LMFDB - Embedded newform 378.2.z.a.293.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			293.17
Character	$\chi$	$=$	378.293
Dual form			378.2.z.a.209.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(-0.811256 - 1.53031i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.307943 - 1.74643i) q^{5} +(-1.71549 + 0.238933i) q^{6} +(2.14467 - 1.54932i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.68373 + 2.48295i) q^{9} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(-0.811256 - 1.53031i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.307943 - 1.74643i) q^{5} +(-1.71549 + 0.238933i) q^{6} +(2.14467 - 1.54932i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.68373 + 2.48295i) q^{9} +(-1.53579 - 0.886687i) q^{10} +(2.04540 - 0.360659i) q^{11} +(-0.362209 + 1.69375i) q^{12} +(-1.92956 - 5.30143i) q^{13} +(-0.722363 - 2.54523i) q^{14} +(-2.92241 + 0.945554i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.73566 + 3.00626i) q^{17} +(1.75735 + 2.43141i) q^{18} +(-0.552273 + 0.318855i) q^{19} +(-1.35848 + 1.13990i) q^{20} +(-4.11082 - 2.02513i) q^{21} +(0.360659 - 2.04540i) q^{22} +(-4.38844 + 5.22994i) q^{23} +(1.46773 + 0.919663i) q^{24} +(1.74326 + 0.634496i) q^{25} -5.64167 q^{26} +(5.16564 + 0.562320i) q^{27} +(-2.63880 - 0.191721i) q^{28} +(-0.536375 + 1.47368i) q^{29} +(-0.110994 + 3.06957i) q^{30} +(-3.11607 + 3.71358i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-2.21127 - 2.83752i) q^{33} +(2.23133 + 2.65919i) q^{34} +(-2.04534 - 4.22262i) q^{35} +(2.88582 - 0.819775i) q^{36} +(3.87432 - 6.71053i) q^{37} +(0.110737 + 0.628021i) q^{38} +(-6.54749 + 7.25366i) q^{39} +(0.606530 + 1.66643i) q^{40} +(11.6113 - 4.22616i) q^{41} +(-3.30898 + 3.17028i) q^{42} +(-2.03601 - 11.5468i) q^{43} +(-1.79869 - 1.03848i) q^{44} +(3.81782 + 3.70512i) q^{45} +(3.41360 + 5.91253i) q^{46} +(-1.88256 + 1.57965i) q^{47} +(1.36619 - 1.06467i) q^{48} +(2.19922 - 6.64556i) q^{49} +(1.19246 - 1.42112i) q^{50} +(6.00859 + 0.217267i) q^{51} +(-1.92956 + 5.30143i) q^{52} -4.08630i q^{53} +(2.29516 - 4.66179i) q^{54} -3.68322i q^{55} +(-1.08268 + 2.41408i) q^{56} +(0.935983 + 0.586478i) q^{57} +(1.20135 + 1.00805i) q^{58} +(-0.784530 + 4.44929i) q^{59} +(2.84649 + 1.15415i) q^{60} +(7.59238 + 9.04825i) q^{61} +(2.42387 + 4.19827i) q^{62} +(0.235849 + 7.93375i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-9.85279 + 1.73731i) q^{65} +(-3.42269 + 1.10742i) q^{66} +(2.59312 - 0.943819i) q^{67} +(3.26198 - 1.18726i) q^{68} +(11.5636 + 2.47287i) q^{69} +(-4.66752 + 0.477772i) q^{70} +(-6.13940 - 3.54459i) q^{71} +(0.216673 - 2.99217i) q^{72} +(7.60752 - 4.39220i) q^{73} +(-4.98073 - 5.93581i) q^{74} +(-0.443255 - 3.18248i) q^{75} +(0.628021 + 0.110737i) q^{76} +(3.82793 - 3.94247i) q^{77} +(4.57684 + 8.63352i) q^{78} +(13.9973 + 5.09459i) q^{79} +1.77337 q^{80} +(-3.33013 - 8.36124i) q^{81} -12.3565i q^{82} +(-2.01086 - 0.731892i) q^{83} +(1.84735 + 4.19372i) q^{84} +(4.71574 + 3.95697i) q^{85} +(-11.5468 - 2.03601i) q^{86} +(2.69033 - 0.374708i) q^{87} +(-1.59104 + 1.33504i) q^{88} +(-2.14895 - 3.72210i) q^{89} +(4.78745 - 2.32035i) q^{90} +(-12.3519 - 8.38031i) q^{91} +(6.72348 - 1.18553i) q^{92} +(8.21088 + 1.75590i) q^{93} +(0.840515 + 2.30930i) q^{94} +(0.386790 + 1.06270i) q^{95} +(-0.533195 - 1.64794i) q^{96} +(15.7571 - 2.77840i) q^{97} +(-5.49260 - 4.33951i) q^{98} +(-2.54840 + 5.68589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	−0.811256	−	1.53031i	−0.468379	−	0.883528i
$3$	−0.811256	−	1.53031i	−0.468379	−	0.883528i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	0.307943	−	1.74643i	0.137716	−	0.781028i	−0.835213	−	0.549926i	$-0.814656\pi$
$5$	0.307943	−	1.74643i	0.137716	−	0.781028i	0.972930	−	0.231102i	$-0.0742331\pi$
$6$	−1.71549	+	0.238933i	−0.700346	+	0.0975439i
$7$	2.14467	−	1.54932i	0.810609	−	0.585587i
$7$	2.14467	−	1.54932i	0.810609	−	0.585587i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−1.68373	+	2.48295i	−0.561242	+	0.827652i
$10$	−1.53579	−	0.886687i	−0.485659	−	0.280395i
$11$	2.04540	−	0.360659i	0.616711	−	0.108743i	0.143439	−	0.989659i	$-0.454184\pi$
$11$	2.04540	−	0.360659i	0.616711	−	0.108743i	0.473272	+	0.880916i	$0.343073\pi$
$12$	−0.362209	+	1.69375i	−0.104561	+	0.488945i
$13$	−1.92956	−	5.30143i	−0.535165	−	1.47035i	−0.852850	−	0.522156i	$-0.825128\pi$
$13$	−1.92956	−	5.30143i	−0.535165	−	1.47035i	0.317685	−	0.948196i	$-0.397094\pi$
$14$	−0.722363	−	2.54523i	−0.193060	−	0.680241i
$15$	−2.92241	+	0.945554i	−0.754564	+	0.244141i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−1.73566	+	3.00626i	−0.420960	+	0.729124i	−0.996034	−	0.0889775i	$-0.971640\pi$
$17$	−1.73566	+	3.00626i	−0.420960	+	0.729124i	0.575074	+	0.818102i	$0.304973\pi$
$18$	1.75735	+	2.43141i	0.414210	+	0.573088i
$19$	−0.552273	+	0.318855i	−0.126700	+	0.0731503i	−0.562010	−	0.827130i	$-0.689972\pi$
$19$	−0.552273	+	0.318855i	−0.126700	+	0.0731503i	0.435310	+	0.900280i	$0.356639\pi$
$20$	−1.35848	+	1.13990i	−0.303766	+	0.254890i
$21$	−4.11082	−	2.02513i	−0.897055	−	0.441919i
$22$	0.360659	−	2.04540i	0.0768928	−	0.436081i
$23$	−4.38844	+	5.22994i	−0.915053	+	1.09052i	0.0805417	+	0.996751i	$0.474335\pi$
$23$	−4.38844	+	5.22994i	−0.915053	+	1.09052i	−0.995594	+	0.0937659i	$0.970109\pi$
$24$	1.46773	+	0.919663i	0.299598	+	0.187726i
$25$	1.74326	+	0.634496i	0.348653	+	0.126899i
$26$	−5.64167			−1.10642
$27$	5.16564	+	0.562320i	0.994127	+	0.108219i
$28$	−2.63880	−	0.191721i	−0.498686	−	0.0362318i
$29$	−0.536375	+	1.47368i	−0.0996023	+	0.273655i	−0.979479	−	0.201548i	$-0.935403\pi$
$29$	−0.536375	+	1.47368i	−0.0996023	+	0.273655i	0.879876	+	0.475202i	$0.157625\pi$
$30$	−0.110994	+	3.06957i	−0.0202646	+	0.560424i
$31$	−3.11607	+	3.71358i	−0.559662	+	0.666979i	−0.969475	−	0.245190i	$-0.921150\pi$
$31$	−3.11607	+	3.71358i	−0.559662	+	0.666979i	0.409813	+	0.912170i	$0.365594\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	−2.21127	−	2.83752i	−0.384932	−	0.493949i
$34$	2.23133	+	2.65919i	0.382669	+	0.456047i
$35$	−2.04534	−	4.22262i	−0.345726	−	0.713754i
$36$	2.88582	−	0.819775i	0.480970	−	0.136629i
$37$	3.87432	−	6.71053i	0.636935	−	1.10320i	−0.349167	−	0.937061i	$-0.613535\pi$
$37$	3.87432	−	6.71053i	0.636935	−	1.10320i	0.986102	−	0.166143i	$-0.0531313\pi$
$38$	0.110737	+	0.628021i	0.0179639	+	0.101879i
$39$	−6.54749	+	7.25366i	−1.04844	+	1.16151i
$40$	0.606530	+	1.66643i	0.0959008	+	0.263485i
$41$	11.6113	−	4.22616i	1.81338	−	0.660016i	0.816842	−	0.576861i	$-0.195723\pi$
$41$	11.6113	−	4.22616i	1.81338	−	0.660016i	0.996537	−	0.0831544i	$-0.0264995\pi$
$42$	−3.30898	+	3.17028i	−0.510587	+	0.489184i
$43$	−2.03601	−	11.5468i	−0.310488	−	1.76087i	−0.596473	−	0.802633i	$-0.703432\pi$
$43$	−2.03601	−	11.5468i	−0.310488	−	1.76087i	0.285985	−	0.958234i	$-0.407679\pi$
$44$	−1.79869	−	1.03848i	−0.271163	−	0.156556i
$45$	3.81782	+	3.70512i	0.569127	+	0.552327i
$46$	3.41360	+	5.91253i	0.503308	+	0.871754i
$47$	−1.88256	+	1.57965i	−0.274599	+	0.230416i	−0.769678	−	0.638432i	$-0.779583\pi$
$47$	−1.88256	+	1.57965i	−0.274599	+	0.230416i	0.495079	+	0.868848i	$0.335139\pi$
$48$	1.36619	−	1.06467i	0.197193	−	0.153672i
$49$	2.19922	−	6.64556i	0.314175	−	0.949365i
$50$	1.19246	−	1.42112i	0.168640	−	0.200977i
$51$	6.00859	+	0.217267i	0.841370	+	0.0304234i
$52$	−1.92956	+	5.30143i	−0.267582	+	0.735176i
$53$		−	4.08630i		−	0.561297i	−0.959811	−	0.280649i	$-0.909450\pi$
$53$		−	4.08630i		−	0.561297i	0.959811	−	0.280649i	$-0.0905495\pi$
$54$	2.29516	−	4.66179i	0.312332	−	0.634389i
$55$		−	3.68322i		−	0.496645i
$56$	−1.08268	+	2.41408i	−0.144679	+	0.322596i
$57$	0.935983	+	0.586478i	0.123974	+	0.0776809i
$58$	1.20135	+	1.00805i	0.157745	+	0.132364i
$59$	−0.784530	+	4.44929i	−0.102137	+	0.579249i	0.890188	+	0.455593i	$0.150573\pi$
$59$	−0.784530	+	4.44929i	−0.102137	+	0.579249i	−0.992325	+	0.123655i	$0.960538\pi$
$60$	2.84649	+	1.15415i	0.367480	+	0.149001i
$61$	7.59238	+	9.04825i	0.972105	+	1.15851i	0.987339	+	0.158626i	$0.0507063\pi$
$61$	7.59238	+	9.04825i	0.972105	+	1.15851i	−0.0152338	+	0.999884i	$0.504849\pi$
$62$	2.42387	+	4.19827i	0.307832	+	0.533180i
$63$	0.235849	+	7.93375i	0.0297142	+	0.999558i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−9.85279	+	1.73731i	−1.22209	+	0.215487i
$66$	−3.42269	+	1.10742i	−0.421304	+	0.136314i
$67$	2.59312	−	0.943819i	0.316800	−	0.115306i	−0.178726	−	0.983899i	$-0.557198\pi$
$67$	2.59312	−	0.943819i	0.316800	−	0.115306i	0.495526	+	0.868593i	$0.334975\pi$
$68$	3.26198	−	1.18726i	0.395573	−	0.143977i
$69$	11.5636	+	2.47287i	1.39209	+	0.297699i
$70$	−4.66752	+	0.477772i	−0.557875	+	0.0571047i
$71$	−6.13940	−	3.54459i	−0.728613	−	0.420665i	0.0893016	−	0.996005i	$-0.471537\pi$
$71$	−6.13940	−	3.54459i	−0.728613	−	0.420665i	−0.817915	+	0.575340i	$0.804870\pi$
$72$	0.216673	−	2.99217i	0.0255352	−	0.352630i
$73$	7.60752	−	4.39220i	0.890393	−	0.514069i	0.0163220	−	0.999867i	$-0.494804\pi$
$73$	7.60752	−	4.39220i	0.890393	−	0.514069i	0.874071	+	0.485798i	$0.161471\pi$
$74$	−4.98073	−	5.93581i	−0.578999	−	0.690024i
$75$	−0.443255	−	3.18248i	−0.0511827	−	0.367481i
$76$	0.628021	+	0.110737i	0.0720390	+	0.0127024i
$77$	3.82793	−	3.94247i	0.436234	−	0.449286i
