LMFDB - Embedded newform 170.2.k.a.111.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(111,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("170.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.k (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			111.1
Root			$-0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	170.111
Dual form			170.2.k.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-2.93755 - 1.21677i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{5} +(2.93755 - 1.21677i) q^{6} +(0.165911 + 0.400544i) q^{7} +(0.707107 + 0.707107i) q^{8} +(5.02734 + 5.02734i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.93755 - 1.21677i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{5} +(2.93755 - 1.21677i) q^{6} +(0.165911 + 0.400544i) q^{7} +(0.707107 + 0.707107i) q^{8} +(5.02734 + 5.02734i) q^{9} +(-0.382683 - 0.923880i) q^{10} +(4.66252 - 1.93128i) q^{11} +(-1.21677 + 2.93755i) q^{12} +5.61313i q^{13} +(-0.400544 - 0.165911i) q^{14} +(2.24830 - 2.24830i) q^{15} -1.00000 q^{16} +(3.76118 - 1.68925i) q^{17} -7.10973 q^{18} +(-4.34549 + 4.34549i) q^{19} +(0.923880 + 0.382683i) q^{20} -1.37849i q^{21} +(-1.93128 + 4.66252i) q^{22} +(4.74603 - 1.96587i) q^{23} +(-1.21677 - 2.93755i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-3.96908 - 3.96908i) q^{26} +(-5.00061 - 12.0725i) q^{27} +(0.400544 - 0.165911i) q^{28} +(-1.02107 + 2.46508i) q^{29} +3.17958i q^{30} +(2.02881 + 0.840361i) q^{31} +(0.707107 - 0.707107i) q^{32} -16.0463 q^{33} +(-1.46508 + 3.85403i) q^{34} -0.433546 q^{35} +(5.02734 - 5.02734i) q^{36} +(1.12132 + 0.464466i) q^{37} -6.14545i q^{38} +(6.82990 - 16.4888i) q^{39} +(-0.923880 + 0.382683i) q^{40} +(1.90602 + 4.60154i) q^{41} +(0.974742 + 0.974742i) q^{42} +(0.638384 + 0.638384i) q^{43} +(-1.93128 - 4.66252i) q^{44} +(-6.56854 + 2.72078i) q^{45} +(-1.96587 + 4.74603i) q^{46} +5.95749i q^{47} +(2.93755 + 1.21677i) q^{48} +(4.81684 - 4.81684i) q^{49} +1.00000 q^{50} +(-13.1041 + 0.385748i) q^{51} +5.61313 q^{52} +(0.0241321 - 0.0241321i) q^{53} +(12.0725 + 5.00061i) q^{54} +5.04667i q^{55} +(-0.165911 + 0.400544i) q^{56} +(18.0526 - 7.47762i) q^{57} +(-1.02107 - 2.46508i) q^{58} +(0.275642 + 0.275642i) q^{59} +(-2.24830 - 2.24830i) q^{60} +(2.72251 + 6.57273i) q^{61} +(-2.02881 + 0.840361i) q^{62} +(-1.17958 + 2.84776i) q^{63} +1.00000i q^{64} +(-5.18585 - 2.14805i) q^{65} +(11.3464 - 11.3464i) q^{66} -3.27677 q^{67} +(-1.68925 - 3.76118i) q^{68} -16.3337 q^{69} +(0.306563 - 0.306563i) q^{70} +(-3.63307 - 1.50487i) q^{71} +7.10973i q^{72} +(-1.30029 + 3.13918i) q^{73} +(-1.12132 + 0.464466i) q^{74} +(1.21677 + 2.93755i) q^{75} +(4.34549 + 4.34549i) q^{76} +(1.54712 + 1.54712i) q^{77} +(6.82990 + 16.4888i) q^{78} +(-12.2090 + 5.05713i) q^{79} +(0.382683 - 0.923880i) q^{80} +20.2191i q^{81} +(-4.60154 - 1.90602i) q^{82} +(0.560528 - 0.560528i) q^{83} -1.37849 q^{84} +(0.121320 + 4.12132i) q^{85} -0.902812 q^{86} +(5.99887 - 5.99887i) q^{87} +(4.66252 + 1.93128i) q^{88} -2.73418i q^{89} +(2.72078 - 6.56854i) q^{90} +(-2.24830 + 0.931278i) q^{91} +(-1.96587 - 4.74603i) q^{92} +(-4.93720 - 4.93720i) q^{93} +(-4.21258 - 4.21258i) q^{94} +(-2.35176 - 5.67766i) q^{95} +(-2.93755 + 1.21677i) q^{96} +(4.95489 - 11.9622i) q^{97} +6.81204i q^{98} +(33.1492 + 13.7309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^9	$ 8 q + 8 q^{9} + 16 q^{11} - 8 q^{12} - 8 q^{14} + 8 q^{15} - 8 q^{16} - 16 q^{18} - 16 q^{19} - 8 q^{22} + 24 q^{23} - 8 q^{24} + 8 q^{28} + 8 q^{29} - 16 q^{31} - 16 q^{33} + 8 q^{36} - 8 q^{37} + 32 q^{39} - 8 q^{43} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 8 q^{49} + 8 q^{50} - 40 q^{51} + 24 q^{52} - 8 q^{53} + 40 q^{54} + 16 q^{57} + 8 q^{58} - 40 q^{59} - 8 q^{60} - 24 q^{61} + 16 q^{62} + 8 q^{63} - 8 q^{65} + 16 q^{66} - 16 q^{69} - 8 q^{70} + 24 q^{71} - 16 q^{73} + 8 q^{74} + 8 q^{75} + 16 q^{76} + 8 q^{77} + 32 q^{78} - 8 q^{79} + 8 q^{82} + 8 q^{83} + 16 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{87} + 16 q^{88} - 8 q^{91} - 8 q^{92} - 32 q^{93} - 8 q^{94} + 16 q^{95} - 32 q^{97} + 72 q^{99}+O(q^{100}) $ 8 * q + 8 * q^9 + 16 * q^11 - 8 * q^12 - 8 * q^14 + 8 * q^15 - 8 * q^16 - 16 * q^18 - 16 * q^19 - 8 * q^22 + 24 * q^23 - 8 * q^24 + 8 * q^28 + 8 * q^29 - 16 * q^31 - 16 * q^33 + 8 * q^36 - 8 * q^37 + 32 * q^39 - 8 * q^43 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 8 * q^49 + 8 * q^50 - 40 * q^51 + 24 * q^52 - 8 * q^53 + 40 * q^54 + 16 * q^57 + 8 * q^58 - 40 * q^59 - 8 * q^60 - 24 * q^61 + 16 * q^62 + 8 * q^63 - 8 * q^65 + 16 * q^66 - 16 * q^69 - 8 * q^70 + 24 * q^71 - 16 * q^73 + 8 * q^74 + 8 * q^75 + 16 * q^76 + 8 * q^77 + 32 * q^78 - 8 * q^79 + 8 * q^82 + 8 * q^83 + 16 * q^84 - 16 * q^85 - 16 * q^86 + 32 * q^87 + 16 * q^88 - 8 * q^91 - 8 * q^92 - 32 * q^93 - 8 * q^94 + 16 * q^95 - 32 * q^97 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−2.93755	−	1.21677i	−1.69599	−	0.702504i	−0.696114	−	0.717931i	$-0.745089\pi$
$3$	−2.93755	−	1.21677i	−1.69599	−	0.702504i	−0.999881	+	0.0154273i	$0.995089\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$6$	2.93755	−	1.21677i	1.19925	−	0.496745i
$7$	0.165911	+	0.400544i	0.0627083	+	0.151391i	0.952128	−	0.305701i	$-0.0988908\pi$
$7$	0.165911	+	0.400544i	0.0627083	+	0.151391i	−0.889419	+	0.457092i	$0.848891\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	5.02734	+	5.02734i	1.67578	+	1.67578i
$10$	−0.382683	−	0.923880i	−0.121015	−	0.292156i
$11$	4.66252	−	1.93128i	1.40580	−	0.582302i	0.454551	−	0.890721i	$-0.349800\pi$
$11$	4.66252	−	1.93128i	1.40580	−	0.582302i	0.951251	+	0.308419i	$0.0997998\pi$
$12$	−1.21677	+	2.93755i	−0.351252	+	0.847997i
$13$			5.61313i			1.55680i	0.627768	+	0.778401i	$0.283969\pi$
$13$			5.61313i			1.55680i	−0.627768	+	0.778401i	$0.716031\pi$
$14$	−0.400544	−	0.165911i	−0.107050	−	0.0443415i
$15$	2.24830	−	2.24830i	0.580509	−	0.580509i
$16$	−1.00000			−0.250000
$17$	3.76118	−	1.68925i	0.912219	−	0.409702i
$17$	3.76118	−	1.68925i	0.912219	−	0.409702i
$18$	−7.10973			−1.67578
$19$	−4.34549	+	4.34549i	−0.996924	+	0.996924i	−0.999995	−	0.00307125i	$-0.999022\pi$
$19$	−4.34549	+	4.34549i	−0.996924	+	0.996924i	0.00307125	+	0.999995i	$0.499022\pi$
$20$	0.923880	+	0.382683i	0.206586	+	0.0855706i
$21$		−	1.37849i		−	0.300812i
$22$	−1.93128	+	4.66252i	−0.411750	+	0.994052i
$23$	4.74603	−	1.96587i	0.989617	−	0.409913i	0.171637	−	0.985160i	$-0.445094\pi$
$23$	4.74603	−	1.96587i	0.989617	−	0.409913i	0.817979	+	0.575248i	$0.195094\pi$
$24$	−1.21677	−	2.93755i	−0.248373	−	0.599625i
$25$	−0.707107	−	0.707107i	−0.141421	−	0.141421i
$26$	−3.96908	−	3.96908i	−0.778401	−	0.778401i
$27$	−5.00061	−	12.0725i	−0.962368	−	2.32336i
$28$	0.400544	−	0.165911i	0.0756957	−	0.0313542i
$29$	−1.02107	+	2.46508i	−0.189608	+	0.457753i	−0.989884	−	0.141878i	$-0.954686\pi$
$29$	−1.02107	+	2.46508i	−0.189608	+	0.457753i	0.800277	+	0.599631i	$0.204686\pi$
$30$			3.17958i			0.580509i
$31$	2.02881	+	0.840361i	0.364385	+	0.150933i	0.557361	−	0.830270i	$-0.311814\pi$
$31$	2.02881	+	0.840361i	0.364385	+	0.150933i	−0.192976	+	0.981204i	$0.561814\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−16.0463			−2.79330
$34$	−1.46508	+	3.85403i	−0.251258	+	0.660961i
$35$	−0.433546			−0.0732826
$36$	5.02734	−	5.02734i	0.837890	−	0.837890i
$37$	1.12132	+	0.464466i	0.184344	+	0.0763578i	0.472946	−	0.881091i	$-0.343191\pi$
$37$	1.12132	+	0.464466i	0.184344	+	0.0763578i	−0.288602	+	0.957449i	$0.593191\pi$
$38$		−	6.14545i		−	0.996924i
$39$	6.82990	−	16.4888i	1.09366	−	2.64033i
$40$	−0.923880	+	0.382683i	−0.146078	+	0.0605076i
$41$	1.90602	+	4.60154i	0.297670	+	0.718639i	0.999977	+	0.00676512i	$0.00215342\pi$
$41$	1.90602	+	4.60154i	0.297670	+	0.718639i	−0.702307	+	0.711874i	$0.747847\pi$
$42$	0.974742	+	0.974742i	0.150406	+	0.150406i
$43$	0.638384	+	0.638384i	0.0973527	+	0.0973527i	0.754106	−	0.656753i	$-0.228071\pi$
$43$	0.638384	+	0.638384i	0.0973527	+	0.0973527i	−0.656753	+	0.754106i	$0.728071\pi$
$44$	−1.93128	−	4.66252i	−0.291151	−	0.702901i
$45$	−6.56854	+	2.72078i	−0.979179	+	0.405589i
$46$	−1.96587	+	4.74603i	−0.289852	+	0.699765i
$47$			5.95749i			0.868989i	0.900674	+	0.434495i	$0.143073\pi$
$47$			5.95749i			0.868989i	−0.900674	+	0.434495i	$0.856927\pi$
$48$	2.93755	+	1.21677i	0.423999	+	0.175626i
$49$	4.81684	−	4.81684i	0.688120	−	0.688120i
$50$	1.00000			0.141421
$51$	−13.1041	+	0.385748i	−1.83494	+	0.0540155i
$52$	5.61313			0.778401
$53$	0.0241321	−	0.0241321i	0.00331480	−	0.00331480i	−0.705447	−	0.708762i	$-0.749254\pi$
$53$	0.0241321	−	0.0241321i	0.00331480	−	0.00331480i	0.708762	+	0.705447i	$0.249254\pi$
$54$	12.0725	+	5.00061i	1.64286	+	0.680497i
$55$			5.04667i			0.680493i
$56$	−0.165911	+	0.400544i	−0.0221707	+	0.0535249i
$57$	18.0526	−	7.47762i	2.39112	−	0.990435i
$58$	−1.02107	−	2.46508i	−0.134073	−	0.323680i
$59$	0.275642	+	0.275642i	0.0358856	+	0.0358856i	0.724822	−	0.688936i	$-0.241922\pi$
$59$	0.275642	+	0.275642i	0.0358856	+	0.0358856i	−0.688936	+	0.724822i	$0.741922\pi$
$60$	−2.24830	−	2.24830i	−0.290255	−	0.290255i
$61$	2.72251	+	6.57273i	0.348582	+	0.841551i	0.996788	+	0.0800863i	$0.0255196\pi$
