LMFDB - Embedded newform 456.2.u.d.11.63

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(11,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("456.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.u (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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.63
Character	$\chi$	$=$	456.11
Dual form			456.2.u.d.83.63

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36421 + 0.372721i) q^{2} +(-1.51141 - 0.845959i) q^{3} +(1.72216 + 1.01694i) q^{4} +(-0.450312 + 0.779964i) q^{5} +(-1.74658 - 1.71740i) q^{6} +3.34959i q^{7} +(1.97036 + 2.02921i) q^{8} +(1.56871 + 2.55718i) q^{9} +O(q^{10})$	\(q+(1.36421 + 0.372721i) q^{2} +(-1.51141 - 0.845959i) q^{3} +(1.72216 + 1.01694i) q^{4} +(-0.450312 + 0.779964i) q^{5} +(-1.74658 - 1.71740i) q^{6} +3.34959i q^{7} +(1.97036 + 2.02921i) q^{8} +(1.56871 + 2.55718i) q^{9} +(-0.905031 + 0.896197i) q^{10} -2.25269i q^{11} +(-1.74259 - 2.99389i) q^{12} +(-4.95554 + 2.86108i) q^{13} +(-1.24846 + 4.56956i) q^{14} +(1.34042 - 0.797898i) q^{15} +(1.93166 + 3.50267i) q^{16} +(1.44663 + 0.835214i) q^{17} +(1.18694 + 4.07323i) q^{18} +(4.11840 - 1.42787i) q^{19} +(-1.56869 + 0.885280i) q^{20} +(2.83362 - 5.06260i) q^{21} +(0.839623 - 3.07314i) q^{22} +(0.706565 + 1.22381i) q^{23} +(-1.26138 - 4.73381i) q^{24} +(2.09444 + 3.62767i) q^{25} +(-7.82680 + 2.05609i) q^{26} +(-0.207688 - 5.19200i) q^{27} +(-3.40634 + 5.76853i) q^{28} +(3.46044 + 5.99366i) q^{29} +(2.12602 - 0.588899i) q^{30} -3.64141i q^{31} +(1.32967 + 5.49836i) q^{32} +(-1.90568 + 3.40473i) q^{33} +(1.66221 + 1.67860i) q^{34} +(-2.61256 - 1.50836i) q^{35} +(0.101059 + 5.99915i) q^{36} +1.11330i q^{37} +(6.15057 - 0.412905i) q^{38} +(9.91019 - 0.132078i) q^{39} +(-2.46999 + 0.623028i) q^{40} +(-1.76368 - 1.01826i) q^{41} +(5.75260 - 5.85032i) q^{42} +(2.58105 - 4.47051i) q^{43} +(2.29085 - 3.87948i) q^{44} +(-2.70092 + 0.0720058i) q^{45} +(0.507767 + 1.93289i) q^{46} +(-5.07311 - 8.78688i) q^{47} +(0.0435944 - 6.92807i) q^{48} -4.21977 q^{49} +(1.50515 + 5.72956i) q^{50} +(-1.47990 - 2.48614i) q^{51} +(-11.4438 - 0.112262i) q^{52} +(-5.20344 - 9.01262i) q^{53} +(1.65184 - 7.16041i) q^{54} +(1.75701 + 1.01441i) q^{55} +(-6.79703 + 6.59989i) q^{56} +(-7.43250 - 1.32590i) q^{57} +(2.48682 + 9.46641i) q^{58} +(-6.51047 - 3.75882i) q^{59} +(3.11984 - 0.0109731i) q^{60} +(11.5988 - 6.69656i) q^{61} +(1.35723 - 4.96766i) q^{62} +(-8.56550 + 5.25453i) q^{63} +(-0.235395 + 7.99654i) q^{64} -5.15352i q^{65} +(-3.86877 + 3.93449i) q^{66} +(-6.46476 - 11.1973i) q^{67} +(1.64197 + 2.90951i) q^{68} +(-0.0326177 - 2.44740i) q^{69} +(-3.00189 - 3.03149i) q^{70} +(-0.450479 + 0.780253i) q^{71} +(-2.09814 + 8.22179i) q^{72} +(-1.44066 + 2.49529i) q^{73} +(-0.414949 + 1.51877i) q^{74} +(-0.0966871 - 7.25470i) q^{75} +(8.54459 + 1.72916i) q^{76} +7.54558 q^{77} +(13.5689 + 3.51355i) q^{78} +(9.98974 + 5.76758i) q^{79} +(-3.60181 - 0.0706732i) q^{80} +(-4.07832 + 8.02292i) q^{81} +(-2.02651 - 2.04648i) q^{82} +8.93124i q^{83} +(10.0283 - 5.83697i) q^{84} +(-1.30287 + 0.752215i) q^{85} +(5.18736 - 5.13672i) q^{86} +(-0.159747 - 11.9863i) q^{87} +(4.57118 - 4.43859i) q^{88} +(4.67642 - 2.69993i) q^{89} +(-3.71146 - 0.908457i) q^{90} +(-9.58345 - 16.5990i) q^{91} +(-0.0277239 + 2.82612i) q^{92} +(-3.08048 + 5.50365i) q^{93} +(-3.64575 - 13.8780i) q^{94} +(-0.740879 + 3.85519i) q^{95} +(2.64171 - 9.43511i) q^{96} +(-1.91639 + 3.31929i) q^{97} +(-5.75666 - 1.57280i) q^{98} +(5.76052 - 3.53380i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9}+O(q^{10}) $ 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9	$ 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9} + 18 q^{12} + 28 q^{16} - 10 q^{18} + 16 q^{19} + 10 q^{22} + 11 q^{24} - 96 q^{25} - 80 q^{27} + 6 q^{28} - 4 q^{30} - 40 q^{33} + 40 q^{34} + q^{36} - 56 q^{40} + 26 q^{42} - 20 q^{43} - 64 q^{46} - 19 q^{48} - 72 q^{49} - 42 q^{51} - 26 q^{52} + 6 q^{54} + 10 q^{57} + 144 q^{58} - 18 q^{60} - 112 q^{64} + 49 q^{66} - 12 q^{67} + 72 q^{70} - 45 q^{72} + 4 q^{73} + 144 q^{75} + 32 q^{76} - 50 q^{78} + 22 q^{81} - 22 q^{82} + 36 q^{84} + 100 q^{88} - 2 q^{90} + 24 q^{91} - 88 q^{94} - 66 q^{96} - 28 q^{97} + 80 q^{99}+O(q^{100}) $ 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9 + 18 * q^12 + 28 * q^16 - 10 * q^18 + 16 * q^19 + 10 * q^22 + 11 * q^24 - 96 * q^25 - 80 * q^27 + 6 * q^28 - 4 * q^30 - 40 * q^33 + 40 * q^34 + q^36 - 56 * q^40 + 26 * q^42 - 20 * q^43 - 64 * q^46 - 19 * q^48 - 72 * q^49 - 42 * q^51 - 26 * q^52 + 6 * q^54 + 10 * q^57 + 144 * q^58 - 18 * q^60 - 112 * q^64 + 49 * q^66 - 12 * q^67 + 72 * q^70 - 45 * q^72 + 4 * q^73 + 144 * q^75 + 32 * q^76 - 50 * q^78 + 22 * q^81 - 22 * q^82 + 36 * q^84 + 100 * q^88 - 2 * q^90 + 24 * q^91 - 88 * q^94 - 66 * q^96 - 28 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	1.36421	+	0.372721i	0.964645	+	0.263554i
$2$	1.36421	+	0.372721i	0.964645	+	0.263554i
$3$	−1.51141	−	0.845959i	−0.872612	−	0.488415i
$3$	−1.51141	−	0.845959i	−0.872612	−	0.488415i
$4$	1.72216	+	1.01694i	0.861079	+	0.508471i
$5$	−0.450312	+	0.779964i	−0.201386	+	0.348811i	−0.948975	−	0.315351i	$-0.897878\pi$
$5$	−0.450312	+	0.779964i	−0.201386	+	0.348811i	0.747589	+	0.664161i	$0.231211\pi$
$6$	−1.74658	−	1.71740i	−0.713037	−	0.701127i
$7$			3.34959i			1.26603i	0.774141	+	0.633013i	$0.218182\pi$
$7$			3.34959i			1.26603i	−0.774141	+	0.633013i	$0.781818\pi$
$8$	1.97036	+	2.02921i	0.696626	+	0.717434i
$9$	1.56871	+	2.55718i	0.522902	+	0.852393i
$10$	−0.905031	+	0.896197i	−0.286196	+	0.283402i
$11$		−	2.25269i		−	0.679210i	−0.940568	−	0.339605i	$-0.889707\pi$
$11$		−	2.25269i		−	0.679210i	0.940568	−	0.339605i	$-0.110293\pi$
$12$	−1.74259	−	2.99389i	−0.503043	−	0.864261i
$13$	−4.95554	+	2.86108i	−1.37442	+	0.793521i	−0.991481	−	0.130253i	$-0.958421\pi$
$13$	−4.95554	+	2.86108i	−1.37442	+	0.793521i	−0.382938	+	0.923774i	$0.625088\pi$
$14$	−1.24846	+	4.56956i	−0.333666	+	1.22127i
$15$	1.34042	−	0.797898i	0.346096	−	0.206016i
$16$	1.93166	+	3.50267i	0.482914	+	0.875668i
$17$	1.44663	+	0.835214i	0.350860	+	0.202569i	0.665064	−	0.746786i	$-0.268404\pi$
$17$	1.44663	+	0.835214i	0.350860	+	0.202569i	−0.314204	+	0.949356i	$0.601738\pi$
$18$	1.18694	+	4.07323i	0.279764	+	0.960069i
$19$	4.11840	−	1.42787i	0.944825	−	0.327576i
$19$	4.11840	−	1.42787i	0.944825	−	0.327576i
$20$	−1.56869	+	0.885280i	−0.350769	+	0.197955i
$21$	2.83362	−	5.06260i	0.618346	−	1.10475i
$22$	0.839623	−	3.07314i	0.179008	−	0.655197i
$23$	0.706565	+	1.22381i	0.147329	+	0.255181i	0.930239	−	0.366953i	$-0.119599\pi$
$23$	0.706565	+	1.22381i	0.147329	+	0.255181i	−0.782910	+	0.622134i	$0.786266\pi$
$24$	−1.26138	−	4.73381i	−0.257478	−	0.966284i
$25$	2.09444	+	3.62767i	0.418887	+	0.725534i
$26$	−7.82680	+	2.05609i	−1.53496	+	0.403233i
$27$	−0.207688	−	5.19200i	−0.0399695	−	0.999201i
$28$	−3.40634	+	5.76853i	−0.643738	+	1.09015i
$29$	3.46044	+	5.99366i	0.642588	+	1.11299i	0.984853	+	0.173391i	$0.0554724\pi$
$29$	3.46044	+	5.99366i	0.642588	+	1.11299i	−0.342266	+	0.939603i	$0.611194\pi$
$30$	2.12602	−	0.588899i	0.388156	−	0.107518i
$31$		−	3.64141i		−	0.654016i	−0.945021	−	0.327008i	$-0.893960\pi$
$31$		−	3.64141i		−	0.654016i	0.945021	−	0.327008i	$-0.106040\pi$
$32$	1.32967	+	5.49836i	0.235055	+	0.971982i
$33$	−1.90568	+	3.40473i	−0.331736	+	0.592687i
$34$	1.66221	+	1.67860i	0.285067	+	0.287878i
$35$	−2.61256	−	1.50836i	−0.441603	−	0.254960i
$36$	0.101059	+	5.99915i	0.0168431	+	0.999858i
$37$			1.11330i			0.183025i	0.995804	+	0.0915124i	$0.0291701\pi$
$37$			1.11330i			0.183025i	−0.995804	+	0.0915124i	$0.970830\pi$
$38$	6.15057	−	0.412905i	0.997754	−	0.0669821i
$39$	9.91019	−	0.132078i	1.58690	−	0.0211494i
$40$	−2.46999	+	0.623028i	−0.390539	+	0.0985093i
$41$	−1.76368	−	1.01826i	−0.275440	−	0.159025i	0.355917	−	0.934518i	$-0.384169\pi$
$41$	−1.76368	−	1.01826i	−0.275440	−	0.159025i	−0.631357	+	0.775492i	$0.717502\pi$
$42$	5.75260	−	5.85032i	0.887645	−	0.902724i
$43$	2.58105	−	4.47051i	0.393607	−	0.681747i	−0.599315	−	0.800513i	$-0.704560\pi$
$43$	2.58105	−	4.47051i	0.393607	−	0.681747i	0.992922	+	0.118766i	$0.0378938\pi$
$44$	2.29085	−	3.87948i	0.345359	−	0.584854i
$45$	−2.70092	+	0.0720058i	−0.402629	+	0.0107340i
$46$	0.507767	+	1.93289i	0.0748662	+	0.284988i
$47$	−5.07311	−	8.78688i	−0.739989	−	1.28170i	−0.952500	−	0.304539i	$-0.901498\pi$
$47$	−5.07311	−	8.78688i	−0.739989	−	1.28170i	0.212511	−	0.977159i	$-0.431836\pi$
$48$	0.0435944	−	6.92807i	0.00629231	−	0.999980i
$49$	−4.21977			−0.602824
$50$	1.50515	+	5.72956i	0.212860	+	0.810282i
$51$	−1.47990	−	2.48614i	−0.207227	−	0.348129i
$52$	−11.4438	−	0.112262i	−1.58697	−	0.0155679i
$53$	−5.20344	−	9.01262i	−0.714747	−	1.23798i	−0.963057	−	0.269298i	$-0.913208\pi$
$53$	−5.20344	−	9.01262i	−0.714747	−	1.23798i	0.248310	−	0.968681i	$-0.420125\pi$
$54$	1.65184	−	7.16041i	0.224787	−	0.974408i
$55$	1.75701	+	1.01441i	0.236916	+	0.136783i
$56$	−6.79703	+	6.59989i	−0.908291	+	0.881947i
$57$	−7.43250	−	1.32590i	−0.984458	−	0.175620i
$58$	2.48682	+	9.46641i	0.326535	+	1.24300i
$59$	−6.51047	−	3.75882i	−0.847591	−	0.489357i	0.0122464	−	0.999925i	$-0.496102\pi$
$59$	−6.51047	−	3.75882i	−0.847591	−	0.489357i	−0.859837	+	0.510568i	$0.829435\pi$
$60$	3.11984	−	0.0109731i	0.402769	−	0.00141662i
$61$	11.5988	−	6.69656i	1.48507	−	0.857406i	0.485215	−	0.874395i	$-0.338741\pi$
