LMFDB - Embedded newform 234.2.y.a.149.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(11,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			149.2
Character	$\chi$	$=$	234.149
Dual form			234.2.y.a.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.57210 - 0.726972i) q^{3} +1.00000i q^{4} +(0.653109 - 0.175000i) q^{5} +(0.597599 + 1.62569i) q^{6} +(-3.90017 + 1.04505i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.94302 + 2.28575i) q^{9} +(-0.585562 - 0.338074i) q^{10} +(-0.502310 + 0.502310i) q^{11} +(0.726972 - 1.57210i) q^{12} +(-2.29871 + 2.77775i) q^{13} +(3.49679 + 2.01888i) q^{14} +(-1.15398 - 0.199673i) q^{15} -1.00000 q^{16} +(3.24443 + 5.61952i) q^{17} +(0.242344 - 2.99020i) q^{18} +(-0.253608 - 0.0679541i) q^{19} +(0.175000 + 0.653109i) q^{20} +(6.89119 + 1.19239i) q^{21} +0.710373 q^{22} +(0.860504 + 1.49044i) q^{23} +(-1.62569 + 0.597599i) q^{24} +(-3.93420 + 2.27141i) q^{25} +(3.58960 - 0.338733i) q^{26} +(-1.39296 - 5.00596i) q^{27} +(-1.04505 - 3.90017i) q^{28} +1.28654i q^{29} +(0.674794 + 0.957175i) q^{30} +(1.04468 + 3.89881i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.15485 - 0.424519i) q^{33} +(1.67944 - 6.26776i) q^{34} +(-2.36435 + 1.36506i) q^{35} +(-2.28575 + 1.94302i) q^{36} +(-7.96159 + 2.13330i) q^{37} +(0.131277 + 0.227379i) q^{38} +(5.63317 - 2.69582i) q^{39} +(0.338074 - 0.585562i) q^{40} +(2.39802 - 8.94954i) q^{41} +(-4.02966 - 5.71595i) q^{42} +(-5.67915 - 3.27886i) q^{43} +(-0.502310 - 0.502310i) q^{44} +(1.66901 + 1.15282i) q^{45} +(0.445430 - 1.66237i) q^{46} +(-9.07214 - 2.43087i) q^{47} +(1.57210 + 0.726972i) q^{48} +(8.05701 - 4.65172i) q^{49} +(4.38803 + 1.17577i) q^{50} +(-1.01535 - 11.1931i) q^{51} +(-2.77775 - 2.29871i) q^{52} -6.34328i q^{53} +(-2.55478 + 4.52472i) q^{54} +(-0.240159 + 0.415967i) q^{55} +(-2.01888 + 3.49679i) q^{56} +(0.349298 + 0.291197i) q^{57} +(0.909720 - 0.909720i) q^{58} +(-3.52351 + 3.52351i) q^{59} +(0.199673 - 1.15398i) q^{60} +(-1.64932 + 2.85670i) q^{61} +(2.01817 - 3.49557i) q^{62} +(-9.96684 - 6.88426i) q^{63} -1.00000i q^{64} +(-1.01520 + 2.21645i) q^{65} +(-1.11678 - 0.516421i) q^{66} +(10.0909 + 2.70385i) q^{67} +(-5.61952 + 3.24443i) q^{68} +(-0.269297 - 2.96868i) q^{69} +(2.63709 + 0.706607i) q^{70} +(-2.09577 + 7.82153i) q^{71} +(2.99020 + 0.242344i) q^{72} +(-1.40415 - 1.40415i) q^{73} +(7.13817 + 4.12122i) q^{74} +(7.83623 - 0.710844i) q^{75} +(0.0679541 - 0.253608i) q^{76} +(1.43416 - 2.48403i) q^{77} +(-5.88948 - 2.07702i) q^{78} +(7.29283 + 12.6316i) q^{79} +(-0.653109 + 0.175000i) q^{80} +(-1.44931 + 8.88254i) q^{81} +(-8.02394 + 4.63262i) q^{82} +(1.04760 - 3.90968i) q^{83} +(-1.19239 + 6.89119i) q^{84} +(3.10238 + 3.10238i) q^{85} +(1.69726 + 6.33427i) q^{86} +(0.935277 - 2.02257i) q^{87} +0.710373i q^{88} +(-2.64065 - 9.85503i) q^{89} +(-0.365007 - 1.99533i) q^{90} +(6.06248 - 13.2360i) q^{91} +(-1.49044 + 0.860504i) q^{92} +(1.19197 - 6.88878i) q^{93} +(4.69609 + 8.13386i) q^{94} -0.177526 q^{95} +(-0.597599 - 1.62569i) q^{96} +(0.520942 + 1.94418i) q^{97} +(-8.98642 - 2.40791i) q^{98} +(-2.12416 - 0.172155i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.57210	−	0.726972i	−0.907655	−	0.419717i
$3$	−1.57210	−	0.726972i	−0.907655	−	0.419717i
$4$			1.00000i			0.500000i
$5$	0.653109	−	0.175000i	0.292079	−	0.0782624i	−0.109804	−	0.993953i	$-0.535022\pi$
$5$	0.653109	−	0.175000i	0.292079	−	0.0782624i	0.401883	+	0.915691i	$0.368356\pi$
$6$	0.597599	+	1.62569i	0.243969	+	0.663686i
$7$	−3.90017	+	1.04505i	−1.47412	+	0.394991i	−0.904343	−	0.426806i	$-0.859639\pi$
$7$	−3.90017	+	1.04505i	−1.47412	+	0.394991i	−0.569781	+	0.821796i	$0.692972\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	1.94302	+	2.28575i	0.647675	+	0.761917i
$10$	−0.585562	−	0.338074i	−0.185171	−	0.106908i
$11$	−0.502310	+	0.502310i	−0.151452	+	0.151452i	−0.778766	−	0.627314i	$-0.784154\pi$
$11$	−0.502310	+	0.502310i	−0.151452	+	0.151452i	0.627314	+	0.778766i	$0.284154\pi$
$12$	0.726972	−	1.57210i	0.209859	−	0.453827i
$13$	−2.29871	+	2.77775i	−0.637548	+	0.770410i
$13$	−2.29871	+	2.77775i	−0.637548	+	0.770410i
$14$	3.49679	+	2.01888i	0.934558	+	0.539567i
$15$	−1.15398	−	0.199673i	−0.297955	−	0.0515555i
$16$	−1.00000			−0.250000
$17$	3.24443	+	5.61952i	0.786890	+	1.36293i	0.927863	+	0.372920i	$0.121644\pi$
$17$	3.24443	+	5.61952i	0.786890	+	1.36293i	−0.140973	+	0.990013i	$0.545023\pi$
$18$	0.242344	−	2.99020i	0.0571210	−	0.704796i
$19$	−0.253608	−	0.0679541i	−0.0581817	−	0.0155897i	0.229611	−	0.973283i	$-0.426255\pi$
$19$	−0.253608	−	0.0679541i	−0.0581817	−	0.0155897i	−0.287792	+	0.957693i	$0.592921\pi$
$20$	0.175000	+	0.653109i	0.0391312	+	0.146040i
$21$	6.89119	+	1.19239i	1.50378	+	0.260200i
$22$	0.710373			0.151452
$23$	0.860504	+	1.49044i	0.179427	+	0.310777i	0.941685	−	0.336497i	$-0.109242\pi$
$23$	0.860504	+	1.49044i	0.179427	+	0.310777i	−0.762257	+	0.647274i	$0.775909\pi$
$24$	−1.62569	+	0.597599i	−0.331843	+	0.121984i
$25$	−3.93420	+	2.27141i	−0.786840	+	0.454282i
$26$	3.58960	−	0.338733i	0.703979	−	0.0664310i
$27$	−1.39296	−	5.00596i	−0.268076	−	0.963398i
$28$	−1.04505	−	3.90017i	−0.197495	−	0.737062i
$29$			1.28654i			0.238904i	0.992840	+	0.119452i	$0.0381138\pi$
$29$			1.28654i			0.238904i	−0.992840	+	0.119452i	$0.961886\pi$
$30$	0.674794	+	0.957175i	0.123200	+	0.174755i
$31$	1.04468	+	3.89881i	0.187630	+	0.700246i	0.994052	+	0.108905i	$0.0347346\pi$
$31$	1.04468	+	3.89881i	0.187630	+	0.700246i	−0.806422	+	0.591341i	$0.798599\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.15485	−	0.424519i	0.201033	−	0.0738992i
$34$	1.67944	−	6.26776i	0.288022	−	1.07491i
$35$	−2.36435	+	1.36506i	−0.399648	+	0.230737i
$36$	−2.28575	+	1.94302i	−0.380958	+	0.323837i
$37$	−7.96159	+	2.13330i	−1.30888	+	0.350713i	−0.844800	−	0.535082i	$-0.820281\pi$
$37$	−7.96159	+	2.13330i	−1.30888	+	0.350713i	−0.464077	+	0.885795i	$0.653614\pi$
$38$	0.131277	+	0.227379i	0.0212960	+	0.0368857i
$39$	5.63317	−	2.69582i	0.902028	−	0.431677i
$40$	0.338074	−	0.585562i	0.0534542	−	0.0925854i
$41$	2.39802	−	8.94954i	0.374508	−	1.39768i	−0.479554	−	0.877512i	$-0.659202\pi$
$41$	2.39802	−	8.94954i	0.374508	−	1.39768i	0.854062	−	0.520171i	$-0.174132\pi$
$42$	−4.02966	−	5.71595i	−0.621790	−	0.881991i
$43$	−5.67915	−	3.27886i	−0.866062	−	0.500021i	−2.44809e−5	−	1.00000i	$-0.500008\pi$
$43$	−5.67915	−	3.27886i	−0.866062	−	0.500021i	−0.866038	+	0.499979i	$0.833341\pi$
$44$	−0.502310	−	0.502310i	−0.0757261	−	0.0757261i
$45$	1.66901	+	1.15282i	0.248802	+	0.171852i
$46$	0.445430	−	1.66237i	0.0656750	−	0.245102i
$47$	−9.07214	−	2.43087i	−1.32331	−	0.354579i	−0.473092	−	0.881013i	$-0.656862\pi$
$47$	−9.07214	−	2.43087i	−1.32331	−	0.354579i	−0.850216	+	0.526434i	$0.823529\pi$
$48$	1.57210	+	0.726972i	0.226914	+	0.104929i
$49$	8.05701	−	4.65172i	1.15100	−	0.664531i
$50$	4.38803	+	1.17577i	0.620561	+	0.166279i
$51$	−1.01535	−	11.1931i	−0.142178	−	1.56735i
$52$	−2.77775	−	2.29871i	−0.385205	−	0.318774i
$53$		−	6.34328i		−	0.871317i	−0.900112	−	0.435658i	$-0.856516\pi$
$53$		−	6.34328i		−	0.871317i	0.900112	−	0.435658i	$-0.143484\pi$
$54$	−2.55478	+	4.52472i	−0.347661	+	0.615737i
$55$	−0.240159	+	0.415967i	−0.0323830	+	0.0560890i
$56$	−2.01888	+	3.49679i	−0.269784	+	0.467279i
$57$	0.349298	+	0.291197i	0.0462656	+	0.0385700i
$58$	0.909720	−	0.909720i	0.119452	−	0.119452i
$59$	−3.52351	+	3.52351i	−0.458722	+	0.458722i	−0.898236	−	0.439514i	$-0.855151\pi$
$59$	−3.52351	+	3.52351i	−0.458722	+	0.458722i	0.439514	+	0.898236i	$0.355151\pi$
$60$	0.199673	−	1.15398i	0.0257777	−	0.148978i
$61$	−1.64932	+	2.85670i	−0.211173	+	0.365763i	−0.952082	−	0.305843i	$-0.901062\pi$
$61$	−1.64932	+	2.85670i	−0.211173	+	0.365763i	0.740909	+	0.671606i	$0.234395\pi$
$62$	2.01817	−	3.49557i	0.256308	−	0.443938i
$63$	−9.96684	−	6.88426i	−1.25570	−	0.867335i
$64$		−	1.00000i		−	0.125000i
$65$	−1.01520	+	2.21645i	−0.125921	+	0.274917i
$66$	−1.11678	−	0.516421i	−0.137466	−	0.0635671i
$67$	10.0909	+	2.70385i	1.23280	+	0.330327i	0.815669	−	0.578520i	$-0.196369\pi$
$67$	10.0909	+	2.70385i	1.23280	+	0.330327i	0.417130	+	0.908847i	$0.363036\pi$
$68$	−5.61952	+	3.24443i	−0.681467	+	0.393445i
$69$	−0.269297	−	2.96868i	−0.0324196	−	0.357388i
$70$	2.63709	+	0.706607i	0.315193	+	0.0844556i
$71$	−2.09577	+	7.82153i	−0.248722	+	0.928245i	0.722753	+	0.691106i	$0.242876\pi$
$71$	−2.09577	+	7.82153i	−0.248722	+	0.928245i	−0.971476	+	0.237139i	$0.923790\pi$
$72$	2.99020	+	0.242344i	0.352398	+	0.0285605i
$73$	−1.40415	−	1.40415i	−0.164343	−	0.164343i	0.620145	−	0.784488i	$-0.287074\pi$
$73$	−1.40415	−	1.40415i	−0.164343	−	0.164343i	−0.784488	+	0.620145i	$0.787074\pi$
$74$	7.13817	+	4.12122i	0.829795	+	0.479082i
$75$	7.83623	−	0.710844i	0.904849	−	0.0820812i
$76$	0.0679541	−	0.253608i	0.00779487	−	0.0290909i
$77$	1.43416	−	2.48403i	0.163437	−	0.283081i
$78$	−5.88948	−	2.07702i	−0.666853	−	0.235176i
$79$	7.29283	+	12.6316i	0.820507	+	1.42116i	0.905305	+	0.424762i	$0.139642\pi$
$79$	7.29283	+	12.6316i	0.820507	+	1.42116i	−0.0847976	+	0.996398i	$0.527024\pi$
$80$	−0.653109	+	0.175000i	−0.0730198	+	0.0195656i