$78$	4.57684	+	8.63352i	0.518225	+	0.977554i
$79$	13.9973	+	5.09459i	1.57481	+	0.573186i	0.974068	−	0.226254i	$-0.0726479\pi$
$79$	13.9973	+	5.09459i	1.57481	+	0.573186i	0.600746	+	0.799440i	$0.294870\pi$
$80$	1.77337			0.198269
$81$	−3.33013	−	8.36124i	−0.370014	−	0.929026i
$82$		−	12.3565i		−	1.36454i
$83$	−2.01086	−	0.731892i	−0.220720	−	0.0803355i	0.229293	−	0.973357i	$-0.426359\pi$
$83$	−2.01086	−	0.731892i	−0.220720	−	0.0803355i	−0.450013	+	0.893022i	$0.648581\pi$
$84$	1.84735	+	4.19372i	0.201562	+	0.457573i
$85$	4.71574	+	3.95697i	0.511494	+	0.429194i
$86$	−11.5468	−	2.03601i	−1.24512	−	0.219548i
$87$	2.69033	−	0.374708i	0.288433	−	0.0401729i
$88$	−1.59104	+	1.33504i	−0.169605	+	0.142316i
$89$	−2.14895	−	3.72210i	−0.227789	−	0.394541i	0.729364	−	0.684126i	$-0.239816\pi$
$89$	−2.14895	−	3.72210i	−0.227789	−	0.394541i	−0.957152	+	0.289585i	$0.906483\pi$
$90$	4.78745	−	2.32035i	0.504642	−	0.244586i
$91$	−12.3519	−	8.38031i	−1.29483	−	0.878496i
$92$	6.72348	−	1.18553i	0.700971	−	0.123600i
$93$	8.21088	+	1.75590i	0.851429	+	0.182078i
$94$	0.840515	+	2.30930i	0.0866925	+	0.238186i
$95$	0.386790	+	1.06270i	0.0396838	+	0.109030i
$96$	−0.533195	−	1.64794i	−0.0544190	−	0.168192i
$97$	15.7571	−	2.77840i	1.59989	−	0.282104i	0.698664	−	0.715450i	$-0.253778\pi$
$97$	15.7571	−	2.77840i	1.59989	−	0.282104i	0.901227	+	0.433346i	$0.142667\pi$
$98$	−5.49260	−	4.33951i	−0.554837	−	0.438356i
$99$	−2.54840	+	5.68589i	−0.256123	+	0.571453i
$100$	−0.927572	−	1.60660i	−0.0927572	−	0.160660i
$101$	−5.70054	+	4.78332i	−0.567225	+	0.475958i	−0.880724	−	0.473631i	$-0.842943\pi$
$101$	−5.70054	+	4.78332i	−0.567225	+	0.475958i	0.313499	+	0.949589i	$0.398499\pi$
$102$	2.25922	−	5.57191i	0.223696	−	0.551702i
$103$	−9.46271	−	1.66853i	−0.932389	−	0.164405i	−0.313236	−	0.949675i	$-0.601413\pi$
$103$	−9.46271	−	1.66853i	−0.932389	−	0.164405i	−0.619153	+	0.785270i	$0.712524\pi$
$104$	4.32177	+	3.62639i	0.423784	+	0.355597i
$105$	−4.80265	+	6.55565i	−0.468690	+	0.639766i
$106$	−3.83987	−	1.39760i	−0.372961	−	0.135747i
$107$			12.3364i			1.19260i	0.802762	+	0.596300i	$0.203363\pi$
$107$			12.3364i			1.19260i	−0.802762	+	0.596300i	$0.796637\pi$
$108$	−3.59565	−	3.75117i	−0.345992	−	0.360956i
$109$	−4.90352			−0.469672			−0.234836	−	0.972035i	$-0.575455\pi$
$109$	−4.90352			−0.469672			−0.234836	+	0.972035i	$0.575455\pi$
$110$	−3.46109	−	1.25973i	−0.330002	−	0.120111i
$111$	−13.4123	−	0.484980i	−1.27304	−	0.0460323i
$112$	1.89820	+	1.84305i	0.179363	+	0.174152i
$113$	2.53983	+	0.447841i	0.238927	+	0.0421293i	0.291829	−	0.956470i	$-0.405736\pi$
$113$	2.53983	+	0.447841i	0.238927	+	0.0421293i	−0.0529022	+	0.998600i	$0.516847\pi$
$114$	0.871234	−	0.678949i	0.0815986	−	0.0635894i
$115$	7.78234	+	9.27464i	0.725707	+	0.864864i
$116$	1.35815	−	0.784127i	0.126101	−	0.0728044i
$117$	16.4121	+	4.13514i	1.51730	+	0.382294i
$118$	3.91264	+	2.25897i	0.360188	+	0.207955i
$119$	0.935225	+	9.13652i	0.0857319	+	0.837544i
$120$	2.05811	−	2.28008i	0.187879	−	0.208142i
$121$	−6.28303	+	2.28684i	−0.571185	+	0.207894i
$122$	11.0993	−	4.03982i	1.00489	−	0.365748i
$123$	−15.8871	−	14.3404i	−1.43249	−	1.29303i
$124$	4.77409	−	0.841801i	0.428726	−	0.0755960i
$125$	6.07837	−	10.5280i	0.543666	−	0.941657i
$126$	7.53595	+	2.49188i	0.671356	+	0.221994i
$127$	−0.604359	−	1.04678i	−0.0536282	−	0.0928867i	0.837965	−	0.545724i	$-0.183745\pi$
$127$	−0.604359	−	1.04678i	−0.0536282	−	0.0928867i	−0.891593	+	0.452837i	$0.850412\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	−16.0185	+	12.4831i	−1.41035	+	1.09908i
$130$	−1.73731	+	9.85279i	−0.152372	+	0.864147i
$131$	10.6817	+	8.96303i	0.933266	+	0.783104i	0.976401	−	0.215966i	$-0.0692900\pi$
$131$	10.6817	+	8.96303i	0.933266	+	0.783104i	−0.0431345	+	0.999069i	$0.513734\pi$
$132$	−0.129994	+	3.59504i	−0.0113146	+	0.312908i
$133$	−0.690435	+	1.53949i	−0.0598683	+	0.133490i
$134$		−	2.75954i		−	0.238388i
$135$	2.57278	−	8.84827i	0.221429	−	0.761538i
$136$		−	3.47133i		−	0.297664i
$137$	0.953154	−	2.61877i	0.0814334	−	0.223737i	−0.892293	−	0.451456i	$-0.850905\pi$
$137$	0.953154	−	2.61877i	0.0814334	−	0.223737i	0.973727	+	0.227720i	$0.0731270\pi$
$138$	6.27872	−	10.0205i	0.534480	−	0.852998i
$139$	1.35238	−	1.61170i	0.114707	−	0.136703i	−0.705635	−	0.708575i	$-0.749338\pi$
$139$	1.35238	−	1.61170i	0.114707	−	0.136703i	0.820343	+	0.571872i	$0.193783\pi$
$140$	−1.14743	+	4.54944i	−0.0969752	+	0.384498i
$141$	3.94460	+	1.59940i	0.332195	+	0.134694i
$142$	−5.43062	+	4.55683i	−0.455727	+	0.382401i
$143$	−5.85874	−	10.1476i	−0.489932	−	0.848588i
$144$	−2.73761	−	1.22699i	−0.228134	−	0.102249i
$145$	2.40850	+	1.39055i	0.200015	+	0.115479i
$146$	−1.52540	−	8.65095i	−0.126243	−	0.715958i
$147$	−11.9539	+	2.02575i	−0.985943	+	0.167081i
$148$	−7.28135	+	2.65019i	−0.598523	+	0.217845i
$149$	−2.27491	−	6.25026i	−0.186368	−	0.512041i	0.810960	−	0.585102i	$-0.198945\pi$
$149$	−2.27491	−	6.25026i	−0.186368	−	0.512041i	−0.997327	+	0.0730609i	$0.976723\pi$
$150$	−3.14216	−	0.671950i	−0.256556	−	0.0548645i
$151$	1.77561	+	10.0700i	0.144497	+	0.819482i	0.967770	+	0.251837i	$0.0810346\pi$
$151$	1.77561	+	10.0700i	0.144497	+	0.819482i	−0.823273	+	0.567646i	$0.807854\pi$
$152$	0.318855	−	0.552273i	0.0258625	−	0.0447952i
$153$	−4.54202	−	9.37129i	−0.367200	−	0.757624i
$154$	−2.39548	−	4.94549i	−0.193033	−	0.398519i
$155$	5.52595	+	6.58557i	0.443855	+	0.528966i
$156$	9.67823	−	1.34798i	0.774878	−	0.107925i
$157$	−17.8492	−	3.14730i	−1.42452	−	0.251182i	−0.592342	−	0.805687i	$-0.701796\pi$
$157$	−17.8492	−	3.14730i	−1.42452	−	0.251182i	−0.832180	+	0.554505i	$0.812908\pi$
$158$	9.57469	−	11.4107i	0.761721	−	0.907784i
$159$	−6.25333	+	3.31504i	−0.495922	+	0.262900i
$160$	0.606530	−	1.66643i	0.0479504	−	0.131743i
$161$	−1.30891	+	18.0156i	−0.103157	+	1.41983i
$162$	−8.99596	+	0.269585i	−0.706789	+	0.0211806i
$163$	2.72302			0.213284			0.106642	−	0.994297i	$-0.465990\pi$
$163$	2.72302			0.213284			0.106642	+	0.994297i	$0.465990\pi$
$164$	−11.6113	−	4.22616i	−0.906689	−	0.330008i
$165$	−5.63648	+	2.98803i	−0.438799	+	0.232618i
$166$	−1.37551	+	1.63926i	−0.106760	+	0.127232i
$167$	−1.81706	+	10.3050i	−0.140608	+	0.797428i	0.830181	+	0.557494i	$0.188237\pi$
$167$	−1.81706	+	10.3050i	−0.140608	+	0.797428i	−0.970789	+	0.239934i	$0.922874\pi$
$168$	4.57264	−	0.301600i	0.352787	−	0.0232690i
$169$	−14.4234	+	12.1027i	−1.10949	+	0.930973i
$170$	5.33122	−	3.07798i	0.408886	−	0.236070i
$171$	0.138174	−	1.90813i	0.0105665	−	0.145919i
$172$	−5.86245	+	10.1541i	−0.447008	+	0.774240i
$173$	1.49457	+	8.47615i	0.113630	+	0.644430i	0.987419	+	0.158124i	$0.0505446\pi$
$173$	1.49457	+	8.47615i	0.113630	+	0.644430i	−0.873789	+	0.486305i	$0.838344\pi$
$174$	0.568036	−	2.65624i	0.0430627	−	0.201369i
$175$	4.72177	−	1.34009i	0.356932	−	0.101301i
$176$	0.710360	+	1.95170i	0.0535454	+	0.147115i
$177$	7.44527	−	2.40894i	0.559621	−	0.181067i
$178$	−4.23261	+	0.746323i	−0.317248	+	0.0559393i
$179$	13.5130	+	7.80172i	1.01001	+	0.583128i	0.911194	−	0.411978i	$-0.135162\pi$
$179$	13.5130	+	7.80172i	1.01001	+	0.583128i	0.0988132	+	0.995106i	$0.468495\pi$
$180$	−0.543012	−	5.29234i	−0.0404737	−	0.394468i
$181$	−8.68844	+	5.01627i	−0.645807	+	0.372857i	−0.786848	−	0.617147i	$-0.788288\pi$
$181$	−8.68844	+	5.01627i	−0.645807	+	0.372857i	0.141041	+	0.990004i	$0.454955\pi$
$182$	−12.0995	+	8.74074i	−0.896876	+	0.647907i
$183$	7.68730	−	18.9592i	0.568262	−	1.40150i
$184$	1.18553	−	6.72348i	0.0873985	−	0.495661i
$185$	−10.5264	−	8.83271i	−0.773917	−	0.649393i
$186$	4.45829	−	7.11515i	0.326898	−	0.521708i
$187$	−2.46589	+	6.77498i	−0.180324	+	0.495436i
$188$	2.45750			0.179232
$189$	11.9498	−	6.79723i	0.869220	−	0.494425i
$190$	1.13090			0.0820440
$191$	0.739074	−	2.03059i	0.0534775	−	0.146928i	−0.910078	−	0.414437i	$-0.863978\pi$
$191$	0.739074	−	2.03059i	0.0534775	−	0.146928i	0.963555	+	0.267509i	$0.0862006\pi$
$192$	−1.73092	−	0.0625890i	−0.124918	−	0.00451697i
$193$	5.11769	+	4.29425i	0.368380	+	0.309107i	0.808120	−	0.589018i	$-0.200485\pi$
$193$	5.11769	+	4.29425i	0.368380	+	0.309107i	−0.439741	+	0.898125i	$0.644930\pi$
$194$	2.77840	−	15.7571i	0.199478	−	1.13129i
$195$	10.6518	+	13.6685i	0.762789	+	0.978819i
$196$	−5.95638	+	3.67716i	−0.425456	+	0.262654i
$197$	16.6682	−	9.62337i	1.18756	−	0.685636i	0.229807	−	0.973236i	$-0.426191\pi$
$197$	16.6682	−	9.62337i	1.18756	−	0.685636i	0.957751	+	0.287600i	$0.0928573\pi$
$198$	4.47138	+	4.33940i	0.317767	+	0.308387i
$199$	−9.61553	−	5.55153i	−0.681627	−	0.393538i	0.118841	−	0.992913i	$-0.462082\pi$
$199$	−9.61553	−	5.55153i	−0.681627	−	0.393538i	−0.800468	+	0.599376i	$0.795416\pi$
$200$	−1.82696	+	0.322142i	−0.129186	+	0.0227789i
$201$	−3.54803	−	3.20261i	−0.250259	−	0.225895i
$202$	2.54515	+	6.99274i	0.179076	+	0.492008i
$203$	1.13285	+	3.99157i	0.0795104	+	0.280153i
$204$	−4.46319	−	4.02868i	−0.312486	−	0.282064i
$205$	−3.80509	−	21.5798i	−0.265759	−	1.50720i
$206$	−4.80435	+	8.32137i	−0.334735	+	0.579777i
$207$	−5.59676	−	19.7021i	−0.389002	−	1.36939i
$208$	4.88583	−	2.82083i	0.338771	−	0.195590i
$209$	−1.01462	+	0.851368i	−0.0701828	+	0.0588904i
$210$	4.51770	+	6.75518i	0.311751	+	0.466152i
$211$	−0.698417	+	3.96092i	−0.0480810	+	0.272681i	−0.999365	−	0.0356355i	$-0.988654\pi$
