LMFDB - Embedded newform 672.2.bu.a.643.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(139,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 0, 4]))

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

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

chi := DirichletCharacter("672.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bu (of order $8$, degree $4$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			643.30
Character	$\chi$	$=$	672.643
Dual form			672.2.bu.a.139.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.189323 + 1.40148i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-1.92831 - 0.530666i) q^{4} +(1.43458 - 0.594222i) q^{5} +(-0.711236 + 1.22235i) q^{6} +(-2.33853 + 1.23745i) q^{7} +(1.10879 - 2.60203i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.189323 + 1.40148i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-1.92831 - 0.530666i) q^{4} +(1.43458 - 0.594222i) q^{5} +(-0.711236 + 1.22235i) q^{6} +(-2.33853 + 1.23745i) q^{7} +(1.10879 - 2.60203i) q^{8} +(0.707107 + 0.707107i) q^{9} +(0.561194 + 2.12304i) q^{10} +(2.06518 + 4.98579i) q^{11} +(-1.57845 - 1.22820i) q^{12} +(-1.54071 - 0.638184i) q^{13} +(-1.29152 - 3.51169i) q^{14} +1.55278 q^{15} +(3.43679 + 2.04658i) q^{16} +4.81274 q^{17} +(-1.12487 + 0.857127i) q^{18} +(-0.795475 + 1.92045i) q^{19} +(-3.08165 + 0.384565i) q^{20} +(-2.63407 + 0.248335i) q^{21} +(-7.37849 + 1.95040i) q^{22} +(-4.69441 + 4.69441i) q^{23} +(2.02015 - 1.97965i) q^{24} +(-1.83061 + 1.83061i) q^{25} +(1.18610 - 2.03846i) q^{26} +(0.382683 + 0.923880i) q^{27} +(5.16609 - 1.14521i) q^{28} +(-2.32291 - 0.962180i) q^{29} +(-0.293976 + 2.17619i) q^{30} +6.87596 q^{31} +(-3.51891 + 4.42914i) q^{32} +5.39658i q^{33} +(-0.911162 + 6.74498i) q^{34} +(-2.61949 + 3.16482i) q^{35} +(-0.988286 - 1.73876i) q^{36} +(0.374146 + 0.903268i) q^{37} +(-2.54087 - 1.47843i) q^{38} +(-1.17921 - 1.17921i) q^{39} +(0.0444660 - 4.39169i) q^{40} +(-2.17710 + 2.17710i) q^{41} +(0.150652 - 3.73862i) q^{42} +(3.96118 + 9.56313i) q^{43} +(-1.33653 - 10.7101i) q^{44} +(1.43458 + 0.594222i) q^{45} +(-5.69038 - 7.46790i) q^{46} -6.43312i q^{47} +(2.39199 + 3.20600i) q^{48} +(3.93745 - 5.78761i) q^{49} +(-2.21900 - 2.91215i) q^{50} +(4.44639 + 1.84176i) q^{51} +(2.63231 + 2.04822i) q^{52} +(-1.39129 + 0.576292i) q^{53} +(-1.36725 + 0.361413i) q^{54} +(5.92534 + 5.92534i) q^{55} +(0.626931 + 7.45701i) q^{56} +(-1.46985 + 1.46985i) q^{57} +(1.78826 - 3.07336i) q^{58} +(-3.67112 - 8.86286i) q^{59} +(-2.99424 - 0.824006i) q^{60} +(-0.816610 + 1.97147i) q^{61} +(-1.30178 + 9.63654i) q^{62} +(-2.52860 - 0.778584i) q^{63} +(-5.54115 - 5.77023i) q^{64} -2.58950 q^{65} +(-7.56322 - 1.02170i) q^{66} +(-1.44090 + 3.47865i) q^{67} +(-9.28048 - 2.55396i) q^{68} +(-6.13354 + 2.54060i) q^{69} +(-3.93952 - 4.27035i) q^{70} +(1.36474 + 1.36474i) q^{71} +(2.62395 - 1.05588i) q^{72} +(10.6715 - 10.6715i) q^{73} +(-1.33675 + 0.353350i) q^{74} +(-2.39181 + 0.990722i) q^{75} +(2.55304 - 3.28109i) q^{76} +(-10.9991 - 9.10387i) q^{77} +(1.87590 - 1.42939i) q^{78} +0.692390 q^{79} +(6.14647 + 0.893766i) q^{80} +1.00000i q^{81} +(-2.63900 - 3.46335i) q^{82} +(4.25470 - 10.2718i) q^{83} +(5.21110 + 0.918944i) q^{84} +(6.90426 - 2.85984i) q^{85} +(-14.1525 + 3.74101i) q^{86} +(-1.77788 - 1.77788i) q^{87} +(15.2631 + 0.154539i) q^{88} +(-5.73747 - 5.73747i) q^{89} +(-1.10439 + 1.89804i) q^{90} +(4.39272 - 0.414137i) q^{91} +(11.5435 - 6.56113i) q^{92} +(6.35256 + 2.63131i) q^{93} +(9.01591 + 1.21794i) q^{94} +3.22772i q^{95} +(-4.94601 + 2.74536i) q^{96} +11.5374i q^{97} +(7.36580 + 6.61400i) q^{98} +(-2.06518 + 4.98579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q+O(q^{10}) $ 256 * q	$ 256 q + 32 q^{14} - 8 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{23} + 40 q^{28} - 48 q^{35} + 16 q^{43} - 8 q^{44} - 48 q^{50} - 32 q^{53} + 64 q^{58} + 48 q^{60} - 144 q^{64} + 16 q^{67} + 72 q^{70} - 128 q^{71} + 232 q^{74} - 48 q^{78} + 176 q^{88} + 48 q^{91} - 152 q^{92} - 32 q^{98}+O(q^{100}) $ 256 * q + 32 * q^14 - 8 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^23 + 40 * q^28 - 48 * q^35 + 16 * q^43 - 8 * q^44 - 48 * q^50 - 32 * q^53 + 64 * q^58 + 48 * q^60 - 144 * q^64 + 16 * q^67 + 72 * q^70 - 128 * q^71 + 232 * q^74 - 48 * q^78 + 176 * q^88 + 48 * q^91 - 152 * q^92 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.189323	+	1.40148i	−0.133871	+	0.990999i
$2$	−0.189323	+	1.40148i	−0.133871	+	0.990999i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$4$	−1.92831	−	0.530666i	−0.964157	−	0.265333i
$5$	1.43458	−	0.594222i	0.641564	−	0.265744i	−0.0380937	−	0.999274i	$-0.512129\pi$
$5$	1.43458	−	0.594222i	0.641564	−	0.265744i	0.679657	+	0.733530i	$0.262129\pi$
$6$	−0.711236	+	1.22235i	−0.290361	+	0.499023i
$7$	−2.33853	+	1.23745i	−0.883881	+	0.467711i
$7$	−2.33853	+	1.23745i	−0.883881	+	0.467711i
$8$	1.10879	−	2.60203i	0.392018	−	0.919958i
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$	0.561194	+	2.12304i	0.177465	+	0.671364i
$11$	2.06518	+	4.98579i	0.622676	+	1.50327i	0.848550	+	0.529116i	$0.177476\pi$
$11$	2.06518	+	4.98579i	0.622676	+	1.50327i	−0.225874	+	0.974157i	$0.572524\pi$
$12$	−1.57845	−	1.22820i	−0.455660	−	0.354552i
$13$	−1.54071	−	0.638184i	−0.427317	−	0.177000i	0.158651	−	0.987335i	$-0.449286\pi$
$13$	−1.54071	−	0.638184i	−0.427317	−	0.177000i	−0.585968	+	0.810334i	$0.699286\pi$
$14$	−1.29152	−	3.51169i	−0.345174	−	0.938539i
$15$	1.55278			0.400926
$16$	3.43679	+	2.04658i	0.859197	+	0.511645i
$17$	4.81274			1.16726			0.583631	−	0.812019i	$-0.301632\pi$
$17$	4.81274			1.16726			0.583631	+	0.812019i	$0.301632\pi$
$18$	−1.12487	+	0.857127i	−0.265134	+	0.202027i
$19$	−0.795475	+	1.92045i	−0.182494	+	0.440580i	−0.988479	−	0.151355i	$-0.951636\pi$
$19$	−0.795475	+	1.92045i	−0.182494	+	0.440580i	0.805985	+	0.591936i	$0.201636\pi$
$20$	−3.08165	+	0.384565i	−0.689079	+	0.0859913i
$21$	−2.63407	+	0.248335i	−0.574801	+	0.0541911i
$22$	−7.37849	+	1.95040i	−1.57310	+	0.415826i
$23$	−4.69441	+	4.69441i	−0.978852	+	0.978852i	−0.999781	−	0.0209287i	$-0.993338\pi$
$23$	−4.69441	+	4.69441i	−0.978852	+	0.978852i	0.0209287	+	0.999781i	$0.493338\pi$
$24$	2.02015	−	1.97965i	0.412361	−	0.404094i
$25$	−1.83061	+	1.83061i	−0.366123	+	0.366123i
$26$	1.18610	−	2.03846i	0.232613	−	0.399775i
$27$	0.382683	+	0.923880i	0.0736475	+	0.177801i
$28$	5.16609	−	1.14521i	0.976299	−	0.216424i
$29$	−2.32291	−	0.962180i	−0.431353	−	0.178672i	0.156433	−	0.987689i	$-0.450000\pi$
$29$	−2.32291	−	0.962180i	−0.431353	−	0.178672i	−0.587786	+	0.809016i	$0.700000\pi$
$30$	−0.293976	+	2.17619i	−0.0536725	+	0.397317i
$31$	6.87596			1.23496			0.617479	−	0.786587i	$-0.288154\pi$
$31$	6.87596			1.23496			0.617479	+	0.786587i	$0.288154\pi$
$32$	−3.51891	+	4.42914i	−0.622062	+	0.782968i
$33$			5.39658i			0.939424i
$34$	−0.911162	+	6.74498i	−0.156263	+	1.15675i
$35$	−2.61949	+	3.16482i	−0.442775	+	0.534953i
$36$	−0.988286	−	1.73876i	−0.164714	−	0.289794i
$37$	0.374146	+	0.903268i	0.0615092	+	0.148496i	0.951646	−	0.307197i	$-0.0993912\pi$
$37$	0.374146	+	0.903268i	0.0615092	+	0.148496i	−0.890137	+	0.455694i	$0.849391\pi$
$38$	−2.54087	−	1.47843i	−0.412184	−	0.239833i
$39$	−1.17921	−	1.17921i	−0.188825	−	0.188825i
$40$	0.0444660	−	4.39169i	0.00703069	−	0.694388i
$41$	−2.17710	+	2.17710i	−0.340006	+	0.340006i	−0.856370	−	0.516363i	$-0.827285\pi$
$41$	−2.17710	+	2.17710i	−0.340006	+	0.340006i	0.516363	+	0.856370i	$0.327285\pi$
$42$	0.150652	−	3.73862i	0.0232462	−	0.576882i
$43$	3.96118	+	9.56313i	0.604074	+	1.45836i	0.869353	+	0.494192i	$0.164536\pi$
$43$	3.96118	+	9.56313i	0.604074	+	1.45836i	−0.265279	+	0.964172i	$0.585464\pi$
$44$	−1.33653	−	10.7101i	−0.201490	−	1.61461i
$45$	1.43458	+	0.594222i	0.213855	+	0.0885814i
$46$	−5.69038	−	7.46790i	−0.839001	−	1.10108i
$47$		−	6.43312i		−	0.938366i	−0.883101	−	0.469183i	$-0.844548\pi$
$47$		−	6.43312i		−	0.938366i	0.883101	−	0.469183i	$-0.155452\pi$
$48$	2.39199	+	3.20600i	0.345253	+	0.462746i
$49$	3.93745	−	5.78761i	0.562493	−	0.826802i
$50$	−2.21900	−	2.91215i	−0.313814	−	0.411841i
$51$	4.44639	+	1.84176i	0.622620	+	0.257898i
$52$	2.63231	+	2.04822i	0.365036	+	0.284037i
$53$	−1.39129	+	0.576292i	−0.191109	+	0.0791598i	−0.476185	−	0.879345i	$-0.657981\pi$
$53$	−1.39129	+	0.576292i	−0.191109	+	0.0791598i	0.285077	+	0.958505i	$0.407981\pi$
$54$	−1.36725	+	0.361413i	−0.186060	+	0.0491821i
$55$	5.92534	+	5.92534i	0.798972	+	0.798972i
$56$	0.626931	+	7.45701i	0.0837772	+	0.996485i
$57$	−1.46985	+	1.46985i	−0.194686	+	0.194686i
$58$	1.78826	−	3.07336i	0.234810	−	0.403551i
$59$	−3.67112	−	8.86286i	−0.477939	−	1.15385i	−0.960574	−	0.278024i	$-0.910320\pi$
$59$	−3.67112	−	8.86286i	−0.477939	−	1.15385i	0.482635	−	0.875821i	$-0.339680\pi$
$60$	−2.99424	−	0.824006i	−0.386555	−	0.106379i
$61$	−0.816610	+	1.97147i	−0.104556	+	0.252421i	−0.967496	−	0.252885i	$-0.918620\pi$
$61$	−0.816610	+	1.97147i	−0.104556	+	0.252421i	0.862940	+	0.505306i	$0.168620\pi$
$62$	−1.30178	+	9.63654i	−0.165326	+	1.22384i
$63$	−2.52860	−	0.778584i	−0.318573	−	0.0980923i
$64$	−5.54115	−	5.77023i	−0.692644	−	0.721279i
$65$	−2.58950			−0.321188
$66$	−7.56322	−	1.02170i	−0.930968	−	0.125762i
