LMFDB - Embedded newform 185.2.u.a.177.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(8,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			177.6
Character	$\chi$	$=$	185.177
Dual form			185.2.u.a.23.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12177 + 0.647656i) q^{2} +(-1.36781 + 0.366504i) q^{3} +(-0.161082 + 0.279003i) q^{4} +(0.928220 + 2.03431i) q^{5} +(1.29701 - 1.29701i) q^{6} +(-0.124317 + 0.0333107i) q^{7} -3.00793i q^{8} +(-0.861493 + 0.497383i) q^{9} +(-2.35879 - 1.68087i) q^{10} +2.33644i q^{11} +(0.118075 - 0.440660i) q^{12} +(-4.96696 - 2.86768i) q^{13} +(0.117882 - 0.117882i) q^{14} +(-2.01521 - 2.44235i) q^{15} +(1.62594 + 2.81621i) q^{16} +(-2.81788 - 4.88071i) q^{17} +(0.644267 - 1.11590i) q^{18} +(-1.92696 + 0.516328i) q^{19} +(-0.717097 - 0.0687149i) q^{20} +(0.157834 - 0.0911256i) q^{21} +(-1.51321 - 2.62096i) q^{22} +9.37639i q^{23} +(1.10242 + 4.11428i) q^{24} +(-3.27681 + 3.77657i) q^{25} +7.42908 q^{26} +(3.99999 - 3.99999i) q^{27} +(0.0107315 - 0.0400506i) q^{28} +(4.17184 - 4.17184i) q^{29} +(3.84242 + 1.43460i) q^{30} +(-2.28474 - 2.28474i) q^{31} +(1.56201 + 0.901828i) q^{32} +(-0.856316 - 3.19581i) q^{33} +(6.32204 + 3.65003i) q^{34} +(-0.183158 - 0.221980i) q^{35} -0.320478i q^{36} +(-5.75402 + 1.97262i) q^{37} +(1.82721 - 1.82721i) q^{38} +(7.84488 + 2.10203i) q^{39} +(6.11905 - 2.79202i) q^{40} +(5.79719 + 3.34701i) q^{41} +(-0.118036 + 0.204445i) q^{42} +9.62176i q^{43} +(-0.651874 - 0.376360i) q^{44} +(-1.81149 - 1.29086i) q^{45} +(-6.07268 - 10.5182i) q^{46} +(7.16056 + 7.16056i) q^{47} +(-3.25613 - 3.25613i) q^{48} +(-6.04783 + 3.49172i) q^{49} +(1.22992 - 6.35871i) q^{50} +(5.64312 + 5.64312i) q^{51} +(1.60018 - 0.923864i) q^{52} +(-2.28658 - 0.612686i) q^{53} +(-1.89646 + 7.07770i) q^{54} +(-4.75305 + 2.16873i) q^{55} +(0.100196 + 0.373938i) q^{56} +(2.44649 - 1.41248i) q^{57} +(-1.97794 + 7.38178i) q^{58} +(-1.04177 + 3.88793i) q^{59} +(1.00604 - 0.168830i) q^{60} +(1.21728 - 0.326171i) q^{61} +(4.04269 + 1.08324i) q^{62} +(0.0905303 - 0.0905303i) q^{63} -8.84006 q^{64} +(1.22330 - 12.7662i) q^{65} +(3.03038 + 3.03038i) q^{66} +(-1.67895 - 6.26591i) q^{67} +1.81564 q^{68} +(-3.43648 - 12.8251i) q^{69} +(0.349229 + 0.130388i) q^{70} +(-3.22082 + 5.57863i) q^{71} +(1.49609 + 2.59131i) q^{72} +(2.20492 + 2.20492i) q^{73} +(5.17714 - 5.93946i) q^{74} +(3.09794 - 6.36660i) q^{75} +(0.166343 - 0.620799i) q^{76} +(-0.0778287 - 0.290460i) q^{77} +(-10.1616 + 2.72279i) q^{78} +(-3.38283 + 0.906427i) q^{79} +(-4.21981 + 5.92173i) q^{80} +(-2.51307 + 4.35277i) q^{81} -8.67085 q^{82} +(-5.39012 - 1.44428i) q^{83} +0.0587149i q^{84} +(7.31325 - 10.2628i) q^{85} +(-6.23159 - 10.7934i) q^{86} +(-4.17729 + 7.23528i) q^{87} +7.02786 q^{88} +(3.70388 + 0.992453i) q^{89} +(2.86811 + 0.274833i) q^{90} +(0.713004 + 0.191049i) q^{91} +(-2.61604 - 1.51037i) q^{92} +(3.96246 + 2.28773i) q^{93} +(-12.6701 - 3.39495i) q^{94} +(-2.83902 - 3.44077i) q^{95} +(-2.46706 - 0.661047i) q^{96} -3.93759 q^{97} +(4.52287 - 7.83384i) q^{98} +(-1.16211 - 2.01283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.12177	+	0.647656i	−0.793214	+	0.457962i	−0.841093	−	0.540891i	$-0.818087\pi$
$2$	−1.12177	+	0.647656i	−0.793214	+	0.457962i	0.0478788	+	0.998853i	$0.484754\pi$
$3$	−1.36781	+	0.366504i	−0.789706	+	0.211601i	−0.631060	−	0.775734i	$-0.717380\pi$
$3$	−1.36781	+	0.366504i	−0.789706	+	0.211601i	−0.158647	+	0.987335i	$0.550713\pi$
$4$	−0.161082	+	0.279003i	−0.0805411	+	0.139501i
$5$	0.928220	+	2.03431i	0.415113	+	0.909770i
$5$	0.928220	+	2.03431i	0.415113	+	0.909770i
$6$	1.29701	−	1.29701i	0.529501	−	0.529501i
$7$	−0.124317	+	0.0333107i	−0.0469875	+	0.0125903i	−0.282236	−	0.959345i	$-0.591076\pi$
$7$	−0.124317	+	0.0333107i	−0.0469875	+	0.0125903i	0.235249	+	0.971935i	$0.424410\pi$
$8$		−	3.00793i		−	1.06346i
$9$	−0.861493	+	0.497383i	−0.287164	+	0.165794i
$10$	−2.35879	−	1.68087i	−0.745914	−	0.531536i
$11$			2.33644i			0.704464i	0.935913	+	0.352232i	$0.114577\pi$
$11$			2.33644i			0.704464i	−0.935913	+	0.352232i	$0.885423\pi$
$12$	0.118075	−	0.440660i	0.0340852	−	0.127208i
$13$	−4.96696	−	2.86768i	−1.37759	−	0.795351i	−0.385719	−	0.922616i	$-0.626047\pi$
$13$	−4.96696	−	2.86768i	−1.37759	−	0.795351i	−0.991869	+	0.127266i	$0.959380\pi$
$14$	0.117882	−	0.117882i	0.0315053	−	0.0315053i
$15$	−2.01521	−	2.44235i	−0.520326	−	0.630613i
$16$	1.62594	+	2.81621i	0.406485	+	0.704053i
$17$	−2.81788	−	4.88071i	−0.683436	−	1.18375i	−0.973926	−	0.226867i	$-0.927152\pi$
$17$	−2.81788	−	4.88071i	−0.683436	−	1.18375i	0.290490	−	0.956878i	$-0.406182\pi$
$18$	0.644267	−	1.11590i	0.151855	−	0.263021i
$19$	−1.92696	+	0.516328i	−0.442076	+	0.118454i	−0.472989	−	0.881068i	$-0.656825\pi$
$19$	−1.92696	+	0.516328i	−0.442076	+	0.118454i	0.0309134	+	0.999522i	$0.490158\pi$
$20$	−0.717097	−	0.0687149i	−0.160348	−	0.0153651i
$21$	0.157834	−	0.0911256i	0.0344422	−	0.0198852i
$22$	−1.51321	−	2.62096i	−0.322618	−	0.558791i
$23$			9.37639i			1.95511i	0.210677	+	0.977556i	$0.432433\pi$
$23$			9.37639i			1.95511i	−0.210677	+	0.977556i	$0.567567\pi$
$24$	1.10242	+	4.11428i	0.225030	+	0.839824i
$25$	−3.27681	+	3.77657i	−0.655363	+	0.755314i
$26$	7.42908			1.45696
$27$	3.99999	−	3.99999i	0.769798	−	0.769798i
$28$	0.0107315	−	0.0400506i	0.00202807	−	0.00756886i
$29$	4.17184	−	4.17184i	0.774691	−	0.774691i	−0.204232	−	0.978923i	$-0.565470\pi$
$29$	4.17184	−	4.17184i	0.774691	−	0.774691i	0.978923	+	0.204232i	$0.0654696\pi$
$30$	3.84242	+	1.43460i	0.701526	+	0.261921i
$31$	−2.28474	−	2.28474i	−0.410351	−	0.410351i	0.471510	−	0.881861i	$-0.343709\pi$
$31$	−2.28474	−	2.28474i	−0.410351	−	0.410351i	−0.881861	+	0.471510i	$0.843709\pi$
$32$	1.56201	+	0.901828i	0.276127	+	0.159422i
$33$	−0.856316	−	3.19581i	−0.149065	−	0.556320i
$34$	6.32204	+	3.65003i	1.08422	+	0.625975i
$35$	−0.183158	−	0.221980i	−0.0309594	−	0.0375215i
$36$		−	0.320478i		−	0.0534131i
$37$	−5.75402	+	1.97262i	−0.945956	+	0.324296i
$37$	−5.75402	+	1.97262i	−0.945956	+	0.324296i
$38$	1.82721	−	1.82721i	0.296413	−	0.296413i
$39$	7.84488	+	2.10203i	1.25619	+	0.336594i
$40$	6.11905	−	2.79202i	0.967507	−	0.441457i
$41$	5.79719	+	3.34701i	0.905370	+	0.522715i	0.878938	−	0.476935i	$-0.158252\pi$
$41$	5.79719	+	3.34701i	0.905370	+	0.522715i	0.0264311	+	0.999651i	$0.491586\pi$
$42$	−0.118036	+	0.204445i	−0.0182134	+	0.0315465i
$43$			9.62176i			1.46730i	0.679525	+	0.733652i	$0.262186\pi$
$43$			9.62176i			1.46730i	−0.679525	+	0.733652i	$0.737814\pi$
$44$	−0.651874	−	0.376360i	−0.0982737	−	0.0567383i
$45$	−1.81149	−	1.29086i	−0.270040	−	0.192430i
$46$	−6.07268	−	10.5182i	−0.895367	−	1.55082i
$47$	7.16056	+	7.16056i	1.04448	+	1.04448i	0.998964	+	0.0455116i	$0.0144918\pi$
$47$	7.16056	+	7.16056i	1.04448	+	1.04448i	0.0455116	+	0.998964i	$0.485508\pi$
$48$	−3.25613	−	3.25613i	−0.469982	−	0.469982i
$49$	−6.04783	+	3.49172i	−0.863976	+	0.498817i
$50$	1.22992	−	6.35871i	0.173938	−	0.899257i
$51$	5.64312	+	5.64312i	0.790195	+	0.790195i
$52$	1.60018	−	0.923864i	0.221905	−	0.128117i
$53$	−2.28658	−	0.612686i	−0.314085	−	0.0841590i	0.0983327	−	0.995154i	$-0.468649\pi$
$53$	−2.28658	−	0.612686i	−0.314085	−	0.0841590i	−0.412418	+	0.910995i	$0.635316\pi$
$54$	−1.89646	+	7.07770i	−0.258076	+	0.963153i
$55$	−4.75305	+	2.16873i	−0.640900	+	0.292432i
$56$	0.100196	+	0.373938i	0.0133893	+	0.0499695i
$57$	2.44649	−	1.41248i	0.324045	−	0.187088i
$58$	−1.97794	+	7.38178i	−0.259716	+	0.969275i
$59$	−1.04177	+	3.88793i	−0.135626	+	0.506165i	0.864368	+	0.502860i	$0.167719\pi$
$59$	−1.04177	+	3.88793i	−0.135626	+	0.506165i	−0.999995	+	0.00330515i	$0.998948\pi$
$60$	1.00604	−	0.168830i	0.129879	−	0.0217958i
$61$	1.21728	−	0.326171i	0.155857	−	0.0417619i	−0.180047	−	0.983658i	$-0.557625\pi$
$61$	1.21728	−	0.326171i	0.155857	−	0.0417619i	0.335904	+	0.941896i	$0.390958\pi$
$62$	4.04269	+	1.08324i	0.513422	+	0.137571i
$63$	0.0905303	−	0.0905303i	0.0114057	−	0.0114057i
$64$	−8.84006			−1.10501
$65$	1.22330	−	12.7662i	0.151732	−	1.58345i
$66$	3.03038	+	3.03038i	0.373014	+	0.373014i
$67$	−1.67895	−	6.26591i	−0.205116	−	0.765503i	−0.989414	−	0.145119i	$-0.953643\pi$
$67$	−1.67895	−	6.26591i	−0.205116	−	0.765503i	0.784298	−	0.620384i	$-0.213023\pi$
$68$	1.81564			0.220179
$69$	−3.43648	−	12.8251i	−0.413704	−	1.54396i
$70$	0.349229	+	0.130388i	0.0417408	+	0.0155843i
$71$	−3.22082	+	5.57863i	−0.382241	+	0.662062i	−0.991382	−	0.131000i	$-0.958181\pi$
$71$	−3.22082	+	5.57863i	−0.382241	+	0.662062i	0.609141	+	0.793062i	$0.291514\pi$
$72$	1.49609	+	2.59131i	0.176316	+	0.305389i
$73$	2.20492	+	2.20492i	0.258066	+	0.258066i	0.824267	−	0.566201i	$-0.191587\pi$
$73$	2.20492	+	2.20492i	0.258066	+	0.258066i	−0.566201	+	0.824267i	$0.691587\pi$
$74$	5.17714	−	5.93946i	0.601830	−	0.690448i
$75$	3.09794	−	6.36660i	0.357719	−	0.735152i
$76$	0.166343	−	0.620799i	0.0190808	−	0.0712105i
$77$	−0.0778287	−	0.290460i	−0.00886940	−	0.0331010i
$78$	−10.1616	+	2.72279i	−1.15057	+	0.308295i
$79$	−3.38283	+	0.906427i	−0.380598	+	0.101981i	−0.444046	−	0.896004i	$-0.646457\pi$
