LMFDB - Embedded newform 804.2.l.a.431.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(431,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("804.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$132$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.2
Character	$\chi$	$=$	804.431
Dual form			804.2.l.a.707.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41390 + 0.0296860i) q^{2} +(-1.00788 + 1.40861i) q^{3} +(1.99824 - 0.0839461i) q^{4} -0.377411i q^{5} +(1.38323 - 2.02155i) q^{6} +(-3.78586 + 2.18577i) q^{7} +(-2.82282 + 0.178011i) q^{8} +(-0.968338 - 2.83942i) q^{9} +O(q^{10})$	\(q+(-1.41390 + 0.0296860i) q^{2} +(-1.00788 + 1.40861i) q^{3} +(1.99824 - 0.0839461i) q^{4} -0.377411i q^{5} +(1.38323 - 2.02155i) q^{6} +(-3.78586 + 2.18577i) q^{7} +(-2.82282 + 0.178011i) q^{8} +(-0.968338 - 2.83942i) q^{9} +(0.0112038 + 0.533622i) q^{10} +(-2.33910 - 4.05143i) q^{11} +(-1.89575 + 2.89934i) q^{12} +(0.889153 - 1.54006i) q^{13} +(5.28795 - 3.20285i) q^{14} +(0.531623 + 0.380387i) q^{15} +(3.98591 - 0.335489i) q^{16} +(5.41332 + 3.12538i) q^{17} +(1.45343 + 3.98592i) q^{18} +(-1.90465 - 1.09965i) q^{19} +(-0.0316822 - 0.754157i) q^{20} +(0.736826 - 7.53579i) q^{21} +(3.42752 + 5.65889i) q^{22} +(0.145547 - 0.252096i) q^{23} +(2.59433 - 4.15565i) q^{24} +4.85756 q^{25} +(-1.21146 + 2.20389i) q^{26} +(4.97560 + 1.49780i) q^{27} +(-7.38157 + 4.68549i) q^{28} +(-3.14894 + 1.81804i) q^{29} +(-0.762955 - 0.522048i) q^{30} +(6.60703 - 3.81457i) q^{31} +(-5.62572 + 0.592674i) q^{32} +(8.06441 + 0.788513i) q^{33} +(-7.74669 - 4.25829i) q^{34} +(0.824933 + 1.42883i) q^{35} +(-2.17333 - 5.59255i) q^{36} +(2.19724 - 3.80573i) q^{37} +(2.72563 + 1.49825i) q^{38} +(1.27317 + 2.80467i) q^{39} +(0.0671834 + 1.06536i) q^{40} +(-7.75760 + 4.47886i) q^{41} +(-0.818092 + 10.6767i) q^{42} +13.0081i q^{43} +(-5.01417 - 7.89937i) q^{44} +(-1.07163 + 0.365462i) q^{45} +(-0.198306 + 0.360759i) q^{46} +(-2.16821 - 3.75545i) q^{47} +(-3.54476 + 5.95270i) q^{48} +(6.05517 - 10.4879i) q^{49} +(-6.86811 + 0.144201i) q^{50} +(-9.85844 + 4.47521i) q^{51} +(1.64746 - 3.15204i) q^{52} -0.977850i q^{53} +(-7.07947 - 1.97004i) q^{54} +(-1.52906 + 0.882801i) q^{55} +(10.2977 - 6.84396i) q^{56} +(3.46863 - 1.57458i) q^{57} +(4.39832 - 2.66401i) q^{58} +10.0101 q^{59} +(1.09424 + 0.715475i) q^{60} +(1.71847 - 2.97648i) q^{61} +(-9.22845 + 5.58956i) q^{62} +(9.87232 + 8.63310i) q^{63} +(7.93662 - 1.00499i) q^{64} +(-0.581235 - 0.335576i) q^{65} +(-11.4257 - 0.875480i) q^{66} +(4.84945 - 6.59415i) q^{67} +(11.0795 + 5.79083i) q^{68} +(0.208408 + 0.459102i) q^{69} +(-1.20879 - 1.99573i) q^{70} +(7.60688 + 13.1755i) q^{71} +(3.23889 + 7.84280i) q^{72} +(-3.85201 + 6.67187i) q^{73} +(-2.99371 + 5.44616i) q^{74} +(-4.89586 + 6.84239i) q^{75} +(-3.89825 - 2.03747i) q^{76} +(17.7110 + 10.2254i) q^{77} +(-1.88340 - 3.92773i) q^{78} +(12.2306 - 7.06135i) q^{79} +(-0.126617 - 1.50432i) q^{80} +(-7.12464 + 5.49904i) q^{81} +(10.8355 - 6.56295i) q^{82} +(4.41566 - 7.64815i) q^{83} +(0.839753 - 15.1201i) q^{84} +(1.17955 - 2.04305i) q^{85} +(-0.386159 - 18.3922i) q^{86} +(0.612864 - 6.26799i) q^{87} +(7.32405 + 11.0201i) q^{88} +0.594091i q^{89} +(1.50433 - 0.548539i) q^{90} +7.77393i q^{91} +(0.269676 - 0.515965i) q^{92} +(-1.28590 + 13.1513i) q^{93} +(3.17712 + 5.24547i) q^{94} +(-0.415019 + 0.718835i) q^{95} +(4.83523 - 8.52177i) q^{96} +(0.271698 - 0.470594i) q^{97} +(-8.25007 + 15.0086i) q^{98} +(-9.23870 + 10.5648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41390	+	0.0296860i	−0.999780	+	0.0209912i
$2$	−1.41390	+	0.0296860i	−0.999780	+	0.0209912i
$3$	−1.00788	+	1.40861i	−0.581902	+	0.813259i
$3$	−1.00788	+	1.40861i	−0.581902	+	0.813259i
$4$	1.99824	−	0.0839461i	0.999119	−	0.0419731i
$5$		−	0.377411i		−	0.168783i	−0.996433	−	0.0843917i	$-0.973105\pi$
$5$		−	0.377411i		−	0.168783i	0.996433	−	0.0843917i	$-0.0268947\pi$
$6$	1.38323	−	2.02155i	0.564703	−	0.825294i
$7$	−3.78586	+	2.18577i	−1.43092	+	0.826143i	−0.997191	−	0.0748998i	$-0.976136\pi$
$7$	−3.78586	+	2.18577i	−1.43092	+	0.826143i	−0.433730	+	0.901043i	$0.642803\pi$
$8$	−2.82282	+	0.178011i	−0.998018	+	0.0629365i
$9$	−0.968338	−	2.83942i	−0.322779	−	0.946474i
$10$	0.0112038	+	0.533622i	0.00354296	+	0.168746i
$11$	−2.33910	−	4.05143i	−0.705264	−	1.22155i	−0.966596	−	0.256304i	$-0.917495\pi$
$11$	−2.33910	−	4.05143i	−0.705264	−	1.22155i	0.261332	−	0.965249i	$-0.415838\pi$
$12$	−1.89575	+	2.89934i	−0.547255	+	0.836966i
$13$	0.889153	−	1.54006i	0.246607	−	0.427135i	−0.715975	−	0.698125i	$-0.754018\pi$
$13$	0.889153	−	1.54006i	0.246607	−	0.427135i	0.962582	+	0.270990i	$0.0873511\pi$
$14$	5.28795	−	3.20285i	1.41326	−	0.855998i
$15$	0.531623	+	0.380387i	0.137265	+	0.0982154i
$16$	3.98591	−	0.335489i	0.996477	−	0.0838722i
$17$	5.41332	+	3.12538i	1.31292	+	0.758017i	0.982579	−	0.185843i	$-0.0595017\pi$
$17$	5.41332	+	3.12538i	1.31292	+	0.758017i	0.330345	+	0.943860i	$0.392835\pi$
$18$	1.45343	+	3.98592i	0.342576	+	0.939490i
$19$	−1.90465	−	1.09965i	−0.436956	−	0.252277i	0.265350	−	0.964152i	$-0.414513\pi$
$19$	−1.90465	−	1.09965i	−0.436956	−	0.252277i	−0.702306	+	0.711876i	$0.747846\pi$
$20$	−0.0316822	−	0.754157i	−0.00708435	−	0.168635i
$21$	0.736826	−	7.53579i	0.160789	−	1.64444i
$22$	3.42752	+	5.65889i	0.730751	+	1.20648i
$23$	0.145547	−	0.252096i	0.0303487	−	0.0525656i	−0.850452	−	0.526052i	$-0.823672\pi$
$23$	0.145547	−	0.252096i	0.0303487	−	0.0525656i	0.880801	+	0.473487i	$0.157005\pi$
$24$	2.59433	−	4.15565i	0.529565	−	0.848269i
$25$	4.85756			0.971512
$26$	−1.21146	+	2.20389i	−0.237586	+	0.432218i
$27$	4.97560	+	1.49780i	0.957554	+	0.288252i
$28$	−7.38157	+	4.68549i	−1.39498	+	0.885475i
$29$	−3.14894	+	1.81804i	−0.584743	+	0.337602i	−0.763016	−	0.646379i	$-0.776282\pi$
$29$	−3.14894	+	1.81804i	−0.584743	+	0.337602i	0.178273	+	0.983981i	$0.442949\pi$
$30$	−0.762955	−	0.522048i	−0.139296	−	0.0953124i
$31$	6.60703	−	3.81457i	1.18666	−	0.685117i	0.229112	−	0.973400i	$-0.426418\pi$
$31$	6.60703	−	3.81457i	1.18666	−	0.685117i	0.957545	+	0.288283i	$0.0930844\pi$
$32$	−5.62572	+	0.592674i	−0.994496	+	0.104771i
$33$	8.06441	+	0.788513i	1.40383	+	0.137262i
$34$	−7.74669	−	4.25829i	−1.32855	−	0.730290i
$35$	0.824933	+	1.42883i	0.139439	+	0.241516i
$36$	−2.17333	−	5.59255i	−0.362221	−	0.932092i
$37$	2.19724	−	3.80573i	0.361224	−	0.625659i	−0.626938	−	0.779069i	$-0.715692\pi$
$37$	2.19724	−	3.80573i	0.361224	−	0.625659i	0.988163	+	0.153410i	$0.0490255\pi$
$38$	2.72563	+	1.49825i	0.442155	+	0.243049i
$39$	1.27317	+	2.80467i	0.203870	+	0.449106i
$40$	0.0671834	+	1.06536i	0.0106226	+	0.168449i
$41$	−7.75760	+	4.47886i	−1.21153	+	0.699480i	−0.963093	−	0.269167i	$-0.913252\pi$
$41$	−7.75760	+	4.47886i	−1.21153	+	0.699480i	−0.248441	+	0.968647i	$0.579918\pi$
$42$	−0.818092	+	10.6767i	−0.126234	+	1.64746i
$43$			13.0081i			1.98372i	0.127326	+	0.991861i	$0.459361\pi$
$43$			13.0081i			1.98372i	−0.127326	+	0.991861i	$0.540639\pi$
$44$	−5.01417	−	7.89937i	−0.755915	−	1.19087i
$45$	−1.07163	+	0.365462i	−0.159749	+	0.0544798i
$46$	−0.198306	+	0.360759i	−0.0292386	+	0.0531910i
$47$	−2.16821	−	3.75545i	−0.316266	−	0.547788i	0.663440	−	0.748230i	$-0.269096\pi$
$47$	−2.16821	−	3.75545i	−0.316266	−	0.547788i	−0.979706	+	0.200441i	$0.935762\pi$
$48$	−3.54476	+	5.95270i	−0.511642	+	0.859199i
$49$	6.05517	−	10.4879i	0.865024	−	1.49827i
$50$	−6.86811	+	0.144201i	−0.971298	+	0.0203932i
$51$	−9.85844	+	4.47521i	−1.38046	+	0.626655i
$52$	1.64746	−	3.15204i	0.228461	−	0.437110i
$53$		−	0.977850i		−	0.134318i	−0.997742	−	0.0671590i	$-0.978607\pi$
$53$		−	0.977850i		−	0.134318i	0.997742	−	0.0671590i	$-0.0213935\pi$
$54$	−7.07947	−	1.97004i	−0.963394	−	0.268089i
$55$	−1.52906	+	0.882801i	−0.206178	+	0.119037i
$56$	10.2977	−	6.84396i	1.37609	−	0.914562i
$57$	3.46863	−	1.57458i	0.459432	−	0.208558i
$58$	4.39832	−	2.66401i	0.577528	−	0.349802i
$59$	10.0101			1.30320			0.651602	−	0.758561i	$-0.274097\pi$
$59$	10.0101			1.30320			0.651602	+	0.758561i	$0.274097\pi$
$60$	1.09424	+	0.715475i	0.141266	+	0.0923674i
$61$	1.71847	−	2.97648i	0.220027	−	0.381099i	−0.734789	−	0.678296i	$-0.762719\pi$
$61$	1.71847	−	2.97648i	0.220027	−	0.381099i	0.954816	+	0.297197i	$0.0960520\pi$
$62$	−9.22845	+	5.58956i	−1.17201	+	0.709875i
$63$	9.87232	+	8.63310i	1.24380	+	1.08767i
$64$	7.93662	−	1.00499i	0.992078	−	0.125623i
$65$	−0.581235	−	0.335576i	−0.0720933	−	0.0416231i
$66$	−11.4257	−	0.875480i	−1.40641	−	0.107764i
$67$	4.84945	−	6.59415i	0.592455	−	0.805604i
$67$	4.84945	−	6.59415i	0.592455	−	0.805604i
$68$	11.0795	+	5.79083i	1.34358	+	0.702242i
$69$	0.208408	+	0.459102i	0.0250894	+	0.0552694i
$70$	−1.20879	−	1.99573i	−0.144478	−	0.238536i
$71$	7.60688	+	13.1755i	0.902770	+	1.56364i	0.823883	+	0.566760i	$0.191803\pi$
$71$	7.60688	+	13.1755i	0.902770	+	1.56364i	0.0788874	+	0.996884i	$0.474863\pi$
$72$	3.23889	+	7.84280i	0.381707	+	0.924283i
$73$	−3.85201	+	6.67187i	−0.450843	+	0.780884i	−0.998439	−	0.0558598i	$-0.982210\pi$
$73$	−3.85201	+	6.67187i	−0.450843	+	0.780884i	0.547595	+	0.836743i	$0.315543\pi$
