LMFDB - Embedded newform 483.2.r.a.34.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			34.6
Character	$\chi$	$=$	483.34
Dual form			483.2.r.a.412.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85697 + 1.19340i) q^{2} +(0.989821 + 0.142315i) q^{3} +(1.19330 - 2.61296i) q^{4} +(-1.10668 + 0.324952i) q^{5} +(-2.00791 + 0.916981i) q^{6} +(1.07924 + 2.41562i) q^{7} +(0.274107 + 1.90645i) q^{8} +(0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-1.85697 + 1.19340i) q^{2} +(0.989821 + 0.142315i) q^{3} +(1.19330 - 2.61296i) q^{4} +(-1.10668 + 0.324952i) q^{5} +(-2.00791 + 0.916981i) q^{6} +(1.07924 + 2.41562i) q^{7} +(0.274107 + 1.90645i) q^{8} +(0.959493 + 0.281733i) q^{9} +(1.66728 - 1.92415i) q^{10} +(-0.0983116 + 0.152976i) q^{11} +(1.55302 - 2.41654i) q^{12} +(3.11702 + 2.70091i) q^{13} +(-4.88694 - 3.19777i) q^{14} +(-1.14167 + 0.164147i) q^{15} +(0.978068 + 1.12875i) q^{16} +(-2.24519 - 4.91628i) q^{17} +(-2.11797 + 0.621892i) q^{18} +(-0.214571 + 0.469846i) q^{19} +(-0.471520 + 3.27949i) q^{20} +(0.724480 + 2.54463i) q^{21} -0.401397i q^{22} +(0.108391 + 4.79461i) q^{23} +1.92606i q^{24} +(-3.08711 + 1.98397i) q^{25} +(-9.01148 - 1.29566i) q^{26} +(0.909632 + 0.415415i) q^{27} +(7.59980 + 0.0625383i) q^{28} +(3.47274 + 7.60424i) q^{29} +(1.92415 - 1.66728i) q^{30} +(3.48170 - 0.500593i) q^{31} +(-6.85938 - 2.01409i) q^{32} +(-0.119082 + 0.137428i) q^{33} +(10.0364 + 6.44997i) q^{34} +(-1.97934 - 2.32263i) q^{35} +(1.88112 - 2.17093i) q^{36} +(-0.139133 + 0.473843i) q^{37} +(-0.162263 - 1.12856i) q^{38} +(2.70091 + 3.11702i) q^{39} +(-0.922855 - 2.02077i) q^{40} +(2.65953 + 9.05751i) q^{41} +(-4.38210 - 3.86070i) q^{42} +(-9.24311 - 1.32896i) q^{43} +(0.282405 + 0.439431i) q^{44} -1.15341 q^{45} +(-5.92318 - 8.77409i) q^{46} -3.91037i q^{47} +(0.807475 + 1.25646i) q^{48} +(-4.67046 + 5.21409i) q^{49} +(3.36500 - 7.36833i) q^{50} +(-1.52268 - 5.18576i) q^{51} +(10.7769 - 4.92166i) q^{52} +(-5.66877 + 4.91202i) q^{53} +(-2.18492 + 0.314144i) q^{54} +(0.0590902 - 0.201243i) q^{55} +(-4.30944 + 2.71967i) q^{56} +(-0.279254 + 0.434527i) q^{57} +(-15.5237 - 9.97647i) q^{58} +(3.29542 + 2.85550i) q^{59} +(-0.933441 + 3.17901i) q^{60} +(-0.757513 - 5.26862i) q^{61} +(-5.86801 + 5.08466i) q^{62} +(0.354968 + 2.62183i) q^{63} +(12.2752 - 3.60432i) q^{64} +(-4.32722 - 1.97618i) q^{65} +(0.0571248 - 0.397312i) q^{66} +(-1.30491 - 2.03047i) q^{67} -15.5253 q^{68} +(-0.575056 + 4.76123i) q^{69} +(6.44742 + 1.95090i) q^{70} +(-7.91478 + 5.08652i) q^{71} +(-0.274107 + 1.90645i) q^{72} +(-5.88839 - 2.68914i) q^{73} +(-0.307120 - 1.04595i) q^{74} +(-3.33804 + 1.52443i) q^{75} +(0.971643 + 1.12134i) q^{76} +(-0.475634 - 0.0723855i) q^{77} +(-8.73537 - 2.56494i) q^{78} +(2.99150 + 2.59215i) q^{79} +(-1.44920 - 0.931346i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-15.7479 - 13.6456i) q^{82} +(8.62357 + 2.53211i) q^{83} +(7.51354 + 1.14347i) q^{84} +(4.08227 + 4.71119i) q^{85} +(18.7502 - 8.56291i) q^{86} +(2.35520 + 8.02106i) q^{87} +(-0.318589 - 0.145495i) q^{88} +(2.58811 - 18.0007i) q^{89} +(2.14184 - 1.37648i) q^{90} +(-3.16036 + 10.4445i) q^{91} +(12.6575 + 5.43819i) q^{92} +3.51751 q^{93} +(4.66665 + 7.26145i) q^{94} +(0.0847856 - 0.589697i) q^{95} +(-6.50292 - 2.96978i) q^{96} +(6.91043 - 2.02908i) q^{97} +(2.45041 - 15.2562i) q^{98} +(-0.137428 + 0.119082i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	−1.85697	+	1.19340i	−1.31308	+	0.843863i	−0.994571	−	0.104058i	$-0.966817\pi$
$2$	−1.85697	+	1.19340i	−1.31308	+	0.843863i	−0.318506	+	0.947921i	$0.603181\pi$
$3$	0.989821	+	0.142315i	0.571474	+	0.0821655i
$3$	0.989821	+	0.142315i	0.571474	+	0.0821655i
$4$	1.19330	−	2.61296i	0.596650	−	1.30648i
$5$	−1.10668	+	0.324952i	−0.494925	+	0.145323i	−0.519664	−	0.854371i	$-0.673943\pi$
$5$	−1.10668	+	0.324952i	−0.494925	+	0.145323i	0.0247390	+	0.999694i	$0.492125\pi$
$6$	−2.00791	+	0.916981i	−0.819725	+	0.374356i
$7$	1.07924	+	2.41562i	0.407916	+	0.913020i
$7$	1.07924	+	2.41562i	0.407916	+	0.913020i
$8$	0.274107	+	1.90645i	0.0969113	+	0.674033i
$9$	0.959493	+	0.281733i	0.319831	+	0.0939109i
$10$	1.66728	−	1.92415i	0.527241	−	0.608469i
$11$	−0.0983116	+	0.152976i	−0.0296421	+	0.0461240i	−0.855758	−	0.517376i	$-0.826909\pi$
$11$	−0.0983116	+	0.152976i	−0.0296421	+	0.0461240i	0.826116	+	0.563500i	$0.190545\pi$
$12$	1.55302	−	2.41654i	0.448318	−	0.697596i
$13$	3.11702	+	2.70091i	0.864505	+	0.749098i	0.969426	−	0.245383i	$-0.0789137\pi$
$13$	3.11702	+	2.70091i	0.864505	+	0.749098i	−0.104921	+	0.994481i	$0.533459\pi$
$14$	−4.88694	−	3.19777i	−1.30609	−	0.854639i
$15$	−1.14167	+	0.164147i	−0.294777	+	0.0423825i
$16$	0.978068	+	1.12875i	0.244517	+	0.282188i
$17$	−2.24519	−	4.91628i	−0.544539	−	1.19237i	−0.959286	−	0.282437i	$-0.908857\pi$
$17$	−2.24519	−	4.91628i	−0.544539	−	1.19237i	0.414747	−	0.909937i	$-0.363870\pi$
$18$	−2.11797	+	0.621892i	−0.499211	+	0.146581i
$19$	−0.214571	+	0.469846i	−0.0492261	+	0.107790i	−0.932647	−	0.360790i	$-0.882507\pi$
$19$	−0.214571	+	0.469846i	−0.0492261	+	0.107790i	0.883421	+	0.468580i	$0.155234\pi$
$20$	−0.471520	+	3.27949i	−0.105435	+	0.733317i
$21$	0.724480	+	2.54463i	0.158094	+	0.555283i
$22$		−	0.401397i		−	0.0855782i
$23$	0.108391	+	4.79461i	0.0226012	+	0.999745i
$23$	0.108391	+	4.79461i	0.0226012	+	0.999745i
$24$			1.92606i			0.393155i
$25$	−3.08711	+	1.98397i	−0.617422	+	0.396793i
$26$	−9.01148	−	1.29566i	−1.76730	−	0.254099i
$27$	0.909632	+	0.415415i	0.175059	+	0.0799467i
$28$	7.59980	+	0.0625383i	1.43623	+	0.0118186i
$29$	3.47274	+	7.60424i	0.644872	+	1.41207i	0.895972	+	0.444111i	$0.146480\pi$
$29$	3.47274	+	7.60424i	0.644872	+	1.41207i	−0.251100	+	0.967961i	$0.580792\pi$
$30$	1.92415	−	1.66728i	0.351300	−	0.304403i
$31$	3.48170	−	0.500593i	0.625333	−	0.0899092i	0.177638	−	0.984096i	$-0.443154\pi$
$31$	3.48170	−	0.500593i	0.625333	−	0.0899092i	0.447694	+	0.894187i	$0.352245\pi$
$32$	−6.85938	−	2.01409i	−1.21258	−	0.356045i
$33$	−0.119082	+	0.137428i	−0.0207295	+	0.0239231i
$34$	10.0364	+	6.44997i	1.72122	+	1.10616i
$35$	−1.97934	−	2.32263i	−0.334570	−	0.392596i
$36$	1.88112	−	2.17093i	0.313520	−	0.361822i
$37$	−0.139133	+	0.473843i	−0.0228733	+	0.0778992i	−0.970139	−	0.242551i	$-0.922016\pi$
$37$	−0.139133	+	0.473843i	−0.0228733	+	0.0778992i	0.947265	+	0.320450i	$0.103834\pi$
$38$	−0.162263	−	1.12856i	−0.0263225	−	0.183077i
$39$	2.70091	+	3.11702i	0.432492	+	0.499122i
$40$	−0.922855	−	2.02077i	−0.145916	−	0.319512i
$41$	2.65953	+	9.05751i	0.415348	+	1.41455i	0.856050	+	0.516892i	$0.172911\pi$
$41$	2.65953	+	9.05751i	0.415348	+	1.41455i	−0.440702	+	0.897653i	$0.645271\pi$
$42$	−4.38210	−	3.86070i	−0.676173	−	0.595719i
$43$	−9.24311	−	1.32896i	−1.40956	−	0.202664i	−0.604854	−	0.796337i	$-0.706768\pi$
$43$	−9.24311	−	1.32896i	−1.40956	−	0.202664i	−0.804707	+	0.593672i	$0.797678\pi$
$44$	0.282405	+	0.439431i	0.0425742	+	0.0662467i
$45$	−1.15341			−0.171940
$46$	−5.92318	−	8.77409i	−0.873325	−	1.29367i
$47$		−	3.91037i		−	0.570387i	−0.958470	−	0.285193i	$-0.907942\pi$
$47$		−	3.91037i		−	0.570387i	0.958470	−	0.285193i	$-0.0920578\pi$
$48$	0.807475	+	1.25646i	0.116549	+	0.181354i
$49$	−4.67046	+	5.21409i	−0.667209	+	0.744870i
$50$	3.36500	−	7.36833i	0.475883	−	1.04204i
$51$	−1.52268	−	5.18576i	−0.213218	−	0.726152i
$52$	10.7769	−	4.92166i	1.49449	−	0.682511i
$53$	−5.66877	+	4.91202i	−0.778665	+	0.674717i	−0.950609	−	0.310389i	$-0.899541\pi$
$53$	−5.66877	+	4.91202i	−0.778665	+	0.674717i	0.171944	+	0.985107i	$0.444995\pi$
$54$	−2.18492	+	0.314144i	−0.297330	+	0.0427495i
$55$	0.0590902	−	0.201243i	0.00796772	−	0.0271356i
$56$	−4.30944	+	2.71967i	−0.575874	+	0.363431i
$57$	−0.279254	+	0.434527i	−0.0369880	+	0.0575545i
$58$	−15.5237	−	9.97647i	−2.03836	−	1.30998i
$59$	3.29542	+	2.85550i	0.429028	+	0.371755i	0.842441	−	0.538789i	$-0.181118\pi$
$59$	3.29542	+	2.85550i	0.429028	+	0.371755i	−0.413413	+	0.910544i	$0.635663\pi$
$60$	−0.933441	+	3.17901i	−0.120507	+	0.410408i
$61$	−0.757513	−	5.26862i	−0.0969896	−	0.674578i	−0.979077	−	0.203491i	$-0.934771\pi$
$61$	−0.757513	−	5.26862i	−0.0969896	−	0.674578i	0.882087	−	0.471086i	$-0.156138\pi$
$62$	−5.86801	+	5.08466i	−0.745239	+	0.645753i
$63$	0.354968	+	2.62183i	0.0447217	+	0.330320i
$64$	12.2752	−	3.60432i	1.53440	−	0.450540i
$65$	−4.32722	−	1.97618i	−0.536726	−	0.245114i
$66$	0.0571248	−	0.397312i	0.00703157	−	0.0489057i
$67$	−1.30491	−	2.03047i	−0.159420	−	0.248062i	0.752350	−	0.658763i	$-0.228920\pi$
$67$	−1.30491	−	2.03047i	−0.159420	−	0.248062i	−0.911770	+	0.410702i	$0.865284\pi$
$68$	−15.5253			−1.88271
$69$	−0.575056	+	4.76123i	−0.0692286	+	0.573185i
$70$	6.44742	+	1.95090i	0.770614	+	0.233177i
$71$	−7.91478	+	5.08652i	−0.939311	+	0.603659i	−0.918199	−	0.396118i	$-0.870357\pi$
$71$	−7.91478	+	5.08652i	−0.939311	+	0.603659i	−0.0211119	+	0.999777i	$0.506721\pi$
$72$	−0.274107	+	1.90645i	−0.0323038	+	0.224678i
$73$	−5.88839	−	2.68914i	−0.689184	−	0.314740i	0.0398614	−	0.999205i	$-0.487308\pi$
$73$	−5.88839	−	2.68914i	−0.689184	−	0.314740i	−0.729045	+	0.684466i	$0.760036\pi$
$74$	−0.307120	−	1.04595i	−0.0357019	−	0.121590i
$75$	−3.33804	+	1.52443i	−0.385443	+	0.176026i
$76$	0.971643	+	1.12134i	0.111455	+	0.128626i