$79$	−3.38283	+	0.906427i	−0.380598	+	0.101981i	0.0634473	+	0.997985i	$0.479791\pi$
$80$	−4.21981	+	5.92173i	−0.471789	+	0.662069i
$81$	−2.51307	+	4.35277i	−0.279230	+	0.483641i
$82$	−8.67085			−0.957536
$83$	−5.39012	−	1.44428i	−0.591642	−	0.158530i	−0.0494387	−	0.998777i	$-0.515743\pi$
$83$	−5.39012	−	1.44428i	−0.591642	−	0.158530i	−0.542204	+	0.840247i	$0.682410\pi$
$84$			0.0587149i			0.00640632i
$85$	7.31325	−	10.2628i	0.793233	−	1.11316i
$86$	−6.23159	−	10.7934i	−0.671970	−	1.16389i
$87$	−4.17729	+	7.23528i	−0.447853	+	0.775704i
$88$	7.02786			0.749172
$89$	3.70388	+	0.992453i	0.392611	+	0.105200i	0.449723	−	0.893168i	$-0.351523\pi$
$89$	3.70388	+	0.992453i	0.392611	+	0.105200i	−0.0571122	+	0.998368i	$0.518189\pi$
$90$	2.86811	+	0.274833i	0.302325	+	0.0289700i
$91$	0.713004	+	0.191049i	0.0747431	+	0.0200274i
$92$	−2.61604	−	1.51037i	−0.272741	−	0.157467i
$93$	3.96246	+	2.28773i	0.410888	+	0.237226i
$94$	−12.6701	−	3.39495i	−1.30682	−	0.350162i
$95$	−2.83902	−	3.44077i	−0.291277	−	0.353016i
$96$	−2.46706	−	0.661047i	−0.251793	−	0.0674678i
$97$	−3.93759			−0.399801			−0.199901	−	0.979816i	$-0.564062\pi$
$97$	−3.93759			−0.399801			−0.199901	+	0.979816i	$0.564062\pi$
$98$	4.52287	−	7.83384i	0.456879	−	0.791337i
$99$	−1.16211	−	2.01283i	−0.116796	−	0.202297i
$100$	−0.525836	−	1.52258i	−0.0525836	−	0.152258i
$101$			6.74555i			0.671208i	0.942003	+	0.335604i	$0.108940\pi$
$101$			6.74555i			0.671208i	−0.942003	+	0.335604i	$0.891060\pi$
$102$	−9.98511	−	2.67550i	−0.988674	−	0.264914i
$103$	8.73530			0.860714			0.430357	−	0.902659i	$-0.358388\pi$
$103$	8.73530			0.860714			0.430357	+	0.902659i	$0.358388\pi$
$104$	−8.62577	+	14.9403i	−0.845827	+	1.46501i
$105$	0.331882	+	0.236499i	0.0323884	+	0.0230799i
$106$	2.96183	−	0.793621i	0.287679	−	0.0770833i
$107$	−0.170923	+	0.0457987i	−0.0165238	+	0.00442753i	−0.267071	−	0.963677i	$-0.586056\pi$
$107$	−0.170923	+	0.0457987i	−0.0165238	+	0.00442753i	0.250548	+	0.968104i	$0.419389\pi$
$108$	0.471680	+	1.76033i	0.0453875	+	0.169388i
$109$	1.53827	−	5.74089i	0.147339	−	0.549878i	−0.852301	−	0.523052i	$-0.824793\pi$
$109$	1.53827	−	5.74089i	0.147339	−	0.549878i	0.999640	−	0.0268258i	$-0.00853995\pi$
$110$	3.92725	−	5.51117i	0.374448	−	0.525469i
$111$	7.14745	−	4.80704i	0.678406	−	0.456264i
$112$	−0.295943	−	0.295943i	−0.0279640	−	0.0279640i
$113$	1.41509	+	2.45101i	0.133121	+	0.230572i	0.924878	−	0.380264i	$-0.124167\pi$
$113$	1.41509	+	2.45101i	0.133121	+	0.230572i	−0.791757	+	0.610836i	$0.790833\pi$
$114$	−1.82960	+	3.16897i	−0.171358	+	0.296801i
$115$	−19.0745	+	8.70335i	−1.77870	+	0.811592i
$116$	0.491945	+	1.83596i	0.0456759	+	0.170465i
$117$	5.70534			0.527459
$118$	−1.34941	−	5.03608i	−0.124224	−	0.463609i
$119$	0.512891	+	0.512891i	0.0470166	+	0.0470166i
$120$	−7.34643	+	6.06162i	−0.670634	+	0.553347i
$121$	5.54103			0.503730
$122$	−1.15427	+	1.15427i	−0.104503	+	0.104503i
$123$	−9.15616	−	2.45339i	−0.825583	−	0.221214i
$124$	1.00548	−	0.269417i	0.0902947	−	0.0241944i
$125$	−10.7243	−	3.16056i	−0.959212	−	0.282689i
$126$	−0.0429220	+	0.160187i	−0.00382380	+	0.0142706i
$127$	−2.59470	+	9.68356i	−0.230243	+	0.859277i	0.749993	+	0.661445i	$0.230057\pi$
$127$	−2.59470	+	9.68356i	−0.230243	+	0.859277i	−0.980236	+	0.197832i	$0.936610\pi$
$128$	6.79253	−	3.92167i	0.600380	−	0.346630i
$129$	−3.52641	−	13.1608i	−0.310483	−	1.15874i
$130$	6.89582	+	15.1130i	0.604804	+	1.32550i
$131$	4.63620	−	17.3025i	0.405066	−	1.51173i	−0.398867	−	0.917009i	$-0.630597\pi$
$131$	4.63620	−	17.3025i	0.405066	−	1.51173i	0.803933	−	0.594719i	$-0.202737\pi$
$132$	1.02958	+	0.275875i	0.0896132	+	0.0240118i
$133$	0.222356	−	0.128377i	0.0192807	−	0.0111317i
$134$	5.94156	+	5.94156i	0.513273	+	0.513273i
$135$	11.8501	+	4.42434i	1.01989	+	0.380786i
$136$	−14.6808	+	8.47598i	−1.25887	+	0.726809i
$137$	13.1909	+	13.1909i	1.12697	+	1.12697i	0.990667	+	0.136305i	$0.0435227\pi$
$137$	13.1909	+	13.1909i	1.12697	+	1.12697i	0.136305	+	0.990667i	$0.456477\pi$
$138$	12.1612	+	12.1612i	1.03523	+	1.03523i
$139$	6.04331	+	10.4673i	0.512587	+	0.887827i	0.999893	+	0.0145956i	$0.00464609\pi$
$139$	6.04331	+	10.4673i	0.512587	+	0.887827i	−0.487307	+	0.873231i	$0.662021\pi$
$140$	0.0914365	−	0.0153446i	0.00772780	−	0.00129685i
$141$	−12.4187	−	7.16993i	−1.04584	−	0.603817i
$142$		−	8.34395i		−	0.700209i
$143$	6.70017	−	11.6050i	0.560296	−	0.970461i
$144$	−2.80147	−	1.61743i	−0.233456	−	0.134786i
$145$	12.3592	+	4.61442i	1.02637	+	0.383207i
$146$	−3.90144	−	1.04539i	−0.322886	−	0.0865170i
$147$	6.99257	−	6.99257i	0.576737	−	0.576737i
$148$	0.376506	−	1.92314i	0.0309486	−	0.158081i
$149$		−	21.8001i		−	1.78594i	−0.450121	−	0.892968i	$-0.648619\pi$
$149$		−	21.8001i		−	1.78594i	0.450121	−	0.892968i	$-0.351381\pi$
$150$	0.648187	+	9.14829i	0.0529242	+	0.746955i
$151$	−0.716854	−	0.413876i	−0.0583368	−	0.0336808i	0.470548	−	0.882374i	$-0.344056\pi$
$151$	−0.716854	−	0.413876i	−0.0583368	−	0.0336808i	−0.528885	+	0.848694i	$0.677390\pi$
$152$	1.55308	+	5.79617i	0.125971	+	0.470132i
$153$	4.85516	+	2.80313i	0.392517	+	0.226620i
$154$	0.275425	+	0.275425i	0.0221944	+	0.0221944i
$155$	2.52712	−	6.76861i	0.202983	−	0.543668i
$156$	−1.85014	+	1.85014i	−0.148130	+	0.148130i
$157$	0.324408	−	1.21071i	0.0258906	−	0.0966251i	−0.951772	−	0.306808i	$-0.900739\pi$
$157$	0.324408	−	1.21071i	0.0258906	−	0.0966251i	0.977662	+	0.210183i	$0.0674058\pi$
$158$	3.20772	−	3.20772i	0.255192	−	0.255192i
$159$	3.35216			0.265843
$160$	−0.384704	+	4.01471i	−0.0304136	+	0.317390i
$161$	−0.312334	−	1.16565i	−0.0246154	−	0.0918659i
$162$		−	6.51042i		−	0.511507i
$163$	−0.247225	−	0.428206i	−0.0193641	−	0.0335397i	0.856181	−	0.516676i	$-0.172831\pi$
$163$	−0.247225	−	0.428206i	−0.0193641	−	0.0335397i	−0.875545	+	0.483136i	$0.839498\pi$
$164$	−1.86765	+	1.07829i	−0.145839	+	0.0842001i
$165$	5.70642	−	4.70843i	0.444244	−	0.366551i
$166$	6.98189	−	1.87079i	0.541900	−	0.145202i
$167$	−8.54937	+	14.8079i	−0.661570	+	1.14587i	0.318633	+	0.947878i	$0.396776\pi$
$167$	−8.54937	+	14.8079i	−0.661570	+	1.14587i	−0.980203	+	0.197995i	$0.936557\pi$
$168$	−0.274099	−	0.474754i	−0.0211472	−	0.0366281i
$169$	9.94715	+	17.2290i	0.765165	+	1.32531i
$170$	−1.55704	+	16.2490i	−0.119420	+	1.24624i
$171$	1.40325	−	1.40325i	0.107309	−	0.107309i
$172$	−2.68450	−	1.54989i	−0.204691	−	0.118178i
$173$	−4.87336	+	18.1876i	−0.370515	+	1.38278i	0.489274	+	0.872130i	$0.337262\pi$
$173$	−4.87336	+	18.1876i	−0.370515	+	1.38278i	−0.859789	+	0.510650i	$0.829405\pi$
$174$		−	10.8218i		−	0.820399i
$175$	0.281565	−	0.578646i	0.0212843	−	0.0437416i
$176$	−6.57992	+	3.79892i	−0.495980	+	0.286354i
$177$		−	5.69976i		−	0.428420i
$178$	−4.79769	+	1.28554i	−0.359602	+	0.0963551i
$179$	0.195467	−	0.195467i	0.0146099	−	0.0146099i	−0.699764	−	0.714374i	$-0.746712\pi$
$179$	0.195467	−	0.195467i	0.0146099	−	0.0146099i	0.714374	+	0.699764i	$0.246712\pi$
$180$	0.651952	−	0.297474i	0.0485936	−	0.0221724i
$181$	3.12916	−	5.41986i	0.232588	−	0.402855i	−0.725981	−	0.687715i	$-0.758614\pi$
$181$	3.12916	−	5.41986i	0.232588	−	0.402855i	0.958569	+	0.284860i	$0.0919472\pi$
$182$	−0.923563	+	0.247468i	−0.0684591	+	0.0183436i
$183$	−1.54547	+	0.892280i	−0.114245	+	0.0659592i
$184$	28.2035			2.07919
$185$	−9.35391	−	9.87443i	−0.687713	−	0.725983i
$186$	−5.92665			−0.434563
$187$	11.4035	−	6.58381i	0.833906	−	0.481456i
$188$	−3.15125	+	0.844376i	−0.229829	+	0.0615825i
$189$	−0.364026	+	0.630511i	−0.0264790	+	0.0458629i
$190$	5.41317	+	2.02106i	0.392713	+	0.146623i
$191$	−3.29529	+	3.29529i	−0.238439	+	0.238439i	−0.816204	−	0.577764i	$-0.803925\pi$
$191$	−3.29529	+	3.29529i	−0.238439	+	0.238439i	0.577764	+	0.816204i	$0.303925\pi$
$192$	12.0915	−	3.23992i	0.872632	−	0.233821i
$193$		−	18.7146i		−	1.34711i	−0.739138	−	0.673554i	$-0.764767\pi$
$193$		−	18.7146i		−	1.34711i	0.739138	−	0.673554i	$-0.235233\pi$
$194$	4.41708	−	2.55020i	0.317128	−	0.183094i
$195$	3.00560	+	17.9101i	0.215236	+	1.28257i
$196$		−	2.24981i		−	0.160701i
$197$	−2.48178	+	9.26213i	−0.176820	+	0.659900i	0.819415	+	0.573201i	$0.194298\pi$
$197$	−2.48178	+	9.26213i	−0.176820	+	0.659900i	−0.996235	+	0.0866988i	$0.972368\pi$
$198$	2.60724	+	1.50529i	0.185289	+	0.106977i
$199$	5.57855	−	5.57855i	0.395453	−	0.395453i	−0.481173	−	0.876626i	$-0.659789\pi$
$199$	5.57855	−	5.57855i	0.395453	−	0.395453i	0.876626	+	0.481173i	$0.159789\pi$
$200$	11.3597	+	9.85643i	0.803249	+	0.696955i
$201$	4.59297	+	7.95525i	0.323963	+	0.561120i
$202$	−4.36880	−	7.56699i	−0.307388	−	0.532411i
$203$	−0.379665	+	0.657599i	−0.0266472	+	0.0461544i
$204$	−2.48345	+	0.665439i	−0.173876	+	0.0465901i
$205$	−1.42778	+	14.9000i	−0.0997204	+	1.04066i
$206$	−9.79903	+	5.65747i	−0.682731	+	0.394175i
$207$	−4.66366	−	8.07769i	−0.324147	−	0.561438i
$208$		−	18.6507i		−	1.29319i
$209$	−1.20637	−	4.50224i	−0.0834465	−	0.311427i
$210$	−0.525467	−	0.0503522i	−0.0362607	−	0.00347463i
$211$	−11.6214			−0.800053			−0.400026	−	0.916504i	$-0.630999\pi$
$211$	−11.6214			−0.800053			−0.400026	+	0.916504i	$0.630999\pi$
$212$	0.539268	−	0.539268i	0.0370371	−	0.0370371i
