LMFDB - Embedded newform 117.2.z.b.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(5,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("117.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.z (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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	117.47
Dual form			117.2.z.b.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.337526 - 1.25966i) q^{2} +(0.425920 - 1.67887i) q^{3} +(0.259225 - 0.149663i) q^{4} +(2.31922 + 0.621434i) q^{5} +(-2.25856 + 0.0301452i) q^{6} +(0.940006 + 3.50815i) q^{7} +(-2.12029 - 2.12029i) q^{8} +(-2.63718 - 1.43012i) q^{9} -3.13119i q^{10} +(-3.85792 + 1.03373i) q^{11} +(-0.140856 - 0.498948i) q^{12} +(-2.31409 + 2.76496i) q^{13} +(4.10181 - 2.36818i) q^{14} +(2.03111 - 3.62898i) q^{15} +(-1.65587 + 2.86806i) q^{16} +1.19872 q^{17} +(-0.911357 + 3.80467i) q^{18} +(2.52470 + 2.52470i) q^{19} +(0.694206 - 0.186012i) q^{20} +(6.29008 - 0.0839540i) q^{21} +(2.60430 + 4.51077i) q^{22} +(-2.51605 - 4.35793i) q^{23} +(-4.46277 + 2.65662i) q^{24} +(0.662484 + 0.382485i) q^{25} +(4.26398 + 1.98173i) q^{26} +(-3.52422 + 3.81836i) q^{27} +(0.768714 + 0.768714i) q^{28} +(2.60252 + 1.50257i) q^{29} +(-5.25684 - 1.33363i) q^{30} +(0.972844 - 3.63070i) q^{31} +(-1.62107 - 0.434363i) q^{32} +(0.0923245 + 6.91722i) q^{33} +(-0.404598 - 1.50998i) q^{34} +8.72033i q^{35} +(-0.897661 + 0.0239665i) q^{36} +(6.60194 - 6.60194i) q^{37} +(2.32812 - 4.03242i) q^{38} +(3.65637 + 5.06270i) q^{39} +(-3.59981 - 6.23506i) q^{40} +(8.58903 + 2.30142i) q^{41} +(-2.22882 - 7.89504i) q^{42} +(-6.32334 - 3.65078i) q^{43} +(-0.845358 + 0.845358i) q^{44} +(-5.22749 - 4.95561i) q^{45} +(-4.64029 + 4.64029i) q^{46} +(-6.61179 + 1.77162i) q^{47} +(4.10982 + 4.00156i) q^{48} +(-5.36132 + 3.09536i) q^{49} +(0.258197 - 0.963605i) q^{50} +(0.510558 - 2.01249i) q^{51} +(-0.186057 + 1.06308i) q^{52} -3.58842i q^{53} +(5.99936 + 3.15053i) q^{54} -9.58978 q^{55} +(5.44522 - 9.43140i) q^{56} +(5.31395 - 3.16331i) q^{57} +(1.01431 - 3.78545i) q^{58} +(-1.46044 + 5.45044i) q^{59} +(-0.0166131 - 1.24470i) q^{60} +(6.49962 - 11.2577i) q^{61} -4.90182 q^{62} +(2.53812 - 10.5960i) q^{63} +8.81210i q^{64} +(-7.08513 + 4.97449i) q^{65} +(8.68221 - 2.45104i) q^{66} +(1.44883 - 5.40710i) q^{67} +(0.310738 - 0.179404i) q^{68} +(-8.38802 + 2.36799i) q^{69} +(10.9847 - 2.94333i) q^{70} +(-4.22627 + 4.22627i) q^{71} +(2.55932 + 8.62389i) q^{72} +(-0.654952 + 0.654952i) q^{73} +(-10.5445 - 6.08790i) q^{74} +(0.924306 - 0.949314i) q^{75} +(1.03232 + 0.276609i) q^{76} +(-7.25294 - 12.5625i) q^{77} +(5.14317 - 6.31459i) q^{78} +(-2.49772 + 4.32618i) q^{79} +(-5.62265 + 5.62265i) q^{80} +(4.90949 + 7.54301i) q^{81} -11.5961i q^{82} +(-0.422504 - 1.57681i) q^{83} +(1.61798 - 0.963158i) q^{84} +(2.78010 + 0.744924i) q^{85} +(-2.46447 + 9.19751i) q^{86} +(3.63107 - 3.72931i) q^{87} +(10.3717 + 5.98813i) q^{88} +(8.82992 + 8.82992i) q^{89} +(-4.47799 + 8.25752i) q^{90} +(-11.8751 - 5.51910i) q^{91} +(-1.30445 - 0.753122i) q^{92} +(-5.68111 - 3.17966i) q^{93} +(4.46330 + 7.73066i) q^{94} +(4.28640 + 7.42427i) q^{95} +(-1.41968 + 2.53655i) q^{96} +(-13.1504 + 3.52364i) q^{97} +(5.70869 + 5.70869i) q^{98} +(11.6524 + 2.79118i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.337526	−	1.25966i	−0.238667	−	0.890716i	−0.976462	−	0.215691i	$-0.930800\pi$
$2$	−0.337526	−	1.25966i	−0.238667	−	0.890716i	0.737795	−	0.675025i	$-0.235867\pi$
$3$	0.425920	−	1.67887i	0.245905	−	0.969294i
$3$	0.425920	−	1.67887i	0.245905	−	0.969294i
$4$	0.259225	−	0.149663i	0.129612	−	0.0748317i
$5$	2.31922	+	0.621434i	1.03719	+	0.277914i	0.736947	−	0.675950i	$-0.236267\pi$
$5$	2.31922	+	0.621434i	1.03719	+	0.277914i	0.300240	+	0.953864i	$0.402933\pi$
$6$	−2.25856	+	0.0301452i	−0.922055	+	0.0123067i
$7$	0.940006	+	3.50815i	0.355289	+	1.32596i	0.880121	+	0.474750i	$0.157461\pi$
$7$	0.940006	+	3.50815i	0.355289	+	1.32596i	−0.524832	+	0.851206i	$0.675872\pi$
$8$	−2.12029	−	2.12029i	−0.749637	−	0.749637i
$9$	−2.63718	−	1.43012i	−0.879062	−	0.476708i
$10$		−	3.13119i		−	0.990168i
$11$	−3.85792	+	1.03373i	−1.16321	+	0.311681i	−0.788246	−	0.615360i	$-0.789011\pi$
$11$	−3.85792	+	1.03373i	−1.16321	+	0.311681i	−0.374961	+	0.927040i	$0.622344\pi$
$12$	−0.140856	−	0.498948i	−0.0406616	−	0.144034i
$13$	−2.31409	+	2.76496i	−0.641813	+	0.766861i
$13$	−2.31409	+	2.76496i	−0.641813	+	0.766861i
$14$	4.10181	−	2.36818i	1.09625	−	0.632923i
$15$	2.03111	−	3.62898i	0.524429	−	0.936999i
$16$	−1.65587	+	2.86806i	−0.413969	+	0.717015i
$17$	1.19872			0.290732			0.145366	−	0.989378i	$-0.453564\pi$
$17$	1.19872			0.290732			0.145366	+	0.989378i	$0.453564\pi$
$18$	−0.911357	+	3.80467i	−0.214809	+	0.896768i
$19$	2.52470	+	2.52470i	0.579205	+	0.579205i	0.934684	−	0.355479i	$-0.115682\pi$
$19$	2.52470	+	2.52470i	0.579205	+	0.579205i	−0.355479	+	0.934684i	$0.615682\pi$
$20$	0.694206	−	0.186012i	0.155229	−	0.0415935i
$21$	6.29008	−	0.0839540i	1.37261	−	0.0183203i
$22$	2.60430	+	4.51077i	0.555238	+	0.961700i
$23$	−2.51605	−	4.35793i	−0.524633	−	0.908691i	−0.999589	−	0.0286816i	$-0.990869\pi$
$23$	−2.51605	−	4.35793i	−0.524633	−	0.908691i	0.474955	−	0.880010i	$-0.342464\pi$
$24$	−4.46277	+	2.65662i	−0.910958	+	0.542279i
$25$	0.662484	+	0.382485i	0.132497	+	0.0764970i
$26$	4.26398	+	1.98173i	0.836235	+	0.388649i
$27$	−3.52422	+	3.81836i	−0.678236	+	0.734844i
$28$	0.768714	+	0.768714i	0.145273	+	0.145273i
$29$	2.60252	+	1.50257i	0.483276	+	0.279020i	0.721781	−	0.692122i	$-0.243324\pi$
$29$	2.60252	+	1.50257i	0.483276	+	0.279020i	−0.238505	+	0.971141i	$0.576657\pi$
$30$	−5.25684	−	1.33363i	−0.959764	−	0.243487i
$31$	0.972844	−	3.63070i	0.174728	−	0.652094i	−0.821870	−	0.569675i	$-0.807069\pi$
$31$	0.972844	−	3.63070i	0.174728	−	0.652094i	0.996598	−	0.0824184i	$-0.0262644\pi$
$32$	−1.62107	−	0.434363i	−0.286567	−	0.0767853i
$33$	0.0923245	+	6.91722i	0.0160716	+	1.20413i
$34$	−0.404598	−	1.50998i	−0.0693880	−	0.258960i
$35$			8.72033i			1.47400i
$36$	−0.897661	+	0.0239665i	−0.149610	+	0.00399442i
$37$	6.60194	−	6.60194i	1.08535	−	1.08535i	0.0893530	−	0.996000i	$-0.471520\pi$
$37$	6.60194	−	6.60194i	1.08535	−	1.08535i	0.996000	−	0.0893530i	$-0.0284799\pi$
$38$	2.32812	−	4.03242i	0.377670	−	0.654144i
$39$	3.65637	+	5.06270i	0.585489	+	0.810681i
$40$	−3.59981	−	6.23506i	−0.569180	−	0.985849i
$41$	8.58903	+	2.30142i	1.34138	+	0.359422i	0.856946	−	0.515406i	$-0.172359\pi$
$41$	8.58903	+	2.30142i	1.34138	+	0.359422i	0.484434	+	0.874828i	$0.339025\pi$
$42$	−2.22882	−	7.89504i	−0.343914	−	1.21823i
$43$	−6.32334	−	3.65078i	−0.964301	−	0.556739i	−0.0668066	−	0.997766i	$-0.521281\pi$
$43$	−6.32334	−	3.65078i	−0.964301	−	0.556739i	−0.897494	+	0.441027i	$0.854614\pi$
$44$	−0.845358	+	0.845358i	−0.127443	+	0.127443i
$45$	−5.22749	−	4.95561i	−0.779268	−	0.738739i
$46$	−4.64029	+	4.64029i	−0.684173	+	0.684173i
$47$	−6.61179	+	1.77162i	−0.964429	+	0.258418i	−0.706474	−	0.707739i	$-0.749715\pi$
$47$	−6.61179	+	1.77162i	−0.964429	+	0.258418i	−0.257955	+	0.966157i	$0.583049\pi$
$48$	4.10982	+	4.00156i	0.593201	+	0.577575i
$49$	−5.36132	+	3.09536i	−0.765902	+	0.442194i
$50$	0.258197	−	0.963605i	0.0365146	−	0.136274i
$51$	0.510558	−	2.01249i	0.0714924	−	0.281805i
$52$	−0.186057	+	1.06308i	−0.0258014	+	0.147423i
$53$		−	3.58842i		−	0.492908i	−0.969155	−	0.246454i	$-0.920735\pi$
$53$		−	3.58842i		−	0.492908i	0.969155	−	0.246454i	$-0.0792654\pi$
$54$	5.99936	+	3.15053i	0.816410	+	0.428733i
$55$	−9.58978			−1.29309
$56$	5.44522	−	9.43140i	0.727648	−	1.26032i
$57$	5.31395	−	3.16331i	0.703850	−	0.418991i
$58$	1.01431	−	3.78545i	0.133185	−	0.497054i
$59$	−1.46044	+	5.45044i	−0.190133	+	0.709587i	0.803340	+	0.595521i	$0.203054\pi$
$59$	−1.46044	+	5.45044i	−0.190133	+	0.709587i	−0.993473	+	0.114066i	$0.963612\pi$
$60$	−0.0166131	−	1.24470i	−0.00214475	−	0.160691i
$61$	6.49962	−	11.2577i	0.832190	−	1.44140i	−0.0641071	−	0.997943i	$-0.520420\pi$
$61$	6.49962	−	11.2577i	0.832190	−	1.44140i	0.896298	−	0.443453i	$-0.146247\pi$
$62$	−4.90182			−0.622532
$63$	2.53812	−	10.5960i	0.319773	−	1.33497i
$64$			8.81210i			1.10151i
$65$	−7.08513	+	4.97449i	−0.878802	+	0.617010i
$66$	8.68221	−	2.45104i	1.06871	−	0.301702i
$67$	1.44883	−	5.40710i	0.177002	−	0.660582i	−0.819200	−	0.573509i	$-0.805582\pi$
$67$	1.44883	−	5.40710i	0.177002	−	0.660582i	0.996202	−	0.0870732i	$-0.0277514\pi$
$68$	0.310738	−	0.179404i	0.0376825	−	0.0217560i
$69$	−8.38802	+	2.36799i	−1.00980	+	0.285072i
$70$	10.9847	−	2.94333i	1.31292	−	0.351796i
$71$	−4.22627	+	4.22627i	−0.501566	+	0.501566i	−0.911924	−	0.410359i	$-0.865404\pi$
$71$	−4.22627	+	4.22627i	−0.501566	+	0.501566i	0.410359	+	0.911924i	$0.365404\pi$
$72$	2.55932	+	8.62389i	0.301619	+	1.01634i
$73$	−0.654952	+	0.654952i	−0.0766564	+	0.0766564i	−0.744395	−	0.667739i	$-0.767262\pi$
$73$	−0.654952	+	0.654952i	−0.0766564	+	0.0766564i	0.667739	+	0.744395i	$0.267262\pi$
$74$	−10.5445	−	6.08790i	−1.22578	−	0.707704i
$75$	0.924306	−	0.949314i	0.106730	−	0.109617i
$76$	1.03232	+	0.276609i	0.118415	+	0.0317292i
