LMFDB - Embedded newform 116.2.l.b.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,2,Mod(3,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 5]))

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

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

chi := DirichletCharacter("116.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$116 = 2^{2} \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	116.l (of order $28$ , degree $12$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$12$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	116.11
Dual form			116.2.l.b.95.7

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.490339 - 1.32649i) q^{2} +(-2.34863 + 0.264627i) q^{3} +(-1.51913 + 1.30086i) q^{4} +(-0.588667 + 1.22238i) q^{5} +(1.50265 + 2.98566i) q^{6} +(2.56130 + 2.04257i) q^{7} +(2.47046 + 1.37725i) q^{8} +(2.52123 - 0.575454i) q^{9} +(1.91012 + 0.181478i) q^{10} +(-5.07822 + 3.19086i) q^{11} +(3.22364 - 3.45723i) q^{12} +(-1.29716 - 0.296069i) q^{13} +(1.45353 - 4.39908i) q^{14} +(1.05908 - 3.02669i) q^{15} +(0.615539 - 3.95236i) q^{16} +(-3.79071 + 3.79071i) q^{17} +(-1.99959 - 3.06221i) q^{18} +(0.151626 - 1.34572i) q^{19} +(-0.695878 - 2.62273i) q^{20} +(-6.55605 - 4.11944i) q^{21} +(6.72268 + 5.17159i) q^{22} +(1.29280 + 2.68452i) q^{23} +(-6.16665 - 2.58089i) q^{24} +(1.96977 + 2.47001i) q^{25} +(0.243319 + 1.86585i) q^{26} +(0.923422 - 0.323119i) q^{27} +(-6.54805 + 0.228950i) q^{28} +(2.93553 - 4.51472i) q^{29} +(-4.53417 + 0.0792436i) q^{30} +(-1.44988 - 4.14352i) q^{31} +(-5.54457 + 1.12149i) q^{32} +(11.0825 - 8.83796i) q^{33} +(6.88707 + 3.16960i) q^{34} +(-4.00455 + 1.92849i) q^{35} +(-3.08150 + 4.15395i) q^{36} +(-3.02614 + 4.81608i) q^{37} +(-1.85942 + 0.458728i) q^{38} +(3.12490 + 0.352092i) q^{39} +(-3.13780 + 2.20910i) q^{40} +(-4.55671 - 4.55671i) q^{41} +(-2.24969 + 10.7164i) q^{42} +(6.65934 + 2.33020i) q^{43} +(3.56365 - 11.4534i) q^{44} +(-0.780741 + 3.42065i) q^{45} +(2.92708 - 3.03121i) q^{46} +(-0.260350 - 0.414345i) q^{47} +(-0.399773 + 9.44549i) q^{48} +(0.830527 + 3.63878i) q^{49} +(2.31058 - 3.82401i) q^{50} +(7.89985 - 9.90609i) q^{51} +(2.35571 - 1.23766i) q^{52} +(5.75234 + 2.77018i) q^{53} +(-0.881404 - 1.06647i) q^{54} +(-0.911059 - 8.08587i) q^{55} +(3.51447 + 8.57364i) q^{56} +3.20071i q^{57} +(-7.42812 - 1.68019i) q^{58} -6.26790i q^{59} +(2.32840 + 5.97567i) q^{60} +(1.38184 + 12.2642i) q^{61} +(-4.78539 + 3.95498i) q^{62} +(7.63303 + 3.67588i) q^{63} +(4.20636 + 6.80489i) q^{64} +(1.12551 - 1.41134i) q^{65} +(-17.1576 - 10.3671i) q^{66} +(0.856051 + 3.75061i) q^{67} +(0.827426 - 10.6898i) q^{68} +(-3.74670 - 5.96283i) q^{69} +(4.52170 + 4.36637i) q^{70} +(-2.73458 + 11.9810i) q^{71} +(7.02115 + 2.05073i) q^{72} +(7.19276 + 2.51686i) q^{73} +(7.87230 + 1.65263i) q^{74} +(-5.27987 - 5.27987i) q^{75} +(1.52025 + 2.24157i) q^{76} +(-19.5244 - 2.19987i) q^{77} +(-1.06522 - 4.31779i) q^{78} +(2.90584 - 4.62461i) q^{79} +(4.46893 + 3.07904i) q^{80} +(-9.07317 + 4.36941i) q^{81} +(-3.81008 + 8.27875i) q^{82} +(-2.50734 + 1.99954i) q^{83} +(15.3183 - 2.27051i) q^{84} +(-2.40222 - 6.86516i) q^{85} +(-0.174352 - 9.97612i) q^{86} +(-5.69974 + 11.3802i) q^{87} +(-16.9402 + 0.888911i) q^{88} +(12.1053 - 4.23583i) q^{89} +(4.92028 - 0.641637i) q^{90} +(-2.71769 - 3.40787i) q^{91} +(-5.45612 - 2.39641i) q^{92} +(4.50171 + 9.34791i) q^{93} +(-0.421963 + 0.548521i) q^{94} +(1.55572 + 0.977524i) q^{95} +(12.7253 - 4.10120i) q^{96} +(0.141905 - 1.25944i) q^{97} +(4.41955 - 2.88592i) q^{98} +(-10.9672 + 10.9672i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$144 q - 12 q^{2} - 14 q^{4} - 28 q^{5} - 14 q^{6} - 12 q^{8} - 28 q^{9} - 8 q^{10} - 12 q^{12} - 28 q^{13} - 14 q^{14} + 2 q^{16} - 4 q^{17} + 14 q^{18} + 14 q^{20} - 28 q^{21} - 14 q^{22} - 22 q^{24} - 12 q^{25}+ \cdots - 110 q^{98}+O(q^{100})$ 144 * q - 12 * q^2 - 14 * q^4 - 28 * q^5 - 14 * q^6 - 12 * q^8 - 28 * q^9 - 8 * q^10 - 12 * q^12 - 28 * q^13 - 14 * q^14 + 2 * q^16 - 4 * q^17 + 14 * q^18 + 14 * q^20 - 28 * q^21 - 14 * q^22 - 22 * q^24 - 12 * q^25 - 30 * q^26 - 36 * q^29 + 16 * q^30 - 12 * q^32 - 28 * q^33 - 56 * q^34 - 50 * q^36 - 36 * q^37 - 14 * q^38 - 60 * q^40 - 12 * q^41 - 14 * q^42 + 30 * q^44 + 36 * q^46 + 136 * q^48 + 12 * q^49 + 56 * q^50 + 66 * q^52 + 48 * q^53 + 56 * q^54 + 52 * q^56 + 184 * q^58 + 108 * q^60 - 28 * q^61 + 84 * q^62 + 112 * q^64 - 68 * q^65 + 92 * q^66 + 68 * q^68 - 44 * q^69 + 46 * q^70 + 4 * q^72 - 148 * q^73 - 32 * q^74 - 14 * q^76 - 60 * q^77 + 2 * q^78 - 14 * q^80 + 36 * q^81 + 6 * q^82 + 28 * q^84 - 92 * q^85 - 48 * q^88 + 28 * q^89 + 28 * q^90 - 14 * q^92 - 28 * q^93 + 62 * q^94 - 56 * q^96 + 184 * q^97 - 110 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$ .

$n$	$59$	$89$
$\chi(n)$	$-1$	$e\left(\frac{25}{28}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.490339	−	1.32649i	−0.346722	−	0.937968i
$2$	−0.490339	−	1.32649i	−0.346722	−	0.937968i
$3$	−2.34863	+	0.264627i	−1.35598	+	0.152782i	−0.759846	−	0.650103i	$-0.774726\pi$
$3$	−2.34863	+	0.264627i	−1.35598	+	0.152782i	−0.596133	+	0.802885i	$0.703297\pi$
$4$	−1.51913	+	1.30086i	−0.759567	+	0.650429i
$5$	−0.588667	+	1.22238i	−0.263260	+	0.546665i	−0.990137	−	0.140103i	$-0.955257\pi$
$5$	−0.588667	+	1.22238i	−0.263260	+	0.546665i	0.726877	+	0.686768i	$0.240971\pi$
$6$	1.50265	+	2.98566i	0.613453	+	1.21889i
$7$	2.56130	+	2.04257i	0.968081	+	0.772019i	0.973669	−	0.227966i	$-0.0732074\pi$
$7$	2.56130	+	2.04257i	0.968081	+	0.772019i	−0.00558836	+	0.999984i	$0.501779\pi$
$8$	2.47046	+	1.37725i	0.873440	+	0.486931i
$9$	2.52123	−	0.575454i	0.840410	−	0.191818i
$10$	1.91012	+	0.181478i	0.604032	+	0.0573884i
$11$	−5.07822	+	3.19086i	−1.53114	+	0.962080i	−0.538285	+	0.842763i	$0.680928\pi$
$11$	−5.07822	+	3.19086i	−1.53114	+	0.962080i	−0.992856	+	0.119317i	$0.961930\pi$
$12$	3.22364	−	3.45723i	0.930584	−	0.998016i
$13$	−1.29716	−	0.296069i	−0.359769	−	0.0821149i	0.0388160	−	0.999246i	$-0.487641\pi$
$13$	−1.29716	−	0.296069i	−0.359769	−	0.0821149i	−0.398585	+	0.917131i	$0.630499\pi$
$14$	1.45353	−	4.39908i	0.388473	−	1.17570i
$15$	1.05908	−	3.02669i	0.273454	−	0.781488i
$16$	0.615539	−	3.95236i	0.153885	−	0.988089i
$17$	−3.79071	+	3.79071i	−0.919383	+	0.919383i	−0.996984	−	0.0776011i	$-0.975274\pi$
$17$	−3.79071	+	3.79071i	−0.919383	+	0.919383i	0.0776011	+	0.996984i	$0.475274\pi$
$18$	−1.99959	−	3.06221i	−0.471308	−	0.721770i
$19$	0.151626	−	1.34572i	0.0347854	−	0.308729i	−0.964257	−	0.264970i	$-0.914638\pi$
$19$	0.151626	−	1.34572i	0.0347854	−	0.308729i	0.999042	−	0.0437590i	$-0.0139334\pi$
$20$	−0.695878	−	2.62273i	−0.155603	−	0.586461i
$21$	−6.55605	−	4.11944i	−1.43065	−	0.898936i
$22$	6.72268	+	5.17159i	1.43328	+	1.10259i
$23$	1.29280	+	2.68452i	0.269567	+	0.559762i	0.991178	−	0.132537i	$-0.0423123\pi$
$23$	1.29280	+	2.68452i	0.269567	+	0.559762i	−0.721611	+	0.692299i	$0.756598\pi$
$24$	−6.16665	−	2.58089i	−1.25876	−	0.526823i
$25$	1.96977	+	2.47001i	0.393953	+	0.494002i
$26$	0.243319	+	1.86585i	0.0477188	+	0.365923i
$27$	0.923422	−	0.323119i	0.177713	−	0.0621844i
$28$	−6.54805	+	0.228950i	−1.23747	+	0.0432675i
$29$	2.93553	−	4.51472i	0.545114	−	0.838362i
$29$	2.93553	−	4.51472i	0.545114	−	0.838362i
$30$	−4.53417	+	0.0792436i	−0.827823	+	0.0144678i
$31$	−1.44988	−	4.14352i	−0.260406	−	0.744199i	−0.997646	−	0.0685678i	$-0.978157\pi$
$31$	−1.44988	−	4.14352i	−0.260406	−	0.744199i	0.737240	−	0.675631i	$-0.236129\pi$
$32$	−5.54457	+	1.12149i	−0.980151	+	0.198253i
$33$	11.0825	−	8.83796i	1.92921	−	1.53849i
$34$	6.88707	+	3.16960i	1.18112	+	0.543581i
$35$	−4.00455	+	1.92849i	−0.676892	+	0.325974i
$36$	−3.08150	+	4.15395i	−0.513584	+	0.692326i
$37$	−3.02614	+	4.81608i	−0.497495	+	0.791759i	−0.997227	−	0.0744214i	$-0.976289\pi$
$37$	−3.02614	+	4.81608i	−0.497495	+	0.791759i	0.499732	+	0.866180i	$0.333432\pi$
$38$	−1.85942	+	0.458728i	−0.301638	+	0.0744155i
$39$	3.12490	+	0.352092i	0.500385	+	0.0563798i
$40$	−3.13780	+	2.20910i	−0.496130	+	0.349290i
$41$	−4.55671	−	4.55671i	−0.711638	−	0.711638i	0.255239	−	0.966878i	$-0.417846\pi$
$41$	−4.55671	−	4.55671i	−0.711638	−	0.711638i	−0.966878	+	0.255239i	$0.917846\pi$
$42$	−2.24969	+	10.7164i	−0.347135	+	1.65358i
$43$	6.65934	+	2.33020i	1.01554	+	0.355353i	0.786186	−	0.617990i	$-0.212053\pi$
$43$	6.65934	+	2.33020i	1.01554	+	0.355353i	0.229354	+	0.973343i	$0.426339\pi$
$44$	3.56365	−	11.4534i	0.537240	−	1.72666i
$45$	−0.780741	+	3.42065i	−0.116386	+	0.509921i
$46$	2.92708	−	3.03121i	0.431574	−	0.446927i
$47$	−0.260350	−	0.414345i	−0.0379760	−	0.0604384i	0.827197	−	0.561912i	$-0.189934\pi$
$47$	−0.260350	−	0.414345i	−0.0379760	−	0.0604384i	−0.865173	+	0.501474i	$0.832791\pi$
$48$	−0.399773	+	9.44549i	−0.0577023	+	1.36334i
$49$	0.830527	+	3.63878i	0.118647	+	0.519825i
$50$	2.31058	−	3.82401i	0.326765	−	0.540797i
$51$	7.89985	−	9.90609i	1.10620	−	1.38713i
$52$	2.35571	−	1.23766i	0.326678	−	0.171632i
$53$	5.75234	+	2.77018i	0.790144	+	0.380513i	0.785018	−	0.619474i	$-0.212654\pi$
$53$	5.75234	+	2.77018i	0.790144	+	0.380513i	0.00512653	+	0.999987i	$0.498368\pi$