$213$	2.36089	−	8.81096i	0.161765	−	0.603717i
$214$	0.162075	−	0.162075i	0.0110792	−	0.0110792i
$215$	−19.5736	+	8.93111i	−1.33491	+	0.609097i
$216$	−12.0317	−	12.0317i	−0.818653	−	0.818653i
$217$	0.360139	+	0.207926i	0.0244478	+	0.0141150i
$218$	1.99254	+	7.43625i	0.134952	+	0.503647i
$219$	−3.82402	−	2.20780i	−0.258403	−	0.149189i
$220$	0.160549	−	1.67546i	0.0108242	−	0.112959i
$221$			32.3231i			2.17428i
$222$	−4.90451	+	10.0215i	−0.329169	+	0.672599i
$223$	19.4912	−	19.4912i	1.30523	−	1.30523i	0.380408	−	0.924819i	$-0.375783\pi$
$223$	19.4912	−	19.4912i	1.30523	−	1.30523i	0.924819	−	0.380408i	$-0.124217\pi$
$224$	−0.224226	−	0.0600811i	−0.0149817	−	0.00401434i
$225$	0.944550	−	4.88332i	0.0629700	−	0.325555i
$226$	−3.17483	−	1.83299i	−0.211187	−	0.121929i
$227$	5.16503	−	8.94610i	0.342815	−	0.593774i	−0.642139	−	0.766588i	$-0.721953\pi$
$227$	5.16503	−	8.94610i	0.342815	−	0.593774i	0.984954	+	0.172815i	$0.0552861\pi$
$228$			0.910101i			0.0602729i
$229$	−6.96829	−	4.02315i	−0.460478	−	0.265857i	0.251767	−	0.967788i	$-0.418988\pi$
$229$	−6.96829	−	4.02315i	−0.460478	−	0.265857i	−0.712245	+	0.701931i	$0.752322\pi$
$230$	15.7604	−	22.1169i	1.03921	−	1.45834i
$231$	0.212910	+	0.368771i	0.0140084	+	0.0242633i
$232$	−12.5486	−	12.5486i	−0.823856	−	0.823856i
$233$	−19.7773	−	19.7773i	−1.29566	−	1.29566i	−0.931234	−	0.364421i	$-0.881267\pi$
$233$	−19.7773	−	19.7773i	−1.29566	−	1.29566i	−0.364421	−	0.931234i	$-0.618733\pi$
$234$	−6.40010	+	3.69510i	−0.418388	+	0.241556i
$235$	−7.92021	+	21.2134i	−0.516657	+	1.38381i
$236$	−0.916931	−	0.916931i	−0.0596871	−	0.0596871i
$237$	4.29487	−	2.47964i	0.278982	−	0.161070i
$238$	−0.907525	−	0.243171i	−0.0588261	−	0.0157624i
$239$	0.895305	−	3.34133i	0.0579125	−	0.216132i	−0.930905	−	0.365260i	$-0.880980\pi$
$239$	0.895305	−	3.34133i	0.0579125	−	0.216132i	0.988818	+	0.149128i	$0.0476466\pi$
$240$	3.60157	−	9.64638i	0.232480	−	0.622671i
$241$	−5.05459	−	18.8640i	−0.325595	−	1.21514i	−0.913713	−	0.406360i	$-0.866798\pi$
$241$	−5.05459	−	18.8640i	−0.325595	−	1.21514i	0.588118	−	0.808775i	$-0.299869\pi$
$242$	−6.21578	+	3.58868i	−0.399566	+	0.230689i
$243$	−2.55019	+	9.51745i	−0.163595	+	0.610545i
$244$	−0.105081	+	0.392166i	−0.00672709	+	0.0251058i
$245$	−12.7169	−	9.06207i	−0.812456	−	0.578954i
$246$	11.8601	−	3.17790i	0.756172	−	0.202616i
$247$	11.0518	+	2.96133i	0.703211	+	0.188425i
$248$	−6.87234	+	6.87234i	−0.436394	+	0.436394i
$249$	7.90200			0.500769
$250$	14.0772	−	3.40024i	0.890321	−	0.215050i
$251$	0.521919	+	0.521919i	0.0329432	+	0.0329432i	0.723387	−	0.690443i	$-0.242584\pi$
$251$	0.521919	+	0.521919i	0.0329432	+	0.0329432i	−0.690443	+	0.723387i	$0.742584\pi$
$252$	0.0106754	+	0.0398410i	0.000672485	+	0.00250975i
$253$	−21.9074			−1.37731
$254$	−3.36095	−	12.5432i	−0.210885	−	0.787033i
$255$	−6.24179	+	16.7179i	−0.390876	+	1.04692i
$256$	3.76027	−	6.51299i	0.235017	−	0.407062i
$257$	5.97412	+	10.3475i	0.372656	+	0.645458i	0.989973	−	0.141256i	$-0.0451140\pi$
$257$	5.97412	+	10.3475i	0.372656	+	0.645458i	−0.617318	+	0.786714i	$0.711781\pi$
$258$	12.4795	+	12.4795i	0.776939	+	0.776939i
$259$	0.649616	−	0.436901i	0.0403652	−	0.0271477i
$260$	3.36474	+	2.39771i	0.208672	+	0.148699i
$261$	−1.51901	+	5.66901i	−0.0940242	+	0.350903i
$262$	6.00532	+	22.4122i	0.371010	+	1.38463i
$263$	1.00296	−	0.268741i	0.0618450	−	0.0165713i	−0.227764	−	0.973716i	$-0.573141\pi$
$263$	1.00296	−	0.268741i	0.0618450	−	0.0165713i	0.289609	+	0.957145i	$0.406475\pi$
$264$	−9.61279	+	2.57574i	−0.591626	+	0.158526i
$265$	−0.876054	−	5.22031i	−0.0538156	−	0.320681i
$266$	−0.166289	+	0.288020i	−0.0101958	+	0.0176597i
$267$	−5.42995			−0.332308
$268$	2.01865	+	0.540897i	0.123309	+	0.0330405i
$269$			11.6789i			0.712074i	0.934472	+	0.356037i	$0.115872\pi$
$269$			11.6789i			0.712074i	−0.934472	+	0.356037i	$0.884128\pi$
$270$	−16.1586	+	2.71167i	−0.983379	+	0.165027i
$271$	12.1102	+	20.9754i	0.735640	+	1.27417i	0.954442	+	0.298396i	$0.0964516\pi$
$271$	12.1102	+	20.9754i	0.735640	+	1.27417i	−0.218803	+	0.975769i	$0.570215\pi$
$272$	9.16340	−	15.8715i	0.555613	−	0.962350i
$273$	−1.04528			−0.0632629
$274$	−23.3403	−	6.25402i	−1.41004	−	0.377819i
$275$	−8.82374	−	7.65609i	−0.532092	−	0.461680i
$276$	4.13180	+	1.10711i	0.248705	+	0.0666403i
$277$	3.20730	+	1.85173i	0.192708	+	0.111260i	0.593250	−	0.805019i	$-0.297845\pi$
$277$	3.20730	+	1.85173i	0.192708	+	0.111260i	−0.400542	+	0.916279i	$0.631178\pi$
$278$	−13.5585	−	7.82798i	−0.813182	−	0.469491i
$279$	3.10468	+	0.831896i	0.185872	+	0.0498043i
$280$	−0.667700	+	0.550927i	−0.0399027	+	0.0329242i
$281$	−24.5233	−	6.57100i	−1.46294	−	0.391993i	−0.562434	−	0.826842i	$-0.690135\pi$
$281$	−24.5233	−	6.57100i	−1.46294	−	0.391993i	−0.900503	+	0.434849i	$0.856802\pi$
$282$	18.5746			1.10610
$283$	1.25913	−	2.18087i	0.0748473	−	0.129639i	−0.826173	−	0.563417i	$-0.809486\pi$
$283$	1.25913	−	2.18087i	0.0748473	−	0.129639i	0.901020	+	0.433778i	$0.142820\pi$
$284$	−1.03763	−	1.79724i	−0.0615723	−	0.106646i
$285$	5.14430	+	3.66581i	0.304722	+	0.217144i
$286$			17.3576i			1.02638i
$287$	−0.832183	−	0.222983i	−0.0491222	−	0.0131623i
$288$	−1.79422			−0.105725
$289$	−7.38086	+	12.7840i	−0.434168	+	0.752002i
$290$	−16.8528	+	2.82817i	−0.989629	+	0.166076i
$291$	5.38587	−	1.44314i	0.315726	−	0.0845984i
$292$	−0.970350	+	0.260004i	−0.0567854	+	0.0152156i
$293$	0.402098	+	1.50065i	0.0234908	+	0.0876688i	0.976676	−	0.214718i	$-0.0688832\pi$
$293$	0.402098	+	1.50065i	0.0234908	+	0.0876688i	−0.953185	+	0.302387i	$0.902217\pi$
$294$	−3.31530	+	12.3729i	−0.193352	+	0.721600i
$295$	−8.87622	+	1.48958i	−0.516794	+	0.0867266i
$296$	5.93349	+	17.3077i	0.344877	+	1.00599i
$297$	9.34575	+	9.34575i	0.542295	+	0.542295i
$298$	14.1190	+	24.4548i	0.817891	+	1.41663i
$299$	26.8885	−	46.5722i	1.55500	−	2.69334i
$300$	1.27728	+	1.88988i	0.0737436	+	0.109112i
$301$	−0.320508	−	1.19615i	−0.0184738	−	0.0689450i
$302$	1.07220			0.0616981
$303$	−2.47227	−	9.22665i	−0.142028	−	0.530057i
$304$	−4.58722	−	4.58722i	−0.263095	−	0.263095i
$305$	1.79344	+	2.17357i	0.102692	+	0.124458i
$306$	−7.26186			−0.415133
$307$	−11.4213	+	11.4213i	−0.651849	+	0.651849i	−0.953438	−	0.301589i	$-0.902483\pi$
$307$	−11.4213	+	11.4213i	−0.651849	+	0.651849i	0.301589	+	0.953438i	$0.402483\pi$
$308$	0.0935760	+	0.0250736i	0.00533199	+	0.00142870i
$309$	−11.9482	+	3.20152i	−0.679712	+	0.182128i
$310$	1.54887	+	9.22955i	0.0879700	+	0.524203i
$311$	5.37302	−	20.0524i	0.304676	−	1.13707i	−0.628548	−	0.777771i	$-0.716351\pi$
$311$	5.37302	−	20.0524i	0.304676	−	1.13707i	0.933224	−	0.359295i	$-0.116983\pi$
$312$	6.32276	−	23.5969i	0.357956	−	1.33591i
$313$	11.8797	−	6.85877i	0.671483	−	0.387681i	−0.125155	−	0.992137i	$-0.539943\pi$
$313$	11.8797	−	6.85877i	0.671483	−	0.387681i	0.796638	+	0.604456i	$0.206610\pi$
$314$	0.420210	+	1.56825i	0.0237138	+	0.0885013i
$315$	0.268199	+	0.100134i	0.0151113	+	0.00564194i
$316$	0.292019	−	1.08983i	0.0164273	−	0.0613076i
$317$	−25.0777	−	6.71956i	−1.40851	−	0.377408i	−0.527115	−	0.849794i	$-0.676726\pi$
$317$	−25.0777	−	6.71956i	−1.40851	−	0.377408i	−0.881392	+	0.472386i	$0.843393\pi$
$318$	−3.76036	+	2.17105i	−0.210871	+	0.121746i
$319$	9.74727	+	9.74727i	0.545742	+	0.545742i
$320$	−8.20552	−	17.9834i	−0.458703	−	1.00530i
$321$	0.217005	−	0.125288i	0.0121121	−	0.00699290i
$322$	1.10531	+	1.10531i	0.0615964	+	0.0615964i
$323$	7.94999	+	7.94999i	0.442349	+	0.442349i
$324$	−0.809622	−	1.40231i	−0.0449790	−	0.0779059i
$325$	27.1058	−	9.36124i	1.50356	−	0.519268i
$326$	0.554660	+	0.320233i	0.0307198	+	0.0177361i
$327$			8.41624i			0.465419i
$328$	10.0676	−	17.4376i	0.555889	−	0.962828i
$329$	−1.12871	−	0.651659i	−0.0622276	−	0.0359271i
$330$	−3.35187	+	8.97759i	−0.184514	+	0.494200i
$331$	−10.6847	−	2.86296i	−0.587284	−	0.157362i	−0.0470725	−	0.998891i	$-0.514989\pi$
$331$	−10.6847	−	2.86296i	−0.587284	−	0.157362i	−0.540212	+	0.841529i	$0.681656\pi$
$332$	1.27121	−	1.27121i	0.0697667	−	0.0697667i
$333$	3.97591	−	4.56135i	0.217878	−	0.249960i
$334$		−	22.1482i		−	1.21190i
$335$	11.1884	−	9.23164i	0.611286	−	0.504379i
$336$	0.513258	+	0.296330i	0.0280005	+	0.0161661i
$337$	4.03650	+	15.0644i	0.219882	+	0.820611i	0.984391	+	0.175997i	$0.0563151\pi$
$337$	4.03650	+	15.0644i	0.219882	+	0.820611i	−0.764509	+	0.644614i	$0.777018\pi$
$338$	−22.3169	−	12.8847i	−1.21388	−	0.700834i
$339$	−2.83389	−	2.83389i	−0.153916	−	0.153916i
$340$	1.68531	+	3.69357i	0.0913989	+	0.200312i
$341$	5.33817	−	5.33817i	0.289078	−	0.289078i
$342$	−0.665307	+	2.48296i	−0.0359757	+	0.134263i
$343$	1.27259	−	1.27259i	0.0687131	−	0.0687131i
$344$	28.9416			1.56042
$345$	22.9004	−	18.8954i	1.23292	−	1.01729i
$346$	−6.31253	−	23.5587i	−0.339364	−	1.26652i
$347$		−	2.11671i		−	0.113631i	−0.998385	−	0.0568155i	$-0.981905\pi$
$347$		−	2.11671i		−	0.113631i	0.998385	−	0.0568155i	$-0.0180947\pi$
$348$	−1.34578	−	2.33095i	−0.0721411	−	0.124952i
$349$	−7.13388	+	4.11875i	−0.381868	+	0.220472i	−0.678631	−	0.734480i	$-0.737426\pi$
$349$	−7.13388	+	4.11875i	−0.381868	+	0.220472i	0.296763	+	0.954951i	$0.404093\pi$
