LMFDB - Embedded newform 840.2.bj.b.13.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(13,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bj (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [184] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.16
Character	$\chi$	$=$	840.13
Dual form			840.2.bj.b.517.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27271 - 0.616616i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.23957 + 1.56954i) q^{4} +(-2.03587 - 0.924781i) q^{5} +(-0.463927 - 1.33595i) q^{6} +(2.06648 + 1.65217i) q^{7} +(-0.609805 - 2.76191i) q^{8} +1.00000i q^{9} +(2.02084 + 2.43233i) q^{10} -0.314048i q^{11} +(-0.233327 + 1.98634i) q^{12} +(-0.233997 - 0.233997i) q^{13} +(-1.61127 - 3.37695i) q^{14} +(-0.785661 - 2.09350i) q^{15} +(-0.926934 + 3.89112i) q^{16} +(3.61664 + 3.61664i) q^{17} +(0.616616 - 1.27271i) q^{18} +0.420252i q^{19} +(-1.07212 - 4.34172i) q^{20} +(0.292962 + 2.62948i) q^{21} +(-0.193647 + 0.399691i) q^{22} +(-3.21095 - 3.21095i) q^{23} +(1.52177 - 2.38416i) q^{24} +(3.28956 + 3.76547i) q^{25} +(0.153523 + 0.442096i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.0316061 + 5.29141i) q^{28} +0.956189 q^{29} +(-0.290968 + 3.14886i) q^{30} +4.90241i q^{31} +(3.57904 - 4.38069i) q^{32} +(0.222065 - 0.222065i) q^{33} +(-2.37285 - 6.83300i) q^{34} +(-2.67920 - 5.27465i) q^{35} +(-1.56954 + 1.23957i) q^{36} +(2.11212 + 2.11212i) q^{37} +(0.259134 - 0.534858i) q^{38} -0.330921i q^{39} +(-1.31268 + 6.18683i) q^{40} +8.14513i q^{41} +(1.24853 - 3.52721i) q^{42} +(2.64605 - 2.64605i) q^{43} +(0.492912 - 0.389284i) q^{44} +(0.924781 - 2.03587i) q^{45} +(2.10668 + 6.06652i) q^{46} +(2.75601 + 2.75601i) q^{47} +(-3.40688 + 2.09599i) q^{48} +(1.54067 + 6.82835i) q^{49} +(-1.86480 - 6.82074i) q^{50} +5.11470i q^{51} +(0.0772128 - 0.657323i) q^{52} +(1.45815 - 1.45815i) q^{53} +(1.33595 - 0.463927i) q^{54} +(-0.290425 + 0.639361i) q^{55} +(3.30299 - 6.71493i) q^{56} +(-0.297163 + 0.297163i) q^{57} +(-1.21695 - 0.589601i) q^{58} +14.3820i q^{59} +(2.31196 - 3.82817i) q^{60} -1.53895 q^{61} +(3.02290 - 6.23933i) q^{62} +(-1.65217 + 2.06648i) q^{63} +(-7.25628 + 3.36845i) q^{64} +(0.259992 + 0.692784i) q^{65} +(-0.419553 + 0.145695i) q^{66} +(-1.82064 - 1.82064i) q^{67} +(-1.19340 + 10.1596i) q^{68} -4.54097i q^{69} +(0.157401 + 8.36512i) q^{70} -11.2013 q^{71} +(2.76191 - 0.609805i) q^{72} +(1.69657 - 1.69657i) q^{73} +(-1.38575 - 3.99048i) q^{74} +(-0.336522 + 4.98866i) q^{75} +(-0.659604 + 0.520932i) q^{76} +(0.518860 - 0.648973i) q^{77} +(-0.204051 + 0.421166i) q^{78} +6.94492i q^{79} +(5.48555 - 7.06461i) q^{80} -1.00000 q^{81} +(5.02241 - 10.3664i) q^{82} +(8.91058 + 8.91058i) q^{83} +(-3.76394 + 3.71924i) q^{84} +(-4.01842 - 10.7076i) q^{85} +(-4.99924 + 1.73605i) q^{86} +(0.676128 + 0.676128i) q^{87} +(-0.867371 + 0.191508i) q^{88} +14.3917 q^{89} +(-2.43233 + 2.02084i) q^{90} +(-0.0969472 - 0.870152i) q^{91} +(1.05953 - 9.01992i) q^{92} +(-3.46652 + 3.46652i) q^{93} +(-1.80820 - 5.20700i) q^{94} +(0.388641 - 0.855580i) q^{95} +(5.62838 - 0.566854i) q^{96} +(3.90303 + 3.90303i) q^{97} +(2.24964 - 9.64049i) q^{98} +0.314048 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) $ 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.27271	−	0.616616i	−0.899940	−	0.436013i
$2$	−1.27271	−	0.616616i	−0.899940	−	0.436013i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	1.23957	+	1.56954i	0.619785	+	0.784772i
$5$	−2.03587	−	0.924781i	−0.910470	−	0.413575i
$5$	−2.03587	−	0.924781i	−0.910470	−	0.413575i
$6$	−0.463927	−	1.33595i	−0.189397	−	0.545401i
$7$	2.06648	+	1.65217i	0.781056	+	0.624461i
$7$	2.06648	+	1.65217i	0.781056	+	0.624461i
$8$	−0.609805	−	2.76191i	−0.215598	−	0.976482i
$9$			1.00000i			0.333333i
$10$	2.02084	+	2.43233i	0.639045	+	0.769170i
$11$		−	0.314048i		−	0.0946890i	−0.998879	−	0.0473445i	$-0.984924\pi$
$11$		−	0.314048i		−	0.0946890i	0.998879	−	0.0473445i	$-0.0150759\pi$
$12$	−0.233327	+	1.98634i	−0.0673556	+	0.573408i
$13$	−0.233997	−	0.233997i	−0.0648990	−	0.0648990i	0.673912	−	0.738811i	$-0.264613\pi$
$13$	−0.233997	−	0.233997i	−0.0648990	−	0.0648990i	−0.738811	+	0.673912i	$0.764613\pi$
$14$	−1.61127	−	3.37695i	−0.430630	−	0.902528i
$15$	−0.785661	−	2.09350i	−0.202857	−	0.540539i
$16$	−0.926934	+	3.89112i	−0.231733	+	0.972779i
$17$	3.61664	+	3.61664i	0.877164	+	0.877164i	0.993240	−	0.116076i	$-0.0370317\pi$
$17$	3.61664	+	3.61664i	0.877164	+	0.877164i	−0.116076	+	0.993240i	$0.537032\pi$
$18$	0.616616	−	1.27271i	0.145338	−	0.299980i
$19$			0.420252i			0.0964125i	0.998837	+	0.0482062i	$0.0153505\pi$
$19$			0.420252i			0.0964125i	−0.998837	+	0.0482062i	$0.984650\pi$
$20$	−1.07212	−	4.34172i	−0.239734	−	0.970839i
$21$	0.292962	+	2.62948i	0.0639294	+	0.573800i
$22$	−0.193647	+	0.399691i	−0.0412856	+	0.0852144i
$23$	−3.21095	−	3.21095i	−0.669530	−	0.669530i	0.288078	−	0.957607i	$-0.406984\pi$
$23$	−3.21095	−	3.21095i	−0.669530	−	0.669530i	−0.957607	+	0.288078i	$0.906984\pi$
$24$	1.52177	−	2.38416i	0.310629	−	0.486665i
$25$	3.28956	+	3.76547i	0.657912	+	0.753095i
$26$	0.153523	+	0.442096i	0.0301084	+	0.0867021i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.0316061	+	5.29141i	−0.00597300	+	0.999982i
$29$	0.956189			0.177560			0.0887799	−	0.996051i	$-0.471703\pi$
$29$	0.956189			0.177560			0.0887799	+	0.996051i	$0.471703\pi$
$30$	−0.290968	+	3.14886i	−0.0531232	+	0.574901i
$31$			4.90241i			0.880498i	0.897876	+	0.440249i	$0.145110\pi$
$31$			4.90241i			0.880498i	−0.897876	+	0.440249i	$0.854890\pi$
$32$	3.57904	−	4.38069i	0.632691	−	0.774404i
$33$	0.222065	−	0.222065i	0.0386566	−	0.0386566i
$34$	−2.37285	−	6.83300i	−0.406940	−	1.17185i
$35$	−2.67920	−	5.27465i	−0.452867	−	0.891578i
$36$	−1.56954	+	1.23957i	−0.261591	+	0.206595i
$37$	2.11212	+	2.11212i	0.347231	+	0.347231i	0.859077	−	0.511846i	$-0.171038\pi$
$37$	2.11212	+	2.11212i	0.347231	+	0.347231i	−0.511846	+	0.859077i	$0.671038\pi$
$38$	0.259134	−	0.534858i	0.0420371	−	0.0867655i
$39$		−	0.330921i		−	0.0529898i
$40$	−1.31268	+	6.18683i	−0.207552	+	0.978224i
$41$			8.14513i			1.27205i	0.771666	+	0.636027i	$0.219424\pi$
$41$			8.14513i			1.27205i	−0.771666	+	0.636027i	$0.780576\pi$
$42$	1.24853	−	3.52721i	0.192652	−	0.544260i
$43$	2.64605	−	2.64605i	0.403518	−	0.403518i	−0.475953	−	0.879471i	$-0.657897\pi$
$43$	2.64605	−	2.64605i	0.403518	−	0.403518i	0.879471	+	0.475953i	$0.157897\pi$
$44$	0.492912	−	0.389284i	0.0743092	−	0.0586868i
$45$	0.924781	−	2.03587i	0.137858	−	0.303490i
$46$	2.10668	+	6.06652i	0.310613	+	0.894460i
$47$	2.75601	+	2.75601i	0.402005	+	0.402005i	0.878939	−	0.476934i	$-0.158252\pi$
$47$	2.75601	+	2.75601i	0.402005	+	0.402005i	−0.476934	+	0.878939i	$0.658252\pi$
$48$	−3.40688	+	2.09599i	−0.491740	+	0.302531i
$49$	1.54067	+	6.82835i	0.220096	+	0.975478i
$50$	−1.86480	−	6.82074i	−0.263722	−	0.964599i
$51$			5.11470i			0.716201i
$52$	0.0772128	−	0.657323i	0.0107075	−	0.0911544i
$53$	1.45815	−	1.45815i	0.200292	−	0.200292i	−0.599833	−	0.800125i	$-0.704766\pi$
$53$	1.45815	−	1.45815i	0.200292	−	0.200292i	0.800125	+	0.599833i	$0.204766\pi$
$54$	1.33595	−	0.463927i	0.181800	−	0.0631325i
$55$	−0.290425	+	0.639361i	−0.0391610	+	0.0862115i
$56$	3.30299	−	6.71493i	0.441381	−	0.897320i
$57$	−0.297163	+	0.297163i	−0.0393602	+	0.0393602i
$58$	−1.21695	−	0.589601i	−0.159793	−	0.0774185i
$59$			14.3820i			1.87238i	0.351491	+	0.936191i	$0.385675\pi$
$59$			14.3820i			1.87238i	−0.351491	+	0.936191i	$0.614325\pi$
$60$	2.31196	−	3.82817i	0.298472	−	0.494214i
$61$	−1.53895			−0.197043			−0.0985213	−	0.995135i	$-0.531411\pi$
$61$	−1.53895			−0.197043			−0.0985213	+	0.995135i	$0.531411\pi$
$62$	3.02290	−	6.23933i	0.383909	−	0.792396i
$63$	−1.65217	+	2.06648i	−0.208154	+	0.260352i
$64$	−7.25628	+	3.36845i	−0.907035	+	0.421056i
$65$	0.259992	+	0.692784i	0.0322480	+	0.0859292i
$66$	−0.419553	+	0.145695i	−0.0516434	+	0.0179338i
$67$	−1.82064	−	1.82064i	−0.222427	−	0.222427i	0.587093	−	0.809520i	$-0.300272\pi$
$67$	−1.82064	−	1.82064i	−0.222427	−	0.222427i	−0.809520	+	0.587093i	$0.800272\pi$
$68$	−1.19340	+	10.1596i	−0.144721	+	1.23203i
$69$		−	4.54097i		−	0.546669i
$70$	0.157401	+	8.36512i	0.0188130	+	0.999823i
$71$	−11.2013			−1.32935			−0.664674	−	0.747133i	$-0.731430\pi$
$71$	−11.2013			−1.32935			−0.664674	+	0.747133i	$0.731430\pi$
$72$	2.76191	−	0.609805i	0.325494	−	0.0718662i
$73$	1.69657	−	1.69657i	0.198569	−	0.198569i	−0.600817	−	0.799386i	$-0.705158\pi$
$73$	1.69657	−	1.69657i	0.198569	−	0.198569i	0.799386	+	0.600817i	$0.205158\pi$
$74$	−1.38575	−	3.99048i	−0.161090	−	0.463884i
$75$	−0.336522	+	4.98866i	−0.0388582	+	0.576041i
$76$	−0.659604	+	0.520932i	−0.0756618	+	0.0597550i
$77$	0.518860	−	0.648973i	0.0591296	−	0.0739574i
$78$	−0.204051	+	0.421166i	−0.0231043	+	0.0476877i
$79$			6.94492i			0.781364i	0.920526	+	0.390682i	$0.127761\pi$
