LMFDB - Embedded newform 731.2.f.c.259.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.17
Character	$\chi$	$=$	731.259
Dual form			731.2.f.c.302.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.401786i q^{2} +(1.92935 - 1.92935i) q^{3} +1.83857 q^{4} +(1.46367 - 1.46367i) q^{5} +(0.775185 + 0.775185i) q^{6} +(0.274168 + 0.274168i) q^{7} +1.54228i q^{8} -4.44476i q^{9} +O(q^{10})$	\(q+0.401786i q^{2} +(1.92935 - 1.92935i) q^{3} +1.83857 q^{4} +(1.46367 - 1.46367i) q^{5} +(0.775185 + 0.775185i) q^{6} +(0.274168 + 0.274168i) q^{7} +1.54228i q^{8} -4.44476i q^{9} +(0.588082 + 0.588082i) q^{10} +(-0.770867 - 0.770867i) q^{11} +(3.54723 - 3.54723i) q^{12} -4.56847 q^{13} +(-0.110157 + 0.110157i) q^{14} -5.64785i q^{15} +3.05747 q^{16} +(0.0756394 + 4.12241i) q^{17} +1.78584 q^{18} -2.35515i q^{19} +(2.69105 - 2.69105i) q^{20} +1.05793 q^{21} +(0.309724 - 0.309724i) q^{22} +(0.550792 + 0.550792i) q^{23} +(2.97560 + 2.97560i) q^{24} +0.715351i q^{25} -1.83555i q^{26} +(-2.78744 - 2.78744i) q^{27} +(0.504076 + 0.504076i) q^{28} +(-2.50509 + 2.50509i) q^{29} +2.26923 q^{30} +(-5.88953 + 5.88953i) q^{31} +4.31302i q^{32} -2.97454 q^{33} +(-1.65633 + 0.0303909i) q^{34} +0.802582 q^{35} -8.17199i q^{36} +(1.41346 - 1.41346i) q^{37} +0.946268 q^{38} +(-8.81417 + 8.81417i) q^{39} +(2.25739 + 2.25739i) q^{40} +(-0.232003 - 0.232003i) q^{41} +0.425062i q^{42} +1.00000i q^{43} +(-1.41729 - 1.41729i) q^{44} +(-6.50565 - 6.50565i) q^{45} +(-0.221301 + 0.221301i) q^{46} +3.39724 q^{47} +(5.89891 - 5.89891i) q^{48} -6.84966i q^{49} -0.287418 q^{50} +(8.09950 + 7.80763i) q^{51} -8.39944 q^{52} +1.38658i q^{53} +(1.11995 - 1.11995i) q^{54} -2.25659 q^{55} +(-0.422845 + 0.422845i) q^{56} +(-4.54391 - 4.54391i) q^{57} +(-1.00651 - 1.00651i) q^{58} +4.80189i q^{59} -10.3839i q^{60} +(-4.99744 - 4.99744i) q^{61} +(-2.36633 - 2.36633i) q^{62} +(1.21861 - 1.21861i) q^{63} +4.38202 q^{64} +(-6.68673 + 6.68673i) q^{65} -1.19513i q^{66} +5.38818 q^{67} +(0.139068 + 7.57933i) q^{68} +2.12534 q^{69} +0.322466i q^{70} +(4.61938 - 4.61938i) q^{71} +6.85508 q^{72} +(-10.4474 + 10.4474i) q^{73} +(0.567907 + 0.567907i) q^{74} +(1.38016 + 1.38016i) q^{75} -4.33011i q^{76} -0.422694i q^{77} +(-3.54141 - 3.54141i) q^{78} +(-6.03374 - 6.03374i) q^{79} +(4.47512 - 4.47512i) q^{80} +2.57840 q^{81} +(0.0932158 - 0.0932158i) q^{82} -5.03830i q^{83} +1.94508 q^{84} +(6.14455 + 5.92313i) q^{85} -0.401786 q^{86} +9.66636i q^{87} +(1.18890 - 1.18890i) q^{88} +5.78979 q^{89} +(2.61388 - 2.61388i) q^{90} +(-1.25253 - 1.25253i) q^{91} +(1.01267 + 1.01267i) q^{92} +22.7259i q^{93} +1.36497i q^{94} +(-3.44716 - 3.44716i) q^{95} +(8.32130 + 8.32130i) q^{96} +(9.71090 - 9.71090i) q^{97} +2.75210 q^{98} +(-3.42632 + 3.42632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$			0.401786i			0.284106i	0.989859	+	0.142053i	$0.0453703\pi$
$2$			0.401786i			0.284106i	−0.989859	+	0.142053i	$0.954630\pi$
$3$	1.92935	−	1.92935i	1.11391	−	1.11391i	0.121292	−	0.992617i	$-0.461296\pi$
$3$	1.92935	−	1.92935i	1.11391	−	1.11391i	0.992617	−	0.121292i	$-0.0387037\pi$
$4$	1.83857			0.919284
$5$	1.46367	−	1.46367i	0.654572	−	0.654572i	−0.299518	−	0.954091i	$-0.596826\pi$
$5$	1.46367	−	1.46367i	0.654572	−	0.654572i	0.954091	+	0.299518i	$0.0968260\pi$
$6$	0.775185	+	0.775185i	0.316468	+	0.316468i
$7$	0.274168	+	0.274168i	0.103626	+	0.103626i	0.757019	−	0.653393i	$-0.226655\pi$
$7$	0.274168	+	0.274168i	0.103626	+	0.103626i	−0.653393	+	0.757019i	$0.726655\pi$
$8$			1.54228i			0.545280i
$9$		−	4.44476i		−	1.48159i
$10$	0.588082	+	0.588082i	0.185968	+	0.185968i
$11$	−0.770867	−	0.770867i	−0.232425	−	0.232425i	0.581279	−	0.813704i	$-0.302552\pi$
$11$	−0.770867	−	0.770867i	−0.232425	−	0.232425i	−0.813704	+	0.581279i	$0.802552\pi$
$12$	3.54723	−	3.54723i	1.02400	−	1.02400i
$13$	−4.56847			−1.26707			−0.633533	−	0.773716i	$-0.718396\pi$
$13$	−4.56847			−1.26707			−0.633533	+	0.773716i	$0.718396\pi$
$14$	−0.110157	+	0.110157i	−0.0294407	+	0.0294407i
$15$		−	5.64785i		−	1.45827i
$16$	3.05747			0.764367
$17$	0.0756394	+	4.12241i	0.0183453	+	0.999832i
$17$	0.0756394	+	4.12241i	0.0183453	+	0.999832i
$18$	1.78584			0.420927
$19$		−	2.35515i		−	0.540309i	−0.962817	−	0.270155i	$-0.912925\pi$
$19$		−	2.35515i		−	0.540309i	0.962817	−	0.270155i	$-0.0870748\pi$
$20$	2.69105	−	2.69105i	0.601738	−	0.601738i
$21$	1.05793			0.230859
$22$	0.309724	−	0.309724i	0.0660334	−	0.0660334i
$23$	0.550792	+	0.550792i	0.114848	+	0.114848i	0.762195	−	0.647347i	$-0.224122\pi$
$23$	0.550792	+	0.550792i	0.114848	+	0.114848i	−0.647347	+	0.762195i	$0.724122\pi$
$24$	2.97560	+	2.97560i	0.607392	+	0.607392i
$25$			0.715351i			0.143070i
$26$		−	1.83555i		−	0.359981i
$27$	−2.78744	−	2.78744i	−0.536443	−	0.536443i
$28$	0.504076	+	0.504076i	0.0952615	+	0.0952615i
$29$	−2.50509	+	2.50509i	−0.465183	+	0.465183i	−0.900350	−	0.435167i	$-0.856689\pi$
$29$	−2.50509	+	2.50509i	−0.465183	+	0.465183i	0.435167	+	0.900350i	$0.356689\pi$
$30$	2.26923			0.414302
$31$	−5.88953	+	5.88953i	−1.05779	+	1.05779i	−0.0595668	+	0.998224i	$0.518972\pi$
$31$	−5.88953	+	5.88953i	−1.05779	+	1.05779i	−0.998224	+	0.0595668i	$0.981028\pi$
$32$			4.31302i			0.762441i
$33$	−2.97454			−0.517801
$34$	−1.65633	+	0.0303909i	−0.284058	+	0.00521199i
$35$	0.802582			0.135661
$36$		−	8.17199i		−	1.36200i
$37$	1.41346	−	1.41346i	0.232371	−	0.232371i	−0.581311	−	0.813682i	$-0.697460\pi$
$37$	1.41346	−	1.41346i	0.232371	−	0.232371i	0.813682	+	0.581311i	$0.197460\pi$
$38$	0.946268			0.153505
$39$	−8.81417	+	8.81417i	−1.41140	+	1.41140i
$40$	2.25739	+	2.25739i	0.356925	+	0.356925i
$41$	−0.232003	−	0.232003i	−0.0362329	−	0.0362329i	0.688758	−	0.724991i	$-0.258156\pi$
$41$	−0.232003	−	0.232003i	−0.0362329	−	0.0362329i	−0.724991	+	0.688758i	$0.758156\pi$
$42$			0.425062i			0.0655885i
$43$			1.00000i			0.152499i
$43$			1.00000i			0.152499i
$44$	−1.41729	−	1.41729i	−0.213665	−	0.213665i
$45$	−6.50565	−	6.50565i	−0.969805	−	0.969805i
$46$	−0.221301	+	0.221301i	−0.0326290	+	0.0326290i
$47$	3.39724			0.495539			0.247769	−	0.968819i	$-0.420302\pi$
$47$	3.39724			0.495539			0.247769	+	0.968819i	$0.420302\pi$
$48$	5.89891	−	5.89891i	0.851435	−	0.851435i
$49$		−	6.84966i		−	0.978523i
$50$	−0.287418			−0.0406471
$51$	8.09950	+	7.80763i	1.13416	+	1.09329i
$52$	−8.39944			−1.16479
$53$			1.38658i			0.190461i	0.995455	+	0.0952305i	$0.0303588\pi$
$53$			1.38658i			0.190461i	−0.995455	+	0.0952305i	$0.969641\pi$
$54$	1.11995	−	1.11995i	0.152406	−	0.152406i
$55$	−2.25659			−0.304278
$56$	−0.422845	+	0.422845i	−0.0565050	+	0.0565050i
$57$	−4.54391	−	4.54391i	−0.601855	−	0.601855i
$58$	−1.00651	−	1.00651i	−0.132161	−	0.132161i
$59$			4.80189i			0.625153i	0.949893	+	0.312577i	$0.101192\pi$
$59$			4.80189i			0.625153i	−0.949893	+	0.312577i	$0.898808\pi$
$60$		−	10.3839i		−	1.34056i
$61$	−4.99744	−	4.99744i	−0.639857	−	0.639857i	0.310663	−	0.950520i	$-0.399449\pi$
$61$	−4.99744	−	4.99744i	−0.639857	−	0.639857i	−0.950520	+	0.310663i	$0.899449\pi$
$62$	−2.36633	−	2.36633i	−0.300525	−	0.300525i
$63$	1.21861	−	1.21861i	0.153530	−	0.153530i
$64$	4.38202			0.547753
$65$	−6.68673	+	6.68673i	−0.829386	+	0.829386i
$66$		−	1.19513i		−	0.147110i
$67$	5.38818			0.658271			0.329136	−	0.944283i	$-0.393243\pi$
$67$	5.38818			0.658271			0.329136	+	0.944283i	$0.393243\pi$
$68$	0.139068	+	7.57933i	0.0168645	+	0.919129i
$69$	2.12534			0.255861
$70$			0.322466i			0.0385421i
$71$	4.61938	−	4.61938i	0.548220	−	0.548220i	−0.377706	−	0.925926i	$-0.623287\pi$
$71$	4.61938	−	4.61938i	0.548220	−	0.548220i	0.925926	+	0.377706i	$0.123287\pi$
$72$	6.85508			0.807879
$73$	−10.4474	+	10.4474i	−1.22278	+	1.22278i	−0.256134	+	0.966641i	$0.582449\pi$
$73$	−10.4474	+	10.4474i	−1.22278	+	1.22278i	−0.966641	+	0.256134i	$0.917551\pi$
$74$	0.567907	+	0.567907i	0.0660178	+	0.0660178i
$75$	1.38016	+	1.38016i	0.159367	+	0.159367i
$76$		−	4.33011i		−	0.496698i
$77$		−	0.422694i		−	0.0481705i