$350$	0.0589123	+	0.831467i	0.00314899	+	0.0444438i
$351$	−31.3385	+	8.39712i	−1.67272	+	0.448205i
$352$	−2.10707	+	3.64955i	−0.112307	+	0.194522i
$353$	9.03032	+	15.6410i	0.480636	+	0.832485i	0.999753	−	0.0222176i	$-0.00707266\pi$
$353$	9.03032	+	15.6410i	0.480636	+	0.832485i	−0.519118	+	0.854703i	$0.673739\pi$
$354$	3.69149	+	6.39384i	0.196200	+	0.339829i
$355$	−14.3383	−	1.37395i	−0.760997	−	0.0729216i
$356$	−0.873527	+	0.873527i	−0.0462968	+	0.0462968i
$357$	−0.889515	−	0.513562i	−0.0470781	−	0.0271806i
$358$	−0.0926742	+	0.345865i	−0.00489799	+	0.0182795i
$359$			16.1578i			0.852775i	0.904541	+	0.426387i	$0.140214\pi$
$359$			16.1578i			0.852775i	−0.904541	+	0.426387i	$0.859786\pi$
$360$	−3.88282	+	5.44882i	−0.204642	+	0.287178i
$361$	−13.0079	+	7.51011i	−0.684626	+	0.395269i
$362$			8.10647i			0.426067i
$363$	−7.57909	+	2.03081i	−0.397799	+	0.106590i
$364$	−0.168155	+	0.168155i	−0.00881374	+	0.00881374i
$365$	−2.43883	+	6.53212i	−0.127654	+	0.341907i
$366$	1.15578	−	2.00187i	0.0604137	−	0.104640i
$367$	7.66168	−	2.05294i	0.399936	−	0.107163i	−0.0532439	−	0.998582i	$-0.516956\pi$
$367$	7.66168	−	2.05294i	0.399936	−	0.107163i	0.453180	+	0.891419i	$0.350289\pi$
$368$	−26.4059	+	15.2454i	−1.37650	+	0.794724i
$369$	−6.65899			−0.346653
$370$	16.8882	+	5.01876i	0.877976	+	0.260913i
$371$	0.304670			0.0158177
$372$	−1.27656	+	0.737024i	−0.0661867	+	0.0382129i
$373$	−15.5022	+	4.15381i	−0.802674	+	0.215076i	−0.636758	−	0.771064i	$-0.719725\pi$
$373$	−15.5022	+	4.15381i	−0.802674	+	0.215076i	−0.165916	+	0.986140i	$0.553058\pi$
$374$	−8.52810	+	14.7711i	−0.440977	+	0.763795i
$375$	15.8272	+	0.392547i	0.817313	+	0.0202710i
$376$	21.5385	−	21.5385i	1.11076	−	1.11076i
$377$	−32.6849	+	8.75788i	−1.68336	+	0.451054i
$378$		−	0.943054i		−	0.0485055i
$379$	−20.0536	+	11.5779i	−1.03008	+	0.594718i	−0.917008	−	0.398868i	$-0.869403\pi$
$379$	−20.0536	+	11.5779i	−1.03008	+	0.594718i	−0.113074	+	0.993587i	$0.536070\pi$
$380$	1.41730	−	0.237846i	0.0727059	−	0.0122013i
$381$		−	14.1963i		−	0.727296i
$382$	1.56236	−	5.83079i	0.0799371	−	0.298329i
$383$	20.2619	+	11.6982i	1.03534	+	0.597751i	0.918509	−	0.395401i	$-0.129394\pi$
$383$	20.2619	+	11.6982i	1.03534	+	0.597751i	0.116827	+	0.993152i	$0.462728\pi$
$384$	−7.85359	+	7.85359i	−0.400777	+	0.400777i
$385$	0.518644	−	0.427939i	0.0264325	−	0.0218098i
$386$	12.1206	+	20.9936i	0.616924	+	1.06854i
$387$	−4.78570	−	8.28908i	−0.243271	−	0.421357i
$388$	0.634275	−	1.09860i	0.0322004	−	0.0557728i
$389$	33.1396	−	8.87973i	1.68024	−	0.450220i	0.712401	−	0.701773i	$-0.247608\pi$
$389$	33.1396	−	8.87973i	1.68024	−	0.450220i	0.967844	+	0.251553i	$0.0809412\pi$
$390$	−14.9712	−	18.1444i	−0.758095	−	0.918779i
$391$	45.7634	−	26.4215i	2.31435	−	1.33619i
$392$	10.5028	+	18.1915i	0.530474	+	0.918807i
$393$			25.3658i			1.27953i
$394$	−3.21468	−	11.9974i	−0.161953	−	0.604418i
$395$	−4.98396	−	6.04036i	−0.250770	−	0.303923i
$396$	0.748780			0.0376276
$397$	18.9636	−	18.9636i	0.951756	−	0.951756i	−0.0471326	−	0.998889i	$-0.515008\pi$
$397$	18.9636	−	18.9636i	0.951756	−	0.951756i	0.998889	+	0.0471326i	$0.0150083\pi$
$398$	−2.64489	+	9.87085i	−0.132576	+	0.494781i
$399$	−0.257090	+	0.257090i	−0.0128706	+	0.0128706i
$400$	−15.9635	−	3.08772i	−0.798176	−	0.154386i
$401$	22.4812	+	22.4812i	1.12266	+	1.12266i	0.991340	+	0.131318i	$0.0419209\pi$
$401$	22.4812	+	22.4812i	1.12266	+	1.12266i	0.131318	+	0.991340i	$0.458079\pi$
$402$	−10.3045	−	5.94933i	−0.513944	−	0.296725i
$403$	4.79632	+	17.9001i	0.238922	+	0.891668i
$404$	−1.88203	−	1.08659i	−0.0936343	−	0.0540598i
$405$	−11.1875	−	1.07203i	−0.555914	−	0.0532698i
$406$		−	0.983570i		−	0.0488137i
$407$	−4.60891	−	13.4440i	−0.228455	−	0.666392i
$408$	16.9741	−	16.9741i	0.840344	−	0.840344i
$409$	12.0283	+	3.22296i	0.594759	+	0.159365i	0.543627	−	0.839327i	$-0.317051\pi$
$409$	12.0283	+	3.22296i	0.594759	+	0.159365i	0.0511316	+	0.998692i	$0.483717\pi$
$410$	−8.04846	−	17.6392i	−0.397485	−	0.871137i
$411$	−22.8771	−	13.2081i	−1.12845	−	0.651508i
$412$	−1.40710	+	2.43717i	−0.0693229	+	0.120071i
$413$		−	0.518039i		−	0.0254910i
$414$	10.4631	+	6.04090i	0.514235	+	0.296894i
$415$	−2.06511	−	12.3058i	−0.101372	−	0.604066i
$416$	−5.17230	−	8.95869i	−0.253593	−	0.439236i
$417$	−12.1024	−	12.1024i	−0.592658	−	0.592658i
$418$	4.26918	+	4.26918i	0.208813	+	0.208813i
$419$	1.24515	−	0.718890i	0.0608297	−	0.0351201i	−0.469277	−	0.883051i	$-0.655485\pi$
$419$	1.24515	−	0.718890i	0.0608297	−	0.0351201i	0.530106	+	0.847931i	$0.322152\pi$
$420$	−0.119444	+	0.0545003i	−0.00582827	+	0.00265934i
$421$	10.4616	+	10.4616i	0.509869	+	0.509869i	0.914486	−	0.404617i	$-0.132595\pi$
$421$	10.4616	+	10.4616i	0.509869	+	0.509869i	−0.404617	+	0.914486i	$0.632595\pi$
$422$	13.0366	−	7.52670i	0.634613	−	0.366394i
$423$	−9.73032	−	2.60723i	−0.473104	−	0.126768i
$424$	−1.84292	+	6.87786i	−0.0895000	+	0.334019i
$425$	27.6660	+	5.35126i	1.34200	+	0.259574i
$426$	3.05809	+	11.4129i	0.148165	+	0.552959i
$427$	−0.140465	+	0.0810973i	−0.00679756	+	0.00392457i
$428$	0.0147547	−	0.0550654i	0.000713197	−	0.00266169i
$429$	−4.91128	+	18.3291i	−0.237119	+	0.884939i
$430$	16.1729	−	22.6957i	0.779925	−	1.09448i
$431$	26.1684	−	7.01180i	1.26049	−	0.337746i	0.434108	−	0.900861i	$-0.357064\pi$
$431$	26.1684	−	7.01180i	1.26049	−	0.337746i	0.826379	+	0.563115i	$0.190397\pi$
$432$	17.7686	+	4.76107i	0.854890	+	0.229067i
$433$	4.83311	−	4.83311i	0.232265	−	0.232265i	−0.581373	−	0.813637i	$-0.697484\pi$
$433$	4.83311	−	4.83311i	0.232265	−	0.232265i	0.813637	+	0.581373i	$0.197484\pi$
$434$	−0.538660			−0.0258565
$435$	−18.5962	−	1.78196i	−0.891621	−	0.0854386i
$436$	1.35394	+	1.35394i	0.0648418	+	0.0648418i
$437$	−4.84129	−	18.0680i	−0.231590	−	0.864307i
$438$	5.71958			0.273292
$439$	4.13514	+	15.4326i	0.197359	+	0.736555i	0.991643	+	0.129009i	$0.0411796\pi$
$439$	4.13514	+	15.4326i	0.197359	+	0.736555i	−0.794284	+	0.607547i	$0.792154\pi$
$440$	6.52340	+	14.2968i	0.310991	+	0.681574i
$441$	3.47344	−	6.01618i	0.165402	−	0.286485i
$442$	−20.9342	−	36.2592i	−0.995740	−	1.72467i
$443$	19.7718	+	19.7718i	0.939389	+	0.939389i	0.998265	−	0.0588766i	$-0.0187518\pi$
$443$	19.7718	+	19.7718i	0.939389	+	0.939389i	−0.0588766	+	0.998265i	$0.518752\pi$
$444$	0.189849	+	2.76849i	0.00900986	+	0.131386i
$445$	1.41907	+	8.45606i	0.0672702	+	0.400855i
$446$	−9.24111	+	34.4883i	−0.437579	+	1.63307i
$447$	7.98983	+	29.8185i	0.377906	+	1.41036i
$448$	1.09897	−	0.294469i	0.0519216	−	0.0139123i
$449$	−6.40280	+	1.71562i	−0.302167	+	0.0809653i	−0.406717	−	0.913554i	$-0.633326\pi$
$449$	−6.40280	+	1.71562i	−0.302167	+	0.0809653i	0.104550	+	0.994520i	$0.466660\pi$
$450$	2.10314	+	6.08973i	0.0991431	+	0.287072i
$451$	−7.82010	+	13.5448i	−0.368234	+	0.637801i
$452$	−0.911786			−0.0428868
$453$	1.13221	+	0.303374i	0.0531958	+	0.0142538i
$454$			13.3807i			0.627986i
$455$	0.273173	+	1.62781i	0.0128065	+	0.0763127i
$456$	−4.24864	−	7.35886i	−0.198961	−	0.344610i
$457$	0.164533	−	0.284979i	0.00769651	−	0.0133307i	−0.862152	−	0.506651i	$-0.830883\pi$
$457$	0.164533	−	0.284979i	0.00769651	−	0.0133307i	0.869848	+	0.493320i	$0.164217\pi$
$458$	10.4225			0.487010
$459$	−30.7943	−	8.25130i	−1.43735	−	0.385138i
$460$	0.644298	−	6.72378i	0.0300405	−	0.313498i
$461$	25.7263	+	6.89335i	1.19819	+	0.321055i	0.802120	−	0.597163i	$-0.203705\pi$
$461$	25.7263	+	6.89335i	1.19819	+	0.321055i	0.396075	+	0.918218i	$0.370372\pi$
$462$	−0.477673	−	0.275785i	−0.0222234	−	0.0128307i
$463$	23.7468	+	13.7102i	1.10361	+	0.637169i	0.937167	−	0.348882i	$-0.113439\pi$
$463$	23.7468	+	13.7102i	1.10361	+	0.637169i	0.166442	+	0.986051i	$0.446772\pi$
$464$	18.5319	+	4.96562i	0.860324	+	0.230523i
$465$	−0.975906	+	10.1844i	−0.0452565	+	0.472289i
$466$	34.9946	+	9.37677i	1.62109	+	0.434371i
$467$	−34.8407			−1.61224			−0.806118	−	0.591754i	$-0.798436\pi$
$467$	−34.8407			−1.61224			−0.806118	+	0.591754i	$0.798436\pi$
$468$	−0.919029	+	1.59180i	−0.0424821	+	0.0735812i
$469$	0.417444	+	0.723035i	0.0192758	+	0.0333867i
$470$	−4.85429	−	28.9262i	−0.223912	−	1.33426i
$471$			1.77492i			0.0817839i
$472$	11.6946	+	3.13356i	0.538288	+	0.144234i
$473$	−22.4807			−1.03366
$474$	−3.21191	+	5.56320i	−0.147528	+	0.255526i
$475$	4.36435	−	8.96923i	0.200250	−	0.411536i
$476$	−0.225715	+	0.0604803i	−0.0103457	+	0.00277211i
$477$	2.27461	−	0.609480i	0.104147	−	0.0279062i
$478$	1.15970	+	4.32806i	0.0530435	+	0.197961i
$479$	−7.33422	+	27.3717i	−0.335109	+	1.25064i	0.568642	+	0.822585i	$0.307469\pi$
$479$	−7.33422	+	27.3717i	−0.335109	+	1.25064i	−0.903751	+	0.428059i	$0.859198\pi$
$480$	−0.945203	−	5.63236i	−0.0431424	−	0.257081i
$481$	34.2368	+	6.70278i	1.56107	+	0.305620i
$482$	17.8875	+	17.8875i	0.814752	+	0.814752i
$483$	0.854429	+	1.47991i	0.0388779	+	0.0673384i
$484$	−0.892561	+	1.54596i	−0.0405710	+	0.0702710i
$485$	−3.65495	−	8.01026i	−0.165963	−	0.363727i
$486$	−3.30330	−	12.3281i	−0.149841	−	0.559213i
$487$	−9.06800			−0.410910			−0.205455	−	0.978667i	$-0.565867\pi$