$74$	−2.99371	+	5.44616i	−0.348011	+	0.633104i
$75$	−4.89586	+	6.84239i	−0.565325	+	0.790091i
$76$	−3.89825	−	2.03747i	−0.447160	−	0.233714i
$77$	17.7110	+	10.2254i	2.01836	+	1.16530i
$78$	−1.88340	−	3.92773i	−0.213253	−	0.444728i
$79$	12.2306	−	7.06135i	1.37605	−	0.794464i	0.384371	−	0.923179i	$-0.374419\pi$
$79$	12.2306	−	7.06135i	1.37605	−	0.794464i	0.991682	+	0.128715i	$0.0410852\pi$
$80$	−0.126617	−	1.50432i	−0.0141562	−	0.168189i
$81$	−7.12464	+	5.49904i	−0.791627	+	0.611005i
$82$	10.8355	−	6.56295i	1.19658	−	0.724757i
$83$	4.41566	−	7.64815i	0.484682	−	0.839493i	−0.515164	−	0.857092i	$-0.672269\pi$
$83$	4.41566	−	7.64815i	0.484682	−	0.839493i	0.999845	+	0.0175988i	$0.00560215\pi$
$84$	0.839753	−	15.1201i	0.0916245	−	1.64974i
$85$	1.17955	−	2.04305i	0.127941	−	0.221600i
$86$	−0.386159	−	18.3922i	−0.0416406	−	1.98328i
$87$	0.612864	−	6.26799i	0.0657059	−	0.671999i
$88$	7.32405	+	11.0201i	0.780746	+	1.17474i
$89$			0.594091i			0.0629735i	0.999504	+	0.0314867i	$0.0100242\pi$
$89$			0.594091i			0.0629735i	−0.999504	+	0.0314867i	$0.989976\pi$
$90$	1.50433	−	0.548539i	0.158570	−	0.0578211i
$91$			7.77393i			0.814929i
$92$	0.269676	−	0.515965i	0.0281157	−	0.0537931i
$93$	−1.28590	+	13.1513i	−0.133341	+	1.36373i
$94$	3.17712	+	5.24547i	0.327695	+	0.541029i
$95$	−0.415019	+	0.718835i	−0.0425801	+	0.0737509i
$96$	4.83523	−	8.52177i	0.493494	−	0.869749i
$97$	0.271698	−	0.470594i	0.0275867	−	0.0477816i	−0.851902	−	0.523701i	$-0.824551\pi$
$97$	0.271698	−	0.470594i	0.0275867	−	0.0477816i	0.879489	+	0.475919i	$0.157884\pi$
$98$	−8.25007	+	15.0086i	−0.833383	+	1.51609i
$99$	−9.23870	+	10.5648i	−0.928524	+	1.06181i
$100$	9.70656	−	0.407773i	0.970656	−	0.0407773i
$101$	4.92436	−	2.84308i	0.489993	−	0.282897i	−0.234579	−	0.972097i	$-0.575371\pi$
$101$	4.92436	−	2.84308i	0.489993	−	0.282897i	0.724571	+	0.689200i	$0.242038\pi$
$102$	13.8060	−	6.62017i	1.36700	−	0.655494i
$103$	4.94497	−	2.85498i	0.487243	−	0.281310i	−0.236187	−	0.971708i	$-0.575898\pi$
$103$	4.94497	−	2.85498i	0.487243	−	0.281310i	0.723430	+	0.690398i	$0.242565\pi$
$104$	−2.23577	+	4.50559i	−0.219235	+	0.441809i
$105$	−2.84409	−	0.278086i	−0.277555	−	0.0271384i
$106$	0.0290284	+	1.38258i	0.00281949	+	0.134288i
$107$	−4.24265			−0.410152			−0.205076	−	0.978746i	$-0.565744\pi$
$107$	−4.24265			−0.410152			−0.205076	+	0.978746i	$0.565744\pi$
$108$	10.0682	+	2.57528i	0.968809	+	0.247807i
$109$	−5.94324			−0.569259			−0.284630	−	0.958638i	$-0.591871\pi$
$109$	−5.94324			−0.569259			−0.284630	+	0.958638i	$0.591871\pi$
$110$	2.13573	−	1.29359i	0.203634	−	0.123339i
$111$	3.14621	+	6.93079i	0.298625	+	0.657841i
$112$	−14.3568	+	9.98238i	−1.35659	+	0.943246i
$113$	15.3316	−	8.85169i	1.44227	−	0.832697i	0.444272	−	0.895892i	$-0.353463\pi$
$113$	15.3316	−	8.85169i	1.44227	−	0.832697i	0.998001	+	0.0631956i	$0.0201292\pi$
$114$	−4.85756	+	2.32927i	−0.454953	+	0.218156i
$115$	−0.0951437	−	0.0549312i	−0.00887219	−	0.00512236i
$116$	−6.13971	+	3.89722i	−0.570058	+	0.361848i
$117$	−5.23388	−	1.03338i	−0.483872	−	0.0955363i
$118$	−14.1533	+	0.297160i	−1.30292	+	0.0273558i
$119$	−27.3255			−2.50492
$120$	−1.56839	−	0.979128i	−0.143174	−	0.0893818i
$121$	−5.44275	+	9.42712i	−0.494795	+	0.857011i
$122$	−2.34139	+	4.25946i	−0.211979	+	0.385633i
$123$	1.50983	−	15.4416i	0.136137	−	1.39232i
$124$	12.8822	−	8.17705i	1.15686	−	0.734321i
$125$		−	3.72035i		−	0.332758i
$126$	−14.2148	−	11.9133i	−1.26635	−	1.06132i
$127$	7.57112	−	4.37119i	0.671828	−	0.387880i	−0.124941	−	0.992164i	$-0.539874\pi$
$127$	7.57112	−	4.37119i	0.671828	−	0.387880i	0.796769	+	0.604284i	$0.206541\pi$
$128$	−11.1918	+	1.65656i	−0.989222	+	0.146421i
$129$	−18.3233	−	13.1107i	−1.61328	−	1.15433i
$130$	0.831771	+	0.457217i	0.0729511	+	0.0401006i
$131$	14.2007			1.24072			0.620361	−	0.784317i	$-0.286986\pi$
$131$	14.2007			1.24072			0.620361	+	0.784317i	$0.286986\pi$
$132$	16.1808	+	0.898660i	1.40836	+	0.0782183i
$133$	9.61431			0.833666
$134$	−6.66089	+	9.46744i	−0.575414	+	0.817863i
$135$	0.565287	−	1.87785i	0.0486522	−	0.161619i
$136$	−15.8372	−	7.85876i	−1.35803	−	0.673883i
$137$			10.0688i			0.860239i	0.902772	+	0.430119i	$0.141529\pi$
$137$			10.0688i			0.860239i	−0.902772	+	0.430119i	$0.858471\pi$
$138$	−0.308298	−	0.642939i	−0.0262440	−	0.0547306i
$139$		−	9.89643i		−	0.839404i	−0.907662	−	0.419702i	$-0.862135\pi$
$139$		−	9.89643i		−	0.839404i	0.907662	−	0.419702i	$-0.137865\pi$
$140$	1.76836	+	2.78588i	0.149453	+	0.235450i
$141$	7.47525	+	0.730906i	0.629530	+	0.0615534i
$142$	−11.1465	−	18.4030i	−0.935394	−	1.54435i
$143$	−8.31926			−0.695691
$144$	−4.81230	−	10.9928i	−0.401025	−	0.916067i
$145$	0.686148	+	1.18844i	0.0569815	+	0.0986949i
$146$	5.24830	−	9.54772i	0.434352	−	0.790175i
$147$	8.67035	+	19.0999i	0.715118	+	1.57533i
$148$	4.07113	−	7.78921i	0.334645	−	0.640269i
$149$		−	14.5590i		−	1.19272i	−0.802718	−	0.596359i	$-0.796613\pi$
$149$		−	14.5590i		−	1.19272i	0.802718	−	0.596359i	$-0.203387\pi$
$150$	6.71914	−	9.81980i	0.548616	−	0.801783i
$151$	−15.7197	−	9.07577i	−1.27925	−	0.738576i	−0.302540	−	0.953137i	$-0.597835\pi$
$151$	−15.7197	−	9.07577i	−1.27925	−	0.738576i	−0.976711	+	0.214561i	$0.931168\pi$
$152$	5.57222	+	2.76506i	0.451967	+	0.224276i
$153$	3.63236	−	18.3971i	0.293659	−	1.48732i
$154$	−25.3452	−	13.9320i	−2.04237	−	1.12267i
$155$	−1.43966	−	2.49357i	−0.115636	−	0.200288i
$156$	2.77954	+	5.49751i	0.222541	+	0.440153i
$157$	9.07333	−	15.7155i	0.724131	−	1.25423i	−0.235200	−	0.971947i	$-0.575574\pi$
$157$	9.07333	−	15.7155i	0.724131	−	1.25423i	0.959331	−	0.282284i	$-0.0910922\pi$
$158$	−17.0833	+	10.3471i	−1.35907	+	0.823174i
$159$	1.37741	+	0.985560i	0.109235	+	0.0781600i
$160$	0.223682	+	2.12321i	0.0176836	+	0.167854i
$161$			1.27253i			0.100290i
$162$	9.91030	−	7.98661i	0.778627	−	0.627487i
$163$	−1.81168	+	1.04597i	−0.141902	+	0.0819270i	−0.569270	−	0.822151i	$-0.692774\pi$
$163$	−1.81168	+	1.04597i	−0.141902	+	0.0819270i	0.427368	+	0.904078i	$0.359441\pi$
$164$	−15.1256	+	9.60104i	−1.18111	+	0.749715i
$165$	0.297593	−	3.04360i	0.0231676	−	0.236944i
$166$	−6.01627	+	10.9448i	−0.466953	+	0.849482i
$167$	−2.37626	−	4.11581i	−0.183881	−	0.318491i	0.759318	−	0.650720i	$-0.225533\pi$
$167$	−2.37626	−	4.11581i	−0.183881	−	0.318491i	−0.943199	+	0.332229i	$0.892199\pi$
$168$	−0.738471	+	21.4033i	−0.0569743	+	1.65130i
$169$	4.91881	+	8.51964i	0.378370	+	0.655357i
$170$	−1.60712	+	2.92369i	−0.123261	+	0.224236i
$171$	−1.27802	+	6.47293i	−0.0977329	+	0.494997i
$172$	1.09198	+	25.9933i	0.0832629	+	1.98197i
$173$	4.25557	+	2.45695i	0.323545	+	0.186799i	0.652972	−	0.757382i	$-0.273522\pi$
$173$	4.25557	+	2.45695i	0.323545	+	0.186799i	−0.329427	+	0.944181i	$0.606855\pi$
$174$	−0.680458	+	8.88051i	−0.0515854	+	0.673230i
$175$	−18.3901	+	10.6175i	−1.39016	+	0.802608i
$176$	−10.6826	−	15.3639i	−0.805234	−	1.15810i
$177$	−10.0890	+	14.1003i	−0.758337	+	1.05984i
$178$	−0.0176362	−	0.839986i	−0.00132189	−	0.0629596i
$179$	−2.75577			−0.205976			−0.102988	−	0.994683i	$-0.532840\pi$
$179$	−2.75577			−0.205976			−0.102988	+	0.994683i	$0.532840\pi$
$180$	−2.11069	+	0.820238i	−0.157322	+	0.0611369i
$181$	−4.94048	−	8.55715i	−0.367223	−	0.636048i	0.621908	−	0.783091i	$-0.286358\pi$
$181$	−4.94048	−	8.55715i	−0.367223	−	0.636048i	−0.989130	+	0.147042i	$0.953025\pi$
$182$	−0.230777	−	10.9916i	−0.0171063	−	0.814750i
$183$	2.46066	+	5.42059i	0.181897	+	0.400701i
$184$	−0.365978	+	0.737530i	−0.0269803	+	0.0543714i
$185$	−1.43633	−	0.829263i	−0.105601	−	0.0609686i
$186$	1.42772	−	18.6329i	0.104686	−	1.36623i
$187$		−	29.2423i		−	2.13841i
$188$	−4.64785	−	7.32227i	−0.338979	−	0.534031i
$189$	−22.1108	+	5.20503i	−1.60832	+	0.378610i
$190$	0.565457	−	1.02868i	0.0410226	−	0.0746284i
$191$	0.227076	−	0.393308i	0.0164307	−	0.0284588i	−0.857693	−	0.514162i	$-0.828103\pi$
$191$	0.227076	−	0.393308i	0.0164307	−	0.0284588i	0.874124	+	0.485703i	$0.161436\pi$
$192$	−6.58357	+	12.1925i	−0.475128	+	0.879917i
$193$	2.15409			0.155055			0.0775275	−	0.996990i	$-0.475297\pi$
$193$	2.15409			0.155055			0.0775275	+	0.996990i	$0.475297\pi$
$194$	−0.370184	+	0.673440i	−0.0265777	+	0.0483502i
$195$	1.05851	−	0.480509i	0.0758016	−	0.0344099i
$196$	11.2193	−	21.4655i	0.801375	−	1.53325i
$197$	−6.11883	+	3.53271i	−0.435948	+	0.251695i	−0.701878	−	0.712298i	$-0.747655\pi$
$197$	−6.11883	+	3.53271i	−0.435948	+	0.251695i	0.265929	+	0.963993i	$0.414321\pi$
$198$	12.7490	−	15.2119i	0.906031	−	1.08106i
$199$	−24.1367	−	13.9353i	−1.71100	−	0.987848i	−0.933214	−	0.359321i	$-0.883008\pi$
$199$	−24.1367	−	13.9353i	−1.71100	−	0.987848i	−0.777788	−	0.628527i	$-0.783658\pi$
$200$	−13.7120	+	0.864700i	−0.969586	+	0.0611436i
$201$	4.40087	+	13.4771i	0.310413	+	0.950602i
$202$	−6.87817	+	4.16603i	−0.483946	+	0.293120i
$203$	7.94763	−	13.7657i	0.557814	−	0.966163i
$204$	−19.3238	+	9.77011i	−1.35294	+	0.684045i
$205$	1.69037	+	2.92781i	0.118061	+	0.204487i
$206$	−6.90695	+	4.18346i	−0.481230	+	0.291475i
$207$	−0.856745	−	0.169157i	−0.0595479	−	0.0117572i
$208$	3.02741	−	6.43683i	0.209913	−	0.446314i
$209$			10.2887i			0.711687i
