LMFDB - Embedded newform 95.2.p.a.9.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,2,Mod(4,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.p (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			9.7
Character	$\chi$	$=$	95.9
Dual form			95.2.p.a.74.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.45670 - 0.256855i) q^{2} +(-1.59617 - 1.90225i) q^{3} +(0.176607 - 0.0642796i) q^{4} +(0.658585 - 2.13688i) q^{5} +(-2.81374 - 2.36101i) q^{6} +(2.81448 + 1.62494i) q^{7} +(-2.32124 + 1.34017i) q^{8} +(-0.549824 + 3.11821i) q^{9} +(0.410490 - 3.28195i) q^{10} +(2.09200 + 3.62344i) q^{11} +(-0.404171 - 0.233348i) q^{12} +(1.14682 - 1.36673i) q^{13} +(4.51721 + 1.64413i) q^{14} +(-5.11609 + 2.15805i) q^{15} +(-3.32506 + 2.79006i) q^{16} +(-6.23606 + 1.09959i) q^{17} +4.68351i q^{18} +(4.09399 - 1.49640i) q^{19} +(-0.0210474 - 0.419722i) q^{20} +(-1.40136 - 7.94751i) q^{21} +(3.97810 + 4.74092i) q^{22} +(0.490346 + 1.34721i) q^{23} +(6.25444 + 2.27643i) q^{24} +(-4.13253 - 2.81464i) q^{25} +(1.31952 - 2.28547i) q^{26} +(0.357658 - 0.206494i) q^{27} +(0.601506 + 0.106062i) q^{28} +(0.0589345 - 0.334234i) q^{29} +(-6.89829 + 4.45771i) q^{30} +(1.38932 - 2.40638i) q^{31} +(-0.681187 + 0.811808i) q^{32} +(3.55349 - 9.76313i) q^{33} +(-8.80161 + 3.20352i) q^{34} +(5.32587 - 4.94404i) q^{35} +(0.103335 + 0.586040i) q^{36} -2.70482i q^{37} +(5.57935 - 3.23137i) q^{38} -4.43037 q^{39} +(1.33505 + 5.84284i) q^{40} +(-5.46819 + 4.58835i) q^{41} +(-4.08271 - 11.2172i) q^{42} +(-3.38403 + 9.29755i) q^{43} +(0.602374 + 0.505452i) q^{44} +(6.30114 + 3.22852i) q^{45} +(1.06032 + 1.83654i) q^{46} +(-0.438674 - 0.0773501i) q^{47} +(10.6148 + 1.87167i) q^{48} +(1.78085 + 3.08452i) q^{49} +(-6.74280 - 3.03861i) q^{50} +(12.0455 + 10.1074i) q^{51} +(0.114683 - 0.315090i) q^{52} +(-2.47532 - 6.80087i) q^{53} +(0.467960 - 0.392665i) q^{54} +(9.12062 - 2.08400i) q^{55} -8.71078 q^{56} +(-9.38125 - 5.39926i) q^{57} -0.502015i q^{58} +(-0.545712 - 3.09489i) q^{59} +(-0.764818 + 0.709986i) q^{60} +(2.88074 - 1.04850i) q^{61} +(1.40573 - 3.86222i) q^{62} +(-6.61436 + 7.88269i) q^{63} +(3.55679 - 6.16055i) q^{64} +(-2.16526 - 3.35072i) q^{65} +(2.66865 - 15.1347i) q^{66} +(8.42261 + 1.48513i) q^{67} +(-1.03065 + 0.595046i) q^{68} +(1.78006 - 3.08315i) q^{69} +(6.48828 - 8.56995i) q^{70} +(-12.1153 - 4.40959i) q^{71} +(-2.90266 - 7.97498i) q^{72} +(1.17133 + 1.39594i) q^{73} +(-0.694747 - 3.94011i) q^{74} +(1.24211 + 12.3537i) q^{75} +(0.626839 - 0.527435i) q^{76} +13.5974i q^{77} +(-6.45371 + 1.13796i) q^{78} +(-0.535235 + 0.449116i) q^{79} +(3.77219 + 8.94276i) q^{80} +(7.96239 + 2.89807i) q^{81} +(-6.78695 + 8.08837i) q^{82} +(-0.478899 - 0.276493i) q^{83} +(-0.758353 - 1.31351i) q^{84} +(-1.75729 + 14.0499i) q^{85} +(-2.54139 + 14.4129i) q^{86} +(-0.729865 + 0.421388i) q^{87} +(-9.71206 - 5.60726i) q^{88} +(-5.23109 - 4.38940i) q^{89} +(10.0081 + 3.08449i) q^{90} +(5.44854 - 1.98311i) q^{91} +(0.173197 + 0.206408i) q^{92} +(-6.79513 + 1.19816i) q^{93} -0.658883 q^{94} +(-0.501395 - 9.73389i) q^{95} +2.63155 q^{96} +(13.0001 - 2.29226i) q^{97} +(3.38643 + 4.03579i) q^{98} +(-12.4489 + 4.53102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34}+ \cdots - 36 q^{99}+O(q^{100}) $ 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$-1$

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 $

$2$	1.45670	−	0.256855i	1.03004	−	0.181624i	0.367010	−	0.930217i	$-0.380381\pi$
$2$	1.45670	−	0.256855i	1.03004	−	0.181624i	0.663030	+	0.748593i	$0.269270\pi$
$3$	−1.59617	−	1.90225i	−0.921552	−	1.09826i	−0.994891	−	0.100955i	$-0.967810\pi$
$3$	−1.59617	−	1.90225i	−0.921552	−	1.09826i	0.0733394	−	0.997307i	$-0.476634\pi$
$4$	0.176607	−	0.0642796i	0.0883034	−	0.0321398i
$5$	0.658585	−	2.13688i	0.294528	−	0.955643i
$5$	0.658585	−	2.13688i	0.294528	−	0.955643i
$6$	−2.81374	−	2.36101i	−1.14871	−	0.963879i
$7$	2.81448	+	1.62494i	1.06377	+	0.614169i	0.926473	−	0.376361i	$-0.122825\pi$
$7$	2.81448	+	1.62494i	1.06377	+	0.614169i	0.137298	+	0.990530i	$0.456158\pi$
$8$	−2.32124	+	1.34017i	−0.820684	+	0.473822i
$9$	−0.549824	+	3.11821i	−0.183275	+	1.03940i
$10$	0.410490	−	3.28195i	0.129808	−	1.03784i
$11$	2.09200	+	3.62344i	0.630760	+	1.09251i	0.987397	+	0.158265i	$0.0505902\pi$
$11$	2.09200	+	3.62344i	0.630760	+	1.09251i	−0.356636	+	0.934243i	$0.616076\pi$
$12$	−0.404171	−	0.233348i	−0.116674	−	0.0673618i
$13$	1.14682	−	1.36673i	0.318070	−	0.379062i	−0.583193	−	0.812334i	$-0.698197\pi$
$13$	1.14682	−	1.36673i	0.318070	−	0.379062i	0.901263	+	0.433272i	$0.142641\pi$
$14$	4.51721	+	1.64413i	1.20728	+	0.439412i
$15$	−5.11609	+	2.15805i	−1.32097	+	0.557205i
$16$	−3.32506	+	2.79006i	−0.831266	+	0.697515i
$17$	−6.23606	+	1.09959i	−1.51247	+	0.266689i	−0.867467	−	0.497495i	$-0.834253\pi$
$17$	−6.23606	+	1.09959i	−1.51247	+	0.266689i	−0.644999	+	0.764183i	$0.723142\pi$
$18$			4.68351i			1.10391i
$19$	4.09399	−	1.49640i	0.939226	−	0.343298i
$19$	4.09399	−	1.49640i	0.939226	−	0.343298i
$20$	−0.0210474	−	0.419722i	−0.00470635	−	0.0938526i
$21$	−1.40136	−	7.94751i	−0.305802	−	1.73429i
$22$	3.97810	+	4.74092i	0.848134	+	1.01077i
$23$	0.490346	+	1.34721i	0.102244	+	0.280914i	0.980258	−	0.197721i	$-0.0633540\pi$
$23$	0.490346	+	1.34721i	0.102244	+	0.280914i	−0.878014	+	0.478635i	$0.841132\pi$
$24$	6.25444	+	2.27643i	1.27668	+	0.464675i
$25$	−4.13253	−	2.81464i	−0.826506	−	0.562927i
$26$	1.31952	−	2.28547i	0.258779	−	0.448218i
$27$	0.357658	−	0.206494i	0.0688313	−	0.0397398i
$28$	0.601506	+	0.106062i	0.113674	+	0.0200438i
$29$	0.0589345	−	0.334234i	0.0109439	−	0.0620657i	−0.978847	−	0.204595i	$-0.934412\pi$
$29$	0.0589345	−	0.334234i	0.0109439	−	0.0620657i	0.989791	+	0.142529i	$0.0455235\pi$
$30$	−6.89829	+	4.45771i	−1.25945	+	0.813863i
$31$	1.38932	−	2.40638i	0.249530	−	0.432199i	−0.713866	−	0.700283i	$-0.753057\pi$
$31$	1.38932	−	2.40638i	0.249530	−	0.432199i	0.963395	+	0.268084i	$0.0863906\pi$
$32$	−0.681187	+	0.811808i	−0.120418	+	0.143509i
$33$	3.55349	−	9.76313i	0.618583	−	1.69954i
$34$	−8.80161	+	3.20352i	−1.50946	+	0.549400i
$35$	5.32587	−	4.94404i	0.900237	−	0.835696i
$36$	0.103335	+	0.586040i	0.0172224	+	0.0976733i
$37$		−	2.70482i		−	0.444670i	−0.974970	−	0.222335i	$-0.928632\pi$
$37$		−	2.70482i		−	0.444670i	0.974970	−	0.222335i	$-0.0713679\pi$
$38$	5.57935	−	3.23137i	0.905090	−	0.524197i
$39$	−4.43037			−0.709427
$40$	1.33505	+	5.84284i	0.211090	+	0.923834i
$41$	−5.46819	+	4.58835i	−0.853987	+	0.716581i	−0.960664	−	0.277713i	$-0.910423\pi$
$41$	−5.46819	+	4.58835i	−0.853987	+	0.716581i	0.106677	+	0.994294i	$0.465979\pi$
$42$	−4.08271	−	11.2172i	−0.629977	−	1.73085i
$43$	−3.38403	+	9.29755i	−0.516060	+	1.41786i	0.358767	+	0.933427i	$0.383197\pi$
$43$	−3.38403	+	9.29755i	−0.516060	+	1.41786i	−0.874827	+	0.484436i	$0.839025\pi$
$44$	0.602374	+	0.505452i	0.0908113	+	0.0761997i
$45$	6.30114	+	3.22852i	0.939318	+	0.481279i
$46$	1.06032	+	1.83654i	0.156336	+	0.270782i
$47$	−0.438674	−	0.0773501i	−0.0639872	−	0.0112827i	0.141563	−	0.989929i	$-0.454787\pi$
$47$	−0.438674	−	0.0773501i	−0.0639872	−	0.0112827i	−0.205550	+	0.978647i	$0.565898\pi$
$48$	10.6148	+	1.87167i	1.53211	+	0.270152i
$49$	1.78085	+	3.08452i	0.254407	+	0.440645i
$50$	−6.74280	−	3.03861i	−0.953576	−	0.429725i
$51$	12.0455	+	10.1074i	1.68671	+	1.41532i
$52$	0.114683	−	0.315090i	0.0159037	−	0.0436952i
$53$	−2.47532	−	6.80087i	−0.340011	−	0.934172i	−0.985391	−	0.170310i	$-0.945523\pi$
$53$	−2.47532	−	6.80087i	−0.340011	−	0.934172i	0.645380	−	0.763862i	$-0.276699\pi$
$54$	0.467960	−	0.392665i	0.0636813	−	0.0534350i
$55$	9.12062	−	2.08400i	1.22982	−	0.281007i
$56$	−8.71078			−1.16403
$57$	−9.38125	−	5.39926i	−1.24258	−	0.715150i
$58$		−	0.502015i		−	0.0659178i
$59$	−0.545712	−	3.09489i	−0.0710457	−	0.402920i	−0.999504	−	0.0314842i	$-0.989977\pi$
$59$	−0.545712	−	3.09489i	−0.0710457	−	0.402920i	0.928459	−	0.371436i	$-0.121134\pi$
$60$	−0.764818	+	0.709986i	−0.0987376	+	0.0916588i
$61$	2.88074	−	1.04850i	0.368841	−	0.134247i	−0.150948	−	0.988542i	$-0.548233\pi$
$61$	2.88074	−	1.04850i	0.368841	−	0.134247i	0.519789	+	0.854295i	$0.326010\pi$
$62$	1.40573	−	3.86222i	0.178528	−	0.490503i
$63$	−6.61436	+	7.88269i	−0.833331	+	0.993126i
$64$	3.55679	−	6.16055i	0.444599	−	0.770068i
$65$	−2.16526	−	3.35072i	−0.268567	−	0.415606i
$66$	2.66865	−	15.1347i	0.328488	−	1.86295i
$67$	8.42261	+	1.48513i	1.02899	+	0.181438i	0.662559	−	0.749009i	$-0.269470\pi$
$67$	8.42261	+	1.48513i	1.02899	+	0.181438i	0.366426	+	0.930447i	$0.380581\pi$
$68$	−1.03065	+	0.595046i	−0.124985	+	0.0721599i
$69$	1.78006	−	3.08315i	0.214294	−	0.371167i
$70$	6.48828	−	8.56995i	0.775498	−	1.02430i
$71$	−12.1153	−	4.40959i	−1.43782	−	0.523322i	−0.498656	−	0.866800i	$-0.666173\pi$
$71$	−12.1153	−	4.40959i	−1.43782	−	0.523322i	−0.939161	+	0.343478i	$0.888395\pi$
$72$	−2.90266	−	7.97498i	−0.342081	−	0.939861i
$73$	1.17133	+	1.39594i	0.137094	+	0.163382i	0.830223	−	0.557431i	$-0.188213\pi$
$73$	1.17133	+	1.39594i	0.137094	+	0.163382i	−0.693129	+	0.720813i	$0.743768\pi$
$74$	−0.694747	−	3.94011i	−0.0807627	−	0.458028i
$75$	1.24211	+	12.3537i	0.143426	+	1.42649i
$76$	0.626839	−	0.527435i	0.0719034	−	0.0605010i
$77$			13.5974i			1.54957i
$78$	−6.45371	+	1.13796i	−0.730739	+	0.128849i