$77$	−0.475634	−	0.0723855i	−0.0542036	−	0.00824909i
$78$	−8.73537	−	2.56494i	−0.989086	−	0.290422i
$79$	2.99150	+	2.59215i	0.336570	+	0.291640i	0.806704	−	0.590955i	$-0.201249\pi$
$79$	2.99150	+	2.59215i	0.336570	+	0.291640i	−0.470134	+	0.882595i	$0.655795\pi$
$80$	−1.44920	−	0.931346i	−0.162026	−	0.104128i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−15.7479	−	13.6456i	−1.73907	−	1.50691i
$83$	8.62357	+	2.53211i	0.946560	+	0.277935i	0.718354	−	0.695678i	$-0.244896\pi$
$83$	8.62357	+	2.53211i	0.946560	+	0.277935i	0.228206	+	0.973613i	$0.426714\pi$
$84$	7.51354	+	1.14347i	0.819795	+	0.124762i
$85$	4.08227	+	4.71119i	0.442785	+	0.511001i
$86$	18.7502	−	8.56291i	2.02188	−	0.923363i
$87$	2.35520	+	8.02106i	0.252504	+	0.859948i
$88$	−0.318589	−	0.145495i	−0.0339617	−	0.0155098i
$89$	2.58811	−	18.0007i	0.274339	−	1.90807i	−0.126575	−	0.991957i	$-0.540398\pi$
$89$	2.58811	−	18.0007i	0.274339	−	1.90807i	0.400914	−	0.916116i	$-0.368693\pi$
$90$	2.14184	−	1.37648i	0.225770	−	0.145094i
$91$	−3.16036	+	10.4445i	−0.331296	+	1.09488i
$92$	12.6575	+	5.43819i	1.31963	+	0.566970i
$93$	3.51751			0.364749
$94$	4.66665	+	7.26145i	0.481328	+	0.748961i
$95$	0.0847856	−	0.589697i	0.00869882	−	0.0605016i
$96$	−6.50292	−	2.96978i	−0.663702	−	0.303102i
$97$	6.91043	−	2.02908i	0.701648	−	0.206022i	0.0885988	−	0.996067i	$-0.471761\pi$
$97$	6.91043	−	2.02908i	0.701648	−	0.206022i	0.613049	+	0.790045i	$0.289943\pi$
$98$	2.45041	−	15.2562i	0.247528	−	1.54111i
$99$	−0.137428	+	0.119082i	−0.0138120	+	0.0119682i
$100$	1.50018	+	10.4340i	0.150018	+	1.04340i
$101$	−1.51269	+	5.15175i	−0.150518	+	0.512618i	−0.999885	−	0.0151854i	$-0.995166\pi$
$101$	−1.51269	+	5.15175i	−0.150518	+	0.512618i	0.849366	+	0.527804i	$0.176984\pi$
$102$	9.01627	+	7.81265i	0.892744	+	0.773567i
$103$	4.97030	+	3.19422i	0.489738	+	0.314735i	0.762100	−	0.647459i	$-0.224168\pi$
$103$	4.97030	+	3.19422i	0.489738	+	0.314735i	−0.272362	+	0.962195i	$0.587805\pi$
$104$	−4.29476	+	6.68278i	−0.421136	+	0.655301i
$105$	−1.62865	−	2.58068i	−0.158940	−	0.251849i
$106$	4.66472	−	15.8866i	0.453078	−	1.54304i
$107$	12.2353	−	1.75917i	1.18283	−	0.170066i	0.477299	−	0.878741i	$-0.341616\pi$
$107$	12.2353	−	1.75917i	1.18283	−	0.170066i	0.705535	+	0.708675i	$0.250707\pi$
$108$	2.17093	−	1.88112i	0.208898	−	0.181011i
$109$	18.3624	−	8.38584i	1.75880	−	0.803217i	0.773193	−	0.634171i	$-0.218659\pi$
$109$	18.3624	−	8.38584i	1.75880	−	0.803217i	0.985608	−	0.169046i	$-0.0540687\pi$
$110$	0.130435	+	0.444220i	0.0124365	+	0.0423547i
$111$	−0.205151	+	0.449219i	−0.0194721	+	0.0426380i
$112$	−1.67106	+	3.58084i	−0.157900	+	0.338358i
$113$	6.35765	+	9.89269i	0.598077	+	0.930626i	0.999889	+	0.0149039i	$0.00474424\pi$
$113$	6.35765	+	9.89269i	0.598077	+	0.930626i	−0.401812	+	0.915722i	$0.631619\pi$
$114$		−	1.14017i		−	0.106786i
$115$	−1.67797	−	5.27090i	−0.156472	−	0.491514i
$116$	24.0136			2.22961
$117$	2.22982	+	3.46967i	0.206147	+	0.320771i
$118$	−9.52727	−	1.36981i	−0.877056	−	0.126102i
$119$	9.45277	−	10.7294i	0.866534	−	0.983562i
$120$	−0.625876	−	2.13154i	−0.0571344	−	0.194582i
$121$	4.55583	+	9.97587i	0.414166	+	0.906898i
$122$	7.69427	+	8.87966i	0.696606	+	0.803926i
$123$	1.34344	+	9.34381i	0.121134	+	0.842503i
$124$	2.84669	−	9.69493i	0.255640	−	0.870630i
$125$	6.54837	−	7.55722i	0.585704	−	0.675938i
$126$	−3.78806	−	4.44504i	−0.337468	−	0.395996i
$127$	−6.94984	−	4.46639i	−0.616699	−	0.396328i	0.194665	−	0.980870i	$-0.437638\pi$
$127$	−6.94984	−	4.46639i	−0.616699	−	0.396328i	−0.811364	+	0.584541i	$0.801274\pi$
$128$	−9.13011	+	10.5367i	−0.806995	+	0.931322i
$129$	−8.95989	−	2.63086i	−0.788875	−	0.231635i
$130$	10.3939	−	1.49442i	0.911605	−	0.131069i
$131$	6.70266	−	5.80789i	0.585614	−	0.507438i	−0.310906	−	0.950441i	$-0.600632\pi$
$131$	6.70266	−	5.80789i	0.585614	−	0.507438i	0.896520	+	0.443003i	$0.146087\pi$
$132$	0.216993	+	0.475149i	0.0188868	+	0.0413564i
$133$	−1.36655	−	0.0112452i	−0.118495	−	0.000975085i
$134$	4.84634	+	2.21325i	0.418660	+	0.191196i
$135$	−1.14167	−	0.164147i	−0.0982590	−	0.0141275i
$136$	8.75724	−	5.62793i	0.750927	−	0.482591i
$137$		−	3.32339i		−	0.283936i	−0.989871	−	0.141968i	$-0.954657\pi$
$137$		−	3.32339i		−	0.283936i	0.989871	−	0.141968i	$-0.0453431\pi$
$138$	−4.61420	−	9.52774i	−0.392787	−	0.811055i
$139$		−	10.6931i		−	0.906976i	−0.891262	−	0.453488i	$-0.850180\pi$
$139$		−	10.6931i		−	0.906976i	0.891262	−	0.453488i	$-0.149820\pi$
$140$	−8.43091	+	2.40036i	−0.712542	+	0.202867i
$141$	0.556504	−	3.87057i	0.0468661	−	0.325961i
$142$	8.62725	−	18.8910i	0.723983	−	1.58530i
$143$	−0.719613	+	0.211297i	−0.0601771	+	0.0176696i
$144$	0.620444	+	1.35858i	0.0517036	+	0.113215i
$145$	−6.31424	−	7.28702i	−0.524369	−	0.605154i
$146$	14.1438	−	2.03357i	1.17055	−	0.168299i
$147$	−5.36497	+	4.49634i	−0.442495	+	0.370852i
$148$	1.07211	+	0.928986i	0.0881266	+	0.0763622i
$149$	−2.10182	+	3.27050i	−0.172188	+	0.267929i	−0.916612	−	0.399777i	$-0.869088\pi$
$149$	−2.10182	+	3.27050i	−0.172188	+	0.267929i	0.744425	+	0.667707i	$0.232724\pi$
$150$	4.37938	−	6.81444i	0.357575	−	0.556397i
$151$	13.1219	−	15.1434i	1.06784	−	1.23235i	0.0963332	−	0.995349i	$-0.469289\pi$
$151$	13.1219	−	15.1434i	1.06784	−	1.23235i	0.971508	−	0.237006i	$-0.0761660\pi$
$152$	−0.954555	−	0.280283i	−0.0774246	−	0.0227339i
$153$	−0.769168	−	5.34968i	−0.0621835	−	0.432496i
$154$	0.969624	−	0.433206i	0.0781345	−	0.0349087i
$155$	−3.69048	+	1.68539i	−0.296427	+	0.135373i
$156$	11.3677	−	3.33784i	0.910141	−	0.267241i
$157$	−1.32273	+	2.89637i	−0.105565	+	0.231156i	−0.955042	−	0.296470i	$-0.904190\pi$
$157$	−1.32273	+	2.89637i	−0.105565	+	0.231156i	0.849477	+	0.527626i	$0.176918\pi$
$158$	−8.64861	−	1.24348i	−0.688046	−	0.0989261i
$159$	−6.31012	+	4.05527i	−0.500425	+	0.321604i
$160$	8.24565			0.651876
$161$	−11.4650	+	5.43638i	−0.903567	+	0.428447i
$162$	−2.20739			−0.173429
$163$	−14.0629	+	9.03769i	−1.10149	+	0.707886i	−0.959423	−	0.281970i	$-0.909012\pi$
$163$	−14.0629	+	9.03769i	−1.10149	+	0.707886i	−0.142069	+	0.989857i	$0.545376\pi$
$164$	26.8406	+	3.85909i	2.09590	+	0.301344i
$165$	0.0871286	−	0.190785i	0.00678295	−	0.0148526i
$166$	−19.0355	+	5.58934i	−1.47744	+	0.433817i
$167$	13.0994	−	5.98228i	1.01366	−	0.462923i	0.161873	−	0.986812i	$-0.448247\pi$
$167$	13.0994	−	5.98228i	1.01366	−	0.462923i	0.851787	+	0.523889i	$0.175519\pi$
$168$	−4.65263	+	2.07869i	−0.358958	+	0.160374i
$169$	0.570783	+	3.96988i	0.0439064	+	0.305376i
$170$	−13.2030	−	3.87676i	−1.01263	−	0.297334i
$171$	−0.338251	+	0.390362i	−0.0258667	+	0.0298517i
$172$	−14.5023	+	22.5661i	−1.10579	+	1.72065i
$173$	−3.10099	+	4.82523i	−0.235764	+	0.366856i	−0.938895	−	0.344205i	$-0.888148\pi$
$173$	−3.10099	+	4.82523i	−0.235764	+	0.366856i	0.703131	+	0.711061i	$0.251785\pi$
$174$	−13.9459	−	12.0842i	−1.05724	−	0.916099i
$175$	−8.12426	−	5.31611i	−0.614136	−	0.401860i
$176$	−0.268827	+	0.0386515i	−0.0202636	+	0.00291347i
$177$	2.85550	+	3.29542i	0.214633	+	0.247699i
$178$	16.6761	+	36.5155i	1.24992	+	2.73695i
$179$	−9.02379	+	2.64962i	−0.674469	+	0.198042i	−0.600992	−	0.799255i	$-0.705228\pi$
$179$	−9.02379	+	2.64962i	−0.674469	+	0.198042i	−0.0734772	+	0.997297i	$0.523410\pi$
$180$	−1.37636	+	3.01381i	−0.102588	+	0.224636i
$181$	−0.948189	+	6.59480i	−0.0704783	+	0.490187i	0.923758	+	0.382977i	$0.125101\pi$
$181$	−0.948189	+	6.59480i	−0.0704783	+	0.490187i	−0.994236	+	0.107211i	$0.965808\pi$
$182$	−6.59577	−	23.1667i	−0.488911	−	1.71723i
$183$		−	5.32280i		−	0.393473i
$184$	−9.11098	+	1.52088i	−0.671670	+	0.112120i
$185$		−	0.569606i		−	0.0418783i
$186$	−6.53191	+	4.19780i	−0.478943	+	0.307798i
$187$	0.972801	+	0.139868i	0.0711382	+	0.0102281i
$188$	−10.2177	−	4.66625i	−0.745200	−	0.340321i
$189$	−0.0217710	+	2.64566i	−0.00158361	+	0.192444i
$190$	0.546302	+	1.19623i	0.0396329	+	0.0867839i
$191$	6.67328	−	5.78243i	0.482861	−	0.418402i	−0.379116	−	0.925349i	$-0.623772\pi$
$191$	6.67328	−	5.78243i	0.482861	−	0.418402i	0.861977	+	0.506948i	$0.169226\pi$
$192$	12.6632	−	1.82069i	0.913887	−	0.131397i
$193$	−11.9587	−	3.51141i	−0.860810	−	0.252756i	−0.178608	−	0.983920i	$-0.557159\pi$
$193$	−11.9587	−	3.51141i	−0.860810	−	0.252756i	−0.682202	+	0.731164i	$0.738977\pi$
$194$	−10.4109	+	12.0149i	−0.747462	+	0.862618i
$195$	−4.00194	−	2.57189i	−0.286585	−	0.184177i
$196$	8.05097	+	18.4257i	0.575069	+	1.31612i
$197$	13.4387	−	15.5091i	0.957471	−	1.10498i	−0.0369310	−	0.999318i	$-0.511758\pi$
$197$	13.4387	−	15.5091i	0.957471	−	1.10498i	0.994402	−	0.105663i	$-0.0336964\pi$
$198$	0.113087	−	0.385138i	0.00803672	−	0.0273706i
$199$	0.0332438	+	0.231215i	0.00235659	+	0.0163904i	0.990966	−	0.134115i	$-0.0428191\pi$
$199$	0.0332438	+	0.231215i	0.00235659	+	0.0163904i	−0.988609	+	0.150505i	$0.951910\pi$
$200$	−4.62853	−	5.34161i	−0.327287	−	0.377709i
$201$	−1.00266	−	2.19551i	−0.0707220	−	0.154859i
$202$	−3.33909	−	11.3719i	−0.234938	−	0.800124i
$203$	−14.6210	+	16.5957i	−1.02620	+	1.16479i
$204$	−15.3672	−	2.20947i	−1.07592	−	0.154694i
$205$	−5.88651	−	9.15959i	−0.411132	−	0.639734i
$206$	−13.0417			−0.908657
$207$	−1.24680	+	4.63093i	−0.0866583	+	0.321872i
$208$			6.16001i			0.427120i
$209$	−0.0507802	−	0.0790156i	−0.00351254	−	0.00546562i
$210$	6.10415	+	2.84861i	0.421226	+	0.196573i
