LMFDB - Embedded newform 756.2.bi.c.559.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(307,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("756.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bi (of order $6$, degree $2$, not 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.18
Character	$\chi$	$=$	756.559
Dual form			756.2.bi.c.307.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.294095 + 1.38330i) q^{2} +(-1.82702 - 0.813640i) q^{4} +(0.416111 - 0.240242i) q^{5} +(-1.52257 - 2.16374i) q^{7} +(1.66282 - 2.28802i) q^{8} +O(q^{10})$	\(q+(-0.294095 + 1.38330i) q^{2} +(-1.82702 - 0.813640i) q^{4} +(0.416111 - 0.240242i) q^{5} +(-1.52257 - 2.16374i) q^{7} +(1.66282 - 2.28802i) q^{8} +(0.209950 + 0.646259i) q^{10} +(2.31311 + 1.33548i) q^{11} +(-5.48694 + 3.16789i) q^{13} +(3.44088 - 1.46982i) q^{14} +(2.67598 + 2.97307i) q^{16} +2.37005i q^{17} -4.20225 q^{19} +(-0.955712 + 0.100361i) q^{20} +(-2.52763 + 2.80696i) q^{22} +(-4.15320 + 2.39785i) q^{23} +(-2.38457 + 4.13019i) q^{25} +(-2.76845 - 8.52173i) q^{26} +(1.02125 + 5.19202i) q^{28} +(-1.45060 + 2.51250i) q^{29} +(-3.14399 - 5.44556i) q^{31} +(-4.89962 + 2.82731i) q^{32} +(-3.27848 - 0.697018i) q^{34} +(-1.15338 - 0.534572i) q^{35} +4.69467 q^{37} +(1.23586 - 5.81295i) q^{38} +(0.142241 - 1.35155i) q^{40} +(-10.1295 + 5.84827i) q^{41} +(1.16280 + 0.671344i) q^{43} +(-3.13950 - 4.32198i) q^{44} +(-2.09550 - 6.45030i) q^{46} +(3.72876 - 6.45840i) q^{47} +(-2.36356 + 6.58890i) q^{49} +(-5.01199 - 4.51323i) q^{50} +(12.6023 - 1.32339i) q^{52} +8.99689 q^{53} +1.28335 q^{55} +(-7.48244 - 0.114250i) q^{56} +(-3.04893 - 2.74552i) q^{58} +(-0.140454 - 0.243273i) q^{59} +(-9.52219 - 5.49764i) q^{61} +(8.45745 - 2.74757i) q^{62} +(-2.47005 - 7.60913i) q^{64} +(-1.52212 + 2.63639i) q^{65} +(1.89068 - 1.09159i) q^{67} +(1.92837 - 4.33012i) q^{68} +(1.07867 - 1.43825i) q^{70} +0.198757i q^{71} +4.84941i q^{73} +(-1.38068 + 6.49412i) q^{74} +(7.67758 + 3.41912i) q^{76} +(-0.632248 - 7.03833i) q^{77} +(-3.42117 - 1.97521i) q^{79} +(1.82776 + 0.594244i) q^{80} +(-5.11086 - 15.7321i) q^{82} +(-5.09429 + 8.82356i) q^{83} +(0.569384 + 0.986203i) q^{85} +(-1.27064 + 1.41106i) q^{86} +(6.90188 - 3.07178i) q^{88} +2.67188i q^{89} +(15.2087 + 7.04900i) q^{91} +(9.53895 - 1.00170i) q^{92} +(7.83727 + 7.05736i) q^{94} +(-1.74860 + 1.00956i) q^{95} +(-1.87526 - 1.08268i) q^{97} +(-8.41929 - 5.20727i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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 $

$2$	−0.294095	+	1.38330i	−0.207956	+	0.978138i
$2$	−0.294095	+	1.38330i	−0.207956	+	0.978138i
$3$		0			0
$3$		0			0
$4$	−1.82702	−	0.813640i	−0.913508	−	0.406820i
$5$	0.416111	−	0.240242i	0.186091	−	0.107439i	−0.404061	−	0.914732i	$-0.632402\pi$
$5$	0.416111	−	0.240242i	0.186091	−	0.107439i	0.590151	+	0.807293i	$0.299068\pi$
$6$		0			0
$7$	−1.52257	−	2.16374i	−0.575477	−	0.817818i
$7$	−1.52257	−	2.16374i	−0.575477	−	0.817818i
$8$	1.66282	−	2.28802i	0.587896	−	0.808937i
$9$		0			0
$10$	0.209950	+	0.646259i	0.0663919	+	0.204365i
$11$	2.31311	+	1.33548i	0.697429	+	0.402661i	0.806389	−	0.591385i	$-0.201419\pi$
$11$	2.31311	+	1.33548i	0.697429	+	0.402661i	−0.108960	+	0.994046i	$0.534752\pi$
$12$		0			0
$13$	−5.48694	+	3.16789i	−1.52180	+	0.878614i	−0.522136	+	0.852862i	$0.674865\pi$
$13$	−5.48694	+	3.16789i	−1.52180	+	0.878614i	−0.999668	+	0.0257515i	$0.991802\pi$
$14$	3.44088	−	1.46982i	0.919613	−	0.392826i
$15$		0			0
$16$	2.67598	+	2.97307i	0.668995	+	0.743267i
$17$			2.37005i			0.574821i	0.957808	+	0.287410i	$0.0927944\pi$
$17$			2.37005i			0.574821i	−0.957808	+	0.287410i	$0.907206\pi$
$18$		0			0
$19$	−4.20225			−0.964062			−0.482031	−	0.876154i	$-0.660101\pi$
$19$	−4.20225			−0.964062			−0.482031	+	0.876154i	$0.660101\pi$
$20$	−0.955712	+	0.100361i	−0.213704	+	0.0224414i
$21$		0			0
$22$	−2.52763	+	2.80696i	−0.538893	+	0.598446i
$23$	−4.15320	+	2.39785i	−0.866001	+	0.499986i	−0.866017	−	0.500014i	$-0.833328\pi$
$23$	−4.15320	+	2.39785i	−0.866001	+	0.499986i	1.59909e−5		1.00000i	$0.499995\pi$
$24$		0			0
$25$	−2.38457	+	4.13019i	−0.476914	+	0.826038i
$26$	−2.76845	−	8.52173i	−0.542937	−	1.67125i
$27$		0			0
$28$	1.02125	+	5.19202i	0.192999	+	0.981199i
$29$	−1.45060	+	2.51250i	−0.269369	+	0.466560i	−0.968699	−	0.248238i	$-0.920148\pi$
$29$	−1.45060	+	2.51250i	−0.269369	+	0.466560i	0.699330	+	0.714799i	$0.253482\pi$
$30$		0			0
$31$	−3.14399	−	5.44556i	−0.564678	−	0.978051i	−0.997080	−	0.0763698i	$-0.975667\pi$
$31$	−3.14399	−	5.44556i	−0.564678	−	0.978051i	0.432402	−	0.901681i	$-0.357666\pi$
$32$	−4.89962	+	2.82731i	−0.866139	+	0.499802i
$33$		0			0
$34$	−3.27848	−	0.697018i	−0.562254	−	0.119538i
$35$	−1.15338	−	0.534572i	−0.194957	−	0.0903592i
$36$		0			0
$37$	4.69467			0.771799			0.385900	−	0.922541i	$-0.373891\pi$
$37$	4.69467			0.771799			0.385900	+	0.922541i	$0.373891\pi$
$38$	1.23586	−	5.81295i	0.200483	−	0.942986i
$39$		0			0
$40$	0.142241	−	1.35155i	0.0224902	−	0.213699i
$41$	−10.1295	+	5.84827i	−1.58196	+	0.913347i	−0.587390	+	0.809304i	$0.699845\pi$
$41$	−10.1295	+	5.84827i	−1.58196	+	0.913347i	−0.994573	+	0.104043i	$0.966822\pi$
$42$		0			0
$43$	1.16280	+	0.671344i	0.177326	+	0.102379i	0.586036	−	0.810285i	$-0.300688\pi$
$43$	1.16280	+	0.671344i	0.177326	+	0.102379i	−0.408710	+	0.912664i	$0.634021\pi$
$44$	−3.13950	−	4.32198i	−0.473297	−	0.651562i
$45$		0			0
$46$	−2.09550	−	6.45030i	−0.308965	−	0.951044i
$47$	3.72876	−	6.45840i	0.543895	−	0.942054i	−0.454780	−	0.890604i	$-0.650282\pi$
$47$	3.72876	−	6.45840i	0.543895	−	0.942054i	0.998676	−	0.0514505i	$-0.0163844\pi$
$48$		0			0
$49$	−2.36356	+	6.58890i	−0.337652	+	0.941271i
$50$	−5.01199	−	4.51323i	−0.708803	−	0.638267i
$51$		0			0
$52$	12.6023	−	1.32339i	1.74762	−	0.183521i
$53$	8.99689			1.23582			0.617909	−	0.786250i	$-0.287980\pi$
$53$	8.99689			1.23582			0.617909	+	0.786250i	$0.287980\pi$
$54$		0			0
$55$	1.28335			0.173047
$56$	−7.48244	−	0.114250i	−0.999883	−	0.0152673i
$57$		0			0
$58$	−3.04893	−	2.74552i	−0.400344	−	0.360504i
$59$	−0.140454	−	0.243273i	−0.0182855	−	0.0316715i	0.856738	−	0.515752i	$-0.172487\pi$
$59$	−0.140454	−	0.243273i	−0.0182855	−	0.0316715i	−0.875023	+	0.484081i	$0.839154\pi$
$60$		0			0
$61$	−9.52219	−	5.49764i	−1.21919	−	0.703900i	−0.254446	−	0.967087i	$-0.581893\pi$
$61$	−9.52219	−	5.49764i	−1.21919	−	0.703900i	−0.964745	+	0.263186i	$0.915227\pi$
$62$	8.45745	−	2.74757i	1.07410	−	0.348941i
$63$		0			0
$64$	−2.47005	−	7.60913i	−0.308757	−	0.951141i
$65$	−1.52212	+	2.63639i	−0.188796	+	0.327003i
$66$		0			0
$67$	1.89068	−	1.09159i	0.230984	−	0.133358i	−0.380042	−	0.924969i	$-0.624091\pi$
$67$	1.89068	−	1.09159i	0.230984	−	0.133358i	0.611026	+	0.791611i	$0.290757\pi$
$68$	1.92837	−	4.33012i	0.233849	−	0.525104i
$69$		0			0
$70$	1.07867	−	1.43825i	0.128926	−	0.171904i
$71$			0.198757i			0.0235881i	0.999930	+	0.0117940i	$0.00375425\pi$
$71$			0.198757i			0.0235881i	−0.999930	+	0.0117940i	$0.996246\pi$
$72$		0			0
$73$			4.84941i			0.567580i	0.958886	+	0.283790i	$0.0915919\pi$
$73$			4.84941i			0.567580i	−0.958886	+	0.283790i	$0.908408\pi$
$74$	−1.38068	+	6.49412i	−0.160501	+	0.754926i
$75$		0			0
$76$	7.67758	+	3.41912i	0.880679	+	0.392200i
$77$	−0.632248	−	7.03833i	−0.0720514	−	0.802092i
$78$		0			0
$79$	−3.42117	−	1.97521i	−0.384912	−	0.222229i	0.295041	−	0.955484i	$-0.404667\pi$
$79$	−3.42117	−	1.97521i	−0.384912	−	0.222229i	−0.679953	+	0.733256i	$0.738000\pi$
