LMFDB - Embedded newform 15.11.f.a.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,11,Mod(7,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("15.7");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	15.f (of order $4$, 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:	$9.53035879011$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 49316 x^{17} + 18276332 x^{16} - 230627572 x^{15} + 1992333560 x^{14} + \cdots + 14\!\cdots\!04 $ x^20 - 4x^19 + 8x^18 - 49316x^17 + 18276332x^16 - 230627572x^15 + 1992333560x^14 - 394917674060x^13 + 80687382741790x^12 - 1533501926122980x^11 + 15146257542506232x^10 - 328741228253604588x^9 + 82447502291888584636x^8 - 1645271725800808466812x^7 + 16207307909588298724904x^6 + 13012195729526348972284x^5 + 16940236408526758395395273x^4 - 319136657167982267954012296x^3 + 2999193261390255504529305632x^2 + 9416677726299921146630526016*x + 14782945224391593673997322304
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{34}\cdot 5^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.10
Root			$-44.2389 + 44.2389i$ of defining polynomial
Character	$\chi$	$=$	15.7
Dual form			15.11.f.a.13.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(42.4637 + 42.4637i) q^{2} +(-99.2043 + 99.2043i) q^{3} +2582.33i q^{4} +(3082.93 + 511.056i) q^{5} -8425.16 q^{6} +(-3582.02 - 3582.02i) q^{7} +(-66172.3 + 66172.3i) q^{8} -19683.0i q^{9} +O(q^{10})$	\(q+(42.4637 + 42.4637i) q^{2} +(-99.2043 + 99.2043i) q^{3} +2582.33i q^{4} +(3082.93 + 511.056i) q^{5} -8425.16 q^{6} +(-3582.02 - 3582.02i) q^{7} +(-66172.3 + 66172.3i) q^{8} -19683.0i q^{9} +(109211. + 152614. i) q^{10} -162794. q^{11} +(-256178. - 256178. i) q^{12} +(395604. - 395604. i) q^{13} -304211. i q^{14} +(-356539. + 255141. i) q^{15} -2.97553e6 q^{16} +(1.74668e6 + 1.74668e6i) q^{17} +(835812. - 835812. i) q^{18} +826980. i q^{19} +(-1.31971e6 + 7.96113e6i) q^{20} +710704. q^{21} +(-6.91285e6 - 6.91285e6i) q^{22} +(-816679. + 816679. i) q^{23} -1.31292e7i q^{24} +(9.24327e6 + 3.15110e6i) q^{25} +3.35976e7 q^{26} +(1.95264e6 + 1.95264e6i) q^{27} +(9.24994e6 - 9.24994e6i) q^{28} -4.13627e6i q^{29} +(-2.59742e7 - 4.30573e6i) q^{30} +2.32774e7 q^{31} +(-5.85916e7 - 5.85916e7i) q^{32} +(1.61499e7 - 1.61499e7i) q^{33} +1.48341e8i q^{34} +(-9.21249e6 - 1.28737e7i) q^{35} +5.08279e7 q^{36} +(-3.90169e7 - 3.90169e7i) q^{37} +(-3.51166e7 + 3.51166e7i) q^{38} +7.84913e7i q^{39} +(-2.37822e8 + 1.70187e8i) q^{40} +1.24880e8 q^{41} +(3.01791e7 + 3.01791e7i) q^{42} +(-2.03844e6 + 2.03844e6i) q^{43} -4.20388e8i q^{44} +(1.00591e7 - 6.06813e7i) q^{45} -6.93583e7 q^{46} +(-2.81589e8 - 2.81589e8i) q^{47} +(2.95186e8 - 2.95186e8i) q^{48} -2.56814e8i q^{49} +(2.58696e8 + 5.26310e8i) q^{50} -3.46557e8 q^{51} +(1.02158e9 + 1.02158e9i) q^{52} +(-1.42946e8 + 1.42946e8i) q^{53} +1.65832e8i q^{54} +(-5.01883e8 - 8.31970e7i) q^{55} +4.74061e8 q^{56} +(-8.20400e7 - 8.20400e7i) q^{57} +(1.75641e8 - 1.75641e8i) q^{58} -2.82797e8i q^{59} +(-6.58857e8 - 9.20700e8i) q^{60} -7.06822e8 q^{61} +(9.88442e8 + 9.88442e8i) q^{62} +(-7.05049e7 + 7.05049e7i) q^{63} -1.92909e9i q^{64} +(1.42179e9 - 1.01744e9i) q^{65} +1.37157e9 q^{66} +(-7.04107e8 - 7.04107e8i) q^{67} +(-4.51051e9 + 4.51051e9i) q^{68} -1.62036e8i q^{69} +(1.55469e8 - 9.37862e8i) q^{70} +2.19034e9 q^{71} +(1.30247e9 + 1.30247e9i) q^{72} +(-2.52807e8 + 2.52807e8i) q^{73} -3.31360e9i q^{74} +(-1.22957e9 + 6.04370e8i) q^{75} -2.13553e9 q^{76} +(5.83133e8 + 5.83133e8i) q^{77} +(-3.33303e9 + 3.33303e9i) q^{78} +1.09973e7i q^{79} +(-9.17335e9 - 1.52066e9i) q^{80} -3.87420e8 q^{81} +(5.30286e9 + 5.30286e9i) q^{82} +(4.24856e9 - 4.24856e9i) q^{83} +1.83527e9i q^{84} +(4.49225e9 + 6.27755e9i) q^{85} -1.73119e8 q^{86} +(4.10336e8 + 4.10336e8i) q^{87} +(1.07725e10 - 1.07725e10i) q^{88} +1.52482e9i q^{89} +(3.00390e9 - 2.14960e9i) q^{90} -2.83412e9 q^{91} +(-2.10893e9 - 2.10893e9i) q^{92} +(-2.30922e9 + 2.30922e9i) q^{93} -2.39146e10i q^{94} +(-4.22633e8 + 2.54952e9i) q^{95} +1.16251e10 q^{96} +(-6.39534e9 - 6.39534e9i) q^{97} +(1.09052e10 - 1.09052e10i) q^{98} +3.20428e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 64 q^{2} + 10676 q^{5} - 4860 q^{6} + 10604 q^{7} - 39948 q^{8}+O(q^{10}) $ 20 * q - 64 * q^2 + 10676 * q^5 - 4860 * q^6 + 10604 * q^7 - 39948 * q^8	\( 20 q - 64 q^{2} + 10676 q^{5} - 4860 q^{6} + 10604 q^{7} - 39948 q^{8} + 153704 q^{10} + 32080 q^{11} - 620136 q^{12} - 69352 q^{13} + 662904 q^{15} - 3111700 q^{16} + 347360 q^{17} - 1259712 q^{18} + 24132564 q^{20} + 1448280 q^{21} - 27255980 q^{22} - 30995704 q^{23} + 36824936 q^{25} + 80977840 q^{26} - 104897636 q^{28} - 6436584 q^{30} - 8846480 q^{31} - 81249676 q^{32} + 86048244 q^{33} + 91578920 q^{35} + 177540660 q^{36} - 27635896 q^{37} + 44187744 q^{38} - 887009352 q^{40} + 149264920 q^{41} + 442105452 q^{42} + 675552392 q^{43} - 183996684 q^{45} - 1916100680 q^{46} - 257112832 q^{47} + 1182772368 q^{48} + 909704384 q^{50} - 711183240 q^{51} + 1397512520 q^{52} - 152646064 q^{53} - 1181518004 q^{55} + 1735516800 q^{56} + 342507528 q^{57} - 1947576252 q^{58} - 1084331124 q^{60} + 2582791000 q^{61} - 969372632 q^{62} + 208718532 q^{63} + 7250334488 q^{65} - 1968290280 q^{66} - 6731030200 q^{67} - 12869460704 q^{68} + 7421027700 q^{70} + 7511442640 q^{71} + 786296484 q^{72} + 1660222316 q^{73} + 72454824 q^{75} + 9998646360 q^{76} - 13264676792 q^{77} - 5574993480 q^{78} - 15692039116 q^{80} - 7748409780 q^{81} + 27089146528 q^{82} + 30753878864 q^{83} - 2653017808 q^{85} - 46532117120 q^{86} + 3048661476 q^{87} + 5813201532 q^{88} + 8161910244 q^{90} + 14175275920 q^{91} + 30045377384 q^{92} - 6062778072 q^{93} - 58265269776 q^{95} - 18513718020 q^{96} - 32149992820 q^{97} + 54432471592 q^{98}+O(q^{100}) \) 20 * q - 64 * q^2 + 10676 * q^5 - 4860 * q^6 + 10604 * q^7 - 39948 * q^8 + 153704 * q^10 + 32080 * q^11 - 620136 * q^12 - 69352 * q^13 + 662904 * q^15 - 3111700 * q^16 + 347360 * q^17 - 1259712 * q^18 + 24132564 * q^20 + 1448280 * q^21 - 27255980 * q^22 - 30995704 * q^23 + 36824936 * q^25 + 80977840 * q^26 - 104897636 * q^28 - 6436584 * q^30 - 8846480 * q^31 - 81249676 * q^32 + 86048244 * q^33 + 91578920 * q^35 + 177540660 * q^36 - 27635896 * q^37 + 44187744 * q^38 - 887009352 * q^40 + 149264920 * q^41 + 442105452 * q^42 + 675552392 * q^43 - 183996684 * q^45 - 1916100680 * q^46 - 257112832 * q^47 + 1182772368 * q^48 + 909704384 * q^50 - 711183240 * q^51 + 1397512520 * q^52 - 152646064 * q^53 - 1181518004 * q^55 + 1735516800 * q^56 + 342507528 * q^57 - 1947576252 * q^58 - 1084331124 * q^60 + 2582791000 * q^61 - 969372632 * q^62 + 208718532 * q^63 + 7250334488 * q^65 - 1968290280 * q^66 - 6731030200 * q^67 - 12869460704 * q^68 + 7421027700 * q^70 + 7511442640 * q^71 + 786296484 * q^72 + 1660222316 * q^73 + 72454824 * q^75 + 9998646360 * q^76 - 13264676792 * q^77 - 5574993480 * q^78 - 15692039116 * q^80 - 7748409780 * q^81 + 27089146528 * q^82 + 30753878864 * q^83 - 2653017808 * q^85 - 46532117120 * q^86 + 3048661476 * q^87 + 5813201532 * q^88 + 8161910244 * q^90 + 14175275920 * q^91 + 30045377384 * q^92 - 6062778072 * q^93 - 58265269776 * q^95 - 18513718020 * q^96 - 32149992820 * q^97 + 54432471592 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	42.4637	+	42.4637i	1.32699	+	1.32699i	0.907983	+	0.419006i	$0.137622\pi$
$2$	42.4637	+	42.4637i	1.32699	+	1.32699i	0.419006	+	0.907983i	$0.362378\pi$
$3$	−99.2043	+	99.2043i	−0.408248	+	0.408248i
$3$	−99.2043	+	99.2043i	−0.408248	+	0.408248i
$4$			2582.33i			2.52180i
$5$	3082.93	+	511.056i	0.986537	+	0.163538i
$5$	3082.93	+	511.056i	0.986537	+	0.163538i
$6$	−8425.16			−1.08348
$7$	−3582.02	−	3582.02i	−0.213127	−	0.213127i	0.592468	−	0.805594i	$-0.298154\pi$
$7$	−3582.02	−	3582.02i	−0.213127	−	0.213127i	−0.805594	+	0.592468i	$0.798154\pi$
$8$	−66172.3	+	66172.3i	−2.01942	+	2.01942i
$9$		−	19683.0i		−	0.333333i
$10$	109211.	+	152614.i	1.09211	+	1.52614i
$11$	−162794.			−1.01083			−0.505413	−	0.862878i	$-0.668660\pi$
$11$	−162794.			−1.01083			−0.505413	+	0.862878i	$0.668660\pi$
$12$	−256178.	−	256178.i	−1.02952	−	1.02952i
$13$	395604.	−	395604.i	1.06548	−	1.06548i	0.0677762	−	0.997701i	$-0.478410\pi$
$13$	395604.	−	395604.i	1.06548	−	1.06548i	0.997701	−	0.0677762i	$-0.0215904\pi$
$14$		−	304211.i		−	0.565634i
$15$	−356539.	+	255141.i	−0.469516	+	0.335988i
$16$	−2.97553e6			−2.83769
$17$	1.74668e6	+	1.74668e6i	1.23018	+	1.23018i	0.963893	+	0.266289i	$0.0857977\pi$
$17$	1.74668e6	+	1.74668e6i	1.23018	+	1.23018i	0.266289	+	0.963893i	$0.414202\pi$
$18$	835812.	−	835812.i	0.442330	−	0.442330i
$19$			826980.i			0.333985i	0.985958	+	0.166993i	$0.0534056\pi$
$19$			826980.i			0.333985i	−0.985958	+	0.166993i	$0.946594\pi$
$20$	−1.31971e6	+	7.96113e6i	−0.412410	+	2.48785i
$21$	710704.			0.174017
$22$	−6.91285e6	−	6.91285e6i	−1.34135	−	1.34135i
$23$	−816679.	+	816679.i	−0.126885	+	0.126885i	−0.767698	−	0.640812i	$-0.778598\pi$
$23$	−816679.	+	816679.i	−0.126885	+	0.126885i	0.640812	+	0.767698i	$0.278598\pi$
$24$		−	1.31292e7i		−	1.64885i
$25$	9.24327e6	+	3.15110e6i	0.946511	+	0.322672i
$26$	3.35976e7			2.82775
$27$	1.95264e6	+	1.95264e6i	0.136083	+	0.136083i
$28$	9.24994e6	−	9.24994e6i	0.537463	−	0.537463i
$29$		−	4.13627e6i		−	0.201660i	−0.994904	−	0.100830i	$-0.967850\pi$
$29$		−	4.13627e6i		−	0.201660i	0.994904	−	0.100830i	$-0.0321497\pi$
$30$	−2.59742e7	−	4.30573e6i	−1.06890	−	0.177190i
$31$	2.32774e7			0.813065			0.406533	−	0.913636i	$-0.366738\pi$
$31$	2.32774e7			0.813065			0.406533	+	0.913636i	$0.366738\pi$
$32$	−5.85916e7	−	5.85916e7i	−1.74617	−	1.74617i
$33$	1.61499e7	−	1.61499e7i	0.412668	−	0.412668i
$34$			1.48341e8i			3.26488i
$35$	−9.21249e6	−	1.28737e7i	−0.175403	−	0.245112i