$79$	−0.535235	+	0.449116i	−0.0602187	+	0.0505295i	−0.672400	−	0.740188i	$-0.734737\pi$
$79$	−0.535235	+	0.449116i	−0.0602187	+	0.0505295i	0.612182	+	0.790717i	$0.290292\pi$
$80$	3.77219	+	8.94276i	0.421744	+	0.999831i
$81$	7.96239	+	2.89807i	0.884710	+	0.322008i
$82$	−6.78695	+	8.08837i	−0.749493	+	0.893211i
$83$	−0.478899	−	0.276493i	−0.0525660	−	0.0303490i	0.473487	−	0.880801i	$-0.342995\pi$
$83$	−0.478899	−	0.276493i	−0.0525660	−	0.0303490i	−0.526053	+	0.850452i	$0.676329\pi$
$84$	−0.758353	−	1.31351i	−0.0827431	−	0.143315i
$85$	−1.75729	+	14.0499i	−0.190605	+	1.52392i
$86$	−2.54139	+	14.4129i	−0.274045	+	1.55419i
$87$	−0.729865	+	0.421388i	−0.0782497	+	0.0451775i
$88$	−9.71206	−	5.60726i	−1.03531	−	0.597736i
$89$	−5.23109	−	4.38940i	−0.554494	−	0.465276i	0.321965	−	0.946751i	$-0.395657\pi$
$89$	−5.23109	−	4.38940i	−0.554494	−	0.465276i	−0.876459	+	0.481476i	$0.840101\pi$
$90$	10.0081	+	3.08449i	1.05495	+	0.325134i
$91$	5.44854	−	1.98311i	0.571162	−	0.207886i
$92$	0.173197	+	0.206408i	0.0180570	+	0.0215195i
$93$	−6.79513	+	1.19816i	−0.704622	+	0.124244i
$94$	−0.658883			−0.0679586
$95$	−0.501395	−	9.73389i	−0.0514420	−	0.998676i
$96$	2.63155			0.268582
$97$	13.0001	−	2.29226i	1.31996	−	0.232744i	0.531094	−	0.847313i	$-0.321781\pi$
$97$	13.0001	−	2.29226i	1.31996	−	0.232744i	0.788863	+	0.614569i	$0.210670\pi$
$98$	3.38643	+	4.03579i	0.342081	+	0.407676i
$99$	−12.4489	+	4.53102i	−1.25116	+	0.455385i
$100$	−0.910757	−	0.231446i	−0.0910757	−	0.0231446i
$101$	13.2339	+	11.1046i	1.31683	+	1.10495i	0.986968	+	0.160916i	$0.0514450\pi$
$101$	13.2339	+	11.1046i	1.31683	+	1.10495i	0.329857	+	0.944031i	$0.392999\pi$
$102$	20.1428	+	11.6294i	1.99443	+	1.15149i
$103$	−11.9759	+	6.91430i	−1.18002	+	0.681286i	−0.956020	−	0.293302i	$-0.905246\pi$
$103$	−11.9759	+	6.91430i	−1.18002	+	0.681286i	−0.224003	+	0.974589i	$0.571912\pi$
$104$	−0.830401	+	4.70944i	−0.0814275	+	0.461798i
$105$	−17.9058	−	2.23957i	−1.74743	−	0.218559i
$106$	−5.35262	−	9.27101i	−0.519893	−	0.900481i
$107$	2.82722	+	1.63230i	0.273318	+	0.157800i	0.630394	−	0.776275i	$-0.282893\pi$
$107$	2.82722	+	1.63230i	0.273318	+	0.157800i	−0.357077	+	0.934075i	$0.616226\pi$
$108$	0.0498915	−	0.0594584i	0.00480081	−	0.00572138i
$109$	−3.02669	−	1.10163i	−0.289905	−	0.105517i	0.192974	−	0.981204i	$-0.438187\pi$
$109$	−3.02669	−	1.10163i	−0.289905	−	0.105517i	−0.482879	+	0.875687i	$0.660409\pi$
$110$	12.7507	−	5.37844i	1.21573	−	0.512814i
$111$	−5.14524	+	4.31737i	−0.488364	+	0.409786i
$112$	−13.8920	+	2.44953i	−1.31267	+	0.231459i
$113$		−	4.71007i		−	0.443086i	−0.975151	−	0.221543i	$-0.928891\pi$
$113$		−	4.71007i		−	0.443086i	0.975151	−	0.221543i	$-0.0711093\pi$
$114$	−15.0525	−	5.45547i	−1.40979	−	0.510952i
$115$	3.20177	−	0.160557i	0.298567	−	0.0149720i
$116$	−0.0110762	−	0.0628163i	−0.00102840	−	0.00583234i
$117$	3.63119	+	4.32748i	0.335704	+	0.400076i
$118$	−1.58988	−	4.36815i	−0.146360	−	0.402121i
$119$	−19.3380	−	7.03845i	−1.77271	−	0.645214i
$120$	8.98355	−	11.8658i	0.820082	−	1.08319i
$121$	−3.25289	+	5.63416i	−0.295717	+	0.512197i
$122$	3.92705	−	2.26729i	0.355539	−	0.205270i
$123$	17.4564	+	3.07803i	1.57399	+	0.277536i
$124$	0.0906829	−	0.514288i	0.00814356	−	0.0461844i
$125$	−8.73617	+	6.97706i	−0.781387	+	0.624047i
$126$	−7.61042	+	13.1816i	−0.677990	+	1.17431i
$127$	−0.380538	+	0.453507i	−0.0337673	+	0.0402423i	−0.782664	−	0.622445i	$-0.786140\pi$
$127$	−0.380538	+	0.453507i	−0.0337673	+	0.0402423i	0.748897	+	0.662687i	$0.230584\pi$
$128$	4.32371	−	11.8793i	0.382165	−	1.04999i
$129$	23.0877	−	8.40325i	2.03276	−	0.739865i
$130$	−4.01477	−	4.32483i	−0.352119	−	0.379313i
$131$	−3.56830	−	20.2369i	−0.311764	−	1.76810i	−0.589817	−	0.807537i	$-0.700800\pi$
$131$	−3.56830	−	20.2369i	−0.311764	−	1.76810i	0.278053	−	0.960566i	$-0.410311\pi$
$132$		−	1.95265i		−	0.169957i
$133$	13.9540	+	2.44090i	1.20997	+	0.211653i
$134$	12.6507			1.09285
$135$	−0.205705	−	0.900267i	−0.0177043	−	0.0774826i
$136$	13.0018	−	10.9098i	1.11489	−	0.935506i
$137$	−2.99407	−	8.22613i	−0.255800	−	0.702806i	−0.999415	−	0.0341973i	$-0.989113\pi$
$137$	−2.99407	−	8.22613i	−0.255800	−	0.702806i	0.743615	−	0.668608i	$-0.233110\pi$
$138$	1.80108	−	4.94843i	0.153318	−	0.421238i
$139$	−5.89041	−	4.94264i	−0.499618	−	0.419229i	0.357840	−	0.933783i	$-0.383513\pi$
$139$	−5.89041	−	4.94264i	−0.499618	−	0.419229i	−0.857458	+	0.514553i	$0.827958\pi$
$140$	0.622784	−	1.21550i	0.0526349	−	0.102728i
$141$	0.553061	+	0.957930i	0.0465762	+	0.0806723i
$142$	−18.7809	−	3.31158i	−1.57606	−	0.277901i
$143$	7.35139	+	1.29625i	0.614754	+	0.108398i
$144$	−6.87178	−	11.9023i	−0.572649	−	0.991857i
$145$	−0.675405	−	0.346057i	−0.0560893	−	0.0287385i
$146$	2.06483	+	1.73260i	0.170887	+	0.143391i
$147$	3.02497	−	8.31104i	0.249495	−	0.685483i
$148$	−0.173865	−	0.477690i	−0.0142916	−	0.0392659i
$149$	11.4457	−	9.60412i	0.937672	−	0.786800i	−0.0395067	−	0.999219i	$-0.512579\pi$
$149$	11.4457	−	9.60412i	0.937672	−	0.786800i	0.977179	+	0.212419i	$0.0681342\pi$
$150$	4.98250	+	17.6766i	0.406819	+	1.44329i
$151$	13.1424			1.06951			0.534757	−	0.845006i	$-0.320403\pi$
$151$	13.1424			1.06951			0.534757	+	0.845006i	$0.320403\pi$
$152$	−7.49772	+	8.96017i	−0.608145	+	0.726765i
$153$		−	20.0499i		−	1.62094i
$154$	3.49257	+	19.8074i	0.281440	+	1.59612i
$155$	−4.22716	−	4.55363i	−0.339534	−	0.365756i
$156$	−0.782434	+	0.284783i	−0.0626449	+	0.0228009i
$157$	3.70654	−	10.1836i	0.295814	−	0.812742i	−0.699374	−	0.714756i	$-0.746538\pi$
$157$	3.70654	−	10.1836i	0.295814	−	0.812742i	0.995188	−	0.0979861i	$-0.0312401\pi$
$158$	−0.664318	+	0.791704i	−0.0528503	+	0.0629846i
$159$	−8.98590	+	15.5640i	−0.712628	+	1.23431i
$160$	1.28612	+	1.99026i	0.101677	+	0.157344i
$161$	−0.809073	+	4.58848i	−0.0637639	+	0.361623i
$162$	12.3432	+	2.17644i	0.969772	+	0.170997i
$163$	−7.31405	+	4.22277i	−0.572881	+	0.330753i	−0.758299	−	0.651907i	$-0.773969\pi$
$163$	−7.31405	+	4.22277i	−0.572881	+	0.330753i	0.185418	+	0.982660i	$0.440636\pi$
$164$	−0.670782	+	1.16183i	−0.0523792	+	0.0907235i
$165$	−18.5224	−	14.0232i	−1.44197	−	1.09171i
$166$	−0.768630	−	0.279758i	−0.0596573	−	0.0217135i
$167$	6.80663	+	18.7011i	0.526713	+	1.44713i	0.862919	+	0.505343i	$0.168634\pi$
$167$	6.80663	+	18.7011i	0.526713	+	1.44713i	−0.336206	+	0.941788i	$0.609144\pi$
$168$	13.9039	+	16.5700i	1.07271	+	1.27841i
$169$	1.70468	+	9.66772i	0.131129	+	0.743671i
$170$	1.04895	+	20.9178i	0.0804506	+	1.60432i
$171$	2.41512	+	13.5887i	0.184689	+	1.03915i
$172$			1.85954i			0.141788i
$173$	11.5430	−	2.03534i	0.877597	−	0.154744i	0.283340	−	0.959019i	$-0.408557\pi$
$173$	11.5430	−	2.03534i	0.877597	−	0.154744i	0.594257	+	0.804275i	$0.297446\pi$
$174$	−0.954956	+	0.801304i	−0.0723951	+	0.0607467i
$175$	−7.05730	−	14.6368i	−0.533482	−	1.10644i
$176$	−17.0656	−	6.21138i	−1.28637	−	0.468200i
$177$	−5.01619	+	5.97806i	−0.377040	+	0.449339i
$178$	−8.74755	−	5.05040i	−0.655657	−	0.378544i
$179$	3.54189	+	6.13473i	0.264733	+	0.458532i	0.967494	−	0.252895i	$-0.0813827\pi$
$179$	3.54189	+	6.13473i	0.264733	+	0.458532i	−0.702760	+	0.711427i	$0.748049\pi$
$180$	1.32035	+	0.165143i	0.0984132	+	0.0123090i
$181$	1.61176	−	9.14076i	0.119801	−	0.679427i	−0.864459	−	0.502703i	$-0.832339\pi$
$181$	1.61176	−	9.14076i	0.119801	−	0.679427i	0.984260	−	0.176724i	$-0.0565500\pi$
$182$	7.42750	−	4.28827i	0.550563	−	0.317868i
$183$	−6.59268	−	3.80628i	−0.487345	−	0.281369i
$184$	−2.94371	−	2.47007i	−0.217013	−	0.182096i
$185$	−5.77989	−	1.78135i	−0.424946	−	0.130968i
$186$	−9.59069	+	3.49073i	−0.703224	+	0.255952i
$187$	−17.0301	−	20.2957i	−1.24536	−	1.48417i
$188$	−0.0824448	+	0.0145373i	−0.00601291	+	0.00106024i
$189$	1.34216			0.0976277
$190$	−3.23058	−	14.0505i	−0.234371	−	1.01933i
$191$	8.12426			0.587850			0.293925	−	0.955828i	$-0.405038\pi$
$191$	8.12426			0.587850			0.293925	+	0.955828i	$0.405038\pi$
$192$	−17.3961	+	3.06741i	−1.25546	+	0.221371i
$193$	−4.96452	−	5.91649i	−0.357354	−	0.425878i	0.557177	−	0.830394i	$-0.311885\pi$
$193$	−4.96452	−	5.91649i	−0.357354	−	0.425878i	−0.914531	+	0.404516i	$0.867440\pi$
$194$	18.3484	−	6.67827i	1.31734	−	0.479472i
$195$	−2.91778	+	9.46719i	−0.208946	+	0.677959i
$196$	0.512781	+	0.430275i	0.0366272	+	0.0307339i
$197$	−3.08965	−	1.78381i	−0.220129	−	0.127091i	0.385881	−	0.922548i	$-0.373897\pi$
$197$	−3.08965	−	1.78381i	−0.220129	−	0.127091i	−0.606010	+	0.795457i	$0.707231\pi$
$198$	−16.9704	+	9.79788i	−1.20604	+	0.696305i
$199$	1.52279	−	8.63615i	0.107947	−	0.612201i	−0.882055	−	0.471147i	$-0.843840\pi$
$199$	1.52279	−	8.63615i	0.107947	−	0.612201i	0.990002	−	0.141053i	$-0.0450489\pi$
$200$	13.3647	+	0.995159i	0.945028	+	0.0703684i
$201$	−10.6189	−	18.3924i	−0.748997	−	1.29730i
$202$	22.1301	+	12.7768i	1.55707	+	0.898974i
$203$	0.708979	−	0.844928i	0.0497606	−	0.0593023i
$204$	2.77702	+	1.01075i	0.194430	+	0.0707668i
$205$	6.20351	+	14.7067i	0.433272	+	1.02716i
$206$	−15.6693	+	13.1481i	−1.09173	+	0.916073i
$207$	−4.47050	+	0.788270i	−0.310721	+	0.0547885i
$208$			7.74414i			0.536960i
$209$	13.9867	+	11.7039i	0.967483	+	0.809574i
$210$	−26.6586	+	1.33683i	−1.83962	+	0.0922497i
$211$	2.05203	+	11.6376i	0.141267	+	0.801167i	0.970289	+	0.241950i	$0.0777870\pi$
$211$	2.05203	+	11.6376i	0.141267	+	0.801167i	−0.829021	+	0.559217i	$0.811102\pi$
$212$	−0.874315	−	1.04197i	−0.0600482	−	0.0715627i
