LMFDB - Embedded newform 756.2.bj.b.451.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(451,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.9
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.06666 - 0.928568i) q^{2} +(0.275522 + 1.98093i) q^{4} +(-2.33177 - 1.34625i) q^{5} +(1.11915 - 2.39740i) q^{7} +(1.54554 - 2.36882i) q^{8} +(1.23712 + 3.60119i) q^{10} +(1.22399 - 0.706672i) q^{11} +(2.46297 - 1.42199i) q^{13} +(-3.41989 + 1.51800i) q^{14} +(-3.84817 + 1.09158i) q^{16} +(1.23338 + 0.712090i) q^{17} +(1.48153 + 2.56609i) q^{19} +(2.02437 - 4.98999i) q^{20} +(-1.96178 - 0.382782i) q^{22} +(-1.67612 - 0.967709i) q^{23} +(1.12475 + 1.94813i) q^{25} +(-3.94756 - 0.770249i) q^{26} +(5.05743 + 1.55642i) q^{28} +(-0.423772 + 0.733994i) q^{29} -9.87356 q^{31} +(5.11830 + 2.40895i) q^{32} +(-0.654368 - 1.90483i) q^{34} +(-5.83707 + 4.08352i) q^{35} +(-5.49245 - 9.51321i) q^{37} +(0.802498 - 4.11284i) q^{38} +(-6.79285 + 3.44285i) q^{40} +(5.99620 - 3.46191i) q^{41} +(-5.96812 - 3.44570i) q^{43} +(1.73711 + 2.22994i) q^{44} +(0.889265 + 2.58861i) q^{46} -10.6848 q^{47} +(-4.49502 - 5.36608i) q^{49} +(0.609243 - 3.12240i) q^{50} +(3.49547 + 4.48718i) q^{52} +(6.58617 - 11.4076i) q^{53} -3.80542 q^{55} +(-3.94931 - 6.35633i) q^{56} +(1.13358 - 0.389420i) q^{58} -1.42192 q^{59} +2.03270i q^{61} +(10.5317 + 9.16828i) q^{62} +(-3.22261 - 7.32221i) q^{64} -7.65741 q^{65} -8.74356i q^{67} +(-1.07078 + 2.63943i) q^{68} +(10.0180 + 1.06440i) q^{70} -1.95293i q^{71} +(7.16234 + 4.13518i) q^{73} +(-2.97509 + 15.2475i) q^{74} +(-4.67504 + 3.64182i) q^{76} +(-0.324347 - 3.72526i) q^{77} +11.8351i q^{79} +(10.4426 + 2.63528i) q^{80} +(-9.61051 - 1.87521i) q^{82} +(-2.85384 + 4.94299i) q^{83} +(-1.91730 - 3.32085i) q^{85} +(3.16639 + 9.21720i) q^{86} +(0.217752 - 3.99161i) q^{88} +(-5.75795 + 3.32435i) q^{89} +(-0.652664 - 7.49613i) q^{91} +(1.45516 - 3.58690i) q^{92} +(11.3970 + 9.92156i) q^{94} -7.97801i q^{95} +(13.1164 + 7.57275i) q^{97} +(-0.188114 + 9.89771i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37}+ \cdots - 21 q^{98}+O(q^{100}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.06666	−	0.928568i	−0.754242	−	0.656597i
$2$	−1.06666	−	0.928568i	−0.754242	−	0.656597i
$3$		0			0
$3$		0			0
$4$	0.275522	+	1.98093i	0.137761	+	0.990465i
$5$	−2.33177	−	1.34625i	−1.04280	−	0.602059i	−0.122173	−	0.992509i	$-0.538986\pi$
$5$	−2.33177	−	1.34625i	−1.04280	−	0.602059i	−0.920624	+	0.390450i	$0.872320\pi$
$6$		0			0
$7$	1.11915	−	2.39740i	0.422998	−	0.906131i
$7$	1.11915	−	2.39740i	0.422998	−	0.906131i
$8$	1.54554	−	2.36882i	0.546431	−	0.837504i
$9$		0			0
$10$	1.23712	+	3.60119i	0.391211	+	1.13880i
$11$	1.22399	−	0.706672i	0.369048	−	0.213070i	−0.303995	−	0.952674i	$-0.598321\pi$
$11$	1.22399	−	0.706672i	0.369048	−	0.213070i	0.673042	+	0.739604i	$0.264987\pi$
$12$		0			0
$13$	2.46297	−	1.42199i	0.683104	−	0.394390i	−0.117920	−	0.993023i	$-0.537622\pi$
$13$	2.46297	−	1.42199i	0.683104	−	0.394390i	0.801024	+	0.598633i	$0.204289\pi$
$14$	−3.41989	+	1.51800i	−0.914005	+	0.405703i
$15$		0			0
$16$	−3.84817	+	1.09158i	−0.962044	+	0.272895i
$17$	1.23338	+	0.712090i	0.299138	+	0.172707i	0.642055	−	0.766658i	$-0.278082\pi$
$17$	1.23338	+	0.712090i	0.299138	+	0.172707i	−0.342918	+	0.939365i	$0.611415\pi$
$18$		0			0
$19$	1.48153	+	2.56609i	0.339886	+	0.588700i	0.984411	−	0.175883i	$-0.0562781\pi$
$19$	1.48153	+	2.56609i	0.339886	+	0.588700i	−0.644525	+	0.764583i	$0.722945\pi$
$20$	2.02437	−	4.98999i	0.452662	−	1.11579i
$21$		0			0
$22$	−1.96178	−	0.382782i	−0.418252	−	0.0816094i
$23$	−1.67612	−	0.967709i	−0.349495	−	0.201781i	0.314968	−	0.949102i	$-0.398006\pi$
$23$	−1.67612	−	0.967709i	−0.349495	−	0.201781i	−0.664463	+	0.747321i	$0.731340\pi$
$24$		0			0
$25$	1.12475	+	1.94813i	0.224950	+	0.389626i
$26$	−3.94756	−	0.770249i	−0.774181	−	0.151058i
$27$		0			0
$28$	5.05743	+	1.55642i	0.955764	+	0.294135i
$29$	−0.423772	+	0.733994i	−0.0786924	+	0.136299i	−0.902686	−	0.430300i	$-0.858408\pi$
$29$	−0.423772	+	0.733994i	−0.0786924	+	0.136299i	0.823994	+	0.566599i	$0.191741\pi$
$30$		0			0
$31$	−9.87356			−1.77334			−0.886672	−	0.462398i	$-0.846989\pi$
$31$	−9.87356			−1.77334			−0.886672	+	0.462398i	$0.846989\pi$
$32$	5.11830	+	2.40895i	0.904796	+	0.425846i
$33$		0			0
$34$	−0.654368	−	1.90483i	−0.112223	−	0.326676i
$35$	−5.83707	+	4.08352i	−0.986645	+	0.690241i
$36$		0			0
$37$	−5.49245	−	9.51321i	−0.902953	−	1.56396i	−0.823641	−	0.567111i	$-0.808061\pi$
$37$	−5.49245	−	9.51321i	−0.902953	−	1.56396i	−0.0793124	−	0.996850i	$-0.525272\pi$
$38$	0.802498	−	4.11284i	0.130182	−	0.667191i
$39$		0			0
$40$	−6.79285	+	3.44285i	−1.07404	+	0.544363i
$41$	5.99620	−	3.46191i	0.936449	−	0.540659i	0.0476034	−	0.998866i	$-0.484842\pi$
$41$	5.99620	−	3.46191i	0.936449	−	0.540659i	0.888845	+	0.458207i	$0.151508\pi$
$42$		0			0
$43$	−5.96812	−	3.44570i	−0.910131	−	0.525464i	−0.0296574	−	0.999560i	$-0.509442\pi$
$43$	−5.96812	−	3.44570i	−0.910131	−	0.525464i	−0.880473	+	0.474096i	$0.842775\pi$
$44$	1.73711	+	2.22994i	0.261879	+	0.336176i
$45$		0			0
$46$	0.889265	+	2.58861i	0.131115	+	0.381669i
$47$	−10.6848			−1.55854			−0.779269	−	0.626690i	$-0.784409\pi$
$47$	−10.6848			−1.55854			−0.779269	+	0.626690i	$0.784409\pi$
$48$		0			0
$49$	−4.49502	−	5.36608i	−0.642146	−	0.766582i
$50$	0.609243	−	3.12240i	0.0861599	−	0.441574i
$51$		0			0
$52$	3.49547	+	4.48718i	0.484735	+	0.622259i
$53$	6.58617	−	11.4076i	0.904681	−	1.56695i	0.0833354	−	0.996522i	$-0.473443\pi$
$53$	6.58617	−	11.4076i	0.904681	−	1.56695i	0.821345	−	0.570431i	$-0.193224\pi$
$54$		0			0
$55$	−3.80542			−0.513122
$56$	−3.94931	−	6.35633i	−0.527749	−	0.849400i
$57$		0			0
$58$	1.13358	−	0.389420i	0.148847	−	0.0511334i
$59$	−1.42192			−0.185118			−0.0925589	−	0.995707i	$-0.529505\pi$
$59$	−1.42192			−0.185118			−0.0925589	+	0.995707i	$0.529505\pi$
$60$		0			0
$61$			2.03270i			0.260260i	0.991497	+	0.130130i	$0.0415395\pi$
$61$			2.03270i			0.260260i	−0.991497	+	0.130130i	$0.958461\pi$
$62$	10.5317	+	9.16828i	1.33753	+	1.16437i
$63$		0			0
$64$	−3.22261	−	7.32221i	−0.402826	−	0.915277i
$65$	−7.65741			−0.949785
$66$		0			0
$67$		−	8.74356i		−	1.06820i	−0.845423	−	0.534098i	$-0.820651\pi$
$67$		−	8.74356i		−	1.06820i	0.845423	−	0.534098i	$-0.179349\pi$
$68$	−1.07078	+	2.63943i	−0.129851	+	0.320078i
$69$		0			0
$70$	10.0180	+	1.06440i	1.19738	+	0.127220i
$71$		−	1.95293i		−	0.231770i	−0.993263	−	0.115885i	$-0.963030\pi$
$71$		−	1.95293i		−	0.231770i	0.993263	−	0.115885i	$-0.0369704\pi$
$72$		0			0
$73$	7.16234	+	4.13518i	0.838289	+	0.483986i	0.856682	−	0.515844i	$-0.172522\pi$
$73$	7.16234	+	4.13518i	0.838289	+	0.483986i	−0.0183933	+	0.999831i	$0.505855\pi$
$74$	−2.97509	+	15.2475i	−0.345847	+	1.77248i
$75$		0			0
$76$	−4.67504	+	3.64182i	−0.536264	+	0.417746i
$77$	−0.324347	−	3.72526i	−0.0369627	−	0.424533i
$78$		0			0
$79$			11.8351i			1.33155i	0.746151	+	0.665776i	$0.231899\pi$
$79$			11.8351i			1.33155i	−0.746151	+	0.665776i	$0.768101\pi$
$80$	10.4426	+	2.63528i	1.16752	+	0.294633i
$81$		0			0
$82$	−9.61051	−	1.87521i	−1.06130	−	0.207082i
$83$	−2.85384	+	4.94299i	−0.313249	+	0.542563i	−0.979064	−	0.203554i	$-0.934751\pi$
$83$	−2.85384	+	4.94299i	−0.313249	+	0.542563i	0.665815	+	0.746117i	$0.268084\pi$
$84$		0			0
$85$	−1.91730	−	3.32085i	−0.207960	−	0.360197i
$86$	3.16639	+	9.21720i	0.341440	+	0.993916i