$77$	−7.25294	−	12.5625i	−0.826549	−	1.43163i
$78$	5.14317	−	6.31459i	0.582350	−	0.714986i
$79$	−2.49772	+	4.32618i	−0.281016	+	0.486734i	−0.971635	−	0.236485i	$-0.924005\pi$
$79$	−2.49772	+	4.32618i	−0.281016	+	0.486734i	0.690619	+	0.723218i	$0.257338\pi$
$80$	−5.62265	+	5.62265i	−0.628631	+	0.628631i
$81$	4.90949	+	7.54301i	0.545499	+	0.838112i
$82$		−	11.5961i		−	1.28057i
$83$	−0.422504	−	1.57681i	−0.0463758	−	0.173077i	0.938854	−	0.344317i	$-0.111889\pi$
$83$	−0.422504	−	1.57681i	−0.0463758	−	0.173077i	−0.985229	+	0.171240i	$0.945223\pi$
$84$	1.61798	−	0.963158i	0.176536	−	0.105089i
$85$	2.78010	+	0.744924i	0.301544	+	0.0807984i
$86$	−2.46447	+	9.19751i	−0.265750	+	0.991793i
$87$	3.63107	−	3.72931i	0.389292	−	0.399824i
$88$	10.3717	+	5.98813i	1.10563	+	0.638337i
$89$	8.82992	+	8.82992i	0.935970	+	0.935970i	0.998070	−	0.0620998i	$-0.0197797\pi$
$89$	8.82992	+	8.82992i	0.935970	+	0.935970i	−0.0620998	+	0.998070i	$0.519780\pi$
$90$	−4.47799	+	8.25752i	−0.472021	+	0.870419i
$91$	−11.8751	−	5.51910i	−1.24485	−	0.578559i
$92$	−1.30445	−	0.753122i	−0.135998	−	0.0785184i
$93$	−5.68111	−	3.17966i	−0.589104	−	0.329716i
$94$	4.46330	+	7.73066i	0.460354	+	0.797356i
$95$	4.28640	+	7.42427i	0.439776	+	0.761714i
$96$	−1.41968	+	2.53655i	−0.144896	+	0.258885i
$97$	−13.1504	+	3.52364i	−1.33522	+	0.357771i	−0.854659	−	0.519189i	$-0.826234\pi$
$97$	−13.1504	+	3.52364i	−1.33522	+	0.357771i	−0.480562	+	0.876961i	$0.659567\pi$
$98$	5.70869	+	5.70869i	0.576664	+	0.576664i
$99$	11.6524	+	2.79118i	1.17111	+	0.280524i
$100$	0.228976			0.0228976
$101$	−0.754854	+	1.30745i	−0.0751108	+	0.130096i	−0.901134	−	0.433540i	$-0.857264\pi$
$101$	−0.754854	+	1.30745i	−0.0751108	+	0.130096i	0.826024	+	0.563635i	$0.190598\pi$
$102$	−2.70738	+	0.0361356i	−0.268071	+	0.00357796i
$103$	3.53091	−	2.03857i	0.347910	−	0.200866i	−0.315854	−	0.948808i	$-0.602291\pi$
$103$	3.53091	−	2.03857i	0.347910	−	0.200866i	0.663765	+	0.747942i	$0.268958\pi$
$104$	10.7691	−	0.955966i	1.05599	−	0.0937402i
$105$	14.6403	+	3.71416i	1.42874	+	0.362465i
$106$	−4.52020	+	1.21118i	−0.439041	+	0.117641i
$107$		−	1.72856i		−	0.167106i	−0.996503	−	0.0835530i	$-0.973373\pi$
$107$		−	1.72856i		−	0.167106i	0.996503	−	0.0835530i	$-0.0266268\pi$
$108$	−0.342095	+	1.51726i	−0.0329181	+	0.145998i
$109$	11.4331	+	11.4331i	1.09509	+	1.09509i	0.994976	+	0.100114i	$0.0319206\pi$
$109$	11.4331	+	11.4331i	1.09509	+	1.09509i	0.100114	+	0.994976i	$0.468079\pi$
$110$	3.23679	+	12.0799i	0.308616	+	1.15177i
$111$	−8.27188	−	13.8957i	−0.785132	−	1.31892i
$112$	−11.6181	−	3.11306i	−1.09781	−	0.294157i
$113$	−6.85493	+	3.95770i	−0.644858	+	0.372309i	−0.786483	−	0.617611i	$-0.788100\pi$
$113$	−6.85493	+	3.95770i	−0.644858	+	0.372309i	0.141625	+	0.989920i	$0.454767\pi$
$114$	−5.77830	−	5.62608i	−0.541187	−	0.526931i
$115$	−3.12712	−	11.6706i	−0.291605	−	1.08829i
$116$	0.899517			0.0835181
$117$	10.0569	−	3.98226i	0.929762	−	0.368160i
$118$	7.35865			0.677419
$119$	1.12680	+	4.20528i	0.103294	+	0.385498i
$120$	−12.0011	+	3.38797i	−1.09554	+	0.309278i
$121$	4.28870	−	2.47608i	0.389882	−	0.225099i
$122$	−16.3746	−	4.38757i	−1.48249	−	0.397232i
$123$	7.52202	−	13.4396i	0.678237	−	1.21181i
$124$	−0.291199	−	1.08677i	−0.0261504	−	0.0975946i
$125$	−7.19018	−	7.19018i	−0.643110	−	0.643110i
$126$	−14.2040	+	0.379231i	−1.26539	+	0.0337846i
$127$			2.72187i			0.241527i	0.992681	+	0.120764i	$0.0385343\pi$
$127$			2.72187i			0.241527i	−0.992681	+	0.120764i	$0.961466\pi$
$128$	7.85814	−	2.10558i	0.694568	−	0.186109i
$129$	−8.82241	+	9.06111i	−0.776770	+	0.797786i
$130$	8.65759	+	7.24585i	0.759321	+	0.635503i
$131$	5.90384	−	3.40858i	0.515821	−	0.297809i	−0.219402	−	0.975634i	$-0.570411\pi$
$131$	5.90384	−	3.40858i	0.515821	−	0.297809i	0.735223	+	0.677825i	$0.237077\pi$
$132$	1.05919	+	1.77930i	0.0921905	+	0.154868i
$133$	−6.48378	+	11.2302i	−0.562215	+	0.973786i
$134$	−7.30013			−0.630635
$135$	−10.5463	+	6.66556i	−0.907681	+	0.573680i
$136$	−2.54164	−	2.54164i	−0.217944	−	0.217944i
$137$	3.57901	−	0.958992i	0.305775	−	0.0819323i	−0.102669	−	0.994716i	$-0.532738\pi$
$137$	3.57901	−	0.958992i	0.305775	−	0.0819323i	0.408444	+	0.912783i	$0.366071\pi$
$138$	5.81404	+	9.76682i	0.494924	+	0.831407i
$139$	−3.98396	−	6.90042i	−0.337915	−	0.585286i	0.646125	−	0.763231i	$-0.276388\pi$
$139$	−3.98396	−	6.90042i	−0.337915	−	0.585286i	−0.984040	+	0.177945i	$0.943055\pi$
$140$	1.30511	+	2.26052i	0.110302	+	0.191049i
$141$	0.158228	+	11.8549i	0.0133252	+	0.998361i
$142$	6.75014	+	3.89720i	0.566459	+	0.327045i
$143$	6.06938	−	13.0591i	0.507547	−	1.09206i
$144$	8.46853	−	5.19549i	0.705711	−	0.432958i
$145$	5.10208	+	5.10208i	0.423705	+	0.423705i
$146$	1.04608	+	0.603956i	0.0865744	+	0.0499837i
$147$	2.91320	+	10.3193i	0.240277	+	0.851122i
$148$	0.723317	−	2.69946i	0.0594563	−	0.221894i
$149$	−12.0991	−	3.24194i	−0.991197	−	0.265590i	−0.273444	−	0.961888i	$-0.588163\pi$
$149$	−12.0991	−	3.24194i	−0.991197	−	0.265590i	−0.717753	+	0.696298i	$0.754829\pi$
$150$	−1.50779	−	0.843897i	−0.123111	−	0.0689039i
$151$	−0.936624	−	3.49553i	−0.0762214	−	0.284462i	0.917286	−	0.398229i	$-0.130375\pi$
$151$	−0.936624	−	3.49553i	−0.0762214	−	0.284462i	−0.993507	+	0.113767i	$0.963708\pi$
$152$		−	10.7062i		−	0.868388i
$153$	−3.16124	−	1.71432i	−0.255571	−	0.138594i
$154$	−13.3764	+	13.3764i	−1.07790	+	1.07790i
$155$	4.51248	−	7.81585i	0.362451	−	0.627784i
$156$	1.70552	+	0.765151i	0.136551	+	0.0612611i
$157$	4.43780	+	7.68650i	0.354175	+	0.613450i	0.986976	−	0.160865i	$-0.0514283\pi$
$157$	4.43780	+	7.68650i	0.354175	+	0.613450i	−0.632801	+	0.774314i	$0.718095\pi$
$158$	6.29258	+	1.68609i	0.500611	+	0.134138i
$159$	−6.02448	−	1.52838i	−0.477772	−	0.121208i
$160$	−3.48968	−	2.01477i	−0.275884	−	0.159281i
$161$	12.9232	−	12.9232i	1.01849	−	1.01849i
$162$	7.84456	−	8.73025i	0.616327	−	0.685913i
$163$	−1.18102	+	1.18102i	−0.0925049	+	0.0925049i	−0.751845	−	0.659340i	$-0.770836\pi$
$163$	−1.18102	+	1.18102i	−0.0925049	+	0.0925049i	0.659340	+	0.751845i	$0.270836\pi$
$164$	2.57093	−	0.688878i	0.200756	−	0.0537923i
$165$	−4.08447	+	16.1000i	−0.317976	+	1.25338i
$166$	−1.84364	+	1.06442i	−0.143094	+	0.0826154i
$167$	1.33132	−	4.96855i	0.103020	−	0.384478i	−0.895093	−	0.445880i	$-0.852891\pi$
$167$	1.33132	−	4.96855i	0.103020	−	0.384478i	0.998113	+	0.0614027i	$0.0195574\pi$
$168$	−13.5148	−	13.1588i	−1.04269	−	1.01522i
$169$	−2.28996	−	12.7967i	−0.176151	−	0.984363i
$170$		−	3.75341i		−	0.287874i
$171$	−3.04746	−	10.2687i	−0.233045	−	0.785269i
$172$	−2.18556			−0.166647
$173$	0.654332	−	1.13334i	0.0497479	−	0.0861660i	−0.840079	−	0.542464i	$-0.817492\pi$
$173$	0.654332	−	1.13334i	0.0497479	−	0.0861660i	0.889827	+	0.456298i	$0.150825\pi$
$174$	−5.92326	−	3.31519i	−0.449041	−	0.251324i
$175$	−0.719076	+	2.68363i	−0.0543571	+	0.202863i
$176$	3.42345	−	12.7765i	0.258052	−	0.963063i
$177$	8.52853	+	4.77333i	0.641043	+	0.358786i
$178$	8.14240	−	14.1030i	0.610299	−	1.05707i
$179$	11.7525			0.878420			0.439210	−	0.898385i	$-0.355258\pi$
$179$	11.7525			0.878420			0.439210	+	0.898385i	$0.355258\pi$
$180$	−2.09677	−	0.502253i	−0.156284	−	0.0374357i
$181$		−	26.1312i		−	1.94232i	−0.238437	−	0.971158i	$-0.576635\pi$
$181$		−	26.1312i		−	1.94232i	0.238437	−	0.971158i	$-0.423365\pi$
$182$	−2.94404	+	16.8215i	−0.218227	+	1.24689i
$183$	−16.1318	−	15.7068i	−1.19250	−	1.16108i
$184$	−3.90532	+	14.5749i	−0.287904	+	1.07447i
$185$	19.4140	−	11.2087i	1.42735	−	0.824080i
$186$	−2.08778	+	8.22950i	−0.153084	+	0.603416i
$187$	−4.62457	+	1.23915i	−0.338182	+	0.0906155i
$188$	−1.44879	+	1.44879i	−0.105664	+	0.105664i
$189$	−16.7082	−	8.77420i	−1.21534	−	0.638229i
$190$	7.90530	−	7.90530i	0.573511	−	0.573511i
$191$	19.3976	+	11.1992i	1.40356	+	0.810346i	0.994756	−	0.102276i	$-0.0326126\pi$
$191$	19.3976	+	11.1992i	1.40356	+	0.810346i	0.408804	+	0.912622i	$0.365946\pi$
$192$	14.7943	+	3.75325i	1.06769	+	0.270867i
$193$	7.50325	+	2.01049i	0.540096	+	0.144718i	0.518546	−	0.855050i	$-0.326473\pi$
$193$	7.50325	+	2.01049i	0.540096	+	0.144718i	0.0215496	+	0.999768i	$0.493140\pi$
$194$	8.87719	+	15.3758i	0.637345	+	1.10391i
$195$	5.33381	+	14.0137i	0.381962	+	1.00354i
$196$	−0.926524	+	1.60479i	−0.0661803	+	0.114628i
$197$	−7.71355	+	7.71355i	−0.549568	+	0.549568i	−0.926316	−	0.376748i	$-0.877042\pi$
$197$	−7.71355	+	7.71355i	−0.549568	+	0.549568i	0.376748	+	0.926316i	$0.377042\pi$
$198$	−0.417042	−	15.6202i	−0.0296379	−	1.11008i
$199$			17.2849i			1.22530i	0.790356	+	0.612648i	$0.209895\pi$
$199$			17.2849i			1.22530i	−0.790356	+	0.612648i	$0.790105\pi$
$200$	−0.593679	−	2.21564i	−0.0419795	−	0.156670i
$201$	−8.46071	−	4.73538i	−0.596772	−	0.334008i
$202$	1.90172	+	0.509565i	0.133805	+	0.0358529i
$203$	−2.82484	+	10.5425i	−0.198265	+	0.739935i
$204$	−0.168847	−	0.598099i	−0.0118216	−	0.0418753i
$205$	18.4897	+	10.6750i	1.29138	+	0.745576i
$206$	−3.75968	−	3.75968i	−0.261949	−	0.261949i
$207$	0.402911	+	15.0909i	0.0280042	+	1.04889i
$208$	−4.09821	−	11.2154i	−0.284160	−	0.777646i
$209$	−12.3499	−	7.13024i	−0.854263	−	0.493209i
$210$	−0.262876	−	19.6954i	−0.0181401	−	1.35911i
