LMFDB - Embedded newform 756.2.bi.c.307.8

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			307.8
Character	$\chi$	$=$	756.307
Dual form			756.2.bi.c.559.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05092 - 0.946342i) q^{2} +(0.208875 + 1.98906i) q^{4} +(0.416111 + 0.240242i) q^{5} +(1.52257 - 2.16374i) q^{7} +(1.66282 - 2.28802i) q^{8} +(-0.209950 - 0.646259i) q^{10} +(-2.31311 + 1.33548i) q^{11} +(-5.48694 - 3.16789i) q^{13} +(-3.64774 + 0.833054i) q^{14} +(-3.91274 + 0.830933i) q^{16} -2.37005i q^{17} +4.20225 q^{19} +(-0.390941 + 0.877852i) q^{20} +(3.69472 + 0.785512i) q^{22} +(4.15320 + 2.39785i) q^{23} +(-2.38457 - 4.13019i) q^{25} +(2.76845 + 8.52173i) q^{26} +(4.62185 + 2.57653i) q^{28} +(-1.45060 - 2.51250i) q^{29} +(3.14399 - 5.44556i) q^{31} +(4.89833 + 2.82954i) q^{32} +(-2.24287 + 2.49074i) q^{34} +(1.15338 - 0.534572i) q^{35} +4.69467 q^{37} +(-4.41624 - 3.97676i) q^{38} +(1.24160 - 0.552590i) q^{40} +(-10.1295 - 5.84827i) q^{41} +(-1.16280 + 0.671344i) q^{43} +(-3.13950 - 4.32198i) q^{44} +(-2.09550 - 6.45030i) q^{46} +(-3.72876 - 6.45840i) q^{47} +(-2.36356 - 6.58890i) q^{49} +(-1.40258 + 6.59713i) q^{50} +(5.15504 - 11.5756i) q^{52} +8.99689 q^{53} -1.28335 q^{55} +(-2.41892 - 7.08158i) q^{56} +(-0.853225 + 4.01321i) q^{58} +(0.140454 - 0.243273i) q^{59} +(-9.52219 + 5.49764i) q^{61} +(-8.45745 + 2.74757i) q^{62} +(-2.47005 - 7.60913i) q^{64} +(-1.52212 - 2.63639i) q^{65} +(-1.89068 - 1.09159i) q^{67} +(4.71417 - 0.495044i) q^{68} +(-1.71800 - 0.529697i) q^{70} +0.198757i q^{71} -4.84941i q^{73} +(-4.93373 - 4.44276i) q^{74} +(0.877746 + 8.35854i) q^{76} +(-0.632248 + 7.03833i) q^{77} +(3.42117 - 1.97521i) q^{79} +(-1.82776 - 0.594244i) q^{80} +(5.11086 + 15.7321i) q^{82} +(5.09429 + 8.82356i) q^{83} +(0.569384 - 0.986203i) q^{85} +(1.85733 + 0.394877i) q^{86} +(-0.790698 + 7.51310i) q^{88} -2.67188i q^{89} +(-15.2087 + 7.04900i) q^{91} +(-3.90197 + 8.76182i) q^{92} +(-2.19322 + 10.3160i) q^{94} +(1.74860 + 1.00956i) q^{95} +(-1.87526 + 1.08268i) q^{97} +(-3.75143 + 9.16116i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.05092	−	0.946342i	−0.743114	−	0.669165i
$2$	−1.05092	−	0.946342i	−0.743114	−	0.669165i
$3$		0			0
$3$		0			0
$4$	0.208875	+	1.98906i	0.104438	+	0.994531i
$5$	0.416111	+	0.240242i	0.186091	+	0.107439i	0.590151	−	0.807293i	$-0.299068\pi$
$5$	0.416111	+	0.240242i	0.186091	+	0.107439i	−0.404061	+	0.914732i	$0.632402\pi$
$6$		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	$-0.798581\pi$
$11$	−2.31311	+	1.33548i	−0.697429	+	0.402661i	0.108960	+	0.994046i	$0.465248\pi$
$12$		0			0
$13$	−5.48694	−	3.16789i	−1.52180	−	0.878614i	−0.999668	−	0.0257515i	$-0.991802\pi$
$13$	−5.48694	−	3.16789i	−1.52180	−	0.878614i	−0.522136	−	0.852862i	$-0.674865\pi$
$14$	−3.64774	+	0.833054i	−0.974900	+	0.222643i
$15$		0			0
$16$	−3.91274	+	0.830933i	−0.978186	+	0.207733i
$17$		−	2.37005i		−	0.574821i	−0.957808	−	0.287410i	$-0.907206\pi$
$17$		−	2.37005i		−	0.574821i	0.957808	−	0.287410i	$-0.0927944\pi$
$18$		0			0
$19$	4.20225			0.964062			0.482031	−	0.876154i	$-0.339899\pi$
$19$	4.20225			0.964062			0.482031	+	0.876154i	$0.339899\pi$
$20$	−0.390941	+	0.877852i	−0.0874170	+	0.196294i
$21$		0			0
$22$	3.69472	+	0.785512i	0.787716	+	0.167472i
$23$	4.15320	+	2.39785i	0.866001	+	0.499986i	0.866017	−	0.500014i	$-0.166672\pi$
$23$	4.15320	+	2.39785i	0.866001	+	0.499986i	−1.59909e−5		1.00000i	$0.500005\pi$
$24$		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	$-0.0243330\pi$
$32$	4.89833	+	2.82954i	0.865911	+	0.500198i
$33$		0			0
$34$	−2.24287	+	2.49074i	−0.384650	+	0.427158i
$35$	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	$0.373891\pi$
$38$	−4.41624	−	3.97676i	−0.716408	−	0.645116i
$39$		0			0
$40$	1.24160	−	0.552590i	0.196314	−	0.0873722i
$41$	−10.1295	−	5.84827i	−1.58196	−	0.913347i	−0.994573	−	0.104043i	$-0.966822\pi$
$41$	−10.1295	−	5.84827i	−1.58196	−	0.913347i	−0.587390	−	0.809304i	$-0.699845\pi$
$42$		0			0
$43$	−1.16280	+	0.671344i	−0.177326	+	0.102379i	−0.586036	−	0.810285i	$-0.699312\pi$
$43$	−1.16280	+	0.671344i	−0.177326	+	0.102379i	0.408710	+	0.912664i	$0.365979\pi$
$44$	−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
$49$	−2.36356	−	6.58890i	−0.337652	−	0.941271i
$50$	−1.40258	+	6.59713i	−0.198354	+	0.932975i
$51$		0			0
$52$	5.15504	−	11.5756i	0.714875	−	1.60524i
$53$	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
$56$	−2.41892	−	7.08158i	−0.323242	−	0.946316i
$57$		0			0
$58$	−0.853225	+	4.01321i	−0.112034	+	0.526960i
$59$	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	−0.964745	−	0.263186i	$-0.915227\pi$