$67$	−1.44090	+	3.47865i	−0.176034	+	0.424984i	−0.987128	−	0.159932i	$-0.948873\pi$
$67$	−1.44090	+	3.47865i	−0.176034	+	0.424984i	0.811094	+	0.584916i	$0.198873\pi$
$68$	−9.28048	−	2.55396i	−1.12542	−	0.309713i
$69$	−6.13354	+	2.54060i	−0.738392	+	0.305852i
$70$	−3.93952	−	4.27035i	−0.470863	−	0.510404i
$71$	1.36474	+	1.36474i	0.161965	+	0.161965i	0.783437	−	0.621471i	$-0.213465\pi$
$71$	1.36474	+	1.36474i	0.161965	+	0.161965i	−0.621471	+	0.783437i	$0.713465\pi$
$72$	2.62395	−	1.05588i	0.309236	−	0.124437i
$73$	10.6715	−	10.6715i	1.24900	−	1.24900i	0.292843	−	0.956161i	$-0.405399\pi$
$73$	10.6715	−	10.6715i	1.24900	−	1.24900i	0.956161	−	0.292843i	$-0.0946013\pi$
$74$	−1.33675	+	0.353350i	−0.155394	+	0.0410761i
$75$	−2.39181	+	0.990722i	−0.276183	+	0.114399i
$76$	2.55304	−	3.28109i	0.292854	−	0.376367i
$77$	−10.9991	−	9.10387i	−1.25347	−	1.03748i
$78$	1.87590	−	1.42939i	0.212403	−	0.161847i
$79$	0.692390			0.0778999			0.0389500	−	0.999241i	$-0.487599\pi$
$79$	0.692390			0.0778999			0.0389500	+	0.999241i	$0.487599\pi$
$80$	6.14647	+	0.893766i	0.687196	+	0.0999261i
$81$			1.00000i			0.111111i
$82$	−2.63900	−	3.46335i	−0.291428	−	0.382463i
$83$	4.25470	−	10.2718i	0.467014	−	1.12747i	−0.498446	−	0.866921i	$-0.666096\pi$
$83$	4.25470	−	10.2718i	0.467014	−	1.12747i	0.965460	−	0.260551i	$-0.0839041\pi$
$84$	5.21110	+	0.918944i	0.568577	+	0.100265i
$85$	6.90426	−	2.85984i	0.748872	−	0.310193i
$86$	−14.1525	+	3.74101i	−1.52610	+	0.403403i
$87$	−1.77788	−	1.77788i	−0.190608	−	0.190608i
$88$	15.2631	+	0.154539i	1.62705	+	0.0164739i
$89$	−5.73747	−	5.73747i	−0.608171	−	0.608171i	0.334297	−	0.942468i	$-0.391501\pi$
$89$	−5.73747	−	5.73747i	−0.608171	−	0.608171i	−0.942468	+	0.334297i	$0.891501\pi$
$90$	−1.10439	+	1.89804i	−0.116413	+	0.200071i
$91$	4.39272	−	0.414137i	0.460482	−	0.0434133i
$92$	11.5435	−	6.56113i	1.20349	−	0.684045i
$93$	6.35256	+	2.63131i	0.658729	+	0.272855i
$94$	9.01591	+	1.21794i	0.929920	+	0.125620i
$95$			3.22772i			0.331157i
$96$	−4.94601	+	2.74536i	−0.504800	+	0.280197i
$97$			11.5374i			1.17145i	0.810510	+	0.585724i	$0.199190\pi$
$97$			11.5374i			1.17145i	−0.810510	+	0.585724i	$0.800810\pi$
$98$	7.36580	+	6.61400i	0.744058	+	0.668115i
$99$	−2.06518	+	4.98579i	−0.207559	+	0.501091i
$100$	4.50144	−	2.55856i	0.450144	−	0.255856i
$101$	2.48907	−	1.03101i	0.247672	−	0.102589i	−0.255394	−	0.966837i	$-0.582205\pi$
$101$	2.48907	−	1.03101i	0.247672	−	0.102589i	0.503066	+	0.864248i	$0.332205\pi$
$102$	−3.42300	+	5.88286i	−0.338927	+	0.582490i
$103$	5.65864	−	5.65864i	0.557562	−	0.557562i	−0.371050	−	0.928613i	$-0.621002\pi$
$103$	5.65864	−	5.65864i	0.557562	−	0.557562i	0.928613	+	0.371050i	$0.121002\pi$
$104$	−3.36891	+	3.30137i	−0.330349	+	0.323726i
$105$	−3.63122	+	1.92148i	−0.354371	+	0.187517i
$106$	−0.544261	−	2.05898i	−0.0528633	−	0.199986i
$107$	−2.88378	−	6.96207i	−0.278786	−	0.673049i	0.721017	−	0.692918i	$-0.243675\pi$
$107$	−2.88378	−	6.96207i	−0.278786	−	0.673049i	−0.999803	+	0.0198689i	$0.993675\pi$
$108$	−0.247662	−	1.98461i	−0.0238313	−	0.190969i
$109$	7.19317	−	17.3659i	0.688981	−	1.66335i	−0.0578437	−	0.998326i	$-0.518423\pi$
$109$	7.19317	−	17.3659i	0.688981	−	1.66335i	0.746825	−	0.665021i	$-0.231577\pi$
$110$	−9.42607	+	7.18246i	−0.898740	+	0.684821i
$111$			0.977690i			0.0927983i
$112$	−10.5696	−	0.533148i	−0.998730	−	0.0503778i
$113$			1.65834i			0.156004i	0.996953	+	0.0780018i	$0.0248540\pi$
$113$			1.65834i			0.156004i	−0.996953	+	0.0780018i	$0.975146\pi$
$114$	−1.78169	−	2.33824i	−0.166871	−	0.218996i
$115$	−3.94498	+	9.52403i	−0.367872	+	0.888120i
$116$	3.96870	+	3.08807i	0.368485	+	0.286720i
$117$	−0.638184	−	1.54071i	−0.0590001	−	0.142439i
$118$	13.1162	−	3.46707i	1.20744	−	0.319169i
$119$	−11.2547	+	5.95551i	−1.03172	+	0.545941i
$120$	1.72171	−	4.04038i	0.157170	−	0.368835i
$121$	−12.8150	+	12.8150i	−1.16500	+	1.16500i
$122$	−2.60838	−	1.51771i	−0.236152	−	0.137407i
$123$	−2.84452	+	1.17824i	−0.256482	+	0.106238i
$124$	−13.2590	−	3.64883i	−1.19069	−	0.327675i
$125$	−4.50948	+	10.8869i	−0.403340	+	0.973750i
$126$	1.56989	−	3.39639i	0.139857	−	0.302574i
$127$			3.96803i			0.352106i	0.984381	+	0.176053i	$0.0563330\pi$
$127$			3.96803i			0.352106i	−0.984381	+	0.176053i	$0.943667\pi$
$128$	9.13596	−	6.67340i	0.807512	−	0.589851i
$129$			10.3511i			0.911360i
$130$	0.490251	−	3.62914i	0.0429979	−	0.318297i
$131$	11.2520	+	4.66074i	0.983094	+	0.407211i	0.815571	−	0.578657i	$-0.196423\pi$
$131$	11.2520	+	4.66074i	0.983094	+	0.407211i	0.167523	+	0.985868i	$0.446423\pi$
$132$	2.86378	−	10.4063i	0.249260	−	0.905752i
$133$	−0.516208	−	5.47538i	−0.0447609	−	0.474776i
$134$	−4.60247	−	2.67799i	−0.397593	−	0.231343i
$135$	1.09798	+	1.09798i	0.0944991	+	0.0944991i
$136$	5.33634	−	12.5229i	0.457587	−	1.07383i
$137$	0.0844680	+	0.0844680i	0.00721658	+	0.00721658i	0.710706	−	0.703489i	$-0.248376\pi$
$137$	0.0844680	+	0.0844680i	0.00721658	+	0.00721658i	−0.703489	+	0.710706i	$0.748376\pi$
$138$	−2.39939	−	9.07705i	−0.204249	−	0.772690i
$139$	5.49746	−	2.27712i	0.466288	−	0.193143i	−0.137154	−	0.990550i	$-0.543795\pi$
$139$	5.49746	−	2.27712i	0.466288	−	0.193143i	0.603442	+	0.797407i	$0.293795\pi$
$140$	6.73066	−	4.71270i	0.568845	−	0.398296i
$141$	2.46185	−	5.94342i	0.207325	−	0.500527i
$142$	−2.17104	+	1.65429i	−0.182190	+	0.138825i
$143$		−	8.99963i		−	0.752587i
$144$	0.983025	+	3.87733i	0.0819188	+	0.323111i
$145$	−3.90415			−0.324222
$146$	12.9356	+	16.9763i	1.07055	+	1.40497i
$147$	5.85255	−	3.84026i	0.482711	−	0.316739i
$148$	−0.242137	−	1.94033i	−0.0199036	−	0.159494i
$149$	18.4534	−	7.64365i	1.51176	−	0.626192i	0.535841	−	0.844319i	$-0.319995\pi$
$149$	18.4534	−	7.64365i	1.51176	−	0.626192i	0.975920	+	0.218127i	$0.0699946\pi$
$150$	−0.935655	−	3.53965i	−0.0763959	−	0.289012i
$151$	7.43698	−	7.43698i	0.605213	−	0.605213i	−0.336479	−	0.941691i	$-0.609236\pi$
$151$	7.43698	−	7.43698i	0.605213	−	0.605213i	0.941691	+	0.336479i	$0.109236\pi$
$152$	4.11505	+	4.19923i	0.333774	+	0.340602i
$153$	3.40312	+	3.40312i	0.275126	+	0.275126i
$154$	14.8413	−	13.6915i	1.19595	−	1.10330i
$155$	9.86411	−	4.08585i	0.792304	−	0.328183i
$156$	1.64812	+	2.89965i	0.131955	+	0.232158i
$157$	1.48251	−	3.57910i	0.118317	−	0.285643i	−0.853615	−	0.520905i	$-0.825595\pi$
$157$	1.48251	−	3.57910i	0.118317	−	0.285643i	0.971932	+	0.235261i	$0.0755946\pi$
$158$	−0.131085	+	0.970373i	−0.0104286	+	0.0771987i
$159$	−1.50592			−0.119428
$160$	−2.41627	+	8.44497i	−0.191023	+	0.667633i
$161$	5.16894	−	16.7871i	0.407369	−	1.32301i
$162$	−1.40148	−	0.189323i	−0.110111	−	0.0148746i
$163$	−6.52844	+	15.7610i	−0.511347	+	1.23450i	0.431753	+	0.901992i	$0.357895\pi$
$163$	−6.52844	+	15.7610i	−0.511347	+	1.23450i	−0.943100	+	0.332509i	$0.892105\pi$
$164$	5.35345	−	3.04282i	0.418034	−	0.237604i
$165$	3.20677	+	7.74183i	0.249647	+	0.602700i
$166$	13.5902	+	7.90757i	1.05480	+	0.613746i
$167$	−11.5163	+	11.5163i	−0.891155	+	0.891155i	−0.994632	−	0.103477i	$-0.967003\pi$
$167$	−11.5163	+	11.5163i	−0.891155	+	0.891155i	0.103477	+	0.994632i	$0.467003\pi$
$168$	−2.27446	+	7.12929i	−0.175479	+	0.550037i
$169$	−7.22587	−	7.22587i	−0.555836	−	0.555836i
$170$	2.70088	+	10.2176i	0.207148	+	0.783658i
$171$	−1.92045	+	0.795475i	−0.146860	+	0.0608315i
$172$	−2.56357	−	20.5428i	−0.195470	−	1.56637i
$173$	2.54083	+	1.05244i	0.193175	+	0.0800159i	0.477174	−	0.878809i	$-0.341661\pi$
$173$	2.54083	+	1.05244i	0.193175	+	0.0800159i	−0.283999	+	0.958825i	$0.591661\pi$
$174$	2.82826	−	2.15507i	0.214410	−	0.163376i
$175$	2.01566	−	6.54624i	0.152370	−	0.494849i
$176$	−3.10623	+	21.3617i	−0.234141	+	1.61020i
$177$		−	9.59309i		−	0.721061i
$178$	9.12721	−	6.95474i	0.684114	−	0.521280i
$179$	23.0586	+	9.55119i	1.72348	+	0.713889i	0.999716	+	0.0238431i	$0.00759021\pi$
$179$	23.0586	+	9.55119i	1.72348	+	0.713889i	0.723765	+	0.690046i	$0.242410\pi$
$180$	−2.45099	−	1.90713i	−0.182686	−	0.142149i
$181$	−6.09255	−	14.7087i	−0.452855	−	1.09329i	−0.971232	−	0.238137i	$-0.923463\pi$
$181$	−6.09255	−	14.7087i	−0.452855	−	1.09329i	0.518376	−	0.855153i	$-0.326537\pi$
$182$	−0.251236	+	6.23473i	−0.0186229	+	0.462149i
$183$	−1.50890	+	1.50890i	−0.111541	+	0.111541i
$184$	7.00988	+	17.4201i	0.516775	+	1.28423i
$185$	1.07348	+	1.07348i	0.0789241	+	0.0789241i
$186$	−4.89043	+	8.40484i	−0.358584	+	0.616272i
$187$	9.93919	+	23.9953i	0.726826	+	1.75471i
$188$	−3.41383	+	12.4051i	−0.248979	+	0.904732i
$189$	−2.03817	−	1.68697i	−0.148255	−	0.122709i
$190$	−4.52360	−	0.611081i	−0.328176	−	0.0443325i
$191$			0.466374i			0.0337457i	0.999858	+	0.0168728i	$0.00537104\pi$
$191$			0.466374i			0.0337457i	−0.999858	+	0.0168728i	$0.994629\pi$
$192$	−2.91119	−	7.45151i	−0.210097	−	0.537766i
$193$	10.7829			0.776169			0.388085	−	0.921624i	$-0.373137\pi$
$193$	10.7829			0.776169			0.388085	+	0.921624i	$0.373137\pi$
$194$	−16.1695	−	2.18430i	−1.16090	−	0.156824i
$195$	−2.39238	−	0.990958i	−0.171322	−	0.0709640i
$196$	−10.6639	+	9.07087i	−0.761709	+	0.647919i
$197$	−4.52695	−	10.9290i	−0.322532	−	0.778661i	−0.999106	−	0.0422861i	$-0.986536\pi$
$197$	−4.52695	−	10.9290i	−0.322532	−	0.778661i	0.676573	−	0.736375i	$-0.263464\pi$
$198$	−6.59652	−	3.83824i	−0.468794	−	0.272772i
$199$	−5.28090	+	5.28090i	−0.374353	+	0.374353i	−0.869060	−	0.494707i	$-0.835275\pi$