$80$	1.82776	+	0.594244i	0.204350	+	0.0664385i
$81$		0			0
$82$	−5.11086	−	15.7321i	−0.564400	−	1.73731i
$83$	−5.09429	+	8.82356i	−0.559171	+	0.968512i	0.438395	+	0.898782i	$0.355547\pi$
$83$	−5.09429	+	8.82356i	−0.559171	+	0.968512i	−0.997566	+	0.0697297i	$0.977786\pi$
$84$		0			0
$85$	0.569384	+	0.986203i	0.0617584	+	0.106969i
$86$	−1.27064	+	1.41106i	−0.137017	+	0.152159i
$87$		0			0
$88$	6.90188	−	3.07178i	0.735743	−	0.327453i
$89$			2.67188i			0.283219i	0.989923	+	0.141609i	$0.0452277\pi$
$89$			2.67188i			0.283219i	−0.989923	+	0.141609i	$0.954772\pi$
$90$		0			0
$91$	15.2087	+	7.04900i	1.59431	+	0.738936i
$92$	9.53895	−	1.00170i	0.994504	−	0.104435i
$93$		0			0
$94$	7.83727	+	7.05736i	0.808353	+	0.727911i
$95$	−1.74860	+	1.00956i	−0.179403	+	0.103578i
$96$		0			0
$97$	−1.87526	−	1.08268i	−0.190403	−	0.109929i	0.401768	−	0.915741i	$-0.368396\pi$
$97$	−1.87526	−	1.08268i	−0.190403	−	0.109929i	−0.592171	+	0.805812i	$0.701729\pi$
$98$	−8.41929	−	5.20727i	−0.850476	−	0.526013i
$99$		0			0
$100$	7.71713	−	5.60575i	0.771713	−	0.560575i
$101$	4.50341	+	2.60004i	0.448106	+	0.258714i	0.707030	−	0.707184i	$-0.250035\pi$
$101$	4.50341	+	2.60004i	0.448106	+	0.258714i	−0.258924	+	0.965898i	$0.583368\pi$
$102$		0			0
$103$	−1.13040	−	1.95791i	−0.111382	−	0.192919i	0.804946	−	0.593348i	$-0.202194\pi$
$103$	−1.13040	−	1.95791i	−0.111382	−	0.192919i	−0.916328	+	0.400429i	$0.868861\pi$
$104$	−1.87562	+	17.8219i	−0.183920	+	1.74758i
$105$		0			0
$106$	−2.64594	+	12.4454i	−0.256996	+	1.20880i
$107$		−	14.8308i		−	1.43375i	−0.697204	−	0.716873i	$-0.745573\pi$
$107$		−	14.8308i		−	1.43375i	0.697204	−	0.716873i	$-0.254427\pi$
$108$		0			0
$109$	−10.9535			−1.04916			−0.524578	−	0.851363i	$-0.675777\pi$
$109$	−10.9535			−1.04916			−0.524578	+	0.851363i	$0.675777\pi$
$110$	−0.377426	+	1.77525i	−0.0359861	+	0.169264i
$111$		0			0
$112$	2.35859	−	10.3168i	0.222866	−	0.974849i
$113$	4.72782	+	8.18882i	0.444756	+	0.770339i	0.998035	−	0.0626563i	$-0.0199572\pi$
$113$	4.72782	+	8.18882i	0.444756	+	0.770339i	−0.553280	+	0.832996i	$0.686624\pi$
$114$		0			0
$115$	−1.15213	+	1.99554i	−0.107436	+	0.186085i
$116$	4.69454	−	3.41013i	0.435877	−	0.316622i
$117$		0			0
$118$	0.377825	−	0.122744i	0.0347816	−	0.0112995i
$119$	5.12817	−	3.60856i	0.470099	−	0.330796i
$120$		0			0
$121$	−1.93301	−	3.34807i	−0.175728	−	0.304370i
$122$	10.4053	−	11.5552i	0.942050	−	1.04616i
$123$		0			0
$124$	1.31341	+	12.5072i	0.117947	+	1.12318i
$125$			4.69391i			0.419836i
$126$		0			0
$127$			1.45847i			0.129419i	0.997904	+	0.0647093i	$0.0206120\pi$
$127$			1.45847i			0.129419i	−0.997904	+	0.0647093i	$0.979388\pi$
$128$	11.2521	−	1.17901i	0.994555	−	0.104211i
$129$		0			0
$130$	−3.19926	−	2.88089i	−0.280593	−	0.252671i
$131$	−6.19426	−	10.7288i	−0.541195	−	0.937377i	−0.998836	−	0.0482400i	$-0.984639\pi$
$131$	−6.19426	−	10.7288i	−0.541195	−	0.937377i	0.457641	−	0.889137i	$-0.348695\pi$
$132$		0			0
$133$	6.39822	+	9.09258i	0.554796	+	0.788427i
$134$	0.953947	+	2.93640i	0.0824085	+	0.253667i
$135$		0			0
$136$	5.42271	+	3.94096i	0.464994	+	0.337935i
$137$	4.45878	−	7.72284i	0.380939	−	0.659806i	−0.610257	−	0.792203i	$-0.708934\pi$
$137$	4.45878	−	7.72284i	0.380939	−	0.659806i	0.991197	+	0.132397i	$0.0422673\pi$
$138$		0			0
$139$	1.37546	+	2.38237i	0.116665	+	0.202070i	0.918444	−	0.395551i	$-0.129446\pi$
$139$	1.37546	+	2.38237i	0.116665	+	0.202070i	−0.801779	+	0.597621i	$0.796113\pi$
$140$	1.67229	+	1.91511i	0.141335	+	0.161856i
$141$		0			0
$142$	−0.274939	−	0.0584533i	−0.0230724	−	0.00490529i
$143$	−16.9225			−1.41513
$144$		0			0
$145$			1.39397i			0.115763i
$146$	−6.70817	−	1.42618i	−0.555172	−	0.118032i
$147$		0			0
$148$	−8.57724	−	3.81977i	−0.705045	−	0.313983i
$149$	0.0762596	+	0.132086i	0.00624743	+	0.0108209i	0.869132	−	0.494580i	$-0.164678\pi$
$149$	0.0762596	+	0.132086i	0.00624743	+	0.0108209i	−0.862885	+	0.505401i	$0.831345\pi$
$150$		0			0
$151$	−10.8876	−	6.28594i	−0.886017	−	0.511542i	−0.0133797	−	0.999910i	$-0.504259\pi$
$151$	−10.8876	−	6.28594i	−0.886017	−	0.511542i	−0.872638	+	0.488368i	$0.837592\pi$
$152$	−6.98759	+	9.61482i	−0.566768	+	0.779865i
$153$		0			0
$154$	9.92204	+	1.19535i	0.799541	+	0.0963240i
$155$	−2.61650	−	1.51064i	−0.210162	−	0.121337i
$156$		0			0
$157$	9.96123	−	5.75112i	0.794993	−	0.458989i	−0.0467246	−	0.998908i	$-0.514878\pi$
$157$	9.96123	−	5.75112i	0.794993	−	0.458989i	0.841717	+	0.539919i	$0.181545\pi$
$158$	3.73845	−	4.15159i	0.297415	−	0.330283i
$159$		0			0
$160$	−1.35955	+	2.35357i	−0.107482	+	0.186066i
$161$	11.5119	+	5.33556i	0.907262	+	0.420501i
$162$		0			0
$163$			19.9710i			1.56425i	0.623121	+	0.782126i	$0.285865\pi$
$163$			19.9710i			1.56425i	−0.623121	+	0.782126i	$0.714135\pi$
$164$	23.2652	−	2.44312i	1.81670	−	0.190776i
$165$		0			0
$166$	−10.7074	−	9.64187i	−0.831055	−	0.748354i
$167$	10.9749	+	19.0090i	0.849260	+	1.47096i	0.881870	+	0.471493i	$0.156285\pi$
$167$	10.9749	+	19.0090i	0.849260	+	1.47096i	−0.0326095	+	0.999468i	$0.510382\pi$
$168$		0			0
$169$	13.5710	−	23.5057i	1.04392	−	1.80813i
$170$	−1.53166	+	0.497590i	−0.117473	+	0.0381634i
$171$		0			0
$172$	−1.57823	−	2.17266i	−0.120339	−	0.165664i
$173$	13.2462	+	7.64770i	1.00709	+	0.581444i	0.910339	−	0.413864i	$-0.135821\pi$
$173$	13.2462	+	7.64770i	1.00709	+	0.581444i	0.0967521	+	0.995309i	$0.469155\pi$
$174$		0			0
$175$	12.5673	−	1.12891i	0.950002	−	0.0853379i
$176$	2.21938	+	10.4507i	0.167292	+	0.787754i
$177$		0			0
$178$	−3.69600	−	0.785786i	−0.277027	−	0.0588971i
$179$			10.6967i			0.799512i	0.916622	+	0.399756i	$0.130905\pi$
$179$			10.6967i			0.799512i	−0.916622	+	0.399756i	$0.869095\pi$
$180$		0			0
$181$		−	7.23452i		−	0.537738i	−0.963177	−	0.268869i	$-0.913350\pi$
$181$		−	7.23452i		−	0.537738i	0.963177	−	0.268869i	$-0.0866498\pi$
$182$	−14.2237	+	18.9651i	−1.05433	+	1.40579i
$183$		0			0
$184$	−1.41970	+	13.4898i	−0.104662	+	0.994480i
$185$	1.95350	−	1.12786i	0.143624	−	0.0829216i
$186$		0			0
$187$	−3.16514	+	5.48218i	−0.231458	+	0.400897i
$188$	−12.0673	+	8.76573i	−0.880099	+	0.639307i
$189$		0			0
$190$	−0.882260	−	2.71574i	−0.0640059	−	0.197020i
$191$	17.2598	+	9.96493i	1.24887	+	0.721037i	0.970885	−	0.239547i	$-0.0769990\pi$
$191$	17.2598	+	9.96493i	1.24887	+	0.721037i	0.277988	+	0.960584i	$0.410332\pi$
$192$		0			0
$193$	7.12877	+	12.3474i	0.513140	+	0.888784i	0.999884	+	0.0152396i	$0.00485112\pi$
$193$	7.12877	+	12.3474i	0.513140	+	0.888784i	−0.486744	+	0.873545i	$0.661816\pi$
$194$	2.04917	−	2.27562i	0.147122	−	0.163380i
$195$		0			0
$196$	9.67926	−	10.1149i	0.691376	−	0.722495i
$197$	−11.9516			−0.851517			−0.425759	−	0.904837i	$-0.639993\pi$
$197$	−11.9516			−0.851517			−0.425759	+	0.904837i	$0.639993\pi$
$198$		0			0
$199$	−21.9514			−1.55610			−0.778048	−	0.628205i	$-0.783790\pi$
$199$	−21.9514			−1.55610			−0.778048	+	0.628205i	$0.783790\pi$
$200$	5.48485	+	12.3237i	0.387837	+	0.871418i
$201$		0			0
$202$	−4.92106	+	5.46489i	−0.346244	+	0.384508i
$203$	7.64505	−	0.686749i	0.536577	−	0.0482003i
$204$		0			0
$205$	−2.81000	+	4.86706i	−0.196259	+	0.339930i
$206$	3.04082	−	0.987869i	0.211864	−	0.0688281i
$207$		0			0
$208$	−24.1013	−	7.83585i	−1.67112	−	0.543318i
$209$	−9.72027	−	5.61200i	−0.672365	−	0.388190i
$210$		0			0
$211$	8.92341	−	5.15194i	0.614313	−	0.354674i	−0.160338	−	0.987062i	$-0.551259\pi$
$211$	8.92341	−	5.15194i	0.614313	−	0.354674i	0.774652	+	0.632388i	$0.217925\pi$
