LMFDB - Embedded newform 880.2.cm.b.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(17,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 5, 18]))

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

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

chi := DirichletCharacter("880.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cm (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			337.1
Character	$\chi$	$=$	880.337
Dual form			880.2.cm.b.833.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37132 - 2.69137i) q^{3} +(2.10381 + 0.757611i) q^{5} +(0.645435 + 0.328865i) q^{7} +(-3.59960 + 4.95443i) q^{9} +(0.737999 + 3.23347i) q^{11} +(-1.00332 - 6.33471i) q^{13} +(-0.845991 - 6.70107i) q^{15} +(0.422556 - 2.66791i) q^{17} +(2.17270 - 6.68689i) q^{19} -2.18809i q^{21} +(0.399505 - 0.399505i) q^{23} +(3.85205 + 3.18774i) q^{25} +(9.32020 + 1.47617i) q^{27} +(0.400667 + 1.23312i) q^{29} +(-2.43127 - 1.76642i) q^{31} +(7.69045 - 6.42037i) q^{33} +(1.10872 + 1.18086i) q^{35} +(3.77284 - 7.40461i) q^{37} +(-15.6732 + 11.3872i) q^{39} +(-4.24004 - 1.37767i) q^{41} +(-1.85191 - 1.85191i) q^{43} +(-11.3264 + 7.69608i) q^{45} +(0.0618701 - 0.0315244i) q^{47} +(-3.80606 - 5.23860i) q^{49} +(-7.75981 + 2.52131i) q^{51} +(-8.11073 + 1.28461i) q^{53} +(-0.897106 + 7.36174i) q^{55} +(-20.9764 + 3.32233i) q^{57} +(6.46029 - 2.09908i) q^{59} +(6.84018 + 9.41470i) q^{61} +(-3.95265 + 2.01397i) q^{63} +(2.68845 - 14.0872i) q^{65} +(-2.17585 - 2.17585i) q^{67} +(-1.62307 - 0.527366i) q^{69} +(-5.64630 + 4.10228i) q^{71} +(2.20782 - 4.33309i) q^{73} +(3.29700 - 14.7387i) q^{75} +(-0.587048 + 2.32970i) q^{77} +(-3.49465 - 2.53901i) q^{79} +(-3.13079 - 9.63559i) q^{81} +(12.2155 + 1.93474i) q^{83} +(2.91022 - 5.29265i) q^{85} +(2.76935 - 2.76935i) q^{87} -7.03122i q^{89} +(1.43569 - 4.41860i) q^{91} +(-1.42004 + 8.96579i) q^{93} +(9.63702 - 12.4219i) q^{95} +(2.08736 + 13.1791i) q^{97} +(-18.6765 - 7.98286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.37132	−	2.69137i	−0.791733	−	1.55386i	−0.832065	−	0.554678i	$-0.812841\pi$
$3$	−1.37132	−	2.69137i	−0.791733	−	1.55386i	0.0403316	−	0.999186i	$-0.487159\pi$
$4$		0			0
$5$	2.10381	+	0.757611i	0.940853	+	0.338814i
$5$	2.10381	+	0.757611i	0.940853	+	0.338814i
$6$		0			0
$7$	0.645435	+	0.328865i	0.243951	+	0.124299i	0.571692	−	0.820468i	$-0.306287\pi$
$7$	0.645435	+	0.328865i	0.243951	+	0.124299i	−0.327741	+	0.944768i	$0.606287\pi$
$8$		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
$13$	−1.00332	−	6.33471i	−0.278271	−	1.75693i	−0.590605	−	0.806961i	$-0.701111\pi$
$13$	−1.00332	−	6.33471i	−0.278271	−	1.75693i	0.312334	−	0.949972i	$-0.398889\pi$
$14$		0			0
$15$	−0.845991	−	6.70107i	−0.218434	−	1.73021i
$16$		0			0
$17$	0.422556	−	2.66791i	0.102485	−	0.647064i	−0.881954	−	0.471336i	$-0.843772\pi$
$17$	0.422556	−	2.66791i	0.102485	−	0.647064i	0.984439	−	0.175728i	$-0.0562280\pi$
$18$		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	$-0.731239\pi$
$23$	0.399505	−	0.399505i	0.0833026	−	0.0833026i	0.747530	+	0.664228i	$0.231239\pi$
$24$		0			0
$25$	3.85205	+	3.18774i	0.770410	+	0.637549i
$26$		0			0
$27$	9.32020	+	1.47617i	1.79367	+	0.284090i
$28$		0			0
$29$	0.400667	+	1.23312i	0.0744019	+	0.228986i	0.981341	−	0.192277i	$-0.0615872\pi$
$29$	0.400667	+	1.23312i	0.0744019	+	0.228986i	−0.906939	+	0.421262i	$0.861587\pi$
$30$		0			0
$31$	−2.43127	−	1.76642i	−0.436669	−	0.317259i	0.347641	−	0.937628i	$-0.386983\pi$
$31$	−2.43127	−	1.76642i	−0.436669	−	0.317259i	−0.784310	+	0.620369i	$0.786983\pi$
$32$		0			0
$33$	7.69045	−	6.42037i	1.33874	−	1.11764i
$34$		0			0
$35$	1.10872	+	1.18086i	0.187408	+	0.199602i
$36$		0			0
$37$	3.77284	−	7.40461i	0.620250	−	1.21731i	−0.340591	−	0.940211i	$-0.610627\pi$
$37$	3.77284	−	7.40461i	0.620250	−	1.21731i	0.960842	−	0.277098i	$-0.0893728\pi$
$38$		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	0.551657	−	0.834071i	$-0.313996\pi$
$43$	−1.85191	−	1.85191i	−0.282414	−	0.282414i	−0.834071	+	0.551657i	$0.813996\pi$
$44$		0			0
$45$	−11.3264	+	7.69608i	−1.68844	+	1.14726i
$46$		0			0
$47$	0.0618701	−	0.0315244i	0.00902468	−	0.00459830i	−0.449472	−	0.893294i	$-0.648388\pi$
$47$	0.0618701	−	0.0315244i	0.00902468	−	0.00459830i	0.458497	+	0.888696i	$0.348388\pi$
$48$		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
$53$	−8.11073	+	1.28461i	−1.11410	+	0.176455i	−0.686228	−	0.727386i	$-0.740735\pi$
