LMFDB - Embedded newform 7.14.c.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,14,Mod(2,7)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7.2");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	7.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.50616502663$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 12266 x^{14} - 55087 x^{13} + 107030285 x^{12} - 640627660 x^{11} + \cdots + 12\!\cdots\!76 $ x^16 - x^15 + 12266x^14 - 55087x^13 + 107030285x^12 - 640627660x^11 + 438282746176x^10 - 5859940491984x^9 + 1300952456341392x^8 - 14674000482091008x^7 + 1878469861868220672x^6 - 14476511842718976000x^5 + 1885010114115081494784x^4 - 9244597941717380241408x^3 + 656480392494410296000512x^2 + 3883492623114966780739584x + 127864623964939499445682176
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{34}\cdot 3^{7}\cdot 7^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2.3
Root			$20.8043 - 36.0341i$ of defining polynomial
Character	$\chi$	$=$	7.2
Dual form			7.14.c.a.4.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-41.6086 + 72.0682i) q^{2} +(-951.376 - 1647.83i) q^{3} +(633.448 + 1097.16i) q^{4} +(8420.78 - 14585.2i) q^{5} +158342. q^{6} +(92983.2 + 297057. i) q^{7} -787143. q^{8} +(-1.01307e6 + 1.75469e6i) q^{9} +O(q^{10})$	\(q+(-41.6086 + 72.0682i) q^{2} +(-951.376 - 1647.83i) q^{3} +(633.448 + 1097.16i) q^{4} +(8420.78 - 14585.2i) q^{5} +158342. q^{6} +(92983.2 + 297057. i) q^{7} -787143. q^{8} +(-1.01307e6 + 1.75469e6i) q^{9} +(700754. + 1.21374e6i) q^{10} +(4.91981e6 + 8.52136e6i) q^{11} +(1.20529e6 - 2.08763e6i) q^{12} +1.62958e7 q^{13} +(-2.52773e7 - 5.65901e6i) q^{14} -3.20453e7 q^{15} +(2.75627e7 - 4.77400e7i) q^{16} +(3.27734e7 + 5.67652e7i) q^{17} +(-8.43050e7 - 1.46021e8i) q^{18} +(-1.62004e7 + 2.80599e7i) q^{19} +2.13365e7 q^{20} +(4.01039e8 - 4.35834e8i) q^{21} -8.18826e8 q^{22} +(1.71707e8 - 2.97406e8i) q^{23} +(7.48869e8 + 1.29708e9i) q^{24} +(4.68532e8 + 8.11522e8i) q^{25} +(-6.78047e8 + 1.17441e9i) q^{26} +8.21648e8 q^{27} +(-2.67021e8 + 2.90188e8i) q^{28} -4.72528e9 q^{29} +(1.33336e9 - 2.30945e9i) q^{30} +(2.14868e9 + 3.72162e9i) q^{31} +(-9.30445e8 - 1.61158e9i) q^{32} +(9.36118e9 - 1.62140e10i) q^{33} -5.45462e9 q^{34} +(5.11564e9 + 1.14528e9i) q^{35} -2.56691e9 q^{36} +(-9.22577e9 + 1.59795e10i) q^{37} +(-1.34815e9 - 2.33507e9i) q^{38} +(-1.55035e10 - 2.68528e10i) q^{39} +(-6.62836e9 + 1.14807e10i) q^{40} -6.55391e9 q^{41} +(1.47231e10 + 4.70366e10i) q^{42} +6.12124e10 q^{43} +(-6.23288e9 + 1.07957e10i) q^{44} +(1.70617e10 + 2.95518e10i) q^{45} +(1.42890e10 + 2.47493e10i) q^{46} +(5.58512e10 - 9.67371e10i) q^{47} -1.04890e11 q^{48} +(-7.95973e10 + 5.52427e10i) q^{49} -7.79799e10 q^{50} +(6.23596e10 - 1.08010e11i) q^{51} +(1.03226e10 + 1.78792e10i) q^{52} +(-2.45658e10 - 4.25492e10i) q^{53} +(-3.41876e10 + 5.92147e10i) q^{54} +1.65715e11 q^{55} +(-7.31911e10 - 2.33827e11i) q^{56} +6.16507e10 q^{57} +(1.96612e11 - 3.40542e11i) q^{58} +(1.43321e11 + 2.48239e11i) q^{59} +(-2.02990e10 - 3.51589e10i) q^{60} +(-3.11158e11 + 5.38941e11i) q^{61} -3.57614e11 q^{62} +(-6.15443e11 - 1.37784e11i) q^{63} +6.06446e11 q^{64} +(1.37224e11 - 2.37678e11i) q^{65} +(7.79011e11 + 1.34929e12i) q^{66} +(1.36774e11 + 2.36900e11i) q^{67} +(-4.15204e10 + 7.19155e10i) q^{68} -6.53433e11 q^{69} +(-2.95393e11 + 3.21022e11i) q^{70} -5.54168e10 q^{71} +(7.97432e11 - 1.38119e12i) q^{72} +(-4.97306e11 - 8.61359e11i) q^{73} +(-7.67743e11 - 1.32977e12i) q^{74} +(8.91501e11 - 1.54413e12i) q^{75} -4.10484e10 q^{76} +(-2.07387e12 + 2.25381e12i) q^{77} +2.58031e12 q^{78} +(5.68535e11 - 9.84731e11i) q^{79} +(-4.64199e11 - 8.04017e11i) q^{80} +(8.33467e11 + 1.44361e12i) q^{81} +(2.72699e11 - 4.72328e11i) q^{82} -4.20820e12 q^{83} +(7.32218e11 + 1.63927e11i) q^{84} +1.10391e12 q^{85} +(-2.54696e12 + 4.41147e12i) q^{86} +(4.49551e12 + 7.78646e12i) q^{87} +(-3.87259e12 - 6.70753e12i) q^{88} +(2.05471e12 - 3.55886e12i) q^{89} -2.83966e12 q^{90} +(1.51524e12 + 4.84080e12i) q^{91} +4.35070e11 q^{92} +(4.08841e12 - 7.08133e12i) q^{93} +(4.64778e12 + 8.05019e12i) q^{94} +(2.72840e11 + 4.72572e11i) q^{95} +(-1.77041e12 + 3.06643e12i) q^{96} +1.00840e13 q^{97} +(-6.69313e11 - 8.03501e12i) q^{98} -1.99365e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 728 * q^3 - 32588 * q^4 + 46928 * q^5 - 30212 * q^6 + 257992 * q^7 - 1093248 * q^8 - 2910808 * q^9	\( 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9} + 879018 q^{10} + 3746000 q^{11} + 13786276 q^{12} - 63556528 q^{13} - 45497410 q^{14} + 179729504 q^{15} - 158020976 q^{16} + 108548496 q^{17} + 358872748 q^{18} + 617001728 q^{19} - 1844979416 q^{20} + 400815352 q^{21} + 977603772 q^{22} - 274288968 q^{23} - 690136272 q^{24} + 342571888 q^{25} - 1890370748 q^{26} + 1818768224 q^{27} - 2830532012 q^{28} - 1243557136 q^{29} + 8470546342 q^{30} + 1983953552 q^{31} - 18584336224 q^{32} - 3534705832 q^{33} + 35123983356 q^{34} - 15057013664 q^{35} + 2810399728 q^{36} + 3822948680 q^{37} + 48271561702 q^{38} + 5559167432 q^{39} + 20095902624 q^{40} - 186830117264 q^{41} - 160102538512 q^{42} + 147613206080 q^{43} + 146754773860 q^{44} + 167965018760 q^{45} + 33234006318 q^{46} + 136146541776 q^{47} - 918554738528 q^{48} - 279115649456 q^{49} + 446501048144 q^{50} + 374908120992 q^{51} + 920059547960 q^{52} - 365779470792 q^{53} + 142841959918 q^{54} - 335157159792 q^{55} - 2232488591424 q^{56} + 1368890666384 q^{57} + 1968765302052 q^{58} + 1211924963928 q^{59} - 1696452613604 q^{60} - 155263824184 q^{61} - 3267358992324 q^{62} - 4123328121080 q^{63} + 3671045348608 q^{64} + 2491203210104 q^{65} + 6785854381222 q^{66} - 1812819047992 q^{67} + 2300642770860 q^{68} - 9833331511584 q^{69} - 10764563120010 q^{70} + 6413635527072 q^{71} + 9182131417728 q^{72} + 7135229075576 q^{73} - 1240472589270 q^{74} + 3092701132528 q^{75} - 24098923346008 q^{76} - 8899938075392 q^{77} + 16977900019528 q^{78} + 7912090175960 q^{79} + 18767635478704 q^{80} - 2029193868592 q^{81} + 2118830761068 q^{82} - 16937841300576 q^{83} - 32302920082804 q^{84} + 9546866646768 q^{85} + 17052910238024 q^{86} + 16147535411672 q^{87} - 15433836932304 q^{88} + 3654589406888 q^{89} - 6354662390216 q^{90} - 14961004874704 q^{91} + 2966525661672 q^{92} + 10829807426472 q^{93} + 7135101410430 q^{94} - 16751540432680 q^{95} - 4043645970784 q^{96} + 20623672673744 q^{97} + 1374873929086 q^{98} + 1803523183088 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 728 * q^3 - 32588 * q^4 + 46928 * q^5 - 30212 * q^6 + 257992 * q^7 - 1093248 * q^8 - 2910808 * q^9 + 879018 * q^10 + 3746000 * q^11 + 13786276 * q^12 - 63556528 * q^13 - 45497410 * q^14 + 179729504 * q^15 - 158020976 * q^16 + 108548496 * q^17 + 358872748 * q^18 + 617001728 * q^19 - 1844979416 * q^20 + 400815352 * q^21 + 977603772 * q^22 - 274288968 * q^23 - 690136272 * q^24 + 342571888 * q^25 - 1890370748 * q^26 + 1818768224 * q^27 - 2830532012 * q^28 - 1243557136 * q^29 + 8470546342 * q^30 + 1983953552 * q^31 - 18584336224 * q^32 - 3534705832 * q^33 + 35123983356 * q^34 - 15057013664 * q^35 + 2810399728 * q^36 + 3822948680 * q^37 + 48271561702 * q^38 + 5559167432 * q^39 + 20095902624 * q^40 - 186830117264 * q^41 - 160102538512 * q^42 + 147613206080 * q^43 + 146754773860 * q^44 + 167965018760 * q^45 + 33234006318 * q^46 + 136146541776 * q^47 - 918554738528 * q^48 - 279115649456 * q^49 + 446501048144 * q^50 + 374908120992 * q^51 + 920059547960 * q^52 - 365779470792 * q^53 + 142841959918 * q^54 - 335157159792 * q^55 - 2232488591424 * q^56 + 1368890666384 * q^57 + 1968765302052 * q^58 + 1211924963928 * q^59 - 1696452613604 * q^60 - 155263824184 * q^61 - 3267358992324 * q^62 - 4123328121080 * q^63 + 3671045348608 * q^64 + 2491203210104 * q^65 + 6785854381222 * q^66 - 1812819047992 * q^67 + 2300642770860 * q^68 - 9833331511584 * q^69 - 10764563120010 * q^70 + 6413635527072 * q^71 + 9182131417728 * q^72 + 7135229075576 * q^73 - 1240472589270 * q^74 + 3092701132528 * q^75 - 24098923346008 * q^76 - 8899938075392 * q^77 + 16977900019528 * q^78 + 7912090175960 * q^79 + 18767635478704 * q^80 - 2029193868592 * q^81 + 2118830761068 * q^82 - 16937841300576 * q^83 - 32302920082804 * q^84 + 9546866646768 * q^85 + 17052910238024 * q^86 + 16147535411672 * q^87 - 15433836932304 * q^88 + 3654589406888 * q^89 - 6354662390216 * q^90 - 14961004874704 * q^91 + 2966525661672 * q^92 + 10829807426472 * q^93 + 7135101410430 * q^94 - 16751540432680 * q^95 - 4043645970784 * q^96 + 20623672673744 * q^97 + 1374873929086 * q^98 + 1803523183088 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−41.6086	+	72.0682i	−0.459715	+	0.796249i	−0.998946	−	0.0459089i	$-0.985382\pi$
$2$	−41.6086	+	72.0682i	−0.459715	+	0.796249i	0.539231	+	0.842158i	$0.318715\pi$
$3$	−951.376	−	1647.83i	−0.753467	−	1.30504i	−0.946133	−	0.323778i	$-0.895047\pi$
$3$	−951.376	−	1647.83i	−0.753467	−	1.30504i	0.192666	−	0.981264i	$-0.438287\pi$
$4$	633.448	+	1097.16i	0.0773251	+	0.133931i
$5$	8420.78	−	14585.2i	0.241017	−	0.417453i	−0.719987	−	0.693987i	$-0.755852\pi$
$5$	8420.78	−	14585.2i	0.241017	−	0.417453i	0.961004	+	0.276534i	$0.0891858\pi$
$6$	158342.			1.38552
$7$	92983.2	+	297057.i	0.298722	+	0.954340i
$7$	92983.2	+	297057.i	0.298722	+	0.954340i
$8$	−787143.			−1.06162
$9$	−1.01307e6	+	1.75469e6i	−0.635425	+	1.10059i
$10$	700754.	+	1.21374e6i	0.221598	+	0.383819i
$11$	4.91981e6	+	8.52136e6i	0.837328	+	1.45030i	0.892121	+	0.451798i	$0.149217\pi$
$11$	4.91981e6	+	8.52136e6i	0.837328	+	1.45030i	−0.0547921	+	0.998498i	$0.517450\pi$
$12$	1.20529e6	−	2.08763e6i	0.116524	−	0.201825i
$13$	1.62958e7			0.936365			0.468182	−	0.883632i	$-0.344909\pi$
$13$	1.62958e7			0.936365			0.468182	+	0.883632i	$0.344909\pi$
$14$	−2.52773e7	−	5.65901e6i	−0.897219	−	0.200867i
$15$	−3.20453e7			−0.726393
$16$	2.75627e7	−	4.77400e7i	0.410717	−	0.711382i
$17$	3.27734e7	+	5.67652e7i	0.329309	+	0.570380i	0.982375	−	0.186921i	$-0.0598510\pi$
$17$	3.27734e7	+	5.67652e7i	0.329309	+	0.570380i	−0.653066	+	0.757301i	$0.726518\pi$
$18$	−8.43050e7	−	1.46021e8i	−0.584228	−	1.01191i
$19$	−1.62004e7	+	2.80599e7i	−0.0790000	+	0.136832i	−0.902819	−	0.430021i	$-0.858506\pi$
$19$	−1.62004e7	+	2.80599e7i	−0.0790000	+	0.136832i	0.823819	+	0.566853i	$0.191839\pi$
$20$	2.13365e7			0.0745466
$21$	4.01039e8	−	4.35834e8i	1.02038	−	1.10891i
$22$	−8.18826e8			−1.53973
$23$	1.71707e8	−	2.97406e8i	0.241857	−	0.418908i	−0.719387	−	0.694610i	$-0.755577\pi$