$79$			6.94492i			0.781364i	−0.920526	+	0.390682i	$0.872239\pi$
$80$	5.48555	−	7.06461i	0.613303	−	0.789848i
$81$	−1.00000			−0.111111
$82$	5.02241	−	10.3664i	0.554633	−	1.14477i
$83$	8.91058	+	8.91058i	0.978063	+	0.978063i	0.999764	−	0.0217014i	$-0.00690832\pi$
$83$	8.91058	+	8.91058i	0.978063	+	0.978063i	−0.0217014	+	0.999764i	$0.506908\pi$
$84$	−3.76394	+	3.71924i	−0.410679	+	0.405803i
$85$	−4.01842	−	10.7076i	−0.435859	−	1.16140i
$86$	−4.99924	+	1.73605i	−0.539082	+	0.187203i
$87$	0.676128	+	0.676128i	0.0724885	+	0.0724885i
$88$	−0.867371	+	0.191508i	−0.0924621	+	0.0204148i
$89$	14.3917			1.52552			0.762760	−	0.646682i	$-0.223844\pi$
$89$	14.3917			1.52552			0.762760	+	0.646682i	$0.223844\pi$
$90$	−2.43233	+	2.02084i	−0.256390	+	0.213015i
$91$	−0.0969472	−	0.870152i	−0.0101628	−	0.0912167i
$92$	1.05953	−	9.01992i	0.110464	−	0.940392i
$93$	−3.46652	+	3.46652i	−0.359462	+	0.359462i
$94$	−1.80820	−	5.20700i	−0.186501	−	0.537061i
$95$	0.388641	−	0.855580i	0.0398738	−	0.0877807i
$96$	5.62838	−	0.566854i	0.574444	−	0.0578543i
$97$	3.90303	+	3.90303i	0.396293	+	0.396293i	0.876923	−	0.480630i	$-0.159592\pi$
$97$	3.90303	+	3.90303i	0.396293	+	0.396293i	−0.480630	+	0.876923i	$0.659592\pi$
$98$	2.24964	−	9.64049i	0.227248	−	0.973837i
$99$	0.314048			0.0315630
$100$	−1.83244	+	9.83068i	−0.183244	+	0.983068i
$101$	−0.0823669			−0.00819582			−0.00409791	−	0.999992i	$-0.501304\pi$
$101$	−0.0823669			−0.00819582			−0.00409791	+	0.999992i	$0.501304\pi$
$102$	3.15381	−	6.50952i	0.312273	−	0.644538i
$103$	6.41711	−	6.41711i	0.632296	−	0.632296i	−0.316347	−	0.948643i	$-0.602456\pi$
$103$	6.41711	−	6.41711i	0.632296	−	0.632296i	0.948643	+	0.316347i	$0.102456\pi$
$104$	−0.503585	+	0.788970i	−0.0493806	+	0.0773649i
$105$	1.83526	−	5.62422i	0.179103	−	0.548867i
$106$	−2.75491	+	0.956677i	−0.267580	+	0.0929207i
$107$	10.7156	+	10.7156i	1.03592	+	1.03592i	0.999331	+	0.0365845i	$0.0116478\pi$
$107$	10.7156	+	10.7156i	1.03592	+	1.03592i	0.0365845	+	0.999331i	$0.488352\pi$
$108$	−1.98634	−	0.233327i	−0.191136	−	0.0224519i
$109$	−10.7030			−1.02516			−0.512579	−	0.858640i	$-0.671310\pi$
$109$	−10.7030			−1.02516			−0.512579	+	0.858640i	$0.671310\pi$
$110$	0.763867	−	0.634639i	0.0728319	−	0.0605105i
$111$			2.98699i			0.283513i
$112$	−8.34427	+	6.50946i	−0.788460	+	0.615086i
$113$	−12.2162	−	12.2162i	−1.14920	−	1.14920i	−0.986709	−	0.162495i	$-0.948046\pi$
$113$	−12.2162	−	12.2162i	−1.14920	−	1.14920i	−0.162495	−	0.986709i	$-0.551954\pi$
$114$	0.561437	−	0.194966i	0.0525834	−	0.0182603i
$115$	3.56766	+	9.50652i	0.332686	+	0.886487i
$116$	1.18526	+	1.50078i	0.110049	+	0.139344i
$117$	0.233997	−	0.233997i	0.0216330	−	0.0216330i
$118$	8.86820	−	18.3041i	0.816384	−	1.68503i
$119$	1.49841	+	13.4490i	0.137359	+	1.23287i
$120$	−5.30295	+	3.44655i	−0.484091	+	0.314625i
$121$	10.9014			0.991034
$122$	1.95864	+	0.948942i	0.177327	+	0.0859132i
$123$	−5.75947	+	5.75947i	−0.519314	+	0.519314i
$124$	−7.69454	+	6.07687i	−0.690990	+	0.545719i
$125$	−3.21489	−	10.7082i	−0.287548	−	0.957766i
$126$	3.37695	−	1.61127i	0.300843	−	0.143543i
$127$	12.9698	−	12.9698i	1.15089	−	1.15089i	0.164510	−	0.986375i	$-0.447396\pi$
$127$	12.9698	−	12.9698i	1.15089	−	1.15089i	0.986375	−	0.164510i	$-0.0526044\pi$
$128$	11.3122	+	0.187285i	0.999863	+	0.0165538i
$129$	3.74207			0.329471
$130$	0.0962875	−	1.04203i	0.00844497	−	0.0913917i
$131$	−14.3671			−1.25526			−0.627632	−	0.778510i	$-0.715976\pi$
$131$	−14.3671			−1.25526			−0.627632	+	0.778510i	$0.715976\pi$
$132$	0.623807	+	0.0732757i	0.0542954	+	0.00637783i
$133$	−0.694328	+	0.868443i	−0.0602059	+	0.0753035i
$134$	1.19451	+	3.43979i	0.103190	+	0.297152i
$135$	2.09350	−	0.785661i	0.180180	−	0.0676189i
$136$	7.78339	−	12.1943i	0.667420	−	1.04565i
$137$	10.4309	−	10.4309i	0.891169	−	0.891169i	−0.103464	−	0.994633i	$-0.532993\pi$
$137$	10.4309	−	10.4309i	0.891169	−	0.891169i	0.994633	+	0.103464i	$0.0329927\pi$
$138$	−2.80003	+	5.77933i	−0.238355	+	0.491969i
$139$			7.20831i			0.611401i	0.952128	+	0.305700i	$0.0988906\pi$
$139$			7.20831i			0.611401i	−0.952128	+	0.305700i	$0.901109\pi$
$140$	4.95774	−	10.7434i	0.419005	−	0.907984i
$141$			3.89759i			0.328236i
$142$	14.2560	+	6.90689i	1.19633	+	0.579614i
$143$	−0.0734862	+	0.0734862i	−0.00614522	+	0.00614522i
$144$	−3.89112	−	0.926934i	−0.324260	−	0.0772445i
$145$	−1.94668	−	0.884266i	−0.161663	−	0.0734343i
$146$	−3.20537	+	1.11311i	−0.265279	+	0.0921214i
$147$	−3.73895	+	5.91779i	−0.308383	+	0.488091i
$148$	−0.696945	+	5.93319i	−0.0572885	+	0.487705i
$149$	15.7190			1.28775			0.643873	−	0.765132i	$-0.277326\pi$
$149$	15.7190			1.28775			0.643873	+	0.765132i	$0.277326\pi$
$150$	3.50438	−	6.14160i	0.286132	−	0.501460i
$151$	13.2054			1.07464			0.537319	−	0.843379i	$-0.319437\pi$
$151$	13.2054			1.07464			0.537319	+	0.843379i	$0.319437\pi$
$152$	1.16070	−	0.256272i	0.0941451	−	0.0207864i
$153$	−3.61664	+	3.61664i	−0.292388	+	0.292388i
$154$	−1.06052	+	0.506016i	−0.0854595	+	0.0407759i
$155$	4.53365	−	9.98068i	0.364152	−	0.801667i
$156$	0.519396	−	0.410200i	0.0415849	−	0.0328423i
$157$	−1.94184	+	1.94184i	−0.154976	+	0.154976i	−0.780336	−	0.625360i	$-0.784952\pi$
$157$	−1.94184	+	1.94184i	−0.154976	+	0.154976i	0.625360	+	0.780336i	$0.284952\pi$
$158$	4.28235	−	8.83885i	0.340685	−	0.703181i
$159$	2.06213			0.163537
$160$	−11.3377	+	5.60871i	−0.896320	+	0.443407i
$161$	−1.33033	−	11.9404i	−0.104845	−	0.941035i
$162$	1.27271	+	0.616616i	0.0999934	+	0.0484459i
$163$	−13.0576	+	13.0576i	−1.02275	+	1.02275i	−0.0230177	+	0.999735i	$0.507327\pi$
$163$	−13.0576	+	13.0576i	−1.02275	+	1.02275i	−0.999735	+	0.0230177i	$0.992673\pi$
$164$	−12.7841	+	10.0965i	−0.998273	+	0.788400i
$165$	−0.657459	+	0.246735i	−0.0511831	+	0.0192083i
$166$	−5.84616	−	16.8350i	−0.453750	−	1.30665i
$167$	−14.6049	−	14.6049i	−1.13016	−	1.13016i	−0.990150	−	0.140008i	$-0.955287\pi$
$167$	−14.6049	−	14.6049i	−1.13016	−	1.13016i	−0.140008	−	0.990150i	$-0.544713\pi$
$168$	7.08374	−	2.41260i	0.546522	−	0.186136i
$169$		−	12.8905i		−	0.991576i
$170$	−1.48821	+	16.1055i	−0.114141	+	1.23523i
$171$	−0.420252			−0.0321375
$172$	7.43304	+	0.873126i	0.566764	+	0.0665752i
$173$	−12.6266	−	12.6266i	−0.959981	−	0.959981i	0.0392487	−	0.999229i	$-0.487504\pi$
$173$	−12.6266	−	12.6266i	−0.959981	−	0.959981i	−0.999229	+	0.0392487i	$0.987504\pi$
$174$	−0.443602	−	1.27742i	−0.0336294	−	0.0968413i
$175$	0.576609	+	13.2162i	0.0435875	+	0.999050i
$176$	1.22200	+	0.291101i	0.0921115	+	0.0219426i
$177$	−10.1696	+	10.1696i	−0.764397	+	0.764397i
$178$	−18.3165	−	8.87416i	−1.37288	−	0.665147i
$179$	−21.7679			−1.62701			−0.813505	−	0.581558i	$-0.802443\pi$
$179$	−21.7679			−1.62701			−0.813505	+	0.581558i	$0.802443\pi$
$180$	4.34172	−	1.07212i	0.323613	−	0.0799113i
$181$	−8.83687			−0.656839			−0.328420	−	0.944532i	$-0.606516\pi$
$181$	−8.83687			−0.656839			−0.328420	+	0.944532i	$0.606516\pi$
$182$	−0.413164	+	1.16723i	−0.0306257	+	0.0865207i
$183$	−1.08820	−	1.08820i	−0.0804423	−	0.0804423i
$184$	−6.91030	+	10.8264i	−0.509434	+	0.798133i
$185$	−2.34676	−	6.25326i	−0.172537	−	0.459749i
$186$	6.54939	−	2.27436i	0.480224	−	0.166764i
$187$	1.13580	−	1.13580i	0.0830578	−	0.0830578i
$188$	−0.909411	+	7.74195i	−0.0663256	+	0.564639i
$189$	−2.62948	+	0.292962i	−0.191267	+	0.0213098i
$190$	−1.02219	+	0.849261i	−0.0741575	+	0.0616119i
$191$	−9.21404			−0.666704			−0.333352	−	0.942802i	$-0.608180\pi$
$191$	−9.21404			−0.666704			−0.333352	+	0.942802i	$0.608180\pi$
$192$	−7.51282	−	2.74911i	−0.542191	−	0.198400i
$193$	−5.92718	−	5.92718i	−0.426648	−	0.426648i	0.460837	−	0.887485i	$-0.347549\pi$
$193$	−5.92718	−	5.92718i	−0.426648	−	0.426648i	−0.887485	+	0.460837i	$0.847549\pi$
$194$	−2.56075	−	7.37409i	−0.183851	−	0.529429i
$195$	−0.306030	+	0.673714i	−0.0219153	+	0.0482457i
$196$	−8.80762	+	10.8824i	−0.629115	+	0.777312i
$197$	7.26030	+	7.26030i	0.517275	+	0.517275i	0.916746	−	0.399471i	$-0.130806\pi$
$197$	7.26030	+	7.26030i	0.517275	+	0.517275i	−0.399471	+	0.916746i	$0.630806\pi$
$198$	−0.399691	−	0.193647i	−0.0284048	−	0.0137619i
$199$	−23.7349			−1.68252			−0.841262	−	0.540628i	$-0.818187\pi$
$199$	−23.7349			−1.68252			−0.841262	+	0.540628i	$0.818187\pi$
$200$	8.39390	−	11.3817i	0.593539	−	0.804805i
$201$		−	2.57478i		−	0.181611i
$202$	0.104829	+	0.0507888i	0.00737575	+	0.00357348i
$203$	1.97595	+	1.57979i	0.138684	+	0.110879i
$204$	−8.02775	+	6.34003i	−0.562055	+	0.443891i
$205$	7.53246	−	16.5824i	0.526090	−	1.15817i
$206$	−12.1240	+	4.21021i	−0.844719	+	0.293339i
$207$	3.21095	−	3.21095i	0.223177	−	0.223177i
$208$	1.12741	−	0.693609i	0.0781717	−	0.0480932i
$209$	0.131979			0.00912920
$210$	−5.80373	+	6.02633i	−0.400496	+	0.415856i
$211$		−	23.5416i		−	1.62067i	−0.585967	−	0.810335i	$-0.699285\pi$
$211$		−	23.5416i		−	1.62067i	0.585967	−	0.810335i	$-0.300715\pi$