$487$	−9.06800			−0.410910			−0.205455	+	0.978667i	$0.565867\pi$
$488$	−0.981098	−	3.66151i	−0.0444122	−	0.165749i
$489$	0.495096	+	0.495096i	0.0223890	+	0.0223890i
$490$	20.1346	+	1.92938i	0.909591	+	0.0871604i
$491$	−28.3508			−1.27945			−0.639727	−	0.768602i	$-0.720953\pi$
$491$	−28.3508			−1.27945			−0.639727	+	0.768602i	$0.720953\pi$
$492$	2.15940	−	2.15940i	0.0973531	−	0.0973531i
$493$	−32.1172	−	8.60579i	−1.44649	−	0.387585i
$494$	−14.3156	+	3.83584i	−0.644088	+	0.172583i
$495$	3.01602	−	4.23243i	0.135560	−	0.190234i
$496$	2.71946	−	10.1492i	0.122107	−	0.455711i
$497$	0.214576	−	0.800808i	0.00962505	−	0.0359212i
$498$	−8.86426	+	5.11778i	−0.397217	+	0.229333i
$499$	5.49842	+	20.5204i	0.246143	+	0.918618i	0.972806	+	0.231623i	$0.0744037\pi$
$499$	5.49842	+	20.5204i	0.246143	+	0.918618i	−0.726663	+	0.686994i	$0.758930\pi$
$500$	2.60930	−	2.48300i	0.116691	−	0.111043i
$501$	6.26676	−	23.3879i	0.279978	−	1.04489i
$502$	−0.923499	−	0.247451i	−0.0412178	−	0.0110443i
$503$	21.9152	−	12.6528i	0.977151	−	0.564159i	0.0757425	−	0.997127i	$-0.475867\pi$
$503$	21.9152	−	12.6528i	0.977151	−	0.564159i	0.901409	+	0.432969i	$0.142534\pi$
$504$	−0.272309	−	0.272309i	−0.0121296	−	0.0121296i
$505$	−13.7225	+	6.26136i	−0.610645	+	0.278627i
$506$	24.5751	−	14.1885i	1.09250	−	0.630754i
$507$	−19.9203	−	19.9203i	−0.884692	−	0.884692i
$508$	−2.28378	−	2.28378i	−0.101326	−	0.101326i
$509$	7.55145	+	13.0795i	0.334712	+	0.579739i	0.983430	−	0.181291i	$-0.0580275\pi$
$509$	7.55145	+	13.0795i	0.334712	+	0.579739i	−0.648717	+	0.761030i	$0.724694\pi$
$510$	−3.82559	−	22.7962i	−0.169400	−	1.00943i
$511$	−0.347557	−	0.200662i	−0.0153750	−	0.00887676i
$512$			25.4281i			1.12378i
$513$	−5.64253	+	9.77314i	−0.249124	+	0.431495i
$514$	−13.4032	−	7.73836i	−0.591191	−	0.341324i
$515$	8.10828	+	17.7703i	0.357293	+	0.783052i
$516$	4.23993	+	1.13608i	0.186652	+	0.0500133i
$517$	−16.7303	+	16.7303i	−0.735796	+	0.735796i
$518$	−0.445760	+	0.910832i	−0.0195856	+	0.0400197i
$519$		−	26.6634i		−	1.17039i
$520$	−38.3997	−	3.67961i	−1.68394	−	0.161361i
$521$	0.561137	+	0.323973i	0.0245839	+	0.0141935i	0.512242	−	0.858841i	$-0.328815\pi$
$521$	0.561137	+	0.323973i	0.0245839	+	0.0141935i	−0.487658	+	0.873035i	$0.662149\pi$
$522$	−1.96759	−	7.34314i	−0.0861191	−	0.321401i
$523$	−36.0021	−	20.7858i	−1.57426	−	0.908901i	−0.995637	−	0.0933066i	$-0.970256\pi$
$523$	−36.0021	−	20.7858i	−1.57426	−	0.908901i	−0.578625	−	0.815594i	$-0.696410\pi$
$524$	4.08064	+	4.08064i	0.178264	+	0.178264i
$525$	−0.173051	+	0.894674i	−0.00755257	+	0.0390468i
$526$	−0.951039	+	0.951039i	−0.0414673	+	0.0414673i
$527$	−4.71303	+	17.5893i	−0.205303	+	0.766200i
$528$	7.60777	−	7.60777i	0.331086	−	0.331086i
$529$	−64.9166			−2.82246
$530$	4.36370	+	5.28862i	0.189547	+	0.229723i
$531$	−1.03631	−	3.86758i	−0.0449722	−	0.167839i
$532$			0.0827171i			0.00358624i
$533$	−19.1963	−	33.2490i	−0.831484	−	1.44017i
$534$	6.09118	−	3.51675i	0.263591	−	0.152184i
$535$	−0.251823	−	0.305199i	−0.0108873	−	0.0131949i
$536$	−18.8474	+	5.05015i	−0.814085	+	0.218133i
$537$	−0.195722	+	0.339001i	−0.00844605	+	0.0146290i
$538$	−7.56390	−	13.1011i	−0.326103	−	0.564827i
$539$	−8.15820	−	14.1304i	−0.351399	−	0.608640i
$540$	−3.14324	+	2.59352i	−0.135263	+	0.111607i
$541$	−7.92447	+	7.92447i	−0.340700	+	0.340700i	−0.856630	−	0.515931i	$-0.827446\pi$
$541$	−7.92447	+	7.92447i	−0.340700	+	0.340700i	0.515931	+	0.856630i	$0.327446\pi$
$542$	−27.1697	−	15.6864i	−1.16704	−	0.673790i
$543$	−2.29370	+	8.56019i	−0.0984319	+	0.367353i
$544$		−	10.1650i		−	0.435819i
$545$	13.1066	−	2.19950i	0.561425	−	0.0942164i
$546$	1.17256	−	0.676979i	0.0501810	−	0.0289720i
$547$			0.343344i			0.0146803i	0.999973	+	0.00734016i	$0.00233647\pi$
$547$			0.343344i			0.0146803i	−0.999973	+	0.00734016i	$0.997664\pi$
$548$	−5.80510	+	1.55547i	−0.247982	+	0.0664465i
$549$	−0.886451	+	0.886451i	−0.0378328	+	0.0378328i
$550$	14.8568	+	2.87365i	0.633495	+	0.122533i
$551$	−5.88494	+	10.1930i	−0.250707	+	0.434237i
$552$	−38.5771	+	10.3367i	−1.64195	+	0.439959i
$553$	0.390351	−	0.225369i	0.0165994	−	0.00958367i
$554$	−4.79715			−0.203811
$555$	16.4134	+	10.0781i	0.696710	+	0.427792i
$556$	−3.89388			−0.165137
$557$	21.8362	−	12.6071i	0.925229	−	0.534181i	0.0399295	−	0.999203i	$-0.487287\pi$
$557$	21.8362	−	12.6071i	0.925229	−	0.534181i	0.885299	+	0.465021i	$0.153953\pi$
$558$	−4.02153	+	1.07757i	−0.170245	+	0.0456170i
$559$	27.5921	−	47.7909i	1.16702	−	2.02134i
$560$	0.327338	−	0.876738i	0.0138326	−	0.0370490i
$561$	−13.1848	+	13.1848i	−0.556664	+	0.556664i
$562$	31.7654	−	8.51150i	1.33994	−	0.359036i
$563$		−	6.21062i		−	0.261746i	−0.991399	−	0.130873i	$-0.958222\pi$
$563$		−	6.21062i		−	0.261746i	0.991399	−	0.130873i	$-0.0417781\pi$
$564$	4.00086	−	2.30989i	0.168466	−	0.0972641i
$565$	−3.67260	+	5.15382i	−0.154507	+	0.216823i
$566$			3.26193i			0.137109i
$567$	0.167424	−	0.624836i	0.00703116	−	0.0262407i
$568$	16.7801	+	9.68801i	0.704078	+	0.406500i
$569$	2.93374	−	2.93374i	0.122989	−	0.122989i	−0.642933	−	0.765922i	$-0.722283\pi$
$569$	2.93374	−	2.93374i	0.122989	−	0.122989i	0.765922	+	0.642933i	$0.222283\pi$
$570$	−8.14493	−	0.780478i	−0.341153	−	0.0326906i
$571$	−6.05364	−	10.4852i	−0.253337	−	0.438793i	0.711105	−	0.703085i	$-0.248195\pi$
$571$	−6.05364	−	10.4852i	−0.253337	−	0.438793i	−0.964443	+	0.264293i	$0.914861\pi$
$572$	2.15856	+	3.73873i	0.0902537	+	0.156324i
$573$	3.29960	−	5.71508i	0.137843	−	0.238751i
$574$	1.07794	−	0.288833i	0.0449922	−	0.0120556i
$575$	−35.4106	−	30.7247i	−1.47672	−	1.28131i
$576$	7.61565	−	4.39690i	0.317319	−	0.183204i
$577$	−13.8496	−	23.9882i	−0.576567	−	0.998644i	−0.995869	−	0.0907968i	$-0.971059\pi$
$577$	−13.8496	−	23.9882i	−0.576567	−	0.998644i	0.419302	−	0.907847i	$-0.362275\pi$
$578$		−	19.1211i		−	0.795331i
$579$	6.85898	+	25.5981i	0.285049	+	1.06382i
$580$	−3.27828	+	2.70494i	−0.136123	+	0.112317i
$581$	0.718195			0.0297958
$582$	−5.10707	+	5.10707i	−0.211695	+	0.211695i
$583$	1.43151	−	5.34246i	0.0592870	−	0.221262i
$584$	6.63223	−	6.63223i	0.274444	−	0.274444i
$585$	5.29581	+	11.6064i	0.218955	+	0.479866i
$586$	−1.42297	−	1.42297i	−0.0587822	−	0.0587822i
$587$	−26.3189	−	15.1952i	−1.08630	−	0.627175i	−0.153710	−	0.988116i	$-0.549122\pi$
$587$	−26.3189	−	15.1952i	−1.08630	−	0.627175i	−0.932589	+	0.360941i	$0.882455\pi$
$588$	0.824566	+	3.07732i	0.0340045	+	0.126907i
$589$	5.58229	+	3.22294i	0.230014	+	0.132799i
$590$	8.99238	−	7.41971i	0.370211	−	0.305465i
$591$		−	13.5784i		−	0.558542i
$592$	−14.9110	−	12.9972i	−0.612838	−	0.534181i
$593$	−28.2413	+	28.2413i	−1.15973	+	1.15973i	−0.175200	+	0.984533i	$0.556057\pi$
$593$	−28.2413	+	28.2413i	−1.15973	+	1.15973i	−0.984533	+	0.175200i	$0.943943\pi$
$594$	−16.5367	−	4.43098i	−0.678507	−	0.181805i
$595$	−0.567302	+	1.51945i	−0.0232571	+	0.0622915i
$596$	6.08229	+	3.51161i	0.249140	+	0.143841i
$597$	−5.58584	+	9.67496i	−0.228613	+	0.395970i
$598$			69.6579i			2.84852i
$599$	2.99451	+	1.72888i	0.122352	+	0.0706401i	0.559927	−	0.828542i	$-0.310829\pi$
$599$	2.99451	+	1.72888i	0.122352	+	0.0706401i	−0.437575	+	0.899182i	$0.644162\pi$
$600$	−19.1503	−	9.31837i	−0.781807	−	0.380421i
$601$	−11.8190	−	20.4712i	−0.482109	−	0.835037i	0.517680	−	0.855574i	$-0.326796\pi$
$601$	−11.8190	−	20.4712i	−0.482109	−	0.835037i	−0.999789	+	0.0205370i	$0.993462\pi$
$602$	1.13423	+	1.13423i	0.0462279	+	0.0462279i
$603$	4.56296	+	4.56296i	0.185818	+	0.185818i
$604$	0.230945	−	0.133336i	0.00939702	−	0.00542537i
$605$	5.14330	+	11.2722i	0.209105	+	0.458278i
$606$	8.74903	+	8.74903i	0.355405	+	0.355405i
$607$	5.04994	−	2.91558i	0.204971	−	0.118340i	−0.394001	−	0.919110i	$-0.628909\pi$
$607$	5.04994	−	2.91558i	0.204971	−	0.118340i	0.598972	+	0.800770i	$0.295576\pi$
$608$	−3.47558	−	0.931278i	−0.140953	−	0.0377683i
$609$	0.278297	−	1.03862i	0.0112772	−	0.0420870i
$610$	−3.41956	−	1.27673i	−0.138454	−	0.0516931i
$611$	−15.0321	−	56.1004i	−0.608132	−	2.26958i
$612$	−1.56416	+	0.903069i	−0.0632275	+	0.0365044i
$613$	−1.16911	+	4.36320i	−0.0472201	+	0.176228i	−0.985509	−	0.169626i	$-0.945744\pi$
$613$	−1.16911	+	4.36320i	−0.0472201	+	0.176228i	0.938288	+	0.345854i	$0.112411\pi$
$614$	5.41505	−	20.2092i	0.218533	−	0.815578i
$615$	−3.50799	−	20.9037i	−0.141456	−	0.842920i
$616$	−0.873685	+	0.234103i	−0.0352018	+	0.00943228i
$617$	27.2973	+	7.31428i	1.09895	+	0.294462i	0.762336	−	0.647182i	$-0.224052\pi$
$617$	27.2973	+	7.31428i	1.09895	+	0.294462i	0.336611	+	0.941644i	$0.390719\pi$
$618$	11.3297	−	11.3297i	0.455749	−	0.455749i
$619$	−2.82730			−0.113639			−0.0568195	−	0.998384i	$-0.518096\pi$
$619$	−2.82730			−0.113639			−0.0568195	+	0.998384i	$0.518096\pi$
$620$	1.48138	+	1.79538i	0.0594938	+	0.0721040i
$621$	37.5054	+	37.5054i	1.50504	+	1.50504i
$622$	6.95974	+	25.9741i	0.279060	+	1.04147i
$623$	−0.493516			−0.0197723
$624$	6.83555	+	25.5106i	0.273641	+	1.02124i
$625$	−3.52497	−	24.7502i	−0.140999	−	0.990010i
$626$	−8.88426	+	15.3880i	−0.355086	+	0.615028i
$627$	3.30018	+	5.71608i	0.131796	+	0.228278i
$628$	0.285534	+	0.285534i	0.0113941	+	0.0113941i