$212$	−16.4375	−	7.32023i	−1.12893	−	0.502756i
$213$		0			0
$214$	20.5154	+	4.36165i	1.40240	+	0.298156i
$215$	0.645139			0.0439981
$216$		0			0
$217$	−6.99583	+	15.0940i	−0.474908	+	1.02465i
$218$	3.22137	−	15.1519i	0.218179	−	1.02622i
$219$		0			0
$220$	−2.34470	−	1.04418i	−0.158080	−	0.0703988i
$221$	−7.50804	−	13.0043i	−0.505046	−	0.874765i
$222$		0			0
$223$	−7.23332	+	12.5285i	−0.484379	+	0.838969i	−0.999839	−	0.0179449i	$-0.994288\pi$
$223$	−7.23332	+	12.5285i	−0.484379	+	0.838969i	0.515460	+	0.856914i	$0.327621\pi$
$224$	13.5776	+	6.29675i	0.907191	+	0.420719i
$225$		0			0
$226$	−12.7180	+	4.13168i	−0.845988	+	0.274835i
$227$	−9.67633	+	16.7599i	−0.642240	+	1.11239i	0.342691	+	0.939448i	$0.388662\pi$
$227$	−9.67633	+	16.7599i	−0.642240	+	1.11239i	−0.984932	+	0.172945i	$0.944672\pi$
$228$		0			0
$229$	17.0595	−	9.84933i	1.12733	−	0.650862i	0.184065	−	0.982914i	$-0.441074\pi$
$229$	17.0595	−	9.84933i	1.12733	−	0.650862i	0.943261	+	0.332052i	$0.107741\pi$
$230$	−2.42159	−	2.18061i	−0.159675	−	0.143785i
$231$		0			0
$232$	3.33658	+	7.49683i	0.219057	+	0.492191i
$233$	−7.34808			−0.481389			−0.240694	−	0.970601i	$-0.577375\pi$
$233$	−7.34808			−0.481389			−0.240694	+	0.970601i	$0.577375\pi$
$234$		0			0
$235$		−	3.58321i		−	0.233743i
$236$	0.0586747	+	0.558743i	0.00381940	+	0.0363711i
$237$		0			0
$238$	3.48354	+	8.15504i	0.225804	+	0.528613i
$239$	−8.34611	+	4.81863i	−0.539865	+	0.311691i	−0.745024	−	0.667037i	$-0.767562\pi$
$239$	−8.34611	+	4.81863i	−0.539865	+	0.311691i	0.205159	+	0.978729i	$0.434229\pi$
$240$		0			0
$241$	−3.56210	−	2.05658i	−0.229455	−	0.132476i	0.380865	−	0.924630i	$-0.375626\pi$
$241$	−3.56210	−	2.05658i	−0.229455	−	0.132476i	−0.610321	+	0.792154i	$0.708959\pi$
$242$	5.19986	−	1.68928i	0.334260	−	0.108591i
$243$		0			0
$244$	12.9241	+	17.7919i	0.827381	+	1.13901i
$245$	0.599424	+	3.30954i	0.0382958	+	0.211439i
$246$		0			0
$247$	23.0575	−	13.3123i	1.46711	−	0.847038i
$248$	−17.6874	−	1.86147i	−1.12315	−	0.118204i
$249$		0			0
$250$	−6.49307	−	1.38045i	−0.410658	−	0.0873076i
$251$	3.31816			0.209441			0.104720	−	0.994502i	$-0.466605\pi$
$251$	3.31816			0.209441			0.104720	+	0.994502i	$0.466605\pi$
$252$		0			0
$253$	−12.8091			−0.805300
$254$	−2.01750	−	0.428929i	−0.126589	−	0.0269134i
$255$		0			0
$256$	−1.67826	+	15.9117i	−0.104892	+	0.994484i
$257$	14.9497	−	8.63121i	0.932537	−	0.538400i	0.0449237	−	0.998990i	$-0.485696\pi$
$257$	14.9497	−	8.63121i	0.932537	−	0.538400i	0.887613	+	0.460590i	$0.152362\pi$
$258$		0			0
$259$	−7.14796	−	10.1581i	−0.444153	−	0.631191i
$260$	4.92600	−	3.57826i	0.305498	−	0.221915i
$261$		0			0
$262$	16.6628	−	5.41322i	1.02943	−	0.334430i
$263$	−11.4455	−	6.60806i	−0.705760	−	0.407471i	0.103729	−	0.994606i	$-0.466922\pi$
$263$	−11.4455	−	6.60806i	−0.705760	−	0.407471i	−0.809489	+	0.587135i	$0.800256\pi$
$264$		0			0
$265$	3.74371	−	2.16143i	0.229974	−	0.132776i
$266$	−14.4594	+	6.17655i	−0.886564	+	0.378708i
$267$		0			0
$268$	−4.34247	+	0.456011i	−0.265258	+	0.0278553i
$269$		−	27.5600i		−	1.68036i	−0.542304	−	0.840182i	$-0.682448\pi$
$269$		−	27.5600i		−	1.68036i	0.542304	−	0.840182i	$-0.317552\pi$
$270$		0			0
$271$	21.2467			1.29065			0.645323	−	0.763910i	$-0.276723\pi$
$271$	21.2467			1.29065			0.645323	+	0.763910i	$0.276723\pi$
$272$	−7.04631	+	6.34220i	−0.427245	+	0.384552i
$273$		0			0
$274$	9.37167	+	8.43906i	0.566163	+	0.509822i
$275$	−11.0315	+	6.36906i	−0.665227	+	0.384069i
$276$		0			0
$277$	7.26076	−	12.5760i	0.436257	−	0.755619i	−0.561140	−	0.827721i	$-0.689637\pi$
$277$	7.26076	−	12.5760i	0.436257	−	0.755619i	0.997397	+	0.0721016i	$0.0229706\pi$
$278$	−3.70004	+	1.20203i	−0.221914	+	0.0720930i
$279$		0			0
$280$	−3.14097	+	1.75005i	−0.187709	+	0.104586i
$281$	−6.35647	+	11.0097i	−0.379195	+	0.656785i	−0.990945	−	0.134266i	$-0.957132\pi$
$281$	−6.35647	+	11.0097i	−0.379195	+	0.656785i	0.611750	+	0.791051i	$0.290466\pi$
$282$		0			0
$283$	−10.4272	−	18.0605i	−0.619834	−	1.07358i	−0.989516	−	0.144425i	$-0.953867\pi$
$283$	−10.4272	−	18.0605i	−0.619834	−	1.07358i	0.369682	−	0.929158i	$-0.379467\pi$
$284$	0.161716	−	0.363132i	0.00959610	−	0.0215479i
$285$		0			0
$286$	4.97683	−	23.4089i	0.294286	−	1.38420i
$287$	28.0770	+	13.0132i	1.65733	+	0.768147i
$288$		0			0
$289$	11.3829			0.669581
$290$	−1.92828	−	0.409960i	−0.113232	−	0.0240737i
$291$		0			0
$292$	3.94567	−	8.85995i	0.230903	−	0.518489i
$293$	5.80807	−	3.35329i	0.339311	−	0.195901i	−0.320656	−	0.947196i	$-0.603903\pi$
$293$	5.80807	−	3.35329i	0.339311	−	0.195901i	0.659967	+	0.751294i	$0.270570\pi$
$294$		0			0
$295$	−0.116889	−	0.0674857i	−0.00680552	−	0.00392917i
$296$	7.80640	−	10.7415i	0.453738	−	0.624336i
$297$		0			0
$298$	−0.205141	+	0.0666440i	−0.0118835	+	0.00386058i
$299$	15.1922	−	26.3137i	0.878590	−	1.52176i
$300$		0			0
$301$	−0.317831	−	3.53817i	−0.0183195	−	0.203937i
$302$	11.8973	−	13.2121i	0.684612	−	0.760269i
$303$		0			0
$304$	−11.2451	−	12.4936i	−0.644953	−	0.716555i
$305$	−5.28305			−0.302507
$306$		0			0
$307$	12.0792			0.689397			0.344699	−	0.938713i	$-0.387981\pi$
$307$	12.0792			0.689397			0.344699	+	0.938713i	$0.387981\pi$
$308$	−4.57154	+	13.3736i	−0.260488	+	0.762030i
$309$		0			0
$310$	2.85916	−	3.17513i	0.162389	−	0.180335i
$311$	1.01185	+	1.75258i	0.0573769	+	0.0993797i	0.893287	−	0.449486i	$-0.148393\pi$
$311$	1.01185	+	1.75258i	0.0573769	+	0.0993797i	−0.835910	+	0.548866i	$0.815060\pi$
$312$		0			0
$313$	16.8337	+	9.71892i	0.951495	+	0.549346i	0.893545	−	0.448974i	$-0.148210\pi$
$313$	16.8337	+	9.71892i	0.951495	+	0.549346i	0.0579500	+	0.998319i	$0.481544\pi$
$314$	5.02596	+	15.4707i	0.283631	+	0.873062i
$315$		0			0
$316$	4.64342	+	6.39235i	0.261213	+	0.359598i
$317$	5.21828	−	9.03832i	0.293088	−	0.507643i	−0.681451	−	0.731864i	$-0.738651\pi$
$317$	5.21828	−	9.03832i	0.293088	−	0.507643i	0.974538	+	0.224222i	$0.0719839\pi$
$318$		0			0
$319$	−6.71078	+	3.87447i	−0.375731	+	0.216929i
$320$	−2.85585	−	2.57283i	−0.159647	−	0.143826i
$321$		0			0
$322$	−10.7662	+	14.3552i	−0.599979	+	0.799981i
$323$		−	9.95953i		−	0.554163i
$324$		0			0
$325$		−	30.2162i		−	1.67609i
$326$	−27.6258	−	5.87337i	−1.53005	−	0.325296i
$327$		0			0
$328$	−3.46260	+	32.9011i	−0.191190	+	1.81666i
$329$	−19.6516	+	1.76529i	−1.08343	+	0.0973235i
$330$		0			0
$331$	−31.2751	−	18.0567i	−1.71903	−	0.992484i	−0.920704	−	0.390261i	$-0.872385\pi$
$331$	−31.2751	−	18.0567i	−1.71903	−	0.992484i	−0.798328	−	0.602223i	$-0.794282\pi$
$332$	16.4866	−	11.9759i	0.904817	−	0.657262i
$333$		0			0
$334$	−29.5227	+	9.59103i	−1.61541	+	0.524798i
$335$	0.524489	−	0.908442i	0.0286559	−	0.0496335i
$336$		0			0
$337$	3.70539	+	6.41792i	0.201845	+	0.349606i	0.949123	−	0.314905i	$-0.101973\pi$
$337$	3.70539	+	6.41792i	0.201845	+	0.349606i	−0.747278	+	0.664512i	$0.768639\pi$
$338$	28.5242	+	25.6856i	1.55151	+	1.39712i
$339$		0			0
$340$	−0.237861	−	2.26508i	−0.0128998	−	0.122841i
$341$		−	16.7949i		−	0.909495i
$342$		0			0
$343$	17.8554	−	4.91791i	0.964099	−	0.265542i
$344$	3.46958	−	1.54419i	0.187067	−	0.0832570i
$345$		0			0
$346$	−14.4747	+	16.0743i	−0.778163	+	0.864159i
$347$	24.8678	−	14.3574i	1.33497	−	0.770747i	0.348915	−	0.937154i	$-0.386550\pi$
$347$	24.8678	−	14.3574i	1.33497	−	0.770747i	0.986057	+	0.166408i	$0.0532168\pi$
$348$		0			0
$349$	−0.744758	−	0.429986i	−0.0398660	−	0.0230166i	0.479935	−	0.877304i	$-0.340660\pi$
$349$	−0.744758	−	0.429986i	−0.0398660	−	0.0230166i	−0.519801	+	0.854288i	$0.673994\pi$
