LMFDB - Embedded newform 483.2.n.a.47.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(47,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("483.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.n (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.18
Character	$\chi$	$=$	483.47
Dual form			483.2.n.a.185.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07338 - 0.619715i) q^{2} +(-0.722709 - 1.57407i) q^{3} +(-0.231907 - 0.401675i) q^{4} +(-0.273772 + 0.474187i) q^{5} +(-0.199734 + 2.13744i) q^{6} +(2.55123 - 0.700882i) q^{7} +3.05372i q^{8} +(-1.95538 + 2.27519i) q^{9} +(0.587721 - 0.339321i) q^{10} +(-3.30069 + 1.90565i) q^{11} +(-0.464662 + 0.655331i) q^{12} +6.33716i q^{13} +(-3.17278 - 0.828723i) q^{14} +(0.944259 + 0.0882365i) q^{15} +(1.42862 - 2.47445i) q^{16} +(0.532689 + 0.922645i) q^{17} +(3.50883 - 1.23036i) q^{18} +(-3.98747 - 2.30217i) q^{19} +0.253958 q^{20} +(-2.94703 - 3.50927i) q^{21} +4.72385 q^{22} +(-0.866025 - 0.500000i) q^{23} +(4.80677 - 2.20695i) q^{24} +(2.35010 + 4.07049i) q^{25} +(3.92724 - 6.80217i) q^{26} +(4.99447 + 1.43361i) q^{27} +(-0.873174 - 0.862224i) q^{28} +4.33342i q^{29} +(-0.958865 - 0.679883i) q^{30} +(-2.78836 + 1.60986i) q^{31} +(2.22230 - 1.28304i) q^{32} +(5.38507 + 3.81828i) q^{33} -1.32046i q^{34} +(-0.366105 + 1.40164i) q^{35} +(1.36735 + 0.257796i) q^{36} +(1.00493 - 1.74058i) q^{37} +(2.85338 + 4.94219i) q^{38} +(9.97513 - 4.57993i) q^{39} +(-1.44803 - 0.836023i) q^{40} +7.04500 q^{41} +(0.988529 + 5.59310i) q^{42} -7.94253 q^{43} +(1.53091 + 0.883869i) q^{44} +(-0.543535 - 1.55010i) q^{45} +(0.619715 + 1.07338i) q^{46} +(-1.88739 + 3.26905i) q^{47} +(-4.92743 - 0.460445i) q^{48} +(6.01753 - 3.57622i) q^{49} -5.82556i q^{50} +(1.06733 - 1.50529i) q^{51} +(2.54548 - 1.46963i) q^{52} +(1.11654 - 0.644636i) q^{53} +(-4.47253 - 4.63395i) q^{54} -2.08686i q^{55} +(2.14030 + 7.79075i) q^{56} +(-0.741988 + 7.94035i) q^{57} +(2.68549 - 4.65140i) q^{58} +(-2.05599 - 3.56109i) q^{59} +(-0.183538 - 0.399748i) q^{60} +(4.33542 + 2.50306i) q^{61} +3.99062 q^{62} +(-3.39399 + 7.17501i) q^{63} -8.89499 q^{64} +(-3.00500 - 1.73494i) q^{65} +(-3.41397 - 7.43566i) q^{66} +(-4.39855 - 7.61852i) q^{67} +(0.247069 - 0.427935i) q^{68} +(-0.161150 + 1.72454i) q^{69} +(1.26159 - 1.27761i) q^{70} +10.0978i q^{71} +(-6.94779 - 5.97120i) q^{72} +(-9.71333 + 5.60799i) q^{73} +(-2.15733 + 1.24553i) q^{74} +(4.70879 - 6.64100i) q^{75} +2.13555i q^{76} +(-7.08517 + 7.17515i) q^{77} +(-13.5453 - 1.26575i) q^{78} +(0.987846 - 1.71100i) q^{79} +(0.782234 + 1.35487i) q^{80} +(-1.35295 - 8.89773i) q^{81} +(-7.56194 - 4.36589i) q^{82} +5.31573 q^{83} +(-0.726149 + 1.99757i) q^{84} -0.583341 q^{85} +(8.52534 + 4.92211i) q^{86} +(6.82110 - 3.13180i) q^{87} +(-5.81934 - 10.0794i) q^{88} +(-6.24674 + 10.8197i) q^{89} +(-0.377201 + 2.00068i) q^{90} +(4.44161 + 16.1676i) q^{91} +0.463814i q^{92} +(4.54921 + 3.22561i) q^{93} +(4.05176 - 2.33928i) q^{94} +(2.18331 - 1.26054i) q^{95} +(-3.62567 - 2.57078i) q^{96} +6.90019i q^{97} +(-8.67532 + 0.109483i) q^{98} +(2.11839 - 11.2360i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q + 56 q^{4} - 10 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 20 q^{15} - 52 q^{16} - 10 q^{18} + 6 q^{19} - 6 q^{21} - 16 q^{22} - 66 q^{25} + 16 q^{28} - 32 q^{30} - 42 q^{31} - 30 q^{33} + 8 q^{36}+ \cdots + 24 q^{99}+O(q^{100}) $ 116 * q + 56 * q^4 - 10 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 20 * q^15 - 52 * q^16 - 10 * q^18 + 6 * q^19 - 6 * q^21 - 16 * q^22 - 66 * q^25 + 16 * q^28 - 32 * q^30 - 42 * q^31 - 30 * q^33 + 8 * q^36 - 2 * q^37 - 22 * q^39 - 36 * q^40 + 46 * q^42 + 20 * q^43 + 30 * q^45 - 22 * q^49 + 12 * q^51 + 48 * q^52 - 54 * q^54 - 44 * q^57 + 52 * q^58 + 32 * q^60 + 36 * q^61 - 38 * q^63 - 160 * q^64 + 10 * q^67 - 20 * q^70 + 62 * q^72 + 18 * q^73 + 78 * q^75 + 12 * q^78 + 10 * q^79 - 28 * q^81 + 32 * q^84 - 32 * q^85 - 30 * q^87 - 36 * q^88 + 50 * q^91 + 60 * q^94 + 84 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.07338	−	0.619715i	−0.758993	−	0.438205i	0.0699413	−	0.997551i	$-0.477719\pi$
$2$	−1.07338	−	0.619715i	−0.758993	−	0.438205i	−0.828934	+	0.559347i	$0.811052\pi$
$3$	−0.722709	−	1.57407i	−0.417256	−	0.908789i
$3$	−0.722709	−	1.57407i	−0.417256	−	0.908789i
$4$	−0.231907	−	0.401675i	−0.115953	−	0.200837i
$5$	−0.273772	+	0.474187i	−0.122434	+	0.212063i	−0.920727	−	0.390207i	$-0.872403\pi$
$5$	−0.273772	+	0.474187i	−0.122434	+	0.212063i	0.798293	+	0.602270i	$0.205737\pi$
$6$	−0.199734	+	2.13744i	−0.0815410	+	0.872608i
$7$	2.55123	−	0.700882i	0.964274	−	0.264909i
$7$	2.55123	−	0.700882i	0.964274	−	0.264909i
$8$			3.05372i			1.07965i
$9$	−1.95538	+	2.27519i	−0.651794	+	0.758396i
$10$	0.587721	−	0.339321i	0.185854	−	0.107303i
$11$	−3.30069	+	1.90565i	−0.995196	+	0.574576i	−0.906823	−	0.421511i	$-0.861500\pi$
$11$	−3.30069	+	1.90565i	−0.995196	+	0.574576i	−0.0883723	+	0.996088i	$0.528167\pi$
$12$	−0.464662	+	0.655331i	−0.134136	+	0.189178i
$13$			6.33716i			1.75761i	0.477178	+	0.878807i	$0.341660\pi$
$13$			6.33716i			1.75761i	−0.477178	+	0.878807i	$0.658340\pi$
$14$	−3.17278	−	0.828723i	−0.847961	−	0.221485i
$15$	0.944259	+	0.0882365i	0.243807	+	0.0227826i
$16$	1.42862	−	2.47445i	0.357156	−	0.618613i
$17$	0.532689	+	0.922645i	0.129196	+	0.223774i	0.923365	−	0.383922i	$-0.125427\pi$
$17$	0.532689	+	0.922645i	0.129196	+	0.223774i	−0.794169	+	0.607697i	$0.792094\pi$
$18$	3.50883	−	1.23036i	0.827040	−	0.289998i
$19$	−3.98747	−	2.30217i	−0.914789	−	0.528154i	−0.0328199	−	0.999461i	$-0.510449\pi$
$19$	−3.98747	−	2.30217i	−0.914789	−	0.528154i	−0.881969	+	0.471308i	$0.843782\pi$
$20$	0.253958			0.0567868
$21$	−2.94703	−	3.50927i	−0.643095	−	0.765786i
$22$	4.72385			1.00713
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	4.80677	−	2.20695i	0.981178	−	0.450493i
$25$	2.35010	+	4.07049i	0.470020	+	0.814098i
$26$	3.92724	−	6.80217i	0.770194	−	1.33402i
$27$	4.99447	+	1.43361i	0.961187	+	0.275898i
$28$	−0.873174	−	0.862224i	−0.165014	−	0.162945i
$29$			4.33342i			0.804696i	0.915487	+	0.402348i	$0.131806\pi$
$29$			4.33342i			0.804696i	−0.915487	+	0.402348i	$0.868194\pi$
$30$	−0.958865	−	0.679883i	−0.175064	−	0.124129i
$31$	−2.78836	+	1.60986i	−0.500804	+	0.289140i	−0.729046	−	0.684465i	$-0.760036\pi$
$31$	−2.78836	+	1.60986i	−0.500804	+	0.289140i	0.228241	+	0.973605i	$0.426703\pi$
$32$	2.22230	−	1.28304i	0.392850	−	0.226812i
$33$	5.38507	+	3.81828i	0.937420	+	0.664677i
$34$		−	1.32046i		−	0.226457i
$35$	−0.366105	+	1.40164i	−0.0618831	+	0.236920i
$36$	1.36735	+	0.257796i	0.227892	+	0.0429660i
$37$	1.00493	−	1.74058i	0.165209	−	0.286150i	−0.771521	−	0.636204i	$-0.780504\pi$
$37$	1.00493	−	1.74058i	0.165209	−	0.286150i	0.936729	+	0.350054i	$0.113837\pi$
$38$	2.85338	+	4.94219i	0.462879	+	0.801729i
$39$	9.97513	−	4.57993i	1.59730	−	0.733375i
$40$	−1.44803	−	0.836023i	−0.228954	−	0.132187i
$41$	7.04500			1.10024			0.550122	−	0.835084i	$-0.314581\pi$
$41$	7.04500			1.10024			0.550122	+	0.835084i	$0.314581\pi$
$42$	0.988529	+	5.59310i	0.152533	+	0.863033i
$43$	−7.94253			−1.21122			−0.605612	−	0.795760i	$-0.707072\pi$
$43$	−7.94253			−1.21122			−0.605612	+	0.795760i	$0.707072\pi$
$44$	1.53091	+	0.883869i	0.230793	+	0.133248i
$45$	−0.543535	−	1.55010i	−0.0810253	−	0.231075i
$46$	0.619715	+	1.07338i	0.0913720	+	0.158261i
$47$	−1.88739	+	3.26905i	−0.275304	+	0.476840i	−0.970212	−	0.242259i	$-0.922112\pi$
$47$	−1.88739	+	3.26905i	−0.275304	+	0.476840i	0.694908	+	0.719099i	$0.255445\pi$
$48$	−4.92743	−	0.460445i	−0.711214	−	0.0664595i
$49$	6.01753	−	3.57622i	0.859647	−	0.510889i
$50$		−	5.82556i		−	0.823859i
$51$	1.06733	−	1.50529i	0.149456	−	0.210783i
$52$	2.54548	−	1.46963i	0.352994	−	0.203801i
$53$	1.11654	−	0.644636i	0.153369	−	0.0885476i	−0.421352	−	0.906897i	$-0.638444\pi$
$53$	1.11654	−	0.644636i	0.153369	−	0.0885476i	0.574720	+	0.818350i	$0.305111\pi$
$54$	−4.47253	−	4.63395i	−0.608634	−	0.630601i
$55$		−	2.08686i		−	0.281392i
$56$	2.14030	+	7.79075i	0.286010	+	1.04108i
$57$	−0.741988	+	7.94035i	−0.0982787	+	1.05173i
$58$	2.68549	−	4.65140i	0.352622	−	0.610759i
$59$	−2.05599	−	3.56109i	−0.267668	−	0.463614i	0.700591	−	0.713563i	$-0.252920\pi$
$59$	−2.05599	−	3.56109i	−0.267668	−	0.463614i	−0.968259	+	0.249949i	$0.919586\pi$
$60$	−0.183538	−	0.399748i	−0.0236946	−	0.0516072i
$61$	4.33542	+	2.50306i	0.555094	+	0.320484i	0.751174	−	0.660104i	$-0.229488\pi$
$61$	4.33542	+	2.50306i	0.555094	+	0.320484i	−0.196080	+	0.980588i	$0.562821\pi$
$62$	3.99062			0.506809
$63$	−3.39399	+	7.17501i	−0.427603	+	0.903967i
$64$	−8.89499			−1.11187
$65$	−3.00500	−	1.73494i	−0.372724	−	0.215192i
$66$	−3.41397	−	7.43566i	−0.420231	−	0.915267i
$67$	−4.39855	−	7.61852i	−0.537369	−	0.930750i	−0.999045	−	0.0437015i	$-0.986085\pi$
$67$	−4.39855	−	7.61852i	−0.537369	−	0.930750i	0.461676	−	0.887049i	$-0.347248\pi$
$68$	0.247069	−	0.427935i	0.0299615	−	0.0518948i
