LMFDB - Embedded newform 804.2.l.a.431.14

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			431.14
Character	$\chi$	$=$	804.431
Dual form			804.2.l.a.707.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32505 + 0.494196i) q^{2} +(-0.696446 - 1.58586i) q^{3} +(1.51154 - 1.30967i) q^{4} +1.99192i q^{5} +(1.70656 + 1.75718i) q^{6} +(-1.23529 + 0.713198i) q^{7} +(-1.35564 + 2.48239i) q^{8} +(-2.02993 + 2.20894i) q^{9} +O(q^{10})$	\(q+(-1.32505 + 0.494196i) q^{2} +(-0.696446 - 1.58586i) q^{3} +(1.51154 - 1.30967i) q^{4} +1.99192i q^{5} +(1.70656 + 1.75718i) q^{6} +(-1.23529 + 0.713198i) q^{7} +(-1.35564 + 2.48239i) q^{8} +(-2.02993 + 2.20894i) q^{9} +(-0.984400 - 2.63941i) q^{10} +(-0.692977 - 1.20027i) q^{11} +(-3.12967 - 1.48498i) q^{12} +(0.164863 - 0.285552i) q^{13} +(1.28437 - 1.55550i) q^{14} +(3.15892 - 1.38727i) q^{15} +(0.569515 - 3.95925i) q^{16} +(-1.42716 - 0.823973i) q^{17} +(1.59812 - 3.93014i) q^{18} +(-0.409397 - 0.236366i) q^{19} +(2.60877 + 3.01087i) q^{20} +(1.99135 + 1.46231i) q^{21} +(1.51140 + 1.24796i) q^{22} +(4.19361 - 7.26355i) q^{23} +(4.88086 + 0.421014i) q^{24} +1.03224 q^{25} +(-0.0773346 + 0.459846i) q^{26} +(4.91681 + 1.68078i) q^{27} +(-0.933144 + 2.69586i) q^{28} +(-3.64705 + 2.10562i) q^{29} +(-3.50016 + 3.39933i) q^{30} +(3.73671 - 2.15739i) q^{31} +(1.20200 + 5.52767i) q^{32} +(-1.42084 + 1.93489i) q^{33} +(2.29827 + 0.386512i) q^{34} +(-1.42064 - 2.46061i) q^{35} +(-0.175333 + 5.99744i) q^{36} +(2.70308 - 4.68187i) q^{37} +(0.659285 + 0.110875i) q^{38} +(-0.567664 - 0.0625794i) q^{39} +(-4.94472 - 2.70033i) q^{40} +(0.426678 - 0.246343i) q^{41} +(-3.36131 - 0.953518i) q^{42} -5.27202i q^{43} +(-2.61942 - 0.906686i) q^{44} +(-4.40003 - 4.04346i) q^{45} +(-1.96715 + 11.6971i) q^{46} +(-5.12508 - 8.87690i) q^{47} +(-6.67546 + 1.85423i) q^{48} +(-2.48270 + 4.30016i) q^{49} +(-1.36778 + 0.510130i) q^{50} +(-0.312767 + 2.83714i) q^{51} +(-0.124781 - 0.647540i) q^{52} -2.80811i q^{53} +(-7.34567 + 0.202738i) q^{54} +(2.39085 - 1.38036i) q^{55} +(-0.0958152 - 4.03332i) q^{56} +(-0.0897205 + 0.813864i) q^{57} +(3.79195 - 4.59242i) q^{58} +5.40043 q^{59} +(2.95797 - 6.23406i) q^{60} +(1.26218 - 2.18615i) q^{61} +(-3.88517 + 4.70533i) q^{62} +(0.932148 - 4.17643i) q^{63} +(-4.32447 - 6.73045i) q^{64} +(0.568797 + 0.328395i) q^{65} +(0.926483 - 3.26601i) q^{66} +(6.19406 - 5.35104i) q^{67} +(-3.23635 + 0.623647i) q^{68} +(-14.4396 - 1.59183i) q^{69} +(3.09844 + 2.55837i) q^{70} +(-6.22806 - 10.7873i) q^{71} +(-2.73158 - 8.03358i) q^{72} +(5.76733 - 9.98931i) q^{73} +(-1.26797 + 7.53958i) q^{74} +(-0.718901 - 1.63700i) q^{75} +(-0.928383 + 0.178900i) q^{76} +(1.71206 + 0.988459i) q^{77} +(0.783113 - 0.197616i) q^{78} +(-11.4177 + 6.59199i) q^{79} +(7.88652 + 1.13443i) q^{80} +(-0.758803 - 8.96796i) q^{81} +(-0.443630 + 0.537280i) q^{82} +(-1.48522 + 2.57248i) q^{83} +(4.92515 - 0.397682i) q^{84} +(1.64129 - 2.84280i) q^{85} +(2.60541 + 6.98572i) q^{86} +(5.87920 + 4.31726i) q^{87} +(3.91896 - 0.0930986i) q^{88} +1.71334i q^{89} +(7.82854 + 3.18333i) q^{90} +0.470320i q^{91} +(-3.17405 - 16.4714i) q^{92} +(-6.02374 - 4.42341i) q^{93} +(11.1779 + 9.22959i) q^{94} +(0.470822 - 0.815488i) q^{95} +(7.92901 - 5.75594i) q^{96} +(3.16457 - 5.48120i) q^{97} +(1.16459 - 6.92489i) q^{98} +(4.05801 + 0.905719i) 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 $

$2$	−1.32505	+	0.494196i	−0.936955	+	0.349449i
$2$	−1.32505	+	0.494196i	−0.936955	+	0.349449i
$3$	−0.696446	−	1.58586i	−0.402093	−	0.915599i
$3$	−0.696446	−	1.58586i	−0.402093	−	0.915599i
$4$	1.51154	−	1.30967i	0.755771	−	0.654836i
$5$			1.99192i			0.890815i	0.895328	+	0.445408i	$0.146941\pi$
$5$			1.99192i			0.890815i	−0.895328	+	0.445408i	$0.853059\pi$
$6$	1.70656	+	1.75718i	0.696699	+	0.717364i
$7$	−1.23529	+	0.713198i	−0.466898	+	0.269563i	−0.714940	−	0.699186i	$-0.753546\pi$
$7$	−1.23529	+	0.713198i	−0.466898	+	0.269563i	0.248043	+	0.968749i	$0.420213\pi$
$8$	−1.35564	+	2.48239i	−0.479292	+	0.877656i
$9$	−2.02993	+	2.20894i	−0.676642	+	0.736312i
$10$	−0.984400	−	2.63941i	−0.311294	−	0.834654i
$11$	−0.692977	−	1.20027i	−0.208940	−	0.361895i	0.742441	−	0.669912i	$-0.233668\pi$
$11$	−0.692977	−	1.20027i	−0.208940	−	0.361895i	−0.951381	+	0.308017i	$0.900335\pi$
$12$	−3.12967	−	1.48498i	−0.903458	−	0.428677i
$13$	0.164863	−	0.285552i	0.0457248	−	0.0791978i	−0.842257	−	0.539076i	$-0.818774\pi$
$13$	0.164863	−	0.285552i	0.0457248	−	0.0791978i	0.887982	+	0.459878i	$0.152107\pi$
$14$	1.28437	−	1.55550i	0.343263	−	0.415726i
$15$	3.15892	−	1.38727i	0.815629	−	0.358191i
$16$	0.569515	−	3.95925i	0.142379	−	0.989812i
$17$	−1.42716	−	0.823973i	−0.346138	−	0.199843i	0.316845	−	0.948477i	$-0.397377\pi$
$17$	−1.42716	−	0.823973i	−0.346138	−	0.199843i	−0.662983	+	0.748634i	$0.730710\pi$
$18$	1.59812	−	3.93014i	0.376680	−	0.926344i
$19$	−0.409397	−	0.236366i	−0.0939222	−	0.0542260i	0.452303	−	0.891864i	$-0.350602\pi$
$19$	−0.409397	−	0.236366i	−0.0939222	−	0.0542260i	−0.546225	+	0.837638i	$0.683936\pi$
$20$	2.60877	+	3.01087i	0.583338	+	0.673252i
$21$	1.99135	+	1.46231i	0.434548	+	0.319101i
$22$	1.51140	+	1.24796i	0.322232	+	0.266066i
$23$	4.19361	−	7.26355i	0.874429	−	1.51455i	0.0170585	−	0.999854i	$-0.494570\pi$
$23$	4.19361	−	7.26355i	0.874429	−	1.51455i	0.857370	−	0.514700i	$-0.172097\pi$
$24$	4.88086	+	0.421014i	0.996300	+	0.0859392i
$25$	1.03224			0.206449
$26$	−0.0773346	+	0.459846i	−0.0151666	+	0.0901833i
$27$	4.91681	+	1.68078i	0.946240	+	0.323466i
$28$	−0.933144	+	2.69586i	−0.176348	+	0.509470i
$29$	−3.64705	+	2.10562i	−0.677239	+	0.391004i	−0.798814	−	0.601578i	$-0.794539\pi$
$29$	−3.64705	+	2.10562i	−0.677239	+	0.391004i	0.121575	+	0.992582i	$0.461206\pi$
$30$	−3.50016	+	3.39933i	−0.639039	+	0.620630i
$31$	3.73671	−	2.15739i	0.671133	−	0.387479i	−0.125373	−	0.992110i	$-0.540013\pi$
$31$	3.73671	−	2.15739i	0.671133	−	0.387479i	0.796506	+	0.604631i	$0.206679\pi$
$32$	1.20200	+	5.52767i	0.212486	+	0.977164i
$33$	−1.42084	+	1.93489i	−0.247337	+	0.336821i
$34$	2.29827	+	0.386512i	0.394151	+	0.0662863i
$35$	−1.42064	−	2.46061i	−0.240131	−	0.415919i
$36$	−0.175333	+	5.99744i	−0.0292222	+	0.999573i
$37$	2.70308	−	4.68187i	0.444383	−	0.769694i	−0.553626	−	0.832765i	$-0.686756\pi$
$37$	2.70308	−	4.68187i	0.444383	−	0.769694i	0.998009	+	0.0630714i	$0.0200896\pi$
$38$	0.659285	+	0.110875i	0.106950	+	0.0179863i
$39$	−0.567664	−	0.0625794i	−0.0908990	−	0.0100207i
$40$	−4.94472	−	2.70033i	−0.781829	−	0.426960i
$41$	0.426678	−	0.246343i	0.0666359	−	0.0384722i	−0.466312	−	0.884620i	$-0.654418\pi$
$41$	0.426678	−	0.246343i	0.0666359	−	0.0384722i	0.532948	+	0.846148i	$0.321084\pi$
$42$	−3.36131	−	0.953518i	−0.518662	−	0.147131i
$43$		−	5.27202i		−	0.803976i	−0.915645	−	0.401988i	$-0.868319\pi$
$43$		−	5.27202i		−	0.803976i	0.915645	−	0.401988i	$-0.131681\pi$
$44$	−2.61942	−	0.906686i	−0.394893	−	0.136688i
$45$	−4.40003	−	4.04346i	−0.655918	−	0.602763i
$46$	−1.96715	+	11.6971i	−0.290041	+	1.72464i
$47$	−5.12508	−	8.87690i	−0.747570	−	1.29483i	−0.948984	−	0.315323i	$-0.897887\pi$
$47$	−5.12508	−	8.87690i	−0.747570	−	1.29483i	0.201415	−	0.979506i	$-0.435446\pi$
$48$	−6.67546	+	1.85423i	−0.963520	+	0.267635i
$49$	−2.48270	+	4.30016i	−0.354671	+	0.614308i
$50$	−1.36778	+	0.510130i	−0.193433	+	0.0721432i
$51$	−0.312767	+	2.83714i	−0.0437961	+	0.397279i
$52$	−0.124781	−	0.647540i	−0.0173041	−	0.0897976i
$53$		−	2.80811i		−	0.385724i	−0.981226	−	0.192862i	$-0.938223\pi$
$53$		−	2.80811i		−	0.385724i	0.981226	−	0.192862i	$-0.0617770\pi$
$54$	−7.34567	+	0.202738i	−0.999619	+	0.0275891i
$55$	2.39085	−	1.38036i	0.322382	−	0.186127i
$56$	−0.0958152	−	4.03332i	−0.0128038	−	0.538975i
$57$	−0.0897205	+	0.813864i	−0.0118838	+	0.107799i
$58$	3.79195	−	4.59242i	0.497907	−	0.603014i
$59$	5.40043			0.703076			0.351538	−	0.936174i	$-0.385659\pi$
$59$	5.40043			0.703076			0.351538	+	0.936174i	$0.385659\pi$
$60$	2.95797	−	6.23406i	0.381872	−	0.804814i
$61$	1.26218	−	2.18615i	0.161605	−	0.279908i	−0.773839	−	0.633382i	$-0.781666\pi$
$61$	1.26218	−	2.18615i	0.161605	−	0.279908i	0.935444	+	0.353474i	$0.115000\pi$
$62$	−3.88517	+	4.70533i	−0.493418	+	0.597577i
$63$	0.932148	−	4.17643i	0.117440	−	0.526180i
$64$	−4.32447	−	6.73045i	−0.540559	−	0.841306i
$65$	0.568797	+	0.328395i	0.0705506	+	0.0407324i
$66$	0.926483	−	3.26601i	0.114042	−	0.402018i
$67$	6.19406	−	5.35104i	0.756725	−	0.653734i
$67$	6.19406	−	5.35104i	0.756725	−	0.653734i
$68$	−3.23635	+	0.623647i	−0.392465	+	0.0756283i
$69$	−14.4396	−	1.59183i	−1.73833	−	0.191633i
$70$	3.09844	+	2.55837i	0.370335	+	0.305784i
$71$	−6.22806	−	10.7873i	−0.739134	−	1.28022i	−0.952886	−	0.303330i	$-0.901902\pi$
$71$	−6.22806	−	10.7873i	−0.739134	−	1.28022i	0.213751	−	0.976888i	$-0.431432\pi$
$72$	−2.73158	−	8.03358i	−0.321920	−	0.946767i
$73$	5.76733	−	9.98931i	0.675015	−	1.16916i	−0.301449	−	0.953482i	$-0.597470\pi$
$73$	5.76733	−	9.98931i	0.675015	−	1.16916i	0.976464	−	0.215678i	$-0.0691962\pi$
$74$	−1.26797	+	7.53958i	−0.147398	+	0.876458i
$75$	−0.718901	−	1.63700i	−0.0830116	−	0.189024i
