LMFDB - Embedded newform 308.2.l.a.243.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(199,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("308.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			243.7
Character	$\chi$	$=$	308.243
Dual form			308.2.l.a.199.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18817 - 0.766974i) q^{2} +(0.968599 + 1.67766i) q^{3} +(0.823502 + 1.82259i) q^{4} +(2.62593 + 1.51608i) q^{5} +(0.135862 - 2.73624i) q^{6} +(1.13810 - 2.38846i) q^{7} +(0.419420 - 2.79716i) q^{8} +(-0.376366 + 0.651886i) q^{9} +(-1.95726 - 3.81539i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-2.26005 + 3.14692i) q^{12} -1.21076i q^{13} +(-3.18415 + 1.96500i) q^{14} +5.87390i q^{15} +(-2.64369 + 3.00182i) q^{16} +(2.50437 - 1.44590i) q^{17} +(0.947167 - 0.485889i) q^{18} +(-3.58654 + 6.21207i) q^{19} +(-0.600741 + 6.03450i) q^{20} +(5.10939 - 0.404100i) q^{21} +(-1.41247 - 0.0701333i) q^{22} +(-1.33152 - 0.768755i) q^{23} +(5.09893 - 2.00568i) q^{24} +(2.09701 + 3.63213i) q^{25} +(-0.928618 + 1.43859i) q^{26} +4.35340 q^{27} +(5.29041 + 0.107403i) q^{28} -9.30351 q^{29} +(4.50513 - 6.97920i) q^{30} +(-1.61750 - 2.80160i) q^{31} +(5.44347 - 1.53903i) q^{32} +(1.67766 + 0.968599i) q^{33} +(-4.08458 - 0.202811i) q^{34} +(6.60968 - 4.54646i) q^{35} +(-1.49806 - 0.149134i) q^{36} +(-3.02813 + 5.24488i) q^{37} +(9.02591 - 4.63022i) q^{38} +(2.03124 - 1.17274i) q^{39} +(5.34209 - 6.70927i) q^{40} -9.31403i q^{41} +(-6.38076 - 3.43863i) q^{42} +9.31576i q^{43} +(1.62447 + 1.16666i) q^{44} +(-1.97662 + 1.14120i) q^{45} +(0.992462 + 1.93466i) q^{46} +(0.0158873 - 0.0275176i) q^{47} +(-7.59671 - 1.52766i) q^{48} +(-4.40944 - 5.43662i) q^{49} +(0.294141 - 5.92394i) q^{50} +(4.85145 + 2.80099i) q^{51} +(2.20671 - 0.997060i) q^{52} +(0.0965971 + 0.167311i) q^{53} +(-5.17258 - 3.33894i) q^{54} +3.03216 q^{55} +(-6.20354 - 4.18522i) q^{56} -13.8957 q^{57} +(11.0542 + 7.13555i) q^{58} +(0.813975 + 1.40985i) q^{59} +(-10.7057 + 4.83717i) q^{60} +(2.93745 + 1.69594i) q^{61} +(-0.226882 + 4.56936i) q^{62} +(1.12866 + 1.64085i) q^{63} +(-7.64817 - 2.34637i) q^{64} +(1.83561 - 3.17936i) q^{65} +(-1.25046 - 2.43758i) q^{66} +(-6.71872 + 3.87905i) q^{67} +(4.69763 + 3.37374i) q^{68} -2.97846i q^{69} +(-11.3404 + 0.332522i) q^{70} -12.8729i q^{71} +(1.66557 + 1.32617i) q^{72} +(-13.1045 + 7.56586i) q^{73} +(7.62063 - 3.90932i) q^{74} +(-4.06232 + 7.03615i) q^{75} +(-14.2756 - 1.42115i) q^{76} +(-0.208600 - 2.63752i) q^{77} +(-3.31292 - 0.164496i) q^{78} +(8.49120 + 4.90240i) q^{79} +(-11.4931 + 3.87452i) q^{80} +(5.34580 + 9.25919i) q^{81} +(-7.14362 + 11.0667i) q^{82} -1.01001 q^{83} +(4.94410 + 8.97955i) q^{84} +8.76840 q^{85} +(7.14494 - 11.0687i) q^{86} +(-9.01137 - 15.6081i) q^{87} +(-1.03535 - 2.63212i) q^{88} +(-3.85204 - 2.22398i) q^{89} +(3.22384 + 0.160073i) q^{90} +(-2.89184 - 1.37797i) q^{91} +(0.304616 - 3.05990i) q^{92} +(3.13342 - 5.42725i) q^{93} +(-0.0399820 + 0.0205104i) q^{94} +(-18.8360 + 10.8750i) q^{95} +(7.85451 + 7.64160i) q^{96} -6.53865i q^{97} +(1.06942 + 9.84156i) q^{98} +0.752733i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38}+ \cdots + 78 q^{98}+O(q^{100}) $ 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.18817	−	0.766974i	−0.840164	−	0.542332i
$2$	−1.18817	−	0.766974i	−0.840164	−	0.542332i
$3$	0.968599	+	1.67766i	0.559221	+	0.968599i	0.997562	+	0.0697899i	$0.0222329\pi$
$3$	0.968599	+	1.67766i	0.559221	+	0.968599i	−0.438341	+	0.898809i	$0.644434\pi$
$4$	0.823502	+	1.82259i	0.411751	+	0.911296i
$5$	2.62593	+	1.51608i	1.17435	+	0.678013i	0.954701	−	0.297566i	$-0.0961748\pi$
$5$	2.62593	+	1.51608i	1.17435	+	0.678013i	0.219651	+	0.975579i	$0.429508\pi$
$6$	0.135862	−	2.73624i	0.0554654	−	1.11707i
$7$	1.13810	−	2.38846i	0.430163	−	0.902751i
$7$	1.13810	−	2.38846i	0.430163	−	0.902751i
$8$	0.419420	−	2.79716i	0.148287	−	0.988944i
$9$	−0.376366	+	0.651886i	−0.125455	+	0.217295i
$10$	−1.95726	−	3.81539i	−0.618940	−	1.20653i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	−2.26005	+	3.14692i	−0.652421	+	0.908437i
$13$		−	1.21076i		−	0.335803i	−0.985804	−	0.167902i	$-0.946301\pi$
$13$		−	1.21076i		−	0.335803i	0.985804	−	0.167902i	$-0.0536991\pi$
$14$	−3.18415	+	1.96500i	−0.850999	+	0.525168i
$15$			5.87390i			1.51663i
$16$	−2.64369	+	3.00182i	−0.660922	+	0.750454i
$17$	2.50437	−	1.44590i	0.607398	−	0.350682i	−0.164548	−	0.986369i	$-0.552617\pi$
$17$	2.50437	−	1.44590i	0.607398	−	0.350682i	0.771947	+	0.635687i	$0.219283\pi$
$18$	0.947167	−	0.485889i	0.223249	−	0.114525i
$19$	−3.58654	+	6.21207i	−0.822808	+	1.42515i	0.0807748	+	0.996732i	$0.474261\pi$
$19$	−3.58654	+	6.21207i	−0.822808	+	1.42515i	−0.903583	+	0.428413i	$0.859073\pi$
$20$	−0.600741	+	6.03450i	−0.134330	+	1.34936i
$21$	5.10939	−	0.404100i	1.11496	−	0.0881819i
$22$	−1.41247	−	0.0701333i	−0.301140	−	0.0149525i
$23$	−1.33152	−	0.768755i	−0.277642	−	0.160297i	0.354714	−	0.934975i	$-0.384578\pi$
$23$	−1.33152	−	0.768755i	−0.277642	−	0.160297i	−0.632355	+	0.774678i	$0.717912\pi$
$24$	5.09893	−	2.00568i	1.04082	−	0.409407i
$25$	2.09701	+	3.63213i	0.419402	+	0.726426i
$26$	−0.928618	+	1.43859i	−0.182117	+	0.282130i
$27$	4.35340			0.837812
$28$	5.29041	+	0.107403i	0.999794	+	0.0202973i
$29$	−9.30351			−1.72762			−0.863809	−	0.503819i	$-0.831928\pi$
$29$	−9.30351			−1.72762			−0.863809	+	0.503819i	$0.831928\pi$
$30$	4.50513	−	6.97920i	0.822520	−	1.27422i
$31$	−1.61750	−	2.80160i	−0.290512	−	0.503182i	0.683419	−	0.730027i	$-0.260492\pi$
$31$	−1.61750	−	2.80160i	−0.290512	−	0.503182i	−0.973931	+	0.226845i	$0.927159\pi$
$32$	5.44347	−	1.53903i	0.962279	−	0.272065i
$33$	1.67766	+	0.968599i	0.292043	+	0.168611i
$34$	−4.08458	−	0.202811i	−0.700500	−	0.0347818i
$35$	6.60968	−	4.54646i	1.11724	−	0.768492i
$36$	−1.49806	−	0.149134i	−0.249677	−	0.0248556i
$37$	−3.02813	+	5.24488i	−0.497822	+	0.862253i	−0.999997	−	0.00251320i	$-0.999200\pi$
$37$	−3.02813	+	5.24488i	−0.497822	+	0.862253i	0.502175	+	0.864766i	$0.332533\pi$
$38$	9.02591	−	4.63022i	1.46420	−	0.751120i
$39$	2.03124	−	1.17274i	0.325259	−	0.187788i
$40$	5.34209	−	6.70927i	0.844658	−	1.06083i
$41$		−	9.31403i		−	1.45461i	−0.686316	−	0.727303i	$-0.740773\pi$
$41$		−	9.31403i		−	1.45461i	0.686316	−	0.727303i	$-0.259227\pi$
$42$	−6.38076	−	3.43863i	−0.984573	−	0.530592i
$43$			9.31576i			1.42064i	0.703879	+	0.710320i	$0.251450\pi$
$43$			9.31576i			1.42064i	−0.703879	+	0.710320i	$0.748550\pi$
$44$	1.62447	+	1.16666i	0.244898	+	0.175881i
$45$	−1.97662	+	1.14120i	−0.294658	+	0.170121i
$46$	0.992462	+	1.93466i	0.146331	+	0.285250i
$47$	0.0158873	−	0.0275176i	0.00231740	−	0.00401385i	−0.864864	−	0.502006i	$-0.832596\pi$
$47$	0.0158873	−	0.0275176i	0.00231740	−	0.00401385i	0.867182	+	0.497992i	$0.165929\pi$
$48$	−7.59671	−	1.52766i	−1.09649	−	0.220499i
$49$	−4.40944	−	5.43662i	−0.629920	−	0.776660i
$50$	0.294141	−	5.92394i	0.0415978	−	0.837772i
$51$	4.85145	+	2.80099i	0.679339	+	0.392217i
$52$	2.20671	−	0.997060i	0.306016	−	0.138267i
$53$	0.0965971	+	0.167311i	0.0132686	+	0.0229820i	0.872583	−	0.488465i	$-0.162443\pi$
$53$	0.0965971	+	0.167311i	0.0132686	+	0.0229820i	−0.859315	+	0.511447i	$0.829110\pi$
$54$	−5.17258	−	3.33894i	−0.703900	−	0.454373i
$55$	3.03216			0.408857
$56$	−6.20354	−	4.18522i	−0.828983	−	0.559274i
$57$	−13.8957			−1.84053
$58$	11.0542	+	7.13555i	1.45148	+	0.936944i
$59$	0.813975	+	1.40985i	0.105970	+	0.183546i	0.914134	−	0.405412i	$-0.132872\pi$
$59$	0.813975	+	1.40985i	0.105970	+	0.183546i	−0.808164	+	0.588958i	$0.799538\pi$
$60$	−10.7057	+	4.83717i	−1.38210	+	0.624476i
$61$	2.93745	+	1.69594i	0.376102	+	0.217143i	0.676121	−	0.736791i	$-0.263660\pi$
$61$	2.93745	+	1.69594i	0.376102	+	0.217143i	−0.300019	+	0.953933i	$0.596993\pi$
$62$	−0.226882	+	4.56936i	−0.0288140	+	0.580309i
$63$	1.12866	+	1.64085i	0.142197	+	0.206727i
$64$	−7.64817	−	2.34637i	−0.956022	−	0.293296i
$65$	1.83561	−	3.17936i	0.227679	−	0.394351i
$66$	−1.25046	−	2.43758i	−0.153921	−	0.300046i
$67$	−6.71872	+	3.87905i	−0.820822	+	0.473902i	−0.850700	−	0.525652i	$-0.823821\pi$
$67$	−6.71872	+	3.87905i	−0.820822	+	0.473902i	0.0298779	+	0.999554i	$0.490488\pi$
$68$	4.69763	+	3.37374i	0.569672	+	0.409126i
$69$		−	2.97846i		−	0.358565i
$70$	−11.3404	+	0.332522i	−1.35544	+	0.0397440i
$71$		−	12.8729i		−	1.52773i	−0.645377	−	0.763864i	$-0.723300\pi$
$71$		−	12.8729i		−	1.52773i	0.645377	−	0.763864i	$-0.276700\pi$
$72$	1.66557	+	1.32617i	0.196289	+	0.156291i
$73$	−13.1045	+	7.56586i	−1.53376	+	0.885517i	−0.534577	+	0.845120i	$0.679529\pi$
$73$	−13.1045	+	7.56586i	−1.53376	+	0.885517i	−0.999184	+	0.0403969i	$0.987138\pi$
$74$	7.62063	−	3.90932i	0.885880	−	0.454449i
$75$	−4.06232	+	7.03615i	−0.469077	+	0.812465i
$76$	−14.2756	−	1.42115i	−1.63752	−	0.163017i
$77$	−0.208600	−	2.63752i	−0.0237722	−	0.300573i
$78$	−3.31292	−	0.164496i	−0.375114	−	0.0186255i