$78$	−3.54141	−	3.54141i	−0.400986	−	0.400986i
$79$	−6.03374	−	6.03374i	−0.678849	−	0.678849i	0.280891	−	0.959740i	$-0.409370\pi$
$79$	−6.03374	−	6.03374i	−0.678849	−	0.678849i	−0.959740	+	0.280891i	$0.909370\pi$
$80$	4.47512	−	4.47512i	0.500333	−	0.500333i
$81$	2.57840			0.286489
$82$	0.0932158	−	0.0932158i	0.0102940	−	0.0102940i
$83$		−	5.03830i		−	0.553025i	−0.961010	−	0.276513i	$-0.910821\pi$
$83$		−	5.03830i		−	0.553025i	0.961010	−	0.276513i	$-0.0891788\pi$
$84$	1.94508			0.212225
$85$	6.14455	+	5.92313i	0.666470	+	0.642454i
$86$	−0.401786			−0.0433257
$87$			9.66636i			1.03634i
$88$	1.18890	−	1.18890i	0.126737	−	0.126737i
$89$	5.78979			0.613717			0.306858	−	0.951755i	$-0.400722\pi$
$89$	5.78979			0.613717			0.306858	+	0.951755i	$0.400722\pi$
$90$	2.61388	−	2.61388i	0.275527	−	0.275527i
$91$	−1.25253	−	1.25253i	−0.131301	−	0.131301i
$92$	1.01267	+	1.01267i	0.105578	+	0.105578i
$93$			22.7259i			2.35657i
$94$			1.36497i			0.140785i
$95$	−3.44716	−	3.44716i	−0.353672	−	0.353672i
$96$	8.32130	+	8.32130i	0.849289	+	0.849289i
$97$	9.71090	−	9.71090i	0.985992	−	0.985992i	−0.0139108	−	0.999903i	$-0.504428\pi$
$97$	9.71090	−	9.71090i	0.985992	−	0.985992i	0.999903	+	0.0139108i	$0.00442807\pi$
$98$	2.75210			0.278004
$99$	−3.42632	+	3.42632i	−0.344358	+	0.344358i
$100$			1.31522i			0.131522i
$101$	8.04243			0.800252			0.400126	−	0.916460i	$-0.368966\pi$
$101$	8.04243			0.800252			0.400126	+	0.916460i	$0.368966\pi$
$102$	−3.13700	+	3.25427i	−0.310609	+	0.322220i
$103$	−0.274671			−0.0270641			−0.0135320	−	0.999908i	$-0.504308\pi$
$103$	−0.274671			−0.0270641			−0.0135320	+	0.999908i	$0.504308\pi$
$104$		−	7.04588i		−	0.690905i
$105$	1.54846	−	1.54846i	0.151114	−	0.151114i
$106$	−0.557107			−0.0541110
$107$	9.03151	−	9.03151i	0.873109	−	0.873109i	−0.119701	−	0.992810i	$-0.538193\pi$
$107$	9.03151	−	9.03151i	0.873109	−	0.873109i	0.992810	+	0.119701i	$0.0381935\pi$
$108$	−5.12489	−	5.12489i	−0.493143	−	0.493143i
$109$	−6.84961	−	6.84961i	−0.656074	−	0.656074i	0.298375	−	0.954449i	$-0.403555\pi$
$109$	−6.84961	−	6.84961i	−0.656074	−	0.656074i	−0.954449	+	0.298375i	$0.903555\pi$
$110$		−	0.906666i		−	0.0864472i
$111$		−	5.45409i		−	0.517679i
$112$	0.838260	+	0.838260i	0.0792081	+	0.0792081i
$113$	6.93318	+	6.93318i	0.652219	+	0.652219i	0.953527	−	0.301308i	$-0.0974233\pi$
$113$	6.93318	+	6.93318i	0.652219	+	0.652219i	−0.301308	+	0.953527i	$0.597423\pi$
$114$	1.82568	−	1.82568i	0.170991	−	0.170991i
$115$	1.61235			0.150353
$116$	−4.60577	+	4.60577i	−0.427635	+	0.427635i
$117$			20.3057i			1.87727i
$118$	−1.92934			−0.177610
$119$	−1.10950	+	1.15097i	−0.101707	+	0.105509i
$120$	8.71058			0.795164
$121$		−	9.81153i		−	0.891957i
$122$	2.00790	−	2.00790i	0.181787	−	0.181787i
$123$	−0.895230			−0.0807202
$124$	−10.8283	+	10.8283i	−0.972410	+	0.972410i
$125$	8.36538	+	8.36538i	0.748222	+	0.748222i
$126$	0.489621	+	0.489621i	0.0436189	+	0.0436189i
$127$		−	4.73367i		−	0.420046i	−0.977696	−	0.210023i	$-0.932646\pi$
$127$		−	4.73367i		−	0.420046i	0.977696	−	0.210023i	$-0.0673538\pi$
$128$			10.3867i			0.918060i
$129$	1.92935	+	1.92935i	0.169870	+	0.169870i
$130$	−2.68663	−	2.68663i	−0.235633	−	0.235633i
$131$	3.08999	−	3.08999i	0.269973	−	0.269973i	−0.559116	−	0.829089i	$-0.688859\pi$
$131$	3.08999	−	3.08999i	0.269973	−	0.269973i	0.829089	+	0.559116i	$0.188859\pi$
$132$	−5.46889			−0.476006
$133$	0.645708	−	0.645708i	0.0559900	−	0.0559900i
$134$			2.16490i			0.187019i
$135$	−8.15977			−0.702281
$136$	−6.35793	+	0.116657i	−0.545188	+	0.0100033i
$137$	−12.9185			−1.10371			−0.551853	−	0.833941i	$-0.686079\pi$
$137$	−12.9185			−1.10371			−0.551853	+	0.833941i	$0.686079\pi$
$138$			0.853932i			0.0726915i
$139$	−10.0661	+	10.0661i	−0.853794	+	0.853794i	−0.990598	−	0.136804i	$-0.956317\pi$
$139$	−10.0661	+	10.0661i	−0.853794	+	0.853794i	0.136804	+	0.990598i	$0.456317\pi$
$140$	1.47560			0.124711
$141$	6.55446	−	6.55446i	0.551985	−	0.551985i
$142$	1.85600	+	1.85600i	0.155752	+	0.155752i
$143$	3.52169	+	3.52169i	0.294498	+	0.294498i
$144$		−	13.5897i		−	1.13247i
$145$			7.33323i			0.608991i
$146$	−4.19762	−	4.19762i	−0.347398	−	0.347398i
$147$	−13.2154	−	13.2154i	−1.08999	−	1.08999i
$148$	2.59873	−	2.59873i	0.213615	−	0.213615i
$149$	−9.18943			−0.752827			−0.376414	−	0.926452i	$-0.622843\pi$
$149$	−9.18943			−0.752827			−0.376414	+	0.926452i	$0.622843\pi$
$150$	−0.554529	+	0.554529i	−0.0452771	+	0.0452771i
$151$			3.24077i			0.263730i	0.991268	+	0.131865i	$0.0420966\pi$
$151$			3.24077i			0.263730i	−0.991268	+	0.131865i	$0.957903\pi$
$152$	3.63232			0.294620
$153$	18.3231	−	0.336199i	1.48134	−	0.0271801i
$154$	0.169833			0.0136855
$155$			17.2406i			1.38480i
$156$	−16.2054	+	16.2054i	−1.29747	+	1.29747i
$157$	11.2954			0.901474			0.450737	−	0.892657i	$-0.351161\pi$
$157$	11.2954			0.901474			0.450737	+	0.892657i	$0.351161\pi$
$158$	2.42428	−	2.42428i	0.192865	−	0.192865i
$159$	2.67519	+	2.67519i	0.212156	+	0.212156i
$160$	6.31282	+	6.31282i	0.499073	+	0.499073i
$161$			0.302019i			0.0238025i
$162$			1.03597i			0.0813933i
$163$	−13.1696	−	13.1696i	−1.03152	−	1.03152i	−0.999487	−	0.0320380i	$-0.989800\pi$
$163$	−13.1696	−	13.1696i	−1.03152	−	1.03152i	−0.0320380	−	0.999487i	$-0.510200\pi$
$164$	−0.426554	−	0.426554i	−0.0333083	−	0.0333083i
$165$	−4.35374	+	4.35374i	−0.338938	+	0.338938i
$166$	2.02432			0.157118
$167$	−6.78001	+	6.78001i	−0.524653	+	0.524653i	−0.918973	−	0.394320i	$-0.870980\pi$
$167$	−6.78001	+	6.78001i	−0.524653	+	0.524653i	0.394320	+	0.918973i	$0.370980\pi$
$168$			1.63163i			0.125883i
$169$	7.87093			0.605456
$170$	−2.37983	+	2.46880i	−0.182525	+	0.189348i
$171$	−10.4681			−0.800515
$172$			1.83857i			0.140189i
$173$	−12.9762	+	12.9762i	−0.986562	+	0.986562i	−0.999911	−	0.0133486i	$-0.995751\pi$
$173$	−12.9762	+	12.9762i	−0.986562	+	0.986562i	0.0133486	+	0.999911i	$0.495751\pi$
$174$	−3.88381			−0.294431
$175$	−0.196126	+	0.196126i	−0.0148258	+	0.0148258i
$176$	−2.35690	−	2.35690i	−0.177658	−	0.177658i
$177$	9.26452	+	9.26452i	0.696364	+	0.696364i
$178$			2.32626i			0.174360i
$179$			15.2137i			1.13713i	0.822639	+	0.568564i	$0.192501\pi$
$179$			15.2137i			1.13713i	−0.822639	+	0.568564i	$0.807499\pi$
$180$	−11.9611	−	11.9611i	−0.891526	−	0.891526i
$181$	−15.9189	−	15.9189i	−1.18324	−	1.18324i	−0.978899	−	0.204345i	$-0.934494\pi$
$181$	−15.9189	−	15.9189i	−1.18324	−	1.18324i	−0.204345	−	0.978899i	$-0.565506\pi$
$182$	0.503249	−	0.503249i	0.0373033	−	0.0373033i
$183$	−19.2836			−1.42548
$184$	−0.849478	+	0.849478i	−0.0626244	+	0.0626244i
$185$		−	4.13766i		−	0.304207i
$186$	−9.13095			−0.669514
$187$	3.11952	−	3.23614i	0.228122	−	0.236650i
$188$	6.24606			0.455541
$189$		−	1.52845i		−	0.111179i
$190$	1.38502	−	1.38502i	0.100480	−	0.100480i
$191$	−1.72049			−0.124490			−0.0622451	−	0.998061i	$-0.519826\pi$
$191$	−1.72049			−0.124490			−0.0622451	+	0.998061i	$0.519826\pi$
$192$	8.45444	−	8.45444i	0.610147	−	0.610147i
$193$	−8.83947	−	8.83947i	−0.636279	−	0.636279i	0.313356	−	0.949636i	$-0.398547\pi$
$193$	−8.83947	−	8.83947i	−0.636279	−	0.636279i	−0.949636	+	0.313356i	$0.898547\pi$
$194$	3.90171	+	3.90171i	0.280126	+	0.280126i
$195$			25.8020i			1.84772i
$196$		−	12.5936i		−	0.899541i
$197$	−5.73004	−	5.73004i	−0.408249	−	0.408249i	0.472879	−	0.881127i	$-0.343215\pi$
$197$	−5.73004	−	5.73004i	−0.408249	−	0.408249i	−0.881127	+	0.472879i	$0.843215\pi$
$198$	−1.37665	−	1.37665i	−0.0978341	−	0.0978341i
$199$	−0.952721	+	0.952721i	−0.0675366	+	0.0675366i	−0.740068	−	0.672532i	$-0.765207\pi$
$199$	−0.952721	+	0.952721i	−0.0675366	+	0.0675366i	0.672532	+	0.740068i	$0.265207\pi$
$200$	−1.10327			−0.0780133
$201$	10.3957	−	10.3957i	0.733254	−	0.733254i
$202$			3.23134i			0.227356i
$203$	−1.37363			−0.0964098
$204$	14.8915	+	14.3549i	1.04261	+	1.00504i
$205$	−0.679152			−0.0474340
$206$		−	0.110359i		−	0.00768907i
$207$	2.44814	−	2.44814i	0.170157	−	0.170157i
$208$	−13.9680			−0.968503