$210$	4.02952	+	0.308757i	0.278063	+	0.0213063i
$211$	13.2400	+	7.64412i	0.911479	+	0.526243i	0.880907	−	0.473290i	$-0.156934\pi$
$211$	13.2400	+	7.64412i	0.911479	+	0.526243i	0.0305725	+	0.999533i	$0.490267\pi$
$212$	−0.0820868	−	1.95398i	−0.00563774	−	0.134200i
$213$	−26.2259	−	2.56429i	−1.79697	−	0.175702i
$214$	5.99869	−	0.125947i	0.410062	−	0.00860957i
$215$	4.90941			0.334819
$216$	−14.3118	−	3.34231i	−0.973798	−	0.227416i
$217$	−16.6755	+	28.8829i	−1.13201	+	1.96070i
$218$	8.40316	−	0.176431i	0.569134	−	0.0119494i
$219$	−5.51566	−	12.1504i	−0.372714	−	0.821050i
$220$	−2.98131	+	1.89240i	−0.201000	+	0.127586i
$221$	9.62655	−	5.55789i	0.647552	−	0.373864i
$222$	−4.65418	−	9.70605i	−0.312368	−	0.651428i
$223$			23.0216i			1.54164i	0.637053	+	0.770820i	$0.280153\pi$
$223$			23.0216i			1.54164i	−0.637053	+	0.770820i	$0.719847\pi$
$224$	20.0028	−	14.5403i	1.33649	−	0.971515i
$225$	−4.70376	−	13.7927i	−0.313584	−	0.919511i
$226$	−21.4146	+	12.9705i	−1.42448	+	0.862788i
$227$	2.78142	+	4.81755i	0.184609	+	0.319752i	0.943445	−	0.331530i	$-0.107565\pi$
$227$	2.78142	+	4.81755i	0.184609	+	0.319752i	−0.758836	+	0.651282i	$0.774231\pi$
$228$	6.79897	−	3.43756i	0.450273	−	0.227658i
$229$	−0.983694	+	1.70381i	−0.0650043	+	0.112591i	−0.896696	−	0.442647i	$-0.854039\pi$
$229$	−0.983694	+	1.70381i	−0.0650043	+	0.112591i	0.831692	+	0.555238i	$0.187373\pi$
$230$	0.136154	+	0.0748429i	0.00897776	+	0.00493500i
$231$	−32.2543	+	14.6417i	−2.12217	+	0.963356i
$232$	8.56525	−	5.69255i	0.562336	−	0.373734i
$233$	10.2365	−	5.91005i	0.670616	−	0.387180i	−0.125694	−	0.992069i	$-0.540116\pi$
$233$	10.2365	−	5.91005i	0.670616	−	0.387180i	0.796310	+	0.604889i	$0.206782\pi$
$234$	7.43086	+	1.30573i	0.485771	+	0.0853583i
$235$	−1.41735	+	0.818306i	−0.0924576	+	0.0533804i
$236$	20.0026	−	0.840309i	1.30206	−	0.0546995i
$237$	−2.38039	+	24.3451i	−0.154623	+	1.58139i
$238$	38.6355	−	0.811183i	2.50437	−	0.0525812i
$239$	−0.413147	−	0.715592i	−0.0267243	−	0.0462878i	0.852354	−	0.522965i	$-0.175174\pi$
$239$	−0.413147	−	0.715592i	−0.0267243	−	0.0462878i	−0.879078	+	0.476678i	$0.841841\pi$
$240$	2.24662	+	1.33783i	0.145018	+	0.0863567i
$241$	14.0806			0.907013			0.453507	−	0.891253i	$-0.350173\pi$
$241$	14.0806			0.907013			0.453507	+	0.891253i	$0.350173\pi$
$242$	7.41566	−	13.4906i	0.476697	−	0.867208i
$243$	−0.565169	−	15.5782i	−0.0362556	−	0.999343i
$244$	3.18405	−	6.09197i	0.203838	−	0.389998i
$245$	−3.95823	−	2.28529i	−0.252882	−	0.146002i
$246$	−1.67635	+	21.8777i	−0.106880	+	1.39487i
$247$	−3.38704	+	1.95551i	−0.215512	+	0.124426i
$248$	−17.9714	+	11.9440i	−1.14119	+	0.758443i
$249$	6.32275	+	13.9284i	0.400688	+	0.882675i
$250$	0.110442	+	5.26021i	0.00698498	+	0.332685i
$251$	4.45256	−	7.71205i	0.281043	−	0.486780i	−0.690599	−	0.723238i	$-0.742653\pi$
$251$	4.45256	−	7.71205i	0.281043	−	0.486780i	0.971642	+	0.236457i	$0.0759864\pi$
$252$	20.4519	+	16.4222i	1.28835	+	1.03450i
$253$	−1.36180			−0.0856155
$254$	−10.5751	+	6.40519i	−0.663538	+	0.401897i
$255$	1.68899	+	3.72068i	0.105769	+	0.232998i
$256$	15.7749	−	2.67445i	0.985931	−	0.167153i
$257$	−3.77842	+	2.18147i	−0.235691	+	0.136076i	−0.613195	−	0.789932i	$-0.710116\pi$
$257$	−3.77842	+	2.18147i	−0.235691	+	0.136076i	0.377504	+	0.926008i	$0.376783\pi$
$258$	26.2966	+	17.9933i	1.63715	+	1.12021i
$259$			19.2106i			1.19369i
$260$	−1.18962	−	0.621768i	−0.0737768	−	0.0385604i
$261$	8.21142	+	7.18069i	0.508274	+	0.444473i
$262$	−20.0784	+	0.421562i	−1.24045	+	0.0260442i
$263$	27.6694			1.70617			0.853085	−	0.521772i	$-0.174729\pi$
$263$	27.6694			1.70617			0.853085	+	0.521772i	$0.174729\pi$
$264$	−22.9047	−	0.790274i	−1.40969	−	0.0486380i
$265$	−0.369052			−0.0226707
$266$	−13.5937	+	0.285410i	−0.833482	+	0.0174996i
$267$	−0.836839	−	0.598775i	−0.0512137	−	0.0366444i
$268$	9.13680	−	13.5838i	0.558119	−	0.829761i
$269$			17.1004i			1.04263i	0.853365	+	0.521315i	$0.174558\pi$
$269$			17.1004i			1.04263i	−0.853365	+	0.521315i	$0.825442\pi$
$270$	−0.743515	+	2.67187i	−0.0452489	+	0.162605i
$271$		−	12.4151i		−	0.754165i	−0.926180	−	0.377083i	$-0.876927\pi$
$271$		−	12.4151i		−	0.754165i	0.926180	−	0.377083i	$-0.123073\pi$
$272$	22.6255	+	10.6414i	1.37187	+	0.645228i
$273$	−10.9504	−	7.83522i	−0.662748	−	0.474209i
$274$	−0.298903	−	14.2363i	−0.0180574	−	0.860049i
$275$	−11.3623	−	19.6801i	−0.685173	−	1.18675i
$276$	0.454989	+	0.899900i	0.0273871	+	0.0541676i
$277$	−10.9195			−0.656092			−0.328046	−	0.944662i	$-0.606390\pi$
$277$	−10.9195			−0.656092			−0.328046	+	0.944662i	$0.606390\pi$
$278$	0.293785	+	13.9926i	0.0176201	+	0.839219i
$279$	−17.2290	−	15.0664i	−1.03147	−	0.901999i
$280$	−2.58299	−	3.88647i	−0.154363	−	0.232261i
$281$	13.6545	+	7.88340i	0.814556	+	0.470284i	0.848536	−	0.529138i	$-0.177485\pi$
$281$	13.6545	+	7.88340i	0.814556	+	0.470284i	−0.0339793	+	0.999423i	$0.510818\pi$
$282$	−10.5910	−	0.811520i	−0.630683	−	0.0483253i
$283$			6.46794i			0.384479i	0.981348	+	0.192240i	$0.0615751\pi$
$283$			6.46794i			0.384479i	−0.981348	+	0.192240i	$0.938425\pi$
$284$	16.3064	+	25.6892i	0.967606	+	1.52437i
$285$	−0.594263	−	1.30910i	−0.0352011	−	0.0775444i
$286$	11.7626	−	0.246965i	0.695538	−	0.0146034i
$287$	19.5795	−	33.9127i	1.15574	−	2.00180i
$288$	7.13045	+	15.3999i	0.420166	+	0.907447i
$289$	11.0361	+	19.1150i	0.649180	+	1.12441i
$290$	−1.00543	−	1.65997i	−0.0590407	−	0.0974770i
$291$	0.389042	+	0.857019i	0.0228060	+	0.0502394i
$292$	−7.13715	+	13.6553i	−0.417670	+	0.799119i
$293$		−	22.2654i		−	1.30076i	−0.759610	−	0.650379i	$-0.774610\pi$
$293$		−	22.2654i		−	1.30076i	0.759610	−	0.650379i	$-0.225390\pi$
$294$	−12.8260	−	26.7480i	−0.748029	−	1.55997i
$295$		−	3.77792i		−	0.219959i
$296$	−5.52495	+	11.1340i	−0.321131	+	0.647153i
$297$	−5.57016	−	23.6618i	−0.323213	−	1.37300i
$298$	0.432198	+	20.5850i	0.0250366	+	1.19246i
$299$	−0.258828	−	0.448303i	−0.0149684	−	0.0259260i
$300$	−9.20870	+	14.0837i	−0.531664	+	0.813123i
$301$	−28.4328	−	49.2470i	−1.63884	−	2.83855i
$302$	22.4955	+	12.3656i	1.29447	+	0.711560i
$303$	−0.958407	+	9.80198i	−0.0550591	+	0.563109i
$304$	−7.96066	−	3.74411i	−0.456575	−	0.214739i
$305$	−1.12335	−	0.648569i	−0.0643231	−	0.0371370i
$306$	−4.58966	+	26.1196i	−0.262373	+	1.49316i
$307$	−19.5782	−	11.3035i	−1.11738	−	0.645122i	−0.176652	−	0.984273i	$-0.556527\pi$
$307$	−19.5782	−	11.3035i	−1.11738	−	0.645122i	−0.940732	+	0.339151i	$0.889860\pi$
$308$	36.2492	+	18.9461i	2.06549	+	1.07955i
$309$	−0.962418	+	9.84301i	−0.0547501	+	0.559949i
$310$	2.10956	+	3.48292i	0.119815	+	0.197817i
$311$	−15.7388			−0.892464			−0.446232	−	0.894917i	$-0.647234\pi$
$311$	−15.7388			−0.892464			−0.446232	+	0.894917i	$0.647234\pi$
$312$	−4.09319	−	7.69043i	−0.231731	−	0.435385i
$313$	21.3890			1.20898			0.604489	−	0.796614i	$-0.293377\pi$
$313$	21.3890			1.20898			0.604489	+	0.796614i	$0.293377\pi$
$314$	−12.3623	+	22.4895i	−0.697644	+	1.26916i
$315$	3.25823	−	3.72592i	0.183580	−	0.209932i
$316$	23.8469	−	15.1370i	1.34149	−	0.851521i
$317$	−14.7298	−	8.50426i	−0.827309	−	0.477647i	0.0256216	−	0.999672i	$-0.491844\pi$
$317$	−14.7298	−	8.50426i	−0.827309	−	0.477647i	−0.852930	+	0.522025i	$0.825177\pi$
$318$	−1.97677	−	1.35260i	−0.110852	−	0.0758498i
$319$	14.7313	+	8.50514i	0.824797	+	0.476197i
$320$	−0.379293	−	2.99537i	−0.0212031	−	0.167446i
$321$	4.27610	−	5.97622i	0.238669	−	0.333560i
$322$	−0.0377764	−	1.79924i	−0.00210519	−	0.100267i
$323$	−6.87365	−	11.9055i	−0.382460	−	0.662440i
$324$	−13.7751	+	11.5865i	−0.765283	+	0.643693i
$325$	4.31911	−	7.48093i	0.239581	−	0.414967i
$326$	2.53049	−	1.53269i	0.140151	−	0.0848877i
$327$	5.99010	−	8.37168i	0.331253	−	0.462955i
$328$	21.1010	−	14.0239i	1.16511	−	0.774343i
$329$	16.4171	+	9.47841i	0.905103	+	0.522562i
$330$	−0.330416	+	4.31218i	−0.0181888	+	0.237378i
$331$	25.2829	−	14.5971i	1.38968	−	0.802329i	0.396397	−	0.918079i	$-0.370260\pi$
$331$	25.2829	−	14.5971i	1.38968	−	0.802329i	0.993278	+	0.115750i	$0.0369270\pi$
$332$	8.18150	−	15.6535i	0.449018	−	0.859097i
$333$	−12.9338	−	2.55366i	−0.708766	−	0.139940i
$334$	3.48198	+	5.74880i	0.190526	+	0.314561i
$335$	−2.48871	−	1.83024i	−0.135972	−	0.0999965i
$336$	0.408747	−	30.2841i	0.0222990	−	1.65214i
$337$	−17.6212	+	30.5209i	−0.959890	+	1.66258i	−0.237132	+	0.971477i	$0.576207\pi$
$337$	−17.6212	+	30.5209i	−0.959890	+	1.66258i	−0.722758	+	0.691101i	$0.757126\pi$
$338$	−7.20764	−	11.8999i	−0.392044	−	0.647270i
$339$	−2.98392	+	30.5176i	−0.162064	+	1.65749i
$340$	2.18552	−	4.18151i	0.118527	−	0.226774i
$341$	−30.9090	−	17.8453i	−1.67381	−	0.966377i
$342$	1.61484	−	9.19002i	0.0873208	−	0.496940i
$343$			22.3400i			1.20625i
$344$	−2.31559	−	36.7196i	−0.124848	−	1.97979i
$345$	0.173270	−	0.0786556i	0.00932855	−	0.00423467i
$346$	−6.08990	−	3.34756i	−0.327395	−	0.179966i
$347$	−5.16089	−	8.93893i	−0.277051	−	0.479867i	0.693599	−	0.720361i	$-0.256024\pi$
$347$	−5.16089	−	8.93893i	−0.277051	−	0.479867i	−0.970651	+	0.240494i	$0.922690\pi$
$348$	0.698475	−	12.5764i	0.0374422	−	0.674164i
$349$	7.10591			0.380371			0.190185	−	0.981748i	$-0.439091\pi$
