LMFDB - Embedded newform 756.2.bi.c.307.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(307,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [80,6,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			307.17
Character	$\chi$	$=$	756.307
Dual form			756.2.bi.c.559.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.294095 - 1.38330i) q^{2} +(-1.82702 + 0.813640i) q^{4} +(-0.416111 - 0.240242i) q^{5} +(-2.63514 + 0.236713i) q^{7} +(1.66282 + 2.28802i) q^{8} +(-0.209950 + 0.646259i) q^{10} +(2.31311 - 1.33548i) q^{11} +(5.48694 + 3.16789i) q^{13} +(1.10242 + 3.57556i) q^{14} +(2.67598 - 2.97307i) q^{16} +2.37005i q^{17} +4.20225 q^{19} +(0.955712 + 0.100361i) q^{20} +(-2.52763 - 2.80696i) q^{22} +(-4.15320 - 2.39785i) q^{23} +(-2.38457 - 4.13019i) q^{25} +(2.76845 - 8.52173i) q^{26} +(4.62185 - 2.57653i) q^{28} +(-1.45060 - 2.51250i) q^{29} +(3.14399 - 5.44556i) q^{31} +(-4.89962 - 2.82731i) q^{32} +(3.27848 - 0.697018i) q^{34} +(1.15338 + 0.534572i) q^{35} +4.69467 q^{37} +(-1.23586 - 5.81295i) q^{38} +(-0.142241 - 1.35155i) q^{40} +(10.1295 + 5.84827i) q^{41} +(1.16280 - 0.671344i) q^{43} +(-3.13950 + 4.32198i) q^{44} +(-2.09550 + 6.45030i) q^{46} +(-3.72876 - 6.45840i) q^{47} +(6.88793 - 1.24754i) q^{49} +(-5.01199 + 4.51323i) q^{50} +(-12.6023 - 1.32339i) q^{52} +8.99689 q^{53} -1.28335 q^{55} +(-4.92337 - 5.63564i) q^{56} +(-3.04893 + 2.74552i) q^{58} +(0.140454 - 0.243273i) q^{59} +(9.52219 - 5.49764i) q^{61} +(-8.45745 - 2.74757i) q^{62} +(-2.47005 + 7.60913i) q^{64} +(-1.52212 - 2.63639i) q^{65} +(1.89068 + 1.09159i) q^{67} +(-1.92837 - 4.33012i) q^{68} +(0.400269 - 1.75268i) q^{70} -0.198757i q^{71} +4.84941i q^{73} +(-1.38068 - 6.49412i) q^{74} +(-7.67758 + 3.41912i) q^{76} +(-5.77925 + 4.06671i) q^{77} +(-3.42117 + 1.97521i) q^{79} +(-1.82776 + 0.594244i) q^{80} +(5.11086 - 15.7321i) q^{82} +(5.09429 + 8.82356i) q^{83} +(0.569384 - 0.986203i) q^{85} +(-1.27064 - 1.41106i) q^{86} +(6.90188 + 3.07178i) q^{88} +2.67188i q^{89} +(-15.2087 - 7.04900i) q^{91} +(9.53895 + 1.00170i) q^{92} +(-7.83727 + 7.05736i) q^{94} +(-1.74860 - 1.00956i) q^{95} +(1.87526 - 1.08268i) q^{97} +(-3.75143 - 9.16116i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

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	$-0.367598\pi$
$5$	−0.416111	−	0.240242i	−0.186091	−	0.107439i	−0.590151	+	0.807293i	$0.700932\pi$
$6$		0			0
$7$	−2.63514	+	0.236713i	−0.995990	+	0.0894690i
$7$	−2.63514	+	0.236713i	−0.995990	+	0.0894690i
$8$	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	−0.108960	−	0.994046i	$-0.534752\pi$
$11$	2.31311	−	1.33548i	0.697429	−	0.402661i	0.806389	+	0.591385i	$0.201419\pi$
$12$		0			0
$13$	5.48694	+	3.16789i	1.52180	+	0.878614i	0.999668	+	0.0257515i	$0.00819785\pi$
$13$	5.48694	+	3.16789i	1.52180	+	0.878614i	0.522136	+	0.852862i	$0.325135\pi$
$14$	1.10242	+	3.57556i	0.294635	+	0.955610i
$15$		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	$-0.339899\pi$
$19$	4.20225			0.964062			0.482031	+	0.876154i	$0.339899\pi$
$20$	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	1.59909e−5	−	1.00000i	$-0.499995\pi$
$23$	−4.15320	−	2.39785i	−0.866001	−	0.499986i	−0.866017	+	0.500014i	$0.833328\pi$
$24$		0			0
$25$	−2.38457	−	4.13019i	−0.476914	−	0.826038i
$26$	2.76845	−	8.52173i	0.542937	−	1.67125i
$27$		0			0
$28$	4.62185	−	2.57653i	0.873447	−	0.486919i
$29$	−1.45060	−	2.51250i	−0.269369	−	0.466560i	0.699330	−	0.714799i	$-0.253482\pi$
$29$	−1.45060	−	2.51250i	−0.269369	−	0.466560i	−0.968699	+	0.248238i	$0.920148\pi$
$30$		0			0
$31$	3.14399	−	5.44556i	0.564678	−	0.978051i	−0.432402	−	0.901681i	$-0.642334\pi$
$31$	3.14399	−	5.44556i	0.564678	−	0.978051i	0.997080	−	0.0763698i	$-0.0243330\pi$
$32$	−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	0.994573	+	0.104043i	$0.0331779\pi$
$41$	10.1295	+	5.84827i	1.58196	+	0.913347i	0.587390	+	0.809304i	$0.300155\pi$
$42$		0			0
$43$	1.16280	−	0.671344i	0.177326	−	0.102379i	−0.408710	−	0.912664i	$-0.634021\pi$
$43$	1.16280	−	0.671344i	0.177326	−	0.102379i	0.586036	+	0.810285i	$0.300688\pi$
$44$	−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	−0.998676	−	0.0514505i	$-0.983616\pi$
$47$	−3.72876	−	6.45840i	−0.543895	−	0.942054i	0.454780	−	0.890604i	$-0.349718\pi$
$48$		0			0
$49$	6.88793	−	1.24754i	0.983991	−	0.178220i
$50$	−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
$56$	−4.92337	−	5.63564i	−0.657913	−	0.753094i
$57$		0			0
$58$	−3.04893	+	2.74552i	−0.400344	+	0.360504i
$59$	0.140454	−	0.243273i	0.0182855	−	0.0316715i	−0.856738	−	0.515752i	$-0.827513\pi$
$59$	0.140454	−	0.243273i	0.0182855	−	0.0316715i	0.875023	+	0.484081i	$0.160846\pi$
$60$		0			0
$61$	9.52219	−	5.49764i	1.21919	−	0.703900i	0.254446	−	0.967087i	$-0.418107\pi$
