LMFDB - Embedded newform 7.9.d.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,9,Mod(3,7)]

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([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	7.d (of order $6$, 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:	$2.85165027043$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 592x^{6} - 1176x^{5} + 336397x^{4} - 348096x^{3} + 8673408x^{2} + 8271396x + 197880489 $ x^8 + 592x^6 - 1176x^5 + 336397x^4 - 348096x^3 + 8673408x^2 + 8271396x + 197880489
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.2
Root			$-2.23583 + 3.87257i$ of defining polynomial
Character	$\chi$	$=$	7.3
Dual form			7.9.d.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.73583 - 4.73860i) q^{2} +(58.8837 + 33.9965i) q^{3} +(113.030 - 195.774i) q^{4} +(586.541 - 338.640i) q^{5} -372.035i q^{6} +(-168.652 + 2395.07i) q^{7} -2637.67 q^{8} +(-968.977 - 1678.32i) q^{9} +O(q^{10})$	\(q+(-2.73583 - 4.73860i) q^{2} +(58.8837 + 33.9965i) q^{3} +(113.030 - 195.774i) q^{4} +(586.541 - 338.640i) q^{5} -372.035i q^{6} +(-168.652 + 2395.07i) q^{7} -2637.67 q^{8} +(-968.977 - 1678.32i) q^{9} +(-3209.35 - 1852.92i) q^{10} +(-7993.72 + 13845.5i) q^{11} +(13311.3 - 7685.28i) q^{12} -7140.05i q^{13} +(11810.7 - 5753.33i) q^{14} +46050.2 q^{15} +(-21719.6 - 37619.4i) q^{16} +(37697.8 + 21764.8i) q^{17} +(-5301.91 + 9183.18i) q^{18} +(-166506. + 96132.3i) q^{19} -153106. i q^{20} +(-91354.8 + 135297. i) q^{21} +87477.8 q^{22} +(91930.6 + 159228. i) q^{23} +(-155316. - 89671.7i) q^{24} +(34041.0 - 58960.8i) q^{25} +(-33833.8 + 19534.0i) q^{26} -577869. i q^{27} +(449831. + 303734. i) q^{28} +1.23038e6 q^{29} +(-125986. - 218214. i) q^{30} +(-928053. - 535812. i) q^{31} +(-456464. + 790620. i) q^{32} +(-941399. + 543517. i) q^{33} -238180. i q^{34} +(712144. + 1.46192e6i) q^{35} -438095. q^{36} +(-1.10683e6 - 1.91708e6i) q^{37} +(911064. + 526003. i) q^{38} +(242737. - 420432. i) q^{39} +(-1.54710e6 + 893221. i) q^{40} -1.82702e6i q^{41} +(891049. + 62744.3i) q^{42} +3.38628e6 q^{43} +(1.80707e6 + 3.12993e6i) q^{44} +(-1.13669e6 - 656268. i) q^{45} +(503013. - 871244. i) q^{46} +(2.72225e6 - 1.57169e6i) q^{47} -2.95356e6i q^{48} +(-5.70791e6 - 807866. i) q^{49} -372522. q^{50} +(1.47986e6 + 2.56319e6i) q^{51} +(-1.39784e6 - 807043. i) q^{52} +(-2.66308e6 + 4.61259e6i) q^{53} +(-2.73829e6 + 1.58095e6i) q^{54} +1.08280e7i q^{55} +(444849. - 6.31741e6i) q^{56} -1.30726e7 q^{57} +(-3.36611e6 - 5.83028e6i) q^{58} +(1.22494e7 + 7.07217e6i) q^{59} +(5.20508e6 - 9.01546e6i) q^{60} +(1.39025e7 - 8.02662e6i) q^{61} +5.86356e6i q^{62} +(4.18310e6 - 2.03772e6i) q^{63} -6.12518e6 q^{64} +(-2.41790e6 - 4.18793e6i) q^{65} +(5.15102e6 + 2.97394e6i) q^{66} +(1.45154e6 - 2.51415e6i) q^{67} +(8.52200e6 - 4.92018e6i) q^{68} +1.25013e7i q^{69} +(4.97914e6 - 7.37413e6i) q^{70} -1.93711e7 q^{71} +(2.55585e6 + 4.42685e6i) q^{72} +(-1.68891e7 - 9.75096e6i) q^{73} +(-6.05618e6 + 1.04896e7i) q^{74} +(4.00892e6 - 2.31455e6i) q^{75} +4.34635e7i q^{76} +(-3.18128e7 - 2.14806e7i) q^{77} -2.65635e6 q^{78} +(2.39941e7 + 4.15589e7i) q^{79} +(-2.54788e7 - 1.47102e7i) q^{80} +(1.32881e7 - 2.30156e7i) q^{81} +(-8.65752e6 + 4.99842e6i) q^{82} -8.03009e7i q^{83} +(1.61618e7 + 3.31776e7i) q^{84} +2.94817e7 q^{85} +(-9.26429e6 - 1.60462e7i) q^{86} +(7.24493e7 + 4.18286e7i) q^{87} +(2.10848e7 - 3.65200e7i) q^{88} +(-2.83820e7 + 1.63863e7i) q^{89} +7.18175e6i q^{90} +(1.71009e7 + 1.20418e6i) q^{91} +4.15638e7 q^{92} +(-3.64314e7 - 6.31011e7i) q^{93} +(-1.48952e7 - 8.59977e6i) q^{94} +(-6.51084e7 + 1.12771e8i) q^{95} +(-5.37566e7 + 3.10364e7i) q^{96} -6.94505e7i q^{97} +(1.17877e7 + 2.92577e7i) q^{98} +3.09829e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9	\( 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9} + 5796 q^{10} + 1784 q^{11} - 40908 q^{12} - 9856 q^{14} + 131808 q^{15} - 8584 q^{16} - 141456 q^{17} - 121944 q^{18} - 257544 q^{19} + 474012 q^{21} + 1706256 q^{22} - 348940 q^{23} - 895104 q^{24} - 557752 q^{25} - 2913120 q^{26} + 1485092 q^{28} + 4983176 q^{29} - 551112 q^{30} - 2376696 q^{31} - 332016 q^{32} - 5719140 q^{33} + 2491272 q^{35} + 13269408 q^{36} + 492740 q^{37} - 7088088 q^{38} - 2850372 q^{39} - 7601832 q^{40} + 3586128 q^{42} + 4448432 q^{43} - 3678804 q^{44} + 3328164 q^{45} - 226560 q^{46} + 2704128 q^{47} - 3811024 q^{49} - 15628912 q^{50} - 350856 q^{51} + 11135208 q^{52} + 2281460 q^{53} + 24553368 q^{54} - 6573392 q^{56} - 43638408 q^{57} + 11442696 q^{58} + 25291140 q^{59} + 17679564 q^{60} + 59368764 q^{61} - 60081756 q^{63} - 114153056 q^{64} + 16923396 q^{65} + 463428 q^{66} - 107108 q^{67} + 44316972 q^{68} + 19120080 q^{70} - 82809760 q^{71} + 13297584 q^{72} + 116758404 q^{73} + 72690340 q^{74} + 79832424 q^{75} - 58244200 q^{77} - 44122512 q^{78} - 50628092 q^{79} - 93591624 q^{80} - 96868872 q^{81} - 91061712 q^{82} + 154096572 q^{84} + 119231208 q^{85} + 39093088 q^{86} + 26702676 q^{87} + 41392848 q^{88} - 2322516 q^{89} - 151794552 q^{91} + 253819128 q^{92} - 57693204 q^{93} - 345566088 q^{94} - 172787052 q^{95} - 416455200 q^{96} + 373659692 q^{98} + 672244008 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9 + 5796 * q^10 + 1784 * q^11 - 40908 * q^12 - 9856 * q^14 + 131808 * q^15 - 8584 * q^16 - 141456 * q^17 - 121944 * q^18 - 257544 * q^19 + 474012 * q^21 + 1706256 * q^22 - 348940 * q^23 - 895104 * q^24 - 557752 * q^25 - 2913120 * q^26 + 1485092 * q^28 + 4983176 * q^29 - 551112 * q^30 - 2376696 * q^31 - 332016 * q^32 - 5719140 * q^33 + 2491272 * q^35 + 13269408 * q^36 + 492740 * q^37 - 7088088 * q^38 - 2850372 * q^39 - 7601832 * q^40 + 3586128 * q^42 + 4448432 * q^43 - 3678804 * q^44 + 3328164 * q^45 - 226560 * q^46 + 2704128 * q^47 - 3811024 * q^49 - 15628912 * q^50 - 350856 * q^51 + 11135208 * q^52 + 2281460 * q^53 + 24553368 * q^54 - 6573392 * q^56 - 43638408 * q^57 + 11442696 * q^58 + 25291140 * q^59 + 17679564 * q^60 + 59368764 * q^61 - 60081756 * q^63 - 114153056 * q^64 + 16923396 * q^65 + 463428 * q^66 - 107108 * q^67 + 44316972 * q^68 + 19120080 * q^70 - 82809760 * q^71 + 13297584 * q^72 + 116758404 * q^73 + 72690340 * q^74 + 79832424 * q^75 - 58244200 * q^77 - 44122512 * q^78 - 50628092 * q^79 - 93591624 * q^80 - 96868872 * q^81 - 91061712 * q^82 + 154096572 * q^84 + 119231208 * q^85 + 39093088 * q^86 + 26702676 * q^87 + 41392848 * q^88 - 2322516 * q^89 - 151794552 * q^91 + 253819128 * q^92 - 57693204 * q^93 - 345566088 * q^94 - 172787052 * q^95 - 416455200 * q^96 + 373659692 * q^98 + 672244008 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.73583	−	4.73860i	−0.170989	−	0.296162i	0.767777	−	0.640718i	$-0.221363\pi$
$2$	−2.73583	−	4.73860i	−0.170989	−	0.296162i	−0.938766	+	0.344555i	$0.888030\pi$
$3$	58.8837	+	33.9965i	0.726959	+	0.419710i	0.817309	−	0.576200i	$-0.195465\pi$
$3$	58.8837	+	33.9965i	0.726959	+	0.419710i	−0.0903498	+	0.995910i	$0.528799\pi$
$4$	113.030	−	195.774i	0.441525	−	0.764744i
$5$	586.541	−	338.640i	0.938466	−	0.541823i	0.0489866	−	0.998799i	$-0.484401\pi$
$5$	586.541	−	338.640i	0.938466	−	0.541823i	0.889479	+	0.456976i	$0.151068\pi$
$6$		−	372.035i		−	0.287064i
$7$	−168.652	+	2395.07i	−0.0702423	+	0.997530i
$7$	−168.652	+	2395.07i	−0.0702423	+	0.997530i
$8$	−2637.67			−0.643964
$9$	−968.977	−	1678.32i	−0.147687	−	0.255802i
$10$	−3209.35	−	1852.92i	−0.320935	−	0.185292i
$11$	−7993.72	+	13845.5i	−0.545982	+	0.945668i	0.452563	+	0.891733i	$0.350510\pi$
$11$	−7993.72	+	13845.5i	−0.545982	+	0.945668i	−0.998544	+	0.0539354i	$0.982823\pi$
$12$	13311.3	−	7685.28i	0.641941	−	0.370625i
$13$		−	7140.05i		−	0.249993i	−0.992157	−	0.124996i	$-0.960108\pi$
$13$		−	7140.05i		−	0.249993i	0.992157	−	0.124996i	$-0.0398920\pi$
$14$	11810.7	−	5753.33i	0.307442	−	0.149764i
$15$	46050.2			0.909634
$16$	−21719.6	−	37619.4i	−0.331414	−	0.574026i
$17$	37697.8	+	21764.8i	0.451357	+	0.260591i	0.708403	−	0.705808i	$-0.249416\pi$
$17$	37697.8	+	21764.8i	0.451357	+	0.260591i	−0.257046	+	0.966399i	$0.582749\pi$
$18$	−5301.91	+	9183.18i	−0.0505060	+	0.0874789i
$19$	−166506.	+	96132.3i	−1.27766	+	0.737658i	−0.976418	−	0.215890i	$-0.930735\pi$
$19$	−166506.	+	96132.3i	−1.27766	+	0.737658i	−0.301243	+	0.953548i	$0.597401\pi$
$20$		−	153106.i		−	0.956915i
$21$	−91354.8	+	135297.i	−0.469736	+	0.695682i
$22$	87477.8			0.373428
$23$	91930.6	+	159228.i	0.328510	+	0.568996i	0.982216	−	0.187752i	$-0.0601202\pi$
$23$	91930.6	+	159228.i	0.328510	+	0.568996i	−0.653706	+	0.756748i	$0.726787\pi$
$24$	−155316.	−	89671.7i	−0.468135	−	0.270278i
$25$	34041.0	−	58960.8i	0.0871451	−	0.150940i
$26$	−33833.8	+	19534.0i	−0.0740385	+	0.0427462i
$27$		−	577869.i		−	1.08736i
$28$	449831.	+	303734.i	0.731841	+	0.494152i
$29$	1.23038e6			1.73959			0.869796	−	0.493412i	$-0.164251\pi$
$29$	1.23038e6			1.73959			0.869796	+	0.493412i	$0.164251\pi$
$30$	−125986.	−	218214.i	−0.155538	−	0.269399i
$31$	−928053.	−	535812.i	−1.00491	−	0.580184i	−0.0952110	−	0.995457i	$-0.530353\pi$
$31$	−928053.	−	535812.i	−1.00491	−	0.580184i	−0.909697	+	0.415273i	$0.863686\pi$
$32$	−456464.	+	790620.i	−0.435318	+	0.753994i
$33$	−941399.	+	543517.i	−0.793812	+	0.458308i
$34$		−	238180.i		−	0.178233i
$35$	712144.	+	1.46192e6i	0.474565	+	0.974206i
$36$	−438095.			−0.260831
$37$	−1.10683e6	−	1.91708e6i	−0.590571	−	1.02290i	−0.994156	−	0.107957i	$-0.965569\pi$
$37$	−1.10683e6	−	1.91708e6i	−0.590571	−	1.02290i	0.403584	−	0.914943i	$-0.367764\pi$
$38$	911064.	+	526003.i	0.436933	+	0.252263i
$39$	242737.	−	420432.i	0.104924	−	0.181735i
$40$	−1.54710e6	+	893221.i	−0.604338	+	0.348914i
$41$		−	1.82702e6i		−	0.646559i	−0.946304	−	0.323279i	$-0.895215\pi$
$41$		−	1.82702e6i		−	0.646559i	0.946304	−	0.323279i	$-0.104785\pi$
$42$	891049.	+	62744.3i	0.286355	+	0.0201640i
$43$	3.38628e6			0.990488			0.495244	−	0.868754i	$-0.335079\pi$
$43$	3.38628e6			0.990488			0.495244	+	0.868754i	$0.335079\pi$
$44$	1.80707e6	+	3.12993e6i	0.482129	+	0.835073i