$36$	5.08279e7			0.840601
$37$	−3.90169e7	−	3.90169e7i	−0.562657	−	0.562657i	0.367404	−	0.930061i	$-0.380247\pi$
$37$	−3.90169e7	−	3.90169e7i	−0.562657	−	0.562657i	−0.930061	+	0.367404i	$0.880247\pi$
$38$	−3.51166e7	+	3.51166e7i	−0.443195	+	0.443195i
$39$			7.84913e7i			0.869958i
$40$	−2.37822e8	+	1.70187e8i	−2.32248	+	1.66198i
$41$	1.24880e8			1.07789			0.538943	−	0.842342i	$-0.318824\pi$
$41$	1.24880e8			1.07789			0.538943	+	0.842342i	$0.318824\pi$
$42$	3.01791e7	+	3.01791e7i	0.230919	+	0.230919i
$43$	−2.03844e6	+	2.03844e6i	−0.0138661	+	0.0138661i	−0.714006	−	0.700140i	$-0.753121\pi$
$43$	−2.03844e6	+	2.03844e6i	−0.0138661	+	0.0138661i	0.700140	+	0.714006i	$0.253121\pi$
$44$		−	4.20388e8i		−	2.54910i
$45$	1.00591e7	−	6.06813e7i	0.0545126	−	0.328846i
$46$	−6.93583e7			−0.336752
$47$	−2.81589e8	−	2.81589e8i	−1.22779	−	1.22779i	−0.964796	−	0.262998i	$-0.915289\pi$
$47$	−2.81589e8	−	2.81589e8i	−1.22779	−	1.22779i	−0.262998	−	0.964796i	$-0.584711\pi$
$48$	2.95186e8	−	2.95186e8i	1.15848	−	1.15848i
$49$		−	2.56814e8i		−	0.909154i
$50$	2.58696e8	+	5.26310e8i	0.827827	+	1.68419i
$51$	−3.46557e8			−1.00444
$52$	1.02158e9	+	1.02158e9i	2.68692	+	2.68692i
$53$	−1.42946e8	+	1.42946e8i	−0.341817	+	0.341817i	−0.857050	−	0.515233i	$-0.827705\pi$
$53$	−1.42946e8	+	1.42946e8i	−0.341817	+	0.341817i	0.515233	+	0.857050i	$0.327705\pi$
$54$			1.65832e8i			0.361161i
$55$	−5.01883e8	−	8.31970e7i	−0.997216	−	0.165308i
$56$	4.74061e8			0.860783
$57$	−8.20400e7	−	8.20400e7i	−0.136349	−	0.136349i
$58$	1.75641e8	−	1.75641e8i	0.267600	−	0.267600i
$59$		−	2.82797e8i		−	0.395562i	−0.980246	−	0.197781i	$-0.936627\pi$
$59$		−	2.82797e8i		−	0.395562i	0.980246	−	0.197781i	$-0.0633735\pi$
$60$	−6.58857e8	−	9.20700e8i	−0.847296	−	1.18403i
$61$	−7.06822e8			−0.836875			−0.418438	−	0.908246i	$-0.637422\pi$
$61$	−7.06822e8			−0.836875			−0.418438	+	0.908246i	$0.637422\pi$
$62$	9.88442e8	+	9.88442e8i	1.07893	+	1.07893i
$63$	−7.05049e7	+	7.05049e7i	−0.0710422	+	0.0710422i
$64$		−	1.92909e9i		−	1.79660i
$65$	1.42179e9	−	1.01744e9i	1.22538	−	0.876886i
$66$	1.37157e9			1.09521
$67$	−7.04107e8	−	7.04107e8i	−0.521512	−	0.521512i	0.396516	−	0.918028i	$-0.370219\pi$
$67$	−7.04107e8	−	7.04107e8i	−0.521512	−	0.521512i	−0.918028	+	0.396516i	$0.870219\pi$
$68$	−4.51051e9	+	4.51051e9i	−3.10228	+	3.10228i
$69$		−	1.62036e8i		−	0.103602i
$70$	1.55469e8	−	9.37862e8i	0.0925025	−	0.558018i
$71$	2.19034e9			1.21400			0.607001	−	0.794701i	$-0.292372\pi$
$71$	2.19034e9			1.21400			0.607001	+	0.794701i	$0.292372\pi$
$72$	1.30247e9	+	1.30247e9i	0.673139	+	0.673139i
$73$	−2.52807e8	+	2.52807e8i	−0.121948	+	0.121948i	−0.765447	−	0.643499i	$-0.777482\pi$
$73$	−2.52807e8	+	2.52807e8i	−0.121948	+	0.121948i	0.643499	+	0.765447i	$0.277482\pi$
$74$		−	3.31360e9i		−	1.49328i
$75$	−1.22957e9	+	6.04370e8i	−0.518142	+	0.254681i
$76$	−2.13553e9			−0.842245
$77$	5.83133e8	+	5.83133e8i	0.215434	+	0.215434i
$78$	−3.33303e9	+	3.33303e9i	−1.15443	+	1.15443i
$79$			1.09973e7i			0.00357395i	0.999998	+	0.00178698i	$0.000568813\pi$
$79$			1.09973e7i			0.00357395i	−0.999998	+	0.00178698i	$0.999431\pi$
$80$	−9.17335e9	−	1.52066e9i	−2.79949	−	0.464070i
$81$	−3.87420e8			−0.111111
$82$	5.30286e9	+	5.30286e9i	1.43034	+	1.43034i
$83$	4.24856e9	−	4.24856e9i	1.07858	−	1.07858i	0.0819402	−	0.996637i	$-0.473888\pi$
$83$	4.24856e9	−	4.24856e9i	1.07858	−	1.07858i	0.996637	−	0.0819402i	$-0.0261117\pi$
$84$			1.83527e9i			0.438837i
$85$	4.49225e9	+	6.27755e9i	1.01244	+	1.41480i
$86$	−1.73119e8			−0.0368004
$87$	4.10336e8	+	4.10336e8i	0.0823272	+	0.0823272i
$88$	1.07725e10	−	1.07725e10i	2.04128	−	2.04128i
$89$			1.52482e9i			0.273066i	0.990635	+	0.136533i	$0.0435961\pi$
$89$			1.52482e9i			0.273066i	−0.990635	+	0.136533i	$0.956404\pi$
$90$	3.00390e9	−	2.14960e9i	0.508713	−	0.364037i
$91$	−2.83412e9			−0.454163
$92$	−2.10893e9	−	2.10893e9i	−0.319980	−	0.319980i
$93$	−2.30922e9	+	2.30922e9i	−0.331932	+	0.331932i
$94$		−	2.39146e10i		−	3.25854i
$95$	−4.22633e8	+	2.54952e9i	−0.0546192	+	0.329489i
$96$	1.16251e10			1.42574
$97$	−6.39534e9	−	6.39534e9i	−0.744741	−	0.744741i	0.228746	−	0.973486i	$-0.426538\pi$
$97$	−6.39534e9	−	6.39534e9i	−0.744741	−	0.744741i	−0.973486	+	0.228746i	$0.926538\pi$
$98$	1.09052e10	−	1.09052e10i	1.20644	−	1.20644i
$99$			3.20428e9i			0.336942i
$100$	−8.13716e9	+	2.38691e10i	−0.813716	+	2.38691i
$101$	1.11881e10			1.06451			0.532254	−	0.846585i	$-0.321345\pi$
$101$	1.11881e10			1.06451			0.532254	+	0.846585i	$0.321345\pi$
$102$	−1.47161e10	−	1.47161e10i	−1.33288	−	1.33288i
$103$	−1.28328e10	+	1.28328e10i	−1.10697	+	1.10697i	−0.113423	+	0.993547i	$0.536182\pi$
$103$	−1.28328e10	+	1.28328e10i	−1.10697	+	1.10697i	−0.993547	+	0.113423i	$0.963818\pi$
$104$			5.23560e10i			4.30328i
$105$	2.19105e9	+	3.63209e8i	0.171674	+	0.0284584i
$106$	−1.21400e10			−0.907175
$107$	1.73115e8	+	1.73115e8i	0.0123429	+	0.0123429i	0.713251	−	0.700908i	$-0.247222\pi$
$107$	1.73115e8	+	1.73115e8i	0.0123429	+	0.0123429i	−0.700908	+	0.713251i	$0.747222\pi$
$108$	−5.04235e9	+	5.04235e9i	−0.343174	+	0.343174i
$109$		−	8.88457e9i		−	0.577436i	−0.957414	−	0.288718i	$-0.906771\pi$
$109$		−	8.88457e9i		−	0.577436i	0.957414	−	0.288718i	$-0.0932290\pi$
$110$	−1.77790e10	−	2.48447e10i	−1.10393	−	1.54266i
$111$	7.74129e9			0.459408
$112$	1.06584e10	+	1.06584e10i	0.604787	+	0.604787i
$113$	−8.92054e9	+	8.92054e9i	−0.484171	+	0.484171i	−0.906461	−	0.422290i	$-0.861227\pi$
$113$	−8.92054e9	+	8.92054e9i	−0.484171	+	0.484171i	0.422290	+	0.906461i	$0.361227\pi$
$114$		−	6.96744e9i		−	0.361867i
$115$	−2.93513e9	+	2.10039e9i	−0.145928	+	0.104427i
$116$	1.06812e10			0.508546
$117$	−7.78667e9	−	7.78667e9i	−0.355159	−	0.355159i
$118$	1.20086e10	−	1.20086e10i	0.524907	−	0.524907i
$119$		−	1.25133e10i		−	0.524369i
$120$	6.70973e9	−	4.04762e10i	0.269649	−	1.62665i
$121$	5.64587e8			0.0217673
$122$	−3.00142e10	−	3.00142e10i	−1.11052	−	1.11052i
$123$	−1.23886e10	+	1.23886e10i	−0.440045	+	0.440045i
$124$			6.01098e10i			2.05039i
$125$	2.68859e10	+	1.44384e10i	0.880999	+	0.473119i
$126$	−5.98779e9			−0.188545
$127$	−1.01089e10	−	1.01089e10i	−0.305976	−	0.305976i	0.537371	−	0.843346i	$-0.319418\pi$
$127$	−1.01089e10	−	1.01089e10i	−0.305976	−	0.305976i	−0.843346	+	0.537371i	$0.819418\pi$
$128$	2.19183e10	−	2.19183e10i	0.637905	−	0.637905i
$129$		−	4.04443e8i		−	0.0113216i
$130$	1.03579e11	+	1.71703e10i	2.78968	+	0.462445i
$131$	1.37772e10			0.357112			0.178556	−	0.983930i	$-0.442858\pi$
$131$	1.37772e10			0.357112			0.178556	+	0.983930i	$0.442858\pi$
$132$	4.17043e10	+	4.17043e10i	1.04067	+	1.04067i
$133$	2.96226e9	−	2.96226e9i	0.0711811	−	0.0711811i
$134$		−	5.97979e10i		−	1.38408i
$135$	5.02194e9	+	7.01775e9i	0.111996	+	0.156505i
$136$	−2.31164e11			−4.96850
$137$	−3.17751e9	−	3.17751e9i	−0.0658392	−	0.0658392i	0.673420	−	0.739260i	$-0.264824\pi$
$137$	−3.17751e9	−	3.17751e9i	−0.0658392	−	0.0658392i	−0.739260	+	0.673420i	$0.764824\pi$
$138$	6.88065e9	−	6.88065e9i	0.137478	−	0.137478i
$139$		−	2.48093e10i		−	0.478124i	−0.971004	−	0.239062i	$-0.923160\pi$
$139$		−	2.48093e10i		−	0.478124i	0.971004	−	0.239062i	$-0.0768399\pi$
$140$	3.32441e10	−	2.37897e10i	0.618123	−	0.442332i
$141$	5.58696e10			1.00249
$142$	9.30098e10	+	9.30098e10i	1.61097	+	1.61097i
$143$	−6.44021e10	+	6.44021e10i	−1.07701	+	1.07701i
$144$			5.85674e10i			0.945896i
$145$	2.11386e9	−	1.27518e10i	0.0329790	−	0.198945i
$146$	−2.14702e10			−0.323647
$147$	2.54770e10	+	2.54770e10i	0.371161	+	0.371161i
$148$	1.00754e11	−	1.00754e11i	1.41891	−	1.41891i
$149$		−	2.31010e10i		−	0.314557i	−0.987554	−	0.157279i	$-0.949728\pi$
$149$		−	2.31010e10i		−	0.314557i	0.987554	−	0.157279i	$-0.0502721\pi$
$150$	−7.78760e10	−	2.65485e10i	−1.02553	−	0.349610i
$151$	3.72889e10			0.475002			0.237501	−	0.971387i	$-0.423672\pi$
$151$	3.72889e10			0.475002			0.237501	+	0.971387i	$0.423672\pi$
$152$	−5.47231e10	−	5.47231e10i	−0.674455	−	0.674455i
$153$	3.43800e10	−	3.43800e10i	0.410061	−	0.410061i
$154$			4.95239e10i			0.571757i
$155$	7.17624e10	+	1.18960e10i	0.802119	+	0.132967i
$156$	−2.02690e11			−2.19386
$157$	−3.69366e10	−	3.69366e10i	−0.387221	−	0.387221i	0.486474	−	0.873695i	$-0.338283\pi$
$157$	−3.69366e10	−	3.69366e10i	−0.387221	−	0.387221i	−0.873695	+	0.486474i	$0.838283\pi$
$158$	−4.66984e8	+	4.66984e8i	−0.00474260	+	0.00474260i
$159$		−	2.83618e10i		−	0.279092i
$160$	−1.50690e11	−	2.10577e11i	−1.43709	−	2.00822i
$161$	5.85072e9			0.0540853
$162$	−1.64513e10	−	1.64513e10i	−0.147443	−	0.147443i
$163$	−1.04146e11	+	1.04146e11i	−0.905115	+	0.905115i	−0.995873	−	0.0907582i	$-0.971071\pi$
$163$	−1.04146e11	+	1.04146e11i	−0.905115	+	0.905115i	0.0907582	+	0.995873i	$0.471071\pi$
$164$			3.22480e11i			2.71822i
$165$	5.80425e10	−	4.15355e10i	0.474599	−	0.339625i
$166$	3.60819e11			2.86252
$167$	−1.37250e11	−	1.37250e11i	−1.05664	−	1.05664i	−0.998296	−	0.0583477i	$-0.981417\pi$
$167$	−1.37250e11	−	1.37250e11i	−1.05664	−	1.05664i	−0.0583477	−	0.998296i	$-0.518583\pi$
$168$	−4.70289e10	+	4.70289e10i	−0.351413	+	0.351413i
$169$		−	1.75147e11i		−	1.27048i
$170$	−7.58106e10	+	4.57325e11i	−0.533932	+	3.22092i
$171$	1.62774e10			0.111328
$172$	−5.26391e9	−	5.26391e9i	−0.0349676	−	0.0349676i
$173$	−1.32740e11	+	1.32740e11i	−0.856586	+	0.856586i	−0.990934	−	0.134348i	$-0.957106\pi$
$173$	−1.32740e11	+	1.32740e11i	−0.856586	+	0.856586i	0.134348	+	0.990934i	$0.457106\pi$
$174$			3.48487e10i			0.218495i
$175$	−2.18223e10	−	4.43969e10i	−0.132957	−	0.270497i
$176$	4.84400e11			2.86841
$177$	2.80547e10	+	2.80547e10i	0.161487	+	0.161487i
$178$	−6.47494e10	+	6.47494e10i	−0.362356	+	0.362356i
$179$		−	9.44539e9i		−	0.0513990i	−0.999670	−	0.0256995i	$-0.991819\pi$
