LMFDB - Embedded newform 465.2.k.a.32.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(32,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("465.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (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:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.5
Character	$\chi$	$=$	465.32
Dual form			465.2.k.a.218.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36051 + 1.36051i) q^{2} +(-1.70135 - 0.324676i) q^{3} -1.70195i q^{4} +(1.70565 + 1.44595i) q^{5} +(2.75642 - 1.87297i) q^{6} +(2.86044 + 2.86044i) q^{7} +(-0.405497 - 0.405497i) q^{8} +(2.78917 + 1.10477i) q^{9} +O(q^{10})$	\(q+(-1.36051 + 1.36051i) q^{2} +(-1.70135 - 0.324676i) q^{3} -1.70195i q^{4} +(1.70565 + 1.44595i) q^{5} +(2.75642 - 1.87297i) q^{6} +(2.86044 + 2.86044i) q^{7} +(-0.405497 - 0.405497i) q^{8} +(2.78917 + 1.10477i) q^{9} +(-4.28776 + 0.353322i) q^{10} -5.71094i q^{11} +(-0.552582 + 2.89561i) q^{12} +(3.46087 - 3.46087i) q^{13} -7.78328 q^{14} +(-2.43244 - 3.01384i) q^{15} +4.50726 q^{16} +(-0.490844 + 0.490844i) q^{17} +(-5.29773 + 2.29163i) q^{18} -5.62739i q^{19} +(2.46093 - 2.90293i) q^{20} +(-3.93789 - 5.79532i) q^{21} +(7.76977 + 7.76977i) q^{22} +(3.70889 + 3.70889i) q^{23} +(0.558236 + 0.821546i) q^{24} +(0.818466 + 4.93256i) q^{25} +9.41708i q^{26} +(-4.38666 - 2.78518i) q^{27} +(4.86833 - 4.86833i) q^{28} +4.36033 q^{29} +(7.40969 + 0.791009i) q^{30} +1.00000 q^{31} +(-5.32117 + 5.32117i) q^{32} +(-1.85420 + 9.71630i) q^{33} -1.33559i q^{34} +(0.742852 + 9.01494i) q^{35} +(1.88027 - 4.74704i) q^{36} +(2.13002 + 2.13002i) q^{37} +(7.65610 + 7.65610i) q^{38} +(-7.01181 + 4.76449i) q^{39} +(-0.105307 - 1.27796i) q^{40} -3.32241i q^{41} +(13.2421 + 2.52704i) q^{42} +(-0.639167 + 0.639167i) q^{43} -9.71975 q^{44} +(3.15990 + 5.91735i) q^{45} -10.0919 q^{46} +(-1.35238 + 1.35238i) q^{47} +(-7.66843 - 1.46340i) q^{48} +9.36421i q^{49} +(-7.82430 - 5.59724i) q^{50} +(0.994462 - 0.675732i) q^{51} +(-5.89024 - 5.89024i) q^{52} +(2.53623 + 2.53623i) q^{53} +(9.75733 - 2.17882i) q^{54} +(8.25773 - 9.74085i) q^{55} -2.31980i q^{56} +(-1.82708 + 9.57416i) q^{57} +(-5.93226 + 5.93226i) q^{58} -0.0212519 q^{59} +(-5.12942 + 4.13989i) q^{60} -2.98763 q^{61} +(-1.36051 + 1.36051i) q^{62} +(4.81812 + 11.1384i) q^{63} -5.46442i q^{64} +(10.9073 - 0.898785i) q^{65} +(-10.6964 - 15.7417i) q^{66} +(-10.3248 - 10.3248i) q^{67} +(0.835393 + 0.835393i) q^{68} +(-5.10593 - 7.51430i) q^{69} +(-13.2755 - 11.2542i) q^{70} +11.8393i q^{71} +(-0.683018 - 1.57898i) q^{72} +(-7.20430 + 7.20430i) q^{73} -5.79581 q^{74} +(0.208985 - 8.65773i) q^{75} -9.57755 q^{76} +(16.3358 - 16.3358i) q^{77} +(3.05749 - 16.0217i) q^{78} -6.29830i q^{79} +(7.68780 + 6.51727i) q^{80} +(6.55896 + 6.16280i) q^{81} +(4.52016 + 4.52016i) q^{82} +(-4.54181 - 4.54181i) q^{83} +(-9.86335 + 6.70209i) q^{84} +(-1.54694 + 0.127472i) q^{85} -1.73918i q^{86} +(-7.41844 - 1.41569i) q^{87} +(-2.31577 + 2.31577i) q^{88} +5.57897 q^{89} +(-12.3497 - 3.75153i) q^{90} +19.7992 q^{91} +(6.31235 - 6.31235i) q^{92} +(-1.70135 - 0.324676i) q^{93} -3.67985i q^{94} +(8.13692 - 9.59835i) q^{95} +(10.7808 - 7.32550i) q^{96} +(5.70093 + 5.70093i) q^{97} +(-12.7401 - 12.7401i) q^{98} +(6.30929 - 15.9288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6}+O(q^{10}) $ 60 * q - 4 * q^6	$ 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40} + 44 q^{42} + 16 q^{43} + 14 q^{45} + 40 q^{46} - 104 q^{48} - 48 q^{51} - 12 q^{52} - 48 q^{55} + 42 q^{57} + 80 q^{58} + 60 q^{60} - 8 q^{61} - 10 q^{63} - 24 q^{66} - 88 q^{67} - 84 q^{70} + 84 q^{72} + 60 q^{73} + 14 q^{75} + 72 q^{76} - 152 q^{78} - 132 q^{81} - 60 q^{82} - 16 q^{85} + 34 q^{87} + 124 q^{88} + 190 q^{90} + 64 q^{91} - 88 q^{96} - 8 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.36051	+	1.36051i	−0.962023	+	0.962023i	−0.999305	−	0.0372820i	$-0.988130\pi$
$2$	−1.36051	+	1.36051i	−0.962023	+	0.962023i	0.0372820	+	0.999305i	$0.488130\pi$
$3$	−1.70135	−	0.324676i	−0.982274	−	0.187451i
$3$	−1.70135	−	0.324676i	−0.982274	−	0.187451i
$4$		−	1.70195i		−	0.850976i
$5$	1.70565	+	1.44595i	0.762789	+	0.646648i
$5$	1.70565	+	1.44595i	0.762789	+	0.646648i
$6$	2.75642	−	1.87297i	1.12530	−	0.764637i
$7$	2.86044	+	2.86044i	1.08114	+	1.08114i	0.996403	+	0.0847409i	$0.0270063\pi$
$7$	2.86044	+	2.86044i	1.08114	+	1.08114i	0.0847409	+	0.996403i	$0.472994\pi$
$8$	−0.405497	−	0.405497i	−0.143365	−	0.143365i
$9$	2.78917	+	1.10477i	0.929724	+	0.368257i
$10$	−4.28776	+	0.353322i	−1.35591	+	0.111730i
$11$		−	5.71094i		−	1.72191i	−0.508678	−	0.860957i	$-0.669866\pi$
$11$		−	5.71094i		−	1.72191i	0.508678	−	0.860957i	$-0.330134\pi$
$12$	−0.552582	+	2.89561i	−0.159517	+	0.835891i
$13$	3.46087	−	3.46087i	0.959874	−	0.959874i	−0.0393518	−	0.999225i	$-0.512529\pi$
$13$	3.46087	−	3.46087i	0.959874	−	0.959874i	0.999225	+	0.0393518i	$0.0125293\pi$
$14$	−7.78328			−2.08017
$15$	−2.43244	−	3.01384i	−0.628052	−	0.778171i
$16$	4.50726			1.12682
$17$	−0.490844	+	0.490844i	−0.119047	+	0.119047i	−0.764121	−	0.645073i	$-0.776827\pi$
$17$	−0.490844	+	0.490844i	−0.119047	+	0.119047i	0.645073	+	0.764121i	$0.276827\pi$
$18$	−5.29773	+	2.29163i	−1.24869	+	0.540144i
$19$		−	5.62739i		−	1.29101i	−0.763755	−	0.645506i	$-0.776646\pi$
$19$		−	5.62739i		−	1.29101i	0.763755	−	0.645506i	$-0.223354\pi$
$20$	2.46093	−	2.90293i	0.550282	−	0.649115i
$21$	−3.93789	−	5.79532i	−0.859317	−	1.26464i
$22$	7.76977	+	7.76977i	1.65652	+	1.65652i
$23$	3.70889	+	3.70889i	0.773357	+	0.773357i	0.978692	−	0.205334i	$-0.0658282\pi$
$23$	3.70889	+	3.70889i	0.773357	+	0.773357i	−0.205334	+	0.978692i	$0.565828\pi$
$24$	0.558236	+	0.821546i	0.113949	+	0.167697i
$25$	0.818466	+	4.93256i	0.163693	+	0.986511i
$26$			9.41708i			1.84684i
$27$	−4.38666	−	2.78518i	−0.844213	−	0.536008i
$28$	4.86833	−	4.86833i	0.920027	−	0.920027i
$29$	4.36033			0.809693			0.404847	−	0.914385i	$-0.367325\pi$
$29$	4.36033			0.809693			0.404847	+	0.914385i	$0.367325\pi$
$30$	7.40969	+	0.791009i	1.35282	+	0.144418i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−5.32117	+	5.32117i	−0.940658	+	0.940658i
$33$	−1.85420	+	9.71630i	−0.322775	+	1.69139i
$34$		−	1.33559i		−	0.229052i
$35$	0.742852	+	9.01494i	0.125565	+	1.52380i
$36$	1.88027	−	4.74704i	0.313378	−	0.791173i
$37$	2.13002	+	2.13002i	0.350173	+	0.350173i	0.860174	−	0.510001i	$-0.170355\pi$
$37$	2.13002	+	2.13002i	0.350173	+	0.350173i	−0.510001	+	0.860174i	$0.670355\pi$
$38$	7.65610	+	7.65610i	1.24198	+	1.24198i
$39$	−7.01181	+	4.76449i	−1.12279	+	0.762929i
$40$	−0.105307	−	1.27796i	−0.0166505	−	0.202063i
$41$		−	3.32241i		−	0.518874i	−0.965760	−	0.259437i	$-0.916463\pi$
$41$		−	3.32241i		−	0.518874i	0.965760	−	0.259437i	$-0.0835370\pi$
$42$	13.2421	+	2.52704i	2.04330	+	0.389931i
$43$	−0.639167	+	0.639167i	−0.0974720	+	0.0974720i	−0.754161	−	0.656689i	$-0.771956\pi$
$43$	−0.639167	+	0.639167i	−0.0974720	+	0.0974720i	0.656689	+	0.754161i	$0.271956\pi$
$44$	−9.71975			−1.46531
$45$	3.15990	+	5.91735i	0.471050	+	0.882107i
$46$	−10.0919			−1.48798
$47$	−1.35238	+	1.35238i	−0.197265	+	0.197265i	−0.798827	−	0.601561i	$-0.794546\pi$
$47$	−1.35238	+	1.35238i	−0.197265	+	0.197265i	0.601561	+	0.798827i	$0.294546\pi$
$48$	−7.66843	−	1.46340i	−1.10684	−	0.211223i
$49$			9.36421i			1.33774i
$50$	−7.82430	−	5.59724i	−1.10652	−	0.791570i
$51$	0.994462	−	0.675732i	0.139253	−	0.0946214i
$52$	−5.89024	−	5.89024i	−0.816829	−	0.816829i
$53$	2.53623	+	2.53623i	0.348378	+	0.348378i	0.859505	−	0.511127i	$-0.170772\pi$
$53$	2.53623	+	2.53623i	0.348378	+	0.348378i	−0.511127	+	0.859505i	$0.670772\pi$
$54$	9.75733	−	2.17882i	1.32780	−	0.296501i
$55$	8.25773	−	9.74085i	1.11347	−	1.31346i
$56$		−	2.31980i		−	0.309996i
$57$	−1.82708	+	9.57416i	−0.242002	+	1.26813i
$58$	−5.93226	+	5.93226i	−0.778944	+	0.778944i
$59$	−0.0212519			−0.00276676			−0.00138338	−	0.999999i	$-0.500440\pi$
$59$	−0.0212519			−0.00276676			−0.00138338	+	0.999999i	$0.500440\pi$
$60$	−5.12942	+	4.13989i	−0.662205	+	0.534457i
$61$	−2.98763			−0.382527			−0.191264	−	0.981539i	$-0.561259\pi$
$61$	−2.98763			−0.382527			−0.191264	+	0.981539i	$0.561259\pi$
$62$	−1.36051	+	1.36051i	−0.172784	+	0.172784i
$63$	4.81812	+	11.1384i	0.607026	+	1.40330i
$64$		−	5.46442i		−	0.683053i
$65$	10.9073	−	0.898785i	1.35288	−	0.111481i
$66$	−10.6964	−	15.7417i	−1.31664	−	1.93767i
$67$	−10.3248	−	10.3248i	−1.26137	−	1.26137i	−0.950429	−	0.310941i	$-0.899356\pi$
$67$	−10.3248	−	10.3248i	−1.26137	−	1.26137i	−0.310941	−	0.950429i	$-0.600644\pi$
$68$	0.835393	+	0.835393i	0.101306	+	0.101306i
$69$	−5.10593	−	7.51430i	−0.614682	−	0.904616i