$45$	−1.13669e6	−	656268.i	−0.277199	−	0.160041i
$46$	503013.	−	871244.i	0.112344	−	0.194585i
$47$	2.72225e6	−	1.57169e6i	0.557875	−	0.322089i	−0.194417	−	0.980919i	$-0.562282\pi$
$47$	2.72225e6	−	1.57169e6i	0.557875	−	0.322089i	0.752292	+	0.658830i	$0.228948\pi$
$48$		−	2.95356e6i		−	0.556391i
$49$	−5.70791e6	−	807866.i	−0.990132	−	0.140138i
$50$	−372522.			−0.0596036
$51$	1.47986e6	+	2.56319e6i	0.218745	+	0.378878i
$52$	−1.39784e6	−	807043.i	−0.191181	−	0.110378i
$53$	−2.66308e6	+	4.61259e6i	−0.337505	+	0.584576i	−0.983963	−	0.178374i	$-0.942916\pi$
$53$	−2.66308e6	+	4.61259e6i	−0.337505	+	0.584576i	0.646458	+	0.762950i	$0.276250\pi$
$54$	−2.73829e6	+	1.58095e6i	−0.322036	+	0.185928i
$55$			1.08280e7i			1.18330i
$56$	444849.	−	6.31741e6i	0.0452335	−	0.642373i
$57$	−1.30726e7			−1.23841
$58$	−3.36611e6	−	5.83028e6i	−0.297452	−	0.515202i
$59$	1.22494e7	+	7.07217e6i	1.01089	+	0.583640i	0.911453	−	0.411404i	$-0.134961\pi$
$59$	1.22494e7	+	7.07217e6i	1.01089	+	0.583640i	0.0994402	+	0.995044i	$0.468295\pi$
$60$	5.20508e6	−	9.01546e6i	0.401626	−	0.695637i
$61$	1.39025e7	−	8.02662e6i	1.00409	−	0.579713i	0.0946362	−	0.995512i	$-0.469831\pi$
$61$	1.39025e7	−	8.02662e6i	1.00409	−	0.579713i	0.909457	+	0.415799i	$0.136498\pi$
$62$			5.86356e6i			0.396821i
$63$	4.18310e6	−	2.03772e6i	0.265544	−	0.129354i
$64$	−6.12518e6			−0.365089
$65$	−2.41790e6	−	4.18793e6i	−0.135452	−	0.234610i
$66$	5.15102e6	+	2.97394e6i	0.271467	+	0.156732i
$67$	1.45154e6	−	2.51415e6i	0.0720330	−	0.124765i	−0.827759	−	0.561083i	$-0.810385\pi$
$67$	1.45154e6	−	2.51415e6i	0.0720330	−	0.124765i	0.899792	+	0.436319i	$0.143718\pi$
$68$	8.52200e6	−	4.92018e6i	0.398571	−	0.230115i
$69$			1.25013e7i			0.551516i
$70$	4.97914e6	−	7.37413e6i	0.207378	−	0.307127i
$71$	−1.93711e7			−0.762290			−0.381145	−	0.924515i	$-0.624470\pi$
$71$	−1.93711e7			−0.762290			−0.381145	+	0.924515i	$0.624470\pi$
$72$	2.55585e6	+	4.42685e6i	0.0951053	+	0.164727i
$73$	−1.68891e7	−	9.75096e6i	−0.594725	−	0.343365i	0.172238	−	0.985055i	$-0.444900\pi$
$73$	−1.68891e7	−	9.75096e6i	−0.594725	−	0.343365i	−0.766964	+	0.641691i	$0.778233\pi$
$74$	−6.05618e6	+	1.04896e7i	−0.201963	+	0.349810i
$75$	4.00892e6	−	2.31455e6i	0.126702	−	0.0731513i
$76$			4.34635e7i			1.30278i
$77$	−3.18128e7	−	2.14806e7i	−0.904981	−	0.611059i
$78$	−2.65635e6			−0.0717639
$79$	2.39941e7	+	4.15589e7i	0.616021	+	1.06698i	0.990204	+	0.139625i	$0.0445896\pi$
$79$	2.39941e7	+	4.15589e7i	0.616021	+	1.06698i	−0.374184	+	0.927355i	$0.622077\pi$
$80$	−2.54788e7	−	1.47102e7i	−0.622042	−	0.359136i
$81$	1.32881e7	−	2.30156e7i	0.308690	−	0.534666i
$82$	−8.65752e6	+	4.99842e6i	−0.191486	+	0.110555i
$83$		−	8.03009e7i		−	1.69203i	−0.533160	−	0.846015i	$-0.678996\pi$
$83$		−	8.03009e7i		−	1.69203i	0.533160	−	0.846015i	$-0.321004\pi$
$84$	1.61618e7	+	3.31776e7i	0.324618	+	0.666389i
$85$	2.94817e7			0.564778
$86$	−9.26429e6	−	1.60462e7i	−0.169363	−	0.293345i
$87$	7.24493e7	+	4.18286e7i	1.26461	+	0.730124i
$88$	2.10848e7	−	3.65200e7i	0.351592	−	0.608976i
$89$	−2.83820e7	+	1.63863e7i	−0.452358	+	0.261169i	−0.708826	−	0.705384i	$-0.750775\pi$
$89$	−2.83820e7	+	1.63863e7i	−0.452358	+	0.261169i	0.256467	+	0.966553i	$0.417441\pi$
$90$			7.18175e6i			0.109461i
$91$	1.71009e7	+	1.20418e6i	0.249375	+	0.0175601i
$92$	4.15638e7			0.580182
$93$	−3.64314e7	−	6.31011e7i	−0.487018	−	0.843539i
$94$	−1.48952e7	−	8.59977e6i	−0.190781	−	0.110148i
$95$	−6.51084e7	+	1.12771e8i	−0.799360	+	1.38453i
$96$	−5.37566e7	+	3.10364e7i	−0.632917	+	0.365415i
$97$		−	6.94505e7i		−	0.784491i	−0.919861	−	0.392246i	$-0.871698\pi$
$97$		−	6.94505e7i		−	0.784491i	0.919861	−	0.392246i	$-0.128302\pi$
$98$	1.17877e7	+	2.92577e7i	0.127799	+	0.317202i
$99$	3.09829e7			0.322538
$100$	−7.69535e6	−	1.33287e7i	−0.0769535	−	0.133287i
$101$	−5.87470e7	−	3.39176e7i	−0.564547	−	0.325941i	0.190421	−	0.981702i	$-0.439015\pi$
$101$	−5.87470e7	−	3.39176e7i	−0.564547	−	0.325941i	−0.754968	+	0.655761i	$0.772348\pi$
$102$	8.09727e6	−	1.40249e7i	0.0748063	−	0.129568i
$103$	6.70717e6	−	3.87239e6i	0.0595923	−	0.0344056i	−0.469908	−	0.882715i	$-0.655713\pi$
$103$	6.70717e6	−	3.87239e6i	0.0595923	−	0.0344056i	0.529500	+	0.848310i	$0.322380\pi$
$104$			1.88331e7i			0.160986i
$105$	−7.76646e6	+	1.10294e8i	−0.0638948	+	0.907387i
$106$	2.91429e7			0.230839
$107$	−1.32965e6	−	2.30302e6i	−0.0101439	−	0.0175697i	0.860909	−	0.508759i	$-0.169896\pi$
$107$	−1.32965e6	−	2.30302e6i	−0.0101439	−	0.0175697i	−0.871053	+	0.491189i	$0.836562\pi$
$108$	−1.13132e8	−	6.53168e7i	−0.831554	−	0.480098i
$109$	−9.84081e7	+	1.70448e8i	−0.697147	+	1.20749i	0.272304	+	0.962211i	$0.412214\pi$
$109$	−9.84081e7	+	1.70448e8i	−0.697147	+	1.20749i	−0.969451	+	0.245284i	$0.921119\pi$
$110$	5.13093e7	−	2.96235e7i	0.350450	−	0.202332i
$111$		−	1.50513e8i		−	0.991474i
$112$	9.37641e7	−	4.56753e7i	0.595888	−	0.290275i
$113$	1.97591e8			1.21186			0.605931	−	0.795517i	$-0.292801\pi$
$113$	1.97591e8			1.21186			0.605931	+	0.795517i	$0.292801\pi$
$114$	3.57645e7	+	6.19460e7i	0.211755	+	0.366770i
$115$	1.07842e8	+	6.22627e7i	0.616591	+	0.355989i
$116$	1.39070e8	−	2.40877e8i	0.768073	−	1.33034i
$117$	−1.19833e7	+	6.91854e6i	−0.0639487	+	0.0369208i
$118$		−	7.73931e7i		−	0.399185i
$119$	−5.84861e7	+	8.66182e7i	−0.291652	+	0.431938i
$120$	−1.21466e8			−0.585771
$121$	−2.06196e7	−	3.57142e7i	−0.0961919	−	0.166609i
$122$	−7.60698e7	−	4.39189e7i	−0.343379	−	0.198250i
$123$	6.21123e7	−	1.07582e8i	0.271367	−	0.470021i
$124$	−2.09797e8	+	1.21126e8i	−0.887384	+	0.512331i
$125$			2.18452e8i			0.894778i
$126$	−2.11002e7	−	1.42472e7i	−0.0837151	−	0.0565259i
$127$	−2.67617e8			−1.02872			−0.514362	−	0.857573i	$-0.671971\pi$
$127$	−2.67617e8			−1.02872			−0.514362	+	0.857573i	$0.671971\pi$
$128$	1.33612e8	+	2.31423e8i	0.497745	+	0.862119i
$129$	1.99397e8	+	1.15122e8i	0.720044	+	0.415717i
$130$	−1.32299e7	+	2.29149e7i	−0.0463217	+	0.0802316i
$131$	1.06804e7	−	6.16632e6i	0.0362662	−	0.0209383i	−0.481757	−	0.876305i	$-0.660001\pi$
$131$	1.06804e7	−	6.16632e6i	0.0362662	−	0.0209383i	0.518023	+	0.855366i	$0.326668\pi$
$132$			2.45736e8i			0.809418i
$133$	−2.02162e8	−	4.15006e8i	−0.646090	−	1.32632i
$134$	−1.58847e7			−0.0492675
$135$	−1.95689e8	−	3.38944e8i	−0.589159	−	1.02045i
$136$	−9.94345e7	−	5.74086e7i	−0.290658	−	0.167811i
$137$	−4.42245e7	+	7.65991e7i	−0.125540	+	0.217441i	−0.921944	−	0.387324i	$-0.873400\pi$
$137$	−4.42245e7	+	7.65991e7i	−0.125540	+	0.217441i	0.796404	+	0.604765i	$0.206733\pi$
$138$	5.92385e7	−	3.42014e7i	0.163338	−	0.0943034i
$139$			1.24154e8i			0.332583i	0.986077	+	0.166292i	$0.0531793\pi$
$139$			1.24154e8i			0.332583i	−0.986077	+	0.166292i	$0.946821\pi$
$140$	3.66700e8	+	2.58217e7i	0.954551	+	0.0672159i
$141$	2.13728e8			0.540736
$142$	5.29960e7	+	9.17917e7i	0.130344	+	0.225762i
$143$	9.88577e7	+	5.70755e7i	0.236410	+	0.136492i
$144$	−4.20915e7	+	7.29046e7i	−0.0978914	+	0.169553i
$145$	7.21668e8	−	4.16655e8i	1.63255	−	0.942551i
$146$			1.06708e8i			0.234847i
$147$	−3.08638e8	−	2.41619e8i	−0.660968	−	0.517442i
$148$	−5.00420e8			−1.04301
$149$	1.58775e8	+	2.75006e8i	0.322134	+	0.557952i	0.980928	−	0.194371i	$-0.0622666\pi$
$149$	1.58775e8	+	2.75006e8i	0.322134	+	0.557952i	−0.658794	+	0.752323i	$0.728933\pi$
$150$	−2.19355e7	−	1.26645e7i	−0.0433293	−	0.0250162i
$151$	3.98699e7	−	6.90566e7i	0.0766897	−	0.132830i	−0.825130	−	0.564943i	$-0.808898\pi$
$151$	3.98699e7	−	6.90566e7i	0.0766897	−	0.132830i	0.901820	+	0.432112i	$0.142232\pi$
$152$	4.39189e8	−	2.53566e8i	0.822767	−	0.475025i
$153$		−	8.43585e7i		−	0.153944i
$154$	−1.47533e7	+	2.09516e8i	−0.0262305	+	0.372506i
$155$	−7.25788e8			−1.25743
$156$	−5.48733e7	−	9.50433e7i	−0.0926536	−	0.160481i
$157$	4.38495e8	+	2.53165e8i	0.721715	+	0.416682i	0.815384	−	0.578921i	$-0.196526\pi$
$157$	4.38495e8	+	2.53165e8i	0.721715	+	0.416682i	−0.0936684	+	0.995603i	$0.529859\pi$
$158$	1.31287e8	−	2.27396e8i	0.210666	−	0.364884i
$159$	−3.13624e8	+	1.81071e8i	−0.490705	+	0.283309i
$160$			6.18308e8i			0.943463i
$161$	−3.96867e8	+	1.93326e8i	−0.590666	+	0.287731i
$162$	−1.45416e8			−0.211131
$163$	−1.60271e8	−	2.77598e8i	−0.227041	−	0.393247i	0.729889	−	0.683566i	$-0.239572\pi$
$163$	−1.60271e8	−	2.77598e8i	−0.227041	−	0.393247i	−0.956930	+	0.290319i	$0.906239\pi$
$164$	−3.57684e8	−	2.06509e8i	−0.494452	−	0.285472i
$165$	−3.68113e8	+	6.37590e8i	−0.496644	+	0.860212i
$166$	−3.80514e8	+	2.19690e8i	−0.501115	+	0.289319i
$167$		−	4.55139e8i		−	0.585165i	−0.956240	−	0.292582i	$-0.905485\pi$
$167$		−	4.55139e8i		−	0.585165i	0.956240	−	0.292582i	$-0.0945146\pi$
$168$	2.40964e8	−	3.56869e8i	0.302493	−	0.447994i
$169$	7.64750e8			0.937504
$170$	−8.06571e7	−	1.39702e8i	−0.0965710	−	0.167266i
$171$	3.22681e8	+	1.86300e8i	0.377389	+	0.217885i
$172$	3.82753e8	−	6.62947e8i	0.437325	−	0.757470i
$173$	−3.75710e8	+	2.16916e8i	−0.419438	+	0.242163i	−0.694837	−	0.719167i	$-0.744523\pi$
$173$	−3.75710e8	+	2.16916e8i	−0.419438	+	0.242163i	0.275399	+	0.961330i	$0.411190\pi$
$174$		−	4.57744e8i		−	0.499374i
$175$	1.35474e8	+	9.14745e7i	0.144446	+	0.0975322i
$176$	6.94480e8			0.723784
$177$	4.80858e8	+	8.32871e8i	0.489918	+	0.848564i
$178$	1.55297e8	+	8.96605e7i	0.154697	+	0.0893144i
$179$	1.23966e8	−	2.14716e8i	0.120751	−	0.209147i	−0.799313	−	0.600915i	$-0.794803\pi$
$179$	1.23966e8	−	2.14716e8i	0.120751	−	0.209147i	0.920064	+	0.391768i	$0.128136\pi$
$180$	−2.56961e8	+	1.48356e8i	−0.244781	+	0.141324i
$181$		−	8.25075e7i		−	0.0768739i	−0.999261	−	0.0384370i	$-0.987762\pi$
$181$		−	8.25075e7i		−	0.0768739i	0.999261	−	0.0384370i	$-0.0122379\pi$
$182$	−4.10791e7	−	8.43288e7i	−0.0374399	−	0.0768582i
$183$	1.09151e9			0.973245
$184$	−2.42483e8	−	4.19993e8i	−0.211549	−	0.366413i
$185$	−1.29840e9	−	7.49630e8i	−1.10846	−	0.639971i
$186$	−1.99341e8	+	3.45268e8i	−0.166550	+	0.288473i
$187$	−6.02691e8	+	3.47964e8i	−0.492865	+	0.284556i
$188$		−	7.10596e8i		−	0.568842i
$189$	1.38404e9	+	9.74587e7i	1.08468	+	0.0763789i
$190$	7.12502e8			0.546729