$61$	−9.52219	+	5.49764i	−1.21919	+	0.703900i	−0.254446	+	0.967087i	$0.581893\pi$
$62$	−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	$-0.375909\pi$
$67$	−1.89068	−	1.09159i	−0.230984	−	0.133358i	−0.611026	+	0.791611i	$0.709243\pi$
$68$	4.71417	−	0.495044i	0.571677	−	0.0600330i
$69$		0			0
$70$	−1.71800	−	0.529697i	−0.205340	−	0.0633109i
$71$			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	$-0.908408\pi$
$73$		−	4.84941i		−	0.567580i	0.958886	−	0.283790i	$-0.0915919\pi$
$74$	−4.93373	−	4.44276i	−0.573535	−	0.516461i
$75$		0			0
$76$	0.877746	+	8.35854i	0.100684	+	0.958790i
$77$	−0.632248	+	7.03833i	−0.0720514	+	0.802092i
$78$		0			0
$79$	3.42117	−	1.97521i	0.384912	−	0.222229i	−0.295041	−	0.955484i	$-0.595333\pi$
$79$	3.42117	−	1.97521i	0.384912	−	0.222229i	0.679953	+	0.733256i	$0.262000\pi$
$80$	−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
$86$	1.85733	+	0.394877i	0.200282	+	0.0425807i
$87$		0			0
$88$	−0.790698	+	7.51310i	−0.0842887	+	0.800899i
$89$		−	2.67188i		−	0.283219i	−0.989923	−	0.141609i	$-0.954772\pi$
$89$		−	2.67188i		−	0.283219i	0.989923	−	0.141609i	$-0.0452277\pi$
$90$		0			0
$91$	−15.2087	+	7.04900i	−1.59431	+	0.738936i
$92$	−3.90197	+	8.76182i	−0.406809	+	0.913483i
$93$		0			0
$94$	−2.19322	+	10.3160i	−0.226213	+	1.06401i
$95$	1.74860	+	1.00956i	0.179403	+	0.103578i
$96$		0			0
$97$	−1.87526	+	1.08268i	−0.190403	+	0.109929i	−0.592171	−	0.805812i	$-0.701729\pi$
$97$	−1.87526	+	1.08268i	−0.190403	+	0.109929i	0.401768	+	0.915741i	$0.368396\pi$
$98$	−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	−0.258924	−	0.965898i	$-0.583368\pi$
$101$	4.50341	−	2.60004i	0.448106	−	0.258714i	0.707030	+	0.707184i	$0.250035\pi$
$102$		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	$0.131139\pi$
$104$	−16.3720	+	7.28659i	−1.60541	+	0.714509i
$105$		0			0
$106$	−9.45503	−	8.51413i	−0.918354	−	0.826966i
$107$		−	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	$0.675777\pi$
$110$	1.34870	+	1.21449i	0.128593	+	0.115797i
$111$		0			0
$112$	−4.15950	+	9.73132i	−0.393036	+	0.919523i
$113$	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
$119$	−5.12817	−	3.60856i	−0.470099	−	0.330796i
$120$		0			0
$121$	−1.93301	+	3.34807i	−0.175728	+	0.304370i
$122$	15.2097	+	3.23365i	1.37702	+	0.292761i
$123$		0			0
$124$	11.4883	+	5.11616i	1.03168	+	0.459445i
$125$		−	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	$0.979388\pi$
$128$	−4.60500	+	10.3341i	−0.407028	+	0.913415i
$129$		0			0
$130$	−0.895294	+	4.21108i	−0.0785224	+	0.369336i
$131$	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
$133$	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	0.991197	−	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	$0.203887\pi$
$140$	1.30421	+	2.18249i	0.110226	+	0.184454i
$141$		0			0
$142$	0.188092	−	0.208878i	0.0157843	−	0.0175286i
$143$	16.9225			1.41513
$144$		0			0
$145$		−	1.39397i		−	0.115763i
$146$	−4.58919	+	5.09635i	−0.379804	+	0.421777i
$147$		0			0
$148$	0.980601	+	9.33799i	0.0806049	+	0.767578i
$149$	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	0.0133797	−	0.999910i	$-0.495741\pi$
$151$	10.8876	−	6.28594i	0.886017	−	0.511542i	0.872638	+	0.488368i	$0.162408\pi$
$152$	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	0.841717	−	0.539919i	$-0.181545\pi$
$157$	9.96123	+	5.75112i	0.794993	+	0.458989i	−0.0467246	+	0.998908i	$0.514878\pi$
$158$	−5.46461	−	1.16180i	−0.434741	−	0.0924278i
$159$		0			0
$160$	1.35848	+	2.35419i	0.107397	+	0.186115i
$161$	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	$0.714135\pi$
$164$	9.51678	−	21.3698i	0.743135	−	1.66870i
$165$		0			0
$166$	2.99641	−	14.0938i	0.232566	−	1.09389i
$167$	−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	0.0967521	−	0.995309i	$-0.469155\pi$
$173$	13.2462	−	7.64770i	1.00709	−	0.581444i	0.910339	+	0.413864i	$0.135821\pi$
$174$		0			0
$175$	−12.5673	−	1.12891i	−0.950002	−	0.0853379i
$176$	7.94092	−	7.14741i	0.598569	−	0.538756i
$177$		0			0
$178$	−2.52851	+	2.80794i	−0.189520	+	0.210464i
$179$			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	$0.0866498\pi$
$181$			7.23452i			0.537738i	−0.963177	+	0.268869i	$0.913350\pi$
$182$	22.6540	+	6.98471i	1.67922	+	0.517741i
$183$		0			0
$184$	12.3923	−	5.51539i	0.913576	−	0.406600i
$185$	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	$-0.923001\pi$
$191$	−17.2598	+	9.96493i	−1.24887	+	0.721037i	−0.277988	+	0.960584i	$0.589668\pi$
$192$		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	$-0.00485112\pi$
$194$	2.99533	+	0.636820i	0.215052	+	0.0457210i
$195$		0			0
