LMFDB - Embedded newform 220.2.u.a.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(13,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 2]))

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

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

chi := DirichletCharacter("220.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.u (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	220.73
Dual form			220.2.u.a.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.69137 + 1.37132i) q^{3} +(-0.0704176 - 2.23496i) q^{5} +(-0.328865 + 0.645435i) q^{7} +(3.59960 - 4.95443i) q^{9} +(-0.737999 - 3.23347i) q^{11} +(6.33471 - 1.00332i) q^{13} +(3.25437 + 5.91854i) q^{15} +(-2.66791 - 0.422556i) q^{17} +(2.17270 - 6.68689i) q^{19} -2.18809i q^{21} +(-0.399505 - 0.399505i) q^{23} +(-4.99008 + 0.314761i) q^{25} +(-1.47617 + 9.32020i) q^{27} +(-0.400667 - 1.23312i) q^{29} +(2.43127 + 1.76642i) q^{31} +(6.42037 + 7.69045i) q^{33} +(1.46568 + 0.689551i) q^{35} +(-7.40461 - 3.77284i) q^{37} +(-15.6732 + 11.3872i) q^{39} +(-4.24004 - 1.37767i) q^{41} +(-1.85191 + 1.85191i) q^{43} +(-11.3264 - 7.69608i) q^{45} +(0.0315244 + 0.0618701i) q^{47} +(3.80606 + 5.23860i) q^{49} +(7.75981 - 2.52131i) q^{51} +(-1.28461 - 8.11073i) q^{53} +(-7.17471 + 1.87709i) q^{55} +(3.32233 + 20.9764i) q^{57} +(6.46029 - 2.09908i) q^{59} +(6.84018 + 9.41470i) q^{61} +(2.01397 + 3.95265i) q^{63} +(-2.68845 - 14.0872i) q^{65} +(2.17585 - 2.17585i) q^{67} +(1.62307 + 0.527366i) q^{69} +(5.64630 - 4.10228i) q^{71} +(4.33309 + 2.20782i) q^{73} +(12.9985 - 7.69015i) q^{75} +(2.32970 + 0.587048i) q^{77} +(-3.49465 - 2.53901i) q^{79} +(-3.13079 - 9.63559i) q^{81} +(1.93474 - 12.2155i) q^{83} +(-0.756527 + 5.99243i) q^{85} +(2.76935 + 2.76935i) q^{87} +7.03122i q^{89} +(-1.43569 + 4.41860i) q^{91} +(-8.96579 - 1.42004i) q^{93} +(-15.0979 - 4.38502i) q^{95} +(13.1791 - 2.08736i) q^{97} +(-18.6765 - 7.98286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55}+ \cdots + 6 q^{97}+O(q^{100}) $ 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.69137	+	1.37132i	−1.55386	+	0.791733i	−0.999186	−	0.0403316i	$-0.987159\pi$
$3$	−2.69137	+	1.37132i	−1.55386	+	0.791733i	−0.554678	+	0.832065i	$0.687159\pi$
$4$		0			0
$5$	−0.0704176	−	2.23496i	−0.0314917	−	0.999504i
$5$	−0.0704176	−	2.23496i	−0.0314917	−	0.999504i
$6$		0			0
$7$	−0.328865	+	0.645435i	−0.124299	+	0.243951i	−0.944768	−	0.327741i	$-0.893713\pi$
$7$	−0.328865	+	0.645435i	−0.124299	+	0.243951i	0.820468	+	0.571692i	$0.193713\pi$
$8$		0			0
$9$	3.59960	−	4.95443i	1.19987	−	1.65148i
$10$		0			0
$11$	−0.737999	−	3.23347i	−0.222515	−	0.974929i
$11$	−0.737999	−	3.23347i	−0.222515	−	0.974929i
$12$		0			0
$13$	6.33471	−	1.00332i	1.75693	−	0.278271i	0.806961	−	0.590605i	$-0.201111\pi$
$13$	6.33471	−	1.00332i	1.75693	−	0.278271i	0.949972	+	0.312334i	$0.101111\pi$
$14$		0			0
$15$	3.25437	+	5.91854i	0.840275	+	1.52816i
$16$		0			0
$17$	−2.66791	−	0.422556i	−0.647064	−	0.102485i	−0.175728	−	0.984439i	$-0.556228\pi$
$17$	−2.66791	−	0.422556i	−0.647064	−	0.102485i	−0.471336	+	0.881954i	$0.656228\pi$
$18$		0			0
$19$	2.17270	−	6.68689i	0.498452	−	1.53408i	−0.313055	−	0.949735i	$-0.601353\pi$
$19$	2.17270	−	6.68689i	0.498452	−	1.53408i	0.811507	−	0.584342i	$-0.198647\pi$
$20$		0			0
$21$		−	2.18809i		−	0.477479i
$22$		0			0
$23$	−0.399505	−	0.399505i	−0.0833026	−	0.0833026i	0.664228	−	0.747530i	$-0.268761\pi$
$23$	−0.399505	−	0.399505i	−0.0833026	−	0.0833026i	−0.747530	+	0.664228i	$0.768761\pi$
$24$		0			0
$25$	−4.99008	+	0.314761i	−0.998017	+	0.0629522i
$26$		0			0
$27$	−1.47617	+	9.32020i	−0.284090	+	1.79367i
$28$		0			0
$29$	−0.400667	−	1.23312i	−0.0744019	−	0.228986i	0.906939	−	0.421262i	$-0.138413\pi$
$29$	−0.400667	−	1.23312i	−0.0744019	−	0.228986i	−0.981341	+	0.192277i	$0.938413\pi$
$30$		0			0
$31$	2.43127	+	1.76642i	0.436669	+	0.317259i	0.784310	−	0.620369i	$-0.213017\pi$
$31$	2.43127	+	1.76642i	0.436669	+	0.317259i	−0.347641	+	0.937628i	$0.613017\pi$
$32$		0			0
$33$	6.42037	+	7.69045i	1.11764	+	1.33874i
$34$		0			0
$35$	1.46568	+	0.689551i	0.247745	+	0.116555i
$36$		0			0
$37$	−7.40461	−	3.77284i	−1.21731	−	0.620250i	−0.277098	−	0.960842i	$-0.589373\pi$
$37$	−7.40461	−	3.77284i	−1.21731	−	0.620250i	−0.940211	+	0.340591i	$0.889373\pi$
$38$		0			0
$39$	−15.6732	+	11.3872i	−2.50972	+	1.82342i
$40$		0			0
$41$	−4.24004	−	1.37767i	−0.662183	−	0.215156i	−0.0414044	−	0.999142i	$-0.513183\pi$
$41$	−4.24004	−	1.37767i	−0.662183	−	0.215156i	−0.620778	+	0.783986i	$0.713183\pi$
$42$		0			0
$43$	−1.85191	+	1.85191i	−0.282414	+	0.282414i	−0.834071	−	0.551657i	$-0.813996\pi$
$43$	−1.85191	+	1.85191i	−0.282414	+	0.282414i	0.551657	+	0.834071i	$0.313996\pi$
$44$		0			0
$45$	−11.3264	−	7.69608i	−1.68844	−	1.14726i
$46$		0			0
$47$	0.0315244	+	0.0618701i	0.00459830	+	0.00902468i	0.893294	−	0.449472i	$-0.148388\pi$
$47$	0.0315244	+	0.0618701i	0.00459830	+	0.00902468i	−0.888696	+	0.458497i	$0.848388\pi$
$48$		0			0
$49$	3.80606	+	5.23860i	0.543723	+	0.748371i
$50$		0			0
$51$	7.75981	−	2.52131i	1.08659	−	0.353055i
$52$		0			0
$53$	−1.28461	−	8.11073i	−0.176455	−	1.11410i	−0.903842	−	0.427867i	$-0.859265\pi$
$53$	−1.28461	−	8.11073i	−0.176455	−	1.11410i	0.727386	−	0.686228i	$-0.240735\pi$
$54$		0			0
$55$	−7.17471	+	1.87709i	−0.967438	+	0.253107i
$56$		0			0
$57$	3.32233	+	20.9764i	0.440054	+	2.77839i
$58$		0			0
$59$	6.46029	−	2.09908i	0.841058	−	0.273276i	0.143362	−	0.989670i	$-0.454209\pi$
$59$	6.46029	−	2.09908i	0.841058	−	0.273276i	0.697696	+	0.716394i	$0.254209\pi$
$60$		0			0
$61$	6.84018	+	9.41470i	0.875795	+	1.20543i	0.977568	+	0.210621i	$0.0675487\pi$
$61$	6.84018	+	9.41470i	0.875795	+	1.20543i	−0.101772	+	0.994808i	$0.532451\pi$
$62$		0			0
$63$	2.01397	+	3.95265i	0.253737	+	0.497987i
$64$		0			0
$65$	−2.68845	−	14.0872i	−0.333462	−	1.74730i
$66$		0			0
$67$	2.17585	−	2.17585i	0.265822	−	0.265822i	−0.561592	−	0.827414i	$-0.689811\pi$
$67$	2.17585	−	2.17585i	0.265822	−	0.265822i	0.827414	+	0.561592i	$0.189811\pi$
$68$		0			0
$69$	1.62307	+	0.527366i	0.195394	+	0.0634875i
$70$		0			0
$71$	5.64630	−	4.10228i	0.670093	−	0.486851i	−0.199963	−	0.979803i	$-0.564082\pi$
$71$	5.64630	−	4.10228i	0.670093	−	0.486851i	0.870056	+	0.492952i	$0.164082\pi$
$72$		0			0
$73$	4.33309	+	2.20782i	0.507150	+	0.258406i	0.688792	−	0.724959i	$-0.258141\pi$
$73$	4.33309	+	2.20782i	0.507150	+	0.258406i	−0.181642	+	0.983365i	$0.558141\pi$
$74$		0			0
$75$	12.9985	−	7.69015i	1.50094	−	0.887982i
$76$		0			0
$77$	2.32970	+	0.587048i	0.265494	+	0.0669003i
$78$		0			0
$79$	−3.49465	−	2.53901i	−0.393179	−	0.285661i	0.373578	−	0.927599i	$-0.378131\pi$
$79$	−3.49465	−	2.53901i	−0.393179	−	0.285661i	−0.766757	+	0.641937i	$0.778131\pi$