$70$	−13.2755	−	11.2542i	−1.58673	−	1.34514i
$71$			11.8393i			1.40507i	0.711649	+	0.702535i	$0.247949\pi$
$71$			11.8393i			1.40507i	−0.711649	+	0.702535i	$0.752051\pi$
$72$	−0.683018	−	1.57898i	−0.0804945	−	0.186085i
$73$	−7.20430	+	7.20430i	−0.843199	+	0.843199i	−0.989274	−	0.146074i	$-0.953336\pi$
$73$	−7.20430	+	7.20430i	−0.843199	+	0.843199i	0.146074	+	0.989274i	$0.453336\pi$
$74$	−5.79581			−0.673749
$75$	0.208985	−	8.65773i	0.0241316	−	0.999709i
$76$	−9.57755			−1.09862
$77$	16.3358	−	16.3358i	1.86164	−	1.86164i
$78$	3.05749	−	16.0217i	0.346193	−	1.81410i
$79$		−	6.29830i		−	0.708614i	−0.935129	−	0.354307i	$-0.884717\pi$
$79$		−	6.29830i		−	0.708614i	0.935129	−	0.354307i	$-0.115283\pi$
$80$	7.68780	+	6.51727i	0.859522	+	0.728653i
$81$	6.55896	+	6.16280i	0.728773	+	0.684755i
$82$	4.52016	+	4.52016i	0.499168	+	0.499168i
$83$	−4.54181	−	4.54181i	−0.498529	−	0.498529i	0.412451	−	0.910980i	$-0.364673\pi$
$83$	−4.54181	−	4.54181i	−0.498529	−	0.498529i	−0.910980	+	0.412451i	$0.864673\pi$
$84$	−9.86335	+	6.70209i	−1.07618	+	0.731258i
$85$	−1.54694	+	0.127472i	−0.167790	+	0.0138262i
$86$		−	1.73918i		−	0.187541i
$87$	−7.41844	−	1.41569i	−0.795341	−	0.151778i
$88$	−2.31577	+	2.31577i	−0.246862	+	0.246862i
$89$	5.57897			0.591369			0.295685	−	0.955286i	$-0.404452\pi$
$89$	5.57897			0.591369			0.295685	+	0.955286i	$0.404452\pi$
$90$	−12.3497	−	3.75153i	−1.30177	−	0.395446i
$91$	19.7992			2.07552
$92$	6.31235	−	6.31235i	0.658108	−	0.658108i
$93$	−1.70135	−	0.324676i	−0.176422	−	0.0336673i
$94$		−	3.67985i		−	0.379548i
$95$	8.13692	−	9.59835i	0.834831	−	0.984770i
$96$	10.7808	−	7.32550i	1.10031	−	0.747656i
$97$	5.70093	+	5.70093i	0.578841	+	0.578841i	0.934584	−	0.355743i	$-0.115772\pi$
$97$	5.70093	+	5.70093i	0.578841	+	0.578841i	−0.355743	+	0.934584i	$0.615772\pi$
$98$	−12.7401	−	12.7401i	−1.28694	−	1.28694i
$99$	6.30929	−	15.9288i	0.634108	−	1.60090i
$100$	8.39497	−	1.39299i	0.839497	−	0.139299i
$101$			17.0280i			1.69435i	0.531312	+	0.847176i	$0.321699\pi$
$101$			17.0280i			1.69435i	−0.531312	+	0.847176i	$0.678301\pi$
$102$	−0.433634	+	2.27231i	−0.0429362	+	0.224992i
$103$	8.32890	−	8.32890i	0.820671	−	0.820671i	−0.165534	−	0.986204i	$-0.552935\pi$
$103$	8.32890	−	8.32890i	0.820671	−	0.820671i	0.986204	+	0.165534i	$0.0529346\pi$
$104$	−2.80674			−0.275224
$105$	1.66308	−	15.5787i	0.162300	−	1.52033i
$106$	−6.90111			−0.670295
$107$	−2.49965	+	2.49965i	−0.241651	+	0.241651i	−0.817533	−	0.575882i	$-0.804659\pi$
$107$	−2.49965	+	2.49965i	−0.241651	+	0.241651i	0.575882	+	0.817533i	$0.304659\pi$
$108$	−4.74024	+	7.46588i	−0.456130	+	0.718405i
$109$		−	2.35908i		−	0.225959i	−0.993597	−	0.112980i	$-0.963961\pi$
$109$		−	2.35908i		−	0.225959i	0.993597	−	0.112980i	$-0.0360395\pi$
$110$	2.01780	+	24.4872i	0.192390	+	2.33476i
$111$	−2.93234	−	4.31547i	−0.278325	−	0.409606i
$112$	12.8927	+	12.8927i	1.21825	+	1.21825i
$113$	−2.00335	−	2.00335i	−0.188459	−	0.188459i	0.606571	−	0.795030i	$-0.292545\pi$
$113$	−2.00335	−	2.00335i	−0.188459	−	0.188459i	−0.795030	+	0.606571i	$0.792545\pi$
$114$	−10.5399	−	15.5114i	−0.987156	−	1.45278i
$115$	0.963195	+	11.6889i	0.0898184	+	1.09000i
$116$		−	7.42108i		−	0.689030i
$117$	13.4764	−	5.82949i	1.24590	−	0.538937i
$118$	0.0289133	−	0.0289133i	0.00266169	−	0.00266169i
$119$	−2.80806			−0.257414
$120$	−0.235759	+	2.20845i	−0.0215217	+	0.201603i
$121$	−21.6149			−1.96499
$122$	4.06469	−	4.06469i	0.368000	−	0.368000i
$123$	−1.07871	+	5.65258i	−0.0972637	+	0.509676i
$124$		−	1.70195i		−	0.152840i
$125$	−5.73621	+	9.59666i	−0.513062	+	0.858351i
$126$	−21.7089	−	8.59876i	−1.93398	−	0.766038i
$127$	0.00626244	+	0.00626244i	0.000555702	+	0.000555702i	0.707385	−	0.706829i	$-0.249875\pi$
$127$	0.00626244	+	0.00626244i	0.000555702	+	0.000555702i	−0.706829	+	0.707385i	$0.749875\pi$
$128$	−3.20795	−	3.20795i	−0.283545	−	0.283545i
$129$	1.29497	−	0.879924i	0.114016	−	0.0774730i
$130$	−13.6166	+	16.0622i	−1.19426	+	1.40875i
$131$			3.22463i			0.281737i	0.990028	+	0.140869i	$0.0449895\pi$
$131$			3.22463i			0.281737i	−0.990028	+	0.140869i	$0.955010\pi$
$132$	16.5367	+	3.15576i	1.43933	+	0.274674i
$133$	16.0968	−	16.0968i	1.39577	−	1.39577i
$134$	28.0938			2.42693
$135$	−3.45487	−	11.0934i	−0.297348	−	0.954769i
$136$	0.398071			0.0341343
$137$	1.38828	−	1.38828i	0.118609	−	0.118609i	−0.645311	−	0.763920i	$-0.723272\pi$
$137$	1.38828	−	1.38828i	0.118609	−	0.118609i	0.763920	+	0.645311i	$0.223272\pi$
$138$	17.1699	+	3.27661i	1.46160	+	0.278923i
$139$		−	5.35069i		−	0.453840i	−0.973913	−	0.226920i	$-0.927134\pi$
$139$		−	5.35069i		−	0.453840i	0.973913	−	0.226920i	$-0.0728655\pi$
$140$	15.3430	−	1.26430i	1.29672	−	0.106853i
$141$	2.73996	−	1.86179i	0.230746	−	0.156791i
$142$	−16.1075	−	16.1075i	−1.35171	−	1.35171i
$143$	−19.7648	−	19.7648i	−1.65282	−	1.65282i
$144$	12.5715	+	4.97950i	1.04763	+	0.414958i
$145$	7.43719	+	6.30482i	0.617625	+	0.523587i
$146$		−	19.6030i		−	1.62235i
$147$	3.04033	−	15.9318i	0.250762	−	1.31403i
$148$	3.62519	−	3.62519i	0.297989	−	0.297989i
$149$	−14.4469			−1.18354			−0.591768	−	0.806108i	$-0.701570\pi$
$149$	−14.4469			−1.18354			−0.591768	+	0.806108i	$0.701570\pi$
$150$	11.4946	+	12.0632i	0.938528	+	0.984958i
$151$	9.03470			0.735234			0.367617	−	0.929977i	$-0.380174\pi$
$151$	9.03470			0.735234			0.367617	+	0.929977i	$0.380174\pi$
$152$	−2.28189	+	2.28189i	−0.185086	+	0.185086i
$153$	−1.91132	+	0.826778i	−0.154521	+	0.0668410i
$154$			44.4499i			3.58187i
$155$	1.70565	+	1.44595i	0.137001	+	0.116141i
$156$	8.10893	+	11.9338i	0.649234	+	0.955466i
$157$	−3.89981	−	3.89981i	−0.311239	−	0.311239i	0.534150	−	0.845389i	$-0.320632\pi$
$157$	−3.89981	−	3.89981i	−0.311239	−	0.311239i	−0.845389	+	0.534150i	$0.820632\pi$
$158$	8.56887	+	8.56887i	0.681703	+	0.681703i
$159$	−3.49156	−	5.13846i	−0.276899	−	0.407507i
$160$	−16.7702	+	1.38190i	−1.32580	+	0.109249i
$161$			21.2181i			1.67222i
$162$	−17.3080	+	0.538975i	−1.35985	+	0.0423459i
$163$	−9.97434	+	9.97434i	−0.781250	+	0.781250i	−0.980042	−	0.198791i	$-0.936298\pi$
$163$	−9.97434	+	9.97434i	−0.781250	+	0.781250i	0.198791	+	0.980042i	$0.436298\pi$
$164$	−5.65459			−0.441549
$165$	−17.2119	+	13.8915i	−1.33994	+	1.08145i
$166$	12.3583			0.959192
$167$	9.74667	−	9.74667i	0.754220	−	0.754220i	−0.221044	−	0.975264i	$-0.570946\pi$
$167$	9.74667	−	9.74667i	0.754220	−	0.754220i	0.975264	+	0.221044i	$0.0709464\pi$
$168$	−0.753181	+	3.94678i	−0.0581092	+	0.304501i
$169$		−	10.9553i		−	0.842715i
$170$	1.93120	−	2.27805i	0.148116	−	0.174719i
$171$	6.21699	−	15.6958i	0.475425	−	1.20029i
$172$	1.08783	+	1.08783i	0.0829463	+	0.0829463i
$173$	−15.0637	−	15.0637i	−1.14527	−	1.14527i	−0.987471	−	0.157801i	$-0.949559\pi$
$173$	−15.0637	−	15.0637i	−1.14527	−	1.14527i	−0.157801	−	0.987471i	$-0.550441\pi$
$174$	12.0189	−	8.16678i	0.911150	−	0.619122i
$175$	−11.7681	+	16.4504i	−0.889585	+	1.24354i
$176$		−	25.7407i		−	1.94028i
$177$	0.0361569	+	0.00689997i	0.00271772	+	0.000518634i
$178$	−7.59022	+	7.59022i	−0.568911	+	0.568911i
$179$	−1.84810			−0.138133			−0.0690667	−	0.997612i	$-0.522002\pi$
$179$	−1.84810			−0.138133			−0.0690667	+	0.997612i	$0.522002\pi$
$180$	10.0710	−	5.37800i	0.750651	−	0.400852i
$181$	18.6067			1.38302			0.691512	−	0.722365i	$-0.256945\pi$
$181$	18.6067			1.38302			0.691512	+	0.722365i	$0.256945\pi$
$182$	−26.9370	+	26.9370i	−1.99670	+	1.99670i
$183$	5.08300	+	0.970011i	0.375746	+	0.0717053i
$184$		−	3.00789i		−	0.221744i
$185$	0.553163	+	6.71296i	0.0406694	+	0.493547i
$186$	2.75642	−	1.87297i	0.202110	−	0.137333i
$187$	2.80318	+	2.80318i	0.204989	+	0.204989i
$188$	2.30169	+	2.30169i	0.167868	+	0.167868i
$189$	−4.58094	−	20.5146i	−0.333214	−	1.49222i
$190$	1.98828	+	24.1289i	0.144245	+	1.75050i
$191$		−	6.57604i		−	0.475826i	−0.971287	−	0.237913i	$-0.923537\pi$
$191$		−	6.57604i		−	0.475826i	0.971287	−	0.237913i	$-0.0764633\pi$
$192$	−1.77416	+	9.29689i	−0.128039	+	0.670945i
$193$	−10.0273	+	10.0273i	−0.721783	+	0.721783i	−0.968968	−	0.247185i	$-0.920494\pi$
$193$	−10.0273	+	10.0273i	−0.721783	+	0.721783i	0.247185	+	0.968968i	$0.420494\pi$
$194$	−15.5123			−1.11372
$195$	−18.8489	−	2.01218i	−1.34980	−	0.144095i
$196$	15.9374			1.13839
$197$	13.8939	−	13.8939i	0.989901	−	0.989901i	−0.0100481	−	0.999950i	$-0.503198\pi$
$197$	13.8939	−	13.8939i	0.989901	−	0.989901i	0.999950	+	0.0100481i	$0.00319846\pi$
$198$	13.0874	+	30.2550i	0.930081	+	2.15013i
$199$		−	0.351855i		−	0.0249423i	−0.999922	−	0.0124712i	$-0.996030\pi$
$199$		−	0.351855i		−	0.0249423i	0.999922	−	0.0124712i	$-0.00396980\pi$
$200$	1.66825	−	2.33202i	0.117963	−	0.164899i