$196$	12.6120	−	6.07753i	0.900860	−	0.434110i
$197$	−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	$0.216210\pi$
$200$	−13.4151	−	1.41184i	−0.948588	−	0.0998319i
$201$		0			0
$202$	−7.19326	−	1.52932i	−0.506116	−	0.107602i
$203$	−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	$-0.448741\pi$
$211$	−8.92341	−	5.15194i	−0.614313	−	0.354674i	−0.774652	+	0.632388i	$0.782075\pi$
$212$	1.87923	+	17.8954i	0.129066	+	1.22906i
$213$		0			0
$214$	−14.0350	+	15.5860i	−0.959411	+	1.06544i
$215$	−0.645139			−0.0439981
$216$		0			0
$217$	−6.99583	−	15.0940i	−0.474908	−	1.02465i
$218$	11.5113	+	10.3658i	0.779642	+	0.702058i
$219$		0			0
$220$	−0.268060	−	2.55266i	−0.0180726	−	0.172100i
$221$	−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	0.943261	−	0.332052i	$-0.107741\pi$
$229$	17.0595	+	9.84933i	1.12733	+	0.650862i	0.184065	+	0.982914i	$0.441074\pi$
$230$	0.677669	−	3.18747i	0.0446842	−	0.210175i
$231$		0			0
$232$	−8.16074	−	0.858857i	−0.535779	−	0.0563868i
$233$	−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
$236$	0.513223	+	0.228558i	0.0334080	+	0.0148778i
$237$		0			0
$238$	1.97438	+	8.64532i	0.127980	+	0.560393i
$239$	8.34611	+	4.81863i	0.539865	+	0.311691i	0.745024	−	0.667037i	$-0.232438\pi$
$239$	8.34611	+	4.81863i	0.539865	+	0.311691i	−0.205159	+	0.978729i	$0.565771\pi$
$240$		0			0
$241$	−3.56210	+	2.05658i	−0.229455	+	0.132476i	−0.610321	−	0.792154i	$-0.708959\pi$
$241$	−3.56210	+	2.05658i	−0.229455	+	0.132476i	0.380865	+	0.924630i	$0.375626\pi$
$242$	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
$248$	−7.23163	−	16.2485i	−0.459209	−	1.03178i
$249$		0			0
$250$	−4.44204	+	4.93293i	−0.280939	+	0.311986i
$251$	−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
$254$	1.38021	−	1.53274i	0.0866023	−	0.0961728i
$255$		0			0
$256$	14.6191	−	6.50245i	0.913694	−	0.406403i
$257$	14.9497	+	8.63121i	0.932537	+	0.538400i	0.887613	−	0.460590i	$-0.152362\pi$
$257$	14.9497	+	8.63121i	0.932537	+	0.538400i	0.0449237	+	0.998990i	$0.485696\pi$
$258$		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	$-0.533078\pi$
$263$	11.4455	−	6.60806i	0.705760	−	0.407471i	0.809489	+	0.587135i	$0.199744\pi$
$264$		0			0
$265$	3.74371	+	2.16143i	0.229974	+	0.132776i
$266$	−15.3287	+	3.50070i	−0.939864	+	0.214642i
$267$		0			0
$268$	1.77632	−	3.98869i	0.108506	−	0.243648i
$269$			27.5600i			1.68036i	0.542304	+	0.840182i	$0.317552\pi$
$269$			27.5600i			1.68036i	−0.542304	+	0.840182i	$0.682448\pi$
$270$		0			0
$271$	−21.2467			−1.29065			−0.645323	−	0.763910i	$-0.723277\pi$
$271$	−21.2467			−1.29065			−0.645323	+	0.763910i	$0.723277\pi$
$272$	1.96935	+	9.27338i	0.119409	+	0.562281i
$273$		0			0
$274$	2.62261	−	12.3356i	0.158438	−	0.745223i
$275$	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	$-0.0461332\pi$
$284$	−0.395340	+	0.0415154i	−0.0234591	+	0.00246348i
$285$		0			0
$286$	−17.7843	−	16.0145i	−1.05161	−	0.946958i
$287$	−28.0770	+	13.0132i	−1.65733	+	0.768147i
$288$		0			0
$289$	11.3829			0.669581
$290$	−1.31918	+	1.46496i	−0.0774647	+	0.0860253i
$291$		0			0
$292$	9.64577	−	1.01292i	0.564476	−	0.0592768i
$293$	5.80807	+	3.35329i	0.339311	+	0.195901i	0.659967	−	0.751294i	$-0.270570\pi$
$293$	5.80807	+	3.35329i	0.339311	+	0.195901i	−0.320656	+	0.947196i	$0.603903\pi$
$294$		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
$302$	−17.3906	−	3.69732i	−1.00072	−	0.212757i
$303$		0			0
$304$	−16.4423	+	3.49179i	−0.943031	+	0.200268i
$305$	−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	$0.612019\pi$
$308$	−14.1317	+	0.212553i	−0.805231	+	0.0121113i
$309$		0			0
$310$	−4.17932	−	0.888541i	−0.237369	−	0.0504657i
$311$	−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	0.0579500	−	0.998319i	$-0.481544\pi$
$313$	16.8337	−	9.71892i	0.951495	−	0.549346i	0.893545	+	0.448974i	$0.148210\pi$
$314$	−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
$320$	0.800215	−	3.75965i	0.0447334	−	0.210171i
$321$		0			0
$322$	−17.1473	−	5.28690i	−0.955583	−	0.294627i
$323$		−	9.95953i		−	0.554163i
$324$		0			0
$325$			30.2162i			1.67609i
$326$	18.8994	−	20.9880i	1.04674	−	1.16242i
$327$		0			0
$328$	−30.2245	+	13.4519i	−1.66887	+	0.742755i
$329$	−19.6516	−	1.76529i	−1.08343	−	0.0973235i
$330$		0			0
$331$	31.2751	−	18.0567i	1.71903	−	0.992484i	0.798328	−	0.602223i	$-0.205718\pi$
$331$	31.2751	−	18.0567i	1.71903	−	0.992484i	0.920704	−	0.390261i	$-0.127615\pi$
$332$	−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	$0.101973\pi$
$338$	7.98233	−	37.5455i	0.434182	−	2.04221i
$339$		0			0
$340$	2.08055	+	0.926548i	0.112834	+	0.0502491i
$341$			16.7949i			0.909495i