$80$		0			0
$81$	−3.13079	−	9.63559i	−0.347866	−	1.07062i
$82$		0			0
$83$	1.93474	−	12.2155i	0.212365	−	1.34082i	−0.619130	−	0.785288i	$-0.712515\pi$
$83$	1.93474	−	12.2155i	0.212365	−	1.34082i	0.831495	−	0.555532i	$-0.187485\pi$
$84$		0			0
$85$	−0.756527	+	5.99243i	−0.0820569	+	0.649970i
$86$		0			0
$87$	2.76935	+	2.76935i	0.296906	+	0.296906i
$88$		0			0
$89$			7.03122i			0.745308i	0.927970	+	0.372654i	$0.121552\pi$
$89$			7.03122i			0.745308i	−0.927970	+	0.372654i	$0.878448\pi$
$90$		0			0
$91$	−1.43569	+	4.41860i	−0.150501	+	0.463195i
$92$		0			0
$93$	−8.96579	−	1.42004i	−0.929709	−	0.147251i
$94$		0			0
$95$	−15.0979	−	4.38502i	−1.54901	−	0.449894i
$96$		0			0
$97$	13.1791	−	2.08736i	1.33813	−	0.211939i	0.553991	−	0.832522i	$-0.313104\pi$
$97$	13.1791	−	2.08736i	1.33813	−	0.211939i	0.784141	+	0.620583i	$0.213104\pi$
$98$		0			0
$99$	−18.6765	−	7.98286i	−1.87706	−	0.802308i
$100$		0			0
$101$	−2.86963	+	3.94971i	−0.285539	+	0.393011i	−0.927559	−	0.373677i	$-0.878097\pi$
$101$	−2.86963	+	3.94971i	−0.285539	+	0.393011i	0.642020	+	0.766688i	$0.278097\pi$
$102$		0			0
$103$	−2.05633	+	4.03577i	−0.202616	+	0.397656i	−0.969847	−	0.243715i	$-0.921634\pi$
$103$	−2.05633	+	4.03577i	−0.202616	+	0.397656i	0.767231	+	0.641371i	$0.221634\pi$
$104$		0			0
$105$	−4.89028	+	0.154080i	−0.477243	+	0.0150366i
$106$		0			0
$107$	−12.6078	+	6.42400i	−1.21884	+	0.621032i	−0.940613	−	0.339482i	$-0.889748\pi$
$107$	−12.6078	+	6.42400i	−1.21884	+	0.621032i	−0.278231	+	0.960514i	$0.589748\pi$
$108$		0			0
$109$	−9.31654			−0.892363			−0.446181	−	0.894943i	$-0.647216\pi$
$109$	−9.31654			−0.892363			−0.446181	+	0.894943i	$0.647216\pi$
$110$		0			0
$111$	25.1023			2.38261
$112$		0			0
$113$	3.97341	−	2.02455i	0.373787	−	0.190454i	−0.256997	−	0.966412i	$-0.582733\pi$
$113$	3.97341	−	2.02455i	0.373787	−	0.190454i	0.630784	+	0.775958i	$0.282733\pi$
$114$		0			0
$115$	−0.864745	+	0.921010i	−0.0806379	+	0.0858846i
$116$		0			0
$117$	17.8316	−	34.9964i	1.64853	−	3.23542i
$118$		0			0
$119$	1.15012	−	1.58300i	0.105431	−	0.145113i
$120$		0			0
$121$	−9.91072	+	4.77260i	−0.900974	+	0.433873i
$122$		0			0
$123$	13.3007	−	2.10663i	1.19929	−	0.189949i
$124$		0			0
$125$	1.05487	+	11.1305i	0.0943502	+	0.995539i
$126$		0			0
$127$	4.39719	+	0.696447i	0.390188	+	0.0617997i	0.348446	−	0.937329i	$-0.386709\pi$
$127$	4.39719	+	0.696447i	0.390188	+	0.0617997i	0.0417415	+	0.999128i	$0.486709\pi$
$128$		0			0
$129$	2.44461	−	7.52375i	0.215236	−	0.662429i
$130$		0			0
$131$			17.1079i			1.49472i	0.664419	+	0.747360i	$0.268679\pi$
$131$			17.1079i			1.49472i	−0.664419	+	0.747360i	$0.731321\pi$
$132$		0			0
$133$	3.60142	+	3.60142i	0.312283	+	0.312283i
$134$		0			0
$135$	20.9342	+	2.64288i	1.80173	+	0.227463i
$136$		0			0
$137$	−0.501626	+	3.16714i	−0.0428568	+	0.270587i	−0.999807	−	0.0196662i	$-0.993740\pi$
$137$	−0.501626	+	3.16714i	−0.0428568	+	0.270587i	0.956950	+	0.290254i	$0.0937397\pi$
$138$		0			0
$139$	−0.736668	−	2.26723i	−0.0624833	−	0.192304i	0.914942	−	0.403586i	$-0.132236\pi$
$139$	−0.736668	−	2.26723i	−0.0624833	−	0.192304i	−0.977425	+	0.211282i	$0.932236\pi$
$140$		0			0
$141$	−0.169688	−	0.123285i	−0.0142903	−	0.0103825i
$142$		0			0
$143$	−7.91922	−	19.7427i	−0.662239	−	1.65097i
$144$		0			0
$145$	−2.72777	+	0.982307i	−0.226529	+	0.0815762i
$146$		0			0
$147$	−17.4273	−	8.87967i	−1.43738	−	0.732383i
$148$		0			0
$149$	11.5619	−	8.40019i	0.947185	−	0.688170i	−0.00295440	−	0.999996i	$-0.500940\pi$
$149$	11.5619	−	8.40019i	0.947185	−	0.688170i	0.950139	+	0.311825i	$0.100940\pi$
$150$		0			0
$151$	−17.0508	−	5.54015i	−1.38758	−	0.450851i	−0.482424	−	0.875938i	$-0.660244\pi$
$151$	−17.0508	−	5.54015i	−1.38758	−	0.450851i	−0.905153	+	0.425087i	$0.860244\pi$
$152$		0			0
$153$	−11.6969	+	11.6969i	−0.945642	+	0.945642i
$154$		0			0
$155$	3.77668	−	5.55818i	0.303350	−	0.446444i
$156$		0			0
$157$	1.51796	+	2.97917i	0.121147	+	0.237764i	0.943613	−	0.331050i	$-0.107403\pi$
$157$	1.51796	+	2.97917i	0.121147	+	0.237764i	−0.822467	+	0.568813i	$0.807403\pi$
$158$		0			0
$159$	14.5798	+	20.0674i	1.15625	+	1.59145i
$160$		0			0
$161$	0.389238	−	0.126471i	0.0306762	−	0.00996731i
$162$		0			0
$163$	1.99353	+	12.5866i	0.156145	+	0.985862i	0.933962	+	0.357371i	$0.116327\pi$
$163$	1.99353	+	12.5866i	0.156145	+	0.985862i	−0.777817	+	0.628490i	$0.783673\pi$
$164$		0			0
$165$	16.7357	−	14.8908i	1.30287	−	1.15925i
$166$		0			0
$167$	0.0665828	+	0.420387i	0.00515233	+	0.0325306i	0.990131	−	0.140148i	$-0.0447578\pi$
$167$	0.0665828	+	0.420387i	0.00515233	+	0.0325306i	−0.984978	+	0.172679i	$0.944758\pi$
$168$		0			0
$169$	26.7582	−	8.69427i	2.05832	−	0.668790i
$170$		0			0
$171$	−25.3088	−	34.8346i	−1.93542	−	2.66387i
$172$		0			0
$173$	6.05217	+	11.8780i	0.460138	+	0.903071i	0.998189	+	0.0601590i	$0.0191608\pi$
$173$	6.05217	+	11.8780i	0.460138	+	0.903071i	−0.538051	+	0.842912i	$0.680839\pi$
$174$		0			0
$175$	1.43791	−	3.32429i	0.108696	−	0.251292i
$176$		0			0
$177$	−14.5085	+	14.5085i	−1.09053	+	1.09053i
$178$		0			0
$179$	20.3460	+	6.61081i	1.52073	+	0.494115i	0.945983	−	0.324217i	$-0.105101\pi$
$179$	20.3460	+	6.61081i	1.52073	+	0.494115i	0.574746	+	0.818332i	$0.305101\pi$
$180$		0			0
$181$	5.91056	−	4.29427i	0.439328	−	0.319191i	−0.346040	−	0.938220i	$-0.612474\pi$
$181$	5.91056	−	4.29427i	0.439328	−	0.319191i	0.785368	+	0.619029i	$0.212474\pi$
$182$		0			0
$183$	−31.3201	−	15.9584i	−2.31525	−	1.17968i
$184$		0			0
$185$	−7.91072	+	16.8147i	−0.581608	+	1.23624i
$186$		0			0
$187$	0.602593	+	8.93847i	0.0440660	+	0.653646i
$188$		0			0
$189$	−5.53012	−	4.01786i	−0.402257	−	0.292257i
$190$		0			0
$191$	0.115702	+	0.356093i	0.00837188	+	0.0257660i	0.955155	−	0.296106i	$-0.0956880\pi$
$191$	0.115702	+	0.356093i	0.00837188	+	0.0257660i	−0.946783	+	0.321872i	$0.895688\pi$
$192$		0			0
$193$	−2.11650	+	13.3630i	−0.152349	+	0.961893i	0.786507	+	0.617582i	$0.211888\pi$
$193$	−2.11650	+	13.3630i	−0.152349	+	0.961893i	−0.938856	+	0.344311i	$0.888112\pi$
$194$		0			0
$195$	26.5537	+	34.2271i	1.90155	+	2.45105i
$196$		0			0
$197$	−18.0772	−	18.0772i	−1.28795	−	1.28795i	−0.936032	−	0.351916i	$-0.885530\pi$
$197$	−18.0772	−	18.0772i	−1.28795	−	1.28795i	−0.351916	−	0.936032i	$-0.614470\pi$
$198$		0			0
$199$			1.57894i			0.111928i	0.998433	+	0.0559641i	$0.0178233\pi$
$199$			1.57894i			0.111928i	−0.998433	+	0.0559641i	$0.982177\pi$
$200$		0			0
$201$	−2.87223	+	8.83981i	−0.202591	+	0.623512i
$202$		0			0
$203$	0.927667	+	0.146928i	0.0651094	+	0.0103123i
$204$		0			0
$205$	−2.78047	+	9.57332i	−0.194196	+	0.668630i
$206$		0			0
$207$	−3.41738	+	0.541260i	−0.237524	+	0.0376201i
$208$		0			0
$209$	−23.2253	−	2.09046i	−1.60653	−	0.144600i
$210$		0			0