$349$	7.10591			0.380371			0.190185	+	0.981748i	$0.439091\pi$
$350$	25.6865	−	15.5580i	1.37300	−	0.831612i
$351$	6.73077	−	6.33094i	0.359262	−	0.337920i
$352$	15.5603	+	21.4059i	0.829366	+	1.14094i
$353$	−11.7129	−	6.76245i	−0.623415	−	0.359929i	0.154783	−	0.987949i	$-0.450532\pi$
$353$	−11.7129	−	6.76245i	−0.623415	−	0.359929i	−0.778197	+	0.628020i	$0.783866\pi$
$354$	13.8463	−	20.2359i	0.735923	−	1.07553i
$355$	4.97258	−	2.87092i	0.263917	−	0.152373i
$356$	0.0498716	+	1.18713i	0.00264319	+	0.0629180i
$357$	27.5409	−	38.4908i	1.45762	−	2.03715i
$358$	3.89638	−	0.0818076i	0.205930	−	0.00432367i
$359$	15.4691			0.816427			0.408213	−	0.912887i	$-0.366152\pi$
$359$	15.4691			0.816427			0.408213	+	0.912887i	$0.366152\pi$
$360$	2.95996	−	1.22239i	0.156004	−	0.0644258i
$361$	−7.08155	−	12.2656i	−0.372713	−	0.645558i
$362$	7.23938	+	11.9523i	0.380493	+	0.628200i
$363$	−7.79343	−	17.1681i	−0.409049	−	0.901093i
$364$	0.652591	+	15.5342i	0.0342051	+	0.814211i
$365$	2.51804	+	1.45379i	0.131800	+	0.0760948i
$366$	−3.64005	−	7.59113i	−0.190268	−	0.396795i
$367$	−20.5942	+	11.8900i	−1.07501	+	0.620655i	−0.929545	−	0.368709i	$-0.879800\pi$
$367$	−20.5942	+	11.8900i	−1.07501	+	0.620655i	−0.145461	+	0.989364i	$0.546467\pi$
$368$	0.495563	−	1.05366i	0.0258330	−	0.0549258i
$369$	20.2293	+	17.6901i	1.05310	+	0.920908i
$370$	2.05544	+	1.12986i	0.106857	+	0.0587385i
$371$	2.13735	+	3.70201i	0.110966	+	0.192199i
$372$	−1.46552	+	26.3874i	−0.0759838	+	1.36813i
$373$	0.286552	+	0.496323i	0.0148371	+	0.0256986i	0.873349	−	0.487096i	$-0.161944\pi$
$373$	0.286552	+	0.496323i	0.0148371	+	0.0256986i	−0.858512	+	0.512794i	$0.828610\pi$
$374$	0.868087	+	41.3458i	0.0448877	+	2.13794i
$375$	5.24051	+	3.74968i	0.270619	+	0.193633i
$376$	6.78898	+	10.2150i	0.350115	+	0.526798i
$377$			6.46606i			0.333019i
$378$	31.1080	−	8.01579i	1.60002	−	0.412288i
$379$	12.3002	+	7.10150i	0.631817	+	0.364780i	0.781455	−	0.623961i	$-0.214478\pi$
$379$	12.3002	+	7.10150i	0.631817	+	0.364780i	−0.149639	+	0.988741i	$0.547811\pi$
$380$	−0.768964	+	1.47124i	−0.0394470	+	0.0754731i
$381$	−1.47353	+	15.0704i	−0.0754914	+	0.772079i
$382$	−0.309388	+	0.562840i	−0.0158297	+	0.0287974i
$383$	−11.5134	+	19.9418i	−0.588307	+	1.01898i	0.406147	+	0.913808i	$0.366872\pi$
$383$	−11.5134	+	19.9418i	−0.588307	+	1.01898i	−0.994454	+	0.105170i	$0.966461\pi$
$384$	8.94657	−	17.4344i	0.456553	−	0.889696i
$385$	3.85920	−	6.68433i	0.196683	−	0.340665i
$386$	−3.04568	+	0.0639464i	−0.155021	+	0.00325478i
$387$	36.9356	−	12.5963i	1.87754	−	0.640305i
$388$	0.503412	−	0.963167i	0.0255569	−	0.0488974i
$389$	−18.1932	−	10.5039i	−0.922433	−	0.532567i	−0.0380227	−	0.999277i	$-0.512106\pi$
$389$	−18.1932	−	10.5039i	−0.922433	−	0.532567i	−0.884411	+	0.466710i	$0.845439\pi$
$390$	−1.48237	+	0.710815i	−0.0750626	+	0.0359935i
$391$	1.57579	−	0.909783i	0.0796912	−	0.0460097i
$392$	−15.2257	+	30.6832i	−0.769014	+	1.54974i
$393$	−14.3127	+	20.0032i	−0.721979	+	1.00903i
$394$	8.54655	−	5.17655i	0.430569	−	0.260791i
$395$	−2.66503	−	4.61597i	−0.134092	−	0.232255i
$396$	−17.5742	+	21.8866i	−0.883139	+	1.09984i
$397$	6.33409			0.317899			0.158949	−	0.987287i	$-0.449189\pi$
$397$	6.33409			0.317899			0.158949	+	0.987287i	$0.449189\pi$
$398$	34.5405	+	18.9866i	1.73136	+	0.951714i
$399$	−9.69011	+	13.5428i	−0.485112	+	0.677986i
$400$	19.3618	−	1.62966i	0.968089	−	0.0814828i
$401$		−	11.4240i		−	0.570486i	−0.958455	−	0.285243i	$-0.907926\pi$
$401$		−	11.4240i		−	0.570486i	0.958455	−	0.285243i	$-0.0920744\pi$
$402$	−6.62248	−	18.9247i	−0.330299	−	0.943876i
$403$		−	13.5669i		−	0.675817i
$404$	9.60138	−	6.09454i	0.477687	−	0.303215i
$405$	2.07540	+	2.68892i	0.103127	+	0.133613i
$406$	−10.8285	+	19.6993i	−0.537411	+	0.977659i
$407$	−20.5582			−1.01903
$408$	27.0320	−	14.3876i	1.33828	−	0.712294i
$409$	−2.94730	−	5.10487i	−0.145735	−	0.252420i	0.783912	−	0.620872i	$-0.213221\pi$
$409$	−2.94730	−	5.10487i	−0.145735	−	0.252420i	−0.929647	+	0.368452i	$0.879888\pi$
$410$	−2.47693	−	4.08945i	−0.122327	−	0.201964i
$411$	−14.1830	−	10.1482i	−0.699597	−	0.500575i
$412$	9.64157	−	6.12004i	0.475006	−	0.301513i
$413$	−37.8969	+	21.8798i	−1.86478	+	1.07663i
$414$	1.21638	+	0.213738i	0.0597816	+	0.0105046i
$415$	−2.88649	−	1.66652i	−0.141692	−	0.0818062i
$416$	−4.08937	+	9.19091i	−0.200498	+	0.450622i
$417$	13.9402	+	9.97445i	0.682653	+	0.488451i
$418$	−0.305431	−	14.5473i	−0.0149391	−	0.711530i
$419$	3.68835	−	6.38841i	0.180188	−	0.312094i	−0.761757	−	0.647863i	$-0.775663\pi$
$419$	3.68835	−	6.38841i	0.180188	−	0.312094i	0.941944	+	0.335769i	$0.108996\pi$
$420$	−5.70651	−	0.316932i	−0.278449	−	0.0154647i
$421$	−4.24409	+	7.35099i	−0.206844	+	0.358265i	−0.950719	−	0.310054i	$-0.899653\pi$
$421$	−4.24409	+	7.35099i	−0.206844	+	0.358265i	0.743874	+	0.668319i	$0.232986\pi$
$422$	−18.9470	−	10.4150i	−0.922325	−	0.506994i
$423$	−8.56375	+	9.79301i	−0.416384	+	0.476152i
$424$	0.174068	+	2.76030i	0.00845351	+	0.134052i
$425$	26.2956	+	15.1817i	1.27552	+	0.736423i
$426$	37.1570	+	2.84711i	1.80026	+	0.137943i
$427$			15.0247i			0.727096i
$428$	−8.47782	+	0.356154i	−0.409791	+	0.0172153i
$429$	8.38485	−	11.7186i	0.404824	−	0.565777i
$430$	−6.94143	+	0.145741i	−0.334745	+	0.00702824i
$431$	13.0848	+	22.6635i	0.630272	+	1.09166i	0.987496	+	0.157645i	$0.0503900\pi$
$431$	13.0848	+	22.6635i	0.630272	+	1.09166i	−0.357224	+	0.934019i	$0.616277\pi$
$432$	20.3348	+	4.30084i	0.978357	+	0.206924i
$433$	−9.36091	−	16.2136i	−0.449857	−	0.779175i	0.548520	−	0.836138i	$-0.315192\pi$
$433$	−9.36091	−	16.2136i	−0.449857	−	0.779175i	−0.998376	+	0.0569631i	$0.981858\pi$
$434$	22.7202	−	41.3326i	1.09060	−	1.98403i
$435$	−2.36561	−	0.231302i	−0.113422	−	0.0110901i
$436$	−11.8760	+	0.498912i	−0.568758	+	0.0238936i
$437$	−0.554433	+	0.320102i	−0.0265221	+	0.0153126i
$438$	8.15930	+	17.0158i	0.389866	+	0.813046i
$439$	−16.5077	−	9.53071i	−0.787868	−	0.454876i	0.0513434	−	0.998681i	$-0.483650\pi$
$439$	−16.5077	−	9.53071i	−0.787868	−	0.454876i	−0.839211	+	0.543805i	$0.816983\pi$
$440$	4.15910	−	2.76418i	0.198277	−	0.131777i
$441$	−35.6429	−	7.03739i	−1.69728	−	0.335114i
$442$	−13.4460	+	8.14408i	−0.639561	+	0.387375i
$443$	−3.11762	−	5.39987i	−0.148122	−	0.256555i	0.782411	−	0.622762i	$-0.213990\pi$
$443$	−3.11762	−	5.39987i	−0.148122	−	0.256555i	−0.930534	+	0.366207i	$0.880656\pi$
$444$	6.86869	+	13.5852i	0.325974	+	0.644727i
$445$	0.224216			0.0106289
$446$	−0.683418	−	32.5503i	−0.0323608	−	1.54130i
$447$	20.5079	+	14.6738i	0.969989	+	0.694046i
$448$	−27.8503	+	21.1524i	−1.31580	+	0.999355i
$449$	−13.4911	+	7.78908i	−0.636683	+	0.367589i	−0.783336	−	0.621599i	$-0.786483\pi$
$449$	−13.4911	+	7.78908i	−0.636683	+	0.367589i	0.146652	+	0.989188i	$0.453150\pi$
$450$	7.06011	+	19.3618i	0.332817	+	0.912726i
$451$	36.2916	+	20.9530i	1.70890	+	0.986636i
$452$	29.8931	−	18.9748i	1.40605	−	0.892499i
$453$	28.6278	−	12.9955i	1.34505	−	0.610583i
$454$	−4.07566	−	6.72898i	−0.191280	−	0.315807i
$455$	2.93397			0.137546
$456$	−9.51103	+	5.06220i	−0.445395	+	0.237059i
$457$	10.1442	+	17.5702i	0.474525	+	0.821901i	0.999574	−	0.0291705i	$-0.00928658\pi$
$457$	10.1442	+	17.5702i	0.474525	+	0.821901i	−0.525050	+	0.851072i	$0.675953\pi$
$458$	1.34027	−	2.43822i	0.0626266	−	0.113930i
$459$	22.2533	+	23.6588i	1.03870	+	1.10430i
$460$	−0.194731	−	0.101779i	−0.00907937	−	0.00474546i
$461$		−	2.39539i		−	0.111565i	−0.998443	−	0.0557823i	$-0.982235\pi$
$461$		−	2.39539i		−	0.111565i	0.998443	−	0.0557823i	$-0.0177653\pi$
$462$	45.1697	−	21.6595i	2.10149	−	1.00769i
$463$	17.2081	+	9.93512i	0.799730	+	0.461724i	0.843377	−	0.537323i	$-0.180564\pi$
$463$	17.2081	+	9.93512i	0.799730	+	0.461724i	−0.0436470	+	0.999047i	$0.513898\pi$
$464$	−11.9414	+	8.30297i	−0.554367	+	0.385456i
$465$	4.96346	+	0.485312i	0.230175	+	0.0225058i
$466$	−14.2980	+	8.66012i	−0.662341	+	0.401172i
$467$	3.63428	−	6.29476i	0.168174	−	0.291287i	−0.769604	−	0.638522i	$-0.779546\pi$
$467$	3.63428	−	6.29476i	0.168174	−	0.291287i	0.937778	+	0.347235i	$0.112879\pi$
$468$	−10.5453	−	1.62558i	−0.487456	−	0.0751426i
$469$	−3.94607	+	35.5643i	−0.182212	+	1.64221i
$470$	1.97970	−	1.19908i	0.0913167	−	0.0553094i
$471$	12.9920	+	28.6201i	0.598641	+	1.31875i
$472$	−28.2567	+	1.78191i	−1.30062	+	0.0820191i
$473$	52.7016	−	30.4273i	2.42322	−	1.39905i
$474$	2.64293	−	34.4923i	0.121394	−	1.58428i
$475$	−9.25194	−	5.34161i	−0.424508	−	0.245090i
$476$	−54.6028	+	2.29387i	−2.50271	+	0.105139i
$477$	−2.77653	+	0.946890i	−0.127129	+	0.0433551i
$478$	0.605392	+	0.999512i	0.0276900	+	0.0457166i
$479$	6.43715	−	11.1495i	0.294121	−	0.509432i	−0.680659	−	0.732600i	$-0.738306\pi$
$479$	6.43715	−	11.1495i	0.294121	−	0.509432i	0.974780	+	0.223168i	$0.0716398\pi$
$480$	−3.21621	−	1.82487i	−0.146799	−	0.0832936i
$481$	−3.90737	−	6.76776i	−0.178161	−	0.308583i
$482$	−19.9086	+	0.417997i	−0.906813	+	0.0190393i
$483$	−1.79250	−	1.28257i	−0.0815614	−	0.0583587i
$484$	−10.0845	+	19.2945i	−0.458388	+	0.877023i
$485$	−0.177607	−	0.102542i	−0.00806474	−	0.00465618i
$486$	1.26155	+	22.0093i	0.0572249	+	0.998361i