$54$	−0.881404	−	1.06647i	−0.119944	−	0.145128i
$55$	−0.911059	−	8.08587i	−0.122847	−	1.09030i
$56$	3.51447	+	8.57364i	0.469640	+	1.14570i
$57$			3.20071i			0.423944i
$58$	−7.42812	−	1.68019i	−0.975360	−	0.220620i
$59$		−	6.26790i		−	0.816011i	−0.912979	−	0.408006i	$-0.866224\pi$
$59$		−	6.26790i		−	0.816011i	0.912979	−	0.408006i	$-0.133776\pi$
$60$	2.32840	+	5.97567i	0.300595	+	0.771455i
$61$	1.38184	+	12.2642i	0.176926	+	1.57026i	0.697586	+	0.716501i	$0.254257\pi$
$61$	1.38184	+	12.2642i	0.176926	+	1.57026i	−0.520660	+	0.853764i	$0.674314\pi$
$62$	−4.78539	+	3.95498i	−0.607746	+	0.502283i
$63$	7.63303	+	3.67588i	0.961672	+	0.463117i
$64$	4.20636	+	6.80489i	0.525795	+	0.850611i
$65$	1.12551	−	1.41134i	0.139602	−	0.175055i
$66$	−17.1576	−	10.3671i	−2.11195	−	1.27611i
$67$	0.856051	+	3.75061i	0.104583	+	0.458209i	0.999918	+	0.0128152i	$0.00407932\pi$
$67$	0.856051	+	3.75061i	0.104583	+	0.458209i	−0.895335	+	0.445394i	$0.853064\pi$
$68$	0.827426	−	10.6898i	0.100340	−	1.29633i
$69$	−3.74670	−	5.96283i	−0.451049	−	0.717841i
$70$	4.52170	+	4.36637i	0.540447	+	0.521881i
$71$	−2.73458	+	11.9810i	−0.324534	+	1.42188i	0.504853	+	0.863205i	$0.331547\pi$
$71$	−2.73458	+	11.9810i	−0.324534	+	1.42188i	−0.829388	+	0.558673i	$0.811311\pi$
$72$	7.02115	+	2.05073i	0.827450	+	0.241680i
$73$	7.19276	+	2.51686i	0.841849	+	0.294576i	0.716543	−	0.697543i	$-0.245723\pi$
$73$	7.19276	+	2.51686i	0.841849	+	0.294576i	0.125306	+	0.992118i	$0.460009\pi$
$74$	7.87230	+	1.65263i	0.915137	+	0.192114i
$75$	−5.27987	−	5.27987i	−0.609667	−	0.609667i
$76$	1.52025	+	2.24157i	0.174384	+	0.257126i
$77$	−19.5244	−	2.19987i	−2.22501	−	0.250699i
$78$	−1.06522	−	4.31779i	−0.120612	−	0.488893i
$79$	2.90584	−	4.62461i	0.326932	−	0.520309i	−0.642302	−	0.766452i	$-0.722020\pi$
$79$	2.90584	−	4.62461i	0.326932	−	0.520309i	0.969234	+	0.246143i	$0.0791632\pi$
$80$	4.46893	+	3.07904i	0.499642	+	0.344248i
$81$	−9.07317	+	4.36941i	−1.00813	+	0.485490i
$82$	−3.81008	+	8.27875i	−0.420753	+	0.914235i
$83$	−2.50734	+	1.99954i	−0.275216	+	0.219478i	−0.751365	−	0.659887i	$-0.770604\pi$
$83$	−2.50734	+	1.99954i	−0.275216	+	0.219478i	0.476148	+	0.879365i	$0.342033\pi$
$84$	15.3183	−	2.27051i	1.67137	−	0.247733i
$85$	−2.40222	−	6.86516i	−0.260558	−	0.744631i
$86$	−0.174352	−	9.97612i	−0.0188009	−	1.07575i
$87$	−5.69974	+	11.3802i	−0.611076	+	1.22009i
$88$	−16.9402	+	0.888911i	−1.80583	+	0.0947583i
$89$	12.1053	−	4.23583i	1.28316	−	0.448997i	0.399331	−	0.916807i	$-0.369242\pi$
$89$	12.1053	−	4.23583i	1.28316	−	0.448997i	0.883829	+	0.467809i	$0.154957\pi$
$90$	4.92028	−	0.641637i	0.518643	−	0.0676345i
$91$	−2.71769	−	3.40787i	−0.284891	−	0.357242i
$92$	−5.45612	−	2.39641i	−0.568840	−	0.249843i
$93$	4.50171	+	9.34791i	0.466806	+	0.969333i
$94$	−0.421963	+	0.548521i	−0.0435222	+	0.0565756i
$95$	1.55572	+	0.977524i	0.159613	+	0.100292i
$96$	12.7253	−	4.10120i	1.29877	−	0.418577i
$97$	0.141905	−	1.25944i	0.0144082	−	0.127877i	−0.984449	−	0.175671i	$-0.943791\pi$
$97$	0.141905	−	1.25944i	0.0144082	−	0.127877i	0.998857	+	0.0477942i	$0.0152192\pi$
$98$	4.41955	−	2.88592i	0.446442	−	0.291522i
$99$	−10.9672	+	10.9672i	−1.10224	+	1.10224i
$100$	−6.20547	−	1.18989i	−0.620547	−	0.118989i
$101$	1.77842	−	5.08243i	0.176959	−	0.505720i	−0.820903	−	0.571067i	$-0.806530\pi$
$101$	1.77842	−	5.08243i	0.176959	−	0.505720i	0.997863	+	0.0653467i	$0.0208153\pi$
$102$	−17.0139	−	5.62169i	−1.68463	−	0.556631i
$103$	−13.8841	−	3.16896i	−1.36804	−	0.312247i	−0.525462	−	0.850817i	$-0.676107\pi$
$103$	−13.8841	−	3.16896i	−1.36804	−	0.312247i	−0.842580	+	0.538571i	$0.818965\pi$
$104$	−2.79683	−	2.51795i	−0.274252	−	0.246905i
$105$	8.89486	−	5.58901i	0.868049	−	0.545431i
$106$	0.854009	−	8.98873i	0.0829487	−	0.873062i
$107$	15.1947	−	3.46808i	1.46892	−	0.335272i	0.588128	−	0.808768i	$-0.299865\pi$
$107$	15.1947	−	3.46808i	1.46892	−	0.335272i	0.880796	+	0.473496i	$0.157008\pi$
$108$	−0.982470	+	1.69210i	−0.0945382	+	0.162823i
$109$	−3.13660	−	2.50135i	−0.300431	−	0.239586i	0.461658	−	0.887058i	$-0.347255\pi$
$109$	−3.13660	−	2.50135i	−0.300431	−	0.239586i	−0.762089	+	0.647472i	$0.775826\pi$
$110$	−10.2791	+	5.17333i	−0.980071	+	0.493257i
$111$	5.83282	−	12.1120i	0.553626	−	1.14962i
$112$	9.64954	−	8.86589i	0.911796	−	0.837748i
$113$	−0.0605474	+	0.00682206i	−0.00569582	+	0.000641765i	−0.114812	−	0.993387i	$-0.536627\pi$
$113$	−0.0605474	+	0.00682206i	−0.00569582	+	0.000641765i	0.109116	+	0.994029i	$0.465198\pi$
$114$	4.24570	−	1.56943i	0.397646	−	0.146991i
$115$	−4.04254			−0.376968
$116$	1.41354	+	10.6772i	0.131244	+	0.991350i
$117$	−3.44083			−0.318104
$118$	−8.31429	+	3.07340i	−0.765392	+	0.282929i
$119$	−17.4520	+	1.96636i	−1.59982	+	0.180256i
$120$	6.78494	−	6.01870i	0.619377	−	0.549429i
$121$	10.8340	−	22.4971i	0.984912	−	2.04519i
$122$	15.5907	−	7.84659i	1.41151	−	0.710397i
$123$	11.9078	+	9.49618i	1.07369	+	0.856241i
$124$	7.59270	+	4.40848i	0.681844	+	0.395893i
$125$	−10.7924	+	2.46330i	−0.965305	+	0.220325i
$126$	1.13322	−	11.9275i	0.100956	−	1.06259i
$127$	−1.61237	+	1.01312i	−0.143075	+	0.0899001i	−0.601667	−	0.798747i	$-0.705497\pi$
$127$	−1.61237	+	1.01312i	−0.143075	+	0.0899001i	0.458592	+	0.888647i	$0.348354\pi$
$128$	6.96405	−	8.91639i	0.615541	−	0.788105i
$129$	−16.2569	−	3.71054i	−1.43134	−	0.326695i
$130$	−2.42401	−	0.800934i	−0.212599	−	0.0702466i
$131$	−4.51526	+	12.9039i	−0.394500	+	1.12742i	0.559815	+	0.828617i	$0.310872\pi$
$131$	−4.51526	+	12.9039i	−0.394500	+	1.12742i	−0.954316	+	0.298800i	$0.903414\pi$
$132$	−5.33881	+	27.8427i	−0.464684	+	2.42340i
$133$	3.13708	−	3.13708i	0.272019	−	0.272019i
$134$	4.55537	−	2.97461i	0.393524	−	0.256967i
$135$	−0.148614	+	1.31898i	−0.0127906	+	0.113520i
$136$	−14.5856	+	4.14405i	−1.25070	+	0.355350i
$137$	19.0825	+	11.9903i	1.63033	+	1.02440i	0.959065	+	0.283187i	$0.0913918\pi$
$137$	19.0825	+	11.9903i	1.63033	+	1.02440i	0.671266	+	0.741217i	$0.265751\pi$
$138$	−6.07246	+	7.89375i	−0.516923	+	0.671961i
$139$	4.09956	+	8.51283i	0.347720	+	0.722049i	0.999334	−	0.0365027i	$-0.0116217\pi$
$139$	4.09956	+	8.51283i	0.347720	+	0.722049i	−0.651613	+	0.758551i	$0.725907\pi$
$140$	3.57476	−	8.13898i	0.302122	−	0.687870i
$141$	0.721112	+	0.904246i	0.0607286	+	0.0761512i
$142$	17.2335	−	2.24736i	1.44620	−	0.188594i
$143$	7.53201	−	2.63556i	0.629858	−	0.220397i
$144$	−0.722483	−	10.3190i	−0.0602069	−	0.859918i
$145$	3.79065	+	6.24600i	0.314797	+	0.518702i
$146$	−0.188318	−	10.7752i	−0.0155853	−	0.891763i
$147$	−2.91351	−	8.32634i	−0.240302	−	0.686745i
$148$	−1.66791	−	11.2529i	−0.137102	−	0.924979i
$149$	5.12076	−	4.08367i	0.419509	−	0.334547i	−0.390878	−	0.920443i	$-0.627828\pi$
$149$	5.12076	−	4.08367i	0.419509	−	0.334547i	0.810387	+	0.585895i	$0.199257\pi$
$150$	−4.41475	+	9.59261i	−0.360463	+	0.783233i
$151$	1.83267	−	0.882569i	0.149141	−	0.0718225i	−0.357825	−	0.933789i	$-0.616481\pi$
$151$	1.83267	−	0.882569i	0.149141	−	0.0718225i	0.506966	+	0.861966i	$0.330767\pi$
$152$	2.22797	−	3.11571i	0.180713	−	0.252718i
$153$	−7.37588	+	11.7386i	−0.596305	+	0.949013i
$154$	6.65548	+	26.9775i	0.536314	+	2.17391i
$155$	5.91846	+	0.666850i	0.475382	+	0.0535627i
$156$	−5.20517	+	3.53018i	−0.416747	+	0.282640i
$157$	−10.3348	−	10.3348i	−0.824803	−	0.824803i	0.161989	−	0.986793i	$-0.448209\pi$
$157$	−10.3348	−	10.3348i	−0.824803	−	0.824803i	−0.986793	+	0.161989i	$0.948209\pi$
$158$	−7.55933	−	1.58692i	−0.601388	−	0.126249i
$159$	−14.2431	−	4.98389i	−1.12955	−	0.395248i
$160$	1.89302	−	7.43776i	0.149656	−	0.588006i
$161$	−2.17208	+	9.51650i	−0.171184	+	0.750006i
$162$	10.2449	+	9.89294i	0.804915	+	0.777263i
$163$	6.00147	+	9.55129i	0.470072	+	0.748115i	0.994656	−	0.103244i	$-0.0329221\pi$
$163$	6.00147	+	9.55129i	0.470072	+	0.748115i	−0.524584	+	0.851358i	$0.675779\pi$
$164$	12.8499	+	0.994625i	1.00341	+	0.0776671i
$165$	4.27947	+	18.7496i	0.333156	+	1.45965i
$166$	3.88181	+	2.34550i	0.301287	+	0.182046i
$167$	−9.48148	+	11.8894i	−0.733699	+	0.920029i	−0.999026	−	0.0441291i	$-0.985949\pi$
$167$	−9.48148	+	11.8894i	−0.733699	+	0.920029i	0.265327	+	0.964159i	$0.414520\pi$
$168$	−10.5230	−	19.2063i	−0.811866	−	1.48179i
$169$	−10.1176	−	4.87239i	−0.778278	−	0.374799i
$170$	−7.92864	+	6.55278i	−0.608099	+	0.502575i
$171$	−0.392115	−	3.48011i	−0.0299858	−	0.266131i
$172$	−13.1477	+	5.12296i	−1.00250	+	0.390622i
$173$			9.89244i			0.752108i	0.926598	+	0.376054i	$0.122719\pi$
$173$			9.89244i			0.752108i	−0.926598	+	0.376054i	$0.877281\pi$
$174$	17.8905	+	1.98047i	1.35627	+	0.150139i
$175$			10.3498i			0.782373i
$176$	9.48556	+	22.0350i	0.715001	+	1.66095i
$177$	1.65865	+	14.7209i	0.124672	+	1.10649i
$178$	−11.5545	−	13.9805i	−0.866046	−	1.04789i
$179$	−7.06397	−	3.40183i	−0.527986	−	0.254265i	0.150847	−	0.988557i	$-0.451800\pi$
$179$	−7.06397	−	3.40183i	−0.527986	−	0.254265i	−0.678833	+	0.734293i	$0.737514\pi$
$180$	−3.26373	−	6.21206i	−0.243264	−	0.463020i
$181$	−9.23028	+	11.5744i	−0.686081	+	0.860319i	−0.995899	−	0.0904773i	$-0.971161\pi$