$350$	−2.13436	+	17.7164i	−0.114087	+	0.946980i
$351$		0			0
$352$	−15.1092	−	0.00344740i	−0.805322	−	0.000183747i
$353$	−27.7159	−	16.0018i	−1.47517	−	0.851690i	−0.475562	−	0.879682i	$-0.657755\pi$
$353$	−27.7159	−	16.0018i	−1.47517	−	0.851690i	−0.999608	+	0.0279920i	$0.991089\pi$
$354$		0			0
$355$	0.0477497	+	0.0827049i	0.00253429	+	0.00438952i
$356$	2.17395	−	4.88157i	0.115219	−	0.258723i
$357$		0			0
$358$	−14.7968	−	3.14586i	−0.782033	−	0.166264i
$359$			5.52163i			0.291421i	0.989327	+	0.145710i	$0.0465468\pi$
$359$			5.52163i			0.291421i	−0.989327	+	0.145710i	$0.953453\pi$
$360$		0			0
$361$	−1.34111			−0.0705845
$362$	10.0075	+	2.12763i	0.525982	+	0.111826i
$363$		0			0
$364$	−22.0513	−	25.2531i	−1.15580	−	1.32362i
$365$	1.16503	+	2.01789i	0.0609805	+	0.105621i
$366$		0			0
$367$	−11.4766	+	19.8780i	−0.599072	+	1.03762i	0.393886	+	0.919159i	$0.371131\pi$
$367$	−11.4766	+	19.8780i	−0.599072	+	1.03762i	−0.992958	+	0.118465i	$0.962203\pi$
$368$	−18.2428	−	5.93114i	−0.950974	−	0.309182i
$369$		0			0
$370$	0.985644	+	3.03397i	0.0512412	+	0.157729i
$371$	−13.6984	−	19.4670i	−0.711185	−	1.01067i
$372$		0			0
$373$	−14.2688	−	24.7143i	−0.738810	−	1.27966i	−0.953032	−	0.302871i	$-0.902055\pi$
$373$	−14.2688	−	24.7143i	−0.738810	−	1.27966i	0.214222	−	0.976785i	$-0.431278\pi$
$374$	−6.65263	−	5.99061i	−0.343999	−	0.309767i
$375$		0			0
$376$	−8.57667	−	19.2706i	−0.442308	−	0.993807i
$377$		−	18.3813i		−	0.946685i
$378$		0			0
$379$			13.3942i			0.688014i	0.938967	+	0.344007i	$0.111784\pi$
$379$			13.3942i			0.688014i	−0.938967	+	0.344007i	$0.888216\pi$
$380$	4.01614	−	0.421743i	0.206024	−	0.0216349i
$381$		0			0
$382$	−18.8605	+	20.9447i	−0.964985	+	1.07163i
$383$	−11.1930	−	19.3869i	−0.571937	−	0.990625i	−0.996367	−	0.0851637i	$-0.972859\pi$
$383$	−11.1930	−	19.3869i	−0.571937	−	0.990625i	0.424430	−	0.905461i	$-0.360475\pi$
$384$		0			0
$385$	−1.95399	−	2.77684i	−0.0995844	−	0.141521i
$386$	−19.1766	+	6.22990i	−0.976064	+	0.317093i
$387$		0			0
$388$	2.54521	+	3.50386i	0.129214	+	0.177881i
$389$	−13.5306	+	23.4357i	−0.686029	+	1.18824i	0.287083	+	0.957906i	$0.407314\pi$
$389$	−13.5306	+	23.4357i	−0.686029	+	1.18824i	−0.973112	+	0.230332i	$0.926019\pi$
$390$		0			0
$391$	−5.68302	−	9.84327i	−0.287402	−	0.497796i
$392$	11.1453	+	16.3640i	0.562924	+	0.826508i
$393$		0			0
$394$	3.51491	−	16.5326i	0.177078	−	0.832901i
$395$	−1.89812			−0.0955046
$396$		0			0
$397$		−	11.6658i		−	0.585487i	−0.956191	−	0.292744i	$-0.905432\pi$
$397$		−	11.6658i		−	0.585487i	0.956191	−	0.292744i	$-0.0945683\pi$
$398$	6.45580	−	30.3653i	0.323600	−	1.52208i
$399$		0			0
$400$	−18.6604	+	3.96283i	−0.933020	+	0.198142i
$401$	8.33464	+	14.4360i	0.416212	+	0.720901i	0.995555	−	0.0941835i	$-0.0300240\pi$
$401$	8.33464	+	14.4360i	0.416212	+	0.720901i	−0.579343	+	0.815084i	$0.696691\pi$
$402$		0			0
$403$	34.5018	+	19.9196i	1.71866	+	0.992268i
$404$	−6.11230	−	8.41447i	−0.304098	−	0.418636i
$405$		0			0
$406$	−1.29839	+	10.7773i	−0.0644380	+	0.534870i
$407$	10.8593	+	6.26962i	0.538275	+	0.310773i
$408$		0			0
$409$	0.589282	−	0.340222i	0.0291381	−	0.0168229i	−0.485360	−	0.874314i	$-0.661312\pi$
$409$	0.589282	−	0.340222i	0.0291381	−	0.0168229i	0.514498	+	0.857491i	$0.327978\pi$
$410$	−5.90618	−	5.31844i	−0.291686	−	0.262659i
$411$		0			0
$412$	0.472227	+	4.49688i	0.0232649	+	0.221546i
$413$	−0.312530	+	0.674306i	−0.0153786	+	0.0331804i
$414$		0			0
$415$			4.89544i			0.240308i
$416$	17.9274	−	31.0347i	0.878961	−	1.52160i
$417$		0			0
$418$	10.6217	−	11.7956i	0.519526	−	0.576939i
$419$	−5.19926	−	9.00538i	−0.254000	−	0.439941i	0.710623	−	0.703573i	$-0.248413\pi$
$419$	−5.19926	−	9.00538i	−0.254000	−	0.439941i	−0.964624	+	0.263631i	$0.915080\pi$
$420$		0			0
$421$	−3.42772	+	5.93699i	−0.167057	+	0.289351i	−0.937384	−	0.348298i	$-0.886760\pi$
$421$	−3.42772	+	5.93699i	−0.167057	+	0.289351i	0.770327	+	0.637649i	$0.220093\pi$
$422$	4.50232	+	13.8589i	0.219170	+	0.674640i
$423$		0			0
$424$	14.9602	−	20.5850i	0.726532	−	0.999698i
$425$	−9.78875	−	5.65154i	−0.474824	−	0.274140i
$426$		0			0
$427$	2.60272	+	28.9741i	0.125955	+	1.40215i
$428$	−12.0669	+	27.0961i	−0.583276	+	1.30974i
$429$		0			0
$430$	−0.189732	+	0.892419i	−0.00914969	+	0.0430363i
$431$		−	15.2572i		−	0.734914i	−0.930040	−	0.367457i	$-0.880228\pi$
$431$		−	15.2572i		−	0.734914i	0.930040	−	0.367457i	$-0.119772\pi$
$432$		0			0
$433$			34.6459i			1.66498i	0.554042	+	0.832489i	$0.313085\pi$
$433$			34.6459i			1.66498i	−0.554042	+	0.832489i	$0.686915\pi$
$434$	−18.8221	−	14.1164i	−0.903489	−	0.677608i
$435$		0			0
$436$	20.0122	+	8.91221i	0.958412	+	0.426817i
$437$	17.4528	−	10.0764i	0.834879	−	0.482018i
$438$		0			0
$439$	6.12174	−	10.6032i	0.292175	−	0.506061i	−0.682149	−	0.731213i	$-0.738955\pi$
$439$	6.12174	−	10.6032i	0.292175	−	0.506061i	0.974324	+	0.225152i	$0.0722878\pi$
$440$	2.13398	−	2.93632i	0.101733	−	0.139984i
$441$		0			0
$442$	20.1969	−	6.56135i	0.960668	−	0.312091i
$443$	−24.2468	−	13.9989i	−1.15200	−	0.665108i	−0.202627	−	0.979256i	$-0.564948\pi$
$443$	−24.2468	−	13.9989i	−1.15200	−	0.665108i	−0.949374	+	0.314148i	$0.898281\pi$
$444$		0			0
$445$	0.641897	+	1.11180i	0.0304288	+	0.0527043i
$446$	−15.2033	−	13.6904i	−0.719898	−	0.648258i
$447$		0			0
$448$	−12.7034	+	16.9300i	−0.600178	+	0.799867i
$449$	−23.8270			−1.12446			−0.562232	−	0.826979i	$-0.690057\pi$
$449$	−23.8270			−1.12446			−0.562232	+	0.826979i	$0.690057\pi$
$450$		0			0
$451$	−31.2409			−1.47108
$452$	−1.97505	−	18.8079i	−0.0928985	−	0.884647i
$453$		0			0
$454$	−20.3381	−	18.3142i	−0.954516	−	0.859529i
$455$	8.02199	−	0.720609i	0.376077	−	0.0337827i
$456$		0			0
$457$	−11.9100	+	20.6288i	−0.557128	+	0.964974i	0.440607	+	0.897700i	$0.354763\pi$
$457$	−11.9100	+	20.6288i	−0.557128	+	0.964974i	−0.997735	+	0.0672735i	$0.978570\pi$
$458$	8.60742	+	26.4950i	0.402198	+	1.23803i
$459$		0			0
$460$	3.72861	−	2.70847i	0.173847	−	0.126283i
$461$	−0.317557	−	0.183341i	−0.0147901	−	0.00853906i	0.492587	−	0.870263i	$-0.336051\pi$
$461$	−0.317557	−	0.183341i	−0.0147901	−	0.00853906i	−0.507377	+	0.861724i	$0.669385\pi$
$462$		0			0
$463$	−14.3509	+	8.28549i	−0.666943	+	0.385060i	−0.794917	−	0.606718i	$-0.792486\pi$
$463$	−14.3509	+	8.28549i	−0.666943	+	0.385060i	0.127974	+	0.991777i	$0.459152\pi$
$464$	−11.3516	+	2.41069i	−0.526985	+	0.111914i
$465$		0			0
$466$	2.16103	−	10.1646i	0.100108	−	0.470865i
$467$	26.1463			1.20991			0.604953	−	0.796261i	$-0.293192\pi$
$467$	26.1463			1.20991			0.604953	+	0.796261i	$0.293192\pi$
$468$		0			0
$469$	−5.24061	−	2.42893i	−0.241989	−	0.112158i
$470$	4.95665	+	1.05380i	0.228633	+	0.0486084i
$471$		0			0
$472$	−0.790163	−	0.0831588i	−0.0363702	−	0.00382769i
$473$	1.79313	+	3.10579i	0.0824480	+	0.142804i
$474$		0			0
$475$	10.0205	−	17.3561i	0.459774	−	0.796352i
$476$	−12.3053	+	2.42042i	−0.564014	+	0.110940i
$477$		0			0
$478$	−4.21104	−	12.9623i	−0.192609	−	0.592880i
$479$	−19.0772	+	33.0427i	−0.871661	+	1.50976i	−0.0113840	+	0.999935i	$0.503624\pi$
$479$	−19.0772	+	33.0427i	−0.871661	+	1.50976i	−0.860277	+	0.509826i	$0.829710\pi$
$480$		0			0
$481$	−25.7594	+	14.8722i	−1.17453	+	0.678113i
$482$	3.89246	−	4.32261i	0.177297	−	0.196890i
$483$		0			0
$484$	0.807517	+	7.68976i	0.0367053	+	0.349534i
$485$	−1.04042			−0.0472430
$486$		0			0
$487$			8.93817i			0.405027i	0.979279	+	0.202514i	$0.0649110\pi$
$487$			8.93817i			0.405027i	−0.979279	+	0.202514i	$0.935089\pi$
