LMFDB - Embedded newform 153.2.n.a.106.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(4,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("153.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.n (of order $12$, degree $4$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			106.16
Character	$\chi$	$=$	153.106
Dual form			153.2.n.a.13.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.25660 + 1.30285i) q^{2} +(-1.36701 + 1.06362i) q^{3} +(2.39483 + 4.14796i) q^{4} +(-3.16280 - 0.847469i) q^{5} +(-4.47053 + 0.619154i) q^{6} +(3.71932 - 0.996589i) q^{7} +7.26900i q^{8} +(0.737432 - 2.90795i) q^{9} +(-6.03304 - 6.03304i) q^{10} +(0.362642 - 0.0971696i) q^{11} +(-7.68561 - 3.12312i) q^{12} +(1.09097 + 1.88962i) q^{13} +(9.69142 + 2.59681i) q^{14} +(5.22496 - 2.20551i) q^{15} +(-4.68075 + 8.10730i) q^{16} +(-1.79701 - 3.71090i) q^{17} +(5.45271 - 5.60133i) q^{18} -0.425667i q^{19} +(-4.05908 - 15.1487i) q^{20} +(-4.02436 + 5.31828i) q^{21} +(0.944935 + 0.253195i) q^{22} +(0.956920 - 3.57127i) q^{23} +(-7.73144 - 9.93680i) q^{24} +(4.95495 + 2.86074i) q^{25} +5.68550i q^{26} +(2.08488 + 4.75955i) q^{27} +(13.0409 + 13.0409i) q^{28} +(-0.0646729 - 0.241362i) q^{29} +(14.6641 + 1.83037i) q^{30} +(-6.87927 - 1.84329i) q^{31} +(-8.53488 + 4.92762i) q^{32} +(-0.392384 + 0.518545i) q^{33} +(0.779601 - 10.7152i) q^{34} -12.6080 q^{35} +(13.8281 - 3.90521i) q^{36} +(-3.47140 + 3.47140i) q^{37} +(0.554580 - 0.960561i) q^{38} +(-3.50121 - 1.42275i) q^{39} +(6.16025 - 22.9904i) q^{40} +(-1.28678 + 4.80233i) q^{41} +(-16.0103 + 6.75811i) q^{42} +(-6.98686 - 4.03387i) q^{43} +(1.27152 + 1.27152i) q^{44} +(-4.79675 + 8.57231i) q^{45} +(6.81221 - 6.81221i) q^{46} +(0.831435 - 1.44009i) q^{47} +(-2.22444 - 16.0613i) q^{48} +(6.77797 - 3.91326i) q^{49} +(7.45423 + 12.9111i) q^{50} +(6.40351 + 3.16150i) q^{51} +(-5.22539 + 9.05065i) q^{52} +2.95966i q^{53} +(-1.49624 + 13.4567i) q^{54} -1.22931 q^{55} +(7.24420 + 27.0357i) q^{56} +(0.452748 + 0.581892i) q^{57} +(0.168518 - 0.628917i) q^{58} +(-1.53623 + 0.886940i) q^{59} +(21.6613 + 16.3911i) q^{60} +(5.61171 - 1.50365i) q^{61} +(-13.1222 - 13.1222i) q^{62} +(-0.155289 - 11.5505i) q^{63} -6.95675 q^{64} +(-1.84913 - 6.90106i) q^{65} +(-1.56104 + 0.658931i) q^{66} +(-0.487236 - 0.843917i) q^{67} +(11.0891 - 16.3409i) q^{68} +(2.49035 + 5.89976i) q^{69} +(-28.4513 - 16.4264i) q^{70} +(-8.74800 + 8.74800i) q^{71} +(21.1379 + 5.36039i) q^{72} +(2.29636 - 2.29636i) q^{73} +(-12.3563 + 3.31085i) q^{74} +(-9.81620 + 1.35951i) q^{75} +(1.76565 - 1.01940i) q^{76} +(1.25194 - 0.722810i) q^{77} +(-6.04720 - 7.77213i) q^{78} +(9.75186 - 2.61300i) q^{79} +(21.6749 - 21.6749i) q^{80} +(-7.91239 - 4.28884i) q^{81} +(-9.16045 + 9.16045i) q^{82} +(-3.51700 - 2.03054i) q^{83} +(-31.6977 - 3.95651i) q^{84} +(2.53871 + 13.2597i) q^{85} +(-10.5110 - 18.2056i) q^{86} +(0.345126 + 0.261158i) q^{87} +(0.706326 + 2.63605i) q^{88} +14.9784 q^{89} +(-21.9928 + 13.0948i) q^{90} +(5.94086 + 5.94086i) q^{91} +(17.1052 - 4.58332i) q^{92} +(11.3646 - 4.79712i) q^{93} +(3.75243 - 2.16647i) q^{94} +(-0.360740 + 1.34630i) q^{95} +(6.42616 - 15.8140i) q^{96} +(4.46637 + 16.6687i) q^{97} +20.3936 q^{98} +(-0.0151410 - 1.12620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7} - 16 q^{10} - 24 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{17} - 8 q^{18} + 18 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{23} - 2 q^{24} - 10 q^{29} - 36 q^{30}+ \cdots + 6 q^{99}+O(q^{100}) $ 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7 - 16 * q^10 - 24 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^17 - 8 * q^18 + 18 * q^20 - 16 * q^21 - 4 * q^22 - 8 * q^23 - 2 * q^24 - 10 * q^29 - 36 * q^30 - 2 * q^31 + 12 * q^33 + 20 * q^34 - 128 * q^35 - 8 * q^37 - 24 * q^38 + 34 * q^39 - 20 * q^40 + 32 * q^41 + 20 * q^44 + 20 * q^45 - 40 * q^46 - 64 * q^47 + 62 * q^48 + 48 * q^50 + 40 * q^51 + 36 * q^52 - 46 * q^54 - 16 * q^55 + 12 * q^56 + 72 * q^57 - 10 * q^58 - 2 * q^61 - 28 * q^62 + 64 * q^63 - 8 * q^64 + 8 * q^65 - 4 * q^67 - 60 * q^68 - 24 * q^69 - 84 * q^71 + 72 * q^72 - 44 * q^73 - 14 * q^74 + 46 * q^75 - 56 * q^78 + 10 * q^79 + 204 * q^80 + 44 * q^81 - 52 * q^82 - 60 * q^84 + 22 * q^85 + 32 * q^86 + 16 * q^88 + 128 * q^89 - 66 * q^90 + 44 * q^91 + 136 * q^92 + 4 * q^95 - 2 * q^96 - 44 * q^97 + 208 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.25660	+	1.30285i	1.59566	+	0.921253i	0.992310	+	0.123774i	$0.0394998\pi$
$2$	2.25660	+	1.30285i	1.59566	+	0.921253i	0.603347	+	0.797479i	$0.293834\pi$
$3$	−1.36701	+	1.06362i	−0.789244	+	0.614080i
$3$	−1.36701	+	1.06362i	−0.789244	+	0.614080i
$4$	2.39483	+	4.14796i	1.19741	+	2.07398i
$5$	−3.16280	−	0.847469i	−1.41445	−	0.379000i	−0.530936	−	0.847412i	$-0.678159\pi$
$5$	−3.16280	−	0.847469i	−1.41445	−	0.379000i	−0.883510	+	0.468413i	$0.844826\pi$
$6$	−4.47053	+	0.619154i	−1.82509	+	0.252769i
$7$	3.71932	−	0.996589i	1.40577	−	0.376675i	0.525357	−	0.850882i	$-0.323932\pi$
$7$	3.71932	−	0.996589i	1.40577	−	0.376675i	0.880414	+	0.474207i	$0.157265\pi$
$8$			7.26900i			2.56998i
$9$	0.737432	−	2.90795i	0.245811	−	0.969318i
$10$	−6.03304	−	6.03304i	−1.90782	−	1.90782i
$11$	0.362642	−	0.0971696i	0.109341	−	0.0292977i	−0.203734	−	0.979026i	$-0.565308\pi$
$11$	0.362642	−	0.0971696i	0.109341	−	0.0292977i	0.313074	+	0.949729i	$0.398641\pi$
$12$	−7.68561	−	3.12312i	−2.21864	−	0.901569i
$13$	1.09097	+	1.88962i	0.302582	+	0.524087i	0.976720	−	0.214518i	$-0.0688181\pi$
$13$	1.09097	+	1.88962i	0.302582	+	0.524087i	−0.674138	+	0.738605i	$0.735485\pi$
$14$	9.69142	+	2.59681i	2.59014	+	0.694026i
$15$	5.22496	−	2.20551i	1.34908	−	0.569460i
$16$	−4.68075	+	8.10730i	−1.17019	+	2.02682i
$17$	−1.79701	−	3.71090i	−0.435839	−	0.900025i
$17$	−1.79701	−	3.71090i	−0.435839	−	0.900025i
$18$	5.45271	−	5.60133i	1.28522	−	1.32025i
$19$		−	0.425667i		−	0.0976548i	−0.998807	−	0.0488274i	$-0.984452\pi$
$19$		−	0.425667i		−	0.0976548i	0.998807	−	0.0488274i	$-0.0155484\pi$
$20$	−4.05908	−	15.1487i	−0.907639	−	3.38735i
$21$	−4.02436	+	5.31828i	−0.878187	+	1.16054i
$22$	0.944935	+	0.253195i	0.201461	+	0.0539813i
$23$	0.956920	−	3.57127i	0.199532	−	0.744662i	−0.791515	−	0.611149i	$-0.790708\pi$
$23$	0.956920	−	3.57127i	0.199532	−	0.744662i	0.991047	−	0.133513i	$-0.0426258\pi$
$24$	−7.73144	−	9.93680i	−1.57817	−	2.02834i
$25$	4.95495	+	2.86074i	0.990990	+	0.572148i
$26$			5.68550i			1.11502i
$27$	2.08488	+	4.75955i	0.401235	+	0.915975i
$28$	13.0409	+	13.0409i	2.46451	+	2.46451i
$29$	−0.0646729	−	0.241362i	−0.0120094	−	0.0448199i	0.959661	−	0.281159i	$-0.0907189\pi$
$29$	−0.0646729	−	0.241362i	−0.0120094	−	0.0448199i	−0.971671	+	0.236339i	$0.924052\pi$
$30$	14.6641	+	1.83037i	2.67728	+	0.334179i
$31$	−6.87927	−	1.84329i	−1.23555	−	0.331066i	−0.418814	−	0.908072i	$-0.637554\pi$
$31$	−6.87927	−	1.84329i	−1.23555	−	0.331066i	−0.816740	+	0.577007i	$0.804221\pi$
$32$	−8.53488	+	4.92762i	−1.50877	+	0.871088i
$33$	−0.392384	+	0.518545i	−0.0683052	+	0.0902670i
$34$	0.779601	−	10.7152i	0.133700	−	1.83765i
$35$	−12.6080			−2.13115
$36$	13.8281	−	3.90521i	2.30469	−	0.650868i
$37$	−3.47140	+	3.47140i	−0.570694	+	0.570694i	−0.932322	−	0.361628i	$-0.882221\pi$
$37$	−3.47140	+	3.47140i	−0.570694	+	0.570694i	0.361628	+	0.932322i	$0.382221\pi$
$38$	0.554580	−	0.960561i	0.0899648	−	0.155824i
$39$	−3.50121	−	1.42275i	−0.560642	−	0.227823i
$40$	6.16025	−	22.9904i	0.974021	−	3.63510i
$41$	−1.28678	+	4.80233i	−0.200961	+	0.749997i	0.789682	+	0.613517i	$0.210246\pi$
$41$	−1.28678	+	4.80233i	−0.200961	+	0.749997i	−0.990643	+	0.136480i	$0.956421\pi$
$42$	−16.0103	+	6.75811i	−2.47044	+	1.04280i
$43$	−6.98686	−	4.03387i	−1.06549	−	0.615159i	−0.138541	−	0.990357i	$-0.544241\pi$
$43$	−6.98686	−	4.03387i	−1.06549	−	0.615159i	−0.926945	+	0.375198i	$0.877575\pi$
$44$	1.27152	+	1.27152i	0.191689	+	0.191689i
$45$	−4.79675	+	8.57231i	−0.715057	+	1.27789i
$46$	6.81221	−	6.81221i	1.00441	−	1.00441i
$47$	0.831435	−	1.44009i	0.121277	−	0.210058i	−0.798994	−	0.601339i	$-0.794634\pi$
$47$	0.831435	−	1.44009i	0.121277	−	0.210058i	0.920272	+	0.391280i	$0.127968\pi$
$48$	−2.22444	−	16.0613i	−0.321070	−	2.31825i
$49$	6.77797	−	3.91326i	0.968282	−	0.559038i
$50$	7.45423	+	12.9111i	1.05419	+	1.82591i
$51$	6.40351	+	3.16150i	0.896671	+	0.442698i
$52$	−5.22539	+	9.05065i	−0.724632	+	1.25510i
$53$			2.95966i			0.406541i	0.979123	+	0.203270i	$0.0651570\pi$
$53$			2.95966i			0.406541i	−0.979123	+	0.203270i	$0.934843\pi$
$54$	−1.49624	+	13.4567i	−0.203612	+	1.83122i
$55$	−1.22931			−0.165760
$56$	7.24420	+	27.0357i	0.968047	+	3.61280i
$57$	0.452748	+	0.581892i	0.0599679	+	0.0770734i
$58$	0.168518	−	0.628917i	0.0221275	−	0.0825809i
$59$	−1.53623	+	0.886940i	−0.200000	+	0.115470i	−0.596655	−	0.802498i	$-0.703504\pi$
$59$	−1.53623	+	0.886940i	−0.200000	+	0.115470i	0.396656	+	0.917967i	$0.370171\pi$
$60$	21.6613	+	16.3911i	2.79646	+	2.11608i
$61$	5.61171	−	1.50365i	0.718506	−	0.192523i	0.119001	−	0.992894i	$-0.462031\pi$
$61$	5.61171	−	1.50365i	0.718506	−	0.192523i	0.599505	+	0.800371i	$0.295364\pi$
$62$	−13.1222	−	13.1222i	−1.66652	−	1.66652i
$63$	−0.155289	−	11.5505i	−0.0195646	−	1.45523i
$64$	−6.95675			−0.869593
$65$	−1.84913	−	6.90106i	−0.229357	−	0.855971i
$66$	−1.56104	+	0.658931i	−0.192151	+	0.0811088i