$53$	−8.11073	+	1.28461i	−1.11410	+	0.176455i	−0.427867	+	0.903842i	$0.640735\pi$
$54$		0			0
$55$	−0.897106	+	7.36174i	−0.120966	+	0.992657i
$56$		0			0
$57$	−20.9764	+	3.32233i	−2.77839	+	0.440054i
$58$		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
$63$	−3.95265	+	2.01397i	−0.497987	+	0.253737i
$64$		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	$-0.310189\pi$
$67$	−2.17585	−	2.17585i	−0.265822	−	0.265822i	−0.827414	+	0.561592i	$0.810189\pi$
$68$		0			0
$69$	−1.62307	−	0.527366i	−0.195394	−	0.0634875i
$70$		0			0
$71$	−5.64630	+	4.10228i	−0.670093	+	0.486851i	−0.870056	−	0.492952i	$-0.835918\pi$
$71$	−5.64630	+	4.10228i	−0.670093	+	0.486851i	0.199963	+	0.979803i	$0.435918\pi$
$72$		0			0
$73$	2.20782	−	4.33309i	0.258406	−	0.507150i	−0.724959	−	0.688792i	$-0.758141\pi$
$73$	2.20782	−	4.33309i	0.258406	−	0.507150i	0.983365	+	0.181642i	$0.0581413\pi$
$74$		0			0
$75$	3.29700	−	14.7387i	0.380705	−	1.70188i
$76$		0			0
$77$	−0.587048	+	2.32970i	−0.0669003	+	0.265494i
$78$		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
$83$	12.2155	+	1.93474i	1.34082	+	0.212365i	0.785288	−	0.619130i	$-0.212515\pi$
$83$	12.2155	+	1.93474i	1.34082	+	0.212365i	0.555532	+	0.831495i	$0.312515\pi$
$84$		0			0
$85$	2.91022	−	5.29265i	0.315658	−	0.574069i
$86$		0			0
$87$	2.76935	−	2.76935i	0.296906	−	0.296906i
$88$		0			0
$89$		−	7.03122i		−	0.745308i	−0.927970	−	0.372654i	$-0.878448\pi$
$89$		−	7.03122i		−	0.745308i	0.927970	−	0.372654i	$-0.121552\pi$
$90$		0			0
$91$	1.43569	−	4.41860i	0.150501	−	0.463195i
$92$		0			0
$93$	−1.42004	+	8.96579i	−0.147251	+	0.929709i
$94$		0			0
$95$	9.63702	−	12.4219i	0.988737	−	1.27446i
$96$		0			0
$97$	2.08736	+	13.1791i	0.211939	+	1.33813i	0.832522	+	0.553991i	$0.186896\pi$
$97$	2.08736	+	13.1791i	0.211939	+	1.33813i	−0.620583	+	0.784141i	$0.713104\pi$
$98$		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
$103$	−4.03577	−	2.05633i	−0.397656	−	0.202616i	0.243715	−	0.969847i	$-0.421634\pi$
$103$	−4.03577	−	2.05633i	−0.397656	−	0.202616i	−0.641371	+	0.767231i	$0.721634\pi$
$104$		0			0
$105$	1.65772	−	4.60332i	0.161777	−	0.449238i
$106$		0			0
$107$	6.42400	+	12.6078i	0.621032	+	1.21884i	0.960514	+	0.278231i	$0.0897482\pi$
$107$	6.42400	+	12.6078i	0.621032	+	1.21884i	−0.339482	+	0.940613i	$0.610252\pi$
$108$		0			0
$109$	9.31654			0.892363			0.446181	−	0.894943i	$-0.352784\pi$
$109$	9.31654			0.892363			0.446181	+	0.894943i	$0.352784\pi$
$110$		0			0
$111$	−25.1023			−2.38261
$112$		0			0
$113$	−2.02455	−	3.97341i	−0.190454	−	0.373787i	0.775958	−	0.630784i	$-0.217267\pi$
$113$	−2.02455	−	3.97341i	−0.190454	−	0.373787i	−0.966412	+	0.256997i	$0.917267\pi$
$114$		0			0
$115$	1.14315	−	0.537814i	0.106600	−	0.0501514i
$116$		0			0
$117$	34.9964	+	17.8316i	3.23542	+	1.64853i
$118$		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
$123$	2.10663	+	13.3007i	0.189949	+	1.19929i
$124$		0			0
$125$	5.68892	+	9.62477i	0.508832	+	0.860866i
$126$		0			0
$127$	0.696447	−	4.39719i	0.0617997	−	0.390188i	−0.937329	−	0.348446i	$-0.886709\pi$
$127$	0.696447	−	4.39719i	0.0617997	−	0.390188i	0.999128	−	0.0417415i	$-0.0132906\pi$
$128$		0			0
$129$	−2.44461	+	7.52375i	−0.215236	+	0.662429i
$130$		0			0
$131$		−	17.1079i		−	1.49472i	−0.664419	−	0.747360i	$-0.731321\pi$
$131$		−	17.1079i		−	1.49472i	0.664419	−	0.747360i	$-0.268679\pi$
$132$		0			0
$133$	3.60142	−	3.60142i	0.312283	−	0.312283i
$134$		0			0
$135$	18.4896	+	10.1667i	1.59133	+	0.875008i
$136$		0			0
$137$	−3.16714	−	0.501626i	−0.270587	−	0.0428568i	0.0196662	−	0.999807i	$-0.493740\pi$
$137$	−3.16714	−	0.501626i	−0.270587	−	0.0428568i	−0.290254	+	0.956950i	$0.593740\pi$
$138$		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
$143$	19.7427	−	7.91922i	1.65097	−	0.662239i
$144$		0			0
$145$	−0.0913023	+	2.89781i	−0.00758225	+	0.240650i
$146$		0			0
$147$	−8.87967	+	17.4273i	−0.732383	+	1.43738i
$148$		0			0
$149$	−11.5619	+	8.40019i	−0.947185	+	0.688170i	−0.950139	−	0.311825i	$-0.899060\pi$
$149$	−11.5619	+	8.40019i	−0.947185	+	0.688170i	0.00295440	+	0.999996i	$0.499060\pi$
$150$		0			0
$151$	17.0508	+	5.54015i	1.38758	+	0.450851i	0.905153	−	0.425087i	$-0.139756\pi$
$151$	17.0508	+	5.54015i	1.38758	+	0.450851i	0.482424	+	0.875938i	$0.339756\pi$
$152$		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
$157$	−2.97917	+	1.51796i	−0.237764	+	0.121147i	−0.568813	−	0.822467i	$-0.692597\pi$