$487$	−5.36147	−	3.09545i	−0.242952	−	0.140268i	0.373581	−	0.927598i	$-0.378130\pi$
$487$	−5.36147	−	3.09545i	−0.242952	−	0.140268i	−0.616533	+	0.787329i	$0.711463\pi$
$488$	−4.32108	+	8.70796i	−0.195606	+	0.394191i
$489$	0.352599	−	3.60616i	0.0159451	−	0.163076i
$490$	5.66440	+	3.11367i	0.255891	+	0.140661i
$491$	34.0842			1.53820			0.769099	−	0.639130i	$-0.220705\pi$
$491$	34.0842			1.53820			0.769099	+	0.639130i	$0.220705\pi$
$492$	1.72074	−	30.9827i	0.0775768	−	1.39681i
$493$	−22.7283			−1.02363
$494$	4.73090	−	2.86545i	0.212853	−	0.128923i
$495$	3.98729	+	3.48679i	0.179215	+	0.156719i
$496$	25.0552	−	17.4211i	1.12501	−	0.782230i
$497$	−57.5972	−	33.2537i	−2.58359	−	1.49163i
$498$	−9.35322	−	19.5057i	−0.419128	−	0.874069i
$499$	−10.5769	−	6.10659i	−0.473488	−	0.273368i	0.244211	−	0.969722i	$-0.421471\pi$
$499$	−10.5769	−	6.10659i	−0.473488	−	0.273368i	−0.717699	+	0.696354i	$0.754804\pi$
$500$	−0.312309	−	7.43415i	−0.0139669	−	0.332465i
$501$	8.19254	+	0.801041i	0.366016	+	0.0357879i
$502$	−6.06654	+	11.0363i	−0.270763	+	0.492573i
$503$	15.2200	+	26.3618i	0.678626	+	1.17541i	0.975395	+	0.220465i	$0.0707576\pi$
$503$	15.2200	+	26.3618i	0.678626	+	1.17541i	−0.296769	+	0.954949i	$0.595909\pi$
$504$	−29.4046	−	22.6123i	−1.30978	−	1.00723i
$505$	−1.07301	−	1.85851i	−0.0477484	−	0.0827026i
$506$	1.92545	−	0.0404263i	0.0855967	−	0.00179717i
$507$	−16.9584	−	1.65814i	−0.753149	−	0.0736406i
$508$	14.7620	−	9.37024i	0.654956	−	0.415737i
$509$			0.550458i			0.0243986i	0.999926	+	0.0121993i	$0.00388326\pi$
$509$			0.550458i			0.0243986i	−0.999926	+	0.0121993i	$0.996117\pi$
$510$	−2.49852	−	5.21054i	−0.110637	−	0.230727i
$511$		−	33.6784i		−	1.48984i
$512$	−22.2248	+	4.24971i	−0.982205	+	0.187812i
$513$	−7.82970	−	8.32419i	−0.345690	−	0.367522i
$514$	5.27755	−	3.19655i	0.232783	−	0.140994i
$515$	−1.07750	−	1.86629i	−0.0474804	−	0.0822384i
$516$	−37.7150	−	24.6601i	−1.66031	−	1.08560i
$517$	−10.1433	+	17.5687i	−0.446102	+	0.772671i
$518$	−0.570287	−	27.1620i	−0.0250570	−	1.19343i
$519$	−7.75000	+	3.51809i	−0.340187	+	0.154427i
$520$	1.70046	+	0.843805i	0.0745700	+	0.0370033i
$521$			10.8978i			0.477442i	0.971088	+	0.238721i	$0.0767282\pi$
$521$			10.8978i			0.477442i	−0.971088	+	0.238721i	$0.923272\pi$
$522$	−11.8233	−	9.90902i	−0.517492	−	0.433706i
$523$	12.4713	+	7.20030i	0.545331	+	0.314847i	0.747237	−	0.664558i	$-0.231380\pi$
$523$	12.4713	+	7.20030i	0.545331	+	0.314847i	−0.201905	+	0.979405i	$0.564713\pi$
$524$	28.3764	−	1.19209i	1.23963	−	0.0520769i
$525$	3.57918	−	36.6056i	0.156208	−	1.59760i
$526$	−39.1219	+	0.821394i	−1.70579	+	0.0358145i
$527$	47.6880			2.07732
$528$	32.4085	+	0.437420i	1.41040	+	0.0190363i
$529$	11.4576	+	19.8452i	0.498158	+	0.862835i
$530$	0.521803	−	0.0109557i	0.0226657	−	0.000475883i
$531$	−9.69316	−	28.4229i	−0.420647	−	1.23345i
$532$	19.2117	−	0.807084i	0.832931	−	0.0349915i
$533$			15.9295i			0.689985i
$534$	1.20098	+	0.821766i	0.0519717	+	0.0355613i
$535$			1.60122i			0.0692269i
$536$	−12.5153	+	19.4774i	−0.540578	+	0.841294i
$537$	2.77749	−	3.88179i	0.119858	−	0.167511i
$538$	−0.507642	−	24.1783i	−0.0218860	−	1.04240i
$539$	−56.6545			−2.44028
$540$	0.971940	−	3.79984i	0.0418257	−	0.163519i
$541$	−0.144786			−0.00622484			−0.00311242	−	0.999995i	$-0.500991\pi$
$541$	−0.144786			−0.00622484			−0.00311242	+	0.999995i	$0.500991\pi$
$542$	0.368555	+	17.5538i	0.0158308	+	0.753999i
$543$	17.0331	+	1.66544i	0.730960	+	0.0714709i
$544$	−32.3062	−	14.3742i	−1.38512	−	0.616289i
$545$			2.24304i			0.0960815i
$546$	15.7154	+	10.7532i	0.672557	+	0.460193i
$547$	−32.5699	+	18.8043i	−1.39259	+	0.804012i	−0.993601	−	0.112944i	$-0.963972\pi$
$547$	−32.5699	+	18.8043i	−1.39259	+	0.804012i	−0.398989	+	0.916956i	$0.630639\pi$
$548$	0.845240	+	20.1199i	0.0361069	+	0.859481i
$549$	−10.1155	−	1.99722i	−0.431720	−	0.0852395i
$550$	16.6494	+	27.4884i	0.709933	+	1.17211i
$551$	7.99682			0.340676
$552$	−0.670024	−	1.25886i	−0.0285181	−	0.0535808i
$553$	−30.8690	+	53.4666i	−1.31268	+	2.27363i
$554$	15.4392	−	0.324157i	0.655947	−	0.0137721i
$555$	2.61576	−	1.18742i	0.111033	−	0.0504030i
$556$	−0.830767	−	19.7754i	−0.0352324	−	0.838664i
$557$	−2.38326	+	1.37598i	−0.100982	+	0.0583020i	−0.549640	−	0.835401i	$-0.685235\pi$
$557$	−2.38326	+	1.37598i	−0.100982	+	0.0583020i	0.448658	+	0.893703i	$0.351902\pi$
$558$	24.8074	+	20.7909i	1.05018	+	0.880148i
$559$	20.0333	+	11.5662i	0.847317	+	0.489199i
$560$	3.76746	+	5.41841i	0.159204	+	0.228970i
$561$	41.1909	+	29.4729i	1.73908	+	1.24435i
$562$	−19.5401	−	10.7410i	−0.824249	−	0.453082i
$563$	−8.27039			−0.348555			−0.174278	−	0.984697i	$-0.555759\pi$
$563$	−8.27039			−0.348555			−0.174278	+	0.984697i	$0.555759\pi$
$564$	14.9987	+	0.833006i	0.631558	+	0.0350759i
$565$	−3.34072	−	5.78630i	−0.140545	−	0.243432i
$566$	−0.192007	−	9.14504i	−0.00807067	−	0.384395i
$567$	14.9533	−	36.3914i	0.627979	−	1.52830i
$568$	−23.8182	−	35.8379i	−0.999391	−	1.50373i
$569$	−23.6725	+	13.6673i	−0.992403	+	0.572964i	−0.905992	−	0.423296i	$-0.860873\pi$
$569$	−23.6725	+	13.6673i	−0.992403	+	0.572964i	−0.0864112	+	0.996260i	$0.527540\pi$
$570$	0.879091	+	1.83330i	0.0368211	+	0.0767884i
$571$	5.10167	−	2.94545i	0.213498	−	0.123263i	−0.389438	−	0.921053i	$-0.627331\pi$
$571$	5.10167	−	2.94545i	0.213498	−	0.123263i	0.602936	+	0.797790i	$0.293997\pi$
$572$	−16.6239	+	0.698370i	−0.695078	+	0.0292003i
$573$	0.325149	+	0.716270i	0.0135833	+	0.0299226i
$574$	−26.6767	+	48.5304i	−1.11347	+	2.02562i
$575$	0.707006	−	1.22457i	0.0294842	−	0.0510681i
$576$	−10.5389	−	21.5623i	−0.439122	−	0.898428i
$577$	−0.644739	−	1.11672i	−0.0268408	−	0.0464897i	0.852293	−	0.523065i	$-0.175211\pi$
$577$	−0.644739	−	1.11672i	−0.0268408	−	0.0464897i	−0.879134	+	0.476575i	$0.841878\pi$
$578$	−16.1713	−	26.6991i	−0.672639	−	1.11054i
$579$	−2.17108	+	3.03427i	−0.0902269	+	0.126100i
$580$	1.47085	+	2.31719i	0.0610738	+	0.0962162i
$581$			38.6064i			1.60167i
$582$	−0.575508	−	1.20019i	−0.0238556	−	0.0497496i
$583$	−3.96170	+	2.28729i	−0.164077	+	0.0947297i
$584$	9.68585	−	19.5192i	0.400803	−	0.807710i
$585$	−0.390010	+	1.97532i	−0.0161249	+	0.0816695i
$586$	0.660970	+	31.4811i	0.0273044	+	1.30047i
$587$	−1.86014	+	3.22185i	−0.0767760	+	0.132980i	−0.901857	−	0.432034i	$-0.857796\pi$
$587$	−1.86014	+	3.22185i	−0.0767760	+	0.132980i	0.825081	+	0.565014i	$0.191129\pi$
$588$	18.9288	+	37.4383i	0.780610	+	1.54393i
$589$	−16.7787			−0.691356
$590$	0.112151	+	5.34161i	0.00461720	+	0.219911i
$591$	1.19088	−	12.1796i	0.0489863	−	0.501001i
$592$	7.48122	−	15.9064i	0.307476	−	0.653751i
$593$	5.51768	+	3.18563i	0.226584	+	0.130818i	0.608995	−	0.793174i	$-0.291573\pi$
$593$	5.51768	+	3.18563i	0.226584	+	0.130818i	−0.382411	+	0.923992i	$0.624906\pi$
$594$	8.57808	+	33.2901i	0.351963	+	1.36591i
$595$			10.3129i			0.422789i
$596$	−1.22217	−	29.0923i	−0.0500621	−	1.19167i
$597$	43.9563	−	19.9538i	1.79901	−	0.816657i
$598$	0.379266	+	0.626173i	0.0155093	+	0.0256061i
$599$	−16.1302	−	27.9384i	−0.659063	−	1.14153i	−0.980858	−	0.194722i	$-0.937620\pi$
$599$	−16.1302	−	27.9384i	−0.659063	−	1.14153i	0.321795	−	0.946809i	$-0.395714\pi$
$600$	12.6021	−	20.1863i	0.514479	−	0.824104i
$601$	−6.38802	+	11.0644i	−0.260573	+	0.451325i	−0.966394	−	0.257064i	$-0.917245\pi$
$601$	−6.38802	+	11.0644i	−0.260573	+	0.451325i	0.705821	+	0.708390i	$0.250578\pi$
$602$	41.6631	+	68.7864i	1.69806	+	2.80352i
$603$	−23.4195	−	7.38427i	−0.953715	−	0.300711i
$604$	−32.1736	−	16.8159i	−1.30912	−	0.684231i
$605$	3.55790	+	2.05415i	0.144649	+	0.0835132i
$606$	1.06411	−	13.8875i	0.0432266	−	0.564141i
$607$	−36.3071	+	20.9619i	−1.47366	+	0.850817i	−0.999560	−	0.0296556i	$-0.990559\pi$
$607$	−36.3071	+	20.9619i	−1.47366	+	0.850817i	−0.474098	+	0.880472i	$0.657226\pi$
$608$	11.3667	+	5.05748i	0.460982	+	0.205108i
$609$	11.3801	+	25.0693i	0.461147	+	1.01586i
$610$	1.60757	+	0.883665i	0.0650885	+	0.0357786i
$611$	−7.71148			−0.311973
$612$	5.71394	−	37.0668i	0.230972	−	1.49834i
$613$	8.28780	−	14.3549i	0.334741	−	0.579789i	−0.648694	−	0.761049i	$-0.724684\pi$
$613$	8.28780	−	14.3549i	0.334741	−	0.579789i	0.983435	+	0.181261i	$0.0580177\pi$
$614$	28.0171	+	15.4008i	1.13068	+	0.621525i
$615$	−5.82782	−	0.569826i	−0.235000	−	0.0229776i
$616$	−51.8152	−	25.7118i	−2.08769	−	1.03596i
$617$			35.8992i			1.44525i	0.691242	+	0.722623i	$0.257064\pi$
$617$			35.8992i			1.44525i	−0.691242	+	0.722623i	$0.742936\pi$
$618$	1.06857	−	13.9456i	0.0429840	−	0.560975i
$619$	23.6602	+	13.6602i	0.950984	+	0.549051i	0.893386	−	0.449289i	$-0.148323\pi$
$619$	23.6602	+	13.6602i	0.950984	+	0.549051i	0.0575973	+	0.998340i	$0.481656\pi$
$620$	−3.08611	−	4.86188i	−0.123941	−	0.195258i
$621$	1.10178	−	1.03633i	0.0442127	−	0.0415863i
$622$	22.2531	−	0.467221i	0.892268	−	0.0187339i
$623$	−1.29854	−	2.24915i	−0.0520251	−	0.0901101i
$624$	6.01567	+	10.7520i	0.240820	+	0.430424i
$625$	22.8837			0.915348
$626$	−30.2420	+	0.634954i	−1.20871	+	0.0253778i
$627$	−14.4928	−	10.3699i	−0.578785	−	0.414132i
$628$	16.8114	−	32.1649i	0.670849	−	1.28352i
$629$	23.7888	−	13.7344i	0.948520	−	0.547628i