$87$		0			0
$88$	0.217752	−	3.99161i	0.0232124	−	0.425507i
$89$	−5.75795	+	3.32435i	−0.610341	+	0.352381i	−0.773099	−	0.634285i	$-0.781294\pi$
$89$	−5.75795	+	3.32435i	−0.610341	+	0.352381i	0.162758	+	0.986666i	$0.447961\pi$
$90$		0			0
$91$	−0.652664	−	7.49613i	−0.0684177	−	0.785808i
$92$	1.45516	−	3.58690i	0.151710	−	0.373961i
$93$		0			0
$94$	11.3970	+	9.92156i	1.17551	+	1.02333i
$95$		−	7.97801i		−	0.818527i
$96$		0			0
$97$	13.1164	+	7.57275i	1.33177	+	0.768896i	0.985570	−	0.169266i	$-0.0541396\pi$
$97$	13.1164	+	7.57275i	1.33177	+	0.768896i	0.346197	+	0.938162i	$0.387473\pi$
$98$	−0.188114	+	9.89771i	−0.0190024	+	0.999819i
$99$		0			0
$100$	−3.54921	+	2.76481i	−0.354921	+	0.276481i
$101$	−14.5192	+	8.38265i	−1.44471	+	0.834105i	−0.998159	−	0.0606528i	$-0.980682\pi$
$101$	−14.5192	+	8.38265i	−1.44471	+	0.834105i	−0.446553	+	0.894757i	$0.647348\pi$
$102$		0			0
$103$	1.31815	−	2.28310i	0.129881	−	0.224960i	−0.793749	−	0.608245i	$-0.791874\pi$
$103$	1.31815	−	2.28310i	0.129881	−	0.224960i	0.923630	+	0.383285i	$0.125207\pi$
$104$	0.438169	−	8.03207i	0.0429660	−	0.787609i
$105$		0			0
$106$	−17.6179	+	6.05229i	−1.71120	+	0.587851i
$107$	−0.702055	+	0.405332i	−0.0678702	+	0.0391849i	−0.533551	−	0.845768i	$-0.679143\pi$
$107$	−0.702055	+	0.405332i	−0.0678702	+	0.0391849i	0.465681	+	0.884953i	$0.345809\pi$
$108$		0			0
$109$	5.19986	−	9.00642i	0.498056	−	0.862659i	−0.501941	−	0.864902i	$-0.667381\pi$
$109$	5.19986	−	9.00642i	0.498056	−	0.862659i	0.999997	+	0.00224278i	$0.000713901\pi$
$110$	4.05908	+	3.53359i	0.387018	+	0.336914i
$111$		0			0
$112$	−1.68972	+	10.4472i	−0.159663	+	0.987172i
$113$	−4.37629	−	7.57996i	−0.411687	−	0.713063i	0.583387	−	0.812194i	$-0.301727\pi$
$113$	−4.37629	−	7.57996i	−0.411687	−	0.713063i	−0.995074	+	0.0991313i	$0.968394\pi$
$114$		0			0
$115$	2.60555	+	4.51294i	0.242968	+	0.420834i
$116$	−1.57075	−	0.637231i	−0.145840	−	0.0591654i
$117$		0			0
$118$	1.51670	+	1.32035i	0.139624	+	0.121548i
$119$	3.08749	−	2.15996i	0.283030	−	0.198003i
$120$		0			0
$121$	−4.50123	+	7.79636i	−0.409203	+	0.708760i
$122$	1.88750	−	2.16819i	0.170886	−	0.196299i
$123$		0			0
$124$	−2.72039	−	19.5588i	−0.244298	−	1.75644i
$125$			7.40568i			0.662384i
$126$		0			0
$127$			15.2544i			1.35361i	0.736164	+	0.676803i	$0.236635\pi$
$127$			15.2544i			1.35361i	−0.736164	+	0.676803i	$0.763365\pi$
$128$	−3.36175	+	10.8027i	−0.297140	+	0.954834i
$129$		0			0
$130$	8.16785	+	7.11043i	0.716368	+	0.623626i
$131$	0.0339597	−	0.0588199i	0.00296707	−	0.00513912i	−0.864538	−	0.502567i	$-0.832389\pi$
$131$	0.0339597	−	0.0588199i	0.00296707	−	0.00513912i	0.867505	+	0.497428i	$0.165722\pi$
$132$		0			0
$133$	7.80997	−	0.679989i	0.677211	−	0.0589625i
$134$	−8.11899	+	9.32639i	−0.701374	+	0.805678i
$135$		0			0
$136$	3.59305	−	1.82108i	0.308101	−	0.156156i
$137$	2.59483	+	4.49438i	0.221691	+	0.383981i	0.955322	−	0.295568i	$-0.0955089\pi$
$137$	2.59483	+	4.49438i	0.221691	+	0.383981i	−0.733630	+	0.679549i	$0.762176\pi$
$138$		0			0
$139$	−5.27411	−	9.13502i	−0.447344	−	0.774823i	0.550868	−	0.834592i	$-0.314297\pi$
$139$	−5.27411	−	9.13502i	−0.447344	−	0.774823i	−0.998212	+	0.0597697i	$0.980963\pi$
$140$	−9.69741	−	10.4377i	−0.819581	−	0.882150i
$141$		0			0
$142$	−1.81343	+	2.08311i	−0.152179	+	0.174810i
$143$	2.00977	−	3.48102i	0.168065	−	0.291097i
$144$		0			0
$145$	1.97627	−	1.14100i	0.164120	−	0.0947550i
$146$	−3.79998	−	11.0616i	−0.314489	−	0.915461i
$147$		0			0
$148$	17.3317	−	13.5013i	1.42466	−	1.10980i
$149$	9.18336	−	15.9060i	0.752330	−	1.30307i	−0.194361	−	0.980930i	$-0.562263\pi$
$149$	9.18336	−	15.9060i	0.752330	−	1.30307i	0.946691	−	0.322143i	$-0.104403\pi$
$150$		0			0
$151$	4.40011	−	2.54041i	0.358076	−	0.206735i	−0.310160	−	0.950684i	$-0.600383\pi$
$151$	4.40011	−	2.54041i	0.358076	−	0.206735i	0.668236	+	0.743949i	$0.267049\pi$
$152$	8.36836	+	0.456514i	0.678763	+	0.0370282i
$153$		0			0
$154$	−3.11319	+	4.27476i	−0.250868	+	0.344470i
$155$	23.0228	+	13.2922i	1.84924	+	1.06766i
$156$		0			0
$157$		−	2.41701i		−	0.192898i	−0.995338	−	0.0964492i	$-0.969251\pi$
$157$		−	2.41701i		−	0.192898i	0.995338	−	0.0964492i	$-0.0307485\pi$
$158$	10.9897	−	12.6240i	0.874293	−	1.00431i
$159$		0			0
$160$	−8.69163	−	12.5076i	−0.687134	−	0.988811i
$161$	−4.19581	+	2.93532i	−0.330676	+	0.231335i
$162$		0			0
$163$	13.8321	−	7.98598i	1.08342	−	0.625510i	0.151600	−	0.988442i	$-0.451558\pi$
$163$	13.8321	−	7.98598i	1.08342	−	0.625510i	0.931816	+	0.362932i	$0.118224\pi$
$164$	8.50988	+	10.9242i	0.664510	+	0.853038i
$165$		0			0
$166$	7.63397	−	2.62250i	0.592511	−	0.203546i
$167$	6.99445	+	12.1147i	0.541247	+	0.937467i	0.998833	+	0.0483016i	$0.0153809\pi$
$167$	6.99445	+	12.1147i	0.541247	+	0.937467i	−0.457586	+	0.889165i	$0.651286\pi$
$168$		0			0
$169$	−2.45586	+	4.25368i	−0.188913	+	0.327206i
$170$	−1.03854	+	5.32256i	−0.0796523	+	0.408222i
$171$		0			0
$172$	5.18134	−	12.7718i	0.395073	−	0.973841i
$173$		−	24.9568i		−	1.89743i	−0.316131	−	0.948716i	$-0.602384\pi$
$173$		−	24.9568i		−	1.89743i	0.316131	−	0.948716i	$-0.397616\pi$
$174$		0			0
$175$	5.92920	−	0.516236i	0.448205	−	0.0390238i
$176$	−3.93875	+	4.05549i	−0.296894	+	0.305694i
$177$		0			0
$178$	9.22865	+	1.80070i	0.691717	+	0.134968i
$179$	−0.618502	−	0.357092i	−0.0462290	−	0.0266903i	0.476707	−	0.879062i	$-0.341830\pi$
$179$	−0.618502	−	0.357092i	−0.0462290	−	0.0266903i	−0.522936	+	0.852372i	$0.675163\pi$
$180$		0			0
$181$		−	13.5134i		−	1.00445i	−0.864738	−	0.502223i	$-0.832516\pi$
$181$		−	13.5134i		−	1.00445i	0.864738	−	0.502223i	$-0.167484\pi$
$182$	−6.26450	+	8.60185i	−0.464355	+	0.637612i
$183$		0			0
$184$	−4.88284	+	2.47479i	−0.359968	+	0.182444i
$185$			29.5767i			2.17453i
$186$		0			0
$187$	2.01286			0.147195
$188$	−2.94390	−	21.1658i	−0.214706	−	1.54368i
$189$		0			0
$190$	−7.40813	+	8.50982i	−0.537442	+	0.617367i
$191$		−	15.2620i		−	1.10432i	−0.833738	−	0.552161i	$-0.813803\pi$
$191$		−	15.2620i		−	1.10432i	0.833738	−	0.552161i	$-0.186197\pi$
$192$		0			0
$193$	8.93048			0.642830			0.321415	−	0.946938i	$-0.395842\pi$
$193$	8.93048			0.642830			0.321415	+	0.946938i	$0.395842\pi$
$194$	−6.95890	−	20.2570i	−0.499620	−	1.45437i
$195$		0			0
$196$	9.39135	−	10.3828i	0.670811	−	0.741629i
$197$	3.57570			0.254758			0.127379	−	0.991854i	$-0.459344\pi$
$197$	3.57570			0.254758			0.127379	+	0.991854i	$0.459344\pi$
$198$		0			0
$199$	7.27270	−	12.5967i	0.515548	−	0.892955i	−0.484289	−	0.874908i	$-0.660922\pi$
$199$	7.27270	−	12.5967i	0.515548	−	0.892955i	0.999837	−	0.0180470i	$-0.00574485\pi$
$200$	6.35311	+	0.346578i	0.449233	+	0.0245067i
$201$		0			0
$202$	23.2709	+	4.54061i	1.63733	+	0.319477i
$203$	1.28541	+	1.83740i	0.0902182	+	0.128960i
$204$		0			0
$205$	−18.6423			−1.30203
$206$	−3.52602	+	1.21130i	−0.245670	+	0.0843950i
$207$		0			0
$208$	−7.92570	+	8.16061i	−0.549549	+	0.565837i
$209$	3.62676	+	2.09391i	0.250868	+	0.144839i
$210$		0			0
$211$	11.3933	−	6.57792i	0.784347	−	0.452843i	−0.0536217	−	0.998561i	$-0.517077\pi$
$211$	11.3933	−	6.57792i	0.784347	−	0.452843i	0.837969	+	0.545718i	$0.183743\pi$
$212$	24.4123	+	9.90371i	1.67664	+	0.680190i
$213$		0			0
$214$	1.12523	+	0.219555i	0.0769193	+	0.0150085i
$215$	9.27751	+	16.0691i	0.632721	+	1.09590i
$216$		0			0
$217$	−11.0500	+	23.6709i	−0.750121	+	1.60688i
$218$	−13.9096	+	4.77836i	−0.942074	+	0.323631i
$219$		0			0