$181$	−9.23028	+	11.5744i	−0.686081	+	0.860319i	0.309817	+	0.950796i	$0.399732\pi$
$182$	−3.18791	+	5.27599i	−0.236303	+	0.391082i
$183$	−6.49084	−	28.4382i	−0.479817	−	2.10222i
$184$	−0.503451	+	8.41252i	−0.0371149	+	0.620179i
$185$	−4.10569	−	6.53417i	−0.301856	−	0.480401i
$186$	10.1925	−	10.5551i	0.747351	−	0.773938i
$187$	7.15446	−	31.3457i	0.523186	−	2.29223i
$188$	0.934511	+	0.290767i	0.0681562	+	0.0212064i
$189$	3.02516	+	1.05855i	0.220048	+	0.0769980i
$190$	0.533841	−	2.54296i	0.0387289	−	0.184486i
$191$	2.38215	+	2.38215i	0.172366	+	0.172366i	0.788018	−	0.615652i	$-0.211107\pi$
$191$	2.38215	+	2.38215i	0.172366	+	0.172366i	−0.615652	+	0.788018i	$0.711107\pi$
$192$	−11.6799	−	14.8690i	−0.842926	−	1.07308i
$193$	−4.16676	−	0.469481i	−0.299930	−	0.0337940i	−0.0392830	−	0.999228i	$-0.512507\pi$
$193$	−4.16676	−	0.469481i	−0.299930	−	0.0337940i	−0.260647	+	0.965434i	$0.583936\pi$
$194$	−1.74021	+	0.429317i	−0.124940	+	0.0308232i
$195$	−2.26992	+	3.61255i	−0.162552	+	0.258700i
$196$	−5.99521	−	4.44739i	−0.428229	−	0.317671i
$197$	17.0865	−	8.22841i	1.21736	−	0.586250i	0.288785	−	0.957394i	$-0.406749\pi$
$197$	17.0865	−	8.22841i	1.21736	−	0.586250i	0.928575	+	0.371144i	$0.121034\pi$
$198$	19.9254	+	9.17017i	1.41604	+	0.651696i
$199$	2.31781	−	1.84839i	0.164305	−	0.131029i	−0.537886	−	0.843018i	$-0.680777\pi$
$199$	2.31781	−	1.84839i	0.164305	−	0.131029i	0.702191	+	0.711989i	$0.252205\pi$
$200$	1.46441	+	8.81492i	0.103550	+	0.623309i
$201$	−3.00305	−	8.58223i	−0.211819	−	0.605344i
$202$	−7.61380	+	0.133066i	−0.535705	+	0.00936250i
$203$	16.7404	−	5.56754i	1.17495	−	0.390764i
$204$	0.885487	+	25.3253i	0.0619965	+	1.77312i
$205$	8.25241	−	2.88764i	0.576374	−	0.201682i
$206$	2.60435	+	19.9710i	0.181453	+	1.39144i
$207$	4.80426	+	6.02436i	0.333919	+	0.418722i
$208$	−1.96863	+	4.94461i	−0.136500	+	0.342847i
$209$	3.52400	+	7.31766i	0.243760	+	0.506173i
$210$	−11.7752	−	9.05840i	−0.812569	−	0.625089i
$211$	15.0964	+	9.48569i	1.03928	+	0.653022i	0.939697	−	0.342008i	$-0.111107\pi$
$211$	15.0964	+	9.48569i	1.03928	+	0.653022i	0.0995808	+	0.995029i	$0.468250\pi$
$212$	−12.3422	+	3.27469i	−0.847664	+	0.224907i
$213$	3.25201	−	28.8624i	0.222824	−	1.97762i
$214$	−12.0509	−	18.4550i	−0.823783	−	1.26156i
$215$	−6.76853	+	6.76853i	−0.461610	+	0.461610i
$216$	2.72630	+	0.473529i	0.185501	+	0.0322196i
$217$	4.74985	−	13.5743i	0.322441	−	0.921483i
$218$	−1.78001	+	5.38717i	−0.120558	+	0.364865i
$219$	−17.5591	−	4.00776i	−1.18654	−	0.270819i
$220$	11.9026	+	11.0984i	0.802472	+	0.748252i
$221$	6.03950	−	3.79487i	0.406261	−	0.255270i
$222$	−18.9264	−	1.79818i	−1.27026	−	0.120686i
$223$	17.5165	−	3.99802i	1.17299	−	0.267727i	0.408742	−	0.912650i	$-0.365968\pi$
$223$	17.5165	−	3.99802i	1.17299	−	0.267727i	0.764248	+	0.644923i	$0.223110\pi$
$224$	−16.4920	−	8.45269i	−1.10192	−	0.564769i
$225$	6.38761	+	5.09395i	0.425841	+	0.339597i
$226$	0.0387382	+	0.0769703i	0.00257682	+	0.00511998i
$227$	1.01832	−	2.11456i	0.0675881	−	0.140348i	−0.864438	−	0.502740i	$-0.832325\pi$
$227$	1.01832	−	2.11456i	0.0675881	−	0.140348i	0.932026	+	0.362392i	$0.118040\pi$
$228$	−4.16367	−	4.86231i	−0.275745	−	0.322014i
$229$	2.33196	−	0.262749i	0.154100	−	0.0173629i	−0.0345772	−	0.999402i	$-0.511008\pi$
$229$	2.33196	−	0.262749i	0.154100	−	0.0173629i	0.188678	+	0.982039i	$0.439580\pi$
$230$	1.98221	+	5.36237i	0.130703	+	0.353584i
$231$	46.4376			3.05537
$232$	13.4700	−	7.11048i	0.884349	−	0.466826i
$233$	−10.1722			−0.666405			−0.333203	−	0.942855i	$-0.608129\pi$
$233$	−10.1722			−0.666405			−0.333203	+	0.942855i	$0.608129\pi$
$234$	1.68717	+	4.56421i	0.110294	+	0.298372i
$235$	0.659747	−	0.0743356i	0.0430371	−	0.00484912i
$236$	8.15364	+	9.52178i	0.530757	+	0.619815i
$237$	−5.60092	+	11.6304i	−0.363819	+	0.755478i
$238$	11.1657	+	22.1856i	0.723767	+	1.43808i
$239$	−6.95433	−	5.54589i	−0.449838	−	0.358734i	0.372213	−	0.928147i	$-0.378599\pi$
$239$	−6.95433	−	5.54589i	−0.449838	−	0.358734i	−0.822051	+	0.569413i	$0.807170\pi$
$240$	−11.3106	−	6.04892i	−0.730099	−	0.390456i
$241$	5.72199	−	1.30601i	0.368586	−	0.0841274i	−0.0342160	−	0.999414i	$-0.510893\pi$
$241$	5.72199	−	1.30601i	0.368586	−	0.0841274i	0.402802	+	0.915287i	$0.368036\pi$
$242$	−35.1545	−	3.33999i	−2.25981	−	0.214702i
$243$	17.6681	−	11.1016i	1.13341	−	0.712168i
$244$	−18.0531	−	16.8333i	−1.15573	−	1.07764i
$245$	−4.93687	−	1.12681i	−0.315405	−	0.0719891i
$246$	6.75767	−	20.4519i	0.430854	−	1.30397i
$247$	−0.595109	+	1.70072i	−0.0378659	+	0.108215i
$248$	2.12479	−	12.2333i	0.134924	−	0.776813i
$249$	5.35967	−	5.35967i	0.339656	−	0.339656i
$250$	8.55950	+	13.1082i	0.541350	+	0.829034i
$251$	0.592621	−	5.25966i	0.0374059	−	0.331987i	−0.961047	−	0.276385i	$-0.910864\pi$
$251$	0.592621	−	5.25966i	0.0374059	−	0.331987i	0.998453	−	0.0556021i	$-0.0177078\pi$
$252$	−16.3774	+	4.34534i	−1.03168	+	0.273731i
$253$	−15.1310	−	9.50747i	−0.951281	−	0.597729i
$254$	2.13450	+	1.64202i	0.133931	+	0.103030i
$255$	7.45863	+	15.4880i	0.467077	+	0.969896i
$256$	−15.2422	−	4.86566i	−0.952639	−	0.304104i
$257$	−0.685106	−	0.859095i	−0.0427357	−	0.0535889i	0.760004	−	0.649918i	$-0.225197\pi$
$257$	−0.685106	−	0.859095i	−0.0427357	−	0.0535889i	−0.802740	+	0.596329i	$0.796625\pi$
$258$	3.04943	+	23.3840i	0.189849	+	1.45583i
$259$	−17.5880	+	6.15432i	−1.09287	+	0.382411i
$260$	0.126157	+	3.60814i	0.00782394	+	0.223768i
$261$	4.80312	−	13.0719i	0.297306	−	0.809131i
$262$	19.3308	−	0.337844i	1.19426	−	0.0208721i
$263$	0.769315	+	2.19858i	0.0474380	+	0.135570i	0.965165	−	0.261641i	$-0.0842637\pi$
$263$	0.769315	+	2.19858i	0.0474380	+	0.135570i	−0.917727	+	0.397211i	$0.869978\pi$
$264$	39.5509	−	6.57054i	2.43419	−	0.404389i
$265$	−6.77242	+	5.40083i	−0.416027	+	0.331770i
$266$	−5.69953	−	2.62306i	−0.349460	−	0.160830i
$267$	−27.3099	+	13.1518i	−1.67134	+	0.804875i
$268$	−6.17946	−	4.58407i	−0.377471	−	0.280017i
$269$	−7.93074	+	12.6217i	−0.483546	+	0.769559i	−0.996019	−	0.0891445i	$-0.971587\pi$
$269$	−7.93074	+	12.6217i	−0.483546	+	0.769559i	0.512473	+	0.858703i	$0.328730\pi$
$270$	1.82248	−	0.449615i	0.110913	−	0.0273627i
$271$	−17.5508	−	1.97750i	−1.06614	−	0.120125i	−0.438577	−	0.898694i	$-0.644517\pi$
$271$	−17.5508	−	1.97750i	−1.06614	−	0.120125i	−0.627559	+	0.778569i	$0.715946\pi$
$272$	12.6489	+	17.3156i	0.766953	+	1.04991i
$273$	7.28464	+	7.28464i	0.440887	+	0.440887i
$274$	6.54812	−	31.1921i	0.395586	−	1.88438i
$275$	−17.8843	−	6.25800i	−1.07847	−	0.377372i
$276$	13.4485	+	4.18443i	0.809506	+	0.251873i
$277$	−3.49210	+	15.2999i	−0.209820	+	0.919280i	0.754867	+	0.655878i	$0.227702\pi$
$277$	−3.49210	+	15.2999i	−0.209820	+	0.919280i	−0.964686	+	0.263402i	$0.915156\pi$
$278$	9.28198	−	9.61219i	0.556696	−	0.576501i
$279$	−6.03989	−	9.61243i	−0.361599	−	0.575481i
$280$	−12.5491	−	0.751007i	−0.749952	−	0.0448813i
$281$	−1.70279	−	7.46043i	−0.101580	−	0.445052i	−0.999983	−	0.00587900i	$-0.998129\pi$
$281$	−1.70279	−	7.46043i	−0.101580	−	0.445052i	0.898402	−	0.439173i	$-0.144728\pi$
$282$	0.845880	−	1.39993i	0.0503714	−	0.0833648i
$283$	8.32098	−	10.4342i	0.494631	−	0.620247i	−0.470378	−	0.882465i	$-0.655882\pi$
$283$	8.32098	−	10.4342i	0.494631	−	0.620247i	0.965009	+	0.262218i	$0.0844538\pi$
$284$	−11.4313	−	21.7580i	−0.678325	−	1.29110i
$285$	−3.91248	−	1.88415i	−0.231755	−	0.111608i
$286$	−7.18928	−	8.69879i	−0.425111	−	0.514370i
$287$	−2.36371	−	20.9785i	−0.139525	−	1.23832i
$288$	−13.3338	+	6.01818i	−0.785700	+	0.354625i
$289$		−	11.7390i		−	0.690532i
$290$	6.42652	−	8.09091i	0.377378	−	0.475115i
$291$			2.99550i			0.175599i
$292$	−14.2008	+	5.53331i	−0.831041	+	0.323813i
$293$	−3.68352	−	32.6922i	−0.215194	−	1.90990i	−0.382436	−	0.923982i	$-0.624915\pi$
$293$	−3.68352	−	32.6922i	−0.215194	−	1.90990i	0.167242	−	0.985916i	$-0.446514\pi$
$294$	−9.61617	+	7.94747i	−0.560826	+	0.463506i
$295$	7.66175	+	3.68971i	0.446085	+	0.214823i
$296$	−14.1089	+	7.73019i	−0.820064	+	0.449308i
$297$	−3.65831	+	4.58738i	−0.212277	+	0.266187i
$298$	−7.92785	−	4.79024i	−0.459248	−	0.277491i
$299$	−0.882167	−	3.86503i	−0.0510171	−	0.223520i
$300$	14.8892	+	1.15247i	0.859628	+	0.0665381i
$301$	12.2970	+	19.5705i	0.708786	+	1.12803i
$302$	−2.06935	−	1.99826i	−0.119078	−	0.114987i
$303$	−2.83189	+	12.4073i	−0.162688	+	0.712783i
$304$	−5.22542	−	1.42762i	−0.299698	−	0.0818797i
$305$	−15.8049	−	5.53038i	−0.904986	−	0.316668i
$306$	19.1878	+	4.02809i	1.09690	+	0.230270i
$307$	−4.13225	−	4.13225i	−0.235840	−	0.235840i	0.579285	−	0.815125i	$-0.303332\pi$
$307$	−4.13225	−	4.13225i	−0.235840	−	0.235840i	−0.815125	+	0.579285i	$0.803332\pi$
$308$	32.5219	−	22.0566i	1.85311	−	1.25679i
$309$	33.4472	+	3.76859i	1.90274	+	0.214388i
$310$	−2.01748	−	8.17774i	−0.114585	−	0.464464i
$311$	1.17063	−	1.86305i	0.0663804	−	0.105644i	−0.811885	−	0.583818i	$-0.801558\pi$
$311$	1.17063	−	1.86305i	0.0663804	−	0.105644i	0.878265	+	0.478174i	$0.158701\pi$
$312$	7.23503	+	5.17360i	0.409603	+	0.292898i
$313$	−10.0771	+	4.85288i	−0.569592	+	0.274301i	−0.696433	−	0.717622i	$-0.745231\pi$
$313$	−10.0771	+	4.85288i	−0.569592	+	0.274301i	0.126841	+	0.991923i	$0.459516\pi$