$67$	−0.487236	−	0.843917i	−0.0595253	−	0.103101i	0.834727	−	0.550664i	$-0.185625\pi$
$67$	−0.487236	−	0.843917i	−0.0595253	−	0.103101i	−0.894252	+	0.447563i	$0.852292\pi$
$68$	11.0891	−	16.3409i	1.34475	−	1.98163i
$69$	2.49035	+	5.89976i	0.299803	+	0.710248i
$70$	−28.4513	−	16.4264i	−3.40058	−	1.96332i
$71$	−8.74800	+	8.74800i	−1.03820	+	1.03820i	−0.0389551	+	0.999241i	$0.512403\pi$
$71$	−8.74800	+	8.74800i	−1.03820	+	1.03820i	−0.999241	+	0.0389551i	$0.987597\pi$
$72$	21.1379	+	5.36039i	2.49113	+	0.631728i
$73$	2.29636	−	2.29636i	0.268768	−	0.268768i	−0.559836	−	0.828604i	$-0.689136\pi$
$73$	2.29636	−	2.29636i	0.268768	−	0.268768i	0.828604	+	0.559836i	$0.189136\pi$
$74$	−12.3563	+	3.31085i	−1.43639	+	0.384879i
$75$	−9.81620	+	1.35951i	−1.13348	+	0.156983i
$76$	1.76565	−	1.01940i	0.202534	−	0.116933i
$77$	1.25194	−	0.722810i	0.142672	−	0.0823718i
$78$	−6.04720	−	7.77213i	−0.684711	−	0.880021i
$79$	9.75186	−	2.61300i	1.09717	−	0.293986i	0.335558	−	0.942019i	$-0.391075\pi$
$79$	9.75186	−	2.61300i	1.09717	−	0.293986i	0.761612	+	0.648034i	$0.224408\pi$
$80$	21.6749	−	21.6749i	2.42333	−	2.42333i
$81$	−7.91239	−	4.28884i	−0.879154	−	0.476537i
$82$	−9.16045	+	9.16045i	−1.01160	+	1.01160i
$83$	−3.51700	−	2.03054i	−0.386041	−	0.222881i	0.294402	−	0.955682i	$-0.404880\pi$
$83$	−3.51700	−	2.03054i	−0.386041	−	0.222881i	−0.680444	+	0.732801i	$0.738213\pi$
$84$	−31.6977	−	3.95651i	−3.45850	−	0.431691i
$85$	2.53871	+	13.2597i	0.275362	+	1.43822i
$86$	−10.5110	−	18.2056i	−1.13343	−	1.96316i
$87$	0.345126	+	0.261158i	0.0370014	+	0.0279990i
$88$	0.706326	+	2.63605i	0.0752946	+	0.281003i
$89$	14.9784			1.58770			0.793851	−	0.608112i	$-0.208073\pi$
$89$	14.9784			1.58770			0.793851	+	0.608112i	$0.208073\pi$
$90$	−21.9928	+	13.0948i	−2.31824	+	1.38032i
$91$	5.94086	+	5.94086i	0.622771	+	0.622771i
$92$	17.1052	−	4.58332i	1.78334	−	0.477844i
$93$	11.3646	−	4.79712i	1.17845	−	0.497438i
$94$	3.75243	−	2.16647i	0.387034	−	0.223454i
$95$	−0.360740	+	1.34630i	−0.0370111	+	0.138127i
$96$	6.42616	−	15.8140i	0.655868	−	1.61401i
$97$	4.46637	+	16.6687i	0.453491	+	1.69245i	0.692486	+	0.721432i	$0.256516\pi$
$97$	4.46637	+	16.6687i	0.453491	+	1.69245i	−0.238994	+	0.971021i	$0.576818\pi$
$98$	20.3936			2.06006
$99$	−0.0151410	−	1.12620i	−0.00152173	−	0.113188i
$100$			27.4039i			2.74039i
$101$	−4.02170	+	6.96579i	−0.400174	+	0.693122i	−0.993747	−	0.111659i	$-0.964384\pi$
$101$	−4.02170	+	6.96579i	−0.400174	+	0.693122i	0.593572	+	0.804781i	$0.297717\pi$
$102$	10.3312	+	15.4770i	1.02294	+	1.53246i
$103$	−8.25415	−	14.2966i	−0.813306	−	1.40869i	−0.910538	−	0.413425i	$-0.864332\pi$
$103$	−8.25415	−	14.2966i	−0.813306	−	1.40869i	0.0972322	−	0.995262i	$-0.469001\pi$
$104$	−13.7357	+	7.93029i	−1.34689	+	0.777629i
$105$	17.2353	−	13.4101i	1.68199	−	1.30869i
$106$	−3.85599	+	6.67877i	−0.374527	+	0.648700i
$107$	0.164966	−	0.164966i	0.0159478	−	0.0159478i	−0.699088	−	0.715036i	$-0.746410\pi$
$107$	0.164966	−	0.164966i	0.0159478	−	0.0159478i	0.715036	+	0.699088i	$0.246410\pi$
$108$	−14.7495	+	20.0463i	−1.41927	+	1.92896i
$109$	1.52442	+	1.52442i	0.146013	+	0.146013i	0.776334	−	0.630321i	$-0.217077\pi$
$109$	1.52442	+	1.52442i	0.146013	+	0.146013i	−0.630321	+	0.776334i	$0.717077\pi$
$110$	−2.77406	−	1.60161i	−0.264497	−	0.152707i
$111$	1.05319	−	8.43768i	0.0999646	−	0.800869i
$112$	−9.32957	+	34.8184i	−0.881561	+	3.29003i
$113$	−4.11643	+	15.3627i	−0.387241	+	1.44520i	0.447363	+	0.894352i	$0.352363\pi$
$113$	−4.11643	+	15.3627i	−0.387241	+	1.44520i	−0.834604	+	0.550850i	$0.814304\pi$
$114$	0.263554	+	1.90296i	0.0246841	+	0.178228i
$115$	−6.05309	+	10.4843i	−0.564453	+	0.977662i
$116$	0.846282	−	0.846282i	0.0785753	−	0.0785753i
$117$	6.29946	−	1.77903i	0.582385	−	0.164472i
$118$	−4.62219			−0.425508
$119$	−10.3819	−	12.0111i	−0.951707	−	1.10106i
$120$	16.0319	+	37.9802i	1.46350	+	3.46710i
$121$	−9.40421	+	5.42952i	−0.854928	+	0.493593i
$122$	14.6224	+	3.91807i	1.32385	+	0.354725i
$123$	−3.34880	−	7.93347i	−0.301951	−	0.715337i
$124$	−8.82875	−	32.9493i	−0.792845	−	2.95894i
$125$	−1.67047	−	1.67047i	−0.149412	−	0.149412i
$126$	14.6982	−	26.2672i	1.30942	−	2.34007i
$127$		−	1.43670i		−	0.127486i	−0.997966	−	0.0637431i	$-0.979696\pi$
$127$		−	1.43670i		−	0.127486i	0.997966	−	0.0637431i	$-0.0203038\pi$
$128$	1.37117	+	0.791644i	0.121195	+	0.0699721i
$129$	13.8416	−	1.91702i	1.21868	−	0.168784i
$130$	4.81828	−	17.9821i	0.422591	−	1.57713i
$131$	19.0361	+	5.10071i	1.66319	+	0.445651i	0.963263	−	0.268559i	$-0.0865476\pi$
$131$	19.0361	+	5.10071i	1.66319	+	0.445651i	0.699931	+	0.714211i	$0.253214\pi$
$132$	−3.09060	−	0.385769i	−0.269002	−	0.0335769i
$133$	−0.424215	−	1.58319i	−0.0367841	−	0.137280i
$134$		−	2.53918i		−	0.219351i
$135$	−2.56047	−	16.8203i	−0.220370	−	1.44766i
$136$	26.9745	−	13.0625i	2.31305	−	1.12010i
$137$	8.22976	−	14.2544i	0.703116	−	1.21783i	−0.264251	−	0.964454i	$-0.585125\pi$
$137$	8.22976	−	14.2544i	0.703116	−	1.21783i	0.967367	−	0.253379i	$-0.0815420\pi$
$138$	−2.06677	+	16.5580i	−0.175935	+	1.40951i
$139$	5.63220	+	1.50914i	0.477717	+	0.128004i	0.489639	−	0.871925i	$-0.337128\pi$
$139$	5.63220	+	1.50914i	0.477717	+	0.128004i	−0.0119224	+	0.999929i	$0.503795\pi$
$140$	−30.1941	−	52.2977i	−2.55186	−	4.41996i
$141$	0.395124	+	2.85294i	0.0332754	+	0.240261i
$142$	−31.1380	+	8.34341i	−2.61305	+	0.700164i
$143$	0.579247	+	0.579247i	0.0484391	+	0.0484391i
$144$	20.1239	+	19.5900i	1.67699	+	1.63250i
$145$			0.818188i			0.0679468i
$146$	8.17376	−	2.19015i	0.676465	−	0.181258i
$147$	−5.10333	+	12.5586i	−0.420916	+	1.03582i
$148$	−22.7126	−	6.08583i	−1.86697	−	0.500252i
$149$	−2.73466	−	4.73656i	−0.224032	−	0.388034i	0.731997	−	0.681308i	$-0.238589\pi$
$149$	−2.73466	−	4.73656i	−0.224032	−	0.388034i	−0.956029	+	0.293274i	$0.905255\pi$
$150$	−23.9225	−	9.72115i	−1.95326	−	0.793728i
$151$	−1.30522	−	0.753569i	−0.106217	−	0.0613246i	0.445950	−	0.895058i	$-0.352866\pi$
$151$	−1.30522	−	0.753569i	−0.106217	−	0.0613246i	−0.552168	+	0.833733i	$0.686199\pi$
$152$	3.09418			0.250971
$153$	−12.1163	+	2.48909i	−0.979544	+	0.201231i
$154$	3.76685			0.303541
$155$	20.1956	+	11.6599i	1.62215	+	0.936548i
$156$	−2.48327	−	17.9301i	−0.198821	−	1.43556i
$157$	3.44410	+	5.96535i	0.274869	+	0.476087i	0.970102	−	0.242697i	$-0.0780322\pi$
$157$	3.44410	+	5.96535i	0.274869	+	0.476087i	−0.695233	+	0.718784i	$0.744699\pi$
$158$	25.4104	+	6.80870i	2.02154	+	0.541671i
$159$	−3.14795	−	4.04589i	−0.249649	−	0.320860i
$160$	31.1701	−	8.35200i	2.46421	−	0.660284i
$161$		−	14.2364i		−	1.12198i
$162$	−12.2674	−	19.9868i	−0.963817	−	1.57031i
$163$	−10.1202	−	10.1202i	−0.792678	−	0.792678i	0.189250	−	0.981929i	$-0.439394\pi$
$163$	−10.1202	−	10.1202i	−0.792678	−	0.792678i	−0.981929	+	0.189250i	$0.939394\pi$
$164$	−23.0015	+	6.16323i	−1.79612	+	0.481268i
$165$	1.68048	−	1.30752i	0.130825	−	0.101790i
$166$	−5.29098	−	9.16425i	−0.410660	−	0.711284i
$167$	−15.4273	−	4.13374i	−1.19380	−	0.319878i	−0.393414	−	0.919361i	$-0.628706\pi$
$167$	−15.4273	−	4.13374i	−1.19380	−	0.319878i	−0.800387	+	0.599483i	$0.795373\pi$
$168$	−38.6586	−	29.2531i	−2.98258	−	2.25692i
$169$	4.11955	−	7.13527i	0.316888	−	0.548867i
$170$	−11.5466	+	33.2294i	−0.885580	+	2.54858i
$171$	−1.23782	−	0.313901i	−0.0946585	−	0.0240046i
$172$		−	38.6417i		−	2.94640i
$173$	−2.53743	−	9.46980i	−0.192917	−	0.719976i	−0.992796	−	0.119815i	$-0.961770\pi$
$173$	−2.53743	−	9.46980i	−0.192917	−	0.719976i	0.799879	−	0.600161i	$-0.204897\pi$
$174$	0.438562	+	1.03897i	0.0332473	+	0.0787645i
$175$	21.2800	+	5.70197i	1.60862	+	0.431028i
$176$	−0.909654	+	3.39487i	−0.0685677	+	0.255898i
$177$	1.15667	−	2.84641i	0.0869406	−	0.213950i
$178$	33.8002	+	19.5145i	2.53343	+	1.46268i
$179$			17.6727i			1.32092i	0.750862	+	0.660459i	$0.229638\pi$
$179$			17.6727i			1.32092i	−0.750862	+	0.660459i	$0.770362\pi$
$180$	−47.0450	+	0.632488i	−3.50653	+	0.0471429i
$181$	−13.4076	−	13.4076i	−0.996581	−	0.996581i	0.00341362	−	0.999994i	$-0.498913\pi$
$181$	−13.4076	−	13.4076i	−0.996581	−	0.996581i	−0.999994	+	0.00341362i	$0.998913\pi$
$182$	5.66610	+	21.1462i	0.419999	+	1.56746i
$183$	−6.07195	+	8.02423i	−0.448852	+	0.593168i
$184$	25.9596	+	6.95585i	1.91377	+	0.512792i
$185$	13.9212	−	8.03742i	1.02351	−	0.590923i
$186$	31.8953	+	3.98117i	2.33867	+	0.291914i
$187$	−1.01226	−	1.17111i	−0.0740236	−	0.0856402i
$188$	7.96458			0.580877
$189$	12.4976	+	15.6245i	0.909069	+	1.13652i
$190$	−2.56807	+	2.56807i	−0.186307	+	0.186307i
$191$	1.55753	−	2.69772i	0.112699	−	0.195200i	−0.804159	−	0.594415i	$-0.797384\pi$
$191$	1.55753	−	2.69772i	0.112699	−	0.195200i	0.916858	+	0.399215i	$0.130717\pi$
$192$	9.50994	−	7.39932i	0.686321	−	0.534000i
$193$	−4.48499	+	16.7382i	−0.322837	+	1.20484i	0.593632	+	0.804736i	$0.297693\pi$
$193$	−4.48499	+	16.7382i	−0.322837	+	1.20484i	−0.916469	+	0.400106i	$0.868973\pi$
$194$	−11.6380	+	43.4337i	−0.835561	+	3.11835i
$195$	9.86788	+	7.46704i	0.706653	+	0.534726i
$196$	32.4642	+	18.7432i	2.31887	+	1.33880i
$197$	−10.7748	−	10.7748i	−0.767670	−	0.767670i	0.210025	−	0.977696i	$-0.432645\pi$
$197$	−10.7748	−	10.7748i	−0.767670	−	0.767670i	−0.977696	+	0.210025i	$0.932645\pi$
$198$	1.43310	−	2.56111i	0.101846	−	0.182010i
$199$	17.3294	−	17.3294i	1.22845	−	1.22845i	0.263901	−	0.964550i	$-0.414991\pi$