$199$	−5.28090	+	5.28090i	−0.374353	+	0.374353i	0.494707	+	0.869060i	$0.335275\pi$
$200$	2.73355	+	6.79309i	0.193291	+	0.480344i
$201$	−2.66244	+	2.66244i	−0.187794	+	0.187794i
$202$	0.973703	+	3.68359i	0.0685095	+	0.259176i
$203$	6.62284	−	0.624388i	0.464832	−	0.0438235i
$204$	−7.59669	−	5.91103i	−0.531874	−	0.413855i
$205$	−1.82954	+	4.41691i	−0.127781	+	0.308490i
$206$	6.85918	+	9.00180i	0.477902	+	0.627185i
$207$	−6.63890			−0.461435
$208$	−3.98901	−	5.34649i	−0.276588	−	0.370713i
$209$	−11.2177			−0.775947
$210$	−2.00545	−	5.45287i	−0.138389	−	0.376284i
$211$	24.5780	+	10.1805i	1.69202	+	0.700857i	0.999783	−	0.0208136i	$-0.00662565\pi$
$211$	24.5780	+	10.1805i	1.69202	+	0.700857i	0.692236	+	0.721671i	$0.256626\pi$
$212$	2.98867	−	0.372961i	0.205262	−	0.0256151i
$213$	0.738594	+	1.78312i	0.0506076	+	0.122178i
$214$	10.3032	−	2.72350i	0.704312	−	0.186174i
$215$	11.3653	+	11.3653i	0.775104	+	0.775104i
$216$	2.82828	+	0.0286364i	0.192440	+	0.00194846i
$217$	−16.0796	+	8.50863i	−1.09156	+	0.577603i
$218$	22.9761	+	13.3689i	1.55614	+	0.905454i
$219$	13.9430	−	5.77537i	0.942179	−	0.390263i
$220$	−8.28153	−	14.5703i	−0.558341	−	0.982328i
$221$	−7.41505	−	3.07141i	−0.498790	−	0.206606i
$222$	−1.37022	−	0.185099i	−0.0919629	−	0.0124230i
$223$	−25.7254			−1.72270			−0.861349	−	0.508014i	$-0.830380\pi$
$223$	−25.7254			−1.72270			−0.861349	+	0.508014i	$0.830380\pi$
$224$	2.74826	−	14.7121i	0.183626	−	0.982996i
$225$	−2.58888			−0.172592
$226$	−2.32414	−	0.313962i	−0.154599	−	0.0208844i
$227$	18.0273	+	7.46717i	1.19652	+	0.495613i	0.889872	−	0.456211i	$-0.150794\pi$
$227$	18.0273	+	7.46717i	1.19652	+	0.495613i	0.306644	+	0.951824i	$0.400794\pi$
$228$	3.61432	−	2.05433i	0.239364	−	0.136051i
$229$	13.1663	−	5.45366i	0.870053	−	0.360388i	0.0974223	−	0.995243i	$-0.468940\pi$
$229$	13.1663	−	5.45366i	0.870053	−	0.360388i	0.772631	+	0.634855i	$0.218940\pi$
$230$	−12.6009	−	7.33195i	−0.830879	−	0.483454i
$231$	−6.67798	−	12.6201i	−0.439379	−	0.830340i
$232$	−5.07925	+	4.97743i	−0.333469	+	0.326784i
$233$	−18.7573	−	18.7573i	−1.22883	−	1.22883i	−0.964406	−	0.264424i	$-0.914818\pi$
$233$	−18.7573	−	18.7573i	−1.22883	−	1.22883i	−0.264424	−	0.964406i	$-0.585182\pi$
$234$	2.28011	−	0.602712i	0.149055	−	0.0394005i
$235$	−3.82270	−	9.22882i	−0.249366	−	0.602022i
$236$	2.37585	+	19.0385i	0.154655	+	1.23930i
$237$	0.639685	+	0.264966i	0.0415520	+	0.0172114i
$238$	−6.21577	−	16.9009i	−0.402909	−	1.09552i
$239$	2.45787			0.158986			0.0794932	−	0.996835i	$-0.474670\pi$
$239$	2.45787			0.158986			0.0794932	+	0.996835i	$0.474670\pi$
$240$	5.33657	+	3.17788i	0.344474	+	0.205132i
$241$	−2.11219			−0.136058			−0.0680291	−	0.997683i	$-0.521671\pi$
$241$	−2.11219			−0.136058			−0.0680291	+	0.997683i	$0.521671\pi$
$242$	−15.5338	−	20.3861i	−0.998550	−	1.31047i
$243$	−0.382683	+	0.923880i	−0.0245492	+	0.0592669i
$244$	2.62087	−	3.36827i	0.167784	−	0.215631i
$245$	2.20946	−	10.6425i	0.141157	−	0.679925i
$246$	−1.11275	−	4.20962i	−0.0709463	−	0.268395i
$247$	2.45120	−	2.45120i	0.155966	−	0.155966i
$248$	7.62401	−	17.8915i	0.484125	−	1.13611i
$249$	7.86166	−	7.86166i	0.498212	−	0.498212i
$250$	−14.4040	−	8.38110i	−0.910989	−	0.530067i
$251$	−9.84068	−	23.7575i	−0.621138	−	1.49956i	−0.850368	−	0.526188i	$-0.823621\pi$
$251$	−9.84068	−	23.7575i	−0.621138	−	1.49956i	0.229230	−	0.973372i	$-0.426379\pi$
$252$	4.46276	+	2.84319i	0.281128	+	0.179104i
$253$	−33.1002	−	13.7105i	−2.08099	−	0.861974i
$254$	−5.56114	−	0.751240i	−0.348937	−	0.0471370i
$255$	7.47312			0.467985
$256$	7.62302	+	14.0673i	0.476439	+	0.879208i
$257$		−	12.9375i		−	0.807019i	−0.914975	−	0.403510i	$-0.867790\pi$
$257$		−	12.9375i		−	0.807019i	0.914975	−	0.403510i	$-0.132210\pi$
$258$	−14.5068	−	1.95969i	−0.903156	−	0.122005i
$259$	−1.99270	−	1.64933i	−0.123820	−	0.102485i
$260$	4.99336	+	1.37416i	0.309675	+	0.0852217i
$261$	−0.962180	−	2.32291i	−0.0595575	−	0.143784i
$262$	−8.66222	+	14.8872i	−0.535154	+	0.919731i
$263$	−22.4894	−	22.4894i	−1.38676	−	1.38676i	−0.832037	−	0.554720i	$-0.812825\pi$
$263$	−22.4894	−	22.4894i	−1.38676	−	1.38676i	−0.554720	−	0.832037i	$-0.687175\pi$
$264$	14.0421	+	5.98369i	0.864230	+	0.368271i
$265$	−1.65347	+	1.65347i	−0.101572	+	0.101572i
$266$	7.77138	+	0.313158i	0.476494	+	0.0192009i
$267$	−3.10510	−	7.49637i	−0.190029	−	0.458771i
$268$	4.62451	−	5.94328i	0.282487	−	0.363044i
$269$	17.6655	+	7.31727i	1.07708	+	0.446142i	0.849485	−	0.527613i	$-0.176913\pi$
$269$	17.6655	+	7.31727i	1.07708	+	0.446142i	0.227597	+	0.973755i	$0.426913\pi$
$270$	−1.74667	+	1.33093i	−0.106299	+	0.0809977i
$271$			30.9631i			1.88087i	0.339971	+	0.940436i	$0.389583\pi$
$271$			30.9631i			1.88087i	−0.339971	+	0.940436i	$0.610417\pi$
$272$	16.5404	+	9.84966i	1.00291	+	0.597224i
$273$	4.21683	+	1.29841i	0.255214	+	0.0785833i
$274$	−0.134372	+	0.102389i	−0.00811772	+	0.00618553i
$275$	−12.9076	−	5.34651i	−0.778359	−	0.322407i
$276$	13.1756	−	1.64421i	0.793078	−	0.0989696i
$277$	14.0545	−	5.82157i	0.844454	−	0.349784i	0.0818455	−	0.996645i	$-0.473919\pi$
$277$	14.0545	−	5.82157i	0.844454	−	0.349784i	0.762608	+	0.646861i	$0.223919\pi$
$278$	2.15056	+	8.13571i	0.128982	+	0.487948i
$279$	4.86204	+	4.86204i	0.291082	+	0.291082i
$280$	5.33050	+	10.3251i	0.318558	+	0.617045i
$281$	−18.4743	+	18.4743i	−1.10208	+	1.10208i	−0.107925	+	0.994159i	$0.534421\pi$
$281$	−18.4743	+	18.4743i	−1.10208	+	1.10208i	−0.994159	+	0.107925i	$0.965579\pi$
$282$	7.86353	+	4.57546i	0.468266	+	0.272465i
$283$	−7.84749	−	18.9455i	−0.466485	−	1.12619i	−0.965687	−	0.259709i	$-0.916373\pi$
$283$	−7.84749	−	18.9455i	−0.466485	−	1.12619i	0.499202	−	0.866486i	$-0.333627\pi$
$284$	−1.90743	−	3.35588i	−0.113185	−	0.199135i
$285$	−1.23520	+	2.98203i	−0.0731667	+	0.176640i
$286$	12.6128	+	1.70384i	0.745813	+	0.100750i
$287$	2.39717	−	7.78527i	0.141501	−	0.459550i
$288$	−5.62012	+	0.643627i	−0.331169	+	0.0379261i
$289$	6.16249			0.362499
$290$	0.739144	−	5.47160i	0.0434040	−	0.321303i
$291$	−4.41518	+	10.6592i	−0.258823	+	0.624853i
$292$	−26.2410	+	14.9150i	−1.53564	+	0.872834i
$293$	−2.42790	+	1.00567i	−0.141839	+	0.0587518i	−0.452474	−	0.891778i	$-0.649458\pi$
$293$	−2.42790	+	1.00567i	−0.141839	+	0.0587518i	0.310635	+	0.950529i	$0.399458\pi$
$294$	4.27404	+	8.92931i	0.249267	+	0.520768i
$295$	−10.5330	−	10.5330i	−0.613256	−	0.613256i
$296$	2.76518	+	0.0279975i	0.160723	+	0.00162732i
$297$	−3.81596	+	3.81596i	−0.221424	+	0.221424i
$298$	7.21880	+	27.3093i	0.418174	+	1.58198i
$299$	10.2286	−	4.23684i	0.591537	−	0.245023i
$300$	5.13791	−	0.641169i	0.296637	−	0.0370179i
$301$	−21.0972	−	17.4619i	−1.21602	−	1.00649i
$302$	9.01481	+	11.8308i	0.518744	+	0.680786i
$303$	2.69415			0.154775
$304$	−6.66422	+	4.97216i	−0.382219	+	0.285173i
$305$			3.31348i			0.189729i
$306$	−5.41371	+	4.12513i	−0.309481	+	0.235818i
$307$	−9.47909	+	22.8846i	−0.541001	+	1.30609i	0.383017	+	0.923741i	$0.374885\pi$
$307$	−9.47909	+	22.8846i	−0.541001	+	1.30609i	−0.924018	+	0.382350i	$0.875115\pi$
$308$	16.3787	+	23.3920i	0.933262	+	1.33288i
$309$	7.39337	−	3.06243i	0.420594	−	0.174216i
$310$	3.85875	+	14.5979i	0.219162	+	0.829107i
$311$	−16.7183	−	16.7183i	−0.948006	−	0.948006i	0.0507076	−	0.998714i	$-0.483852\pi$
$311$	−16.7183	−	16.7183i	−0.948006	−	0.948006i	−0.998714	+	0.0507076i	$0.983852\pi$
$312$	−4.37584	+	1.76084i	−0.247733	+	0.0996881i
$313$	9.89789	+	9.89789i	0.559462	+	0.559462i	0.929154	−	0.369692i	$-0.120537\pi$
$313$	9.89789	+	9.89789i	0.559462	+	0.559462i	−0.369692	+	0.929154i	$0.620537\pi$
$314$	4.73538	+	2.75532i	0.267233	+	0.155492i
$315$	−4.09013	+	0.385609i	−0.230453	+	0.0217266i
$316$	−1.33514	−	0.367428i	−0.0751078	−	0.0206694i
$317$	−13.3436	−	5.52708i	−0.749449	−	0.310432i	−0.0249322	−	0.999689i	$-0.507937\pi$
$317$	−13.3436	−	5.52708i	−0.749449	−	0.310432i	−0.724517	+	0.689257i	$0.757937\pi$
$318$	0.285106	−	2.11053i	0.0159879	−	0.118353i
$319$		−	13.5686i		−	0.759697i
$320$	−11.3780	−	4.98518i	−0.636051	−	0.278680i
$321$		−	7.53569i		−	0.420601i
$322$	22.5483	+	10.4224i	1.25657	+	0.580816i
$323$	−3.82841	+	9.24261i	−0.213019	+	0.514273i
$324$	0.530666	−	1.92831i	0.0294814	−	0.107129i
$325$	3.98872	−	1.65218i	0.221254	−	0.0916466i
$326$	−20.8529	−	12.1334i	−1.15493	−	0.672009i
$327$	13.2912	−	13.2912i	0.735008	−	0.735008i
$328$	3.25093	+	8.07885i	0.179503	+	0.446080i
$329$	7.96064	+	15.0440i	0.438884	+	0.829405i
$330$	−11.4572	+	3.02853i	−0.630696	+	0.166715i
$331$	−4.23767	−	10.2307i	−0.232924	−	0.562328i	0.763595	−	0.645695i	$-0.223432\pi$
$331$	−4.23767	−	10.2307i	−0.232924	−	0.562328i	−0.996519	+	0.0833678i	$0.973432\pi$
$332$	−13.6553	+	17.5493i	−0.749430	+	0.963145i
$333$	−0.374146	+	0.903268i	−0.0205031	+	0.0494988i
$334$	−13.9596	−	18.3202i	−0.763834	−	1.00243i
$335$			5.84661i			0.319435i
$336$	−9.56098	−	4.53736i	−0.521594	−	0.247533i
$337$		−	4.17986i		−	0.227692i	−0.993498	−	0.113846i	$-0.963683\pi$
$337$		−	4.17986i		−	0.227692i	0.993498	−	0.113846i	$-0.0363170\pi$
$338$	11.4950	−	8.75892i	0.625244	−	0.476422i
$339$	−0.634619	+	1.53211i	−0.0344678	+	0.0832126i
$340$	−14.8312	+	1.85081i	−0.804335	+	0.100374i
$341$	14.2001	+	34.2821i	0.768979	+	1.85648i
$342$	−0.751261	−	2.84208i	−0.0406235	−	0.153682i
$343$	−2.04598	+	18.4069i	−0.110473	+	0.993879i