$61$	9.52219	−	5.49764i	1.21919	−	0.703900i	0.964745	+	0.263186i	$0.0847735\pi$
$62$	−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	0.611026	−	0.791611i	$-0.290757\pi$
$67$	1.89068	+	1.09159i	0.230984	+	0.133358i	−0.380042	+	0.924969i	$0.624091\pi$
$68$	−1.92837	−	4.33012i	−0.233849	−	0.525104i
$69$		0			0
$70$	0.400269	−	1.75268i	0.0478413	−	0.209485i
$71$		−	0.198757i		−	0.0235881i	−0.999930	−	0.0117940i	$-0.996246\pi$
$71$		−	0.198757i		−	0.0235881i	0.999930	−	0.0117940i	$-0.00375425\pi$
$72$		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
$77$	−5.77925	+	4.06671i	−0.658607	+	0.463444i
$78$		0			0
$79$	−3.42117	+	1.97521i	−0.384912	+	0.222229i	−0.679953	−	0.733256i	$-0.738000\pi$
$79$	−3.42117	+	1.97521i	−0.384912	+	0.222229i	0.295041	+	0.955484i	$0.404667\pi$
$80$	−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	0.997566	+	0.0697297i	$0.0222137\pi$
$83$	5.09429	+	8.82356i	0.559171	+	0.968512i	−0.438395	+	0.898782i	$0.644453\pi$
$84$		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	$-0.631604\pi$
$97$	1.87526	−	1.08268i	0.190403	−	0.109929i	0.592171	+	0.805812i	$0.298271\pi$
$98$	−3.75143	−	9.16116i	−0.378951	−	0.925417i
$99$		0			0
$100$	7.71713	+	5.60575i	0.771713	+	0.560575i
$101$	−4.50341	+	2.60004i	−0.448106	+	0.258714i	−0.707030	−	0.707184i	$-0.749965\pi$
$101$	−4.50341	+	2.60004i	−0.448106	+	0.258714i	0.258924	+	0.965898i	$0.416632\pi$
$102$		0			0
$103$	1.13040	−	1.95791i	0.111382	−	0.192919i	−0.804946	−	0.593348i	$-0.797806\pi$
$103$	1.13040	−	1.95791i	0.111382	−	0.192919i	0.916328	+	0.400429i	$0.131139\pi$
$104$	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	$0.254427\pi$
$107$			14.8308i			1.43375i	−0.697204	+	0.716873i	$0.745573\pi$
$108$		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
$112$	−6.34782	+	8.46789i	−0.599813	+	0.800140i
$113$	4.72782	−	8.18882i	0.444756	−	0.770339i	−0.553280	−	0.832996i	$-0.686624\pi$
$113$	4.72782	−	8.18882i	0.444756	−	0.770339i	0.998035	+	0.0626563i	$0.0199572\pi$
$114$		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
$119$	−0.561020	−	6.24541i	−0.0514286	−	0.572516i
$120$		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	$-0.979388\pi$
$127$		−	1.45847i		−	0.129419i	0.997904	−	0.0647093i	$-0.0206120\pi$
$128$	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	−0.457641	−	0.889137i	$-0.651305\pi$
$131$	6.19426	−	10.7288i	0.541195	−	0.937377i	0.998836	−	0.0482400i	$-0.0153612\pi$
$132$		0			0
$133$	−11.0735	+	0.994726i	−0.960196	+	0.0862537i
$134$	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	0.991197	−	0.132397i	$-0.0422673\pi$
$137$	4.45878	+	7.72284i	0.380939	+	0.659806i	−0.610257	+	0.792203i	$0.708934\pi$
$138$		0			0
$139$	−1.37546	+	2.38237i	−0.116665	+	0.202070i	−0.918444	−	0.395551i	$-0.870554\pi$
$139$	−1.37546	+	2.38237i	−0.116665	+	0.202070i	0.801779	+	0.597621i	$0.203887\pi$
$140$	−2.54219	−	0.0382367i	−0.214855	−	0.00323159i
$141$		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	−0.862885	−	0.505401i	$-0.831345\pi$
$149$	0.0762596	−	0.132086i	0.00624743	−	0.0108209i	0.869132	+	0.494580i	$0.164678\pi$
$150$		0			0
$151$	−10.8876	+	6.28594i	−0.886017	+	0.511542i	−0.872638	−	0.488368i	$-0.837592\pi$
$151$	−10.8876	+	6.28594i	−0.886017	+	0.511542i	−0.0133797	+	0.999910i	$0.504259\pi$
$152$	6.98759	+	9.61482i	0.566768	+	0.779865i
$153$		0			0
$154$	7.32511	+	6.79842i	0.590274	+	0.547832i
$155$	−2.61650	+	1.51064i	−0.210162	+	0.121337i
$156$		0			0
$157$	−9.96123	−	5.75112i	−0.794993	−	0.458989i	0.0467246	−	0.998908i	$-0.485122\pi$
$157$	−9.96123	−	5.75112i	−0.794993	−	0.458989i	−0.841717	+	0.539919i	$0.818455\pi$
$158$	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	$-0.714135\pi$
$163$		−	19.9710i		−	1.56425i	0.623121	−	0.782126i	$-0.285865\pi$
$164$	−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	0.0326095	+	0.999468i	$0.489618\pi$
$167$	−10.9749	+	19.0090i	−0.849260	+	1.47096i	−0.881870	+	0.471493i	$0.843715\pi$
$168$		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	$-0.864179\pi$
$173$	−13.2462	+	7.64770i	−1.00709	+	0.581444i	−0.0967521	+	0.995309i	$0.530845\pi$
$174$		0			0
$175$	7.26134	+	10.3192i	0.548906	+	0.780057i
$176$	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	$-0.869095\pi$
$179$		−	10.6967i		−	0.799512i	0.916622	−	0.399756i	$-0.130905\pi$
$180$		0			0
$181$		−	7.23452i		−	0.537738i	−0.963177	−	0.268869i	$-0.913350\pi$
$181$		−	7.23452i		−	0.537738i	0.963177	−	0.268869i	$-0.0866498\pi$
$182$	−5.27805	+	23.1113i	−0.391235	+	1.71312i
$183$		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	0.277988	−	0.960584i	$-0.410332\pi$
$191$	17.2598	−	9.96493i	1.24887	−	0.721037i	0.970885	+	0.239547i	$0.0769990\pi$
$192$		0			0