$61$	11.5988	−	6.69656i	1.48507	−	0.857406i	0.999856	+	0.0169886i	$0.00540790\pi$
$62$	1.35723	−	4.96766i	0.172368	−	0.630894i
$63$	−8.56550	+	5.25453i	−1.07915	+	0.662008i
$64$	−0.235395	+	7.99654i	−0.0294244	+	0.999567i
$65$		−	5.15352i		−	0.639216i
$66$	−3.86877	+	3.93449i	−0.476212	+	0.484302i
$67$	−6.46476	−	11.1973i	−0.789796	−	1.36797i	−0.926091	−	0.377299i	$-0.876853\pi$
$67$	−6.46476	−	11.1973i	−0.789796	−	1.36797i	0.136295	−	0.990668i	$-0.456480\pi$
$68$	1.64197	+	2.90951i	0.199118	+	0.352830i
$69$	−0.0326177	−	2.44740i	−0.00392671	−	0.294632i
$70$	−3.00189	−	3.03149i	−0.358795	−	0.362332i
$71$	−0.450479	+	0.780253i	−0.0534621	+	0.0925990i	−0.891518	−	0.452985i	$-0.850359\pi$
$71$	−0.450479	+	0.780253i	−0.0534621	+	0.0925990i	0.838056	+	0.545584i	$0.183692\pi$
$72$	−2.09814	+	8.22179i	−0.247269	+	0.968947i
$73$	−1.44066	+	2.49529i	−0.168616	+	0.292052i	−0.937934	−	0.346815i	$-0.887263\pi$
$73$	−1.44066	+	2.49529i	−0.168616	+	0.292052i	0.769317	+	0.638867i	$0.220597\pi$
$74$	−0.414949	+	1.51877i	−0.0482368	+	0.176554i
$75$	−0.0966871	−	7.25470i	−0.0111645	−	0.837701i
$76$	8.54459	+	1.72916i	0.980132	+	0.198348i
$77$	7.54558			0.859898
$78$	13.5689	+	3.51355i	1.53637	+	0.397832i
$79$	9.98974	+	5.76758i	1.12393	+	0.648903i	0.942402	−	0.334482i	$-0.108561\pi$
$79$	9.98974	+	5.76758i	1.12393	+	0.648903i	0.181531	+	0.983385i	$0.441895\pi$
$80$	−3.60181	−	0.0706732i	−0.402694	−	0.00790150i
$81$	−4.07832	+	8.02292i	−0.453146	+	0.891436i
$82$	−2.02651	−	2.04648i	−0.223790	−	0.225996i
$83$			8.93124i			0.980331i	0.871629	+	0.490165i	$0.163064\pi$
$83$			8.93124i			0.980331i	−0.871629	+	0.490165i	$0.836936\pi$
$84$	10.0283	−	5.83697i	1.09418	−	0.636866i
$85$	−1.30287	+	0.752215i	−0.141316	+	0.0815891i
$86$	5.18736	−	5.13672i	0.559368	−	0.553907i
$87$	−0.159747	−	11.9863i	−0.0171267	−	1.28506i
$88$	4.57118	−	4.43859i	0.487289	−	0.473156i
$89$	4.67642	−	2.69993i	0.495699	−	0.286192i	−0.231237	−	0.972898i	$-0.574277\pi$
$89$	4.67642	−	2.69993i	0.495699	−	0.286192i	0.726936	+	0.686705i	$0.240944\pi$
$90$	−3.71146	−	0.908457i	−0.391223	−	0.0957597i
$91$	−9.58345	−	16.5990i	−1.00462	−	1.74005i
$92$	−0.0277239	+	2.82612i	−0.00289041	+	0.294644i
$93$	−3.08048	+	5.50365i	−0.319431	+	0.570702i
$94$	−3.64575	−	13.8780i	−0.376030	−	1.43141i
$95$	−0.740879	+	3.85519i	−0.0760126	+	0.395534i
$96$	2.64171	−	9.43511i	0.269618	−	0.962967i
$97$	−1.91639	+	3.31929i	−0.194580	+	0.337022i	−0.946763	−	0.321932i	$-0.895668\pi$
$97$	−1.91639	+	3.31929i	−0.194580	+	0.337022i	0.752183	+	0.658955i	$0.229001\pi$
$98$	−5.75666	−	1.57280i	−0.581511	−	0.158876i
$99$	5.76052	−	3.53380i	0.578954	−	0.355161i
$100$	−0.0821806	+	8.37735i	−0.00821806	+	0.837735i
$101$	3.98870	+	6.90863i	0.396890	+	0.687434i	0.993340	−	0.115216i	$-0.0367560\pi$
$101$	3.98870	+	6.90863i	0.396890	+	0.687434i	−0.596450	+	0.802650i	$0.703423\pi$
$102$	−1.09226	−	3.94322i	−0.108150	−	0.390437i
$103$		−	6.80308i		−	0.670328i	−0.942160	−	0.335164i	$-0.891208\pi$
$103$		−	6.80308i		−	0.670328i	0.942160	−	0.335164i	$-0.108792\pi$
$104$	−15.5699	−	4.41848i	−1.52676	−	0.433268i
$105$	2.67263	+	4.48987i	0.260822	+	0.438167i
$106$	−3.73941	−	14.2346i	−0.363203	−	1.38258i
$107$			16.6943i			1.61390i	0.590619	+	0.806951i	$0.298884\pi$
$107$			16.6943i			1.61390i	−0.590619	+	0.806951i	$0.701116\pi$
$108$	4.92229	−	9.15265i	0.473648	−	0.880714i
$109$	−8.65673	−	4.99797i	−0.829165	−	0.478718i	0.0244019	−	0.999702i	$-0.492232\pi$
$109$	−8.65673	−	4.99797i	−0.829165	−	0.478718i	−0.853567	+	0.520984i	$0.825565\pi$
$110$	2.01885	+	2.03875i	0.192490	+	0.194387i
$111$	0.941803	−	1.68264i	0.0893920	−	0.159710i
$112$	−11.7325	+	6.47026i	−1.10862	+	0.611382i
$113$		−	2.41156i		−	0.226860i	−0.993546	−	0.113430i	$-0.963816\pi$
$113$		−	2.41156i		−	0.226860i	0.993546	−	0.113430i	$-0.0361838\pi$
$114$	−9.64532	−	4.57906i	−0.903367	−	0.428868i
$115$	−1.27270			−0.118680
$116$	−0.135779	+	13.8411i	−0.0126068	+	1.28511i
$117$	−15.0901	−	8.18399i	−1.39508	−	0.756610i
$118$	−7.48068	−	7.55442i	−0.688652	−	0.695441i
$119$	−2.79763	+	4.84563i	−0.256458	+	0.444198i
$120$	4.26021	+	1.14786i	0.388903	+	0.104785i
$121$	5.92541			0.538673
$122$	18.3192	−	4.81243i	1.65854	−	0.435697i
$123$	1.80423	+	3.03101i	0.162682	+	0.273297i
$124$	3.70310	−	6.27108i	0.332548	−	0.563160i
$125$	−8.27573			−0.740204
$126$	−13.6436	+	3.97576i	−1.21547	+	0.354188i
$127$	16.9627	−	9.79344i	1.50520	−	0.869027i	0.505217	−	0.862992i	$-0.331412\pi$
$127$	16.9627	−	9.79344i	1.50520	−	0.869027i	0.999982	−	0.00603472i	$-0.00192092\pi$
$128$	−3.30161	+	10.8212i	−0.291824	+	0.956472i
$129$	−7.68289	+	4.57330i	−0.676441	+	0.402657i
$130$	1.92083	−	7.03050i	0.168468	−	0.616616i
$131$	15.9093	+	9.18525i	1.39000	+	0.802519i	0.993315	−	0.115434i	$-0.0368258\pi$
$131$	15.9093	+	9.18525i	1.39000	+	0.802519i	0.396689	+	0.917953i	$0.370159\pi$
$132$	−6.74429	+	3.92551i	−0.587015	+	0.341672i
$133$	4.78278	+	13.7949i	0.414719	+	1.19617i
$134$	−4.64585	−	17.6851i	−0.401340	−	1.52776i
$135$	4.14310	+	2.17603i	0.356581	+	0.187283i
$136$	1.15556	+	4.58119i	0.0990882	+	0.392834i
$137$	11.0774	−	6.39554i	0.946406	−	0.546408i	0.0544432	−	0.998517i	$-0.482662\pi$
$137$	11.0774	−	6.39554i	0.946406	−	0.546408i	0.891963	+	0.452109i	$0.149328\pi$
$138$	0.867699	−	3.35093i	0.0738634	−	0.285250i
$139$	0.708235	+	1.22670i	0.0600717	+	0.104047i	0.894497	−	0.447073i	$-0.147534\pi$
$139$	0.708235	+	1.22670i	0.0600717	+	0.104047i	−0.834426	+	0.551121i	$0.814200\pi$
$140$	−2.96533	−	5.25446i	−0.250616	−	0.444083i
$141$	0.234194	+	17.5722i	0.0197227	+	1.47985i
$142$	−0.905367	+	0.896529i	−0.0759767	+	0.0752350i
$143$	6.44512	+	11.1633i	0.538968	+	0.933519i
$144$	−5.92675	+	10.4343i	−0.493896	+	0.869521i
$145$	−6.23312			−0.517632
$146$	−2.89541	+	2.86715i	−0.239626	+	0.237287i
$147$	6.37779	+	3.56975i	0.526031	+	0.294428i
$148$	−1.13216	+	1.91727i	−0.0930628	+	0.157599i
$149$	6.85354	−	11.8707i	0.561464	−	0.972484i	−0.435905	−	0.899993i	$-0.643572\pi$
$149$	6.85354	−	11.8707i	0.561464	−	0.972484i	0.997369	−	0.0724914i	$-0.0230950\pi$
$150$	2.57208	−	9.93300i	0.210009	−	0.811026i
$151$		−	2.18534i		−	0.177840i	−0.996039	−	0.0889201i	$-0.971658\pi$
$151$		−	2.18534i		−	0.177840i	0.996039	−	0.0889201i	$-0.0283416\pi$
$152$	11.0122	+	5.54369i	0.893204	+	0.449652i
$153$	0.133552	+	5.00950i	0.0107971	+	0.404994i
$154$	10.2938	+	2.81240i	0.829497	+	0.226629i
$155$	2.84017	+	1.63977i	0.228128	+	0.131710i
$156$	17.2012	+	9.85063i	1.37720	+	0.788682i
$157$	−10.0469	−	5.80056i	−0.801826	−	0.462935i	0.0422829	−	0.999106i	$-0.486537\pi$
$157$	−10.0469	−	5.80056i	−0.801826	−	0.462935i	−0.844109	+	0.536171i	$0.819870\pi$
$158$	11.4784	+	11.5916i	0.913176	+	0.922178i
$159$	0.240210	+	18.0236i	0.0190499	+	1.42937i
$160$	−4.88729	−	1.43888i	−0.386374	−	0.113754i
$161$	−4.09925	+	2.36671i	−0.323066	+	0.186522i
$162$	−8.55401	+	9.42491i	−0.672067	+	0.740491i
$163$	13.2843			1.04051			0.520255	−	0.854011i	$-0.325837\pi$
$163$	13.2843			1.04051			0.520255	+	0.854011i	$0.325837\pi$
$164$	−2.00182	−	3.54716i	−0.156316	−	0.276987i
$165$	−1.79741	−	3.01955i	−0.139928	−	0.235072i
$166$	−3.32886	+	12.1841i	−0.258370	+	0.945671i
$167$	−3.88950	−	6.73682i	−0.300979	−	0.521311i	0.675379	−	0.737471i	$-0.263980\pi$
$167$	−3.88950	−	6.73682i	−0.300979	−	0.521311i	−0.976358	+	0.216160i	$0.930647\pi$
$168$	15.8563	−	4.22511i	1.22334	−	0.325975i
$169$	9.87156	−	17.0981i	0.759351	−	1.31523i
$170$	−2.05776	+	0.540573i	−0.157823	+	0.0414601i
$171$	10.1119	+	8.29157i	0.773274	+	0.634072i
$172$	8.99123	−	5.07415i	0.685575	−	0.386900i
$173$	−8.48256	+	14.6922i	−0.644917	+	1.11703i	0.339403	+	0.940641i	$0.389775\pi$
$173$	−8.48256	+	14.6922i	−0.644917	+	1.11703i	−0.984321	+	0.176389i	$0.943558\pi$
$174$	4.24960	−	16.4113i	0.322161	−	1.24414i
$175$	−12.1512	+	7.01551i	−0.918546	+	0.530323i
$176$	7.89042	−	4.35142i	0.594763	−	0.328000i
$177$	6.66016	+	11.1887i	0.500609	+	0.840994i
$178$	7.38595	−	1.94028i	0.553601	−	0.145430i
$179$			1.71726i			0.128354i	0.997939	+	0.0641769i	$0.0204422\pi$
$179$			1.71726i			0.128354i	−0.997939	+	0.0641769i	$0.979558\pi$
$180$	−4.72463	−	2.62267i	−0.352153	−	0.195482i
$181$	16.4480	−	9.49625i	1.22257	−	0.705851i	0.257104	−	0.966384i	$-0.417232\pi$
$181$	16.4480	−	9.49625i	1.22257	−	0.705851i	0.965465	+	0.260533i	$0.0838982\pi$
$182$	−6.88707	−	26.2166i	−0.510504	−	1.94330i
$183$	−23.1955	+	0.309138i	−1.71466	+	0.0228522i
$184$	−1.09118	+	3.84511i	−0.0804427	+	0.283465i
$185$	−0.868331	−	0.501331i	−0.0638410	−	0.0368586i
$186$	−6.25377	+	6.36000i	−0.458548	+	0.466338i
$187$	1.88147	−	3.25881i	0.137587	−	0.238308i
$188$	0.199056	−	20.2914i	0.0145177	−	1.47991i
$189$	17.3911	−	0.695669i	1.26502	−	0.0506025i
$190$	−2.44763	+	4.98316i	−0.177570	+	0.361516i
$191$	−13.5012			−0.976912			−0.488456	−	0.872588i	$-0.662440\pi$
$191$	−13.5012			−0.976912			−0.488456	+	0.872588i	$0.662440\pi$
$192$	7.12052	−	11.8869i	0.513879	−	0.857863i
$193$	−9.24460	+	16.0121i	−0.665441	+	1.15258i	0.313725	+	0.949514i	$0.398423\pi$
$193$	−9.24460	+	16.0121i	−0.665441	+	1.15258i	−0.979166	+	0.203063i	$0.934910\pi$
$194$	−3.85153	+	3.81394i	−0.276524	+	0.273825i
$195$	−4.35967	+	7.78907i	−0.312202	+	0.557787i
$196$	−7.26710	−	4.29126i	−0.519079	−	0.306518i
$197$	−7.62653			−0.543367			−0.271684	−	0.962387i	$-0.587580\pi$
$197$	−7.62653			−0.543367			−0.271684	+	0.962387i	$0.587580\pi$