$61$	2.72251	+	6.57273i	0.348582	+	0.841551i	−0.648206	+	0.761465i	$0.724480\pi$
$62$	−2.02881	+	0.840361i	−0.257659	+	0.106726i
$63$	−1.17958	+	2.84776i	−0.148613	+	0.358784i
$64$			1.00000i			0.125000i
$65$	−5.18585	−	2.14805i	−0.643226	−	0.266433i
$66$	11.3464	−	11.3464i	1.39665	−	1.39665i
$67$	−3.27677			−0.400321			−0.200161	−	0.979763i	$-0.564146\pi$
$67$	−3.27677			−0.400321			−0.200161	+	0.979763i	$0.564146\pi$
$68$	−1.68925	−	3.76118i	−0.204851	−	0.456110i
$69$	−16.3337			−1.96635
$70$	0.306563	−	0.306563i	0.0366413	−	0.0366413i
$71$	−3.63307	−	1.50487i	−0.431166	−	0.178595i	0.156536	−	0.987672i	$-0.449967\pi$
$71$	−3.63307	−	1.50487i	−0.431166	−	0.178595i	−0.587702	+	0.809078i	$0.699967\pi$
$72$			7.10973i			0.837890i
$73$	−1.30029	+	3.13918i	−0.152188	+	0.367413i	−0.981525	−	0.191335i	$-0.938718\pi$
$73$	−1.30029	+	3.13918i	−0.152188	+	0.367413i	0.829337	+	0.558748i	$0.188718\pi$
$74$	−1.12132	+	0.464466i	−0.130351	+	0.0539931i
$75$	1.21677	+	2.93755i	0.140501	+	0.339199i
$76$	4.34549	+	4.34549i	0.498462	+	0.498462i
$77$	1.54712	+	1.54712i	0.176311	+	0.176311i
$78$	6.82990	+	16.4888i	0.773334	+	1.86699i
$79$	−12.2090	+	5.05713i	−1.37362	+	0.568972i	−0.942768	−	0.333450i	$-0.891787\pi$
$79$	−12.2090	+	5.05713i	−1.37362	+	0.568972i	−0.430852	+	0.902422i	$0.641787\pi$
$80$	0.382683	−	0.923880i	0.0427853	−	0.103293i
$81$			20.2191i			2.24657i
$82$	−4.60154	−	1.90602i	−0.508155	−	0.210485i
$83$	0.560528	−	0.560528i	0.0615259	−	0.0615259i	−0.675674	−	0.737200i	$-0.736147\pi$
$83$	0.560528	−	0.560528i	0.0615259	−	0.0615259i	0.737200	+	0.675674i	$0.236147\pi$
$84$	−1.37849			−0.150406
$85$	0.121320	+	4.12132i	0.0131590	+	0.447020i
$86$	−0.902812			−0.0973527
$87$	5.99887	−	5.99887i	0.643147	−	0.643147i
$88$	4.66252	+	1.93128i	0.497026	+	0.205875i
$89$		−	2.73418i		−	0.289823i	−0.989445	−	0.144911i	$-0.953710\pi$
$89$		−	2.73418i		−	0.289823i	0.989445	−	0.144911i	$-0.0462897\pi$
$90$	2.72078	−	6.56854i	0.286795	−	0.692384i
$91$	−2.24830	+	0.931278i	−0.235686	+	0.0976244i
$92$	−1.96587	−	4.74603i	−0.204956	−	0.494808i
$93$	−4.93720	−	4.93720i	−0.511964	−	0.511964i
$94$	−4.21258	−	4.21258i	−0.434495	−	0.434495i
$95$	−2.35176	−	5.67766i	−0.241286	−	0.582515i
$96$	−2.93755	+	1.21677i	−0.299812	+	0.124186i
$97$	4.95489	−	11.9622i	0.503093	−	1.21457i	−0.444697	−	0.895681i	$-0.646689\pi$
$97$	4.95489	−	11.9622i	0.503093	−	1.21457i	0.947791	−	0.318893i	$-0.103311\pi$
$98$			6.81204i			0.688120i
$99$	33.1492	+	13.7309i	3.33162	+	1.38000i
$100$	−0.707107	+	0.707107i	−0.0707107	+	0.0707107i
$101$	1.24718			0.124099			0.0620494	−	0.998073i	$-0.480236\pi$
$101$	1.24718			0.124099			0.0620494	+	0.998073i	$0.480236\pi$
$102$	8.99321	−	9.53874i	0.890461	−	0.944476i
$103$	8.15571			0.803606			0.401803	−	0.915726i	$-0.368384\pi$
$103$	8.15571			0.803606			0.401803	+	0.915726i	$0.368384\pi$
$104$	−3.96908	+	3.96908i	−0.389200	+	0.389200i
$105$	1.27356	+	0.527526i	0.124287	+	0.0514813i
$106$			0.0341280i			0.00331480i
$107$	1.57287	−	3.79724i	0.152055	−	0.367093i	−0.829436	−	0.558602i	$-0.811338\pi$
$107$	1.57287	−	3.79724i	0.152055	−	0.367093i	0.981491	+	0.191509i	$0.0613380\pi$
$108$	−12.0725	+	5.00061i	−1.16168	+	0.481184i
$109$	−4.90230	−	11.8352i	−0.469555	−	1.13361i	−0.964358	−	0.264600i	$-0.914760\pi$
$109$	−4.90230	−	11.8352i	−0.469555	−	1.13361i	0.494803	−	0.869005i	$-0.335240\pi$
$110$	−3.56854	−	3.56854i	−0.340247	−	0.340247i
$111$	−2.72878	−	2.72878i	−0.259005	−	0.259005i
$112$	−0.165911	−	0.400544i	−0.0156771	−	0.0378478i
$113$	16.5938	−	6.87336i	1.56101	−	0.646592i	0.575746	−	0.817629i	$-0.304712\pi$
$113$	16.5938	−	6.87336i	1.56101	−	0.646592i	0.985265	+	0.171037i	$0.0547119\pi$
$114$	−7.47762	+	18.0526i	−0.700343	+	1.69078i
$115$			5.13707i			0.479034i
$116$	2.46508	+	1.02107i	0.228877	+	0.0948038i
$117$	−28.2191	+	28.2191i	−2.60886	+	2.60886i
$118$	−0.389817			−0.0358856
$119$	1.30064	+	1.22625i	0.119229	+	0.112410i
$120$	3.17958			0.290255
$121$	10.2311	−	10.2311i	0.930096	−	0.930096i
$122$	−6.57273	−	2.72251i	−0.595067	−	0.246485i
$123$		−	15.8364i		−	1.42792i
$124$	0.840361	−	2.02881i	0.0754667	−	0.182193i
$125$	0.923880	−	0.382683i	0.0826343	−	0.0342282i
$126$	−1.17958	−	2.84776i	−0.105085	−	0.253699i
$127$	10.7285	+	10.7285i	0.952002	+	0.952002i	0.998900	−	0.0468975i	$-0.0149334\pi$
$127$	10.7285	+	10.7285i	0.952002	+	0.952002i	−0.0468975	+	0.998900i	$0.514933\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−1.09852	−	2.65205i	−0.0967190	−	0.233500i
$130$	5.18585	−	2.14805i	0.454829	−	0.188396i
$131$	3.33229	−	8.04485i	0.291143	−	0.702882i	−0.708854	−	0.705356i	$-0.750787\pi$
$131$	3.33229	−	8.04485i	0.291143	−	0.702882i	0.999997	+	0.00247343i	$0.000787318\pi$
$132$			16.0463i			1.39665i
$133$	−2.46152	−	1.01960i	−0.213441	−	0.0884102i
$134$	2.31703	−	2.31703i	0.200161	−	0.200161i
$135$	13.0672			1.12465
$136$	3.85403	+	1.46508i	0.330480	+	0.125629i
$137$	−10.8065			−0.923259			−0.461629	−	0.887073i	$-0.652735\pi$
$137$	−10.8065			−0.923259			−0.461629	+	0.887073i	$0.652735\pi$
$138$	11.5497	−	11.5497i	0.983175	−	0.983175i
$139$	−17.9161	−	7.42109i	−1.51962	−	0.629449i	−0.542108	−	0.840309i	$-0.682374\pi$
$139$	−17.9161	−	7.42109i	−1.51962	−	0.629449i	−0.977516	+	0.210860i	$0.932374\pi$
$140$			0.433546i			0.0366413i
$141$	7.24891	−	17.5004i	0.610469	−	1.47380i
$142$	3.63307	−	1.50487i	0.304880	−	0.126286i
$143$	10.8405	+	26.1713i	0.906528	+	2.18855i
$144$	−5.02734	−	5.02734i	−0.418945	−	0.418945i
$145$	−1.88669	−	1.88669i	−0.156681	−	0.156681i
$146$	−1.30029	−	3.13918i	−0.107613	−	0.259800i
$147$	−20.0107	+	8.28870i	−1.65045	+	0.683641i
$148$	0.464466	−	1.12132i	0.0381789	−	0.0921720i
$149$		−	18.6030i		−	1.52402i	−0.647566	−	0.762009i	$-0.724213\pi$
$149$		−	18.6030i		−	1.52402i	0.647566	−	0.762009i	$-0.275787\pi$
$150$	−2.93755	−	1.21677i	−0.239850	−	0.0993491i
$151$	−8.87351	+	8.87351i	−0.722116	+	0.722116i	−0.969036	−	0.246920i	$-0.920581\pi$
$151$	−8.87351	+	8.87351i	−0.722116	+	0.722116i	0.246920	+	0.969036i	$0.420581\pi$
$152$	−6.14545			−0.498462
$153$	27.4011	+	10.4163i	2.21525	+	0.842108i
$154$	−2.18796			−0.176311
$155$	−1.55278	+	1.55278i	−0.124723	+	0.124723i
$156$	−16.4888	−	6.82990i	−1.32016	−	0.546830i
$157$			14.7634i			1.17825i	0.808043	+	0.589124i	$0.200527\pi$
$157$			14.7634i			1.17825i	−0.808043	+	0.589124i	$0.799473\pi$
$158$	5.05713	−	12.2090i	0.402324	−	0.971296i
$159$	−0.100253	+	0.0415260i	−0.00795055	+	0.00329322i
$160$	0.382683	+	0.923880i	0.0302538	+	0.0730391i
$161$	1.57484	+	1.57484i	0.124114	+	0.124114i
$162$	−14.2971	−	14.2971i	−1.12328	−	1.12328i
$163$	−5.52848	−	13.3469i	−0.433024	−	1.04541i	−0.978307	−	0.207160i	$-0.933578\pi$
$163$	−5.52848	−	13.3469i	−0.433024	−	1.04541i	0.545283	−	0.838252i	$-0.316422\pi$
$164$	4.60154	−	1.90602i	0.359320	−	0.148835i
$165$	6.14065	−	14.8248i	0.478049	−	1.15411i
$166$			0.792706i			0.0615259i
$167$	−16.2497	−	6.73087i	−1.25744	−	0.520850i	−0.348319	−	0.937376i	$-0.613247\pi$
$167$	−16.2497	−	6.73087i	−1.25744	−	0.520850i	−0.909124	+	0.416526i	$0.863247\pi$
$168$	0.974742	−	0.974742i	0.0752029	−	0.0752029i
$169$	−18.5072			−1.42363
$170$	−3.00000	−	2.82843i	−0.230089	−	0.216930i
$171$	−43.6925			−3.34125
$172$	0.638384	−	0.638384i	0.0486763	−	0.0486763i
$173$	−17.4154	−	7.21371i	−1.32407	−	0.548448i	−0.395113	−	0.918633i	$-0.629294\pi$
$173$	−17.4154	−	7.21371i	−1.32407	−	0.548448i	−0.928958	+	0.370185i	$0.879294\pi$
$174$			8.48369i			0.643147i
$175$	0.165911	−	0.400544i	0.0125417	−	0.0302783i
$176$	−4.66252	+	1.93128i	−0.351450	+	0.145576i
$177$	−0.474319	−	1.14511i	−0.0356520	−	0.0860715i
$178$	1.93336	+	1.93336i	0.144911	+	0.144911i
$179$	12.1689	+	12.1689i	0.909550	+	0.909550i	0.996236	−	0.0866859i	$-0.0276277\pi$
$179$	12.1689	+	12.1689i	0.909550	+	0.909550i	−0.0866859	+	0.996236i	$0.527628\pi$
$180$	2.72078	+	6.56854i	0.202795	+	0.489590i
$181$	14.6821	−	6.08153i	1.09131	−	0.452037i	0.236848	−	0.971547i	$-0.423886\pi$
$181$	14.6821	−	6.08153i	1.09131	−	0.452037i	0.854464	+	0.519510i	$0.173886\pi$
$182$	0.931278	−	2.24830i	0.0690309	−	0.166655i
$183$		−	22.6204i		−	1.67215i
$184$	4.74603	+	1.96587i	0.349882	+	0.144926i
$185$	−0.858221	+	0.858221i	−0.0630977	+	0.0630977i
$186$	6.98226			0.511964
$187$	14.2741	−	15.1400i	1.04383	−	1.10715i
$188$	5.95749			0.434495
$189$	4.00593	−	4.00593i	0.291388	−	0.291388i
$190$	5.67766	+	2.35176i	0.411901	+	0.170615i
$191$			10.2092i			0.738710i	0.929288	+	0.369355i	$0.120421\pi$
$191$			10.2092i			0.738710i	−0.929288	+	0.369355i	$0.879579\pi$
$192$	1.21677	−	2.93755i	0.0878130	−	0.211999i
$193$	−1.78768	+	0.740482i	−0.128680	+	0.0533011i	−0.446094	−	0.894986i	$-0.647185\pi$
$193$	−1.78768	+	0.740482i	−0.128680	+	0.0533011i	0.317414	+	0.948287i	$0.397185\pi$
$194$	4.95489	+	11.9622i	0.355741	+	0.858834i
$195$	12.6200	+	12.6200i	0.903737	+	0.903737i
$196$	−4.81684	−	4.81684i	−0.344060	−	0.344060i
$197$	−2.33625	−	5.64020i	−0.166451	−	0.401848i	0.818541	−	0.574448i	$-0.194783\pi$
$197$	−2.33625	−	5.64020i	−0.166451	−	0.401848i	−0.984992	+	0.172600i	$0.944783\pi$
$198$	−33.1492	+	13.7309i	−2.35581	+	0.975810i