$488$	−28.4124	+	12.6454i	−1.28617	+	0.572428i
$489$		0			0
$490$	−4.75436	−	0.144137i	−0.214780	−	0.00651146i
$491$	8.03087	−	4.63662i	0.362428	−	0.209248i	−0.307717	−	0.951478i	$-0.599565\pi$
$491$	8.03087	−	4.63662i	0.362428	−	0.209248i	0.670145	+	0.742230i	$0.266232\pi$
$492$		0			0
$493$	−5.95475	−	3.43798i	−0.268189	−	0.154839i
$494$	11.6337	+	35.8104i	0.523425	+	1.61119i
$495$		0			0
$496$	7.77675	−	23.9195i	0.349186	−	1.07402i
$497$	0.430058	−	0.302621i	0.0192908	−	0.0135744i
$498$		0			0
$499$	15.0365	−	8.68131i	0.673125	−	0.388629i	−0.124135	−	0.992265i	$-0.539615\pi$
$499$	15.0365	−	8.68131i	0.673125	−	0.388629i	0.797260	+	0.603636i	$0.206282\pi$
$500$	3.81915	−	8.57585i	0.170798	−	0.383524i
$501$		0			0
$502$	−0.975855	+	4.59000i	−0.0435545	+	0.204862i
$503$	−6.23388			−0.277955			−0.138978	−	0.990296i	$-0.544382\pi$
$503$	−6.23388			−0.277955			−0.138978	+	0.990296i	$0.544382\pi$
$504$		0			0
$505$	2.49856			0.111184
$506$	3.76708	−	17.7187i	0.167467	−	0.787694i
$507$		0			0
$508$	1.18667	−	2.66465i	0.0526500	−	0.118225i
$509$	3.52873	−	2.03731i	0.156408	−	0.0903023i	−0.419753	−	0.907638i	$-0.637883\pi$
$509$	3.52873	−	2.03731i	0.156408	−	0.0903023i	0.576161	+	0.817336i	$0.304550\pi$
$510$		0			0
$511$	10.4929	−	7.38356i	0.464177	−	0.326629i
$512$	−21.5171	−	7.00109i	−0.950930	−	0.309408i
$513$		0			0
$514$	7.54290	+	23.2183i	0.332703	+	1.02411i
$515$	−0.940746	−	0.543140i	−0.0414542	−	0.0239336i
$516$		0			0
$517$	17.2501	−	9.95933i	0.758657	−	0.438011i
$518$	16.1538	−	6.90032i	0.709756	−	0.303183i
$519$		0			0
$520$	3.50109	+	7.86647i	0.153533	+	0.344968i
$521$			27.2193i			1.19250i	0.802798	+	0.596251i	$0.203344\pi$
$521$			27.2193i			1.19250i	−0.802798	+	0.596251i	$0.796656\pi$
$522$		0			0
$523$	−3.44794			−0.150768			−0.0753838	−	0.997155i	$-0.524018\pi$
$523$	−3.44794			−0.150768			−0.0753838	+	0.997155i	$0.524018\pi$
$524$	2.58766	+	24.6415i	0.113042	+	1.07647i
$525$		0			0
$526$	12.5070	−	13.8891i	0.545330	−	0.605595i
$527$	12.9062	−	7.45141i	0.562204	−	0.324589i
$528$		0			0
$529$	−0.000637027		0.00110336i	−2.76968e−5		4.79723e-5i
$530$	1.88889	+	5.81432i	0.0820483	+	0.252558i
$531$		0			0
$532$	−4.29156	−	21.8181i	−0.186063	−	0.945937i
$533$	37.0533	−	64.1783i	1.60496	−	2.77987i
$534$		0			0
$535$	−3.56297	−	6.17125i	−0.154041	−	0.266806i
$536$	0.646298	−	6.14103i	0.0279158	−	0.265252i
$537$		0			0
$538$	38.1237	+	8.10525i	1.64363	+	0.349442i
$539$	−14.2665	+	12.0844i	−0.614502	+	0.520511i
$540$		0			0
$541$	5.99277			0.257649			0.128825	−	0.991667i	$-0.458880\pi$
$541$	5.99277			0.257649			0.128825	+	0.991667i	$0.458880\pi$
$542$	−6.24854	+	29.3905i	−0.268398	+	1.26243i
$543$		0			0
$544$	−6.70086	−	11.6123i	−0.287297	−	0.497875i
$545$	−4.55787	+	2.63149i	−0.195238	+	0.112721i
$546$		0			0
$547$	−5.72221	−	3.30372i	−0.244664	−	0.141257i	0.372654	−	0.927970i	$-0.378448\pi$
$547$	−5.72221	−	3.30372i	−0.244664	−	0.141257i	−0.617319	+	0.786713i	$0.711781\pi$
$548$	−14.4299	+	10.4819i	−0.616414	+	0.447765i
$549$		0			0
$550$	−5.56598	−	17.1330i	−0.237334	−	0.730553i
$551$	6.09576	−	10.5582i	0.259688	−	0.449793i
$552$		0			0
$553$	0.935116	+	10.4099i	0.0397652	+	0.442675i
$554$	15.2610	+	13.7423i	0.648377	+	0.583855i
$555$		0			0
$556$	−0.574601	−	5.47176i	−0.0243685	−	0.232055i
$557$	−6.08351			−0.257767			−0.128883	−	0.991660i	$-0.541139\pi$
$557$	−6.08351			−0.257767			−0.128883	+	0.991660i	$0.541139\pi$
$558$		0			0
$559$	−8.50697			−0.359806
$560$	−1.49710	−	4.85958i	−0.0632640	−	0.205355i
$561$		0			0
$562$	−13.3603	−	12.0308i	−0.563571	−	0.507488i
$563$	13.1561	+	22.7871i	0.554465	+	0.960361i	0.997945	+	0.0640767i	$0.0204102\pi$
$563$	13.1561	+	22.7871i	0.554465	+	0.960361i	−0.443480	+	0.896284i	$0.646256\pi$
$564$		0			0
$565$	3.93459	+	2.27164i	0.165530	+	0.0955686i
$566$	28.0496	−	9.11244i	1.17901	−	0.383024i
$567$		0			0
$568$	0.454759	+	0.330497i	0.0190813	+	0.0138673i
$569$	0.683478	−	1.18382i	0.0286529	−	0.0496283i	−0.851343	−	0.524609i	$-0.824212\pi$
$569$	0.683478	−	1.18382i	0.0286529	−	0.0496283i	0.879996	+	0.474981i	$0.157545\pi$
$570$		0			0
$571$	−14.6500	+	8.45818i	−0.613083	+	0.353964i	−0.774171	−	0.632976i	$-0.781833\pi$
$571$	−14.6500	+	8.45818i	−0.613083	+	0.353964i	0.161088	+	0.986940i	$0.448500\pi$
$572$	30.9178	+	13.7689i	1.29274	+	0.575705i
$573$		0			0
$574$	−26.2585	+	35.0117i	−1.09601	+	1.46136i
$575$		−	22.8713i		−	0.953801i
$576$		0			0
$577$		−	0.277722i		−	0.0115617i	−0.999983	−	0.00578087i	$-0.998160\pi$
$577$		−	0.277722i		−	0.0115617i	0.999983	−	0.00578087i	$-0.00184012\pi$
$578$	−3.34764	+	15.7459i	−0.139244	+	0.654943i
$579$		0			0
$580$	1.13419	−	2.54681i	0.0470948	−	0.105751i
$581$	26.8483	−	2.41176i	1.11386	−	0.100057i
$582$		0			0
$583$	20.8108	+	12.0151i	0.861896	+	0.497616i
$584$	11.0955	+	8.06369i	0.459136	+	0.333678i
$585$		0			0
$586$	2.93047	+	9.02046i	0.121057	+	0.372632i
$587$	−13.6979	+	23.7254i	−0.565372	+	0.979253i	0.431643	+	0.902044i	$0.357934\pi$
$587$	−13.6979	+	23.7254i	−0.565372	+	0.979253i	−0.997015	+	0.0772082i	$0.975399\pi$
$588$		0			0
$589$	13.2118	+	22.8836i	0.544385	+	0.942902i
$590$	0.127729	−	0.141845i	0.00525852	−	0.00583965i
$591$		0			0
$592$	12.5628	+	13.9576i	0.516330	+	0.573653i
$593$			32.0154i			1.31471i	0.753579	+	0.657357i	$0.228326\pi$
$593$			32.0154i			1.31471i	−0.753579	+	0.657357i	$0.771674\pi$
$594$		0			0
$595$	1.26696	−	2.73356i	0.0519403	−	0.112065i
$596$	−0.0318575	−	0.303370i	−0.00130494	−	0.0124265i
$597$		0			0
$598$	31.9317	+	28.7541i	1.30578	+	1.17584i
$599$	−15.8709	+	9.16306i	−0.648467	+	0.374392i	−0.787869	−	0.615843i	$-0.788815\pi$
$599$	−15.8709	+	9.16306i	−0.648467	+	0.374392i	0.139402	+	0.990236i	$0.455482\pi$
$600$		0			0
$601$	19.1583	+	11.0611i	0.781485	+	0.451190i	0.836956	−	0.547270i	$-0.184333\pi$
$601$	19.1583	+	11.0611i	0.781485	+	0.451190i	−0.0554716	+	0.998460i	$0.517666\pi$
$602$	4.98781	+	0.600902i	0.203288	+	0.0244910i
$603$		0			0
$604$	14.7773	+	20.3431i	0.601279	+	0.827748i
$605$	−1.60869	−	0.928780i	−0.0654027	−	0.0377603i
$606$		0			0
$607$	7.92507	+	13.7266i	0.321669	+	0.557146i	0.980832	−	0.194853i	$-0.0624230\pi$
$607$	7.92507	+	13.7266i	0.321669	+	0.557146i	−0.659164	+	0.751999i	$0.729090\pi$
$608$	20.5894	−	11.8811i	0.835012	−	0.481840i
$609$		0			0
$610$	1.55372	−	7.30802i	0.0629082	−	0.295893i
$611$			47.2491i			1.91150i
$612$		0			0
$613$	24.5067			0.989818			0.494909	−	0.868945i	$-0.335201\pi$
$613$	24.5067			0.989818			0.494909	+	0.868945i	$0.335201\pi$
$614$	−3.55243	+	16.7091i	−0.143365	+	0.674326i
$615$		0			0
$616$	−17.1551	−	10.2569i	−0.691201	−	0.413262i
$617$	15.9608	+	27.6449i	0.642557	+	1.11294i	0.984860	+	0.173352i	$0.0554599\pi$
$617$	15.9608	+	27.6449i	0.642557	+	1.11294i	−0.342303	+	0.939590i	$0.611207\pi$
$618$		0			0
$619$	−0.227459	+	0.393971i	−0.00914236	+	0.0158350i	−0.870560	−	0.492062i	$-0.836243\pi$
$619$	−0.227459	+	0.393971i	−0.00914236	+	0.0158350i	0.861418	+	0.507897i	$0.169577\pi$
$620$	3.55128	+	4.88885i	0.142623	+	0.196341i
$621$		0			0
$622$	−2.72192	+	0.884267i	−0.109139	+	0.0354559i
$623$	5.78126	−	4.06812i	0.231621	−	0.162986i
$624$		0			0
$625$	−10.7952	−	18.6978i	−0.431807	−	0.747911i
$626$	−18.3948	+	20.4277i	−0.735206	+	0.816454i
$627$		0			0
$628$	−22.8787	+	2.40253i	−0.912958	+	0.0958716i
$629$			11.1266i			0.443646i
$630$		0			0
$631$		−	28.8331i		−	1.14783i	−0.818916	−	0.573913i	$-0.805425\pi$