$213$	10.9499	+	30.0847i	0.750277	+	2.06137i
$214$	4.53767	+	1.65158i	0.310189	+	0.112899i
$215$	17.6391	+	13.3545i	1.20298	+	0.910770i
$216$	−0.553474	+	0.958646i	−0.0376592	+	0.0652276i
$217$	7.82043	−	4.51513i	0.530886	−	0.306507i
$218$	−4.69193	−	0.827314i	−0.317778	−	0.0560328i
$219$	0.785770	−	4.45633i	0.0530974	−	0.301131i
$220$	1.47681	−	0.954320i	0.0995662	−	0.0643402i
$221$	−5.64880	+	9.78401i	−0.379979	+	0.658144i
$222$	−6.38611	+	7.61067i	−0.428608	+	0.510795i
$223$	−3.04316	+	8.36101i	−0.203785	+	0.559895i	−0.998916	−	0.0465426i	$-0.985180\pi$
$223$	−3.04316	+	8.36101i	−0.203785	+	0.559895i	0.795131	+	0.606437i	$0.207402\pi$
$224$	−3.23632	+	1.17792i	−0.216236	+	0.0787034i
$225$	11.0488	−	11.3385i	0.736586	−	0.755903i
$226$	−1.20980	−	6.86114i	−0.0804750	−	0.456396i
$227$		−	26.4080i		−	1.75276i	−0.481620	−	0.876380i	$-0.659951\pi$
$227$		−	26.4080i		−	1.75276i	0.481620	−	0.876380i	$-0.340049\pi$
$228$	−2.00386	−	0.350523i	−0.132709	−	0.0232140i
$229$	−21.7852			−1.43961			−0.719804	−	0.694177i	$-0.755768\pi$
$229$	−21.7852			−1.43961			−0.719804	+	0.694177i	$0.755768\pi$
$230$	4.62277	−	1.05627i	0.304817	−	0.0696486i
$231$	25.8657	−	21.7039i	1.70184	−	1.42801i
$232$	0.311129	+	0.854821i	0.0204266	+	0.0561217i
$233$	−3.42052	+	9.39780i	−0.224086	+	0.615670i	−0.999883	−	0.0153122i	$-0.995126\pi$
$233$	−3.42052	+	9.39780i	−0.224086	+	0.615670i	0.775797	+	0.630982i	$0.217348\pi$
$234$	6.40108	+	5.37114i	0.418452	+	0.351123i
$235$	−0.454192	+	0.886453i	−0.0296282	+	0.0578258i
$236$	−0.295315	−	0.511500i	−0.0192234	−	0.0332958i
$237$	1.70866	+	0.301282i	0.110989	+	0.0195704i
$238$	−29.9774	−	5.28583i	−1.94315	−	0.342630i
$239$	8.91823	+	15.4468i	0.576872	+	0.999172i	0.995835	+	0.0911689i	$0.0290603\pi$
$239$	8.91823	+	15.4468i	0.576872	+	0.999172i	−0.418963	+	0.908003i	$0.637606\pi$
$240$	10.9903	−	21.4498i	0.709418	−	1.38458i
$241$	−13.1332	−	11.0201i	−0.845984	−	0.709864i	0.112918	−	0.993604i	$-0.463980\pi$
$241$	−13.1332	−	11.0201i	−0.845984	−	0.709864i	−0.958901	+	0.283740i	$0.908425\pi$
$242$	−3.29131	+	9.04279i	−0.211573	+	0.581293i
$243$	−7.62027	−	20.9365i	−0.488840	−	1.34308i
$244$	0.441361	−	0.370346i	0.0282552	−	0.0237090i
$245$	7.76409	−	1.77404i	0.496029	−	0.113339i
$246$	26.2192			1.67168
$247$	2.64990	−	7.31147i	0.168609	−	0.465218i
$248$			7.44772i			0.472931i
$249$	0.238450	+	1.35232i	0.0151111	+	0.0856995i
$250$	−10.9339	+	12.4074i	−0.691518	+	0.784712i
$251$	−9.11112	+	3.31618i	−0.575089	+	0.209315i	−0.613159	−	0.789960i	$-0.710101\pi$
$251$	−9.11112	+	3.31618i	−0.575089	+	0.209315i	0.0380697	+	0.999275i	$0.487879\pi$
$252$	−0.661445	+	1.81731i	−0.0416671	+	0.114480i
$253$	−3.85575	+	4.59511i	−0.242409	+	0.288892i
$254$	−0.437843	+	0.758366i	−0.0274727	+	0.0475841i
$255$	29.5313	−	19.0833i	1.84932	−	1.19504i
$256$	0.776555	−	4.40406i	0.0485347	−	0.275254i
$257$	−9.89795	−	1.74528i	−0.617417	−	0.108867i	−0.143813	−	0.989605i	$-0.545936\pi$
$257$	−9.89795	−	1.74528i	−0.617417	−	0.108867i	−0.473605	+	0.880738i	$0.657047\pi$
$258$	31.4734	−	18.1712i	1.95945	−	1.13129i
$259$	4.39517	−	7.61265i	0.273102	−	0.473027i
$260$	−0.597782	−	0.452579i	−0.0370729	−	0.0280677i
$261$	1.00981	+	0.367540i	0.0625055	+	0.0227501i
$262$	−10.3959	−	28.5624i	−0.642259	−	1.76459i
$263$	14.0324	+	16.7232i	0.865276	+	1.03120i	0.999192	+	0.0402026i	$0.0128003\pi$
$263$	14.0324	+	16.7232i	0.865276	+	1.03120i	−0.133916	+	0.990993i	$0.542755\pi$
$264$	4.83575	+	27.4249i	0.297620	+	1.68789i
$265$	−16.1629	+	0.810506i	−0.992877	+	0.0497890i
$266$	20.9537	−	0.0285081i	1.28475	−	0.00174794i
$267$			16.9571i			1.03776i
$268$	1.58295	−	0.279117i	0.0966943	−	0.0170498i
$269$	−11.8393	+	9.93433i	−0.721853	+	0.605707i	−0.927897	−	0.372836i	$-0.878385\pi$
$269$	−11.8393	+	9.93433i	−0.721853	+	0.605707i	0.206044	+	0.978543i	$0.433941\pi$
$270$	−0.530888	−	1.25858i	−0.0323088	−	0.0765947i
$271$	−4.85182	−	1.76592i	−0.294727	−	0.107272i	0.190425	−	0.981702i	$-0.439013\pi$
$271$	−4.85182	−	1.76592i	−0.294727	−	0.107272i	−0.485152	+	0.874430i	$0.661236\pi$
$272$	17.6674	−	21.0552i	1.07124	−	1.27666i
$273$	−12.4692	−	7.19908i	−0.754669	−	0.435708i
$274$	−6.47437	−	11.2139i	−0.391131	−	0.677459i
$275$	1.55343	−	20.8622i	0.0936756	−	1.25804i
$276$	0.116186	−	0.658926i	0.00699360	−	0.0396627i
$277$	−4.82402	+	2.78515i	−0.289847	+	0.167343i	−0.637873	−	0.770142i	$-0.720186\pi$
$277$	−4.82402	+	2.78515i	−0.289847	+	0.167343i	0.348026	+	0.937485i	$0.386852\pi$
$278$	−9.85009	−	5.68695i	−0.590769	−	0.341081i
$279$	6.73971	+	5.65529i	0.403496	+	0.338573i
$280$	−5.73679	+	18.6139i	−0.342839	+	1.11239i
$281$	−25.6282	+	9.32789i	−1.52885	+	0.556455i	−0.963339	−	0.268287i	$-0.913542\pi$
$281$	−25.6282	+	9.32789i	−1.52885	+	0.556455i	−0.565509	+	0.824742i	$0.691320\pi$
$282$	1.05169	+	1.25336i	0.0626273	+	0.0746363i
$283$	14.8172	−	2.61267i	0.880792	−	0.155307i	0.285078	−	0.958504i	$-0.407980\pi$
$283$	14.8172	−	2.61267i	0.880792	−	0.155307i	0.595714	+	0.803197i	$0.296869\pi$
$284$	−2.42308			−0.143784
$285$	−17.7159	+	16.4908i	−1.04940	+	0.976828i
$286$	11.0417			0.652910
$287$	−22.8459	+	4.02834i	−1.34855	+	0.237786i
$288$	−2.15685	−	2.57044i	−0.127094	−	0.151464i
$289$	21.7045	−	7.89981i	1.27674	−	0.464694i
$290$	−1.07275	−	0.330620i	−0.0629939	−	0.0194147i
$291$	−25.1108	−	21.0705i	−1.47202	−	1.23517i
$292$	0.296596	+	0.171240i	0.0173570	+	0.0100210i
$293$	−6.77995	+	3.91441i	−0.396089	+	0.228682i	−0.684795	−	0.728736i	$-0.740108\pi$
$293$	−6.77995	+	3.91441i	−0.396089	+	0.228682i	0.288706	+	0.957418i	$0.406775\pi$
$294$	2.27173	−	12.8836i	0.132490	−	0.751389i
$295$	−6.97281	−	0.872124i	−0.405973	−	0.0507770i
$296$	3.62492	+	6.27855i	0.210694	+	0.364933i
$297$	1.49644	+	0.863969i	0.0868321	+	0.0501325i
$298$	14.2061	−	16.9302i	0.822938	−	0.980740i
$299$	2.40361	+	0.874843i	0.139004	+	0.0505935i
$300$	1.01346	+	2.10191i	0.0585121	+	0.121354i
$301$	−24.6322	+	20.6689i	−1.41978	+	1.19133i
$302$	19.1445	−	3.37569i	1.10164	−	0.194249i
$303$		−	42.8990i		−	2.46449i
$304$	−9.43773	+	16.3981i	−0.541291	+	0.940496i
$305$	−0.343317	−	6.84633i	−0.0196583	−	0.392020i
$306$	−5.14992	−	29.2066i	−0.294401	−	1.66963i
$307$	10.1011	+	12.0381i	0.576503	+	0.687049i	0.972952	−	0.231008i	$-0.0742022\pi$
$307$	10.1011	+	12.0381i	0.576503	+	0.687049i	−0.396449	+	0.918057i	$0.629758\pi$
$308$	0.874039	+	2.40140i	0.0498030	+	0.136833i
$309$	32.2684	+	11.7447i	1.83568	+	0.668134i
$310$	−7.32732	−	5.54749i	−0.416164	−	0.315076i
$311$	−8.99061	+	15.5722i	−0.509810	+	0.883018i	0.490125	+	0.871652i	$0.336951\pi$
$311$	−8.99061	+	15.5722i	−0.509810	+	0.883018i	−0.999935	+	0.0113654i	$0.996382\pi$
$312$	10.2840	−	5.93746i	0.582216	−	0.336142i
$313$	20.8784	+	3.68143i	1.18012	+	0.208087i	0.729087	−	0.684422i	$-0.239945\pi$
$313$	20.8784	+	3.68143i	1.18012	+	0.208087i	0.451031	+	0.892508i	$0.351056\pi$
$314$	2.78359	−	15.7865i	0.157087	−	0.890884i
$315$	12.4883	+	19.3255i	0.703634	+	1.08887i
$316$	−0.0656572	+	0.113722i	−0.00369351	+	0.00639734i
$317$	1.96977	−	2.34748i	0.110633	−	0.131848i	−0.707886	−	0.706327i	$-0.750351\pi$
$317$	1.96977	−	2.34748i	0.110633	−	0.131848i	0.818519	+	0.574479i	$0.194795\pi$
$318$	−9.09203	+	24.9802i	−0.509856	+	1.40082i
$319$	1.33437	−	0.485670i	0.0747102	−	0.0271923i
$320$	−10.8219	−	11.6577i	−0.604963	−	0.651685i
$321$	−1.40771	−	7.98350i	−0.0785706	−	0.445596i
$322$			6.89184i			0.384067i
$323$	−23.8850	+	13.8333i	−1.32899	+	0.769708i
$324$	1.59250			0.0884722
$325$	−8.58611	+	2.42016i	−0.476271	+	0.134246i
$326$	−9.56972	+	8.02995i	−0.530018	+	0.444738i
$327$	2.73556	+	7.51590i	0.151277	+	0.415630i
$328$	6.54382	−	17.9790i	0.361322	−	0.992724i
$329$	−1.10895	−	0.930518i	−0.0611383	−	0.0513011i
$330$	−30.5835	−	15.6700i	−1.68356	−	0.862608i
$331$	12.9754	+	22.4741i	0.713195	+	1.23529i	0.963652	+	0.267162i	$0.0860858\pi$
$331$	12.9754	+	22.4741i	0.713195	+	1.23529i	−0.250457	+	0.968128i	$0.580581\pi$
$332$	−0.102350	−	0.0180470i	−0.00561717	−	0.000990459i
$333$	8.43420	+	1.48718i	0.462191	+	0.0814968i
$334$	14.7187	+	25.4935i	0.805369	+	1.39494i
$335$	8.72056	−	17.0200i	0.476455	−	0.929904i
$336$	26.8336	+	22.5161i	1.46389	+	1.22835i
$337$	−3.43986	+	9.45093i	−0.187381	+	0.514825i	−0.997439	−	0.0715252i	$-0.977213\pi$
$337$	−3.43986	+	9.45093i	−0.187381	+	0.514825i	0.810058	+	0.586350i	$0.199436\pi$
$338$	4.96641	+	13.6451i	0.270137	+	0.742195i
$339$	−8.95971	+	7.51809i	−0.486624	+	0.408326i
$340$	0.592773	+	2.59426i	0.0321476	+	0.140694i
$341$	11.6258			0.629574
$342$	7.00842	+	19.1743i	0.378972	+	1.03683i
$343$		−	11.1741i		−	0.603343i
$344$	−4.60514	−	26.1171i	−0.248293	−	1.40814i
$345$	−5.41600	−	5.83428i	−0.291588	−	0.314107i
$346$	16.2918	−	5.92975i	0.875855	−	0.318785i
$347$	−2.33190	+	6.40683i	−0.125183	+	0.343937i	−0.986414	−	0.164276i	$-0.947471\pi$
$347$	−2.33190	+	6.40683i	−0.125183	+	0.343937i	0.861232	+	0.508213i	$0.169694\pi$
$348$	−0.101812	+	0.121335i	−0.00545772	+	0.00650426i
$349$	15.7983	−	27.3634i	0.845663	−	1.46473i	−0.0393817	−	0.999224i	$-0.512539\pi$
$349$	15.7983	−	27.3634i	0.845663	−	1.46473i	0.885044	−	0.465507i	$-0.154128\pi$
$350$	−14.0399	−	19.5087i	−0.750464	−	1.04279i
$351$	0.127948	−	0.725632i	0.00682938	−	0.0387314i
$352$	−4.36658	−	0.769945i	−0.232739	−	0.0410382i
