LMFDB - Embedded newform 115.2.e.a.22.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(22,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("115.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{18} + 3 x^{16} + 80 x^{14} - 600 x^{12} + 3500 x^{10} - 15000 x^{8} + 50000 x^{6} + \cdots + 9765625 $ x^20 - 6x^18 + 3x^16 + 80x^14 - 600x^12 + 3500x^10 - 15000x^8 + 50000x^6 + 46875x^4 - 2343750*x^2 + 9765625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.10
Root			$-1.20735 + 1.88210i$ of defining polynomial
Character	$\chi$	$=$	115.22
Dual form			115.2.e.a.68.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40095 + 1.40095i) q^{2} +(-1.47890 + 1.47890i) q^{3} +1.92534i q^{4} +(1.88210 - 1.20735i) q^{5} -4.14375 q^{6} +(-2.58659 + 2.58659i) q^{7} +(0.104596 - 0.104596i) q^{8} -1.37431i q^{9} +O(q^{10})$	\(q+(1.40095 + 1.40095i) q^{2} +(-1.47890 + 1.47890i) q^{3} +1.92534i q^{4} +(1.88210 - 1.20735i) q^{5} -4.14375 q^{6} +(-2.58659 + 2.58659i) q^{7} +(0.104596 - 0.104596i) q^{8} -1.37431i q^{9} +(4.32817 + 0.945306i) q^{10} -4.24585i q^{11} +(-2.84739 - 2.84739i) q^{12} +(1.82074 - 1.82074i) q^{13} -7.24738 q^{14} +(-0.997903 + 4.56900i) q^{15} +4.14375 q^{16} +(-0.884201 + 0.884201i) q^{17} +(1.92534 - 1.92534i) q^{18} +0.524079 q^{19} +(2.32455 + 3.62369i) q^{20} -7.65063i q^{21} +(5.94824 - 5.94824i) q^{22} +(2.91521 + 3.80809i) q^{23} +0.309375i q^{24} +(2.08463 - 4.54470i) q^{25} +5.10155 q^{26} +(-2.40424 - 2.40424i) q^{27} +(-4.98006 - 4.98006i) q^{28} -4.01110i q^{29} +(-7.79896 + 5.00293i) q^{30} -7.49669 q^{31} +(5.59600 + 5.59600i) q^{32} +(6.27920 + 6.27920i) q^{33} -2.47745 q^{34} +(-1.74532 + 7.99114i) q^{35} +2.64601 q^{36} +(-5.58812 + 5.58812i) q^{37} +(0.734210 + 0.734210i) q^{38} +5.38541i q^{39} +(0.0705771 - 0.323144i) q^{40} -4.85068 q^{41} +(10.7182 - 10.7182i) q^{42} +(-6.47232 - 6.47232i) q^{43} +8.17471 q^{44} +(-1.65926 - 2.58659i) q^{45} +(-1.25087 + 9.41903i) q^{46} +(-2.08135 - 2.08135i) q^{47} +(-6.12820 + 6.12820i) q^{48} -6.38088i q^{49} +(9.28739 - 3.44644i) q^{50} -2.61530i q^{51} +(3.50555 + 3.50555i) q^{52} +(0.553239 + 0.553239i) q^{53} -6.73646i q^{54} +(-5.12621 - 7.99114i) q^{55} +0.541094i q^{56} +(-0.775062 + 0.775062i) q^{57} +(5.61936 - 5.61936i) q^{58} +13.5774i q^{59} +(-8.79687 - 1.92130i) q^{60} +3.54262i q^{61} +(-10.5025 - 10.5025i) q^{62} +(3.55477 + 3.55477i) q^{63} +7.39198i q^{64} +(1.22856 - 5.62510i) q^{65} +17.5937i q^{66} +(9.83397 - 9.83397i) q^{67} +(-1.70239 - 1.70239i) q^{68} +(-9.94311 - 1.32047i) q^{69} +(-13.6403 + 8.75009i) q^{70} +6.28522 q^{71} +(-0.143747 - 0.143747i) q^{72} +(-3.78828 + 3.78828i) q^{73} -15.6574 q^{74} +(3.63820 + 9.80414i) q^{75} +1.00903i q^{76} +(10.9823 + 10.9823i) q^{77} +(-7.54470 + 7.54470i) q^{78} +10.4842 q^{79} +(7.79896 - 5.00293i) q^{80} +11.2342 q^{81} +(-6.79557 - 6.79557i) q^{82} +(8.53483 + 8.53483i) q^{83} +14.7301 q^{84} +(-0.596623 + 2.73170i) q^{85} -18.1348i q^{86} +(5.93202 + 5.93202i) q^{87} +(-0.444099 - 0.444099i) q^{88} -10.8704 q^{89} +(1.29914 - 5.94824i) q^{90} +9.41903i q^{91} +(-7.33186 + 5.61278i) q^{92} +(11.0869 - 11.0869i) q^{93} -5.83173i q^{94} +(0.986371 - 0.632744i) q^{95} -16.5519 q^{96} +(-2.73658 + 2.73658i) q^{97} +(8.93932 - 8.93932i) q^{98} -5.83510 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.40095	+	1.40095i	0.990623	+	0.990623i	0.999956	−	0.00933298i	$-0.00297082\pi$
$2$	1.40095	+	1.40095i	0.990623	+	0.990623i	−0.00933298	+	0.999956i	$0.502971\pi$
$3$	−1.47890	+	1.47890i	−0.853845	+	0.853845i	−0.990604	−	0.136759i	$-0.956331\pi$
$3$	−1.47890	+	1.47890i	−0.853845	+	0.853845i	0.136759	+	0.990604i	$0.456331\pi$
$4$			1.92534i			0.962670i
$5$	1.88210	−	1.20735i	0.841703	−	0.539941i
$5$	1.88210	−	1.20735i	0.841703	−	0.539941i
$6$	−4.14375			−1.69168
$7$	−2.58659	+	2.58659i	−0.977639	+	0.977639i	−0.999755	−	0.0221167i	$-0.992959\pi$
$7$	−2.58659	+	2.58659i	−0.977639	+	0.977639i	0.0221167	+	0.999755i	$0.492959\pi$
$8$	0.104596	−	0.104596i	0.0369803	−	0.0369803i
$9$		−	1.37431i		−	0.458102i
$10$	4.32817	+	0.945306i	1.36869	+	0.298932i
$11$		−	4.24585i		−	1.28017i	−0.768303	−	0.640086i	$-0.778899\pi$
$11$		−	4.24585i		−	1.28017i	0.768303	−	0.640086i	$-0.221101\pi$
$12$	−2.84739	−	2.84739i	−0.821971	−	0.821971i
$13$	1.82074	−	1.82074i	0.504983	−	0.504983i	−0.407999	−	0.912982i	$-0.633773\pi$
$13$	1.82074	−	1.82074i	0.504983	−	0.504983i	0.912982	+	0.407999i	$0.133773\pi$
$14$	−7.24738			−1.93694
$15$	−0.997903	+	4.56900i	−0.257657	+	1.17971i
$16$	4.14375			1.03594
$17$	−0.884201	+	0.884201i	−0.214450	+	0.214450i	−0.806155	−	0.591705i	$-0.798455\pi$
$17$	−0.884201	+	0.884201i	−0.214450	+	0.214450i	0.591705	+	0.806155i	$0.298455\pi$
$18$	1.92534	−	1.92534i	0.453807	−	0.453807i
$19$	0.524079			0.120232			0.0601160	−	0.998191i	$-0.480853\pi$
$19$	0.524079			0.120232			0.0601160	+	0.998191i	$0.480853\pi$
$20$	2.32455	+	3.62369i	0.519785	+	0.810282i
$21$		−	7.65063i		−	1.66950i
$22$	5.94824	−	5.94824i	1.26817	−	1.26817i
$23$	2.91521	+	3.80809i	0.607864	+	0.794041i
$23$	2.91521	+	3.80809i	0.607864	+	0.794041i
$24$			0.309375i			0.0631508i
$25$	2.08463	−	4.54470i	0.416927	−	0.908940i
$26$	5.10155			1.00050
$27$	−2.40424	−	2.40424i	−0.462697	−	0.462697i
$28$	−4.98006	−	4.98006i	−0.941143	−	0.941143i
$29$		−	4.01110i		−	0.744842i	−0.928064	−	0.372421i	$-0.878528\pi$
$29$		−	4.01110i		−	0.744842i	0.928064	−	0.372421i	$-0.121472\pi$
$30$	−7.79896	+	5.00293i	−1.42389	+	0.913407i
$31$	−7.49669			−1.34644			−0.673222	−	0.739440i	$-0.735090\pi$
$31$	−7.49669			−1.34644			−0.673222	+	0.739440i	$0.735090\pi$
$32$	5.59600	+	5.59600i	0.989243	+	0.989243i
$33$	6.27920	+	6.27920i	1.09307	+	1.09307i
$34$	−2.47745			−0.424879
$35$	−1.74532	+	7.99114i	−0.295014	+	1.35075i
$36$	2.64601			0.441001
$37$	−5.58812	+	5.58812i	−0.918681	+	0.918681i	−0.996934	−	0.0782528i	$-0.975066\pi$
$37$	−5.58812	+	5.58812i	−0.918681	+	0.918681i	0.0782528	+	0.996934i	$0.475066\pi$
$38$	0.734210	+	0.734210i	0.119105	+	0.119105i
$39$			5.38541i			0.862355i
$40$	0.0705771	−	0.323144i	0.0111592	−	0.0510936i
$41$	−4.85068			−0.757549			−0.378774	−	0.925489i	$-0.623654\pi$
$41$	−4.85068			−0.757549			−0.378774	+	0.925489i	$0.623654\pi$
$42$	10.7182	−	10.7182i	1.65385	−	1.65385i
$43$	−6.47232	−	6.47232i	−0.987019	−	0.987019i	0.0128975	−	0.999917i	$-0.495894\pi$
$43$	−6.47232	−	6.47232i	−0.987019	−	0.987019i	−0.999917	+	0.0128975i	$0.995894\pi$
$44$	8.17471			1.23238
$45$	−1.65926	−	2.58659i	−0.247348	−	0.385586i
$46$	−1.25087	+	9.41903i	−0.184431	+	1.38876i
$47$	−2.08135	−	2.08135i	−0.303595	−	0.303595i	0.538823	−	0.842419i	$-0.318869\pi$
$47$	−2.08135	−	2.08135i	−0.303595	−	0.303595i	−0.842419	+	0.538823i	$0.818869\pi$
$48$	−6.12820	+	6.12820i	−0.884529	+	0.884529i
$49$		−	6.38088i		−	0.911555i
$50$	9.28739	−	3.44644i	1.31343	−	0.487400i
$51$		−	2.61530i		−	0.366215i
$52$	3.50555	+	3.50555i	0.486132	+	0.486132i
$53$	0.553239	+	0.553239i	0.0759932	+	0.0759932i	0.744082	−	0.668089i	$-0.232887\pi$
$53$	0.553239	+	0.553239i	0.0759932	+	0.0759932i	−0.668089	+	0.744082i	$0.732887\pi$
$54$		−	6.73646i		−	0.916716i
$55$	−5.12621	−	7.99114i	−0.691218	−	1.07752i
$56$			0.541094i			0.0723067i
$57$	−0.775062	+	0.775062i	−0.102659	+	0.102659i
$58$	5.61936	−	5.61936i	0.737858	−	0.737858i
$59$			13.5774i			1.76763i	0.467838	+	0.883814i	$0.345033\pi$
$59$			13.5774i			1.76763i	−0.467838	+	0.883814i	$0.654967\pi$
$60$	−8.79687	−	1.92130i	−1.13567	−	0.248039i
$61$			3.54262i			0.453586i	0.973943	+	0.226793i	$0.0728241\pi$
$61$			3.54262i			0.453586i	−0.973943	+	0.226793i	$0.927176\pi$
$62$	−10.5025	−	10.5025i	−1.33382	−	1.33382i
$63$	3.55477	+	3.55477i	0.447859	+	0.447859i
$64$			7.39198i			0.923998i
$65$	1.22856	−	5.62510i	0.152385	−	0.697707i
$66$			17.5937i			2.16564i
$67$	9.83397	−	9.83397i	1.20141	−	1.20141i	0.227673	−	0.973738i	$-0.426888\pi$
$67$	9.83397	−	9.83397i	1.20141	−	1.20141i	0.973738	−	0.227673i	$-0.0731117\pi$
$68$	−1.70239	−	1.70239i	−0.206445	−	0.206445i
$69$	−9.94311	−	1.32047i	−1.19701	−	0.158966i
$70$	−13.6403	+	8.75009i	−1.63033	+	1.04584i
$71$	6.28522			0.745919			0.372959	−	0.927848i	$-0.378343\pi$
$71$	6.28522			0.745919			0.372959	+	0.927848i	$0.378343\pi$