$314$	−8.64138	+	18.7765i	−0.487661	+	1.05962i
$315$	−8.98663	+	7.16660i	−0.506339	+	0.403792i
$316$	1.60160	+	10.8055i	0.0900973	+	0.607856i
$317$	4.08640	+	11.6783i	0.229515	+	0.655916i	0.999833	+	0.0182567i	$0.00581160\pi$
$317$	4.08640	+	11.6783i	0.229515	+	0.655916i	−0.770318	+	0.637660i	$0.779903\pi$
$318$	0.372908	+	21.3371i	0.0209117	+	1.19653i
$319$	−0.501431	+	32.2936i	−0.0280747	+	1.80809i
$320$	−10.7943	+	1.13596i	−0.603420	+	0.0635021i
$321$	−34.7688	+	12.1661i	−1.94061	+	0.679048i
$322$	13.6886	−	1.78508i	0.762834	−	0.0994787i
$323$	4.52646	+	5.67600i	0.251859	+	0.315821i
$324$	8.09939	−	18.4406i	0.449966	−	1.02448i
$325$	−1.82382	−	3.78719i	−0.101167	−	0.210076i
$326$	9.72690	−	12.6442i	0.538723	−	0.700300i
$327$	8.02862	+	5.04471i	0.443983	+	0.278973i
$328$	−4.98145	−	17.5329i	−0.275054	−	0.968093i
$329$	0.179493	−	1.59305i	0.00989578	−	0.0878275i
$330$	22.7727	−	14.8703i	1.25359	−	0.818584i
$331$	−14.9146	+	14.9146i	−0.819782	+	0.819782i	−0.986076	−	0.166294i	$-0.946820\pi$
$331$	−14.9146	+	14.9146i	−0.819782	+	0.819782i	0.166294	+	0.986076i	$0.446820\pi$
$332$	1.20787	−	6.29926i	0.0662907	−	0.345717i
$333$	−4.85817	+	13.8839i	−0.266226	+	0.760831i
$334$	20.4203	+	6.74722i	1.11735	+	0.369191i
$335$	−5.08859	−	1.16144i	−0.278020	−	0.0634562i
$336$	−20.3170	+	23.3762i	−1.10838	+	1.27528i
$337$	−16.8237	+	10.5710i	−0.916446	+	0.575841i	−0.905615	−	0.424100i	$-0.860590\pi$
$337$	−16.8237	+	10.5710i	−0.916446	+	0.575841i	−0.0108308	+	0.999941i	$0.503448\pi$
$338$	−1.50209	+	15.8100i	−0.0817030	+	0.859951i
$339$	0.140398	−	0.0320449i	0.00762537	−	0.00174044i
$340$	12.5799	+	7.30415i	0.682241	+	0.396123i
$341$	20.5842	+	16.4154i	1.11470	+	0.888942i
$342$	−4.42406	+	2.22657i	−0.239226	+	0.120399i
$343$	4.64468	−	9.64478i	0.250789	−	0.520769i
$344$	13.2424	+	14.9283i	0.713981	+	0.804878i
$345$	9.49440	−	1.06976i	0.511161	−	0.0575941i
$346$	13.1222	−	4.85065i	0.705454	−	0.260773i
$347$	16.7210			0.897629			0.448814	−	0.893625i	$-0.351846\pi$
$347$	16.7210			0.897629			0.448814	+	0.893625i	$0.351846\pi$
$348$	−6.14535	−	24.7026i	−0.329425	−	1.32420i
$349$	3.96295			0.212132			0.106066	−	0.994359i	$-0.466175\pi$
$349$	3.96295			0.212132			0.106066	+	0.994359i	$0.466175\pi$
$350$	13.7289	−	5.07492i	0.733840	−	0.271266i
$351$	−1.29350	+	0.145742i	−0.0690417	+	0.00777914i
$352$	24.5780	−	23.3871i	1.31001	−	1.24654i
$353$	−7.95794	+	16.5248i	−0.423559	+	0.879528i	0.574575	+	0.818452i	$0.305168\pi$
$353$	−7.95794	+	16.5248i	−0.423559	+	0.879528i	−0.998133	+	0.0610761i	$0.980547\pi$
$354$	18.7138	−	9.41844i	0.994629	−	0.500585i
$355$	−13.0355	−	10.3955i	−0.691854	−	0.551735i
$356$	−12.8794	+	22.1821i	−0.682606	+	1.17565i
$357$	40.4678	−	9.23650i	2.14178	−	0.488848i
$358$	−1.04874	+	11.0383i	−0.0554275	+	0.583393i
$359$	−2.35090	+	1.47717i	−0.124076	+	0.0779621i	−0.592640	−	0.805467i	$-0.701914\pi$
$359$	−2.35090	+	1.47717i	−0.124076	+	0.0779621i	0.468564	+	0.883429i	$0.344771\pi$
$360$	−6.63989	+	7.37531i	−0.349953	+	0.388713i
$361$	16.7357	+	3.81981i	0.880825	+	0.201042i
$362$	19.8793	+	6.56846i	1.04483	+	0.345231i
$363$	−19.4918	+	55.7042i	−1.02305	+	2.92371i
$364$	8.56169	+	1.64169i	0.448754	+	0.0860481i
$365$	−7.31070	+	7.31070i	−0.382659	+	0.382659i
$366$	−34.5402	+	22.5544i	−1.80545	+	1.17894i
$367$	0.150160	−	1.33270i	0.00783827	−	0.0695666i	−0.989184	−	0.146679i	$-0.953142\pi$
$367$	0.150160	−	1.33270i	0.00783827	−	0.0695666i	0.997022	+	0.0771126i	$0.0245701\pi$
$368$	11.4060	−	3.45717i	0.594577	−	0.180217i
$369$	−14.1107	−	8.86633i	−0.734573	−	0.461563i
$370$	−6.65430	+	8.65010i	−0.345941	+	0.449697i
$371$	9.07518	+	18.8448i	0.471160	+	0.978374i
$372$	−18.9990	−	8.34464i	−0.985052	−	0.432649i
$373$	0.852893	+	1.06949i	0.0441611	+	0.0553763i	0.803422	−	0.595411i	$-0.203011\pi$
$373$	0.852893	+	1.06949i	0.0441611	+	0.0553763i	−0.759260	+	0.650787i	$0.774439\pi$
$374$	−45.0878	+	5.87975i	−2.33143	+	0.304035i
$375$	24.6955	−	8.64134i	1.27527	−	0.446237i
$376$	−0.0725286	−	1.38219i	−0.00374037	−	0.0712811i
$377$	−5.14453	+	4.98721i	−0.264957	+	0.256855i
$378$	−0.0792034	−	4.53188i	−0.00407378	−	0.233095i
$379$	−11.3860	−	32.5395i	−0.584862	−	1.67144i	−0.731166	−	0.682200i	$-0.761023\pi$
$379$	−11.3860	−	32.5395i	−0.584862	−	1.67144i	0.146304	−	0.989240i	$-0.453262\pi$
$380$	−3.63497	+	0.538780i	−0.186470	+	0.0276388i
$381$	3.51877	−	2.80612i	0.180272	−	0.143762i
$382$	1.99183	−	4.32795i	0.101911	−	0.221437i
$383$	−3.17316	+	1.52812i	−0.162141	+	0.0780831i	−0.513194	−	0.858273i	$-0.671538\pi$
$383$	−3.17316	+	1.52812i	−0.162141	+	0.0780831i	0.351053	+	0.936356i	$0.385824\pi$
$384$	−13.9964	+	22.7841i	−0.714252	+	1.16270i
$385$	14.1825	−	22.5712i	0.722805	−	1.15034i
$386$	1.42037	+	5.75736i	0.0722948	+	0.293042i
$387$	18.1307	+	2.04283i	0.921633	+	0.103843i
$388$	1.42278	+	2.09785i	0.0722305	+	0.106502i
$389$	12.4654	+	12.4654i	0.632022	+	0.632022i	0.948575	−	0.316553i	$-0.102526\pi$
$389$	12.4654	+	12.4654i	0.632022	+	0.632022i	−0.316553	+	0.948575i	$0.602526\pi$
$390$	5.90503	+	1.23964i	0.299013	+	0.0627715i
$391$	−15.0769	−	5.27563i	−0.762471	−	0.266800i
$392$	−2.95972	+	10.1333i	−0.149488	+	0.511809i
$393$	7.18995	−	31.5012i	0.362685	−	1.58903i
$394$	−19.2931	−	18.6303i	−0.971970	−	0.938579i
$395$	3.94246	+	6.27439i	0.198367	+	0.315699i
$396$	2.39388	−	30.9273i	0.120297	−	1.55416i
$397$	−8.10411	−	35.5064i	−0.406734	−	1.78202i	−0.599080	−	0.800689i	$-0.704467\pi$
$397$	−8.10411	−	35.5064i	−0.406734	−	1.78202i	0.192347	−	0.981327i	$-0.438390\pi$
$398$	−3.58837	−	2.16820i	−0.179869	−	0.108682i
$399$	−6.53767	+	8.19798i	−0.327293	+	0.410412i
$400$	10.9748	−	6.26483i	0.548741	−	0.313241i
$401$	12.2141	+	5.88201i	0.609944	+	0.293733i	0.713243	−	0.700917i	$-0.247226\pi$
$401$	12.2141	+	5.88201i	0.609944	+	0.293733i	−0.103299	+	0.994650i	$0.532940\pi$
$402$	−9.91170	+	8.19172i	−0.494351	+	0.408566i
$403$	0.653965	+	5.80410i	0.0325763	+	0.289123i
$404$	3.90986	+	10.0344i	0.194523	+	0.499228i
$405$		−	13.6630i		−	0.678919i
$406$	−15.5937	−	19.4759i	−0.773904	−	0.966574i
$407$		−	34.1131i		−	1.69092i
$408$	33.1594	−	13.5926i	1.64164	−	0.672932i
$409$	2.43294	+	21.5929i	0.120301	+	1.06770i	0.898284	+	0.439416i	$0.144815\pi$
$409$	2.43294	+	21.5929i	0.120301	+	1.06770i	−0.777982	+	0.628286i	$0.783757\pi$
$410$	−7.87691	−	9.53079i	−0.389013	−	0.470692i
$411$	−47.9907	−	23.1111i	−2.36720	−	1.13999i
$412$	25.2142	−	13.2472i	1.24221	−	0.652642i
$413$	12.8026	−	16.0540i	0.629976	−	0.789965i
$414$	5.63551	−	9.32677i	0.276970	−	0.458386i
$415$	−0.968206	−	4.24199i	−0.0475273	−	0.208231i
$416$	7.52426	+	0.186819i	0.368907	+	0.00915958i
$417$	−11.8811	−	18.9086i	−0.581818	−	0.925958i
$418$	7.97883	−	8.26268i	0.390257	−	0.404141i
$419$	7.39689	−	32.4079i	0.361362	−	1.58323i	−0.388380	−	0.921499i	$-0.626965\pi$
$419$	7.39689	−	32.4079i	0.361362	−	1.58323i	0.749742	−	0.661730i	$-0.230178\pi$
$420$	−6.24198	+	20.0614i	−0.304577	+	0.978896i
$421$	−25.5561	−	8.94248i	−1.24553	−	0.435830i	−0.374577	−	0.927196i	$-0.622212\pi$
$421$	−25.5561	−	8.94248i	−1.24553	−	0.435830i	−0.870953	+	0.491366i	$0.836498\pi$
$422$	5.18029	−	24.6764i	0.252172	−	1.20123i
$423$	−0.894839	−	0.894839i	−0.0435086	−	0.0435086i
$424$	10.3957	+	14.7660i	0.504860	+	0.717102i
$425$	−16.8299	−	1.89628i	−0.816371	−	0.0919829i
$426$	−39.8802	+	9.83863i	−1.93220	+	0.476683i
$427$	−21.5111	+	34.2347i	−1.04099	+	1.65673i
$428$	−18.5713	+	25.0346i	−0.897676	+	1.21009i
$429$	−16.9924	+	8.18312i	−0.820402	+	0.395085i
$430$	12.2972	+	5.65949i	0.593026	+	0.272925i
$431$	10.9810	−	8.75704i	0.528935	−	0.421812i	−0.322268	−	0.946649i	$-0.604445\pi$
$431$	10.9810	−	8.75704i	0.528935	−	0.421812i	0.851203	+	0.524837i	$0.175874\pi$
$432$	−0.708680	−	3.84858i	−0.0340964	−	0.185165i
$433$	7.97828	+	22.8006i	0.383412	+	1.09573i	0.960316	+	0.278916i	$0.0899751\pi$
$433$	7.97828	+	22.8006i	0.383412	+	1.09573i	−0.576904	+	0.816812i	$0.695739\pi$
$434$	−20.3352	+	0.355397i	−0.976119	+	0.0170596i
$435$	−10.5557	−	13.6664i	−0.506106	−	0.655254i
$436$	8.01882	−	0.280375i	0.384032	−	0.0134275i
$437$	3.80863	−	1.33270i	0.182191	−	0.0637516i
$438$	3.29370	+	25.2571i	0.157379	+	1.20683i
$439$	17.1754	+	21.5373i	0.819737	+	1.02792i	0.999026	+	0.0441209i	$0.0140487\pi$
$439$	17.1754	+	21.5373i	0.819737	+	1.02792i	−0.179290	+	0.983796i	$0.557380\pi$
$440$	8.88553	−	21.2306i	0.423601	−	1.01213i
$441$	4.18790	+	8.69626i	0.199424	+	0.414108i
$442$	−7.99524	−	6.15054i	−0.380295	−	0.292551i
$443$	19.2138	+	12.0728i	0.912873	+	0.573596i	0.904549	−	0.426369i	$-0.140208\pi$
$443$	19.2138	+	12.0728i	0.912873	+	0.573596i	0.00832387	+	0.999965i	$0.497350\pi$
$444$	6.89511	+	25.9874i	0.327227	+	1.23331i
$445$	−1.94820	+	17.2908i	−0.0923537	+	0.819662i
$446$	−13.8923	−	21.2750i	−0.657821	−	1.00740i
$447$	−10.9461	+	10.9461i	−0.517733	+	0.517733i
$448$	−3.12569	+	26.0212i	−0.147675	+	1.22938i
$449$	0.624960	−	1.78603i	0.0294937	−	0.0842881i	−0.928195	−	0.372094i	$-0.878640\pi$
$449$	0.624960	−	1.78603i	0.0294937	−	0.0842881i	0.957689	+	0.287806i	$0.0929257\pi$