$191$	−3.03757e6	−	5.26122e6i	−0.00228240	−	0.00395324i	0.864882	−	0.501975i	$-0.167393\pi$
$191$	−3.03757e6	−	5.26122e6i	−0.00228240	−	0.00395324i	−0.867164	+	0.498022i	$0.834060\pi$
$192$	−3.60673e8	−	2.08235e8i	−0.265405	−	0.153231i
$193$	−3.57777e8	+	6.19688e8i	−0.257860	+	0.446626i	−0.965668	−	0.259778i	$-0.916351\pi$
$193$	−3.57777e8	+	6.19688e8i	−0.257860	+	0.446626i	0.707809	+	0.706404i	$0.249684\pi$
$194$	−3.29098e8	+	1.90005e8i	−0.232337	+	0.134140i
$195$		−	3.28801e8i		−	0.227402i
$196$	−8.03328e8	+	1.02615e9i	−0.544338	+	0.695323i
$197$	−1.99131e9			−1.32213			−0.661066	−	0.750328i	$-0.729896\pi$
$197$	−1.99131e9			−1.32213			−0.661066	+	0.750328i	$0.729896\pi$
$198$	−8.47640e7	−	1.46816e8i	−0.0551507	−	0.0955237i
$199$	1.81056e8	+	1.04533e8i	0.115452	+	0.0666562i	0.556614	−	0.830771i	$-0.312100\pi$
$199$	1.81056e8	+	1.04533e8i	0.115452	+	0.0666562i	−0.441162	+	0.897427i	$0.645434\pi$
$200$	−8.97892e7	+	1.55519e8i	−0.0561183	+	0.0971997i
$201$	1.70945e8	−	9.86949e7i	0.104730	−	0.0604659i
$202$			3.71171e8i			0.222930i
$203$	−2.07506e8	+	2.94685e9i	−0.122193	+	1.73529i
$204$	6.69075e8			0.386326
$205$	−6.18701e8	−	1.07162e9i	−0.350321	−	0.606773i
$206$	−3.66994e7	−	2.11884e7i	−0.0203793	−	0.0117660i
$207$	1.78157e8	−	3.08577e8i	0.0970336	−	0.168067i
$208$	−2.68604e8	+	1.55079e8i	−0.143503	+	0.0828512i
$209$		−	3.07382e9i		−	1.61099i
$210$	5.43884e8	−	2.64942e8i	0.279659	−	0.136230i
$211$	1.35092e9			0.681553			0.340776	−	0.940144i	$-0.389310\pi$
$211$	1.35092e9			0.681553			0.340776	+	0.940144i	$0.389310\pi$
$212$	6.02018e8	+	1.04273e9i	0.298034	+	0.516210i
$213$	−1.14064e9	−	6.58548e8i	−0.554153	−	0.319941i
$214$	−7.27541e6	+	1.26014e7i	−0.00346898	+	0.00600846i
$215$	1.98619e9	−	1.14673e9i	0.929539	−	0.536669i
$216$			1.52423e9i			0.700222i
$217$	1.43982e9	−	2.13239e9i	0.649338	−	0.961672i
$218$	1.07691e9			0.476819
$219$	−6.62997e8	−	1.14834e9i	−0.288227	−	0.499224i
$220$	2.11984e9	+	1.22389e9i	0.904924	+	0.522458i
$221$	1.55402e8	−	2.69164e8i	0.0651459	−	0.112836i
$222$	−7.13220e8	+	4.11778e8i	−0.293637	+	0.169532i
$223$			1.79377e9i			0.725349i	0.931916	+	0.362674i	$0.118136\pi$
$223$			1.79377e9i			0.725349i	−0.931916	+	0.362674i	$0.881864\pi$
$224$	−1.81661e9	−	1.22660e9i	−0.721553	−	0.487205i
$225$	−1.31940e8			−0.0514809
$226$	−5.40575e8	−	9.36304e8i	−0.207216	−	0.358908i
$227$	9.31425e8	+	5.37758e8i	0.350788	+	0.202527i	0.665032	−	0.746815i	$-0.268418\pi$
$227$	9.31425e8	+	5.37758e8i	0.350788	+	0.202527i	−0.314244	+	0.949342i	$0.601751\pi$
$228$	−1.47761e9	+	2.55929e9i	−0.546789	+	0.947066i
$229$	−2.35264e9	+	1.35830e9i	−0.855489	+	0.493917i	−0.862499	−	0.506059i	$-0.831102\pi$
$229$	−2.35264e9	+	1.35830e9i	−0.855489	+	0.493917i	0.00701039	+	0.999975i	$0.497769\pi$
$230$		−	6.81361e8i		−	0.243481i
$231$	−1.14299e9	−	2.34638e9i	−0.401416	−	0.824044i
$232$	−3.24534e9			−1.12023
$233$	2.37662e9	+	4.11642e9i	0.806372	+	1.39668i	0.915361	+	0.402634i	$0.131905\pi$
$233$	2.37662e9	+	4.11642e9i	0.806372	+	1.39668i	−0.108989	+	0.994043i	$0.534761\pi$
$234$	6.55684e7	+	3.78559e7i	0.0218691	+	0.0126261i
$235$	1.06447e9	−	1.84372e9i	0.349031	−	0.604539i
$236$	2.76910e9	−	1.59874e9i	0.892670	−	0.515383i
$237$			3.26286e9i			1.03420i
$238$	5.70457e8	+	4.01694e7i	0.177793	+	0.0125195i
$239$	−1.10087e9			−0.337401			−0.168700	−	0.985667i	$-0.553957\pi$
$239$	−1.10087e9			−0.337401			−0.168700	+	0.985667i	$0.553957\pi$
$240$	−1.00019e9	−	1.73238e9i	−0.301466	−	0.522154i
$241$	−1.64257e9	−	9.48338e8i	−0.486918	−	0.281122i	0.236377	−	0.971661i	$-0.424040\pi$
$241$	−1.64257e9	−	9.48338e8i	−0.486918	−	0.281122i	−0.723295	+	0.690539i	$0.757373\pi$
$242$	−1.12823e8	+	1.95416e8i	−0.0328956	+	0.0569769i
$243$	−1.71855e9	+	9.92204e8i	−0.492875	+	0.284561i
$244$		−	3.62901e9i		−	1.02383i
$245$	−3.62150e9	+	1.45908e9i	−1.00513	+	0.404962i
$246$	−6.79715e8			−0.185604
$247$	6.86389e8	+	1.18886e9i	0.184409	+	0.319406i
$248$	2.44790e9	+	1.41330e9i	0.647124	+	0.373617i
$249$	2.72995e9	−	4.72841e9i	0.710161	−	1.23004i
$250$	1.03515e9	−	5.97647e8i	0.265000	−	0.152998i
$251$			6.93531e9i			1.74731i	0.486543	+	0.873657i	$0.338258\pi$
$251$			6.93531e9i			1.74731i	−0.486543	+	0.873657i	$0.661742\pi$
$252$	7.38856e7	−	1.04927e9i	0.0183214	−	0.260186i
$253$	−2.93947e9			−0.717442
$254$	7.32154e8	+	1.26813e9i	0.175901	+	0.304669i
$255$	1.73599e9	+	1.00228e9i	0.410570	+	0.237043i
$256$	−5.29410e7	+	9.16965e7i	−0.0123263	+	0.0213498i
$257$	7.12542e9	−	4.11386e9i	1.63335	−	0.943013i	0.650295	−	0.759682i	$-0.274645\pi$
$257$	7.12542e9	−	4.11386e9i	1.63335	−	0.943013i	0.983051	−	0.183331i	$-0.0586879\pi$
$258$		−	1.25981e9i		−	0.284333i
$259$	4.77820e9	−	2.32761e9i	1.06186	−	0.517262i
$260$	−1.09319e9			−0.239222
$261$	−1.19221e9	−	2.06497e9i	−0.256916	−	0.444991i
$262$	−5.84394e7	−	3.37400e7i	−0.0124023	−	0.00716045i
$263$	4.72089e8	−	8.17682e8i	0.0986735	−	0.170908i	−0.812462	−	0.583014i	$-0.801873\pi$
$263$	4.72089e8	−	8.17682e8i	0.0986735	−	0.170908i	0.911136	+	0.412106i	$0.135207\pi$
$264$	2.48310e9	−	1.43362e9i	0.511186	−	0.295133i
$265$			3.60730e9i			0.731473i
$266$	−1.41347e9	+	2.09335e9i	−0.282331	+	0.418134i
$267$	−2.22831e9			−0.438461
$268$	−3.28138e8	−	5.68351e8i	−0.0636087	−	0.110174i
$269$	−5.70184e9	−	3.29196e9i	−1.08895	−	0.628703i	−0.155650	−	0.987812i	$-0.549747\pi$
$269$	−5.70184e9	−	3.29196e9i	−1.08895	−	0.628703i	−0.933296	+	0.359109i	$0.883081\pi$
$270$	−1.07075e9	+	1.85459e9i	−0.201480	+	0.348973i
$271$	−3.88464e9	+	2.24280e9i	−0.720235	+	0.415828i	−0.814839	−	0.579687i	$-0.803175\pi$
$271$	−3.88464e9	+	2.24280e9i	−0.720235	+	0.415828i	0.0946042	+	0.995515i	$0.469841\pi$
$272$		−	1.89089e9i		−	0.345454i
$273$	9.66026e8	+	6.52278e8i	0.173915	+	0.117431i
$274$	4.83963e8			0.0858638
$275$	5.44229e8	+	9.42632e8i	0.0951592	+	0.164821i
$276$	2.44743e9	+	1.41302e9i	0.421768	+	0.243508i
$277$	−2.70975e9	+	4.69343e9i	−0.460267	+	0.797206i	−0.998974	−	0.0452869i	$-0.985580\pi$
$277$	−2.70975e9	+	4.69343e9i	−0.460267	+	0.797206i	0.538707	+	0.842493i	$0.318913\pi$
$278$	5.88315e8	−	3.39664e8i	0.0984987	−	0.0568683i
$279$			2.07676e9i			0.342743i
$280$	−1.87840e9	−	3.85607e9i	−0.305603	−	0.627353i
$281$	2.99551e9			0.480447			0.240224	−	0.970718i	$-0.422779\pi$
$281$	2.99551e9			0.480447			0.240224	+	0.970718i	$0.422779\pi$
$282$	−5.84724e8	−	1.01277e9i	−0.0924601	−	0.160146i
$283$	−1.20764e9	−	6.97230e8i	−0.188274	−	0.108700i	0.402900	−	0.915244i	$-0.368002\pi$
$283$	−1.20764e9	−	6.97230e8i	−0.188274	−	0.108700i	−0.591174	+	0.806544i	$0.701335\pi$
$284$	−2.18952e9	+	3.79236e9i	−0.336570	+	0.582957i
$285$	−7.66764e9	+	4.42691e9i	−1.16220	+	0.670999i
$286$		−	6.24596e8i		−	0.0933545i
$287$	4.37584e9	+	3.08130e8i	0.644962	+	0.0454158i
$288$	1.76921e9			0.257164
$289$	−2.54046e9	−	4.40021e9i	−0.364184	−	0.630786i
$290$	−3.94872e9	−	2.27980e9i	−0.558296	−	0.322333i
$291$	2.36107e9	−	4.08950e9i	0.329259	−	0.570293i
$292$	−3.81798e9	+	2.20431e9i	−0.525172	+	0.303208i
$293$		−	7.92885e9i		−	1.07582i	−0.843002	−	0.537910i	$-0.819214\pi$
$293$		−	7.92885e9i		−	1.07582i	0.843002	−	0.537910i	$-0.180786\pi$
$294$	−3.00554e8	+	2.12354e9i	−0.0402284	+	0.284231i
$295$	9.57967e9			1.26492
$296$	2.91945e9	+	5.05663e9i	0.380306	+	0.658710i
$297$	8.00090e9	+	4.61932e9i	1.02828	+	0.593680i
$298$	8.68761e8	−	1.50474e9i	0.110163	−	0.190808i
$299$	1.13690e9	−	6.56389e8i	0.142245	−	0.0821252i
$300$		−	1.04646e9i		−	0.129193i
$301$	−5.71102e8	+	8.11038e9i	−0.0695742	+	0.988041i
$302$	−4.36309e8			−0.0524525
$303$	−2.30616e9	−	3.99438e9i	−0.273602	−	0.473892i
$304$	7.23287e9	+	4.17590e9i	0.846870	+	0.488940i
$305$	5.43626e9	−	9.41588e9i	0.628204	−	1.08808i
$306$	−3.99741e8	+	2.30791e8i	−0.0455924	+	0.0263228i
$307$		−	1.30887e10i		−	1.47347i	−0.676181	−	0.736735i	$-0.736366\pi$
$307$		−	1.30887e10i		−	1.47347i	0.676181	−	0.736735i	$-0.263634\pi$
$308$	−7.80117e9	+	3.80018e9i	−0.866876	+	0.422281i
$309$	5.26590e8			0.0577615
$310$	1.98563e9	+	3.43922e9i	0.215007	+	0.372403i
$311$	−1.48190e10	−	8.55574e9i	−1.58408	−	0.914568i	−0.994255	−	0.107035i	$-0.965864\pi$
$311$	−1.48190e10	−	8.55574e9i	−1.58408	−	0.914568i	−0.589822	−	0.807533i	$-0.700802\pi$
$312$	−6.40260e8	+	1.10896e9i	−0.0675675	+	0.117030i
$313$	3.40303e9	−	1.96474e9i	0.354559	−	0.204705i	−0.312132	−	0.950039i	$-0.601043\pi$
$313$	3.40303e9	−	1.96474e9i	0.354559	−	0.204705i	0.666691	+	0.745334i	$0.267710\pi$
$314$		−	2.77047e9i		−	0.284993i
$315$	1.76351e9	−	2.61177e9i	0.179117	−	0.265273i
$316$	1.08482e10			1.08795
$317$	5.31219e9	+	9.20098e9i	0.526061	+	0.911165i	0.999539	+	0.0303594i	$0.00966517\pi$
$317$	5.31219e9	+	9.20098e9i	0.526061	+	0.911165i	−0.473478	+	0.880806i	$0.657001\pi$
$318$	1.71604e9	+	9.90758e8i	0.167811	+	0.0968855i
$319$	−9.83531e9	+	1.70353e10i	−0.949785	+	1.64508i
$320$	−3.59267e9	+	2.07423e9i	−0.342623	+	0.197814i
$321$		−	1.80814e8i		−	0.0170299i
$322$	2.00186e9	+	1.35169e9i	0.186213	+	0.125734i
$323$	−8.36921e9			−0.768908
$324$	−3.00391e9	−	5.20293e9i	−0.272588	−	0.472137i
$325$	−4.20983e8	−	2.43055e8i	−0.0377339	−	0.0217857i
$326$	−8.76949e8	+	1.51892e9i	−0.0776433	+	0.134482i
$327$	−1.15893e10	+	6.69106e9i	−1.01359	+	0.585199i
$328$			4.81908e9i			0.416360i
$329$	3.30520e9	+	6.78505e9i	0.282107	+	0.579121i
$330$	4.02838e9			0.339683
$331$	−5.92885e9	−	1.02691e10i	−0.493922	−	0.855499i	0.506053	−	0.862502i	$-0.331104\pi$
$331$	−5.92885e9	−	1.02691e10i	−0.493922	−	0.855499i	−0.999975	+	0.00700357i	$0.997771\pi$
$332$	−1.57209e10	−	9.07644e9i	−1.29397	−	0.747073i
$333$	−2.14498e9	+	3.71521e9i	−0.174440	+	0.302139i
$334$	−2.15672e9	+	1.24518e9i	−0.173304	+	0.100057i
$335$		−	1.96620e9i		−	0.156117i
$336$	7.07397e9	+	4.98123e8i	0.555017	+	0.0390822i
$337$	6.57267e9			0.509591			0.254796	−	0.966995i	$-0.417992\pi$
$337$	6.57267e9			0.509591			0.254796	+	0.966995i	$0.417992\pi$
$338$	−2.09223e9	−	3.62385e9i	−0.160303	−	0.277653i
$339$	1.16349e10	+	6.71739e9i	0.880973	+	0.508630i
$340$	3.33233e9	−	5.77177e9i	0.249364	−	0.431910i