$199$	3.62665	−	8.75551i	0.257087	−	0.620662i	−0.741657	−	0.670780i	$-0.765960\pi$
$199$	3.62665	−	8.75551i	0.257087	−	0.620662i	0.998743	+	0.0501177i	$0.0159596\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	9.62567	+	3.98708i	0.678942	+	0.281227i
$202$	−0.881887	+	0.881887i	−0.0620494	+	0.0620494i
$203$	−1.15678			−0.0811898
$204$	0.385748	+	13.1041i	0.0270077	+	0.917468i
$205$	−4.98067			−0.347865
$206$	−5.76696	+	5.76696i	−0.401803	+	0.401803i
$207$	33.7430	+	13.9768i	2.34530	+	0.971456i
$208$		−	5.61313i		−	0.389200i
$209$	−11.8686	+	28.6533i	−0.820966	+	1.98199i
$210$	−1.27356	+	0.527526i	−0.0878841	+	0.0364028i
$211$	5.21212	+	12.5832i	0.358817	+	0.866260i	0.995467	+	0.0951077i	$0.0303196\pi$
$211$	5.21212	+	12.5832i	0.358817	+	0.866260i	−0.636650	+	0.771153i	$0.719680\pi$
$212$	−0.0241321	−	0.0241321i	−0.00165740	−	0.00165740i
$213$	8.84123	+	8.84123i	0.605791	+	0.605791i
$214$	1.57287	+	3.79724i	0.107519	+	0.259574i
$215$	−0.834089	+	0.345491i	−0.0568844	+	0.0235623i
$216$	5.00061	−	12.0725i	0.340248	−	0.821432i
$217$			0.952053i			0.0646295i
$218$	11.8352	+	4.90230i	0.801580	+	0.332025i
$219$	7.63934	−	7.63934i	0.516219	−	0.516219i
$220$	5.04667			0.340247
$221$	9.48195	+	21.1120i	0.637825	+	1.42014i
$222$	3.85908			0.259005
$223$	−5.65573	+	5.65573i	−0.378736	+	0.378736i	−0.870646	−	0.491910i	$-0.836299\pi$
$223$	−5.65573	+	5.65573i	−0.378736	+	0.378736i	0.491910	+	0.870646i	$0.336299\pi$
$224$	0.400544	+	0.165911i	0.0267625	+	0.0110854i
$225$		−	7.10973i		−	0.473982i
$226$	−6.87336	+	16.5938i	−0.457209	+	1.10380i
$227$	−13.9610	+	5.78285i	−0.926627	+	0.383821i	−0.794398	−	0.607398i	$-0.792213\pi$
$227$	−13.9610	+	5.78285i	−0.926627	+	0.383821i	−0.132229	+	0.991219i	$0.542213\pi$
$228$	−7.47762	−	18.0526i	−0.495217	−	1.19556i
$229$	11.0538	+	11.0538i	0.730457	+	0.730457i	0.970710	−	0.240253i	$-0.0772305\pi$
$229$	11.0538	+	11.0538i	0.730457	+	0.730457i	−0.240253	+	0.970710i	$0.577231\pi$
$230$	−3.63246	−	3.63246i	−0.239517	−	0.239517i
$231$	−2.66225	−	6.42725i	−0.175163	−	0.422882i
$232$	−2.46508	+	1.02107i	−0.161840	+	0.0670364i
$233$	−10.2517	+	24.7497i	−0.671608	+	1.62141i	0.107270	+	0.994230i	$0.465789\pi$
$233$	−10.2517	+	24.7497i	−0.671608	+	1.62141i	−0.778878	+	0.627176i	$0.784211\pi$
$234$		−	39.9078i		−	2.60886i
$235$	−5.50400	−	2.27983i	−0.359042	−	0.148720i
$236$	0.275642	−	0.275642i	0.0179428	−	0.0179428i
$237$	42.0179			2.72936
$238$	−1.78678	+	0.0525979i	−0.115820	+	0.00340941i
$239$	20.0977			1.30002			0.650008	−	0.759928i	$-0.274766\pi$
$239$	20.0977			1.30002			0.650008	+	0.759928i	$0.274766\pi$
$240$	−2.24830	+	2.24830i	−0.145127	+	0.145127i
$241$	−15.6571	−	6.48539i	−1.00856	−	0.417761i	−0.183633	−	0.982995i	$-0.558786\pi$
$241$	−15.6571	−	6.48539i	−1.00856	−	0.417761i	−0.824931	+	0.565234i	$0.808786\pi$
$242$			14.4689i			0.930096i
$243$	9.60021	−	23.1770i	0.615854	−	1.48680i
$244$	6.57273	−	2.72251i	0.420776	−	0.174291i
$245$	2.60685	+	6.29350i	0.166546	+	0.402077i
$246$	11.1981	+	11.1981i	0.713962	+	0.713962i
$247$	−24.3918	−	24.3918i	−1.55201	−	1.55201i
$248$	0.840361	+	2.02881i	0.0533630	+	0.128830i
$249$	−2.32861	+	0.964543i	−0.147570	+	0.0611255i
$250$	−0.382683	+	0.923880i	−0.0242030	+	0.0584313i
$251$		−	22.8890i		−	1.44474i	−0.691507	−	0.722370i	$-0.743053\pi$
$251$		−	22.8890i		−	1.44474i	0.691507	−	0.722370i	$-0.256947\pi$
$252$	2.84776	+	1.17958i	0.179392	+	0.0743066i
$253$	18.3318	−	18.3318i	1.15251	−	1.15251i
$254$	−15.1724			−0.952002
$255$	4.65833	−	12.2542i	0.291716	−	0.767388i
$256$	1.00000			0.0625000
$257$	12.0629	−	12.0629i	0.752460	−	0.752460i	−0.222477	−	0.974938i	$-0.571414\pi$
$257$	12.0629	−	12.0629i	0.752460	−	0.752460i	0.974938	+	0.222477i	$0.0714144\pi$
$258$	2.65205	+	1.09852i	0.165110	+	0.0683907i
$259$			0.526198i			0.0326963i
$260$	−2.14805	+	5.18585i	−0.133216	+	0.321613i
$261$	−17.5260	+	7.25952i	−1.08483	+	0.449353i
$262$	3.33229	+	8.04485i	0.205869	+	0.497013i
$263$	6.71303	+	6.71303i	0.413943	+	0.413943i	0.883110	−	0.469166i	$-0.155446\pi$
$263$	6.71303	+	6.71303i	0.413943	+	0.413943i	−0.469166	+	0.883110i	$0.655446\pi$
$264$	−11.3464	−	11.3464i	−0.698325	−	0.698325i
$265$	0.0130602	+	0.0315301i	0.000802282	+	0.00193688i
$266$	2.46152	−	1.01960i	0.150926	−	0.0625155i
$267$	−3.32688	+	8.03179i	−0.203602	+	0.491538i
$268$			3.27677i			0.200161i
$269$	14.4995	+	6.00590i	0.884051	+	0.366186i	0.778067	−	0.628182i	$-0.216201\pi$
$269$	14.4995	+	6.00590i	0.884051	+	0.366186i	0.105985	+	0.994368i	$0.466201\pi$
$270$	−9.23992	+	9.23992i	−0.562324	+	0.562324i
$271$	2.16929			0.131775			0.0658875	−	0.997827i	$-0.479012\pi$
$271$	2.16929			0.131775			0.0658875	+	0.997827i	$0.479012\pi$
$272$	−3.76118	+	1.68925i	−0.228055	+	0.102426i
$273$	7.73765			0.468304
$274$	7.64133	−	7.64133i	0.461629	−	0.461629i
$275$	−4.66252	−	1.93128i	−0.281160	−	0.116460i
$276$			16.3337i			0.983175i
$277$	−2.11999	+	5.11811i	−0.127378	+	0.307518i	−0.974684	−	0.223588i	$-0.928223\pi$
$277$	−2.11999	+	5.11811i	−0.127378	+	0.307518i	0.847306	+	0.531105i	$0.178223\pi$
$278$	17.9161	−	7.42109i	1.07454	−	0.445088i
$279$	5.97474	+	14.4243i	0.357698	+	0.863560i
$280$	−0.306563	−	0.306563i	−0.0183206	−	0.0183206i
$281$	−14.0868	−	14.0868i	−0.840349	−	0.840349i	0.148555	−	0.988904i	$-0.452538\pi$
$281$	−14.0868	−	14.0868i	−0.840349	−	0.840349i	−0.988904	+	0.148555i	$0.952538\pi$
$282$	7.24891	+	17.5004i	0.431666	+	1.04214i
$283$	−17.9961	+	7.45422i	−1.06976	+	0.443107i	−0.846904	−	0.531745i	$-0.821536\pi$
$283$	−17.9961	+	7.45422i	−1.06976	+	0.443107i	−0.222851	+	0.974852i	$0.571536\pi$
$284$	−1.50487	+	3.63307i	−0.0892974	+	0.215583i
$285$			19.5400i			1.15745i
$286$	−26.1713	−	10.8405i	−1.54754	−	0.641012i
$287$	−1.52689	+	1.52689i	−0.0901294	+	0.0901294i
$288$	7.10973			0.418945
$289$	11.2929	−	12.7071i	0.664288	−	0.747477i
$290$	2.66818			0.156681
$291$	−29.1105	+	29.1105i	−1.70649	+	1.70649i
$292$	3.13918	+	1.30029i	0.183707	+	0.0760938i
$293$		−	4.29544i		−	0.250942i	−0.992097	−	0.125471i	$-0.959956\pi$
$293$		−	4.29544i		−	0.250942i	0.992097	−	0.125471i	$-0.0400443\pi$
$294$	8.28870	−	20.0107i	0.483407	−	1.16705i
$295$	−0.360144	+	0.149177i	−0.0209684	+	0.00868540i
$296$	0.464466	+	1.12132i	0.0269965	+	0.0651754i
$297$	−46.6308	−	46.6308i	−2.70580	−	2.70580i
$298$	13.1543	+	13.1543i	0.762009	+	0.762009i
$299$	11.0347	+	26.6401i	0.638152	+	1.54064i
$300$	2.93755	−	1.21677i	0.169599	−	0.0702504i
$301$	−0.149786	+	0.361616i	−0.00863353	+	0.0208432i
$302$		−	12.5490i		−	0.722116i
$303$	−3.66364	−	1.51753i	−0.210471	−	0.0871798i
$304$	4.34549	−	4.34549i	0.249231	−	0.249231i
$305$	−7.11427			−0.407362
$306$	−26.7410	+	12.0101i	−1.52868	+	0.686571i
$307$	15.4654			0.882658			0.441329	−	0.897345i	$-0.354507\pi$
$307$	15.4654			0.882658			0.441329	+	0.897345i	$0.354507\pi$
$308$	1.54712	−	1.54712i	0.0881555	−	0.0881555i
$309$	−23.9578	−	9.92365i	−1.36291	−	0.564537i
$310$		−	2.19597i		−	0.124723i
$311$	4.34992	−	10.5016i	0.246661	−	0.595493i	−0.751255	−	0.660012i	$-0.770551\pi$
$311$	4.34992	−	10.5016i	0.246661	−	0.595493i	0.997916	+	0.0645189i	$0.0205513\pi$
$312$	16.4888	−	6.82990i	0.933496	−	0.386667i
$313$	−3.27922	−	7.91675i	−0.185353	−	0.447481i	0.803702	−	0.595032i	$-0.202861\pi$
$313$	−3.27922	−	7.91675i	−0.185353	−	0.447481i	−0.989054	+	0.147551i	$0.952861\pi$
$314$	−10.4393	−	10.4393i	−0.589124	−	0.589124i
$315$	−2.17958	−	2.17958i	−0.122805	−	0.122805i
$316$	5.05713	+	12.2090i	0.284486	+	0.686810i
$317$	−5.48112	+	2.27035i	−0.307850	+	0.127516i	−0.531260	−	0.847209i	$-0.678281\pi$
$317$	−5.48112	+	2.27035i	−0.307850	+	0.127516i	0.223410	+	0.974725i	$0.428281\pi$
$318$	0.0415260	−	0.100253i	0.00232866	−	0.00562189i
$319$			13.4654i			0.753919i
$320$	−0.923880	−	0.382683i	−0.0516464	−	0.0213927i
$321$	−9.24076	+	9.24076i	−0.515769	+	0.515769i
$322$	−2.22715			−0.124114
$323$	−9.00355	+	23.6848i	−0.500971	+	1.31786i
$324$	20.2191			1.12328
$325$	3.96908	−	3.96908i	0.220165	−	0.220165i
$326$	13.3469	+	5.52848i	0.739218	+	0.306194i
$327$			40.7314i			2.25245i
$328$	−1.90602	+	4.60154i	−0.105242	+	0.254077i
$329$	−2.38624	+	0.988411i	−0.131557	+	0.0544929i
$330$	6.14065	+	14.8248i	0.338032	+	0.816081i
$331$	11.6200	+	11.6200i	0.638693	+	0.638693i	0.950233	−	0.311540i	$-0.100845\pi$
$331$	11.6200	+	11.6200i	0.638693	+	0.638693i	−0.311540	+	0.950233i	$0.600845\pi$
$332$	−0.560528	−	0.560528i	−0.0307630	−	0.0307630i
$333$	3.30223	+	7.97229i	0.180961	+	0.436879i
$334$	16.2497	−	6.73087i	0.889147	−	0.368297i
$335$	1.25397	−	3.02734i	0.0685114	−	0.165401i
$336$			1.37849i			0.0752029i
$337$	2.74728	+	1.13796i	0.149654	+	0.0619887i	0.456253	−	0.889850i	$-0.349191\pi$
$337$	2.74728	+	1.13796i	0.149654	+	0.0619887i	−0.306599	+	0.951839i	$0.599191\pi$
$338$	13.0866	−	13.0866i	0.711815	−	0.711815i
$339$	−57.1083			−3.10170
$340$	4.12132	−	0.121320i	0.223510	−	0.00657952i
$341$	11.0823			0.600142
$342$	30.8953	−	30.8953i	1.67063	−	1.67063i
$343$	5.53233	+	2.29156i	0.298718	+	0.123733i
$344$			0.902812i			0.0486763i
$345$	6.25065	−	15.0904i	0.336524	−	0.812440i
$346$	17.4154	−	7.21371i	0.936259	−	0.387811i