$69$	−0.161150	+	1.72454i	−0.0194002	+	0.207610i
$70$	1.26159	−	1.27761i	0.150788	−	0.152703i
$71$			10.0978i			1.19838i	0.800606	+	0.599192i	$0.204511\pi$
$71$			10.0978i			1.19838i	−0.800606	+	0.599192i	$0.795489\pi$
$72$	−6.94779	−	5.97120i	−0.818805	−	0.703713i
$73$	−9.71333	+	5.60799i	−1.13686	+	0.656366i	−0.945651	−	0.325183i	$-0.894574\pi$
$73$	−9.71333	+	5.60799i	−1.13686	+	0.656366i	−0.191208	+	0.981549i	$0.561241\pi$
$74$	−2.15733	+	1.24553i	−0.250785	+	0.144791i
$75$	4.70879	−	6.64100i	0.543724	−	0.766836i
$76$			2.13555i			0.244965i
$77$	−7.08517	+	7.17515i	−0.807431	+	0.817685i
$78$	−13.5453	−	1.26575i	−1.53371	−	0.143318i
$79$	0.987846	−	1.71100i	0.111141	−	0.192502i	−0.805089	−	0.593154i	$-0.797883\pi$
$79$	0.987846	−	1.71100i	0.111141	−	0.192502i	0.916231	+	0.400651i	$0.131216\pi$
$80$	0.782234	+	1.35487i	0.0874564	+	0.151479i
$81$	−1.35295	−	8.89773i	−0.150328	−	0.988636i
$82$	−7.56194	−	4.36589i	−0.835077	−	0.482132i
$83$	5.31573			0.583477			0.291738	−	0.956498i	$-0.405766\pi$
$83$	5.31573			0.583477			0.291738	+	0.956498i	$0.405766\pi$
$84$	−0.726149	+	1.99757i	−0.0792293	+	0.217953i
$85$	−0.583341			−0.0632722
$86$	8.52534	+	4.92211i	0.919311	+	0.530764i
$87$	6.82110	−	3.13180i	0.731299	−	0.335765i
$88$	−5.81934	−	10.0794i	−0.620344	−	1.07447i
$89$	−6.24674	+	10.8197i	−0.662153	+	1.14688i	0.317896	+	0.948126i	$0.397024\pi$
$89$	−6.24674	+	10.8197i	−0.662153	+	1.14688i	−0.980049	+	0.198757i	$0.936310\pi$
$90$	−0.377201	+	2.00068i	−0.0397605	+	0.210890i
$91$	4.44161	+	16.1676i	0.465607	+	1.69482i
$92$			0.463814i			0.0483559i
$93$	4.54921	+	3.22561i	0.471731	+	0.334480i
$94$	4.05176	−	2.33928i	0.417907	−	0.241279i
$95$	2.18331	−	1.26054i	0.224003	−	0.129328i
$96$	−3.62567	−	2.57078i	−0.370044	−	0.262379i
$97$			6.90019i			0.700608i	0.936636	+	0.350304i	$0.113922\pi$
$97$			6.90019i			0.700608i	−0.936636	+	0.350304i	$0.886078\pi$
$98$	−8.67532	+	0.109483i	−0.876339	+	0.0110594i
$99$	2.11839	−	11.2360i	0.212907	−	1.12926i
$100$	1.09001	−	1.88795i	0.109001	−	0.188795i
$101$	1.87785	+	3.25253i	0.186853	+	0.323639i	0.944199	−	0.329375i	$-0.106838\pi$
$101$	1.87785	+	3.25253i	0.186853	+	0.323639i	−0.757346	+	0.653013i	$0.773505\pi$
$102$	−2.07850	+	0.954310i	−0.205802	+	0.0944908i
$103$	15.7418	+	9.08853i	1.55109	+	0.895520i	0.998054	+	0.0623598i	$0.0198626\pi$
$103$	15.7418	+	9.08853i	1.55109	+	0.895520i	0.553032	+	0.833160i	$0.313471\pi$
$104$	−19.3520			−1.89762
$105$	2.47086	−	0.436703i	0.241132	−	0.0426179i
$106$	−1.59796			−0.155208
$107$	−12.6008	−	7.27509i	−1.21817	−	0.703309i	−0.253641	−	0.967298i	$-0.581628\pi$
$107$	−12.6008	−	7.27509i	−1.21817	−	0.703309i	−0.964526	+	0.263989i	$0.914962\pi$
$108$	−0.582409	−	2.33862i	−0.0560423	−	0.225033i
$109$	−4.10001	−	7.10143i	−0.392710	−	0.680194i	0.600096	−	0.799928i	$-0.295129\pi$
$109$	−4.10001	−	7.10143i	−0.392710	−	0.680194i	−0.992806	+	0.119734i	$0.961796\pi$
$110$	−1.29326	+	2.23999i	−0.123307	+	0.213574i
$111$	−3.46607	−	0.323887i	−0.328984	−	0.0307420i
$112$	1.91045	−	7.31418i	0.180520	−	0.691125i
$113$		−	9.47546i		−	0.891377i	−0.895188	−	0.445688i	$-0.852959\pi$
$113$		−	9.47546i		−	0.891377i	0.895188	−	0.445688i	$-0.147041\pi$
$114$	5.71719	−	8.06317i	0.535464	−	0.755186i
$115$	0.474187	−	0.273772i	0.0442181	−	0.0255293i
$116$	1.74063	−	1.00495i	0.161613	−	0.0933073i
$117$	−14.4182	−	12.3916i	−1.33297	−	1.14560i
$118$			5.09652i			0.469173i
$119$	2.00568	+	1.98053i	0.183860	+	0.181554i
$120$	−0.269450	+	2.88351i	−0.0245973	+	0.263227i
$121$	1.76304	−	3.05367i	0.160276	−	0.277606i
$122$	−3.10236	−	5.37345i	−0.280875	−	0.486490i
$123$	−5.09149	−	11.0893i	−0.459084	−	0.999889i
$124$	1.29328	+	0.746676i	0.116140	+	0.0670535i
$125$	−5.31128			−0.475055
$126$	8.08950	−	5.59819i	0.720670	−	0.498727i
$127$	−12.8702			−1.14204			−0.571022	−	0.820935i	$-0.693453\pi$
$127$	−12.8702			−1.14204			−0.571022	+	0.820935i	$0.693453\pi$
$128$	5.10308	+	2.94627i	0.451053	+	0.260416i
$129$	5.74014	+	12.5021i	0.505391	+	1.10075i
$130$	2.15033	+	3.72448i	0.188597	+	0.326659i
$131$	−7.77280	+	13.4629i	−0.679112	+	1.17626i	0.296136	+	0.955146i	$0.404302\pi$
$131$	−7.77280	+	13.4629i	−0.679112	+	1.17626i	−0.975249	+	0.221111i	$0.929032\pi$
$132$	0.284870	−	3.04853i	0.0247948	−	0.265340i
$133$	−11.7865	−	3.07861i	−1.02202	−	0.266949i
$134$			10.9034i			0.941910i
$135$	−2.04714	+	1.97583i	−0.176190	+	0.170052i
$136$	−2.81750	+	1.62669i	−0.241599	+	0.139487i
$137$	4.10733	−	2.37137i	0.350913	−	0.202600i	−0.314174	−	0.949365i	$-0.601728\pi$
$137$	4.10733	−	2.37137i	0.350913	−	0.202600i	0.665087	+	0.746766i	$0.268394\pi$
$138$	1.24170	−	1.75121i	0.105700	−	0.149073i
$139$			3.82666i			0.324573i	0.986744	+	0.162287i	$0.0518869\pi$
$139$			3.82666i			0.324573i	−0.986744	+	0.162287i	$0.948113\pi$
$140$	0.647905	−	0.177995i	0.0547580	−	0.0150433i
$141$	6.50974	+	0.608304i	0.548219	+	0.0512284i
$142$	6.25773	−	10.8387i	0.525137	−	0.909564i
$143$	−12.0764	−	20.9170i	−1.00988	−	1.74917i
$144$	2.83633	+	8.08889i	0.236361	+	0.674074i
$145$	−2.05485	−	1.18637i	−0.170646	−	0.0985225i
$146$	13.9014			1.15049
$147$	−9.97814	−	6.88744i	−0.822983	−	0.568066i
$148$	−0.932197			−0.0766261
$149$	12.5343	+	7.23670i	1.02685	+	0.592853i	0.916081	−	0.400993i	$-0.131335\pi$
$149$	12.5343	+	7.23670i	1.02685	+	0.592853i	0.110771	+	0.993846i	$0.464668\pi$
$150$	−9.16984	+	4.21019i	−0.748714	+	0.343760i
$151$	3.37078	+	5.83836i	0.274310	+	0.475119i	0.969961	−	0.243261i	$-0.0782173\pi$
$151$	3.37078	+	5.83836i	0.274310	+	0.475119i	−0.695651	+	0.718380i	$0.744884\pi$
$152$	7.03019	−	12.1766i	0.570223	−	0.987656i
$153$	−3.14080	−	0.592156i	−0.253919	−	0.0478730i
$154$	12.0516	−	3.31086i	0.971147	−	0.266797i
$155$		−	1.76294i		−	0.141603i
$156$	−4.15294	−	2.94464i	−0.332501	−	0.235760i
$157$	−14.4516	+	8.34364i	−1.15336	+	0.665895i	−0.949705	−	0.313147i	$-0.898617\pi$
$157$	−14.4516	+	8.34364i	−1.15336	+	0.665895i	−0.203659	+	0.979042i	$0.565283\pi$
$158$	−2.12066	+	1.22437i	−0.168711	+	0.0974053i
$159$	−1.82164	−	1.29163i	−0.144465	−	0.102433i
$160$			1.40504i			0.111079i
$161$	−2.55987	−	0.668632i	−0.201746	−	0.0526956i
$162$	−4.06182	+	10.3891i	−0.319127	+	0.816242i
$163$	3.54867	−	6.14648i	0.277954	−	0.481430i	−0.692922	−	0.721012i	$-0.743677\pi$
$163$	3.54867	−	6.14648i	0.277954	−	0.481430i	0.970876	+	0.239582i	$0.0770105\pi$
$164$	−1.63378	−	2.82980i	−0.127577	−	0.220970i
$165$	−3.28486	+	1.50819i	−0.255726	+	0.117412i
$166$	−5.70578	−	3.29423i	−0.442854	−	0.255682i
$167$	16.7797			1.29845			0.649227	−	0.760594i	$-0.275092\pi$
$167$	16.7797			1.29845			0.649227	+	0.760594i	$0.275092\pi$
$168$	10.7164	−	8.99942i	0.826785	−	0.694321i
$169$	−27.1597			−2.08920
$170$	0.626145	+	0.361505i	0.0480232	+	0.0277262i
$171$	13.0349	−	4.57062i	0.996803	−	0.349524i
$172$	1.84193	+	3.19031i	0.140446	+	0.243259i
$173$	5.79102	−	10.0303i	0.440283	−	0.762593i	−0.557427	−	0.830226i	$-0.688211\pi$
$173$	5.79102	−	10.0303i	0.440283	−	0.762593i	0.997710	+	0.0676328i	$0.0215446\pi$
$174$	−9.26245	−	0.865531i	−0.702184	−	0.0656157i
$175$	8.84857	+	8.73760i	0.668889	+	0.660501i
$176$			10.8899i			0.820854i
$177$	−4.11951	+	5.80991i	−0.309641	+	0.436699i
$178$	13.4102	−	7.74239i	1.00514	−	0.580317i
$179$	−7.52422	+	4.34411i	−0.562387	+	0.324694i	−0.754103	−	0.656756i	$-0.771928\pi$
$179$	−7.52422	+	4.34411i	−0.562387	+	0.324694i	0.191716	+	0.981450i	$0.438595\pi$
$180$	−0.496586	+	0.577802i	−0.0370133	+	0.0430668i
$181$			9.53741i			0.708910i	0.935073	+	0.354455i	$0.115334\pi$
$181$			9.53741i			0.708910i	−0.935073	+	0.354455i	$0.884666\pi$
$182$	5.25175	−	20.1064i	0.389286	−	1.49039i
$183$	0.806734	−	8.63324i	0.0596355	−	0.638187i
$184$	1.52686	−	2.64460i	0.112562	−	0.194963i
$185$	0.550241	+	0.953045i	0.0404545	+	0.0700692i
$186$	−2.88406	−	6.28151i	−0.211469	−	0.460583i
$187$	−3.51648	−	2.03024i	−0.257151	−	0.148466i
$188$	1.75079			0.127690
$189$	13.7468	+	0.156924i	0.999935	+	0.0114145i
$190$	−3.12469			−0.226689
$191$	21.0141	+	12.1325i	1.52053	+	0.877876i	0.999707	+	0.0242079i	$0.00770638\pi$
$191$	21.0141	+	12.1325i	1.52053	+	0.877876i	0.520818	+	0.853668i	$0.325627\pi$
$192$	6.42849	+	14.0013i	0.463936	+	1.01046i
$193$	3.06634	+	5.31106i	0.220720	+	0.382299i	0.955027	−	0.296519i	$-0.0958259\pi$
$193$	3.06634	+	5.31106i	0.220720	+	0.382299i	−0.734307	+	0.678818i	$0.762493\pi$
$194$	4.27615	−	7.40651i	0.307010	−	0.531757i
$195$	−0.559169	+	5.98393i	−0.0400429	+	0.428518i
$196$	−2.83198	−	1.58774i	−0.202284	−	0.113410i
$197$			1.59205i			0.113429i	0.998390	+	0.0567144i	$0.0180624\pi$
$197$			1.59205i			0.113429i	−0.998390	+	0.0567144i	$0.981938\pi$
$198$	−9.23694	+	10.7476i	−0.656440	+	0.763802i
$199$	14.2021	−	8.19959i	1.00676	−	0.581253i	0.0965188	−	0.995331i	$-0.469229\pi$
$199$	14.2021	−	8.19959i	1.00676	−	0.581253i	0.910241	+	0.414078i	$0.135896\pi$
$200$	−12.4302	+	7.17655i	−0.878944	+	0.507459i
$201$	−8.81320	+	12.4296i	−0.621635	+	0.876716i