$344$	29.2757	+	0.296417i	1.57844	+	0.0159817i
$345$	−7.28938	+	7.28938i	−0.392447	+	0.392447i
$346$	−1.95602	+	3.36167i	−0.105156	+	0.180725i
$347$	−24.2514	+	10.0453i	−1.30188	+	0.539257i	−0.922505	−	0.385985i	$-0.873862\pi$
$347$	−24.2514	+	10.0453i	−1.30188	+	0.539257i	−0.379377	+	0.925242i	$0.623862\pi$
$348$	2.48485	+	4.37176i	0.133202	+	0.234351i
$349$	5.25458	−	12.6857i	0.281271	−	0.679049i	−0.718594	−	0.695429i	$-0.755214\pi$
$349$	5.25458	−	12.6857i	0.281271	−	0.679049i	0.999866	+	0.0163802i	$0.00521423\pi$
$350$	8.79284	+	4.06427i	0.469997	+	0.217244i
$351$		−	1.66765i		−	0.0890128i
$352$	−29.3499	−	8.39758i	−1.56436	−	0.447592i
$353$			15.8057i			0.841255i	0.907233	+	0.420628i	$0.138190\pi$
$353$			15.8057i			0.841255i	−0.907233	+	0.420628i	$0.861810\pi$
$354$	13.4446	+	1.81619i	0.714570	+	0.0965294i
$355$	2.76880	+	1.14687i	0.146952	+	0.0608697i
$356$	8.01897	+	14.1083i	0.425005	+	0.747740i
$357$	−12.6771	+	1.19517i	−0.670944	+	0.0632552i
$358$	−17.7514	+	30.5080i	−0.938188	+	1.61240i
$359$	−20.2342	−	20.2342i	−1.06792	−	1.06792i	−0.997519	−	0.0703990i	$-0.977573\pi$
$359$	−20.2342	−	20.2342i	−1.06792	−	1.06792i	−0.0703990	−	0.997519i	$-0.522427\pi$
$360$	3.13684	−	3.07395i	0.165326	−	0.162012i
$361$	10.3797	+	10.3797i	0.546300	+	0.546300i
$362$	21.7675	−	5.75391i	1.14407	−	0.302419i
$363$	−16.7435	+	6.93540i	−0.878808	+	0.364014i
$364$	−8.69031	−	1.53248i	−0.455496	−	0.0803238i
$365$	8.96787	−	21.6503i	0.469400	−	1.13323i
$366$	−1.82903	−	2.40037i	−0.0956048	−	0.125469i
$367$		−	18.5335i		−	0.967443i	−0.875222	−	0.483721i	$-0.839285\pi$
$367$		−	18.5335i		−	0.967443i	0.875222	−	0.483721i	$-0.160715\pi$
$368$	−25.7412	+	6.52620i	−1.34185	+	0.340202i
$369$	−3.07889			−0.160280
$370$	−1.70771	+	1.30124i	−0.0887794	+	0.0676480i
$371$	2.54045	−	3.06933i	0.131894	−	0.159352i
$372$	−10.8534	−	8.44508i	−0.562721	−	0.437857i
$373$	−5.22582	+	2.16461i	−0.270583	+	0.112079i	−0.513849	−	0.857880i	$-0.671781\pi$
$373$	−5.22582	+	2.16461i	−0.270583	+	0.112079i	0.243267	+	0.969959i	$0.421781\pi$
$374$	−35.5108	+	9.38675i	−1.83622	+	0.485377i
$375$	−8.33244	+	8.33244i	−0.430285	+	0.430285i
$376$	−16.7392	−	7.13300i	−0.863257	−	0.367856i
$377$	2.96489	+	2.96489i	0.152699	+	0.152699i
$378$	2.75013	−	2.53708i	0.141452	−	0.130493i
$379$	20.0699	−	8.31324i	1.03092	−	0.427022i	0.197877	−	0.980227i	$-0.436595\pi$
$379$	20.0699	−	8.31324i	1.03092	−	0.427022i	0.833045	+	0.553205i	$0.186595\pi$
$380$	1.71284	−	6.22406i	0.0878669	−	0.319288i
$381$	−1.51850	+	3.66599i	−0.0777952	+	0.187814i
$382$	−0.653616	−	0.0882953i	−0.0334419	−	0.00451758i
$383$	−12.6077			−0.644224			−0.322112	−	0.946702i	$-0.604393\pi$
$383$	−12.6077			−0.644224			−0.322112	+	0.946702i	$0.604393\pi$
$384$	10.9943	−	2.66924i	0.561052	−	0.136214i
$385$	−21.1889	−	6.52429i	−1.07988	−	0.332509i
$386$	−2.04145	+	15.1120i	−0.103907	+	0.769183i
$387$	−3.96118	+	9.56313i	−0.201358	+	0.486121i
$388$	6.12252	−	22.2478i	0.310824	−	1.12946i
$389$	6.08470	+	14.6898i	0.308507	+	0.744801i	0.999754	+	0.0221825i	$0.00706150\pi$
$389$	6.08470	+	14.6898i	0.308507	+	0.744801i	−0.691247	+	0.722618i	$0.742938\pi$
$390$	1.84174	−	3.16528i	0.0932604	−	0.160280i
$391$	−22.5930	+	22.5930i	−1.14258	+	1.14258i
$392$	−10.6937	−	16.6626i	−0.540116	−	0.841591i
$393$	8.61193	+	8.61193i	0.434414	+	0.434414i
$394$	16.1739	−	4.27534i	0.814830	−	0.215388i
$395$	0.993288	−	0.411434i	0.0499778	−	0.0207015i
$396$	6.62811	−	8.51825i	0.333075	−	0.428058i
$397$	−24.2925	−	10.0623i	−1.21920	−	0.505011i	−0.322048	−	0.946723i	$-0.604371\pi$
$397$	−24.2925	−	10.0623i	−1.21920	−	0.505011i	−0.897157	+	0.441712i	$0.854371\pi$
$398$	−6.40130	−	8.40089i	−0.320868	−	0.421098i
$399$	1.61842	−	5.25613i	0.0810225	−	0.263136i
$400$	−10.0379	+	2.54493i	−0.501897	+	0.127247i
$401$			3.08227i			0.153921i	0.997034	+	0.0769607i	$0.0245216\pi$
$401$			3.08227i			0.153921i	−0.997034	+	0.0769607i	$0.975478\pi$
$402$	−3.22731	−	4.23543i	−0.160963	−	0.211244i
$403$	−10.5939	−	4.38812i	−0.527718	−	0.218588i
$404$	−5.34683	+	0.667241i	−0.266015	+	0.0331965i
$405$	0.594222	+	1.43458i	0.0295271	+	0.0712848i
$406$	−0.378785	+	9.40001i	−0.0187988	+	0.466515i
$407$	−3.73083	+	3.73083i	−0.184930	+	0.184930i
$408$	9.72244	−	9.52754i	0.481333	−	0.471683i
$409$	16.0488	+	16.0488i	0.793563	+	0.793563i	0.982072	−	0.188508i	$-0.0603653\pi$
$409$	16.0488	+	16.0488i	0.793563	+	0.793563i	−0.188508	+	0.982072i	$0.560365\pi$
$410$	−5.84385	−	3.40030i	−0.288607	−	0.167929i
$411$	0.0457137	+	0.110363i	0.00225489	+	0.00544379i
$412$	−13.9145	+	7.90879i	−0.685517	+	0.389638i
$413$	19.5523	+	16.1833i	0.962107	+	0.796326i
$414$	1.25690	−	9.30431i	0.0617730	−	0.457282i
$415$		−	17.2639i		−	0.847451i
$416$	8.24823	−	4.57831i	0.404403	−	0.224470i
$417$	5.95041			0.291393
$418$	2.12377	−	15.7215i	0.103877	−	0.768963i
$419$	−19.7907	−	8.19758i	−0.966840	−	0.400478i	−0.157305	−	0.987550i	$-0.550281\pi$
$419$	−19.7907	−	8.19758i	−0.966840	−	0.400478i	−0.809535	+	0.587072i	$0.800281\pi$
$420$	8.02179	−	1.77825i	0.391423	−	0.0867699i
$421$	10.6938	+	25.8171i	0.521183	+	1.25825i	0.937169	+	0.348876i	$0.113436\pi$
$421$	10.6938	+	25.8171i	0.521183	+	1.25825i	−0.415986	+	0.909371i	$0.636564\pi$
$422$	−18.9210	+	32.5183i	−0.921062	+	1.58296i
$423$	4.54890	−	4.54890i	0.221175	−	0.221175i
$424$	−0.0431242	+	4.25918i	−0.00209430	+	0.206844i
$425$	−8.81028	+	8.81028i	−0.427361	+	0.427361i
$426$	−2.63885	+	0.697542i	−0.127853	+	0.0337960i
$427$	−0.529923	−	5.62086i	−0.0256448	−	0.272012i
$428$	1.86631	+	14.9554i	0.0902114	+	0.722896i
$429$	3.44401	−	8.31458i	0.166278	−	0.401432i
$430$	−18.0799	+	13.7765i	−0.871891	+	0.664362i
$431$	25.9613			1.25051			0.625255	−	0.780421i	$-0.284995\pi$
$431$	25.9613			1.25051			0.625255	+	0.780421i	$0.284995\pi$
$432$	−0.575592	+	3.95837i	−0.0276932	+	0.190447i
$433$	−17.1787			−0.825554			−0.412777	−	0.910832i	$-0.635441\pi$
$433$	−17.1787			−0.825554			−0.412777	+	0.910832i	$0.635441\pi$
$434$	−8.88047	−	24.1462i	−0.426276	−	1.15906i
$435$	−3.60696	−	1.49405i	−0.172941	−	0.0716343i
$436$	−23.0862	+	29.6696i	−1.10563	+	1.42092i
$437$	−5.28108	−	12.7496i	−0.252628	−	0.609898i
$438$	5.45436	+	20.6343i	0.260620	+	0.985943i
$439$	24.5842	+	24.5842i	1.17334	+	1.17334i	0.981408	+	0.191933i	$0.0614756\pi$
$439$	24.5842	+	24.5842i	1.17334	+	1.17334i	0.191933	+	0.981408i	$0.438524\pi$
$440$	21.9879	−	8.84795i	1.04823	−	0.421809i
$441$	6.87666	−	1.30826i	0.327460	−	0.0622983i
$442$	5.70838	−	9.81059i	0.271520	−	0.466642i
$443$	−2.27638	+	0.942909i	−0.108154	+	0.0447990i	−0.436104	−	0.899896i	$-0.643642\pi$
$443$	−2.27638	+	0.942909i	−0.108154	+	0.0447990i	0.327950	+	0.944695i	$0.393642\pi$
$444$	0.518827	−	1.88529i	0.0246224	−	0.0894721i
$445$	−11.6402	−	4.82153i	−0.551798	−	0.228562i
$446$	4.87040	−	36.0537i	0.230620	−	1.70719i
$447$	19.9738			0.944729
$448$	20.0985	+	6.63698i	0.949566	+	0.313568i
$449$	−5.47124			−0.258204			−0.129102	−	0.991631i	$-0.541209\pi$
$449$	−5.47124			−0.258204			−0.129102	+	0.991631i	$0.541209\pi$
$450$	0.490134	−	3.62827i	0.0231051	−	0.171038i
$451$	−15.3507	−	6.35846i	−0.722835	−	0.299408i
$452$	0.880024	−	3.19780i	0.0413929	−	0.150412i
$453$	9.71688	−	4.02486i	0.456539	−	0.189105i
$454$	−13.8781	+	23.8513i	−0.651331	+	1.11940i
$455$	6.05562	−	3.20437i	0.283892	−	0.150223i
$456$	2.19483	+	5.45434i	0.102782	+	0.255423i
$457$	6.84922	+	6.84922i	0.320393	+	0.320393i	0.848918	−	0.528525i	$-0.177255\pi$
$457$	6.84922	+	6.84922i	0.320393	+	0.320393i	−0.528525	+	0.848918i	$0.677255\pi$
$458$	5.15053	+	19.4849i	0.240669	+	0.910467i
$459$	1.84176	+	4.44639i	0.0859658	+	0.207540i
$460$	12.6612	−	16.2719i	0.590333	−	0.758679i
$461$	37.7970	+	15.6560i	1.76038	+	0.729174i	0.996479	+	0.0838421i	$0.0267191\pi$
$461$	37.7970	+	15.6560i	1.76038	+	0.729174i	0.763902	+	0.645332i	$0.223281\pi$
$462$	18.9511	−	6.96982i	0.881686	−	0.324265i
$463$	−11.3907			−0.529369			−0.264684	−	0.964335i	$-0.585268\pi$
$463$	−11.3907			−0.529369			−0.264684	+	0.964335i	$0.585268\pi$
$464$	−6.01417	−	8.06083i	−0.279201	−	0.374215i
$465$	10.6768			0.495126
$466$	29.8392	−	22.7369i	1.38228	−	1.05326i
$467$	12.9878	−	31.3553i	0.601004	−	1.45095i	−0.271545	−	0.962426i	$-0.587535\pi$
$467$	12.9878	−	31.3553i	0.601004	−	1.45095i	0.872549	−	0.488527i	$-0.162465\pi$
$468$	0.413016	+	3.30964i	0.0190917	+	0.152988i
$469$	−0.935045	−	9.91796i	−0.0431764	−	0.457969i
$470$	13.6578	−	3.61023i	0.629986	−	0.166527i
$471$	2.73933	−	2.73933i	0.126221	−	0.126221i
$472$	−27.1320	−	0.274712i	−1.24885	−	0.0126446i
$473$	−39.4992	+	39.4992i	−1.81618	+	1.81618i
$474$	−0.492453	+	0.846344i	−0.0226191	+	0.0388739i
$475$	−2.05939	−	4.97180i	−0.0944912	−	0.228122i
$476$	24.8631	−	5.51159i	1.13960	−	0.252623i
$477$	−1.39129	−	0.576292i	−0.0637029	−	0.0263866i
$478$	−0.465331	+	3.44466i	−0.0212837	+	0.157555i
$479$	−26.9562			−1.23166			−0.615831	−	0.787879i	$-0.711179\pi$
$479$	−26.9562			−1.23166			−0.615831	+	0.787879i	$0.711179\pi$
$480$	−5.46409	+	6.87747i	−0.249400	+	0.313912i
$481$		−	1.63045i		−	0.0743421i
$482$	0.399886	−	2.96020i	0.0182143	−	0.134833i
$483$	11.1996	−	13.5312i	0.509601	−	0.615691i
$484$	31.5117	−	17.9108i	1.43235	−	0.814127i
$485$	6.85580	+	16.5514i	0.311306	+	0.751559i