$23$	1.71707e8	−	2.97406e8i	0.241857	−	0.418908i	0.961243	+	0.275702i	$0.0889103\pi$
$24$	7.48869e8	+	1.29708e9i	0.799895	+	1.38546i
$25$	4.68532e8	+	8.11522e8i	0.383822	+	0.664799i
$26$	−6.78047e8	+	1.17441e9i	−0.430460	+	0.745579i
$27$	8.21648e8			0.408152
$28$	−2.67021e8	+	2.90188e8i	−0.104717	+	0.113803i
$29$	−4.72528e9			−1.47516			−0.737582	−	0.675258i	$-0.764032\pi$
$29$	−4.72528e9			−1.47516			−0.737582	+	0.675258i	$0.764032\pi$
$30$	1.33336e9	−	2.30945e9i	0.333933	−	0.578389i
$31$	2.14868e9	+	3.72162e9i	0.434831	+	0.753150i	0.997282	−	0.0736812i	$-0.0234747\pi$
$31$	2.14868e9	+	3.72162e9i	0.434831	+	0.753150i	−0.562451	+	0.826831i	$0.690141\pi$
$32$	−9.30445e8	−	1.61158e9i	−0.153185	−	0.265324i
$33$	9.36118e9	−	1.62140e10i	1.26180	−	2.18550i
$34$	−5.45462e9			−0.605552
$35$	5.11564e9	+	1.14528e9i	0.470390	+	0.105310i
$36$	−2.56691e9			−0.196537
$37$	−9.22577e9	+	1.59795e10i	−0.591141	+	1.02389i	0.402938	+	0.915227i	$0.367989\pi$
$37$	−9.22577e9	+	1.59795e10i	−0.591141	+	1.02389i	−0.994079	+	0.108659i	$0.965344\pi$
$38$	−1.34815e9	−	2.33507e9i	−0.0726349	−	0.125807i
$39$	−1.55035e10	−	2.68528e10i	−0.705520	−	1.22200i
$40$	−6.62836e9	+	1.14807e10i	−0.255868	+	0.443176i
$41$	−6.55391e9			−0.215479			−0.107740	−	0.994179i	$-0.534361\pi$
$41$	−6.55391e9			−0.215479			−0.107740	+	0.994179i	$0.534361\pi$
$42$	1.47231e10	+	4.70366e10i	0.413885	+	1.32226i
$43$	6.12124e10			1.47671			0.738354	−	0.674414i	$-0.235604\pi$
$43$	6.12124e10			1.47671			0.738354	+	0.674414i	$0.235604\pi$
$44$	−6.23288e9	+	1.07957e10i	−0.129493	+	0.224289i
$45$	1.70617e10	+	2.95518e10i	0.306296	+	0.530520i
$46$	1.42890e10	+	2.47493e10i	0.222370	+	0.385156i
$47$	5.58512e10	−	9.67371e10i	0.755782	−	1.30905i	−0.189203	−	0.981938i	$-0.560590\pi$
$47$	5.58512e10	−	9.67371e10i	0.755782	−	1.30905i	0.944985	−	0.327114i	$-0.106076\pi$
$48$	−1.04890e11			−1.23785
$49$	−7.95973e10	+	5.52427e10i	−0.821530	+	0.570165i
$50$	−7.79799e10			−0.705794
$51$	6.23596e10	−	1.08010e11i	0.496247	−	0.859524i
$52$	1.03226e10	+	1.78792e10i	0.0724045	+	0.125408i
$53$	−2.45658e10	−	4.25492e10i	−0.152243	−	0.263693i	0.779809	−	0.626018i	$-0.215316\pi$
$53$	−2.45658e10	−	4.25492e10i	−0.152243	−	0.263693i	−0.932052	+	0.362325i	$0.881983\pi$
$54$	−3.41876e10	+	5.92147e10i	−0.187633	+	0.324990i
$55$	1.65715e11			0.807241
$56$	−7.31911e10	−	2.33827e11i	−0.317129	−	1.01315i
$57$	6.16507e10			0.238096
$58$	1.96612e11	−	3.40542e11i	0.678154	−	1.17460i
$59$	1.43321e11	+	2.48239e11i	0.442355	+	0.766181i	0.997864	−	0.0653297i	$-0.0208099\pi$
$59$	1.43321e11	+	2.48239e11i	0.442355	+	0.766181i	−0.555509	+	0.831510i	$0.687477\pi$
$60$	−2.02990e10	−	3.51589e10i	−0.0561684	−	0.0972865i
$61$	−3.11158e11	+	5.38941e11i	−0.773279	+	1.33936i	0.162477	+	0.986712i	$0.448052\pi$
$61$	−3.11158e11	+	5.38941e11i	−0.773279	+	1.33936i	−0.935757	+	0.352647i	$0.885282\pi$
$62$	−3.57614e11			−0.799593
$63$	−6.15443e11	−	1.37784e11i	−1.24015	−	0.277641i
$64$	6.06446e11			1.10312
$65$	1.37224e11	−	2.37678e11i	0.225680	−	0.390889i
$66$	7.79011e11	+	1.34929e12i	1.16013	+	2.00941i
$67$	1.36774e11	+	2.36900e11i	0.184721	+	0.319947i	0.943483	−	0.331422i	$-0.107528\pi$
$67$	1.36774e11	+	2.36900e11i	0.184721	+	0.319947i	−0.758761	+	0.651369i	$0.774195\pi$
$68$	−4.15204e10	+	7.19155e10i	−0.0509277	+	0.0882094i
$69$	−6.53433e11			−0.728924
$70$	−2.95393e11	+	3.21022e11i	−0.300097	+	0.326135i
$71$	−5.54168e10			−0.0513408			−0.0256704	−	0.999670i	$-0.508172\pi$
$71$	−5.54168e10			−0.0513408			−0.0256704	+	0.999670i	$0.508172\pi$
$72$	7.97432e11	−	1.38119e12i	0.674579	−	1.16840i
$73$	−4.97306e11	−	8.61359e11i	−0.384614	−	0.666170i	0.607102	−	0.794624i	$-0.292332\pi$
$73$	−4.97306e11	−	8.61359e11i	−0.384614	−	0.666170i	−0.991716	+	0.128454i	$0.958999\pi$
$74$	−7.67743e11	−	1.32977e12i	−0.543512	−	0.941391i
$75$	8.91501e11	−	1.54413e12i	0.578394	−	1.00181i
$76$	−4.10484e10			−0.0244347
$77$	−2.07387e12	+	2.25381e12i	−1.13395	+	1.23233i
$78$	2.58031e12			1.29735
$79$	5.68535e11	−	9.84731e11i	0.263136	−	0.455766i	−0.703937	−	0.710262i	$-0.748576\pi$
$79$	5.68535e11	−	9.84731e11i	0.263136	−	0.455766i	0.967074	+	0.254497i	$0.0819098\pi$
$80$	−4.64199e11	−	8.04017e11i	−0.197979	−	0.342910i
$81$	8.33467e11	+	1.44361e12i	0.327896	+	0.567932i
$82$	2.72699e11	−	4.72328e11i	0.0990589	−	0.171575i
$83$	−4.20820e12			−1.41283			−0.706413	−	0.707800i	$-0.749688\pi$
$83$	−4.20820e12			−1.41283			−0.706413	+	0.707800i	$0.749688\pi$
$84$	7.32218e11	+	1.63927e11i	0.227418	+	0.0509138i
$85$	1.10391e12			0.317476
$86$	−2.54696e12	+	4.41147e12i	−0.678864	+	1.17583i
$87$	4.49551e12	+	7.78646e12i	1.11149	+	1.92515i
$88$	−3.87259e12	−	6.70753e12i	−0.888924	−	1.53966i
$89$	2.05471e12	−	3.55886e12i	0.438243	−	0.759059i	−0.559311	−	0.828958i	$-0.688934\pi$
$89$	2.05471e12	−	3.55886e12i	0.438243	−	0.759059i	0.997554	+	0.0698990i	$0.0222677\pi$
$90$	−2.83966e12			−0.563235
$91$	1.51524e12	+	4.84080e12i	0.279713	+	0.893610i
$92$	4.35070e11			0.0748064
$93$	4.08841e12	−	7.08133e12i	0.655262	−	1.13495i
$94$	4.64778e12	+	8.05019e12i	0.694888	+	1.20358i
$95$	2.72840e11	+	4.72572e11i	0.0380807	+	0.0659576i
$96$	−1.77041e12	+	3.06643e12i	−0.230839	+	0.399825i
$97$	1.00840e13			1.22918			0.614592	−	0.788845i	$-0.289321\pi$
$97$	1.00840e13			1.22918			0.614592	+	0.788845i	$0.289321\pi$
$98$	−6.69313e11	−	8.03501e12i	−0.0763237	−	0.916256i
$99$	−1.99365e13			−2.12824
$100$	−5.93581e11	+	1.02811e12i	−0.0593581	+	0.102811i
$101$	−7.38323e12	−	1.27881e13i	−0.692082	−	1.19872i	−0.971155	−	0.238451i	$-0.923360\pi$
$101$	−7.38323e12	−	1.27881e13i	−0.692082	−	1.19872i	0.279073	−	0.960270i	$-0.409973\pi$
$102$	5.18940e12	+	8.98830e12i	0.456263	+	0.790271i
$103$	4.11166e12	−	7.12161e12i	0.339293	−	0.587674i	−0.645007	−	0.764177i	$-0.723145\pi$
$103$	4.11166e12	−	7.12161e12i	0.339293	−	0.587674i	0.984300	+	0.176503i	$0.0564787\pi$
$104$	−1.28272e13			−0.994062
$105$	−2.97968e12	−	9.51930e12i	−0.216989	−	0.693226i
$106$	4.08859e12			0.279953
$107$	3.81271e12	−	6.60381e12i	0.245606	−	0.425402i	−0.716696	−	0.697386i	$-0.754346\pi$
$107$	3.81271e12	−	6.60381e12i	0.245606	−	0.425402i	0.962302	+	0.271984i	$0.0876797\pi$
$108$	5.20471e11	+	9.01482e11i	0.0315604	+	0.0546642i
$109$	2.61388e12	+	4.52738e12i	0.149284	+	0.258568i	0.930963	−	0.365113i	$-0.118970\pi$
$109$	2.61388e12	+	4.52738e12i	0.149284	+	0.258568i	−0.781679	+	0.623681i	$0.785636\pi$
$110$	−6.89515e12	+	1.19428e13i	−0.371100	+	0.642765i
$111$	3.51087e13			1.78162
$112$	1.67444e13	+	3.74869e12i	0.801590	+	0.179458i
$113$	−7.56531e11			−0.0341835			−0.0170918	−	0.999854i	$-0.505441\pi$
$113$	−7.56531e11			−0.0341835			−0.0170918	+	0.999854i	$0.505441\pi$
$114$	−2.56520e12	+	4.44305e12i	−0.109456	+	0.189583i
$115$	−2.89182e12	−	5.00878e12i	−0.116583	−	0.201928i
$116$	−2.99321e12	−	5.18440e12i	−0.114067	−	0.197570i
$117$	−1.65089e13	+	2.85942e13i	−0.594989	+	1.03055i
$118$	−2.38535e13			−0.813427
$119$	−1.38151e13	+	1.50138e13i	−0.445964	+	0.484658i
$120$	2.52242e13			0.771152
$121$	−3.11477e13	+	5.39494e13i	−0.902238	+	1.56272i
$122$	−2.58937e13	−	4.48491e13i	−0.710975	−	1.23145i
$123$	6.23523e12	+	1.07997e13i	0.162356	+	0.281210i
$124$	−2.72215e12	+	4.71490e12i	−0.0672468	+	0.116475i
$125$	3.63402e13			0.852064
$126$	3.55376e13	−	3.86209e13i	0.791187	−	0.859832i
$127$	5.61372e13			1.18721			0.593603	−	0.804758i	$-0.297705\pi$
$127$	5.61372e13			1.18721			0.593603	+	0.804758i	$0.297705\pi$
$128$	−1.76112e13	+	3.05034e13i	−0.353935	+	0.613033i
$129$	−5.82360e13	−	1.00868e14i	−1.11265	−	1.92717i
$130$	1.14194e13	+	1.97789e13i	0.207496	+	0.359394i
$131$	1.26349e13	−	2.18843e13i	0.218428	−	0.378328i	−0.735900	−	0.677091i	$-0.763240\pi$
$131$	1.26349e13	−	2.18843e13i	0.218428	−	0.378328i	0.954328	+	0.298762i	$0.0965738\pi$
$132$	2.37193e13			0.390275
$133$	−9.84177e12	−	2.20335e12i	−0.154183	−	0.0345181i
$134$	−2.27639e13			−0.339677
$135$	6.91892e12	−	1.19839e13i	0.0983714	−	0.170384i
$136$	−2.57973e13	−	4.46823e13i	−0.349600	−	0.605526i
$137$	−3.30185e12	−	5.71898e12i	−0.0426652	−	0.0738984i	0.843904	−	0.536494i	$-0.180252\pi$
$137$	−3.30185e12	−	5.71898e12i	−0.0426652	−	0.0738984i	−0.886569	+	0.462596i	$0.846918\pi$
$138$	2.71884e13	−	4.70918e13i	0.335097	−	0.580405i
$139$	−1.89757e12			−0.0223152			−0.0111576	−	0.999938i	$-0.503552\pi$
$139$	−1.89757e12			−0.0223152			−0.0111576	+	0.999938i	$0.503552\pi$
$140$	1.98394e12	+	6.33816e12i	0.0222687	+	0.0711428i
$141$	−2.12542e14			−2.27783
$142$	2.30582e12	−	3.99379e12i	0.0236021	−	0.0408800i
$143$	8.01724e13	+	1.38863e14i	0.784045	+	1.35801i
$144$	5.58460e13	+	9.67282e13i	0.521959	+	0.904059i
$145$	−3.97905e13	+	6.89192e13i	−0.355539	+	0.615812i
$146$	8.27688e13			0.707250
$147$	1.66758e14	+	7.86063e13i	1.36309	+	0.642532i
$148$	−2.33762e13			−0.182840
$149$	−1.48865e13	+	2.57842e13i	−0.111450	+	0.193038i	−0.916355	−	0.400366i	$-0.868883\pi$
$149$	−1.48865e13	+	2.57842e13i	−0.111450	+	0.193038i	0.804905	+	0.593404i	$0.202216\pi$
$150$	7.41883e13	+	1.28498e14i	0.531792	+	0.921091i
$151$	−9.56796e13	−	1.65722e14i	−0.656854	−	1.13771i	−0.981425	−	0.191844i	$-0.938553\pi$
$151$	−9.56796e13	−	1.65722e14i	−0.656854	−	1.13771i	0.324571	−	0.945861i	$-0.394780\pi$
$152$	1.27520e13	−	2.20872e13i	0.0838679	−	0.145263i
$153$	−1.32807e14			−0.837004
$154$	−7.61370e13	−	2.43238e14i	−0.459951	−	1.46942i
$155$	7.23742e13			0.419206
$156$	1.96413e13	−	3.40197e13i	0.109109	−	0.188982i
$157$	2.08358e13	+	3.60886e13i	0.111036	+	0.192319i	0.916188	−	0.400749i	$-0.131250\pi$
$157$	2.08358e13	+	3.60886e13i	0.111036	+	0.192319i	−0.805152	+	0.593068i	$0.797917\pi$
$158$	4.73119e13	+	8.19466e13i	0.241935	+	0.419044i
$159$	−4.67426e13	+	8.09606e13i	−0.229420	+	0.397368i
$160$	−3.13403e13			−0.147680
$161$	1.04313e14	+	2.33532e13i	0.472028	+	0.105676i
$162$	−1.38718e14			−0.602954
$163$	6.00965e13	−	1.04090e14i	0.250975	−	0.434701i	−0.712820	−	0.701347i	$-0.752582\pi$
$163$	6.00965e13	−	1.04090e14i	0.250975	−	0.434701i	0.963794	+	0.266646i	$0.0859156\pi$
$164$	−4.15156e12	−	7.19071e12i	−0.0166620	−	0.0288594i
$165$	−1.57657e14	−	2.73070e14i	−0.608229	−	1.05348i
$166$	1.75097e14	−	3.03277e14i	0.649496	−	1.12496i
$167$	3.31297e14			1.18184			0.590922	−	0.806729i	$-0.298764\pi$
$167$	3.31297e14			1.18184			0.590922	+	0.806729i	$0.298764\pi$
$168$	−3.15675e14	+	3.43064e14i	−1.08325	+	1.17724i
$169$	−3.73207e13			−0.123221