$79$	8.49120	+	4.90240i	0.955335	+	0.551563i	0.894734	−	0.446599i	$-0.147365\pi$
$79$	8.49120	+	4.90240i	0.955335	+	0.551563i	0.0606007	+	0.998162i	$0.480698\pi$
$80$	−11.4931	+	3.87452i	−1.28497	+	0.433184i
$81$	5.34580	+	9.25919i	0.593977	+	1.02880i
$82$	−7.14362	+	11.0667i	−0.788880	+	1.22211i
$83$	−1.01001			−0.110863			−0.0554315	−	0.998462i	$-0.517653\pi$
$83$	−1.01001			−0.110863			−0.0554315	+	0.998462i	$0.517653\pi$
$84$	4.94410	+	8.97955i	0.539446	+	0.979750i
$85$	8.76840			0.951066
$86$	7.14494	−	11.0687i	0.770459	−	1.19357i
$87$	−9.01137	−	15.6081i	−0.966120	−	1.67337i
$88$	−1.03535	−	2.63212i	−0.110369	−	0.280585i
$89$	−3.85204	−	2.22398i	−0.408316	−	0.235741i	0.281750	−	0.959488i	$-0.409085\pi$
$89$	−3.85204	−	2.22398i	−0.408316	−	0.235741i	−0.690066	+	0.723747i	$0.742418\pi$
$90$	3.22384	+	0.160073i	0.339823	+	0.0168732i
$91$	−2.89184	−	1.37797i	−0.303147	−	0.144450i
$92$	0.304616	−	3.05990i	0.0317584	−	0.319016i
$93$	3.13342	−	5.42725i	0.324921	−	0.562779i
$94$	−0.0399820	+	0.0205104i	−0.00412383	+	0.00211549i
$95$	−18.8360	+	10.8750i	−1.93253	+	1.11575i
$96$	7.85451	+	7.64160i	0.801648	+	0.779918i
$97$		−	6.53865i		−	0.663899i	−0.943297	−	0.331950i	$-0.892294\pi$
$97$		−	6.53865i		−	0.663899i	0.943297	−	0.331950i	$-0.107706\pi$
$98$	1.06942	+	9.84156i	0.108028	+	0.994148i
$99$			0.752733i			0.0756525i
$100$	−4.89300	+	6.81306i	−0.489300	+	0.681306i
$101$	9.70849	−	5.60520i	0.966031	−	0.557738i	0.0680070	−	0.997685i	$-0.478336\pi$
$101$	9.70849	−	5.60520i	0.966031	−	0.557738i	0.898024	+	0.439947i	$0.145003\pi$
$102$	−3.61607	−	7.04899i	−0.358045	−	0.697954i
$103$	7.04543	−	12.2030i	0.694207	−	1.20240i	−0.276240	−	0.961089i	$-0.589088\pi$
$103$	7.04543	−	12.2030i	0.694207	−	1.20240i	0.970447	−	0.241314i	$-0.0775782\pi$
$104$	−3.38667	−	0.507815i	−0.332091	−	0.0497954i
$105$	14.0295	+	6.68511i	1.36914	+	0.652400i
$106$	0.0135494	−	0.272882i	0.00131603	−	0.0265046i
$107$	−11.7622	−	6.79089i	−1.13709	−	0.656501i	−0.191383	−	0.981515i	$-0.561297\pi$
$107$	−11.7622	−	6.79089i	−1.13709	−	0.656501i	−0.945709	+	0.325015i	$0.894631\pi$
$108$	3.58503	+	7.93447i	0.344970	+	0.763495i
$109$	−4.07735	−	7.06218i	−0.390540	−	0.676434i	0.601981	−	0.798510i	$-0.294378\pi$
$109$	−4.07735	−	7.06218i	−0.390540	−	0.676434i	−0.992521	+	0.122076i	$0.961045\pi$
$110$	−3.60273	−	2.32559i	−0.343507	−	0.221736i
$111$	−11.7322			−1.11357
$112$	4.16091	+	9.73071i	0.393169	+	0.919466i
$113$	10.7208			1.00853			0.504265	−	0.863549i	$-0.331764\pi$
$113$	10.7208			1.00853			0.504265	+	0.863549i	$0.331764\pi$
$114$	16.5104	+	10.6576i	1.54634	+	0.998177i
$115$	−2.33099	−	4.03740i	−0.217366	−	0.376489i
$116$	−7.66146	−	16.9565i	−0.711349	−	1.57437i
$117$	0.789274	+	0.455688i	0.0729685	+	0.0421284i
$118$	0.114173	−	2.29943i	0.0105105	−	0.211680i
$119$	−0.603230	−	7.62715i	−0.0552980	−	0.699180i
$120$	16.4302	+	2.46363i	1.49987	+	0.224898i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−2.18945	−	4.26801i	−0.198224	−	0.386408i
$123$	15.6258	−	9.02155i	1.40893	−	0.813446i
$124$	3.77415	−	5.25517i	0.338929	−	0.471928i
$125$		−	2.44386i		−	0.218585i
$126$	−0.0825484	−	2.81526i	−0.00735400	−	0.250803i
$127$		−	4.53478i		−	0.402397i	−0.979551	−	0.201198i	$-0.935516\pi$
$127$		−	4.53478i		−	0.402397i	0.979551	−	0.201198i	$-0.0644836\pi$
$128$	7.28774	+	8.65384i	0.644151	+	0.764898i
$129$	−15.6287	+	9.02323i	−1.37603	+	0.794451i
$130$	−4.61950	+	2.36976i	−0.405157	+	0.207842i
$131$	−5.50659	+	9.53769i	−0.481113	+	0.833312i	−0.999765	−	0.0216735i	$-0.993101\pi$
$131$	−5.50659	+	9.53769i	−0.481113	+	0.833312i	0.518652	+	0.854985i	$0.326434\pi$
$132$	−0.383803	+	3.85534i	−0.0334058	+	0.335564i
$133$	10.7554	+	15.6363i	0.932610	+	1.35584i
$134$	10.9581	+	0.544102i	0.946637	+	0.0470032i
$135$	11.4317	+	6.60011i	0.983887	+	0.568047i
$136$	−2.99402	−	7.61155i	−0.256735	−	0.652685i
$137$	9.52910	+	16.5049i	0.814126	+	1.41011i	0.909954	+	0.414709i	$0.136117\pi$
$137$	9.52910	+	16.5049i	0.814126	+	1.41011i	−0.0958284	+	0.995398i	$0.530550\pi$
$138$	−2.28440	+	3.53892i	−0.194461	+	0.301253i
$139$	−5.12323			−0.434547			−0.217274	−	0.976111i	$-0.569716\pi$
$139$	−5.12323			−0.434547			−0.217274	+	0.976111i	$0.569716\pi$
$140$	13.7294	+	8.30273i	1.16035	+	0.701709i
$141$	0.0615535			0.00518374
$142$	−9.87315	+	15.2952i	−0.828537	+	1.28354i
$143$	−0.605378	−	1.04855i	−0.0506242	−	0.0876838i
$144$	−0.961846	−	2.85317i	−0.0801538	−	0.237764i
$145$	−24.4304	−	14.1049i	−2.02883	−	1.17135i
$146$	21.3732	+	1.06124i	1.76885	+	0.0878286i
$147$	4.84984	−	12.6634i	0.400008	−	1.04446i
$148$	−12.0530	−	1.19988i	−0.990747	−	0.0986299i
$149$	7.25957	−	12.5740i	0.594727	−	1.03010i	−0.398858	−	0.917013i	$-0.630593\pi$
$149$	7.25957	−	12.5740i	0.594727	−	1.03010i	0.993585	−	0.113085i	$-0.0360734\pi$
$150$	10.2233	−	5.24446i	0.834727	−	0.428208i
$151$	1.89507	−	1.09412i	0.154218	−	0.0890381i	−0.420905	−	0.907105i	$-0.638287\pi$
$151$	1.89507	−	1.09412i	0.154218	−	0.0890381i	0.575123	+	0.818067i	$0.304954\pi$
$152$	15.8719	+	12.6376i	1.28738	+	1.02504i
$153$			2.17675i			0.175980i
$154$	−1.77505	+	3.29381i	−0.143038	+	0.265423i
$155$		−	9.80907i		−	0.787883i
$156$	3.81015	+	2.73637i	0.305056	+	0.219085i
$157$	−11.5015	+	6.64040i	−0.917920	+	0.529961i	−0.882971	−	0.469428i	$-0.844460\pi$
$157$	−11.5015	+	6.64040i	−0.917920	+	0.529961i	−0.0349492	+	0.999389i	$0.511127\pi$
$158$	−6.32899	−	12.3374i	−0.503507	−	0.981512i
$159$	−0.187128	+	0.324115i	−0.0148402	+	0.0257040i
$160$	16.6275	+	4.21136i	1.31452	+	0.332937i
$161$	−3.35155	+	2.30536i	−0.264139	+	0.181688i
$162$	0.749837	−	15.1016i	0.0589127	−	1.18649i
$163$	1.69069	+	0.976119i	0.132425	+	0.0764555i	0.564749	−	0.825263i	$-0.308973\pi$
$163$	1.69069	+	0.976119i	0.132425	+	0.0764555i	−0.432324	+	0.901718i	$0.642306\pi$
$164$	16.9757	−	7.67012i	1.32558	−	0.598936i
$165$	2.93695	+	5.08695i	0.228641	+	0.396018i
$166$	1.20007	+	0.774652i	0.0931431	+	0.0601246i
$167$	7.16391			0.554360			0.277180	−	0.960818i	$-0.410600\pi$
$167$	7.16391			0.554360			0.277180	+	0.960818i	$0.410600\pi$
$168$	1.01265	−	14.4612i	0.0781274	−	1.11571i
$169$	11.5341			0.887236
$170$	−10.4184	−	6.72513i	−0.799051	−	0.515794i
$171$	−2.69970	−	4.67603i	−0.206452	−	0.357585i
$172$	−16.9788	+	7.67154i	−1.29462	+	0.584950i
$173$	13.2712	+	7.66210i	1.00899	+	0.582539i	0.910895	−	0.412638i	$-0.135393\pi$
$173$	13.2712	+	7.66210i	1.00899	+	0.582539i	0.0980921	+	0.995177i	$0.468726\pi$
$174$	−1.26399	+	25.4566i	−0.0958231	+	1.92986i
$175$	11.0618	−	0.874875i	0.836193	−	0.0661343i
$176$	−0.788593	+	3.92149i	−0.0594425	+	0.295594i
$177$	−1.57683	+	2.73115i	−0.118522	+	0.205286i
$178$	2.87115	+	5.59688i	0.215202	+	0.419504i
$179$	5.86211	−	3.38449i	0.438155	−	0.252969i	−0.264660	−	0.964342i	$-0.585260\pi$
$179$	5.86211	−	3.38449i	0.438155	−	0.252969i	0.702815	+	0.711373i	$0.251926\pi$
$180$	−3.70771	−	2.66280i	−0.276356	−	0.198473i
$181$		−	7.28989i		−	0.541853i	−0.962600	−	0.270927i	$-0.912670\pi$
$181$		−	7.28989i		−	0.541853i	0.962600	−	0.270927i	$-0.0873301\pi$
$182$	2.37913	+	3.85522i	0.176353	+	0.285768i
$183$			6.57073i			0.485723i
$184$	−2.70880	+	3.40205i	−0.199695	+	0.250802i
$185$	−15.9033	+	9.18180i	−1.16924	+	0.675059i
$186$	−7.88560	+	4.04524i	−0.578200	+	0.296612i
$187$	1.44590	−	2.50437i	0.105734	−	0.183137i
$188$	0.0632365	+	0.00629526i	0.00461200	+	0.000459129i
$189$	4.95462	−	10.3979i	0.360396	−	0.756336i
$190$	30.7212	+	1.52540i	2.22875	+	0.110664i
$191$	−5.49130	−	3.17040i	−0.397336	−	0.229402i	0.287998	−	0.957631i	$-0.407010\pi$
$191$	−5.49130	−	3.17040i	−0.397336	−	0.229402i	−0.685334	+	0.728229i	$0.740344\pi$
$192$	−3.47160	−	15.1037i	−0.250541	−	1.09002i
$193$	4.19927	+	7.27335i	0.302270	+	0.523547i	0.976650	−	0.214837i	$-0.0689222\pi$
$193$	4.19927	+	7.27335i	0.302270	+	0.523547i	−0.674380	+	0.738385i	$0.735589\pi$
$194$	−5.01497	+	7.76904i	−0.360054	+	0.557784i
$195$	7.11186			0.509291
$196$	6.27757	−	12.5137i	0.448398	−	0.893834i
$197$	2.51693			0.179324			0.0896620	−	0.995972i	$-0.471421\pi$
$197$	2.51693			0.179324			0.0896620	+	0.995972i	$0.471421\pi$
$198$	0.577326	−	0.894376i	0.0410288	−	0.0635605i
$199$	4.32482	+	7.49080i	0.306578	+	0.531009i	0.977611	−	0.210418i	$-0.0674826\pi$
$199$	4.32482	+	7.49080i	0.306578	+	0.531009i	−0.671033	+	0.741427i	$0.734149\pi$
$200$	11.0392	−	4.34228i	0.780587	−	0.307046i
$201$	−13.0155	−	7.51449i	−0.918041	−	0.530031i
$202$	−15.8344	−	0.786222i	−1.11410	−	0.0553184i
$203$	−10.5884	+	22.2210i	−0.743157	+	1.55961i
$204$	−1.10988	+	11.1488i	−0.0777071	+	0.780575i
$205$	14.1208	−	24.4580i	0.986242	−	1.70822i
$206$	−17.7306	+	9.09565i	−1.23535	+	0.633724i
$207$	1.00228	−	0.578667i	0.0696634	−	0.0402202i
$208$	3.63447	+	3.20086i	0.252005	+	0.221940i
$209$			7.17308i			0.496172i
$210$	−11.5422	−	18.7034i	−0.796487	−	1.29065i
$211$		−	8.11611i		−	0.558736i	−0.960184	−	0.279368i	$-0.909875\pi$