$212$	4.09610	+	0.481150i	0.281321	+	0.0330455i
$213$	−7.92051	−	7.92051i	−0.542704	−	0.542704i
$214$	−7.03041	−	20.2452i	−0.480589	−	1.38393i
$215$	−7.83403	+	2.94000i	−0.534276	+	0.200506i
$216$	2.38416	+	1.52177i	0.162222	+	0.103543i
$217$	−8.09960	+	10.1307i	−0.549837	+	0.687718i
$218$	13.6218	+	6.59962i	0.922582	+	0.446983i
$219$	2.39932			0.162131
$220$	−1.36351	+	0.336698i	−0.0919277	+	0.0227002i
$221$		−	1.69256i		−	0.113854i
$222$	1.84183	−	3.80157i	0.123615	−	0.255144i
$223$	12.4423	−	12.4423i	0.833199	−	0.833199i	−0.154754	−	0.987953i	$-0.549459\pi$
$223$	12.4423	−	12.4423i	0.833199	−	0.833199i	0.987953	+	0.154754i	$0.0494586\pi$
$224$	14.6337	−	3.13943i	0.977752	−	0.209762i
$225$	−3.76547	+	3.28956i	−0.251032	+	0.219304i
$226$	8.01496	+	23.0804i	0.533147	+	1.53528i
$227$	3.49963	−	3.49963i	0.232278	−	0.232278i	−0.581365	−	0.813643i	$-0.697481\pi$
$227$	3.49963	−	3.49963i	0.232278	−	0.232278i	0.813643	+	0.581365i	$0.197481\pi$
$228$	−0.834765	−	0.0980561i	−0.0552837	−	0.00649392i
$229$		−	21.3009i		−	1.40760i	−0.710397	−	0.703801i	$-0.751485\pi$
$229$		−	21.3009i		−	1.40760i	0.710397	−	0.703801i	$-0.248515\pi$
$230$	1.32128	−	14.2989i	0.0871224	−	0.942841i
$231$	0.825783	−	0.0920039i	0.0543325	−	0.00605341i
$232$	−0.583089	−	2.64091i	−0.0382816	−	0.173384i
$233$	−12.2948	−	12.2948i	−0.805459	−	0.805459i	0.178484	−	0.983943i	$-0.442881\pi$
$233$	−12.2948	−	12.2948i	−0.805459	−	0.805459i	−0.983943	+	0.178484i	$0.942881\pi$
$234$	−0.442096	+	0.153523i	−0.0289007	+	0.0100361i
$235$	−3.06218	−	8.15959i	−0.199755	−	0.532273i
$236$	−22.5732	+	17.8275i	−1.46939	+	1.16047i
$237$	−4.91080	+	4.91080i	−0.318991	+	0.318991i
$238$	6.38584	−	18.0406i	0.413932	−	1.16940i
$239$			18.6532i			1.20657i	0.797525	+	0.603287i	$0.206142\pi$
$239$			18.6532i			1.20657i	−0.797525	+	0.603287i	$0.793858\pi$
$240$	8.87430	−	1.11656i	0.572834	−	0.0720739i
$241$			0.672629i			0.0433278i	0.999765	+	0.0216639i	$0.00689638\pi$
$241$			0.672629i			0.0433278i	−0.999765	+	0.0216639i	$0.993104\pi$
$242$	−13.8743	−	6.72196i	−0.891871	−	0.432104i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−1.90764	−	2.41545i	−0.122124	−	0.154633i
$245$	3.17811	−	15.3264i	0.203042	−	0.979170i
$246$	10.8815	−	3.77874i	0.693780	−	0.240924i
$247$	0.0983377	−	0.0983377i	0.00625708	−	0.00625708i
$248$	13.5400	−	2.98951i	0.859791	−	0.189834i
$249$			12.6015i			0.798585i
$250$	−2.51120	+	15.6107i	−0.158822	+	0.987307i
$251$	5.56688			0.351379			0.175689	−	0.984446i	$-0.443785\pi$
$251$	5.56688			0.351379			0.175689	+	0.984446i	$0.443785\pi$
$252$	−5.29141	−	0.0316061i	−0.333327	−	0.00199100i
$253$	−1.00839	+	1.00839i	−0.0633971	+	0.0633971i
$254$	−24.5042	+	8.50939i	−1.53753	+	0.533927i
$255$	4.72998	−	10.4129i	0.296203	−	0.652080i
$256$	−14.2816	−	7.21361i	−0.892599	−	0.450851i
$257$	−17.1043	−	17.1043i	−1.06693	−	1.06693i	−0.997593	−	0.0693411i	$-0.977910\pi$
$257$	−17.1043	−	17.1043i	−1.06693	−	1.06693i	−0.0693411	−	0.997593i	$-0.522090\pi$
$258$	−4.76257	−	2.30742i	−0.296504	−	0.143654i
$259$	0.875074	+	7.85424i	0.0543744	+	0.488039i
$260$	−0.765076	+	1.26682i	−0.0474480	+	0.0785650i
$261$			0.956189i			0.0591866i
$262$	18.2852	+	8.85901i	1.12966	+	0.547312i
$263$	2.45798	+	2.45798i	0.151566	+	0.151566i	0.778817	−	0.627251i	$-0.215820\pi$
$263$	2.45798	+	2.45798i	0.151566	+	0.151566i	−0.627251	+	0.778817i	$0.715820\pi$
$264$	−0.748740	−	0.477908i	−0.0460818	−	0.0294132i
$265$	−4.31706	+	1.62013i	−0.265195	+	0.0995240i
$266$	1.41917	−	0.677140i	0.0870150	−	0.0415181i
$267$	10.1765	+	10.1765i	0.622791	+	0.622791i
$268$	0.600765	−	5.11440i	0.0366976	−	0.312412i
$269$		−	0.379458i		−	0.0231360i	−0.999933	−	0.0115680i	$-0.996318\pi$
$269$		−	0.379458i		−	0.0231360i	0.999933	−	0.0115680i	$-0.00368229\pi$
$270$	−3.14886	−	0.290968i	−0.191634	−	0.0177077i
$271$		−	0.263843i		−	0.0160273i	−0.999968	−	0.00801365i	$-0.997449\pi$
$271$		−	0.263843i		−	0.0160273i	0.999968	−	0.00801365i	$-0.00255085\pi$
$272$	−17.4252	+	10.7204i	−1.05656	+	0.650019i
$273$	0.546738	−	0.683842i	0.0330901	−	0.0413880i
$274$	−19.7073	+	6.84361i	−1.19056	+	0.413437i
$275$	1.18254	−	1.03308i	0.0713098	−	0.0622970i
$276$	7.12725	−	5.62885i	0.429010	−	0.338817i
$277$	−1.76560	−	1.76560i	−0.106085	−	0.106085i	0.652072	−	0.758157i	$-0.273900\pi$
$277$	−1.76560	−	1.76560i	−0.106085	−	0.106085i	−0.758157	+	0.652072i	$0.773900\pi$
$278$	4.44476	−	9.17407i	0.266579	−	0.550224i
$279$	−4.90241			−0.293499
$280$	−12.9343	+	10.6162i	−0.772973	+	0.634439i
$281$	21.8598			1.30404			0.652022	−	0.758200i	$-0.273921\pi$
$281$	21.8598			1.30404			0.652022	+	0.758200i	$0.273921\pi$
$282$	2.40331	−	4.96049i	0.143115	−	0.295393i
$283$	−9.60390	−	9.60390i	−0.570892	−	0.570892i	0.361485	−	0.932378i	$-0.382270\pi$
$283$	−9.60390	−	9.60390i	−0.570892	−	0.570892i	−0.932378	+	0.361485i	$0.882270\pi$
$284$	−13.8848	−	17.5809i	−0.823910	−	1.04324i
$285$	0.879798	−	0.330176i	0.0521147	−	0.0195579i
$286$	0.138839	−	0.0482137i	0.00820973	−	0.00285093i
$287$	−13.4571	+	16.8317i	−0.794349	+	0.993546i
$288$	4.38069	+	3.57904i	0.258135	+	0.210897i
$289$			9.16017i			0.538833i
$290$	1.93230	+	2.32577i	0.113469	+	0.136574i
$291$			5.51972i			0.323572i
$292$	4.76586	+	0.559824i	0.278901	+	0.0327612i
$293$	17.0503	+	17.0503i	0.996092	+	0.996092i	0.999992	−	0.00390077i	$-0.00124166\pi$
$293$	17.0503	+	17.0503i	0.996092	+	0.996092i	−0.00390077	+	0.999992i	$0.501242\pi$
$294$	8.40759	−	5.22612i	0.490341	−	0.304794i
$295$	13.3002	−	29.2800i	0.774370	−	1.70475i
$296$	4.54551	−	7.12147i	0.264202	−	0.413927i
$297$	0.222065	+	0.222065i	0.0128855	+	0.0128855i
$298$	−20.0056	−	9.69256i	−1.15890	−	0.561475i
$299$			1.50270i			0.0869036i
$300$	−8.24706	+	5.65561i	−0.476145	+	0.326527i
$301$	9.83972	−	1.09628i	0.567152	−	0.0631888i
$302$	−16.8066	−	8.14264i	−0.967110	−	0.468556i
$303$	−0.0582422	−	0.0582422i	−0.00334593	−	0.00334593i
$304$	−1.63525	−	0.389546i	−0.0937881	−	0.0223420i
$305$	3.13311	+	1.42319i	0.179401	+	0.0814918i
$306$	6.83300	−	2.37285i	0.390617	−	0.135647i
$307$	0.410345	−	0.410345i	0.0234196	−	0.0234196i	−0.695300	−	0.718720i	$-0.744728\pi$
$307$	0.410345	−	0.410345i	0.0234196	−	0.0234196i	0.718720	+	0.695300i	$0.244728\pi$
$308$	1.66175	+	0.00992583i	0.0946873	+	0.000565577i
$309$	9.07516			0.516268
$310$	−11.9243	+	9.90696i	−0.677252	+	0.562678i
$311$		−	6.15475i		−	0.349004i	−0.984657	−	0.174502i	$-0.944168\pi$
$311$		−	6.15475i		−	0.349004i	0.984657	−	0.174502i	$-0.0558315\pi$
$312$	−0.913975	+	0.201797i	−0.0517436	+	0.0114245i
$313$	10.4885	−	10.4885i	0.592846	−	0.592846i	−0.345553	−	0.938399i	$-0.612309\pi$
$313$	10.4885	−	10.4885i	0.592846	−	0.592846i	0.938399	+	0.345553i	$0.112309\pi$
$314$	3.66877	−	1.27403i	0.207040	−	0.0718975i
$315$	5.27465	−	2.67920i	0.297193	−	0.150956i
$316$	−10.9004	+	8.60871i	−0.613193	+	0.484278i
$317$	13.8113	+	13.8113i	0.775722	+	0.775722i	0.979100	−	0.203379i	$-0.0651922\pi$
$317$	13.8113	+	13.8113i	0.775722	+	0.775722i	−0.203379	+	0.979100i	$0.565192\pi$
$318$	−2.62449	−	1.27154i	−0.147174	−	0.0713045i
$319$		−	0.300289i		−	0.0168130i
$320$	17.8879	−	0.147268i	0.999966	−	0.00823255i
$321$			15.1541i			0.845821i
$322$	−5.66952	+	16.0169i	−0.315950	+	0.892589i
$323$	−1.51990	+	1.51990i	−0.0845696	+	0.0845696i
$324$	−1.23957	−	1.56954i	−0.0688650	−	0.0871969i
$325$	0.111362	−	1.65086i	0.00617726	−	0.0915730i
$326$	24.6701	−	8.56701i	1.36635	−	0.474483i
$327$	−7.56814	−	7.56814i	−0.418519	−	0.418519i
$328$	22.4961	−	4.96694i	1.24214	−	0.274253i
$329$	1.14184	+	10.2486i	0.0629518	+	0.565025i
$330$	0.988893	+	0.0913778i	0.0544368	+	0.00503018i
$331$			4.06088i			0.223206i	0.993753	+	0.111603i	$0.0355985\pi$
$331$			4.06088i			0.223206i	−0.993753	+	0.111603i	$0.964402\pi$
$332$	−2.94026	+	25.0308i	−0.161368	+	1.37374i
$333$	−2.11212	+	2.11212i	−0.115744	+	0.115744i
$334$	9.58213	+	27.5933i	0.524311	+	1.50984i
$335$	2.02290	+	5.39030i	0.110523	+	0.294503i
$336$	−10.5032	−	1.29741i	−0.572995	−	0.0707794i
$337$	−1.71147	+	1.71147i	−0.0932295	+	0.0932295i	−0.752183	−	0.658954i	$-0.770999\pi$
$337$	−1.71147	+	1.71147i	−0.0932295	+	0.0932295i	0.658954	+	0.752183i	$0.270999\pi$
$338$	−7.94848	+	16.4058i	−0.432340	+	0.892359i
$339$		−	17.2763i		−	0.938322i
$340$	11.8250	−	19.5799i	0.641299	−	1.06187i
$341$	1.53959			0.0833735
$342$	0.534858	+	0.259134i	0.0289218	+	0.0140124i
$343$	−8.09781	+	16.6561i	−0.437241	+	0.899344i
$344$	−8.92171	−	5.69457i	−0.481026	−	0.307030i
$345$	−4.19940	+	9.24484i	−0.226088	+	0.497725i
$346$	8.28419	+	23.8557i	0.445361	+	1.28249i
$347$	5.86939	+	5.86939i	0.315085	+	0.315085i	0.846876	−	0.531791i	$-0.178481\pi$
$347$	5.86939	+	5.86939i	0.315085	+	0.315085i	−0.531791	+	0.846876i	$0.678481\pi$
$348$	−0.223104	+	1.89932i	−0.0119597	+	0.101814i
$349$		−	12.5472i		−	0.671636i	−0.941927	−	0.335818i	$-0.890987\pi$