$157$	−2.97917	+	1.51796i	−0.237764	+	0.121147i	0.331050	+	0.943613i	$0.392597\pi$
$158$		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
$163$	−12.5866	+	1.99353i	−0.985862	+	0.156145i	−0.628490	−	0.777817i	$-0.716327\pi$
$163$	−12.5866	+	1.99353i	−0.985862	+	0.156145i	−0.357371	+	0.933962i	$0.616327\pi$
$164$		0			0
$165$	21.0434	−	7.68087i	1.63823	−	0.597955i
$166$		0			0
$167$	0.420387	−	0.0665828i	0.0325306	−	0.00515233i	−0.140148	−	0.990131i	$-0.544758\pi$
$167$	0.420387	−	0.0665828i	0.0325306	−	0.00515233i	0.172679	+	0.984978i	$0.444758\pi$
$168$		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
$173$	11.8780	−	6.05217i	0.903071	−	0.460138i	0.0601590	−	0.998189i	$-0.480839\pi$
$173$	11.8780	−	6.05217i	0.903071	−	0.460138i	0.842912	+	0.538051i	$0.180839\pi$
$174$		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
$183$	15.9584	−	31.3201i	1.17968	−	2.31525i
$184$		0			0
$185$	13.5472	−	12.7196i	0.996006	−	0.935161i
$186$		0			0
$187$	8.93847	−	0.602593i	0.653646	−	0.0440660i
$188$		0			0
$189$	5.53012	+	4.01786i	0.402257	+	0.292257i
$190$		0			0
$191$	−0.115702	−	0.356093i	−0.00837188	−	0.0257660i	0.946783	−	0.321872i	$-0.104312\pi$
$191$	−0.115702	−	0.356093i	−0.00837188	−	0.0257660i	−0.955155	+	0.296106i	$0.904312\pi$
$192$		0			0
$193$	13.3630	+	2.11650i	0.961893	+	0.152349i	0.617582	−	0.786507i	$-0.288112\pi$
$193$	13.3630	+	2.11650i	0.961893	+	0.152349i	0.344311	+	0.938856i	$0.388112\pi$
$194$		0			0
$195$	−41.6006	+	12.0824i	−2.97908	+	0.865241i
$196$		0			0
$197$	18.0772	−	18.0772i	1.28795	−	1.28795i	0.351916	−	0.936032i	$-0.385530\pi$
$197$	18.0772	−	18.0772i	1.28795	−	1.28795i	0.936032	−	0.351916i	$-0.114470\pi$
$198$		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
$203$	−0.146928	+	0.927667i	−0.0103123	+	0.0651094i
$204$		0			0
$205$	−7.87650	−	6.11066i	−0.550119	−	0.426787i
$206$		0			0
$207$	0.541260	+	3.41738i	0.0376201	+	0.237524i
$208$		0			0
$209$	23.2253	+	2.09046i	1.60653	+	0.144600i
$210$		0			0
$211$	9.31244	−	12.8175i	0.641095	−	0.882391i	−0.357579	−	0.933883i	$-0.616398\pi$
$211$	9.31244	−	12.8175i	0.641095	−	0.882391i	0.998673	+	0.0514920i	$0.0163977\pi$
$212$		0			0
$213$	18.7837	+	9.57076i	1.28704	+	0.655777i
$214$		0			0
$215$	−2.49304	−	5.29910i	−0.170024	−	0.361396i
$216$		0			0
$217$	−0.988311	−	1.93967i	−0.0670910	−	0.131673i
$218$		0			0
$219$	−14.6896			−0.992630
$220$		0			0
$221$	−17.3244			−1.16537
$222$		0			0
$223$	7.94888	+	15.6005i	0.532296	+	1.04469i	0.987985	+	0.154551i	$0.0493930\pi$
$223$	7.94888	+	15.6005i	0.532296	+	1.04469i	−0.455689	+	0.890139i	$0.650607\pi$
$224$		0			0
$225$	−29.6593	+	7.61009i	−1.97729	+	0.507339i
$226$		0			0
$227$	−1.98201	−	1.00988i	−0.131550	−	0.0670283i	0.386977	−	0.922090i	$-0.373519\pi$
$227$	−1.98201	−	1.00988i	−0.131550	−	0.0670283i	−0.518527	+	0.855061i	$0.673519\pi$
$228$		0			0
$229$	−4.26974	+	5.87679i	−0.282152	+	0.388349i	−0.926445	−	0.376429i	$-0.877152\pi$
$229$	−4.26974	+	5.87679i	−0.282152	+	0.388349i	0.644293	+	0.764779i	$0.277152\pi$
$230$		0			0
$231$	7.07512	−	1.61480i	0.465509	−	0.106246i
$232$		0			0
$233$	1.02469	+	6.46966i	0.0671299	+	0.423841i	0.998250	+	0.0591295i	$0.0188325\pi$
$233$	1.02469	+	6.46966i	0.0671299	+	0.423841i	−0.931120	+	0.364712i	$0.881168\pi$
$234$		0			0
$235$	0.154046	−	0.0194479i	0.0100489	−	0.00126864i
$236$		0			0
$237$	−2.04113	+	12.8872i	−0.132586	+	0.837115i
$238$		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
$245$	−4.03842	−	13.9045i	−0.258005	−	0.888328i
$246$		0			0
$247$	−44.5394	−	7.05435i	−2.83398	−	0.448858i
$248$		0			0
$249$	−11.5442	−	35.5295i	−0.731586	−	2.25159i
$250$		0			0
$251$	−10.2704	−	7.46191i	−0.648264	−	0.470992i	0.214415	−	0.976743i	$-0.431215\pi$
$251$	−10.2704	−	7.46191i	−0.648264	−	0.470992i	−0.862680	+	0.505751i	$0.831215\pi$
$252$		0			0
$253$	1.58662	+	0.996955i	0.0997502	+	0.0626780i
$254$		0			0
$255$	−18.2353	−	0.574547i	−1.14194	−	0.0359795i
$256$		0			0
$257$	−0.542953	+	1.06560i	−0.0338685	+	0.0664706i	−0.907321	−	0.420439i	$-0.861876\pi$
$257$	−0.542953	+	1.06560i	−0.0338685	+	0.0664706i	0.873452	+	0.486910i	$0.161876\pi$
$258$		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	0.921853	+	0.387540i	$0.126675\pi$
$263$	21.2348	+	21.2348i	1.30939	+	1.30939i	0.387540	+	0.921853i	$0.373325\pi$
$264$		0			0
$265$	−18.0367	−	3.44220i	−1.10799	−	0.211453i
$266$		0			0
$267$	−18.9236	+	9.64207i	−1.15811	+	0.590085i