$193$	7.12877	−	12.3474i	0.513140	−	0.888784i	−0.486744	−	0.873545i	$-0.661816\pi$
$193$	7.12877	−	12.3474i	0.513140	−	0.888784i	0.999884	−	0.0152396i	$-0.00485112\pi$
$194$	−2.04917	−	2.27562i	−0.147122	−	0.163380i
$195$		0			0
$196$	−11.5693	+	7.88358i	−0.826380	+	0.563113i
$197$	−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	$-0.216210\pi$
$199$	21.9514			1.55610			0.778048	+	0.628205i	$0.216210\pi$
$200$	5.48485	−	12.3237i	0.387837	−	0.871418i
$201$		0			0
$202$	4.92106	+	5.46489i	0.346244	+	0.384508i
$203$	4.41726	+	6.27743i	0.310031	+	0.440589i
$204$		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	0.774652	−	0.632388i	$-0.217925\pi$
$211$	8.92341	+	5.15194i	0.614313	+	0.354674i	−0.160338	+	0.987062i	$0.551259\pi$
$212$	−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	$-0.00571235\pi$
$223$	7.23332	+	12.5285i	0.484379	+	0.838969i	−0.515460	+	0.856914i	$0.672379\pi$
$224$	13.5805	+	6.29055i	0.907383	+	0.420305i
$225$		0			0
$226$	−12.7180	−	4.13168i	−0.845988	−	0.274835i
$227$	9.67633	+	16.7599i	0.642240	+	1.11239i	0.984932	+	0.172945i	$0.0553282\pi$
$227$	9.67633	+	16.7599i	0.642240	+	1.11239i	−0.342691	+	0.939448i	$0.611338\pi$
$228$		0			0
$229$	−17.0595	−	9.84933i	−1.12733	−	0.650862i	−0.184065	−	0.982914i	$-0.558926\pi$
$229$	−17.0595	−	9.84933i	−1.12733	−	0.650862i	−0.943261	+	0.332052i	$0.892259\pi$
$230$	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
$238$	−8.47426	+	2.61280i	−0.549304	+	0.169363i
$239$	−8.34611	−	4.81863i	−0.539865	−	0.311691i	0.205159	−	0.978729i	$-0.434229\pi$
$239$	−8.34611	−	4.81863i	−0.539865	−	0.311691i	−0.745024	+	0.667037i	$0.767562\pi$
$240$		0			0
$241$	3.56210	−	2.05658i	0.229455	−	0.132476i	−0.380865	−	0.924630i	$-0.624374\pi$
$241$	3.56210	−	2.05658i	0.229455	−	0.132476i	0.610321	+	0.792154i	$0.291041\pi$
$242$	5.19986	+	1.68928i	0.334260	+	0.108591i
$243$		0			0
$244$	−12.9241	+	17.7919i	−0.827381	+	1.13901i
$245$	−3.16586	−	1.13565i	−0.202259	−	0.0725542i
$246$		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	$-0.533395\pi$
$251$	−3.31816			−0.209441			−0.104720	+	0.994502i	$0.533395\pi$
$252$		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	$-0.514304\pi$
$257$	−14.9497	−	8.63121i	−0.932537	−	0.538400i	−0.887613	+	0.460590i	$0.847638\pi$
$258$		0			0
$259$	−12.3711	+	1.11129i	−0.768704	+	0.0690521i
$260$	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	−0.809489	−	0.587135i	$-0.800256\pi$
$263$	−11.4455	+	6.60806i	−0.705760	+	0.407471i	0.103729	+	0.994606i	$0.466922\pi$
$264$		0			0
$265$	−3.74371	−	2.16143i	−0.229974	−	0.132776i
$266$	4.63266	+	15.0254i	0.284047	+	0.921267i
$267$		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	$-0.723277\pi$
$271$	−21.2467			−1.29065			−0.645323	+	0.763910i	$0.723277\pi$
$272$	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	0.997397	−	0.0721016i	$-0.0229706\pi$
$277$	7.26076	+	12.5760i	0.436257	+	0.755619i	−0.561140	+	0.827721i	$0.689637\pi$
$278$	3.70004	+	1.20203i	0.221914	+	0.0720930i
$279$		0			0
$280$	0.694753	+	3.52785i	0.0415194	+	0.210829i
$281$	−6.35647	−	11.0097i	−0.379195	−	0.656785i	0.611750	−	0.791051i	$-0.290466\pi$
$281$	−6.35647	−	11.0097i	−0.379195	−	0.656785i	−0.990945	+	0.134266i	$0.957132\pi$
$282$		0			0
$283$	10.4272	−	18.0605i	0.619834	−	1.07358i	−0.369682	−	0.929158i	$-0.620533\pi$
$283$	10.4272	−	18.0605i	0.619834	−	1.07358i	0.989516	−	0.144425i	$-0.0461332\pi$
$284$	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	$-0.396097\pi$
$293$	−5.80807	−	3.35329i	−0.339311	−	0.195901i	−0.659967	+	0.751294i	$0.729430\pi$
$294$		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
$301$	−2.90523	+	2.04434i	−0.167455	+	0.117834i
$302$	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	$-0.612019\pi$
$307$	−12.0792			−0.689397			−0.344699	+	0.938713i	$0.612019\pi$
$308$	7.24995	−	12.1322i	0.413104	−	0.691295i
$309$		0			0
$310$	2.85916	+	3.17513i	0.162389	+	0.180335i
$311$	−1.01185	+	1.75258i	−0.0573769	+	0.0993797i	−0.893287	−	0.449486i	$-0.851607\pi$
$311$	−1.01185	+	1.75258i	−0.0573769	+	0.0993797i	0.835910	+	0.548866i	$0.184940\pi$
$312$		0			0
$313$	−16.8337	+	9.71892i	−0.951495	+	0.549346i	−0.893545	−	0.448974i	$-0.851790\pi$
$313$	−16.8337	+	9.71892i	−0.951495	+	0.549346i	−0.0579500	+	0.998319i	$0.518456\pi$
$314$	−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	0.974538	−	0.224222i	$-0.0719839\pi$
$317$	5.21828	+	9.03832i	0.293088	+	0.507643i	−0.681451	+	0.731864i	$0.738651\pi$
$318$		0			0
$319$	−6.71078	−	3.87447i	−0.375731	−	0.216929i
$320$	2.85585	−	2.57283i	0.159647	−	0.143826i
$321$		0			0
$322$	3.99508	−	17.4935i	0.222637	−	0.974873i
$323$			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
$329$	11.3546	+	16.1361i	0.625999	+	0.889614i
$330$		0			0