$199$	17.3294	−	17.3294i	1.22845	−	1.22845i	0.964550	−	0.263901i	$-0.0850093\pi$
$200$	−20.7947	+	36.0175i	−1.47041	+	2.54682i
$201$	1.56366	+	0.635410i	0.110292	+	0.0448184i
$202$	−18.1507	+	10.4793i	−1.27708	+	0.737323i
$203$	−0.481078	−	0.833252i	−0.0337651	−	0.0584828i
$204$	2.22153	+	34.1328i	0.155538	+	2.38977i
$205$	8.13964	−	14.0983i	0.568497	−	0.984666i
$206$		−	43.0156i		−	2.99704i
$207$	−9.67944	−	5.41625i	−0.672767	−	0.376455i
$208$	−20.4263			−1.41631
$209$	−0.0413619	−	0.154365i	−0.00286107	−	0.0106776i
$210$	56.3645	−	7.80631i	3.88952	−	0.538687i
$211$	2.64507	−	9.87152i	0.182094	−	0.679584i	−0.813140	−	0.582068i	$-0.802244\pi$
$211$	2.64507	−	9.87152i	0.182094	−	0.679584i	0.995234	−	0.0975156i	$-0.0310896\pi$
$212$	−12.2766	+	7.08788i	−0.843158	+	0.486798i
$213$	2.65407	−	21.2631i	0.181854	−	1.45693i
$214$	0.587187	−	0.157336i	0.0401392	−	0.0107553i
$215$	18.6794	+	18.6794i	1.27393	+	1.27393i
$216$	−34.5972	+	15.1550i	−2.35404	+	1.03116i
$217$	−27.4232			−1.86161
$218$	1.45392	+	5.42610i	0.0984718	+	0.367502i
$219$	−0.696695	+	5.58159i	−0.0470783	+	0.377169i
$220$	−2.94399	−	5.09914i	−0.198484	−	0.343784i
$221$	5.05170	−	7.44417i	0.339814	−	0.500749i
$222$	13.3696	−	17.6683i	0.897312	−	1.18582i
$223$	−4.94348	−	2.85412i	−0.331040	−	0.191126i	0.325263	−	0.945624i	$-0.394547\pi$
$223$	−4.94348	−	2.85412i	−0.331040	−	0.191126i	−0.656303	+	0.754498i	$0.727881\pi$
$224$	−26.8331	+	26.8331i	−1.79286	+	1.79286i
$225$	11.9728	−	12.2992i	0.798190	−	0.819944i
$226$	−29.3044	+	29.3044i	−1.94930	+	1.94930i
$227$	4.47545	−	1.19919i	0.297046	−	0.0795933i	−0.107218	−	0.994236i	$-0.534194\pi$
$227$	4.47545	−	1.19919i	0.297046	−	0.0795933i	0.404264	+	0.914642i	$0.367528\pi$
$228$	−1.32941	+	3.27151i	−0.0880425	+	0.216661i
$229$	−18.1949	+	10.5049i	−1.20236	+	0.694180i	−0.961078	−	0.276276i	$-0.910900\pi$
$229$	−18.1949	+	10.5049i	−1.20236	+	0.694180i	−0.241277	+	0.970456i	$0.577566\pi$
$230$	−27.3188	+	15.7725i	−1.80135	+	1.04001i
$231$	−0.942625	+	2.31968i	−0.0620202	+	0.152624i
$232$	1.75446	−	0.470107i	0.115186	−	0.0308640i
$233$	−0.144906	+	0.144906i	−0.00949310	+	0.00949310i	−0.711837	−	0.702344i	$-0.752137\pi$
$233$	−0.144906	+	0.144906i	−0.00949310	+	0.00949310i	0.702344	+	0.711837i	$0.252137\pi$
$234$	16.5332	+	4.19267i	1.08081	+	0.274083i
$235$	−3.85009	+	3.85009i	−0.251152	+	0.251152i
$236$	−7.35799	−	4.24814i	−0.478965	−	0.276530i
$237$	−10.5517	+	13.9443i	−0.685404	+	0.905777i
$238$	−7.77910	−	40.6303i	−0.504244	−	2.63367i
$239$	8.32743	+	14.4235i	0.538657	+	0.932981i	0.998977	+	0.0452278i	$0.0144014\pi$
$239$	8.32743	+	14.4235i	0.538657	+	0.932981i	−0.460320	+	0.887753i	$0.652265\pi$
$240$	−6.57599	+	52.6837i	−0.424478	+	3.40072i
$241$	5.68761	+	21.2265i	0.366371	+	1.36732i	0.865552	+	0.500819i	$0.166968\pi$
$241$	5.68761	+	21.2265i	0.366371	+	1.36732i	−0.499181	+	0.866498i	$0.666366\pi$
$242$	−28.2954			−1.81890
$243$	15.3780	−	2.55288i	0.986499	−	0.163767i
$244$	19.6762	+	19.6762i	1.25964	+	1.25964i
$245$	−24.7537	+	6.63274i	−1.58146	+	0.423750i
$246$	2.77920	−	22.2656i	0.177195	−	1.41961i
$247$	0.804351	−	0.464392i	0.0511796	−	0.0295486i
$248$	13.3989	−	50.0054i	0.850832	−	3.17535i
$249$	6.96750	−	0.964978i	0.441548	−	0.0611530i
$250$	−1.59322	−	5.94596i	−0.100764	−	0.376056i
$251$	10.2742			0.648499			0.324250	−	0.945972i	$-0.394888\pi$
$251$	10.2742			0.648499			0.324250	+	0.945972i	$0.394888\pi$
$252$	47.5393	−	28.3057i	2.99469	−	1.78309i
$253$		−	1.38808i		−	0.0872677i
$254$	1.87180	−	3.24205i	0.117447	−	0.203424i
$255$	−17.5737	−	15.4259i	−1.10051	−	0.966010i
$256$	9.01953	+	15.6223i	0.563721	+	0.976393i
$257$	−18.7148	+	10.8050i	−1.16740	+	0.673997i	−0.953066	−	0.302764i	$-0.902091\pi$
$257$	−18.7148	+	10.8050i	−1.16740	+	0.673997i	−0.214331	+	0.976761i	$0.568757\pi$
$258$	33.7325	+	13.7076i	2.10010	+	0.853396i
$259$	−9.45168	+	16.3708i	−0.587299	+	1.01723i
$260$	24.1970	−	24.1970i	1.50063	−	1.50063i
$261$	−0.749562	+	0.0100774i	−0.0463968	+	0.000623772i
$262$	36.3115	+	36.3115i	2.24333	+	2.24333i
$263$	−15.1829	−	8.76588i	−0.936220	−	0.540527i	−0.0474469	−	0.998874i	$-0.515108\pi$
$263$	−15.1829	−	8.76588i	−0.936220	−	0.540527i	−0.888774	+	0.458347i	$0.848442\pi$
$264$	−3.76930	−	2.85224i	−0.231984	−	0.175543i
$265$	2.50822	−	9.36081i	0.154079	−	0.575030i
$266$	1.10538	−	4.12532i	0.0677750	−	0.252940i
$267$	−20.4756	+	15.9313i	−1.25308	+	0.974977i
$268$	2.33369	−	4.04207i	0.142553	−	0.246909i
$269$	4.56547	−	4.56547i	0.278361	−	0.278361i	−0.554093	−	0.832455i	$-0.686935\pi$
$269$	4.56547	−	4.56547i	0.278361	−	0.278361i	0.832455	+	0.554093i	$0.186935\pi$
$270$	16.1364	−	41.2927i	0.982030	−	2.51299i
$271$	12.6954			0.771193			0.385597	−	0.922667i	$-0.373996\pi$
$271$	12.6954			0.771193			0.385597	+	0.922667i	$0.373996\pi$
$272$	38.4967	+	2.80088i	2.33421	+	0.169828i
$273$	−14.4400	−	1.80241i	−0.873950	−	0.109087i
$274$	37.1426	−	21.4443i	2.24386	−	1.29550i
$275$	2.07485	+	0.555955i	0.125118	+	0.0335253i
$276$	−18.5080	+	24.4588i	−1.11405	+	1.47225i
$277$	−5.40862	−	20.1853i	−0.324973	−	1.21281i	−0.914339	−	0.404949i	$-0.867289\pi$
$277$	−5.40862	−	20.1853i	−0.324973	−	1.21281i	0.589367	−	0.807866i	$-0.299377\pi$
$278$	10.7434	+	10.7434i	0.644348	+	0.644348i
$279$	−10.4332	+	18.6453i	−0.624620	+	1.11626i
$280$		−	91.6478i		−	5.47700i
$281$	17.0716	+	9.85632i	1.01841	+	0.587978i	0.913643	−	0.406518i	$-0.133257\pi$
$281$	17.0716	+	9.85632i	1.01841	+	0.587978i	0.104766	+	0.994497i	$0.466591\pi$
$282$	−2.82532	+	6.95274i	−0.168245	+	0.414030i
$283$	−6.61525	+	24.6885i	−0.393236	+	1.46758i	0.431528	+	0.902100i	$0.357975\pi$
$283$	−6.61525	+	24.6885i	−0.393236	+	1.46758i	−0.824764	+	0.565477i	$0.808692\pi$
$284$	−57.2363	−	15.3364i	−3.39635	−	0.910050i
$285$	−0.938814	−	2.22409i	−0.0556105	−	0.131744i
$286$	0.552458	+	2.06180i	0.0326675	+	0.121917i
$287$			19.1438i			1.13002i
$288$	8.03539	+	28.4528i	0.473490	+	1.67660i
$289$	−10.5415	+	13.3370i	−0.620088	+	0.784532i
$290$	−1.06598	+	1.84632i	−0.0625962	+	0.108420i
$291$	−23.8347	−	18.0358i	−1.39722	−	1.05728i
$292$	15.0246	+	4.02583i	0.879247	+	0.235594i
$293$	10.3865	+	17.9899i	0.606783	+	1.05098i	0.991767	+	0.128056i	$0.0408738\pi$
$293$	10.3865	+	17.9899i	0.606783	+	1.05098i	−0.384983	+	0.922923i	$0.625793\pi$
$294$	−27.8782	+	21.6910i	−1.62589	+	1.26504i
$295$	5.61042	−	1.50331i	0.326651	−	0.0875260i
$296$	−25.2336	−	25.2336i	−1.46667	−	1.46667i
$297$	1.21855	+	1.52343i	0.0707073	+	0.0883981i
$298$		−	14.2514i		−	0.825560i
$299$	7.79234	−	2.08795i	0.450643	−	0.120749i
$300$	−29.1473	−	37.4615i	−1.68282	−	2.16284i
$301$	−30.0065	−	8.04021i	−1.72954	−	0.463430i
$302$	−1.96357	−	3.40101i	−0.112991	−	0.195706i
$303$	−1.91124	−	13.7999i	−0.109798	−	0.792781i
$304$	3.45101	+	1.99244i	0.197929	+	0.114274i
$305$	−19.0230			−1.08925
$306$	−30.5845	−	10.1688i	−1.74840	−	0.581312i
$307$	−20.2734			−1.15707			−0.578533	−	0.815659i	$-0.696374\pi$
$307$	−20.2734			−1.15707			−0.578533	+	0.815659i	$0.696374\pi$
$308$	5.99638	+	3.46201i	0.341675	+	0.197266i
$309$	26.4896	+	10.7643i	1.50694	+	0.612362i
$310$	30.3823	+	52.6236i	1.72560	+	2.98882i
$311$	18.1027	+	4.85062i	1.02651	+	0.275053i	0.732513	−	0.680753i	$-0.238347\pi$
$311$	18.1027	+	4.85062i	1.02651	+	0.275053i	0.293999	+	0.955806i	$0.405014\pi$
$312$	10.3420	−	25.4503i	0.585500	−	1.44084i
$313$	1.78873	−	0.479289i	0.101105	−	0.0270910i	−0.207912	−	0.978148i	$-0.566667\pi$
$313$	1.78873	−	0.479289i	0.101105	−	0.0270910i	0.309017	+	0.951057i	$0.400000\pi$
$314$			17.9485i			1.01290i
$315$	−9.29756	+	36.6636i	−0.523858	+	2.06576i
$316$	34.1927	+	34.1927i	1.92349	+	1.92349i
$317$	6.29984	−	1.68804i	0.353834	−	0.0948097i	−0.0775235	−	0.996991i	$-0.524701\pi$
$317$	6.29984	−	1.68804i	0.353834	−	0.0948097i	0.431358	+	0.902181i	$0.358035\pi$
$318$	−1.83249	−	13.2312i	−0.102761	−	0.741972i
$319$	−0.0469062	−	0.0812439i	−0.00262624	−	0.00454879i
$320$	22.0028	+	5.89563i	1.22999	+	0.329576i
$321$	−0.0500492	+	0.400970i	−0.00279347	+	0.0223800i
$322$	18.5478	−	32.1258i	1.03363	−	1.79030i
$323$	−1.57961	+	0.764929i	−0.0878917	+	0.0425618i
$324$	−1.15888	−	43.0913i	−0.0643820	−	2.39396i
$325$			12.4840i			0.692487i
$326$	−9.65219	−	36.0225i	−0.534585	−	1.99510i
$327$	−3.70530	−	0.462497i	−0.204904	−	0.0255761i
$328$	−34.9081	−	9.35360i	−1.92748	−	0.516466i
$329$	1.65720	−	6.18475i	0.0913643	−	0.340976i
$330$	5.49567	−	0.761133i	0.302527	−	0.0418990i
$331$	−16.1563	−	9.32787i	−0.888033	−	0.512706i	−0.0147342	−	0.999891i	$-0.504690\pi$
$331$	−16.1563	−	9.32787i	−0.888033	−	0.512706i	−0.873298	+	0.487186i	$0.838024\pi$
$332$		−	19.4512i		−	1.06752i
$333$	7.53474	+	12.6546i	0.412901	+	0.693467i
$334$	−29.4276	−	29.4276i	−1.61021	−	1.61021i
$335$	0.825834	+	3.08205i	0.0451201	+	0.168391i
$336$	−24.2799	−	57.5202i	−1.32458	−	3.13798i
$337$	−8.54839	−	2.29053i	−0.465660	−	0.124773i	0.0183574	−	0.999831i	$-0.494156\pi$
$337$	−8.54839	−	2.29053i	−0.465660	−	0.124773i	−0.484018	+	0.875058i	$0.660823\pi$
$338$	18.5923	−	10.7343i	1.01129	−	0.583869i
$339$	−10.7129	−	25.3793i	−0.581843	−	1.37841i
$340$	−48.9211	+	42.2852i	−2.65312	+	2.29324i
$341$	−2.67382			−0.144796
$342$	−2.38430	−	2.32104i	−0.128928	−	0.125508i
$343$	2.25041	−	2.25041i	0.121511	−	0.121511i