$170$	−4.59322e13	+	7.95568e13i	−0.145948	+	0.252790i
$171$	−3.28243e13	−	5.68534e13i	−0.100397	−	0.173893i
$172$	3.87748e13	+	6.71600e13i	0.114187	+	0.197777i
$173$	1.02303e14	−	1.77194e14i	0.290128	−	0.502516i	−0.683712	−	0.729752i	$-0.739635\pi$
$173$	1.02303e14	−	1.77194e14i	0.290128	−	0.502516i	0.973840	+	0.227236i	$0.0729688\pi$
$174$	−7.48208e14			−2.04387
$175$	−1.97503e14	+	2.14639e14i	−0.519788	+	0.564887i
$176$	5.42413e14			1.37562
$177$	2.72704e14	−	4.72337e14i	0.666599	−	1.15458i
$178$	1.70987e14	+	2.96158e14i	0.402933	+	0.697901i
$179$	2.45397e13	+	4.25040e13i	0.0557602	+	0.0965794i	0.892558	−	0.450932i	$-0.148908\pi$
$179$	2.45397e13	+	4.25040e13i	0.0557602	+	0.0965794i	−0.836798	+	0.547512i	$0.815575\pi$
$180$	−2.16154e13	+	3.74390e13i	−0.0473688	+	0.0820451i
$181$	−2.76761e14			−0.585052			−0.292526	−	0.956258i	$-0.594496\pi$
$181$	−2.76761e14			−0.585052			−0.292526	+	0.956258i	$0.594496\pi$
$182$	−4.11915e14	−	9.22184e13i	−0.840124	−	0.188085i
$183$	1.18411e15			2.33056
$184$	−1.35158e14	+	2.34101e14i	−0.256760	+	0.444721i
$185$	1.55376e14	+	2.69120e14i	0.284950	+	0.493548i
$186$	3.40226e14	+	5.89288e14i	0.602467	+	1.04350i
$187$	−3.22478e14	+	5.58548e14i	−0.551479	+	0.955190i
$188$	1.41515e14			0.233764
$189$	7.63995e13	+	2.44077e14i	0.121924	+	0.389515i
$190$	−4.54099e13			−0.0700249
$191$	−5.03968e13	+	8.72899e13i	−0.0751080	+	0.130091i	−0.901133	−	0.433542i	$-0.857263\pi$
$191$	−5.03968e13	+	8.72899e13i	−0.0751080	+	0.130091i	0.826025	+	0.563633i	$0.190597\pi$
$192$	−5.76958e14	−	9.99320e14i	−0.831163	−	1.43962i
$193$	−4.67676e14	−	8.10038e14i	−0.651362	−	1.12819i	−0.982793	−	0.184712i	$-0.940865\pi$
$193$	−4.67676e14	−	8.10038e14i	−0.651362	−	1.12819i	0.331431	−	0.943479i	$-0.392469\pi$
$194$	−4.19581e14	+	7.26736e14i	−0.565073	+	0.978736i
$195$	−5.22205e14			−0.680168
$196$	−1.11031e14	−	5.23378e13i	−0.139888	−	0.0659404i
$197$	−7.49362e14			−0.913401			−0.456700	−	0.889621i	$-0.650969\pi$
$197$	−7.49362e14			−0.913401			−0.456700	+	0.889621i	$0.650969\pi$
$198$	8.29529e14	−	1.43679e15i	0.978381	−	1.69461i
$199$	7.13069e14	+	1.23507e15i	0.813929	+	1.40977i	0.910094	+	0.414402i	$0.136009\pi$
$199$	7.13069e14	+	1.23507e15i	0.813929	+	1.40977i	−0.0961646	+	0.995365i	$0.530658\pi$
$200$	−3.68802e14	−	6.38784e14i	−0.407473	−	0.705763i
$201$	2.60247e14	−	4.50761e14i	0.278363	−	0.482139i
$202$	1.22882e15			1.27264
$203$	−4.39371e14	−	1.40368e15i	−0.440664	−	1.40781i
$204$	1.58006e14			0.153489
$205$	−5.51890e13	+	9.55902e13i	−0.0519341	+	0.0899525i
$206$	3.42161e14	+	5.92640e14i	0.311956	+	0.540324i
$207$	3.47904e14	+	6.02587e14i	0.307363	+	0.532369i
$208$	4.49158e14	−	7.77964e14i	0.384580	−	0.666113i
$209$	−3.18811e14			−0.264596
$210$	8.10019e14	+	1.81345e14i	0.651733	+	0.145908i
$211$	−1.68891e15			−1.31756			−0.658781	−	0.752335i	$-0.728928\pi$
$211$	−1.68891e15			−1.31756			−0.658781	+	0.752335i	$0.728928\pi$
$212$	3.11223e13	−	5.39054e13i	0.0235444	−	0.0407802i
$213$	5.27222e13	+	9.13176e13i	0.0386836	+	0.0670019i
$214$	3.17283e14	+	5.49551e14i	0.225817	+	0.391127i
$215$	5.15456e14	−	8.92796e14i	0.355911	−	0.616456i
$216$	−6.46755e14			−0.433301
$217$	−9.05745e14	+	9.84330e14i	−0.588867	+	0.639959i
$218$	−4.35040e14			−0.274513
$219$	−9.46249e14	+	1.63895e15i	−0.579587	+	1.00387i
$220$	1.04971e14	+	1.81816e14i	0.0624200	+	0.108115i
$221$	5.34070e14	+	9.25036e14i	0.308353	+	0.534083i
$222$	−1.46082e15	+	2.53022e15i	−0.819037	+	1.41861i
$223$	2.16237e15			1.17747			0.588733	−	0.808328i	$-0.299627\pi$
$223$	2.16237e15			1.17747			0.588733	+	0.808328i	$0.299627\pi$
$224$	3.92215e14	−	4.26245e14i	0.207450	−	0.225448i
$225$	−1.89863e15			−0.975559
$226$	3.14782e13	−	5.45218e13i	0.0157147	−	0.0272186i
$227$	−8.75379e14	−	1.51620e15i	−0.424647	−	0.735510i	0.571741	−	0.820435i	$-0.306268\pi$
$227$	−8.75379e14	−	1.51620e15i	−0.424647	−	0.735510i	−0.996387	+	0.0849246i	$0.972935\pi$
$228$	3.90525e13	+	6.76408e13i	0.0184108	+	0.0318884i
$229$	1.17823e15	−	2.04075e15i	0.539882	−	0.935103i	−0.459028	−	0.888422i	$-0.651802\pi$
$229$	1.17823e15	−	2.04075e15i	0.539882	−	0.935103i	0.998910	−	0.0466814i	$-0.0148645\pi$
$230$	4.81298e14			0.214380
$231$	5.68693e15	+	1.27317e15i	2.46264	+	0.551328i
$232$	3.71947e15			1.56606
$233$	−1.58793e15	+	2.75037e15i	−0.650155	+	1.12610i	0.332930	+	0.942952i	$0.391963\pi$
$233$	−1.58793e15	+	2.75037e15i	−0.650155	+	1.12610i	−0.983085	+	0.183150i	$0.941371\pi$
$234$	−1.37382e15	−	2.37953e15i	−0.547050	−	0.947519i
$235$	−9.40621e14	−	1.62920e15i	−0.364312	−	0.631007i
$236$	−1.81572e14	+	3.14492e14i	−0.0684103	+	0.118490i
$237$	−2.16356e15			−0.793058
$238$	−5.07188e14	−	1.62034e15i	−0.180892	−	0.577903i
$239$	−1.58045e15			−0.548522			−0.274261	−	0.961655i	$-0.588433\pi$
$239$	−1.58045e15			−0.548522			−0.274261	+	0.961655i	$0.588433\pi$
$240$	−8.83256e14	+	1.52984e15i	−0.298341	+	0.516743i
$241$	−8.07668e14	−	1.39892e15i	−0.265535	−	0.459920i	0.702169	−	0.712011i	$-0.252215\pi$
$241$	−8.07668e14	−	1.39892e15i	−0.265535	−	0.459920i	−0.967704	+	0.252090i	$0.918882\pi$
$242$	−2.59202e15	−	4.48952e15i	−0.829543	−	1.43681i
$243$	2.24087e15	−	3.88130e15i	0.698193	−	1.20931i
$244$	−7.88408e14			−0.239176
$245$	1.35456e14	+	1.62613e15i	0.0400146	+	0.480370i
$246$	−1.03776e15			−0.298550
$247$	−2.63999e14	+	4.57260e14i	−0.0739728	+	0.128125i
$248$	−1.69132e15	−	2.92945e15i	−0.461625	−	0.799558i
$249$	4.00358e15	+	6.93440e15i	1.06452	+	1.84380i
$250$	−1.51206e15	+	2.61897e15i	−0.391706	+	0.678455i
$251$	7.12402e14			0.179823			0.0899116	−	0.995950i	$-0.471342\pi$
$251$	7.12402e14			0.179823			0.0899116	+	0.995950i	$0.471342\pi$
$252$	−2.38680e14	−	7.62520e14i	−0.0587100	−	0.187563i
$253$	3.37907e15			0.810053
$254$	−2.33579e15	+	4.04571e15i	−0.545776	+	0.945312i
$255$	−1.05023e15	−	1.81906e15i	−0.239207	−	0.414320i
$256$	1.01845e15	+	1.76401e15i	0.226141	+	0.391688i
$257$	5.38091e14	−	9.32002e14i	0.116491	−	0.201768i	−0.801884	−	0.597480i	$-0.796169\pi$
$257$	5.38091e14	−	9.32002e14i	0.116491	−	0.201768i	0.918375	+	0.395712i	$0.129502\pi$
$258$	9.69248e15			2.04601
$259$	−5.60467e15	−	1.25476e15i	−1.15372	−	0.258292i
$260$	3.47696e14			0.0698028
$261$	4.78704e15	−	8.29140e15i	0.937355	−	1.62355i
$262$	1.05144e15	+	1.82115e15i	0.200829	+	0.347846i
$263$	3.01929e14	+	5.22956e14i	0.0562590	+	0.0974434i	0.892783	−	0.450486i	$-0.148749\pi$
$263$	3.01929e14	+	5.22956e14i	0.0562590	+	0.0974434i	−0.836524	+	0.547930i	$0.815416\pi$
$264$	−7.36859e15	+	1.27628e16i	−1.33955	+	2.32017i
$265$	−8.27453e14			−0.146773
$266$	5.68294e14	−	6.17600e14i	0.0983653	−	0.106900i
$267$	−7.81920e15			−1.32081
$268$	−1.73278e14	+	3.00127e14i	−0.0285672	+	0.0494799i
$269$	9.65510e14	+	1.67231e15i	0.155370	+	0.269109i	0.933194	−	0.359374i	$-0.117010\pi$
$269$	9.65510e14	+	1.67231e15i	0.155370	+	0.269109i	−0.777824	+	0.628483i	$0.783676\pi$
$270$	5.75773e14	+	9.97269e14i	0.0904455	+	0.156656i
$271$	1.76015e15	−	3.04867e15i	0.269929	−	0.467530i	−0.698915	−	0.715205i	$-0.746333\pi$
$271$	1.76015e15	−	3.04867e15i	0.269929	−	0.467530i	0.968843	+	0.247675i	$0.0796666\pi$
$272$	3.61329e15			0.541010
$273$	6.53526e15	−	7.10228e15i	0.955446	−	1.03834i
$274$	5.49542e14			0.0784553
$275$	−4.61018e15	+	7.98507e15i	−0.642770	+	1.11331i
$276$	−4.13916e14	−	7.16923e14i	−0.0563641	−	0.0976255i
$277$	6.01940e14	+	1.04259e15i	0.0800635	+	0.138674i	0.903277	−	0.429058i	$-0.141154\pi$
$277$	6.01940e14	+	1.04259e15i	0.0800635	+	0.138674i	−0.823213	+	0.567732i	$0.807821\pi$
$278$	7.89551e13	−	1.36754e14i	0.0102586	−	0.0177684i
$279$	−8.70707e15			−1.10521
$280$	−4.02674e15	−	9.01495e14i	−0.499374	−	0.111799i
$281$	1.86038e15			0.225429			0.112714	−	0.993627i	$-0.464045\pi$
$281$	1.86038e15			0.225429			0.112714	+	0.993627i	$0.464045\pi$
$282$	8.84358e15	−	1.53175e16i	1.04715	−	1.81372i
$283$	6.56238e15	+	1.13664e16i	0.759363	+	1.31526i	0.943176	+	0.332295i	$0.107823\pi$
$283$	6.56238e15	+	1.13664e16i	0.759363	+	1.31526i	−0.183812	+	0.982961i	$0.558844\pi$
$284$	−3.51036e13	−	6.08013e13i	−0.00396993	−	0.00687612i
$285$	5.19147e14	−	8.99188e14i	0.0573850	−	0.0993938i
$286$	−1.33435e16			−1.44175
$287$	−6.09403e14	−	1.94689e15i	−0.0643684	−	0.205640i
$288$	3.77043e15			0.389350
$289$	2.80410e15	−	4.85684e15i	0.283111	−	0.490363i
$290$	−3.31126e15	−	5.73526e15i	−0.326893	−	0.566195i
$291$	−9.59368e15	−	1.66167e16i	−0.926149	−	1.60414i
$292$	6.30034e14	−	1.09125e15i	0.0594806	−	0.103023i
$293$	5.77987e15			0.533677			0.266838	−	0.963741i	$-0.414021\pi$
$293$	5.77987e15			0.533677			0.266838	+	0.963741i	$0.414021\pi$
$294$	−1.26036e16	+	8.74723e15i	−1.13825	+	0.789974i
$295$	4.82749e15			0.426460
$296$	7.26200e15	−	1.25781e16i	0.627567	−	1.08698i
$297$	4.04235e15	+	7.00156e15i	0.341757	+	0.591940i
$298$	−1.23881e15	−	2.14569e15i	−0.102471	−	0.177485i
$299$	2.79812e15	−	4.84648e15i	0.226466	−	0.392250i
$300$	2.25888e15			0.178898
$301$	5.69173e15	+	1.81836e16i	0.441125	+	1.40928i
$302$	1.59244e16			1.20786
$303$	−1.40485e16	+	2.43326e16i	−1.04292	+	1.80639i
$304$	8.93054e14	+	1.54681e15i	0.0648932	+	0.112398i
$305$	5.24038e15	+	9.07660e15i	0.372747	+	0.645616i
$306$	5.52592e15	−	9.57118e15i	0.384783	−	0.666463i
$307$	−1.16092e16			−0.791411			−0.395706	−	0.918377i	$-0.629500\pi$
$307$	−1.16092e16			−0.791411			−0.395706	+	0.918377i	$0.629500\pi$
$308$	−3.78649e15	−	8.47708e14i	−0.252730	−	0.0565805i
$309$	−1.56470e16			−1.02259
$310$	−3.01139e15	+	5.21588e15i	−0.192715	+	0.333793i
$311$	9.24446e15	+	1.60119e16i	0.579348	+	1.00346i	0.995554	+	0.0941894i	$0.0300259\pi$
$311$	9.24446e15	+	1.60119e16i	0.579348	+	1.00346i	−0.416207	+	0.909270i	$0.636641\pi$
$312$	1.22035e16	+	2.11370e16i	0.748993	+	1.29729i
$313$	7.41510e15	−	1.28433e16i	0.445737	−	0.772039i	−0.552366	−	0.833602i	$-0.686275\pi$
$313$	7.41510e15	−	1.28433e16i	0.445737	−	0.772039i	0.998103	+	0.0615623i	$0.0196083\pi$
$314$	−3.46779e15			−0.204179
$315$	−7.19212e15	+	7.81613e15i	−0.414799	+	0.450789i
$316$	1.44055e15			0.0813882
$317$	8.87574e14	−	1.53732e15i	0.0491269	−	0.0850903i	−0.840416	−	0.541941i	$-0.817689\pi$
$317$	8.87574e14	−	1.53732e15i	0.0491269	−	0.0850903i	0.889543	+	0.456851i	$0.151023\pi$
$318$	−3.88979e15	−	6.73732e15i	−0.210936	−	0.365351i
$319$	−2.32475e16	−	4.02658e16i	−1.23520	−	2.13942i
$320$	5.10675e15	−	8.84514e15i	0.265870	−	0.460500i
$321$	−1.45093e16			−0.740224
$322$	−6.02332e15	+	6.54592e15i	−0.301143	+	0.327271i
$323$	−2.12377e15			−0.104062