$353$	−5.46165	+	3.15328i	−0.290694	+	0.167832i	−0.638255	−	0.769825i	$-0.720343\pi$
$353$	−5.46165	+	3.15328i	−0.290694	+	0.167832i	0.347561	+	0.937658i	$0.387010\pi$
$354$	−5.77157	+	9.99666i	−0.306756	+	0.531316i
$355$	−17.4017	+	22.9848i	−0.923587	+	1.21991i
$356$	−1.20600	−	0.438946i	−0.0639176	−	0.0232641i
$357$	17.4779	+	48.0202i	0.925030	+	2.54150i
$358$	6.73520	+	8.02670i	0.355966	+	0.424224i
$359$	−0.725269	−	4.11321i	−0.0382782	−	0.217087i	0.959669	−	0.281134i	$-0.0907104\pi$
$359$	−0.725269	−	4.11321i	−0.0382782	−	0.217087i	−0.997947	+	0.0640469i	$0.979599\pi$
$360$	−18.9532	+	0.950432i	−0.998924	+	0.0500922i
$361$	14.5216	−	12.2525i	0.764293	−	0.644870i
$362$		−	13.7293i		−	0.721596i
$363$	15.9097	−	2.80532i	0.835045	−	0.147241i
$364$	0.834776	−	0.700460i	0.0437542	−	0.0367141i
$365$	3.75438	−	1.58365i	0.196513	−	0.0828923i
$366$	−10.5812	−	3.85124i	−0.553088	−	0.201308i
$367$	−10.6516	+	12.6941i	−0.556010	+	0.662627i	−0.968697	−	0.248246i	$-0.920146\pi$
$367$	−10.6516	+	12.6941i	−0.556010	+	0.662627i	0.412687	+	0.910873i	$0.364590\pi$
$368$	−5.38924	−	3.11148i	−0.280933	−	0.162197i
$369$	−11.3009	−	19.5737i	−0.588302	−	1.01897i
$370$	−8.87709	−	1.11030i	−0.461498	−	0.0577218i
$371$	4.08428	−	23.1631i	0.212045	−	1.20257i
$372$	−1.12305	+	0.648392i	−0.0582274	+	0.0336176i
$373$	32.0433	+	18.5002i	1.65914	+	0.957905i	0.973113	+	0.230330i	$0.0739804\pi$
$373$	32.0433	+	18.5002i	1.65914	+	0.957905i	0.686028	+	0.727576i	$0.259353\pi$
$374$	−30.0207	−	25.1904i	−1.55233	−	1.30256i
$375$	27.2165	+	5.48175i	1.40546	+	0.283076i
$376$	1.12193	−	0.408350i	0.0578592	−	0.0210590i
$377$	−0.389219	−	0.463853i	−0.0200458	−	0.0238897i
$378$	1.95512	−	0.344740i	0.100561	−	0.0177315i
$379$	−31.5147			−1.61880			−0.809400	−	0.587257i	$-0.800208\pi$
$379$	−31.5147			−1.61880			−0.809400	+	0.587257i	$0.800208\pi$
$380$	−0.714241	−	1.68684i	−0.0366398	−	0.0865332i
$381$	1.47009			0.0753148
$382$	11.8346	−	2.08676i	0.605510	−	0.106768i
$383$	−1.99144	−	2.37331i	−0.101758	−	0.121270i	0.712762	−	0.701406i	$-0.247444\pi$
$383$	−1.99144	−	2.37331i	−0.101758	−	0.121270i	−0.814520	+	0.580136i	$0.803000\pi$
$384$	−29.4987	+	10.7367i	−1.50535	+	0.547903i
$385$	29.0561	+	8.95507i	1.48084	+	0.456393i
$386$	−8.75148	−	7.34337i	−0.445439	−	0.373768i
$387$	−27.1311	−	15.6641i	−1.37915	−	0.796253i
$388$	2.14856	−	1.24047i	0.109076	−	0.0629753i
$389$	−4.52037	+	25.6363i	−0.229192	+	1.29981i	0.625316	+	0.780372i	$0.284970\pi$
$389$	−4.52037	+	25.6363i	−0.229192	+	1.29981i	−0.854507	+	0.519439i	$0.826141\pi$
$390$	−1.81862	+	14.5403i	−0.0920895	+	0.736275i
$391$	−4.53920	−	7.86213i	−0.229557	−	0.397605i
$392$	−8.26756	−	4.77328i	−0.417575	−	0.241087i
$393$	−32.7999	+	39.0893i	−1.65453	+	1.97180i
$394$	−4.95887	−	1.80488i	−0.249824	−	0.0909285i
$395$	0.607210	+	1.43952i	0.0305520	+	0.0724299i
$396$	−1.90730	+	1.60042i	−0.0958457	+	0.0804241i
$397$	12.4684	−	2.19851i	0.625770	−	0.110340i	0.148234	−	0.988952i	$-0.452641\pi$
$397$	12.4684	−	2.19851i	0.625770	−	0.110340i	0.477536	+	0.878612i	$0.341530\pi$
$398$		−	12.9714i		−	0.650197i
$399$	−17.6298	−	30.4400i	−0.882595	−	1.52391i
$400$	21.5939	−	2.17116i	1.07970	−	0.108558i
$401$	−1.60135	−	9.08170i	−0.0799675	−	0.453518i	−0.998330	−	0.0577770i	$-0.981599\pi$
$401$	−1.60135	−	9.08170i	−0.0799675	−	0.453518i	0.918362	−	0.395741i	$-0.129512\pi$
$402$	−20.1926	−	24.0647i	−1.00712	−	1.20024i
$403$	−1.69556	−	4.65851i	−0.0844618	−	0.232057i
$404$	3.05100	+	1.11047i	0.151793	+	0.0552481i
$405$	11.4368	−	15.1061i	0.568297	−	0.750627i
$406$	0.815744	−	1.41291i	0.0404847	−	0.0701215i
$407$	9.80076	−	5.65847i	0.485806	−	0.280480i
$408$	−41.5062	−	7.31866i	−2.05486	−	0.362328i
$409$	−5.98343	+	33.9337i	−0.295861	+	1.67791i	0.367819	+	0.929897i	$0.380105\pi$
$409$	−5.98343	+	33.9337i	−0.295861	+	1.67791i	−0.663680	+	0.748016i	$0.731007\pi$
$410$	12.8141	+	19.8298i	0.632844	+	0.979324i
$411$	−10.8691	+	18.8258i	−0.536132	+	0.928607i
$412$	−1.67058	+	1.99092i	−0.0823036	+	0.0980856i
$413$	3.49311	−	9.59724i	0.171885	−	0.472249i
$414$	−6.30969	+	2.29654i	−0.310104	+	0.112869i
$415$	−0.906228	+	0.841258i	−0.0444850	+	0.0412957i
$416$	0.328320	+	1.86199i	0.0160972	+	0.0912917i
$417$			19.0943i			0.935053i
$418$	23.3806	+	13.4564i	1.14358	+	0.658176i
$419$	7.86047			0.384009			0.192005	−	0.981394i	$-0.438501\pi$
$419$	7.86047			0.384009			0.192005	+	0.981394i	$0.438501\pi$
$420$	−3.30625	+	0.755456i	−0.161328	+	0.0368625i
$421$	8.03752	−	6.74428i	0.391725	−	0.328696i	−0.425560	−	0.904930i	$-0.639923\pi$
$421$	8.03752	−	6.74428i	0.391725	−	0.328696i	0.817285	+	0.576234i	$0.195478\pi$
$422$	5.97836	+	16.4254i	0.291022	+	0.799577i
$423$	0.482387	−	1.32535i	0.0234545	−	0.0644406i
$424$	14.8601	+	12.4691i	0.721672	+	0.605555i
$425$	28.8656	+	13.0082i	1.40019	+	0.630989i
$426$	23.6781	+	41.0117i	1.14721	+	1.98702i
$427$	9.81153	+	1.73004i	0.474813	+	0.0837223i
$428$	0.604230	+	0.106542i	0.0292066	+	0.00514991i
$429$	−9.26832	−	16.0532i	−0.447479	−	0.775056i
$430$	29.1250	+	14.9228i	1.40453	+	0.719640i
$431$	22.8988	+	19.2144i	1.10300	+	0.925525i	0.997623	−	0.0689073i	$-0.0219513\pi$
$431$	22.8988	+	19.2144i	1.10300	+	0.925525i	0.105375	+	0.994433i	$0.466396\pi$
$432$	−0.613105	+	1.68449i	−0.0294980	+	0.0810452i
$433$	−2.32566	−	6.38969i	−0.111764	−	0.307069i	0.871183	−	0.490959i	$-0.163353\pi$
$433$	−2.32566	−	6.38969i	−0.111764	−	0.307069i	−0.982947	+	0.183890i	$0.941131\pi$
$434$	10.2323	−	8.58589i	0.491165	−	0.412136i
$435$	0.419778	+	1.83715i	0.0201268	+	0.0880848i
$436$	−0.605347			−0.0289908
$437$	4.02345	+	4.78173i	0.192468	+	0.228741i
$438$		−	6.69335i		−	0.319820i
$439$	−1.38329	−	7.84504i	−0.0660209	−	0.374423i	−0.999860	−	0.0167300i	$-0.994674\pi$
$439$	−1.38329	−	7.84504i	−0.0660209	−	0.374423i	0.933839	−	0.357693i	$-0.116437\pi$
$440$	−18.3783	+	17.0607i	−0.876150	+	0.813336i
$441$	−10.5973	+	3.85711i	−0.504634	+	0.183672i
$442$	−5.71552	+	15.7033i	−0.271859	+	0.746928i
$443$	14.0059	−	16.6916i	0.665440	−	0.793041i	−0.322715	−	0.946496i	$-0.604596\pi$
$443$	14.0059	−	16.6916i	0.665440	−	0.793041i	0.988156	+	0.153455i	$0.0490401\pi$
$444$	−0.631165	+	1.09321i	−0.0299538	+	0.0518815i
$445$	−12.8248	+	8.28742i	−0.607952	+	0.392862i
$446$	−2.28539	+	12.9611i	−0.108217	+	0.613726i
$447$	−36.5388	−	6.44278i	−1.72823	−	0.304733i
$448$	20.0210	−	11.5591i	0.945904	−	0.546118i
$449$	9.39185	−	16.2672i	0.443229	−	0.767695i	−0.554698	−	0.832052i	$-0.687166\pi$
$449$	9.39185	−	16.2672i	0.443229	−	0.767695i	0.997927	+	0.0643569i	$0.0204996\pi$
$450$	13.1824	−	19.3548i	0.621423	−	0.912392i
$451$	−28.0651	−	10.2148i	−1.32153	−	0.480998i
$452$	−0.302761	−	0.831830i	−0.0142407	−	0.0391260i
$453$	−20.9776	−	25.0001i	−0.985612	−	1.17461i
$454$	−6.78303	−	38.4685i	−0.318343	−	1.80541i
$455$	−0.649339	−	12.9489i	−0.0304415	−	0.607055i
$456$	29.0121	−	0.0394717i	1.35862	−	0.00184843i
$457$		−	28.2368i		−	1.32086i	−0.750887	−	0.660431i	$-0.770373\pi$
$457$		−	28.2368i		−	1.32086i	0.750887	−	0.660431i	$-0.229627\pi$
$458$	−31.7345	+	5.59564i	−1.48285	+	0.261467i
$459$	−2.00332	+	1.68098i	−0.0935069	+	0.0784616i
$460$	0.555134	−	0.234164i	0.0258833	−	0.0109180i
$461$	0.184187	+	0.0670386i	0.00857845	+	0.00312230i	0.346306	−	0.938122i	$-0.387436\pi$
$461$	0.184187	+	0.0670386i	0.00857845	+	0.00312230i	−0.337727	+	0.941244i	$0.609658\pi$
$462$	32.1037	−	38.2597i	1.49360	−	1.78000i
$463$	−12.0933	−	6.98206i	−0.562022	−	0.324484i	0.191935	−	0.981408i	$-0.438524\pi$
$463$	−12.0933	−	6.98206i	−0.562022	−	0.324484i	−0.753957	+	0.656924i	$0.771857\pi$
$464$	0.736571	+	1.27578i	0.0341945	+	0.0592266i
$465$	−1.91483	+	15.3095i	−0.0887982	+	0.709960i
$466$	−2.56879	+	14.5683i	−0.118997	+	0.674865i
$467$	27.8016	−	16.0512i	1.28650	−	0.742763i	0.308474	−	0.951233i	$-0.400182\pi$
$467$	27.8016	−	16.0512i	1.28650	−	0.742763i	0.978029	+	0.208470i	$0.0668483\pi$
$468$	0.919462	+	0.530851i	0.0425021	+	0.0245386i
$469$	21.2920	+	17.8661i	0.983172	+	0.824979i
$470$	−0.433930	+	1.40796i	−0.0200157	+	0.0649441i
$471$	−25.2881	+	9.20410i	−1.16521	+	0.424102i
$472$	5.41441	+	6.45264i	0.249218	+	0.297007i
$473$	−40.7685	+	7.18859i	−1.87454	+	0.330532i
$474$	2.56638			0.117878
$475$	−21.1304	−	5.33917i	−0.969529	−	0.244978i
$476$	−3.86765			−0.177273
$477$	22.5675	−	3.97926i	1.03330	−	0.182198i
$478$	16.9588	+	20.2107i	0.775675	+	0.924414i
$479$	−1.86271	+	0.677972i	−0.0851095	+	0.0309773i	−0.384224	−	0.923240i	$-0.625531\pi$
$479$	−1.86271	+	0.677972i	−0.0851095	+	0.0309773i	0.299114	+	0.954217i	$0.403309\pi$
$480$	1.73310	−	5.62332i	0.0791048	−	0.256668i
$481$	−3.69675	−	3.10194i	−0.168557	−	0.141436i
$482$	−21.9616	−	12.6796i	−1.00033	−	0.577538i
$483$	10.0198	−	5.78496i	0.455919	−	0.263225i
$484$	−0.212320	+	1.20413i	−0.00965091	+	0.0547330i
$485$	3.66335	−	29.2893i	0.166344	−	1.32996i
$486$	−16.4781	−	28.5409i	−0.747460	−	1.29464i
$487$	7.43843	+	4.29458i	0.337068	+	0.194606i	0.658975	−	0.752165i	$-0.270990\pi$
$487$	7.43843	+	4.29458i	0.337068	+	0.194606i	−0.321907	+	0.946771i	$0.604324\pi$
$488$	−5.28173	+	6.29452i	−0.239093	+	0.284939i
$489$	19.7072	+	7.17285i	0.891192	+	0.324367i
$490$	10.8543	−	4.57849i	0.490345	−	0.206835i
$491$	19.8407	−	16.6483i	0.895398	−	0.751328i	−0.0738874	−	0.997267i	$-0.523541\pi$