$268$		0			0
$269$	8.55891	+	11.7803i	0.521846	+	0.718259i	0.985860	−	0.167568i	$-0.0535915\pi$
$269$	8.55891	+	11.7803i	0.521846	+	0.718259i	−0.464015	+	0.885828i	$0.653591\pi$
$270$		0			0
$271$	−12.7061	+	4.12848i	−0.771844	+	0.250787i	−0.668354	−	0.743843i	$-0.733001\pi$
$271$	−12.7061	+	4.12848i	−0.771844	+	0.250787i	−0.103490	+	0.994631i	$0.533001\pi$
$272$		0			0
$273$	−13.8609	+	2.19535i	−0.838899	+	0.132869i
$274$		0			0
$275$	−7.46468	+	14.8081i	−0.450137	+	0.892959i
$276$		0			0
$277$	−21.0789	+	3.33857i	−1.26651	+	0.200595i	−0.753305	−	0.657671i	$-0.771542\pi$
$277$	−21.0789	+	3.33857i	−1.26651	+	0.200595i	−0.513205	+	0.858266i	$0.671542\pi$
$278$		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
$283$	12.7430	−	6.49288i	0.757493	−	0.385962i	−0.0321865	−	0.999482i	$-0.510247\pi$
$283$	12.7430	−	6.49288i	0.757493	−	0.385962i	0.789679	+	0.613520i	$0.210247\pi$
$284$		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
$293$	−10.7590	+	21.1158i	−0.628548	+	1.23360i	0.328729	+	0.944424i	$0.393380\pi$
$293$	−10.7590	+	21.1158i	−0.628548	+	1.23360i	−0.957277	+	0.289171i	$0.906620\pi$
$294$		0			0
$295$	15.1815	+	0.478329i	0.883902	+	0.0278494i
$296$		0			0
$297$	2.10512	+	31.2260i	0.122152	+	1.81192i
$298$		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
$303$	14.5653	+	2.30692i	0.836757	+	0.132529i
$304$		0			0
$305$	7.25777	+	24.9890i	0.415579	+	1.43086i
$306$		0			0
$307$	−10.5579	+	10.5579i	−0.602570	+	0.602570i	−0.940994	−	0.338424i	$-0.890106\pi$
$307$	−10.5579	+	10.5579i	−0.602570	+	0.602570i	0.338424	+	0.940994i	$0.390106\pi$
$308$		0			0
$309$			13.6816i			0.778322i
$310$		0			0
$311$	1.32389	−	4.07451i	0.0750708	−	0.231044i	−0.906479	−	0.422251i	$-0.861240\pi$
$311$	1.32389	−	4.07451i	0.0750708	−	0.231044i	0.981550	+	0.191207i	$0.0612401\pi$
$312$		0			0
$313$	4.53183	−	28.6128i	0.256154	−	1.61729i	−0.439038	−	0.898468i	$-0.644681\pi$
$313$	4.53183	−	28.6128i	0.256154	−	1.61729i	0.695192	−	0.718824i	$-0.255319\pi$
$314$		0			0
$315$	−9.84144	+	1.24245i	−0.554502	+	0.0700043i
$316$		0			0
$317$	1.28923	+	8.13986i	0.0724102	+	0.457180i	0.997077	+	0.0764028i	$0.0243435\pi$
$317$	1.28923	+	8.13986i	0.0724102	+	0.457180i	−0.924667	+	0.380777i	$0.875657\pi$
$318$		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
$323$	−16.9219	−	8.62216i	−0.941562	−	0.479750i
$324$		0			0
$325$	16.3286	−	27.6000i	0.905748	−	1.53097i
$326$		0			0
$327$	−12.7760	−	25.0743i	−0.706514	−	1.38661i
$328$		0			0
$329$	0.0503004			0.00277315
$330$		0			0
$331$	−24.6521			−1.35500			−0.677502	−	0.735521i	$-0.736937\pi$
$331$	−24.6521			−1.35500			−0.677502	+	0.735521i	$0.736937\pi$
$332$		0			0
$333$	23.1049	+	45.3459i	1.26614	+	2.48494i
$334$		0			0
$335$	−2.92913	−	6.22602i	−0.160035	−	0.340164i
$336$		0			0
$337$	2.27308	+	1.15819i	0.123822	+	0.0630907i	0.514804	−	0.857308i	$-0.327865\pi$
$337$	2.27308	+	1.15819i	0.123822	+	0.0630907i	−0.390982	+	0.920398i	$0.627865\pi$
$338$		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
$343$	−1.52701	−	9.64114i	−0.0824506	−	0.520573i
$344$		0			0
$345$	−3.01509	−	2.33913i	−0.162327	−	0.125935i
$346$		0			0
$347$	3.33435	−	21.0523i	0.178997	−	1.13015i	−0.720576	−	0.693376i	$-0.756123\pi$
$347$	3.33435	−	21.0523i	0.178997	−	1.13015i	0.899573	−	0.436769i	$-0.143877\pi$
$348$		0			0
$349$	−4.10120	+	12.6222i	−0.219532	+	0.675651i	0.779268	+	0.626690i	$0.215591\pi$
$349$	−4.10120	+	12.6222i	−0.219532	+	0.675651i	−0.998801	+	0.0489608i	$0.984409\pi$
$350$		0			0
$351$		−	60.5218i		−	3.23042i
$352$		0			0
$353$	5.35710	−	5.35710i	0.285130	−	0.285130i	−0.550021	−	0.835151i	$-0.685380\pi$
$353$	5.35710	−	5.35710i	0.285130	−	0.285130i	0.835151	+	0.550021i	$0.185380\pi$
$354$		0			0
$355$	−14.9867	+	4.35272i	−0.795411	+	0.231018i
$356$		0			0
$357$	−5.83762	−	0.924588i	−0.308960	−	0.0489344i
$358$		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
$363$	26.4356	+	20.1286i	1.38751	+	1.05648i
$364$		0			0
$365$	7.92763	−	7.44334i	0.414951	−	0.389602i
$366$		0			0
$367$	−0.307872	+	0.604234i	−0.0160708	+	0.0315407i	−0.898902	−	0.438149i	$-0.855634\pi$
$367$	−0.307872	+	0.604234i	−0.0160708	+	0.0315407i	0.882832	+	0.469690i	$0.155634\pi$
$368$		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	$-0.163391\pi$
$373$	7.34024	+	7.34024i	0.380063	+	0.380063i	−0.491061	+	0.871125i	$0.663391\pi$
$374$		0			0
$375$	18.1025	−	28.5097i	0.934809	−	1.47223i