$72$	−0.143747	−	0.143747i	−0.0169407	−	0.0169407i
$73$	−3.78828	+	3.78828i	−0.443384	+	0.443384i	−0.893148	−	0.449763i	$-0.851508\pi$
$73$	−3.78828	+	3.78828i	−0.443384	+	0.443384i	0.449763	+	0.893148i	$0.351508\pi$
$74$	−15.6574			−1.82013
$75$	3.63820	+	9.80414i	0.420103	+	1.13208i
$76$			1.00903i			0.115744i
$77$	10.9823	+	10.9823i	1.25155	+	1.25155i
$78$	−7.54470	+	7.54470i	−0.854269	+	0.854269i
$79$	10.4842			1.17956			0.589782	−	0.807562i	$-0.299213\pi$
$79$	10.4842			1.17956			0.589782	+	0.807562i	$0.299213\pi$
$80$	7.79896	−	5.00293i	0.871951	−	0.559345i
$81$	11.2342			1.24824
$82$	−6.79557	−	6.79557i	−0.750446	−	0.750446i
$83$	8.53483	+	8.53483i	0.936819	+	0.936819i	0.998119	−	0.0613002i	$-0.0195247\pi$
$83$	8.53483	+	8.53483i	0.936819	+	0.936819i	−0.0613002	+	0.998119i	$0.519525\pi$
$84$	14.7301			1.60718
$85$	−0.596623	+	2.73170i	−0.0647128	+	0.296294i
$86$		−	18.1348i		−	1.95553i
$87$	5.93202	+	5.93202i	0.635980	+	0.635980i
$88$	−0.444099	−	0.444099i	−0.0473411	−	0.0473411i
$89$	−10.8704			−1.15226			−0.576132	−	0.817357i	$-0.695439\pi$
$89$	−10.8704			−1.15226			−0.576132	+	0.817357i	$0.695439\pi$
$90$	1.29914	−	5.94824i	0.136941	−	0.626999i
$91$			9.41903i			0.987383i
$92$	−7.33186	+	5.61278i	−0.764399	+	0.585172i
$93$	11.0869	−	11.0869i	1.14965	−	1.14965i
$94$		−	5.83173i		−	0.601498i
$95$	0.986371	−	0.632744i	0.101200	−	0.0649182i
$96$	−16.5519			−1.68932
$97$	−2.73658	+	2.73658i	−0.277858	+	0.277858i	−0.832253	−	0.554396i	$-0.812949\pi$
$97$	−2.73658	+	2.73658i	−0.277858	+	0.277858i	0.554396	+	0.832253i	$0.312949\pi$
$98$	8.93932	−	8.93932i	0.903008	−	0.903008i
$99$	−5.83510			−0.586450
$100$	8.75009	+	4.01363i	0.875009	+	0.401363i
$101$	0.488012			0.0485590			0.0242795	−	0.999705i	$-0.492271\pi$
$101$	0.488012			0.0485590			0.0242795	+	0.999705i	$0.492271\pi$
$102$	3.66391	−	3.66391i	0.362781	−	0.362781i
$103$	−3.91489	−	3.91489i	−0.385746	−	0.385746i	0.487421	−	0.873167i	$-0.337938\pi$
$103$	−3.91489	−	3.91489i	−0.385746	−	0.385746i	−0.873167	+	0.487421i	$0.837938\pi$
$104$		−	0.380885i		−	0.0373488i
$105$	−9.23695	−	14.3993i	−0.901434	−	1.40523i
$106$			1.55012i			0.150561i
$107$	−4.87092	+	4.87092i	−0.470890	+	0.470890i	−0.902203	−	0.431313i	$-0.858051\pi$
$107$	−4.87092	+	4.87092i	−0.470890	+	0.470890i	0.431313	+	0.902203i	$0.358051\pi$
$108$	4.62898	−	4.62898i	0.445424	−	0.445424i
$109$	6.58545			0.630772			0.315386	−	0.948963i	$-0.397866\pi$
$109$	6.58545			0.630772			0.315386	+	0.948963i	$0.397866\pi$
$110$	4.01363	−	18.3768i	0.382685	−	1.75216i
$111$		−	16.5286i		−	1.56882i
$112$	−10.7182	+	10.7182i	−1.01277	+	1.01277i
$113$	3.11067	+	3.11067i	0.292627	+	0.292627i	0.838117	−	0.545490i	$-0.183656\pi$
$113$	3.11067	+	3.11067i	0.292627	+	0.292627i	−0.545490	+	0.838117i	$0.683656\pi$
$114$	−2.17165			−0.203394
$115$	10.0844	+	3.64755i	0.940376	+	0.340136i
$116$	7.72273			0.717037
$117$	−2.50226	−	2.50226i	−0.231334	−	0.231334i
$118$	−19.0213	+	19.0213i	−1.75105	+	1.75105i
$119$		−	4.57413i		−	0.419310i
$120$	0.373522	+	0.582275i	0.0340977	+	0.0531542i
$121$	−7.02726			−0.638842
$122$	−4.96305	+	4.96305i	−0.449333	+	0.449333i
$123$	7.17368	−	7.17368i	0.646829	−	0.646829i
$124$		−	14.4337i		−	1.29618i
$125$	−1.56352	−	11.0705i	−0.139846	−	0.990173i
$126$			9.96012i			0.887318i
$127$	−11.5902	−	11.5902i	−1.02846	−	1.02846i	−0.999583	−	0.0288796i	$-0.990806\pi$
$127$	−11.5902	−	11.5902i	−1.02846	−	1.02846i	−0.0288796	−	0.999583i	$-0.509194\pi$
$128$	0.836185	−	0.836185i	0.0739090	−	0.0739090i
$129$	19.1439			1.68552
$130$	9.60165	−	6.15934i	0.842121	−	0.540209i
$131$	7.75071			0.677183			0.338591	−	0.940934i	$-0.390050\pi$
$131$	7.75071			0.677183			0.338591	+	0.940934i	$0.390050\pi$
$132$	−12.0896	+	12.0896i	−1.05226	+	1.05226i
$133$	−1.35558	+	1.35558i	−0.117543	+	0.117543i
$134$	27.5539			2.38029
$135$	−7.42779	−	1.62228i	−0.639282	−	0.139624i
$136$			0.184968i			0.0158609i
$137$	−7.12655	+	7.12655i	−0.608862	+	0.608862i	−0.942649	−	0.333787i	$-0.891674\pi$
$137$	−7.12655	+	7.12655i	−0.608862	+	0.608862i	0.333787	+	0.942649i	$0.391674\pi$
$138$	−12.0799	−	15.7797i	−1.02831	−	1.34326i
$139$		−	9.78245i		−	0.829737i	−0.909881	−	0.414868i	$-0.863828\pi$
$139$		−	9.78245i		−	0.829737i	0.909881	−	0.414868i	$-0.136172\pi$
$140$	−15.3857	−	3.36034i	−1.30032	−	0.284001i
$141$	6.15622			0.518447
$142$	8.80530	+	8.80530i	0.738925	+	0.738925i
$143$	−7.73061	−	7.73061i	−0.646466	−	0.646466i
$144$		−	5.69478i		−	0.474565i
$145$	−4.84278	−	7.54931i	−0.402171	−	0.626936i
$146$	−10.6144			−0.878454
$147$	9.43671	+	9.43671i	0.778327	+	0.778327i
$148$	−10.7590	−	10.7590i	−0.884386	−	0.884386i
$149$	17.5133			1.43475			0.717373	−	0.696689i	$-0.245344\pi$
$149$	17.5133			1.43475			0.717373	+	0.696689i	$0.245344\pi$
$150$	−8.63820	+	18.8321i	−0.705306	+	1.53763i
$151$	8.88661			0.723182			0.361591	−	0.932337i	$-0.382234\pi$
$151$	8.88661			0.723182			0.361591	+	0.932337i	$0.382234\pi$
$152$	0.0548165	−	0.0548165i	0.00444621	−	0.00444621i
$153$	1.21516	+	1.21516i	0.0982402	+	0.0982402i
$154$			30.7713i			2.47962i
$155$	−14.1095	+	9.05109i	−1.13331	+	0.727001i
$156$	−10.3687			−0.830163
$157$	−4.46767	+	4.46767i	−0.356559	+	0.356559i	−0.862543	−	0.505984i	$-0.831130\pi$
$157$	−4.46767	+	4.46767i	−0.356559	+	0.356559i	0.505984	+	0.862543i	$0.331130\pi$
$158$	14.6879	+	14.6879i	1.16850	+	1.16850i
$159$	−1.63637			−0.129773
$160$	17.2886	+	3.77595i	1.36678	+	0.298515i
$161$	−17.3904	−	2.30950i	−1.37056	−	0.182014i
$162$	15.7386	+	15.7386i	1.23654	+	1.23654i
$163$	−16.1787	+	16.1787i	−1.26721	+	1.26721i	−0.319691	+	0.947522i	$0.603579\pi$
$163$	−16.1787	+	16.1787i	−1.26721	+	1.26721i	−0.947522	+	0.319691i	$0.896421\pi$
$164$		−	9.33920i		−	0.729269i
$165$	19.3993	+	4.23695i	1.51023	+	0.329846i
$166$			23.9138i			1.85607i
$167$	4.56719	+	4.56719i	0.353420	+	0.353420i	0.861380	−	0.507960i	$-0.169600\pi$
$167$	4.56719	+	4.56719i	0.353420	+	0.353420i	−0.507960	+	0.861380i	$0.669600\pi$
$168$	−0.800225	−	0.800225i	−0.0617387	−	0.0617387i
$169$			6.36979i			0.489984i
$170$	−4.66282	+	2.99114i	−0.357622	+	0.229410i
$171$		−	0.720245i		−	0.0550785i
$172$	12.4614	−	12.4614i	0.950174	−	0.950174i
$173$	−5.73382	+	5.73382i	−0.435935	+	0.435935i	−0.890641	−	0.454707i	$-0.849744\pi$
$173$	−5.73382	+	5.73382i	−0.435935	+	0.435935i	0.454707	+	0.890641i	$0.349744\pi$
$174$			16.6210i			1.26003i
$175$	6.36318	+	17.1474i	0.481011	+	1.29622i
$176$		−	17.5937i		−	1.32618i
$177$	−20.0797	−	20.0797i	−1.50928	−	1.50928i
$178$	−15.2290	−	15.2290i	−1.14146	−	1.14146i
$179$			3.90640i			0.291978i	0.989286	+	0.145989i	$0.0466364\pi$
$179$			3.90640i			0.291978i	−0.989286	+	0.145989i	$0.953364\pi$
$180$	4.98006	−	3.19464i	0.371192	−	0.238115i
$181$		−	21.2572i		−	1.58003i	−0.613085	−	0.790017i	$-0.710072\pi$
$181$		−	21.2572i		−	1.58003i	0.613085	−	0.790017i	$-0.289928\pi$
$182$	−13.1956	+	13.1956i	−0.978124	+	0.978124i
$183$	−5.23919	−	5.23919i	−0.387292	−	0.387292i
$184$	0.703230	+	0.0933910i	0.0518428	+	0.00688487i
$185$	−3.77063	+	17.2642i	−0.277222	+	1.26929i
$186$	31.0644			2.27775
$187$	3.75419	+	3.75419i	0.274533	+	0.274533i
$188$	4.00730	−	4.00730i	0.292262	−	0.292262i
$189$	12.4376			0.904700
$190$	2.26830	+	0.495415i	0.164560	+	0.0359412i
$191$		−	2.78325i		−	0.201389i	−0.994917	−	0.100694i	$-0.967894\pi$
$191$		−	2.78325i		−	0.201389i	0.994917	−	0.100694i	$-0.0321064\pi$
$192$	−10.9320	−	10.9320i	−0.788951	−	0.788951i
$193$	9.50337	−	9.50337i	0.684068	−	0.684068i	−0.276847	−	0.960914i	$-0.589289\pi$
$193$	9.50337	−	9.50337i	0.684068	−	0.684068i	0.960914	+	0.276847i	$0.0892894\pi$
$194$	−7.66764			−0.550505
$195$	6.50204	+	10.1359i	0.465621	+	0.725847i
$196$	12.2854			0.877526
$197$	−1.97143	−	1.97143i	−0.140459	−	0.140459i	0.633381	−	0.773840i	$-0.281667\pi$
$197$	−1.97143	−	1.97143i	−0.140459	−	0.140459i	−0.773840	+	0.633381i	$0.781667\pi$
$198$	−8.17471	−	8.17471i	−0.580951	−	0.580951i
$199$	−10.5829			−0.750203			−0.375102	−	0.926984i	$-0.622392\pi$
$199$	−10.5829			−0.750203			−0.375102	+	0.926984i	$0.622392\pi$
$200$	−0.257313	−	0.693402i	−0.0181948	−	0.0490309i
$201$			29.0870i			2.05164i
$202$	0.683681	+	0.683681i	0.0481037	+	0.0481037i
$203$	10.3751	+	10.3751i	0.728187	+	0.728187i