$491$	19.8407	−	16.6483i	0.895398	−	0.751328i	0.969285	+	0.245938i	$0.0790961\pi$
$492$	3.28077	−	0.578488i	0.147908	−	0.0260802i
$493$			2.14910i			0.0967908i
$494$	1.98211	−	11.3312i	0.0891794	−	0.509817i
$495$	1.48362	+	29.5858i	0.0666836	+	1.32979i
$496$	2.09435	+	11.8777i	0.0940391	+	0.533322i
$497$	−26.9328	−	32.0972i	−1.20810	−	1.43976i
$498$	0.694698	+	1.90867i	0.0311302	+	0.0855294i
$499$	−19.9251	−	7.25214i	−0.891970	−	0.324650i	−0.144939	−	0.989441i	$-0.546299\pi$
$499$	−19.9251	−	7.25214i	−0.891970	−	0.324650i	−0.747030	+	0.664790i	$0.768521\pi$
$500$	−1.09438	+	1.79375i	−0.0489424	+	0.0802191i
$501$	24.7094	−	42.7980i	1.10394	−	1.91207i
$502$	−12.4204	+	7.17090i	−0.554348	+	0.320053i
$503$	25.1285	+	4.43084i	1.12043	+	0.197561i	0.703028	−	0.711162i	$-0.251831\pi$
$503$	25.1285	+	4.43084i	1.12043	+	0.197561i	0.417398	+	0.908724i	$0.362942\pi$
$504$	4.78940	−	27.1620i	0.213337	−	1.20989i
$505$	32.4449	−	20.9660i	1.44378	−	0.932976i
$506$	−4.43639	+	7.68405i	−0.197221	+	0.341597i
$507$	15.6694	−	18.6741i	0.695904	−	0.829346i
$508$	−0.0380543	+	0.104553i	−0.00168839	+	0.00463880i
$509$	−16.0130	+	5.82825i	−0.709763	+	0.258333i	−0.671574	−	0.740938i	$-0.734381\pi$
$509$	−16.0130	+	5.82825i	−0.709763	+	0.258333i	−0.0381894	+	0.999271i	$0.512159\pi$
$510$	38.1165	−	35.3838i	1.68783	−	1.56682i
$511$	1.02837	+	5.83218i	0.0454924	+	0.258000i
$512$			18.6685i			0.825039i
$513$	1.15525	−	1.38059i	0.0510056	−	0.0609543i
$514$	−14.8666			−0.655738
$515$	6.88789	+	30.1448i	0.303517	+	1.32834i
$516$	3.53729	−	2.96814i	0.155721	−	0.130665i
$517$	−0.637430	−	1.75133i	−0.0280342	−	0.0770232i
$518$	4.44708	−	12.2183i	0.195393	−	0.536839i
$519$	−22.2963	−	18.7088i	−0.978700	−	0.821227i
$520$	9.51663	+	4.87603i	0.417332	+	0.213828i
$521$	−10.8909	−	18.8635i	−0.477137	−	0.826426i	0.522520	−	0.852627i	$-0.324992\pi$
$521$	−10.8909	−	18.8635i	−0.477137	−	0.826426i	−0.999657	+	0.0262016i	$0.991659\pi$
$522$	1.56539	+	0.276020i	0.0685152	+	0.0120811i
$523$	−17.2199	−	3.03633i	−0.752973	−	0.132769i	−0.216028	−	0.976387i	$-0.569310\pi$
$523$	−17.2199	−	3.03633i	−0.752973	−	0.132769i	−0.536944	+	0.843618i	$0.680422\pi$
$524$	−1.93100	−	3.34460i	−0.0843563	−	0.146109i
$525$	−16.5782	+	36.7877i	−0.723531	+	1.60554i
$526$	24.7364	+	20.7563i	1.07856	+	0.905018i
$527$	−6.01788	+	16.5340i	−0.262143	+	0.720232i
$528$	15.4241	+	42.3775i	0.671249	+	1.84424i
$529$	16.0445	−	13.4629i	0.697586	−	0.585344i
$530$	−23.3362	+	5.33218i	−1.01366	+	0.231615i
$531$	9.95056			0.431817
$532$	2.62127	−	0.465879i	0.113647	−	0.0201984i
$533$			12.7355i			0.551637i
$534$	4.35551	+	24.7013i	0.188481	+	1.06893i
$535$	5.34999	−	4.96644i	0.231300	−	0.214718i
$536$	−21.5413	+	7.84038i	−0.930441	+	0.338653i
$537$	6.01630	−	16.5297i	0.259623	−	0.713307i
$538$	−14.6945	+	17.5123i	−0.633527	+	0.755008i
$539$	−7.45104	+	12.9056i	−0.320939	+	0.555883i
$540$	−0.0941978	−	0.145771i	−0.00405363	−	0.00627297i
$541$	2.57157	−	14.5841i	0.110560	−	0.627018i	−0.878293	−	0.478123i	$-0.841317\pi$
$541$	2.57157	−	14.5841i	0.110560	−	0.627018i	0.988853	−	0.148895i	$-0.0475717\pi$
$542$	−7.52121	−	1.32619i	−0.323064	−	0.0569648i
$543$	−19.9606	+	11.5243i	−0.856592	+	0.494554i
$544$	3.35527	−	5.81150i	0.143856	−	0.249166i
$545$	−4.34738	+	5.74217i	−0.186221	+	0.245968i
$546$	−20.0129	−	7.28411i	−0.856474	−	0.311731i
$547$	−9.08867	−	24.9709i	−0.388603	−	1.06768i	−0.967631	−	0.252371i	$-0.918790\pi$
$547$	−9.08867	−	24.9709i	−0.388603	−	1.06768i	0.579027	−	0.815308i	$-0.303433\pi$
$548$	−1.05754	−	1.26033i	−0.0451761	−	0.0538388i
$549$	1.68555	+	9.55924i	0.0719376	+	0.407979i
$550$	−3.09568	−	30.7889i	−0.132000	−	1.31284i
$551$	−0.258871	−	1.45654i	−0.0110283	−	0.0620507i
$552$			9.54231i			0.406148i
$553$	−2.23619	+	0.394301i	−0.0950926	+	0.0167674i
$554$	−6.31176	+	5.29619i	−0.268161	+	0.225014i
$555$	5.83713	+	13.8381i	0.247772	+	0.587395i
$556$	−1.35800	−	0.494271i	−0.0575919	−	0.0209618i
$557$	−10.3330	+	12.3143i	−0.437821	+	0.521775i	−0.939162	−	0.343475i	$-0.888396\pi$
$557$	−10.3330	+	12.3143i	−0.437821	+	0.521775i	0.501340	+	0.865250i	$0.332840\pi$
$558$	11.2703	+	6.50691i	0.477110	+	0.275460i
$559$	8.82633	+	15.2877i	0.373314	+	0.646599i
$560$	−3.91469	+	31.2987i	−0.165426	+	1.32261i
$561$	−11.4244	+	64.7908i	−0.482337	+	2.73547i
$562$	−34.9365	+	20.1706i	−1.47371	+	0.850847i
$563$	1.75929	+	1.01573i	0.0741452	+	0.0428078i	0.536614	−	0.843828i	$-0.319703\pi$
$563$	1.75929	+	1.01573i	0.0741452	+	0.0428078i	−0.462469	+	0.886635i	$0.653036\pi$
$564$	0.159250	+	0.133626i	0.00670562	+	0.00562669i
$565$	−10.0649	−	3.10198i	−0.423432	−	0.130501i
$566$	20.9131	−	7.61175i	0.879044	−	0.319946i
$567$	17.7008	+	21.0950i	0.743362	+	0.885905i
$568$	34.0321	−	6.00077i	1.42795	−	0.251787i
$569$	12.8224			0.537543			0.268772	−	0.963204i	$-0.413382\pi$
$569$	12.8224			0.537543			0.268772	+	0.963204i	$0.413382\pi$
$570$	−21.5710	+	28.5725i	−0.903511	+	1.19677i
$571$	12.9168			0.540551			0.270276	−	0.962783i	$-0.412885\pi$
$571$	12.9168			0.540551			0.270276	+	0.962783i	$0.412885\pi$
$572$	1.38163	−	0.243618i	0.0577688	−	0.0101862i
$573$	−12.9677	−	15.4543i	−0.541735	−	0.645614i
$574$	−32.2448	+	11.7362i	−1.34587	+	0.489858i
$575$	1.76555	−	6.94755i	0.0736285	−	0.289733i
$576$	17.2543	+	14.4780i	0.718928	+	0.603252i
$577$	−7.02658	−	4.05680i	−0.292520	−	0.168887i	0.346558	−	0.938029i	$-0.387351\pi$
$577$	−7.02658	−	4.05680i	−0.292520	−	0.168887i	−0.639078	+	0.769142i	$0.720684\pi$
$578$	29.5878	−	17.0825i	1.23069	−	0.710540i
$579$	−3.33037	+	18.8875i	−0.138406	+	0.784937i
$580$	−0.141526	−	0.0177013i	−0.00587653	−	0.000735007i
$581$	−0.898567	−	1.55636i	−0.0372788	−	0.0645689i
$582$	−41.9909	−	24.2435i	−1.74058	−	1.00492i
$583$	19.4642	−	23.1966i	0.806126	−	0.960703i
$584$	−4.58975	−	1.67053i	−0.189925	−	0.0691271i
$585$	11.6388	−	4.90941i	0.481204	−	0.202979i
$586$	−8.87090	+	7.44357i	−0.366454	+	0.307491i
$587$	32.0670	−	5.65427i	1.32355	−	0.233377i	0.533174	−	0.846005i	$-0.320999\pi$
$587$	32.0670	−	5.65427i	1.32355	−	0.233377i	0.790371	+	0.612629i	$0.209888\pi$
$588$		−	1.66223i		−	0.0685492i
$589$	2.08697	−	11.9307i	0.0859921	−	0.491595i
$590$	−10.3813	+	0.520581i	−0.427391	+	0.0214320i
$591$	1.53837	+	8.72455i	0.0632802	+	0.358880i
$592$	7.54661	+	8.99370i	0.310164	+	0.369639i
$593$	−3.92476	−	10.7832i	−0.161171	−	0.442812i	0.832652	−	0.553797i	$-0.186822\pi$
$593$	−3.92476	−	10.7832i	−0.161171	−	0.442812i	−0.993822	+	0.110985i	$0.964599\pi$
$594$	2.40177	+	0.874173i	0.0985459	+	0.0358678i
$595$	−27.7760	+	36.6876i	−1.13871	+	1.50404i
$596$	1.40405	−	2.43188i	0.0575120	−	0.0996138i
$597$	−18.8587	+	10.8881i	−0.771836	+	0.445620i
$598$	3.72604	+	0.657002i	0.152369	+	0.0268668i
$599$	−5.76684	+	32.7054i	−0.235627	+	1.33631i	0.605663	+	0.795721i	$0.292908\pi$
$599$	−5.76684	+	32.7054i	−0.235627	+	1.33631i	−0.841290	+	0.540584i	$0.818203\pi$
$600$	−19.4394	−	27.0114i	−0.793609	−	1.10274i
$601$	−13.6590	+	23.6581i	−0.557163	+	0.965034i	0.440569	+	0.897719i	$0.354777\pi$
$601$	−13.6590	+	23.6581i	−0.557163	+	0.965034i	−0.997732	+	0.0673154i	$0.978557\pi$
$602$	−30.5728	+	36.4352i	−1.24605	+	1.48499i
$603$	−9.26191	+	25.4469i	−0.377174	+	1.03628i
$604$	2.32104	−	0.844789i	0.0944417	−	0.0343740i
$605$	9.89725	+	10.6616i	0.402380	+	0.433456i
$606$	−11.0188	−	62.4909i	−0.447609	−	2.53852i
$607$			25.7405i			1.04478i	0.852708	+	0.522388i	$0.174959\pi$
$607$			25.7405i			1.04478i	−0.852708	+	0.522388i	$0.825041\pi$
$608$	−1.57399	+	4.34286i	−0.0638335	+	0.176126i
$609$	−2.73892			−0.110986
$610$	−2.25862	−	9.88485i	−0.0914490	−	0.400226i
$611$	−0.608796	+	0.510841i	−0.0246293	+	0.0206664i
$612$	−1.28880	−	3.54095i	−0.0520967	−	0.143134i
$613$	−13.8873	+	38.1551i	−0.560904	+	1.54107i	0.257411	+	0.966302i	$0.417131\pi$
$613$	−13.8873	+	38.1551i	−0.560904	+	1.54107i	−0.818315	+	0.574770i	$0.805092\pi$
$614$	17.8063	+	14.9413i	0.718606	+	0.602982i
$615$	18.0739	−	35.2750i	0.728809	−	1.42243i
$616$	−18.2229	−	31.5630i	−0.734222	−	1.27171i
$617$	13.9954	+	2.46776i	0.563433	+	0.0993485i	0.448108	−	0.893979i	$-0.352098\pi$
$617$	13.9954	+	2.46776i	0.563433	+	0.0993485i	0.115325	+	0.993328i	$0.463209\pi$
$618$	50.0219	+	8.82021i	2.01218	+	0.354801i
$619$	−14.7818	−	25.6028i	−0.594129	−	1.02906i	−0.993669	−	0.112346i	$-0.964164\pi$
$619$	−14.7818	−	25.6028i	−0.594129	−	1.02906i	0.399540	−	0.916716i	$-0.369170\pi$
$620$	−1.03925	−	0.532481i	−0.0417373	−	0.0213850i
$621$	0.453568	+	0.380589i	0.0182010	+	0.0152725i
$622$	−9.09680	+	24.9932i	−0.364748	+	1.00214i
$623$	−7.59026	−	20.8541i	−0.304097	−	0.835500i
$624$	14.7313	−	12.3610i	0.589723	−	0.494836i
$625$	9.15564	+	23.2632i	0.366226	+	0.930526i
$626$	31.3591			1.25336
$627$	−0.0616150	−	45.2877i	−0.00246067	−	1.80861i
$628$		−	2.03675i		−	0.0812753i
$629$	2.97418	+	16.8674i	0.118588	+	0.672548i
$630$	23.1555	+	24.9438i	0.922536	+	0.993784i
$631$	1.60465	−	0.584045i	0.0638801	−	0.0232505i	−0.309882	−	0.950775i	$-0.600290\pi$
$631$	1.60465	−	0.584045i	0.0638801	−	0.0232505i	0.373763	+	0.927524i	$0.378067\pi$
$632$	0.640520	−	1.75981i	0.0254785	−	0.0700017i
$633$	18.8622	−	22.4791i	0.749706	−	0.893465i
$634$	2.26640	−	3.92552i	0.0900102	−	0.155902i
$635$	0.718475	+	1.11184i	0.0285118	+	0.0441219i