$344$	29.3222	−	50.7875i	1.58095	−	2.73828i
$345$	−2.87662	−	20.7703i	−0.154872	−	1.11823i
$346$	6.61176	−	24.6754i	0.355451	−	1.32656i
$347$	2.88567	−	10.7695i	0.154911	−	0.578136i	−0.844202	−	0.536025i	$-0.819925\pi$
$347$	2.88567	−	10.7695i	0.154911	−	0.578136i	0.999113	−	0.0421105i	$-0.0134082\pi$
$348$	−0.256755	+	2.05700i	−0.0137635	+	0.110267i
$349$	3.20796	+	1.85211i	0.171718	+	0.0991414i	0.583396	−	0.812188i	$-0.301724\pi$
$349$	3.20796	+	1.85211i	0.171718	+	0.0991414i	−0.411678	+	0.911330i	$0.635057\pi$
$350$	40.5917	+	40.5917i	2.16972	+	2.16972i
$351$	−6.71920	+	9.13217i	−0.358645	+	0.487439i
$352$	−2.61629	+	2.61629i	−0.139449	+	0.139449i
$353$	−3.90737	+	6.76776i	−0.207968	+	0.360211i	−0.951074	−	0.308962i	$-0.900018\pi$
$353$	−3.90737	+	6.76776i	−0.207968	+	0.360211i	0.743106	+	0.669174i	$0.233352\pi$
$354$	6.31859	−	4.91625i	0.335829	−	0.261296i
$355$	35.0818	−	20.2545i	1.86195	−	1.07500i
$356$	35.8706	+	62.1297i	1.90114	+	3.29287i
$357$	26.9674	+	5.37696i	1.42727	+	0.284579i
$358$	−23.0248	+	39.8802i	−1.21690	+	2.10773i
$359$		−	16.5375i		−	0.872818i	−0.899748	−	0.436409i	$-0.856250\pi$
$359$		−	16.5375i		−	0.872818i	0.899748	−	0.436409i	$-0.143750\pi$
$360$	−62.3122	−	34.8676i	−3.28414	−	1.83768i
$361$	18.8188			0.990464
$362$	−12.7875	−	47.7237i	−0.672098	−	2.50830i
$363$	7.08071	−	17.4247i	0.371641	−	0.914560i
$364$	−10.4151	+	38.8698i	−0.545901	+	2.03733i
$365$	−9.20900	+	5.31682i	−0.482021	+	0.278295i
$366$	−24.1563	+	10.1966i	−1.26267	+	0.532987i
$367$	2.60393	−	0.697722i	0.135924	−	0.0364208i	−0.190215	−	0.981742i	$-0.560919\pi$
$367$	2.60393	−	0.697722i	0.135924	−	0.0364208i	0.326140	+	0.945322i	$0.394252\pi$
$368$	24.4743	+	24.4743i	1.27581	+	1.27581i
$369$	13.0160	+	7.28328i	0.677587	+	0.379153i
$370$	41.8862			2.17756
$371$	2.94957	+	11.0079i	0.153134	+	0.571503i
$372$	47.1145	+	35.6517i	2.44277	+	1.84845i
$373$	8.40225	+	14.5531i	0.435052	+	0.753533i	0.997300	−	0.0734363i	$-0.0233966\pi$
$373$	8.40225	+	14.5531i	0.435052	+	0.753533i	−0.562248	+	0.826969i	$0.690063\pi$
$374$	−0.758480	−	3.96155i	−0.0392201	−	0.204847i
$375$	4.06030	+	0.506807i	0.209673	+	0.0261714i
$376$	10.4680	+	6.04370i	0.539846	+	0.311680i
$377$	0.385528	−	0.385528i	0.0198557	−	0.0198557i
$378$	7.84578	+	51.5408i	0.403543	+	2.65097i
$379$	25.6646	−	25.6646i	1.31830	−	1.31830i	0.403181	−	0.915120i	$-0.367904\pi$
$379$	25.6646	−	25.6646i	1.31830	−	1.31830i	0.915120	−	0.403181i	$-0.132096\pi$
$380$	−6.44831	+	1.72782i	−0.330791	+	0.0886353i
$381$	1.52810	+	1.96398i	0.0782868	+	0.100618i
$382$	7.02943	−	4.05845i	0.359657	−	0.207648i
$383$	29.0417	−	16.7673i	1.48396	−	0.856766i	0.484129	−	0.874997i	$-0.339136\pi$
$383$	29.0417	−	16.7673i	1.48396	−	0.856766i	0.999834	+	0.0182301i	$0.00580313\pi$
$384$	−2.71641	+	0.376214i	−0.138621	+	0.0191986i
$385$	−4.57220	+	1.22512i	−0.233021	+	0.0624378i
$386$	−31.9282	+	31.9282i	−1.62510	+	1.62510i
$387$	−16.8826	+	17.3428i	−0.858192	+	0.881582i
$388$	−58.4451	+	58.4451i	−2.96710	+	2.96710i
$389$	−3.96820	−	2.29104i	−0.201196	−	0.116160i	0.396017	−	0.918243i	$-0.370392\pi$
$389$	−3.96820	−	2.29104i	−0.201196	−	0.116160i	−0.597213	+	0.802083i	$0.703725\pi$
$390$	12.5394	+	29.7065i	0.634958	+	1.50425i
$391$	−14.9722	+	2.86659i	−0.757178	+	0.144970i
$392$	28.4455	+	49.2691i	1.43672	+	2.48846i
$393$	−31.4478	+	13.2744i	−1.58633	+	0.669607i
$394$	−10.2764	−	38.3522i	−0.517720	−	1.93216i
$395$	−33.0576			−1.66331
$396$	4.63519	−	2.75987i	0.232927	−	0.138688i
$397$	−13.1180	−	13.1180i	−0.658372	−	0.658372i	0.296623	−	0.954995i	$-0.404140\pi$
$397$	−13.1180	−	13.1180i	−0.658372	−	0.658372i	−0.954995	+	0.296623i	$0.904140\pi$
$398$	61.6832	−	16.5280i	3.09190	−	0.828472i
$399$	2.26382	+	1.71304i	0.113333	+	0.0857591i
$400$	−46.3858	+	26.7808i	−2.31929	+	1.33904i
$401$	2.43404	−	9.08398i	0.121550	−	0.453632i	−0.878143	−	0.478398i	$-0.841218\pi$
$401$	2.43404	−	9.08398i	0.121550	−	0.453632i	0.999693	+	0.0247663i	$0.00788417\pi$
$402$	2.70071	+	3.47108i	0.134699	+	0.173122i
$403$	−4.02198	−	15.0102i	−0.200349	−	0.747712i
$404$	−38.5251			−1.91670
$405$	21.3906	+	20.2702i	1.06291	+	1.00724i
$406$		−	2.50709i		−	0.124425i
$407$	−0.921560	+	1.59619i	−0.0456800	+	0.0791202i
$408$	−22.9809	+	46.5471i	−1.13773	+	2.30443i
$409$	2.97314	+	5.14963i	0.147012	+	0.254633i	0.930122	−	0.367251i	$-0.119701\pi$
$409$	2.97314	+	5.14963i	0.147012	+	0.254633i	−0.783110	+	0.621884i	$0.786368\pi$
$410$	36.7358	−	21.2094i	1.81425	−	1.04746i
$411$	3.91104	+	28.2392i	0.192917	+	1.39294i
$412$	39.5346	−	68.4759i	1.94773	−	3.37356i
$413$	−4.82980	+	4.82980i	−0.237659	+	0.237659i
$414$	−14.7861	−	24.8331i	−0.726695	−	1.22048i
$415$	9.40275	+	9.40275i	0.461563	+	0.461563i
$416$	−18.6227	−	10.7518i	−0.913052	−	0.527151i
$417$	−9.30443	+	3.92750i	−0.455640	+	0.192330i
$418$	0.107777	−	0.402228i	0.00527153	−	0.0196736i
$419$	7.14243	−	26.6559i	0.348931	−	1.30223i	−0.539022	−	0.842292i	$-0.681206\pi$
$419$	7.14243	−	26.6559i	0.348931	−	1.30223i	0.887952	−	0.459935i	$-0.152127\pi$
$420$	96.9003	+	39.3764i	4.72825	+	1.92137i
$421$	6.14578	−	10.6448i	0.299527	−	0.518796i	−0.676501	−	0.736442i	$-0.736504\pi$
$421$	6.14578	−	10.6448i	0.299527	−	0.518796i	0.976028	+	0.217646i	$0.0698378\pi$
$422$	18.8300	−	18.8300i	0.916628	−	0.916628i
$423$	−3.57458	−	3.47974i	−0.173802	−	0.169191i
$424$	−21.5138			−1.04480
$425$	1.71182	−	23.5281i	0.0830353	−	1.14128i
$426$	33.6918	−	44.5245i	1.63237	−	2.15722i
$427$	19.3732	−	11.1851i	0.937536	−	0.541287i
$428$	1.07934	+	0.289207i	0.0521717	+	0.0139794i
$429$	−1.40793	−	0.175739i	−0.0679757	−	0.00848474i
$430$	17.8155	+	66.4885i	0.859142	+	3.20636i
$431$	7.62840	+	7.62840i	0.367447	+	0.367447i	0.866545	−	0.499098i	$-0.166335\pi$
$431$	7.62840	+	7.62840i	0.367447	+	0.367447i	−0.499098	+	0.866545i	$0.666335\pi$
$432$	−48.3459	−	5.37554i	−2.32604	−	0.258631i
$433$			17.7075i			0.850968i	0.904966	+	0.425484i	$0.139896\pi$
$433$			17.7075i			0.850968i	−0.904966	+	0.425484i	$0.860104\pi$
$434$	−61.8832	−	35.7283i	−2.97049	−	1.71501i
$435$	−0.870240	−	1.11847i	−0.0417248	−	0.0536266i
$436$	−2.67252	+	9.97398i	−0.127990	+	0.477667i
$437$	−1.52017	−	0.407330i	−0.0727198	−	0.0194852i
$438$	−8.84413	+	11.6877i	−0.422589	+	0.558461i
$439$	0.848708	+	3.16742i	0.0405066	+	0.151173i	0.983217	−	0.182439i	$-0.0583992\pi$
$439$	0.848708	+	3.16742i	0.0405066	+	0.151173i	−0.942711	+	0.333612i	$0.891733\pi$
$440$		−	8.93586i		−	0.426001i
$441$	−6.38130	−	22.5958i	−0.303871	−	1.07599i
$442$	21.0983	−	10.2169i	1.00354	−	0.485968i
$443$	−0.922573	+	1.59794i	−0.0438328	+	0.0759206i	−0.887109	−	0.461559i	$-0.847290\pi$
$443$	−0.922573	+	1.59794i	−0.0438328	+	0.0759206i	0.843277	+	0.537480i	$0.180624\pi$
$444$	37.5214	−	15.8382i	1.78069	−	0.751647i
$445$	−47.3735	−	12.6937i	−2.24572	−	0.601739i
$446$	−7.43697	−	12.8812i	−0.352151	−	0.609943i
$447$	8.77620	+	3.56630i	0.415100	+	0.168680i
$448$	−25.8744	+	6.93302i	−1.22245	+	0.327554i
$449$	10.2493	+	10.2493i	0.483694	+	0.483694i	0.906309	−	0.422615i	$-0.138888\pi$
$449$	10.2493	+	10.2493i	0.483694	+	0.483694i	−0.422615	+	0.906309i	$0.638888\pi$
$450$	43.0419	−	12.1555i	2.02901	−	0.573015i
$451$			1.86656i			0.0878929i
$452$	−73.5821	+	19.7163i	−3.46101	+	0.927376i
$453$	2.58576	−	0.358120i	0.121490	−	0.0168259i
$454$	11.6617	+	3.12474i	0.547309	+	0.146651i
$455$	−13.7550	−	23.8244i	−0.644846	−	1.11691i
$456$	−4.22977	+	3.29102i	−0.198077	+	0.154116i
$457$	16.6268	+	9.59950i	0.777770	+	0.449046i	0.835639	−	0.549278i	$-0.185097\pi$
$457$	16.6268	+	9.59950i	0.777770	+	0.449046i	−0.0578694	+	0.998324i	$0.518431\pi$
$458$	−54.7449			−2.55806
$459$	13.9156	−	16.2897i	0.649526	−	0.760339i
$460$	−57.9844			−2.70354
$461$	11.4955	+	6.63691i	0.535397	+	0.309112i	0.743211	−	0.669057i	$-0.233302\pi$
$461$	11.4955	+	6.63691i	0.535397	+	0.309112i	−0.207814	+	0.978168i	$0.566635\pi$
$462$	−5.14932	+	4.00649i	−0.239568	+	0.186399i
$463$	2.01245	+	3.48567i	0.0935265	+	0.161993i	0.908993	−	0.416812i	$-0.136853\pi$
$463$	2.01245	+	3.48567i	0.0935265	+	0.161993i	−0.815466	+	0.578805i	$0.803519\pi$
$464$	2.25951	+	0.605435i	0.104895	+	0.0281066i
$465$	−40.0093	+	5.54116i	−1.85539	+	0.256965i
$466$	−0.515785	+	0.138204i	−0.0238933	+	0.00640218i
$467$		−	28.0545i		−	1.29821i	−0.760700	−	0.649103i	$-0.775144\pi$
$467$		−	28.0545i		−	1.29821i	0.760700	−	0.649103i	$-0.224856\pi$
$468$	22.4655	+	21.8694i	1.03847	+	1.01092i
$469$	−2.65322	−	2.65322i	−0.122514	−	0.122514i
$470$	−13.7042	+	3.67203i	−0.632127	+	0.169378i
$471$	−11.0530	−	4.49149i	−0.509294	−	0.206957i
$472$	−6.44717	−	11.1668i	−0.296755	−	0.513995i
$473$	−2.92570	−	0.783938i	−0.134524	−	0.0360455i
$474$	−41.9781	+	17.7194i	−1.92812	+	0.813880i
$475$	1.21772	−	2.10916i	0.0558730	−	0.0967749i
$476$	24.9589	−	71.8283i	1.14399	−	3.29225i
$477$	8.60656	+	2.18255i	0.394067	+	0.0999320i
$478$			43.3975i			1.98496i
$479$	2.93123	+	10.9395i	0.133931	+	0.499839i	1.00000		8.62574e-5i	$-2.74566e-5\pi$
$479$	2.93123	+	10.9395i	0.133931	+	0.499839i	−0.866069	+	0.499925i	$0.833361\pi$
$480$	−33.7265	+	44.5704i	−1.53940	+	2.03435i
$481$	−10.3468	−	2.77243i	−0.471775	−	0.126412i
$482$	−14.8202	+	55.3097i	−0.675042	+	2.51929i
$483$	15.1421	+	19.4613i	0.688988	+	0.885518i
$484$	−45.0430	−	26.0056i	−2.04741	−	1.18207i