$342$		0			0
$343$	−17.8554	−	4.91791i	−0.964099	−	0.265542i
$344$	−0.397484	+	3.77684i	−0.0214309	+	0.203633i
$345$		0			0
$346$	−21.1581	−	4.49830i	−1.13747	−	0.241830i
$347$	−24.8678	−	14.3574i	−1.33497	−	0.770747i	−0.348915	−	0.937154i	$-0.613450\pi$
$347$	−24.8678	−	14.3574i	−1.33497	−	0.770747i	−0.986057	+	0.166408i	$0.946783\pi$
$348$		0			0
$349$	−0.744758	+	0.429986i	−0.0398660	+	0.0230166i	−0.519801	−	0.854288i	$-0.673994\pi$
$349$	−0.744758	+	0.429986i	−0.0398660	+	0.0230166i	0.479935	+	0.877304i	$0.340660\pi$
$350$	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	−0.999608	−	0.0279920i	$-0.991089\pi$
$353$	−27.7159	+	16.0018i	−1.47517	+	0.851690i	−0.475562	+	0.879682i	$0.657755\pi$
$354$		0			0
$355$	−0.0477497	+	0.0827049i	−0.00253429	+	0.00438952i
$356$	5.31454	−	0.558090i	0.281670	−	0.0295787i
$357$		0			0
$358$	10.1228	−	11.2414i	0.535005	−	0.594129i
$359$			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
$362$	6.84633	−	7.60292i	0.359835	−	0.399601i
$363$		0			0
$364$	−17.1976	−	28.7788i	−0.901401	−	1.50842i
$365$	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
$371$	13.6984	−	19.4670i	0.711185	−	1.01067i
$372$		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	$0.902055\pi$
$374$	1.86170	−	8.75665i	0.0962663	−	0.452796i
$375$		0			0
$376$	−20.9772	−	2.20769i	−1.08182	−	0.113853i
$377$			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	$0.888216\pi$
$380$	−1.64283	+	3.68895i	−0.0842754	+	0.189239i
$381$		0			0
$382$	27.5689	+	5.86127i	1.41055	+	0.299889i
$383$	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
$385$	−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	−0.973112	−	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
$392$	−19.0057	−	5.54828i	−0.959933	−	0.280231i
$393$		0			0
$394$	12.5602	+	11.3103i	0.632775	+	0.569805i
$395$	1.89812			0.0955046
$396$		0			0
$397$			11.6658i			0.585487i	0.956191	+	0.292744i	$0.0945683\pi$
$397$			11.6658i			0.585487i	−0.956191	+	0.292744i	$0.905432\pi$
$398$	−23.0692	−	20.7735i	−1.15636	−	1.04128i
$399$		0			0
$400$	12.7621	+	14.1790i	0.638106	+	0.708948i
$401$	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	0.514498	−	0.857491i	$-0.327978\pi$
$409$	0.589282	+	0.340222i	0.0291381	+	0.0168229i	−0.485360	+	0.874314i	$0.661312\pi$
$410$	−1.65281	+	7.77412i	−0.0816265	+	0.383937i
$411$		0			0
$412$	4.13053	+	1.83948i	0.203497	+	0.0906247i
$413$	−0.312530	−	0.674306i	−0.0153786	−	0.0331804i
$414$		0			0
$415$			4.89544i			0.240308i
$416$	−17.9132	−	31.0429i	−0.878267	−	1.52200i
$417$		0			0
$418$	15.5261	+	3.30092i	0.759407	+	0.161453i
$419$	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
$427$	−2.60272	+	28.9741i	−0.125955	+	1.40215i
$428$	29.4993	−	3.09778i	1.42590	−	0.149737i
$429$		0			0
$430$	0.677991	+	0.610522i	0.0326956	+	0.0294420i
$431$		−	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	$-0.686915\pi$
$433$		−	34.6459i		−	1.66498i	0.554042	−	0.832489i	$-0.313085\pi$
$434$	−6.93203	+	22.4831i	−0.332748	+	1.07922i
$435$		0			0
$436$	−2.28792	−	21.7872i	−0.109571	−	1.04342i
$437$	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	0.202627	−	0.979256i	$-0.435052\pi$
$443$	24.2468	−	13.9989i	1.15200	−	0.665108i	0.949374	+	0.314148i	$0.101719\pi$
$444$		0			0
$445$	0.641897	−	1.11180i	0.0304288	−	0.0527043i
$446$	4.25456	−	20.0116i	0.201459	−	0.947579i
$447$		0			0
$448$	−20.2250	−	6.24087i	−0.955543	−	0.294853i
$449$	−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
$452$	17.2756	+	7.69348i	0.812576	+	0.361871i
$453$		0			0
$454$	5.69151	−	26.7705i	0.267116	−	1.25640i
$455$	−8.02199	−	0.720609i	−0.376077	−	0.0337827i
$456$		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	−0.507377	−	0.861724i	$-0.669385\pi$
$461$	−0.317557	+	0.183341i	−0.0147901	+	0.00853906i	0.492587	+	0.870263i	$0.336051\pi$
$462$		0			0
$463$	14.3509	+	8.28549i	0.666943	+	0.385060i	0.794917	−	0.606718i	$-0.207514\pi$
$463$	14.3509	+	8.28549i	0.666943	+	0.385060i	−0.127974	+	0.991777i	$0.540848\pi$
$464$	7.76353	+	8.62544i	0.360413	+	0.400426i
$465$		0			0
$466$	7.72226	+	6.95379i	0.357727	+	0.322128i
$467$	−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
$470$	−3.39094	+	3.76568i	−0.156413	+	0.173698i
$471$		0			0
$472$	−0.323064	−	0.725880i	−0.0148702	−	0.0334113i
$473$	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
$482$	5.68972	+	1.20966i	0.259160	+	0.0550985i
$483$		0			0
$484$	−7.06328	−	3.14555i	−0.321058	−	0.142979i
$485$	−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	$0.935089\pi$
$488$	−3.25500	+	30.9285i	−0.147347	+	1.40007i