$211$	−0.698417	+	3.96092i	−0.0480810	+	0.272681i	0.951284	+	0.308316i	$0.0997656\pi$
$212$	−2.62663	+	3.13029i	−0.180397	+	0.214989i
$213$	−0.443704	+	12.2708i	−0.0304021	+	0.840780i
$214$	11.5924	+	4.21928i	0.792439	+	0.288424i
$215$	−20.7926			−1.41805
$216$	−4.75473	+	2.09583i	−0.323519	+	0.142603i
$217$	−0.929411	+	12.7922i	−0.0630925	+	0.868391i
$218$	−1.67710	+	4.60780i	−0.113588	+	0.312080i
$219$	−12.8931	−	8.07870i	−0.871235	−	0.545908i
$220$	−2.36753	+	2.82151i	−0.159619	+	0.190226i
$221$	19.2865	+	3.40074i	1.29735	+	0.228758i
$222$	−5.04300	+	12.4376i	−0.338464	+	0.834754i
$223$	−1.44632	−	1.72366i	−0.0968530	−	0.115425i	0.715441	−	0.698673i	$-0.246226\pi$
$223$	−1.44632	−	1.72366i	−0.0968530	−	0.115425i	−0.812294	+	0.583248i	$0.801781\pi$
$224$	2.38112	−	1.15336i	0.159096	−	0.0770623i
$225$	−4.51061	+	3.26013i	−0.300707	+	0.217342i
$226$	1.28951	−	2.23349i	0.0857767	−	0.148570i
$227$	2.28067	+	12.9343i	0.151373	+	0.858480i	0.962027	+	0.272954i	$0.0880008\pi$
$227$	2.28067	+	12.9343i	0.151373	+	0.858480i	−0.810654	+	0.585526i	$0.800888\pi$
$228$	−0.340024	−	1.05091i	−0.0225186	−	0.0695980i
$229$	0.999818	+	2.74698i	0.0660699	+	0.181525i	0.968334	−	0.249658i	$-0.0803183\pi$
$229$	0.999818	+	2.74698i	0.0660699	+	0.181525i	−0.902264	+	0.431184i	$0.858096\pi$
$230$	11.3770	−	4.14090i	0.750179	−	0.273043i
$231$	−9.13866	−	2.65959i	−0.601280	−	0.174988i
$232$	−0.272324	−	1.54443i	−0.0178790	−	0.101397i
$233$	−25.8229	−	14.9089i	−1.69172	−	0.976713i	−0.953133	−	0.302552i	$-0.902161\pi$
$233$	−25.8229	−	14.9089i	−1.69172	−	0.976713i	−0.738584	−	0.674161i	$-0.764505\pi$
$234$	9.49902	−	14.0080i	0.620971	−	0.915731i
$235$	2.17904	+	3.77420i	0.142145	+	0.246202i
$236$	3.46094	−	2.90407i	0.225288	−	0.189039i
$237$	−3.55904	−	25.5532i	−0.231185	−	1.65986i
$238$	8.90539	+	2.24605i	0.577251	+	0.145590i
$239$	−10.7539	+	12.8161i	−0.695615	+	0.829002i	−0.992023	−	0.126060i	$-0.959767\pi$
$239$	−10.7539	+	12.8161i	−0.695615	+	0.829002i	0.296408	+	0.955062i	$0.404211\pi$
$240$	−1.43866	−	2.71382i	−0.0928652	−	0.175176i
$241$	−0.255351	+	0.701570i	−0.0164486	+	0.0451921i	−0.947645	−	0.319325i	$-0.896544\pi$
$241$	−0.255351	+	0.701570i	−0.0164486	+	0.0451921i	0.931197	+	0.364517i	$0.118766\pi$
$242$			6.68626i			0.429809i
$243$	−10.0937	+	11.8792i	−0.647513	+	0.762054i
$244$		−	11.8117i		−	0.756163i
$245$	−10.9288	−	5.88725i	−0.698214	−	0.376122i
$246$	−18.9093	+	10.0243i	−1.20561	+	0.639124i
$247$	2.75603	+	2.31259i	0.175362	+	0.147146i
$248$	0.841801	−	4.77409i	0.0534544	−	0.303155i
$249$	0.511294	+	3.67099i	0.0324020	+	0.232640i
$250$	−7.81420	−	9.31260i	−0.494213	−	0.588981i
$251$	−12.0464	−	20.8649i	−0.760359	−	1.31698i	−0.942665	−	0.333739i	$-0.891689\pi$
$251$	−12.0464	−	20.8649i	−0.760359	−	1.31698i	0.182306	−	0.983242i	$-0.441644\pi$
$252$	4.91904	−	6.22921i	0.309871	−	0.392403i
$253$	−7.08989	+	12.2800i	−0.445737	+	0.772040i
$254$	−1.19035	+	0.209892i	−0.0746895	+	0.0131698i
$255$	2.22974	−	10.4267i	0.139632	−	0.652944i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	6.70776	−	2.44142i	0.418418	−	0.152292i	−0.124227	−	0.992254i	$-0.539645\pi$
$257$	6.70776	−	2.44142i	0.418418	−	0.152292i	0.542645	+	0.839962i	$0.317423\pi$
$258$	6.25166	+	19.3219i	0.389211	+	1.20293i
$259$	−2.08760	−	20.3944i	−0.129717	−	1.26725i
$260$	8.66440	+	5.00239i	0.537343	+	0.310235i
$261$	−2.75596	−	3.81306i	−0.170590	−	0.236023i
$262$	12.0759	−	6.97200i	0.746049	−	0.430732i
$263$	6.30630	+	7.51556i	0.388863	+	0.463429i	0.924591	−	0.380962i	$-0.124407\pi$
$263$	6.30630	+	7.51556i	0.388863	+	0.463429i	−0.535728	+	0.844391i	$0.679963\pi$
$264$	3.33377	+	1.35173i	0.205179	+	0.0831933i
$265$	−7.13646	−	1.25835i	−0.438389	−	0.0772998i
$266$	1.21050	+	1.17533i	0.0742205	+	0.0720642i
$267$	−3.95263	+	6.30815i	−0.241897	+	0.386052i
$268$	−2.59312	−	0.943819i	−0.158400	−	0.0576529i
$269$	12.9911			0.792081			0.396040	−	0.918233i	$-0.370384\pi$
$269$	12.9911			0.792081			0.396040	+	0.918233i	$0.370384\pi$
$270$	−7.43472	−	5.44391i	−0.452462	−	0.331306i
$271$		−	1.36547i		−	0.0829461i	−0.999140	−	0.0414731i	$-0.986795\pi$
$271$		−	1.36547i		−	0.0829461i	0.999140	−	0.0414731i	$-0.0132051\pi$
$272$	−3.26198	−	1.18726i	−0.197787	−	0.0719884i
$273$	−2.80398	+	25.7009i	−0.169704	+	1.55549i
$274$	−2.13484	−	1.79134i	−0.128970	−	0.108219i
$275$	3.79451	+	0.669075i	0.228818	+	0.0403467i
$276$	−7.26870	−	9.32727i	−0.437524	−	0.561436i
$277$	−20.8788	+	17.5194i	−1.25449	+	1.05264i	−0.258239	+	0.966081i	$0.583142\pi$
$277$	−20.8788	+	17.5194i	−1.25449	+	1.05264i	−0.996247	+	0.0865576i	$0.972413\pi$
$278$	−1.05196	−	1.82206i	−0.0630926	−	0.109280i
$279$	−3.97405	−	13.9897i	−0.237920	−	0.837542i
$280$	3.88263	+	2.63423i	0.232032	+	0.157425i
$281$	19.3156	−	3.40587i	1.15227	−	0.203177i	0.435306	−	0.900283i	$-0.356640\pi$
$281$	19.3156	−	3.40587i	1.15227	−	0.203177i	0.716969	+	0.697106i	$0.245529\pi$
$282$	2.85208	−	3.15968i	0.169839	−	0.188156i
$283$	−1.69987	−	4.67036i	−0.101047	−	0.277624i	0.878860	−	0.477080i	$-0.158305\pi$
$283$	−1.69987	−	4.67036i	−0.101047	−	0.277624i	−0.979907	+	0.199456i	$0.936083\pi$
$284$	2.42464	+	6.66164i	0.143876	+	0.395296i
$285$	1.31247	−	1.45403i	0.0777443	−	0.0861293i
$286$	−11.5395	+	2.03472i	−0.682343	+	0.120315i
$287$	18.3547	−	27.0533i	1.08344	−	1.59691i
$288$	−2.08931	+	2.15286i	−0.123114	+	0.126858i
$289$	2.47495	+	4.28674i	0.145585	+	0.252161i
$290$	2.13045	−	1.78766i	0.125104	−	0.104975i
$291$	−17.0349	−	21.8593i	−0.998602	−	1.28142i
$292$	−8.65095	−	1.52540i	−0.506259	−	0.0892671i
$293$	10.9098	+	9.15438i	0.637355	+	0.534805i	0.903205	−	0.429210i	$-0.141208\pi$
$293$	10.9098	+	9.15438i	0.637355	+	0.534805i	−0.265850	+	0.964015i	$0.585652\pi$
$294$	−2.18491	+	11.9259i	−0.127426	+	0.695530i
$295$	7.52880	+	2.74026i	0.438344	+	0.159544i
$296$			7.74865i			0.450381i
$297$	10.7686	−	0.712865i	0.624858	−	0.0413646i
$298$	−6.65138			−0.385304
$299$	36.1939	+	13.1735i	2.09315	+	0.761844i
$300$	−1.70611	+	2.72284i	−0.0985022	+	0.157203i
$301$	−22.2562	−	21.6096i	−1.28283	−	1.24556i
$302$	10.0700	+	1.77561i	0.579462	+	0.102175i
$303$	11.9446	+	4.84312i	0.686198	+	0.278230i
$304$	−0.409912	−	0.488514i	−0.0235101	−	0.0280182i
$305$	18.1402	−	10.4732i	1.03870	−	0.599696i
$306$	−10.3596	+	1.06293i	−0.592218	+	0.0607636i
$307$	26.1304	+	15.0864i	1.49134	+	0.861024i	0.999951	−	0.00991695i	$-0.00315672\pi$
$307$	26.1304	+	15.0864i	1.49134	+	0.861024i	0.491387	+	0.870941i	$0.336490\pi$
$308$	−5.46654	+	0.559561i	−0.311485	+	0.0318839i
$309$	5.12331	+	15.8345i	0.291455	+	0.900795i
$310$	8.07840	−	2.94030i	0.458822	−	0.166998i
$311$	−29.6384	+	10.7875i	−1.68064	+	0.611703i	−0.993397	−	0.114725i	$-0.963401\pi$
$311$	−29.6384	+	10.7875i	−1.68064	+	0.611703i	−0.687242	+	0.726428i	$0.741179\pi$
$312$	2.04346	−	9.55560i	0.115688	−	0.540979i
$313$	18.0348	−	3.18002i	1.01939	−	0.179745i	0.361111	−	0.932523i	$-0.382398\pi$
$313$	18.0348	−	3.18002i	1.01939	−	0.179745i	0.658275	+	0.752778i	$0.271286\pi$
$314$	−9.06228	+	15.6963i	−0.511414	+	0.885795i
$315$	13.9284	+	2.03125i	0.784776	+	0.114448i
$316$	−7.44779	−	12.8999i	−0.418971	−	0.725679i
$317$	10.9318	+	13.0280i	0.613988	+	0.731723i	0.980024	−	0.198878i	$-0.0637297\pi$
$317$	10.9318	+	13.0280i	0.613988	+	0.731723i	−0.366036	+	0.930601i	$0.619285\pi$
$318$	0.976353	+	7.01002i	0.0547511	+	0.393102i
$319$	−0.565605	+	3.20771i	−0.0316678	+	0.179597i
$320$	−1.35848	−	1.13990i	−0.0759415	−	0.0637225i
$321$	18.8785	−	10.0079i	1.05370	−	0.558589i
$322$	16.4814	+	7.39167i	0.918474	+	0.411922i
$323$		−	2.21370i		−	0.123173i
$324$	−2.82347	+	8.54564i	−0.156860	+	0.474758i
$325$		−	10.4661i		−	0.580555i
$326$	0.931329	−	2.55881i	0.0515816	−	0.141719i
$327$	3.97801	+	7.50393i	0.219985	+	0.414968i
$328$	−7.94259	+	9.46561i	−0.438556	+	0.522651i
$329$	−1.59008	+	6.30451i	−0.0876638	+	0.347579i
$330$	0.880042	+	6.31853i	0.0484447	+	0.347823i
$331$	−4.20543	+	3.52877i	−0.231151	+	0.193959i	−0.751005	−	0.660296i	$-0.770431\pi$
$331$	−4.20543	+	3.52877i	−0.231151	+	0.193959i	0.519854	+	0.854255i	$0.325986\pi$
$332$	1.06995	+	1.85321i	0.0587213	+	0.101708i
$333$	10.1386	+	20.9185i	0.555593	+	1.14632i
$334$	9.06210	+	5.23200i	0.495856	+	0.286283i
$335$	−0.849783	−	4.81936i	−0.0464286	−	0.263310i
$336$	1.28052	−	4.40003i	0.0698583	−	0.240041i
$337$	−20.0754	+	7.30684i	−1.09358	+	0.398029i	−0.824944	−	0.565214i	$-0.808794\pi$
$337$	−20.0754	+	7.30684i	−1.09358	+	0.398029i	−0.268632	+	0.963243i	$0.586571\pi$
$338$	6.43969	+	17.6929i	0.350273	+	0.962367i
$339$	−1.37512	−	4.25005i	−0.0746861	−	0.230831i
$340$	−1.06897	−	6.06244i	−0.0579731	−	0.328782i
$341$	−5.03427	+	8.71960i	−0.272621	+	0.472193i
$342$	−1.74580	−	0.782461i	−0.0944020	−	0.0423107i
$343$	−5.57948	−	17.6598i	−0.301264	−	0.953541i
$344$	7.53662	+	8.98180i	0.406348	+	0.484266i
$345$	7.87964	−	19.4335i	0.424225	−	1.04627i
$346$	8.47615	+	1.49457i	0.455680	+	0.0803488i
$347$	9.29360	−	11.0757i	0.498907	−	0.594574i	−0.456553	−	0.889696i	$-0.650916\pi$
$347$	9.29360	−	11.0757i	0.498907	−	0.594574i	0.955459	+	0.295123i	$0.0953605\pi$
$348$	−2.30177	−	1.44227i	−0.123388	−	0.0773136i