$349$		−	12.5472i		−	0.671636i	0.941927	−	0.335818i	$-0.109013\pi$
$350$	7.41545	−	17.1759i	0.396373	−	0.918090i
$351$	0.330921			0.0176633
$352$	−1.37575	−	1.12399i	−0.0733276	−	0.0599088i
$353$	−0.298475	+	0.298475i	−0.0158862	+	0.0158862i	−0.715005	−	0.699119i	$-0.753576\pi$
$353$	−0.298475	+	0.298475i	−0.0158862	+	0.0158862i	0.699119	+	0.715005i	$0.253576\pi$
$354$	19.2137	−	6.67222i	1.02120	−	0.354624i
$355$	22.8044	+	10.3587i	1.21033	+	0.549785i
$356$	17.8395	+	22.5884i	0.945494	+	1.19718i
$357$	−8.45035	+	10.5694i	−0.447240	+	0.559393i
$358$	27.7042	+	13.4224i	1.46421	+	0.709398i
$359$			7.62049i			0.402194i	0.979571	+	0.201097i	$0.0644507\pi$
$359$			7.62049i			0.402194i	−0.979571	+	0.201097i	$0.935549\pi$
$360$	−6.18683	−	1.31268i	−0.326075	−	0.0691841i
$361$	18.8234			0.990705
$362$	11.2467	+	5.44895i	0.591116	+	0.286391i
$363$	7.70844	+	7.70844i	0.404588	+	0.404588i
$364$	1.24557	−	1.23078i	0.0652855	−	0.0645102i
$365$	−5.02296	+	1.88505i	−0.262914	+	0.0986679i
$366$	0.713961	+	2.05597i	0.0373194	+	0.107467i
$367$	4.60964	+	4.60964i	0.240621	+	0.240621i	0.817107	−	0.576486i	$-0.195576\pi$
$367$	4.60964	+	4.60964i	0.240621	+	0.240621i	−0.576486	+	0.817107i	$0.695576\pi$
$368$	15.4705	−	9.51785i	0.806457	−	0.496152i
$369$	−8.14513			−0.424018
$370$	−0.869118	+	9.40563i	−0.0451833	+	0.488975i
$371$	5.42233	−	0.604124i	0.281513	−	0.0313646i
$372$	−9.73786	−	1.14386i	−0.504885	−	0.0593065i
$373$	15.3495	−	15.3495i	0.794765	−	0.794765i	−0.187500	−	0.982265i	$-0.560038\pi$
$373$	15.3495	−	15.3495i	0.794765	−	0.794765i	0.982265	+	0.187500i	$0.0600384\pi$
$374$	−2.14589	+	0.745188i	−0.110961	+	0.0385327i
$375$	5.29854	−	9.84508i	0.273615	−	0.508398i
$376$	5.93122	−	9.29248i	0.305879	−	0.479223i
$377$	−0.223745	−	0.223745i	−0.0115235	−	0.0115235i
$378$	3.52721	+	1.24853i	0.181420	+	0.0642172i
$379$	35.1087			1.80341			0.901706	−	0.432350i	$-0.142316\pi$
$379$	35.1087			1.80341			0.901706	+	0.432350i	$0.142316\pi$
$380$	1.82462	−	0.450562i	0.0936010	−	0.0231133i
$381$	18.3421			0.939694
$382$	11.7268	+	5.68152i	0.599994	+	0.290692i
$383$	−12.8931	+	12.8931i	−0.658809	+	0.658809i	−0.955098	−	0.296289i	$-0.904251\pi$
$383$	−12.8931	+	12.8931i	−0.658809	+	0.658809i	0.296289	+	0.955098i	$0.404251\pi$
$384$	7.86647	+	8.13133i	0.401434	+	0.414950i
$385$	−1.65649	+	0.841395i	−0.0844226	+	0.0428815i
$386$	3.88878	+	11.1984i	0.197934	+	0.569982i
$387$	2.64605	+	2.64605i	0.134506	+	0.134506i
$388$	−1.28790	+	10.9641i	−0.0653831	+	0.556616i
$389$	5.55375			0.281586			0.140793	−	0.990039i	$-0.455035\pi$
$389$	5.55375			0.281586			0.140793	+	0.990039i	$0.455035\pi$
$390$	0.804909	−	0.668738i	0.0407582	−	0.0338629i
$391$		−	23.2257i		−	1.17457i
$392$	17.9198	−	8.41916i	0.905085	−	0.425232i
$393$	−10.1591	−	10.1591i	−0.512459	−	0.512459i
$394$	−4.76342	−	13.7171i	−0.239978	−	0.691055i
$395$	6.42253	−	14.1390i	0.323152	−	0.711409i
$396$	0.389284	+	0.492912i	0.0195623	+	0.0247697i
$397$	16.8508	−	16.8508i	0.845716	−	0.845716i	−0.143879	−	0.989595i	$-0.545958\pi$
$397$	16.8508	−	16.8508i	0.845716	−	0.845716i	0.989595	+	0.143879i	$0.0459577\pi$
$398$	30.2076	+	14.6353i	1.51417	+	0.733603i
$399$	−1.10505	+	0.123118i	−0.0553215	+	0.00616360i
$400$	−17.7011	+	9.30972i	−0.885055	+	0.465486i
$401$	34.1171			1.70373			0.851864	−	0.523763i	$-0.175472\pi$
$401$	34.1171			1.70373			0.851864	+	0.523763i	$0.175472\pi$
$402$	−1.58765	+	3.27694i	−0.0791848	+	0.163439i
$403$	1.14715	−	1.14715i	0.0571435	−	0.0571435i
$404$	−0.102100	−	0.129278i	−0.00507964	−	0.00643185i
$405$	2.03587	+	0.924781i	0.101163	+	0.0459527i
$406$	−1.54068	−	3.22901i	−0.0764626	−	0.160253i
$407$	0.663307	−	0.663307i	0.0328789	−	0.0328789i
$408$	14.1263	−	3.11897i	0.699358	−	0.154412i
$409$	−24.3436			−1.20371			−0.601856	−	0.798605i	$-0.705572\pi$
$409$	−24.3436			−1.20371			−0.601856	+	0.798605i	$0.705572\pi$
$410$	−19.8116	+	16.4600i	−0.978426	+	0.812900i
$411$	14.7515			0.727636
$412$	18.0264	+	2.11748i	0.888096	+	0.104321i
$413$	−23.7616	+	29.7202i	−1.16923	+	1.46244i
$414$	−6.06652	+	2.10668i	−0.298153	+	0.103538i
$415$	−9.90048	−	26.3811i	−0.485995	−	1.29500i
$416$	−1.86255	+	0.187584i	−0.0913191	+	0.00919707i
$417$	−5.09704	+	5.09704i	−0.249603	+	0.249603i
$418$	−0.167971	−	0.0813805i	−0.00821573	−	0.00398045i
$419$		−	14.3069i		−	0.698939i	−0.936948	−	0.349469i	$-0.886362\pi$
$419$		−	14.3069i		−	0.698939i	0.936948	−	0.349469i	$-0.113638\pi$
$420$	11.1024	−	4.09109i	0.541741	−	0.199625i
$421$			17.6128i			0.858394i	0.903211	+	0.429197i	$0.141203\pi$
$421$			17.6128i			0.858394i	−0.903211	+	0.429197i	$0.858797\pi$
$422$	−14.5161	+	29.9615i	−0.706633	+	1.45851i
$423$	−2.75601	+	2.75601i	−0.134002	+	0.134002i
$424$	−4.91645	−	3.13808i	−0.238764	−	0.152399i
$425$	−1.72121	+	25.5155i	−0.0834908	+	1.23768i
$426$	5.19658	+	14.9644i	0.251775	+	0.725028i
$427$	−3.18021	−	2.54261i	−0.153901	−	0.123045i
$428$	−3.53586	+	30.1013i	−0.170912	+	1.45500i
$429$	−0.103925			−0.00501755
$430$	11.7833	+	1.08882i	0.568240	+	0.0525077i
$431$	−22.6824			−1.09257			−0.546287	−	0.837598i	$-0.683959\pi$
$431$	−22.6824			−1.09257			−0.546287	+	0.837598i	$0.683959\pi$
$432$	−2.09599	−	3.40688i	−0.100844	−	0.163913i
$433$	2.56603	−	2.56603i	0.123315	−	0.123315i	−0.642756	−	0.766071i	$-0.722209\pi$
$433$	2.56603	−	2.56603i	0.123315	−	0.123315i	0.766071	+	0.642756i	$0.222209\pi$
$434$	16.5552	−	7.89910i	0.794675	−	0.379169i
$435$	−0.751240	−	2.00178i	−0.0360192	−	0.0959780i
$436$	−13.2671	−	16.7988i	−0.635378	−	0.804516i
$437$	1.34941	−	1.34941i	0.0645510	−	0.0645510i
$438$	−3.05363	−	1.47946i	−0.145908	−	0.0706911i
$439$	−3.59528			−0.171593			−0.0857967	−	0.996313i	$-0.527344\pi$
$439$	−3.59528			−0.171593			−0.0857967	+	0.996313i	$0.527344\pi$
$440$	1.94296	+	0.412243i	0.0926270	+	0.0196529i
$441$	−6.82835	+	1.54067i	−0.325159	+	0.0733654i
$442$	−1.04366	+	2.15414i	−0.0496419	+	0.102462i
$443$	−18.7645	+	18.7645i	−0.891528	+	0.891528i	−0.994667	−	0.103139i	$-0.967111\pi$
$443$	−18.7645	+	18.7645i	−0.891528	+	0.891528i	0.103139	+	0.994667i	$0.467111\pi$
$444$	−4.68821	+	3.70258i	−0.222493	+	0.175717i
$445$	−29.2997	−	13.3092i	−1.38894	−	0.630916i
$446$	−23.5075	+	8.16330i	−1.11311	+	0.386543i
$447$	11.1150	+	11.1150i	0.525720	+	0.525720i
$448$	−20.5602	−	5.02777i	−0.971378	−	0.237540i
$449$		−	33.7366i		−	1.59213i	−0.605211	−	0.796065i	$-0.706911\pi$
$449$		−	33.7366i		−	1.59213i	0.605211	−	0.796065i	$-0.293089\pi$
$450$	6.82074	−	1.86480i	0.321533	−	0.0879074i
$451$	2.55796			0.120450
$452$	4.03103	−	34.3167i	0.189604	−	1.61412i
$453$	9.33761	+	9.33761i	0.438719	+	0.438719i
$454$	−6.61193	+	2.29608i	−0.310313	+	0.107760i
$455$	−0.607328	+	1.86117i	−0.0284720	+	0.0872532i
$456$	1.00195	+	0.639526i	0.0469206	+	0.0299486i
$457$	−11.4620	+	11.4620i	−0.536171	+	0.536171i	−0.922402	−	0.386231i	$-0.873777\pi$
$457$	−11.4620	+	11.4620i	−0.536171	+	0.536171i	0.386231	+	0.922402i	$0.373777\pi$
$458$	−13.1345	+	27.1098i	−0.613733	+	1.26676i
$459$	−5.11470			−0.238734
$460$	−10.4985	+	17.3836i	−0.489496	+	0.810514i
$461$	3.84261			0.178968			0.0894840	−	0.995988i	$-0.471478\pi$
$461$	3.84261			0.178968			0.0894840	+	0.995988i	$0.471478\pi$
$462$	−1.10771	−	0.392097i	−0.0515354	−	0.0182420i
$463$	3.59451	+	3.59451i	0.167051	+	0.167051i	0.785682	−	0.618631i	$-0.212312\pi$
$463$	3.59451	+	3.59451i	0.167051	+	0.167051i	−0.618631	+	0.785682i	$0.712312\pi$
$464$	−0.886324	+	3.72064i	−0.0411466	+	0.172727i
$465$	10.2632	−	3.85163i	0.475944	−	0.178615i
$466$	8.06652	+	23.2289i	0.373674	+	1.07606i
$467$	1.22842	−	1.22842i	0.0568446	−	0.0568446i	−0.678113	−	0.734958i	$-0.737202\pi$
$467$	1.22842	−	1.22842i	0.0568446	−	0.0568446i	0.734958	+	0.678113i	$0.237202\pi$
$468$	0.657323	+	0.0772128i	0.0303848	+	0.00356916i
$469$	−0.754312	−	6.77034i	−0.0348309	−	0.312625i
$470$	−1.13407	+	12.2730i	−0.0523109	+	0.566110i
$471$	−2.74618			−0.126537
$472$	39.7219	−	8.77024i	1.82835	−	0.403683i
$473$	−0.830985	−	0.830985i	−0.0382087	−	0.0382087i
$474$	9.27809	−	3.22193i	0.426157	−	0.147988i
$475$	−1.58245	+	1.38245i	−0.0726077	+	0.0634309i
$476$	−19.2514	+	19.0228i	−0.882388	+	0.871909i
$477$	1.45815	+	1.45815i	0.0667639	+	0.0667639i
$478$	11.5018	−	23.7400i	0.526082	−	1.08584i
$479$	27.0344			1.23523			0.617617	−	0.786479i	$-0.288098\pi$
$479$	27.0344			1.23523			0.617617	+	0.786479i	$0.288098\pi$
$480$	−11.9829	−	4.05098i	−0.546941	−	0.184901i
$481$		−	0.988460i		−	0.0450699i
$482$	0.414754	−	0.856060i	0.0188915	−	0.0389925i
$483$	7.50245	−	9.38382i	0.341373	−	0.426979i
$484$	13.5130	+	17.1102i	0.614228	+	0.777735i
$485$	−4.33663	−	11.5555i	−0.196916	−	0.524710i
$486$	0.463927	+	1.33595i	0.0210442	+	0.0606001i
$487$	1.07144	−	1.07144i	0.0485517	−	0.0485517i	−0.682414	−	0.730966i	$-0.739070\pi$
$487$	1.07144	−	1.07144i	0.0485517	−	0.0485517i	0.730966	+	0.682414i	$0.239070\pi$