$76$	−0.928383	+	0.178900i	−0.106493	+	0.0205212i
$77$	1.71206	+	0.988459i	0.195107	+	0.112645i
$78$	0.783113	−	0.197616i	0.0886701	−	0.0223756i
$79$	−11.4177	+	6.59199i	−1.28459	+	0.741657i	−0.977683	−	0.210084i	$-0.932626\pi$
$79$	−11.4177	+	6.59199i	−1.28459	+	0.741657i	−0.306904	+	0.951741i	$0.599293\pi$
$80$	7.88652	+	1.13443i	0.881740	+	0.126833i
$81$	−0.758803	−	8.96796i	−0.0843114	−	0.996439i
$82$	−0.443630	+	0.537280i	−0.0489908	+	0.0593326i
$83$	−1.48522	+	2.57248i	−0.163025	+	0.282367i	−0.935952	−	0.352128i	$-0.885458\pi$
$83$	−1.48522	+	2.57248i	−0.163025	+	0.282367i	0.772927	+	0.634494i	$0.218792\pi$
$84$	4.92515	−	0.397682i	0.537378	−	0.0433907i
$85$	1.64129	−	2.84280i	0.178023	−	0.308345i
$86$	2.60541	+	6.98572i	0.280949	+	0.753290i
$87$	5.87920	+	4.31726i	0.630317	+	0.462859i
$88$	3.91896	−	0.0930986i	0.417763	−	0.00992434i
$89$			1.71334i			0.181614i	0.995869	+	0.0908071i	$0.0289447\pi$
$89$			1.71334i			0.181614i	−0.995869	+	0.0908071i	$0.971055\pi$
$90$	7.82854	+	3.18333i	0.825201	+	0.335552i
$91$			0.470320i			0.0493030i
$92$	−3.17405	−	16.4714i	−0.330918	−	1.71726i
$93$	−6.02374	−	4.42341i	−0.624633	−	0.458686i
$94$	11.1779	+	9.22959i	1.15292	+	0.951959i
$95$	0.470822	−	0.815488i	0.0483053	−	0.0836673i
$96$	7.92901	−	5.75594i	0.809251	−	0.587463i
$97$	3.16457	−	5.48120i	0.321314	−	0.556532i	−0.659446	−	0.751752i	$-0.729209\pi$
$97$	3.16457	−	5.48120i	0.321314	−	0.556532i	0.980759	+	0.195220i	$0.0625422\pi$
$98$	1.16459	−	6.92489i	0.117642	−	0.699519i
$99$	4.05801	+	0.905719i	0.407846	+	0.0910282i
$100$	1.56028	−	1.35190i	0.156028	−	0.135190i
$101$	3.04147	−	1.75600i	0.302638	−	0.174728i	−0.340989	−	0.940067i	$-0.610762\pi$
$101$	3.04147	−	1.75600i	0.302638	−	0.174728i	0.643627	+	0.765339i	$0.277429\pi$
$102$	−0.987669	−	3.91393i	−0.0977938	−	0.387537i
$103$	4.35646	−	2.51521i	0.429255	−	0.247831i	−0.269774	−	0.962924i	$-0.586949\pi$
$103$	4.35646	−	2.51521i	0.429255	−	0.247831i	0.699029	+	0.715093i	$0.253616\pi$
$104$	0.485354	+	0.796360i	0.0475928	+	0.0780895i
$105$	−2.91280	+	3.96662i	−0.284260	+	0.387102i
$106$	1.38776	+	3.72090i	0.134791	+	0.361406i
$107$	1.16258			0.112391			0.0561953	−	0.998420i	$-0.482103\pi$
$107$	1.16258			0.112391			0.0561953	+	0.998420i	$0.482103\pi$
$108$	9.63323	−	3.89884i	0.926958	−	0.375166i
$109$	6.69659			0.641417			0.320709	−	0.947178i	$-0.396079\pi$
$109$	6.69659			0.641417			0.320709	+	0.947178i	$0.396079\pi$
$110$	−2.48584	+	3.01059i	−0.237015	+	0.287049i
$111$	−9.30735	−	1.02604i	−0.883414	−	0.0973877i
$112$	2.12021	+	5.29702i	0.200341	+	0.500521i
$113$	−0.132726	+	0.0766293i	−0.0124858	+	0.00720868i	−0.506230	−	0.862399i	$-0.668961\pi$
$113$	−0.132726	+	0.0766293i	−0.0124858	+	0.00720868i	0.493744	+	0.869607i	$0.335628\pi$
$114$	−0.283324	−	1.12275i	−0.0265357	−	0.105156i
$115$	14.4684	+	8.35335i	1.34919	+	0.778954i
$116$	−2.75498	+	7.95917i	−0.255794	+	0.738991i
$117$	0.296105	+	0.943821i	0.0273749	+	0.0872563i
$118$	−7.15587	+	2.66887i	−0.658751	+	0.245689i
$119$	2.35062			0.215481
$120$	−0.838628	+	9.72229i	−0.0765559	+	0.887519i
$121$	4.53957	−	7.86276i	0.412688	−	0.714796i
$122$	−0.592066	+	3.52054i	−0.0536031	+	0.318734i
$123$	−0.687824	−	0.505088i	−0.0620190	−	0.0455423i
$124$	2.82272	−	8.15485i	0.253487	−	0.732327i
$125$			12.0158i			1.07472i
$126$	0.828824	+	5.99466i	0.0738375	+	0.534047i
$127$	−15.9092	+	9.18517i	−1.41171	+	0.815052i	−0.995550	−	0.0942380i	$-0.969959\pi$
$127$	−15.9092	+	9.18517i	−1.41171	+	0.815052i	−0.416162	+	0.909290i	$0.636625\pi$
$128$	9.05632	+	6.78108i	0.800473	+	0.599368i
$129$	−8.36071	+	3.67168i	−0.736119	+	0.323273i
$130$	−0.915978	−	0.154045i	−0.0803366	−	0.0135106i
$131$	−7.31128			−0.638789			−0.319395	−	0.947622i	$-0.603480\pi$
$131$	−7.31128			−0.638789			−0.319395	+	0.947622i	$0.603480\pi$
$132$	0.386407	+	4.78551i	0.0336324	+	0.416525i
$133$	0.674302			0.0584694
$134$	−5.56301	+	10.1515i	−0.480571	+	0.876956i
$135$	−3.34798	+	9.79390i	−0.288149	+	0.842925i
$136$	3.98014	−	2.42576i	0.341294	−	0.208007i
$137$		−	10.6697i		−	0.911576i	−0.890088	−	0.455788i	$-0.849358\pi$
$137$		−	10.6697i		−	0.911576i	0.890088	−	0.455788i	$-0.150642\pi$
$138$	19.9200	−	5.02674i	1.69570	−	0.427905i
$139$			4.97462i			0.421942i	0.977492	+	0.210971i	$0.0676625\pi$
$139$			4.97462i			0.421942i	−0.977492	+	0.210971i	$0.932338\pi$
$140$	−5.36995	−	1.85875i	−0.453843	−	0.157093i
$141$	−10.5082	+	14.3100i	−0.884951	+	1.20512i
$142$	13.5836	+	11.2159i	1.13991	+	0.941217i
$143$	−0.456986			−0.0382151
$144$	7.58966	+	9.29500i	0.632471	+	0.774584i
$145$	−4.19424	−	7.26463i	−0.348313	−	0.603295i
$146$	−2.70536	+	16.0866i	−0.223897	+	1.33133i
$147$	8.54853	+	0.942391i	0.705071	+	0.0777271i
$148$	−2.04590	−	10.6170i	−0.168172	−	0.872710i
$149$		−	11.3134i		−	0.926827i	−0.886142	−	0.463413i	$-0.846625\pi$
$149$		−	11.3134i		−	0.926827i	0.886142	−	0.463413i	$-0.153375\pi$
$150$	1.76158	+	1.81383i	0.143832	+	0.148099i
$151$	3.79093	+	2.18869i	0.308501	+	0.178113i	0.646256	−	0.763121i	$-0.276334\pi$
$151$	3.79093	+	2.18869i	0.308501	+	0.178113i	−0.337754	+	0.941234i	$0.609667\pi$
$152$	1.14175	−	0.695855i	0.0926079	−	0.0564413i
$153$	4.71714	−	1.47991i	0.381358	−	0.119644i
$154$	−2.75707	−	0.463669i	−0.222171	−	0.0373635i
$155$	4.29736	+	7.44324i	0.345172	+	0.597855i
$156$	−0.940006	+	0.648863i	−0.0752608	+	0.0519506i
$157$	−1.99496	+	3.45537i	−0.159215	+	0.275768i	−0.934586	−	0.355738i	$-0.884230\pi$
$157$	−1.99496	+	3.45537i	−0.159215	+	0.275768i	0.775371	+	0.631506i	$0.217563\pi$
$158$	11.8713	−	14.3773i	0.944429	−	1.14380i
$159$	−4.45328	+	1.95570i	−0.353168	+	0.155097i
$160$	−11.0107	+	2.39430i	−0.870472	+	0.189286i
$161$			11.9635i			0.942856i
$162$	5.43738	+	11.5080i	0.427201	+	0.904157i
$163$	−8.57914	+	4.95317i	−0.671970	+	0.387962i	−0.796823	−	0.604213i	$-0.793487\pi$
$163$	−8.57914	+	4.95317i	−0.671970	+	0.387962i	0.124853	+	0.992175i	$0.460154\pi$
$164$	0.322313	−	0.931165i	0.0251684	−	0.0727118i
$165$	−3.85415	−	2.83021i	−0.300045	−	0.220332i
$166$	0.696694	−	4.14267i	0.0540739	−	0.321534i
$167$	−3.88145	−	6.72287i	−0.300356	−	0.520231i	0.675861	−	0.737029i	$-0.263772\pi$
$167$	−3.88145	−	6.72287i	−0.300356	−	0.520231i	−0.976216	+	0.216798i	$0.930439\pi$
$168$	−6.32956	+	2.96094i	−0.488336	+	0.228441i
$169$	6.44564	+	11.1642i	0.495818	+	0.858783i
$170$	−0.769902	+	4.57799i	−0.0590488	+	0.351115i
$171$	1.35316	−	0.424528i	0.103479	−	0.0324645i
$172$	−6.90463	−	7.96888i	−0.526473	−	0.607622i
$173$	−3.25324	−	1.87826i	−0.247339	−	0.142801i	0.371206	−	0.928551i	$-0.378944\pi$
$173$	−3.25324	−	1.87826i	−0.247339	−	0.142801i	−0.618545	+	0.785749i	$0.712278\pi$
$174$	−9.92384	−	2.81514i	−0.752324	−	0.213415i
$175$	−1.27512	+	0.736193i	−0.0963903	+	0.0556510i
$176$	−5.14683	+	2.06009i	−0.387957	+	0.155285i
$177$	−3.76111	−	8.56434i	−0.282702	−	0.643735i
$178$	−0.846727	−	2.27028i	−0.0634649	−	0.170164i
$179$	2.73310			0.204281			0.102141	−	0.994770i	$-0.467431\pi$
$179$	2.73310			0.204281			0.102141	+	0.994770i	$0.467431\pi$
$180$	−11.9464	−	0.349250i	−0.890435	−	0.0260316i
$181$	3.31351	+	5.73916i	0.246291	+	0.426589i	0.962494	−	0.271304i	$-0.0874548\pi$
$181$	3.31351	+	5.73916i	0.246291	+	0.426589i	−0.716203	+	0.697892i	$0.754121\pi$
$182$	−0.232430	−	0.623201i	−0.0172289	−	0.0461947i
$183$	−4.34598	−	0.479101i	−0.321264	−	0.0354162i
$184$	12.3459	+	20.2569i	0.910152	+	1.49336i
$185$	9.32592	+	5.38432i	0.685655	+	0.395863i
$186$	10.1678	+	2.88435i	0.745541	+	0.211491i
$187$			2.28398i			0.167021i
$188$	−19.3726	−	6.70562i	−1.41289	−	0.489058i
$189$	−7.27243	+	1.43040i	−0.528992	+	0.104046i
$190$	−0.220855	+	1.31324i	−0.0160225	+	0.0952728i
$191$	6.55281	−	11.3498i	0.474145	−	0.821243i	−0.525417	−	0.850845i	$-0.676091\pi$
$191$	6.55281	−	11.3498i	0.474145	−	0.821243i	0.999562	+	0.0296019i	$0.00942394\pi$
$192$	−7.66181	+	11.5454i	−0.552943	+	0.833219i
$193$	−13.9775			−1.00612			−0.503061	−	0.864251i	$-0.667793\pi$
$193$	−13.9775			−1.00612			−0.503061	+	0.864251i	$0.667793\pi$
$194$	−1.48445	+	8.82682i	−0.106577	+	0.633728i
$195$	0.124653	−	1.13074i	0.00892661	−	0.0809742i
$196$	1.87910	+	9.75139i	0.134221	+	0.696528i
$197$	3.33681	−	1.92651i	0.237738	−	0.137258i	−0.376399	−	0.926458i	$-0.622838\pi$
$197$	3.33681	−	1.92651i	0.237738	−	0.137258i	0.614136	+	0.789200i	$0.289504\pi$
$198$	−5.82469	+	0.805325i	−0.413943	+	0.0572319i
$199$	−12.3000	−	7.10141i	−0.871924	−	0.503405i	−0.00393668	−	0.999992i	$-0.501253\pi$
$199$	−12.3000	−	7.10141i	−0.871924	−	0.503405i	−0.867987	+	0.496587i	$0.834586\pi$
$200$	−1.39935	+	2.56242i	−0.0989490	+	0.181191i
$201$	−12.7998	−	6.09622i	−0.902832	−	0.429994i
$202$	−3.16232	+	3.82987i	−0.222500	+	0.269469i
$203$	3.00345	−	5.20213i	0.210801	−	0.365118i
$204$	3.24296	+	4.69808i	0.227053	+	0.328931i
$205$	0.490695	+	0.849909i	0.0342717	+	0.0593602i
$206$	−4.52955	+	5.48573i	−0.315589	+	0.382209i
$207$	7.53200	+	24.0079i	0.523510	+	1.66866i
$208$	−1.03668	−	0.815361i	−0.0718807	−	0.0565351i
$209$			0.655184i			0.0453200i
$210$	1.89933	−	6.69548i	0.131067	−	0.462032i