$631$		−	28.8331i		−	1.14783i	0.818916	−	0.573913i	$-0.194575\pi$
$632$	−10.2081	+	4.54327i	−0.406057	+	0.180722i
$633$		0			0
$634$	10.9680	+	9.87654i	0.435595	+	0.392248i
$635$	0.350386	+	0.606887i	0.0139046	+	0.0240836i
$636$		0			0
$637$	−7.90415	−	43.6404i	−0.313174	−	1.72910i
$638$	−3.38593	−	10.4225i	−0.134050	−	0.412629i
$639$		0			0
$640$	4.39888	−	3.19383i	0.173881	−	0.126247i
$641$	−3.90266	+	6.75961i	−0.154146	+	0.266989i	−0.932748	−	0.360530i	$-0.882596\pi$
$641$	−3.90266	+	6.75961i	−0.154146	+	0.266989i	0.778602	+	0.627518i	$0.215929\pi$
$642$		0			0
$643$	2.26137	+	3.91681i	0.0891797	+	0.154464i	0.907165	−	0.420776i	$-0.138242\pi$
$643$	2.26137	+	3.91681i	0.0891797	+	0.154464i	−0.817985	+	0.575240i	$0.804909\pi$
$644$	−16.6911	−	19.1147i	−0.657723	−	0.753223i
$645$		0			0
$646$	13.7770	+	2.92904i	0.542048	+	0.115242i
$647$	−32.4931			−1.27744			−0.638718	−	0.769441i	$-0.720535\pi$
$647$	−32.4931			−1.27744			−0.638718	+	0.769441i	$0.720535\pi$
$648$		0			0
$649$		−	0.750290i		−	0.0294515i
$650$	41.7979	+	8.88641i	1.63945	+	0.348554i
$651$		0			0
$652$	16.2492	−	36.4874i	0.636369	−	1.42896i
$653$	−3.99865	−	6.92587i	−0.156479	−	0.271030i	0.777117	−	0.629356i	$-0.216681\pi$
$653$	−3.99865	−	6.92587i	−0.156479	−	0.271030i	−0.933597	+	0.358325i	$0.883348\pi$
$654$		0			0
$655$	−5.15500	−	2.97624i	−0.201422	−	0.116291i
$656$	−44.4937	−	14.4658i	−1.73719	−	0.564796i
$657$		0			0
$658$	3.33751	−	27.7031i	0.130110	−	1.07998i
$659$	6.89888	+	3.98307i	0.268742	+	0.155158i	0.628316	−	0.777958i	$-0.283745\pi$
$659$	6.89888	+	3.98307i	0.268742	+	0.155158i	−0.359574	+	0.933117i	$0.617078\pi$
$660$		0			0
$661$	0.220771	−	0.127462i	0.00858700	−	0.00495771i	−0.495700	−	0.868494i	$-0.665089\pi$
$661$	0.220771	−	0.127462i	0.00858700	−	0.00495771i	0.504287	+	0.863536i	$0.331755\pi$
$662$	34.1755	−	37.9523i	1.32827	−	1.47506i
$663$		0			0
$664$	11.7176	+	26.3278i	0.454731	+	1.02172i
$665$	4.84679	+	2.24641i	0.187950	+	0.0871119i
$666$		0			0
$667$		−	13.9132i		−	0.538723i
$668$	−4.58476	−	43.6594i	−0.177390	−	1.68923i
$669$		0			0
$670$	1.10239	+	0.992692i	0.0425892	+	0.0383510i
$671$	−14.6839	−	25.4333i	−0.566867	−	0.981842i
$672$		0			0
$673$	−0.198313	+	0.343488i	−0.00764441	+	0.0132405i	−0.869822	−	0.493365i	$-0.835767\pi$
$673$	−0.198313	+	0.343488i	−0.00764441	+	0.0132405i	0.862178	+	0.506606i	$0.169100\pi$
$674$	−9.96762	+	3.23817i	−0.383938	+	0.124730i
$675$		0			0
$676$	−43.9197	+	31.9034i	−1.68922	+	1.22705i
$677$	43.1462	+	24.9105i	1.65824	+	0.957388i	0.973525	+	0.228582i	$0.0734090\pi$
$677$	43.1462	+	24.9105i	1.65824	+	0.957388i	0.684720	+	0.728806i	$0.259924\pi$
$678$		0			0
$679$	0.512568	+	5.70602i	0.0196706	+	0.218977i
$680$	3.20323	+	0.337117i	0.122838	+	0.0129278i
$681$		0			0
$682$	23.2323	+	4.93929i	0.889612	+	0.189135i
$683$			28.4508i			1.08864i	0.838878	+	0.544320i	$0.183212\pi$
$683$			28.4508i			1.08864i	−0.838878	+	0.544320i	$0.816788\pi$
$684$		0			0
$685$		−	4.28474i		−	0.163712i
$686$	1.55176	+	26.1456i	0.0592465	+	0.998243i
$687$		0			0
$688$	1.11568	+	5.25359i	0.0425350	+	0.200291i
$689$	−49.3654	+	28.5011i	−1.88067	+	1.08581i
$690$		0			0
$691$	−6.08340	+	10.5368i	−0.231423	+	0.400837i	−0.958227	−	0.286008i	$-0.907672\pi$
$691$	−6.08340	+	10.5368i	−0.231423	+	0.400837i	0.726804	+	0.686845i	$0.241005\pi$
$692$	−17.9786	−	24.7501i	−0.683443	−	0.940859i
$693$		0			0
$694$	12.5471	+	38.6219i	0.476281	+	1.46607i
$695$	1.14469	+	0.660887i	0.0434206	+	0.0250689i
$696$		0			0
$697$	−13.8607	−	24.0074i	−0.525011	−	0.909345i
$698$	0.813827	−	0.903764i	0.0308038	−	0.0342080i
$699$		0			0
$700$	−23.8793	−	8.16275i	−0.902552	−	0.308523i
$701$	9.67651			0.365477			0.182738	−	0.983162i	$-0.441504\pi$
$701$	9.67651			0.365477			0.182738	+	0.983162i	$0.441504\pi$
$702$		0			0
$703$	−19.7282			−0.744062
$704$	4.44830	−	20.8995i	0.167652	−	0.787678i
$705$		0			0
$706$	30.2863	−	33.6333i	1.13984	−	1.26581i
$707$	−1.23093	−	13.7030i	−0.0462938	−	0.515353i
$708$		0			0
$709$	−22.5400	+	39.0404i	−0.846507	+	1.46619i	0.0377999	+	0.999285i	$0.487965\pi$
$709$	−22.5400	+	39.0404i	−0.846507	+	1.46619i	−0.884306	+	0.466907i	$0.845368\pi$
$710$	−0.128448	+	0.0417289i	−0.00482058	+	0.00156606i
$711$		0			0
$712$	6.11331	+	4.44286i	0.229106	+	0.166503i
$713$	26.1153	+	15.0776i	0.978024	+	0.564662i
$714$		0			0
$715$	−7.04166	+	4.06550i	−0.263343	+	0.152041i
$716$	8.70330	−	19.5431i	0.325258	−	0.730361i
$717$		0			0
$718$	−7.63805	−	1.62388i	−0.285050	−	0.0606028i
$719$	12.1609			0.453526			0.226763	−	0.973950i	$-0.427186\pi$
$719$	12.1609			0.453526			0.226763	+	0.973950i	$0.427186\pi$
$720$		0			0
$721$	−2.51531	+	5.42696i	−0.0936749	+	0.202111i
$722$	0.394412	−	1.85515i	0.0146785	−	0.0690414i
$723$		0			0
$724$	−5.88630	+	13.2176i	−0.218762	+	0.491228i
$725$	−6.91809	−	11.9825i	−0.256931	−	0.445018i
$726$		0			0
$727$	8.39590	−	14.5421i	0.311387	−	0.539337i	−0.667276	−	0.744810i	$-0.732540\pi$
$727$	8.39590	−	14.5421i	0.311387	−	0.539337i	0.978663	+	0.205473i	$0.0658733\pi$
$728$	41.4177	−	23.0767i	1.53504	−	0.855278i
$729$		0			0
$730$	−3.13397	+	1.01813i	−0.115993	+	0.0376827i
$731$	−1.59112	+	2.75589i	−0.0588496	+	0.101930i
$732$		0			0
$733$	−18.4832	+	10.6713i	−0.682693	+	0.394153i	−0.800869	−	0.598840i	$-0.795629\pi$
$733$	−18.4832	+	10.6713i	−0.682693	+	0.394153i	0.118176	+	0.992993i	$0.462295\pi$
$734$	−24.1220	−	21.7215i	−0.890359	−	0.801756i
$735$		0			0
$736$	13.5696	−	23.4909i	0.500184	−	0.865887i
$737$	5.83114			0.214793
$738$		0			0
$739$		−	50.5558i		−	1.85973i	−0.367907	−	0.929863i	$-0.619926\pi$
$739$		−	50.5558i		−	1.85973i	0.367907	−	0.929863i	$-0.380074\pi$
$740$	−4.48675	+	0.471163i	−0.164936	+	0.0173203i
$741$		0			0
$742$	30.9572	−	13.2238i	1.13647	−	0.485461i
$743$	−32.1395	+	18.5558i	−1.17909	+	0.680745i	−0.955803	−	0.294009i	$-0.905011\pi$
$743$	−32.1395	+	18.5558i	−1.17909	+	0.680745i	−0.223282	+	0.974754i	$0.571677\pi$
$744$		0			0
$745$	0.0634650	+	0.0366415i	0.00232518	+	0.00134244i
$746$	38.3835	−	12.4696i	1.40532	−	0.456545i
$747$		0			0
$748$	10.2433	−	7.44075i	0.374532	−	0.272061i
$749$	−32.0900	+	22.5809i	−1.17254	+	0.825088i
$750$		0			0
$751$	−37.8228	+	21.8370i	−1.38017	+	0.796843i	−0.992180	−	0.124819i	$-0.960165\pi$
$751$	−37.8228	+	21.8370i	−1.38017	+	0.796843i	−0.387993	+	0.921662i	$0.626832\pi$
$752$	29.1793	−	6.19669i	1.06406	−	0.225970i
$753$		0			0
$754$	25.4268	+	5.40584i	0.925988	+	0.196869i
$755$	−6.04058			−0.219839
$756$		0			0
$757$	−53.5207			−1.94524			−0.972622	−	0.232392i	$-0.925345\pi$
$757$	−53.5207			−1.94524			−0.972622	+	0.232392i	$0.925345\pi$
$758$	−18.5281	−	3.93916i	−0.672972	−	0.143077i
$759$		0			0
$760$	−0.597730	+	5.67954i	−0.0216820	+	0.206019i
$761$	−19.6964	+	11.3717i	−0.713994	+	0.412225i	−0.812538	−	0.582908i	$-0.801915\pi$
$761$	−19.6964	+	11.3717i	−0.713994	+	0.412225i	0.0985439	+	0.995133i	$0.468582\pi$
$762$		0			0
$763$	16.6775	+	23.7006i	0.603765	+	0.858018i
$764$	−23.4260	−	32.2493i	−0.847524	−	1.16674i
$765$		0			0
$766$	30.1096	−	9.78170i	1.08791	−	0.353427i
$767$	1.54132	+	0.889883i	0.0556540	+	0.0321318i
$768$		0			0
$769$	−9.86460	+	5.69533i	−0.355726	+	0.205379i	−0.667204	−	0.744875i	$-0.732509\pi$
$769$	−9.86460	+	5.69533i	−0.355726	+	0.205379i	0.311478	+	0.950253i	$0.399176\pi$
$770$	4.41584	−	1.88629i	0.159136	−	0.0679772i
$771$		0			0
$772$	−2.97805	−	28.3591i	−0.107182	−	1.02067i
$773$			30.6663i			1.10299i	0.834178	+	0.551495i	$0.185942\pi$