$488$	0.938460	+	4.25044i	0.0424821	+	0.192409i
$489$	−18.4663			−0.835074
$490$	−13.4953	+	17.5464i	−0.609657	+	0.792666i
$491$		−	14.9484i		−	0.674611i	−0.941395	−	0.337306i	$-0.890484\pi$
$491$		−	14.9484i		−	0.674611i	0.941395	−	0.337306i	$-0.109516\pi$
$492$	−16.1790	−	1.90048i	−0.729406	−	0.0856800i
$493$	3.45819	+	3.45819i	0.155749	+	0.155749i
$494$	−0.185792	+	0.0645185i	−0.00835916	+	0.00290283i
$495$	−0.639361	−	0.290425i	−0.0287372	−	0.0130537i
$496$	−19.0758	−	4.54420i	−0.856530	−	0.204041i
$497$	−23.1472	−	18.5064i	−1.03830	−	0.830127i
$498$	7.77026	−	16.0380i	0.348194	−	0.718679i
$499$	−17.1579			−0.768092			−0.384046	−	0.923314i	$-0.625470\pi$
$499$	−17.1579			−0.768092			−0.384046	+	0.923314i	$0.625470\pi$
$500$	12.8218	−	18.3194i	0.573410	−	0.819269i
$501$		−	20.6544i		−	0.922771i
$502$	−7.08501	−	3.43263i	−0.316220	−	0.153206i
$503$	−9.65949	+	9.65949i	−0.430695	+	0.430695i	−0.888865	−	0.458170i	$-0.848505\pi$
$503$	−9.65949	+	9.65949i	−0.430695	+	0.430695i	0.458170	+	0.888865i	$0.348505\pi$
$504$	6.71493	+	3.30299i	0.299107	+	0.147127i
$505$	0.167689	+	0.0761714i	0.00746205	+	0.00338958i
$506$	1.90518	−	0.661598i	0.0846955	−	0.0294116i
$507$	9.11495	−	9.11495i	0.404809	−	0.404809i
$508$	36.4337	+	4.27970i	1.61648	+	0.189881i
$509$			30.4834i			1.35115i	0.737289	+	0.675577i	$0.236105\pi$
$509$			30.4834i			1.35115i	−0.737289	+	0.675577i	$0.763895\pi$
$510$	−12.4406	+	10.3360i	−0.550880	+	0.457685i
$511$	6.30896	−	0.702907i	0.279092	−	0.0310948i
$512$	13.7283	+	17.9871i	0.606709	+	0.794924i
$513$	−0.297163	−	0.297163i	−0.0131201	−	0.0131201i
$514$	11.2220	+	32.3155i	0.494980	+	1.42537i
$515$	−18.9988	+	7.13000i	−0.837189	+	0.314185i
$516$	4.63856	+	5.87335i	0.204201	+	0.258560i
$517$	0.865519	−	0.865519i	0.0380655	−	0.0380655i
$518$	3.72934	−	10.5357i	0.163858	−	0.462914i
$519$		−	17.8567i		−	0.783821i
$520$	1.75486	−	1.14054i	0.0769557	−	0.0500158i
$521$			18.2589i			0.799938i	0.916529	+	0.399969i	$0.130979\pi$
$521$			18.2589i			0.799938i	−0.916529	+	0.399969i	$0.869021\pi$
$522$	0.589601	−	1.21695i	0.0258062	−	0.0532644i
$523$	−20.0977	−	20.0977i	−0.878811	−	0.878811i	0.114601	−	0.993412i	$-0.463441\pi$
$523$	−20.0977	−	20.0977i	−0.878811	−	0.878811i	−0.993412	+	0.114601i	$0.963441\pi$
$524$	−17.8091	−	22.5499i	−0.777993	−	0.985095i
$525$	−8.93753	+	9.75298i	−0.390066	+	0.425655i
$526$	−1.61266	−	4.64393i	−0.0703155	−	0.202485i
$527$	−17.7302	+	17.7302i	−0.772341	+	0.772341i
$528$	0.658242	+	1.06992i	0.0286463	+	0.0465624i
$529$		−	2.37959i		−	0.103460i
$530$	6.49336	+	0.600013i	0.282054	+	0.0260629i
$531$	−14.3820			−0.624127
$532$	−2.22373	−	0.0132825i	−0.0964108	−	0.000575871i
$533$	1.90593	−	1.90593i	0.0825551	−	0.0825551i
$534$	−6.67671	−	19.2267i	−0.288929	−	0.832019i
$535$	−11.9060	−	31.7252i	−0.514742	−	1.37160i
$536$	−3.91822	+	6.13869i	−0.169241	+	0.265151i
$537$	−15.3922	−	15.3922i	−0.664224	−	0.664224i
$538$	−0.233980	+	0.482940i	−0.0100876	+	0.0208210i
$539$	2.14443	−	0.483845i	0.0923670	−	0.0208407i
$540$	3.82817	+	2.31196i	0.164738	+	0.0994907i
$541$		−	26.8650i		−	1.15502i	−0.816384	−	0.577509i	$-0.804025\pi$
$541$		−	26.8650i		−	1.15502i	0.816384	−	0.577509i	$-0.195975\pi$
$542$	−0.162689	+	0.335794i	−0.00698811	+	0.0144236i
$543$	−6.24861	−	6.24861i	−0.268153	−	0.268153i
$544$	28.7875	−	2.89929i	1.23425	−	0.124306i
$545$	21.7899	+	9.89790i	0.933376	+	0.423980i
$546$	−1.11751	+	0.533204i	−0.0478248	+	0.0228190i
$547$	12.0710	+	12.0710i	0.516118	+	0.516118i	0.916394	−	0.400277i	$-0.131086\pi$
$547$	12.0710	+	12.0710i	0.516118	+	0.516118i	−0.400277	+	0.916394i	$0.631086\pi$
$548$	29.3015	+	3.44191i	1.25170	+	0.147031i
$549$		−	1.53895i		−	0.0656809i
$550$	−2.14204	+	0.585636i	−0.0913368	+	0.0249716i
$551$			0.401841i			0.0171190i
$552$	−12.5417	+	2.76910i	−0.533812	+	0.117861i
$553$	−11.4742	+	14.3515i	−0.487932	+	0.610289i
$554$	1.15840	+	3.33579i	0.0492155	+	0.141724i
$555$	2.76231	−	6.08114i	0.117254	−	0.258130i
$556$	−11.3138	+	8.93520i	−0.479810	+	0.378937i
$557$	−4.58669	−	4.58669i	−0.194344	−	0.194344i	0.603226	−	0.797570i	$-0.293882\pi$
$557$	−4.58669	−	4.58669i	−0.194344	−	0.194344i	−0.797570	+	0.603226i	$0.793882\pi$
$558$	6.23933	+	3.02290i	0.264132	+	0.127970i
$559$	−1.23833			−0.0523759
$560$	23.0077	−	5.53582i	0.972253	−	0.233931i
$561$	1.60626			0.0678164
$562$	−27.8211	−	13.4791i	−1.17356	−	0.568581i
$563$	−23.7113	−	23.7113i	−0.999313	−	0.999313i	0.000686267	−	1.00000i	$-0.499782\pi$
$563$	−23.7113	−	23.7113i	−0.999313	−	0.999313i	−1.00000		0.000686267i	$0.999782\pi$
$564$	−6.11743	+	4.83133i	−0.257590	+	0.203436i
$565$	13.5733	+	36.1680i	0.571035	+	1.52160i
$566$	6.30104	+	18.1449i	0.264852	+	0.762686i
$567$	−2.06648	−	1.65217i	−0.0867840	−	0.0693846i
$568$	6.83060	+	30.9369i	0.286606	+	1.29809i
$569$		−	35.2163i		−	1.47634i	−0.674613	−	0.738172i	$-0.735689\pi$
$569$		−	35.2163i		−	1.47634i	0.674613	−	0.738172i	$-0.264311\pi$
$570$	−1.32332	−	0.122280i	−0.0554276	−	0.00512174i
$571$		−	16.0688i		−	0.672458i	−0.941780	−	0.336229i	$-0.890848\pi$
$571$		−	16.0688i		−	0.672458i	0.941780	−	0.336229i	$-0.109152\pi$
$572$	−0.206431	−	0.0242485i	−0.00863131	−	0.00101388i
$573$	−6.51531	−	6.51531i	−0.272181	−	0.272181i
$574$	27.5057	−	13.1240i	1.14807	−	0.547785i
$575$	1.52813	−	22.6534i	0.0637276	−	0.944711i
$576$	−3.36845	−	7.25628i	−0.140352	−	0.302345i
$577$	25.1070	+	25.1070i	1.04522	+	1.04522i	0.998928	+	0.0462885i	$0.0147394\pi$
$577$	25.1070	+	25.1070i	1.04522	+	1.04522i	0.0462885	+	0.998928i	$0.485261\pi$
$578$	5.64831	−	11.6582i	0.234939	−	0.484918i
$579$		−	8.38230i		−	0.348357i
$580$	−1.02515	−	4.15151i	−0.0425671	−	0.172382i
$581$	3.69174	+	33.1353i	0.153159	+	1.37468i
$582$	3.40355	−	7.02499i	0.141082	−	0.291195i
$583$	−0.457927	−	0.457927i	−0.0189654	−	0.0189654i
$584$	−5.72035	−	3.65120i	−0.236710	−	0.151088i
$585$	−0.692784	+	0.259992i	−0.0286431	+	0.0107493i
$586$	−11.1866	−	32.2136i	−0.462114	−	1.33073i
$587$	24.8114	−	24.8114i	1.02408	−	1.02408i	0.0243736	−	0.999703i	$-0.492241\pi$
$587$	24.8114	−	24.8114i	1.02408	−	1.02408i	0.999703	−	0.0243736i	$-0.00775913\pi$
$588$	−13.9229	+	1.46707i	−0.574172	+	0.0605010i
$589$	−2.06025			−0.0848910
$590$	−34.9818	+	29.0638i	−1.44018	+	1.19654i
$591$			10.2676i			0.422353i
$592$	−10.1763	+	6.26072i	−0.418244	+	0.257314i
$593$	−6.40266	+	6.40266i	−0.262926	+	0.262926i	−0.826242	−	0.563316i	$-0.809525\pi$
$593$	−6.40266	+	6.40266i	−0.262926	+	0.262926i	0.563316	+	0.826242i	$0.309525\pi$
$594$	−0.145695	−	0.419553i	−0.00597795	−	0.0172145i
$595$	9.38682	−	28.7662i	0.384822	−	1.17930i
$596$	19.4847	+	24.6716i	0.798126	+	1.01059i
$597$	−16.7831	−	16.7831i	−0.686887	−	0.686887i
$598$	0.926591	−	1.91250i	0.0378911	−	0.0782081i
$599$			41.5479i			1.69760i	0.528713	+	0.848801i	$0.322675\pi$
$599$			41.5479i			1.69760i	−0.528713	+	0.848801i	$0.677325\pi$
$600$	13.9834	−	2.11267i	0.570872	−	0.0862493i
$601$		−	19.6459i		−	0.801374i	−0.916215	−	0.400687i	$-0.868771\pi$
$601$		−	19.6459i		−	0.801374i	0.916215	−	0.400687i	$-0.131229\pi$
$602$	−13.1991	−	4.67208i	−0.537954	−	0.190420i
$603$	1.82064	−	1.82064i	0.0741424	−	0.0741424i
$604$	16.3690	+	20.7264i	0.666044	+	0.843345i
$605$	−22.1938	−	10.0814i	−0.902307	−	0.409867i
$606$	0.0382122	+	0.110038i	0.00155227	+	0.00447000i
$607$	28.0661	+	28.0661i	1.13917	+	1.13917i	0.988600	+	0.150569i	$0.0481104\pi$
$607$	28.0661	+	28.0661i	1.13917	+	1.13917i	0.150569	+	0.988600i	$0.451890\pi$
$608$	1.84100	+	1.50410i	0.0746622	+	0.0609993i
$609$	0.280127	+	2.51428i	0.0113513	+	0.101884i
$610$	−3.10997	−	3.74323i	−0.125919	−	0.151559i
$611$		−	1.28980i		−	0.0521795i
$612$	−10.1596	−	1.19340i	−0.410676	−	0.0482402i
$613$	−16.2272	+	16.2272i	−0.655409	+	0.655409i	−0.954290	−	0.298881i	$-0.903387\pi$
$613$	−16.2272	+	16.2272i	−0.655409	+	0.655409i	0.298881	+	0.954290i	$0.403387\pi$
$614$	−0.775275	+	0.269224i	−0.0312875	+	0.0108650i
$615$	17.0518	−	6.39931i	0.687595	−	0.258045i
$616$	−2.10881	−	1.03730i	−0.0849663	−	0.0417939i
$617$	−1.20048	+	1.20048i	−0.0483295	+	0.0483295i	−0.730859	−	0.682529i	$-0.760880\pi$
$617$	−1.20048	+	1.20048i	−0.0483295	+	0.0483295i	0.682529	+	0.730859i	$0.260880\pi$
$618$	−11.5500	−	5.59589i	−0.464610	−	0.225100i
$619$			17.5621i			0.705881i	0.935646	+	0.352941i	$0.114818\pi$
$619$			17.5621i			0.705881i	−0.935646	+	0.352941i	$0.885182\pi$
$620$	21.2849	−	5.25598i	0.854822	−	0.211085i
$621$	4.54097			0.182223
$622$	−3.79512	+	7.83320i	−0.152170	+	0.314083i
$623$	29.7402	+	23.7776i	1.19152	+	0.952628i
$624$	1.28765	+	0.306742i	0.0515474	+	0.0122795i
$625$	−3.35759	+	24.7735i	−0.134303	+	0.990940i
$626$	−19.8162	+	6.88143i	−0.792015	+	0.275037i
$627$	0.0933234	+	0.0933234i	0.00372698	+	0.00372698i
$628$	−5.45485	−	0.640757i	−0.217672	−	0.0255690i
$629$			15.2776i			0.609157i