$211$		−	8.11611i		−	0.558736i	0.960184	−	0.279368i	$-0.0901249\pi$
$212$	−0.225392	+	0.313838i	−0.0154800	+	0.0215545i
$213$	21.5963	−	12.4686i	1.47976	−	0.854337i
$214$	8.76704	+	17.0900i	0.599302	+	1.16825i
$215$	−14.1235	+	24.4625i	−0.963212	+	1.66833i
$216$	1.82590	−	12.1771i	0.124237	−	0.828550i
$217$	−8.53238	+	0.674824i	−0.579215	+	0.0458100i
$218$	−0.571916	+	11.5183i	−0.0387351	+	0.780118i
$219$	−25.3859	−	14.6566i	−1.71542	−	0.990399i
$220$	2.49699	+	5.52640i	0.168347	+	0.372590i
$221$	−1.75063	−	3.03218i	−0.117760	−	0.203966i
$222$	13.9398	+	8.99828i	0.935581	+	0.603925i
$223$	−1.32883			−0.0889850			−0.0444925	−	0.999010i	$-0.514167\pi$
$223$	−1.32883			−0.0889850			−0.0444925	+	0.999010i	$0.514167\pi$
$224$	2.51933	−	14.7531i	0.168330	−	0.985731i
$225$	−3.15698			−0.210465
$226$	−12.7382	−	8.22259i	−0.847330	−	0.546958i
$227$	−4.94143	−	8.55881i	−0.327974	−	0.568068i	0.654135	−	0.756377i	$-0.273033\pi$
$227$	−4.94143	−	8.55881i	−0.327974	−	0.568068i	−0.982110	+	0.188309i	$0.939699\pi$
$228$	−11.4431	−	25.3261i	−0.757838	−	1.67726i
$229$	−12.2246	−	7.05790i	−0.807828	−	0.466399i	0.0383733	−	0.999263i	$-0.487782\pi$
$229$	−12.2246	−	7.05790i	−0.807828	−	0.466399i	−0.846201	+	0.532864i	$0.821116\pi$
$230$	−0.326960	+	6.58493i	−0.0215591	+	0.434197i
$231$	4.22281	−	2.90465i	0.277840	−	0.191112i
$232$	−3.90208	+	26.0234i	−0.256184	+	1.70852i
$233$	−11.5490	+	20.0034i	−0.756599	+	1.31047i	0.187977	+	0.982173i	$0.439807\pi$
$233$	−11.5490	+	20.0034i	−0.756599	+	1.31047i	−0.944576	+	0.328294i	$0.893526\pi$
$234$	−0.588293	−	1.14679i	−0.0384579	−	0.0749679i
$235$	0.0834378	−	0.0481728i	0.00544288	−	0.00314245i
$236$	−1.89926	+	2.64455i	−0.123632	+	0.172146i
$237$			18.9938i			1.23378i
$238$	−5.13309	+	9.52502i	−0.332729	+	0.617416i
$239$			5.79987i			0.375163i	0.982249	+	0.187581i	$0.0600648\pi$
$239$			5.79987i			0.375163i	−0.982249	+	0.187581i	$0.939935\pi$
$240$	−17.6324	−	15.5288i	−1.13816	−	1.00238i
$241$	−23.3005	+	13.4525i	−1.50092	+	0.866554i	−0.500917	+	0.865495i	$0.667004\pi$
$241$	−23.3005	+	13.4525i	−1.50092	+	0.866554i	−0.999999	+	0.00105905i	$0.999663\pi$
$242$	−1.25830	+	0.645500i	−0.0808869	+	0.0414943i
$243$	−3.82576	+	6.62641i	−0.245423	+	0.425085i
$244$	−0.672008	+	6.75039i	−0.0430209	+	0.432149i
$245$	−3.33651	−	20.9613i	−0.213162	−	1.33917i
$246$	−25.4854	−	1.26542i	−1.62489	−	0.0806804i
$247$	7.52129	+	4.34242i	0.478569	+	0.276302i
$248$	−8.51492	+	3.34936i	−0.540698	+	0.212685i
$249$	−0.978295	−	1.69446i	−0.0619969	−	0.107382i
$250$	−1.87438	+	2.90372i	−0.118546	+	0.183648i
$251$	−24.5604			−1.55024			−0.775121	−	0.631813i	$-0.782311\pi$
$251$	−24.5604			−1.55024			−0.775121	+	0.631813i	$0.782311\pi$
$252$	−2.06115	+	3.40832i	−0.129840	+	0.214704i
$253$	−1.53751			−0.0966625
$254$	−3.47806	+	5.38810i	−0.218233	+	0.338079i
$255$	8.49306	+	14.7104i	0.531856	+	0.921201i
$256$	−2.02181	−	15.8717i	−0.126363	−	0.991984i
$257$	14.6194	+	8.44052i	0.911933	+	0.526505i	0.881053	−	0.473018i	$-0.156835\pi$
$257$	14.6194	+	8.44052i	0.911933	+	0.526505i	0.0308807	+	0.999523i	$0.490169\pi$
$258$	25.4901	+	1.26566i	1.58695	+	0.0787964i
$259$	9.08083	+	13.2018i	0.564255	+	0.820319i
$260$	7.30631	+	0.727351i	0.453118	+	0.0451084i
$261$	3.50153	−	6.06483i	0.216739	−	0.375403i
$262$	13.8579	−	7.10900i	0.856146	−	0.439195i
$263$	−6.85759	+	3.95923i	−0.422857	+	0.244137i	−0.696299	−	0.717752i	$-0.745171\pi$
$263$	−6.85759	+	3.95923i	−0.422857	+	0.244137i	0.273442	+	0.961889i	$0.411838\pi$
$264$	3.41297	−	4.28643i	0.210054	−	0.263812i
$265$			0.585797i			0.0359852i
$266$	−0.786635	−	26.8277i	−0.0482317	−	1.64491i
$267$		−	8.61657i		−	0.527326i
$268$	−12.6028	−	9.05108i	−0.769839	−	0.552883i
$269$	−13.6178	+	7.86224i	−0.830292	+	0.479369i	−0.853953	−	0.520351i	$-0.825801\pi$
$269$	−13.6178	+	7.86224i	−0.830292	+	0.479369i	0.0236606	+	0.999720i	$0.492468\pi$
$270$	−8.52074	−	16.6099i	−0.518556	−	1.01085i
$271$	14.6813	−	25.4287i	0.891823	−	1.54468i	0.0541356	−	0.998534i	$-0.482760\pi$
$271$	14.6813	−	25.4287i	0.891823	−	1.54468i	0.837688	−	0.546150i	$-0.183907\pi$
$272$	−2.28045	+	11.3402i	−0.138273	+	0.687598i
$273$	−0.489267	−	6.18622i	−0.0296118	−	0.374407i
$274$	1.33661	−	26.9192i	0.0807478	−	1.62625i
$275$	3.63213	+	2.09701i	0.219026	+	0.126455i
$276$	5.42852	−	2.45277i	0.326759	−	0.147639i
$277$	11.6409	+	20.1627i	0.699435	+	1.21146i	0.968663	+	0.248380i	$0.0798982\pi$
$277$	11.6409	+	20.1627i	0.699435	+	1.21146i	−0.269228	+	0.963077i	$0.586768\pi$
$278$	6.08728	+	3.92939i	0.365091	+	0.235669i
$279$	2.43510			0.145785
$280$	−9.94493	−	20.3952i	−0.594323	−	1.21885i
$281$	−0.00517271			−0.000308578			−0.000154289	−	1.00000i	$-0.500049\pi$
$281$	−0.00517271			−0.000308578			−0.000154289		1.00000i	$0.500049\pi$
$282$	−0.0731362	−	0.0472100i	−0.00435519	−	0.00281131i
$283$	3.19534	+	5.53450i	0.189943	+	0.328992i	0.945231	−	0.326402i	$-0.105836\pi$
$283$	3.19534	+	5.53450i	0.189943	+	0.328992i	−0.755288	+	0.655393i	$0.772503\pi$
$284$	23.4620	−	10.6008i	1.39221	−	0.629043i
$285$	−36.4891	−	21.0670i	−2.16143	−	1.24790i
$286$	−0.0849143	+	1.71016i	−0.00502109	+	0.101124i
$287$	−22.2461	−	10.6003i	−1.31315	−	0.625718i
$288$	−1.04547	+	4.12776i	−0.0616047	+	0.243231i
$289$	−4.31876	+	7.48032i	−0.254045	+	0.440019i
$290$	18.2094	+	35.4965i	1.06929	+	2.08443i
$291$	10.9696	−	6.33333i	0.643052	−	0.371266i
$292$	−24.5810	−	17.6536i	−1.43850	−	1.03310i
$293$		−	22.3888i		−	1.30797i	−0.756507	−	0.653985i	$-0.773096\pi$
$293$		−	22.3888i		−	1.30797i	0.756507	−	0.653985i	$-0.226904\pi$
$294$	−15.4750	+	11.3266i	−0.902519	+	0.660583i
$295$			4.93621i			0.287397i
$296$	13.4007	+	10.6700i	0.778899	+	0.620179i
$297$	3.77015	−	2.17670i	0.218767	−	0.126305i
$298$	−18.2695	+	9.37210i	−1.05832	+	0.542911i
$299$	−0.930775	+	1.61215i	−0.0538281	+	0.0932330i
$300$	−16.1694	−	1.60968i	−0.933539	−	0.0929348i
$301$	22.2503	+	10.6023i	1.28248	+	0.611107i
$302$	−3.09083	−	0.153468i	−0.177857	−	0.00883110i
$303$	18.8073	+	10.8584i	1.08045	+	0.623797i
$304$	−9.16579	−	27.1889i	−0.525694	−	1.55939i
$305$	5.14236	+	8.90683i	0.294451	+	0.510004i
$306$	1.66951	−	2.58635i	0.0954395	−	0.147852i
$307$	27.8438			1.58913			0.794564	−	0.607181i	$-0.207700\pi$
$307$	27.8438			1.58913			0.794564	+	0.607181i	$0.207700\pi$
$308$	4.63533	−	2.55219i	0.264123	−	0.145425i
$309$	27.2968			1.55286
$310$	−7.52330	+	11.6549i	−0.427295	+	0.661951i
$311$	11.0264	+	19.0983i	0.625251	+	1.08297i	0.988492	+	0.151272i	$0.0483369\pi$
$311$	11.0264	+	19.0983i	0.625251	+	1.08297i	−0.363241	+	0.931695i	$0.618330\pi$
$312$	−2.42839	−	6.17356i	−0.137480	−	0.349509i
$313$	9.23866	+	5.33394i	0.522200	+	0.301492i	0.737834	−	0.674982i	$-0.235849\pi$
$313$	9.23866	+	5.33394i	0.522200	+	0.301492i	−0.215634	+	0.976474i	$0.569182\pi$
$314$	18.7588	+	0.931426i	1.05862	+	0.0525634i
$315$	0.476112	+	6.01989i	0.0268259	+	0.339182i
$316$	−1.94255	+	19.5131i	−0.109277	+	1.09770i
$317$	8.93799	−	15.4811i	0.502008	−	0.869503i	−0.497990	−	0.867183i	$-0.665928\pi$
$317$	8.93799	−	15.4811i	0.502008	−	0.869503i	0.999997	−	0.00231992i	$-0.000738453\pi$
$318$	0.470927	−	0.241582i	0.0264083	−	0.0135472i
$319$	−8.05708	+	4.65175i	−0.451110	+	0.260448i
$320$	−16.5263	−	17.7567i	−0.923848	−	0.992627i
$321$		−	26.3106i		−	1.46851i
$322$	5.75037	−	0.168611i	0.320455	−	0.00939632i
$323$			20.7431i			1.15417i
$324$	−12.4735	+	17.3682i	−0.692970	+	0.964898i
$325$	4.39762	−	2.53897i	0.243936	−	0.140837i
$326$	−1.26017	−	2.45651i	−0.0697943	−	0.136053i
$327$	7.89864	−	13.6808i	0.436796	−	0.756552i
$328$	−26.0528	−	3.90649i	−1.43852	−	0.215700i
$329$	−0.0476431	−	0.0692639i	−0.00262665	−	0.00381864i
$330$	0.411956	−	8.29673i	0.0226774	−	0.456720i
$331$	29.7644	+	17.1845i	1.63600	+	0.944545i	0.982191	+	0.187886i	$0.0601636\pi$
$331$	29.7644	+	17.1845i	1.63600	+	0.944545i	0.653810	+	0.756659i	$0.273170\pi$
$332$	−0.831745	−	1.84084i	−0.0456480	−	0.101029i
$333$	−2.27937	−	3.94799i	−0.124909	−	0.216349i
$334$	−8.51195	−	5.49453i	−0.465753	−	0.300647i
$335$	−23.5239			−1.28525
$336$	−12.2946	+	16.4058i	−0.670725	+	0.895008i
$337$	1.99597			0.108727			0.0543636	−	0.998521i	$-0.482687\pi$
$337$	1.99597			0.108727			0.0543636	+	0.998521i	$0.482687\pi$
$338$	−13.7045	−	8.84633i	−0.745424	−	0.481177i
$339$	10.3842	+	17.9859i	0.563990	+	0.976860i
$340$	7.22079	+	15.9812i	0.391602	+	0.866703i
$341$	−2.80160	−	1.61750i	−0.151715	−	0.0875927i
$342$	−0.378678	+	7.62652i	−0.0204766	+	0.412395i
$343$	−18.0035	+	4.34430i	−0.972099	+	0.234570i
$344$	26.0576	+	3.90721i	1.40493	+	0.210663i
$345$	4.51559	−	7.82123i	0.243111	−	0.421081i
$346$	−9.89177	−	19.2825i	−0.531785	−	1.03663i
$347$	21.1514	−	12.2118i	1.13547	−	0.655561i	0.190162	−	0.981753i	$-0.439099\pi$
$347$	21.1514	−	12.2118i	1.13547	−	0.655561i	0.945304	+	0.326191i	$0.105765\pi$
$348$	21.0264	−	29.2774i	1.12713	−	1.56943i