$211$	4.33229	−	9.48639i	0.298247	−	0.653070i	−0.699879	−	0.714262i	$-0.746763\pi$
$211$	4.33229	−	9.48639i	0.298247	−	0.653070i	0.998126	+	0.0611914i	$0.0194900\pi$
$212$	6.07038	+	20.6738i	0.416915	+	1.41988i
$213$	−8.55810	+	3.90836i	−0.586392	+	0.267796i
$214$	−20.6212	+	17.8684i	−1.40964	+	1.22146i
$215$	10.6611	−	1.53283i	0.727078	−	0.104538i
$216$	−0.542633	+	1.84804i	−0.0369215	+	0.125743i
$217$	4.96685	+	7.87022i	0.337172	+	0.534265i
$218$	−24.0908	+	37.4860i	−1.63163	+	2.53887i
$219$	−5.44575	−	3.49977i	−0.367990	−	0.236493i
$220$	−0.455328	−	0.394544i	−0.0306982	−	0.0266001i
$221$	6.28014	−	21.3882i	0.422448	−	1.43873i
$222$	−0.155139	−	1.07901i	−0.0104122	−	0.0724187i
$223$	−13.8261	+	11.9804i	−0.925863	+	0.802265i	−0.980556	−	0.196238i	$-0.937127\pi$
$223$	−13.8261	+	11.9804i	−0.925863	+	0.802265i	0.0546933	+	0.998503i	$0.482582\pi$
$224$	−2.53765	−	18.7434i	−0.169554	−	1.25234i
$225$	−3.52101	+	1.03386i	−0.234734	+	0.0689241i
$226$	−23.6119	−	10.7832i	−1.57064	−	0.717288i
$227$	0.574083	−	3.99283i	0.0381032	−	0.265014i	−0.961860	−	0.273541i	$-0.911805\pi$
$227$	0.574083	−	3.99283i	0.0381032	−	0.265014i	0.999964	+	0.00852707i	$0.00271428\pi$
$228$	0.802170	+	1.24820i	0.0531250	+	0.0826641i
$229$	22.0179			1.45498			0.727491	−	0.686117i	$-0.240686\pi$
$229$	22.0179			1.45498			0.727491	+	0.686117i	$0.240686\pi$
$230$	9.40625	+	7.78541i	0.620230	+	0.513354i
$231$	−0.460491	−	0.139339i	−0.0302981	−	0.00916780i
$232$	−13.5452	+	8.70499i	−0.889288	+	0.571510i
$233$	−0.571226	+	3.97296i	−0.0374223	+	0.260277i	−0.999940	−	0.0109407i	$-0.996517\pi$
$233$	−0.571226	+	3.97296i	−0.0374223	+	0.260277i	0.962518	+	0.271218i	$0.0874265\pi$
$234$	−8.28143	−	3.78200i	−0.541374	−	0.247237i
$235$	1.27068	+	4.32755i	0.0828903	+	0.282298i
$236$	11.3938	−	5.20336i	0.741670	−	0.338710i
$237$	2.59215	+	2.99150i	0.168378	+	0.194319i
$238$	−4.74903	+	31.2051i	−0.307834	+	2.02273i
$239$	−12.2132	−	3.58612i	−0.790007	−	0.231967i	−0.138253	−	0.990397i	$-0.544149\pi$
$239$	−12.2132	−	3.58612i	−0.790007	−	0.231967i	−0.651755	+	0.758430i	$0.725967\pi$
$240$	−1.30191	−	1.12811i	−0.0840378	−	0.0728192i
$241$	17.0271	+	10.9426i	1.09681	+	0.704878i	0.958380	−	0.285495i	$-0.0921579\pi$
$241$	17.0271	+	10.9426i	1.09681	+	0.704878i	0.138431	+	0.990372i	$0.455794\pi$
$242$	−20.3653	−	13.0880i	−1.30913	−	0.841326i
$243$	0.755750	+	0.654861i	0.0484814	+	0.0420093i
$244$	−14.6707	−	4.30769i	−0.939193	−	0.275772i
$245$	3.47440	−	7.28803i	0.221971	−	0.465615i
$246$	−13.6456	−	15.7479i	−0.870015	−	1.00405i
$247$	−1.93783	+	0.884980i	−0.123301	+	0.0563099i
$248$	1.90872	+	6.50049i	0.121204	+	0.412781i
$249$	8.17544	+	3.73360i	0.518097	+	0.236607i
$250$	−3.14132	+	21.8484i	−0.198675	+	1.38181i
$251$	2.78381	−	1.78905i	0.175712	−	0.112924i	−0.449828	−	0.893115i	$-0.648515\pi$
$251$	2.78381	−	1.78905i	0.175712	−	0.112924i	0.625541	+	0.780192i	$0.284878\pi$
$252$	7.27433	+	2.20112i	0.458240	+	0.138657i
$253$	−0.744115	−	0.454784i	−0.0467821	−	0.0285920i
$254$	18.2359			1.14422
$255$	3.37025	+	5.24421i	0.211053	+	0.328405i
$256$	0.738429	−	5.13589i	0.0461518	−	0.320993i
$257$	−4.26711	−	1.94872i	−0.266175	−	0.121558i	0.277857	−	0.960622i	$-0.410376\pi$
$257$	−4.26711	−	1.94872i	−0.266175	−	0.121558i	−0.544032	+	0.839064i	$0.683103\pi$
$258$	19.7779	−	5.80733i	1.23132	−	0.361548i
$259$	−1.29478	+	0.175300i	−0.0804539	+	0.0108926i
$260$	−10.3274	+	8.94870i	−0.640475	+	0.554975i
$261$	1.18971	+	8.27460i	0.0736411	+	0.512185i
$262$	−5.51550	+	18.7841i	−0.340749	+	1.16048i
$263$	−9.47672	−	8.21162i	−0.584359	−	0.506350i	0.311761	−	0.950160i	$-0.399081\pi$
$263$	−9.47672	−	8.21162i	−0.584359	−	0.506350i	−0.896121	+	0.443810i	$0.853626\pi$
$264$	−0.294640	−	0.189354i	−0.0181339	−	0.0116539i
$265$	4.67737	−	7.27813i	0.287329	−	0.447092i
$266$	2.55106	−	1.60996i	0.156415	−	0.0987128i
$267$	5.12354	−	17.4492i	0.313556	−	1.06787i
$268$	−6.86270	+	0.986707i	−0.419206	+	0.0602727i
$269$	14.2497	−	12.3474i	0.868819	−	0.752836i	−0.101456	−	0.994840i	$-0.532350\pi$
$269$	14.2497	−	12.3474i	0.868819	−	0.752836i	0.970275	+	0.242004i	$0.0778047\pi$
$270$	2.31593	−	1.05765i	0.140943	−	0.0643666i
$271$	−8.86135	−	30.1790i	−0.538289	−	1.83324i	−0.552749	−	0.833348i	$-0.686421\pi$
$271$	−8.86135	−	30.1790i	−0.538289	−	1.83324i	0.0144607	−	0.999895i	$-0.495397\pi$
$272$	3.35331	−	7.34272i	0.203324	−	0.445218i
$273$	−4.61459	+	9.88840i	−0.279288	+	0.598473i
$274$	3.96614	+	6.17144i	0.239603	+	0.372830i
$275$		−	0.667300i		−	0.0402397i
$276$	11.7547	+	7.18418i	0.707550	+	0.432437i
$277$	3.73824			0.224609			0.112305	−	0.993674i	$-0.464177\pi$
$277$	3.73824			0.224609			0.112305	+	0.993674i	$0.464177\pi$
$278$	12.7612	+	19.8567i	0.765363	+	1.19093i
$279$	3.48170	+	0.500593i	0.208444	+	0.0299697i
$280$	3.88543	−	4.41018i	0.232199	−	0.263558i
$281$	0.146799	+	0.499952i	0.00875730	+	0.0298246i	0.963756	−	0.266786i	$-0.0859618\pi$
$281$	0.146799	+	0.499952i	0.00875730	+	0.0298246i	−0.954998	+	0.296611i	$0.904144\pi$
$282$	3.58574	+	7.85167i	0.213528	+	0.467560i
$283$	−13.5035	−	15.5838i	−0.802698	−	0.926363i	0.195828	−	0.980638i	$-0.437261\pi$
$283$	−13.5035	−	15.5838i	−0.802698	−	0.926363i	−0.998526	+	0.0542754i	$0.982715\pi$
$284$	3.84618	+	26.7508i	0.228229	+	1.58737i
$285$	0.167845	−	0.571628i	0.00994229	−	0.0338603i
$286$	1.08414	−	1.25116i	0.0641064	−	0.0739827i
$287$	−19.0093	+	16.1997i	−1.12208	+	0.956236i
$288$	−6.01409	−	3.86502i	−0.354383	−	0.227748i
$289$	−7.99631	+	9.22823i	−0.470371	+	0.542837i
$290$	20.4217	+	5.99636i	1.19920	+	0.352118i
$291$	7.12886	−	1.02498i	0.417901	−	0.0600851i
$292$	−14.0532	+	12.1772i	−0.822404	+	0.712617i
$293$	−13.8642	−	30.3583i	−0.809953	−	1.77355i	−0.607611	−	0.794235i	$-0.707872\pi$
$293$	−13.8642	−	30.3583i	−0.809953	−	1.77355i	−0.202342	−	0.979315i	$-0.564855\pi$
$294$	4.59664	−	14.7521i	0.268082	−	0.860363i
$295$	−4.57490	−	2.08929i	−0.266361	−	0.121643i
$296$	−0.941496	−	0.135367i	−0.0547233	−	0.00786803i
$297$	−0.152976	+	0.0983116i	−0.00887656	+	0.00570462i
$298$		−	8.58153i		−	0.497115i
$299$	−12.6119	+	15.2376i	−0.729368	+	0.881214i
$300$			10.5413i			0.608601i
$301$	−6.76531	−	23.7621i	−0.389946	−	1.36963i
$302$	−6.29470	+	43.7806i	−0.362219	+	2.51929i
$303$	−2.23046	+	4.88403i	−0.128137	+	0.280580i
$304$	−0.740205	+	0.217344i	−0.0424536	+	0.0124655i
$305$	2.55038	+	5.58455i	0.146034	+	0.319770i
$306$	7.81265	+	9.01627i	0.446619	+	0.515426i
$307$	−20.0223	+	2.87877i	−1.14273	+	0.164300i	−0.687577	−	0.726112i	$-0.741326\pi$
$307$	−20.0223	+	2.87877i	−1.14273	+	0.164300i	−0.455156	+	0.890412i	$0.650416\pi$
$308$	−0.756716	+	1.15644i	−0.0431179	+	0.0658942i
$309$	4.46512	+	3.86905i	0.254012	+	0.220103i
$310$	4.84177	−	7.53394i	0.274994	−	0.427899i
$311$	−15.9969	+	24.8916i	−0.907100	+	1.41148i	0.00431606	+	0.999991i	$0.498626\pi$
$311$	−15.9969	+	24.8916i	−0.907100	+	1.41148i	−0.911416	+	0.411485i	$0.865010\pi$
$312$	−5.20211	+	6.00355i	−0.294511	+	0.339884i
$313$	31.4011	+	9.22018i	1.77489	+	0.521156i	0.994556	−	0.104204i	$-0.0332294\pi$
$313$	31.4011	+	9.22018i	1.77489	+	0.521156i	0.780337	+	0.625359i	$0.215048\pi$
$314$	−1.00027	−	6.95702i	−0.0564484	−	0.392607i
$315$	−1.24481	−	2.78619i	−0.0701369	−	0.156984i
$316$	10.3430	−	4.72347i	0.581837	−	0.265716i
$317$	22.0417	−	6.47203i	1.23799	−	0.363506i	0.403728	−	0.914879i	$-0.367714\pi$
$317$	22.0417	−	6.47203i	1.23799	−	0.363506i	0.834258	+	0.551374i	$0.185896\pi$
$318$	6.87814	−	15.0610i	0.385707	−	0.844581i
$319$	−1.50468	−	0.216340i	−0.0842457	−	0.0121127i
$320$	−12.4135	+	7.97769i	−0.693937	+	0.445966i
$321$	12.3611			0.689932
$322$	14.8023	−	23.7775i	0.824902	−	1.32507i
$323$	2.79165			0.155332
$324$	2.41654	−	1.55302i	0.134252	−	0.0862788i
$325$	−14.9811	−	2.15395i	−0.831001	−	0.119480i
$326$	15.3288	−	33.5654i	0.848985	−	1.85902i
$327$	19.3689	−	5.68724i	1.07111	−	0.314505i
$328$	−16.5387	+	7.55298i	−0.913198	+	0.417044i
$329$	9.44598	−	4.22025i	0.520774	−	0.232670i
$330$	0.0658881	+	0.458262i	0.00362702	+	0.0252265i
$331$	−11.8576	−	3.48170i	−0.651752	−	0.191372i	−0.0608904	−	0.998144i	$-0.519394\pi$
$331$	−11.8576	−	3.48170i	−0.651752	−	0.191372i	−0.590862	+	0.806773i	$0.701212\pi$
$332$	16.9068	−	19.5115i	0.927882	−	1.07083i
$333$	−0.266994	+	0.415450i	−0.0146312	+	0.0227665i
$334$	−17.1859	+	26.7417i	−0.940369	+	1.46324i
$335$	2.10392	+	1.82306i	0.114950	+	0.0996045i
$336$	−2.16366	+	3.30658i	−0.118037	+	0.180389i
$337$	−7.17478	+	1.03158i	−0.390835	+	0.0561936i	−0.334931	−	0.942243i	$-0.608713\pi$
$337$	−7.17478	+	1.03158i	−0.390835	+	0.0561936i	−0.0559039	+	0.998436i	$0.517804\pi$
$338$	−5.79760	−	6.69079i	−0.315348	−	0.363931i
$339$	4.88506	+	10.6968i	0.265320	+	0.580970i
$340$	17.1816	−	5.04496i	0.931801	−	0.273602i
$341$	−0.265713	+	0.581831i	−0.0143892	+	0.0315079i
$342$	0.162263	−	1.12856i	0.00877415	−	0.0610256i
$343$	−17.6359	−	5.65480i	−0.952246	−	0.305331i
$344$		−	17.9858i		−	0.969731i
$345$	−0.910766	−	5.45605i	−0.0490340	−	0.293744i
$346$		−	12.6610i		−	0.680662i
$347$	−3.63509	+	2.33613i	−0.195142	+	0.125410i	−0.634563	−	0.772871i	$-0.718820\pi$
$347$	−3.63509	+	2.33613i	−0.195142	+	0.125410i	0.439421	+	0.898281i	$0.355184\pi$