$630$	−8.36512	+	0.157401i	−0.333274	+	0.00627101i
$631$	−34.9881			−1.39285			−0.696427	−	0.717628i	$-0.745228\pi$
$631$	−34.9881			−1.39285			−0.696427	+	0.717628i	$0.745228\pi$
$632$	19.1812	−	4.23504i	0.762988	−	0.168461i
$633$	16.6464	−	16.6464i	0.661635	−	0.661635i
$634$	−9.06150	−	26.0941i	−0.359878	−	1.03633i
$635$	−38.3992	+	14.4107i	−1.52382	+	0.571870i
$636$	2.55615	+	3.23660i	0.101358	+	0.128340i
$637$	1.23730	−	1.95832i	0.0490236	−	0.0775916i
$638$	−0.185163	+	0.382180i	−0.00733067	+	0.0151307i
$639$		−	11.2013i		−	0.443116i
$640$	−22.8569	−	10.8426i	−0.903499	−	0.428590i
$641$	30.7424			1.21425			0.607125	−	0.794606i	$-0.292323\pi$
$641$	30.7424			1.21425			0.607125	+	0.794606i	$0.292323\pi$
$642$	9.34428	−	19.2868i	0.368789	−	0.761188i
$643$	−3.91154	−	3.91154i	−0.154256	−	0.154256i	0.625760	−	0.780016i	$-0.284789\pi$
$643$	−3.91154	−	3.91154i	−0.154256	−	0.154256i	−0.780016	+	0.625760i	$0.784789\pi$
$644$	17.0919	−	16.8890i	0.673517	−	0.665518i
$645$	−7.61839	−	3.46060i	−0.299974	−	0.136261i
$646$	2.87158	−	0.997195i	0.112981	−	0.0392341i
$647$	−6.74642	−	6.74642i	−0.265229	−	0.265229i	0.561945	−	0.827174i	$-0.310053\pi$
$647$	−6.74642	−	6.74642i	−0.265229	−	0.265229i	−0.827174	+	0.561945i	$0.810053\pi$
$648$	0.609805	+	2.76191i	0.0239554	+	0.108498i
$649$	4.51665			0.177294
$650$	−1.15968	+	2.03239i	−0.0454862	+	0.0797168i
$651$	−12.8908	+	1.43622i	−0.505230	+	0.0562898i
$652$	−36.6804	−	4.30868i	−1.43651	−	0.168741i
$653$	20.9900	−	20.9900i	0.821402	−	0.821402i	−0.164907	−	0.986309i	$-0.552732\pi$
$653$	20.9900	−	20.9900i	0.821402	−	0.821402i	0.986309	+	0.164907i	$0.0527324\pi$
$654$	4.96540	+	14.2987i	0.194162	+	0.559122i
$655$	29.2497	+	13.2865i	1.14288	+	0.519145i
$656$	−31.6936	−	7.54999i	−1.23743	−	0.294778i
$657$	1.69657	+	1.69657i	0.0661896	+	0.0661896i
$658$	4.86624	−	13.7476i	0.189706	−	0.535937i
$659$	28.7344			1.11933			0.559666	−	0.828718i	$-0.310929\pi$
$659$	28.7344			1.11933			0.559666	+	0.828718i	$0.310929\pi$
$660$	−1.20223	−	0.726065i	−0.0467966	−	0.0282620i
$661$	−18.6873			−0.726851			−0.363426	−	0.931623i	$-0.618393\pi$
$661$	−18.6873			−0.726851			−0.363426	+	0.931623i	$0.618393\pi$
$662$	2.50400	−	5.16831i	0.0973208	−	0.200872i
$663$	1.19682	−	1.19682i	0.0464808	−	0.0464808i
$664$	19.1765	−	30.0439i	0.744192	−	1.16593i
$665$	2.21668	−	1.12594i	0.0859593	−	0.0436620i
$666$	3.99048	−	1.38575i	0.154628	−	0.0536966i
$667$	−3.07028	−	3.07028i	−0.118882	−	0.118882i
$668$	4.81922	−	41.0267i	0.186461	−	1.58737i
$669$	17.5961			0.680304
$670$	0.749178	−	8.10763i	0.0289433	−	0.313225i
$671$			0.483304i			0.0186578i
$672$	12.5675	+	8.12765i	0.484801	+	0.313531i
$673$	−26.9412	−	26.9412i	−1.03851	−	1.03851i	−0.999228	−	0.0392774i	$-0.987494\pi$
$673$	−26.9412	−	26.9412i	−1.03851	−	1.03851i	−0.0392774	−	0.999228i	$-0.512506\pi$
$674$	3.23351	−	1.12288i	0.124550	−	0.0432517i
$675$	−4.98866	−	0.336522i	−0.192014	−	0.0129527i
$676$	20.2322	−	15.9787i	0.778161	−	0.614564i
$677$	−24.4650	+	24.4650i	−0.940265	+	0.940265i	−0.998314	−	0.0580485i	$-0.981512\pi$
$677$	−24.4650	+	24.4650i	−0.940265	+	0.940265i	0.0580485	+	0.998314i	$0.481512\pi$
$678$	−10.6529	+	21.9877i	−0.409121	+	0.844433i
$679$	1.61707	+	14.5140i	0.0620573	+	0.556997i
$680$	−27.1230	+	17.6281i	−1.04012	+	0.676006i
$681$	4.94922			0.189654
$682$	−1.95945	−	0.949335i	−0.0750311	−	0.0363519i
$683$	−22.6957	+	22.6957i	−0.868428	+	0.868428i	−0.992298	−	0.123871i	$-0.960469\pi$
$683$	−22.6957	+	22.6957i	−0.868428	+	0.868428i	0.123871	+	0.992298i	$0.460469\pi$
$684$	−0.520932	−	0.659604i	−0.0199183	−	0.0252206i
$685$	−30.8822	+	11.5897i	−1.17995	+	0.442818i
$686$	20.5766	−	16.2051i	0.785617	−	0.618713i
$687$	15.0620	−	15.0620i	0.574651	−	0.574651i
$688$	7.84337	+	12.7488i	0.299026	+	0.486043i
$689$	−0.682403			−0.0259975
$690$	11.0451	−	9.17656i	0.420481	−	0.349346i
$691$	25.4561			0.968397			0.484199	−	0.874958i	$-0.339111\pi$
$691$	25.4561			0.968397			0.484199	+	0.874958i	$0.339111\pi$
$692$	4.16644	−	35.4695i	0.158384	−	1.34835i
$693$	0.648973	+	0.518860i	0.0246525	+	0.0197099i
$694$	−3.85086	−	11.0892i	−0.146177	−	0.420939i
$695$	6.66611	−	14.6752i	0.252860	−	0.556662i
$696$	1.45510	−	2.27971i	0.0551553	−	0.0864122i
$697$	−29.4580	+	29.4580i	−1.11580	+	1.11580i
$698$	−7.73680	+	15.9689i	−0.292842	+	0.604432i
$699$		−	17.3875i		−	0.657655i
$700$	−20.0286	+	17.2874i	−0.757011	+	0.653402i
$701$			44.5420i			1.68233i	0.540780	+	0.841164i	$0.318129\pi$
$701$			44.5420i			1.68233i	−0.540780	+	0.841164i	$0.681871\pi$
$702$	−0.421166	−	0.204051i	−0.0158959	−	0.00770142i
$703$	−0.887624	+	0.887624i	−0.0334774	+	0.0334774i
$704$	1.05785	+	2.27882i	0.0398694	+	0.0858862i
$705$	3.60441	−	7.93499i	0.135750	−	0.298849i
$706$	0.563915	−	0.195827i	0.0212232	−	0.00737004i
$707$	−0.170210	−	0.136084i	−0.00640139	−	0.00511797i
$708$	−28.5677	−	3.35571i	−1.07364	−	0.126115i
$709$	50.4496			1.89467			0.947337	−	0.320238i	$-0.103763\pi$
$709$	50.4496			1.89467			0.947337	+	0.320238i	$0.103763\pi$
$710$	−22.6360	−	27.2452i	−0.849513	−	1.02249i
$711$	−6.94492			−0.260455
$712$	−8.77614	−	39.7486i	−0.328900	−	1.48964i
$713$	15.7414	−	15.7414i	0.589519	−	0.589519i
$714$	17.2721	−	8.24117i	0.646392	−	0.308418i
$715$	0.217567	−	0.0816499i	0.00813655	−	0.00305353i
$716$	−26.9828	−	34.1657i	−1.00840	−	1.27683i
$717$	−13.1898	+	13.1898i	−0.492581	+	0.492581i
$718$	4.69892	−	9.69866i	0.175362	−	0.361951i
$719$	38.8346			1.44829			0.724143	−	0.689650i	$-0.242236\pi$
$719$	38.8346			1.44829			0.724143	+	0.689650i	$0.242236\pi$
$720$	7.06461	+	5.48555i	0.263283	+	0.204434i
$721$	23.8630	−	2.65867i	0.888703	−	0.0990141i
$722$	−23.9567	−	11.6068i	−0.891575	−	0.431960i
$723$	−0.475620	+	0.475620i	−0.0176885	+	0.0176885i
$724$	−10.9539	−	13.8698i	−0.407099	−	0.515469i
$725$	3.14544	+	3.60051i	0.116819	+	0.133719i
$726$	−5.05744	−	14.5637i	−0.187699	−	0.540511i
$727$	5.54152	+	5.54152i	0.205524	+	0.205524i	0.802362	−	0.596838i	$-0.203577\pi$
$727$	5.54152	+	5.54152i	0.205524	+	0.205524i	−0.596838	+	0.802362i	$0.703577\pi$
$728$	−2.34416	+	0.798382i	−0.0868804	+	0.0295900i
$729$		−	1.00000i		−	0.0370370i
$730$	7.55512	+	0.698124i	0.279627	+	0.0258387i
$731$	19.1396			0.707903
$732$	0.359078	−	3.05689i	0.0132719	−	0.112986i
$733$	17.4972	+	17.4972i	0.646274	+	0.646274i	0.952090	−	0.305817i	$-0.0989294\pi$
$733$	17.4972	+	17.4972i	0.646274	+	0.646274i	−0.305817	+	0.952090i	$0.598929\pi$
$734$	−3.02435	−	8.70910i	−0.111631	−	0.321459i
$735$	13.0847	−	8.59016i	0.482636	−	0.316853i
$736$	−25.5583	+	2.57407i	−0.942092	+	0.0948814i
$737$	−0.571769	+	0.571769i	−0.0210614	+	0.0210614i
$738$	10.3664	+	5.02241i	0.381591	+	0.184878i
$739$	2.09227			0.0769653			0.0384827	−	0.999259i	$-0.487748\pi$
$739$	2.09227			0.0769653			0.0384827	+	0.999259i	$0.487748\pi$
$740$	6.90579	−	11.4347i	0.253862	−	0.420348i
$741$	0.139070			0.00510888
$742$	−7.27355	−	2.57462i	−0.267021	−	0.0945173i
$743$	−2.51303	−	2.51303i	−0.0921940	−	0.0921940i	0.659506	−	0.751700i	$-0.270766\pi$
$743$	−2.51303	−	2.51303i	−0.0921940	−	0.0921940i	−0.751700	+	0.659506i	$0.770766\pi$
$744$	11.6881	+	7.46032i	0.428507	+	0.273509i
$745$	−32.0018	−	14.5366i	−1.17246	−	0.532579i
$746$	−29.0001	+	10.0707i	−1.06177	+	0.368713i
$747$	−8.91058	+	8.91058i	−0.326021	+	0.326021i
$748$	3.19058	+	0.374783i	0.116659	+	0.0137034i
$749$	4.43958	+	39.8475i	0.162219	+	1.45600i
$750$	−12.8141	+	9.26274i	−0.467905	+	0.338228i
$751$	−17.5165			−0.639187			−0.319594	−	0.947555i	$-0.603546\pi$
$751$	−17.5165			−0.639187			−0.319594	+	0.947555i	$0.603546\pi$
$752$	−13.2786	+	8.16932i	−0.484221	+	0.297904i
$753$	3.93638	+	3.93638i	0.143450	+	0.143450i
$754$	0.146797	+	0.422727i	0.00534605	+	0.0153948i
$755$	−26.8845	−	12.2121i	−0.978426	−	0.444443i
$756$	−3.71924	−	3.76394i	−0.135268	−	0.136893i
$757$	31.2912	+	31.2912i	1.13730	+	1.13730i	0.988933	+	0.148365i	$0.0474011\pi$
$757$	31.2912	+	31.2912i	1.13730	+	1.13730i	0.148365	+	0.988933i	$0.452599\pi$
$758$	−44.6831	−	21.6486i	−1.62296	−	0.786311i
$759$	−1.42608			−0.0517635
$760$	−2.60003	−	0.551655i	−0.0943130	−	0.0200106i
$761$			28.0208i			1.01575i	0.861429	+	0.507877i	$0.169570\pi$
$761$			28.0208i			1.01575i	−0.861429	+	0.507877i	$0.830430\pi$
$762$	−23.3441	−	11.3100i	−0.845669	−	0.409719i
$763$	−22.1175	−	17.6831i	−0.800706	−	0.640172i
$764$	−11.4214	−	14.4618i	−0.413213	−	0.523211i
$765$	10.7076	−	4.01842i	0.387135	−	0.145286i
$766$	24.3593	−	8.45909i	0.880138	−	0.305639i
$767$	3.36535	−	3.36535i	0.121516	−	0.121516i
$768$	−4.99781	−	15.1994i	−0.180343	−	0.548461i
$769$	−32.9481			−1.18814			−0.594069	−	0.804414i	$-0.702479\pi$
$769$	−32.9481			−1.18814			−0.594069	+	0.804414i	$0.702479\pi$
$770$	2.62705	−	0.0494315i	0.0946722	−	0.00178139i
$771$		−	24.1891i		−	0.871148i
$772$	1.95582	−	16.6501i	0.0703913	−	0.599251i