$204$	5.03533			0.352544
$205$	−9.12948	+	5.85644i	−0.637631	+	0.409032i
$206$		−	10.9692i		−	0.764257i
$207$	5.23348	−	4.00640i	0.363752	−	0.278464i
$208$	7.54470	−	7.54470i	0.523131	−	0.523131i
$209$		−	2.22516i		−	0.153918i
$210$	7.23218	−	33.1132i	0.499068	−	2.28503i
$211$	−7.53925			−0.519023			−0.259512	−	0.965740i	$-0.583562\pi$
$211$	−7.53925			−0.519023			−0.259512	+	0.965740i	$0.583562\pi$
$212$	−1.06517	+	1.06517i	−0.0731563	+	0.0731563i
$213$	−9.29523	+	9.29523i	−0.636899	+	0.636899i
$214$	−13.6479			−0.932949
$215$	−19.9959	−	4.36726i	−1.36371	−	0.297844i
$216$	−0.502948			−0.0342213
$217$	19.3908	−	19.3908i	1.31634	−	1.31634i
$218$	9.22591	+	9.22591i	0.624858	+	0.624858i
$219$		−	11.2050i		−	0.757163i
$220$	15.3857	−	9.86969i	1.03730	−	0.665415i
$221$			3.21981i			0.216588i
$222$	23.1557	−	23.1557i	1.55411	−	1.55411i
$223$	10.7644	−	10.7644i	0.720838	−	0.720838i	−0.247938	−	0.968776i	$-0.579753\pi$
$223$	10.7644	−	10.7644i	0.720838	−	0.720838i	0.968776	+	0.247938i	$0.0797529\pi$
$224$	−28.9491			−1.93424
$225$	−6.24581	−	2.86493i	−0.416387	−	0.190995i
$226$			8.71580i			0.579766i
$227$	15.6982	−	15.6982i	1.04193	−	1.04193i	0.0428466	−	0.999082i	$-0.486357\pi$
$227$	15.6982	−	15.6982i	1.04193	−	1.04193i	0.999082	−	0.0428466i	$-0.0136427\pi$
$228$	−1.49226	−	1.49226i	−0.0988271	−	0.0988271i
$229$	−0.305799			−0.0202078			−0.0101039	−	0.999949i	$-0.503216\pi$
$229$	−0.305799			−0.0202078			−0.0101039	+	0.999949i	$0.503216\pi$
$230$	9.01775	+	19.2378i	0.594613	+	1.26851i
$231$	−32.4834			−2.13725
$232$	−0.419545	−	0.419545i	−0.0275445	−	0.0275445i
$233$	−12.4523	+	12.4523i	−0.815779	+	0.815779i	−0.985493	−	0.169714i	$-0.945716\pi$
$233$	−12.4523	+	12.4523i	−0.815779	+	0.815779i	0.169714	+	0.985493i	$0.445716\pi$
$234$		−	7.01110i		−	0.458330i
$235$	−6.43021	−	1.40441i	−0.419461	−	0.0916134i
$236$	−26.1411			−1.70164
$237$	−15.5051	+	15.5051i	−1.00717	+	1.00717i
$238$	6.40814	−	6.40814i	0.415378	−	0.415378i
$239$			9.23593i			0.597423i	0.954344	+	0.298711i	$0.0965568\pi$
$239$			9.23593i			0.597423i	−0.954344	+	0.298711i	$0.903443\pi$
$240$	−4.13506	+	18.9328i	−0.266917	+	1.22210i
$241$			2.91528i			0.187790i	0.995582	+	0.0938948i	$0.0299317\pi$
$241$			2.91528i			0.187790i	−0.995582	+	0.0938948i	$0.970068\pi$
$242$	−9.84486	−	9.84486i	−0.632852	−	0.632852i
$243$	−9.40156	+	9.40156i	−0.603111	+	0.603111i
$244$	−6.82075			−0.436654
$245$	−7.70393	−	12.0095i	−0.492186	−	0.767258i
$246$	20.1000			1.28153
$247$	0.954213	−	0.954213i	0.0607151	−	0.0607151i
$248$	−0.784123	+	0.784123i	−0.0497919	+	0.0497919i
$249$	−25.2444			−1.59980
$250$	13.3188	−	17.6996i	0.842354	−	1.11942i
$251$			19.1830i			1.21082i	0.795914	+	0.605410i	$0.206991\pi$
$251$			19.1830i			1.21082i	−0.795914	+	0.605410i	$0.793009\pi$
$252$	−6.84413	+	6.84413i	−0.431140	+	0.431140i
$253$	16.1686	−	12.3776i	1.01651	−	0.778171i
$254$		−	32.4746i		−	2.03764i
$255$	−3.15756	−	4.92226i	−0.197734	−	0.308244i
$256$	17.1269			1.07043
$257$	−5.08878	−	5.08878i	−0.317429	−	0.317429i	0.530350	−	0.847779i	$-0.322061\pi$
$257$	−5.08878	−	5.08878i	−0.317429	−	0.317429i	−0.847779	+	0.530350i	$0.822061\pi$
$258$	26.8196	+	26.8196i	1.66972	+	1.66972i
$259$		−	28.9083i		−	1.79628i
$260$	10.8302	+	2.36540i	0.671662	+	0.146696i
$261$	−5.51248			−0.341214
$262$	10.8584	+	10.8584i	0.670833	+	0.670833i
$263$	−5.79825	−	5.79825i	−0.357535	−	0.357535i	0.505368	−	0.862904i	$-0.331357\pi$
$263$	−5.79825	−	5.79825i	−0.357535	−	0.357535i	−0.862904	+	0.505368i	$0.831357\pi$
$264$	1.31356			0.0808439
$265$	1.70920	+	0.373303i	0.104996	+	0.0229318i
$266$	−3.79820			−0.232882
$267$	16.0763	−	16.0763i	0.983855	−	0.983855i
$268$	18.9337	+	18.9337i	1.15656	+	1.15656i
$269$			6.52449i			0.397805i	0.980019	+	0.198902i	$0.0637377\pi$
$269$			6.52449i			0.397805i	−0.980019	+	0.198902i	$0.936262\pi$
$270$	−8.13324	−	12.6787i	−0.494973	−	0.771603i
$271$	15.6908			0.953148			0.476574	−	0.879134i	$-0.341879\pi$
$271$	15.6908			0.953148			0.476574	+	0.879134i	$0.341879\pi$
$272$	−3.66391	+	3.66391i	−0.222157	+	0.222157i
$273$	−13.9298	−	13.9298i	−0.843072	−	0.843072i
$274$	−19.9679			−1.20631
$275$	−19.2961	−	8.85105i	−1.16360	−	0.533738i
$276$	2.54236	−	19.1439i	0.153032	−	1.15232i
$277$	12.5541	+	12.5541i	0.754300	+	0.754300i	0.975279	−	0.220979i	$-0.0709251\pi$
$277$	12.5541	+	12.5541i	0.754300	+	0.754300i	−0.220979	+	0.975279i	$0.570925\pi$
$278$	13.7048	−	13.7048i	0.821956	−	0.821956i
$279$			10.3027i			0.616809i
$280$	0.653287	+	1.01839i	0.0390414	+	0.0608607i
$281$		−	5.68024i		−	0.338855i	−0.985543	−	0.169427i	$-0.945808\pi$
$281$		−	5.68024i		−	0.338855i	0.985543	−	0.169427i	$-0.0541918\pi$
$282$	8.62457	+	8.62457i	0.513586	+	0.513586i
$283$	4.72681	+	4.72681i	0.280979	+	0.280979i	0.833500	−	0.552520i	$-0.186334\pi$
$283$	4.72681	+	4.72681i	0.280979	+	0.280979i	−0.552520	+	0.833500i	$0.686334\pi$
$284$			12.1012i			0.718073i
$285$	−0.522980	+	2.39451i	−0.0309787	+	0.141839i
$286$		−	21.6604i		−	1.28081i
$287$	12.5467	−	12.5467i	0.740609	−	0.740609i
$288$	7.69063	−	7.69063i	0.453174	−	0.453174i
$289$			15.4364i			0.908022i
$290$	3.79171	−	17.3607i	0.222657	−	1.01946i
$291$		−	8.09427i		−	0.474495i
$292$	−7.29372	−	7.29372i	−0.426833	−	0.426833i
$293$	15.5891	+	15.5891i	0.910724	+	0.910724i	0.996329	−	0.0856047i	$-0.0272822\pi$
$293$	15.5891	+	15.5891i	0.910724	+	0.910724i	−0.0856047	+	0.996329i	$0.527282\pi$
$294$			26.4408i			1.54206i
$295$	16.3926	+	25.5541i	0.954416	+	1.48782i
$296$			1.16899i			0.0679461i
$297$	−10.2081	+	10.2081i	−0.592331	+	0.592331i
$298$	24.5353	+	24.5353i	1.42129	+	1.42129i
$299$	12.2414	+	1.62569i	0.707939	+	0.0940163i
$300$	−18.8763	+	7.00477i	−1.08982	+	0.404420i
$301$	33.4825			1.92990
$302$	12.4497	+	12.4497i	0.716401	+	0.716401i
$303$	−0.721722	+	0.721722i	−0.0414618	+	0.0414618i
$304$	2.17165			0.124553
$305$	4.27717	+	6.66758i	0.244910	+	0.381785i
$306$			3.40478i			0.194638i
$307$	−0.539934	−	0.539934i	−0.0308157	−	0.0308157i	0.691531	−	0.722347i	$-0.256937\pi$
$307$	−0.539934	−	0.539934i	−0.0308157	−	0.0308157i	−0.722347	+	0.691531i	$0.756937\pi$
$308$	−21.1446	+	21.1446i	−1.20483	+	1.20483i
$309$	11.5795			0.658734
$310$	−32.4470	−	7.08666i	−1.84286	−	0.402495i
$311$	13.9115			0.788846			0.394423	−	0.918929i	$-0.370944\pi$
$311$	13.9115			0.788846			0.394423	+	0.918929i	$0.370944\pi$
$312$	0.563292	+	0.563292i	0.0318901	+	0.0318901i
$313$	−16.3093	−	16.3093i	−0.921858	−	0.921858i	0.0753025	−	0.997161i	$-0.476008\pi$
$313$	−16.3093	−	16.3093i	−0.921858	−	0.921858i	−0.997161	+	0.0753025i	$0.976008\pi$
$314$	−12.5180			−0.706432
$315$	10.9823	+	2.39861i	0.618781	+	0.135146i
$316$			20.1856i			1.13553i
$317$	−10.0129	−	10.0129i	−0.562378	−	0.562378i	0.367604	−	0.929982i	$-0.380178\pi$
$317$	−10.0129	−	10.0129i	−0.562378	−	0.562378i	−0.929982	+	0.367604i	$0.880178\pi$
$318$	−2.29248	−	2.29248i	−0.128556	−	0.128556i
$319$	−17.0305			−0.953527
$320$	8.92468	+	13.9125i	0.498905	+	0.777732i
$321$		−	14.4072i		−	0.804134i
$322$	−21.1277	−	27.5987i	−1.17740	−	1.53801i
$323$	−0.463391	+	0.463391i	−0.0257838	+	0.0257838i
$324$			21.6297i			1.20165i
$325$	−4.47915	−	12.0703i	−0.248458	−	0.669541i
$326$	−45.3312			−2.51066
$327$	−9.73925	+	9.73925i	−0.538582	+	0.538582i
$328$	−0.507361	+	0.507361i	−0.0280144	+	0.0280144i
$329$	10.7672			0.593613
$330$	21.2417	+	33.1132i	1.16932	+	1.82282i
$331$	−14.0712			−0.773422			−0.386711	−	0.922201i	$-0.626389\pi$
$331$	−14.0712			−0.773422			−0.386711	+	0.922201i	$0.626389\pi$
$332$	−16.4324	+	16.4324i	−0.901847	+	0.901847i
$333$	7.67979	+	7.67979i	0.420850	+	0.420850i
$334$			12.7968i			0.700212i
$335$	6.63556	−	30.3816i	0.362539	−	1.65992i
$336$		−	31.7023i		−	1.72950i
$337$	2.71142	−	2.71142i	0.147700	−	0.147700i	−0.629390	−	0.777090i	$-0.716695\pi$
$337$	2.71142	−	2.71142i	0.147700	−	0.147700i	0.777090	+	0.629390i	$0.216695\pi$
$338$	−8.92377	+	8.92377i	−0.485389	+	0.485389i
$339$	−9.20075			−0.499716
$340$	−5.25944	−	1.14870i	−0.285233	−	0.0622971i
$341$			31.8298i			1.72368i
$342$	1.00903	−	1.00903i	0.0545621	−	0.0545621i
$343$	−1.60140	−	1.60140i	−0.0864673	−	0.0864673i
$344$	−1.35396			−0.0730005
$345$	−20.3082	+	9.51950i	−1.09336	+	0.512513i
$346$	−16.0656			−0.863694