$349$	8.89459	−	24.4377i	0.476117	−	1.30812i	−0.436647	−	0.899633i	$-0.643834\pi$
$349$	8.89459	−	24.4377i	0.476117	−	1.30812i	0.912764	−	0.408487i	$-0.133944\pi$
$350$	0.355669	−	4.89535i	0.0190113	−	0.261667i
$351$	−6.98632	−	28.4703i	−0.372902	−	1.51963i
$352$	2.07695			0.110702
$353$	30.9320	+	11.2583i	1.64634	+	0.599220i	0.988131	−	0.153612i	$-0.0490906\pi$
$353$	30.9320	+	11.2583i	1.64634	+	0.599220i	0.658213	+	0.752832i	$0.271313\pi$
$354$	0.282773	−	7.82017i	0.0150292	−	0.415638i
$355$	−8.08097	+	9.63052i	−0.428893	+	0.511135i
$356$	−0.746323	+	4.23261i	−0.0395551	+	0.224328i
$357$	13.2231	−	8.84325i	0.699838	−	0.468034i
$358$	11.9529	−	10.0297i	0.631732	−	0.530086i
$359$	−22.2968	+	12.8731i	−1.17678	+	0.679414i	−0.955267	−	0.295744i	$-0.904433\pi$
$359$	−22.2968	+	12.8731i	−1.17678	+	0.679414i	−0.221512	+	0.975158i	$0.571099\pi$
$360$	−5.15889	−	1.29982i	−0.271898	−	0.0685066i
$361$	−9.29666	+	16.1023i	−0.489298	+	0.847489i
$362$	1.74213	+	9.88013i	0.0915645	+	0.519288i
$363$	8.59673	+	7.75981i	0.451211	+	0.407284i
$364$	4.07533	+	14.3593i	0.213605	+	0.752633i
$365$	−5.32801	−	14.6386i	−0.278881	−	0.766218i
$366$	−15.1866	−	13.7081i	−0.793816	−	0.716535i
$367$	−3.84666	+	0.678270i	−0.200794	+	0.0354054i	−0.273141	−	0.961974i	$-0.588062\pi$
$367$	−3.84666	+	0.678270i	−0.200794	+	0.0354054i	0.0723464	+	0.997380i	$0.476951\pi$
$368$	−5.91253	−	3.41360i	−0.308212	−	0.177946i
$369$	−9.05687	+	35.9460i	−0.471482	+	1.87127i
$370$	−11.9003	+	6.87063i	−0.618666	+	0.357187i
$371$	−6.33099	−	8.76378i	−0.328689	−	0.454993i
$372$	−5.16123	−	6.62295i	−0.267597	−	0.343384i
$373$	−0.674656	+	3.82617i	−0.0349324	+	0.198111i	−0.997280	−	0.0737118i	$-0.976515\pi$
$373$	−0.674656	+	3.82617i	−0.0349324	+	0.198111i	0.962347	+	0.271823i	$0.0876266\pi$
$374$	5.52301	+	4.63436i	0.285588	+	0.239637i
$375$	−21.0423	−	0.760878i	−1.08662	−	0.0392916i
$376$	0.840515	−	2.30930i	0.0433463	−	0.119093i
$377$	8.84757			0.455673
$378$	−2.30023	−	13.5539i	−0.118311	−	0.697139i
$379$	21.8630			1.12303			0.561513	−	0.827468i	$-0.310220\pi$
$379$	21.8630			1.12303			0.561513	+	0.827468i	$0.310220\pi$
$380$	0.386790	−	1.06270i	0.0198419	−	0.0545152i
$381$	−1.11161	+	1.77407i	−0.0569497	+	0.0908881i
$382$	−1.65535	−	1.38900i	−0.0846952	−	0.0710677i
$383$	4.06119	−	23.0321i	0.207517	−	1.17689i	−0.685912	−	0.727684i	$-0.740597\pi$
$383$	4.06119	−	23.0321i	0.207517	−	1.17689i	0.893429	−	0.449204i	$-0.148292\pi$
$384$	−0.650824	+	1.60513i	−0.0332122	+	0.0819112i
$385$	−5.70648	−	7.89929i	−0.290829	−	0.402585i
$386$	5.78563	−	3.34034i	0.294481	−	0.170019i
$387$	32.0982	+	14.3863i	1.63164	+	0.731297i
$388$	−13.8566	−	8.00009i	−0.703460	−	0.406143i
$389$	32.2633	−	5.68889i	1.63581	−	0.288438i	0.721188	−	0.692739i	$-0.243596\pi$
$389$	32.2633	−	5.68889i	1.63581	−	0.288438i	0.914626	+	0.404301i	$0.132485\pi$
$390$	16.4873	−	5.33450i	0.834866	−	0.270123i
$391$	−8.10568	−	22.2702i	−0.409922	−	1.12625i
$392$	1.41820	+	6.85483i	0.0716297	+	0.346221i
$393$	5.05064	−	23.6177i	0.254771	−	1.19136i
$394$	−3.34216	−	18.9543i	−0.168376	−	0.954905i
$395$	13.2077	−	22.8764i	0.664552	−	1.15104i
$396$	5.60700	−	2.71757i	0.281762	−	0.136563i
$397$	10.4953	−	6.05944i	0.526742	−	0.304115i	−0.212947	−	0.977064i	$-0.568306\pi$
$397$	10.4953	−	6.05944i	0.526742	−	0.304115i	0.739689	+	0.672949i	$0.234973\pi$
$398$	−8.50544	+	7.13691i	−0.426339	+	0.357741i
$399$	2.91602	−	0.192333i	0.145983	−	0.00962871i
$400$	−0.322142	+	1.82696i	−0.0161071	+	0.0913480i
$401$	−2.94532	+	3.51010i	−0.147082	+	0.175286i	−0.834556	−	0.550924i	$-0.814275\pi$
$401$	−2.94532	+	3.51010i	−0.147082	+	0.175286i	0.687473	+	0.726210i	$0.258720\pi$
$402$	−4.22297	+	2.23870i	−0.210623	+	0.111656i
$403$	25.7000	+	9.35402i	1.28021	+	0.465957i
$404$	7.44152			0.370230
$405$	−15.6278	+	3.24106i	−0.776553	+	0.161049i
$406$	4.13830	+	0.300666i	0.205381	+	0.0149218i
$407$	5.50433	−	15.1230i	0.272839	−	0.749620i
$408$	−5.31222	+	2.81613i	−0.262994	+	0.139419i
$409$	−8.25267	+	9.83515i	−0.408068	+	0.486317i	−0.930462	−	0.366387i	$-0.880595\pi$
$409$	−8.25267	+	9.83515i	−0.408068	+	0.486317i	0.522394	+	0.852704i	$0.325039\pi$
$410$	−21.5798	−	3.80509i	−1.06575	−	0.187920i
$411$	−4.78079	+	0.665867i	−0.235819	+	0.0328448i
$412$	6.17635	+	7.36069i	0.304287	+	0.362635i
$413$	5.21081	+	10.7578i	0.256407	+	0.529354i
$414$	−20.4281	−	1.47927i	−1.00399	−	0.0727021i
$415$	−1.89743	+	3.28644i	−0.0931411	+	0.161325i
$416$	−0.979665	−	5.55596i	−0.0480320	−	0.272403i
$417$	−3.56354	−	0.762062i	−0.174507	−	0.0373184i
$418$	0.453004	+	1.24462i	0.0221571	+	0.0608762i
$419$	−30.7085	+	11.1770i	−1.50021	+	0.546032i	−0.956115	−	0.292991i	$-0.905349\pi$
$419$	−30.7085	+	11.1770i	−1.50021	+	0.546032i	−0.544095	+	0.839023i	$0.683127\pi$
$420$	7.89293	−	1.93484i	0.385136	−	0.0944104i
$421$	1.00354	+	5.69138i	0.0489097	+	0.277381i	0.999448	−	0.0332271i	$-0.0105785\pi$
$421$	1.00354	+	5.69138i	0.0489097	+	0.277381i	−0.950538	+	0.310608i	$0.899467\pi$
$422$	3.48317	+	2.01101i	0.169558	+	0.0978945i
$423$	−0.752494	−	7.33400i	−0.0365875	−	0.356591i
$424$	2.04315	+	3.53884i	0.0992243	+	0.171861i
$425$	−4.93318	+	4.13943i	−0.239294	+	0.200792i
$426$	11.3790	+	4.61380i	0.551315	+	0.223539i
$427$	30.3018	+	7.64249i	1.46641	+	0.369846i
$428$	7.92965	−	9.45019i	0.383294	−	0.456792i
$429$	−10.7761	+	17.1980i	−0.520277	+	0.830329i
$430$	−7.11150	+	19.5387i	−0.342947	+	0.942240i
$431$			13.0385i			0.628042i	0.949416	+	0.314021i	$0.101676\pi$
$431$			13.0385i			0.628042i	−0.949416	+	0.314021i	$0.898324\pi$
$432$	0.343226	+	5.18480i	0.0165135	+	0.249454i
$433$			29.6219i			1.42354i	0.702414	+	0.711769i	$0.252106\pi$
$433$			29.6219i			1.42354i	−0.702414	+	0.711769i	$0.747894\pi$
$434$	11.7029	+	5.24855i	0.561755	+	0.251938i
$435$	0.174066	−	4.81386i	0.00834584	−	0.230807i
$436$	3.75632	+	3.15192i	0.179895	+	0.150950i
$437$	0.756024	−	4.28763i	0.0361655	−	0.205105i
$438$	−12.0012	+	9.35248i	−0.573439	+	0.446879i
$439$	16.7245	+	19.9315i	0.798217	+	0.951279i	0.999601	−	0.0282339i	$-0.00898831\pi$
$439$	16.7245	+	19.9315i	0.798217	+	0.951279i	−0.201384	+	0.979512i	$0.564544\pi$
$440$	1.84161	+	3.18976i	0.0877952	+	0.152066i
$441$	12.7977	+	16.6499i	0.609415	+	0.792851i
$442$	9.79203	−	16.9603i	0.465759	−	0.806719i
$443$	−37.1349	+	6.54788i	−1.76433	+	0.311099i	−0.959354	−	0.282206i	$-0.908934\pi$
$443$	−37.1349	+	6.54788i	−1.76433	+	0.311099i	−0.804978	+	0.593305i	$0.797823\pi$
$444$	9.96267	+	8.99277i	0.472807	+	0.426778i
$445$	−7.16214	+	2.60681i	−0.339518	+	0.123575i
$446$	−2.11438	+	0.769573i	−0.100119	+	0.0364403i
$447$	−7.71933	+	8.55188i	−0.365112	+	0.404490i
$448$	−0.269414	−	2.63200i	−0.0127286	−	0.124350i
$449$	−9.24683	−	5.33866i	−0.436385	−	0.251947i	0.265678	−	0.964062i	$-0.414404\pi$
$449$	−9.24683	−	5.33866i	−0.436385	−	0.251947i	−0.702063	+	0.712115i	$0.747737\pi$
$450$	1.52080	+	5.35361i	0.0716912	+	0.252372i
$451$	22.2255	−	12.8319i	1.04656	−	0.604231i
$452$	−1.65776	−	1.97564i	−0.0779743	−	0.0929262i
$453$	13.9698	−	10.8866i	0.656356	−	0.511495i
$454$	12.9343	+	2.28067i	0.607037	+	0.107037i
$455$	−18.4393	+	18.9911i	−0.864449	+	0.890315i
$456$	−1.10382	−	0.0399136i	−0.0516913	−	0.00186913i
$457$	1.92677	+	0.701287i	0.0901306	+	0.0328048i	0.386692	−	0.922209i	$-0.373618\pi$
$457$	1.92677	+	0.701287i	0.0901306	+	0.0328048i	−0.296561	+	0.955014i	$0.595840\pi$
$458$	2.92327			0.136596
$459$	−10.6563	+	14.5532i	−0.497393	+	0.679286i
$460$		−	12.1072i		−	0.564500i
$461$	−35.9523	−	13.0856i	−1.67447	−	0.609456i	−0.681931	−	0.731417i	$-0.738859\pi$
$461$	−35.9523	−	13.0856i	−1.67447	−	0.609456i	−0.992535	+	0.121961i	$0.961082\pi$
$462$	−5.62480	+	7.67790i	−0.261689	+	0.357208i
$463$	18.9148	+	15.8714i	0.879047	+	0.737608i	0.965983	−	0.258606i	$-0.0832632\pi$
$463$	18.9148	+	15.8714i	0.879047	+	0.737608i	−0.0869363	+	0.996214i	$0.527708\pi$
$464$	−1.54443	−	0.272324i	−0.0716983	−	0.0126423i
$465$	5.59504	−	13.7990i	0.259464	−	0.639915i
$466$	−22.8417	+	19.1665i	−1.05812	+	0.887870i
$467$	12.3557	+	21.4006i	0.571752	+	0.990303i	0.996386	+	0.0849381i	$0.0270692\pi$
$467$	12.3557	+	21.4006i	0.571752	+	0.990303i	−0.424635	+	0.905365i	$0.639597\pi$
$468$	−9.91435	−	13.7172i	−0.458291	−	0.634077i
$469$	4.09912	−	6.04175i	0.189280	−	0.278982i
$470$	4.29186	−	0.756771i	0.197969	−	0.0349072i
$471$	9.66393	+	29.8682i	0.445290	+	1.37625i
$472$	−1.54522	−	4.24547i	−0.0711247	−	0.195413i
$473$	−8.32890	−	22.8835i	−0.382963	−	1.05218i
$474$	−25.2294	−	5.39531i	−1.15883	−	0.247815i
$475$	−1.16507	+	0.205433i	−0.0534571	+	0.00942592i
$476$	5.15642	−	7.60013i	0.236344	−	0.348352i
$477$	10.1461	+	6.88022i	0.464558	+	0.315024i
$478$	8.36509	+	14.4888i	0.382610	+	0.662700i
$479$	17.7163	−	14.8657i	0.809478	−	0.679233i	−0.141005	−	0.990009i	$-0.545033\pi$
$479$	17.7163	−	14.8657i	0.809478	−	0.679233i	0.950483	+	0.310776i	$0.100589\pi$
$480$	−3.04221	+	0.423717i	−0.138857	+	0.0193400i
$481$	−43.0511	−	7.59108i	−1.96296	−	0.346123i
$482$	0.571925	+	0.479902i	0.0260505	+	0.0218590i
$483$	28.6314	−	12.6122i	1.30277	−	0.573875i
$484$	6.28303	+	2.28684i	0.285592	+	0.103947i
$485$		−	28.3743i		−	1.28841i
$486$	7.71058	+	13.5480i	0.349759	+	0.614548i
$487$	−8.83685			−0.400436			−0.200218	−	0.979751i	$-0.564165\pi$