$81$	−1.44931	+	8.88254i	−0.161034	+	0.986949i
$82$	−8.02394	+	4.63262i	−0.886096	+	0.511588i
$83$	1.04760	−	3.90968i	0.114989	−	0.429144i	−0.884297	−	0.466924i	$-0.845362\pi$
$83$	1.04760	−	3.90968i	0.114989	−	0.429144i	0.999286	+	0.0377806i	$0.0120288\pi$
$84$	−1.19239	+	6.89119i	−0.130100	+	0.751891i
$85$	3.10238	+	3.10238i	0.336501	+	0.336501i
$86$	1.69726	+	6.33427i	0.183020	+	0.683042i
$87$	0.935277	−	2.02257i	0.100272	−	0.216843i
$88$			0.710373i			0.0757261i
$89$	−2.64065	−	9.85503i	−0.279908	−	1.04463i	−0.952481	−	0.304600i	$-0.901477\pi$
$89$	−2.64065	−	9.85503i	−0.279908	−	1.04463i	0.672573	−	0.740031i	$-0.265189\pi$
$90$	−0.365007	−	1.99533i	−0.0384752	−	0.210327i
$91$	6.06248	−	13.2360i	0.635521	−	1.38751i
$92$	−1.49044	+	0.860504i	−0.155389	+	0.0897137i
$93$	1.19197	−	6.88878i	0.123602	−	0.714334i
$94$	4.69609	+	8.13386i	0.484364	+	0.838944i
$95$	−0.177526			−0.0182138
$96$	−0.597599	−	1.62569i	−0.0609922	−	0.165922i
$97$	0.520942	+	1.94418i	0.0528937	+	0.197402i	0.987317	−	0.158763i	$-0.0507507\pi$
$97$	0.520942	+	1.94418i	0.0528937	+	0.197402i	−0.934423	+	0.356165i	$0.884084\pi$
$98$	−8.98642	−	2.40791i	−0.907766	−	0.243235i
$99$	−2.12416	−	0.172155i	−0.213486	−	0.0173022i
$100$	−2.27141	−	3.93420i	−0.227141	−	0.393420i
$101$	14.5201			1.44481			0.722404	−	0.691472i	$-0.243037\pi$
$101$	14.5201			1.44481			0.722404	+	0.691472i	$0.243037\pi$
$102$	−7.19674	+	8.63267i	−0.712584	+	0.854761i
$103$	−16.7121	−	9.64874i	−1.64669	−	0.950719i	−0.978374	−	0.206844i	$-0.933681\pi$
$103$	−16.7121	−	9.64874i	−1.64669	−	0.950719i	−0.668319	−	0.743874i	$-0.732986\pi$
$104$	0.338733	+	3.58960i	0.0332155	+	0.351990i
$105$	4.70937	−	0.427199i	0.459587	−	0.0416904i
$106$	−4.48538	+	4.48538i	−0.435658	+	0.435658i
$107$	11.5211	+	6.65169i	1.11378	+	0.643043i	0.939807	−	0.341706i	$-0.111005\pi$
$107$	11.5211	+	6.65169i	1.11378	+	0.643043i	0.173977	+	0.984750i	$0.444338\pi$
$108$	5.00596	−	1.39296i	0.481699	−	0.134038i
$109$	7.63616	−	7.63616i	0.731412	−	0.731412i	−0.239488	−	0.970899i	$-0.576979\pi$
$109$	7.63616	−	7.63616i	0.731412	−	0.731412i	0.970899	+	0.239488i	$0.0769794\pi$
$110$	0.463951	−	0.124315i	0.0442360	−	0.0118530i
$111$	14.0673	+	2.43408i	1.33521	+	0.231032i
$112$	3.90017	−	1.04505i	0.368531	−	0.0987476i
$113$			15.2122i			1.43105i	0.698588	+	0.715524i	$0.253812\pi$
$113$			15.2122i			1.43105i	−0.698588	+	0.715524i	$0.746188\pi$
$114$	−0.0410836	−	0.452898i	−0.00384783	−	0.0424178i
$115$	0.822829	+	0.822829i	0.0767292	+	0.0767292i
$116$	−1.28654			−0.119452
$117$	−10.8157	+	0.142959i	−0.999913	+	0.0132166i
$118$	4.98300			0.458722
$119$	−18.5265	−	18.5265i	−1.69832	−	1.69832i
$120$	−0.957175	+	0.674794i	−0.0873777	+	0.0616000i
$121$			10.4954i			0.954125i
$122$	3.18623	−	0.853749i	0.288468	−	0.0772948i
$123$	−10.2760	+	12.3263i	−0.926556	+	1.11143i
$124$	−3.89881	+	1.04468i	−0.350123	+	0.0938152i
$125$	−4.56251	+	4.56251i	−0.408083	+	0.408083i
$126$	2.17971	+	11.9155i	0.194184	+	1.06152i
$127$	16.8933	+	9.75334i	1.49904	+	0.865469i	0.999999	−	0.00111133i	$-0.000353747\pi$
$127$	16.8933	+	9.75334i	1.49904	+	0.865469i	0.499037	+	0.866581i	$0.333687\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	6.54458	+	9.28329i	0.576218	+	0.817348i
$130$	2.28513	−	0.849411i	0.200419	−	0.0744982i
$131$	−4.87564	−	2.81495i	−0.425986	−	0.245943i	0.271649	−	0.962396i	$-0.412431\pi$
$131$	−4.87564	−	2.81495i	−0.425986	−	0.245943i	−0.697635	+	0.716453i	$0.745764\pi$
$132$	0.424519	+	1.15485i	0.0369496	+	0.100517i
$133$	1.06013			0.0919249
$134$	−5.22343	−	9.04724i	−0.451236	−	0.781563i
$135$	−1.78580	−	3.02567i	−0.153697	−	0.260408i
$136$	6.26776	+	1.67944i	0.537456	+	0.144011i
$137$	3.04445	+	11.3621i	0.260105	+	0.970726i	0.965179	+	0.261592i	$0.0842474\pi$
$137$	3.04445	+	11.3621i	0.260105	+	0.970726i	−0.705073	+	0.709134i	$0.749086\pi$
$138$	−1.90875	+	2.28960i	−0.162484	+	0.194904i
$139$	2.96212			0.251244			0.125622	−	0.992078i	$-0.459907\pi$
$139$	2.96212			0.251244			0.125622	+	0.992078i	$0.459907\pi$
$140$	−1.36506	−	2.36435i	−0.115369	−	0.199824i
$141$	12.4952	+	10.4168i	1.05228	+	0.877251i
$142$	7.01259	−	4.04872i	0.588484	−	0.339761i
$143$	−0.240627	−	2.54996i	−0.0201222	−	0.213238i
$144$	−1.94302	−	2.28575i	−0.161919	−	0.190479i
$145$	0.225144	+	0.840250i	0.0186972	+	0.0697790i
$146$			1.98576i			0.164343i
$147$	−16.0481	+	1.45577i	−1.32363	+	0.120070i
$148$	−2.13330	−	7.96159i	−0.175356	−	0.654439i
$149$	−16.4140	−	16.4140i	−1.34469	−	1.34469i	−0.891329	−	0.453358i	$-0.850226\pi$
$149$	−16.4140	−	16.4140i	−1.34469	−	1.34469i	−0.453358	−	0.891329i	$-0.649774\pi$
$150$	−6.04369	−	5.03841i	−0.493465	−	0.411384i
$151$	−1.78383	+	6.65733i	−0.145166	+	0.541766i	0.854582	+	0.519316i	$0.173813\pi$
$151$	−1.78383	+	6.65733i	−0.145166	+	0.541766i	−0.999748	+	0.0224496i	$0.992853\pi$
$152$	−0.227379	+	0.131277i	−0.0184429	+	0.0106480i
$153$	−6.54081	+	18.3348i	−0.528793	+	1.48228i
$154$	−2.77058	+	0.742373i	−0.223259	+	0.0598222i
$155$	1.36458	+	2.36353i	0.109606	+	0.189843i
$156$	2.69582	+	5.63317i	0.215838	+	0.451014i
$157$	−5.48299	+	9.49681i	−0.437590	+	0.757928i	−0.997503	−	0.0706232i	$-0.977501\pi$
$157$	−5.48299	+	9.49681i	−0.437590	+	0.757928i	0.559913	+	0.828551i	$0.310835\pi$
$158$	3.77505	−	14.0887i	0.300327	−	1.12083i
$159$	−4.61139	+	9.97230i	−0.365707	+	0.790855i
$160$	0.585562	+	0.338074i	0.0462927	+	0.0267271i
$161$	−4.91369	−	4.91369i	−0.387253	−	0.387253i
$162$	7.30572	−	5.25609i	0.573992	−	0.412957i
$163$	3.31255	−	12.3626i	0.259459	−	0.968315i	−0.706096	−	0.708116i	$-0.749545\pi$
$163$	3.31255	−	12.3626i	0.259459	−	0.968315i	0.965555	−	0.260198i	$-0.0837880\pi$
$164$	8.94954	+	2.39802i	0.698842	+	0.187254i
$165$	0.679951	−	0.479355i	0.0529341	−	0.0373178i
$166$	−3.50533	+	2.02380i	−0.272066	+	0.157077i
$167$	−0.811408	−	0.217416i	−0.0627886	−	0.0168242i	0.227288	−	0.973828i	$-0.427014\pi$
$167$	−0.811408	−	0.217416i	−0.0627886	−	0.0168242i	−0.290077	+	0.957003i	$0.593681\pi$
$168$	5.71595	−	4.02966i	0.440995	−	0.310895i
$169$	−2.43183	−	12.7705i	−0.187064	−	0.982348i
$170$		−	4.38743i		−	0.336501i
$171$	−0.337441	−	0.711722i	−0.0258047	−	0.0544267i
$172$	3.27886	−	5.67915i	0.250011	−	0.433031i
$173$	10.6585	−	18.4610i	0.810349	−	1.40356i	−0.102272	−	0.994757i	$-0.532611\pi$
$173$	10.6585	−	18.4610i	0.810349	−	1.40356i	0.912620	−	0.408808i	$-0.134056\pi$
$174$	−2.09152	+	0.768834i	−0.158557	+	0.0582852i
$175$	12.9703	−	12.9703i	0.980463	−	0.980463i
$176$	0.502310	−	0.502310i	0.0378630	−	0.0378630i
$177$	8.10082	−	2.97783i	0.608895	−	0.223828i
$178$	−5.10134	+	8.83578i	−0.382361	+	0.662269i
$179$	0.120767	−	0.209175i	0.00902656	−	0.0156345i	−0.861477	−	0.507797i	$-0.830460\pi$
$179$	0.120767	−	0.209175i	0.00902656	−	0.0156345i	0.870503	+	0.492162i	$0.163793\pi$
$180$	−1.15282	+	1.66901i	−0.0859258	+	0.124401i
$181$			1.73952i			0.129298i	0.997908	+	0.0646488i	$0.0205927\pi$
$181$			1.73952i			0.129298i	−0.997908	+	0.0646488i	$0.979407\pi$
$182$	−13.6461	+	5.07242i	−1.01151	+	0.375993i
$183$	4.66964	−	3.29202i	0.345189	−	0.243353i
$184$	1.66237	+	0.445430i	0.122551	+	0.0328375i
$185$	−4.82646	+	2.78656i	−0.354848	+	0.204872i
$186$	−5.71396	+	4.02825i	−0.418968	+	0.295366i
$187$	−4.45245	−	1.19303i	−0.325595	−	0.0872430i
$188$	2.43087	−	9.07214i	0.177290	−	0.661654i
$189$	10.6643	+	18.0684i	0.775710	+	1.31428i
$190$	0.125530	+	0.125530i	0.00910688	+	0.00910688i
$191$	7.31652	+	4.22419i	0.529404	+	0.305652i	0.740774	−	0.671754i	$-0.234459\pi$
$191$	7.31652	+	4.22419i	0.529404	+	0.305652i	−0.211369	+	0.977406i	$0.567792\pi$
$192$	−0.726972	+	1.57210i	−0.0524647	+	0.113457i
$193$	0.0138895	−	0.0518362i	0.000999786	−	0.00373125i	−0.965424	−	0.260684i	$-0.916052\pi$
$193$	0.0138895	−	0.0518362i	0.000999786	−	0.00373125i	0.966424	+	0.256953i	$0.0827185\pi$
$194$	1.00638	−	1.74311i	0.0722541	−	0.125148i
$195$	3.20730	−	2.74647i	0.229680	−	0.196679i
$196$	4.65172	+	8.05701i	0.332265	+	0.575501i
$197$	2.56942	−	0.688475i	0.183064	−	0.0490518i	−0.166122	−	0.986105i	$-0.553125\pi$
$197$	2.56942	−	0.688475i	0.183064	−	0.0490518i	0.349186	+	0.937053i	$0.386458\pi$
$198$	1.38027	+	1.62374i	0.0980917	+	0.115394i
$199$	−1.51087	+	0.872302i	−0.107103	+	0.0618359i	−0.552595	−	0.833450i	$-0.686362\pi$
$199$	−1.51087	+	0.872302i	−0.107103	+	0.0618359i	0.445492	+	0.895286i	$0.353029\pi$
$200$	−1.17577	+	4.38803i	−0.0831394	+	0.310281i
$201$	−13.8983	−	11.5865i	−0.980311	−	0.817250i
$202$	−10.2673	−	10.2673i	−0.722404	−	0.722404i
$203$	−1.34449	−	5.01771i	−0.0943649	−	0.352175i
$204$	11.1931	−	1.01535i	0.783673	−	0.0710890i
$205$		−	6.26468i		−	0.437544i
$206$	4.99456	+	18.6399i	0.347987	+	1.29871i
$207$	−1.73479	+	4.86285i	−0.120576	+	0.337992i
$208$	2.29871	−	2.77775i	0.159387	−	0.192603i
$209$	0.161524	−	0.0932559i	0.0111728	−	0.00645064i
$210$	−3.63210	−	3.02795i	−0.250639	−	0.208948i
$211$	0.651117	+	1.12777i	0.0448248	+	0.0776388i	0.887567	−	0.460678i	$-0.152394\pi$
$211$	0.651117	+	1.12777i	0.0448248	+	0.0776388i	−0.842743	+	0.538317i	$0.819060\pi$
$212$	6.34328			0.435658