$347$	−2.71461	−	6.55366i	−0.145728	−	0.351819i	0.834114	−	0.551592i	$-0.185979\pi$
$347$	−2.71461	−	6.55366i	−0.145728	−	0.351819i	−0.979842	+	0.199773i	$0.935979\pi$
$348$	−5.99887	−	5.99887i	−0.321573	−	0.321573i
$349$	−14.1387	−	14.1387i	−0.756825	−	0.756825i	0.218918	−	0.975743i	$-0.429747\pi$
$349$	−14.1387	−	14.1387i	−0.756825	−	0.756825i	−0.975743	+	0.218918i	$0.929747\pi$
$350$	0.165911	+	0.400544i	0.00886830	+	0.0214100i
$351$	67.7647	−	28.0691i	3.61701	−	1.49822i
$352$	1.93128	−	4.66252i	0.102937	−	0.248513i
$353$		−	3.74153i		−	0.199142i	−0.995030	−	0.0995708i	$-0.968253\pi$
$353$		−	3.74153i		−	0.199142i	0.995030	−	0.0995708i	$-0.0317470\pi$
$354$	1.14511	+	0.474319i	0.0608618	+	0.0252098i
$355$	2.78063	−	2.78063i	0.147580	−	0.147580i
$356$	−2.73418			−0.144911
$357$	−2.32861	−	5.18475i	−0.123243	−	0.274406i
$358$	−17.2095			−0.909550
$359$	0.411759	−	0.411759i	0.0217318	−	0.0217318i	−0.696157	−	0.717889i	$-0.745108\pi$
$359$	0.411759	−	0.411759i	0.0217318	−	0.0217318i	0.717889	+	0.696157i	$0.245108\pi$
$360$	−6.56854	−	2.72078i	−0.346192	−	0.143398i
$361$		−	18.7666i		−	0.987715i
$362$	−6.08153	+	14.6821i	−0.319638	+	0.771675i
$363$	−42.5031	+	17.6054i	−2.23083	+	0.924041i
$364$	0.931278	+	2.24830i	0.0488122	+	0.117843i
$365$	−2.40262	−	2.40262i	−0.125759	−	0.125759i
$366$	15.9950	+	15.9950i	0.836074	+	0.836074i
$367$	−10.5677	−	25.5126i	−0.551628	−	1.33175i	−0.916255	−	0.400594i	$-0.868804\pi$
$367$	−10.5677	−	25.5126i	−0.551628	−	1.33175i	0.364627	−	0.931154i	$-0.381196\pi$
$368$	−4.74603	+	1.96587i	−0.247404	+	0.102478i
$369$	−13.5513	+	32.7157i	−0.705452	+	1.70311i
$370$		−	1.21371i		−	0.0630977i
$371$	0.0136697	+	0.00566219i	0.000709698	+	0.000293966i
$372$	−4.93720	+	4.93720i	−0.255982	+	0.255982i
$373$	33.5706			1.73822			0.869109	−	0.494621i	$-0.164693\pi$
$373$	33.5706			1.73822			0.869109	+	0.494621i	$0.164693\pi$
$374$	0.612264	+	20.7989i	0.0316594	+	1.07549i
$375$	−3.17958			−0.164193
$376$	−4.21258	+	4.21258i	−0.217247	+	0.217247i
$377$	−13.8368	−	5.73138i	−0.712630	−	0.295181i
$378$			5.66524i			0.291388i
$379$	−8.55128	+	20.6446i	−0.439250	+	1.06044i	0.536958	+	0.843609i	$0.319573\pi$
$379$	−8.55128	+	20.6446i	−0.439250	+	1.06044i	−0.976208	+	0.216835i	$0.930427\pi$
$380$	−5.67766	+	2.35176i	−0.291258	+	0.120643i
$381$	−18.4614	−	44.5697i	−0.945805	−	2.28338i
$382$	−7.21898	−	7.21898i	−0.369355	−	0.369355i
$383$	−20.3162	−	20.3162i	−1.03811	−	1.03811i	−0.999245	−	0.0388641i	$-0.987626\pi$
$383$	−20.3162	−	20.3162i	−1.03811	−	1.03811i	−0.0388641	−	0.999245i	$-0.512374\pi$
$384$	1.21677	+	2.93755i	0.0620932	+	0.149906i
$385$	−2.02141	+	0.837297i	−0.103021	+	0.0426726i
$386$	0.740482	−	1.78768i	0.0376896	−	0.0909906i
$387$			6.41875i			0.326283i
$388$	−11.9622	−	4.95489i	−0.607287	−	0.251547i
$389$	14.2668	−	14.2668i	0.723355	−	0.723355i	−0.245932	−	0.969287i	$-0.579094\pi$
$389$	14.2668	−	14.2668i	0.723355	−	0.723355i	0.969287	+	0.245932i	$0.0790940\pi$
$390$	−17.8474			−0.903737
$391$	14.5298	−	15.4112i	0.734805	−	0.779379i
$392$	6.81204			0.344060
$393$	−19.5775	+	19.5775i	−0.987555	+	0.987555i
$394$	5.64020	+	2.33625i	0.284149	+	0.117698i
$395$		−	13.2149i		−	0.664915i
$396$	13.7309	−	33.1492i	0.690002	−	1.66581i
$397$	19.4621	−	8.06147i	0.976775	−	0.404593i	0.163545	−	0.986536i	$-0.447707\pi$
$397$	19.4621	−	8.06147i	0.976775	−	0.404593i	0.813230	+	0.581942i	$0.197707\pi$
$398$	3.62665	+	8.75551i	0.181788	+	0.438874i
$399$	5.99023	+	5.99023i	0.299887	+	0.299887i
$400$	0.707107	+	0.707107i	0.0353553	+	0.0353553i
$401$	−2.01999	−	4.87669i	−0.100874	−	0.243530i	0.865383	−	0.501110i	$-0.167075\pi$
$401$	−2.01999	−	4.87669i	−0.100874	−	0.243530i	−0.966257	+	0.257580i	$0.917075\pi$
$402$	−9.62567	+	3.98708i	−0.480085	+	0.198858i
$403$	−4.71705	+	11.3880i	−0.234973	+	0.567275i
$404$		−	1.24718i		−	0.0620494i
$405$	−18.6800	−	7.73751i	−0.928217	−	0.384480i
$406$	0.817965	−	0.817965i	0.0405949	−	0.0405949i
$407$	6.12519			0.303614
$408$	−9.53874	−	8.99321i	−0.472238	−	0.445230i
$409$	−29.6056			−1.46390			−0.731952	−	0.681356i	$-0.761390\pi$
$409$	−29.6056			−1.46390			−0.731952	+	0.681356i	$0.761390\pi$
$410$	3.52186	−	3.52186i	0.173932	−	0.173932i
$411$	31.7445	+	13.1490i	1.56584	+	0.648593i
$412$		−	8.15571i		−	0.401803i
$413$	−0.0646748	+	0.156139i	−0.00318244	+	0.00768309i
$414$	−33.7430	+	13.9768i	−1.65838	+	0.686923i
$415$	0.303356	+	0.732365i	0.0148911	+	0.0359504i
$416$	3.96908	+	3.96908i	0.194600	+	0.194600i
$417$	43.5997	+	43.5997i	2.13508	+	2.13508i
$418$	−11.8686	−	28.6533i	−0.580511	−	1.40148i
$419$	30.8284	−	12.7695i	1.50606	−	0.623832i	0.531323	−	0.847169i	$-0.321695\pi$
$419$	30.8284	−	12.7695i	1.50606	−	0.623832i	0.974741	+	0.223337i	$0.0716950\pi$
$420$	0.527526	−	1.27356i	0.0257407	−	0.0621434i
$421$		−	13.7226i		−	0.668799i	−0.942431	−	0.334400i	$-0.891466\pi$
$421$		−	13.7226i		−	0.668799i	0.942431	−	0.334400i	$-0.108534\pi$
$422$	−12.5832	−	5.21212i	−0.612539	−	0.253722i
$423$	−29.9503	+	29.9503i	−1.45623	+	1.45623i
$424$	0.0341280			0.00165740
$425$	−3.85403	−	1.46508i	−0.186948	−	0.0710666i
$426$	−12.5034			−0.605791
$427$	−2.18097	+	2.18097i	−0.105545	+	0.105545i
$428$	−3.79724	−	1.57287i	−0.183547	−	0.0760275i
$429$		−	90.0699i		−	4.34862i
$430$	0.345491	−	0.834089i	0.0166611	−	0.0402234i
$431$	11.3125	−	4.68579i	0.544903	−	0.225706i	−0.0932131	−	0.995646i	$-0.529714\pi$
$431$	11.3125	−	4.68579i	0.544903	−	0.225706i	0.638117	+	0.769940i	$0.279714\pi$
$432$	5.00061	+	12.0725i	0.240592	+	0.580840i
$433$	−20.7523	−	20.7523i	−0.997291	−	0.997291i	0.00270549	−	0.999996i	$-0.499139\pi$
$433$	−20.7523	−	20.7523i	−0.997291	−	0.997291i	−0.999996	+	0.00270549i	$0.999139\pi$
$434$	−0.673203	−	0.673203i	−0.0323148	−	0.0323148i
$435$	3.24657	+	7.83791i	0.155661	+	0.375799i
$436$	−11.8352	+	4.90230i	−0.566803	+	0.234777i
$437$	−12.0812	+	29.1665i	−0.577921	+	1.39522i
$438$			10.8037i			0.516219i
$439$	1.97810	+	0.819355i	0.0944095	+	0.0391057i	0.429388	−	0.903120i	$-0.358729\pi$
$439$	1.97810	+	0.819355i	0.0944095	+	0.0391057i	−0.334979	+	0.942226i	$0.608729\pi$
$440$	−3.56854	+	3.56854i	−0.170123	+	0.170123i
$441$	48.4318			2.30627
$442$	−21.6332	−	8.22365i	−1.02898	−	0.391159i
$443$	1.26810			0.0602493			0.0301247	−	0.999546i	$-0.490410\pi$
$443$	1.26810			0.0602493			0.0301247	+	0.999546i	$0.490410\pi$
$444$	−2.72878	+	2.72878i	−0.129502	+	0.129502i
$445$	2.52605	+	1.04633i	0.119746	+	0.0496006i
$446$		−	7.99841i		−	0.378736i
$447$	−22.6356	+	54.6473i	−1.07063	+	2.58473i
$448$	−0.400544	+	0.165911i	−0.0189239	+	0.00783854i
$449$	−1.18345	−	2.85710i	−0.0558503	−	0.134835i	0.893491	−	0.449081i	$-0.148248\pi$
$449$	−1.18345	−	2.85710i	−0.0558503	−	0.134835i	−0.949342	+	0.314246i	$0.898248\pi$
$450$	5.02734	+	5.02734i	0.236991	+	0.236991i
$451$	17.7737	+	17.7737i	0.836930	+	0.836930i
$452$	−6.87336	−	16.5938i	−0.323296	−	0.780505i
$453$	36.8634	−	15.2693i	1.73199	−	0.717415i
$454$	5.78285	−	13.9610i	0.271403	−	0.655224i
$455$		−	2.43355i		−	0.114086i
$456$	18.0526	+	7.47762i	0.845389	+	0.350172i
$457$	−7.46615	+	7.46615i	−0.349252	+	0.349252i	−0.859831	−	0.510579i	$-0.829431\pi$
$457$	−7.46615	+	7.46615i	−0.349252	+	0.349252i	0.510579	+	0.859831i	$0.329431\pi$
$458$	−15.6325			−0.730457
$459$	−39.2017	−	36.9597i	−1.82978	−	1.72513i
$460$	5.13707			0.239517
$461$	−14.1820	+	14.1820i	−0.660522	+	0.660522i	−0.955503	−	0.294981i	$-0.904687\pi$
$461$	−14.1820	+	14.1820i	−0.660522	+	0.660522i	0.294981	+	0.955503i	$0.404687\pi$
$462$	6.42725	+	2.66225i	0.299023	+	0.123859i
$463$			1.96882i			0.0914986i	0.998953	+	0.0457493i	$0.0145675\pi$
$463$			1.96882i			0.0914986i	−0.998953	+	0.0457493i	$0.985432\pi$
$464$	1.02107	−	2.46508i	0.0474019	−	0.114438i
$465$	6.45077	−	2.67200i	0.299147	−	0.123911i
$466$	−10.2517	−	24.7497i	−0.474899	−	1.14651i
$467$	−17.1719	−	17.1719i	−0.794622	−	0.794622i	0.187620	−	0.982242i	$-0.439923\pi$
$467$	−17.1719	−	17.1719i	−0.794622	−	0.794622i	−0.982242	+	0.187620i	$0.939923\pi$
$468$	28.2191	+	28.2191i	1.30443	+	1.30443i
$469$	−0.543651	−	1.31249i	−0.0251035	−	0.0606051i
$470$	5.50400	−	2.27983i	0.253881	−	0.105161i
$471$	17.9637	−	43.3682i	0.827724	−	1.99830i
$472$			0.389817i			0.0179428i
$473$	4.20937	+	1.74358i	0.193547	+	0.0801699i
$474$	−29.7112	+	29.7112i	−1.36468	+	1.36468i
$475$	6.14545			0.281973
$476$	1.22625	−	1.30064i	0.0562052	−	0.0596146i
$477$	0.242641			0.0111098
$478$	−14.2113	+	14.2113i	−0.650008	+	0.650008i
$479$	30.4291	+	12.6041i	1.39034	+	0.575898i	0.947226	−	0.320568i	$-0.103874\pi$
$479$	30.4291	+	12.6041i	1.39034	+	0.575898i	0.443114	+	0.896465i	$0.353874\pi$
$480$		−	3.17958i		−	0.145127i
$481$	−2.60711	+	6.29411i	−0.118874	+	0.286987i
$482$	15.6571	−	6.48539i	0.713162	−	0.295401i
$483$	−2.70994	−	6.54237i	−0.123307	−	0.297688i
$484$	−10.2311	−	10.2311i	−0.465048	−	0.465048i
$485$	9.15545	+	9.15545i	0.415727	+	0.415727i
$486$	9.60021	+	23.1770i	0.435474	+	1.05133i
$487$	−4.68569	+	1.94088i	−0.212329	+	0.0879496i	−0.486313	−	0.873785i	$-0.661658\pi$
$487$	−4.68569	+	1.94088i	−0.212329	+	0.0879496i	0.273984	+	0.961734i	$0.411658\pi$