$179$		−	9.44539e9i		−	0.0513990i	0.999670	−	0.0256995i	$-0.00818131\pi$
$180$	1.56699e11	+	2.59759e10i	0.829284	+	0.137470i
$181$	−8.03812e10			−0.413773			−0.206886	−	0.978365i	$-0.566333\pi$
$181$	−8.03812e10			−0.413773			−0.206886	+	0.978365i	$0.566333\pi$
$182$	−1.20347e11	−	1.20347e11i	−0.602669	−	0.602669i
$183$	7.01198e10	−	7.01198e10i	0.341653	−	0.341653i
$184$		−	1.08083e11i		−	0.512470i
$185$	−1.00346e11	−	1.40226e11i	−0.463066	−	0.647098i
$186$	−1.96116e11			−0.880942
$187$	−2.84350e11	−	2.84350e11i	−1.24350	−	1.24350i
$188$	7.27154e11	−	7.27154e11i	3.09626	−	3.09626i
$189$		−	1.39888e10i		−	0.0580057i
$190$	−1.26209e11	+	9.03154e10i	−0.509707	+	0.364749i
$191$	−1.94198e11			−0.763972			−0.381986	−	0.924168i	$-0.624760\pi$
$191$	−1.94198e11			−0.763972			−0.381986	+	0.924168i	$0.624760\pi$
$192$	1.91374e11	+	1.91374e11i	0.733460	+	0.733460i
$193$	1.37567e11	−	1.37567e11i	0.513722	−	0.513722i	−0.401943	−	0.915665i	$-0.631665\pi$
$193$	1.37567e11	−	1.37567e11i	0.513722	−	0.513722i	0.915665	+	0.401943i	$0.131665\pi$
$194$		−	5.43139e11i		−	1.97653i
$195$	−4.01134e10	+	2.41983e11i	−0.142271	+	0.858246i
$196$	6.63176e11			2.29271
$197$	3.88115e11	+	3.88115e11i	1.30807	+	1.30807i	0.922810	+	0.385256i	$0.125887\pi$
$197$	3.88115e11	+	3.88115e11i	1.30807	+	1.30807i	0.385256	+	0.922810i	$0.374113\pi$
$198$	−1.36066e11	+	1.36066e11i	−0.447118	+	0.447118i
$199$			4.42640e11i			1.41835i	0.705030	+	0.709177i	$0.250933\pi$
$199$			4.42640e11i			1.41835i	−0.705030	+	0.709177i	$0.749067\pi$
$200$	−8.20163e11	+	4.03133e11i	−2.56301	+	1.25979i
$201$	1.39701e11			0.425813
$202$	4.75087e11	+	4.75087e11i	1.41259	+	1.41259i
$203$	−1.48162e10	+	1.48162e10i	−0.0429790	+	0.0429790i
$204$		−	8.94924e11i		−	2.53300i
$205$	3.84995e11	+	6.38206e10i	1.06337	+	0.176275i
$206$	−1.08986e12			−2.93788
$207$	1.60747e10	+	1.60747e10i	0.0422952	+	0.0422952i
$208$	−1.17713e12	+	1.17713e12i	−3.02349	+	3.02349i
$209$		−	1.34628e11i		−	0.337600i
$210$	7.76167e10	+	1.08463e11i	0.190046	+	0.265574i
$211$	−1.63373e11			−0.390633			−0.195317	−	0.980740i	$-0.562573\pi$
$211$	−1.63373e11			−0.390633			−0.195317	+	0.980740i	$0.562573\pi$
$212$	−3.69134e11	−	3.69134e11i	−0.861995	−	0.861995i
$213$	−2.17291e11	+	2.17291e11i	−0.495614	+	0.495614i
$214$			1.47022e10i			0.0327578i
$215$	−7.32610e9	+	5.24260e9i	−0.0159471	+	0.0114118i
$216$	−2.58421e11			−0.549616
$217$	−8.33799e10	−	8.33799e10i	−0.173286	−	0.173286i
$218$	3.77272e11	−	3.77272e11i	0.766252	−	0.766252i
$219$		−	5.01591e10i		−	0.0995701i
$220$	2.14842e11	−	1.29603e12i	0.416875	−	2.51478i
$221$	1.38199e12			2.62146
$222$	3.28723e11	+	3.28723e11i	0.609629	+	0.609629i
$223$	−5.72278e11	+	5.72278e11i	−1.03773	+	1.03773i	−0.0384669	+	0.999260i	$0.512247\pi$
$223$	−5.72278e11	+	5.72278e11i	−1.03773	+	1.03773i	−0.999260	+	0.0384669i	$0.987753\pi$
$224$			4.19753e11i			0.744309i
$225$	6.20231e10	−	1.81935e11i	0.107557	−	0.315504i
$226$	−7.57598e11			−1.28498
$227$	3.51000e11	+	3.51000e11i	0.582341	+	0.582341i	0.935546	−	0.353205i	$-0.114908\pi$
$227$	3.51000e11	+	3.51000e11i	0.582341	+	0.582341i	−0.353205	+	0.935546i	$0.614908\pi$
$228$	2.11854e11	−	2.11854e11i	0.343845	−	0.343845i
$229$			5.00223e11i			0.794303i	0.917753	+	0.397151i	$0.130001\pi$
$229$			5.00223e11i			0.794303i	−0.917753	+	0.397151i	$0.869999\pi$
$230$	−2.13827e11	−	3.54460e10i	−0.332218	−	0.0550716i
$231$	−1.15699e11			−0.175901
$232$	2.73706e11	+	2.73706e11i	0.407235	+	0.407235i
$233$	5.92603e11	−	5.92603e11i	0.862947	−	0.862947i	−0.128733	−	0.991679i	$-0.541091\pi$
$233$	5.92603e11	−	5.92603e11i	0.862947	−	0.862947i	0.991679	+	0.128733i	$0.0410909\pi$
$234$		−	6.61302e11i		−	0.942584i
$235$	−7.24210e11	−	1.01202e12i	−1.01047	−	1.41206i
$236$	7.30274e11			0.997529
$237$	−1.09098e9	−	1.09098e9i	−0.00145906	−	0.00145906i
$238$	5.31361e11	−	5.31361e11i	0.695833	−	0.695833i
$239$			1.49610e12i			1.91854i	0.282495	+	0.959269i	$0.408838\pi$
$239$			1.49610e12i			1.91854i	−0.282495	+	0.959269i	$0.591162\pi$
$240$	1.06089e12	−	7.59180e11i	1.33234	−	0.953429i
$241$	8.30603e11			1.02166			0.510832	−	0.859681i	$-0.329337\pi$
$241$	8.30603e11			1.02166			0.510832	+	0.859681i	$0.329337\pi$
$242$	2.39744e10	+	2.39744e10i	0.0288849	+	0.0288849i
$243$	3.84338e10	−	3.84338e10i	0.0453609	−	0.0453609i
$244$		−	1.82524e12i		−	2.11043i
$245$	1.31246e11	−	7.91738e11i	0.148681	−	0.896914i
$246$	−1.05213e12			−1.16787
$247$	3.27157e11	+	3.27157e11i	0.355853	+	0.355853i
$248$	−1.54032e12	+	1.54032e12i	−1.64192	+	1.64192i
$249$			8.42951e11i			0.880655i
$250$	5.28567e11	+	1.75479e12i	0.541253	+	1.79690i
$251$	−1.06167e12			−1.06566			−0.532830	−	0.846222i	$-0.678872\pi$
$251$	−1.06167e12			−1.06566			−0.532830	+	0.846222i	$0.678872\pi$
$252$	−1.82067e11	−	1.82067e11i	−0.179154	−	0.179154i
$253$	1.32951e11	−	1.32951e11i	0.128259	−	0.128259i
$254$		−	8.58525e11i		−	0.812053i
$255$	−1.06841e12	−	1.77110e11i	−0.990917	−	0.164264i
$256$	−1.13925e11			−0.103615
$257$	−3.90930e11	−	3.90930e11i	−0.348685	−	0.348685i	0.510934	−	0.859620i	$-0.329300\pi$
$257$	−3.90930e11	−	3.90930e11i	−0.348685	−	0.348685i	−0.859620	+	0.510934i	$0.829300\pi$
$258$	1.71741e10	−	1.71741e10i	0.0150237	−	0.0150237i
$259$			2.79518e11i			0.239834i
$260$	2.62737e12	+	3.67154e12i	2.21134	+	3.09016i
$261$	−8.14142e10			−0.0672198
$262$	5.85030e11	+	5.85030e11i	0.473883	+	0.473883i
$263$	1.85780e11	−	1.85780e11i	0.147645	−	0.147645i	−0.629420	−	0.777065i	$-0.716707\pi$
$263$	1.85780e11	−	1.85780e11i	0.147645	−	0.147645i	0.777065	+	0.629420i	$0.216707\pi$
$264$			2.13735e12i			1.66670i
$265$	−5.13747e11	+	3.67640e11i	−0.393115	+	0.281315i
$266$	2.51577e11			0.188913
$267$	−1.51269e11	−	1.51269e11i	−0.111479	−	0.111479i
$268$	1.81823e12	−	1.81823e12i	1.31515	−	1.31515i
$269$		−	2.37850e12i		−	1.68866i	−0.535822	−	0.844331i	$-0.679998\pi$
$269$		−	2.37850e12i		−	1.68866i	0.535822	−	0.844331i	$-0.320002\pi$
$270$	−8.47497e10	+	5.11249e11i	−0.0590635	+	0.356299i
$271$	−6.60998e11			−0.452224			−0.226112	−	0.974101i	$-0.572602\pi$
$271$	−6.60998e11			−0.452224			−0.226112	+	0.974101i	$0.572602\pi$
$272$	−5.19731e12	−	5.19731e12i	−3.49088	−	3.49088i
$273$	2.81157e11	−	2.81157e11i	0.185411	−	0.185411i
$274$		−	2.69858e11i		−	0.174736i
$275$	−1.50475e12	−	5.12981e11i	−0.956757	−	0.326165i
$276$	4.18430e11			0.261263
$277$	−1.42192e12	−	1.42192e12i	−0.871919	−	0.871919i	0.120762	−	0.992681i	$-0.461466\pi$
$277$	−1.42192e12	−	1.42192e12i	−0.871919	−	0.871919i	−0.992681	+	0.120762i	$0.961466\pi$
$278$	1.05349e12	−	1.05349e12i	0.634465	−	0.634465i
$279$		−	4.58168e11i		−	0.271022i
$280$	1.46149e12	+	2.42272e11i	0.849194	+	0.140771i
$281$	8.03190e11			0.458444			0.229222	−	0.973374i	$-0.426382\pi$
$281$	8.03190e11			0.458444			0.229222	+	0.973374i	$0.426382\pi$
$282$	2.37243e12	+	2.37243e12i	1.33029	+	1.33029i
$283$	1.66776e12	−	1.66776e12i	0.918757	−	0.918757i	−0.0781823	−	0.996939i	$-0.524912\pi$
$283$	1.66776e12	−	1.66776e12i	0.918757	−	0.918757i	0.996939	+	0.0781823i	$0.0249116\pi$
$284$			5.65617e12i			3.06148i
$285$	−2.10996e11	−	2.94850e11i	−0.112215	−	0.156811i
$286$	−5.46950e12			−2.85836
$287$	−4.47322e11	−	4.47322e11i	−0.229726	−	0.229726i
$288$	−1.15326e12	+	1.15326e12i	−0.582056	+	0.582056i
$289$			4.08581e12i			2.02670i
$290$	6.31252e11	−	4.51727e11i	0.307760	−	0.220235i
$291$	1.26889e12			0.608078
$292$	−6.52830e11	−	6.52830e11i	−0.307529	−	0.307529i
$293$	−1.29386e12	+	1.29386e12i	−0.599167	+	0.599167i	−0.940091	−	0.340924i	$-0.889260\pi$
$293$	−1.29386e12	+	1.29386e12i	−0.599167	+	0.599167i	0.340924	+	0.940091i	$0.389260\pi$
$294$			2.16370e12i			0.985053i
$295$	1.44525e11	−	8.71842e11i	0.0646894	−	0.390236i
$296$	5.16367e12			2.27248
$297$	−3.17879e11	−	3.17879e11i	−0.137556	−	0.137556i
$298$	9.80954e11	−	9.80954e11i	0.417414	−	0.417414i
$299$			6.46163e11i			0.270387i
$300$	−1.56068e12	−	3.17516e12i	−0.642255	−	1.30665i
$301$	1.46034e10			0.00591047
$302$	1.58342e12	+	1.58342e12i	0.630322	+	0.630322i
$303$	−1.10991e12	+	1.10991e12i	−0.434583	+	0.434583i
$304$		−	2.46071e12i		−	0.947746i
$305$	−2.17908e12	−	3.61225e11i	−0.825608	−	0.136861i
$306$	2.91980e12			1.08829
$307$	1.83926e12	+	1.83926e12i	0.674452	+	0.674452i	0.958739	−	0.284287i	$-0.0917569\pi$
$307$	1.83926e12	+	1.83926e12i	0.674452	+	0.674452i	−0.284287	+	0.958739i	$0.591757\pi$
$308$	−1.50584e12	+	1.50584e12i	−0.543281	+	0.543281i
$309$		−	2.54614e12i		−	0.903837i
$310$	2.54215e12	+	3.55245e12i	0.887958	+	1.24085i
$311$	2.60157e12			0.894197			0.447099	−	0.894485i	$-0.352457\pi$
$311$	2.60157e12			0.894197			0.447099	+	0.894485i	$0.352457\pi$
$312$	−5.19395e12	−	5.19395e12i	−1.75681	−	1.75681i
$313$	3.33218e12	−	3.33218e12i	1.10919	−	1.10919i	0.115935	−	0.993257i	$-0.463014\pi$
$313$	3.33218e12	−	3.33218e12i	1.10919	−	1.10919i	0.993257	−	0.115935i	$-0.0369864\pi$
$314$		−	3.13693e12i		−	1.02768i
$315$	−2.53393e11	+	1.81330e11i	−0.0817039	+	0.0584677i
$316$	−2.83985e10			−0.00901281
$317$	1.73834e12	+	1.73834e12i	0.543049	+	0.543049i	0.924421	−	0.381372i	$-0.124548\pi$
$317$	1.73834e12	+	1.73834e12i	0.543049	+	0.543049i	−0.381372	+	0.924421i	$0.624548\pi$
$318$	1.20435e12	−	1.20435e12i	0.370353	−	0.370353i
$319$			6.73361e11i			0.203843i
$320$	9.85871e11	−	5.94723e12i	0.293812	−	1.77241i
$321$	−3.43476e10			−0.0100779
$322$	2.48443e11	+	2.48443e11i	0.0717707	+	0.0717707i
$323$	−1.44447e12	+	1.44447e12i	−0.410863	+	0.410863i
$324$		−	1.00045e12i		−	0.280200i
$325$	4.90326e12	−	2.41009e12i	1.35229	−	0.664685i
$326$	−8.84482e12			−2.40216
$327$	8.81388e11	+	8.81388e11i	0.235737	+	0.235737i
$328$	−8.26358e12	+	8.26358e12i	−2.17670	+	2.17670i
$329$			2.01731e12i			0.523351i
$330$	4.22845e12	+	7.00948e11i	1.08047	+	0.179109i