$213$	8.98080	−	10.7727i	0.615354	−	0.738133i
$214$	−3.44317	−	12.8501i	−0.235370	−	0.878414i
$215$	−4.28290	−	1.14760i	−0.292092	−	0.0782657i
$216$	−4.52472	−	2.55478i	−0.307868	−	0.173831i
$217$	−8.14887	−	14.1143i	−0.553181	−	0.958138i
$218$	−10.7992			−0.731412
$219$	1.18669	+	3.22824i	0.0801891	+	0.218144i
$220$	−0.415967	−	0.240159i	−0.0280445	−	0.0161915i
$221$	−23.0677	−	3.90543i	−1.55170	−	0.262708i
$222$	−8.22593	−	11.6682i	−0.552088	−	0.783121i
$223$	−13.4964	+	13.4964i	−0.903785	+	0.903785i	−0.995761	−	0.0919766i	$-0.970682\pi$
$223$	−13.4964	+	13.4964i	−0.903785	+	0.903785i	0.0919766	+	0.995761i	$0.470682\pi$
$224$	−3.49679	−	2.01888i	−0.233639	−	0.134892i
$225$	−12.8361	−	4.57919i	−0.855742	−	0.305279i
$226$	10.7567	−	10.7567i	0.715524	−	0.715524i
$227$	15.8751	−	4.25372i	1.05367	−	0.282329i	0.309901	−	0.950769i	$-0.399704\pi$
$227$	15.8751	−	4.25372i	1.05367	−	0.282329i	0.743766	+	0.668440i	$0.233037\pi$
$228$	−0.291197	+	0.349298i	−0.0192850	+	0.0231328i
$229$	−13.1402	+	3.52092i	−0.868332	+	0.232669i	−0.665366	−	0.746517i	$-0.731725\pi$
$229$	−13.1402	+	3.52092i	−0.868332	+	0.232669i	−0.202965	+	0.979186i	$0.565058\pi$
$230$		−	1.16366i		−	0.0767292i
$231$	−4.06046	+	2.86256i	−0.267159	+	0.188343i
$232$	0.909720	+	0.909720i	0.0597260	+	0.0597260i
$233$	3.89618			0.255247			0.127623	−	0.991823i	$-0.459265\pi$
$233$	3.89618			0.255247			0.127623	+	0.991823i	$0.459265\pi$
$234$	7.74895	+	7.54677i	0.506565	+	0.493348i
$235$	−6.35050			−0.414261
$236$	−3.52351	−	3.52351i	−0.229361	−	0.229361i
$237$	−2.28231	−	25.1598i	−0.148252	−	1.63430i
$238$			26.2004i			1.69832i
$239$	1.52259	−	0.407977i	0.0984882	−	0.0263898i	−0.209238	−	0.977865i	$-0.567098\pi$
$239$	1.52259	−	0.407977i	0.0984882	−	0.0263898i	0.307727	+	0.951475i	$0.400432\pi$
$240$	1.15398	+	0.199673i	0.0744888	+	0.0128889i
$241$	−4.98879	+	1.33674i	−0.321356	+	0.0861071i	−0.415891	−	0.909414i	$-0.636530\pi$
$241$	−4.98879	+	1.33674i	−0.321356	+	0.0861071i	0.0945350	+	0.995522i	$0.469864\pi$
$242$	7.42135	−	7.42135i	0.477062	−	0.477062i
$243$	8.73582	−	12.9107i	0.560403	−	0.828220i
$244$	−2.85670	−	1.64932i	−0.182881	−	0.105587i
$245$	4.44806	−	4.44806i	0.284176	−	0.284176i
$246$	15.9823	−	1.44979i	1.01899	−	0.0924353i
$247$	0.771732	−	0.548254i	0.0491042	−	0.0348846i
$248$	3.49557	+	2.01817i	0.221969	+	0.128154i
$249$	−4.48916	+	5.38486i	−0.284489	+	0.341252i
$250$	6.45236			0.408083
$251$	3.50515	+	6.07109i	0.221243	+	0.383204i	0.955186	−	0.296007i	$-0.0956553\pi$
$251$	3.50515	+	6.07109i	0.221243	+	0.383204i	−0.733943	+	0.679211i	$0.762322\pi$
$252$	6.88426	−	9.96684i	0.433668	−	0.627852i
$253$	−1.18090	−	0.316421i	−0.0742426	−	0.0198932i
$254$	−5.04870	−	18.8420i	−0.316784	−	1.18225i
$255$	−2.62193	−	7.13262i	−0.164191	−	0.446662i
$256$	1.00000			0.0625000
$257$	1.89609	+	3.28412i	0.118275	+	0.204858i	0.919084	−	0.394062i	$-0.128930\pi$
$257$	1.89609	+	3.28412i	0.118275	+	0.204858i	−0.800809	+	0.598919i	$0.795597\pi$
$258$	1.93656	−	11.1920i	0.120565	−	0.696783i
$259$	28.8221	−	16.6405i	1.79092	−	1.03399i
$260$	−2.21645	−	1.01520i	−0.137458	−	0.0629603i
$261$	−2.94071	+	2.49978i	−0.182025	+	0.154732i
$262$	1.45713	+	5.43807i	0.0900215	+	0.335965i
$263$			8.35425i			0.515145i	0.966259	+	0.257573i	$0.0829226\pi$
$263$			8.35425i			0.515145i	−0.966259	+	0.257573i	$0.917077\pi$
$264$	0.516421	−	1.11678i	0.0317835	−	0.0687331i
$265$	−1.11007	−	4.14286i	−0.0681914	−	0.254494i
$266$	−0.749625	−	0.749625i	−0.0459625	−	0.0459625i
$267$	−3.01295	+	17.4128i	−0.184390	+	1.06565i
$268$	−2.70385	+	10.0909i	−0.165164	+	0.616399i
$269$	3.60032	−	2.07864i	0.219515	−	0.126737i	−0.386211	−	0.922411i	$-0.626216\pi$
$269$	3.60032	−	2.07864i	0.219515	−	0.126737i	0.605726	+	0.795674i	$0.292883\pi$
$270$	−0.876721	+	3.40222i	−0.0533556	+	0.207053i
$271$	−20.1972	+	5.41182i	−1.22689	+	0.328745i	−0.813368	−	0.581749i	$-0.802369\pi$
$271$	−20.1972	+	5.41182i	−1.22689	+	0.328745i	−0.413523	+	0.910494i	$0.635702\pi$
$272$	−3.24443	−	5.61952i	−0.196723	−	0.340733i
$273$	−19.1530	+	16.4011i	−1.15919	+	0.992638i
$274$	5.88143	−	10.1869i	0.355310	−	0.615416i
$275$	0.835235	−	3.11714i	0.0503666	−	0.187971i
$276$	2.96868	−	0.269297i	0.178694	−	0.0162098i
$277$	13.1496	+	7.59192i	0.790082	+	0.456154i	0.839991	−	0.542600i	$-0.182560\pi$
$277$	13.1496	+	7.59192i	0.790082	+	0.456154i	−0.0499093	+	0.998754i	$0.515893\pi$
$278$	−2.09454	−	2.09454i	−0.125622	−	0.125622i
$279$	−6.88186	+	9.96336i	−0.412006	+	0.596491i
$280$	−0.706607	+	2.63709i	−0.0422278	+	0.157596i
$281$	29.2088	+	7.82648i	1.74245	+	0.466889i	0.982990	−	0.183662i	$-0.0587951\pi$
$281$	29.2088	+	7.82648i	1.74245	+	0.466889i	0.759463	+	0.650550i	$0.225462\pi$
$282$	−1.46965	−	16.2012i	−0.0875166	−	0.964768i
$283$	17.0472	−	9.84221i	1.01335	−	0.585059i	0.101180	−	0.994868i	$-0.467738\pi$
$283$	17.0472	−	9.84221i	1.01335	−	0.585059i	0.912171	+	0.409810i	$0.134405\pi$
$284$	−7.82153	−	2.09577i	−0.464122	−	0.124361i
$285$	0.279089	+	0.129056i	0.0165318	+	0.00764463i
$286$	−1.63294	+	1.97324i	−0.0965580	+	0.116680i
$287$			37.4107i			2.20829i
$288$	−0.242344	+	2.99020i	−0.0142802	+	0.176199i
$289$	−12.5527	+	21.7419i	−0.738393	+	1.27893i
$290$	0.434945	−	0.753347i	0.0255409	−	0.0442381i
$291$	0.594390	−	3.43517i	0.0348438	−	0.201373i
$292$	1.40415	−	1.40415i	0.0821715	−	0.0821715i
$293$	7.02611	−	7.02611i	0.410470	−	0.410470i	−0.471433	−	0.881902i	$-0.656263\pi$
$293$	7.02611	−	7.02611i	0.410470	−	0.410470i	0.881902	+	0.471433i	$0.156263\pi$
$294$	12.3771	+	10.3184i	0.721848	+	0.601779i
$295$	−1.68462	+	2.91785i	−0.0980825	+	0.169884i
$296$	−4.12122	+	7.13817i	−0.239541	+	0.414897i
$297$	3.21424	+	1.81485i	0.186509	+	0.105308i
$298$			23.2129i			1.34469i
$299$	−6.11812	−	1.03582i	−0.353820	−	0.0599029i
$300$	0.710844	+	7.83623i	0.0410406	+	0.452425i
$301$	25.5762	+	6.85312i	1.47419	+	0.395007i
$302$	5.96880	−	3.44609i	0.343466	−	0.198300i
$303$	−22.8272	−	10.5557i	−1.31139	−	0.606411i
$304$	0.253608	+	0.0679541i	0.0145454	+	0.00389744i
$305$	−0.577261	+	2.15437i	−0.0330539	+	0.123359i
$306$	17.5897	−	8.33963i	1.00554	−	0.476745i
$307$	14.4825	+	14.4825i	0.826560	+	0.826560i	0.987039	−	0.160479i	$-0.0513040\pi$
$307$	14.4825	+	14.4825i	0.826560	+	0.826560i	−0.160479	+	0.987039i	$0.551304\pi$
$308$	2.48403	+	1.43416i	0.141541	+	0.0817186i
$309$	19.2588	+	27.3181i	1.09560	+	1.55407i
$310$	0.706360	−	2.63617i	0.0401186	−	0.149724i
$311$	−11.3091	+	19.5879i	−0.641281	+	1.11073i	0.343866	+	0.939019i	$0.388263\pi$
$311$	−11.3091	+	19.5879i	−0.641281	+	1.11073i	−0.985147	+	0.171712i	$0.945070\pi$
$312$	2.07702	−	5.88948i	0.117588	−	0.333426i
$313$	−9.43419	−	16.3405i	−0.533252	−	0.923619i	−0.999246	−	0.0388313i	$-0.987636\pi$
$313$	−9.43419	−	16.3405i	−0.533252	−	0.923619i	0.465994	−	0.884788i	$-0.345697\pi$
$314$	10.5923	−	2.83820i	0.597759	−	0.160169i
$315$	−7.71418	−	2.75197i	−0.434645	−	0.155056i
$316$	−12.6316	+	7.29283i	−0.710580	+	0.410254i
$317$	−4.92071	+	18.3643i	−0.276375	+	1.03144i	0.678540	+	0.734563i	$0.262613\pi$
$317$	−4.92071	+	18.3643i	−0.276375	+	1.03144i	−0.954915	+	0.296881i	$0.904054\pi$
$318$	10.3122	−	3.79074i	0.578281	−	0.212574i
$319$	−0.646241	−	0.646241i	−0.0361825	−	0.0361825i
$320$	−0.175000	−	0.653109i	−0.00978280	−	0.0365099i
$321$	−13.2767	−	18.8326i	−0.741035	−	1.05114i
$322$			6.94900i			0.387253i
$323$	−0.440945	−	1.64563i	−0.0245348	−	0.0915652i
$324$	−8.88254	−	1.44931i	−0.493474	−	0.0805172i
$325$	2.73418	−	16.1496i	0.151665	−	0.895817i
$326$	−11.0840	+	6.39936i	−0.613887	+	0.354428i
$327$	−17.5561	+	6.45357i	−0.970856	+	0.356883i
$328$	−4.63262	−	8.02394i	−0.255794	−	0.443048i
$329$	37.9233			2.09078
$330$	−0.819754	−	0.141843i	−0.0451260	−	0.00780818i
$331$	−6.85161	−	25.5705i	−0.376598	−	1.40548i	−0.850995	−	0.525173i	$-0.824001\pi$
$331$	−6.85161	−	25.5705i	−0.376598	−	1.40548i	0.474397	−	0.880311i	$-0.342666\pi$
$332$	3.90968	+	1.04760i	0.214572	+	0.0574943i
$333$	−20.3458	−	14.0531i	−1.11494	−	0.770108i
$334$	0.420016	+	0.727488i	0.0229822	+	0.0398064i
$335$	7.06363			0.385927
$336$	−6.89119	−	1.19239i	−0.375945	−	0.0650501i
$337$	−19.6500	−	11.3449i	−1.07040	−	0.617996i	−0.142110	−	0.989851i	$-0.545389\pi$
$337$	−19.6500	−	11.3449i	−1.07040	−	0.617996i	−0.928291	+	0.371854i	$0.878722\pi$
$338$	−7.31055	+	10.7497i	−0.397642	+	0.584706i
$339$	11.0589	−	23.9152i	0.600635	−	1.29890i
$340$	−3.10238	+	3.10238i	−0.168250	+	0.168250i
$341$	−2.48316	−	1.43365i	−0.134471	−	0.0776368i
$342$	−0.264656	+	0.741870i	−0.0143110	+	0.0401157i
$343$	−6.57658	+	6.57658i	−0.355102	+	0.355102i
$344$	−6.33427	+	1.69726i	−0.341521	+	0.0915102i
$345$	−0.695400	−	1.89175i	−0.0374391	−	0.101848i
$346$	−20.5906	+	5.51723i	−1.10696	+	0.296608i
$347$			16.6116i			0.891759i	0.895093	+	0.445879i	$0.147109\pi$
$347$			16.6116i			0.891759i	−0.895093	+	0.445879i	$0.852891\pi$
$348$	2.02257	+	0.935277i	0.108421	+	0.0501361i
$349$	−1.58754	−	1.58754i	−0.0849789	−	0.0849789i	0.663340	−	0.748318i	$-0.269139\pi$
$349$	−1.58754	−	1.58754i	−0.0849789	−	0.0849789i	−0.748318	+	0.663340i	$0.769139\pi$