$630$	−4.49621	+	5.36481i	−0.179133	+	0.213739i
$631$	−1.05892	−	0.611367i	−0.0421549	−	0.0243381i	0.478774	−	0.877938i	$-0.341081\pi$
$631$	−1.05892	−	0.611367i	−0.0421549	−	0.0243381i	−0.520929	+	0.853600i	$0.674414\pi$
$632$	−33.2678	+	22.1101i	−1.32332	+	0.879493i
$633$	−24.1119	+	10.9456i	−0.958363	+	0.435047i
$634$	21.0790	+	11.5869i	0.837153	+	0.460176i
$635$	−1.64973	−	2.85742i	−0.0654677	−	0.113393i
$636$	2.83512	+	1.85376i	0.112420	+	0.0735062i
$637$	−10.7679	−	18.6506i	−0.426641	−	0.738965i
$638$	−21.0812	−	11.5881i	−0.834611	−	0.458778i
$639$	30.0448	−	34.3575i	1.18855	−	1.35916i
$640$	0.625204	+	4.22390i	0.0247134	+	0.166964i
$641$	38.8179	−	22.4115i	1.53322	−	0.885203i	0.534005	−	0.845481i	$-0.320686\pi$
$641$	38.8179	−	22.4115i	1.53322	−	0.885203i	0.999211	−	0.0397214i	$-0.0126470\pi$
$642$	−5.86857	+	8.57672i	−0.231614	+	0.338496i
$643$			18.0381i			0.711352i	0.934609	+	0.355676i	$0.115749\pi$
$643$			18.0381i			0.711352i	−0.934609	+	0.355676i	$0.884251\pi$
$644$	0.106824	+	2.54282i	0.00420946	+	0.100201i
$645$	−4.94812	+	6.91543i	−0.194832	+	0.272295i
$646$	10.0721	+	16.6292i	0.396281	+	0.654266i
$647$	−11.3005	+	19.5730i	−0.444267	+	0.769492i	−0.998001	−	0.0632011i	$-0.979869\pi$
$647$	−11.3005	+	19.5730i	−0.444267	+	0.769492i	0.553734	+	0.832694i	$0.313202\pi$
$648$	19.1327	−	16.7911i	0.751603	−	0.659616i
$649$	−23.4146	−	40.5553i	−0.919103	−	1.59193i
$650$	−5.88473	+	10.7055i	−0.230818	+	0.419905i
$651$	−23.8776	−	52.5998i	−0.935835	−	2.06155i
$652$	−3.53236	+	2.24219i	−0.138338	+	0.0878109i
$653$	0.736578	+	0.425264i	0.0288245	+	0.0166419i	0.514343	−	0.857585i	$-0.328036\pi$
$653$	0.736578	+	0.425264i	0.0288245	+	0.0166419i	−0.485518	+	0.874226i	$0.661369\pi$
$654$	−8.22089	+	12.0146i	−0.321462	+	0.469806i
$655$		−	5.35950i		−	0.209413i
$656$	−29.4185	+	20.4549i	−1.14860	+	0.798629i
$657$	22.6743	+	4.47685i	0.884609	+	0.174658i
$658$	−23.4935	−	12.9142i	−0.915873	−	0.503447i
$659$	4.62126	+	8.00426i	0.180019	+	0.311802i	0.941887	−	0.335931i	$-0.109051\pi$
$659$	4.62126	+	8.00426i	0.180019	+	0.311802i	−0.761868	+	0.647732i	$0.775717\pi$
$660$	0.339164	−	6.10681i	0.0132019	−	0.237707i
$661$	43.7657			1.70229			0.851144	−	0.524932i	$-0.175909\pi$
$661$	43.7657			1.70229			0.851144	+	0.524932i	$0.175909\pi$
$662$	−35.3143	+	21.3894i	−1.37253	+	0.831324i
$663$	−1.87357	+	19.1617i	−0.0727635	+	0.744179i
$664$	−11.1032	+	22.3754i	−0.430886	+	0.868333i
$665$		−	3.62854i		−	0.140709i
$666$	18.3629	+	3.22667i	0.711547	+	0.125031i
$667$			1.05844i			0.0409831i
$668$	−5.09384	−	8.02488i	−0.197087	−	0.310492i
$669$	−32.4283	−	23.2031i	−1.25375	−	0.897084i
$670$	3.57312	+	2.51390i	0.138042	+	0.0971202i
$671$	−16.0787			−0.620710
$672$	0.321086	+	42.8309i	0.0123862	+	1.65224i
$673$	21.2587			0.819462			0.409731	−	0.912206i	$-0.365622\pi$
$673$	21.2587			0.819462			0.409731	+	0.912206i	$0.365622\pi$
$674$	24.0087	−	43.6766i	0.924779	−	1.68236i
$675$	24.1693	+	7.27567i	0.930276	+	0.280041i
$676$	10.5441	+	16.6113i	0.405544	+	0.638898i
$677$	41.1960	−	23.7845i	1.58329	−	0.914115i	0.588918	−	0.808193i	$-0.299554\pi$
$677$	41.1960	−	23.7845i	1.58329	−	0.914115i	0.994374	−	0.105922i	$-0.0337794\pi$
$678$	3.31302	−	43.2375i	0.127236	−	1.66053i
$679$			2.37547i			0.0911623i
$680$	−2.96598	+	5.97713i	−0.113740	+	0.229213i
$681$	−9.58938	−	0.937620i	−0.367466	−	0.0359297i
$682$	44.2320	+	24.3139i	1.69373	+	0.931029i
$683$	−7.24397	+	12.5469i	−0.277183	+	0.480095i	−0.970684	−	0.240361i	$-0.922734\pi$
$683$	−7.24397	+	12.5469i	−0.277183	+	0.480095i	0.693501	+	0.720456i	$0.256067\pi$
$684$	−2.01042	+	13.0417i	−0.0768702	+	0.498663i
$685$	3.80009			0.145194
$686$	−0.663186	−	31.5866i	−0.0253206	−	1.20598i
$687$	−1.40854	−	3.10288i	−0.0537393	−	0.118382i
$688$	4.36408	+	51.8492i	0.166379	+	1.97673i
$689$	−1.50595	−	0.869459i	−0.0573720	−	0.0331237i
$690$	−0.242652	+	0.116355i	−0.00923761	+	0.00442956i
$691$	21.0968	−	12.1803i	0.802562	−	0.463359i	−0.0418045	−	0.999126i	$-0.513311\pi$
$691$	21.0968	−	12.1803i	0.802562	−	0.463359i	0.844366	+	0.535767i	$0.179977\pi$
$692$	8.70989	+	4.55234i	0.331100	+	0.173054i
$693$	11.8841	−	60.1907i	0.451441	−	2.28646i
$694$	7.56236	+	12.4856i	0.287063	+	0.473945i
$695$	−3.73502			−0.141677
$696$	−0.614233	+	17.8025i	−0.0232824	+	0.674802i
$697$	−55.9926			−2.12087
$698$	−10.0471	+	0.210946i	−0.380287	+	0.00798442i
$699$	−1.99229	+	20.3759i	−0.0753552	+	0.770686i
$700$	−35.8564	+	22.7601i	−1.35524	+	0.860250i
$701$	26.1439	−	15.0942i	0.987443	−	0.570100i	0.0829339	−	0.996555i	$-0.473571\pi$
$701$	26.1439	−	15.0942i	0.987443	−	0.570100i	0.904509	+	0.426455i	$0.140238\pi$
$702$	−9.32871	+	9.15113i	−0.352089	+	0.345387i
$703$	−8.36994	+	4.83239i	−0.315678	+	0.182257i
$704$	−22.6362	−	29.8040i	−0.853133	−	1.12328i
$705$	0.275852	−	2.82124i	0.0103892	−	0.106254i
$706$	16.7616	+	9.21373i	0.630833	+	0.346763i
$707$	−12.4286	+	21.5270i	−0.467427	+	0.809608i
$708$	−18.9766	+	29.0226i	−0.713184	+	1.09074i
$709$	8.98746	−	15.5667i	0.337531	−	0.584621i	−0.646436	−	0.762968i	$-0.723741\pi$
$709$	8.98746	−	15.5667i	0.337531	−	0.584621i	0.983968	+	0.178347i	$0.0570748\pi$
$710$	−6.94551	+	4.20681i	−0.260660	+	0.157879i
$711$	−31.8935	−	27.8901i	−1.19610	−	1.04596i
$712$	−0.105755	−	1.67701i	−0.00396333	−	0.0628487i
$713$		−	2.22080i		−	0.0831697i
$714$	−37.7975	+	55.2398i	−1.41454	+	2.06730i
$715$			3.13978i			0.117421i
$716$	−5.50668	+	0.231336i	−0.205794	+	0.00864543i
$717$	1.42439	+	0.139272i	0.0531948	+	0.00520123i
$718$	−21.8718	+	0.459215i	−0.816247	+	0.0171377i
$719$	6.36715	−	11.0282i	0.237455	−	0.411284i	−0.722529	−	0.691341i	$-0.757020\pi$
$719$	6.36715	−	11.0282i	0.237455	−	0.411284i	0.959983	+	0.280057i	$0.0903535\pi$
$720$	−4.14881	+	1.81622i	−0.154617	+	0.0676863i
$721$	−12.4807	+	21.6171i	−0.464804	+	0.805064i
$722$	10.3767	+	17.1321i	0.386182	+	0.637592i
$723$	−14.1916	+	19.8341i	−0.527793	+	0.737636i
$724$	−10.5906	−	16.6845i	−0.393596	−	0.620074i
$725$	−15.2962	+	8.83124i	−0.568085	+	0.327984i
$726$	11.5288	+	24.0427i	0.427874	+	0.892308i
$727$	−15.2859	−	8.82534i	−0.566924	−	0.327314i	0.188996	−	0.981978i	$-0.439477\pi$
$727$	−15.2859	−	8.82534i	−0.566924	−	0.327314i	−0.755920	+	0.654664i	$0.772810\pi$
$728$	−1.38385	−	21.9444i	−0.0512888	−	0.813314i
$729$	22.5132	+	14.9049i	0.833821	+	0.552035i
$730$	−3.60342	−	1.98077i	−0.133368	−	0.0733114i
$731$	−40.6554	+	70.4172i	−1.50369	+	2.60448i
$732$	5.37202	+	10.6251i	0.198556	+	0.392714i
$733$	12.7204	+	22.0324i	0.469839	+	0.813786i	0.999405	−	0.0344830i	$-0.0109785\pi$
$733$	12.7204	+	22.0324i	0.469839	+	0.813786i	−0.529566	+	0.848269i	$0.677645\pi$
$734$	28.7652	−	17.4227i	1.06174	−	0.643084i
$735$	7.20851	−	3.27229i	0.265890	−	0.120700i
$736$	−0.669399	+	1.50448i	−0.0246744	+	0.0554559i
$737$	−38.0591	−	4.22288i	−1.40193	−	0.155552i
$738$	−29.1275	−	24.4115i	−1.07220	−	0.898600i
$739$	−13.6545	−	7.88342i	−0.502288	−	0.289996i	0.227370	−	0.973808i	$-0.426987\pi$
$739$	−13.6545	−	7.88342i	−0.502288	−	0.289996i	−0.729658	+	0.683812i	$0.760321\pi$
$740$	−2.93973	−	1.53649i	−0.108067	−	0.0564825i
$741$	0.659205	−	6.74194i	0.0242165	−	0.247671i
$742$	−3.13191	−	5.17083i	−0.114976	−	0.189827i
$743$	20.0041	−	34.6482i	0.733880	−	1.27112i	−0.221333	−	0.975198i	$-0.571041\pi$
$743$	20.0041	−	34.6482i	0.733880	−	1.27112i	0.955213	−	0.295919i	$-0.0956260\pi$
$744$	1.28877	−	37.3528i	0.0472486	−	1.36942i
$745$	−5.49472			−0.201311
$746$	−0.419891	−	0.693246i	−0.0153733	−	0.0253815i
$747$	−25.9922	−	5.13193i	−0.951004	−	0.187767i
$748$	−2.45478	−	58.4331i	−0.0897556	−	2.13652i
$749$	16.0621	−	9.27345i	0.586896	−	0.338844i
$750$	−7.52088	−	5.14612i	−0.274624	−	0.187910i
$751$			14.3262i			0.522770i	0.965235	+	0.261385i	$0.0841792\pi$
$751$			14.3262i			0.522770i	−0.965235	+	0.261385i	$0.915821\pi$
$752$	−9.90219	−	14.2415i	−0.361096	−	0.519332i
$753$	6.37558	+	14.0448i	0.232339	+	0.511819i
$754$	−0.191951	−	9.14238i	−0.00699046	−	0.332946i
$755$	−3.42530	+	5.93279i	−0.124659	+	0.215916i
$756$	−43.7457	+	12.2570i	−1.59101	+	0.445783i
$757$	−10.8821	−	18.8483i	−0.395515	−	0.685053i	0.597651	−	0.801756i	$-0.296101\pi$
$757$	−10.8821	−	18.8483i	−0.395515	−	0.685053i	−0.993167	+	0.116703i	$0.962767\pi$
$758$	−17.6020	−	9.67568i	−0.639335	−	0.351437i
$759$	1.37254	−	1.91824i	0.0498199	−	0.0696276i
$760$	1.04356	−	2.10302i	0.0378541	−	0.0762845i
$761$			3.60463i			0.130668i	0.997863	+	0.0653340i	$0.0208113\pi$
$761$			3.60463i			0.130668i	−0.997863	+	0.0653340i	$0.979189\pi$
$762$	1.63605	−	21.3518i	0.0592680	−	0.773493i
$763$	22.5003	−	12.9905i	0.814565	−	0.470289i
$764$	0.420736	−	0.804985i	0.0152217	−	0.0291233i
$765$	−6.94329	−	1.37089i	−0.251035	−	0.0495647i
$766$	15.6868	−	28.5375i	0.566788	−	1.03110i
$767$	8.90051	−	15.4161i	0.321379	−	0.556644i
$768$	−12.1320	+	24.9161i	−0.437777	+	0.899084i
$769$	−13.3864	−	23.1859i	−0.482724	−	0.836103i	0.517079	−	0.855938i	$-0.327019\pi$
$769$	−13.3864	−	23.1859i	−0.482724	−	0.836103i	−0.999803	+	0.0198345i	$0.993686\pi$
$770$	−5.25810	+	9.56555i	−0.189489	+	0.344718i
$771$	0.735377	−	7.52097i	0.0264839	−	0.270861i