$324$	−1.05592e15	+	1.82890e15i	−0.0507092	+	0.0878309i
$325$	7.63513e15	+	1.32244e16i	0.359397	+	0.622494i
$326$	5.00107e15	+	8.66210e15i	0.230753	+	0.399677i
$327$	4.97357e15	−	8.61448e15i	0.224961	−	0.389645i
$328$	5.15886e15			0.228757
$329$	3.39297e16	+	7.59609e15i	1.47505	+	0.330230i
$330$	2.62395e16			1.11845
$331$	2.36300e16	−	4.09283e16i	0.987600	−	1.71057i	0.357844	−	0.933781i	$-0.383512\pi$
$331$	2.36300e16	−	4.09283e16i	0.987600	−	1.71057i	0.629756	−	0.776793i	$-0.283155\pi$
$332$	−2.66567e15	−	4.61708e15i	−0.109247	−	0.189221i
$333$	−1.86927e16	−	3.23768e16i	−0.751251	−	1.30121i
$334$	−1.37848e16	+	2.38760e16i	−0.543311	+	0.941042i
$335$	4.60698e15			0.178084
$336$	−9.75301e15	−	3.11584e16i	−0.369772	−	1.18133i
$337$	−1.02033e16			−0.379442			−0.189721	−	0.981838i	$-0.560758\pi$
$337$	−1.02033e16			−0.379442			−0.189721	+	0.981838i	$0.560758\pi$
$338$	1.55286e15	−	2.68963e15i	0.0566466	−	0.0981148i
$339$	7.19746e14	+	1.24664e15i	0.0257562	+	0.0446110i
$340$	6.99269e14	+	1.21117e15i	0.0245489	+	0.0425199i
$341$	−2.11422e16	+	3.66193e16i	−0.728193	+	1.26127i
$342$	5.46310e15			0.184616
$343$	−2.38115e16	−	1.85083e16i	−0.789540	−	0.613699i
$344$	−4.81829e16			−1.56770
$345$	−5.50242e15	+	9.53046e15i	−0.175683	+	0.304292i
$346$	8.51339e15	+	1.47456e16i	0.266752	+	0.462028i
$347$	2.73702e16	+	4.74066e16i	0.841660	+	1.45780i	0.888490	+	0.458896i	$0.151755\pi$
$347$	2.73702e16	+	4.74066e16i	0.841660	+	1.45780i	−0.0468296	+	0.998903i	$0.514912\pi$
$348$	−5.69535e15	+	9.86463e15i	−0.171892	+	0.297725i
$349$	−4.37861e15			−0.129709			−0.0648546	−	0.997895i	$-0.520658\pi$
$349$	−4.37861e15			−0.129709			−0.0648546	+	0.997895i	$0.520658\pi$
$350$	−7.25082e15	−	2.31645e16i	−0.210836	−	0.673567i
$351$	1.33895e16			0.382179
$352$	9.15522e15	−	1.58573e16i	0.256532	−	0.444326i
$353$	−1.45702e16	−	2.52363e16i	−0.400802	−	0.694209i	0.593021	−	0.805187i	$-0.297935\pi$
$353$	−1.45702e16	−	2.52363e16i	−0.400802	−	0.694209i	−0.993823	+	0.110978i	$0.964602\pi$
$354$	2.26936e16	+	3.93065e16i	0.612891	+	1.06156i
$355$	−4.66653e14	+	8.08266e14i	−0.0123740	+	0.0214324i
$356$	5.20619e15			0.135549
$357$	3.78836e16	+	8.48128e15i	0.968518	+	0.216829i
$358$	−4.08425e15			−0.102535
$359$	−1.59646e16	+	2.76515e16i	−0.393590	+	0.681717i	−0.992920	−	0.118785i	$-0.962100\pi$
$359$	−1.59646e16	+	2.76515e16i	−0.393590	+	0.681717i	0.599330	+	0.800502i	$0.295434\pi$
$360$	−1.34300e16	−	2.32615e16i	−0.325170	−	0.563210i
$361$	2.05016e16	+	3.55098e16i	0.487518	+	0.844406i
$362$	1.15156e16	−	1.99457e16i	0.268957	−	0.465847i
$363$	1.18533e17			2.71922
$364$	−4.35132e15	+	4.72886e15i	−0.0980534	+	0.106561i
$365$	−1.67508e16			−0.370793
$366$	−4.92692e16	+	8.53368e16i	−1.07139	+	1.85571i
$367$	−5.62784e15	−	9.74771e15i	−0.120230	−	0.208244i	0.799628	−	0.600495i	$-0.205030\pi$
$367$	−5.62784e15	−	9.74771e15i	−0.120230	−	0.208244i	−0.919858	+	0.392251i	$0.871696\pi$
$368$	−9.46544e15	−	1.63946e16i	−0.198669	−	0.344105i
$369$	6.63958e15	−	1.15001e16i	0.136921	−	0.237154i
$370$	−2.58600e16			−0.523982
$371$	1.03554e16	−	1.12538e16i	0.206174	−	0.224063i
$372$	1.03592e16			0.202673
$373$	3.11427e16	−	5.39408e16i	0.598755	−	1.03707i	−0.394250	−	0.919003i	$-0.628996\pi$
$373$	3.11427e16	−	5.39408e16i	0.598755	−	1.03707i	0.993005	−	0.118071i	$-0.0376711\pi$
$374$	−2.68357e16	−	4.64808e16i	−0.507046	−	0.878229i
$375$	−3.45732e16	−	5.98825e16i	−0.642002	−	1.11198i
$376$	−4.39629e16	+	7.61459e16i	−0.802352	+	1.38971i
$377$	−7.70023e16			−1.38129
$378$	−2.07691e16	−	4.64972e15i	−0.366201	−	0.0819842i
$379$	3.17976e16			0.551112			0.275556	−	0.961285i	$-0.411138\pi$
$379$	3.17976e16			0.551112			0.275556	+	0.961285i	$0.411138\pi$
$380$	−3.45659e14	+	5.98700e14i	−0.00588918	+	0.0102004i
$381$	−5.34076e16	−	9.25046e16i	−0.894521	−	1.54936i
$382$	−4.19388e15	−	7.26402e15i	−0.0690565	−	0.119609i
$383$	9.81826e15	−	1.70057e16i	0.158943	−	0.275298i	−0.775545	−	0.631293i	$-0.782525\pi$
$383$	9.81826e15	−	1.70057e16i	0.158943	−	0.275298i	0.934488	+	0.355995i	$0.115858\pi$
$384$	6.70193e16			1.06671
$385$	1.54087e16	+	4.92267e16i	0.241141	+	0.770382i
$386$	7.78373e16			1.19776
$387$	−6.20126e16	+	1.07409e17i	−0.938336	+	1.62525i
$388$	6.38769e15	+	1.10638e16i	0.0950468	+	0.164626i
$389$	3.45207e15	+	5.97916e15i	0.0505135	+	0.0874919i	0.890177	−	0.455616i	$-0.150581\pi$
$389$	3.45207e15	+	5.97916e15i	0.0505135	+	0.0874919i	−0.839663	+	0.543108i	$0.817248\pi$
$390$	2.17282e16	−	3.76344e16i	0.312683	−	0.541583i
$391$	2.25097e16			0.318582
$392$	6.26544e16	−	4.34839e16i	0.872152	−	0.605298i
$393$	−4.80822e16			−0.658313
$394$	3.11799e16	−	5.40052e16i	0.419904	−	0.727295i
$395$	−9.57501e15	−	1.65844e16i	−0.126841	−	0.219694i
$396$	−1.26287e16	−	2.18736e16i	−0.164566	−	0.285037i
$397$	2.84521e16	−	4.92805e16i	0.364734	−	0.631738i	−0.623999	−	0.781425i	$-0.714493\pi$
$397$	2.84521e16	−	4.92805e16i	0.364734	−	0.631738i	0.988733	+	0.149687i	$0.0478266\pi$
$398$	−1.18679e17			−1.49670
$399$	5.73248e15	+	1.83138e16i	0.0711244	+	0.227224i
$400$	5.16561e16			0.630568
$401$	−4.74904e15	+	8.22557e15i	−0.0570384	+	0.0987933i	−0.893135	−	0.449789i	$-0.851499\pi$
$401$	−4.74904e15	+	8.22557e15i	−0.0570384	+	0.0987933i	0.836096	+	0.548583i	$0.184832\pi$
$402$	2.16570e16	+	3.75111e16i	0.255935	+	0.443292i
$403$	3.50145e16	+	6.06470e16i	0.407161	+	0.705223i
$404$	9.35378e15	−	1.62012e16i	0.107031	−	0.185383i
$405$	2.80738e16			0.316114
$406$	1.19442e17	+	2.67404e16i	1.32354	+	0.296312i
$407$	−1.81556e17			−1.97992
$408$	−4.90860e16	+	8.50194e16i	−0.526825	+	0.912487i
$409$	2.59014e16	+	4.48626e16i	0.273604	+	0.473896i	0.969782	−	0.243973i	$-0.0784510\pi$
$409$	2.59014e16	+	4.48626e16i	0.273604	+	0.473896i	−0.696178	+	0.717869i	$0.745118\pi$
$410$	−4.59268e15	−	7.95475e15i	−0.0477497	−	0.0827049i
$411$	−6.28261e15	+	1.08818e16i	−0.0642937	+	0.111360i
$412$	1.04181e16			0.104944
$413$	−6.04147e16	+	6.56565e16i	−0.599056	+	0.651032i
$414$	−5.79032e16			−0.565197
$415$	−3.54363e16	+	6.13775e16i	−0.340515	+	0.589789i
$416$	−1.51624e16	−	2.62620e16i	−0.143437	−	0.248440i
$417$	1.80530e15	+	3.12687e15i	0.0168138	+	0.0291223i
$418$	1.32653e16	−	2.29762e16i	0.121639	−	0.210684i
$419$	1.73717e17			1.56838			0.784190	−	0.620521i	$-0.213079\pi$
$419$	1.73717e17			1.56838			0.784190	+	0.620521i	$0.213079\pi$
$420$	8.55676e15	−	9.29917e15i	0.0760657	−	0.0826654i
$421$	−8.72237e16			−0.763486			−0.381743	−	0.924269i	$-0.624676\pi$
$421$	−8.72237e16			−0.763486			−0.381743	+	0.924269i	$0.624676\pi$
$422$	7.02733e16	−	1.21717e17i	0.605702	−	1.04911i
$423$	1.13163e17	+	1.96003e17i	0.960485	+	1.66361i
$424$	1.93368e16	+	3.34923e16i	0.161624	+	0.279941i
$425$	−3.07108e16	+	5.31927e16i	−0.252792	+	0.437848i
$426$	−8.77480e15			−0.0711336
$427$	−1.89029e17	−	4.23192e16i	−1.50920	−	0.337875i
$428$	9.66061e15			0.0759661
$429$	1.52548e17	−	2.64221e17i	1.18150	−	2.04642i
$430$	4.28948e16	+	7.42960e16i	0.327235	+	0.566788i
$431$	−5.20204e15	−	9.01019e15i	−0.0390905	−	0.0677067i	0.845818	−	0.533471i	$-0.179113\pi$
$431$	−5.20204e15	−	9.01019e15i	−0.0390905	−	0.0677067i	−0.884909	+	0.465764i	$0.845779\pi$
$432$	2.26469e16	−	3.92255e16i	0.167635	−	0.290352i
$433$	−2.25162e17			−1.64181			−0.820907	−	0.571062i	$-0.806532\pi$
$433$	−2.25162e17			−1.64181			−0.820907	+	0.571062i	$0.806532\pi$
$434$	−3.32521e16	−	1.06232e17i	−0.238856	−	0.763083i
$435$	1.51423e17			1.07155
$436$	−3.31152e15	+	5.73571e15i	−0.0230868	+	0.0399876i
$437$	5.56345e15	+	9.63618e15i	0.0382133	+	0.0661874i
$438$	−7.87442e16	−	1.36389e17i	−0.532889	−	0.922992i
$439$	1.07414e17	−	1.86046e17i	0.716209	−	1.24051i	−0.246283	−	0.969198i	$-0.579209\pi$
$439$	1.07414e17	−	1.86046e17i	0.716209	−	1.24051i	0.962492	−	0.271312i	$-0.0874574\pi$
$440$	−1.30441e17			−0.856982
$441$	−1.62962e16	−	1.95634e17i	−0.105496	−	1.26646i
$442$	−8.88876e16			−0.567018
$443$	−3.55148e16	+	6.15134e16i	−0.223247	+	0.386675i	−0.955792	−	0.294044i	$-0.904999\pi$
$443$	−3.55148e16	+	6.15134e16i	−0.223247	+	0.386675i	0.732545	+	0.680718i	$0.238332\pi$
$444$	2.22395e16	+	3.85200e16i	0.137764	+	0.238614i
$445$	−3.46045e16	−	5.99367e16i	−0.211248	−	0.365892i
$446$	−8.99732e16	+	1.55838e17i	−0.541298	+	0.937556i
$447$	5.66507e16			0.335897
$448$	5.63893e16	+	1.80149e17i	0.329526	+	1.05275i
$449$	3.06317e17			1.76429			0.882146	−	0.470976i	$-0.156098\pi$
$449$	3.06317e17			1.76429			0.882146	+	0.470976i	$0.156098\pi$
$450$	7.89993e16	−	1.36831e17i	0.448479	−	0.776788i
$451$	−3.22440e16	−	5.58482e16i	−0.180427	−	0.312508i
$452$	−4.79223e14	−	8.30038e14i	−0.00264325	−	0.00457824i
$453$	−1.82055e17	+	3.15328e17i	−0.989836	+	1.71445i
$454$	1.45693e17			0.780865
$455$	8.33636e16	+	1.86632e16i	0.440456	+	0.0986081i
$456$	−4.85279e16			−0.252767
$457$	2.82957e16	−	4.90095e16i	0.145300	−	0.251666i	−0.784185	−	0.620527i	$-0.786919\pi$
$457$	2.82957e16	−	4.90095e16i	0.145300	−	0.251666i	0.929485	+	0.368861i	$0.120252\pi$
$458$	9.80489e16	+	1.69826e17i	0.496383	+	0.859761i
$459$	2.69282e16	+	4.66410e16i	0.134408	+	0.232801i
$460$	3.66363e15	−	6.34560e15i	0.0180296	−	0.0312282i
$461$	−2.39909e17			−1.16410			−0.582050	−	0.813153i	$-0.697749\pi$
$461$	−2.39909e17			−1.16410			−0.582050	+	0.813153i	$0.697749\pi$
$462$	−3.28381e17	+	3.56872e17i	−1.57110	+	1.70742i
$463$	1.95497e17			0.922283			0.461142	−	0.887327i	$-0.347440\pi$
$463$	1.95497e17			0.922283			0.461142	+	0.887327i	$0.347440\pi$
$464$	−1.30241e17	+	2.25585e17i	−0.605874	+	1.04940i
$465$	−6.88551e16	−	1.19261e17i	−0.315858	−	0.547082i
$466$	−1.32143e17	−	2.28878e17i	−0.597771	−	1.03537i
$467$	1.08558e17	−	1.88027e17i	0.484285	−	0.838806i	−0.515552	−	0.856858i	$-0.672413\pi$
$467$	1.08558e17	−	1.88027e17i	0.484285	−	0.838806i	0.999837	+	0.0180524i	$0.00574657\pi$
$468$	−4.18300e16			−0.184030
$469$	−5.76551e16	+	6.26574e16i	−0.250158	+	0.271862i
$470$	1.56552e17			0.669918
$471$	3.96453e16	−	6.86678e16i	0.167323	−	0.289812i
$472$	−1.12814e17	−	1.95399e17i	−0.469612	−	0.813392i
$473$	3.01153e17	+	5.21613e17i	1.23649	+	2.14166i
$474$	9.00228e16	−	1.55924e17i	0.364580	−	0.631472i
$475$	−3.03616e16			−0.121288
$476$	−2.52237e16	−	5.64702e15i	−0.0993950	−	0.0222523i
$477$	9.95477e16			0.386956
$478$	6.57603e16	−	1.13900e17i	0.252163	−	0.436760i
$479$	−5.96895e16	−	1.03385e17i	−0.225796	−	0.391091i	0.730762	−	0.682633i	$-0.239165\pi$
$479$	−5.96895e16	−	1.03385e17i	−0.225796	−	0.391091i	−0.956558	+	0.291542i	$0.905832\pi$