$211$	−9.31244	+	12.8175i	−0.641095	+	0.882391i	−0.998673	−	0.0514920i	$-0.983602\pi$
$211$	−9.31244	+	12.8175i	−0.641095	+	0.882391i	0.357579	+	0.933883i	$0.383602\pi$
$212$		0			0
$213$	−9.57076	+	18.7837i	−0.655777	+	1.28704i
$214$		0			0
$215$	4.26935	+	4.00854i	0.291167	+	0.273380i
$216$		0			0
$217$	−1.93967	+	0.988311i	−0.131673	+	0.0670910i
$218$		0			0
$219$	−14.6896			−0.992630
$220$		0			0
$221$	−17.3244			−1.16537
$222$		0			0
$223$	15.6005	−	7.94888i	1.04469	−	0.532296i	0.154551	−	0.987985i	$-0.450607\pi$
$223$	15.6005	−	7.94888i	1.04469	−	0.532296i	0.890139	+	0.455689i	$0.150607\pi$
$224$		0			0
$225$	−16.4029	+	25.8560i	−1.09352	+	1.72373i
$226$		0			0
$227$	1.00988	−	1.98201i	0.0670283	−	0.131550i	−0.855061	−	0.518527i	$-0.826481\pi$
$227$	1.00988	−	1.98201i	0.0670283	−	0.131550i	0.922090	+	0.386977i	$0.126481\pi$
$228$		0			0
$229$	4.26974	−	5.87679i	0.282152	−	0.388349i	−0.644293	−	0.764779i	$-0.722848\pi$
$229$	4.26974	−	5.87679i	0.282152	−	0.388349i	0.926445	+	0.376429i	$0.122848\pi$
$230$		0			0
$231$	−7.07512	+	1.61480i	−0.465509	+	0.106246i
$232$		0			0
$233$	−6.46966	+	1.02469i	−0.423841	+	0.0671299i	−0.364712	−	0.931120i	$-0.618832\pi$
$233$	−6.46966	+	1.02469i	−0.423841	+	0.0671299i	−0.0591295	+	0.998250i	$0.518832\pi$
$234$		0			0
$235$	0.136057	−	0.0748124i	0.00887540	−	0.00488023i
$236$		0			0
$237$	12.8872	+	2.04113i	0.837115	+	0.132586i
$238$		0			0
$239$	−5.04062	+	15.5134i	−0.326051	+	1.00348i	0.644913	+	0.764256i	$0.276893\pi$
$239$	−5.04062	+	15.5134i	−0.326051	+	1.00348i	−0.970964	+	0.239225i	$0.923107\pi$
$240$		0			0
$241$		−	4.18134i		−	0.269344i	−0.990890	−	0.134672i	$-0.957002\pi$
$241$		−	4.18134i		−	0.269344i	0.990890	−	0.134672i	$-0.0429980\pi$
$242$		0			0
$243$	1.62206	+	1.62206i	0.104055	+	0.104055i
$244$		0			0
$245$	11.4400	−	8.87528i	0.730877	−	0.567021i
$246$		0			0
$247$	7.05435	−	44.5394i	0.448858	−	2.83398i
$248$		0			0
$249$	11.5442	+	35.5295i	0.731586	+	2.25159i
$250$		0			0
$251$	10.2704	+	7.46191i	0.648264	+	0.470992i	0.862680	−	0.505751i	$-0.168785\pi$
$251$	10.2704	+	7.46191i	0.648264	+	0.470992i	−0.214415	+	0.976743i	$0.568785\pi$
$252$		0			0
$253$	−0.996955	+	1.58662i	−0.0626780	+	0.0997502i
$254$		0			0
$255$	−6.18146	−	17.1653i	−0.387098	−	1.07493i
$256$		0			0
$257$	1.06560	+	0.542953i	0.0664706	+	0.0338685i	0.486910	−	0.873452i	$-0.338124\pi$
$257$	1.06560	+	0.542953i	0.0664706	+	0.0338685i	−0.420439	+	0.907321i	$0.638124\pi$
$258$		0			0
$259$	4.87024	−	3.53843i	0.302622	−	0.219868i
$260$		0			0
$261$	−7.55167	−	2.45369i	−0.467436	−	0.151879i
$262$		0			0
$263$	21.2348	−	21.2348i	1.30939	−	1.30939i	0.387540	−	0.921853i	$-0.373325\pi$
$263$	21.2348	−	21.2348i	1.30939	−	1.30939i	0.921853	−	0.387540i	$-0.126675\pi$
$264$		0			0
$265$	−18.0367	+	3.44220i	−1.10799	+	0.211453i
$266$		0			0
$267$	−9.64207	−	18.9236i	−0.590085	−	1.15811i
$268$		0			0
$269$	−8.55891	−	11.7803i	−0.521846	−	0.718259i	0.464015	−	0.885828i	$-0.346409\pi$
$269$	−8.55891	−	11.7803i	−0.521846	−	0.718259i	−0.985860	+	0.167568i	$0.946409\pi$
$270$		0			0
$271$	12.7061	−	4.12848i	0.771844	−	0.250787i	0.103490	−	0.994631i	$-0.466999\pi$
$271$	12.7061	−	4.12848i	0.771844	−	0.250787i	0.668354	+	0.743843i	$0.266999\pi$
$272$		0			0
$273$	−2.19535	−	13.8609i	−0.132869	−	0.838899i
$274$		0			0
$275$	4.70045	+	15.9030i	0.283448	+	0.958988i
$276$		0			0
$277$	3.33857	+	21.0789i	0.200595	+	1.26651i	0.858266	+	0.513205i	$0.171542\pi$
$277$	3.33857	+	21.0789i	0.200595	+	1.26651i	−0.657671	+	0.753305i	$0.728458\pi$
$278$		0			0
$279$	17.5032	−	5.68714i	1.04789	−	0.340480i
$280$		0			0
$281$	14.0944	+	19.3993i	0.840801	+	1.15726i	0.985815	+	0.167834i	$0.0536771\pi$
$281$	14.0944	+	19.3993i	0.840801	+	1.15726i	−0.145014	+	0.989430i	$0.546323\pi$
$282$		0			0
$283$	−6.49288	−	12.7430i	−0.385962	−	0.757493i	0.613520	−	0.789679i	$-0.289753\pi$
$283$	−6.49288	−	12.7430i	−0.385962	−	0.757493i	−0.999482	+	0.0321865i	$0.989753\pi$
$284$		0			0
$285$	46.6474	−	8.90238i	2.76315	−	0.527332i
$286$		0			0
$287$	2.28360	−	2.28360i	0.134797	−	0.134797i
$288$		0			0
$289$	−9.22876	−	2.99860i	−0.542868	−	0.176389i
$290$		0			0
$291$	−32.6073	+	23.6906i	−1.91148	+	1.38877i
$292$		0			0
$293$	−21.1158	−	10.7590i	−1.23360	−	0.628548i	−0.289171	−	0.957277i	$-0.593380\pi$
$293$	−21.1158	−	10.7590i	−1.23360	−	0.628548i	−0.944424	+	0.328729i	$0.893380\pi$
$294$		0			0
$295$	−5.14627	−	14.2907i	−0.299627	−	0.832035i
$296$		0			0
$297$	31.2260	−	2.10512i	1.81192	−	0.122152i
$298$		0			0
$299$	−2.93158	−	2.12992i	−0.169538	−	0.123176i
$300$		0			0
$301$	−0.586258	−	1.80432i	−0.0337913	−	0.103999i
$302$		0			0
$303$	2.30692	−	14.5653i	0.132529	−	0.836757i
$304$		0			0
$305$	20.5598	−	15.9505i	1.17725	−	0.913322i
$306$		0			0
$307$	−10.5579	−	10.5579i	−0.602570	−	0.602570i	0.338424	−	0.940994i	$-0.390106\pi$
$307$	−10.5579	−	10.5579i	−0.602570	−	0.602570i	−0.940994	+	0.338424i	$0.890106\pi$
$308$		0			0
$309$		−	13.6816i		−	0.778322i
$310$		0			0
$311$	−1.32389	+	4.07451i	−0.0750708	+	0.231044i	−0.981550	−	0.191207i	$-0.938760\pi$
$311$	−1.32389	+	4.07451i	−0.0750708	+	0.231044i	0.906479	+	0.422251i	$0.138760\pi$
$312$		0			0
$313$	28.6128	+	4.53183i	1.61729	+	0.256154i	0.898468	−	0.439038i	$-0.144681\pi$
$313$	28.6128	+	4.53183i	1.61729	+	0.256154i	0.718824	+	0.695192i	$0.244681\pi$
$314$		0			0
$315$	8.69219	−	4.77949i	0.489749	−	0.269294i
$316$		0			0
$317$	8.13986	−	1.28923i	0.457180	−	0.0724102i	0.0764028	−	0.997077i	$-0.475657\pi$
$317$	8.13986	−	1.28923i	0.457180	−	0.0724102i	0.380777	+	0.924667i	$0.375657\pi$
$318$		0			0
$319$	−3.69159	+	2.20559i	−0.206689	+	0.123489i
$320$		0			0
$321$	25.1229	−	34.5788i	1.40223	−	1.93000i
$322$		0			0
$323$	−8.62216	+	16.9219i	−0.479750	+	0.941562i
$324$		0			0
$325$	−31.2949	+	7.00057i	−1.73593	+	0.388322i
$326$		0			0
$327$	25.0743	−	12.7760i	1.38661	−	0.706514i
$328$		0			0
$329$	−0.0503004			−0.00277315
$330$		0			0
$331$	24.6521			1.35500			0.677502	−	0.735521i	$-0.263063\pi$
$331$	24.6521			1.35500			0.677502	+	0.735521i	$0.263063\pi$
$332$		0			0
$333$	−45.3459	+	23.1049i	−2.48494	+	1.26614i
$334$		0			0
$335$	−5.01615	−	4.70971i	−0.274062	−	0.257319i
$336$		0			0
$337$	1.15819	−	2.27308i	0.0630907	−	0.123822i	−0.857308	−	0.514804i	$-0.827865\pi$
$337$	1.15819	−	2.27308i	0.0630907	−	0.123822i	0.920398	+	0.390982i	$0.127865\pi$
$338$		0			0
$339$	−7.91761	+	10.8977i	−0.430025	+	0.591879i
$340$		0			0
$341$	3.91740	−	9.16507i	0.212139	−	0.496316i
$342$		0			0
$343$	−9.64114	+	1.52701i	−0.520573	+	0.0824506i
$344$		0			0
$345$	1.06435	−	3.66462i	0.0573027	−	0.197297i
$346$		0			0
$347$	21.0523	+	3.33435i	1.13015	+	0.178997i	0.693376	−	0.720576i	$-0.256123\pi$