$450$	3.62496	−	10.9708i	0.170882	−	0.517170i
$451$	37.6798	+	8.60017i	1.77427	+	0.404966i
$452$	0.0831052	−	0.0891272i	0.00390894	−	0.00419219i
$453$	−4.07071	+	2.55780i	−0.191259	+	0.120176i
$454$	−3.30426	−	0.313934i	−0.155076	−	0.0147336i
$455$	5.76553	−	1.31594i	0.270292	−	0.0616924i
$456$	−4.40818	+	7.90723i	−0.206432	+	0.370290i
$457$	−12.1203	−	9.66562i	−0.566964	−	0.452138i	0.297579	−	0.954697i	$-0.403821\pi$
$457$	−12.1203	−	9.66562i	−0.566964	−	0.452138i	−0.864543	+	0.502559i	$0.832392\pi$
$458$	−1.49199	−	2.96448i	−0.0697159	−	0.138521i
$459$	−2.27558	+	4.72528i	−0.106215	+	0.220557i
$460$	6.14116	−	5.25876i	0.286333	−	0.245191i
$461$	16.2172	−	1.82724i	0.755310	−	0.0851030i	0.274091	−	0.961704i	$-0.411623\pi$
$461$	16.2172	−	1.82724i	0.755310	−	0.0851030i	0.481219	+	0.876601i	$0.340194\pi$
$462$	−22.7702	−	61.5989i	−1.05937	−	2.86584i
$463$	−33.3937			−1.55194			−0.775969	−	0.630771i	$-0.782739\pi$
$463$	−33.3937			−1.55194			−0.775969	+	0.630771i	$0.782739\pi$
$464$	−16.0368	−	14.3812i	−0.744491	−	0.667632i
$465$	−14.0767			−0.652791
$466$	4.98785	+	13.4933i	0.231058	+	0.625067i
$467$	11.8946	−	1.34019i	0.550414	−	0.0620168i	0.167622	−	0.985851i	$-0.446391\pi$
$467$	11.8946	−	1.34019i	0.550414	−	0.0620168i	0.382792	+	0.923834i	$0.374963\pi$
$468$	5.22708	−	4.47602i	0.241622	−	0.206904i
$469$	−5.46827	+	11.3550i	−0.252501	+	0.524324i
$470$	−0.422105	−	0.838696i	−0.0194702	−	0.0386861i
$471$	27.0073	+	21.5376i	1.24443	+	0.992401i
$472$	8.63247	−	15.4846i	0.397341	−	0.712737i
$473$	−41.2530	+	9.41572i	−1.89681	+	0.432935i
$474$	18.1740	+	1.72669i	0.834758	+	0.0793095i
$475$	3.62260	−	2.27623i	0.166216	−	0.104441i
$476$	23.9539	−	25.6897i	1.09793	−	1.17748i
$477$	16.0971	+	3.67405i	0.737034	+	0.168223i
$478$	−3.94657	+	11.9442i	−0.180512	+	0.546314i
$479$	8.56686	−	24.4827i	0.391430	−	1.11864i	−0.564598	−	0.825366i	$-0.690969\pi$
$479$	8.56686	−	24.4827i	0.391430	−	1.11864i	0.956028	−	0.293276i	$-0.0947454\pi$
$480$	−2.47776	+	17.9694i	−0.113094	+	0.820189i
$481$	5.35130	−	5.35130i	0.243998	−	0.243998i
$482$	−4.53812	−	6.94976i	−0.206706	−	0.316553i
$483$	2.58308	−	22.9255i	0.117534	−	1.04315i
$484$	12.8072	+	48.2697i	0.582144	+	2.19408i
$485$	1.45598	+	0.914851i	0.0661125	+	0.0415412i
$486$	−23.3895	−	17.9930i	−1.06097	−	0.816177i
$487$	−1.80844	−	3.75527i	−0.0819484	−	0.170168i	0.855968	−	0.517029i	$-0.172962\pi$
$487$	−1.80844	−	3.75527i	−0.0819484	−	0.170168i	−0.937917	+	0.346861i	$0.887248\pi$
$488$	−13.4770	+	32.2013i	−0.610077	+	1.45768i
$489$	−16.6227	−	20.8443i	−0.751706	−	0.942610i
$490$	0.926045	+	7.10121i	0.0418345	+	0.320800i
$491$	15.3723	−	5.37898i	0.693740	−	0.242750i	0.0397018	−	0.999212i	$-0.487359\pi$
$491$	15.3723	−	5.37898i	0.693740	−	0.242750i	0.654038	+	0.756461i	$0.273074\pi$
$492$	−30.4428	+	1.06442i	−1.37247	+	0.0479877i
$493$	5.98626	+	28.2418i	0.269608	+	1.27194i
$494$	2.54779	−	0.0445277i	0.114631	−	0.00200340i
$495$	−6.95004	−	19.8621i	−0.312381	−	0.892733i
$496$	−17.2691	+	3.17994i	−0.775407	+	0.142784i
$497$	−31.4760	+	25.1013i	−1.41189	+	1.12595i
$498$	−9.73760	−	4.48148i	−0.436352	−	0.200820i
$499$	4.64060	−	2.23479i	0.207742	−	0.100043i	−0.327120	−	0.944983i	$-0.606078\pi$
$499$	4.64060	−	2.23479i	0.207742	−	0.100043i	0.534861	+	0.844940i	$0.320364\pi$
$500$	13.1908	−	17.7815i	0.589909	−	0.795214i
$501$	19.1222	−	30.4328i	0.854317	−	1.35964i
$502$	−7.26746	+	1.79291i	−0.324362	+	0.0800217i
$503$	2.97694	+	0.335420i	0.132735	+	0.0149556i	0.178082	−	0.984016i	$-0.443011\pi$
$503$	2.97694	+	0.335420i	0.132735	+	0.0149556i	−0.0453470	+	0.998971i	$0.514439\pi$
$504$	13.7945	+	19.5937i	0.614457	+	0.872773i
$505$	5.16576	+	5.16576i	0.229873	+	0.229873i
$506$	−5.19218	+	24.7330i	−0.230821	+	1.09952i
$507$	25.0519	+	8.76602i	1.11259	+	0.389313i
$508$	1.13149	−	3.63654i	0.0502016	−	0.161345i
$509$	4.07185	−	17.8400i	0.180482	−	0.790742i	−0.800919	−	0.598772i	$-0.795655\pi$
$509$	4.07185	−	17.8400i	0.180482	−	0.790742i	0.981401	−	0.191969i	$-0.0614875\pi$
$510$	16.8874	−	17.4882i	0.747785	−	0.774388i
$511$	13.2820	+	21.1381i	0.587560	+	0.935096i
$512$	1.01963	+	22.6044i	0.0450616	+	0.998984i
$513$	−0.294812	−	1.29166i	−0.0130163	−	0.0570281i
$514$	−0.803644	+	1.33003i	−0.0354472	+	0.0586652i
$515$	12.0468	−	15.1062i	0.530845	−	0.665659i
$516$	29.5233	−	15.5111i	1.29969	−	0.682840i
$517$	2.64423	+	1.27340i	0.116293	+	0.0560038i
$518$	16.7877	+	20.3126i	0.737611	+	0.892484i
$519$	−2.61780	−	23.2336i	−0.114909	−	1.01984i
$520$	4.72429	−	1.93656i	0.207174	−	0.0849238i
$521$		−	16.9894i		−	0.744321i	−0.928168	−	0.372161i	$-0.878617\pi$
$521$		−	16.9894i		−	0.744321i	0.928168	−	0.372161i	$-0.121383\pi$
$522$	−19.6949	+	0.0383887i	−0.862021	+	0.00168023i
$523$		−	10.8616i		−	0.474943i	−0.971395	−	0.237471i	$-0.923681\pi$
$523$		−	10.8616i		−	0.474943i	0.971395	−	0.237471i	$-0.0763186\pi$
$524$	−9.92682	−	25.4764i	−0.433655	−	1.11294i
$525$	−2.73884	−	24.3078i	−0.119533	−	1.06088i
$526$	2.53916	−	2.09853i	0.110712	−	0.0915004i
$527$	21.2030	+	10.2108i	0.923617	+	0.444791i
$528$	−28.1091	−	49.2419i	−1.22329	−	2.14298i
$529$	8.80493	−	11.0410i	0.382823	−	0.480045i
$530$	10.4849	+	6.33529i	0.455435	+	0.275187i
$531$	−3.60689	−	15.8028i	−0.156526	−	0.685784i
$532$	−0.684752	+	8.84654i	−0.0296878	+	0.383546i
$533$	4.56170	+	7.25990i	0.197589	+	0.314461i
$534$	30.8368	+	29.7774i	1.33444	+	1.28860i
$535$	−4.70528	+	20.6152i	−0.203427	+	0.891273i
$536$	−3.05068	+	10.4447i	−0.131769	+	0.451143i
$537$	17.4908	+	6.12031i	0.754785	+	0.264111i
$538$	20.6313	+	4.33111i	0.889478	+	0.186727i
$539$	−15.8284	−	15.8284i	−0.681778	−	0.681778i
$540$	−1.49004	−	2.19704i	−0.0641213	−	0.0945454i
$541$	16.6052	+	1.87095i	0.713912	+	0.0804385i	0.461447	−	0.887168i	$-0.347330\pi$
$541$	16.6052	+	1.87095i	0.713912	+	0.0804385i	0.252465	+	0.967606i	$0.418759\pi$
$542$	5.98272	+	24.2506i	0.256980	+	1.04165i
$543$	18.6156	−	29.6265i	0.798871	−	1.27140i
$544$	16.7666	−	25.2691i	0.718863	−	1.08341i
$545$	4.90401	−	2.36165i	0.210065	−	0.101162i
$546$	6.09104	−	13.2349i	0.260672	−	0.566403i
$547$	−5.45356	+	4.34907i	−0.233177	+	0.185953i	−0.733107	−	0.680113i	$-0.761931\pi$
$547$	−5.45356	+	4.34907i	−0.233177	+	0.185953i	0.499930	+	0.866066i	$0.333359\pi$
$548$	−44.5867	+	6.60870i	−1.90465	+	0.282310i
$549$	10.5414	+	30.1256i	0.449896	+	1.28573i
$550$	0.468241	+	26.7919i	0.0199659	+	1.14241i
$551$	−5.63043	−	4.63494i	−0.239864	−	0.197455i
$552$	−1.04376	−	19.8911i	−0.0444253	−	0.846621i
$553$	16.8888	−	5.90965i	0.718185	−	0.251304i
$554$	22.0074	−	2.86991i	0.935004	−	0.121931i
$555$	11.3718	+	14.2598i	0.482708	+	0.605296i
$556$	−17.3018	−	7.59919i	−0.733758	−	0.322277i
$557$	−13.1670	−	27.3416i	−0.557905	−	1.15850i	−0.969035	−	0.246925i	$-0.920580\pi$
$557$	−13.1670	−	27.3416i	−0.557905	−	1.15850i	0.411129	−	0.911577i	$-0.365134\pi$
$558$	−9.78917	+	12.7252i	−0.414409	+	0.538700i
$559$	−7.94836	−	4.99429i	−0.336180	−	0.211236i
$560$	5.15712	+	17.0145i	0.217928	+	0.718992i
$561$	−8.50823	+	75.5126i	−0.359218	+	3.18814i
$562$	−9.06122	+	5.91688i	−0.382224	+	0.249588i
$563$	−1.97550	+	1.97550i	−0.0832575	+	0.0832575i	−0.747509	−	0.664252i	$-0.768750\pi$
$563$	−1.97550	+	1.97550i	−0.0832575	+	0.0832575i	0.664252	+	0.747509i	$0.268750\pi$
$564$	−2.27176	−	0.435607i	−0.0956584	−	0.0183424i
$565$	0.0273031	−	0.0780279i	0.00114865	−	0.00328266i
$566$	−17.9209	−	5.92138i	−0.753272	−	0.248894i
$567$	−32.1639	−	7.34121i	−1.35076	−	0.308302i
$568$	−23.2564	+	25.8323i	−0.975819	+	1.08390i
$569$	8.20150	−	5.15334i	0.343825	−	0.216039i	−0.349039	−	0.937108i	$-0.613492\pi$
$569$	8.20150	−	5.15334i	0.343825	−	0.216039i	0.692863	+	0.721069i	$0.256349\pi$
$570$	−0.580859	+	6.11373i	−0.0243295	+	0.256076i
$571$	18.4067	−	4.20122i	0.770298	−	0.175815i	0.180728	−	0.983533i	$-0.442155\pi$
$571$	18.4067	−	4.20122i	0.770298	−	0.175815i	0.589570	+	0.807718i	$0.299297\pi$
$572$	−8.01364	+	13.8018i	−0.335067	+	0.577084i
$573$	−6.22515	−	4.96439i	−0.260059	−	0.207390i
$574$	−26.6687	+	13.4220i	−1.11313	+	0.560224i
$575$	−4.08428	+	8.48110i	−0.170326	+	0.353686i
$576$	14.5211	+	14.7361i	0.605046	+	0.614005i
$577$	31.8330	−	3.58672i	1.32523	−	0.149317i	0.579173	−	0.815205i	$-0.303376\pi$
$577$	31.8330	−	3.58672i	1.32523	−	0.149317i	0.746052	+	0.665888i	$0.231947\pi$
$578$	−15.5717	+	5.75611i	−0.647696	+	0.239423i
$579$	9.91040			0.411862
$580$	−13.8837	−	4.55741i	−0.576488	−	0.189236i
$581$	−10.5063			−0.435873
$582$	3.97349	−	1.46881i	0.164706	−	0.0608842i
$583$	−38.0509	+	4.28730i	−1.57591	+	0.177562i
$584$	14.3031	+	16.1240i	0.591866	+	0.667217i
$585$	2.02550	−	4.20600i	0.0837441	−	0.173897i
$586$	−41.5596	+	20.9164i	−1.71681	+	0.864049i
$587$	−0.356758	−	0.284505i	−0.0147250	−	0.0117428i	0.616100	−	0.787668i	$-0.288712\pi$
$587$	−0.356758	−	0.284505i	−0.0147250	−	0.0117428i	−0.630825	+	0.775925i	$0.717283\pi$
$588$	15.2574	+	8.85877i	0.629205	+	0.365329i
$589$	−5.79585	+	1.32286i	−0.238814	+	0.0545077i
$590$	1.13749	−	11.9724i	0.0468296	−	0.492897i
$591$	−37.9523	+	23.8470i	−1.56115	+	0.980934i