$209$	−1.81551	+	1.81551i	−0.125582	+	0.125582i
$210$	0.622149	+	0.622149i	0.0429324	+	0.0429324i
$211$	9.68852	+	9.68852i	0.666986	+	0.666986i	0.957017	−	0.290032i	$-0.0936658\pi$
$211$	9.68852	+	9.68852i	0.666986	+	0.666986i	−0.290032	+	0.957017i	$0.593666\pi$
$212$			2.54931i			0.175088i
$213$		−	17.8248i		−	1.22133i
$214$	3.62874	+	3.62874i	0.248055	+	0.248055i
$215$	1.46367	+	1.46367i	0.0998213	+	0.0998213i
$216$	4.29902	−	4.29902i	0.292511	−	0.292511i
$217$	−3.22944			−0.219229
$218$	2.75208	−	2.75208i	0.186394	−	0.186394i
$219$			40.3133i			2.72412i
$220$	−4.14889			−0.279718
$221$	−0.345557	−	18.8331i	−0.0232447	−	1.26685i
$222$	2.19138			0.147076
$223$		−	14.3807i		−	0.963001i	−0.876446	−	0.481501i	$-0.840092\pi$
$223$		−	14.3807i		−	0.963001i	0.876446	−	0.481501i	$-0.159908\pi$
$224$	−1.18249	+	1.18249i	−0.0790085	+	0.0790085i
$225$	3.17956			0.211971
$226$	−2.78566	+	2.78566i	−0.185299	+	0.185299i
$227$	17.2397	+	17.2397i	1.14424	+	1.14424i	0.987667	+	0.156570i	$0.0500438\pi$
$227$	17.2397	+	17.2397i	1.14424	+	1.14424i	0.156570	+	0.987667i	$0.449956\pi$
$228$	−8.35428	−	8.35428i	−0.553276	−	0.553276i
$229$			11.4056i			0.753703i	0.926274	+	0.376852i	$0.122993\pi$
$229$			11.4056i			0.753703i	−0.926274	+	0.376852i	$0.877007\pi$
$230$			0.647822i			0.0427161i
$231$	−0.815524	−	0.815524i	−0.0536575	−	0.0536575i
$232$	−3.86355	−	3.86355i	−0.253655	−	0.253655i
$233$	9.88915	−	9.88915i	0.647860	−	0.647860i	−0.304615	−	0.952475i	$-0.598528\pi$
$233$	9.88915	−	9.88915i	0.647860	−	0.647860i	0.952475	+	0.304615i	$0.0985279\pi$
$234$	−8.15857			−0.533342
$235$	4.97244	−	4.97244i	0.324366	−	0.324366i
$236$			8.82861i			0.574693i
$237$	−23.2824			−1.51235
$238$	−0.462444	−	0.445780i	−0.0299758	−	0.0288956i
$239$	−12.7392			−0.824028			−0.412014	−	0.911178i	$-0.635175\pi$
$239$	−12.7392			−0.824028			−0.412014	+	0.911178i	$0.635175\pi$
$240$		−	17.2681i		−	1.11465i
$241$	−14.0879	+	14.0879i	−0.907484	+	0.907484i	−0.996069	−	0.0885848i	$-0.971766\pi$
$241$	−14.0879	+	14.0879i	−0.907484	+	0.907484i	0.0885848	+	0.996069i	$0.471766\pi$
$242$	3.94214			0.253410
$243$	13.3369	−	13.3369i	0.855566	−	0.855566i
$244$	−9.18813	−	9.18813i	−0.588210	−	0.588210i
$245$	−10.0256	−	10.0256i	−0.640514	−	0.640514i
$246$		−	0.359691i		−	0.0229331i
$247$			10.7595i			0.684608i
$248$	−9.08333	−	9.08333i	−0.576792	−	0.576792i
$249$	−9.72063	−	9.72063i	−0.616020	−	0.616020i
$250$	−3.36109	+	3.36109i	−0.212574	+	0.212574i
$251$	−6.16337			−0.389028			−0.194514	−	0.980900i	$-0.562313\pi$
$251$	−6.16337			−0.389028			−0.194514	+	0.980900i	$0.562313\pi$
$252$	2.24050	−	2.24050i	0.141138	−	0.141138i
$253$		−	0.849176i		−	0.0533872i
$254$	1.90193			0.119337
$255$	23.2827	−	0.427200i	1.45802	−	0.0267523i
$256$	4.59083			0.286927
$257$			18.8776i			1.17755i	0.808296	+	0.588777i	$0.200390\pi$
$257$			18.8776i			1.17755i	−0.808296	+	0.588777i	$0.799610\pi$
$258$	−0.775185	+	0.775185i	−0.0482609	+	0.0482609i
$259$	0.775048			0.0481592
$260$	−12.2940	+	12.2940i	−0.762442	+	0.762442i
$261$	11.1345	+	11.1345i	0.689208	+	0.689208i
$262$	1.24151	+	1.24151i	0.0767010	+	0.0767010i
$263$			14.3958i			0.887681i	0.896106	+	0.443840i	$0.146384\pi$
$263$			14.3958i			0.887681i	−0.896106	+	0.443840i	$0.853616\pi$
$264$		−	4.58759i		−	0.282346i
$265$	2.02949	+	2.02949i	0.124670	+	0.124670i
$266$	0.259436	+	0.259436i	0.0159071	+	0.0159071i
$267$	11.1705	−	11.1705i	0.683624	−	0.683624i
$268$	9.90654			0.605138
$269$	0.657444	−	0.657444i	0.0400851	−	0.0400851i	−0.686780	−	0.726865i	$-0.740976\pi$
$269$	0.657444	−	0.657444i	0.0400851	−	0.0400851i	0.726865	+	0.686780i	$0.240976\pi$
$270$		−	3.27848i		−	0.199522i
$271$	−3.84623			−0.233642			−0.116821	−	0.993153i	$-0.537270\pi$
$271$	−3.84623			−0.233642			−0.116821	+	0.993153i	$0.537270\pi$
$272$	0.231265	+	12.6041i	0.0140225	+	0.764238i
$273$	−4.83312			−0.292514
$274$		−	5.19049i		−	0.313569i
$275$	0.551441	−	0.551441i	0.0332531	−	0.0332531i
$276$	3.90758			0.235209
$277$	16.6827	−	16.6827i	1.00237	−	1.00237i	0.00237028	−	0.999997i	$-0.499246\pi$
$277$	16.6827	−	16.6827i	1.00237	−	1.00237i	0.999997	−	0.00237028i	$-0.000754484\pi$
$278$	−4.04441	−	4.04441i	−0.242568	−	0.242568i
$279$	26.1775	+	26.1775i	1.56721	+	1.56721i
$280$			1.23781i			0.0739732i
$281$			6.89532i			0.411341i	0.978621	+	0.205670i	$0.0659374\pi$
$281$			6.89532i			0.411341i	−0.978621	+	0.205670i	$0.934063\pi$
$282$	2.63349	+	2.63349i	0.156822	+	0.156822i
$283$	−5.77320	−	5.77320i	−0.343181	−	0.343181i	0.514381	−	0.857562i	$-0.328022\pi$
$283$	−5.77320	−	5.77320i	−0.343181	−	0.343181i	−0.857562	+	0.514381i	$0.828022\pi$
$284$	8.49305	−	8.49305i	0.503970	−	0.503970i
$285$	−13.3015			−0.787916
$286$	−1.41496	+	1.41496i	−0.0836686	+	0.0836686i
$287$		−	0.127216i		−	0.00750931i
$288$	19.1703			1.12962
$289$	−16.9886	+	0.623634i	−0.999327	+	0.0366843i
$290$	−2.94639			−0.173018
$291$		−	37.4714i		−	2.19661i
$292$	−19.2082	+	19.2082i	−1.12408	+	1.12408i
$293$	18.4674			1.07888			0.539438	−	0.842025i	$-0.318637\pi$
$293$	18.4674			1.07888			0.539438	+	0.842025i	$0.318637\pi$
$294$	5.30976	−	5.30976i	0.309671	−	0.309671i
$295$	7.02838	+	7.02838i	0.409208	+	0.409208i
$296$	2.17995	+	2.17995i	0.126707	+	0.126707i
$297$			4.29749i			0.249366i
$298$		−	3.69219i		−	0.213883i
$299$	−2.51628	−	2.51628i	−0.145520	−	0.145520i
$300$	2.53752	+	2.53752i	0.146504	+	0.146504i
$301$	−0.274168	+	0.274168i	−0.0158028	+	0.0158028i
$302$	−1.30210			−0.0749273
$303$	15.5166	−	15.5166i	0.891408	−	0.891408i
$304$		−	7.20081i		−	0.412995i
$305$	−14.6292			−0.837665
$306$	0.135080	+	7.36198i	0.00772202	+	0.420856i
$307$	11.2897			0.644339			0.322170	−	0.946682i	$-0.395588\pi$
$307$	11.2897			0.644339			0.322170	+	0.946682i	$0.395588\pi$
$308$		−	0.777152i		−	0.0442823i
$309$	−0.529935	+	0.529935i	−0.0301469	+	0.0301469i
$310$	−6.92705			−0.393430
$311$	−6.18811	+	6.18811i	−0.350896	+	0.350896i	−0.860443	−	0.509547i	$-0.829813\pi$
$311$	−6.18811	+	6.18811i	−0.350896	+	0.350896i	0.509547	+	0.860443i	$0.329813\pi$
$312$	−13.5939	−	13.5939i	−0.769606	−	0.769606i
$313$	−13.6200	−	13.6200i	−0.769849	−	0.769849i	0.208230	−	0.978080i	$-0.433230\pi$
$313$	−13.6200	−	13.6200i	−0.769849	−	0.769849i	−0.978080	+	0.208230i	$0.933230\pi$
$314$			4.53835i			0.256114i
$315$		−	3.56728i		−	0.200994i
$316$	−11.0934	−	11.0934i	−0.624055	−	0.624055i
$317$	−15.5763	−	15.5763i	−0.874854	−	0.874854i	0.118143	−	0.992997i	$-0.462306\pi$
$317$	−15.5763	−	15.5763i	−0.874854	−	0.874854i	−0.992997	+	0.118143i	$0.962306\pi$
$318$	−1.07485	+	1.07485i	−0.0602748	+	0.0602748i
$319$	3.86218			0.216240
$320$	6.41383	−	6.41383i	0.358544	−	0.358544i
$321$		−	34.8498i		−	1.94513i
$322$	−0.121347			−0.00676242
$323$	9.70891	−	0.178143i	0.540218	−	0.00991212i
$324$	4.74057			0.263365
$325$		−	3.26806i		−	0.181279i
$326$	5.29137	−	5.29137i	0.293062	−	0.293062i
$327$	−26.4306			−1.46161
$328$	0.357815	−	0.357815i	0.0197570	−	0.0197570i
$329$	0.931415	+	0.931415i	0.0513506	+	0.0513506i
$330$	−1.74927	−	1.74927i	−0.0962943	−	0.0962943i
$331$		−	0.818708i		−	0.0450003i	−0.999747	−	0.0225001i	$-0.992837\pi$
$331$		−	0.818708i		−	0.0450003i	0.999747	−	0.0225001i	$-0.00716262\pi$
$332$		−	9.26326i		−	0.508387i
$333$	−6.28247	−	6.28247i	−0.344277	−	0.344277i
$334$	−2.72412	−	2.72412i	−0.149057	−	0.149057i
$335$	7.88651	−	7.88651i	0.430886	−	0.430886i
$336$	3.23459			0.176461
$337$	20.7177	−	20.7177i	1.12857	−	1.12857i	0.138154	−	0.990411i	$-0.455883\pi$
$337$	20.7177	−	20.7177i	1.12857	−	1.12857i	0.990411	−	0.138154i	$-0.0441170\pi$
$338$			3.16243i			0.172014i
$339$	26.7530			1.45302
$340$	11.2972	+	10.8901i	0.612676	+	0.590597i
$341$	9.08009			0.491715
$342$		−	4.20593i		−	0.227431i
$343$	3.79713	−	3.79713i	0.205026	−	0.205026i
$344$	−1.54228			−0.0831544
$345$	3.11079	−	3.11079i	0.167479	−	0.167479i
$346$	−5.21366	−	5.21366i	−0.280288	−	0.280288i
$347$	10.0053	+	10.0053i	0.537115	+	0.537115i	0.922680	−	0.385566i	$-0.125994\pi$