$347$	21.0523	+	3.33435i	1.13015	+	0.178997i	0.436769	+	0.899573i	$0.356123\pi$
$348$		0			0
$349$	4.10120	−	12.6222i	0.219532	−	0.675651i	−0.779268	−	0.626690i	$-0.784409\pi$
$349$	4.10120	−	12.6222i	0.219532	−	0.675651i	0.998801	−	0.0489608i	$-0.0155910\pi$
$350$		0			0
$351$			60.5218i			3.23042i
$352$		0			0
$353$	5.35710	+	5.35710i	0.285130	+	0.285130i	0.835151	−	0.550021i	$-0.185380\pi$
$353$	5.35710	+	5.35710i	0.285130	+	0.285130i	−0.550021	+	0.835151i	$0.685380\pi$
$354$		0			0
$355$	−9.56603	−	12.3304i	−0.507712	−	0.654429i
$356$		0			0
$357$	−0.924588	+	5.83762i	−0.0489344	+	0.308960i
$358$		0			0
$359$	9.21704	+	28.3671i	0.486457	+	1.49716i	0.829860	+	0.557971i	$0.188420\pi$
$359$	9.21704	+	28.3671i	0.486457	+	1.49716i	−0.343404	+	0.939188i	$0.611580\pi$
$360$		0			0
$361$	−24.6225	−	17.8893i	−1.29592	−	0.941542i
$362$		0			0
$363$	20.1286	−	26.4356i	1.05648	−	1.38751i
$364$		0			0
$365$	4.62926	−	9.83974i	0.242306	−	0.515036i
$366$		0			0
$367$	−0.604234	−	0.307872i	−0.0315407	−	0.0160708i	0.438149	−	0.898902i	$-0.355634\pi$
$367$	−0.604234	−	0.307872i	−0.0315407	−	0.0160708i	−0.469690	+	0.882832i	$0.655634\pi$
$368$		0			0
$369$	−22.0880	+	16.0479i	−1.14986	+	0.835420i
$370$		0			0
$371$	5.65741	+	1.83821i	0.293718	+	0.0954349i
$372$		0			0
$373$	−7.34024	+	7.34024i	−0.380063	+	0.380063i	−0.871125	−	0.491061i	$-0.836609\pi$
$373$	−7.34024	+	7.34024i	−0.380063	+	0.380063i	0.491061	+	0.871125i	$0.336609\pi$
$374$		0			0
$375$	−18.1025	−	28.5097i	−0.934809	−	1.47223i
$376$		0			0
$377$	−3.77533	−	7.40950i	−0.194439	−	0.381608i
$378$		0			0
$379$	−8.97797	−	12.3571i	−0.461167	−	0.634742i	0.513583	−	0.858040i	$-0.328318\pi$
$379$	−8.97797	−	12.3571i	−0.461167	−	0.634742i	−0.974750	+	0.223298i	$0.928318\pi$
$380$		0			0
$381$	−12.7895	+	4.15557i	−0.655228	+	0.212896i
$382$		0			0
$383$	3.28863	+	20.7636i	0.168041	+	1.06097i	0.917156	+	0.398529i	$0.130479\pi$
$383$	3.28863	+	20.7636i	0.168041	+	1.06097i	−0.749114	+	0.662441i	$0.769521\pi$
$384$		0			0
$385$	1.14798	−	5.24812i	0.0585063	−	0.267469i
$386$		0			0
$387$	2.50901	+	15.8413i	0.127540	+	0.805258i
$388$		0			0
$389$	−16.6876	+	5.42213i	−0.846096	+	0.274913i	−0.699810	−	0.714329i	$-0.746732\pi$
$389$	−16.6876	+	5.42213i	−0.846096	+	0.274913i	−0.146286	+	0.989242i	$0.546732\pi$
$390$		0			0
$391$	0.897032	+	1.23466i	0.0453648	+	0.0624393i
$392$		0			0
$393$	−23.4604	−	46.0436i	−1.18342	−	2.32259i
$394$		0			0
$395$	−5.42851	+	7.98920i	−0.273138	+	0.401980i
$396$		0			0
$397$	10.1338	−	10.1338i	0.508603	−	0.508603i	−0.405495	−	0.914097i	$-0.632901\pi$
$397$	10.1338	−	10.1338i	0.508603	−	0.508603i	0.914097	+	0.405495i	$0.132901\pi$
$398$		0			0
$399$	−14.6315	−	4.75406i	−0.732490	−	0.238000i
$400$		0			0
$401$	31.6798	−	23.0167i	1.58201	−	1.14940i	0.667671	−	0.744456i	$-0.267291\pi$
$401$	31.6798	−	23.0167i	1.58201	−	1.14940i	0.914342	−	0.404943i	$-0.132709\pi$
$402$		0			0
$403$	17.1737	+	8.75043i	0.855482	+	0.435890i
$404$		0			0
$405$	−21.3147	+	7.67571i	−1.05914	+	0.381409i
$406$		0			0
$407$	−6.73478	+	26.7270i	−0.333830	+	1.32481i
$408$		0			0
$409$	−17.3141	−	12.5794i	−0.856128	−	0.622013i	0.0707012	−	0.997498i	$-0.477476\pi$
$409$	−17.3141	−	12.5794i	−0.856128	−	0.622013i	−0.926829	+	0.375484i	$0.877476\pi$
$410$		0			0
$411$	−2.99311	−	9.21185i	−0.147639	−	0.454387i
$412$		0			0
$413$	−0.769750	+	4.86001i	−0.0378769	+	0.239145i
$414$		0			0
$415$	−27.4373	−	3.46388i	−1.34684	−	0.170035i
$416$		0			0
$417$	5.09175	+	5.09175i	0.249344	+	0.249344i
$418$		0			0
$419$			14.5036i			0.708548i	0.935142	+	0.354274i	$0.115272\pi$
$419$			14.5036i			0.708548i	−0.935142	+	0.354274i	$0.884728\pi$
$420$		0			0
$421$	−6.22588	+	19.1613i	−0.303431	+	0.933864i	0.676827	+	0.736142i	$0.263354\pi$
$421$	−6.22588	+	19.1613i	−0.303431	+	0.933864i	−0.980258	+	0.197722i	$0.936646\pi$
$422$		0			0
$423$	0.420006	+	0.0665224i	0.0204214	+	0.00323443i
$424$		0			0
$425$	13.4461	+	1.26883i	0.652232	+	0.0615475i
$426$		0			0
$427$	−8.32607	+	1.31872i	−0.402927	+	0.0638174i
$428$		0			0
$429$	48.3872	+	42.2751i	2.33615	+	2.04106i
$430$		0			0
$431$	10.8439	−	14.9254i	0.522334	−	0.718931i	−0.463604	−	0.886042i	$-0.653444\pi$
$431$	10.8439	−	14.9254i	0.522334	−	0.718931i	0.985938	+	0.167112i	$0.0534440\pi$
$432$		0			0
$433$	12.8954	−	25.3087i	0.619715	−	1.21626i	−0.341350	−	0.939936i	$-0.610884\pi$
$433$	12.8954	−	25.3087i	0.619715	−	1.21626i	0.961065	−	0.276323i	$-0.0891158\pi$
$434$		0			0
$435$	5.99438	−	6.38441i	0.287409	−	0.306109i
$436$		0			0
$437$	−3.53945	+	1.80344i	−0.169315	+	0.0862703i
$438$		0			0
$439$	16.1551			0.771040			0.385520	−	0.922699i	$-0.374022\pi$
$439$	16.1551			0.771040			0.385520	+	0.922699i	$0.374022\pi$
$440$		0			0
$441$	39.6546			1.88831
$442$		0			0
$443$	−24.1154	+	12.2874i	−1.14576	+	0.583791i	−0.920590	−	0.390529i	$-0.872292\pi$
$443$	−24.1154	+	12.2874i	−1.14576	+	0.583791i	−0.225165	+	0.974321i	$0.572292\pi$
$444$		0			0
$445$	15.7145	−	0.495121i	0.744938	−	0.0234710i
$446$		0			0
$447$	−19.5979	+	38.4631i	−0.926950	+	1.81924i
$448$		0			0
$449$	7.68659	−	10.5797i	0.362752	−	0.499286i	−0.588161	−	0.808744i	$-0.700148\pi$
$449$	7.68659	−	10.5797i	0.362752	−	0.499286i	0.950913	+	0.309458i	$0.100148\pi$
$450$		0			0
$451$	−1.32552	+	14.7268i	−0.0624165	+	0.693457i
$452$		0			0
$453$	53.4875	−	8.47158i	2.51306	−	0.398030i
$454$		0			0
$455$	9.97649	+	2.89756i	0.467705	+	0.135840i
$456$		0			0
$457$	25.9795	+	4.11475i	1.21527	+	0.192480i	0.730962	−	0.682418i	$-0.239072\pi$
$457$	25.9795	+	4.11475i	1.21527	+	0.192480i	0.484307	+	0.874898i	$0.339072\pi$
$458$		0			0
$459$	7.87661	−	24.2417i	0.367649	−	1.13151i
$460$		0			0
$461$		−	16.1463i		−	0.752009i	−0.926618	−	0.376004i	$-0.877298\pi$
$461$		−	16.1463i		−	0.752009i	0.926618	−	0.376004i	$-0.122702\pi$
$462$		0			0
$463$	13.3994	+	13.3994i	0.622724	+	0.622724i	0.946227	−	0.323503i	$-0.104861\pi$
$463$	13.3994	+	13.3994i	0.622724	+	0.622724i	−0.323503	+	0.946227i	$0.604861\pi$
$464$		0			0
$465$	−2.54238	+	20.1382i	−0.117900	+	0.933885i
$466$		0			0
$467$	−1.10504	+	6.97693i	−0.0511350	+	0.322854i	0.948840	+	0.315758i	$0.102259\pi$
$467$	−1.10504	+	6.97693i	−0.0511350	+	0.322854i	−0.999975	+	0.00709589i	$0.997741\pi$
$468$		0			0
$469$	0.688807	+	2.11993i	0.0318061	+	0.0978892i
$470$		0			0
$471$	−8.17080	−	5.93644i	−0.376491	−	0.273537i
$472$		0			0
$473$	7.35481	+	4.62140i	0.338175	+	0.212492i
$474$		0			0
$475$	−8.73719	+	34.0520i	−0.400890	+	1.56241i
$476$		0			0
$477$	−44.8081	−	22.8309i	−2.05162	−	1.04535i
$478$		0			0
$479$	−11.6472	+	8.46222i	−0.532176	+	0.386649i	−0.821171	−	0.570682i	$-0.806679\pi$
$479$	−11.6472	+	8.46222i	−0.532176	+	0.386649i	0.288995	+	0.957331i	$0.406679\pi$
$480$		0			0