$201$	14.2138	+	20.9182i	1.00257	+	1.47546i
$202$	−23.1667	−	23.1667i	−1.63001	−	1.63001i
$203$	12.4725	+	12.4725i	0.875395	+	0.875395i
$204$	−1.15006	−	1.69253i	−0.0805205	−	0.118501i
$205$	4.80404	−	5.66687i	0.335529	−	0.395791i
$206$			22.6630i			1.57901i
$207$	6.24726	+	14.4422i	0.434214	+	1.00380i
$208$	15.5991	−	15.5991i	1.08160	−	1.08160i
$209$	−32.1377			−2.22301
$210$	18.9323	+	23.4576i	1.30646	+	1.61873i
$211$	0.289633			0.0199391			0.00996956	−	0.999950i	$-0.496827\pi$
$211$	0.289633			0.0199391			0.00996956	+	0.999950i	$0.496827\pi$
$212$	4.31654	−	4.31654i	0.296461	−	0.296461i
$213$	3.84394	−	20.1428i	0.263383	−	1.38016i
$214$		−	6.80158i		−	0.464947i
$215$	−2.01440	+	0.165991i	−0.137381	+	0.0113205i
$216$	0.649395	+	2.90816i	0.0441857	+	0.197875i
$217$	2.86044	+	2.86044i	0.194179	+	0.194179i
$218$	3.20955	+	3.20955i	0.217378	+	0.217378i
$219$	14.5961	−	9.91796i	0.986311	−	0.670194i
$220$	−16.5785	−	14.0543i	−1.11772	−	0.947538i
$221$			3.39750i			0.228541i
$222$	9.86068	+	1.88176i	0.661806	+	0.126295i
$223$	−19.2774	+	19.2774i	−1.29091	+	1.29091i	−0.356687	+	0.934224i	$0.616094\pi$
$223$	−19.2774	+	19.2774i	−1.29091	+	1.29091i	−0.934224	+	0.356687i	$0.883906\pi$
$224$	−30.4417			−2.03397
$225$	−3.16651	+	14.6620i	−0.211101	+	0.977464i
$226$	5.45113			0.362604
$227$	−15.8563	+	15.8563i	−1.05242	+	1.05242i	−0.0538715	+	0.998548i	$0.517156\pi$
$227$	−15.8563	+	15.8563i	−1.05242	+	1.05242i	−0.998548	+	0.0538715i	$0.982844\pi$
$228$	16.2948	+	3.10960i	1.07915	+	0.205938i
$229$			21.0650i			1.39201i	0.718035	+	0.696007i	$0.245042\pi$
$229$			21.0650i			1.39201i	−0.718035	+	0.696007i	$0.754958\pi$
$230$	−17.2133	−	14.5924i	−1.13501	−	0.962196i
$231$	−33.0967	+	22.4890i	−2.17760	+	1.47967i
$232$	−1.76810	−	1.76810i	−0.116081	−	0.116081i
$233$	15.4472	+	15.4472i	1.01198	+	1.01198i	0.999927	+	0.0120544i	$0.00383712\pi$
$233$	15.4472	+	15.4472i	1.01198	+	1.01198i	0.0120544	+	0.999927i	$0.496163\pi$
$234$	−10.4037	+	26.2658i	−0.680113	+	1.71705i
$235$	−4.26217	+	0.351212i	−0.278033	+	0.0229106i
$236$			0.0361697i			0.00235445i
$237$	−2.04490	+	10.7156i	−0.132831	+	0.696053i
$238$	3.82038	−	3.82038i	0.247639	−	0.247639i
$239$	0.0253725			0.00164121			0.000820605	−	1.00000i	$-0.499739\pi$
$239$	0.0253725			0.00164121			0.000820605		1.00000i	$0.499739\pi$
$240$	−10.9636	−	13.5842i	−0.707699	−	0.876856i
$241$	−3.19735			−0.205960			−0.102980	−	0.994683i	$-0.532838\pi$
$241$	−3.19735			−0.205960			−0.102980	+	0.994683i	$0.532838\pi$
$242$	29.4071	−	29.4071i	1.89036	−	1.89036i
$243$	−9.15816	−	12.6146i	−0.587496	−	0.809227i
$244$			5.08481i			0.325521i
$245$	−13.5402	+	15.9720i	−0.865050	+	1.02042i
$246$	−6.22278	−	9.15796i	−0.396750	−	0.583890i
$247$	−19.4757	−	19.4757i	−1.23921	−	1.23921i
$248$	−0.405497	−	0.405497i	−0.0257491	−	0.0257491i
$249$	6.25259	+	9.20182i	0.396242	+	0.583142i
$250$	−5.25217	−	20.8605i	−0.332176	−	1.31933i
$251$		−	3.53773i		−	0.223300i	−0.993748	−	0.111650i	$-0.964386\pi$
$251$		−	3.53773i		−	0.223300i	0.993748	−	0.111650i	$-0.0356135\pi$
$252$	18.9570	−	8.20021i	1.19418	−	0.516565i
$253$	21.1813	−	21.1813i	1.33165	−	1.33165i
$254$	−0.0170402			−0.00106920
$255$	2.67328	+	0.285381i	0.167407	+	0.0178712i
$256$	19.6577			1.22861
$257$	19.9803	−	19.9803i	1.24634	−	1.24634i	0.289013	−	0.957325i	$-0.406673\pi$
$257$	19.9803	−	19.9803i	1.24634	−	1.24634i	0.957325	−	0.289013i	$-0.0933271\pi$
$258$	−0.564669	+	2.95895i	−0.0351548	+	0.184216i
$259$			12.1856i			0.757175i
$260$	−1.52969	−	18.5637i	−0.0948672	−	1.15127i
$261$	12.1617	+	4.81717i	0.752791	+	0.298176i
$262$	−4.38713	−	4.38713i	−0.271038	−	0.271038i
$263$	−9.34970	−	9.34970i	−0.576527	−	0.576527i	0.357418	−	0.933945i	$-0.383657\pi$
$263$	−9.34970	−	9.34970i	−0.576527	−	0.576527i	−0.933945	+	0.357418i	$0.883657\pi$
$264$	4.69180	−	3.18805i	0.288760	−	0.196211i
$265$	0.658656	+	7.99318i	0.0404609	+	0.491017i
$266$			43.7996i			2.68553i
$267$	−9.49176	−	1.81135i	−0.580887	−	0.110853i
$268$	−17.5722	+	17.5722i	−1.07340	+	1.07340i
$269$	8.91936			0.543823			0.271911	−	0.962322i	$-0.412344\pi$
$269$	8.91936			0.543823			0.271911	+	0.962322i	$0.412344\pi$
$270$	19.7930	+	10.3923i	1.20457	+	0.632454i
$271$	23.5173			1.42858			0.714288	−	0.699852i	$-0.246751\pi$
$271$	23.5173			1.42858			0.714288	+	0.699852i	$0.246751\pi$
$272$	−2.21237	+	2.21237i	−0.134144	+	0.134144i
$273$	−33.6854	−	6.42832i	−2.03873	−	0.389060i
$274$			3.77753i			0.228209i
$275$	28.1695	−	4.67421i	1.69869	−	0.281865i
$276$	−12.7890	+	8.69005i	−0.769806	+	0.523079i
$277$	6.25253	+	6.25253i	0.375678	+	0.375678i	0.869540	−	0.493862i	$-0.164415\pi$
$277$	6.25253	+	6.25253i	0.375678	+	0.375678i	−0.493862	+	0.869540i	$0.664415\pi$
$278$	7.27964	+	7.27964i	0.436604	+	0.436604i
$279$	2.78917	+	1.10477i	0.166983	+	0.0661410i
$280$	3.35430	−	3.95675i	0.200458	−	0.236461i
$281$			5.62779i			0.335726i	0.985810	+	0.167863i	$0.0536866\pi$
$281$			5.62779i			0.335726i	−0.985810	+	0.167863i	$0.946313\pi$
$282$	−1.19476	+	6.26071i	−0.0711468	+	0.372820i
$283$	11.5507	−	11.5507i	0.686615	−	0.686615i	−0.274867	−	0.961482i	$-0.588634\pi$
$283$	11.5507	−	11.5507i	0.686615	−	0.686615i	0.961482	+	0.274867i	$0.0886339\pi$
$284$	20.1500			1.19568
$285$	−16.9601	+	13.6883i	−1.00463	+	0.810823i
$286$	53.7804			3.18010
$287$	9.50356	−	9.50356i	0.560977	−	0.560977i
$288$	−20.7203	+	8.96297i	−1.22096	+	0.528148i
$289$			16.5181i			0.971656i
$290$	−18.6961	+	1.54060i	−1.09787	+	0.0904671i
$291$	−7.84831	−	11.5502i	−0.460076	−	0.677085i
$292$	12.2614	+	12.2614i	0.717542	+	0.717542i
$293$	19.8604	+	19.8604i	1.16025	+	1.16025i	0.984420	+	0.175835i	$0.0562625\pi$
$293$	19.8604	+	19.8604i	1.16025	+	1.16025i	0.175835	+	0.984420i	$0.443738\pi$
$294$	17.5389	+	25.8117i	1.02289	+	1.50537i
$295$	−0.0362483	−	0.0307292i	−0.00211045	−	0.00178912i
$296$		−	1.72743i		−	0.100405i
$297$	−15.9060	+	25.0520i	−0.922959	+	1.45366i
$298$	19.6551	−	19.6551i	1.13859	−	1.13859i
$299$	25.6720			1.48465
$300$	−14.7350	−	0.355683i	−0.850728	−	0.0205354i
$301$	−3.65659			−0.210763
$302$	−12.2918	+	12.2918i	−0.707312	+	0.707312i
$303$	5.52858	−	28.9706i	0.317609	−	1.66432i
$304$		−	25.3641i		−	1.45473i
$305$	−5.09585	−	4.31996i	−0.291787	−	0.247360i
$306$	1.47553	−	3.72520i	0.0843502	−	0.212955i
$307$	−17.7179	−	17.7179i	−1.01121	−	1.01121i	−0.999936	−	0.0112748i	$-0.996411\pi$
$307$	−17.7179	−	17.7179i	−1.01121	−	1.01121i	−0.0112748	−	0.999936i	$-0.503589\pi$
$308$	−27.8027	−	27.8027i	−1.58421	−	1.58421i
$309$	−16.8745	+	11.4662i	−0.959959	+	0.652287i
$310$	−4.28776	+	0.353322i	−0.243529	+	0.0200673i
$311$			7.41299i			0.420352i	0.977664	+	0.210176i	$0.0674037\pi$
$311$			7.41299i			0.420352i	−0.977664	+	0.210176i	$0.932596\pi$
$312$	4.77525	+	0.911281i	0.270345	+	0.0515911i
$313$	−9.99286	+	9.99286i	−0.564830	+	0.564830i	−0.930675	−	0.365846i	$-0.880780\pi$
$313$	−9.99286	+	9.99286i	−0.564830	+	0.564830i	0.365846	+	0.930675i	$0.380780\pi$
$314$	10.6114			0.598838
$315$	−7.88752	+	25.9649i	−0.444411	+	1.46296i
$316$	−10.7194			−0.603014
$317$	9.83924	−	9.83924i	0.552627	−	0.552627i	−0.374571	−	0.927198i	$-0.622210\pi$
$317$	9.83924	−	9.83924i	0.552627	−	0.552627i	0.927198	+	0.374571i	$0.122210\pi$
$318$	11.7412	+	2.24062i	0.658414	+	0.125648i
$319$		−	24.9016i		−	1.39422i
$320$	7.90128	−	9.32038i	0.441695	−	0.521025i
$321$	5.06436	−	3.44120i	0.282665	−	0.192069i
$322$	−28.8674	−	28.8674i	−1.60872	−	1.60872i
$323$	2.76217	+	2.76217i	0.153691	+	0.153691i
$324$	10.4888	−	11.1630i	0.582710	−	0.620168i
$325$	19.9036	+	14.2383i	1.10405	+	0.789801i
$326$		−	27.1403i		−	1.50316i
$327$	−0.765937	+	4.01362i	−0.0423564	+	0.221954i
$328$	−1.34723	+	1.34723i	−0.0743882	+	0.0743882i
$329$	−7.73682			−0.426545
$330$	4.51741	−	42.3163i	0.248675	−	2.32944i
$331$	−21.0997			−1.15974			−0.579872	−	0.814708i	$-0.696897\pi$
$331$	−21.0997			−1.15974			−0.579872	+	0.814708i	$0.696897\pi$
$332$	−7.72994	+	7.72994i	−0.424236	+	0.424236i
$333$	3.58780	+	8.29417i	0.196610	+	0.454518i
$334$			26.5208i			1.45115i
$335$	−2.68133	−	32.5395i	−0.146497	−	1.77782i
$336$	−17.7491	−	26.1210i	−0.968293	−	1.42502i
$337$	−2.46144	−	2.46144i	−0.134083	−	0.134083i	0.636880	−	0.770963i	$-0.280225\pi$
$337$	−2.46144	−	2.46144i	−0.134083	−	0.134083i	−0.770963	+	0.636880i	$0.780225\pi$
$338$	14.9047	+	14.9047i	0.810711	+	0.810711i
$339$	2.75796	+	4.05883i	0.149792	+	0.220445i
$340$	0.216951	+	2.63282i	0.0117658	+	0.142785i
$341$		−	5.71094i		−	0.309265i
$342$	12.8959	+	29.8124i	0.697332	+	1.61207i
$343$	−6.76268	+	6.76268i	−0.365150	+	0.365150i
$344$	0.518360			0.0279481
$345$	2.15638	−	20.1997i	0.116096	−	1.08751i