$198$	9.17570	−	2.67380i	0.652089	−	0.190018i
$199$	−4.55778	+	2.63144i	−0.323093	+	0.186538i	−0.652770	−	0.757556i	$-0.726393\pi$
$199$	−4.55778	+	2.63144i	−0.323093	+	0.186538i	0.329678	+	0.944094i	$0.393060\pi$
$200$	−3.23452	+	11.3979i	−0.228715	+	0.805950i
$201$	0.298438	+	22.3926i	0.0210502	+	1.57945i
$202$	2.86645	+	10.9115i	0.201682	+	0.767732i
$203$	−20.0763	+	11.5911i	−1.40908	+	0.813533i
$204$	−0.0203523	−	5.78650i	−0.00142494	−	0.405136i
$205$	1.58841	−	0.917070i	0.110940	−	0.0640510i
$206$	2.53565	−	9.28086i	0.176667	−	0.646628i
$207$	−2.02110	+	3.72661i	−0.140476	+	0.259017i
$208$	−19.5938	−	11.8310i	−1.35859	−	0.820331i
$209$	−3.21654	−	9.27745i	−0.222493	−	0.641735i
$210$	1.97257	+	7.12129i	0.136120	+	0.491416i
$211$	−0.502877	+	0.871008i	−0.0346195	+	0.0599627i	−0.882816	−	0.469719i	$-0.844355\pi$
$211$	−0.502877	+	0.871008i	−0.0346195	+	0.0599627i	0.848197	+	0.529682i	$0.177689\pi$
$212$	0.204170	−	20.8127i	0.0140225	−	1.42943i
$213$	1.34092	−	0.798194i	0.0918783	−	0.0546913i
$214$	−6.22233	+	22.7746i	−0.425350	+	1.55684i
$215$	2.32456	+	4.02626i	0.158534	+	0.274588i
$216$	10.1264	−	10.6515i	0.689017	−	0.724745i
$217$	12.1972			0.828002
$218$	−9.94679	−	10.0448i	−0.673681	−	0.680323i
$219$	4.28834	−	2.55267i	0.289779	−	0.172493i
$220$	1.99426	+	3.53376i	0.134453	+	0.238246i
$221$	−9.55846			−0.642971
$222$	1.91198	−	1.94446i	0.128323	−	0.130503i
$223$	−2.69913	−	1.55834i	−0.180747	−	0.104354i	0.406897	−	0.913474i	$-0.366611\pi$
$223$	−2.69913	−	1.55834i	−0.180747	−	0.104354i	−0.587644	+	0.809120i	$0.699944\pi$
$224$	−18.4173	+	4.45387i	−1.23056	+	0.297586i
$225$	−5.99104	+	11.0466i	−0.399403	+	0.736440i
$226$	0.898839	−	3.28988i	0.0597899	−	0.218840i
$227$		−	2.57211i		−	0.170717i	−0.996350	−	0.0853585i	$-0.972796\pi$
$227$		−	2.57211i		−	0.170717i	0.996350	−	0.0853585i	$-0.0272036\pi$
$228$	−11.4516	−	9.84183i	−0.758398	−	0.651791i
$229$		−	1.65752i		−	0.109532i	−0.998499	−	0.0547659i	$-0.982559\pi$
$229$		−	1.65752i		−	0.109532i	0.998499	−	0.0547659i	$-0.0174413\pi$
$230$	−1.73624	−	0.474362i	−0.114484	−	0.0312785i
$231$	−11.4044	−	6.38325i	−0.750357	−	0.419987i
$232$	−5.34410	+	18.8316i	−0.350857	+	1.23636i
$233$	5.84455	+	3.37435i	0.382889	+	0.221061i	0.679075	−	0.734069i	$-0.262381\pi$
$233$	5.84455	+	3.37435i	0.382889	+	0.221061i	−0.296185	+	0.955130i	$0.595715\pi$
$234$	−17.5357	−	16.7891i	−1.14635	−	1.09754i
$235$	9.13793			0.596093
$236$	−7.38955	−	13.0941i	−0.481019	−	0.852350i
$237$	−10.2194	−	17.1681i	−0.663824	−	1.11519i
$238$	−5.62263	+	5.56774i	−0.364461	+	0.360903i
$239$	16.2391			1.05042			0.525210	−	0.850973i	$-0.323987\pi$
$239$	16.2391			1.05042			0.525210	+	0.850973i	$0.323987\pi$
$240$	5.38401	+	3.15380i	0.347536	+	0.203577i
$241$	−11.6202	−	20.1267i	−0.748520	−	1.29647i	−0.948532	−	0.316681i	$-0.897431\pi$
$241$	−11.6202	−	20.1267i	−0.748520	−	1.29647i	0.200012	−	0.979793i	$-0.435902\pi$
$242$	8.08352	+	2.20852i	0.519628	+	0.141969i
$243$	12.9511	−	8.67582i	0.830811	−	0.556554i
$244$	26.7849	+	0.262756i	1.71473	+	0.0168213i
$245$	1.90021	−	3.29127i	0.121400	−	0.210271i
$246$	1.33164	+	4.80741i	0.0849020	+	0.306509i
$247$	−16.3236	+	18.8589i	−1.03865	+	1.19996i
$248$	7.38919	−	7.17487i	0.469214	−	0.455605i
$249$	7.55546	−	13.4987i	0.478808	−	0.855448i
$250$	−11.2899	−	3.08454i	−0.714034	−	0.195083i
$251$	−20.2687	+	11.7022i	−1.27935	+	0.738634i	−0.976729	−	0.214476i	$-0.931195\pi$
$251$	−20.2687	+	11.7022i	−1.27935	+	0.738634i	−0.302623	+	0.953110i	$0.597862\pi$
$252$	−20.0947	+	0.338505i	−1.26585	+	0.0213238i
$253$	2.75685	−	1.59167i	0.173322	−	0.100067i
$254$	26.7910	−	7.03797i	1.68102	−	0.441602i
$255$	2.60552	−	0.0347251i	0.163164	−	0.00217457i
$256$	−8.53740	+	13.5319i	−0.533588	+	0.845745i
$257$	22.5800	−	13.0366i	1.40850	−	0.813200i	0.413260	−	0.910613i	$-0.364390\pi$
$257$	22.5800	−	13.0366i	1.40850	−	0.813200i	0.995244	+	0.0974124i	$0.0310566\pi$
$258$	−12.1857	+	3.37539i	−0.758647	+	0.210143i
$259$	−3.72909			−0.231714
$260$	5.24083	−	8.87518i	0.325023	−	0.550415i
$261$	−9.89843	+	18.2513i	−0.612698	+	1.12972i
$262$	18.2802	+	18.4604i	1.12935	+	1.14049i
$263$	13.1646	−	22.8018i	0.811766	−	1.40602i	−0.0998617	−	0.995001i	$-0.531840\pi$
$263$	13.1646	−	22.8018i	0.811766	−	1.40602i	0.911627	−	0.411018i	$-0.134827\pi$
$264$	−10.6638	+	2.84150i	−0.656310	+	0.174882i
$265$	9.37269			0.575760
$266$	1.38306	+	20.6019i	0.0848011	+	1.26318i
$267$	−9.35200	+	0.124639i	−0.572333	+	0.00762778i
$268$	0.253661	−	25.8578i	0.0154948	−	1.57952i
$269$	6.02342	−	10.4329i	0.367255	−	0.636104i	−0.621881	−	0.783112i	$-0.713631\pi$
$269$	6.02342	−	10.4329i	0.367255	−	0.636104i	0.989135	+	0.147008i	$0.0469644\pi$
$270$	4.84102	+	4.51279i	0.294615	+	0.274640i
$271$	−9.65859	−	5.57639i	−0.586717	−	0.338741i	0.177081	−	0.984196i	$-0.443335\pi$
$271$	−9.65859	−	5.57639i	−0.586717	−	0.338741i	−0.763798	+	0.645455i	$0.776668\pi$
$272$	−0.131081	+	6.68043i	−0.00794793	+	0.405060i
$273$	0.442408	+	33.1951i	0.0267758	+	2.00906i
$274$	17.4957	−	4.59610i	1.05695	−	0.277661i
$275$	8.17201	−	4.71811i	0.492790	−	0.284513i
$276$	2.43269	−	4.24797i	0.146431	−	0.255698i
$277$			29.5643i			1.77635i	0.459508	+	0.888173i	$0.348026\pi$
$277$			29.5643i			1.77635i	−0.459508	+	0.888173i	$0.651974\pi$
$278$	0.508967	+	1.93745i	0.0305258	+	0.116201i
$279$	9.31173	−	5.71230i	0.557479	−	0.341987i
$280$	−2.08689	−	8.27345i	−0.124715	−	0.494433i
$281$	−12.1436	+	7.01110i	−0.724425	+	0.418247i	−0.816379	−	0.577516i	$-0.804022\pi$
$281$	−12.1436	+	7.01110i	−0.724425	+	0.418247i	0.0919540	+	0.995763i	$0.470689\pi$
$282$	−6.23004	+	24.0595i	−0.370993	+	1.43272i
$283$	−8.67618	+	15.0276i	−0.515745	+	0.893297i	0.484088	+	0.875019i	$0.339152\pi$
$283$	−8.67618	+	15.0276i	−0.515745	+	0.893297i	−0.999833	+	0.0182774i	$0.994182\pi$
$284$	−1.56927	+	0.885608i	−0.0931190	+	0.0525512i
$285$	4.38110	−	5.20001i	0.259514	−	0.308022i
$286$	4.63173	+	17.6313i	0.273880	+	1.04256i
$287$	3.41076	−	5.90760i	0.201331	−	0.348715i
$288$	−11.9744	+	12.0255i	−0.705599	+	0.708611i
$289$	−7.10484	−	12.3059i	−0.417931	−	0.723879i
$290$	−8.50330	−	2.32321i	−0.499331	−	0.136424i
$291$	5.70443	−	3.39561i	0.334399	−	0.199054i
$292$	−5.01861	+	2.83222i	−0.293692	+	0.165743i
$293$	13.8403			0.808556			0.404278	−	0.914636i	$-0.367523\pi$
$293$	13.8403			0.808556			0.404278	+	0.914636i	$0.367523\pi$
$294$	7.37014	+	7.24704i	0.429836	+	0.422656i
$295$	5.86349	−	3.38529i	0.341386	−	0.197099i
$296$	−2.25911	+	2.19359i	−0.131308	+	0.127500i
$297$	−11.6959	+	0.467855i	−0.678668	+	0.0271477i
$298$	13.7741	−	13.6397i	0.797915	−	0.790126i
$299$	−7.00282	−	4.04308i	−0.404984	−	0.233817i
$300$	7.21110	−	12.5921i	0.416333	−	0.727003i
$301$	14.9744	+	8.64547i	0.863110	+	0.498317i
$302$	0.814521	−	2.98127i	0.0468704	−	0.171553i
$303$	−0.184133	−	13.8160i	−0.0105782	−	0.793710i
$304$	12.9567	+	11.6672i	0.743117	+	0.669162i
$305$			12.0622i			0.690678i
$306$	−1.68495	+	6.88381i	−0.0963224	+	0.393521i
$307$	−10.5347	+	18.2467i	−0.601249	+	1.04139i	0.391383	+	0.920228i	$0.371997\pi$
$307$	−10.5347	+	18.2467i	−0.601249	+	1.04139i	−0.992632	+	0.121166i	$0.961337\pi$
$308$	12.9947	+	7.67342i	0.740441	+	0.437234i
$309$	−5.75513	+	10.2822i	−0.327398	+	0.584936i
$310$	3.26342	+	3.29559i	0.185350	+	0.187177i
$311$	−27.6195			−1.56616			−0.783080	−	0.621922i	$-0.786352\pi$
$311$	−27.6195			−1.56616			−0.783080	+	0.621922i	$0.786352\pi$
$312$	19.7946	+	19.8496i	1.12065	+	1.12376i
$313$	−0.873467	−	1.51289i	−0.0493713	−	0.0855135i	0.840284	−	0.542147i	$-0.182388\pi$
$313$	−0.873467	−	1.51289i	−0.0493713	−	0.0855135i	−0.889655	+	0.456633i	$0.849055\pi$
$314$	−11.5441	−	11.6579i	−0.651470	−	0.657892i
$315$	−0.241190	−	9.04696i	−0.0135895	−	0.509739i
$316$	11.3386	+	20.0917i	0.637847	+	1.13024i
$317$	9.49625	+	16.4480i	0.533362	+	0.923811i	0.999241	+	0.0389620i	$0.0124051\pi$
$317$	9.49625	+	16.4480i	0.533362	+	0.923811i	−0.465878	+	0.884849i	$0.654262\pi$
$318$	−6.39009	+	24.6776i	−0.358338	+	1.38385i
$319$	13.5018	−	7.79528i	0.755957	−	0.436452i
$320$	−6.13101	−	3.78454i	−0.342734	−	0.211562i
$321$	14.1227	−	25.2319i	0.788253	−	1.40831i
$322$	−6.47438	+	1.70081i	−0.360803	+	0.0947826i
$323$	7.15038	+	1.37414i	0.397858	+	0.0764592i
$324$	−15.1824	+	9.66933i	−0.843464	+	0.537185i
$325$	−20.7581	−	11.9847i	−1.15145	−	0.664792i
$326$	18.1227	+	4.95135i	1.00372	+	0.274230i
$327$	8.85578	+	14.8772i	0.489726	+	0.822712i
$328$	−1.40881	−	5.58521i	−0.0777885	−	0.308392i
$329$	29.4325	−	16.9928i	1.62266	−	0.936845i
$330$	−1.32660	−	4.78925i	−0.0730272	−	0.263639i
$331$	14.7327			0.809784			0.404892	−	0.914365i	$-0.367309\pi$
$331$	14.7327			0.809784			0.404892	+	0.914365i	$0.367309\pi$
$332$	−9.08255	+	15.3810i	−0.498470	+	0.844142i
$333$	−2.84690	+	1.74643i	−0.156009	+	0.0957040i
$334$	−2.79516	−	10.6402i	−0.152944	−	0.582204i
$335$	11.6447			0.636215
$336$	23.2062	+	0.146024i	1.26600	+	0.00796624i
$337$	−7.30511	+	12.6528i	−0.397934	+	0.689243i	−0.993471	−	0.114086i	$-0.963606\pi$
$337$	−7.30511	+	12.6528i	−0.397934	+	0.689243i	0.595536	+	0.803328i	$0.296940\pi$
$338$	19.8397	−	19.6461i	1.07914	−	1.06860i
$339$	−2.04008	+	3.64485i	−0.110802	+	0.197961i
$340$	−3.00871	−	0.0295150i	−0.163170	−	0.00160068i
$341$	−8.20295			−0.444215
$342$	10.7043	+	15.0804i	0.578823	+	0.815453i
$343$			9.31265i			0.502836i
$344$	14.1572	−	3.57100i	0.763305	−	0.192536i