$486$	−1.22235	−	0.711236i	−0.0554470	−	0.0322623i
$487$	1.85082	+	1.85082i	0.0838687	+	0.0838687i	0.747797	−	0.663928i	$-0.231112\pi$
$487$	1.85082	+	1.85082i	0.0838687	+	0.0838687i	−0.663928	+	0.747797i	$0.731112\pi$
$488$	4.22438	+	4.31080i	0.191229	+	0.195141i
$489$	−12.0630	+	12.0630i	−0.545507	+	0.545507i
$490$	14.4970	+	5.11139i	0.654908	+	0.230909i
$491$	−12.2832	−	29.6542i	−0.554332	−	1.33828i	−0.914196	−	0.405271i	$-0.867177\pi$
$491$	−12.2832	−	29.6542i	−0.554332	−	1.33828i	0.359864	−	0.933005i	$-0.382823\pi$
$492$	6.11038	−	0.762525i	0.275477	−	0.0343773i
$493$	−11.1796	−	4.63073i	−0.503502	−	0.208557i
$494$	2.97124	+	3.89938i	0.133683	+	0.175441i
$495$			8.37969i			0.376639i
$496$	23.6312	+	14.0722i	1.06107	+	0.631860i
$497$	−4.88029	−	1.50270i	−0.218911	−	0.0674052i
$498$	9.52960	+	12.5064i	0.427031	+	0.560424i
$499$	19.7174	+	8.16722i	0.882672	+	0.365615i	0.777533	−	0.628843i	$-0.216471\pi$
$499$	19.7174	+	8.16722i	0.882672	+	0.365615i	0.105140	+	0.994457i	$0.466471\pi$
$500$	14.4730	−	18.6002i	0.647251	−	0.831828i
$501$	−15.0467	+	6.23256i	−0.672238	+	0.278450i
$502$	35.1588	−	9.29372i	1.56922	−	0.414799i
$503$	−9.05289	−	9.05289i	−0.403648	−	0.403648i	0.475868	−	0.879517i	$-0.342134\pi$
$503$	−9.05289	−	9.05289i	−0.403648	−	0.403648i	−0.879517	+	0.475868i	$0.842134\pi$
$504$	−4.82959	+	5.71621i	−0.215127	+	0.254620i
$505$	2.95813	−	2.95813i	0.131635	−	0.131635i
$506$	25.4817	−	43.7936i	1.13280	−	1.94686i
$507$	−3.91061	−	9.44106i	−0.173676	−	0.419292i
$508$	2.10570	−	7.65162i	0.0934253	−	0.339486i
$509$	4.28201	−	10.3377i	0.189797	−	0.458210i	−0.800124	−	0.599835i	$-0.795233\pi$
$509$	4.28201	−	10.3377i	0.189797	−	0.458210i	0.989920	+	0.141625i	$0.0452328\pi$
$510$	−1.41483	+	10.4735i	−0.0626498	+	0.463772i
$511$	−11.7502	+	38.1610i	−0.519798	+	1.68814i
$512$	−21.1583	+	8.02027i	−0.935075	+	0.354449i
$513$	−2.07868			−0.0917758
$514$	18.1317	+	2.44936i	0.799755	+	0.108037i
$515$	4.75528	−	11.4803i	0.209543	−	0.505881i
$516$	5.49295	−	19.9601i	0.241814	−	0.878694i
$517$	32.0742	−	13.2856i	1.41062	−	0.584298i
$518$	2.68878	−	2.48048i	0.118138	−	0.108986i
$519$	1.94466	+	1.94466i	0.0853613	+	0.0853613i
$520$	−2.87122	+	6.73796i	−0.125911	+	0.295479i
$521$	22.8145	−	22.8145i	0.999520	−	0.999520i	−0.000479629	−	1.00000i	$-0.500153\pi$
$521$	22.8145	−	22.8145i	0.999520	−	0.999520i	1.00000		0.000479629i	$0.000152671\pi$
$522$	3.43768	−	0.908701i	0.150463	−	0.0397727i
$523$	−1.29852	+	0.537863i	−0.0567801	+	0.0235191i	−0.410893	−	0.911684i	$-0.634783\pi$
$523$	−1.29852	+	0.537863i	−0.0567801	+	0.0235191i	0.354113	+	0.935203i	$0.384783\pi$
$524$	−19.2241	−	14.9584i	−0.839811	−	0.653463i
$525$	4.36736	−	5.27658i	0.190607	−	0.230289i
$526$	35.7763	−	27.2608i	1.55992	−	1.18863i
$527$	33.0922			1.44152
$528$	−11.0445	+	18.5469i	−0.480652	+	0.807150i
$529$		−	21.0750i		−	0.916304i
$530$	−2.00428	−	2.63036i	−0.0870602	−	0.114255i
$531$	3.67112	−	8.86286i	0.159313	−	0.384615i
$532$	−1.91019	+	10.8322i	−0.0828171	+	0.469635i
$533$	4.74368	−	1.96490i	0.205471	−	0.0851091i
$534$	11.0939	−	2.93251i	0.480080	−	0.126902i
$535$	−8.27404	−	8.27404i	−0.357718	−	0.357718i
$536$	7.45389	+	7.60638i	0.321959	+	0.328545i
$537$	17.6483	+	17.6483i	0.761580	+	0.761580i
$538$	−13.5995	+	23.3725i	−0.586317	+	1.00766i
$539$	36.9874	+	7.67883i	1.59316	+	0.330750i
$540$	−1.53459	−	2.69991i	−0.0660382	−	0.116186i
$541$	23.5916	+	9.77195i	1.01428	+	0.420129i	0.827015	−	0.562180i	$-0.190037\pi$
$541$	23.5916	+	9.77195i	1.01428	+	0.420129i	0.187266	+	0.982309i	$0.440037\pi$
$542$	−43.3942	−	5.86201i	−1.86394	−	0.251795i
$543$		−	15.9206i		−	0.683218i
$544$	−16.9356	+	21.3163i	−0.726108	+	0.913929i
$545$		−	29.1870i		−	1.25024i
$546$	−2.61804	+	5.66400i	−0.112042	+	0.242397i
$547$	−8.44151	+	20.3796i	−0.360933	+	0.871370i	0.634231	+	0.773144i	$0.281317\pi$
$547$	−8.44151	+	20.3796i	−0.360933	+	0.871370i	−0.995164	+	0.0982260i	$0.968683\pi$
$548$	−0.118056	−	0.207705i	−0.00504312	−	0.00887272i
$549$	−1.97147	+	0.816610i	−0.0841403	+	0.0348521i
$550$	9.93675	−	17.0776i	0.423705	−	0.728191i
$551$	3.69563	−	3.69563i	0.157439	−	0.157439i
$552$	−0.190114	+	18.7767i	−0.00809180	+	0.799189i
$553$	−1.61917	+	0.856796i	−0.0688543	+	0.0364347i
$554$	5.49799	+	20.7993i	0.233587	+	0.883678i
$555$	0.580965	+	1.40257i	0.0246606	+	0.0595360i
$556$	−11.8092	+	1.47369i	−0.500822	+	0.0624985i
$557$	3.84831	−	9.29063i	0.163058	−	0.393657i	−0.821140	−	0.570726i	$-0.806662\pi$
$557$	3.84831	−	9.29063i	0.163058	−	0.393657i	0.984198	+	0.177070i	$0.0566617\pi$
$558$	−7.73456	+	5.89357i	−0.327430	+	0.249495i
$559$		−	17.2620i		−	0.730104i
$560$	−15.4797	+	5.51583i	−0.654137	+	0.233086i
$561$			25.9724i			1.09655i
$562$	−22.3938	−	29.3890i	−0.944626	−	1.23970i
$563$	10.7247	−	25.8918i	0.451994	−	1.09121i	−0.519569	−	0.854429i	$-0.673907\pi$
$563$	10.7247	−	25.8918i	0.451994	−	1.09121i	0.971563	−	0.236782i	$-0.0760927\pi$
$564$	−7.90118	+	10.1544i	−0.332700	+	0.427576i
$565$	0.985423	+	2.37902i	0.0414570	+	0.100086i
$566$	28.0376	−	7.41131i	1.17851	−	0.311521i
$567$	−1.23745	−	2.33853i	−0.0519679	−	0.0982091i
$568$	5.06433	−	2.03789i	0.212494	−	0.0855080i
$569$	16.2078	−	16.2078i	0.679466	−	0.679466i	−0.280413	−	0.959879i	$-0.590472\pi$
$569$	16.2078	−	16.2078i	0.679466	−	0.679466i	0.959879	+	0.280413i	$0.0904715\pi$
$570$	−3.94541	−	2.29567i	−0.165255	−	0.0961551i
$571$	6.79609	−	2.81503i	0.284407	−	0.117805i	−0.235919	−	0.971773i	$-0.575810\pi$
$571$	6.79609	−	2.81503i	0.284407	−	0.117805i	0.520327	+	0.853967i	$0.325810\pi$
$572$	−4.77580	+	17.3541i	−0.199686	+	0.725612i
$573$	−0.178474	+	0.430874i	−0.00745584	+	0.0180000i
$574$	10.4571	+	4.83352i	0.436470	+	0.201747i
$575$		−	17.1873i		−	0.716761i
$576$	0.161984	−	7.99836i	0.00674932	−	0.333265i
$577$			10.5226i			0.438062i	0.975718	+	0.219031i	$0.0702896\pi$
$577$			10.5226i			0.438062i	−0.975718	+	0.219031i	$0.929710\pi$
$578$	−1.16670	+	8.63663i	−0.0485283	+	0.359236i
$579$	9.96209	+	4.12643i	0.414010	+	0.171489i
$580$	7.52842	+	2.07180i	0.312601	+	0.0860267i
$581$	2.76100	+	29.2858i	0.114546	+	1.21498i
$582$	−14.1028	−	8.20584i	−0.584580	−	0.340143i
$583$	−5.74654	−	5.74654i	−0.237998	−	0.237998i
$584$	−15.9351	−	39.6000i	−0.659399	−	1.63866i
$585$	−1.83105	−	1.83105i	−0.0757047	−	0.0757047i
$586$	−0.949771	−	3.59306i	−0.0392347	−	0.148428i
$587$	18.1867	−	7.53316i	0.750644	−	0.310927i	0.0256396	−	0.999671i	$-0.491838\pi$
$587$	18.1867	−	7.53316i	0.750644	−	0.310927i	0.725004	+	0.688744i	$0.241838\pi$
$588$	−13.3235	+	4.29948i	−0.549450	+	0.177308i
$589$	−5.46965	+	13.2049i	−0.225373	+	0.544099i
$590$	16.7560	−	12.7677i	0.689833	−	0.525638i
$591$		−	11.8295i		−	0.486601i
$592$	−0.562751	+	3.87006i	−0.0231289	+	0.159058i
$593$	4.49362			0.184531			0.0922655	−	0.995734i	$-0.470589\pi$
$593$	4.49362			0.184531			0.0922655	+	0.995734i	$0.470589\pi$
$594$	−4.62556	−	6.07045i	−0.189789	−	0.249074i
$595$	−12.6069	+	15.2315i	−0.516834	+	0.624430i
$596$	−39.6402	+	4.94676i	−1.62372	+	0.202627i
$597$	−6.89983	+	2.85800i	−0.282391	+	0.116970i
$598$	4.00135	+	15.1374i	0.163627	+	0.619014i
$599$	−12.7681	+	12.7681i	−0.521691	+	0.521691i	−0.918082	−	0.396391i	$-0.870262\pi$
$599$	−12.7681	+	12.7681i	−0.521691	+	0.521691i	0.396391	+	0.918082i	$0.370262\pi$
$600$	−0.0741362	+	7.32208i	−0.00302660	+	0.298923i
$601$	−21.2762	−	21.2762i	−0.867876	−	0.867876i	0.124361	−	0.992237i	$-0.460312\pi$
$601$	−21.2762	−	21.2762i	−0.867876	−	0.867876i	−0.992237	+	0.124361i	$0.960312\pi$
$602$	28.4668	−	26.2614i	1.16022	−	1.07034i
$603$	−3.47865	+	1.44090i	−0.141661	+	0.0586781i
$604$	−18.2874	+	10.3943i	−0.744103	+	0.422937i
$605$	−10.7691	+	25.9990i	−0.437828	+	1.05701i
$606$	−0.510065	+	3.77581i	−0.0207200	+	0.153382i
$607$	42.4045			1.72114			0.860572	−	0.509328i	$-0.170106\pi$
$607$	42.4045			1.72114			0.860572	+	0.509328i	$0.170106\pi$
$608$	−5.70671	−	10.2811i	−0.231438	−	0.416956i
$609$	6.35765	+	1.95759i	0.257625	+	0.0793256i
$610$	−4.64379	−	0.627318i	−0.188022	−	0.0253993i
$611$	−4.10551	+	9.91158i	−0.166091	+	0.400980i
$612$	−4.75637	−	8.36821i	−0.192265	−	0.338265i
$613$	5.76199	+	13.9107i	0.232724	+	0.561846i	0.996496	−	0.0836401i	$-0.0266546\pi$
$613$	5.76199	+	13.9107i	0.232724	+	0.561846i	−0.763772	+	0.645487i	$0.776655\pi$
$614$	−30.2777	−	17.6174i	−1.22191	−	0.710979i
$615$	−3.38056	+	3.38056i	−0.136317	+	0.136317i
$616$	−35.8843	+	18.5258i	−1.44582	+	0.746427i
$617$	1.65723	+	1.65723i	0.0667175	+	0.0667175i	0.739678	−	0.672961i	$-0.234978\pi$
$617$	1.65723	+	1.65723i	0.0667175	+	0.0667175i	−0.672961	+	0.739678i	$0.734978\pi$
$618$	2.89222	+	10.9415i	0.116342	+	0.440131i
$619$	−27.8885	+	11.5518i	−1.12093	+	0.464306i	−0.864690	−	0.502306i	$-0.832485\pi$
$619$	−27.8885	+	11.5518i	−1.12093	+	0.464306i	−0.256244	+	0.966612i	$0.582485\pi$
$620$	−21.1893	+	2.64425i	−0.850983	+	0.106196i
$621$	−6.13354	−	2.54060i	−0.246131	−	0.101951i
$622$	26.5955	−	20.2652i	1.06638	−	0.812562i
$623$	20.5171	+	6.31744i	0.821999	+	0.253103i
$624$	−1.63935	−	6.46604i	−0.0656264	−	0.258849i
$625$			5.35330i			0.214132i
$626$	−15.7456	+	11.9978i	−0.629322	+	0.479530i
$627$	−10.3638	−	4.29284i	−0.413892	−	0.171440i
$628$	−4.75806	+	6.11491i	−0.189867	+	0.244012i
$629$	1.80067	+	4.34720i	0.0717973	+	0.173334i