$331$	8.29809e11			0.208852			0.104426	−	0.994533i	$-0.466699\pi$
$331$	8.29809e11			0.208852			0.104426	+	0.994533i	$0.466699\pi$
$332$	1.09712e13	+	1.09712e13i	2.71996	+	2.71996i
$333$	−7.67969e11	+	7.67969e11i	−0.187552	+	0.187552i
$334$		−	1.16562e13i		−	2.80431i
$335$	−1.81087e12	−	2.53055e12i	−0.429204	−	0.599778i
$336$	−2.11472e12			−0.493807
$337$	−2.64990e11	−	2.64990e11i	−0.0609649	−	0.0609649i	0.675967	−	0.736932i	$-0.263726\pi$
$337$	−2.64990e11	−	2.64990e11i	−0.0609649	−	0.0609649i	−0.736932	+	0.675967i	$0.763726\pi$
$338$	7.43737e12	−	7.43737e12i	1.68592	−	1.68592i
$339$		−	1.76991e12i		−	0.395324i
$340$	−1.62107e13	+	1.16004e13i	−3.56785	+	2.55317i
$341$	−3.78942e12			−0.821867
$342$	6.91200e11	+	6.91200e11i	0.147732	+	0.147732i
$343$	−1.93174e12	+	1.93174e12i	−0.406892	+	0.406892i
$344$		−	2.69776e11i		−	0.0560029i
$345$	8.28095e10	−	4.99546e11i	0.0169428	−	0.102207i
$346$	−1.12732e13			−2.27336
$347$	−3.53051e12	−	3.53051e12i	−0.701762	−	0.701762i	0.263026	−	0.964789i	$-0.415279\pi$
$347$	−3.53051e12	−	3.53051e12i	−0.701762	−	0.701762i	−0.964789	+	0.263026i	$0.915279\pi$
$348$	−1.05962e12	+	1.05962e12i	−0.207613	+	0.207613i
$349$			2.47275e12i			0.477588i	0.971070	+	0.238794i	$0.0767521\pi$
$349$			2.47275e12i			0.477588i	−0.971070	+	0.238794i	$0.923248\pi$
$350$	9.58600e11	−	2.81191e12i	0.182514	−	0.535378i
$351$	1.54494e12			0.289986
$352$	9.53839e12	+	9.53839e12i	1.76507	+	1.76507i
$353$	−3.61840e12	+	3.61840e12i	−0.660151	+	0.660151i	−0.955416	−	0.295265i	$-0.904592\pi$
$353$	−3.61840e12	+	3.61840e12i	−0.660151	+	0.660151i	0.295265	+	0.955416i	$0.404592\pi$
$354$			2.38261e12i			0.428584i
$355$	6.75266e12	+	1.11939e12i	1.19766	+	0.198535i
$356$	−3.93758e12			−0.688620
$357$	1.24137e12	+	1.24137e12i	0.214073	+	0.214073i
$358$	4.01086e11	−	4.01086e11i	0.0682059	−	0.0682059i
$359$			5.63993e12i			0.945805i	0.881115	+	0.472903i	$0.156794\pi$
$359$			5.63993e12i			0.945805i	−0.881115	+	0.472903i	$0.843206\pi$
$360$	3.34978e12	+	4.68105e12i	0.553993	+	0.774161i
$361$	5.44717e12			0.888454
$362$	−3.41328e12	−	3.41328e12i	−0.549072	−	0.549072i
$363$	−5.60095e10	+	5.60095e10i	−0.00888645	+	0.00888645i
$364$		−	7.31863e12i		−	1.14531i
$365$	−9.08584e11	+	6.50187e11i	−0.140249	+	0.100363i
$366$	5.95509e12			0.906740
$367$	−3.20007e12	−	3.20007e12i	−0.480651	−	0.480651i	0.424689	−	0.905339i	$-0.360384\pi$
$367$	−3.20007e12	−	3.20007e12i	−0.480651	−	0.480651i	−0.905339	+	0.424689i	$0.860384\pi$
$368$	2.43005e12	−	2.43005e12i	0.360062	−	0.360062i
$369$		−	2.45801e12i		−	0.359295i
$370$	1.69343e12	−	1.02156e13i	0.244208	−	1.47318i
$371$	1.02407e12			0.145701
$372$	−5.96315e12	−	5.96315e12i	−0.837068	−	0.837068i
$373$	−9.71574e12	+	9.71574e12i	−1.34565	+	1.34565i	−0.455322	+	0.890327i	$0.650476\pi$
$373$	−9.71574e12	+	9.71574e12i	−1.34565	+	1.34565i	−0.890327	+	0.455322i	$0.849524\pi$
$374$		−	2.41491e13i		−	3.30022i
$375$	−4.09956e12	+	1.23485e12i	−0.552816	+	0.166516i
$376$	3.72667e13			4.95886
$377$	−1.63632e12	−	1.63632e12i	−0.214864	−	0.214864i
$378$	5.94015e11	−	5.94015e11i	0.0769730	−	0.0769730i
$379$			2.32857e12i			0.297778i	0.988854	+	0.148889i	$0.0475697\pi$
$379$			2.32857e12i			0.297778i	−0.988854	+	0.148889i	$0.952430\pi$
$380$	−6.58369e12	−	1.09138e12i	−0.830905	−	0.137739i
$381$	2.00570e12			0.249828
$382$	−8.24635e12	−	8.24635e12i	−1.01378	−	1.01378i
$383$	−4.79797e11	+	4.79797e11i	−0.0582188	+	0.0582188i	−0.735617	−	0.677398i	$-0.763108\pi$
$383$	−4.79797e11	+	4.79797e11i	−0.0582188	+	0.0582188i	0.677398	+	0.735617i	$0.263108\pi$
$384$			4.34877e12i			0.520847i
$385$	1.49974e12	+	2.09577e12i	0.177302	+	0.247765i
$386$	1.16832e13			1.36341
$387$	4.01225e10	+	4.01225e10i	0.00462204	+	0.00462204i
$388$	1.65149e13	−	1.65149e13i	1.87809	−	1.87809i
$389$		−	9.01075e12i		−	1.01161i	−0.862648	−	0.505805i	$-0.831196\pi$
$389$		−	9.01075e12i		−	1.01161i	0.862648	−	0.505805i	$-0.168804\pi$
$390$	−1.19788e13	+	8.57212e12i	−1.32768	+	0.950091i
$391$	−2.85296e12			−0.312185
$392$	1.69939e13	+	1.69939e13i	1.83596	+	1.83596i
$393$	−1.36676e12	+	1.36676e12i	−0.145790	+	0.145790i
$394$			3.29616e13i			3.47158i
$395$	−5.62021e9	+	3.39037e10i	−0.000584477	+	0.00352584i
$396$	−8.27450e12			−0.849701
$397$	−7.97878e12	−	7.97878e12i	−0.809066	−	0.809066i	0.175427	−	0.984492i	$-0.443869\pi$
$397$	−7.97878e12	−	7.97878e12i	−0.809066	−	0.809066i	−0.984492	+	0.175427i	$0.943869\pi$
$398$	−1.87961e13	+	1.87961e13i	−1.88214	+	1.88214i
$399$			5.87738e11i			0.0581191i
$400$	−2.75036e13	−	9.37620e12i	−2.68590	−	0.915644i
$401$	7.03227e12			0.678225			0.339112	−	0.940746i	$-0.389873\pi$
$401$	7.03227e12			0.678225			0.339112	+	0.940746i	$0.389873\pi$
$402$	5.93221e12	+	5.93221e12i	0.565050	+	0.565050i
$403$	9.20862e12	−	9.20862e12i	0.866302	−	0.866302i
$404$			2.88913e13i			2.68448i
$405$	−1.19439e12	−	1.97994e11i	−0.109615	−	0.0181709i
$406$	−1.25830e12			−0.114065
$407$	6.35173e12	+	6.35173e12i	0.568748	+	0.568748i
$408$	2.29325e13	−	2.29325e13i	2.02838	−	2.02838i
$409$			1.01262e13i			0.884773i	0.896825	+	0.442386i	$0.145868\pi$
$409$			1.01262e13i			0.884773i	−0.896825	+	0.442386i	$0.854132\pi$
$410$	1.36383e13	+	1.90584e13i	1.17717	+	1.64500i
$411$	6.30446e11			0.0537575
$412$	−3.31385e13	−	3.31385e13i	−2.79156	−	2.79156i
$413$	−1.01298e12	+	1.01298e12i	−0.0843048	+	0.0843048i
$414$			1.36518e12i			0.112251i
$415$	1.52693e13	−	1.09268e13i	1.24044	−	0.887668i
$416$	−4.63582e13			−3.72100
$417$	2.46119e12	+	2.46119e12i	0.195193	+	0.195193i
$418$	5.71679e12	−	5.71679e12i	0.447992	−	0.447992i
$419$		−	2.20744e13i		−	1.70930i	−0.519202	−	0.854651i	$-0.673771\pi$
$419$		−	2.20744e13i		−	1.70930i	0.519202	−	0.854651i	$-0.326229\pi$
$420$	−9.37925e11	+	5.65800e12i	−0.0717665	+	0.432929i
$421$	−9.25428e12			−0.699733			−0.349866	−	0.936800i	$-0.613773\pi$
$421$	−9.25428e12			−0.699733			−0.349866	+	0.936800i	$0.613773\pi$
$422$	−6.93743e12	−	6.93743e12i	−0.518366	−	0.518366i
$423$	−5.54251e12	+	5.54251e12i	−0.409265	+	0.409265i
$424$		−	1.89182e13i		−	1.38054i
$425$	1.06411e13	+	2.16490e13i	0.767435	+	1.56133i
$426$	−1.84540e13			−1.31535
$427$	2.53185e12	+	2.53185e12i	0.178360	+	0.178360i
$428$	−4.47041e11	+	4.47041e11i	−0.0311263	+	0.0311263i
$429$		−	1.27779e13i		−	0.879375i
$430$	−5.33713e11	−	8.84734e10i	−0.0363049	−	0.00601826i
$431$	2.61070e13			1.75538			0.877689	−	0.479230i	$-0.159084\pi$
$431$	2.61070e13			1.75538			0.877689	+	0.479230i	$0.159084\pi$
$432$	−5.81014e12	−	5.81014e12i	−0.386161	−	0.386161i
$433$	−1.76337e13	+	1.76337e13i	−1.15852	+	1.15852i	−0.173725	+	0.984794i	$0.555580\pi$
$433$	−1.76337e13	+	1.76337e13i	−1.15852	+	1.15852i	−0.984794	+	0.173725i	$0.944420\pi$
$434$		−	7.08124e12i		−	0.459897i
$435$	1.05533e12	+	1.47474e12i	0.0677552	+	0.0946824i
$436$	2.29429e13			1.45618
$437$	−6.75377e11	−	6.75377e11i	−0.0423779	−	0.0423779i
$438$	2.12994e12	−	2.12994e12i	0.132128	−	0.132128i
$439$		−	2.42529e12i		−	0.148744i	−0.997231	−	0.0743722i	$-0.976305\pi$
$439$		−	2.42529e12i		−	0.148744i	0.997231	−	0.0743722i	$-0.0236953\pi$
$440$	3.87161e13	−	2.77054e13i	2.34762	−	1.67997i
$441$	−5.05486e12			−0.303051
$442$	5.86844e13	+	5.86844e13i	3.47865	+	3.47865i
$443$	1.45079e13	−	1.45079e13i	0.850326	−	0.850326i	−0.139847	−	0.990173i	$-0.544661\pi$
$443$	1.45079e13	−	1.45079e13i	0.850326	−	0.850326i	0.990173	+	0.139847i	$0.0446610\pi$
$444$			1.99905e13i			1.15854i
$445$	−7.79268e11	+	4.70091e12i	−0.0446567	+	0.269390i
$446$	−4.86021e13			−2.75411
$447$	2.29172e12	+	2.29172e12i	0.128417	+	0.128417i
$448$	−6.91002e12	+	6.91002e12i	−0.382904	+	0.382904i
$449$		−	1.37462e13i		−	0.753269i	−0.926362	−	0.376634i	$-0.877081\pi$
$449$		−	1.37462e13i		−	0.753269i	0.926362	−	0.376634i	$-0.122919\pi$
$450$	1.03594e13	−	5.09191e12i	0.561398	−	0.275942i
$451$	−2.03297e13			−1.08955
$452$	−2.30358e13	−	2.30358e13i	−1.22098	−	1.22098i
$453$	−3.69922e12	+	3.69922e12i	−0.193919	+	0.193919i
$454$			2.98095e13i			1.54552i
$455$	−8.73740e12	−	1.44840e12i	−0.448048	−	0.0742728i
$456$	1.08575e13			0.550690
$457$	−2.74057e13	−	2.74057e13i	−1.37486	−	1.37486i	−0.853077	−	0.521786i	$-0.825266\pi$
$457$	−2.74057e13	−	2.74057e13i	−1.37486	−	1.37486i	−0.521786	−	0.853077i	$-0.674734\pi$
$458$	−2.12413e13	+	2.12413e13i	−1.05403	+	1.05403i
$459$			6.82128e12i			0.334813i
$460$	−5.42390e12	−	7.57946e12i	−0.263343	−	0.368001i
$461$	−1.29927e13			−0.624016			−0.312008	−	0.950080i	$-0.601002\pi$
$461$	−1.29927e13			−0.624016			−0.312008	+	0.950080i	$0.601002\pi$
$462$	−4.91298e12	−	4.91298e12i	−0.233419	−	0.233419i
$463$	1.68924e13	−	1.68924e13i	0.793938	−	0.793938i	−0.188194	−	0.982132i	$-0.560263\pi$
$463$	1.68924e13	−	1.68924e13i	0.793938	−	0.793938i	0.982132	+	0.188194i	$0.0602634\pi$
$464$			1.23076e13i			0.572247i
$465$	−8.29928e12	+	5.93901e12i	−0.381747	+	0.273180i
$466$	5.03282e13			2.29024
$467$	1.82599e13	+	1.82599e13i	0.822078	+	0.822078i	0.986406	−	0.164327i	$-0.0525454\pi$
$467$	1.82599e13	+	1.82599e13i	0.822078	+	0.822078i	−0.164327	+	0.986406i	$0.552545\pi$
$468$	2.01077e13	−	2.01077e13i	0.895641	−	0.895641i
$469$			5.04425e12i			0.222296i
$470$	1.22217e13	−	7.37269e13i	0.532895	−	3.21467i
$471$	7.32854e12			0.316164
$472$	1.87133e13	+	1.87133e13i	0.798805	+	0.798805i
$473$	3.31846e11	−	3.31846e11i	0.0140162	−	0.0140162i
$474$		−	9.26536e10i		−	0.00387232i
$475$	−2.60589e12	+	7.64400e12i	−0.107768	+	0.316120i
$476$	3.23134e13			1.32236
$477$	2.81361e12	+	2.81361e12i	0.113939	+	0.113939i
$478$	−6.35298e13	+	6.35298e13i	−2.54588	+	2.54588i
$479$		−	2.46898e12i		−	0.0979129i	−0.998801	−	0.0489564i	$-0.984410\pi$
$479$		−	2.46898e12i		−	0.0979129i	0.998801	−	0.0489564i	$-0.0155895\pi$