$488$	−2.72251	+	6.57273i	−0.123242	+	0.297533i
$489$			45.9342i			2.07722i
$490$	−6.29350	−	2.60685i	−0.284311	−	0.117766i
$491$	10.8893	−	10.8893i	0.491427	−	0.491427i	−0.417329	−	0.908756i	$-0.637034\pi$
$491$	10.8893	−	10.8893i	0.491427	−	0.491427i	0.908756	+	0.417329i	$0.137034\pi$
$492$	−15.8364			−0.713962
$493$	0.323704	+	10.9964i	0.0145789	+	0.495254i
$494$	34.4952			1.55201
$495$	−25.3713	+	25.3713i	−1.14036	+	1.14036i
$496$	−2.02881	−	0.840361i	−0.0910963	−	0.0377333i
$497$		−	1.70488i		−	0.0764741i
$498$	0.964543	−	2.32861i	0.0432222	−	0.104348i
$499$	16.2218	−	6.71929i	0.726188	−	0.300797i	0.0112035	−	0.999937i	$-0.496434\pi$
$499$	16.2218	−	6.71929i	0.726188	−	0.300797i	0.714984	+	0.699140i	$0.246434\pi$
$500$	−0.382683	−	0.923880i	−0.0171141	−	0.0413171i
$501$	39.5445	+	39.5445i	1.76672	+	1.76672i
$502$	16.1850	+	16.1850i	0.722370	+	0.722370i
$503$	−5.85455	−	14.1341i	−0.261041	−	0.630210i	0.737962	−	0.674842i	$-0.235788\pi$
$503$	−5.85455	−	14.1341i	−0.261041	−	0.630210i	−0.999003	+	0.0446325i	$0.985788\pi$
$504$	−2.84776	+	1.17958i	−0.126849	+	0.0525427i
$505$	−0.477274	+	1.15224i	−0.0212384	+	0.0512740i
$506$			25.9251i			1.15251i
$507$	54.3658	+	22.5190i	2.41447	+	1.00011i
$508$	10.7285	−	10.7285i	0.476001	−	0.476001i
$509$	27.0994			1.20116			0.600580	−	0.799565i	$-0.294937\pi$
$509$	27.0994			1.20116			0.600580	+	0.799565i	$0.294937\pi$
$510$	5.37109	+	11.9590i	0.237836	+	0.529552i
$511$	−1.47311			−0.0651666
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	74.1912	+	30.7310i	3.27562	+	1.35681i
$514$			17.0595i			0.752460i
$515$	−3.12106	+	7.53490i	−0.137530	+	0.332027i
$516$	−2.65205	+	1.09852i	−0.116750	+	0.0483595i
$517$	11.5056	+	27.7769i	0.506014	+	1.22163i
$518$	−0.372078	−	0.372078i	−0.0163482	−	0.0163482i
$519$	42.3812	+	42.3812i	1.86033	+	1.86033i
$520$	−2.14805	−	5.18585i	−0.0941982	−	0.227415i
$521$	−11.7666	+	4.87388i	−0.515503	+	0.213529i	−0.625241	−	0.780432i	$-0.714999\pi$
$521$	−11.7666	+	4.87388i	−0.515503	+	0.213529i	0.109737	+	0.993961i	$0.464999\pi$
$522$	7.25952	−	17.5260i	0.317740	−	0.767093i
$523$		−	13.5049i		−	0.590528i	−0.955416	−	0.295264i	$-0.904592\pi$
$523$		−	13.5049i		−	0.590528i	0.955416	−	0.295264i	$-0.0954076\pi$
$524$	−8.04485	−	3.33229i	−0.351441	−	0.145572i
$525$	−0.974742	+	0.974742i	−0.0425412	+	0.0425412i
$526$	−9.49366			−0.413943
$527$	9.05029	−	0.266416i	0.394237	−	0.0116053i
$528$	16.0463			0.698325
$529$	2.39674	−	2.39674i	0.104206	−	0.104206i
$530$	−0.0315301	−	0.0130602i	−0.00136958	−	0.000567299i
$531$			2.77150i			0.120273i
$532$	−1.01960	+	2.46152i	−0.0442051	+	0.106721i
$533$	−25.8290	+	10.6987i	−1.11878	+	0.463413i
$534$	−3.32688	−	8.03179i	−0.143968	−	0.347570i
$535$	2.90628	+	2.90628i	0.125650	+	0.125650i
$536$	−2.31703	−	2.31703i	−0.100080	−	0.100080i
$537$	−20.9400	−	50.5537i	−0.903629	−	2.18155i
$538$	−14.4995	+	6.00590i	−0.625119	+	0.258933i
$539$	13.1559	−	31.7612i	0.566666	−	1.36805i
$540$		−	13.0672i		−	0.562324i
$541$	−37.5819	−	15.5669i	−1.61577	−	0.669275i	−0.622241	−	0.782826i	$-0.713778\pi$
$541$	−37.5819	−	15.5669i	−1.61577	−	0.669275i	−0.993532	+	0.113551i	$0.963778\pi$
$542$	−1.53392	+	1.53392i	−0.0658875	+	0.0658875i
$543$	−50.5293			−2.16842
$544$	1.46508	−	3.85403i	0.0628146	−	0.165240i
$545$	12.8103			0.548734
$546$	−5.47135	+	5.47135i	−0.234152	+	0.234152i
$547$	15.2150	+	6.30228i	0.650549	+	0.269466i	0.683455	−	0.729992i	$-0.260476\pi$
$547$	15.2150	+	6.30228i	0.650549	+	0.269466i	−0.0329067	+	0.999458i	$0.510476\pi$
$548$			10.8065i			0.461629i
$549$	−19.3563	+	46.7303i	−0.826108	+	1.99440i
$550$	4.66252	−	1.93128i	0.198810	−	0.0823500i
$551$	−6.27492	−	15.1490i	−0.267321	−	0.645369i
$552$	−11.5497	−	11.5497i	−0.491588	−	0.491588i
$553$	−4.05121	−	4.05121i	−0.172275	−	0.172275i
$554$	−2.11999	−	5.11811i	−0.0900698	−	0.217448i
$555$	3.56533	−	1.47681i	0.151340	−	0.0626870i
$556$	−7.42109	+	17.9161i	−0.314725	+	0.759812i
$557$		−	15.8158i		−	0.670138i	−0.942194	−	0.335069i	$-0.891240\pi$
$557$		−	15.8158i		−	0.670138i	0.942194	−	0.335069i	$-0.108760\pi$
$558$	−14.4243	−	5.97474i	−0.610629	−	0.252931i
$559$	−3.58333	+	3.58333i	−0.151559	+	0.151559i
$560$	0.433546			0.0183206
$561$	−60.3530	+	27.1062i	−2.54810	+	1.14442i
$562$	19.9218			0.840349
$563$	12.6018	−	12.6018i	0.531103	−	0.531103i	−0.389798	−	0.920900i	$-0.627455\pi$
$563$	12.6018	−	12.6018i	0.531103	−	0.531103i	0.920900	+	0.389798i	$0.127455\pi$
$564$	−17.5004	−	7.24891i	−0.736901	−	0.305234i
$565$			17.9610i			0.755623i
$566$	7.45422	−	17.9961i	0.313324	−	0.756431i
$567$	−8.09863	+	3.35456i	−0.340111	+	0.140878i
$568$	−1.50487	−	3.63307i	−0.0631428	−	0.152440i
$569$	−24.2079	−	24.2079i	−1.01485	−	1.01485i	−0.999888	−	0.0149588i	$-0.995238\pi$
$569$	−24.2079	−	24.2079i	−1.01485	−	1.01485i	−0.0149588	−	0.999888i	$-0.504762\pi$
$570$	−13.8168	−	13.8168i	−0.578724	−	0.578724i
$571$	−1.09381	−	2.64069i	−0.0457745	−	0.110509i	0.899338	−	0.437253i	$-0.144049\pi$
$571$	−1.09381	−	2.64069i	−0.0457745	−	0.110509i	−0.945113	+	0.326744i	$0.894049\pi$
$572$	26.1713	−	10.8405i	1.09428	−	0.453264i
$573$	12.4222	−	29.9899i	0.518947	−	1.25285i
$574$		−	2.15935i		−	0.0901294i
$575$	−4.74603	−	1.96587i	−0.197923	−	0.0819825i
$576$	−5.02734	+	5.02734i	−0.209472	+	0.209472i
$577$	1.44744			0.0602577			0.0301288	−	0.999546i	$-0.490408\pi$
$577$	1.44744			0.0602577			0.0301288	+	0.999546i	$0.490408\pi$
$578$	1.00000	+	16.9706i	0.0415945	+	0.705882i
$579$	6.15240			0.255685
$580$	−1.88669	+	1.88669i	−0.0783404	+	0.0783404i
$581$	0.317514	+	0.131518i	0.0131727	+	0.00545630i
$582$		−	41.1684i		−	1.70649i
$583$	0.0659106	−	0.159122i	0.00272974	−	0.00659017i
$584$	−3.13918	+	1.30029i	−0.129900	+	0.0538064i
$585$	−15.2721	−	36.8700i	−0.631422	−	1.52439i
$586$	3.03734	+	3.03734i	0.125471	+	0.125471i
$587$	−29.6925	−	29.6925i	−1.22554	−	1.22554i	−0.965633	−	0.259908i	$-0.916308\pi$
$587$	−29.6925	−	29.6925i	−1.22554	−	1.22554i	−0.259908	−	0.965633i	$-0.583692\pi$
$588$	8.28870	+	20.0107i	0.341820	+	0.825227i
$589$	−12.4680	+	5.16440i	−0.513733	+	0.212795i
$590$	0.149177	−	0.360144i	0.00614150	−	0.0148269i
$591$			19.4111i			0.798464i
$592$	−1.12132	−	0.464466i	−0.0460860	−	0.0190894i
$593$	−21.8918	+	21.8918i	−0.898989	+	0.898989i	−0.995347	−	0.0963581i	$-0.969281\pi$
$593$	−21.8918	+	21.8918i	−0.898989	+	0.898989i	0.0963581	+	0.995347i	$0.469281\pi$
$594$	65.9460			2.70580
$595$	−1.63064	+	0.732365i	−0.0668498	+	0.0300240i
$596$	−18.6030			−0.762009
$597$	−21.3069	+	21.3069i	−0.872035	+	0.872035i
$598$	−26.6401	−	11.0347i	−1.08939	−	0.451242i
$599$			25.0444i			1.02328i	0.859198	+	0.511642i	$0.170963\pi$
$599$			25.0444i			1.02328i	−0.859198	+	0.511642i	$0.829037\pi$
$600$	−1.21677	+	2.93755i	−0.0496745	+	0.119925i
$601$	36.9233	−	15.2941i	1.50613	−	0.623861i	0.531377	−	0.847135i	$-0.321675\pi$
$601$	36.9233	−	15.2941i	1.50613	−	0.623861i	0.974756	+	0.223274i	$0.0716746\pi$
$602$	−0.149786	−	0.361616i	−0.00610483	−	0.0147384i
$603$	−16.4734	−	16.4734i	−0.670850	−	0.670850i
$604$	8.87351	+	8.87351i	0.361058	+	0.361058i
$605$	5.53701	+	13.3675i	0.225111	+	0.543467i
$606$	3.66364	−	1.51753i	0.148825	−	0.0616455i
$607$	−6.44562	+	15.5611i	−0.261620	+	0.631606i	−0.999039	−	0.0438293i	$-0.986044\pi$
$607$	−6.44562	+	15.5611i	−0.261620	+	0.631606i	0.737419	+	0.675435i	$0.236044\pi$
$608$			6.14545i			0.249231i
$609$	3.39809	+	1.40753i	0.137698	+	0.0570362i
$610$	5.03055	−	5.03055i	0.203681	−	0.203681i
$611$	−33.4401			−1.35284
$612$	10.4163	−	27.4011i	0.421054	−	1.10762i
$613$	8.76471			0.354003			0.177002	−	0.984211i	$-0.443360\pi$
$613$	8.76471			0.354003			0.177002	+	0.984211i	$0.443360\pi$
$614$	−10.9357	+	10.9357i	−0.441329	+	0.441329i
$615$	14.6310	+	6.06034i	0.589977	+	0.244377i
$616$			2.18796i			0.0881555i
$617$	3.14929	−	7.60305i	0.126785	−	0.306087i	−0.847723	−	0.530440i	$-0.822027\pi$
$617$	3.14929	−	7.60305i	0.126785	−	0.306087i	0.974508	+	0.224353i	$0.0720268\pi$
$618$	23.9578	−	9.92365i	0.963724	−	0.399188i
$619$	−2.89480	−	6.98868i	−0.116352	−	0.280899i	0.854965	−	0.518685i	$-0.173578\pi$
$619$	−2.89480	−	6.98868i	−0.116352	−	0.280899i	−0.971317	+	0.237786i	$0.923578\pi$
$620$	1.55278	+	1.55278i	0.0623613	+	0.0623613i
$621$	−47.4661	−	47.4661i	−1.90475	−	1.90475i
$622$	4.34992	+	10.5016i	0.174416	+	0.421077i
$623$	1.09516	−	0.453630i	0.0438766	−	0.0181743i
$624$	−6.82990	+	16.4888i	−0.273415	+	0.660082i
$625$			1.00000i			0.0400000i
$626$	7.91675	+	3.27922i	0.316417	+	0.131064i
$627$	69.7290	−	69.7290i	2.78471	−	2.78471i
$628$	14.7634			0.589124
$629$	5.00208	−	0.147248i	0.199446	−	0.00587114i
$630$	3.08239			0.122805
$631$	−20.7927	+	20.7927i	−0.827745	+	0.827745i	−0.987204	−	0.159460i	$-0.949025\pi$
$631$	−20.7927	+	20.7927i	−0.827745	+	0.827745i	0.159460	+	0.987204i	$0.449025\pi$
$632$	−12.2090	−	5.05713i	−0.485648	−	0.201162i
$633$		−	43.3056i		−	1.72124i
$634$	2.27035	−	5.48112i	0.0901673	−	0.217683i
$635$	−14.0175	+	5.80623i	−0.556267	+	0.230413i
$636$	0.0415260	+	0.100253i	0.00164661	+	0.00397527i
$637$	27.0375	+	27.0375i	1.07127	+	1.07127i
$638$	−9.52149	−	9.52149i	−0.376959	−	0.376959i
$639$	−10.6992	−	25.8301i	−0.423253	−	1.02182i