$773$	−14.0146	−	14.0146i	−0.504070	−	0.504070i	0.408630	−	0.912700i	$-0.366007\pi$
$773$	−14.0146	−	14.0146i	−0.504070	−	0.504070i	−0.912700	+	0.408630i	$0.866007\pi$
$774$	−1.73605	−	4.99924i	−0.0624010	−	0.179694i
$775$	−18.4599	+	16.1268i	−0.663099	+	0.579290i
$776$	8.39973	−	13.1599i	0.301533	−	0.472413i
$777$	−4.93502	+	6.17256i	−0.177043	+	0.221439i
$778$	−7.06830	−	3.42453i	−0.253411	−	0.122775i
$779$	−3.42301			−0.122642
$780$	−1.43677	+	0.354788i	−0.0514446	+	0.0127035i
$781$			3.51774i			0.125875i
$782$	−14.3213	+	29.5595i	−0.512130	+	1.05705i
$783$	−0.676128	+	0.676128i	−0.0241628	+	0.0241628i
$784$	−27.9980	−	0.334482i	−0.999929	−	0.0119458i
$785$	5.74912	−	2.15757i	0.205195	−	0.0770068i
$786$	6.66531	+	19.1938i	0.237744	+	0.684622i
$787$	−20.2653	+	20.2653i	−0.722380	+	0.722380i	−0.969089	−	0.246710i	$-0.920651\pi$
$787$	−20.2653	+	20.2653i	−0.722380	+	0.722380i	0.246710	+	0.969089i	$0.420651\pi$
$788$	−2.39571	+	20.3950i	−0.0853436	+	0.726542i
$789$			3.47611i			0.123753i
$790$	−16.8923	+	14.0345i	−0.601002	+	0.499327i
$791$	−5.06130	−	45.4278i	−0.179959	−	1.61523i
$792$	−0.191508	−	0.867371i	−0.00680493	−	0.0308207i
$793$	0.360110	+	0.360110i	0.0127879	+	0.0127879i
$794$	−31.8366	+	11.0557i	−1.12984	+	0.392351i
$795$	−4.19823	−	1.90702i	−0.148896	−	0.0676349i
$796$	−29.4211	−	37.2530i	−1.04280	−	1.32040i
$797$	18.1757	−	18.1757i	0.643815	−	0.643815i	−0.307676	−	0.951491i	$-0.599551\pi$
$797$	18.1757	−	18.1757i	0.643815	−	0.643815i	0.951491	+	0.307676i	$0.0995513\pi$
$798$	1.48232	+	0.524696i	0.0524734	+	0.0185740i
$799$			19.9350i			0.705249i
$800$	28.2689	−	0.933772i	0.999455	−	0.0330138i
$801$			14.3917i			0.508506i
$802$	−43.4211	−	21.0372i	−1.53325	−	0.742848i
$803$	−0.532805	−	0.532805i	−0.0188023	−	0.0188023i
$804$	4.04123	−	3.19162i	0.142523	−	0.112560i
$805$	−8.33387	+	25.5394i	−0.293730	+	0.900146i
$806$	−2.16733	+	0.752634i	−0.0763410	+	0.0265104i
$807$	0.268318	−	0.268318i	0.00944523	−	0.00944523i
$808$	0.0502277	+	0.227490i	0.00176701	+	0.00800307i
$809$			4.01249i			0.141072i	0.997509	+	0.0705359i	$0.0224709\pi$
$809$			4.01249i			0.141072i	−0.997509	+	0.0705359i	$0.977529\pi$
$810$	−2.02084	−	2.43233i	−0.0710050	−	0.0854633i
$811$	−38.9358			−1.36722			−0.683611	−	0.729847i	$-0.739591\pi$
$811$	−38.9358			−1.36722			−0.683611	+	0.729847i	$0.739591\pi$
$812$	−0.0302214	+	5.05959i	−0.00106056	+	0.177557i
$813$	0.186565	−	0.186565i	0.00654312	−	0.00654312i
$814$	−1.25320	+	0.435190i	−0.0439247	+	0.0152534i
$815$	38.6591	−	14.5082i	1.35417	−	0.508201i
$816$	−19.9019	−	4.74099i	−0.696706	−	0.165968i
$817$	1.11201	+	1.11201i	0.0389042	+	0.0389042i
$818$	30.9822	+	15.0106i	1.08327	+	0.524834i
$819$	0.870152	−	0.0969472i	0.0304056	−	0.00338761i
$820$	35.3639	−	8.73258i	1.23496	−	0.304955i
$821$		−	46.7693i		−	1.63226i	−0.577868	−	0.816130i	$-0.696115\pi$
$821$		−	46.7693i		−	1.63226i	0.577868	−	0.816130i	$-0.303885\pi$
$822$	−18.7743	−	9.09599i	−0.654829	−	0.317259i
$823$	1.40906	+	1.40906i	0.0491166	+	0.0491166i	0.731238	−	0.682122i	$-0.238943\pi$
$823$	1.40906	+	1.40906i	0.0491166	+	0.0491166i	−0.682122	+	0.731238i	$0.738943\pi$
$824$	−21.6366	−	13.8103i	−0.753748	−	0.481104i
$825$	1.56668	+	0.105684i	0.0545447	+	0.00367944i
$826$	48.5675	−	23.1734i	1.68988	−	0.806304i
$827$	−34.0551	−	34.0551i	−1.18421	−	1.18421i	−0.978643	−	0.205569i	$-0.934096\pi$
$827$	−34.0551	−	34.0551i	−1.18421	−	1.18421i	−0.205569	−	0.978643i	$-0.565904\pi$
$828$	9.01992	+	1.05953i	0.313464	+	0.0368212i
$829$			54.4136i			1.88986i	0.327270	+	0.944931i	$0.393871\pi$
$829$			54.4136i			1.88986i	−0.327270	+	0.944931i	$0.606129\pi$
$830$	−3.66662	+	39.6803i	−0.127270	+	1.37732i
$831$		−	2.49694i		−	0.0866177i
$832$	2.48615	+	0.909739i	0.0861918	+	0.0315395i
$833$	−19.1236	+	30.2677i	−0.662594	+	1.04871i
$834$	9.62996	−	3.34413i	0.333458	−	0.115798i
$835$	16.2274	+	43.2400i	0.561571	+	1.49638i
$836$	0.163598	+	0.207147i	0.00565814	+	0.00716434i
$837$	−3.46652	−	3.46652i	−0.119821	−	0.119821i
$838$	−8.82187	+	18.2085i	−0.304746	+	0.629003i
$839$	−48.2650			−1.66629			−0.833147	−	0.553051i	$-0.813463\pi$
$839$	−48.2650			−1.66629			−0.833147	+	0.553051i	$0.813463\pi$
$840$	−16.6527	−	1.63915i	−0.574574	−	0.0565561i
$841$	−28.0857			−0.968472
$842$	10.8603	−	22.4159i	0.374271	−	0.772503i
$843$	15.4572	+	15.4572i	0.532374	+	0.532374i
$844$	36.9495	−	29.1814i	1.27186	−	1.00447i
$845$	−11.9209	+	26.2434i	−0.410091	+	0.902801i
$846$	5.20700	−	1.80820i	0.179020	−	0.0621671i
$847$	22.5275	+	18.0109i	0.774053	+	0.618862i
$848$	4.32221	+	7.02542i	0.148425	+	0.241254i
$849$		−	13.5820i		−	0.466132i
$850$	17.9239	−	31.4125i	0.614784	−	1.07744i
$851$		−	13.5638i		−	0.464962i
$852$	2.61356	−	22.2496i	0.0895391	−	0.762259i
$853$	35.3474	+	35.3474i	1.21027	+	1.21027i	0.970937	+	0.239334i	$0.0769292\pi$
$853$	35.3474	+	35.3474i	1.21027	+	1.21027i	0.239334	+	0.970937i	$0.423071\pi$
$854$	2.47967	+	5.19697i	0.0848525	+	0.177837i
$855$	0.855580	+	0.388641i	0.0292602	+	0.0132913i
$856$	23.0611	−	36.1299i	0.788211	−	1.23489i
$857$	14.2303	+	14.2303i	0.486098	+	0.486098i	0.907072	−	0.420975i	$-0.138312\pi$
$857$	14.2303	+	14.2303i	0.486098	+	0.486098i	−0.420975	+	0.907072i	$0.638312\pi$
$858$	0.132266	+	0.0640819i	0.00451550	+	0.00218772i
$859$		−	36.9876i		−	1.26200i	−0.775783	−	0.631000i	$-0.782645\pi$
$859$		−	36.9876i		−	1.26200i	0.775783	−	0.631000i	$-0.217355\pi$
$860$	−14.3253	−	8.65151i	−0.488488	−	0.295014i
$861$	−21.4175	+	2.38621i	−0.729905	+	0.0813218i
$862$	28.8681	+	13.9863i	0.983251	+	0.476377i
$863$	−1.71517	−	1.71517i	−0.0583850	−	0.0583850i	0.677311	−	0.735696i	$-0.263145\pi$
$863$	−1.71517	−	1.71517i	−0.0583850	−	0.0583850i	−0.735696	+	0.677311i	$0.763145\pi$
$864$	0.566854	+	5.62838i	0.0192848	+	0.191481i
$865$	14.0293	+	37.3829i	0.477010	+	1.27106i
$866$	−4.84805	+	1.68355i	−0.164744	+	0.0572093i
$867$	−6.47722	+	6.47722i	−0.219978	+	0.219978i
$868$	−25.9406	−	0.154946i	−0.880482	−	0.00525921i
$869$	2.18104			0.0739866
$870$	−0.278220	+	3.01091i	−0.00943255	+	0.102079i
$871$			0.852050i			0.0288706i
$872$	6.52672	+	29.5606i	0.221023	+	1.00105i
$873$	−3.90303	+	3.90303i	−0.132098	+	0.132098i
$874$	−2.54947	+	0.885336i	−0.0862371	+	0.0299469i
$875$	11.0482	−	27.4397i	0.373496	−	0.927632i
$876$	2.97412	+	3.76583i	0.100486	+	0.127236i
$877$	−34.0477	−	34.0477i	−1.14971	−	1.14971i	−0.986610	−	0.163099i	$-0.947851\pi$
$877$	−34.0477	−	34.0477i	−1.14971	−	1.14971i	−0.163099	−	0.986610i	$-0.552149\pi$
$878$	4.57574	+	2.21691i	0.154424	+	0.0748170i
$879$			24.1128i			0.813305i
$880$	−2.21863	−	1.72272i	−0.0747898	−	0.0580730i
$881$		−	50.3745i		−	1.69716i	−0.529067	−	0.848580i	$-0.677458\pi$
$881$		−	50.3745i		−	1.69716i	0.529067	−	0.848580i	$-0.322542\pi$
$882$	9.64049	+	2.24964i	0.324612	+	0.0757493i
$883$	28.7389	−	28.7389i	0.967142	−	0.967142i	−0.0323349	−	0.999477i	$-0.510294\pi$
$883$	28.7389	−	28.7389i	0.967142	−	0.967142i	0.999477	+	0.0323349i	$0.0102943\pi$
$884$	2.65655	−	2.09805i	0.0893496	−	0.0705651i
$885$	30.1088	−	11.2994i	1.01210	−	0.379825i
$886$	35.4522	−	12.3112i	1.19104	−	0.413604i
$887$	−23.3304	−	23.3304i	−0.783357	−	0.783357i	0.197039	−	0.980396i	$-0.436868\pi$
$887$	−23.3304	−	23.3304i	−0.783357	−	0.783357i	−0.980396	+	0.197039i	$0.936868\pi$
$888$	8.24980	−	1.82148i	0.276845	−	0.0611249i
$889$	48.2302	−	5.37353i	1.61759	−	0.180222i
$890$	29.0833	+	35.0054i	0.974875	+	1.17338i
$891$			0.314048i			0.0105210i
$892$	34.9519	+	4.10564i	1.17027	+	0.137467i
$893$	−1.15822	+	1.15822i	−0.0387583	+	0.0387583i
$894$	−7.29245	−	20.9998i	−0.243896	−	0.702338i
$895$	44.3167	+	20.1305i	1.48134	+	0.672890i
$896$	23.0669	+	19.0766i	0.770612	+	0.637305i
$897$	−1.06257	+	1.06257i	−0.0354783	+	0.0354783i
$898$	−20.8025	+	42.9369i	−0.694190	+	1.43282i
$899$			4.68763i			0.156341i
$900$	−9.83068	−	1.83244i	−0.327689	−	0.0610812i
$901$	10.5472			0.351377
$902$	−3.25553	−	1.57728i	−0.108397	−	0.0525176i
$903$	7.73292	+	6.18254i	0.257335	+	0.205742i
$904$	−26.2906	+	41.1896i	−0.874411	+	1.36994i
$905$	17.9907	+	8.17217i	0.598032	+	0.271652i
$906$	−6.12633	−	17.6418i	−0.203534	−	0.586108i
$907$	25.9831	+	25.9831i	0.862754	+	0.862754i	0.991657	−	0.128904i	$-0.0411458\pi$
$907$	25.9831	+	25.9831i	0.862754	+	0.862754i	−0.128904	+	0.991657i	$0.541146\pi$
$908$	9.83084	+	1.15478i	0.326248	+	0.0383229i
$909$		−	0.0823669i		−	0.00273194i
$910$	1.92058	−	1.99424i	0.0636666	−	0.0661085i
$911$	12.9407			0.428745			0.214373	−	0.976752i	$-0.431229\pi$
$911$	12.9407			0.428745			0.214373	+	0.976752i	$0.431229\pi$
$912$	−0.880846	−	1.43175i	−0.0291677	−	0.0474099i
$913$	2.79835	−	2.79835i	0.0926118	−	0.0926118i
$914$	21.6555	−	7.52015i	0.716300	−	0.248744i
$915$	1.20909	+	3.22179i	0.0399714	+	0.106509i
$916$	33.4327	−	26.4039i	1.10465	−	0.872410i
$917$	−29.6894	−	23.7370i	−0.980431	−	0.783863i
