LMFDB - Embedded newform 368.2.j.d.277.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(93,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("368.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.j (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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.6
Character	$\chi$	$=$	368.277
Dual form			368.2.j.d.93.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.408999 + 1.35378i) q^{2} +(-1.35709 + 1.35709i) q^{3} +(-1.66544 - 1.10739i) q^{4} +(-0.944781 - 0.944781i) q^{5} +(-1.28215 - 2.39224i) q^{6} -1.03914i q^{7} +(2.18032 - 1.80172i) q^{8} -0.683369i q^{9} +(1.66544 - 0.892612i) q^{10} +(-2.32083 - 2.32083i) q^{11} +(3.76297 - 0.757325i) q^{12} +(3.04566 - 3.04566i) q^{13} +(1.40676 + 0.425006i) q^{14} +2.56430 q^{15} +(1.54738 + 3.68858i) q^{16} +2.64059 q^{17} +(0.925131 + 0.279497i) q^{18} +(-0.723364 + 0.723364i) q^{19} +(0.527237 + 2.61972i) q^{20} +(1.41020 + 1.41020i) q^{21} +(4.09111 - 2.19268i) q^{22} +1.00000i q^{23} +(-0.513797 + 5.40398i) q^{24} -3.21478i q^{25} +(2.87749 + 5.36883i) q^{26} +(-3.14387 - 3.14387i) q^{27} +(-1.15073 + 1.73062i) q^{28} +(2.38258 - 2.38258i) q^{29} +(-1.04880 + 3.47150i) q^{30} +4.88133 q^{31} +(-5.62640 + 0.586193i) q^{32} +6.29914 q^{33} +(-1.08000 + 3.57478i) q^{34} +(-0.981759 + 0.981759i) q^{35} +(-0.756755 + 1.13811i) q^{36} +(1.04169 + 1.04169i) q^{37} +(-0.683421 - 1.27513i) q^{38} +8.26646i q^{39} +(-3.76216 - 0.357697i) q^{40} -2.62724i q^{41} +(-2.48587 + 1.33233i) q^{42} +(-2.55653 - 2.55653i) q^{43} +(1.29514 + 6.43527i) q^{44} +(-0.645634 + 0.645634i) q^{45} +(-1.35378 - 0.408999i) q^{46} -0.736160 q^{47} +(-7.10565 - 2.90579i) q^{48} +5.92019 q^{49} +(4.35210 + 1.31484i) q^{50} +(-3.58351 + 3.58351i) q^{51} +(-8.44511 + 1.69964i) q^{52} +(-6.95536 - 6.95536i) q^{53} +(5.54195 - 2.97027i) q^{54} +4.38536i q^{55} +(-1.87224 - 2.26566i) q^{56} -1.96334i q^{57} +(2.25101 + 4.19995i) q^{58} +(-7.67379 - 7.67379i) q^{59} +(-4.27069 - 2.83968i) q^{60} +(6.85611 - 6.85611i) q^{61} +(-1.99646 + 6.60824i) q^{62} -0.710115 q^{63} +(1.50761 - 7.85666i) q^{64} -5.75497 q^{65} +(-2.57634 + 8.52765i) q^{66} +(5.25714 - 5.25714i) q^{67} +(-4.39775 - 2.92416i) q^{68} +(-1.35709 - 1.35709i) q^{69} +(-0.927547 - 1.73062i) q^{70} +1.12865i q^{71} +(-1.23124 - 1.48997i) q^{72} -14.8204i q^{73} +(-1.83627 + 0.984169i) q^{74} +(4.36273 + 4.36273i) q^{75} +(2.00576 - 0.403675i) q^{76} +(-2.41166 + 2.41166i) q^{77} +(-11.1910 - 3.38097i) q^{78} +6.88664 q^{79} +(2.02296 - 4.94684i) q^{80} +10.5831 q^{81} +(3.55671 + 1.07454i) q^{82} +(-7.58934 + 7.58934i) q^{83} +(-0.786966 - 3.91025i) q^{84} +(-2.49478 - 2.49478i) q^{85} +(4.50659 - 2.41536i) q^{86} +6.46672i q^{87} +(-9.24165 - 0.878674i) q^{88} +7.82916i q^{89} +(-0.609983 - 1.13811i) q^{90} +(-3.16487 - 3.16487i) q^{91} +(1.10739 - 1.66544i) q^{92} +(-6.62438 + 6.62438i) q^{93} +(0.301089 - 0.996599i) q^{94} +1.36684 q^{95} +(6.84000 - 8.43103i) q^{96} -14.5175 q^{97} +(-2.42135 + 8.01464i) q^{98} +(-1.58598 + 1.58598i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 4 q^{3} + 4 q^{5} + 2 q^{8} - 4 q^{11} + 38 q^{12} - 12 q^{13} - 6 q^{14} + 40 q^{17} - 8 q^{18} + 8 q^{19} - 2 q^{20} + 34 q^{22} - 10 q^{24} - 2 q^{26} - 28 q^{27} + 10 q^{28} - 16 q^{29}+ \cdots + 4 q^{99}+O(q^{100}) $ 24 * q - 4 * q^2 - 4 * q^3 + 4 * q^5 + 2 * q^8 - 4 * q^11 + 38 * q^12 - 12 * q^13 - 6 * q^14 + 40 * q^17 - 8 * q^18 + 8 * q^19 - 2 * q^20 + 34 * q^22 - 10 * q^24 - 2 * q^26 - 28 * q^27 + 10 * q^28 - 16 * q^29 - 30 * q^30 - 12 * q^31 + 16 * q^32 - 28 * q^33 + 4 * q^34 + 8 * q^35 - 24 * q^36 - 4 * q^37 + 20 * q^38 + 40 * q^42 - 28 * q^43 + 50 * q^44 + 20 * q^45 - 4 * q^47 + 20 * q^48 - 24 * q^49 + 10 * q^50 - 12 * q^51 - 44 * q^52 + 32 * q^53 + 38 * q^54 - 40 * q^56 - 40 * q^58 + 24 * q^59 + 34 * q^60 - 16 * q^61 - 42 * q^62 - 4 * q^63 + 24 * q^64 + 4 * q^65 - 12 * q^66 - 10 * q^68 - 4 * q^69 + 14 * q^70 + 4 * q^74 + 44 * q^75 + 8 * q^76 - 20 * q^77 + 4 * q^78 + 12 * q^79 - 4 * q^80 - 48 * q^81 - 4 * q^82 - 16 * q^83 - 66 * q^84 + 8 * q^85 - 28 * q^88 - 40 * q^90 - 72 * q^91 + 4 * q^93 - 26 * q^94 - 40 * q^95 - 32 * q^96 - 124 * q^97 + 54 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.408999	+	1.35378i	−0.289206	+	0.957267i
$2$	−0.408999	+	1.35378i	−0.289206	+	0.957267i
$3$	−1.35709	+	1.35709i	−0.783514	+	0.783514i	−0.980422	−	0.196908i	$-0.936910\pi$
$3$	−1.35709	+	1.35709i	−0.783514	+	0.783514i	0.196908	+	0.980422i	$0.436910\pi$
$4$	−1.66544	−	1.10739i	−0.832720	−	0.553694i
$5$	−0.944781	−	0.944781i	−0.422519	−	0.422519i	0.463551	−	0.886070i	$-0.346575\pi$
$5$	−0.944781	−	0.944781i	−0.422519	−	0.422519i	−0.886070	+	0.463551i	$0.846575\pi$
$6$	−1.28215	−	2.39224i	−0.523436	−	0.976629i
$7$		−	1.03914i		−	0.392757i	−0.980528	−	0.196379i	$-0.937082\pi$
$7$		−	1.03914i		−	0.392757i	0.980528	−	0.196379i	$-0.0629182\pi$
$8$	2.18032	−	1.80172i	0.770860	−	0.637004i
$9$		−	0.683369i		−	0.227790i
$10$	1.66544	−	0.892612i	0.526658	−	0.282269i
$11$	−2.32083	−	2.32083i	−0.699757	−	0.699757i	0.264601	−	0.964358i	$-0.414760\pi$
$11$	−2.32083	−	2.32083i	−0.699757	−	0.699757i	−0.964358	+	0.264601i	$0.914760\pi$
$12$	3.76297	−	0.757325i	1.08628	−	0.218621i
$13$	3.04566	−	3.04566i	0.844715	−	0.844715i	−0.144753	−	0.989468i	$-0.546239\pi$
$13$	3.04566	−	3.04566i	0.844715	−	0.844715i	0.989468	+	0.144753i	$0.0462386\pi$
$14$	1.40676	+	0.425006i	0.375974	+	0.113588i
$15$	2.56430			0.662100
$16$	1.54738	+	3.68858i	0.386846	+	0.922144i
$17$	2.64059			0.640438			0.320219	−	0.947344i	$-0.396244\pi$
$17$	2.64059			0.640438			0.320219	+	0.947344i	$0.396244\pi$
$18$	0.925131	+	0.279497i	0.218056	+	0.0658781i
$19$	−0.723364	+	0.723364i	−0.165951	+	0.165951i	−0.785197	−	0.619246i	$-0.787438\pi$
$19$	−0.723364	+	0.723364i	−0.165951	+	0.165951i	0.619246	+	0.785197i	$0.287438\pi$
$20$	0.527237	+	2.61972i	0.117894	+	0.585786i
$21$	1.41020	+	1.41020i	0.307731	+	0.307731i
$22$	4.09111	−	2.19268i	0.872228	−	0.467480i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−0.513797	+	5.40398i	−0.104878	+	1.10308i
$25$		−	3.21478i		−	0.642955i
$26$	2.87749	+	5.36883i	0.564322	+	1.05291i
$27$	−3.14387	−	3.14387i	−0.605038	−	0.605038i
$28$	−1.15073	+	1.73062i	−0.217467	+	0.327057i
$29$	2.38258	−	2.38258i	0.442433	−	0.442433i	−0.450396	−	0.892829i	$-0.648717\pi$
$29$	2.38258	−	2.38258i	0.442433	−	0.442433i	0.892829	+	0.450396i	$0.148717\pi$
$30$	−1.04880	+	3.47150i	−0.191483	+	0.633806i
$31$	4.88133			0.876712			0.438356	−	0.898801i	$-0.355561\pi$
$31$	4.88133			0.876712			0.438356	+	0.898801i	$0.355561\pi$
$32$	−5.62640	+	0.586193i	−0.994616	+	0.103625i
$33$	6.29914			1.09654
$34$	−1.08000	+	3.57478i	−0.185218	+	0.613070i
$35$	−0.981759	+	0.981759i	−0.165947	+	0.165947i
$36$	−0.756755	+	1.13811i	−0.126126	+	0.189685i
$37$	1.04169	+	1.04169i	0.171253	+	0.171253i	0.787530	−	0.616277i	$-0.211360\pi$
$37$	1.04169	+	1.04169i	0.171253	+	0.171253i	−0.616277	+	0.787530i	$0.711360\pi$
$38$	−0.683421	−	1.27513i	−0.110865	−	0.206853i
$39$			8.26646i			1.32369i
$40$	−3.76216	−	0.357697i	−0.594850	−	0.0565569i
$41$		−	2.62724i		−	0.410306i	−0.978730	−	0.205153i	$-0.934231\pi$
$41$		−	2.62724i		−	0.410306i	0.978730	−	0.205153i	$-0.0657693\pi$
$42$	−2.48587	+	1.33233i	−0.383578	+	0.205583i
$43$	−2.55653	−	2.55653i	−0.389867	−	0.389867i	0.484773	−	0.874640i	$-0.338902\pi$
$43$	−2.55653	−	2.55653i	−0.389867	−	0.389867i	−0.874640	+	0.484773i	$0.838902\pi$
$44$	1.29514	+	6.43527i	0.195250	+	0.970153i
$45$	−0.645634	+	0.645634i	−0.0962455	+	0.0962455i
$46$	−1.35378	−	0.408999i	−0.199604	−	0.0603036i
$47$	−0.736160			−0.107380			−0.0536900	−	0.998558i	$-0.517098\pi$
$47$	−0.736160			−0.107380			−0.0536900	+	0.998558i	$0.517098\pi$
$48$	−7.10565	−	2.90579i	−1.02561	−	0.419414i
$49$	5.92019			0.845742
$50$	4.35210	+	1.31484i	0.615480	+	0.185946i
$51$	−3.58351	+	3.58351i	−0.501792	+	0.501792i
$52$	−8.44511	+	1.69964i	−1.17113	+	0.235698i
$53$	−6.95536	−	6.95536i	−0.955392	−	0.955392i	0.0436542	−	0.999047i	$-0.486100\pi$
$53$	−6.95536	−	6.95536i	−0.955392	−	0.955392i	−0.999047	+	0.0436542i	$0.986100\pi$
$54$	5.54195	−	2.97027i	0.754163	−	0.404202i
$55$			4.38536i			0.591321i
$56$	−1.87224	−	2.26566i	−0.250188	−	0.302761i
$57$		−	1.96334i		−	0.260050i
$58$	2.25101	+	4.19995i	0.295572	+	0.551481i
$59$	−7.67379	−	7.67379i	−0.999043	−	0.999043i	0.000956675	−	1.00000i	$-0.499695\pi$
$59$	−7.67379	−	7.67379i	−0.999043	−	0.999043i	−1.00000		0.000956675i	$0.999695\pi$
$60$	−4.27069	−	2.83968i	−0.551344	−	0.366601i
$61$	6.85611	−	6.85611i	0.877834	−	0.877834i	−0.115476	−	0.993310i	$-0.536839\pi$
$61$	6.85611	−	6.85611i	0.877834	−	0.877834i	0.993310	+	0.115476i	$0.0368393\pi$
$62$	−1.99646	+	6.60824i	−0.253550	+	0.839248i
$63$	−0.710115			−0.0894661