$345$	1.92357	+	1.07665i	0.103561	+	0.0579650i
$346$	−17.0481	+	16.8817i	−0.916513	+	0.907567i
$347$	−24.1056	−	13.9174i	−1.29405	−	0.747123i	−0.314684	−	0.949196i	$-0.601899\pi$
$347$	−24.1056	−	13.9174i	−1.29405	−	0.747123i	−0.979370	+	0.202074i	$0.935232\pi$
$348$	11.9142	−	20.8047i	0.638669	−	1.11525i
$349$		−	3.35519i		−	0.179599i	−0.995960	−	0.0897995i	$-0.971377\pi$
$349$		−	3.35519i		−	0.179599i	0.995960	−	0.0897995i	$-0.0286226\pi$
$350$	−19.1917	+	5.04164i	−1.02584	+	0.269487i
$351$	15.8839	+	25.1349i	0.847822	+	1.34160i
$352$	12.3861	−	2.99534i	0.660180	−	0.159652i
$353$			8.80445i			0.468614i	0.972163	+	0.234307i	$0.0752820\pi$
$353$			8.80445i			0.468614i	−0.972163	+	0.234307i	$0.924718\pi$
$354$	4.91562	+	17.7462i	0.261262	+	0.943198i
$355$	−0.405713	−	0.702715i	−0.0215330	−	0.0372963i
$356$	10.7992	+	0.105939i	0.572357	+	0.00561474i
$357$	8.32756	−	4.95705i	0.440741	−	0.262355i
$358$	−0.640058	+	2.34271i	−0.0338281	+	0.123816i
$359$	−4.26344	+	7.38450i	−0.225016	+	0.389739i	−0.956324	−	0.292308i	$-0.905577\pi$
$359$	−4.26344	+	7.38450i	−0.225016	+	0.389739i	0.731308	+	0.682047i	$0.238910\pi$
$360$	−5.46788	−	5.33885i	−0.288183	−	0.281382i
$361$	14.9224	−	11.7611i	0.785388	−	0.619003i
$362$	25.9780	−	6.82440i	1.36537	−	0.358683i
$363$	−8.95571	−	5.01265i	−0.470053	−	0.263096i
$364$	0.376031	−	38.3320i	0.0197094	−	2.00914i
$365$	−1.29749	−	2.24732i	−0.0679138	−	0.117630i
$366$	−31.7588	−	8.22372i	−1.66006	−	0.429861i
$367$	−0.625884	+	0.361354i	−0.0326709	+	0.0188625i	−0.516246	−	0.856440i	$-0.672671\pi$
$367$	−0.625884	+	0.361354i	−0.0326709	+	0.0188625i	0.483576	+	0.875303i	$0.339338\pi$
$368$	−2.92175	+	4.83884i	−0.152307	+	0.252242i
$369$	−0.162822	−	6.10739i	−0.00847615	−	0.317938i
$370$	−0.997732	−	1.00757i	−0.0518696	−	0.0523810i
$371$	30.1886	−	17.4294i	1.56731	−	0.904889i
$372$	−10.9020	+	6.34549i	−0.565241	+	0.328998i
$373$		−	12.3012i		−	0.636934i	−0.947934	−	0.318467i	$-0.896832\pi$
$373$		−	12.3012i		−	0.636934i	0.947934	−	0.318467i	$-0.103168\pi$
$374$	3.78136	−	3.74445i	0.195529	−	0.193621i
$375$	12.5080	+	7.00093i	0.645910	+	0.361526i
$376$	7.83460	−	27.6077i	0.404039	−	1.42376i
$377$	−34.2967	−	19.8012i	−1.76637	−	1.01981i
$378$	23.9844	+	5.53298i	1.23363	+	0.284586i
$379$	−26.6862			−1.37078			−0.685389	−	0.728177i	$-0.740368\pi$
$379$	−26.6862			−1.37078			−0.685389	+	0.728177i	$0.740368\pi$
$380$	−5.19641	+	5.88581i	−0.266570	+	0.301936i
$381$	−33.9224	+	0.452102i	−1.73790	+	0.0231619i
$382$	−18.4185	−	5.03218i	−0.942373	−	0.257469i
$383$	−9.35056	+	16.1956i	−0.477791	+	0.827559i	−0.999676	−	0.0254572i	$-0.991896\pi$
$383$	−9.35056	+	16.1956i	−0.477791	+	0.827559i	0.521885	+	0.853016i	$0.325229\pi$
$384$	14.1444	−	13.5623i	0.721804	−	0.692098i
$385$	−3.39787	+	5.88528i	−0.173171	+	0.299942i
$386$	−18.5797	+	18.3983i	−0.945680	+	0.936448i
$387$	15.4808	−	0.412715i	0.786934	−	0.0209795i
$388$	−6.67585	+	3.76748i	−0.338915	+	0.191265i
$389$	15.6849	+	27.1671i	0.795258	+	1.37743i	0.922675	+	0.385579i	$0.125998\pi$
$389$	15.6849	+	27.1671i	0.795258	+	1.37743i	−0.127416	+	0.991849i	$0.540668\pi$
$390$	−8.85067	+	9.00102i	−0.448171	+	0.455784i
$391$			2.36053i			0.119377i
$392$	−8.31444	−	8.56280i	−0.419943	−	0.432487i
$393$	−16.2751	−	27.3413i	−0.820972	−	1.37919i
$394$	−10.4042	−	2.84257i	−0.524157	−	0.143206i
$395$	−8.99701	+	5.19443i	−0.452689	+	0.261360i
$396$	13.5142	−	0.227654i	0.679114	−	0.0114400i
$397$	4.65546	+	2.68783i	0.233651	+	0.134899i	0.612255	−	0.790660i	$-0.290262\pi$
$397$	4.65546	+	2.68783i	0.233651	+	0.134899i	−0.378604	+	0.925559i	$0.623596\pi$
$398$	−7.19858	+	1.89106i	−0.360832	+	0.0947903i
$399$	4.44123	−	24.8958i	0.222340	−	1.24635i
$400$	−8.66081	+	14.3435i	−0.433040	+	0.717177i
$401$	1.74921	+	1.00991i	0.0873515	+	0.0504324i	0.543039	−	0.839707i	$-0.317273\pi$
$401$	1.74921	+	1.00991i	0.0873515	+	0.0504324i	−0.455688	+	0.890140i	$0.650607\pi$
$402$	−7.93906	+	30.6595i	−0.395964	+	1.52916i
$403$	10.4184	+	18.0451i	0.518976	+	0.898892i
$404$	−0.156507	+	15.9540i	−0.00778650	+	0.793743i
$405$	−4.42108	−	6.79376i	−0.219685	−	0.337585i
$406$	−31.7086	+	8.32982i	−1.57367	+	0.413402i
$407$	2.50791			0.124312
$408$	2.12898	−	7.90160i	0.105400	−	0.391188i
$409$	−9.99301	−	17.3084i	−0.494123	−	0.855846i	0.505854	−	0.862619i	$-0.331177\pi$
$409$	−9.99301	−	17.3084i	−0.494123	−	0.855846i	−0.999977	+	0.00677328i	$0.997844\pi$
$410$	2.50875	−	0.659045i	0.123898	−	0.0325479i
$411$	−22.1528	+	0.295242i	−1.09272	+	0.0145632i
$412$	6.91834	−	11.7160i	0.340842	−	0.577205i
$413$	12.5905	−	21.8074i	0.619539	−	1.07307i
$414$	−4.14619	+	4.33058i	−0.203774	+	0.212837i
$415$	−6.96604	−	4.02185i	−0.341950	−	0.197425i
$416$	−22.3205	−	23.4430i	−1.09435	−	1.14939i
$417$	−0.0326948	−	2.45318i	−0.00160107	−	0.120133i
$418$	−0.930146	−	13.8553i	−0.0454949	−	0.677685i
$419$		−	11.3318i		−	0.553596i	−0.960928	−	0.276798i	$-0.910727\pi$
$419$		−	11.3318i		−	0.553596i	0.960928	−	0.276798i	$-0.0892733\pi$
$420$	0.0367554	+	10.4502i	0.00179348	+	0.509917i
$421$	−8.94068	−	5.16191i	−0.435742	−	0.251576i	0.266048	−	0.963960i	$-0.414282\pi$
$421$	−8.94068	−	5.16191i	−0.435742	−	0.251576i	−0.701790	+	0.712384i	$0.747615\pi$
$422$	−1.01067	+	1.00081i	−0.0491989	+	0.0487186i
$423$	14.5114	−	26.7569i	0.705568	−	1.30096i
$424$	8.03588	−	28.3169i	0.390257	−	1.37519i
$425$			6.99721i			0.339415i
$426$	2.12681	−	0.589118i	0.103044	−	0.0285428i
$427$	22.4307	+	38.8512i	1.08550	+	1.88014i
$428$	−16.9772	+	28.7503i	−0.820622	+	1.38970i
$429$	−0.297531	−	22.3246i	−0.0143649	−	1.07784i
$430$	1.67053	+	6.35909i	0.0805599	+	0.306662i
$431$	−12.5941	−	21.8137i	−0.606639	−	1.05073i	−0.991790	−	0.127876i	$-0.959184\pi$
$431$	−12.5941	−	21.8137i	−0.606639	−	1.05073i	0.385152	−	0.922853i	$-0.374149\pi$
$432$	17.7847	−	10.7566i	0.855666	−	0.517528i
$433$	−2.27451	−	3.93956i	−0.109306	−	0.189323i	0.806183	−	0.591666i	$-0.201529\pi$
$433$	−2.27451	−	3.93956i	−0.109306	−	0.189323i	−0.915489	+	0.402342i	$0.868196\pi$
$434$	16.6396	+	4.54617i	0.798728	+	0.218223i
$435$	9.42078	+	5.27296i	0.451692	+	0.252819i
$436$	−9.82562	−	17.4107i	−0.470562	−	0.833821i
$437$	4.65735	+	4.03124i	0.222791	+	0.192840i
$438$	6.80164	−	1.88403i	0.324995	−	0.0900224i
$439$	5.91049	+	3.41242i	0.282092	+	0.162866i	0.634370	−	0.773029i	$-0.281260\pi$
$439$	5.91049	+	3.41242i	0.282092	+	0.162866i	−0.352278	+	0.935895i	$0.614593\pi$
$440$	1.40349	+	5.56411i	0.0669086	+	0.265258i
$441$	−6.61958	−	10.7907i	−0.315218	−	0.513843i
$442$	−13.0398	−	3.56264i	−0.620239	−	0.169457i
$443$	−13.0931	+	7.55928i	−0.622070	+	0.359152i	−0.777675	−	0.628667i	$-0.783601\pi$
$443$	−13.0931	+	7.55928i	−0.622070	+	0.359152i	0.155604	+	0.987819i	$0.450268\pi$
$444$	3.33309	−	1.94002i	0.158181	−	0.0920693i
$445$			4.86325i			0.230540i
$446$	−3.10136	−	3.13193i	−0.146854	−	0.148301i
$447$	−20.4006	+	12.1436i	−0.964915	+	0.574374i
$448$	−26.7851	−	0.788477i	−1.26548	−	0.0372520i
$449$		−	36.3902i		−	1.71736i	−0.512511	−	0.858681i	$-0.671285\pi$
$449$		−	36.3902i		−	1.71736i	0.512511	−	0.858681i	$-0.328715\pi$
$450$	−12.2904	+	12.8369i	−0.579373	+	0.605139i
$451$	−2.29382	+	3.97301i	−0.108012	+	0.187082i
$452$	2.45242	−	4.15309i	0.115352	−	0.195345i
$453$	−1.84871	+	3.30294i	−0.0868598	+	0.155185i
$454$	0.958680	−	3.50891i	0.0449931	−	0.164681i
$455$	17.2622			0.809264
$456$	−11.9541	−	17.6946i	−0.559803	−	0.828626i
$457$	28.0694			1.31303			0.656516	−	0.754312i	$-0.272029\pi$
$457$	28.0694			1.31303			0.656516	+	0.754312i	$0.272029\pi$
$458$	0.617791	−	2.26121i	0.0288675	−	0.105659i
$459$	4.03598	−	7.68438i	0.188384	−	0.358676i
$460$	−2.19179	−	1.29426i	−0.102193	−	0.0603453i
$461$	16.8613	−	29.2046i	0.785309	−	1.36020i	−0.143505	−	0.989650i	$-0.545837\pi$
$461$	16.8613	−	29.2046i	0.785309	−	1.36020i	0.928814	−	0.370546i	$-0.120829\pi$
$462$	−13.1789	−	12.9588i	−0.613139	−	0.602898i
$463$		−	22.8946i		−	1.06400i	−0.846744	−	0.532001i	$-0.821440\pi$
$463$		−	22.8946i		−	1.06400i	0.846744	−	0.532001i	$-0.178560\pi$
$464$	−14.3094	+	23.6985i	−0.664298	+	1.10017i
$465$	−2.90547	−	4.88103i	−0.134738	−	0.226352i
$466$	6.71552	+	6.78172i	0.311091	+	0.314157i
$467$		−	1.41380i		−	0.0654231i	−0.999465	−	0.0327115i	$-0.989586\pi$
$467$		−	1.41380i		−	0.0654231i	0.999465	−	0.0327115i	$-0.0104143\pi$
$468$	−17.6648	−	29.4399i	−0.816558	−	1.36086i
$469$	37.5064	−	21.6543i	1.73188	−	0.999903i
$470$	12.4661	+	3.40590i	0.575018	+	0.157102i
$471$	10.2779	+	17.2662i	0.473579	+	0.795586i
$472$	−5.20050	−	20.6173i	−0.239372	−	0.948990i
$473$	−10.0707	−	5.81430i	−0.463050	−	0.267342i
$474$	−7.54259	−	27.2299i	−0.346443	−	1.25071i
$475$	13.8056	+	11.9496i	0.633443	+	0.548286i
$476$	−9.74568	+	5.49992i	−0.446693	+	0.252088i
$477$	14.8842	−	27.4443i	0.681501	−	1.25659i
$478$	22.1536	+	6.05265i	1.01328	+	0.276842i
$479$	−10.2894	−	17.8218i	−0.470136	−	0.814299i	0.529281	−	0.848446i	$-0.322462\pi$
$479$	−10.2894	−	17.8218i	−0.470136	−	0.814299i	−0.999417	+	0.0341477i	$0.989128\pi$
$480$	6.16946	+	6.30919i	0.281596	+	0.287974i
$481$	−3.18523	−	5.51698i	−0.145234	−	0.251553i
$482$	−8.35073	−	31.7882i	−0.380365	−	1.44791i
$483$	8.19778	−	0.109256i	0.373012	−	0.00497132i
$484$	10.2045	+	6.02580i	0.463840	+	0.273900i
$485$	−1.72595	−	2.98943i	−0.0783713	−	0.135743i
$486$	20.9017	−	7.00854i	0.948120	−	0.317914i
$487$			1.96933i			0.0892388i	0.999004	+	0.0446194i	$0.0142075\pi$