$480$	2.98164e16	+	5.16435e16i	0.111272	+	0.192729i
$481$	−1.50342e17	+	2.60399e17i	−0.553524	+	0.958731i
$482$	1.34424e17			0.488281
$483$	−6.07583e16	−	1.94107e17i	−0.217746	−	0.695641i
$484$	−7.89217e16			−0.279063
$485$	8.49152e16	−	1.47077e17i	0.296254	−	0.513127i
$486$	1.86479e17	+	3.22991e17i	0.641939	+	1.11187i
$487$	−8.25455e16	−	1.42973e17i	−0.280385	−	0.485641i	0.691094	−	0.722765i	$-0.257129\pi$
$487$	−8.25455e16	−	1.42973e17i	−0.280385	−	0.485641i	−0.971480	+	0.237123i	$0.923796\pi$
$488$	2.44925e17	−	4.24223e17i	0.820928	−	1.42189i
$489$	−2.28698e17			−0.756405
$490$	−1.22828e17	−	5.78989e16i	−0.400889	−	0.188971i
$491$	4.88215e17			1.57247			0.786233	−	0.617930i	$-0.212028\pi$
$491$	4.88215e17			1.57247			0.786233	+	0.617930i	$0.212028\pi$
$492$	−7.89938e15	+	1.36821e16i	−0.0251085	+	0.0434891i
$493$	−1.54863e17	−	2.68231e17i	−0.485784	−	0.841403i
$494$	−2.19693e16	−	3.80519e16i	−0.0680127	−	0.117802i
$495$	−1.67881e17	+	2.90778e17i	−0.512941	+	0.888439i
$496$	2.36894e17			0.714369
$497$	−5.15283e15	−	1.64620e16i	−0.0153366	−	0.0489965i
$498$	−6.66333e17			−1.95750
$499$	−9.10541e16	+	1.57710e17i	−0.264025	+	0.457306i	−0.967308	−	0.253605i	$-0.918384\pi$
$499$	−9.10541e16	+	1.57710e17i	−0.264025	+	0.457306i	0.703282	+	0.710911i	$0.251717\pi$
$500$	2.30196e16	+	3.98711e16i	0.0658859	+	0.114118i
$501$	−3.15188e17	−	5.45921e17i	−0.890480	−	1.54236i
$502$	−2.96420e16	+	5.13415e16i	−0.0826673	+	0.143184i
$503$	−3.60834e17			−0.993381			−0.496691	−	0.867928i	$-0.665452\pi$
$503$	−3.60834e17			−0.993381			−0.496691	+	0.867928i	$0.665452\pi$
$504$	4.84442e17	+	1.08455e17i	1.31657	+	0.294749i
$505$	−2.48690e17			−0.667213
$506$	−1.40598e17	+	2.43523e17i	−0.372393	+	0.645004i
$507$	3.55060e16	+	6.14982e16i	0.0928431	+	0.160809i
$508$	3.55600e16	+	6.15916e16i	0.0918009	+	0.159004i
$509$	1.94391e17	−	3.36694e17i	0.495461	−	0.858164i	−0.504525	−	0.863397i	$-0.668332\pi$
$509$	1.94391e17	−	3.36694e17i	0.495461	−	0.858164i	0.999986	+	0.00523331i	$0.00166582\pi$
$510$	1.74795e17			0.439869
$511$	2.09632e17	−	2.27820e17i	0.520861	−	0.566052i
$512$	−4.58046e17			−1.12371
$513$	−1.33110e16	+	2.30554e16i	−0.0322440	+	0.0558482i
$514$	4.47785e16	+	7.75586e16i	0.107105	+	0.185511i
$515$	−6.92468e16	−	1.19939e17i	−0.163551	−	0.283278i
$516$	7.37789e16	−	1.27789e17i	0.172072	−	0.298037i
$517$	1.09911e18			2.53135
$518$	3.23631e17	−	3.51710e17i	0.736048	−	0.799910i
$519$	−3.89315e17			−0.874407
$520$	−1.08015e17	+	1.87087e17i	−0.239586	+	0.414975i
$521$	4.54401e17	+	7.87045e17i	0.995391	+	1.72407i	0.580745	+	0.814086i	$0.302761\pi$
$521$	4.54401e17	+	7.87045e17i	0.995391	+	1.72407i	0.414646	+	0.909983i	$0.363905\pi$
$522$	3.98364e17	+	6.89987e17i	0.861831	+	1.49274i
$523$	−3.96325e17	+	6.86456e17i	−0.846820	+	1.46673i	0.0372122	+	0.999307i	$0.488152\pi$
$523$	−3.96325e17	+	6.86456e17i	−0.846820	+	1.46673i	−0.884032	+	0.467427i	$0.845181\pi$
$524$	3.20142e16			0.0675599
$525$	5.41589e17	+	1.21249e17i	1.12884	+	0.252723i
$526$	−5.02513e16			−0.103452
$527$	−1.40839e17	+	2.43940e17i	−0.286387	+	0.496038i
$528$	−5.16039e17	−	8.93806e17i	−1.03648	−	1.79524i
$529$	1.93051e17	+	3.34375e17i	0.383011	+	0.663394i
$530$	3.44292e16	−	5.96330e16i	0.0674735	−	0.116868i
$531$	−5.80776e17			−1.12433
$532$	−3.81681e15	−	1.21937e16i	−0.00729920	−	0.0233191i
$533$	−1.06801e17			−0.201767
$534$	3.25346e17	−	5.63516e17i	0.607193	−	1.05169i
$535$	−6.42120e16	−	1.11218e17i	−0.118390	−	0.205058i
$536$	−1.07661e17	−	1.86474e17i	−0.196104	−	0.339662i
$537$	4.66929e16	−	8.08745e16i	0.0840269	−	0.145539i
$538$	−1.60694e17			−0.285703
$539$	−8.62346e17	−	4.06493e17i	−1.51480	−	0.714046i
$540$	1.75311e16			0.0304263
$541$	−4.75223e17	+	8.23111e17i	−0.814921	+	1.41148i	0.0944639	+	0.995528i	$0.469886\pi$
$541$	−4.75223e17	+	8.23111e17i	−0.814921	+	1.41148i	−0.909385	+	0.415956i	$0.863447\pi$
$542$	1.46475e17	+	2.53702e17i	0.248180	+	0.429861i
$543$	2.63304e17	+	4.56056e17i	0.440817	+	0.763517i
$544$	6.09876e16	−	1.05634e17i	0.100890	−	0.174747i
$545$	8.80437e16			0.143920
$546$	2.39926e17	+	7.66501e17i	0.387547	+	1.23811i
$547$	−2.19471e17			−0.350316			−0.175158	−	0.984540i	$-0.556044\pi$
$547$	−2.19471e17			−0.350316			−0.175158	+	0.984540i	$0.556044\pi$
$548$	4.18310e15	−	7.24535e15i	0.00659819	−	0.0114284i
$549$	−6.30450e17	−	1.09197e18i	−0.982721	−	1.70212i
$550$	−3.83646e17	−	6.64495e17i	−0.590981	−	1.02361i
$551$	7.65513e16	−	1.32591e17i	0.116538	−	0.201850i
$552$	5.14345e17			0.773839
$553$	3.45386e17	+	7.73240e16i	0.513560	+	0.114974i
$554$	−1.00184e17			−0.147225
$555$	2.95643e17	−	5.12068e17i	0.429401	−	0.743744i
$556$	−1.20201e15	−	2.08194e15i	−0.00172553	−	0.00298870i
$557$	1.91160e17	+	3.31099e17i	0.271231	+	0.469785i	0.969177	−	0.246365i	$-0.0792361\pi$
$557$	1.91160e17	+	3.31099e17i	0.271231	+	0.469785i	−0.697947	+	0.716150i	$0.745903\pi$
$558$	3.62289e17	−	6.27503e17i	0.508081	−	0.880022i
$559$	9.97508e17			1.38274
$560$	1.95676e17	−	2.12654e17i	0.268112	−	0.291374i
$561$	1.22719e18			1.66209
$562$	−7.74076e16	+	1.34074e17i	−0.103633	+	0.179497i
$563$	−6.27572e17	−	1.08699e18i	−0.830536	−	1.43853i	−0.897613	−	0.440783i	$-0.854701\pi$
$563$	−6.27572e17	−	1.08699e18i	−0.830536	−	1.43853i	0.0670771	−	0.997748i	$-0.478633\pi$
$564$	−1.34634e17	−	2.33193e17i	−0.176133	−	0.305072i
$565$	−6.37058e15	+	1.10342e16i	−0.00823880	+	0.0142700i
$566$	−1.09221e18			−1.39636
$567$	−3.51336e17	+	3.81819e17i	−0.444051	+	0.482578i
$568$	4.36209e16			0.0545043
$569$	−3.62232e17	+	6.27405e17i	−0.447463	+	0.775029i	−0.998220	−	0.0596364i	$-0.981006\pi$
$569$	−3.62232e17	+	6.27405e17i	−0.447463	+	0.775029i	0.550757	+	0.834666i	$0.314339\pi$
$570$	4.32019e16	+	7.48280e16i	0.0527614	+	0.0913855i
$571$	−4.79287e17	−	8.30149e17i	−0.578710	−	1.00235i	−0.995628	−	0.0934105i	$-0.970223\pi$
$571$	−4.79287e17	−	8.30149e17i	−0.578710	−	1.00235i	0.416918	−	0.908944i	$-0.363110\pi$
$572$	−1.01570e17	+	1.75925e17i	−0.121253	+	0.210016i
$573$	1.91785e17			0.226366
$574$	1.65665e17	+	3.70886e16i	0.193332	+	0.0432826i
$575$	3.21802e17			0.371319
$576$	−6.14373e17	+	1.06413e18i	−0.700948	+	1.21408i
$577$	−2.63120e17	−	4.55736e17i	−0.296832	−	0.514128i	0.678578	−	0.734529i	$-0.262597\pi$
$577$	−2.63120e17	−	4.55736e17i	−0.296832	−	0.514128i	−0.975409	+	0.220401i	$0.929263\pi$
$578$	2.33349e17	+	4.04173e17i	0.260301	+	0.450854i
$579$	−8.89871e17	+	1.54130e18i	−0.981559	+	1.70011i
$580$	−1.00821e17			−0.109968
$581$	−3.91292e17	−	1.25008e18i	−0.422042	−	1.34832i
$582$	1.59672e18			1.70306
$583$	2.41718e17	−	4.18668e17i	0.254955	−	0.441595i
$584$	3.91451e17	+	6.78012e17i	0.408313	+	0.707219i
$585$	2.78035e17	+	4.81571e17i	0.286805	+	0.496760i
$586$	−2.40492e17	+	4.16545e17i	−0.245339	+	0.424939i
$587$	−1.14736e18			−1.15758			−0.578790	−	0.815476i	$-0.696475\pi$
$587$	−1.14736e18			−1.15758			−0.578790	+	0.815476i	$0.696475\pi$
$588$	1.93883e16	+	2.32753e17i	0.0193458	+	0.232243i
$589$	−1.39238e17			−0.137407
$590$	−2.00865e17	+	3.47908e17i	−0.196050	+	0.339568i
$591$	7.12926e17	+	1.23482e18i	0.688217	+	1.19203i
$592$	5.08574e17	+	8.80877e17i	0.485583	+	0.841054i
$593$	2.38082e17	−	4.12370e17i	0.224839	−	0.389432i	−0.731432	−	0.681914i	$-0.761148\pi$
$593$	2.38082e17	−	4.12370e17i	0.224839	−	0.389432i	0.956271	+	0.292482i	$0.0944812\pi$
$594$	−6.72787e17			−0.628442
$595$	1.02645e17	+	3.27925e17i	0.0948370	+	0.302980i
$596$	−3.77193e16			−0.0344717
$597$	1.35679e18	−	2.35004e18i	1.22654	−	2.12443i
$598$	2.32851e17	+	4.03310e17i	0.208219	+	0.360646i
$599$	3.73199e17	+	6.46400e17i	0.330116	+	0.571778i	0.982534	−	0.186081i	$-0.0595788\pi$
$599$	3.73199e17	+	6.46400e17i	0.330116	+	0.571778i	−0.652418	+	0.757859i	$0.726245\pi$
$600$	−7.01739e17	+	1.21545e18i	−0.614034	+	1.06354i
$601$	1.84451e18			1.59661			0.798303	−	0.602257i	$-0.205732\pi$
$601$	1.84451e18			1.59661			0.798303	+	0.602257i	$0.205732\pi$
$602$	−1.54728e18	−	3.46402e17i	−1.32493	−	0.296622i
$603$	−5.54248e17			−0.469506
$604$	1.21216e17	−	2.09952e17i	0.101583	−	0.175946i
$605$	5.24576e17	+	9.08592e17i	0.434909	+	0.753284i
$606$	−1.16907e18	−	2.02489e18i	−0.958892	−	1.66085i
$607$	9.71234e17	−	1.68223e18i	0.788129	−	1.36508i	−0.138982	−	0.990295i	$-0.544383\pi$
$607$	9.71234e17	−	1.68223e18i	0.788129	−	1.36508i	0.927112	−	0.374785i	$-0.122284\pi$
$608$	6.02943e16			0.0484064
$609$	−1.89502e18	+	2.05944e18i	−1.50522	+	1.63582i
$610$	−8.72179e17			−0.685428
$611$	9.10142e17	−	1.57641e18i	0.707687	−	1.22575i
$612$	−8.41264e16	−	1.45711e17i	−0.0647214	−	0.112101i
$613$	−7.58251e16	−	1.31333e17i	−0.0577191	−	0.0999724i	0.835722	−	0.549153i	$-0.185049\pi$
$613$	−7.58251e16	−	1.31333e17i	−0.0577191	−	0.0999724i	−0.893441	+	0.449180i	$0.851716\pi$
$614$	4.83042e17	−	8.36653e17i	0.363823	−	0.630160i
$615$	2.10022e17			0.156522
$616$	1.63244e18	−	1.77407e18i	1.20382	−	1.30827i
$617$	−1.23313e18			−0.899816			−0.449908	−	0.893075i	$-0.648543\pi$
$617$	−1.23313e18			−0.899816			−0.449908	+	0.893075i	$0.648543\pi$
$618$	6.51048e17	−	1.12765e18i	0.470097	−	0.814233i
$619$	−2.20877e17	−	3.82569e17i	−0.157819	−	0.273351i	0.776263	−	0.630410i	$-0.217113\pi$
$619$	−2.20877e17	−	3.82569e17i	−0.157819	−	0.273351i	−0.934082	+	0.357058i	$0.883780\pi$
$620$	4.58453e16	+	7.94064e16i	0.0324152	+	0.0561448i
$621$	1.41083e17	−	2.44363e17i	0.0987141	−	0.170978i
$622$	−1.53860e18			−1.06534
$623$	1.24824e18	+	2.79452e17i	0.855313	+	0.191485i
$624$	−1.70927e18			−1.15907
$625$	−2.65926e17	+	4.60598e17i	−0.178460	+	0.309102i
$626$	6.17064e17	+	1.06879e18i	0.409824	+	0.709835i
$627$	3.03310e17	+	5.25347e17i	0.199364	+	0.345309i
$628$	−2.63968e16	+	4.57205e16i	−0.0171717	+	0.0297422i
$629$	−1.20944e18			−0.778672
$630$	−2.64040e17	−	8.43541e17i	−0.168251	−	0.537518i
$631$	−9.80756e16			−0.0618543			−0.0309272	−	0.999522i	$-0.509846\pi$
$631$	−9.80756e16			−0.0618543			−0.0309272	+	0.999522i	$0.509846\pi$
$632$	−4.47518e17	+	7.75124e17i	−0.279351	+	0.483849i
$633$	1.60679e18	+	2.78304e18i	0.992739	+	1.71947i
$634$	7.38615e16	+	1.27932e17i	0.0451687	+	0.0782345i
$635$	4.72719e17	−	8.18773e17i	0.286137	−	0.495603i
$636$	−1.18436e17			−0.0709598
$637$	−1.29710e18	+	9.00226e17i	−0.769252	+	0.533882i
$638$	3.86918e18			2.27135
$639$	5.61412e16	−	9.72394e16i	0.0326232	−	0.0565050i
$640$	2.96599e17	+	5.13725e17i	0.170608	+	0.295502i
$641$	−1.15218e18	−	1.99564e18i	−0.656060	−	1.13633i	−0.981627	−	0.190811i	$-0.938888\pi$