$347$	10.0053	+	10.0053i	0.537115	+	0.537115i	−0.385566	+	0.922680i	$0.625994\pi$
$348$			17.7723i			0.952693i
$349$			12.0417i			0.644576i	0.946642	+	0.322288i	$0.104452\pi$
$349$			12.0417i			0.644576i	−0.946642	+	0.322288i	$0.895548\pi$
$350$	−0.0788009	−	0.0788009i	−0.00421208	−	0.00421208i
$351$	12.7343	+	12.7343i	0.679708	+	0.679708i
$352$	3.32476	−	3.32476i	0.177210	−	0.177210i
$353$	22.5689			1.20122			0.600611	−	0.799542i	$-0.294924\pi$
$353$	22.5689			1.20122			0.600611	+	0.799542i	$0.294924\pi$
$354$	−3.72236	+	3.72236i	−0.197841	+	0.197841i
$355$		−	13.5225i		−	0.717699i
$356$	10.6449			0.564180
$357$	0.0800212	+	4.36122i	0.00423517	+	0.230820i
$358$	−6.11266			−0.323064
$359$			1.87403i			0.0989077i	0.998776	+	0.0494538i	$0.0157481\pi$
$359$			1.87403i			0.0989077i	−0.998776	+	0.0494538i	$0.984252\pi$
$360$	10.0336	−	10.0336i	0.528815	−	0.528815i
$361$	13.4533			0.708066
$362$	6.39600	−	6.39600i	0.336166	−	0.336166i
$363$	−18.9298	−	18.9298i	−0.993559	−	0.993559i
$364$	−2.30286	−	2.30286i	−0.120703	−	0.120703i
$365$			30.5830i			1.60079i
$366$		−	7.74788i		−	0.404988i
$367$	24.9702	+	24.9702i	1.30343	+	1.30343i	0.926062	+	0.377371i	$0.123172\pi$
$367$	24.9702	+	24.9702i	1.30343	+	1.30343i	0.377371	+	0.926062i	$0.376828\pi$
$368$	1.68403	+	1.68403i	0.0877861	+	0.0877861i
$369$	−1.03120	+	1.03120i	−0.0536821	+	0.0536821i
$370$	1.66245			0.0864269
$371$	−0.380155	+	0.380155i	−0.0197367	+	0.0197367i
$372$			41.7831i			2.16635i
$373$	18.6417			0.965232			0.482616	−	0.875832i	$-0.339687\pi$
$373$	18.6417			0.965232			0.482616	+	0.875832i	$0.339687\pi$
$374$	1.30024	+	1.25338i	0.0672336	+	0.0648108i
$375$	32.2794			1.66690
$376$			5.23951i			0.270207i
$377$	11.4444	−	11.4444i	0.589417	−	0.589417i
$378$	0.614111			0.0315865
$379$	−25.5132	+	25.5132i	−1.31053	+	1.31053i	−0.389501	+	0.921026i	$0.627353\pi$
$379$	−25.5132	+	25.5132i	−1.31053	+	1.31053i	−0.921026	+	0.389501i	$0.872647\pi$
$380$	−6.33784	−	6.33784i	−0.325125	−	0.325125i
$381$	−9.13290	−	9.13290i	−0.467893	−	0.467893i
$382$		−	0.691269i		−	0.0353684i
$383$			12.5898i			0.643311i	0.946857	+	0.321655i	$0.104239\pi$
$383$			12.5898i			0.643311i	−0.946857	+	0.321655i	$0.895761\pi$
$384$	20.0395	+	20.0395i	1.02264	+	1.02264i
$385$	−0.618684	−	0.618684i	−0.0315311	−	0.0315311i
$386$	3.55158	−	3.55158i	0.180771	−	0.180771i
$387$	4.44476			0.225940
$388$	17.8541	−	17.8541i	0.906407	−	0.906407i
$389$		−	23.6625i		−	1.19974i	−0.800098	−	0.599869i	$-0.795219\pi$
$389$		−	23.6625i		−	1.19974i	0.800098	−	0.599869i	$-0.204781\pi$
$390$	−10.3669			−0.524948
$391$	−2.22893	+	2.31225i	−0.112722	+	0.116936i
$392$	10.5641			0.533569
$393$		−	11.9233i		−	0.601452i
$394$	2.30225	−	2.30225i	0.115986	−	0.115986i
$395$	−17.6628			−0.888712
$396$	−6.29952	+	6.29952i	−0.316563	+	0.316563i
$397$	7.98656	+	7.98656i	0.400834	+	0.400834i	0.878527	−	0.477693i	$-0.158527\pi$
$397$	7.98656	+	7.98656i	0.400834	+	0.400834i	−0.477693	+	0.878527i	$0.658527\pi$
$398$	−0.382790	−	0.382790i	−0.0191875	−	0.0191875i
$399$		−	2.49159i		−	0.124735i
$400$			2.18716i			0.109358i
$401$	−3.16581	−	3.16581i	−0.158093	−	0.158093i	0.623628	−	0.781721i	$-0.285658\pi$
$401$	−3.16581	−	3.16581i	−0.158093	−	0.158093i	−0.781721	+	0.623628i	$0.785658\pi$
$402$	4.17684	+	4.17684i	0.208322	+	0.208322i
$403$	26.9062	−	26.9062i	1.34029	−	1.34029i
$404$	14.7866			0.735659
$405$	3.77393	−	3.77393i	0.187528	−	0.187528i
$406$		−	0.551905i		−	0.0273906i
$407$	−2.17917			−0.108018
$408$	−12.0416	+	12.4917i	−0.596147	+	0.618432i
$409$	4.72146			0.233461			0.116731	−	0.993164i	$-0.462759\pi$
$409$	4.72146			0.233461			0.116731	+	0.993164i	$0.462759\pi$
$410$		−	0.272874i		−	0.0134763i
$411$	−24.9244	+	24.9244i	−1.22943	+	1.22943i
$412$	−0.505000			−0.0248796
$413$	−1.31653	+	1.31653i	−0.0647820	+	0.0647820i
$414$	0.983629	+	0.983629i	0.0483427	+	0.0483427i
$415$	−7.37440	−	7.37440i	−0.361995	−	0.361995i
$416$		−	19.7039i		−	0.966063i
$417$			38.8419i			1.90210i
$418$	−0.729447	−	0.729447i	−0.0356784	−	0.0356784i
$419$	3.25713	+	3.25713i	0.159121	+	0.159121i	0.782177	−	0.623056i	$-0.214109\pi$
$419$	3.25713	+	3.25713i	0.159121	+	0.159121i	−0.623056	+	0.782177i	$0.714109\pi$
$420$	2.84695	−	2.84695i	0.138917	−	0.138917i
$421$	−15.2474			−0.743113			−0.371557	−	0.928410i	$-0.621176\pi$
$421$	−15.2474			−0.743113			−0.371557	+	0.928410i	$0.621176\pi$
$422$	−3.89272	+	3.89272i	−0.189494	+	0.189494i
$423$		−	15.0999i		−	0.734183i
$424$	−2.13849			−0.103854
$425$	−2.94897	+	0.0541088i	−0.143046	+	0.00262466i
$426$	7.16175			0.346988
$427$		−	2.74028i		−	0.132611i
$428$	16.6050	−	16.6050i	0.802635	−	0.802635i
$429$	13.5891			0.656088
$430$	−0.588082	+	0.588082i	−0.0283598	+	0.0283598i
$431$	−19.2732	−	19.2732i	−0.928357	−	0.928357i	0.0692425	−	0.997600i	$-0.477942\pi$
$431$	−19.2732	−	19.2732i	−0.928357	−	0.928357i	−0.997600	+	0.0692425i	$0.977942\pi$
$432$	−8.52250	−	8.52250i	−0.410039	−	0.410039i
$433$		−	15.2884i		−	0.734713i	−0.930080	−	0.367357i	$-0.880263\pi$
$433$		−	15.2884i		−	0.734713i	0.930080	−	0.367357i	$-0.119737\pi$
$434$		−	1.29755i		−	0.0622842i
$435$	14.1483	+	14.1483i	0.678361	+	0.678361i
$436$	−12.5935	−	12.5935i	−0.603118	−	0.603118i
$437$	1.29720	−	1.29720i	0.0620535	−	0.0620535i
$438$	−16.1973			−0.773938
$439$	−12.9033	+	12.9033i	−0.615839	+	0.615839i	−0.944461	−	0.328622i	$-0.893416\pi$
$439$	−12.9033	+	12.9033i	−0.615839	+	0.615839i	0.328622	+	0.944461i	$0.393416\pi$
$440$		−	3.48030i		−	0.165917i
$441$	−30.4451			−1.44977
$442$	7.56689	−	0.138840i	0.359920	−	0.00660394i
$443$	39.6029			1.88159			0.940795	−	0.338975i	$-0.110080\pi$
$443$	39.6029			1.88159			0.940795	+	0.338975i	$0.110080\pi$
$444$		−	10.0277i		−	0.475894i
$445$	8.47433	−	8.47433i	0.401722	−	0.401722i
$446$	5.77796			0.273594
$447$	−17.7296	+	17.7296i	−0.838581	+	0.838581i
$448$	1.20141	+	1.20141i	0.0567613	+	0.0567613i
$449$	−14.7308	−	14.7308i	−0.695189	−	0.695189i	0.268180	−	0.963369i	$-0.413578\pi$
$449$	−14.7308	−	14.7308i	−0.695189	−	0.695189i	−0.963369	+	0.268180i	$0.913578\pi$
$450$			1.27750i			0.0602221i
$451$			0.357688i			0.0168429i
$452$	12.7471	+	12.7471i	0.599574	+	0.599574i
$453$	6.25257	+	6.25257i	0.293771	+	0.293771i
$454$	−6.92666	+	6.92666i	−0.325084	+	0.325084i
$455$	−3.66657			−0.171892
$456$	7.00800	−	7.00800i	0.328179	−	0.328179i
$457$		−	36.3014i		−	1.69811i	−0.528305	−	0.849055i	$-0.677172\pi$
$457$		−	36.3014i		−	1.69811i	0.528305	−	0.849055i	$-0.322828\pi$
$458$	−4.58261			−0.214132
$459$	11.2801	−	11.7018i	0.526511	−	0.546194i
$460$	2.96442			0.138217
$461$		−	22.1331i		−	1.03084i	−0.856937	−	0.515421i	$-0.827636\pi$
$461$		−	22.1331i		−	1.03084i	0.856937	−	0.515421i	$-0.172364\pi$
$462$	0.327666	−	0.327666i	0.0152444	−	0.0152444i
$463$	−26.4750			−1.23040			−0.615199	−	0.788372i	$-0.710924\pi$
$463$	−26.4750			−1.23040			−0.615199	+	0.788372i	$0.710924\pi$
$464$	−7.65922	+	7.65922i	−0.355570	+	0.355570i
$465$	33.2632	+	33.2632i	1.54254	+	1.54254i
$466$	3.97333	+	3.97333i	0.184061	+	0.184061i
$467$			33.2189i			1.53719i	0.639736	+	0.768594i	$0.279043\pi$
$467$			33.2189i			1.53719i	−0.639736	+	0.768594i	$0.720957\pi$
$468$			37.3335i			1.72574i
$469$	1.47727	+	1.47727i	0.0682138	+	0.0682138i
$470$	1.99786	+	1.99786i	0.0921543	+	0.0921543i
$471$	21.7928	−	21.7928i	1.00416	−	1.00416i
$472$	−7.40588			−0.340883
$473$	0.770867	−	0.770867i	0.0354445	−	0.0354445i
$474$		−	9.35453i		−	0.429668i
$475$	1.68476			0.0773022
$476$	−2.03988	+	2.11614i	−0.0934979	+	0.0969930i
$477$	6.16300			0.282184
$478$		−	5.11842i		−	0.234111i
$479$	6.78856	−	6.78856i	0.310177	−	0.310177i	−0.534801	−	0.844978i	$-0.679613\pi$
$479$	6.78856	−	6.78856i	0.310177	−	0.310177i	0.844978	+	0.534801i	$0.179613\pi$
$480$	24.3593			1.11184
$481$	−6.45733	+	6.45733i	−0.294429	+	0.294429i
$482$	−5.66034	−	5.66034i	−0.257821	−	0.257821i
$483$	0.582700	+	0.582700i	0.0265138	+	0.0265138i