$487$			1.96933i			0.0892388i	−0.999004	+	0.0446194i	$0.985792\pi$
$488$	36.4424	+	10.3418i	1.64967	+	0.468150i
$489$	−20.0780	−	11.2380i	−0.907961	−	0.508200i
$490$	3.81902	−	3.78174i	0.172526	−	0.170842i
$491$	−33.2196	−	19.1793i	−1.49918	−	0.865551i	−0.499180	−	0.866499i	$-0.666365\pi$
$491$	−33.2196	−	19.1793i	−1.49918	−	0.865551i	−1.00000		0.000947089i	$0.999699\pi$
$492$	0.0248127	+	7.05467i	0.00111864	+	0.318049i
$493$			11.5608i			0.520674i
$494$	−29.2980	+	19.6434i	−1.31818	+	0.883800i
$495$	0.162206	+	6.08431i	0.00729064	+	0.273470i
$496$	12.7547	−	7.03395i	0.572701	−	0.315834i
$497$	−2.61353	−	1.50892i	−0.117233	−	0.0676844i
$498$	15.3385	−	15.5991i	0.687336	−	0.699012i
$499$	−8.11222	+	14.0508i	−0.363153	+	0.628999i	−0.988478	−	0.151365i	$-0.951633\pi$
$499$	−8.11222	+	14.0508i	−0.363153	+	0.628999i	0.625325	+	0.780364i	$0.284966\pi$
$500$	−14.2521	−	8.41594i	−0.637374	−	0.376372i
$501$	0.179554	+	13.4724i	0.00802189	+	0.601904i
$502$	−32.0125	+	8.40967i	−1.42879	+	0.375342i
$503$	−6.88557	−	11.9262i	−0.307012	−	0.531761i	0.670695	−	0.741733i	$-0.265996\pi$
$503$	−6.88557	−	11.9262i	−0.307012	−	0.531761i	−0.977707	+	0.209972i	$0.932663\pi$
$504$	−27.5396	−	7.02792i	−1.22671	−	0.313049i
$505$	−7.18464			−0.319712
$506$	4.35418	−	1.14384i	0.193567	−	0.0508499i
$507$	−29.3842	+	17.4912i	−1.30500	+	0.776811i
$508$	39.1719	+	0.384270i	1.73797	+	0.0170492i
$509$	0.384202	+	0.665458i	0.0170295	+	0.0294959i	0.874415	−	0.485180i	$-0.161246\pi$
$509$	0.384202	+	0.665458i	0.0170295	+	0.0294959i	−0.857385	+	0.514675i	$0.827912\pi$
$510$	3.56742	+	0.923758i	0.157968	+	0.0409047i
$511$	−8.35821	−	4.82561i	−0.369745	−	0.213473i
$512$	−16.6905	+	15.2784i	−0.737622	+	0.675214i
$513$	−8.26884	−	21.0862i	−0.365078	−	0.930977i
$514$	35.6630	−	9.36864i	1.57303	−	0.413233i
$515$	5.30616	+	3.06351i	0.233817	+	0.134995i
$516$	−17.8819	+	0.0628944i	−0.787209	+	0.00276877i
$517$	−19.7941	+	11.4281i	−0.870542	+	0.502608i
$518$	−5.08727	−	1.38991i	−0.223522	−	0.0610691i
$519$	25.2496	−	15.0301i	1.10834	−	0.659746i
$520$	10.4576	−	10.1543i	0.458595	−	0.445294i
$521$			36.0874i			1.58102i	0.612452	+	0.790508i	$0.290183\pi$
$521$			36.0874i			1.58102i	−0.612452	+	0.790508i	$0.709817\pi$
$522$	−20.3062	+	21.2093i	−0.888778	+	0.928304i
$523$	1.69398	+	2.93407i	0.0740728	+	0.128298i	0.900683	−	0.434478i	$-0.143067\pi$
$523$	1.69398	+	2.93407i	0.0740728	+	0.128298i	−0.826610	+	0.562775i	$0.809734\pi$
$524$	18.0575	+	31.9973i	0.788846	+	1.39781i
$525$	24.3003	−	0.323862i	1.06055	−	0.0141345i
$526$	26.4581	−	26.1998i	1.15363	−	1.14237i
$527$	3.04136	−	5.26778i	0.132484	−	0.229468i
$528$	−15.6068	−	0.0982045i	−0.679197	−	0.00427380i
$529$	10.5015	−	18.1892i	0.456588	−	0.790834i
$530$	12.7864	+	3.49340i	0.555404	+	0.151744i
$531$	−0.601042	−	22.5449i	−0.0260830	−	0.978366i
$532$	−5.79197	+	28.6209i	−0.251114	+	1.24087i
$533$	11.6533			0.504760
$534$	−12.8046	−	3.31565i	−0.554109	−	0.143482i
$535$	−13.0210	−	7.51767i	−0.562946	−	0.325017i
$536$	9.98380	−	35.1810i	0.431234	−	1.51959i
$537$	1.45273	−	2.59548i	0.0626899	−	0.112003i
$538$	12.1058	−	11.9876i	0.521918	−	0.516823i
$539$			9.50581i			0.409444i
$540$	4.92217	+	7.96077i	0.211816	+	0.342577i
$541$	−30.4170	+	17.5613i	−1.30773	+	0.755018i	−0.981717	−	0.190347i	$-0.939039\pi$
$541$	−30.4170	+	17.5613i	−1.30773	+	0.755018i	−0.326013	+	0.945365i	$0.605705\pi$
$542$	−11.0979	−	11.2073i	−0.476697	−	0.481397i
$543$	−32.8931	+	0.438383i	−1.41158	+	0.0188128i
$544$	−2.66876	+	9.06467i	−0.114422	+	0.388645i
$545$	7.79647	−	4.50129i	0.333964	−	0.192814i
$546$	−11.7690	+	45.4501i	−0.503666	+	1.94509i
$547$	−14.3236	−	24.8092i	−0.612432	−	1.06076i	−0.990829	−	0.135120i	$-0.956858\pi$
$547$	−14.3236	−	24.8092i	−0.612432	−	1.06076i	0.378397	−	0.925643i	$-0.376475\pi$
$548$	25.5809	+	0.250945i	1.09276	+	0.0107198i
$549$	35.3194	+	19.1552i	1.50739	+	0.817524i
$550$	12.9069	−	3.39063i	0.550352	−	0.144577i
$551$	22.8096	+	19.7432i	0.971722	+	0.841089i
$552$	4.90202	−	4.88843i	0.208644	−	0.208065i
$553$	−19.3190	+	33.4616i	−0.821529	+	1.42293i
$554$	−11.0192	+	40.3320i	−0.468163	+	1.71354i
$555$	0.888296	+	1.49229i	0.0377061	+	0.0633441i
$556$	−0.0277894	+	2.83280i	−0.00117853	+	0.120138i
$557$	8.37521	+	14.5063i	0.354869	+	0.614651i	0.987096	−	0.160132i	$-0.0511921\pi$
$557$	8.37521	+	14.5063i	0.354869	+	0.614651i	−0.632226	+	0.774784i	$0.717859\pi$
$558$	14.8323	−	4.32212i	0.627901	−	0.182970i
$559$			29.5384i			1.24934i
$560$	0.236726	−	12.0646i	0.0100035	−	0.509822i
$561$	−5.60049	+	3.33374i	−0.236453	+	0.140751i
$562$	−19.1796	+	5.03847i	−0.809044	+	0.212535i
$563$			14.0058i			0.590276i	0.955455	+	0.295138i	$0.0953656\pi$
$563$			14.0058i			0.590276i	−0.955455	+	0.295138i	$0.904634\pi$
$564$	−17.4666	+	30.5003i	−0.735476	+	1.28429i
$565$	1.88093	+	1.08596i	0.0791313	+	0.0456865i
$566$	−17.4373	+	17.2670i	−0.732942	+	0.725788i
$567$	−26.8735	−	13.6607i	−1.12858	−	0.573696i
$568$	−2.47090	+	0.623259i	−0.103677	+	0.0261514i
$569$		−	36.3905i		−	1.52557i	−0.646654	−	0.762784i	$-0.723832\pi$
$569$		−	36.3905i		−	1.52557i	0.646654	−	0.762784i	$-0.276168\pi$
$570$	7.91491	−	5.46099i	0.331519	−	0.228736i
$571$	−38.5836			−1.61467			−0.807337	−	0.590091i	$-0.799092\pi$
$571$	−38.5836			−1.61467			−0.807337	+	0.590091i	$0.799092\pi$
$572$	−0.252890	+	25.7792i	−0.0105739	+	1.07788i
$573$	20.4058	+	11.4215i	0.852465	+	0.477138i
$574$	6.85489	−	6.78797i	0.286117	−	0.283324i
$575$	−2.95971	+	5.12637i	−0.123429	+	0.213785i
$576$	−20.8178	+	11.9423i	−0.867410	+	0.497595i
$577$	−17.1512			−0.714015			−0.357008	−	0.934101i	$-0.616203\pi$
$577$	−17.1512			−0.714015			−0.357008	+	0.934101i	$0.616203\pi$
$578$	−5.10583	−	19.4360i	−0.212375	−	0.808433i
$579$	27.5179	−	16.3803i	1.14361	−	0.680741i
$580$	−10.7344	−	6.33872i	−0.445722	−	0.263201i
$581$	−29.9160			−1.24112
$582$	9.04767	−	2.50617i	0.375038	−	0.103884i
$583$	−20.3026	+	11.7217i	−0.840848	+	0.485464i
$584$	−7.90208	+	1.99322i	−0.326990	+	0.0824798i
$585$	13.1785	−	8.08436i	0.544863	−	0.334247i
$586$	18.8811	+	5.15855i	0.779970	+	0.213098i
$587$	19.9864	+	11.5392i	0.824928	+	0.476272i	0.852113	−	0.523358i	$-0.175321\pi$
$587$	19.9864	+	11.5392i	0.824928	+	0.476272i	−0.0271852	+	0.999630i	$0.508654\pi$
$588$	7.35333	+	12.6335i	0.303246	+	0.520997i
$589$	−5.19946	−	14.9968i	−0.214240	−	0.617931i
$590$	9.26082	−	2.43281i	0.381262	−	0.100157i
$591$	11.5268	+	6.45173i	0.474149	+	0.265389i
$592$	−3.89951	+	2.15051i	−0.160269	+	0.0883852i
$593$	−20.7612	+	11.9865i	−0.852562	+	0.492227i	−0.861514	−	0.507733i	$-0.830484\pi$
$593$	−20.7612	+	11.9865i	−0.852562	+	0.492227i	0.00895249	+	0.999960i	$0.497150\pi$
$594$	−16.1301	−	3.72107i	−0.661828	−	0.152677i
$595$	−2.51961	−	4.36410i	−0.103294	−	0.178910i
$596$	23.8747	−	13.4735i	0.977945	−	0.551897i
$597$	9.11475	−	0.121477i	0.373042	−	0.00497172i
$598$	−8.04640	−	8.12572i	−0.329042	−	0.332286i
$599$	14.2475	+	24.6774i	0.582138	+	1.00829i	0.995226	+	0.0976017i	$0.0311171\pi$
$599$	14.2475	+	24.6774i	0.582138	+	1.00829i	−0.413087	+	0.910691i	$0.635550\pi$
$600$	14.5308	−	14.4905i	0.593218	−	0.591574i
$601$	31.9927			1.30501			0.652505	−	0.757784i	$-0.273718\pi$
$601$	31.9927			1.30501			0.652505	+	0.757784i	$0.273718\pi$
$602$	17.2059	+	17.3755i	0.701261	+	0.708174i
$603$	18.4922	−	34.0968i	0.753059	−	1.38853i
$604$	2.22236	−	3.76350i	0.0904266	−	0.153135i
$605$	−2.66828	+	4.62160i	−0.108481	+	0.187895i
$606$	4.89833	−	18.9166i	0.198981	−	0.768436i
$607$		−	9.37060i		−	0.380341i	−0.981751	−	0.190170i	$-0.939096\pi$
$607$		−	9.37060i		−	0.380341i	0.981751	−	0.190170i	$-0.0609040\pi$
$608$	13.3271	+	20.7458i	0.540484	+	0.841354i
$609$	40.1490	−	0.535087i	1.62692	−	0.0216828i
$610$	−4.49582	+	16.4554i	−0.182031	+	0.666259i
$611$	50.2799	+	29.0291i	2.03411	+	1.17439i
$612$	−4.86438	+	8.76297i	−0.196631	+	0.354222i
$613$	−12.9392	−	7.47047i	−0.522610	−	0.301729i	0.215392	−	0.976528i	$-0.430897\pi$
$613$	−12.9392	−	7.47047i	−0.522610	−	0.301729i	−0.738002	+	0.674798i	$0.764231\pi$
$614$	−21.1726	+	20.9659i	−0.854455	+	0.846114i
$615$	−3.17654	+	0.0423354i	−0.128091	+	0.00170713i
$616$	14.8675	+	15.3116i	0.599028	+	0.616921i
$617$	26.6731	−	15.3997i	1.07382	−	0.619969i	0.144595	−	0.989491i	$-0.453812\pi$
$617$	26.6731	−	15.3997i	1.07382	−	0.619969i	0.929222	+	0.369522i	$0.120479\pi$
$618$	−11.6836	+	11.8821i	−0.469985	+	0.477968i
$619$	14.3745			0.577760			0.288880	−	0.957365i	$-0.406717\pi$
$619$	14.3745			0.577760			0.288880	+	0.957365i	$0.406717\pi$
$620$	3.22367	+	5.71223i	0.129466	+	0.229409i
$621$	6.20726	−	3.92266i	0.249089	−	0.157411i
$622$	−37.6789	−	10.2944i	−1.51079	−	0.412767i
$623$	9.04367	+	15.6641i	0.362327	+	0.627568i
$624$	19.6057	+	34.4570i	0.784857	+	1.37938i
$625$	−6.74552	+	11.6836i	−0.269821	+	0.467343i
$626$	−0.627710	−	2.38946i	−0.0250883	−	0.0955021i
$627$	−2.98684	+	16.7431i	−0.119283	+	0.668654i
$628$	−11.4034	−	20.2065i	−0.455047	−	0.806329i
$629$	−0.929840	+	1.61053i	−0.0370752	+	0.0642161i
$630$	3.04296	−	12.4319i	0.121234	−	0.495298i
$631$	15.0954	−	8.71533i	0.600938	−	0.346952i	−0.168472	−	0.985706i	$-0.553883\pi$
$631$	15.0954	−	8.71533i	0.600938	−	0.346952i	0.769411	+	0.638755i	$0.220550\pi$
$632$	7.97971	+	31.6355i	0.317416	+	1.25839i
$633$	1.49689	−	0.891036i	0.0594960	−	0.0354155i
$634$	6.82440	+	25.9780i	0.271032	+	1.03172i