$480$	3.58393e13	+	5.94107e12i	1.40654	+	0.233162i
$481$	−3.08705e13			−1.19900
$482$	3.52704e13	+	3.52704e13i	1.35574	+	1.35574i
$483$	−5.80416e11	+	5.80416e11i	−0.0220803	+	0.0220803i
$484$			1.45795e12i			0.0548928i
$485$	−1.64480e13	−	2.29848e13i	−0.612921	−	0.856507i
$486$	3.26408e12			0.120387
$487$	−2.99466e13	−	2.99466e13i	−1.09321	−	1.09321i	−0.995184	−	0.0980243i	$-0.968748\pi$
$487$	−2.99466e13	−	2.99466e13i	−1.09321	−	1.09321i	−0.0980243	−	0.995184i	$-0.531252\pi$
$488$	4.67720e13	−	4.67720e13i	1.69000	−	1.69000i
$489$		−	2.06634e13i		−	0.739023i
$490$	3.91933e13	−	2.80469e13i	1.38749	−	0.992898i
$491$	−9.96879e12			−0.349329			−0.174665	−	0.984628i	$-0.555884\pi$
$491$	−9.96879e12			−0.349329			−0.174665	+	0.984628i	$0.555884\pi$
$492$	−3.19915e13	−	3.19915e13i	−1.10971	−	1.10971i
$493$	7.22475e12	−	7.22475e12i	0.248078	−	0.248078i
$494$			2.77845e13i			0.944427i
$495$	−1.63757e12	+	9.87857e12i	−0.0551027	+	0.332405i
$496$	−6.92626e13			−2.30723
$497$	−7.84583e12	−	7.84583e12i	−0.258736	−	0.258736i
$498$	−3.57948e13	+	3.57948e13i	−1.16862	+	1.16862i
$499$			1.50953e12i			0.0487909i	0.999702	+	0.0243954i	$0.00776608\pi$
$499$			1.50953e12i			0.0487909i	−0.999702	+	0.0243954i	$0.992234\pi$
$500$	−3.72848e13	+	6.94283e13i	−1.19311	+	2.22171i
$501$	2.72315e13			0.862746
$502$	−4.50822e13	−	4.50822e13i	−1.41412	−	1.41412i
$503$	−7.23559e12	+	7.23559e12i	−0.224716	+	0.224716i	−0.810481	−	0.585765i	$-0.800794\pi$
$503$	−7.23559e12	+	7.23559e12i	−0.224716	+	0.224716i	0.585765	+	0.810481i	$0.300794\pi$
$504$		−	9.33094e12i		−	0.286928i
$505$	3.44920e13	+	5.71773e12i	1.05018	+	0.174087i
$506$	1.12911e13			0.340397
$507$	1.73753e13	+	1.73753e13i	0.518672	+	0.518672i
$508$	2.61046e13	−	2.61046e13i	0.771610	−	0.771610i
$509$			3.39585e13i			0.993940i	0.867768	+	0.496970i	$0.165554\pi$
$509$			3.39585e13i			0.993940i	−0.867768	+	0.496970i	$0.834446\pi$
$510$	−3.78479e13	−	5.28894e13i	−1.09696	−	1.53291i
$511$	1.81112e12			0.0519807
$512$	−2.72820e13	−	2.72820e13i	−0.775401	−	0.775401i
$513$	−1.61479e12	+	1.61479e12i	−0.0454496	+	0.0454496i
$514$		−	3.32007e13i		−	0.925404i
$515$	−4.61209e13	+	3.30044e13i	−1.27310	+	0.911036i
$516$	1.04440e12			0.0285509
$517$	4.58410e13	+	4.58410e13i	1.24109	+	1.24109i
$518$	−1.18694e13	+	1.18694e13i	−0.318258	+	0.318258i
$519$		−	2.63368e13i		−	0.699400i
$520$	−2.67569e13	+	1.61410e14i	−0.703750	+	4.24535i
$521$	−1.65322e13			−0.430668			−0.215334	−	0.976540i	$-0.569084\pi$
$521$	−1.65322e13			−0.430668			−0.215334	+	0.976540i	$0.569084\pi$
$522$	−3.45714e12	−	3.45714e12i	−0.0892000	−	0.0892000i
$523$	3.99932e13	−	3.99932e13i	1.02206	−	1.02206i	0.0223111	−	0.999751i	$-0.492898\pi$
$523$	3.99932e13	−	3.99932e13i	1.02206	−	1.02206i	0.999751	−	0.0223111i	$-0.00710243\pi$
$524$			3.55772e13i			0.900565i
$525$	6.56922e12	+	2.23950e12i	0.164709	+	0.0561505i
$526$	1.57778e13			0.391848
$527$	4.06582e13	+	4.06582e13i	1.00022	+	1.00022i
$528$	−4.80546e13	+	4.80546e13i	−1.17102	+	1.17102i
$529$			4.00926e13i			0.967800i
$530$	−3.74269e13	−	6.20424e12i	−0.894962	−	0.148357i
$531$	−5.56629e12			−0.131854
$532$	7.64952e12	+	7.64952e12i	0.179505	+	0.179505i
$533$	4.94030e13	−	4.94030e13i	1.14846	−	1.14846i
$534$		−	1.28468e13i		−	0.295863i
$535$	4.45231e11	+	6.22174e11i	0.0101582	+	0.0141952i
$536$	9.31847e13			2.10630
$537$	9.37023e11	+	9.37023e11i	0.0209836	+	0.0209836i
$538$	1.01000e14	−	1.01000e14i	2.24084	−	2.24084i
$539$			4.18078e13i			0.918996i
$540$	−1.81221e13	+	1.29683e13i	−0.394676	+	0.282432i
$541$	−7.39850e13			−1.59646			−0.798229	−	0.602354i	$-0.794230\pi$
$541$	−7.39850e13			−1.59646			−0.798229	+	0.602354i	$0.794230\pi$
$542$	−2.80684e13	−	2.80684e13i	−0.600097	−	0.600097i
$543$	7.97417e12	−	7.97417e12i	0.168922	−	0.168922i
$544$		−	2.04682e14i		−	4.29621i
$545$	4.54051e12	−	2.73905e13i	0.0944327	−	0.569662i
$546$	2.38779e13			0.492078
$547$	−1.09106e13	−	1.09106e13i	−0.222798	−	0.222798i	0.586878	−	0.809676i	$-0.300357\pi$
$547$	−1.09106e13	−	1.09106e13i	−0.222798	−	0.222798i	−0.809676	+	0.586878i	$0.800357\pi$
$548$	8.20538e12	−	8.20538e12i	0.166034	−	0.166034i
$549$			1.39124e13i			0.278958i
$550$	−4.21142e13	−	8.56804e13i	−0.836788	−	1.70242i
$551$	3.42061e12			0.0673513
$552$	1.07223e13	+	1.07223e13i	0.209215	+	0.209215i
$553$	3.93924e10	−	3.93924e10i	0.000761704	−	0.000761704i
$554$		−	1.20760e14i		−	2.31406i
$555$	2.38658e13	+	3.95623e12i	0.453223	+	0.0751306i
$556$	6.40657e13			1.20573
$557$	6.41787e12	+	6.41787e12i	0.119706	+	0.119706i	0.764422	−	0.644716i	$-0.223024\pi$
$557$	6.41787e12	+	6.41787e12i	0.119706	+	0.119706i	−0.644716	+	0.764422i	$0.723024\pi$
$558$	1.94555e13	−	1.94555e13i	0.359643	−	0.359643i
$559$			1.61283e12i			0.0295480i
$560$	2.74121e13	+	3.83062e13i	0.497739	+	0.695550i
$561$	5.64175e13			1.01531
$562$	3.41064e13	+	3.41064e13i	0.608351	+	0.608351i
$563$	−5.24025e13	+	5.24025e13i	−0.926425	+	0.926425i	−0.997473	−	0.0710479i	$-0.977366\pi$
$563$	−5.24025e13	+	5.24025e13i	−0.926425	+	0.926425i	0.0710479	+	0.997473i	$0.477366\pi$
$564$			1.44274e14i			2.52808i
$565$	−3.20603e13	+	2.29425e13i	−0.556833	+	0.398473i
$566$	1.41638e14			2.43836
$567$	1.38775e12	+	1.38775e12i	0.0236807	+	0.0236807i
$568$	−1.44940e14	+	1.44940e14i	−2.45158	+	2.45158i
$569$			2.89296e13i			0.485044i	0.970146	+	0.242522i	$0.0779747\pi$
$569$			2.89296e13i			0.485044i	−0.970146	+	0.242522i	$0.922025\pi$
$570$	3.56075e12	−	2.14801e13i	0.0591790	−	0.356995i
$571$	7.02567e13			1.15746			0.578731	−	0.815518i	$-0.303548\pi$
$571$	7.02567e13			1.15746			0.578731	+	0.815518i	$0.303548\pi$
$572$	−1.66307e14	−	1.66307e14i	−2.71601	−	2.71601i
$573$	1.92653e13	−	1.92653e13i	0.311890	−	0.311890i
$574$		−	3.79899e13i		−	0.609689i
$575$	−1.01222e13	+	4.97535e12i	−0.161041	+	0.0791560i
$576$	−3.79702e13			−0.598867
$577$	5.78006e13	+	5.78006e13i	0.903761	+	0.903761i	0.995759	−	0.0919986i	$-0.0293255\pi$
$577$	5.78006e13	+	5.78006e13i	0.903761	+	0.903761i	−0.0919986	+	0.995759i	$0.529326\pi$
$578$	−1.73499e14	+	1.73499e14i	−2.68941	+	2.68941i
$579$			2.72945e13i			0.419452i
$580$	3.29294e13	+	5.45869e12i	0.501699	+	0.0831665i
$581$	−3.04368e13			−0.459747
$582$	5.38818e13	+	5.38818e13i	0.806913	+	0.806913i
$583$	2.32708e13	−	2.32708e13i	0.345517	−	0.345517i
$584$		−	3.34576e13i		−	0.492528i
$585$	−2.00263e13	−	2.79852e13i	−0.292295	−	0.408459i
$586$	−1.09884e14			−1.59018
$587$	−6.06284e12	−	6.06284e12i	−0.0869933	−	0.0869933i	0.662271	−	0.749264i	$-0.269593\pi$
$587$	−6.06284e12	−	6.06284e12i	−0.0869933	−	0.0869933i	−0.749264	+	0.662271i	$0.769593\pi$
$588$	−6.57900e13	+	6.57900e13i	−0.935994	+	0.935994i
$589$			1.92499e13i			0.271552i
$590$	4.31587e13	−	3.08846e13i	0.603682	−	0.431998i
$591$	−7.70054e13			−1.06803
$592$	1.16096e14	+	1.16096e14i	1.59665	+	1.59665i
$593$	6.73070e13	−	6.73070e13i	0.917882	−	0.917882i	−0.0789927	−	0.996875i	$-0.525170\pi$
$593$	6.73070e13	−	6.73070e13i	0.917882	−	0.917882i	0.996875	+	0.0789927i	$0.0251704\pi$
$594$		−	2.69966e13i		−	0.365070i
$595$	6.39500e12	−	3.85776e13i	0.0857542	−	0.517310i
$596$	5.96544e13			0.793252
$597$	−4.39118e13	−	4.39118e13i	−0.579041	−	0.579041i
$598$	−2.74384e13	+	2.74384e13i	−0.358801	+	0.358801i
$599$		−	7.55262e13i		−	0.979408i	−0.871889	−	0.489704i	$-0.837105\pi$
$599$		−	7.55262e13i		−	0.979408i	0.871889	−	0.489704i	$-0.162895\pi$
$600$	4.13712e13	−	1.21356e14i	0.532038	−	1.56065i
$601$	−4.98527e13			−0.635793			−0.317897	−	0.948125i	$-0.602977\pi$
$601$	−4.98527e13			−0.635793			−0.317897	+	0.948125i	$0.602977\pi$
$602$	6.20115e11	+	6.20115e11i	0.00784314	+	0.00784314i
$603$	−1.38589e13	+	1.38589e13i	−0.173837	+	0.173837i
$604$			9.62922e13i			1.19786i
$605$	1.74058e12	+	2.88536e11i	0.0214742	+	0.00355977i
$606$	−9.42613e13			−1.15337
$607$	−1.54260e13	−	1.54260e13i	−0.187202	−	0.187202i	0.607283	−	0.794485i	$-0.292259\pi$
$607$	−1.54260e13	−	1.54260e13i	−0.187202	−	0.187202i	−0.794485	+	0.607283i	$0.792259\pi$
$608$	4.84541e13	−	4.84541e13i	0.583194	−	0.583194i
$609$		−	2.93966e12i		−	0.0350922i
$610$	−7.71928e13	−	1.07871e14i	−0.913961	−	1.27719i
$611$	−2.22795e14			−2.61637
$612$	8.87803e13	+	8.87803e13i	1.03409	+	1.03409i
$613$	4.83397e13	−	4.83397e13i	0.558472	−	0.558472i	−0.370400	−	0.928872i	$-0.620779\pi$
$613$	4.83397e13	−	4.83397e13i	0.558472	−	0.558472i	0.928872	+	0.370400i	$0.120779\pi$
$614$			1.56203e14i			1.78998i
$615$	−4.45245e13	+	3.18619e13i	−0.506085	+	0.362157i
$616$	−7.71744e13			−0.870101
$617$	6.42172e13	+	6.42172e13i	0.718167	+	0.718167i	0.968230	−	0.250062i	$-0.0804512\pi$
$617$	6.42172e13	+	6.42172e13i	0.718167	+	0.718167i	−0.250062	+	0.968230i	$0.580451\pi$
$618$	1.08119e14	−	1.08119e14i	1.19938	−	1.19938i
$619$		−	1.54974e14i		−	1.70531i	−0.522471	−	0.852657i	$-0.674990\pi$
$619$		−	1.54974e14i		−	1.70531i	0.522471	−	0.852657i	$-0.325010\pi$
$620$	−3.07195e13	+	1.85314e14i	−0.335317	+	2.02279i
$621$	−3.18936e12			−0.0345339
$622$	1.10472e14	+	1.10472e14i	1.18659	+	1.18659i
$623$	5.46193e12	−	5.46193e12i	0.0581977	−	0.0581977i
$624$		−	2.33553e14i		−	2.46867i
$625$	7.55086e13	+	5.82529e13i	0.791765	+	0.610826i
$626$	2.82993e14			2.94377
$627$	1.33557e13	+	1.33557e13i	0.137825	+	0.137825i
$628$	9.53823e13	−	9.53823e13i	0.976494	−	0.976494i
$629$		−	1.36300e14i		−	1.38434i
$630$	−1.84599e13	−	3.06010e12i	−0.186006	−	0.0308342i
$631$	−9.43001e13			−0.942682			−0.471341	−	0.881951i	$-0.656230\pi$
$631$	−9.43001e13			−0.942682			−0.471341	+	0.881951i	$0.656230\pi$
$632$	−7.27713e11	−	7.27713e11i	−0.00721730	−	0.00721730i
$633$	1.62073e13	−	1.62073e13i	0.159475	−	0.159475i
$634$			1.47633e14i			1.44124i
$635$	−2.59989e13	−	3.63313e13i	−0.251818	−	0.351895i
$636$	7.32394e13			0.703816