$64$	1.50761	−	7.85666i	0.188452	−	0.982082i
$65$	−5.75497			−0.713817
$66$	−2.57634	+	8.52765i	−0.317125	+	1.04968i
$67$	5.25714	−	5.25714i	0.642261	−	0.642261i	−0.308850	−	0.951111i	$-0.599944\pi$
$67$	5.25714	−	5.25714i	0.642261	−	0.642261i	0.951111	+	0.308850i	$0.0999439\pi$
$68$	−4.39775	−	2.92416i	−0.533305	−	0.354607i
$69$	−1.35709	−	1.35709i	−0.163374	−	0.163374i
$70$	−0.927547	−	1.73062i	−0.110863	−	0.206849i
$71$			1.12865i			0.133946i	0.997755	+	0.0669728i	$0.0213341\pi$
$71$			1.12865i			0.133946i	−0.997755	+	0.0669728i	$0.978666\pi$
$72$	−1.23124	−	1.48997i	−0.145103	−	0.175594i
$73$		−	14.8204i		−	1.73459i	−0.497791	−	0.867297i	$-0.665855\pi$
$73$		−	14.8204i		−	1.73459i	0.497791	−	0.867297i	$-0.334145\pi$
$74$	−1.83627	+	0.984169i	−0.213462	+	0.114407i
$75$	4.36273	+	4.36273i	0.503765	+	0.503765i
$76$	2.00576	−	0.403675i	0.230077	−	0.0463047i
$77$	−2.41166	+	2.41166i	−0.274835	+	0.274835i
$78$	−11.1910	−	3.38097i	−1.26713	−	0.382820i
$79$	6.88664			0.774807			0.387403	−	0.921910i	$-0.373372\pi$
$79$	6.88664			0.774807			0.387403	+	0.921910i	$0.373372\pi$
$80$	2.02296	−	4.94684i	0.226174	−	0.553073i
$81$	10.5831			1.17590
$82$	3.55671	+	1.07454i	0.392773	+	0.118663i
$83$	−7.58934	+	7.58934i	−0.833039	+	0.833039i	−0.987931	−	0.154893i	$-0.950497\pi$
$83$	−7.58934	+	7.58934i	−0.833039	+	0.833039i	0.154893	+	0.987931i	$0.450497\pi$
$84$	−0.786966	−	3.91025i	−0.0858650	−	0.426643i
$85$	−2.49478	−	2.49478i	−0.270597	−	0.270597i
$86$	4.50659	−	2.41536i	0.485958	−	0.260455i
$87$			6.46672i			0.693306i
$88$	−9.24165	−	0.878674i	−0.985163	−	0.0936669i
$89$			7.82916i			0.829889i	0.909847	+	0.414944i	$0.136199\pi$
$89$			7.82916i			0.829889i	−0.909847	+	0.414944i	$0.863801\pi$
$90$	−0.609983	−	1.13811i	−0.0642979	−	0.119967i
$91$	−3.16487	−	3.16487i	−0.331768	−	0.331768i
$92$	1.10739	−	1.66544i	0.115453	−	0.173634i
$93$	−6.62438	+	6.62438i	−0.686917	+	0.686917i
$94$	0.301089	−	0.996599i	0.0310549	−	0.102791i
$95$	1.36684			0.140235
$96$	6.84000	−	8.43103i	0.698104	−	0.860488i
$97$	−14.5175			−1.47403			−0.737013	−	0.675878i	$-0.763765\pi$
$97$	−14.5175			−1.47403			−0.737013	+	0.675878i	$0.763765\pi$
$98$	−2.42135	+	8.01464i	−0.244593	+	0.809601i
$99$	−1.58598	+	1.58598i	−0.159397	+	0.159397i
$100$	−3.56001	+	5.35402i	−0.356001	+	0.535402i
$101$	−2.65938	−	2.65938i	−0.264619	−	0.264619i	0.562309	−	0.826927i	$-0.309913\pi$
$101$	−2.65938	−	2.65938i	−0.264619	−	0.264619i	−0.826927	+	0.562309i	$0.809913\pi$
$102$	−3.38564	−	6.31694i	−0.335228	−	0.625470i
$103$			5.78991i			0.570497i	0.958454	+	0.285248i	$0.0920761\pi$
$103$			5.78991i			0.570497i	−0.958454	+	0.285248i	$0.907924\pi$
$104$	1.15310	−	12.1280i	0.113071	−	1.18924i
$105$		−	2.66466i		−	0.260044i
$106$	12.2608	−	6.57130i	1.19087	−	0.638261i
$107$	−2.22067	−	2.22067i	−0.214680	−	0.214680i	0.591572	−	0.806252i	$-0.298508\pi$
$107$	−2.22067	−	2.22067i	−0.214680	−	0.214680i	−0.806252	+	0.591572i	$0.798508\pi$
$108$	1.75444	+	8.71741i	0.168821	+	0.838833i
$109$	−9.38645	+	9.38645i	−0.899059	+	0.899059i	−0.995353	−	0.0962942i	$-0.969301\pi$
$109$	−9.38645	+	9.38645i	−0.899059	+	0.899059i	0.0962942	+	0.995353i	$0.469301\pi$
$110$	−5.93681	−	1.79360i	−0.566052	−	0.171013i
$111$	−2.82733			−0.268358
$112$	3.83294	−	1.60794i	0.362179	−	0.151937i
$113$	1.89466			0.178234			0.0891172	−	0.996021i	$-0.471595\pi$
$113$	1.89466			0.178234			0.0891172	+	0.996021i	$0.471595\pi$
$114$	2.65792	+	0.803001i	0.248937	+	0.0752080i
$115$	0.944781	−	0.944781i	0.0881013	−	0.0881013i
$116$	−6.60647	+	1.32960i	−0.613396	+	0.123450i
$117$	−2.08131	−	2.08131i	−0.192417	−	0.192417i
$118$	13.5272	−	7.25006i	1.24528	−	0.667422i
$119$		−	2.74394i		−	0.251537i
$120$	5.59100	−	4.62015i	0.510386	−	0.421760i
$121$		−	0.227490i		−	0.0206809i
$122$	6.47752	+	12.0858i	0.586447	+	1.09420i
$123$	3.56540	+	3.56540i	0.321481	+	0.321481i
$124$	−8.12956	−	5.40552i	−0.730056	−	0.485430i
$125$	−7.76117	+	7.76117i	−0.694180	+	0.694180i
$126$	0.290436	−	0.961340i	0.0258741	−	0.0856429i
$127$	1.62302			0.144019			0.0720096	−	0.997404i	$-0.477059\pi$
$127$	1.62302			0.144019			0.0720096	+	0.997404i	$0.477059\pi$
$128$	10.0196	+	5.25434i	0.885614	+	0.464422i
$129$	6.93886			0.610933
$130$	2.35378	−	7.79097i	0.206440	−	0.683313i
$131$	0.00207687	−	0.00207687i	0.000181457	−	0.000181457i	−0.707016	−	0.707198i	$-0.749959\pi$
$131$	0.00207687	−	0.00207687i	0.000181457	−	0.000181457i	0.707198	+	0.707016i	$0.249959\pi$
$132$	−10.4908	−	6.97559i	−0.913110	−	0.607147i
$133$	0.751675	+	0.751675i	0.0651785	+	0.0651785i
$134$	4.96684	+	9.26717i	0.429070	+	0.800561i
$135$			5.94054i			0.511280i
$136$	5.75734	−	4.75761i	0.493688	−	0.407961i
$137$			9.54941i			0.815861i	0.913013	+	0.407931i	$0.133749\pi$
$137$			9.54941i			0.815861i	−0.913013	+	0.407931i	$0.866251\pi$
$138$	2.39224	−	1.28215i	0.203641	−	0.109144i
$139$	9.01775	+	9.01775i	0.764876	+	0.764876i	0.977199	−	0.212324i	$-0.0681031\pi$
$139$	9.01775	+	9.01775i	0.764876	+	0.764876i	−0.212324	+	0.977199i	$0.568103\pi$
$140$	2.72225	−	0.547872i	0.230072	−	0.0463037i
$141$	0.999033	−	0.999033i	0.0841338	−	0.0841338i
$142$	−1.52794	−	0.461615i	−0.128222	−	0.0387378i
$143$	−14.1369			−1.18219
$144$	2.52066	−	1.05743i	0.210055	−	0.0881195i
$145$	−4.50203			−0.373873
$146$	20.0635	+	6.06151i	1.66047	+	0.501654i
$147$	−8.03421	+	8.03421i	−0.662651	+	0.662651i
$148$	−0.581317	−	2.88843i	−0.0477840	−	0.237427i
$149$	11.5838	+	11.5838i	0.948985	+	0.948985i	0.998760	−	0.0497750i	$-0.0158504\pi$
$149$	11.5838	+	11.5838i	0.948985	+	0.948985i	−0.0497750	+	0.998760i	$0.515850\pi$
$150$	−7.69053	+	4.12183i	−0.627929	+	0.336546i
$151$		−	22.2288i		−	1.80895i	−0.426522	−	0.904477i	$-0.640261\pi$
$151$		−	22.2288i		−	1.80895i	0.426522	−	0.904477i	$-0.359739\pi$
$152$	−0.273868	+	2.88047i	−0.0222136	+	0.233637i
$153$		−	1.80450i		−	0.145885i
$154$	−2.27850	−	4.25123i	−0.183606	−	0.342574i
$155$	−4.61179	−	4.61179i	−0.370428	−	0.370428i
$156$	9.15418	−	13.7673i	0.732921	−	1.10227i
$157$	−11.9676	+	11.9676i	−0.955119	+	0.955119i	−0.999035	−	0.0439160i	$-0.986017\pi$
$157$	−11.9676	+	11.9676i	−0.955119	+	0.955119i	0.0439160	+	0.999035i	$0.486017\pi$
$158$	−2.81662	+	9.32299i	−0.224079	+	0.741697i
$159$	18.8781			1.49713
$160$	5.86954	+	4.76189i	0.464028	+	0.376461i
$161$	1.03914			0.0818956
$162$	−4.32848	+	14.3272i	−0.340077	+	1.12565i
$163$	6.67263	−	6.67263i	0.522641	−	0.522641i	−0.395727	−	0.918368i	$-0.629507\pi$
$163$	6.67263	−	6.67263i	0.522641	−	0.522641i	0.918368	+	0.395727i	$0.129507\pi$
$164$	−2.90938	+	4.37552i	−0.227184	+	0.341670i
$165$	−5.95131	−	5.95131i	−0.463309	−	0.463309i
$166$	−7.17027	−	13.3783i	−0.556521	−	1.03836i
$167$			16.4261i			1.27109i	0.772062	+	0.635547i	$0.219225\pi$
$167$			16.4261i			1.27109i	−0.772062	+	0.635547i	$0.780775\pi$
$168$	5.61548	+	0.533907i	0.433244	+	0.0411918i
$169$		−	5.55215i		−	0.427088i
$170$	4.39775	−	2.35702i	0.337292	−	0.180775i
$171$	0.494325	+	0.494325i	0.0378019	+	0.0378019i
$172$	1.42668	+	7.08881i	0.108783	+	0.540517i
$173$	0.408306	−	0.408306i	0.0310429	−	0.0310429i	−0.691415	−	0.722458i	$-0.743012\pi$
$173$	0.408306	−	0.408306i	0.0310429	−	0.0310429i	0.722458	+	0.691415i	$0.243012\pi$
$174$	−8.75452	−	2.64488i	−0.663679	−	0.200508i
$175$	−3.34060			−0.252525
$176$	4.96935	−	12.1518i	0.374579	−	0.915975i
$177$	20.8280			1.56553
$178$	−10.5990	−	3.20211i	−0.794425	−	0.240009i
$179$	0.793254	−	0.793254i	0.0592906	−	0.0592906i	−0.676840	−	0.736130i	$-0.736651\pi$
$179$	0.793254	−	0.793254i	0.0592906	−	0.0592906i	0.736130	+	0.676840i	$0.236651\pi$
$180$	1.79023	−	0.360298i	0.133436	−	0.0268550i
$181$	4.26161	+	4.26161i	0.316763	+	0.316763i	0.847522	−	0.530760i	$-0.178093\pi$
$181$	4.26161	+	4.26161i	0.316763	+	0.316763i	−0.530760	+	0.847522i	$0.678093\pi$
$182$	5.57896	−	2.99011i	0.413540	−	0.221641i
$183$			18.6087i			1.37559i
$184$	1.80172	+	2.18032i	0.132825	+	0.160736i
$185$		−	1.96834i		−	0.144715i
$186$	−6.25859	−	11.6773i	−0.458902	−	0.856223i
$187$	−6.12837	−	6.12837i	−0.448151	−	0.448151i
$188$	1.22603	+	0.815215i	0.0894175	+	0.0594557i
$189$	−3.26691	+	3.26691i	−0.237633	+	0.237633i
$190$	−0.559036	+	1.85040i	−0.0405568	+	0.134242i
$191$	−17.9897			−1.30169			−0.650846	−	0.759210i	$-0.725586\pi$
$191$	−17.9897			−1.30169			−0.650846	+	0.759210i	$0.725586\pi$
$192$	8.61621	+	12.7081i	0.621821	+	0.917130i
$193$	6.61497			0.476156			0.238078	−	0.971246i	$-0.423483\pi$
$193$	6.61497			0.476156			0.238078	+	0.971246i	$0.423483\pi$
$194$	5.93763	−	19.6535i	0.426297	−	1.41104i
$195$	7.81000	−	7.81000i	0.559286	−	0.559286i
$196$	−9.85973	−	6.55595i	−0.704266	−	0.468282i
$197$	10.7577	+	10.7577i	0.766455	+	0.766455i	0.977480	−	0.211026i	$-0.0676804\pi$
$197$	10.7577	+	10.7577i	0.766455	+	0.766455i	−0.211026	+	0.977480i	$0.567680\pi$