$347$	−22.3073	−	22.3073i	−1.19752	−	1.19752i	−0.974908	−	0.222609i	$-0.928543\pi$
$347$	−22.3073	−	22.3073i	−1.19752	−	1.19752i	−0.222609	−	0.974908i	$-0.571457\pi$
$348$	−11.4212	+	11.4212i	−0.612238	+	0.612238i
$349$			5.25900i			0.281508i	0.990045	+	0.140754i	$0.0449526\pi$
$349$			5.25900i			0.281508i	−0.990045	+	0.140754i	$0.955047\pi$
$350$	−15.1081	+	32.9372i	−0.807564	+	1.76057i
$351$	−8.75502			−0.467308
$352$	23.7598	−	23.7598i	1.26640	−	1.26640i
$353$	22.9940	−	22.9940i	1.22385	−	1.22385i	0.257595	−	0.966253i	$-0.417070\pi$
$353$	22.9940	−	22.9940i	1.22385	−	1.22385i	0.966253	−	0.257595i	$-0.0829301\pi$
$354$		−	56.2614i		−	2.99026i
$355$	11.8294	−	7.58843i	0.627842	−	0.402752i
$356$		−	20.9293i		−	1.10925i
$357$	6.76469	+	6.76469i	0.358026	+	0.358026i
$358$	−5.47268	+	5.47268i	−0.289240	+	0.289240i
$359$	6.80373			0.359087			0.179544	−	0.983750i	$-0.442538\pi$
$359$	6.80373			0.359087			0.179544	+	0.983750i	$0.442538\pi$
$360$	−0.444099	−	0.0969946i	−0.0234061	−	0.00511206i
$361$	−18.7253			−0.985544
$362$	29.7803	−	29.7803i	1.56522	−	1.56522i
$363$	10.3926	−	10.3926i	0.545472	−	0.545472i
$364$	−18.1348			−0.950523
$365$	−2.55617	+	11.7037i	−0.133796	+	0.612599i
$366$		−	14.6797i		−	0.767322i
$367$	3.54662	−	3.54662i	0.185132	−	0.185132i	−0.608456	−	0.793588i	$-0.708211\pi$
$367$	3.54662	−	3.54662i	0.185132	−	0.185132i	0.793588	+	0.608456i	$0.208211\pi$
$368$	12.0799	+	15.7797i	0.629709	+	0.822576i
$369$			6.66632i			0.347035i
$370$	−29.4688	+	18.9039i	−1.53201	+	0.982765i
$371$	−2.86200			−0.148588
$372$	21.3460	+	21.3460i	1.10674	+	1.10674i
$373$	−4.61812	−	4.61812i	−0.239117	−	0.239117i	0.577367	−	0.816485i	$-0.304080\pi$
$373$	−4.61812	−	4.61812i	−0.239117	−	0.239117i	−0.816485	+	0.577367i	$0.804080\pi$
$374$			10.5189i			0.543918i
$375$	18.6845	+	14.0599i	0.964861	+	0.726048i
$376$	−0.435401			−0.0224541
$377$	−7.30318	−	7.30318i	−0.376133	−	0.376133i
$378$	17.4245	+	17.4245i	0.896217	+	0.896217i
$379$	−28.0276			−1.43968			−0.719841	−	0.694139i	$-0.755785\pi$
$379$	−28.0276			−1.43968			−0.719841	+	0.694139i	$0.755785\pi$
$380$	1.21825	+	1.89910i	0.0624948	+	0.0974217i
$381$	34.2815			1.75629
$382$	3.89920	−	3.89920i	0.199500	−	0.199500i
$383$	−24.8950	−	24.8950i	−1.27207	−	1.27207i	−0.944998	−	0.327076i	$-0.893937\pi$
$383$	−24.8950	−	24.8950i	−1.27207	−	1.27207i	−0.327076	−	0.944998i	$-0.606063\pi$
$384$			2.47327i			0.126214i
$385$	33.9292	+	7.41039i	1.72919	+	0.377668i
$386$	26.6276			1.35531
$387$	−8.89495	+	8.89495i	−0.452156	+	0.452156i
$388$	−5.26885	−	5.26885i	−0.267485	−	0.267485i
$389$	12.7847			0.648209			0.324104	−	0.946021i	$-0.394937\pi$
$389$	12.7847			0.648209			0.324104	+	0.946021i	$0.394937\pi$
$390$	−5.09086	+	23.3090i	−0.257785	+	1.18030i
$391$	−5.94475	−	0.789480i	−0.300639	−	0.0399257i
$392$	−0.667415	−	0.667415i	−0.0337095	−	0.0337095i
$393$	−11.4625	+	11.4625i	−0.578209	+	0.578209i
$394$		−	5.52377i		−	0.278284i
$395$	19.7324	−	12.6581i	0.992843	−	0.636896i
$396$		−	11.2346i		−	0.564558i
$397$	27.1558	+	27.1558i	1.36291	+	1.36291i	0.870184	+	0.492727i	$0.164000\pi$
$397$	27.1558	+	27.1558i	1.36291	+	1.36291i	0.492727	+	0.870184i	$0.336000\pi$
$398$	−14.8262	−	14.8262i	−0.743169	−	0.743169i
$399$		−	4.00953i		−	0.200728i
$400$	8.63820	−	18.8321i	0.431910	−	0.941604i
$401$			10.6634i			0.532502i	0.963904	+	0.266251i	$0.0857851\pi$
$401$			10.6634i			0.532502i	−0.963904	+	0.266251i	$0.914215\pi$
$402$	−40.7495	+	40.7495i	−2.03240	+	2.03240i
$403$	−13.6495	+	13.6495i	−0.679932	+	0.679932i
$404$			0.939588i			0.0467462i
$405$	21.1439	−	13.5636i	1.05065	−	0.673979i
$406$			29.0700i			1.44272i
$407$	23.7263	+	23.7263i	1.17607	+	1.17607i
$408$	−0.273549	−	0.273549i	−0.0135427	−	0.0135427i
$409$		−	23.2475i		−	1.14951i	−0.818324	−	0.574757i	$-0.805096\pi$
$409$		−	23.2475i		−	1.14951i	0.818324	−	0.574757i	$-0.194904\pi$
$410$	−20.9946	−	4.58538i	−1.03685	−	0.226456i
$411$		−	21.0789i		−	1.03975i
$412$	7.53749	−	7.53749i	0.371346	−	0.371346i
$413$	−35.1192	−	35.1192i	−1.72810	−	1.72810i
$414$	12.9446	+	1.71908i	0.636194	+	0.0844884i
$415$	26.3679	+	5.75895i	1.29435	+	0.282696i
$416$	20.3778			0.999103
$417$	14.4673	+	14.4673i	0.708466	+	0.708466i
$418$	3.11735	−	3.11735i	0.152474	−	0.152474i
$419$	−29.1857			−1.42581			−0.712907	−	0.701259i	$-0.752622\pi$
$419$	−29.1857			−1.42581			−0.712907	+	0.701259i	$0.752622\pi$
$420$	27.7235	−	17.7843i	1.35277	−	0.867783i
$421$			1.45722i			0.0710206i	0.999369	+	0.0355103i	$0.0113057\pi$
$421$			1.45722i			0.0710206i	−0.999369	+	0.0355103i	$0.988694\pi$
$422$	−10.5621	−	10.5621i	−0.514156	−	0.514156i
$423$	−2.86041	+	2.86041i	−0.139078	+	0.139078i
$424$	0.115733			0.00562050
$425$	2.17519	+	5.86167i	0.105512	+	0.284333i
$426$	−26.0444			−1.26185
$427$	−9.16331	−	9.16331i	−0.443443	−	0.443443i
$428$	−9.37818	−	9.37818i	−0.453311	−	0.453311i
$429$	22.8656			1.10396
$430$	−21.8950	−	34.1316i	−1.05587	−	1.64597i
$431$		−	0.582399i		−	0.0280532i	−0.999902	−	0.0140266i	$-0.995535\pi$
$431$		−	0.582399i		−	0.0280532i	0.999902	−	0.0140266i	$-0.00446495\pi$
$432$	−9.96257	−	9.96257i	−0.479324	−	0.479324i
$433$	−10.9710	−	10.9710i	−0.527231	−	0.527231i	0.392515	−	0.919746i	$-0.371605\pi$
$433$	−10.9710	−	10.9710i	−0.527231	−	0.527231i	−0.919746	+	0.392515i	$0.871605\pi$
$434$	54.3313			2.60799
$435$	18.3267	+	4.00269i	0.878698	+	0.191914i
$436$			12.6792i			0.607225i
$437$	1.52780	+	1.99574i	0.0730847	+	0.0954691i
$438$	15.6977	−	15.6977i	0.750063	−	0.750063i
$439$			16.6345i			0.793923i	0.917835	+	0.396962i	$0.129935\pi$
$439$			16.6345i			0.793923i	−0.917835	+	0.396962i	$0.870065\pi$
$440$	−1.37202	−	0.299660i	−0.0654086	−	0.0142857i
$441$	−8.76929			−0.417585
$442$	−4.51080	+	4.51080i	−0.214557	+	0.214557i
$443$	10.7205	−	10.7205i	0.509347	−	0.509347i	−0.404979	−	0.914326i	$-0.632721\pi$
$443$	10.7205	−	10.7205i	0.509347	−	0.509347i	0.914326	+	0.404979i	$0.132721\pi$
$444$	31.8231			1.51026
$445$	−20.4593	+	13.1244i	−0.969864	+	0.622155i
$446$	30.1609			1.42816
$447$	−25.9005	+	25.9005i	−1.22505	+	1.22505i
$448$	−19.1200	−	19.1200i	−0.903336	−	0.903336i
$449$		−	6.41439i		−	0.302714i	−0.988479	−	0.151357i	$-0.951636\pi$
$449$		−	6.41439i		−	0.302714i	0.988479	−	0.151357i	$-0.0483643\pi$
$450$	−4.73646	−	12.7637i	−0.223279	−	0.601687i
$451$			20.5953i			0.969793i
$452$	−5.98909	+	5.98909i	−0.281703	+	0.281703i
$453$	−13.1424	+	13.1424i	−0.617485	+	0.617485i
$454$	43.9850			2.06432
$455$	11.3720	+	17.7276i	0.533129	+	0.831083i
$456$			0.162137i			0.00759274i
$457$	−10.2641	+	10.2641i	−0.480134	+	0.480134i	−0.905175	−	0.425040i	$-0.860260\pi$
$457$	−10.2641	+	10.2641i	−0.480134	+	0.480134i	0.425040	+	0.905175i	$0.360260\pi$
$458$	−0.428411	−	0.428411i	−0.0200183	−	0.0200183i
$459$	4.25167			0.198451
$460$	−7.02277	+	19.4159i	−0.327438	+	0.905272i
$461$	15.0573			0.701286			0.350643	−	0.936509i	$-0.385963\pi$
$461$	15.0573			0.701286			0.350643	+	0.936509i	$0.385963\pi$
$462$	−45.5078	−	45.5078i	−2.11721	−	2.11721i
$463$	8.68190	−	8.68190i	0.403482	−	0.403482i	−0.475976	−	0.879458i	$-0.657905\pi$
$463$	8.68190	−	8.68190i	0.403482	−	0.403482i	0.879458	+	0.475976i	$0.157905\pi$
$464$		−	16.6210i		−	0.771609i
$465$	7.48097	−	34.2523i	0.346922	−	1.58841i
$466$	−34.8903			−1.61626
$467$	20.4003	−	20.4003i	0.944015	−	0.944015i	−0.0544992	−	0.998514i	$-0.517356\pi$
$467$	20.4003	−	20.4003i	0.944015	−	0.944015i	0.998514	+	0.0544992i	$0.0173562\pi$
$468$	4.81770	−	4.81770i	0.222698	−	0.222698i
$469$			50.8729i			2.34909i
$470$	−7.04092	−	10.9759i	−0.324773	−	0.506282i
$471$		−	13.2145i		−	0.608893i
$472$	1.42014	+	1.42014i	0.0653674	+	0.0653674i
$473$	−27.4805	+	27.4805i	−1.26355	+	1.26355i
$474$	−43.4439			−1.99544
$475$	1.09251	−	2.38178i	0.0501279	−	0.109284i
$476$	8.80675			0.403657
$477$	0.760320	−	0.760320i	0.0348127	−	0.0348127i
$478$	−12.9391	+	12.9391i	−0.591821	+	0.591821i
$479$	22.4278			1.02475			0.512376	−	0.858761i	$-0.328765\pi$
$479$	22.4278			1.02475			0.512376	+	0.858761i	$0.328765\pi$
$480$	−31.1524	+	19.9838i	−1.42191	+	0.912134i
$481$			20.3491i			0.927837i
$482$	−4.08417	+	4.08417i	−0.186029	+	0.186029i
$483$	29.1343	−	22.3032i	1.32565	−	1.01483i
$484$		−	13.5299i		−	0.614993i