$349$			1.83470i			0.0982092i	0.998794	+	0.0491046i	$0.0156368\pi$
$349$			1.83470i			0.0982092i	−0.998794	+	0.0491046i	$0.984363\pi$
$350$	−13.8143	−	7.44461i	−0.738406	−	0.397931i
$351$		−	5.27090i		−	0.281340i
$352$	3.94467	−	4.05458i	0.210252	−	0.216110i
$353$	−3.34020	+	1.92847i	−0.177781	+	0.102642i	−0.586250	−	0.810130i	$-0.699396\pi$
$353$	−3.34020	+	1.92847i	−0.177781	+	0.102642i	0.408469	+	0.912772i	$0.366063\pi$
$354$	3.96826	−	2.03569i	0.210911	−	0.108195i
$355$	19.5163	−	33.8033i	1.03582	−	1.79409i
$356$	0.881242	−	8.85216i	0.0467057	−	0.469163i
$357$	12.2115	−	8.39966i	0.646301	−	0.444557i
$358$	−9.56101	−	0.474731i	−0.505315	−	0.0250903i
$359$	15.8124	+	9.12929i	0.834546	+	0.481825i	0.855407	−	0.517957i	$-0.173307\pi$
$359$	15.8124	+	9.12929i	0.834546	+	0.481825i	−0.0208606	+	0.999782i	$0.506641\pi$
$360$	2.36309	+	6.00757i	0.124546	+	0.316627i
$361$	−16.2265	−	28.1051i	−0.854027	−	1.47922i
$362$	−5.59116	+	8.66164i	−0.293865	+	0.455246i
$363$	1.93720			0.101676
$364$	0.130039	−	6.40540i	0.00681590	−	0.335734i
$365$	−45.8819			−2.40157
$366$	5.03958	−	7.80716i	0.263423	−	0.408087i
$367$	1.60190	+	2.77457i	0.0836185	+	0.144831i	0.904802	−	0.425833i	$-0.140019\pi$
$367$	1.60190	+	2.77457i	0.0836185	+	0.144831i	−0.821183	+	0.570665i	$0.806686\pi$
$368$	5.82780	−	1.96464i	0.303795	−	0.102414i
$369$	6.07168	+	3.50549i	0.316079	+	0.182488i
$370$	25.9381	+	1.28790i	1.34846	+	0.0669547i
$371$	0.509553	−	0.0403004i	0.0264547	−	0.00209229i
$372$	12.4720	+	1.24161i	0.646645	+	0.0643742i
$373$	−14.5880	+	25.2672i	−0.755341	+	1.30829i	0.189864	+	0.981810i	$0.439195\pi$
$373$	−14.5880	+	25.2672i	−0.755341	+	1.30829i	−0.945205	+	0.326478i	$0.894138\pi$
$374$	−3.63876	+	1.86665i	−0.188156	+	0.0965223i
$375$	4.09997	−	2.36712i	0.211722	−	0.122237i
$376$	−0.0703075	−	0.0559806i	−0.00362583	−	0.00288698i
$377$			11.2643i			0.580140i
$378$	−13.8619	+	8.55442i	−0.712977	+	0.439992i
$379$		−	2.04691i		−	0.105143i	−0.998617	−	0.0525714i	$-0.983258\pi$
$379$		−	2.04691i		−	0.105143i	0.998617	−	0.0525714i	$-0.0167417\pi$
$380$	−35.3321	−	25.3748i	−1.81250	−	1.30170i
$381$	7.60783	−	4.39238i	0.389761	−	0.225029i
$382$	4.09299	+	7.97867i	0.209415	+	0.408224i
$383$	−1.62742	+	2.81877i	−0.0831572	+	0.144033i	−0.904604	−	0.426252i	$-0.859834\pi$
$383$	−1.62742	+	2.81877i	−0.0831572	+	0.144033i	0.821447	+	0.570285i	$0.193167\pi$
$384$	−7.45932	+	20.6085i	−0.380657	+	1.05167i
$385$	3.45092	−	7.24219i	0.175875	−	0.369096i
$386$	0.589018	−	11.8627i	0.0299802	−	0.603797i
$387$	−6.07281	−	3.50614i	−0.308698	−	0.178227i
$388$	11.9173	−	5.38459i	0.605009	−	0.273361i
$389$	17.9495	+	31.0894i	0.910075	+	1.57630i	0.813957	+	0.580926i	$0.197309\pi$
$389$	17.9495	+	31.0894i	0.910075	+	1.57630i	0.0961181	+	0.995370i	$0.469357\pi$
$390$	−8.45011	−	5.45461i	−0.427888	−	0.276205i
$391$	−4.44616			−0.224852
$392$	−17.0565	+	10.0537i	−0.861483	+	0.507787i
$393$	−21.3347			−1.07619
$394$	−2.99055	−	1.93042i	−0.150662	−	0.0972532i
$395$	14.8649	+	25.7467i	0.747933	+	1.29546i
$396$	−1.37193	+	0.619877i	−0.0689418	+	0.0311500i
$397$	14.9710	+	8.64352i	0.751374	+	0.433806i	0.826190	−	0.563391i	$-0.190504\pi$
$397$	14.9710	+	8.64352i	0.751374	+	0.433806i	−0.0748161	+	0.997197i	$0.523837\pi$
$398$	0.606627	−	12.2174i	0.0304075	−	0.612402i
$399$	−15.8147	+	33.1892i	−0.791726	+	1.66154i
$400$	−16.4468	−	3.30738i	−0.822342	−	0.165369i
$401$	−7.06579	+	12.2383i	−0.352848	+	0.611151i	−0.986747	−	0.162265i	$-0.948120\pi$
$401$	−7.06579	+	12.2383i	−0.352848	+	0.611151i	0.633899	+	0.773416i	$0.281454\pi$
$402$	9.70120	+	18.9110i	0.483852	+	0.943197i
$403$	−3.39205	+	1.95840i	−0.168970	+	0.0975549i
$404$	18.2110	+	13.0787i	0.906029	+	0.650691i
$405$			32.4187i			1.61090i
$406$	29.6237	−	18.2814i	1.47020	−	0.907289i
$407$			6.05627i			0.300198i
$408$	9.86960	−	12.3955i	0.488618	−	0.613668i
$409$	27.7231	−	16.0059i	1.37082	−	0.791442i	0.379786	−	0.925074i	$-0.375998\pi$
$409$	27.7231	−	16.0059i	1.37082	−	0.791442i	0.991031	+	0.133633i	$0.0426643\pi$
$410$	−35.5366	+	18.2300i	−1.75503	+	0.900314i
$411$	−18.4597	+	31.9732i	−0.910552	+	1.57712i
$412$	28.0431	+	2.79172i	1.38159	+	0.137538i
$413$	4.29374	−	0.339591i	0.211281	−	0.0167102i
$414$	−1.63470	−	0.0811677i	−0.0803413	−	0.00398917i
$415$	−2.65222	−	1.53126i	−0.130192	−	0.0751665i
$416$	−1.86339	−	6.59071i	−0.0913603	−	0.323136i
$417$	−4.96236	−	8.59505i	−0.243008	−	0.420902i
$418$	5.50156	−	8.52284i	0.269090	−	0.416866i
$419$	−29.4416			−1.43832			−0.719159	−	0.694845i	$-0.755473\pi$
$419$	−29.4416			−1.43832			−0.719159	+	0.694845i	$0.755473\pi$
$420$	−0.630876	+	31.0754i	−0.0307836	+	1.51632i
$421$	−9.79886			−0.477567			−0.238784	−	0.971073i	$-0.576749\pi$
$421$	−9.79886			−0.477567			−0.238784	+	0.971073i	$0.576749\pi$
$422$	−6.22485	+	9.64333i	−0.303021	+	0.469430i
$423$	0.0119589	+	0.0207134i	0.000581460	+	0.00100712i
$424$	0.508510	−	0.200024i	0.0246954	−	0.00971401i
$425$	10.5034	+	6.06412i	0.509488	+	0.294153i
$426$	−35.2232	−	1.74893i	−1.70657	−	0.0847361i
$427$	7.39380	−	5.08582i	0.357811	−	0.246120i
$428$	2.69086	−	27.0300i	0.130068	−	1.30654i
$429$	1.17274	−	2.03124i	0.0566202	−	0.0980691i
$430$	35.5432	−	18.2334i	1.71405	−	0.879291i
$431$	−14.1926	+	8.19411i	−0.683634	+	0.394696i	−0.801223	−	0.598366i	$-0.795817\pi$
$431$	−14.1926	+	8.19411i	−0.683634	+	0.394696i	0.117589	+	0.993062i	$0.462484\pi$
$432$	−11.5090	+	13.0681i	−0.553729	+	0.628740i
$433$		−	10.9264i		−	0.525090i	−0.964920	−	0.262545i	$-0.915438\pi$
$433$		−	10.9264i		−	0.525090i	0.964920	−	0.262545i	$-0.0845619\pi$
$434$	10.6555	+	5.74230i	0.511480	+	0.275639i
$435$		−	54.6479i		−	2.62017i
$436$	9.51377	−	13.2471i	0.455627	−	0.634420i
$437$	9.55112	−	5.51434i	0.456892	−	0.263787i
$438$	18.9216	+	36.8848i	0.904109	+	1.76243i
$439$	−0.525692	+	0.910525i	−0.0250899	+	0.0434570i	−0.878298	−	0.478114i	$-0.841321\pi$
$439$	−0.525692	+	0.910525i	−0.0250899	+	0.0434570i	0.853208	+	0.521571i	$0.174654\pi$
$440$	1.27175	−	8.48144i	0.0606283	−	0.404337i
$441$	5.20362	−	0.828287i	0.247791	−	0.0394423i
$442$	−0.245555	+	4.94543i	−0.0116798	+	0.235230i
$443$	−20.2117	−	11.6692i	−0.960285	−	0.554421i	−0.0640244	−	0.997948i	$-0.520394\pi$
$443$	−20.2117	−	11.6692i	−0.960285	−	0.554421i	−0.896261	+	0.443527i	$0.853727\pi$
$444$	−9.66147	−	21.3830i	−0.458513	−	1.01479i
$445$	−6.74347	−	11.6800i	−0.319671	−	0.553687i
$446$	1.57888	+	1.01918i	0.0747620	+	0.0482595i
$447$	28.1265			1.33034
$448$	−14.3086	+	15.5969i	−0.676018	+	0.736885i
$449$	−14.8300			−0.699873			−0.349937	−	0.936773i	$-0.613797\pi$
$449$	−14.8300			−0.699873			−0.349937	+	0.936773i	$0.613797\pi$
$450$	3.75103	+	2.42132i	0.176825	+	0.114142i
$451$	−4.65701	−	8.06618i	−0.219290	−	0.379822i
$452$	8.82861	+	19.5397i	0.415263	+	0.919069i
$453$	3.67112	+	2.11952i	0.172484	+	0.0995838i
$454$	−0.693118	+	13.9593i	−0.0325296	+	0.655142i
$455$	−5.50465	−	8.00271i	−0.258062	−	0.375173i
$456$	−5.82812	+	38.8683i	−0.272927	+	1.82018i
$457$	−21.2467	+	36.8004i	−0.993880	+	1.72145i	−0.401277	+	0.915957i	$0.631434\pi$
$457$	−21.2467	+	36.8004i	−0.993880	+	1.72145i	−0.592603	+	0.805495i	$0.701900\pi$
$458$	9.11175	+	17.7620i	0.425764	+	0.829963i
$459$	10.9025	−	6.29457i	0.508886	−	0.293805i
$460$	5.43895	−	7.57325i	0.253593	−	0.353105i
$461$		−	18.6535i		−	0.868781i	−0.900725	−	0.434391i	$-0.856964\pi$
$461$		−	18.6535i		−	0.868781i	0.900725	−	0.434391i	$-0.143036\pi$
$462$	−7.24521	+	0.212443i	−0.337078	+	0.00988372i
$463$		−	2.38449i		−	0.110817i	−0.998464	−	0.0554083i	$-0.982354\pi$
$463$		−	2.38449i		−	0.110817i	0.998464	−	0.0554083i	$-0.0176460\pi$
$464$	24.5956	−	27.9274i	1.14182	−	1.29650i
$465$	16.4563	−	9.50105i	0.763143	−	0.440601i
$466$	29.0643	−	14.9097i	1.34638	−	0.690679i
$467$	8.66684	−	15.0114i	0.401053	−	0.694645i	−0.592800	−	0.805350i	$-0.701978\pi$
$467$	8.66684	−	15.0114i	0.401053	−	0.694645i	0.993853	+	0.110705i	$0.0353109\pi$
$468$	−0.180564	+	1.81379i	−0.00834659	+	0.0838423i
$469$	1.61834	+	20.4621i	0.0747282	+	0.944853i
$470$	−0.136086	−	0.00675704i	−0.00627716	−	0.000311679i
$471$	−22.2807	−	12.8638i	−1.02664	−	0.592731i
$472$	4.28496	−	1.68550i	0.197231	−	0.0775813i
$473$	4.65788	+	8.06768i	0.214170	+	0.370952i
$474$	14.5678	−	22.5679i	0.669120	−	1.03658i
$475$	−30.0840			−1.38035
$476$	13.4044	−	7.38042i	0.614391	−	0.338281i
$477$	−0.145424			−0.00665849
$478$	4.44835	−	6.89124i	0.203463	−	0.315198i
$479$	−14.2764	−	24.7274i	−0.652304	−	1.12982i	−0.982562	−	0.185933i	$-0.940469\pi$
$479$	−14.2764	−	24.7274i	−0.652304	−	1.12982i	0.330259	−	0.943890i	$-0.392864\pi$
$480$	9.04012	+	31.9744i	0.412623	+	1.45943i
$481$	6.35027	+	3.66633i	0.289547	+	0.167170i
$482$	38.0027	+	1.88694i	1.73098	+	0.0859479i
$483$	−7.11392	−	3.38980i	−0.323695	−	0.154241i
$484$	1.99016	+	0.198123i	0.0904619	+	0.00900558i
$485$	9.91313	−	17.1700i	0.450132	−	0.779652i