$211$	2.94333	+	5.09799i	0.202627	+	0.350960i	0.949374	−	0.314148i	$-0.101719\pi$
$211$	2.94333	+	5.09799i	0.202627	+	0.350960i	−0.746747	+	0.665108i	$0.768385\pi$
$212$	−0.537056	−	0.930208i	−0.0368851	−	0.0638869i
$213$	5.29529	+	8.89539i	0.362827	+	0.609502i
$214$	−2.17740	+	0.583433i	−0.148844	+	0.0398826i
$215$	−12.3965	−	12.3965i	−0.845435	−	0.845435i
$216$	15.5684	−	0.623674i	1.05930	−	0.0424357i
$217$	13.6515			0.926726
$218$	10.5429	−	18.2608i	0.714052	−	1.23677i
$219$	0.820620	+	1.37853i	0.0554524	+	0.0931527i
$220$	−2.48591	+	1.43524i	−0.167600	+	0.0967638i
$221$	−2.77394	+	3.31441i	−0.186596	+	0.222951i
$222$	−14.7119	+	15.1099i	−0.987398	+	1.01411i
$223$	−25.5629	+	6.84955i	−1.71182	+	0.458680i	−0.975869	−	0.218357i	$-0.929930\pi$
$223$	−25.5629	+	6.84955i	−1.71182	+	0.458680i	−0.735949	+	0.677037i	$0.763263\pi$
$224$		−	6.09524i		−	0.407255i
$225$	−1.20009	−	1.95612i	−0.0800060	−	0.130408i
$226$	7.29908	+	7.29908i	0.485528	+	0.485528i
$227$	1.44276	+	5.38445i	0.0957592	+	0.357378i	0.997133	−	0.0756627i	$-0.0241072\pi$
$227$	1.44276	+	5.38445i	0.0957592	+	0.357378i	−0.901374	+	0.433041i	$0.857441\pi$
$228$	0.904075	−	1.61531i	0.0598738	−	0.106977i
$229$	−4.23155	−	1.13384i	−0.279629	−	0.0749263i	0.116279	−	0.993217i	$-0.462903\pi$
$229$	−4.23155	−	1.13384i	−0.279629	−	0.0749263i	−0.395908	+	0.918290i	$0.629570\pi$
$230$	−13.6455	+	7.87823i	−0.899757	+	0.519475i
$231$	−24.1799	+	6.82612i	−1.59092	+	0.449126i
$232$	−2.33223	−	8.70399i	−0.153118	−	0.571445i
$233$	2.35632			0.154367			0.0771837	−	0.997017i	$-0.475407\pi$
$233$	2.35632			0.154367			0.0771837	+	0.997017i	$0.475407\pi$
$234$	−8.41077	−	11.3242i	−0.549829	−	0.740287i
$235$	−16.4352			−1.07211
$236$	0.437149	+	1.63146i	0.0284560	+	0.106199i
$237$	6.19925	+	6.03595i	0.402685	+	0.392077i
$238$	4.91691	−	2.83878i	0.318716	−	0.184011i
$239$	−26.8963	−	7.20684i	−1.73978	−	0.466172i	−0.757379	−	0.652975i	$-0.773520\pi$
$239$	−26.8963	−	7.20684i	−1.73978	−	0.466172i	−0.982397	+	0.186804i	$0.940187\pi$
$240$	7.04488	+	11.8345i	0.454745	+	0.763912i
$241$	4.14633	+	15.4743i	0.267089	+	0.996789i	0.960959	+	0.276690i	$0.0892374\pi$
$241$	4.14633	+	15.4743i	0.267089	+	0.996789i	−0.693870	+	0.720100i	$0.744096\pi$
$242$	−4.56658	−	4.56658i	−0.293551	−	0.293551i
$243$	14.7547	−	5.02966i	0.946517	−	0.322653i
$244$		−	3.89102i		−	0.249097i
$245$	−14.3576	+	3.84712i	−0.917276	+	0.245783i
$246$	−19.4682	−	4.93899i	−1.24125	−	0.314899i
$247$	−12.8231	+	1.13830i	−0.815912	+	0.0724281i
$248$	−9.76088	+	5.63545i	−0.619816	+	0.357851i
$249$	−2.82720	+	0.0377348i	−0.179167	+	0.00239134i
$250$	−6.63033	+	11.4841i	−0.419339	+	0.726317i
$251$	10.8482			0.684734			0.342367	−	0.939566i	$-0.388771\pi$
$251$	10.8482			0.684734			0.342367	+	0.939566i	$0.388771\pi$
$252$	−0.927884	−	3.12660i	−0.0584512	−	0.196957i
$253$	14.2117	+	14.2117i	0.893479	+	0.893479i
$254$	3.42864	−	0.918702i	0.215132	−	0.0576445i
$255$	2.43473	−	4.35013i	0.152468	−	0.272416i
$256$	3.50745	+	6.07509i	0.219216	+	0.379693i
$257$	4.68578	+	8.11602i	0.292291	+	0.506263i	0.974351	−	0.225033i	$-0.0722490\pi$
$257$	4.68578	+	8.11602i	0.292291	+	0.506263i	−0.682060	+	0.731296i	$0.738916\pi$
$258$	14.3917	+	8.05491i	0.895990	+	0.501477i
$259$	29.3665	+	16.9547i	1.82474	+	1.05352i
$260$	−1.09214	+	2.34990i	−0.0677317	+	0.145734i
$261$	−4.71447	−	7.68448i	−0.291819	−	0.475657i
$262$	−6.28636	−	6.28636i	−0.388373	−	0.388373i
$263$	24.3584	+	14.0633i	1.50200	+	0.867182i	0.999997	+	0.00231808i	$0.000737870\pi$
$263$	24.3584	+	14.0633i	1.50200	+	0.867182i	0.502006	+	0.864864i	$0.332595\pi$
$264$	14.4708	−	14.8623i	0.890616	−	0.914712i
$265$	2.22997	−	8.32235i	0.136986	−	0.511238i
$266$	16.3348	+	4.37689i	1.00155	+	0.268364i
$267$	18.5851	−	11.0634i	1.13739	−	0.677071i
$268$	−0.433673	−	1.61849i	−0.0264908	−	0.0988650i
$269$		−	12.7454i		−	0.777099i	−0.921428	−	0.388550i	$-0.872976\pi$
$269$		−	12.7454i		−	0.777099i	0.921428	−	0.388550i	$-0.127024\pi$
$270$	11.9560	+	11.0350i	0.727619	+	0.671568i
$271$	−2.93224	+	2.93224i	−0.178121	+	0.178121i	−0.790536	−	0.612415i	$-0.790198\pi$
$271$	−2.93224	+	2.93224i	−0.178121	+	0.178121i	0.612415	+	0.790536i	$0.290198\pi$
$272$	−1.98493	+	3.43800i	−0.120354	+	0.208459i
$273$	−14.3237	+	17.5861i	−0.866909	+	1.06436i
$274$	−2.41601	−	4.18466i	−0.145957	−	0.252804i
$275$	−2.95120	−	0.790771i	−0.177964	−	0.0476853i
$276$	−1.81998	+	1.86922i	−0.109550	+	0.112514i
$277$	15.2173	+	8.78570i	0.914318	+	0.527881i	0.881818	−	0.471590i	$-0.156320\pi$
$277$	15.2173	+	8.78570i	0.914318	+	0.527881i	0.0324997	+	0.999472i	$0.489653\pi$
$278$	−7.34752	+	7.34752i	−0.440675	+	0.440675i
$279$	−7.75793	+	8.18355i	−0.464455	+	0.489936i
$280$	18.4897	−	18.4897i	1.10497	−	1.10497i
$281$	−31.5194	+	8.44560i	−1.88029	+	0.503822i	−0.880748	+	0.473586i	$0.842959\pi$
$281$	−31.5194	+	8.44560i	−1.88029	+	0.503822i	−0.999543	+	0.0302362i	$0.990374\pi$
$282$	14.8797	−	4.20064i	0.886076	−	0.250144i
$283$	7.54552	−	4.35641i	0.448535	−	0.258962i	−0.258677	−	0.965964i	$-0.583286\pi$
$283$	7.54552	−	4.35641i	0.448535	−	0.258962i	0.707211	+	0.707002i	$0.249953\pi$
$284$	−0.463035	+	1.72807i	−0.0274761	+	0.102542i
$285$	14.2900	−	4.03416i	0.846468	−	0.238963i
$286$	−18.4987	−	3.23758i	−1.09385	−	0.191442i
$287$			32.2949i			1.90631i
$288$	3.65386	+	3.46382i	0.215305	+	0.204108i
$289$	−15.5631			−0.915475
$290$	4.70482	−	8.14898i	0.276276	−	0.478525i
$291$	0.314704	+	23.5786i	0.0184483	+	1.38220i
$292$	−0.0717574	+	0.267802i	−0.00419929	+	0.0156719i
$293$	−0.673169	+	2.51230i	−0.0393269	+	0.146770i	−0.982798	−	0.184686i	$-0.940873\pi$
$293$	−0.673169	+	2.51230i	−0.0393269	+	0.146770i	0.943471	+	0.331456i	$0.107540\pi$
$294$	12.0156	−	7.15268i	0.700762	−	0.417153i
$295$	−6.77417	+	11.7332i	−0.394408	+	0.683134i
$296$	−27.9961			−1.62724
$297$	9.64902	−	18.3740i	0.559893	−	1.06617i
$298$			16.3350i			0.946263i
$299$	17.8719	+	3.12787i	1.03356	+	0.180890i
$300$	0.0975255	−	0.384421i	0.00563064	−	0.0221945i
$301$	6.86351	−	25.6150i	0.395606	−	1.47642i
$302$	−4.08705	+	2.35966i	−0.235183	+	0.135783i
$303$	1.87352	+	1.82417i	0.107631	+	0.104796i
$304$	−11.4216	+	3.06040i	−0.655072	+	0.175526i
$305$	22.0699	−	22.0699i	1.26372	−	1.26372i
$306$	−1.09246	+	4.56073i	−0.0624518	+	0.260719i
$307$	17.2807	−	17.2807i	0.986261	−	0.986261i	−0.0136454	−	0.999907i	$-0.504344\pi$
$307$	17.2807	−	17.2807i	0.986261	−	0.986261i	0.999907	+	0.0136454i	$0.00434362\pi$
$308$	−3.76028	−	2.17100i	−0.214262	−	0.123704i
$309$	−1.91860	−	6.79619i	−0.109146	−	0.386622i
$310$	−11.3684	−	3.04616i	−0.645682	−	0.173010i
$311$	−7.95837	−	13.7843i	−0.451278	−	0.781636i	0.547188	−	0.837010i	$-0.315698\pi$
$311$	−7.95837	−	13.7843i	−0.451278	−	0.781636i	−0.998466	+	0.0553736i	$0.982365\pi$
$312$	2.98182	−	18.4870i	0.168812	−	1.04662i
$313$	4.72787	−	8.18891i	0.267235	−	0.462865i	−0.700912	−	0.713248i	$-0.747223\pi$
$313$	4.72787	−	8.18891i	0.267235	−	0.462865i	0.968147	+	0.250383i	$0.0805566\pi$
$314$	8.18453	−	8.18453i	0.461879	−	0.461879i
$315$	12.4712	−	22.9971i	0.702670	−	1.29574i
$316$			1.49527i			0.0841156i
$317$	0.586685	+	2.18954i	0.0329515	+	0.122977i	0.980442	−	0.196806i	$-0.0630568\pi$
$317$	0.586685	+	2.18954i	0.0329515	+	0.122977i	−0.947491	+	0.319782i	$0.896390\pi$
$318$	0.108174	+	8.10468i	0.00606607	+	0.454488i
$319$	−11.5936	−	3.10649i	−0.649116	−	0.173930i
$320$	−5.47614	+	20.4372i	−0.306125	+	1.14248i
$321$	−2.90202	−	0.736227i	−0.161975	−	0.0410922i
$322$	−20.6407	−	11.9169i	−1.15026	−	0.664104i
$323$	3.02640	+	3.02640i	0.168394	+	0.168394i
$324$	2.40157	+	1.22056i	0.133421	+	0.0678091i
$325$	−2.59060	+	0.946633i	−0.143701	+	0.0525097i
$326$	1.88632	+	1.08907i	0.104473	+	0.0603177i
$327$	24.0642	−	14.3250i	1.33075	−	0.792176i
$328$	−13.3316	−	23.0910i	−0.736113	−	1.27498i
$329$	−12.4302	−	21.5298i	−0.685301	−	1.18698i
$330$	21.6591	−	0.289085i	1.19230	−	0.0159136i
$331$	33.3627	−	8.93950i	1.83378	−	0.491359i	0.835472	−	0.549533i	$-0.185194\pi$
$331$	33.3627	−	8.93950i	1.83378	−	0.491359i	0.998306	+	0.0581739i	$0.0185278\pi$
$332$	−0.345514	−	0.345514i	−0.0189625	−	0.0189625i
$333$	−26.8522	+	7.96894i	−1.47149	+	0.436695i
$334$	−6.70804			−0.367048
$335$	6.72030	−	11.6399i	0.367169	−	0.635956i
$336$	−10.1748	+	18.1793i	−0.555081	+	0.991764i
$337$	−18.8669	+	10.8928i	−1.02774	+	0.593369i	−0.916338	−	0.400406i	$-0.868869\pi$
$337$	−18.8669	+	10.8928i	−1.02774	+	0.593369i	−0.111407	+	0.993775i	$0.535536\pi$
$338$	−15.3466	+	7.20380i	−0.834747	+	0.391835i
$339$	3.72479	+	13.1942i	0.202303	+	0.716610i
$340$	0.832158	−	0.222976i	0.0451301	−	0.0120926i
$341$			15.0126i			0.812980i
$342$	−11.9065	+	7.30473i	−0.643832	+	0.394995i
$343$	2.07836	+	2.07836i	0.112221	+	0.112221i
$344$	5.66661	+	21.1481i	0.305523	+	1.14023i
$345$	−20.9252	+	0.279290i	−1.12658	+	0.0150365i
$346$	−1.64847	−	0.441708i	−0.0886226	−	0.0237463i
$347$	−15.1832	+	8.76603i	−0.815078	+	0.470585i	−0.848716	−	0.528849i	$-0.822624\pi$
$347$	−15.1832	+	8.76603i	−0.815078	+	0.470585i	0.0336384	+	0.999434i	$0.489291\pi$