$202$		−	4.65492i		−	0.327519i
$203$	3.03722	+	11.0556i	0.213171	+	0.775947i
$204$	−0.852158	−	0.0796301i	−0.0596630	−	0.00557522i
$205$	−1.92872	+	3.34064i	−0.134708	+	0.233321i
$206$	−11.2646	−	19.5109i	−0.784842	−	1.35939i
$207$	2.83101	−	0.992678i	0.196768	−	0.0689959i
$208$	15.6810	+	9.05343i	1.08728	+	0.627742i
$209$	17.5485			1.21386
$210$	−2.92280	−	1.06248i	−0.201692	−	0.0733184i
$211$	19.1386			1.31756			0.658778	−	0.752338i	$-0.271074\pi$
$211$	19.1386			1.31756			0.658778	+	0.752338i	$0.271074\pi$
$212$	−0.517868	−	0.298991i	−0.0355673	−	0.0205348i
$213$	15.8946	−	7.29774i	1.08908	−	0.500033i
$214$	9.01696	+	15.6178i	0.616387	+	1.06761i
$215$	2.17444	−	3.76624i	0.148296	−	0.256856i
$216$	−4.37784	+	15.2517i	−0.297875	+	1.03775i
$217$	−5.98542	+	6.06143i	−0.406317	+	0.411477i
$218$			10.1634i			0.688349i
$219$	15.8473	+	11.2365i	1.07086	+	0.759292i
$220$	−0.838237	+	0.483957i	−0.0565139	+	0.0326283i
$221$	−5.84695	+	3.37574i	−0.393309	+	0.227077i
$222$	3.51968	+	2.49563i	0.236225	+	0.167495i
$223$			18.5980i			1.24541i	0.782455	+	0.622707i	$0.213967\pi$
$223$			18.5980i			1.24541i	−0.782455	+	0.622707i	$0.786033\pi$
$224$	4.77033	−	4.83091i	0.318731	−	0.322779i
$225$	−13.8565	−	2.61245i	−0.923765	−	0.174163i
$226$	−5.87209	+	10.1708i	−0.390605	+	0.676548i
$227$	−12.3781	−	21.4395i	−0.821565	−	1.42299i	−0.904516	−	0.426439i	$-0.859768\pi$
$227$	−12.3781	−	21.4395i	−0.821565	−	1.42299i	0.0829509	−	0.996554i	$-0.473566\pi$
$228$	3.36151	−	1.54338i	0.222621	−	0.102213i
$229$	20.0583	+	11.5807i	1.32549	+	0.765273i	0.984599	−	0.174829i	$-0.0559373\pi$
$229$	20.0583	+	11.5807i	1.32549	+	0.765273i	0.340893	+	0.940102i	$0.389271\pi$
$230$	−0.678642			−0.0447483
$231$	16.4147	+	5.96700i	1.08001	+	0.392600i
$232$	−13.2331			−0.868794
$233$	−23.8163	−	13.7503i	−1.56026	−	0.900814i	−0.997230	−	0.0743752i	$-0.976304\pi$
$233$	−23.8163	−	13.7503i	−1.56026	−	0.900814i	−0.563026	−	0.826439i	$-0.690363\pi$
$234$	7.79696	+	22.2360i	0.509704	+	1.45362i
$235$	−1.03343	−	1.78995i	−0.0674133	−	0.116763i
$236$	−0.953599	+	1.65168i	−0.0620740	+	0.107515i
$237$	−3.40715	−	0.318382i	−0.221318	−	0.0206811i
$238$	−0.925488	−	3.36880i	−0.0599905	−	0.218367i
$239$		−	22.9298i		−	1.48320i	−0.670841	−	0.741602i	$-0.734067\pi$
$239$		−	22.9298i		−	1.48320i	0.670841	−	0.741602i	$-0.265933\pi$
$240$	1.56733	−	2.21047i	0.101171	−	0.142685i
$241$	−1.35185	+	0.780489i	−0.0870800	+	0.0502757i	−0.542908	−	0.839792i	$-0.682677\pi$
$241$	−1.35185	+	0.780489i	−0.0870800	+	0.0502757i	0.455828	+	0.890068i	$0.349343\pi$
$242$	−3.78481	+	2.18516i	−0.243297	+	0.140467i
$243$	−13.0278	+	8.56011i	−0.835736	+	0.549131i
$244$		−	2.32191i		−	0.148645i
$245$	0.0483661	+	3.83250i	0.00309000	+	0.244849i
$246$	−1.40712	+	15.0583i	−0.0897150	+	0.960081i
$247$	14.5892	−	25.2693i	0.928290	−	1.60784i
$248$	−4.91607	−	8.51489i	−0.312171	−	0.540696i
$249$	−3.84172	−	8.36732i	−0.243459	−	0.530257i
$250$	5.70101	+	3.29148i	0.360563	+	0.208171i
$251$	−9.88617			−0.624010			−0.312005	−	0.950081i	$-0.601000\pi$
$251$	−9.88617			−0.624010			−0.312005	+	0.950081i	$0.601000\pi$
$252$	3.66911	−	0.300656i	0.231132	−	0.0189395i
$253$	3.81131			0.239615
$254$	13.8146	+	7.97585i	0.866804	+	0.500449i
$255$	0.421586	+	0.918219i	0.0264007	+	0.0575011i
$256$	5.24329	+	9.08165i	0.327706	+	0.567603i
$257$	−13.6017	+	23.5589i	−0.848454	+	1.46956i	0.0341342	+	0.999417i	$0.489133\pi$
$257$	−13.6017	+	23.5589i	−0.848454	+	1.46956i	−0.882588	+	0.470148i	$0.844201\pi$
$258$	1.58639	−	16.9767i	0.0987645	−	1.05692i
$259$	1.34385	−	5.14496i	0.0835029	−	0.319692i
$260$			1.60937i			0.0998092i
$261$	−9.85935	−	8.47350i	−0.610278	−	0.524497i
$262$	16.6863	−	9.63384i	1.03088	−	0.595180i
$263$	0.722249	−	0.416991i	0.0445358	−	0.0257128i	−0.477567	−	0.878595i	$-0.658481\pi$
$263$	0.722249	−	0.416991i	0.0445358	−	0.0257128i	0.522103	+	0.852883i	$0.325148\pi$
$264$	−11.6600	+	16.4445i	−0.717622	+	1.01209i
$265$			0.705932i			0.0433651i
$266$	10.7435	+	10.6088i	0.658727	+	0.650466i
$267$	21.5455	+	2.01332i	1.31856	+	0.123213i
$268$	−2.04011	+	3.53357i	−0.124620	+	0.215847i
$269$	10.5551	+	18.2820i	0.643556	+	1.11467i	0.984633	+	0.174636i	$0.0558750\pi$
$269$	10.5551	+	18.2820i	0.643556	+	1.11467i	−0.341077	+	0.940035i	$0.610792\pi$
$270$	3.42181	−	0.852167i	0.208245	−	0.0518613i
$271$	−3.36816	−	1.94461i	−0.204601	−	0.118127i	0.394199	−	0.919025i	$-0.371022\pi$
$271$	−3.36816	−	1.94461i	−0.204601	−	0.118127i	−0.598800	+	0.800899i	$0.704356\pi$
$272$	3.04405			0.184573
$273$	22.2388	−	18.6758i	1.34596	−	1.13031i
$274$	−5.87829			−0.355121
$275$	−15.5139	−	8.95695i	−0.935523	−	0.540124i
$276$	0.730075	−	0.335202i	0.0439453	−	0.0201768i
$277$	−7.35738	−	12.7434i	−0.442062	−	0.765674i	0.555780	−	0.831329i	$-0.312420\pi$
$277$	−7.35738	−	12.7434i	−0.442062	−	0.765674i	−0.997842	+	0.0656553i	$0.979086\pi$
$278$	2.37144	−	4.10746i	0.142230	−	0.246349i
$279$	1.78958	−	9.49194i	0.107139	−	0.568267i
$280$	−4.28022	−	1.11798i	−0.255792	−	0.0668123i
$281$		−	26.9261i		−	1.60628i	−0.595793	−	0.803138i	$-0.703162\pi$
$281$		−	26.9261i		−	1.60628i	0.595793	−	0.803138i	$-0.296838\pi$
$282$	−6.61043	−	4.68712i	−0.393645	−	0.279114i
$283$	8.82803	−	5.09686i	0.524772	−	0.302977i	−0.214113	−	0.976809i	$-0.568686\pi$
$283$	8.82803	−	5.09686i	0.524772	−	0.302977i	0.738885	+	0.673832i	$0.235353\pi$
$284$	4.05601	−	2.34174i	0.240680	−	0.138957i
$285$	−3.56207	−	2.52568i	−0.210999	−	0.149609i
$286$			29.9358i			1.77014i
$287$	17.9734	−	4.93771i	1.06094	−	0.291464i
$288$	−1.42628	+	7.56499i	−0.0840442	+	0.445771i
$289$	7.93248	−	13.7395i	0.466617	−	0.808204i
$290$	1.47042	+	2.54684i	0.0863461	+	0.149556i
$291$	10.8614	−	4.98683i	0.636705	−	0.292333i
$292$	4.50518	+	2.60106i	0.263646	+	0.152216i
$293$	−10.6250			−0.620719			−0.310359	−	0.950619i	$-0.600449\pi$
$293$	−10.6250			−0.620719			−0.310359	+	0.950619i	$0.600449\pi$
$294$	6.44206	+	13.5764i	0.375709	+	0.791793i
$295$	2.25149			0.131087
$296$	5.31526	+	3.06877i	0.308943	+	0.178368i
$297$	−19.2172	+	4.78584i	−1.11509	+	0.277703i
$298$	−8.96938	−	15.5354i	−0.519582	−	0.899943i
$299$	3.16858	−	5.48815i	0.183244	−	0.317388i
$300$	−3.75952	−	0.351309i	−0.217056	−	0.0202828i
$301$	−20.2632	+	5.56678i	−1.16795	+	0.320864i
$302$		−	8.35568i		−	0.480815i
$303$	3.76257	−	5.30650i	0.216154	−	0.304850i
$304$	−11.3932	+	6.57787i	−0.653445	+	0.377267i
$305$	−2.37383	+	1.37053i	−0.135925	+	0.0784765i
$306$	3.00430	+	2.58201i	0.171744	+	0.147604i
$307$			0.198539i			0.0113312i	0.999984	+	0.00566562i	$0.00180343\pi$
$307$			0.198539i			0.0113312i	−0.999984	+	0.00566562i	$0.998197\pi$
$308$	4.52518	+	1.18197i	0.257846	+	0.0673488i
$309$	2.92923	−	31.3470i	0.166638	−	1.78327i
$310$	−1.09252	+	1.89230i	−0.0620509	+	0.107475i
$311$	3.24806	+	5.62580i	0.184180	+	0.319010i	0.943300	−	0.331941i	$-0.107704\pi$
$311$	3.24806	+	5.62580i	0.184180	+	0.319010i	−0.759120	+	0.650951i	$0.774370\pi$
$312$	13.9858	+	30.4613i	0.791792	+	1.72453i
$313$	25.3654	+	14.6447i	1.43374	+	0.827768i	0.997403	−	0.0720180i	$-0.0229439\pi$
$313$	25.3654	+	14.6447i	1.43374	+	0.827768i	0.436332	+	0.899786i	$0.356277\pi$
$314$	20.6827			1.16719
$315$	−2.47312	−	3.57370i	−0.139344	−	0.201355i
$316$	−0.916353			−0.0515489
$317$	−9.67058	−	5.58331i	−0.543154	−	0.313590i	0.203202	−	0.979137i	$-0.434865\pi$
$317$	−9.67058	−	5.58331i	−0.543154	−	0.313590i	−0.746356	+	0.665547i	$0.768198\pi$
$318$	1.15486	+	2.51530i	0.0647614	+	0.141051i
$319$	−8.25801	−	14.3033i	−0.462360	−	0.800830i
$320$	2.43520	−	4.21788i	0.136132	−	0.235787i
$321$	−2.34476	+	25.0923i	−0.130872	+	1.40052i
$322$	2.33335	+	2.30408i	0.130032	+	0.128402i
$323$		−	4.90536i		−	0.272942i
$324$	−3.26023	+	2.60689i	−0.181124	+	0.144827i
$325$	−25.7954	+	14.8930i	−1.43087	+	0.826113i
$326$	−7.61813	+	4.39833i	−0.421929	+	0.243601i
$327$	−8.21502	+	11.5860i	−0.454292	+	0.640705i
$328$			21.5135i			1.18788i
$329$	−2.52393	+	9.66292i	−0.139149	+	0.532734i
$330$	4.46054	+	0.416816i	0.245545	+	0.0229450i
$331$	−0.290175	+	0.502598i	−0.0159495	+	0.0276253i	−0.873890	−	0.486124i	$-0.838410\pi$
$331$	−0.290175	+	0.502598i	−0.0159495	+	0.0276253i	0.857941	+	0.513749i	$0.171744\pi$
$332$	−1.23275	−	2.13519i	−0.0676561	−	0.117184i
$333$	1.99514	+	5.68990i	0.109333	+	0.311805i
$334$	−18.0110	−	10.3987i	−0.985518	−	0.568989i
$335$	4.81680			0.263170
$336$	−12.8937	+	2.27885i	−0.703410	+	0.124321i
$337$	14.4437			0.786798			0.393399	−	0.919368i	$-0.371299\pi$
$337$	14.4437			0.786798			0.393399	+	0.919368i	$0.371299\pi$
$338$	29.1526	+	16.8312i	1.58569	+	0.915499i
$339$	−14.9150	+	6.84800i	−0.810073	+	0.371933i
$340$	0.135281	+	0.234313i	0.00733663	+	0.0127074i
$341$	6.13568	−	10.6273i	0.332266	−	0.575501i
$342$	−16.8239	−	3.17191i	−0.909730	−	0.171517i
$343$	12.8456	−	13.3413i	0.693596	−	0.720364i
$344$		−	24.2543i		−	1.30770i
$345$	−0.773634	−	0.548545i	−0.0416511	−	0.0295327i