$331$	−31.2751	+	18.0567i	−1.71903	+	0.992484i	−0.798328	+	0.602223i	$0.794282\pi$
$331$	−31.2751	+	18.0567i	−1.71903	+	0.992484i	−0.920704	+	0.390261i	$0.872385\pi$
$332$	−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	−0.747278	−	0.664512i	$-0.768639\pi$
$337$	3.70539	−	6.41792i	0.201845	−	0.349606i	0.949123	+	0.314905i	$0.101973\pi$
$338$	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	0.986057	−	0.166408i	$-0.0532168\pi$
$347$	24.8678	+	14.3574i	1.33497	+	0.770747i	0.348915	+	0.937154i	$0.386550\pi$
$348$		0			0
$349$	0.744758	−	0.429986i	0.0398660	−	0.0230166i	−0.479935	−	0.877304i	$-0.659340\pi$
$349$	0.744758	−	0.429986i	0.0398660	−	0.0230166i	0.519801	+	0.854288i	$0.326006\pi$
$350$	12.1390	−	13.0794i	0.648855	−	0.699123i
$351$		0			0
$352$	−15.1092	+	0.00344740i	−0.805322	+	0.000183747i
$353$	27.7159	−	16.0018i	1.47517	−	0.851690i	0.475562	−	0.879682i	$-0.342245\pi$
$353$	27.7159	−	16.0018i	1.47517	−	0.851690i	0.999608	+	0.0279920i	$0.00891130\pi$
$354$		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	$-0.953453\pi$
$359$		−	5.52163i		−	0.291421i	0.989327	−	0.145710i	$-0.0465468\pi$
$360$		0			0
$361$	−1.34111			−0.0705845
$362$	−10.0075	+	2.12763i	−0.525982	+	0.111826i
$363$		0			0
$364$	33.5220	+	0.504199i	1.75703	+	0.0264272i
$365$	1.16503	−	2.01789i	0.0609805	−	0.105621i
$366$		0			0
$367$	11.4766	+	19.8780i	0.599072	+	1.03762i	0.992958	+	0.118465i	$0.0377972\pi$
$367$	11.4766	+	19.8780i	0.599072	+	1.03762i	−0.393886	+	0.919159i	$0.628869\pi$
$368$	−18.2428	+	5.93114i	−0.950974	+	0.309182i
$369$		0			0
$370$	−0.985644	+	3.03397i	−0.0512412	+	0.157729i
$371$	−23.7081	+	2.12968i	−1.23086	+	0.110567i
$372$		0			0
$373$	−14.2688	+	24.7143i	−0.738810	+	1.27966i	0.214222	+	0.976785i	$0.431278\pi$
$373$	−14.2688	+	24.7143i	−0.738810	+	1.27966i	−0.953032	+	0.302871i	$0.902055\pi$
$374$	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	$-0.888216\pi$
$379$		−	13.3942i		−	0.688014i	0.938967	−	0.344007i	$-0.111784\pi$
$380$	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	−0.424430	−	0.905461i	$-0.639525\pi$
$383$	11.1930	−	19.3869i	0.571937	−	0.990625i	0.996367	−	0.0851637i	$-0.0271413\pi$
$384$		0			0
$385$	3.38180	−	0.303785i	0.172353	−	0.0154823i
$386$	−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	−0.973112	−	0.230332i	$-0.926019\pi$
$389$	−13.5306	−	23.4357i	−0.686029	−	1.18824i	0.287083	−	0.957906i	$-0.407314\pi$
$390$		0			0
$391$	5.68302	−	9.84327i	0.287402	−	0.497796i
$392$	14.3078	+	13.6853i	0.722653	+	0.691211i
$393$		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	−0.579343	−	0.815084i	$-0.696691\pi$
$401$	8.33464	−	14.4360i	0.416212	−	0.720901i	0.995555	+	0.0941835i	$0.0300240\pi$
$402$		0			0
$403$	34.5018	−	19.9196i	1.71866	−	0.992268i
$404$	6.11230	−	8.41447i	0.304098	−	0.418636i
$405$		0			0
$406$	7.38445	−	7.95654i	0.366484	−	0.394877i
$407$	10.8593	−	6.26962i	0.538275	−	0.310773i
$408$		0			0
$409$	−0.589282	−	0.340222i	−0.0291381	−	0.0168229i	0.485360	−	0.874314i	$-0.338688\pi$
$409$	−0.589282	−	0.340222i	−0.0291381	−	0.0168229i	−0.514498	+	0.857491i	$0.672022\pi$
$410$	−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	$-0.751587\pi$
$419$	5.19926	−	9.00538i	0.254000	−	0.439941i	0.964624	+	0.263631i	$0.0849202\pi$
$420$		0			0
$421$	−3.42772	−	5.93699i	−0.167057	−	0.289351i	0.770327	−	0.637649i	$-0.220093\pi$
$421$	−3.42772	−	5.93699i	−0.167057	−	0.289351i	−0.937384	+	0.348298i	$0.886760\pi$
$422$	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
$427$	−23.7909	+	16.7411i	−1.15132	+	0.810157i
$428$	−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	$0.119772\pi$
$431$			15.2572i			0.734914i	−0.930040	+	0.367457i	$0.880228\pi$
$432$		0			0
$433$			34.6459i			1.66498i	0.554042	+	0.832489i	$0.313085\pi$
$433$			34.6459i			1.66498i	−0.554042	+	0.832489i	$0.686915\pi$
$434$	22.9370	+	5.23824i	1.10101	+	0.251443i
$435$		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	$-0.261045\pi$
$439$	−6.12174	−	10.6032i	−0.292175	−	0.506061i	−0.974324	+	0.225152i	$0.927712\pi$
$440$	−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	−0.949374	−	0.314148i	$-0.898281\pi$
$443$	−24.2468	+	13.9989i	−1.15200	+	0.665108i	−0.202627	+	0.979256i	$0.564948\pi$
$444$		0			0
$445$	0.641897	−	1.11180i	0.0304288	−	0.0527043i
$446$	15.2033	−	13.6904i	0.719898	−	0.648258i
$447$		0			0
$448$	4.70776	−	20.6358i	0.222421	−	0.974951i
$449$	−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
$455$	4.63506	+	6.58694i	0.217295	+	0.308801i
$456$		0			0
$457$	−11.9100	−	20.6288i	−0.557128	−	0.964974i	−0.997735	−	0.0672735i	$-0.978570\pi$
$457$	−11.9100	−	20.6288i	−0.557128	−	0.964974i	0.440607	−	0.897700i	$-0.354763\pi$
$458$	−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	$-0.663949\pi$