$348$	0.383122	−	1.51017i	0.0205375	−	0.0809536i
$349$	0.936616	+	3.49550i	0.0501359	+	0.187110i	0.986452	−	0.164047i	$-0.0524550\pi$
$349$	0.936616	+	3.49550i	0.0501359	+	0.187110i	−0.936317	+	0.351157i	$0.885788\pi$
$350$	3.62317			0.193667
$351$	−2.40224	−	18.5803i	−0.128222	−	0.991745i
$352$	6.70296			0.357269
$353$	−5.69115	−	21.2397i	−0.302910	−	1.13047i	−0.934730	−	0.355359i	$-0.884359\pi$
$353$	−5.69115	−	21.2397i	−0.302910	−	1.13047i	0.631820	−	0.775115i	$-0.282308\pi$
$354$	3.13419	−	12.3542i	0.166581	−	0.656618i
$355$	−12.4280	+	7.17531i	−0.659610	+	0.380826i
$356$	3.61045	+	0.967418i	0.191354	+	0.0512730i
$357$	7.54004	−	0.100637i	0.399061	−	0.00532629i
$358$	−3.96675	−	14.8041i	−0.209649	−	0.782422i
$359$	9.99668	+	9.99668i	0.527604	+	0.527604i	0.919857	−	0.392253i	$-0.128304\pi$
$359$	9.99668	+	9.99668i	0.527604	+	0.527604i	−0.392253	+	0.919857i	$0.628304\pi$
$360$	0.576460	+	21.5912i	0.0303821	+	1.13795i
$361$		−	6.25180i		−	0.329042i
$362$	−32.9165	+	8.81994i	−1.73005	+	0.463566i
$363$	−2.33037	−	8.25478i	−0.122313	−	0.433263i
$364$	−3.90434	+	0.346586i	−0.204643	+	0.0181661i
$365$	−1.92599	+	1.11197i	−0.100811	+	0.0582032i
$366$	−14.3404	+	25.6221i	−0.749586	+	1.33929i
$367$	15.2290	−	26.3774i	0.794946	−	1.37689i	−0.127928	−	0.991783i	$-0.540833\pi$
$367$	15.2290	−	26.3774i	0.794946	−	1.37689i	0.922874	−	0.385103i	$-0.125834\pi$
$368$	16.6651			0.868727
$369$	−19.3595	−	18.3527i	−1.00782	−	0.955401i
$370$	−20.6719	−	20.6719i	−1.07468	−	1.07468i
$371$	12.5887	−	3.37314i	0.653574	−	0.175124i
$372$	−1.94856	+	0.0260076i	−0.101028	+	0.00134843i
$373$	−6.72100	−	11.6411i	−0.348000	−	0.602754i	0.637894	−	0.770124i	$-0.279806\pi$
$373$	−6.72100	−	11.6411i	−0.348000	−	0.602754i	−0.985894	+	0.167370i	$0.946472\pi$
$374$	3.12182	+	5.40715i	0.161425	+	0.279597i
$375$	−15.1338	+	9.00892i	−0.781506	+	0.465218i
$376$	17.7753	+	10.2626i	0.916692	+	0.529252i
$377$	−10.1770	+	3.71878i	−0.524142	+	0.191527i
$378$	−5.41309	+	24.0082i	−0.278419	+	1.23485i
$379$	−4.10894	−	4.10894i	−0.211062	−	0.211062i	0.593656	−	0.804719i	$-0.297684\pi$
$379$	−4.10894	−	4.10894i	−0.211062	−	0.211062i	−0.804719	+	0.593656i	$0.797684\pi$
$380$	2.22228	+	1.28304i	0.114001	+	0.0658184i
$381$	4.56966	+	1.15930i	0.234111	+	0.0593927i
$382$	7.56003	−	28.2144i	0.386805	−	1.44358i
$383$	5.92608	+	1.58789i	0.302809	+	0.0811373i	0.407024	−	0.913417i	$-0.366566\pi$
$383$	5.92608	+	1.58789i	0.302809	+	0.0811373i	−0.104215	+	0.994555i	$0.533233\pi$
$384$	−0.188054	−	14.0896i	−0.00959661	−	0.719006i
$385$	−9.01444	−	33.6424i	−0.459418	−	1.71457i
$386$		−	10.1302i		−	0.515611i
$387$	11.4547	+	18.6710i	0.582277	+	0.949098i
$388$	−2.88155	+	2.88155i	−0.146289	+	0.146289i
$389$	12.9546	−	22.4381i	0.656826	−	1.13766i	−0.324607	−	0.945849i	$-0.605232\pi$
$389$	12.9546	−	22.4381i	0.656826	−	1.13766i	0.981433	−	0.191807i	$-0.0614347\pi$
$390$	15.8523	−	11.4488i	0.802710	−	0.579732i
$391$	−3.01604	−	5.22393i	−0.152528	−	0.264186i
$392$	17.9306	+	4.80450i	0.905634	+	0.242664i
$393$	−3.20799	−	11.3635i	−0.161822	−	0.573215i
$394$	12.3200	+	7.11295i	0.620672	+	0.358345i
$395$	−8.48121	+	8.48121i	−0.426736	+	0.426736i
$396$	3.43833	−	1.02040i	0.172783	−	0.0512769i
$397$	−7.05730	+	7.05730i	−0.354196	+	0.354196i	−0.861668	−	0.507472i	$-0.830580\pi$
$397$	−7.05730	+	7.05730i	−0.354196	+	0.354196i	0.507472	+	0.861668i	$0.330580\pi$
$398$	21.7732	−	5.83410i	1.09139	−	0.292437i
$399$	16.0925	+	15.6686i	0.805633	+	0.784411i
$400$	−2.19398	+	1.26670i	−0.109699	+	0.0633348i
$401$	3.05777	−	11.4118i	0.152698	−	0.569876i	−0.846594	−	0.532240i	$-0.821351\pi$
$401$	3.05777	−	11.4118i	0.152698	−	0.569876i	0.999292	−	0.0376361i	$-0.0119828\pi$
$402$	−3.10927	+	12.2559i	−0.155076	+	0.611271i
$403$	7.78749	+	11.0917i	0.387922	+	0.552515i
$404$			0.451896i			0.0224827i
$405$	6.69871	+	20.5448i	0.332862	+	1.02088i
$406$	14.2334			0.706391
$407$	−18.6452	+	32.2944i	−0.924208	+	1.60077i
$408$	−5.34960	+	3.18454i	−0.264845	+	0.157658i
$409$	−6.26991	+	23.3996i	−0.310027	+	1.15704i	0.618504	+	0.785782i	$0.287739\pi$
$409$	−6.26991	+	23.3996i	−0.310027	+	1.15704i	−0.928531	+	0.371255i	$0.878928\pi$
$410$	7.20618	−	26.8938i	0.355888	−	1.32819i
$411$	−0.0856498	−	6.41713i	−0.00422479	−	0.316534i
$412$	0.610199	−	1.05690i	0.0300623	−	0.0520695i
$413$	−20.4938			−1.00843
$414$	18.8735	−	5.60111i	0.927582	−	0.275279i
$415$		−	3.91952i		−	0.192402i
$416$	4.95229	−	3.47702i	0.242806	−	0.170475i
$417$	−13.2817	+	3.74951i	−0.650410	+	0.183614i
$418$	−4.81328	+	17.9634i	−0.235425	+	0.878619i
$419$	12.2475	−	7.07112i	0.598331	−	0.345447i	−0.170054	−	0.985435i	$-0.554394\pi$
$419$	12.2475	−	7.07112i	0.598331	−	0.345447i	0.768385	+	0.639988i	$0.221061\pi$
$420$	4.35099	−	1.22831i	0.212307	−	0.0599354i
$421$	−0.0303363	+	0.00812858i	−0.00147850	+	0.000396163i	−0.259558	−	0.965727i	$-0.583577\pi$
$421$	−0.0303363	+	0.00812858i	−0.00147850	+	0.000396163i	0.258080	+	0.966124i	$0.416910\pi$
$422$	5.42830	−	5.42830i	0.264246	−	0.264246i
$423$	19.9702	+	4.78359i	0.970982	+	0.232586i
$424$	−7.60851	+	7.60851i	−0.369502	+	0.369502i
$425$	0.794132	+	0.458492i	0.0385211	+	0.0222401i
$426$	9.41789	−	9.67269i	0.456298	−	0.468644i
$427$	45.6032	+	12.2193i	2.20689	+	0.591336i
$428$	−0.258702	−	0.448085i	−0.0125048	−	0.0216590i
$429$	−19.3395	−	15.7518i	−0.933718	−	0.760505i
$430$	−11.4313	+	19.7996i	−0.551265	+	0.954820i
$431$	−5.86423	+	5.86423i	−0.282470	+	0.282470i	−0.834093	−	0.551623i	$-0.814009\pi$
$431$	−5.86423	+	5.86423i	−0.282470	+	0.282470i	0.551623	+	0.834093i	$0.314009\pi$
$432$	−5.11563	−	16.4304i	−0.246126	−	0.790508i
$433$			26.9940i			1.29725i	0.761110	+	0.648623i	$0.224655\pi$
$433$			26.9940i			1.29725i	−0.761110	+	0.648623i	$0.775345\pi$
$434$	−4.60774	−	17.1963i	−0.221179	−	0.825450i
$435$	10.7388	−	6.39263i	0.514885	−	0.306503i
$436$	4.67485	+	1.25262i	0.223885	+	0.0599897i
$437$	4.65019	−	17.3547i	0.222449	−	0.830189i
$438$	1.45951	−	1.49900i	0.0697380	−	0.0716248i
$439$	−23.7589	−	13.7172i	−1.13395	−	0.654685i	−0.189023	−	0.981973i	$-0.560532\pi$
$439$	−23.7589	−	13.7172i	−1.13395	−	0.654685i	−0.944925	+	0.327287i	$0.893866\pi$
$440$	20.3331	+	20.3331i	0.969345	+	0.969345i
$441$	18.5655	−	0.495678i	0.884073	−	0.0236037i
$442$	5.11131	+	2.37554i	0.243120	+	0.112993i
$443$	−2.52266	−	1.45646i	−0.119855	−	0.0691983i	0.438874	−	0.898549i	$-0.355377\pi$
$443$	−2.52266	−	1.45646i	−0.119855	−	0.0691983i	−0.558729	+	0.829350i	$0.688711\pi$
$444$	−4.22395	−	2.36411i	−0.200460	−	0.112195i
$445$	14.9913	+	25.9658i	0.710658	+	1.23090i
$446$	17.2563	+	29.8887i	0.817107	+	1.41527i
$447$	−10.5960	+	18.9320i	−0.501175	+	0.895451i
$448$	−30.9142	+	8.28343i	−1.46056	+	0.391355i
$449$	23.3661	+	23.3661i	1.10272	+	1.10272i	0.994082	+	0.108634i	$0.0346476\pi$
$449$	23.3661	+	23.3661i	1.10272	+	1.10272i	0.108634	+	0.994082i	$0.465352\pi$
$450$	−2.05899	+	2.17195i	−0.0970616	+	0.102387i
$451$	−35.5149			−1.67233
$452$	−1.18465	+	2.05187i	−0.0557210	+	0.0965117i
$453$	−6.26745	+	0.0836520i	−0.294471	+	0.00393032i
$454$	6.29562	−	3.63478i	0.295468	−	0.170589i
$455$	−24.1113	−	20.1796i	−1.13036	−	0.946036i
$456$	−17.9743	−	4.55998i	−0.841723	−	0.213541i
$457$	−7.49418	+	2.00806i	−0.350563	+	0.0939331i	−0.429804	−	0.902922i	$-0.641417\pi$
$457$	−7.49418	+	2.00806i	−0.350563	+	0.0939331i	0.0792404	+	0.996856i	$0.474751\pi$
$458$			5.71303i			0.266952i
$459$	−4.22455	+	4.57714i	−0.197185	+	0.213643i
$460$	−2.55728	−	2.55728i	−0.119234	−	0.119234i
$461$	−7.48096	−	27.9193i	−0.348423	−	1.30033i	−0.888562	−	0.458757i	$-0.848295\pi$
$461$	−7.48096	−	27.9193i	−0.348423	−	1.30033i	0.540138	−	0.841576i	$-0.318372\pi$
$462$	16.7599	+	28.1545i	0.779742	+	1.30986i
$463$	11.6030	+	3.10900i	0.539235	+	0.144488i	0.518149	−	0.855290i	$-0.326621\pi$
$463$	11.6030	+	3.10900i	0.539235	+	0.144488i	0.0210856	+	0.999778i	$0.493288\pi$
$464$	−8.61890	+	4.97612i	−0.400122	+	0.231011i
$465$	−11.1998	−	10.9048i	−0.519379	−	0.505697i
$466$	−0.795317	−	2.96816i	−0.0368423	−	0.137497i
$467$	−34.1817			−1.58174			−0.790870	−	0.611985i	$-0.790371\pi$
$467$	−34.1817			−1.58174			−0.790870	+	0.611985i	$0.790371\pi$
$468$	2.01100	−	2.53745i	0.0929586	−	0.117294i
$469$	20.3308			0.938789
$470$	5.54729	+	20.7028i	0.255877	+	0.954947i
$471$	14.7948	−	4.17665i	0.681706	−	0.192450i
$472$	14.6531	−	8.45997i	0.674464	−	0.389402i
$473$	28.1689	+	7.54783i	1.29521	+	0.347050i
$474$	5.51085	−	9.84626i	0.253122	−	0.452254i
$475$	0.706912	+	2.63823i	0.0324353	+	0.121050i
$476$	0.921473	+	0.921473i	0.0422356	+	0.0422356i
$477$	−5.13189	+	9.46333i	−0.234973	+	0.433296i
$478$			36.3127i			1.66091i
$479$	−4.69806	+	1.25884i	−0.214660	+	0.0575179i	−0.364546	−	0.931185i	$-0.618776\pi$
$479$	−4.69806	+	1.25884i	−0.214660	+	0.0575179i	0.149886	+	0.988703i	$0.452109\pi$
$480$	−4.86885	+	5.00058i	−0.222232	+	0.228244i
$481$	2.97658	+	33.5316i	0.135721	+	1.52891i
$482$	18.0929	−	10.4460i	0.824111	−	0.475801i
$483$	−16.1920	−	27.2005i	−0.736763	−	1.23767i
$484$	0.741159	−	1.28373i	0.0336890	−	0.0583511i
$485$	−32.6884			−1.48430