$211$	19.8880	+	11.4823i	1.36915	+	0.790476i	0.990819	−	0.135196i	$-0.0431664\pi$
$211$	19.8880	+	11.4823i	1.36915	+	0.790476i	0.378326	+	0.925672i	$0.376500\pi$
$212$	−3.67771	−	4.24458i	−0.252586	−	0.291519i
$213$	−12.7697	+	17.3896i	−0.874965	+	1.19152i
$214$	−1.54048	+	0.574540i	−0.105305	+	0.0392748i
$215$	10.5015			0.716194
$216$	−10.8378	+	9.92687i	−0.737417	+	0.675438i
$217$	−3.07729	+	5.33003i	−0.208900	+	0.361826i
$218$	−8.87336	+	3.30943i	−0.600979	+	0.224143i
$219$	−19.8583	−	2.18918i	−1.34190	−	0.147931i
$220$	1.80605	−	5.21769i	0.121764	−	0.351777i
$221$	−0.470574	+	0.271686i	−0.0316542	+	0.0182756i
$222$	12.8398	−	3.24009i	0.861752	−	0.217460i
$223$		−	15.3161i		−	1.02564i	−0.858495	−	0.512822i	$-0.828600\pi$
$223$		−	15.3161i		−	1.02564i	0.858495	−	0.512822i	$-0.171400\pi$
$224$	−5.42715	−	5.97104i	−0.362617	−	0.398957i
$225$	−2.09538	+	2.28016i	−0.139692	+	0.152011i
$226$	0.137999	−	0.167131i	0.00917957	−	0.0111174i
$227$	0.587994	+	1.01844i	0.0390265	+	0.0675959i	0.884879	−	0.465821i	$-0.154241\pi$
$227$	0.587994	+	1.01844i	0.0390265	+	0.0675959i	−0.845852	+	0.533417i	$0.820908\pi$
$228$	0.930280	+	1.34769i	0.0616093	+	0.0892532i
$229$	−14.9215	+	25.8448i	−0.986040	+	1.70787i	−0.348819	+	0.937190i	$0.613417\pi$
$229$	−14.9215	+	25.8448i	−0.986040	+	1.70787i	−0.637221	+	0.770681i	$0.719916\pi$
$230$	−23.2997	−	3.91842i	−1.53633	−	0.258373i
$231$	0.375203	−	3.40350i	0.0246865	−	0.223934i
$232$	−0.282882	−	11.9078i	−0.0185721	−	0.781788i
$233$	12.8283	−	7.40645i	0.840413	−	0.485213i	−0.0169916	−	0.999856i	$-0.505409\pi$
$233$	12.8283	−	7.40645i	0.840413	−	0.485213i	0.857405	+	0.514643i	$0.172076\pi$
$234$	−0.858788	−	1.10428i	−0.0561407	−	0.0721891i
$235$	17.6821	−	10.2088i	1.15345	−	0.665946i
$236$	8.16297	−	7.07279i	0.531364	−	0.460400i
$237$	18.4058	+	13.5159i	1.19558	+	0.877951i
$238$	−3.11471	+	1.16167i	−0.201896	+	0.0752997i
$239$	4.17131	+	7.22491i	0.269819	+	0.467341i	0.968815	−	0.247785i	$-0.0797027\pi$
$239$	4.17131	+	7.22491i	0.269819	+	0.467341i	−0.698996	+	0.715126i	$0.746369\pi$
$240$	−3.69348	−	13.2970i	−0.238413	−	0.858318i
$241$	27.1398			1.74823			0.874114	−	0.485721i	$-0.161443\pi$
$241$	27.1398			1.74823			0.874114	+	0.485721i	$0.161443\pi$
$242$	−2.12943	+	12.6620i	−0.136885	+	0.813946i
$243$	−13.6935	+	7.44905i	−0.878438	+	0.477857i
$244$	−0.955314	−	4.95750i	−0.0611577	−	0.317371i
$245$	−8.56559	−	4.94534i	−0.547235	−	0.315946i
$246$	1.16102	+	0.329351i	0.0740237	+	0.0209986i
$247$	−0.134989	+	0.0779361i	−0.00858916	+	0.00495895i
$248$	0.289837	+	12.2006i	0.0184046	+	0.774739i
$249$	5.11399	+	0.563767i	0.324086	+	0.0357273i
$250$	−5.93814	−	15.9215i	−0.375561	−	1.00697i
$251$	−13.1244	+	22.7322i	−0.828407	+	1.43484i	0.0708799	+	0.997485i	$0.477419\pi$
$251$	−13.1244	+	22.7322i	−0.828407	+	1.43484i	−0.899287	+	0.437359i	$0.855914\pi$
$252$	−4.06077	−	7.53365i	−0.255805	−	0.474575i
$253$	−11.6243			−0.730814
$254$	16.5413	−	20.0331i	1.03789	−	1.25699i
$255$	−5.65136	−	0.623007i	−0.353902	−	0.0390142i
$256$	−15.3513	−	4.50971i	−0.959457	−	0.281857i
$257$	24.5268	−	14.1606i	1.52994	−	0.883311i	0.530576	−	0.847637i	$-0.321975\pi$
$257$	24.5268	−	14.1606i	1.52994	−	0.883311i	0.999363	−	0.0356741i	$-0.0113578\pi$
$258$	9.26387	−	8.99700i	0.576744	−	0.560129i
$259$			7.71131i			0.479158i
$260$	1.28985	−	0.248555i	0.0799931	−	0.0154147i
$261$	2.75204	−	12.3304i	0.170347	−	0.763230i
$262$	9.68785	−	3.61320i	0.598517	−	0.223224i
$263$	−4.97630			−0.306852			−0.153426	−	0.988160i	$-0.549031\pi$
$263$	−4.97630			−0.306852			−0.153426	+	0.988160i	$0.549031\pi$
$264$	−2.87699	−	6.15010i	−0.177066	−	0.378513i
$265$	5.59354			0.343609
$266$	−0.893487	+	0.333237i	−0.0547832	+	0.0204321i
$267$	2.71713	−	1.19325i	0.166286	−	0.0730258i
$268$	2.35446	−	16.2005i	0.143822	−	0.989604i
$269$			15.5156i			0.946006i	0.881061	+	0.473003i	$0.156830\pi$
$269$			15.5156i			0.946006i	−0.881061	+	0.473003i	$0.843170\pi$
$270$	−0.403838	−	14.6320i	−0.0245768	−	0.890476i
$271$			13.8798i			0.843137i	0.906797	+	0.421569i	$0.138520\pi$
$271$			13.8798i			0.843137i	−0.906797	+	0.421569i	$0.861480\pi$
$272$	−4.07511	+	5.18123i	−0.247090	+	0.314158i
$273$	0.745864	−	0.327553i	0.0451417	−	0.0198244i
$274$	5.27293	+	14.1380i	0.318549	+	0.854106i
$275$	−0.715320	−	1.23897i	−0.0431354	−	0.0747127i
$276$	−23.9109	+	16.5051i	−1.43926	+	0.993488i
$277$	−22.4983			−1.35179			−0.675894	−	0.736998i	$-0.736242\pi$
$277$	−22.4983			−1.35179			−0.675894	+	0.736998i	$0.736242\pi$
$278$	−2.45843	−	6.59164i	−0.147447	−	0.395340i
$279$	−2.81970	+	12.6335i	−0.168811	+	0.756348i
$280$	8.03406	−	0.190857i	0.480127	−	0.0114059i
$281$	19.1482	+	11.0552i	1.14229	+	0.659500i	0.946996	−	0.321245i	$-0.104101\pi$
$281$	19.1482	+	11.0552i	1.14229	+	0.659500i	0.195292	+	0.980745i	$0.437435\pi$
$282$	6.85204	−	24.1546i	0.408033	−	1.43839i
$283$			1.96701i			0.116926i	0.998290	+	0.0584632i	$0.0186200\pi$
$283$			1.96701i			0.116926i	−0.998290	+	0.0584632i	$0.981380\pi$
$284$	−23.5418	−	8.14875i	−1.39695	−	0.483539i
$285$	−1.62116	−	0.178716i	−0.0960289	−	0.0105862i
$286$	0.605531	−	0.225840i	0.0358058	−	0.0133542i
$287$	−0.351382	+	0.608611i	−0.0207414	+	0.0359252i
$288$	−14.6503	−	8.56562i	−0.863275	−	0.504734i
$289$	−7.14214	−	12.3705i	−0.420126	−	0.727679i
$290$	9.14775	+	7.55327i	0.537174	+	0.443543i
$291$	−10.8964	−	1.20122i	−0.638758	−	0.0704168i
$292$	−4.36517	−	22.6526i	−0.255452	−	1.32564i
$293$		−	31.9164i		−	1.86457i	−0.361718	−	0.932287i	$-0.617810\pi$
$293$		−	31.9164i		−	1.86457i	0.361718	−	0.932287i	$-0.382190\pi$
$294$	−11.7930	+	2.97593i	−0.687782	+	0.173560i
$295$			10.7572i			0.626311i
$296$	7.95779	+	13.0570i	0.462537	+	0.758923i
$297$	−1.38984	−	7.06624i	−0.0806467	−	0.410025i
$298$	5.59101	+	14.9908i	0.323879	+	0.868395i
$299$	−1.38275	−	2.39499i	−0.0799662	−	0.138506i
$300$	−3.23058	−	1.53286i	−0.186517	−	0.0884998i
$301$	3.76000	+	6.51250i	0.216723	+	0.375374i
$302$	−6.10483	−	1.02668i	−0.351294	−	0.0590787i
$303$	−4.90299	−	3.60041i	−0.281670	−	0.206838i
$304$	−1.16899	+	1.48629i	−0.0670461	+	0.0852447i
$305$	4.35465	+	2.51416i	0.249347	+	0.143960i
$306$	−5.51911	+	4.29215i	−0.315506	+	0.245366i
$307$	−7.17571	−	4.14290i	−0.409539	−	0.236448i	0.281053	−	0.959692i	$-0.409316\pi$
$307$	−7.17571	−	4.14290i	−0.409539	−	0.236448i	−0.690592	+	0.723245i	$0.742650\pi$
$308$	3.88241	−	0.748143i	0.221221	−	0.0426294i
$309$	−7.02282	−	5.15705i	−0.399514	−	0.293374i
$310$	−9.37265	−	7.73897i	−0.532331	−	0.439544i
$311$	19.9145			1.12925			0.564624	−	0.825348i	$-0.309021\pi$
$311$	19.9145			1.12925			0.564624	+	0.825348i	$0.309021\pi$
$312$	0.924895	−	1.32433i	0.0523619	−	0.0749752i
$313$	15.8649			0.896739			0.448369	−	0.893848i	$-0.352005\pi$
$313$	15.8649			0.896739			0.448369	+	0.893848i	$0.352005\pi$
$314$	0.935801	−	5.56445i	0.0528103	−	0.314020i
$315$	8.31912	+	1.85677i	0.468729	+	0.104617i
$316$	−8.62492	+	24.9175i	−0.485190	+	1.40172i
$317$	20.0863	+	11.5968i	1.12816	+	0.651342i	0.943471	−	0.331456i	$-0.107540\pi$
$317$	20.0863	+	11.5968i	1.12816	+	0.651342i	0.184686	+	0.982797i	$0.440873\pi$
$318$	4.93435	−	4.79220i	0.276704	−	0.268733i
$319$	5.05463	+	2.91829i	0.283005	+	0.163393i
$320$	13.4065	−	8.61402i	0.749448	−	0.481538i
$321$	−0.809672	−	1.84369i	−0.0451915	−	0.102905i
$322$	−5.91231	−	15.8523i	−0.329480	−	0.883414i
$323$	0.389518	+	0.674665i	0.0216734	+	0.0375394i
$324$	−12.8920	−	12.5617i	−0.716225	−	0.697870i
$325$	0.170179	−	0.294758i	0.00943983	−	0.0163503i
$326$	8.92000	−	10.8030i	0.494033	−	0.598322i
$327$	−4.66382	−	10.6199i	−0.257910	−	0.587281i
$328$	0.0330951	+	1.39313i	0.00182737	+	0.0769228i
$329$	12.6620	+	7.31039i	0.698077	+	0.403035i
$330$	6.50564	+	1.84548i	0.358124	+	0.101590i
$331$	−0.715909	+	0.413330i	−0.0393499	+	0.0227187i	−0.519546	−	0.854443i	$-0.673899\pi$
$331$	−0.715909	+	0.413330i	−0.0393499	+	0.0227187i	0.480196	+	0.877161i	$0.340566\pi$
$332$	1.12413	+	5.83357i	0.0616948	+	0.320159i
$333$	4.85490	+	15.4748i	0.266047	+	0.848012i
$334$	8.46555	+	6.98998i	0.463214	+	0.382475i
$335$	10.6589	+	12.3381i	0.582356	+	0.674102i
$336$	6.92373	−	7.05145i	0.377721	−	0.384688i
$337$	−7.76102	+	13.4425i	−0.422770	+	0.732259i	−0.996209	−	0.0869891i	$-0.972275\pi$
$337$	−7.76102	+	13.4425i	−0.422770	+	0.732259i	0.573439	+	0.819248i	$0.305609\pi$
$338$	−14.0581	−	11.6077i	−0.764661	−	0.631378i
$339$	0.213960	+	0.157117i	0.0116207	+	0.00853342i
$340$	−1.24226	−	6.44656i	−0.0673709	−	0.349614i
$341$	−5.17891	−	2.99004i	−0.280453	−	0.161920i
$342$	−1.58322	+	1.23125i	−0.0856105	+	0.0665784i
$343$		−	17.0674i		−	0.921552i
$344$	13.0872	+	7.14697i	0.705614	+	0.385339i
$345$	3.17080	−	28.7626i	0.170710	−	1.54853i
$346$	5.23895	+	0.881059i	0.281648	+	0.0473660i
$347$	1.37180	+	2.37602i	0.0736420	+	0.127552i	0.900495	−	0.434867i	$-0.143204\pi$
$347$	1.37180	+	2.37602i	0.0736420	+	0.127552i	−0.826853	+	0.562418i	$0.809871\pi$
$348$	14.5409	−	1.17411i	0.779472	−	0.0629386i
$349$	28.5466			1.52806			0.764031	−	0.645179i	$-0.223217\pi$
$349$	28.5466			1.52806			0.764031	+	0.645179i	$0.223217\pi$