$376$		0			0
$377$	7.40950	−	3.77533i	0.381608	−	0.194439i
$378$		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
$383$	−20.7636	+	3.28863i	−1.06097	+	0.168041i	−0.662441	−	0.749114i	$-0.730479\pi$
$383$	−20.7636	+	3.28863i	−1.06097	+	0.168041i	−0.398529	+	0.917156i	$0.630479\pi$
$384$		0			0
$385$	−3.00004	+	4.45649i	−0.152896	+	0.227124i
$386$		0			0
$387$	15.8413	−	2.50901i	0.805258	−	0.127540i
$388$		0			0
$389$	16.6876	−	5.42213i	0.846096	−	0.274913i	0.146286	−	0.989242i	$-0.453268\pi$
$389$	16.6876	−	5.42213i	0.846096	−	0.274913i	0.699810	+	0.714329i	$0.253268\pi$
$390$		0			0
$391$	−0.897032	−	1.23466i	−0.0453648	−	0.0624393i
$392$		0			0
$393$	−46.0436	+	23.4604i	−2.32259	+	1.18342i
$394$		0			0
$395$	−5.42851	−	7.98920i	−0.273138	−	0.401980i
$396$		0			0
$397$	10.1338	+	10.1338i	0.508603	+	0.508603i	0.914097	−	0.405495i	$-0.132901\pi$
$397$	10.1338	+	10.1338i	0.508603	+	0.508603i	−0.405495	+	0.914097i	$0.632901\pi$
$398$		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
$403$	−8.75043	+	17.1737i	−0.435890	+	0.855482i
$404$		0			0
$405$	0.713433	−	22.6434i	0.0354508	−	1.12516i
$406$		0			0
$407$	26.7270	+	6.73478i	1.32481	+	0.333830i
$408$		0			0
$409$	17.3141	+	12.5794i	0.856128	+	0.622013i	0.926829	−	0.375484i	$-0.122524\pi$
$409$	17.3141	+	12.5794i	0.856128	+	0.622013i	−0.0707012	+	0.997498i	$0.522524\pi$
$410$		0			0
$411$	2.99311	+	9.21185i	0.147639	+	0.454387i
$412$		0			0
$413$	4.86001	+	0.769750i	0.239145	+	0.0378769i
$414$		0			0
$415$	24.2332	+	13.3249i	1.18956	+	0.654093i
$416$		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
$423$	−0.0665224	+	0.420006i	−0.00323443	+	0.0204214i
$424$		0			0
$425$	10.1323	−	8.92993i	0.491490	−	0.433165i
$426$		0			0
$427$	1.31872	+	8.32607i	0.0638174	+	0.402927i
$428$		0			0
$429$	−48.3872	−	42.2751i	−2.33615	−	2.04106i
$430$		0			0
$431$	−10.8439	+	14.9254i	−0.522334	+	0.718931i	−0.985938	−	0.167112i	$-0.946556\pi$
$431$	−10.8439	+	14.9254i	−0.522334	+	0.718931i	0.463604	+	0.886042i	$0.346556\pi$
$432$		0			0
$433$	−25.3087	−	12.8954i	−1.21626	−	0.619715i	−0.276323	−	0.961065i	$-0.589116\pi$
$433$	−25.3087	−	12.8954i	−1.21626	−	0.619715i	−0.939936	+	0.341350i	$0.889116\pi$
$434$		0			0
$435$	7.92430	−	3.72811i	0.379941	−	0.178749i
$436$		0			0
$437$	−1.80344	−	3.53945i	−0.0862703	−	0.169315i
$438$		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
$443$	−12.2874	−	24.1154i	−0.583791	−	1.14576i	−0.974321	−	0.225165i	$-0.927708\pi$
$443$	−12.2874	−	24.1154i	−0.583791	−	1.14576i	0.390529	−	0.920590i	$-0.372292\pi$
$444$		0			0
$445$	5.32693	−	14.7924i	0.252521	−	0.701225i
$446$		0			0
$447$	38.4631	+	19.5979i	1.81924	+	0.926950i
$448$		0			0
$449$	−7.68659	+	10.5797i	−0.362752	+	0.499286i	−0.950913	−	0.309458i	$-0.899852\pi$
$449$	−7.68659	+	10.5797i	−0.362752	+	0.499286i	0.588161	+	0.808744i	$0.299852\pi$
$450$		0			0
$451$	1.32552	−	14.7268i	0.0624165	−	0.693457i
$452$		0			0
$453$	−8.47158	−	53.4875i	−0.398030	−	2.51306i
$454$		0			0
$455$	6.36801	−	8.20821i	0.298537	−	0.384807i
$456$		0			0
$457$	−4.11475	+	25.9795i	−0.192480	+	1.21527i	0.682418	+	0.730962i	$0.260928\pi$
$457$	−4.11475	+	25.9795i	−0.192480	+	1.21527i	−0.874898	+	0.484307i	$0.839072\pi$
$458$		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	$-0.895139\pi$
$463$	−13.3994	+	13.3994i	−0.622724	+	0.622724i	0.323503	+	0.946227i	$0.395139\pi$
$464$		0			0
$465$	−9.78008	+	17.7865i	−0.453540	+	0.824829i
$466$		0			0
$467$	6.97693	+	1.10504i	0.322854	+	0.0511350i	0.315758	−	0.948840i	$-0.397741\pi$
$467$	6.97693	+	1.10504i	0.322854	+	0.0511350i	0.00709589	+	0.999975i	$0.497741\pi$
$468$		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
$473$	4.62140	−	7.35481i	0.212492	−	0.338175i
$474$		0			0
$475$	29.6854	−	18.8322i	1.36206	−	0.864081i
$476$		0			0
$477$	22.8309	−	44.8081i	1.04535	−	2.05162i
$478$		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
$487$	−31.9458	+	16.2772i	−1.44760	+	0.737590i	−0.988561	−	0.150825i	$-0.951807\pi$
$487$	−31.9458	+	16.2772i	−1.44760	+	0.737590i	−0.459042	+	0.888415i	$0.651807\pi$
$488$		0			0
$489$	22.6257	+	31.1416i	1.02317	+	1.40827i
$490$		0			0
$491$	17.6291	−	5.72805i	0.795591	−	0.258503i	0.117108	−	0.993119i	$-0.462638\pi$
$491$	17.6291	−	5.72805i	0.795591	−	0.258503i	0.678483	+	0.734616i	$0.262638\pi$
$492$		0			0
$493$	3.45917	−	0.547879i	0.155793	−	0.0246752i
$494$		0			0