$641$	−1.15218e18	−	1.99564e18i	−0.656060	−	1.13633i	0.325566	−	0.945519i	$-0.394445\pi$
$642$	6.03711e17	−	1.04566e18i	0.340292	−	0.589403i
$643$	−2.77921e17			−0.155078			−0.0775389	−	0.996989i	$-0.524706\pi$
$643$	−2.77921e17			−0.155078			−0.0775389	+	0.996989i	$0.524706\pi$
$644$	4.04542e16	+	1.29241e17i	0.0223463	+	0.0713907i
$645$	−1.96157e18			−1.07267
$646$	8.83670e16	−	1.53056e17i	0.0478386	−	0.0828589i
$647$	−5.20991e17	−	9.02382e17i	−0.279224	−	0.483629i	0.691968	−	0.721928i	$-0.256744\pi$
$647$	−5.20991e17	−	9.02382e17i	−0.279224	−	0.483629i	−0.971192	+	0.238298i	$0.923410\pi$
$648$	−6.56058e17	−	1.13633e18i	−0.348100	−	0.602928i
$649$	−1.41022e18	+	2.44257e18i	−0.740792	+	1.28309i
$650$	−1.27075e18			−0.660880
$651$	2.48371e18	+	5.56047e17i	1.27887	+	0.286309i
$652$	1.52272e17			0.0776266
$653$	−9.52198e17	+	1.64926e18i	−0.480609	+	0.832439i	−0.999752	−	0.0222483i	$-0.992918\pi$
$653$	−9.52198e17	+	1.64926e18i	−0.480609	+	0.832439i	0.519144	+	0.854687i	$0.326251\pi$
$654$	4.13887e17	+	7.16873e17i	0.206836	+	0.358251i
$655$	−2.12791e17	−	3.68566e17i	−0.105290	−	0.182367i
$656$	−1.80644e17	+	3.12884e17i	−0.0885008	+	0.153288i
$657$	2.01523e18			0.977572
$658$	−1.95920e18	+	2.12919e18i	−0.941047	+	1.02270i
$659$	1.61004e18			0.765741			0.382871	−	0.923802i	$-0.374935\pi$
$659$	1.61004e18			0.765741			0.382871	+	0.923802i	$0.374935\pi$
$660$	1.99735e17	−	3.45951e17i	0.0940628	−	0.162922i
$661$	−9.91684e17	−	1.71765e18i	−0.462449	−	0.800985i	0.536633	−	0.843815i	$-0.319696\pi$
$661$	−9.91684e17	−	1.71765e18i	−0.462449	−	0.800985i	−0.999082	+	0.0428304i	$0.986362\pi$
$662$	1.96642e18	+	3.40594e18i	0.908028	+	1.57275i
$663$	1.01620e18	−	1.76012e18i	0.464668	−	0.804828i
$664$	3.31245e18			1.49988
$665$	−1.15012e17	+	1.24990e17i	−0.0515705	+	0.0560449i
$666$	3.11111e18			1.38144
$667$	−8.11364e17	+	1.40532e18i	−0.356778	+	0.617958i
$668$	2.09859e17	+	3.63487e17i	0.0913862	+	0.158286i
$669$	−2.05723e18	−	3.56322e18i	−0.887181	−	1.53664i
$670$	−1.91690e17	+	3.32017e17i	−0.0818678	+	0.141799i
$671$	−6.12334e18			−2.58995
$672$	−1.07552e18	−	2.40786e17i	−0.450526	−	0.100863i
$673$	1.31549e18			0.545745			0.272872	−	0.962050i	$-0.412026\pi$
$673$	1.31549e18			0.545745			0.272872	+	0.962050i	$0.412026\pi$
$674$	4.24545e17	−	7.35333e17i	0.174435	−	0.302130i
$675$	3.84969e17	+	6.66786e17i	0.156657	+	0.271339i
$676$	−2.36407e16	−	4.09469e16i	−0.00952810	−	0.0165032i
$677$	2.06222e18	−	3.57187e18i	0.823206	−	1.42583i	−0.0800770	−	0.996789i	$-0.525517\pi$
$677$	2.06222e18	−	3.57187e18i	0.823206	−	1.42583i	0.903283	−	0.429046i	$-0.141150\pi$
$678$	−1.19790e17			−0.0473619
$679$	9.37643e17	+	2.99553e18i	0.367184	+	1.17306i
$680$	−8.68935e17			−0.337038
$681$	−1.66563e18	+	2.88495e18i	−0.639915	+	1.10836i
$682$	−1.75939e18	−	3.04736e18i	−0.669522	−	1.15965i
$683$	2.06153e18	+	3.57067e18i	0.777060	+	1.34591i	0.933630	+	0.358240i	$0.116623\pi$
$683$	2.06153e18	+	3.57067e18i	0.777060	+	1.34591i	−0.156570	+	0.987667i	$0.550044\pi$
$684$	4.15850e16	−	7.20273e16i	0.0155264	−	0.0268926i
$685$	−1.11217e17			−0.0411322
$686$	2.32462e18	−	9.45945e17i	0.851620	−	0.346545i
$687$	−4.48376e18			−1.62713
$688$	1.68718e18	−	2.92228e18i	0.606508	−	1.05050i
$689$	−4.00320e17	−	6.93375e17i	−0.142555	−	0.246913i
$690$	−4.57896e17	−	7.93099e17i	−0.161528	−	0.279775i
$691$	−1.38872e18	+	2.40534e18i	−0.485298	+	0.840562i	−0.999857	−	0.0168935i	$-0.994622\pi$
$691$	−1.38872e18	+	2.40534e18i	−0.485298	+	0.840562i	0.514559	+	0.857455i	$0.327956\pi$
$692$	2.59215e17			0.0897367
$693$	−1.85376e18	−	5.92228e18i	−0.635751	−	2.03106i
$694$	−4.55535e18			−1.54769
$695$	−1.59790e16	+	2.76764e16i	−0.00537834	+	0.00931555i
$696$	−3.53861e18	−	6.12906e18i	−1.17998	−	2.04378i
$697$	−2.14794e17	−	3.72034e17i	−0.0709592	−	0.122905i
$698$	1.82188e17	−	3.15559e17i	0.0596292	−	0.103281i
$699$	6.04286e18			1.95948
$700$	−3.60602e17	−	8.07305e16i	−0.115849	−	0.0259359i
$701$	4.70460e18			1.49746			0.748730	−	0.662875i	$-0.230664\pi$
$701$	4.70460e18			1.49746			0.748730	+	0.662875i	$0.230664\pi$
$702$	−5.57116e17	+	9.64954e17i	−0.175693	+	0.304309i
$703$	−2.98922e17	−	5.17748e17i	−0.0934003	−	0.161774i
$704$	2.98360e18	+	5.16774e18i	0.923672	+	1.59985i
$705$	−1.78977e18	+	3.09997e18i	−0.548994	+	0.950886i
$706$	2.42498e18			0.737017
$707$	3.11229e18	−	3.38232e18i	0.937247	−	1.01857i
$708$	6.90974e17			0.206179
$709$	7.67108e17	−	1.32867e18i	0.226807	−	0.392841i	−0.730053	−	0.683390i	$-0.760505\pi$
$709$	7.67108e17	−	1.32867e18i	0.226807	−	0.392841i	0.956860	+	0.290549i	$0.0938381\pi$
$710$	−3.88335e16	−	6.72617e16i	−0.0113770	−	0.0197055i
$711$	1.15193e18	+	1.99521e18i	0.334407	+	0.579209i
$712$	−1.61735e18	+	2.80133e18i	−0.465247	+	0.805831i
$713$	1.47578e18			0.420667
$714$	−2.18751e18	+	2.37731e18i	−0.617892	+	0.671502i
$715$	2.70046e18			0.755872
$716$	−3.10892e16	+	5.38481e16i	−0.00862332	+	0.0149360i
$717$	1.50360e18	+	2.60431e18i	0.413293	+	0.715845i
$718$	−1.32853e18	−	2.30108e18i	−0.361878	−	0.626790i
$719$	−1.14227e18	+	1.97847e18i	−0.308341	+	0.534063i	−0.978000	−	0.208607i	$-0.933107\pi$
$719$	−1.14227e18	+	1.97847e18i	−0.308341	+	0.534063i	0.669658	+	0.742669i	$0.266441\pi$
$720$	1.88107e18			0.503203
$721$	2.49784e18	+	5.59210e17i	0.662195	+	0.148250i
$722$	−3.41217e18			−0.896476
$723$	−1.53679e18	+	2.66180e18i	−0.400144	+	0.693069i
$724$	−1.75314e17	−	3.03652e17i	−0.0452392	−	0.0783566i
$725$	−2.21394e18	−	3.83467e18i	−0.566200	−	0.980687i
$726$	−4.93198e18	+	8.54244e18i	−1.25007	+	2.16518i
$727$	−3.35392e18			−0.842519			−0.421259	−	0.906940i	$-0.638412\pi$
$727$	−3.35392e18			−0.842519			−0.421259	+	0.906940i	$0.638412\pi$
$728$	−1.19271e18	−	3.81040e18i	−0.296948	−	0.948674i
$729$	−5.87000e18			−1.44847
$730$	6.96978e17	−	1.20720e18i	0.170459	−	0.295244i
$731$	2.00614e18	+	3.47473e18i	0.486293	+	0.842284i
$732$	7.50073e17	+	1.29916e18i	0.180211	+	0.312135i
$733$	2.26376e18	−	3.92095e18i	0.539082	−	0.933717i	−0.459872	−	0.887985i	$-0.652105\pi$
$733$	2.26376e18	−	3.92095e18i	0.539082	−	0.933717i	0.998954	−	0.0457317i	$-0.0145619\pi$
$734$	9.36666e17			0.221086
$735$	2.55072e18	−	1.77027e18i	0.596754	−	0.414164i
$736$	−6.39057e17			−0.148195
$737$	−1.34580e18	+	2.33100e18i	−0.309345	+	0.535801i
$738$	5.52527e17	+	9.57005e17i	0.125889	+	0.218046i
$739$	−6.34508e17	−	1.09900e18i	−0.143301	−	0.248204i	0.785437	−	0.618942i	$-0.212438\pi$
$739$	−6.34508e17	−	1.09900e18i	−0.143301	−	0.248204i	−0.928738	+	0.370737i	$0.879105\pi$
$740$	−1.96845e17	+	3.40946e17i	−0.0440676	+	0.0763273i
$741$	1.00465e18			0.222944
$742$	3.80171e17	+	1.21455e18i	0.0836283	+	0.267171i
$743$	4.06623e17			0.0886676			0.0443338	−	0.999017i	$-0.485883\pi$
$743$	4.06623e17			0.0886676			0.0443338	+	0.999017i	$0.485883\pi$
$744$	−3.21816e18	+	5.57402e18i	−0.695638	+	1.20488i
$745$	2.50712e17	+	4.34246e17i	0.0537229	+	0.0930507i
$746$	2.59161e18	+	4.48880e18i	0.550513	+	0.953516i
$747$	4.26321e18	−	7.38409e18i	0.897744	−	1.55494i
$748$	−8.17091e17			−0.170573
$749$	2.31623e18	+	5.18551e17i	0.479347	+	0.107315i
$750$	5.75417e18			1.18055
$751$	3.90597e18	−	6.76533e18i	0.794454	−	1.37604i	−0.128731	−	0.991680i	$-0.541090\pi$
$751$	3.90597e18	−	6.76533e18i	0.794454	−	1.37604i	0.923185	−	0.384356i	$-0.125576\pi$
$752$	−3.07882e18	−	5.33268e18i	−0.620824	−	1.07530i
$753$	−6.77762e17	−	1.17392e18i	−0.135491	−	0.234677i
$754$	3.20396e18	−	5.54942e18i	0.634999	−	1.09985i
$755$	−3.22279e18			−0.633252
$756$	−2.19397e17	+	2.38433e17i	−0.0427404	+	0.0464487i
$757$	−4.91857e18			−0.949982			−0.474991	−	0.879991i	$-0.657549\pi$
$757$	−4.91857e18			−0.949982			−0.474991	+	0.879991i	$0.657549\pi$
$758$	−1.32305e18	+	2.29160e18i	−0.253354	+	0.438822i
$759$	−3.21477e18	−	5.56814e18i	−0.610348	−	1.05715i
$760$	−2.14764e17	−	3.71982e17i	−0.0404271	−	0.0700219i
$761$	1.19821e18	−	2.07536e18i	0.223632	−	0.387341i	−0.732276	−	0.681008i	$-0.761542\pi$
$761$	1.19821e18	−	2.07536e18i	0.223632	−	0.387341i	0.955908	+	0.293666i	$0.0948754\pi$
$762$	8.88886e18			1.64490
$763$	−1.10184e18	+	1.19744e18i	−0.202167	+	0.219708i
$764$	−1.27695e17			−0.0232310
$765$	−1.11834e18	+	1.93702e18i	−0.201732	+	0.349410i
$766$	8.17048e17	+	1.41517e18i	0.146137	+	0.253117i
$767$	2.33553e18	+	4.04526e18i	0.414205	+	0.717425i
$768$	1.93786e18	−	3.35647e18i	0.340780	−	0.590248i
$769$	−1.78932e18			−0.312009			−0.156004	−	0.987756i	$-0.549861\pi$
$769$	−1.78932e18			−0.312009			−0.156004	+	0.987756i	$0.549861\pi$
$770$	−4.18882e18	−	9.37781e17i	−0.724272	−	0.162148i
$771$	−2.04771e18			−0.351087
$772$	5.92496e17	−	1.02623e18i	0.100733	−	0.174475i
$773$	−2.50662e18	−	4.34160e18i	−0.422593	−	0.731952i	0.573599	−	0.819136i	$-0.305547\pi$
$773$	−2.50662e18	−	4.34160e18i	−0.422593	−	0.731952i	−0.996192	+	0.0871837i	$0.972213\pi$
$774$	−5.16051e18	−	8.93827e18i	−0.862734	−	1.49430i
$775$	−2.01345e18	+	3.48740e18i	−0.333795	+	0.578151i
$776$	−7.93755e18			−1.30492
$777$	3.26452e18	+	1.04293e19i	0.532209	+	1.70027i
$778$	−5.74543e17			−0.0928871
$779$	1.06176e17	−	1.83902e17i	0.0170229	−	0.0294844i
$780$	−3.30790e17	−	5.72945e17i	−0.0525941	−	0.0910957i
$781$	−2.72640e17	−	4.72227e17i	−0.0429891	−	0.0744593i
$782$	−9.36598e17	+	1.62224e18i	−0.146457	+	0.253671i
$783$	−3.88251e18			−0.602090
$784$	4.43372e17	+	5.32261e18i	0.0681889	+	0.818598i
$785$	7.01814e17			0.107046
$786$	2.00063e18	−	3.46520e18i	0.302636	−	0.524181i
$787$	5.31061e18	+	9.19824e18i	0.796725	+	1.37997i	0.921738	+	0.387813i	$0.126769\pi$
$787$	5.31061e18	+	9.19824e18i	0.796725	+	1.37997i	−0.125013	+	0.992155i	$0.539897\pi$
$788$	−4.74682e17	−	8.22173e17i	−0.0706289	−	0.122333i
$789$	5.74495e17	−	9.95055e17i	0.0847786	−	0.146841i
$790$	1.59361e18			0.233242
$791$	−7.03447e16	−	2.24733e17i	−0.0102114	−	0.0326227i
$792$	1.56929e19			2.25938
$793$	−5.07057e18	+	8.78249e18i	−0.724071	+	1.25413i
$794$	2.36771e18	+	4.10099e18i	0.335347	+	0.580838i
$795$	7.87219e17	+	1.36350e18i	0.110588	+	0.191545i
$796$	−9.03384e17	+	1.56471e18i	−0.125874	+	0.218021i
$797$	−7.42730e18			−1.02648			−0.513242	−	0.858244i	$-0.671556\pi$
$797$	−7.42730e18			−1.02648			−0.513242	+	0.858244i	$0.671556\pi$
$798$	−1.55836e18	−	3.48882e17i	−0.213624	−	0.0478255i
$799$	7.32173e18			0.995542
$800$	8.71887e17	−	1.51015e18i	0.117591	−	0.203674i
$801$	4.16313e18	+	7.21075e18i	0.556940	+	0.964649i
$802$	−3.95202e17	−	6.84509e17i	−0.0524427	−	0.0908335i