$346$	−12.4319	+	7.17757i	−0.668344	+	0.385868i
$347$	−16.9273	+	9.77295i	−0.908703	+	0.524640i	−0.880013	−	0.474949i	$-0.842467\pi$
$347$	−16.9273	+	9.77295i	−0.908703	+	0.524640i	−0.0286890	+	0.999588i	$0.509133\pi$
$348$	−2.83983	−	2.01358i	−0.152231	−	0.107939i
$349$		−	25.1362i		−	1.34551i	−0.739865	−	0.672755i	$-0.765111\pi$
$349$		−	25.1362i		−	1.34551i	0.739865	−	0.672755i	$-0.234889\pi$
$350$	−4.08303	−	14.8623i	−0.218247	−	0.794425i
$351$	−9.08501	+	31.6508i	−0.484922	+	1.68939i
$352$	−4.89008	+	8.46986i	−0.260642	+	0.451445i
$353$	4.51404	+	7.81855i	0.240258	+	0.416140i	0.960788	−	0.277285i	$-0.0894345\pi$
$353$	4.51404	+	7.81855i	0.240258	+	0.416140i	−0.720529	+	0.693424i	$0.756101\pi$
$354$	8.02227	−	3.68330i	0.426379	−	0.195765i
$355$	−4.78822	−	2.76448i	−0.254132	−	0.146723i
$356$	5.79465			0.307116
$357$	1.66796	−	4.58842i	0.0882779	−	0.242845i
$358$	10.7684			0.569130
$359$	−19.1553	−	11.0593i	−1.01098	−	0.583689i	−0.0995006	−	0.995038i	$-0.531725\pi$
$359$	−19.1553	−	11.0593i	−1.01098	−	0.583689i	−0.911478	+	0.411349i	$0.865058\pi$
$360$	4.73357	−	1.65980i	0.249481	−	0.0874794i
$361$	1.09995	+	1.90517i	0.0578923	+	0.100272i
$362$	5.91048	−	10.2372i	0.310648	−	0.538058i
$363$	−6.08085	−	0.568226i	−0.319162	−	0.0298241i
$364$	5.46405	−	5.53345i	0.286394	−	0.290031i
$365$		−	6.14124i		−	0.321447i
$366$	−6.21608	+	8.76678i	−0.324919	+	0.458247i
$367$	2.23888	−	1.29262i	0.116868	−	0.0674740i	−0.440426	−	0.897789i	$-0.645173\pi$
$367$	2.23888	−	1.29262i	0.116868	−	0.0674740i	0.557295	+	0.830315i	$0.311839\pi$
$368$	−2.47445	+	1.42862i	−0.128990	+	0.0744722i
$369$	−13.7757	+	16.0287i	−0.717133	+	0.834420i
$370$		−	1.36397i		−	0.0709094i
$371$	2.39674	−	2.42718i	0.124433	−	0.126013i
$372$	0.240653	−	2.57534i	0.0124773	−	0.133525i
$373$	1.23274	−	2.13517i	0.0638291	−	0.110555i	−0.832345	−	0.554258i	$-0.813002\pi$
$373$	1.23274	−	2.13517i	0.0638291	−	0.110555i	0.896174	+	0.443703i	$0.146335\pi$
$374$	2.51634	+	4.35844i	0.130117	+	0.225369i
$375$	3.83851	+	8.36032i	0.198220	+	0.431725i
$376$	−9.98277	−	5.76356i	−0.514822	−	0.297233i
$377$	−27.4616			−1.41435
$378$	−14.6583	−	8.68756i	−0.753941	−	0.446840i
$379$	15.7553			0.809298			0.404649	−	0.914472i	$-0.367394\pi$
$379$	15.7553			0.809298			0.404649	+	0.914472i	$0.367394\pi$
$380$	−1.01265	−	0.584654i	−0.0519479	−	0.0299921i
$381$	9.30140	+	20.2586i	0.476525	+	1.03788i
$382$	−15.0374	−	26.0455i	−0.769378	−	1.33260i
$383$	17.6955	−	30.6495i	0.904198	−	1.56612i	0.0822080	−	0.996615i	$-0.473803\pi$
$383$	17.6955	−	30.6495i	0.904198	−	1.56612i	0.821990	−	0.569502i	$-0.192864\pi$
$384$	0.949580	−	10.1619i	0.0484581	−	0.518572i
$385$	−1.46264	−	5.32405i	−0.0745431	−	0.271339i
$386$		−	7.60104i		−	0.386883i
$387$	15.5307	−	18.0707i	0.789470	−	0.918588i
$388$	2.77163	−	1.60020i	0.140708	−	0.0812379i
$389$	−28.4609	+	16.4319i	−1.44302	+	0.833129i	−0.998050	−	0.0624150i	$-0.980120\pi$
$389$	−28.4609	+	16.4319i	−1.44302	+	0.833129i	−0.444972	+	0.895544i	$0.646786\pi$
$390$	4.30853	−	6.07649i	0.218171	−	0.307695i
$391$		−	1.06538i		−	0.0538785i
$392$	10.9208	+	18.3759i	0.551583	+	0.928122i
$393$	26.8090	+	2.50517i	1.35233	+	0.126369i
$394$	0.986617	−	1.70887i	0.0497050	−	0.0860916i
$395$	0.540888	+	0.936846i	0.0272150	+	0.0471378i
$396$	−5.00447	+	1.75479i	−0.251484	+	0.0881818i
$397$	−21.6571	−	12.5037i	−1.08694	−	0.627544i	−0.154179	−	0.988043i	$-0.549273\pi$
$397$	−21.6571	−	12.5037i	−1.08694	−	0.627544i	−0.932760	+	0.360499i	$0.882607\pi$
$398$	−20.3256			−1.01883
$399$	3.67227	+	20.7777i	0.183843	+	1.04019i
$400$	13.4296			0.671482
$401$	12.7549	+	7.36405i	0.636950	+	0.367743i	0.783439	−	0.621469i	$-0.213464\pi$
$401$	12.7549	+	7.36405i	0.636950	+	0.367743i	−0.146489	+	0.989212i	$0.546797\pi$
$402$	17.1627	−	7.87999i	0.855997	−	0.393018i
$403$	−10.2020	−	17.6703i	−0.508196	−	0.880221i
$404$	0.870972	−	1.50857i	0.0433325	−	0.0750541i
$405$	4.58958	+	1.79439i	0.228058	+	0.0891641i
$406$	3.59121	−	13.7490i	0.178229	−	0.682351i
$407$			7.66017i			0.379700i
$408$	4.59675	+	3.25932i	0.227573	+	0.161360i
$409$	7.90852	−	4.56599i	0.391051	−	0.225773i	−0.291564	−	0.956551i	$-0.594176\pi$
$409$	7.90852	−	4.56599i	0.391051	−	0.225773i	0.682615	+	0.730778i	$0.260842\pi$
$410$	4.14049	−	2.39051i	0.204484	−	0.118059i
$411$	−6.70110	−	4.75141i	−0.330541	−	0.234370i
$412$		−	8.43077i		−	0.415354i
$413$	−7.74121	−	7.64413i	−0.380920	−	0.376143i
$414$	−3.65392	−	0.688897i	−0.179580	−	0.0338574i
$415$	−1.45530	+	2.52065i	−0.0714376	+	0.123734i
$416$	8.13086	+	14.0831i	0.398648	+	0.690479i
$417$	6.02343	−	2.76556i	0.294969	−	0.135430i
$418$	−18.8362	−	10.8751i	−0.921309	−	0.531918i
$419$	0.194362			0.00949520			0.00474760	−	0.999989i	$-0.498489\pi$
$419$	0.194362			0.00949520			0.00474760	+	0.999989i	$0.498489\pi$
$420$	−0.748423	−	0.891209i	−0.0365193	−	0.0434865i
$421$	−33.4270			−1.62913			−0.814567	−	0.580070i	$-0.803025\pi$
$421$	−33.4270			−1.62913			−0.814567	+	0.580070i	$0.803025\pi$
$422$	−20.5429	−	11.8605i	−1.00001	−	0.577359i
$423$	−3.74713	−	10.6864i	−0.182192	−	0.519590i
$424$	1.96854	+	3.40961i	0.0956008	+	0.165585i
$425$	−2.50374	+	4.33661i	−0.121449	+	0.210357i
$426$	−21.5834	−	2.01686i	−1.04572	−	0.0977174i
$427$	12.8150	+	3.34725i	0.620161	+	0.161985i
$428$			6.74857i			0.326204i
$429$	−24.1971	+	34.1261i	−1.16825	+	1.64762i
$430$	−4.66799	+	2.69507i	−0.225111	+	0.129968i
$431$	−10.1276	+	5.84719i	−0.487831	+	0.281649i	−0.723674	−	0.690142i	$-0.757548\pi$
$431$	−10.1276	+	5.84719i	−0.487831	+	0.281649i	0.235843	+	0.971791i	$0.424215\pi$
$432$	10.6826	−	10.3105i	0.513968	−	0.496064i
$433$		−	24.0346i		−	1.15503i	−0.816381	−	0.577514i	$-0.804023\pi$
$433$		−	24.0346i		−	1.15503i	0.816381	−	0.577514i	$-0.195977\pi$
$434$	10.1810	−	2.79695i	0.488703	−	0.134258i
$435$	−0.382366	+	4.09188i	−0.0183330	+	0.196190i
$436$	−1.90164	+	3.29374i	−0.0910721	+	0.157742i
$437$	2.30217	+	3.98747i	0.110128	+	0.190747i
$438$	−10.0467	−	21.8818i	−0.480049	−	1.04555i
$439$	−10.2684	−	5.92844i	−0.490082	−	0.282949i	0.234527	−	0.972110i	$-0.424646\pi$
$439$	−10.2684	−	5.92844i	−0.490082	−	0.282949i	−0.724608	+	0.689161i	$0.757979\pi$
$440$	6.37269			0.303806
$441$	−3.63000	+	20.6839i	−0.172857	+	0.984947i
$442$	8.36799			0.398025
$443$	−14.0631	−	8.11936i	−0.668160	−	0.385762i	0.127219	−	0.991875i	$-0.459395\pi$
$443$	−14.0631	−	8.11936i	−0.668160	−	0.385762i	−0.795379	+	0.606112i	$0.792728\pi$
$444$	0.673707	+	1.46734i	0.0319727	+	0.0696370i
$445$	−3.42036	−	5.92424i	−0.162141	−	0.280836i
$446$	11.5255	−	19.9627i	0.545746	−	0.945260i
$447$	2.33238	−	24.9599i	0.110318	−	1.18056i
$448$	−22.6931	+	6.23434i	−1.07215	+	0.294545i
$449$		−	42.1940i		−	1.99126i	−0.0934083	−	0.995628i	$-0.529776\pi$
$449$		−	42.1940i		−	1.99126i	0.0934083	−	0.995628i	$-0.470224\pi$
$450$	13.2542	+	11.3912i	0.624811	+	0.536987i
$451$	−23.2534	+	13.4253i	−1.09496	+	0.632174i
$452$	−3.80605	+	2.19743i	−0.179022	+	0.103358i
$453$	6.75388	−	9.52527i	0.317325	−	0.447536i
$454$			30.6836i			1.44005i
$455$	−8.88242	−	2.32007i	−0.416414	−	0.108767i
$456$	−24.2476	−	2.26583i	−1.13550	−	0.106107i
$457$	14.3031	−	24.7737i	0.669071	−	1.15887i	−0.309093	−	0.951032i	$-0.600025\pi$
$457$	14.3031	−	24.7737i	0.669071	−	1.15887i	0.978164	−	0.207834i	$-0.0666413\pi$
$458$	−14.3534	−	24.8609i	−0.670692	−	1.16167i
$459$	1.33779	+	5.37179i	0.0624428	+	0.250734i
$460$	−0.219934	−	0.126979i	−0.0102545	−	0.00592043i
$461$	11.7607			0.547749			0.273874	−	0.961765i	$-0.411695\pi$
$461$	11.7607			0.547749			0.273874	+	0.961765i	$0.411695\pi$
$462$	−13.9213	−	16.5773i	−0.647679	−	0.771245i
$463$	−24.2008			−1.12471			−0.562354	−	0.826896i	$-0.690104\pi$
$463$	−24.2008			−1.12471			−0.562354	+	0.826896i	$0.690104\pi$
$464$	10.7228	+	6.19083i	0.497795	+	0.287402i
$465$	−2.77498	+	1.27409i	−0.128687	+	0.0590846i
$466$	17.0426	+	29.5186i	0.789482	+	1.36742i
$467$	−17.7761	+	30.7892i	−0.822581	+	1.42475i	0.0811727	+	0.996700i	$0.474133\pi$
$467$	−17.7761	+	30.7892i	−0.822581	+	1.42475i	−0.903754	+	0.428052i	$0.859200\pi$
$468$	−1.63370	+	8.66513i	−0.0755176	+	0.400546i
$469$	−16.5614	−	16.3537i	−0.764734	−	0.755144i
$470$			2.56172i			0.118163i
$471$	23.5778	+	16.7178i	1.08641	+	0.770315i
$472$	10.8746	−	6.27844i	0.500543	−	0.288989i
$473$	26.2158	−	15.1357i	1.20541	−	0.695941i
$474$	3.45986	+	2.45321i	0.158917	+	0.112680i
$475$		−	21.6413i		−	0.992970i
$476$	0.330396	−	1.26493i	0.0151437	−	0.0579778i
$477$	−0.716600	+	3.80085i	−0.0328109	+	0.174029i
$478$	−14.2099	+	24.6123i	−0.649946	+	1.12574i
$479$	10.5126	+	18.2084i	0.480335	+	0.831964i	0.999745	−	0.0225604i	$-0.00718181\pi$
$479$	10.5126	+	18.2084i	0.480335	+	0.831964i	−0.519411	+	0.854525i	$0.673848\pi$
$480$	2.21164	−	1.01544i	0.100947	−	0.0463482i
$481$	11.0304	+	6.36838i	0.502941	+	0.290373i
$482$	1.93472			0.0881241
$483$	0.797568	+	4.51264i	0.0362906	+	0.205332i
$484$	−1.63544			−0.0743383