$346$	40.9885			2.20356
$347$	−11.0624	+	11.0624i	−0.593861	+	0.593861i	−0.938672	−	0.344811i	$-0.887943\pi$
$347$	−11.0624	+	11.0624i	−0.593861	+	0.593861i	0.344811	+	0.938672i	$0.387943\pi$
$348$	−2.40944	+	12.6258i	−0.129160	+	0.676816i
$349$		−	18.7587i		−	1.00413i	−0.864829	−	0.502066i	$-0.832574\pi$
$349$		−	18.7587i		−	1.00413i	0.864829	−	0.502066i	$-0.167426\pi$
$350$	−6.37035	−	38.3915i	−0.340510	−	2.05211i
$351$	−24.8208	+	5.54253i	−1.32484	+	0.295838i
$352$	30.3889	+	30.3889i	1.61973	+	1.61973i
$353$	−21.4656	−	21.4656i	−1.14250	−	1.14250i	−0.987991	−	0.154509i	$-0.950620\pi$
$353$	−21.4656	−	21.4656i	−1.14250	−	1.14250i	−0.154509	−	0.987991i	$-0.549380\pi$
$354$	−0.0585791	+	0.0398042i	−0.00311344	+	0.00211557i
$355$	−17.1191	+	20.1937i	−0.908586	+	1.07177i
$356$		−	9.49513i		−	0.503241i
$357$	4.77749	+	0.911708i	0.252851	+	0.0482527i
$358$	2.51435	−	2.51435i	0.132888	−	0.132888i
$359$	6.63720			0.350298			0.175149	−	0.984542i	$-0.443959\pi$
$359$	6.63720			0.350298			0.175149	+	0.984542i	$0.443959\pi$
$360$	1.11814	−	3.68079i	0.0589310	−	0.193995i
$361$	−12.6676			−0.666714
$362$	−25.3145	+	25.3145i	−1.33050	+	1.33050i
$363$	36.7744	+	7.01782i	1.93016	+	0.368340i
$364$		−	33.6973i		−	1.76622i
$365$	−22.7050	+	1.87095i	−1.18844	+	0.0979298i
$366$	−8.23516	+	5.59575i	−0.430459	+	0.292495i
$367$	−18.6578	−	18.6578i	−0.973927	−	0.973927i	0.0257414	−	0.999669i	$-0.491805\pi$
$367$	−18.6578	−	18.6578i	−0.973927	−	0.973927i	−0.999669	+	0.0257414i	$0.991805\pi$
$368$	16.7170	+	16.7170i	0.871432	+	0.871432i
$369$	3.67051	−	9.26678i	0.191079	−	0.482409i
$370$	−9.88560	−	8.38044i	−0.513928	−	0.435678i
$371$			14.5095i			0.753294i
$372$	−0.552582	+	2.89561i	−0.0286500	+	0.150131i
$373$	−10.6265	+	10.6265i	−0.550218	+	0.550218i	−0.926504	−	0.376285i	$-0.877201\pi$
$373$	−10.6265	+	10.6265i	−0.550218	+	0.550218i	0.376285	+	0.926504i	$0.377201\pi$
$374$	−7.62750			−0.394408
$375$	12.8751	−	14.4649i	0.664867	−	0.746962i
$376$	1.09677			0.0565618
$377$	15.0906	−	15.0906i	0.777203	−	0.777203i
$378$	34.1426	+	21.6778i	1.75611	+	1.11499i
$379$			37.2519i			1.91350i	0.290910	+	0.956750i	$0.406042\pi$
$379$			37.2519i			1.91350i	−0.290910	+	0.956750i	$0.593958\pi$
$380$	−16.3359	−	13.8486i	−0.838015	−	0.710421i
$381$	−0.00862134	−	0.0126879i	−0.000441684	−	0.000650019i
$382$	8.94674	+	8.94674i	0.457755	+	0.457755i
$383$	−14.9605	−	14.9605i	−0.764446	−	0.764446i	0.212676	−	0.977123i	$-0.431782\pi$
$383$	−14.9605	−	14.9605i	−0.764446	−	0.764446i	−0.977123	+	0.212676i	$0.931782\pi$
$384$	4.41630	+	6.49938i	0.225368	+	0.331670i
$385$	51.4838	−	4.24239i	2.62386	−	0.216212i
$386$		−	27.2845i		−	1.38874i
$387$	−2.48888	+	1.07661i	−0.126517	+	0.0547273i
$388$	9.70270	−	9.70270i	0.492580	−	0.492580i
$389$	13.3991			0.679363			0.339682	−	0.940541i	$-0.389681\pi$
$389$	13.3991			0.679363			0.339682	+	0.940541i	$0.389681\pi$
$390$	28.3816	−	22.9064i	1.43716	−	1.15991i
$391$	−3.64098			−0.184132
$392$	3.79716	−	3.79716i	0.191785	−	0.191785i
$393$	1.04696	−	5.48622i	0.0528121	−	0.276743i
$394$			37.8055i			1.90462i
$395$	9.10702	−	10.7427i	0.458224	−	0.540523i
$396$	−27.1100	−	10.7381i	−1.36233	−	0.539610i
$397$	6.97511	+	6.97511i	0.350071	+	0.350071i	0.860136	−	0.510065i	$-0.170379\pi$
$397$	6.97511	+	6.97511i	0.350071	+	0.350071i	−0.510065	+	0.860136i	$0.670379\pi$
$398$	0.478701	+	0.478701i	0.0239951	+	0.0239951i
$399$	−32.6125	+	22.1600i	−1.63267	+	1.10939i
$400$	3.68904	+	22.2323i	0.184452	+	1.11162i
$401$		−	28.1715i		−	1.40682i	−0.710786	−	0.703409i	$-0.751660\pi$
$401$		−	28.1715i		−	1.40682i	0.710786	−	0.703409i	$-0.248340\pi$
$402$	−47.7973	−	9.12137i	−2.38391	−	0.454932i
$403$	3.46087	−	3.46087i	0.172398	−	0.172398i
$404$	28.9809			1.44185
$405$	2.27618	+	19.9955i	0.113104	+	0.993583i
$406$	−33.9377			−1.68430
$407$	12.1644	−	12.1644i	0.602968	−	0.602968i
$408$	−0.677258	−	0.129244i	−0.0335293	−	0.00639853i
$409$		−	13.4796i		−	0.666523i	−0.942834	−	0.333262i	$-0.891851\pi$
$409$		−	13.4796i		−	0.666523i	0.942834	−	0.333262i	$-0.108149\pi$
$410$	1.17388	+	14.2457i	0.0579738	+	0.703546i
$411$	−2.81269	+	1.91121i	−0.138740	+	0.0942730i
$412$	−14.1754	−	14.1754i	−0.698371	−	0.698371i
$413$	−0.0607898	−	0.0607898i	−0.00299127	−	0.00299127i
$414$	−28.1481	−	11.1493i	−1.38341	−	0.547958i
$415$	−1.17950	−	14.3140i	−0.0578995	−	0.702644i
$416$			36.8318i			1.80583i
$417$	−1.73724	+	9.10339i	−0.0850729	+	0.445795i
$418$	43.7236	−	43.7236i	2.13859	−	2.13859i
$419$	−26.7477			−1.30671			−0.653355	−	0.757052i	$-0.726639\pi$
$419$	−26.7477			−1.30671			−0.653355	+	0.757052i	$0.726639\pi$
$420$	−26.5143	−	2.83048i	−1.29376	−	0.138113i
$421$	−30.8965			−1.50580			−0.752902	−	0.658133i	$-0.771346\pi$
$421$	−30.8965			−1.50580			−0.752902	+	0.658133i	$0.771346\pi$
$422$	−0.394047	+	0.394047i	−0.0191819	+	0.0191819i
$423$	−5.26611	+	2.27795i	−0.256047	+	0.110758i
$424$		−	2.05687i		−	0.0998902i
$425$	−2.82286	−	2.01938i	−0.136929	−	0.0979542i
$426$	22.1747	+	32.6341i	1.07437	+	1.58113i
$427$	−8.54594	−	8.54594i	−0.413567	−	0.413567i
$428$	4.25429	+	4.25429i	0.205639	+	0.205639i
$429$	27.2097	+	40.0441i	1.31370	+	1.93335i
$430$	2.51477	−	2.96643i	0.121273	−	0.143054i
$431$		−	23.3707i		−	1.12573i	−0.826550	−	0.562864i	$-0.809699\pi$
$431$		−	23.3707i		−	1.12573i	0.826550	−	0.562864i	$-0.190301\pi$
$432$	−19.7718	−	12.5535i	−0.951273	−	0.603982i
$433$	5.31806	−	5.31806i	0.255570	−	0.255570i	−0.567680	−	0.823250i	$-0.692159\pi$
$433$	5.31806	−	5.31806i	0.255570	−	0.255570i	0.823250	+	0.567680i	$0.192159\pi$
$434$	−7.78328			−0.373610
$435$	−10.6062	−	13.1414i	−0.508530	−	0.630080i
$436$	−4.01505			−0.192286
$437$	20.8714	−	20.8714i	0.998414	−	0.998414i
$438$	−6.36461	+	33.3515i	−0.304113	+	1.59360i
$439$			6.60252i			0.315121i	0.987509	+	0.157560i	$0.0503629\pi$
$439$			6.60252i			0.315121i	−0.987509	+	0.157560i	$0.949637\pi$
$440$	−7.29836	+	0.601402i	−0.347936	+	0.0286707i
$441$	−10.3453	+	26.1184i	−0.492634	+	1.24373i
$442$	−4.62232	−	4.62232i	−0.219861	−	0.219861i
$443$	24.9156	+	24.9156i	1.18378	+	1.18378i	0.978758	+	0.205017i	$0.0657251\pi$
$443$	24.9156	+	24.9156i	1.18378	+	1.18378i	0.205017	+	0.978758i	$0.434275\pi$
$444$	−7.34472	+	4.99070i	−0.348565	+	0.236848i
$445$	9.51575	+	8.06690i	0.451090	+	0.382408i
$446$		−	52.4541i		−	2.48377i
$447$	24.5792	+	4.69055i	1.16256	+	0.221856i
$448$	15.6306	−	15.6306i	0.738479	−	0.738479i
$449$	−38.6476			−1.82389			−0.911947	−	0.410307i	$-0.865422\pi$
$449$	−38.6476			−1.82389			−0.911947	+	0.410307i	$0.865422\pi$
$450$	−15.6396	−	24.2557i	−0.737259	−	1.14343i
$451$	−18.9741			−0.893456
$452$	−3.40960	+	3.40960i	−0.160374	+	0.160374i
$453$	−15.3712	−	2.93335i	−0.722201	−	0.137821i
$454$		−	43.1452i		−	2.02490i
$455$	33.7705	+	28.6287i	1.58319	+	1.34213i
$456$	4.62316	−	3.14141i	0.216499	−	0.147110i
$457$	−30.0518	−	30.0518i	−1.40576	−	1.40576i	−0.780065	−	0.625699i	$-0.784814\pi$
$457$	−30.0518	−	30.0518i	−1.40576	−	1.40576i	−0.625699	−	0.780065i	$-0.715186\pi$
$458$	−28.6590	−	28.6590i	−1.33915	−	1.33915i
$459$	3.52026	−	0.786078i	0.164311	−	0.0366910i
$460$	19.8940	−	1.63931i	0.927562	−	0.0764333i
$461$			2.85868i			0.133142i	0.997782	+	0.0665711i	$0.0212059\pi$
$461$			2.85868i			0.133142i	−0.997782	+	0.0665711i	$0.978794\pi$
$462$	14.4318	−	75.6247i	0.671428	−	3.51838i
$463$	−23.1625	+	23.1625i	−1.07645	+	1.07645i	−0.0796292	+	0.996825i	$0.525374\pi$
$463$	−23.1625	+	23.1625i	−1.07645	+	1.07645i	−0.996825	+	0.0796292i	$0.974626\pi$
$464$	19.6532			0.912376
$465$	−2.43244	−	3.01384i	−0.112802	−	0.139764i
$466$	−42.0321			−1.94710
$467$	−14.8328	+	14.8328i	−0.686382	+	0.686382i	−0.961430	−	0.275048i	$-0.911306\pi$
$467$	−14.8328	+	14.8328i	−0.686382	+	0.686382i	0.275048	+	0.961430i	$0.411306\pi$
$468$	−9.92152	−	22.9363i	−0.458622	−	1.06023i
$469$		−	59.0667i		−	2.72745i
$470$	5.32087	−	6.27653i	0.245434	−	0.289515i
$471$	5.36877	+	7.90111i	0.247380	+	0.364064i
$472$	0.00861757	+	0.00861757i	0.000396656	+	0.000396656i
$473$	3.65025	+	3.65025i	0.167838	+	0.167838i
$474$	−11.7965	−	17.3607i	−0.541833	−	0.797405i
$475$	27.7574	−	4.60583i	1.27360	−	0.211330i
$476$			4.77918i			0.219053i
$477$	4.27203	+	9.87594i	0.195603	+	0.452188i
$478$	−0.0345194	+	0.0345194i	−0.00157888	+	0.00157888i
$479$	16.1490			0.737868			0.368934	−	0.929456i	$-0.379723\pi$
$479$	16.1490			0.737868			0.368934	+	0.929456i	$0.379723\pi$
$480$	28.9806	+	3.09377i	1.32278	+	0.141211i
$481$	14.7435			0.672244
$482$	4.35002	−	4.35002i	0.198138	−	0.198138i
$483$	6.88900	−	36.0994i	0.313460	−	1.64258i
$484$			36.7875i			1.67216i