$198$	−1.49841	−	2.79574i	−0.106487	−	0.198685i
$199$			9.31387i			0.660242i	0.943939	+	0.330121i	$0.107090\pi$
$199$			9.31387i			0.660242i	−0.943939	+	0.330121i	$0.892910\pi$
$200$	−5.79213	−	7.00925i	−0.409565	−	0.495629i
$201$			14.2688i			1.00644i
$202$	4.68791	−	2.51254i	0.329840	−	0.176781i
$203$	−2.47583	−	2.47583i	−0.173769	−	0.173769i
$204$	9.93647	−	1.99979i	0.695692	−	0.140013i
$205$	−2.48217	+	2.48217i	−0.173362	+	0.173362i
$206$	−7.83826	−	2.36806i	−0.546118	−	0.164991i
$207$	0.683369			0.0474974
$208$	15.9470	+	6.52136i	1.10572	+	0.452175i
$209$	3.35761			0.232251
$210$	3.60737	+	1.08984i	0.248932	+	0.0752063i
$211$	18.8579	−	18.8579i	1.29823	−	1.29823i	0.368669	−	0.929561i	$-0.379814\pi$
$211$	18.8579	−	18.8579i	1.29823	−	1.29823i	0.929561	−	0.368669i	$-0.120186\pi$
$212$	3.88145	+	19.2860i	0.266579	+	1.32457i
$213$	−1.53167	−	1.53167i	−0.104948	−	0.104948i
$214$	3.91455	−	2.09805i	0.267593	−	0.143420i
$215$			4.83072i			0.329452i
$216$	−12.5190	−	1.19028i	−0.851811	−	0.0809882i
$217$		−	5.07237i		−	0.344335i
$218$	−8.86814	−	16.5462i	−0.600626	−	1.12065i
$219$	20.1125	+	20.1125i	1.35908	+	1.35908i
$220$	4.85629	−	7.30355i	0.327411	−	0.492405i
$221$	8.04236	−	8.04236i	0.540988	−	0.540988i
$222$	1.15637	−	3.82758i	0.0776107	−	0.256890i
$223$	−13.8120			−0.924923			−0.462461	−	0.886639i	$-0.653034\pi$
$223$	−13.8120			−0.924923			−0.462461	+	0.886639i	$0.653034\pi$
$224$	0.609135	+	5.84661i	0.0406996	+	0.390643i
$225$	−2.19688			−0.146459
$226$	−0.774913	+	2.56495i	−0.0515464	+	0.170618i
$227$	1.69489	−	1.69489i	0.112494	−	0.112494i	−0.648619	−	0.761113i	$-0.724653\pi$
$227$	1.69489	−	1.69489i	0.112494	−	0.112494i	0.761113	+	0.648619i	$0.224653\pi$
$228$	−2.17417	+	3.26982i	−0.143988	+	0.216549i
$229$	12.9935	+	12.9935i	0.858636	+	0.858636i	0.991177	−	0.132542i	$-0.0423138\pi$
$229$	12.9935	+	12.9935i	0.858636	+	0.858636i	−0.132542	+	0.991177i	$0.542314\pi$
$230$	0.892612	+	1.66544i	0.0588571	+	0.109816i
$231$		−	6.54568i		−	0.430674i
$232$	0.902051	−	9.48752i	0.0592225	−	0.622886i
$233$		−	20.6606i		−	1.35352i	−0.736202	−	0.676762i	$-0.763383\pi$
$233$		−	20.6606i		−	1.35352i	0.736202	−	0.676762i	$-0.236617\pi$
$234$	3.66889	−	1.96639i	0.239843	−	0.128547i
$235$	0.695511	+	0.695511i	0.0453701	+	0.0453701i
$236$	4.28238	+	21.2781i	0.278759	+	1.38509i
$237$	−9.34576	+	9.34576i	−0.607072	+	0.607072i
$238$	3.71469	+	1.12227i	0.240788	+	0.0727458i
$239$	23.3888			1.51290			0.756448	−	0.654054i	$-0.226933\pi$
$239$	23.3888			1.51290			0.756448	+	0.654054i	$0.226933\pi$
$240$	3.96795	+	9.45862i	0.256130	+	0.610551i
$241$	3.48282			0.224348			0.112174	−	0.993689i	$-0.464219\pi$
$241$	3.48282			0.224348			0.112174	+	0.993689i	$0.464219\pi$
$242$	0.307972	+	0.0930431i	0.0197972	+	0.00598104i
$243$	−4.93060	+	4.93060i	−0.316298	+	0.316298i
$244$	−19.0108	+	3.82606i	−1.21704	+	0.244939i
$245$	−5.59329	−	5.59329i	−0.357342	−	0.357342i
$246$	−6.28501	+	3.36852i	−0.400717	+	0.214769i
$247$			4.40625i			0.280363i
$248$	10.6429	−	8.79478i	0.675823	−	0.558469i
$249$		−	20.5988i		−	1.30540i
$250$	−7.33261	−	13.6812i	−0.463755	−	0.865276i
$251$	−20.7487	−	20.7487i	−1.30964	−	1.30964i	−0.921670	−	0.387974i	$-0.873175\pi$
$251$	−20.7487	−	20.7487i	−1.30964	−	1.30964i	−0.387974	−	0.921670i	$-0.626825\pi$
$252$	1.18265	+	0.786373i	0.0745002	+	0.0495368i
$253$	2.32083	−	2.32083i	0.145909	−	0.145909i
$254$	−0.663811	+	2.19721i	−0.0416512	+	0.137865i
$255$	6.77127			0.424034
$256$	−11.2112	+	11.4153i	−0.700701	+	0.713455i
$257$	−2.99626			−0.186901			−0.0934507	−	0.995624i	$-0.529790\pi$
$257$	−2.99626			−0.186901			−0.0934507	+	0.995624i	$0.529790\pi$
$258$	−2.83798	+	9.39369i	−0.176685	+	0.584826i
$259$	1.08246	−	1.08246i	0.0672608	−	0.0672608i
$260$	9.58457	+	6.37299i	0.594410	+	0.395236i
$261$	−1.62818	−	1.62818i	−0.100782	−	0.100782i
$262$	0.00196218	+	0.00366105i	0.000121224	+	0.000226181i
$263$		−	12.6198i		−	0.778170i	−0.921202	−	0.389085i	$-0.872791\pi$
$263$		−	12.6198i		−	0.778170i	0.921202	−	0.389085i	$-0.127209\pi$
$264$	13.7342	−	11.3493i	0.845279	−	0.698500i
$265$			13.1426i			0.807343i
$266$	−1.32504	+	0.710169i	−0.0812432	+	0.0435432i
$267$	−10.6248	−	10.6248i	−0.650230	−	0.650230i
$268$	−14.5771	+	2.93376i	−0.890440	+	0.179208i
$269$	−7.66183	+	7.66183i	−0.467150	+	0.467150i	−0.900990	−	0.433840i	$-0.857158\pi$
$269$	−7.66183	+	7.66183i	−0.467150	+	0.467150i	0.433840	+	0.900990i	$0.357158\pi$
$270$	−8.04218	−	2.42967i	−0.489432	−	0.147865i
$271$	14.6836			0.891965			0.445982	−	0.895042i	$-0.352854\pi$
$271$	14.6836			0.891965			0.445982	+	0.895042i	$0.352854\pi$
$272$	4.08601	+	9.74003i	0.247751	+	0.590576i
$273$	8.59000			0.519890
$274$	−12.9278	−	3.90570i	−0.780997	−	0.235952i
$275$	−7.46095	+	7.46095i	−0.449912	+	0.449912i
$276$	0.757325	+	3.76297i	0.0455856	+	0.226504i
$277$	−1.64422	−	1.64422i	−0.0987914	−	0.0987914i	0.655984	−	0.754775i	$-0.272254\pi$
$277$	−1.64422	−	1.64422i	−0.0987914	−	0.0987914i	−0.754775	+	0.655984i	$0.772254\pi$
$278$	−15.8963	+	8.51980i	−0.953397	+	0.510984i
$279$		−	3.33575i		−	0.199706i
$280$	−0.371697	+	3.90940i	−0.0222131	+	0.233632i
$281$			0.247492i			0.0147641i	0.999973	+	0.00738207i	$0.00234981\pi$
$281$			0.247492i			0.0147641i	−0.999973	+	0.00738207i	$0.997650\pi$
$282$	0.943868	+	1.76107i	0.0562065	+	0.104870i
$283$	−17.4833	−	17.4833i	−1.03927	−	1.03927i	−0.999197	−	0.0400784i	$-0.987239\pi$
$283$	−17.4833	−	17.4833i	−1.03927	−	1.03927i	−0.0400784	−	0.999197i	$-0.512761\pi$
$284$	1.24985	−	1.87969i	0.0741649	−	0.111539i
$285$	−1.85492	+	1.85492i	−0.109876	+	0.109876i
$286$	5.78199	−	19.1383i	0.341896	−	1.13167i
$287$	−2.73007			−0.161151
$288$	0.400586	+	3.84491i	0.0236048	+	0.226563i
$289$	−10.0273			−0.589840
$290$	1.84132	−	6.09475i	0.108126	−	0.357896i
$291$	19.7015	−	19.7015i	1.15492	−	1.15492i
$292$	−16.4119	+	24.6825i	−0.960435	+	1.44443i
$293$	22.8784	+	22.8784i	1.33657	+	1.33657i	0.899358	+	0.437214i	$0.144035\pi$
$293$	22.8784	+	22.8784i	1.33657	+	1.33657i	0.437214	+	0.899358i	$0.355965\pi$
$294$	−7.59058	−	14.1625i	−0.442691	−	0.825976i
$295$			14.5001i			0.844229i
$296$	4.14805	+	0.394387i	0.241101	+	0.0229233i
$297$			14.5928i			0.846759i
$298$	−20.4198	+	10.9442i	−1.18288	+	0.633980i
$299$	3.04566	+	3.04566i	0.176135	+	0.176135i
$300$	−2.43463	−	12.0971i	−0.140563	−	0.698427i
$301$	−2.65659	+	2.65659i	−0.153123	+	0.153123i
$302$	30.0929	+	9.09155i	1.73165	+	0.523160i
$303$	7.21803			0.414665
$304$	−3.78751	−	1.54886i	−0.217228	−	0.0888334i
$305$	−12.9550			−0.741804
$306$	2.44290	+	0.738038i	0.139651	+	0.0421908i
$307$	−13.2707	+	13.2707i	−0.757399	+	0.757399i	−0.975848	−	0.218449i	$-0.929900\pi$
$307$	−13.2707	+	13.2707i	−0.757399	+	0.757399i	0.218449	+	0.975848i	$0.429900\pi$
$308$	6.68713	−	1.34583i	0.381035	−	0.0766860i
$309$	−7.85741	−	7.85741i	−0.446992	−	0.446992i
$310$	8.12956	−	4.35713i	0.461728	−	0.247468i
$311$		−	25.7509i		−	1.46020i	−0.683339	−	0.730101i	$-0.739473\pi$
$311$		−	25.7509i		−	1.46020i	0.683339	−	0.730101i	$-0.260527\pi$
$312$	14.8938	+	18.0236i	0.843198	+	1.02038i
$313$		−	23.6082i		−	1.33441i	−0.744873	−	0.667206i	$-0.767490\pi$
$313$		−	23.6082i		−	1.33441i	0.744873	−	0.667206i	$-0.232510\pi$
$314$	−11.3068	−	21.0962i	−0.638078	−	1.19053i
$315$	0.670904	+	0.670904i	0.0378011	+	0.0378011i
$316$	−11.4693	−	7.62618i	−0.645197	−	0.429006i
$317$	0.887639	−	0.887639i	0.0498548	−	0.0498548i	−0.681740	−	0.731595i	$-0.738776\pi$
$317$	0.887639	−	0.887639i	0.0498548	−	0.0498548i	0.731595	+	0.681740i	$0.238776\pi$
$318$	−7.72110	+	25.5567i	−0.432978	+	1.43315i
$319$	−11.0591			−0.619191
$320$	−8.84719	+	5.99846i	−0.494573	+	0.335324i
$321$	6.02729			0.336410
$322$	−0.425006	+	1.40676i	−0.0236847	+	0.0783959i
$323$	−1.91011	+	1.91011i	−0.106281	+	0.106281i
$324$	−17.6255	−	11.7196i	−0.979197	−	0.651090i
$325$	−9.79113	−	9.79113i	−0.543114	−	0.543114i
$326$	6.30418	+	11.7624i	0.349156	+	0.651458i
$327$		−	25.4765i		−	1.40885i
$328$	−4.73356	−	5.72824i	−0.261367	−	0.316289i
$329$			0.764972i			0.0421743i
$330$	10.4908	−	5.62268i	0.577502	−	0.309519i
$331$	22.2908	+	22.2908i	1.22521	+	1.22521i	0.965755	+	0.259456i	$0.0835433\pi$
$331$	22.2908	+	22.2908i	1.22521	+	1.22521i	0.259456	+	0.965755i	$0.416457\pi$
$332$	21.0439	−	4.23525i	1.15494	−	0.232439i
$333$	0.711859	−	0.711859i	0.0390096	−	0.0390096i
$334$	−22.2374	−	6.71827i	−1.21678	−	0.367607i
$335$	−9.93369			−0.542735
$336$	−3.01952	+	7.38376i	−0.164728	+	0.402817i
$337$	−15.3503			−0.836183			−0.418091	−	0.908405i	$-0.637301\pi$
$337$	−15.3503			−0.836183			−0.418091	+	0.908405i	$0.637301\pi$
$338$	7.51638	+	2.27082i	0.408837	+	0.123516i
$339$	−2.57122	+	2.57122i	−0.139649	+	0.139649i
$340$	1.39222	+	6.91760i	0.0755037	+	0.375160i
$341$	−11.3287	−	11.3287i	−0.613485	−	0.613485i