$486$	−11.3158	−	16.8884i	−0.513294	−	0.766072i
$487$	−11.0540	−	11.0540i	−0.500905	−	0.500905i	0.410814	−	0.911719i	$-0.365245\pi$
$487$	−11.0540	−	11.0540i	−0.500905	−	0.500905i	−0.911719	+	0.410814i	$0.865245\pi$
$488$	−37.6507	+	10.0885i	−1.70437	+	0.456683i
$489$	1.47976	+	2.48580i	0.0669170	+	0.112412i
$490$	9.69214	+	16.7873i	0.437846	+	0.758372i
$491$	17.8924	+	30.9906i	0.807474	+	1.39859i	0.914608	+	0.404342i	$0.132499\pi$
$491$	17.8924	+	30.9906i	0.807474	+	1.39859i	−0.107134	+	0.994245i	$0.534167\pi$
$492$	−0.0615252	−	4.60965i	−0.00277377	−	0.207819i
$493$	3.11969	+	1.80115i	0.140504	+	0.0811199i
$494$	5.76198	+	15.7685i	0.259244	+	0.709459i
$495$	25.2900	+	13.7146i	1.13670	+	0.616424i
$496$	8.80217	+	8.80217i	0.395229	+	0.395229i
$497$	−18.7991	−	10.8537i	−0.843254	−	0.486853i
$498$	1.00179	+	3.54858i	0.0448911	+	0.159016i
$499$	0.551893	−	2.05969i	0.0247061	−	0.0922045i	−0.952472	−	0.304626i	$-0.901468\pi$
$499$	0.551893	−	2.05969i	0.0247061	−	0.0922045i	0.977178	+	0.212422i	$0.0681351\pi$
$500$	−2.93998	−	0.787766i	−0.131480	−	0.0352300i
$501$	−7.77449	−	4.35131i	−0.347339	−	0.194402i
$502$	−3.66155	−	13.6651i	−0.163423	−	0.609904i
$503$		−	40.5278i		−	1.80704i	−0.428542	−	0.903522i	$-0.640972\pi$
$503$		−	40.5278i		−	1.80704i	0.428542	−	0.903522i	$-0.359028\pi$
$504$	−27.8481	+	17.0850i	−1.24045	+	0.761026i
$505$	−2.56316	+	2.56316i	−0.114059	+	0.114059i
$506$	13.1051	−	22.6987i	0.582592	−	1.00908i
$507$	−22.4593	−	1.60583i	−0.997454	−	0.0713175i
$508$	0.407365	+	0.705577i	0.0180739	+	0.0313049i
$509$	11.0733	+	2.96707i	0.490814	+	0.131513i	0.495734	−	0.868475i	$-0.334899\pi$
$509$	11.0733	+	2.96707i	0.490814	+	0.131513i	−0.00491945	+	0.999988i	$0.501566\pi$
$510$	−6.30148	−	1.59865i	−0.279034	−	0.0707895i
$511$	−2.91333	−	1.68201i	−0.128878	−	0.0744078i
$512$	17.9738	−	17.9738i	0.794338	−	0.794338i
$513$	−18.5378	+	0.742627i	−0.818464	+	0.0327878i
$514$	8.64187	−	8.64187i	0.381177	−	0.381177i
$515$	9.45579	−	2.53367i	0.416672	−	0.111647i
$516$	−0.930871	+	3.66926i	−0.0409793	+	0.161530i
$517$	23.6764	−	13.6696i	1.04129	−	0.601188i
$518$	11.4453	−	42.7145i	0.502878	−	1.87677i
$519$	−1.62403	−	1.58125i	−0.0712869	−	0.0694090i
$520$	25.5699	+	4.47517i	1.12132	+	0.196249i
$521$			10.9569i			0.480031i	0.970769	+	0.240016i	$0.0771525\pi$
$521$			10.9569i			0.480031i	−0.970769	+	0.240016i	$0.922847\pi$
$522$	−8.08859	+	8.53235i	−0.354028	+	0.373451i
$523$	11.1030			0.485500			0.242750	−	0.970089i	$-0.421950\pi$
$523$	11.1030			0.485500			0.242750	+	0.970089i	$0.421950\pi$
$524$	1.02028	−	1.76718i	0.0445712	−	0.0771995i
$525$	4.19919	+	2.35024i	0.183268	+	0.102573i
$526$	9.49347	−	35.4301i	0.413935	−	1.54483i
$527$	1.16617	−	4.35219i	0.0507990	−	0.189585i
$528$	−19.9919	−	11.1893i	−0.870035	−	0.486950i
$529$	−1.16104	+	2.01099i	−0.0504801	+	0.0874341i
$530$	−11.2360			−0.488061
$531$	11.6463	−	12.2852i	0.505405	−	0.533132i
$532$			3.88154i			0.168286i
$533$	−26.2391	+	18.4226i	−1.13654	+	0.797970i
$534$	−20.2091	−	19.6768i	−0.874534	−	0.851497i
$535$	1.07418	−	4.00891i	0.0464410	−	0.173320i
$536$	−14.5366	+	8.39269i	−0.627884	+	0.362509i
$537$	5.00560	−	19.7308i	0.216008	−	0.851447i
$538$	−16.0549	+	4.30189i	−0.692175	+	0.185468i
$539$	17.4838	−	17.4838i	0.753080	−	0.753080i
$540$	−1.73627	+	3.30628i	−0.0747172	+	0.142279i
$541$	−0.544451	+	0.544451i	−0.0234078	+	0.0234078i	−0.718714	−	0.695306i	$-0.755269\pi$
$541$	−0.544451	+	0.544451i	−0.0234078	+	0.0234078i	0.695306	+	0.718714i	$0.255269\pi$
$542$	4.68334	+	2.70393i	0.201167	+	0.116144i
$543$	−43.8708	−	11.1298i	−1.88268	−	0.477625i
$544$	−1.94320	−	0.520679i	−0.0833141	−	0.0223239i
$545$	19.4109	+	33.6207i	0.831473	+	1.44015i
$546$	26.9871	+	12.1073i	1.15494	+	0.518143i
$547$	−5.24035	+	9.07656i	−0.224061	+	0.388086i	−0.956037	−	0.293245i	$-0.905265\pi$
$547$	−5.24035	+	9.07656i	−0.224061	+	0.388086i	0.731976	+	0.681330i	$0.238598\pi$
$548$	0.784241	−	0.784241i	0.0335011	−	0.0335011i
$549$	−33.2405	+	20.3933i	−1.41867	+	0.870364i
$550$			3.98442i			0.169896i
$551$	2.77705	+	10.3641i	0.118306	+	0.441526i
$552$	22.8059	+	12.7642i	0.970684	+	0.543282i
$553$	−17.5248	−	4.69575i	−0.745229	−	0.199683i
$554$	5.93080	−	22.1340i	0.251975	−	0.940385i
$555$	−10.5491	−	37.3676i	−0.447784	−	1.58617i
$556$	−2.06548	−	1.19251i	−0.0875960	−	0.0505736i
$557$	2.47553	+	2.47553i	0.104891	+	0.104891i	0.757605	−	0.652713i	$-0.226369\pi$
$557$	2.47553	+	2.47553i	0.104891	+	0.104891i	−0.652713	+	0.757605i	$0.726369\pi$
$558$	12.9270	+	7.01022i	0.547244	+	0.296766i
$559$	24.7270	−	9.03552i	1.04584	−	0.382162i
$560$	−25.0104	−	14.4398i	−1.05688	−	0.610192i
$561$	0.110671	+	8.29181i	0.00467254	+	0.350080i
$562$	21.2772	+	36.8532i	0.897525	+	1.55456i
$563$	−10.1220	−	17.5318i	−0.426592	−	0.738879i	0.569976	−	0.821662i	$-0.306953\pi$
$563$	−10.1220	−	17.5318i	−0.426592	−	0.738879i	−0.996568	+	0.0827826i	$0.973619\pi$
$564$	1.81526	+	3.04940i	0.0764362	+	0.128403i
$565$	−18.3576	+	4.91889i	−0.772308	+	0.206939i
$566$	−8.03441	−	8.03441i	−0.337711	−	0.337711i
$567$	−21.8470	+	24.3137i	−0.917489	+	1.02108i
$568$	17.9219			0.751985
$569$	11.2366	−	19.4623i	0.471061	−	0.815902i	−0.528391	−	0.849001i	$-0.677204\pi$
$569$	11.2366	−	19.4623i	0.471061	−	0.815902i	0.999452	+	0.0330993i	$0.0105378\pi$
$570$	−9.90492	−	16.6390i	−0.414871	−	0.696930i
$571$	−34.8548	+	20.1234i	−1.45863	+	0.842140i	−0.998944	−	0.0459422i	$-0.985371\pi$
$571$	−34.8548	+	20.1234i	−1.45863	+	0.842140i	−0.459685	+	0.888082i	$0.652038\pi$
$572$	−0.381142	−	4.29361i	−0.0159364	−	0.179525i
$573$	27.0638	−	27.7960i	1.13061	−	1.16119i
$574$	40.6807	−	10.9004i	1.69798	−	0.454972i
$575$		−	3.84941i		−	0.160532i
$576$	12.6024	−	23.2391i	0.525100	−	0.968298i
$577$	−26.0823	−	26.0823i	−1.08582	−	1.08582i	−0.995954	−	0.0898664i	$-0.971356\pi$
$577$	−26.0823	−	26.0823i	−1.08582	−	1.08582i	−0.0898664	−	0.995954i	$-0.528644\pi$
$578$	5.25293	+	19.6042i	0.218493	+	0.815428i
$579$	6.57113	−	11.7407i	0.273087	−	0.487925i
$580$	2.08618	+	0.558990i	0.0866239	+	0.0232108i
$581$	5.13451	−	2.96441i	0.213016	−	0.122985i
$582$	29.5948	−	8.35479i	1.22674	−	0.346317i
$583$	3.70945	+	13.8439i	0.153630	+	0.573354i
$584$	2.77738			0.114929
$585$	25.7989	−	2.98604i	1.06665	−	0.123458i
$586$	3.39186			0.140116
$587$	−2.22592	−	8.30726i	−0.0918737	−	0.342877i	0.904653	−	0.426149i	$-0.140130\pi$
$587$	−2.22592	−	8.30726i	−0.0918737	−	0.342877i	−0.996527	+	0.0832712i	$0.973463\pi$
$588$	2.29960	+	2.23902i	0.0948338	+	0.0923356i
$589$	11.6226	−	6.71029i	0.478900	−	0.276493i
$590$	17.0663	+	4.57291i	0.702610	+	0.188264i
$591$	9.66467	+	16.2354i	0.397551	+	0.667834i
$592$	8.00277	+	29.8668i	0.328912	+	1.22752i
$593$	11.6059	+	11.6059i	0.476599	+	0.476599i	0.904042	−	0.427443i	$-0.140586\pi$
$593$	11.6059	+	11.6059i	0.476599	+	0.476599i	−0.427443	+	0.904042i	$0.640586\pi$
$594$	−26.4019	−	5.95280i	−1.08328	−	0.244246i
$595$			10.4532i			0.428540i
$596$	−3.62159	+	0.970401i	−0.148346	+	0.0397492i
$597$	29.0191	+	7.36199i	1.18767	+	0.301306i
$598$	−2.09214	−	23.5683i	−0.0855541	−	0.963778i
$599$	11.1719	−	6.45010i	0.456471	−	0.263544i	−0.254088	−	0.967181i	$-0.581775\pi$
$599$	11.1719	−	6.45010i	0.456471	−	0.263544i	0.710559	+	0.703637i	$0.248442\pi$
$600$	−3.97263	+	0.0530228i	−0.162182	+	0.00216465i
$601$	1.62052	−	2.80681i	0.0661022	−	0.114492i	−0.831080	−	0.556153i	$-0.812277\pi$
$601$	1.62052	−	2.80681i	0.0661022	−	0.114492i	0.897182	+	0.441660i	$0.145610\pi$
$602$	−34.5828			−1.40949
$603$	−11.5536	+	12.1875i	−0.470501	+	0.496314i
$604$	−0.765949	−	0.765949i	−0.0311660	−	0.0311660i
$605$	11.4852	−	3.07744i	0.466939	−	0.125116i
$606$	1.66547	−	2.97570i	0.0676552	−	0.120880i
$607$	2.64465	+	4.58067i	0.107343	+	0.185924i	0.914693	−	0.404149i	$-0.132432\pi$
$607$	2.64465	+	4.58067i	0.107343	+	0.185924i	−0.807350	+	0.590073i	$0.799099\pi$
$608$	−2.99606	−	5.18934i	−0.121506	−	0.210455i
$609$	16.4962	+	9.23277i	0.668460	+	0.374131i
$610$	−35.2498	−	20.3515i	−1.42722	−	0.824008i
$611$	10.4018	−	22.3810i	0.420813	−	0.905439i
$612$	−1.07604	+	0.0287291i	−0.0434965	+	0.00116131i
$613$	−21.9191	−	21.9191i	−0.885304	−	0.885304i	0.108764	−	0.994068i	$-0.465311\pi$
$613$	−21.9191	−	21.9191i	−0.885304	−	0.885304i	−0.994068	+	0.108764i	$0.965311\pi$
$614$	−27.6005	−	15.9352i	−1.11387	−	0.643091i
$615$	25.7970	−	26.4950i	1.04024	−	1.06838i
$616$	−11.2577	+	42.0145i	−0.453587	+	1.69281i
$617$	2.37338	+	0.635946i	0.0955488	+	0.0256022i	0.306277	−	0.951943i	$-0.400917\pi$
$617$	2.37338	+	0.635946i	0.0955488	+	0.0256022i	−0.210728	+	0.977545i	$0.567583\pi$
$618$	−7.91332	+	4.71068i	−0.318321	+	0.189491i
$619$	4.42746	+	16.5235i	0.177955	+	0.664136i	0.996029	+	0.0890241i	$0.0283748\pi$
$619$	4.42746	+	16.5235i	0.177955	+	0.664136i	−0.818075	+	0.575112i	$0.804959\pi$
$620$		−	2.70142i		−	0.108491i
$621$	25.5073	+	5.75110i	1.02357	+	0.230784i
$622$	−14.6774	+	14.6774i	−0.588511	+	0.588511i
$623$	−22.6765	+	39.2769i	−0.908515	+	1.57359i
$624$	−20.5746	+	2.10350i	−0.823644	+	0.0842075i
$625$	−14.1198	−	24.4563i	−0.564793	−	0.978251i