$485$	1.48052	+	17.9670i	0.0672271	+	0.815840i
$486$	29.6220	+	4.70251i	1.34368	+	0.213310i
$487$	8.19344	+	8.19344i	0.371280	+	0.371280i	0.867943	−	0.496663i	$-0.165442\pi$
$487$	8.19344	+	8.19344i	0.371280	+	0.371280i	−0.496663	+	0.867943i	$0.665442\pi$
$488$	1.21147	+	1.21147i	0.0548409	+	0.0548409i
$489$	20.2082	−	13.7314i	0.913848	−	0.620955i
$490$	−3.30858	−	40.1515i	−0.149466	−	1.81386i
$491$			16.6770i			0.752625i	0.926493	+	0.376312i	$0.122808\pi$
$491$			16.6770i			0.752625i	−0.926493	+	0.376312i	$0.877192\pi$
$492$	9.62042	+	1.83591i	0.433722	+	0.0827690i
$493$	−2.14024	+	2.14024i	−0.0963918	+	0.0963918i
$494$	52.9936			2.38429
$495$	33.7936	−	18.0460i	1.51891	−	0.811108i
$496$	4.50726			0.202382
$497$	−33.8657	+	33.8657i	−1.51908	+	1.51908i
$498$	−21.0258	−	4.01244i	−0.942189	−	0.179802i
$499$			3.48440i			0.155983i	0.996954	+	0.0779915i	$0.0248507\pi$
$499$			3.48440i			0.155983i	−0.996954	+	0.0779915i	$0.975149\pi$
$500$	16.3331	+	9.76275i	0.730436	+	0.436604i
$501$	−19.7470	+	13.4180i	−0.882230	+	0.599471i
$502$	4.81311	+	4.81311i	0.214819	+	0.214819i
$503$	−8.12172	−	8.12172i	−0.362129	−	0.362129i	0.502467	−	0.864596i	$-0.332426\pi$
$503$	−8.12172	−	8.12172i	−0.362129	−	0.362129i	−0.864596	+	0.502467i	$0.832426\pi$
$504$	2.56285	−	6.47031i	0.114158	−	0.288210i
$505$	−24.6217	+	29.0438i	−1.09565	+	1.29243i
$506$			57.6345i			2.56216i
$507$	−3.55691	+	18.6388i	−0.157968	+	0.827777i
$508$	0.0106584	−	0.0106584i	0.000472889	−	0.000472889i
$509$	−13.8597			−0.614319			−0.307159	−	0.951658i	$-0.599378\pi$
$509$	−13.8597			−0.614319			−0.307159	+	0.951658i	$0.599378\pi$
$510$	−4.02527	+	3.24874i	−0.178242	+	0.143857i
$511$	−41.2149			−1.82324
$512$	−20.3285	+	20.3285i	−0.898403	+	0.898403i
$513$	−15.6733	+	24.6855i	−0.691993	+	1.08989i
$514$			54.3667i			2.39801i
$515$	26.2493	−	2.16300i	1.15668	−	0.0953133i
$516$	−1.49759	−	2.20397i	−0.0659276	−	0.0970244i
$517$	7.72338	+	7.72338i	0.339674	+	0.339674i
$518$	−16.5785	−	16.5785i	−0.728419	−	0.728419i
$519$	20.7378	+	30.5194i	0.910288	+	1.33965i
$520$	−4.78732	−	4.05841i	−0.209938	−	0.177973i
$521$		−	0.863902i		−	0.0378482i	−0.999821	−	0.0189241i	$-0.993976\pi$
$521$		−	0.863902i		−	0.0378482i	0.999821	−	0.0189241i	$-0.00602410\pi$
$522$	−23.0999	+	9.99229i	−1.01105	+	0.437351i
$523$	13.4869	−	13.4869i	0.589743	−	0.589743i	−0.347819	−	0.937562i	$-0.613078\pi$
$523$	13.4869	−	13.4869i	0.589743	−	0.589743i	0.937562	+	0.347819i	$0.113078\pi$
$524$	5.48816			0.239752
$525$	25.3627	−	24.1671i	1.10692	−	1.05474i
$526$	25.4406			1.10926
$527$	−0.490844	+	0.490844i	−0.0213815	+	0.0213815i
$528$	−8.35738	+	43.7939i	−0.363708	+	1.90589i
$529$			4.51176i			0.196163i
$530$	−11.7709	−	9.97866i	−0.511294	−	0.433445i
$531$	−0.0592752	−	0.0234785i	−0.00257232	−	0.00101888i
$532$	−27.3960	−	27.3960i	−1.18777	−	1.18777i
$533$	−11.4985	−	11.4985i	−0.498053	−	0.498053i
$534$	15.3780	−	10.4492i	0.665469	−	0.452183i
$535$	−7.87790	+	0.649157i	−0.340591	+	0.0280655i
$536$			8.37331i			0.361672i
$537$	3.14426	+	0.600033i	0.135685	+	0.0258933i
$538$	−12.1348	+	12.1348i	−0.523170	+	0.523170i
$539$	53.4785			2.30348
$540$	−18.8805	+	5.88002i	−0.812486	+	0.253036i
$541$	14.9202			0.641471			0.320735	−	0.947169i	$-0.396070\pi$
$541$	14.9202			0.641471			0.320735	+	0.947169i	$0.396070\pi$
$542$	−31.9954	+	31.9954i	−1.37432	+	1.37432i
$543$	−31.6564	−	6.04113i	−1.35851	−	0.259250i
$544$		−	5.22373i		−	0.223965i
$545$	3.41111	−	4.02377i	0.146116	−	0.172359i
$546$	54.5749	−	37.0834i	2.33559	−	1.58702i
$547$	21.8292	+	21.8292i	0.933350	+	0.933350i	0.997914	−	0.0645638i	$-0.0205656\pi$
$547$	21.8292	+	21.8292i	0.933350	+	0.933350i	−0.0645638	+	0.997914i	$0.520566\pi$
$548$	−2.36279	−	2.36279i	−0.100933	−	0.100933i
$549$	−8.33302	−	3.30065i	−0.355645	−	0.140868i
$550$	−31.9655	+	44.6841i	−1.36302	+	1.90534i
$551$		−	24.5373i		−	1.04532i
$552$	−0.976587	+	5.11746i	−0.0415663	+	0.217814i
$553$	18.0159	−	18.0159i	0.766114	−	0.766114i
$554$	−17.0132			−0.722822
$555$	1.23841	−	11.6007i	0.0525676	−	0.492421i
$556$	−9.10662			−0.386207
$557$	−15.9248	+	15.9248i	−0.674756	+	0.674756i	−0.958809	−	0.284053i	$-0.908321\pi$
$557$	−15.9248	+	15.9248i	−0.674756	+	0.674756i	0.284053	+	0.958809i	$0.408321\pi$
$558$	−5.29773	+	2.29163i	−0.224271	+	0.0970126i
$559$			4.42415i			0.187122i
$560$	3.34823	+	40.6327i	0.141489	+	1.71705i
$561$	−3.85907	−	5.67932i	−0.162930	−	0.239781i
$562$	−7.65664	−	7.65664i	−0.322976	−	0.322976i
$563$	−14.8060	−	14.8060i	−0.623998	−	0.623998i	0.322553	−	0.946551i	$-0.395459\pi$
$563$	−14.8060	−	14.8060i	−0.623998	−	0.623998i	−0.946551	+	0.322553i	$0.895459\pi$
$564$	−3.16868	−	4.66328i	−0.133425	−	0.196360i
$565$	−0.520267	−	6.31374i	−0.0218878	−	0.265621i
$566$			31.4295i			1.32108i
$567$	1.13319	+	36.3898i	0.0475893	+	1.52823i
$568$	4.80081	−	4.80081i	0.201437	−	0.201437i
$569$	−15.9178			−0.667309			−0.333654	−	0.942695i	$-0.608282\pi$
$569$	−15.9178			−0.667309			−0.333654	+	0.942695i	$0.608282\pi$
$570$	4.45132	−	41.6973i	0.186445	−	1.74651i
$571$	16.9392			0.708882			0.354441	−	0.935078i	$-0.384671\pi$
$571$	16.9392			0.708882			0.354441	+	0.935078i	$0.384671\pi$
$572$	−33.6388	+	33.6388i	−1.40651	+	1.40651i
$573$	−2.13508	+	11.1881i	−0.0891942	+	0.467391i
$574$			25.8593i			1.07935i
$575$	−15.2587	+	21.3299i	−0.636333	+	0.889519i
$576$	6.03694	−	15.2412i	0.251539	−	0.635051i
$577$	−5.19332	−	5.19332i	−0.216201	−	0.216201i	0.590694	−	0.806895i	$-0.298854\pi$
$577$	−5.19332	−	5.19332i	−0.216201	−	0.216201i	−0.806895	+	0.590694i	$0.798854\pi$
$578$	−22.4730	−	22.4730i	−0.934755	−	0.934755i
$579$	20.3156	−	13.8044i	0.844288	−	0.573689i
$580$	10.7305	−	12.6577i	0.445559	−	0.525584i
$581$		−	25.9831i		−	1.07796i
$582$	26.3918	+	5.03646i	1.09398	+	0.208768i
$583$	14.4843	−	14.4843i	0.599877	−	0.599877i
$584$	5.84263			0.241770
$585$	31.4152	+	9.54319i	1.29886	+	0.394562i
$586$	−54.0403			−2.23238
$587$	−1.46914	+	1.46914i	−0.0606377	+	0.0606377i	−0.736775	−	0.676138i	$-0.763652\pi$
$587$	−1.46914	+	1.46914i	−0.0606377	+	0.0606377i	0.676138	+	0.736775i	$0.263652\pi$
$588$	−27.1151	−	5.17450i	−1.11821	−	0.213393i
$589$		−	5.62739i		−	0.231873i
$590$	0.0911231	−	0.00750876i	0.00375148	−	0.000309131i
$591$	−28.1494	+	19.1274i	−1.15791	+	0.786796i
$592$	9.60056	+	9.60056i	0.394581	+	0.394581i
$593$	−5.76791	−	5.76791i	−0.236859	−	0.236859i	0.578689	−	0.815548i	$-0.303565\pi$
$593$	−5.76791	−	5.76791i	−0.236859	−	0.236859i	−0.815548	+	0.578689i	$0.803565\pi$
$594$	−12.4431	−	55.7235i	−0.510548	−	2.28636i
$595$	−4.78956	−	4.06031i	−0.196353	−	0.166456i
$596$			24.5879i			1.00716i
$597$	−0.114239	+	0.598628i	−0.00467548	+	0.0245002i
$598$	−34.9269	+	34.9269i	−1.42827	+	1.42827i
$599$	−3.49711			−0.142888			−0.0714439	−	0.997445i	$-0.522761\pi$
$599$	−3.49711			−0.142888			−0.0714439	+	0.997445i	$0.522761\pi$
$600$	−3.59542	+	3.42594i	−0.146783	+	0.139863i
$601$	−25.7127			−1.04884			−0.524421	−	0.851459i	$-0.675718\pi$
$601$	−25.7127			−1.04884			−0.524421	+	0.851459i	$0.675718\pi$
$602$	4.97482	−	4.97482i	0.202758	−	0.202758i
$603$	−17.3910	−	40.2040i	−0.708217	−	1.63724i
$604$		−	15.3766i		−	0.625666i
$605$	−36.8673	−	31.2540i	−1.49887	−	1.27066i
$606$	31.8930	+	46.9364i	1.29556	+	1.90666i
$607$	32.1952	+	32.1952i	1.30676	+	1.30676i	0.923738	+	0.383024i	$0.125117\pi$
$607$	32.1952	+	32.1952i	1.30676	+	1.30676i	0.383024	+	0.923738i	$0.374883\pi$
$608$	29.9443	+	29.9443i	1.21440	+	1.21440i
$609$	−17.1705	−	25.2695i	−0.695784	−	1.02397i
$610$	12.8103	−	1.05560i	0.518672	−	0.0427398i
$611$			9.36086i			0.378700i
$612$	1.40714	+	3.25297i	0.0568801	+	0.131494i
$613$	−28.1927	+	28.1927i	−1.13869	+	1.13869i	−0.150010	+	0.988685i	$0.547931\pi$
$613$	−28.1927	+	28.1927i	−1.13869	+	1.13869i	−0.988685	+	0.150010i	$0.952069\pi$
$614$	48.2105			1.94562
$615$	−10.0132	+	8.08156i	−0.403773	+	0.325880i
$616$	−13.2482			−0.533786
$617$	11.6452	−	11.6452i	0.468816	−	0.468816i	−0.432715	−	0.901531i	$-0.642444\pi$
$617$	11.6452	−	11.6452i	0.468816	−	0.468816i	0.901531	+	0.432715i	$0.142444\pi$
$618$	7.35813	−	38.5577i	0.295987	−	1.55102i
$619$		−	14.6322i		−	0.588117i	−0.955787	−	0.294058i	$-0.904994\pi$
$619$		−	14.6322i		−	0.588117i	0.955787	−	0.294058i	$-0.0950060\pi$
$620$	2.46093	−	2.90293i	0.0988335	−	0.116584i
$621$	−5.93972	−	26.5996i	−0.238353	−	1.06740i
$622$	−10.0854	−	10.0854i	−0.404388	−	0.404388i
$623$	15.9583	+	15.9583i	0.639355	+	0.639355i
$624$	−31.6041	+	21.4748i	−1.26518	+	0.859681i
$625$	−23.6602	+	8.07426i	−0.946409	+	0.322970i
$626$		−	27.1907i		−	1.08676i
$627$	54.6775	+	10.4343i	2.18361	+	0.416707i