$348$	23.7692	+	3.41750i	1.27416	+	0.183197i
$349$	11.8794	+	5.42516i	0.635892	+	0.290402i	0.707158	−	0.707055i	$-0.249977\pi$
$349$	11.8794	+	5.42516i	0.635892	+	0.290402i	−0.0712667	+	0.997457i	$0.522704\pi$
$350$	21.4308	+	0.176353i	1.14552	+	0.00942644i
$351$	1.71334	+	3.75169i	0.0914513	+	0.200250i
$352$	0.982464	−	0.851310i	0.0523655	−	0.0453750i
$353$	13.0707	−	1.87929i	0.695685	−	0.100024i	0.214605	−	0.976701i	$-0.431154\pi$
$353$	13.0707	−	1.87929i	0.695685	−	0.100024i	0.481080	+	0.876677i	$0.340245\pi$
$354$	−9.23535	−	2.71174i	−0.490853	−	0.144128i
$355$	7.10629	−	8.20110i	0.377163	−	0.435269i
$356$	−43.9469	−	28.2429i	−2.32918	−	1.49687i
$357$	10.8835	−	9.27492i	0.576016	−	0.490881i
$358$	13.5948	−	15.6893i	0.718510	−	0.829204i
$359$	3.71903	−	12.6659i	0.196283	−	0.668479i	−0.801253	−	0.598326i	$-0.795833\pi$
$359$	3.71903	−	12.6659i	0.196283	−	0.668479i	0.997536	−	0.0701533i	$-0.0223489\pi$
$360$	−0.316156	−	2.19891i	−0.0166629	−	0.115893i
$361$	12.2676	+	14.1576i	0.645665	+	0.745137i
$362$	−6.10949	−	13.3779i	−0.321108	−	0.703128i
$363$	3.08974	+	10.5227i	0.162169	+	0.552298i
$364$	23.5198	+	20.7213i	1.23277	+	1.08609i
$365$	7.39043	+	1.06258i	0.386833	+	0.0556182i
$366$	6.35224	+	9.88428i	0.332037	+	0.516660i
$367$	−19.4708			−1.01637			−0.508183	−	0.861249i	$-0.669682\pi$
$367$	−19.4708			−1.01637			−0.508183	+	0.861249i	$0.669682\pi$
$368$	−5.30590	+	4.81180i	−0.276589	+	0.250832i
$369$			9.43989i			0.491421i
$370$	0.679769	+	1.05774i	0.0353395	+	0.0549894i
$371$	−17.9836	−	8.39234i	−0.933660	−	0.435709i
$372$	4.19744	−	9.19112i	0.217627	−	0.476537i
$373$	−9.56478	−	32.5747i	−0.495246	−	1.68665i	−0.705256	−	0.708953i	$-0.749168\pi$
$373$	−9.56478	−	32.5747i	−0.495246	−	1.68665i	0.210011	−	0.977699i	$-0.432650\pi$
$374$	−1.97338	+	0.901213i	−0.102041	+	0.0466006i
$375$	7.55722	−	6.54837i	0.390253	−	0.338156i
$376$	7.45494	−	1.07186i	0.384459	−	0.0552769i
$377$	−9.71378	+	33.0821i	−0.500285	+	1.70381i
$378$	−3.11691	−	4.93890i	−0.160317	−	0.254030i
$379$	0.131640	−	0.204837i	0.00676191	−	0.0105217i	−0.837856	−	0.545891i	$-0.816191\pi$
$379$	0.131640	−	0.204837i	0.00676191	−	0.0105217i	0.844618	+	0.535369i	$0.179828\pi$
$380$	−1.43968	−	0.925228i	−0.0738542	−	0.0474632i
$381$	−6.24347	−	5.41000i	−0.319863	−	0.277163i
$382$	−5.49132	+	18.7017i	−0.280960	+	0.956862i
$383$	2.06449	+	14.3589i	0.105491	+	0.733704i	0.972074	+	0.234673i	$0.0754018\pi$
$383$	2.06449	+	14.3589i	0.105491	+	0.733704i	−0.866584	+	0.499032i	$0.833689\pi$
$384$	−10.5367	+	9.13011i	−0.537699	+	0.465919i
$385$	0.549899	−	0.0744504i	0.0280255	−	0.00379434i
$386$	26.3976	−	7.75103i	1.34360	−	0.394517i
$387$	−8.49429	−	3.87921i	−0.431789	−	0.197191i
$388$	2.94429	−	20.4780i	0.149474	−	1.03961i
$389$	−14.6822	−	22.8460i	−0.744418	−	1.15834i	−0.982349	−	0.187055i	$-0.940106\pi$
$389$	−14.6822	−	22.8460i	−0.744418	−	1.15834i	0.237931	−	0.971282i	$-0.423531\pi$
$390$	10.5008			0.531728
$391$	23.3283	−	11.2977i	1.17976	−	0.571349i
$392$	−11.2206	−	7.47480i	−0.566727	−	0.377535i
$393$	7.46099	−	4.79489i	0.376357	−	0.241870i
$394$	−6.44671	+	44.8379i	−0.324781	+	2.25890i
$395$	−4.15297	−	1.89660i	−0.208959	−	0.0954282i
$396$	0.147164	+	0.501194i	0.00739526	+	0.0251859i
$397$	−12.4054	+	5.66535i	−0.622609	+	0.284336i	−0.701635	−	0.712537i	$-0.747546\pi$
$397$	−12.4054	+	5.66535i	−0.622609	+	0.284336i	0.0790260	+	0.996873i	$0.474819\pi$
$398$	−0.337666	−	0.389687i	−0.0169257	−	0.0195332i
$399$	−1.35104	−	0.205610i	−0.0676364	−	0.0102934i
$400$	−5.25881	−	1.54412i	−0.262940	−	0.0772062i
$401$	10.3538	+	8.97165i	0.517046	+	0.448023i	0.873878	−	0.486146i	$-0.161598\pi$
$401$	10.3538	+	8.97165i	0.517046	+	0.448023i	−0.356832	+	0.934169i	$0.616143\pi$
$402$	4.48203	+	2.88043i	0.223544	+	0.143663i
$403$	12.2046	+	7.84341i	0.607954	+	0.390708i
$404$	11.6562	+	10.1002i	0.579920	+	0.502503i
$405$	−1.10668	−	0.324952i	−0.0549916	−	0.0161470i
$406$	7.34554	−	48.2664i	0.364553	−	2.39542i
$407$	−0.0588081	−	0.0678682i	−0.00291501	−	0.00336410i
$408$	9.46904	−	4.32437i	0.468787	−	0.214088i
$409$	2.34551	+	7.98808i	0.115978	+	0.394985i	0.996937	−	0.0782073i	$-0.0249196\pi$
$409$	2.34551	+	7.98808i	0.115978	+	0.394985i	−0.880959	+	0.473193i	$0.843101\pi$
$410$	21.8622	+	9.98412i	1.07970	+	0.493080i
$411$	0.472968	−	3.28956i	0.0233298	−	0.162262i
$412$	14.2774	−	9.17555i	0.703399	−	0.452047i
$413$	−3.34125	+	11.0423i	−0.164412	+	0.543355i
$414$	−3.21130	−	10.0874i	−0.157827	−	0.495770i
$415$	−10.3664			−0.508866
$416$	−15.9409	−	24.8045i	−0.781567	−	1.21614i
$417$	1.52178	−	10.5842i	0.0745221	−	0.518313i
$418$	0.188595	+	0.0861284i	0.00922448	+	0.00421268i
$419$	4.67543	−	1.37283i	0.228410	−	0.0670672i	−0.165525	−	0.986206i	$-0.552932\pi$
$419$	4.67543	−	1.37283i	0.228410	−	0.0670672i	0.393935	+	0.919138i	$0.371114\pi$
$420$	−8.68670	+	1.17608i	−0.423867	+	0.0573871i
$421$	20.5656	−	17.8202i	1.00231	−	0.868505i	0.0109832	−	0.999940i	$-0.496504\pi$
$421$	20.5656	−	17.8202i	1.00231	−	0.868505i	0.991325	+	0.131435i	$0.0419584\pi$
$422$	3.27615	+	22.7861i	0.159480	+	1.10921i
$423$	1.10168	−	3.75198i	0.0535655	−	0.182427i
$424$	−10.9184	−	9.46082i	−0.530243	−	0.459458i
$425$	16.6849	+	10.7227i	0.809336	+	0.520128i
$426$	11.2279	−	17.4710i	0.543994	−	0.846471i
$427$	11.9095	−	7.51599i	0.576339	−	0.363724i
$428$	10.0038	−	34.0697i	0.483550	−	1.64682i
$429$	−0.742359	+	0.106735i	−0.0358414	+	0.00515322i
$430$	−17.9680	+	15.5693i	−0.866493	+	0.750821i
$431$	−17.8362	+	8.14552i	−0.859139	+	0.392356i	−0.795744	−	0.605633i	$-0.792920\pi$
$431$	−17.8362	+	8.14552i	−0.859139	+	0.392356i	−0.0633949	+	0.997989i	$0.520193\pi$
$432$	0.420782	+	1.43305i	0.0202449	+	0.0689477i
$433$	−2.89909	+	6.34811i	−0.139321	+	0.305071i	−0.966412	−	0.256997i	$-0.917267\pi$
$433$	−2.89909	+	6.34811i	−0.139321	+	0.305071i	0.827091	+	0.562068i	$0.189994\pi$
$434$	−18.6156	−	8.68731i	−0.893580	−	0.417004i
$435$	−5.21292	−	8.11146i	−0.249940	−	0.388915i
$436$		−	57.9872i		−	2.77708i
$437$	−2.27598	−	0.977859i	−0.108875	−	0.0467773i
$438$	14.2892			0.682766
$439$	12.8947	+	20.0646i	0.615431	+	0.957629i	0.999412	+	0.0342879i	$0.0109163\pi$
$439$	12.8947	+	20.0646i	0.615431	+	0.957629i	−0.383981	+	0.923341i	$0.625447\pi$
$440$	0.399857	+	0.0574907i	0.0190624	+	0.00274076i
$441$	−5.95026	+	3.68706i	−0.283346	+	0.175574i
$442$	13.8627	+	47.2120i	0.659381	+	2.24564i
$443$	12.7530	+	27.9251i	0.605911	+	1.32676i	0.925336	+	0.379149i	$0.123783\pi$
$443$	12.7530	+	27.9251i	0.605911	+	1.32676i	−0.319425	+	0.947612i	$0.603490\pi$
$444$	0.928986	+	1.07211i	0.0440877	+	0.0508799i
$445$	2.98515	+	20.7621i	0.141509	+	0.984220i
$446$	11.3772	−	38.7473i	0.538727	−	1.83474i
$447$	−2.54587	+	2.93809i	−0.120415	+	0.138967i
$448$	21.9546	+	25.7623i	1.03726	+	1.21715i
$449$	20.7980	+	13.3661i	0.981520	+	0.630785i	0.929873	−	0.367881i	$-0.119917\pi$
$449$	20.7980	+	13.3661i	0.981520	+	0.630785i	0.0516471	+	0.998665i	$0.483553\pi$
$450$	5.30460	−	6.12183i	0.250061	−	0.288586i
$451$	−1.64704	−	0.483615i	−0.0775562	−	0.0227726i
$452$	33.4358	−	4.80735i	1.57269	−	0.226119i
$453$	15.1434	−	13.1219i	0.711500	−	0.616519i
$454$	3.69900	+	8.09969i	0.173603	+	0.380137i
$455$	0.103567	−	12.5857i	0.00485530	−	0.590027i
$456$	−0.904950	−	0.413277i	−0.0423782	−	0.0193535i
$457$	3.80759	+	0.547448i	0.178111	+	0.0256085i	0.230793	−	0.973003i	$-0.425868\pi$
$457$	3.80759	+	0.547448i	0.178111	+	0.0256085i	−0.0526820	+	0.998611i	$0.516777\pi$
$458$	−40.8866	+	26.2762i	−1.91050	+	1.22781i
$459$		−	5.40469i		−	0.252269i
$460$	−15.7750	−	1.90528i	−0.735513	−	0.0888343i
$461$			17.2774i			0.804689i	0.915488	+	0.402344i	$0.131805\pi$
$461$			17.2774i			0.804689i	−0.915488	+	0.402344i	$0.868195\pi$
$462$	1.02141	−	0.290804i	0.0475201	−	0.0135294i
$463$	−4.72660	+	32.8742i	−0.219664	+	1.52779i	0.519619	+	0.854398i	$0.326074\pi$
$463$	−4.72660	+	32.8742i	−0.219664	+	1.52779i	−0.739282	+	0.673395i	$0.764835\pi$
$464$	−5.18671	+	11.3573i	−0.240787	+	0.527250i
$465$	−3.89277	+	1.14302i	−0.180523	+	0.0530063i
$466$	−3.68060	−	8.05938i	−0.170500	−	0.373344i
$467$	5.25407	+	6.06352i	0.243129	+	0.280586i	0.864178	−	0.503185i	$-0.167839\pi$
$467$	5.25407	+	6.06352i	0.243129	+	0.280586i	−0.621049	+	0.783772i	$0.713293\pi$
$468$	11.7270	−	1.68608i	0.542079	−	0.0779393i
$469$	3.49654	−	5.34353i	0.161455	−	0.246741i
$470$	−7.52413	−	6.51970i	−0.347062	−	0.300731i
$471$	−1.72146	+	2.67865i	−0.0793207	+	0.123425i
$472$	−4.54058	+	7.06528i	−0.208997	+	0.325206i
$473$	1.11200	−	1.28332i	0.0511300	−	0.0590071i
$474$	−8.38361	−	2.46165i	−0.385072	−	0.113067i
$475$	−0.269752	−	1.87617i	−0.0123771	−	0.0860845i
$476$	−16.7555	−	37.5032i	−0.767989	−	1.71895i
$477$	−6.82302	+	3.11597i	−0.312405	+	0.142670i
$478$	26.9593	−	7.91596i	1.23309	−	0.362067i
$479$	0.337016	−	0.737963i	0.0153987	−	0.0337184i	−0.901776	−	0.432203i	$-0.857736\pi$
$479$	0.337016	−	0.737963i	0.0153987	−	0.0337184i	0.917175	+	0.398484i	$0.130464\pi$
$480$	8.16172	+	1.17348i	0.372530	+	0.0535617i
$481$	−1.71349	+	1.10119i	−0.0781282	+	0.0502099i
$482$	−44.6778			−2.03502
$483$	−12.1220	+	3.74941i	−0.551568	+	0.170604i
$484$	31.5031			1.43196
$485$	−6.98831	+	4.49111i	−0.317323	+	0.203931i