$461$	0.317557	−	0.183341i	0.0147901	−	0.00853906i	0.507377	+	0.861724i	$0.330615\pi$
$462$		0			0
$463$	−14.3509	−	8.28549i	−0.666943	−	0.385060i	0.127974	−	0.991777i	$-0.459152\pi$
$463$	−14.3509	−	8.28549i	−0.666943	−	0.385060i	−0.794917	+	0.606718i	$0.792486\pi$
$464$	−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	$-0.706808\pi$
$467$	−26.1463			−1.20991			−0.604953	+	0.796261i	$0.706808\pi$
$468$		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
$476$	6.10651	+	10.9540i	0.279891	+	0.502076i
$477$		0			0
$478$	−4.21104	+	12.9623i	−0.192609	+	0.592880i
$479$	19.0772	+	33.0427i	0.871661	+	1.50976i	0.860277	+	0.509826i	$0.170290\pi$
$479$	19.0772	+	33.0427i	0.871661	+	1.50976i	0.0113840	+	0.999935i	$0.496376\pi$
$480$		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	$-0.935089\pi$
$487$		−	8.93817i		−	0.405027i	0.979279	−	0.202514i	$-0.0649110\pi$
$488$	28.4124	+	12.6454i	1.28617	+	0.572428i
$489$		0			0
$490$	−0.639884	+	4.71331i	−0.0289070	+	0.212926i
$491$	8.03087	+	4.63662i	0.362428	+	0.209248i	0.670145	−	0.742230i	$-0.266232\pi$
$491$	8.03087	+	4.63662i	0.362428	+	0.209248i	−0.307717	+	0.951478i	$0.599565\pi$
$492$		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
$497$	0.0470482	+	0.523752i	0.00211040	+	0.0234935i
$498$		0			0
$499$	15.0365	+	8.68131i	0.673125	+	0.388629i	0.797260	−	0.603636i	$-0.206282\pi$
$499$	15.0365	+	8.68131i	0.673125	+	0.388629i	−0.124135	+	0.992265i	$0.539615\pi$
$500$	−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	$-0.455618\pi$
$503$	6.23388			0.277955			0.138978	+	0.990296i	$0.455618\pi$
$504$		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	$-0.362117\pi$
$509$	−3.52873	−	2.03731i	−0.156408	−	0.0903023i	−0.576161	+	0.817336i	$0.695450\pi$
$510$		0			0
$511$	−1.14792	−	12.7789i	−0.0507808	−	0.565304i
$512$	−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
$518$	5.17552	+	16.7861i	0.227399	+	0.737539i
$519$		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	$-0.475982\pi$
$523$	3.44794			0.150768			0.0753838	+	0.997155i	$0.475982\pi$
$524$	−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
$532$	19.4222	−	10.8272i	0.842057	−	0.469420i
$533$	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	−0.617319	−	0.786713i	$-0.711781\pi$
$547$	−5.72221	+	3.30372i	−0.244664	+	0.141257i	0.372654	+	0.927970i	$0.378448\pi$
$548$	−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
$553$	8.54771	−	6.01480i	0.363485	−	0.255775i
$554$	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
$560$	4.67574	−	1.99857i	0.197586	−	0.0844550i
$561$		0			0
$562$	−13.3603	+	12.0308i	−0.563571	+	0.507488i
$563$	−13.1561	+	22.7871i	−0.554465	+	0.960361i	0.443480	+	0.896284i	$0.353744\pi$
$563$	−13.1561	+	22.7871i	−0.554465	+	0.960361i	−0.997945	+	0.0640767i	$0.979590\pi$
$564$		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	0.879996	−	0.474981i	$-0.157545\pi$
$569$	0.683478	+	1.18382i	0.0286529	+	0.0496283i	−0.851343	+	0.524609i	$0.824212\pi$
$570$		0			0
$571$	−14.6500	−	8.45818i	−0.613083	−	0.353964i	0.161088	−	0.986940i	$-0.448500\pi$
$571$	−14.6500	−	8.45818i	−0.613083	−	0.353964i	−0.774171	+	0.632976i	$0.781833\pi$
$572$	−30.9178	+	13.7689i	−1.29274	+	0.575705i
$573$		0			0
$574$	−9.74386	+	42.6660i	−0.406701	+	1.78084i
$575$			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
$581$	−15.5128	−	22.0455i	−0.643580	−	0.914599i
$582$		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	0.997015	+	0.0772082i	$0.0246006\pi$
$587$	13.6979	+	23.7254i	0.565372	+	0.979253i	−0.431643	+	0.902044i	$0.642066\pi$
$588$		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	0.139402	−	0.990236i	$-0.455482\pi$
$599$	−15.8709	−	9.16306i	−0.648467	−	0.374392i	−0.787869	+	0.615843i	$0.788815\pi$
$600$		0			0
$601$	−19.1583	+	11.0611i	−0.781485	+	0.451190i	−0.836956	−	0.547270i	$-0.815667\pi$
$601$	−19.1583	+	11.0611i	−0.781485	+	0.451190i	0.0554716	+	0.998460i	$0.482334\pi$
$602$	3.68233	+	3.41757i	0.150081	+	0.139290i
$603$		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	$-0.937577\pi$
$607$	−7.92507	+	13.7266i	−0.321669	+	0.557146i	0.659164	+	0.751999i	$0.270910\pi$
$608$	−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
$616$	−18.9146	−	6.46082i	−0.762089	−	0.260314i
$617$	15.9608	−	27.6449i	0.642557	−	1.11294i	−0.342303	−	0.939590i	$-0.611207\pi$
$617$	15.9608	−	27.6449i	0.642557	−	1.11294i	0.984860	−	0.173352i	$-0.0554599\pi$
$618$		0			0
$619$	0.227459	+	0.393971i	0.00914236	+	0.0158350i	0.870560	−	0.492062i	$-0.163757\pi$
$619$	0.227459	+	0.393971i	0.00914236	+	0.0158350i	−0.861418	+	0.507897i	$0.830423\pi$
$620$	3.55128	−	4.88885i	0.142623	−	0.196341i
$621$		0			0
$622$	2.72192	+	0.884267i	0.109139	+	0.0354559i