$636$	−0.586521	+	3.32633i	−0.0232571	+	0.131897i
$637$	6.25800	+	1.10345i	0.247951	+	0.0437204i
$638$	1.81902	−	1.05021i	0.0720158	−	0.0415783i
$639$	20.4113	−	35.3534i	0.807459	−	1.39856i
$640$	−22.5371	−	17.0628i	−0.890858	−	0.674465i
$641$	−2.59543	−	0.944659i	−0.102513	−	0.0373118i	0.290254	−	0.956950i	$-0.406260\pi$
$641$	−2.59543	−	0.944659i	−0.102513	−	0.0373118i	−0.392768	+	0.919638i	$0.628482\pi$
$642$	−4.10121	−	11.2680i	−0.161862	−	0.444711i
$643$	−13.9466	−	16.6209i	−0.550000	−	0.655465i	0.417398	−	0.908724i	$-0.362942\pi$
$643$	−13.9466	−	16.6209i	−0.550000	−	0.655465i	−0.967398	+	0.253259i	$0.918497\pi$
$644$	0.152058	+	0.862364i	0.00599193	+	0.0339819i
$645$	−2.75152	−	54.8700i	−0.108341	−	2.16050i
$646$	−31.2400	+	26.2860i	−1.22912	+	1.03421i
$647$		−	28.0268i		−	1.10185i	−0.834556	−	0.550923i	$-0.814276\pi$
$647$		−	28.0268i		−	1.10185i	0.834556	−	0.550923i	$-0.185724\pi$
$648$	−22.3666	+	3.94383i	−0.878642	+	0.154928i
$649$	10.0725	−	8.45185i	0.395381	−	0.331764i
$650$	−11.8857	+	5.73082i	−0.466196	+	0.224781i
$651$	−21.0717	−	7.66946i	−0.825864	−	0.300590i
$652$	−1.02027	+	1.21591i	−0.0399570	+	0.0476189i
$653$	6.57580	+	3.79654i	0.257331	+	0.148570i	0.623116	−	0.782129i	$-0.285866\pi$
$653$	6.57580	+	3.79654i	0.257331	+	0.148570i	−0.365785	+	0.930699i	$0.619200\pi$
$654$	5.91538	+	10.2457i	0.231310	+	0.400640i
$655$	−45.5938	−	5.70264i	−1.78150	−	0.222821i
$656$	5.38029	−	30.5131i	0.210065	−	1.19134i
$657$	−4.99686	+	2.88494i	−0.194946	+	0.112552i
$658$	−1.85441	−	1.07064i	−0.0722924	−	0.0417380i
$659$	−5.50322	−	4.61775i	−0.214375	−	0.179882i	0.529277	−	0.848449i	$-0.322463\pi$
$659$	−5.50322	−	4.61775i	−0.214375	−	0.179882i	−0.743652	+	0.668567i	$0.766908\pi$
$660$	−4.17259	−	1.28599i	−0.162418	−	0.0500570i
$661$	27.1268	−	9.87335i	1.05511	−	0.384029i	0.244521	−	0.969644i	$-0.421369\pi$
$661$	27.1268	−	9.87335i	1.05511	−	0.384029i	0.810589	+	0.585615i	$0.199147\pi$
$662$	24.6739	+	29.4052i	0.958978	+	1.14287i
$663$	27.6281	−	4.87157i	1.07298	−	0.189196i
$664$	1.48219			0.0575201
$665$	14.4058	−	28.2105i	0.558633	−	1.09396i
$666$	12.6681			0.490877
$667$	0.479183	−	0.0844929i	0.0185540	−	0.00327158i
$668$	2.40419	+	2.86521i	0.0930210	+	0.110858i
$669$	20.7621	−	7.55679i	0.802710	−	0.292162i
$670$	8.33153	−	27.0330i	0.321875	−	1.04437i
$671$	9.82569	+	8.24473i	0.379316	+	0.318284i
$672$	7.40644	+	4.27611i	0.285709	+	0.164954i
$673$	20.1949	−	11.6595i	0.778457	−	0.449442i	−0.0574263	−	0.998350i	$-0.518289\pi$
$673$	20.1949	−	11.6595i	0.778457	−	0.449442i	0.835883	+	0.548907i	$0.184956\pi$
$674$	−2.58331	+	14.6507i	−0.0995054	+	0.564323i
$675$	−2.05924	−	0.153334i	−0.0792601	−	0.00590185i
$676$	0.922496	+	1.59781i	0.0354806	+	0.0614542i
$677$	−15.1640	−	8.75493i	−0.582799	−	0.336479i	0.179446	−	0.983768i	$-0.442570\pi$
$677$	−15.1640	−	8.75493i	−0.582799	−	0.336479i	−0.762245	+	0.647289i	$0.775903\pi$
$678$	−11.1205	+	13.2529i	−0.427081	+	0.508975i
$679$	40.3132	+	14.6728i	1.54708	+	0.563090i
$680$	−14.7502	−	34.9683i	−0.565643	−	1.34097i
$681$	−50.2345	+	42.1518i	−1.92499	+	1.61526i
$682$	16.9353	−	2.98615i	0.648487	−	0.114346i
$683$			22.0114i			0.842243i	0.907004	+	0.421122i	$0.138363\pi$
$683$			22.0114i			0.842243i	−0.907004	+	0.421122i	$0.861637\pi$
$684$	1.30000	+	2.24461i	0.0497068	+	0.0858249i
$685$	−19.5501	+	0.980363i	−0.746971	+	0.0374577i
$686$	−2.87012	−	16.2772i	−0.109582	−	0.621468i
$687$	34.7730	+	41.4409i	1.32667	+	1.58107i
$688$	−14.6886	−	40.3566i	−0.559997	−	1.53858i
$689$	−12.1337	−	4.41629i	−0.462256	−	0.168247i
$690$	−9.38804	−	7.10766i	−0.357397	−	0.270584i
$691$	1.32811	−	2.30036i	0.0505238	−	0.0875098i	−0.839657	−	0.543116i	$-0.817244\pi$
$691$	1.32811	−	2.30036i	0.0505238	−	0.0875098i	0.890181	+	0.455607i	$0.150578\pi$
$692$	1.90774	−	1.10143i	0.0725214	−	0.0418702i
$693$	−42.3997	−	7.47621i	−1.61063	−	0.283998i
$694$	−1.75124	+	9.93178i	−0.0664762	+	0.377005i
$695$	−14.4412	+	9.33197i	−0.547785	+	0.353982i
$696$	1.12946	−	1.95629i	0.0428122	−	0.0741529i
$697$	29.0546	−	34.6260i	1.10052	−	1.31155i
$698$	15.9849	−	43.9181i	0.605037	−	1.66232i
$699$	23.3367	−	8.49385i	0.882674	−	0.321267i
$700$	−2.18722	−	2.13132i	−0.0826690	−	0.0805565i
$701$	−1.27931	−	7.25535i	−0.0483190	−	0.274031i	0.951070	−	0.308975i	$-0.0999859\pi$
$701$	−1.27931	−	7.25535i	−0.0483190	−	0.274031i	−0.999389	+	0.0349439i	$0.988875\pi$
$702$		−	1.08989i		−	0.0411352i
$703$	−4.04750	−	11.0735i	−0.152654	−	0.417646i
$704$	29.7632			1.12174
$705$	2.41122	−	0.550948i	0.0908119	−	0.0207499i
$706$	−7.14603	+	5.99623i	−0.268944	+	0.225671i
$707$	19.2023	+	52.7579i	0.722177	+	1.98416i
$708$	−0.501626	+	1.37821i	−0.0188522	+	0.0517961i
$709$	4.58997	+	3.85144i	0.172380	+	0.144644i	0.724896	−	0.688858i	$-0.241888\pi$
$709$	4.58997	+	3.85144i	0.172380	+	0.144644i	−0.552516	+	0.833502i	$0.686332\pi$
$710$	−19.4453	+	37.9516i	−0.729768	+	1.42430i
$711$	−1.10615	−	1.91591i	−0.0414839	−	0.0718523i
$712$	18.0252	+	3.17833i	0.675522	+	0.119113i
$713$	3.92316	+	0.691759i	0.146923	+	0.0259066i
$714$	37.7943	+	65.4616i	1.41441	+	2.44984i
$715$	7.61145	−	14.8554i	0.284652	−	0.555559i
$716$	1.01986	+	0.855765i	0.0381140	+	0.0319814i
$717$	15.1486	−	41.6205i	0.565736	−	1.55435i
$718$	−2.11300	−	5.80541i	−0.0788563	−	0.216656i
$719$	−10.4040	+	8.73002i	−0.388005	+	0.325575i	−0.815835	−	0.578284i	$-0.803722\pi$
$719$	−10.4040	+	8.73002i	−0.388005	+	0.325575i	0.427831	+	0.903859i	$0.359278\pi$
$720$	−29.9594	+	6.84553i	−1.11652	+	0.255118i
$721$	−44.9412			−1.67370
$722$	18.0064	−	21.5782i	0.670128	−	0.803056i
$723$			42.5725i			1.58329i
$724$	−0.302916	−	1.71792i	−0.0112578	−	0.0638461i
$725$	−1.18430	+	1.21535i	−0.0439836	+	0.0451371i
$726$	22.4551	−	8.17299i	0.833387	−	0.303328i
$727$	−14.1065	+	38.7574i	−0.523183	+	1.43743i	0.343776	+	0.939052i	$0.388294\pi$
$727$	−14.1065	+	38.7574i	−0.523183	+	1.43743i	−0.866958	+	0.498381i	$0.833928\pi$
$728$	−9.98969	+	11.9052i	−0.370242	+	0.441238i
$729$	−14.9530	+	25.8994i	−0.553816	+	0.959237i
$730$	5.06223	−	3.27124i	0.187361	−	0.121074i
$731$	10.8796	−	61.7011i	0.402395	−	2.28210i
$732$	−1.40898	−	0.248441i	−0.0520773	−	0.00918264i
$733$	0.107256	−	0.0619240i	0.00396158	−	0.00228722i	−0.498018	−	0.867167i	$-0.665939\pi$
$733$	0.107256	−	0.0619240i	0.00396158	−	0.00228722i	0.501979	+	0.864880i	$0.332605\pi$
$734$	−12.2556	+	21.2274i	−0.452364	+	0.783517i
$735$	−15.7675	−	11.9375i	−0.581593	−	0.440322i
$736$	−1.42770	−	0.519639i	−0.0526256	−	0.0191541i
$737$	12.2388	+	33.6257i	0.450821	+	1.23862i
$738$	−21.4896	−	25.6103i	−0.791043	−	0.942729i
$739$	6.34049	+	35.9587i	0.233239	+	1.32276i	0.846291	+	0.532720i	$0.178830\pi$
$739$	6.34049	+	35.9587i	0.233239	+	1.32276i	−0.613053	+	0.790042i	$0.710059\pi$
$740$	−1.13527	+	0.0569295i	−0.0417334	+	0.00209277i
$741$	−18.1379	+	6.62962i	−0.666313	+	0.243545i
$742$		−	34.7907i		−	1.27721i
$743$	8.92430	−	1.57359i	0.327401	−	0.0577296i	−0.00753195	−	0.999972i	$-0.502398\pi$
$743$	8.92430	−	1.57359i	0.327401	−	0.0577296i	0.334933	+	0.942242i	$0.391286\pi$
$744$	14.1674	−	11.8879i	0.519402	−	0.435830i
$745$	−12.9849	−	30.7833i	−0.475729	−	1.12781i
$746$	51.4293	+	18.7187i	1.88296	+	0.685341i
$747$	1.12547	−	1.34129i	0.0411789	−	0.0490751i
$748$	−4.31223	−	2.48967i	−0.157671	−	0.0910312i
$749$	5.30476	+	9.18812i	0.193832	+	0.335727i
$750$	41.0543	+	0.994544i	1.49909	+	0.0363156i
$751$	−0.709544	+	4.02402i	−0.0258916	+	0.146839i	−0.995013	−	0.0997456i	$-0.968197\pi$
$751$	−0.709544	+	4.02402i	−0.0258916	+	0.146839i	0.969121	+	0.246584i	$0.0793082\pi$
$752$	1.67443	−	0.966732i	0.0610602	−	0.0352531i
$753$	20.8511	+	12.0384i	0.759857	+	0.438704i
$754$	−0.686117	−	0.575721i	−0.0249869	−	0.0209665i
$755$	8.65539	−	28.0838i	0.315002	−	1.02207i
$756$	0.237035	−	0.0862735i	0.00862086	−	0.00313774i
$757$	−22.1503	−	26.3977i	−0.805066	−	0.959441i	0.194704	−	0.980862i	$-0.437625\pi$
$757$	−22.1503	−	26.3977i	−0.805066	−	0.959441i	−0.999771	+	0.0214214i	$0.993181\pi$
$758$	−45.9073	+	8.09470i	−1.66743	+	0.294013i
$759$	14.8955			0.540671
$760$	14.2089	+	21.9228i	0.515412	+	0.795223i
$761$	20.5813			0.746072			0.373036	−	0.927817i	$-0.378317\pi$
$761$	20.5813			0.746072			0.373036	+	0.927817i	$0.378317\pi$
$762$	2.14147	−	0.377599i	0.0775773	−	0.0136790i
$763$	−6.72848	−	8.01868i	−0.243587	−	0.290296i
$764$	1.43480	−	0.522224i	0.0519092	−	0.0188934i
$765$	−42.8443	−	13.2046i	−1.54904	−	0.477412i
$766$	−3.51052	−	2.94568i	−0.126840	−	0.106432i
$767$	−4.85570	−	2.80344i	−0.175329	−	0.101226i
$768$	−9.61713	+	5.55245i	−0.347028	+	0.200357i
$769$	5.27109	−	29.8939i	0.190081	−	1.07800i	−0.729172	−	0.684331i	$-0.760094\pi$
$769$	5.27109	−	29.8939i	0.190081	−	1.07800i	0.919252	−	0.393669i	$-0.128794\pi$
$770$	44.6262	+	5.58161i	1.60822	+	0.201147i
$771$	12.4789	+	21.6141i	0.449417	+	0.778413i
$772$	−1.25708	−	0.725774i	−0.0452432	−	0.0261212i
$773$	12.5488	−	14.9551i	0.451350	−	0.537898i	−0.491605	−	0.870818i	$-0.663590\pi$
$773$	12.5488	−	14.9551i	0.451350	−	0.537898i	0.942955	+	0.332921i	$0.108034\pi$
$774$	−43.5452	−	15.8491i	−1.56520	−	0.569686i
$775$	−12.5145	+	6.03400i	−0.449534	+	0.216748i
$776$	−27.1043	+	22.7432i	−0.972988	+	0.816434i
$777$	−21.4966	+	3.79043i	−0.771186	+	0.135981i
$778$			38.5054i			1.38048i
$779$	−15.5207	+	26.9673i	−0.556087	+	0.966204i