$630$	0.233930	−	5.80525i	0.00931999	−	0.231287i
$631$	−3.54779	+	3.54779i	−0.141235	+	0.141235i	−0.774189	−	0.632954i	$-0.781842\pi$
$631$	−3.54779	+	3.54779i	−0.141235	+	0.141235i	0.632954	+	0.774189i	$0.281842\pi$
$632$	0.767717	−	1.80162i	0.0305381	−	0.0716646i
$633$	18.8112	+	18.8112i	0.747678	+	0.747678i
$634$	10.2724	−	17.6544i	0.407967	−	0.701145i
$635$	2.35790	+	5.69246i	0.0935702	+	0.225898i
$636$	2.90389	+	0.799142i	0.115147	+	0.0316881i
$637$	−9.76004	+	6.40423i	−0.386707	+	0.253745i
$638$	19.0162	+	2.56885i	0.752858	+	0.101702i
$639$			1.93004i			0.0763512i
$640$	9.14077	−	15.0023i	0.361321	−	0.593019i
$641$	32.8641			1.29805			0.649027	−	0.760765i	$-0.275176\pi$
$641$	32.8641			1.29805			0.649027	+	0.760765i	$0.275176\pi$
$642$	10.5611	+	1.42668i	0.416815	+	0.0563065i
$643$	−31.5004	−	13.0479i	−1.24226	−	0.514559i	−0.337837	−	0.941205i	$-0.609695\pi$
$643$	−31.5004	−	13.0479i	−1.24226	−	0.514559i	−0.904419	+	0.426645i	$0.859695\pi$
$644$	−18.8757	+	29.6278i	−0.743806	+	1.16750i
$645$	6.15083	+	14.8494i	0.242189	+	0.584695i
$646$	−12.2286	−	7.11530i	−0.481126	−	0.279948i
$647$	−17.5760	+	17.5760i	−0.690983	+	0.690983i	−0.962448	−	0.271465i	$-0.912492\pi$
$647$	−17.5760	+	17.5760i	−0.690983	+	0.690983i	0.271465	+	0.962448i	$0.412492\pi$
$648$	2.60203	+	1.10879i	0.102218	+	0.0435575i
$649$	36.6068	−	36.6068i	1.43694	−	1.43694i
$650$	1.56035	+	5.90292i	0.0612020	+	0.231532i
$651$	−18.1118	+	1.70754i	−0.709856	+	0.0669238i
$652$	20.9527	−	26.9278i	0.820572	−	1.05458i
$653$	−4.15906	+	10.0409i	−0.162757	+	0.392929i	−0.984127	−	0.177466i	$-0.943210\pi$
$653$	−4.15906	+	10.0409i	−0.162757	+	0.392929i	0.821370	+	0.570395i	$0.193210\pi$
$654$	16.1111	+	21.1438i	0.629995	+	0.826788i
$655$	18.9115			0.738932
$656$	−11.9378	+	3.02662i	−0.466095	+	0.118170i
$657$	15.0918			0.588786
$658$	−22.5911	+	8.30853i	−0.880693	+	0.323900i
$659$	−30.9444	−	12.8176i	−1.20542	−	0.499302i	−0.312675	−	0.949860i	$-0.601225\pi$
$659$	−30.9444	−	12.8176i	−1.20542	−	0.499302i	−0.892747	+	0.450558i	$0.851225\pi$
$660$	−2.07534	−	16.6304i	−0.0807823	−	0.647337i
$661$	7.46838	+	18.0303i	0.290486	+	0.701296i	0.999994	−	0.00340153i	$-0.00108274\pi$
$661$	7.46838	+	18.0303i	0.290486	+	0.701296i	−0.709508	+	0.704697i	$0.751083\pi$
$662$	15.1404	−	4.00214i	0.588448	−	0.155547i
$663$	−5.67523	−	5.67523i	−0.220408	−	0.220408i
$664$	−22.0099	−	22.4601i	−0.854148	−	0.871622i
$665$	−3.99413	−	7.54813i	−0.154886	−	0.292704i
$666$	−1.19508	−	0.695369i	−0.0463085	−	0.0269450i
$667$	15.4216	−	6.38782i	0.597125	−	0.247337i
$668$	28.3183	−	16.0957i	1.09567	−	0.622761i
$669$	−23.7671	−	9.84467i	−0.918891	−	0.380617i
$670$	−8.19393	−	1.10690i	−0.316559	−	0.0427632i
$671$	−11.5158			−0.444562
$672$	8.16915	−	12.5405i	0.315132	−	0.483762i
$673$	44.2142			1.70433			0.852167	−	0.523271i	$-0.175288\pi$
$673$	44.2142			1.70433			0.852167	+	0.523271i	$0.175288\pi$
$674$	5.85801	+	0.791343i	0.225642	+	0.0304814i
$675$	−2.39181	−	0.990722i	−0.0920610	−	0.0381329i
$676$	10.0992	+	17.7683i	0.388432	+	0.683395i
$677$	0.458739	−	0.190016i	0.0176308	−	0.00730290i	−0.373851	−	0.927489i	$-0.621963\pi$
$677$	0.458739	−	0.190016i	0.0176308	−	0.00730290i	0.391481	+	0.920186i	$0.371963\pi$
$678$	−2.02707	−	1.17947i	−0.0778493	−	0.0452973i
$679$	−14.2770	−	26.9806i	−0.547899	−	1.03542i
$680$	0.214003	−	21.1361i	0.00820665	−	0.810532i
$681$	13.7975	+	13.7975i	0.528722	+	0.528722i
$682$	−50.7342	+	13.4108i	−1.94271	+	0.513527i
$683$	8.06512	+	19.4709i	0.308603	+	0.745034i	0.999751	+	0.0223205i	$0.00710544\pi$
$683$	8.06512	+	19.4709i	0.308603	+	0.745034i	−0.691148	+	0.722714i	$0.742895\pi$
$684$	4.12535	−	0.514810i	0.157737	−	0.0196842i
$685$	0.171369	+	0.0709833i	0.00654766	+	0.00271213i
$686$	−25.4096	−	6.35226i	−0.970144	−	0.242530i
$687$	14.2511			0.543713
$688$	−5.95798	+	40.9733i	−0.227146	+	1.56209i
$689$	2.51136			0.0956752
$690$	−8.83590	−	11.5960i	−0.336377	−	0.441452i
$691$	4.06087	−	9.80380i	0.154483	−	0.372954i	−0.827623	−	0.561284i	$-0.810307\pi$
$691$	4.06087	−	9.80380i	0.154483	−	0.372954i	0.982106	+	0.188330i	$0.0603075\pi$
$692$	−4.34101	−	3.37777i	−0.165021	−	0.128404i
$693$	−1.34016	−	14.2150i	−0.0509084	−	0.539982i
$694$	−9.48692	−	35.8897i	−0.360118	−	1.36235i
$695$	6.53343	−	6.53343i	0.247827	−	0.247827i
$696$	−6.59740	+	2.65480i	−0.250074	+	0.100630i
$697$	−10.4778	+	10.4778i	−0.396876	+	0.396876i
$698$	16.7840	+	9.76590i	0.635283	+	0.369645i
$699$	−10.1514	−	24.5076i	−0.383960	−	0.926962i
$700$	−7.36069	+	11.5536i	−0.278208	+	0.436683i
$701$	2.97354	+	1.23168i	0.112309	+	0.0465200i	0.438131	−	0.898911i	$-0.355641\pi$
$701$	2.97354	+	1.23168i	0.112309	+	0.0465200i	−0.325821	+	0.945431i	$0.605641\pi$
$702$	2.33719	+	0.315725i	0.0882116	+	0.0119163i
$703$	−2.03230			−0.0766497
$704$	17.3257	−	39.5436i	0.652986	−	1.49036i
$705$		−	9.98920i		−	0.376215i
$706$	−22.1515	−	2.99239i	−0.833683	−	0.112620i
$707$	−4.54496	+	5.49114i	−0.170931	+	0.206516i
$708$	−5.09072	+	18.4985i	−0.191321	+	0.695216i
$709$	12.2154	+	29.4906i	0.458759	+	1.10754i	0.968900	+	0.247451i	$0.0795931\pi$
$709$	12.2154	+	29.4906i	0.458759	+	1.10754i	−0.510141	+	0.860091i	$0.670407\pi$
$710$	−2.13152	+	3.66329i	−0.0799945	+	0.137481i
$711$	0.489594	+	0.489594i	0.0183612	+	0.0183612i
$712$	−21.2908	+	8.56743i	−0.797905	+	0.321078i
$713$	−32.2786	+	32.2786i	−1.20884	+	1.20884i
$714$	0.725051	−	17.9930i	0.0271344	−	0.673372i
$715$	−5.34778	−	12.9107i	−0.199996	−	0.482833i
$716$	−39.3957	−	30.6541i	−1.47229	−	1.14560i
$717$	2.27077	+	0.940586i	0.0848036	+	0.0351268i
$718$	32.1886	−	24.5271i	1.20127	−	0.915342i
$719$			53.2379i			1.98544i	0.120451	+	0.992719i	$0.461566\pi$
$719$			53.2379i			1.98544i	−0.120451	+	0.992719i	$0.538434\pi$
$720$	3.71422	+	4.97820i	0.138421	+	0.185527i
$721$	−6.23064	+	20.2352i	−0.232041	+	0.753597i
$722$	−16.5121	+	12.5819i	−0.614516	+	0.468248i
$723$	−1.95141	−	0.808300i	−0.0725737	−	0.0300610i
$724$	3.94293	+	31.5961i	0.146538	+	1.17426i
$725$	6.01373	−	2.49097i	0.223344	−	0.0925123i
$726$	−6.54992	−	24.7788i	−0.243090	−	0.919629i
$727$	14.6860	+	14.6860i	0.544674	+	0.544674i	0.924896	−	0.380221i	$-0.124152\pi$
$727$	14.6860	+	14.6860i	0.544674	+	0.544674i	−0.380221	+	0.924896i	$0.624152\pi$
$728$	3.79302	−	11.8892i	0.140579	−	0.440643i
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$	28.6448	+	16.6672i	1.06019	+	0.616882i
$731$	19.0641	+	46.0249i	0.705112	+	1.70229i
$732$	3.71035	−	2.10891i	0.137139	−	0.0779475i
$733$	9.60453	−	23.1874i	0.354751	−	0.856446i	−0.641269	−	0.767317i	$-0.721592\pi$
$733$	9.60453	−	23.1874i	0.354751	−	0.856446i	0.996020	−	0.0891294i	$-0.0284085\pi$
$734$	25.9744	+	3.50882i	0.958734	+	0.129513i
$735$	6.11399	−	8.98688i	0.225518	−	0.331486i
$736$	−4.27298	−	37.3114i	−0.157504	−	1.37532i
$737$	−20.3195			−0.748479
$738$	0.582903	−	4.31501i	0.0214570	−	0.158838i
$739$	1.92698	−	4.65213i	0.0708849	−	0.171131i	−0.884466	−	0.466604i	$-0.845477\pi$
$739$	1.92698	−	4.65213i	0.0708849	−	0.171131i	0.955351	+	0.295473i	$0.0954772\pi$
$740$	−1.50035	−	2.63968i	−0.0551541	−	0.0970364i
$741$	3.20264	−	1.32658i	0.117652	−	0.0487330i
$742$	3.82065	+	4.14149i	0.140260	+	0.152039i
$743$	−0.344089	−	0.344089i	−0.0126234	−	0.0126234i	0.700767	−	0.713390i	$-0.252841\pi$
$743$	−0.344089	−	0.344089i	−0.0126234	−	0.0126234i	−0.713390	+	0.700767i	$0.752841\pi$
$744$	13.8904	−	13.6120i	0.509248	−	0.499039i
$745$	21.9308	−	21.9308i	0.803484	−	0.803484i
$746$	−2.04429	−	7.73371i	−0.0748469	−	0.283151i
$747$	10.2718	−	4.25470i	0.375824	−	0.155671i
$748$	−6.43238	−	51.5449i	−0.235191	−	1.88467i
$749$	15.3590	+	12.7125i	0.561206	+	0.464504i
$750$	−10.1003	−	13.2553i	−0.368809	−	0.484015i
$751$	−4.67369			−0.170545			−0.0852726	−	0.996358i	$-0.527176\pi$
$751$	−4.67369			−0.170545			−0.0852726	+	0.996358i	$0.527176\pi$
$752$	13.1659	−	22.1093i	0.480111	−	0.806242i
$753$		−	25.7149i		−	0.937104i
$754$	−4.71656	+	3.59392i	−0.171767	+	0.130883i
$755$	6.24972	−	15.0882i	0.227451	−	0.549114i
$756$	3.03501	+	4.33459i	0.110382	+	0.157648i
$757$	−15.1275	+	6.26601i	−0.549818	+	0.227742i	−0.640258	−	0.768160i	$-0.721173\pi$
$757$	−15.1275	+	6.26601i	−0.549818	+	0.227742i	0.0904402	+	0.995902i	$0.471173\pi$
$758$	7.85117	+	29.7016i	0.285167	+	1.07881i
$759$	−25.3338	−	25.3338i	−0.919557	−	0.919557i
$760$	8.39864	+	3.57888i	0.304651	+	0.129819i
$761$	−2.40923	−	2.40923i	−0.0873344	−	0.0873344i	0.662090	−	0.749424i	$-0.269670\pi$
$761$	−2.40923	−	2.40923i	−0.0873344	−	0.0873344i	−0.749424	+	0.662090i	$0.769670\pi$
$762$	−4.85033	−	2.82221i	−0.175709	−	0.102238i
$763$	4.66787	+	49.5117i	0.168988	+	1.79245i
$764$	0.247489	−	0.899316i	0.00895383	−	0.0325361i
$765$	6.90426	+	2.85984i	0.249624	+	0.103398i
$766$	2.38693	−	17.6695i	0.0862432	−	0.638425i
$767$			15.9980i			0.577653i
$768$	1.65942	+	15.9137i	0.0598792	+	0.574237i
$769$		−	12.7315i		−	0.459111i	−0.973296	−	0.229556i	$-0.926273\pi$
$769$		−	12.7315i		−	0.459111i	0.973296	−	0.229556i	$-0.0737273\pi$
$770$	13.1552	−	28.4607i	0.474081	−	1.02565i
$771$	4.95097	−	11.9527i	0.178305	−	0.430466i
$772$	−20.7928	−	5.72211i	−0.748349	−	0.205943i
$773$	−23.0295	+	9.53911i	−0.828312	+	0.343098i	−0.756234	−	0.654301i	$-0.772963\pi$