$350$	1.32579	−	1.60566i	0.0708662	−	0.0858260i
$351$	1.29055	−	1.12690i	0.0688845	−	0.0601496i
$352$	5.80174	−	5.27328i	0.309234	−	0.281067i
$353$	18.7577	+	10.8298i	0.998371	+	0.576410i	0.907766	−	0.419477i	$-0.137786\pi$
$353$	18.7577	+	10.8298i	0.998371	+	0.576410i	0.0906054	+	0.995887i	$0.471120\pi$
$354$	9.21614	+	9.48950i	0.489832	+	0.504361i
$355$	21.4875	−	12.4058i	1.14044	−	0.658432i
$356$	2.24392	+	2.58979i	0.118928	+	0.137259i
$357$	−1.63708	−	3.72777i	−0.0866436	−	0.197294i
$358$	−3.62150	+	1.35068i	−0.191402	+	0.0713859i
$359$	−0.888052			−0.0468696			−0.0234348	−	0.999725i	$-0.507460\pi$
$359$	−0.888052			−0.0468696			−0.0234348	+	0.999725i	$0.507460\pi$
$360$	16.0023	−	5.44110i	0.843394	−	0.286771i
$361$	−9.38826	−	16.2609i	−0.494119	−	0.855839i
$362$	−7.22685	−	5.96719i	−0.379835	−	0.313628i
$363$	−15.6308	−	1.72314i	−0.820406	−	0.0904416i
$364$	0.615966	+	0.710909i	0.0322854	+	0.0372618i
$365$	19.8979	+	11.4881i	1.04151	+	0.601314i
$366$	5.99543	−	1.51293i	0.313386	−	0.0790820i
$367$	19.2020	−	11.0863i	1.00234	−	0.578699i	0.0933975	−	0.995629i	$-0.470227\pi$
$367$	19.2020	−	11.0863i	1.00234	−	0.578699i	0.908939	+	0.416930i	$0.136894\pi$
$368$	−26.3699	−	20.7403i	−1.37462	−	1.08116i
$369$	−0.321969	+	1.44256i	−0.0167610	+	0.0750967i
$370$	−15.0183	−	2.52569i	−0.780762	−	0.131305i
$371$	2.00274	+	3.46885i	0.103977	+	0.180094i
$372$	−14.8984	+	1.20297i	−0.772444	+	0.0623711i
$373$	11.7933	+	20.4265i	0.610632	+	1.05765i	0.991134	+	0.132865i	$0.0424177\pi$
$373$	11.7933	+	20.4265i	0.610632	+	1.05765i	−0.380502	+	0.924780i	$0.624249\pi$
$374$	−1.12873	−	3.02639i	−0.0583653	−	0.156491i
$375$	19.0554	−	8.36833i	0.984015	−	0.432139i
$376$	28.9837	−	0.688534i	1.49472	−	0.0355084i
$377$			1.38856i			0.0715145i
$378$	8.92948	−	5.48936i	0.459283	−	0.282342i
$379$	−25.1790	−	14.5371i	−1.29336	−	0.746722i	−0.314112	−	0.949386i	$-0.601707\pi$
$379$	−25.1790	−	14.5371i	−1.29336	−	0.746722i	−0.979248	+	0.202664i	$0.935040\pi$
$380$	−0.356355	−	1.84927i	−0.0182806	−	0.0948654i
$381$	25.6463	+	18.8328i	1.31390	+	0.964835i
$382$	−3.07381	+	18.2775i	−0.157270	+	0.935158i
$383$	5.82460	−	10.0885i	0.297623	−	0.515499i	−0.677968	−	0.735091i	$-0.737139\pi$
$383$	5.82460	−	10.0885i	0.297623	−	0.515499i	0.975592	+	0.219592i	$0.0704727\pi$
$384$	4.44662	−	19.0847i	0.226916	−	0.973914i
$385$	−1.96893	+	3.41029i	−0.100346	+	0.173805i
$386$	18.5210	−	6.90762i	0.942692	−	0.351589i
$387$	11.6456	+	10.7018i	0.591977	+	0.544004i
$388$	−2.39520	−	12.4296i	−0.121598	−	0.631019i
$389$	−19.8472	−	11.4588i	−1.00629	−	0.580984i	−0.0961899	−	0.995363i	$-0.530666\pi$
$389$	−19.8472	−	11.4588i	−1.00629	−	0.580984i	−0.910105	+	0.414379i	$0.863999\pi$
$390$	0.393636	+	1.55990i	0.0199325	+	0.0789886i
$391$	−11.9699	+	6.91085i	−0.605346	+	0.349497i
$392$	−7.30900	−	11.9925i	−0.369160	−	0.605712i
$393$	5.09191	+	11.5947i	0.256853	+	0.584875i
$394$	−3.46938	+	4.20176i	−0.174785	+	0.211682i
$395$	−13.1307	−	22.7431i	−0.660679	−	1.14433i
$396$	7.32005	−	3.94564i	0.367846	−	0.198276i
$397$	−17.7162			−0.889153			−0.444576	−	0.895741i	$-0.646646\pi$
$397$	−17.7162			−0.889153			−0.444576	+	0.895741i	$0.646646\pi$
$398$	19.8077	+	3.33115i	0.992868	+	0.166975i
$399$	−0.469615	−	1.06935i	−0.0235102	−	0.0535345i
$400$	0.587878	−	4.08691i	0.0293939	−	0.204345i
$401$		−	3.64702i		−	0.182124i	−0.995845	−	0.0910618i	$-0.970974\pi$
$401$		−	3.64702i		−	0.182124i	0.995845	−	0.0910618i	$-0.0290261\pi$
$402$	19.9732	+	1.75220i	0.996174	+	0.0873917i
$403$		−	1.42270i		−	0.0708696i
$404$	2.29753	−	6.63760i	0.114307	−	0.330233i
$405$	17.8635	−	1.51148i	0.887643	−	0.0751059i
$406$	−1.40887	+	8.37740i	−0.0699210	+	0.415763i
$407$	−7.49268			−0.371398
$408$	−6.61887	−	4.62255i	−0.327683	−	0.228850i
$409$	−16.2971	−	28.2274i	−0.805841	−	1.39576i	−0.915722	−	0.401812i	$-0.868380\pi$
$409$	−16.2971	−	28.2274i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$410$	−1.07022	−	0.883677i	−0.0528544	−	0.0436417i
$411$	−16.9207	+	7.43089i	−0.834638	+	0.366539i
$412$	3.29088	−	9.50738i	0.162130	−	0.468395i
$413$	−6.67112	+	3.85157i	−0.328264	+	0.189524i
$414$	−21.8449	−	28.0895i	−1.07362	−	1.38052i
$415$	−5.12419	−	2.95845i	−0.251537	−	0.145225i
$416$	1.77660	+	0.568076i	0.0871051	+	0.0278522i
$417$	7.88906	−	3.46455i	0.386329	−	0.169660i
$418$	−0.323789	−	0.868154i	−0.0158370	−	0.0424628i
$419$	−6.19276	+	10.7262i	−0.302536	+	0.524008i	−0.976710	−	0.214565i	$-0.931167\pi$
$419$	−6.19276	+	10.7262i	−0.302536	+	0.524008i	0.674174	+	0.738573i	$0.264500\pi$
$420$	0.792153	+	9.81052i	0.0386531	+	0.478704i
$421$	−6.48480	+	11.2320i	−0.316050	+	0.547414i	−0.979660	−	0.200664i	$-0.935690\pi$
$421$	−6.48480	+	11.2320i	−0.316050	+	0.547414i	0.663610	+	0.748078i	$0.269023\pi$
$422$	−32.0272	−	5.38617i	−1.55906	−	0.262195i
$423$	30.0120	+	6.69847i	1.45924	+	0.325691i
$424$	6.97082	+	3.80679i	0.338533	+	0.184874i
$425$	−1.47318	−	0.850540i	−0.0714597	−	0.0412573i
$426$	8.32667	−	29.3529i	0.403429	−	1.42215i
$427$			3.60073i			0.174251i
$428$	1.75728	−	1.52259i	0.0849415	−	0.0735974i
$429$	0.318266	+	0.724717i	0.0153660	+	0.0349897i
$430$	−13.9150	+	5.18978i	−0.671042	+	0.250273i
$431$	−19.8155	−	34.3214i	−0.954477	−	1.65320i	−0.735561	−	0.677459i	$-0.763081\pi$
$431$	−19.8155	−	34.3214i	−0.954477	−	1.65320i	−0.218916	−	0.975744i	$-0.570252\pi$
$432$	9.45482	−	18.5096i	0.454895	−	0.890545i
$433$	0.905785	+	1.56887i	0.0435292	+	0.0753949i	0.886969	−	0.461829i	$-0.152806\pi$
$433$	0.905785	+	1.56887i	0.0435292	+	0.0753949i	−0.843440	+	0.537224i	$0.819473\pi$
$434$	1.44351	−	8.58336i	0.0692905	−	0.412015i
$435$	−8.59966	+	11.7109i	−0.412322	+	0.561495i
$436$	10.1222	−	8.77035i	0.484764	−	0.420023i
$437$	−3.43371	+	1.98245i	−0.164257	+	0.0948336i
$438$	27.3953	−	6.91310i	1.30900	−	0.330321i
$439$	−20.8055	−	12.0120i	−0.992991	−	0.573304i	−0.0868242	−	0.996224i	$-0.527672\pi$
$439$	−20.8055	−	12.0120i	−0.992991	−	0.573304i	−0.906167	+	0.422920i	$0.861005\pi$
$440$	0.185445	+	7.80627i	0.00884076	+	0.372149i
$441$	−4.45909	−	14.2131i	−0.212337	−	0.676816i
$442$	0.489270	−	0.592554i	0.0232722	−	0.0281849i
$443$	15.7377	+	27.2584i	0.747719	+	1.29509i	0.948914	+	0.315536i	$0.102184\pi$
$443$	15.7377	+	27.2584i	0.747719	+	1.29509i	−0.201195	+	0.979551i	$0.564482\pi$
$444$	−15.4122	+	10.6387i	−0.731432	+	0.504889i
$445$	−3.41285			−0.161785
$446$	7.56916	+	20.2947i	0.358410	+	0.960982i
$447$	−17.9414	+	7.87914i	−0.848601	+	0.372671i
$448$	10.1421	+	5.22988i	0.479171	+	0.247089i
$449$	−13.8124	+	7.97460i	−0.651848	+	0.376345i	−0.789164	−	0.614182i	$-0.789486\pi$
$449$	−13.8124	+	7.97460i	−0.651848	+	0.376345i	0.137316	+	0.990527i	$0.456153\pi$
$450$	1.64964	−	4.05686i	0.0777650	−	0.191242i
$451$	−0.591355	−	0.341419i	−0.0278458	−	0.0160768i
$452$	−0.100261	+	0.289656i	−0.00471590	+	0.0136243i
$453$	0.830792	−	7.53620i	0.0390340	−	0.354082i
$454$	−1.28243	−	1.05890i	−0.0601875	−	0.0496966i
$455$	−0.936842			−0.0439198
$456$	−1.89870	−	1.32603i	−0.0889146	−	0.0620970i
$457$	8.25472	+	14.2976i	0.386139	+	0.668813i	0.991927	−	0.126814i	$-0.0404751\pi$
$457$	8.25472	+	14.2976i	0.386139	+	0.668813i	−0.605787	+	0.795627i	$0.707142\pi$
$458$	6.99942	−	41.6199i	0.327061	−	1.94477i
$459$	−5.63217	−	6.45006i	−0.262887	−	0.301063i
$460$	32.8098	−	6.32247i	1.52976	−	0.294787i
$461$		−	16.7014i		−	0.777861i	−0.921267	−	0.388931i	$-0.872845\pi$
$461$		−	16.7014i		−	0.777861i	0.921267	−	0.388931i	$-0.127155\pi$
$462$	1.18483	+	4.69525i	0.0551234	+	0.218443i
$463$	−26.6243	−	15.3715i	−1.23734	−	0.714376i	−0.268787	−	0.963200i	$-0.586623\pi$
$463$	−26.6243	−	15.3715i	−1.23734	−	0.714376i	−0.968549	+	0.248824i	$0.919956\pi$
$464$	6.25964	+	15.6387i	0.290596	+	0.726011i
$465$	8.81108	−	11.9988i	0.408604	−	0.556433i
$466$	−13.3380	+	16.1537i	−0.617872	+	0.748304i
$467$	−15.6445	+	27.0971i	−0.723942	+	1.25390i	0.235467	+	0.971882i	$0.424338\pi$
$467$	−15.6445	+	27.0971i	−0.723942	+	1.25390i	−0.959408	+	0.282021i	$0.908995\pi$
$468$	1.68367	+	1.03882i	0.0778278	+	0.0480197i
$469$	−3.83514	+	11.0277i	−0.177090	+	0.509212i
$470$	−18.3846	+	22.2656i	−0.848020	+	1.02704i
$471$	6.86912	+	0.757253i	0.316512	+	0.0348924i
$472$	−7.32104	+	13.4059i	−0.336978	+	0.617059i
$473$	−6.32786	+	3.65339i	−0.290955	+	0.167983i
$474$	−31.0682	−	8.81324i	−1.42701	−	0.404805i
$475$	−0.422597	−	0.243987i	−0.0193901	−	0.0111949i
$476$	3.55306	−	3.07855i	0.162854	−	0.141105i
$477$	6.20294	+	5.70026i	0.284013	+	0.260997i
$478$	−9.09773	−	7.51197i	−0.416120	−	0.343589i
$479$	−13.2988	+	23.0342i	−0.607638	+	1.05246i	0.383991	+	0.923337i	$0.374549\pi$
$479$	−13.2988	+	23.0342i	−0.607638	+	1.05246i	−0.991629	+	0.129123i	$0.958784\pi$
$480$	11.4654	+	15.7940i	0.523321	+	0.720893i
$481$	−0.891276	−	1.54374i	−0.0406387	−	0.0703883i
$482$	−35.9617	+	13.4124i	−1.63801	+	0.610916i
$483$	18.9725	−	8.33193i	0.863278	−	0.379116i
$484$	−3.43590	−	17.8302i	−0.156177	−	0.810465i
$485$	10.9181	+	6.30359i	0.495767	+	0.286231i
$486$	14.4633	−	16.6377i	0.656070	−	0.754700i
$487$	−24.3776	−	14.0744i	−1.10465	−	0.637772i	−0.167214	−	0.985921i	$-0.553477\pi$