$640$	0.923880	−	0.382683i	0.0365195	−	0.0151269i
$641$	−17.4083	+	42.0273i	−0.687585	+	1.65998i	0.0620050	+	0.998076i	$0.480251\pi$
$641$	−17.4083	+	42.0273i	−0.687585	+	1.65998i	−0.749590	+	0.661902i	$0.769749\pi$
$642$		−	13.0684i		−	0.515769i
$643$	−13.8772	−	5.74812i	−0.547263	−	0.226684i	0.0918824	−	0.995770i	$-0.470712\pi$
$643$	−13.8772	−	5.74812i	−0.547263	−	0.226684i	−0.639145	+	0.769086i	$0.720712\pi$
$644$	1.57484	−	1.57484i	0.0620572	−	0.0620572i
$645$	2.87056			0.113028
$646$	−10.3812	−	23.1141i	−0.408442	−	0.909413i
$647$	16.5065			0.648938			0.324469	−	0.945896i	$-0.394814\pi$
$647$	16.5065			0.648938			0.324469	+	0.945896i	$0.394814\pi$
$648$	−14.2971	+	14.2971i	−0.561641	+	0.561641i
$649$	1.81753	+	0.752845i	0.0713443	+	0.0295518i
$650$			5.61313i			0.220165i
$651$	1.15843	−	2.79670i	0.0454025	−	0.109611i
$652$	−13.3469	+	5.52848i	−0.522706	+	0.216512i
$653$	16.4862	+	39.8013i	0.645156	+	1.55755i	0.819636	+	0.572884i	$0.194176\pi$
$653$	16.4862	+	39.8013i	0.645156	+	1.55755i	−0.174480	+	0.984661i	$0.555824\pi$
$654$	−28.8015	−	28.8015i	−1.12623	−	1.12623i
$655$	6.15727	+	6.15727i	0.240584	+	0.240584i
$656$	−1.90602	−	4.60154i	−0.0744175	−	0.179660i
$657$	−22.3187	+	9.24472i	−0.870737	+	0.360671i
$658$	0.988411	−	2.38624i	0.0385323	−	0.0930252i
$659$		−	25.7250i		−	1.00210i	−0.865417	−	0.501051i	$-0.832947\pi$
$659$		−	25.7250i		−	1.00210i	0.865417	−	0.501051i	$-0.167053\pi$
$660$	−14.8248	−	6.14065i	−0.577056	−	0.239025i
$661$	4.57274	−	4.57274i	0.177859	−	0.177859i	−0.612563	−	0.790422i	$-0.709861\pi$
$661$	4.57274	−	4.57274i	0.177859	−	0.177859i	0.790422	+	0.612563i	$0.209861\pi$
$662$	−16.4332			−0.638693
$663$	−2.16525	−	73.5548i	−0.0840914	−	2.85663i
$664$	0.792706			0.0307630
$665$	1.88397	−	1.88397i	0.0730572	−	0.0730572i
$666$	−7.97229	−	3.30223i	−0.308920	−	0.127959i
$667$			13.7066i			0.530723i
$668$	−6.73087	+	16.2497i	−0.260425	+	0.628722i
$669$	23.4957	−	9.73224i	0.908397	−	0.376270i
$670$	1.25397	+	3.02734i	0.0484449	+	0.116956i
$671$	25.3875	+	25.3875i	0.980074	+	0.980074i
$672$	−0.974742	−	0.974742i	−0.0376015	−	0.0376015i
$673$	9.91983	+	23.9486i	0.382381	+	0.923150i	0.991504	+	0.130074i	$0.0415216\pi$
$673$	9.91983	+	23.9486i	0.382381	+	0.923150i	−0.609123	+	0.793076i	$0.708478\pi$
$674$	−2.74728	+	1.13796i	−0.105821	+	0.0438326i
$675$	−5.00061	+	12.0725i	−0.192474	+	0.464672i
$676$			18.5072i			0.711815i
$677$	−16.4725	−	6.82312i	−0.633089	−	0.262234i	0.0429762	−	0.999076i	$-0.486316\pi$
$677$	−16.4725	−	6.82312i	−0.633089	−	0.262234i	−0.676065	+	0.736842i	$0.736316\pi$
$678$	40.3817	−	40.3817i	1.55085	−	1.55085i
$679$	5.61344			0.215424
$680$	−2.82843	+	3.00000i	−0.108465	+	0.115045i
$681$	48.0477			1.84119
$682$	−7.83639	+	7.83639i	−0.300071	+	0.300071i
$683$	−15.6108	−	6.46620i	−0.597330	−	0.247422i	0.0634704	−	0.997984i	$-0.479783\pi$
$683$	−15.6108	−	6.46620i	−0.597330	−	0.247422i	−0.660801	+	0.750561i	$0.729783\pi$
$684$			43.6925i			1.67063i
$685$	4.13546	−	9.98388i	0.158008	−	0.381464i
$686$	−5.53233	+	2.29156i	−0.211225	+	0.0874923i
$687$	−19.0211	−	45.9211i	−0.725702	−	1.75200i
$688$	−0.638384	−	0.638384i	−0.0243382	−	0.0243382i
$689$	0.135457	+	0.135457i	0.00516049	+	0.00516049i
$690$	6.25065	+	15.0904i	0.237958	+	0.574482i
$691$	−9.05490	+	3.75066i	−0.344465	+	0.142682i	−0.548207	−	0.836343i	$-0.684689\pi$
$691$	−9.05490	+	3.75066i	−0.344465	+	0.142682i	0.203742	+	0.979025i	$0.434689\pi$
$692$	−7.21371	+	17.4154i	−0.274224	+	0.662035i
$693$			15.5558i			0.590917i
$694$	6.55366	+	2.71461i	0.248773	+	0.103045i
$695$	13.7124	−	13.7124i	0.520141	−	0.520141i
$696$	8.48369			0.321573
$697$	14.9420	+	14.0875i	0.565969	+	0.533600i
$698$	19.9951			0.756825
$699$	60.2295	−	60.2295i	2.27809	−	2.27809i
$700$	−0.400544	−	0.165911i	−0.0151391	−	0.00627083i
$701$			20.2236i			0.763836i	0.924196	+	0.381918i	$0.124736\pi$
$701$			20.2236i			0.763836i	−0.924196	+	0.381918i	$0.875264\pi$
$702$	−28.0691	+	67.7647i	−1.05940	+	2.55761i
$703$	−6.89102	+	2.85435i	−0.259900	+	0.107654i
$704$	1.93128	+	4.66252i	0.0727878	+	0.175725i
$705$	13.3942	+	13.3942i	0.504456	+	0.504456i
$706$	2.64566	+	2.64566i	0.0995708	+	0.0995708i
$707$	0.206920	+	0.499549i	0.00778202	+	0.0187875i
$708$	−1.14511	+	0.474319i	−0.0430358	+	0.0178260i
$709$	4.90625	−	11.8447i	0.184258	−	0.444839i	−0.804578	−	0.593848i	$-0.797608\pi$
$709$	4.90625	−	11.8447i	0.184258	−	0.444839i	0.988836	+	0.149009i	$0.0476082\pi$
$710$			3.93240i			0.147580i
$711$	−86.8027	−	35.9549i	−3.25536	−	1.34841i
$712$	1.93336	−	1.93336i	0.0724557	−	0.0724557i
$713$	11.2809			0.422471
$714$	5.31275	+	2.01960i	0.198825	+	0.0755815i
$715$	−28.3276			−1.05939
$716$	12.1689	−	12.1689i	0.454775	−	0.454775i
$717$	−59.0381	−	24.4544i	−2.20482	−	0.913266i
$718$			0.582315i			0.0217318i
$719$	−2.87400	+	6.93845i	−0.107182	+	0.258761i	−0.968367	−	0.249532i	$-0.919723\pi$
$719$	−2.87400	+	6.93845i	−0.107182	+	0.258761i	0.861184	+	0.508293i	$0.169723\pi$
$720$	6.56854	−	2.72078i	0.244795	−	0.101397i
$721$	1.35312	+	3.26672i	0.0503928	+	0.121659i
$722$	13.2700	+	13.2700i	0.493858	+	0.493858i
$723$	38.1023	+	38.1023i	1.41704	+	1.41704i
$724$	−6.08153	−	14.6821i	−0.226018	−	0.545656i
$725$	2.46508	−	1.02107i	0.0915506	−	0.0379215i
$726$	17.6054	−	42.5031i	0.653396	−	1.57744i
$727$		−	13.7314i		−	0.509269i	−0.967037	−	0.254635i	$-0.918045\pi$
$727$		−	13.7314i		−	0.509269i	0.967037	−	0.254635i	$-0.0819552\pi$
$728$	−2.24830	−	0.931278i	−0.0833276	−	0.0345154i
$729$	−13.5110	+	13.5110i	−0.500408	+	0.500408i
$730$	3.39782			0.125759
$731$	3.47946	+	1.32269i	0.128693	+	0.0489214i
$732$	−22.6204			−0.836074
$733$	22.6233	−	22.6233i	0.835612	−	0.835612i	−0.152666	−	0.988278i	$-0.548786\pi$
$733$	22.6233	−	22.6233i	0.835612	−	0.835612i	0.988278	+	0.152666i	$0.0487859\pi$
$734$	25.5126	+	10.5677i	0.941688	+	0.390060i
$735$		−	21.6594i		−	0.798920i
$736$	1.96587	−	4.74603i	0.0724630	−	0.174941i
$737$	−15.2780	+	6.32835i	−0.562772	+	0.233108i
$738$	−13.5513	−	32.7157i	−0.498830	−	1.20428i
$739$	4.06591	+	4.06591i	0.149567	+	0.149567i	0.777925	−	0.628358i	$-0.216273\pi$
$739$	4.06591	+	4.06591i	0.149567	+	0.149567i	−0.628358	+	0.777925i	$0.716273\pi$
$740$	0.858221	+	0.858221i	0.0315488	+	0.0315488i
$741$	41.9728	+	101.331i	1.54191	+	3.72250i
$742$	−0.0136697	+	0.00566219i	−0.000501832	+	0.000207866i
$743$	20.2655	−	48.9253i	0.743470	−	1.79490i	0.152327	−	0.988330i	$-0.451323\pi$
$743$	20.2655	−	48.9253i	0.743470	−	1.79490i	0.591144	−	0.806566i	$-0.298677\pi$
$744$		−	6.98226i		−	0.255982i
$745$	17.1869	+	7.11907i	0.629681	+	0.260822i
$746$	−23.7380	+	23.7380i	−0.869109	+	0.869109i
$747$	5.63593			0.206208
$748$	−15.1400	−	14.2741i	−0.553574	−	0.521914i
$749$	1.78192			0.0651099
$750$	2.24830	−	2.24830i	0.0820964	−	0.0820964i
$751$	−31.8455	−	13.1909i	−1.16206	−	0.481341i	−0.283500	−	0.958972i	$-0.591496\pi$
$751$	−31.8455	−	13.1909i	−1.16206	−	0.481341i	−0.878560	+	0.477631i	$0.841496\pi$
$752$		−	5.95749i		−	0.217247i
$753$	−27.8507	+	67.2375i	−1.01494	+	2.45027i
$754$	13.8368	−	5.73138i	0.503906	−	0.208725i
$755$	−4.80231	−	11.5938i	−0.174774	−	0.421941i
$756$	−4.00593	−	4.00593i	−0.145694	−	0.145694i
$757$	35.4440	+	35.4440i	1.28823	+	1.28823i	0.935858	+	0.352376i	$0.114626\pi$
$757$	35.4440	+	35.4440i	1.28823	+	1.28823i	0.352376	+	0.935858i	$0.385374\pi$
$758$	−8.55128	−	20.6446i	−0.310597	−	0.749847i
$759$	−76.1563	+	31.5450i	−2.76430	+	1.14501i
$760$	2.35176	−	5.67766i	0.0853074	−	0.205950i
$761$		−	50.1987i		−	1.81970i	−0.414935	−	0.909851i	$-0.636196\pi$
$761$		−	50.1987i		−	1.81970i	0.414935	−	0.909851i	$-0.363804\pi$
$762$	44.5697	+	18.4614i	1.61459	+	0.668785i
$763$	3.92717	−	3.92717i	0.142173	−	0.142173i
$764$	10.2092			0.369355
$765$	−20.1094	+	21.3292i	−0.727055	+	0.771159i
$766$	28.7314			1.03811
$767$	−1.54722	+	1.54722i	−0.0558667	+	0.0558667i
$768$	−2.93755	−	1.21677i	−0.106000	−	0.0439065i
$769$			55.0520i			1.98523i	0.121321	+	0.992613i	$0.461287\pi$
$769$			55.0520i			1.98523i	−0.121321	+	0.992613i	$0.538713\pi$
$770$	0.837297	−	2.02141i	0.0301741	−	0.0728467i
$771$	−50.1130	+	20.7575i	−1.80478	+	0.747562i
$772$	0.740482	+	1.78768i	0.0266505	+	0.0643401i
$773$	−16.5300	−	16.5300i	−0.594542	−	0.594542i	0.344313	−	0.938855i	$-0.388112\pi$
$773$	−16.5300	−	16.5300i	−0.594542	−	0.594542i	−0.938855	+	0.344313i	$0.888112\pi$
$774$	−4.53874	−	4.53874i	−0.163142	−	0.163142i
$775$	−0.840361	−	2.02881i	−0.0301867	−	0.0728770i
$776$	11.9622	−	4.95489i	0.429417	−	0.177870i
$777$	0.640263	−	1.54573i	0.0229693	−	0.0554528i
$778$			20.1763i			0.723355i
$779$	−28.2785	−	11.7134i	−1.01318	−	0.419674i
$780$	12.6200	−	12.6200i	0.451869	−	0.451869i
$781$	−19.8456			−0.710130
$782$	0.623231	+	21.1715i	0.0222867	+	0.757092i
$783$	34.8657			1.24600
$784$	−4.81684	+	4.81684i	−0.172030	+	0.172030i
$785$	−13.6396	−	5.64971i	−0.486818	−	0.201647i
$786$		−	27.6868i		−	0.987555i
$787$	0.00854607	−	0.0206320i	0.000304634	−	0.000735452i	−0.923727	−	0.383051i	$-0.874873\pi$
$787$	0.00854607	−	0.0206320i	0.000304634	−	0.000735452i	0.924032	+	0.382316i	$0.124873\pi$