$350$	−18.3428			−0.980463
$351$	17.1074	+	7.63797i	0.913123	+	0.407684i
$352$	−0.710373			−0.0378630
$353$	−6.34497	−	6.34497i	−0.337709	−	0.337709i	0.517796	−	0.855504i	$-0.326753\pi$
$353$	−6.34497	−	6.34497i	−0.337709	−	0.337709i	−0.855504	+	0.517796i	$0.826753\pi$
$354$	−7.83379	−	3.62250i	−0.416361	−	0.192534i
$355$			5.47507i			0.290587i
$356$	9.85503	−	2.64065i	0.522315	−	0.139954i
$357$	15.6573	+	42.5938i	0.828675	+	2.25430i
$358$	−0.233304	+	0.0625136i	−0.0123305	+	0.00330395i
$359$	−25.1620	+	25.1620i	−1.32800	+	1.32800i	−0.420885	+	0.907114i	$0.638280\pi$
$359$	−25.1620	+	25.1620i	−1.32800	+	1.32800i	−0.907114	+	0.420885i	$0.861720\pi$
$360$	1.99533	−	0.365007i	0.105163	−	0.0192376i
$361$	−16.3948	−	9.46553i	−0.862883	−	0.498186i
$362$	1.23003	−	1.23003i	0.0646488	−	0.0646488i
$363$	7.62984	−	16.4998i	0.400463	−	0.866016i
$364$	13.2360	+	6.06248i	0.693753	+	0.317761i
$365$	−1.16279	−	0.671335i	−0.0608631	−	0.0351393i
$366$	−5.62974	−	0.974119i	−0.294271	−	0.0509180i
$367$	23.1998			1.21102			0.605509	−	0.795839i	$-0.292970\pi$
$367$	23.1998			1.21102			0.605509	+	0.795839i	$0.292970\pi$
$368$	−0.860504	−	1.49044i	−0.0448569	−	0.0776944i
$369$	25.1158	−	11.9079i	1.30748	−	0.619900i
$370$	5.38322	+	1.44243i	0.279860	+	0.0749883i
$371$	6.62903	+	24.7399i	0.344162	+	1.28443i
$372$	6.88878	+	1.19197i	0.357167	+	0.0618009i
$373$	−30.0462			−1.55573			−0.777866	−	0.628430i	$-0.783698\pi$
$373$	−30.0462			−1.55573			−0.777866	+	0.628430i	$0.783698\pi$
$374$	2.30476	+	3.99196i	0.119176	+	0.206419i
$375$	10.4896	−	3.85593i	0.541678	−	0.199119i
$376$	−8.13386	+	4.69609i	−0.419472	+	0.242182i
$377$	−3.57369	−	2.95738i	−0.184054	−	0.152313i
$378$	5.23551	−	20.3170i	0.269286	−	1.04500i
$379$	7.34807	+	27.4234i	0.377445	+	1.40864i	0.849739	+	0.527203i	$0.176759\pi$
$379$	7.34807	+	27.4234i	0.377445	+	1.40864i	−0.472294	+	0.881441i	$0.656574\pi$
$380$		−	0.177526i		−	0.00910688i
$381$	−19.4676	−	27.6142i	−0.997356	−	1.41472i
$382$	−2.18660	−	8.16051i	−0.111876	−	0.417528i
$383$	−2.62509	−	2.62509i	−0.134136	−	0.134136i	0.636851	−	0.770987i	$-0.280237\pi$
$383$	−2.62509	−	2.62509i	−0.134136	−	0.134136i	−0.770987	+	0.636851i	$0.780237\pi$
$384$	1.62569	−	0.597599i	0.0829608	−	0.0304961i
$385$	0.501955	−	1.87332i	0.0255820	−	0.0954732i
$386$	−0.0464751	+	0.0268324i	−0.00236552	+	0.00136573i
$387$	−3.54007	−	19.3520i	−0.179952	−	0.983718i
$388$	−1.94418	+	0.520942i	−0.0987009	+	0.0264468i
$389$	1.01593	+	1.75965i	0.0515099	+	0.0892178i	0.890631	−	0.454727i	$-0.150263\pi$
$389$	1.01593	+	1.75965i	0.0515099	+	0.0892178i	−0.839121	+	0.543945i	$0.816930\pi$
$390$	−4.20995	−	0.325859i	−0.213179	−	0.0165005i
$391$	−5.58369	+	9.67124i	−0.282379	+	0.489096i
$392$	2.40791	−	8.98642i	0.121618	−	0.453883i
$393$	5.61862	+	7.96985i	0.283422	+	0.402026i
$394$	−2.30368	−	1.33003i	−0.116058	−	0.0670060i
$395$	6.97354	+	6.97354i	0.350877	+	0.350877i
$396$	0.172155	−	2.12416i	0.00865109	−	0.106743i
$397$	−2.23806	+	8.35257i	−0.112325	+	0.419203i	−0.999073	−	0.0430503i	$-0.986292\pi$
$397$	−2.23806	+	8.35257i	−0.112325	+	0.419203i	0.886748	+	0.462254i	$0.152959\pi$
$398$	1.68516	+	0.451537i	0.0844694	+	0.0226335i
$399$	−1.66663	−	0.770684i	−0.0834361	−	0.0385825i
$400$	3.93420	−	2.27141i	0.196710	−	0.113571i
$401$	37.9864	+	10.1784i	1.89695	+	0.508286i	0.997450	+	0.0713636i	$0.0227351\pi$
$401$	37.9864	+	10.1784i	1.89695	+	0.508286i	0.899499	+	0.436923i	$0.143932\pi$
$402$	1.63469	+	18.0205i	0.0815307	+	0.898781i
$403$	−13.2313	−	6.06037i	−0.659100	−	0.301888i
$404$			14.5201i			0.722404i
$405$	0.607887	+	6.05490i	0.0302061	+	0.300870i
$406$	−2.59736	+	4.49876i	−0.128905	+	0.223270i
$407$	2.92761	−	5.07076i	0.145116	−	0.251348i
$408$	−8.63267	−	7.19674i	−0.427381	−	0.356292i
$409$	−21.0344	+	21.0344i	−1.04008	+	1.04008i	−0.0409222	+	0.999162i	$0.513030\pi$
$409$	−21.0344	+	21.0344i	−1.04008	+	1.04008i	−0.999162	+	0.0409222i	$0.986970\pi$
$410$	−4.42980	+	4.42980i	−0.218772	+	0.218772i
$411$	3.47369	−	20.0756i	0.171345	−	0.990255i
$412$	9.64874	−	16.7121i	0.475359	−	0.823347i
$413$	10.0600	−	17.4245i	0.495023	−	0.857404i
$414$	4.66523	−	2.21188i	0.229284	−	0.108708i
$415$		−	2.73678i		−	0.134343i
$416$	−3.58960	+	0.338733i	−0.175995	+	0.0166077i
$417$	−4.65677	−	2.15338i	−0.228043	−	0.105451i
$418$	−0.180157	−	0.0482728i	−0.00881174	−	0.00236110i
$419$	−12.1901	+	7.03797i	−0.595527	+	0.343827i	−0.767280	−	0.641313i	$-0.778390\pi$
$419$	−12.1901	+	7.03797i	−0.595527	+	0.343827i	0.171753	+	0.985140i	$0.445057\pi$
$420$	0.427199	+	4.70937i	0.0208452	+	0.229794i
$421$	4.66713	+	1.25055i	0.227462	+	0.0609482i	0.370750	−	0.928733i	$-0.379101\pi$
$421$	4.66713	+	1.25055i	0.227462	+	0.0609482i	−0.143288	+	0.989681i	$0.545767\pi$
$422$	0.337043	−	1.25786i	0.0164070	−	0.0612318i
$423$	−12.0710	−	25.4599i	−0.586914	−	1.23790i
$424$	−4.48538	−	4.48538i	−0.217829	−	0.217829i
$425$	−25.5285	−	14.7389i	−1.23831	−	0.714941i
$426$	−13.9678	+	1.26706i	−0.676744	+	0.0613892i
$427$	3.44722	−	12.8652i	0.166823	−	0.622591i
$428$	−6.65169	+	11.5211i	−0.321522	+	0.556892i
$429$	−1.47546	+	4.18373i	−0.0712358	+	0.201992i
$430$	2.21699	+	3.83995i	0.106913	+	0.185179i
$431$	16.0936	−	4.31228i	0.775203	−	0.207715i	0.150534	−	0.988605i	$-0.451901\pi$
$431$	16.0936	−	4.31228i	0.775203	−	0.207715i	0.624669	+	0.780890i	$0.285234\pi$
$432$	1.39296	+	5.00596i	0.0670189	+	0.240849i
$433$	5.53229	−	3.19407i	0.265865	−	0.153497i	−0.361142	−	0.932511i	$-0.617613\pi$
$433$	5.53229	−	3.19407i	0.265865	−	0.153497i	0.627007	+	0.779014i	$0.284280\pi$
$434$	−4.21817	+	15.7424i	−0.202478	+	0.755660i
$435$	0.256887	−	1.48463i	0.0123168	−	0.0711828i
$436$	7.63616	+	7.63616i	0.365706	+	0.365706i
$437$	−0.116950	−	0.436462i	−0.00559446	−	0.0208788i
$438$	1.44359	−	3.12183i	0.0689776	−	0.149167i
$439$		−	13.2838i		−	0.633999i	−0.948426	−	0.317000i	$-0.897325\pi$
$439$		−	13.2838i		−	0.633999i	0.948426	−	0.317000i	$-0.102675\pi$
$440$	0.124315	+	0.463951i	0.00592650	+	0.0221180i
$441$	26.2876	+	9.37791i	1.25179	+	0.446567i
$442$	13.5497	+	19.0729i	0.644496	+	0.907203i
$443$	19.0340	−	10.9893i	0.904332	−	0.522117i	0.0257292	−	0.999669i	$-0.491809\pi$
$443$	19.0340	−	10.9893i	0.904332	−	0.522117i	0.878603	+	0.477552i	$0.158476\pi$
$444$	−2.43408	+	14.0673i	−0.115516	+	0.667604i
$445$	−3.44926	−	5.97429i	−0.163511	−	0.283209i
$446$	19.0868			0.903785
$447$	13.8720	+	37.7370i	0.656123	+	1.78490i
$448$	1.04505	+	3.90017i	0.0493738	+	0.184266i
$449$	8.04520	+	2.15570i	0.379676	+	0.101734i	0.443609	−	0.896220i	$-0.353698\pi$
$449$	8.04520	+	2.15570i	0.379676	+	0.101734i	−0.0639330	+	0.997954i	$0.520364\pi$
$450$	5.83854	+	12.3145i	0.275231	+	0.580511i
$451$	3.29089	+	5.69999i	0.154962	+	0.268402i
$452$	−15.2122			−0.715524
$453$	7.64405	−	9.16922i	0.359149	−	0.430808i
$454$	−14.2332	−	8.21756i	−0.667998	−	0.385669i
$455$	1.64317	−	9.70547i	0.0770329	−	0.454999i
$456$	0.452898	−	0.0410836i	0.0212089	−	0.00192391i
$457$	9.62978	−	9.62978i	0.450462	−	0.450462i	−0.445046	−	0.895508i	$-0.646813\pi$
$457$	9.62978	−	9.62978i	0.450462	−	0.450462i	0.895508	+	0.445046i	$0.146813\pi$
$458$	11.7812	+	6.80189i	0.550500	+	0.317831i
$459$	23.6117	−	24.0693i	1.10210	−	1.12346i
$460$	−0.822829	+	0.822829i	−0.0383646	+	0.0383646i
$461$	−34.5408	+	9.25517i	−1.60872	+	0.431056i	−0.947662	−	0.319275i	$-0.896561\pi$
$461$	−34.5408	+	9.25517i	−1.60872	+	0.431056i	−0.661062	+	0.750331i	$0.729894\pi$
$462$	4.89532	+	0.847041i	0.227751	+	0.0394079i
$463$	12.0689	−	3.23386i	0.560891	−	0.150290i	0.0327754	−	0.999463i	$-0.489565\pi$
$463$	12.0689	−	3.23386i	0.560891	−	0.150290i	0.528116	+	0.849172i	$0.322899\pi$
$464$		−	1.28654i		−	0.0597260i
$465$	−0.427050	−	4.70772i	−0.0198040	−	0.218315i
$466$	−2.75501	−	2.75501i	−0.127623	−	0.127623i
$467$	11.9847			0.554587			0.277293	−	0.960785i	$-0.410563\pi$
$467$	11.9847			0.554587			0.277293	+	0.960785i	$0.410563\pi$
$468$	−0.142959	−	10.8157i	−0.00660830	−	0.499956i
$469$	−42.1818			−1.94777
$470$	4.49048	+	4.49048i	0.207131	+	0.207131i
$471$	15.5237	−	10.9440i	0.715296	−	0.504273i
$472$			4.98300i			0.229361i
$473$	4.49970	−	1.20569i	0.206896	−	0.0554377i
$474$	−16.1768	+	19.4045i	−0.743026	+	0.891278i
$475$	1.15210	−	0.308704i	0.0528618	−	0.0141643i
$476$	18.5265	−	18.5265i	0.849160	−	0.849160i
$477$	14.4992	−	12.3252i	0.663871	−	0.564330i
$478$	−1.36512	−	0.788151i	−0.0624390	−	0.0360492i
$479$	10.1637	−	10.1637i	0.464393	−	0.464393i	−0.435699	−	0.900092i	$-0.643499\pi$
$479$	10.1637	−	10.1637i	0.464393	−	0.464393i	0.900092	+	0.435699i	$0.143499\pi$
$480$	−0.674794	−	0.957175i	−0.0308000	−	0.0436888i
$481$	12.3756	−	27.0192i	0.564280	−	1.23197i
$482$	4.47282	+	2.58239i	0.203732	+	0.117624i
$483$	4.15272	+	11.2969i	0.188955	+	0.514028i
$484$	−10.4954			−0.477062
$485$	0.680464	+	1.17860i	0.0308983	+	0.0535174i
$486$	−15.3064	+	2.95207i	−0.694312	+	0.133908i
$487$	21.7160	+	5.81879i	0.984047	+	0.263675i	0.714748	−	0.699382i	$-0.246541\pi$
$487$	21.7160	+	5.81879i	0.984047	+	0.263675i	0.269299	+	0.963057i	$0.413208\pi$