$637$	−1.01596e14	−	1.01596e14i	−0.968683	−	0.968683i
$638$	−2.85934e13	+	2.85934e13i	−0.270497	+	0.270497i
$639$		−	4.31124e13i		−	0.404667i
$640$	7.87739e13	−	5.63710e13i	0.733639	−	0.524995i
$641$	3.08930e13			0.285476			0.142738	−	0.989761i	$-0.454409\pi$
$641$	3.08930e13			0.285476			0.142738	+	0.989761i	$0.454409\pi$
$642$	−1.45853e12	−	1.45853e12i	−0.0133733	−	0.0133733i
$643$	−1.28779e14	+	1.28779e14i	−1.17163	+	1.17163i	−0.189808	+	0.981821i	$0.560787\pi$
$643$	−1.28779e14	+	1.28779e14i	−1.17163	+	1.17163i	−0.981821	+	0.189808i	$0.939213\pi$
$644$			1.51085e13i			0.136393i
$645$	2.06693e11	−	1.24687e12i	0.00185152	−	0.0111692i
$646$	−1.22675e14			−1.09042
$647$	3.87896e13	+	3.87896e13i	0.342132	+	0.342132i	0.857168	−	0.515036i	$-0.172222\pi$
$647$	3.87896e13	+	3.87896e13i	0.342132	+	0.342132i	−0.515036	+	0.857168i	$0.672222\pi$
$648$	2.56365e13	−	2.56365e13i	0.224380	−	0.224380i
$649$			4.60377e13i			0.399844i
$650$	3.10552e14	+	1.05869e14i	2.67650	+	0.912438i
$651$	1.65433e13			0.141487
$652$	−2.68938e14	−	2.68938e14i	−2.28252	−	2.28252i
$653$	8.34857e13	−	8.34857e13i	0.703147	−	0.703147i	−0.261938	−	0.965085i	$-0.584361\pi$
$653$	8.34857e13	−	8.34857e13i	0.703147	−	0.703147i	0.965085	+	0.261938i	$0.0843615\pi$
$654$			7.48539e13i			0.625642i
$655$	4.24741e13	+	7.04091e12i	0.352304	+	0.0584013i
$656$	−3.71584e14			−3.05871
$657$	4.97600e12	+	4.97600e12i	0.0406493	+	0.0406493i
$658$	−8.56624e13	+	8.56624e13i	−0.694482	+	0.694482i
$659$			1.34428e14i			1.08159i	0.841155	+	0.540795i	$0.181876\pi$
$659$			1.34428e14i			1.08159i	−0.841155	+	0.540795i	$0.818124\pi$
$660$	1.07258e14	+	1.49885e14i	0.856468	+	1.19684i
$661$	2.17607e14			1.72451			0.862256	−	0.506473i	$-0.169051\pi$
$661$	2.17607e14			1.72451			0.862256	+	0.506473i	$0.169051\pi$
$662$	3.52367e13	+	3.52367e13i	0.277144	+	0.277144i
$663$	−1.37099e14	+	1.37099e14i	−1.07021	+	1.07021i
$664$			5.62274e14i			4.35620i
$665$	1.06463e13	−	7.61855e12i	0.0818636	−	0.0585820i
$666$	−6.52216e13			−0.497760
$667$	3.37800e12	+	3.37800e12i	0.0255877	+	0.0255877i
$668$	3.54423e14	−	3.54423e14i	2.66465	−	2.66465i
$669$		−	1.13545e14i		−	0.847300i
$670$	3.05601e13	−	1.84353e14i	0.226350	−	1.36545i
$671$	1.15067e14			0.845934
$672$	−4.16413e13	−	4.16413e13i	−0.303863	−	0.303863i
$673$	−1.01113e14	+	1.01113e14i	−0.732373	+	0.732373i	−0.971089	−	0.238716i	$-0.923273\pi$
$673$	−1.01113e14	+	1.01113e14i	−0.732373	+	0.732373i	0.238716	+	0.971089i	$0.423273\pi$
$674$		−	2.25049e13i		−	0.161800i
$675$	1.18958e13	+	2.42017e13i	0.0848936	+	0.172714i
$676$	4.52286e14			3.20390
$677$	−1.16455e14	−	1.16455e14i	−0.818869	−	0.818869i	0.167075	−	0.985944i	$-0.446568\pi$
$677$	−1.16455e14	−	1.16455e14i	−0.818869	−	0.818869i	−0.985944	+	0.167075i	$0.946568\pi$
$678$	7.51570e13	−	7.51570e13i	0.524591	−	0.524591i
$679$			4.58165e13i			0.317448i
$680$	−7.12662e14	−	1.18138e14i	−4.90161	−	0.812539i
$681$	−6.96414e13			−0.475479
$682$	−1.60913e14	−	1.60913e14i	−1.09061	−	1.09061i
$683$	8.53406e13	−	8.53406e13i	0.574185	−	0.574185i	−0.359110	−	0.933295i	$-0.616920\pi$
$683$	8.53406e13	−	8.53406e13i	0.574185	−	0.574185i	0.933295	+	0.359110i	$0.116920\pi$
$684$			4.20337e13i			0.280748i
$685$	−8.17216e12	−	1.14199e13i	−0.0541856	−	0.0757200i
$686$	−1.64058e14			−1.07988
$687$	−4.96243e13	−	4.96243e13i	−0.324273	−	0.324273i
$688$	6.06543e12	−	6.06543e12i	0.0393477	−	0.0393477i
$689$			1.13100e14i			0.728396i
$690$	2.47289e13	−	1.76961e13i	0.158110	−	0.113144i
$691$	2.92481e14			1.85655			0.928275	−	0.371894i	$-0.121291\pi$
$691$	2.92481e14			1.85655			0.928275	+	0.371894i	$0.121291\pi$
$692$	−3.42778e14	−	3.42778e14i	−2.16014	−	2.16014i
$693$	1.14778e13	−	1.14778e13i	0.0718112	−	0.0718112i
$694$		−	2.99837e14i		−	1.86246i
$695$	1.26789e13	−	7.64853e13i	0.0781914	−	0.471687i
$696$	−5.43057e13			−0.332506
$697$	2.18125e14	+	2.18125e14i	1.32600	+	1.32600i
$698$	−1.05002e14	+	1.05002e14i	−0.633755	+	0.633755i
$699$			1.17577e14i			0.704593i
$700$	1.14647e14	−	5.63522e13i	0.682139	−	0.335290i
$701$	1.51507e14			0.895043			0.447522	−	0.894273i	$-0.352307\pi$
$701$	1.51507e14			0.895043			0.447522	+	0.894273i	$0.352307\pi$
$702$	6.56040e13	+	6.56040e13i	0.384809	+	0.384809i
$703$	3.22662e13	−	3.22662e13i	0.187919	−	0.187919i
$704$			3.14044e14i			1.81605i
$705$	1.72242e14	+	2.85525e13i	0.988994	+	0.163945i
$706$	−3.07301e14			−1.75203
$707$	−4.00759e13	−	4.00759e13i	−0.226875	−	0.226875i
$708$	−7.24463e13	+	7.24463e13i	−0.407240	+	0.407240i
$709$		−	8.42190e13i		−	0.470088i	−0.971985	−	0.235044i	$-0.924477\pi$
$709$		−	8.42190e13i		−	0.470088i	0.971985	−	0.235044i	$-0.0755234\pi$
$710$	2.39209e14	+	3.34276e14i	1.32583	+	1.85273i
$711$	2.16459e11			0.00119132
$712$	−1.00901e14	−	1.00901e14i	−0.551435	−	0.551435i
$713$	−1.90101e13	+	1.90101e13i	−0.103166	+	0.103166i
$714$			1.05427e14i			0.568145i
$715$	−2.31460e14	+	1.65634e14i	−1.23864	+	0.886379i
$716$	2.43911e13			0.129618
$717$	−1.48419e14	−	1.48419e14i	−0.783240	−	0.783240i
$718$	−2.39492e14	+	2.39492e14i	−1.25507	+	1.25507i
$719$			8.19435e13i			0.426452i	0.977003	+	0.213226i	$0.0683971\pi$
$719$			8.19435e13i			0.426452i	−0.977003	+	0.213226i	$0.931603\pi$
$720$	−2.99312e13	+	1.80559e14i	−0.154690	+	0.933162i
$721$	9.19348e13			0.471850
$722$	2.31307e14	+	2.31307e14i	1.17897	+	1.17897i
$723$	−8.23994e13	+	8.23994e13i	−0.417093	+	0.417093i
$724$		−	2.07571e14i		−	1.04345i
$725$	1.30338e13	−	3.82326e13i	0.0650700	−	0.190873i
$726$	−4.75674e12			−0.0235845
$727$	−5.94817e13	−	5.94817e13i	−0.292895	−	0.292895i	0.545328	−	0.838223i	$-0.316405\pi$
$727$	−5.94817e13	−	5.94817e13i	−0.292895	−	0.292895i	−0.838223	+	0.545328i	$0.816405\pi$
$728$	1.87540e14	−	1.87540e14i	0.917144	−	0.917144i
$729$			7.62560e12i			0.0370370i
$730$	−6.61911e13	−	1.09725e13i	−0.319290	−	0.0529286i
$731$	−7.12100e12			−0.0341157
$732$	1.81072e14	+	1.81072e14i	0.861581	+	0.861581i
$733$	−1.86888e14	+	1.86888e14i	−0.883207	+	0.883207i	−0.993859	−	0.110652i	$-0.964706\pi$
$733$	−1.86888e14	+	1.86888e14i	−0.883207	+	0.883207i	0.110652	+	0.993859i	$0.464706\pi$
$734$		−	2.71774e14i		−	1.27564i
$735$	6.55236e13	+	9.15640e13i	0.305465	+	0.426863i
$736$	9.57011e13			0.443126
$737$	1.14625e14	+	1.14625e14i	0.527158	+	0.527158i
$738$	1.04376e14	−	1.04376e14i	0.476781	−	0.476781i
$739$		−	3.76355e14i		−	1.70756i	−0.520634	−	0.853780i	$-0.674304\pi$
$739$		−	3.76355e14i		−	1.70756i	0.520634	−	0.853780i	$-0.325696\pi$
$740$	3.62109e14	−	2.59127e14i	1.63185	−	1.16776i
$741$	−6.49107e13			−0.290553
$742$	4.34859e13	+	4.34859e13i	0.193343	+	0.193343i
$743$	−2.45945e14	+	2.45945e14i	−1.08616	+	1.08616i	−0.0902415	+	0.995920i	$0.528764\pi$
$743$	−2.45945e14	+	2.45945e14i	−1.08616	+	1.08616i	−0.995920	+	0.0902415i	$0.971236\pi$
$744$		−	3.05612e14i		−	1.34062i
$745$	1.18059e13	−	7.12188e13i	0.0514420	−	0.310322i
$746$	−8.25132e14			−3.57132
$747$	−8.36244e13	−	8.36244e13i	−0.359526	−	0.359526i
$748$	7.34285e14	−	7.34285e14i	3.13586	−	3.13586i
$749$		−	1.24021e12i		−	0.00526120i
$750$	−2.26518e14	−	1.21646e14i	−0.954547	−	0.512616i
$751$	1.04724e14			0.438377			0.219189	−	0.975682i	$-0.429659\pi$
$751$	1.04724e14			0.438377			0.219189	+	0.975682i	$0.429659\pi$
$752$	8.37876e14	+	8.37876e14i	3.48410	+	3.48410i
$753$	1.05322e14	−	1.05322e14i	0.435054	−	0.435054i
$754$		−	1.38969e14i		−	0.570243i
$755$	1.14959e14	+	1.90567e13i	0.468607	+	0.0776808i
$756$	3.61236e13			0.146279
$757$	−2.04593e14	−	2.04593e14i	−0.823020	−	0.823020i	0.163520	−	0.986540i	$-0.447715\pi$
$757$	−2.04593e14	−	2.04593e14i	−0.823020	−	0.823020i	−0.986540	+	0.163520i	$0.947715\pi$
$758$	−9.88795e13	+	9.88795e13i	−0.395148	+	0.395148i
$759$			2.63786e13i			0.104723i
$760$	−1.40741e14	−	1.96674e14i	−0.555076	−	0.775674i
$761$	−1.29776e14			−0.508478			−0.254239	−	0.967141i	$-0.581825\pi$
$761$	−1.29776e14			−0.508478			−0.254239	+	0.967141i	$0.581825\pi$
$762$	8.51694e13	+	8.51694e13i	0.331519	+	0.331519i
$763$	−3.18247e13	+	3.18247e13i	−0.123067	+	0.123067i
$764$		−	5.01482e14i		−	1.92659i
$765$	1.23561e14	−	8.84209e13i	0.471601	−	0.337480i
$766$	−4.07479e13			−0.154512
$767$	−1.11876e14	−	1.11876e14i	−0.421462	−	0.421462i
$768$	1.13019e13	−	1.13019e13i	0.0423005	−	0.0423005i
$769$			4.58140e14i			1.70359i	0.523871	+	0.851797i	$0.324487\pi$
$769$			4.58140e14i			1.70359i	−0.523871	+	0.851797i	$0.675513\pi$
$770$	−2.53095e13	+	1.52679e14i	−0.0935039	+	0.564059i
$771$	7.75640e13			0.284700
$772$	3.55243e14	+	3.55243e14i	1.29551	+	1.29551i
$773$	−9.06480e12	+	9.06480e12i	−0.0328443	+	0.0328443i	−0.723338	−	0.690494i	$-0.757393\pi$
$773$	−9.06480e12	+	9.06480e12i	−0.0328443	+	0.0328443i	0.690494	+	0.723338i	$0.257393\pi$
$774$			3.40750e12i			0.0122668i
$775$	2.15159e14	+	7.33493e13i	0.769575	+	0.262354i
$776$	8.46388e14			3.00788
$777$	−2.77294e13	−	2.77294e13i	−0.0979120	−	0.0979120i
$778$	3.82630e14	−	3.82630e14i	1.34240	−	1.34240i
$779$			1.03273e14i			0.359998i
$780$	−6.24879e14	−	1.03586e14i	−2.16433	−	0.358780i
$781$	−3.56575e14			−1.22714
$782$	−1.21147e14	−	1.21147e14i	−0.414266	−	0.414266i
$783$	8.07664e12	−	8.07664e12i	0.0274424	−	0.0274424i
$784$			7.64157e14i			2.57990i
$785$	−9.49962e13	−	1.32750e14i	−0.318682	−	0.445333i
$786$	−1.16075e14			−0.386924
$787$	2.13797e14	+	2.13797e14i	0.708153	+	0.708153i	0.966147	−	0.257994i	$-0.0830614\pi$
$787$	2.13797e14	+	2.13797e14i	0.708153	+	0.708153i	−0.257994	+	0.966147i	$0.583061\pi$
$788$	−1.00224e15	+	1.00224e15i	−3.29868	+	3.29868i
$789$			3.68604e13i			0.120552i
$790$	−1.67833e12	+	1.20102e12i	−0.00545434	+	0.00390315i
$791$	6.39071e13			0.206380
$792$	−2.12035e14	−	2.12035e14i	−0.680426	−	0.680426i
$793$	−2.79621e14	+	2.79621e14i	−0.891671	+	0.891671i