$788$	−5.64020	+	2.33625i	−0.200924	+	0.0832254i
$789$	−11.5516	−	27.8881i	−0.411249	−	0.992843i
$790$	9.34436	+	9.34436i	0.332458	+	0.332458i
$791$	5.50617	+	5.50617i	0.195777	+	0.195777i
$792$	13.7309	+	33.1492i	0.487905	+	1.17791i
$793$	−36.8935	+	15.2818i	−1.31013	+	0.542673i
$794$	−8.06147	+	19.4621i	−0.286091	+	0.690684i
$795$		−	0.108513i		−	0.00384855i
$796$	−8.75551	−	3.62665i	−0.310331	−	0.128543i
$797$	−15.1850	+	15.1850i	−0.537879	+	0.537879i	−0.922905	−	0.385027i	$-0.874192\pi$
$797$	−15.1850	+	15.1850i	−0.537879	+	0.537879i	0.385027	+	0.922905i	$0.374192\pi$
$798$	−8.47146			−0.299887
$799$	10.0637	+	22.4072i	0.356027	+	0.792709i
$800$	−1.00000			−0.0353553
$801$	13.7457	−	13.7457i	0.485679	−	0.485679i
$802$	4.87669	+	2.01999i	0.172202	+	0.0713284i
$803$			17.1477i			0.605129i
$804$	3.98708	−	9.62567i	0.140614	−	0.339471i
$805$	−2.05762	+	0.852295i	−0.0725216	+	0.0300395i
$806$	−4.71705	−	11.3880i	−0.166151	−	0.401124i
$807$	−35.2852	−	35.2852i	−1.24210	−	1.24210i
$808$	0.881887	+	0.881887i	0.0310247	+	0.0310247i
$809$	−6.21294	−	14.9994i	−0.218435	−	0.527349i	0.776236	−	0.630442i	$-0.217126\pi$
$809$	−6.21294	−	14.9994i	−0.218435	−	0.527349i	−0.994672	+	0.103092i	$0.967126\pi$
$810$	18.6800	−	7.73751i	0.656348	−	0.271868i
$811$	5.46079	−	13.1835i	0.191754	−	0.462936i	−0.798537	−	0.601946i	$-0.794392\pi$
$811$	5.46079	−	13.1835i	0.191754	−	0.462936i	0.990291	+	0.139010i	$0.0443921\pi$
$812$			1.15678i			0.0405949i
$813$	−6.37239	−	2.63953i	−0.223490	−	0.0925724i
$814$	−4.33116	+	4.33116i	−0.151807	+	0.151807i
$815$	14.4466			0.506043
$816$	13.1041	−	0.385748i	0.458734	−	0.0135039i
$817$	−5.54819			−0.194106
$818$	20.9343	−	20.9343i	0.731952	−	0.731952i
$819$	−15.9848	−	6.62113i	−0.558555	−	0.231361i
$820$			4.98067i			0.173932i
$821$	−4.55495	+	10.9966i	−0.158969	+	0.383784i	−0.983216	−	0.182446i	$-0.941599\pi$
$821$	−4.55495	+	10.9966i	−0.158969	+	0.383784i	0.824247	+	0.566230i	$0.191599\pi$
$822$	−31.7445	+	13.1490i	−1.10722	+	0.458625i
$823$	19.6162	+	47.3578i	0.683779	+	1.65079i	0.756954	+	0.653468i	$0.226687\pi$
$823$	19.6162	+	47.3578i	0.683779	+	1.65079i	−0.0731752	+	0.997319i	$0.523313\pi$
$824$	5.76696	+	5.76696i	0.200902	+	0.200902i
$825$	11.3464	+	11.3464i	0.395033	+	0.395033i
$826$	−0.0646748	−	0.156139i	−0.00225033	−	0.00543277i
$827$	22.2204	−	9.20401i	0.772680	−	0.320055i	0.0387228	−	0.999250i	$-0.487671\pi$
$827$	22.2204	−	9.20401i	0.772680	−	0.320055i	0.733958	+	0.679195i	$0.237671\pi$
$828$	13.9768	−	33.7430i	0.485728	−	1.17265i
$829$			21.3366i			0.741050i	0.928822	+	0.370525i	$0.120822\pi$
$829$			21.3366i			0.741050i	−0.928822	+	0.370525i	$0.879178\pi$
$830$	−0.732365	−	0.303356i	−0.0254208	−	0.0105296i
$831$	12.4552	−	12.4552i	0.432065	−	0.432065i
$832$	−5.61313			−0.194600
$833$	9.98015	−	26.2538i	0.345792	−	0.909640i
$834$	−61.6592			−2.13508
$835$	12.4370	−	12.4370i	0.430401	−	0.430401i
$836$	28.6533	+	11.8686i	0.990994	+	0.410483i
$837$		−	28.6952i		−	0.991852i
$838$	−12.7695	+	30.8284i	−0.441116	+	1.06495i
$839$	−12.9128	+	5.34865i	−0.445799	+	0.184656i	−0.594278	−	0.804260i	$-0.702562\pi$
$839$	−12.9128	+	5.34865i	−0.445799	+	0.184656i	0.148479	+	0.988915i	$0.452562\pi$
$840$	0.527526	+	1.27356i	0.0182014	+	0.0439420i
$841$	15.4721	+	15.4721i	0.533520	+	0.533520i
$842$	9.70335	+	9.70335i	0.334400	+	0.334400i
$843$	24.2403	+	58.5212i	0.834879	+	2.01558i
$844$	12.5832	−	5.21212i	0.433130	−	0.179408i
$845$	7.08239	−	17.0984i	0.243642	−	0.588203i
$846$		−	42.3562i		−	1.45623i
$847$	5.79543	+	2.40054i	0.199133	+	0.0824837i
$848$	−0.0241321	+	0.0241321i	−0.000828700	+	0.000828700i
$849$	61.9344			2.12558
$850$	3.76118	−	1.68925i	0.129007	−	0.0579407i
$851$	6.23491			0.213730
$852$	8.84123	−	8.84123i	0.302896	−	0.302896i
$853$	−6.23943	−	2.58446i	−0.213634	−	0.0884902i	0.273300	−	0.961929i	$-0.411885\pi$
$853$	−6.23943	−	2.58446i	−0.213634	−	0.0884902i	−0.486934	+	0.873439i	$0.661885\pi$
$854$		−	3.08436i		−	0.105545i
$855$	16.7204	−	40.3666i	0.571826	−	1.38051i
$856$	3.79724	−	1.57287i	0.129787	−	0.0537596i
$857$	4.15332	+	10.0270i	0.141875	+	0.342516i	0.978805	−	0.204793i	$-0.0656523\pi$
$857$	4.15332	+	10.0270i	0.141875	+	0.342516i	−0.836931	+	0.547309i	$0.815652\pi$
$858$	63.6890	+	63.6890i	2.17431	+	2.17431i
$859$	3.85273	+	3.85273i	0.131453	+	0.131453i	0.769772	−	0.638319i	$-0.220370\pi$
$859$	3.85273	+	3.85273i	0.131453	+	0.131453i	−0.638319	+	0.769772i	$0.720370\pi$
$860$	0.345491	+	0.834089i	0.0117811	+	0.0284422i
$861$	6.34319	−	2.62743i	0.216175	−	0.0895427i
$862$	−4.68579	+	11.3125i	−0.159599	+	0.385305i
$863$		−	31.3583i		−	1.06745i	−0.845659	−	0.533724i	$-0.820792\pi$
$863$		−	31.3583i		−	1.06745i	0.845659	−	0.533724i	$-0.179208\pi$
$864$	−12.0725	−	5.00061i	−0.410716	−	0.170124i
$865$	13.3292	−	13.3292i	0.453206	−	0.453206i
$866$	29.3482			0.997291
$867$	−48.6351	+	23.5869i	−1.65173	+	0.801052i
$868$	0.952053			0.0323148
$869$	−47.1579	+	47.1579i	−1.59972	+	1.59972i
$870$	−7.83791	−	3.24657i	−0.265730	−	0.110069i
$871$		−	18.3929i		−	0.623220i
$872$	4.90230	−	11.8352i	0.166013	−	0.400790i
$873$	85.0478	−	35.2280i	2.87843	−	1.19229i
$874$	−12.0812	−	29.1665i	−0.408652	−	0.986573i
$875$	0.306563	+	0.306563i	0.0103637	+	0.0103637i
$876$	−7.63934	−	7.63934i	−0.258109	−	0.258109i
$877$	0.932426	+	2.25107i	0.0314858	+	0.0760134i	0.938840	−	0.344353i	$-0.111902\pi$
$877$	0.932426	+	2.25107i	0.0314858	+	0.0760134i	−0.907355	+	0.420366i	$0.861902\pi$
$878$	−1.97810	+	0.819355i	−0.0667576	+	0.0276519i
$879$	−5.22658	+	12.6181i	−0.176288	+	0.425597i
$880$		−	5.04667i		−	0.170123i
$881$	−5.85282	−	2.42432i	−0.197187	−	0.0816774i	0.281905	−	0.959442i	$-0.409034\pi$
$881$	−5.85282	−	2.42432i	−0.197187	−	0.0816774i	−0.479091	+	0.877765i	$0.659034\pi$
$882$	−34.2464	+	34.2464i	−1.15314	+	1.15314i
$883$	56.7857			1.91099			0.955496	−	0.295004i	$-0.0953210\pi$
$883$	56.7857			1.91099			0.955496	+	0.295004i	$0.0953210\pi$
$884$	21.1120	−	9.48195i	0.710072	−	0.318913i
$885$	1.23946			0.0416638
$886$	−0.896683	+	0.896683i	−0.0301247	+	0.0301247i
$887$	20.3799	+	8.44165i	0.684291	+	0.283443i	0.697619	−	0.716468i	$-0.254243\pi$
$887$	20.3799	+	8.44165i	0.684291	+	0.283443i	−0.0133282	+	0.999911i	$0.504243\pi$
$888$		−	3.85908i		−	0.129502i
$889$	−2.51727	+	6.07722i	−0.0844264	+	0.203823i
$890$	−2.52605	+	1.04633i	−0.0846735	+	0.0350729i
$891$	39.0487	+	94.2718i	1.30818	+	3.15823i
$892$	5.65573	+	5.65573i	0.189368	+	0.189368i
$893$	−25.8882	−	25.8882i	−0.866316	−	0.866316i
$894$	−22.6356	−	54.6473i	−0.757049	−	1.82768i
$895$	−15.8995	+	6.58579i	−0.531462	+	0.220139i
$896$	0.165911	−	0.400544i	0.00554269	−	0.0133812i
$897$		−	91.6833i		−	3.06122i
$898$	2.85710	+	1.18345i	0.0953425	+	0.0394922i
$899$	−4.14311	+	4.14311i	−0.138180	+	0.138180i
$900$	−7.10973			−0.236991
$901$	0.0500001	−	0.131530i	0.00166574	−	0.00438191i
$902$	−25.1358			−0.836930
$903$	0.880008	−	0.880008i	0.0292848	−	0.0292848i
$904$	16.5938	+	6.87336i	0.551900	+	0.228605i
$905$			15.8918i			0.528261i
$906$	−15.2693	+	36.8634i	−0.507289	+	1.22470i
$907$	−28.9161	+	11.9774i	−0.960144	+	0.397705i	−0.807034	−	0.590505i	$-0.798929\pi$
$907$	−28.9161	+	11.9774i	−0.960144	+	0.397705i	−0.153110	+	0.988209i	$0.548929\pi$
$908$	5.78285	+	13.9610i	0.191911	+	0.463313i
$909$	6.26998	+	6.26998i	0.207962	+	0.207962i
$910$	1.72078	+	1.72078i	0.0570432	+	0.0570432i
$911$	−7.32156	−	17.6758i	−0.242574	−	0.585626i	0.754963	−	0.655768i	$-0.227655\pi$
$911$	−7.32156	−	17.6758i	−0.242574	−	0.585626i	−0.997537	+	0.0701417i	$0.977655\pi$
$912$	−18.0526	+	7.47762i	−0.597780	+	0.247609i
$913$	1.53094	−	3.69601i	0.0506666	−	0.122320i
$914$		−	10.5587i		−	0.349252i
$915$	20.8985	+	8.65645i	0.690883	+	0.286173i
$916$	11.0538	−	11.0538i	0.365228	−	0.365228i
$917$	3.77518			0.124667
$918$	53.8542	−	1.58532i	1.77745	−	0.0523234i
$919$	−11.0668			−0.365062			−0.182531	−	0.983200i	$-0.558429\pi$
$919$	−11.0668			−0.365062			−0.182531	+	0.983200i	$0.558429\pi$
$920$	−3.63246	+	3.63246i	−0.119759	+	0.119759i
$921$	−45.4304	−	18.8179i	−1.49698	−	0.620071i
$922$		−	20.0564i		−	0.660522i
$923$	8.44700	−	20.3929i	0.278036	−	0.671239i
$924$	−6.42725	+	2.66225i	−0.211441	+	0.0875817i
$925$	−0.464466	−	1.12132i	−0.0152716	−	0.0368688i
$926$	−1.39216	−	1.39216i	−0.0457493	−	0.0457493i
$927$	41.0015	+	41.0015i	1.34667	+	1.34667i
$928$	1.02107	+	2.46508i	0.0335182	+	0.0809201i
$929$	−14.6234	+	6.05720i	−0.479777	+	0.198730i	−0.609447	−	0.792827i	$-0.708608\pi$
$929$	−14.6234	+	6.05720i	−0.479777	+	0.198730i	0.129670	+	0.991557i	$0.458608\pi$
$930$	−2.67200	+	6.45077i	−0.0876182	+	0.211529i
$931$			41.8631i			1.37201i
$932$	24.7497	+	10.2517i	0.810703	+	0.335804i
$933$	−25.5562	+	25.5562i	−0.836672	+	0.836672i
$934$	24.2848			0.794622
$935$	8.52507	+	18.9814i	0.278800	+	0.620759i
$936$	−39.9078			−1.30443
$937$	−5.80733	+	5.80733i	−0.189717	+	0.189717i	−0.795574	−	0.605857i	$-0.792831\pi$
$937$	−5.80733	+	5.80733i	−0.189717	+	0.189717i	0.605857	+	0.795574i	$0.292831\pi$
$938$	1.31249	+	0.543651i	0.0428543	+	0.0177508i
$939$			27.2459i			0.889136i
$940$	−2.27983	+	5.50400i	−0.0743600	+	0.179521i