$220$	−1.04848	−	7.53827i	−0.0706883	−	0.508230i
$221$	4.05035			0.272456
$222$		0			0
$223$	−7.88047	+	13.6494i	−0.527715	+	0.914030i	0.471763	+	0.881726i	$0.343618\pi$
$223$	−7.88047	+	13.6494i	−0.527715	+	0.914030i	−0.999478	+	0.0323043i	$0.989715\pi$
$224$	11.5033	−	9.57462i	0.768599	−	0.639731i
$225$		0			0
$226$	−2.37050	+	12.1489i	−0.157683	+	0.808134i
$227$	0.947912	+	1.64183i	0.0629152	+	0.108972i	0.895767	−	0.444523i	$-0.146627\pi$
$227$	0.947912	+	1.64183i	0.0629152	+	0.108972i	−0.832852	+	0.553496i	$0.813294\pi$
$228$		0			0
$229$	7.39322	+	4.26848i	0.488558	+	0.282069i	0.723976	−	0.689825i	$-0.242313\pi$
$229$	7.39322	+	4.26848i	0.488558	+	0.282069i	−0.235418	+	0.971894i	$0.575646\pi$
$230$	1.41134	−	7.23319i	0.0930611	−	0.476943i
$231$		0			0
$232$	1.08374	+	2.13826i	0.0711512	+	0.140383i
$233$	8.18028	+	14.1687i	0.535908	+	0.928220i	0.999119	+	0.0419719i	$0.0133640\pi$
$233$	8.18028	+	14.1687i	0.535908	+	0.928220i	−0.463211	+	0.886248i	$0.653303\pi$
$234$		0			0
$235$	24.9144	+	14.3844i	1.62524	+	0.938332i
$236$	−0.391770	−	2.81672i	−0.0255020	−	0.183353i
$237$		0			0
$238$	−5.29897	−	0.563007i	−0.343481	−	0.0364943i
$239$	5.95333	−	3.43716i	0.385089	−	0.222331i	−0.294941	−	0.955515i	$-0.595300\pi$
$239$	5.95333	−	3.43716i	0.385089	−	0.222331i	0.680030	+	0.733184i	$0.261967\pi$
$240$		0			0
$241$	8.63910	−	4.98779i	0.556493	−	0.321292i	−0.195244	−	0.980755i	$-0.562550\pi$
$241$	8.63910	−	4.98779i	0.556493	−	0.321292i	0.751737	+	0.659463i	$0.229216\pi$
$242$	12.0407	−	4.13636i	0.774007	−	0.265895i
$243$		0			0
$244$	−4.02663	+	0.560053i	−0.257779	+	0.0358537i
$245$	3.25728	+	18.5638i	0.208100	+	1.18600i
$246$		0			0
$247$	7.29792	+	4.21345i	0.464355	+	0.268096i
$248$	−15.2600	+	23.3887i	−0.969011	+	1.48518i
$249$		0			0
$250$	6.87668	−	7.89934i	0.434920	−	0.499598i
$251$	−16.6175			−1.04889			−0.524444	−	0.851445i	$-0.675727\pi$
$251$	−16.6175			−1.04889			−0.524444	+	0.851445i	$0.675727\pi$
$252$		0			0
$253$	−2.73541			−0.171974
$254$	14.1647	−	16.2712i	0.888773	−	1.02095i
$255$		0			0
$256$	13.6169	−	8.40119i	0.851056	−	0.525074i
$257$	−6.63756	−	3.83220i	−0.414040	−	0.239046i	0.278484	−	0.960441i	$-0.410168\pi$
$257$	−6.63756	−	3.83220i	−0.414040	−	0.239046i	−0.692524	+	0.721395i	$0.743501\pi$
$258$		0			0
$259$	−28.9538	+	2.52091i	−1.79910	+	0.156642i
$260$	−2.10979	−	15.1688i	−0.130843	−	0.940729i
$261$		0			0
$262$	−0.0908417	+	0.0312069i	−0.00561222	+	0.00192797i
$263$	9.88765	−	5.70864i	0.609699	−	0.352010i	−0.163149	−	0.986601i	$-0.552165\pi$
$263$	9.88765	−	5.70864i	0.609699	−	0.352010i	0.772848	+	0.634592i	$0.218832\pi$
$264$		0			0
$265$	−30.7148	+	17.7332i	−1.88680	+	1.08934i
$266$	−8.96199	−	6.52678i	−0.549495	−	0.400182i
$267$		0			0
$268$	17.3204	−	2.40905i	1.05801	−	0.147156i
$269$	4.88573	+	2.82078i	0.297888	+	0.171986i	0.641494	−	0.767128i	$-0.278315\pi$
$269$	4.88573	+	2.82078i	0.297888	+	0.171986i	−0.343606	+	0.939114i	$0.611648\pi$
$270$		0			0
$271$	−3.13192	−	5.42464i	−0.190251	−	0.329524i	0.755083	−	0.655630i	$-0.227597\pi$
$271$	−3.13192	−	5.42464i	−0.190251	−	0.329524i	−0.945333	+	0.326106i	$0.894263\pi$
$272$	−5.52355	−	1.39392i	−0.334915	−	0.0845187i
$273$		0			0
$274$	1.40554	−	7.20345i	0.0849117	−	0.435176i
$275$	2.75338	+	1.58966i	0.166035	+	0.0958602i
$276$		0			0
$277$	−10.0179	−	17.3515i	−0.601917	−	1.04255i	−0.992531	−	0.121996i	$-0.961070\pi$
$277$	−10.0179	−	17.3515i	−0.601917	−	1.04255i	0.390614	−	0.920555i	$-0.372263\pi$
$278$	−2.85682	+	14.6413i	−0.171341	+	0.878128i
$279$		0			0
$280$	0.651685	+	20.1382i	0.0389456	+	1.20349i
$281$	9.81283	−	16.9963i	0.585384	−	1.01392i	−0.409443	−	0.912336i	$-0.634277\pi$
$281$	9.81283	−	16.9963i	0.585384	−	1.01392i	0.994827	−	0.101580i	$-0.0323897\pi$
$282$		0			0
$283$	−1.67820			−0.0997585			−0.0498792	−	0.998755i	$-0.515884\pi$
$283$	−1.67820			−0.0997585			−0.0498792	+	0.998755i	$0.515884\pi$
$284$	3.86861	−	0.538075i	0.229560	−	0.0319289i
$285$		0			0
$286$	−5.37610	+	1.84685i	−0.317895	+	0.109207i
$287$	−1.58894	−	18.2496i	−0.0937920	−	1.07724i
$288$		0			0
$289$	−7.48585	−	12.9659i	−0.440344	−	0.762699i
$290$	−3.16751	−	0.618044i	−0.186002	−	0.0362928i
$291$		0			0
$292$	−6.21812	+	15.3274i	−0.363888	+	0.896971i
$293$	9.06774	−	5.23526i	0.529743	−	0.305847i	−0.211169	−	0.977450i	$-0.567727\pi$
$293$	9.06774	−	5.23526i	0.529743	−	0.305847i	0.740912	+	0.671602i	$0.234394\pi$
$294$		0			0
$295$	3.31558	+	1.91425i	0.193040	+	0.111452i
$296$	−31.0239	−	1.69243i	−1.80323	−	0.0983703i
$297$		0			0
$298$	−24.5653	+	8.43895i	−1.42303	+	0.488855i
$299$	−5.50430			−0.318322
$300$		0			0
$301$	−14.9399	+	10.4517i	−0.861122	+	0.602427i
$302$	−7.05236	−	1.37606i	−0.405818	−	0.0791832i
$303$		0			0
$304$	−8.50228	−	8.25753i	−0.487639	−	0.473602i
$305$	2.73651	−	4.73977i	0.156692	−	0.271398i
$306$		0			0
$307$	0.644576			0.0367879			0.0183939	−	0.999831i	$-0.494145\pi$
$307$	0.644576			0.0367879			0.0183939	+	0.999831i	$0.494145\pi$
$308$	7.29013	−	1.66890i	0.415394	−	0.0950945i
$309$		0			0
$310$	−12.2148	−	35.5566i	−0.693752	−	2.01948i
$311$	−18.0913			−1.02586			−0.512931	−	0.858430i	$-0.671440\pi$
$311$	−18.0913			−1.02586			−0.512931	+	0.858430i	$0.671440\pi$
$312$		0			0
$313$			0.0623583i			0.00352470i	0.999998	+	0.00176235i	$0.000560974\pi$
$313$			0.0623583i			0.00352470i	−0.999998	+	0.00176235i	$0.999439\pi$
$314$	−2.24436	+	2.57812i	−0.126656	+	0.145492i
$315$		0			0
$316$	−23.4445	+	3.26083i	−1.31886	+	0.183436i
$317$	8.44530			0.474335			0.237168	−	0.971469i	$-0.423781\pi$
$317$	8.44530			0.474335			0.237168	+	0.971469i	$0.423781\pi$
$318$		0			0
$319$			1.19787i			0.0670679i
$320$	−2.34314	+	21.4121i	−0.130985	+	1.19697i
$321$		0			0
$322$	7.20114	+	0.765109i	0.401304	+	0.0426379i
$323$			4.21993i			0.234803i
$324$		0			0
$325$	5.54045	+	3.19878i	0.307329	+	0.177437i
$326$	−22.1697	−	4.32575i	−1.22787	−	0.239581i
$327$		0			0
$328$	1.06674	−	19.5544i	0.0589009	−	1.07971i
$329$	−11.9579	+	25.6157i	−0.659258	+	1.41224i
$330$		0			0
$331$		−	15.4700i		−	0.850306i	−0.905122	−	0.425153i	$-0.860220\pi$
$331$		−	15.4700i		−	0.850306i	0.905122	−	0.425153i	$-0.139780\pi$
$332$	−10.5780	−	4.29135i	−0.580544	−	0.235518i
$333$		0			0
$334$	3.78867	−	19.4171i	0.207307	−	1.06246i
$335$	−11.7710	+	20.3879i	−0.643117	+	1.11391i
$336$		0			0
$337$	1.49961	+	2.59739i	0.0816887	+	0.141489i	0.903975	−	0.427584i	$-0.140635\pi$
$337$	1.49961	+	2.59739i	0.0816887	+	0.141489i	−0.822287	+	0.569073i	$0.807302\pi$
$338$	6.56940	−	2.25679i	0.357328	−	0.122753i
$339$		0			0
$340$	6.05013	−	4.71300i	0.328114	−	0.255598i
$341$	−12.0852	+	6.97737i	−0.654448	+	0.377846i
$342$		0			0
$343$	−17.8952	+	4.77092i	−0.966250	+	0.257605i
$344$	−17.3862	+	8.81194i	−0.937402	+	0.475108i
$345$		0			0
$346$	−23.1741	+	26.6204i	−1.24585	+	1.43112i
$347$			30.0283i			1.61200i	0.591915	+	0.806001i	$0.298372\pi$
$347$			30.0283i			1.61200i	−0.591915	+	0.806001i	$0.701628\pi$
$348$		0			0
$349$	16.0196	+	9.24890i	0.857507	+	0.495082i	0.863177	−	0.504902i	$-0.168471\pi$
$349$	16.0196	+	9.24890i	0.857507	+	0.495082i	−0.00566949	+	0.999984i	$0.501805\pi$
$350$	−6.80379	−	4.95502i	−0.363678	−	0.264857i
$351$		0			0
$352$	7.96709	−	0.668425i	0.424647	−	0.0356272i
$353$	6.81136	−	3.93254i	0.362532	−	0.209308i	−0.307659	−	0.951497i	$-0.599546\pi$
$353$	6.81136	−	3.93254i	0.362532	−	0.209308i	0.670191	+	0.742189i	$0.266212\pi$