$487$	−24.3776	−	14.0744i	−1.10465	−	0.637772i	−0.937439	+	0.348149i	$0.886810\pi$
$488$	3.71582	+	6.09685i	0.168207	+	0.275991i
$489$	13.8300	+	10.1557i	0.625412	+	0.459258i
$490$	13.7938	+	2.31978i	0.623142	+	0.104797i
$491$	18.0851			0.816168			0.408084	−	0.912944i	$-0.366197\pi$
$491$	18.0851			0.816168			0.408084	+	0.912944i	$0.366197\pi$
$492$	−1.70117	+	0.137362i	−0.0766949	+	0.00619275i
$493$	6.93991			0.312558
$494$	0.140352	−	0.169981i	0.00631476	−	0.00764779i
$495$	−1.80412	+	8.08325i	−0.0810893	+	0.363315i
$496$	−6.41353	−	16.0232i	−0.287976	−	0.719464i
$497$	15.3870	+	8.88367i	0.690200	+	0.398487i
$498$	−7.05492	+	1.78029i	−0.316139	+	0.0797766i
$499$	−25.7656	−	14.8758i	−1.15343	−	0.665932i	−0.203707	−	0.979032i	$-0.565299\pi$
$499$	−25.7656	−	14.8758i	−1.15343	−	0.665932i	−0.949720	+	0.313100i	$0.898632\pi$
$500$	15.7367	+	18.1623i	0.703767	+	0.812244i
$501$	−7.95833	+	10.8376i	−0.355552	+	0.484187i
$502$	6.15645	−	36.6075i	0.274776	−	1.63387i
$503$	−6.65871	−	11.5332i	−0.296897	−	0.514241i	0.678527	−	0.734575i	$-0.262619\pi$
$503$	−6.65871	−	11.5332i	−0.296897	−	0.514241i	−0.975424	+	0.220334i	$0.929285\pi$
$504$	9.10384	+	7.97569i	0.405517	+	0.355265i
$505$	3.49781	+	6.05838i	0.155650	+	0.269594i
$506$	15.4028	−	5.74468i	0.684740	−	0.255382i
$507$	13.2158	−	17.9972i	0.586935	−	0.799282i
$508$	−12.0178	+	34.7196i	−0.533205	+	1.54043i
$509$		−	1.74765i		−	0.0774632i	−0.999250	−	0.0387316i	$-0.987668\pi$
$509$		−	1.74765i		−	0.0774632i	0.999250	−	0.0387316i	$-0.0123317\pi$
$510$	7.79625	−	1.96736i	0.345224	−	0.0871162i
$511$			16.4530i			0.727838i
$512$	22.5700	−	1.61094i	0.997462	−	0.0711941i
$513$	−1.61565	−	1.85027i	−0.0713326	−	0.0816915i
$514$	−25.5013	+	30.8846i	−1.12481	+	1.36226i
$515$	5.01010	+	8.67774i	0.220771	+	0.382387i
$516$	−7.82886	+	16.4997i	−0.344646	+	0.726358i
$517$	−7.10312	+	12.3030i	−0.312395	+	0.541084i
$518$	−3.81090	−	10.2179i	−0.167441	−	0.448949i
$519$	−0.712956	+	6.46730i	−0.0312953	+	0.283883i
$520$	−1.58629	+	0.966787i	−0.0695633	+	0.0423964i
$521$		−	23.0615i		−	1.01034i	−0.863019	−	0.505172i	$-0.831429\pi$
$521$		−	23.0615i		−	1.01034i	0.863019	−	0.505172i	$-0.168571\pi$
$522$	2.44699	+	17.6984i	0.107102	+	0.774640i
$523$	−24.9840	−	14.4245i	−1.09248	−	0.630741i	−0.158241	−	0.987401i	$-0.550582\pi$
$523$	−24.9840	−	14.4245i	−1.09248	−	0.630741i	−0.934234	+	0.356660i	$0.883916\pi$
$524$	−11.0513	+	9.57538i	−0.482778	+	0.418302i
$525$	2.05556	+	1.50945i	0.0897118	+	0.0658779i
$526$	6.59387	−	2.45927i	0.287507	−	0.107229i
$527$	−7.11053			−0.309739
$528$	6.85152	+	6.72743i	0.298174	+	0.292774i
$529$	−23.6728	−	41.0024i	−1.02925	−	1.78271i
$530$	−7.41175	+	2.76430i	−0.321946	+	0.120074i
$531$	−10.9625	+	11.9292i	−0.475731	+	0.517683i
$532$	1.01924	−	0.883115i	0.0441895	−	0.0382879i
$533$		−	0.162451i		−	0.00703655i
$534$	−3.01065	+	2.92392i	−0.130283	+	0.126530i
$535$			2.31576i			0.100119i
$536$	4.88643	+	22.6301i	0.211061	+	0.977473i
$537$	−1.90345	−	4.33432i	−0.0821401	−	0.187040i
$538$	−7.66776	−	20.5591i	−0.330581	−	0.886365i
$539$	6.88181			0.296420
$540$	7.76618	+	19.1886i	0.334203	+	0.825748i
$541$	−16.5932			−0.713397			−0.356699	−	0.934220i	$-0.616098\pi$
$541$	−16.5932			−0.713397			−0.356699	+	0.934220i	$0.616098\pi$
$542$	−6.85933	−	18.3915i	−0.294633	−	0.789982i
$543$	6.79385	−	9.25179i	0.291552	−	0.397032i
$544$	2.83920	−	8.87931i	0.121730	−	0.380697i
$545$			13.3391i			0.571384i
$546$	−0.826436	+	0.802628i	−0.0353682	+	0.0343493i
$547$	−20.6738	+	11.9360i	−0.883949	+	0.510348i	−0.871958	−	0.489580i	$-0.837150\pi$
$547$	−20.6738	+	11.9360i	−0.883949	+	0.510348i	−0.0119903	+	0.999928i	$0.503817\pi$
$548$	−13.9738	−	16.1277i	−0.596933	−	0.688943i
$549$	2.26695	+	7.22580i	0.0967511	+	0.308390i
$550$	1.56013	+	1.28820i	0.0665242	+	0.0549289i
$551$	1.99079			0.0848104
$552$	23.5265	−	33.6868i	1.00135	−	1.43380i
$553$	9.40278	−	16.2861i	0.399847	−	0.692555i
$554$	29.8114	−	11.1185i	1.26657	−	0.472381i
$555$	2.04380	−	18.5395i	0.0867544	−	0.786959i
$556$	6.51512	+	7.51934i	0.276303	+	0.318891i
$557$	−11.2728	+	6.50833i	−0.477642	+	0.275767i	−0.719433	−	0.694562i	$-0.755598\pi$
$557$	−11.2728	+	6.50833i	−0.477642	+	0.275767i	0.241791	+	0.970328i	$0.422265\pi$
$558$	−2.50716	−	18.1336i	−0.106136	−	0.767655i
$559$	−1.50543	−	0.869163i	−0.0636731	−	0.0367617i
$560$	−10.5512	+	4.22329i	−0.445872	+	0.178467i
$561$	3.62208	−	1.59067i	0.152924	−	0.0671580i
$562$	−30.8359	−	5.18583i	−1.30073	−	0.218751i
$563$	7.50206			0.316174			0.158087	−	0.987425i	$-0.449467\pi$
$563$	7.50206			0.316174			0.158087	+	0.987425i	$0.449467\pi$
$564$	2.85777	+	35.3924i	0.120334	+	1.49029i
$565$	−0.152640	−	0.264380i	−0.00642160	−	0.0111225i
$566$	−0.972086	−	2.60639i	−0.0408598	−	0.109555i
$567$	7.33327	+	10.5369i	0.307968	+	0.442508i
$568$	35.2213	−	0.836714i	1.47785	−	0.0351077i
$569$	−25.1152	+	14.5003i	−1.05288	+	0.607883i	−0.923455	−	0.383706i	$-0.874648\pi$
$569$	−25.1152	+	14.5003i	−1.05288	+	0.607883i	−0.129429	+	0.991589i	$0.541314\pi$
$570$	2.23644	−	0.564359i	0.0936742	−	0.0236384i
$571$	6.84793	−	3.95365i	0.286577	−	0.165455i	−0.349820	−	0.936817i	$-0.613757\pi$
$571$	6.84793	−	3.95365i	0.286577	−	0.165455i	0.636397	+	0.771362i	$0.280424\pi$
$572$	−0.690753	+	0.598502i	−0.0288818	+	0.0250246i
$573$	−22.5629	−	2.48734i	−0.942580	−	0.103910i
$574$	0.164827	−	0.980095i	0.00687976	−	0.0409084i
$575$	4.32883	−	7.49775i	0.180524	−	0.312678i
$576$	23.6455	+	4.10982i	0.985229	+	0.171242i
$577$	−9.57722	−	16.5882i	−0.398705	−	0.690577i	0.594862	−	0.803828i	$-0.297207\pi$
$577$	−9.57722	−	16.5882i	−0.398705	−	0.690577i	−0.993566	+	0.113251i	$0.963874\pi$
$578$	15.5772	+	12.8620i	0.647926	+	0.534990i
$579$	9.73458	+	22.1664i	0.404555	+	0.921205i
$580$	−15.8541	−	5.48772i	−0.658304	−	0.227865i
$581$		−	4.23703i		−	0.175782i
$582$	15.0320	−	3.79327i	0.623095	−	0.157236i
$583$	−3.37049	+	1.94596i	−0.139592	+	0.0805933i
$584$	16.9789	+	27.8587i	0.702591	+	1.15280i
$585$	−1.88002	+	0.589819i	−0.0777292	+	0.0243860i
$586$	15.7729	+	42.2910i	0.651574	+	1.74702i
$587$	22.5082	−	38.9853i	0.929013	−	1.60910i	0.144035	−	0.989573i	$-0.453992\pi$
$587$	22.5082	−	38.9853i	0.929013	−	1.60910i	0.784977	−	0.619524i	$-0.212674\pi$
$588$	14.1557	−	9.77131i	0.583770	−	0.402962i
$589$	−2.03973			−0.0840457
$590$	−5.31618	−	14.2539i	−0.218864	−	0.586825i
$591$	−5.37908	−	3.95001i	−0.221266	−	0.162482i
$592$	−16.9972	−	13.3685i	−0.698582	−	0.549444i
$593$	−34.9739	−	20.1922i	−1.43621	−	0.829195i	−0.438624	−	0.898671i	$-0.644534\pi$
$593$	−34.9739	−	20.1922i	−1.43621	−	0.829195i	−0.997584	+	0.0694756i	$0.977867\pi$
$594$	5.33372	+	8.67630i	0.218845	+	0.355993i
$595$			4.68226i			0.191954i
$596$	−14.8168	−	17.1006i	−0.606920	−	0.700468i
$597$	−2.69558	+	24.4519i	−0.110323	+	1.00075i
$598$	3.01580	+	2.49014i	0.123325	+	0.101829i
$599$	9.34904	+	16.1930i	0.381991	+	0.661628i	0.991347	−	0.131269i	$-0.0419051\pi$
$599$	9.34904	+	16.1930i	0.381991	+	0.661628i	−0.609356	+	0.792897i	$0.708572\pi$
$600$	5.03823	+	0.434589i	0.205685	+	0.0177420i
$601$	8.16608	−	14.1441i	0.333101	−	0.576949i	−0.650017	−	0.759920i	$-0.725238\pi$
$601$	8.16608	−	14.1441i	0.333101	−	0.576949i	0.983118	+	0.182971i	$0.0585715\pi$
$602$	−8.20065	−	6.77125i	−0.334234	−	0.275976i
$603$	−0.753368	+	24.5445i	−0.0306795	+	0.999529i
$604$	8.59662	−	1.65657i	0.349791	−	0.0674050i
$605$	15.6620	+	9.04247i	0.636751	+	0.367629i
$606$	8.27604	+	2.34770i	0.336191	+	0.0953688i
$607$	15.8571	−	9.15508i	0.643619	−	0.371593i	−0.142388	−	0.989811i	$-0.545478\pi$
$607$	15.8571	−	9.15508i	0.643619	−	0.371593i	0.786007	+	0.618217i	$0.212145\pi$
$608$	0.814455	−	2.54713i	0.0330305	−	0.103300i
$609$	−10.3416	−	1.14006i	−0.419063	−	0.0461976i
$610$	−7.01264	−	1.17935i	−0.283933	−	0.0477505i
$611$	−3.37975			−0.136730
$612$	5.19196	−	8.41485i	0.209872	−	0.340150i
$613$	−8.86012	+	15.3462i	−0.357857	+	0.619826i	−0.987603	−	0.156975i	$-0.949826\pi$
$613$	−8.86012	+	15.3462i	−0.357857	+	0.619826i	0.629746	+	0.776801i	$0.283159\pi$
$614$	11.5556	+	1.94336i	0.466346	+	0.0784277i
$615$	1.00610	−	1.37009i	0.0405698	−	0.0552474i
$616$	−4.77468	+	2.91000i	−0.192377	+	0.117247i
$617$		−	6.00728i		−	0.241844i	−0.992662	−	0.120922i	$-0.961415\pi$
$617$		−	6.00728i		−	0.241844i	0.992662	−	0.120922i	$-0.0385851\pi$
$618$	11.8542	+	3.36273i	0.476846	+	0.135269i
$619$	30.7325	+	17.7434i	1.23524	+	0.713168i	0.968118	−	0.250494i	$-0.0805930\pi$
$619$	30.7325	+	17.7434i	1.23524	+	0.713168i	0.267125	+	0.963662i	$0.413926\pi$
$620$	16.2438	+	5.62263i	0.652368	+	0.225810i
$621$	32.8276	−	28.6649i	1.31733	−	1.15028i
$622$	−26.3878	+	9.84167i	−1.05806	+	0.394615i
$623$	−1.22195	−	2.11649i	−0.0489565	−	0.0847952i
$624$	−0.571061	+	2.21188i	−0.0228607	+	0.0885462i
$625$	−18.7733			−0.750931
$626$	−21.0219	+	7.84038i	−0.840204	+	0.313364i
$627$	1.03903	−	0.456300i	0.0414949	−	0.0182229i
$628$	1.50994	+	7.83567i	0.0602531	+	0.312677i
$629$	−7.71546	+	4.45453i	−0.307636	+	0.177614i
$630$	−11.9409	+	1.65095i	−0.475737	+	0.0657756i