$803$	4.89330e18	−	8.47544e18i	0.644096	−	1.11561i
$804$	6.59412e17			0.0860978
$805$	1.21900e18	−	1.32477e18i	0.157882	−	0.171580i
$806$	−5.82763e18			−0.748710
$807$	1.83713e18	−	3.18200e18i	0.234132	−	0.405529i
$808$	5.81166e18	+	1.00661e19i	0.734727	+	1.27258i
$809$	−3.64614e17	−	6.31530e17i	−0.0457265	−	0.0792006i	0.842256	−	0.539077i	$-0.181227\pi$
$809$	−3.64614e17	−	6.31530e17i	−0.0457265	−	0.0792006i	−0.887983	+	0.459877i	$0.847894\pi$
$810$	−1.16811e18	+	2.02323e18i	−0.145322	+	0.251705i
$811$	−9.53295e18			−1.17650			−0.588250	−	0.808679i	$-0.700183\pi$
$811$	−9.53295e18			−1.17650			−0.588250	+	0.808679i	$0.700183\pi$
$812$	1.26175e18	−	1.37122e18i	0.154475	−	0.167877i
$813$	−6.69825e18			−0.813529
$814$	7.55429e18	−	1.30844e19i	0.910197	−	1.57651i
$815$	−1.01212e18	−	1.75304e18i	−0.120978	−	0.209540i
$816$	−3.43760e18	−	5.95410e18i	−0.407633	−	0.706042i
$817$	−9.91665e17	+	1.71761e18i	−0.116660	+	0.202061i
$818$	−4.31089e18			−0.503119
$819$	−1.00292e19	−	2.24530e18i	−1.16123	−	0.259974i
$820$	−1.39837e17			−0.0160632
$821$	1.02172e17	−	1.76967e17i	0.0116440	−	0.0201679i	−0.860145	−	0.510050i	$-0.829627\pi$
$821$	1.02172e17	−	1.76967e17i	0.0116440	−	0.0201679i	0.871789	+	0.489882i	$0.162960\pi$
$822$	−5.22821e17	−	9.05553e17i	−0.0591135	−	0.102388i
$823$	1.52052e18	+	2.63362e18i	0.170566	+	0.295429i	0.938618	−	0.344959i	$-0.112107\pi$
$823$	1.52052e18	+	2.63362e18i	0.170566	+	0.295429i	−0.768052	+	0.640388i	$0.778774\pi$
$824$	−3.23647e18	+	5.60572e18i	−0.360200	+	0.623885i
$825$	1.75441e19			1.93722
$826$	−2.21797e18	−	7.08586e18i	−0.242989	−	0.776287i
$827$	−9.54127e18			−1.03710			−0.518550	−	0.855047i	$-0.673528\pi$
$827$	−9.54127e18			−1.03710			−0.518550	+	0.855047i	$0.673528\pi$
$828$	−4.40758e17	+	7.63414e17i	−0.0475338	+	0.0823310i
$829$	2.41893e18	+	4.18971e18i	0.258832	+	0.448311i	0.965929	−	0.258806i	$-0.0833289\pi$
$829$	2.41893e18	+	4.18971e18i	0.258832	+	0.448311i	−0.707097	+	0.707117i	$0.749996\pi$
$830$	−2.94891e18	−	5.10766e18i	−0.313079	−	0.542269i
$831$	1.14534e18	−	1.98379e18i	0.120650	−	0.208973i
$832$	9.88254e18			1.03292
$833$	−5.74453e18	−	2.70786e18i	−0.595748	−	0.280824i
$834$	−3.00464e17			−0.0309181
$835$	2.78978e18	−	4.83204e18i	0.284844	−	0.493365i
$836$	−2.01950e17	−	3.49788e17i	−0.0204599	−	0.0354376i
$837$	1.76546e18	+	3.05786e18i	0.177477	+	0.307399i
$838$	−7.22812e18	+	1.25195e19i	−0.721007	+	1.24882i
$839$	5.31128e18			0.525710			0.262855	−	0.964835i	$-0.415336\pi$
$839$	5.31128e18			0.525710			0.262855	+	0.964835i	$0.415336\pi$
$840$	2.34543e18	+	7.49305e18i	0.230360	+	0.735942i
$841$	1.20676e19			1.17611
$842$	3.62926e18	−	6.28606e18i	0.350985	−	0.607925i
$843$	−1.76992e18	−	3.06559e18i	−0.169853	−	0.294194i
$844$	−1.06984e18	−	1.85301e18i	−0.101881	−	0.176462i
$845$	−3.14269e17	+	5.44330e17i	−0.0296984	+	0.0514391i
$846$	−1.88341e19			−1.76619
$847$	−1.89223e19	−	4.23627e18i	−1.76089	−	0.394222i
$848$	−2.70840e18			−0.250115
$849$	1.24866e19	−	2.16274e19i	1.14431	−	1.98200i
$850$	−2.55567e18	−	4.42654e18i	−0.232424	−	0.402570i
$851$	3.16826e18	+	5.48759e18i	0.285943	+	0.495267i
$852$	−6.67935e16	+	1.15690e17i	−0.00598242	+	0.0103619i
$853$	2.22749e18			0.197992			0.0989960	−	0.995088i	$-0.468437\pi$
$853$	2.22749e18			0.197992			0.0989960	+	0.995088i	$0.468437\pi$
$854$	1.09151e19	−	1.18621e19i	0.962834	−	1.04637i
$855$	−1.10563e18			−0.0967895
$856$	−3.00115e18	+	5.19814e18i	−0.260740	+	0.451615i
$857$	−1.36406e18	−	2.36261e18i	−0.117613	−	0.203712i	0.801208	−	0.598386i	$-0.204191\pi$
$857$	−1.36406e18	−	2.36261e18i	−0.117613	−	0.203712i	−0.918821	+	0.394674i	$0.870858\pi$
$858$	1.26946e19	+	2.19878e19i	1.08631	+	1.88154i
$859$	1.04082e18	−	1.80275e18i	0.0883934	−	0.153102i	−0.818439	−	0.574594i	$-0.805160\pi$
$859$	1.04082e18	−	1.80275e18i	0.0883934	−	0.153102i	0.906832	+	0.421492i	$0.138493\pi$
$860$	1.30606e18			0.110084
$861$	−2.62837e18	+	2.85642e18i	−0.219870	+	0.238947i
$862$	8.65798e17			0.0718819
$863$	−1.00618e19	+	1.74275e19i	−0.829097	+	1.43604i	0.0696510	+	0.997571i	$0.477811\pi$
$863$	−1.00618e19	+	1.74275e19i	−0.829097	+	1.43604i	−0.898748	+	0.438466i	$0.855522\pi$
$864$	−7.64498e17	−	1.32415e18i	−0.0625226	−	0.108292i
$865$	−1.72295e18	−	2.98423e18i	−0.139851	−	0.242230i
$866$	9.36868e18	−	1.62270e19i	0.754766	−	1.30729i
$867$	−1.06710e19			−0.853260
$868$	−1.65371e18	−	3.70228e17i	−0.131245	−	0.0293827i
$869$	1.11883e19			0.881326
$870$	−6.30050e18	+	1.09128e19i	−0.492606	+	0.853219i
$871$	2.22885e18	+	3.86048e18i	0.172967	+	0.299587i
$872$	−2.05750e18	−	3.56369e18i	−0.158483	−	0.274501i
$873$	−1.02158e19	+	1.76943e19i	−0.781053	+	1.35282i
$874$	−9.25950e17			−0.0702689
$875$	3.37903e18	+	1.07951e19i	0.254530	+	0.813159i
$876$	−2.39760e18			−0.179267
$877$	7.85684e18	−	1.36084e19i	0.583110	−	1.00998i	−0.411998	−	0.911185i	$-0.635169\pi$
$877$	7.85684e18	−	1.36084e19i	0.583110	−	1.00998i	0.995108	−	0.0987911i	$-0.0314976\pi$
$878$	8.93865e18	+	1.54822e19i	0.658503	+	1.14056i
$879$	−5.49883e18	−	9.52425e18i	−0.402108	−	0.696471i
$880$	4.56754e18	−	7.91122e18i	0.331547	−	0.574256i
$881$	2.05256e19			1.47895			0.739475	−	0.673184i	$-0.235074\pi$
$881$	2.05256e19			1.47895			0.739475	+	0.673184i	$0.235074\pi$
$882$	1.47770e19	+	6.96560e18i	1.05692	+	0.498210i
$883$	7.91695e18			0.562100			0.281050	−	0.959693i	$-0.409317\pi$
$883$	7.91695e18			0.562100			0.281050	+	0.959693i	$0.409317\pi$
$884$	−6.76611e17	+	1.17192e18i	−0.0476869	+	0.0825961i
$885$	−4.59276e18	−	7.95489e18i	−0.321323	−	0.556548i
$886$	−2.95544e18	−	5.11898e18i	−0.205260	−	0.355520i
$887$	−4.87157e18	+	8.43781e18i	−0.335865	+	0.581736i	−0.983651	−	0.180087i	$-0.942362\pi$
$887$	−4.87157e18	+	8.43781e18i	−0.335865	+	0.581736i	0.647785	+	0.761823i	$0.275695\pi$
$888$	−2.76356e19			−1.89140
$889$	5.21981e18	+	1.66760e19i	0.354645	+	1.13300i
$890$	5.75937e18			0.388455
$891$	−8.20100e18	+	1.42045e19i	−0.549113	+	0.951092i
$892$	1.36975e18	+	2.37247e18i	0.0910477	+	0.157699i
$893$	1.80962e18	+	3.13436e18i	0.119414	+	0.206830i
$894$	−2.35715e18	+	4.08271e18i	−0.154417	+	0.267458i
$895$	8.26573e17			0.0537565
$896$	−1.06988e19	−	2.39522e18i	−0.690770	−	0.154648i
$897$	−1.06482e19			−0.682538
$898$	−1.27454e19	+	2.20757e19i	−0.811071	+	1.40482i
$899$	−1.01531e19	−	1.75857e19i	−0.641447	−	1.11102i
$900$	−1.20268e18	−	2.08311e18i	−0.0754352	−	0.130658i
$901$	1.61021e18	−	2.78896e18i	0.100270	−	0.173673i
$902$	5.36651e18			0.331779
$903$	2.45485e19	−	2.66785e19i	1.50680	−	1.63753i
$904$	5.95498e17			0.0362899
$905$	−2.33054e18	+	4.03662e18i	−0.141007	+	0.244232i
$906$	−1.51501e19	−	2.62407e19i	−0.910084	−	1.57631i
$907$	−1.30717e19	−	2.26409e19i	−0.779624	−	1.35035i	−0.932159	−	0.362050i	$-0.882077\pi$
$907$	−1.30717e19	−	2.26409e19i	−0.779624	−	1.35035i	0.152534	−	0.988298i	$-0.451257\pi$
$908$	1.10901e18	−	1.92087e18i	0.0656718	−	0.113747i
$909$	2.99190e19			1.75906
$910$	−4.81367e18	+	5.23132e18i	−0.281001	+	0.305381i
$911$	4.49567e18			0.260570			0.130285	−	0.991477i	$-0.458411\pi$
$911$	4.49567e18			0.260570			0.130285	+	0.991477i	$0.458411\pi$
$912$	1.69926e18	−	2.94320e18i	0.0977898	−	0.169377i
$913$	−2.07035e19	−	3.58596e19i	−1.18300	−	2.04901i
$914$	2.35469e18	+	4.07844e18i	0.133593	+	0.231389i
$915$	9.97114e18	−	1.72705e19i	0.561704	−	0.972901i
$916$	2.98538e18			0.166986
$917$	7.67572e18	+	1.71842e18i	0.426303	+	0.0954396i
$918$	−4.48178e18			−0.247157
$919$	−4.97026e18	+	8.60874e18i	−0.272162	+	0.471399i	−0.969415	−	0.245426i	$-0.921072\pi$
$919$	−4.97026e18	+	8.60874e18i	−0.272162	+	0.471399i	0.697253	+	0.716825i	$0.254405\pi$
$920$	2.27627e18	+	3.94262e18i	0.123767	+	0.214370i
$921$	1.10447e19	+	1.91300e19i	0.596302	+	1.03283i
$922$	9.98227e18	−	1.72898e19i	0.535153	−	0.926913i
$923$	−9.03064e17			−0.0480737
$924$	2.20549e18	+	7.04598e18i	0.116584	+	0.372455i
$925$	−1.72903e19			−0.907572
$926$	−8.13437e18	+	1.40891e19i	−0.423987	+	0.734367i
$927$	8.33082e18	+	1.44294e19i	0.431191	+	0.746844i
$928$	4.39661e18	+	7.61515e18i	0.225973	+	0.391396i
$929$	−2.72284e18	+	4.71610e18i	−0.138970	+	0.240703i	−0.927107	−	0.374797i	$-0.877712\pi$
$929$	−2.72284e18	+	4.71610e18i	−0.138970	+	0.240703i	0.788137	+	0.615500i	$0.211046\pi$
$930$	1.14599e19			0.580818
$931$	−2.60598e17	−	3.12844e18i	−0.0131159	−	0.157455i
$932$	−4.02347e18			−0.201093
$933$	1.75899e19	−	3.04666e19i	0.873038	−	1.51215i
$934$	9.03387e18	+	1.56471e19i	0.445265	+	0.771222i
$935$	5.43103e18	+	9.40681e18i	0.265832	+	0.460434i
$936$	1.29948e19	−	2.25077e19i	0.631652	−	1.09405i
$937$	−1.75736e19			−0.848307			−0.424153	−	0.905590i	$-0.639428\pi$
$937$	−1.75736e19			−0.848307			−0.424153	+	0.905590i	$0.639428\pi$
$938$	−2.11666e18	−	6.76219e18i	−0.101469	−	0.324167i
$939$	−2.82182e19			−1.34339
$940$	1.19167e18	−	2.06403e18i	0.0563410	−	0.0975854i
$941$	1.68477e19	+	2.91810e19i	0.791057	+	1.37015i	0.925313	+	0.379204i	$0.123802\pi$
$941$	1.68477e19	+	2.91810e19i	0.791057	+	1.37015i	−0.134257	+	0.990947i	$0.542865\pi$
$942$	3.29918e18	+	5.71434e18i	0.153842	+	0.266462i
$943$	−1.12535e18	+	1.94917e18i	−0.0521150	+	0.0902659i
$944$	1.58012e19			0.726730
$945$	4.20326e18	+	9.41013e17i	0.191990	+	0.0429822i
$946$	−5.01223e19			−2.27373
$947$	−2.06394e19	+	3.57484e19i	−0.929868	+	1.61058i	−0.146330	+	0.989236i	$0.546746\pi$
$947$	−2.06394e19	+	3.57484e19i	−0.929868	+	1.61058i	−0.783538	+	0.621343i	$0.786587\pi$
$948$	−1.37050e18	−	2.37378e18i	−0.0613233	−	0.106215i
$949$	−8.10401e18	−	1.40366e19i	−0.360139	−	0.623778i
$950$	1.26331e18	−	2.18811e18i	0.0557577	−	0.0965752i
$951$	−3.37767e18			−0.148062
$952$	1.08745e19	−	1.18180e19i	0.473444	−	0.514522i
$953$	2.39608e19			1.03609			0.518046	−	0.855353i	$-0.326660\pi$
$953$	2.39608e19			1.03609			0.518046	+	0.855353i	$0.326660\pi$
$954$	−4.14204e18	+	7.17422e18i	−0.177889	+	0.308113i
$955$	8.48761e17	+	1.47010e18i	0.0362046	+	0.0627082i
$956$	−1.00113e18	−	1.73401e18i	−0.0424145	−	0.0734641i
$957$	−4.42341e19	+	7.66158e19i	−1.86136	+	3.22397i
$958$	9.93438e18			0.415207
$959$	1.39185e18	−	1.51261e18i	0.0577791	−	0.0627922i
$960$	−1.94337e19			−0.801297
$961$	2.97513e18	−	5.15307e18i	0.121844	−	0.211040i
$962$	−1.25110e19	−	2.16697e19i	−0.508926	−	0.881485i
$963$	7.72510e18	+	1.33803e19i	0.312128	+	0.540622i
$964$	1.02323e18	−	1.77229e18i	0.0410651	−	0.0711268i
$965$	−1.57528e19			−0.627956
$966$	1.65170e19	+	3.69779e18i	0.654004	+	0.146417i
$967$	3.98367e19			1.56679			0.783396	−	0.621524i	$-0.213486\pi$