$628$	−6.63729	+	6.63729i	−0.264857	+	0.264857i
$629$	−2.09102			−0.0833743
$630$	−24.5944	−	46.0564i	−0.979864	−	1.83493i
$631$	23.7042			0.943650			0.471825	−	0.881692i	$-0.343595\pi$
$631$	23.7042			0.943650			0.471825	+	0.881692i	$0.343595\pi$
$632$	−2.55394	+	2.55394i	−0.101590	+	0.101590i
$633$	−0.492766	−	0.0940366i	−0.0195857	−	0.00373762i
$634$			26.7727i			1.06328i
$635$	0.00162635	+	0.0197367i	6.45397e−5	+	0.000783227i
$636$	−8.74542	+	5.94247i	−0.346778	+	0.235634i
$637$	32.4084	+	32.4084i	1.28407	+	1.28407i
$638$	33.8788	+	33.8788i	1.34127	+	1.34127i
$639$	−13.0798	+	33.0219i	−0.517428	+	1.30633i
$640$	−0.833101	−	10.1102i	−0.0329312	−	0.399639i
$641$			10.5628i			0.417205i	0.978001	+	0.208602i	$0.0668915\pi$
$641$			10.5628i			0.417205i	−0.978001	+	0.208602i	$0.933109\pi$
$642$	−2.20831	+	11.5719i	−0.0871550	+	0.456705i
$643$	−6.92783	+	6.92783i	−0.273207	+	0.273207i	−0.830390	−	0.557183i	$-0.811882\pi$
$643$	−6.92783	+	6.92783i	−0.273207	+	0.273207i	0.557183	+	0.830390i	$0.311882\pi$
$644$	36.1122			1.42302
$645$	3.48108	+	0.371617i	0.137067	+	0.0146324i
$646$	−7.51591			−0.295709
$647$	20.9649	−	20.9649i	0.824216	−	0.824216i	−0.162494	−	0.986710i	$-0.551954\pi$
$647$	20.9649	−	20.9649i	0.824216	−	0.824216i	0.986710	+	0.162494i	$0.0519537\pi$
$648$	−0.160641	−	5.15863i	−0.00631056	−	0.202650i
$649$			0.121368i			0.00476413i
$650$	−46.4503	+	7.70755i	−1.82193	+	0.302315i
$651$	−3.93789	−	5.79532i	−0.154338	−	0.227136i
$652$	16.9758	+	16.9758i	0.664825	+	0.664825i
$653$	9.82897	+	9.82897i	0.384637	+	0.384637i	0.872770	−	0.488132i	$-0.162322\pi$
$653$	9.82897	+	9.82897i	0.384637	+	0.384637i	−0.488132	+	0.872770i	$0.662322\pi$
$654$	−4.41850	−	6.50262i	−0.172777	−	0.254273i
$655$	−4.66265	+	5.50008i	−0.182185	+	0.214906i
$656$		−	14.9750i		−	0.584675i
$657$	−28.0531	+	12.1349i	−1.09446	+	0.473428i
$658$	10.5260	−	10.5260i	0.410346	−	0.410346i
$659$	−17.6458			−0.687384			−0.343692	−	0.939082i	$-0.611678\pi$
$659$	−17.6458			−0.687384			−0.343692	+	0.939082i	$0.611678\pi$
$660$	23.6427	+	29.2938i	0.920289	+	1.14026i
$661$	5.45333			0.212110			0.106055	−	0.994360i	$-0.466178\pi$
$661$	5.45333			0.212110			0.106055	+	0.994360i	$0.466178\pi$
$662$	28.7062	−	28.7062i	1.11570	−	1.11570i
$663$	1.10309	−	5.78033i	0.0428403	−	0.224489i
$664$			3.68338i			0.142943i
$665$	50.7306	−	4.18032i	1.96725	−	0.162106i
$666$	−16.1655	−	6.40305i	−0.626400	−	0.248113i
$667$	16.1720	+	16.1720i	0.626182	+	0.626182i
$668$	−16.5884	−	16.5884i	−0.641823	−	0.641823i
$669$	39.0565	−	26.5387i	1.51001	−	1.02604i
$670$	47.9181	+	40.6222i	1.85124	+	1.56937i
$671$			17.0622i			0.658679i
$672$	51.7920	+	9.88368i	1.99792	+	0.381271i
$673$	−28.8327	+	28.8327i	−1.11142	+	1.11142i	−0.118460	+	0.992959i	$0.537796\pi$
$673$	−28.8327	+	28.8327i	−1.11142	+	1.11142i	−0.992959	+	0.118460i	$0.962204\pi$
$674$	6.69760			0.257982
$675$	10.1477	−	23.9170i	0.390586	−	0.920567i
$676$	−18.6454			−0.717130
$677$	32.4631	−	32.4631i	1.24766	−	1.24766i	0.290906	−	0.956752i	$-0.406043\pi$
$677$	32.4631	−	32.4631i	1.24766	−	1.24766i	0.956752	−	0.290906i	$-0.0939566\pi$
$678$	−9.27428	−	1.76985i	−0.356176	−	0.0679707i
$679$			32.6143i			1.25162i
$680$	0.678969	+	0.575591i	0.0260373	+	0.0220729i
$681$	32.1252	−	21.8289i	1.23104	−	0.836486i
$682$	7.76977	+	7.76977i	0.297520	+	0.297520i
$683$	−2.57119	−	2.57119i	−0.0983837	−	0.0983837i	0.656202	−	0.754585i	$-0.272162\pi$
$683$	−2.57119	−	2.57119i	−0.0983837	−	0.0983837i	−0.754585	+	0.656202i	$0.772162\pi$
$684$	−26.7134	−	10.5810i	−1.02141	−	0.404575i
$685$	4.37530	−	0.360535i	0.167172	−	0.0137753i
$686$		−	18.4013i		−	0.702566i
$687$	6.83928	−	35.8389i	0.260935	−	1.36734i
$688$	−2.88089	+	2.88089i	−0.109833	+	0.109833i
$689$	17.5551			0.668798
$690$	24.5480	+	30.4155i	0.934526	+	1.15790i
$691$	21.0615			0.801217			0.400609	−	0.916249i	$-0.368799\pi$
$691$	21.0615			0.801217			0.400609	+	0.916249i	$0.368799\pi$
$692$	−25.6377	+	25.6377i	−0.974599	+	0.974599i
$693$	63.6107	−	27.5160i	2.41637	−	1.04525i
$694$		−	30.1009i		−	1.14262i
$695$	7.73682	−	9.12639i	0.293474	−	0.346184i
$696$	2.43409	+	3.58221i	0.0922641	+	0.135783i
$697$	1.63079	+	1.63079i	0.0617705	+	0.0617705i
$698$	25.5214	+	25.5214i	0.965998	+	0.965998i
$699$	−21.2658	−	31.2965i	−0.804346	−	1.18374i
$700$	27.9979	+	20.0287i	1.05822	+	0.757015i
$701$		−	9.29703i		−	0.351144i	−0.984467	−	0.175572i	$-0.943823\pi$
$701$		−	9.29703i		−	0.351144i	0.984467	−	0.175572i	$-0.0561775\pi$
$702$	26.2282	−	41.3095i	0.989921	−	1.55913i
$703$	11.9865	−	11.9865i	0.452078	−	0.452078i
$704$	−31.2070			−1.17616
$705$	7.36546	+	0.786287i	0.277399	+	0.0296133i
$706$	58.4082			2.19822
$707$	−48.7076	+	48.7076i	−1.83184	+	1.83184i
$708$	0.0117434	−	0.0615373i	0.000441345	−	0.00231271i
$709$		−	28.8012i		−	1.08165i	−0.841135	−	0.540826i	$-0.818112\pi$
$709$		−	28.8012i		−	1.08165i	0.841135	−	0.540826i	$-0.181888\pi$
$710$	−4.18309	−	50.7643i	−0.156989	−	1.90515i
$711$	6.95819	−	17.5670i	0.260952	−	0.658816i
$712$	−2.26225	−	2.26225i	−0.0847815	−	0.0847815i
$713$	3.70889	+	3.70889i	0.138899	+	0.138899i
$714$	−7.74018	+	5.25941i	−0.289669	+	0.196829i
$715$	−5.13291	−	62.2908i	−0.191960	−	2.32954i
$716$			3.14538i			0.117548i
$717$	−0.0431674	−	0.00823783i	−0.00161212	−	0.000307647i
$718$	−9.02994	+	9.02994i	−0.336994	+	0.336994i
$719$	−3.60087			−0.134290			−0.0671449	−	0.997743i	$-0.521389\pi$
$719$	−3.60087			−0.134290			−0.0671449	+	0.997743i	$0.521389\pi$
$720$	14.2425	+	26.6711i	0.530787	+	0.993972i
$721$	47.6486			1.77453
$722$	17.2343	−	17.2343i	0.641394	−	0.641394i
$723$	5.43981	+	1.03810i	0.202309	+	0.0386075i
$724$		−	31.6677i		−	1.17692i
$725$	3.56878	+	21.5076i	0.132541	+	0.798772i
$726$	−59.5796	+	40.4840i	−2.21121	+	1.50250i
$727$	−5.41613	−	5.41613i	−0.200873	−	0.200873i	0.599501	−	0.800374i	$-0.295366\pi$
$727$	−5.41613	−	5.41613i	−0.200873	−	0.200873i	−0.800374	+	0.599501i	$0.795366\pi$
$728$	−8.02852	−	8.02852i	−0.297557	−	0.297557i
$729$	11.4856	+	24.4353i	0.425391	+	0.905009i
$730$	28.3449	−	33.4358i	1.04909	−	1.23751i
$731$		−	0.627463i		−	0.0232076i
$732$	1.65091	−	8.65103i	0.0610195	−	0.319751i
$733$	−2.90074	+	2.90074i	−0.107141	+	0.107141i	−0.758645	−	0.651504i	$-0.774138\pi$
$733$	−2.90074	+	2.90074i	−0.107141	+	0.107141i	0.651504	+	0.758645i	$0.274138\pi$
$734$	50.7680			1.87388
$735$	28.2223	−	22.7778i	1.04099	−	0.840173i
$736$	−39.4713			−1.45493
$737$	−58.9641	+	58.9641i	−2.17197	+	2.17197i
$738$	7.61376	+	17.6013i	0.280266	+	0.647911i
$739$		−	34.4438i		−	1.26704i	−0.773728	−	0.633518i	$-0.781610\pi$
$739$		−	34.4438i		−	1.26704i	0.773728	−	0.633518i	$-0.218390\pi$
$740$	11.4251	−	0.941457i	0.419996	−	0.0346087i
$741$	26.8117	+	39.4582i	0.984951	+	1.44953i
$742$	−19.7402	−	19.7402i	−0.724686	−	0.724686i
$743$	29.9334	+	29.9334i	1.09815	+	1.09815i	0.994627	+	0.103521i	$0.0330109\pi$
$743$	29.9334	+	29.9334i	1.09815	+	1.09815i	0.103521	+	0.994627i	$0.466989\pi$
$744$	0.558236	+	0.821546i	0.0204659	+	0.0301193i
$745$	−24.6413	−	20.8895i	−0.902788	−	0.765331i
$746$		−	28.9148i		−	1.05865i
$747$	−7.65022	−	17.6856i	−0.279907	−	0.647081i
$748$	4.77088	−	4.77088i	0.174441	−	0.174441i
$749$	−14.3002			−0.522518
$750$	2.16288	+	37.1962i	0.0789774	+	1.35821i
$751$	−36.7466			−1.34090			−0.670451	−	0.741954i	$-0.733899\pi$
$751$	−36.7466			−1.34090			−0.670451	+	0.741954i	$0.733899\pi$
$752$	−6.09555	+	6.09555i	−0.222282	+	0.222282i
$753$	−1.14862	+	6.01892i	−0.0418579	+	0.219342i
$754$			41.0616i			1.49537i
$755$	15.4100	+	13.0637i	0.560828	+	0.475437i
$756$	−34.9149	+	7.79654i	−1.26984	+	0.283557i
$757$	−0.745238	−	0.745238i	−0.0270862	−	0.0270862i	0.693434	−	0.720520i	$-0.256097\pi$
$757$	−0.745238	−	0.745238i	−0.0270862	−	0.0270862i	−0.720520	+	0.693434i	$0.756097\pi$
$758$	−50.6814	−	50.6814i	−1.84083	−	1.84083i
$759$	−42.9138	+	29.1597i	−1.55767	+	1.05843i
$760$	−7.19159	+	0.592604i	−0.260866	+	0.0214960i
$761$		−	21.8146i		−	0.790780i	−0.918513	−	0.395390i	$-0.870610\pi$
$761$		−	21.8146i		−	0.790780i	0.918513	−	0.395390i	$-0.129390\pi$
$762$	0.0289913	+	0.00553253i	0.00105024	+	0.000200422i
$763$	6.74801	−	6.74801i	0.244295	−	0.244295i
$764$	−11.1921			−0.404916
$765$	−4.45552	−	1.35348i	−0.161090	−	0.0489351i
$766$	40.7077			1.47083
$767$	−0.0735501	+	0.0735501i	−0.00265574	+	0.00265574i
$768$	−33.4446	−	6.38238i	−1.20683	−	0.230304i
$769$		−	39.7921i		−	1.43494i	−0.696590	−	0.717469i	$-0.745300\pi$
$769$		−	39.7921i		−	1.43494i	0.696590	−	0.717469i	$-0.254700\pi$
$770$	−64.2723	+	75.8158i	−2.31621	+	2.73221i
$771$	−40.4806	+	27.5064i	−1.45787	+	0.990617i