$489$		0			0
$490$	−3.76190	+	2.91081i	−0.169945	+	0.131497i
$491$	−8.03087	−	4.63662i	−0.362428	−	0.209248i	0.307717	−	0.951478i	$-0.400435\pi$
$491$	−8.03087	−	4.63662i	−0.362428	−	0.209248i	−0.670145	+	0.742230i	$0.733768\pi$
$492$		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	$-0.460385\pi$
$499$	−15.0365	−	8.68131i	−0.673125	−	0.388629i	−0.797260	+	0.603636i	$0.793718\pi$
$500$	9.33648	−	0.980442i	0.417540	−	0.0438467i
$501$		0			0
$502$	3.48713	+	3.14012i	0.155638	+	0.140150i
$503$	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
$506$	13.4613	+	12.1218i	0.598430	+	0.538878i
$507$		0			0
$508$	−2.90099	+	0.304639i	−0.128711	+	0.0135162i
$509$	3.52873	+	2.03731i	0.156408	+	0.0903023i	0.576161	−	0.817336i	$-0.304550\pi$
$509$	3.52873	+	2.03731i	0.156408	+	0.0903023i	−0.419753	+	0.907638i	$0.637883\pi$
$510$		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
$518$	−17.1249	+	3.91092i	−0.752427	+	0.171836i
$519$		0			0
$520$	−8.56311	−	0.901204i	−0.375517	−	0.0395204i
$521$		−	27.2193i		−	1.19250i	−0.802798	−	0.596251i	$-0.796656\pi$
$521$		−	27.2193i		−	1.19250i	0.802798	−	0.596251i	$-0.203344\pi$
$522$		0			0
$523$	3.44794			0.150768			0.0753838	−	0.997155i	$-0.475982\pi$
$523$	3.44794			0.150768			0.0753838	+	0.997155i	$0.475982\pi$
$524$	22.6340	+	10.0798i	0.988772	+	0.440338i
$525$		0			0
$526$	−18.2818	−	3.88679i	−0.797125	−	0.169472i
$527$	−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
$536$	−5.64143	+	2.51080i	−0.243673	+	0.108450i
$537$		0			0
$538$	26.0812	−	28.9634i	1.12444	−	1.24870i
$539$	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	$0.458880\pi$
$542$	22.3286	+	20.1066i	0.959097	+	0.863654i
$543$		0			0
$544$	6.70615	−	11.6093i	0.287524	−	0.497744i
$545$	−4.55787	−	2.63149i	−0.195238	−	0.112721i
$546$		0			0
$547$	5.72221	−	3.30372i	0.244664	−	0.141257i	−0.372654	−	0.927970i	$-0.621552\pi$
$547$	5.72221	−	3.30372i	0.244664	−	0.141257i	0.617319	+	0.786713i	$0.288219\pi$
$548$	−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
$554$	4.27070	−	20.0876i	0.181445	−	0.853439i
$555$		0			0
$556$	−5.02599	−	2.23826i	−0.213149	−	0.0949235i
$557$	−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
$560$	−4.06868	+	3.05002i	−0.171933	+	0.128887i
$561$		0			0
$562$	−3.73881	+	17.5858i	−0.157712	+	0.741810i
$563$	−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	0.774171	−	0.632976i	$-0.218167\pi$
$571$	14.6500	+	8.45818i	0.613083	+	0.353964i	−0.161088	+	0.986940i	$0.551500\pi$
$572$	3.53470	+	33.6600i	0.147793	+	1.40740i
$573$		0			0
$574$	41.8218	+	12.8946i	1.74561	+	0.538209i
$575$		−	22.8713i		−	0.953801i
$576$		0			0
$577$			0.277722i			0.0115617i	0.999983	+	0.00578087i	$0.00184012\pi$
$577$			0.277722i			0.0115617i	−0.999983	+	0.00578087i	$0.998160\pi$
$578$	−11.9625	−	10.7721i	−0.497575	−	0.448060i
$579$		0			0
$580$	2.77270	−	0.291167i	0.115130	−	0.0120901i
$581$	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	0.997015	+	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
$590$	−0.186706	−	0.0396944i	−0.00768654	−	0.00163419i
$591$		0			0
$592$	−18.3690	+	3.90095i	−0.754963	+	0.160328i
$593$		−	32.0154i		−	1.31471i	−0.753579	−	0.657357i	$-0.771674\pi$
$593$		−	32.0154i		−	1.31471i	0.753579	−	0.657357i	$-0.228326\pi$
$594$		0			0
$595$	−1.26696	−	2.73356i	−0.0519403	−	0.112065i
$596$	0.278655	+	0.124096i	0.0114142	+	0.00508316i
$597$		0			0
$598$	−8.93591	+	42.0307i	−0.365417	+	1.71876i
$599$	15.8709	+	9.16306i	0.648467	+	0.374392i	0.787869	−	0.615843i	$-0.211185\pi$
$599$	15.8709	+	9.16306i	0.648467	+	0.374392i	−0.139402	+	0.990236i	$0.544518\pi$
$600$		0			0
$601$	19.1583	−	11.0611i	0.781485	−	0.451190i	−0.0554716	−	0.998460i	$-0.517666\pi$
$601$	19.1583	−	11.0611i	0.781485	−	0.451190i	0.836956	+	0.547270i	$0.184333\pi$
$602$	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	$0.270910\pi$
$608$	20.5840	+	11.8905i	0.834792	+	0.482221i
$609$		0			0
$610$	5.55208	+	4.99957i	0.224797	+	0.202427i
$611$			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	$0.335201\pi$
$614$	12.6943	+	11.4311i	0.512301	+	0.461320i
$615$		0			0
$616$	15.0525	+	13.1501i	0.606483	+	0.529832i
$617$	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
$623$	−5.78126	−	4.06812i	−0.231621	−	0.162986i
$624$		0			0
$625$	−10.7952	+	18.6978i	−0.431807	+	0.747911i
$626$	−26.8883	−	5.71657i	−1.07467	−	0.228480i
$627$		0			0
$628$	−9.35868	+	21.0148i	−0.373452	+	0.838581i
$629$		−	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	$-0.194575\pi$
$632$	1.16947	−	11.1121i	0.0465190	−	0.442017i
$633$		0			0