$487$	−8.83685			−0.400436			−0.200218	+	0.979751i	$0.564165\pi$
$488$	−11.0993	−	4.03982i	−0.502443	−	0.182874i
$489$	−2.20907	−	4.16709i	−0.0998976	−	0.188442i
$490$	−9.27007	+	8.25614i	−0.418779	+	0.372974i
$491$	−10.1997	−	1.79848i	−0.460306	−	0.0811645i	−0.0613137	−	0.998119i	$-0.519529\pi$
$491$	−10.1997	−	1.79848i	−0.460306	−	0.0811645i	−0.398993	+	0.916954i	$0.630640\pi$
$492$	2.95237	+	21.1974i	0.133103	+	0.955654i
$493$	−3.49929	−	4.17029i	−0.157600	−	0.187820i
$494$	3.11574	−	1.79887i	0.140184	−	0.0809351i
$495$	9.14526	+	6.20153i	0.411049	+	0.278738i
$496$	−4.19827	−	2.42387i	−0.188508	−	0.108835i
$497$	−18.6587	+	1.90992i	−0.836956	+	0.0856718i
$498$	3.62448	+	0.775094i	0.162417	+	0.0347328i
$499$	18.1616	−	6.61029i	0.813026	−	0.295917i	0.0981526	−	0.995171i	$-0.468707\pi$
$499$	18.1616	−	6.61029i	0.813026	−	0.295917i	0.714873	+	0.699254i	$0.246484\pi$
$500$	−11.4236	+	4.15785i	−0.510879	+	0.185945i
$501$	17.2440	−	5.57936i	0.770407	−	0.249267i
$502$	−23.7267	+	4.18366i	−1.05897	+	0.186726i
$503$	−11.8158	+	20.4656i	−0.526842	+	0.912517i	0.472669	+	0.881240i	$0.343291\pi$
$503$	−11.8158	+	20.4656i	−0.526842	+	0.912517i	−0.999511	+	0.0312769i	$0.990043\pi$
$504$	−4.17113	−	6.75290i	−0.185797	−	0.300798i
$505$	6.59830	+	11.4286i	0.293621	+	0.508566i
$506$	9.11458	+	10.8623i	0.405193	+	0.482890i
$507$	30.2219	+	12.2540i	1.34220	+	0.544217i
$508$	−0.209892	+	1.19035i	−0.00931243	+	0.0528134i
$509$	−24.1538	−	20.2675i	−1.07060	−	0.898340i	−0.0754928	−	0.997146i	$-0.524053\pi$
$509$	−24.1538	−	20.2675i	−1.07060	−	0.898340i	−0.995107	+	0.0988067i	$0.968497\pi$
$510$	−9.03526	−	5.66141i	−0.400088	−	0.250691i
$511$	9.51070	−	21.2063i	0.420729	−	0.938112i
$512$			1.00000i			0.0441942i
$513$	−3.03214	+	1.33653i	−0.133872	+	0.0590094i
$514$		−	7.13824i		−	0.314854i
$515$	−5.82796	+	16.0122i	−0.256810	+	0.705581i
$516$	20.2949	+	0.733850i	0.893432	+	0.0323059i
$517$	−3.28086	+	3.90998i	−0.144292	+	0.171961i
$518$	−19.8785	−	5.01361i	−0.873411	−	0.220285i
$519$	11.7587	−	9.16349i	0.516149	−	0.402233i
$520$	7.66411	−	6.43095i	0.336093	−	0.282016i
$521$	−8.81233	−	15.2634i	−0.386075	−	0.668702i	0.605843	−	0.795585i	$-0.292836\pi$
$521$	−8.81233	−	15.2634i	−0.386075	−	0.668702i	−0.991918	+	0.126883i	$0.959503\pi$
$522$	−4.52570	+	1.28562i	−0.198085	+	0.0562698i
$523$	−19.8219	−	11.4442i	−0.866749	−	0.500418i	−0.000482485	−	1.00000i	$-0.500154\pi$
$523$	−19.8219	−	11.4442i	−0.866749	−	0.500418i	−0.866267	+	0.499582i	$0.833487\pi$
$524$	−2.42135	−	13.7322i	−0.105777	−	0.599892i
$525$	−5.88132	−	6.13863i	−0.256682	−	0.267912i
$526$	9.21920	−	3.35551i	0.401976	−	0.146307i
$527$	−5.75554	−	15.8132i	−0.250715	−	0.688835i
$528$	2.41043	−	2.67040i	0.104900	−	0.116214i
$529$	−4.09994	−	23.2519i	−0.178258	−	1.01095i
$530$	−3.62327	+	6.27569i	−0.157385	+	0.272599i
$531$	−9.72646	−	9.43935i	−0.422092	−	0.409633i
$532$	1.51847	−	0.735511i	0.0658339	−	0.0318884i
$533$	−44.8094	−	53.4018i	−1.94091	−	2.31309i
$534$	4.57584	+	5.87177i	0.198016	+	0.254096i
$535$	21.5446	+	3.79890i	0.931455	+	0.164241i
$536$	−1.77380	+	2.11393i	−0.0766165	+	0.0913080i
$537$	0.976603	−	27.0083i	0.0421435	−	1.16549i
$538$	4.44321	−	12.2076i	0.191561	−	0.526308i
$539$	2.10151	−	14.3860i	0.0905184	−	0.619649i
$540$	−7.65842	+	5.12442i	−0.329566	+	0.220520i
$541$	−15.2548			−0.655856			−0.327928	−	0.944703i	$-0.606350\pi$
$541$	−15.2548			−0.655856			−0.327928	+	0.944703i	$0.606350\pi$
$542$	−1.28312	−	0.467017i	−0.0551146	−	0.0200601i
$543$	14.7250	+	9.22656i	0.631911	+	0.395950i
$544$	−2.23133	+	2.65919i	−0.0956673	+	0.114012i
$545$	−1.51001	+	8.56367i	−0.0646816	+	0.366827i
$546$	23.1919	+	11.4251i	0.992521	+	0.488949i
$547$	−30.2345	+	25.3698i	−1.29273	+	1.08473i	−0.301382	+	0.953503i	$0.597448\pi$
$547$	−30.2345	+	25.3698i	−1.29273	+	1.08473i	−0.991352	+	0.131229i	$0.958108\pi$
$548$	−2.41347	+	1.39342i	−0.103098	+	0.0595239i
$549$	−35.2499	+	3.61676i	−1.50443	+	0.154360i
$550$	1.92652	−	3.33684i	0.0821473	−	0.142283i
$551$	−0.173664	−	0.984897i	−0.00739833	−	0.0419580i
$552$	−11.2508	+	3.64023i	−0.478866	+	0.154938i
$553$	37.9126	−	10.7600i	1.61221	−	0.457562i
$554$	9.32188	+	25.6116i	0.396049	+	1.08813i
$555$	−4.97721	+	23.2743i	−0.211271	+	0.987939i
$556$	−2.07197	+	0.365343i	−0.0878709	+	0.0154940i
$557$	−13.1835	−	7.61149i	−0.558602	−	0.322509i	0.193982	−	0.981005i	$-0.437860\pi$
$557$	−13.1835	−	7.61149i	−0.558602	−	0.322509i	−0.752584	+	0.658496i	$0.771193\pi$
$558$	−14.5052	−	1.05037i	−0.614056	−	0.0444659i
$559$	−57.2858	+	33.0740i	−2.42293	+	1.39888i
$560$	3.80330	−	2.74752i	0.160719	−	0.116104i
$561$	12.3683	−	1.72265i	0.522191	−	0.0727305i
$562$	3.40587	−	19.3156i	0.143668	−	0.814781i
$563$	−5.96327	−	5.00377i	−0.251322	−	0.210884i	0.508420	−	0.861110i	$-0.330230\pi$
$563$	−5.96327	−	5.00377i	−0.251322	−	0.210884i	−0.759741	+	0.650226i	$0.774674\pi$
$564$	−1.99366	−	3.76075i	−0.0839484	−	0.158356i
$565$	1.56425	−	4.29773i	0.0658084	−	0.180807i
$566$	−4.97010			−0.208909
$567$	−20.0962	−	12.7727i	−0.843963	−	0.536402i
$568$	7.08917			0.297455
$569$	−2.01583	+	5.53845i	−0.0845081	+	0.232184i	−0.974748	−	0.223308i	$-0.928314\pi$
$569$	−2.01583	+	5.53845i	−0.0845081	+	0.232184i	0.890240	+	0.455492i	$0.150537\pi$
$570$	−0.917448	−	1.73063i	−0.0384277	−	0.0724881i
$571$	−9.75363	−	8.18427i	−0.408177	−	0.342501i	0.415467	−	0.909608i	$-0.363618\pi$
$571$	−9.75363	−	8.18427i	−0.408177	−	0.342501i	−0.823644	+	0.567107i	$0.808063\pi$
$572$	−2.03472	+	11.5395i	−0.0850759	+	0.482489i
$573$	−3.70702	+	0.516312i	−0.154863	+	0.0215692i
$574$	−19.1441	−	26.5006i	−0.799060	−	1.10611i
$575$	−10.9686	+	6.33272i	−0.457422	+	0.264092i
$576$	1.30844	+	2.69963i	0.0545183	+	0.112484i
$577$	33.6737	+	19.4415i	1.40186	+	0.809362i	0.994583	−	0.103944i	$-0.0331464\pi$
$577$	33.6737	+	19.4415i	1.40186	+	0.809362i	0.407273	+	0.913306i	$0.366480\pi$
$578$	4.87470	−	0.859541i	0.202761	−	0.0357522i
$579$	2.41980	−	11.3154i	0.100563	−	0.470253i
$580$	−0.951193	−	2.61338i	−0.0394961	−	0.108515i
$581$	−5.44656	+	1.54579i	−0.225961	+	0.0641302i
$582$	−26.3673	+	8.53121i	−1.09296	+	0.353630i
$583$	−1.47376	−	8.35813i	−0.0610371	−	0.346158i
$584$	−4.39220	+	7.60752i	−0.181751	+	0.314801i
$585$	12.2757	−	27.3892i	0.507539	−	1.13240i
$586$	12.3337	−	7.12084i	0.509499	−	0.294159i
$587$	16.1574	−	13.5576i	0.666886	−	0.559583i	−0.245256	−	0.969458i	$-0.578872\pi$
$587$	16.1574	−	13.5576i	0.666886	−	0.559583i	0.912142	+	0.409875i	$0.134428\pi$
$588$	10.4594	+	6.13202i	0.431337	+	0.252880i
$589$	0.536825	−	3.04448i	0.0221195	−	0.125446i
$590$	5.15000	−	6.13753i	0.212022	−	0.252678i
$591$	−28.2489	−	17.7005i	−1.16201	−	0.728102i
$592$	7.28135	+	2.65019i	0.299261	+	0.108922i
$593$	−33.5431			−1.37745			−0.688725	−	0.725022i	$-0.741829\pi$
$593$	−33.5431			−1.37745			−0.688725	+	0.725022i	$0.741829\pi$
$594$	3.01320	−	10.3630i	0.123633	−	0.425199i
$595$	16.2443	+	1.18022i	0.665952	+	0.0483845i
$596$	−2.27491	+	6.25026i	−0.0931838	+	0.256020i
$597$	−0.694929	+	19.2185i	−0.0284416	+	0.786561i
$598$	24.7581	−	29.5056i	1.01243	−	1.20657i
$599$	28.1206	+	4.95842i	1.14898	+	0.202595i	0.715529	−	0.698583i	$-0.246186\pi$
$599$	28.1206	+	4.95842i	1.14898	+	0.202595i	0.433447	+	0.901179i	$0.357297\pi$
$600$	1.97511	+	2.53448i	0.0806336	+	0.103470i
$601$	−29.4948	−	35.1505i	−1.20312	−	1.43382i	−0.871493	−	0.490408i	$-0.836848\pi$
$601$	−29.4948	−	35.1505i	−1.20312	−	1.43382i	−0.331624	−	0.943412i	$-0.607597\pi$
$602$	−27.9185	+	13.5231i	−1.13787	+	0.551159i
$603$	−2.02265	+	8.02774i	−0.0823686	+	0.326915i
$604$	5.11266	−	8.85538i	0.208031	−	0.360320i
$605$	2.05899	+	11.6771i	0.0837098	+	0.474742i
$606$	8.63633	−	9.56779i	0.350827	−	0.388665i
$607$	−8.30249	−	22.8109i	−0.336988	−	0.925866i	−0.986244	−	0.165296i	$-0.947142\pi$
$607$	−8.30249	−	22.8109i	−0.336988	−	0.925866i	0.649256	−	0.760570i	$-0.275080\pi$
$608$	−0.599251	+	0.218110i	−0.0243028	+	0.00884551i
$609$	5.18932	−	4.97180i	0.210282	−	0.201467i
$610$	−3.63732	−	20.6283i	−0.147271	−	0.835214i
$611$	12.0069	+	6.93220i	0.485748	+	0.280447i
$612$	−2.54436	+	10.0984i	−0.102850	+	0.408203i
$613$	−0.687800	−	1.19130i	−0.0277800	−	0.0481163i	0.851801	−	0.523865i	$-0.175510\pi$
$613$	−0.687800	−	1.19130i	−0.0277800	−	0.0481163i	−0.879581	+	0.475749i	$0.842177\pi$
$614$	23.1137	−	19.3947i	0.932791	−	0.782705i
$615$	−29.9369	+	23.3297i	−1.20717	+	0.940744i
$616$	−1.34385	+	5.32825i	−0.0541453	+	0.214681i
$617$	−8.29436	+	9.88484i	−0.333918	+	0.397948i	−0.906711	−	0.421752i	$-0.861415\pi$
$617$	−8.29436	+	9.88484i	−0.333918	+	0.397948i	0.572793	+	0.819700i	$0.305860\pi$
$618$	16.6319	+	0.601398i	0.669032	+	0.0241918i
$619$	−1.20175	+	3.30179i	−0.0483025	+	0.132710i	−0.961498	−	0.274811i	$-0.911385\pi$
$619$	−1.20175	+	3.30179i	−0.0483025	+	0.132710i	0.913196	+	0.407521i	$0.133607\pi$
$620$		−	8.59686i		−	0.345258i
$621$	−25.6100	+	24.5482i	−1.02769	+	0.985087i
$622$			31.5405i			1.26466i
$623$	−10.3755	−	4.65325i	−0.415686	−	0.186429i
$624$	−8.28042	−	5.18843i	−0.331482	−	0.207704i
$625$	−9.40911	−	7.89518i	−0.376365	−	0.315807i
$626$	3.18002	−	18.0348i	0.127099	−	0.720815i
$627$	2.12598	+	0.862012i	0.0849034	+	0.0344254i