$772$	17.0660	+	17.0660i	0.614220	+	0.614220i
$773$	−21.4306	−	21.4306i	−0.770805	−	0.770805i	0.207442	−	0.978247i	$-0.433486\pi$
$773$	−21.4306	−	21.4306i	−0.770805	−	0.770805i	−0.978247	+	0.207442i	$0.933486\pi$
$774$	1.92140	−	4.85087i	0.0690632	−	0.174361i
$775$	0.818466	+	4.93256i	0.0294002	+	0.177183i
$776$		−	4.62341i		−	0.165971i
$777$	3.95636	−	20.7319i	0.141934	−	0.743753i
$778$	−18.2296	+	18.2296i	−0.653563	+	0.653563i
$779$	−18.6965			−0.669873
$780$	−3.42463	+	32.0799i	−0.122622	+	1.14864i
$781$	67.6138			2.41941
$782$	4.95357	−	4.95357i	0.177139	−	0.177139i
$783$	−19.1273	−	12.1443i	−0.683554	−	0.434002i
$784$			42.2070i			1.50739i
$785$	−1.01278	−	12.2906i	−0.0361475	−	0.438672i
$786$	6.03964	+	8.88842i	0.215427	+	0.317040i
$787$	−30.4664	−	30.4664i	−1.08601	−	1.08601i	−0.995935	−	0.0900745i	$-0.971289\pi$
$787$	−30.4664	−	30.4664i	−1.08601	−	1.08601i	−0.0900745	−	0.995935i	$-0.528711\pi$
$788$	−23.6468	−	23.6468i	−0.842382	−	0.842382i
$789$	12.8715	+	18.9427i	0.458237	+	0.674378i
$790$	2.22533	+	27.0056i	0.0791736	+	0.960817i
$791$		−	11.4609i		−	0.407503i
$792$	−9.01747	+	3.90068i	−0.320422	+	0.138605i
$793$	−10.3398	+	10.3398i	−0.367178	+	0.367178i
$794$	−18.9794			−0.673553
$795$	1.47459	−	13.8130i	0.0522981	−	0.489897i
$796$	−0.598840			−0.0212253
$797$	−18.4595	+	18.4595i	−0.653870	+	0.653870i	−0.953923	−	0.300053i	$-0.902996\pi$
$797$	−18.4595	+	18.4595i	−0.653870	+	0.653870i	0.300053	+	0.953923i	$0.402996\pi$
$798$	14.2207	−	74.5184i	0.503406	−	2.63792i
$799$		−	1.32762i		−	0.0469678i
$800$	−30.6021	−	21.8918i	−1.08195	−	0.773991i
$801$	15.5607	+	6.16349i	0.549810	+	0.217776i
$802$	38.3275	+	38.3275i	1.35339	+	1.35339i
$803$	41.1433	+	41.1433i	1.45192	+	1.45192i
$804$	35.6018	−	24.1912i	1.25558	−	0.853159i
$805$	−30.6803	+	36.1906i	−1.08134	+	1.27555i
$806$			9.41708i			0.331702i
$807$	−15.1749	−	2.89590i	−0.534183	−	0.101940i
$808$	6.90481	−	6.90481i	0.242910	−	0.242910i
$809$	18.8903			0.664148			0.332074	−	0.943253i	$-0.392252\pi$
$809$	18.8903			0.664148			0.332074	+	0.943253i	$0.392252\pi$
$810$	−30.3007	−	24.1072i	−1.06466	−	0.847041i
$811$	−11.1965			−0.393163			−0.196581	−	0.980487i	$-0.562984\pi$
$811$	−11.1965			−0.393163			−0.196581	+	0.980487i	$0.562984\pi$
$812$	21.2275	−	21.2275i	0.744940	−	0.744940i
$813$	−40.0111	−	7.63550i	−1.40325	−	0.267789i
$814$			33.0995i			1.16014i
$815$	−31.4351	+	2.59032i	−1.10112	+	0.0907351i
$816$	4.48230	−	3.04570i	0.156912	−	0.106621i
$817$	3.59684	+	3.59684i	0.125838	+	0.125838i
$818$	18.3391	+	18.3391i	0.641210	+	0.641210i
$819$	55.2234	+	21.8736i	1.92966	+	0.764327i
$820$	−9.64473	−	8.17624i	−0.336809	−	0.285527i
$821$			23.1207i			0.806917i	0.914998	+	0.403458i	$0.132192\pi$
$821$			23.1207i			0.806917i	−0.914998	+	0.403458i	$0.867808\pi$
$822$	1.22647	−	6.42690i	0.0427781	−	0.224164i
$823$	−20.2204	+	20.2204i	−0.704838	+	0.704838i	−0.965445	−	0.260607i	$-0.916077\pi$
$823$	−20.2204	+	20.2204i	−0.704838	+	0.704838i	0.260607	+	0.965445i	$0.416077\pi$
$824$	−6.75468			−0.235310
$825$	−49.4438	−	1.19350i	−1.72141	−	0.0415525i
$826$	0.165410			0.00575534
$827$	−18.9826	+	18.9826i	−0.660089	+	0.660089i	−0.955401	−	0.295312i	$-0.904576\pi$
$827$	−18.9826	+	18.9826i	−0.660089	+	0.660089i	0.295312	+	0.955401i	$0.404576\pi$
$828$	24.5800	−	10.6325i	0.854212	−	0.369506i
$829$			15.5012i			0.538377i	0.963087	+	0.269189i	$0.0867555\pi$
$829$			15.5012i			0.538377i	−0.963087	+	0.269189i	$0.913245\pi$
$830$	21.0789	+	17.8695i	0.731661	+	0.620259i
$831$	−8.60769	−	12.6678i	−0.298597	−	0.439440i
$832$	−18.9117	−	18.9117i	−0.655645	−	0.655645i
$833$	−4.59637	−	4.59637i	−0.159255	−	0.159255i
$834$	−10.0217	−	14.7487i	−0.347023	−	0.510707i
$835$	30.7176	−	2.53120i	1.06303	−	0.0875957i
$836$			54.6968i			1.89173i
$837$	−4.38666	−	2.78518i	−0.151625	−	0.0962698i
$838$	36.3904	−	36.3904i	1.25708	−	1.25708i
$839$	−7.30546			−0.252212			−0.126106	−	0.992017i	$-0.540248\pi$
$839$	−7.30546			−0.252212			−0.126106	+	0.992017i	$0.540248\pi$
$840$	−6.99150	+	5.64275i	−0.241230	+	0.194693i
$841$	−9.98750			−0.344397
$842$	42.0349	−	42.0349i	1.44862	−	1.44862i
$843$	1.82721	−	9.57483i	0.0629323	−	0.329775i
$844$		−	0.492941i		−	0.0169677i
$845$	15.8408	−	18.6859i	0.544940	−	0.642813i
$846$	4.06540	−	10.2637i	0.139771	−	0.352874i
$847$	−61.8280	−	61.8280i	−2.12443	−	2.12443i
$848$	11.4315	+	11.4315i	0.392558	+	0.392558i
$849$	−23.4019	+	15.9015i	−0.803151	+	0.545737i
$850$	6.58789	−	1.09314i	0.225963	−	0.0374943i
$851$			15.8000i			0.541618i
$852$	−34.2821	−	6.54220i	−1.17449	−	0.224132i
$853$	1.71245	−	1.71245i	0.0586331	−	0.0586331i	−0.677182	−	0.735815i	$-0.736799\pi$
$853$	1.71245	−	1.71245i	0.0586331	−	0.0586331i	0.735815	+	0.677182i	$0.236799\pi$
$854$	23.2536			0.795722
$855$	33.2993	−	17.7820i	1.13881	−	0.608131i
$856$	2.02720			0.0692883
$857$	20.4426	−	20.4426i	0.698305	−	0.698305i	−0.265740	−	0.964045i	$-0.585616\pi$
$857$	20.4426	−	20.4426i	0.698305	−	0.698305i	0.964045	+	0.265740i	$0.0856163\pi$
$858$	−91.4992	−	17.4612i	−3.12373	−	0.596115i
$859$			9.34756i			0.318935i	0.987203	+	0.159467i	$0.0509777\pi$
$859$			9.34756i			0.318935i	−0.987203	+	0.159467i	$0.949022\pi$
$860$	0.282508	+	3.42840i	0.00963346	+	0.116908i
$861$	−19.2544	+	13.0833i	−0.656189	+	0.445877i
$862$	31.7960	+	31.7960i	1.08298	+	1.08298i
$863$	14.8540	+	14.8540i	0.505635	+	0.505635i	0.913184	−	0.407549i	$-0.133616\pi$
$863$	14.8540	+	14.8540i	0.505635	+	0.505635i	−0.407549	+	0.913184i	$0.633616\pi$
$864$	38.1625	−	8.52175i	1.29832	−	0.289916i
$865$	−3.91202	−	47.4747i	−0.133013	−	1.61419i
$866$			14.4705i			0.491728i
$867$	5.36304	−	28.1031i	0.182138	−	0.954432i
$868$	4.86833	−	4.86833i	0.165242	−	0.165242i
$869$	−35.9692			−1.22017
$870$	32.3087	+	3.44906i	1.09537	+	0.116934i
$871$	−71.4654			−2.42151
$872$	−0.956600	+	0.956600i	−0.0323946	+	0.0323946i
$873$	9.60264	+	22.1991i	0.325000	+	0.751325i
$874$			56.7913i			1.92099i
$875$	−43.8587	+	11.0426i	−1.48270	+	0.373307i
$876$	−16.8799	−	24.8418i	−0.570319	−	0.839327i
$877$	10.6100	+	10.6100i	0.358273	+	0.358273i	0.863176	−	0.504903i	$-0.168472\pi$
$877$	10.6100	+	10.6100i	0.358273	+	0.358273i	−0.504903	+	0.863176i	$0.668472\pi$
$878$	−8.98276	−	8.98276i	−0.303154	−	0.303154i
$879$	−27.3412	−	40.2376i	−0.922196	−	1.35718i
$880$	37.2198	−	43.9046i	1.25468	−	1.48002i
$881$			16.1058i			0.542618i	0.962492	+	0.271309i	$0.0874565\pi$
$881$			16.1058i			0.542618i	−0.962492	+	0.271309i	$0.912544\pi$
$882$	−21.4594	−	49.6091i	−0.722574	−	1.67043i
$883$	−7.51527	+	7.51527i	−0.252909	+	0.252909i	−0.822162	−	0.569253i	$-0.807232\pi$
$883$	−7.51527	+	7.51527i	−0.252909	+	0.252909i	0.569253	+	0.822162i	$0.307232\pi$
$884$	5.78238			0.194483
$885$	0.0516939	+	0.0640499i	0.00173767	+	0.00215301i
$886$	−67.7956			−2.27764
$887$	−33.0150	+	33.0150i	−1.10853	+	1.10853i	−0.115191	+	0.993343i	$0.536748\pi$
$887$	−33.0150	+	33.0150i	−1.10853	+	1.10853i	−0.993343	+	0.115191i	$0.963252\pi$
$888$	−0.560854	+	2.93896i	−0.0188210	+	0.0986251i
$889$			0.0358267i			0.00120159i
$890$	−23.9213	+	1.97117i	−0.801844	+	0.0660738i
$891$	35.1954	−	37.4578i	1.17909	−	1.25488i
$892$	32.8092	+	32.8092i	1.09853	+	1.09853i
$893$	7.61039	+	7.61039i	0.254672	+	0.254672i
$894$	−39.8217	+	27.0586i	−1.33184	+	0.904976i
$895$	−3.15221	−	2.67226i	−0.105367	−	0.0893237i
$896$		−	18.3523i		−	0.613107i
$897$	−43.6770	−	8.33507i	−1.45833	−	0.278300i
$898$	52.5803	−	52.5803i	1.75463	−	1.75463i
$899$	4.36033			0.145425
$900$	24.9540	+	5.38925i	0.831798	+	0.179642i
$901$	−2.48979			−0.0829469
$902$	25.8144	−	25.8144i	0.859525	−	0.859525i
$903$	6.22114	+	1.18721i	0.207027	+	0.0395078i
$904$			1.62470i			0.0540368i
$905$	31.7364	+	26.9043i	1.05495	+	0.894329i
$906$	24.9034	−	16.9217i	0.827360	−	0.562187i
$907$	−16.1270	−	16.1270i	−0.535487	−	0.535487i	0.386713	−	0.922200i	$-0.373610\pi$
$907$	−16.1270	−	16.1270i	−0.535487	−	0.535487i	−0.922200	+	0.386713i	$0.873610\pi$
$908$	26.9867	+	26.9867i	0.895583	+	0.895583i
$909$	−18.8121	+	47.4941i	−0.623958	+	1.57528i
$910$	−84.8944	+	6.99550i	−2.81422	+	0.231898i
$911$		−	17.8337i		−	0.590858i	−0.955365	−	0.295429i	$-0.904537\pi$
$911$		−	17.8337i		−	0.590858i	0.955365	−	0.295429i	$-0.0954626\pi$
$912$	−8.23512	+	43.1532i	−0.272692	+	1.42895i
$913$	−25.9380	+	25.9380i	−0.858423	+	0.858423i
$914$	81.7713			2.70475
$915$	7.26722	+	9.00426i	0.240247	+	0.297672i
$916$	35.8516			1.18457
$917$	−9.22385	+	9.22385i	−0.304599	+	0.304599i
$918$	−3.71986	+	5.85879i	−0.122774	+	0.193369i
$919$			50.4473i			1.66410i	0.554699	+	0.832051i	$0.312833\pi$
$919$			50.4473i			1.66410i	−0.554699	+	0.832051i	$0.687167\pi$