$485$		−	56.5049i		−	2.56576i
$486$	38.0280	+	14.2744i	1.72499	+	0.647499i
$487$	−7.32305	−	7.32305i	−0.331839	−	0.331839i	0.521446	−	0.853285i	$-0.325393\pi$
$487$	−7.32305	−	7.32305i	−0.331839	−	0.331839i	−0.853285	+	0.521446i	$0.825393\pi$
$488$	10.9301	+	40.7915i	0.494781	+	1.84655i
$489$	24.5985	+	3.07039i	1.11238	+	0.138848i
$490$	−64.5007	−	17.2829i	−2.91384	−	0.780762i
$491$	−24.7376	+	14.2823i	−1.11639	+	0.644549i	−0.940477	−	0.339856i	$-0.889622\pi$
$491$	−24.7376	+	14.2823i	−1.11639	+	0.644549i	−0.175914	+	0.984405i	$0.556288\pi$
$492$	24.8879	−	32.8900i	1.12204	−	1.48280i
$493$	−0.779453	+	0.673725i	−0.0351048	+	0.0303431i
$494$	2.42013			0.108887
$495$	−0.906533	+	3.57478i	−0.0407456	+	0.160674i
$496$	47.1443	−	47.1443i	2.11684	−	2.11684i
$497$	−23.8184	+	41.2547i	−1.06840	+	1.85053i
$498$	16.9801	+	6.90003i	0.760896	+	0.309198i
$499$	8.15582	−	30.4379i	0.365105	−	1.36259i	−0.502174	−	0.864766i	$-0.667466\pi$
$499$	8.15582	−	30.4379i	0.365105	−	1.36259i	0.867279	−	0.497822i	$-0.165867\pi$
$500$	2.92857	−	10.9296i	0.130969	−	0.488785i
$501$	25.4860	−	10.7579i	1.13863	−	0.480628i
$502$	23.1847	+	13.3857i	1.03478	+	0.597432i
$503$	−15.7710	−	15.7710i	−0.703194	−	0.703194i	0.261901	−	0.965095i	$-0.415651\pi$
$503$	−15.7710	−	15.7710i	−0.703194	−	0.703194i	−0.965095	+	0.261901i	$0.915651\pi$
$504$	83.9608	−	1.12879i	3.73991	−	0.0502805i
$505$	18.6231	−	18.6231i	0.828718	−	0.828718i
$506$	1.80845	−	3.13234i	0.0803956	−	0.139249i
$507$	1.95774	+	14.1356i	0.0869462	+	0.627785i
$508$	5.95937	−	3.44064i	0.264404	−	0.152654i
$509$	−17.8761	−	30.9623i	−0.792343	−	1.37238i	−0.924512	−	0.381152i	$-0.875527\pi$
$509$	−17.8761	−	30.9623i	−0.792343	−	1.37238i	0.132169	−	0.991227i	$-0.457806\pi$
$510$	−19.5592	−	57.7061i	−0.866096	−	2.55527i
$511$	6.25236	−	10.8294i	0.276588	−	0.479065i
$512$			43.8378i			1.93737i
$513$	2.02598	−	0.887464i	0.0894494	−	0.0391825i
$514$	−56.3091			−2.48369
$515$	13.9903	+	52.2124i	0.616485	+	2.30075i
$516$	41.1000	+	52.8235i	1.80933	+	2.32543i
$517$	0.161581	−	0.603027i	0.00710630	−	0.0265211i
$518$	−42.6573	+	24.6282i	−1.87426	+	1.08210i
$519$	13.5409	+	10.2465i	0.594381	+	0.449770i
$520$	50.1638	−	13.4414i	2.19983	−	0.589442i
$521$	24.2680	+	24.2680i	1.06320	+	1.06320i	0.997863	+	0.0653394i	$0.0208130\pi$
$521$	24.2680	+	24.2680i	1.06320	+	1.06320i	0.0653394	+	0.997863i	$0.479187\pi$
$522$	−1.70459	−	0.953826i	−0.0746080	−	0.0417478i
$523$	2.55482			0.111714			0.0558572	−	0.998439i	$-0.482211\pi$
$523$	2.55482			0.111714			0.0558572	+	0.998439i	$0.482211\pi$
$524$	24.4307	+	91.1765i	1.06726	+	3.98306i
$525$	−35.1547	+	14.8392i	−1.53428	+	0.647635i
$526$	−22.8412	−	39.5622i	−0.995924	−	1.72499i
$527$	5.52185	+	28.8407i	0.240535	+	1.25632i
$528$	−2.36734	−	5.60835i	−0.103025	−	0.244072i
$529$	8.08028	+	4.66515i	0.351317	+	0.202833i
$530$	17.8558	−	17.8558i	0.775605	−	0.775605i
$531$	1.44632	+	5.12133i	0.0627649	+	0.222247i
$532$	5.55111	−	5.55111i	0.240671	−	0.240671i
$533$	−10.4784	+	2.80769i	−0.453871	+	0.121614i
$534$	−66.9612	+	9.27391i	−2.89769	+	0.401322i
$535$	−0.661556	+	0.381949i	−0.0286016	+	0.0165131i
$536$	6.13443	−	3.54172i	0.264967	−	0.152979i
$537$	−18.7970	−	24.1587i	−0.811150	−	1.04253i
$538$	16.2505	−	4.35432i	0.700611	−	0.187728i
$539$	2.07773	−	2.07773i	0.0894940	−	0.0894940i
$540$	63.6383	−	50.9026i	2.73856	−	2.19050i
$541$	27.0736	−	27.0736i	1.16399	−	1.16399i	0.180392	−	0.983595i	$-0.442263\pi$
$541$	27.0736	−	27.0736i	1.16399	−	1.16399i	0.983595	−	0.180392i	$-0.0577366\pi$
$542$	28.6485	+	16.5402i	1.23056	+	0.710464i
$543$	32.5889	+	4.06776i	1.39853	+	0.174564i
$544$	33.6231	+	22.8171i	1.44158	+	0.978274i
$545$	−3.52954	−	6.11334i	−0.151189	−	0.261867i
$546$	−30.2371	−	22.8805i	−1.29403	−	0.979194i
$547$	4.94019	+	18.4370i	0.211227	+	0.788311i	0.987461	+	0.157865i	$0.0504611\pi$
$547$	4.94019	+	18.4370i	0.211227	+	0.788311i	−0.776233	+	0.630446i	$0.782872\pi$
$548$	78.8355			3.36769
$549$	−0.234300	−	17.4274i	−0.00999968	−	0.743785i
$550$	3.95778	+	3.95778i	0.168760	+	0.168760i
$551$	−0.102740	+	0.0275291i	−0.00437688	+	0.00117278i
$552$	−42.8854	+	18.1024i	−1.82532	+	0.770489i
$553$	33.6662	−	19.4372i	1.43163	−	0.826553i
$554$	14.0932	−	52.5966i	0.598764	−	2.23462i
$555$	−10.4817	+	25.7941i	−0.444923	+	1.09490i
$556$	7.22828	+	26.9763i	0.306547	+	1.14405i
$557$	25.5409			1.08220			0.541101	−	0.840958i	$-0.318008\pi$
$557$	25.5409			1.08220			0.541101	+	0.840958i	$0.318008\pi$
$558$	−47.8356	+	28.4821i	−2.02504	+	1.20574i
$559$		−	17.6034i		−	0.744543i
$560$	59.0150	−	102.217i	2.49384	−	4.31946i
$561$	2.62938	+	0.524265i	0.111013	+	0.0221345i
$562$	25.6826	+	44.4835i	1.08335	+	1.87642i
$563$	−12.2505	+	7.07283i	−0.516297	+	0.298084i	−0.735418	−	0.677614i	$-0.763014\pi$
$563$	−12.2505	+	7.07283i	−0.516297	+	0.298084i	0.219121	+	0.975698i	$0.429681\pi$
$564$	−10.8877	+	8.47127i	−0.458453	+	0.356705i
$565$	26.0388	−	45.1006i	1.09546	−	1.89740i
$566$	−47.0933	+	47.0933i	−1.97948	+	1.97948i
$567$	−33.7029	−	8.06615i	−1.41539	−	0.338747i
$568$	−63.5892	−	63.5892i	−2.66814	−	2.66814i
$569$	−10.4444	−	6.03010i	−0.437854	−	0.252795i	0.264833	−	0.964294i	$-0.414683\pi$
$569$	−10.4444	−	6.03010i	−0.437854	−	0.252795i	−0.702687	+	0.711499i	$0.748017\pi$
$570$	0.779130	−	6.24202i	0.0326342	−	0.261450i
$571$	−8.28681	+	30.9268i	−0.346792	+	1.29425i	0.543712	+	0.839272i	$0.317018\pi$
$571$	−8.28681	+	30.9268i	−0.346792	+	1.29425i	−0.890504	+	0.454974i	$0.849648\pi$
$572$	−1.01550	+	3.78989i	−0.0424601	+	0.158463i
$573$	0.740186	+	5.34442i	0.0309217	+	0.223266i
$574$	−24.9414	+	43.1998i	−1.04104	+	1.80313i
$575$	14.9580	−	14.9580i	0.623791	−	0.623791i
$576$	−5.13013	+	20.2299i	−0.213755	+	0.842912i
$577$	27.1906			1.13196			0.565980	−	0.824419i	$-0.308498\pi$
$577$	27.1906			1.13196			0.565980	+	0.824419i	$0.308498\pi$
$578$	−41.1641	+	16.3624i	−1.71220	+	0.680586i
$579$	−11.6720	−	27.6516i	−0.485073	−	1.14916i
$580$	−3.39382	+	1.95942i	−0.140921	+	0.0813605i
$581$	−15.1045	−	4.04723i	−0.626639	−	0.167908i
$582$	−30.2876	−	71.7526i	−1.25546	−	2.97424i
$583$	0.287589	+	1.07330i	0.0119107	+	0.0444514i
$584$	16.6922	+	16.6922i	0.690729	+	0.690729i
$585$	−21.4316	+	0.288133i	−0.886086	+	0.0119128i
$586$			54.1279i			2.23600i
$587$	4.32648	+	2.49789i	0.178573	+	0.103099i	0.586622	−	0.809861i	$-0.300457\pi$
$587$	4.32648	+	2.49789i	0.178573	+	0.103099i	−0.408049	+	0.912960i	$0.633791\pi$
$588$	−64.3144	+	8.90735i	−2.65228	+	0.367333i
$589$	−0.784631	+	2.92828i	−0.0323301	+	0.120658i
$590$	14.6191	+	3.91717i	0.601857	+	0.161267i
$591$	26.1895	+	3.26897i	1.07729	+	0.134468i
$592$	−11.8949	−	44.3924i	−0.488878	−	1.82452i
$593$			6.06818i			0.249190i	0.992208	+	0.124595i	$0.0397632\pi$
$593$			6.06818i			0.249190i	−0.992208	+	0.124595i	$0.960237\pi$
$594$	0.764981	+	5.02534i	0.0313876	+	0.206192i
$595$	22.6568	+	46.7871i	0.928837	+	1.91808i
$596$	13.0981	−	22.6865i	0.536518	−	0.929276i
$597$	−5.25760	+	42.1214i	−0.215179	+	1.72391i
$598$	20.3045	+	5.44057i	0.830312	+	0.222481i
$599$	−9.06357	−	15.6986i	−0.370328	−	0.641426i	0.619288	−	0.785164i	$-0.287421\pi$
$599$	−9.06357	−	15.6986i	−0.370328	−	0.641426i	−0.989616	+	0.143738i	$0.954088\pi$
$600$	−9.88231	−	71.3540i	−0.403444	−	2.91301i
$601$	−19.4592	+	5.21406i	−0.793755	+	0.212686i	−0.632841	−	0.774282i	$-0.718111\pi$
$601$	−19.4592	+	5.21406i	−0.793755	+	0.212686i	−0.160915	+	0.986968i	$0.551444\pi$
$602$	−57.2374	−	57.2374i	−2.33282	−	2.33282i
$603$	−2.81337	+	0.794527i	−0.114569	+	0.0323557i
$604$		−	7.21867i		−	0.293724i
$605$	34.3450	−	9.20270i	1.39632	−	0.374143i
$606$	13.6662	−	33.6308i	0.555153	−	1.36616i
$607$	16.7973	+	4.50082i	0.681780	+	0.182682i	0.583056	−	0.812432i	$-0.301857\pi$
$607$	16.7973	+	4.50082i	0.681780	+	0.182682i	0.0987248	+	0.995115i	$0.468524\pi$
$608$	2.09753	+	3.63302i	0.0850659	+	0.147338i
$609$	1.54390	+	0.627380i	0.0625620	+	0.0254227i
$610$	−42.9273	−	24.7841i	−1.73808	−	1.00348i
$611$	3.62830			0.146785
$612$	−39.3411	−	44.2970i	−1.59027	−	1.79060i
$613$	1.92172			0.0776175			0.0388088	−	0.999247i	$-0.487644\pi$
$613$	1.92172			0.0776175			0.0388088	+	0.999247i	$0.487644\pi$
$614$	−45.7490	−	26.4132i	−1.84628	−	1.06595i
$615$	3.86821	+	27.9300i	0.155981	+	1.12624i
$616$	5.25411	+	9.10038i	0.211694	+	0.366665i
$617$	−21.3882	−	5.73094i	−0.861055	−	0.230719i	−0.198839	−	0.980032i	$-0.563717\pi$
$617$	−21.3882	−	5.73094i	−0.861055	−	0.230719i	−0.662216	+	0.749313i	$0.730384\pi$
$618$	45.7522	+	58.8028i	1.84042	+	2.36540i
$619$	4.42225	−	1.18494i	0.177745	−	0.0476267i	−0.168849	−	0.985642i	$-0.554005\pi$
$619$	4.42225	−	1.18494i	0.177745	−	0.0476267i	0.346594	+	0.938015i	$0.387338\pi$
$620$			111.694i			4.48575i
$621$	18.9927	−	2.89116i	0.762151	−	0.116018i
$622$	34.5310	+	34.5310i	1.38457	+	1.38457i
$623$	55.7093	−	14.9273i	2.23195	−	0.598048i
$624$	27.9230	−	21.7258i	1.11781	−	0.869728i
$625$	−10.4360	−	18.0757i	−0.417441	−	0.723029i
$626$	4.66089	+	1.24888i	0.186287	+	0.0499154i
$627$	0.220727	+	0.167025i	0.00881501	+	0.00667033i
$628$	−16.4960	+	28.5720i	−0.658264	+	1.14015i
$629$	19.1201	+	6.64386i	0.762370	+	0.264908i
$630$	−68.7479	+	70.6217i	−2.73898	+	2.81363i
$631$		−	4.32559i		−	0.172199i	−0.996287	−	0.0860996i	$-0.972560\pi$