$484$		−	18.0392i		−	0.819962i
$485$		−	28.4271i		−	1.29081i
$486$	5.35860	+	5.35860i	0.243071	+	0.243071i
$487$	−12.9824	−	12.9824i	−0.588287	−	0.588287i	0.348880	−	0.937167i	$-0.386562\pi$
$487$	−12.9824	−	12.9824i	−0.588287	−	0.588287i	−0.937167	+	0.348880i	$0.886562\pi$
$488$	7.70747	−	7.70747i	0.348901	−	0.348901i
$489$	−50.8175			−2.29805
$490$	4.02816	−	4.02816i	0.181974	−	0.181974i
$491$		−	24.9068i		−	1.12403i	−0.827128	−	0.562014i	$-0.810027\pi$
$491$		−	24.9068i		−	1.12403i	0.827128	−	0.562014i	$-0.189973\pi$
$492$	−1.64594			−0.0742048
$493$	−10.5165	−	10.1375i	−0.473638	−	0.456571i
$494$	−4.32300			−0.194501
$495$			10.0300i			0.450814i
$496$	−18.0070	+	18.0070i	−0.808540	+	0.808540i
$497$	2.53297			0.113619
$498$	3.90562	−	3.90562i	0.175015	−	0.175015i
$499$	4.09364	+	4.09364i	0.183257	+	0.183257i	0.792773	−	0.609517i	$-0.208636\pi$
$499$	4.09364	+	4.09364i	0.183257	+	0.183257i	−0.609517	+	0.792773i	$0.708636\pi$
$500$	15.3803	+	15.3803i	0.687829	+	0.687829i
$501$			26.1620i			1.16883i
$502$		−	2.47636i		−	0.110525i
$503$	−8.05207	−	8.05207i	−0.359024	−	0.359024i	0.504429	−	0.863453i	$-0.331703\pi$
$503$	−8.05207	−	8.05207i	−0.359024	−	0.359024i	−0.863453	+	0.504429i	$0.831703\pi$
$504$	1.87944	+	1.87944i	0.0837170	+	0.0837170i
$505$	11.7715	−	11.7715i	0.523823	−	0.523823i
$506$	0.341187			0.0151676
$507$	15.1858	−	15.1858i	0.674423	−	0.674423i
$508$		−	8.70318i		−	0.386141i
$509$	−42.0815			−1.86523			−0.932614	−	0.360875i	$-0.882478\pi$
$509$	−42.0815			−1.86523			−0.932614	+	0.360875i	$0.882478\pi$
$510$	0.171643	+	9.35469i	0.00760048	+	0.414233i
$511$	−5.72868			−0.253422
$512$			22.6179i			0.999578i
$513$	−6.56484	+	6.56484i	−0.289845	+	0.289845i
$514$	−7.58477			−0.334550
$515$	−0.402027	+	0.402027i	−0.0177154	+	0.0177154i
$516$	3.54723	+	3.54723i	0.156158	+	0.156158i
$517$	−2.61882	−	2.61882i	−0.115176	−	0.115176i
$518$			0.311404i			0.0136823i
$519$			50.0712i			2.19788i
$520$	−10.3128	−	10.3128i	−0.452248	−	0.452248i
$521$	−16.3053	−	16.3053i	−0.714350	−	0.714350i	0.253092	−	0.967442i	$-0.418552\pi$
$521$	−16.3053	−	16.3053i	−0.714350	−	0.714350i	−0.967442	+	0.253092i	$0.918552\pi$
$522$	−4.47369	+	4.47369i	−0.195808	+	0.195808i
$523$	−20.1860			−0.882671			−0.441336	−	0.897342i	$-0.645495\pi$
$523$	−20.1860			−0.882671			−0.441336	+	0.897342i	$0.645495\pi$
$524$	5.68115	−	5.68115i	0.248182	−	0.248182i
$525$			0.756791i			0.0330291i
$526$	−5.78402			−0.252195
$527$	−24.7246	−	23.8336i	−1.07702	−	1.03821i
$528$	−9.09456			−0.395790
$529$		−	22.3933i		−	0.973620i
$530$	−0.815420	+	0.815420i	−0.0354196	+	0.0354196i
$531$	21.3433			0.926218
$532$	1.18718	−	1.18718i	0.0514707	−	0.0514707i
$533$	1.05990	+	1.05990i	0.0459094	+	0.0459094i
$534$	4.48816	+	4.48816i	0.194222	+	0.194222i
$535$		−	26.4383i		−	1.14303i
$536$			8.31010i			0.358942i
$537$	29.3525	+	29.3525i	1.26666	+	1.26666i
$538$	0.264152	+	0.264152i	0.0113884	+	0.0113884i
$539$	−5.28018	+	5.28018i	−0.227434	+	0.227434i
$540$	−15.0023			−0.645596
$541$	22.3126	−	22.3126i	0.959295	−	0.959295i	−0.0399085	−	0.999203i	$-0.512707\pi$
$541$	22.3126	−	22.3126i	0.959295	−	0.959295i	0.999203	+	0.0399085i	$0.0127066\pi$
$542$		−	1.54536i		−	0.0663790i
$543$	−61.4262			−2.63605
$544$	−17.7800	+	0.326234i	−0.762312	+	0.0139872i
$545$	−20.0511			−0.858896
$546$		−	1.94188i		−	0.0831049i
$547$	16.0171	−	16.0171i	0.684841	−	0.684841i	−0.276246	−	0.961087i	$-0.589090\pi$
$547$	16.0171	−	16.0171i	0.684841	−	0.684841i	0.961087	+	0.276246i	$0.0890903\pi$
$548$	−23.7516			−1.01462
$549$	−22.2124	+	22.2124i	−0.948003	+	0.948003i
$550$	0.221561	+	0.221561i	0.00944741	+	0.00944741i
$551$	5.89986	+	5.89986i	0.251343	+	0.251343i
$552$			3.27788i			0.139516i
$553$		−	3.30852i		−	0.140692i
$554$	6.70289	+	6.70289i	0.284778	+	0.284778i
$555$	−7.98298	−	7.98298i	−0.338859	−	0.338859i
$556$	−18.5072	+	18.5072i	−0.784879	+	0.784879i
$557$	38.8682			1.64690			0.823449	−	0.567390i	$-0.192047\pi$
$557$	38.8682			1.64690			0.823449	+	0.567390i	$0.192047\pi$
$558$	−10.5178	+	10.5178i	−0.445253	+	0.445253i
$559$		−	4.56847i		−	0.193226i
$560$	2.45387			0.103695
$561$	−0.224993	−	12.2623i	−0.00949919	−	0.517714i
$562$	−2.77045			−0.116864
$563$			43.8292i			1.84718i	0.383381	+	0.923590i	$0.374760\pi$
$563$			43.8292i			1.84718i	−0.383381	+	0.923590i	$0.625240\pi$
$564$	12.0508	−	12.0508i	0.507431	−	0.507431i
$565$	20.2957			0.853848
$566$	2.31959	−	2.31959i	0.0974998	−	0.0974998i
$567$	0.706916	+	0.706916i	0.0296877	+	0.0296877i
$568$	7.12440	+	7.12440i	0.298933	+	0.298933i
$569$			3.34213i			0.140109i	0.997543	+	0.0700547i	$0.0223174\pi$
$569$			3.34213i			0.140109i	−0.997543	+	0.0700547i	$0.977683\pi$
$570$		−	5.34438i		−	0.223851i
$571$	−17.7847	−	17.7847i	−0.744267	−	0.744267i	0.229129	−	0.973396i	$-0.426412\pi$
$571$	−17.7847	−	17.7847i	−0.744267	−	0.744267i	−0.973396	+	0.229129i	$0.926412\pi$
$572$	6.47486	+	6.47486i	0.270727	+	0.270727i
$573$	−3.31942	+	3.31942i	−0.138671	+	0.138671i
$574$	0.0511136			0.00213344
$575$	−0.394010	+	0.394010i	−0.0164314	+	0.0164314i
$576$		−	19.4770i		−	0.811543i
$577$	−38.7990			−1.61523			−0.807613	−	0.589713i	$-0.799241\pi$
$577$	−38.7990			−1.61523			−0.807613	+	0.589713i	$0.799241\pi$
$578$	−0.250568	−	6.82577i	−0.0104222	−	0.283915i
$579$	−34.1088			−1.41751
$580$			13.4826i			0.559836i
$581$	1.38134	−	1.38134i	0.0573077	−	0.0573077i
$582$	15.0555			0.624070
$583$	1.06887	−	1.06887i	0.0442679	−	0.0442679i
$584$	−16.1129	−	16.1129i	−0.666755	−	0.666755i
$585$	29.7209	+	29.7209i	1.22881	+	1.22881i
$586$			7.41994i			0.306515i
$587$		−	1.00613i		−	0.0415275i	−0.999784	−	0.0207637i	$-0.993390\pi$
$587$		−	1.00613i		−	0.0415275i	0.999784	−	0.0207637i	$-0.00660978\pi$
$588$	−24.2974	−	24.2974i	−1.00201	−	1.00201i
$589$	13.8708	+	13.8708i	0.571534	+	0.571534i
$590$	−2.82391	+	2.82391i	−0.116258	+	0.116258i
$591$	−22.1105			−0.909503
$592$	4.32159	−	4.32159i	0.177616	−	0.177616i
$593$		−	41.4743i		−	1.70314i	−0.524237	−	0.851572i	$-0.675650\pi$
$593$		−	41.4743i		−	1.70314i	0.524237	−	0.851572i	$-0.324350\pi$
$594$	−1.72667			−0.0708462
$595$	0.0607068	+	3.30857i	0.00248874	+	0.135638i
$596$	−16.8954			−0.692062
$597$			3.67626i			0.150459i
$598$	1.01101	−	1.01101i	0.0413431	−	0.0413431i
$599$	−28.3901			−1.15999			−0.579993	−	0.814621i	$-0.696945\pi$
$599$	−28.3901			−1.15999			−0.579993	+	0.814621i	$0.696945\pi$
$600$	−2.12860	+	2.12860i	−0.0868997	+	0.0868997i
$601$	24.6581	+	24.6581i	1.00582	+	1.00582i	0.999983	+	0.00584200i	$0.00185958\pi$
$601$	24.6581	+	24.6581i	1.00582	+	1.00582i	0.00584200	+	0.999983i	$0.498140\pi$
$602$	−0.110157	−	0.110157i	−0.00448966	−	0.00448966i
$603$		−	23.9492i		−	0.975285i
$604$			5.95838i			0.242443i
$605$	−14.3608	−	14.3608i	−0.583850	−	0.583850i
$606$	6.23437	+	6.23437i	0.253254	+	0.253254i
$607$	−27.1262	+	27.1262i	−1.10102	+	1.10102i	−0.106730	+	0.994288i	$0.534038\pi$
$607$	−27.1262	+	27.1262i	−1.10102	+	1.10102i	−0.994288	+	0.106730i	$0.965962\pi$
$608$	10.1578			0.411954
$609$	−2.65021	+	2.65021i	−0.107392	+	0.107392i
$610$		−	5.87781i		−	0.237985i
$611$	−15.5202			−0.627880
$612$	33.6883	−	0.618125i	1.36177	−	0.0249862i
$613$	−19.6964			−0.795532			−0.397766	−	0.917487i	$-0.630214\pi$
$613$	−19.6964			−0.795532			−0.397766	+	0.917487i	$0.630214\pi$
$614$			4.53606i			0.183060i
$615$	−1.31032	+	1.31032i	−0.0528372	+	0.0528372i
$616$	0.651914			0.0262664
$617$	−11.8727	+	11.8727i	−0.477975	+	0.477975i	−0.904484	−	0.426508i	$-0.859744\pi$
$617$	−11.8727	+	11.8727i	−0.477975	+	0.477975i	0.426508	+	0.904484i	$0.359744\pi$
$618$	−0.212921	−	0.212921i	−0.00856492	−	0.00856492i
$619$	9.32788	+	9.32788i	0.374919	+	0.374919i	0.869265	−	0.494346i	$-0.164592\pi$
$619$	9.32788	+	9.32788i	0.374919	+	0.374919i	−0.494346	+	0.869265i	$0.664592\pi$
$620$			31.6981i			1.27303i
$621$		−	3.07060i		−	0.123219i
$622$	−2.48630	−	2.48630i	−0.0996914	−	0.0996914i