$629$	25.8419	+	22.5251i	1.03038	+	0.898135i
$630$	−0.365711	+	0.0613723i	−0.0145703	+	0.00244513i
$631$	−1.95373	+	7.29142i	−0.0777767	+	0.290267i	−0.993849	−	0.110747i	$-0.964676\pi$
$631$	−1.95373	+	7.29142i	−0.0777767	+	0.290267i	0.916072	+	0.401014i	$0.131342\pi$
$632$	2.72647	+	10.1753i	0.108453	+	0.404753i
$633$	15.8959	−	4.25930i	0.631807	−	0.169292i
$634$	32.4835	−	8.70394i	1.29009	−	0.345677i
$635$	−22.1078	+	3.71005i	−0.877321	+	0.147229i
$636$	−0.539973	+	0.935261i	−0.0214113	+	0.0370855i
$637$	40.0525			1.58694
$638$	−17.2471	−	4.62135i	−0.682820	−	0.182961i
$639$		−	6.40793i		−	0.253494i
$640$	14.2828	+	10.1779i	0.564579	+	0.402318i
$641$	2.03182	+	3.51921i	0.0802519	+	0.139000i	0.903358	−	0.428887i	$-0.141094\pi$
$641$	2.03182	+	3.51921i	0.0802519	+	0.139000i	−0.823106	+	0.567888i	$0.807761\pi$
$642$	−0.162287	+	0.281090i	−0.00640497	+	0.0110937i
$643$	−0.831741			−0.0328007			−0.0164003	−	0.999866i	$-0.505221\pi$
$643$	−0.831741			−0.0328007			−0.0164003	+	0.999866i	$0.505221\pi$
$644$	0.375530	+	0.100623i	0.0147980	+	0.00396510i
$645$	23.4997	−	19.3899i	0.925301	−	0.763476i
$646$	−14.0670	−	3.76923i	−0.553457	−	0.148298i
$647$	15.5775	+	8.99368i	0.612415	+	0.353578i	0.773910	−	0.633295i	$-0.218298\pi$
$647$	15.5775	+	8.99368i	0.612415	+	0.353578i	−0.161495	+	0.986874i	$0.551632\pi$
$648$	13.0928	+	7.55914i	0.514334	+	0.296951i
$649$	−9.08392	−	2.43403i	−0.356575	−	0.0955440i
$650$	−24.3437	+	28.0564i	−0.954839	+	1.10046i
$651$	−0.568808	−	0.152412i	−0.0222934	−	0.00597349i
$652$	0.159294			0.00623844
$653$	16.8353	−	29.1596i	0.658816	−	1.14110i	−0.322107	−	0.946703i	$-0.604391\pi$
$653$	16.8353	−	29.1596i	0.658816	−	1.14110i	0.980923	−	0.194399i	$-0.0622756\pi$
$654$	−5.45083	−	9.44112i	−0.213144	−	0.369177i
$655$	39.5021	−	6.62910i	1.54347	−	0.259020i
$656$			21.7682i			0.849904i
$657$	−2.99621	−	0.802831i	−0.116893	−	0.0313214i
$658$	1.68820			0.0658130
$659$	17.0098	−	29.4618i	0.662606	−	1.14767i	−0.317322	−	0.948318i	$-0.602784\pi$
$659$	17.0098	−	29.4618i	0.662606	−	1.14767i	0.979928	−	0.199350i	$-0.0638830\pi$
$660$	0.394461	+	2.35055i	0.0153544	+	0.0914950i
$661$	−27.2321	+	7.29681i	−1.05920	+	0.283813i	−0.746051	−	0.665889i	$-0.768052\pi$
$661$	−27.2321	+	7.29681i	−1.05920	+	0.283813i	−0.313154	+	0.949702i	$0.601386\pi$
$662$	13.8400	−	3.70843i	0.537908	−	0.144132i
$663$	−11.8465	−	44.2118i	−0.460081	−	1.71705i
$664$	−4.34429	+	16.2131i	−0.168591	+	0.629190i
$665$	0.467554	+	0.333178i	0.0181310	+	0.0129201i
$666$	−1.50588	+	7.69182i	−0.0583516	+	0.298052i
$667$	39.1168	+	39.1168i	1.51461	+	1.51461i
$668$	−2.75430	−	4.77059i	−0.106567	−	0.184580i
$669$	−19.5167	+	33.8039i	−0.754558	+	1.30693i
$670$	−6.57188	+	17.6020i	−0.253894	+	0.680026i
$671$	0.762079	+	2.84412i	0.0294197	+	0.109796i
$672$	0.328718			0.0126806
$673$	8.83302	+	32.9653i	0.340488	+	1.27072i	0.897796	+	0.440412i	$0.145168\pi$
$673$	8.83302	+	32.9653i	0.340488	+	1.27072i	−0.557308	+	0.830306i	$0.688166\pi$
$674$	−14.2846	−	14.2846i	−0.550222	−	0.550222i
$675$	1.99902	+	28.2135i	0.0769423	+	1.08594i
$676$	−6.40924			−0.246509
$677$	25.5280	−	25.5280i	0.981123	−	0.981123i	−0.0187025	−	0.999825i	$-0.505954\pi$
$677$	25.5280	−	25.5280i	0.981123	−	0.981123i	0.999825	+	0.0187025i	$0.00595355\pi$
$678$	5.01437	+	1.34360i	0.192576	+	0.0516005i
$679$	0.489510	−	0.131164i	0.0187857	−	0.00503361i
$680$	−30.8698	−	21.9977i	−1.18380	−	0.843575i
$681$	−3.78601	+	14.1296i	−0.145080	+	0.541447i
$682$	−2.53092	+	9.44551i	−0.0969139	+	0.361687i
$683$	−26.8851	+	15.5221i	−1.02873	+	0.593938i	−0.916621	−	0.399758i	$-0.869094\pi$
$683$	−26.8851	+	15.5221i	−1.02873	+	0.593938i	−0.112109	+	0.993696i	$0.535761\pi$
$684$	0.165472	+	0.617550i	0.00632698	+	0.0236126i
$685$	−14.5903	+	39.0783i	−0.557465	+	1.49311i
$686$	−0.603355	+	2.25175i	−0.0230362	+	0.0859722i
$687$	11.0058	+	2.94900i	0.419898	+	0.112511i
$688$	−27.0969	+	15.6444i	−1.03306	+	0.596437i
$689$	9.60036	+	9.60036i	0.365744	+	0.365744i
$690$	−13.4514	+	36.0280i	−0.512086	+	1.37156i
$691$	−25.5510	+	14.7519i	−0.972007	+	0.561189i	−0.899848	−	0.436205i	$-0.856322\pi$
$691$	−25.5510	+	14.7519i	−0.972007	+	0.561189i	−0.0721595	+	0.997393i	$0.522989\pi$
$692$	−4.28939	−	4.28939i	−0.163058	−	0.163058i
$693$	0.211519	+	0.211519i	0.00803494	+	0.00803494i
$694$	1.37090	+	2.37447i	0.0520387	+	0.0901337i
$695$	−15.6842	+	22.0099i	−0.594937	+	0.834884i
$696$	21.7632	+	12.5650i	0.824933	+	0.476275i
$697$		−	37.7259i		−	1.42897i
$698$	5.33507	−	9.24061i	0.201935	−	0.349762i
$699$	34.3001	+	19.8032i	1.29735	+	0.749025i
$700$	0.116089	+	0.171767i	0.00438774	+	0.00649218i
$701$	25.5146	+	6.83662i	0.963673	+	0.258216i	0.706155	−	0.708058i	$-0.250428\pi$
$701$	25.5146	+	6.83662i	0.963673	+	0.258216i	0.257519	+	0.966273i	$0.417095\pi$
$702$	29.7162	−	29.7162i	1.12157	−	1.12157i
$703$	10.0693	−	6.77212i	0.379770	−	0.255415i
$704$		−	20.6543i		−	0.778438i
$705$	3.05857	−	31.9187i	0.115192	−	1.20213i
$706$	−20.2600	−	11.6971i	−0.762494	−	0.440226i
$707$	−0.224699	−	0.838589i	−0.00845069	−	0.0315384i
$708$	1.59025	+	0.918130i	0.0597652	+	0.0345054i
$709$	14.5369	+	14.5369i	0.545946	+	0.545946i	0.925266	−	0.379320i	$-0.123842\pi$
$709$	14.5369	+	14.5369i	0.545946	+	0.545946i	−0.379320	+	0.925266i	$0.623842\pi$
$710$	16.9742	−	7.74502i	0.637029	−	0.290665i
$711$	2.46344	−	2.46344i	0.0923864	−	0.0923864i
$712$	2.98523	−	11.1410i	0.111876	−	0.417528i
$713$	21.4226	−	21.4226i	0.802283	−	0.802283i
$714$	1.33045			0.0497907
$715$	29.8274	+	2.85818i	1.11548	+	0.106890i
$716$	0.0230495	+	0.0860220i	0.000861401	+	0.00321479i
$717$			4.89844i			0.182935i
$718$	−10.4647	−	18.1254i	−0.390539	−	0.676433i
$719$	6.85837	−	3.95968i	0.255774	−	0.147671i	−0.366631	−	0.930366i	$-0.619489\pi$
$719$	6.85837	−	3.95968i	0.255774	−	0.147671i	0.622405	+	0.782695i	$0.286156\pi$
$720$	0.689969	−	7.20039i	0.0257136	−	0.268343i
$721$	−1.08595	+	0.290979i	−0.0404428	+	0.0108366i
$722$	9.72794	−	16.8493i	0.362036	−	0.627066i
$723$	13.8274	+	23.9498i	0.514248	+	0.890704i
$724$	1.00810	+	1.74608i	0.0374658	+	0.0648927i
$725$	2.08490	+	29.4256i	0.0774313	+	1.09284i
$726$	7.18675	−	7.18675i	0.266725	−	0.266725i
$727$	−40.0005	−	23.0943i	−1.48354	−	0.856520i	−0.483712	−	0.875227i	$-0.660712\pi$
$727$	−40.0005	−	23.0943i	−1.48354	−	0.856520i	−0.999825	+	0.0187071i	$0.994045\pi$
$728$	0.574662	−	2.14467i	0.0212984	−	0.0794866i
$729$		−	29.0312i		−	1.07523i
$730$	−1.49476	−	8.90709i	−0.0553234	−	0.329666i
$731$	46.9610	−	27.1129i	1.73691	−	1.00281i
$732$		−	0.574921i		−	0.0212497i
$733$	11.1693	−	2.99280i	0.412547	−	0.110542i	−0.0465753	−	0.998915i	$-0.514831\pi$
$733$	11.1693	−	2.99280i	0.412547	−	0.110542i	0.459122	+	0.888373i	$0.348164\pi$
$734$	−7.26507	+	7.26507i	−0.268159	+	0.268159i
$735$	20.7157	+	7.73439i	0.764109	+	0.285287i
$736$	−8.45588	+	14.6460i	−0.311688	+	0.539860i
$737$	14.6400	−	3.92276i	0.539270	−	0.144497i
$738$	7.46988	−	4.31274i	0.274970	−	0.158754i
$739$	−30.6774			−1.12849			−0.564244	−	0.825608i	$-0.690832\pi$
$739$	−30.6774			−1.12849			−0.564244	+	0.825608i	$0.690832\pi$
$740$	4.26174	−	1.01917i	0.156665	−	0.0374654i
$741$	−16.2021			−0.595201
$742$	−0.341771	+	0.197322i	−0.0125468	+	0.00724390i
$743$	−40.8742	+	10.9522i	−1.49953	+	0.401797i	−0.912942	−	0.408090i	$-0.866195\pi$
$743$	−40.8742	+	10.9522i	−1.49953	+	0.401797i	−0.586586	+	0.809887i	$0.699528\pi$
$744$	6.88132	−	11.9188i	0.252282	−	0.436964i
$745$	44.3481	−	20.2353i	1.62479	−	0.741364i
$746$	14.6997	−	14.6997i	0.538196	−	0.538196i
$747$	5.36191	−	1.43672i	0.196182	−	0.0525668i
$748$			4.24214i			0.155108i
$749$	0.0197231	−	0.0113872i	0.000720668	−	0.000416078i
$750$	−18.0088	+	9.81024i	−0.657587	+	0.358219i
$751$			28.9353i			1.05586i	0.849287	+	0.527932i	$0.177032\pi$
$751$			28.9353i			1.05586i	−0.849287	+	0.527932i	$0.822968\pi$
$752$	−8.52301	+	31.8083i	−0.310802	+	1.15993i
$753$	−0.905172	−	0.522601i	−0.0329863	−	0.0190446i
$754$	30.9929	−	30.9929i	1.12870	−	1.12870i
$755$	0.176553	−	1.84247i	0.00642540	−	0.0670544i
$756$	−0.117276	−	0.203128i	−0.00426529	−	0.00738770i
$757$	1.55486	+	2.69309i	0.0565122	+	0.0978820i	0.892898	−	0.450260i	$-0.148669\pi$
$757$	1.55486	+	2.69309i	0.0565122	+	0.0978820i	−0.836385	+	0.548142i	$0.815335\pi$
$758$	14.9970	−	25.9756i	0.544717	−	0.943477i
$759$	29.9652	−	8.02915i	1.08767	−	0.291440i
$760$	−10.3496	+	8.53956i	−0.375419	+	0.309763i
$761$	7.38889	−	4.26598i	0.267847	−	0.154642i	−0.360062	−	0.932928i	$-0.617244\pi$
$761$	7.38889	−	4.26598i	0.267847	−	0.154642i	0.627909	+	0.778287i	$0.283911\pi$
$762$	9.19429	+	15.9250i	0.333074	+	0.576901i
$763$			0.764933i			0.0276924i
$764$	−0.388582	−	1.45021i	−0.0140584	−	0.0524667i
$765$	−1.19577	+	12.4788i	−0.0432331	+	0.451173i
$766$	−30.3057			−1.09499
$767$	16.3237	−	16.3237i	0.589416	−	0.589416i
$768$	−2.75631	+	10.2867i	−0.0994598	+	0.371189i
$769$	−28.2158	+	28.2158i	−1.01749	+	1.01749i	−0.0176427	+	0.999844i	$0.505616\pi$
$769$	−28.2158	+	28.2158i	−1.01749	+	1.01749i	−0.999844	+	0.0176427i	$0.994384\pi$