$341$	1.48372e10	−	8.56626e9i	1.09732	−	0.633539i
$342$		−	2.03874e9i		−	0.149024i
$343$	2.89754e9	−	1.35346e10i	0.209341	−	0.977843i
$344$	−8.93191e9			−0.637838
$345$	4.23343e9	+	7.33251e9i	0.298824	+	0.517578i
$346$	2.05576e9	+	1.18689e9i	0.143439	+	0.0828146i
$347$	3.09380e8	−	5.35861e8i	0.0213390	−	0.0369602i	−0.855159	−	0.518366i	$-0.826540\pi$
$347$	3.09380e8	−	5.35861e8i	0.0213390	−	0.0369602i	0.876498	+	0.481406i	$0.159874\pi$
$348$	1.63779e10	−	9.45581e9i	1.11672	−	0.644736i
$349$			1.97851e10i			1.33364i	0.745220	+	0.666818i	$0.232344\pi$
$349$			1.97851e10i			1.33364i	−0.745220	+	0.666818i	$0.767656\pi$
$350$	6.28266e7	−	8.92217e8i	0.00418669	−	0.0594563i
$351$	−4.12601e9			−0.271833
$352$	−7.29770e9	−	1.26400e10i	−0.475352	−	0.823333i
$353$	6.63393e9	+	3.83010e9i	0.427240	+	0.246667i	0.698170	−	0.715932i	$-0.253998\pi$
$353$	6.63393e9	+	3.83010e9i	0.427240	+	0.246667i	−0.270930	+	0.962599i	$0.587331\pi$
$354$	2.63109e9	−	4.55719e9i	0.167542	−	0.290191i
$355$	−1.13619e10	+	6.55981e9i	−0.715383	+	0.413026i
$356$			7.40862e9i			0.461251i
$357$	−6.38859e9	+	3.11207e9i	−0.393307	+	0.191592i
$358$	−1.35660e9			−0.0825887
$359$	7.16213e9	+	1.24052e10i	0.431186	+	0.746836i	0.996976	−	0.0777138i	$-0.0247620\pi$
$359$	7.16213e9	+	1.24052e10i	0.431186	+	0.746836i	−0.565790	+	0.824549i	$0.691429\pi$
$360$	2.99822e9	+	1.73102e9i	0.178506	+	0.103061i
$361$	9.99104e9	−	1.73050e10i	0.588277	−	1.01893i
$362$	−3.90970e8	+	2.25727e8i	−0.0227672	+	0.0131446i
$363$		−	2.80398e9i		−	0.161491i
$364$	2.16867e9	−	3.21181e9i	0.123535	−	0.182955i
$365$	−1.32082e10			−0.744172
$366$	−2.98618e9	−	5.17222e9i	−0.166415	−	0.288239i
$367$	5.21666e9	+	3.01184e9i	0.287560	+	0.166023i	0.636841	−	0.770995i	$-0.280241\pi$
$367$	5.21666e9	+	3.01184e9i	0.287560	+	0.166023i	−0.349281	+	0.937018i	$0.613574\pi$
$368$	3.99338e9	−	6.91674e9i	0.217746	−	0.377147i
$369$	−3.06632e9	+	1.77034e9i	−0.165391	+	0.0954885i
$370$			8.20345e9i			0.437713i
$371$	−1.05983e10	−	7.15618e9i	−0.559425	−	0.377734i
$372$	−1.64715e10			−0.860122
$373$	4.89096e9	+	8.47139e9i	0.252673	+	0.437642i	0.964261	−	0.264955i	$-0.0853570\pi$
$373$	4.89096e9	+	8.47139e9i	0.252673	+	0.437642i	−0.711588	+	0.702597i	$0.752024\pi$
$374$	3.29772e9	+	1.90394e9i	0.168550	+	0.0973121i
$375$	−7.42659e9	+	1.28632e10i	−0.375547	+	0.650466i
$376$	−7.18041e9	+	4.14561e9i	−0.359251	+	0.207414i
$377$		−	8.78497e9i		−	0.434885i
$378$	−3.32467e9	−	6.82503e9i	−0.162848	−	0.334301i
$379$	−9.29163e9			−0.450334			−0.225167	−	0.974320i	$-0.572293\pi$
$379$	−9.29163e9			−0.450334			−0.225167	+	0.974320i	$0.572293\pi$
$380$	1.47185e10	+	2.54931e10i	0.705875	+	1.22261i
$381$	−1.57583e10	−	9.09803e9i	−0.747839	−	0.431765i
$382$	−1.66206e7	+	2.87876e7i	−0.000780534	+	0.00135193i
$383$	2.52434e10	−	1.45743e10i	1.17315	−	0.677317i	0.218728	−	0.975786i	$-0.429809\pi$
$383$	2.52434e10	−	1.45743e10i	1.17315	−	0.677317i	0.954419	+	0.298469i	$0.0964760\pi$
$384$			1.81694e10i			0.835634i
$385$	−2.59337e10	−	1.82615e9i	−1.18038	−	0.0831179i
$386$	3.91527e9			0.176365
$387$	−3.28123e9	−	5.68325e9i	−0.146283	−	0.253369i
$388$	−1.35966e10	−	7.85002e9i	−0.599935	−	0.346373i
$389$	−1.01545e9	+	1.75881e9i	−0.0443464	+	0.0768103i	−0.887347	−	0.461103i	$-0.847454\pi$
$389$	−1.01545e9	+	1.75881e9i	−0.0443464	+	0.0768103i	0.843000	+	0.537913i	$0.180787\pi$
$390$	−1.55806e9	+	8.99544e8i	−0.0673480	+	0.0388834i
$391$			8.00342e9i			0.342427i
$392$	1.50556e10	+	2.13089e9i	0.637609	+	0.0902435i
$393$	8.38533e8			0.0351520
$394$	5.44790e9	+	9.43604e9i	0.226071	+	0.391566i
$395$	2.81470e10	+	1.62507e10i	1.15623	+	0.667549i
$396$	3.50201e9	−	6.06566e9i	0.142409	−	0.246659i
$397$	3.03359e10	−	1.75144e10i	1.22122	−	0.705072i	0.256043	−	0.966666i	$-0.417581\pi$
$397$	3.03359e10	−	1.75144e10i	1.22122	−	0.705072i	0.965178	+	0.261593i	$0.0842479\pi$
$398$		−	1.14394e9i		−	0.0455900i
$399$	2.20472e9	−	3.13099e10i	0.0869887	−	1.23535i
$400$	−2.95743e9			−0.115524
$401$	−5.98305e9	−	1.03629e10i	−0.231390	−	0.400780i	0.726827	−	0.686820i	$-0.240994\pi$
$401$	−5.98305e9	−	1.03629e10i	−0.231390	−	0.400780i	−0.958218	+	0.286041i	$0.907661\pi$
$402$	−9.35351e8	−	5.40025e8i	−0.0358154	−	0.0206781i
$403$	−3.82572e9	+	6.62634e9i	−0.145042	+	0.251220i
$404$	−1.32804e10	+	7.66744e9i	−0.498523	+	0.287823i
$405$		−	1.79995e10i		−	0.669021i
$406$	1.45316e10	−	7.07878e9i	0.534823	−	0.260528i
$407$	3.53906e10			1.28976
$408$	−3.90338e9	−	6.76085e9i	−0.140864	−	0.243984i
$409$	1.63230e10	+	9.42408e9i	0.583319	+	0.336780i	0.762451	−	0.647045i	$-0.223996\pi$
$409$	1.63230e10	+	9.42408e9i	0.583319	+	0.336780i	−0.179132	+	0.983825i	$0.557329\pi$
$410$	−3.38533e9	+	5.86355e9i	−0.119802	+	0.207504i
$411$	−5.20820e9	+	3.00696e9i	−0.182524	+	0.105380i
$412$		−	1.75079e9i		−	0.0607638i
$413$	−1.90042e10	+	2.81453e10i	−0.653205	+	0.967400i
$414$	−1.94963e9			−0.0663669
$415$	−2.71930e10	−	4.70997e10i	−0.916781	−	1.58791i
$416$	5.64506e9	+	3.25918e9i	0.188493	+	0.108827i
$417$	−4.22079e9	+	7.31063e9i	−0.139589	+	0.241774i
$418$	−1.45656e10	+	8.40944e9i	−0.477115	+	0.275462i
$419$			2.35329e10i			0.763517i	0.924262	+	0.381758i	$0.124681\pi$
$419$			2.35329e10i			0.763517i	−0.924262	+	0.381758i	$0.875319\pi$
$420$	2.07148e10	+	1.39870e10i	0.665708	+	0.449498i
$421$	−4.83123e10			−1.53790			−0.768952	−	0.639306i	$-0.779222\pi$
$421$	−4.83123e10			−1.53790			−0.768952	+	0.639306i	$0.779222\pi$
$422$	−3.69589e9	−	6.40146e9i	−0.116538	−	0.201850i
$423$	−5.27560e9	−	3.04587e9i	−0.164782	−	0.0951370i
$424$	7.02434e9	−	1.21665e10i	0.217341	−	0.376446i
$425$	2.56655e9	−	1.48180e9i	0.0786671	−	0.0454185i
$426$			7.20671e9i			0.218826i
$427$	1.68796e10	+	3.46512e10i	0.507752	+	1.04233i
$428$	−6.01165e8			−0.0179151
$429$	3.88074e9	+	6.72163e9i	0.114574	+	0.198447i
$430$	−1.08678e10	−	6.27451e9i	−0.317883	−	0.183530i
$431$	−1.04309e10	+	1.80668e10i	−0.302281	+	0.523566i	−0.976652	−	0.214826i	$-0.931081\pi$
$431$	−1.04309e10	+	1.80668e10i	−0.302281	+	0.523566i	0.674371	+	0.738393i	$0.264415\pi$
$432$	−2.17391e10	+	1.25511e10i	−0.624175	+	0.360368i
$433$		−	5.95075e10i		−	1.69286i	−0.532502	−	0.846429i	$-0.678748\pi$
$433$		−	5.95075e10i		−	1.69286i	0.532502	−	0.846429i	$-0.321252\pi$
$434$	−1.40436e10	−	9.88900e8i	−0.395841	−	0.0278736i
$435$	5.66593e10			1.58239
$436$	2.22462e10	+	3.85316e10i	0.615616	+	1.06628i
$437$	−3.06140e10	−	1.76750e10i	−0.839449	−	0.484656i
$438$	−3.62769e9	+	6.28335e9i	−0.0985676	+	0.170724i
$439$	−2.14593e10	+	1.23895e10i	−0.577773	+	0.333577i	−0.760248	−	0.649633i	$-0.774922\pi$
$439$	−2.14593e10	+	1.23895e10i	−0.577773	+	0.333577i	0.182475	+	0.983210i	$0.441589\pi$
$440$		−	2.85606e10i		−	0.762004i
$441$	4.17498e9	+	1.03625e10i	0.110382	+	0.273974i
$442$	−1.70061e9			−0.0445571
$443$	−8.14966e9	−	1.41156e10i	−0.211604	−	0.366509i	0.740612	−	0.671932i	$-0.234535\pi$
$443$	−8.14966e9	−	1.41156e10i	−0.211604	−	0.366509i	−0.952217	+	0.305423i	$0.901202\pi$
$444$	−2.94666e10	−	1.70125e10i	−0.758224	−	0.437761i
$445$	−1.10981e10	+	1.92225e10i	−0.283015	+	0.490197i
$446$	8.49995e9	−	4.90745e9i	0.214821	−	0.124027i
$447$			2.15911e10i			0.540811i
$448$	1.03302e9	−	1.46702e10i	0.0256447	−	0.364187i
$449$	2.04087e10			0.502146			0.251073	−	0.967968i	$-0.419217\pi$
$449$	2.04087e10			0.502146			0.251073	+	0.967968i	$0.419217\pi$
$450$	3.60965e8	+	6.25210e8i	0.00880269	+	0.0152467i
$451$	2.52961e10	+	1.46047e10i	0.611430	+	0.353009i
$452$	2.23338e10	−	3.86832e10i	0.535067	−	0.926764i
$453$	4.69537e9	−	2.71087e9i	0.111500	−	0.0643748i
$454$		−	5.88486e9i		−	0.138520i
$455$	1.04382e10	−	5.08474e9i	0.243545	−	0.118638i
$456$	3.44814e10			0.797490
$457$	3.31394e10	+	5.73991e10i	0.759765	+	1.31595i	0.942970	+	0.332877i	$0.108020\pi$
$457$	3.31394e10	+	5.73991e10i	0.759765	+	1.31595i	−0.183205	+	0.983075i	$0.558647\pi$
$458$	1.28729e10	+	7.43216e9i	0.292559	+	0.168909i
$459$	1.25772e10	−	2.17844e10i	0.283357	−	0.490789i
$460$	2.43789e10	−	1.40752e10i	0.544481	−	0.314356i
$461$		−	4.73317e10i		−	1.04797i	−0.851728	−	0.523985i	$-0.824445\pi$
$461$		−	4.73317e10i		−	1.04797i	0.851728	−	0.523985i	$-0.175555\pi$
$462$	−7.99152e9	+	1.18355e10i	−0.175413	+	0.259787i
$463$	4.12318e10			0.897238			0.448619	−	0.893723i	$-0.351916\pi$
$463$	4.12318e10			0.897238			0.448619	+	0.893723i	$0.351916\pi$
$464$	−2.67233e10	−	4.62861e10i	−0.576525	−	0.998571i
$465$	−4.27371e10	−	2.46743e10i	−0.914098	−	0.527755i
$466$	1.30040e10	−	2.25237e10i	0.275762	−	0.477634i
$467$	−7.64151e10	+	4.41183e10i	−1.60661	+	0.927579i	−0.616494	+	0.787360i	$0.711448\pi$
$467$	−7.64151e10	+	4.41183e10i	−1.60661	+	0.927579i	−0.990120	+	0.140220i	$0.955219\pi$
$468$			3.12802e9i			0.0652058i
$469$	5.77676e9	+	3.90057e9i	0.119397	+	0.0806188i
$470$	−1.16489e10			−0.238722
$471$	1.72135e10	+	2.98146e10i	0.349771	+	0.605822i
$472$	−3.23098e10	−	1.86541e10i	−0.650978	−	0.375843i
$473$	−2.70690e10	+	4.68848e10i	−0.540788	+	0.936673i
$474$	1.54614e10	−	8.92662e9i	0.306291	−	0.176837i
$475$			1.30898e10i			0.257133i
$476$	1.03469e10	+	2.12406e10i	0.201550	+	0.413750i
$477$	1.03218e10			0.199381
$478$	3.01180e9	+	5.21660e9i	0.0576919	+	0.0999254i
$479$	3.02343e10	+	1.74558e10i	0.574324	+	0.331586i	0.758875	−	0.651237i	$-0.225749\pi$
$479$	3.02343e10	+	1.74558e10i	0.574324	+	0.331586i	−0.184550	+	0.982823i	$0.559083\pi$
$480$	−2.10203e10	+	3.64082e10i	−0.395981	+	0.685858i
$481$	−1.36880e10	+	7.90279e9i	−0.255718	+	0.147639i
$482$			1.03780e10i			0.192276i
$483$	−2.99414e10	−	2.10836e9i	−0.550153	−	0.0387397i
$484$	−9.32257e9			−0.169885
$485$	−2.35187e10	−	4.07355e10i	−0.425056	−	0.736218i
$486$	9.40332e9	+	5.42901e9i	0.168553	+	0.0973140i
$487$	1.49369e10	−	2.58714e10i	0.265549	−	0.459944i	−0.702159	−	0.712021i	$-0.747780\pi$
$487$	1.49369e10	−	2.58714e10i	0.265549	−	0.459944i	0.967707	+	0.252077i	$0.0811136\pi$
$488$	−3.66703e10	+	2.11716e10i	−0.646599	+	0.373314i
$489$		−	2.17946e10i		−	0.381166i
$490$	1.68218e10	+	1.31690e10i	0.291802	+	0.228439i