$626$	−11.9110	−	3.19155i	−0.476061	−	0.127560i
$627$	−17.2308	+	17.6970i	−0.688132	+	0.706750i
$628$	2.30078	+	1.32835i	0.0918110	+	0.0530071i
$629$	7.91388	−	7.91388i	0.315547	−	0.315547i
$630$	−33.1779	−	7.94733i	−1.32184	−	0.316629i
$631$	−6.93764	+	6.93764i	−0.276183	+	0.276183i	−0.831583	−	0.555400i	$-0.812565\pi$
$631$	−6.93764	+	6.93764i	−0.276183	+	0.276183i	0.555400	+	0.831583i	$0.312565\pi$
$632$	14.4687	−	3.87687i	0.575534	−	0.154214i
$633$	9.81247	−	2.77012i	0.390011	−	0.110102i
$634$	2.56006	−	1.47805i	0.101673	−	0.0587009i
$635$	−1.69146	+	6.31263i	−0.0671237	+	0.250509i
$636$	−1.79044	+	0.505451i	−0.0709954	+	0.0200424i
$637$	3.84805	−	21.9867i	0.152465	−	0.871146i
$638$			15.6525i			0.619689i
$639$	17.1895	−	5.10136i	0.680008	−	0.201807i
$640$	19.5333			0.772120
$641$	13.6931	−	23.7171i	0.540843	−	0.936768i	−0.458013	−	0.888946i	$-0.651439\pi$
$641$	13.6931	−	23.7171i	0.540843	−	0.936768i	0.998856	−	0.0478223i	$-0.0152281\pi$
$642$	0.0521077	+	3.90406i	0.00205653	+	0.154081i
$643$	−5.55334	+	20.7253i	−0.219002	+	0.817328i	0.765717	+	0.643178i	$0.222384\pi$
$643$	−5.55334	+	20.7253i	−0.219002	+	0.817328i	−0.984719	+	0.174150i	$0.944282\pi$
$644$	1.41588	−	5.28413i	0.0557934	−	0.208224i
$645$	−26.0920	+	15.5322i	−1.02737	+	0.611579i
$646$	2.79076	−	4.83374i	0.109801	−	0.190181i
$647$	45.0052			1.76934			0.884669	−	0.466219i	$-0.154384\pi$
$647$	45.0052			1.76934			0.884669	+	0.466219i	$0.154384\pi$
$648$	5.58384	−	26.4029i	0.219354	−	1.03721i
$649$		−	22.5371i		−	0.884658i
$650$	2.06683	+	2.94377i	0.0810678	+	0.115464i
$651$	5.81446	−	22.9191i	0.227886	−	0.898270i
$652$	−0.129394	+	0.482907i	−0.00506748	+	0.0189121i
$653$	10.2668	−	5.92754i	0.401771	−	0.231963i	−0.285477	−	0.958386i	$-0.592152\pi$
$653$	10.2668	−	5.92754i	0.401771	−	0.231963i	0.687248	+	0.726423i	$0.258819\pi$
$654$	−26.1670	−	25.4777i	−1.02321	−	0.996256i
$655$	15.8105	−	4.23642i	0.617768	−	0.165530i
$656$	−20.8230	+	20.8230i	−0.813000	+	0.813000i
$657$	2.66389	−	0.790567i	0.103928	−	0.0308430i
$658$	−22.9248	+	22.9248i	−0.893700	+	0.893700i
$659$	31.6578	+	18.2776i	1.23321	+	0.711995i	0.967698	−	0.252112i	$-0.0811253\pi$
$659$	31.6578	+	18.2776i	1.23321	+	0.711995i	0.265513	+	0.964107i	$0.414459\pi$
$660$	1.35078	+	4.78480i	0.0525790	+	0.186248i
$661$	−26.1261	−	7.00047i	−1.01619	−	0.272287i	−0.287975	−	0.957638i	$-0.592982\pi$
$661$	−26.1261	−	7.00047i	−1.01619	−	0.272287i	−0.728213	+	0.685351i	$0.759649\pi$
$662$	−22.5215	−	39.0084i	−0.875323	−	1.51610i
$663$	4.38297	+	6.06875i	0.170220	+	0.235691i
$664$	−2.44746	+	4.23913i	−0.0949799	+	0.164510i
$665$	−22.0162	+	22.0162i	−0.853751	+	0.853751i
$666$	19.1015	+	31.1349i	0.740167	+	1.20645i
$667$		−	15.1221i		−	0.585532i
$668$	−0.398499	−	1.48722i	−0.0154184	−	0.0575423i
$669$	0.611749	+	45.8340i	0.0236516	+	1.77205i
$670$	−16.9306	−	4.53655i	−0.654087	−	0.175262i
$671$	−13.4377	+	50.1500i	−0.518755	+	1.93602i
$672$	−10.2331	−	2.59608i	−0.394750	−	0.100146i
$673$	8.95874	+	5.17233i	0.345334	+	0.199379i	0.662628	−	0.748948i	$-0.269441\pi$
$673$	8.95874	+	5.17233i	0.345334	+	0.199379i	−0.317294	+	0.948327i	$0.602774\pi$
$674$	20.0893	+	20.0893i	0.773811	+	0.773811i
$675$	−3.79520	+	1.18164i	−0.146077	+	0.0454814i
$676$	−2.50882	−	2.97450i	−0.0964930	−	0.114404i
$677$	26.6682	+	15.3969i	1.02494	+	0.591751i	0.915532	−	0.402245i	$-0.131770\pi$
$677$	26.6682	+	15.3969i	1.02494	+	0.591751i	0.109411	+	0.993997i	$0.465103\pi$
$678$	15.3630	−	9.14536i	0.590012	−	0.351225i
$679$	−24.7229	−	42.8213i	−0.948778	−	1.64333i
$680$	−4.31516	−	7.47408i	−0.165479	−	0.286618i
$681$	9.65427	−	0.128856i	0.369952	−	0.00493777i
$682$	18.9109	−	5.06715i	0.724134	−	0.194031i
$683$	4.77976	+	4.77976i	0.182893	+	0.182893i	0.792615	−	0.609722i	$-0.208719\pi$
$683$	4.77976	+	4.77976i	0.182893	+	0.182893i	−0.609722	+	0.792615i	$0.708719\pi$
$684$	−2.32683	−	2.20581i	−0.0889686	−	0.0843414i
$685$	8.89647			0.339916
$686$	1.91653	−	3.31953i	0.0731735	−	0.126740i
$687$	−3.70587	+	6.62128i	−0.141388	+	0.252618i
$688$	20.9413	−	12.0905i	0.798380	−	0.460945i
$689$	9.92183	+	8.30393i	0.377992	+	0.316355i
$690$	7.41461	+	26.2645i	0.282269	+	0.999871i
$691$	5.93946	−	1.59147i	0.225948	−	0.0605425i	−0.144069	−	0.989568i	$-0.546019\pi$
$691$	5.93946	−	1.59147i	0.225948	−	0.0605425i	0.370017	+	0.929025i	$0.379352\pi$
$692$		−	0.391718i		−	0.0148909i
$693$	1.16146	+	43.5021i	0.0441201	+	1.65251i
$694$	16.1670	+	16.1670i	0.613690	+	0.613690i
$695$	−4.95154	−	18.4794i	−0.187822	−	0.700963i
$696$	−15.6062	+	0.208297i	−0.591551	+	0.00789546i
$697$	10.2958	+	2.75876i	0.389982	+	0.104495i
$698$	4.08702	−	2.35964i	0.154696	−	0.0893137i
$699$	1.00360	−	3.95594i	0.0379597	−	0.149627i
$700$	0.215239	+	0.803283i	0.00813527	+	0.0303612i
$701$	−11.6684			−0.440711			−0.220355	−	0.975420i	$-0.570722\pi$
$701$	−11.6684			−0.440711			−0.220355	+	0.975420i	$0.570722\pi$
$702$	−22.5941	+	9.29736i	−0.852761	+	0.350906i
$703$	33.3358			1.25728
$704$	−9.10931	−	33.9964i	−0.343320	−	1.28129i
$705$	−7.00006	+	27.5924i	−0.263637	+	1.03919i
$706$	−24.8339	+	14.3379i	−0.934637	+	0.539613i
$707$	−5.29628	−	1.41913i	−0.199187	−	0.0533720i
$708$	2.92520	−	0.0390428i	0.109936	−	0.00146732i
$709$	−2.50829	−	9.36105i	−0.0942006	−	0.351562i	0.902696	−	0.430278i	$-0.141584\pi$
$709$	−2.50829	−	9.36105i	−0.0942006	−	0.351562i	−0.996897	+	0.0787165i	$0.974918\pi$
$710$	13.2332	+	13.2332i	0.496634	+	0.496634i
$711$	12.7739	−	7.83689i	0.479060	−	0.293906i
$712$		−	37.4441i		−	1.40328i
$713$	−18.2701	+	4.89545i	−0.684220	+	0.183336i
$714$	−2.67172	−	9.46393i	−0.0999868	−	0.354179i
$715$	22.1916	−	26.5153i	0.829919	−	0.991616i
$716$	3.04653	−	1.75891i	0.113854	−	0.0657337i
$717$	−23.5550	+	42.0857i	−0.879677	+	1.57172i
$718$	9.21831	−	15.9666i	0.344024	−	0.595867i
$719$	−12.1983			−0.454918			−0.227459	−	0.973788i	$-0.573042\pi$
$719$	−12.1983			−0.454918			−0.227459	+	0.973788i	$0.573042\pi$
$720$	22.8691	−	6.78688i	0.852279	−	0.252932i
$721$	10.4707	+	10.4707i	0.389948	+	0.389948i
$722$	−7.87516	+	2.11014i	−0.293083	+	0.0785314i
$723$	27.7453	−	0.370318i	1.03186	−	0.0137723i
$724$	−3.91088	−	6.77385i	−0.145347	−	0.251748i
$725$	1.14942	+	1.99085i	0.0426883	+	0.0739384i
$726$	−9.61167	+	5.72168i	−0.356723	+	0.212351i
$727$	−29.3434	−	16.9414i	−1.08829	−	0.628322i	−0.155166	−	0.987888i	$-0.549591\pi$
$727$	−29.3434	−	16.9414i	−1.08829	−	0.628322i	−0.933119	+	0.359567i	$0.882925\pi$
$728$	13.4767	+	36.8809i	0.499478	+	1.36690i
$729$	−2.15978	−	26.9135i	−0.0799920	−	0.996796i
$730$	2.05078	+	2.05078i	0.0759027	+	0.0759027i
$731$	−7.57991	−	4.37626i	−0.280353	−	0.161862i
$732$	−6.53250	−	1.65726i	−0.241448	−	0.0612542i
$733$	−1.66693	+	6.22108i	−0.0615696	+	0.229781i	−0.989854	−	0.142091i	$-0.954617\pi$
$733$	−1.66693	+	6.22108i	−0.0615696	+	0.229781i	0.928284	+	0.371872i	$0.121284\pi$
$734$	−38.3667	−	10.2803i	−1.41614	−	0.379454i
$735$	0.343595	+	25.7431i	0.0126737	+	0.949550i
$736$	2.18576	+	8.15737i	0.0805682	+	0.300685i
$737$			22.3579i			0.823562i
$738$	−16.5838	+	30.5810i	−0.610459	+	1.12570i
$739$	6.62890	−	6.62890i	0.243848	−	0.243848i	−0.574592	−	0.818440i	$-0.694839\pi$
$739$	6.62890	−	6.62890i	0.243848	−	0.243848i	0.818440	+	0.574592i	$0.194839\pi$
$740$	3.35507	−	5.81115i	0.123335	−	0.213622i
$741$	−3.55055	+	22.0130i	−0.130433	+	0.808669i
$742$	−8.49803	−	14.7190i	−0.311972	−	0.540352i
$743$	18.8322	+	5.04607i	0.690886	+	0.185122i	0.587145	−	0.809482i	$-0.300252\pi$
$743$	18.8322	+	5.04607i	0.690886	+	0.185122i	0.103741	+	0.994604i	$0.466919\pi$
$744$	5.30381	+	18.7875i	0.194447	+	0.688782i
$745$	−26.0459	−	15.0376i	−0.954246	−	0.550934i
$746$	−12.3954	+	12.3954i	−0.453826	+	0.453826i
$747$	−1.14081	+	4.76256i	−0.0417400	+	0.174253i
$748$	−1.01335	+	1.01335i	−0.0370516	+	0.0370516i
$749$	6.06404	−	1.62485i	0.221575	−	0.0593709i
$750$	16.4562	+	16.0227i	0.600897	+	0.585068i
$751$	−24.3100	+	14.0354i	−0.887086	+	0.512159i	−0.872988	−	0.487741i	$-0.837821\pi$
$751$	−24.3100	+	14.0354i	−0.887086	+	0.512159i	−0.0140977	+	0.999901i	$0.504488\pi$
$752$	5.86718	−	21.8966i	0.213954	−	0.798487i
$753$	4.62047	−	18.2127i	0.168379	−	0.663709i
$754$	8.11941	+	11.5644i	0.295691	+	0.421151i
$755$		−	8.68896i		−	0.316224i
$756$	−5.64435	+	0.226114i	−0.205283	+	0.00822367i
$757$	−46.4797			−1.68933			−0.844667	−	0.535292i	$-0.820201\pi$
$757$	−46.4797			−1.68933			−0.844667	+	0.535292i	$0.820201\pi$
$758$	−3.78901	+	6.56275i	−0.137623	+	0.238370i
$759$	29.9125	−	17.8064i	1.08575	−	0.646333i
$760$	6.65320	−	24.8301i	0.241337	−	0.900681i
$761$	−9.00310	+	33.6000i	−0.326362	+	1.21800i	0.586574	+	0.809896i	$0.300476\pi$
$761$	−9.00310	+	33.6000i	−0.326362	+	1.21800i	−0.912936	+	0.408104i	$0.866190\pi$
$762$	−0.0820513	−	6.14752i	−0.00297240	−	0.222701i
$763$	−29.3618	+	50.8561i	−1.06297	+	1.84111i
$764$	6.70445			0.242558
$765$	−6.26629	−	5.94039i	−0.226558	−	0.214775i
$766$		−	8.00082i		−	0.289081i
$767$	−11.6906	−	16.6509i	−0.422124	−	0.601228i
$768$	11.6932	−	3.30105i	0.421940	−	0.119116i