$634$	3.06933	−	14.4368i	0.121899	−	0.573360i
$635$	−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	0.778602	−	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	$0.195091\pi$
$644$	13.0173	+	21.7833i	0.512954	+	0.858384i
$645$		0			0
$646$	−9.42511	+	10.4667i	−0.370826	+	0.411806i
$647$	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
$650$	28.5948	−	31.7548i	1.12158	−	1.24553i
$651$		0			0
$652$	−39.7236	+	4.17146i	−1.55570	+	0.163367i
$653$	−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	−0.628316	−	0.777958i	$-0.716255\pi$
$659$	−6.89888	+	3.98307i	−0.268742	+	0.155158i	0.359574	+	0.933117i	$0.382922\pi$
$660$		0			0
$661$	0.220771	+	0.127462i	0.00858700	+	0.00495771i	0.504287	−	0.863536i	$-0.331755\pi$
$661$	0.220771	+	0.127462i	0.00858700	+	0.00495771i	−0.495700	+	0.868494i	$0.665089\pi$
$662$	−49.9554	−	10.6207i	−1.94157	−	0.412787i
$663$		0			0
$664$	28.6594	+	3.01619i	1.11220	+	0.117051i
$665$	4.84679	−	2.24641i	0.187950	−	0.0871119i
$666$		0			0
$667$		−	13.9132i		−	0.538723i
$668$	−40.1025	−	17.8592i	−1.55161	−	0.690992i
$669$		0			0
$670$	−0.308499	+	1.45105i	−0.0119184	+	0.0560589i
$671$	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	$-0.259924\pi$
$677$	43.1462	−	24.9105i	1.65824	−	0.957388i	0.973525	−	0.228582i	$-0.0734090\pi$
$678$		0			0
$679$	−0.512568	+	5.70602i	−0.0196706	+	0.218977i
$680$	−1.30967	−	2.94264i	−0.0502234	−	0.112845i
$681$		0			0
$682$	15.8937	−	17.6501i	0.608602	−	0.675859i
$683$			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
$686$	14.1106	+	22.0656i	0.538744	+	0.842469i
$687$		0			0
$688$	3.99190	−	3.59301i	0.152190	−	0.136982i
$689$	−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
$698$	1.18960	+	0.252913i	0.0450269	+	0.00957291i
$699$		0			0
$700$	−0.379526	−	25.2330i	−0.0143447	−	0.953719i
$701$	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
$704$	15.8753	+	14.3021i	0.598323	+	0.539029i
$705$		0			0
$706$	44.2705	+	9.41209i	1.66614	+	0.354229i
$707$	1.23093	−	13.7030i	0.0462938	−	0.515353i
$708$		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
$716$	−21.2765	+	2.23429i	−0.795140	+	0.0834992i
$717$		0			0
$718$	5.22535	−	5.80281i	0.195008	−	0.216559i
$719$	−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
$722$	1.40940	+	1.26914i	0.0524524	+	0.0472326i
$723$		0			0
$724$	−14.3899	+	1.51111i	−0.534797	+	0.0561601i
$725$	−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	0.118176	−	0.992993i	$-0.462295\pi$
$733$	−18.4832	−	10.6713i	−0.682693	−	0.394153i	−0.800869	+	0.598840i	$0.795629\pi$
$734$	6.75040	−	31.7510i	0.249162	−	1.17195i
$735$		0			0
$736$	13.5589	+	23.4971i	0.499789	+	0.866115i
$737$	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	$-0.380074\pi$
$740$	−1.83534	+	4.12122i	−0.0674684	+	0.151499i
$741$		0			0
$742$	−32.8183	+	7.49490i	−1.20480	+	0.275146i
$743$	32.1395	+	18.5558i	1.17909	+	0.680745i	0.955803	−	0.294009i	$-0.0949895\pi$
$743$	32.1395	+	18.5558i	1.17909	+	0.680745i	0.223282	+	0.974754i	$0.428323\pi$
$744$		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	$-0.0398350\pi$
$751$	37.8228	+	21.8370i	1.38017	+	0.796843i	0.387993	+	0.921662i	$0.373168\pi$
$752$	19.9562	+	22.1717i	0.727726	+	0.808519i
$753$		0			0
$754$	17.3950	−	19.3173i	0.633488	−	0.703495i
$755$	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	$0.925345\pi$
$758$	12.6755	−	14.0763i	0.460394	−	0.511273i
$759$		0			0
$760$	5.21749	−	2.32212i	0.189258	−	0.0842322i
$761$	−19.6964	−	11.3717i	−0.713994	−	0.412225i	0.0985439	−	0.995133i	$-0.468582\pi$
$761$	−19.6964	−	11.3717i	−0.713994	−	0.412225i	−0.812538	+	0.582908i	$0.801915\pi$
$762$		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	0.311478	−	0.950253i	$-0.399176\pi$
$769$	−9.86460	−	5.69533i	−0.355726	−	0.205379i	−0.667204	+	0.744875i	$0.732509\pi$
$770$	4.68132	−	1.06910i	0.168703	−	0.0385277i
$771$		0			0
$772$	26.0488	+	11.6005i	0.937515	+	0.417511i
$773$		−	30.6663i		−	1.10299i	−0.834178	−	0.551495i	$-0.814058\pi$
$773$		−	30.6663i		−	1.10299i	0.834178	−	0.551495i	$-0.185942\pi$
$774$		0			0
$775$	−29.9883			−1.07721
$776$	−0.641025	+	6.09092i	−0.0230114	+	0.218651i
$777$		0			0
$778$	−7.95856	+	37.4337i	−0.285328	+	1.34206i
$779$	−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	$0.0535957\pi$
$788$	−2.49640	−	23.7725i	−0.0889305	−	0.846861i
$789$		0			0
$790$	−1.99477	−	1.79627i	−0.0709708	−	0.0639083i
$791$	−10.5201	−	22.6978i	−0.374050	−	0.807042i
$792$		0			0
$793$	69.6636			2.47383
$794$	11.0398	−	12.2598i	0.391787	−	0.435084i
$795$		0			0
$796$	4.58511	+	43.6628i	0.162515	+	1.54759i