$628$	11.6502	+	13.8842i	0.464895	+	0.554041i
$629$	13.4490	+	23.2944i	0.536248	+	0.928809i
$630$	6.67254	−	12.3937i	0.265840	−	0.493776i
$631$	−2.33391	+	4.04244i	−0.0929113	+	0.160927i	−0.908735	−	0.417374i	$-0.862951\pi$
$631$	−2.33391	+	4.04244i	−0.0929113	+	0.160927i	0.815824	+	0.578301i	$0.196284\pi$
$632$	−14.6693	+	2.58659i	−0.583512	+	0.102889i
$633$	6.62805	−	2.14452i	0.263441	−	0.0852371i
$634$	15.9812	−	5.81666i	0.634693	−	0.231009i
$635$	−2.01424	+	0.733123i	−0.0799326	+	0.0290931i
$636$	6.92120	+	1.48010i	0.274443	+	0.0586897i
$637$	−39.4745	+	1.16399i	−1.56404	+	0.0461191i
$638$	2.82081	+	1.62860i	0.111677	+	0.0644767i
$639$	19.1381	−	9.27574i	0.757092	−	0.366943i
$640$	−1.53579	+	0.886687i	−0.0607073	+	0.0350494i
$641$	−18.6911	−	22.2752i	−0.738253	−	0.879816i	0.258014	−	0.966141i	$-0.416932\pi$
$641$	−18.6911	−	22.2752i	−0.738253	−	0.879816i	−0.996267	+	0.0863251i	$0.972488\pi$
$642$	−2.94756	−	21.1629i	−0.116331	−	0.835233i
$643$	8.08087	+	1.42488i	0.318678	+	0.0561916i	0.330699	−	0.943736i	$-0.392715\pi$
$643$	8.08087	+	1.42488i	0.318678	+	0.0561916i	−0.0120210	+	0.999928i	$0.503827\pi$
$644$	12.5829	−	12.9594i	0.495835	−	0.510671i
$645$	16.8682	+	31.8193i	0.664183	+	1.25288i
$646$	−2.08020	−	0.757129i	−0.0818442	−	0.0297889i
$647$	35.6194			1.40034			0.700171	−	0.713976i	$-0.253107\pi$
$647$	35.6194			1.40034			0.700171	+	0.713976i	$0.253107\pi$
$648$	7.06459	+	5.57598i	0.277523	+	0.219045i
$649$			9.38353i			0.368336i
$650$	−9.83492	−	3.57962i	−0.385757	−	0.140404i
$651$	20.3301	−	8.95545i	0.796798	−	0.350992i
$652$	−2.08596	−	1.75033i	−0.0816924	−	0.0685481i
$653$	−8.97416	−	1.58239i	−0.351186	−	0.0619236i	−0.00472742	−	0.999989i	$-0.501505\pi$
$653$	−8.97416	−	1.58239i	−0.351186	−	0.0619236i	−0.346459	+	0.938065i	$0.612616\pi$
$654$	8.41195	−	1.17161i	0.328933	−	0.0458137i
$655$	18.9427	−	15.8948i	0.740152	−	0.621061i
$656$	6.17824	+	10.7010i	0.241220	+	0.417805i
$657$	−1.90334	+	26.2844i	−0.0742565	+	1.02545i
$658$	5.38046	+	3.65045i	0.209752	+	0.142309i
$659$	−15.4505	+	2.72435i	−0.601867	+	0.106125i	−0.466276	−	0.884639i	$-0.654405\pi$
$659$	−15.4505	+	2.72435i	−0.601867	+	0.106125i	−0.135591	+	0.990765i	$0.543293\pi$
$660$	6.23847	+	1.33409i	0.242832	+	0.0519296i
$661$	11.1178	+	30.5460i	0.432433	+	1.18810i	0.944314	+	0.329045i	$0.106727\pi$
$661$	11.1178	+	30.5460i	0.432433	+	1.18810i	−0.511881	+	0.859056i	$0.671051\pi$
$662$	1.87762	+	5.15872i	0.0729758	+	0.200499i
$663$	−10.4421	−	32.2733i	−0.405538	−	1.25339i
$664$	2.10740	−	0.371591i	0.0817829	−	0.0144205i
$665$	2.47599	+	1.67987i	0.0960149	+	0.0651427i
$666$	23.1245	−	2.37266i	0.896058	−	0.0919386i
$667$	−5.35339	−	9.27234i	−0.207284	−	0.359027i
$668$	8.01590	−	6.72614i	0.310144	−	0.260242i
$669$	−1.46441	+	3.61166i	−0.0566172	+	0.139635i
$670$	−4.81936	−	0.849783i	−0.186188	−	0.0328300i
$671$	18.7928	+	15.7690i	0.725488	+	0.608757i
$672$	−3.69671	−	2.70820i	−0.142604	−	0.104471i
$673$	40.7097	+	14.8171i	1.56924	+	0.571158i	0.972830	−	0.231520i	$-0.0743699\pi$
$673$	40.7097	+	14.8171i	1.56924	+	0.571158i	0.596413	+	0.802678i	$0.296592\pi$
$674$			21.3638i			0.822902i
$675$	8.64828	+	4.25785i	0.332872	+	0.163885i
$676$	18.8284			0.724169
$677$	4.64649	+	1.69118i	0.178579	+	0.0649975i	0.429762	−	0.902942i	$-0.358597\pi$
$677$	4.64649	+	1.69118i	0.178579	+	0.0649975i	−0.251183	+	0.967940i	$0.580820\pi$
$678$	−4.46406	−	0.161418i	−0.171441	−	0.00619921i
$679$	29.4892	−	30.3715i	1.13169	−	1.16555i
$680$	−6.06244	−	1.06897i	−0.232484	−	0.0409932i
$681$	17.9434	−	13.9832i	0.687591	−	0.535836i
$682$	6.47193	+	7.71294i	0.247823	+	0.295344i
$683$	2.24559	−	1.29649i	0.0859252	−	0.0496089i	−0.456422	−	0.889764i	$-0.650869\pi$
$683$	2.24559	−	1.29649i	0.0859252	−	0.0496089i	0.542347	+	0.840155i	$0.317536\pi$
$684$	−1.33237	+	1.37290i	−0.0509445	+	0.0524941i
$685$	−4.27999	−	2.47105i	−0.163530	−	0.0944140i
$686$	−18.5031	−	0.797021i	−0.706452	−	0.0304304i
$687$	3.39263	−	3.75854i	0.129437	−	0.143397i
$688$	11.0178	−	4.01015i	0.420050	−	0.152886i
$689$	−21.6633	+	7.88478i	−0.825305	+	0.300386i
$690$	−15.5666	−	14.0511i	−0.592609	−	0.534916i
$691$	7.11072	−	1.25381i	0.270505	−	0.0476973i	−0.0367504	−	0.999324i	$-0.511701\pi$
$691$	7.11072	−	1.25381i	0.270505	−	0.0476973i	0.307255	+	0.951627i	$0.400590\pi$
$692$	4.30345	−	7.45380i	0.163593	−	0.283351i
$693$	3.34379	+	16.1426i	0.127020	+	0.613208i
$694$	−7.22914	−	12.5212i	−0.274414	−	0.475300i
$695$	−2.39827	−	2.85815i	−0.0909717	−	0.108416i
$696$	−2.14254	+	1.66967i	−0.0812127	+	0.0632887i
$697$	−7.44835	+	42.2417i	−0.282126	+	1.60002i
$698$	−19.9218	−	16.7164i	−0.754051	−	0.632724i
$699$	−1.86626	+	51.6121i	−0.0705886	+	1.95215i
$700$	−4.47847	−	2.00853i	−0.169270	−	0.0759152i
$701$			6.06592i			0.229107i	0.993417	+	0.114553i	$0.0365437\pi$
$701$			6.06592i			0.229107i	−0.993417	+	0.114553i	$0.963456\pi$
$702$	−29.1428	−	3.17242i	−1.09992	−	0.119735i
$703$			4.94139i			0.186368i
$704$	0.710360	−	1.95170i	0.0267727	−	0.0735574i
$705$	4.00796	−	6.39645i	0.150948	−	0.240904i
$706$	21.1587	−	25.2160i	0.796319	−	0.949016i
$707$	−4.81489	+	19.0906i	−0.181082	+	0.717976i
$708$	−7.25185	−	2.94038i	−0.272541	−	0.110506i
$709$	−15.5152	+	13.0188i	−0.582684	+	0.488930i	−0.885827	−	0.464015i	$-0.846408\pi$
$709$	−15.5152	+	13.0188i	−0.582684	+	0.488930i	0.303143	+	0.952945i	$0.401964\pi$
$710$	6.28588	+	10.8875i	0.235905	+	0.408599i
$711$	−36.2172	+	26.1767i	−1.35825	+	0.981702i
$712$	3.72210	+	2.14895i	0.139491	+	0.0805354i
$713$	−5.74714	−	32.5937i	−0.215232	−	1.22064i
$714$	−3.78739	−	15.4502i	−0.141739	−	0.578208i
$715$	−19.5263	+	7.10700i	−0.730243	+	0.265787i
$716$	−5.33669	−	14.6624i	−0.199441	−	0.547961i
$717$	28.3368	+	6.05982i	1.05826	+	0.226308i
$718$	4.47076	+	25.3550i	0.166847	+	0.946239i
$719$	−16.8482	+	29.1820i	−0.628333	+	1.08830i	0.359553	+	0.933124i	$0.382929\pi$
$719$	−16.8482	+	29.1820i	−0.628333	+	1.08830i	−0.987886	+	0.155180i	$0.950404\pi$
$720$	−2.98588	+	4.40321i	−0.111277	+	0.164098i
$721$	−22.8795	+	11.0823i	−0.852077	+	0.412727i
$722$	11.9516	+	14.2433i	0.444791	+	0.530081i
$723$	1.28078	−	0.178386i	0.0476327	−	0.00663426i
$724$	9.88013	+	1.74213i	0.367192	+	0.0647459i
$725$	−1.87009	+	2.22868i	−0.0694532	+	0.0827711i
$726$	10.2321	−	5.42427i	0.379748	−	0.201314i
$727$	−1.61305	+	4.43181i	−0.0598246	+	0.164367i	−0.966004	−	0.258526i	$-0.916763\pi$
$727$	−1.61305	+	4.43181i	−0.0598246	+	0.164367i	0.906180	+	0.422893i	$0.138985\pi$
$728$	14.8872	+	1.08162i	0.551756	+	0.0400876i
$729$	26.3676	+	5.80948i	0.976577	+	0.215166i
$730$	−15.5780			−0.576569
$731$	38.2464	+	13.9205i	1.41459	+	0.514870i
$732$	−18.0755	+	9.58227i	−0.668091	+	0.354171i
$733$	17.3476	−	20.6741i	0.640750	−	0.763616i	−0.343739	−	0.939065i	$-0.611693\pi$
$733$	17.3476	−	20.6741i	0.640750	−	0.763616i	0.984488	+	0.175450i	$0.0561379\pi$
$734$	−0.678270	+	3.84666i	−0.0250354	+	0.141983i
$735$	−0.143302	+	21.5005i	−0.00528576	+	0.793059i
$736$	−5.22994	+	4.38844i	−0.192778	+	0.161760i
$737$	4.96358	−	2.86572i	0.182836	−	0.105560i
$738$	30.6806	+	20.8049i	1.12937	+	0.765840i
$739$	19.1933	−	33.2438i	0.706037	−	1.22289i	−0.260279	−	0.965533i	$-0.583815\pi$
$739$	19.1933	−	33.2438i	0.706037	−	1.22289i	0.966316	−	0.257358i	$-0.0828520\pi$
$740$	2.38614	+	13.5325i	0.0877164	+	0.497464i
$741$	1.30314	−	6.09370i	0.0478719	−	0.223858i
$742$	−10.4006	+	2.95180i	−0.381817	+	0.108364i
$743$	−15.7088	−	43.1597i	−0.576301	−	1.58337i	−0.794366	−	0.607440i	$-0.792197\pi$
$743$	−15.7088	−	43.1597i	−0.576301	−	1.58337i	0.218065	−	0.975934i	$-0.430026\pi$
$744$	−7.98878	+	2.58479i	−0.292883	+	0.0947630i
$745$	−11.6162	+	2.04825i	−0.425584	+	0.0750420i
$746$	3.36467	+	1.94260i	0.123189	+	0.0711235i
$747$	5.20298	−	3.76056i	0.190367	−	0.137592i
$748$	6.24386	−	3.60489i	0.228298	−	0.131808i
$749$	19.1129	+	26.4574i	0.698372	+	0.966733i
$750$	−7.91189	+	19.5131i	−0.288901	+	0.712517i
$751$	1.92199	−	10.9002i	0.0701345	−	0.397752i	−0.929451	−	0.368947i	$-0.879718\pi$
$751$	1.92199	−	10.9002i	0.0701345	−	0.397752i	0.999585	−	0.0288057i	$-0.00917040\pi$
$752$	−1.88256	−	1.57965i	−0.0686497	−	0.0576040i
$753$	−22.1572	+	35.3615i	−0.807453	+	1.28864i
$754$	3.02605	−	8.31399i	0.110202	−	0.302778i
$755$	18.1333			0.659939
$756$	−13.5233	−	2.47421i	−0.491836	−	0.0899860i
$757$	−28.5741			−1.03854			−0.519272	−	0.854609i	$-0.673797\pi$
$757$	−28.5741			−1.03854			−0.519272	+	0.854609i	$0.673797\pi$
$758$	7.47757	−	20.5445i	0.271598	−	0.746209i
$759$	24.5440	+	0.887498i	0.890893	+	0.0322141i
$760$	−0.866318	−	0.726927i	−0.0314247	−	0.0263684i
$761$	3.54108	−	20.0824i	0.128364	−	0.727988i	−0.850889	−	0.525346i	$-0.823936\pi$
$761$	3.54108	−	20.0824i	0.128364	−	0.727988i	0.979253	−	0.202642i	$-0.0649529\pi$
$762$	1.28688	+	1.65134i	0.0466188	+	0.0598218i
$763$	−10.5164	+	7.59712i	−0.380721	+	0.275034i
$764$	−1.87140	+	1.08045i	−0.0677049	+	0.0390895i
$765$	−17.7650	+	5.04650i	−0.642295	+	0.182457i
$766$	−20.2541	−	11.6937i	−0.731812	−	0.422512i
$767$	25.1014	−	4.42606i	0.906360	−	0.159816i
$768$	1.28573	+	1.16056i	0.0463948	+	0.0418781i
$769$	8.13521	+	22.3513i	0.293363	+	0.806009i	0.995569	+	0.0940346i	$0.0299764\pi$