$354$		0			0
$355$	−2.62912	+	4.55377i	−0.139539	+	0.241689i
$356$	−8.17175	−	10.4902i	−0.433102	−	0.555977i
$357$		0			0
$358$	0.328146	+	0.955216i	0.0173430	+	0.0504847i
$359$	15.0238	−	8.67397i	0.792924	−	0.457795i	−0.0480670	−	0.998844i	$-0.515306\pi$
$359$	15.0238	−	8.67397i	0.792924	−	0.457795i	0.840991	+	0.541049i	$0.181973\pi$
$360$		0			0
$361$	5.11014	−	8.85102i	0.268955	−	0.465843i
$362$	−12.5482	+	14.4142i	−0.659516	+	0.757595i
$363$		0			0
$364$	14.6695	−	3.35823i	0.768890	−	0.176019i
$365$	−11.1339	−	19.2845i	−0.582777	−	1.00940i
$366$		0			0
$367$	0.510070	+	0.883467i	0.0266254	+	0.0461166i	0.879031	−	0.476764i	$-0.158191\pi$
$367$	0.510070	+	0.883467i	0.0266254	+	0.0461166i	−0.852406	+	0.522881i	$0.824857\pi$
$368$	7.50634	+	1.89429i	0.391295	+	0.0987467i
$369$		0			0
$370$	27.4640	−	31.5483i	1.42779	−	1.64012i
$371$	−19.9776	−	28.5564i	−1.03719	−	1.48258i
$372$		0			0
$373$	0.0376831	−	0.0652691i	0.00195116	−	0.00337951i	−0.865048	−	0.501689i	$-0.832712\pi$
$373$	0.0376831	−	0.0652691i	0.00195116	−	0.00337951i	0.866999	+	0.498309i	$0.166046\pi$
$374$	−2.14703	−	1.86908i	−0.111020	−	0.0966476i
$375$		0			0
$376$	−16.5138	+	25.3104i	−0.851634	+	1.30528i
$377$			2.41040i			0.124142i
$378$		0			0
$379$			29.5406i			1.51740i	0.651442	+	0.758699i	$0.274165\pi$
$379$			29.5406i			1.51740i	−0.651442	+	0.758699i	$0.725835\pi$
$380$	15.8039	−	2.19812i	0.810722	−	0.112761i
$381$		0			0
$382$	−14.1718	+	16.2794i	−0.725094	+	0.832925i
$383$	14.2357	−	24.6569i	0.727410	−	1.25991i	−0.230564	−	0.973057i	$-0.574057\pi$
$383$	14.2357	−	24.6569i	0.727410	−	1.25991i	0.957974	−	0.286854i	$-0.0926095\pi$
$384$		0			0
$385$	−4.25882	+	9.12309i	−0.217050	+	0.464956i
$386$	−9.52577	−	8.29256i	−0.484849	−	0.422080i
$387$		0			0
$388$	−11.3872	+	28.0691i	−0.578099	+	1.42499i
$389$	10.8878	+	18.8582i	0.552032	+	0.956148i	0.998128	+	0.0611628i	$0.0194809\pi$
$389$	10.8878	+	18.8582i	0.552032	+	0.956148i	−0.446095	+	0.894985i	$0.647186\pi$
$390$		0			0
$391$	−1.37819	−	2.38710i	−0.0696982	−	0.120721i
$392$	−19.6585	+	2.35440i	−0.992904	+	0.118915i
$393$		0			0
$394$	−3.81405	−	3.32028i	−0.192149	−	0.167273i
$395$	15.9329	−	27.5967i	0.801673	−	1.38854i
$396$		0			0
$397$	−1.28100	+	0.739586i	−0.0642915	+	0.0371187i	−0.531801	−	0.846869i	$-0.678485\pi$
$397$	−1.28100	+	0.739586i	−0.0642915	+	0.0371187i	0.467510	+	0.883988i	$0.345151\pi$
$398$	−19.4544	+	6.68317i	−0.975159	+	0.334997i
$399$		0			0
$400$	−6.45478	−	6.26898i	−0.322739	−	0.313449i
$401$	−12.4003	+	21.4780i	−0.619242	+	1.07256i	0.370382	+	0.928879i	$0.379227\pi$
$401$	−12.4003	+	21.4780i	−0.619242	+	1.07256i	−0.989624	+	0.143679i	$0.954107\pi$
$402$		0			0
$403$	−24.3183	+	14.0402i	−1.21138	+	0.699390i
$404$	−20.6058	−	26.4519i	−1.02518	−	1.31603i
$405$		0			0
$406$	0.335051	−	3.15347i	0.0166283	−	0.156504i
$407$	−13.4454	−	7.76273i	−0.666465	−	0.384784i
$408$		0			0
$409$			9.36239i			0.462941i	0.972842	+	0.231470i	$0.0743536\pi$
$409$			9.36239i			0.462941i	−0.972842	+	0.231470i	$0.925646\pi$
$410$	19.8850	+	17.3106i	0.982049	+	0.854912i
$411$		0			0
$412$	4.88584	+	1.98211i	0.240708	+	0.0976517i
$413$	−1.59133	+	3.40890i	−0.0783044	+	0.167741i
$414$		0			0
$415$	13.3089	−	7.68392i	0.653311	−	0.377189i
$416$	16.0317	−	1.34503i	0.786019	−	0.0659456i
$417$		0			0
$418$	−1.92418	−	5.60119i	−0.0941146	−	0.273963i
$419$	−5.21230	−	9.02797i	−0.254637	−	0.441045i	0.710160	−	0.704041i	$-0.248623\pi$
$419$	−5.21230	−	9.02797i	−0.254637	−	0.441045i	−0.964797	+	0.262996i	$0.915289\pi$
$420$		0			0
$421$	−3.45213	+	5.97927i	−0.168247	+	0.291412i	−0.937803	−	0.347167i	$-0.887144\pi$
$421$	−3.45213	+	5.97927i	−0.168247	+	0.291412i	0.769557	+	0.638578i	$0.220477\pi$
$422$	−18.2608	−	3.56305i	−0.888922	−	0.173447i
$423$		0			0
$424$	−16.8433	−	33.2324i	−0.817983	−	1.61391i
$425$			3.20370i			0.155402i
$426$		0			0
$427$	4.87318	+	2.27488i	0.235830	+	0.110089i
$428$	−0.996366	−	1.27905i	−0.0481612	−	0.0618250i
$429$		0			0
$430$	5.02533	−	25.7551i	0.242343	−	1.24202i
$431$	12.4348	+	7.17921i	0.598961	+	0.345810i	0.768633	−	0.639690i	$-0.220937\pi$
$431$	12.4348	+	7.17921i	0.598961	+	0.345810i	−0.169672	+	0.985501i	$0.554271\pi$
$432$		0			0
$433$			25.8458i			1.24207i	0.783783	+	0.621035i	$0.213288\pi$
$433$			25.8458i			1.24207i	−0.783783	+	0.621035i	$0.786712\pi$
$434$	33.7665	−	14.9881i	1.62085	−	0.719451i
$435$		0			0
$436$	19.2738	+	7.81910i	0.923047	+	0.374467i
$437$		−	5.73476i		−	0.274331i
$438$		0			0
$439$	14.5869			0.696195			0.348097	−	0.937458i	$-0.386828\pi$
$439$	14.5869			0.696195			0.348097	+	0.937458i	$0.386828\pi$
$440$	−5.88143	+	9.01434i	−0.280386	+	0.429742i
$441$		0			0
$442$	−4.32035	−	3.76103i	−0.205498	−	0.178894i
$443$		−	35.3820i		−	1.68105i	−0.541775	−	0.840524i	$-0.682247\pi$
$443$		−	35.3820i		−	1.68105i	0.541775	−	0.840524i	$-0.317753\pi$
$444$		0			0
$445$	17.9016			0.848616
$446$	21.0801	−	7.24167i	0.998174	−	0.342903i
$447$		0			0
$448$	−21.1608	−	0.468769i	−0.999755	−	0.0221473i
$449$	0.329740			0.0155614			0.00778070	−	0.999970i	$-0.497523\pi$
$449$	0.329740			0.0155614			0.00778070	+	0.999970i	$0.497523\pi$
$450$		0			0
$451$	4.89287	−	8.47469i	0.230396	−	0.399058i
$452$	13.8096	−	10.7576i	0.649550	−	0.505994i
$453$		0			0
$454$	0.513454	−	2.63148i	0.0240976	−	0.123501i
$455$	−8.56977	+	18.3579i	−0.401757	+	0.860629i
$456$		0			0
$457$	25.8843			1.21081			0.605407	−	0.795916i	$-0.293010\pi$
$457$	25.8843			1.21081			0.605407	+	0.795916i	$0.293010\pi$
$458$	−3.92247	−	11.4181i	−0.183285	−	0.533533i
$459$		0			0
$460$	−8.22193	+	6.40482i	−0.383350	+	0.298626i
$461$	24.3535	+	14.0605i	1.13426	+	0.654863i	0.945002	−	0.327065i	$-0.106060\pi$
$461$	24.3535	+	14.0605i	1.13426	+	0.654863i	0.189254	+	0.981928i	$0.439393\pi$
$462$		0			0
$463$	−17.0012	+	9.81564i	−0.790112	+	0.456171i	−0.840002	−	0.542583i	$-0.817446\pi$
$463$	−17.0012	+	9.81564i	−0.790112	+	0.456171i	0.0498901	+	0.998755i	$0.484113\pi$
$464$	0.829533	−	3.28712i	0.0385101	−	0.152601i
$465$		0			0
$466$	4.43100	−	22.7091i	0.205262	−	1.05198i
$467$	10.9101	+	18.8969i	0.504861	+	0.874446i	0.999984	+	0.00562261i	$0.00178974\pi$
$467$	10.9101	+	18.8969i	0.504861	+	0.874446i	−0.495123	+	0.868823i	$0.664877\pi$
$468$		0			0
$469$	−20.9618	−	9.78532i	−0.967925	−	0.451844i
$470$	−13.2184	−	38.4780i	−0.609717	−	1.77486i
$471$		0			0
$472$	−2.19763	+	3.36826i	−0.101154	+	0.155037i
$473$	−9.73992			−0.447842
$474$		0			0
$475$	−3.33271	+	5.77242i	−0.152915	+	0.264857i
$476$	5.12940	+	5.52099i	0.235106	+	0.253054i
$477$		0			0
$478$	−9.54181	−	1.86180i	−0.436432	−	0.0851568i
$479$	14.7030	+	25.4664i	0.671799	+	1.16359i	0.977393	+	0.211429i	$0.0678116\pi$
$479$	14.7030	+	25.4664i	0.671799	+	1.16359i	−0.305594	+	0.952162i	$0.598855\pi$
$480$		0			0
$481$	−27.0554	−	15.6205i	−1.23362	−	0.712232i
$482$	−13.8465	−	2.70173i	−0.630689	−	0.123060i
$483$		0			0
$484$	−16.6842	−	6.76855i	−0.758374	−	0.307662i
$485$	−20.3896	−	35.3157i	−0.925842	−	1.60361i
$486$		0			0
$487$	3.83992	+	2.21698i	0.174003	+	0.100461i	0.584472	−	0.811414i	$-0.301302\pi$
$487$	3.83992	+	2.21698i	0.174003	+	0.100461i	−0.410469	+	0.911875i	$0.634635\pi$
$488$	4.81509	+	3.14161i	0.217969	+	0.142214i
$489$		0			0
$490$	13.7634	−	22.8259i	0.621766	−	1.03117i
$491$	0.492024	−	0.284070i	0.0222047	−	0.0128199i	−0.488857	−	0.872364i	$-0.662586\pi$