$592$	17.1721	+	14.9249i	0.705771	+	0.613409i
$593$	14.8290	+	3.38463i	0.608955	+	0.138990i	0.515868	−	0.856668i	$-0.327469\pi$
$593$	14.8290	+	3.38463i	0.608955	+	0.138990i	0.0930870	+	0.995658i	$0.470327\pi$
$594$	7.87891	+	2.60333i	0.323276	+	0.106816i
$595$	7.86975	−	22.4905i	0.322628	−	0.922019i
$596$	−2.46685	+	12.8650i	−0.101046	+	0.526972i
$597$	−4.95452	+	4.95452i	−0.202775	+	0.202775i
$598$	−4.69435	+	3.06536i	−0.191966	+	0.125352i
$599$	−3.68671	+	32.7205i	−0.150635	+	1.33692i	0.659953	+	0.751307i	$0.270576\pi$
$599$	−3.68671	+	32.7205i	−0.150635	+	1.33692i	−0.810588	+	0.585616i	$0.800852\pi$
$600$	−5.77202	−	20.3154i	−0.235642	−	0.829374i
$601$	22.3617	+	14.0508i	0.912155	+	0.573145i	0.904334	−	0.426825i	$-0.140368\pi$
$601$	22.3617	+	14.0508i	0.912155	+	0.573145i	0.00782019	+	0.999969i	$0.497511\pi$
$602$	19.9303	−	25.9080i	0.812300	−	1.05593i
$603$	4.31660	+	8.96352i	0.175786	+	0.365023i
$604$	−1.63598	+	3.72479i	−0.0665671	+	0.151560i
$605$	21.1224	+	26.4866i	0.858746	+	1.07683i
$606$	17.8468	−	2.32734i	0.724975	−	0.0945416i
$607$	−29.3456	+	10.2685i	−1.19110	+	0.416785i	−0.851787	−	0.523888i	$-0.824481\pi$
$607$	−29.3456	+	10.2685i	−1.19110	+	0.416785i	−0.339315	+	0.940673i	$0.610195\pi$
$608$	0.668508	+	7.63147i	0.0271116	+	0.309497i
$609$	−37.8436	+	17.5060i	−1.53350	+	0.709379i
$610$	0.413798	+	23.6768i	0.0167542	+	0.958644i
$611$	0.215042	+	0.614556i	0.00869968	+	0.0248623i
$612$	−4.06535	−	27.4276i	−0.164332	−	1.10869i
$613$	−19.6640	+	15.6815i	−0.794220	+	0.633369i	−0.934186	−	0.356787i	$-0.883872\pi$
$613$	−19.6640	+	15.6815i	−0.794220	+	0.633369i	0.139966	+	0.990156i	$0.455301\pi$
$614$	−3.45517	+	7.50758i	−0.139439	+	0.302981i
$615$	−18.6177	+	8.96580i	−0.750737	+	0.361536i
$616$	−45.2045	−	32.3247i	−1.82134	−	1.30240i
$617$	18.5673	−	29.5496i	0.747490	−	1.18962i	−0.228866	−	0.973458i	$-0.573502\pi$
$617$	18.5673	−	29.5496i	0.747490	−	1.18962i	0.976357	−	0.216166i	$-0.0693553\pi$
$618$	−11.4015	−	46.2151i	−0.458635	−	1.85904i
$619$	18.3917	+	2.07225i	0.739226	+	0.0832908i	0.473544	−	0.880770i	$-0.342974\pi$
$619$	18.3917	+	2.07225i	0.739226	+	0.0832908i	0.265682	+	0.964061i	$0.414403\pi$
$620$	−9.85841	+	6.68603i	−0.395923	+	0.268518i
$621$	2.06122	+	2.06122i	0.0827139	+	0.0827139i
$622$	−3.04532	−	0.639301i	−0.122106	−	0.0256336i
$623$	39.6573	+	13.8767i	1.58884	+	0.555958i
$624$	3.31509	−	12.1340i	0.132710	−	0.485749i
$625$	−0.172945	+	0.757720i	−0.00691778	+	0.0303088i
$626$	11.3785	+	10.9876i	0.454776	+	0.439153i
$627$	−10.2130	−	16.2539i	−0.407868	−	0.649118i
$628$	29.1439	+	2.25584i	1.16297	+	0.0900178i
$629$	−6.78514	−	29.7276i	−0.270541	−	1.18532i
$630$	13.9129	+	8.40658i	0.554303	+	0.334926i
$631$	20.2570	−	25.4015i	0.806419	−	1.01122i	−0.193129	−	0.981173i	$-0.561864\pi$
$631$	20.2570	−	25.4015i	0.806419	−	1.01122i	0.999549	−	0.0300445i	$-0.00956489\pi$
$632$	13.5480	−	7.42286i	0.538911	−	0.295266i
$633$	−37.9659	−	18.2834i	−1.50901	−	0.726701i
$634$	13.4873	−	11.1469i	0.535650	−	0.442698i
$635$	−0.289268	−	2.56733i	−0.0114793	−	0.101881i
$636$	28.1206	−	10.9571i	1.11505	−	0.434477i
$637$		−	4.96598i		−	0.196759i
$638$	43.0829	−	15.1697i	1.70567	−	0.600573i
$639$			31.7804i			1.25721i
$640$	6.79971	+	13.7615i	0.268782	+	0.543971i
$641$	−3.71681	−	32.9876i	−0.146805	−	1.30293i	−0.823773	−	0.566919i	$-0.808135\pi$
$641$	−3.71681	−	32.9876i	−0.146805	−	1.30293i	0.676968	−	0.736012i	$-0.263293\pi$
$642$	33.1867	+	40.1548i	1.30978	+	1.58479i
$643$	26.1204	+	12.5789i	1.03009	+	0.496064i	0.871043	−	0.491207i	$-0.163444\pi$
$643$	26.1204	+	12.5789i	1.03009	+	0.496064i	0.159045	+	0.987271i	$0.449158\pi$
$644$	−9.07993	−	17.2824i	−0.357800	−	0.681023i
$645$	14.1056	−	17.6879i	0.555408	−	0.696459i
$646$	5.30964	−	8.78745i	0.208905	−	0.345738i
$647$	0.928892	+	4.06974i	0.0365185	+	0.159998i	0.989899	−	0.141772i	$-0.0452798\pi$
$647$	0.928892	+	4.06974i	0.0365185	+	0.159998i	−0.953381	+	0.301770i	$0.902423\pi$
$648$	−28.4327	−	1.70157i	−1.11694	−	0.0668439i
$649$	20.0000	+	31.8298i	0.785068	+	1.24943i
$650$	−4.12937	+	4.27628i	−0.161967	+	0.167729i
$651$	−7.56350	+	33.1379i	−0.296437	+	1.29878i
$652$	−21.5419	−	6.70263i	−0.843646	−	0.262495i
$653$	−2.24407	−	0.785233i	−0.0878171	−	0.0307285i	0.286013	−	0.958226i	$-0.407670\pi$
$653$	−2.24407	−	0.785233i	−0.0878171	−	0.0307285i	−0.373830	+	0.927497i	$0.621956\pi$
$654$	2.75500	−	13.1235i	0.107729	−	0.513168i
$655$	−13.1155	−	13.1155i	−0.512463	−	0.512463i
$656$	−20.8146	+	15.2049i	−0.812672	+	0.593652i
$657$	19.5829	+	2.20647i	0.764003	+	0.0860825i
$658$	−2.20117	+	0.543038i	−0.0858104	+	0.0211698i
$659$	−9.83419	+	15.6510i	−0.383086	+	0.609677i	−0.981489	−	0.191518i	$-0.938659\pi$
$659$	−9.83419	+	15.6510i	−0.383086	+	0.609677i	0.598404	+	0.801195i	$0.295802\pi$
$660$	−30.8916	−	22.9162i	−1.20246	−	0.892010i
$661$	1.98958	−	0.958132i	0.0773857	−	0.0372670i	−0.394791	−	0.918771i	$-0.629183\pi$
$661$	1.98958	−	0.958132i	0.0773857	−	0.0372670i	0.472176	+	0.881504i	$0.343469\pi$
$662$	27.0973	+	12.4708i	1.05317	+	0.484692i
$663$	−13.1803	+	10.5109i	−0.511880	+	0.408211i
$664$	−8.94815	+	1.48655i	−0.347256	+	0.0576892i
$665$	1.98801	+	5.68140i	0.0770916	+	0.220315i
$666$	20.7989	−	0.363502i	0.805941	−	0.0140854i
$667$	15.9149	+	2.04387i	0.616228	+	0.0791390i
$668$	−1.06277	−	30.3957i	−0.0411199	−	1.17604i
$669$	−40.0816	+	14.0252i	−1.54965	+	0.542245i
$670$	0.954505	+	7.31945i	0.0368758	+	0.282775i
$671$	−46.1505	−	57.8709i	−1.78162	−	2.23408i
$672$	40.9704	+	15.4880i	1.58047	+	0.597462i
$673$	−8.26809	−	17.1689i	−0.318711	−	0.661811i	0.678646	−	0.734466i	$-0.262567\pi$
$673$	−8.26809	−	17.1689i	−0.318711	−	0.661811i	−0.997357	+	0.0726548i	$0.976853\pi$
$674$	22.2717	+	17.1330i	0.857873	+	0.659940i
$675$	2.61703	+	1.64439i	0.100730	+	0.0632926i
$676$	21.7083	−	5.75977i	0.834935	−	0.221529i
$677$	3.13527	−	27.8263i	0.120498	−	1.06945i	−0.777326	−	0.629098i	$-0.783424\pi$
$677$	3.13527	−	27.8263i	0.120498	−	1.06945i	0.897824	−	0.440354i	$-0.145147\pi$
$678$	−0.111350	−	0.170523i	−0.00427636	−	0.00654890i
$679$	2.93595	−	2.93595i	0.112671	−	0.112671i
$680$	3.52044	−	20.2686i	0.135003	−	0.777265i
$681$	−1.83208	+	5.23578i	−0.0702054	+	0.200636i
$682$	11.6815	−	35.3538i	0.447308	−	1.35377i
$683$	−16.9597	−	3.87094i	−0.648945	−	0.148117i	−0.114637	−	0.993407i	$-0.536571\pi$
$683$	−16.9597	−	3.87094i	−0.648945	−	0.148117i	−0.534308	+	0.845290i	$0.679428\pi$
$684$	5.12281	+	4.77668i	0.195875	+	0.182641i
$685$	−25.8900	+	16.2678i	−0.989207	+	0.621560i
$686$	−15.0711	−	1.43189i	−0.575419	−	0.0546699i
$687$	−5.40737	+	1.23420i	−0.206304	+	0.0470876i
$688$	13.3089	−	24.8857i	0.507396	−	0.948760i
$689$	−6.64156	−	5.29647i	−0.253023	−	0.201779i
$690$	−6.07450	−	12.0697i	−0.231252	−	0.459484i
$691$	−9.21194	+	19.1288i	−0.350439	+	0.727694i	−0.999453	−	0.0330829i	$-0.989467\pi$
$691$	−9.21194	+	19.1288i	−0.350439	+	0.727694i	0.649014	+	0.760777i	$0.275182\pi$
$692$	−12.8687	−	15.0280i	−0.489193	−	0.571277i
$693$	−50.4914	+	5.68902i	−1.91801	+	0.216108i
$694$	−8.19895	−	22.1802i	−0.311228	−	0.841947i
$695$	−12.8192			−0.486260
$696$	−29.7544	+	20.2644i	−1.12784	+	0.768119i
$697$	34.5464			1.30854
$698$	−1.94319	−	5.25680i	−0.0735509	−	0.198973i
$699$	23.8908	−	2.69184i	0.903632	−	0.101815i
$700$	−13.4636	−	15.7228i	−0.508878	−	0.594265i
$701$	−6.87657	+	14.2793i	−0.259724	+	0.539323i	−0.989529	−	0.144332i	$-0.953897\pi$
$701$	−6.87657	+	14.2793i	−0.259724	+	0.539323i	0.729805	+	0.683656i	$0.239611\pi$
$702$	0.827577	+	1.64434i	0.0312349	+	0.0620617i
$703$	6.02224	+	4.80257i	0.227133	+	0.181133i
$704$	−43.0743	−	21.1348i	−1.62342	−	0.796548i
$705$	−1.52983	+	0.349173i	−0.0576166	+	0.0131506i
$706$	25.8221	+	2.45333i	0.971826	+	0.0923322i
$707$	14.9363	−	9.38508i	0.561736	−	0.352962i
$708$	−21.6696	−	20.2054i	−0.814392	−	0.759367i
$709$	−9.00190	−	2.05463i	−0.338073	−	0.0771631i	0.0501140	−	0.998744i	$-0.484042\pi$
$709$	−9.00190	−	2.05463i	−0.338073	−	0.0771631i	−0.388187	+	0.921580i	$0.626899\pi$
$710$	−7.39764	+	22.3888i	−0.277629	+	0.840236i
$711$	4.66503	−	13.3319i	0.174952	−	0.499985i
$712$	35.7395	+	6.20758i	1.33940	+	0.232639i
$713$	9.24898	−	9.24898i	0.346377	−	0.346377i
$714$	−32.0950	−	49.1509i	−1.20113	−	1.83943i
$715$	−1.21219	+	10.7584i	−0.0453332	+	0.402343i
$716$	15.1564	−	4.02138i	0.566422	−	0.150286i
$717$	17.8007	+	11.1849i	0.664779	+	0.417708i
$718$	3.11219	+	2.39413i	0.116146	+	0.0893481i
$719$	−1.80570	−	3.74958i	−0.0673413	−	0.139836i	0.864581	−	0.502493i	$-0.167584\pi$
$719$	−1.80570	−	3.74958i	−0.0673413	−	0.139836i	−0.931922	+	0.362657i	$0.881869\pi$
$720$	13.0391	+	5.19131i	0.485937	+	0.193469i
$721$	−29.0886	−	36.4759i	−1.08331	−	1.35843i
$722$	−3.13923	−	24.0726i	−0.116830	−	0.895891i
$723$	−13.0932	+	4.58151i	−0.486942	+	0.170388i
$724$	−1.03461	−	29.5904i	−0.0384512	−	1.09972i
$725$	16.9337	−	1.64216i	0.628901	−	0.0609884i
$726$	83.4485	−	1.45843i	3.09706	−	0.0541273i
$727$	−2.68664	−	7.67798i	−0.0996421	−	0.284761i	0.883262	−	0.468880i	$-0.155342\pi$