$635$			17.6404i			0.700039i
$636$	−17.9153	+	31.2838i	−0.710388	+	1.24048i
$637$	20.9112	−	12.0731i	0.828532	−	0.478353i
$638$	21.3248	−	5.60202i	0.844259	−	0.221786i
$639$	−2.70192	+	0.0720325i	−0.106886	+	0.00284956i
$640$	−6.95343	−	7.44808i	−0.274858	−	0.294411i
$641$	−28.5631	−	16.4909i	−1.12818	−	0.651353i	−0.184701	−	0.982795i	$-0.559132\pi$
$641$	−28.5631	−	16.4909i	−1.12818	−	0.651353i	−0.943476	+	0.331442i	$0.892465\pi$
$642$	28.6709	−	29.1579i	1.13155	−	1.15077i
$643$	5.29581	−	9.17261i	0.208846	−	0.361732i	−0.742505	−	0.669840i	$-0.766363\pi$
$643$	5.29581	−	9.17261i	0.208846	−	0.361732i	0.951351	+	0.308108i	$0.0996958\pi$
$644$	−9.46637	−	0.0928637i	−0.373027	−	0.00365934i
$645$	−0.107310	−	8.05180i	−0.00422535	−	0.317039i
$646$	9.24248	+	4.53972i	0.363641	+	0.178613i
$647$	−23.7725			−0.934595			−0.467298	−	0.884100i	$-0.654772\pi$
$647$	−23.7725			−0.934595			−0.467298	+	0.884100i	$0.654772\pi$
$648$	−24.3159	+	7.53225i	−0.955221	+	0.295895i
$649$	−8.46744	+	14.6660i	−0.332376	+	0.575692i
$650$	−23.8516	−	24.0867i	−0.935535	−	0.944758i
$651$	−18.4350	−	10.3184i	−0.722525	−	0.404408i
$652$	22.8777	+	13.5094i	0.895961	+	0.529069i
$653$	−27.1994			−1.06440			−0.532198	−	0.846620i	$-0.678634\pi$
$653$	−27.1994			−1.06440			−0.532198	+	0.846620i	$0.678634\pi$
$654$	6.53613	+	23.5964i	0.255583	+	0.922693i
$655$	−14.3283	+	8.27247i	−0.559854	+	0.323232i
$656$	0.159808	−	8.14451i	0.00623947	−	0.317990i
$657$	−8.64087	+	0.230364i	−0.337113	+	0.00898734i
$658$	46.4857	−	12.2118i	1.81220	−	0.476064i
$659$	4.47087	−	2.58126i	0.174160	−	0.100551i	−0.410386	−	0.911912i	$-0.634606\pi$
$659$	4.47087	−	2.58126i	0.174160	−	0.100551i	0.584546	+	0.811361i	$0.301273\pi$
$660$	−0.0247189	−	7.02801i	−0.000962183	−	0.273565i
$661$	−8.55505	+	4.93926i	−0.332753	+	0.192115i	−0.657063	−	0.753836i	$-0.728201\pi$
$661$	−8.55505	+	4.93926i	−0.332753	+	0.192115i	0.324310	+	0.945951i	$0.394868\pi$
$662$	20.0986	+	5.49120i	0.781154	+	0.213421i
$663$	14.4467	+	8.08606i	0.561064	+	0.314037i
$664$	−18.1234	+	17.5977i	−0.703323	+	0.682924i
$665$	−12.9133	−	2.48164i	−0.500757	−	0.0962340i
$666$	−4.53471	+	1.32141i	−0.175716	+	0.0512037i
$667$	−4.89005	+	8.46982i	−0.189344	+	0.327953i
$668$	0.152615	−	15.5573i	0.00590483	−	0.601929i
$669$	2.76119	+	4.63864i	0.106754	+	0.179340i
$670$	15.8858	+	4.34021i	0.613722	+	0.167677i
$671$	−15.0852	−	26.1284i	−0.582359	−	1.00868i
$672$	31.6038	+	8.84864i	1.21914	+	0.341344i
$673$	−9.43154			−0.363559			−0.181779	−	0.983339i	$-0.558186\pi$
$673$	−9.43154			−0.363559			−0.181779	+	0.983339i	$0.558186\pi$
$674$	−14.6817	+	14.5384i	−0.565518	+	0.559997i
$675$	18.3999	−	11.6277i	0.708212	−	0.447552i
$676$	34.3881	−	19.4067i	1.32262	−	0.746413i
$677$	9.36875			0.360070			0.180035	−	0.983660i	$-0.442379\pi$
$677$	9.36875			0.360070			0.180035	+	0.983660i	$0.442379\pi$
$678$	−4.14162	+	4.21197i	−0.159058	+	0.161760i
$679$	−11.1183	−	6.41913i	−0.426679	−	0.246343i
$680$	−4.09353	−	1.16168i	−0.156980	−	0.0445482i
$681$	−2.17590	+	3.88751i	−0.0833807	+	0.148970i
$682$	−11.1906	−	3.05741i	−0.428509	−	0.117074i
$683$		−	25.7563i		−	0.985536i	−0.870161	−	0.492768i	$-0.835985\pi$
$683$		−	25.7563i		−	0.985536i	0.870161	−	0.492768i	$-0.164015\pi$
$684$	8.98220	+	24.5626i	0.343443	+	0.939174i
$685$			11.5200i			0.440155i
$686$	−3.47102	+	12.7044i	−0.132524	+	0.485058i
$687$	−1.40219	+	2.50518i	−0.0534969	+	0.0955787i
$688$	20.6444	+	0.405077i	0.787062	+	0.0154434i
$689$	51.5716	+	29.7749i	1.96472	+	1.13433i
$690$	2.22287	+	2.18574i	0.0846232	+	0.0832097i
$691$	22.7402			0.865077			0.432539	−	0.901615i	$-0.357618\pi$
$691$	22.7402			0.865077			0.432539	+	0.901615i	$0.357618\pi$
$692$	−29.5495	+	16.6761i	−1.12330	+	0.633929i
$693$	11.8368	+	19.2954i	0.449643	+	0.732971i
$694$	−27.6979	−	27.9709i	−1.05140	−	1.06176i
$695$	−1.27571			−0.0483904
$696$	24.0079	−	23.9413i	0.910016	−	0.907494i
$697$	−1.70093	−	2.94610i	−0.0644273	−	0.111591i
$698$	1.25055	−	4.57719i	0.0473340	−	0.173249i
$699$	−5.97893	−	10.0443i	−0.226144	−	0.379909i
$700$	−28.0607	−	0.275271i	−1.06059	−	0.0104043i
$701$	−6.13608	+	10.6280i	−0.231757	+	0.401414i	−0.958325	−	0.285680i	$-0.907781\pi$
$701$	−6.13608	+	10.6280i	−0.231757	+	0.401414i	0.726569	+	0.687094i	$0.241114\pi$
$702$	12.3008	+	40.2097i	0.464262	+	1.51762i
$703$	1.58964	+	4.58499i	0.0599544	+	0.172926i
$704$	18.0137	+	0.530271i	0.678916	+	0.0199853i
$705$	−13.8111	−	7.73032i	−0.520158	−	0.291141i
$706$	−3.28160	+	12.0111i	−0.123505	+	0.452046i
$707$	−23.1411	+	13.3605i	−0.870310	+	0.502474i
$708$	0.0915940	+	26.0417i	0.00344231	+	0.978708i
$709$	−12.7569	+	7.36520i	−0.479096	+	0.276606i	−0.720040	−	0.693933i	$-0.755876\pi$
$709$	−12.7569	+	7.36520i	−0.479096	+	0.276606i	0.240944	+	0.970539i	$0.422543\pi$
$710$	−0.291562	−	1.10987i	−0.0109421	−	0.0416527i
$711$	0.922246	+	34.5932i	0.0345869	+	1.29735i
$712$	14.6929	+	4.16961i	0.550641	+	0.156263i
$713$	4.45638	−	2.57289i	0.166893	−	0.0963556i
$714$	13.2082	−	3.65861i	0.494303	−	0.136920i
$715$	−11.6093			−0.434162
$716$	−1.74635	+	2.95739i	−0.0652642	+	0.110523i
$717$	−24.5439	−	13.7376i	−0.916608	−	0.513040i
$718$	−8.56860	+	8.48496i	−0.319777	+	0.316656i
$719$	−18.3375	+	31.7614i	−0.683872	+	1.18450i	0.289917	+	0.957052i	$0.406372\pi$
$719$	−18.3375	+	31.7614i	−0.683872	+	1.18450i	−0.973790	+	0.227450i	$0.926961\pi$
$720$	−5.46945	−	9.32133i	−0.203835	−	0.347385i
$721$	22.7876			0.848653
$722$	24.7409	−	10.4827i	0.920761	−	0.390126i
$723$	0.536430	+	40.2498i	0.0199501	+	1.49691i
$724$	37.9832	+	0.372609i	1.41163	+	0.0138479i
$725$	−14.4953	+	25.1067i	−0.538344	+	0.932439i
$726$	−10.3492	−	10.1763i	−0.384094	−	0.377678i
$727$	−3.83143	−	2.21208i	−0.142100	−	0.0820414i	0.427265	−	0.904127i	$-0.359477\pi$
$727$	−3.83143	−	2.21208i	−0.142100	−	0.0820414i	−0.569364	+	0.822085i	$0.692811\pi$
$728$	14.8001	−	52.1528i	0.548529	−	1.93291i
$729$	−26.9137	+	2.15663i	−0.996805	+	0.0798752i
$730$	−0.932432	−	3.54943i	−0.0345109	−	0.131370i
$731$	7.46767	−	4.31146i	0.276202	−	0.159465i
$732$	−40.2607	−	23.0561i	−1.48808	−	0.852178i
$733$		−	33.3684i		−	1.23249i	−0.787554	−	0.616246i	$-0.788653\pi$
$733$		−	33.3684i		−	1.23249i	0.787554	−	0.616246i	$-0.211347\pi$
$734$	−0.988523	+	0.259684i	−0.0364871	+	0.00958512i
$735$	−5.65627	+	3.36694i	−0.208635	+	0.124192i
$736$	−5.78943	+	5.51221i	−0.213401	+	0.203183i
$737$	−25.2240	+	14.5631i	−0.929138	+	0.536438i
$738$	2.05423	−	8.39247i	0.0756172	−	0.308931i
$739$	−9.06998	+	15.7097i	−0.333645	+	0.577889i	−0.983224	−	0.182405i	$-0.941612\pi$
$739$	−9.06998	+	15.7097i	−0.333645	+	0.577889i	0.649579	+	0.760294i	$0.274945\pi$
$740$	−0.985578	−	1.74641i	−0.0362306	−	0.0641994i
$741$	40.6255	−	14.6944i	1.49242	−	0.539813i
$742$	47.6800	−	12.5255i	1.75039	−	0.459825i
$743$	9.28618	−	16.0841i	0.340677	−	0.590070i	−0.643882	−	0.765125i	$-0.722677\pi$
$743$	9.28618	−	16.0841i	0.340677	−	0.590070i	0.984559	+	0.175055i	$0.0560105\pi$
$744$	−17.2377	+	4.59321i	−0.631966	+	0.168395i
$745$	6.17247	+	10.6910i	0.226142	+	0.391689i
$746$	4.58493	−	16.7815i	0.167866	−	0.614415i
$747$	−22.8388	+	14.0105i	−0.835627	+	0.512617i
$748$	6.55422	−	3.69883i	0.239646	−	0.135243i
$749$	−55.9192			−2.04324
$750$	14.4542	+	14.2128i	0.527793	+	0.518977i
$751$	36.1548	−	20.8740i	1.31931	−	0.761702i	0.335689	−	0.941973i	$-0.391031\pi$
$751$	36.1548	−	20.8740i	1.31931	−	0.761702i	0.983617	+	0.180271i	$0.0576976\pi$
$752$	20.9780	−	34.7427i	0.764990	−	1.26693i
$753$	40.5339	−	0.540216i	1.47714	−	0.0196866i
$754$	−39.4077	−	39.7962i	−1.43514	−	1.44929i
$755$	1.70448	+	0.984085i	0.0620326	+	0.0358145i
$756$	30.6576	+	16.4877i	1.11501	+	0.599651i
$757$	−1.99877	−	1.15399i	−0.0726466	−	0.0419425i	0.463237	−	0.886235i	$-0.346688\pi$
$757$	−1.99877	−	1.15399i	−0.0726466	−	0.0419425i	−0.535883	+	0.844292i	$0.680021\pi$
$758$	−36.4057	−	9.94651i	−1.32231	−	0.361274i
$759$	−5.51322	+	0.0734775i	−0.200117	+	0.00266706i
$760$	−9.28279	+	6.09269i	−0.336722	+	0.221005i
$761$			44.0208i			1.59575i	0.602822	+	0.797876i	$0.294043\pi$
$761$			44.0208i			1.59575i	−0.602822	+	0.797876i	$0.705957\pi$
$762$	−46.4460	−	12.0268i	−1.68256	−	0.435687i
$763$	16.7412	−	28.9965i	0.606070	−	1.04974i
$764$	−23.2512	−	13.7299i	−0.841199	−	0.496732i
$765$	−3.96737	−	2.15168i	−0.143441	−	0.0777940i
$766$	−18.7926	+	18.6092i	−0.679005	+	0.672377i
$767$	43.0172			1.55326
$768$	24.3509	−	13.2300i	0.878689	−	0.477395i
$769$	−6.76572	−	11.7186i	−0.243978	−	0.422582i	0.717866	−	0.696182i	$-0.245119\pi$
$769$	−6.76572	−	11.7186i	−0.243978	−	0.422582i	−0.961844	+	0.273599i	$0.911786\pi$
$770$	−6.82899	+	6.76232i	−0.246100	+	0.243697i
$771$	−45.1561	+	0.601818i	−1.62626	+	0.0216740i
$772$	−32.2040	+	18.1742i	−1.15905	+	0.654103i
$773$	−26.9539	−	46.6856i	−0.969465	−	1.67916i	−0.697107	−	0.716967i	$-0.745530\pi$
$773$	−26.9539	−	46.6856i	−0.969465	−	1.67916i	−0.272358	−	0.962196i	$-0.587803\pi$
$774$	21.2730	+	5.20699i	0.764641	+	0.187161i
$775$	13.2098	−	7.62670i	0.474511	−	0.273959i
$776$	−10.5115	+	2.65141i	−0.377341	+	0.0951802i
$777$	5.63617	+	3.15465i	0.202197	+	0.113173i
$778$	11.2719	+	42.9079i	0.404116	+	1.53832i
$779$	−8.71747	−	1.67530i	−0.312336	−	0.0600238i
$780$	−15.4291	+	8.98048i	−0.552449	+	0.321553i
$781$	1.75767	+	1.01479i	0.0628942	+	0.0363120i
$782$	−0.879820	+	3.22027i	−0.0314623	+	0.115157i
$783$	30.4004	−	19.2114i	1.08642	−	0.686560i