$485$	−1.84653	+	8.45453i	−0.0838467	+	0.383900i
$486$	−26.3423			−1.19491
$487$	−3.84312	−	3.84312i	−0.174148	−	0.174148i	0.614651	−	0.788799i	$-0.289297\pi$
$487$	−3.84312	−	3.84312i	−0.174148	−	0.174148i	−0.788799	+	0.614651i	$0.789297\pi$
$488$	0.370544	+	0.370544i	0.0167737	+	0.0167737i
$489$		−	47.8534i		−	2.16401i
$490$	6.03189	−	27.6176i	0.272493	−	1.24764i
$491$	22.5199			1.01631			0.508155	−	0.861266i	$-0.330328\pi$
$491$	22.5199			1.01631			0.508155	+	0.861266i	$0.330328\pi$
$492$	13.8118	+	13.8118i	0.622683	+	0.622683i
$493$	3.54662	+	3.54662i	0.159732	+	0.159732i
$494$	2.67362			0.120292
$495$	−10.9823	+	7.04498i	−0.493616	+	0.316649i
$496$	−31.0644			−1.39483
$497$	−16.2573	+	16.2573i	−0.729239	+	0.729239i
$498$	−35.3662	−	35.3662i	−1.58480	−	1.58480i
$499$		−	8.97150i		−	0.401620i	−0.979630	−	0.200810i	$-0.935643\pi$
$499$		−	8.97150i		−	0.401620i	0.979630	−	0.200810i	$-0.0643573\pi$
$500$	21.3144	−	3.01031i	0.953210	−	0.134625i
$501$	−13.5089			−0.603532
$502$	−26.8745	+	26.8745i	−1.19947	+	1.19947i
$503$	19.4362	+	19.4362i	0.866619	+	0.866619i	0.992096	−	0.125477i	$-0.0400462\pi$
$503$	19.4362	+	19.4362i	0.866619	+	0.866619i	−0.125477	+	0.992096i	$0.540046\pi$
$504$	0.743629			0.0331239
$505$	0.918489	−	0.589198i	0.0408722	−	0.0262190i
$506$	39.9918	+	5.31102i	1.77785	+	0.236104i
$507$	−9.42030	−	9.42030i	−0.418370	−	0.418370i
$508$	22.3150	−	22.3150i	0.990070	−	0.990070i
$509$		−	14.8111i		−	0.656491i	−0.944592	−	0.328246i	$-0.893543\pi$
$509$		−	14.8111i		−	0.656491i	0.944592	−	0.328246i	$-0.106457\pi$
$510$	2.47225	−	11.3195i	0.109473	−	0.501234i
$511$		−	19.5974i		−	0.866939i
$512$	22.3216	+	22.3216i	0.986484	+	0.986484i
$513$	−1.26001	−	1.26001i	−0.0556309	−	0.0556309i
$514$		−	14.2583i		−	0.628906i
$515$	−12.0949	−	2.64161i	−0.532963	−	0.116403i
$516$			36.8584i			1.62260i
$517$	−8.83708	+	8.83708i	−0.388655	+	0.388655i
$518$	40.4992	−	40.4992i	1.77943	−	1.77943i
$519$		−	16.9595i		−	0.744441i
$520$	−0.459860	−	0.716865i	−0.0201662	−	0.0314366i
$521$			14.1668i			0.620661i	0.950629	+	0.310330i	$0.100440\pi$
$521$			14.1668i			0.620661i	−0.950629	+	0.310330i	$0.899560\pi$
$522$	−7.72273	−	7.72273i	−0.338015	−	0.338015i
$523$	12.7188	+	12.7188i	0.556155	+	0.556155i	0.928211	−	0.372055i	$-0.121347\pi$
$523$	12.7188	+	12.7188i	0.556155	+	0.556155i	−0.372055	+	0.928211i	$0.621347\pi$
$524$			14.9227i			0.651903i
$525$	−34.7698	−	15.9488i	−1.51748	−	0.696061i
$526$		−	16.2461i		−	0.708366i
$527$	6.62858	−	6.62858i	0.288745	−	0.288745i
$528$	26.0194	+	26.0194i	1.13235	+	1.13235i
$529$	−6.00306	+	22.2028i	−0.261002	+	0.965338i
$530$	1.87153	+	2.91749i	0.0812942	+	0.126728i
$531$	18.6595			0.809755
$532$	−2.60994	−	2.60994i	−0.113155	−	0.113155i
$533$	−8.83184	+	8.83184i	−0.382550	+	0.382550i
$534$	45.0443			1.94926
$535$	−3.28670	+	15.0485i	−0.142096	+	0.650602i
$536$		−	2.05719i		−	0.0888570i
$537$	−5.77718	−	5.77718i	−0.249304	−	0.249304i
$538$	−9.14050	+	9.14050i	−0.394075	+	0.394075i
$539$	−27.0923			−1.16695
$540$	3.12345	−	14.3010i	0.134412	−	0.615417i
$541$	5.11180			0.219773			0.109887	−	0.993944i	$-0.464951\pi$
$541$	5.11180			0.219773			0.109887	+	0.993944i	$0.464951\pi$
$542$	21.9821	+	21.9821i	0.944210	+	0.944210i
$543$	31.4373	+	31.4373i	1.34910	+	1.34910i
$544$	−9.89599			−0.424287
$545$	12.3945	−	7.95092i	0.530923	−	0.340580i
$546$		−	39.0301i		−	1.67033i
$547$	−13.4172	−	13.4172i	−0.573680	−	0.573680i	0.359475	−	0.933155i	$-0.382956\pi$
$547$	−13.4172	−	13.4172i	−0.573680	−	0.573680i	−0.933155	+	0.359475i	$0.882956\pi$
$548$	−13.7210	−	13.7210i	−0.586133	−	0.586133i
$549$	4.86865			0.207789
$550$	−14.6331	−	39.4329i	−0.623956	−	1.68142i
$551$		−	2.10213i		−	0.0895538i
$552$	−1.17813	+	0.901893i	−0.0501443	+	0.0383871i
$553$	−27.1183	+	27.1183i	−1.15319	+	1.15319i
$554$			35.1753i			1.49445i
$555$	−19.9557	−	31.1085i	−0.847072	−	1.32048i
$556$	18.8345			0.798762
$557$	14.6983	−	14.6983i	0.622787	−	0.622787i	−0.323456	−	0.946243i	$-0.604845\pi$
$557$	14.6983	−	14.6983i	0.622787	−	0.622787i	0.946243	+	0.323456i	$0.104845\pi$
$558$	−14.4337	+	14.4337i	−0.611026	+	0.611026i
$559$	−23.5689			−0.996857
$560$	−7.23218	+	33.1132i	−0.305616	+	1.39929i
$561$	−11.1042			−0.468818
$562$	7.95775	−	7.95775i	0.335678	−	0.335678i
$563$	5.00617	+	5.00617i	0.210985	+	0.210985i	0.804686	−	0.593701i	$-0.202334\pi$
$563$	5.00617	+	5.00617i	0.210985	+	0.210985i	−0.593701	+	0.804686i	$0.702334\pi$
$564$			11.8528i			0.499093i
$565$	9.61025	+	2.09895i	0.404306	+	0.0883036i
$566$			13.2441i			0.556690i
$567$	−29.0583	+	29.0583i	−1.22033	+	1.22033i
$568$	0.657409	−	0.657409i	0.0275843	−	0.0275843i
$569$	15.2554			0.639540			0.319770	−	0.947495i	$-0.396394\pi$
$569$	15.2554			0.639540			0.319770	+	0.947495i	$0.396394\pi$
$570$	−4.08727	+	2.62193i	−0.171197	+	0.109821i
$571$		−	31.6677i		−	1.32525i	−0.748951	−	0.662626i	$-0.769442\pi$
$571$		−	31.6677i		−	1.32525i	0.748951	−	0.662626i	$-0.230558\pi$
$572$	14.8840	−	14.8840i	0.622333	−	0.622333i
$573$	4.11615	+	4.11615i	0.171955	+	0.171955i
$574$	35.1547			1.46733
$575$	23.3838	−	5.31030i	0.975171	−	0.221455i
$576$	10.1589			0.423286
$577$	2.19187	+	2.19187i	0.0912488	+	0.0912488i	0.751258	−	0.660009i	$-0.229448\pi$
$577$	2.19187	+	2.19187i	0.0912488	+	0.0912488i	−0.660009	+	0.751258i	$0.729448\pi$
$578$	−21.6256	+	21.6256i	−0.899508	+	0.899508i
$579$			28.1091i			1.16818i
$580$	14.5350	−	9.32400i	0.603532	−	0.387158i
$581$	−44.1522			−1.83174
$582$	11.3397	−	11.3397i	0.470046	−	0.470046i
$583$	2.34897	−	2.34897i	0.0972844	−	0.0972844i
$584$			0.792477i			0.0327929i
$585$	−7.73061	−	1.68842i	−0.319621	−	0.0698077i
$586$			43.6792i			1.80437i
$587$	0.610131	+	0.610131i	0.0251828	+	0.0251828i	0.719586	−	0.694403i	$-0.244332\pi$
$587$	0.610131	+	0.610131i	0.0251828	+	0.0251828i	−0.694403	+	0.719586i	$0.744332\pi$
$588$	−18.1689	+	18.1689i	−0.749271	+	0.749271i
$589$	−3.92885			−0.161886
$590$	−12.8348	+	58.7654i	−0.528401	+	2.41933i
$591$	5.83112			0.239860
$592$	−23.1557	+	23.1557i	−0.951695	+	0.951695i
$593$	−20.2560	+	20.2560i	−0.831816	+	0.831816i	−0.987765	−	0.155950i	$-0.950156\pi$
$593$	−20.2560	+	20.2560i	−0.831816	+	0.831816i	0.155950	+	0.987765i	$0.450156\pi$
$594$	−28.6020			−1.17355
$595$	−5.52256	−	8.60899i	−0.226403	−	0.352934i
$596$			33.7191i			1.38119i
$597$	15.6511	−	15.6511i	0.640557	−	0.640557i
$598$	14.8721	+	19.4272i	0.608166	+	0.794436i
$599$			14.9856i			0.612293i	0.951984	+	0.306147i	$0.0990398\pi$
$599$			14.9856i			0.612293i	−0.951984	+	0.306147i	$0.900960\pi$
$600$	1.40601	+	0.644933i	0.0574003	+	0.0263293i
$601$	−9.54167			−0.389213			−0.194606	−	0.980881i	$-0.562343\pi$
$601$	−9.54167			−0.389213			−0.194606	+	0.980881i	$0.562343\pi$
$602$	46.9073	+	46.9073i	1.91180	+	1.91180i
$603$	−13.5149	−	13.5149i	−0.550369	−	0.550369i
$604$			17.1097i			0.696186i
$605$	−13.2260	+	8.48433i	−0.537715	+	0.344937i
$606$	−2.02220			−0.0821461
$607$	−4.08607	−	4.08607i	−0.165849	−	0.165849i	0.619303	−	0.785152i	$-0.287415\pi$
$607$	−4.08607	−	4.08607i	−0.165849	−	0.165849i	−0.785152	+	0.619303i	$0.787415\pi$
$608$	2.93275	+	2.93275i	0.118939	+	0.118939i
$609$	−30.6874			−1.24352
$610$	−3.34886	+	15.3331i	−0.135591	+	0.620818i
$611$	−7.57919			−0.306621
$612$	−2.33960	+	2.33960i	−0.0945728	+	0.0945728i
$613$	28.0640	+	28.0640i	1.13349	+	1.13349i	0.989592	+	0.143901i	$0.0459647\pi$
$613$	28.0640	+	28.0640i	1.13349	+	1.13349i	0.143901	+	0.989592i	$0.454035\pi$
$614$		−	1.51285i		−	0.0610535i
$615$	4.84051	−	22.1627i	0.195188	−	0.893688i
$616$	2.29740			0.0925650
$617$	24.8729	−	24.8729i	1.00134	−	1.00134i	0.00134503	−	0.999999i	$-0.499572\pi$
$617$	24.8729	−	24.8729i	1.00134	−	1.00134i	0.999999	−	0.00134503i	$-0.000428137\pi$
$618$	16.2223	+	16.2223i	0.652557	+	0.652557i
$619$	−13.5552			−0.544831			−0.272416	−	0.962180i	$-0.587823\pi$
$619$	−13.5552			−0.544831			−0.272416	+	0.962180i	$0.587823\pi$
$620$	−17.4264	−	27.1657i	−0.699862	−	1.09100i
$621$	2.14668	−	16.1644i	0.0861434	−	0.648657i
$622$	19.4893	+	19.4893i	0.781450	+	0.781450i
$623$	28.1173	−	28.1173i	1.12650	−	1.12650i
$624$			22.3158i			0.893345i
$625$	−16.3086	−	18.9481i	−0.652344	−	0.757923i
$626$		−	45.6972i		−	1.82643i
$627$	3.29080	+	3.29080i	0.131422	+	0.131422i