$797$	25.9632	+	14.9898i	0.919663	+	0.530968i	0.883528	−	0.468379i	$-0.155162\pi$
$797$	25.9632	+	14.9898i	0.919663	+	0.530968i	0.0361355	+	0.999347i	$0.488495\pi$
$798$		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
$806$	55.1095	+	11.7165i	1.94115	+	0.412697i
$807$		0			0
$808$	1.53941	−	14.6273i	0.0541564	−	0.514586i
$809$	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	$0.400527\pi$
$812$	−0.230876	−	15.3499i	−0.00810215	−	0.538677i
$813$		0			0
$814$	17.3455	+	3.68772i	0.607959	+	0.129255i
$815$	−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	0.345639	−	0.938367i	$-0.387662\pi$
$823$	−8.43975	−	4.87269i	−0.294191	−	0.169851i	−0.639831	+	0.768516i	$0.720995\pi$
$824$	−2.60009	−	5.84204i	−0.0905783	−	0.203517i
$825$		0			0
$826$	−0.309679	+	1.00440i	−0.0107751	+	0.0349476i
$827$			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	$0.0450266\pi$
$829$			8.11853i			0.281968i	−0.990012	+	0.140984i	$0.954973\pi$
$830$	4.63276	−	5.14473i	0.160805	−	0.178576i
$831$		0			0
$832$	−10.5518	+	49.5757i	−0.365819	+	1.71873i
$833$	−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	$-0.322065\pi$
$839$	−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
$842$	−2.01615	+	9.48311i	−0.0694811	+	0.326810i
$843$		0			0
$844$	8.38364	−	18.8253i	0.288577	−	0.647995i
$845$			13.0413i			0.448635i
$846$		0			0
$847$	4.30122	+	9.28021i	0.147792	+	0.318872i
$848$	−35.2025	+	7.47581i	−1.20886	+	0.256720i
$849$		0			0
$850$	15.6355	+	3.32417i	0.536293	+	0.114018i
$851$	19.4979	+	11.2571i	0.668379	+	0.385889i
$852$		0			0
$853$	−20.4384	+	11.8001i	−0.699797	+	0.404028i	−0.807272	−	0.590180i	$-0.799057\pi$
$853$	−20.4384	+	11.8001i	−0.699797	+	0.404028i	0.107475	+	0.994208i	$0.465724\pi$
$854$	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	−0.248717	−	0.968576i	$-0.580009\pi$
$857$	13.6342	−	7.87173i	0.465737	−	0.268893i	0.714453	+	0.699683i	$0.246675\pi$
$858$		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	$0.317442\pi$
$860$	−0.134754	−	1.28322i	−0.00459506	−	0.0437575i
$861$		0			0
$862$	−14.4385	+	16.0341i	−0.491778	+	0.546125i
$863$		−	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
$866$	−32.7869	+	36.4102i	−1.11414	+	1.23727i
$867$		0			0
$868$	28.5617	−	17.0679i	0.969448	−	0.579323i
$869$	−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	−0.728293	−	0.685266i	$-0.759686\pi$
$877$	6.79088	−	11.7621i	0.229312	−	0.397179i	0.957604	+	0.288087i	$0.0930192\pi$
$878$	−3.60074	+	16.9363i	−0.121519	+	0.571574i
$879$		0			0
$880$	5.02141	−	1.06638i	0.169272	−	0.0359475i
$881$		−	5.11905i		−	0.172465i	−0.996275	−	0.0862325i	$-0.972517\pi$
$881$		−	5.11905i		−	0.172465i	0.996275	−	0.0862325i	$-0.0274828\pi$
$882$		0			0
$883$		−	36.5196i		−	1.22898i	−0.788924	−	0.614491i	$-0.789361\pi$
$883$		−	36.5196i		−	1.22898i	0.788924	−	0.614491i	$-0.210639\pi$
$884$	−27.4346	−	12.2177i	−0.922727	−	0.410925i
$885$		0			0
$886$	−38.7293	−	8.23400i	−1.30113	−	0.276627i
$887$	−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
$889$	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
$896$	15.3489	+	25.6984i	0.512772	+	0.858525i
$897$		0			0
$898$	25.0403	+	22.5485i	0.835606	+	0.752452i
$899$	−18.2427			−0.608426
$900$		0			0
$901$		−	21.3231i		−	0.710374i
$902$	−32.8318	−	29.5646i	−1.09318	−	0.984392i
$903$		0			0
$904$	−10.8747	−	24.4339i	−0.361686	−	0.812658i
$905$	−1.73803	+	3.01036i	−0.0577742	+	0.100068i
$906$		0			0
$907$	24.3819	−	14.0769i	0.809588	−	0.467416i	−0.0372246	−	0.999307i	$-0.511852\pi$
$907$	24.3819	−	14.0769i	0.809588	−	0.467416i	0.846813	+	0.531891i	$0.178518\pi$
$908$	−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	−0.936934	−	0.349507i	$-0.886349\pi$
$911$	−33.2831	+	19.2160i	−1.10272	+	0.636655i	−0.165785	+	0.986162i	$0.553016\pi$
$912$		0			0
$913$	−23.5673	−	13.6066i	−0.779964	−	0.450312i
$914$	−7.00535	+	32.9502i	−0.231717	+	1.08990i
$915$		0			0
$916$	−16.0276	+	35.9898i	−0.529567	+	1.18914i
$917$	−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	$0.907676\pi$
$920$	6.48162	+	0.682143i	0.213693	+	0.0224896i
$921$		0			0
$922$	0.507231	+	0.107839i	0.0167048	+	0.00355150i
$923$	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	$0.708490\pi$
$929$	−48.7835	+	28.1651i	−1.60053	+	0.924068i	−0.991380	+	0.131016i	$0.958176\pi$
$930$		0			0
$931$	−9.93228	−	27.6882i	−0.325517	−	0.907444i
$932$	−1.53483	−	14.6158i	−0.0502751	−	0.478756i
$933$		0			0
$934$	27.4777	+	24.7433i	0.899099	+	0.809627i
$935$			3.04160i			0.0994708i
$936$		0			0
$937$			36.1315i			1.18036i	0.807270	+	0.590182i	$0.200944\pi$
$937$			36.1315i			1.18036i	−0.807270	+	0.590182i	$0.799056\pi$