$486$	−2.18492	−	0.314144i	−0.0991099	−	0.0142498i
$487$	−1.16815	+	2.55788i	−0.0529338	+	0.115909i	−0.934251	−	0.356617i	$-0.883930\pi$
$487$	−1.16815	+	2.55788i	−0.0529338	+	0.115909i	0.881317	+	0.472525i	$0.156658\pi$
$488$	9.83674	−	2.88833i	0.445288	−	0.130748i
$489$	−15.2060	+	6.94433i	−0.687638	+	0.314034i
$490$	2.24569	+	17.6800i	0.101450	+	0.798702i
$491$	−0.789073	−	5.48813i	−0.0356104	−	0.247676i	0.964239	−	0.265034i	$-0.0853833\pi$
$491$	−0.789073	−	5.48813i	−0.0356104	−	0.247676i	−0.999849	+	0.0173588i	$0.994474\pi$
$492$	26.0182	+	7.63962i	1.17299	+	0.344421i
$493$	29.5876	−	34.1459i	1.33256	−	1.53786i
$494$	2.54237	−	3.95600i	0.114386	−	0.177989i
$495$	0.113393	−	0.176443i	0.00509665	−	0.00793054i
$496$	3.97039	+	3.44036i	0.178276	+	0.154477i
$497$	−20.8291	−	13.6295i	−0.934312	−	0.611368i
$498$	−19.6372	+	2.82341i	−0.879966	+	0.126520i
$499$	−21.6534	−	24.9894i	−0.969341	−	1.11868i	−0.992899	−	0.118957i	$-0.962045\pi$
$499$	−21.6534	−	24.9894i	−0.969341	−	1.11868i	0.0235580	−	0.999722i	$-0.492501\pi$
$500$	−11.9326	−	26.1287i	−0.533641	−	1.16851i
$501$	13.8174	−	4.05715i	0.617316	−	0.181260i
$502$	−3.03440	+	6.64441i	−0.135432	+	0.296555i
$503$	−1.81101	+	12.5959i	−0.0807491	+	0.561623i	0.908778	+	0.417279i	$0.137016\pi$
$503$	−1.81101	+	12.5959i	−0.0807491	+	0.561623i	−0.989528	+	0.144344i	$0.953893\pi$
$504$	−4.90110	+	1.39539i	−0.218312	+	0.0621556i
$505$		−	6.19292i		−	0.275581i
$506$	1.92454	−	0.0435080i	0.0855563	−	0.00193417i
$507$			4.01071i			0.178122i
$508$	−19.9638	+	12.8299i	−0.885750	+	0.569237i
$509$	13.4497	+	1.93377i	0.596146	+	0.0857129i	0.433782	−	0.901018i	$-0.357179\pi$
$509$	13.4497	+	1.93377i	0.596146	+	0.0857129i	0.162365	+	0.986731i	$0.448088\pi$
$510$	−12.5169	−	5.71628i	−0.554258	−	0.253121i
$511$	0.140932	−	17.1264i	0.00623446	−	0.757626i
$512$	−6.82555	−	14.9459i	−0.301649	−	0.660520i
$513$	−0.390362	+	0.338251i	−0.0172349	+	0.0149341i
$514$	10.2495	−	1.47366i	0.452087	−	0.0650002i
$515$	−6.53852	−	1.91988i	−0.288122	−	0.0846001i
$516$	−17.5662	+	20.2725i	−0.773309	+	0.892446i
$517$	0.598193	+	0.384435i	0.0263085	+	0.0169074i
$518$	2.19517	−	1.87072i	0.0964503	−	0.0821949i
$519$	−3.75613	+	4.33480i	−0.164876	+	0.190277i
$520$	2.58137	−	8.79133i	0.113200	−	0.385525i
$521$	0.205262	+	1.42763i	0.00899270	+	0.0625456i	0.993824	−	0.110971i	$-0.0353961\pi$
$521$	0.205262	+	1.42763i	0.00899270	+	0.0625456i	−0.984831	+	0.173517i	$0.944487\pi$
$522$	−12.0842	−	13.9459i	−0.528910	−	0.610395i
$523$	10.3203	+	22.5983i	0.451274	+	0.988153i	0.989390	+	0.145282i	$0.0464089\pi$
$523$	10.3203	+	22.5983i	0.451274	+	0.988153i	−0.538116	+	0.842871i	$0.680864\pi$
$524$	−7.17752	−	24.4444i	−0.313551	−	1.06786i
$525$	−7.28500	−	6.41820i	−0.317944	−	0.280113i
$526$	27.3978	+	3.93920i	1.19460	+	0.171757i
$527$	−10.2781	−	15.9931i	−0.447723	−	0.696671i
$528$	−0.271592			−0.0118195
$529$	−22.9765	+	1.03939i	−0.998978	+	0.0451908i
$530$			19.0973i			0.829532i
$531$	2.35745	+	3.66826i	0.102305	+	0.159189i
$532$	−1.66008	+	3.55732i	−0.0719738	+	0.154229i
$533$	−16.1737	+	35.4155i	−0.700562	+	1.53402i
$534$	11.3096	+	38.5171i	0.489415	+	1.66680i
$535$	−12.9690	+	5.92275i	−0.560699	+	0.256063i
$536$	3.51332	−	3.04431i	0.151752	−	0.131494i
$537$	−9.30902	+	1.33843i	−0.401714	+	0.0577577i
$538$	−11.7258	+	39.9344i	−0.505536	+	1.72170i
$539$	−0.338469	−	1.22707i	−0.0145789	−	0.0528538i
$540$	−1.79126	+	2.78726i	−0.0770836	+	0.119944i
$541$	−2.54177	−	1.63350i	−0.109279	−	0.0702296i	0.484860	−	0.874592i	$-0.338871\pi$
$541$	−2.54177	−	1.63350i	−0.109279	−	0.0702296i	−0.594139	+	0.804362i	$0.702507\pi$
$542$	52.4710	+	45.4663i	2.25382	+	1.95295i
$543$	−1.87707	+	6.39273i	−0.0805530	+	0.274338i
$544$	5.49875	+	38.2446i	0.235757	+	1.63973i
$545$	−17.5964	+	15.2474i	−0.753748	+	0.653126i
$546$	−3.23168	−	23.8695i	−0.138303	−	1.02152i
$547$	−7.35915	+	2.16084i	−0.314655	+	0.0923909i	−0.435247	−	0.900311i	$-0.643339\pi$
$547$	−7.35915	+	2.16084i	−0.314655	+	0.0923909i	0.120592	+	0.992702i	$0.461521\pi$
$548$	−8.68390	−	3.96580i	−0.370958	−	0.169411i
$549$	0.757513	−	5.26862i	0.0323299	−	0.224859i
$550$	0.796358	+	1.23916i	0.0339568	+	0.0528378i
$551$	−4.31797			−0.183952
$552$	−9.23469	+	0.208768i	−0.393054	+	0.00888575i
$553$	−3.03310	+	10.0239i	−0.128980	+	0.426259i
$554$	−6.94181	+	4.46123i	−0.294929	+	0.189539i
$555$	0.0810634	−	0.563808i	0.00344095	−	0.0239323i
$556$	−27.9407	−	12.7601i	−1.18495	−	0.541147i
$557$	4.74966	+	16.1758i	0.201249	+	0.685393i	0.996831	+	0.0795464i	$0.0253472\pi$
$557$	4.74966	+	16.1758i	0.201249	+	0.685393i	−0.795582	+	0.605846i	$0.792835\pi$
$558$	−7.06283	+	3.22549i	−0.298994	+	0.136546i
$559$	−25.2215	−	29.1072i	−1.06676	−	1.23110i
$560$	0.685737	−	4.50588i	0.0289777	−	0.190408i
$561$	0.942994	+	0.276888i	0.0398132	+	0.0116902i
$562$	−0.869246	−	0.753206i	−0.0366669	−	0.0317721i
$563$	−31.8865	−	20.4922i	−1.34385	−	0.863642i	−0.346622	−	0.938005i	$-0.612671\pi$
$563$	−31.8865	−	20.4922i	−1.34385	−	0.863642i	−0.997231	+	0.0743625i	$0.976308\pi$
$564$	−9.44959	−	6.07288i	−0.397899	−	0.255714i
$565$	−10.2506	−	8.88216i	−0.431244	−	0.373675i
$566$	43.6733	+	12.8237i	1.83573	+	0.539018i
$567$	−0.398066	+	2.61563i	−0.0167172	+	0.109846i
$568$	−11.8667	−	13.6949i	−0.497916	−	0.574625i
$569$	−30.8000	+	14.0659i	−1.29120	+	0.589672i	−0.938246	−	0.345968i	$-0.887551\pi$
$569$	−30.8000	+	14.0659i	−1.29120	+	0.589672i	−0.352956	+	0.935640i	$0.614823\pi$
$570$	0.370499	+	1.26180i	0.0155185	+	0.0528512i
$571$	−13.3561	−	6.09952i	−0.558934	−	0.255257i	0.115856	−	0.993266i	$-0.463039\pi$
$571$	−13.3561	−	6.09952i	−0.558934	−	0.255257i	−0.674791	+	0.738009i	$0.735766\pi$
$572$	−0.306602	+	2.13247i	−0.0128197	+	0.0891629i
$573$	7.42828	−	4.77386i	0.310321	−	0.199431i
$574$	15.9669	−	52.7680i	0.666445	−	2.20249i
$575$	−9.84695	−	14.5864i	−0.410646	−	0.608296i
$576$	12.7934			0.533059
$577$	−4.34932	−	6.76768i	−0.181065	−	0.281742i	0.738843	−	0.673878i	$-0.235373\pi$
$577$	−4.34932	−	6.76768i	−0.181065	−	0.281742i	−0.919907	+	0.392136i	$0.871736\pi$
$578$	3.83591	−	26.6794i	0.159553	−	1.10972i
$579$	−11.3373	−	5.17757i	−0.471162	−	0.215173i
$580$	−26.5755	+	7.80328i	−1.10349	+	0.324013i
$581$	3.19032	+	23.5641i	0.132357	+	0.977602i
$582$	−12.0149	+	10.4109i	−0.498033	+	0.431548i
$583$	−0.194114	−	1.35009i	−0.00803938	−	0.0559151i
$584$	3.51267	−	11.9630i	0.145355	−	0.495034i
$585$	−3.59519	−	3.11525i	−0.148643	−	0.128800i
$586$	61.9750	+	39.8289i	2.56016	+	1.64532i
$587$	10.9306	−	17.0083i	0.451153	−	0.702008i	−0.538952	−	0.842337i	$-0.681179\pi$
$587$	10.9306	−	17.0083i	0.451153	−	0.702008i	0.990105	+	0.140328i	$0.0448158\pi$
$588$	5.34677	+	19.3840i	0.220497	+	0.799381i
$589$	−0.511873	+	1.74328i	−0.0210913	+	0.0718305i
$590$	10.9888	−	1.57995i	0.452402	−	0.0650456i
$591$	15.5091	−	13.4387i	0.637961	−	0.552796i
$592$	−0.670931	+	0.306404i	−0.0275751	+	0.0125931i
$593$	−5.76555	−	19.6357i	−0.236763	−	0.806340i	−0.989060	−	0.147516i	$-0.952872\pi$
$593$	−5.76555	−	19.6357i	−0.236763	−	0.806340i	0.752297	−	0.658824i	$-0.228946\pi$
$594$	0.166746	−	0.365124i	0.00684169	−	0.0149812i
$595$	−6.97470	+	14.9458i	−0.285935	+	0.612716i
$596$	6.03759	+	9.39467i	0.247309	+	0.384821i
$597$			0.233593i			0.00956033i
$598$	5.23539	−	43.3470i	0.214091	−	1.77259i
$599$	−42.0998			−1.72015			−0.860076	−	0.510166i	$-0.829584\pi$
$599$	−42.0998			−1.72015			−0.860076	+	0.510166i	$0.829584\pi$
$600$	−3.82123	−	5.94595i	−0.156001	−	0.242742i
$601$	43.0800	+	6.19397i	1.75727	+	0.252657i	0.944168	−	0.329464i	$-0.106868\pi$
$601$	43.0800	+	6.19397i	1.75727	+	0.252657i	0.813102	+	0.582122i	$0.197777\pi$
$602$	40.9208	+	36.0518i	1.66781	+	1.46936i
$603$	−0.679997	−	2.31586i	−0.0276916	−	0.0943090i
$604$	−23.9109	−	52.3576i	−0.972922	−	2.13040i
$605$	−8.28355	−	9.55972i	−0.336774	−	0.388658i
$606$	−1.68671	−	11.7314i	−0.0685181	−	0.476554i
$607$	11.9954	−	40.8525i	0.486877	−	1.65815i	−0.239531	−	0.970889i	$-0.576994\pi$
$607$	11.9954	−	40.8525i	0.486877	−	1.65815i	0.726409	−	0.687263i	$-0.241188\pi$
$608$	2.41814	−	2.79068i	0.0980686	−	0.113177i
$609$	−16.8340	+	14.3459i	−0.682149	+	0.581327i
$610$	−11.4006	−	7.32671i	−0.461596	−	0.296650i
$611$	10.5616	−	12.1887i	0.427275	−	0.493102i
$612$	−14.8964	−	4.37397i	−0.602150	−	0.176807i
$613$	24.3624	−	3.50278i	0.983987	−	0.141476i	0.368504	−	0.929626i	$-0.379870\pi$
$613$	24.3624	−	3.50278i	0.983987	−	0.141476i	0.615483	+	0.788150i	$0.288961\pi$
$614$	33.7453	−	29.2405i	1.36185	−	1.18005i
$615$	−4.52305	−	9.90410i	−0.182387	−	0.399372i
$616$	0.00762507	−	0.926616i	0.000307223	−	0.0373344i
$617$	−24.6619	−	11.2627i	−0.992852	−	0.453420i	−0.148328	−	0.988938i	$-0.547389\pi$
$617$	−24.6619	−	11.2627i	−0.992852	−	0.453420i	−0.844524	+	0.535518i	$0.820116\pi$
$618$	−12.9089	−	1.85603i	−0.519274	−	0.0746603i
$619$	−7.04889	+	4.53005i	−0.283319	+	0.182078i	−0.674580	−	0.738202i	$-0.735675\pi$
$619$	−7.04889	+	4.53005i	−0.283319	+	0.182078i	0.391261	+	0.920280i	$0.372039\pi$
$620$			11.6543i			0.468047i
$621$	−1.89316	+	4.40635i	−0.0759697	+	0.176821i
$622$		−	65.3138i		−	2.61884i
$623$	46.2762	−	13.1753i	1.85402	−	0.527856i
$624$	−0.876661	+	6.09731i	−0.0350945	+	0.244088i
$625$	2.83090	−	6.19881i	0.113236	−	0.247953i