$488$	0.853749	+	3.18623i	0.0386474	+	0.144234i
$489$	−14.1949	+	17.0272i	−0.641918	+	0.769996i
$490$	−6.29050			−0.284176
$491$	−21.6874	−	37.5637i	−0.978738	−	1.69522i	−0.667003	−	0.745055i	$-0.732423\pi$
$491$	−21.6874	−	37.5637i	−0.978738	−	1.69522i	−0.311735	−	0.950169i	$-0.600910\pi$
$492$	−12.3263	−	10.2760i	−0.555713	−	0.463278i
$493$	−7.22973	+	4.17409i	−0.325611	+	0.187991i
$494$	−0.933371	−	0.158023i	−0.0419944	−	0.00710979i
$495$	−1.41743	+	0.259292i	−0.0637088	+	0.0116543i
$496$	−1.04468	−	3.89881i	−0.0469076	−	0.175062i
$497$		−	32.6955i		−	1.46659i
$498$	6.98198	−	0.633354i	0.312870	−	0.0283813i
$499$	7.45370	+	27.8176i	0.333673	+	1.24529i	0.905300	+	0.424772i	$0.139646\pi$
$499$	7.45370	+	27.8176i	0.333673	+	1.24529i	−0.571627	+	0.820514i	$0.693687\pi$
$500$	−4.56251	−	4.56251i	−0.204042	−	0.204042i
$501$	1.11756	+	0.931671i	0.0499290	+	0.0416240i
$502$	1.81440	−	6.77143i	0.0809805	−	0.302224i
$503$	13.3453	−	7.70492i	0.595038	−	0.343545i	−0.172049	−	0.985088i	$-0.555039\pi$
$503$	13.3453	−	7.70492i	0.595038	−	0.343545i	0.767087	+	0.641543i	$0.221705\pi$
$504$	−11.9155	+	2.17971i	−0.530760	+	0.0970921i
$505$	9.48323	−	2.54102i	0.421998	−	0.113074i
$506$	0.611279	+	1.05877i	0.0271747	+	0.0470679i
$507$	−5.46071	+	21.8445i	−0.242519	+	0.970147i
$508$	−9.75334	+	16.8933i	−0.432735	+	0.749518i
$509$	1.81959	−	6.79081i	0.0806519	−	0.300997i	−0.913803	−	0.406157i	$-0.866869\pi$
$509$	1.81959	−	6.79081i	0.0806519	−	0.300997i	0.994455	+	0.105160i	$0.0335353\pi$
$510$	−3.18954	+	6.89750i	−0.141235	+	0.305427i
$511$	6.94381	+	4.00901i	0.307176	+	0.177348i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.0130909	+	1.36421i	0.000577976	+	0.0602314i
$514$	0.981486	−	3.66296i	0.0432915	−	0.161566i
$515$	−12.6034	−	3.37706i	−0.555371	−	0.148811i
$516$	−9.28329	+	6.54458i	−0.408674	+	0.288109i
$517$	5.77808	−	3.33598i	0.254120	−	0.146716i
$518$	−32.1469	−	8.61374i	−1.41245	−	0.378466i
$519$	−30.1769	+	21.2742i	−1.32462	+	0.933835i
$520$	0.849411	+	2.28513i	0.0372491	+	0.100209i
$521$		−	42.4222i		−	1.85855i	−0.369391	−	0.929274i	$-0.620434\pi$
$521$		−	42.4222i		−	1.85855i	0.369391	−	0.929274i	$-0.379566\pi$
$522$	3.84700	+	0.311785i	0.168379	+	0.0136464i
$523$	1.58272	−	2.74135i	0.0692074	−	0.119871i	−0.829345	−	0.558737i	$-0.811286\pi$
$523$	1.58272	−	2.74135i	0.0692074	−	0.119871i	0.898553	+	0.438866i	$0.144620\pi$
$524$	2.81495	−	4.87564i	0.122972	−	0.212993i
$525$	−29.8197	+	10.9616i	−1.30144	+	0.478405i
$526$	5.90735	−	5.90735i	0.257573	−	0.257573i
$527$	−18.5200	+	18.5200i	−0.806745	+	0.806745i
$528$	−1.15485	+	0.424519i	−0.0502583	+	0.0184748i
$529$	10.0191	−	17.3535i	0.435612	−	0.754501i
$530$	−2.14450	+	3.71438i	−0.0931511	+	0.161342i
$531$	−14.9001	−	1.20760i	−0.646611	−	0.0524053i
$532$			1.06013i			0.0459625i
$533$	19.3473	+	27.2335i	0.838023	+	1.17962i
$534$	14.4432	−	10.1822i	0.625018	−	0.440628i
$535$	8.68856	+	2.32809i	0.375639	+	0.100652i
$536$	9.04724	−	5.22343i	0.390781	−	0.225618i
$537$	−0.341923	+	0.241050i	−0.0147550	+	0.0104021i
$538$	−4.01563	−	1.07599i	−0.173126	−	0.0463890i
$539$	−1.71051	+	6.38372i	−0.0736770	+	0.274966i
$540$	3.02567	−	1.78580i	0.130204	−	0.0768486i
$541$	−5.91918	−	5.91918i	−0.254486	−	0.254486i	0.568321	−	0.822807i	$-0.307593\pi$
$541$	−5.91918	−	5.91918i	−0.254486	−	0.254486i	−0.822807	+	0.568321i	$0.807593\pi$
$542$	18.1083	+	10.4548i	0.777818	+	0.449074i
$543$	1.26458	−	2.73471i	0.0542684	−	0.117358i
$544$	−1.67944	+	6.26776i	−0.0720055	+	0.268728i
$545$	3.65092	−	6.32358i	0.156388	−	0.270872i
$546$	25.1405	+	1.94593i	1.07592	+	0.0832781i
$547$	16.9449	+	29.3493i	0.724510	+	1.25489i	0.959176	+	0.282811i	$0.0912670\pi$
$547$	16.9449	+	29.3493i	0.724510	+	1.25489i	−0.234666	+	0.972076i	$0.575400\pi$
$548$	−11.3621	+	3.04445i	−0.485363	+	0.130053i
$549$	−9.73436	+	1.78071i	−0.415452	+	0.0759989i
$550$	−2.79475	+	1.61355i	−0.119169	+	0.0688020i
$551$	0.0874256	−	0.326277i	0.00372445	−	0.0138999i
$552$	−2.28960	−	1.90875i	−0.0974518	−	0.0812420i
$553$	−41.6438	−	41.6438i	−1.77088	−	1.77088i
$554$	−3.92987	−	14.6665i	−0.166964	−	0.623118i
$555$	9.61344	−	0.872061i	0.408068	−	0.0370169i
$556$			2.96212i			0.125622i
$557$	−2.17805	−	8.12858i	−0.0922868	−	0.344419i	0.904307	−	0.426882i	$-0.140388\pi$
$557$	−2.17805	−	8.12858i	−0.0922868	−	0.344419i	−0.996594	+	0.0824630i	$0.973721\pi$
$558$	11.9114	−	2.17895i	0.504248	−	0.0922424i
$559$	22.1626	−	8.23812i	0.937378	−	0.348436i
$560$	2.36435	−	1.36506i	0.0999121	−	0.0576843i
$561$	6.13242	+	5.11237i	0.258911	+	0.215845i
$562$	−15.1196	−	26.1879i	−0.637782	−	1.10467i
$563$	31.8876			1.34390			0.671951	−	0.740596i	$-0.265457\pi$
$563$	31.8876			1.34390			0.671951	+	0.740596i	$0.265457\pi$
$564$	−10.4168	+	12.4952i	−0.438625	+	0.526142i
$565$	2.66214	+	9.93526i	0.111997	+	0.417979i
$566$	−19.0137	−	5.09470i	−0.799205	−	0.214146i
$567$	−3.63011	−	36.1580i	−0.152450	−	1.51849i
$568$	4.04872	+	7.01259i	0.169881	+	0.294242i
$569$	−32.4802			−1.36164			−0.680821	−	0.732450i	$-0.738377\pi$
$569$	−32.4802			−1.36164			−0.680821	+	0.732450i	$0.738377\pi$
$570$	−0.106089	−	0.288602i	−0.00444359	−	0.0120882i
$571$	−27.2576	−	15.7372i	−1.14070	−	0.658582i	−0.194094	−	0.980983i	$-0.562177\pi$
$571$	−27.2576	−	15.7372i	−1.14070	−	0.658582i	−0.946603	+	0.322401i	$0.895510\pi$
$572$	2.54996	−	0.240627i	0.106619	−	0.0100611i
$573$	−8.43146	−	11.9598i	−0.352229	−	0.499627i
$574$	26.4534	−	26.4534i	1.10414	−	1.10414i
$575$	−6.77079	−	3.90912i	−0.282361	−	0.163021i
$576$	2.28575	−	1.94302i	0.0952396	−	0.0809594i
$577$	3.78292	−	3.78292i	0.157485	−	0.157485i	−0.623966	−	0.781451i	$-0.714480\pi$
$577$	3.78292	−	3.78292i	0.157485	−	0.157485i	0.781451	+	0.623966i	$0.214480\pi$
$578$	24.2499	−	6.49774i	1.00866	−	0.270270i
$579$	−0.0595192	+	0.0713947i	−0.00247353	+	0.00296706i
$580$	−0.840250	+	0.225144i	−0.0348895	+	0.00934861i
$581$			16.3432i			0.678031i
$582$	−2.84933	+	2.00873i	−0.118108	+	0.0832647i
$583$	3.18629	+	3.18629i	0.131963	+	0.131963i
$584$	−1.98576			−0.0821715
$585$	−7.03882	+	1.98612i	−0.291019	+	0.0821159i
$586$	−9.93642			−0.410470
$587$	−30.8578	−	30.8578i	−1.27364	−	1.27364i	−0.944165	−	0.329474i	$-0.893129\pi$
$587$	−30.8578	−	30.8578i	−1.27364	−	1.27364i	−0.329474	−	0.944165i	$-0.606871\pi$
$588$	−1.45577	−	16.0481i	−0.0600348	−	0.661813i
$589$		−	1.05976i		−	0.0436666i
$590$	3.25444	−	0.872025i	0.133983	−	0.0359007i
$591$	−4.53990	−	0.785543i	−0.186747	−	0.0323129i
$592$	7.96159	−	2.13330i	0.327219	−	0.0876781i
$593$	−3.43157	+	3.43157i	−0.140918	+	0.140918i	−0.774047	−	0.633129i	$-0.781770\pi$
$593$	−3.43157	+	3.43157i	−0.140918	+	0.140918i	0.633129	+	0.774047i	$0.281770\pi$
$594$	−0.989523	−	3.55610i	−0.0406006	−	0.145909i
$595$	−15.3420	−	8.85768i	−0.628959	−	0.363130i
$596$	16.4140	−	16.4140i	0.672343	−	0.672343i
$597$	3.00939	−	0.272989i	0.123166	−	0.0111727i
$598$	3.59373	+	5.05860i	0.146958	+	0.206861i
$599$	6.49912	+	3.75227i	0.265547	+	0.153313i	0.626862	−	0.779130i	$-0.284339\pi$
$599$	6.49912	+	3.75227i	0.265547	+	0.153313i	−0.361315	+	0.932444i	$0.617672\pi$
$600$	5.03841	−	6.04369i	0.205692	−	0.246733i
$601$	17.4262			0.710831			0.355416	−	0.934708i	$-0.384339\pi$
$601$	17.4262			0.710831			0.355416	+	0.934708i	$0.384339\pi$
$602$	−13.2392	−	22.9310i	−0.539590	−	0.934597i
$603$	13.4265	+	28.3189i	0.546771	+	1.15323i
$604$	−6.65733	−	1.78383i	−0.270883	−	0.0725828i
$605$	1.83669	+	6.85462i	0.0746721	+	0.278680i
$606$	8.67722	+	23.6053i	0.352488	+	0.958899i
$607$	−30.9125			−1.25470			−0.627350	−	0.778737i	$-0.715861\pi$
$607$	−30.9125			−1.25470			−0.627350	+	0.778737i	$0.715861\pi$
$608$	−0.131277	−	0.227379i	−0.00532400	−	0.00922143i
$609$	−1.53405	+	8.86578i	−0.0621630	+	0.359260i
$610$	1.93155	−	1.11518i	0.0782063	−	0.0451524i
$611$	27.6066	−	19.6123i	1.11684	−	0.793429i
$612$	−18.3348	−	6.54081i	−0.741141	−	0.264397i
$613$	11.1528	+	41.6227i	0.450456	+	1.68113i	0.701113	+	0.713050i	$0.252687\pi$
$613$	11.1528	+	41.6227i	0.450456	+	1.68113i	−0.250657	+	0.968076i	$0.580646\pi$
$614$		−	20.4813i		−	0.826560i
$615$	−4.55424	+	9.84873i	−0.183645	+	0.397139i
$616$	−0.742373	−	2.77058i	−0.0299111	−	0.111630i
$617$	−8.95150	−	8.95150i	−0.360374	−	0.360374i	0.503577	−	0.863950i	$-0.332017\pi$
$617$	−8.95150	−	8.95150i	−0.360374	−	0.360374i	−0.863950	+	0.503577i	$0.832017\pi$
$618$	5.69874	−	32.9348i	0.229237	−	1.32483i
$619$	0.291078	−	1.08632i	0.0116994	−	0.0436628i	−0.959829	−	0.280584i	$-0.909472\pi$
$619$	0.291078	−	1.08632i	0.0116994	−	0.0436628i	0.971529	+	0.236922i	$0.0761384\pi$
$620$	−2.36353	+	1.36458i	−0.0949215	+	0.0548030i
$621$	6.26242	−	6.38377i	0.251302	−	0.256172i
$622$	21.8475	−	5.85403i	0.876006	−	0.234725i
$623$	20.5979	+	35.6767i	0.825239	+	1.42936i
$624$	−5.63317	+	2.69582i	−0.225507	+	0.107919i
$625$	9.17568	−	15.8927i	0.367027	−	0.635710i
$626$	−4.88349	+	18.2255i	−0.195184	+	0.728436i
$627$	−0.321727	+	0.0291847i	−0.0128485	+	0.00116552i
$628$	−9.49681	−	5.48299i	−0.378964	−	0.218795i
$629$	−37.8190	−	37.8190i	−1.50794	−	1.50794i
$630$	3.50881	+	7.40069i	0.139794	+	0.294850i