$773$			30.6663i			1.10299i	−0.834178	+	0.551495i	$0.814058\pi$
$774$		0			0
$775$	29.9883			1.07721
$776$	−5.59540	+	2.49032i	−0.200863	+	0.0893972i
$777$		0			0
$778$	−28.4392	−	25.6092i	−1.01960	−	0.918133i
$779$	42.5667	−	24.5759i	1.52511	−	0.880523i
$780$		0			0
$781$	−0.265435	+	0.459746i	−0.00949800	+	0.0164510i
$782$	15.2875	−	4.96644i	0.546680	−	0.177600i
$783$		0			0
$784$	−25.9141	+	10.6047i	−0.925503	+	0.378740i
$785$	2.76332	−	4.78621i	0.0986271	−	0.170827i
$786$		0			0
$787$	−9.75700	−	16.8996i	−0.347799	−	0.602406i	0.638059	−	0.769988i	$-0.279738\pi$
$787$	−9.75700	−	16.8996i	−0.347799	−	0.602406i	−0.985858	+	0.167581i	$0.946404\pi$
$788$	21.8358	+	9.72431i	0.777868	+	0.346414i
$789$		0			0
$790$	0.558226	−	2.62566i	0.0198608	−	0.0934166i
$791$	10.5201	−	22.6978i	0.374050	−	0.807042i
$792$		0			0
$793$	69.6636			2.47383
$794$	16.1372	+	3.43084i	0.572688	+	0.121756i
$795$		0			0
$796$	40.1056	+	17.8606i	1.42151	+	0.633051i
$797$	25.9632	−	14.9898i	0.919663	−	0.530968i	0.0361355	−	0.999347i	$-0.488495\pi$
$797$	25.9632	−	14.9898i	0.919663	−	0.530968i	0.883528	+	0.468379i	$0.155162\pi$
$798$		0			0
$799$	15.3067	+	8.83733i	0.541512	+	0.312642i
$800$	0.00615553	−	26.9783i	0.000217631	−	0.953827i
$801$		0			0
$802$	−22.4205	+	7.28372i	−0.791694	+	0.257197i
$803$	−6.47626	+	11.2172i	−0.228542	+	0.395847i
$804$		0			0
$805$	6.07204	−	0.545446i	0.214011	−	0.0192245i
$806$	−37.7016	+	41.8680i	−1.32798	+	1.47474i
$807$		0			0
$808$	13.4373	−	5.98047i	0.472723	−	0.210392i
$809$	54.5869			1.91917			0.959586	−	0.281415i	$-0.0908038\pi$
$809$	54.5869			1.91917			0.959586	+	0.281415i	$0.0908038\pi$
$810$		0			0
$811$	−17.5107			−0.614883			−0.307442	−	0.951567i	$-0.599473\pi$
$811$	−17.5107			−0.614883			−0.307442	+	0.951567i	$0.599473\pi$
$812$	−14.5264	−	4.96561i	−0.509776	−	0.174259i
$813$		0			0
$814$	−11.8664	+	13.1778i	−0.415917	+	0.461880i
$815$	4.79788	+	8.31016i	0.168062	+	0.291092i
$816$		0			0
$817$	−4.88638	−	2.82115i	−0.170953	−	0.0986997i
$818$	0.297323	+	0.915209i	0.0103957	+	0.0319995i
$819$		0			0
$820$	9.09395	−	6.60587i	0.317575	−	0.230687i
$821$	9.47071	−	16.4037i	0.330530	−	0.572495i	−0.652086	−	0.758145i	$-0.726106\pi$
$821$	9.47071	−	16.4037i	0.330530	−	0.572495i	0.982616	+	0.185650i	$0.0594392\pi$
$822$		0			0
$823$	8.43975	−	4.87269i	0.294191	−	0.169851i	−0.345639	−	0.938367i	$-0.612338\pi$
$823$	8.43975	−	4.87269i	0.294191	−	0.169851i	0.639831	+	0.768516i	$0.279005\pi$
$824$	−6.35940	−	0.669280i	−0.221540	−	0.0233155i
$825$		0			0
$826$	−0.840852	−	0.630631i	−0.0292570	−	0.0219425i
$827$			38.9872i			1.35572i	0.735193	+	0.677858i	$0.237092\pi$
$827$			38.9872i			1.35572i	−0.735193	+	0.677858i	$0.762908\pi$
$828$		0			0
$829$		−	8.11853i		−	0.281968i	−0.990012	−	0.140984i	$-0.954973\pi$
$829$		−	8.11853i		−	0.281968i	0.990012	−	0.140984i	$-0.0450266\pi$
$830$	−6.77185	−	1.43972i	−0.235054	−	0.0499735i
$831$		0			0
$832$	37.6579	+	33.9260i	1.30555	+	1.17617i
$833$	−15.6160	−	5.60176i	−0.541062	−	0.194089i
$834$		0			0
$835$	9.13352	+	5.27324i	0.316078	+	0.182488i
$836$	13.1929	+	18.1620i	0.456288	+	0.628147i
$837$		0			0
$838$	13.9862	−	4.54368i	0.483144	−	0.156959i
$839$	13.5859	−	23.5314i	0.469036	−	0.812394i	−0.530337	−	0.847787i	$-0.677935\pi$
$839$	13.5859	−	23.5314i	0.469036	−	0.812394i	0.999373	+	0.0353923i	$0.0112681\pi$
$840$		0			0
$841$	10.2915	+	17.8255i	0.354881	+	0.614672i
$842$	−7.20454	−	6.48759i	−0.248285	−	0.223577i
$843$		0			0
$844$	−20.4950	+	2.15223i	−0.705469	+	0.0740826i
$845$		−	13.0413i		−	0.448635i
$846$		0			0
$847$	−4.30122	+	9.28021i	−0.147792	+	0.318872i
$848$	24.0755	+	26.7484i	0.826756	+	0.918543i
$849$		0			0
$850$	10.6966	−	11.8787i	0.366889	−	0.407434i
$851$	−19.4979	+	11.2571i	−0.668379	+	0.385889i
$852$		0			0
$853$	−20.4384	−	11.8001i	−0.699797	−	0.404028i	0.107475	−	0.994208i	$-0.465724\pi$
$853$	−20.4384	−	11.8001i	−0.699797	−	0.404028i	−0.807272	+	0.590180i	$0.799057\pi$
$854$	−40.8452	−	4.92079i	−1.39769	−	0.168386i
$855$		0			0
$856$	−33.9331	−	24.6609i	−1.15981	−	0.842893i
$857$	13.6342	+	7.87173i	0.465737	+	0.268893i	0.714453	−	0.699683i	$-0.246675\pi$
$857$	13.6342	+	7.87173i	0.465737	+	0.268893i	−0.248717	+	0.968576i	$0.580009\pi$
$858$		0			0
$859$	13.3695	+	23.1566i	0.456160	+	0.790093i	0.998754	−	0.0499024i	$-0.0158910\pi$
$859$	13.3695	+	23.1566i	0.456160	+	0.790093i	−0.542594	+	0.839995i	$0.682558\pi$
$860$	−1.17868	−	0.524911i	−0.0401927	−	0.0178993i
$861$		0			0
$862$	21.1052	+	4.48706i	0.718847	+	0.152830i
$863$		−	50.8477i		−	1.73088i	−0.501015	−	0.865438i	$-0.667040\pi$
$863$		−	50.8477i		−	1.73088i	0.501015	−	0.865438i	$-0.332960\pi$
$864$		0			0
$865$	7.34919			0.249880
$866$	−47.9256	−	10.1892i	−1.62858	−	0.346243i
$867$		0			0
$868$	25.0626	−	21.8850i	0.850681	−	0.742824i
$869$	−5.27570	−	9.13778i	−0.178966	−	0.309978i
$870$		0			0
$871$	−6.91604	+	11.9789i	−0.234341	+	0.405891i
$872$	−18.2137	+	25.0618i	−0.616794	+	0.848700i
$873$		0			0
$874$	8.80582	+	27.1057i	0.297861	+	0.916866i
$875$	10.1564	−	7.14680i	0.343349	−	0.241606i
$876$		0			0
$877$	6.79088	+	11.7621i	0.229312	+	0.397179i	0.957604	−	0.288087i	$-0.0930192\pi$
$877$	6.79088	+	11.7621i	0.229312	+	0.397179i	−0.728293	+	0.685266i	$0.759686\pi$
$878$	12.8669	+	11.5865i	0.434238	+	0.391026i
$879$		0			0
$880$	3.43421	+	3.81548i	0.115767	+	0.128620i
$881$			5.11905i			0.172465i	0.996275	+	0.0862325i	$0.0274828\pi$
$881$			5.11905i			0.172465i	−0.996275	+	0.0862325i	$0.972517\pi$
$882$		0			0
$883$		−	36.5196i		−	1.22898i	−0.788924	−	0.614491i	$-0.789361\pi$
$883$		−	36.5196i		−	1.22898i	0.788924	−	0.614491i	$-0.210639\pi$
$884$	3.13649	+	29.8679i	0.105492	+	1.00457i
$885$		0			0
$886$	26.4955	−	29.4235i	0.890133	−	0.988502i
$887$	16.1245	+	27.9284i	0.541407	+	0.937744i	0.998824	+	0.0484917i	$0.0154415\pi$
$887$	16.1245	+	27.9284i	0.541407	+	0.937744i	−0.457417	+	0.889252i	$0.651225\pi$
$888$		0			0
$889$	3.15576	−	2.22063i	0.105841	−	0.0744774i
$890$	−1.72673	+	0.560960i	−0.0578800	+	0.0188034i
$891$		0			0
$892$	23.4091	−	17.0044i	0.783793	−	0.569350i
$893$	−15.6692	+	27.1398i	−0.524349	+	0.908199i
$894$		0			0
$895$	2.56981	+	4.45103i	0.0858991	+	0.148782i
$896$	−19.6832	−	22.5515i	−0.657569	−	0.753394i
$897$		0			0
$898$	7.00739	−	32.9598i	0.233840	−	1.09988i
$899$	18.2427			0.608426
$900$		0			0
$901$			21.3231i			0.710374i
$902$	9.18778	−	43.2154i	0.305920	−	1.43892i
$903$		0			0
$904$	26.5977	+	2.79921i	0.884626	+	0.0931003i
$905$	−1.73803	−	3.01036i	−0.0577742	−	0.100068i
$906$		0			0
$907$	−24.3819	−	14.0769i	−0.809588	−	0.467416i	0.0372246	−	0.999307i	$-0.488148\pi$
$907$	−24.3819	−	14.0769i	−0.809588	−	0.467416i	−0.846813	+	0.531891i	$0.821482\pi$
$908$	31.3153	−	22.7475i	1.03924	−	0.754904i
$909$		0			0
$910$	−1.36241	+	11.3087i	−0.0451634	+	0.374880i
$911$	33.2831	+	19.2160i	1.10272	+	0.636655i	0.936934	−	0.349507i	$-0.113651\pi$
$911$	33.2831	+	19.2160i	1.10272	+	0.636655i	0.165785	+	0.986162i	$0.446984\pi$
$912$		0			0
$913$	−23.5673	+	13.6066i	−0.779964	+	0.450312i
$914$	−25.0330	−	22.5419i	−0.828019	−	0.745620i
$915$		0			0
$916$	−39.1819	+	4.11456i	−1.29461	+	0.135949i
$917$	−13.7831	+	29.7381i	−0.455158	+	0.982038i
$918$		0			0
$919$			17.3398i			0.571988i	0.958231	+	0.285994i	$0.0923238\pi$
$919$			17.3398i			0.571988i	−0.958231	+	0.285994i	$0.907676\pi$
$920$	2.65006	+	5.95432i	0.0873698	+	0.196308i
$921$		0			0