$481$	−50.6914	−	16.4706i	−2.31133	−	0.750997i
$482$		0			0
$483$	−0.874151	+	0.874151i	−0.0397753	+	0.0397753i
$484$		0			0
$485$	−5.59320	−	29.3077i	−0.253974	−	1.33079i
$486$		0			0
$487$	−16.2772	−	31.9458i	−0.737590	−	1.44760i	−0.888415	−	0.459042i	$-0.848193\pi$
$487$	−16.2772	−	31.9458i	−0.737590	−	1.44760i	0.150825	−	0.988561i	$-0.451807\pi$
$488$		0			0
$489$	−22.6257	−	31.1416i	−1.02317	−	1.40827i
$490$		0			0
$491$	−17.6291	+	5.72805i	−0.795591	+	0.258503i	−0.678483	−	0.734616i	$-0.737362\pi$
$491$	−17.6291	+	5.72805i	−0.795591	+	0.258503i	−0.117108	+	0.993119i	$0.537362\pi$
$492$		0			0
$493$	0.547879	+	3.45917i	0.0246752	+	0.155793i
$494$		0			0
$495$	−16.5262	+	42.3034i	−0.742798	+	1.90140i
$496$		0			0
$497$	0.790880	+	4.99342i	0.0354758	+	0.223985i
$498$		0			0
$499$	10.8573	−	3.52775i	0.486040	−	0.157924i	−0.0557384	−	0.998445i	$-0.517751\pi$
$499$	10.8573	−	3.52775i	0.486040	−	0.157924i	0.541778	+	0.840522i	$0.317751\pi$
$500$		0			0
$501$	−0.755686	−	1.04011i	−0.0337616	−	0.0464688i
$502$		0			0
$503$	10.3079	+	20.2304i	0.459608	+	0.902031i	0.998229	+	0.0594833i	$0.0189453\pi$
$503$	10.3079	+	20.2304i	0.459608	+	0.902031i	−0.538621	+	0.842548i	$0.681055\pi$
$504$		0			0
$505$	9.02952	+	6.13538i	0.401808	+	0.273021i
$506$		0			0
$507$	−60.0937	+	60.0937i	−2.66885	+	2.66885i
$508$		0			0
$509$	−15.5927	−	5.06639i	−0.691136	−	0.224564i	−0.0576716	−	0.998336i	$-0.518368\pi$
$509$	−15.5927	−	5.06639i	−0.691136	−	0.224564i	−0.633464	+	0.773772i	$0.718368\pi$
$510$		0			0
$511$	−2.85001	+	2.07065i	−0.126077	+	0.0916002i
$512$		0			0
$513$	59.1158	+	30.1210i	2.61003	+	1.32988i
$514$		0			0
$515$	9.16458	+	4.31162i	0.403840	+	0.189993i
$516$		0			0
$517$	0.176790	−	0.147593i	0.00777523	−	0.00649115i
$518$		0			0
$519$	−32.5773	−	23.6688i	−1.42998	−	1.03894i
$520$		0			0
$521$	11.4206	+	35.1490i	0.500346	+	1.53991i	0.808456	+	0.588556i	$0.200303\pi$
$521$	11.4206	+	35.1490i	0.500346	+	1.53991i	−0.308110	+	0.951351i	$0.599697\pi$
$522$		0			0
$523$	−2.08688	+	13.1761i	−0.0912530	+	0.576149i	0.899118	+	0.437707i	$0.144209\pi$
$523$	−2.08688	+	13.1761i	−0.0912530	+	0.576149i	−0.990371	+	0.138442i	$0.955791\pi$
$524$		0			0
$525$	0.688724	+	10.9187i	0.0300584	+	0.476532i
$526$		0			0
$527$	−5.74001	−	5.74001i	−0.250039	−	0.250039i
$528$		0			0
$529$		−	22.6808i		−	0.986121i
$530$		0			0
$531$	12.8548	−	39.5629i	0.557849	−	1.71688i
$532$		0			0
$533$	−28.2417	−	4.47304i	−1.22328	−	0.193749i
$534$		0			0
$535$	15.2452	+	27.7256i	0.659107	+	1.19868i
$536$		0			0
$537$	−63.8241	+	10.1087i	−2.75421	+	0.436225i
$538$		0			0
$539$	14.1300	−	16.1729i	0.608622	−	0.696616i
$540$		0			0
$541$	5.17033	−	7.11635i	0.222290	−	0.305956i	−0.683277	−	0.730159i	$-0.739446\pi$
$541$	5.17033	−	7.11635i	0.222290	−	0.305956i	0.905567	+	0.424203i	$0.139446\pi$
$542$		0			0
$543$	−10.0187	+	19.6628i	−0.429943	+	0.843810i
$544$		0			0
$545$	0.656049	+	20.8221i	0.0281020	+	0.891920i
$546$		0			0
$547$	19.1062	−	9.73509i	0.816922	−	0.416242i	0.00498489	−	0.999988i	$-0.498413\pi$
$547$	19.1062	−	9.73509i	0.816922	−	0.416242i	0.811937	+	0.583745i	$0.198413\pi$
$548$		0			0
$549$	71.2664			3.04158
$550$		0			0
$551$	−9.11630			−0.388367
$552$		0			0
$553$	2.78804	−	1.42058i	0.118559	−	0.0604091i
$554$		0			0
$555$	−1.76765	−	56.1027i	−0.0750324	−	2.38143i
$556$		0			0
$557$	−5.19678	+	10.1993i	−0.220195	+	0.432156i	−0.974506	−	0.224360i	$-0.927971\pi$
$557$	−5.19678	+	10.1993i	−0.220195	+	0.432156i	0.754312	+	0.656517i	$0.227971\pi$
$558$		0			0
$559$	−9.87326	+	13.5894i	−0.417594	+	0.574769i
$560$		0			0
$561$	−13.8793	−	23.2304i	−0.585986	−	0.980789i
$562$		0			0
$563$	−13.6659	+	2.16446i	−0.575948	+	0.0912213i	−0.437612	−	0.899164i	$-0.644176\pi$
$563$	−13.6659	+	2.16446i	−0.575948	+	0.0912213i	−0.138337	+	0.990385i	$0.544176\pi$
$564$		0			0
$565$	−4.80459	−	8.73784i	−0.202131	−	0.367604i
$566$		0			0
$567$	7.24875	+	1.14809i	0.304419	+	0.0482152i
$568$		0			0
$569$	−7.89984	+	24.3132i	−0.331179	+	1.01926i	0.637395	+	0.770537i	$0.280012\pi$
$569$	−7.89984	+	24.3132i	−0.331179	+	1.01926i	−0.968574	+	0.248726i	$0.919988\pi$
$570$		0			0
$571$		−	29.7381i		−	1.24450i	−0.782818	−	0.622251i	$-0.786218\pi$
$571$		−	29.7381i		−	1.24450i	0.782818	−	0.622251i	$-0.213782\pi$
$572$		0			0
$573$	−0.799715	−	0.799715i	−0.0334086	−	0.0334086i
$574$		0			0
$575$	2.11931	+	1.86781i	0.0883814	+	0.0778933i
$576$		0			0
$577$	−4.52857	+	28.5923i	−0.188527	+	1.19031i	0.693974	+	0.720000i	$0.255858\pi$
$577$	−4.52857	+	28.5923i	−0.188527	+	1.19031i	−0.882500	+	0.470311i	$0.844142\pi$
$578$		0			0
$579$	−12.6288	−	38.8673i	−0.524833	−	1.61527i
$580$		0			0
$581$	7.24801	+	5.26599i	0.300698	+	0.218470i
$582$		0			0
$583$	−25.2778	+	10.1395i	−1.04690	+	0.419934i
$584$		0			0
$585$	−79.4712	−	37.3885i	−3.28573	−	1.54582i
$586$		0			0
$587$	35.5782	+	18.1280i	1.46847	+	0.748222i	0.991427	−	0.130659i	$-0.0417094\pi$
$587$	35.5782	+	18.1280i	1.46847	+	0.748222i	0.477041	+	0.878881i	$0.341709\pi$
$588$		0			0
$589$	17.0943	−	12.4197i	0.704358	−	0.511746i
$590$		0			0
$591$	73.4422	+	23.8628i	3.02101	+	0.981585i
$592$		0			0
$593$	−15.3021	+	15.3021i	−0.628383	+	0.628383i	−0.947661	−	0.319278i	$-0.896560\pi$
$593$	−15.3021	+	15.3021i	−0.628383	+	0.628383i	0.319278	+	0.947661i	$0.396560\pi$
$594$		0			0
$595$	−3.61893	−	2.45899i	−0.148362	−	0.100809i
$596$		0			0
$597$	−2.16524	−	4.24952i	−0.0886174	−	0.173921i
$598$		0			0
$599$	10.9535	+	15.0762i	0.447547	+	0.615996i	0.971868	−	0.235525i	$-0.0756808\pi$
$599$	10.9535	+	15.0762i	0.447547	+	0.615996i	−0.524321	+	0.851521i	$0.675681\pi$
$600$		0			0
$601$	−9.80318	+	3.18525i	−0.399880	+	0.129929i	−0.502051	−	0.864838i	$-0.667421\pi$
$601$	−9.80318	+	3.18525i	−0.399880	+	0.129929i	0.102171	+	0.994767i	$0.467421\pi$
$602$		0			0
$603$	−2.94789	−	18.6123i	−0.120048	−	0.757950i
$604$		0			0
$605$	11.3645	+	21.8140i	0.462031	+	0.886864i
$606$		0			0
$607$	0.752433	+	4.75068i	0.0305403	+	0.192824i	0.998242	−	0.0592754i	$-0.0188790\pi$
$607$	0.752433	+	4.75068i	0.0305403	+	0.192824i	−0.967701	+	0.252099i	$0.918879\pi$
$608$		0			0
$609$	−2.69818	+	0.876693i	−0.109336	+	0.0355254i
$610$		0			0
$611$	0.261773	+	0.360300i	0.0105902	+	0.0145762i
$612$		0			0
$613$	5.12125	+	10.0510i	0.206846	+	0.405957i	0.971001	−	0.239075i	$-0.0768441\pi$
$613$	5.12125	+	10.0510i	0.206846	+	0.405957i	−0.764156	+	0.645032i	$0.776844\pi$
$614$		0			0
$615$	−5.64484	−	29.5783i	−0.227622	−	1.19271i
$616$		0			0
$617$	−11.3680	+	11.3680i	−0.457659	+	0.457659i	−0.897886	−	0.440227i	$-0.854898\pi$
$617$	−11.3680	+	11.3680i	−0.457659	+	0.457659i	0.440227	+	0.897886i	$0.354898\pi$
$618$		0			0
$619$	24.0772	+	7.82317i	0.967746	+	0.314440i	0.749906	−	0.661545i	$-0.230099\pi$