$920$	4.34925	−	5.13039i	0.143390	−	0.169144i
$921$	24.3917	+	35.8968i	0.803733	+	1.18284i
$922$	−3.88926	−	3.88926i	−0.128086	−	0.128086i
$923$	40.9744	+	40.9744i	1.34869	+	1.34869i
$924$	38.2753	+	56.3290i	1.25916	+	1.85309i
$925$	−8.76309	+	12.2498i	−0.288129	+	0.402771i
$926$		−	63.0255i		−	2.07115i
$927$	32.4323	−	14.0292i	1.06522	−	0.460779i
$928$	−23.2021	+	23.2021i	−0.761645	+	0.761645i
$929$	1.25894			0.0413044			0.0206522	−	0.999787i	$-0.493426\pi$
$929$	1.25894			0.0413044			0.0206522	+	0.999787i	$0.493426\pi$
$930$	7.40969	+	0.791009i	0.242973	+	0.0259382i
$931$	52.6961			1.72705
$932$	26.2904	−	26.2904i	0.861172	−	0.861172i
$933$	2.40682	−	12.6121i	0.0787956	−	0.412901i
$934$		−	40.3603i		−	1.32063i
$935$	0.727983	+	8.83450i	0.0238076	+	0.288919i
$936$	−7.82849	−	3.10081i	−0.255882	−	0.101353i
$937$	15.9541	+	15.9541i	0.521197	+	0.521197i	0.917933	−	0.396736i	$-0.129857\pi$
$937$	15.9541	+	15.9541i	0.521197	+	0.521197i	−0.396736	+	0.917933i	$0.629857\pi$
$938$	80.3606	+	80.3606i	2.62387	+	2.62387i
$939$	20.2458	−	13.7569i	0.660696	−	0.448939i
$940$	0.597746	+	7.25400i	0.0194963	+	0.236599i
$941$		−	28.2553i		−	0.921097i	−0.887634	−	0.460549i	$-0.847653\pi$
$941$		−	28.2553i		−	0.921097i	0.887634	−	0.460549i	$-0.152347\pi$
$942$	−18.0537	−	3.44527i	−0.588223	−	0.112253i
$943$	12.3225	−	12.3225i	0.401275	−	0.401275i
$944$	−0.0957879			−0.00311763
$945$	21.8496	−	41.6145i	0.710767	−	1.35372i
$946$	−9.93236			−0.322929
$947$	−0.522614	+	0.522614i	−0.0169827	+	0.0169827i	−0.715547	−	0.698564i	$-0.753823\pi$
$947$	−0.522614	+	0.522614i	−0.0169827	+	0.0169827i	0.698564	+	0.715547i	$0.253823\pi$
$948$	18.2374	+	3.48033i	0.592324	+	0.113036i
$949$			49.8663i			1.61873i
$950$	−31.4979	+	44.0304i	−1.02193	+	1.42854i
$951$	−19.9345	+	13.5454i	−0.646422	+	0.439240i
$952$	1.13866	+	1.13866i	0.0369041	+	0.0369041i
$953$	−9.68784	−	9.68784i	−0.313820	−	0.313820i	0.532568	−	0.846388i	$-0.321227\pi$
$953$	−9.68784	−	9.68784i	−0.313820	−	0.313820i	−0.846388	+	0.532568i	$0.821227\pi$
$954$	−19.2484	−	7.62416i	−0.623190	−	0.246841i
$955$	9.50862	−	11.2164i	0.307692	−	0.362954i
$956$		−	0.0431827i		−	0.00139663i
$957$	−8.08494	+	42.3663i	−0.261349	+	1.36951i
$958$	−21.9708	+	21.9708i	−0.709846	+	0.709846i
$959$	7.94219			0.256467
$960$	−16.4689	+	13.2919i	−0.531532	+	0.428993i
$961$	1.00000			0.0322581
$962$	−20.0586	+	20.0586i	−0.646714	+	0.646714i
$963$	−9.73351	+	4.21041i	−0.313658	+	0.135679i
$964$			5.44174i			0.175267i
$965$	−31.6021	+	2.60409i	−1.01731	+	0.0838285i
$966$	39.7409	+	58.4860i	1.27864	+	1.88175i
$967$	−7.65027	−	7.65027i	−0.246016	−	0.246016i	0.573317	−	0.819333i	$-0.305656\pi$
$967$	−7.65027	−	7.65027i	−0.246016	−	0.246016i	−0.819333	+	0.573317i	$0.805656\pi$
$968$	8.76475	+	8.76475i	0.281710	+	0.281710i
$969$	−3.80261	−	5.59623i	−0.122157	−	0.179777i
$970$	−26.4585	−	22.4300i	−0.849531	−	0.720183i
$971$			20.6772i			0.663563i	0.943356	+	0.331782i	$0.107650\pi$
$971$			20.6772i			0.663563i	−0.943356	+	0.331782i	$0.892350\pi$
$972$	−21.4694	+	15.5867i	−0.688633	+	0.499945i
$973$	15.3053	−	15.3053i	0.490666	−	0.490666i
$974$	−22.2944			−0.714360
$975$	−29.2400	−	30.6866i	−0.936431	−	0.982757i
$976$	−13.4660			−0.431038
$977$	18.6805	−	18.6805i	0.597641	−	0.597641i	−0.342044	−	0.939684i	$-0.611119\pi$
$977$	18.6805	−	18.6805i	0.597641	−	0.597641i	0.939684	+	0.342044i	$0.111119\pi$
$978$	−8.81179	+	46.1751i	−0.281770	+	1.47652i
$979$		−	31.8612i		−	1.01829i
$980$	27.1836	+	23.0447i	0.868350	+	0.736136i
$981$	2.60625	−	6.57989i	0.0832112	−	0.210080i
$982$	−22.6892	−	22.6892i	−0.724042	−	0.724042i
$983$	−0.387463	−	0.387463i	−0.0123581	−	0.0123581i	0.700901	−	0.713259i	$-0.252782\pi$
$983$	−0.387463	−	0.387463i	−0.0123581	−	0.0123581i	−0.713259	+	0.700901i	$0.752782\pi$
$984$	2.72951	−	1.85469i	0.0870137	−	0.0591254i
$985$	43.7880	−	3.60824i	1.39520	−	0.114968i
$986$		−	5.82363i		−	0.185462i
$987$	13.1630	+	2.51196i	0.418984	+	0.0799564i
$988$	−33.1467	+	33.1467i	−1.05454	+	1.05454i
$989$	−4.74120			−0.150761
$990$	−21.4248	+	70.5281i	−0.680924	+	2.24153i
$991$	−33.8637			−1.07572			−0.537858	−	0.843035i	$-0.680767\pi$
$991$	−33.8637			−1.07572			−0.537858	+	0.843035i	$0.680767\pi$
$992$	−5.32117	+	5.32117i	−0.168947	+	0.168947i
$993$	35.8979	+	6.85055i	1.13919	+	0.217396i
$994$		−	92.1489i		−	2.92279i
$995$	0.508764	−	0.600141i	0.0161289	−	0.0190257i
$996$	15.6610	−	10.6416i	0.496239	−	0.337192i
$997$	−16.9345	−	16.9345i	−0.536323	−	0.536323i	0.386124	−	0.922447i	$-0.373814\pi$
$997$	−16.9345	−	16.9345i	−0.536323	−	0.536323i	−0.922447	+	0.386124i	$0.873814\pi$
$998$	−4.74054	−	4.74054i	−0.150059	−	0.150059i
$999$	−3.41119	−	15.2762i	−0.107925	−	0.483316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.a.32.5	✓	60
3.2	odd	2	inner	465.2.k.a.32.26	yes	60
5.3	odd	4	inner	465.2.k.a.218.26	yes	60
15.8	even	4	inner	465.2.k.a.218.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.5	✓	60	1.1	even	1	trivial
465.2.k.a.32.26	yes	60	3.2	odd	2	inner
465.2.k.a.218.5	yes	60	15.8	even	4	inner
465.2.k.a.218.26	yes	60	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36051 + 1.36051i) q^{2} +(-1.70135 - 0.324676i) q^{3} -1.70195i q^{4} +(1.70565 + 1.44595i) q^{5} +(2.75642 - 1.87297i) q^{6} +(2.86044 + 2.86044i) q^{7} +(-0.405497 - 0.405497i) q^{8} +(2.78917 + 1.10477i) q^{9} +O(q^{10})\)	\(q+(-1.36051 + 1.36051i) q^{2} +(-1.70135 - 0.324676i) q^{3} -1.70195i q^{4} +(1.70565 + 1.44595i) q^{5} +(2.75642 - 1.87297i) q^{6} +(2.86044 + 2.86044i) q^{7} +(-0.405497 - 0.405497i) q^{8} +(2.78917 + 1.10477i) q^{9} +(-4.28776 + 0.353322i) q^{10} -5.71094i q^{11} +(-0.552582 + 2.89561i) q^{12} +(3.46087 - 3.46087i) q^{13} -7.78328 q^{14} +(-2.43244 - 3.01384i) q^{15} +4.50726 q^{16} +(-0.490844 + 0.490844i) q^{17} +(-5.29773 + 2.29163i) q^{18} -5.62739i q^{19} +(2.46093 - 2.90293i) q^{20} +(-3.93789 - 5.79532i) q^{21} +(7.76977 + 7.76977i) q^{22} +(3.70889 + 3.70889i) q^{23} +(0.558236 + 0.821546i) q^{24} +(0.818466 + 4.93256i) q^{25} +9.41708i q^{26} +(-4.38666 - 2.78518i) q^{27} +(4.86833 - 4.86833i) q^{28} +4.36033 q^{29} +(7.40969 + 0.791009i) q^{30} +1.00000 q^{31} +(-5.32117 + 5.32117i) q^{32} +(-1.85420 + 9.71630i) q^{33} -1.33559i q^{34} +(0.742852 + 9.01494i) q^{35} +(1.88027 - 4.74704i) q^{36} +(2.13002 + 2.13002i) q^{37} +(7.65610 + 7.65610i) q^{38} +(-7.01181 + 4.76449i) q^{39} +(-0.105307 - 1.27796i) q^{40} -3.32241i q^{41} +(13.2421 + 2.52704i) q^{42} +(-0.639167 + 0.639167i) q^{43} -9.71975 q^{44} +(3.15990 + 5.91735i) q^{45} -10.0919 q^{46} +(-1.35238 + 1.35238i) q^{47} +(-7.66843 - 1.46340i) q^{48} +9.36421i q^{49} +(-7.82430 - 5.59724i) q^{50} +(0.994462 - 0.675732i) q^{51} +(-5.89024 - 5.89024i) q^{52} +(2.53623 + 2.53623i) q^{53} +(9.75733 - 2.17882i) q^{54} +(8.25773 - 9.74085i) q^{55} -2.31980i q^{56} +(-1.82708 + 9.57416i) q^{57} +(-5.93226 + 5.93226i) q^{58} -0.0212519 q^{59} +(-5.12942 + 4.13989i) q^{60} -2.98763 q^{61} +(-1.36051 + 1.36051i) q^{62} +(4.81812 + 11.1384i) q^{63} -5.46442i q^{64} +(10.9073 - 0.898785i) q^{65} +(-10.6964 - 15.7417i) q^{66} +(-10.3248 - 10.3248i) q^{67} +(0.835393 + 0.835393i) q^{68} +(-5.10593 - 7.51430i) q^{69} +(-13.2755 - 11.2542i) q^{70} +11.8393i q^{71} +(-0.683018 - 1.57898i) q^{72} +(-7.20430 + 7.20430i) q^{73} -5.79581 q^{74} +(0.208985 - 8.65773i) q^{75} -9.57755 q^{76} +(16.3358 - 16.3358i) q^{77} +(3.05749 - 16.0217i) q^{78} -6.29830i q^{79} +(7.68780 + 6.51727i) q^{80} +(6.55896 + 6.16280i) q^{81} +(4.52016 + 4.52016i) q^{82} +(-4.54181 - 4.54181i) q^{83} +(-9.86335 + 6.70209i) q^{84} +(-1.54694 + 0.127472i) q^{85} -1.73918i q^{86} +(-7.41844 - 1.41569i) q^{87} +(-2.31577 + 2.31577i) q^{88} +5.57897 q^{89} +(-12.3497 - 3.75153i) q^{90} +19.7992 q^{91} +(6.31235 - 6.31235i) q^{92} +(-1.70135 - 0.324676i) q^{93} -3.67985i q^{94} +(8.13692 - 9.59835i) q^{95} +(10.7808 - 7.32550i) q^{96} +(5.70093 + 5.70093i) q^{97} +(-12.7401 - 12.7401i) q^{98} +(6.30929 - 15.9288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6}+O(q^{10}) \) 60 * q - 4 * q^6	\( 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40} + 44 q^{42} + 16 q^{43} + 14 q^{45} + 40 q^{46} - 104 q^{48} - 48 q^{51} - 12 q^{52} - 48 q^{55} + 42 q^{57} + 80 q^{58} + 60 q^{60} - 8 q^{61} - 10 q^{63} - 24 q^{66} - 88 q^{67} - 84 q^{70} + 84 q^{72} + 60 q^{73} + 14 q^{75} + 72 q^{76} - 152 q^{78} - 132 q^{81} - 60 q^{82} - 16 q^{85} + 34 q^{87} + 124 q^{88} + 190 q^{90} + 64 q^{91} - 88 q^{96} - 8 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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