$631$		−	4.32559i		−	0.172199i	0.996287	−	0.0860996i	$-0.0274403\pi$
$632$	18.9939	+	70.8863i	0.755538	+	2.81971i
$633$	6.88370	+	16.3078i	0.273603	+	0.648177i
$634$	16.4155	+	4.39852i	0.651942	+	0.174687i
$635$	−1.21756	+	4.54398i	−0.0483172	+	0.180322i
$636$	9.24339	−	22.7468i	0.366524	−	0.901969i
$637$	14.7892	+	8.53854i	0.585969	+	0.338309i
$638$		−	0.244447i		−	0.00967773i
$639$	18.9877	+	31.8898i	0.751142	+	1.26154i
$640$	−3.66583	−	3.66583i	−0.144905	−	0.144905i
$641$	−3.13383	−	11.6956i	−0.123779	−	0.461949i	0.876014	−	0.482285i	$-0.160193\pi$
$641$	−3.13383	−	11.6956i	−0.123779	−	0.461949i	−0.999793	+	0.0203363i	$0.993526\pi$
$642$	−0.635344	+	0.839623i	−0.0250750	+	0.0331373i
$643$	1.89006	+	0.506439i	0.0745366	+	0.0199720i	0.295895	−	0.955221i	$-0.404382\pi$
$643$	1.89006	+	0.506439i	0.0745366	+	0.0199720i	−0.221358	+	0.975193i	$0.571049\pi$
$644$	59.0519	−	34.0937i	2.32697	−	1.34348i
$645$	−45.4028	−	5.66718i	−1.78773	−	0.223145i
$646$	−4.56113	−	0.331851i	−0.179455	−	0.0130565i
$647$	−5.94573			−0.233751			−0.116875	−	0.993147i	$-0.537288\pi$
$647$	−5.94573			−0.233751			−0.116875	+	0.993147i	$0.537288\pi$
$648$	31.1755	−	57.5152i	1.22469	−	2.25941i
$649$	−0.470916	+	0.470916i	−0.0184851	+	0.0184851i
$650$	−16.2647	+	28.1714i	−0.637956	+	1.10497i
$651$	37.4878	−	29.1678i	1.46926	−	1.14318i
$652$	17.7422	−	66.2146i	0.694837	−	2.59317i
$653$	−1.41863	+	5.29438i	−0.0555151	+	0.207185i	−0.988112	−	0.153734i	$-0.950870\pi$
$653$	−1.41863	+	5.29438i	−0.0555151	+	0.207185i	0.932597	+	0.360919i	$0.117537\pi$
$654$	−7.75882	−	5.87112i	−0.303394	−	0.229579i
$655$	−55.8847	−	32.2650i	−2.18360	−	1.26070i
$656$	−32.9108	−	32.9108i	−1.28495	−	1.28495i
$657$	−4.98429	−	8.37110i	−0.194456	−	0.326588i
$658$	11.7974	−	11.7974i	0.459911	−	0.459911i
$659$	−21.3196	+	36.9266i	−0.830492	+	1.43845i	0.0671560	+	0.997742i	$0.478607\pi$
$659$	−21.3196	+	36.9266i	−0.830492	+	1.43845i	−0.897648	+	0.440712i	$0.854726\pi$
$660$	9.44800	+	3.83929i	0.367763	+	0.149444i
$661$	−32.8370	+	18.9585i	−1.27721	+	0.737399i	−0.976335	−	0.216264i	$-0.930613\pi$
$661$	−32.8370	+	18.9585i	−1.27721	+	0.737399i	−0.300877	+	0.953663i	$0.597279\pi$
$662$	−24.3056	−	42.0985i	−0.944664	−	1.63621i
$663$	1.01203	+	15.5493i	0.0393038	+	0.603886i
$664$	14.7600	−	25.5651i	0.572800	−	0.992119i
$665$			5.36683i			0.208117i
$666$	0.515898	+	38.3730i	0.0199906	+	1.48692i
$667$	−0.923858			−0.0357719
$668$	−19.7992	−	73.8915i	−0.766053	−	2.85895i
$669$	9.79348	−	1.35637i	0.378638	−	0.0524402i
$670$	−2.15187	+	8.03090i	−0.0831341	+	0.310261i
$671$	1.88893	−	1.09058i	0.0729215	−	0.0421012i
$672$	8.14095	−	65.2214i	0.314044	−	2.51597i
$673$	−18.1478	+	4.86270i	−0.699548	+	0.187443i	−0.591028	−	0.806651i	$-0.701278\pi$
$673$	−18.1478	+	4.86270i	−0.699548	+	0.187443i	−0.108520	+	0.994094i	$0.534611\pi$
$674$	−16.3061	−	16.3061i	−0.628087	−	0.628087i
$675$	−3.28538	+	29.5476i	−0.126454	+	1.13729i
$676$	39.4625			1.51779
$677$	−11.8479	−	44.2171i	−0.455353	−	1.69940i	−0.687049	−	0.726611i	$-0.741094\pi$
$677$	−11.8479	−	44.2171i	−0.455353	−	1.69940i	0.231696	−	0.972788i	$-0.425572\pi$
$678$	8.89071	−	71.2281i	0.341446	−	2.73550i
$679$	33.2237	+	57.5452i	1.27501	+	2.20838i
$680$	−96.3849	+	18.4539i	−3.69619	+	0.707675i
$681$	−4.84250	+	6.39948i	−0.185565	+	0.245229i
$682$	−6.03375	−	3.48359i	−0.231044	−	0.133393i
$683$	34.7238	−	34.7238i	1.32867	−	1.32867i	0.422135	−	0.906533i	$-0.361281\pi$
$683$	34.7238	−	34.7238i	1.32867	−	1.32867i	0.906533	−	0.422135i	$-0.138719\pi$
$684$	−1.66232	−	5.88618i	−0.0635604	−	0.225064i
$685$	−38.1092	+	38.1092i	−1.45608	+	1.45608i
$686$	8.01022	−	2.14633i	0.305832	−	0.0819473i
$687$	13.6995	−	33.7127i	0.522669	−	1.28622i
$688$	65.4075	−	37.7630i	2.49364	−	1.43970i
$689$	−5.59265	+	3.22892i	−0.213063	+	0.123012i
$690$	20.5691	−	50.6179i	0.783053	−	1.92699i
$691$	−39.4346	+	10.5665i	−1.50016	+	0.401967i	−0.913154	−	0.407615i	$-0.866361\pi$
$691$	−39.4346	+	10.5665i	−1.50016	+	0.401967i	−0.587007	+	0.809582i	$0.699694\pi$
$692$	33.2037	−	33.2037i	1.26222	−	1.26222i
$693$	−1.17867	−	4.17362i	−0.0447741	−	0.158543i
$694$	20.5428	−	20.5428i	0.779794	−	0.779794i
$695$	−16.5346	−	9.54623i	−0.627191	−	0.362109i
$696$	−1.89835	+	2.50872i	−0.0719569	+	0.0950928i
$697$	20.1333	−	3.85473i	0.762603	−	0.146008i
$698$	4.82605	+	8.35896i	0.182669	+	0.316391i
$699$	0.0439632	−	0.352212i	0.00166284	−	0.0133219i
$700$	27.3105	+	101.924i	1.03224	+	3.85237i
$701$	−22.1494			−0.836571			−0.418286	−	0.908316i	$-0.637369\pi$
$701$	−22.1494			−0.836571			−0.418286	+	0.908316i	$0.637369\pi$
$702$	−27.0604	+	11.8536i	−1.02133	+	0.447384i
$703$	1.47766	+	1.47766i	0.0557310	+	0.0557310i
$704$	−2.52281	+	0.675985i	−0.0950819	+	0.0254771i
$705$	1.16808	−	9.35814i	0.0439926	−	0.352448i
$706$	−17.6347	+	10.1814i	−0.663692	+	0.383183i
$707$	−8.01596	+	29.9160i	−0.301471	+	1.12511i
$708$	14.5768	−	2.01885i	0.547832	−	0.0758730i
$709$	11.7630	+	43.9000i	0.441768	+	1.64870i	0.724332	+	0.689452i	$0.242148\pi$
$709$	11.7630	+	43.9000i	0.441768	+	1.64870i	−0.282564	+	0.959248i	$0.591185\pi$
$710$	105.554			3.96137
$711$	−0.407159	−	30.2849i	−0.0152697	−	1.13577i
$712$			108.878i			4.08036i
$713$	−13.1658	+	22.8039i	−0.493064	+	0.854012i
$714$	53.8493	+	47.2681i	2.01526	+	1.76896i
$715$	−1.34115	−	2.32293i	−0.0501560	−	0.0868728i
$716$	−73.3057	+	42.3230i	−2.73956	+	1.58169i
$717$	−26.7248	−	10.8599i	−0.998057	−	0.405571i
$718$	21.5459	−	37.3186i	0.804087	−	1.39272i
$719$	9.92847	−	9.92847i	0.370269	−	0.370269i	−0.497306	−	0.867575i	$-0.665677\pi$
$719$	9.92847	−	9.92847i	0.370269	−	0.370269i	0.867575	+	0.497306i	$0.165677\pi$
$720$	−47.0459	−	79.0135i	−1.75330	−	2.94466i
$721$	−44.9477	−	44.9477i	−1.67394	−	1.67394i
$722$	42.4665	+	24.5181i	1.58044	+	0.912468i
$723$	−30.3519	−	22.9673i	−1.12880	−	0.854164i
$724$	23.5054	−	87.7233i	0.873571	−	3.26021i
$725$	0.370025	−	1.38095i	0.0137424	−	0.0512872i
$726$	38.6801	−	30.0955i	1.43555	−	1.11695i
$727$	19.9610	−	34.5735i	0.740313	−	1.28226i	−0.212039	−	0.977261i	$-0.568011\pi$
$727$	19.9610	−	34.5735i	0.740313	−	1.28226i	0.952353	−	0.304999i	$-0.0986561\pi$
$728$	−43.1841	+	43.1841i	−1.60051	+	1.60051i
$729$	−18.3066	+	19.8461i	−0.678022	+	0.735042i
$730$	−27.7080			−1.02552
$731$	−2.41379	+	33.1764i	−0.0892773	+	1.22707i
$732$	−47.8255	−	5.96959i	−1.76768	−	0.220642i
$733$	9.82815	−	5.67429i	0.363011	−	0.209585i	−0.307390	−	0.951584i	$-0.599456\pi$
$733$	9.82815	−	5.67429i	0.363011	−	0.209585i	0.670401	+	0.741999i	$0.266122\pi$
$734$	6.78506	+	1.81805i	0.250441	+	0.0671055i
$735$	26.7839	−	35.3955i	0.987938	−	1.30558i
$736$	9.43067	+	35.1957i	0.347619	+	1.29733i
$737$	−0.258695	−	0.258695i	−0.00952916	−	0.00952916i
$738$	19.8830	+	33.3934i	0.731902	+	1.22923i
$739$			29.2150i			1.07469i	0.843362	+	0.537346i	$0.180573\pi$
$739$			29.2150i			1.07469i	−0.843362	+	0.537346i	$0.819427\pi$
$740$	66.6779	+	38.4965i	2.45113	+	1.41516i
$741$	−0.605620	+	1.49035i	−0.0222480	+	0.0547494i
$742$	−7.68567	+	28.6833i	−0.282150	+	1.05300i
$743$	−0.664956	−	0.178174i	−0.0243949	−	0.00653658i	0.246601	−	0.969117i	$-0.420686\pi$
$743$	−0.664956	−	0.178174i	−0.0243949	−	0.00653658i	−0.270996	+	0.962581i	$0.587353\pi$
$744$	34.8702	+	82.6092i	1.27841	+	3.02860i
$745$	4.63507	+	17.2983i	0.169816	+	0.633761i
$746$			43.7875i			1.60317i
$747$	−8.49828	+	8.72990i	−0.310936	+	0.319410i
$748$	2.43355	−	7.00342i	0.0889793	−	0.256071i
$749$	0.449157	−	0.777963i	0.0164118	−	0.0284261i
$750$	8.50218	+	6.43361i	0.310456	+	0.234922i
$751$	−39.6945	−	10.6361i	−1.44847	−	0.388117i	−0.552980	−	0.833195i	$-0.686509\pi$
$751$	−39.6945	−	10.6361i	−1.44847	−	0.388117i	−0.895492	+	0.445078i	$0.853176\pi$
$752$	7.78348	+	13.4814i	0.283834	+	0.491616i
$753$	−14.0449	+	10.9278i	−0.511824	+	0.398231i
$754$	1.37227	−	0.367697i	0.0499750	−	0.0133907i
$755$	3.48952	+	3.48952i	0.126997	+	0.126997i
$756$	−34.8802	+	89.2578i	−1.26858	+	3.24627i
$757$			19.2641i			0.700165i	0.936719	+	0.350083i	$0.113846\pi$
$757$			19.2641i			0.700165i	−0.936719	+	0.350083i	$0.886154\pi$
$758$	91.3518	−	24.4776i	3.31805	−	0.889068i
$759$	1.47638	+	1.89752i	0.0535894	+	0.0688755i
$760$	−9.78625	−	2.62222i	−0.354985	−	0.0951178i
$761$	−4.81683	−	8.34299i	−0.174610	−	0.302433i	0.765416	−	0.643535i	$-0.222533\pi$
$761$	−4.81683	−	8.34299i	−0.174610	−	0.302433i	−0.940026	+	0.341102i	$0.889200\pi$
$762$	0.889537	+	6.42280i	0.0322245	+	0.232673i
$763$	7.18903	+	4.15059i	0.260260	+	0.150261i
$764$	14.9200			0.539788
$765$	40.4308	+	2.39569i	1.46178	+	0.0866162i
$766$	87.3807			3.15719
$767$	−3.35197	−	1.93526i	−0.121032	−	0.0698781i
$768$	−28.9459	−	11.7625i	−1.04450	−	0.424442i
$769$	3.71625	+	6.43674i	0.134011	+	0.232115i	0.925219	−	0.379433i	$-0.123881\pi$
$769$	3.71625	+	6.43674i	0.134011	+	0.232115i	−0.791208	+	0.611547i	$0.790547\pi$
$770$	−11.9138	−	3.19228i	−0.429342	−	0.115042i
$771$	14.0909	−	34.6759i	0.507472	−	1.24882i
$772$	−80.1703	+	21.4816i	−2.88539	+	0.773138i
$773$		−	42.8996i		−	1.54299i	−0.636235	−	0.771495i	$-0.719509\pi$
$773$		−	42.8996i		−	1.54299i	0.636235	−	0.771495i	$-0.280491\pi$
$774$	−60.6923	+	17.1402i	−2.18154	+	0.616091i
$775$	−28.8133	−	28.8133i	−1.03500	−	1.03500i
$776$	−121.165	+	32.4661i	−4.34957	+	1.16546i
$777$	−4.49173	−	32.4320i	−0.161140	−	1.16349i