$628$	−8.60179	−	8.60179i	−0.343249	−	0.343249i
$629$		−	9.88204i		−	0.394023i
$630$	12.0253	+	18.7460i	0.479100	+	0.746858i
$631$		−	16.9812i		−	0.676012i	−0.941144	−	0.338006i	$-0.890248\pi$
$631$		−	16.9812i		−	0.676012i	0.941144	−	0.338006i	$-0.109752\pi$
$632$	1.09661	−	1.09661i	0.0436206	−	0.0436206i
$633$	11.1498	−	11.1498i	0.443165	−	0.443165i
$634$		−	28.0551i		−	1.11421i
$635$	−35.8073	−	7.82058i	−1.42097	−	0.310350i
$636$		−	3.15057i		−	0.124928i
$637$	−11.6180	−	11.6180i	−0.460320	−	0.460320i
$638$	−23.8590	−	23.8590i	−0.944586	−	0.944586i
$639$		−	8.63782i		−	0.341707i
$640$	0.564223	−	2.58335i	0.0223029	−	0.102116i
$641$			48.2196i			1.90456i	0.305225	+	0.952280i	$0.401268\pi$
$641$			48.2196i			1.90456i	−0.305225	+	0.952280i	$0.598732\pi$
$642$	20.1839	−	20.1839i	0.796594	−	0.796594i
$643$	19.8040	+	19.8040i	0.780992	+	0.780992i	0.979998	−	0.199006i	$-0.0637714\pi$
$643$	19.8040	+	19.8040i	0.780992	+	0.780992i	−0.199006	+	0.979998i	$0.563771\pi$
$644$	4.44656	−	33.4825i	0.175219	−	1.31939i
$645$	36.0307	−	23.1132i	1.41871	−	0.910083i
$646$	−1.29838			−0.0510840
$647$	7.63032	+	7.63032i	0.299979	+	0.299979i	0.841005	−	0.541027i	$-0.181964\pi$
$647$	7.63032	+	7.63032i	0.299979	+	0.299979i	−0.541027	+	0.841005i	$0.681964\pi$
$648$	1.17505	−	1.17505i	0.0461604	−	0.0461604i
$649$	57.6477			2.26287
$650$	10.6349	−	23.1850i	0.417134	−	0.909392i
$651$			57.3543i			2.24789i
$652$	−31.1495	−	31.1495i	−1.21991	−	1.21991i
$653$	28.6922	−	28.6922i	1.12281	−	1.12281i	0.131497	−	0.991317i	$-0.458022\pi$
$653$	28.6922	−	28.6922i	1.12281	−	1.12281i	0.991317	−	0.131497i	$-0.0419784\pi$
$654$	−27.2885			−1.06706
$655$	14.5876	−	9.35778i	0.569986	−	0.365639i
$656$	−20.1000			−0.784773
$657$	5.20626	+	5.20626i	0.203115	+	0.203115i
$658$	15.0843	+	15.0843i	0.588047	+	0.588047i
$659$	−42.3419			−1.64941			−0.824704	−	0.565564i	$-0.808658\pi$
$659$	−42.3419			−1.64941			−0.824704	+	0.565564i	$0.808658\pi$
$660$	−8.15756	+	37.3502i	−0.317533	+	1.45385i
$661$		−	16.0529i		−	0.624385i	−0.950019	−	0.312192i	$-0.898937\pi$
$661$		−	16.0529i		−	0.624385i	0.950019	−	0.312192i	$-0.101063\pi$
$662$	−19.7131	−	19.7131i	−0.766170	−	0.766170i
$663$	−4.76178	−	4.76178i	−0.184932	−	0.184932i
$664$	1.78542			0.0692876
$665$	−0.914688	+	4.18799i	−0.0354701	+	0.162403i
$666$			21.5180i			0.833807i
$667$	15.2746	−	11.6932i	0.591435	−	0.452763i
$668$	−8.79340	+	8.79340i	−0.340227	+	0.340227i
$669$			31.8390i			1.23097i
$670$	51.8592	−	33.2670i	2.00350	−	1.28522i
$671$	15.0414			0.580669
$672$	42.8129	−	42.8129i	1.65154	−	1.65154i
$673$	12.1544	−	12.1544i	0.468518	−	0.468518i	−0.432916	−	0.901434i	$-0.642515\pi$
$673$	12.1544	−	12.1544i	0.468518	−	0.468518i	0.901434	+	0.432916i	$0.142515\pi$
$674$	7.59714			0.292631
$675$	−15.9385	+	5.91459i	−0.613474	+	0.227653i
$676$	−12.2640			−0.471692
$677$	−9.71268	+	9.71268i	−0.373289	+	0.373289i	−0.868674	−	0.495385i	$-0.835027\pi$
$677$	−9.71268	+	9.71268i	−0.373289	+	0.373289i	0.495385	+	0.868674i	$0.335027\pi$
$678$	−12.8898	−	12.8898i	−0.495031	−	0.495031i
$679$		−	14.1568i		−	0.543289i
$680$	0.223320	+	0.348129i	0.00856393	+	0.0133501i
$681$			46.4323i			1.77929i
$682$	−44.5921	+	44.5921i	−1.70752	+	1.70752i
$683$	−6.18689	+	6.18689i	−0.236735	+	0.236735i	−0.815497	−	0.578762i	$-0.803536\pi$
$683$	−6.18689	+	6.18689i	−0.236735	+	0.236735i	0.578762	+	0.815497i	$0.303536\pi$
$684$	1.38672			0.0530224
$685$	−4.80870	+	22.0171i	−0.183731	+	0.841231i
$686$		−	4.48696i		−	0.171313i
$687$	0.452247	−	0.452247i	0.0172543	−	0.0172543i
$688$	−26.8196	−	26.8196i	−1.02249	−	1.02249i
$689$	2.01461			0.0767506
$690$	−41.7873	−	15.1145i	−1.59081	−	0.575400i
$691$	−4.66320			−0.177396			−0.0886982	−	0.996059i	$-0.528271\pi$
$691$	−4.66320			−0.177396			−0.0886982	+	0.996059i	$0.528271\pi$
$692$	−11.0396	−	11.0396i	−0.419661	−	0.419661i
$693$	15.0930	−	15.0930i	0.573336	−	0.573336i
$694$		−	62.5029i		−	2.37258i
$695$	−11.8108	−	18.4116i	−0.448009	−	0.698391i
$696$	1.24093			0.0470374
$697$	4.28898	−	4.28898i	0.162457	−	0.162457i
$698$	−7.36761	+	7.36761i	−0.278868	+	0.278868i
$699$		−	36.8316i		−	1.39310i
$700$	−33.0145	+	12.2513i	−1.24783	+	0.463055i
$701$		−	13.2720i		−	0.501276i	−0.968081	−	0.250638i	$-0.919360\pi$
$701$		−	13.2720i		−	0.501276i	0.968081	−	0.250638i	$-0.0806404\pi$
$702$	−12.2654	−	12.2654i	−0.462926	−	0.462926i
$703$	−2.92861	+	2.92861i	−0.110455	+	0.110455i
$704$	31.3853			1.18288
$705$	11.5866	−	7.43268i	0.436378	−	0.279931i
$706$	64.4271			2.42475
$707$	−1.26229	+	1.26229i	−0.0474731	+	0.0474731i
$708$	38.6602	−	38.6602i	1.45294	−	1.45294i
$709$	−29.4992			−1.10787			−0.553934	−	0.832561i	$-0.686874\pi$
$709$	−29.4992			−1.10787			−0.553934	+	0.832561i	$0.686874\pi$
$710$	27.2035	+	5.94146i	1.02093	+	0.222979i
$711$		−	14.4085i		−	0.540361i
$712$	−1.13700	+	1.13700i	−0.0426110	+	0.0426110i
$713$	−21.8544	−	28.5480i	−0.818455	−	1.06913i
$714$			18.9540i			0.709337i
$715$	−23.8833	−	5.21630i	−0.893186	−	0.195078i
$716$	−7.52114			−0.281078
$717$	−13.6590	−	13.6590i	−0.510106	−	0.510106i
$718$	9.53171	+	9.53171i	0.355720	+	0.355720i
$719$		−	13.9897i		−	0.521729i	−0.965375	−	0.260865i	$-0.915992\pi$
$719$		−	13.9897i		−	0.521729i	0.965375	−	0.260865i	$-0.0840076\pi$
$720$	−6.87557	−	10.7182i	−0.256237	−	0.399443i
$721$	20.2524			0.754239
$722$	−26.2333	−	26.2333i	−0.976303	−	0.976303i
$723$	−4.31141	−	4.31141i	−0.160343	−	0.160343i
$724$	40.9273			1.52105
$725$	−18.2292	−	8.36167i	−0.677017	−	0.310545i
$726$	29.1192			1.08071
$727$	−6.81675	+	6.81675i	−0.252819	+	0.252819i	−0.822126	−	0.569306i	$-0.807212\pi$
$727$	−6.81675	+	6.81675i	−0.252819	+	0.252819i	0.569306	+	0.822126i	$0.307212\pi$
$728$	0.985193	+	0.985193i	0.0365137	+	0.0365137i
$729$			5.89460i			0.218319i
$730$	−19.9774	+	12.8152i	−0.739397	+	0.474313i
$731$	11.4457			0.423333
$732$	10.0872	−	10.0872i	0.372835	−	0.372835i
$733$	−19.6235	−	19.6235i	−0.724812	−	0.724812i	0.244769	−	0.969581i	$-0.421288\pi$
$733$	−19.6235	−	19.6235i	−0.724812	−	0.724812i	−0.969581	+	0.244769i	$0.921288\pi$
$734$	9.93729			0.366792
$735$	29.1542	+	6.36751i	1.07537	+	0.234869i
$736$	−4.99652	+	37.6236i	−0.184174	+	1.38682i
$737$	−41.7536	−	41.7536i	−1.53801	−	1.53801i
$738$	−9.33920	+	9.33920i	−0.343781	+	0.343781i
$739$			20.0313i			0.736864i	0.929655	+	0.368432i	$0.120105\pi$
$739$			20.0313i			0.736864i	−0.929655	+	0.368432i	$0.879895\pi$
$740$	−33.2395	−	7.25975i	−1.22191	−	0.266874i
$741$			2.82238i			0.103683i
$742$	−4.00953	−	4.00953i	−0.147195	−	0.147195i
$743$	18.2305	+	18.2305i	0.668812	+	0.668812i	0.957441	−	0.288629i	$-0.0931994\pi$
$743$	18.2305	+	18.2305i	0.668812	+	0.668812i	−0.288629	+	0.957441i	$0.593199\pi$
$744$		−	2.31928i		−	0.0850291i
$745$	32.9619	−	21.1446i	1.20763	−	0.774678i
$746$		−	12.9395i		−	0.473750i
$747$	11.7295	−	11.7295i	0.429159	−	0.429159i
$748$	−7.22809	+	7.22809i	−0.264285	+	0.264285i
$749$		−	25.1981i		−	0.920720i
$750$	6.47884	+	45.8732i	0.236574	+	1.67505i
$751$			24.9495i			0.910419i	0.890384	+	0.455210i	$0.150436\pi$
$751$			24.9495i			0.910419i	−0.890384	+	0.455210i	$0.849564\pi$
$752$	−8.62457	−	8.62457i	−0.314506	−	0.314506i
$753$	−28.3698	−	28.3698i	−1.03385	−	1.03385i
$754$		−	20.4628i		−	0.745212i
$755$	16.7255	−	10.7292i	0.608704	−	0.390476i
$756$			23.9465i			0.870928i
$757$	−14.3452	+	14.3452i	−0.521386	+	0.521386i	−0.917990	−	0.396604i	$-0.870189\pi$
$757$	−14.3452	+	14.3452i	−0.521386	+	0.521386i	0.396604	+	0.917990i	$0.370189\pi$
$758$	−39.2654	−	39.2654i	−1.42618	−	1.42618i
$759$	−5.60653	+	42.2170i	−0.203504	+	1.53238i
$760$	0.0369880	−	0.169353i	0.00134169	−	0.00614308i
$761$	−17.8213			−0.646023			−0.323012	−	0.946395i	$-0.604695\pi$
$761$	−17.8213			−0.646023			−0.323012	+	0.946395i	$0.604695\pi$
$762$	48.0268	+	48.0268i	1.73983	+	1.73983i
$763$	−17.0339	+	17.0339i	−0.616667	+	0.616667i
$764$	5.35870			0.193871
$765$	3.75419	+	0.819943i	0.135733	+	0.0296451i
$766$		−	69.7534i		−	2.52029i
$767$	24.7210	+	24.7210i	0.892623	+	0.892623i
$768$	−25.3290	+	25.3290i	−0.913981	+	0.913981i
$769$	−10.1694			−0.366717			−0.183359	−	0.983046i	$-0.558697\pi$
$769$	−10.1694			−0.366717			−0.183359	+	0.983046i	$0.558697\pi$
$770$	37.1516	+	57.9148i	1.33885	+	2.08710i