$727$	−2.68664	−	7.67798i	−0.0996421	−	0.284761i	−0.982904	+	0.184119i	$0.941057\pi$
$728$	−2.02045	−	12.1620i	−0.0748829	−	0.450752i
$729$	−14.9378	+	11.9125i	−0.553251	+	0.441203i
$730$	13.2823	+	6.11282i	0.491599	+	0.226246i
$731$	−34.0768	+	16.4105i	−1.26038	+	0.606965i
$732$	46.8546	+	34.7579i	1.73179	+	1.28469i
$733$	−13.3022	+	21.1703i	−0.491328	+	0.781944i	−0.996718	−	0.0809466i	$-0.974206\pi$
$733$	−13.3022	+	21.1703i	−0.491328	+	0.781944i	0.505390	+	0.862891i	$0.331349\pi$
$734$	−1.84144	+	0.454292i	−0.0679689	+	0.0167682i
$735$	11.8930	+	1.34002i	0.438681	+	0.0494275i
$736$	−10.1787	−	13.4347i	−0.375191	−	0.495208i
$737$	−16.3149	−	16.3149i	−0.600966	−	0.600966i
$738$	−4.84205	+	23.0652i	−0.178238	+	0.849040i
$739$	−30.6055	−	10.7093i	−1.12584	−	0.393949i	−0.297807	−	0.954626i	$-0.596255\pi$
$739$	−30.6055	−	10.7093i	−1.12584	−	0.393949i	−0.828034	+	0.560677i	$0.810541\pi$
$740$	14.7371	+	4.58536i	0.541747	+	0.168561i
$741$	0.947632	−	4.15185i	0.0348121	−	0.152522i
$742$	20.5475	−	21.2785i	0.754321	−	0.781157i
$743$	5.55297	+	8.83750i	0.203719	+	0.324217i	0.932921	−	0.360082i	$-0.117251\pi$
$743$	5.55297	+	8.83750i	0.203719	+	0.324217i	−0.729202	+	0.684299i	$0.760108\pi$
$744$	−1.75309	+	29.2936i	−0.0642715	+	1.07396i
$745$	1.97737	+	8.66344i	0.0724454	+	0.317404i
$746$	1.00046	−	1.65577i	0.0366295	−	0.0606219i
$747$	−5.17094	+	6.48416i	−0.189195	+	0.237243i
$748$	29.9077	+	56.9253i	1.09354	+	2.08139i
$749$	46.0019	+	22.1533i	1.68087	+	0.809466i
$750$	−23.5718	−	28.5211i	−0.860721	−	1.04144i
$751$	3.57577	+	31.7358i	0.130482	+	1.15806i	0.872823	+	0.488036i	$0.162287\pi$
$751$	3.57577	+	31.7358i	0.130482	+	1.15806i	−0.742342	+	0.670021i	$0.766285\pi$
$752$	−1.79789	+	0.773951i	−0.0655625	+	0.0282231i
$753$			12.5098i			0.455882i
$754$	9.13804	+	4.37873i	0.332788	+	0.159464i
$755$			2.75976i			0.100438i
$756$	−5.97264	+	2.32722i	−0.217223	+	0.0846402i
$757$	−1.78210	−	15.8166i	−0.0647717	−	0.574864i	−0.983620	−	0.180254i	$-0.942308\pi$
$757$	−1.78210	−	15.8166i	−0.0647717	−	0.574864i	0.918848	−	0.394611i	$-0.129121\pi$
$758$	−37.5801	+	31.0588i	−1.36497	+	1.12811i
$759$	38.0531	+	18.3254i	1.38124	+	0.665170i
$760$	2.49705	+	4.55755i	0.0905776	+	0.165320i
$761$	−24.9327	+	31.2647i	−0.903811	+	1.13334i	0.0867441	+	0.996231i	$0.472354\pi$
$761$	−24.9327	+	31.2647i	−0.903811	+	1.13334i	−0.990555	+	0.137113i	$0.956218\pi$
$762$	−5.44767	−	3.29164i	−0.197348	−	0.119244i
$763$	−2.92458	−	12.8134i	−0.105877	−	0.463877i
$764$	−6.71763	−	0.519968i	−0.243035	−	0.0188118i
$765$	−10.0071	−	15.9263i	−0.361809	−	0.575816i
$766$	3.58295	+	3.45987i	0.129457	+	0.125010i
$767$	−1.85573	+	8.13050i	−0.0670066	+	0.293575i
$768$	37.0859	+	7.39412i	1.33822	+	0.266812i
$769$	22.7352	+	7.95539i	0.819853	+	0.286879i	0.707432	−	0.706782i	$-0.249854\pi$
$769$	22.7352	+	7.95539i	0.819853	+	0.286879i	0.112421	+	0.993661i	$0.464139\pi$
$770$	−36.8947	−	7.74527i	−1.32959	−	0.279120i
$771$	1.83640	+	1.83640i	0.0661362	+	0.0661362i
$772$	6.94060	−	4.70716i	0.249798	−	0.169414i
$773$	24.9831	+	2.81492i	0.898580	+	0.101246i	0.549157	−	0.835719i	$-0.314949\pi$
$773$	24.9831	+	2.81492i	0.898580	+	0.101246i	0.349423	+	0.936965i	$0.386378\pi$
$774$	−6.18038	−	25.0518i	−0.222149	−	0.900467i
$775$	7.37861	−	11.7430i	0.265047	−	0.421820i
$776$	2.08513	−	2.91595i	0.0748518	−	0.104677i
$777$	39.6791	−	19.1085i	1.42348	−	0.685512i
$778$	10.4229	−	22.6475i	0.373680	−	0.811952i
$779$	−6.82295	+	5.44112i	−0.244458	+	0.194948i
$780$	−1.25111	−	8.44079i	−0.0447968	−	0.302229i
$781$	−24.3428	−	69.5676i	−0.871052	−	2.48932i
$782$	0.394737	+	22.5862i	0.0141158	+	0.807679i
$783$	1.25194	−	5.11752i	0.0447406	−	0.182885i
$784$	14.8930	−	1.04273i	0.531891	−	0.0372402i
$785$	18.7167	−	6.54927i	0.668029	−	0.233753i
$786$	−45.3115	+	5.90892i	−1.61621	+	0.210764i
$787$	15.5671	+	19.5205i	0.554907	+	0.695832i	0.977607	−	0.210438i	$-0.0674890\pi$
$787$	15.5671	+	19.5205i	0.554907	+	0.695832i	−0.422700	+	0.906270i	$0.638918\pi$
$788$	−15.2527	+	34.7271i	−0.543353	+	1.23710i
$789$	−2.38863	−	4.96005i	−0.0850376	−	0.176582i
$790$	6.38975	−	8.30620i	0.227337	−	0.295521i
$791$	−0.169015	−	0.106199i	−0.00600947	−	0.00377600i
$792$	−42.1985	+	11.9894i	−1.49946	+	0.426026i
$793$	1.83857	−	16.3178i	0.0652895	−	0.579460i
$794$	−43.1250	+	28.1602i	−1.53045	+	0.999368i
$795$	14.4767	−	14.4767i	0.513435	−	0.513435i
$796$	−1.11657	+	5.82308i	−0.0395757	+	0.206394i
$797$	−14.1924	+	40.5595i	−0.502720	+	1.43669i	0.360927	+	0.932594i	$0.382460\pi$
$797$	−14.1924	+	40.5595i	−0.502720	+	1.43669i	−0.863647	+	0.504097i	$0.831825\pi$
$798$	14.0802	+	4.65234i	0.498433	+	0.164691i
$799$	2.55758	+	0.583750i	0.0904806	+	0.0206516i
$800$	−13.6916	−	11.4861i	−0.484071	−	0.406093i
$801$	28.0828	−	17.6456i	0.992255	−	0.623475i
$802$	1.81334	−	19.0860i	0.0640314	−	0.673952i
$803$	−44.5574	+	10.1699i	−1.57239	+	0.358889i
$804$	15.7263	+	9.13102i	0.554624	+	0.322026i
$805$	−10.3542	−	8.25716i	−0.364936	−	0.291027i
$806$	7.37839	−	3.71345i	0.259893	−	0.130801i
$807$	15.2863	−	31.7423i	0.538103	−	1.11738i
$808$	11.3933	−	10.1066i	0.400814	−	0.355550i
$809$	−36.0729	+	4.06444i	−1.26826	+	0.142898i	−0.720331	−	0.693630i	$-0.756010\pi$
$809$	−36.0729	+	4.06444i	−1.26826	+	0.142898i	−0.547924	+	0.836528i	$0.684582\pi$
$810$	−18.1238	+	6.69950i	−0.636804	+	0.235396i
$811$	−7.59558			−0.266717			−0.133358	−	0.991068i	$-0.542576\pi$
$811$	−7.59558			−0.266717			−0.133358	+	0.991068i	$0.542576\pi$
$812$	−18.1883	+	30.2347i	−0.638286	+	1.06103i
$813$	41.7436			1.46401
$814$	−45.2506	+	16.7270i	−1.58603	+	0.586281i
$815$	−15.2082	+	1.71355i	−0.532719	+	0.0600230i
$816$	−34.2897	−	37.3206i	−1.20038	−	1.30648i
$817$	4.14552	−	8.60827i	0.145033	−	0.301165i
$818$	27.4498	−	13.8151i	0.959759	−	0.483035i
$819$	−8.81299	−	7.02812i	−0.307951	−	0.245583i
$820$	−8.78011	+	15.1219i	−0.306615	+	0.528081i
$821$	−3.23648	+	0.738705i	−0.112954	+	0.0257810i	−0.278624	−	0.960400i	$-0.589878\pi$
$821$	−3.23648	+	0.738705i	−0.112954	+	0.0257810i	0.165670	+	0.986181i	$0.447021\pi$
$822$	−7.12484	+	74.9913i	−0.248507	+	2.61562i
$823$	−18.4749	+	11.6085i	−0.643994	+	0.404648i	−0.814057	−	0.580785i	$-0.802746\pi$
$823$	−18.4749	+	11.6085i	−0.643994	+	0.404648i	0.170063	+	0.985433i	$0.445603\pi$
$824$	−29.9357	−	26.9507i	−1.04286	−	0.938872i
$825$	43.6597	+	9.96503i	1.52003	+	0.346938i
$826$	−27.5730	−	9.11061i	−0.959388	−	0.316999i
$827$	−9.91985	+	28.3493i	−0.344947	+	0.985802i	0.632489	+	0.774569i	$0.282033\pi$
$827$	−9.91985	+	28.3493i	−0.344947	+	0.985802i	−0.977436	+	0.211232i	$0.932252\pi$
$828$	−15.1351	−	2.90214i	−0.525983	−	0.100856i
$829$	11.3244	−	11.3244i	0.393313	−	0.393313i	−0.482554	−	0.875866i	$-0.660291\pi$
$829$	11.3244	−	11.3244i	0.393313	−	0.393313i	0.875866	+	0.482554i	$0.160291\pi$
$830$	−5.15219	+	3.36432i	−0.178835	+	0.116777i
$831$	4.15287	−	36.8578i	0.144062	−	1.27858i
$832$	−3.44163	−	10.0724i	−0.119317	−	0.349199i
$833$	−16.9418	−	10.6453i	−0.587000	−	0.368837i
$834$	−19.2562	+	25.0317i	−0.666789	+	0.866777i
$835$	−8.95193	−	18.5889i	−0.309794	−	0.643294i
$836$	−14.8727	−	6.53229i	−0.514382	−	0.225924i
$837$	−2.67770	−	3.35774i	−0.0925550	−	0.116060i
$838$	−46.6156	+	6.07899i	−1.61031	+	0.209995i
$839$	46.2406	−	16.1803i	1.59640	−	0.558606i	0.621923	−	0.783078i	$-0.286352\pi$
$839$	46.2406	−	16.1803i	1.59640	−	0.558606i	0.974480	+	0.224473i	$0.0720659\pi$
$840$	29.6719	−	1.55699i	1.02378	−	0.0537213i
$841$	−11.7654	−	26.5062i	−0.405702	−	0.914005i
$842$	0.669101	+	38.2847i	0.0230587	+	1.31938i
$843$	5.97346	+	17.0712i	0.205737	+	0.587962i
$844$	−35.2730	+	5.22821i	−1.21415	+	0.179962i
$845$	11.9118	−	9.49936i	0.409779	−	0.326788i
$846$	−0.748218	+	1.62577i	−0.0257243	+	0.0558950i
$847$	73.7011	−	35.4926i	2.53240	−	1.21954i
$848$	14.4895	−	21.0301i	0.497572	−	0.722177i
$849$	−16.7817	+	26.7079i	−0.575946	+	0.916613i
$850$	5.73698	+	23.2545i	0.196777	+	0.797622i
$851$	−16.8411	−	1.89753i	−0.577305	−	0.0650466i
$852$	32.6057	+	48.0763i	1.11705	+	1.64707i
$853$	40.3424	+	40.3424i	1.38130	+	1.38130i	0.842318	+	0.538981i	$0.181190\pi$
$853$	40.3424	+	40.3424i	1.38130	+	1.38130i	0.538981	+	0.842318i	$0.318810\pi$
$854$	55.9596	+	11.7476i	1.91490	+	0.401993i
$855$	4.48485	+	1.56932i	0.153379	+	0.0536695i
$856$	42.3143	+	12.3591i	1.44627	+	0.422425i
$857$	−1.70941	+	7.48940i	−0.0583922	+	0.255833i	−0.995696	−	0.0926808i	$-0.970456\pi$
$857$	−1.70941	+	7.48940i	−0.0583922	+	0.255833i	0.937304	+	0.348514i	$0.113314\pi$
$858$	19.1868	+	18.5277i	0.655028	+	0.632526i
$859$	−19.2950	−	30.7078i	−0.658337	−	1.04774i	−0.994378	−	0.105890i	$-0.966231\pi$
$859$	−19.2950	−	30.7078i	−0.658337	−	1.04774i	0.336041	−	0.941848i	$-0.390912\pi$
$860$	1.47741	−	19.0872i	0.0503794	−	0.650868i
$861$	11.1029	+	48.6451i	0.378387	+	1.65782i
$862$	−17.0005	−	10.2722i	−0.579040	−	0.349873i
$863$	5.47768	−	6.86880i	0.186463	−	0.233817i	−0.679810	−	0.733388i	$-0.737938\pi$
$863$	5.47768	−	6.86880i	0.186463	−	0.233817i	0.866273	+	0.499572i	$0.166509\pi$
$864$	−4.75760	+	2.82717i	−0.161857	+	0.0961822i