$769$	8.13521	+	22.3513i	0.293363	+	0.806009i	−0.702206	+	0.711974i	$0.747801\pi$
$770$	−9.37463	+	2.66062i	−0.337838	+	0.0958821i
$771$	−9.17785	−	8.28436i	−0.330532	−	0.298354i
$772$	−1.16009	−	6.57918i	−0.0417524	−	0.236790i
$773$	−23.6803	+	41.0154i	−0.851720	+	1.47522i	0.0279342	+	0.999610i	$0.491107\pi$
$773$	−23.6803	+	41.0154i	−0.851720	+	1.47522i	−0.879655	+	0.475613i	$0.842226\pi$
$774$	24.4969	−	25.2420i	0.880524	−	0.907306i
$775$	−7.78838	+	4.49663i	−0.279767	+	0.161524i
$776$	−12.2568	+	10.2847i	−0.439995	+	0.369200i
$777$	−29.5163	+	19.7398i	−1.05889	+	0.708161i
$778$	5.68889	−	32.2633i	0.203957	−	1.15670i
$779$	−5.06507	+	6.03631i	−0.181475	+	0.216273i
$780$	0.626189	−	17.3175i	0.0224212	−	0.620065i
$781$	−13.8359	−	5.03586i	−0.495088	−	0.180197i
$782$	−23.6994			−0.847490
$783$	−3.59939	+	7.31086i	−0.128632	+	0.261269i
$784$	6.92649	+	1.01182i	0.247375	+	0.0361365i
$785$	−10.9931	+	30.2033i	−0.392360	+	1.07800i
$786$	−20.4660	−	12.8238i	−0.729997	−	0.457409i
$787$	16.7240	−	19.9309i	0.596147	−	0.710460i	−0.380628	−	0.924728i	$-0.624292\pi$
$787$	16.7240	−	19.9309i	0.596147	−	0.710460i	0.976775	+	0.214268i	$0.0687366\pi$
$788$	−18.9543	−	3.34216i	−0.675220	−	0.119060i
$789$	6.38514	−	15.7477i	0.227317	−	0.560632i
$790$	−16.9795	−	20.2354i	−0.604104	−	0.719943i
$791$	6.14095	−	2.97454i	0.218347	−	0.105762i
$792$	−0.635969	−	6.19832i	−0.0225982	−	0.220248i
$793$	33.3187	−	57.7097i	1.18318	−	2.04933i
$794$	−2.10442	−	11.9348i	−0.0746831	−	0.423549i
$795$	3.86382	+	11.9419i	0.137036	+	0.423534i
$796$	3.79747	+	10.4335i	0.134598	+	0.369804i
$797$	12.8463	−	4.67566i	0.455038	−	0.165620i	−0.104325	−	0.994543i	$-0.533268\pi$
$797$	12.8463	−	4.67566i	0.455038	−	0.165620i	0.559363	+	0.828923i	$0.311046\pi$
$798$	0.816602	−	2.80594i	0.0289074	−	0.0993292i
$799$	−1.48136	−	8.40119i	−0.0524066	−	0.297213i
$800$	1.60660	+	0.927572i	0.0568019	+	0.0327946i
$801$	12.8600	+	0.931240i	0.454387	+	0.0329038i
$802$	2.29106	+	3.96822i	0.0809000	+	0.140123i
$803$	13.9763	−	11.7275i	0.493214	−	0.413856i
$804$	0.659346	+	4.73397i	0.0232533	+	0.166954i
$805$	31.0599	+	7.83371i	1.09472	+	0.276102i
$806$	17.5798	−	20.9508i	0.619222	−	0.737960i
$807$	−10.5391	−	19.8805i	−0.370994	−	0.699825i
$808$	2.54515	−	6.99274i	0.0895381	−	0.246004i
$809$			2.87226i			0.100983i	0.998724	+	0.0504917i	$0.0160788\pi$
$809$			2.87226i			0.100983i	−0.998724	+	0.0504917i	$0.983921\pi$
$810$	−2.29943	+	15.7939i	−0.0807939	+	0.554940i
$811$			44.9274i			1.57761i	0.614640	+	0.788807i	$0.289301\pi$
$811$			44.9274i			1.57761i	−0.614640	+	0.788807i	$0.710699\pi$
$812$	1.69792	−	3.78590i	0.0595852	−	0.132859i
$813$	−2.08959	+	1.10774i	−0.0732852	+	0.0388502i
$814$	−12.3284	−	10.3448i	−0.432110	−	0.362584i
$815$	0.838537	−	4.75558i	0.0293727	−	0.166581i
$816$	0.829414	+	5.95503i	0.0290353	+	0.208468i
$817$	4.80618	+	5.72778i	0.168147	+	0.200390i
$818$	6.41944	+	11.1188i	0.224450	+	0.388759i
$819$	41.6051	−	16.5590i	1.45380	−	0.578618i
$820$	−10.9563	+	18.9769i	−0.382612	+	0.662703i
$821$	35.9698	−	6.34245i	1.25536	−	0.221353i	0.493870	−	0.869536i	$-0.335582\pi$
$821$	35.9698	−	6.34245i	1.25536	−	0.221353i	0.761485	+	0.648183i	$0.224471\pi$
$822$	−1.00942	+	4.72022i	−0.0352075	+	0.164636i
$823$	3.16027	−	1.15024i	0.110160	−	0.0400950i	−0.286352	−	0.958124i	$-0.592443\pi$
$823$	3.16027	−	1.15024i	0.110160	−	0.0400950i	0.396512	+	0.918030i	$0.370220\pi$
$824$	9.02922	−	3.28637i	0.314548	−	0.114486i
$825$	−2.05443	−	6.34959i	−0.0715259	−	0.221064i
$826$	11.8912	−	1.21719i	0.413747	−	0.0423516i
$827$	3.07794	+	1.77705i	0.107030	+	0.0617940i	0.552560	−	0.833473i	$-0.313651\pi$
$827$	3.07794	+	1.77705i	0.107030	+	0.0617940i	−0.445529	+	0.895267i	$0.646984\pi$
$828$	−8.37688	+	18.6902i	−0.291117	+	0.649529i
$829$	−32.9537	+	19.0258i	−1.14453	+	0.660795i	−0.947548	−	0.319612i	$-0.896447\pi$
$829$	−32.9537	+	19.0258i	−1.14453	+	0.660795i	−0.196982	+	0.980407i	$0.563114\pi$
$830$	2.43929	+	2.90703i	0.0846689	+	0.100904i
$831$	43.7483	+	17.7384i	1.51761	+	0.615339i
$832$	−5.55596	−	0.979665i	−0.192618	−	0.0339638i
$833$	16.1611	+	18.1459i	0.559950	+	0.628717i
$834$	−1.93491	+	3.08799i	−0.0670003	+	0.106928i
$835$	17.4375	+	6.34673i	0.603450	+	0.219638i
$836$	1.32449			0.0458086
$837$	−18.1847	+	17.4308i	−0.628555	+	0.602496i
$838$			32.6793i			1.12889i
$839$	−17.6700	−	6.43136i	−0.610037	−	0.222035i	0.0184824	−	0.999829i	$-0.494117\pi$
$839$	−17.6700	−	6.43136i	−0.610037	−	0.222035i	−0.628519	+	0.777794i	$0.716339\pi$
$840$	0.881389	−	8.07868i	0.0304108	−	0.278741i
$841$	20.3313	+	17.0600i	0.701078	+	0.588274i
$842$	5.69138	+	1.00354i	0.196138	+	0.0345844i
$843$	−20.8820	−	26.7960i	−0.719214	−	0.922903i
$844$	3.08105	−	2.58531i	0.106054	−	0.0889899i
$845$	16.6949	+	28.9164i	0.574322	+	0.994754i
$846$	−7.14908	−	1.80126i	−0.245790	−	0.0619287i
$847$	−9.93199	+	14.6389i	−0.341267	+	0.503000i
$848$	4.02422	−	0.709579i	0.138192	−	0.0243671i
$849$	−5.76809	+	6.39020i	−0.197960	+	0.219311i
$850$	2.20254	+	6.05144i	0.0755466	+	0.207563i
$851$	18.0934	+	49.7112i	0.620234	+	1.70408i
$852$	8.22740	−	9.11476i	0.281866	−	0.312266i
$853$	−13.7339	+	2.42166i	−0.470240	+	0.0829160i	−0.403747	−	0.914871i	$-0.632292\pi$
$853$	−13.7339	+	2.42166i	−0.470240	+	0.0829160i	−0.0664935	+	0.997787i	$0.521181\pi$
$854$	17.5454	−	25.8605i	0.600392	−	0.884927i
$855$	−3.28988	−	0.828909i	−0.112511	−	0.0283481i
$856$	−6.16818	−	10.6836i	−0.210824	−	0.365158i
$857$	−12.4915	+	10.4816i	−0.426702	+	0.358046i	−0.830706	−	0.556712i	$-0.812063\pi$
$857$	−12.4915	+	10.4816i	−0.426702	+	0.358046i	0.404003	+	0.914757i	$0.367618\pi$
$858$	12.4752	+	16.0083i	0.425897	+	0.546516i
$859$	35.4401	+	6.24905i	1.20920	+	0.213215i	0.741672	−	0.670763i	$-0.234033\pi$
$859$	35.4401	+	6.24905i	1.20920	+	0.213215i	0.467529	+	0.883978i	$0.345144\pi$
$860$	15.9281	+	13.3653i	0.543143	+	0.455751i
$861$	−56.2905	−	6.14132i	−1.91837	−	0.209296i
$862$	12.2522	+	4.45943i	0.417311	+	0.151889i
$863$		−	34.7617i		−	1.18330i	−0.806195	−	0.591650i	$-0.798477\pi$
$863$		−	34.7617i		−	1.18330i	0.806195	−	0.591650i	$-0.201523\pi$
$864$	4.98951	+	1.45078i	0.169747	+	0.0493566i
$865$	15.2633			0.518967
$866$	27.8355	+	10.1313i	0.945888	+	0.344275i
$867$	4.55224	−	7.26509i	0.154602	−	0.246736i
$868$	8.93463	−	9.20197i	0.303261	−	0.312335i
$869$	30.4674	+	5.37223i	1.03354	+	0.182240i
$870$	−4.46402	−	1.81001i	−0.151344	−	0.0613650i
$871$	−10.0072	−	11.9261i	−0.339081	−	0.404100i
$872$	4.24658	−	2.45176i	0.143807	−	0.0830271i
$873$	−19.6320	+	43.8022i	−0.664443	+	1.48248i
$874$	−3.77048	−	2.17688i	−0.127538	−	0.0736342i
$875$	−3.27520	−	31.9965i	−0.110722	−	1.08168i
$876$	4.68380	+	14.4762i	0.158251	+	0.489105i
$877$	−19.4061	+	7.06325i	−0.655298	+	0.238509i	−0.648205	−	0.761466i	$-0.724480\pi$
$877$	−19.4061	+	7.06325i	−0.655298	+	0.238509i	−0.00709328	+	0.999975i	$0.502258\pi$
$878$	24.4496	−	8.89893i	0.825134	−	0.300324i
$879$	5.15847	−	24.1219i	0.173991	−	0.813612i
$880$	3.62726	−	0.639584i	0.122275	−	0.0215604i
$881$	8.54818	−	14.8059i	0.287995	−	0.498823i	−0.685336	−	0.728227i	$-0.740345\pi$
$881$	8.54818	−	14.8059i	0.287995	−	0.498823i	0.973331	+	0.229405i	$0.0736779\pi$
$882$	20.0228	−	6.33134i	0.674204	−	0.213187i
$883$	24.2114	+	41.9353i	0.814777	+	1.41124i	0.909488	+	0.415730i	$0.136474\pi$
$883$	24.2114	+	41.9353i	0.814777	+	1.41124i	−0.0947111	+	0.995505i	$0.530193\pi$
$884$	−12.5884	−	15.0023i	−0.423393	−	0.504581i
$885$	−1.91433	−	13.7445i	−0.0643494	−	0.462016i
$886$	−6.54788	+	37.1349i	−0.219980	+	1.24757i
$887$	−40.9329	−	34.3468i	−1.37439	−	1.15325i	−0.971235	−	0.238121i	$-0.923468\pi$
$887$	−40.9329	−	34.3468i	−1.37439	−	1.15325i	−0.403157	−	0.915131i	$-0.632087\pi$
$888$	11.8579	−	6.28614i	0.397924	−	0.210949i
$889$	−2.91795	−	1.30865i	−0.0978648	−	0.0438908i
$890$			7.62179i			0.255483i
$891$	−9.82700	−	15.9010i	−0.329217	−	0.532705i
$892$			2.25008i			0.0753383i
$893$	0.536005	−	1.47266i	0.0179367	−	0.0492807i
$894$	5.39598	+	10.1787i	0.180468	+	0.340427i
$895$	17.7864	−	21.1970i	0.594534	−	0.708538i
$896$	−2.56541	−	0.647030i	−0.0857045	−	0.0216158i
$897$	−9.20292	−	66.0752i	−0.307277	−	2.20619i
$898$	−8.17930	+	6.86325i	−0.272947	+	0.229030i
$899$	−3.80124	−	6.58395i	−0.126779	−	0.219587i
$900$	5.55090	+	0.401960i	0.185030	+	0.0133987i
$901$	12.2845	+	7.09245i	0.409255	+	0.236284i
$902$	−4.45648	−	25.2739i	−0.148384	−	0.841530i
$903$	−15.0140	+	51.5899i	−0.499635	+	1.71681i
$904$	−2.42348	+	0.882074i	−0.0806037	+	0.0293373i
$905$	6.08504	+	16.7185i	0.202273	+	0.555742i
$906$	−5.45209	−	16.8507i	−0.181133	−	0.559827i
$907$	−5.44985	−	30.9076i	−0.180959	−	1.02627i	−0.931038	−	0.364922i	$-0.881096\pi$
$907$	−5.44985	−	30.9076i	−0.180959	−	1.02627i	0.750079	−	0.661349i	$-0.230016\pi$
$908$	6.56692	−	11.3742i	0.217931	−	0.377467i
$909$	−2.27861	−	22.2080i	−0.0755769	−	0.736592i
$910$	11.5391	+	23.8226i	0.382519	+	0.789713i
$911$	26.1793	+	31.1993i	0.867359	+	1.03368i	0.999101	+	0.0423942i	$0.0134985\pi$
$911$	26.1793	+	31.1993i	0.867359	+	1.03368i	−0.131742	+	0.991284i	$0.542057\pi$
$912$	−0.415037	+	1.02360i	−0.0137432	+	0.0338949i
$913$	−4.37697	−	0.771778i	−0.144856	−	0.0255421i
$914$	1.31799	−	1.57072i	0.0435952	−	0.0519547i