$485$	−3.27198	−	1.88908i	−0.148573	−	0.0857786i
$486$	19.2886	−	1.11469i	0.874949	−	0.0505632i
$487$	14.1314	+	24.4763i	0.640355	+	1.10913i	0.985353	+	0.170524i	$0.0545461\pi$
$487$	14.1314	+	24.4763i	0.640355	+	1.10913i	−0.344998	+	0.938603i	$0.612121\pi$
$488$	−7.64365	+	13.2392i	−0.346012	+	0.599310i
$489$	−12.2396	−	1.14374i	−0.553496	−	0.0517215i
$490$	2.32314	−	4.14369i	0.104949	−	0.187193i
$491$			10.3880i			0.468802i	0.972140	+	0.234401i	$0.0753129\pi$
$491$			10.3880i			0.468802i	−0.972140	+	0.234401i	$0.924687\pi$
$492$	−3.27354	+	4.61681i	−0.147583	+	0.208142i
$493$	−3.99821	+	2.30837i	−0.180070	+	0.103964i
$494$	−31.3195	+	18.0823i	−1.40913	+	0.813562i
$495$	4.74799	+	4.08060i	0.213406	+	0.183410i
$496$			9.19955i			0.413072i
$497$	7.07734	+	25.7617i	0.317462	+	1.15557i
$498$	−1.06173	+	11.3621i	−0.0475773	+	0.509146i
$499$	14.6851	−	25.4353i	0.657394	−	1.13864i	−0.323894	−	0.946093i	$-0.604992\pi$
$499$	14.6851	−	25.4353i	0.657394	−	1.13864i	0.981288	−	0.192547i	$-0.0616747\pi$
$500$	1.23172	+	2.13341i	0.0550843	+	0.0954088i
$501$	−12.1269	−	26.4125i	−0.541789	−	1.18002i
$502$	10.6116	+	6.12661i	0.473619	+	0.273444i
$503$	9.43320			0.420606			0.210303	−	0.977636i	$-0.432555\pi$
$503$	9.43320			0.420606			0.210303	+	0.977636i	$0.432555\pi$
$504$	−21.9105	−	10.3643i	−0.975972	−	0.461663i
$505$	−2.05641			−0.0915090
$506$	−4.09097	−	2.36192i	−0.181866	−	0.105000i
$507$	19.6285	+	42.7512i	0.871734	+	1.89865i
$508$	2.98469	+	5.16963i	0.132424	+	0.229365i
$509$	16.4669	−	28.5215i	0.729882	−	1.26419i	−0.227051	−	0.973883i	$-0.572908\pi$
$509$	16.4669	−	28.5215i	0.729882	−	1.26419i	0.956933	−	0.290310i	$-0.0937583\pi$
$510$	0.116513	−	1.24686i	0.00515928	−	0.0552118i
$511$	−20.8504	+	21.1152i	−0.922366	+	0.934080i
$512$		−	24.7825i		−	1.09524i
$513$	−16.6149	−	17.2146i	−0.733566	−	0.760043i
$514$	29.1996	−	16.8584i	1.28794	−	0.743593i
$515$	−8.61932	+	4.97637i	−0.379813	+	0.219285i
$516$	3.69059	−	5.20499i	0.162469	−	0.229137i
$517$		−	14.3868i		−	0.632732i
$518$	−4.63087	+	4.68968i	−0.203469	+	0.206053i
$519$	−19.9737	−	1.86644i	−0.876747	−	0.0819278i
$520$	5.29802	−	9.17644i	0.232333	−	0.402413i
$521$	9.56796	+	16.5722i	0.419180	+	0.726041i	0.995857	−	0.0909312i	$-0.0289843\pi$
$521$	9.56796	+	16.5722i	0.419180	+	0.726041i	−0.576677	+	0.816972i	$0.695651\pi$
$522$	5.33165	+	15.2053i	0.233360	+	0.665516i
$523$	−20.2581	−	11.6960i	−0.885824	−	0.511430i	−0.0132494	−	0.999912i	$-0.504218\pi$
$523$	−20.2581	−	11.6960i	−0.885824	−	0.511430i	−0.872574	+	0.488482i	$0.837551\pi$
$524$	7.21026			0.314982
$525$	7.35865	−	20.2430i	0.321158	−	0.883477i
$526$	−1.03366			−0.0450698
$527$	−2.97066	−	1.71511i	−0.129404	−	0.0747114i
$528$	17.1414	−	7.87020i	0.745983	−	0.342507i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	0.437477	−	0.757732i	0.0190028	−	0.0329138i
$531$	12.1224	+	2.28552i	0.526067	+	0.0991830i
$532$	1.49677	+	5.44829i	0.0648933	+	0.236213i
$533$			44.6453i			1.93380i
$534$	−21.8787	−	15.5131i	−0.946786	−	0.671318i
$535$	6.89949	−	3.98343i	0.298291	−	0.172218i
$536$	23.2649	−	13.4320i	1.00489	−	0.580173i
$537$	12.2758	+	8.70411i	0.529738	+	0.375610i
$538$		−	26.1646i		−	1.12804i
$539$	−13.0470	+	23.2713i	−0.561972	+	1.00237i
$540$	1.26839	+	0.364076i	0.0545827	+	0.0156674i
$541$	−17.3442	+	30.0410i	−0.745685	+	1.29156i	0.204189	+	0.978932i	$0.434544\pi$
$541$	−17.3442	+	30.0410i	−0.745685	+	1.29156i	−0.949874	+	0.312633i	$0.898789\pi$
$542$	2.41021	+	4.17460i	0.103527	+	0.179315i
$543$	15.0125	−	6.89277i	0.644250	−	0.295797i
$544$	2.36759	+	1.36693i	0.101510	+	0.0586066i
$545$	4.48987			0.192325
$546$	−35.4444	+	6.26447i	−1.51688	+	0.268095i
$547$	42.1534			1.80235			0.901174	−	0.433458i	$-0.142707\pi$
$547$	42.1534			1.80235			0.901174	+	0.433458i	$0.142707\pi$
$548$	−1.90504	−	1.09987i	−0.0813792	−	0.0469843i
$549$	−14.1723	+	4.96946i	−0.604861	+	0.212092i
$550$	11.1015	+	19.2284i	0.473370	+	0.819901i
$551$	9.97627	−	17.2794i	0.425003	−	0.736127i
$552$	−5.26626	−	0.492107i	−0.224147	−	0.0209455i
$553$	1.32101	−	5.05751i	0.0561751	−	0.215067i
$554$			18.2379i			0.774854i
$555$	1.10249	−	1.55489i	0.0467982	−	0.0660014i
$556$	1.53707	−	0.887430i	0.0651864	−	0.0376354i
$557$	32.4461	−	18.7327i	1.37478	−	0.793732i	0.383258	−	0.923641i	$-0.374802\pi$
$557$	32.4461	−	18.7327i	1.37478	−	0.793732i	0.991526	+	0.129910i	$0.0414688\pi$
$558$	−7.80319	+	9.07941i	−0.330335	+	0.384362i
$559$		−	50.3331i		−	2.12886i
$560$	2.94526	+	2.90833i	0.124460	+	0.122899i
$561$	−0.654347	+	7.00246i	−0.0276265	+	0.295644i
$562$	−16.6865	+	28.9019i	−0.703878	+	1.21915i
$563$	−0.550026	−	0.952674i	−0.0231808	−	0.0401504i	0.854202	−	0.519941i	$-0.174046\pi$
$563$	−0.550026	−	0.952674i	−0.0231808	−	0.0401504i	−0.877383	+	0.479790i	$0.840713\pi$
$564$	−1.26531	−	2.75587i	−0.0532793	−	0.116043i
$565$	4.49314	+	2.59411i	0.189028	+	0.109135i
$566$	−12.6344			−0.531064
$567$	−9.68795	−	21.7519i	−0.406856	−	0.913492i
$568$	−30.8358			−1.29384
$569$	13.1710	+	7.60428i	0.552157	+	0.318788i	0.749991	−	0.661448i	$-0.230058\pi$
$569$	13.1710	+	7.60428i	0.552157	+	0.318788i	−0.197835	+	0.980235i	$0.563391\pi$
$570$	2.25824	+	4.91848i	0.0945875	+	0.206013i
$571$	22.1498	+	38.3646i	0.926941	+	1.60551i	0.788409	+	0.615151i	$0.210905\pi$
$571$	22.1498	+	38.3646i	0.926941	+	1.60551i	0.138532	+	0.990358i	$0.455762\pi$
$572$	−5.60122	+	9.70160i	−0.234199	+	0.405644i
$573$	3.91029	−	41.8458i	0.163355	−	1.74814i
$574$	−22.3522	−	5.83835i	−0.932964	−	0.243688i
$575$		−	4.70020i		−	0.196012i
$576$	17.3931	−	20.2378i	0.724713	−	0.843240i
$577$	−15.0823	+	8.70776i	−0.627884	+	0.362509i	−0.779932	−	0.625864i	$-0.784746\pi$
$577$	−15.0823	+	8.70776i	−0.627884	+	0.362509i	0.152048	+	0.988373i	$0.451413\pi$
$578$	−17.0291	+	9.83176i	−0.708317	+	0.408947i
$579$	6.14390	−	8.66499i	0.255332	−	0.360105i
$580$			1.10051i			0.0456961i
$581$	13.5616	−	3.72570i	0.562631	−	0.154568i
$582$	−14.7488	−	1.37820i	−0.611356	−	0.0571283i
$583$	−2.45691	+	4.25549i	−0.101755	+	0.176244i
$584$	−17.1253	−	29.6618i	−0.708649	−	1.22742i
$585$	9.82323	−	3.44447i	0.406140	−	0.142411i
$586$	11.4046	+	6.58447i	0.471121	+	0.272002i
$587$	45.7535			1.88845			0.944226	−	0.329300i	$-0.106813\pi$
$587$	45.7535			1.88845			0.944226	+	0.329300i	$0.106813\pi$
$588$	−0.452508	+	5.60521i	−0.0186611	+	0.231155i
$589$	14.8247			0.610840
$590$	−2.41670	−	1.39528i	−0.0994940	−	0.0574429i
$591$	2.50599	−	1.15059i	0.103083	−	0.0473289i
$592$	−2.87132	−	4.97328i	−0.118011	−	0.204400i
$593$	7.66023	−	13.2679i	0.314568	−	0.544848i	−0.664778	−	0.747041i	$-0.731474\pi$
$593$	7.66023	−	13.2679i	0.314568	−	0.544848i	0.979346	+	0.202194i	$0.0648070\pi$
$594$	23.5931	+	6.77215i	0.968038	+	0.277865i
$595$	−1.48824	+	0.408853i	−0.0610117	+	0.0167614i
$596$		−	6.71296i		−	0.274973i
$597$	−23.1707	−	16.4292i	−0.948314	−	0.672401i
$598$	−6.80217	+	3.92724i	−0.278161	+	0.160597i
$599$	−22.1487	+	12.7876i	−0.904972	+	0.522486i	−0.878810	−	0.477172i	$-0.841662\pi$
$599$	−22.1487	+	12.7876i	−0.904972	+	0.522486i	−0.0261618	+	0.999658i	$0.508329\pi$
$600$	20.2798	+	14.3794i	0.827918	+	0.587035i
$601$		−	29.0013i		−	1.18299i	−0.806309	−	0.591495i	$-0.798538\pi$
$601$		−	29.0013i		−	1.18299i	0.806309	−	0.591495i	$-0.201462\pi$
$602$	25.1999	+	6.58216i	1.02707	+	0.268269i
$603$	25.9344	+	4.88959i	1.05613	+	0.199119i
$604$	1.56341	−	2.70791i	0.0636143	−	0.110183i
$605$	0.965339	+	1.67202i	0.0392466	+	0.0679772i
$606$	−7.32717	+	3.36416i	−0.297646	+	0.136660i
$607$	7.91183	+	4.56790i	0.321131	+	0.185405i	0.651897	−	0.758308i	$-0.273974\pi$
$607$	7.91183	+	4.56790i	0.321131	+	0.185405i	−0.330765	+	0.943713i	$0.607307\pi$
$608$	−11.8151			−0.479167
$609$	15.2072	−	12.7707i	0.616226	−	0.517496i
$610$	3.39736			0.137555
$611$	−20.7165	−	11.9607i	−0.838100	−	0.483877i
$612$	0.490519	+	1.39891i	0.0198281	+	0.0565474i
$613$	−12.4459	−	21.5568i	−0.502683	−	0.870673i	−0.999995	−	0.00310109i	$-0.999013\pi$
$613$	−12.4459	−	21.5568i	−0.502683	−	0.870673i	0.497312	−	0.867572i	$-0.334320\pi$
$614$	0.123038	−	0.213108i	0.00496540	−	0.00860033i
$615$	6.65231	+	0.621626i	0.268247	+	0.0250664i
$616$	−21.9109	−	21.6362i	−0.882817	−	0.871746i
$617$			26.4642i			1.06541i	0.846301	+	0.532704i	$0.178824\pi$
$617$			26.4642i			1.06541i	−0.846301	+	0.532704i	$0.821176\pi$
$618$	−22.5704	+	31.8319i	−0.907915	+	1.28047i
$619$	−2.28633	+	1.32001i	−0.0918953	+	0.0530558i	−0.545243	−	0.838278i	$-0.683563\pi$
$619$	−2.28633	+	1.32001i	−0.0918953	+	0.0530558i	0.453348	+	0.891334i	$0.350229\pi$
$620$	−0.708127	+	0.408837i	−0.0284391	+	0.0164193i
$621$	−3.60854	−	3.73878i	−0.144806	−	0.150032i
$622$		−	8.05148i		−	0.322835i
$623$	−8.35354	+	31.9817i	−0.334678	+	1.28132i
$624$	2.91792	−	31.2260i	0.116810	−	1.25004i
$625$	−10.2964	+	17.8339i	−0.411857	+	0.713356i
$626$	−18.1511	−	31.4386i	−0.725463	−	1.25654i
$627$	−12.6825	−	27.6226i	−0.506490	−	1.10314i