$771$	15.0516			0.542071
$772$	18.2972	+	18.2972i	0.658531	+	0.658531i
$773$	−0.320217	−	0.320217i	−0.0115174	−	0.0115174i	0.701325	−	0.712842i	$-0.252592\pi$
$773$	−0.320217	−	0.320217i	−0.0115174	−	0.0115174i	−0.712842	+	0.701325i	$0.752592\pi$
$774$	−24.9228			−0.895832
$775$	−15.6278	+	34.0702i	−0.561369	+	1.22384i
$776$			0.572471i			0.0205505i
$777$	42.7526	+	42.7526i	1.53374	+	1.53374i
$778$	17.9107	+	17.9107i	0.642131	+	0.642131i
$779$	−2.54214			−0.0910815
$780$	−19.5150	+	12.5186i	−0.698750	+	0.448239i
$781$		−	26.6861i		−	0.954905i
$782$	−7.22229	−	9.43434i	−0.258269	−	0.337371i
$783$	−9.64365	+	9.64365i	−0.344636	+	0.344636i
$784$		−	26.4408i		−	0.944313i
$785$	−3.01460	+	13.8027i	−0.107596	+	0.492638i
$786$	−32.1170			−1.14557
$787$	14.4826	−	14.4826i	0.516249	−	0.516249i	−0.400185	−	0.916434i	$-0.631054\pi$
$787$	14.4826	−	14.4826i	0.516249	−	0.516249i	0.916434	+	0.400185i	$0.131054\pi$
$788$	3.79568	−	3.79568i	0.135216	−	0.135216i
$789$	17.1501			0.610559
$790$	45.3775	+	9.91078i	1.61446	+	0.352610i
$791$	−16.0920			−0.572167
$792$	−0.610328	+	0.610328i	−0.0216871	+	0.0216871i
$793$	6.45021	+	6.45021i	0.229053	+	0.229053i
$794$			76.0880i			2.70026i
$795$	−3.07982	+	1.97567i	−0.109230	+	0.0700697i
$796$		−	20.3757i		−	0.722198i
$797$	14.6932	−	14.6932i	0.520460	−	0.520460i	−0.397250	−	0.917710i	$-0.630036\pi$
$797$	14.6932	−	14.6932i	0.520460	−	0.520460i	0.917710	+	0.397250i	$0.130036\pi$
$798$	5.61717	−	5.61717i	0.198846	−	0.198846i
$799$	3.68066			0.130212
$800$	37.0978	−	13.7665i	1.31160	−	0.486721i
$801$			14.9393i			0.527855i
$802$	−14.9389	+	14.9389i	−0.527509	+	0.527509i
$803$	16.0845	+	16.0845i	0.567608	+	0.567608i
$804$	−56.0023			−1.97505
$805$	−35.5189	+	16.6495i	−1.25188	+	0.586819i
$806$	−38.2447			−1.34711
$807$	−9.64908	−	9.64908i	−0.339664	−	0.339664i
$808$	0.0510440	−	0.0510440i	0.00179572	−	0.00179572i
$809$			33.3168i			1.17136i	0.810544	+	0.585678i	$0.199172\pi$
$809$			33.3168i			1.17136i	−0.810544	+	0.585678i	$0.800828\pi$
$810$	48.6236	+	10.6198i	1.70846	+	0.373140i
$811$	24.0519			0.844575			0.422288	−	0.906462i	$-0.361227\pi$
$811$	24.0519			0.844575			0.422288	+	0.906462i	$0.361227\pi$
$812$	−19.9755	+	19.9755i	−0.701003	+	0.701003i
$813$	−23.2052	+	23.2052i	−0.813840	+	0.813840i
$814$			66.4789i			2.33008i
$815$	−10.9167	+	49.9833i	−0.382396	+	1.75084i
$816$		−	10.8371i		−	0.379375i
$817$	−3.39200	−	3.39200i	−0.118671	−	0.118671i
$818$	32.5687	−	32.5687i	1.13874	−	1.13874i
$819$	12.9446			0.452322
$820$	−11.2756	−	17.5774i	−0.393763	−	0.613828i
$821$	−11.2195			−0.391563			−0.195781	−	0.980648i	$-0.562724\pi$
$821$	−11.2195			−0.391563			−0.195781	+	0.980648i	$0.562724\pi$
$822$	29.5306	−	29.5306i	1.03000	−	1.03000i
$823$	−16.9341	+	16.9341i	−0.590286	+	0.590286i	−0.937709	−	0.347423i	$-0.887057\pi$
$823$	−16.9341	+	16.9341i	−0.590286	+	0.590286i	0.347423	+	0.937709i	$0.387057\pi$
$824$	−0.818963			−0.0285299
$825$	41.6269	−	15.4472i	1.44926	−	0.537804i
$826$		−	98.4007i		−	3.42380i
$827$	2.86855	−	2.86855i	0.0997493	−	0.0997493i	−0.655471	−	0.755220i	$-0.727530\pi$
$827$	2.86855	−	2.86855i	0.0997493	−	0.0997493i	0.755220	+	0.655471i	$0.227530\pi$
$828$	7.71368	+	10.0762i	0.268069	+	0.350173i
$829$		−	43.1039i		−	1.49706i	−0.663100	−	0.748531i	$-0.730760\pi$
$829$		−	43.1039i		−	1.49706i	0.663100	−	0.748531i	$-0.269240\pi$
$830$	28.8722	+	45.0083i	1.00217	+	1.56226i
$831$	−37.1325			−1.28811
$832$	13.4589	+	13.4589i	0.466604	+	0.466604i
$833$	5.64199	+	5.64199i	0.195483	+	0.195483i
$834$			40.5360i			1.40365i
$835$	14.1101	+	3.08175i	0.488301	+	0.106649i
$836$	4.28419			0.148172
$837$	18.0238	+	18.0238i	0.622995	+	0.622995i
$838$	−40.8878	−	40.8878i	−1.41244	−	1.41244i
$839$	−3.14028			−0.108415			−0.0542073	−	0.998530i	$-0.517263\pi$
$839$	−3.14028			−0.108415			−0.0542073	+	0.998530i	$0.517263\pi$
$840$	−2.47225	−	0.539959i	−0.0853009	−	0.0186304i
$841$	12.9111			0.445210
$842$	−2.04150	+	2.04150i	−0.0703547	+	0.0703547i
$843$	8.40053	+	8.40053i	0.289329	+	0.289329i
$844$		−	14.5156i		−	0.499648i
$845$	7.69053	+	11.9886i	0.264562	+	0.412421i
$846$	−8.01459			−0.275547
$847$	18.1766	−	18.1766i	0.624556	−	0.624556i
$848$	2.29248	+	2.29248i	0.0787241	+	0.0787241i
$849$	−13.9810			−0.479826
$850$	−5.16458	+	11.2593i	−0.177143	+	0.386190i
$851$	−37.5706	−	4.98948i	−1.28790	−	0.171037i
$852$	−17.8965	−	17.8965i	−0.613123	−	0.613123i
$853$	25.8718	−	25.8718i	0.885834	−	0.885834i	−0.108286	−	0.994120i	$-0.534536\pi$
$853$	25.8718	−	25.8718i	0.885834	−	0.885834i	0.994120	+	0.108286i	$0.0345361\pi$
$854$		−	25.6747i		−	0.878571i
$855$	−0.869584	−	1.35558i	−0.0297392	−	0.0463597i
$856$			1.01896i			0.0348273i
$857$	−4.61744	−	4.61744i	−0.157729	−	0.157729i	0.623831	−	0.781560i	$-0.285575\pi$
$857$	−4.61744	−	4.61744i	−0.157729	−	0.157729i	−0.781560	+	0.623831i	$0.785575\pi$
$858$	32.0337	+	32.0337i	1.09361	+	1.09361i
$859$			14.4628i			0.493464i	0.969084	+	0.246732i	$0.0793568\pi$
$859$			14.4628i			0.493464i	−0.969084	+	0.246732i	$0.920643\pi$
$860$	8.40845	−	38.4989i	0.286726	−	1.31280i
$861$			37.1107i			1.26473i
$862$	0.815913	−	0.815913i	0.0277901	−	0.0277901i
$863$	0.0304482	−	0.0304482i	0.00103647	−	0.00103647i	−0.706588	−	0.707625i	$-0.749767\pi$
$863$	0.0304482	−	0.0304482i	0.00103647	−	0.00103647i	0.707625	+	0.706588i	$0.249767\pi$
$864$		−	26.9083i		−	0.915439i
$865$	−3.86895	+	17.7144i	−0.131548	+	0.602306i
$866$		−	30.7396i		−	1.04458i
$867$	−22.8289	−	22.8289i	−0.775310	−	0.775310i
$868$	37.3340	+	37.3340i	1.26720	+	1.26720i
$869$		−	44.5144i		−	1.51005i
$870$	20.0673	+	31.2824i	0.680344	+	1.06057i
$871$		−	35.8103i		−	1.21338i
$872$	0.688812	−	0.688812i	0.0233261	−	0.0233261i
$873$	3.76090	+	3.76090i	0.127287	+	0.127287i
$874$	−0.655556	+	4.93631i	−0.0221745	+	0.166973i
$875$	32.6790	+	24.5906i	1.10475	+	0.831313i
$876$	21.5734			0.728898
$877$	10.1873	+	10.1873i	0.344000	+	0.344000i	0.857869	−	0.513869i	$-0.171788\pi$
$877$	10.1873	+	10.1873i	0.344000	+	0.344000i	−0.513869	+	0.857869i	$0.671788\pi$
$878$	−23.3042	+	23.3042i	−0.786479	+	0.786479i
$879$	−46.1095			−1.55523
$880$	−21.2417	−	33.1132i	−0.716058	−	1.11625i
$881$		−	13.2383i		−	0.446008i	−0.974818	−	0.223004i	$-0.928414\pi$
$881$		−	13.2383i		−	0.446008i	0.974818	−	0.223004i	$-0.0715863\pi$
$882$	−12.2854	−	12.2854i	−0.413670	−	0.413670i
$883$	1.75780	−	1.75780i	0.0591547	−	0.0591547i	−0.676911	−	0.736065i	$-0.736682\pi$
$883$	1.75780	−	1.75780i	0.0591547	−	0.0591547i	0.736065	+	0.676911i	$0.236682\pi$
$884$	−6.19922			−0.208502
$885$	−62.0351	−	13.5489i	−2.08529	−	0.455443i
$886$	30.0379			1.00914
$887$	7.26411	+	7.26411i	0.243905	+	0.243905i	0.818464	−	0.574558i	$-0.194826\pi$
$887$	7.26411	+	7.26411i	0.243905	+	0.243905i	−0.574558	+	0.818464i	$0.694826\pi$
$888$	−1.72882	−	1.72882i	−0.0580154	−	0.0580154i
$889$	59.9581			2.01093
$890$	−47.0491	−	10.2759i	−1.57709	−	0.344448i
$891$		−	47.6988i		−	1.59797i
$892$	20.7251	+	20.7251i	0.693929	+	0.693929i
$893$	−1.09079	−	1.09079i	−0.0365019	−	0.0365019i
$894$	−72.5707			−2.42713
$895$	4.71637	+	7.35224i	0.157651	+	0.245758i
$896$			4.32573i			0.144513i
$897$	−20.5081	+	15.6996i	−0.684745	+	0.524195i
$898$	8.98626	−	8.98626i	0.299876	−	0.299876i
$899$			30.0699i			1.00289i
$900$	5.51596	−	12.0253i	0.183865	−	0.400844i
$901$	−0.978349			−0.0325935
$902$	−28.8530	+	28.8530i	−0.960700	+	0.960700i
$903$	−49.5173	+	49.5173i	−1.64783	+	1.64783i
$904$	0.650727			0.0216428
$905$	−25.6648	−	40.0083i	−0.853126	−	1.32992i
$906$	−36.8239			−1.22339
$907$	−33.1581	+	33.1581i	−1.10100	+	1.10100i	−0.106707	+	0.994291i	$0.534031\pi$
$907$	−33.1581	+	33.1581i	−1.10100	+	1.10100i	−0.994291	+	0.106707i	$0.965969\pi$
$908$	30.2244	+	30.2244i	1.00303	+	1.00303i
$909$		−	0.670678i		−	0.0222450i
$910$	−8.90386	+	40.7672i	−0.295160	+	1.35142i
$911$		−	15.3817i		−	0.509618i	−0.966991	−	0.254809i	$-0.917987\pi$
$911$		−	15.3817i		−	0.509618i	0.966991	−	0.254809i	$-0.0820126\pi$
$912$	−3.21166	+	3.21166i	−0.106349	+	0.106349i
$913$	36.2376	−	36.2376i	1.19929	−	1.19929i
$914$	−28.7591			−0.951265
$915$	−16.1862	−	3.53519i	−0.535100	−	0.116870i
$916$		−	0.588767i		−	0.0194534i
$917$	−20.0479	+	20.0479i	−0.662040	+	0.662040i