$626$	−69.3143	+	20.3525i	−2.77035	+	0.813450i
$627$	−0.0390183	−	0.0854381i	−0.00155824	−	0.00341207i
$628$	5.98970	+	6.91248i	0.239015	+	0.275838i
$629$	2.64192	−	0.379851i	0.105340	−	0.0151457i
$630$	5.63662	+	3.68832i	0.224568	+	0.146946i
$631$	−10.4959	−	9.09477i	−0.417836	−	0.362057i	0.420424	−	0.907328i	$-0.361881\pi$
$631$	−10.4959	−	9.09477i	−0.417836	−	0.362057i	−0.838260	+	0.545271i	$0.816427\pi$
$632$	−4.12182	+	6.41368i	−0.163957	+	0.255122i
$633$	5.63825	−	8.77328i	0.224100	−	0.348707i
$634$	−33.2071	+	38.3230i	−1.31882	+	1.52200i
$635$	9.14265	+	2.68452i	0.362815	+	0.106532i
$636$	3.06640	+	21.3273i	0.121591	+	0.845682i
$637$	−28.6407	+	3.63791i	−1.13479	+	0.144139i
$638$	3.05232	−	1.39395i	0.120843	−	0.0551869i
$639$	−9.02721	+	2.65063i	−0.357111	+	0.104857i
$640$	6.68023	−	14.6277i	0.264059	−	0.578209i
$641$	−6.88192	−	0.989471i	−0.271820	−	0.0390818i	0.00505709	−	0.999987i	$-0.498390\pi$
$641$	−6.88192	−	0.989471i	−0.271820	−	0.0390818i	−0.276877	+	0.960905i	$0.589299\pi$
$642$	−22.9543	+	14.7518i	−0.905934	+	0.582208i
$643$	12.7776			0.503899			0.251950	−	0.967740i	$-0.418928\pi$
$643$	12.7776			0.503899			0.251950	+	0.967740i	$0.418928\pi$
$644$	0.523906	+	36.4448i	0.0206448	+	1.43613i
$645$	10.7707			0.424095
$646$	−5.18401	+	3.33156i	−0.203962	+	0.131079i
$647$	41.7192	+	5.99831i	1.64015	+	0.235818i	0.899768	−	0.436369i	$-0.143736\pi$
$647$	41.7192	+	5.99831i	1.64015	+	0.235818i	0.740382	+	0.672187i	$0.234645\pi$
$648$	−0.800113	+	1.75200i	−0.0314314	+	0.0688252i
$649$	−0.760802	+	0.223391i	−0.0298641	+	0.00876888i
$650$	30.3900	−	13.8786i	1.19199	−	0.544365i
$651$	3.79625	+	8.49697i	0.148787	+	0.333023i
$652$	6.83387	+	47.5306i	0.267635	+	1.86144i
$653$	40.2287	+	11.8122i	1.57427	+	0.462248i	0.948241	−	0.317551i	$-0.102861\pi$
$653$	40.2287	+	11.8122i	1.57427	+	0.462248i	0.626030	+	0.779799i	$0.284679\pi$
$654$	−29.1804	+	33.6760i	−1.14104	+	1.31684i
$655$	−5.53045	+	8.60555i	−0.216093	+	0.336247i
$656$	−7.62247	+	11.8608i	−0.297608	+	0.463087i
$657$	−4.89225	−	4.23916i	−0.190865	−	0.165385i
$658$	−12.5045	+	19.1097i	−0.487475	+	0.744975i
$659$	26.5223	−	3.81333i	1.03316	−	0.148546i	0.395185	−	0.918602i	$-0.370681\pi$
$659$	26.5223	−	3.81333i	1.03316	−	0.148546i	0.637977	+	0.770055i	$0.279771\pi$
$660$	−0.394544	−	0.455328i	−0.0153576	−	0.0177236i
$661$	11.5124	+	25.2086i	0.447781	+	0.980503i	0.990104	+	0.140333i	$0.0448173\pi$
$661$	11.5124	+	25.2086i	0.447781	+	0.980503i	−0.542324	+	0.840170i	$0.682455\pi$
$662$	26.1743	−	7.68546i	1.01729	−	0.298704i
$663$	9.26007	−	20.2767i	0.359631	−	0.787483i
$664$	−2.46357	+	17.1345i	−0.0956050	+	0.664947i
$665$	1.51599	−	0.431617i	0.0587876	−	0.0167374i
$666$		−	1.09011i		−	0.0422409i
$667$	−36.0829	+	17.4747i	−1.39714	+	0.676621i
$668$		−	41.3668i		−	1.60053i
$669$	−15.3903	+	9.89077i	−0.595025	+	0.382399i
$670$	−6.08257	−	0.874542i	−0.234990	−	0.0337865i
$671$	0.880444	+	0.402085i	0.0339892	+	0.0155223i
$672$	0.155640	−	18.9137i	0.00600394	−	0.729613i
$673$	16.0175	+	35.0735i	0.617430	+	1.35198i	0.917374	+	0.398026i	$0.130305\pi$
$673$	16.0175	+	35.0735i	0.617430	+	1.35198i	−0.299945	+	0.953957i	$0.596968\pi$
$674$	12.0923	−	10.4780i	0.465777	−	0.403598i
$675$	−3.63230	+	0.522246i	−0.139807	+	0.0201013i
$676$	11.0543	+	3.24583i	0.425165	+	0.124840i
$677$	−21.2009	+	24.4671i	−0.814816	+	0.940347i	−0.999095	−	0.0425266i	$-0.986459\pi$
$677$	−21.2009	+	24.4671i	−0.814816	+	0.940347i	0.184280	+	0.982874i	$0.441005\pi$
$678$	−21.8370	−	14.0338i	−0.838644	−	0.538964i
$679$	12.3595	+	14.5031i	0.474316	+	0.556578i
$680$	−7.86269	+	9.07403i	−0.301521	+	0.347973i
$681$	1.13648	−	3.87049i	0.0435500	−	0.148318i
$682$	−0.200937	−	1.39755i	−0.00769427	−	0.0535148i
$683$	6.60020	+	7.61703i	0.252550	+	0.291458i	0.867841	−	0.496842i	$-0.165507\pi$
$683$	6.60020	+	7.61703i	0.252550	+	0.291458i	−0.615291	+	0.788300i	$0.710962\pi$
$684$	0.616368	+	1.34966i	0.0235674	+	0.0516054i
$685$	1.07994	+	3.67794i	0.0412625	+	0.140527i
$686$	39.4977	−	10.5459i	1.50803	−	0.402643i
$687$	21.7938	+	3.13347i	0.831484	+	0.119549i
$688$	−7.54033	−	11.7330i	−0.287472	−	0.447315i
$689$	−30.9366			−1.17859
$690$	8.20253	+	9.04481i	0.312265	+	0.344330i
$691$		−	47.5765i		−	1.80990i	−0.425523	−	0.904948i	$-0.639910\pi$
$691$		−	47.5765i		−	1.80990i	0.425523	−	0.904948i	$-0.360090\pi$
$692$	8.90775	+	13.8607i	0.338622	+	0.526906i
$693$	−0.435974	−	0.203455i	−0.0165613	−	0.00772862i
$694$	3.96232	−	8.67626i	0.150408	−	0.329346i
$695$	3.47474	+	11.8339i	0.131804	+	0.448884i
$696$	−14.6462	+	6.68870i	−0.555163	+	0.253534i
$697$	38.5581	−	33.4108i	1.46049	−	1.26552i
$698$	−28.5342	+	4.10259i	−1.08003	+	0.155285i
$699$	−1.13082	+	3.85123i	−0.0427717	+	0.145667i
$700$	−23.5855	+	14.8847i	−0.891448	+	0.562588i
$701$	21.7919	−	33.9089i	0.823069	−	1.28072i	−0.134035	−	0.990977i	$-0.542793\pi$
$701$	21.7919	−	33.9089i	0.823069	−	1.28072i	0.957104	−	0.289744i	$-0.0935702\pi$
$702$	−7.65890	−	4.92208i	−0.289066	−	0.185772i
$703$	−0.192779	−	0.167044i	−0.00727080	−	0.00630019i
$704$	−0.655419	+	2.23215i	−0.0247021	+	0.0841275i
$705$	0.641875	+	4.46434i	0.0241744	+	0.168137i
$706$	−22.0292	+	19.0884i	−0.829081	+	0.718403i
$707$	−14.0772	+	1.90591i	−0.529429	+	0.0716790i
$708$	12.0183	−	3.52889i	0.451675	−	0.132624i
$709$	31.5689	+	14.4170i	1.18559	+	0.541443i	0.907884	−	0.419222i	$-0.137697\pi$
$709$	31.5689	+	14.4170i	1.18559	+	0.541443i	0.277711	+	0.960665i	$0.410424\pi$
$710$	−3.40896	+	23.7099i	−0.127936	+	0.889815i
$711$	2.14003	+	3.32995i	0.0802574	+	0.124883i
$712$	35.0270			1.31269
$713$	2.77754	+	16.6391i	0.104020	+	0.623141i
$714$	−9.14164	+	30.2117i	−0.342117	+	1.13064i
$715$	0.727723	−	0.467679i	0.0272153	−	0.0174902i
$716$	−3.84472	+	26.7406i	−0.143684	+	0.999344i
$717$	−11.5785	−	5.28774i	−0.432409	−	0.197474i
$718$	8.20934	+	27.9585i	0.306370	+	1.04340i
$719$	45.7299	−	20.8841i	1.70544	−	0.778847i	0.708084	−	0.706129i	$-0.249560\pi$
$719$	45.7299	−	20.8841i	1.70544	−	0.778847i	0.997353	−	0.0727180i	$-0.0231673\pi$
$720$	−1.12811	−	1.30191i	−0.0420422	−	0.0485192i
$721$	−2.35186	+	15.4537i	−0.0875877	+	0.575526i
$722$	−39.6764	−	11.6500i	−1.47660	−	0.433569i
$723$	15.2965	+	13.2545i	0.568882	+	0.492939i
$724$	16.1005	+	10.3472i	0.598370	+	0.384549i
$725$	−25.8073	−	16.5853i	−0.958458	−	0.615964i
$726$	−18.2954	−	15.8530i	−0.679005	−	0.588361i
$727$	−46.9637	−	13.7898i	−1.74179	−	0.511434i	−0.752647	−	0.658424i	$-0.771223\pi$
$727$	−46.9637	−	13.7898i	−1.74179	−	0.511434i	−0.989138	+	0.146989i	$0.953042\pi$
$728$	−20.7782	−	3.16217i	−0.770091	−	0.117198i
$729$	0.654861	+	0.755750i	0.0242541	+	0.0279907i
$730$	−14.9919	+	6.84657i	−0.554875	+	0.253403i
$731$	14.2190	+	48.4255i	0.525909	+	1.79108i
$732$	−13.9083	−	6.35170i	−0.514065	−	0.234766i
$733$	7.12408	−	49.5491i	0.263134	−	1.83014i	−0.245788	−	0.969324i	$-0.579047\pi$
$733$	7.12408	−	49.5491i	0.263134	−	1.83014i	0.508921	−	0.860813i	$-0.330044\pi$
$734$	36.1566	−	23.2365i	1.33457	−	0.857673i
$735$	4.47623	−	6.71939i	0.165108	−	0.247849i
$736$	8.91329	−	33.1063i	0.328548	−	1.22032i
$737$	0.438901			0.0161671
$738$	−11.2656	−	17.5296i	−0.414692	−	0.645274i
$739$	−2.65326	+	18.4538i	−0.0976016	+	0.678834i	0.881007	+	0.473103i	$0.156866\pi$
$739$	−2.65326	+	18.4538i	−0.0976016	+	0.678834i	−0.978609	+	0.205731i	$0.934043\pi$
$740$	−1.48836	−	0.679711i	−0.0547132	−	0.0249867i
$741$	−2.04406	+	0.600189i	−0.0750903	+	0.0220485i
$742$	43.4104	−	5.87730i	1.59365	−	0.215762i
$743$	14.8752	−	12.8894i	0.545717	−	0.472867i	−0.337831	−	0.941207i	$-0.609693\pi$
$743$	14.8752	−	12.8894i	0.545717	−	0.472867i	0.883548	+	0.468340i	$0.155148\pi$
$744$	0.964172	+	6.70596i	0.0353483	+	0.245852i
$745$	1.26330	−	4.30240i	0.0462837	−	0.157628i
$746$	56.6362	+	49.0756i	2.07360	+	1.79678i
$747$	7.56088	+	4.85908i	0.276638	+	0.177784i
$748$	1.52631	−	2.37499i	0.0558075	−	0.0868382i
$749$	17.4544	+	27.6574i	0.637770	+	1.01058i
$750$	−6.21869	+	21.1789i	−0.227075	+	0.773345i
$751$	36.0102	−	5.17749i	1.31403	−	0.188929i	0.550574	−	0.834786i	$-0.314409\pi$
$751$	36.0102	−	5.17749i	1.31403	−	0.188929i	0.763458	+	0.645857i	$0.223500\pi$
$752$	4.41384	−	3.82461i	0.160956	−	0.139469i
$753$	3.01008	−	1.37466i	0.109693	−	0.0500953i
$754$	−21.4421	−	73.0249i	−0.780874	−	2.65941i
$755$	−9.60087	+	21.0230i	−0.349412	+	0.765104i
$756$	6.88704	+	3.21396i	0.250479	+	0.116891i
$757$	−8.12756	−	12.6467i	−0.295401	−	0.459653i	0.661550	−	0.749901i	$-0.269899\pi$
$757$	−8.12756	−	12.6467i	−0.295401	−	0.459653i	−0.956952	+	0.290247i	$0.906262\pi$
$758$			0.537475i			0.0195220i
$759$	−0.671819	−	0.556054i	−0.0243855	−	0.0201835i
$760$	1.14747			0.0416231
$761$	4.05170	+	6.30456i	0.146874	+	0.228540i	0.906894	−	0.421360i	$-0.138447\pi$
$761$	4.05170	+	6.30456i	0.146874	+	0.228540i	−0.760020	+	0.649900i	$0.774811\pi$
$762$	18.0503	+	2.59523i	0.653892	+	0.0940154i
$763$	40.0745	+	35.3063i	1.45080	+	1.27817i
$764$	−7.14605	−	24.3372i	−0.258535	−	0.880489i
$765$	2.58962	+	5.67047i	0.0936278	+	0.205016i
$766$	−20.9696	−	24.2002i	−0.757664	−	0.874390i
$767$	2.55944	+	17.8013i	0.0924160	+	0.642767i
$768$	1.46183	−	4.97852i	0.0527491	−	0.179647i