$623$	−0.632468	−	7.04078i	−0.0253393	−	0.282083i
$624$		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	$0.194575\pi$
$631$			28.8331i			1.14783i	−0.818916	+	0.573913i	$0.805425\pi$
$632$	−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
$637$	41.7458	+	14.9750i	1.65403	+	0.593331i
$638$	−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	0.778602	−	0.627518i	$-0.215929\pi$
$641$	−3.90266	−	6.75961i	−0.154146	−	0.266989i	−0.932748	+	0.360530i	$0.882596\pi$
$642$		0			0
$643$	−2.26137	+	3.91681i	−0.0891797	+	0.154464i	−0.907165	−	0.420776i	$-0.861758\pi$
$643$	−2.26137	+	3.91681i	−0.0891797	+	0.154464i	0.817985	+	0.575240i	$0.195091\pi$
$644$	−25.3736	−	0.381640i	−0.999859	−	0.0150387i
$645$		0			0
$646$	13.7770	−	2.92904i	0.542048	−	0.115242i
$647$	32.4931			1.27744			0.638718	−	0.769441i	$-0.279465\pi$
$647$	32.4931			1.27744			0.638718	+	0.769441i	$0.279465\pi$
$648$		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	−0.933597	−	0.358325i	$-0.883348\pi$
$653$	−3.99865	+	6.92587i	−0.156479	+	0.271030i	0.777117	+	0.629356i	$0.216681\pi$
$654$		0			0
$655$	−5.15500	+	2.97624i	−0.201422	+	0.116291i
$656$	44.4937	−	14.4658i	1.73719	−	0.564796i
$657$		0			0
$658$	18.9817	−	20.4523i	0.739985	−	0.797314i
$659$	6.89888	−	3.98307i	0.268742	−	0.155158i	−0.359574	−	0.933117i	$-0.617078\pi$
$659$	6.89888	−	3.98307i	0.268742	−	0.155158i	0.628316	+	0.777958i	$0.283745\pi$
$660$		0			0
$661$	−0.220771	−	0.127462i	−0.00858700	−	0.00495771i	0.495700	−	0.868494i	$-0.334911\pi$
$661$	−0.220771	−	0.127462i	−0.00858700	−	0.00495771i	−0.504287	+	0.863536i	$0.668245\pi$
$662$	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	0.862178	−	0.506606i	$-0.169100\pi$
$673$	−0.198313	−	0.343488i	−0.00764441	−	0.0132405i	−0.869822	+	0.493365i	$0.835767\pi$
$674$	−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	−0.684720	+	0.728806i	$0.740076\pi$
$677$	−43.1462	+	24.9105i	−1.65824	+	0.957388i	−0.973525	+	0.228582i	$0.926591\pi$
$678$		0			0
$679$	−4.68528	+	3.29691i	−0.179804	+	0.126524i
$680$	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	$-0.816788\pi$
$683$		−	28.4508i		−	1.08864i	0.838878	−	0.544320i	$-0.183212\pi$
$684$		0			0
$685$		−	4.28474i		−	0.163712i
$686$	12.0541	+	23.2529i	0.460228	+	0.887801i
$687$		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	$-0.0923284\pi$
$691$	6.08340	+	10.5368i	0.231423	+	0.400837i	−0.726804	+	0.686845i	$0.758995\pi$
$692$	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
$700$	−21.6627	−	12.9452i	−0.818773	−	0.489283i
$701$	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
$707$	11.2516	−	7.91749i	0.423162	−	0.297768i
$708$		0			0
$709$	−22.5400	−	39.0404i	−0.846507	−	1.46619i	−0.884306	−	0.466907i	$-0.845368\pi$
$709$	−22.5400	−	39.0404i	−0.846507	−	1.46619i	0.0377999	−	0.999285i	$-0.487965\pi$
$710$	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	$-0.572814\pi$
$719$	−12.1609			−0.453526			−0.226763	+	0.973950i	$0.572814\pi$
$720$		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	$-0.267460\pi$
$727$	−8.39590	−	14.5421i	−0.311387	−	0.539337i	−0.978663	+	0.205473i	$0.934127\pi$
$728$	−9.16118	−	46.5191i	−0.339536	−	1.72411i
$729$		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	$-0.204371\pi$
$733$	18.4832	+	10.6713i	0.682693	+	0.394153i	−0.118176	+	0.992993i	$0.537705\pi$
$734$	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	$0.380074\pi$
$739$			50.5558i			1.85973i	−0.367907	+	0.929863i	$0.619926\pi$
$740$	4.48675	+	0.471163i	0.164936	+	0.0173203i
$741$		0			0
$742$	9.91839	+	32.1690i	0.364116	+	1.18096i
$743$	−32.1395	−	18.5558i	−1.17909	−	0.680745i	−0.223282	−	0.974754i	$-0.571677\pi$
$743$	−32.1395	−	18.5558i	−1.17909	−	0.680745i	−0.955803	+	0.294009i	$0.905011\pi$
$744$		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
$749$	−3.51063	−	39.0812i	−0.128276	−	1.42800i
$750$		0			0
$751$	−37.8228	−	21.8370i	−1.38017	−	0.796843i	−0.387993	−	0.921662i	$-0.626832\pi$
$751$	−37.8228	−	21.8370i	−1.38017	−	0.796843i	−0.992180	+	0.124819i	$0.960165\pi$
$752$	−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	$-0.198085\pi$
$761$	19.6964	+	11.3717i	0.713994	+	0.412225i	−0.0985439	+	0.995133i	$0.531418\pi$
$762$		0			0
$763$	28.8640	−	2.59283i	1.04495	−	0.0938669i
$764$	−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	$-0.267491\pi$
$769$	9.86460	+	5.69533i	0.355726	+	0.205379i	−0.311478	+	0.950253i	$0.600824\pi$
$770$	−1.41479	−	4.58869i	−0.0509857	−	0.165365i
$771$		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
$784$	14.7229	−	23.8167i	0.525819	−	0.850596i
$785$	2.76332	+	4.78621i	0.0986271	+	0.170827i
$786$		0			0
$787$	9.75700	−	16.8996i	0.347799	−	0.602406i	−0.638059	−	0.769988i	$-0.720262\pi$