$491$	0.492024	−	0.284070i	0.0222047	−	0.0128199i	0.511061	+	0.859544i	$0.329253\pi$
$492$		0			0
$493$	−1.04534	+	0.603527i	−0.0470798	+	0.0271815i
$494$	−3.87191	−	11.2709i	−0.174205	−	0.507103i
$495$		0			0
$496$	37.9952	−	10.7778i	1.70604	−	0.483937i
$497$	−4.68194	−	2.18561i	−0.210014	−	0.0980381i
$498$		0			0
$499$	−7.10975	−	4.10482i	−0.318276	−	0.183757i	0.332348	−	0.943157i	$-0.392159\pi$
$499$	−7.10975	−	4.10482i	−0.318276	−	0.183757i	−0.650624	+	0.759400i	$0.725493\pi$
$500$	−14.6701	+	2.04043i	−0.656069	+	0.0912508i
$501$		0			0
$502$	17.7252	+	15.4305i	0.791116	+	0.688697i
$503$	23.6082			1.05264			0.526319	−	0.850287i	$-0.323572\pi$
$503$	23.6082			1.05264			0.526319	+	0.850287i	$0.323572\pi$
$504$		0			0
$505$	45.1404			2.00872
$506$	2.91775	+	2.54002i	0.129710	+	0.112917i
$507$		0			0
$508$	−30.2178	+	4.20292i	−1.34070	+	0.186474i
$509$	27.4898	+	15.8713i	1.21847	+	0.703482i	0.964590	−	0.263755i	$-0.0849611\pi$
$509$	27.4898	+	15.8713i	1.21847	+	0.703482i	0.253876	+	0.967237i	$0.418294\pi$
$510$		0			0
$511$	17.9294	−	12.5431i	0.793149	−	0.554874i
$512$	−22.3257	−	3.68301i	−0.986664	−	0.162768i
$513$		0			0
$514$	3.52156	+	10.2511i	0.155329	+	0.452156i
$515$	−6.14722	+	3.54910i	−0.270879	+	0.156392i
$516$		0			0
$517$	−13.0781	+	7.55065i	−0.575175	+	0.332077i
$518$	33.2247	+	24.1966i	1.45981	+	1.06314i
$519$		0			0
$520$	−11.8348	+	18.1390i	−0.518992	+	0.795449i
$521$	2.09032	+	1.20685i	0.0915786	+	0.0528730i	0.545090	−	0.838378i	$-0.316495\pi$
$521$	2.09032	+	1.20685i	0.0915786	+	0.0528730i	−0.453511	+	0.891251i	$0.649829\pi$
$522$		0			0
$523$	−4.85017	−	8.40075i	−0.212083	−	0.367339i	0.740283	−	0.672295i	$-0.234691\pi$
$523$	−4.85017	−	8.40075i	−0.212083	−	0.367339i	−0.952366	+	0.304956i	$0.901358\pi$
$524$	0.125875	+	0.0510656i	0.00549887	+	0.00223081i
$525$		0			0
$526$	−15.8476	−	3.09219i	−0.690989	−	0.134826i
$527$	−12.1778	−	7.03087i	−0.530474	−	0.306270i
$528$		0			0
$529$	−9.62708	−	16.6746i	−0.418569	−	0.724982i
$530$	49.2287	+	9.60552i	2.13836	+	0.417237i
$531$		0			0
$532$	3.49883	+	15.2837i	0.151694	+	0.662631i
$533$	9.84562	−	17.0531i	0.426461	−	0.738653i
$534$		0			0
$535$	2.18270			0.0943665
$536$	−20.7119	−	13.5135i	−0.894618	−	0.583696i
$537$		0			0
$538$	−2.59212	−	7.54555i	−0.111754	−	0.325312i
$539$	−9.29393	−	3.39153i	−0.400318	−	0.146084i
$540$		0			0
$541$	−2.43786	−	4.22250i	−0.104812	−	0.181539i	0.808850	−	0.588016i	$-0.200091\pi$
$541$	−2.43786	−	4.22250i	−0.104812	−	0.181539i	−0.913661	+	0.406476i	$0.866757\pi$
$542$	−1.69646	+	8.69444i	−0.0728693	+	0.373458i
$543$		0			0
$544$	4.59740	+	6.61583i	0.197112	+	0.283651i
$545$	−24.2497	+	14.0006i	−1.03874	+	0.599719i
$546$		0			0
$547$	22.7649	+	13.1433i	0.973356	+	0.561967i	0.900258	−	0.435357i	$-0.143378\pi$
$547$	22.7649	+	13.1433i	0.973356	+	0.561967i	0.0730983	+	0.997325i	$0.476711\pi$
$548$	−8.18812	+	6.37849i	−0.349779	+	0.272475i
$549$		0			0
$550$	−1.46080	−	4.25232i	−0.0622888	−	0.181320i
$551$	−2.51132			−0.106986
$552$		0			0
$553$	28.3734	+	13.2452i	1.20656	+	0.563244i
$554$	−5.42638	+	27.8104i	−0.230545	+	1.18155i
$555$		0			0
$556$	16.6427	−	12.9645i	0.705808	−	0.549819i
$557$	0.740402	−	1.28241i	0.0313719	−	0.0543377i	−0.849913	−	0.526923i	$-0.823346\pi$
$557$	0.740402	−	1.28241i	0.0313719	−	0.0543377i	0.881285	+	0.472585i	$0.156679\pi$
$558$		0			0
$559$	−19.5991			−0.828952
$560$	18.0046	−	22.0857i	0.760832	−	0.933293i
$561$		0			0
$562$	−26.2492	+	9.01739i	−1.10725	+	0.380376i
$563$	0.200896			0.00846677			0.00423339	−	0.999991i	$-0.498652\pi$
$563$	0.200896			0.00846677			0.00423339	+	0.999991i	$0.498652\pi$
$564$		0			0
$565$			23.5663i			0.991440i
$566$	1.79006	+	1.55832i	0.0752420	+	0.0655011i
$567$		0			0
$568$	−4.62613	−	3.01833i	−0.194108	−	0.126646i
$569$	−43.8164			−1.83688			−0.918441	−	0.395559i	$-0.870551\pi$
$569$	−43.8164			−1.83688			−0.918441	+	0.395559i	$0.870551\pi$
$570$		0			0
$571$			13.2983i			0.556516i	0.960506	+	0.278258i	$0.0897570\pi$
$571$			13.2983i			0.556516i	−0.960506	+	0.278258i	$0.910243\pi$
$572$	7.44940	+	3.02211i	0.311475	+	0.126361i
$573$		0			0
$574$	−15.2512	+	20.9416i	−0.636572	+	0.874085i
$575$		−	4.35373i		−	0.181563i
$576$		0			0
$577$	7.21473	+	4.16543i	0.300353	+	0.173409i	0.642602	−	0.766201i	$-0.277855\pi$
$577$	7.21473	+	4.16543i	0.300353	+	0.173409i	−0.342248	+	0.939610i	$0.611188\pi$
$578$	−4.05485	+	20.7813i	−0.168660	+	0.864388i
$579$		0			0
$580$	2.80475	+	3.60049i	0.116461	+	0.149502i
$581$	8.65644	+	12.3737i	0.359130	+	0.513348i
$582$		0			0
$583$		−	18.6171i		−	0.771040i
$584$	20.8652	−	10.5752i	0.863408	−	0.437605i
$585$		0			0
$586$	−14.5335	−	2.83578i	−0.600373	−	0.117145i
$587$	−4.37925	+	7.58509i	−0.180751	+	0.313070i	−0.942137	−	0.335229i	$-0.891186\pi$
$587$	−4.37925	+	7.58509i	−0.180751	+	0.313070i	0.761385	+	0.648299i	$0.224520\pi$
$588$		0			0
$589$	−14.6280	−	25.3364i	−0.602736	−	1.04397i
$590$	−1.75908	−	5.12059i	−0.0724201	−	0.210811i
$591$		0			0
$592$	31.5204	+	30.6130i	1.29548	+	1.25819i
$593$	10.4931	−	6.05820i	0.430900	−	0.248780i	−0.268830	−	0.963188i	$-0.586637\pi$
$593$	10.4931	−	6.05820i	0.430900	−	0.248780i	0.699730	+	0.714407i	$0.253304\pi$
$594$		0			0
$595$	−10.1071	+	0.879996i	−0.414352	+	0.0360763i
$596$	34.0390	+	13.8091i	1.39429	+	0.565644i
$597$		0			0
$598$	5.87121	+	5.11112i	0.240092	+	0.209009i
$599$		−	39.4741i		−	1.61287i	−0.591323	−	0.806434i	$-0.701394\pi$
$599$		−	39.4741i		−	1.61287i	0.591323	−	0.806434i	$-0.298606\pi$
$600$		0			0
$601$	−3.43670	−	1.98418i	−0.140186	−	0.0809363i	0.428267	−	0.903652i	$-0.359124\pi$
$601$	−3.43670	−	1.98418i	−0.140186	−	0.0809363i	−0.568453	+	0.822716i	$0.692458\pi$
$602$	25.6409	+	2.72431i	1.04505	+	0.111035i
$603$		0			0
$604$	6.24470	+	8.01638i	0.254093	+	0.326182i
$605$	20.9916	−	12.1195i	0.853431	−	0.492728i
$606$		0			0
$607$	−14.3423	+	24.8416i	−0.582136	+	1.00829i	0.413089	+	0.910690i	$0.364450\pi$
$607$	−14.3423	+	24.8416i	−0.582136	+	1.00829i	−0.995226	+	0.0975993i	$0.968884\pi$
$608$	1.40135	+	16.7029i	0.0568321	+	0.677393i
$609$		0			0
$610$	−7.32012	+	2.51468i	−0.296383	+	0.101817i
$611$	−26.3163	+	15.1937i	−1.06464	+	0.614672i
$612$		0			0
$613$	−1.55941	+	2.70099i	−0.0629842	+	0.109092i	−0.895798	−	0.444461i	$-0.853395\pi$
$613$	−1.55941	+	2.70099i	−0.0629842	+	0.109092i	0.832814	+	0.553553i	$0.186728\pi$
$614$	−0.687542	−	0.598532i	−0.0277469	−	0.0241548i
$615$		0			0
$616$	−9.32577	−	4.98923i	−0.375746	−	0.201022i
$617$	−1.30847	−	2.26634i	−0.0526770	−	0.0912393i	0.838485	−	0.544925i	$-0.183442\pi$
$617$	−1.30847	−	2.26634i	−0.0526770	−	0.0912393i	−0.891162	+	0.453686i	$0.850109\pi$
$618$		0			0
$619$	12.3184	+	21.3361i	0.495119	+	0.857571i	0.999984	−	0.00562710i	$-0.00179117\pi$
$619$	12.3184	+	21.3361i	0.495119	+	0.857571i	−0.504865	+	0.863198i	$0.668458\pi$
$620$	−19.9877	+	49.2690i	−0.802725	+	1.97869i
$621$		0			0
$622$	19.2972	+	16.7990i	0.773748	+	0.673578i
$623$	1.52580	+	17.5245i	0.0611300	+	0.702105i
$624$		0			0
$625$	15.5936	−	27.0090i	0.623745	−	1.08036i
$626$	0.0579040	−	0.0665151i	0.00231431	−	0.00265848i
$627$		0			0
$628$	4.78793	−	0.665940i	0.191059	−	0.0265739i
$629$		−	15.6445i		−	0.623787i
$630$		0			0
$631$		−	8.86244i		−	0.352808i	−0.984318	−	0.176404i	$-0.943553\pi$
$631$		−	8.86244i		−	0.352808i	0.984318	−	0.176404i	$-0.0564466\pi$