$486$	9.62795	−	4.93905i	0.436732	−	0.224040i
$487$	−4.39234	+	2.53592i	−0.199036	+	0.114913i	−0.596206	−	0.802832i	$-0.703326\pi$
$487$	−4.39234	+	2.53592i	−0.199036	+	0.114913i	0.397170	+	0.917745i	$0.369992\pi$
$488$	5.97583	−	7.50520i	0.270513	−	0.339745i
$489$			3.78187i			0.171022i
$490$	−12.1124	+	27.4646i	−0.547182	+	1.24072i
$491$			1.22666i			0.0553584i	0.999617	+	0.0276792i	$0.00881169\pi$
$491$			1.22666i			0.0553584i	−0.999617	+	0.0276792i	$0.991188\pi$
$492$	29.3105	+	21.0502i	1.32142	+	0.949016i
$493$	−23.2994	+	13.4519i	−1.04935	+	0.605844i
$494$	−5.60606	−	10.9282i	−0.252229	−	0.491682i
$495$	−1.14120	+	1.97662i	−0.0512933	+	0.0888427i
$496$	12.6861	+	2.55110i	0.569621	+	0.114548i
$497$	−30.7463	−	14.6507i	−1.37916	−	0.657172i
$498$	−0.137222	+	2.76363i	−0.00614907	+	0.123841i
$499$	−32.2699	−	18.6310i	−1.44460	−	0.834039i	−0.446447	−	0.894810i	$-0.647311\pi$
$499$	−32.2699	−	18.6310i	−1.44460	−	0.834039i	−0.998152	+	0.0607709i	$0.980644\pi$
$500$	4.45416	−	2.01252i	0.199196	−	0.0900028i
$501$	6.93895	+	12.0186i	0.310009	+	0.536952i
$502$	29.1820	+	18.8372i	1.30246	+	0.840746i
$503$	18.0021			0.802674			0.401337	−	0.915931i	$-0.368546\pi$
$503$	18.0021			0.802674			0.401337	+	0.915931i	$0.368546\pi$
$504$	5.06309	−	2.46882i	0.225528	−	0.109970i
$505$	33.9918			1.51261
$506$	1.82683	+	1.17923i	0.0812123	+	0.0524232i
$507$	11.1719	+	19.3503i	0.496161	+	0.859376i
$508$	8.26506	−	3.73440i	0.366703	−	0.165687i
$509$	−5.00347	−	2.88875i	−0.221775	−	0.128042i	0.384997	−	0.922918i	$-0.374203\pi$
$509$	−5.00347	−	2.88875i	−0.221775	−	0.128042i	−0.606772	+	0.794876i	$0.707536\pi$
$510$	1.19129	−	23.9924i	0.0527513	−	1.06240i
$511$	3.15648	+	39.9101i	0.139635	+	1.76552i
$512$	−9.77095	+	20.4090i	−0.431819	+	0.901960i
$513$	−15.6136	+	27.0436i	−0.689359	+	1.19400i
$514$	−10.8967	−	21.2415i	−0.480633	−	0.936922i
$515$	37.0017	−	21.3629i	1.63049	−	0.941363i
$516$	−29.3159	−	21.0541i	−1.29056	−	0.926855i
$517$		−	0.0317745i		−	0.00139744i
$518$	−0.664160	−	22.6507i	−0.0291815	−	0.995216i
$519$			29.6860i			1.30307i
$520$	−8.12328	−	6.46796i	−0.356230	−	0.283639i
$521$	−14.1393	+	8.16331i	−0.619453	+	0.357641i	−0.776656	−	0.629925i	$-0.783086\pi$
$521$	−14.1393	+	8.16331i	−0.619453	+	0.357641i	0.157203	+	0.987566i	$0.449752\pi$
$522$	−8.81198	+	4.52047i	−0.385690	+	0.197856i
$523$	4.29244	−	7.43472i	0.187695	−	0.325098i	−0.756786	−	0.653662i	$-0.773232\pi$
$523$	4.29244	−	7.43472i	0.187695	−	0.325098i	0.944481	+	0.328565i	$0.106565\pi$
$524$	−21.9180	−	2.18196i	−0.957493	−	0.0953194i
$525$	12.1822	+	17.7106i	0.531674	+	0.772952i
$526$	11.1846	+	0.555348i	0.487673	+	0.0242143i
$527$	−8.10164	−	4.67749i	−0.352913	−	0.203754i
$528$	−7.34277	+	2.47536i	−0.319553	+	0.107726i
$529$	−10.3180	−	17.8714i	−0.448610	−	0.777015i
$530$	0.449291	−	0.696027i	0.0195160	−	0.0302335i
$531$	−1.22541			−0.0531783
$532$	−19.6415	+	32.4792i	−0.851565	+	1.40815i
$533$	−11.2770			−0.488462
$534$	−6.60868	+	10.2380i	−0.285986	+	0.443040i
$535$	−20.5911	−	35.6648i	−0.890231	−	1.54193i
$536$	8.03236	+	20.4203i	0.346945	+	0.882021i
$537$	11.3561	+	6.55643i	0.490050	+	0.282931i
$538$	22.2104	+	1.10281i	0.957559	+	0.0475455i
$539$	−6.53700	−	2.50353i	−0.281568	−	0.107835i
$540$	−2.61527	+	26.2706i	−0.112543	+	1.13051i
$541$	6.74071	−	11.6752i	0.289806	−	0.501958i	−0.683958	−	0.729522i	$-0.739743\pi$
$541$	6.74071	−	11.6752i	0.289806	−	0.501958i	0.973763	+	0.227564i	$0.0730760\pi$
$542$	−36.9470	+	18.9535i	−1.58701	+	0.814122i
$543$	12.2300	−	7.06098i	0.524839	−	0.303016i
$544$	11.4072	−	11.7250i	0.489078	−	0.502705i
$545$		−	24.7264i		−	1.05916i
$546$	−4.16334	+	7.72554i	−0.178174	+	0.330623i
$547$			16.0797i			0.687517i	0.939058	+	0.343759i	$0.111700\pi$
$547$			16.0797i			0.687517i	−0.939058	+	0.343759i	$0.888300\pi$
$548$	−22.2344	+	30.9595i	−0.949808	+	1.32252i
$549$	−2.21112	+	1.27659i	−0.0943681	+	0.0544835i
$550$	−2.70724	−	5.27736i	−0.115437	−	0.225027i
$551$	33.3674	−	57.7940i	1.42150	−	2.46211i
$552$	−8.33122	−	1.24923i	−0.354600	−	0.0531706i
$553$	21.3730	−	14.7014i	0.908874	−	0.625168i
$554$	1.63283	−	32.8850i	0.0693724	−	1.39715i
$555$	−30.8079	−	17.7869i	−1.30772	−	0.755014i
$556$	−4.21899	−	9.33757i	−0.178925	−	0.396001i
$557$	−9.16076	−	15.8669i	−0.388154	−	0.672302i	0.604048	−	0.796948i	$-0.293554\pi$
$557$	−9.16076	−	15.8669i	−0.388154	−	0.672302i	−0.992201	+	0.124646i	$0.960220\pi$
$558$	−2.89331	−	1.86765i	−0.122484	−	0.0790641i
$559$	11.2791			0.477055
$560$	−3.82629	+	31.8605i	−0.161690	+	1.34635i
$561$	5.60198			0.236516
$562$	0.00614607	+	0.00396734i	0.000259256	+	0.000167352i
$563$	−9.92026	−	17.1824i	−0.418089	−	0.724152i	0.577658	−	0.816279i	$-0.303967\pi$
$563$	−9.92026	−	17.1824i	−0.418089	−	0.724152i	−0.995747	+	0.0921272i	$0.970633\pi$
$564$	0.0506895	+	0.112187i	0.00213441	+	0.00472393i
$565$	28.1521	+	16.2536i	1.18437	+	0.683796i
$566$	0.448200	−	9.02668i	0.0188393	−	0.379420i
$567$	28.1992	−	2.23027i	1.18426	−	0.0936626i
$568$	−36.0074	−	5.39914i	−1.51084	−	0.226543i
$569$	9.96780	−	17.2647i	0.417872	−	0.723775i	−0.577853	−	0.816141i	$-0.696109\pi$
$569$	9.96780	−	17.2647i	0.417872	−	0.723775i	0.995725	+	0.0923652i	$0.0294427\pi$
$570$	27.1974	+	53.0173i	1.13918	+	2.22065i
$571$	−28.6734	+	16.5546i	−1.19994	+	0.692788i	−0.960543	−	0.278132i	$-0.910285\pi$
$571$	−28.6734	+	16.5546i	−1.19994	+	0.692788i	−0.239402	+	0.970921i	$0.576951\pi$
$572$	1.41254	−	1.96684i	0.0590613	−	0.0822376i
$573$		−	12.2834i		−	0.513146i
$574$	18.3020	+	29.6572i	0.763912	+	1.23787i
$575$		−	6.44835i		−	0.268915i
$576$	4.40808	−	4.10264i	0.183670	−	0.170943i
$577$	9.06358	−	5.23286i	0.377322	−	0.217847i	−0.299331	−	0.954149i	$-0.596763\pi$
$577$	9.06358	−	5.23286i	0.377322	−	0.217847i	0.676652	+	0.736303i	$0.263430\pi$
$578$	10.8686	−	5.57552i	0.452076	−	0.231911i
$579$	−8.13482	+	14.0899i	−0.338071	+	0.585557i
$580$	5.58900	−	56.1420i	0.232071	−	2.33117i
$581$	−1.14950	+	2.41236i	−0.0476892	+	0.100082i
$582$	−17.8913	−	0.888354i	−0.741619	−	0.0368235i
$583$	0.167311	+	0.0965971i	0.00692932	+	0.00400065i
$584$	15.6666	+	39.8285i	0.648290	+	1.64811i
$585$	1.38172	+	2.39321i	0.0571271	+	0.0989471i
$586$	−17.1717	+	26.6018i	−0.709355	+	1.09891i
$587$	24.0746			0.993666			0.496833	−	0.867846i	$-0.334496\pi$
$587$	24.0746			0.993666			0.496833	+	0.867846i	$0.334496\pi$
$588$	27.0742	−	1.58909i	1.11652	−	0.0655330i
$589$	23.2049			0.956143
$590$	3.78594	−	5.86506i	0.155865	−	0.241461i
$591$	2.43790	+	4.22256i	0.100282	+	0.173693i
$592$	−7.73873	−	22.9557i	−0.318060	−	0.943475i
$593$	15.6499	+	9.03548i	0.642665	+	0.371043i	0.785640	−	0.618683i	$-0.212334\pi$
$593$	15.6499	+	9.03548i	0.642665	+	0.371043i	−0.142975	+	0.989726i	$0.545667\pi$
$594$	−6.14906	−	0.305318i	−0.252299	−	0.0125274i
$595$	9.97935	−	20.9429i	0.409113	−	0.858576i
$596$	28.8955	+	2.87657i	1.18360	+	0.117829i
$597$	−8.37802	+	14.5112i	−0.342890	+	0.593902i
$598$	2.34240	−	1.20163i	0.0957877	−	0.0491383i
$599$	−34.8453	+	20.1180i	−1.42374	+	0.821997i	−0.996616	−	0.0821953i	$-0.973807\pi$
$599$	−34.8453	+	20.1180i	−1.42374	+	0.821997i	−0.427125	+	0.904193i	$0.640474\pi$
$600$	17.9774	+	14.3141i	0.733924	+	0.584369i
$601$		−	33.6518i		−	1.37268i	−0.727279	−	0.686342i	$-0.759215\pi$
$601$		−	33.6518i		−	1.37268i	0.727279	−	0.686342i	$-0.240785\pi$
$602$	−18.3054	−	29.6627i	−0.746074	−	1.20896i
$603$		−	5.83978i		−	0.237814i
$604$	3.55472	+	2.55293i	0.144640	+	0.103877i
$605$	2.62593	−	1.51608i	0.106759	−	0.0616375i
$606$	−14.0182	−	27.3263i	−0.569449	−	1.11005i
$607$	−5.88299	+	10.1896i	−0.238783	+	0.413584i	−0.960365	−	0.278744i	$-0.910082\pi$
$607$	−5.88299	+	10.1896i	−0.238783	+	0.413584i	0.721582	+	0.692329i	$0.243415\pi$
$608$	−9.96265	+	39.3350i	−0.404039	+	1.59524i
$609$	−47.5352	+	3.75955i	−1.92622	+	0.152345i
$610$	0.721302	−	14.5269i	0.0292047	−	0.588177i
$611$	−0.0333170	−	0.0192356i	−0.00134786	−	0.000778189i
$612$	−3.96733	+	1.79256i	−0.160370	+	0.0724598i
$613$	−12.2457	−	21.2101i	−0.494598	−	0.856669i	0.505383	−	0.862895i	$-0.331351\pi$
$613$	−12.2457	−	21.2101i	−0.494598	−	0.856669i	−0.999981	+	0.00622640i	$0.998018\pi$
$614$	−33.0832	−	21.3554i	−1.33513	−	0.861836i
$615$	54.7097			2.20611
$616$	−7.46503	−	0.522738i	−0.300775	−	0.0210617i
$617$	35.7466			1.43911			0.719553	−	0.694438i	$-0.244347\pi$
$617$	35.7466			1.43911			0.719553	+	0.694438i	$0.244347\pi$
$618$	−32.4333	−	20.9359i	−1.30466	−	0.842166i
$619$	−1.77949	−	3.08217i	−0.0715239	−	0.123883i	0.828045	−	0.560661i	$-0.189453\pi$
$619$	−1.77949	−	3.08217i	−0.0715239	−	0.123883i	−0.899569	+	0.436778i	$0.856120\pi$
$620$	17.8779	−	8.07779i	0.717995	−	0.324412i
$621$	−5.79665	−	3.34670i	−0.232612	−	0.134298i
$622$	1.54664	−	31.1491i	0.0620146	−	1.24896i
$623$	−9.69590	+	6.66931i	−0.388458	+	0.267200i
$624$	−1.84962	+	9.19776i	−0.0740442	+	0.368205i