$769$	15.1660	−	17.5025i	0.546901	−	0.631157i	−0.413257	−	0.910614i	$-0.635609\pi$
$769$	15.1660	−	17.5025i	0.546901	−	0.631157i	0.960158	+	0.279457i	$0.0901545\pi$
$770$	−0.932297	+	0.794503i	−0.0335977	+	0.0286319i
$771$	−3.94634	−	2.53616i	−0.142124	−	0.0913376i
$772$	−23.4456	+	27.0576i	−0.843824	+	0.973825i
$773$	−21.7140	−	6.37579i	−0.780997	−	0.229321i	−0.133154	−	0.991095i	$-0.542510\pi$
$773$	−21.7140	−	6.37579i	−0.780997	−	0.229321i	−0.647843	+	0.761774i	$0.724329\pi$
$774$	20.4031	−	2.93352i	0.733374	−	0.105443i
$775$	−9.75524	+	8.45297i	−0.350419	+	0.303640i
$776$	5.76255	+	12.6182i	0.206863	+	0.452968i
$777$	−1.30655	−	0.0107515i	−0.0468723	−	0.000385709i
$778$	54.5289	+	24.9025i	1.95496	+	0.892799i
$779$	−4.82629	−	0.693916i	−0.172920	−	0.0248621i
$780$	−11.4958	+	7.38788i	−0.411615	+	0.264529i
$781$		−	1.71083i		−	0.0612185i
$782$	−29.8372	+	48.8195i	−1.06698	+	1.74578i
$783$			8.35969i			0.298751i
$784$	−10.4534	−	0.172053i	−0.373337	−	0.00614476i
$785$	0.522662	−	3.63519i	0.0186546	−	0.129746i
$786$	−8.13261	+	17.8079i	−0.290081	+	0.635188i
$787$	−25.6891	+	7.54301i	−0.915718	+	0.268879i	−0.705446	−	0.708764i	$-0.749253\pi$
$787$	−25.6891	+	7.54301i	−0.915718	+	0.268879i	−0.210272	+	0.977643i	$0.567435\pi$
$788$	−24.4884	−	53.6220i	−0.872362	−	1.91021i
$789$	−8.21162	−	9.47672i	−0.292341	−	0.337380i
$790$	9.97535	−	1.43424i	0.354907	−	0.0510279i
$791$	−17.0356	+	26.0343i	−0.605715	+	0.925673i
$792$	−0.264693	−	0.229358i	−0.00940547	−	0.00814989i
$793$	11.8689	−	18.4684i	0.421477	−	0.655830i
$794$	16.2754	−	25.3250i	0.577593	−	0.898752i
$795$	5.66555	−	6.53839i	0.200936	−	0.231893i
$796$	0.643827	+	0.189045i	0.0228199	+	0.00670052i
$797$	0.237894	+	1.65459i	0.00842663	+	0.0586085i	0.993601	−	0.112948i	$-0.0360294\pi$
$797$	0.237894	+	1.65459i	0.00842663	+	0.0586085i	−0.985174	+	0.171557i	$0.945120\pi$
$798$	2.75421	−	1.23052i	0.0974980	−	0.0435598i
$799$	−19.2245	+	8.77953i	−0.680114	+	0.310597i
$800$	25.1715	−	7.39103i	0.889948	−	0.261312i
$801$	7.55467	−	16.5424i	0.266931	−	0.584497i
$802$	−29.9336	−	4.30380i	−1.05699	−	0.151972i
$803$	0.990270	−	0.636408i	0.0349459	−	0.0224584i
$804$	−6.93327			−0.244517
$805$	10.9216	−	9.74193i	0.384934	−	0.343358i
$806$	−32.0239			−1.12799
$807$	15.8619	−	10.1938i	0.558365	−	0.358839i
$808$	−10.2362	−	1.47174i	−0.360108	−	0.0517758i
$809$	−11.6184	+	25.4407i	−0.408480	+	0.894446i	0.587860	+	0.808963i	$0.299971\pi$
$809$	−11.6184	+	25.4407i	−0.408480	+	0.894446i	−0.996340	+	0.0854832i	$0.972757\pi$
$810$	2.44288	−	0.717294i	0.0858341	−	0.0252032i
$811$	1.77460	−	0.810431i	0.0623145	−	0.0284581i	−0.384014	−	0.923327i	$-0.625459\pi$
$811$	1.77460	−	0.810431i	0.0623145	−	0.0284581i	0.446329	+	0.894869i	$0.352731\pi$
$812$	25.9166	+	58.0079i	0.909493	+	2.03568i
$813$	−4.47624	−	31.1329i	−0.156988	−	1.09188i
$814$	0.190199	+	0.0558475i	0.00666647	+	0.00195745i
$815$	12.6264	−	14.5716i	0.442284	−	0.510422i
$816$	4.36415	−	6.79075i	0.152776	−	0.237724i
$817$	2.60771	−	4.05768i	0.0912323	−	0.141960i
$818$	−13.8886	−	12.0345i	−0.485602	−	0.420776i
$819$	−5.97489	+	9.13103i	−0.208780	+	0.319064i
$820$	−30.9581	+	4.45110i	−1.08110	+	0.155439i
$821$	5.51599	+	6.36579i	0.192509	+	0.222168i	0.843796	−	0.536664i	$-0.180316\pi$
$821$	5.51599	+	6.36579i	0.192509	+	0.222168i	−0.651286	+	0.758832i	$0.725770\pi$
$822$	3.04749	+	6.67306i	0.106293	+	0.232750i
$823$	−14.2944	+	4.19721i	−0.498271	+	0.146306i	−0.521205	−	0.853431i	$-0.674517\pi$
$823$	−14.2944	+	4.19721i	−0.498271	+	0.146306i	0.0229343	+	0.999737i	$0.492699\pi$
$824$	−4.72723	+	10.3512i	−0.164681	+	0.360601i
$825$	0.0949667	−	0.660508i	0.00330632	−	0.0229959i
$826$	−6.97330	−	24.4927i	−0.242632	−	0.852209i
$827$		−	38.7585i		−	1.34777i	−0.738838	−	0.673883i	$-0.764625\pi$
$827$		−	38.7585i		−	1.34777i	0.738838	−	0.673883i	$-0.235375\pi$
$828$	10.6126	+	8.78393i	0.368815	+	0.305263i
$829$			12.5550i			0.436054i	0.975943	+	0.218027i	$0.0699621\pi$
$829$			12.5550i			0.436054i	−0.975943	+	0.218027i	$0.930038\pi$
$830$	19.2501	−	12.3713i	0.668180	−	0.429413i
$831$	3.70019	+	0.532007i	0.128358	+	0.0184551i
$832$	47.9969	+	21.9194i	1.66399	+	0.759920i
$833$	36.1200	+	11.2547i	1.25148	+	0.389952i
$834$	9.80536	+	21.4707i	0.339532	+	0.743471i
$835$	−12.5529	+	10.8772i	−0.434412	+	0.376420i
$836$	−0.267061	+	0.0383976i	−0.00923650	+	0.00132801i
$837$	3.37502	+	0.990996i	0.116658	+	0.0342538i
$838$	−7.04381	+	8.12899i	−0.243324	+	0.280811i
$839$	−23.9856	−	15.4146i	−0.828074	−	0.532171i	0.0565913	−	0.998397i	$-0.481977\pi$
$839$	−23.9856	−	15.4146i	−0.828074	−	0.532171i	−0.884665	+	0.466227i	$0.845613\pi$
$840$	4.47352	−	3.81233i	0.154351	−	0.131538i
$841$	−26.7736	+	30.8984i	−0.923227	+	1.06546i
$842$	−16.9231	+	57.6347i	−0.583208	+	1.98622i
$843$	0.0741544	+	0.515755i	0.00255401	+	0.0177635i
$844$	−19.6179	−	22.6402i	−0.675275	−	0.779309i
$845$	−1.92170	−	4.20793i	−0.0661085	−	0.144757i
$846$	2.43183	+	8.28206i	0.0836081	+	0.284743i
$847$	−19.1811	+	21.7716i	−0.659070	+	0.748080i
$848$	−11.0889	−	1.59434i	−0.380794	−	0.0547499i
$849$	−11.1482	−	17.3470i	−0.382606	−	0.595346i
$850$	−43.7799			−1.50164
$851$	−2.28697	−	0.615726i	−0.0783963	−	0.0211068i
$852$			27.0259i			0.925891i
$853$	0.156822	+	0.244020i	0.00536948	+	0.00835508i	0.843928	−	0.536457i	$-0.180237\pi$
$853$	0.156822	+	0.244020i	0.00536948	+	0.00835508i	−0.838558	+	0.544812i	$0.816601\pi$
$854$	−13.1459	+	28.1698i	−0.449844	+	0.963949i
$855$	0.247488	−	0.541923i	0.00846391	−	0.0185334i
$856$	6.70757	+	22.8439i	0.229260	+	0.780788i
$857$	−17.1735	+	7.84288i	−0.586636	+	0.267908i	−0.686543	−	0.727089i	$-0.740873\pi$
$857$	−17.1735	+	7.84288i	−0.586636	+	0.267908i	0.0999070	+	0.994997i	$0.468145\pi$
$858$	1.25116	−	1.08414i	0.0427140	−	0.0370119i
$859$	−17.5304	+	2.52049i	−0.598129	+	0.0859980i	−0.434728	−	0.900562i	$-0.643156\pi$
$859$	−17.5304	+	2.52049i	−0.598129	+	0.0859980i	−0.163401	+	0.986560i	$0.552246\pi$
$860$	8.71662	−	29.6861i	0.297234	−	1.01229i
$861$	−21.1212	+	13.3295i	−0.719809	+	0.454268i
$862$	23.4004	−	36.4117i	0.797021	−	1.24019i
$863$	14.3305	+	9.20968i	0.487817	+	0.313501i	0.761327	−	0.648368i	$-0.224548\pi$
$863$	14.3305	+	9.20968i	0.487817	+	0.313501i	−0.273510	+	0.961869i	$0.588185\pi$
$864$	−5.40282	−	4.68157i	−0.183808	−	0.159270i
$865$	1.86385	−	6.34768i	0.0633727	−	0.215828i
$866$	−2.19234	−	15.2480i	−0.0744986	−	0.518149i
$867$	−9.22823	+	7.99631i	−0.313407	+	0.271569i
$868$	26.4916	−	3.58667i	0.899182	−	0.121740i
$869$	−0.690636	+	0.202789i	−0.0234282	+	0.00687914i
$870$	19.3605	+	8.84164i	0.656382	+	0.299760i
$871$	1.41671	−	9.85345i	0.0480034	−	0.333871i
$872$	21.0205	+	32.7085i	0.711843	+	1.10765i
$873$	7.20217			0.243756
$874$	5.39342	−	0.900311i	0.182435	−	0.0304535i
$875$	25.3227	+	7.66230i	0.856062	+	0.259033i
$876$	−15.6432	+	10.0533i	−0.528535	+	0.339669i
$877$	4.91141	−	34.1596i	0.165846	−	1.15349i	−0.721510	−	0.692404i	$-0.756552\pi$
$877$	4.91141	−	34.1596i	0.165846	−	1.15349i	0.887357	−	0.461083i	$-0.152539\pi$
$878$	−47.8902	−	21.8707i	−1.61622	−	0.738101i
$879$	−9.40261	−	32.0224i	−0.317142	−	1.08009i
$880$	0.284947	−	0.130131i	0.00960556	−	0.00438671i
$881$	−3.93826	−	4.54500i	−0.132683	−	0.153125i	0.685520	−	0.728054i	$-0.259575\pi$
$881$	−3.93826	−	4.54500i	−0.132683	−	0.153125i	−0.818203	+	0.574929i	$0.805030\pi$
$882$	6.64930	−	13.9478i	0.223894	−	0.469648i
$883$	40.5792	+	11.9151i	1.36560	+	0.400976i	0.880733	−	0.473613i	$-0.157050\pi$
$883$	40.5792	+	11.9151i	1.36560	+	0.400976i	0.484866	+	0.874589i	$0.338869\pi$
$884$	−48.3925	−	41.9323i	−1.62762	−	1.41034i
$885$	−4.23100	−	2.71910i	−0.142223	−	0.0914014i
$886$	−57.0077	−	36.6366i	−1.91521	−	1.23083i
$887$	−40.2463	−	34.8736i	−1.35134	−	1.17094i	−0.969041	−	0.246901i	$-0.920588\pi$
$887$	−40.2463	−	34.8736i	−1.35134	−	1.17094i	−0.382297	−	0.924040i	$-0.624867\pi$
$888$	−0.912648	−	0.267978i	−0.0306265	−	0.00899274i
$889$	3.28854	−	21.6085i	0.110294	−	0.724727i
$890$	−30.3209	−	34.9922i	−1.01636	−	1.17294i
$891$	−0.165410	+	0.0755402i	−0.00554144	+	0.00253069i
$892$	14.8056	+	50.4232i	0.495728	+	1.68830i
$893$	1.83727	+	0.839055i	0.0614820	+	0.0280779i
$894$	1.22128	−	8.49419i	0.0408457	−	0.284088i
$895$	9.12549	−	5.86460i	0.305031	−	0.196032i
$896$	−35.3063	−	10.6832i	−1.17950	−	0.356901i
$897$	−14.6521	+	13.2877i	−0.489220	+	0.443662i
$898$	−54.5725			−1.82111
$899$	15.8977	+	24.7373i	0.530217	+	0.825035i
$900$	−1.50018	+	10.4340i	−0.0500060	+	0.347799i
$901$	36.8763	+	16.8408i	1.22853	+	0.561050i
$902$	3.63566	−	1.06753i	0.121054	−	0.0355447i
$903$	−3.31474	−	24.4831i	−0.110308	−	0.814745i
$904$	−17.1173	+	14.8322i	−0.569312	+	0.493312i
$905$	−1.09365	−	7.60648i	−0.0363540	−	0.252848i
$906$	−12.4612	+	42.4391i	−0.413997	+	1.40995i
$907$	−9.75040	−	8.44877i	−0.323757	−	0.280537i	0.477784	−	0.878478i	$-0.341440\pi$
$907$	−9.75040	−	8.44877i	−0.323757	−	0.280537i	−0.801540	+	0.597941i	$0.795986\pi$
$908$	−9.74808	−	6.26471i	−0.323501	−	0.207902i
$909$	−2.90283	+	4.51689i	−0.0962808	+	0.149816i
$910$	14.8275	+	23.4949i	0.491527	+	0.778848i
$911$	−7.11810	+	24.2420i	−0.235833	+	0.803174i	0.753493	+	0.657456i	$0.228367\pi$
$911$	−7.11810	+	24.2420i	−0.235833	+	0.803174i	−0.989326	+	0.145718i	$0.953451\pi$