$794$		−	6.77616e14i		−	2.14724i
$795$	1.44945e13	−	8.74373e13i	0.0456422	−	0.275335i
$796$	−1.14304e15			−3.57681
$797$	−2.50564e14	−	2.50564e14i	−0.779159	−	0.779159i	0.200528	−	0.979688i	$-0.435734\pi$
$797$	−2.50564e14	−	2.50564e14i	−0.779159	−	0.779159i	−0.979688	+	0.200528i	$0.935734\pi$
$798$	−2.49575e13	+	2.49575e13i	−0.0771235	+	0.0771235i
$799$		−	9.83692e14i		−	3.02082i
$800$	−3.56950e14	−	7.26206e14i	−1.08933	−	2.21621i
$801$	3.00130e13			0.0910222
$802$	2.98616e14	+	2.98616e14i	0.899997	+	0.899997i
$803$	4.11555e13	−	4.11555e13i	0.123268	−	0.123268i
$804$			3.60753e14i			1.07382i
$805$	1.80373e13	+	2.99004e12i	0.0533572	+	0.00884500i
$806$	7.82064e14			2.29915
$807$	2.35958e14	+	2.35958e14i	0.689393	+	0.689393i
$808$	−7.40340e14	+	7.40340e14i	−2.14968	+	2.14968i
$809$			5.72086e14i			1.65089i	0.564482	+	0.825446i	$0.309076\pi$
$809$			5.72086e14i			1.65089i	−0.564482	+	0.825446i	$0.690924\pi$
$810$	−4.23106e13	−	5.91257e13i	−0.121346	−	0.169571i
$811$	6.54228e14			1.86477			0.932384	−	0.361469i	$-0.117725\pi$
$811$	6.54228e14			1.86477			0.932384	+	0.361469i	$0.117725\pi$
$812$	−3.82602e13	−	3.82602e13i	−0.108385	−	0.108385i
$813$	6.55739e13	−	6.55739e13i	0.184620	−	0.184620i
$814$			5.39435e14i			1.50945i
$815$	−3.74298e14	+	2.67850e14i	−1.04095	+	0.744909i
$816$	1.03119e15			2.85029
$817$	−1.68575e12	−	1.68575e12i	−0.00463107	−	0.00463107i
$818$	−4.29997e14	+	4.29997e14i	−1.17408	+	1.17408i
$819$			5.57840e13i			0.151388i
$820$	−1.64806e14	+	9.94184e14i	−0.444532	+	2.68162i
$821$	−4.04180e14			−1.08357			−0.541787	−	0.840516i	$-0.682252\pi$
$821$	−4.04180e14			−1.08357			−0.541787	+	0.840516i	$0.682252\pi$
$822$	2.67711e13	+	2.67711e13i	0.0713357	+	0.0713357i
$823$	2.79663e13	−	2.79663e13i	0.0740688	−	0.0740688i	−0.669102	−	0.743171i	$-0.733321\pi$
$823$	2.79663e13	−	2.79663e13i	0.0740688	−	0.0740688i	0.743171	+	0.669102i	$0.233321\pi$
$824$		−	1.69835e15i		−	4.47087i
$825$	2.00168e14	−	9.83880e13i	0.523751	−	0.257438i
$826$	−8.60300e13			−0.223743
$827$	−6.20961e13	−	6.20961e13i	−0.160523	−	0.160523i	0.622276	−	0.782798i	$-0.286208\pi$
$827$	−6.20961e13	−	6.20961e13i	−0.160523	−	0.160523i	−0.782798	+	0.622276i	$0.786208\pi$
$828$	−4.15101e13	+	4.15101e13i	−0.106660	+	0.106660i
$829$			1.86840e14i			0.477196i	0.971118	+	0.238598i	$0.0766879\pi$
$829$			1.86840e14i			0.477196i	−0.971118	+	0.238598i	$0.923312\pi$
$830$	1.11238e15	+	1.84399e14i	2.82398	+	0.468131i
$831$	2.82121e14			0.711919
$832$	−7.63154e14	−	7.63154e14i	−1.91424	−	1.91424i
$833$	4.48572e14	−	4.48572e14i	1.11843	−	1.11843i
$834$			2.09022e14i			0.518039i
$835$	−3.52988e14	−	4.93273e14i	−0.869617	−	1.21522i
$836$	3.47653e14			0.851362
$837$	4.54523e13	+	4.54523e13i	0.110644	+	0.110644i
$838$	9.37360e14	−	9.37360e14i	2.26823	−	2.26823i
$839$			4.27733e14i			1.02888i	0.857528	+	0.514438i	$0.171999\pi$
$839$			4.27733e14i			1.02888i	−0.857528	+	0.514438i	$0.828001\pi$
$840$	−1.69021e14	+	1.20952e14i	−0.404152	+	0.289213i
$841$	4.03599e14			0.959333
$842$	−3.92971e14	−	3.92971e14i	−0.928538	−	0.928538i
$843$	−7.96799e13	+	7.96799e13i	−0.187159	+	0.187159i
$844$		−	4.21883e14i		−	0.985100i
$845$	8.95097e13	−	5.39965e14i	0.207772	−	1.25338i
$846$	−4.70710e14			−1.08618
$847$	−2.02236e12	−	2.02236e12i	−0.00463918	−	0.00463918i
$848$	4.25341e14	−	4.25341e14i	0.969970	−	0.969970i
$849$			3.30897e14i			0.750162i
$850$	−4.67438e14	+	1.37116e15i	−1.05349	+	3.09024i
$851$	6.37285e13			0.142786
$852$	−5.61117e14	−	5.61117e14i	−1.24984	−	1.24984i
$853$	3.06134e14	−	3.06134e14i	0.677900	−	0.677900i	−0.281624	−	0.959525i	$-0.590873\pi$
$853$	3.06134e14	−	3.06134e14i	0.677900	−	0.677900i	0.959525	+	0.281624i	$0.0908732\pi$
$854$			2.15023e14i			0.473365i
$855$	5.01822e13	+	8.31869e12i	0.109830	+	0.0182064i
$856$	−2.29109e13			−0.0498509
$857$	1.14204e14	+	1.14204e14i	0.247046	+	0.247046i	0.819757	−	0.572711i	$-0.194108\pi$
$857$	1.14204e14	+	1.14204e14i	0.247046	+	0.247046i	−0.572711	+	0.819757i	$0.694108\pi$
$858$	5.42598e14	−	5.42598e14i	1.16692	−	1.16692i
$859$		−	4.58961e14i		−	0.981319i	−0.871351	−	0.490660i	$-0.836756\pi$
$859$		−	4.58961e14i		−	0.981319i	0.871351	−	0.490660i	$-0.163244\pi$
$860$	−1.35381e13	−	1.89184e13i	−0.0287783	−	0.0402154i
$861$	8.87525e13			0.187571
$862$	1.10860e15	+	1.10860e15i	2.32937	+	2.32937i
$863$	7.27259e13	−	7.27259e13i	0.151927	−	0.151927i	−0.627051	−	0.778978i	$-0.715738\pi$
$863$	7.27259e13	−	7.27259e13i	0.151927	−	0.151927i	0.778978	+	0.627051i	$0.215738\pi$
$864$		−	2.28817e14i		−	0.475246i
$865$	−4.77065e14	+	3.41390e14i	−0.985138	+	0.704970i
$866$	−1.49758e15			−3.07469
$867$	−4.05330e14	−	4.05330e14i	−0.827396	−	0.827396i
$868$	2.15314e14	−	2.15314e14i	0.436993	−	0.436993i
$869$		−	1.79029e12i		−	0.00361264i
$870$	−1.78097e13	+	1.07436e14i	−0.0357321	+	0.215553i
$871$	−5.57095e14			−1.11132
$872$	5.87912e14	+	5.87912e14i	1.16608	+	1.16608i
$873$	−1.25879e14	+	1.25879e14i	−0.248247	+	0.248247i
$874$		−	5.73580e13i		−	0.112470i
$875$	−4.45872e13	−	1.48025e14i	−0.0869301	−	0.288598i
$876$	1.29527e14			0.251096
$877$	−1.33051e14	−	1.33051e14i	−0.256461	−	0.256461i	0.567152	−	0.823613i	$-0.308045\pi$
$877$	−1.33051e14	−	1.33051e14i	−0.256461	−	0.256461i	−0.823613	+	0.567152i	$0.808045\pi$
$878$	1.02987e14	−	1.02987e14i	0.197382	−	0.197382i
$879$		−	2.56712e14i		−	0.489218i
$880$	1.49337e15	+	2.47556e14i	2.82979	+	0.469093i
$881$	−8.12081e13			−0.153010			−0.0765050	−	0.997069i	$-0.524376\pi$
$881$	−8.12081e13			−0.153010			−0.0765050	+	0.997069i	$0.524376\pi$
$882$	−2.14648e14	−	2.14648e14i	−0.402146	−	0.402146i
$883$	−2.35225e14	+	2.35225e14i	−0.438207	+	0.438207i	−0.891408	−	0.453201i	$-0.850282\pi$
$883$	−2.35225e14	+	2.35225e14i	−0.438207	+	0.438207i	0.453201	+	0.891408i	$0.350282\pi$
$884$			3.56875e15i			6.61081i
$885$	7.21530e13	+	1.00828e14i	0.132904	+	0.185723i
$886$	1.23212e15			2.25675
$887$	6.53317e14	+	6.53317e14i	1.18989	+	1.18989i	0.977098	+	0.212788i	$0.0682545\pi$
$887$	6.53317e14	+	6.53317e14i	1.18989	+	1.18989i	0.212788	+	0.977098i	$0.431745\pi$
$888$	−5.12259e14	+	5.12259e14i	−0.927736	+	0.927736i
$889$			7.24208e13i			0.130423i
$890$	−2.32708e14	+	1.66527e14i	−0.416737	+	0.298219i
$891$	6.30699e13			0.112314
$892$	−1.47781e15	−	1.47781e15i	−2.61694	−	2.61694i
$893$	2.32868e14	−	2.32868e14i	0.410065	−	0.410065i
$894$			1.94630e14i			0.340817i
$895$	4.82712e12	−	2.91195e13i	0.00840569	−	0.0507070i
$896$	−1.57023e14			−0.271909
$897$	−6.41021e13	−	6.41021e13i	−0.110385	−	0.110385i
$898$	5.83713e14	−	5.83713e14i	0.999580	−	0.999580i
$899$		−	9.62814e13i		−	0.163962i
$900$	4.69816e14	+	1.60164e14i	0.795638	+	0.271239i
$901$	−4.99364e14			−0.840994
$902$	−8.63275e14	−	8.63275e14i	−1.44583	−	1.44583i
$903$	−1.44872e12	+	1.44872e12i	−0.00241294	+	0.00241294i
$904$		−	1.18059e15i		−	1.95549i
$905$	−2.47810e14	−	4.10793e13i	−0.408202	−	0.0676675i
$906$	−3.14165e14			−0.514656
$907$	1.34413e14	+	1.34413e14i	0.218981	+	0.218981i	0.808069	−	0.589088i	$-0.200513\pi$
$907$	1.34413e14	+	1.34413e14i	0.218981	+	0.218981i	−0.589088	+	0.808069i	$0.700513\pi$
$908$	−9.06396e14	+	9.06396e14i	−1.46855	+	1.46855i
$909$		−	2.20215e14i		−	0.354836i
$910$	−3.09518e14	−	4.32526e14i	−0.495996	−	0.693115i
$911$	4.38601e14			0.699001			0.349501	−	0.936936i	$-0.386351\pi$
$911$	4.38601e14			0.699001			0.349501	+	0.936936i	$0.386351\pi$
$912$	2.44113e14	+	2.44113e14i	0.386916	+	0.386916i
$913$	−6.91642e14	+	6.91642e14i	−1.09025	+	1.09025i
$914$		−	2.32749e15i		−	3.64886i
$915$	2.52009e14	−	1.80339e14i	0.392926	−	0.281180i
$916$	−1.29174e15			−2.00308
$917$	−4.93501e13	−	4.93501e13i	−0.0761100	−	0.0761100i
$918$	−2.89657e14	+	2.89657e14i	−0.444294	+	0.444294i
$919$			5.64641e13i			0.0861381i	0.999072	+	0.0430690i	$0.0137135\pi$
$919$			5.64641e13i			0.0861381i	−0.999072	+	0.0430690i	$0.986286\pi$
$920$	5.52364e13	−	3.33212e14i	0.0838082	−	0.505570i
$921$	−3.64925e14			−0.550688
$922$	−5.51719e14	−	5.51719e14i	−0.828062	−	0.828062i
$923$	8.66507e14	−	8.66507e14i	1.29349	−	1.29349i
$924$		−	2.98771e14i		−	0.443587i
$925$	−2.37697e14	−	4.83589e14i	−0.351007	−	0.714115i
$926$	1.43463e15			2.10709
$927$	2.52588e14	+	2.52588e14i	0.368990	+	0.368990i
$928$	−2.42351e14	+	2.42351e14i	−0.352131	+	0.352131i
$929$			1.17784e15i			1.70219i	0.525014	+	0.851094i	$0.324060\pi$
$929$			1.17784e15i			1.70219i	−0.525014	+	0.851094i	$0.675940\pi$
$930$	−6.04610e14	−	1.00226e14i	−0.869082	−	0.144067i
$931$	2.12380e14			0.303644
$932$	1.53029e15	+	1.53029e15i	2.17618	+	2.17618i
$933$	−2.58087e14	+	2.58087e14i	−0.365054	+	0.365054i
$934$			1.55076e15i			2.18178i
$935$	−7.31312e14	−	1.02195e15i	−1.02340	−	1.43012i
$936$	1.03052e15			1.43443
$937$	−4.99559e14	−	4.99559e14i	−0.691654	−	0.691654i	0.270942	−	0.962596i	$-0.412665\pi$
$937$	−4.99559e14	−	4.99559e14i	−0.691654	−	0.691654i	−0.962596	+	0.270942i	$0.912665\pi$
$938$	−2.14197e14	+	2.14197e14i	−0.294985	+	0.294985i
$939$			6.61133e14i			0.905651i
$940$	2.61338e15	−	1.87015e15i	3.56093	−	2.54822i
$941$	−6.50267e14			−0.881340			−0.440670	−	0.897669i	$-0.645259\pi$
$941$	−6.50267e14			−0.881340			−0.440670	+	0.897669i	$0.645259\pi$
$942$	3.11197e14	+	3.11197e14i	0.419547	+	0.419547i
$943$	−1.01987e14	+	1.01987e14i	−0.136768	+	0.136768i
$944$			8.41471e14i			1.12248i
$945$	7.14905e12	−	4.31264e13i	0.00948613	−	0.0572248i
$946$	2.81828e13			0.0371987
$947$	6.06122e14	+	6.06122e14i	0.795811	+	0.795811i	0.982432	−	0.186621i	$-0.0597535\pi$
$947$	6.06122e14	+	6.06122e14i	0.795811	+	0.795811i	−0.186621	+	0.982432i	$0.559754\pi$
$948$	2.81725e12	−	2.81725e12i	0.00367946	−	0.00367946i
$949$			2.00023e14i			0.259865i
$950$	−4.35248e14	+	2.13936e14i	−0.562495	+	0.276482i