$625$	14.1901	−	24.5781i	0.567606	−	0.983122i
$626$	−6.88611	−	13.4234i	−0.275224	−	0.536509i
$627$	−12.0340	+	6.94783i	−0.480591	+	0.277470i
$628$	−21.5743	−	15.4942i	−0.860906	−	0.618285i
$629$			17.5135i			0.698308i
$630$	4.05140	−	7.51783i	0.161412	−	0.299517i
$631$			12.9012i			0.513590i	0.966466	+	0.256795i	$0.0826666\pi$
$631$			12.9012i			0.513590i	−0.966466	+	0.256795i	$0.917333\pi$
$632$	17.2742	−	21.6951i	0.687129	−	0.862983i
$633$	13.6161	−	7.86125i	0.541191	−	0.312457i
$634$	−22.4934	+	11.5389i	−0.893329	+	0.458270i
$635$	6.87510	−	11.9080i	0.272830	−	0.472556i
$636$	−0.744829	−	0.0741486i	−0.0295344	−	0.00294018i
$637$	−6.58242	+	5.33875i	−0.260805	+	0.211529i
$638$	13.1410	+	0.652486i	0.520256	+	0.0258322i
$639$	8.39164	+	4.84491i	0.331968	+	0.191662i
$640$	6.01717	+	33.7732i	0.237850	+	1.33500i
$641$	12.1474	+	21.0400i	0.479794	+	0.831028i	0.999731	−	0.0231764i	$-0.00737795\pi$
$641$	12.1474	+	21.0400i	0.479794	+	0.831028i	−0.519937	+	0.854205i	$0.674045\pi$
$642$	−20.1795	+	31.2615i	−0.796423	+	1.23379i
$643$	16.5783			0.653783			0.326891	−	0.945062i	$-0.393999\pi$
$643$	16.5783			0.653783			0.326891	+	0.945062i	$0.393999\pi$
$644$	−6.96174	−	4.21004i	−0.274331	−	0.165899i
$645$	−54.7198			−2.15459
$646$	15.9094	−	24.6463i	0.625946	−	0.969696i
$647$	−3.45823	−	5.98982i	−0.135957	−	0.235484i	0.790006	−	0.613099i	$-0.210078\pi$
$647$	−3.45823	−	5.98982i	−0.135957	−	0.235484i	−0.925963	+	0.377615i	$0.876744\pi$
$648$	28.1415	−	11.0695i	1.10550	−	0.434853i
$649$	1.40985	+	0.813975i	0.0553413	+	0.0319513i
$650$	−7.17245	−	0.356132i	−0.281327	−	0.0139687i
$651$	−9.39657	−	13.6608i	−0.368281	−	0.535409i
$652$	−0.386783	+	3.88527i	−0.0151476	+	0.152159i
$653$	−2.07749	+	3.59833i	−0.0812986	+	0.140813i	−0.903808	−	0.427938i	$-0.859240\pi$
$653$	−2.07749	+	3.59833i	−0.0812986	+	0.140813i	0.822509	+	0.568752i	$0.192573\pi$
$654$	−19.8778	+	10.1971i	−0.777283	+	0.398739i
$655$	−28.9198	+	16.6969i	−1.12999	+	0.652401i
$656$	27.9590	+	24.6234i	1.09162	+	0.961382i
$657$		−	11.3901i		−	0.444372i
$658$	0.00348455	+	0.118838i	0.000135842	+	0.00463280i
$659$			36.7871i			1.43302i	0.697576	+	0.716511i	$0.254262\pi$
$659$			36.7871i			1.43302i	−0.697576	+	0.716511i	$0.745738\pi$
$660$	−6.85285	+	9.54197i	−0.266747	+	0.371421i
$661$	−24.4729	+	14.1294i	−0.951885	+	0.549571i	−0.893666	−	0.448733i	$-0.851875\pi$
$661$	−24.4729	+	14.1294i	−0.951885	+	0.549571i	−0.0582190	+	0.998304i	$0.518542\pi$
$662$	−22.1852	−	43.2467i	−0.862251	−	1.68083i
$663$	3.39131	−	5.87393i	0.131708	−	0.228124i
$664$	−0.423618	+	2.82516i	−0.0164396	+	0.109637i
$665$	4.53705	+	57.3658i	0.175939	+	2.22455i
$666$	−0.319720	+	6.43911i	−0.0123889	+	0.249511i
$667$	12.3878	+	7.15212i	0.479659	+	0.276931i
$668$	5.89949	+	13.0569i	0.228258	+	0.505186i
$669$	−1.28710	−	2.22933i	−0.0497623	−	0.0861908i
$670$	27.9504	+	18.0422i	1.07982	+	0.697030i
$671$	3.39188			0.130942
$672$	27.1909	−	10.0632i	1.04891	−	0.388197i
$673$	−5.76323			−0.222156			−0.111078	−	0.993812i	$-0.535430\pi$
$673$	−5.76323			−0.222156			−0.111078	+	0.993812i	$0.535430\pi$
$674$	−2.37155	−	1.53085i	−0.0913487	−	0.0589663i
$675$	9.12913	+	15.8121i	0.351380	+	0.608608i
$676$	9.49833	+	21.0219i	0.365320	+	0.808535i
$677$	−4.06025	−	2.34419i	−0.156048	−	0.0900945i	0.419943	−	0.907551i	$-0.362050\pi$
$677$	−4.06025	−	2.34419i	−0.156048	−	0.0900945i	−0.575991	+	0.817456i	$0.695384\pi$
$678$	1.45655	−	29.3347i	0.0559385	−	1.12659i
$679$	−15.6173	−	7.44167i	−0.599336	−	0.285585i
$680$	3.67764	−	24.5266i	0.141031	−	0.940551i
$681$	9.57253	−	16.5801i	0.366820	−	0.635351i
$682$	2.08819	+	4.07062i	0.0799611	+	0.155872i
$683$	23.9085	−	13.8036i	0.914835	−	0.528180i	0.0328513	−	0.999460i	$-0.489541\pi$
$683$	23.9085	−	13.8036i	0.914835	−	0.528180i	0.881984	+	0.471280i	$0.156208\pi$
$684$	6.29928	−	8.77118i	0.240859	−	0.335374i
$685$			57.7876i			2.20795i
$686$	24.7232	+	8.64646i	0.943938	+	0.330124i
$687$		−	27.3451i		−	1.04328i
$688$	−27.9642	−	24.6280i	−1.06613	−	0.938933i
$689$	0.202573	−	0.116956i	0.00771742	−	0.00445565i
$690$	−11.3640	+	5.82962i	−0.432619	+	0.221930i
$691$	−24.4174	+	42.2922i	−0.928883	+	1.60887i	−0.143689	+	0.989623i	$0.545897\pi$
$691$	−24.4174	+	42.2922i	−0.928883	+	1.60887i	−0.785194	+	0.619250i	$0.787437\pi$
$692$	−3.03608	+	30.4977i	−0.115414	+	1.15935i
$693$	1.79787	+	0.856688i	0.0682954	+	0.0325429i
$694$	−34.4976	−	1.71290i	−1.30951	−	0.0650209i
$695$	−13.4533	−	7.76724i	−0.510311	−	0.294628i
$696$	−47.4380	+	18.6598i	−1.79813	+	0.707299i
$697$	−13.4671	−	23.3257i	−0.510104	−	0.883526i
$698$	1.40717	−	2.17994i	0.0532620	−	0.0825118i
$699$	−44.7453			−1.69242
$700$	10.7039	+	19.4407i	0.404571	+	0.734789i
$701$	−45.1931			−1.70692			−0.853459	−	0.521159i	$-0.825500\pi$
$701$	−45.1931			−1.70692			−0.853459	+	0.521159i	$0.825500\pi$
$702$	−4.04265	+	6.26274i	−0.152580	+	0.236372i
$703$	−21.7210	−	37.6219i	−0.819224	−	1.41894i
$704$	−7.79670	+	1.79207i	−0.293849	+	0.0675413i
$705$	0.161635	+	0.0933202i	0.00608754	+	0.00351464i
$706$	5.44782	+	0.270500i	0.205031	+	0.0101804i
$707$	−2.33849	−	29.5676i	−0.0879481	−	1.11200i
$708$	−6.27629	−	0.624812i	−0.235878	−	0.0234819i
$709$	17.4950	−	30.3023i	0.657039	−	1.13803i	−0.324339	−	0.945941i	$-0.605142\pi$
$709$	17.4950	−	30.3023i	0.657039	−	1.13803i	0.981378	−	0.192085i	$-0.0615249\pi$
$710$	−49.1150	+	25.1956i	−1.84325	+	0.945572i
$711$	−6.39161	+	3.69020i	−0.239704	+	0.138393i
$712$	−7.83644	+	9.84199i	−0.293683	+	0.368844i
$713$			4.97386i			0.186272i
$714$	−20.9517	+	0.614340i	−0.784097	+	0.0229911i
$715$		−	3.67121i		−	0.137296i
$716$	10.9960	+	7.89710i	0.410940	+	0.295129i
$717$	−9.73023	+	5.61775i	−0.363382	+	0.209799i
$718$	−11.7859	−	22.9748i	−0.439846	−	0.857414i
$719$	19.7111	−	34.1406i	0.735100	−	1.27323i	−0.219579	−	0.975595i	$-0.570468\pi$
$719$	19.7111	−	34.1406i	0.735100	−	1.27323i	0.954679	−	0.297637i	$-0.0961983\pi$
$720$	1.79989	−	8.95046i	0.0670781	−	0.333564i
$721$	−21.1280	−	30.7160i	−0.786848	−	1.14393i
$722$	−2.27604	+	45.8390i	−0.0847053	+	1.70595i
$723$	−45.1376	−	26.0602i	−1.67869	−	0.969190i
$724$	13.2865	−	6.00324i	0.493789	−	0.223109i
$725$	−19.5096	−	33.7916i	−0.724567	−	1.25499i
$726$	−2.30172	−	1.48578i	−0.0854249	−	0.0551425i
$727$	13.3265			0.494251			0.247125	−	0.968984i	$-0.420514\pi$
$727$	13.3265			0.494251			0.247125	+	0.968984i	$0.420514\pi$
$728$	−5.06728	+	7.51097i	−0.187806	+	0.278375i
$729$	17.2523			0.638973
$730$	54.5155	+	35.1902i	2.01771	+	1.30245i
$731$	13.4696	+	23.3301i	0.498192	+	0.862894i
$732$	−11.9758	+	5.41101i	−0.442637	+	0.199997i
$733$	−27.2761	−	15.7478i	−1.00746	−	0.581660i	−0.0970164	−	0.995283i	$-0.530930\pi$
$733$	−27.2761	−	15.7478i	−1.00746	−	0.581660i	−0.910448	+	0.413623i	$0.864263\pi$
$734$	0.224693	−	4.52528i	0.00829357	−	0.167031i
$735$	31.9342	−	25.9006i	1.17791	−	0.955358i
$736$	−8.43125	−	2.13544i	−0.310780	−	0.0787134i
$737$	−3.87905	+	6.71872i	−0.142887	+	0.247487i
$738$	−4.52558	−	8.82194i	−0.166589	−	0.324740i
$739$	−0.0327094	+	0.0188848i	−0.00120324	+	0.000694688i	−0.500601	−	0.865678i	$-0.666888\pi$
$739$	−0.0327094	+	0.0188848i	−0.00120324	+	0.000694688i	0.499398	+	0.866373i	$0.333554\pi$
$740$	−29.8311	−	21.4241i	−1.09661	−	0.787565i
$741$			16.8243i			0.618054i
$742$	−0.636345	−	0.342930i	−0.0233610	−	0.0125894i
$743$			43.1535i			1.58315i	0.611073	+	0.791574i	$0.290738\pi$
$743$			43.1535i			1.58315i	−0.611073	+	0.791574i	$0.709262\pi$
$744$	−13.8666	−	11.0410i	−0.508376	−	0.404782i
$745$	38.1263	−	22.0122i	1.39684	−	0.806465i
$746$	36.7124	−	18.8332i	1.34414	−	0.689531i
$747$	0.380134	−	0.658411i	0.0139084	−	0.0240900i
$748$	5.75514	+	0.572931i	0.210429	+	0.0209484i
$749$	−29.6063	+	20.3647i	−1.08179	+	0.744109i
$750$	−6.68698	−	0.332028i	−0.244174	−	0.0121239i
$751$	−17.5004	−	10.1039i	−0.638600	−	0.368696i	0.145475	−	0.989362i	$-0.453529\pi$
$751$	−17.5004	−	10.1039i	−0.638600	−	0.368696i	−0.784075	+	0.620666i	$0.786862\pi$
$752$	0.0406017	+	0.120439i	0.00148059	+	0.00439194i
$753$	−23.7892	−	41.2041i	−0.866927	−	1.50156i
$754$	8.63941	−	13.3839i	0.314629	−	0.487413i
$755$	6.63509			0.241476
$756$	23.0313	+	0.467569i	0.837640	+	0.0170053i
$757$	41.3750			1.50380			0.751899	−	0.659278i	$-0.229138\pi$
$757$	41.3750			1.50380			0.751899	+	0.659278i	$0.229138\pi$
$758$	−1.56993	+	2.43208i	−0.0570223	+	0.0883371i
$759$	−1.48923	−	2.57942i	−0.0540556	−	0.0936271i
$760$	22.5188	+	57.2484i	0.816843	+	2.07662i
$761$	16.9535	+	9.78814i	0.614566	+	0.354820i	0.774750	−	0.632267i	$-0.217876\pi$
$761$	16.9535	+	9.78814i	0.614566	+	0.354820i	−0.160185	+	0.987087i	$0.551209\pi$
$762$	−12.4083	−	0.616105i	−0.449504	−	0.0223191i
$763$	−21.5082	+	1.70107i	−0.778648	+	0.0615830i
$764$	1.25626	−	12.6192i	0.0454498	−	0.456548i
$765$	−3.30013	+	5.71599i	−0.119316	+	0.206662i
$766$	4.09558	−	2.10100i	0.147979	−	0.0759121i