$773$	−23.0295	+	9.53911i	−0.828312	+	0.343098i	−0.0720778	+	0.997399i	$0.522963\pi$
$774$	−12.6526	−	7.36204i	−0.454789	−	0.264623i
$775$	−12.5872	+	12.5872i	−0.452147	+	0.452147i
$776$	30.0208	+	12.7926i	1.07768	+	0.459229i
$777$	−1.20984	−	2.28636i	−0.0434028	−	0.0820227i
$778$	−21.7394	+	5.74650i	−0.779397	+	0.206022i
$779$	−2.44918	−	5.91283i	−0.0877508	−	0.211849i
$780$	4.08740	+	3.18043i	0.146352	+	0.113878i
$781$	−3.98588	+	9.62277i	−0.142626	+	0.344330i
$782$	−27.3863	−	35.9411i	−0.979334	−	1.28525i
$783$		−	2.51430i		−	0.0898537i
$784$	25.3770	−	11.8325i	0.906321	−	0.422589i
$785$		−	6.01545i		−	0.214701i
$786$	−13.6999	+	10.4390i	−0.488660	+	0.372348i
$787$	−15.3866	+	37.1465i	−0.548473	+	1.32413i	0.370141	+	0.928976i	$0.379309\pi$
$787$	−15.3866	+	37.1465i	−0.548473	+	1.32413i	−0.918614	+	0.395156i	$0.870691\pi$
$788$	2.92972	+	23.4769i	0.104367	+	0.836330i
$789$	−12.1712	−	29.3838i	−0.433306	−	1.04609i
$790$	0.388565	+	1.46997i	0.0138245	+	0.0522992i
$791$	−2.05211	−	3.87808i	−0.0729645	−	0.137889i
$792$	10.6833	+	10.9019i	0.379616	+	0.387382i
$793$	2.51632	−	2.51632i	0.0893572	−	0.0893572i
$794$	18.7012	−	32.1405i	0.663682	−	1.14062i
$795$	−2.16037	+	0.894854i	−0.0766204	+	0.0317372i
$796$	12.9856	−	7.38084i	0.460263	−	0.261607i
$797$	−10.2283	+	24.6932i	−0.362304	+	0.874678i	0.632659	+	0.774431i	$0.281964\pi$
$797$	−10.2283	+	24.6932i	−0.362304	+	0.874678i	−0.994963	+	0.100248i	$0.968036\pi$
$798$	7.05998	+	3.26330i	0.249921	+	0.115520i
$799$		−	30.9609i		−	1.09532i
$800$	−1.66627	−	14.5498i	−0.0589117	−	0.514414i
$801$		−	8.11401i		−	0.286695i
$802$	−4.31976	−	0.583545i	−0.152536	−	0.0206057i
$803$	75.2444	+	31.1672i	2.65532	+	1.09987i
$804$	6.54689	−	3.72115i	0.230891	−	0.131235i
$805$	−2.56002	−	27.1539i	−0.0902288	−	0.957051i
$806$	8.15555	−	14.0164i	0.287267	−	0.493705i
$807$	13.5206	+	13.5206i	0.475946	+	0.475946i
$808$	0.0771509	−	7.61983i	0.00271416	−	0.268065i
$809$	21.7961	+	21.7961i	0.766309	+	0.766309i	0.977455	−	0.211146i	$-0.0677195\pi$
$809$	21.7961	+	21.7961i	0.766309	+	0.766309i	−0.211146	+	0.977455i	$0.567719\pi$
$810$	−2.12304	+	0.561194i	−0.0745960	+	0.0197184i
$811$	14.0120	−	5.80397i	0.492028	−	0.203805i	−0.122852	−	0.992425i	$-0.539204\pi$
$811$	14.0120	−	5.80397i	0.492028	−	0.203805i	0.614881	+	0.788620i	$0.289204\pi$
$812$	−13.1023	−	2.31050i	−0.459799	−	0.0810826i
$813$	−11.8490	+	28.6061i	−0.415564	+	1.00326i
$814$	−4.52236	−	5.93502i	−0.158509	−	0.208022i
$815$			26.4898i			0.927898i
$816$	11.5120	+	15.4296i	0.403001	+	0.540145i
$817$	−21.5165			−0.752767
$818$	−25.5306	+	19.4538i	−0.892656	+	0.680185i
$819$	3.39896	+	2.81328i	0.118769	+	0.0983041i
$820$	5.87184	−	7.54631i	0.205053	−	0.263529i
$821$	23.1021	−	9.56921i	0.806270	−	0.333968i	0.0588050	−	0.998269i	$-0.481271\pi$
$821$	23.1021	−	9.56921i	0.806270	−	0.333968i	0.747465	+	0.664302i	$0.231271\pi$
$822$	−0.163326	+	0.0431729i	−0.00569666	+	0.00150583i
$823$	4.46424	−	4.46424i	0.155613	−	0.155613i	−0.625006	−	0.780620i	$-0.714904\pi$
$823$	4.46424	−	4.46424i	0.155613	−	0.155613i	0.780620	+	0.625006i	$0.214904\pi$
$824$	−8.44971	−	20.9982i	−0.294360	−	0.731508i
$825$	−9.87906	−	9.87906i	−0.343945	−	0.343945i
$826$	−26.3823	+	24.3384i	−0.917957	+	0.846842i
$827$	20.2131	−	8.37254i	0.702878	−	0.291142i	−0.00247578	−	0.999997i	$-0.500788\pi$
$827$	20.2131	−	8.37254i	0.702878	−	0.291142i	0.705354	+	0.708855i	$0.250788\pi$
$828$	12.8019	+	3.52304i	0.444896	+	0.122434i
$829$	−6.41676	+	15.4914i	−0.222863	+	0.538040i	−0.995277	−	0.0970806i	$-0.969050\pi$
$829$	−6.41676	+	15.4914i	−0.222863	+	0.538040i	0.772413	+	0.635120i	$0.219050\pi$
$830$	24.1951	+	3.26845i	0.839823	+	0.113449i
$831$	15.2125			0.527715
$832$	4.85485	+	12.4265i	0.168312	+	0.430813i
$833$	18.9499	−	27.8543i	0.656576	−	0.965094i
$834$	−1.12655	+	8.33940i	−0.0390092	+	0.288770i
$835$	−9.67778	+	23.3642i	−0.334913	+	0.808552i
$836$	21.6313	+	5.95287i	0.748135	+	0.205884i
$837$	2.63131	+	6.35256i	0.0909515	+	0.219576i
$838$	15.2356	−	26.1844i	0.526305	−	0.904524i
$839$	2.11601	−	2.11601i	0.0730527	−	0.0730527i	−0.669636	−	0.742689i	$-0.733550\pi$
$839$	2.11601	−	2.11601i	0.0730527	−	0.0730527i	0.742689	+	0.669636i	$0.233550\pi$
$840$	0.973484	+	11.5791i	0.0335884	+	0.399516i
$841$	−16.0360	−	16.0360i	−0.552965	−	0.552965i
$842$	−38.2068	+	10.0994i	−1.31669	+	0.348048i
$843$	−24.1378	+	9.99822i	−0.831351	+	0.344357i
$844$	−41.9916	−	32.6740i	−1.44541	−	1.12468i
$845$	−14.6599	−	6.07232i	−0.504315	−	0.208894i
$846$	5.51400	+	7.23642i	0.189575	+	0.248793i
$847$	14.1103	−	45.8260i	0.484837	−	1.57460i
$848$	−5.96100	−	0.866797i	−0.204702	−	0.0297659i
$849$		−	20.5065i		−	0.703781i
$850$	−10.6795	−	14.0154i	−0.366303	−	0.480726i
$851$	−5.99671	−	2.48392i	−0.205564	−	0.0851476i
$852$	−0.477998	−	3.83037i	−0.0163760	−	0.131226i
$853$	9.32298	+	22.5077i	0.319213	+	0.770648i	0.999296	+	0.0375131i	$0.0119436\pi$
$853$	9.32298	+	22.5077i	0.319213	+	0.770648i	−0.680083	+	0.733135i	$0.738056\pi$
$854$	7.97787	+	0.321478i	0.272997	+	0.0110007i
$855$	−2.28234	+	2.28234i	−0.0780545	+	0.0780545i
$856$	−21.3131	−	0.215795i	−0.728465	−	0.00737572i
$857$	8.53327	+	8.53327i	0.291491	+	0.291491i	0.837669	−	0.546178i	$-0.183918\pi$
$857$	8.53327	+	8.53327i	0.291491	+	0.291491i	−0.546178	+	0.837669i	$0.683918\pi$
$858$	11.0007	+	6.40087i	0.375558	+	0.218522i
$859$	−17.9356	−	43.3003i	−0.611954	−	1.47739i	−0.860851	−	0.508858i	$-0.830068\pi$
$859$	−17.9356	−	43.3003i	−0.611954	−	1.47739i	0.248897	−	0.968530i	$-0.419932\pi$
$860$	−15.8846	−	27.9469i	−0.541661	−	0.952982i
$861$	5.19399	−	6.27529i	0.177011	−	0.213861i
$862$	−4.91506	+	36.3843i	−0.167408	+	1.23925i
$863$			39.0318i			1.32866i	0.747441	+	0.664328i	$0.231282\pi$
$863$			39.0318i			1.32866i	−0.747441	+	0.664328i	$0.768718\pi$
$864$	−5.43862	−	1.55609i	−0.185026	−	0.0529393i
$865$	4.27040			0.145198
$866$	3.25232	−	24.0756i	0.110518	−	0.818123i
$867$	5.69340	+	2.35828i	0.193358	+	0.0800915i
$868$	35.5218	−	7.87440i	1.20569	−	0.267274i
$869$	1.42991	+	3.45211i	0.0485064	+	0.117105i
$870$	2.77677	−	4.77224i	0.0941413	−	0.161794i
$871$	4.44003	−	4.44003i	0.150445	−	0.150445i
$872$	−37.2108	−	37.9720i	−1.26012	−	1.28589i
$873$	−8.15820	+	8.15820i	−0.276113	+	0.276113i
$874$	18.8683	−	4.98754i	0.638228	−	0.168706i
$875$	−2.92634	−	31.0395i	−0.0989284	−	1.04933i
$876$	−29.9512	+	3.73766i	−1.01196	+	0.126284i
$877$	−13.7665	+	33.2353i	−0.464861	+	1.12227i	0.501516	+	0.865148i	$0.332776\pi$
$877$	−13.7665	+	33.2353i	−0.464861	+	1.12227i	−0.966378	+	0.257127i	$0.917224\pi$
$878$	−39.1087	+	29.8000i	−1.31986	+	1.00570i
$879$	−2.62794			−0.0886382
$880$	8.23745	+	32.4908i	0.277684	+	1.09526i
$881$	−15.3066			−0.515691			−0.257846	−	0.966186i	$-0.583013\pi$
$881$	−15.3066			−0.515691			−0.257846	+	0.966186i	$0.583013\pi$
$882$	0.531601	+	9.88521i	0.0179000	+	0.332852i
$883$	36.6261	+	15.1710i	1.23257	+	0.510546i	0.901384	−	0.433021i	$-0.142552\pi$
$883$	36.6261	+	15.1710i	1.23257	+	0.510546i	0.331183	+	0.943567i	$0.392552\pi$
$884$	12.6687	+	9.85757i	0.426093	+	0.331546i
$885$	−5.70043	−	13.7621i	−0.191618	−	0.462606i
$886$	−0.890500	−	3.36883i	−0.0299169	−	0.113178i
$887$	−22.3363	−	22.3363i	−0.749979	−	0.749979i	0.224496	−	0.974475i	$-0.427926\pi$
$887$	−22.3363	−	22.3363i	−0.749979	−	0.749979i	−0.974475	+	0.224496i	$0.927926\pi$
$888$	2.54398	+	1.08406i	0.0853705	+	0.0363786i
$889$	−4.91023	−	9.27937i	−0.164684	−	0.311220i
$890$	8.96105	−	15.4007i	0.300375	−	0.516234i
$891$	−4.98579	+	2.06518i	−0.167030	+	0.0691862i
$892$	49.6066	+	13.6516i	1.66095	+	0.457088i
$893$	12.3545	+	5.11738i	0.413426	+	0.171247i
$894$	−3.78150	+	27.9930i	−0.126472	+	0.936225i
$895$	38.7549			1.29543
$896$	−13.1067	+	26.9112i	−0.437865	+	0.899041i
$897$	11.0714			0.369663
$898$	1.03583	−	7.66785i	0.0345661	−	0.255879i
$899$	−15.9722	−	6.61591i	−0.532703	−	0.220653i
$900$	4.99217	+	1.37383i	0.166406	+	0.0457943i
$901$	−6.69593	+	2.77355i	−0.223074	+	0.0924002i
$902$	11.8175	−	20.3099i	0.393480	−	0.676247i
$903$	−12.8089	−	24.2063i	−0.426253	−	0.805534i
$904$	4.31506	+	1.83876i	0.143517	+	0.0611561i
$905$	−17.4805	−	17.4805i	−0.581071	−	0.581071i
$906$	3.80115	+	14.3800i	0.126285	+	0.477745i
$907$	−12.0495	−	29.0900i	−0.400096	−	0.965918i	−0.987642	−	0.156727i	$-0.949906\pi$
$907$	−12.0495	−	29.0900i	−0.400096	−	0.965918i	0.587546	−	0.809191i	$-0.300094\pi$
$908$	−30.7998	−	23.9655i	−1.02213	−	0.795324i
$909$	2.48907	+	1.03101i	0.0825574	+	0.0341964i
$910$	3.34440	+	9.09351i	0.110866	+	0.301447i
$911$	−43.7738			−1.45029			−0.725146	−	0.688596i	$-0.758228\pi$
$911$	−43.7738			−1.45029			−0.725146	+	0.688596i	$0.758228\pi$
$912$	−8.05970	+	2.04339i	−0.266883	+	0.0676634i
$913$	59.9995			1.98569
$914$	−10.8958	+	8.30236i	−0.360401	+	0.274618i
$915$	−1.26801	+	3.06126i	−0.0419193	+	0.101202i
$916$	−28.2828	+	3.52946i	−0.934491	+	0.116617i
$917$	−32.0806	+	3.02450i	−1.05940	+	0.0998777i
$918$	−6.58024	+	1.73939i	−0.217180	+	0.0574084i
$919$	−18.8850	+	18.8850i	−0.622960	+	0.622960i	−0.946287	−	0.323327i	$-0.895199\pi$
$919$	−18.8850	+	18.8850i	−0.622960	+	0.622960i	0.323327	+	0.946287i	$0.395199\pi$
$920$	20.4077	+	20.8252i	0.672821	+	0.686585i
$921$	−17.5151	+	17.5151i	−0.577142	+	0.577142i