$951$	−3.44902e14			−0.443398
$952$	8.28034e14	+	8.28034e14i	1.05892	+	1.05892i
$953$	1.47764e14	−	1.47764e14i	0.187976	−	0.187976i	−0.606844	−	0.794821i	$-0.707565\pi$
$953$	1.47764e14	−	1.47764e14i	0.187976	−	0.187976i	0.794821	+	0.606844i	$0.207565\pi$
$954$			2.38953e14i			0.302392i
$955$	−5.98698e14	−	9.92460e13i	−0.753687	−	0.124938i
$956$	−3.86341e15			−4.83818
$957$	−6.68004e13	−	6.68004e13i	−0.0832184	−	0.0832184i
$958$	1.04842e14	−	1.04842e14i	0.129929	−	0.129929i
$959$			2.27638e13i			0.0280642i
$960$	4.92189e14	+	6.87794e14i	0.603637	+	0.843533i
$961$	−2.77793e14			−0.338925
$962$	−1.31087e15	−	1.31087e15i	−1.59106	−	1.59106i
$963$	3.40743e12	−	3.40743e12i	0.00411430	−	0.00411430i
$964$			2.14489e15i			2.57644i
$965$	4.94414e14	−	3.53805e14i	0.590819	−	0.422793i
$966$	−4.92932e13			−0.0586005
$967$	7.76544e14	+	7.76544e14i	0.918404	+	0.918404i	0.996913	−	0.0785097i	$-0.0250162\pi$
$967$	7.76544e14	+	7.76544e14i	0.918404	+	0.918404i	−0.0785097	+	0.996913i	$0.525016\pi$
$968$	−3.73600e13	+	3.73600e13i	−0.0439572	+	0.0439572i
$969$		−	2.86596e14i		−	0.335468i
$970$	2.77575e14	−	1.67446e15i	0.323237	−	1.94992i
$971$	5.29961e14			0.613970			0.306985	−	0.951714i	$-0.400680\pi$
$971$	5.29961e14			0.613970			0.306985	+	0.951714i	$0.400680\pi$
$972$	9.92486e13	+	9.92486e13i	0.114391	+	0.114391i
$973$	−8.88673e13	+	8.88673e13i	−0.101901	+	0.101901i
$974$		−	2.54329e15i		−	2.90135i
$975$	−2.47334e14	+	7.25516e14i	−0.280712	+	0.823425i
$976$	2.10317e15			2.37479
$977$	2.27752e14	+	2.27752e14i	0.255852	+	0.255852i	0.823365	−	0.567513i	$-0.192094\pi$
$977$	2.27752e14	+	2.27752e14i	0.255852	+	0.255852i	−0.567513	+	0.823365i	$0.692094\pi$
$978$	8.77445e14	−	8.77445e14i	0.980676	−	0.980676i
$979$		−	2.48232e14i		−	0.276022i
$980$	2.04453e15	+	3.38920e14i	2.26184	+	0.374945i
$981$	−1.74875e14			−0.192479
$982$	−4.23312e14	−	4.23312e14i	−0.463557	−	0.463557i
$983$	3.56857e14	−	3.56857e14i	0.388801	−	0.388801i	−0.485459	−	0.874259i	$-0.661347\pi$
$983$	3.56857e14	−	3.56857e14i	0.388801	−	0.388801i	0.874259	+	0.485459i	$0.161347\pi$
$984$		−	1.63957e15i		−	1.77727i
$985$	9.98183e14	+	1.39488e15i	1.07654	+	1.50437i
$986$	6.13579e14			0.658394
$987$	−2.00126e14	−	2.00126e14i	−0.213657	−	0.213657i
$988$	−8.44825e14	+	8.44825e14i	−0.897392	+	0.897392i
$989$		−	3.32949e12i		−	0.00351882i
$990$	−4.89018e14	+	3.49943e14i	−0.514219	+	0.367978i
$991$	1.46822e15			1.53611			0.768056	−	0.640383i	$-0.221224\pi$
$991$	1.46822e15			1.53611			0.768056	+	0.640383i	$0.221224\pi$
$992$	−1.36386e15	−	1.36386e15i	−1.41975	−	1.41975i
$993$	−8.23207e13	+	8.23207e13i	−0.0852634	+	0.0852634i
$994$		−	6.66326e14i		−	0.686681i
$995$	−2.26214e14	+	1.36463e15i	−0.231955	+	1.39926i
$996$	−2.17678e15			−2.22084
$997$	3.44362e14	+	3.44362e14i	0.349574	+	0.349574i	0.859951	−	0.510377i	$-0.170494\pi$
$997$	3.44362e14	+	3.44362e14i	0.349574	+	0.349574i	−0.510377	+	0.859951i	$0.670494\pi$
$998$	−6.41001e13	+	6.41001e13i	−0.0647450	+	0.0647450i
$999$		−	1.52372e14i		−	0.153136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.f.a.7.10	✓	20
3.2	odd	2		45.11.g.c.37.1		20
5.2	odd	4		75.11.f.d.43.1		20
5.3	odd	4	inner	15.11.f.a.13.10	yes	20
5.4	even	2		75.11.f.d.7.1		20
15.8	even	4		45.11.g.c.28.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.f.a.7.10	✓	20	1.1	even	1	trivial
15.11.f.a.13.10	yes	20	5.3	odd	4	inner
45.11.g.c.28.1		20	15.8	even	4
45.11.g.c.37.1		20	3.2	odd	2
75.11.f.d.7.1		20	5.4	even	2
75.11.f.d.43.1		20	5.2	odd	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	15.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(42.4637 + 42.4637i) q^{2} +(-99.2043 + 99.2043i) q^{3} +2582.33i q^{4} +(3082.93 + 511.056i) q^{5} -8425.16 q^{6} +(-3582.02 - 3582.02i) q^{7} +(-66172.3 + 66172.3i) q^{8} -19683.0i q^{9} +O(q^{10})\)	\(q+(42.4637 + 42.4637i) q^{2} +(-99.2043 + 99.2043i) q^{3} +2582.33i q^{4} +(3082.93 + 511.056i) q^{5} -8425.16 q^{6} +(-3582.02 - 3582.02i) q^{7} +(-66172.3 + 66172.3i) q^{8} -19683.0i q^{9} +(109211. + 152614. i) q^{10} -162794. q^{11} +(-256178. - 256178. i) q^{12} +(395604. - 395604. i) q^{13} -304211. i q^{14} +(-356539. + 255141. i) q^{15} -2.97553e6 q^{16} +(1.74668e6 + 1.74668e6i) q^{17} +(835812. - 835812. i) q^{18} +826980. i q^{19} +(-1.31971e6 + 7.96113e6i) q^{20} +710704. q^{21} +(-6.91285e6 - 6.91285e6i) q^{22} +(-816679. + 816679. i) q^{23} -1.31292e7i q^{24} +(9.24327e6 + 3.15110e6i) q^{25} +3.35976e7 q^{26} +(1.95264e6 + 1.95264e6i) q^{27} +(9.24994e6 - 9.24994e6i) q^{28} -4.13627e6i q^{29} +(-2.59742e7 - 4.30573e6i) q^{30} +2.32774e7 q^{31} +(-5.85916e7 - 5.85916e7i) q^{32} +(1.61499e7 - 1.61499e7i) q^{33} +1.48341e8i q^{34} +(-9.21249e6 - 1.28737e7i) q^{35} +5.08279e7 q^{36} +(-3.90169e7 - 3.90169e7i) q^{37} +(-3.51166e7 + 3.51166e7i) q^{38} +7.84913e7i q^{39} +(-2.37822e8 + 1.70187e8i) q^{40} +1.24880e8 q^{41} +(3.01791e7 + 3.01791e7i) q^{42} +(-2.03844e6 + 2.03844e6i) q^{43} -4.20388e8i q^{44} +(1.00591e7 - 6.06813e7i) q^{45} -6.93583e7 q^{46} +(-2.81589e8 - 2.81589e8i) q^{47} +(2.95186e8 - 2.95186e8i) q^{48} -2.56814e8i q^{49} +(2.58696e8 + 5.26310e8i) q^{50} -3.46557e8 q^{51} +(1.02158e9 + 1.02158e9i) q^{52} +(-1.42946e8 + 1.42946e8i) q^{53} +1.65832e8i q^{54} +(-5.01883e8 - 8.31970e7i) q^{55} +4.74061e8 q^{56} +(-8.20400e7 - 8.20400e7i) q^{57} +(1.75641e8 - 1.75641e8i) q^{58} -2.82797e8i q^{59} +(-6.58857e8 - 9.20700e8i) q^{60} -7.06822e8 q^{61} +(9.88442e8 + 9.88442e8i) q^{62} +(-7.05049e7 + 7.05049e7i) q^{63} -1.92909e9i q^{64} +(1.42179e9 - 1.01744e9i) q^{65} +1.37157e9 q^{66} +(-7.04107e8 - 7.04107e8i) q^{67} +(-4.51051e9 + 4.51051e9i) q^{68} -1.62036e8i q^{69} +(1.55469e8 - 9.37862e8i) q^{70} +2.19034e9 q^{71} +(1.30247e9 + 1.30247e9i) q^{72} +(-2.52807e8 + 2.52807e8i) q^{73} -3.31360e9i q^{74} +(-1.22957e9 + 6.04370e8i) q^{75} -2.13553e9 q^{76} +(5.83133e8 + 5.83133e8i) q^{77} +(-3.33303e9 + 3.33303e9i) q^{78} +1.09973e7i q^{79} +(-9.17335e9 - 1.52066e9i) q^{80} -3.87420e8 q^{81} +(5.30286e9 + 5.30286e9i) q^{82} +(4.24856e9 - 4.24856e9i) q^{83} +1.83527e9i q^{84} +(4.49225e9 + 6.27755e9i) q^{85} -1.73119e8 q^{86} +(4.10336e8 + 4.10336e8i) q^{87} +(1.07725e10 - 1.07725e10i) q^{88} +1.52482e9i q^{89} +(3.00390e9 - 2.14960e9i) q^{90} -2.83412e9 q^{91} +(-2.10893e9 - 2.10893e9i) q^{92} +(-2.30922e9 + 2.30922e9i) q^{93} -2.39146e10i q^{94} +(-4.22633e8 + 2.54952e9i) q^{95} +1.16251e10 q^{96} +(-6.39534e9 - 6.39534e9i) q^{97} +(1.09052e10 - 1.09052e10i) q^{98} +3.20428e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 64 q^{2} + 10676 q^{5} - 4860 q^{6} + 10604 q^{7} - 39948 q^{8}+O(q^{10}) \) 20 * q - 64 * q^2 + 10676 * q^5 - 4860 * q^6 + 10604 * q^7 - 39948 * q^8	\( 20 q - 64 q^{2} + 10676 q^{5} - 4860 q^{6} + 10604 q^{7} - 39948 q^{8} + 153704 q^{10} + 32080 q^{11} - 620136 q^{12} - 69352 q^{13} + 662904 q^{15} - 3111700 q^{16} + 347360 q^{17} - 1259712 q^{18} + 24132564 q^{20} + 1448280 q^{21} - 27255980 q^{22} - 30995704 q^{23} + 36824936 q^{25} + 80977840 q^{26} - 104897636 q^{28} - 6436584 q^{30} - 8846480 q^{31} - 81249676 q^{32} + 86048244 q^{33} + 91578920 q^{35} + 177540660 q^{36} - 27635896 q^{37} + 44187744 q^{38} - 887009352 q^{40} + 149264920 q^{41} + 442105452 q^{42} + 675552392 q^{43} - 183996684 q^{45} - 1916100680 q^{46} - 257112832 q^{47} + 1182772368 q^{48} + 909704384 q^{50} - 711183240 q^{51} + 1397512520 q^{52} - 152646064 q^{53} - 1181518004 q^{55} + 1735516800 q^{56} + 342507528 q^{57} - 1947576252 q^{58} - 1084331124 q^{60} + 2582791000 q^{61} - 969372632 q^{62} + 208718532 q^{63} + 7250334488 q^{65} - 1968290280 q^{66} - 6731030200 q^{67} - 12869460704 q^{68} + 7421027700 q^{70} + 7511442640 q^{71} + 786296484 q^{72} + 1660222316 q^{73} + 72454824 q^{75} + 9998646360 q^{76} - 13264676792 q^{77} - 5574993480 q^{78} - 15692039116 q^{80} - 7748409780 q^{81} + 27089146528 q^{82} + 30753878864 q^{83} - 2653017808 q^{85} - 46532117120 q^{86} + 3048661476 q^{87} + 5813201532 q^{88} + 8161910244 q^{90} + 14175275920 q^{91} + 30045377384 q^{92} - 6062778072 q^{93} - 58265269776 q^{95} - 18513718020 q^{96} - 32149992820 q^{97} + 54432471592 q^{98}+O(q^{100}) \) 20 * q - 64 * q^2 + 10676 * q^5 - 4860 * q^6 + 10604 * q^7 - 39948 * q^8 + 153704 * q^10 + 32080 * q^11 - 620136 * q^12 - 69352 * q^13 + 662904 * q^15 - 3111700 * q^16 + 347360 * q^17 - 1259712 * q^18 + 24132564 * q^20 + 1448280 * q^21 - 27255980 * q^22 - 30995704 * q^23 + 36824936 * q^25 + 80977840 * q^26 - 104897636 * q^28 - 6436584 * q^30 - 8846480 * q^31 - 81249676 * q^32 + 86048244 * q^33 + 91578920 * q^35 + 177540660 * q^36 - 27635896 * q^37 + 44187744 * q^38 - 887009352 * q^40 + 149264920 * q^41 + 442105452 * q^42 + 675552392 * q^43 - 183996684 * q^45 - 1916100680 * q^46 - 257112832 * q^47 + 1182772368 * q^48 + 909704384 * q^50 - 711183240 * q^51 + 1397512520 * q^52 - 152646064 * q^53 - 1181518004 * q^55 + 1735516800 * q^56 + 342507528 * q^57 - 1947576252 * q^58 - 1084331124 * q^60 + 2582791000 * q^61 - 969372632 * q^62 + 208718532 * q^63 + 7250334488 * q^65 - 1968290280 * q^66 - 6731030200 * q^67 - 12869460704 * q^68 + 7421027700 * q^70 + 7511442640 * q^71 + 786296484 * q^72 + 1660222316 * q^73 + 72454824 * q^75 + 9998646360 * q^76 - 13264676792 * q^77 - 5574993480 * q^78 - 15692039116 * q^80 - 7748409780 * q^81 + 27089146528 * q^82 + 30753878864 * q^83 - 2653017808 * q^85 - 46532117120 * q^86 + 3048661476 * q^87 + 5813201532 * q^88 + 8161910244 * q^90 + 14175275920 * q^91 + 30045377384 * q^92 - 6062778072 * q^93 - 58265269776 * q^95 - 18513718020 * q^96 - 32149992820 * q^97 + 54432471592 * q^98

Introduction

L-functions

Modular forms

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