$631$	35.8386	+	20.6914i	1.42671	+	0.823713i	0.996860	−	0.0791851i	$-0.0252318\pi$
$631$	35.8386	+	20.6914i	1.42671	+	0.823713i	0.429854	+	0.902899i	$0.358565\pi$
$632$	−0.885607	−	37.2794i	−0.0352276	−	1.48289i
$633$	4.35850	−	39.5364i	0.173235	−	1.57143i
$634$	−32.3465	−	5.43987i	−1.28464	−	0.216045i
$635$	−18.2962	−	31.6899i	−0.726061	−	1.25757i
$636$	−4.17000	+	8.78846i	−0.165351	+	0.348485i
$637$	0.818611	+	1.41788i	0.0324346	+	0.0561783i
$638$	−8.13988	−	1.36892i	−0.322261	−	0.0541962i
$639$	36.4710	+	8.14006i	1.44277	+	0.322016i
$640$	−13.5074	+	18.0395i	−0.533926	+	0.713074i
$641$	−21.1332	+	12.2013i	−0.834713	+	0.481922i	−0.855464	−	0.517863i	$-0.826728\pi$
$641$	−21.1332	+	12.2013i	−0.834713	+	0.481922i	0.0207506	+	0.999785i	$0.493394\pi$
$642$	1.98400	+	2.04285i	0.0783023	+	0.0806249i
$643$			14.9319i			0.588858i	0.955673	+	0.294429i	$0.0951295\pi$
$643$			14.9319i			0.588858i	−0.955673	+	0.294429i	$0.904870\pi$
$644$	15.6683	+	18.0833i	0.617416	+	0.712583i
$645$	−7.31370	−	16.6539i	−0.287977	−	0.655746i
$646$	−0.849549	−	0.701470i	−0.0334251	−	0.0275990i
$647$	−17.5853	+	30.4586i	−0.691348	+	1.19745i	0.280048	+	0.959986i	$0.409650\pi$
$647$	−17.5853	+	30.4586i	−0.691348	+	1.19745i	−0.971396	+	0.237464i	$0.923684\pi$
$648$	23.2906	+	10.2737i	0.914941	+	0.403589i
$649$	−3.74237	−	6.48198i	−0.146901	−	0.254440i
$650$	−0.0798281	+	0.474673i	−0.00313111	+	0.0186182i
$651$	10.5959	+	1.16809i	0.415285	+	0.0457810i
$652$	−6.48069	+	18.7228i	−0.253804	+	0.733241i
$653$	16.9833	+	9.80532i	0.664608	+	0.383712i	0.794031	−	0.607878i	$-0.207979\pi$
$653$	16.9833	+	9.80532i	0.664608	+	0.383712i	−0.129422	+	0.991590i	$0.541312\pi$
$654$	11.4281	+	11.7671i	0.446875	+	0.460130i
$655$		−	14.5635i		−	0.569043i
$656$	−0.732332	−	1.82962i	−0.0285928	−	0.0714346i
$657$	10.3585	+	33.0172i	0.404124	+	1.28812i
$658$	−20.3906	−	3.42918i	−0.794907	−	0.133683i
$659$	1.36621	+	2.36634i	0.0532199	+	0.0921796i	0.891408	−	0.453202i	$-0.149718\pi$
$659$	1.36621	+	2.36634i	0.0532199	+	0.0921796i	−0.838188	+	0.545381i	$0.816385\pi$
$660$	−9.53236	+	0.769693i	−0.371047	+	0.0299603i
$661$	−14.4867			−0.563466			−0.281733	−	0.959493i	$-0.590909\pi$
$661$	−14.4867			−0.563466			−0.281733	+	0.959493i	$0.590909\pi$
$662$	0.744353	−	0.901484i	0.0289301	−	0.0350372i
$663$	0.758586	+	0.557051i	0.0294610	+	0.0216341i
$664$	−4.37247	−	7.17426i	−0.169685	−	0.278415i
$665$			1.34316i			0.0520854i
$666$	−14.0806	−	18.1056i	−0.545611	−	0.701580i
$667$			35.3207i			1.36762i
$668$	−14.6717	−	5.07847i	−0.567666	−	0.196492i
$669$	−24.2893	+	10.6668i	−0.939077	+	0.412404i
$670$	−20.2210	−	11.0811i	−0.781206	−	0.428100i
$671$	−3.49863			−0.135063
$672$	−5.68953	+	12.7652i	−0.219479	+	0.492430i
$673$	−16.1943			−0.624246			−0.312123	−	0.950042i	$-0.601040\pi$
$673$	−16.1943			−0.624246			−0.312123	+	0.950042i	$0.601040\pi$
$674$	3.64057	−	21.6475i	0.140229	−	0.833830i
$675$	5.07534	+	1.73497i	0.195350	+	0.0667791i
$676$	24.3643	+	8.43344i	0.937087	+	0.324363i
$677$	−24.7363	+	14.2815i	−0.950693	+	0.548883i	−0.893296	−	0.449469i	$-0.851613\pi$
$677$	−24.7363	+	14.2815i	−0.950693	+	0.548883i	−0.0573966	+	0.998351i	$0.518280\pi$
$678$	−0.361155	−	0.102450i	−0.0138701	−	0.00393459i
$679$			9.02787i			0.346458i
$680$	4.83192	+	7.92813i	0.185296	+	0.304030i
$681$	1.20559	−	1.64176i	0.0461984	−	0.0629125i
$682$	8.34000	+	1.40258i	0.319355	+	0.0537075i
$683$	5.56048	−	9.63103i	0.212766	−	0.368521i	−0.739813	−	0.672812i	$-0.765086\pi$
$683$	5.56048	−	9.63103i	0.212766	−	0.368521i	0.952579	+	0.304291i	$0.0984195\pi$
$684$	1.48937	−	2.41389i	0.0569475	−	0.0922975i
$685$	21.2533			0.812046
$686$	8.43463	+	22.6152i	0.322036	+	0.863453i
$687$	51.3783	+	5.66395i	1.96020	+	0.216093i
$688$	−20.8733	−	3.00250i	−0.795785	−	0.114469i
$689$	−0.801861	−	0.462955i	−0.0305485	−	0.0176372i
$690$	10.0129	+	39.6790i	0.381184	+	1.51056i
$691$	34.9997	−	20.2071i	1.33145	−	0.768714i	0.345929	−	0.938261i	$-0.387564\pi$
$691$	34.9997	−	20.2071i	1.33145	−	0.768714i	0.985522	+	0.169547i	$0.0542305\pi$
$692$	−7.37731	+	1.42161i	−0.280443	+	0.0540416i
$693$	−5.65880	+	1.77534i	−0.214960	+	0.0674394i
$694$	−2.99193	−	2.47042i	−0.113572	−	0.0937760i
$695$	−9.90905			−0.375872
$696$	−18.6872	+	8.74178i	−0.708337	+	0.331356i
$697$	−0.811919			−0.0307536
$698$	−37.8258	+	14.1076i	−1.43173	+	0.533980i
$699$	−20.6799	−	15.1858i	−0.782184	−	0.574380i
$700$	−0.963231	+	2.78278i	−0.0364067	+	0.105179i
$701$	−35.0240	+	20.2211i	−1.32284	+	0.763741i	−0.984181	−	0.177169i	$-0.943306\pi$
$701$	−35.0240	+	20.2211i	−1.32284	+	0.763741i	−0.338658	+	0.940910i	$0.609973\pi$
$702$	−1.15314	+	2.13099i	−0.0435224	+	0.0804291i
$703$	−2.21327	+	1.27783i	−0.0834749	+	0.0481942i
$704$	−5.08160	+	9.85458i	−0.191520	+	0.371409i
$705$	−28.5043	−	20.9315i	−1.07354	−	0.788328i
$706$	−30.2070	−	5.08006i	−1.13686	−	0.191191i
$707$	−2.50474	+	4.33835i	−0.0942006	+	0.163160i
$708$	−16.9016	−	8.01954i	−0.635199	−	0.301393i
$709$	22.7819	−	39.4595i	0.855593	−	1.48193i	−0.0205005	−	0.999790i	$-0.506526\pi$
$709$	22.7819	−	39.4595i	0.855593	−	1.48193i	0.876094	−	0.482141i	$-0.160141\pi$
$710$	−22.3412	+	27.0574i	−0.838451	+	1.01545i
$711$	8.61571	−	38.6021i	0.323115	−	1.44769i
$712$	−4.25318	−	2.32268i	−0.159395	−	0.0870461i
$713$		−	36.1890i		−	1.35529i
$714$	4.01147	+	4.13046i	0.150126	+	0.154579i
$715$		−	0.910280i		−	0.0340425i
$716$	4.13119	−	3.57946i	0.154390	−	0.133771i
$717$	8.55264	−	11.6469i	0.319404	−	0.434961i
$718$	1.17672	−	0.438871i	0.0439147	−	0.0163785i
$719$	−6.93163	+	12.0059i	−0.258506	+	0.447746i	−0.965842	−	0.259132i	$-0.916564\pi$
$719$	−6.93163	+	12.0059i	−0.258506	+	0.447746i	0.707336	+	0.706878i	$0.249897\pi$
$720$	−18.5149	+	15.1180i	−0.690011	+	0.563415i
$721$	−3.58768	+	6.21404i	−0.133612	+	0.231423i
$722$	20.4761	+	16.9070i	0.762040	+	0.629214i
$723$	−18.9014	−	43.0400i	−0.702951	−	1.60067i
$724$	12.5249	+	4.33537i	0.465485	+	0.161123i
$725$	−3.76464	+	2.17351i	−0.139815	+	0.0807223i
$726$	21.5633	−	5.44142i	0.800288	−	0.201950i
$727$	−0.630923	−	0.364264i	−0.0233997	−	0.0135098i	0.488255	−	0.872701i	$-0.337634\pi$
$727$	−0.630923	−	0.364264i	−0.0233997	−	0.0135098i	−0.511654	+	0.859191i	$0.670967\pi$
$728$	−1.16752	−	0.637586i	−0.0432710	−	0.0236305i
$729$	21.3500	+	16.5281i	0.790739	+	0.612153i
$730$	−32.0432	−	5.38887i	−1.18597	−	0.199451i
$731$	−4.34401	+	7.52404i	−0.160669	+	0.278287i
$732$	−7.19659	+	4.96763i	−0.265994	+	0.183609i
$733$	8.03225	+	13.9123i	0.296678	+	0.513861i	0.975374	−	0.220558i	$-0.0707879\pi$
$733$	8.03225	+	13.9123i	0.296678	+	0.513861i	−0.678696	+	0.734419i	$0.737455\pi$
$734$	−19.9649	+	24.1795i	−0.736918	+	0.892481i
$735$	−1.87717	+	17.0280i	−0.0692405	+	0.628088i
$736$	45.1913	+	14.4501i	1.66577	+	0.532638i
$737$	−10.7150	−	3.72640i	−0.394693	−	0.137264i
$738$	−0.286281	−	2.07059i	−0.0105381	−	0.0762194i
$739$	42.1943	+	24.3609i	1.55214	+	0.896130i	0.997967	+	0.0637294i	$0.0202994\pi$
$739$	42.1943	+	24.3609i	1.55214	+	0.896130i	0.554175	+	0.832400i	$0.313034\pi$
$740$	21.1482	−	4.07527i	0.777424	−	0.149810i
$741$	0.217609	+	0.159796i	0.00799405	+	0.00587026i
$742$	−4.36803	−	3.60667i	−0.160355	−	0.132405i
$743$	10.7259	−	18.5778i	0.393494	−	0.681552i	−0.599413	−	0.800440i	$-0.704599\pi$
$743$	10.7259	−	18.5778i	0.393494	−	0.681552i	0.992908	+	0.118887i	$0.0379327\pi$
$744$	19.1466	−	8.95670i	0.701950	−	0.328369i
$745$	22.5353			0.825631
$746$	−25.7214	−	21.2381i	−0.941728	−	0.777582i
$747$	−2.66756	−	8.50272i	−0.0976009	−	0.311098i
$748$	2.99126	+	3.45233i	0.109371	+	0.126230i
$749$	−1.43612	+	0.829147i	−0.0524749	+	0.0302964i
$750$	−21.1138	+	20.5056i	−0.770967	+	0.748758i
$751$			22.1836i			0.809490i	0.914430	+	0.404745i	$0.132640\pi$
$751$			22.1836i			0.809490i	−0.914430	+	0.404745i	$0.867360\pi$
$752$	−38.0647	+	15.2359i	−1.38808	+	0.555598i
$753$	45.1906	+	4.98182i	1.64684	+	0.181548i
$754$	−0.686220	−	1.83992i	−0.0249907	−	0.0670059i
$755$	−4.35971	+	7.55124i	−0.158666	+	0.274818i
$756$	−9.11923	+	11.6866i	−0.331663	+	0.425038i
$757$	22.7105	+	39.3358i	0.825428	+	1.42968i	0.901592	+	0.432588i	$0.142400\pi$
$757$	22.7105	+	39.3358i	0.825428	+	1.42968i	−0.0761632	+	0.997095i	$0.524267\pi$
$758$	40.5478	+	6.81912i	1.47276	+	0.247682i
$759$	8.09570	+	18.4346i	0.293855	+	0.669132i
$760$	1.38609	+	2.27427i	0.0502788	+	0.0824965i
$761$			11.0424i			0.400286i	0.979767	+	0.200143i	$0.0641407\pi$
$761$			11.0424i			0.400286i	−0.979767	+	0.200143i	$0.935859\pi$
$762$	−43.2899	−	12.2802i	−1.56823	−	0.444866i
$763$	−8.27227	+	4.77600i	−0.299476	+	0.172903i
$764$	−4.95968	−	25.7377i	−0.179435	−	0.931159i
$765$	2.94787	+	9.39618i	0.106580	+	0.339720i
$766$	−2.73222	+	16.2463i	−0.0987192	+	0.587003i
$767$	0.890333	−	1.54210i	0.0321480	−	0.0556820i
$768$	3.53958	+	27.4858i	0.127724	+	0.991810i
$769$	7.44757	+	12.8996i	0.268566	+	0.465170i	0.968492	−	0.249045i	$-0.0801169\pi$
$769$	7.44757	+	12.8996i	0.268566	+	0.465170i	−0.699926	+	0.714216i	$0.746784\pi$
$770$	0.923594	−	5.49186i	0.0332840	−	0.197913i
$771$	−39.5383	−	29.0341i	−1.42394	−	1.04564i
$772$	−21.1276	+	18.3060i	−0.760398	+	0.658846i