$342$	−0.871385	+	0.467029i	−0.0471191	+	0.0252540i
$343$		−	13.4259i		−	0.724929i
$344$	−10.1802	−	0.967910i	−0.548880	−	0.0521862i
$345$			2.56430i			0.138057i
$346$	0.385760	+	0.719753i	0.0207386	+	0.0386942i
$347$	−8.55518	−	8.55518i	−0.459266	−	0.459266i	0.439148	−	0.898415i	$-0.355280\pi$
$347$	−8.55518	−	8.55518i	−0.459266	−	0.459266i	−0.898415	+	0.439148i	$0.855280\pi$
$348$	7.16117	−	10.7699i	0.383879	−	0.577330i
$349$	6.27907	−	6.27907i	0.336111	−	0.336111i	−0.518791	−	0.854901i	$-0.673618\pi$
$349$	6.27907	−	6.27907i	0.336111	−	0.336111i	0.854901	+	0.518791i	$0.173618\pi$
$350$	1.36630	−	4.52243i	0.0730318	−	0.241734i
$351$	−19.1503			−1.02217
$352$	14.4184	+	11.6975i	0.768502	+	0.623477i
$353$	−30.2465			−1.60986			−0.804930	−	0.593370i	$-0.797797\pi$
$353$	−30.2465			−1.60986			−0.804930	+	0.593370i	$0.797797\pi$
$354$	−8.51863	+	28.1965i	−0.452760	+	1.49863i
$355$	1.06632	−	1.06632i	0.0565946	−	0.0565946i
$356$	8.66991	−	13.0390i	0.459505	−	0.691065i
$357$	3.72377	+	3.72377i	0.197083	+	0.197083i
$358$	0.749452	+	1.39833i	0.0396098	+	0.0739041i
$359$		−	6.80471i		−	0.359139i	−0.983745	−	0.179569i	$-0.942530\pi$
$359$		−	6.80471i		−	0.359139i	0.983745	−	0.179569i	$-0.0574704\pi$
$360$	−0.244439	+	2.57094i	−0.0128831	+	0.135501i
$361$			17.9535i			0.944920i
$362$	−7.51227	+	4.02629i	−0.394836	+	0.211617i
$363$	0.308724	+	0.308724i	0.0162038	+	0.0162038i
$364$	1.76616	+	8.77563i	0.0925720	+	0.459968i
$365$	−14.0020	+	14.0020i	−0.732899	+	0.732899i
$366$	−25.1920	−	7.61092i	−1.31681	−	0.397829i
$367$	17.0408			0.889523			0.444761	−	0.895649i	$-0.353288\pi$
$367$	17.0408			0.889523			0.444761	+	0.895649i	$0.353288\pi$
$368$	−3.68858	+	1.54738i	−0.192280	+	0.0806629i
$369$	−1.79538			−0.0934636
$370$	2.66470	+	0.805048i	0.138531	+	0.0418524i
$371$	−7.22758	+	7.22758i	−0.375237	+	0.375237i
$372$	18.3683	−	3.69675i	0.952351	−	0.191668i
$373$	−9.22733	−	9.22733i	−0.477773	−	0.477773i	0.426646	−	0.904419i	$-0.359695\pi$
$373$	−9.22733	−	9.22733i	−0.477773	−	0.477773i	−0.904419	+	0.426646i	$0.859695\pi$
$374$	10.8030	−	5.78997i	0.558607	−	0.299392i
$375$		−	21.0652i		−	1.08780i
$376$	−1.60507	+	1.32635i	−0.0827750	+	0.0684015i
$377$		−	14.5131i		−	0.747460i
$378$	−3.08652	−	5.75885i	−0.158753	−	0.296203i
$379$	22.6596	+	22.6596i	1.16395	+	1.16395i	0.983604	+	0.180342i	$0.0577205\pi$
$379$	22.6596	+	22.6596i	1.16395	+	1.16395i	0.180342	+	0.983604i	$0.442280\pi$
$380$	−2.27639	−	1.51362i	−0.116776	−	0.0776473i
$381$	−2.20257	+	2.20257i	−0.112841	+	0.112841i
$382$	7.35777	−	24.3541i	0.376457	−	1.24607i
$383$	−12.2027			−0.623531			−0.311766	−	0.950159i	$-0.600920\pi$
$383$	−12.2027			−0.623531			−0.311766	+	0.950159i	$0.600920\pi$
$384$	−20.7280	+	6.46684i	−1.05777	+	0.330010i
$385$	4.55699			0.232246
$386$	−2.70552	+	8.95522i	−0.137707	+	0.455809i
$387$	−1.74705	+	1.74705i	−0.0888077	+	0.0888077i
$388$	24.1780	+	16.0765i	1.22745	+	0.816160i
$389$	13.4433	+	13.4433i	0.681601	+	0.681601i	0.960361	−	0.278760i	$-0.0899234\pi$
$389$	13.4433	+	13.4433i	0.681601	+	0.681601i	−0.278760	+	0.960361i	$0.589923\pi$
$390$	7.37874	+	13.7673i	0.373637	+	0.697134i
$391$			2.64059i			0.133540i
$392$	12.9079	−	10.6665i	0.651949	−	0.538741i
$393$			0.00563697i			0.000284348i
$394$	−18.9634	+	10.1637i	−0.955365	+	0.512039i
$395$	−6.50636	−	6.50636i	−0.327371	−	0.327371i
$396$	4.39766	−	0.885062i	0.220991	−	0.0444760i
$397$	5.80463	−	5.80463i	0.291326	−	0.291326i	−0.546278	−	0.837604i	$-0.683956\pi$
$397$	5.80463	−	5.80463i	0.291326	−	0.291326i	0.837604	+	0.546278i	$0.183956\pi$
$398$	−12.6089	−	3.80936i	−0.632028	−	0.190946i
$399$	−2.04018			−0.102137
$400$	11.8580	−	4.97449i	0.592898	−	0.248724i
$401$	29.9626			1.49626			0.748132	−	0.663550i	$-0.230951\pi$
$401$	29.9626			1.49626			0.748132	+	0.663550i	$0.230951\pi$
$402$	−19.3168	−	5.83591i	−0.963434	−	0.291069i
$403$	14.8669	−	14.8669i	0.740572	−	0.740572i
$404$	1.48408	+	7.37402i	0.0738355	+	0.366871i
$405$	−9.99873	−	9.99873i	−0.496841	−	0.496841i
$406$	4.36433	−	2.33911i	0.216598	−	0.116088i
$407$		−	4.83517i		−	0.239671i
$408$	−1.35673	+	14.2697i	−0.0671681	+	0.706455i
$409$			32.7649i			1.62012i	0.586348	+	0.810059i	$0.300565\pi$
$409$			32.7649i			1.62012i	−0.586348	+	0.810059i	$0.699435\pi$
$410$	−2.34511	−	4.37552i	−0.115817	−	0.216091i
$411$	−12.9594	−	12.9594i	−0.639239	−	0.639239i
$412$	6.41168	−	9.64275i	0.315881	−	0.475064i
$413$	−7.97413	+	7.97413i	−0.392381	+	0.392381i
$414$	−0.279497	+	0.925131i	−0.0137365	+	0.0454677i
$415$	14.3405			0.703949
$416$	−15.3508	+	18.9215i	−0.752634	+	0.927702i
$417$	−24.4757			−1.19858
$418$	−1.37326	+	4.54547i	−0.0671682	+	0.222326i
$419$	7.29280	−	7.29280i	0.356277	−	0.356277i	−0.506162	−	0.862439i	$-0.668936\pi$
$419$	7.29280	−	7.29280i	0.356277	−	0.356277i	0.862439	+	0.506162i	$0.168936\pi$
$420$	−2.95082	+	4.43784i	−0.143985	+	0.216544i
$421$	−28.3286	−	28.3286i	−1.38065	−	1.38065i	−0.843465	−	0.537184i	$-0.819488\pi$
$421$	−28.3286	−	28.3286i	−1.38065	−	1.38065i	−0.537184	−	0.843465i	$-0.680512\pi$
$422$	17.8166	+	33.2423i	0.867297	+	1.61821i
$423$			0.503069i			0.0244601i
$424$	−27.6965	−	2.63332i	−1.34506	−	0.127885i
$425$		−	8.48891i		−	0.411773i
$426$	2.70000	−	1.44709i	0.130815	−	0.0701119i
$427$	−7.12444	−	7.12444i	−0.344776	−	0.344776i
$428$	1.23925	+	6.15754i	0.0599014	+	0.297636i
$429$	19.1851	−	19.1851i	0.926263	−	0.926263i
$430$	−6.53973	−	1.97576i	−0.315374	−	0.0952795i
$431$	28.6230			1.37872			0.689360	−	0.724419i	$-0.257892\pi$
$431$	28.6230			1.37872			0.689360	+	0.724419i	$0.257892\pi$
$432$	6.73164	−	16.4612i	0.323876	−	0.791989i
$433$	−20.1257			−0.967182			−0.483591	−	0.875294i	$-0.660668\pi$
$433$	−20.1257			−0.967182			−0.483591	+	0.875294i	$0.660668\pi$
$434$	6.86688	+	2.07459i	0.329621	+	0.0995837i
$435$	6.10964	−	6.10964i	0.292935	−	0.292935i
$436$	26.0270	−	5.23813i	1.24647	−	0.250861i
$437$	−0.723364	−	0.723364i	−0.0346032	−	0.0346032i
$438$	−35.4540	+	19.0020i	−1.69406	+	0.907948i
$439$			29.2451i			1.39579i	0.716198	+	0.697897i	$0.245881\pi$
$439$			29.2451i			1.39579i	−0.716198	+	0.697897i	$0.754119\pi$
$440$	7.90118	+	9.56149i	0.376674	+	0.455826i
$441$		−	4.04568i		−	0.192651i
$442$	7.59827	+	14.1769i	0.361413	+	0.674326i
$443$	22.0509	+	22.0509i	1.04767	+	1.04767i	0.998805	+	0.0488650i	$0.0155604\pi$
$443$	22.0509	+	22.0509i	1.04767	+	1.04767i	0.0488650	+	0.998805i	$0.484440\pi$
$444$	4.70875	+	3.13095i	0.223467	+	0.148588i
$445$	7.39684	−	7.39684i	0.350644	−	0.350644i
$446$	5.64911	−	18.6985i	0.267493	−	0.885398i
$447$	−31.4406			−1.48709
$448$	−8.16416	−	1.56662i	−0.385720	−	0.0740158i
$449$	−14.7479			−0.695994			−0.347997	−	0.937496i	$-0.613138\pi$
$449$	−14.7479			−0.695994			−0.347997	+	0.937496i	$0.613138\pi$
$450$	0.898520	−	2.97409i	0.0423567	−	0.140200i
$451$	−6.09739	+	6.09739i	−0.287115	+	0.287115i
$452$	−3.15544	−	2.09812i	−0.148419	−	0.0986874i
$453$	30.1664	+	30.1664i	1.41734	+	1.41734i
$454$	1.60130	+	2.98771i	0.0751526	+	0.140220i
$455$			5.98021i			0.280357i
$456$	−3.53738	−	4.28070i	−0.165653	−	0.200462i
$457$			38.4217i			1.79729i	0.438675	+	0.898646i	$0.355448\pi$
$457$			38.4217i			1.79729i	−0.438675	+	0.898646i	$0.644552\pi$
$458$	−22.9047	+	12.2760i	−1.07027	+	0.573621i
$459$	−8.30168	−	8.30168i	−0.387489	−	0.387489i
$460$	−2.61972	+	0.527237i	−0.122145	+	0.0245826i
$461$	−13.6064	+	13.6064i	−0.633711	+	0.633711i	−0.948997	−	0.315286i	$-0.897900\pi$
$461$	−13.6064	+	13.6064i	−0.633711	+	0.633711i	0.315286	+	0.948997i	$0.397900\pi$
$462$	8.86140	+	2.67717i	0.412270	+	0.124553i
$463$	26.3626			1.22517			0.612586	−	0.790404i	$-0.290129\pi$
$463$	26.3626			1.22517			0.612586	+	0.790404i	$0.290129\pi$
$464$	12.4751	+	5.10156i	0.579141	+	0.236834i
$465$	12.5172			0.580471
$466$	27.9700	+	8.45017i	1.29568	+	0.391447i
$467$	7.32038	−	7.32038i	0.338747	−	0.338747i	−0.517149	−	0.855896i	$-0.673007\pi$
$467$	7.32038	−	7.32038i	0.338747	−	0.338747i	0.855896	+	0.517149i	$0.173007\pi$
$468$	1.16148	+	5.77112i	0.0536895	+	0.266770i
$469$	−5.46289	−	5.46289i	−0.252253	−	0.252253i
$470$	−1.22603	+	0.657105i	−0.0565526	+	0.0303100i
$471$		−	32.4822i		−	1.49670i
$472$	−30.5574	−	2.90532i	−1.40652	−	0.133728i
$473$			11.8665i			0.545624i
$474$	−8.82970	−	16.4745i	−0.405562	−	0.756699i
$475$	2.32545	+	2.32545i	0.106699	+	0.106699i
$476$	−3.03861	+	4.56987i	−0.139274	+	0.209460i
$477$	−4.75308	+	4.75308i	−0.217629	+	0.217629i
$478$	−9.56599	+	31.6633i	−0.437538	+	1.44825i
$479$	37.5883			1.71745			0.858727	−	0.512433i	$-0.171256\pi$
$479$	37.5883			1.71745			0.858727	+	0.512433i	$0.171256\pi$
$480$	−14.4278	+	1.50317i	−0.658535	+	0.0686102i
$481$	6.34528			0.289320
$482$	−1.42447	+	4.71498i	−0.0648828	+	0.214761i
$483$	−1.41020	+	1.41020i	−0.0641664	+	0.0641664i
$484$	−0.251920	+	0.378871i	−0.0114509	+	0.0172214i