$915$	−30.7437	−	19.2637i	−1.01635	−	0.636839i
$916$	0.999818	−	2.74698i	0.0330349	−	0.0907627i
$917$	36.7954	+	2.67335i	1.21509	+	0.0882818i
$918$	10.0309	+	14.9911i	0.331069	+	0.494781i
$919$	−41.2268			−1.35995			−0.679973	−	0.733237i	$-0.738009\pi$
$919$	−41.2268			−1.35995			−0.679973	+	0.733237i	$0.738009\pi$
$920$	−11.3770	−	4.14090i	−0.375089	−	0.136521i
$921$	1.88848	−	52.2266i	0.0622276	−	1.72092i
$922$	−24.5928	+	29.3086i	−0.809922	+	0.965227i
$923$	−6.94501	+	39.3871i	−0.228598	+	1.29644i
$924$	5.29107	+	7.91158i	0.174063	+	0.260272i
$925$	11.0118	−	9.23998i	0.362065	−	0.303809i
$926$	21.3835	−	12.3458i	0.702706	−	0.405707i
$927$	20.0755	−	20.6861i	0.659366	−	0.679422i
$928$	−0.784127	+	1.35815i	−0.0257402	+	0.0445834i
$929$	−10.2577	−	58.1741i	−0.336543	−	1.90863i	−0.411435	−	0.911439i	$-0.634972\pi$
$929$	−10.2577	−	58.1741i	−0.336543	−	1.90863i	0.0748920	−	0.997192i	$-0.476139\pi$
$930$	−11.0532	−	9.97716i	−0.362450	−	0.327164i
$931$	0.904397	+	4.37139i	0.0296404	+	0.143267i
$932$	10.1983	+	28.0195i	0.334056	+	0.917810i
$933$	40.5526	+	36.6047i	1.32763	+	1.19838i
$934$	24.3359	−	4.29107i	0.796295	−	0.140408i
$935$	11.0727	+	6.39282i	0.362116	+	0.209068i
$936$	−16.2808	+	4.62489i	−0.532156	+	0.151169i
$937$	35.8334	−	20.6884i	1.17063	−	0.675862i	0.216799	−	0.976216i	$-0.430438\pi$
$937$	35.8334	−	20.6884i	1.17063	−	0.675862i	0.953828	+	0.300355i	$0.0971050\pi$
$938$	−4.27541	−	5.91831i	−0.139597	−	0.193240i
$939$	−19.4973	−	25.0191i	−0.636269	−	0.816467i
$940$	0.756771	−	4.29186i	0.0246831	−	0.139985i
$941$	−22.9762	−	19.2793i	−0.749003	−	0.628488i	0.186236	−	0.982505i	$-0.440371\pi$
$941$	−22.9762	−	19.2793i	−0.749003	−	0.628488i	−0.935239	+	0.354017i	$0.884816\pi$
$942$	31.3722	+	1.13440i	1.02216	+	0.0369607i
$943$	−28.8529	+	79.2726i	−0.939578	+	2.58147i
$944$	−4.51793			−0.147046
$945$	−8.19104	−	22.9627i	−0.266454	−	0.746976i
$946$	−24.3521			−0.791755
$947$	8.28570	−	22.7648i	0.269249	−	0.739755i	−0.729212	−	0.684288i	$-0.760113\pi$
$947$	8.28570	−	22.7648i	0.269249	−	0.739755i	0.998461	−	0.0554671i	$-0.0176648\pi$
$948$	−13.6989	+	21.8626i	−0.444920	+	0.710065i
$949$	−37.9642	−	31.8557i	−1.23237	−	1.03408i
$950$	−0.205433	+	1.16507i	−0.00666514	+	0.0377999i
$951$	11.0684	−	27.2980i	0.358918	−	0.885199i
$952$	−5.37819	−	7.44485i	−0.174308	−	0.241289i
$953$	−22.4553	+	12.9646i	−0.727399	+	0.419964i	−0.817470	−	0.575971i	$-0.804624\pi$
$953$	−22.4553	+	12.9646i	−0.727399	+	0.419964i	0.0900709	+	0.995935i	$0.471291\pi$
$954$	9.93547	−	7.18105i	0.321673	−	0.232495i
$955$	−3.31869	−	1.91605i	−0.107390	−	0.0620019i
$956$	16.4760	−	2.90516i	0.532872	−	0.0939597i
$957$	5.36765	−	1.73672i	0.173512	−	0.0561401i
$958$	−7.90989	−	21.7322i	−0.255557	−	0.702137i
$959$	−2.01311	−	7.09314i	−0.0650066	−	0.229049i
$960$	−0.642332	+	3.00366i	−0.0207312	+	0.0969427i
$961$	1.30226	+	7.38549i	0.0420085	+	0.238242i
$962$	−21.8576	+	37.8585i	−0.704718	+	1.22061i
$963$	−30.6306	−	20.7710i	−0.987057	−	0.669338i
$964$	0.646571	−	0.373298i	0.0208246	−	0.0120231i
$965$	9.07558	−	7.61532i	0.292153	−	0.245146i
$966$	−2.05908	−	31.2183i	−0.0662500	−	1.00443i
$967$	9.62637	−	54.5939i	0.309563	−	1.75562i	−0.291643	−	0.956527i	$-0.594202\pi$
$967$	9.62637	−	54.5939i	0.309563	−	1.75562i	0.601207	−	0.799094i	$-0.294687\pi$
$968$	4.29785	−	5.12197i	0.138138	−	0.164626i
$969$	−3.38765	+	1.79588i	−0.108827	+	0.0576918i
$970$	−26.6631	−	9.70458i	−0.856101	−	0.311595i
$971$	−26.2141			−0.841250			−0.420625	−	0.907234i	$-0.638189\pi$
$971$	−26.2141			−0.841250			−0.420625	+	0.907234i	$0.638189\pi$
$972$	15.3681	−	2.61190i	0.492931	−	0.0837768i
$973$	0.403366	−	5.55184i	0.0129313	−	0.177984i
$974$	−3.02238	+	8.30392i	−0.0968433	+	0.266075i
$975$	−16.0164	+	8.49069i	−0.512936	+	0.271920i
$976$	−7.59238	+	9.04825i	−0.243026	+	0.289627i
$977$	−2.66762	−	0.470373i	−0.0853447	−	0.0150486i	0.130813	−	0.991407i	$-0.458241\pi$
$977$	−2.66762	−	0.470373i	−0.0853447	−	0.0150486i	−0.216157	+	0.976359i	$0.569352\pi$
$978$	−4.67133	+	0.650620i	−0.149373	+	0.0208045i
$979$	−5.73788	−	6.83813i	−0.183383	−	0.218548i
$980$	4.58768	+	11.5348i	0.146548	+	0.368465i
$981$	8.25619	−	12.1752i	0.263600	−	0.388725i
$982$	−5.17853	+	8.96947i	−0.165253	+	0.286227i
$983$	0.625772	+	3.54893i	0.0199590	+	0.113193i	0.993160	−	0.116765i	$-0.0372523\pi$
$983$	0.625772	+	3.54893i	0.0199590	+	0.113193i	−0.973201	+	0.229958i	$0.926141\pi$
$984$	20.9288	+	4.47563i	0.667187	+	0.142678i
$985$	−11.6737	−	32.0733i	−0.371956	−	1.02194i
$986$	−5.11561	+	1.86193i	−0.162914	+	0.0592960i
$987$	10.9378	−	2.68125i	0.348155	−	0.0853453i
$988$	−0.624742	−	3.54309i	−0.0198757	−	0.112721i
$989$	69.3238	+	40.0241i	2.20437	+	1.27269i
$990$	8.95540	−	6.47268i	0.284621	−	0.205715i
$991$	6.15949	+	10.6686i	0.195663	+	0.338898i	0.947118	−	0.320887i	$-0.103981\pi$
$991$	6.15949	+	10.6686i	0.195663	+	0.338898i	−0.751455	+	0.659784i	$0.770648\pi$
$992$	−3.71358	+	3.11607i	−0.117906	+	0.0989352i
$993$	8.81181	+	3.57289i	0.279634	+	0.113382i
$994$	−4.58691	+	18.1867i	−0.145488	+	0.576846i
$995$	−12.6564	+	15.0833i	−0.401235	+	0.478174i
$996$	1.96799	−	3.14080i	0.0623583	−	0.0995200i
$997$	10.4339	−	28.6668i	0.330444	−	0.907886i	−0.657553	−	0.753408i	$-0.728408\pi$
$997$	10.4339	−	28.6668i	0.330444	−	0.907886i	0.987996	−	0.154478i	$-0.0493695\pi$
$998$		−	19.3272i		−	0.611791i
$999$	23.7868	−	32.4855i	0.752581	−	1.02780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.293.17	yes	144
7.6	odd	2	inner	378.2.z.a.293.20	yes	144
27.20	odd	18	inner	378.2.z.a.209.20	yes	144
189.20	even	18	inner	378.2.z.a.209.17	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.209.17	✓	144	189.20	even	18	inner
378.2.z.a.209.20	yes	144	27.20	odd	18	inner
378.2.z.a.293.17	yes	144	1.1	even	1	trivial
378.2.z.a.293.20	yes	144	7.6	odd	2	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(-0.811256 - 1.53031i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.307943 - 1.74643i) q^{5} +(-1.71549 + 0.238933i) q^{6} +(2.14467 - 1.54932i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.68373 + 2.48295i) q^{9} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(-0.811256 - 1.53031i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.307943 - 1.74643i) q^{5} +(-1.71549 + 0.238933i) q^{6} +(2.14467 - 1.54932i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.68373 + 2.48295i) q^{9} +(-1.53579 - 0.886687i) q^{10} +(2.04540 - 0.360659i) q^{11} +(-0.362209 + 1.69375i) q^{12} +(-1.92956 - 5.30143i) q^{13} +(-0.722363 - 2.54523i) q^{14} +(-2.92241 + 0.945554i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.73566 + 3.00626i) q^{17} +(1.75735 + 2.43141i) q^{18} +(-0.552273 + 0.318855i) q^{19} +(-1.35848 + 1.13990i) q^{20} +(-4.11082 - 2.02513i) q^{21} +(0.360659 - 2.04540i) q^{22} +(-4.38844 + 5.22994i) q^{23} +(1.46773 + 0.919663i) q^{24} +(1.74326 + 0.634496i) q^{25} -5.64167 q^{26} +(5.16564 + 0.562320i) q^{27} +(-2.63880 - 0.191721i) q^{28} +(-0.536375 + 1.47368i) q^{29} +(-0.110994 + 3.06957i) q^{30} +(-3.11607 + 3.71358i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-2.21127 - 2.83752i) q^{33} +(2.23133 + 2.65919i) q^{34} +(-2.04534 - 4.22262i) q^{35} +(2.88582 - 0.819775i) q^{36} +(3.87432 - 6.71053i) q^{37} +(0.110737 + 0.628021i) q^{38} +(-6.54749 + 7.25366i) q^{39} +(0.606530 + 1.66643i) q^{40} +(11.6113 - 4.22616i) q^{41} +(-3.30898 + 3.17028i) q^{42} +(-2.03601 - 11.5468i) q^{43} +(-1.79869 - 1.03848i) q^{44} +(3.81782 + 3.70512i) q^{45} +(3.41360 + 5.91253i) q^{46} +(-1.88256 + 1.57965i) q^{47} +(1.36619 - 1.06467i) q^{48} +(2.19922 - 6.64556i) q^{49} +(1.19246 - 1.42112i) q^{50} +(6.00859 + 0.217267i) q^{51} +(-1.92956 + 5.30143i) q^{52} -4.08630i q^{53} +(2.29516 - 4.66179i) q^{54} -3.68322i q^{55} +(-1.08268 + 2.41408i) q^{56} +(0.935983 + 0.586478i) q^{57} +(1.20135 + 1.00805i) q^{58} +(-0.784530 + 4.44929i) q^{59} +(2.84649 + 1.15415i) q^{60} +(7.59238 + 9.04825i) q^{61} +(2.42387 + 4.19827i) q^{62} +(0.235849 + 7.93375i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-9.85279 + 1.73731i) q^{65} +(-3.42269 + 1.10742i) q^{66} +(2.59312 - 0.943819i) q^{67} +(3.26198 - 1.18726i) q^{68} +(11.5636 + 2.47287i) q^{69} +(-4.66752 + 0.477772i) q^{70} +(-6.13940 - 3.54459i) q^{71} +(0.216673 - 2.99217i) q^{72} +(7.60752 - 4.39220i) q^{73} +(-4.98073 - 5.93581i) q^{74} +(-0.443255 - 3.18248i) q^{75} +(0.628021 + 0.110737i) q^{76} +(3.82793 - 3.94247i) q^{77} +(4.57684 + 8.63352i) q^{78} +(13.9973 + 5.09459i) q^{79} +1.77337 q^{80} +(-3.33013 - 8.36124i) q^{81} -12.3565i q^{82} +(-2.01086 - 0.731892i) q^{83} +(1.84735 + 4.19372i) q^{84} +(4.71574 + 3.95697i) q^{85} +(-11.5468 - 2.03601i) q^{86} +(2.69033 - 0.374708i) q^{87} +(-1.59104 + 1.33504i) q^{88} +(-2.14895 - 3.72210i) q^{89} +(4.78745 - 2.32035i) q^{90} +(-12.3519 - 8.38031i) q^{91} +(6.72348 - 1.18553i) q^{92} +(8.21088 + 1.75590i) q^{93} +(0.840515 + 2.30930i) q^{94} +(0.386790 + 1.06270i) q^{95} +(-0.533195 - 1.64794i) q^{96} +(15.7571 - 2.77840i) q^{97} +(-5.49260 - 4.33951i) q^{98} +(-2.54840 + 5.68589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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