$495$	−33.2440	−	30.9440i	−1.49421	−	1.39083i
$496$		0			0
$497$	−4.99342	+	0.790880i	−0.223985	+	0.0354758i
$498$		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
$503$	−20.2304	+	10.3079i	−0.902031	+	0.459608i	−0.842548	−	0.538621i	$-0.818945\pi$
$503$	−20.2304	+	10.3079i	−0.902031	+	0.459608i	−0.0594833	+	0.998229i	$0.518945\pi$
$504$		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	0.633464	−	0.773772i	$-0.281632\pi$
$509$	15.5927	+	5.06639i	0.691136	+	0.224564i	0.0576716	+	0.998336i	$0.481632\pi$
$510$		0			0
$511$	2.85001	−	2.07065i	0.126077	−	0.0916002i
$512$		0			0
$513$	30.1210	−	59.1158i	1.32988	−	2.61003i
$514$		0			0
$515$	−6.93260	−	7.38367i	−0.305487	−	0.325363i
$516$		0			0
$517$	0.147593	+	0.176790i	0.00649115	+	0.00777523i
$518$		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
$523$	−13.1761	−	2.08688i	−0.576149	−	0.0912530i	−0.138442	−	0.990371i	$-0.544209\pi$
$523$	−13.1761	−	2.08688i	−0.576149	−	0.0912530i	−0.437707	+	0.899118i	$0.644209\pi$
$524$		0			0
$525$	6.97506	−	8.42861i	0.304416	−	0.367855i
$526$		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
$533$	−4.47304	+	28.2417i	−0.193749	+	1.22328i
$534$		0			0
$535$	3.96307	+	31.3914i	0.171338	+	1.35717i
$536$		0			0
$537$	−10.1087	−	63.8241i	−0.436225	−	2.75421i
$538$		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
$543$	−19.6628	−	10.0187i	−0.843810	−	0.429943i
$544$		0			0
$545$	19.6003	+	7.05832i	0.839583	+	0.302345i
$546$		0			0
$547$	−9.73509	−	19.1062i	−0.416242	−	0.816922i	−0.999988	−	0.00498489i	$-0.998413\pi$
$547$	−9.73509	−	19.1062i	−0.416242	−	0.816922i	0.583745	−	0.811937i	$-0.301587\pi$
$548$		0			0
$549$	−71.2664			−3.04158
$550$		0			0
$551$	9.11630			0.388367
$552$		0			0
$553$	−1.42058	−	2.78804i	−0.0604091	−	0.118559i
$554$		0			0
$555$	−52.8106	−	19.0178i	−2.24168	−	0.807261i
$556$		0			0
$557$	−10.1993	−	5.19678i	−0.432156	−	0.220195i	0.224360	−	0.974506i	$-0.427971\pi$
$557$	−10.1993	−	5.19678i	−0.432156	−	0.220195i	−0.656517	+	0.754312i	$0.727971\pi$
$558$		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
$563$	−2.16446	−	13.6659i	−0.0912213	−	0.575948i	−0.990385	−	0.138337i	$-0.955824\pi$
$563$	−2.16446	−	13.6659i	−0.0912213	−	0.575948i	0.899164	−	0.437612i	$-0.144176\pi$
$564$		0			0
$565$	−1.24898	−	9.89313i	−0.0525450	−	0.416207i
$566$		0			0
$567$	1.14809	−	7.24875i	0.0482152	−	0.304419i
$568$		0			0
$569$	7.89984	−	24.3132i	0.331179	−	1.01926i	−0.637395	−	0.770537i	$-0.719988\pi$
$569$	7.89984	−	24.3132i	0.331179	−	1.01926i	0.968574	−	0.248726i	$-0.0800119\pi$
$570$		0			0
$571$			29.7381i			1.24450i	0.782818	+	0.622251i	$0.213782\pi$
$571$			29.7381i			1.24450i	−0.782818	+	0.622251i	$0.786218\pi$
$572$		0			0
$573$	−0.799715	+	0.799715i	−0.0334086	+	0.0334086i
$574$		0			0
$575$	2.81243	−	0.265394i	0.117287	−	0.0110677i
$576$		0			0
$577$	−28.5923	−	4.52857i	−1.19031	−	0.188527i	−0.470311	−	0.882500i	$-0.655858\pi$
$577$	−28.5923	−	4.52857i	−1.19031	−	0.188527i	−0.720000	+	0.693974i	$0.755858\pi$
$578$		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
$583$	−10.1395	−	25.2778i	−0.419934	−	1.04690i
$584$		0			0
$585$	60.1165	+	64.0280i	2.48551	+	2.64723i
$586$		0			0
$587$	18.1280	−	35.5782i	0.748222	−	1.46847i	−0.130659	−	0.991427i	$-0.541709\pi$
$587$	18.1280	−	35.5782i	0.748222	−	1.46847i	0.878881	−	0.477041i	$-0.158291\pi$
$588$		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	$-0.103440\pi$
$593$	15.3021	+	15.3021i	0.628383	+	0.628383i	−0.319278	+	0.947661i	$0.603440\pi$
$594$		0			0
$595$	3.61893	−	2.45899i	0.148362	−	0.100809i
$596$		0			0
$597$	4.24952	−	2.16524i	0.173921	−	0.0886174i
$598$		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
$603$	18.6123	−	2.94789i	0.757950	−	0.120048i
$604$		0			0
$605$	−24.4661	+	2.53218i	−0.994687	+	0.102948i
$606$		0			0
$607$	4.75068	−	0.752433i	0.192824	−	0.0305403i	−0.0592754	−	0.998242i	$-0.518879\pi$
$607$	4.75068	−	0.752433i	0.192824	−	0.0305403i	0.252099	+	0.967701i	$0.418879\pi$
$608$		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
$613$	10.0510	−	5.12125i	0.405957	−	0.206846i	−0.239075	−	0.971001i	$-0.576844\pi$
$613$	10.0510	−	5.12125i	0.405957	−	0.206846i	0.645032	+	0.764156i	$0.276844\pi$
$614$		0			0
$615$	−5.64484	+	29.5783i	−0.227622	+	1.19271i
$616$		0			0
$617$	−11.3680	−	11.3680i	−0.457659	−	0.457659i	0.440227	−	0.897886i	$-0.354898\pi$
$617$	−11.3680	−	11.3680i	−0.457659	−	0.457659i	−0.897886	+	0.440227i	$0.854898\pi$