$491$	−7.80581e10			−1.34305			−0.671525	−	0.740982i	$-0.734360\pi$
$491$	−7.80581e10			−1.34305			−0.671525	+	0.740982i	$0.734360\pi$
$492$	−1.40412e10	−	2.43200e10i	−0.239631	−	0.415053i
$493$	4.63826e10	+	2.67790e10i	0.785177	+	0.453322i
$494$	3.75569e9	−	6.50504e9i	0.0630640	−	0.109230i
$495$	1.81727e10	−	1.04920e10i	0.302691	−	0.174759i
$496$			4.65504e10i			0.769125i
$497$	3.26697e9	−	4.63950e10i	0.0535450	−	0.760407i
$498$	−2.98747e10			−0.485720
$499$	−4.04951e10	−	7.01395e10i	−0.653130	−	1.13125i	−0.982359	−	0.187005i	$-0.940122\pi$
$499$	−4.04951e10	−	7.01395e10i	−0.653130	−	1.13125i	0.329229	−	0.944250i	$-0.393211\pi$
$500$	4.27673e10	+	2.46917e10i	0.684276	+	0.395067i
$501$	1.54731e10	−	2.68002e10i	0.245599	−	0.425391i
$502$	3.28636e10	−	1.89738e10i	0.517489	−	0.298772i
$503$			3.15283e10i			0.492525i	0.969203	+	0.246263i	$0.0792026\pi$
$503$			3.15283e10i			0.492525i	−0.969203	+	0.246263i	$0.920797\pi$
$504$	−1.10337e10	+	5.37483e9i	−0.171001	+	0.0832995i
$505$	−4.59434e10			−0.706411
$506$	8.04189e9	+	1.39290e10i	0.122675	+	0.212479i
$507$	4.50313e10	+	2.59988e10i	0.681526	+	0.393479i
$508$	−3.02489e10	+	5.23925e10i	−0.454207	+	0.786710i
$509$	8.16281e10	−	4.71280e10i	1.21610	−	0.702114i	0.252017	−	0.967723i	$-0.418906\pi$
$509$	8.16281e10	−	4.71280e10i	1.21610	−	0.702114i	0.964081	+	0.265608i	$0.0855728\pi$
$510$		−	1.09682e10i		−	0.162127i
$511$	2.62026e10	−	3.88062e10i	0.384292	−	0.569137i
$512$	6.89889e10			1.00392
$513$	5.55519e10	+	9.62187e10i	0.802101	+	1.38928i
$514$	−3.89879e10	−	2.25097e10i	−0.558570	−	0.322490i
$515$	2.62269e9	−	4.54263e9i	0.0372836	−	0.0645770i
$516$	4.50758e10	−	2.60245e10i	0.635835	−	0.367099i
$517$			5.02547e10i			0.703419i
$518$	−2.41020e10	−	1.62741e10i	−0.334760	−	0.226036i
$519$	−2.94976e10			−0.406553
$520$	6.37764e9	+	1.10464e10i	0.0872261	+	0.151080i
$521$	−9.63420e10	−	5.56231e10i	−1.30757	−	0.754925i	−0.325879	−	0.945411i	$-0.605660\pi$
$521$	−9.63420e10	−	5.56231e10i	−1.30757	−	0.754925i	−0.981690	+	0.190486i	$0.938994\pi$
$522$	−6.52337e9	+	1.12988e10i	−0.0878597	+	0.152177i
$523$	5.93671e10	−	3.42756e10i	0.793486	−	0.458119i	−0.0477023	−	0.998862i	$-0.515190\pi$
$523$	5.93671e10	−	3.42756e10i	0.793486	−	0.458119i	0.841188	+	0.540742i	$0.181857\pi$
$524$		−	2.78793e9i		−	0.0369791i
$525$	4.86740e9	+	9.99200e9i	0.0640708	+	0.131527i
$526$	−5.16622e9			−0.0674885
$527$	−2.33237e10	−	4.03979e10i	−0.302381	−	0.523740i
$528$	4.08935e10	+	2.36099e10i	0.526161	+	0.303779i
$529$	2.22530e10	−	3.85434e10i	0.284162	−	0.492183i
$530$	1.70935e10	−	9.86895e9i	0.216635	−	0.125074i
$531$		−	2.74111e10i		−	0.344785i
$532$	−1.04098e11	−	7.33020e9i	−1.29956	−	0.0915101i
$533$	−1.30450e10			−0.161635
$534$	6.09629e9	+	1.05591e10i	0.0749722	+	0.129856i
$535$	−1.55979e9	−	9.00546e8i	−0.0190393	−	0.0109924i
$536$	−3.82870e9	+	6.63151e9i	−0.0463866	+	0.0803439i
$537$	1.45992e10	−	8.42883e9i	0.175562	−	0.101361i
$538$			3.60250e10i			0.430006i
$539$	5.68128e10	−	7.25712e10i	0.673118	−	0.859824i
$540$	−8.84755e10			−1.04051
$541$	5.64941e10	+	9.78506e10i	0.659499	+	1.14228i	0.980746	+	0.195290i	$0.0625647\pi$
$541$	5.64941e10	+	9.78506e10i	0.659499	+	1.14228i	−0.321247	+	0.946995i	$0.604102\pi$
$542$	2.12555e10	+	1.22718e10i	0.246305	+	0.142204i
$543$	2.80496e9	−	4.85834e9i	0.0322647	−	0.0558842i
$544$	−3.44154e10	+	1.98697e10i	−0.392968	+	0.226880i
$545$			1.33299e11i			1.51092i
$546$	4.47997e8	−	6.36213e9i	0.00504086	−	0.0715867i
$547$	−3.33041e10			−0.372004			−0.186002	−	0.982549i	$-0.559553\pi$
$547$	−3.33041e10			−0.372004			−0.186002	+	0.982549i	$0.559553\pi$
$548$	9.99743e9	+	1.73161e10i	0.110858	+	0.192011i
$549$	−2.69424e10	−	1.55552e10i	−0.296584	−	0.171233i
$550$	2.97784e9	−	5.15777e9i	0.0325424	−	0.0563652i
$551$	−2.04866e11	+	1.18279e11i	−2.22261	+	1.28322i
$552$		−	3.29743e10i		−	0.355156i
$553$	−1.03583e11	+	5.04585e10i	−1.10761	+	0.539552i
$554$	2.96537e10			0.314803
$555$	−5.09696e10	−	8.82819e10i	−0.537204	−	0.930465i
$556$	2.43061e10	+	1.40332e10i	0.254341	+	0.146844i
$557$	3.91823e10	−	6.78657e10i	0.407070	−	0.705066i	−0.587490	−	0.809231i	$-0.699884\pi$
$557$	3.91823e10	−	6.78657e10i	0.407070	−	0.705066i	0.994560	+	0.104165i	$0.0332171\pi$
$558$	9.84092e9	−	5.68166e9i	0.101508	−	0.0586055i
$559$		−	2.41782e10i		−	0.247615i
$560$	3.95290e10	−	5.85427e10i	0.401943	−	0.595279i
$561$	−4.73182e10			−0.477724
$562$	−8.19521e9	−	1.41945e10i	−0.0821514	−	0.142290i
$563$	1.16350e11	+	6.71745e10i	1.15806	+	0.668607i	0.950839	−	0.309686i	$-0.100224\pi$
$563$	1.16350e11	+	6.71745e10i	1.15806	+	0.668607i	0.207223	+	0.978294i	$0.433557\pi$
$564$	2.41578e10	−	4.18425e10i	0.238749	−	0.413525i
$565$	1.15895e11	−	6.69121e10i	1.13729	−	0.656615i
$566$			7.63001e9i			0.0743463i
$567$	5.28829e10	+	3.57075e10i	0.511662	+	0.345483i
$568$	5.10946e10			0.490887
$569$	3.03498e10	+	5.25674e10i	0.289539	+	0.501496i	0.973700	−	0.227835i	$-0.0731647\pi$
$569$	3.03498e10	+	5.25674e10i	0.289539	+	0.501496i	−0.684161	+	0.729331i	$0.739831\pi$
$570$	4.19547e10	+	2.42226e10i	0.397449	+	0.229467i
$571$	1.72325e10	−	2.98475e10i	0.162108	−	0.280779i	−0.773517	−	0.633776i	$-0.781504\pi$
$571$	1.72325e10	−	2.98475e10i	0.162108	−	0.280779i	0.935624	+	0.352997i	$0.114838\pi$
$572$	2.23479e10	−	1.29025e10i	0.208762	−	0.120529i
$573$		−	4.13067e8i		−	0.00383179i
$574$	−1.05115e10	−	2.15783e10i	−0.0968312	−	0.198779i
$575$	1.25177e10			0.114512
$576$	5.93515e9	+	1.02800e10i	0.0539190	+	0.0933905i
$577$	−1.46492e11	−	8.45769e10i	−1.32163	−	0.763042i	−0.337640	−	0.941275i	$-0.609629\pi$
$577$	−1.46492e11	−	8.45769e10i	−1.32163	−	0.763042i	−0.983988	+	0.178233i	$0.942962\pi$
$578$	−1.39006e10	+	2.40765e10i	−0.124543	+	0.215716i
$579$	−4.21344e10	+	2.43263e10i	−0.374907	+	0.216452i
$580$		−	1.88379e11i		−	1.66464i
$581$	1.92326e11	+	1.35429e10i	1.68785	+	0.118852i
$582$	−2.58380e10			−0.225199
$583$	−4.25758e10	−	7.37435e10i	−0.368543	−	0.638336i
$584$	4.45481e10	+	2.57198e10i	0.382981	+	0.221114i
$585$	−4.68578e9	+	8.11601e9i	−0.0400091	+	0.0692978i
$586$	−3.75716e10	+	2.16920e10i	−0.318617	+	0.183954i
$587$			1.76504e11i			1.48662i	0.668945	+	0.743312i	$0.266746\pi$
$587$			1.76504e11i			1.48662i	−0.668945	+	0.743312i	$0.733254\pi$
$588$	−8.21884e10	+	3.31132e10i	−0.687545	+	0.277007i
$589$	2.06035e11			1.71191
$590$	−2.62084e10	−	4.53942e10i	−0.216288	−	0.374621i
$591$	−1.17256e11	−	6.76977e10i	−0.961135	−	0.554912i
$592$	−4.80795e10	+	8.32762e10i	−0.391448	+	0.678007i
$593$	−1.09392e10	+	6.31578e9i	−0.0884644	+	0.0510749i	−0.543580	−	0.839358i	$-0.682931\pi$
$593$	−1.09392e10	+	6.31578e9i	−0.0884644	+	0.0510749i	0.455115	+	0.890433i	$0.349598\pi$
$594$		−	5.05508e10i		−	0.406052i
$595$	−4.97215e9	+	7.06108e10i	−0.0396713	+	0.563382i
$596$	7.17855e10			0.568920
$597$	7.10750e9	+	1.23106e10i	0.0559525	+	0.0969126i
$598$	−6.22073e9	−	3.59154e9i	−0.0486448	−	0.0280851i
$599$	−4.30339e10	+	7.45370e10i	−0.334275	+	0.578981i	−0.983345	−	0.181747i	$-0.941825\pi$
$599$	−4.30339e10	+	7.45370e10i	−0.334275	+	0.578981i	0.649070	+	0.760728i	$0.275158\pi$
$600$	−1.05742e10	+	6.10504e9i	−0.0815913	+	0.0471068i
$601$		−	2.52446e10i		−	0.193496i	−0.995309	−	0.0967478i	$-0.969156\pi$
$601$		−	2.52446e10i		−	0.193496i	0.995309	−	0.0967478i	$-0.0308440\pi$
$602$	3.99943e10	−	1.94824e10i	0.304517	−	0.148339i
$603$	−5.62605e9			−0.0425534
$604$	−9.01301e9	−	1.56110e10i	−0.0677208	−	0.117296i
$605$	−2.41885e10	−	1.39652e10i	−0.180546	−	0.104238i
$606$	−1.26185e10	+	2.18559e10i	−0.0935660	+	0.162061i
$607$	−1.19612e10	+	6.90578e9i	−0.0881087	+	0.0508696i	−0.543407	−	0.839469i	$-0.682866\pi$
$607$	−1.19612e10	+	6.90578e9i	−0.0881087	+	0.0508696i	0.455298	+	0.890339i	$0.349533\pi$
$608$		−	1.75524e11i		−	1.28446i
$609$	−1.12401e11	+	1.66467e11i	−0.817149	+	1.21020i
$610$	−5.94908e10			−0.429665
$611$	−1.12220e10	−	1.94370e10i	−0.0805200	−	0.139465i
$612$	−1.65152e10	−	9.53508e9i	−0.117728	−	0.0679702i
$613$	−6.33909e10	+	1.09796e11i	−0.448937	+	0.777581i	−0.998317	−	0.0579914i	$-0.981530\pi$
$613$	−6.33909e10	+	1.09796e11i	−0.448937	+	0.777581i	0.549381	+	0.835572i	$0.314864\pi$
$614$	−6.20219e10	+	3.58083e10i	−0.436387	+	0.251948i
$615$		−	8.41347e10i		−	0.588132i
$616$	8.39119e10	+	5.66588e10i	0.582775	+	0.393500i
$617$	4.32247e10			0.298258			0.149129	−	0.988818i	$-0.452353\pi$
$617$	4.32247e10			0.298258			0.149129	+	0.988818i	$0.452353\pi$
$618$	−1.44066e9	−	2.49530e9i	−0.00987661	−	0.0171068i
$619$	−1.25261e11	−	7.23196e10i	−0.853206	−	0.492599i	0.00852520	−	0.999964i	$-0.497286\pi$
$619$	−1.25261e11	−	7.23196e10i	−0.853206	−	0.492599i	−0.861731	+	0.507365i	$0.830620\pi$
$620$	−8.20362e10	+	1.42091e11i	−0.555186	+	0.961611i
$621$	9.20132e10	−	5.31239e10i	0.618705	−	0.357210i
$622$			9.36282e10i			0.625526i
$623$	−3.44598e10	−	7.07404e10i	−0.228749	−	0.469586i
$624$	−2.10885e10			−0.139094
$625$	8.72736e10	+	1.51162e11i	0.571957	+	0.990658i
$626$	−1.86202e10	−	1.07504e10i	−0.121252	−	0.0700047i
$627$	1.04499e11	−	1.80998e11i	0.676148	−	1.17112i
$628$	9.91265e10	−	5.72307e10i	0.637311	−	0.367952i
$629$		−	9.63595e10i		−	0.615591i
$630$	−1.72008e10	−	1.21122e9i	−0.109191	−	0.00768881i
$631$	1.68699e9			0.0106413			0.00532066	−	0.999986i	$-0.498306\pi$
$631$	1.68699e9			0.0106413			0.00532066	+	0.999986i	$0.498306\pi$
$632$	−6.32885e10	−	1.09619e11i	−0.396695	−	0.687096i
$633$	7.95471e10	+	4.59265e10i	0.495461	+	0.286054i
$634$	2.90665e10	−	5.03447e10i	0.179902	−	0.311599i
$635$	−1.56968e11	+	9.06257e10i	−0.965421	+	0.557386i
$636$			8.18660e10i			0.500351i
$637$	−5.76820e9	+	4.07548e10i	−0.0350334	+	0.247526i
$638$	1.07631e11			0.649613
$639$	1.87701e10	+	3.25108e10i	0.112581	+	0.194995i
$640$	1.56738e11	+	9.04929e10i	0.934233	+	0.539380i
$641$	1.15349e11	−	1.99790e11i	0.683251	−	1.18343i	−0.290732	−	0.956804i	$-0.593899\pi$
$641$	1.15349e11	−	1.99790e11i	0.683251	−	1.18343i	0.973983	−	0.226621i	$-0.0727678\pi$
$642$	−8.56805e8	+	4.94677e8i	−0.00504362	+	0.00291193i