$787$	9.75700	−	16.8996i	0.347799	−	0.602406i	0.985858	+	0.167581i	$0.0535957\pi$
$788$	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	$-0.511505\pi$
$797$	−25.9632	−	14.9898i	−0.919663	−	0.530968i	−0.883528	+	0.468379i	$0.844838\pi$
$798$		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
$805$	−3.50839	−	4.98581i	−0.123654	−	0.175727i
$806$	−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	$-0.400527\pi$
$811$	17.5107			0.614883			0.307442	+	0.951567i	$0.400527\pi$
$812$	−13.1780	−	7.87490i	−0.462457	−	0.276355i
$813$		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	0.982616	−	0.185650i	$-0.0594392\pi$
$821$	9.47071	+	16.4037i	0.330530	+	0.572495i	−0.652086	+	0.758145i	$0.726106\pi$
$822$		0			0
$823$	8.43975	+	4.87269i	0.294191	+	0.169851i	0.639831	−	0.768516i	$-0.279005\pi$
$823$	8.43975	+	4.87269i	0.294191	+	0.169851i	−0.345639	+	0.938367i	$0.612338\pi$
$824$	6.35940	−	0.669280i	0.221540	−	0.0233155i
$825$		0			0
$826$	1.02468	+	0.234011i	0.0356531	+	0.00814229i
$827$		−	38.9872i		−	1.35572i	−0.735193	−	0.677858i	$-0.762908\pi$
$827$		−	38.9872i		−	1.35572i	0.735193	−	0.677858i	$-0.237092\pi$
$828$		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
$833$	2.95673	+	16.3247i	0.102445	+	0.565618i
$834$		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	$-0.322065\pi$
$839$	−13.5859	−	23.5314i	−0.469036	−	0.812394i	−0.999373	+	0.0353923i	$0.988732\pi$
$840$		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	$-0.534276\pi$
$853$	20.4384	−	11.8001i	0.699797	−	0.404028i	0.807272	+	0.590180i	$0.200943\pi$
$854$	30.1547	+	27.9865i	1.03187	+	0.957677i
$855$		0			0
$856$	−33.9331	+	24.6609i	−1.15981	+	0.842893i
$857$	−13.6342	+	7.87173i	−0.465737	+	0.268893i	−0.714453	−	0.699683i	$-0.753325\pi$
$857$	−13.6342	+	7.87173i	−0.465737	+	0.268893i	0.248717	+	0.968576i	$0.419991\pi$
$858$		0			0
$859$	−13.3695	+	23.1566i	−0.456160	+	0.790093i	−0.998754	−	0.0499024i	$-0.984109\pi$
$859$	−13.3695	+	23.1566i	−0.456160	+	0.790093i	0.542594	+	0.839995i	$0.317442\pi$
$860$	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	$0.332960\pi$
$863$			50.8477i			1.73088i	−0.501015	+	0.865438i	$0.667040\pi$
$864$		0			0
$865$	7.34919			0.249880
$866$	47.9256	−	10.1892i	1.62858	−	0.346243i
$867$		0			0
$868$	0.500396	−	33.2691i	0.0169845	−	1.12923i
$869$	−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
$875$	−1.11111	−	12.3691i	−0.0375623	−	0.418152i
$876$		0			0
$877$	6.79088	−	11.7621i	0.229312	−	0.397179i	−0.728293	−	0.685266i	$-0.759686\pi$
$877$	6.79088	−	11.7621i	0.229312	−	0.397179i	0.957604	+	0.288087i	$0.0930192\pi$
$878$	−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	$0.210639\pi$
$883$			36.5196i			1.22898i	−0.788924	+	0.614491i	$0.789361\pi$
$884$	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	0.457417	+	0.889252i	$0.348775\pi$
$887$	−16.1245	+	27.9284i	−0.541407	+	0.937744i	−0.998824	+	0.0484917i	$0.984559\pi$
$888$		0			0
$889$	0.345239	+	3.84328i	0.0115789	+	0.128899i
$890$	−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
$896$	−29.9300	−	0.443341i	−0.999890	−	0.0148110i
$897$		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	−0.846813	−	0.531891i	$-0.821482\pi$
$907$	−24.3819	+	14.0769i	−0.809588	+	0.467416i	0.0372246	+	0.999307i	$0.488148\pi$
$908$	−31.3153	−	22.7475i	−1.03924	−	0.754904i
$909$		0			0
$910$	7.74855	−	8.34885i	0.256862	−	0.276762i
$911$	33.2831	−	19.2160i	1.10272	−	0.636655i	0.165785	−	0.986162i	$-0.446984\pi$
$911$	33.2831	−	19.2160i	1.10272	−	0.636655i	0.936934	+	0.349507i	$0.113651\pi$
$912$		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	$-0.907676\pi$
$919$		−	17.3398i		−	0.571988i	0.958231	−	0.285994i	$-0.0923238\pi$
$920$	−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	0.609153	−	0.793053i	$-0.291510\pi$
$929$	48.7835	−	28.1651i	1.60053	−	0.924068i	0.991380	−	0.131016i	$-0.0418238\pi$
$930$		0			0
$931$	28.9448	−	5.24248i	0.948628	−	0.171815i
$932$	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	$-0.200944\pi$
$938$	−1.81870	+	7.96365i	−0.0593827	+	0.260022i
$939$		0			0
$940$	−2.91545	−	6.54659i	−0.0950914	−	0.213526i
$941$	12.0974	+	6.98446i	0.394365	+	0.227687i	0.684050	−	0.729435i	$-0.260217\pi$
$941$	12.0974	+	6.98446i	0.394365	+	0.227687i	−0.289684	+	0.957122i	$0.593550\pi$
$942$		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	−0.309528	−	0.950890i	$-0.600171\pi$
$947$	11.0539	−	6.38196i	0.359203	−	0.207386i	0.668731	+	0.743505i	$0.266838\pi$
$948$		0			0
$949$	−15.3624	+	26.6084i	−0.498684	+	0.863746i
$950$	−21.0616	+	18.9657i	−0.683330	+	0.615329i
$951$		0			0
$952$	13.3567	−	11.6686i	0.432894	−	0.378182i
$953$	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
$959$	−13.5776	−	19.2953i	−0.438444	−	0.623078i