$784$	−8.15114	−	14.7805i	−0.291112	−	0.527873i
$785$	9.04845	−	5.22413i	0.322953	−	0.186457i
$786$	−12.0121	−	43.3655i	−0.428457	−	1.54679i
$787$	20.9623			0.747225			0.373613	−	0.927585i	$-0.378119\pi$
$787$	20.9623			0.747225			0.373613	+	0.927585i	$0.378119\pi$
$788$	−13.1341	−	7.75574i	−0.467882	−	0.276287i
$789$	−39.1865	+	23.3261i	−1.39508	+	0.830431i
$790$	−14.2099	+	3.73293i	−0.505566	+	0.132812i
$791$	8.07774			0.287211
$792$	18.5211	+	4.72646i	0.658119	+	0.167947i
$793$	−38.3188	+	66.3701i	−1.36074	+	2.35687i
$794$	5.34924	+	5.40197i	0.189837	+	0.191709i
$795$	−14.1660	−	7.92891i	−0.502415	−	0.281210i
$796$	−10.5252	−	0.103251i	−0.373057	−	0.00365964i
$797$	39.0796			1.38427			0.692135	−	0.721768i	$-0.256670\pi$
$797$	39.0796			1.38427			0.692135	+	0.721768i	$0.256670\pi$
$798$	15.3380	−	32.3079i	0.542959	−	1.14369i
$799$		−	16.9485i		−	0.599595i
$800$	−17.1613	+	16.3396i	−0.606745	+	0.577692i
$801$	14.2401	+	7.72303i	0.503150	+	0.272880i
$802$	2.00989	+	2.02970i	0.0709715	+	0.0716712i
$803$	5.62111	+	3.24535i	0.198365	+	0.114526i
$804$	−22.2580	+	38.8671i	−0.784980	+	1.37074i
$805$		−	4.26303i		−	0.150252i
$806$	7.48708	+	28.5006i	0.263721	+	1.00389i
$807$	−17.9296	+	10.6728i	−0.631153	+	0.375699i
$808$	−6.15991	+	21.7064i	−0.216705	+	0.763627i
$809$			31.0137i			1.09038i	0.838312	+	0.545191i	$0.183543\pi$
$809$			31.0137i			1.09038i	−0.838312	+	0.545191i	$0.816457\pi$
$810$	−3.49911	−	10.9160i	−0.122946	−	0.383548i
$811$	20.4283	+	35.3829i	0.717335	+	1.24246i	0.962052	+	0.272866i	$0.0879715\pi$
$811$	20.4283	+	35.3829i	0.717335	+	1.24246i	−0.244717	+	0.969594i	$0.578695\pi$
$812$	−46.3620	−	0.454805i	−1.62699	−	0.0159605i
$813$	9.88067	+	16.5990i	0.346530	+	0.582151i
$814$	3.42132	+	0.934749i	0.119917	+	0.0327629i
$815$	−5.98210	+	10.3613i	−0.209544	+	0.362941i
$816$	5.84948	−	9.98596i	0.204773	−	0.349578i
$817$	4.24649	−	22.0968i	0.148566	−	0.773068i
$818$	−7.18140	−	27.3370i	−0.251092	−	0.955815i
$819$	27.4130	−	50.5456i	0.957889	−	1.76621i
$820$	3.66810	+	0.0359836i	0.128096	+	0.00125660i
$821$	−5.77185	−	9.99714i	−0.201439	−	0.348903i	0.747553	−	0.664202i	$-0.231228\pi$
$821$	−5.77185	−	9.99714i	−0.201439	−	0.348903i	−0.948992	+	0.315299i	$0.897895\pi$
$822$	−30.3312	−	7.85405i	−1.05792	−	0.273941i
$823$	−12.3332	+	7.12057i	−0.429908	+	0.248208i	−0.699307	−	0.714821i	$-0.746508\pi$
$823$	−12.3332	+	7.12057i	−0.429908	+	0.248208i	0.269399	+	0.963029i	$0.413175\pi$
$824$	13.8049	−	13.4045i	0.480916	−	0.466968i
$825$	−16.3426	+	0.217806i	−0.568975	+	0.00758302i
$826$	25.3042	−	25.0572i	0.880447	−	0.871852i
$827$	8.22779	−	4.75032i	0.286108	−	0.165185i	−0.350077	−	0.936721i	$-0.613845\pi$
$827$	8.22779	−	4.75032i	0.286108	−	0.165185i	0.636186	+	0.771536i	$0.280511\pi$
$828$	−7.27040	+	4.36247i	−0.252664	+	0.151606i
$829$			57.3151i			1.99064i	0.0966587	+	0.995318i	$0.469184\pi$
$829$			57.3151i			1.99064i	−0.0966587	+	0.995318i	$0.530816\pi$
$830$	−8.00415	−	8.08305i	−0.277828	−	0.280567i
$831$	25.0102	−	44.6837i	0.867594	−	1.55006i
$832$	−21.7122	−	40.3006i	−0.752736	−	1.39717i
$833$	−6.10445	−	3.52441i	−0.211507	−	0.122113i
$834$	0.869749	−	3.35885i	0.0301169	−	0.116307i
$835$	7.00597			0.242452
$836$	3.89524	−	19.2483i	0.134720	−	0.665716i
$837$	−18.9062	+	0.756276i	−0.653494	+	0.0261407i
$838$	4.22361	−	15.4590i	0.145902	−	0.534024i
$839$	−0.686151	+	1.18845i	−0.0236886	+	0.0410298i	−0.877627	−	0.479345i	$-0.840874\pi$
$839$	−0.686151	+	1.18845i	−0.0236886	+	0.0410298i	0.853938	+	0.520375i	$0.174208\pi$
$840$	−3.84486	+	14.2700i	−0.132660	+	0.492361i
$841$	−9.44929	+	16.3666i	−0.325837	+	0.564367i
$842$	−10.2731	−	10.3743i	−0.354033	−	0.357523i
$843$	24.2850	−	0.323659i	0.836420	−	0.0111474i
$844$	−1.75180	+	0.988617i	−0.0602994	+	0.0340296i
$845$	8.89058	+	15.3989i	0.305845	+	0.529739i
$846$	29.7695	−	31.0934i	1.02350	−	1.06901i
$847$			19.8477i			0.681975i
$848$	21.5170	−	35.6352i	0.738896	−	1.22372i
$849$	25.8260	−	15.3731i	0.886345	−	0.527604i
$850$	−2.60801	+	9.54569i	−0.0894539	+	0.327415i
$851$	−1.36246	+	0.786616i	−0.0467045	+	0.0269649i
$852$	3.12099	−	0.0109772i	0.106923	−	0.000376071i
$853$	−22.0514	−	12.7314i	−0.755027	−	0.435915i	0.0724806	−	0.997370i	$-0.476908\pi$
$853$	−22.0514	−	12.7314i	−0.755027	−	0.435915i	−0.827507	+	0.561455i	$0.810242\pi$
$854$	16.1197	+	61.3617i	0.551604	+	2.09975i
$855$	−11.0206	+	4.15310i	−0.376897	+	0.142033i
$856$	−33.8763	+	32.8938i	−1.15787	+	1.12429i
$857$	22.2026	+	12.8187i	0.758425	+	0.437877i	0.828730	−	0.559649i	$-0.189064\pi$
$857$	22.2026	+	12.8187i	0.758425	+	0.437877i	−0.0703051	+	0.997526i	$0.522397\pi$
$858$	7.91493	−	30.5664i	0.270211	−	1.04352i
$859$	−14.0752	−	24.3789i	−0.480239	−	0.831798i	0.519504	−	0.854468i	$-0.326117\pi$
$859$	−14.0752	−	24.3789i	−0.480239	−	0.831798i	−0.999743	+	0.0226700i	$0.992783\pi$
$860$	−0.0912100	+	9.29779i	−0.00311024	+	0.317052i
$861$	−10.1526	+	6.04344i	−0.346001	+	0.205960i
$862$	−9.05068	−	34.4526i	−0.308267	−	1.17346i
$863$	−37.2932			−1.26947			−0.634737	−	0.772728i	$-0.718892\pi$
$863$	−37.2932			−1.26947			−0.634737	+	0.772728i	$0.718892\pi$
$864$	28.2713	−	8.04561i	0.961810	−	0.273717i
$865$	−7.63961	−	13.2322i	−0.259754	−	0.449908i
$866$	−1.63456	−	6.22216i	−0.0555445	−	0.211438i
$867$	0.327986	+	24.6097i	0.0111390	+	0.835789i
$868$	21.0056	+	12.4039i	0.712975	+	0.421015i
$869$	12.9925	−	22.5037i	0.440742	−	0.763387i
$870$	10.8866	+	10.7048i	0.369091	+	0.362926i
$871$	64.0727	+	36.9924i	2.17102	+	1.25344i
$872$	−6.91492	−	27.4141i	−0.234169	−	0.928359i
$873$	−11.4943	+	0.306434i	−0.389022	+	0.0103712i
$874$	4.85110	+	7.23537i	0.164091	+	0.244740i
$875$		−	27.7203i		−	0.937118i
$876$	9.98111	−	0.0351056i	0.337230	−	0.00118611i
$877$	12.9560	+	7.48013i	0.437492	+	0.252586i	0.702533	−	0.711651i	$-0.252052\pi$
$877$	12.9560	+	7.48013i	0.437492	+	0.252586i	−0.265041	+	0.964237i	$0.585386\pi$
$878$	6.79129	+	6.85824i	0.229195	+	0.231454i
$879$	−20.9183	−	11.7083i	−0.705556	−	0.394911i
$880$	−0.159205	+	8.11374i	−0.00536678	+	0.273514i
$881$			49.1641i			1.65638i	0.560446	+	0.828191i	$0.310630\pi$
$881$			49.1641i			1.65638i	−0.560446	+	0.828191i	$0.689370\pi$
$882$	−5.00860	−	17.1881i	−0.168648	−	0.578752i
$883$	−6.96120	−	12.0571i	−0.234263	−	0.405755i	0.724795	−	0.688964i	$-0.241934\pi$
$883$	−6.96120	−	12.0571i	−0.234263	−	0.405755i	−0.959058	+	0.283209i	$0.908601\pi$
$884$	−16.4612	−	9.72040i	−0.553649	−	0.326932i
$885$	−11.7259	+	0.156278i	−0.394163	+	0.00525322i
$886$	−20.6792	+	5.43242i	−0.694733	+	0.182506i
$887$	−5.94863	−	10.3033i	−0.199735	−	0.345952i	0.748707	−	0.662901i	$-0.230675\pi$
$887$	−5.94863	−	10.3033i	−0.199735	−	0.345952i	−0.948443	+	0.316949i	$0.897342\pi$
$888$	5.27013	−	1.40429i	0.176854	−	0.0471249i
$889$	32.8040	+	56.8182i	1.10021	+	1.90562i
$890$	−1.81264	+	6.63451i	−0.0607597	+	0.222389i
$891$	18.0731	+	9.18717i	0.605473	+	0.307782i
$892$	−3.06358	−	5.42856i	−0.102576	−	0.181762i
$893$	−33.4396	−	28.9441i	−1.11901	−	0.968578i
$894$	−32.3570	+	8.96277i	−1.08218	+	0.299760i
$895$	−1.33940	−	0.773302i	−0.0447712	−	0.0258487i
$896$	−36.2468	−	11.0590i	−1.21092	−	0.369456i
$897$	7.16384	+	12.0348i	0.239194	+	0.401832i
$898$	13.5634	−	49.6440i	0.452617	−	1.65664i
$899$	21.8254	−	12.6009i	0.727917	−	0.420263i
$900$	−21.5513	+	12.9314i	−0.718376	+	0.431048i
$901$		−	17.3839i		−	0.579143i
$902$	−4.61009	+	4.56508i	−0.153499	+	0.152001i
$903$	−15.3187	−	25.7346i	−0.509775	−	0.856392i
$904$	4.89356	−	4.75163i	0.162758	−	0.158037i
$905$			17.1051i			0.568593i
$906$	−3.75310	+	3.81686i	−0.124689	+	0.126807i
$907$	17.9002	−	31.0040i	0.594366	−	1.02947i	−0.399270	−	0.916833i	$-0.630736\pi$
$907$	17.9002	−	31.0040i	0.594366	−	1.02947i	0.993636	−	0.112639i	$-0.0359303\pi$
$908$	2.61569	−	4.42958i	0.0868047	−	0.147001i
$909$	−11.4095	+	21.0374i	−0.378429	+	0.697767i
$910$	23.5493	+	6.43398i	0.780652	+	0.213284i
$911$	8.84213			0.292953			0.146476	−	0.989214i	$-0.453207\pi$
$911$	8.84213			0.292953			0.146476	+	0.989214i	$0.453207\pi$
$912$	−9.71283	−	28.5948i	−0.321624	−	0.946867i
$913$	20.1193			0.665851
$914$	38.2927	+	10.4621i	1.26661	+	0.346054i
$915$	10.2041	−	18.2309i	0.337337	−	0.602694i
$916$	1.68560	−	2.85451i	0.0556938	−	0.0943155i
$917$	−30.7668	+	53.2897i	−1.01601	+	1.75978i
$918$	8.37007	−	8.97884i	0.276254	−	0.296346i
$919$			15.3158i			0.505221i	0.967568	+	0.252611i	$0.0812891\pi$
$919$			15.3158i			0.505221i	−0.967568	+	0.252611i	$0.918711\pi$
$920$	−2.50767	−	2.58258i	−0.0826755	−	0.0851451i
$921$	31.3582	−	18.6662i	1.03329	−	0.615074i
$922$	33.8876	−	33.5568i	1.11603	−	1.10513i
$923$		−	5.15543i		−	0.169693i
$924$	−13.1489	−	22.5906i	−0.432566	−	0.743177i
$925$	−4.03867	+	2.33173i	−0.132791	+	0.0766668i
$926$	8.53329	−	31.2331i	0.280421	−	1.02638i
$927$	17.3967	−	10.6720i	0.571383	−	0.350516i
$928$	−28.3540	+	26.9964i	−0.930767	+	0.886199i
$929$	19.9751	+	11.5326i	0.655362	+	0.378373i	0.790507	−	0.612452i	$-0.209817\pi$
$929$	19.9751	+	11.5326i	0.655362	+	0.378373i	−0.135146	+	0.990826i	$0.543150\pi$
$930$	−2.14442	−	7.74170i	−0.0703184	−	0.253860i
$931$	−17.3787	+	6.02527i	−0.569563	+	0.197470i
$932$	6.63372	+	11.7547i	0.217295	+	0.385039i
$933$	41.7443	+	23.3650i	1.36665	+	0.764935i
$934$	0.526955	−	1.92873i	0.0172425	−	0.0631100i
$935$	1.69450	+	2.93497i	0.0554162	+	0.0959836i
$936$	−13.1258	−	46.7463i	−0.429029	−	1.52795i