$769$	−3.54846	+	13.2430i	−0.127961	+	0.477556i	−0.999928	−	0.0120081i	$-0.996178\pi$
$769$	−3.54846	+	13.2430i	−0.127961	+	0.477556i	0.871967	+	0.489565i	$0.162844\pi$
$770$	−39.3354	+	22.7103i	−1.41755	+	0.818423i
$771$	15.6215	−	4.41003i	0.562594	−	0.158823i
$772$	2.24593	−	0.601794i	0.0808326	−	0.0216590i
$773$	−15.1145	+	15.1145i	−0.543631	+	0.543631i	−0.924591	−	0.380960i	$-0.875593\pi$
$773$	−15.1145	+	15.1145i	−0.543631	+	0.543631i	0.380960	+	0.924591i	$0.375593\pi$
$774$	19.6528	−	20.7310i	0.706407	−	0.745162i
$775$	2.03318	−	2.03318i	0.0730341	−	0.0730341i
$776$	35.3539	+	20.4116i	1.26913	+	0.732733i
$777$	40.9725	−	42.0810i	1.46988	−	1.50965i
$778$	−32.6369	−	8.74504i	−1.17009	−	0.313525i
$779$	15.8743	+	27.4951i	0.568756	+	0.985114i
$780$	3.48000	+	2.83443i	0.124604	+	0.101489i
$781$	11.9358	−	20.6734i	0.427097	−	0.739753i
$782$	−5.56240	+	5.56240i	−0.198911	+	0.198911i
$783$	−14.9092	+	4.64200i	−0.532811	+	0.165892i
$784$		−	20.5021i		−	0.732218i
$785$	5.51560	+	20.5845i	0.196860	+	0.734692i
$786$	−13.2314	+	7.87647i	−0.471950	+	0.280945i
$787$	−7.40236	−	1.98346i	−0.263866	−	0.0707026i	0.124461	−	0.992225i	$-0.460280\pi$
$787$	−7.40236	−	1.98346i	−0.263866	−	0.0707026i	−0.388326	+	0.921522i	$0.626947\pi$
$788$	−0.845107	+	3.15398i	−0.0301057	+	0.112356i
$789$	33.9852	−	34.9047i	1.20990	−	1.24264i
$790$	13.5461	+	7.82084i	0.481948	+	0.278253i
$791$	−20.3279	−	20.3279i	−0.722776	−	0.722776i
$792$	−18.7884	−	30.6247i	−0.667618	−	1.08820i
$793$	16.0862	+	44.0224i	0.571239	+	1.56328i
$794$	11.2718	+	6.50780i	0.400022	+	0.230953i
$795$	−13.0223	−	7.28847i	−0.461854	−	0.258495i
$796$	2.58692	+	4.48068i	0.0916910	+	0.158813i
$797$	11.2181	+	19.4304i	0.397367	+	0.688259i	0.993400	−	0.114700i	$-0.0365908\pi$
$797$	11.2181	+	19.4304i	0.397367	+	0.688259i	−0.596033	+	0.802960i	$0.703257\pi$
$798$	14.3055	−	25.5597i	0.506409	−	0.904803i
$799$	−7.92568	+	2.12368i	−0.280390	+	0.0751304i
$800$	−0.907792	−	0.907792i	−0.0320953	−	0.0320953i
$801$	−10.6582	−	35.9140i	−0.376591	−	1.26896i
$802$	−15.4070			−0.544041
$803$	1.84971	−	3.20380i	0.0652750	−	0.113060i
$804$	−2.90194	+	0.0387323i	−0.102343	+	0.00136598i
$805$	38.0026	−	21.9408i	1.33941	−	0.773312i
$806$	11.3433	−	13.5533i	0.399549	−	0.477395i
$807$	−21.3978	−	5.42851i	−0.753238	−	0.191093i
$808$	4.37268	−	1.17166i	0.153830	−	0.0412187i
$809$			29.7930i			1.04747i	0.851883	+	0.523733i	$0.175461\pi$
$809$			29.7930i			1.04747i	−0.851883	+	0.523733i	$0.824539\pi$
$810$	23.6186	−	15.3725i	0.829872	−	0.540135i
$811$	8.70198	+	8.70198i	0.305568	+	0.305568i	0.843187	−	0.537620i	$-0.180676\pi$
$811$	8.70198	+	8.70198i	0.305568	+	0.305568i	−0.537620	+	0.843187i	$0.680676\pi$
$812$	0.845551	+	3.15564i	0.0296730	+	0.110741i
$813$	3.67394	+	6.17173i	0.128851	+	0.216452i
$814$	46.9733	+	12.5865i	1.64641	+	0.441155i
$815$	−3.47298	+	2.00513i	−0.121653	+	0.0702366i
$816$	4.92652	+	4.79674i	0.172463	+	0.167920i
$817$	−6.74740	−	25.1817i	−0.236062	−	0.880995i
$818$	31.5919			1.10458
$819$	23.4239	+	31.5378i	0.818498	+	1.10202i
$820$	6.39064			0.223171
$821$	−8.99938	−	33.5861i	−0.314080	−	1.17216i	−0.924843	−	0.380350i	$-0.875804\pi$
$821$	−8.99938	−	33.5861i	−0.314080	−	1.17216i	0.610762	−	0.791814i	$-0.290863\pi$
$822$	−8.05451	+	2.27384i	−0.280933	+	0.0793091i
$823$	−4.48030	+	2.58670i	−0.156173	+	0.0901667i	−0.576050	−	0.817414i	$-0.695407\pi$
$823$	−4.48030	+	2.58670i	−0.156173	+	0.0901667i	0.419877	+	0.907581i	$0.362073\pi$
$824$	−11.8089	−	3.16419i	−0.411383	−	0.110230i
$825$	−2.58457	+	4.61786i	−0.0899833	+	0.160773i
$826$	6.91717	+	25.8152i	0.240679	+	0.898227i
$827$	−25.7643	−	25.7643i	−0.895912	−	0.895912i	0.0991598	−	0.995072i	$-0.468385\pi$
$827$	−25.7643	−	25.7643i	−0.895912	−	0.895912i	−0.995072	+	0.0991598i	$0.968385\pi$
$828$	2.36301	+	3.85164i	0.0821202	+	0.133854i
$829$		−	2.79539i		−	0.0970878i	−0.998821	−	0.0485439i	$-0.984542\pi$
$829$		−	2.79539i		−	0.0970878i	0.998821	−	0.0485439i	$-0.0154581\pi$
$830$	−4.93727	+	1.32294i	−0.171375	+	0.0459199i
$831$	21.2314	−	21.8058i	0.736507	−	0.756434i
$832$	−24.3651	−	20.3920i	−0.844707	−	0.706966i
$833$	−6.42671	+	3.71046i	−0.222672	+	0.128560i
$834$	9.20605	+	15.4650i	0.318779	+	0.535507i
$835$	6.17524	−	10.6958i	0.213703	−	0.370145i
$836$	−4.26855			−0.147631
$837$	10.4348	+	16.5101i	0.360680	+	0.570671i
$838$	−13.0411	−	13.0411i	−0.450497	−	0.450497i
$839$	−22.1519	+	5.93559i	−0.764769	+	0.204919i	−0.620060	−	0.784555i	$-0.712892\pi$
$839$	−22.1519	+	5.93559i	−0.764769	+	0.204919i	−0.144710	+	0.989474i	$0.546225\pi$
$840$	−23.1666	−	38.9168i	−0.799322	−	1.34276i
$841$	−9.98459	−	17.2938i	−0.344296	−	0.596338i
$842$	0.0204785	+	0.0354699i	0.000705737	+	0.00122237i
$843$	0.754296	+	56.5140i	0.0259793	+	1.94645i
$844$	1.52597	+	0.881018i	0.0525260	+	0.0303259i
$845$	2.64138	−	31.1015i	0.0908662	−	1.06992i
$846$	−0.714735	−	26.7702i	−0.0245731	−	0.920380i
$847$	12.7179	+	12.7179i	0.436992	+	0.436992i
$848$	10.2918	+	5.94198i	0.353422	+	0.204048i
$849$	−4.10004	−	14.5234i	−0.140713	−	0.498442i
$850$	0.309506	−	1.15509i	0.0106160	−	0.0396193i
$851$	−45.3817	−	12.1600i	−1.55566	−	0.416839i
$852$	2.70398	+	1.51339i	0.0926370	+	0.0518480i
$853$	10.8069	+	40.3318i	0.370020	+	1.38093i	0.860487	+	0.509473i	$0.170160\pi$
$853$	10.8069	+	40.3318i	0.370020	+	1.38093i	−0.490467	+	0.871460i	$0.663174\pi$
$854$		−	61.5690i		−	2.10685i
$855$	−0.686408	−	25.7093i	−0.0234746	−	0.879238i
$856$	−3.66505	+	3.66505i	−0.125269	+	0.125269i
$857$	−28.9446	+	50.1335i	−0.988729	+	1.71253i	−0.364704	+	0.931124i	$0.618830\pi$
$857$	−28.9446	+	50.1335i	−0.988729	+	1.71253i	−0.624025	+	0.781404i	$0.714504\pi$
$858$	−13.3144	+	29.6778i	−0.454546	+	1.01318i
$859$	2.91461	+	5.04825i	0.0994452	+	0.172244i	0.911455	−	0.411399i	$-0.134960\pi$
$859$	2.91461	+	5.04825i	0.0994452	+	0.172244i	−0.812010	+	0.583644i	$0.801627\pi$
$860$	−5.06879	−	1.35818i	−0.172844	−	0.0463135i
$861$	54.2189	+	13.7550i	1.84777	+	0.468771i
$862$	9.36628	+	5.40763i	0.319017	+	0.184184i
$863$	6.14702	−	6.14702i	0.209247	−	0.209247i	−0.594700	−	0.803947i	$-0.702729\pi$
$863$	6.14702	−	6.14702i	0.209247	−	0.209247i	0.803947	+	0.594700i	$0.202729\pi$
$864$	7.37154	−	4.65902i	0.250785	−	0.158503i
$865$	2.22183	−	2.22183i	0.0755446	−	0.0755446i
$866$	34.0033	−	9.11115i	1.15548	−	0.309609i
$867$	−6.62862	+	26.1283i	−0.225120	+	0.887364i
$868$	3.53881	−	2.04314i	0.120115	−	0.0693485i
$869$	5.16393	−	19.2721i	0.175174	−	0.653760i
$870$	−11.6772	−	11.3696i	−0.395893	−	0.385465i
$871$	11.5977	+	16.5185i	0.392972	+	0.559706i
$872$		−	48.4829i		−	1.64184i
$873$	39.7193	+	9.51423i	1.34429	+	0.322008i
$874$	−23.4307			−0.792554
$875$	18.4654	−	31.9830i	0.624245	−	1.08122i
$876$	0.419041	+	0.234533i	0.0141581	+	0.00792415i
$877$	1.53858	−	5.74207i	0.0519543	−	0.193896i	−0.935071	−	0.354460i	$-0.884665\pi$
$877$	1.53858	−	5.74207i	0.0519543	−	0.193896i	0.987025	+	0.160564i	$0.0513313\pi$
$878$	−9.25980	+	34.5580i	−0.312503	+	1.16628i
$879$	3.93110	+	2.20020i	0.132593	+	0.0742108i
$880$	15.8795	−	27.5040i	0.535297	−	0.927161i
$881$	−49.0408			−1.65223			−0.826113	−	0.563504i	$-0.809453\pi$
$881$	−49.0408			−1.65223			−0.826113	+	0.563504i	$0.809453\pi$
$882$	−6.89073	−	23.2190i	−0.232023	−	0.781824i
$883$		−	30.0126i		−	1.01001i	−0.863118	−	0.505003i	$-0.831491\pi$
$883$		−	30.0126i		−	1.01001i	0.863118	−	0.505003i	$-0.168509\pi$
$884$	−0.223030	+	1.27433i	−0.00750130	+	0.0428605i
$885$	16.8132	+	16.3703i	0.565171	+	0.550283i
$886$	−0.983183	+	3.66929i	−0.0330307	+	0.123272i
$887$	−28.0225	+	16.1788i	−0.940902	+	0.543230i	−0.890243	−	0.455486i	$-0.849466\pi$
$887$	−28.0225	+	16.1788i	−0.940902	+	0.543230i	−0.0506591	+	0.998716i	$0.516132\pi$
$888$	−11.9241	+	47.0018i	−0.400147	+	1.57728i
$889$	−9.54873	+	2.55858i	−0.320254	+	0.0858119i
$890$	27.6481	−	27.6481i	0.926768	−	0.926768i
$891$	−26.7378	−	24.0253i	−0.895751	−	0.804877i
$892$	−5.60140	+	5.60140i	−0.187549	+	0.187549i
$893$	−21.1656	−	12.2200i	−0.708280	−	0.408925i
$894$	27.4243	+	6.95741i	0.917207	+	0.232691i
$895$	27.2565	+	7.30337i	0.911086	+	0.244125i
$896$	14.7734	+	25.5883i	0.493545	+	0.854844i
$897$	12.8633	−	28.6722i	0.429492	−	0.957338i
$898$	21.5468	−	37.3201i	0.719025	−	1.24539i
$899$	7.98722	−	7.98722i	0.266389	−	0.266389i
$900$	−0.603853	−	0.327465i	−0.0201284	−	0.0109155i
$901$		−	4.30151i		−	0.143304i
$902$	11.9872	+	44.7367i	0.399129	+	1.48957i
$903$	−40.0808	−	22.4328i	−1.33381	−	0.746518i
$904$	22.9260	+	6.14299i	0.762506	+	0.204313i
$905$	16.2388	−	60.6040i	0.539796	−	2.01455i
$906$	2.22080	+	7.86664i	0.0737811	+	0.261352i
$907$	−7.97950	−	4.60697i	−0.264955	−	0.152972i	0.361638	−	0.932319i	$-0.382218\pi$
$907$	−7.97950	−	4.60697i	−0.264955	−	0.152972i	−0.626593	+	0.779347i	$0.715551\pi$
$908$	1.17985	+	1.17985i	0.0391548	+	0.0391548i
$909$	3.86050	−	2.36844i	0.128045	−	0.0785562i
$910$	−17.2813	+	37.1833i	−0.572871	+	1.23261i
$911$	−33.4540	−	19.3147i	−1.10838	−	0.639924i	−0.169971	−	0.985449i	$-0.554367\pi$
$911$	−33.4540	−	19.3147i	−1.10838	−	0.639924i	−0.938409	+	0.345525i	$0.887701\pi$