$619$	24.0772	+	7.82317i	0.967746	+	0.314440i	0.217840	+	0.975984i	$0.430099\pi$
$620$		0			0
$621$	4.31320	−	3.13373i	0.173083	−	0.125752i
$622$		0			0
$623$	−4.53819	−	2.31232i	−0.181819	−	0.0926413i
$624$		0			0
$625$	24.8019	−	3.14137i	0.992074	−	0.125655i
$626$		0			0
$627$	65.3747	−	26.2232i	2.61081	−	1.04725i
$628$		0			0
$629$	18.1606	+	13.1945i	0.724111	+	0.526097i
$630$		0			0
$631$	−15.0120	−	46.2023i	−0.597620	−	1.83929i	−0.541227	−	0.840877i	$-0.682040\pi$
$631$	−15.0120	−	46.2023i	−0.597620	−	1.83929i	−0.0563932	−	0.998409i	$-0.517960\pi$
$632$		0			0
$633$	7.48635	−	47.2669i	0.297556	−	1.87869i
$634$		0			0
$635$	1.24689	−	9.87659i	0.0494813	−	0.391940i
$636$		0			0
$637$	29.3663	+	29.3663i	1.16354	+	1.16354i
$638$		0			0
$639$		−	42.7408i		−	1.69080i
$640$		0			0
$641$	−6.22570	+	19.1607i	−0.245900	+	0.756804i	0.749587	+	0.661906i	$0.230252\pi$
$641$	−6.22570	+	19.1607i	−0.245900	+	0.756804i	−0.995487	+	0.0948974i	$0.969748\pi$
$642$		0			0
$643$	19.4799	+	3.08531i	0.768213	+	0.121673i	0.528227	−	0.849103i	$-0.322857\pi$
$643$	19.4799	+	3.08531i	0.768213	+	0.121673i	0.239986	+	0.970776i	$0.422857\pi$
$644$		0			0
$645$	−16.9874	−	4.93381i	−0.668878	−	0.194268i
$646$		0			0
$647$	−4.97430	+	0.787851i	−0.195560	+	0.0309736i	−0.253446	−	0.967350i	$-0.581564\pi$
$647$	−4.97430	+	0.787851i	−0.195560	+	0.0309736i	0.0578861	+	0.998323i	$0.481564\pi$
$648$		0			0
$649$	−11.5550	−	19.3401i	−0.453573	−	0.759164i
$650$		0			0
$651$	3.86508	−	5.31983i	0.151484	−	0.208500i
$652$		0			0
$653$	7.31163	−	14.3499i	0.286126	−	0.561554i	−0.702547	−	0.711637i	$-0.747954\pi$
$653$	7.31163	−	14.3499i	0.286126	−	0.561554i	0.988673	+	0.150083i	$0.0479541\pi$
$654$		0			0
$655$	38.2354	−	1.20469i	1.49398	−	0.0470713i
$656$		0			0
$657$	26.5359	−	13.5207i	1.03526	−	0.527493i
$658$		0			0
$659$	13.1583			0.512575			0.256287	−	0.966601i	$-0.417501\pi$
$659$	13.1583			0.512575			0.256287	+	0.966601i	$0.417501\pi$
$660$		0			0
$661$	16.6065			0.645919			0.322960	−	0.946413i	$-0.395322\pi$
$661$	16.6065			0.645919			0.322960	+	0.946413i	$0.395322\pi$
$662$		0			0
$663$	46.6265	−	23.7574i	1.81082	−	0.922660i
$664$		0			0
$665$	7.79543	−	8.30264i	0.302294	−	0.321962i
$666$		0			0
$667$	−0.332571	+	0.652708i	−0.0128772	+	0.0252730i
$668$		0			0
$669$	−31.0864	+	42.7868i	−1.20187	+	1.65423i
$670$		0			0
$671$	25.3942	−	29.0656i	0.980330	−	1.12206i
$672$		0			0
$673$	−8.18656	+	1.29662i	−0.315569	+	0.0499812i	−0.312210	−	0.950013i	$-0.601069\pi$
$673$	−8.18656	+	1.29662i	−0.315569	+	0.0499812i	−0.00335891	+	0.999994i	$0.501069\pi$
$674$		0			0
$675$	4.43260	−	46.9732i	0.170611	−	1.80800i
$676$		0			0
$677$	−22.9582	−	3.63622i	−0.882354	−	0.139751i	−0.301216	−	0.953556i	$-0.597392\pi$
$677$	−22.9582	−	3.63622i	−0.882354	−	0.139751i	−0.581138	+	0.813805i	$0.697392\pi$
$678$		0			0
$679$	−2.98689	+	9.19269i	−0.114626	+	0.352783i
$680$		0			0
$681$			6.71919i			0.257480i
$682$		0			0
$683$	10.7294	+	10.7294i	0.410548	+	0.410548i	0.881929	−	0.471382i	$-0.156245\pi$
$683$	10.7294	+	10.7294i	0.410548	+	0.410548i	−0.471382	+	0.881929i	$0.656245\pi$
$684$		0			0
$685$	7.11376	+	0.898092i	0.271803	+	0.0343143i
$686$		0			0
$687$	−3.43248	+	21.6718i	−0.130957	+	0.826832i
$688$		0			0
$689$	−16.2753	−	50.0903i	−0.620041	−	1.90829i
$690$		0			0
$691$	6.67401	+	4.84895i	0.253891	+	0.184463i	0.707450	−	0.706764i	$-0.249846\pi$
$691$	6.67401	+	4.84895i	0.253891	+	0.184463i	−0.453558	+	0.891227i	$0.649846\pi$
$692$		0			0
$693$	11.2945	−	9.42918i	0.429042	−	0.358185i
$694$		0			0
$695$	−5.01529	+	1.80607i	−0.190241	+	0.0685083i
$696$		0			0
$697$	10.7299	+	5.46716i	0.406424	+	0.207083i
$698$		0			0
$699$	16.0071	−	11.6298i	0.605443	−	0.439880i
$700$		0			0
$701$	−17.4538	−	5.67108i	−0.659220	−	0.214194i	−0.0397449	−	0.999210i	$-0.512655\pi$
$701$	−17.4538	−	5.67108i	−0.659220	−	0.214194i	−0.619475	+	0.785016i	$0.712655\pi$
$702$		0			0
$703$	−41.3165	+	41.3165i	−1.55828	+	1.55828i
$704$		0			0
$705$	−0.263589	+	0.387926i	−0.00992732	+	0.0146102i
$706$		0			0
$707$	−1.60556	−	3.15108i	−0.0603832	−	0.118509i
$708$		0			0
$709$	−9.81584	−	13.5103i	−0.368641	−	0.507391i	0.583890	−	0.811833i	$-0.301530\pi$
$709$	−9.81584	−	13.5103i	−0.368641	−	0.507391i	−0.952531	+	0.304442i	$0.901530\pi$
$710$		0			0
$711$	−25.1587	+	8.17456i	−0.943526	+	0.306570i
$712$		0			0
$713$	−0.265611	−	1.67700i	−0.00994720	−	0.0628041i
$714$		0			0
$715$	−43.5664	+	19.0894i	−1.62929	+	0.713902i
$716$		0			0
$717$	−7.70774	−	48.6647i	−0.287851	−	1.81742i
$718$		0			0
$719$	−41.7628	+	13.5696i	−1.55749	+	0.506059i	−0.956136	−	0.292924i	$-0.905372\pi$
$719$	−41.7628	+	13.5696i	−1.55749	+	0.506059i	−0.601354	+	0.798983i	$0.705372\pi$
$720$		0			0
$721$	−1.92857	−	2.65445i	−0.0718237	−	0.0988569i
$722$		0			0
$723$	5.73396	+	11.2535i	0.213248	+	0.418523i
$724$		0			0
$725$	2.38750	+	6.02728i	0.0886695	+	0.223848i
$726$		0			0
$727$	−16.0350	+	16.0350i	−0.594705	+	0.594705i	−0.938899	−	0.344194i	$-0.888152\pi$
$727$	−16.0350	+	16.0350i	−0.594705	+	0.594705i	0.344194	+	0.938899i	$0.388152\pi$
$728$		0			0
$729$	22.3168	+	7.25118i	0.826550	+	0.268562i
$730$		0			0
$731$	5.72327	−	4.15820i	0.211683	−	0.153797i
$732$		0			0
$733$	6.19423	+	3.15612i	0.228789	+	0.116574i	0.564628	−	0.825346i	$-0.309020\pi$
$733$	6.19423	+	3.15612i	0.228789	+	0.116574i	−0.335839	+	0.941919i	$0.609020\pi$
$734$		0			0
$735$	−18.6185	+	39.5747i	−0.686754	+	1.45973i
$736$		0			0
$737$	−8.64132	−	5.42978i	−0.318307	−	0.200008i
$738$		0			0
$739$	−18.2947	−	13.2919i	−0.672981	−	0.488949i	0.198041	−	0.980194i	$-0.436542\pi$
$739$	−18.2947	−	13.2919i	−0.672981	−	0.488949i	−0.871022	+	0.491245i	$0.836542\pi$
$740$		0			0
$741$	42.0920	+	129.546i	1.54629	+	4.75899i
$742$		0			0
$743$	7.69739	−	48.5994i	0.282390	−	1.78294i	−0.284022	−	0.958818i	$-0.591669\pi$
$743$	7.69739	−	48.5994i	0.282390	−	1.78294i	0.566412	−	0.824122i	$-0.308331\pi$
$744$		0			0
$745$	−19.5882	−	25.2488i	−0.717657	−	0.925044i
$746$		0			0
$747$	−53.5563	−	53.5563i	−1.95952	−	1.95952i
$748$		0			0
$749$		−	10.2502i		−	0.374533i
$750$		0			0
$751$	−7.00769	+	21.5674i	−0.255714	+	0.787007i	0.737974	+	0.674829i	$0.235783\pi$
$751$	−7.00769	+	21.5674i	−0.255714	+	0.787007i	−0.993688	+	0.112178i	$0.964217\pi$
$752$		0			0
$753$	−37.8743	−	5.99869i	−1.38021	−	0.218605i
$754$		0			0
$755$	−11.1813	+	38.4980i	−0.406930	+	1.40109i
$756$		0			0
$757$	1.74836	−	0.276914i	0.0635454	−	0.0100646i	−0.124581	−	0.992209i	$-0.539759\pi$
$757$	1.74836	−	0.276914i	0.0635454	−	0.0100646i	0.188126	+	0.982145i	$0.439759\pi$
$758$		0			0
$759$	0.507404	−	5.63734i	0.0184176	−	0.204623i
$760$		0			0
$761$	19.3732	−	26.6649i	0.702279	−	0.966604i	−0.297650	−	0.954675i	$-0.596203\pi$