$628$	6.70286	+	3.86990i	0.267473	+	0.154426i
$629$	2.14125			0.0853774
$630$	0.439913	+	5.36856i	0.0175266	+	0.213888i
$631$	41.6250			1.65706			0.828532	−	0.559941i	$-0.189176\pi$
$631$	41.6250			1.65706			0.828532	+	0.559941i	$0.189176\pi$
$632$	5.22492	+	3.01661i	0.207836	+	0.119994i
$633$	−13.8316	−	30.1255i	−0.549758	−	1.19738i
$634$	6.92012	+	11.9860i	0.274833	+	0.476025i
$635$	3.52349	−	6.10287i	0.139826	−	0.242185i
$636$	−0.0963647	+	1.03124i	−0.00382111	+	0.0408914i
$637$	22.6631	+	38.1341i	0.897945	+	1.51093i
$638$			20.4704i			0.810432i
$639$	−22.9743	−	19.7450i	−0.908849	−	0.781100i
$640$	−2.79416	+	1.61321i	−0.110449	+	0.0637677i
$641$	2.90920	−	1.67963i	0.114907	−	0.0663413i	−0.441445	−	0.897288i	$-0.645534\pi$
$641$	2.90920	−	1.67963i	0.114907	−	0.0663413i	0.556352	+	0.830947i	$0.312201\pi$
$642$	18.0669	−	25.4805i	0.713043	−	1.00563i
$643$			32.8061i			1.29375i	0.762597	+	0.646873i	$0.223924\pi$
$643$			32.8061i			1.29375i	−0.762597	+	0.646873i	$0.776076\pi$
$644$	0.325079	+	1.18329i	0.0128099	+	0.0466283i
$645$	−7.49981	−	0.700821i	−0.295305	−	0.0275948i
$646$	−3.03993	+	5.26530i	−0.119604	+	0.207161i
$647$	−20.0214	−	34.6781i	−0.787124	−	1.36334i	−0.927722	−	0.373272i	$-0.878236\pi$
$647$	−20.0214	−	34.6781i	−0.787124	−	1.36334i	0.140598	−	0.990067i	$-0.455098\pi$
$648$	27.1712	−	4.13155i	1.06739	−	0.162303i
$649$	13.5724	+	7.83603i	0.532763	+	0.307591i
$650$	36.9176			1.44803
$651$	13.8668	+	5.04081i	0.543484	+	0.197565i
$652$	−3.29185			−0.128919
$653$	25.2259	+	14.5642i	0.987167	+	0.569941i	0.904426	−	0.426630i	$-0.140299\pi$
$653$	25.2259	+	14.5642i	0.987167	+	0.569941i	0.0827410	+	0.996571i	$0.473633\pi$
$654$	15.9978	−	7.34515i	0.625564	−	0.287218i
$655$	−4.25594	−	7.37151i	−0.166293	−	0.288029i
$656$	10.0647	−	17.4325i	0.392959	−	0.680625i
$657$	6.23405	−	33.0654i	0.243213	−	1.29001i
$658$	8.69739	−	8.80785i	0.339060	−	0.343366i
$659$			27.9586i			1.08911i	0.838725	+	0.544556i	$0.183302\pi$
$659$			27.9586i			1.08911i	−0.838725	+	0.544556i	$0.816698\pi$
$660$	1.36758	+	0.969683i	0.0532331	+	0.0377449i
$661$	15.2715	−	8.81703i	0.593994	−	0.342943i	−0.172681	−	0.984978i	$-0.555243\pi$
$661$	15.2715	−	8.81703i	0.593994	−	0.342943i	0.766675	+	0.642035i	$0.221910\pi$
$662$	0.622934	−	0.359651i	0.0242110	−	0.0139782i
$663$	9.53929	+	6.76383i	0.370475	+	0.262685i
$664$			16.2328i			0.629953i
$665$	4.68664	−	4.74616i	0.181740	−	0.184048i
$666$	1.38458	−	7.34383i	0.0536514	−	0.284568i
$667$	2.16671	−	3.75285i	0.0838954	−	0.145311i
$668$	−3.89134	−	6.73999i	−0.150560	−	0.260778i
$669$	29.2745	−	13.4409i	1.13182	−	0.519657i
$670$	−5.17024	−	2.98504i	−0.199744	−	0.115322i
$671$	−19.0799			−0.736570
$672$	−11.0517	−	4.01748i	−0.426330	−	0.154978i
$673$	15.3086			0.590104			0.295052	−	0.955481i	$-0.404663\pi$
$673$	15.3086			0.590104			0.295052	+	0.955481i	$0.404663\pi$
$674$	−15.5035	−	8.95098i	−0.597174	−	0.344779i
$675$	5.90202	+	23.6991i	0.227169	+	0.912178i
$676$	6.29851	+	10.9093i	0.242250	+	0.419590i
$677$	−25.8457	+	44.7660i	−0.993330	+	1.72050i	−0.396805	+	0.917903i	$0.629881\pi$
$677$	−25.8457	+	44.7660i	−0.993330	+	1.72050i	−0.596525	+	0.802595i	$0.703452\pi$
$678$	20.2533	+	1.89257i	0.777822	+	0.0726837i
$679$	4.83622	+	17.6040i	0.185597	+	0.675578i
$680$		−	1.78136i		−	0.0683121i
$681$	−24.8015	+	34.9786i	−0.950397	+	1.34038i
$682$	−13.1718	+	7.60474i	−0.504374	+	0.291201i
$683$	−40.0443	+	23.1196i	−1.53225	+	0.884647i	−0.532995	+	0.846118i	$0.678934\pi$
$683$	−40.0443	+	23.1196i	−1.53225	+	0.884647i	−0.999258	+	0.0385283i	$0.987733\pi$
$684$	−4.85879	−	4.17583i	−0.185780	−	0.159667i
$685$			2.59686i			0.0992207i
$686$	−22.0560	+	6.35969i	−0.842101	+	0.242814i
$687$	3.73245	−	39.9427i	0.142402	−	1.52391i
$688$	−11.3469	+	19.6534i	−0.432596	+	0.749279i
$689$	4.08517	+	7.07571i	0.155632	+	0.269563i
$690$	0.490460	+	1.06823i	0.0186715	+	0.0406668i
$691$	7.50502	+	4.33303i	0.285505	+	0.164836i	0.635913	−	0.771761i	$-0.280624\pi$
$691$	7.50502	+	4.33303i	0.285505	+	0.164836i	−0.350408	+	0.936597i	$0.613957\pi$
$692$	−5.37191			−0.204210
$693$	−2.47059	−	30.1503i	−0.0938499	−	1.14531i
$694$	24.2258			0.919598
$695$	−1.81455	−	1.04763i	−0.0688299	−	0.0397390i
$696$	9.56367	+	20.8298i	0.362510	+	0.789550i
$697$	3.75280	+	6.50003i	0.142147	+	0.246206i
$698$	−15.5773	+	26.9806i	−0.589609	+	1.02123i
$699$	−4.43173	+	47.4259i	−0.167623	+	1.79381i
$700$	1.45763	−	5.58056i	0.0550932	−	0.210925i
$701$			20.7724i			0.784562i	0.919845	+	0.392281i	$0.128314\pi$
$701$			20.7724i			0.784562i	−0.919845	+	0.392281i	$0.871686\pi$
$702$	29.3661	−	28.3431i	1.10835	−	1.06974i
$703$	−8.01423	+	4.62702i	−0.302262	+	0.174511i
$704$	29.3596	−	16.9508i	1.10653	−	0.638856i
$705$	−2.07063	+	2.92029i	−0.0779845	+	0.109985i
$706$		−	11.1897i		−	0.421129i
$707$	7.07046	+	6.98180i	0.265912	+	0.262577i
$708$	3.28903	+	0.307344i	0.123609	+	0.0115507i
$709$	3.87341	−	6.70895i	0.145469	−	0.251960i	−0.784079	−	0.620661i	$-0.786864\pi$
$709$	3.87341	−	6.70895i	0.145469	−	0.251960i	0.929548	+	0.368702i	$0.120198\pi$
$710$	3.42638	+	5.93466i	0.128590	+	0.222724i
$711$	1.96123	+	5.59319i	0.0735517	+	0.209761i
$712$	−33.0403	−	19.0758i	−1.23824	−	0.714896i
$713$	3.21972			0.120580
$714$	−4.63386	+	3.89144i	−0.173418	+	0.145634i
$715$	13.2248			0.494578
$716$	3.48984	+	2.01486i	0.130421	+	0.0752988i
$717$	−36.0930	+	16.5716i	−1.34792	+	0.618876i
$718$	13.7073	+	23.7417i	0.511550	+	0.886031i
$719$	−4.79846	+	8.31118i	−0.178952	+	0.309955i	−0.941522	−	0.336952i	$-0.890604\pi$
$719$	−4.79846	+	8.31118i	−0.178952	+	0.309955i	0.762570	+	0.646906i	$0.223937\pi$
$720$	−4.61215	−	0.869559i	−0.171885	−	0.0324066i
$721$	46.5309	+	12.1538i	1.73290	+	0.452630i
$722$		−	2.72663i		−	0.101475i
$723$	2.20553	+	1.56383i	0.0820247	+	0.0581595i
$724$	3.83094	−	2.21179i	0.142376	−	0.0822006i
$725$	−17.6392	+	10.1840i	−0.655102	+	0.378223i
$726$	6.17491	+	4.37831i	0.229172	+	0.162494i
$727$		−	16.8710i		−	0.625711i	−0.949801	−	0.312855i	$-0.898715\pi$
$727$		−	16.8710i		−	0.625711i	0.949801	−	0.312855i	$-0.101285\pi$
$728$	−49.3712	+	13.5634i	−1.82982	+	0.502694i
$729$	22.8895	+	14.3202i	0.847761	+	0.530379i
$730$	−3.80582	+	6.59187i	−0.140860	+	0.243976i
$731$	−4.23090	−	7.32814i	−0.156486	−	0.271041i
$732$	−3.65484	+	1.67806i	−0.135087	+	0.0620230i
$733$	−2.45955	−	1.42002i	−0.0908454	−	0.0524496i	0.453889	−	0.891058i	$-0.350036\pi$
$733$	−2.45955	−	1.42002i	−0.0908454	−	0.0524496i	−0.544735	+	0.838609i	$0.683370\pi$
$734$	−3.20421			−0.118270
$735$	5.99766	−	2.84591i	0.221227	−	0.104973i
$736$	−2.56609			−0.0945873
$737$	29.0365	+	16.7642i	1.06957	+	0.617519i
$738$	24.7197	−	8.66785i	0.909945	−	0.319068i
$739$	20.9524	+	36.2906i	0.770746	+	1.33497i	0.937155	+	0.348914i	$0.113450\pi$
$739$	20.9524	+	36.2906i	0.770746	+	1.33497i	−0.166409	+	0.986057i	$0.553217\pi$
$740$	0.255209	−	0.442035i	0.00938167	−	0.0162495i
$741$	−50.3193	−	4.70210i	−1.84853	−	0.172736i
$742$	−4.07677	+	1.11998i	−0.149663	+	0.0411159i
$743$		−	20.2170i		−	0.741689i	−0.928695	−	0.370844i	$-0.879068\pi$
$743$		−	20.2170i		−	0.741689i	0.928695	−	0.370844i	$-0.120932\pi$
$744$	−9.85012	+	13.8920i	−0.361123	+	0.509306i
$745$	−6.86309	+	3.96241i	−0.251444	+	0.145171i
$746$	−2.64640	+	1.52790i	−0.0968916	+	0.0559404i
$747$	−10.3943	+	12.0943i	−0.380307	+	0.442506i
$748$			1.88331i			0.0688606i
$749$	−37.2465	−	9.72871i	−1.36096	−	0.355479i
$750$	1.06084	−	11.3526i	0.0387365	−	0.414537i
$751$	−10.5323	+	18.2424i	−0.384328	+	0.665675i	−0.991676	−	0.128761i	$-0.958900\pi$
$751$	−10.5323	+	18.2424i	−0.384328	+	0.665675i	0.607348	+	0.794436i	$0.292233\pi$
$752$	5.39273	+	9.34049i	0.196653	+	0.340612i
$753$	7.14483	+	15.5615i	0.260372	+	0.567093i
$754$	29.4767	+	17.0184i	1.07348	+	0.619773i
$755$	−3.69129			−0.134340
$756$	−3.12495	−	5.55814i	−0.113653	−	0.202148i
$757$	−4.82700			−0.175440			−0.0877202	−	0.996145i	$-0.527958\pi$
$757$	−4.82700			−0.175440			−0.0877202	+	0.996145i	$0.527958\pi$
$758$	−16.9114	−	9.76383i	−0.614251	−	0.354638i
$759$	−2.75447	−	5.99926i	−0.0999808	−	0.217759i
$760$	3.84933	+	6.66724i	0.139630	+	0.241846i
$761$	10.4988	−	18.1845i	0.380582	−	0.659187i	−0.610564	−	0.791967i	$-0.709057\pi$
$761$	10.4988	−	18.1845i	0.380582	−	0.659187i	0.991146	+	0.132780i	$0.0423904\pi$
$762$	2.57061	−	27.5093i	0.0931235	−	0.996557i
$763$	−15.4373	−	15.2437i	−0.558869	−	0.551860i
$764$		−	11.2544i		−	0.407171i
$765$	1.14066	−	1.32721i	0.0412405	−	0.0479854i
$766$	−37.9879	+	21.9323i	−1.37256	+	0.792448i
$767$	22.5672	−	13.0292i	0.814854	−	0.470456i
$768$	10.5058	−	14.8167i	0.379094	−	0.534652i
$769$			18.9829i			0.684540i	0.939602	+	0.342270i	$0.111196\pi$
$769$			18.9829i			0.684540i	−0.939602	+	0.342270i	$0.888804\pi$
$770$	−1.72943	+	6.62113i	−0.0623242	+	0.238609i
$771$	46.9135	+	4.38384i	1.68955	+	0.157880i
$772$	1.42221	−	2.46334i	0.0511865	−	0.0886577i
$773$	−6.40223	−	11.0890i	−0.230272	−	0.398843i	0.727616	−	0.685985i	$-0.240628\pi$