$922$	0.347007	−	0.385355i	0.0114281	−	0.0126910i
$923$	−0.629639	−	1.09057i	−0.0207248	−	0.0358964i
$924$		0			0
$925$	−11.1948	+	19.3899i	−0.368081	+	0.637536i
$926$	−7.24077	−	22.2883i	−0.237946	−	0.732438i
$927$		0			0
$928$	0.00374457	−	16.4116i	0.000122922	−	0.538738i
$929$	−48.7835	−	28.1651i	−1.60053	−	0.924068i	−0.991380	−	0.131016i	$-0.958176\pi$
$929$	−48.7835	−	28.1651i	−1.60053	−	0.924068i	−0.609153	−	0.793053i	$-0.708490\pi$
$930$		0			0
$931$	9.93228	−	27.6882i	0.325517	−	0.907444i
$932$	13.4251	+	5.97869i	0.439753	+	0.195839i
$933$		0			0
$934$	−7.68949	+	36.1681i	−0.251608	+	1.18346i
$935$			3.04160i			0.0994708i
$936$		0			0
$937$		−	36.1315i		−	1.18036i	−0.807270	−	0.590182i	$-0.799056\pi$
$937$		−	36.1315i		−	1.18036i	0.807270	−	0.590182i	$-0.200944\pi$
$938$	4.90117	−	6.53497i	0.160029	−	0.213374i
$939$		0			0
$940$	−2.91545	+	6.54659i	−0.0950914	+	0.213526i
$941$	−12.0974	+	6.98446i	−0.394365	+	0.227687i	−0.684050	−	0.729435i	$-0.739783\pi$
$941$	−12.0974	+	6.98446i	−0.394365	+	0.227687i	0.289684	+	0.957122i	$0.406450\pi$
$942$		0			0
$943$	28.0466	−	48.5781i	0.913321	−	1.58192i
$944$	0.347416	−	1.06857i	0.0113074	−	0.0347791i
$945$		0			0
$946$	−4.82357	+	1.56703i	−0.156828	+	0.0509485i
$947$	11.0539	+	6.38196i	0.359203	+	0.207386i	0.668731	−	0.743505i	$-0.266838\pi$
$947$	11.0539	+	6.38196i	0.359203	+	0.207386i	−0.309528	+	0.950890i	$0.600171\pi$
$948$		0			0
$949$	−15.3624	−	26.6084i	−0.498684	−	0.863746i
$950$	21.0616	+	18.9657i	0.683330	+	0.615329i
$951$		0			0
$952$	0.270777	−	17.7337i	0.00877595	−	0.574754i
$953$	3.91673			0.126875			0.0634377	−	0.997986i	$-0.479794\pi$
$953$	3.91673			0.126875			0.0634377	+	0.997986i	$0.479794\pi$
$954$		0			0
$955$	9.57597			0.309871
$956$	19.1691	−	2.01299i	0.619973	−	0.0651046i
$957$		0			0
$958$	−40.0974	−	36.1072i	−1.29549	−	1.16657i
$959$	−23.4990	+	2.11090i	−0.758823	+	0.0681645i
$960$		0			0
$961$	−4.26940	+	7.39481i	−0.137722	+	0.238542i
$962$	−12.9969	−	40.0067i	−0.419038	−	1.28987i
$963$		0			0
$964$	4.83470	+	6.65568i	0.155715	+	0.214365i
$965$	5.93272	+	3.42526i	0.190981	+	0.110263i
$966$		0			0
$967$	−20.2799	+	11.7086i	−0.652158	+	0.376524i	−0.789283	−	0.614030i	$-0.789547\pi$
$967$	−20.2799	+	11.7086i	−0.652158	+	0.376524i	0.137125	+	0.990554i	$0.456214\pi$
$968$	−10.8747	−	1.14448i	−0.349526	−	0.0367850i
$969$		0			0
$970$	0.305982	−	1.43921i	0.00982448	−	0.0462102i
$971$	−25.1209			−0.806167			−0.403084	−	0.915163i	$-0.632062\pi$
$971$	−25.1209			−0.806167			−0.403084	+	0.915163i	$0.632062\pi$
$972$		0			0
$973$	3.06060	−	6.60347i	0.0981184	−	0.211698i
$974$	−12.3641	−	2.62867i	−0.396173	−	0.0842280i
$975$		0			0
$976$	−9.13633	−	43.0217i	−0.292447	−	1.37709i
$977$	1.21770	+	2.10911i	0.0389575	+	0.0674764i	0.884847	−	0.465882i	$-0.154263\pi$
$977$	1.21770	+	2.10911i	0.0389575	+	0.0674764i	−0.845889	+	0.533359i	$0.820930\pi$
$978$		0			0
$979$	−3.56823	+	6.18036i	−0.114041	+	0.197525i
$980$	1.59762	−	6.53430i	0.0510340	−	0.208731i
$981$		0			0
$982$	4.05199	+	12.4727i	0.129304	+	0.398019i
$983$	−9.60279	+	16.6325i	−0.306281	+	0.530495i	−0.977546	−	0.210723i	$-0.932418\pi$
$983$	−9.60279	+	16.6325i	−0.306281	+	0.530495i	0.671264	+	0.741218i	$0.265752\pi$
$984$		0			0
$985$	−4.97320	+	2.87128i	−0.158459	+	0.0914865i
$986$	6.50700	−	7.22610i	0.207225	−	0.230126i
$987$		0			0
$988$	−52.9578	+	5.56120i	−1.68481	+	0.176925i
$989$	−6.43913			−0.204752
$990$		0			0
$991$			29.4493i			0.935489i	0.883864	+	0.467745i	$0.154933\pi$
$991$			29.4493i			0.935489i	−0.883864	+	0.467745i	$0.845067\pi$
$992$	30.8007	+	17.7921i	0.977922	+	0.564901i
$993$		0			0
$994$	0.292137	+	0.683897i	0.00926601	+	0.0216919i
$995$	−9.13423	+	5.27365i	−0.289575	+	0.167186i
$996$		0			0
$997$	13.3933	+	7.73264i	0.424171	+	0.244895i	0.696860	−	0.717207i	$-0.254580\pi$
$997$	13.3933	+	7.73264i	0.424171	+	0.244895i	−0.272689	+	0.962102i	$0.587913\pi$
$998$	7.58668	+	23.3530i	0.240152	+	0.739227i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bi.c.559.18		80
3.2	odd	2		252.2.bi.c.223.23	yes	80
4.3	odd	2	inner	756.2.bi.c.559.8		80
7.6	odd	2	inner	756.2.bi.c.559.17		80
9.4	even	3	inner	756.2.bi.c.307.7		80
9.5	odd	6		252.2.bi.c.139.33	yes	80
12.11	even	2		252.2.bi.c.223.34	yes	80
21.20	even	2		252.2.bi.c.223.24	yes	80
28.27	even	2	inner	756.2.bi.c.559.7		80
36.23	even	6		252.2.bi.c.139.24	yes	80
36.31	odd	6	inner	756.2.bi.c.307.17		80
63.13	odd	6	inner	756.2.bi.c.307.8		80
63.41	even	6		252.2.bi.c.139.34	yes	80
84.83	odd	2		252.2.bi.c.223.33	yes	80
252.139	even	6	inner	756.2.bi.c.307.18		80
252.167	odd	6		252.2.bi.c.139.23	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.23	✓	80	252.167	odd	6
252.2.bi.c.139.24	yes	80	36.23	even	6
252.2.bi.c.139.33	yes	80	9.5	odd	6
252.2.bi.c.139.34	yes	80	63.41	even	6
252.2.bi.c.223.23	yes	80	3.2	odd	2
252.2.bi.c.223.24	yes	80	21.20	even	2
252.2.bi.c.223.33	yes	80	84.83	odd	2
252.2.bi.c.223.34	yes	80	12.11	even	2
756.2.bi.c.307.7		80	9.4	even	3	inner
756.2.bi.c.307.8		80	63.13	odd	6	inner
756.2.bi.c.307.17		80	36.31	odd	6	inner
756.2.bi.c.307.18		80	252.139	even	6	inner
756.2.bi.c.559.7		80	28.27	even	2	inner
756.2.bi.c.559.8		80	4.3	odd	2	inner
756.2.bi.c.559.17		80	7.6	odd	2	inner
756.2.bi.c.559.18		80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.294095 + 1.38330i) q^{2} +(-1.82702 - 0.813640i) q^{4} +(0.416111 - 0.240242i) q^{5} +(-1.52257 - 2.16374i) q^{7} +(1.66282 - 2.28802i) q^{8} +O(q^{10})\)	\(q+(-0.294095 + 1.38330i) q^{2} +(-1.82702 - 0.813640i) q^{4} +(0.416111 - 0.240242i) q^{5} +(-1.52257 - 2.16374i) q^{7} +(1.66282 - 2.28802i) q^{8} +(0.209950 + 0.646259i) q^{10} +(2.31311 + 1.33548i) q^{11} +(-5.48694 + 3.16789i) q^{13} +(3.44088 - 1.46982i) q^{14} +(2.67598 + 2.97307i) q^{16} +2.37005i q^{17} -4.20225 q^{19} +(-0.955712 + 0.100361i) q^{20} +(-2.52763 + 2.80696i) q^{22} +(-4.15320 + 2.39785i) q^{23} +(-2.38457 + 4.13019i) q^{25} +(-2.76845 - 8.52173i) q^{26} +(1.02125 + 5.19202i) q^{28} +(-1.45060 + 2.51250i) q^{29} +(-3.14399 - 5.44556i) q^{31} +(-4.89962 + 2.82731i) q^{32} +(-3.27848 - 0.697018i) q^{34} +(-1.15338 - 0.534572i) q^{35} +4.69467 q^{37} +(1.23586 - 5.81295i) q^{38} +(0.142241 - 1.35155i) q^{40} +(-10.1295 + 5.84827i) q^{41} +(1.16280 + 0.671344i) q^{43} +(-3.13950 - 4.32198i) q^{44} +(-2.09550 - 6.45030i) q^{46} +(3.72876 - 6.45840i) q^{47} +(-2.36356 + 6.58890i) q^{49} +(-5.01199 - 4.51323i) q^{50} +(12.6023 - 1.32339i) q^{52} +8.99689 q^{53} +1.28335 q^{55} +(-7.48244 - 0.114250i) q^{56} +(-3.04893 - 2.74552i) q^{58} +(-0.140454 - 0.243273i) q^{59} +(-9.52219 - 5.49764i) q^{61} +(8.45745 - 2.74757i) q^{62} +(-2.47005 - 7.60913i) q^{64} +(-1.52212 + 2.63639i) q^{65} +(1.89068 - 1.09159i) q^{67} +(1.92837 - 4.33012i) q^{68} +(1.07867 - 1.43825i) q^{70} +0.198757i q^{71} +4.84941i q^{73} +(-1.38068 + 6.49412i) q^{74} +(7.67758 + 3.41912i) q^{76} +(-0.632248 - 7.03833i) q^{77} +(-3.42117 - 1.97521i) q^{79} +(1.82776 + 0.594244i) q^{80} +(-5.11086 - 15.7321i) q^{82} +(-5.09429 + 8.82356i) q^{83} +(0.569384 + 0.986203i) q^{85} +(-1.27064 + 1.41106i) q^{86} +(6.90188 - 3.07178i) q^{88} +2.67188i q^{89} +(15.2087 + 7.04900i) q^{91} +(9.53895 - 1.00170i) q^{92} +(7.83727 + 7.05736i) q^{94} +(-1.74860 + 1.00956i) q^{95} +(-1.87526 - 1.08268i) q^{97} +(-8.41929 - 5.20727i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

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