$631$	−3.51015	+	13.1000i	−0.139737	+	0.521505i	0.860197	+	0.509962i	$0.170341\pi$
$631$	−3.51015	+	13.1000i	−0.139737	+	0.521505i	−0.999933	+	0.0115421i	$0.996326\pi$
$632$	14.0887	+	3.77505i	0.560417	+	0.150163i
$633$	−0.203769	−	2.24631i	−0.00809909	−	0.0892829i
$634$	16.4650	−	9.50608i	0.653909	−	0.377535i
$635$	12.7400	+	3.41367i	0.505571	+	0.135467i
$636$	−9.97230	−	4.61139i	−0.395428	−	0.182853i
$637$	−5.59943	+	33.0733i	−0.221857	+	1.31041i
$638$			0.913923i			0.0361825i
$639$	−21.9502	+	10.4070i	−0.868336	+	0.411695i
$640$	−0.338074	+	0.585562i	−0.0133636	+	0.0231464i
$641$	−23.6580	+	40.9769i	−0.934436	+	1.61849i	−0.158801	+	0.987311i	$0.550763\pi$
$641$	−23.6580	+	40.9769i	−0.934436	+	1.61849i	−0.775636	+	0.631181i	$0.782571\pi$
$642$	−3.92862	+	22.7048i	−0.155050	+	0.896085i
$643$	6.73860	−	6.73860i	0.265745	−	0.265745i	−0.561638	−	0.827383i	$-0.689829\pi$
$643$	6.73860	−	6.73860i	0.265745	−	0.265745i	0.827383	+	0.561638i	$0.189829\pi$
$644$	4.91369	−	4.91369i	0.193626	−	0.193626i
$645$	5.89890	+	4.91770i	0.232269	+	0.193634i
$646$	−0.851840	+	1.47543i	−0.0335152	+	0.0580500i
$647$	−8.42061	+	14.5849i	−0.331048	+	0.573392i	−0.982718	−	0.185111i	$-0.940736\pi$
$647$	−8.42061	+	14.5849i	−0.331048	+	0.573392i	0.651669	+	0.758503i	$0.274069\pi$
$648$	5.25609	+	7.30572i	0.206479	+	0.286996i
$649$		−	3.53979i		−	0.138949i
$650$	−13.3528	+	9.48611i	−0.523741	+	0.372076i
$651$	2.55021	+	28.1131i	0.0999506	+	1.10184i
$652$	12.3626	+	3.31255i	0.484157	+	0.129730i
$653$	−25.2989	+	14.6063i	−0.990022	+	0.571589i	−0.905281	−	0.424814i	$-0.860340\pi$
$653$	−25.2989	+	14.6063i	−0.990022	+	0.571589i	−0.0847408	+	0.996403i	$0.527006\pi$
$654$	16.9774	+	7.85069i	0.663870	+	0.306986i
$655$	−3.67694	−	0.985233i	−0.143670	−	0.0384962i
$656$	−2.39802	+	8.94954i	−0.0936270	+	0.349421i
$657$	0.481237	−	5.93782i	0.0187749	−	0.231657i
$658$	−26.8158	−	26.8158i	−1.04539	−	1.04539i
$659$	−12.4412	−	7.18293i	−0.484641	−	0.279807i	0.237708	−	0.971337i	$-0.423604\pi$
$659$	−12.4412	−	7.18293i	−0.484641	−	0.279807i	−0.722348	+	0.691529i	$0.756937\pi$
$660$	0.479355	+	0.679951i	0.0186589	+	0.0264671i
$661$	−10.7255	+	40.0282i	−0.417174	+	1.55692i	0.363267	+	0.931685i	$0.381661\pi$
$661$	−10.7255	+	40.0282i	−0.417174	+	1.55692i	−0.780441	+	0.625230i	$0.785005\pi$
$662$	−13.2363	+	22.9259i	−0.514443	+	0.891041i
$663$	33.4256	+	22.9093i	1.29814	+	0.889723i
$664$	−2.02380	−	3.50533i	−0.0785387	−	0.136033i
$665$	0.692380	−	0.185523i	0.0268494	−	0.00719426i
$666$	4.44955	+	24.3237i	0.172416	+	0.942524i
$667$	−1.91750	+	1.10707i	−0.0742460	+	0.0428660i
$668$	0.217416	−	0.811408i	0.00841208	−	0.0313943i
$669$	31.0292	−	11.4062i	1.19966	−	0.440991i
$670$	−4.99474	−	4.99474i	−0.192964	−	0.192964i
$671$	−0.606480	−	2.26342i	−0.0234129	−	0.0873782i
$672$	4.02966	+	5.71595i	0.155448	+	0.220498i
$673$			39.4913i			1.52228i	0.648588	+	0.761140i	$0.275360\pi$
$673$			39.4913i			1.52228i	−0.648588	+	0.761140i	$0.724640\pi$
$674$	5.87256	+	21.9167i	0.226202	+	0.844199i
$675$	16.8508	+	16.5305i	0.648587	+	0.636258i
$676$	12.7705	−	2.43183i	0.491174	−	0.0935321i
$677$	14.7062	−	8.49064i	0.565206	−	0.326322i	−0.190026	−	0.981779i	$-0.560857\pi$
$677$	14.7062	−	8.49064i	0.565206	−	0.326322i	0.755232	+	0.655457i	$0.227524\pi$
$678$	−24.7304	+	9.09083i	−0.949766	+	0.349131i
$679$	−4.06352	−	7.03823i	−0.155944	−	0.270103i
$680$	4.38743			0.168250
$681$	−28.0496	−	4.85345i	−1.07486	−	0.185985i
$682$	0.742114	+	2.76961i	0.0284170	+	0.106054i
$683$	−1.34228	−	0.359662i	−0.0513607	−	0.0137621i	0.233047	−	0.972465i	$-0.425130\pi$
$683$	−1.34228	−	0.359662i	−0.0513607	−	0.0137621i	−0.284408	+	0.958703i	$0.591797\pi$
$684$	0.711722	−	0.337441i	0.0272134	−	0.0129024i
$685$	3.97672	+	6.88788i	0.151943	+	0.263173i
$686$	9.30068			0.355102
$687$	23.2174	+	4.01733i	0.885800	+	0.153271i
$688$	5.67915	+	3.27886i	0.216516	+	0.125005i
$689$	17.6201	+	14.5814i	0.671272	+	0.555507i
$690$	−0.845945	+	1.82939i	−0.0322046	+	0.0696437i
$691$	−7.28822	+	7.28822i	−0.277257	+	0.277257i	−0.832013	−	0.554756i	$-0.812812\pi$
$691$	−7.28822	+	7.28822i	−0.277257	+	0.277257i	0.554756	+	0.832013i	$0.312812\pi$
$692$	18.4610	+	10.6585i	0.701782	+	0.405174i
$693$	8.46447	−	1.54841i	0.321539	−	0.0588192i
$694$	11.7462	−	11.7462i	0.445879	−	0.445879i
$695$	1.93459	−	0.518372i	0.0733832	−	0.0196630i
$696$	−0.768834	−	2.09152i	−0.0291426	−	0.0792787i
$697$	58.0723	−	15.5604i	2.19965	−	0.589393i
$698$			2.24512i			0.0849789i
$699$	−6.12519	−	2.83241i	−0.231676	−	0.107132i
$700$	12.9703	+	12.9703i	0.490232	+	0.490232i
$701$	−26.3023			−0.993423			−0.496712	−	0.867916i	$-0.665459\pi$
$701$	−26.3023			−0.993423			−0.496712	+	0.867916i	$0.665459\pi$
$702$	−6.69587	−	17.4976i	−0.252719	−	0.660404i
$703$	2.16409			0.0816202
$704$	0.502310	+	0.502310i	0.0189315	+	0.0189315i
$705$	9.98365	+	4.61664i	0.376006	+	0.173873i
$706$			8.97314i			0.337709i
$707$	−56.6310	+	15.1742i	−2.12983	+	0.570685i
$708$	2.97783	+	8.10082i	0.111914	+	0.304447i
$709$	31.3179	−	8.39161i	1.17617	−	0.315154i	0.382763	−	0.923846i	$-0.374972\pi$
$709$	31.3179	−	8.39161i	1.17617	−	0.315154i	0.793406	+	0.608693i	$0.208306\pi$
$710$	3.87146	−	3.87146i	0.145293	−	0.145293i
$711$	−14.7024	+	41.2130i	−0.551384	+	1.54561i
$712$	−8.83578	−	5.10134i	−0.331135	−	0.191181i
$713$	−4.91197	+	4.91197i	−0.183955	+	0.183955i
$714$	19.0470	−	41.1898i	0.712814	−	1.54149i
$715$	−0.603399	−	1.62329i	−0.0225658	−	0.0607077i
$716$	0.209175	+	0.120767i	0.00781723	+	0.00451328i
$717$	−2.69026	−	0.465498i	−0.100470	−	0.0173843i
$718$	35.5844			1.32800
$719$	8.65353	+	14.9884i	0.322722	+	0.558971i	0.981049	−	0.193761i	$-0.0620687\pi$
$719$	8.65353	+	14.9884i	0.322722	+	0.558971i	−0.658326	+	0.752733i	$0.728735\pi$
$720$	−1.66901	−	1.15282i	−0.0622005	−	0.0429629i
$721$	75.2634	+	20.1668i	2.80296	+	0.751050i
$722$	4.89972	+	18.2860i	0.182349	+	0.680535i
$723$	8.81467	+	1.52521i	0.327821	+	0.0567232i
$724$	−1.73952			−0.0646488
$725$	−2.92226	−	5.06150i	−0.108530	−	0.187979i
$726$	−17.0622	+	6.27202i	−0.633239	+	0.232777i
$727$	8.04825	−	4.64666i	0.298493	−	0.172335i	−0.343273	−	0.939236i	$-0.611536\pi$
$727$	8.04825	−	4.64666i	0.298493	−	0.172335i	0.641766	+	0.766901i	$0.278202\pi$
$728$	−5.07242	−	13.6461i	−0.187996	−	0.505757i
$729$	−23.1193	+	13.9462i	−0.856271	+	0.516527i
$730$	0.347509	+	1.29692i	0.0128619	+	0.0480012i
$731$		−	42.5521i		−	1.57385i
$732$	3.29202	+	4.66964i	0.121677	+	0.172595i
$733$	9.12426	+	34.0522i	0.337012	+	1.25775i	0.901671	+	0.432422i	$0.142341\pi$
$733$	9.12426	+	34.0522i	0.337012	+	1.25775i	−0.564659	+	0.825324i	$0.690992\pi$
$734$	−16.4047	−	16.4047i	−0.605509	−	0.605509i
$735$	−10.2264	+	3.75920i	−0.377207	+	0.138660i
$736$	−0.445430	+	1.66237i	−0.0164188	+	0.0612756i
$737$	−6.42692	+	3.71058i	−0.236739	+	0.136681i
$738$	−26.1797	−	9.33942i	−0.963689	−	0.343789i
$739$	32.7392	−	8.77244i	1.20433	−	0.322699i	0.399795	−	0.916604i	$-0.369081\pi$
$739$	32.7392	−	8.77244i	1.20433	−	0.322699i	0.804535	+	0.593905i	$0.202415\pi$
$740$	−2.78656	−	4.82646i	−0.102436	−	0.177424i
$741$	−1.61181	+	0.300885i	−0.0592113	+	0.0110533i
$742$	12.8063	−	22.1812i	0.470134	−	0.814296i
$743$	−2.77031	+	10.3389i	−0.101633	+	0.379299i	−0.997941	−	0.0641321i	$-0.979572\pi$
$743$	−2.77031	+	10.3389i	−0.101633	+	0.379299i	0.896309	+	0.443431i	$0.146239\pi$
$744$	−4.02825	−	5.71396i	−0.147683	−	0.209484i
$745$	−13.5926	−	7.84768i	−0.497993	−	0.287517i
$746$	21.2459	+	21.2459i	0.777866	+	0.777866i
$747$	10.9721	−	5.20207i	0.401447	−	0.190334i
$748$	1.19303	−	4.45245i	0.0436215	−	0.162798i
$749$	−51.8854	−	13.9027i	−1.89585	−	0.507992i
$750$	−10.1438	−	4.69069i	−0.370399	−	0.171280i
$751$	−12.1245	+	7.00006i	−0.442428	+	0.255436i	−0.704627	−	0.709578i	$-0.748886\pi$
$751$	−12.1245	+	7.00006i	−0.442428	+	0.255436i	0.262199	+	0.965014i	$0.415552\pi$
$752$	9.07214	+	2.43087i	0.330827	+	0.0886448i
$753$	−1.09695	−	12.0925i	−0.0399749	−	0.440677i
$754$	0.435793	+	4.61816i	0.0158706	+	0.168184i
$755$			4.66013i			0.169600i
$756$	−18.0684	+	10.6643i	−0.657141	+	0.387855i
$757$	−4.20269	+	7.27928i	−0.152749	+	0.264570i	−0.932237	−	0.361848i	$-0.882146\pi$
$757$	−4.20269	+	7.27928i	−0.152749	+	0.264570i	0.779488	+	0.626417i	$0.215479\pi$
$758$	14.1954	−	24.5871i	0.515600	−	0.893045i
$759$	1.62647	+	1.35593i	0.0590371	+	0.0492171i
$760$	−0.125530	+	0.125530i	−0.00455344	+	0.00455344i
$761$	20.7884	−	20.7884i	0.753578	−	0.753578i	−0.221567	−	0.975145i	$-0.571117\pi$
$761$	20.7884	−	20.7884i	0.753578	−	0.753578i	0.975145	+	0.221567i	$0.0711171\pi$
$762$	−5.76052	+	33.2919i	−0.208682	+	1.20604i
$763$	−21.8022	+	37.7625i	−0.789292	+	1.36709i
$764$	−4.22419	+	7.31652i	−0.152826	+	0.264702i
$765$	−1.06327	+	13.1193i	−0.0384425	+	0.474329i
$766$			3.71244i			0.134136i
$767$	−1.68790	−	17.8870i	−0.0609467	−	0.645862i
$768$	−1.57210	−	0.726972i	−0.0567284	−	0.0262323i
$769$	35.1291	+	9.41282i	1.26679	+	0.339435i	0.828800	−	0.559545i	$-0.189024\pi$
$769$	35.1291	+	9.41282i	1.26679	+	0.339435i	0.437989	+	0.898980i	$0.355691\pi$