$643$		−	3.19437e11i		−	1.86871i	−0.356343	−	0.934355i	$-0.615977\pi$
$643$		−	3.19437e11i		−	1.86871i	0.356343	−	0.934355i	$-0.384023\pi$
$644$	−7.00981e9	+	9.95482e10i	−0.0407533	+	0.578749i
$645$	1.55939e11			0.900982
$646$	2.28968e10	+	3.96583e10i	0.131475	+	0.227722i
$647$	1.79087e11	+	1.03396e11i	1.02199	+	0.590046i	0.914680	−	0.404179i	$-0.132443\pi$
$647$	1.79087e11	+	1.03396e11i	1.02199	+	0.590046i	0.107310	+	0.994226i	$0.465776\pi$
$648$	−3.50496e10	+	6.07077e10i	−0.198785	+	0.344305i
$649$	−1.95836e11	+	1.13066e11i	−1.10386	+	0.637313i
$650$			2.65983e9i			0.0149005i
$651$	1.57276e11	−	7.66137e10i	0.875665	−	0.426562i
$652$	−7.24621e10			−0.400978
$653$	−1.75448e11	−	3.03884e11i	−0.964928	−	1.67130i	−0.709809	−	0.704394i	$-0.751219\pi$
$653$	−1.75448e11	−	3.03884e11i	−0.964928	−	1.67130i	−0.255118	−	0.966910i	$-0.582114\pi$
$654$	6.34125e10	+	3.66112e10i	0.346628	+	0.200126i
$655$	4.17632e9	−	7.23360e9i	0.0226897	−	0.0392997i
$656$	−6.87314e10	+	3.96821e10i	−0.371142	+	0.214279i
$657$			3.77938e10i			0.202843i
$658$	2.31092e10	−	3.42248e10i	0.123277	−	0.182573i
$659$	2.26943e10			0.120330			0.0601652	−	0.998188i	$-0.480837\pi$
$659$	2.26943e10			0.120330			0.0601652	+	0.998188i	$0.480837\pi$
$660$	8.32159e10	+	1.44134e11i	0.438561	+	0.759611i
$661$	−1.80869e11	−	1.04425e11i	−0.947456	−	0.547014i	−0.0551663	−	0.998477i	$-0.517569\pi$
$661$	−1.80869e11	−	1.04425e11i	−0.947456	−	0.547014i	−0.892290	+	0.451463i	$0.850902\pi$
$662$	−3.24407e10	+	5.61889e10i	−0.168911	+	0.292563i
$663$	1.83013e10	−	1.05662e10i	0.0947168	−	0.0546848i
$664$			2.11808e11i			1.08960i
$665$	−2.59114e11	−	1.74958e11i	−1.32496	−	0.894638i
$666$	2.34732e10			0.119309
$667$	1.13110e11	+	1.95911e11i	0.571473	+	0.989821i
$668$	−8.91046e10	−	5.14446e10i	−0.447501	−	0.258365i
$669$	−6.09818e10	+	1.05624e11i	−0.304436	+	0.527299i
$670$	−9.31704e9	+	5.37920e9i	−0.0462359	+	0.0266943i
$671$			2.56650e11i			1.26605i
$672$	−6.52681e10	−	1.33985e11i	−0.320055	−	0.657021i
$673$	−1.55269e11			−0.756877			−0.378438	−	0.925627i	$-0.623539\pi$
$673$	−1.55269e11			−0.756877			−0.378438	+	0.925627i	$0.623539\pi$
$674$	−1.79817e10	−	3.11452e10i	−0.0871348	−	0.150922i
$675$	−3.40716e10	−	1.96713e10i	−0.164126	−	0.0947583i
$676$	8.64401e10	−	1.49719e11i	0.413931	−	0.716950i
$677$	1.81122e11	−	1.04571e11i	0.862216	−	0.497801i	−0.00253760	−	0.999997i	$-0.500808\pi$
$677$	1.81122e11	−	1.04571e11i	0.862216	−	0.497801i	0.864754	+	0.502196i	$0.167474\pi$
$678$		−	7.35106e10i		−	0.347882i
$679$	1.66339e11	+	1.17129e10i	0.782554	+	0.0551045i
$680$	−7.77632e10			−0.363696
$681$	3.65638e10	+	6.33304e10i	0.170005	+	0.294458i
$682$	−8.11841e10	−	4.68717e10i	−0.375261	−	0.216657i
$683$	−1.02352e11	+	1.77279e11i	−0.470343	+	0.814658i	−0.999425	−	0.0339132i	$-0.989203\pi$
$683$	−1.02352e11	+	1.77279e11i	−0.470343	+	0.814658i	0.529082	+	0.848571i	$0.322536\pi$
$684$	7.29455e10	−	4.21151e10i	0.333253	−	0.192404i
$685$			5.99047e10i			0.272081i
$686$	−7.20622e10	+	2.32981e10i	−0.325395	+	0.105202i
$687$	−1.84710e11			−0.829206
$688$	−7.35485e10	−	1.27390e11i	−0.328262	−	0.568566i
$689$	3.29341e10	+	1.90145e10i	0.146140	+	0.0843739i
$690$	2.31639e10	−	4.01210e10i	0.102192	−	0.177001i
$691$	1.36082e11	−	7.85668e10i	0.596881	−	0.344609i	−0.170933	−	0.985283i	$-0.554678\pi$
$691$	1.36082e11	−	7.85668e10i	0.596881	−	0.344609i	0.767813	+	0.640674i	$0.221345\pi$
$692$			9.80725e10i			0.427684i
$693$	−5.22532e9	+	7.42062e10i	−0.0226558	+	0.321742i
$694$	−3.38564e9			−0.0145950
$695$	4.20434e10	+	7.28212e10i	0.180201	+	0.312118i
$696$	−1.91098e11	−	1.10330e11i	−0.814363	−	0.470173i
$697$	3.97648e10	−	6.88746e10i	0.168487	−	0.291829i
$698$	9.37539e10	−	5.41288e10i	0.394973	−	0.228038i
$699$			3.23186e11i			1.35377i
$700$	3.32211e10	−	1.61830e10i	0.138364	−	0.0674010i
$701$	−4.32646e11			−1.79168			−0.895840	−	0.444377i	$-0.853425\pi$
$701$	−4.32646e11			−1.79168			−0.895840	+	0.444377i	$0.853425\pi$
$702$	1.12881e10	+	1.95515e10i	0.0464806	+	0.0805067i
$703$	3.68586e11	+	2.12803e11i	1.50910	+	0.871279i
$704$	4.89629e10	−	8.48063e10i	0.199332	−	0.345253i
$705$	1.25360e11	−	7.23768e10i	0.507462	−	0.292983i
$706$		−	4.19140e10i		−	0.168710i
$707$	9.11428e10	−	1.34983e11i	0.364791	−	0.540258i
$708$	2.17406e11			0.865245
$709$	2.03523e10	+	3.52513e10i	0.0805432	+	0.139505i	0.903483	−	0.428623i	$-0.141001\pi$
$709$	2.03523e10	+	3.52513e10i	0.0805432	+	0.139505i	−0.822940	+	0.568128i	$0.807668\pi$
$710$	6.21686e10	+	3.58931e10i	0.244646	+	0.141246i
$711$	4.64994e10	−	8.05393e10i	0.181957	−	0.315159i
$712$	7.48624e10	−	4.32218e10i	0.291302	−	0.168183i
$713$		−	1.97030e11i		−	0.762385i
$714$	3.22250e10	+	2.17589e10i	0.123994	+	0.0837227i
$715$	7.73121e10			0.295817
$716$	−2.80239e10	−	4.85389e10i	−0.106629	−	0.184687i
$717$	−6.48235e10	−	3.74258e10i	−0.245276	−	0.141610i
$718$	3.91888e10	−	6.78769e10i	0.147456	−	0.255402i
$719$	2.18425e11	−	1.26108e11i	0.817311	−	0.471875i	−0.0321770	−	0.999482i	$-0.510244\pi$
$719$	2.18425e11	−	1.26108e11i	0.817311	−	0.471875i	0.849488	+	0.527607i	$0.176911\pi$
$720$			5.70154e10i			0.212159i
$721$	8.14346e9	+	1.67172e10i	0.0301348	+	0.0618619i
$722$	−1.09335e11			−0.402357
$723$	−6.44803e10	−	1.11683e11i	−0.235979	−	0.408728i
$724$	−1.61529e10	−	9.32586e9i	−0.0587889	−	0.0339418i
$725$	4.18834e10	−	7.25442e10i	0.151597	−	0.262573i
$726$	−1.32869e10	+	7.67121e9i	−0.0478275	+	0.0276132i
$727$			5.00088e10i			0.179023i	0.995986	+	0.0895115i	$0.0285306\pi$
$727$			5.00088e10i			0.179023i	−0.995986	+	0.0895115i	$0.971469\pi$
$728$	−4.51066e10	−	3.17624e9i	−0.160589	−	0.0113081i
$729$	−3.09292e11			−1.09511
$730$	3.61355e10	+	6.25885e10i	0.127246	+	0.220396i
$731$	1.27655e11	+	7.37018e10i	0.447064	+	0.258112i
$732$	1.23374e11	−	2.13689e11i	0.429712	−	0.744284i
$733$	−4.41005e10	+	2.54615e10i	−0.152766	+	0.0881997i	−0.574435	−	0.818550i	$-0.694778\pi$
$733$	−4.41005e10	+	2.54615e10i	−0.152766	+	0.0881997i	0.421668	+	0.906750i	$0.361445\pi$
$734$		−	3.29595e10i		−	0.113553i
$735$	−2.62851e11	−	3.72024e10i	−0.900658	−	0.127474i
$736$	−1.67852e11			−0.572026
$737$	2.32065e10	+	4.01948e10i	0.0786573	+	0.136239i
$738$	1.67779e10	+	9.68670e9i	0.0565602	+	0.0326551i
$739$	−2.72715e11	+	4.72356e11i	−0.914389	+	1.58377i	−0.106595	+	0.994303i	$0.533995\pi$
$739$	−2.72715e11	+	4.72356e11i	−0.914389	+	1.58377i	−0.807794	+	0.589465i	$0.799339\pi$
$740$	−2.93517e11	+	1.69462e11i	−0.978828	+	0.565126i
$741$			9.33393e10i			0.309593i
$742$	−4.91501e9	+	6.97994e10i	−0.0162147	+	0.230269i
$743$	3.27091e11			1.07328			0.536641	−	0.843811i	$-0.319693\pi$
$743$	3.27091e11			1.07328			0.536641	+	0.843811i	$0.319693\pi$
$744$	9.60943e10	+	1.66440e11i	0.313622	+	0.543208i
$745$	1.86256e11	+	1.07535e11i	0.604623	+	0.349079i
$746$	2.67617e10	−	4.63526e10i	0.0864088	−	0.149664i
$747$	−1.34770e11	+	7.78097e10i	−0.432824	+	0.249891i
$748$			1.57322e11i			0.502555i
$749$	5.74015e9	−	2.79620e9i	0.0182388	−	0.00888466i
$750$	8.12716e10			0.256858
$751$	−2.04416e11	−	3.54059e11i	−0.642621	−	1.11305i	−0.984845	−	0.173434i	$-0.944514\pi$
$751$	−2.04416e11	−	3.54059e11i	−0.642621	−	1.11305i	0.342224	−	0.939618i	$-0.388820\pi$
$752$	−1.18252e11	−	6.82729e10i	−0.369775	−	0.213490i
$753$	−2.35776e11	+	4.08376e11i	−0.733365	+	1.27023i
$754$	−4.16285e10	+	2.40342e10i	−0.128797	+	0.0743608i
$755$		−	5.40060e10i		−	0.166209i
$756$	1.75518e11	−	2.59943e11i	0.537323	−	0.795777i
$757$	4.82594e10			0.146960			0.0734799	−	0.997297i	$-0.476590\pi$
$757$	4.82594e10			0.146960			0.0734799	+	0.997297i	$0.476590\pi$
$758$	2.54203e10	+	4.40293e10i	0.0770024	+	0.133372i
$759$	−1.73087e11	−	9.99316e10i	−0.521551	−	0.301117i
$760$	1.71735e11	−	2.97453e11i	0.514759	−	0.891588i
$761$	−1.73821e11	+	1.00355e11i	−0.518278	+	0.299228i	−0.736230	−	0.676732i	$-0.763396\pi$
$761$	−1.73821e11	+	1.00355e11i	−0.518278	+	0.299228i	0.217952	+	0.975960i	$0.430062\pi$
$762$			9.95627e10i			0.295309i
$763$	−3.91637e11	−	2.64440e11i	−1.15554	−	0.780243i
$764$	−1.37335e9			−0.00403096
$765$	−2.85671e10	−	4.94797e10i	−0.0834105	−	0.144471i
$766$	−1.38123e11	−	7.97455e10i	−0.401191	−	0.231628i
$767$	5.04956e10	−	8.74610e10i	0.145906	−	0.252716i
$768$	−6.23472e9	+	3.59962e9i	−0.0179214	+	0.0103469i
$769$		−	4.61218e11i		−	1.31887i	−0.751762	−	0.659434i	$-0.770796\pi$
$769$		−	4.61218e11i		−	1.31887i	0.751762	−	0.659434i	$-0.229204\pi$
$770$	6.22968e10	+	1.27885e11i	0.177216	+	0.363796i
$771$	5.59428e11			1.58317
$772$	8.08794e10	+	1.40087e11i	0.227703	+	0.394393i
$773$	4.10904e11	+	2.37235e11i	1.15086	+	0.664448i	0.949096	−	0.314986i	$-0.102000\pi$
$773$	4.10904e11	+	2.37235e11i	1.15086	+	0.664448i	0.201762	+	0.979435i	$0.435333\pi$
$774$	−1.79538e10	+	3.10968e10i	−0.0500255	+	0.0866468i
$775$	−6.31838e10	+	3.64792e10i	−0.175145	+	0.101120i
$776$			1.83188e11i			0.505184i
$777$	3.60489e11	+	2.53843e10i	0.989025	+	0.0696435i
$778$	1.11124e10			0.0303311
$779$	1.75636e11	+	3.04210e11i	0.476939	+	0.826082i
$780$	−6.43708e10	−	3.71645e10i	−0.173904	−	0.100404i
$781$	1.54847e11	−	2.68203e11i	0.416196	−	0.720873i
$782$	3.79250e10	−	2.18960e10i	0.101414	−	0.0585515i
$783$		−	7.10999e11i		−	1.89157i
$784$	9.35820e10	+	2.32275e11i	0.247701	+	0.614805i
$785$	3.42927e11			0.903073
$786$	−2.29409e9	−	3.97347e9i	−0.00601062	−	0.0104107i
$787$	−3.89508e11	−	2.24883e11i	−1.01536	−	0.586216i	−0.102600	−	0.994723i	$-0.532716\pi$
$787$	−3.89508e11	−	2.24883e11i	−1.01536	−	0.586216i	−0.912755	+	0.408507i	$0.866049\pi$
$788$	−2.25079e11	+	3.89848e11i	−0.583755	+	1.01109i
$789$	5.55966e10	−	3.20987e10i	0.143463	−	0.0828285i
$790$		−	1.77836e11i		−	0.456575i
$791$	−3.33240e10	+	4.73244e11i	−0.0851240	+	1.20887i
$792$	−8.17228e10			−0.207703
$793$	−5.73104e10	−	9.92646e10i	−0.144924	−	0.251016i
$794$	−1.65988e11	−	9.58330e10i	−0.417632	−	0.241120i
$795$	−1.22635e11	+	2.12411e11i	−0.307006	+	0.531751i
$796$	4.09298e10	−	2.36308e10i	0.101950	−	0.0588608i