$772$	4.30439	−	0.180828i	0.154918	−	0.00650813i
$773$	−38.1348	+	22.0171i	−1.37161	+	0.791901i	−0.991131	−	0.132888i	$-0.957575\pi$
$773$	−38.1348	+	22.0171i	−1.37161	+	0.791901i	−0.380481	+	0.924789i	$0.624242\pi$
$774$	−51.8494	+	18.9064i	−1.86369	+	0.679575i
$775$	32.0940	−	18.5295i	1.15285	−	0.665599i
$776$	−0.683183	+	1.37677i	−0.0245248	+	0.0494231i
$777$	−27.0602	−	19.3621i	−0.970780	−	0.694612i
$778$	26.0353	+	14.3114i	0.933409	+	0.513087i
$779$	19.7007			0.705849
$780$	2.07482	−	1.04903i	0.0742905	−	0.0375612i
$781$	35.5864	−	61.6375i	1.27338	−	2.20556i
$782$	−2.20101	+	1.33312i	−0.0787078	+	0.0476724i
$783$	−18.3909	+	4.32935i	−0.657238	+	0.154718i
$784$	20.6168	−	43.8351i	0.736314	−	1.56554i
$785$	−5.93119	−	3.42438i	−0.211693	−	0.122221i
$786$	19.6429	−	28.7074i	0.700639	−	1.02396i
$787$	−34.9969	−	20.2055i	−1.24751	−	0.720248i	−0.276894	−	0.960900i	$-0.589305\pi$
$787$	−34.9969	−	20.2055i	−1.24751	−	0.720248i	−0.970611	+	0.240653i	$0.922639\pi$
$788$	−11.9303	+	7.57284i	−0.425000	+	0.269771i
$789$	−27.8876	+	38.9753i	−0.992824	+	1.38756i
$790$	3.90512	+	6.44742i	0.138938	+	0.229389i
$791$	−38.6955	+	67.0225i	−1.37585	+	2.38305i
$792$	24.1985	−	31.4672i	0.859857	−	1.11814i
$793$	−3.05596	−	5.29308i	−0.108520	−	0.187963i
$794$	−8.95578	+	0.188034i	−0.317829	+	0.00667306i
$795$	0.371961	−	0.519848i	0.0131921	−	0.0184371i
$796$	−49.4006	−	25.8199i	−1.75096	−	0.915161i
$797$	−23.8596	+	13.7754i	−0.845152	+	0.487949i	−0.859012	−	0.511955i	$-0.828921\pi$
$797$	−23.8596	+	13.7754i	−0.845152	+	0.487949i	0.0138604	+	0.999904i	$0.495588\pi$
$798$	13.2988	−	19.4358i	0.470774	−	0.688020i
$799$		−	27.1059i		−	0.958939i
$800$	−27.3273	+	2.87895i	−0.966165	+	0.101786i
$801$	1.68687	−	0.575281i	0.0596028	−	0.0203266i
$802$	0.339132	+	16.1524i	0.0119752	+	0.570361i
$803$	36.0409			1.27185
$804$	9.92534	+	26.5610i	0.350040	+	0.936735i
$805$	0.480268			0.0169272
$806$	0.402748	+	19.1823i	0.0141862	+	0.675669i
$807$	−24.0877	−	17.2352i	−0.847927	−	0.606708i
$808$	−13.3945	+	8.90210i	−0.471217	+	0.313175i
$809$		−	6.13267i		−	0.215613i	−0.994172	−	0.107807i	$-0.965617\pi$
$809$		−	6.13267i		−	0.215613i	0.994172	−	0.107807i	$-0.0343828\pi$
$810$	−3.01424	−	3.74026i	−0.105909	−	0.131419i
$811$	−5.42111	+	3.12988i	−0.190361	+	0.109905i	−0.592152	−	0.805827i	$-0.701721\pi$
$811$	−5.42111	+	3.12988i	−0.190361	+	0.109905i	0.401791	+	0.915732i	$0.368388\pi$
$812$	14.7257	−	28.1743i	0.516770	−	0.988725i
$813$	17.4880	+	12.5130i	0.613332	+	0.438851i
$814$	29.0673	−	0.610292i	1.01881	−	0.0213907i
$815$	0.394762	+	0.683748i	0.0138279	+	0.0239507i
$816$	−37.7934	+	21.1452i	−1.32303	+	0.740229i
$817$	14.3044	−	24.7759i	0.500447	−	0.866799i
$818$	4.31874	+	7.13030i	0.151001	+	0.249305i
$819$	22.0735	−	7.52779i	0.771310	−	0.263042i
$820$	3.62354	+	5.70855i	0.126539	+	0.199351i
$821$	23.8916	+	13.7938i	0.833821	+	0.481407i	0.855159	−	0.518365i	$-0.173459\pi$
$821$	23.8916	+	13.7938i	0.833821	+	0.481407i	−0.0213380	+	0.999772i	$0.506793\pi$
$822$	20.3547	+	13.9276i	0.709950	+	0.485779i
$823$	−13.4281	−	7.75272i	−0.468074	−	0.270243i	0.247359	−	0.968924i	$-0.420437\pi$
$823$	−13.4281	−	7.75272i	−0.468074	−	0.270243i	−0.715433	+	0.698681i	$0.753771\pi$
$824$	−13.4505	+	8.93936i	−0.468572	+	0.311417i
$825$	39.1734	+	3.83025i	1.36384	+	0.133352i
$826$	52.9329	−	32.0608i	1.84177	−	1.11554i
$827$	−14.1168	+	24.4511i	−0.490890	+	0.850247i	−0.999945	−	0.0104870i	$-0.996662\pi$
$827$	−14.1168	+	24.4511i	−0.490890	+	0.850247i	0.509055	+	0.860734i	$0.329995\pi$
$828$	−1.72618	−	0.266095i	−0.0599889	−	0.00924745i
$829$	17.0599			0.592516			0.296258	−	0.955108i	$-0.404261\pi$
$829$	17.0599			0.592516			0.296258	+	0.955108i	$0.404261\pi$
$830$	4.13069	+	2.27061i	0.143378	+	0.0788139i
$831$	11.0056	−	15.3813i	0.381781	−	0.533572i
$832$	5.50913	−	13.1164i	0.190995	−	0.454731i
$833$	65.5572	−	37.8495i	2.27142	−	1.31141i
$834$	−20.0061	−	13.6891i	−0.692755	−	0.474014i
$835$	−1.55335	+	0.896827i	−0.0537559	+	0.0310360i
$836$	0.863699	+	20.5593i	0.0298717	+	0.711059i
$837$	38.5874	−	9.08374i	1.33378	−	0.313980i
$838$	−5.02532	+	9.14207i	−0.173597	+	0.315808i
$839$	−6.75324	−	11.6970i	−0.233148	−	0.403824i	0.725585	−	0.688132i	$-0.241569\pi$
$839$	−6.75324	−	11.6970i	−0.233148	−	0.403824i	−0.958733	+	0.284309i	$0.908236\pi$
$840$	8.07786	+	0.278707i	0.278712	+	0.00961631i
$841$	−7.88946	+	13.6649i	−0.272050	+	0.471205i
$842$	5.78251	−	10.5196i	0.199278	−	0.362528i
$843$	−24.8667	+	11.2882i	−0.856455	+	0.388786i
$844$	27.0984	+	14.1633i	0.932764	+	0.487521i
$845$	3.21540	−	1.85641i	0.110613	−	0.0638626i
$846$	11.8176	−	14.1006i	0.406297	−	0.484788i
$847$		−	47.5864i		−	1.63509i
$848$	−0.328058	−	3.89762i	−0.0112655	−	0.133845i
$849$	−9.11078	−	6.51894i	−0.312681	−	0.223729i
$850$	−37.6300	−	20.6849i	−1.29070	−	0.709486i
$851$	−0.639606	−	1.10783i	−0.0219254	−	0.0379759i
$852$	−52.6209	−	2.92249i	−1.80276	−	0.100123i
$853$	20.3659	−	35.2747i	0.697314	−	1.20778i	−0.272081	−	0.962274i	$-0.587712\pi$
$853$	20.3659	−	35.2747i	0.697314	−	1.20778i	0.969395	−	0.245508i	$-0.0789548\pi$
$854$	−0.446023	−	21.2435i	−0.0152626	−	0.726936i
$855$	2.44295	+	0.482340i	0.0835473	+	0.0164957i
$856$	11.9762	−	0.755239i	0.409339	−	0.0258135i
$857$			13.5669i			0.463435i	0.972783	+	0.231718i	$0.0744345\pi$
$857$			13.5669i			0.463435i	−0.972783	+	0.231718i	$0.925565\pi$
$858$	−11.5075	+	16.8178i	−0.392859	+	0.574150i
$859$	14.6340	−	8.44895i	0.499306	−	0.288274i	−0.229121	−	0.973398i	$-0.573585\pi$
$859$	14.6340	−	8.44895i	0.499306	−	0.288274i	0.728427	+	0.685124i	$0.240252\pi$
$860$	9.81017	−	0.412126i	0.334524	−	0.0140534i
$861$	28.0357	+	61.7598i	0.955454	+	2.10477i
$862$	−19.1734	−	31.6556i	−0.653049	−	1.07819i
$863$	−14.4556			−0.492073			−0.246037	−	0.969261i	$-0.579128\pi$
$863$	−14.4556			−0.492073			−0.246037	+	0.969261i	$0.579128\pi$
$864$	−28.8790	−	5.47731i	−0.982485	−	0.186342i
$865$	0.927282	−	1.60610i	0.0315285	−	0.0546090i
$866$	13.7167	+	22.6465i	0.466113	+	0.769560i
$867$	−38.0486	−	3.72027i	−1.29220	−	0.126347i
$868$	−30.8971	+	59.1147i	−1.04871	+	2.00648i
$869$	−57.2172	−	33.0344i	−1.94096	−	1.12061i
$870$	3.35160	+	0.256812i	0.113630	+	0.00870676i
$871$	−5.84347	−	13.3316i	−0.197998	−	0.451726i
$872$	16.7767	−	1.05796i	0.568131	−	0.0358272i
$873$	−1.59931	−	0.315770i	−0.0541285	−	0.0106872i
$874$	0.774411	−	0.469052i	0.0261948	−	0.0158659i
$875$	8.13183	+	14.0847i	0.274906	+	0.476151i
$876$	−12.0416	−	23.8164i	−0.406847	−	0.804683i
$877$	14.2845	−	24.7415i	0.482354	−	0.835462i	−0.517441	−	0.855719i	$-0.673115\pi$
$877$	14.2845	−	24.7415i	0.482354	−	0.835462i	0.999795	+	0.0202574i	$0.00644858\pi$
$878$	23.6232	+	12.9854i	0.797243	+	0.438237i
$879$	31.3631	+	22.4409i	1.05785	+	0.756914i
$880$	−5.79850	+	4.03174i	−0.195468	+	0.135910i
$881$	43.0522	+	24.8562i	1.45046	+	0.837426i	0.998508	−	0.0546133i	$-0.0173926\pi$
$881$	43.0522	+	24.8562i	1.45046	+	0.837426i	0.451957	+	0.892040i	$0.350726\pi$
$882$	50.6045	+	8.89208i	1.70394	+	0.299412i
$883$	28.9580	−	16.7189i	0.974513	−	0.562635i	0.0739040	−	0.997265i	$-0.476454\pi$
$883$	28.9580	−	16.7189i	0.974513	−	0.562635i	0.900609	+	0.434630i	$0.143121\pi$
$884$	18.7696	−	11.9141i	0.631289	−	0.400714i
$885$	5.32160	+	3.80771i	0.178884	+	0.127995i
$886$	4.56830	+	7.54233i	0.153475	+	0.253390i
$887$	−17.0812	+	29.5855i	−0.573531	+	0.993385i	0.422668	+	0.906284i	$0.361094\pi$
$887$	−17.0812	+	29.5855i	−0.573531	+	0.993385i	−0.996200	+	0.0871007i	$0.972240\pi$
$888$	−10.1149	−	19.0043i	−0.339435	−	0.637743i
$889$	−19.1088	+	33.0974i	−0.640889	+	1.11005i
$890$	−0.317020	+	0.00665608i	−0.0106265	+	0.000223112i
$891$	38.9442	+	16.0022i	1.30468	+	0.536095i
$892$	1.93257	+	46.0026i	0.0647073	+	1.54028i
$893$			9.53707i			0.319146i
$894$	−29.4317	−	20.1385i	−0.984344	−	0.673532i
$895$			1.04006i			0.0347653i
$896$	38.7497	−	30.7341i	1.29454	−	1.02676i
$897$	0.892351	+	0.0872512i	0.0297947	+	0.00291323i
$898$	18.8438	−	11.4135i	0.628827	−	0.380873i
$899$	−13.8701	+	24.0237i	−0.462593	+	0.801235i
$900$	−10.5571	−	27.1662i	−0.351903	−	0.905539i
$901$	3.05616	−	5.29342i	0.101815	−	0.176349i
$902$	−51.9347	−	28.5481i	−1.72924	−	0.950547i
$903$	98.0265	+	9.58473i	3.26212	+	0.318960i
$904$	−41.7026	+	27.7159i	−1.38701	+	0.921817i
$905$	−3.22956	+	1.86459i	−0.107354	+	0.0619811i
$906$	−40.0911	+	19.2242i	−1.33194	+	0.638683i
$907$	−15.7178	+	9.07470i	−0.521902	+	0.301320i	−0.737713	−	0.675115i	$-0.764094\pi$
$907$	−15.7178	+	9.07470i	−0.521902	+	0.301320i	0.215810	+	0.976435i	$0.430761\pi$
$908$	5.96235	+	9.39313i	0.197867	+	0.311722i
$909$	−12.8412	−	11.2293i	−0.425915	−	0.372452i
$910$	−4.14834	+	0.0870977i	−0.137516	+	0.00288726i
$911$	−15.9585			−0.528729			−0.264365	−	0.964423i	$-0.585162\pi$
$911$	−15.9585			−0.528729			−0.264365	+	0.964423i	$0.585162\pi$
$912$	13.2974	−	7.43980i	0.440321	−	0.246357i
$913$	−41.3146			−1.36731
$914$	−14.8645	−	24.5415i	−0.491673	−	0.811759i
$915$	2.04579	−	0.928681i	0.0676317	−	0.0307012i
$916$	−1.82263	+	3.48719i	−0.0602212	+	0.115220i