$912$	−0.763602	+	0.109789i	−0.0252854	+	0.00363549i
$913$	−1.23515	+	1.07026i	−0.0408775	+	0.0354205i
$914$	−7.72390	+	3.52739i	−0.255484	+	0.116676i
$915$	1.72965	+	5.89066i	0.0571806	+	0.194739i
$916$	26.2739	−	57.5319i	0.868116	−	1.90091i
$917$	21.2635	+	9.92297i	0.702182	+	0.327685i
$918$	6.44997	+	10.0364i	0.212881	+	0.331249i
$919$			29.2461i			0.964739i	0.875968	+	0.482370i	$0.160224\pi$
$919$			29.2461i			0.964739i	−0.875968	+	0.482370i	$0.839776\pi$
$920$	9.58877	−	4.64376i	0.316132	−	0.153100i
$921$	−20.2282			−0.666541
$922$	−20.6189	−	32.0836i	−0.679047	−	1.05662i
$923$	−38.4087	−	5.52234i	−1.26424	−	0.181770i
$924$	−0.913592	+	1.03698i	−0.0300550	+	0.0341140i
$925$	−0.510569	−	1.73884i	−0.0167874	−	0.0571727i
$926$	−30.4550	−	66.6872i	−1.00081	−	2.19148i
$927$	3.86905	+	4.46512i	0.127076	+	0.146654i
$928$	−8.50517	−	59.1548i	−0.279196	−	1.94185i
$929$	15.6860	−	53.4215i	0.514640	−	1.75270i	−0.133364	−	0.991067i	$-0.542578\pi$
$929$	15.6860	−	53.4215i	0.514640	−	1.75270i	0.648004	−	0.761637i	$-0.275604\pi$
$930$	5.86468	−	6.76820i	0.192310	−	0.221938i
$931$	−1.44767	−	3.31319i	−0.0474455	−	0.108586i
$932$	9.69957	+	6.23353i	0.317720	+	0.204186i
$933$	−19.3765	+	22.3617i	−0.634359	+	0.732089i
$934$	−16.9929	−	4.98956i	−0.556024	−	0.163263i
$935$	−1.12203	+	0.161324i	−0.0366944	+	0.00527586i
$936$	−6.00355	+	5.20211i	−0.196232	+	0.170036i
$937$	21.4162	+	46.8950i	0.699637	+	1.53199i	0.840411	+	0.541950i	$0.182314\pi$
$937$	21.4162	+	46.8950i	0.699637	+	1.53199i	−0.140773	+	0.990042i	$0.544959\pi$
$938$	−0.115992	+	14.0956i	−0.00378726	+	0.460237i
$939$	29.7693	+	13.5952i	0.971484	+	0.443662i
$940$	12.8240	+	1.84382i	0.418274	+	0.0601388i
$941$	10.5316	−	6.76823i	0.343320	−	0.220638i	−0.357606	−	0.933873i	$-0.616407\pi$
$941$	10.5316	−	6.76823i	0.343320	−	0.220638i	0.700925	+	0.713235i	$0.252771\pi$
$942$		−	7.02856i		−	0.229003i
$943$	−43.1389	+	13.7331i	−1.40480	+	0.447212i
$944$			6.51259i			0.211967i
$945$	−0.835619	−	2.93499i	−0.0271827	−	0.0954752i
$946$	−0.533440	+	3.71016i	−0.0173436	+	0.120628i
$947$	4.64235	−	10.1653i	0.150856	−	0.330329i	−0.819084	−	0.573674i	$-0.805518\pi$
$947$	4.64235	−	10.1653i	0.150856	−	0.330329i	0.969940	+	0.243345i	$0.0782448\pi$
$948$	10.9099	−	3.20343i	0.354337	−	0.104043i
$949$	−11.0911	−	24.2861i	−0.360032	−	0.788360i
$950$	2.73995	+	3.16207i	0.0888956	+	0.102591i
$951$	22.7384	−	3.26929i	0.737344	−	0.106014i
$952$	23.0462	+	15.0803i	0.746930	+	0.488754i
$953$	−31.5042	−	27.2986i	−1.02052	−	0.884288i	−0.0271965	−	0.999630i	$-0.508658\pi$
$953$	−31.5042	−	27.2986i	−1.02052	−	0.884288i	−0.993326	+	0.115343i	$0.963203\pi$
$954$	8.95154	−	13.9289i	0.289817	−	0.450964i
$955$	−5.50620	+	8.56782i	−0.178177	+	0.277248i
$956$	−23.9445	+	27.6334i	−0.774419	+	0.893727i
$957$	−1.45857	−	0.428275i	−0.0471489	−	0.0138442i
$958$	0.254857	+	1.77257i	0.00823407	+	0.0572692i
$959$	8.02805	−	3.58675i	0.259239	−	0.115822i
$960$	−13.4225	+	6.12986i	−0.433210	+	0.197840i
$961$	−17.8726	+	5.24787i	−0.576536	+	0.169286i
$962$	1.86773	−	4.08976i	0.0602180	−	0.131859i
$963$	12.2353	+	1.75917i	0.394278	+	0.0566886i
$964$	48.9112	−	31.4333i	1.57532	−	1.01240i
$965$	14.3756			0.462767
$966$	18.0356	−	21.4289i	0.580285	−	0.689464i
$967$	−23.5532			−0.757419			−0.378710	−	0.925516i	$-0.623632\pi$
$967$	−23.5532			−0.757419			−0.378710	+	0.925516i	$0.623632\pi$
$968$	−17.7698	+	11.4199i	−0.571141	+	0.367050i
$969$	2.76323	+	0.397293i	0.0887679	+	0.0127629i
$970$	7.61738	−	16.6797i	0.244579	−	0.535554i
$971$	−13.7305	+	4.03165i	−0.440634	+	0.129382i	−0.494522	−	0.869165i	$-0.664657\pi$
$971$	−13.7305	+	4.03165i	−0.440634	+	0.129382i	0.0538881	+	0.998547i	$0.482839\pi$
$972$	2.61296	−	1.19330i	0.0838109	−	0.0382751i
$973$	25.8305	−	11.5404i	0.828086	−	0.369970i
$974$	−0.883372	−	6.14399i	−0.0283051	−	0.196866i
$975$	−14.5221	−	4.26406i	−0.465078	−	0.136559i
$976$	5.20606	−	6.00811i	0.166642	−	0.192315i
$977$	−22.8922	+	35.6210i	−0.732387	+	1.13962i	0.252697	+	0.967545i	$0.418682\pi$
$977$	−22.8922	+	35.6210i	−0.732387	+	1.13962i	−0.985084	+	0.172072i	$0.944954\pi$
$978$	19.9497	−	31.0423i	0.637920	−	0.992623i
$979$	2.49924	+	2.16560i	0.0798759	+	0.0692129i
$980$	−14.8974	−	17.7753i	−0.475879	−	0.567811i
$981$	19.9812	−	2.87286i	0.637950	−	0.0917233i
$982$	8.01483	+	9.24961i	0.255764	+	0.295167i
$983$	11.0524	+	24.2014i	0.352517	+	0.771905i	0.999952	+	0.00978405i	$0.00311441\pi$
$983$	11.0524	+	24.2014i	0.352517	+	0.771905i	−0.647435	+	0.762121i	$0.724158\pi$
$984$	−17.4453	+	5.12240i	−0.556135	+	0.163296i
$985$	−9.83273	+	21.5307i	−0.313297	+	0.686024i
$986$	−14.1935	+	98.7179i	−0.452013	+	3.14382i
$987$	9.95044	−	2.83299i	0.316726	−	0.0901750i
$988$			6.11954i			0.194689i
$989$	5.36996	−	44.4611i	0.170755	−	1.41378i
$990$			0.462974i			0.0147143i
$991$	21.7184	−	13.9576i	0.689908	−	0.443377i	−0.148145	−	0.988966i	$-0.547330\pi$
$991$	21.7184	−	13.9576i	0.689908	−	0.443377i	0.838053	+	0.545589i	$0.183694\pi$
$992$	−24.8906	−	3.57872i	−0.790276	−	0.113625i
$993$	−11.2414	−	5.13378i	−0.356735	−	0.162915i
$994$	54.9445	+	0.452135i	1.74273	+	0.0143409i
$995$	−0.111924	−	0.245080i	−0.00354824	−	0.00776956i
$996$	19.5115	−	16.9068i	0.618246	−	0.535713i
$997$	12.1463	−	1.74637i	0.384677	−	0.0553082i	0.0527362	−	0.998608i	$-0.483206\pi$
$997$	12.1463	−	1.74637i	0.384677	−	0.0553082i	0.331941	+	0.943300i	$0.392297\pi$
$998$	70.0323	+	20.5633i	2.21683	+	0.650921i
$999$	−0.323401	+	0.373225i	−0.0102320	+	0.0118083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.34.6	yes	320
7.6	odd	2	inner	483.2.r.a.34.5	✓	320
23.21	odd	22	inner	483.2.r.a.412.5	yes	320
161.90	even	22	inner	483.2.r.a.412.6	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.34.5	✓	320	7.6	odd	2	inner
483.2.r.a.34.6	yes	320	1.1	even	1	trivial
483.2.r.a.412.5	yes	320	23.21	odd	22	inner
483.2.r.a.412.6	yes	320	161.90	even	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85697 + 1.19340i) q^{2} +(0.989821 + 0.142315i) q^{3} +(1.19330 - 2.61296i) q^{4} +(-1.10668 + 0.324952i) q^{5} +(-2.00791 + 0.916981i) q^{6} +(1.07924 + 2.41562i) q^{7} +(0.274107 + 1.90645i) q^{8} +(0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-1.85697 + 1.19340i) q^{2} +(0.989821 + 0.142315i) q^{3} +(1.19330 - 2.61296i) q^{4} +(-1.10668 + 0.324952i) q^{5} +(-2.00791 + 0.916981i) q^{6} +(1.07924 + 2.41562i) q^{7} +(0.274107 + 1.90645i) q^{8} +(0.959493 + 0.281733i) q^{9} +(1.66728 - 1.92415i) q^{10} +(-0.0983116 + 0.152976i) q^{11} +(1.55302 - 2.41654i) q^{12} +(3.11702 + 2.70091i) q^{13} +(-4.88694 - 3.19777i) q^{14} +(-1.14167 + 0.164147i) q^{15} +(0.978068 + 1.12875i) q^{16} +(-2.24519 - 4.91628i) q^{17} +(-2.11797 + 0.621892i) q^{18} +(-0.214571 + 0.469846i) q^{19} +(-0.471520 + 3.27949i) q^{20} +(0.724480 + 2.54463i) q^{21} -0.401397i q^{22} +(0.108391 + 4.79461i) q^{23} +1.92606i q^{24} +(-3.08711 + 1.98397i) q^{25} +(-9.01148 - 1.29566i) q^{26} +(0.909632 + 0.415415i) q^{27} +(7.59980 + 0.0625383i) q^{28} +(3.47274 + 7.60424i) q^{29} +(1.92415 - 1.66728i) q^{30} +(3.48170 - 0.500593i) q^{31} +(-6.85938 - 2.01409i) q^{32} +(-0.119082 + 0.137428i) q^{33} +(10.0364 + 6.44997i) q^{34} +(-1.97934 - 2.32263i) q^{35} +(1.88112 - 2.17093i) q^{36} +(-0.139133 + 0.473843i) q^{37} +(-0.162263 - 1.12856i) q^{38} +(2.70091 + 3.11702i) q^{39} +(-0.922855 - 2.02077i) q^{40} +(2.65953 + 9.05751i) q^{41} +(-4.38210 - 3.86070i) q^{42} +(-9.24311 - 1.32896i) q^{43} +(0.282405 + 0.439431i) q^{44} -1.15341 q^{45} +(-5.92318 - 8.77409i) q^{46} -3.91037i q^{47} +(0.807475 + 1.25646i) q^{48} +(-4.67046 + 5.21409i) q^{49} +(3.36500 - 7.36833i) q^{50} +(-1.52268 - 5.18576i) q^{51} +(10.7769 - 4.92166i) q^{52} +(-5.66877 + 4.91202i) q^{53} +(-2.18492 + 0.314144i) q^{54} +(0.0590902 - 0.201243i) q^{55} +(-4.30944 + 2.71967i) q^{56} +(-0.279254 + 0.434527i) q^{57} +(-15.5237 - 9.97647i) q^{58} +(3.29542 + 2.85550i) q^{59} +(-0.933441 + 3.17901i) q^{60} +(-0.757513 - 5.26862i) q^{61} +(-5.86801 + 5.08466i) q^{62} +(0.354968 + 2.62183i) q^{63} +(12.2752 - 3.60432i) q^{64} +(-4.32722 - 1.97618i) q^{65} +(0.0571248 - 0.397312i) q^{66} +(-1.30491 - 2.03047i) q^{67} -15.5253 q^{68} +(-0.575056 + 4.76123i) q^{69} +(6.44742 + 1.95090i) q^{70} +(-7.91478 + 5.08652i) q^{71} +(-0.274107 + 1.90645i) q^{72} +(-5.88839 - 2.68914i) q^{73} +(-0.307120 - 1.04595i) q^{74} +(-3.33804 + 1.52443i) q^{75} +(0.971643 + 1.12134i) q^{76} +(-0.475634 - 0.0723855i) q^{77} +(-8.73537 - 2.56494i) q^{78} +(2.99150 + 2.59215i) q^{79} +(-1.44920 - 0.931346i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-15.7479 - 13.6456i) q^{82} +(8.62357 + 2.53211i) q^{83} +(7.51354 + 1.14347i) q^{84} +(4.08227 + 4.71119i) q^{85} +(18.7502 - 8.56291i) q^{86} +(2.35520 + 8.02106i) q^{87} +(-0.318589 - 0.145495i) q^{88} +(2.58811 - 18.0007i) q^{89} +(2.14184 - 1.37648i) q^{90} +(-3.16036 + 10.4445i) q^{91} +(12.6575 + 5.43819i) q^{92} +3.51751 q^{93} +(4.66665 + 7.26145i) q^{94} +(0.0847856 - 0.589697i) q^{95} +(-6.50292 - 2.96978i) q^{96} +(6.91043 - 2.02908i) q^{97} +(2.45041 - 15.2562i) q^{98} +(-0.137428 + 0.119082i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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