$912$	0.273331	+	20.4788i	0.00905090	+	0.678120i
$913$	3.25998	+	5.64644i	0.107889	+	0.186870i
$914$	5.05896	+	8.76237i	0.167335	+	0.289833i
$915$	−27.6525	−	46.4525i	−0.914162	−	1.53567i
$916$	−1.26662	+	0.339389i	−0.0418502	+	0.0112137i
$917$	17.5075	+	17.5075i	0.578147	+	0.578147i
$918$	7.19155	+	3.77660i	0.237356	+	0.124646i
$919$	−9.77449			−0.322431			−0.161215	−	0.986919i	$-0.551541\pi$
$919$	−9.77449			−0.322431			−0.161215	+	0.986919i	$0.551541\pi$
$920$	−18.1146	+	31.3755i	−0.597222	+	1.03442i
$921$	−21.6518	−	36.3722i	−0.713451	−	1.19850i
$922$	−32.6439	+	18.8470i	−1.07507	+	0.620692i
$923$	−1.90548	−	21.4654i	−0.0627195	−	0.706543i
$924$	−5.24640	+	5.38834i	−0.172594	+	0.177263i
$925$	6.89883	−	1.84854i	0.226832	−	0.0607795i
$926$		−	15.6652i		−	0.514790i
$927$	−12.2271	+	0.326449i	−0.401589	+	0.0107220i
$928$	−3.56620	−	3.56620i	−0.117066	−	0.117066i
$929$	6.95657	+	25.9623i	0.228238	+	0.851794i	0.981082	+	0.193595i	$0.0620148\pi$
$929$	6.95657	+	25.9623i	0.228238	+	0.851794i	−0.752844	+	0.658199i	$0.771319\pi$
$930$	−9.95612	+	17.7886i	−0.326474	+	0.583312i
$931$	−21.3505	−	5.72086i	−0.699736	−	0.187494i
$932$	0.610815	−	0.352654i	0.0200079	−	0.0115516i
$933$	−26.5316	+	7.49004i	−0.868607	+	0.245213i
$934$	11.5372	+	43.0574i	0.377508	+	1.40888i
$935$	−11.4954			−0.375941
$936$	−29.7672	−	12.8801i	−0.972971	−	0.420998i
$937$	−17.6915			−0.577955			−0.288977	−	0.957336i	$-0.593315\pi$
$937$	−17.6915			−0.577955			−0.288977	+	0.957336i	$0.593315\pi$
$938$	−6.86216	−	25.6099i	−0.224058	−	0.836194i
$939$	−11.7344	−	11.4253i	−0.382938	−	0.372850i
$940$	−4.26040	+	2.45974i	−0.138959	+	0.0802280i
$941$	−8.80815	−	2.36014i	−0.287137	−	0.0769382i	0.112375	−	0.993666i	$-0.464154\pi$
$941$	−8.80815	−	2.36014i	−0.287137	−	0.0769382i	−0.399513	+	0.916728i	$0.630821\pi$
$942$	−10.2548	−	17.2267i	−0.334119	−	0.561275i
$943$	−11.5810	−	43.2209i	−0.377129	−	1.40747i
$944$	−13.2139	−	13.2139i	−0.430075	−	0.430075i
$945$	−33.2974	−	30.7323i	−1.08316	−	0.999723i
$946$		−	38.0309i		−	1.23649i
$947$	−2.04283	+	0.547375i	−0.0663831	+	0.0177873i	−0.291858	−	0.956462i	$-0.594273\pi$
$947$	−2.04283	+	0.547375i	−0.0663831	+	0.0177873i	0.225475	+	0.974249i	$0.427607\pi$
$948$	2.51036	+	0.636866i	0.0815328	+	0.0206844i
$949$	−0.295295	−	3.32653i	−0.00958568	−	0.107984i
$950$	3.08468	−	1.78094i	0.100080	−	0.0577813i
$951$	3.92582	−	0.0523981i	0.127304	−	0.00169913i
$952$	6.52729	−	11.3056i	0.211551	−	0.366416i
$953$	45.0716			1.46001			0.730007	−	0.683440i	$-0.239517\pi$
$953$	45.0716			1.46001			0.730007	+	0.683440i	$0.239517\pi$
$954$	13.6527	+	3.27033i	0.442024	+	0.105881i
$955$	38.0277	+	38.0277i	1.23055	+	1.23055i
$956$	−8.05078	+	2.15720i	−0.260381	+	0.0697689i
$957$	−10.1533	+	18.1409i	−0.328210	+	0.586414i
$958$	3.17143	+	5.49308i	0.102464	+	0.177473i
$959$	6.72858	+	11.6542i	0.217277	+	0.376335i
$960$	31.9790	+	17.8983i	1.03212	+	0.577666i
$961$	14.6112	+	8.43578i	0.471329	+	0.272122i
$962$	41.2338	−	15.0673i	1.32943	−	0.485788i
$963$	−2.47205	+	4.55853i	−0.0796608	+	0.146896i
$964$	3.39078	+	3.39078i	0.109210	+	0.109210i
$965$	16.1523	+	9.32555i	0.519962	+	0.300200i
$966$	−28.7982	+	29.5774i	−0.926568	+	0.951636i
$967$	−0.493189	+	1.84061i	−0.0158599	+	0.0591900i	−0.973402	−	0.229103i	$-0.926421\pi$
$967$	−0.493189	+	1.84061i	−0.0158599	+	0.0591900i	0.957542	+	0.288293i	$0.0930876\pi$
$968$	−14.3433	−	3.84329i	−0.461013	−	0.123528i
$969$	6.36993	−	3.79192i	0.204632	−	0.121814i
$970$	11.0332	+	41.1764i	0.354254	+	1.32209i
$971$			43.0782i			1.38245i	0.722642	+	0.691223i	$0.242928\pi$
$971$			43.0782i			1.38245i	−0.722642	+	0.691223i	$0.757072\pi$
$972$	3.07204	−	3.51206i	0.0985357	−	0.112649i
$973$	20.4628	−	20.4628i	0.656006	−	0.656006i
$974$	−10.1933	+	17.6553i	−0.326615	+	0.565714i
$975$	0.485881	+	4.75247i	0.0155607	+	0.152201i
$976$	21.5251	+	37.2826i	0.689002	+	1.19339i
$977$	−14.9050	−	3.99377i	−0.476852	−	0.127772i	0.0123844	−	0.999923i	$-0.496058\pi$
$977$	−14.9050	−	3.99377i	−0.476852	−	0.127772i	−0.489236	+	0.872151i	$0.662725\pi$
$978$	2.63181	−	2.70302i	0.0841561	−	0.0864330i
$979$	−43.1929	−	24.9374i	−1.38045	−	0.797004i
$980$	−3.14608	+	3.14608i	−0.100498	+	0.100498i
$981$	−13.8004	−	46.5018i	−0.440613	−	1.48469i
$982$	32.9985	−	32.9985i	1.05303	−	1.05303i
$983$	54.3666	−	14.5675i	1.73403	−	0.464631i	0.752922	−	0.658110i	$-0.228644\pi$
$983$	54.3666	−	14.5675i	1.73403	−	0.464631i	0.981105	+	0.193479i	$0.0619770\pi$
$984$	−44.4448	+	12.5470i	−1.41685	+	0.399985i
$985$	−22.6829	+	13.0960i	−0.722737	+	0.417273i
$986$	1.21587	−	4.53769i	0.0387212	−	0.144510i
$987$	−41.4400	+	11.6987i	−1.31905	+	0.372375i
$988$	−3.15369	+	2.21422i	−0.100332	+	0.0704437i
$989$			36.7423i			1.16834i
$990$	8.73971	−	36.4859i	0.277766	−	1.15960i
$991$	34.3792			1.09209			0.546046	−	0.837755i	$-0.316132\pi$
$991$	34.3792			1.09209			0.546046	+	0.837755i	$0.316132\pi$
$992$	−3.15409	+	5.46304i	−0.100142	+	0.173452i
$993$	−0.798407	−	59.8190i	−0.0253367	−	1.89830i
$994$	−7.32677	+	27.3439i	−0.232391	+	0.867295i
$995$	−10.7414	+	40.0876i	−0.340526	+	1.27086i
$996$	−0.727233	+	0.432910i	−0.0230433	+	0.0137173i
$997$	−25.4741	+	44.1224i	−0.806773	+	1.39737i	0.108315	+	0.994117i	$0.465455\pi$
$997$	−25.4741	+	44.1224i	−0.806773	+	1.39737i	−0.915088	+	0.403255i	$0.867879\pi$
$998$	−2.78080			−0.0880246
$999$	1.94193	+	48.4753i	0.0614399	+	1.53369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.z.b.47.3	yes	44
3.2	odd	2		351.2.bc.b.8.9		44
9.4	even	3		351.2.bc.b.125.9		44
9.5	odd	6	inner	117.2.z.b.86.3	yes	44
13.5	odd	4	inner	117.2.z.b.83.3	yes	44
39.5	even	4		351.2.bc.b.278.9		44
117.5	even	12	inner	117.2.z.b.5.3	✓	44
117.31	odd	12		351.2.bc.b.44.9		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.z.b.5.3	✓	44	117.5	even	12	inner
117.2.z.b.47.3	yes	44	1.1	even	1	trivial
117.2.z.b.83.3	yes	44	13.5	odd	4	inner
117.2.z.b.86.3	yes	44	9.5	odd	6	inner
351.2.bc.b.8.9		44	3.2	odd	2
351.2.bc.b.44.9		44	117.31	odd	12
351.2.bc.b.125.9		44	9.4	even	3
351.2.bc.b.278.9		44	39.5	even	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.337526 - 1.25966i) q^{2} +(0.425920 - 1.67887i) q^{3} +(0.259225 - 0.149663i) q^{4} +(2.31922 + 0.621434i) q^{5} +(-2.25856 + 0.0301452i) q^{6} +(0.940006 + 3.50815i) q^{7} +(-2.12029 - 2.12029i) q^{8} +(-2.63718 - 1.43012i) q^{9} -3.13119i q^{10} +(-3.85792 + 1.03373i) q^{11} +(-0.140856 - 0.498948i) q^{12} +(-2.31409 + 2.76496i) q^{13} +(4.10181 - 2.36818i) q^{14} +(2.03111 - 3.62898i) q^{15} +(-1.65587 + 2.86806i) q^{16} +1.19872 q^{17} +(-0.911357 + 3.80467i) q^{18} +(2.52470 + 2.52470i) q^{19} +(0.694206 - 0.186012i) q^{20} +(6.29008 - 0.0839540i) q^{21} +(2.60430 + 4.51077i) q^{22} +(-2.51605 - 4.35793i) q^{23} +(-4.46277 + 2.65662i) q^{24} +(0.662484 + 0.382485i) q^{25} +(4.26398 + 1.98173i) q^{26} +(-3.52422 + 3.81836i) q^{27} +(0.768714 + 0.768714i) q^{28} +(2.60252 + 1.50257i) q^{29} +(-5.25684 - 1.33363i) q^{30} +(0.972844 - 3.63070i) q^{31} +(-1.62107 - 0.434363i) q^{32} +(0.0923245 + 6.91722i) q^{33} +(-0.404598 - 1.50998i) q^{34} +8.72033i q^{35} +(-0.897661 + 0.0239665i) q^{36} +(6.60194 - 6.60194i) q^{37} +(2.32812 - 4.03242i) q^{38} +(3.65637 + 5.06270i) q^{39} +(-3.59981 - 6.23506i) q^{40} +(8.58903 + 2.30142i) q^{41} +(-2.22882 - 7.89504i) q^{42} +(-6.32334 - 3.65078i) q^{43} +(-0.845358 + 0.845358i) q^{44} +(-5.22749 - 4.95561i) q^{45} +(-4.64029 + 4.64029i) q^{46} +(-6.61179 + 1.77162i) q^{47} +(4.10982 + 4.00156i) q^{48} +(-5.36132 + 3.09536i) q^{49} +(0.258197 - 0.963605i) q^{50} +(0.510558 - 2.01249i) q^{51} +(-0.186057 + 1.06308i) q^{52} -3.58842i q^{53} +(5.99936 + 3.15053i) q^{54} -9.58978 q^{55} +(5.44522 - 9.43140i) q^{56} +(5.31395 - 3.16331i) q^{57} +(1.01431 - 3.78545i) q^{58} +(-1.46044 + 5.45044i) q^{59} +(-0.0166131 - 1.24470i) q^{60} +(6.49962 - 11.2577i) q^{61} -4.90182 q^{62} +(2.53812 - 10.5960i) q^{63} +8.81210i q^{64} +(-7.08513 + 4.97449i) q^{65} +(8.68221 - 2.45104i) q^{66} +(1.44883 - 5.40710i) q^{67} +(0.310738 - 0.179404i) q^{68} +(-8.38802 + 2.36799i) q^{69} +(10.9847 - 2.94333i) q^{70} +(-4.22627 + 4.22627i) q^{71} +(2.55932 + 8.62389i) q^{72} +(-0.654952 + 0.654952i) q^{73} +(-10.5445 - 6.08790i) q^{74} +(0.924306 - 0.949314i) q^{75} +(1.03232 + 0.276609i) q^{76} +(-7.25294 - 12.5625i) q^{77} +(5.14317 - 6.31459i) q^{78} +(-2.49772 + 4.32618i) q^{79} +(-5.62265 + 5.62265i) q^{80} +(4.90949 + 7.54301i) q^{81} -11.5961i q^{82} +(-0.422504 - 1.57681i) q^{83} +(1.61798 - 0.963158i) q^{84} +(2.78010 + 0.744924i) q^{85} +(-2.46447 + 9.19751i) q^{86} +(3.63107 - 3.72931i) q^{87} +(10.3717 + 5.98813i) q^{88} +(8.82992 + 8.82992i) q^{89} +(-4.47799 + 8.25752i) q^{90} +(-11.8751 - 5.51910i) q^{91} +(-1.30445 - 0.753122i) q^{92} +(-5.68111 - 3.17966i) q^{93} +(4.46330 + 7.73066i) q^{94} +(4.28640 + 7.42427i) q^{95} +(-1.41968 + 2.53655i) q^{96} +(-13.1504 + 3.52364i) q^{97} +(5.70869 + 5.70869i) q^{98} +(11.6524 + 2.79118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Introduction

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