$767$	1.70698	−	0.985524i	0.0616354	−	0.0355852i
$768$	24.6691	−	18.7653i	0.890169	−	0.677133i
$769$			37.8267i			1.36406i	0.731322	+	0.682032i	$0.238904\pi$
$769$			37.8267i			1.36406i	−0.731322	+	0.682032i	$0.761096\pi$
$770$	−9.65485	+	5.95820i	−0.347937	+	0.214718i
$771$			32.7019i			1.17773i
$772$	−9.79825	+	13.6432i	−0.352647	+	0.491029i
$773$	32.3825	−	18.6960i	1.16472	−	0.672450i	0.212287	−	0.977207i	$-0.431909\pi$
$773$	32.3825	−	18.6960i	1.16472	−	0.672450i	0.952430	+	0.304757i	$0.0985754\pi$
$774$	4.52642	+	8.82358i	0.162699	+	0.317157i
$775$	6.78384	−	11.7500i	0.243683	−	0.422071i
$776$	−18.2896	−	2.74244i	−0.656559	−	0.0984479i
$777$	−13.3524	+	28.0218i	−0.479016	+	1.00528i
$778$	2.51771	−	50.7063i	0.0902644	−	1.81791i
$779$	57.8593	+	33.4051i	2.07303	+	1.19686i
$780$	5.85663	+	12.9620i	0.209701	+	0.464115i
$781$	−6.43643	−	11.1482i	−0.230314	−	0.398915i
$782$	5.28280	+	3.41009i	0.188913	+	0.121945i
$783$	−40.5019			−1.44742
$784$	27.9769	+	1.13641i	0.999176	+	0.0405862i
$785$	−40.2696			−1.43728
$786$	25.3493	+	16.3632i	0.904178	+	0.583654i
$787$	12.4098	+	21.4944i	0.442361	+	0.766191i	0.997864	−	0.0653228i	$-0.0208077\pi$
$787$	12.4098	+	21.4944i	0.442361	+	0.766191i	−0.555503	+	0.831514i	$0.687474\pi$
$788$	2.07270	+	4.58734i	0.0738368	+	0.163417i
$789$	−13.2845	−	7.66981i	−0.472941	−	0.273053i
$790$	2.08505	−	41.9925i	0.0741826	−	1.49403i
$791$	12.2014	−	25.6062i	0.433832	−	0.910451i
$792$	2.10551	+	0.315711i	0.0748161	+	0.0112183i
$793$	2.05337	−	3.55654i	0.0729172	−	0.126296i
$794$	−11.1588	−	21.7524i	−0.396010	−	0.771963i
$795$	−0.982769	+	0.567402i	−0.0348552	+	0.0201237i
$796$	−10.0912	+	14.0511i	−0.357673	+	0.498027i
$797$			3.76524i			0.133372i	0.997774	+	0.0666859i	$0.0212425\pi$
$797$			3.76524i			0.133372i	−0.997774	+	0.0666859i	$0.978757\pi$
$798$	44.2458	−	27.3049i	1.56628	−	0.966584i
$799$		−	0.0918854i		−	0.00325067i
$800$	17.0050	+	16.5440i	0.601217	+	0.584920i
$801$	2.89956	−	1.67406i	0.102451	−	0.0591501i
$802$	17.7818	−	9.12192i	0.627898	−	0.322106i
$803$	−7.56586	+	13.1045i	−0.266993	+	0.462446i
$804$	2.97758	−	29.9101i	0.105011	−	1.05485i
$805$	−12.2961	+	0.972492i	−0.433379	+	0.0342758i
$806$	5.53238	+	0.274698i	0.194870	+	0.00967583i
$807$	−26.3804	−	15.2307i	−0.928633	−	0.536146i
$808$	−11.6067	−	29.5071i	−0.408322	−	1.03806i
$809$	15.7289	+	27.2433i	0.553000	+	0.957824i	0.998056	+	0.0623216i	$0.0198504\pi$
$809$	15.7289	+	27.2433i	0.553000	+	0.957824i	−0.445056	+	0.895503i	$0.646816\pi$
$810$	24.8643	−	38.5189i	0.873641	−	1.35342i
$811$	33.5457			1.17795			0.588975	−	0.808152i	$-0.299532\pi$
$811$	33.5457			1.17795			0.588975	+	0.808152i	$0.299532\pi$
$812$	−49.2194	−	0.999227i	−1.72726	−	0.0350660i
$813$	56.8810			1.99490
$814$	4.64500	−	7.19588i	0.162807	−	0.252215i
$815$	2.95975	+	5.12644i	0.103676	+	0.179571i
$816$	−21.2338	+	7.15823i	−0.743331	+	0.250588i
$817$	−57.8701	−	33.4113i	−2.02462	−	1.16891i
$818$	−45.2159	−	2.24510i	−1.58094	−	0.0784979i
$819$	1.98667	−	1.36653i	0.0694198	−	0.0477503i
$820$	56.2055	+	5.59532i	1.96278	+	0.195397i
$821$	−10.2939	+	17.8296i	−0.359261	+	0.622259i	−0.987838	−	0.155489i	$-0.950305\pi$
$821$	−10.2939	+	17.8296i	−0.359261	+	0.622259i	0.628576	+	0.777748i	$0.283638\pi$
$822$	46.4559	−	23.8315i	1.62034	−	0.831219i
$823$	−21.9623	+	12.6799i	−0.765557	+	0.441995i	−0.831288	−	0.555843i	$-0.812396\pi$
$823$	−21.9623	+	12.6799i	−0.765557	+	0.441995i	0.0657301	+	0.997837i	$0.479062\pi$
$824$	−31.1788	−	24.8254i	−1.08617	−	0.864833i
$825$			8.12465i			0.282864i
$826$	−5.36216	−	2.88969i	−0.186573	−	0.100545i
$827$		−	11.9688i		−	0.416195i	−0.978108	−	0.208097i	$-0.933273\pi$
$827$		−	11.9688i		−	0.416195i	0.978108	−	0.208097i	$-0.0667271\pi$
$828$	1.88006	+	1.35022i	0.0653364	+	0.0469233i
$829$	16.1068	−	9.29927i	0.559413	−	0.322977i	−0.193497	−	0.981101i	$-0.561983\pi$
$829$	16.1068	−	9.29927i	0.559413	−	0.322977i	0.752910	+	0.658124i	$0.228650\pi$
$830$	1.97685	+	3.85358i	0.0686176	+	0.133760i
$831$	−22.5507	+	39.0590i	−0.782277	+	1.35494i
$832$	−2.84088	+	9.26007i	−0.0984897	+	0.321035i
$833$	−18.9036	−	7.23971i	−0.654973	−	0.250841i
$834$	−0.696053	+	14.0184i	−0.0241023	+	0.485417i
$835$	18.8119	+	10.8611i	0.651014	+	0.375863i
$836$	−13.0736	+	5.90704i	−0.452160	+	0.204299i
$837$	−7.04164	−	12.1965i	−0.243395	−	0.421572i
$838$	34.9817	+	22.5810i	1.20842	+	0.780047i
$839$	−11.3662			−0.392403			−0.196202	−	0.980564i	$-0.562861\pi$
$839$	−11.3662			−0.392403			−0.196202	+	0.980564i	$0.562861\pi$
$840$	24.5836	−	36.4390i	0.848214	−	1.25726i
$841$	57.5553			1.98467
$842$	11.6427	+	7.51547i	0.401235	+	0.259000i
$843$	−0.00501028	−	0.00867806i	−0.000172563	−	0.000298888i
$844$	14.7924	−	6.68363i	0.509174	−	0.230060i
$845$	30.2877	+	17.4866i	1.04193	+	0.601557i
$846$	0.00167743	−	0.0337832i	5.76712e−5	−	0.00116149i
$847$	−1.49941	−	2.17985i	−0.0515204	−	0.0749007i
$848$	−0.757610	−	0.152352i	−0.0260164	−	0.00523178i
$849$	−6.19001	+	10.7214i	−0.212441	+	0.367958i
$850$	−7.82878	−	15.2610i	−0.268525	−	0.523449i
$851$	8.06406	−	4.65579i	0.276432	−	0.159598i
$852$	40.5099	+	29.0933i	1.38784	+	0.996721i
$853$		−	7.18205i		−	0.245909i	−0.992412	−	0.122954i	$-0.960763\pi$
$853$		−	7.18205i		−	0.245909i	0.992412	−	0.122954i	$-0.0392369\pi$
$854$	−12.6858	+	0.371970i	−0.434099	+	0.0127285i
$855$		−	16.3719i		−	0.559907i
$856$	−23.9285	+	30.0524i	−0.817859	+	1.02717i
$857$	10.8284	−	6.25178i	0.369891	−	0.213557i	−0.303520	−	0.952825i	$-0.598162\pi$
$857$	10.8284	−	6.25178i	0.369891	−	0.213557i	0.673411	+	0.739269i	$0.264829\pi$
$858$	−2.95132	+	1.51400i	−0.100756	+	0.0516872i
$859$	−11.5203	+	19.9537i	−0.393066	+	0.680811i	−0.992852	−	0.119350i	$-0.961919\pi$
$859$	−11.5203	+	19.9537i	−0.393066	+	0.680811i	0.599786	+	0.800161i	$0.295252\pi$
$860$	−56.2159	−	5.59636i	−1.91695	−	0.190834i
$861$	−3.76380	−	47.5890i	−0.128270	−	1.62183i
$862$	23.1479	+	1.14936i	0.788421	+	0.0391473i
$863$	26.7862	+	15.4650i	0.911814	+	0.526436i	0.881014	−	0.473089i	$-0.156861\pi$
$863$	26.7862	+	15.4650i	0.911814	+	0.526436i	0.0307999	+	0.999526i	$0.490195\pi$
$864$	23.6976	−	6.70002i	0.806209	−	0.227939i
$865$	23.2328	+	40.2403i	0.789937	+	1.36821i
$866$	−8.38028	+	12.9825i	−0.284774	+	0.441162i
$867$	−16.7326			−0.568269
$868$	−8.25636	−	14.9953i	−0.280239	−	0.508975i
$869$	9.80480			0.332605
$870$	−41.9135	+	64.9311i	−1.42100	+	2.20137i
$871$	4.69659	+	8.13473i	0.159138	+	0.275635i
$872$	−21.4642	+	8.44298i	−0.726868	+	0.285915i
$873$	4.26245	+	2.46093i	0.144262	+	0.0832898i
$874$	−15.5777	−	0.773478i	−0.526924	−	0.0261633i
$875$	−5.83705	−	2.78137i	−0.197328	−	0.0940274i
$876$	5.80760	−	58.3379i	0.196221	−	1.97105i
$877$	−6.25110	+	10.8272i	−0.211085	+	0.365610i	−0.952054	−	0.305929i	$-0.901033\pi$
$877$	−6.25110	+	10.8272i	−0.211085	+	0.365610i	0.740970	+	0.671539i	$0.234366\pi$
$878$	1.32296	−	0.678668i	0.0446478	−	0.0229039i
$879$	37.5609	−	21.6858i	1.26690	−	0.731444i
$880$	−8.01610	+	9.10200i	−0.270223	+	0.306828i
$881$			8.31333i			0.280083i	0.990146	+	0.140042i	$0.0447237\pi$
$881$			8.31333i			0.280083i	−0.990146	+	0.140042i	$0.955276\pi$
$882$	−6.81807	−	3.00689i	−0.229576	−	0.101247i
$883$			29.6843i			0.998956i	0.866327	+	0.499478i	$0.166475\pi$
$883$			29.6843i			0.998956i	−0.866327	+	0.499478i	$0.833525\pi$
$884$	4.08478	−	5.68769i	0.137386	−	0.191298i
$885$	−8.28129	+	4.78121i	−0.278373	+	0.160718i
$886$	15.0649	+	29.3668i	0.506117	+	0.986598i
$887$	−10.4329	+	18.0703i	−0.350303	+	0.606743i	−0.986302	−	0.164947i	$-0.947255\pi$
$887$	−10.4329	+	18.0703i	−0.350303	+	0.606743i	0.635999	+	0.771690i	$0.280588\pi$
$888$	−4.92071	+	32.8167i	−0.165128	+	1.10126i
$889$	−10.8311	−	5.16106i	−0.363264	−	0.173096i
$890$	−0.945883	+	19.0499i	−0.0317061	+	0.638555i
$891$	9.25919	+	5.34580i	0.310195	+	0.179091i
$892$	−1.09429	−	2.42192i	−0.0366397	−	0.0810918i
$893$	0.113961	+	0.197386i	0.00381355	+	0.00660525i
$894$	−33.4190	−	21.5723i	−1.11770	−	0.721484i
$895$	20.5247			0.686064
$896$	28.9635	−	7.55747i	0.967603	−	0.252477i
$897$	−3.60619			−0.120407
$898$	17.6206	+	11.3743i	0.588008	+	0.379564i
$899$	15.0485	+	26.0647i	0.501894	+	0.869306i
$900$	−2.59978	−	5.75388i	−0.0866592	−	0.191796i
$901$	0.483829	+	0.279339i	0.0161187	+	0.00930613i
$902$	−0.653223	+	13.1558i	−0.0217500	+	0.438041i
$903$	3.76450	+	47.5978i	0.125275	+	1.58396i
$904$	4.49652	−	29.9878i	0.149552	−	0.997379i
$905$	11.0521	−	19.1428i	0.367383	−	0.636327i
$906$	−2.73630	−	5.33401i	−0.0909075	−	0.177211i
$907$	38.3818	−	22.1597i	1.27445	−	0.735802i	0.298625	−	0.954370i	$-0.403472\pi$
$907$	38.3818	−	22.1597i	1.27445	−	0.735802i	0.975822	+	0.218568i	$0.0701387\pi$
$908$	11.5299	−	16.0544i	0.382635	−	0.532784i
$909$			8.43844i			0.279885i
$910$	0.402603	+	13.7305i	0.0133462	+	0.455162i
$911$		−	27.7739i		−	0.920192i	−0.887869	−	0.460096i	$-0.847815\pi$