$918$	6.50952	+	3.15381i	0.214846	+	0.104091i
$919$		−	26.8121i		−	0.884448i	−0.896905	−	0.442224i	$-0.854190\pi$
$919$		−	26.8121i		−	0.884448i	0.896905	−	0.442224i	$-0.145810\pi$
$920$	24.0805	−	15.6507i	0.793912	−	0.515987i
$921$	0.580316			0.0191220
$922$	−4.89051	−	2.36941i	−0.161061	−	0.0780324i
$923$	2.62107	+	2.62107i	0.0862734	+	0.0862734i
$924$	1.16802	+	1.18206i	0.0384250	+	0.0388868i
$925$	−1.00519	+	14.9011i	−0.0330504	+	0.489945i
$926$	−2.35833	−	6.79119i	−0.0774994	−	0.223172i
$927$	6.41711	+	6.41711i	0.210765	+	0.210765i
$928$	3.42224	−	4.18877i	0.112341	−	0.137503i
$929$	22.5517			0.739898			0.369949	−	0.929052i	$-0.379375\pi$
$929$	22.5517			0.739898			0.369949	+	0.929052i	$0.379375\pi$
$930$	−15.4370	−	1.42644i	−0.506199	−	0.0467749i
$931$	−2.86963	+	0.647472i	−0.0940483	+	0.0212200i
$932$	4.05696	−	34.5375i	0.132890	−	1.13131i
$933$	4.35206	−	4.35206i	0.142480	−	0.142480i
$934$	−2.32089	+	0.805957i	−0.0759417	+	0.0263717i
$935$	−3.36270	+	1.26198i	−0.109972	+	0.0412710i
$936$	−0.788970	−	0.503585i	−0.0257883	−	0.0164602i
$937$	0.565943	+	0.565943i	0.0184885	+	0.0184885i	0.716291	−	0.697802i	$-0.245838\pi$
$937$	0.565943	+	0.565943i	0.0184885	+	0.0184885i	−0.697802	+	0.716291i	$0.745838\pi$
$938$	−3.21468	+	9.08178i	−0.104963	+	0.296531i
$939$	14.8330			0.484057
$940$	9.01105	−	14.9206i	0.293908	−	0.486657i
$941$	43.3340			1.41265			0.706325	−	0.707888i	$-0.250352\pi$
$941$	43.3340			1.41265			0.706325	+	0.707888i	$0.250352\pi$
$942$	3.49508	+	1.69334i	0.113876	+	0.0551719i
$943$	26.1536	−	26.1536i	0.851678	−	0.851678i
$944$	−55.9622	−	13.3312i	−1.82141	−	0.433894i
$945$	5.62422	+	1.83526i	0.182956	+	0.0597011i
$946$	0.545202	+	1.57000i	0.0177261	+	0.0510451i
$947$	−10.2202	−	10.2202i	−0.332111	−	0.332111i	0.521276	−	0.853388i	$-0.325456\pi$
$947$	−10.2202	−	10.2202i	−0.332111	−	0.332111i	−0.853388	+	0.521276i	$0.825456\pi$
$948$	−13.7950	−	1.62043i	−0.448040	−	0.0526293i
$949$	−0.793985			−0.0257738
$950$	2.86643	−	0.783685i	0.0929993	−	0.0254261i
$951$			19.5322i			0.633374i
$952$	36.2312	−	12.3397i	1.17426	−	0.399933i
$953$	−22.0614	−	22.0614i	−0.714640	−	0.714640i	0.252862	−	0.967502i	$-0.418628\pi$
$953$	−22.0614	−	22.0614i	−0.714640	−	0.714640i	−0.967502	+	0.252862i	$0.918628\pi$
$954$	−0.956677	−	2.75491i	−0.0309736	−	0.0891934i
$955$	18.7586	+	8.52096i	0.607014	+	0.275732i
$956$	−29.2770	+	23.1219i	−0.946884	+	0.747816i
$957$	0.212336	−	0.212336i	0.00686386	−	0.00686386i
$958$	−34.4069	−	16.6699i	−1.11164	−	0.538579i
$959$	38.7887	−	4.32161i	1.25255	−	0.139552i
$960$	12.7528	+	12.5445i	0.411595	+	0.404874i
$961$	6.96641			0.224723
$962$	−0.609500	+	1.25802i	−0.0196511	+	0.0405602i
$963$	−10.7156	+	10.7156i	−0.345305	+	0.345305i
$964$	−1.05572	+	0.833770i	−0.0340025	+	0.0268539i
$965$	6.58565	+	17.5483i	0.212000	+	0.564901i
$966$	−15.3346	+	7.31673i	−0.493384	+	0.235412i
$967$	1.07274	−	1.07274i	0.0344970	−	0.0344970i	−0.689648	−	0.724145i	$-0.742235\pi$
$967$	1.07274	−	1.07274i	0.0344970	−	0.0344970i	0.724145	+	0.689648i	$0.242235\pi$
$968$	−6.64771	−	30.1086i	−0.213665	−	0.967727i
$969$	−2.14946			−0.0690508
$970$	−1.60606	+	17.3809i	−0.0515675	+	0.558065i
$971$	13.6823			0.439085			0.219543	−	0.975603i	$-0.429543\pi$
$971$	13.6823			0.439085			0.219543	+	0.975603i	$0.429543\pi$
$972$	0.233327	−	1.98634i	0.00748396	−	0.0637120i
$973$	−11.9093	+	14.8958i	−0.381796	+	0.477538i
$974$	−2.02430	+	0.702965i	−0.0648628	+	0.0225244i
$975$	1.24608	−	1.08859i	0.0399064	−	0.0348627i
$976$	1.42651	−	5.98824i	0.0456613	−	0.191679i
$977$	−0.781646	+	0.781646i	−0.0250071	+	0.0250071i	−0.719500	−	0.694493i	$-0.755629\pi$
$977$	−0.781646	+	0.781646i	−0.0250071	+	0.0250071i	0.694493	+	0.719500i	$0.255629\pi$
$978$	23.5022	+	11.3866i	0.751517	+	0.364103i
$979$		−	4.51969i		−	0.144450i
$980$	27.9950	−	14.0100i	0.894267	−	0.447533i
$981$		−	10.7030i		−	0.341720i
$982$	−9.21741	+	19.0249i	−0.294140	+	0.607110i
$983$	5.08472	−	5.08472i	0.162178	−	0.162178i	−0.621353	−	0.783531i	$-0.713417\pi$
$983$	5.08472	−	5.08472i	0.162178	−	0.162178i	0.783531	+	0.621353i	$0.213417\pi$
$984$	19.4193	+	12.3950i	0.619064	+	0.395138i
$985$	−8.06686	−	21.4952i	−0.257032	−	0.684895i
$986$	−2.26889	−	6.53364i	−0.0722562	−	0.208074i
$987$	−6.43947	+	8.05428i	−0.204971	+	0.256371i
$988$	0.276242	+	0.0324488i	0.00878842	+	0.00103234i
$989$	−16.9926			−0.540335
$990$	0.634639	+	0.763867i	0.0201702	+	0.0242773i
$991$	−47.5202			−1.50953			−0.754765	−	0.655995i	$-0.772249\pi$
$991$	−47.5202			−1.50953			−0.754765	+	0.655995i	$0.772249\pi$
$992$	21.4759	+	17.5459i	0.681862	+	0.557083i
$993$	−2.87147	+	2.87147i	−0.0911235	+	0.0911235i
$994$	18.0483	+	37.8262i	0.572458	+	1.19978i
$995$	48.3213	+	21.9496i	1.53189	+	0.695849i
$996$	−19.7785	+	15.6204i	−0.626707	+	0.494951i
$997$	−31.5302	+	31.5302i	−0.998571	+	0.998571i	−0.999999	−	0.00142762i	$-0.999546\pi$
$997$	−31.5302	+	31.5302i	−0.998571	+	0.998571i	0.00142762	+	0.999999i	$0.499546\pi$
$998$	21.8370	+	10.5798i	0.691237	+	0.334898i
$999$	−2.98699			−0.0945042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bj.b.13.16	yes	184
5.2	odd	4	inner	840.2.bj.b.517.62	yes	184
7.6	odd	2	inner	840.2.bj.b.13.15	✓	184
8.5	even	2	inner	840.2.bj.b.13.61	yes	184
35.27	even	4	inner	840.2.bj.b.517.61	yes	184
40.37	odd	4	inner	840.2.bj.b.517.15	yes	184
56.13	odd	2	inner	840.2.bj.b.13.62	yes	184
280.237	even	4	inner	840.2.bj.b.517.16	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.15	✓	184	7.6	odd	2	inner
840.2.bj.b.13.16	yes	184	1.1	even	1	trivial
840.2.bj.b.13.61	yes	184	8.5	even	2	inner
840.2.bj.b.13.62	yes	184	56.13	odd	2	inner
840.2.bj.b.517.15	yes	184	40.37	odd	4	inner
840.2.bj.b.517.16	yes	184	280.237	even	4	inner
840.2.bj.b.517.61	yes	184	35.27	even	4	inner
840.2.bj.b.517.62	yes	184	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27271 - 0.616616i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.23957 + 1.56954i) q^{4} +(-2.03587 - 0.924781i) q^{5} +(-0.463927 - 1.33595i) q^{6} +(2.06648 + 1.65217i) q^{7} +(-0.609805 - 2.76191i) q^{8} +1.00000i q^{9} +(2.02084 + 2.43233i) q^{10} -0.314048i q^{11} +(-0.233327 + 1.98634i) q^{12} +(-0.233997 - 0.233997i) q^{13} +(-1.61127 - 3.37695i) q^{14} +(-0.785661 - 2.09350i) q^{15} +(-0.926934 + 3.89112i) q^{16} +(3.61664 + 3.61664i) q^{17} +(0.616616 - 1.27271i) q^{18} +0.420252i q^{19} +(-1.07212 - 4.34172i) q^{20} +(0.292962 + 2.62948i) q^{21} +(-0.193647 + 0.399691i) q^{22} +(-3.21095 - 3.21095i) q^{23} +(1.52177 - 2.38416i) q^{24} +(3.28956 + 3.76547i) q^{25} +(0.153523 + 0.442096i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.0316061 + 5.29141i) q^{28} +0.956189 q^{29} +(-0.290968 + 3.14886i) q^{30} +4.90241i q^{31} +(3.57904 - 4.38069i) q^{32} +(0.222065 - 0.222065i) q^{33} +(-2.37285 - 6.83300i) q^{34} +(-2.67920 - 5.27465i) q^{35} +(-1.56954 + 1.23957i) q^{36} +(2.11212 + 2.11212i) q^{37} +(0.259134 - 0.534858i) q^{38} -0.330921i q^{39} +(-1.31268 + 6.18683i) q^{40} +8.14513i q^{41} +(1.24853 - 3.52721i) q^{42} +(2.64605 - 2.64605i) q^{43} +(0.492912 - 0.389284i) q^{44} +(0.924781 - 2.03587i) q^{45} +(2.10668 + 6.06652i) q^{46} +(2.75601 + 2.75601i) q^{47} +(-3.40688 + 2.09599i) q^{48} +(1.54067 + 6.82835i) q^{49} +(-1.86480 - 6.82074i) q^{50} +5.11470i q^{51} +(0.0772128 - 0.657323i) q^{52} +(1.45815 - 1.45815i) q^{53} +(1.33595 - 0.463927i) q^{54} +(-0.290425 + 0.639361i) q^{55} +(3.30299 - 6.71493i) q^{56} +(-0.297163 + 0.297163i) q^{57} +(-1.21695 - 0.589601i) q^{58} +14.3820i q^{59} +(2.31196 - 3.82817i) q^{60} -1.53895 q^{61} +(3.02290 - 6.23933i) q^{62} +(-1.65217 + 2.06648i) q^{63} +(-7.25628 + 3.36845i) q^{64} +(0.259992 + 0.692784i) q^{65} +(-0.419553 + 0.145695i) q^{66} +(-1.82064 - 1.82064i) q^{67} +(-1.19340 + 10.1596i) q^{68} -4.54097i q^{69} +(0.157401 + 8.36512i) q^{70} -11.2013 q^{71} +(2.76191 - 0.609805i) q^{72} +(1.69657 - 1.69657i) q^{73} +(-1.38575 - 3.99048i) q^{74} +(-0.336522 + 4.98866i) q^{75} +(-0.659604 + 0.520932i) q^{76} +(0.518860 - 0.648973i) q^{77} +(-0.204051 + 0.421166i) q^{78} +6.94492i q^{79} +(5.48555 - 7.06461i) q^{80} -1.00000 q^{81} +(5.02241 - 10.3664i) q^{82} +(8.91058 + 8.91058i) q^{83} +(-3.76394 + 3.71924i) q^{84} +(-4.01842 - 10.7076i) q^{85} +(-4.99924 + 1.73605i) q^{86} +(0.676128 + 0.676128i) q^{87} +(-0.867371 + 0.191508i) q^{88} +14.3917 q^{89} +(-2.43233 + 2.02084i) q^{90} +(-0.0969472 - 0.870152i) q^{91} +(1.05953 - 9.01992i) q^{92} +(-3.46652 + 3.46652i) q^{93} +(-1.80820 - 5.20700i) q^{94} +(0.388641 - 0.855580i) q^{95} +(5.62838 - 0.566854i) q^{96} +(3.90303 + 3.90303i) q^{97} +(2.24964 - 9.64049i) q^{98} +0.314048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) \) 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Introduction

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