$632$	28.0352	+	18.2916i	1.11518	+	0.727602i
$633$		0			0
$634$	−9.00826	−	7.84204i	−0.357764	−	0.311447i
$635$	20.5361	−	35.5696i	0.814951	−	1.41154i
$636$		0			0
$637$	−18.7016	−	6.82457i	−0.740985	−	0.270399i
$638$	1.11230	−	1.27772i	0.0440366	−	0.0505854i
$639$		0			0
$640$	22.3819	−	20.6636i	0.884723	−	0.816802i
$641$	−18.3397	−	31.7654i	−0.724376	−	1.25466i	−0.959230	−	0.282626i	$-0.908795\pi$
$641$	−18.3397	−	31.7654i	−0.724376	−	1.25466i	0.234854	−	0.972031i	$-0.424539\pi$
$642$		0			0
$643$	−10.9509	−	18.9675i	−0.431860	−	0.748004i	0.565173	−	0.824972i	$-0.308809\pi$
$643$	−10.9509	−	18.9675i	−0.431860	−	0.748004i	−0.997034	+	0.0769685i	$0.975476\pi$
$644$	−6.97070	−	7.50286i	−0.274684	−	0.295654i
$645$		0			0
$646$	3.91850	−	4.50123i	0.154171	−	0.177098i
$647$	−15.1436	+	26.2296i	−0.595358	+	1.03119i	0.398138	+	0.917326i	$0.369657\pi$
$647$	−15.1436	+	26.2296i	−0.595358	+	1.03119i	−0.993496	+	0.113865i	$0.963677\pi$
$648$		0			0
$649$	−1.74042	+	1.00483i	−0.0683173	+	0.0394430i
$650$	−2.93949	−	8.55670i	−0.115296	−	0.335621i
$651$		0			0
$652$	19.6307	+	25.2002i	0.768799	+	0.986914i
$653$	4.36506	−	7.56050i	0.170818	−	0.295865i	−0.767888	−	0.640584i	$-0.778692\pi$
$653$	4.36506	−	7.56050i	0.170818	−	0.295865i	0.938706	+	0.344719i	$0.112026\pi$
$654$		0			0
$655$	−0.158372	+	0.0914362i	−0.00618811	+	0.00357271i
$656$	−19.2955	+	19.8674i	−0.753361	+	0.775690i
$657$		0			0
$658$	36.5409	−	16.2195i	1.42451	−	0.632303i
$659$	38.1510	+	22.0265i	1.48615	+	0.858030i	0.999876	−	0.0157758i	$-0.00502180\pi$
$659$	38.1510	+	22.0265i	1.48615	+	0.858030i	0.486276	+	0.873806i	$0.338355\pi$
$660$		0			0
$661$		−	38.9747i		−	1.51594i	−0.652289	−	0.757971i	$-0.726191\pi$
$661$		−	38.9747i		−	1.51594i	0.652289	−	0.757971i	$-0.273809\pi$
$662$	−14.3649	+	16.5012i	−0.558308	+	0.641336i
$663$		0			0
$664$	7.29832	+	14.3998i	0.283230	+	0.558821i
$665$	−19.1265	−	8.92856i	−0.741692	−	0.346235i
$666$		0			0
$667$	1.42058	−	0.820175i	0.0550053	−	0.0317573i
$668$	−22.0713	+	17.1934i	−0.853966	+	0.665233i
$669$		0			0
$670$	31.4872	−	10.8168i	1.21646	−	0.417890i
$671$	1.43645	+	2.48800i	0.0554535	+	0.0960483i
$672$		0			0
$673$	6.18407	−	10.7111i	0.238379	−	0.412884i	−0.721871	−	0.692028i	$-0.756717\pi$
$673$	6.18407	−	10.7111i	0.238379	−	0.412884i	0.960249	+	0.279144i	$0.0900508\pi$
$674$	0.812289	−	4.16302i	0.0312882	−	0.160353i
$675$		0			0
$676$	−9.10290	−	3.69291i	−0.350111	−	0.142035i
$677$			13.4525i			0.517022i	0.966008	+	0.258511i	$0.0832317\pi$
$677$			13.4525i			0.517022i	−0.966008	+	0.258511i	$0.916768\pi$
$678$		0			0
$679$	32.8340	−	22.9702i	1.26005	−	0.881514i
$680$	−10.8298	−	0.590790i	−0.415303	−	0.0226558i
$681$		0			0
$682$	19.3697	+	3.77942i	0.741705	+	0.144722i
$683$	−13.0760	−	7.54945i	−0.500340	−	0.288872i	0.228514	−	0.973541i	$-0.426613\pi$
$683$	−13.0760	−	7.54945i	−0.500340	−	0.288872i	−0.728854	+	0.684669i	$0.759947\pi$
$684$		0			0
$685$		−	13.9731i		−	0.533886i
$686$	23.5182	+	11.5280i	0.897929	+	0.440140i
$687$		0			0
$688$	26.7276	+	6.74496i	1.01898	+	0.257149i
$689$		−	37.4620i		−	1.42719i
$690$		0			0
$691$	26.4012			1.00435			0.502175	−	0.864766i	$-0.332533\pi$
$691$	26.4012			1.00435			0.502175	+	0.864766i	$0.332533\pi$
$692$	49.4377	−	6.87616i	1.87934	−	0.261392i
$693$		0			0
$694$	27.8833	−	32.0299i	1.05843	−	1.21584i
$695$			28.4010i			1.07731i
$696$		0			0
$697$	9.86076			0.373503
$698$	−8.49917	−	24.7407i	−0.321698	−	0.936448i
$699$		0			0
$700$	2.65625	+	11.6031i	0.100397	+	0.438556i
$701$	9.14551			0.345421			0.172711	−	0.984973i	$-0.444747\pi$
$701$	9.14551			0.345421			0.172711	+	0.984973i	$0.444747\pi$
$702$		0			0
$703$	16.2745	−	28.1882i	0.613803	−	1.06314i
$704$	−9.11885	−	6.68501i	−0.343680	−	0.251951i
$705$		0			0
$706$	−10.9170	−	2.13013i	−0.410868	−	0.0801686i
$707$	3.84745	+	44.1896i	0.144698	+	1.66192i
$708$		0			0
$709$	−19.1952			−0.720890			−0.360445	−	0.932781i	$-0.617375\pi$
$709$	−19.1952			−0.720890			−0.360445	+	0.932781i	$0.617375\pi$
$710$	7.03286	−	2.41600i	0.263938	−	0.0906709i
$711$		0			0
$712$	−1.02436	+	18.7775i	−0.0383893	+	0.703715i
$713$	16.5493	+	9.55473i	0.619776	+	0.357828i
$714$		0			0
$715$	−9.37261	+	5.41128i	−0.350516	+	0.202370i
$716$	0.536964	−	1.32360i	0.0200673	−	0.0494651i
$717$		0			0
$718$	−24.0796	−	4.69842i	−0.898643	−	0.175343i
$719$	−2.31150	−	4.00364i	−0.0862046	−	0.149311i	0.819699	−	0.572794i	$-0.194141\pi$
$719$	−2.31150	−	4.00364i	−0.0862046	−	0.149311i	−0.905904	+	0.423483i	$0.860807\pi$
$720$		0			0
$721$	−3.99829	−	5.71524i	−0.148904	−	0.212847i
$722$	−13.6695	+	4.69591i	−0.508728	+	0.174764i
$723$		0			0
$724$	26.7692	−	3.72326i	0.994870	−	0.138374i
$725$	−1.90655			−0.0708076
$726$		0			0
$727$	4.10913	−	7.11723i	0.152399	−	0.263963i	−0.779710	−	0.626141i	$-0.784633\pi$
$727$	4.10913	−	7.11723i	0.152399	−	0.263963i	0.932109	+	0.362178i	$0.117967\pi$
$728$	−18.7657	−	10.0395i	−0.695503	−	0.372090i
$729$		0			0
$730$	−6.03090	+	30.9086i	−0.223214	+	1.14398i
$731$	−4.90730	−	8.49969i	−0.181503	−	0.314372i
$732$		0			0
$733$	18.9227	+	10.9250i	0.698927	+	0.403526i	0.806948	−	0.590623i	$-0.201118\pi$
$733$	18.9227	+	10.9250i	0.698927	+	0.403526i	−0.108021	+	0.994149i	$0.534451\pi$
$734$	0.276289	−	1.41599i	0.0101980	−	0.0522652i
$735$		0			0
$736$	−6.24772	−	8.99071i	−0.230294	−	0.331402i
$737$	−6.17883	−	10.7020i	−0.227600	−	0.394215i
$738$		0			0
$739$	−16.9483	−	9.78511i	−0.623454	−	0.359951i	0.154759	−	0.987952i	$-0.450540\pi$
$739$	−16.9483	−	9.78511i	−0.623454	−	0.359951i	−0.778212	+	0.628001i	$0.783873\pi$
$740$	−58.5895	+	8.14905i	−2.15379	+	0.299565i
$741$		0			0
$742$	−5.20730	+	49.0106i	−0.191166	+	1.79923i
$743$	7.26557	−	4.19478i	0.266548	−	0.153892i	−0.360770	−	0.932655i	$-0.617486\pi$
$743$	7.26557	−	4.19478i	0.266548	−	0.153892i	0.627318	+	0.778763i	$0.284153\pi$
$744$		0			0
$745$	−42.8269	+	24.7261i	−1.56905	+	0.905894i
$746$	−0.100802	+	0.0346285i	−0.00369062	+	0.00126784i
$747$		0			0
$748$	0.554587	+	3.98733i	0.0202777	+	0.145791i
$749$	0.186038	+	2.13673i	0.00679769	+	0.0780744i
$750$		0			0
$751$	11.8250	+	6.82717i	0.431501	+	0.249127i	0.699986	−	0.714157i	$-0.253190\pi$
$751$	11.8250	+	6.82717i	0.431501	+	0.249127i	−0.268485	+	0.963284i	$0.586523\pi$
$752$	41.1170	−	11.6633i	1.49938	−	0.425318i
$753$		0			0
$754$	2.23822	−	2.57108i	0.0815113	−	0.0936331i
$755$	−13.6800			−0.497868
$756$		0			0
$757$	22.0851			0.802697			0.401348	−	0.915925i	$-0.368542\pi$
$757$	22.0851			0.802697			0.401348	+	0.915925i	$0.368542\pi$
$758$	27.4304	−	31.5097i	0.996318	−	1.14448i
$759$		0			0
$760$	−18.8985	−	12.3303i	−0.685519	−	0.447269i
$761$	22.6153	+	13.0569i	0.819804	+	0.473314i	0.850349	−	0.526220i	$-0.176391\pi$
$761$	22.6153	+	13.0569i	0.819804	+	0.473314i	−0.0305452	+	0.999533i	$0.509724\pi$
$762$		0			0
$763$	−15.7726	−	22.5456i	−0.571005	−	0.816207i
$764$	30.2330	−	4.20503i	1.09379	−	0.152133i
$765$		0			0
$766$	−38.0803	+	13.0817i	−1.37590	+	0.472662i
$767$	−3.50213	+	2.02196i	−0.126455	+	0.0730087i
$768$		0			0
$769$	14.6518	−	8.45923i	0.528358	−	0.305048i	−0.211989	−	0.977272i	$-0.567994\pi$
$769$	14.6518	−	8.45923i	0.528358	−	0.305048i	0.740348	+	0.672224i	$0.234661\pi$
$770$	13.0141	−	5.77662i	0.468996	−	0.208175i
$771$		0			0
$772$	2.46055	+	17.6907i	0.0885570	+	0.636701i
$773$	−18.8030	−	10.8559i	−0.676298	−	0.390461i	0.122161	−	0.992510i	$-0.461018\pi$