$485$	13.7158	+	13.7158i	0.622804	+	0.622804i
$486$	−4.65834	−	8.69155i	−0.211306	−	0.394257i
$487$		−	0.799551i		−	0.0362311i	−0.999836	−	0.0181156i	$-0.994233\pi$
$487$		−	0.799551i		−	0.0362311i	0.999836	−	0.0181156i	$-0.00576667\pi$
$488$	2.59574	−	27.3013i	0.117504	−	1.23587i
$489$			18.1107i			0.818993i
$490$	9.85973	−	5.28443i	0.445417	−	0.238726i
$491$	−6.00074	−	6.00074i	−0.270809	−	0.270809i	0.558617	−	0.829426i	$-0.311332\pi$
$491$	−6.00074	−	6.00074i	−0.270809	−	0.270809i	−0.829426	+	0.558617i	$0.811332\pi$
$492$	−1.98968	−	9.88623i	−0.0897016	−	0.445706i
$493$	6.29141	−	6.29141i	0.283351	−	0.283351i
$494$	−5.96509	−	1.80215i	−0.268382	−	0.0810825i
$495$	2.99682			0.134697
$496$	7.55328	+	18.0052i	0.339152	+	0.808455i
$497$	1.17282			0.0526081
$498$	27.8862	+	8.42488i	1.24961	+	0.377528i
$499$	11.7126	−	11.7126i	0.524326	−	0.524326i	−0.394549	−	0.918875i	$-0.629099\pi$
$499$	11.7126	−	11.7126i	0.524326	−	0.524326i	0.918875	+	0.394549i	$0.129099\pi$
$500$	21.5204	−	4.33114i	0.962421	−	0.193694i
$501$	−22.2917	−	22.2917i	−0.995920	−	0.995920i
$502$	36.5753	−	19.6030i	1.63244	−	0.874923i
$503$		−	34.7455i		−	1.54922i	−0.632436	−	0.774612i	$-0.717945\pi$
$503$		−	34.7455i		−	1.54922i	0.632436	−	0.774612i	$-0.282055\pi$
$504$	−1.54828	+	1.27943i	−0.0689659	+	0.0569903i
$505$			5.02507i			0.223613i
$506$	2.19268	+	4.09111i	0.0974764	+	0.181872i
$507$	7.53474	+	7.53474i	0.334630	+	0.334630i
$508$	−2.70303	−	1.79731i	−0.119928	−	0.0797426i
$509$	17.9923	−	17.9923i	0.797494	−	0.797494i	−0.185206	−	0.982700i	$-0.559295\pi$
$509$	17.9923	−	17.9923i	0.797494	−	0.797494i	0.982700	+	0.185206i	$0.0592951\pi$
$510$	−2.76944	+	9.16681i	−0.122633	+	0.405913i
$511$	−15.4004			−0.681275
$512$	−10.8684	−	19.8464i	−0.480320	−	0.877093i
$513$	4.54832			0.200813
$514$	1.22547	−	4.05627i	0.0540530	−	0.178915i
$515$	5.47020	−	5.47020i	0.241046	−	0.241046i
$516$	−11.5563	−	7.68401i	−0.508736	−	0.338270i
$517$	1.70850	+	1.70850i	0.0751399	+	0.0751399i
$518$	1.02269	+	1.90814i	0.0449343	+	0.0838388i
$519$			1.10821i			0.0486452i
$520$	−12.5477	+	10.3688i	−0.550253	+	0.454704i
$521$			29.4574i			1.29055i	0.763950	+	0.645275i	$0.223257\pi$
$521$			29.4574i			1.29055i	−0.763950	+	0.645275i	$0.776743\pi$
$522$	2.87012	−	1.53827i	0.125622	−	0.0673284i
$523$	17.8554	+	17.8554i	0.780762	+	0.780762i	0.979959	−	0.199197i	$-0.0638334\pi$
$523$	17.8554	+	17.8554i	0.780762	+	0.780762i	−0.199197	+	0.979959i	$0.563833\pi$
$524$	−0.00575879	+	0.00115900i	−0.000251574	+	5.06311e-5i
$525$	4.53348	−	4.53348i	0.197857	−	0.197857i
$526$	17.0844	+	5.16148i	0.744917	+	0.225051i
$527$	12.8896			0.561479
$528$	9.74718	+	23.2349i	0.424191	+	1.01117i
$529$	−1.00000			−0.0434783
$530$	−17.7922	−	5.37530i	−0.772843	−	0.233488i
$531$	−5.24403	+	5.24403i	−0.227572	+	0.227572i
$532$	−0.419474	−	2.08427i	−0.0181865	−	0.0903644i
$533$	−8.00170	−	8.00170i	−0.346592	−	0.346592i
$534$	18.7292	−	10.0382i	0.810494	−	0.434393i
$535$			4.19610i			0.181413i
$536$	1.99037	−	20.9341i	0.0859708	−	0.904217i
$537$			2.15303i			0.0929101i
$538$	−7.23875	−	13.5061i	−0.312085	−	0.582289i
$539$	−13.7398	−	13.7398i	−0.591813	−	0.591813i
$540$	6.57848	−	9.89361i	0.283093	−	0.425753i
$541$	27.0332	−	27.0332i	1.16225	−	1.16225i	0.178265	−	0.983982i	$-0.442951\pi$
$541$	27.0332	−	27.0332i	1.16225	−	1.16225i	0.983982	−	0.178265i	$-0.0570485\pi$
$542$	−6.00557	+	19.8784i	−0.257961	+	0.853848i
$543$	−11.5667			−0.496377
$544$	−14.8570	+	1.54790i	−0.636990	+	0.0663655i
$545$	17.7363			0.759739
$546$	−3.51330	+	11.6290i	−0.150355	+	0.497674i
$547$	10.7547	−	10.7547i	0.459837	−	0.459837i	−0.438765	−	0.898602i	$-0.644584\pi$
$547$	10.7547	−	10.7547i	0.459837	−	0.459837i	0.898602	+	0.438765i	$0.144584\pi$
$548$	10.5749	−	15.9040i	0.451738	−	0.679384i
$549$	−4.68525	−	4.68525i	−0.199962	−	0.199962i
$550$	−7.04897	−	13.1520i	−0.300569	−	0.560803i
$551$			3.44694i			0.146845i
$552$	−5.40398	−	0.513797i	−0.230009	−	0.0218687i
$553$		−	7.15617i		−	0.304311i
$554$	2.89839	−	1.55342i	0.123141	−	0.0659987i
$555$	2.67121	+	2.67121i	0.113386	+	0.113386i
$556$	−5.03238	−	25.0047i	−0.213420	−	1.06043i
$557$	20.3767	−	20.3767i	0.863388	−	0.863388i	−0.128342	−	0.991730i	$-0.540966\pi$
$557$	20.3767	−	20.3767i	0.863388	−	0.863388i	0.991730	+	0.128342i	$0.0409656\pi$
$558$	4.51587	+	1.36432i	0.191172	+	0.0577561i
$559$	−15.5727			−0.658653
$560$	−5.14045	−	2.10214i	−0.217224	−	0.0888315i
$561$	16.6335			0.702265
$562$	−0.335050	−	0.101224i	−0.0141332	−	0.00426987i
$563$	0.0151291	−	0.0151291i	0.000637614	−	0.000637614i	−0.706788	−	0.707426i	$-0.749856\pi$
$563$	0.0151291	−	0.0151291i	0.000637614	−	0.000637614i	0.707426	+	0.706788i	$0.249856\pi$
$564$	−2.77015	+	0.557513i	−0.116644	+	0.0234755i
$565$	−1.79004	−	1.79004i	−0.0753075	−	0.0753075i
$566$	30.8192	−	16.5179i	1.29543	−	0.694299i
$567$		−	10.9973i		−	0.461844i
$568$	2.03350	+	2.46081i	0.0853239	+	0.103253i
$569$		−	28.2556i		−	1.18453i	−0.805742	−	0.592267i	$-0.798233\pi$
$569$		−	28.2556i		−	1.18453i	0.805742	−	0.592267i	$-0.201767\pi$
$570$	−1.75250	−	3.26982i	−0.0734040	−	0.136958i
$571$	20.3606	+	20.3606i	0.852064	+	0.852064i	0.990387	−	0.138323i	$-0.0441712\pi$
$571$	20.3606	+	20.3606i	0.852064	+	0.852064i	−0.138323	+	0.990387i	$0.544171\pi$
$572$	23.5442	+	15.6551i	0.984434	+	0.654572i
$573$	24.4136	−	24.4136i	1.01989	−	1.01989i
$574$	1.11659	−	3.69591i	0.0466058	−	0.154264i
$575$	3.21478			0.134065
$576$	−5.36900	−	1.03026i	−0.223708	−	0.0429274i
$577$	−12.2293			−0.509111			−0.254555	−	0.967058i	$-0.581929\pi$
$577$	−12.2293			−0.509111			−0.254555	+	0.967058i	$0.581929\pi$
$578$	4.10114	−	13.5747i	0.170585	−	0.564634i
$579$	−8.97709	+	8.97709i	−0.373075	+	0.373075i
$580$	7.49786	+	4.98549i	0.311332	+	0.207011i
$581$	7.88638	+	7.88638i	0.327182	+	0.327182i
$582$	18.6136	+	34.7293i	0.771558	+	1.43958i
$583$			32.2844i			1.33708i
$584$	−26.7022	−	32.3132i	−1.10494	−	1.33713i
$585$			3.93277i			0.162600i
$586$	−40.3296	+	21.6151i	−1.66600	+	0.892912i
$587$	−0.477560	−	0.477560i	−0.0197110	−	0.0197110i	0.697183	−	0.716894i	$-0.254437\pi$
$587$	−0.477560	−	0.477560i	−0.0197110	−	0.0197110i	−0.716894	+	0.697183i	$0.754437\pi$
$588$	22.2775	−	4.48351i	0.918708	−	0.184897i
$589$	−3.53098	+	3.53098i	−0.145491	+	0.145491i
$590$	−19.6300	−	5.93053i	−0.808153	−	0.244156i
$591$	−29.1983			−1.20106
$592$	−2.23046	+	5.45425i	−0.0916714	+	0.224168i
$593$	−44.7662			−1.83833			−0.919164	−	0.393874i	$-0.871135\pi$
$593$	−44.7662			−1.83833			−0.919164	+	0.393874i	$0.871135\pi$
$594$	−19.7554	−	5.96842i	−0.810574	−	0.244887i
$595$	−2.59242	+	2.59242i	−0.106279	+	0.106279i
$596$	−6.46439	−	32.1200i	−0.264792	−	1.31569i
$597$	−12.6397	−	12.6397i	−0.517309	−	0.517309i
$598$	−5.36883	+	2.87749i	−0.219548	+	0.117669i
$599$		−	0.331335i		−	0.0135380i	−0.999977	−	0.00676899i	$-0.997845\pi$
$599$		−	0.331335i		−	0.0135380i	0.999977	−	0.00676899i	$-0.00215465\pi$
$600$	17.3726	+	1.65174i	0.709232	+	0.0674322i
$601$		−	15.2465i		−	0.621918i	−0.950423	−	0.310959i	$-0.899350\pi$
$601$		−	15.2465i		−	0.621918i	0.950423	−	0.310959i	$-0.100650\pi$
$602$	−2.50989	−	4.68297i	−0.102296	−	0.190864i
$603$	−3.59256	−	3.59256i	−0.146301	−	0.146301i
$604$	−24.6159	+	37.0207i	−1.00161	+	1.50635i
$605$	−0.214928	+	0.214928i	−0.00873808	+	0.00873808i
$606$	−2.95216	+	9.77163i	−0.119924	+	0.396945i
$607$	3.73658			0.151663			0.0758315	−	0.997121i	$-0.475839\pi$
$607$	3.73658			0.151663			0.0758315	+	0.997121i	$0.475839\pi$
$608$	3.64590	−	4.49397i	0.147861	−	0.182254i
$609$	6.71982			0.272301
$610$	5.29859	−	17.5383i	0.214534	−	0.710104i
$611$	−2.24210	+	2.24210i	−0.0907055	+	0.0907055i
$612$	−1.99828	+	3.00529i	−0.0807757	+	0.121481i
$613$	−2.71214	−	2.71214i	−0.109542	−	0.109542i	0.650211	−	0.759753i	$-0.274680\pi$
$613$	−2.71214	−	2.71214i	−0.109542	−	0.109542i	−0.759753	+	0.650211i	$0.774680\pi$
$614$	−12.5379	−	23.3933i	−0.505989	−	0.944077i
$615$		−	6.73704i		−	0.271664i
$616$	−0.913064	+	9.60335i	−0.0367884	+	0.386930i
$617$		−	35.3903i		−	1.42476i	−0.701795	−	0.712379i	$-0.747618\pi$
$617$		−	35.3903i		−	1.42476i	0.701795	−	0.712379i	$-0.252382\pi$
$618$	13.8509	−	7.42353i	0.557164	−	0.298618i
$619$	−2.08383	−	2.08383i	−0.0837563	−	0.0837563i	0.663987	−	0.747744i	$-0.268863\pi$
$619$	−2.08383	−	2.08383i	−0.0837563	−	0.0837563i	−0.747744	+	0.663987i	$0.768863\pi$
$620$	2.57362	+	12.7877i	0.103359	+	0.513566i
$621$	3.14387	−	3.14387i	0.126159	−	0.126159i
$622$	34.8611	+	10.5321i	1.39780	+	0.422299i
$623$	8.13558			0.325945
$624$	−30.4915	+	12.7914i	−1.22064	+	0.512065i
$625$	−1.40867			−0.0563468
$626$	31.9603	+	9.65571i	1.27739	+	0.385920i
$627$	−4.55657	+	4.55657i	−0.181972	+	0.181972i
$628$	33.1841	−	6.67855i	1.32419	−	0.266503i
$629$	2.75068	+	2.75068i	0.109677	+	0.109677i