$623$	1.58738	+	1.58738i	0.0635968	+	0.0635968i
$624$	−26.9490	+	26.9490i	−1.07882	+	1.07882i
$625$	20.9115			0.836461
$626$	5.47234	−	5.47234i	0.218719	−	0.218719i
$627$			7.00550i			0.279773i
$628$	20.7674			0.828711
$629$	5.93376	+	5.71993i	0.236594	+	0.228069i
$630$	1.43328			0.0571034
$631$			28.9000i			1.15049i	0.817981	+	0.575246i	$0.195094\pi$
$631$			28.9000i			1.15049i	−0.817981	+	0.575246i	$0.804906\pi$
$632$	9.30574	−	9.30574i	0.370163	−	0.370163i
$633$	37.3850			1.48592
$634$	6.25835	−	6.25835i	0.248551	−	0.248551i
$635$	−6.92853	−	6.92853i	−0.274950	−	0.274950i
$636$	4.91851	+	4.91851i	0.195032	+	0.195032i
$637$			31.2925i			1.23985i
$638$			1.55177i			0.0614352i
$639$	−20.5320	−	20.5320i	−0.812235	−	0.812235i
$640$	15.2026	+	15.2026i	0.600937	+	0.600937i
$641$	17.6066	−	17.6066i	0.695418	−	0.695418i	−0.268001	−	0.963419i	$-0.586363\pi$
$641$	17.6066	−	17.6066i	0.695418	−	0.695418i	0.963419	+	0.268001i	$0.0863630\pi$
$642$	14.0022			0.552622
$643$	4.66728	−	4.66728i	0.184060	−	0.184060i	−0.609063	−	0.793122i	$-0.708454\pi$
$643$	4.66728	−	4.66728i	0.184060	−	0.184060i	0.793122	+	0.609063i	$0.208454\pi$
$644$			0.555283i			0.0218812i
$645$	5.64785			0.222384
$646$	0.0715752	+	3.90091i	0.00281609	+	0.153479i
$647$	−4.20273			−0.165226			−0.0826132	−	0.996582i	$-0.526327\pi$
$647$	−4.20273			−0.165226			−0.0826132	+	0.996582i	$0.526327\pi$
$648$			3.97663i			0.156217i
$649$	3.70162	−	3.70162i	0.145301	−	0.145301i
$650$	1.31306			0.0515025
$651$	−6.23071	+	6.23071i	−0.244201	+	0.244201i
$652$	−24.2132	−	24.2132i	−0.948264	−	0.948264i
$653$	−17.1836	−	17.1836i	−0.672448	−	0.672448i	0.285832	−	0.958280i	$-0.407730\pi$
$653$	−17.1836	−	17.1836i	−0.672448	−	0.672448i	−0.958280	+	0.285832i	$0.907730\pi$
$654$		−	10.6194i		−	0.415253i
$655$		−	9.04543i		−	0.353434i
$656$	−0.709343	−	0.709343i	−0.0276952	−	0.0276952i
$657$	46.4361	+	46.4361i	1.81165	+	1.81165i
$658$	−0.374230	+	0.374230i	−0.0145890	+	0.0145890i
$659$	43.4281			1.69172			0.845859	−	0.533407i	$-0.179088\pi$
$659$	43.4281			1.69172			0.845859	+	0.533407i	$0.179088\pi$
$660$	−8.00465	+	8.00465i	−0.311580	+	0.311580i
$661$			7.05666i			0.274472i	0.990538	+	0.137236i	$0.0438219\pi$
$661$			7.05666i			0.274472i	−0.990538	+	0.137236i	$0.956178\pi$
$662$	0.328946			0.0127848
$663$	−37.0023	−	35.6689i	−1.43705	−	1.38527i
$664$	7.77049			0.301553
$665$		−	1.89020i		−	0.0732989i
$666$	2.52421	−	2.52421i	0.0978111	−	0.0978111i
$667$	−2.75956			−0.106851
$668$	−12.4655	+	12.4655i	−0.482305	+	0.482305i
$669$	−27.7453	−	27.7453i	−1.07270	−	1.07270i
$670$	3.16869	+	3.16869i	0.122417	+	0.122417i
$671$			7.70473i			0.297438i
$672$			4.56287i			0.176017i
$673$	14.8091	+	14.8091i	0.570849	+	0.570849i	0.932366	−	0.361517i	$-0.117741\pi$
$673$	14.8091	+	14.8091i	0.570849	+	0.570849i	−0.361517	+	0.932366i	$0.617741\pi$
$674$	8.32409	+	8.32409i	0.320632	+	0.320632i
$675$	1.99400	−	1.99400i	0.0767490	−	0.0767490i
$676$	14.4712			0.556586
$677$	20.9352	−	20.9352i	0.804606	−	0.804606i	−0.179206	−	0.983812i	$-0.557353\pi$
$677$	20.9352	−	20.9352i	0.804606	−	0.804606i	0.983812	+	0.179206i	$0.0573528\pi$
$678$			10.7490i			0.412813i
$679$	5.32484			0.204348
$680$	−9.13515	+	9.47665i	−0.350317	+	0.363413i
$681$	66.5226			2.54915
$682$			3.64826i			0.139699i
$683$	27.8874	−	27.8874i	1.06708	−	1.06708i	0.0695000	−	0.997582i	$-0.477860\pi$
$683$	27.8874	−	27.8874i	1.06708	−	1.06708i	0.997582	−	0.0695000i	$-0.0221404\pi$
$684$	−19.2463			−0.735900
$685$	−18.9085	+	18.9085i	−0.722455	+	0.722455i
$686$	1.52564	+	1.52564i	0.0582491	+	0.0582491i
$687$	22.0054	+	22.0054i	0.839557	+	0.839557i
$688$			3.05747i			0.116565i
$689$		−	6.33453i		−	0.241327i
$690$	1.24987	+	1.24987i	0.0475819	+	0.0475819i
$691$	17.4763	+	17.4763i	0.664829	+	0.664829i	0.956514	−	0.291685i	$-0.0942159\pi$
$691$	17.4763	+	17.4763i	0.664829	+	0.664829i	−0.291685	+	0.956514i	$0.594216\pi$
$692$	−23.8576	+	23.8576i	−0.906931	+	0.906931i
$693$	−1.87877			−0.0713687
$694$	−4.02001	+	4.02001i	−0.152597	+	0.152597i
$695$			29.4668i			1.11774i
$696$	−14.9083			−0.565096
$697$	0.938865	−	0.973962i	0.0355621	−	0.0368915i
$698$	−4.83818			−0.183128
$699$		−	38.1592i		−	1.44331i
$700$	−0.360592	+	0.360592i	−0.0136291	+	0.0136291i
$701$	44.3699			1.67583			0.837913	−	0.545803i	$-0.183775\pi$
$701$	44.3699			1.67583			0.837913	+	0.545803i	$0.183775\pi$
$702$	−5.11648	+	5.11648i	−0.193109	+	0.193109i
$703$	−3.32890	−	3.32890i	−0.125552	−	0.125552i
$704$	−3.37796	−	3.37796i	−0.127312	−	0.127312i
$705$		−	19.1871i		−	0.722628i
$706$			9.06788i			0.341274i
$707$	2.20498	+	2.20498i	0.0829267	+	0.0829267i
$708$	17.0334	+	17.0334i	0.640156	+	0.640156i
$709$	19.2496	−	19.2496i	0.722932	−	0.722932i	−0.246269	−	0.969201i	$-0.579205\pi$
$709$	19.2496	−	19.2496i	0.722932	−	0.722932i	0.969201	+	0.246269i	$0.0792047\pi$
$710$	5.43315			0.203902
$711$	−26.8185	+	26.8185i	−1.00577	+	1.00577i
$712$			8.92950i			0.334647i
$713$	−6.48782			−0.242971
$714$	−1.75228	+	0.0321514i	−0.0655774	+	0.00120324i
$715$	10.3092			0.385541
$716$			27.9715i			1.04534i
$717$	−24.5783	+	24.5783i	−0.917892	+	0.917892i
$718$	−0.752961			−0.0281002
$719$	21.8915	−	21.8915i	0.816414	−	0.816414i	−0.169172	−	0.985586i	$-0.554109\pi$
$719$	21.8915	−	21.8915i	0.816414	−	0.816414i	0.985586	+	0.169172i	$0.0541095\pi$
$720$	−19.8908	−	19.8908i	−0.741287	−	0.741287i
$721$	−0.0753059	−	0.0753059i	−0.00280454	−	0.00280454i
$722$			5.40533i			0.201166i
$723$			54.3610i			2.02171i
$724$	−29.2680	−	29.2680i	−1.08774	−	1.08774i
$725$	−1.79202	−	1.79202i	−0.0665538	−	0.0665538i
$726$	7.60575	−	7.60575i	0.282276	−	0.282276i
$727$	−30.2303			−1.12118			−0.560591	−	0.828093i	$-0.689426\pi$
$727$	−30.2303			−1.12118			−0.560591	+	0.828093i	$0.689426\pi$
$728$	1.93175	−	1.93175i	0.0715956	−	0.0715956i
$729$		−	43.7280i		−	1.61955i
$730$	−12.2878			−0.454794
$731$	−4.12241	+	0.0756394i	−0.152473	+	0.00279763i
$732$	−35.4542			−1.31042
$733$			19.8398i			0.732800i	0.930457	+	0.366400i	$0.119410\pi$
$733$			19.8398i			0.732800i	−0.930457	+	0.366400i	$0.880590\pi$
$734$	−10.0327	+	10.0327i	−0.370313	+	0.370313i
$735$	−38.6859			−1.42695
$736$	−2.37558	+	2.37558i	−0.0875649	+	0.0875649i
$737$	−4.15357	−	4.15357i	−0.152999	−	0.152999i
$738$	−0.414322	−	0.414322i	−0.0152514	−	0.0152514i
$739$		−	31.0709i		−	1.14296i	−0.820615	−	0.571482i	$-0.806369\pi$
$739$		−	31.0709i		−	1.14296i	0.820615	−	0.571482i	$-0.193631\pi$
$740$		−	7.60737i		−	0.279652i
$741$	20.7587	+	20.7587i	0.762590	+	0.762590i
$742$	−0.152741	−	0.152741i	−0.00560730	−	0.00560730i
$743$	−15.8071	+	15.8071i	−0.579904	+	0.579904i	−0.934877	−	0.354972i	$-0.884490\pi$
$743$	−15.8071	+	15.8071i	−0.579904	+	0.579904i	0.354972	+	0.934877i	$0.384490\pi$
$744$	−35.0498			−1.28499
$745$	−13.4503	+	13.4503i	−0.492780	+	0.492780i
$746$			7.48999i			0.274228i
$747$	−22.3940			−0.819354
$748$	5.73546	−	5.94986i	0.209709	−	0.217549i
$749$	4.95230			0.180953
$750$			12.9694i			0.473577i
$751$	−12.0523	+	12.0523i	−0.439795	+	0.439795i	−0.891943	−	0.452148i	$-0.850658\pi$
$751$	−12.0523	+	12.0523i	−0.439795	+	0.439795i	0.452148	+	0.891943i	$0.350658\pi$
$752$	10.3870			0.378773
$753$	−11.8913	+	11.8913i	−0.433342	+	0.433342i
$754$	4.59821	+	4.59821i	0.167457	+	0.167457i
$755$	4.74341	+	4.74341i	0.172630	+	0.172630i
$756$		−	2.81016i		−	0.102205i
$757$			42.1101i			1.53052i	0.643723	+	0.765258i	$0.277389\pi$
$757$			42.1101i			1.53052i	−0.643723	+	0.765258i	$0.722611\pi$
$758$	−10.2509	−	10.2509i	−0.372328	−	0.372328i
$759$	−1.63835	−	1.63835i	−0.0594685	−	0.0594685i
$760$	5.31650	−	5.31650i	0.192850	−	0.192850i
$761$	17.9989			0.652458			0.326229	−	0.945291i	$-0.394222\pi$
$761$	17.9989			0.652458			0.326229	+	0.945291i	$0.394222\pi$
$762$	3.66947	−	3.66947i	0.132931	−	0.132931i
$763$		−	3.75589i		−	0.135972i
$764$	−3.16324			−0.114442
$765$	26.3269	−	27.3111i	0.951850	−	0.987433i
$766$	−5.05843			−0.182768