$773$	−18.8030	−	10.8559i	−0.676298	−	0.390461i	−0.798459	+	0.602049i	$0.794351\pi$
$774$		0			0
$775$	−11.1053	−	19.2350i	−0.398915	−	0.690940i
$776$	38.2104	−	19.3663i	1.37167	−	0.695211i
$777$		0			0
$778$	5.89757	−	30.2253i	0.211438	−	1.08363i
$779$	17.7671	+	10.2578i	0.636572	+	0.367525i
$780$		0			0
$781$	−1.38008	−	2.39037i	−0.0493831	−	0.0855341i
$782$	−0.746523	+	3.82596i	−0.0266956	+	0.136816i
$783$		0			0
$784$	23.1551	+	15.7429i	0.826969	+	0.562247i
$785$	−3.25389	+	5.63590i	−0.116136	+	0.201154i
$786$		0			0
$787$	19.5188			0.695769			0.347884	−	0.937537i	$-0.386900\pi$
$787$	19.5188			0.695769			0.347884	+	0.937537i	$0.386900\pi$
$788$	0.985184	+	7.08321i	0.0350957	+	0.252329i
$789$		0			0
$790$	−42.6204	+	14.6414i	−1.51637	+	0.520918i
$791$	−23.0699	+	2.00862i	−0.820271	+	0.0714183i
$792$		0			0
$793$	2.89048	+	5.00646i	0.102644	+	0.177785i
$794$	2.05315	+	0.400610i	0.0728634	+	0.0142171i
$795$		0			0
$796$	26.9569	+	10.9360i	0.955463	+	0.387618i
$797$	23.1795	−	13.3827i	0.821059	−	0.474039i	−0.0297223	−	0.999558i	$-0.509462\pi$
$797$	23.1795	−	13.3827i	0.821059	−	0.474039i	0.850782	+	0.525519i	$0.176129\pi$
$798$		0			0
$799$	−13.1784	−	7.60854i	−0.466218	−	0.269171i
$800$	1.06388	+	12.6806i	0.0376138	+	0.448326i
$801$		0			0
$802$	33.1707	−	11.3951i	1.17130	−	0.402376i
$803$	11.6889			0.412491
$804$		0			0
$805$	13.7353	−	1.19589i	0.484105	−	0.0421495i
$806$	38.9765	+	7.60511i	1.37289	+	0.267878i
$807$		0			0
$808$	−2.58300	+	47.3490i	−0.0908697	+	1.66573i
$809$	−13.9813	+	24.2164i	−0.491557	+	0.851402i	−0.999953	−	0.00972146i	$-0.996906\pi$
$809$	−13.9813	+	24.2164i	−0.491557	+	0.851402i	0.508395	+	0.861124i	$0.330239\pi$
$810$		0			0
$811$	−44.1723			−1.55110			−0.775550	−	0.631286i	$-0.782527\pi$
$811$	−44.1723			−1.55110			−0.775550	+	0.631286i	$0.782527\pi$
$812$	−3.28559	+	3.05256i	−0.115302	+	0.107124i
$813$		0			0
$814$	7.13347	+	20.7652i	0.250028	+	0.727819i
$815$	−43.0043			−1.50638
$816$		0			0
$817$		−	20.4196i		−	0.714392i
$818$	8.69362	−	9.98648i	0.303965	−	0.349169i
$819$		0			0
$820$	−5.13637	−	36.9291i	−0.179370	−	1.28962i
$821$	10.5891			0.369562			0.184781	−	0.982780i	$-0.440842\pi$
$821$	10.5891			0.369562			0.184781	+	0.982780i	$0.440842\pi$
$822$		0			0
$823$		−	1.56546i		−	0.0545685i	−0.999628	−	0.0272843i	$-0.991314\pi$
$823$		−	1.56546i		−	0.0545685i	0.999628	−	0.0272843i	$-0.00868593\pi$
$824$	−3.37099	−	6.65107i	−0.117434	−	0.231701i
$825$		0			0
$826$	4.86281	−	2.15847i	0.169199	−	0.0751028i
$827$			1.44507i			0.0502499i	0.999684	+	0.0251249i	$0.00799836\pi$
$827$			1.44507i			0.0502499i	−0.999684	+	0.0251249i	$0.992002\pi$
$828$		0			0
$829$	−33.2429	−	19.1928i	−1.15457	−	0.666594i	−0.204577	−	0.978851i	$-0.565582\pi$
$829$	−33.2429	−	19.1928i	−1.15457	−	0.666594i	−0.949998	+	0.312257i	$0.898915\pi$
$830$	−21.3312	−	4.16214i	−0.740415	−	0.144470i
$831$		0			0
$832$	−18.3493	−	13.4518i	−0.636148	−	0.466359i
$833$	−1.72292	−	9.81926i	−0.0596957	−	0.340217i
$834$		0			0
$835$		−	37.6650i		−	1.30345i
$836$	−3.14864	+	7.76129i	−0.108898	+	0.268430i
$837$		0			0
$838$	−2.82334	+	14.4697i	−0.0975306	+	0.499849i
$839$	−8.96149	+	15.5217i	−0.309385	+	0.535870i	−0.978228	−	0.207533i	$-0.933456\pi$
$839$	−8.96149	+	15.5217i	−0.309385	+	0.535870i	0.668843	+	0.743404i	$0.266790\pi$
$840$		0			0
$841$	14.1408	+	24.4926i	0.487615	+	0.844574i
$842$	9.23441	−	3.17230i	0.318239	−	0.109325i
$843$		0			0
$844$	16.1695	+	20.7570i	0.556578	+	0.714484i
$845$	11.4530	−	6.61239i	0.393995	−	0.227473i
$846$		0			0
$847$	13.6534	+	19.5165i	0.469137	+	0.670595i
$848$	−12.8924	+	51.0877i	−0.442728	+	1.75436i
$849$		0			0
$850$	2.97485	−	3.41726i	0.102037	−	0.117211i
$851$			21.2604i			0.728796i
$852$		0			0
$853$	13.3860	+	7.72843i	0.458329	+	0.264616i	0.711341	−	0.702847i	$-0.248088\pi$
$853$	13.3860	+	7.72843i	0.458329	+	0.264616i	−0.253013	+	0.967463i	$0.581421\pi$
$854$	−3.08563	−	6.95160i	−0.105588	−	0.237879i
$855$		0			0
$856$	−0.124898	+	2.28950i	−0.00426892	+	0.0782535i
$857$	−19.7121	+	11.3808i	−0.673352	+	0.388760i	−0.797346	−	0.603523i	$-0.793763\pi$
$857$	−19.7121	+	11.3808i	−0.673352	+	0.388760i	0.123993	+	0.992283i	$0.460430\pi$
$858$		0			0
$859$	−0.444083	+	0.769174i	−0.0151519	+	0.0262439i	−0.873502	−	0.486821i	$-0.838157\pi$
$859$	−0.444083	+	0.769174i	−0.0151519	+	0.0262439i	0.858350	+	0.513065i	$0.171490\pi$
$860$	−29.2757	+	22.8055i	−0.998292	+	0.777661i
$861$		0			0
$862$	−6.59726	−	19.2043i	−0.224703	−	0.654101i
$863$	−39.6368	+	22.8843i	−1.34925	+	0.778992i	−0.988144	−	0.153531i	$-0.950935\pi$
$863$	−39.6368	+	22.8843i	−1.34925	+	0.778992i	−0.361110	+	0.932523i	$0.617602\pi$
$864$		0			0
$865$	−33.5980	+	58.1934i	−1.14237	+	1.97864i
$866$	23.9996	−	27.5687i	0.815539	−	0.936821i
$867$		0			0
$868$	−49.9348	−	15.3674i	−1.69490	−	0.521603i
$869$	8.36353	+	14.4861i	0.283713	+	0.491406i
$870$		0			0
$871$	−12.4333	−	21.5351i	−0.421286	−	0.729689i
$872$	−13.2980	−	26.2373i	−0.450327	−	0.888508i
$873$		0			0
$874$	−5.32511	+	6.11703i	−0.180125	+	0.206912i
$875$	17.7544	+	8.28805i	0.600207	+	0.280187i
$876$		0			0
$877$	15.7434	−	27.2683i	0.531616	−	0.920786i	−0.467703	−	0.883886i	$-0.654918\pi$
$877$	15.7434	−	27.2683i	0.531616	−	0.920786i	0.999319	−	0.0369000i	$-0.0117483\pi$
$878$	−15.5592	−	13.5449i	−0.525099	−	0.457119i
$879$		0			0
$880$	14.6439	−	4.15392i	0.493646	−	0.140029i
$881$			12.0700i			0.406649i	0.979111	+	0.203324i	$0.0651746\pi$
$881$			12.0700i			0.406649i	−0.979111	+	0.203324i	$0.934825\pi$
$882$		0			0
$883$		−	26.0164i		−	0.875522i	−0.899091	−	0.437761i	$-0.855772\pi$
$883$		−	26.0164i		−	0.875522i	0.899091	−	0.437761i	$-0.144228\pi$
$884$	1.11596	+	8.02347i	0.0375339	+	0.269859i
$885$		0			0
$886$	−32.8546	+	37.7405i	−1.10377	+	1.26792i
$887$	−12.7190	+	22.0300i	−0.427063	+	0.739694i	−0.996611	−	0.0822640i	$-0.973785\pi$
$887$	−12.7190	+	22.0300i	−0.427063	+	0.739694i	0.569548	+	0.821958i	$0.307118\pi$
$888$		0			0
$889$	36.5707	+	17.0719i	1.22654	+	0.572572i
$890$	−19.0949	−	16.6228i	−0.640061	−	0.557198i
$891$		0			0
$892$	−29.2097	−	11.8500i	−0.978014	−	0.396766i
$893$	−15.8299	−	27.4181i	−0.529726	−	0.917512i
$894$		0			0
$895$	0.961467	+	1.66531i	0.0321383	+	0.0556652i
$896$	22.1361	+	20.1493i	0.739515	+	0.673140i
$897$		0			0
$898$	−0.351720	−	0.306186i	−0.0117371	−	0.0102176i
$899$	4.18414	−	7.24714i	0.139549	−	0.241706i
$900$		0			0
$901$	16.2465	−	9.37990i	0.541248	−	0.312490i
$902$	−13.0883	+	4.49625i	−0.435794	+	0.149709i
$903$		0			0
$904$	−24.7193	−	1.34850i	−0.822152	−	0.0448504i
$905$	−18.1924	+	31.5102i	−0.604736	+	1.04743i
$906$		0			0
$907$	25.3966	−	14.6627i	0.843281	−	0.486868i	−0.0150974	−	0.999886i	$-0.504806\pi$
$907$	25.3966	−	14.6627i	0.843281	−	0.486868i	0.858378	+	0.513018i	$0.171472\pi$
$908$	−2.99119	+	2.33011i	−0.0992660	+	0.0773274i
$909$		0			0
$910$	26.1875	−	11.6240i	0.868108	−	0.385330i
$911$	12.1668	+	7.02448i	0.403103	+	0.232731i	0.687822	−	0.725880i	$-0.258567\pi$
$911$	12.1668	+	7.02448i	0.403103	+	0.232731i	−0.284719	+	0.958611i	$0.591900\pi$
$912$		0			0
$913$			8.06690i			0.266976i
$914$	−27.6097	−	24.0353i	−0.913247	−	0.795017i
$915$		0			0
$916$	−6.41856	+	15.8215i	−0.212075	+	0.522758i
$917$	−0.103009	−	0.147243i	−0.00340165	−	0.00486239i
$918$		0			0