$778$	−5.96976	−	10.3399i	−0.214026	−	0.370704i
$779$	2.04419	+	0.547740i	0.0732408	+	0.0196248i
$780$	−7.34116	+	58.8139i	−0.262856	+	2.10588i
$781$	−2.32235	+	4.02243i	−0.0831003	+	0.143934i
$782$	−37.5210	−	13.0378i	−1.34175	−	0.466231i
$783$	1.01394	−	0.811024i	0.0362353	−	0.0289836i
$784$			73.2680i			2.61672i
$785$	−5.83753	−	21.7860i	−0.208350	−	0.777574i
$786$	−88.2596	−	11.0166i	−3.14812	−	0.392949i
$787$	−34.9590	−	9.36723i	−1.24615	−	0.333906i	−0.425304	−	0.905051i	$-0.639833\pi$
$787$	−34.9590	−	9.36723i	−1.24615	−	0.333906i	−0.820849	+	0.571145i	$0.806499\pi$
$788$	18.8896	−	70.4971i	0.672915	−	2.51135i
$789$	30.0788	−	4.16582i	1.07083	−	0.148307i
$790$	−74.5978	−	43.0690i	−2.65407	−	1.53233i
$791$			61.2412i			2.17749i
$792$	8.18636	−	0.110060i	0.290890	−	0.00391081i
$793$	8.96357	+	8.96357i	0.318306	+	0.318306i
$794$	−12.5113	−	46.6927i	−0.444008	−	1.65706i
$795$	6.52756	+	15.4641i	0.231509	+	0.548455i
$796$	113.383	+	30.3809i	4.01875	+	1.07682i
$797$	32.7431	−	18.9042i	1.15982	−	0.669623i	0.208560	−	0.978010i	$-0.433122\pi$
$797$	32.7431	−	18.9042i	1.15982	−	0.669623i	0.951261	+	0.308387i	$0.0997891\pi$
$798$	2.87671	+	6.81505i	0.101834	+	0.241250i
$799$	−6.83812	−	0.497516i	−0.241915	−	0.0176008i
$800$	−56.3866			−1.99357
$801$	11.0455	−	43.5564i	0.390274	−	1.53899i
$802$	17.3277	−	17.3277i	0.611863	−	0.611863i
$803$	0.609619	−	1.05589i	0.0215130	−	0.0372616i
$804$	1.10904	+	8.00771i	0.0391129	+	0.282410i
$805$	−12.0649	+	45.0267i	−0.425231	+	1.58698i
$806$	10.4800	−	39.1121i	0.369144	−	1.37766i
$807$	−1.38512	+	11.0970i	−0.0487587	+	0.390631i
$808$	−50.6343	−	29.2337i	−1.78131	−	1.02844i
$809$	13.6821	+	13.6821i	0.481038	+	0.481038i	0.905463	−	0.424425i	$-0.139524\pi$
$809$	13.6821	+	13.6821i	0.481038	+	0.481038i	−0.424425	+	0.905463i	$0.639524\pi$
$810$	21.8610	+	73.6105i	0.768119	+	2.58641i
$811$	3.31583	−	3.31583i	0.116435	−	0.116435i	−0.646489	−	0.762923i	$-0.723763\pi$
$811$	3.31583	−	3.31583i	0.116435	−	0.116435i	0.762923	+	0.646489i	$0.223763\pi$
$812$	2.30420	−	3.99099i	0.0808615	−	0.140056i
$813$	−17.3548	+	13.5031i	−0.608659	+	0.473575i
$814$	−4.15919	+	2.40131i	−0.145779	+	0.0841658i
$815$	23.4317	+	40.5848i	0.820776	+	1.42163i
$816$	−55.6044	+	37.1170i	−1.94654	+	1.29935i
$817$	−1.71708	+	2.97408i	−0.0600732	+	0.104050i
$818$			15.4942i			0.541742i
$819$	21.6567	−	12.8948i	0.756747	−	0.450580i
$820$	77.9722			2.72291
$821$	4.84071	+	18.0658i	0.168942	+	0.630500i	0.997504	+	0.0706034i	$0.0224925\pi$
$821$	4.84071	+	18.0658i	0.168942	+	0.630500i	−0.828563	+	0.559897i	$0.810841\pi$
$822$	−27.9657	+	68.8201i	−0.975417	+	2.40038i
$823$	−0.851421	+	3.17755i	−0.0296787	+	0.110762i	−0.979176	−	0.203012i	$-0.934927\pi$
$823$	−0.851421	+	3.17755i	−0.0296787	+	0.110762i	0.949498	+	0.313774i	$0.101594\pi$
$824$	103.922	−	59.9994i	3.62030	−	2.09018i
$825$	−3.42766	+	1.44685i	−0.119336	+	0.0503730i
$826$	−17.1914	+	4.60643i	−0.598166	+	0.160278i
$827$	12.9036	+	12.9036i	0.448703	+	0.448703i	0.894923	−	0.446220i	$-0.147230\pi$
$827$	12.9036	+	12.9036i	0.448703	+	0.448703i	−0.446220	+	0.894923i	$0.647230\pi$
$828$	−0.714175	−	53.1210i	−0.0248193	−	1.84608i
$829$	−49.8284			−1.73061			−0.865306	−	0.501245i	$-0.832876\pi$
$829$	−49.8284			−1.73061			−0.865306	+	0.501245i	$0.832876\pi$
$830$	8.96788	+	33.4686i	0.311280	+	1.16171i
$831$	28.8630	+	21.8407i	1.00125	+	0.757646i
$832$	−7.58963	−	13.1456i	−0.263123	−	0.455743i
$833$	−26.7018	−	18.1202i	−0.925163	−	0.627827i
$834$	−26.1133	−	3.25947i	−0.904230	−	0.112866i
$835$	45.2902	+	26.1483i	1.56733	+	0.904900i
$836$	0.541245	−	0.541245i	0.0187194	−	0.0187194i
$837$	−5.56918	−	36.5853i	−0.192499	−	1.26457i
$838$	50.8463	−	50.8463i	1.75645	−	1.75645i
$839$	−12.1196	+	3.24744i	−0.418415	+	0.112114i	−0.461883	−	0.886941i	$-0.652826\pi$
$839$	−12.1196	+	3.24744i	−0.418415	+	0.112114i	0.0434681	+	0.999055i	$0.486159\pi$
$840$	97.4783	+	125.283i	3.36332	+	4.32269i
$841$	25.0607	−	14.4688i	0.864161	−	0.498923i
$842$	27.7371	−	16.0140i	0.955885	−	0.551881i
$843$	−33.8205	+	4.68403i	−1.16484	+	0.161327i
$844$	47.2812	−	12.6690i	1.62749	−	0.436084i
$845$	−19.0762	+	19.0762i	−0.656242	+	0.656242i
$846$	−3.53283	−	12.5095i	−0.121461	−	0.430086i
$847$	−29.5663	+	29.5663i	−1.01591	+	1.01591i
$848$	−23.9949	−	13.8534i	−0.823987	−	0.475729i
$849$	−17.2160	−	40.7855i	−0.590851	−	1.39975i
$850$	34.5164	−	50.8633i	1.18390	−	1.74460i
$851$	9.07546	+	15.7192i	0.311103	+	0.538846i
$852$	94.5547	−	39.9126i	3.23939	−	1.36738i
$853$	1.84383	+	6.88125i	0.0631314	+	0.235609i	0.990281	−	0.139082i	$-0.0444152\pi$
$853$	1.84383	+	6.88125i	0.0631314	+	0.235609i	−0.927149	+	0.374692i	$0.877749\pi$
$854$	58.2902			1.99465
$855$	3.64895	+	2.04182i	0.124792	+	0.0698287i
$856$	1.19914	+	1.19914i	0.0409856	+	0.0409856i
$857$	−22.0979	+	5.92112i	−0.754851	+	0.202262i	−0.615669	−	0.788005i	$-0.711114\pi$
$857$	−22.0979	+	5.92112i	−0.754851	+	0.202262i	−0.139182	+	0.990267i	$0.544447\pi$
$858$	−2.94818	−	2.23090i	−0.100649	−	0.0761616i
$859$	28.7745	−	16.6130i	0.981775	−	0.566828i	0.0789693	−	0.996877i	$-0.474837\pi$
$859$	28.7745	−	16.6130i	0.981775	−	0.566828i	0.902805	+	0.430049i	$0.141504\pi$
$860$	−32.7476	+	122.216i	−1.11668	+	4.16752i
$861$	−20.3617	−	26.1697i	−0.693924	−	0.891862i
$862$	7.27560	+	27.1529i	0.247808	+	0.924831i
$863$	−18.6692			−0.635506			−0.317753	−	0.948174i	$-0.602928\pi$
$863$	−18.6692			−0.635506			−0.317753	+	0.948174i	$0.602928\pi$
$864$	−41.2474	−	30.3487i	−1.40326	−	1.03248i
$865$			32.1015i			1.09148i
$866$	−23.0702	+	39.9587i	−0.783957	+	1.35785i
$867$	0.224814	−	29.4440i	0.00763507	−	0.999971i
$868$	−65.6739	−	113.751i	−2.22912	−	3.86094i
$869$	3.28253	−	1.89517i	0.111352	−	0.0642892i
$870$	−0.506585	−	3.65773i	−0.0171748	−	0.124009i
$871$	1.06312	−	1.84138i	0.0360226	−	0.0623929i
$872$	−11.0810	+	11.0810i	−0.375251	+	0.375251i
$873$	51.7655	−	0.695952i	1.75200	−	0.0235544i
$874$	−2.89974	−	2.89974i	−0.0980851	−	0.0980851i
$875$	−7.87780	−	4.54825i	−0.266318	−	0.153759i
$876$	−24.8207	+	10.4771i	−0.838614	+	0.353988i
$877$	2.05372	−	7.66459i	0.0693492	−	0.258815i	−0.922543	−	0.385893i	$-0.873893\pi$
$877$	2.05372	−	7.66459i	0.0693492	−	0.258815i	0.991893	+	0.127078i	$0.0405600\pi$
$878$	−2.21148	+	8.25334i	−0.0746337	+	0.278537i
$879$	−33.3328	−	13.5451i	−1.12429	−	0.456865i
$880$	5.75410	−	9.96639i	0.193971	−	0.335967i
$881$	−12.0874	+	12.0874i	−0.407233	+	0.407233i	−0.880773	−	0.473539i	$-0.842976\pi$
$881$	−12.0874	+	12.0874i	−0.407233	+	0.407233i	0.473539	+	0.880773i	$0.342976\pi$
$882$	15.0389	−	59.3035i	0.506385	−	1.99685i
$883$	−20.7084			−0.696893			−0.348446	−	0.937329i	$-0.613291\pi$
$883$	−20.7084			−0.696893			−0.348446	+	0.937329i	$0.613291\pi$
$884$	42.9761	+	3.12678i	1.44544	+	0.105165i
$885$	−6.07056	+	8.02239i	−0.204060	+	0.269670i
$886$	−4.16376	+	2.40395i	−0.139884	+	0.0807622i
$887$	−17.6885	−	4.73962i	−0.593922	−	0.159141i	−0.0506772	−	0.998715i	$-0.516138\pi$
$887$	−17.6885	−	4.73962i	−0.593922	−	0.159141i	−0.543245	+	0.839574i	$0.682805\pi$
$888$	61.3335	+	7.65566i	2.05822	+	0.256907i
$889$	−1.43180	−	5.34354i	−0.0480209	−	0.179216i
$890$	−90.3651	−	90.3651i	−3.02904	−	3.02904i
$891$	−3.28611	−	0.786468i	−0.110089	−	0.0263477i
$892$		−	27.3405i		−	0.915428i
$893$	−0.612999	−	0.353915i	−0.0205132	−	0.0118433i
$894$	15.1580	+	19.4818i	0.506960	+	0.651568i
$895$	14.9770	−	55.8951i	0.500628	−	1.86837i
$896$	5.88875	+	1.57789i	0.196729	+	0.0527135i
$897$	−8.43142	+	11.1423i	−0.281517	+	0.372031i
$898$	9.77527	+	36.4818i	0.326205	+	1.21741i
$899$			1.77961i			0.0593533i
$900$	79.6894	+	20.2085i	2.65631	+	0.673618i
$901$	10.9830	−	5.31854i	0.365897	−	0.177186i
$902$	−2.43185	+	4.21208i	−0.0809716	+	0.140247i
$903$	49.5708	−	20.9244i	1.64961	−	0.696320i
$904$	−111.672	−	29.9223i	−3.71414	−	0.995201i
$905$	31.0430	+	53.7681i	1.03191	+	1.78731i
$906$	6.30160	+	2.56072i	0.209357	+	0.0850742i
$907$	−3.88215	+	1.04022i	−0.128905	+	0.0345399i	−0.322695	−	0.946503i	$-0.604589\pi$
$907$	−3.88215	+	1.04022i	−0.128905	+	0.0345399i	0.193790	+	0.981043i	$0.437922\pi$
$908$	15.6922	+	15.6922i	0.520762	+	0.520762i
$909$	17.2905	+	16.8317i	0.573489	+	0.558273i
$910$		−	71.6829i		−	2.37627i
$911$	−2.00346	+	0.536824i	−0.0663774	+	0.0177858i	−0.291855	−	0.956463i	$-0.594272\pi$
$911$	−2.00346	+	0.536824i	−0.0663774	+	0.0177858i	0.225478	+	0.974248i	$0.427606\pi$
$912$	−6.83677	+	0.946871i	−0.226388	+	0.0313540i
$913$	−1.47272	−	0.394614i	−0.0487399	−	0.0130598i
$914$	25.0134	+	43.3245i	0.827369	+	1.43305i
$915$	26.0046	−	20.2332i	0.859687	−	0.668890i
$916$	−87.1475	−	50.3147i	−2.87944	−	1.66244i
$917$	75.8847			2.50593
$918$	52.6251	−	18.6294i	1.73689	−	0.614862i
$919$	−3.62133			−0.119457			−0.0597283	−	0.998215i	$-0.519023\pi$
$919$	−3.62133			−0.119457			−0.0597283	+	0.998215i	$0.519023\pi$
$920$	−76.2100	−	43.9999i	−2.51257	−	1.45063i
$921$	27.7140	−	21.5632i	0.913206	−	0.710531i
$922$	17.2938	+	29.9537i	0.569540	+	0.986472i
$923$	−26.0743	−	6.98658i	−0.858245	−	0.229966i
$924$	−11.8794	+	1.64526i	−0.390803	+	0.0541249i
$925$	−27.1314	+	7.26983i	−0.892074	+	0.239031i
$926$			10.4877i			0.344646i
$927$	−47.6608	+	13.4599i	−1.56538	+	0.442082i
$928$	1.74132	+	1.74132i	0.0571615	+	0.0571615i