$797$		−	3.34628e11i		−	0.829332i	−0.909974	−	0.414666i	$-0.863898\pi$
$797$		−	3.34628e11i		−	0.829332i	0.909974	−	0.414666i	$-0.136102\pi$
$798$	−1.54397e11	+	7.52112e10i	−0.380738	+	0.185469i
$799$	1.36830e11			0.335734
$800$	3.10771e10	+	5.38270e10i	0.0758717	+	0.131414i
$801$	5.50030e10	+	3.17560e10i	0.133615	+	0.0771428i
$802$	−3.27372e10	+	5.67026e10i	−0.0791306	+	0.137058i
$803$	2.70014e11	−	1.55893e11i	0.649418	−	0.374942i
$804$		−	4.46221e10i		−	0.106789i
$805$	−1.67311e11	+	2.47789e11i	−0.398420	+	0.590062i
$806$	4.18661e10			0.0992025
$807$	−2.23830e11	−	3.87685e11i	−0.527746	−	0.914082i
$808$	1.54955e11	+	8.94636e10i	0.363548	+	0.209894i
$809$	2.94569e11	−	5.10208e11i	0.687689	−	1.19111i	−0.284894	−	0.958559i	$-0.591958\pi$
$809$	2.94569e11	−	5.10208e11i	0.687689	−	1.19111i	0.972583	−	0.232554i	$-0.0747083\pi$
$810$	−8.52923e10	+	4.92435e10i	−0.198139	+	0.114396i
$811$			5.45293e11i			1.26051i	0.776388	+	0.630256i	$0.217050\pi$
$811$			5.45293e11i			1.26051i	−0.776388	+	0.630256i	$0.782950\pi$
$812$	5.53463e11	+	3.73708e11i	1.27310	+	0.859623i
$813$	−3.04989e11			−0.698108
$814$	−9.68227e10	−	1.67702e11i	−0.220536	−	0.381980i
$815$	−1.88011e11	−	1.08548e11i	−0.426141	−	0.246032i
$816$	6.42837e10	−	1.11343e11i	0.144991	−	0.251131i
$817$	−5.63836e11	+	3.25531e11i	−1.26551	+	0.730641i
$818$		−	1.03131e11i		−	0.230343i
$819$	−1.45494e10	−	2.98676e10i	−0.0323377	−	0.0663841i
$820$	−2.79728e11			−0.618701
$821$	5.86383e10	+	1.01564e11i	0.129065	+	0.223547i	0.923315	−	0.384044i	$-0.125469\pi$
$821$	5.86383e10	+	1.01564e11i	0.129065	+	0.223547i	−0.794250	+	0.607592i	$0.792136\pi$
$822$	2.84975e10	+	1.64530e10i	0.0624194	+	0.0360379i
$823$	−1.17880e11	+	2.04175e11i	−0.256946	+	0.445044i	−0.965422	−	0.260691i	$-0.916050\pi$
$823$	−1.17880e11	+	2.04175e11i	−0.256946	+	0.445044i	0.708476	+	0.705735i	$0.249383\pi$
$824$	−1.76913e10	+	1.02141e10i	−0.0383753	+	0.0221560i
$825$			7.40075e10i			0.159757i
$826$	1.85362e11	+	1.30525e10i	0.398199	+	0.0280397i
$827$	−2.86783e11			−0.613100			−0.306550	−	0.951855i	$-0.599175\pi$
$827$	−2.86783e11			−0.613100			−0.306550	+	0.951855i	$0.599175\pi$
$828$	−4.02744e10	−	6.97573e10i	−0.0856855	−	0.148412i
$829$	7.49482e10	+	4.32714e10i	0.158688	+	0.0916184i	0.577241	−	0.816574i	$-0.304129\pi$
$829$	7.49482e10	+	4.32714e10i	0.158688	+	0.0916184i	−0.418553	+	0.908192i	$0.637463\pi$
$830$	−1.48791e11	+	2.57714e11i	−0.313520	+	0.543032i
$831$	−3.19120e11	+	1.84244e11i	−0.669191	+	0.386357i
$832$			4.37341e10i			0.0912697i
$833$	−1.97593e11	−	1.54687e11i	−0.410385	−	0.321272i
$834$	4.61895e10			0.0954727
$835$	−1.54128e11	−	2.66958e11i	−0.317056	−	0.549157i
$836$	−6.01775e11	−	3.47435e11i	−1.23200	−	0.711293i
$837$	−3.09629e11	+	5.36293e11i	−0.630870	+	1.09270i
$838$	1.11513e11	−	6.43819e10i	0.226125	−	0.130553i
$839$		−	3.59935e10i		−	0.0726401i	−0.999340	−	0.0363201i	$-0.988436\pi$
$839$		−	3.59935e10i		−	0.0726401i	0.999340	−	0.0363201i	$-0.0115636\pi$
$840$	2.04854e10	−	2.90918e11i	0.0411459	−	0.584324i
$841$	1.01359e12			2.02618
$842$	1.32174e11	+	2.28933e11i	0.262966	+	0.455470i
$843$	1.76387e11	+	1.01837e11i	0.349265	+	0.201648i
$844$	1.52695e11	−	2.64476e11i	0.300923	−	0.521214i
$845$	4.48557e11	−	2.58975e11i	0.879815	−	0.507961i
$846$			3.33319e10i			0.0650697i
$847$	8.90155e10	−	4.33621e10i	0.172955	−	0.0842513i
$848$	2.31364e11			0.447416
$849$	−4.74067e10	−	8.21109e10i	−0.0912450	−	0.158041i
$850$	−1.40433e10	−	8.10788e9i	−0.0269025	−	0.0155322i
$851$	2.03502e11	−	3.52476e11i	0.388017	−	0.672066i
$852$	−2.57854e11	+	1.48872e11i	−0.489345	+	0.282524i
$853$			3.95346e11i			0.746761i	0.927678	+	0.373380i	$0.121801\pi$
$853$			3.95346e11i			0.746761i	−0.927678	+	0.373380i	$0.878199\pi$
$854$	1.18018e11	−	1.74786e11i	0.221880	−	0.328605i
$855$	2.52354e11			0.472222
$856$	3.50719e9	+	6.07463e9i	0.00653227	+	0.0113142i
$857$	−8.56602e9	−	4.94560e9i	−0.0158802	−	0.00916844i	0.492039	−	0.870573i	$-0.336252\pi$
$857$	−8.56602e9	−	4.94560e9i	−0.0158802	−	0.00916844i	−0.507919	+	0.861405i	$0.669585\pi$
$858$	2.12341e10	−	3.67785e10i	0.0391818	−	0.0678648i
$859$	2.85199e11	−	1.64660e11i	0.523812	−	0.302423i	−0.214681	−	0.976684i	$-0.568871\pi$
$859$	2.85199e11	−	1.64660e11i	0.523812	−	0.302423i	0.738493	+	0.674261i	$0.235538\pi$
$860$		−	5.18461e11i		−	0.947812i
$861$	2.47190e11	+	1.66907e11i	0.449799	+	0.303712i
$862$	1.14148e11			0.206748
$863$	3.95706e11	+	6.85383e11i	0.713394	+	1.23563i	0.963576	+	0.267435i	$0.0861762\pi$
$863$	3.95706e11	+	6.85383e11i	0.713394	+	1.23563i	−0.250182	+	0.968199i	$0.580490\pi$
$864$	4.56875e11	+	2.63777e11i	0.819865	+	0.473349i
$865$	−1.46913e11	+	2.54460e11i	−0.262419	+	0.454523i
$866$	−2.81982e11	+	1.62803e11i	−0.501361	+	0.289461i
$867$		−	3.45467e11i		−	0.611407i
$868$	−2.54723e11	−	5.22905e11i	−0.448734	−	0.921180i
$869$	−7.67207e11			−1.34534
$870$	−1.55010e11	−	2.68486e11i	−0.270572	−	0.468645i
$871$	−1.79511e10	−	1.03641e10i	−0.0311903	−	0.0180077i
$872$	2.59568e11	−	4.49586e11i	0.448938	−	0.777583i
$873$	−1.16560e11	+	6.72959e10i	−0.200674	+	0.115859i
$874$			1.93423e11i			0.331484i
$875$	−5.23207e11	−	3.68423e10i	−0.892568	−	0.0628513i
$876$	−2.99755e11			−0.509038
$877$	1.60444e10	+	2.77897e10i	0.0271222	+	0.0469770i	0.879268	−	0.476328i	$-0.158032\pi$
$877$	1.60444e10	+	2.77897e10i	0.0271222	+	0.0469770i	−0.852146	+	0.523305i	$0.824699\pi$
$878$	1.17418e11	+	6.77913e10i	0.197586	+	0.114076i
$879$	2.69553e11	−	4.66880e11i	0.451532	−	0.782077i
$880$	4.07341e11	−	2.35178e11i	0.679247	−	0.392163i
$881$			7.47336e11i			1.24054i	0.784387	+	0.620272i	$0.212978\pi$
$881$			7.47336e11i			1.24054i	−0.784387	+	0.620272i	$0.787022\pi$
$882$	3.76816e10	−	4.81336e10i	0.0622666	−	0.0795379i
$883$	−6.32325e11			−1.04015			−0.520077	−	0.854120i	$-0.674097\pi$
$883$	−6.32325e11			−1.04015			−0.520077	+	0.854120i	$0.674097\pi$
$884$	−3.51303e10	−	6.08475e10i	−0.0575272	−	0.0996400i
$885$	5.64086e11	+	3.25675e11i	0.919543	+	0.530899i
$886$	−4.45922e10	+	7.72359e10i	−0.0723642	+	0.125338i
$887$	1.20690e11	−	6.96802e10i	0.194974	−	0.112568i	−0.399335	−	0.916805i	$-0.630759\pi$
$887$	1.20690e11	−	6.96802e10i	0.194974	−	0.112568i	0.594309	+	0.804237i	$0.297426\pi$
$888$			3.97004e11i			0.638473i
$889$	4.51341e10	−	6.40961e11i	0.0722599	−	1.02618i
$890$	1.21450e11			0.193570
$891$	2.12442e11	+	3.67961e11i	0.337078	+	0.583836i
$892$	3.51174e11	+	2.02750e11i	0.554706	+	0.320260i
$893$	−3.02181e11	+	5.23392e11i	−0.475183	+	0.823041i
$894$	1.02312e11	−	5.90697e10i	0.160168	−	0.0924729i
$895$		−	1.67919e11i		−	0.261703i
$896$	−5.76809e11	+	2.80981e11i	−0.894953	+	0.435958i
$897$	8.92597e10			0.137875
$898$	−5.58348e10	−	9.67087e10i	−0.0858617	−	0.148717i
$899$	−1.14186e12	−	6.59252e11i	−1.74813	−	1.00928i
$900$	−1.49132e10	+	2.58305e10i	−0.0227301	+	0.0393697i
$901$	−2.00784e11	+	1.15923e11i	−0.304671	+	0.175902i
$902$		−	1.59824e11i		−	0.241443i
$903$	−3.09353e11	+	4.58153e11i	−0.465268	+	0.689064i
$904$	−5.21180e11			−0.780395
$905$	−2.79403e10	−	4.83940e10i	−0.0416521	−	0.0721435i
$906$	−2.56915e10	−	1.48330e10i	−0.0381308	−	0.0220148i
$907$	9.40093e10	−	1.62829e11i	0.138913	−	0.240604i	−0.788173	−	0.615454i	$-0.788973\pi$
$907$	9.40093e10	−	1.62829e11i	0.138913	−	0.240604i	0.927085	+	0.374850i	$0.122306\pi$
$908$	2.10559e11	−	1.21566e11i	0.309763	−	0.178842i
$909$			1.31461e11i			0.192550i
$910$	−5.26516e10	−	3.55513e10i	−0.0767797	−	0.0518430i
$911$	−1.25216e12			−1.81797			−0.908985	−	0.416828i	$-0.863142\pi$
$911$	−1.25216e12			−1.81797			−0.908985	+	0.416828i	$0.863142\pi$
$912$	2.83932e11	+	4.91785e11i	0.410426	+	0.710879i
$913$	1.11181e12	+	6.41902e11i	1.60010	+	0.923817i
$914$	1.81327e11	−	3.14068e11i	0.259824	−	0.450028i
$915$	6.40214e11	−	3.69628e11i	0.913357	−	0.527327i
$916$			6.14117e11i			0.872306i
$917$	1.29675e10	+	2.66202e10i	0.0183391	+	0.0376473i
$918$	−1.37637e11			−0.193804
$919$	1.21272e11	+	2.10049e11i	0.170019	+	0.294482i	0.938426	−	0.345479i	$-0.112284\pi$
$919$	1.21272e11	+	2.10049e11i	0.170019	+	0.294482i	−0.768407	+	0.639961i	$0.778950\pi$
$920$	−2.84452e11	−	1.64229e11i	−0.397062	−	0.229244i
$921$	4.44968e11	−	7.70708e11i	0.618430	−	1.07115i
$922$	−2.24286e11	+	1.29492e11i	−0.310369	+	0.179192i
$923$			1.38310e11i			0.190567i
$924$	−5.88554e11	−	4.14438e10i	−0.807418	−	0.0568554i
$925$	−1.50710e11			−0.205862
$926$	−1.12803e11	−	1.95381e11i	−0.153418	−	0.265728i
$927$	−1.29982e10	−	7.50450e9i	−0.0176021	−	0.0101626i
$928$	−5.61625e11	+	9.72762e11i	−0.757276	+	1.31164i
$929$	1.10052e12	−	6.35385e11i	1.47753	−	0.853050i	0.477848	−	0.878443i	$-0.341417\pi$
$929$	1.10052e12	−	6.35385e11i	1.47753	−	0.853050i	0.999678	+	0.0253933i	$0.00808380\pi$
$930$			2.70018e11i			0.360962i
$931$	1.02806e12	−	4.14200e11i	1.36843	−	0.551330i
$932$	1.07452e12			1.42413
$933$	−5.81730e11	−	1.00759e12i	−0.767706	−	1.32971i
$934$	4.18118e11	+	2.41400e11i	0.549428	+	0.317213i
$935$	−2.35669e11	+	4.08190e11i	−0.308358	+	0.534092i
$936$	3.16079e10	−	1.82489e10i	0.0411806	−	0.0237756i
$937$		−	2.85353e11i		−	0.370189i	−0.982721	−	0.185095i	$-0.940741\pi$
$937$		−	2.85353e11i		−	0.370189i	0.982721	−	0.185095i	$-0.0592591\pi$
$938$	2.67899e9	−	3.80450e10i	0.00346066	−	0.0491458i
$939$	2.67177e11			0.343666
$940$	−2.40636e11	−	4.16794e11i	−0.308212	−	0.533839i
$941$	−9.63566e11	−	5.56315e11i	−1.22892	−	0.709516i	−0.262114	−	0.965037i	$-0.584420\pi$
$941$	−9.63566e11	−	5.56315e11i	−1.22892	−	0.709516i	−0.966804	+	0.255521i	$0.917753\pi$
$942$	9.41862e10	−	1.63135e11i	0.119614	−	0.207178i
$943$	2.90914e11	−	1.67959e11i	0.367889	−	0.212401i
$944$		−	6.14418e11i		−	0.773706i
$945$	8.44798e11	−	4.11526e11i	1.05932	−	0.516024i
$946$	2.96225e11			0.369876
$947$	1.33170e11	+	2.30657e11i	0.165579	+	0.286791i	0.936861	−	0.349703i	$-0.113717\pi$
$947$	1.33170e11	+	2.30657e11i	0.165579	+	0.286791i	−0.771282	+	0.636494i	$0.780384\pi$
$948$	6.38784e11	+	3.68802e11i	0.790898	+	0.456625i
$949$	−6.96223e10	+	1.20589e11i	−0.0858388	+	0.148677i