$773$	35.4873	−	20.4886i	1.27639	−	0.736924i	0.300207	−	0.953874i	$-0.402944\pi$
$773$	35.4873	−	20.4886i	1.27639	−	0.736924i	0.976183	+	0.216950i	$0.0696109\pi$
$774$	−20.7198	−	8.42531i	−0.744758	−	0.302841i
$775$	3.85719	−	2.22695i	0.138554	−	0.0799944i
$776$	9.31643	+	15.2862i	0.334440	+	0.548744i
$777$	12.2291	−	5.37051i	0.438716	−	0.192666i
$778$	31.9616	+	5.37513i	1.14588	+	0.192708i
$779$	−0.232908			−0.00834478
$780$	−1.29249	−	1.87242i	−0.0462784	−	0.0670434i
$781$	−8.63179	+	14.9507i	−0.308870	+	0.534978i
$782$	12.4455	−	15.0727i	0.445051	−	0.539000i
$783$	−21.4709	+	4.22306i	−0.767308	+	0.150920i
$784$	15.6115	+	12.2786i	0.557552	+	0.438522i
$785$	−6.88282	−	3.97380i	−0.245659	−	0.141831i
$786$	−12.4771	−	12.8472i	−0.445044	−	0.458244i
$787$	−6.40792	−	3.69961i	−0.228418	−	0.131877i	0.381424	−	0.924400i	$-0.375434\pi$
$787$	−6.40792	−	3.69961i	−0.228418	−	0.131877i	−0.609842	+	0.792523i	$0.708767\pi$
$788$	2.52063	−	7.28212i	0.0897937	−	0.259415i
$789$	3.46573	+	7.89173i	0.123383	+	0.280953i
$790$	28.6385	+	23.6467i	1.01891	+	0.841312i
$791$	0.109304	−	0.189320i	0.00388639	−	0.00673143i
$792$	−7.74955	+	8.84572i	−0.275368	+	0.314319i
$793$	−0.416173	−	0.720833i	−0.0147787	−	0.0255975i
$794$	23.4750	−	8.75529i	0.833097	−	0.310714i
$795$	−3.89560	−	8.87060i	−0.138163	−	0.314608i
$796$	−27.8925	+	5.37490i	−0.988623	+	0.190508i
$797$	19.0155	−	10.9786i	0.673562	−	0.388881i	−0.123863	−	0.992299i	$-0.539528\pi$
$797$	19.0155	−	10.9786i	0.673562	−	0.388881i	0.797425	+	0.603418i	$0.206195\pi$
$798$	1.15073	+	1.18487i	0.0407355	+	0.0419438i
$799$			16.8917i			0.597586i
$800$	1.24076	+	5.70590i	0.0438675	+	0.201734i
$801$	−3.78467	−	3.47796i	−0.133725	−	0.122888i
$802$	1.80234	+	4.83251i	0.0636429	+	0.170642i
$803$	−15.9865			−0.564151
$804$	−27.3316	+	7.54892i	−0.963910	+	0.266230i
$805$	−23.8304			−0.839910
$806$	0.703091	+	1.88515i	0.0247653	+	0.0664017i
$807$	24.6057	−	10.8058i	0.866162	−	0.380383i
$808$	0.235911	+	9.93061i	0.00829932	+	0.349358i
$809$		−	18.5363i		−	0.651700i	−0.945421	−	0.325850i	$-0.894350\pi$
$809$		−	18.5363i		−	0.651700i	0.945421	−	0.325850i	$-0.105650\pi$
$810$	−22.9231	+	10.8308i	−0.805436	+	0.380557i
$811$	30.4329	−	17.5705i	1.06864	−	0.616982i	0.140834	−	0.990033i	$-0.455022\pi$
$811$	30.4329	−	17.5705i	1.06864	−	0.616982i	0.927811	+	0.373051i	$0.121688\pi$
$812$	−2.27325	−	11.7968i	−0.0797753	−	0.413986i
$813$	22.0115	−	9.66653i	0.771975	−	0.339020i
$814$	9.92821	−	3.70285i	0.347983	−	0.129785i
$815$	−9.86633	−	17.0890i	−0.345602	−	0.598601i
$816$	11.0548	+	2.85412i	0.386996	+	0.0999140i
$817$	−1.24613	+	2.15835i	−0.0435964	+	0.0755112i
$818$	35.5445	+	29.3489i	1.24278	+	1.02616i
$819$	−1.03891	−	0.954716i	−0.0363024	−	0.0333605i
$820$	1.85481	+	0.642023i	0.0647728	+	0.0224204i
$821$	−31.0419	−	17.9220i	−1.08337	−	0.625484i	−0.151566	−	0.988447i	$-0.548432\pi$
$821$	−31.0419	−	17.9220i	−1.08337	−	0.625484i	−0.931803	+	0.362963i	$0.881765\pi$
$822$	18.7486	−	18.2085i	0.653932	−	0.635094i
$823$	−12.7693	−	7.37237i	−0.445110	−	0.256985i	0.260653	−	0.965433i	$-0.416062\pi$
$823$	−12.7693	−	7.37237i	−0.445110	−	0.256985i	−0.705763	+	0.708448i	$0.749396\pi$
$824$	0.337908	+	14.2241i	0.0117716	+	0.495521i
$825$	−1.46666	+	1.99728i	−0.0510624	+	0.0695362i
$826$	6.93617	−	8.40039i	0.241340	−	0.292287i
$827$	9.94886	−	17.2319i	0.345956	−	0.599213i	−0.639571	−	0.768732i	$-0.720888\pi$
$827$	9.94886	−	17.2319i	0.345956	−	0.599213i	0.985527	+	0.169519i	$0.0542214\pi$
$828$	42.8274	+	26.4245i	1.48836	+	0.918314i
$829$	−18.2214			−0.632855			−0.316428	−	0.948617i	$-0.602483\pi$
$829$	−18.2214			−0.632855			−0.316428	+	0.948617i	$0.602483\pi$
$830$	8.25189	+	1.38776i	0.286427	+	0.0481699i
$831$	15.6688	+	35.6792i	0.543545	+	1.23770i
$832$	−2.63484	+	0.125257i	−0.0913465	+	0.00434250i
$833$	7.08643	−	4.09135i	0.245530	−	0.141757i
$834$	−8.74128	+	8.48946i	−0.302686	+	0.293966i
$835$	13.3914	−	7.73155i	0.463430	−	0.267561i
$836$	0.858076	+	0.990337i	0.0296772	+	0.0342515i
$837$	21.9988	−	4.32688i	0.760389	−	0.149559i
$838$	2.90492	−	17.2732i	0.100349	−	0.596693i
$839$	3.26910	+	5.66224i	0.112862	+	0.195482i	0.916923	−	0.399064i	$-0.130665\pi$
$839$	3.26910	+	5.66224i	0.112862	+	0.195482i	−0.804061	+	0.594547i	$0.797332\pi$
$840$	−5.89796	−	12.6080i	−0.203499	−	0.435017i
$841$	−5.63270	+	9.75613i	−0.194231	+	0.336418i
$842$	3.04191	−	18.0878i	0.104831	−	0.623346i
$843$	4.19639	−	38.0659i	0.144531	−	1.31106i
$844$	45.0996	−	8.69073i	1.55239	−	0.299147i
$845$	−22.2382	+	12.8392i	−0.765017	+	0.441683i
$846$	−43.0780	+	5.95598i	−1.48105	+	0.204771i
$847$			12.9504i			0.444982i
$848$	−11.1180	−	1.59926i	−0.381794	−	0.0549189i
$849$	3.11940	−	1.36991i	0.107058	−	0.0470153i
$850$	2.37238	+	0.398974i	0.0813718	+	0.0136847i
$851$	−22.6713	−	39.2679i	−0.777163	−	1.34609i
$852$	3.47279	+	43.0093i	0.118976	+	1.47347i
$853$	−18.0019	+	31.1802i	−0.616372	+	1.06759i	0.373770	+	0.927521i	$0.378065\pi$
$853$	−18.0019	+	31.1802i	−0.616372	+	1.06759i	−0.990142	+	0.140067i	$0.955268\pi$
$854$	−1.77946	−	4.77116i	−0.0608920	−	0.163266i
$855$	0.845627	+	2.69540i	0.0289198	+	0.0921806i
$856$	−1.57604	+	2.88596i	−0.0538678	+	0.0986402i
$857$			21.0556i			0.719246i	0.933098	+	0.359623i	$0.117095\pi$
$857$			21.0556i			0.719246i	−0.933098	+	0.359623i	$0.882905\pi$
$858$	−0.779871	−	0.803004i	−0.0266244	−	0.0274141i
$859$	17.8142	−	10.2850i	0.607813	−	0.350921i	−0.164296	−	0.986411i	$-0.552535\pi$
$859$	17.8142	−	10.2850i	0.607813	−	0.350921i	0.772109	+	0.635490i	$0.219202\pi$
$860$	15.8734	−	13.7535i	0.541278	−	0.468990i
$861$	1.20989	+	0.133379i	0.0412330	+	0.00454554i
$862$	43.2180	+	35.6850i	1.47201	+	1.21544i
$863$	5.60035			0.190638			0.0953191	−	0.995447i	$-0.469613\pi$
$863$	5.60035			0.190638			0.0953191	+	0.995447i	$0.469613\pi$
$864$	−3.38078	+	29.1988i	−0.115017	+	0.993364i
$865$	3.74135	−	6.48020i	0.127210	−	0.220333i
$866$	−1.97554	−	1.63120i	−0.0671316	−	0.0554304i
$867$	−14.6439	+	19.9419i	−0.497332	+	0.677261i
$868$	2.32913	+	12.0868i	0.0790560	+	0.410253i
$869$	15.8243	+	9.13619i	0.536804	+	0.309924i
$870$	5.60754	−	19.7675i	0.190113	−	0.670182i
$871$	−0.506825	−	2.65091i	−0.0171731	−	0.0898228i
$872$	−9.07818	+	16.6235i	−0.307426	+	0.562944i
$873$	5.68378	+	18.1168i	0.192367	+	0.613160i
$874$	3.57013	−	4.32378i	0.120762	−	0.146254i
$875$	−8.56962	−	14.8430i	−0.289706	−	0.501785i
$876$	−32.8838	+	22.6989i	−1.11104	+	0.766923i
$877$	−18.0758	+	31.3082i	−0.610376	+	1.05720i	0.380801	+	0.924657i	$0.375648\pi$
$877$	−18.0758	+	31.3082i	−0.610376	+	1.05720i	−0.991177	+	0.132545i	$0.957685\pi$
$878$	33.5047	+	5.63465i	1.13073	+	0.190160i
$879$	−50.6150	+	22.2280i	−1.70720	+	0.749733i
$880$	−4.10355	−	10.2521i	−0.138331	−	0.345598i
$881$	−40.3986	−	23.3241i	−1.36106	−	0.785810i	−0.371297	−	0.928514i	$-0.621087\pi$
$881$	−40.3986	−	23.3241i	−1.36106	−	0.785810i	−0.989765	+	0.142704i	$0.954420\pi$
$882$	12.9326	+	16.6295i	0.435463	+	0.559945i
$883$	−4.59847	+	2.65493i	−0.154751	+	0.0893455i	−0.575376	−	0.817889i	$-0.695144\pi$
$883$	−4.59847	+	2.65493i	−0.154751	+	0.0893455i	0.420625	+	0.907235i	$0.361811\pi$
$884$	−0.355472	+	1.02696i	−0.0119558	+	0.0345405i
$885$	17.0595	−	7.49184i	0.573449	−	0.251835i
$886$	−34.3243	−	28.3414i	−1.15315	−	0.952149i
$887$	0.957307	−	1.65811i	0.0321432	−	0.0556737i	−0.849506	−	0.527578i	$-0.823100\pi$
$887$	0.957307	−	1.65811i	0.0321432	−	0.0556737i	0.881650	+	0.471905i	$0.156433\pi$
$888$	15.1645	−	21.7135i	0.508886	−	0.728657i
$889$	13.1017	−	22.6928i	0.439417	−	0.761092i
$890$	4.52221	−	1.68662i	0.151585	−	0.0565355i
$891$	−10.2381	+	7.12535i	−0.342991	+	0.238708i
$892$	−20.0591	−	23.1509i	−0.671628	−	0.775151i
$893$			4.84557i			0.162151i
$894$	19.8796	−	19.3069i	0.664872	−	0.645719i
$895$			5.44412i			0.181977i
$896$	−16.0235	−	1.91768i	−0.535307	−	0.0640652i
$897$	−2.83511	+	3.86082i	−0.0946616	+	0.128909i
$898$	14.3612	−	17.3928i	0.479240	−	0.580406i
$899$	−9.08530	+	15.7362i	−0.303012	+	0.524832i
$900$	−0.180986	+	6.19081i	−0.00603287	+	0.206360i
$901$	−2.31381	+	4.00764i	−0.0770842	+	0.133514i
$902$	0.952306	+	0.160154i	0.0317083	+	0.00533255i
$903$	7.70931	−	10.4984i	0.256550	−	0.349366i
$904$	−0.0102948	−	0.433359i	−0.000342401	−	0.0144133i
$905$	−11.4320	+	6.60025i	−0.380012	+	0.219400i
$906$	2.62351	+	10.3965i	0.0871604	+	0.345399i
$907$	24.1972	−	13.9703i	0.803455	−	0.463875i	−0.0412230	−	0.999150i	$-0.513125\pi$
$907$	24.1972	−	13.9703i	0.803455	−	0.463875i	0.844678	+	0.535275i	$0.179792\pi$
$908$	2.22259	+	0.769328i	0.0737594	+	0.0255310i
$909$	−2.29508	+	10.2830i	−0.0761231	+	0.341064i
$910$	1.24137	−	0.462983i	0.0411509	−	0.0153477i
$911$	28.0830			0.930432			0.465216	−	0.885197i	$-0.345977\pi$
$911$	28.0830			0.930432			0.465216	+	0.885197i	$0.345977\pi$
$912$	3.17119	+	0.818734i	0.105009	+	0.0271110i
$913$	4.11690			0.136250
$914$	−18.0038	−	14.8656i	−0.595511	−	0.491712i
$915$	0.954333	−	8.65686i	0.0315493	−	0.286187i
$916$	11.2938	+	58.6077i	0.373156	+	1.93645i
$917$	9.03158	−	5.21439i	0.298249	−	0.172194i