$917$	−53.7619	+	31.0395i	−1.77538	+	1.02501i
$918$	−32.1663	−	32.7905i	−1.06165	−	1.08225i
$919$	16.1514	+	9.32501i	0.532785	+	0.307604i	0.742150	−	0.670234i	$-0.233806\pi$
$919$	16.1514	+	9.32501i	0.532785	+	0.307604i	−0.209365	+	0.977838i	$0.567140\pi$
$920$	0.278352	+	0.138124i	0.00917699	+	0.00455382i
$921$	35.6546	−	16.1853i	1.17486	−	0.533324i
$922$	0.0711096	+	3.38685i	0.00234187	+	0.111540i
$923$	27.0547			0.890516
$924$	−63.2226	+	31.9653i	−2.07987	+	1.05158i
$925$	10.6732	−	18.4866i	0.350934	−	0.607835i
$926$	−24.6255	−	13.5364i	−0.809245	−	0.444835i
$927$	−12.8949	−	11.2763i	−0.423524	−	0.370362i
$928$	16.6375	−	12.0941i	0.546154	−	0.397008i
$929$			23.8334i			0.781949i	0.920402	+	0.390974i	$0.127862\pi$
$929$			23.8334i			0.781949i	−0.920402	+	0.390974i	$0.872138\pi$
$930$	−7.03225	−	0.538838i	−0.230597	−	0.0176692i
$931$	−23.0659	+	13.3171i	−0.755955	+	0.436451i
$932$	19.9589	−	12.6690i	0.653774	−	0.414987i
$933$	15.8629	−	22.1697i	0.519327	−	0.725804i
$934$	−4.95165	+	9.00806i	−0.162023	+	0.294753i
$935$	−11.0364			−0.360928
$936$	14.9582	+	1.98537i	0.488925	+	0.0648937i
$937$	29.5310			0.964737			0.482368	−	0.875968i	$-0.339777\pi$
$937$	29.5310			0.964737			0.482368	+	0.875968i	$0.339777\pi$
$938$	4.52359	−	50.4016i	0.147700	−	1.64567i
$939$	−21.5576	+	30.1287i	−0.703507	+	0.983212i
$940$	−2.76350	+	1.75415i	−0.0901356	+	0.0572141i
$941$			45.7910i			1.49274i	0.665529	+	0.746372i	$0.268206\pi$
$941$			45.7910i			1.49274i	−0.665529	+	0.746372i	$0.731794\pi$
$942$	−19.2191	−	40.0804i	−0.626191	−	1.30589i
$943$			2.60754i			0.0849133i
$944$	39.8993	−	3.35827i	1.29861	−	0.109303i
$945$	1.96444	+	8.34485i	0.0639031	+	0.271458i
$946$	−73.6116	+	44.5857i	−2.39332	+	1.44961i
$947$	40.2540			1.30808			0.654040	−	0.756460i	$-0.273073\pi$
$947$	40.2540			1.30808			0.654040	+	0.756460i	$0.273073\pi$
$948$	−2.71291	+	48.8472i	−0.0881111	+	1.58648i
$949$	6.85005	+	11.8646i	0.222362	+	0.385142i
$950$	13.2399	+	7.27786i	0.429559	+	0.236125i
$951$	26.8251	−	12.1772i	0.869863	−	0.394872i
$952$	77.1349	−	4.86424i	2.49996	−	0.157651i
$953$		−	29.6896i		−	0.961741i	−0.876792	−	0.480870i	$-0.840321\pi$
$953$		−	29.6896i		−	0.961741i	0.876792	−	0.480870i	$-0.159679\pi$
$954$	3.89763	−	1.42123i	0.126191	−	0.0460141i
$955$	−0.148439	−	0.0857012i	−0.00480337	−	0.00277322i
$956$	−0.885637	−	1.39524i	−0.0286436	−	0.0451253i
$957$	−26.8279	+	12.1784i	−0.867222	+	0.393673i
$958$	−8.77052	+	15.9554i	−0.283363	+	0.515494i
$959$	−22.0081	−	38.1192i	−0.710680	−	1.23093i
$960$	4.60158	+	2.48471i	0.148515	+	0.0801937i
$961$	13.6019	−	23.5591i	0.438770	−	0.759972i
$962$	5.72554	+	9.45295i	0.184599	+	0.304775i
$963$	4.10832	+	12.0467i	0.132389	+	0.388198i
$964$	28.1364	−	1.18201i	0.906214	−	0.0380701i
$965$		−	0.812978i		−	0.0261707i
$966$	2.57249	+	1.76021i	0.0827684	+	0.0566338i
$967$	41.9759	−	24.2348i	1.34985	−	0.779338i	0.361625	−	0.932324i	$-0.382222\pi$
$967$	41.9759	−	24.2348i	1.34985	−	0.779338i	0.988228	+	0.152986i	$0.0488888\pi$
$968$	13.6858	−	27.5799i	0.439877	−	0.886452i
$969$	23.6980	+	2.31712i	0.761289	+	0.0744365i
$970$	0.254164	+	0.139711i	0.00816070	+	0.00448586i
$971$	7.34713	+	12.7256i	0.235781	+	0.408384i	0.959499	−	0.281711i	$-0.0909020\pi$
$971$	7.34713	+	12.7256i	0.235781	+	0.408384i	−0.723719	+	0.690095i	$0.757569\pi$
$972$	−2.43707	−	31.0815i	−0.0781691	−	0.996940i
$973$	21.6313	+	37.4665i	0.693468	+	1.20112i
$974$	7.67249	+	4.21750i	0.245842	+	0.135137i
$975$	6.18450	+	13.6238i	0.198063	+	0.436312i
$976$	5.85108	−	12.4405i	0.187289	−	0.398210i
$977$	11.2164	+	6.47578i	0.358844	+	0.207178i	0.668573	−	0.743646i	$-0.266905\pi$
$977$	11.2164	+	6.47578i	0.358844	+	0.207178i	−0.309730	+	0.950825i	$0.600239\pi$
$978$	−0.391488	+	5.10923i	−0.0125184	+	0.163375i
$979$	2.40692	−	1.38964i	0.0769255	−	0.0444130i
$980$	−8.10133	−	4.23427i	−0.258788	−	0.135259i
$981$	5.75507	+	16.8754i	0.183745	+	0.538789i
$982$	−48.1917	+	1.01182i	−1.53786	+	0.0322886i
$983$	37.0696			1.18234			0.591168	−	0.806549i	$-0.298667\pi$
$983$	37.0696			1.18234			0.591168	+	0.806549i	$0.298667\pi$
$984$	−1.51320	+	43.8575i	−0.0482391	+	1.39813i
$985$	1.33328	+	2.30931i	0.0424819	+	0.0735808i
$986$	32.1356	−	0.674712i	1.02341	−	0.0214872i
$987$	−29.8979	+	13.5721i	−0.951659	+	0.432003i
$988$	−6.60396	+	4.19190i	−0.210100	+	0.133362i
$989$	3.27929	+	1.89330i	0.104275	+	0.0602035i
$990$	−5.74114	−	4.81161i	−0.182466	−	0.152923i
$991$			2.30461i			0.0732084i	0.999330	+	0.0366042i	$0.0116541\pi$
$991$			2.30461i			0.0732084i	−0.999330	+	0.0366042i	$0.988346\pi$
$992$	−34.9085	+	25.3755i	−1.10835	+	0.805673i
$993$	−4.92071	+	50.3259i	−0.156154	+	1.59704i
$994$	82.4239	+	45.3077i	2.61433	+	1.43707i
$995$	−5.25934	+	9.10944i	−0.166732	+	0.288789i
$996$	13.8036	+	27.3014i	0.437383	+	0.865079i
$997$	−22.4235			−0.710160			−0.355080	−	0.934836i	$-0.615546\pi$
$997$	−22.4235			−0.710160			−0.355080	+	0.934836i	$0.615546\pi$
$998$	15.1360	+	8.32013i	0.479122	+	0.263369i
$999$	16.6328	−	15.6448i	0.526240	−	0.494979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.l.a.431.2	✓	264
3.2	odd	2	inner	804.2.l.a.431.131	yes	264
4.3	odd	2	inner	804.2.l.a.431.45	yes	264
12.11	even	2	inner	804.2.l.a.431.88	yes	264
67.37	even	3	inner	804.2.l.a.707.88	yes	264
201.104	odd	6	inner	804.2.l.a.707.45	yes	264
268.171	odd	6	inner	804.2.l.a.707.131	yes	264
804.707	even	6	inner	804.2.l.a.707.2	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.l.a.431.2	✓	264	1.1	even	1	trivial
804.2.l.a.431.45	yes	264	4.3	odd	2	inner
804.2.l.a.431.88	yes	264	12.11	even	2	inner
804.2.l.a.431.131	yes	264	3.2	odd	2	inner
804.2.l.a.707.2	yes	264	804.707	even	6	inner
804.2.l.a.707.45	yes	264	201.104	odd	6	inner
804.2.l.a.707.88	yes	264	67.37	even	3	inner
804.2.l.a.707.131	yes	264	268.171	odd	6	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41390 + 0.0296860i) q^{2} +(-1.00788 + 1.40861i) q^{3} +(1.99824 - 0.0839461i) q^{4} -0.377411i q^{5} +(1.38323 - 2.02155i) q^{6} +(-3.78586 + 2.18577i) q^{7} +(-2.82282 + 0.178011i) q^{8} +(-0.968338 - 2.83942i) q^{9} +O(q^{10})\)	\(q+(-1.41390 + 0.0296860i) q^{2} +(-1.00788 + 1.40861i) q^{3} +(1.99824 - 0.0839461i) q^{4} -0.377411i q^{5} +(1.38323 - 2.02155i) q^{6} +(-3.78586 + 2.18577i) q^{7} +(-2.82282 + 0.178011i) q^{8} +(-0.968338 - 2.83942i) q^{9} +(0.0112038 + 0.533622i) q^{10} +(-2.33910 - 4.05143i) q^{11} +(-1.89575 + 2.89934i) q^{12} +(0.889153 - 1.54006i) q^{13} +(5.28795 - 3.20285i) q^{14} +(0.531623 + 0.380387i) q^{15} +(3.98591 - 0.335489i) q^{16} +(5.41332 + 3.12538i) q^{17} +(1.45343 + 3.98592i) q^{18} +(-1.90465 - 1.09965i) q^{19} +(-0.0316822 - 0.754157i) q^{20} +(0.736826 - 7.53579i) q^{21} +(3.42752 + 5.65889i) q^{22} +(0.145547 - 0.252096i) q^{23} +(2.59433 - 4.15565i) q^{24} +4.85756 q^{25} +(-1.21146 + 2.20389i) q^{26} +(4.97560 + 1.49780i) q^{27} +(-7.38157 + 4.68549i) q^{28} +(-3.14894 + 1.81804i) q^{29} +(-0.762955 - 0.522048i) q^{30} +(6.60703 - 3.81457i) q^{31} +(-5.62572 + 0.592674i) q^{32} +(8.06441 + 0.788513i) q^{33} +(-7.74669 - 4.25829i) q^{34} +(0.824933 + 1.42883i) q^{35} +(-2.17333 - 5.59255i) q^{36} +(2.19724 - 3.80573i) q^{37} +(2.72563 + 1.49825i) q^{38} +(1.27317 + 2.80467i) q^{39} +(0.0671834 + 1.06536i) q^{40} +(-7.75760 + 4.47886i) q^{41} +(-0.818092 + 10.6767i) q^{42} +13.0081i q^{43} +(-5.01417 - 7.89937i) q^{44} +(-1.07163 + 0.365462i) q^{45} +(-0.198306 + 0.360759i) q^{46} +(-2.16821 - 3.75545i) q^{47} +(-3.54476 + 5.95270i) q^{48} +(6.05517 - 10.4879i) q^{49} +(-6.86811 + 0.144201i) q^{50} +(-9.85844 + 4.47521i) q^{51} +(1.64746 - 3.15204i) q^{52} -0.977850i q^{53} +(-7.07947 - 1.97004i) q^{54} +(-1.52906 + 0.882801i) q^{55} +(10.2977 - 6.84396i) q^{56} +(3.46863 - 1.57458i) q^{57} +(4.39832 - 2.66401i) q^{58} +10.0101 q^{59} +(1.09424 + 0.715475i) q^{60} +(1.71847 - 2.97648i) q^{61} +(-9.22845 + 5.58956i) q^{62} +(9.87232 + 8.63310i) q^{63} +(7.93662 - 1.00499i) q^{64} +(-0.581235 - 0.335576i) q^{65} +(-11.4257 - 0.875480i) q^{66} +(4.84945 - 6.59415i) q^{67} +(11.0795 + 5.79083i) q^{68} +(0.208408 + 0.459102i) q^{69} +(-1.20879 - 1.99573i) q^{70} +(7.60688 + 13.1755i) q^{71} +(3.23889 + 7.84280i) q^{72} +(-3.85201 + 6.67187i) q^{73} +(-2.99371 + 5.44616i) q^{74} +(-4.89586 + 6.84239i) q^{75} +(-3.89825 - 2.03747i) q^{76} +(17.7110 + 10.2254i) q^{77} +(-1.88340 - 3.92773i) q^{78} +(12.2306 - 7.06135i) q^{79} +(-0.126617 - 1.50432i) q^{80} +(-7.12464 + 5.49904i) q^{81} +(10.8355 - 6.56295i) q^{82} +(4.41566 - 7.64815i) q^{83} +(0.839753 - 15.1201i) q^{84} +(1.17955 - 2.04305i) q^{85} +(-0.386159 - 18.3922i) q^{86} +(0.612864 - 6.26799i) q^{87} +(7.32405 + 11.0201i) q^{88} +0.594091i q^{89} +(1.50433 - 0.548539i) q^{90} +7.77393i q^{91} +(0.269676 - 0.515965i) q^{92} +(-1.28590 + 13.1513i) q^{93} +(3.17712 + 5.24547i) q^{94} +(-0.415019 + 0.718835i) q^{95} +(4.83523 - 8.52177i) q^{96} +(0.271698 - 0.470594i) q^{97} +(-8.25007 + 15.0086i) q^{98} +(-9.23870 + 10.5648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

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