$767$		−	21.9373i		−	0.792111i
$768$	8.85730	−	8.85730i	0.319610	−	0.319610i
$769$	−10.2282			−0.368837			−0.184419	−	0.982848i	$-0.559040\pi$
$769$	−10.2282			−0.368837			−0.184419	+	0.982848i	$0.559040\pi$
$770$	0.248579	−	0.248579i	0.00895816	−	0.00895816i
$771$	36.4215	+	36.4215i	1.31169	+	1.31169i
$772$	−16.2520	−	16.2520i	−0.584921	−	0.584921i
$773$		−	18.0648i		−	0.649745i	−0.945758	−	0.324873i	$-0.894679\pi$
$773$		−	18.0648i		−	0.649745i	0.945758	−	0.324873i	$-0.105321\pi$
$774$			1.78584i			0.0641908i
$775$	−4.21308	−	4.21308i	−0.151338	−	0.151338i
$776$	14.9770	+	14.9770i	0.537642	+	0.537642i
$777$	1.49534	−	1.49534i	0.0536449	−	0.0536449i
$778$	9.50728			0.340852
$779$	−0.546404	+	0.546404i	−0.0195770	+	0.0195770i
$780$			47.4388i			1.69858i
$781$	−7.12186			−0.254840
$782$	−0.929032	−	0.895554i	−0.0332221	−	0.0320250i
$783$	13.9655			0.499088
$784$		−	20.9426i		−	0.747951i
$785$	16.5328	−	16.5328i	0.590080	−	0.590080i
$786$	4.79062			0.170876
$787$	21.6010	−	21.6010i	0.769992	−	0.769992i	−0.208113	−	0.978105i	$-0.566732\pi$
$787$	21.6010	−	21.6010i	0.769992	−	0.769992i	0.978105	+	0.208113i	$0.0667321\pi$
$788$	−10.5351	−	10.5351i	−0.375296	−	0.375296i
$789$	27.7744	+	27.7744i	0.988795	+	0.988795i
$790$		−	7.09667i		−	0.252488i
$791$			3.80171i			0.135173i
$792$	−5.28435	−	5.28435i	−0.187771	−	0.187771i
$793$	22.8307	+	22.8307i	0.810741	+	0.810741i
$794$	−3.20889	+	3.20889i	−0.113879	+	0.113879i
$795$	7.83117			0.277743
$796$	−1.75164	+	1.75164i	−0.0620853	+	0.0620853i
$797$		−	3.58754i		−	0.127077i	−0.997979	−	0.0635385i	$-0.979761\pi$
$797$		−	3.58754i		−	0.127077i	0.997979	−	0.0635385i	$-0.0202386\pi$
$798$	1.00109			0.0354381
$799$	0.256966	+	14.0048i	0.00909079	+	0.495455i
$800$	−3.08532			−0.109083
$801$		−	25.7342i		−	0.909274i
$802$	1.27198	−	1.27198i	0.0449151	−	0.0449151i
$803$	16.1071			0.568408
$804$	19.1131	−	19.1131i	0.674069	−	0.674069i
$805$	0.442056	+	0.442056i	0.0155804	+	0.0155804i
$806$	10.8105	+	10.8105i	0.380785	+	0.380785i
$807$		−	2.53687i		−	0.0893022i
$808$			12.4037i			0.436361i
$809$	12.9975	+	12.9975i	0.456968	+	0.456968i	0.897659	−	0.440691i	$-0.145266\pi$
$809$	12.9975	+	12.9975i	0.456968	+	0.456968i	−0.440691	+	0.897659i	$0.645266\pi$
$810$	1.51631	+	1.51631i	0.0532778	+	0.0532778i
$811$	−13.9393	+	13.9393i	−0.489475	+	0.489475i	−0.908140	−	0.418666i	$-0.862498\pi$
$811$	−13.9393	+	13.9393i	−0.489475	+	0.489475i	0.418666	+	0.908140i	$0.362498\pi$
$812$	−2.52551			−0.0886280
$813$	−7.42071	+	7.42071i	−0.260256	+	0.260256i
$814$		−	0.875562i		−	0.0306884i
$815$	−38.5519			−1.35041
$816$	24.7639	+	23.8716i	0.866911	+	0.835672i
$817$	2.35515			0.0823964
$818$			1.89702i			0.0663277i
$819$	−5.56719	+	5.56719i	−0.194533	+	0.194533i
$820$	−1.24867			−0.0436054
$821$	21.9334	−	21.9334i	0.765481	−	0.765481i	−0.211826	−	0.977307i	$-0.567941\pi$
$821$	21.9334	−	21.9334i	0.765481	−	0.765481i	0.977307	+	0.211826i	$0.0679410\pi$
$822$	−10.0143	−	10.0143i	−0.349288	−	0.349288i
$823$	−21.7996	−	21.7996i	−0.759887	−	0.759887i	0.216414	−	0.976302i	$-0.430564\pi$
$823$	−21.7996	−	21.7996i	−0.759887	−	0.759887i	−0.976302	+	0.216414i	$0.930564\pi$
$824$		−	0.423620i		−	0.0147575i
$825$		−	2.12784i		−	0.0740819i
$826$	−0.528962	−	0.528962i	−0.0184049	−	0.0184049i
$827$	17.5884	+	17.5884i	0.611609	+	0.611609i	0.943365	−	0.331756i	$-0.107641\pi$
$827$	17.5884	+	17.5884i	0.611609	+	0.611609i	−0.331756	+	0.943365i	$0.607641\pi$
$828$	4.50107	−	4.50107i	0.156423	−	0.156423i
$829$	6.27396			0.217904			0.108952	−	0.994047i	$-0.465251\pi$
$829$	6.27396			0.217904			0.108952	+	0.994047i	$0.465251\pi$
$830$	2.96293	−	2.96293i	0.102845	−	0.102845i
$831$		−	64.3735i		−	2.23309i
$832$	−20.0192			−0.694039
$833$	28.2371	−	0.518105i	0.978359	−	0.0179513i
$834$	−15.6061			−0.540397
$835$			19.8474i			0.686847i
$836$	−3.33794	+	3.33794i	−0.115445	+	0.115445i
$837$	32.8334			1.13489
$838$	−1.30867	+	1.30867i	−0.0452073	+	0.0452073i
$839$	−15.3049	−	15.3049i	−0.528384	−	0.528384i	0.391706	−	0.920090i	$-0.371885\pi$
$839$	−15.3049	−	15.3049i	−0.528384	−	0.528384i	−0.920090	+	0.391706i	$0.871885\pi$
$840$	2.38816	+	2.38816i	0.0823994	+	0.0823994i
$841$			16.4491i			0.567210i
$842$		−	6.12620i		−	0.211123i
$843$	13.3035	+	13.3035i	0.458196	+	0.458196i
$844$	17.8130	+	17.8130i	0.613149	+	0.613149i
$845$	11.5204	−	11.5204i	0.396315	−	0.396315i
$846$	6.06694			0.208586
$847$	2.69001	−	2.69001i	0.0924297	−	0.0924297i
$848$			4.23941i			0.145582i
$849$	−22.2770			−0.764545
$850$	−0.0217402	−	1.18486i	−0.000745681	−	0.0406402i
$851$	1.55704			0.0533747
$852$		−	32.7721i		−	1.12275i
$853$	2.20550	−	2.20550i	0.0755150	−	0.0755150i	−0.668340	−	0.743856i	$-0.732995\pi$
$853$	2.20550	−	2.20550i	0.0755150	−	0.0755150i	0.743856	+	0.668340i	$0.232995\pi$
$854$	1.10101			0.0376756
$855$	−15.3218	+	15.3218i	−0.523995	+	0.523995i
$856$	13.9292	+	13.9292i	0.476089	+	0.476089i
$857$	18.8446	+	18.8446i	0.643719	+	0.643719i	0.951468	−	0.307749i	$-0.0995756\pi$
$857$	18.8446	+	18.8446i	0.643719	+	0.643719i	−0.307749	+	0.951468i	$0.599576\pi$
$858$			5.45992i			0.186398i
$859$			5.88401i			0.200760i	0.994949	+	0.100380i	$0.0320058\pi$
$859$			5.88401i			0.200760i	−0.994949	+	0.100380i	$0.967994\pi$
$860$	2.69105	+	2.69105i	0.0917641	+	0.0917641i
$861$	−0.245443	−	0.245443i	−0.00836469	−	0.00836469i
$862$	7.74371	−	7.74371i	0.263752	−	0.263752i
$863$	−41.6967			−1.41937			−0.709686	−	0.704518i	$-0.751163\pi$
$863$	−41.6967			−1.41937			−0.709686	+	0.704518i	$0.751163\pi$
$864$	12.0223	−	12.0223i	0.409006	−	0.409006i
$865$			37.9857i			1.29155i
$866$	6.14267			0.208736
$867$	−31.5736	+	33.9800i	−1.07230	+	1.15402i
$868$	−5.93755			−0.201533
$869$			9.30243i			0.315563i
$870$	−5.68461	+	5.68461i	−0.192726	+	0.192726i
$871$	−24.6158			−0.834073
$872$	10.5641	−	10.5641i	0.357744	−	0.357744i
$873$	−43.1626	−	43.1626i	−1.46083	−	1.46083i
$874$	0.521198	+	0.521198i	0.0176298	+	0.0176298i
$875$			4.58704i			0.155070i
$876$			74.1187i			2.50424i
$877$	9.49036	+	9.49036i	0.320467	+	0.320467i	0.848946	−	0.528479i	$-0.177238\pi$
$877$	9.49036	+	9.49036i	0.320467	+	0.320467i	−0.528479	+	0.848946i	$0.677238\pi$
$878$	−5.18435	−	5.18435i	−0.174963	−	0.174963i
$879$	35.6300	−	35.6300i	1.20177	−	1.20177i
$880$	−6.89944			−0.232580
$881$	6.03203	−	6.03203i	0.203224	−	0.203224i	−0.598156	−	0.801380i	$-0.704100\pi$
$881$	6.03203	−	6.03203i	0.203224	−	0.203224i	0.801380	+	0.598156i	$0.204100\pi$
$882$		−	12.2324i		−	0.411887i
$883$	43.0476			1.44867			0.724333	−	0.689450i	$-0.242148\pi$
$883$	43.0476			1.44867			0.724333	+	0.689450i	$0.242148\pi$
$884$	−0.635329	−	34.6260i	−0.0213684	−	1.16460i
$885$	27.1204			0.911641
$886$			15.9119i			0.534571i
$887$	18.2736	−	18.2736i	0.613567	−	0.613567i	−0.330307	−	0.943874i	$-0.607152\pi$
$887$	18.2736	−	18.2736i	0.613567	−	0.613567i	0.943874	+	0.330307i	$0.107152\pi$
$888$	8.41176			0.282280
$889$	1.29782	−	1.29782i	0.0435275	−	0.0435275i
$890$	3.40487	+	3.40487i	0.114132	+	0.114132i
$891$	−1.98761	−	1.98761i	−0.0665873	−	0.0665873i
$892$		−	26.4399i		−	0.885272i
$893$		−	8.00103i		−	0.267744i
$894$	−7.12351	−	7.12351i	−0.238246	−	0.238246i
$895$	22.2678	+	22.2678i	0.744332	+	0.744332i
$896$	−2.84769	+	2.84769i	−0.0951347	+	0.0951347i
$897$	−9.70955			−0.324193
$898$	5.91863	−	5.91863i	0.197507	−	0.197507i
$899$		−	29.5076i		−	0.984132i
$900$	5.84584			0.194861
$901$	−5.71604	+	0.104880i	−0.190429	+	0.00349406i
$902$	−0.143714			−0.00478515
$903$			1.05793i			0.0352057i
$904$	−10.6929	+	10.6929i	−0.355641	+	0.355641i
$905$	−46.6000			−1.54904
$906$	−2.51220	+	2.51220i	−0.0834622	+	0.0834622i
$907$	27.9726	+	27.9726i	0.928813	+	0.928813i	0.997629	−	0.0688160i	$-0.0219221\pi$
$907$	27.9726	+	27.9726i	0.928813	+	0.928813i	−0.0688160	+	0.997629i	$0.521922\pi$
$908$	31.6963	+	31.6963i	1.05188	+	1.05188i
$909$		−	35.7467i		−	1.18564i
$910$		−	1.47318i		−	0.0488354i