$770$	−0.304644	+	0.815953i	−0.0109786	+	0.0294049i
$771$	−11.9639	−	11.9639i	−0.430868	−	0.430868i
$772$	5.22142	+	3.01459i	0.187923	+	0.108498i
$773$	0.0273642	+	0.102125i	0.000984222	+	0.00367317i	0.966416	−	0.256982i	$-0.0827281\pi$
$773$	0.0273642	+	0.102125i	0.000984222	+	0.00367317i	−0.965432	+	0.260655i	$0.916061\pi$
$774$	10.7369	+	6.19898i	0.385932	+	0.222818i
$775$	16.1152	−	1.14181i	0.578873	−	0.0410151i
$776$			11.8440i			0.425174i
$777$	−0.728426	+	0.835685i	−0.0261321	+	0.0299800i
$778$	−31.4241	+	31.4241i	−1.12661	+	1.12661i
$779$	−12.8991	−	3.45631i	−0.462160	−	0.123835i
$780$	−5.48110	−	2.04642i	−0.196255	−	0.0732736i
$781$	−13.0342	−	7.52527i	−0.466399	−	0.269275i
$782$	−34.2241	+	59.2779i	−1.22385	+	2.11977i
$783$		−	33.3746i		−	1.19271i
$784$	−19.6668	−	11.3547i	−0.702387	−	0.405523i
$785$	2.76408	−	0.463858i	0.0986541	−	0.0165558i
$786$	−16.4283	−	28.4547i	−0.585978	−	1.01494i
$787$	−9.62366	−	9.62366i	−0.343046	−	0.343046i	0.514465	−	0.857511i	$-0.327991\pi$
$787$	−9.62366	−	9.62366i	−0.343046	−	0.343046i	−0.857511	+	0.514465i	$0.827991\pi$
$788$	−2.18439	−	2.18439i	−0.0778156	−	0.0778156i
$789$	−1.27336	+	0.735175i	−0.0453329	+	0.0261729i
$790$	9.50296	+	3.54802i	0.338100	+	0.126233i
$791$	−0.257566	−	0.257566i	−0.00915799	−	0.00915799i
$792$	−6.05445	+	3.49554i	−0.215136	+	0.124209i
$793$	−6.98156	−	1.87070i	−0.247923	−	0.0664306i
$794$	−8.99098	+	33.5548i	−0.319078	+	1.19081i
$795$	3.11154	+	6.81932i	0.110355	+	0.241856i
$796$	0.657824	+	2.45503i	0.0233160	+	0.0870164i
$797$	8.63407	−	4.98488i	0.305834	−	0.176574i	−0.339227	−	0.940705i	$-0.610165\pi$
$797$	8.63407	−	4.98488i	0.305834	−	0.176574i	0.645061	+	0.764131i	$0.276832\pi$
$798$	0.121891	−	0.454903i	0.00431489	−	0.0161034i
$799$	14.7710	−	55.1262i	0.522561	−	1.95022i
$800$	−8.52424	+	2.94392i	−0.301377	+	0.104083i
$801$	−3.68450	+	0.987259i	−0.130185	+	0.0348831i
$802$	−39.7789	−	10.6587i	−1.40464	−	0.376373i
$803$	−5.15166	+	5.15166i	−0.181798	+	0.181798i
$804$	−2.95938			−0.104369
$805$	2.08137	−	1.71736i	0.0733587	−	0.0605290i
$806$	−16.9735	−	16.9735i	−0.597867	−	0.597867i
$807$	−4.28035	−	15.9745i	−0.150676	−	0.562329i
$808$	20.2902			0.713805
$809$	4.88219	+	18.2206i	0.171649	+	0.640601i	0.997098	+	0.0761254i	$0.0242549\pi$
$809$	4.88219	+	18.2206i	0.171649	+	0.640601i	−0.825450	+	0.564476i	$0.809078\pi$
$810$	13.2442	−	6.04311i	0.465354	−	0.212333i
$811$	−2.72608	+	4.72171i	−0.0957256	+	0.165802i	−0.909911	−	0.414803i	$-0.863850\pi$
$811$	−2.72608	+	4.72171i	−0.0957256	+	0.165802i	0.814186	+	0.580605i	$0.197184\pi$
$812$	−0.122315	−	0.211855i	−0.00429240	−	0.00743465i
$813$	−24.2520	−	24.2520i	−0.850554	−	0.850554i
$814$	13.8772	+	12.0961i	0.486396	+	0.423968i
$815$	0.641623	−	0.900400i	0.0224751	−	0.0315396i
$816$	−6.71685	+	25.0676i	−0.235137	+	0.877542i
$817$	−4.96799	−	18.5408i	−0.173808	−	0.648660i
$818$	−15.5804	+	4.17474i	−0.544754	+	0.145966i
$819$	−0.709273	+	0.190049i	−0.0247840	+	0.00664085i
$820$	−3.92716	−	2.79849i	−0.137142	−	0.0977273i
$821$	−12.7492	+	22.0823i	−0.444951	+	0.770678i	−0.998049	−	0.0624382i	$-0.980112\pi$
$821$	−12.7492	+	22.0823i	−0.444951	+	0.770678i	0.553098	+	0.833117i	$0.313446\pi$
$822$	34.2173			1.19346
$823$	14.8087	+	3.96797i	0.516197	+	0.138315i	0.507507	−	0.861648i	$-0.330567\pi$
$823$	14.8087	+	3.96797i	0.516197	+	0.138315i	0.00869031	+	0.999962i	$0.497234\pi$
$824$		−	26.2752i		−	0.915338i
$825$	14.8752	+	7.23815i	0.517888	+	0.252000i
$826$	0.335511	+	0.581122i	0.0116739	+	0.0202198i
$827$	13.2735	−	22.9903i	0.461564	−	0.799452i	−0.537475	−	0.843280i	$-0.680622\pi$
$827$	13.2735	−	22.9903i	0.461564	−	0.799452i	0.999039	+	0.0438273i	$0.0139551\pi$
$828$	3.00493			0.104428
$829$	−22.2969	−	5.97444i	−0.774404	−	0.207501i	−0.150088	−	0.988673i	$-0.547956\pi$
$829$	−22.2969	−	5.97444i	−0.774404	−	0.207501i	−0.624316	+	0.781172i	$0.714622\pi$
$830$	10.2865	+	12.4668i	0.357050	+	0.432729i
$831$	−5.06565	−	1.35734i	−0.175725	−	0.0470855i
$832$	43.9083	+	25.3504i	1.52224	+	0.878868i
$833$	34.0841	+	19.6785i	1.18094	+	0.681818i
$834$	21.4144	+	5.73797i	0.741520	+	0.198690i
$835$	−38.0596	−	3.64702i	−1.31711	−	0.126210i
$836$	1.45046	+	0.388650i	0.0501653	+	0.0134417i
$837$	−18.2779			−0.631776
$838$	−0.931187	+	1.61286i	−0.0321673	+	0.0557154i
$839$	−9.23203	−	15.9903i	−0.318725	−	0.552048i	0.661497	−	0.749948i	$-0.269921\pi$
$839$	−9.23203	−	15.9903i	−0.318725	−	0.552048i	−0.980222	+	0.197900i	$0.936588\pi$
$840$	0.711371	−	0.998279i	0.0245446	−	0.0344439i
$841$		−	5.80847i		−	0.200292i
$842$	−18.5111	−	4.96005i	−0.637936	−	0.170934i
$843$	35.9516			1.23824
$844$	1.87201	−	3.24241i	0.0644372	−	0.111608i
$845$	−25.8159	+	36.2278i	−0.888093	+	1.24628i
$846$	12.6038	−	3.37718i	0.433328	−	0.116110i
$847$	−0.688846	+	0.184576i	−0.0236690	+	0.00634210i
$848$	−1.99238	−	7.43568i	−0.0684187	−	0.255342i
$849$	−0.922950	+	3.44450i	−0.0316756	+	0.118215i
$850$	−34.5008	+	11.9152i	−1.18337	+	0.408687i
$851$	−18.4960	−	53.9519i	−0.634035	−	1.84945i
$852$	2.07798	+	2.07798i	0.0711905	+	0.0711905i
$853$	4.84103	+	8.38490i	0.165754	+	0.287094i	0.936923	−	0.349537i	$-0.113661\pi$
$853$	4.84103	+	8.38490i	0.165754	+	0.287094i	−0.771169	+	0.636630i	$0.780328\pi$
$854$	0.105046	−	0.181946i	0.00359461	−	0.00622605i
$855$	4.15717	+	1.55212i	0.142172	+	0.0530814i
$856$	0.137759	+	0.514125i	0.00470852	+	0.0175724i
$857$	−6.51247			−0.222462			−0.111231	−	0.993795i	$-0.535479\pi$
$857$	−6.51247			−0.222462			−0.111231	+	0.993795i	$0.535479\pi$
$858$	−6.36164	−	23.7420i	−0.217183	−	0.810537i
$859$	−6.00846	−	6.00846i	−0.205006	−	0.205006i	0.597135	−	0.802141i	$-0.296306\pi$
$859$	−6.00846	−	6.00846i	−0.205006	−	0.205006i	−0.802141	+	0.597135i	$0.796306\pi$
$860$	0.661158	−	6.89973i	0.0225453	−	0.235279i
$861$	1.21999			0.0415773
$862$	−24.8138	+	24.8138i	−0.845160	+	0.845160i
$863$	54.1135	+	14.4997i	1.84205	+	0.493575i	0.999018	−	0.0442964i	$-0.0141046\pi$
$863$	54.1135	+	14.4997i	1.84205	+	0.493575i	0.843027	+	0.537871i	$0.180771\pi$
$864$	9.85533	−	2.64073i	0.335285	−	0.0898394i
$865$	−41.5228	+	6.96821i	−1.41182	+	0.236926i
$866$	−2.29146	+	8.55186i	−0.0778671	+	0.290604i
$867$	5.41023	−	20.1913i	0.183741	−	0.685731i
$868$	−0.116024	+	0.0669865i	−0.00393811	+	0.00227367i
$869$	−2.11782	−	7.90380i	−0.0718420	−	0.268118i
$870$	22.0149	−	10.0450i	0.746374	−	0.340558i
$871$	−9.62936	+	35.9372i	−0.326278	+	1.21769i
$872$	−17.2682	−	4.62700i	−0.584775	−	0.156690i
$873$	3.39220	−	1.95849i	0.114809	−	0.0662848i
$874$	17.1327	+	17.1327i	0.579521	+	0.579521i
$875$	1.43850	+	0.0356777i	0.0486301	+	0.00120613i
$876$	1.23196	−	0.711274i	0.0416242	−	0.0240317i
$877$	18.7975	+	18.7975i	0.634747	+	0.634747i	0.949255	−	0.314508i	$-0.101840\pi$
$877$	18.7975	+	18.7975i	0.634747	+	0.634747i	−0.314508	+	0.949255i	$0.601840\pi$
$878$	−14.6337	−	14.6337i	−0.493863	−	0.493863i
$879$	−1.09999	−	1.90523i	−0.0371017	−	0.0642620i
$880$	−13.8358	−	9.85935i	−0.466404	−	0.332359i
$881$	−20.3900	−	11.7722i	−0.686958	−	0.396616i	0.115513	−	0.993306i	$-0.463149\pi$
$881$	−20.3900	−	11.7722i	−0.686958	−	0.396616i	−0.802472	+	0.596690i	$0.796482\pi$
$882$			8.99839i			0.302992i
$883$	24.9625	−	43.2363i	0.840054	−	1.45502i	−0.0497942	−	0.998760i	$-0.515857\pi$
$883$	24.9625	−	43.2363i	0.840054	−	1.45502i	0.889848	−	0.456257i	$-0.150810\pi$
$884$	−9.01822	−	5.20667i	−0.303315	−	0.175119i
$885$	11.5951	−	5.29063i	0.389764	−	0.177843i
$886$	−34.9849	−	9.37418i	−1.17534	−	0.314932i
$887$	−21.2888	+	21.2888i	−0.714807	+	0.714807i	−0.967537	−	0.252730i	$-0.918671\pi$
$887$	−21.2888	+	21.2888i	−0.714807	+	0.714807i	0.252730	+	0.967537i	$0.418671\pi$
$888$	−14.4592	−	21.4990i	−0.485220	−	0.721460i
$889$		−	1.29027i		−	0.0432741i
$890$	−7.06849	−	8.56672i	−0.236936	−	0.287157i
$891$	−10.1700	−	5.87165i	−0.340708	−	0.196708i
$892$	2.29841	+	8.57778i	0.0769564	+	0.287205i
$893$	−17.4953	−	10.1009i	−0.585459	−	0.338015i
$894$	−28.2749	−	28.2749i	−0.945654	−	0.945654i
$895$	0.579076	+	0.216203i	0.0193564	+	0.00722688i
$896$	−0.713795	+	0.713795i	−0.0238462	+	0.0238462i
$897$	−19.7094	+	73.5567i	−0.658079	+	2.45599i
$898$	6.07136	−	6.07136i	0.202604	−	0.202604i
$899$	−19.0631			−0.635791
$900$	1.21031	+	1.05015i	0.0403436	+	0.0350049i
$901$	3.45295	+	12.8866i	0.115034	+	0.429314i
$902$		−	20.2590i		−	0.674550i
$903$	0.876788	+	1.51864i	0.0291777	+	0.0505372i
$904$	7.37248	−	4.25650i	0.245205	−	0.141569i
$905$	13.9302	+	1.33484i	0.463055	+	0.0443717i
$906$	−1.46656	+	0.392965i	−0.0487234	+	0.0130554i
$907$	−0.540942	+	0.936940i	−0.0179617	+	0.0311106i	−0.874867	−	0.484364i	$-0.839051\pi$
$907$	−0.540942	+	0.936940i	−0.0179617	+	0.0311106i	0.856905	+	0.515475i	$0.172384\pi$
$908$	1.66399	+	2.88212i	0.0552215	+	0.0956464i
$909$	−3.35513	−	5.81125i	−0.111282	−	0.192747i
$910$	−1.36070	−	1.64911i	−0.0451066	−	0.0546674i
$911$	−9.98581	+	9.98581i	−0.330845	+	0.330845i	−0.852907	−	0.522062i	$-0.825163\pi$
$911$	−9.98581	+	9.98581i	−0.330845	+	0.330845i	0.522062	+	0.852907i	$0.325163\pi$
$912$	7.95568	+	4.59322i	0.263439	+	0.152097i