$918$	5.95639	+	5.95639i	0.196590	+	0.196590i
$919$	−38.8730			−1.28230			−0.641152	−	0.767414i	$-0.721543\pi$
$919$	−38.8730			−1.28230			−0.641152	+	0.767414i	$0.721543\pi$
$920$	1.43631	−	0.673270i	0.0473537	−	0.0221971i
$921$	1.59702			0.0526236
$922$	21.0945	+	21.0945i	0.694711	+	0.694711i
$923$	11.4438	−	11.4438i	0.376677	−	0.376677i
$924$		−	62.5416i		−	2.05747i
$925$	13.7471	+	37.0455i	0.452003	+	1.21805i
$926$	24.3259			0.799398
$927$	−5.38026	+	5.38026i	−0.176711	+	0.176711i
$928$	22.4461	−	22.4461i	0.736830	−	0.736830i
$929$			6.87353i			0.225513i	0.993623	+	0.112757i	$0.0359680\pi$
$929$			6.87353i			0.225513i	−0.993623	+	0.112757i	$0.964032\pi$
$930$	58.4664	−	37.5054i	1.91719	−	1.22985i
$931$		−	3.34409i		−	0.109598i
$932$	−23.9750	−	23.9750i	−0.785326	−	0.785326i
$933$	−20.5737	+	20.5737i	−0.673552	+	0.673552i
$934$	57.1598			1.87033
$935$	11.5984	+	2.53317i	0.379307	+	0.0828436i
$936$	−0.523453			−0.0171096
$937$	8.27388	−	8.27388i	0.270296	−	0.270296i	−0.558923	−	0.829219i	$-0.688785\pi$
$937$	8.27388	−	8.27388i	0.270296	−	0.270296i	0.829219	+	0.558923i	$0.188785\pi$
$938$	−71.2705	+	71.2705i	−2.32706	+	2.32706i
$939$	48.2398			1.57425
$940$	2.70396	−	12.3803i	0.0881934	−	0.403802i
$941$		−	54.9307i		−	1.79069i	−0.445372	−	0.895346i	$-0.646929\pi$
$941$		−	54.9307i		−	1.79069i	0.445372	−	0.895346i	$-0.353071\pi$
$942$	18.5129	−	18.5129i	0.603183	−	0.603183i
$943$	−14.1408	−	18.4718i	−0.460487	−	0.601525i
$944$			56.2614i			1.83115i
$945$	23.4088	−	15.0164i	0.761489	−	0.488485i
$946$	−76.9978			−2.50341
$947$	29.9981	+	29.9981i	0.974808	+	0.974808i	0.999690	−	0.0248820i	$-0.00792099\pi$
$947$	29.9981	+	29.9981i	0.974808	+	0.974808i	−0.0248820	+	0.999690i	$0.507921\pi$
$948$	−29.8526	−	29.8526i	−0.969568	−	0.969568i
$949$			13.7950i			0.447803i
$950$	4.86732	−	1.80620i	0.157917	−	0.0586010i
$951$	29.6161			0.960367
$952$	−0.478436	−	0.478436i	−0.0155062	−	0.0155062i
$953$	−17.8604	−	17.8604i	−0.578555	−	0.578555i	0.355950	−	0.934505i	$-0.384157\pi$
$953$	−17.8604	−	17.8604i	−0.578555	−	0.578555i	−0.934505	+	0.355950i	$0.884157\pi$
$954$	2.13034			0.0689725
$955$	−3.36034	−	5.23836i	−0.108738	−	0.169509i
$956$	−17.7823			−0.575121
$957$	25.1865	−	25.1865i	0.814164	−	0.814164i
$958$	31.4203	+	31.4203i	1.01514	+	1.01514i
$959$		−	36.8669i		−	1.19049i
$960$	−33.7739	−	7.37648i	−1.09005	−	0.238075i
$961$	25.2003			0.812913
$962$	−28.5081	+	28.5081i	−0.919137	+	0.919137i
$963$	6.69414	+	6.69414i	0.215716	+	0.215716i
$964$	−5.61290			−0.180779
$965$	6.41249	−	29.3602i	0.206425	−	0.945138i
$966$	72.0615	+	9.56997i	2.31854	+	0.307909i
$967$	−41.0798	−	41.0798i	−1.32104	−	1.32104i	−0.912938	−	0.408098i	$-0.866192\pi$
$967$	−41.0798	−	41.0798i	−1.32104	−	1.32104i	−0.408098	−	0.912938i	$-0.633808\pi$
$968$	−0.735023	+	0.735023i	−0.0236245	+	0.0236245i
$969$		−	1.37062i		−	0.0440307i
$970$	−14.4313	+	9.25749i	−0.463361	+	0.297240i
$971$			60.3006i			1.93514i	0.252604	+	0.967570i	$0.418713\pi$
$971$			60.3006i			1.93514i	−0.252604	+	0.967570i	$0.581287\pi$
$972$	−18.1012	−	18.1012i	−0.580596	−	0.580596i
$973$	25.3032	+	25.3032i	0.811183	+	0.811183i
$974$		−	10.7680i		−	0.345031i
$975$	24.4751	+	11.2266i	0.783829	+	0.359539i
$976$			14.6797i			0.469887i
$977$	9.21244	−	9.21244i	0.294732	−	0.294732i	−0.544214	−	0.838946i	$-0.683172\pi$
$977$	9.21244	−	9.21244i	0.294732	−	0.294732i	0.838946	+	0.544214i	$0.183172\pi$
$978$	67.0404	−	67.0404i	2.14372	−	2.14372i
$979$			46.1543i			1.47510i
$980$	23.1223	−	14.8327i	0.738616	−	0.473813i
$981$		−	9.05044i		−	0.288958i
$982$	31.5493	+	31.5493i	1.00678	+	1.00678i
$983$	−0.800718	−	0.800718i	−0.0255389	−	0.0255389i	0.694222	−	0.719761i	$-0.255749\pi$
$983$	−0.800718	−	0.800718i	−0.0255389	−	0.0255389i	−0.719761	+	0.694222i	$0.755749\pi$
$984$		−	1.50068i		−	0.0478398i
$985$	−6.09065	−	1.33024i	−0.194064	−	0.0423851i
$986$			9.93729i			0.316468i
$987$	−15.9236	+	15.9236i	−0.506854	+	0.506854i
$988$	1.83718	+	1.83718i	0.0584486	+	0.0584486i
$989$	5.77896	−	43.5153i	0.183760	−	1.38371i
$990$	−25.2553	−	5.51596i	−0.802668	−	0.175309i
$991$	−45.5190			−1.44596			−0.722979	−	0.690870i	$-0.757228\pi$
$991$	−45.5190			−1.44596			−0.722979	+	0.690870i	$0.757228\pi$
$992$	−41.9515	−	41.9515i	−1.33196	−	1.33196i
$993$	20.8099	−	20.8099i	0.660383	−	0.660383i
$994$	−45.5514			−1.44480
$995$	−19.9182	+	12.7772i	−0.631448	+	0.405066i
$996$		−	48.6040i		−	1.54008i
$997$	−16.3776	−	16.3776i	−0.518683	−	0.518683i	0.398490	−	0.917173i	$-0.369534\pi$
$997$	−16.3776	−	16.3776i	−0.518683	−	0.518683i	−0.917173	+	0.398490i	$0.869534\pi$
$998$	12.5687	−	12.5687i	0.397854	−	0.397854i
$999$	26.8704			0.850141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.e.a.22.10	yes	20
5.2	odd	4		575.2.e.d.68.1		20
5.3	odd	4	inner	115.2.e.a.68.9	yes	20
5.4	even	2		575.2.e.d.482.2		20
23.22	odd	2	inner	115.2.e.a.22.9	✓	20
115.22	even	4		575.2.e.d.68.2		20
115.68	even	4	inner	115.2.e.a.68.10	yes	20
115.114	odd	2		575.2.e.d.482.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.e.a.22.9	✓	20	23.22	odd	2	inner
115.2.e.a.22.10	yes	20	1.1	even	1	trivial
115.2.e.a.68.9	yes	20	5.3	odd	4	inner
115.2.e.a.68.10	yes	20	115.68	even	4	inner
575.2.e.d.68.1		20	5.2	odd	4
575.2.e.d.68.2		20	115.22	even	4
575.2.e.d.482.1		20	115.114	odd	2
575.2.e.d.482.2		20	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40095 + 1.40095i) q^{2} +(-1.47890 + 1.47890i) q^{3} +1.92534i q^{4} +(1.88210 - 1.20735i) q^{5} -4.14375 q^{6} +(-2.58659 + 2.58659i) q^{7} +(0.104596 - 0.104596i) q^{8} -1.37431i q^{9} +O(q^{10})\)	\(q+(1.40095 + 1.40095i) q^{2} +(-1.47890 + 1.47890i) q^{3} +1.92534i q^{4} +(1.88210 - 1.20735i) q^{5} -4.14375 q^{6} +(-2.58659 + 2.58659i) q^{7} +(0.104596 - 0.104596i) q^{8} -1.37431i q^{9} +(4.32817 + 0.945306i) q^{10} -4.24585i q^{11} +(-2.84739 - 2.84739i) q^{12} +(1.82074 - 1.82074i) q^{13} -7.24738 q^{14} +(-0.997903 + 4.56900i) q^{15} +4.14375 q^{16} +(-0.884201 + 0.884201i) q^{17} +(1.92534 - 1.92534i) q^{18} +0.524079 q^{19} +(2.32455 + 3.62369i) q^{20} -7.65063i q^{21} +(5.94824 - 5.94824i) q^{22} +(2.91521 + 3.80809i) q^{23} +0.309375i q^{24} +(2.08463 - 4.54470i) q^{25} +5.10155 q^{26} +(-2.40424 - 2.40424i) q^{27} +(-4.98006 - 4.98006i) q^{28} -4.01110i q^{29} +(-7.79896 + 5.00293i) q^{30} -7.49669 q^{31} +(5.59600 + 5.59600i) q^{32} +(6.27920 + 6.27920i) q^{33} -2.47745 q^{34} +(-1.74532 + 7.99114i) q^{35} +2.64601 q^{36} +(-5.58812 + 5.58812i) q^{37} +(0.734210 + 0.734210i) q^{38} +5.38541i q^{39} +(0.0705771 - 0.323144i) q^{40} -4.85068 q^{41} +(10.7182 - 10.7182i) q^{42} +(-6.47232 - 6.47232i) q^{43} +8.17471 q^{44} +(-1.65926 - 2.58659i) q^{45} +(-1.25087 + 9.41903i) q^{46} +(-2.08135 - 2.08135i) q^{47} +(-6.12820 + 6.12820i) q^{48} -6.38088i q^{49} +(9.28739 - 3.44644i) q^{50} -2.61530i q^{51} +(3.50555 + 3.50555i) q^{52} +(0.553239 + 0.553239i) q^{53} -6.73646i q^{54} +(-5.12621 - 7.99114i) q^{55} +0.541094i q^{56} +(-0.775062 + 0.775062i) q^{57} +(5.61936 - 5.61936i) q^{58} +13.5774i q^{59} +(-8.79687 - 1.92130i) q^{60} +3.54262i q^{61} +(-10.5025 - 10.5025i) q^{62} +(3.55477 + 3.55477i) q^{63} +7.39198i q^{64} +(1.22856 - 5.62510i) q^{65} +17.5937i q^{66} +(9.83397 - 9.83397i) q^{67} +(-1.70239 - 1.70239i) q^{68} +(-9.94311 - 1.32047i) q^{69} +(-13.6403 + 8.75009i) q^{70} +6.28522 q^{71} +(-0.143747 - 0.143747i) q^{72} +(-3.78828 + 3.78828i) q^{73} -15.6574 q^{74} +(3.63820 + 9.80414i) q^{75} +1.00903i q^{76} +(10.9823 + 10.9823i) q^{77} +(-7.54470 + 7.54470i) q^{78} +10.4842 q^{79} +(7.79896 - 5.00293i) q^{80} +11.2342 q^{81} +(-6.79557 - 6.79557i) q^{82} +(8.53483 + 8.53483i) q^{83} +14.7301 q^{84} +(-0.596623 + 2.73170i) q^{85} -18.1348i q^{86} +(5.93202 + 5.93202i) q^{87} +(-0.444099 - 0.444099i) q^{88} -10.8704 q^{89} +(1.29914 - 5.94824i) q^{90} +9.41903i q^{91} +(-7.33186 + 5.61278i) q^{92} +(11.0869 - 11.0869i) q^{93} -5.83173i q^{94} +(0.986371 - 0.632744i) q^{95} -16.5519 q^{96} +(-2.73658 + 2.73658i) q^{97} +(8.93932 - 8.93932i) q^{98} -5.83510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Introduction

L-functions

Modular forms

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Database

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