$630$	−1.18265	+	0.633857i	−0.0471181	+	0.0252535i
$631$			9.64495i			0.383960i	0.981399	+	0.191980i	$0.0614908\pi$
$631$			9.64495i			0.383960i	−0.981399	+	0.191980i	$0.938509\pi$
$632$	15.0151	−	12.4078i	0.597268	−	0.493555i
$633$			51.1835i			2.03436i
$634$	0.838624	+	1.56471i	0.0333060	+	0.0621426i
$635$	−1.53339	−	1.53339i	−0.0608509	−	0.0608509i
$636$	−31.4403	−	20.9053i	−1.24669	−	0.828951i
$637$	18.0309	−	18.0309i	0.714411	−	0.714411i
$638$	4.52316	−	14.9716i	0.179074	−	0.592731i
$639$	0.771282			0.0305114
$640$	−4.50211	−	14.4305i	−0.177961	−	0.570416i
$641$	−12.4528			−0.491854			−0.245927	−	0.969288i	$-0.579092\pi$
$641$	−12.4528			−0.491854			−0.245927	+	0.969288i	$0.579092\pi$
$642$	−2.46515	+	8.15962i	−0.0972918	+	0.322034i
$643$	−29.4591	+	29.4591i	−1.16175	+	1.16175i	−0.177660	+	0.984092i	$0.556853\pi$
$643$	−29.4591	+	29.4591i	−1.16175	+	1.16175i	−0.984092	+	0.177660i	$0.943147\pi$
$644$	−1.73062	−	1.15073i	−0.0681961	−	0.0453451i
$645$	−6.55571	−	6.55571i	−0.258131	−	0.258131i
$646$	−1.80464	−	3.36710i	−0.0710024	−	0.132477i
$647$			20.4981i			0.805864i	0.915230	+	0.402932i	$0.132009\pi$
$647$			20.4981i			0.805864i	−0.915230	+	0.402932i	$0.867991\pi$
$648$	23.0746	−	19.0678i	0.906456	−	0.749054i
$649$			35.6192i			1.39817i
$650$	17.2596	−	9.25048i	0.676977	−	0.362834i
$651$	6.88365	+	6.88365i	0.269792	+	0.269792i
$652$	−18.5021	+	3.72368i	−0.724597	+	0.145830i
$653$	20.5538	−	20.5538i	0.804331	−	0.804331i	−0.179439	−	0.983769i	$-0.557428\pi$
$653$	20.5538	−	20.5538i	0.804331	−	0.804331i	0.983769	+	0.179439i	$0.0574281\pi$
$654$	34.4895	+	10.4198i	1.34865	+	0.407448i
$655$	−0.00392437			−0.000153338
$656$	9.69079	−	4.06535i	0.378362	−	0.158725i
$657$	−10.1278			−0.395123
$658$	−1.03560	−	0.312873i	−0.0403721	−	0.0121970i
$659$	−22.8047	+	22.8047i	−0.888345	+	0.888345i	−0.994364	−	0.106019i	$-0.966190\pi$
$659$	−22.8047	+	22.8047i	−0.888345	+	0.888345i	0.106019	+	0.994364i	$0.466190\pi$
$660$	3.32114	+	16.5020i	0.129275	+	0.642338i
$661$	26.5982	+	26.5982i	1.03455	+	1.03455i	0.999381	+	0.0351672i	$0.0111964\pi$
$661$	26.5982	+	26.5982i	1.03455	+	1.03455i	0.0351672	+	0.999381i	$0.488804\pi$
$662$	−39.2937	+	21.0599i	−1.52719	+	0.818516i
$663$			21.8284i			0.847743i
$664$	−2.87335	+	30.2211i	−0.111508	+	1.17281i
$665$		−	1.42034i		−	0.0550783i
$666$	0.672551	+	1.25485i	0.0260608	+	0.0486244i
$667$	2.38258	+	2.38258i	0.0922537	+	0.0922537i
$668$	18.1901	−	27.3568i	0.703797	−	1.05847i
$669$	18.7441	−	18.7441i	0.724690	−	0.724690i
$670$	4.06286	−	13.4480i	0.156962	−	0.519543i
$671$	−31.8237			−1.22854
$672$	−8.76100	−	7.10771i	−0.337963	−	0.274186i
$673$	−3.50318			−0.135038			−0.0675188	−	0.997718i	$-0.521508\pi$
$673$	−3.50318			−0.135038			−0.0675188	+	0.997718i	$0.521508\pi$
$674$	6.27824	−	20.7809i	0.241829	−	0.800450i
$675$	−10.1068	+	10.1068i	−0.389012	+	0.389012i
$676$	−6.14838	+	9.24677i	−0.236476	+	0.355645i
$677$	19.1608	+	19.1608i	0.736411	+	0.736411i	0.971881	−	0.235471i	$-0.0756632\pi$
$677$	19.1608	+	19.1608i	0.736411	+	0.736411i	−0.235471	+	0.971881i	$0.575663\pi$
$678$	−2.42924	−	4.53248i	−0.0932943	−	0.174069i
$679$			15.0857i			0.578935i
$680$	−9.93433	−	0.944533i	−0.380964	−	0.0362212i
$681$			4.60022i			0.176281i
$682$	19.9700	−	10.7032i	0.764693	−	0.409846i
$683$	25.0664	+	25.0664i	0.959141	+	0.959141i	0.999197	−	0.0400569i	$-0.0127539\pi$
$683$	25.0664	+	25.0664i	0.959141	+	0.959141i	−0.0400569	+	0.999197i	$0.512754\pi$
$684$	−0.275859	−	1.37068i	−0.0105477	−	0.0524092i
$685$	9.02211	−	9.02211i	0.344717	−	0.344717i
$686$	18.1757	+	5.49116i	0.693950	+	0.209653i
$687$	−35.2667			−1.34551
$688$	5.47403	−	13.3859i	0.208695	−	0.510332i
$689$	−42.3674			−1.61407
$690$	−3.47150	−	1.04880i	−0.132158	−	0.0399270i
$691$	−17.8490	+	17.8490i	−0.679006	+	0.679006i	−0.959775	−	0.280769i	$-0.909411\pi$
$691$	−17.8490	+	17.8490i	−0.679006	+	0.679006i	0.280769	+	0.959775i	$0.409411\pi$
$692$	−1.13216	+	0.227856i	−0.0430384	+	0.00866179i
$693$	1.64806	+	1.64806i	0.0626045	+	0.0626045i
$694$	15.0809	−	8.08278i	0.572463	−	0.306818i
$695$		−	17.0396i		−	0.646349i
$696$	11.6512	+	14.0995i	0.441638	+	0.534442i
$697$		−	6.93748i		−	0.262776i
$698$	5.93235	+	11.0686i	0.224543	+	0.418953i
$699$	28.0383	+	28.0383i	1.06050	+	1.06050i
$700$	5.56357	+	3.69934i	0.210283	+	0.139822i
$701$	−17.2434	+	17.2434i	−0.651275	+	0.651275i	−0.953300	−	0.302025i	$-0.902337\pi$
$701$	−17.2434	+	17.2434i	−0.651275	+	0.651275i	0.302025	+	0.953300i	$0.402337\pi$
$702$	7.83246	−	25.9253i	0.295617	−	0.978489i
$703$	−1.50704			−0.0568392
$704$	−21.7329	+	14.7351i	−0.819089	+	0.555348i
$705$	−1.88774			−0.0710963
$706$	12.3708	−	40.9471i	0.465580	−	1.54107i
$707$	−2.76347	+	2.76347i	−0.103931	+	0.103931i
$708$	−34.6878	−	23.0647i	−1.30365	−	0.866824i
$709$	−22.7158	−	22.7158i	−0.853109	−	0.853109i	0.137406	−	0.990515i	$-0.456123\pi$
$709$	−22.7158	−	22.7158i	−0.853109	−	0.853109i	−0.990515	+	0.137406i	$0.956123\pi$
$710$	1.00744	+	1.87969i	0.0378087	+	0.0705436i
$711$		−	4.70611i		−	0.176493i
$712$	14.1059	+	17.0701i	0.528643	+	0.639729i
$713$			4.88133i			0.182807i
$714$	−6.56417	+	3.51814i	−0.245658	+	0.131663i
$715$	13.3563	+	13.3563i	0.499498	+	0.499498i
$716$	−2.19956	+	0.442677i	−0.0822013	+	0.0165436i
$717$	−31.7406	+	31.7406i	−1.18538	+	1.18538i
$718$	9.21207	+	2.78312i	0.343792	+	0.103865i
$719$	−5.56231			−0.207439			−0.103720	−	0.994607i	$-0.533074\pi$
$719$	−5.56231			−0.207439			−0.103720	+	0.994607i	$0.533074\pi$
$720$	−3.38052	−	1.38243i	−0.125984	−	0.0515201i
$721$	6.01652			0.224067
$722$	−24.3051	−	7.34295i	−0.904541	−	0.273276i
$723$	−4.72650	+	4.72650i	−0.175780	+	0.175780i
$724$	−2.37820	−	11.8167i	−0.0883851	−	0.439165i
$725$	−7.65945	−	7.65945i	−0.284465	−	0.284465i
$726$	−0.544212	+	0.291676i	−0.0201976	+	0.0108251i
$727$			24.9482i			0.925276i	0.886547	+	0.462638i	$0.153097\pi$
$727$			24.9482i			0.925276i	−0.886547	+	0.462638i	$0.846903\pi$
$728$	−12.6026	−	1.19823i	−0.467085	−	0.0444093i
$729$			18.3668i			0.680254i
$730$	−13.2288	−	24.6825i	−0.489622	−	0.913539i
$731$	−6.75075	−	6.75075i	−0.249685	−	0.249685i
$732$	20.6070	−	30.9916i	0.761657	−	1.14548i
$733$	−4.28174	+	4.28174i	−0.158150	+	0.158150i	−0.781746	−	0.623597i	$-0.785671\pi$
$733$	−4.28174	+	4.28174i	−0.158150	+	0.158150i	0.623597	+	0.781746i	$0.285671\pi$
$734$	−6.96967	+	23.0695i	−0.257255	+	0.851511i
$735$	15.1812			0.559965
$736$	−0.586193	−	5.62640i	−0.0216073	−	0.207392i
$737$	−24.4018			−0.898854
$738$	0.734307	−	2.43055i	0.0270302	−	0.0894696i
$739$	−22.1800	+	22.1800i	−0.815904	+	0.815904i	−0.985512	−	0.169608i	$-0.945750\pi$
$739$	−22.1800	+	22.1800i	−0.815904	+	0.815904i	0.169608	+	0.985512i	$0.445750\pi$
$740$	−2.17972	+	3.27815i	−0.0801279	+	0.120507i
$741$	−5.97966	−	5.97966i	−0.219668	−	0.219668i
$742$	−6.82849	−	12.7406i	−0.250682	−	0.467723i
$743$		−	6.84629i		−	0.251166i	−0.992083	−	0.125583i	$-0.959920\pi$
$743$		−	6.84629i		−	0.251166i	0.992083	−	0.125583i	$-0.0400801\pi$
$744$	−2.50801	+	26.3786i	−0.0919482	+	0.967085i
$745$		−	21.8884i		−	0.801929i
$746$	16.2657	−	8.71781i	0.595531	−	0.319182i
$747$	5.18632	+	5.18632i	0.189758	+	0.189758i
$748$	3.41995	+	16.9929i	0.125046	+	0.621322i
$749$	−2.30758	+	2.30758i	−0.0843173	+	0.0843173i
$750$	28.5176	+	8.61562i	1.04132	+	0.314598i
$751$	−23.1178			−0.843580			−0.421790	−	0.906693i	$-0.638598\pi$
$751$	−23.1178			−0.843580			−0.421790	+	0.906693i	$0.638598\pi$
$752$	−1.13912	−	2.71538i	−0.0415395	−	0.0990199i
$753$	56.3155			2.05225
$754$	19.6475	+	5.93582i	0.715519	+	0.216170i
$755$	−21.0014	+	21.0014i	−0.764318	+	0.764318i
$756$	9.05859	−	1.82311i	0.329458	−	0.0663058i
$757$	21.7823	+	21.7823i	0.791691	+	0.791691i	0.981769	−	0.190078i	$-0.0608741\pi$
$757$	21.7823	+	21.7823i	0.791691	+	0.791691i	−0.190078	+	0.981769i	$0.560874\pi$
$758$	−39.9439	+	21.4084i	−1.45083	+	0.777587i
$759$			6.29914i			0.228644i
$760$	2.98016	−	2.46267i	0.108102	−	0.0893302i
$761$			20.6449i			0.748378i	0.927353	+	0.374189i	$0.122079\pi$
$761$			20.6449i			0.748378i	−0.927353	+	0.374189i	$0.877921\pi$
$762$	−2.08095	−	3.88265i	−0.0753848	−	0.140653i
$763$	9.75382	+	9.75382i	0.353112	+	0.353112i
$764$	29.9608	+	19.9216i	1.08394	+	0.720739i
$765$	−1.70486	+	1.70486i	−0.0616392	+	0.0616392i
$766$	4.99090	−	16.5198i	0.180329	−	0.596886i
$767$	−46.7436			−1.68781
$768$	−0.276942	−	30.7061i	−0.00999329	−	1.10801i
$769$	−18.1582			−0.654803			−0.327402	−	0.944885i	$-0.606173\pi$
$769$	−18.1582			−0.654803			−0.327402	+	0.944885i	$0.606173\pi$
$770$	−1.86380	+	6.16916i	−0.0671668	+	0.222321i
$771$	4.06618	−	4.06618i	0.146440	−	0.146440i
$772$	−11.0168	−	7.32534i	−0.396505	−	0.263645i
$773$	27.1002	+	27.1002i	0.974727	+	0.974727i	0.999688	−	0.0249615i	$-0.00794632\pi$
$773$	27.1002	+	27.1002i	0.974727	+	0.974727i	−0.0249615	+	0.999688i	$0.507946\pi$