$941$	0.191365	−	0.0792658i	0.00623831	−	0.00258399i	−0.379562	−	0.925166i	$-0.623925\pi$
$941$	0.191365	−	0.0792658i	0.00623831	−	0.00258399i	0.385800	+	0.922582i	$0.373925\pi$
$942$	17.9637	+	43.3682i	0.585289	+	1.41301i
$943$	18.0921	+	18.0921i	0.589159	+	0.589159i
$944$	−0.275642	−	0.275642i	−0.00897140	−	0.00897140i
$945$	2.16799	+	5.23400i	0.0705248	+	0.170262i
$946$	−4.20937	+	1.74358i	−0.136859	+	0.0566887i
$947$	−10.2893	+	24.8407i	−0.334359	+	0.807214i	0.663877	+	0.747842i	$0.268910\pi$
$947$	−10.2893	+	24.8407i	−0.334359	+	0.807214i	−0.998236	+	0.0593719i	$0.981090\pi$
$948$		−	42.0179i		−	1.36468i
$949$	−17.6206	−	7.29870i	−0.571989	−	0.236926i
$950$	−4.34549	+	4.34549i	−0.140986	+	0.140986i
$951$	18.8636			0.611693
$952$	0.0525979	+	1.78678i	0.00170471	+	0.0579099i
$953$	−26.6131			−0.862084			−0.431042	−	0.902332i	$-0.641854\pi$
$953$	−26.6131			−0.862084			−0.431042	+	0.902332i	$0.641854\pi$
$954$	−0.171573	+	0.171573i	−0.00555488	+	0.00555488i
$955$	−9.43205	−	3.90688i	−0.305214	−	0.126424i
$956$		−	20.0977i		−	0.650008i
$957$	16.3844	−	39.5553i	0.529631	−	1.27864i
$958$	−30.4291	+	12.6041i	−0.983119	+	0.407221i
$959$	−1.79291	−	4.32846i	−0.0578960	−	0.139773i
$960$	2.24830	+	2.24830i	0.0725637	+	0.0725637i
$961$	−18.5104	−	18.5104i	−0.597111	−	0.597111i
$962$	−2.60711	−	6.29411i	−0.0840565	−	0.202930i
$963$	26.9974	−	11.1827i	0.869978	−	0.360357i
$964$	−6.48539	+	15.6571i	−0.208880	+	0.504282i
$965$		−	1.93497i		−	0.0622890i
$966$	6.54237	+	2.70994i	0.210497	+	0.0871909i
$967$	−5.18409	+	5.18409i	−0.166709	+	0.166709i	−0.785531	−	0.618822i	$-0.787610\pi$
$967$	−5.18409	+	5.18409i	−0.166709	+	0.166709i	0.618822	+	0.785531i	$0.287610\pi$
$968$	14.4689			0.465048
$969$	55.2674	−	58.6199i	1.77544	−	1.88314i
$970$	−12.9478			−0.415727
$971$	−35.1312	+	35.1312i	−1.12741	+	1.12741i	−0.136818	+	0.990596i	$0.543687\pi$
$971$	−35.1312	+	35.1312i	−1.12741	+	1.12741i	−0.990596	+	0.136818i	$0.956313\pi$
$972$	−23.1770	−	9.60021i	−0.743401	−	0.307927i
$973$		−	8.40743i		−	0.269530i
$974$	1.94088	−	4.68569i	0.0621897	−	0.150139i
$975$	−16.4888	+	6.82990i	−0.528065	+	0.218732i
$976$	−2.72251	−	6.57273i	−0.0871455	−	0.210388i
$977$	−32.2010	−	32.2010i	−1.03020	−	1.03020i	−0.999530	−	0.0306715i	$-0.990235\pi$
$977$	−32.2010	−	32.2010i	−1.03020	−	1.03020i	−0.0306715	−	0.999530i	$-0.509765\pi$
$978$	−32.4804	−	32.4804i	−1.03861	−	1.03861i
$979$	−5.28046	−	12.7482i	−0.168764	−	0.407433i
$980$	6.29350	−	2.60685i	0.201039	−	0.0832729i
$981$	34.8540	−	84.1450i	1.11280	−	2.68654i
$982$			15.3998i			0.491427i
$983$	53.2587	+	22.0605i	1.69869	+	0.703621i	0.999931	−	0.0117365i	$-0.00373592\pi$
$983$	53.2587	+	22.0605i	1.69869	+	0.703621i	0.698759	+	0.715357i	$0.253736\pi$
$984$	11.1981	−	11.1981i	0.356981	−	0.356981i
$985$	6.10491			0.194519
$986$	−8.00454	−	7.54675i	−0.254916	−	0.240337i
$987$	8.21236			0.261402
$988$	−24.3918	+	24.3918i	−0.776006	+	0.776006i
$989$	4.28478	+	1.77481i	0.136248	+	0.0564358i
$990$		−	35.8805i		−	1.14036i
$991$	14.2488	−	34.3997i	0.452628	−	1.09274i	−0.518691	−	0.854962i	$-0.673581\pi$
$991$	14.2488	−	34.3997i	0.452628	−	1.09274i	0.971319	−	0.237779i	$-0.0764195\pi$
$992$	2.02881	−	0.840361i	0.0644148	−	0.0266815i
$993$	−19.9954	−	48.2733i	−0.634536	−	1.53191i
$994$	1.20553	+	1.20553i	0.0382371	+	0.0382371i
$995$	6.70118	+	6.70118i	0.212442	+	0.212442i
$996$	0.964543	+	2.32861i	0.0305627	+	0.0737850i
$997$	−30.5077	+	12.6367i	−0.966188	+	0.400208i	−0.809292	−	0.587407i	$-0.800149\pi$
$997$	−30.5077	+	12.6367i	−0.966188	+	0.400208i	−0.156896	+	0.987615i	$0.550149\pi$
$998$	−6.71929	+	16.2218i	−0.212696	+	0.513492i
$999$		−	15.8598i		−	0.501782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.a.111.1	✓	8
5.2	odd	4		850.2.o.c.349.1		8
5.3	odd	4		850.2.o.f.349.2		8
5.4	even	2		850.2.l.d.451.2		8
17.2	even	8	inner	170.2.k.a.121.1	yes	8
17.6	odd	16		2890.2.a.bc.1.1		4
17.7	odd	16		2890.2.b.p.2311.8		8
17.10	odd	16		2890.2.b.p.2311.1		8
17.11	odd	16		2890.2.a.bf.1.4		4
85.2	odd	8		850.2.o.f.699.2		8
85.19	even	8		850.2.l.d.801.2		8
85.53	odd	8		850.2.o.c.699.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.a.111.1	✓	8	1.1	even	1	trivial
170.2.k.a.121.1	yes	8	17.2	even	8	inner
850.2.l.d.451.2		8	5.4	even	2
850.2.l.d.801.2		8	85.19	even	8
850.2.o.c.349.1		8	5.2	odd	4
850.2.o.c.699.1		8	85.53	odd	8
850.2.o.f.349.2		8	5.3	odd	4
850.2.o.f.699.2		8	85.2	odd	8
2890.2.a.bc.1.1		4	17.6	odd	16
2890.2.a.bf.1.4		4	17.11	odd	16
2890.2.b.p.2311.1		8	17.10	odd	16
2890.2.b.p.2311.8		8	17.7	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.k (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.93755 - 1.21677i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{5} +(2.93755 - 1.21677i) q^{6} +(0.165911 + 0.400544i) q^{7} +(0.707107 + 0.707107i) q^{8} +(5.02734 + 5.02734i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.93755 - 1.21677i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{5} +(2.93755 - 1.21677i) q^{6} +(0.165911 + 0.400544i) q^{7} +(0.707107 + 0.707107i) q^{8} +(5.02734 + 5.02734i) q^{9} +(-0.382683 - 0.923880i) q^{10} +(4.66252 - 1.93128i) q^{11} +(-1.21677 + 2.93755i) q^{12} +5.61313i q^{13} +(-0.400544 - 0.165911i) q^{14} +(2.24830 - 2.24830i) q^{15} -1.00000 q^{16} +(3.76118 - 1.68925i) q^{17} -7.10973 q^{18} +(-4.34549 + 4.34549i) q^{19} +(0.923880 + 0.382683i) q^{20} -1.37849i q^{21} +(-1.93128 + 4.66252i) q^{22} +(4.74603 - 1.96587i) q^{23} +(-1.21677 - 2.93755i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-3.96908 - 3.96908i) q^{26} +(-5.00061 - 12.0725i) q^{27} +(0.400544 - 0.165911i) q^{28} +(-1.02107 + 2.46508i) q^{29} +3.17958i q^{30} +(2.02881 + 0.840361i) q^{31} +(0.707107 - 0.707107i) q^{32} -16.0463 q^{33} +(-1.46508 + 3.85403i) q^{34} -0.433546 q^{35} +(5.02734 - 5.02734i) q^{36} +(1.12132 + 0.464466i) q^{37} -6.14545i q^{38} +(6.82990 - 16.4888i) q^{39} +(-0.923880 + 0.382683i) q^{40} +(1.90602 + 4.60154i) q^{41} +(0.974742 + 0.974742i) q^{42} +(0.638384 + 0.638384i) q^{43} +(-1.93128 - 4.66252i) q^{44} +(-6.56854 + 2.72078i) q^{45} +(-1.96587 + 4.74603i) q^{46} +5.95749i q^{47} +(2.93755 + 1.21677i) q^{48} +(4.81684 - 4.81684i) q^{49} +1.00000 q^{50} +(-13.1041 + 0.385748i) q^{51} +5.61313 q^{52} +(0.0241321 - 0.0241321i) q^{53} +(12.0725 + 5.00061i) q^{54} +5.04667i q^{55} +(-0.165911 + 0.400544i) q^{56} +(18.0526 - 7.47762i) q^{57} +(-1.02107 - 2.46508i) q^{58} +(0.275642 + 0.275642i) q^{59} +(-2.24830 - 2.24830i) q^{60} +(2.72251 + 6.57273i) q^{61} +(-2.02881 + 0.840361i) q^{62} +(-1.17958 + 2.84776i) q^{63} +1.00000i q^{64} +(-5.18585 - 2.14805i) q^{65} +(11.3464 - 11.3464i) q^{66} -3.27677 q^{67} +(-1.68925 - 3.76118i) q^{68} -16.3337 q^{69} +(0.306563 - 0.306563i) q^{70} +(-3.63307 - 1.50487i) q^{71} +7.10973i q^{72} +(-1.30029 + 3.13918i) q^{73} +(-1.12132 + 0.464466i) q^{74} +(1.21677 + 2.93755i) q^{75} +(4.34549 + 4.34549i) q^{76} +(1.54712 + 1.54712i) q^{77} +(6.82990 + 16.4888i) q^{78} +(-12.2090 + 5.05713i) q^{79} +(0.382683 - 0.923880i) q^{80} +20.2191i q^{81} +(-4.60154 - 1.90602i) q^{82} +(0.560528 - 0.560528i) q^{83} -1.37849 q^{84} +(0.121320 + 4.12132i) q^{85} -0.902812 q^{86} +(5.99887 - 5.99887i) q^{87} +(4.66252 + 1.93128i) q^{88} -2.73418i q^{89} +(2.72078 - 6.56854i) q^{90} +(-2.24830 + 0.931278i) q^{91} +(-1.96587 - 4.74603i) q^{92} +(-4.93720 - 4.93720i) q^{93} +(-4.21258 - 4.21258i) q^{94} +(-2.35176 - 5.67766i) q^{95} +(-2.93755 + 1.21677i) q^{96} +(4.95489 - 11.9622i) q^{97} +6.81204i q^{98} +(33.1492 + 13.7309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^9	\( 8 q + 8 q^{9} + 16 q^{11} - 8 q^{12} - 8 q^{14} + 8 q^{15} - 8 q^{16} - 16 q^{18} - 16 q^{19} - 8 q^{22} + 24 q^{23} - 8 q^{24} + 8 q^{28} + 8 q^{29} - 16 q^{31} - 16 q^{33} + 8 q^{36} - 8 q^{37} + 32 q^{39} - 8 q^{43} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 8 q^{49} + 8 q^{50} - 40 q^{51} + 24 q^{52} - 8 q^{53} + 40 q^{54} + 16 q^{57} + 8 q^{58} - 40 q^{59} - 8 q^{60} - 24 q^{61} + 16 q^{62} + 8 q^{63} - 8 q^{65} + 16 q^{66} - 16 q^{69} - 8 q^{70} + 24 q^{71} - 16 q^{73} + 8 q^{74} + 8 q^{75} + 16 q^{76} + 8 q^{77} + 32 q^{78} - 8 q^{79} + 8 q^{82} + 8 q^{83} + 16 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{87} + 16 q^{88} - 8 q^{91} - 8 q^{92} - 32 q^{93} - 8 q^{94} + 16 q^{95} - 32 q^{97} + 72 q^{99}+O(q^{100}) \) 8 * q + 8 * q^9 + 16 * q^11 - 8 * q^12 - 8 * q^14 + 8 * q^15 - 8 * q^16 - 16 * q^18 - 16 * q^19 - 8 * q^22 + 24 * q^23 - 8 * q^24 + 8 * q^28 + 8 * q^29 - 16 * q^31 - 16 * q^33 + 8 * q^36 - 8 * q^37 + 32 * q^39 - 8 * q^43 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 8 * q^49 + 8 * q^50 - 40 * q^51 + 24 * q^52 - 8 * q^53 + 40 * q^54 + 16 * q^57 + 8 * q^58 - 40 * q^59 - 8 * q^60 - 24 * q^61 + 16 * q^62 + 8 * q^63 - 8 * q^65 + 16 * q^66 - 16 * q^69 - 8 * q^70 + 24 * q^71 - 16 * q^73 + 8 * q^74 + 8 * q^75 + 16 * q^76 + 8 * q^77 + 32 * q^78 - 8 * q^79 + 8 * q^82 + 8 * q^83 + 16 * q^84 - 16 * q^85 - 16 * q^86 + 32 * q^87 + 16 * q^88 - 8 * q^91 - 8 * q^92 - 32 * q^93 - 8 * q^94 + 16 * q^95 - 32 * q^97 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more