$960$		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	0.137125	−	0.990554i	$-0.456214\pi$
$967$	−20.2799	−	11.7086i	−0.652158	−	0.376524i	−0.789283	+	0.614030i	$0.789547\pi$
$968$	−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	$-0.367938\pi$
$971$	25.1209			0.806167			0.403084	+	0.915163i	$0.367938\pi$
$972$		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	−0.845889	−	0.533359i	$-0.820930\pi$
$977$	1.21770	−	2.10911i	0.0389575	−	0.0674764i	0.884847	+	0.465882i	$0.154263\pi$
$978$		0			0
$979$	3.56823	+	6.18036i	0.114041	+	0.197525i
$980$	6.70809	−	0.501010i	0.214282	−	0.0160042i
$981$		0			0
$982$	4.05199	−	12.4727i	0.129304	−	0.398019i
$983$	9.60279	+	16.6325i	0.306281	+	0.530495i	0.977546	−	0.210723i	$-0.0675818\pi$
$983$	9.60279	+	16.6325i	0.306281	+	0.530495i	−0.671264	+	0.741218i	$0.734248\pi$
$984$		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	$-0.845067\pi$
$991$		−	29.4493i		−	0.935489i	0.883864	−	0.467745i	$-0.154933\pi$
$992$	−30.8007	+	17.7921i	−0.977922	+	0.564901i
$993$		0			0
$994$	0.710667	−	0.219114i	0.0225410	−	0.00694988i
$995$	−9.13423	−	5.27365i	−0.289575	−	0.167186i
$996$		0			0
$997$	−13.3933	+	7.73264i	−0.424171	+	0.244895i	−0.696860	−	0.717207i	$-0.745420\pi$
$997$	−13.3933	+	7.73264i	−0.424171	+	0.244895i	0.272689	+	0.962102i	$0.412087\pi$
$998$	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.307.17		80
3.2	odd	2		252.2.bi.c.139.24	yes	80
4.3	odd	2	inner	756.2.bi.c.307.7		80
7.6	odd	2	inner	756.2.bi.c.307.18		80
9.2	odd	6		252.2.bi.c.223.34	yes	80
9.7	even	3	inner	756.2.bi.c.559.8		80
12.11	even	2		252.2.bi.c.139.33	yes	80
21.20	even	2		252.2.bi.c.139.23	✓	80
28.27	even	2	inner	756.2.bi.c.307.8		80
36.7	odd	6	inner	756.2.bi.c.559.18		80
36.11	even	6		252.2.bi.c.223.23	yes	80
63.20	even	6		252.2.bi.c.223.33	yes	80
63.34	odd	6	inner	756.2.bi.c.559.7		80
84.83	odd	2		252.2.bi.c.139.34	yes	80
252.83	odd	6		252.2.bi.c.223.24	yes	80
252.223	even	6	inner	756.2.bi.c.559.17		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.23	✓	80	21.20	even	2
252.2.bi.c.139.24	yes	80	3.2	odd	2
252.2.bi.c.139.33	yes	80	12.11	even	2
252.2.bi.c.139.34	yes	80	84.83	odd	2
252.2.bi.c.223.23	yes	80	36.11	even	6
252.2.bi.c.223.24	yes	80	252.83	odd	6
252.2.bi.c.223.33	yes	80	63.20	even	6
252.2.bi.c.223.34	yes	80	9.2	odd	6
756.2.bi.c.307.7		80	4.3	odd	2	inner
756.2.bi.c.307.8		80	28.27	even	2	inner
756.2.bi.c.307.17		80	1.1	even	1	trivial
756.2.bi.c.307.18		80	7.6	odd	2	inner
756.2.bi.c.559.7		80	63.34	odd	6	inner
756.2.bi.c.559.8		80	9.7	even	3	inner
756.2.bi.c.559.17		80	252.223	even	6	inner
756.2.bi.c.559.18		80	36.7	odd	6	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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(-0.294095 - 1.38330i) q^{2} +(-1.82702 + 0.813640i) q^{4} +(-0.416111 - 0.240242i) q^{5} +(-2.63514 + 0.236713i) q^{7} +(1.66282 + 2.28802i) q^{8} +(-0.209950 + 0.646259i) q^{10} +(2.31311 - 1.33548i) q^{11} +(5.48694 + 3.16789i) q^{13} +(1.10242 + 3.57556i) q^{14} +(2.67598 - 2.97307i) q^{16} +2.37005i q^{17} +4.20225 q^{19} +(0.955712 + 0.100361i) q^{20} +(-2.52763 - 2.80696i) q^{22} +(-4.15320 - 2.39785i) q^{23} +(-2.38457 - 4.13019i) q^{25} +(2.76845 - 8.52173i) q^{26} +(4.62185 - 2.57653i) q^{28} +(-1.45060 - 2.51250i) q^{29} +(3.14399 - 5.44556i) q^{31} +(-4.89962 - 2.82731i) q^{32} +(3.27848 - 0.697018i) q^{34} +(1.15338 + 0.534572i) q^{35} +4.69467 q^{37} +(-1.23586 - 5.81295i) q^{38} +(-0.142241 - 1.35155i) q^{40} +(10.1295 + 5.84827i) q^{41} +(1.16280 - 0.671344i) q^{43} +(-3.13950 + 4.32198i) q^{44} +(-2.09550 + 6.45030i) q^{46} +(-3.72876 - 6.45840i) q^{47} +(6.88793 - 1.24754i) q^{49} +(-5.01199 + 4.51323i) q^{50} +(-12.6023 - 1.32339i) q^{52} +8.99689 q^{53} -1.28335 q^{55} +(-4.92337 - 5.63564i) q^{56} +(-3.04893 + 2.74552i) q^{58} +(0.140454 - 0.243273i) q^{59} +(9.52219 - 5.49764i) q^{61} +(-8.45745 - 2.74757i) q^{62} +(-2.47005 + 7.60913i) q^{64} +(-1.52212 - 2.63639i) q^{65} +(1.89068 + 1.09159i) q^{67} +(-1.92837 - 4.33012i) q^{68} +(0.400269 - 1.75268i) q^{70} -0.198757i q^{71} +4.84941i q^{73} +(-1.38068 - 6.49412i) q^{74} +(-7.67758 + 3.41912i) q^{76} +(-5.77925 + 4.06671i) q^{77} +(-3.42117 + 1.97521i) q^{79} +(-1.82776 + 0.594244i) q^{80} +(5.11086 - 15.7321i) q^{82} +(5.09429 + 8.82356i) q^{83} +(0.569384 - 0.986203i) q^{85} +(-1.27064 - 1.41106i) q^{86} +(6.90188 + 3.07178i) q^{88} +2.67188i q^{89} +(-15.2087 - 7.04900i) q^{91} +(9.53895 + 1.00170i) q^{92} +(-7.83727 + 7.05736i) q^{94} +(-1.74860 - 1.00956i) q^{95} +(1.87526 - 1.08268i) q^{97} +(-3.75143 - 9.16116i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56}+ \cdots - 20 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

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