$774$	−1.65058	−	3.07967i	−0.0593290	−	0.110696i
$775$		−	15.6924i		−	0.563687i
$776$	−31.6528	+	26.1564i	−1.13627	+	0.938961i
$777$			2.93798i			0.105400i
$778$	−23.6975	+	12.7010i	−0.849597	+	0.455351i
$779$	1.90045	+	1.90045i	0.0680908	+	0.0680908i
$780$	−21.6558	+	4.35839i	−0.775402	+	0.156055i
$781$	2.61940	−	2.61940i	0.0937294	−	0.0937294i
$782$	−3.57478	−	1.08000i	−0.127834	−	0.0386207i
$783$	−14.9810			−0.535378
$784$	9.16080	+	21.8371i	0.327172	+	0.779896i
$785$	22.6135			0.807112
$786$	−0.00763122	−	0.00230551i	−0.000272197	−	8.22350e-5i
$787$	14.0686	−	14.0686i	0.501490	−	0.501490i	−0.410411	−	0.911901i	$-0.634615\pi$
$787$	14.0686	−	14.0686i	0.501490	−	0.501490i	0.911901	+	0.410411i	$0.134615\pi$
$788$	−6.00336	−	29.8293i	−0.213861	−	1.06262i
$789$	17.1262	+	17.1262i	0.609708	+	0.609708i
$790$	11.4693	−	6.14709i	0.408059	−	0.218704i
$791$		−	1.96881i		−	0.0700029i
$792$	−0.600459	+	6.31546i	−0.0213364	+	0.224410i
$793$		−	41.7628i		−	1.48304i
$794$	5.48410	+	10.2323i	0.194624	+	0.363130i
$795$	−17.8356	−	17.8356i	−0.632565	−	0.632565i
$796$	10.3141	−	15.5117i	0.365572	−	0.549797i
$797$	34.3747	−	34.3747i	1.21761	−	1.21761i	0.249148	−	0.968465i	$-0.419849\pi$
$797$	34.3747	−	34.3747i	1.21761	−	1.21761i	0.968465	−	0.249148i	$-0.0801505\pi$
$798$	0.834430	−	2.76195i	0.0295385	−	0.0977720i
$799$	−1.94390			−0.0687702
$800$	1.88448	+	18.0876i	0.0666264	+	0.639494i
$801$	5.35020			0.189040
$802$	−12.2547	+	40.5628i	−0.432728	+	1.43232i
$803$	−34.3956	+	34.3956i	−1.21379	+	1.21379i
$804$	15.8011	−	23.7638i	0.557261	−	0.838085i
$805$	−0.981759	−	0.981759i	−0.0346024	−	0.0346024i
$806$	14.0460	+	26.2070i	0.494748	+	0.923103i
$807$		−	20.7955i		−	0.732037i
$808$	−10.5898	−	1.00685i	−0.372547	−	0.0354209i
$809$		−	19.8794i		−	0.698922i	−0.936951	−	0.349461i	$-0.886365\pi$
$809$		−	19.8794i		−	0.698922i	0.936951	−	0.349461i	$-0.113635\pi$
$810$	17.6255	−	9.44661i	0.619299	−	0.331920i
$811$	18.6464	+	18.6464i	0.654763	+	0.654763i	0.954136	−	0.299373i	$-0.0967776\pi$
$811$	18.6464	+	18.6464i	0.654763	+	0.654763i	−0.299373	+	0.954136i	$0.596778\pi$
$812$	1.38164	+	6.86504i	0.0484861	+	0.240916i
$813$	−19.9269	+	19.9269i	−0.698867	+	0.698867i
$814$	6.54576	+	1.97758i	0.229429	+	0.0693141i
$815$	−12.6084			−0.441651
$816$	−18.7631	−	7.67300i	−0.656841	−	0.268609i
$817$	3.69860			0.129398
$818$	−44.3564	−	13.4008i	−1.55089	−	0.468547i
$819$	−2.16277	+	2.16277i	−0.0755734	+	0.0755734i
$820$	6.88263	−	1.38518i	0.240352	−	0.0483726i
$821$	14.7887	+	14.7887i	0.516129	+	0.516129i	0.916398	−	0.400269i	$-0.131083\pi$
$821$	14.7887	+	14.7887i	0.516129	+	0.516129i	−0.400269	+	0.916398i	$0.631083\pi$
$822$	22.8445	−	12.2438i	0.796794	−	0.427051i
$823$			11.6401i			0.405749i	0.979205	+	0.202875i	$0.0650284\pi$
$823$			11.6401i			0.405749i	−0.979205	+	0.202875i	$0.934972\pi$
$824$	10.4318	+	12.6239i	0.363409	+	0.439773i
$825$		−	20.2503i		−	0.705026i
$826$	−7.53381	−	14.0566i	−0.262135	−	0.489093i
$827$	−22.7061	−	22.7061i	−0.789569	−	0.789569i	0.191855	−	0.981423i	$-0.438550\pi$
$827$	−22.7061	−	22.7061i	−0.789569	−	0.789569i	−0.981423	+	0.191855i	$0.938550\pi$
$828$	−1.13811	−	0.756755i	−0.0395521	−	0.0262991i
$829$	4.08997	−	4.08997i	0.142051	−	0.142051i	−0.632505	−	0.774556i	$-0.717973\pi$
$829$	4.08997	−	4.08997i	0.142051	−	0.142051i	0.774556	+	0.632505i	$0.217973\pi$
$830$	−5.86526	+	19.4139i	−0.203586	+	0.673868i
$831$	4.46269			0.154809
$832$	−19.3371	−	28.5204i	−0.670392	−	0.988768i
$833$	15.6328			0.541645
$834$	10.0105	−	33.1348i	0.346637	−	1.14736i
$835$	15.5191	−	15.5191i	0.537061	−	0.537061i
$836$	−5.59190	−	3.71818i	−0.193400	−	0.128596i
$837$	−15.3463	−	15.3463i	−0.530444	−	0.530444i
$838$	6.89010	+	12.8556i	0.238015	+	0.444089i
$839$		−	1.07505i		−	0.0371149i	−0.999828	−	0.0185575i	$-0.994093\pi$
$839$		−	1.07505i		−	0.0371149i	0.999828	−	0.0185575i	$-0.00590736\pi$
$840$	−4.80098	−	5.80983i	−0.165649	−	0.200458i
$841$			17.6467i			0.608506i
$842$	49.9370	−	26.7643i	1.72094	−	0.922358i
$843$	−0.335868	−	0.335868i	−0.0115679	−	0.0115679i
$844$	−52.2896	+	10.5237i	−1.79988	+	0.362240i
$845$	−5.24556	+	5.24556i	−0.180453	+	0.180453i
$846$	−0.681045	−	0.205755i	−0.0234148	−	0.00707399i
$847$	−0.236394			−0.00812258
$848$	14.8928	−	36.4180i	0.511420	−	1.25060i
$849$	47.4527			1.62857
$850$	11.4921	+	3.47195i	0.394176	+	0.119087i
$851$	−1.04169	+	1.04169i	−0.0357087	+	0.0357087i
$852$	0.854752	+	4.24706i	0.0292833	+	0.145502i
$853$	10.5166	+	10.5166i	0.360081	+	0.360081i	0.863843	−	0.503762i	$-0.168051\pi$
$853$	10.5166	+	10.5166i	0.360081	+	0.360081i	−0.503762	+	0.863843i	$0.668051\pi$
$854$	12.5588	−	6.73104i	0.429754	−	0.230331i
$855$		−	0.934057i		−	0.0319441i
$856$	−8.84280	−	0.840753i	−0.302241	−	0.0287363i
$857$		−	9.90117i		−	0.338218i	−0.985597	−	0.169109i	$-0.945911\pi$
$857$		−	9.90117i		−	0.338218i	0.985597	−	0.169109i	$-0.0540889\pi$
$858$	18.1257	+	33.8190i	0.618801	+	1.15456i
$859$	−15.9867	−	15.9867i	−0.545458	−	0.545458i	0.379666	−	0.925124i	$-0.376039\pi$
$859$	−15.9867	−	15.9867i	−0.545458	−	0.545458i	−0.925124	+	0.379666i	$0.876039\pi$
$860$	5.34948	−	8.04528i	0.182416	−	0.274342i
$861$	3.70494	−	3.70494i	0.126264	−	0.126264i
$862$	−11.7067	+	38.7492i	−0.398733	+	1.31980i
$863$	−10.6622			−0.362944			−0.181472	−	0.983396i	$-0.558086\pi$
$863$	−10.6622			−0.362944			−0.181472	+	0.983396i	$0.558086\pi$
$864$	19.5316	+	15.8458i	0.664478	+	0.539083i
$865$	−0.771520			−0.0262325
$866$	8.23140	−	27.2458i	0.279714	−	0.925851i
$867$	13.6079	−	13.6079i	0.462148	−	0.462148i
$868$	−5.61709	+	8.44773i	−0.190656	+	0.286735i
$869$	−15.9827	−	15.9827i	−0.542176	−	0.542176i
$870$	5.77227	+	10.7699i	0.195698	+	0.365135i
$871$		−	32.0229i		−	1.08506i
$872$	−3.55374	+	37.3772i	−0.120345	+	1.26575i
$873$			9.92080i			0.335768i
$874$	1.27513	−	0.683421i	0.0431319	−	0.0231171i
$875$	8.06493	+	8.06493i	0.272644	+	0.272644i
$876$	−11.2238	−	55.7686i	−0.379219	−	1.88425i
$877$	−33.6382	+	33.6382i	−1.13588	+	1.13588i	−0.146702	+	0.989181i	$0.546866\pi$
$877$	−33.6382	+	33.6382i	−1.13588	+	1.13588i	−0.989181	+	0.146702i	$0.953134\pi$
$878$	−39.5915	−	11.9612i	−1.33615	−	0.403672i
$879$	−62.0960			−2.09445
$880$	−16.1757	+	6.78582i	−0.545284	+	0.228750i
$881$	−26.5560			−0.894695			−0.447348	−	0.894360i	$-0.647631\pi$
$881$	−26.5560			−0.894695			−0.447348	+	0.894360i	$0.647631\pi$
$882$	5.47696	+	1.65468i	0.184419	+	0.0557158i
$883$	13.3950	−	13.3950i	0.450777	−	0.450777i	−0.444835	−	0.895612i	$-0.646738\pi$
$883$	13.3950	−	13.3950i	0.450777	−	0.450777i	0.895612	+	0.444835i	$0.146738\pi$
$884$	−22.3001	+	4.48806i	−0.750033	+	0.150950i
$885$	−19.6779	−	19.6779i	−0.661466	−	0.661466i
$886$	−38.8709	+	20.8333i	−1.30589	+	0.699908i
$887$			21.3699i			0.717532i	0.933428	+	0.358766i	$0.116802\pi$
$887$			21.3699i			0.717532i	−0.933428	+	0.358766i	$0.883198\pi$
$888$	−6.16449	+	5.09405i	−0.206867	+	0.170945i
$889$		−	1.68654i		−	0.0565646i
$890$	6.98840	+	13.0390i	0.234252	+	0.437068i
$891$	−24.5616	−	24.5616i	−0.822845	−	0.822845i
$892$	23.0031	+	15.2953i	0.770202	+	0.512124i
$893$	0.532512	−	0.532512i	0.0178198	−	0.0178198i
$894$	12.8591	−	42.5636i	0.430074	−	1.42354i
$895$	−1.49890			−0.0501028
$896$	5.45999	−	10.4117i	0.182405	−	0.347831i
$897$	−8.26646			−0.276009
$898$	6.03185	−	19.9653i	0.201285	−	0.666252i
$899$	11.6301	−	11.6301i	0.387887	−	0.387887i
$900$	3.65877	+	2.43280i	0.121959	+	0.0810933i
$901$	−18.3663	−	18.3663i	−0.611869	−	0.611869i
$902$	−5.76070	−	10.7483i	−0.191810	−	0.357881i
$903$		−	7.21044i		−	0.239948i
$904$	4.13097	−	3.41364i	0.137394	−	0.113536i
$905$		−	8.05258i		−	0.267677i
$906$	−53.1767	+	28.5007i	−1.76668	+	0.946871i
$907$	−31.9140	−	31.9140i	−1.05969	−	1.05969i	−0.998102	−	0.0615842i	$-0.980385\pi$
$907$	−31.9140	−	31.9140i	−1.05969	−	1.05969i	−0.0615842	−	0.998102i	$-0.519615\pi$
$908$	−4.69963	+	0.945835i	−0.155963	+	0.0313886i
$909$	−1.81734	+	1.81734i	−0.0602774	+	0.0602774i
$910$	−8.09589	−	2.44590i	−0.268376	−	0.0810808i
$911$	2.44657			0.0810584			0.0405292	−	0.999178i	$-0.487096\pi$
$911$	2.44657			0.0810584			0.0405292	+	0.999178i	$0.487096\pi$
$912$	7.24192	−	3.03803i	0.239804	−	0.100599i
$913$	35.2272			1.16585
$914$	−52.0145	−	15.7144i	−1.72049	−	0.519787i
$915$	17.5811	−	17.5811i	0.581214	−	0.581214i
$916$	−7.25106	−	36.0288i	−0.239582	−	1.19042i
$917$	−0.00215815	−	0.00215815i	−7.12684e−5	−	7.12684e-5i
$918$	14.6340	−	7.84327i	0.482995	−	0.258866i
$919$			3.55117i			0.117142i	0.998283	+	0.0585712i	$0.0186545\pi$
$919$			3.55117i			0.117142i	−0.998283	+	0.0585712i	$0.981346\pi$
$920$	0.357697	−	3.76216i	0.0117929	−	0.124035i
$921$		−	36.0190i		−	1.18687i
$922$	−12.8550	−	23.9850i	−0.423358	−	0.789903i
$923$	3.43748	+	3.43748i	0.113146	+	0.113146i
$924$	−7.24860	+	10.9014i	−0.238462	+	0.358631i