$773$	−6.40223	−	11.0890i	−0.230272	−	0.398843i	−0.957888	+	0.287141i	$0.907295\pi$
$774$	−27.8690	+	9.77214i	−1.00173	+	0.351252i
$775$	−13.1058	−	7.56666i	−0.470776	−	0.271803i
$776$	−21.0713			−0.756415
$777$	−9.06973	+	1.60299i	−0.325375	+	0.0575071i
$778$	40.7323			1.46032
$779$	−28.0917	−	16.2188i	−1.00649	−	0.581098i
$780$	2.53327	−	1.16311i	0.0907055	−	0.0416460i
$781$	−19.2428	−	33.3296i	−0.688563	−	1.19263i
$782$	−0.660231	+	1.14355i	−0.0236098	+	0.0408934i
$783$	−6.21243	+	21.6432i	−0.222014	+	0.773464i
$784$	−0.252389	−	19.9992i	−0.00901391	−	0.714255i
$785$		−	9.13701i		−	0.326114i
$786$	−27.2237	−	19.3029i	−0.971035	−	0.688512i
$787$	−14.5438	+	8.39687i	−0.518431	+	0.299316i	−0.736292	−	0.676664i	$-0.763425\pi$
$787$	−14.5438	+	8.39687i	−0.518431	+	0.299316i	0.217862	+	0.975980i	$0.430092\pi$
$788$	0.639486	−	0.369207i	0.0227807	−	0.0131525i
$789$	−1.17835	−	0.835507i	−0.0419503	−	0.0297448i
$790$		−	1.34079i		−	0.0477030i
$791$	−6.64118	−	24.1741i	−0.236133	−	0.859531i
$792$	34.3116	+	6.46899i	1.21921	+	0.229865i
$793$	−15.8623	+	27.4743i	−0.563286	+	0.975641i
$794$	15.4975	+	26.8425i	0.549986	+	0.952603i
$795$	1.11119	−	0.510184i	0.0394097	−	0.0180944i
$796$	−6.58713	−	3.80308i	−0.233475	−	0.134797i
$797$	16.0474			0.568429			0.284215	−	0.958761i	$-0.408267\pi$
$797$	16.0474			0.568429			0.284215	+	0.958761i	$0.408267\pi$
$798$	8.93451	−	24.5781i	0.316278	−	0.870054i
$799$	−4.02156			−0.142273
$800$	10.4452	+	6.03056i	0.369295	+	0.213212i
$801$	−12.4020	−	35.3691i	−0.438203	−	1.24971i
$802$	−9.12723	−	15.8088i	−0.322294	−	0.558229i
$803$	21.3738	−	37.0205i	0.754265	−	1.30643i
$804$	7.03649	+	0.657526i	0.248158	+	0.0231892i
$805$	1.01788	−	1.03080i	0.0358754	−	0.0363310i
$806$			25.2892i			0.890775i
$807$	21.1488	−	29.8270i	0.744473	−	1.04996i
$808$	−9.93233	+	5.73443i	−0.349418	+	0.201737i
$809$	17.5345	−	10.1235i	0.616479	−	0.355924i	−0.159018	−	0.987276i	$-0.550833\pi$
$809$	17.5345	−	10.1235i	0.616479	−	0.355924i	0.775497	+	0.631352i	$0.217499\pi$
$810$	−3.81434	−	4.77029i	−0.134022	−	0.167611i
$811$			17.8989i			0.628517i	0.949337	+	0.314259i	$0.101756\pi$
$811$			17.8989i			0.628517i	−0.949337	+	0.314259i	$0.898244\pi$
$812$	3.73638	−	3.78383i	0.131121	−	0.132786i
$813$	−0.626747	+	6.70711i	−0.0219810	+	0.235229i
$814$	4.74712	−	8.22225i	0.166386	−	0.288190i
$815$	1.94305	+	3.36547i	0.0680622	+	0.117887i
$816$	−2.19996	−	4.79155i	−0.0770142	−	0.167738i
$817$	31.6706	+	18.2850i	1.10801	+	0.639713i
$818$	−11.3184			−0.395740
$819$	−45.4692	−	21.5083i	−1.58882	−	0.751560i
$820$	1.78914			0.0624793
$821$	29.4993	+	17.0314i	1.02953	+	0.594401i	0.916851	−	0.399230i	$-0.130722\pi$
$821$	29.4993	+	17.0314i	1.02953	+	0.594401i	0.112682	+	0.993631i	$0.464056\pi$
$822$	4.24829	+	9.25283i	0.148176	+	0.322730i
$823$	−4.67941	−	8.10498i	−0.163114	−	0.282522i	0.772870	−	0.634564i	$-0.218821\pi$
$823$	−4.67941	−	8.10498i	−0.163114	−	0.282522i	−0.935984	+	0.352043i	$0.885487\pi$
$824$	−27.7539	+	48.0711i	−0.966852	+	1.67464i
$825$	−2.88682	+	30.8932i	−0.100506	+	1.07556i
$826$	3.57206	+	13.0024i	0.124288	+	0.452411i
$827$			34.5150i			1.20021i	0.799923	+	0.600103i	$0.204874\pi$
$827$			34.5150i			1.20021i	−0.799923	+	0.600103i	$0.795126\pi$
$828$	−1.05526	−	0.906934i	−0.0366729	−	0.0315181i
$829$	5.66067	−	3.26819i	0.196603	−	0.113509i	−0.398467	−	0.917183i	$-0.630458\pi$
$829$	5.66067	−	3.26819i	0.196603	−	0.113509i	0.595070	+	0.803674i	$0.297124\pi$
$830$	3.12416	−	1.80374i	0.108441	−	0.0626086i
$831$	−14.7417	+	20.7908i	−0.511383	+	0.721223i
$832$		−	56.3690i		−	1.95424i
$833$	6.50505	+	3.64703i	0.225387	+	0.126362i
$834$	−8.17928	−	0.764314i	−0.283225	−	0.0264660i
$835$	−4.59382	+	7.95672i	−0.158976	+	0.275354i
$836$	−4.06963	−	7.04880i	−0.140751	−	0.243788i
$837$	−16.2343	+	4.04299i	−0.561140	+	0.139746i
$838$	−0.208624	−	0.120449i	−0.00720679	−	0.00416084i
$839$	13.9472			0.481512			0.240756	−	0.970586i	$-0.422605\pi$
$839$	13.9472			0.481512			0.240756	+	0.970586i	$0.422605\pi$
$840$	1.33357	+	7.54534i	0.0460126	+	0.260339i
$841$	10.2214			0.352464
$842$	35.8798	+	20.7152i	1.23650	+	0.713894i
$843$	−42.3835	+	19.4597i	−1.45977	+	0.670229i
$844$	−4.43837	−	7.68749i	−0.152775	−	0.264614i
$845$	7.43555	−	12.8787i	0.255791	−	0.443042i
$846$	−2.60043	+	13.7927i	−0.0894046	+	0.474203i
$847$	2.35765	−	9.02629i	0.0810097	−	0.310147i
$848$		−	3.68377i		−	0.126501i
$849$	−14.4029	−	10.2124i	−0.494306	−	0.350488i
$850$	5.37493	−	3.10322i	0.184358	−	0.106439i
$851$	−1.74058	+	1.00493i	−0.0596664	+	0.0344484i
$852$	−6.61738	−	4.69204i	−0.226708	−	0.160747i
$853$			22.4565i			0.768895i	0.923147	+	0.384447i	$0.125608\pi$
$853$			22.4565i			0.768895i	−0.923147	+	0.384447i	$0.874392\pi$
$854$	−11.6810	−	11.5345i	−0.399715	−	0.394703i
$855$	−1.40126	+	7.43228i	−0.0479220	+	0.254179i
$856$	22.2161	−	38.4794i	0.759331	−	1.31520i
$857$	−11.1858	−	19.3744i	−0.382100	−	0.661817i	0.609262	−	0.792969i	$-0.291466\pi$
$857$	−11.1858	−	19.3744i	−0.382100	−	0.661817i	−0.991362	+	0.131152i	$0.958132\pi$
$858$	47.1210	−	21.6349i	1.60869	−	0.738603i
$859$	21.8186	+	12.5970i	0.744441	+	0.429803i	0.823682	−	0.567053i	$-0.191916\pi$
$859$	21.8186	+	12.5970i	0.744441	+	0.429803i	−0.0792411	+	0.996855i	$0.525250\pi$
$860$	−2.01707			−0.0687816
$861$	−20.7618	−	24.7228i	−0.707562	−	0.842552i
$862$	14.4944			0.493680
$863$	10.4439	+	6.02980i	0.355515	+	0.205257i	0.667112	−	0.744958i	$-0.267530\pi$
$863$	10.4439	+	6.02980i	0.355515	+	0.205257i	−0.311597	+	0.950215i	$0.600864\pi$
$864$	12.9386	−	3.22223i	0.440180	−	0.109622i
$865$	3.17084	+	5.49205i	0.107812	+	0.186735i
$866$	−14.8946	+	25.7982i	−0.506139	+	0.876658i
$867$	−27.3597	−	2.55664i	−0.929185	−	0.0868279i
$868$	3.82278	+	0.998503i	0.129754	+	0.0338914i
$869$			7.52997i			0.255437i
$870$	2.94622	−	4.15517i	0.0998862	−	0.140873i
$871$	48.2798	−	27.8744i	1.63590	−	0.944487i
$872$	21.6858	−	12.5203i	0.734374	−	0.423991i
$873$	−15.6992	−	13.4925i	−0.531338	−	0.456652i
$874$		−	5.70675i		−	0.193034i
$875$	−13.5503	+	3.72258i	−0.458083	+	0.125846i
$876$	0.838322	−	8.97127i	0.0283243	−	0.303111i
$877$	−13.4006	+	23.2105i	−0.452505	+	0.783761i	−0.998541	−	0.0540002i	$-0.982803\pi$
$877$	−13.4006	+	23.2105i	−0.452505	+	0.783761i	0.546036	+	0.837762i	$0.316136\pi$
$878$	7.34788	+	12.7269i	0.247979	+	0.429512i
$879$	7.67878	+	16.7245i	0.258999	+	0.564102i
$880$	−5.16382	−	2.98134i	−0.174072	−	0.100501i
$881$	33.2685			1.12084			0.560421	−	0.828208i	$-0.310639\pi$
$881$	33.2685			1.12084			0.560421	+	0.828208i	$0.310639\pi$
$882$	16.7145	−	19.9521i	0.562806	−	0.671821i
$883$	23.6137			0.794665			0.397332	−	0.917675i	$-0.369936\pi$
$883$	23.6137			0.794665			0.397332	+	0.917675i	$0.369936\pi$
$884$	2.71190	+	1.56571i	0.0912110	+	0.0526607i
$885$	−1.62717	−	3.54400i	−0.0546969	−	0.119130i
$886$	10.0634	+	17.4303i	0.338086	+	0.585582i
$887$	21.3836	−	37.0376i	0.717993	−	1.24360i	−0.243801	−	0.969825i	$-0.578394\pi$
$887$	21.3836	−	37.0376i	0.717993	−	1.24360i	0.961794	−	0.273774i	$-0.0882722\pi$
$888$	0.989062	−	10.5844i	0.0331907	−	0.355189i
$889$	−32.8348	+	9.02049i	−1.10124	+	0.302537i
$890$			8.47859i			0.284203i
$891$	21.4217	+	26.7904i	0.717653	+	0.897511i
$892$	7.47034	−	4.31301i	0.250126	−	0.144410i
$893$	15.0518	−	8.69016i	0.503689	−	0.290805i
$894$	−17.9716	+	25.3460i	−0.601059	+	0.847697i
$895$		−	4.75718i		−	0.159015i
$896$	15.0841	+	3.93994i	0.503925	+	0.131624i
$897$	−10.9287	−	1.02123i	−0.364898	−	0.0340980i
$898$	−26.1482	+	45.2900i	−0.872577	+	1.51135i
$899$	−6.97621	−	12.0831i	−0.232670	−	0.402996i
$900$	2.16405	+	6.17164i	0.0721352	+	0.205721i
$901$	1.18954	+	0.686782i	0.0396293	+	0.0228800i
$902$	33.2795			1.10809
$903$	23.4069	+	27.8725i	0.778933	+	0.927539i
$904$	28.9355			0.962379
$905$	−4.52251	−	2.61107i	−0.150333	−	0.0867950i
$906$	−13.1524	+	6.03873i	−0.436960	+	0.200623i
$907$	−27.7607	−	48.0829i	−0.921779	−	1.59657i	−0.796662	−	0.604426i	$-0.793403\pi$
$907$	−27.7607	−	48.0829i	−0.921779	−	1.59657i	−0.125117	−	0.992142i	$-0.539931\pi$
$908$	−5.74115	+	9.94396i	−0.190527	+	0.330002i
$909$	−11.0720	−	2.08748i	−0.367236	−	0.0692375i
$910$	8.09641	+	7.99488i	0.268393	+	0.265028i
$911$		−	13.5029i		−	0.447372i	−0.974661	−	0.223686i	$-0.928191\pi$
$911$		−	13.5029i		−	0.447372i	0.974661	−	0.223686i	$-0.0718090\pi$
$912$	18.5880	+	13.1798i	0.615510	+	0.436427i
$913$	−17.5456	+	10.1299i	−0.580673	+	0.335252i
$914$	−30.7053	+	17.7277i	−1.01564	+	0.586380i
$915$	3.87290	+	2.74608i	0.128034	+	0.0907825i
$916$		−	10.7426i		−	0.354944i
$917$	−10.3943	+	39.7947i	−0.343250	+	1.31414i
$918$	1.89303	−	6.59501i	0.0624791	−	0.217668i
$919$	−6.35325	+	11.0041i	−0.209574	+	0.362993i	−0.951580	−	0.307400i	$-0.900541\pi$
$919$	−6.35325	+	11.0041i	−0.209574	+	0.362993i	0.742006	+	0.670393i	$0.233874\pi$
$920$	0.836023	+	1.44803i	0.0275629	+	0.0477403i
$921$	0.312515	−	0.143486i	0.0102977	−	0.00472803i