$918$	10.6505	+	5.76330i	0.351520	+	0.190217i
$919$	15.3701	+	8.87395i	0.507014	+	0.292725i	0.731605	−	0.681728i	$-0.238771\pi$
$919$	15.3701	+	8.87395i	0.507014	+	0.292725i	−0.224592	+	0.974453i	$0.572105\pi$
$920$	−40.3502	+	24.5921i	−1.33031	+	0.810777i
$921$	−1.57257	+	14.2650i	−0.0518181	+	0.470048i
$922$	8.25376	+	22.1303i	0.271823	+	0.728821i
$923$	−4.10711			−0.135187
$924$	−3.89034	−	5.63593i	−0.127983	−	0.185408i
$925$	2.79023	−	4.83282i	0.0917422	−	0.158902i
$926$	42.8752	+	7.21053i	1.40897	+	0.236953i
$927$	−3.28737	+	14.7288i	−0.107971	+	0.483758i
$928$	−16.0230	−	17.6287i	−0.525980	−	0.578691i
$929$		−	19.3553i		−	0.635027i	−0.948254	−	0.317513i	$-0.897152\pi$
$929$		−	19.3553i		−	0.635027i	0.948254	−	0.317513i	$-0.102848\pi$
$930$	−5.74540	+	20.2535i	−0.188399	+	0.664139i
$931$	2.03282	−	1.17365i	0.0666230	−	0.0384648i
$932$	9.69055	−	27.9961i	0.317425	−	0.917042i
$933$	−13.8694	−	31.5817i	−0.454063	−	1.03394i
$934$	7.33858	−	43.6366i	0.240126	−	1.42783i
$935$	−4.54951			−0.148785
$936$	−2.74434	−	0.544436i	−0.0897016	−	0.0177954i
$937$	50.7074			1.65654			0.828270	−	0.560330i	$-0.189326\pi$
$937$	50.7074			1.65654			0.828270	+	0.560330i	$0.189326\pi$
$938$	−0.368073	−	16.5076i	−0.0120180	−	0.538993i
$939$	−11.0491	−	25.1596i	−0.360573	−	0.821053i
$940$	13.3571	−	38.5887i	0.435660	−	1.25863i
$941$		−	12.4089i		−	0.404520i	−0.979332	−	0.202260i	$-0.935171\pi$
$941$		−	12.4089i		−	0.404520i	0.979332	−	0.202260i	$-0.0648286\pi$
$942$	−9.47619	+	2.39129i	−0.308751	+	0.0779123i
$943$		−	4.13226i		−	0.134565i
$944$	3.07563	−	21.3816i	0.100103	−	0.695913i
$945$	−2.84924	−	14.4861i	−0.0926858	−	0.471234i
$946$	6.57927	−	7.96814i	0.213910	−	0.259067i
$947$	−39.0257			−1.26816			−0.634082	−	0.773266i	$-0.718622\pi$
$947$	−39.0257			−1.26816			−0.634082	+	0.773266i	$0.718622\pi$
$948$	45.5225	−	3.67572i	1.47850	−	0.119382i
$949$	−1.90164	−	3.29374i	−0.0617299	−	0.106919i
$950$	0.680542	+	0.114450i	0.0220797	+	0.00371325i
$951$	4.40196	−	39.9306i	0.142743	−	1.29484i
$952$	−3.18660	+	5.83515i	−0.103278	+	0.189118i
$953$		−	15.2322i		−	0.493419i	−0.969089	−	0.246710i	$-0.920651\pi$
$953$		−	15.2322i		−	0.493419i	0.969089	−	0.246710i	$-0.0793494\pi$
$954$	−11.0363	−	4.48769i	−0.357313	−	0.145294i
$955$	22.6079	+	13.0527i	0.731576	+	0.422375i
$956$	15.7674	+	5.45771i	0.509953	+	0.176515i
$957$	1.10774	−	10.0484i	0.0358080	−	0.324819i
$958$	6.23825	−	37.0938i	0.201549	−	1.19845i
$959$	7.60962	+	13.1803i	0.245728	+	0.425613i
$960$	−22.9976	−	15.2617i	−0.742244	−	0.492570i
$961$	−6.19133	+	10.7237i	−0.199720	+	0.345926i
$962$	1.94390	+	1.60507i	0.0626738	+	0.0517495i
$963$	−2.35994	+	2.56806i	−0.0760481	+	0.0827545i
$964$	41.0229	−	35.5442i	1.32126	−	1.14480i
$965$		−	27.8421i		−	0.896269i
$966$	−21.0220	+	20.4164i	−0.676371	+	0.656886i
$967$	−3.25303	+	1.87814i	−0.104610	+	0.0603968i	−0.551392	−	0.834246i	$-0.685903\pi$
$967$	−3.25303	+	1.87814i	−0.104610	+	0.0603968i	0.446782	+	0.894643i	$0.352570\pi$
$968$	13.3644	+	21.9280i	0.429547	+	0.704794i
$969$	0.798648	−	1.08759i	0.0256563	−	0.0349384i
$970$	−17.5823	−	2.95691i	−0.564535	−	0.0949406i
$971$	9.65737	+	16.7271i	0.309920	+	0.536797i	0.978345	−	0.206983i	$-0.0663645\pi$
$971$	9.65737	+	16.7271i	0.309920	+	0.536797i	−0.668425	+	0.743780i	$0.733031\pi$
$972$	−10.9425	+	29.1935i	−0.350979	+	0.936383i
$973$	−3.54789	−	6.14512i	−0.113740	−	0.197003i
$974$	39.2571	+	6.60206i	1.25788	+	0.211544i
$975$	−0.585967	−	0.0645971i	−0.0187660	−	0.00206876i
$976$	−7.93670	−	6.24232i	−0.254048	−	0.199812i
$977$	1.99449	+	1.15152i	0.0638092	+	0.0368403i	0.531565	−	0.847017i	$-0.321604\pi$
$977$	1.99449	+	1.15152i	0.0638092	+	0.0368403i	−0.467756	+	0.883858i	$0.654937\pi$
$978$	−23.3444	−	6.62219i	−0.746470	−	0.211754i
$979$	2.05648	−	1.18731i	0.0657253	−	0.0379465i
$980$	−19.4240	+	3.74302i	−0.620478	+	0.119566i
$981$	−13.5936	+	14.7924i	−0.434010	+	0.472283i
$982$	−23.9637	+	8.93756i	−0.764713	+	0.285209i
$983$	0.822824			0.0262440			0.0131220	−	0.999914i	$-0.495823\pi$
$983$	0.822824			0.0262440			0.0131220	+	0.999914i	$0.495823\pi$
$984$	2.18627	−	1.02272i	0.0696956	−	0.0326033i
$985$	3.83745	+	6.64666i	0.122271	+	0.211780i
$986$	−9.19576	+	3.42967i	−0.292853	+	0.109223i
$987$	2.77490	−	25.1715i	0.0883262	−	0.801216i
$988$	−0.101971	+	0.294595i	−0.00324413	+	0.00937232i
$989$	−38.2936	−	22.1088i	−1.21767	−	0.703020i
$990$	−1.60414	−	11.6023i	−0.0509831	−	0.368747i
$991$		−	30.7335i		−	0.976281i	−0.872765	−	0.488140i	$-0.837675\pi$
$991$		−	30.7335i		−	0.976281i	0.872765	−	0.488140i	$-0.162325\pi$
$992$	16.4169	+	18.0621i	0.521237	+	0.573473i
$993$	1.15408	+	0.847472i	0.0366235	+	0.0268937i
$994$	−24.7789	−	4.16718i	−0.785937	−	0.132175i
$995$	14.1455	−	24.5006i	0.448441	−	0.776723i
$996$	8.46835	−	5.84549i	0.268330	−	0.185221i
$997$	15.8715			0.502655			0.251328	−	0.967902i	$-0.419133\pi$
$997$	15.8715			0.502655			0.251328	+	0.967902i	$0.419133\pi$
$998$	41.4924	+	6.97798i	1.31342	+	0.220884i
$999$	21.1597	−	18.4765i	0.669463	−	0.584572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.l.a.431.14	✓	264
3.2	odd	2	inner	804.2.l.a.431.119	yes	264
4.3	odd	2	inner	804.2.l.a.431.59	yes	264
12.11	even	2	inner	804.2.l.a.431.74	yes	264
67.37	even	3	inner	804.2.l.a.707.74	yes	264
201.104	odd	6	inner	804.2.l.a.707.59	yes	264
268.171	odd	6	inner	804.2.l.a.707.119	yes	264
804.707	even	6	inner	804.2.l.a.707.14	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.l.a.431.14	✓	264	1.1	even	1	trivial
804.2.l.a.431.59	yes	264	4.3	odd	2	inner
804.2.l.a.431.74	yes	264	12.11	even	2	inner
804.2.l.a.431.119	yes	264	3.2	odd	2	inner
804.2.l.a.707.14	yes	264	804.707	even	6	inner
804.2.l.a.707.59	yes	264	201.104	odd	6	inner
804.2.l.a.707.74	yes	264	67.37	even	3	inner
804.2.l.a.707.119	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)

\(f(q)\)	\(=\)	\(q+(-1.32505 + 0.494196i) q^{2} +(-0.696446 - 1.58586i) q^{3} +(1.51154 - 1.30967i) q^{4} +1.99192i q^{5} +(1.70656 + 1.75718i) q^{6} +(-1.23529 + 0.713198i) q^{7} +(-1.35564 + 2.48239i) q^{8} +(-2.02993 + 2.20894i) q^{9} +O(q^{10})\)	\(q+(-1.32505 + 0.494196i) q^{2} +(-0.696446 - 1.58586i) q^{3} +(1.51154 - 1.30967i) q^{4} +1.99192i q^{5} +(1.70656 + 1.75718i) q^{6} +(-1.23529 + 0.713198i) q^{7} +(-1.35564 + 2.48239i) q^{8} +(-2.02993 + 2.20894i) q^{9} +(-0.984400 - 2.63941i) q^{10} +(-0.692977 - 1.20027i) q^{11} +(-3.12967 - 1.48498i) q^{12} +(0.164863 - 0.285552i) q^{13} +(1.28437 - 1.55550i) q^{14} +(3.15892 - 1.38727i) q^{15} +(0.569515 - 3.95925i) q^{16} +(-1.42716 - 0.823973i) q^{17} +(1.59812 - 3.93014i) q^{18} +(-0.409397 - 0.236366i) q^{19} +(2.60877 + 3.01087i) q^{20} +(1.99135 + 1.46231i) q^{21} +(1.51140 + 1.24796i) q^{22} +(4.19361 - 7.26355i) q^{23} +(4.88086 + 0.421014i) q^{24} +1.03224 q^{25} +(-0.0773346 + 0.459846i) q^{26} +(4.91681 + 1.68078i) q^{27} +(-0.933144 + 2.69586i) q^{28} +(-3.64705 + 2.10562i) q^{29} +(-3.50016 + 3.39933i) q^{30} +(3.73671 - 2.15739i) q^{31} +(1.20200 + 5.52767i) q^{32} +(-1.42084 + 1.93489i) q^{33} +(2.29827 + 0.386512i) q^{34} +(-1.42064 - 2.46061i) q^{35} +(-0.175333 + 5.99744i) q^{36} +(2.70308 - 4.68187i) q^{37} +(0.659285 + 0.110875i) q^{38} +(-0.567664 - 0.0625794i) q^{39} +(-4.94472 - 2.70033i) q^{40} +(0.426678 - 0.246343i) q^{41} +(-3.36131 - 0.953518i) q^{42} -5.27202i q^{43} +(-2.61942 - 0.906686i) q^{44} +(-4.40003 - 4.04346i) q^{45} +(-1.96715 + 11.6971i) q^{46} +(-5.12508 - 8.87690i) q^{47} +(-6.67546 + 1.85423i) q^{48} +(-2.48270 + 4.30016i) q^{49} +(-1.36778 + 0.510130i) q^{50} +(-0.312767 + 2.83714i) q^{51} +(-0.124781 - 0.647540i) q^{52} -2.80811i q^{53} +(-7.34567 + 0.202738i) q^{54} +(2.39085 - 1.38036i) q^{55} +(-0.0958152 - 4.03332i) q^{56} +(-0.0897205 + 0.813864i) q^{57} +(3.79195 - 4.59242i) q^{58} +5.40043 q^{59} +(2.95797 - 6.23406i) q^{60} +(1.26218 - 2.18615i) q^{61} +(-3.88517 + 4.70533i) q^{62} +(0.932148 - 4.17643i) q^{63} +(-4.32447 - 6.73045i) q^{64} +(0.568797 + 0.328395i) q^{65} +(0.926483 - 3.26601i) q^{66} +(6.19406 - 5.35104i) q^{67} +(-3.23635 + 0.623647i) q^{68} +(-14.4396 - 1.59183i) q^{69} +(3.09844 + 2.55837i) q^{70} +(-6.22806 - 10.7873i) q^{71} +(-2.73158 - 8.03358i) q^{72} +(5.76733 - 9.98931i) q^{73} +(-1.26797 + 7.53958i) q^{74} +(-0.718901 - 1.63700i) q^{75} +(-0.928383 + 0.178900i) q^{76} +(1.71206 + 0.988459i) q^{77} +(0.783113 - 0.197616i) q^{78} +(-11.4177 + 6.59199i) q^{79} +(7.88652 + 1.13443i) q^{80} +(-0.758803 - 8.96796i) q^{81} +(-0.443630 + 0.537280i) q^{82} +(-1.48522 + 2.57248i) q^{83} +(4.92515 - 0.397682i) q^{84} +(1.64129 - 2.84280i) q^{85} +(2.60541 + 6.98572i) q^{86} +(5.87920 + 4.31726i) q^{87} +(3.91896 - 0.0930986i) q^{88} +1.71334i q^{89} +(7.82854 + 3.18333i) q^{90} +0.470320i q^{91} +(-3.17405 - 16.4714i) q^{92} +(-6.02374 - 4.42341i) q^{93} +(11.1779 + 9.22959i) q^{94} +(0.470822 - 0.815488i) q^{95} +(7.92901 - 5.75594i) q^{96} +(3.16457 - 5.48120i) q^{97} +(1.16459 - 6.92489i) q^{98} +(4.05801 + 0.905719i) 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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