$911$		−	27.7739i		−	0.920192i	0.887869	−	0.460096i	$-0.152185\pi$
$912$	36.7358	−	41.7122i	1.21644	−	1.38123i
$913$	−0.874695	+	0.505005i	−0.0289482	+	0.0167132i
$914$	53.4697	−	27.4295i	1.76862	−	0.907288i
$915$	−9.96177	+	17.2543i	−0.329326	+	0.570409i
$916$	2.79666	−	28.0928i	0.0924044	−	0.928211i
$917$	16.5133	+	24.0071i	0.545316	+	0.792785i
$918$	−17.7818	−	0.882918i	−0.586888	−	0.0291406i
$919$	19.7627	+	11.4100i	0.651911	+	0.376381i	0.789188	−	0.614152i	$-0.210502\pi$
$919$	19.7627	+	11.4100i	0.651911	+	0.376381i	−0.137277	+	0.990533i	$0.543835\pi$
$920$	−12.2709	+	4.82679i	−0.404560	+	0.159134i
$921$	26.9694	+	46.7124i	0.888673	+	1.53923i
$922$	−14.3068	+	22.1636i	−0.471168	+	0.729919i
$923$	−15.5859			−0.513016
$924$	8.77149	+	5.30447i	0.288561	+	0.174504i
$925$	−25.4001			−0.835150
$926$	−1.82884	+	2.83318i	−0.0600994	+	0.0931041i
$927$	5.30333	+	9.18564i	0.174184	+	0.301696i
$928$	−50.6434	+	14.3184i	−1.66245	+	0.470025i
$929$	−9.85306	−	5.68867i	−0.323268	−	0.186639i	0.329580	−	0.944128i	$-0.393093\pi$
$929$	−9.85306	−	5.68867i	−0.323268	−	0.186639i	−0.652848	+	0.757489i	$0.726426\pi$
$930$	−26.8400	−	1.33268i	−0.880117	−	0.0437003i
$931$	49.5873	−	7.89306i	1.62516	−	0.258685i
$932$	−45.9687	−	4.57623i	−1.50575	−	0.149899i
$933$	−21.3604	+	36.9972i	−0.699307	+	1.21124i
$934$	−21.8110	+	11.1889i	−0.713679	+	0.366111i
$935$	7.59365	−	4.38420i	0.248339	−	0.143379i
$936$	1.60567	−	2.01660i	0.0524829	−	0.0659146i
$937$			9.04406i			0.295456i	0.989028	+	0.147728i	$0.0471961\pi$
$937$			9.04406i			0.295456i	−0.989028	+	0.147728i	$0.952804\pi$
$938$	13.7710	−	25.5537i	0.449641	−	0.834359i
$939$			20.6658i			0.674403i
$940$	0.156511	+	0.112403i	0.00510481	+	0.00366617i
$941$	20.5833	−	11.8838i	0.670998	−	0.387401i	−0.125457	−	0.992099i	$-0.540040\pi$
$941$	20.5833	−	11.8838i	0.670998	−	0.387401i	0.796455	+	0.604698i	$0.206706\pi$
$942$	16.6071	+	32.3731i	0.541089	+	1.05477i
$943$	−7.16021	+	12.4018i	−0.233168	+	0.403860i
$944$	−6.38399	−	1.28379i	−0.207781	−	0.0417838i
$945$	28.7746	−	19.7926i	0.936037	−	0.643852i
$946$	0.653345	−	13.1583i	0.0212421	−	0.427812i
$947$	10.6966	+	6.17566i	0.347592	+	0.200682i	0.663624	−	0.748066i	$-0.269018\pi$
$947$	10.6966	+	6.17566i	0.347592	+	0.200682i	−0.316032	+	0.948748i	$0.602351\pi$
$948$	−34.6180	+	15.6414i	−1.12434	+	0.508011i
$949$	9.16041	+	15.8663i	0.297359	+	0.515042i
$950$	35.7450	+	23.0737i	1.15972	+	0.748609i
$951$	34.6293			1.12293
$952$	−21.5873	−	1.51165i	−0.699650	−	0.0489929i
$953$	16.0439			0.519713			0.259857	−	0.965647i	$-0.416325\pi$
$953$	16.0439			0.519713			0.259857	+	0.965647i	$0.416325\pi$
$954$	0.172788	+	0.111536i	0.00559423	+	0.00361112i
$955$	−9.61318	−	16.6505i	−0.311075	−	0.538798i
$956$	−10.5708	+	4.77621i	−0.341884	+	0.154474i
$957$	−15.6081	−	9.01137i	−0.504540	−	0.291296i
$958$	−2.00250	+	40.3300i	−0.0646977	+	1.30300i
$959$	50.2663	−	3.97555i	1.62318	−	0.128377i
$960$	13.7823	−	44.9246i	0.444823	−	1.44994i
$961$	10.2674	−	17.7836i	0.331205	−	0.573665i
$962$	−4.73323	−	9.22672i	−0.152605	−	0.297481i
$963$	8.85377	−	5.11173i	0.285309	−	0.164723i
$964$	−43.7065	−	31.3891i	−1.40769	−	1.01098i
$965$			25.4658i			0.819772i
$966$	5.85267	+	9.48385i	0.188307	+	0.305138i
$967$		−	44.3866i		−	1.42738i	−0.700463	−	0.713689i	$-0.747023\pi$
$967$		−	44.3866i		−	1.42738i	0.700463	−	0.713689i	$-0.252977\pi$
$968$	−2.21270	−	1.76181i	−0.0711188	−	0.0566266i
$969$	−34.7998	+	20.0917i	−1.11793	+	0.645438i
$970$	−24.9475	+	12.7978i	−0.801015	+	0.410914i
$971$	−8.69266	+	15.0561i	−0.278961	+	0.483174i	−0.971127	−	0.238564i	$-0.923323\pi$
$971$	−8.69266	+	15.0561i	−0.278961	+	0.483174i	0.692166	+	0.721738i	$0.256657\pi$
$972$	−15.2278	−	1.51594i	−0.488431	−	0.0486238i
$973$	−5.83077	+	12.2366i	−0.186926	+	0.392288i
$974$	7.16383	+	0.355705i	0.229544	+	0.0113975i
$975$	8.51906	+	4.91848i	0.272828	+	0.157517i
$976$	−12.8566	+	4.33416i	−0.411530	+	0.138733i
$977$	−21.9430	−	38.0064i	−0.702019	−	1.21593i	−0.967757	−	0.251888i	$-0.918949\pi$
$977$	−21.9430	−	38.0064i	−0.702019	−	1.21593i	0.265737	−	0.964045i	$-0.414385\pi$
$978$	2.90060	−	4.49351i	0.0927508	−	0.143687i
$979$	−4.44796			−0.142157
$980$	35.4562	−	23.3427i	1.13261	−	0.745657i
$981$	6.13831			0.195981
$982$	0.940816	−	1.45748i	0.0300227	−	0.0465101i
$983$	11.8381	+	20.5042i	0.377577	+	0.653982i	0.990709	−	0.135998i	$-0.0434241\pi$
$983$	11.8381	+	20.5042i	0.377577	+	0.653982i	−0.613132	+	0.789980i	$0.710091\pi$
$984$	−18.6809	−	47.4916i	−0.595526	−	1.51398i
$985$	6.60929	+	3.81588i	0.210589	+	0.121584i
$986$	38.0010	+	1.88685i	1.21020	+	0.0600897i
$987$	0.0700544	−	0.147018i	0.00222985	−	0.00467963i
$988$	−1.72067	+	17.2843i	−0.0547417	+	0.549885i
$989$	7.16154	−	12.4041i	0.227724	−	0.394429i
$990$	2.87197	−	1.47329i	0.0912771	−	0.0468244i
$991$	2.28215	−	1.31760i	0.0724950	−	0.0418550i	−0.463314	−	0.886194i	$-0.653340\pi$
$991$	2.28215	−	1.31760i	0.0724950	−	0.0418550i	0.535809	+	0.844339i	$0.320007\pi$
$992$	−13.1166	−	12.7610i	−0.416452	−	0.405163i
$993$			66.5795i			2.11284i
$994$	25.2951	+	40.9891i	0.802313	+	1.30009i
$995$			26.2271i			0.831455i
$996$	2.28268	−	3.17842i	0.0723293	−	0.100712i
$997$	49.7834	−	28.7424i	1.57665	−	0.910282i	0.581333	−	0.813666i	$-0.302531\pi$
$997$	49.7834	−	28.7424i	1.57665	−	0.910282i	0.995322	−	0.0966165i	$-0.0308020\pi$
$998$	24.0526	+	46.8870i	0.761373	+	1.48418i
$999$	−13.1827	+	22.8331i	−0.417081	+	0.722406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.l.a.243.7	yes	80
4.3	odd	2	inner	308.2.l.a.243.35	yes	80
7.3	odd	6	inner	308.2.l.a.199.35	yes	80
28.3	even	6	inner	308.2.l.a.199.7	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.l.a.199.7	✓	80	28.3	even	6	inner
308.2.l.a.199.35	yes	80	7.3	odd	6	inner
308.2.l.a.243.7	yes	80	1.1	even	1	trivial
308.2.l.a.243.35	yes	80	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18817 - 0.766974i) q^{2} +(0.968599 + 1.67766i) q^{3} +(0.823502 + 1.82259i) q^{4} +(2.62593 + 1.51608i) q^{5} +(0.135862 - 2.73624i) q^{6} +(1.13810 - 2.38846i) q^{7} +(0.419420 - 2.79716i) q^{8} +(-0.376366 + 0.651886i) q^{9} +(-1.95726 - 3.81539i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-2.26005 + 3.14692i) q^{12} -1.21076i q^{13} +(-3.18415 + 1.96500i) q^{14} +5.87390i q^{15} +(-2.64369 + 3.00182i) q^{16} +(2.50437 - 1.44590i) q^{17} +(0.947167 - 0.485889i) q^{18} +(-3.58654 + 6.21207i) q^{19} +(-0.600741 + 6.03450i) q^{20} +(5.10939 - 0.404100i) q^{21} +(-1.41247 - 0.0701333i) q^{22} +(-1.33152 - 0.768755i) q^{23} +(5.09893 - 2.00568i) q^{24} +(2.09701 + 3.63213i) q^{25} +(-0.928618 + 1.43859i) q^{26} +4.35340 q^{27} +(5.29041 + 0.107403i) q^{28} -9.30351 q^{29} +(4.50513 - 6.97920i) q^{30} +(-1.61750 - 2.80160i) q^{31} +(5.44347 - 1.53903i) q^{32} +(1.67766 + 0.968599i) q^{33} +(-4.08458 - 0.202811i) q^{34} +(6.60968 - 4.54646i) q^{35} +(-1.49806 - 0.149134i) q^{36} +(-3.02813 + 5.24488i) q^{37} +(9.02591 - 4.63022i) q^{38} +(2.03124 - 1.17274i) q^{39} +(5.34209 - 6.70927i) q^{40} -9.31403i q^{41} +(-6.38076 - 3.43863i) q^{42} +9.31576i q^{43} +(1.62447 + 1.16666i) q^{44} +(-1.97662 + 1.14120i) q^{45} +(0.992462 + 1.93466i) q^{46} +(0.0158873 - 0.0275176i) q^{47} +(-7.59671 - 1.52766i) q^{48} +(-4.40944 - 5.43662i) q^{49} +(0.294141 - 5.92394i) q^{50} +(4.85145 + 2.80099i) q^{51} +(2.20671 - 0.997060i) q^{52} +(0.0965971 + 0.167311i) q^{53} +(-5.17258 - 3.33894i) q^{54} +3.03216 q^{55} +(-6.20354 - 4.18522i) q^{56} -13.8957 q^{57} +(11.0542 + 7.13555i) q^{58} +(0.813975 + 1.40985i) q^{59} +(-10.7057 + 4.83717i) q^{60} +(2.93745 + 1.69594i) q^{61} +(-0.226882 + 4.56936i) q^{62} +(1.12866 + 1.64085i) q^{63} +(-7.64817 - 2.34637i) q^{64} +(1.83561 - 3.17936i) q^{65} +(-1.25046 - 2.43758i) q^{66} +(-6.71872 + 3.87905i) q^{67} +(4.69763 + 3.37374i) q^{68} -2.97846i q^{69} +(-11.3404 + 0.332522i) q^{70} -12.8729i q^{71} +(1.66557 + 1.32617i) q^{72} +(-13.1045 + 7.56586i) q^{73} +(7.62063 - 3.90932i) q^{74} +(-4.06232 + 7.03615i) q^{75} +(-14.2756 - 1.42115i) q^{76} +(-0.208600 - 2.63752i) q^{77} +(-3.31292 - 0.164496i) q^{78} +(8.49120 + 4.90240i) q^{79} +(-11.4931 + 3.87452i) q^{80} +(5.34580 + 9.25919i) q^{81} +(-7.14362 + 11.0667i) q^{82} -1.01001 q^{83} +(4.94410 + 8.97955i) q^{84} +8.76840 q^{85} +(7.14494 - 11.0687i) q^{86} +(-9.01137 - 15.6081i) q^{87} +(-1.03535 - 2.63212i) q^{88} +(-3.85204 - 2.22398i) q^{89} +(3.22384 + 0.160073i) q^{90} +(-2.89184 - 1.37797i) q^{91} +(0.304616 - 3.05990i) q^{92} +(3.13342 - 5.42725i) q^{93} +(-0.0399820 + 0.0205104i) q^{94} +(-18.8360 + 10.8750i) q^{95} +(7.85451 + 7.64160i) q^{96} -6.53865i q^{97} +(1.06942 + 9.84156i) q^{98} +0.752733i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38}+ \cdots + 78 q^{98}+O(q^{100}) \) 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Introduction

L-functions

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