$911$	−25.1267	−	25.1267i	−0.832484	−	0.832484i	0.155372	−	0.987856i	$-0.450342\pi$
$911$	−25.1267	−	25.1267i	−0.832484	−	0.832484i	−0.987856	+	0.155372i	$0.950342\pi$
$912$	−13.8928	−	13.8928i	−0.460038	−	0.460038i
$913$	−3.88386	+	3.88386i	−0.128537	+	0.128537i
$914$	14.5854			0.482443
$915$	−28.2248	+	28.2248i	−0.933082	+	0.933082i
$916$			20.9700i			0.692867i
$917$	1.69435			0.0559524
$918$	4.70163	+	4.53220i	0.155177	+	0.149585i
$919$	−3.20251			−0.105641			−0.0528205	−	0.998604i	$-0.516821\pi$
$919$	−3.20251			−0.105641			−0.0528205	+	0.998604i	$0.516821\pi$
$920$			2.48671i			0.0819844i
$921$	21.7818	−	21.7818i	0.717735	−	0.717735i
$922$	8.89277			0.292868
$923$	−21.1035	+	21.1035i	−0.694631	+	0.694631i
$924$	−1.49940	−	1.49940i	−0.0493265	−	0.0493265i
$925$	1.01112	+	1.01112i	0.0332453	+	0.0332453i
$926$		−	10.6373i		−	0.349563i
$927$			1.22084i			0.0400978i
$928$	−10.8045	−	10.8045i	−0.354674	−	0.354674i
$929$	−36.6703	−	36.6703i	−1.20311	−	1.20311i	−0.973215	−	0.229898i	$-0.926161\pi$
$929$	−36.6703	−	36.6703i	−1.20311	−	1.20311i	−0.229898	−	0.973215i	$-0.573839\pi$
$930$	−13.3647	+	13.3647i	−0.438245	+	0.438245i
$931$	−16.1320			−0.528705
$932$	18.1819	−	18.1819i	0.595567	−	0.595567i
$933$			23.8780i			0.781731i
$934$	−13.3469			−0.436724
$935$	−0.170687	−	9.30258i	−0.00558206	−	0.304227i
$936$	−31.3172			−1.02364
$937$		−	51.6605i		−	1.68767i	−0.536599	−	0.843837i	$-0.680291\pi$
$937$		−	51.6605i		−	1.68767i	0.536599	−	0.843837i	$-0.319709\pi$
$938$	−0.593545	+	0.593545i	−0.0193799	+	0.0193799i
$939$	−52.5555			−1.71508
$940$	9.14216	−	9.14216i	0.298184	−	0.298184i
$941$	−11.0231	−	11.0231i	−0.359342	−	0.359342i	0.504228	−	0.863571i	$-0.331777\pi$
$941$	−11.0231	−	11.0231i	−0.359342	−	0.359342i	−0.863571	+	0.504228i	$0.831777\pi$
$942$	8.75606	+	8.75606i	0.285288	+	0.285288i
$943$		−	0.255572i		−	0.00832255i
$944$			14.6816i			0.477846i
$945$	−2.23715	−	2.23715i	−0.0727744	−	0.0727744i
$946$	0.309724	+	0.309724i	0.0100700	+	0.0100700i
$947$	−16.0361	+	16.0361i	−0.521103	+	0.521103i	−0.917905	−	0.396801i	$-0.870120\pi$
$947$	−16.0361	+	16.0361i	−0.521103	+	0.521103i	0.396801	+	0.917905i	$0.370120\pi$
$948$	−42.8062			−1.39028
$949$	47.7286	−	47.7286i	1.54934	−	1.54934i
$950$			0.676914i			0.0219620i
$951$	−60.1043			−1.94901
$952$	−1.77512	−	1.71116i	−0.0575321	−	0.0554589i
$953$	−8.00940			−0.259450			−0.129725	−	0.991550i	$-0.541409\pi$
$953$	−8.00940			−0.259450			−0.129725	+	0.991550i	$0.541409\pi$
$954$			2.47621i			0.0801702i
$955$	−2.51823	+	2.51823i	−0.0814879	+	0.0814879i
$956$	−23.4218			−0.757516
$957$	7.45148	−	7.45148i	0.240872	−	0.240872i
$958$	2.72755	+	2.72755i	0.0881231	+	0.0881231i
$959$	−3.54185	−	3.54185i	−0.114372	−	0.114372i
$960$		−	24.7490i		−	0.798770i
$961$		−	38.3732i		−	1.23784i
$962$	−2.59447	−	2.59447i	−0.0836490	−	0.0836490i
$963$	−40.1429	−	40.1429i	−1.29359	−	1.29359i
$964$	−25.9016	+	25.9016i	−0.834235	+	0.834235i
$965$	−25.8761			−0.832981
$966$	−0.234121	+	0.234121i	−0.00753271	+	0.00753271i
$967$		−	35.7709i		−	1.15032i	−0.818043	−	0.575158i	$-0.804941\pi$
$967$		−	35.7709i		−	1.15032i	0.818043	−	0.575158i	$-0.195059\pi$
$968$	15.1322			0.486366
$969$	18.3882	−	19.0756i	0.590713	−	0.612795i
$970$	11.4216			0.366726
$971$			30.0097i			0.963057i	0.876430	+	0.481529i	$0.159918\pi$
$971$			30.0097i			0.963057i	−0.876430	+	0.481529i	$0.840082\pi$
$972$	24.5209	−	24.5209i	0.786508	−	0.786508i
$973$	−5.51959			−0.176950
$974$	5.21613	−	5.21613i	0.167136	−	0.167136i
$975$	−6.30522	−	6.30522i	−0.201929	−	0.201929i
$976$	−15.2795	−	15.2795i	−0.489085	−	0.489085i
$977$			9.86818i			0.315711i	0.987462	+	0.157856i	$0.0504580\pi$
$977$			9.86818i			0.315711i	−0.987462	+	0.157856i	$0.949542\pi$
$978$		−	20.4178i		−	0.652889i
$979$	−4.46316	−	4.46316i	−0.142643	−	0.142643i
$980$	−18.4328	−	18.4328i	−0.588814	−	0.588814i
$981$	−30.4449	+	30.4449i	−0.972030	+	0.972030i
$982$	10.0072			0.319343
$983$	−32.9809	+	32.9809i	−1.05193	+	1.05193i	−0.0533528	+	0.998576i	$0.516991\pi$
$983$	−32.9809	+	32.9809i	−1.05193	+	1.05193i	−0.998576	+	0.0533528i	$0.983009\pi$
$984$		−	1.38070i		−	0.0440151i
$985$	−16.7738			−0.534456
$986$	4.07311	−	4.22538i	0.129714	−	0.134563i
$987$	3.59405			0.114400
$988$			19.7820i			0.629349i
$989$	−0.550792	+	0.550792i	−0.0175142	+	0.0175142i
$990$	−4.02991			−0.128079
$991$	−21.9572	+	21.9572i	−0.697492	+	0.697492i	−0.963869	−	0.266377i	$-0.914173\pi$
$991$	−21.9572	+	21.9572i	−0.697492	+	0.697492i	0.266377	+	0.963869i	$0.414173\pi$
$992$	−25.4016	−	25.4016i	−0.806503	−	0.806503i
$993$	−1.57957	−	1.57957i	−0.0501262	−	0.0501262i
$994$			1.01771i			0.0322799i
$995$			2.78893i			0.0884152i
$996$	−17.8720	−	17.8720i	−0.566297	−	0.566297i
$997$	23.7218	+	23.7218i	0.751278	+	0.751278i	0.974718	−	0.223440i	$-0.0717287\pi$
$997$	23.7218	+	23.7218i	0.751278	+	0.751278i	−0.223440	+	0.974718i	$0.571729\pi$
$998$	−1.64477	+	1.64477i	−0.0520642	+	0.0520642i
$999$	−7.87984			−0.249307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.c.259.17	✓	56
17.13	even	4	inner	731.2.f.c.302.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.c.259.17	✓	56	1.1	even	1	trivial
731.2.f.c.302.12	yes	56	17.13	even	4	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.401786i q^{2} +(1.92935 - 1.92935i) q^{3} +1.83857 q^{4} +(1.46367 - 1.46367i) q^{5} +(0.775185 + 0.775185i) q^{6} +(0.274168 + 0.274168i) q^{7} +1.54228i q^{8} -4.44476i q^{9} +O(q^{10})\)	\(q+0.401786i q^{2} +(1.92935 - 1.92935i) q^{3} +1.83857 q^{4} +(1.46367 - 1.46367i) q^{5} +(0.775185 + 0.775185i) q^{6} +(0.274168 + 0.274168i) q^{7} +1.54228i q^{8} -4.44476i q^{9} +(0.588082 + 0.588082i) q^{10} +(-0.770867 - 0.770867i) q^{11} +(3.54723 - 3.54723i) q^{12} -4.56847 q^{13} +(-0.110157 + 0.110157i) q^{14} -5.64785i q^{15} +3.05747 q^{16} +(0.0756394 + 4.12241i) q^{17} +1.78584 q^{18} -2.35515i q^{19} +(2.69105 - 2.69105i) q^{20} +1.05793 q^{21} +(0.309724 - 0.309724i) q^{22} +(0.550792 + 0.550792i) q^{23} +(2.97560 + 2.97560i) q^{24} +0.715351i q^{25} -1.83555i q^{26} +(-2.78744 - 2.78744i) q^{27} +(0.504076 + 0.504076i) q^{28} +(-2.50509 + 2.50509i) q^{29} +2.26923 q^{30} +(-5.88953 + 5.88953i) q^{31} +4.31302i q^{32} -2.97454 q^{33} +(-1.65633 + 0.0303909i) q^{34} +0.802582 q^{35} -8.17199i q^{36} +(1.41346 - 1.41346i) q^{37} +0.946268 q^{38} +(-8.81417 + 8.81417i) q^{39} +(2.25739 + 2.25739i) q^{40} +(-0.232003 - 0.232003i) q^{41} +0.425062i q^{42} +1.00000i q^{43} +(-1.41729 - 1.41729i) q^{44} +(-6.50565 - 6.50565i) q^{45} +(-0.221301 + 0.221301i) q^{46} +3.39724 q^{47} +(5.89891 - 5.89891i) q^{48} -6.84966i q^{49} -0.287418 q^{50} +(8.09950 + 7.80763i) q^{51} -8.39944 q^{52} +1.38658i q^{53} +(1.11995 - 1.11995i) q^{54} -2.25659 q^{55} +(-0.422845 + 0.422845i) q^{56} +(-4.54391 - 4.54391i) q^{57} +(-1.00651 - 1.00651i) q^{58} +4.80189i q^{59} -10.3839i q^{60} +(-4.99744 - 4.99744i) q^{61} +(-2.36633 - 2.36633i) q^{62} +(1.21861 - 1.21861i) q^{63} +4.38202 q^{64} +(-6.68673 + 6.68673i) q^{65} -1.19513i q^{66} +5.38818 q^{67} +(0.139068 + 7.57933i) q^{68} +2.12534 q^{69} +0.322466i q^{70} +(4.61938 - 4.61938i) q^{71} +6.85508 q^{72} +(-10.4474 + 10.4474i) q^{73} +(0.567907 + 0.567907i) q^{74} +(1.38016 + 1.38016i) q^{75} -4.33011i q^{76} -0.422694i q^{77} +(-3.54141 - 3.54141i) q^{78} +(-6.03374 - 6.03374i) q^{79} +(4.47512 - 4.47512i) q^{80} +2.57840 q^{81} +(0.0932158 - 0.0932158i) q^{82} -5.03830i q^{83} +1.94508 q^{84} +(6.14455 + 5.92313i) q^{85} -0.401786 q^{86} +9.66636i q^{87} +(1.18890 - 1.18890i) q^{88} +5.78979 q^{89} +(2.61388 - 2.61388i) q^{90} +(-1.25253 - 1.25253i) q^{91} +(1.01267 + 1.01267i) q^{92} +22.7259i q^{93} +1.36497i q^{94} +(-3.44716 - 3.44716i) q^{95} +(8.32130 + 8.32130i) q^{96} +(9.71090 - 9.71090i) q^{97} +2.75210 q^{98} +(-3.42632 + 3.42632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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