$922$	−29.0975	+	50.0078i	−0.958275	+	1.64692i
$923$	−1.23172	−	2.97364i	−0.0405426	−	0.0978784i
$924$	6.18021	+	27.8792i	0.203314	+	0.917159i
$925$	−2.33845	−	0.968619i	−0.0768879	−	0.0318480i
$926$	2.15651	−	15.9638i	0.0708674	−	0.524604i
$927$	8.00253			0.262837
$928$	12.4357	−	6.90266i	0.408223	−	0.226591i
$929$			26.5571i			0.871309i	0.900114	+	0.435654i	$0.143483\pi$
$929$			26.5571i			0.871309i	−0.900114	+	0.435654i	$0.856517\pi$
$930$	−2.02137	+	14.9634i	−0.0662833	+	0.490670i
$931$	7.98266	+	12.1656i	0.261621	+	0.398710i
$932$	26.2161	+	46.1238i	0.858736	+	1.51083i
$933$	−9.04786	−	21.8435i	−0.296214	−	0.715123i
$934$	41.4851	+	24.1385i	1.35743	+	0.789835i
$935$	28.5171	+	28.5171i	0.932610	+	0.932610i
$936$	−4.71660	−	0.0477556i	−0.154167	−	0.00156094i
$937$	−22.8688	+	22.8688i	−0.747092	+	0.747092i	−0.973932	−	0.226840i	$-0.927160\pi$
$937$	−22.8688	+	22.8688i	−0.747092	+	0.747092i	0.226840	+	0.973932i	$0.427160\pi$
$938$	14.0769	+	0.567246i	0.459627	+	0.0185212i
$939$	5.35670	+	12.9322i	0.174809	+	0.422027i
$940$	2.47395	+	19.8246i	0.0806914	+	0.646608i
$941$	32.8250	+	13.5966i	1.07006	+	0.443235i	0.847013	−	0.531572i	$-0.178398\pi$
$941$	32.8250	+	13.5966i	1.07006	+	0.443235i	0.223051	+	0.974807i	$0.428398\pi$
$942$	3.32050	+	4.35774i	0.108188	+	0.141983i
$943$		−	20.4404i		−	0.665631i
$944$	5.52170	−	37.9730i	0.179716	−	1.23592i
$945$	−3.92635	−	1.20897i	−0.127724	−	0.0393277i
$946$	−47.8794	−	62.8356i	−1.55669	−	2.04296i
$947$	6.99318	+	2.89667i	0.227248	+	0.0941291i	0.493402	−	0.869801i	$-0.335753\pi$
$947$	6.99318	+	2.89667i	0.227248	+	0.0941291i	−0.266154	+	0.963930i	$0.585753\pi$
$948$	−1.09290	−	0.850397i	−0.0354959	−	0.0276196i
$949$	−23.2521	+	9.63132i	−0.754794	+	0.312646i
$950$	7.35779	−	1.94492i	0.238718	−	0.0631017i
$951$	−10.2127	−	10.2127i	−0.331170	−	0.331170i
$952$	3.01726	+	35.8887i	0.0977899	+	1.16316i
$953$	−10.2438	+	10.2438i	−0.331830	+	0.331830i	−0.853281	−	0.521451i	$-0.825391\pi$
$953$	−10.2438	+	10.2438i	−0.331830	+	0.331830i	0.521451	+	0.853281i	$0.325391\pi$
$954$	1.07107	−	1.84077i	0.0346771	−	0.0595971i
$955$	0.277130	+	0.669051i	0.00896772	+	0.0216500i
$956$	−4.73954	−	1.30431i	−0.153288	−	0.0421843i
$957$	5.19248	−	12.5358i	0.167849	−	0.405224i
$958$	5.10343	−	37.7787i	0.164884	−	1.22057i
$959$	−0.302055	−	0.0930063i	−0.00975388	−	0.00300333i
$960$	−8.60418	−	8.95989i	−0.277699	−	0.289179i
$961$	16.2788			0.525122
$962$	2.28505	+	0.308681i	0.0736729	+	0.00995229i
$963$	2.88378	−	6.96207i	0.0929286	−	0.224350i
$964$	4.07297	+	1.12087i	0.131181	+	0.0361007i
$965$	15.4689	−	6.40743i	0.497962	−	0.206263i
$966$	16.8434	+	18.2579i	0.541928	+	0.587437i
$967$	37.8233	+	37.8233i	1.21631	+	1.21631i	0.968913	+	0.247401i	$0.0795765\pi$
$967$	37.8233	+	37.8233i	1.21631	+	1.21631i	0.247401	+	0.968913i	$0.420424\pi$
$968$	19.1358	+	47.5541i	0.615048	+	1.52845i
$969$	−7.07399	+	7.07399i	−0.227249	+	0.227249i
$970$	−24.4944	+	6.47474i	−0.786469	+	0.207891i
$971$	−41.0265	+	16.9938i	−1.31660	+	0.545355i	−0.926805	−	0.375544i	$-0.877456\pi$
$971$	−41.0265	+	16.9938i	−1.31660	+	0.545355i	−0.389800	+	0.920900i	$0.627456\pi$
$972$	1.22820	−	1.57845i	0.0393947	−	0.0506289i
$973$	−10.0382	+	12.1279i	−0.321809	+	0.388804i
$974$	−2.94430	+	2.24349i	−0.0943414	+	0.0718862i
$975$	4.31736			0.138266
$976$	−6.84129	+	5.10427i	−0.218984	+	0.163384i
$977$		−	16.8550i		−	0.539239i	−0.962967	−	0.269619i	$-0.913102\pi$
$977$		−	16.8550i		−	0.539239i	0.962967	−	0.269619i	$-0.0868979\pi$
$978$	−14.6223	−	19.1899i	−0.467569	−	0.613625i
$979$	16.7569	−	40.4548i	0.535553	−	1.29294i
$980$	−9.90815	+	19.3496i	−0.316504	+	0.618101i
$981$	17.3659	−	7.19317i	0.554449	−	0.229660i
$982$	43.8854	−	11.6005i	1.40044	−	0.370185i
$983$	−3.99215	−	3.99215i	−0.127330	−	0.127330i	0.640570	−	0.767900i	$-0.278698\pi$
$983$	−3.99215	−	3.99215i	−0.127330	−	0.127330i	−0.767900	+	0.640570i	$0.778698\pi$
$984$	−0.0881682	+	8.70796i	−0.00281070	+	0.277600i
$985$	−12.9886	−	12.9886i	−0.413850	−	0.413850i
$986$	8.60643	−	14.7913i	0.274085	−	0.471050i
$987$	1.59757	+	16.9453i	0.0508511	+	0.539374i
$988$	−6.02744	+	3.42591i	−0.191758	+	0.108993i
$989$	−63.4886	−	26.2979i	−2.01882	−	0.836223i
$990$	−11.7440	−	1.58647i	−0.373249	−	0.0504212i
$991$		−	7.27399i		−	0.231066i	−0.993304	−	0.115533i	$-0.963142\pi$
$991$		−	7.27399i		−	0.231066i	0.993304	−	0.115533i	$-0.0368576\pi$
$992$	−24.1959	+	30.4546i	−0.768220	+	0.966933i
$993$		−	11.0736i		−	0.351409i
$994$	3.02996	−	6.55516i	0.0961044	−	0.207917i
$995$	−4.43784	+	10.7139i	−0.140689	+	0.339653i
$996$	−19.3317	+	10.9878i	−0.612547	+	0.348163i
$997$	9.57450	−	3.96589i	0.303228	−	0.125601i	−0.225882	−	0.974155i	$-0.572526\pi$
$997$	9.57450	−	3.96589i	0.303228	−	0.125601i	0.529109	+	0.848554i	$0.322526\pi$
$998$	−15.1792	+	26.0874i	−0.480488	+	0.825782i
$999$	−0.691331	+	0.691331i	−0.0218728	+	0.0218728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bu.a.643.30	yes	256
7.6	odd	2	inner	672.2.bu.a.643.29	yes	256
32.11	odd	8	inner	672.2.bu.a.139.29	✓	256
224.139	even	8	inner	672.2.bu.a.139.30	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bu.a.139.29	✓	256	32.11	odd	8	inner
672.2.bu.a.139.30	yes	256	224.139	even	8	inner
672.2.bu.a.643.29	yes	256	7.6	odd	2	inner
672.2.bu.a.643.30	yes	256	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bu (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.189323 + 1.40148i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-1.92831 - 0.530666i) q^{4} +(1.43458 - 0.594222i) q^{5} +(-0.711236 + 1.22235i) q^{6} +(-2.33853 + 1.23745i) q^{7} +(1.10879 - 2.60203i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.189323 + 1.40148i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-1.92831 - 0.530666i) q^{4} +(1.43458 - 0.594222i) q^{5} +(-0.711236 + 1.22235i) q^{6} +(-2.33853 + 1.23745i) q^{7} +(1.10879 - 2.60203i) q^{8} +(0.707107 + 0.707107i) q^{9} +(0.561194 + 2.12304i) q^{10} +(2.06518 + 4.98579i) q^{11} +(-1.57845 - 1.22820i) q^{12} +(-1.54071 - 0.638184i) q^{13} +(-1.29152 - 3.51169i) q^{14} +1.55278 q^{15} +(3.43679 + 2.04658i) q^{16} +4.81274 q^{17} +(-1.12487 + 0.857127i) q^{18} +(-0.795475 + 1.92045i) q^{19} +(-3.08165 + 0.384565i) q^{20} +(-2.63407 + 0.248335i) q^{21} +(-7.37849 + 1.95040i) q^{22} +(-4.69441 + 4.69441i) q^{23} +(2.02015 - 1.97965i) q^{24} +(-1.83061 + 1.83061i) q^{25} +(1.18610 - 2.03846i) q^{26} +(0.382683 + 0.923880i) q^{27} +(5.16609 - 1.14521i) q^{28} +(-2.32291 - 0.962180i) q^{29} +(-0.293976 + 2.17619i) q^{30} +6.87596 q^{31} +(-3.51891 + 4.42914i) q^{32} +5.39658i q^{33} +(-0.911162 + 6.74498i) q^{34} +(-2.61949 + 3.16482i) q^{35} +(-0.988286 - 1.73876i) q^{36} +(0.374146 + 0.903268i) q^{37} +(-2.54087 - 1.47843i) q^{38} +(-1.17921 - 1.17921i) q^{39} +(0.0444660 - 4.39169i) q^{40} +(-2.17710 + 2.17710i) q^{41} +(0.150652 - 3.73862i) q^{42} +(3.96118 + 9.56313i) q^{43} +(-1.33653 - 10.7101i) q^{44} +(1.43458 + 0.594222i) q^{45} +(-5.69038 - 7.46790i) q^{46} -6.43312i q^{47} +(2.39199 + 3.20600i) q^{48} +(3.93745 - 5.78761i) q^{49} +(-2.21900 - 2.91215i) q^{50} +(4.44639 + 1.84176i) q^{51} +(2.63231 + 2.04822i) q^{52} +(-1.39129 + 0.576292i) q^{53} +(-1.36725 + 0.361413i) q^{54} +(5.92534 + 5.92534i) q^{55} +(0.626931 + 7.45701i) q^{56} +(-1.46985 + 1.46985i) q^{57} +(1.78826 - 3.07336i) q^{58} +(-3.67112 - 8.86286i) q^{59} +(-2.99424 - 0.824006i) q^{60} +(-0.816610 + 1.97147i) q^{61} +(-1.30178 + 9.63654i) q^{62} +(-2.52860 - 0.778584i) q^{63} +(-5.54115 - 5.77023i) q^{64} -2.58950 q^{65} +(-7.56322 - 1.02170i) q^{66} +(-1.44090 + 3.47865i) q^{67} +(-9.28048 - 2.55396i) q^{68} +(-6.13354 + 2.54060i) q^{69} +(-3.93952 - 4.27035i) q^{70} +(1.36474 + 1.36474i) q^{71} +(2.62395 - 1.05588i) q^{72} +(10.6715 - 10.6715i) q^{73} +(-1.33675 + 0.353350i) q^{74} +(-2.39181 + 0.990722i) q^{75} +(2.55304 - 3.28109i) q^{76} +(-10.9991 - 9.10387i) q^{77} +(1.87590 - 1.42939i) q^{78} +0.692390 q^{79} +(6.14647 + 0.893766i) q^{80} +1.00000i q^{81} +(-2.63900 - 3.46335i) q^{82} +(4.25470 - 10.2718i) q^{83} +(5.21110 + 0.918944i) q^{84} +(6.90426 - 2.85984i) q^{85} +(-14.1525 + 3.74101i) q^{86} +(-1.77788 - 1.77788i) q^{87} +(15.2631 + 0.154539i) q^{88} +(-5.73747 - 5.73747i) q^{89} +(-1.10439 + 1.89804i) q^{90} +(4.39272 - 0.414137i) q^{91} +(11.5435 - 6.56113i) q^{92} +(6.35256 + 2.63131i) q^{93} +(9.01591 + 1.21794i) q^{94} +3.22772i q^{95} +(-4.94601 + 2.74536i) q^{96} +11.5374i q^{97} +(7.36580 + 6.61400i) q^{98} +(-2.06518 + 4.98579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q+O(q^{10}) \) 256 * q	\( 256 q + 32 q^{14} - 8 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{23} + 40 q^{28} - 48 q^{35} + 16 q^{43} - 8 q^{44} - 48 q^{50} - 32 q^{53} + 64 q^{58} + 48 q^{60} - 144 q^{64} + 16 q^{67} + 72 q^{70} - 128 q^{71} + 232 q^{74} - 48 q^{78} + 176 q^{88} + 48 q^{91} - 152 q^{92} - 32 q^{98}+O(q^{100}) \) 256 * q + 32 * q^14 - 8 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^23 + 40 * q^28 - 48 * q^35 + 16 * q^43 - 8 * q^44 - 48 * q^50 - 32 * q^53 + 64 * q^58 + 48 * q^60 - 144 * q^64 + 16 * q^67 + 72 * q^70 - 128 * q^71 + 232 * q^74 - 48 * q^78 + 176 * q^88 + 48 * q^91 - 152 * q^92 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more