$967$	3.98367e19			1.56679			0.783396	+	0.621524i	$0.213486\pi$
$968$	2.45177e19	−	4.24659e19i	0.957833	−	1.65901i
$969$	2.02050e18	+	3.49961e18i	0.0784069	+	0.135805i
$970$	7.06640e18	+	1.22394e19i	0.272384	+	0.471784i
$971$	−4.21778e18	+	7.30541e18i	−0.161495	+	0.279717i	−0.935405	−	0.353578i	$-0.884965\pi$
$971$	−4.21778e18	+	7.30541e18i	−0.161495	+	0.279717i	0.773910	+	0.633295i	$0.218298\pi$
$972$	5.67789e18			0.215952
$973$	−1.76442e17	−	5.63686e17i	−0.00666604	−	0.0212963i
$974$	1.37384e19			0.515589
$975$	1.45278e19	−	2.51628e19i	0.541588	−	0.938057i
$976$	1.71527e19	+	2.97093e19i	0.635197	+	1.10019i
$977$	−1.62268e19	−	2.81056e19i	−0.596923	−	1.03390i	−0.993272	−	0.115801i	$-0.963057\pi$
$977$	−1.62268e19	−	2.81056e19i	−0.596923	−	1.03390i	0.396350	−	0.918100i	$-0.370277\pi$
$978$	9.51579e18	−	1.64818e19i	0.347730	−	0.602286i
$979$	4.04351e19			1.46781
$980$	−1.69833e18	+	1.17869e18i	−0.0612423	+	0.0425039i
$981$	−1.05922e19			−0.379435
$982$	−2.03140e19	+	3.51848e19i	−0.722886	+	1.25208i
$983$	−3.36194e18	−	5.82305e18i	−0.118848	−	0.205851i	0.800463	−	0.599382i	$-0.204587\pi$
$983$	−3.36194e18	−	5.82305e18i	−0.118848	−	0.205851i	−0.919311	+	0.393531i	$0.871253\pi$
$984$	−4.90802e18	−	8.50094e18i	−0.172361	−	0.298537i
$985$	−6.31022e18	+	1.09296e19i	−0.220145	+	0.381302i
$986$	2.57746e19			0.893288
$987$	−1.97628e19	−	6.31372e19i	−0.680437	−	2.17382i
$988$	−6.68918e17			−0.0228798
$989$	1.05106e19	−	1.82049e19i	0.357151	−	0.618604i
$990$	−1.39706e19	−	2.41977e19i	−0.471612	−	0.816857i
$991$	2.20384e19	+	3.81716e19i	0.739096	+	1.28015i	0.952903	+	0.303276i	$0.0980803\pi$
$991$	2.20384e19	+	3.81716e19i	0.739096	+	1.28015i	−0.213807	+	0.976876i	$0.568586\pi$
$992$	3.99845e18	−	6.92553e18i	0.133219	−	0.230742i
$993$	−8.99240e19			−2.97650
$994$	1.40079e18	+	3.13604e17i	0.0460639	+	0.0103127i
$995$	2.40184e19			0.784683
$996$	−5.07212e18	+	8.78516e18i	−0.164628	+	0.285144i
$997$	−3.00283e19	−	5.20105e19i	−0.968304	−	1.67715i	−0.700465	−	0.713687i	$-0.747024\pi$
$997$	−3.00283e19	−	5.20105e19i	−0.968304	−	1.67715i	−0.267839	−	0.963464i	$-0.586310\pi$
$998$	−7.57727e18	−	1.31242e19i	−0.242753	−	0.420460i
$999$	−7.58034e18	+	1.31295e19i	−0.241275	+	0.417901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.14.c.a.2.3	✓	16
3.2	odd	2		63.14.e.c.37.6		16
7.2	even	3		49.14.a.e.1.6		8
7.3	odd	6		49.14.c.g.18.3		16
7.4	even	3	inner	7.14.c.a.4.3	yes	16
7.5	odd	6		49.14.a.f.1.6		8
7.6	odd	2		49.14.c.g.30.3		16
21.11	odd	6		63.14.e.c.46.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.14.c.a.2.3	✓	16	1.1	even	1	trivial
7.14.c.a.4.3	yes	16	7.4	even	3	inner
49.14.a.e.1.6		8	7.2	even	3
49.14.a.f.1.6		8	7.5	odd	6
49.14.c.g.18.3		16	7.3	odd	6
49.14.c.g.30.3		16	7.6	odd	2
63.14.e.c.37.6		16	3.2	odd	2
63.14.e.c.46.6		16	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-41.6086 + 72.0682i) q^{2} +(-951.376 - 1647.83i) q^{3} +(633.448 + 1097.16i) q^{4} +(8420.78 - 14585.2i) q^{5} +158342. q^{6} +(92983.2 + 297057. i) q^{7} -787143. q^{8} +(-1.01307e6 + 1.75469e6i) q^{9} +O(q^{10})\)	\(q+(-41.6086 + 72.0682i) q^{2} +(-951.376 - 1647.83i) q^{3} +(633.448 + 1097.16i) q^{4} +(8420.78 - 14585.2i) q^{5} +158342. q^{6} +(92983.2 + 297057. i) q^{7} -787143. q^{8} +(-1.01307e6 + 1.75469e6i) q^{9} +(700754. + 1.21374e6i) q^{10} +(4.91981e6 + 8.52136e6i) q^{11} +(1.20529e6 - 2.08763e6i) q^{12} +1.62958e7 q^{13} +(-2.52773e7 - 5.65901e6i) q^{14} -3.20453e7 q^{15} +(2.75627e7 - 4.77400e7i) q^{16} +(3.27734e7 + 5.67652e7i) q^{17} +(-8.43050e7 - 1.46021e8i) q^{18} +(-1.62004e7 + 2.80599e7i) q^{19} +2.13365e7 q^{20} +(4.01039e8 - 4.35834e8i) q^{21} -8.18826e8 q^{22} +(1.71707e8 - 2.97406e8i) q^{23} +(7.48869e8 + 1.29708e9i) q^{24} +(4.68532e8 + 8.11522e8i) q^{25} +(-6.78047e8 + 1.17441e9i) q^{26} +8.21648e8 q^{27} +(-2.67021e8 + 2.90188e8i) q^{28} -4.72528e9 q^{29} +(1.33336e9 - 2.30945e9i) q^{30} +(2.14868e9 + 3.72162e9i) q^{31} +(-9.30445e8 - 1.61158e9i) q^{32} +(9.36118e9 - 1.62140e10i) q^{33} -5.45462e9 q^{34} +(5.11564e9 + 1.14528e9i) q^{35} -2.56691e9 q^{36} +(-9.22577e9 + 1.59795e10i) q^{37} +(-1.34815e9 - 2.33507e9i) q^{38} +(-1.55035e10 - 2.68528e10i) q^{39} +(-6.62836e9 + 1.14807e10i) q^{40} -6.55391e9 q^{41} +(1.47231e10 + 4.70366e10i) q^{42} +6.12124e10 q^{43} +(-6.23288e9 + 1.07957e10i) q^{44} +(1.70617e10 + 2.95518e10i) q^{45} +(1.42890e10 + 2.47493e10i) q^{46} +(5.58512e10 - 9.67371e10i) q^{47} -1.04890e11 q^{48} +(-7.95973e10 + 5.52427e10i) q^{49} -7.79799e10 q^{50} +(6.23596e10 - 1.08010e11i) q^{51} +(1.03226e10 + 1.78792e10i) q^{52} +(-2.45658e10 - 4.25492e10i) q^{53} +(-3.41876e10 + 5.92147e10i) q^{54} +1.65715e11 q^{55} +(-7.31911e10 - 2.33827e11i) q^{56} +6.16507e10 q^{57} +(1.96612e11 - 3.40542e11i) q^{58} +(1.43321e11 + 2.48239e11i) q^{59} +(-2.02990e10 - 3.51589e10i) q^{60} +(-3.11158e11 + 5.38941e11i) q^{61} -3.57614e11 q^{62} +(-6.15443e11 - 1.37784e11i) q^{63} +6.06446e11 q^{64} +(1.37224e11 - 2.37678e11i) q^{65} +(7.79011e11 + 1.34929e12i) q^{66} +(1.36774e11 + 2.36900e11i) q^{67} +(-4.15204e10 + 7.19155e10i) q^{68} -6.53433e11 q^{69} +(-2.95393e11 + 3.21022e11i) q^{70} -5.54168e10 q^{71} +(7.97432e11 - 1.38119e12i) q^{72} +(-4.97306e11 - 8.61359e11i) q^{73} +(-7.67743e11 - 1.32977e12i) q^{74} +(8.91501e11 - 1.54413e12i) q^{75} -4.10484e10 q^{76} +(-2.07387e12 + 2.25381e12i) q^{77} +2.58031e12 q^{78} +(5.68535e11 - 9.84731e11i) q^{79} +(-4.64199e11 - 8.04017e11i) q^{80} +(8.33467e11 + 1.44361e12i) q^{81} +(2.72699e11 - 4.72328e11i) q^{82} -4.20820e12 q^{83} +(7.32218e11 + 1.63927e11i) q^{84} +1.10391e12 q^{85} +(-2.54696e12 + 4.41147e12i) q^{86} +(4.49551e12 + 7.78646e12i) q^{87} +(-3.87259e12 - 6.70753e12i) q^{88} +(2.05471e12 - 3.55886e12i) q^{89} -2.83966e12 q^{90} +(1.51524e12 + 4.84080e12i) q^{91} +4.35070e11 q^{92} +(4.08841e12 - 7.08133e12i) q^{93} +(4.64778e12 + 8.05019e12i) q^{94} +(2.72840e11 + 4.72572e11i) q^{95} +(-1.77041e12 + 3.06643e12i) q^{96} +1.00840e13 q^{97} +(-6.69313e11 - 8.03501e12i) q^{98} -1.99365e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 728 * q^3 - 32588 * q^4 + 46928 * q^5 - 30212 * q^6 + 257992 * q^7 - 1093248 * q^8 - 2910808 * q^9	\( 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9} + 879018 q^{10} + 3746000 q^{11} + 13786276 q^{12} - 63556528 q^{13} - 45497410 q^{14} + 179729504 q^{15} - 158020976 q^{16} + 108548496 q^{17} + 358872748 q^{18} + 617001728 q^{19} - 1844979416 q^{20} + 400815352 q^{21} + 977603772 q^{22} - 274288968 q^{23} - 690136272 q^{24} + 342571888 q^{25} - 1890370748 q^{26} + 1818768224 q^{27} - 2830532012 q^{28} - 1243557136 q^{29} + 8470546342 q^{30} + 1983953552 q^{31} - 18584336224 q^{32} - 3534705832 q^{33} + 35123983356 q^{34} - 15057013664 q^{35} + 2810399728 q^{36} + 3822948680 q^{37} + 48271561702 q^{38} + 5559167432 q^{39} + 20095902624 q^{40} - 186830117264 q^{41} - 160102538512 q^{42} + 147613206080 q^{43} + 146754773860 q^{44} + 167965018760 q^{45} + 33234006318 q^{46} + 136146541776 q^{47} - 918554738528 q^{48} - 279115649456 q^{49} + 446501048144 q^{50} + 374908120992 q^{51} + 920059547960 q^{52} - 365779470792 q^{53} + 142841959918 q^{54} - 335157159792 q^{55} - 2232488591424 q^{56} + 1368890666384 q^{57} + 1968765302052 q^{58} + 1211924963928 q^{59} - 1696452613604 q^{60} - 155263824184 q^{61} - 3267358992324 q^{62} - 4123328121080 q^{63} + 3671045348608 q^{64} + 2491203210104 q^{65} + 6785854381222 q^{66} - 1812819047992 q^{67} + 2300642770860 q^{68} - 9833331511584 q^{69} - 10764563120010 q^{70} + 6413635527072 q^{71} + 9182131417728 q^{72} + 7135229075576 q^{73} - 1240472589270 q^{74} + 3092701132528 q^{75} - 24098923346008 q^{76} - 8899938075392 q^{77} + 16977900019528 q^{78} + 7912090175960 q^{79} + 18767635478704 q^{80} - 2029193868592 q^{81} + 2118830761068 q^{82} - 16937841300576 q^{83} - 32302920082804 q^{84} + 9546866646768 q^{85} + 17052910238024 q^{86} + 16147535411672 q^{87} - 15433836932304 q^{88} + 3654589406888 q^{89} - 6354662390216 q^{90} - 14961004874704 q^{91} + 2966525661672 q^{92} + 10829807426472 q^{93} + 7135101410430 q^{94} - 16751540432680 q^{95} - 4043645970784 q^{96} + 20623672673744 q^{97} + 1374873929086 q^{98} + 1803523183088 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 728 * q^3 - 32588 * q^4 + 46928 * q^5 - 30212 * q^6 + 257992 * q^7 - 1093248 * q^8 - 2910808 * q^9 + 879018 * q^10 + 3746000 * q^11 + 13786276 * q^12 - 63556528 * q^13 - 45497410 * q^14 + 179729504 * q^15 - 158020976 * q^16 + 108548496 * q^17 + 358872748 * q^18 + 617001728 * q^19 - 1844979416 * q^20 + 400815352 * q^21 + 977603772 * q^22 - 274288968 * q^23 - 690136272 * q^24 + 342571888 * q^25 - 1890370748 * q^26 + 1818768224 * q^27 - 2830532012 * q^28 - 1243557136 * q^29 + 8470546342 * q^30 + 1983953552 * q^31 - 18584336224 * q^32 - 3534705832 * q^33 + 35123983356 * q^34 - 15057013664 * q^35 + 2810399728 * q^36 + 3822948680 * q^37 + 48271561702 * q^38 + 5559167432 * q^39 + 20095902624 * q^40 - 186830117264 * q^41 - 160102538512 * q^42 + 147613206080 * q^43 + 146754773860 * q^44 + 167965018760 * q^45 + 33234006318 * q^46 + 136146541776 * q^47 - 918554738528 * q^48 - 279115649456 * q^49 + 446501048144 * q^50 + 374908120992 * q^51 + 920059547960 * q^52 - 365779470792 * q^53 + 142841959918 * q^54 - 335157159792 * q^55 - 2232488591424 * q^56 + 1368890666384 * q^57 + 1968765302052 * q^58 + 1211924963928 * q^59 - 1696452613604 * q^60 - 155263824184 * q^61 - 3267358992324 * q^62 - 4123328121080 * q^63 + 3671045348608 * q^64 + 2491203210104 * q^65 + 6785854381222 * q^66 - 1812819047992 * q^67 + 2300642770860 * q^68 - 9833331511584 * q^69 - 10764563120010 * q^70 + 6413635527072 * q^71 + 9182131417728 * q^72 + 7135229075576 * q^73 - 1240472589270 * q^74 + 3092701132528 * q^75 - 24098923346008 * q^76 - 8899938075392 * q^77 + 16977900019528 * q^78 + 7912090175960 * q^79 + 18767635478704 * q^80 - 2029193868592 * q^81 + 2118830761068 * q^82 - 16937841300576 * q^83 - 32302920082804 * q^84 + 9546866646768 * q^85 + 17052910238024 * q^86 + 16147535411672 * q^87 - 15433836932304 * q^88 + 3654589406888 * q^89 - 6354662390216 * q^90 - 14961004874704 * q^91 + 2966525661672 * q^92 + 10829807426472 * q^93 + 7135101410430 * q^94 - 16751540432680 * q^95 - 4043645970784 * q^96 + 20623672673744 * q^97 + 1374873929086 * q^98 + 1803523183088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more