$780$	0.0932479	+	1.85952i	0.00333881	+	0.0665816i
$781$	−9.36716	−	53.1238i	−0.335183	−	1.90092i
$782$	−8.63167	−	10.2868i	−0.308668	−	0.367856i
$783$	−0.0479389	−	0.131711i	−0.00171320	−	0.00470697i
$784$	−14.5274	−	5.28754i	−0.518836	−	0.188841i
$785$	−19.3201	−	14.6272i	−0.689566	−	0.522068i
$786$	−37.7392	+	65.3661i	−1.34611	+	2.33153i
$787$	−30.5046	+	17.6118i	−1.08737	+	0.627793i	−0.932875	−	0.360200i	$-0.882708\pi$
$787$	−30.5046	+	17.6118i	−1.08737	+	0.627793i	−0.154495	+	0.987994i	$0.549375\pi$
$788$	−0.660316	−	0.116432i	−0.0235228	−	0.00414770i
$789$	9.41343	−	53.3862i	0.335127	−	1.90060i
$790$	1.25427	+	1.94097i	0.0446248	+	0.0690568i
$791$	7.65357	−	13.2564i	0.272129	−	0.471342i
$792$	22.8245	−	27.2012i	0.811035	−	0.966554i
$793$	1.87067	−	5.13963i	0.0664295	−	0.182514i
$794$	17.5979	−	6.40513i	0.624528	−	0.227309i
$795$	27.3405	+	29.4520i	0.969669	+	1.04456i
$796$	−0.286194	−	1.62309i	−0.0101439	−	0.0575288i
$797$			28.7940i			1.01994i	0.860193	+	0.509969i	$0.170343\pi$
$797$			28.7940i			1.01994i	−0.860193	+	0.509969i	$0.829657\pi$
$798$	−33.5000	−	39.8136i	−1.18589	−	1.40939i
$799$	2.82065			0.0997874
$800$	5.09997	−	1.43753i	0.180311	−	0.0508242i
$801$	16.5633	−	13.8982i	0.585234	−	0.491070i
$802$	−4.66536	−	12.8180i	−0.164740	−	0.452618i
$803$	−2.60768	+	7.16455i	−0.0920232	+	0.252832i
$804$	−3.05762	−	2.56565i	−0.107834	−	0.0904834i
$805$	9.27220	+	4.75080i	0.326802	+	0.167444i
$806$	−3.66648	−	6.35052i	−0.129146	−	0.223688i
$807$	37.7951	+	6.66429i	1.33045	+	0.234594i
$808$	−45.6012	−	8.04072i	−1.60425	−	0.282872i
$809$	−24.0034	−	41.5751i	−0.843915	−	1.46170i	−0.886560	−	0.462613i	$-0.846912\pi$
$809$	−24.0034	−	41.5751i	−0.843915	−	1.46170i	0.0426458	−	0.999090i	$-0.486421\pi$
$810$	12.7798	−	24.9426i	0.449037	−	0.876392i
$811$	−7.37613	−	6.18931i	−0.259011	−	0.217336i	0.504030	−	0.863686i	$-0.331850\pi$
$811$	−7.37613	−	6.18931i	−0.259011	−	0.217336i	−0.763041	+	0.646350i	$0.776295\pi$
$812$	0.0708988	−	0.194793i	0.00248806	−	0.00683589i
$813$	4.38513	+	12.0481i	0.153793	+	0.422544i
$814$	12.8233	−	10.7601i	0.449458	−	0.377140i
$815$	4.20664	+	18.4103i	0.147352	+	0.644885i
$816$	−68.2523			−2.38931
$817$	0.0586768	+	43.1280i	0.00205284	+	1.50886i
$818$			50.9680i			1.78205i
$819$	3.18800	+	18.0800i	0.111398	+	0.631768i
$820$	2.04092	+	2.19854i	0.0712721	+	0.0767765i
$821$	24.1743	−	8.79872i	0.843688	−	0.307077i	0.116224	−	0.993223i	$-0.462921\pi$
$821$	24.1743	−	8.79872i	0.843688	−	0.307077i	0.727464	+	0.686146i	$0.240699\pi$
$822$	−10.9974	+	30.2152i	−0.383580	+	1.05388i
$823$	−8.65091	+	10.3098i	−0.301552	+	0.359376i	−0.895448	−	0.445166i	$-0.853145\pi$
$823$	−8.65091	+	10.3098i	−0.301552	+	0.359376i	0.593896	+	0.804542i	$0.297589\pi$
$824$	18.5327	−	32.0996i	0.645617	−	1.11824i
$825$	−42.1646	+	30.3447i	−1.46798	+	1.05647i
$826$	2.62330	−	14.8775i	0.0912764	−	0.517654i
$827$	0.169788	+	0.0299383i	0.00590412	+	0.00104106i	0.176599	−	0.984283i	$-0.443490\pi$
$827$	0.169788	+	0.0299383i	0.00590412	+	0.00104106i	−0.170695	+	0.985324i	$0.554601\pi$
$828$	−0.738851	+	0.426576i	−0.0256769	+	0.0148245i
$829$	−21.1895	+	36.7014i	−0.735943	+	1.27469i	0.218365	+	0.975867i	$0.429928\pi$
$829$	−21.1895	+	36.7014i	−0.735943	+	1.27469i	−0.954308	+	0.298824i	$0.903406\pi$
$830$	−1.10402	+	1.45823i	−0.0383211	+	0.0506158i
$831$	12.9980	+	4.73089i	0.450896	+	0.164113i
$832$	−4.34078	−	11.9262i	−0.150490	−	0.413467i
$833$	−14.4971	−	17.2770i	−0.502296	−	0.598614i
$834$	4.90447	+	27.8147i	0.169828	+	0.963143i
$835$	44.4447	−	2.22873i	1.53807	−	0.0771284i
$836$	3.22247	+	1.16792i	0.111452	+	0.0403934i
$837$		−	1.14755i		−	0.0396651i
$838$	11.4503	−	2.01900i	0.395545	−	0.0697452i
$839$	−34.5791	+	29.0153i	−1.19380	+	1.00172i	−0.194019	+	0.980998i	$0.562152\pi$
$839$	−34.5791	+	29.0153i	−1.19380	+	1.00172i	−0.999785	+	0.0207231i	$0.993403\pi$
$840$	44.5651	−	18.7983i	1.53764	−	0.648601i
$841$	27.1428	+	9.87919i	0.935960	+	0.340662i
$842$	9.97593	−	11.8888i	0.343793	−	0.409717i
$843$	58.6509	+	33.8621i	2.02005	+	1.16627i
$844$	1.11046	+	1.92338i	0.0382237	+	0.0662055i
$845$	21.7815	+	2.72431i	0.749305	+	0.0937193i
$846$	0.362270	−	2.05453i	0.0124551	−	0.0706363i
$847$	−18.3103	+	10.5715i	−0.629151	+	0.363240i
$848$	27.2054	+	15.7070i	0.934238	+	0.539382i
$849$	−28.6208	−	24.0157i	−0.982263	−	0.824217i
$850$	45.3897	+	11.5347i	1.55685	+	0.395636i
$851$	3.64397	−	1.32630i	0.124914	−	0.0454649i
$852$	3.86766	+	4.60930i	0.132504	+	0.157912i
$853$	−45.6364	+	8.04694i	−1.56256	+	0.275522i	−0.886996	−	0.461778i	$-0.847212\pi$
$853$	−45.6364	+	8.04694i	−1.56256	+	0.275522i	−0.675566	+	0.737299i	$0.736101\pi$
$854$	14.7368			0.504283
$855$	30.6280	+	3.78848i	1.04745	+	0.129563i
$856$	−8.75023			−0.299077
$857$	−21.5607	+	3.80174i	−0.736501	+	0.129865i	−0.529302	−	0.848434i	$-0.677546\pi$
$857$	−21.5607	+	3.80174i	−0.736501	+	0.129865i	−0.207199	+	0.978299i	$0.566435\pi$
$858$	−17.6245	−	21.0040i	−0.601690	−	0.717066i
$859$	31.3876	−	11.4242i	1.07093	−	0.389787i	0.254406	−	0.967097i	$-0.418120\pi$
$859$	31.3876	−	11.4242i	1.07093	−	0.389787i	0.816525	+	0.577310i	$0.195898\pi$
$860$	3.97361	+	1.22466i	0.135499	+	0.0417606i
$861$	44.1289	+	37.0285i	1.50391	+	1.26193i
$862$	38.2920	+	22.1079i	1.30423	+	0.752998i
$863$	23.4913	−	13.5627i	0.799653	−	0.461680i	−0.0436971	−	0.999045i	$-0.513914\pi$
$863$	23.4913	−	13.5627i	0.799653	−	0.461680i	0.843350	+	0.537365i	$0.180580\pi$
$864$	−0.0759988	+	0.431011i	−0.00258553	+	0.0146633i
$865$	3.25275	−	26.0064i	0.110597	−	0.884246i
$866$	−5.02900	−	8.71049i	−0.170892	−	0.295994i
$867$	−49.6716	−	28.6779i	−1.68694	−	0.973953i
$868$	1.09091	−	1.30010i	0.0370279	−	0.0441282i
$869$	−2.74705	−	0.999846i	−0.0931875	−	0.0339175i
$870$	1.08337	+	2.56836i	0.0367297	+	0.0870754i
$871$	11.6890	−	9.80822i	0.396066	−	0.332339i
$872$	8.50206	−	1.49914i	0.287916	−	0.0507674i
$873$			41.7973i			1.41462i
$874$	7.08916	+	5.93209i	0.239794	+	0.200656i
$875$	−35.9250	+	5.44102i	−1.21449	+	0.183940i
$876$	−0.147679	−	0.837527i	−0.00498960	−	0.0282974i
$877$	−31.5495	−	37.5992i	−1.06535	−	1.26963i	−0.961430	−	0.275049i	$-0.911306\pi$
$877$	−31.5495	−	37.5992i	−1.06535	−	1.26963i	−0.103920	−	0.994586i	$-0.533139\pi$
$878$	−4.03008	−	11.0725i	−0.136008	−	0.373680i
$879$	18.2682	+	6.64906i	0.616169	+	0.224267i
$880$	−24.5122	+	32.3765i	−0.826304	+	1.09141i
$881$	−18.9889	+	32.8898i	−0.639753	+	1.10808i	0.345734	+	0.938332i	$0.387630\pi$
$881$	−18.9889	+	32.8898i	−0.639753	+	1.10808i	−0.985487	+	0.169751i	$0.945704\pi$
$882$	−14.4464	+	8.34062i	−0.486435	+	0.280843i
$883$	−32.7055	−	5.76686i	−1.10063	−	0.194070i	−0.406307	−	0.913737i	$-0.633184\pi$
$883$	−32.7055	−	5.76686i	−1.10063	−	0.194070i	−0.694320	+	0.719666i	$0.744295\pi$
$884$	−0.368704	+	2.09103i	−0.0124009	+	0.0703288i
$885$	9.47083	+	14.6561i	0.318358	+	0.492658i
$886$	16.1150	−	27.9121i	0.541395	−	0.937724i
$887$	−16.8748	+	20.1106i	−0.566601	+	0.675248i	−0.970930	−	0.239365i	$-0.923061\pi$
$887$	−16.8748	+	20.1106i	−0.566601	+	0.675248i	0.404329	+	0.914614i	$0.367505\pi$
$888$	6.15734	−	16.9172i	0.206627	−	0.567703i
$889$	−1.80794	+	0.658035i	−0.0606362	+	0.0220698i
$890$	−16.5531	+	15.3664i	−0.554862	+	0.515082i
$891$	6.15629	+	34.9140i	0.206243	+	1.16966i
$892$			1.67222i			0.0559902i
$893$	−1.91167	+	0.339762i	−0.0639718	+	0.0113697i
$894$	−54.8808			−1.83549
$895$	15.4418	−	3.52836i	0.516164	−	0.117940i
$896$	31.4721	−	26.4082i	1.05141	−	0.882236i
$897$	−2.17242	−	5.96866i	−0.0725348	−	0.199288i
$898$	9.50278	−	26.1087i	0.317112	−	0.871258i
$899$	−0.722415	−	0.606178i	−0.0240939	−	0.0202172i
$900$	1.22245	−	2.71268i	0.0407485	−	0.0904225i
$901$	22.9143	+	39.6888i	0.763387	+	1.32223i
$902$	−43.5060	−	7.67129i	−1.44859	−	0.255426i
$903$	78.6346	+	13.8654i	2.61680	+	0.461412i
$904$	6.31229	+	10.9332i	0.209944	+	0.363633i
$905$	−18.4712	−	9.46411i	−0.614005	−	0.314598i
$906$	−36.9793	−	31.0294i	−1.22856	−	1.03088i
$907$	2.71140	−	7.44950i	0.0900305	−	0.247357i	−0.886503	−	0.462723i	$-0.846872\pi$
$907$	2.71140	−	7.44950i	0.0900305	−	0.247357i	0.976533	+	0.215366i	$0.0690946\pi$
$908$	−1.69750	−	4.66383i	−0.0563334	−	0.154775i
$909$	−41.9027	+	35.1606i	−1.38983	+	1.16620i
$910$	−4.27189	−	18.6959i	−0.141612	−	0.619763i
$911$	−0.619746			−0.0205331			−0.0102665	−	0.999947i	$-0.503268\pi$
$911$	−0.619746			−0.0205331			−0.0102665	+	0.999947i	$0.503268\pi$
$912$	46.2575	−	8.22135i	1.53174	−	0.272236i
$913$		−	2.31369i		−	0.0765718i
$914$	−7.25277	−	41.1325i	−0.239900	−	1.36054i
$915$	−12.4754	+	11.5810i	−0.412425	+	0.382856i
$916$	−3.84742	+	1.40035i	−0.127122	+	0.0462687i
$917$	22.8407	−	62.7544i	0.754268	−	2.07233i
$918$	−2.48646	+	2.96325i	−0.0820654	+	0.0978017i
$919$	−17.5287	+	30.3606i	−0.578219	+	1.00150i	0.417465	+	0.908693i	$0.362919\pi$
$919$	−17.5287	+	30.3606i	−0.578219	+	1.00150i	−0.995684	+	0.0928113i	$0.970415\pi$
$920$	−7.21692	+	4.66361i	−0.237935	+	0.153755i
$921$	6.77620	−	38.4297i	0.223283	−	1.26630i
$922$	0.285524	+	0.0503456i	0.00940324	+	0.00165804i
$923$	−19.9207	+	11.5012i	−0.655699	+	0.378568i
$924$	3.17294	−	5.49569i	0.104382	−	0.180795i
$925$	−7.61309	+	11.1778i	−0.250317	+	0.367523i
$926$	−19.4096	−	7.06452i	−0.637840	−	0.232155i
$927$	−14.9756	−	41.1451i	−0.491863	−	1.35138i