$761$	19.3732	−	26.6649i	0.702279	−	0.966604i	0.999929	−	0.0119286i	$-0.00379709\pi$
$762$		0			0
$763$	3.06389	−	6.01322i	0.110920	−	0.217693i
$764$		0			0
$765$	26.9659	+	25.3185i	0.974953	+	0.915393i
$766$		0			0
$767$	38.8180	−	19.7788i	1.40164	−	0.714170i
$768$		0			0
$769$	−37.5969			−1.35578			−0.677889	−	0.735164i	$-0.737105\pi$
$769$	−37.5969			−1.35578			−0.677889	+	0.735164i	$0.737105\pi$
$770$		0			0
$771$	−3.61250			−0.130101
$772$		0			0
$773$	11.4475	−	5.83278i	0.411737	−	0.209790i	−0.235838	−	0.971792i	$-0.575783\pi$
$773$	11.4475	−	5.83278i	0.411737	−	0.209790i	0.647575	+	0.762002i	$0.275783\pi$
$774$		0			0
$775$	−12.6882	−	8.04932i	−0.455775	−	0.289140i
$776$		0			0
$777$	−8.25529	+	16.2019i	−0.296157	+	0.581240i
$778$		0			0
$779$	−18.4247	+	25.3594i	−0.660132	+	0.908594i
$780$		0			0
$781$	−17.4316	−	15.2297i	−0.623751	−	0.544962i
$782$		0			0
$783$	12.0844	−	1.91398i	0.431862	−	0.0684002i
$784$		0			0
$785$	6.55143	−	3.60237i	0.233831	−	0.128574i
$786$		0			0
$787$	14.4723	+	2.29218i	0.515881	+	0.0817075i	0.408946	−	0.912559i	$-0.365896\pi$
$787$	14.4723	+	2.29218i	0.515881	+	0.0817075i	0.106935	+	0.994266i	$0.465896\pi$
$788$		0			0
$789$	−28.0310	+	86.2704i	−0.997929	+	3.07131i
$790$		0			0
$791$			3.23038i			0.114859i
$792$		0			0
$793$	52.7765	+	52.7765i	1.87415	+	1.87415i
$794$		0			0
$795$	43.8231	−	33.9984i	1.55425	−	1.20580i
$796$		0			0
$797$	−0.264802	+	1.67189i	−0.00937977	+	0.0592215i	−0.991934	−	0.126753i	$-0.959544\pi$
$797$	−0.264802	+	1.67189i	−0.00937977	+	0.0592215i	0.982554	+	0.185975i	$0.0595443\pi$
$798$		0			0
$799$	−0.0579607	−	0.178385i	−0.00205050	−	0.00631080i
$800$		0			0
$801$	34.8357	+	25.3096i	1.23086	+	0.894270i
$802$		0			0
$803$	3.94111	−	15.6403i	0.139079	−	0.551934i
$804$		0			0
$805$	−0.310067	−	0.861025i	−0.0109284	−	0.0303471i
$806$		0			0
$807$	39.1898	+	19.9682i	1.37955	+	0.702915i
$808$		0			0
$809$	3.29877	−	2.39669i	0.115978	−	0.0842633i	−0.528284	−	0.849068i	$-0.677164\pi$
$809$	3.29877	−	2.39669i	0.115978	−	0.0842633i	0.644263	+	0.764804i	$0.277164\pi$
$810$		0			0
$811$	0.365104	+	0.118629i	0.0128205	+	0.00416564i	0.315420	−	0.948952i	$-0.397855\pi$
$811$	0.365104	+	0.118629i	0.0128205	+	0.00416564i	−0.302600	+	0.953118i	$0.597855\pi$
$812$		0			0
$813$	−28.5355	+	28.5355i	−1.00078	+	1.00078i
$814$		0			0
$815$	27.9902	−	5.34177i	0.980455	−	0.187114i
$816$		0			0
$817$	8.35987	+	16.4072i	0.292475	+	0.574014i
$818$		0			0
$819$	16.7237	+	23.0182i	0.584374	+	0.804322i
$820$		0			0
$821$	−37.9513	+	12.3311i	−1.32451	+	0.430359i	−0.884041	−	0.467410i	$-0.845187\pi$
$821$	−37.9513	+	12.3311i	−1.32451	+	0.430359i	−0.440467	+	0.897769i	$0.645187\pi$
$822$		0			0
$823$	5.16364	+	32.6020i	0.179993	+	1.13643i	0.897869	+	0.440262i	$0.145114\pi$
$823$	5.16364	+	32.6020i	0.179993	+	1.13643i	−0.717876	+	0.696171i	$0.754886\pi$
$824$		0			0
$825$	−34.4588	−	36.3551i	−1.19970	−	1.26572i
$826$		0			0
$827$	4.33802	+	27.3892i	0.150848	+	0.952415i	0.940730	+	0.339157i	$0.110142\pi$
$827$	4.33802	+	27.3892i	0.150848	+	0.952415i	−0.789882	+	0.613259i	$0.789858\pi$
$828$		0			0
$829$	−48.8463	+	15.8711i	−1.69650	+	0.551227i	−0.987996	−	0.154477i	$-0.950631\pi$
$829$	−48.8463	+	15.8711i	−1.69650	+	0.551227i	−0.708507	+	0.705704i	$0.750631\pi$
$830$		0			0
$831$	−37.8914	−	52.1530i	−1.31444	−	1.80917i
$832$		0			0
$833$	−7.94065	−	15.5844i	−0.275127	−	0.539967i
$834$		0			0
$835$	0.934860	−	0.178413i	0.0323522	−	0.00617422i
$836$		0			0
$837$	−20.0524	+	20.0524i	−0.693111	+	0.693111i
$838$		0			0
$839$	−1.93080	−	0.627354i	−0.0666585	−	0.0216587i	0.275498	−	0.961302i	$-0.411157\pi$
$839$	−1.93080	−	0.627354i	−0.0666585	−	0.0216587i	−0.342156	+	0.939643i	$0.611157\pi$
$840$		0			0
$841$	22.1014	−	16.0576i	0.762118	−	0.553711i
$842$		0			0
$843$	−64.5359	−	32.8827i	−2.22273	−	1.13254i
$844$		0			0
$845$	−21.3156	−	59.1913i	−0.733278	−	2.03624i
$846$		0			0
$847$	0.178889	−	7.96626i	0.00614670	−	0.273724i
$848$		0			0
$849$	34.9495	+	25.3923i	1.19946	+	0.871462i
$850$		0			0
$851$	1.45091	+	4.46545i	0.0497366	+	0.153073i
$852$		0			0
$853$	3.62270	−	22.8728i	0.124039	−	0.783150i	−0.844731	−	0.535190i	$-0.820240\pi$
$853$	3.62270	−	22.8728i	0.124039	−	0.783150i	0.968770	−	0.247960i	$-0.0797602\pi$
$854$		0			0
$855$	−76.0718	+	59.0172i	−2.60160	+	2.01835i
$856$		0			0
$857$	−2.65045	−	2.65045i	−0.0905378	−	0.0905378i	0.660387	−	0.750925i	$-0.270392\pi$
$857$	−2.65045	−	2.65045i	−0.0905378	−	0.0905378i	−0.750925	+	0.660387i	$0.770392\pi$
$858$		0			0
$859$			29.9156i			1.02071i	0.859965	+	0.510353i	$0.170485\pi$
$859$			29.9156i			1.02071i	−0.859965	+	0.510353i	$0.829515\pi$
$860$		0			0
$861$	−3.01446	+	9.27756i	−0.102733	+	0.316178i
$862$		0			0
$863$	−30.7625	−	4.87230i	−1.04717	−	0.165855i	−0.390939	−	0.920417i	$-0.627850\pi$
$863$	−30.7625	−	4.87230i	−1.04717	−	0.165855i	−0.656229	+	0.754561i	$0.727850\pi$
$864$		0			0
$865$	26.1208	−	14.3628i	0.888133	−	0.488349i
$866$		0			0
$867$	28.9501	−	4.58524i	0.983196	−	0.155723i
$868$		0			0
$869$	−5.63079	+	13.1737i	−0.191011	+	0.446886i
$870$		0			0
$871$	11.6003	−	15.9664i	0.393061	−	0.541002i
$872$		0			0
$873$	37.0977	−	72.8084i	1.25557	−	2.46419i
$874$		0			0
$875$	−7.53090	−	2.97958i	−0.254591	−	0.100728i
$876$		0			0
$877$	4.01742	−	2.04698i	0.135659	−	0.0691215i	−0.384844	−	0.922982i	$-0.625745\pi$
$877$	4.01742	−	2.04698i	0.135659	−	0.0691215i	0.520502	+	0.853860i	$0.325745\pi$
$878$		0			0
$879$	71.5844			2.41448
$880$		0			0
$881$	−12.6932			−0.427646			−0.213823	−	0.976872i	$-0.568592\pi$
$881$	−12.6932			−0.427646			−0.213823	+	0.976872i	$0.568592\pi$
$882$		0			0
$883$	−12.0876	+	6.15894i	−0.406780	+	0.207265i	−0.645394	−	0.763850i	$-0.723307\pi$
$883$	−12.0876	+	6.15894i	−0.406780	+	0.207265i	0.238614	+	0.971114i	$0.423307\pi$
$884$		0			0
$885$	33.4476	+	31.4043i	1.12433	+	1.05564i
$886$		0			0
$887$	11.6610	−	22.8860i	0.391538	−	0.768436i	−0.608140	−	0.793830i	$-0.708084\pi$
$887$	11.6610	−	22.8860i	0.391538	−	0.768436i	0.999678	+	0.0253938i	$0.00808397\pi$
$888$		0			0
$889$	−1.89560	+	2.60906i	−0.0635762	+	0.0875052i
$890$		0			0
$891$	−28.8459	+	17.2344i	−0.966374	+	0.577374i
$892$		0			0
$893$	0.482211	−	0.0763748i	0.0161366	−	0.00255578i
$894$		0			0
$895$	13.3422	−	45.9379i	0.445979	−	1.53554i
$896$		0			0
$897$	10.8108	+	1.71226i	0.360962	+	0.0571707i
$898$		0			0
$899$	1.20409	−	3.70581i	0.0401586	−	0.123596i
$900$		0			0
$901$			22.1816i			0.738975i
$902$		0			0
$903$	4.05214	+	4.05214i	0.134847	+	0.134847i
$904$		0			0
$905$	−10.0137	−	12.9075i	−0.332868	−	0.429059i
$906$		0			0
$907$	0.636482	−	4.01859i	0.0211340	−	0.133435i	−0.974865	−	0.222795i	$-0.928482\pi$