$913$	3.37447	−	12.5937i	0.111679	−	0.416791i
$914$			0.426242i			0.0140988i
$915$	−3.24971	−	2.31574i	−0.107432	−	0.0765559i
$916$	2.24494	−	1.29611i	0.0741748	−	0.0428248i
$917$			2.30544i			0.0761323i
$918$	39.8882	−	10.6880i	1.31651	−	0.352757i
$919$	−25.3108	+	25.3108i	−0.834927	+	0.834927i	−0.988186	−	0.153259i	$-0.951023\pi$
$919$	−25.3108	+	25.3108i	−0.834927	+	0.834927i	0.153259	+	0.988186i	$0.451023\pi$
$920$	26.1791	+	57.3746i	0.863098	+	1.89158i
$921$	11.4363	−	19.8082i	0.376837	−	0.652701i
$922$	−33.3237	+	8.92905i	−1.09746	+	0.294062i
$923$	31.9954	−	18.4726i	1.05314	−	0.608032i
$924$	−0.137184			−0.00451302
$925$	11.4051	−	28.1944i	0.374999	−	0.927025i
$926$	−35.5181			−1.16720
$927$	−7.52540	+	4.34479i	−0.247166	+	0.142702i
$928$	10.2787	−	2.75418i	0.337416	−	0.0904104i
$929$	5.69135	−	9.85771i	0.186727	−	0.323421i	−0.757430	−	0.652916i	$-0.773545\pi$
$929$	5.69135	−	9.85771i	0.186727	−	0.323421i	0.944157	+	0.329495i	$0.106879\pi$
$930$	−5.50123	−	12.0566i	−0.180393	−	0.395352i
$931$	9.85108	−	9.85108i	0.322856	−	0.322856i
$932$	8.70370	−	2.33215i	0.285099	−	0.0763921i
$933$			29.3971i			0.962418i
$934$	39.0834	−	22.5648i	1.27885	−	0.738344i
$935$	23.9785	+	17.0870i	0.784179	+	0.558804i
$936$		−	17.1613i		−	0.560933i
$937$	14.5367	−	54.2517i	0.474893	−	1.77233i	−0.146907	−	0.989150i	$-0.546932\pi$
$937$	14.5367	−	54.2517i	0.474893	−	1.77233i	0.621801	−	0.783176i	$-0.286401\pi$
$938$	−0.936556	−	0.540721i	−0.0305797	−	0.0176552i
$939$	−13.7355	+	13.7355i	−0.448241	+	0.448241i
$940$	−4.64278	−	5.62685i	−0.151431	−	0.183528i
$941$	13.1083	+	22.7042i	0.427318	+	0.740136i	0.996634	−	0.0819829i	$-0.0261253\pi$
$941$	13.1083	+	22.7042i	0.427318	+	0.740136i	−0.569316	+	0.822119i	$0.692792\pi$
$942$	−1.14954	−	1.99106i	−0.0374539	−	0.0648721i
$943$	−31.3829	+	54.3567i	−1.02197	+	1.77010i
$944$	−12.6431	+	3.38770i	−0.411497	+	0.110260i
$945$	−1.62055	−	0.155287i	−0.0527164	−	0.00505149i
$946$	25.2183	−	14.5598i	0.819916	−	0.473379i
$947$	5.68265	+	9.84264i	0.184661	+	0.319843i	0.943462	−	0.331480i	$-0.107548\pi$
$947$	5.68265	+	9.84264i	0.184661	+	0.319843i	−0.758801	+	0.651323i	$0.774215\pi$
$948$			1.59771i			0.0518911i
$949$	−4.62875	−	17.2747i	−0.150255	−	0.560761i
$950$	0.913161	+	12.8880i	0.0296269	+	0.418143i
$951$	36.7644			1.19217
$952$	1.54274	−	1.54274i	0.0500005	−	0.0500005i
$953$	−2.55701	+	9.54288i	−0.0828296	+	0.309124i	−0.994894	−	0.100922i	$-0.967821\pi$
$953$	−2.55701	+	9.54288i	−0.0828296	+	0.309124i	0.912065	+	0.410046i	$0.134487\pi$
$954$	−2.15686	+	2.15686i	−0.0698311	+	0.0698311i
$955$	−9.76240	−	3.64488i	−0.315904	−	0.117946i
$956$	0.788021	+	0.788021i	0.0254864	+	0.0254864i
$957$	−16.9048	−	9.76001i	−0.546456	−	0.315496i
$958$	−9.50011	−	35.4549i	−0.306935	−	1.14550i
$959$	−2.07925	−	1.20046i	−0.0671425	−	0.0387648i
$960$	17.8146	+	21.5905i	0.574964	+	0.696832i
$961$		−	20.5599i		−	0.663223i
$962$	−42.7471	+	14.6547i	−1.37822	+	0.472487i
$963$	0.124470	−	0.124470i	0.00401098	−	0.00401098i
$964$	6.07730	+	1.62841i	0.195737	+	0.0524475i
$965$	38.0713	−	17.3713i	1.22556	−	0.559201i
$966$	−1.91695	−	1.10675i	−0.0616769	−	0.0356092i
$967$	−12.4215	+	21.5147i	−0.399449	+	0.691866i	−0.993658	−	0.112445i	$-0.964132\pi$
$967$	−12.4215	+	21.5147i	−0.399449	+	0.691866i	0.594209	+	0.804311i	$0.297465\pi$
$968$		−	16.6670i		−	0.535699i
$969$	−13.7878	−	7.96039i	−0.442928	−	0.255725i
$970$	9.28792	+	6.61855i	0.298217	+	0.212509i
$971$	−18.8570	−	32.6613i	−0.605151	−	1.04815i	−0.992028	−	0.126020i	$-0.959780\pi$
$971$	−18.8570	−	32.6613i	−0.605151	−	1.04815i	0.386877	−	0.922131i	$-0.373554\pi$
$972$	−2.24460	−	2.24460i	−0.0719957	−	0.0719957i
$973$	−1.09996	−	1.09996i	−0.0352632	−	0.0352632i
$974$	10.1722	−	5.87295i	0.325940	−	0.188181i
$975$	−33.6447	+	22.7388i	−1.07749	+	0.728224i
$976$	2.89780	+	2.89780i	0.0927563	+	0.0927563i
$977$	−33.4281	+	19.2997i	−1.06946	+	0.617453i	−0.928034	−	0.372496i	$-0.878502\pi$
$977$	−33.4281	+	19.2997i	−1.06946	+	0.617453i	−0.141426	+	0.989949i	$0.545169\pi$
$978$	−0.876038	−	0.234734i	−0.0280126	−	0.00750595i
$979$	−2.31881	+	8.65392i	−0.0741095	+	0.276580i
$980$	4.57681	−	2.08832i	0.146201	−	0.0667090i
$981$	1.53022	+	5.71085i	0.0488561	+	0.182333i
$982$	31.8032	−	18.3616i	1.01488	−	0.585942i
$983$	−5.47948	+	20.4497i	−0.174768	+	0.652244i	0.821823	+	0.569743i	$0.192957\pi$
$983$	−5.47948	+	20.4497i	−0.174768	+	0.652244i	−0.996591	+	0.0825010i	$0.973709\pi$
$984$	−7.37961	+	27.5411i	−0.235253	+	0.877978i
$985$	−21.1457	+	3.54859i	−0.673757	+	0.113068i
$986$	41.6019	−	11.1472i	1.32487	−	0.354999i
$987$	1.78269	+	0.477671i	0.0567437	+	0.0152044i
$988$	−2.60647	+	2.60647i	−0.0829228	+	0.0829228i
$989$	−90.2173			−2.86874
$990$	−0.642133	+	6.70118i	−0.0204083	+	0.212978i
$991$	−23.0224	−	23.0224i	−0.731329	−	0.731329i	0.239554	−	0.970883i	$-0.422999\pi$
$991$	−23.0224	−	23.0224i	−0.731329	−	0.731329i	−0.970883	+	0.239554i	$0.922999\pi$
$992$	−1.50835	−	5.62923i	−0.0478901	−	0.178728i
$993$	15.6639			0.497080
$994$	0.277943	+	1.03730i	0.00881582	+	0.0329011i
$995$	16.5266	+	6.17036i	0.523928	+	0.195614i
$996$	−1.27287	+	2.20468i	−0.0403325	+	0.0698579i
$997$	10.1472	+	17.5754i	0.321364	+	0.556618i	0.980770	−	0.195169i	$-0.0625255\pi$
$997$	10.1472	+	17.5754i	0.321364	+	0.556618i	−0.659406	+	0.751787i	$0.729192\pi$
$998$	−19.4581	−	19.4581i	−0.615936	−	0.615936i
$999$	−15.1256	+	30.9065i	−0.478553	+	0.977838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.u.a.177.6	yes	68
5.2	odd	4		925.2.t.b.843.6		68
5.3	odd	4		185.2.p.a.103.12	yes	68
5.4	even	2		925.2.y.b.732.12		68
37.23	odd	12		185.2.p.a.97.12	✓	68
185.23	even	12	inner	185.2.u.a.23.6	yes	68
185.97	even	12		925.2.y.b.393.12		68
185.134	odd	12		925.2.t.b.282.6		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.12	✓	68	37.23	odd	12
185.2.p.a.103.12	yes	68	5.3	odd	4
185.2.u.a.23.6	yes	68	185.23	even	12	inner
185.2.u.a.177.6	yes	68	1.1	even	1	trivial
925.2.t.b.282.6		68	185.134	odd	12
925.2.t.b.843.6		68	5.2	odd	4
925.2.y.b.393.12		68	185.97	even	12
925.2.y.b.732.12		68	5.4	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12177 + 0.647656i) q^{2} +(-1.36781 + 0.366504i) q^{3} +(-0.161082 + 0.279003i) q^{4} +(0.928220 + 2.03431i) q^{5} +(1.29701 - 1.29701i) q^{6} +(-0.124317 + 0.0333107i) q^{7} -3.00793i q^{8} +(-0.861493 + 0.497383i) q^{9} +(-2.35879 - 1.68087i) q^{10} +2.33644i q^{11} +(0.118075 - 0.440660i) q^{12} +(-4.96696 - 2.86768i) q^{13} +(0.117882 - 0.117882i) q^{14} +(-2.01521 - 2.44235i) q^{15} +(1.62594 + 2.81621i) q^{16} +(-2.81788 - 4.88071i) q^{17} +(0.644267 - 1.11590i) q^{18} +(-1.92696 + 0.516328i) q^{19} +(-0.717097 - 0.0687149i) q^{20} +(0.157834 - 0.0911256i) q^{21} +(-1.51321 - 2.62096i) q^{22} +9.37639i q^{23} +(1.10242 + 4.11428i) q^{24} +(-3.27681 + 3.77657i) q^{25} +7.42908 q^{26} +(3.99999 - 3.99999i) q^{27} +(0.0107315 - 0.0400506i) q^{28} +(4.17184 - 4.17184i) q^{29} +(3.84242 + 1.43460i) q^{30} +(-2.28474 - 2.28474i) q^{31} +(1.56201 + 0.901828i) q^{32} +(-0.856316 - 3.19581i) q^{33} +(6.32204 + 3.65003i) q^{34} +(-0.183158 - 0.221980i) q^{35} -0.320478i q^{36} +(-5.75402 + 1.97262i) q^{37} +(1.82721 - 1.82721i) q^{38} +(7.84488 + 2.10203i) q^{39} +(6.11905 - 2.79202i) q^{40} +(5.79719 + 3.34701i) q^{41} +(-0.118036 + 0.204445i) q^{42} +9.62176i q^{43} +(-0.651874 - 0.376360i) q^{44} +(-1.81149 - 1.29086i) q^{45} +(-6.07268 - 10.5182i) q^{46} +(7.16056 + 7.16056i) q^{47} +(-3.25613 - 3.25613i) q^{48} +(-6.04783 + 3.49172i) q^{49} +(1.22992 - 6.35871i) q^{50} +(5.64312 + 5.64312i) q^{51} +(1.60018 - 0.923864i) q^{52} +(-2.28658 - 0.612686i) q^{53} +(-1.89646 + 7.07770i) q^{54} +(-4.75305 + 2.16873i) q^{55} +(0.100196 + 0.373938i) q^{56} +(2.44649 - 1.41248i) q^{57} +(-1.97794 + 7.38178i) q^{58} +(-1.04177 + 3.88793i) q^{59} +(1.00604 - 0.168830i) q^{60} +(1.21728 - 0.326171i) q^{61} +(4.04269 + 1.08324i) q^{62} +(0.0905303 - 0.0905303i) q^{63} -8.84006 q^{64} +(1.22330 - 12.7662i) q^{65} +(3.03038 + 3.03038i) q^{66} +(-1.67895 - 6.26591i) q^{67} +1.81564 q^{68} +(-3.43648 - 12.8251i) q^{69} +(0.349229 + 0.130388i) q^{70} +(-3.22082 + 5.57863i) q^{71} +(1.49609 + 2.59131i) q^{72} +(2.20492 + 2.20492i) q^{73} +(5.17714 - 5.93946i) q^{74} +(3.09794 - 6.36660i) q^{75} +(0.166343 - 0.620799i) q^{76} +(-0.0778287 - 0.290460i) q^{77} +(-10.1616 + 2.72279i) q^{78} +(-3.38283 + 0.906427i) q^{79} +(-4.21981 + 5.92173i) q^{80} +(-2.51307 + 4.35277i) q^{81} -8.67085 q^{82} +(-5.39012 - 1.44428i) q^{83} +0.0587149i q^{84} +(7.31325 - 10.2628i) q^{85} +(-6.23159 - 10.7934i) q^{86} +(-4.17729 + 7.23528i) q^{87} +7.02786 q^{88} +(3.70388 + 0.992453i) q^{89} +(2.86811 + 0.274833i) q^{90} +(0.713004 + 0.191049i) q^{91} +(-2.61604 - 1.51037i) q^{92} +(3.96246 + 2.28773i) q^{93} +(-12.6701 - 3.39495i) q^{94} +(-2.83902 - 3.44077i) q^{95} +(-2.46706 - 0.661047i) q^{96} -3.93759 q^{97} +(4.52287 - 7.83384i) q^{98} +(-1.16211 - 2.01283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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