$922$	−12.6236	−	7.28826i	−0.415737	−	0.240026i
$923$	−63.9912			−2.10629
$924$	−1.40989	−	7.97716i	−0.0463820	−	0.262429i
$925$	9.44670			0.310605
$926$	25.9766	+	14.9976i	0.853646	+	0.492852i
$927$	−51.4594	+	18.0440i	−1.69015	+	0.592642i
$928$	5.55997	+	9.63016i	0.182515	+	0.316125i
$929$	1.72148	−	2.98169i	0.0564799	−	0.0978260i	−0.836403	−	0.548115i	$-0.815346\pi$
$929$	1.72148	−	2.98169i	0.0564799	−	0.0978260i	0.892883	+	0.450289i	$0.148679\pi$
$930$	3.76818	+	0.352118i	0.123563	+	0.0115464i
$931$	−32.2278	+	0.406715i	−1.05622	+	0.0133295i
$932$			12.7552i			0.417810i
$933$	6.50799	−	9.17848i	0.213062	−	0.300490i
$934$	38.1610	−	22.0323i	1.24867	−	0.720918i
$935$	1.92543	−	1.11165i	0.0629682	−	0.0363547i
$936$	37.8405	−	44.0293i	1.23685	−	1.43914i
$937$			18.7536i			0.612654i	0.951926	+	0.306327i	$0.0991001\pi$
$937$			18.7536i			0.612654i	−0.951926	+	0.306327i	$0.900900\pi$
$938$	7.64200	+	27.8171i	0.249520	+	0.908259i
$939$	4.71998	−	50.5107i	0.154031	−	1.64835i
$940$	−0.479317	+	0.830202i	−0.0156336	+	0.0270782i
$941$	−6.38634	−	11.0615i	−0.208189	−	0.360593i	0.742955	−	0.669341i	$-0.233423\pi$
$941$	−6.38634	−	11.0615i	−0.208189	−	0.360593i	−0.951144	+	0.308748i	$0.900090\pi$
$942$	−14.9476	−	32.5560i	−0.487019	−	1.06073i
$943$	−6.10115	−	3.52250i	−0.198681	−	0.114708i
$944$	−11.7490			−0.382397
$945$	−3.83790	+	6.47560i	−0.124847	+	0.210651i
$946$	−37.5193			−1.21986
$947$	26.1686	+	15.1085i	0.850366	+	0.490959i	0.860774	−	0.508987i	$-0.169980\pi$
$947$	26.1686	+	15.1085i	0.850366	+	0.490959i	−0.0104083	+	0.999946i	$0.503313\pi$
$948$	0.662257	+	1.44240i	0.0215091	+	0.0468470i
$949$	−35.5388	−	61.5550i	−1.15364	−	1.99816i
$950$	−13.4114	+	23.2293i	−0.435124	+	0.753657i
$951$	−1.79950	+	19.2573i	−0.0583527	+	0.624459i
$952$	−6.04798	+	6.12479i	−0.196016	+	0.198505i
$953$			2.80134i			0.0907444i	0.998970	+	0.0453722i	$0.0144474\pi$
$953$			2.80134i			0.0907444i	−0.998970	+	0.0453722i	$0.985553\pi$
$954$	3.12463	−	3.63566i	0.101164	−	0.117709i
$955$	−11.5061	+	6.64306i	−0.372329	+	0.214964i
$956$	−9.21030	+	5.31757i	−0.297882	+	0.171983i
$957$	−16.5462	+	23.3358i	−0.534863	+	0.754339i
$958$		−	26.0594i		−	0.841940i
$959$	8.81669	−	8.92866i	0.284706	−	0.288321i
$960$	−8.39917	−	0.784862i	−0.271082	−	0.0253313i
$961$	−10.3167	+	17.8690i	−0.332797	+	0.576421i
$962$	−7.89316	−	13.6714i	−0.254486	−	0.440782i
$963$	41.1916	−	14.4436i	1.32738	−	0.465440i
$964$	0.627005	+	0.362001i	0.0201945	+	0.0116593i
$965$	−3.35791			−0.108095
$966$	1.94046	−	5.33803i	0.0624332	−	0.171748i
$967$	−43.3260			−1.39327			−0.696636	−	0.717425i	$-0.745321\pi$
$967$	−43.3260			−1.39327			−0.696636	+	0.717425i	$0.745321\pi$
$968$	9.32507	+	5.38383i	0.299719	+	0.173043i
$969$	−7.72137	+	3.54515i	−0.248046	+	0.113887i
$970$	2.34138	+	4.05539i	0.0751771	+	0.130211i
$971$	−0.0862921	+	0.149462i	−0.00276925	+	0.00479648i	−0.867407	−	0.497600i	$-0.834215\pi$
$971$	−0.0862921	+	0.149462i	−0.00276925	+	0.00479648i	0.864637	+	0.502396i	$0.167548\pi$
$972$	6.45962	+	3.24780i	0.207193	+	0.104173i
$973$	2.68204	+	9.76269i	0.0859822	+	0.312977i
$974$		−	35.0298i		−	1.12243i
$975$	42.0851	+	29.8404i	1.34780	+	0.955657i
$976$	12.3874	−	7.15186i	0.396511	−	0.228925i
$977$	19.0647	−	11.0070i	0.609933	−	0.352145i	−0.163006	−	0.986625i	$-0.552119\pi$
$977$	19.0647	−	11.0070i	0.609933	−	0.352145i	0.772939	+	0.634480i	$0.218786\pi$
$978$	12.4290	+	8.81275i	0.397435	+	0.281801i
$979$		−	47.6165i		−	1.52183i
$980$	1.52820	−	0.908210i	0.0488166	−	0.0290117i
$981$	24.1742	+	4.55772i	0.771822	+	0.145517i
$982$	6.43758	−	11.1502i	0.205431	−	0.355818i
$983$	−12.1030	−	20.9630i	−0.386026	−	0.668617i	0.605885	−	0.795552i	$-0.292819\pi$
$983$	−12.1030	−	20.9630i	−0.386026	−	0.668617i	−0.991911	+	0.126935i	$0.959486\pi$
$984$	33.8637	−	15.5480i	1.07954	−	0.495652i
$985$	−0.754928	−	0.435858i	−0.0240540	−	0.0138876i
$986$	5.72212			0.182229
$987$	17.0342	−	3.01064i	0.542204	−	0.0958296i
$988$	−13.5334			−0.430554
$989$	6.87843	+	3.97127i	0.218722	+	0.126279i
$990$	−2.56758	−	7.32243i	−0.0816029	−	0.232722i
$991$	27.7487	+	48.0622i	0.881467	+	1.52675i	0.849710	+	0.527250i	$0.176777\pi$
$991$	27.7487	+	48.0622i	0.881467	+	1.52675i	0.0317570	+	0.999496i	$0.489890\pi$
$992$	−4.13105	+	7.15518i	−0.131161	+	0.227177i
$993$	1.00084	+	0.0935232i	0.0317605	+	0.00296787i
$994$	8.36824	−	32.0379i	0.265425	−	1.01618i
$995$			8.97926i			0.284662i
$996$	−2.47002	+	3.48356i	−0.0782654	+	0.110381i
$997$	17.8870	−	10.3271i	0.566488	−	0.327062i	−0.189257	−	0.981927i	$-0.560608\pi$
$997$	17.8870	−	10.3271i	0.566488	−	0.327062i	0.755745	+	0.654866i	$0.227275\pi$
$998$	−31.5253	+	18.2011i	−0.997915	+	0.576146i
$999$	7.51439	−	7.25262i	0.237745	−	0.229463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.n.a.47.18	✓	116
3.2	odd	2	inner	483.2.n.a.47.41	yes	116
7.3	odd	6	inner	483.2.n.a.185.41	yes	116
21.17	even	6	inner	483.2.n.a.185.18	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.n.a.47.18	✓	116	1.1	even	1	trivial
483.2.n.a.47.41	yes	116	3.2	odd	2	inner
483.2.n.a.185.18	yes	116	21.17	even	6	inner
483.2.n.a.185.41	yes	116	7.3	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07338 - 0.619715i) q^{2} +(-0.722709 - 1.57407i) q^{3} +(-0.231907 - 0.401675i) q^{4} +(-0.273772 + 0.474187i) q^{5} +(-0.199734 + 2.13744i) q^{6} +(2.55123 - 0.700882i) q^{7} +3.05372i q^{8} +(-1.95538 + 2.27519i) q^{9} +(0.587721 - 0.339321i) q^{10} +(-3.30069 + 1.90565i) q^{11} +(-0.464662 + 0.655331i) q^{12} +6.33716i q^{13} +(-3.17278 - 0.828723i) q^{14} +(0.944259 + 0.0882365i) q^{15} +(1.42862 - 2.47445i) q^{16} +(0.532689 + 0.922645i) q^{17} +(3.50883 - 1.23036i) q^{18} +(-3.98747 - 2.30217i) q^{19} +0.253958 q^{20} +(-2.94703 - 3.50927i) q^{21} +4.72385 q^{22} +(-0.866025 - 0.500000i) q^{23} +(4.80677 - 2.20695i) q^{24} +(2.35010 + 4.07049i) q^{25} +(3.92724 - 6.80217i) q^{26} +(4.99447 + 1.43361i) q^{27} +(-0.873174 - 0.862224i) q^{28} +4.33342i q^{29} +(-0.958865 - 0.679883i) q^{30} +(-2.78836 + 1.60986i) q^{31} +(2.22230 - 1.28304i) q^{32} +(5.38507 + 3.81828i) q^{33} -1.32046i q^{34} +(-0.366105 + 1.40164i) q^{35} +(1.36735 + 0.257796i) q^{36} +(1.00493 - 1.74058i) q^{37} +(2.85338 + 4.94219i) q^{38} +(9.97513 - 4.57993i) q^{39} +(-1.44803 - 0.836023i) q^{40} +7.04500 q^{41} +(0.988529 + 5.59310i) q^{42} -7.94253 q^{43} +(1.53091 + 0.883869i) q^{44} +(-0.543535 - 1.55010i) q^{45} +(0.619715 + 1.07338i) q^{46} +(-1.88739 + 3.26905i) q^{47} +(-4.92743 - 0.460445i) q^{48} +(6.01753 - 3.57622i) q^{49} -5.82556i q^{50} +(1.06733 - 1.50529i) q^{51} +(2.54548 - 1.46963i) q^{52} +(1.11654 - 0.644636i) q^{53} +(-4.47253 - 4.63395i) q^{54} -2.08686i q^{55} +(2.14030 + 7.79075i) q^{56} +(-0.741988 + 7.94035i) q^{57} +(2.68549 - 4.65140i) q^{58} +(-2.05599 - 3.56109i) q^{59} +(-0.183538 - 0.399748i) q^{60} +(4.33542 + 2.50306i) q^{61} +3.99062 q^{62} +(-3.39399 + 7.17501i) q^{63} -8.89499 q^{64} +(-3.00500 - 1.73494i) q^{65} +(-3.41397 - 7.43566i) q^{66} +(-4.39855 - 7.61852i) q^{67} +(0.247069 - 0.427935i) q^{68} +(-0.161150 + 1.72454i) q^{69} +(1.26159 - 1.27761i) q^{70} +10.0978i q^{71} +(-6.94779 - 5.97120i) q^{72} +(-9.71333 + 5.60799i) q^{73} +(-2.15733 + 1.24553i) q^{74} +(4.70879 - 6.64100i) q^{75} +2.13555i q^{76} +(-7.08517 + 7.17515i) q^{77} +(-13.5453 - 1.26575i) q^{78} +(0.987846 - 1.71100i) q^{79} +(0.782234 + 1.35487i) q^{80} +(-1.35295 - 8.89773i) q^{81} +(-7.56194 - 4.36589i) q^{82} +5.31573 q^{83} +(-0.726149 + 1.99757i) q^{84} -0.583341 q^{85} +(8.52534 + 4.92211i) q^{86} +(6.82110 - 3.13180i) q^{87} +(-5.81934 - 10.0794i) q^{88} +(-6.24674 + 10.8197i) q^{89} +(-0.377201 + 2.00068i) q^{90} +(4.44161 + 16.1676i) q^{91} +0.463814i q^{92} +(4.54921 + 3.22561i) q^{93} +(4.05176 - 2.33928i) q^{94} +(2.18331 - 1.26054i) q^{95} +(-3.62567 - 2.57078i) q^{96} +6.90019i q^{97} +(-8.67532 + 0.109483i) q^{98} +(2.11839 - 11.2360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q + 56 q^{4} - 10 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 20 q^{15} - 52 q^{16} - 10 q^{18} + 6 q^{19} - 6 q^{21} - 16 q^{22} - 66 q^{25} + 16 q^{28} - 32 q^{30} - 42 q^{31} - 30 q^{33} + 8 q^{36}+ \cdots + 24 q^{99}+O(q^{100}) \) 116 * q + 56 * q^4 - 10 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 20 * q^15 - 52 * q^16 - 10 * q^18 + 6 * q^19 - 6 * q^21 - 16 * q^22 - 66 * q^25 + 16 * q^28 - 32 * q^30 - 42 * q^31 - 30 * q^33 + 8 * q^36 - 2 * q^37 - 22 * q^39 - 36 * q^40 + 46 * q^42 + 20 * q^43 + 30 * q^45 - 22 * q^49 + 12 * q^51 + 48 * q^52 - 54 * q^54 - 44 * q^57 + 52 * q^58 + 32 * q^60 + 36 * q^61 - 38 * q^63 - 160 * q^64 + 10 * q^67 - 20 * q^70 + 62 * q^72 + 18 * q^73 + 78 * q^75 + 12 * q^78 + 10 * q^79 - 28 * q^81 + 32 * q^84 - 32 * q^85 - 30 * q^87 - 36 * q^88 + 50 * q^91 + 60 * q^94 + 84 * q^96 + 24 * q^99

Introduction

L-functions

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