$937$	5.78196	+	10.0147i	0.188888	+	0.327164i	0.944880	−	0.327417i	$-0.106178\pi$
$937$	5.78196	+	10.0147i	0.188888	+	0.327164i	−0.755991	+	0.654581i	$0.772845\pi$
$938$	59.2377	−	15.5617i	1.93418	−	0.508108i
$939$	0.0403225	+	3.02551i	0.00131588	+	0.0987337i
$940$	15.7370	+	9.29275i	0.513283	+	0.303096i
$941$	20.0143	+	34.6658i	0.652448	+	1.13007i	0.982527	+	0.186120i	$0.0595913\pi$
$941$	20.0143	+	34.6658i	0.652448	+	1.13007i	−0.330079	+	0.943953i	$0.607075\pi$
$942$	7.58572	+	27.3856i	0.247156	+	0.892271i
$943$		−	2.87787i		−	0.0937163i
$944$	0.589919	−	30.0648i	0.0192002	−	0.978525i
$945$	−7.28882	+	13.8777i	−0.237105	+	0.451441i
$946$	−11.5714	−	11.6855i	−0.376219	−	0.379928i
$947$	18.7273	+	10.8122i	0.608555	+	0.351350i	0.772400	−	0.635137i	$-0.219056\pi$
$947$	18.7273	+	10.8122i	0.608555	+	0.351350i	−0.163845	+	0.986486i	$0.552390\pi$
$948$	−0.140543	−	39.9587i	−0.00456462	−	1.29780i
$949$		−	16.4873i		−	0.535202i
$950$	14.3799	+	21.4474i	0.466545	+	0.695847i
$951$	−0.438383	−	32.8930i	−0.0142155	−	1.06663i
$952$	−15.3451	+	3.87064i	−0.497338	+	0.125448i
$953$	−13.4636	−	7.77324i	−0.436130	−	0.251800i	0.265825	−	0.964021i	$-0.414356\pi$
$953$	−13.4636	−	7.77324i	−0.436130	−	0.251800i	−0.701955	+	0.712222i	$0.747689\pi$
$954$	30.5343	−	31.8922i	0.988584	−	1.03255i
$955$	6.07976	−	10.5305i	0.196736	−	0.340757i
$956$	27.9663	+	16.5142i	0.904494	+	0.534108i
$957$	−27.0013	+	0.359860i	−0.872827	+	0.0116326i
$958$	−7.39441	−	28.1478i	−0.238903	−	0.909415i
$959$	21.4224	+	37.1048i	0.691767	+	1.19818i
$960$	6.06489	+	10.9066i	0.195743	+	0.352008i
$961$	17.7401			0.572262
$962$	−2.28904	−	8.71354i	−0.0738016	−	0.280936i
$963$	−42.6904	+	26.1885i	−1.37568	+	0.843913i
$964$	0.455946	−	46.4784i	0.0146850	−	1.49697i
$965$	−8.32591	−	14.4209i	−0.268021	−	0.464225i
$966$	11.2242	+	2.90644i	0.361134	+	0.0935130i
$967$	−29.3347	−	16.9364i	−0.943339	−	0.544637i	−0.0523335	−	0.998630i	$-0.516666\pi$
$967$	−29.3347	−	16.9364i	−0.943339	−	0.544637i	−0.891005	+	0.453993i	$0.849999\pi$
$968$	11.6752	+	12.0239i	0.375254	+	0.386463i
$969$	−9.64468	−	8.12582i	−0.309832	−	0.261039i
$970$	−1.24034	−	4.72152i	−0.0398249	−	0.151599i
$971$	−33.8005	−	19.5147i	−1.08471	−	0.626258i	−0.152547	−	0.988296i	$-0.548747\pi$
$971$	−33.8005	−	19.5147i	−1.08471	−	0.626258i	−0.932163	+	0.362039i	$0.882081\pi$
$972$	31.1266	−	1.77065i	0.998386	−	0.0567935i
$973$	−4.10894	+	2.37230i	−0.131727	+	0.0760524i
$974$	−0.734010	+	2.68658i	−0.0235192	+	0.0860837i
$975$	21.2354	+	35.6743i	0.680078	+	1.14249i
$976$	45.8607	+	27.6912i	1.46796	+	0.886375i
$977$			25.4748i			0.815012i	0.913202	+	0.407506i	$0.133601\pi$
$977$			25.4748i			0.815012i	−0.913202	+	0.407506i	$0.866399\pi$
$978$	−23.2021	−	22.8146i	−0.741922	−	0.729529i
$979$	−6.08210	−	10.5345i	−0.194385	−	0.336684i
$980$	6.61950	−	3.73567i	0.211452	−	0.119332i
$981$	−0.799184	−	29.9772i	−0.0255160	−	0.957097i
$982$	−38.1701	−	38.5464i	−1.21806	−	1.23006i
$983$	−18.9236	+	32.7767i	−0.603570	+	1.04541i	0.388706	+	0.921362i	$0.372922\pi$
$983$	−18.9236	+	32.7767i	−0.603570	+	1.04541i	−0.992276	+	0.124052i	$0.960411\pi$
$984$	−2.59557	+	9.63332i	−0.0827438	+	0.307099i
$985$	3.43432	−	5.94842i	0.109427	−	0.189532i
$986$	−4.30896	+	15.7714i	−0.137225	+	0.502265i
$987$	−58.8597	+	0.784453i	−1.87352	+	0.0249694i
$988$	−47.2903	+	15.8779i	−1.50450	+	0.505142i
$989$	7.29473			0.231959
$990$	−2.04647	+	8.36076i	−0.0650410	+	0.265722i
$991$	−26.8003	−	15.4731i	−0.851338	−	0.491520i	0.00976378	−	0.999952i	$-0.496892\pi$
$991$	−26.8003	−	15.4731i	−0.851338	−	0.491520i	−0.861102	+	0.508432i	$0.830225\pi$
$992$	20.0218	−	4.84189i	0.635692	−	0.153730i
$993$	−22.2672	−	12.4633i	−0.706627	−	0.395510i
$994$	−3.00301	−	3.03261i	−0.0952496	−	0.0961885i
$995$		−	4.73987i		−	0.150264i
$996$	26.7391	−	15.5635i	0.847262	−	0.493148i
$997$	27.3591	−	15.7958i	0.866472	−	0.500258i	0.000297633	−	1.00000i	$-0.499905\pi$
$997$	27.3591	−	15.7958i	0.866472	−	0.500258i	0.866174	+	0.499742i	$0.166572\pi$
$998$	−16.3038	+	16.1447i	−0.516088	+	0.511050i
$999$	5.78023	−	0.231218i	0.182878	−	0.00731541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.u.d.11.63	yes	136
3.2	odd	2	inner	456.2.u.d.11.6	✓	136
8.3	odd	2	inner	456.2.u.d.11.52	yes	136
19.7	even	3	inner	456.2.u.d.83.17	yes	136
24.11	even	2	inner	456.2.u.d.11.17	yes	136
57.26	odd	6	inner	456.2.u.d.83.52	yes	136
152.83	odd	6	inner	456.2.u.d.83.6	yes	136
456.83	even	6	inner	456.2.u.d.83.63	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.u.d.11.6	✓	136	3.2	odd	2	inner
456.2.u.d.11.17	yes	136	24.11	even	2	inner
456.2.u.d.11.52	yes	136	8.3	odd	2	inner
456.2.u.d.11.63	yes	136	1.1	even	1	trivial
456.2.u.d.83.6	yes	136	152.83	odd	6	inner
456.2.u.d.83.17	yes	136	19.7	even	3	inner
456.2.u.d.83.52	yes	136	57.26	odd	6	inner
456.2.u.d.83.63	yes	136	456.83	even	6	inner

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36421 + 0.372721i) q^{2} +(-1.51141 - 0.845959i) q^{3} +(1.72216 + 1.01694i) q^{4} +(-0.450312 + 0.779964i) q^{5} +(-1.74658 - 1.71740i) q^{6} +3.34959i q^{7} +(1.97036 + 2.02921i) q^{8} +(1.56871 + 2.55718i) q^{9} +O(q^{10})\)	\(q+(1.36421 + 0.372721i) q^{2} +(-1.51141 - 0.845959i) q^{3} +(1.72216 + 1.01694i) q^{4} +(-0.450312 + 0.779964i) q^{5} +(-1.74658 - 1.71740i) q^{6} +3.34959i q^{7} +(1.97036 + 2.02921i) q^{8} +(1.56871 + 2.55718i) q^{9} +(-0.905031 + 0.896197i) q^{10} -2.25269i q^{11} +(-1.74259 - 2.99389i) q^{12} +(-4.95554 + 2.86108i) q^{13} +(-1.24846 + 4.56956i) q^{14} +(1.34042 - 0.797898i) q^{15} +(1.93166 + 3.50267i) q^{16} +(1.44663 + 0.835214i) q^{17} +(1.18694 + 4.07323i) q^{18} +(4.11840 - 1.42787i) q^{19} +(-1.56869 + 0.885280i) q^{20} +(2.83362 - 5.06260i) q^{21} +(0.839623 - 3.07314i) q^{22} +(0.706565 + 1.22381i) q^{23} +(-1.26138 - 4.73381i) q^{24} +(2.09444 + 3.62767i) q^{25} +(-7.82680 + 2.05609i) q^{26} +(-0.207688 - 5.19200i) q^{27} +(-3.40634 + 5.76853i) q^{28} +(3.46044 + 5.99366i) q^{29} +(2.12602 - 0.588899i) q^{30} -3.64141i q^{31} +(1.32967 + 5.49836i) q^{32} +(-1.90568 + 3.40473i) q^{33} +(1.66221 + 1.67860i) q^{34} +(-2.61256 - 1.50836i) q^{35} +(0.101059 + 5.99915i) q^{36} +1.11330i q^{37} +(6.15057 - 0.412905i) q^{38} +(9.91019 - 0.132078i) q^{39} +(-2.46999 + 0.623028i) q^{40} +(-1.76368 - 1.01826i) q^{41} +(5.75260 - 5.85032i) q^{42} +(2.58105 - 4.47051i) q^{43} +(2.29085 - 3.87948i) q^{44} +(-2.70092 + 0.0720058i) q^{45} +(0.507767 + 1.93289i) q^{46} +(-5.07311 - 8.78688i) q^{47} +(0.0435944 - 6.92807i) q^{48} -4.21977 q^{49} +(1.50515 + 5.72956i) q^{50} +(-1.47990 - 2.48614i) q^{51} +(-11.4438 - 0.112262i) q^{52} +(-5.20344 - 9.01262i) q^{53} +(1.65184 - 7.16041i) q^{54} +(1.75701 + 1.01441i) q^{55} +(-6.79703 + 6.59989i) q^{56} +(-7.43250 - 1.32590i) q^{57} +(2.48682 + 9.46641i) q^{58} +(-6.51047 - 3.75882i) q^{59} +(3.11984 - 0.0109731i) q^{60} +(11.5988 - 6.69656i) q^{61} +(1.35723 - 4.96766i) q^{62} +(-8.56550 + 5.25453i) q^{63} +(-0.235395 + 7.99654i) q^{64} -5.15352i q^{65} +(-3.86877 + 3.93449i) q^{66} +(-6.46476 - 11.1973i) q^{67} +(1.64197 + 2.90951i) q^{68} +(-0.0326177 - 2.44740i) q^{69} +(-3.00189 - 3.03149i) q^{70} +(-0.450479 + 0.780253i) q^{71} +(-2.09814 + 8.22179i) q^{72} +(-1.44066 + 2.49529i) q^{73} +(-0.414949 + 1.51877i) q^{74} +(-0.0966871 - 7.25470i) q^{75} +(8.54459 + 1.72916i) q^{76} +7.54558 q^{77} +(13.5689 + 3.51355i) q^{78} +(9.98974 + 5.76758i) q^{79} +(-3.60181 - 0.0706732i) q^{80} +(-4.07832 + 8.02292i) q^{81} +(-2.02651 - 2.04648i) q^{82} +8.93124i q^{83} +(10.0283 - 5.83697i) q^{84} +(-1.30287 + 0.752215i) q^{85} +(5.18736 - 5.13672i) q^{86} +(-0.159747 - 11.9863i) q^{87} +(4.57118 - 4.43859i) q^{88} +(4.67642 - 2.69993i) q^{89} +(-3.71146 - 0.908457i) q^{90} +(-9.58345 - 16.5990i) q^{91} +(-0.0277239 + 2.82612i) q^{92} +(-3.08048 + 5.50365i) q^{93} +(-3.64575 - 13.8780i) q^{94} +(-0.740879 + 3.85519i) q^{95} +(2.64171 - 9.43511i) q^{96} +(-1.91639 + 3.31929i) q^{97} +(-5.75666 - 1.57280i) q^{98} +(5.76052 - 3.53380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9}+O(q^{10}) \) 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9	\( 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9} + 18 q^{12} + 28 q^{16} - 10 q^{18} + 16 q^{19} + 10 q^{22} + 11 q^{24} - 96 q^{25} - 80 q^{27} + 6 q^{28} - 4 q^{30} - 40 q^{33} + 40 q^{34} + q^{36} - 56 q^{40} + 26 q^{42} - 20 q^{43} - 64 q^{46} - 19 q^{48} - 72 q^{49} - 42 q^{51} - 26 q^{52} + 6 q^{54} + 10 q^{57} + 144 q^{58} - 18 q^{60} - 112 q^{64} + 49 q^{66} - 12 q^{67} + 72 q^{70} - 45 q^{72} + 4 q^{73} + 144 q^{75} + 32 q^{76} - 50 q^{78} + 22 q^{81} - 22 q^{82} + 36 q^{84} + 100 q^{88} - 2 q^{90} + 24 q^{91} - 88 q^{94} - 66 q^{96} - 28 q^{97} + 80 q^{99}+O(q^{100}) \) 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9 + 18 * q^12 + 28 * q^16 - 10 * q^18 + 16 * q^19 + 10 * q^22 + 11 * q^24 - 96 * q^25 - 80 * q^27 + 6 * q^28 - 4 * q^30 - 40 * q^33 + 40 * q^34 + q^36 - 56 * q^40 + 26 * q^42 - 20 * q^43 - 64 * q^46 - 19 * q^48 - 72 * q^49 - 42 * q^51 - 26 * q^52 + 6 * q^54 + 10 * q^57 + 144 * q^58 - 18 * q^60 - 112 * q^64 + 49 * q^66 - 12 * q^67 + 72 * q^70 - 45 * q^72 + 4 * q^73 + 144 * q^75 + 32 * q^76 - 50 * q^78 + 22 * q^81 - 22 * q^82 + 36 * q^84 + 100 * q^88 - 2 * q^90 + 24 * q^91 - 88 * q^94 - 66 * q^96 - 28 * q^97 + 80 * q^99

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