$770$	−1.67957	+	0.969702i	−0.0605276	+	0.0349456i
$771$	−0.593385	−	6.54137i	−0.0213702	−	0.235582i
$772$	0.0518362	+	0.0138895i	0.00186563	+	0.000499893i
$773$	−1.91671	+	7.15325i	−0.0689391	+	0.257284i	−0.991791	−	0.127871i	$-0.959186\pi$
$773$	−1.91671	+	7.15325i	−0.0689391	+	0.257284i	0.922852	+	0.385156i	$0.125852\pi$
$774$	−11.1807	+	16.1872i	−0.401883	+	0.581835i
$775$	−12.9658	−	12.9658i	−0.465745	−	0.465745i
$776$	1.74311	+	1.00638i	0.0625739	+	0.0361271i
$777$	−57.4085	+	5.20768i	−2.05952	+	0.186824i
$778$	0.525886	−	1.96263i	0.0188539	−	0.0703638i
$779$	−1.21632	+	2.10672i	−0.0435790	+	0.0754811i
$780$	2.74647	+	3.20730i	0.0983394	+	0.114840i
$781$	−2.87610	−	4.98156i	−0.102915	−	0.178254i
$782$	10.7869	−	2.89033i	0.385738	−	0.103358i
$783$	6.44036	−	1.79210i	0.230160	−	0.0640444i
$784$	−8.05701	+	4.65172i	−0.287750	+	0.166133i
$785$	−1.91905	+	7.16198i	−0.0684937	+	0.255622i
$786$	1.66257	−	9.60850i	0.0593018	−	0.342724i
$787$	−8.59029	−	8.59029i	−0.306211	−	0.306211i	0.537227	−	0.843438i	$-0.319472\pi$
$787$	−8.59029	−	8.59029i	−0.306211	−	0.306211i	−0.843438	+	0.537227i	$0.819472\pi$
$788$	0.688475	+	2.56942i	0.0245259	+	0.0915319i
$789$	6.07330	−	13.1338i	0.216215	−	0.467574i
$790$		−	9.86207i		−	0.350877i
$791$	−15.8975	−	59.3303i	−0.565250	−	2.10954i
$792$	−1.62374	+	1.38027i	−0.0576970	+	0.0490459i
$793$	−4.14390	−	11.1481i	−0.147154	−	0.395881i
$794$	7.48871	−	4.32361i	0.265764	−	0.153439i
$795$	−1.26658	+	7.32000i	−0.0449211	+	0.259613i
$796$	−0.872302	−	1.51087i	−0.0309179	−	0.0535514i
$797$	−32.4028			−1.14777			−0.573883	−	0.818937i	$-0.694564\pi$
$797$	−32.4028			−1.14777			−0.573883	+	0.818937i	$0.694564\pi$
$798$	0.633533	+	1.72344i	0.0224268	+	0.0610093i
$799$	−15.7736	−	58.8679i	−0.558030	−	2.08260i
$800$	−4.38803	−	1.17577i	−0.155140	−	0.0415697i
$801$	17.3953	−	25.1844i	0.614632	−	0.889848i
$802$	−19.6632	−	34.0577i	−0.694332	−	1.20262i
$803$	1.41063			0.0497802
$804$	11.5865	−	13.8983i	0.408625	−	0.490156i
$805$	−4.06907	−	2.34928i	−0.143416	−	0.0828012i
$806$	5.07065	+	13.6413i	0.178606	+	0.480494i
$807$	−7.17119	+	0.650517i	−0.252438	+	0.0228993i
$808$	10.2673	−	10.2673i	0.361202	−	0.361202i
$809$	−16.9078	−	9.76174i	−0.594448	−	0.343205i	0.172406	−	0.985026i	$-0.444846\pi$
$809$	−16.9078	−	9.76174i	−0.594448	−	0.343205i	−0.766854	+	0.641821i	$0.778179\pi$
$810$	3.85162	−	4.71130i	0.135332	−	0.165538i
$811$	−22.8460	+	22.8460i	−0.802232	+	0.802232i	−0.983444	−	0.181212i	$-0.941998\pi$
$811$	−22.8460	+	22.8460i	−0.802232	+	0.802232i	0.181212	+	0.983444i	$0.441998\pi$
$812$	5.01771	−	1.34449i	0.176087	−	0.0471824i
$813$	35.6863	+	6.17483i	1.25157	+	0.216561i
$814$	−5.65570	+	1.51544i	−0.198232	+	0.0531162i
$815$		−	8.65383i		−	0.303131i
$816$	1.01535	+	11.1931i	0.0355445	+	0.391836i
$817$	1.21747	+	1.21747i	0.0425938	+	0.0425938i
$818$	29.7471			1.04008
$819$	42.0337	−	11.8605i	1.46878	−	0.414439i
$820$	6.26468			0.218772
$821$	26.9448	+	26.9448i	0.940379	+	0.940379i	0.998320	−	0.0579409i	$-0.0184535\pi$
$821$	26.9448	+	26.9448i	0.940379	+	0.940379i	−0.0579409	+	0.998320i	$0.518453\pi$
$822$	−16.6518	+	11.7393i	−0.580800	+	0.409455i
$823$			7.48458i			0.260896i	0.991455	+	0.130448i	$0.0416416\pi$
$823$			7.48458i			0.260896i	−0.991455	+	0.130448i	$0.958358\pi$
$824$	−18.6399	+	4.99456i	−0.649353	+	0.173994i
$825$	−3.57915	+	4.29328i	−0.124610	+	0.149473i
$826$	−19.4345	+	5.20746i	−0.676214	+	0.181191i
$827$	−7.82102	+	7.82102i	−0.271963	+	0.271963i	−0.829890	−	0.557927i	$-0.811597\pi$
$827$	−7.82102	+	7.82102i	−0.271963	+	0.271963i	0.557927	+	0.829890i	$0.311597\pi$
$828$	−4.86285	−	1.73479i	−0.168996	−	0.0602880i
$829$	−8.88429	−	5.12935i	−0.308564	−	0.178150i	0.337720	−	0.941247i	$-0.390344\pi$
$829$	−8.88429	−	5.12935i	−0.308564	−	0.178150i	−0.646284	+	0.763097i	$0.723678\pi$
$830$	−1.93520	+	1.93520i	−0.0671716	+	0.0671716i
$831$	−15.1534	−	21.4947i	−0.525666	−	0.745642i
$832$	2.77775	+	2.29871i	0.0963013	+	0.0796935i
$833$	52.2808	+	30.1843i	1.81142	+	1.04583i
$834$	1.77016	+	4.81550i	0.0612957	+	0.166747i
$835$	−0.567986			−0.0196560
$836$	0.0932559	+	0.161524i	0.00322532	+	0.00558642i
$837$	18.0621	−	10.6605i	0.624317	−	0.368482i
$838$	13.5963	+	3.64312i	0.469677	+	0.125850i
$839$	3.05007	+	11.3830i	0.105300	+	0.392985i	0.998379	−	0.0569146i	$-0.0181263\pi$
$839$	3.05007	+	11.3830i	0.105300	+	0.392985i	−0.893079	+	0.449900i	$0.851460\pi$
$840$	3.02795	−	3.63210i	0.104474	−	0.125319i
$841$	27.3448			0.942925
$842$	−2.41588	−	4.18443i	−0.0832568	−	0.144205i
$843$	−40.2297	−	33.5380i	−1.38558	−	1.15511i
$844$	−1.12777	+	0.651117i	−0.0388194	+	0.0224124i
$845$	−3.82310	−	7.91497i	−0.131518	−	0.272283i
$846$	−9.46737	+	26.5384i	−0.325495	+	0.912408i
$847$	−10.9682	−	40.9337i	−0.376870	−	1.40650i
$848$			6.34328i			0.217829i
$849$	−33.9550	+	3.08015i	−1.16533	+	0.105710i
$850$	7.62941	+	28.4733i	0.261686	+	0.976627i
$851$	−10.0305	−	10.0305i	−0.343842	−	0.343842i
$852$	10.7727	+	8.98080i	0.369066	+	0.307677i
$853$	−6.39301	+	23.8590i	−0.218892	+	0.816918i	0.765868	+	0.642998i	$0.222310\pi$
$853$	−6.39301	+	23.8590i	−0.218892	+	0.816918i	−0.984760	+	0.173919i	$0.944357\pi$
$854$	−11.5346	+	6.65953i	−0.394707	+	0.227884i
$855$	−0.344937	−	0.405780i	−0.0117966	−	0.0138774i
$856$	12.8501	−	3.44317i	0.439207	−	0.117685i
$857$	24.8560	+	43.0518i	0.849063	+	1.47062i	0.882045	+	0.471165i	$0.156166\pi$
$857$	24.8560	+	43.0518i	0.849063	+	1.47062i	−0.0329818	+	0.999456i	$0.510500\pi$
$858$	4.00165	−	1.91504i	0.136614	−	0.0653783i
$859$	−11.5341	+	19.9776i	−0.393538	+	0.681628i	−0.992913	−	0.118840i	$-0.962082\pi$
$859$	−11.5341	+	19.9776i	−0.393538	+	0.681628i	0.599375	+	0.800468i	$0.295416\pi$
$860$	1.14760	−	4.28290i	0.0391329	−	0.146046i
$861$	27.1965	−	58.8136i	0.926856	−	2.00436i
$862$	−14.4292	−	8.33068i	−0.491459	−	0.283744i
$863$	−4.06937	−	4.06937i	−0.138523	−	0.138523i	0.634445	−	0.772968i	$-0.281229\pi$
$863$	−4.06937	−	4.06937i	−0.138523	−	0.138523i	−0.772968	+	0.634445i	$0.781229\pi$
$864$	2.55478	−	4.52472i	0.0869153	−	0.153934i
$865$	3.73047	−	13.9223i	0.126840	−	0.473372i
$866$	−6.17046	−	1.65337i	−0.209681	−	0.0561838i
$867$	35.5398	−	25.0550i	1.20700	−	0.850914i
$868$	14.1143	−	8.14887i	0.479069	−	0.276591i
$869$	−10.0082	−	2.68169i	−0.339505	−	0.0909702i
$870$	−1.23144	+	0.868148i	−0.0417498	+	0.0294330i
$871$	−30.7067	+	21.8146i	−1.04046	+	0.739161i
$872$		−	10.7992i		−	0.365706i
$873$	−3.43171	+	4.96834i	−0.116146	+	0.168153i
$874$	−0.225929	+	0.391321i	−0.00764217	+	0.0132366i
$875$	13.0265	−	22.5626i	0.440377	−	0.762755i
$876$	−3.22824	+	1.18669i	−0.109072	+	0.0400946i
$877$	−25.0480	+	25.0480i	−0.845812	+	0.845812i	−0.989607	−	0.143796i	$-0.954069\pi$
$877$	−25.0480	+	25.0480i	−0.845812	+	0.845812i	0.143796	+	0.989607i	$0.454069\pi$
$878$	−9.39304	+	9.39304i	−0.317000	+	0.317000i
$879$	−16.1536	+	5.93799i	−0.544846	+	0.200284i
$880$	0.240159	−	0.415967i	0.00809575	−	0.0140223i
$881$	−9.78090	+	16.9410i	−0.329527	+	0.570757i	−0.982418	−	0.186695i	$-0.940223\pi$
$881$	−9.78090	+	16.9410i	−0.329527	+	0.570757i	0.652891	+	0.757452i	$0.273556\pi$
$882$	−11.9570	−	25.2193i	−0.402612	−	0.849179i
$883$			7.96488i			0.268040i	0.990979	+	0.134020i	$0.0427886\pi$
$883$			7.96488i			0.268040i	−0.990979	+	0.134020i	$0.957211\pi$
$884$	3.90543	−	23.0677i	0.131354	−	0.775849i
$885$	4.76960	−	3.36249i	0.160328	−	0.113029i
$886$	−21.2297	−	5.68847i	−0.713225	−	0.191108i
$887$	44.3470	−	25.6038i	1.48903	−	0.859690i	0.489105	−	0.872225i	$-0.337323\pi$
$887$	44.3470	−	25.6038i	1.48903	−	0.859690i	0.999921	+	0.0125348i	$0.00399005\pi$
$888$	11.6682	−	8.22593i	0.391560	−	0.276044i
$889$	−76.0793	−	20.3854i	−2.55162	−	0.683704i
$890$	−1.78547	+	6.66346i	−0.0598490	+	0.223360i
$891$	−3.73378	−	5.18979i	−0.125086	−	0.173864i
$892$	−13.4964	−	13.4964i	−0.451892	−	0.451892i
$893$	2.13558	+	1.23298i	0.0714645	+	0.0412601i
$894$	16.8751	−	36.4931i	0.564388	−	1.22051i
$895$	0.0422685	−	0.157748i	0.00141288	−	0.00527294i
$896$	2.01888	−	3.49679i	0.0674459	−	0.116820i
$897$	8.86531	+	6.07611i	0.296004	+	0.202875i
$898$	−4.16450	−	7.21313i	−0.138971	−	0.240705i
$899$	−5.01596	+	1.34402i	−0.167292	+	0.0448257i
$900$	4.57919	−	12.8361i	0.152640	−	0.427871i
$901$	35.6462	−	20.5803i	1.18755	−	0.685631i
$902$	1.70349	−	6.35751i	0.0567200	−	0.211682i
$903$	−35.2264	−	29.3670i	−1.17226	−	0.977272i
$904$	10.7567	+	10.7567i	0.357762	+	0.357762i
$905$	0.304416	+	1.13610i	0.0101191	+	0.0377652i
$906$	−11.8888	+	1.07846i	−0.394978	+	0.0358295i
$907$			12.9015i			0.428388i	0.976791	+	0.214194i	$0.0687125\pi$
$907$			12.9015i			0.428388i	−0.976791	+	0.214194i	$0.931288\pi$
$908$	4.25372	+	15.8751i	0.141165	+	0.526834i
$909$	28.2130	+	33.1894i	0.935765	+	1.10082i
$910$	−8.02470	+	5.70091i	−0.266016	+	0.188983i
$911$	−6.52125	+	3.76504i	−0.216059	+	0.124741i	−0.604124	−	0.796890i	$-0.706477\pi$
$911$	−6.52125	+	3.76504i	−0.216059	+	0.124741i	0.388065	+	0.921632i	$0.373143\pi$
$912$	−0.349298	−	0.291197i	−0.0115664	−	0.00964249i
$913$	1.43765	+	2.49009i	0.0475794	+	0.0824100i