$928$	0.231188	+	0.275519i	0.00758912	+	0.00904437i
$929$	−2.09132	−	11.8605i	−0.0686140	−	0.389129i	−0.999704	−	0.0243392i	$-0.992252\pi$
$929$	−2.09132	−	11.8605i	−0.0686140	−	0.389129i	0.931090	−	0.364790i	$-0.118859\pi$
$930$	1.14299	+	22.7931i	0.0374800	+	0.747416i
$931$	11.9065	+	9.96313i	0.390218	+	0.326528i
$932$			1.87959i			0.0615679i
$933$	43.9727	−	7.75357i	1.43960	−	0.253841i
$934$	36.3756	−	30.5228i	1.19025	−	0.998735i
$935$	−54.5852	+	23.0249i	−1.78513	+	0.752994i
$936$	−14.2284	−	5.17873i	−0.465071	−	0.169272i
$937$	−9.59711	+	11.4374i	−0.313524	+	0.373643i	−0.899676	−	0.436558i	$-0.856198\pi$
$937$	−9.59711	+	11.4374i	−0.313524	+	0.373643i	0.586152	+	0.810201i	$0.300642\pi$
$938$	35.6049	+	20.5565i	1.16254	+	0.671194i
$939$	−26.3226	−	45.5921i	−0.859006	−	1.48784i
$940$	−0.0232325	+	0.185749i	−0.000757762	+	0.00605846i
$941$	3.37221	−	19.1248i	0.109931	−	0.623450i	−0.879205	−	0.476444i	$-0.841925\pi$
$941$	3.37221	−	19.1248i	0.109931	−	0.623450i	0.989136	−	0.147006i	$-0.0469635\pi$
$942$	−34.4729	+	19.9029i	−1.12319	+	0.648473i
$943$	−8.86280	−	5.11694i	−0.288612	−	0.166630i
$944$	10.4494	+	8.76813i	0.340101	+	0.285378i
$945$	0.883926	−	2.86804i	0.0287541	−	0.0932972i
$946$	−57.5409	+	20.9432i	−1.87082	+	0.680922i
$947$	10.7583	+	12.8212i	0.349598	+	0.416634i	0.911975	−	0.410247i	$-0.134557\pi$
$947$	10.7583	+	12.8212i	0.349598	+	0.416634i	−0.562377	+	0.826881i	$0.690113\pi$
$948$	0.321127	−	0.0566233i	0.0104297	−	0.00183904i
$949$	3.25117			0.105538
$950$	−32.1520	−	2.35011i	−1.04315	−	0.0762476i
$951$	−7.60959			−0.246758
$952$	54.3209	−	9.57824i	1.76055	−	0.310433i
$953$	34.1817	+	40.7361i	1.10725	+	1.31957i	0.942864	+	0.333177i	$0.108121\pi$
$953$	34.1817	+	40.7361i	1.10725	+	1.31957i	0.164389	+	0.986396i	$0.447435\pi$
$954$	31.8520	−	11.5932i	1.03125	−	0.375343i
$955$	5.35051	−	17.3606i	0.173138	−	0.561775i
$956$	2.56794	+	2.15475i	0.0830530	+	0.0696897i
$957$	−3.05375	−	1.76308i	−0.0987136	−	0.0569923i
$958$	−2.53927	+	1.46605i	−0.0820400	+	0.0473658i
$959$	4.94022	−	28.0174i	0.159528	−	0.904729i
$960$	−4.90214	+	39.1936i	−0.158216	+	1.26497i
$961$	11.6396	+	20.1603i	0.375470	+	0.650332i
$962$	−6.18179	−	3.56906i	−0.199309	−	0.115071i
$963$	−6.64432	+	7.91839i	−0.214110	+	0.255167i
$964$	−3.02778	−	1.10202i	−0.0975181	−	0.0354937i
$965$	−15.9124	+	6.71209i	−0.512238	+	0.216070i
$966$	13.1100	−	11.0006i	0.421807	−	0.353938i
$967$	−29.5719	+	5.21432i	−0.950967	+	0.167681i	−0.627551	−	0.778576i	$-0.715943\pi$
$967$	−29.5719	+	5.21432i	−0.950967	+	0.167681i	−0.323416	+	0.946257i	$0.604831\pi$
$968$		−	17.4377i		−	0.560469i
$969$	64.4390	+	23.3546i	2.07008	+	0.750259i
$970$	−2.18670	−	43.6065i	−0.0702107	−	1.40012i
$971$	4.19210	+	23.7746i	0.134531	+	0.762962i	0.975185	+	0.221390i	$0.0710595\pi$
$971$	4.19210	+	23.7746i	0.134531	+	0.762962i	−0.840654	+	0.541572i	$0.817829\pi$
$972$	−2.69158	−	3.20770i	−0.0863325	−	0.102887i
$973$	−8.54693	−	23.4825i	−0.274002	−	0.752814i
$974$	11.9386	+	4.34531i	0.382538	+	0.139233i
$975$	18.3087	+	12.4699i	0.586346	+	0.399356i
$976$	−6.65325	+	11.5238i	−0.212965	+	0.368867i
$977$	−8.29375	+	4.78840i	−0.265341	+	0.153195i	−0.626768	−	0.779206i	$-0.715623\pi$
$977$	−8.29375	+	4.78840i	−0.265341	+	0.153195i	0.361428	+	0.932400i	$0.382289\pi$
$978$	30.5499	+	5.38677i	0.976877	+	0.172250i
$979$	4.96134	−	28.1372i	0.158565	−	0.899267i
$980$	1.25716	−	0.812381i	0.0401584	−	0.0259506i
$981$	5.09925	−	8.83216i	0.162806	−	0.281989i
$982$	24.6257	−	29.3477i	0.785837	−	0.936524i
$983$	−10.6613	+	29.2916i	−0.340042	+	0.934257i	0.645340	+	0.763896i	$0.276716\pi$
$983$	−10.6613	+	29.2916i	−0.340042	+	0.934257i	−0.985382	+	0.170362i	$0.945506\pi$
$984$	−44.6455	+	16.2497i	−1.42325	+	0.518020i
$985$	−5.84659	+	5.42743i	−0.186288	+	0.172932i
$986$	0.552008	+	3.13060i	0.0175795	+	0.0996985i
$987$			3.59476i			0.114422i
$988$	−0.00198853	−	1.46159i	−6.32636e−5	−	0.0464994i
$989$	−14.1851			−0.451061
$990$	9.76045	+	42.7165i	0.310208	+	1.35762i
$991$	−37.2791	+	31.2808i	−1.18421	+	0.993669i	−0.184266	+	0.982876i	$0.558991\pi$
$991$	−37.2791	+	31.2808i	−1.18421	+	0.993669i	−0.999942	+	0.0107922i	$0.996565\pi$
$992$	1.00713	+	2.76706i	0.0319763	+	0.0878542i
$993$	22.0403	−	60.5551i	0.699426	−	1.92166i
$994$	−47.4772	−	39.8381i	−1.50589	−	1.26359i
$995$	−17.4516	−	8.94165i	−0.553252	−	0.283469i
$996$	0.129038	+	0.223501i	0.00408873	+	0.00708189i
$997$	31.4108	+	5.53857i	0.994790	+	0.175408i	0.647267	−	0.762263i	$-0.275912\pi$
$997$	31.4108	+	5.53857i	0.994790	+	0.175408i	0.347523	+	0.937672i	$0.387023\pi$
$998$	−30.8876	−	5.44631i	−0.977729	−	0.172400i
$999$	−0.558529	−	0.967401i	−0.0176711	−	0.0306072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.p.a.9.7	yes	48
3.2	odd	2		855.2.da.b.199.2		48
5.2	odd	4		475.2.l.f.351.7		48
5.3	odd	4		475.2.l.f.351.2		48
5.4	even	2	inner	95.2.p.a.9.2	✓	48
15.14	odd	2		855.2.da.b.199.7		48
19.6	even	9		1805.2.b.k.1084.7		24
19.13	odd	18		1805.2.b.l.1084.18		24
19.17	even	9	inner	95.2.p.a.74.2	yes	48
57.17	odd	18		855.2.da.b.739.7		48
95.13	even	36		9025.2.a.ct.1.18		24
95.17	odd	36		475.2.l.f.226.7		48
95.32	even	36		9025.2.a.ct.1.7		24
95.44	even	18		1805.2.b.k.1084.18		24
95.63	odd	36		9025.2.a.cu.1.7		24
95.74	even	18	inner	95.2.p.a.74.7	yes	48
95.82	odd	36		9025.2.a.cu.1.18		24
95.89	odd	18		1805.2.b.l.1084.7		24
95.93	odd	36		475.2.l.f.226.2		48
285.74	odd	18		855.2.da.b.739.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.2	✓	48	5.4	even	2	inner
95.2.p.a.9.7	yes	48	1.1	even	1	trivial
95.2.p.a.74.2	yes	48	19.17	even	9	inner
95.2.p.a.74.7	yes	48	95.74	even	18	inner
475.2.l.f.226.2		48	95.93	odd	36
475.2.l.f.226.7		48	95.17	odd	36
475.2.l.f.351.2		48	5.3	odd	4
475.2.l.f.351.7		48	5.2	odd	4
855.2.da.b.199.2		48	3.2	odd	2
855.2.da.b.199.7		48	15.14	odd	2
855.2.da.b.739.2		48	285.74	odd	18
855.2.da.b.739.7		48	57.17	odd	18
1805.2.b.k.1084.7		24	19.6	even	9
1805.2.b.k.1084.18		24	95.44	even	18
1805.2.b.l.1084.7		24	95.89	odd	18
1805.2.b.l.1084.18		24	19.13	odd	18
9025.2.a.ct.1.7		24	95.32	even	36
9025.2.a.ct.1.18		24	95.13	even	36
9025.2.a.cu.1.7		24	95.63	odd	36
9025.2.a.cu.1.18		24	95.82	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45670 - 0.256855i) q^{2} +(-1.59617 - 1.90225i) q^{3} +(0.176607 - 0.0642796i) q^{4} +(0.658585 - 2.13688i) q^{5} +(-2.81374 - 2.36101i) q^{6} +(2.81448 + 1.62494i) q^{7} +(-2.32124 + 1.34017i) q^{8} +(-0.549824 + 3.11821i) q^{9} +(0.410490 - 3.28195i) q^{10} +(2.09200 + 3.62344i) q^{11} +(-0.404171 - 0.233348i) q^{12} +(1.14682 - 1.36673i) q^{13} +(4.51721 + 1.64413i) q^{14} +(-5.11609 + 2.15805i) q^{15} +(-3.32506 + 2.79006i) q^{16} +(-6.23606 + 1.09959i) q^{17} +4.68351i q^{18} +(4.09399 - 1.49640i) q^{19} +(-0.0210474 - 0.419722i) q^{20} +(-1.40136 - 7.94751i) q^{21} +(3.97810 + 4.74092i) q^{22} +(0.490346 + 1.34721i) q^{23} +(6.25444 + 2.27643i) q^{24} +(-4.13253 - 2.81464i) q^{25} +(1.31952 - 2.28547i) q^{26} +(0.357658 - 0.206494i) q^{27} +(0.601506 + 0.106062i) q^{28} +(0.0589345 - 0.334234i) q^{29} +(-6.89829 + 4.45771i) q^{30} +(1.38932 - 2.40638i) q^{31} +(-0.681187 + 0.811808i) q^{32} +(3.55349 - 9.76313i) q^{33} +(-8.80161 + 3.20352i) q^{34} +(5.32587 - 4.94404i) q^{35} +(0.103335 + 0.586040i) q^{36} -2.70482i q^{37} +(5.57935 - 3.23137i) q^{38} -4.43037 q^{39} +(1.33505 + 5.84284i) q^{40} +(-5.46819 + 4.58835i) q^{41} +(-4.08271 - 11.2172i) q^{42} +(-3.38403 + 9.29755i) q^{43} +(0.602374 + 0.505452i) q^{44} +(6.30114 + 3.22852i) q^{45} +(1.06032 + 1.83654i) q^{46} +(-0.438674 - 0.0773501i) q^{47} +(10.6148 + 1.87167i) q^{48} +(1.78085 + 3.08452i) q^{49} +(-6.74280 - 3.03861i) q^{50} +(12.0455 + 10.1074i) q^{51} +(0.114683 - 0.315090i) q^{52} +(-2.47532 - 6.80087i) q^{53} +(0.467960 - 0.392665i) q^{54} +(9.12062 - 2.08400i) q^{55} -8.71078 q^{56} +(-9.38125 - 5.39926i) q^{57} -0.502015i q^{58} +(-0.545712 - 3.09489i) q^{59} +(-0.764818 + 0.709986i) q^{60} +(2.88074 - 1.04850i) q^{61} +(1.40573 - 3.86222i) q^{62} +(-6.61436 + 7.88269i) q^{63} +(3.55679 - 6.16055i) q^{64} +(-2.16526 - 3.35072i) q^{65} +(2.66865 - 15.1347i) q^{66} +(8.42261 + 1.48513i) q^{67} +(-1.03065 + 0.595046i) q^{68} +(1.78006 - 3.08315i) q^{69} +(6.48828 - 8.56995i) q^{70} +(-12.1153 - 4.40959i) q^{71} +(-2.90266 - 7.97498i) q^{72} +(1.17133 + 1.39594i) q^{73} +(-0.694747 - 3.94011i) q^{74} +(1.24211 + 12.3537i) q^{75} +(0.626839 - 0.527435i) q^{76} +13.5974i q^{77} +(-6.45371 + 1.13796i) q^{78} +(-0.535235 + 0.449116i) q^{79} +(3.77219 + 8.94276i) q^{80} +(7.96239 + 2.89807i) q^{81} +(-6.78695 + 8.08837i) q^{82} +(-0.478899 - 0.276493i) q^{83} +(-0.758353 - 1.31351i) q^{84} +(-1.75729 + 14.0499i) q^{85} +(-2.54139 + 14.4129i) q^{86} +(-0.729865 + 0.421388i) q^{87} +(-9.71206 - 5.60726i) q^{88} +(-5.23109 - 4.38940i) q^{89} +(10.0081 + 3.08449i) q^{90} +(5.44854 - 1.98311i) q^{91} +(0.173197 + 0.206408i) q^{92} +(-6.79513 + 1.19816i) q^{93} -0.658883 q^{94} +(-0.501395 - 9.73389i) q^{95} +2.63155 q^{96} +(13.0001 - 2.29226i) q^{97} +(3.38643 + 4.03579i) q^{98} +(-12.4489 + 4.53102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34}+ \cdots - 36 q^{99}+O(q^{100}) \) 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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