$925$	3.34880	−	3.34880i	0.110108	−	0.110108i
$926$	−10.7823	+	35.6891i	−0.354327	+	1.17282i
$927$	3.95665			0.129953
$928$	−12.0087	+	14.8020i	−0.394204	+	0.485899i
$929$	1.01716			0.0333718			0.0166859	−	0.999861i	$-0.494688\pi$
$929$	1.01716			0.0333718			0.0166859	+	0.999861i	$0.494688\pi$
$930$	−5.11951	+	16.9455i	−0.167875	+	0.555665i
$931$	−4.28245	+	4.28245i	−0.140352	+	0.140352i
$932$	−22.8793	+	34.4091i	−0.749438	+	1.12711i
$933$	34.9463	+	34.9463i	1.14409	+	1.14409i
$934$	6.91616	+	12.9042i	0.226304	+	0.422239i
$935$			11.5799i			0.378704i
$936$	−8.28788	−	0.787992i	−0.270898	−	0.0257563i
$937$		−	36.5659i		−	1.19456i	−0.802034	−	0.597278i	$-0.796249\pi$
$937$		−	36.5659i		−	1.19456i	0.802034	−	0.597278i	$-0.203751\pi$
$938$	9.62987	−	5.16124i	0.314426	−	0.168520i
$939$	32.0383	+	32.0383i	1.04553	+	1.04553i
$940$	−0.388131	−	1.92853i	−0.0126594	−	0.0629018i
$941$	−16.9584	+	16.9584i	−0.552827	+	0.552827i	−0.927256	−	0.374429i	$-0.877839\pi$
$941$	−16.9584	+	16.9584i	−0.552827	+	0.552827i	0.374429	+	0.927256i	$0.377839\pi$
$942$	43.9737	+	13.2852i	1.43274	+	0.432854i
$943$	2.62724			0.0855548
$944$	16.4311	−	40.1797i	0.534786	−	1.30774i
$945$	6.17304			0.200809
$946$	−16.0647	−	4.85340i	−0.522308	−	0.157798i
$947$	−11.7928	+	11.7928i	−0.383215	+	0.383215i	−0.872259	−	0.489044i	$-0.837346\pi$
$947$	−11.7928	+	11.7928i	−0.383215	+	0.383215i	0.489044	+	0.872259i	$0.337346\pi$
$948$	25.9142	−	5.21542i	0.841654	−	0.169389i
$949$	−45.1379	−	45.1379i	−1.46524	−	1.46524i
$950$	−4.09926	+	2.19704i	−0.132998	+	0.0712816i
$951$			2.40921i			0.0781238i
$952$	−4.94381	−	5.98268i	−0.160230	−	0.193900i
$953$		−	55.4065i		−	1.79479i	−0.441224	−	0.897397i	$-0.645456\pi$
$953$		−	55.4065i		−	1.79479i	0.441224	−	0.897397i	$-0.354544\pi$
$954$	−4.49062	−	8.37863i	−0.145389	−	0.271268i
$955$	16.9964	+	16.9964i	0.549989	+	0.549989i
$956$	−38.9527	−	25.9005i	−1.25982	−	0.837682i
$957$	15.0082	−	15.0082i	0.485145	−	0.485145i
$958$	−15.3736	+	50.8863i	−0.496698	+	1.64406i
$959$	9.92316			0.320436
$960$	3.86598	−	20.1468i	0.124774	−	0.650236i
$961$	−7.17265			−0.231376
$962$	−2.59521	+	8.59011i	−0.0836729	+	0.276956i
$963$	−1.51754	+	1.51754i	−0.0489020	+	0.0489020i
$964$	−5.80044	−	3.85684i	−0.186819	−	0.124220i
$965$	−6.24970	−	6.24970i	−0.201185	−	0.201185i
$966$	−1.33233	−	2.48587i	−0.0428671	−	0.0799816i
$967$			38.1599i			1.22714i	0.789640	+	0.613570i	$0.210267\pi$
$967$			38.1599i			1.22714i	−0.789640	+	0.613570i	$0.789733\pi$
$968$	−0.409873	−	0.496002i	−0.0131738	−	0.0159421i
$969$		−	5.18437i		−	0.166546i
$970$	−24.1780	+	12.9585i	−0.776309	+	0.416071i
$971$	22.9272	+	22.9272i	0.735768	+	0.735768i	0.971756	−	0.235988i	$-0.0758325\pi$
$971$	22.9272	+	22.9272i	0.735768	+	0.735768i	−0.235988	+	0.971756i	$0.575832\pi$
$972$	13.6717	−	2.75153i	0.438520	−	0.0882554i
$973$	9.37069	−	9.37069i	0.300411	−	0.300411i
$974$	1.08242	+	0.327015i	0.0346828	+	0.0104782i
$975$	26.5748			0.851076
$976$	35.8983	+	14.6803i	1.14908	+	0.469904i
$977$	10.6791			0.341656			0.170828	−	0.985301i	$-0.445356\pi$
$977$	10.6791			0.341656			0.170828	+	0.985301i	$0.445356\pi$
$978$	−24.5179	−	7.40724i	−0.783995	−	0.236858i
$979$	18.1701	−	18.1701i	0.580720	−	0.580720i
$980$	3.12135	+	15.5092i	0.0997077	+	0.495424i
$981$	6.41441	+	6.41441i	0.204796	+	0.204796i
$982$	10.5780	−	5.66938i	0.337557	−	0.180917i
$983$		−	48.9907i		−	1.56256i	−0.624180	−	0.781280i	$-0.714567\pi$
$983$		−	48.9907i		−	1.56256i	0.624180	−	0.781280i	$-0.285433\pi$
$984$	14.1976	+	1.34987i	0.452602	+	0.0430323i
$985$		−	20.3274i		−	0.647683i
$986$	5.94401	+	11.0904i	0.189296	+	0.353189i
$987$	−1.03813	−	1.03813i	−0.0330442	−	0.0330442i
$988$	4.87943	−	7.33834i	0.155235	−	0.233464i
$989$	2.55653	−	2.55653i	0.0812929	−	0.0812929i
$990$	−1.22569	+	4.05703i	−0.0389551	+	0.128941i
$991$	52.6490			1.67245			0.836225	−	0.548386i	$-0.184757\pi$
$991$	52.6490			1.67245			0.836225	+	0.548386i	$0.184757\pi$
$992$	−27.4643	+	2.86140i	−0.871992	+	0.0908495i
$993$	−60.5010			−1.91994
$994$	−0.479681	+	1.58774i	−0.0152146	+	0.0503600i
$995$	8.79957	−	8.79957i	0.278965	−	0.278965i
$996$	−22.8109	+	34.3061i	−0.722790	+	1.08703i
$997$	−26.0987	−	26.0987i	−0.826554	−	0.826554i	0.160485	−	0.987038i	$-0.448694\pi$
$997$	−26.0987	−	26.0987i	−0.826554	−	0.826554i	−0.987038	+	0.160485i	$0.948694\pi$
$998$	11.0658	+	20.6467i	0.350282	+	0.653558i
$999$		−	6.54988i		−	0.207229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.j.d.277.6	yes	24
4.3	odd	2		1472.2.j.d.369.9		24
16.3	odd	4		1472.2.j.d.1105.9		24
16.13	even	4	inner	368.2.j.d.93.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.j.d.93.6	✓	24	16.13	even	4	inner
368.2.j.d.277.6	yes	24	1.1	even	1	trivial
1472.2.j.d.369.9		24	4.3	odd	2
1472.2.j.d.1105.9		24	16.3	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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.408999 + 1.35378i) q^{2} +(-1.35709 + 1.35709i) q^{3} +(-1.66544 - 1.10739i) q^{4} +(-0.944781 - 0.944781i) q^{5} +(-1.28215 - 2.39224i) q^{6} -1.03914i q^{7} +(2.18032 - 1.80172i) q^{8} -0.683369i q^{9} +(1.66544 - 0.892612i) q^{10} +(-2.32083 - 2.32083i) q^{11} +(3.76297 - 0.757325i) q^{12} +(3.04566 - 3.04566i) q^{13} +(1.40676 + 0.425006i) q^{14} +2.56430 q^{15} +(1.54738 + 3.68858i) q^{16} +2.64059 q^{17} +(0.925131 + 0.279497i) q^{18} +(-0.723364 + 0.723364i) q^{19} +(0.527237 + 2.61972i) q^{20} +(1.41020 + 1.41020i) q^{21} +(4.09111 - 2.19268i) q^{22} +1.00000i q^{23} +(-0.513797 + 5.40398i) q^{24} -3.21478i q^{25} +(2.87749 + 5.36883i) q^{26} +(-3.14387 - 3.14387i) q^{27} +(-1.15073 + 1.73062i) q^{28} +(2.38258 - 2.38258i) q^{29} +(-1.04880 + 3.47150i) q^{30} +4.88133 q^{31} +(-5.62640 + 0.586193i) q^{32} +6.29914 q^{33} +(-1.08000 + 3.57478i) q^{34} +(-0.981759 + 0.981759i) q^{35} +(-0.756755 + 1.13811i) q^{36} +(1.04169 + 1.04169i) q^{37} +(-0.683421 - 1.27513i) q^{38} +8.26646i q^{39} +(-3.76216 - 0.357697i) q^{40} -2.62724i q^{41} +(-2.48587 + 1.33233i) q^{42} +(-2.55653 - 2.55653i) q^{43} +(1.29514 + 6.43527i) q^{44} +(-0.645634 + 0.645634i) q^{45} +(-1.35378 - 0.408999i) q^{46} -0.736160 q^{47} +(-7.10565 - 2.90579i) q^{48} +5.92019 q^{49} +(4.35210 + 1.31484i) q^{50} +(-3.58351 + 3.58351i) q^{51} +(-8.44511 + 1.69964i) q^{52} +(-6.95536 - 6.95536i) q^{53} +(5.54195 - 2.97027i) q^{54} +4.38536i q^{55} +(-1.87224 - 2.26566i) q^{56} -1.96334i q^{57} +(2.25101 + 4.19995i) q^{58} +(-7.67379 - 7.67379i) q^{59} +(-4.27069 - 2.83968i) q^{60} +(6.85611 - 6.85611i) q^{61} +(-1.99646 + 6.60824i) q^{62} -0.710115 q^{63} +(1.50761 - 7.85666i) q^{64} -5.75497 q^{65} +(-2.57634 + 8.52765i) q^{66} +(5.25714 - 5.25714i) q^{67} +(-4.39775 - 2.92416i) q^{68} +(-1.35709 - 1.35709i) q^{69} +(-0.927547 - 1.73062i) q^{70} +1.12865i q^{71} +(-1.23124 - 1.48997i) q^{72} -14.8204i q^{73} +(-1.83627 + 0.984169i) q^{74} +(4.36273 + 4.36273i) q^{75} +(2.00576 - 0.403675i) q^{76} +(-2.41166 + 2.41166i) q^{77} +(-11.1910 - 3.38097i) q^{78} +6.88664 q^{79} +(2.02296 - 4.94684i) q^{80} +10.5831 q^{81} +(3.55671 + 1.07454i) q^{82} +(-7.58934 + 7.58934i) q^{83} +(-0.786966 - 3.91025i) q^{84} +(-2.49478 - 2.49478i) q^{85} +(4.50659 - 2.41536i) q^{86} +6.46672i q^{87} +(-9.24165 - 0.878674i) q^{88} +7.82916i q^{89} +(-0.609983 - 1.13811i) q^{90} +(-3.16487 - 3.16487i) q^{91} +(1.10739 - 1.66544i) q^{92} +(-6.62438 + 6.62438i) q^{93} +(0.301089 - 0.996599i) q^{94} +1.36684 q^{95} +(6.84000 - 8.43103i) q^{96} -14.5175 q^{97} +(-2.42135 + 8.01464i) q^{98} +(-1.58598 + 1.58598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 4 q^{3} + 4 q^{5} + 2 q^{8} - 4 q^{11} + 38 q^{12} - 12 q^{13} - 6 q^{14} + 40 q^{17} - 8 q^{18} + 8 q^{19} - 2 q^{20} + 34 q^{22} - 10 q^{24} - 2 q^{26} - 28 q^{27} + 10 q^{28} - 16 q^{29}+ \cdots + 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 - 4 * q^3 + 4 * q^5 + 2 * q^8 - 4 * q^11 + 38 * q^12 - 12 * q^13 - 6 * q^14 + 40 * q^17 - 8 * q^18 + 8 * q^19 - 2 * q^20 + 34 * q^22 - 10 * q^24 - 2 * q^26 - 28 * q^27 + 10 * q^28 - 16 * q^29 - 30 * q^30 - 12 * q^31 + 16 * q^32 - 28 * q^33 + 4 * q^34 + 8 * q^35 - 24 * q^36 - 4 * q^37 + 20 * q^38 + 40 * q^42 - 28 * q^43 + 50 * q^44 + 20 * q^45 - 4 * q^47 + 20 * q^48 - 24 * q^49 + 10 * q^50 - 12 * q^51 - 44 * q^52 + 32 * q^53 + 38 * q^54 - 40 * q^56 - 40 * q^58 + 24 * q^59 + 34 * q^60 - 16 * q^61 - 42 * q^62 - 4 * q^63 + 24 * q^64 + 4 * q^65 - 12 * q^66 - 10 * q^68 - 4 * q^69 + 14 * q^70 + 4 * q^74 + 44 * q^75 + 8 * q^76 - 20 * q^77 + 4 * q^78 + 12 * q^79 - 4 * q^80 - 48 * q^81 - 4 * q^82 - 16 * q^83 - 66 * q^84 + 8 * q^85 - 28 * q^88 - 40 * q^90 - 72 * q^91 + 4 * q^93 - 26 * q^94 - 40 * q^95 - 32 * q^96 - 124 * q^97 + 54 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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