$914$	−13.6186			−0.450462
$915$	2.47368	−	2.96724i	0.0817772	−	0.0980938i
$916$	−3.52092	−	13.1402i	−0.116334	−	0.434166i
$917$	21.9576	+	5.88351i	0.725103	+	0.194291i
$918$	−33.7156	+	0.323532i	−1.11278	+	0.0106782i
$919$	−9.25517	−	16.0304i	−0.305300	−	0.528795i	0.672028	−	0.740526i	$-0.265423\pi$
$919$	−9.25517	−	16.0304i	−0.305300	−	0.528795i	−0.977328	+	0.211731i	$0.932090\pi$
$920$	1.16366			0.0383646
$921$	−12.2396	−	33.2964i	−0.403310	−	1.09715i
$922$	30.9684	+	17.8796i	1.01989	+	0.588834i
$923$	−16.9087	−	23.8010i	−0.556557	−	0.783419i
$924$	−2.86256	−	4.06046i	−0.0941714	−	0.133579i
$925$	26.4769	−	26.4769i	0.870555	−	0.870555i
$926$	−10.8207	−	6.24734i	−0.355591	−	0.205300i
$927$	−10.4174	−	56.9475i	−0.342153	−	1.87040i
$928$	−0.909720	+	0.909720i	−0.0298630	+	0.0298630i
$929$	1.65623	−	0.443784i	0.0543390	−	0.0145601i	−0.231547	−	0.972824i	$-0.574379\pi$
$929$	1.65623	−	0.443784i	0.0543390	−	0.0145601i	0.285886	+	0.958264i	$0.407712\pi$
$930$	−3.02689	+	3.63083i	−0.0992557	+	0.119060i
$931$	−2.35943	+	0.632206i	−0.0773271	+	0.0207197i
$932$			3.89618i			0.127623i
$933$	32.0190	−	22.5729i	1.04825	−	0.739004i
$934$	−8.47448	−	8.47448i	−0.277293	−	0.277293i
$935$	−3.11672			−0.101928
$936$	−7.54677	+	7.74895i	−0.246674	+	0.253282i
$937$	−25.3011			−0.826552			−0.413276	−	0.910606i	$-0.635616\pi$
$937$	−25.3011			−0.826552			−0.413276	+	0.910606i	$0.635616\pi$
$938$	29.8270	+	29.8270i	0.973887	+	0.973887i
$939$	2.95245	+	32.5473i	0.0963497	+	1.06214i
$940$		−	6.35050i		−	0.207131i
$941$	45.8826	−	12.2942i	1.49573	−	0.400779i	0.584062	−	0.811709i	$-0.301462\pi$
$941$	45.8826	−	12.2942i	1.49573	−	0.400779i	0.911667	+	0.410929i	$0.134796\pi$
$942$	−18.7155	−	3.23836i	−0.609785	−	0.105512i
$943$	15.4022	−	4.12701i	0.501565	−	0.134394i
$944$	3.52351	−	3.52351i	0.114681	−	0.114681i
$945$	10.1269	+	9.93438i	0.329428	+	0.323165i
$946$	−4.03432	−	2.32921i	−0.131167	−	0.0757293i
$947$	−29.0592	+	29.0592i	−0.944299	+	0.944299i	−0.998528	−	0.0542299i	$-0.982730\pi$
$947$	−29.0592	+	29.0592i	−0.944299	+	0.944299i	0.0542299	+	0.998528i	$0.482730\pi$
$948$	25.1598	−	2.28231i	0.817152	−	0.0741260i
$949$	7.12811	−	0.672644i	0.231388	−	0.0218349i
$950$	−1.03294	−	0.596369i	−0.0335131	−	0.0193488i
$951$	21.0862	−	25.2934i	0.683768	−	0.820196i
$952$	−26.2004			−0.849160
$953$	18.5200	+	32.0775i	0.599921	+	1.03909i	0.992832	+	0.119517i	$0.0381346\pi$
$953$	18.5200	+	32.0775i	0.599921	+	1.03909i	−0.392911	+	0.919576i	$0.628532\pi$
$954$	−18.9677	−	1.53726i	−0.614101	−	0.0497705i
$955$	5.51772	+	1.47847i	0.178549	+	0.0478421i
$956$	0.407977	+	1.52259i	0.0131949	+	0.0492441i
$957$	0.546159	+	1.48576i	0.0176548	+	0.0480277i
$958$	−14.3737			−0.464393
$959$	−23.7478	−	41.1323i	−0.766855	−	1.32823i
$960$	−0.199673	+	1.15398i	−0.00644443	+	0.0372444i
$961$	12.7375	−	7.35397i	0.410886	−	0.237225i
$962$	−27.8563	+	10.3546i	−0.898124	+	0.333844i
$963$	7.18161	+	39.2587i	0.231424	+	1.26509i
$964$	−1.33674	−	4.98879i	−0.0430536	−	0.160678i
$965$		−	0.0362854i		−	0.00116807i
$966$	5.05173	−	10.9246i	0.162537	−	0.351492i
$967$	1.54647	+	5.77149i	0.0497310	+	0.185599i	0.986323	−	0.164822i	$-0.0527051\pi$
$967$	1.54647	+	5.77149i	0.0497310	+	0.185599i	−0.936592	+	0.350421i	$0.886038\pi$
$968$	7.42135	+	7.42135i	0.238531	+	0.238531i
$969$	−0.503114	+	2.90765i	−0.0161623	+	0.0934073i
$970$	0.352234	−	1.31456i	0.0113096	−	0.0422079i
$971$	1.66482	−	0.961183i	0.0534266	−	0.0308458i	−0.473049	−	0.881036i	$-0.656847\pi$
$971$	1.66482	−	0.961183i	0.0534266	−	0.0308458i	0.526475	+	0.850190i	$0.323513\pi$
$972$	12.9107	+	8.73582i	0.414110	+	0.280202i
$973$	−11.5528	+	3.09556i	−0.370365	+	0.0992390i
$974$	−11.2410	−	19.4701i	−0.360186	−	0.623861i
$975$	−16.0387	+	23.4011i	−0.513649	+	0.749436i
$976$	1.64932	−	2.85670i	0.0527933	−	0.0914407i
$977$	1.06347	−	3.96893i	0.0340235	−	0.126977i	−0.946825	−	0.321748i	$-0.895730\pi$
$977$	1.06347	−	3.96893i	0.0340235	−	0.126977i	0.980849	+	0.194771i	$0.0623963\pi$
$978$	22.0774	−	2.00270i	0.705957	−	0.0640392i
$979$	6.27670	+	3.62385i	0.200604	+	0.115819i
$980$	4.44806	+	4.44806i	0.142088	+	0.142088i
$981$	32.2916	+	2.61711i	1.03099	+	0.0835579i
$982$	−11.2262	+	41.8968i	−0.358243	+	1.33698i
$983$	14.8251	+	3.97238i	0.472848	+	0.126699i	0.487370	−	0.873195i	$-0.337956\pi$
$983$	14.8251	+	3.97238i	0.472848	+	0.126699i	−0.0145225	+	0.999895i	$0.504623\pi$
$984$	1.44979	+	15.9823i	0.0462177	+	0.509496i
$985$	1.55763	−	0.899299i	0.0496302	−	0.0286540i
$986$	8.06371	+	2.16067i	0.256801	+	0.0688096i
$987$	−59.6193	−	27.5691i	−1.89770	−	0.877535i
$988$	0.548254	+	0.771732i	0.0174423	+	0.0245521i
$989$		−	11.2859i		−	0.358870i
$990$	1.18562	+	0.818929i	0.0376816	+	0.0260273i
$991$	−2.52005	+	4.36486i	−0.0800521	+	0.138654i	−0.903272	−	0.429068i	$-0.858842\pi$
$991$	−2.52005	+	4.36486i	−0.0800521	+	0.138654i	0.823220	+	0.567722i	$0.192175\pi$
$992$	−2.01817	+	3.49557i	−0.0640770	+	0.110985i
$993$	−7.81762	+	45.1805i	−0.248085	+	1.43376i
$994$	−23.1192	+	23.1192i	−0.733296	+	0.733296i
$995$	−0.834111	+	0.834111i	−0.0264431	+	0.0264431i
$996$	−5.38486	−	4.48916i	−0.170626	−	0.142244i
$997$	5.85786	−	10.1461i	0.185520	−	0.321331i	−0.758231	−	0.651986i	$-0.773936\pi$
$997$	5.85786	−	10.1461i	0.185520	−	0.321331i	0.943752	+	0.330655i	$0.107270\pi$
$998$	14.3994	−	24.9406i	0.455806	−	0.789480i
$999$	21.7694	+	36.8838i	0.688754	+	1.16695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.y.a.149.2	yes	56
3.2	odd	2		702.2.bb.a.71.11		56
9.2	odd	6		234.2.z.a.227.13	yes	56
9.7	even	3		702.2.bc.a.305.4		56
13.11	odd	12		234.2.z.a.167.13	yes	56
39.11	even	12		702.2.bc.a.557.4		56
117.11	even	12	inner	234.2.y.a.11.2	✓	56
117.115	odd	12		702.2.bb.a.89.11		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.2	✓	56	117.11	even	12	inner
234.2.y.a.149.2	yes	56	1.1	even	1	trivial
234.2.z.a.167.13	yes	56	13.11	odd	12
234.2.z.a.227.13	yes	56	9.2	odd	6
702.2.bb.a.71.11		56	3.2	odd	2
702.2.bb.a.89.11		56	117.115	odd	12
702.2.bc.a.305.4		56	9.7	even	3
702.2.bc.a.557.4		56	39.11	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.57210 - 0.726972i) q^{3} +1.00000i q^{4} +(0.653109 - 0.175000i) q^{5} +(0.597599 + 1.62569i) q^{6} +(-3.90017 + 1.04505i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.94302 + 2.28575i) q^{9} +(-0.585562 - 0.338074i) q^{10} +(-0.502310 + 0.502310i) q^{11} +(0.726972 - 1.57210i) q^{12} +(-2.29871 + 2.77775i) q^{13} +(3.49679 + 2.01888i) q^{14} +(-1.15398 - 0.199673i) q^{15} -1.00000 q^{16} +(3.24443 + 5.61952i) q^{17} +(0.242344 - 2.99020i) q^{18} +(-0.253608 - 0.0679541i) q^{19} +(0.175000 + 0.653109i) q^{20} +(6.89119 + 1.19239i) q^{21} +0.710373 q^{22} +(0.860504 + 1.49044i) q^{23} +(-1.62569 + 0.597599i) q^{24} +(-3.93420 + 2.27141i) q^{25} +(3.58960 - 0.338733i) q^{26} +(-1.39296 - 5.00596i) q^{27} +(-1.04505 - 3.90017i) q^{28} +1.28654i q^{29} +(0.674794 + 0.957175i) q^{30} +(1.04468 + 3.89881i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.15485 - 0.424519i) q^{33} +(1.67944 - 6.26776i) q^{34} +(-2.36435 + 1.36506i) q^{35} +(-2.28575 + 1.94302i) q^{36} +(-7.96159 + 2.13330i) q^{37} +(0.131277 + 0.227379i) q^{38} +(5.63317 - 2.69582i) q^{39} +(0.338074 - 0.585562i) q^{40} +(2.39802 - 8.94954i) q^{41} +(-4.02966 - 5.71595i) q^{42} +(-5.67915 - 3.27886i) q^{43} +(-0.502310 - 0.502310i) q^{44} +(1.66901 + 1.15282i) q^{45} +(0.445430 - 1.66237i) q^{46} +(-9.07214 - 2.43087i) q^{47} +(1.57210 + 0.726972i) q^{48} +(8.05701 - 4.65172i) q^{49} +(4.38803 + 1.17577i) q^{50} +(-1.01535 - 11.1931i) q^{51} +(-2.77775 - 2.29871i) q^{52} -6.34328i q^{53} +(-2.55478 + 4.52472i) q^{54} +(-0.240159 + 0.415967i) q^{55} +(-2.01888 + 3.49679i) q^{56} +(0.349298 + 0.291197i) q^{57} +(0.909720 - 0.909720i) q^{58} +(-3.52351 + 3.52351i) q^{59} +(0.199673 - 1.15398i) q^{60} +(-1.64932 + 2.85670i) q^{61} +(2.01817 - 3.49557i) q^{62} +(-9.96684 - 6.88426i) q^{63} -1.00000i q^{64} +(-1.01520 + 2.21645i) q^{65} +(-1.11678 - 0.516421i) q^{66} +(10.0909 + 2.70385i) q^{67} +(-5.61952 + 3.24443i) q^{68} +(-0.269297 - 2.96868i) q^{69} +(2.63709 + 0.706607i) q^{70} +(-2.09577 + 7.82153i) q^{71} +(2.99020 + 0.242344i) q^{72} +(-1.40415 - 1.40415i) q^{73} +(7.13817 + 4.12122i) q^{74} +(7.83623 - 0.710844i) q^{75} +(0.0679541 - 0.253608i) q^{76} +(1.43416 - 2.48403i) q^{77} +(-5.88948 - 2.07702i) q^{78} +(7.29283 + 12.6316i) q^{79} +(-0.653109 + 0.175000i) q^{80} +(-1.44931 + 8.88254i) q^{81} +(-8.02394 + 4.63262i) q^{82} +(1.04760 - 3.90968i) q^{83} +(-1.19239 + 6.89119i) q^{84} +(3.10238 + 3.10238i) q^{85} +(1.69726 + 6.33427i) q^{86} +(0.935277 - 2.02257i) q^{87} +0.710373i q^{88} +(-2.64065 - 9.85503i) q^{89} +(-0.365007 - 1.99533i) q^{90} +(6.06248 - 13.2360i) q^{91} +(-1.49044 + 0.860504i) q^{92} +(1.19197 - 6.88878i) q^{93} +(4.69609 + 8.13386i) q^{94} -0.177526 q^{95} +(-0.597599 - 1.62569i) q^{96} +(0.520942 + 1.94418i) q^{97} +(-8.98642 - 2.40791i) q^{98} +(-2.12416 - 0.172155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Introduction

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