$950$	6.20272e10	−	3.58114e10i	0.0761531	−	0.0439670i
$951$			7.22383e11i			0.883173i
$952$	1.54267e11	−	2.28471e11i	0.187813	−	0.278152i
$953$	3.02193e11			0.366364			0.183182	−	0.983079i	$-0.441360\pi$
$953$	3.02193e11			0.366364			0.183182	+	0.983079i	$0.441360\pi$
$954$	−2.82388e10	−	4.89111e10i	−0.0340921	−	0.0590492i
$955$	−3.56332e9	−	2.05728e9i	−0.00428392	−	0.00247332i
$956$	−1.24432e11	+	2.15523e11i	−0.148971	+	0.258025i
$957$	−1.15828e12	+	6.68732e11i	−1.38091	+	0.797268i
$958$		−	1.91024e11i		−	0.226791i
$959$	−1.76002e11	−	1.18839e11i	−0.208086	−	0.140503i
$960$	−2.82066e11			−0.332098
$961$	1.47743e11	+	2.55898e11i	0.173226	+	0.300037i
$962$	7.48963e10	+	4.32414e10i	0.0874500	+	0.0504893i
$963$	−2.57680e9	+	4.46315e9i	−0.00299624	+	0.00518963i
$964$	−3.71321e11	+	2.14382e11i	−0.429973	+	0.248245i
$965$			4.84630e11i			0.558857i
$966$	7.19240e10	+	1.47648e11i	0.0825972	+	0.169559i
$967$	−6.58881e11			−0.753531			−0.376765	−	0.926309i	$-0.622964\pi$
$967$	−6.58881e11			−0.753531			−0.376765	+	0.926309i	$0.622964\pi$
$968$	5.43878e10	+	9.42024e10i	0.0619441	+	0.107290i
$969$	−4.92810e11	−	2.84524e11i	−0.558964	−	0.322718i
$970$	−1.28686e11	+	2.22891e11i	−0.145360	+	0.251771i
$971$	5.37947e9	−	3.10584e9i	0.00605149	−	0.00349383i	−0.496971	−	0.867767i	$-0.665555\pi$
$971$	5.37947e9	−	3.10584e9i	0.00605149	−	0.00349383i	0.503023	+	0.864273i	$0.332221\pi$
$972$			4.48597e11i			0.502564i
$973$	−2.97357e11	−	2.09388e10i	−0.331762	−	0.0233614i
$974$	−1.63459e11			−0.181624
$975$	−1.65260e10	−	2.86239e10i	−0.0182873	−	0.0316745i
$976$	−6.03913e11	−	3.48669e11i	−0.665541	−	0.384250i
$977$	2.97186e11	−	5.14741e11i	0.326174	−	0.564951i	−0.655575	−	0.755130i	$-0.727574\pi$
$977$	2.97186e11	−	5.14741e11i	0.326174	−	0.564951i	0.981749	+	0.190179i	$0.0609070\pi$
$978$	−1.03276e11	+	5.96264e10i	−0.112887	+	0.0651753i
$979$		−	5.23951e11i		−	0.570374i
$980$	−1.23689e11	+	8.73918e11i	−0.134100	+	0.947472i
$981$	3.81420e11			0.411839
$982$	2.13554e11	+	3.69886e11i	0.229647	+	0.397761i
$983$	5.00006e11	+	2.88678e11i	0.535502	+	0.309172i	0.743254	−	0.669009i	$-0.233281\pi$
$983$	5.00006e11	+	2.88678e11i	0.535502	+	0.309172i	−0.207752	+	0.978181i	$0.566615\pi$
$984$	−1.63832e11	+	2.83765e11i	−0.174750	+	0.302677i
$985$	−1.16799e12	+	6.74338e11i	−1.24078	+	0.716362i
$986$		−	2.93051e11i		−	0.310053i
$987$	−3.60456e10	+	5.11894e11i	−0.0379825	+	0.539400i
$988$	3.10331e11			0.325685
$989$	3.11303e11	+	5.39192e11i	0.325385	+	0.563584i
$990$	−9.94351e10	−	5.74089e10i	−0.103514	−	0.0597638i
$991$	9.01496e11	−	1.56144e12i	0.934693	−	1.61894i	0.159513	−	0.987196i	$-0.449008\pi$
$991$	9.01496e11	−	1.56144e12i	0.934693	−	1.61894i	0.775180	−	0.631740i	$-0.217659\pi$
$992$	8.47247e11	−	4.89158e11i	0.874910	−	0.505129i
$993$		−	8.06241e11i		−	0.829216i
$994$	−2.28785e11	+	1.11448e11i	−0.234360	+	0.114164i
$995$	1.41596e11			0.144464
$996$	−6.17134e11	−	1.06891e12i	−0.627108	−	1.08618i
$997$	−1.40124e12	−	8.09008e11i	−1.41818	−	0.818789i	−0.422045	−	0.906575i	$-0.638687\pi$
$997$	−1.40124e12	−	8.09008e11i	−1.41818	−	0.818789i	−0.996139	+	0.0877862i	$0.972021\pi$
$998$	−2.21575e11	+	3.83780e11i	−0.223357	+	0.386865i
$999$	−1.10782e12	+	6.39601e11i	−1.11226	+	0.642165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.9.d.a.3.2	✓	8
3.2	odd	2		63.9.m.b.10.3		8
4.3	odd	2		112.9.s.a.17.1		8
7.2	even	3		49.9.d.c.19.2		8
7.3	odd	6		49.9.b.a.48.6		8
7.4	even	3		49.9.b.a.48.5		8
7.5	odd	6	inner	7.9.d.a.5.2	yes	8
7.6	odd	2		49.9.d.c.31.2		8
21.5	even	6		63.9.m.b.19.3		8
28.19	even	6		112.9.s.a.33.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.9.d.a.3.2	✓	8	1.1	even	1	trivial
7.9.d.a.5.2	yes	8	7.5	odd	6	inner
49.9.b.a.48.5		8	7.4	even	3
49.9.b.a.48.6		8	7.3	odd	6
49.9.d.c.19.2		8	7.2	even	3
49.9.d.c.31.2		8	7.6	odd	2
63.9.m.b.10.3		8	3.2	odd	2
63.9.m.b.19.3		8	21.5	even	6
112.9.s.a.17.1		8	4.3	odd	2
112.9.s.a.33.1		8	28.19	even	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.73583 - 4.73860i) q^{2} +(58.8837 + 33.9965i) q^{3} +(113.030 - 195.774i) q^{4} +(586.541 - 338.640i) q^{5} -372.035i q^{6} +(-168.652 + 2395.07i) q^{7} -2637.67 q^{8} +(-968.977 - 1678.32i) q^{9} +O(q^{10})\)	\(q+(-2.73583 - 4.73860i) q^{2} +(58.8837 + 33.9965i) q^{3} +(113.030 - 195.774i) q^{4} +(586.541 - 338.640i) q^{5} -372.035i q^{6} +(-168.652 + 2395.07i) q^{7} -2637.67 q^{8} +(-968.977 - 1678.32i) q^{9} +(-3209.35 - 1852.92i) q^{10} +(-7993.72 + 13845.5i) q^{11} +(13311.3 - 7685.28i) q^{12} -7140.05i q^{13} +(11810.7 - 5753.33i) q^{14} +46050.2 q^{15} +(-21719.6 - 37619.4i) q^{16} +(37697.8 + 21764.8i) q^{17} +(-5301.91 + 9183.18i) q^{18} +(-166506. + 96132.3i) q^{19} -153106. i q^{20} +(-91354.8 + 135297. i) q^{21} +87477.8 q^{22} +(91930.6 + 159228. i) q^{23} +(-155316. - 89671.7i) q^{24} +(34041.0 - 58960.8i) q^{25} +(-33833.8 + 19534.0i) q^{26} -577869. i q^{27} +(449831. + 303734. i) q^{28} +1.23038e6 q^{29} +(-125986. - 218214. i) q^{30} +(-928053. - 535812. i) q^{31} +(-456464. + 790620. i) q^{32} +(-941399. + 543517. i) q^{33} -238180. i q^{34} +(712144. + 1.46192e6i) q^{35} -438095. q^{36} +(-1.10683e6 - 1.91708e6i) q^{37} +(911064. + 526003. i) q^{38} +(242737. - 420432. i) q^{39} +(-1.54710e6 + 893221. i) q^{40} -1.82702e6i q^{41} +(891049. + 62744.3i) q^{42} +3.38628e6 q^{43} +(1.80707e6 + 3.12993e6i) q^{44} +(-1.13669e6 - 656268. i) q^{45} +(503013. - 871244. i) q^{46} +(2.72225e6 - 1.57169e6i) q^{47} -2.95356e6i q^{48} +(-5.70791e6 - 807866. i) q^{49} -372522. q^{50} +(1.47986e6 + 2.56319e6i) q^{51} +(-1.39784e6 - 807043. i) q^{52} +(-2.66308e6 + 4.61259e6i) q^{53} +(-2.73829e6 + 1.58095e6i) q^{54} +1.08280e7i q^{55} +(444849. - 6.31741e6i) q^{56} -1.30726e7 q^{57} +(-3.36611e6 - 5.83028e6i) q^{58} +(1.22494e7 + 7.07217e6i) q^{59} +(5.20508e6 - 9.01546e6i) q^{60} +(1.39025e7 - 8.02662e6i) q^{61} +5.86356e6i q^{62} +(4.18310e6 - 2.03772e6i) q^{63} -6.12518e6 q^{64} +(-2.41790e6 - 4.18793e6i) q^{65} +(5.15102e6 + 2.97394e6i) q^{66} +(1.45154e6 - 2.51415e6i) q^{67} +(8.52200e6 - 4.92018e6i) q^{68} +1.25013e7i q^{69} +(4.97914e6 - 7.37413e6i) q^{70} -1.93711e7 q^{71} +(2.55585e6 + 4.42685e6i) q^{72} +(-1.68891e7 - 9.75096e6i) q^{73} +(-6.05618e6 + 1.04896e7i) q^{74} +(4.00892e6 - 2.31455e6i) q^{75} +4.34635e7i q^{76} +(-3.18128e7 - 2.14806e7i) q^{77} -2.65635e6 q^{78} +(2.39941e7 + 4.15589e7i) q^{79} +(-2.54788e7 - 1.47102e7i) q^{80} +(1.32881e7 - 2.30156e7i) q^{81} +(-8.65752e6 + 4.99842e6i) q^{82} -8.03009e7i q^{83} +(1.61618e7 + 3.31776e7i) q^{84} +2.94817e7 q^{85} +(-9.26429e6 - 1.60462e7i) q^{86} +(7.24493e7 + 4.18286e7i) q^{87} +(2.10848e7 - 3.65200e7i) q^{88} +(-2.83820e7 + 1.63863e7i) q^{89} +7.18175e6i q^{90} +(1.71009e7 + 1.20418e6i) q^{91} +4.15638e7 q^{92} +(-3.64314e7 - 6.31011e7i) q^{93} +(-1.48952e7 - 8.59977e6i) q^{94} +(-6.51084e7 + 1.12771e8i) q^{95} +(-5.37566e7 + 3.10364e7i) q^{96} -6.94505e7i q^{97} +(1.17877e7 + 2.92577e7i) q^{98} +3.09829e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9	\( 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9} + 5796 q^{10} + 1784 q^{11} - 40908 q^{12} - 9856 q^{14} + 131808 q^{15} - 8584 q^{16} - 141456 q^{17} - 121944 q^{18} - 257544 q^{19} + 474012 q^{21} + 1706256 q^{22} - 348940 q^{23} - 895104 q^{24} - 557752 q^{25} - 2913120 q^{26} + 1485092 q^{28} + 4983176 q^{29} - 551112 q^{30} - 2376696 q^{31} - 332016 q^{32} - 5719140 q^{33} + 2491272 q^{35} + 13269408 q^{36} + 492740 q^{37} - 7088088 q^{38} - 2850372 q^{39} - 7601832 q^{40} + 3586128 q^{42} + 4448432 q^{43} - 3678804 q^{44} + 3328164 q^{45} - 226560 q^{46} + 2704128 q^{47} - 3811024 q^{49} - 15628912 q^{50} - 350856 q^{51} + 11135208 q^{52} + 2281460 q^{53} + 24553368 q^{54} - 6573392 q^{56} - 43638408 q^{57} + 11442696 q^{58} + 25291140 q^{59} + 17679564 q^{60} + 59368764 q^{61} - 60081756 q^{63} - 114153056 q^{64} + 16923396 q^{65} + 463428 q^{66} - 107108 q^{67} + 44316972 q^{68} + 19120080 q^{70} - 82809760 q^{71} + 13297584 q^{72} + 116758404 q^{73} + 72690340 q^{74} + 79832424 q^{75} - 58244200 q^{77} - 44122512 q^{78} - 50628092 q^{79} - 93591624 q^{80} - 96868872 q^{81} - 91061712 q^{82} + 154096572 q^{84} + 119231208 q^{85} + 39093088 q^{86} + 26702676 q^{87} + 41392848 q^{88} - 2322516 q^{89} - 151794552 q^{91} + 253819128 q^{92} - 57693204 q^{93} - 345566088 q^{94} - 172787052 q^{95} - 416455200 q^{96} + 373659692 q^{98} + 672244008 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9 + 5796 * q^10 + 1784 * q^11 - 40908 * q^12 - 9856 * q^14 + 131808 * q^15 - 8584 * q^16 - 141456 * q^17 - 121944 * q^18 - 257544 * q^19 + 474012 * q^21 + 1706256 * q^22 - 348940 * q^23 - 895104 * q^24 - 557752 * q^25 - 2913120 * q^26 + 1485092 * q^28 + 4983176 * q^29 - 551112 * q^30 - 2376696 * q^31 - 332016 * q^32 - 5719140 * q^33 + 2491272 * q^35 + 13269408 * q^36 + 492740 * q^37 - 7088088 * q^38 - 2850372 * q^39 - 7601832 * q^40 + 3586128 * q^42 + 4448432 * q^43 - 3678804 * q^44 + 3328164 * q^45 - 226560 * q^46 + 2704128 * q^47 - 3811024 * q^49 - 15628912 * q^50 - 350856 * q^51 + 11135208 * q^52 + 2281460 * q^53 + 24553368 * q^54 - 6573392 * q^56 - 43638408 * q^57 + 11442696 * q^58 + 25291140 * q^59 + 17679564 * q^60 + 59368764 * q^61 - 60081756 * q^63 - 114153056 * q^64 + 16923396 * q^65 + 463428 * q^66 - 107108 * q^67 + 44316972 * q^68 + 19120080 * q^70 - 82809760 * q^71 + 13297584 * q^72 + 116758404 * q^73 + 72690340 * q^74 + 79832424 * q^75 - 58244200 * q^77 - 44122512 * q^78 - 50628092 * q^79 - 93591624 * q^80 - 96868872 * q^81 - 91061712 * q^82 + 154096572 * q^84 + 119231208 * q^85 + 39093088 * q^86 + 26702676 * q^87 + 41392848 * q^88 - 2322516 * q^89 - 151794552 * q^91 + 253819128 * q^92 - 57693204 * q^93 - 345566088 * q^94 - 172787052 * q^95 - 416455200 * q^96 + 373659692 * q^98 + 672244008 * q^99

Introduction

L-functions

Modular forms

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Database

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