$618$		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
$623$	2.31232	−	4.53819i	0.0926413	−	0.181819i
$624$		0			0
$625$	4.67658	+	24.5587i	0.187063	+	0.982348i
$626$		0			0
$627$	−26.2232	−	65.3747i	−1.04725	−	2.61081i
$628$		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	$0.317960\pi$
$631$	15.0120	+	46.2023i	0.597620	+	1.83929i	0.0563932	+	0.998409i	$0.482040\pi$
$632$		0			0
$633$	−47.2669	−	7.48635i	−1.87869	−	0.297556i
$634$		0			0
$635$	4.79656	−	8.72323i	0.190346	−	0.346171i
$636$		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
$643$	−3.08531	+	19.4799i	−0.121673	+	0.768213i	0.849103	+	0.528227i	$0.177143\pi$
$643$	−3.08531	+	19.4799i	−0.121673	+	0.768213i	−0.970776	+	0.239986i	$0.922857\pi$
$644$		0			0
$645$	−10.8431	+	13.9765i	−0.426946	+	0.550323i
$646$		0			0
$647$	0.787851	+	4.97430i	0.0309736	+	0.195560i	0.998323	−	0.0578861i	$-0.0184360\pi$
$647$	0.787851	+	4.97430i	0.0309736	+	0.195560i	−0.967350	+	0.253446i	$0.918436\pi$
$648$		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
$653$	−14.3499	−	7.31163i	−0.561554	−	0.286126i	0.150083	−	0.988673i	$-0.452046\pi$
$653$	−14.3499	−	7.31163i	−0.561554	−	0.286126i	−0.711637	+	0.702547i	$0.752046\pi$
$654$		0			0
$655$	12.9611	−	35.9917i	0.506433	−	1.40631i
$656$		0			0
$657$	13.5207	+	26.5359i	0.527493	+	1.03526i
$658$		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
$663$	23.7574	+	46.6265i	0.922660	+	1.81082i
$664$		0			0
$665$	10.3052	−	4.84824i	0.399618	−	0.188007i
$666$		0			0
$667$	0.652708	+	0.332571i	0.0252730	+	0.0128772i
$668$		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
$673$	1.29662	+	8.18656i	0.0499812	+	0.315569i	0.999994	+	0.00335891i	$0.00106918\pi$
$673$	1.29662	+	8.18656i	0.0499812	+	0.315569i	−0.950013	+	0.312210i	$0.898931\pi$
$674$		0			0
$675$	31.1962	+	35.3967i	1.20074	+	1.36242i
$676$		0			0
$677$	3.63622	−	22.9582i	0.139751	−	0.882354i	−0.813805	−	0.581138i	$-0.802608\pi$
$677$	3.63622	−	22.9582i	0.139751	−	0.882354i	0.953556	−	0.301216i	$-0.0973925\pi$
$678$		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	$-0.843755\pi$
$683$	−10.7294	+	10.7294i	−0.410548	+	0.410548i	0.471382	+	0.881929i	$0.343755\pi$
$684$		0			0
$685$	−6.28304	−	3.45479i	−0.240063	−	0.132001i
$686$		0			0
$687$	21.6718	+	3.43248i	0.826832	+	0.130957i
$688$		0			0
$689$	16.2753	+	50.0903i	0.620041	+	1.90829i
$690$		0			0
$691$	−6.67401	−	4.84895i	−0.253891	−	0.184463i	0.453558	−	0.891227i	$-0.350154\pi$
$691$	−6.67401	−	4.84895i	−0.253891	−	0.184463i	−0.707450	+	0.706764i	$0.750154\pi$
$692$		0			0
$693$	−9.42918	−	11.2945i	−0.358185	−	0.429042i
$694$		0			0
$695$	0.167869	−	5.32793i	0.00636763	−	0.202100i
$696$		0			0
$697$	−5.46716	+	10.7299i	−0.207083	+	0.406424i
$698$		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
$707$	−3.15108	+	1.60556i	−0.118509	+	0.0603832i
$708$		0			0
$709$	9.81584	+	13.5103i	0.368641	+	0.507391i	0.952531	−	0.304442i	$-0.0984699\pi$
$709$	9.81584	+	13.5103i	0.368641	+	0.507391i	−0.583890	+	0.811833i	$0.698470\pi$
$710$		0			0
$711$	25.1587	−	8.17456i	0.943526	−	0.306570i
$712$		0			0
$713$	−1.67700	+	0.265611i	−0.0628041	+	0.00994720i
$714$		0			0
$715$	47.5346	−	1.70327i	1.77769	−	0.0636986i
$716$		0			0
$717$	48.6647	−	7.70774i	1.81742	−	0.287851i
$718$		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
$723$	−11.2535	+	5.73396i	−0.418523	+	0.213248i
$724$		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	$-0.111848\pi$
$727$	16.0350	+	16.0350i	0.594705	+	0.594705i	−0.344194	+	0.938899i	$0.611848\pi$
$728$		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
$733$	3.15612	−	6.19423i	0.116574	−	0.228789i	−0.825346	−	0.564628i	$-0.809020\pi$
$733$	3.15612	−	6.19423i	0.116574	−	0.228789i	0.941919	+	0.335839i	$0.109020\pi$
$734$		0			0
$735$	−31.8843	+	29.9365i	−1.17607	+	1.10422i
$736$		0			0
$737$	5.42978	−	8.64132i	0.200008	−	0.318307i
$738$		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
$743$	48.5994	+	7.69739i	1.78294	+	0.282390i	0.958818	−	0.284022i	$-0.0916687\pi$
$743$	48.5994	+	7.69739i	1.78294	+	0.282390i	0.824122	+	0.566412i	$0.191669\pi$
$744$		0			0
$745$	−30.6881	+	8.91301i	−1.12432	+	0.326548i
$746$		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	$-0.764217\pi$
$751$	7.00769	−	21.5674i	0.255714	−	0.787007i	0.993688	−	0.112178i	$-0.0357827\pi$
$752$		0			0