$929$	5.81405	−	1.55787i	0.190753	−	0.0511120i	−0.162178	−	0.986762i	$-0.551852\pi$
$929$	5.81405	−	1.55787i	0.190753	−	0.0511120i	0.352931	+	0.935650i	$0.385185\pi$
$930$	−97.5043	−	39.6219i	−3.19729	−	1.29925i
$931$	−1.66575	−	2.88516i	−0.0545927	−	0.0945573i
$932$	−0.948089	−	0.254040i	−0.0310557	−	0.00832134i
$933$	−29.9058	+	12.6236i	−0.979073	+	0.413277i
$934$	36.5507	−	63.3077i	1.19598	−	2.07149i
$935$	2.20909	+	4.56185i	0.0722448	+	0.149188i
$936$	12.9318	+	45.7908i	0.422689	+	1.49672i
$937$		−	54.4438i		−	1.77860i	−0.457321	−	0.889301i	$-0.651191\pi$
$937$		−	54.4438i		−	1.77860i	0.457321	−	0.889301i	$-0.348809\pi$
$938$	−2.53051	−	9.44401i	−0.0826242	−	0.308358i
$939$	−1.93543	+	2.55772i	−0.0631604	+	0.0834680i
$940$	−25.1903	−	6.74973i	−0.821618	−	0.220152i
$941$	1.79293	−	6.69132i	0.0584480	−	0.218131i	−0.930525	−	0.366229i	$-0.880649\pi$
$941$	1.79293	−	6.69132i	0.0584480	−	0.218131i	0.988973	+	0.148098i	$0.0473153\pi$
$942$	−19.0904	−	24.5358i	−0.621999	−	0.799421i
$943$	15.9191	+	9.19088i	0.518397	+	0.299296i
$944$		−	16.6062i		−	0.540485i
$945$	−26.2862	−	60.0085i	−0.855089	−	1.95208i
$946$	−5.58078	−	5.58078i	−0.181447	−	0.181447i
$947$	−3.98843	−	14.8850i	−0.129606	−	0.483698i	0.870356	−	0.492424i	$-0.163889\pi$
$947$	−3.98843	−	14.8850i	−0.129606	−	0.483698i	−0.999962	+	0.00872616i	$0.997222\pi$
$948$	−83.1097	−	10.3738i	−2.69928	−	0.336924i
$949$	6.84451	+	1.83398i	0.222182	+	0.0595336i
$950$	5.49583	−	3.17302i	0.178308	−	0.102946i
$951$	−6.81652	+	9.00819i	−0.221041	+	0.292111i
$952$	87.3089	−	75.4660i	2.82970	−	2.44587i
$953$	−40.4381			−1.30992			−0.654959	−	0.755665i	$-0.727314\pi$
$953$	−40.4381			−1.30992			−0.654959	+	0.755665i	$0.727314\pi$
$954$	16.5780	+	16.1382i	0.536733	+	0.522493i
$955$	−7.21237	+	7.21237i	−0.233387	+	0.233387i
$956$	−39.8855	+	69.0838i	−1.28999	+	2.23433i
$957$	0.150534	+	0.0611709i	0.00486606	+	0.00197738i
$958$	−7.63791	+	28.5051i	−0.246770	+	0.920956i
$959$	16.4034	−	61.2182i	0.529693	−	1.97684i
$960$	−36.3487	+	15.3432i	−1.17315	+	0.495199i
$961$	17.0798	+	9.86105i	0.550963	+	0.318098i
$962$	−19.7366	−	19.7366i	−0.636334	−	0.636334i
$963$	−0.358061	−	0.601363i	−0.0115384	−	0.0193787i
$964$	−74.4258	+	74.4258i	−2.39709	+	2.39709i
$965$	28.3702	−	49.1386i	0.913269	−	1.58183i
$966$	8.81451	+	63.6441i	0.283602	+	2.04771i
$967$	33.7565	−	19.4893i	1.08554	−	0.626734i	0.153151	−	0.988203i	$-0.451058\pi$
$967$	33.7565	−	19.4893i	1.08554	−	0.626734i	0.932384	+	0.361469i	$0.117725\pi$
$968$	−39.4672	−	68.3592i	−1.26852	−	2.19715i
$969$	1.34575	−	2.72577i	0.0432316	−	0.0875642i
$970$	73.6173	−	127.509i	2.36371	−	4.09407i
$971$			7.44981i			0.239076i	0.992830	+	0.119538i	$0.0381413\pi$
$971$			7.44981i			0.239076i	−0.992830	+	0.119538i	$0.961859\pi$
$972$	47.4169	+	57.6737i	1.52090	+	1.84988i
$973$	22.4519			0.719776
$974$	−6.98437	−	26.0660i	−0.223794	−	0.835209i
$975$	−13.2782	−	17.0657i	−0.425243	−	0.546541i
$976$	−14.0765	+	52.5341i	−0.450576	+	1.68157i
$977$	6.63437	−	3.83036i	0.212252	−	0.122544i	−0.390105	−	0.920770i	$-0.627561\pi$
$977$	6.63437	−	3.83036i	0.212252	−	0.122544i	0.602358	+	0.798226i	$0.294228\pi$
$978$	51.5088	+	38.9768i	1.64707	+	1.24634i
$979$	5.43178	−	1.45544i	0.173600	−	0.0465161i
$980$	−86.7933	−	86.7933i	−2.77251	−	2.77251i
$981$	5.55710	−	3.30879i	0.177425	−	0.105642i
$982$	−74.4304			−2.37517
$983$	−5.51781	−	20.5928i	−0.175991	−	0.656807i	−0.996381	−	0.0850025i	$-0.972910\pi$
$983$	−5.51781	−	20.5928i	−0.175991	−	0.656807i	0.820390	−	0.571805i	$-0.193756\pi$
$984$	57.6684	−	24.3424i	1.83840	−	0.776009i
$985$	24.9471	+	43.2097i	0.794881	+	1.37677i
$986$	−2.63668	+	0.504819i	−0.0839688	+	0.0160767i
$987$	4.31280	+	10.2172i	0.137278	+	0.325218i
$988$	3.85257	+	2.22428i	0.122566	+	0.0707638i
$989$	−21.0919	+	21.0919i	−0.670684	+	0.670684i
$990$	−6.70308	+	6.88577i	−0.213038	+	0.218844i
$991$	−7.31959	+	7.31959i	−0.232515	+	0.232515i	−0.813741	−	0.581227i	$-0.802573\pi$
$991$	−7.31959	+	7.31959i	−0.232515	+	0.232515i	0.581227	+	0.813741i	$0.302573\pi$
$992$	67.7968	−	18.1661i	2.15255	−	0.576774i
$993$	32.0072	−	4.43289i	1.01572	−	0.140674i
$994$	−107.497	+	62.0636i	−3.40961	+	1.96854i
$995$	−69.4956	+	40.1233i	−2.20316	+	1.27199i
$996$	20.6887	+	26.5900i	0.655546	+	0.842536i
$997$	26.6394	−	7.13800i	0.843678	−	0.226063i	0.189006	−	0.981976i	$-0.439473\pi$
$997$	26.6394	−	7.13800i	0.843678	−	0.226063i	0.654672	+	0.755913i	$0.272807\pi$
$998$	58.0604	−	58.0604i	1.83787	−	1.83787i
$999$	−23.7597	−	9.28485i	−0.751724	−	0.293760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.n.a.106.16	yes	64
3.2	odd	2		459.2.o.a.208.1		64
9.4	even	3	inner	153.2.n.a.4.1	✓	64
9.5	odd	6		459.2.o.a.361.16		64
17.13	even	4	inner	153.2.n.a.115.1	yes	64
51.47	odd	4		459.2.o.a.370.16		64
153.13	even	12	inner	153.2.n.a.13.16	yes	64
153.149	odd	12		459.2.o.a.64.1		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.n.a.4.1	✓	64	9.4	even	3	inner
153.2.n.a.13.16	yes	64	153.13	even	12	inner
153.2.n.a.106.16	yes	64	1.1	even	1	trivial
153.2.n.a.115.1	yes	64	17.13	even	4	inner
459.2.o.a.64.1		64	153.149	odd	12
459.2.o.a.208.1		64	3.2	odd	2
459.2.o.a.361.16		64	9.5	odd	6
459.2.o.a.370.16		64	51.47	odd	4

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.25660 + 1.30285i) q^{2} +(-1.36701 + 1.06362i) q^{3} +(2.39483 + 4.14796i) q^{4} +(-3.16280 - 0.847469i) q^{5} +(-4.47053 + 0.619154i) q^{6} +(3.71932 - 0.996589i) q^{7} +7.26900i q^{8} +(0.737432 - 2.90795i) q^{9} +(-6.03304 - 6.03304i) q^{10} +(0.362642 - 0.0971696i) q^{11} +(-7.68561 - 3.12312i) q^{12} +(1.09097 + 1.88962i) q^{13} +(9.69142 + 2.59681i) q^{14} +(5.22496 - 2.20551i) q^{15} +(-4.68075 + 8.10730i) q^{16} +(-1.79701 - 3.71090i) q^{17} +(5.45271 - 5.60133i) q^{18} -0.425667i q^{19} +(-4.05908 - 15.1487i) q^{20} +(-4.02436 + 5.31828i) q^{21} +(0.944935 + 0.253195i) q^{22} +(0.956920 - 3.57127i) q^{23} +(-7.73144 - 9.93680i) q^{24} +(4.95495 + 2.86074i) q^{25} +5.68550i q^{26} +(2.08488 + 4.75955i) q^{27} +(13.0409 + 13.0409i) q^{28} +(-0.0646729 - 0.241362i) q^{29} +(14.6641 + 1.83037i) q^{30} +(-6.87927 - 1.84329i) q^{31} +(-8.53488 + 4.92762i) q^{32} +(-0.392384 + 0.518545i) q^{33} +(0.779601 - 10.7152i) q^{34} -12.6080 q^{35} +(13.8281 - 3.90521i) q^{36} +(-3.47140 + 3.47140i) q^{37} +(0.554580 - 0.960561i) q^{38} +(-3.50121 - 1.42275i) q^{39} +(6.16025 - 22.9904i) q^{40} +(-1.28678 + 4.80233i) q^{41} +(-16.0103 + 6.75811i) q^{42} +(-6.98686 - 4.03387i) q^{43} +(1.27152 + 1.27152i) q^{44} +(-4.79675 + 8.57231i) q^{45} +(6.81221 - 6.81221i) q^{46} +(0.831435 - 1.44009i) q^{47} +(-2.22444 - 16.0613i) q^{48} +(6.77797 - 3.91326i) q^{49} +(7.45423 + 12.9111i) q^{50} +(6.40351 + 3.16150i) q^{51} +(-5.22539 + 9.05065i) q^{52} +2.95966i q^{53} +(-1.49624 + 13.4567i) q^{54} -1.22931 q^{55} +(7.24420 + 27.0357i) q^{56} +(0.452748 + 0.581892i) q^{57} +(0.168518 - 0.628917i) q^{58} +(-1.53623 + 0.886940i) q^{59} +(21.6613 + 16.3911i) q^{60} +(5.61171 - 1.50365i) q^{61} +(-13.1222 - 13.1222i) q^{62} +(-0.155289 - 11.5505i) q^{63} -6.95675 q^{64} +(-1.84913 - 6.90106i) q^{65} +(-1.56104 + 0.658931i) q^{66} +(-0.487236 - 0.843917i) q^{67} +(11.0891 - 16.3409i) q^{68} +(2.49035 + 5.89976i) q^{69} +(-28.4513 - 16.4264i) q^{70} +(-8.74800 + 8.74800i) q^{71} +(21.1379 + 5.36039i) q^{72} +(2.29636 - 2.29636i) q^{73} +(-12.3563 + 3.31085i) q^{74} +(-9.81620 + 1.35951i) q^{75} +(1.76565 - 1.01940i) q^{76} +(1.25194 - 0.722810i) q^{77} +(-6.04720 - 7.77213i) q^{78} +(9.75186 - 2.61300i) q^{79} +(21.6749 - 21.6749i) q^{80} +(-7.91239 - 4.28884i) q^{81} +(-9.16045 + 9.16045i) q^{82} +(-3.51700 - 2.03054i) q^{83} +(-31.6977 - 3.95651i) q^{84} +(2.53871 + 13.2597i) q^{85} +(-10.5110 - 18.2056i) q^{86} +(0.345126 + 0.261158i) q^{87} +(0.706326 + 2.63605i) q^{88} +14.9784 q^{89} +(-21.9928 + 13.0948i) q^{90} +(5.94086 + 5.94086i) q^{91} +(17.1052 - 4.58332i) q^{92} +(11.3646 - 4.79712i) q^{93} +(3.75243 - 2.16647i) q^{94} +(-0.360740 + 1.34630i) q^{95} +(6.42616 - 15.8140i) q^{96} +(4.46637 + 16.6687i) q^{97} +20.3936 q^{98} +(-0.0151410 - 1.12620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7} - 16 q^{10} - 24 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{17} - 8 q^{18} + 18 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{23} - 2 q^{24} - 10 q^{29} - 36 q^{30}+ \cdots + 6 q^{99}+O(q^{100}) \) 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7 - 16 * q^10 - 24 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^17 - 8 * q^18 + 18 * q^20 - 16 * q^21 - 4 * q^22 - 8 * q^23 - 2 * q^24 - 10 * q^29 - 36 * q^30 - 2 * q^31 + 12 * q^33 + 20 * q^34 - 128 * q^35 - 8 * q^37 - 24 * q^38 + 34 * q^39 - 20 * q^40 + 32 * q^41 + 20 * q^44 + 20 * q^45 - 40 * q^46 - 64 * q^47 + 62 * q^48 + 48 * q^50 + 40 * q^51 + 36 * q^52 - 46 * q^54 - 16 * q^55 + 12 * q^56 + 72 * q^57 - 10 * q^58 - 2 * q^61 - 28 * q^62 + 64 * q^63 - 8 * q^64 + 8 * q^65 - 4 * q^67 - 60 * q^68 - 24 * q^69 - 84 * q^71 + 72 * q^72 - 44 * q^73 - 14 * q^74 + 46 * q^75 - 56 * q^78 + 10 * q^79 + 204 * q^80 + 44 * q^81 - 52 * q^82 - 60 * q^84 + 22 * q^85 + 32 * q^86 + 16 * q^88 + 128 * q^89 - 66 * q^90 + 44 * q^91 + 136 * q^92 + 4 * q^95 - 2 * q^96 - 44 * q^97 + 208 * q^98 + 6 * q^99

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