$907$	0.636482	−	4.01859i	0.0211340	−	0.133435i	0.995999	+	0.0893597i	$0.0284821\pi$
$908$		0			0
$909$	9.23902	+	28.4348i	0.306439	+	0.943122i
$910$		0			0
$911$	−39.9673	−	29.0380i	−1.32418	−	0.962070i	−0.999870	−	0.0161180i	$-0.994869\pi$
$911$	−39.9673	−	29.0380i	−1.32418	−	0.962070i	−0.324306	−	0.945952i	$-0.605131\pi$
$912$		0			0
$913$	−40.9262	+	2.75907i	−1.35446	+	0.0913118i
$914$		0			0
$915$	−33.4608	+	71.1228i	−1.10618	+	2.35125i
$916$		0			0
$917$	−11.0420	−	5.62618i	−0.364639	−	0.185793i
$918$		0			0
$919$	9.17092	−	6.66307i	0.302521	−	0.219794i	−0.426160	−	0.904648i	$-0.640134\pi$
$919$	9.17092	−	6.66307i	0.302521	−	0.219794i	0.728681	+	0.684854i	$0.240134\pi$
$920$		0			0
$921$	42.8935	+	13.9369i	1.41339	+	0.459237i
$922$		0			0
$923$	31.6518	−	31.6518i	1.04183	−	1.04183i
$924$		0			0
$925$	38.1371	+	16.4961i	1.25394	+	0.542388i
$926$		0			0
$927$	12.5930	+	24.7151i	0.413607	+	0.811750i
$928$		0			0
$929$	10.3144	+	14.1966i	0.338404	+	0.465774i	0.943975	−	0.330018i	$-0.107055\pi$
$929$	10.3144	+	14.1966i	0.338404	+	0.465774i	−0.605570	+	0.795792i	$0.707055\pi$
$930$		0			0
$931$	43.2993	−	14.0688i	1.41908	−	0.461087i
$932$		0			0
$933$	−2.02439	−	12.7815i	−0.0662755	−	0.418447i
$934$		0			0
$935$	19.9347	−	1.97620i	0.651934	−	0.0646285i
$936$		0			0
$937$	−6.90315	−	43.5848i	−0.225516	−	1.42385i	−0.797367	−	0.603495i	$-0.793774\pi$
$937$	−6.90315	−	43.5848i	−0.225516	−	1.42385i	0.571851	−	0.820357i	$-0.306226\pi$
$938$		0			0
$939$	−83.2223	+	27.0406i	−2.71586	+	0.882436i
$940$		0			0
$941$	−7.71688	−	10.6214i	−0.251563	−	0.346247i	0.664495	−	0.747293i	$-0.268647\pi$
$941$	−7.71688	−	10.6214i	−0.251563	−	0.346247i	−0.916058	+	0.401046i	$0.868647\pi$
$942$		0			0
$943$	1.14353	+	2.24430i	0.0372384	+	0.0730846i
$944$		0			0
$945$	−8.59034	+	12.6425i	−0.279444	+	0.411261i
$946$		0			0
$947$	−14.1055	+	14.1055i	−0.458367	+	0.458367i	−0.898119	−	0.439752i	$-0.855066\pi$
$947$	−14.1055	+	14.1055i	−0.458367	+	0.458367i	0.439752	+	0.898119i	$0.355066\pi$
$948$		0			0
$949$	29.6640	+	9.63843i	0.962935	+	0.312877i
$950$		0			0
$951$	−20.1394	+	14.6322i	−0.653066	+	0.474480i
$952$		0			0
$953$	38.2426	+	19.4856i	1.23880	+	0.631199i	0.945749	−	0.324898i	$-0.105330\pi$
$953$	38.2426	+	19.4856i	1.23880	+	0.631199i	0.293050	+	0.956097i	$0.405330\pi$
$954$		0			0
$955$	0.787706	−	0.283664i	0.0254896	−	0.00917915i
$956$		0			0
$957$	6.91086	−	10.9984i	0.223396	−	0.355528i
$958$		0			0
$959$	−1.87922	−	1.36533i	−0.0606831	−	0.0440888i
$960$		0			0
$961$	−6.78870	−	20.8935i	−0.218990	−	0.673982i
$962$		0			0
$963$	−13.5559	+	85.5884i	−0.436832	+	2.75805i
$964$		0			0
$965$	30.0149	+	3.78929i	0.966214	+	0.121982i
$966$		0			0
$967$	−10.8777	−	10.8777i	−0.349803	−	0.349803i	0.510233	−	0.860036i	$-0.329559\pi$
$967$	−10.8777	−	10.8777i	−0.349803	−	0.349803i	−0.860036	+	0.510233i	$0.829559\pi$
$968$		0			0
$969$		−	57.3670i		−	1.84289i
$970$		0			0
$971$	6.16511	−	18.9743i	0.197848	−	0.608913i	−0.802084	−	0.597212i	$-0.796275\pi$
$971$	6.16511	−	18.9743i	0.197848	−	0.608913i	0.999932	−	0.0117013i	$-0.00372472\pi$
$972$		0			0
$973$	1.70561	+	0.270143i	0.0546794	+	0.00866037i
$974$		0			0
$975$	74.6263	−	61.7566i	2.38995	−	1.97779i
$976$		0			0
$977$	24.5475	−	3.88795i	0.785345	−	0.124386i	0.249133	−	0.968469i	$-0.419854\pi$
$977$	24.5475	−	3.88795i	0.785345	−	0.124386i	0.536213	+	0.844083i	$0.319854\pi$
$978$		0			0
$979$	22.7353	−	5.18903i	0.726622	−	0.165842i
$980$		0			0
$981$	−33.5358	+	46.1581i	−1.07072	+	1.47372i
$982$		0			0
$983$	−13.2129	+	25.9317i	−0.421424	+	0.827092i	0.578510	+	0.815675i	$0.303634\pi$
$983$	−13.2129	+	25.9317i	−0.421424	+	0.827092i	−0.999935	+	0.0114171i	$0.996366\pi$
$984$		0			0
$985$	−39.1289	+	41.6748i	−1.24675	+	1.32787i
$986$		0			0
$987$	0.135377	−	0.0689780i	0.00430910	−	0.00219560i
$988$		0			0
$989$	1.47970			0.0470516
$990$		0			0
$991$	−48.5379			−1.54186			−0.770929	−	0.636921i	$-0.780208\pi$
$991$	−48.5379			−1.54186			−0.770929	+	0.636921i	$0.780208\pi$
$992$		0			0
$993$	−66.3481	+	33.8060i	−2.10549	+	1.07280i
$994$		0			0
$995$	3.52887	−	0.111185i	0.111873	−	0.00352481i
$996$		0			0
$997$	11.8187	−	23.1955i	0.374303	−	0.734610i	−0.624624	−	0.780925i	$-0.714748\pi$
$997$	11.8187	−	23.1955i	0.374303	−	0.734610i	0.998927	+	0.0463152i	$0.0147479\pi$
$998$		0			0
$999$	46.0941	−	63.4430i	1.45835	−	2.00725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.u.a.73.1	✓	48
4.3	odd	2		880.2.cm.b.513.6		48
5.2	odd	4	inner	220.2.u.a.117.6	yes	48
11.8	odd	10	inner	220.2.u.a.173.6	yes	48
20.7	even	4		880.2.cm.b.337.1		48
44.19	even	10		880.2.cm.b.833.1		48
55.52	even	20	inner	220.2.u.a.217.1	yes	48
220.107	odd	20		880.2.cm.b.657.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.73.1	✓	48	1.1	even	1	trivial
220.2.u.a.117.6	yes	48	5.2	odd	4	inner
220.2.u.a.173.6	yes	48	11.8	odd	10	inner
220.2.u.a.217.1	yes	48	55.52	even	20	inner
880.2.cm.b.337.1		48	20.7	even	4
880.2.cm.b.513.6		48	4.3	odd	2
880.2.cm.b.657.6		48	220.107	odd	20
880.2.cm.b.833.1		48	44.19	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.69137 + 1.37132i) q^{3} +(-0.0704176 - 2.23496i) q^{5} +(-0.328865 + 0.645435i) q^{7} +(3.59960 - 4.95443i) q^{9} +(-0.737999 - 3.23347i) q^{11} +(6.33471 - 1.00332i) q^{13} +(3.25437 + 5.91854i) q^{15} +(-2.66791 - 0.422556i) q^{17} +(2.17270 - 6.68689i) q^{19} -2.18809i q^{21} +(-0.399505 - 0.399505i) q^{23} +(-4.99008 + 0.314761i) q^{25} +(-1.47617 + 9.32020i) q^{27} +(-0.400667 - 1.23312i) q^{29} +(2.43127 + 1.76642i) q^{31} +(6.42037 + 7.69045i) q^{33} +(1.46568 + 0.689551i) q^{35} +(-7.40461 - 3.77284i) q^{37} +(-15.6732 + 11.3872i) q^{39} +(-4.24004 - 1.37767i) q^{41} +(-1.85191 + 1.85191i) q^{43} +(-11.3264 - 7.69608i) q^{45} +(0.0315244 + 0.0618701i) q^{47} +(3.80606 + 5.23860i) q^{49} +(7.75981 - 2.52131i) q^{51} +(-1.28461 - 8.11073i) q^{53} +(-7.17471 + 1.87709i) q^{55} +(3.32233 + 20.9764i) q^{57} +(6.46029 - 2.09908i) q^{59} +(6.84018 + 9.41470i) q^{61} +(2.01397 + 3.95265i) q^{63} +(-2.68845 - 14.0872i) q^{65} +(2.17585 - 2.17585i) q^{67} +(1.62307 + 0.527366i) q^{69} +(5.64630 - 4.10228i) q^{71} +(4.33309 + 2.20782i) q^{73} +(12.9985 - 7.69015i) q^{75} +(2.32970 + 0.587048i) q^{77} +(-3.49465 - 2.53901i) q^{79} +(-3.13079 - 9.63559i) q^{81} +(1.93474 - 12.2155i) q^{83} +(-0.756527 + 5.99243i) q^{85} +(2.76935 + 2.76935i) q^{87} +7.03122i q^{89} +(-1.43569 + 4.41860i) q^{91} +(-8.96579 - 1.42004i) q^{93} +(-15.0979 - 4.38502i) q^{95} +(13.1791 - 2.08736i) q^{97} +(-18.6765 - 7.98286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55}+ \cdots + 6 q^{97}+O(q^{100}) \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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