$865$	−12.0923	−	5.82336i	−0.411151	−	0.198000i
$866$	26.3327	−	21.7631i	0.894820	−	0.739541i
$867$	3.10646	+	27.5706i	0.105501	+	0.936347i
$868$	10.4426	+	26.8001i	0.354444	+	0.909653i
$869$			32.7569i			1.11120i
$870$	−12.9524	+	20.7031i	−0.439128	+	0.701902i
$871$		−	5.11860i		−	0.173437i
$872$	−4.30385	−	10.4994i	−0.145747	−	0.355554i
$873$	−0.366975	−	3.25699i	−0.0124202	−	0.110232i
$874$	−3.63533	−	4.39862i	−0.122967	−	0.148786i
$875$	−32.6742	−	15.7350i	−1.10459	−	0.531942i
$876$	31.8882	−	16.7536i	1.07740	−	0.566052i
$877$	−23.9137	+	29.9868i	−0.807507	+	1.01258i	0.192006	+	0.981394i	$0.438501\pi$
$877$	−23.9137	+	29.9868i	−0.807507	+	1.01258i	−0.999514	+	0.0311883i	$0.990071\pi$
$878$	20.1471	−	33.3435i	0.679932	−	1.12529i
$879$	17.3024	+	75.8069i	0.583597	+	2.55690i
$880$	−32.5190	−	1.37634i	−1.09622	−	0.0463965i
$881$	23.8183	+	37.9066i	0.802458	+	1.27710i	0.957280	+	0.289162i	$0.0933768\pi$
$881$	23.8183	+	37.9066i	0.802458	+	1.27710i	−0.154822	+	0.987942i	$0.549480\pi$
$882$	9.48198	−	9.81931i	0.319275	−	0.330633i
$883$	6.84148	−	29.9745i	0.230234	−	1.00872i	−0.719212	−	0.694791i	$-0.755497\pi$
$883$	6.84148	−	29.9745i	0.230234	−	1.00872i	0.949446	−	0.313931i	$-0.101646\pi$
$884$	−4.23823	+	13.6214i	−0.142547	+	0.458139i
$885$	−18.9710	−	6.63823i	−0.637703	−	0.223142i
$886$	6.59315	−	31.4066i	0.221501	−	1.05512i
$887$	36.2012	+	36.2012i	1.21552	+	1.21552i	0.969186	+	0.246330i	$0.0792247\pi$
$887$	36.2012	+	36.2012i	1.21552	+	1.21552i	0.246330	+	0.969186i	$0.420775\pi$
$888$	31.0910	−	21.8889i	1.04334	−	0.734544i
$889$	−6.19915	−	0.698476i	−0.207913	−	0.0234261i
$890$	23.8913	−	5.89409i	0.800838	−	0.197570i
$891$	32.1334	−	51.1400i	1.07651	−	1.71325i
$892$	−21.4090	+	28.8600i	−0.716827	+	0.966303i
$893$	−0.597067	+	0.287532i	−0.0199801	+	0.00962190i
$894$	19.8872	+	9.15256i	0.665126	+	0.306107i
$895$	8.31665	−	6.63231i	0.277995	−	0.221694i
$896$	36.0494	−	8.61301i	1.20433	−	0.287740i
$897$	3.09467	+	8.84406i	0.103328	+	0.295294i
$898$	−2.67559	+	0.0467612i	−0.0892856	+	0.00156044i
$899$	−22.9630	−	5.61762i	−0.765859	−	0.187358i
$900$	−16.3301	+	0.570977i	−0.544338	+	0.0190326i
$901$	−32.3064	+	11.3045i	−1.07628	+	0.376608i
$902$	−7.06788	−	54.1987i	−0.235335	−	1.80462i
$903$	−34.0599	−	42.7097i	−1.13344	−	1.42129i
$904$	−0.158976	−	0.0665353i	−0.00528746	−	0.00221293i
$905$	−8.71476	−	18.0964i	−0.289688	−	0.601544i
$906$	5.38892	+	4.14556i	0.179035	+	0.137727i
$907$	−19.5641	−	12.2930i	−0.649616	−	0.408181i	0.166522	−	0.986038i	$-0.446746\pi$
$907$	−19.5641	−	12.2930i	−0.649616	−	0.408181i	−0.816138	+	0.577857i	$0.803889\pi$
$908$	1.20378	+	4.53699i	0.0399488	+	0.150565i
$909$	1.55910	−	13.8374i	0.0517120	−	0.458956i
$910$	−4.57265	−	7.00264i	−0.151582	−	0.232135i
$911$	15.7666	−	15.7666i	0.522371	−	0.522371i	−0.395916	−	0.918287i	$-0.629573\pi$
$911$	15.7666	−	15.7666i	0.522371	−	0.522371i	0.918287	+	0.395916i	$0.129573\pi$
$912$	12.6503	+	1.97016i	0.418894	+	0.0652386i
$913$	6.35259	−	18.1547i	0.210240	−	0.600832i
$914$	−6.87825	+	20.8168i	−0.227512	+	0.688560i
$915$	38.5833	+	8.80638i	1.27552	+	0.291130i
$916$	−3.20076	+	3.43270i	−0.105756	+	0.113420i
$917$	−37.9220	+	23.8280i	−1.25230	+	0.786869i
$918$	7.38383	+	0.701530i	0.243703	+	0.0231539i
$919$	47.5748	−	10.8586i	1.56935	−	0.358194i	0.652614	−	0.757690i	$-0.273672\pi$
$919$	47.5748	−	10.8586i	1.56935	−	0.358194i	0.916735	+	0.399497i	$0.130815\pi$
$920$	−9.98693	−	5.56758i	−0.329259	−	0.183558i
$921$	10.7986	+	8.61161i	0.355826	+	0.283762i
$922$	−10.3757	−	20.6159i	−0.341707	−	0.678949i
$923$	7.09439	−	14.7317i	0.233515	−	0.484898i
$924$	−70.5450	+	60.4088i	−2.32076	+	1.98730i
$925$	−17.8565	+	2.01195i	−0.587120	+	0.0661525i
$926$	16.3743	+	44.2963i	0.538091	+	1.45567i
$927$	−36.8286			−1.20961
$928$	−11.2130	+	28.3243i	−0.368085	+	0.929792i
$929$	17.7945			0.583820			0.291910	−	0.956446i	$-0.405709\pi$
$929$	17.7945			0.583820			0.291910	+	0.956446i	$0.405709\pi$
$930$	6.90236	+	18.6726i	0.226337	+	0.612297i
$931$	5.02269	−	0.565921i	0.164612	−	0.0185473i
$932$	15.4530	−	13.2326i	0.506180	−	0.433449i
$933$	−2.25636	+	4.68539i	−0.0738700	+	0.153393i
$934$	−7.61012	−	15.1208i	−0.249011	−	0.494768i
$935$	34.1048	+	27.1977i	1.11535	+	0.889458i
$936$	−8.50043	−	4.73888i	−0.277845	−	0.154895i
$937$	23.7318	−	5.41664i	0.775285	−	0.176954i	0.183468	−	0.983026i	$-0.441268\pi$
$937$	23.7318	−	5.41664i	0.775285	−	0.176954i	0.591818	+	0.806072i	$0.298411\pi$
$938$	17.7435	+	1.68579i	0.579347	+	0.0550431i
$939$	22.3832	−	14.0643i	0.730447	−	0.458970i
$940$	−0.905544	+	0.971162i	−0.0295356	+	0.0316758i
$941$	−55.4467	−	12.6554i	−1.80751	−	0.412553i	−0.820295	−	0.571940i	$-0.806191\pi$
$941$	−55.4467	−	12.6554i	−1.80751	−	0.412553i	−0.987216	+	0.159388i	$0.949048\pi$
$942$	15.3266	−	46.3856i	0.499368	−	1.51132i
$943$	6.34169	−	18.1235i	0.206514	−	0.590182i
$944$	−24.7730	−	3.85814i	−0.806291	−	0.125572i
$945$	−3.07476	+	3.07476i	−0.100022	+	0.100022i
$946$	32.7178	+	50.1046i	1.06375	+	1.62904i
$947$	−1.70840	+	15.1625i	−0.0555155	+	0.492714i	0.934932	+	0.354826i	$0.115460\pi$
$947$	−1.70840	+	15.1625i	−0.0555155	+	0.492714i	−0.990448	+	0.137888i	$0.955969\pi$
$948$	−6.62099	−	24.9542i	−0.215040	−	0.810475i
$949$	−8.58503	−	5.39433i	−0.278682	−	0.175107i
$950$	−4.79569	−	3.68920i	−0.155593	−	0.119694i
$951$	−12.6878	−	26.3465i	−0.411430	−	0.854343i
$952$	−45.8226	−	19.1779i	−1.48512	−	0.621559i
$953$	29.9243	+	37.5239i	0.969343	+	1.21552i	0.976494	+	0.215544i	$0.0691524\pi$
$953$	29.9243	+	37.5239i	0.969343	+	1.21552i	−0.00715083	+	0.999974i	$0.502276\pi$
$954$	−3.01945	−	23.1541i	−0.0977582	−	0.749641i
$955$	−4.31418	+	1.50960i	−0.139604	+	0.0488494i
$956$	17.7790	−	0.621634i	0.575013	−	0.0201051i
$957$	−7.36807	−	75.9782i	−0.238176	−	2.45603i
$958$	−36.6766	+	0.640995i	−1.18497	+	0.0207096i
$959$	24.3850	+	69.6883i	0.787432	+	2.25035i
$960$	25.0512	−	5.52441i	0.808523	−	0.178299i
$961$	9.17015	−	7.31295i	0.295811	−	0.235902i
$962$	−9.72239	−	4.47448i	−0.313462	−	0.144263i
$963$	36.3135	−	17.4877i	1.17019	−	0.563532i
$964$	−6.99355	+	9.42750i	−0.225247	+	0.303639i
$965$	3.02672	−	4.81700i	0.0974336	−	0.155065i
$966$	−31.6769	+	7.81485i	−1.01919	+	0.251439i
$967$	−41.9356	−	4.72501i	−1.34856	−	0.151946i	−0.592035	−	0.805912i	$-0.701675\pi$
$967$	−41.9356	−	4.72501i	−1.34856	−	0.151946i	−0.756524	+	0.653966i	$0.773104\pi$
$968$	57.7492	−	40.6571i	1.85613	−	1.30677i
$969$	−12.1330	−	12.1330i	−0.389767	−	0.389767i
$970$	0.499615	−	2.37992i	0.0160417	−	0.0764147i
$971$	−19.6281	−	6.86817i	−0.629895	−	0.220410i	−0.00359722	−	0.999994i	$-0.501145\pi$
$971$	−19.6281	−	6.86817i	−0.629895	−	0.220410i	−0.626298	+	0.779584i	$0.715431\pi$
$972$	−12.3986	+	39.8485i	−0.397686	+	1.27814i
$973$	−6.88783	+	30.1776i	−0.220814	+	0.967448i
$974$	−4.09457	+	4.24023i	−0.131198	+	0.135866i
$975$	5.28565	+	8.41207i	0.169276	+	0.269402i
$976$	49.3229	+	2.08756i	1.57879	+	0.0668210i
$977$	1.47420	+	6.45891i	0.0471639	+	0.206639i	0.993020	−	0.117948i	$-0.0376318\pi$
$977$	1.47420	+	6.45891i	0.0471639	+	0.206639i	−0.945856	+	0.324587i	$0.894775\pi$
$978$	−19.4988	+	32.2706i	−0.623504	+	1.03190i
$979$	−47.9575	+	60.1368i	−1.53273	+	1.92198i
$980$	8.96559	−	4.71039i	0.286395	−	0.150468i
$981$	−9.34750	−	4.50152i	−0.298443	−	0.143722i
$982$	−14.6728	−	17.7536i	−0.468227	−	0.566539i
$983$	−2.15147	−	19.0948i	−0.0686213	−	0.609031i	−0.980215	−	0.197938i	$-0.936576\pi$
$983$	−2.15147	−	19.0948i	−0.0686213	−	0.609031i	0.911593	−	0.411093i	$-0.134853\pi$
$984$	16.3392	+	39.8600i	0.520875	+	1.27069i
$985$			25.7300i			0.819825i
$986$	34.5270	−	21.7887i	1.09956	−	0.693895i
$987$			3.78897i			0.120604i
$988$	−1.30835	−	3.35778i	−0.0416241	−	0.106825i
$989$	2.35370	+	20.8896i	0.0748432	+	0.664252i
$990$	−22.9389	+	18.9583i	−0.729046	+	0.602534i
$991$	4.35015	+	2.09492i	0.138187	+	0.0665474i	0.501700	−	0.865042i	$-0.332708\pi$
$991$	4.35015	+	2.09492i	0.138187	+	0.0665474i	−0.363512	+	0.931589i	$0.618423\pi$
$992$	12.6859	+	21.3480i	0.402777	+	0.677800i
$993$	31.0820	−	38.9757i	0.986359	−	1.23686i
$994$	48.7305	+	29.4444i	1.54564	+	0.933919i
$995$	0.895017	+	3.92132i	0.0283739	+	0.124314i
$996$	−1.16989	+	15.1142i	−0.0370695	+	0.478913i
$997$	−23.2987	−	37.0796i	−0.737876	−	1.17432i	−0.979006	−	0.203831i	$-0.934661\pi$
$997$	−23.2987	−	37.0796i	−0.737876	−	1.17432i	0.241130	−	0.970493i	$-0.422482\pi$
$998$	−5.23989	−	5.05988i	−0.165866	−	0.160168i
$999$	−1.23824	+	5.42508i	−0.0391762	+	0.171642i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.l.b.11.7	✓	144
4.3	odd	2	inner	116.2.l.b.11.9	yes	144
29.8	odd	28	inner	116.2.l.b.95.9	yes	144
116.95	even	28	inner	116.2.l.b.95.7	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.l.b.11.7	✓	144	1.1	even	1	trivial
116.2.l.b.11.9	yes	144	4.3	odd	2	inner
116.2.l.b.95.7	yes	144	116.95	even	28	inner
116.2.l.b.95.9	yes	144	29.8	odd	28	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	116.2.l.b.11.7

Level	$116$
Weight	$2$
Character	116.11
Analytic conductor	$0.926$
Analytic rank	$0$
Dimension	$144$
Inner twists	$4$