$938$	7.80607	+	2.40678i	0.254877	+	0.0785842i
$939$		0			0
$940$	7.12724	−	0.748445i	0.232465	−	0.0244116i
$941$	−12.0974	−	6.98446i	−0.394365	−	0.227687i	0.289684	−	0.957122i	$-0.406450\pi$
$941$	−12.0974	−	6.98446i	−0.394365	−	0.227687i	−0.684050	+	0.729435i	$0.739783\pi$
$942$		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	$-0.733162\pi$
$947$	−11.0539	+	6.38196i	−0.359203	+	0.207386i	0.309528	+	0.950890i	$0.399829\pi$
$948$		0			0
$949$	−15.3624	+	26.6084i	−0.498684	+	0.863746i
$950$	−5.89398	+	27.7228i	−0.191226	+	0.899445i
$951$		0			0
$952$	−16.7837	+	5.73296i	−0.543962	+	0.185806i
$953$	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
$956$	−7.84126	+	17.6074i	−0.253604	+	0.569465i
$957$		0			0
$958$	11.2210	−	52.7789i	0.362535	−	1.70521i
$959$	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	$-0.210453\pi$
$967$	20.2799	+	11.7086i	0.652158	+	0.376524i	−0.137125	+	0.990554i	$0.543786\pi$
$968$	4.44620	+	9.99001i	0.142906	+	0.321091i
$969$		0			0
$970$	1.09340	+	0.984592i	0.0351070	+	0.0316133i
$971$	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
$974$	8.45856	−	9.39332i	0.271030	−	0.300982i
$975$		0			0
$976$	32.6897	−	29.4231i	1.04637	−	0.941812i
$977$	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
$986$	9.51149	+	2.02218i	0.302907	+	0.0643994i
$987$		0			0
$988$	21.6628	−	48.6434i	0.689184	−	1.54755i
$989$	−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	$0.845067\pi$
$992$	30.8088	−	17.7781i	0.978180	−	0.564455i
$993$		0			0
$994$	−0.165575	−	0.725013i	−0.00525172	−	0.0229960i
$995$	9.13423	+	5.27365i	0.289575	+	0.167186i
$996$		0			0
$997$	13.3933	−	7.73264i	0.424171	−	0.244895i	−0.272689	−	0.962102i	$-0.587913\pi$
$997$	13.3933	−	7.73264i	0.424171	−	0.244895i	0.696860	+	0.717207i	$0.254580\pi$
$998$	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.307.8		80
3.2	odd	2		252.2.bi.c.139.34	yes	80
4.3	odd	2	inner	756.2.bi.c.307.18		80
7.6	odd	2	inner	756.2.bi.c.307.7		80
9.2	odd	6		252.2.bi.c.223.24	yes	80
9.7	even	3	inner	756.2.bi.c.559.17		80
12.11	even	2		252.2.bi.c.139.23	✓	80
21.20	even	2		252.2.bi.c.139.33	yes	80
28.27	even	2	inner	756.2.bi.c.307.17		80
36.7	odd	6	inner	756.2.bi.c.559.7		80
36.11	even	6		252.2.bi.c.223.33	yes	80
63.20	even	6		252.2.bi.c.223.23	yes	80
63.34	odd	6	inner	756.2.bi.c.559.18		80
84.83	odd	2		252.2.bi.c.139.24	yes	80
252.83	odd	6		252.2.bi.c.223.34	yes	80
252.223	even	6	inner	756.2.bi.c.559.8		80

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

\(f(q)\)	\(=\)	\(q+(-1.05092 - 0.946342i) q^{2} +(0.208875 + 1.98906i) q^{4} +(0.416111 + 0.240242i) q^{5} +(1.52257 - 2.16374i) q^{7} +(1.66282 - 2.28802i) q^{8} +(-0.209950 - 0.646259i) q^{10} +(-2.31311 + 1.33548i) q^{11} +(-5.48694 - 3.16789i) q^{13} +(-3.64774 + 0.833054i) q^{14} +(-3.91274 + 0.830933i) q^{16} -2.37005i q^{17} +4.20225 q^{19} +(-0.390941 + 0.877852i) q^{20} +(3.69472 + 0.785512i) q^{22} +(4.15320 + 2.39785i) q^{23} +(-2.38457 - 4.13019i) q^{25} +(2.76845 + 8.52173i) q^{26} +(4.62185 + 2.57653i) q^{28} +(-1.45060 - 2.51250i) q^{29} +(3.14399 - 5.44556i) q^{31} +(4.89833 + 2.82954i) q^{32} +(-2.24287 + 2.49074i) q^{34} +(1.15338 - 0.534572i) q^{35} +4.69467 q^{37} +(-4.41624 - 3.97676i) q^{38} +(1.24160 - 0.552590i) q^{40} +(-10.1295 - 5.84827i) q^{41} +(-1.16280 + 0.671344i) q^{43} +(-3.13950 - 4.32198i) q^{44} +(-2.09550 - 6.45030i) q^{46} +(-3.72876 - 6.45840i) q^{47} +(-2.36356 - 6.58890i) q^{49} +(-1.40258 + 6.59713i) q^{50} +(5.15504 - 11.5756i) q^{52} +8.99689 q^{53} -1.28335 q^{55} +(-2.41892 - 7.08158i) q^{56} +(-0.853225 + 4.01321i) q^{58} +(0.140454 - 0.243273i) q^{59} +(-9.52219 + 5.49764i) q^{61} +(-8.45745 + 2.74757i) q^{62} +(-2.47005 - 7.60913i) q^{64} +(-1.52212 - 2.63639i) q^{65} +(-1.89068 - 1.09159i) q^{67} +(4.71417 - 0.495044i) q^{68} +(-1.71800 - 0.529697i) q^{70} +0.198757i q^{71} -4.84941i q^{73} +(-4.93373 - 4.44276i) q^{74} +(0.877746 + 8.35854i) q^{76} +(-0.632248 + 7.03833i) q^{77} +(3.42117 - 1.97521i) q^{79} +(-1.82776 - 0.594244i) q^{80} +(5.11086 + 15.7321i) q^{82} +(5.09429 + 8.82356i) q^{83} +(0.569384 - 0.986203i) q^{85} +(1.85733 + 0.394877i) q^{86} +(-0.790698 + 7.51310i) q^{88} -2.67188i q^{89} +(-15.2087 + 7.04900i) q^{91} +(-3.90197 + 8.76182i) q^{92} +(-2.19322 + 10.3160i) q^{94} +(1.74860 + 1.00956i) q^{95} +(-1.87526 + 1.08268i) q^{97} +(-3.75143 + 9.16116i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56}+ \cdots - 20 q^{98}+O(q^{100}) \) 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

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