$919$	−43.1553	+	24.9157i	−1.42356	+	0.821894i	−0.996601	−	0.0823755i	$-0.973749\pi$
$919$	−43.1553	+	24.9157i	−1.42356	+	0.821894i	−0.426961	+	0.904270i	$0.640416\pi$
$920$	14.7173	+	0.802865i	0.485215	+	0.0264697i
$921$		0			0
$922$	−12.9208	−	37.6117i	−0.425522	−	1.23867i
$923$	−2.77705	−	4.80999i	−0.0914078	−	0.158323i
$924$		0			0
$925$	12.3553	−	21.4000i	0.406240	−	0.703628i
$926$	27.2489	+	5.31682i	0.895456	+	0.174722i
$927$		0			0
$928$	−3.93714	+	2.73596i	−0.129243	+	0.0898122i
$929$			27.6268i			0.906406i	0.891407	+	0.453203i	$0.149719\pi$
$929$			27.6268i			0.906406i	−0.891407	+	0.453203i	$0.850281\pi$
$930$		0			0
$931$	7.11030	−	19.4846i	0.233031	−	0.638582i
$932$	−25.8133	+	20.1084i	−0.845543	+	0.658671i
$933$		0			0
$934$	5.90968	−	30.2874i	0.193371	−	0.991034i
$935$	−4.69351	−	2.70980i	−0.153494	−	0.0886199i
$936$		0			0
$937$			5.47306i			0.178797i	0.995996	+	0.0893986i	$0.0284945\pi$
$937$			5.47306i			0.178797i	−0.995996	+	0.0893986i	$0.971505\pi$
$938$	13.2727	+	29.9020i	0.433370	+	0.976336i
$939$		0			0
$940$	−21.6299	+	53.3170i	−0.705491	+	1.73901i
$941$		−	14.4602i		−	0.471388i	−0.971827	−	0.235694i	$-0.924264\pi$
$941$		−	14.4602i		−	0.471388i	0.971827	−	0.235694i	$-0.0757363\pi$
$942$		0			0
$943$	−13.4005			−0.436379
$944$	5.47178	−	1.55214i	0.178091	−	0.0505178i
$945$		0			0
$946$	10.3892	+	9.04418i	0.337781	+	0.294052i
$947$		−	42.3981i		−	1.37775i	−0.724879	−	0.688877i	$-0.758104\pi$
$947$		−	42.3981i		−	1.37775i	0.724879	−	0.688877i	$-0.241896\pi$
$948$		0			0
$949$	23.5208			0.763518
$950$	8.91495	−	3.06256i	0.289239	−	0.0993624i
$951$		0			0
$952$	−0.344706	−	10.6520i	−0.0111720	−	0.345234i
$953$	11.7969			0.382138			0.191069	−	0.981577i	$-0.438804\pi$
$953$	11.7969			0.382138			0.191069	+	0.981577i	$0.438804\pi$
$954$		0			0
$955$	−20.5464	+	35.5875i	−0.664867	+	1.15158i
$956$	8.44905	+	10.8461i	0.273262	+	0.350789i
$957$		0			0
$958$	7.96418	−	40.8168i	0.257311	−	1.31873i
$959$	13.6788	−	1.19097i	0.441712	−	0.0384584i
$960$		0			0
$961$	66.4873			2.14475
$962$	14.3543	+	41.7845i	0.462800	+	1.34719i
$963$		0			0
$964$	12.2607	+	15.7392i	0.394891	+	0.506926i
$965$	−20.8238	−	12.0226i	−0.670341	−	0.387022i
$966$		0			0
$967$	−9.83637	+	5.67903i	−0.316316	+	0.182625i	−0.649749	−	0.760148i	$-0.725126\pi$
$967$	−9.83637	+	5.67903i	−0.316316	+	0.182625i	0.333433	+	0.942774i	$0.391793\pi$
$968$	11.5113	+	22.7122i	0.369988	+	0.729997i
$969$		0			0
$970$	−11.0444	+	56.6029i	−0.354614	+	1.81741i
$971$	−9.77591	−	16.9324i	−0.313724	−	0.543386i	0.665442	−	0.746450i	$-0.268243\pi$
$971$	−9.77591	−	16.9324i	−0.313724	−	0.543386i	−0.979165	+	0.203064i	$0.934910\pi$
$972$		0			0
$973$	−27.8028	+	2.42070i	−0.891316	+	0.0776040i
$974$	−2.03727	−	5.93038i	−0.0652782	−	0.190022i
$975$		0			0
$976$	−2.21885	−	7.82217i	−0.0710237	−	0.250381i
$977$	4.26325			0.136393			0.0681967	−	0.997672i	$-0.478275\pi$
$977$	4.26325			0.136393			0.0681967	+	0.997672i	$0.478275\pi$
$978$		0			0
$979$	−4.69845	+	8.13796i	−0.150163	+	0.260090i
$980$	−35.8762	+	11.5672i	−1.14602	+	0.369500i
$981$		0			0
$982$	−0.788600	−	0.153872i	−0.0251652	−	0.00491025i
$983$	−17.8283	−	30.8795i	−0.568633	−	0.984902i	−0.996701	−	0.0811554i	$-0.974139\pi$
$983$	−17.8283	−	30.8795i	−0.568633	−	0.984902i	0.428068	−	0.903746i	$-0.359194\pi$
$984$		0			0
$985$	−8.33768	−	4.81376i	−0.265661	−	0.153379i
$986$	1.67544	+	0.326912i	0.0533568	+	0.0104110i
$987$		0			0
$988$	−6.33582	+	15.6176i	−0.201569	+	0.496861i
$989$	6.66886	+	11.5508i	0.212058	+	0.367294i
$990$		0			0
$991$	21.9593	+	12.6782i	0.697561	+	0.402737i	0.806438	−	0.591318i	$-0.201392\pi$
$991$	21.9593	+	12.6782i	0.697561	+	0.402737i	−0.108877	+	0.994055i	$0.534726\pi$
$992$	−50.5358	−	23.7849i	−1.60451	−	0.755171i
$993$		0			0
$994$	2.96454	+	6.67880i	0.0940296	+	0.211839i
$995$	−33.9164	+	19.5817i	−1.07522	+	0.620780i
$996$		0			0
$997$	−23.4164	+	13.5195i	−0.741606	+	0.428166i	−0.822653	−	0.568544i	$-0.807507\pi$
$997$	−23.4164	+	13.5195i	−0.741606	+	0.428166i	0.0810469	+	0.996710i	$0.474174\pi$
$998$	3.77208	+	10.9803i	0.119403	+	0.347576i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bj.b.451.9		84
3.2	odd	2		252.2.bj.b.115.34	yes	84
4.3	odd	2	inner	756.2.bj.b.451.10		84
7.5	odd	6		756.2.n.b.19.19		84
9.4	even	3		756.2.n.b.199.38		84
9.5	odd	6		252.2.n.b.31.5	✓	84
12.11	even	2		252.2.bj.b.115.33	yes	84
21.5	even	6		252.2.n.b.187.24	yes	84
28.19	even	6		756.2.n.b.19.38		84
36.23	even	6		252.2.n.b.31.24	yes	84
36.31	odd	6		756.2.n.b.199.19		84
63.5	even	6		252.2.bj.b.103.34	yes	84
63.40	odd	6	inner	756.2.bj.b.523.9		84
84.47	odd	6		252.2.n.b.187.5	yes	84
252.103	even	6	inner	756.2.bj.b.523.10		84
252.131	odd	6		252.2.bj.b.103.33	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.5	✓	84	9.5	odd	6
252.2.n.b.31.24	yes	84	36.23	even	6
252.2.n.b.187.5	yes	84	84.47	odd	6
252.2.n.b.187.24	yes	84	21.5	even	6
252.2.bj.b.103.33	yes	84	252.131	odd	6
252.2.bj.b.103.34	yes	84	63.5	even	6
252.2.bj.b.115.33	yes	84	12.11	even	2
252.2.bj.b.115.34	yes	84	3.2	odd	2
756.2.n.b.19.19		84	7.5	odd	6
756.2.n.b.19.38		84	28.19	even	6
756.2.n.b.199.19		84	36.31	odd	6
756.2.n.b.199.38		84	9.4	even	3
756.2.bj.b.451.9		84	1.1	even	1	trivial
756.2.bj.b.451.10		84	4.3	odd	2	inner
756.2.bj.b.523.9		84	63.40	odd	6	inner
756.2.bj.b.523.10		84	252.103	even	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.bj (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.06666 - 0.928568i) q^{2} +(0.275522 + 1.98093i) q^{4} +(-2.33177 - 1.34625i) q^{5} +(1.11915 - 2.39740i) q^{7} +(1.54554 - 2.36882i) q^{8} +(1.23712 + 3.60119i) q^{10} +(1.22399 - 0.706672i) q^{11} +(2.46297 - 1.42199i) q^{13} +(-3.41989 + 1.51800i) q^{14} +(-3.84817 + 1.09158i) q^{16} +(1.23338 + 0.712090i) q^{17} +(1.48153 + 2.56609i) q^{19} +(2.02437 - 4.98999i) q^{20} +(-1.96178 - 0.382782i) q^{22} +(-1.67612 - 0.967709i) q^{23} +(1.12475 + 1.94813i) q^{25} +(-3.94756 - 0.770249i) q^{26} +(5.05743 + 1.55642i) q^{28} +(-0.423772 + 0.733994i) q^{29} -9.87356 q^{31} +(5.11830 + 2.40895i) q^{32} +(-0.654368 - 1.90483i) q^{34} +(-5.83707 + 4.08352i) q^{35} +(-5.49245 - 9.51321i) q^{37} +(0.802498 - 4.11284i) q^{38} +(-6.79285 + 3.44285i) q^{40} +(5.99620 - 3.46191i) q^{41} +(-5.96812 - 3.44570i) q^{43} +(1.73711 + 2.22994i) q^{44} +(0.889265 + 2.58861i) q^{46} -10.6848 q^{47} +(-4.49502 - 5.36608i) q^{49} +(0.609243 - 3.12240i) q^{50} +(3.49547 + 4.48718i) q^{52} +(6.58617 - 11.4076i) q^{53} -3.80542 q^{55} +(-3.94931 - 6.35633i) q^{56} +(1.13358 - 0.389420i) q^{58} -1.42192 q^{59} +2.03270i q^{61} +(10.5317 + 9.16828i) q^{62} +(-3.22261 - 7.32221i) q^{64} -7.65741 q^{65} -8.74356i q^{67} +(-1.07078 + 2.63943i) q^{68} +(10.0180 + 1.06440i) q^{70} -1.95293i q^{71} +(7.16234 + 4.13518i) q^{73} +(-2.97509 + 15.2475i) q^{74} +(-4.67504 + 3.64182i) q^{76} +(-0.324347 - 3.72526i) q^{77} +11.8351i q^{79} +(10.4426 + 2.63528i) q^{80} +(-9.61051 - 1.87521i) q^{82} +(-2.85384 + 4.94299i) q^{83} +(-1.91730 - 3.32085i) q^{85} +(3.16639 + 9.21720i) q^{86} +(0.217752 - 3.99161i) q^{88} +(-5.75795 + 3.32435i) q^{89} +(-0.652664 - 7.49613i) q^{91} +(1.45516 - 3.58690i) q^{92} +(11.3970 + 9.92156i) q^{94} -7.97801i q^{95} +(13.1164 + 7.57275i) q^{97} +(-0.188114 + 9.89771i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37}+ \cdots - 21 q^{98}+O(q^{100}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more