$753$	−5.99869	+	37.8743i	−0.218605	+	1.38021i
$754$		0			0
$755$	31.6745	+	24.5733i	1.15275	+	0.894315i
$756$		0			0
$757$	0.276914	+	1.74836i	0.0100646	+	0.0635454i	0.992209	−	0.124581i	$-0.0397586\pi$
$757$	0.276914	+	1.74836i	0.0100646	+	0.0635454i	−0.982145	+	0.188126i	$0.939759\pi$
$758$		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
$763$	6.01322	+	3.06389i	0.217693	+	0.110920i
$764$		0			0
$765$	15.7464	+	33.4699i	0.569314	+	1.21011i
$766$		0			0
$767$	−19.7788	−	38.8180i	−0.714170	−	1.40164i
$768$		0			0
$769$	37.5969			1.35578			0.677889	−	0.735164i	$-0.262895\pi$
$769$	37.5969			1.35578			0.677889	+	0.735164i	$0.262895\pi$
$770$		0			0
$771$	3.61250			0.130101
$772$		0			0
$773$	−5.83278	−	11.4475i	−0.209790	−	0.411737i	0.762002	−	0.647575i	$-0.224217\pi$
$773$	−5.83278	−	11.4475i	−0.209790	−	0.411737i	−0.971792	+	0.235838i	$0.924217\pi$
$774$		0			0
$775$	−3.73448	−	14.5546i	−0.134146	−	0.522817i
$776$		0			0
$777$	−16.2019	−	8.25529i	−0.581240	−	0.296157i
$778$		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
$783$	1.91398	+	12.0844i	0.0684002	+	0.431862i
$784$		0			0
$785$	−7.41764	+	0.936455i	−0.264747	+	0.0334235i
$786$		0			0
$787$	2.29218	−	14.4723i	0.0817075	−	0.515881i	−0.912559	−	0.408946i	$-0.865896\pi$
$787$	2.29218	−	14.4723i	0.0817075	−	0.515881i	0.994266	−	0.106935i	$-0.0341035\pi$
$788$		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
$795$	15.4699	+	53.2638i	0.548661	+	1.88907i
$796$		0			0
$797$	−1.67189	−	0.264802i	−0.0592215	−	0.00937977i	0.126753	−	0.991934i	$-0.459544\pi$
$797$	−1.67189	−	0.264802i	−0.0592215	−	0.00937977i	−0.185975	+	0.982554i	$0.559544\pi$
$798$		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
$803$	15.6403	+	3.94111i	0.551934	+	0.139079i
$804$		0			0
$805$	0.914699	+	0.0288197i	0.0322389	+	0.00101576i
$806$		0			0
$807$	19.9682	−	39.1898i	0.702915	−	1.37955i
$808$		0			0
$809$	−3.29877	+	2.39669i	−0.115978	+	0.0842633i	−0.644263	−	0.764804i	$-0.722836\pi$
$809$	−3.29877	+	2.39669i	−0.115978	+	0.0842633i	0.528284	+	0.849068i	$0.322836\pi$
$810$		0			0
$811$	−0.365104	−	0.118629i	−0.0128205	−	0.00416564i	0.302600	−	0.953118i	$-0.402145\pi$
$811$	−0.365104	−	0.118629i	−0.0128205	−	0.00416564i	−0.315420	+	0.948952i	$0.602145\pi$
$812$		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
$817$	−16.4072	+	8.35987i	−0.574014	+	0.292475i
$818$		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
$823$	−32.6020	+	5.16364i	−1.13643	+	0.179993i	−0.696171	−	0.717876i	$-0.745114\pi$
$823$	−32.6020	+	5.16364i	−1.13643	+	0.179993i	−0.440262	+	0.897869i	$0.645114\pi$
$824$		0			0
$825$	50.0905	−	0.216390i	1.74393	−	0.00753374i
$826$		0			0
$827$	27.3892	−	4.33802i	0.952415	−	0.150848i	0.339157	−	0.940730i	$-0.389858\pi$
$827$	27.3892	−	4.33802i	0.952415	−	0.150848i	0.613259	+	0.789882i	$0.289858\pi$
$828$		0			0
$829$	48.8463	−	15.8711i	1.69650	−	0.551227i	0.708507	−	0.705704i	$-0.249369\pi$
$829$	48.8463	−	15.8711i	1.69650	−	0.551227i	0.987996	+	0.154477i	$0.0493692\pi$
$830$		0			0
$831$	37.8914	+	52.1530i	1.31444	+	1.80917i
$832$		0			0
$833$	−15.5844	+	7.94065i	−0.539967	+	0.275127i
$834$		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
$843$	32.8827	−	64.5359i	1.13254	−	2.22273i
$844$		0			0
$845$	−62.8811	−	1.98122i	−2.16318	−	0.0681559i
$846$		0			0
$847$	−7.96626	−	0.178889i	−0.273724	−	0.00614670i
$848$		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
$853$	−22.8728	−	3.62270i	−0.783150	−	0.124039i	−0.247960	−	0.968770i	$-0.579760\pi$
$853$	−22.8728	−	3.62270i	−0.783150	−	0.124039i	−0.535190	+	0.844731i	$0.679760\pi$
$854$		0			0
$855$	26.8539	+	92.4598i	0.918385	+	3.16206i
$856$		0			0
$857$	2.65045	−	2.65045i	0.0905378	−	0.0905378i	−0.660387	−	0.750925i	$-0.729608\pi$
$857$	2.65045	−	2.65045i	0.0905378	−	0.0905378i	0.750925	+	0.660387i	$0.229608\pi$
$858$		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
$863$	4.87230	−	30.7625i	0.165855	−	1.04717i	−0.754561	−	0.656229i	$-0.772150\pi$
$863$	4.87230	−	30.7625i	0.165855	−	1.04717i	0.920417	−	0.390939i	$-0.127850\pi$
$864$		0			0
$865$	29.5744	−	3.73368i	1.00556	−	0.126949i
$866$		0			0
$867$	−4.58524	−	28.9501i	−0.155723	−	0.983196i
$868$		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
$873$	−72.8084	−	37.0977i	−2.46419	−	1.25557i
$874$		0			0
$875$	0.506571	+	8.08305i	0.0171252	+	0.273257i
$876$		0			0
$877$	2.04698	+	4.01742i	0.0691215	+	0.135659i	0.922982	−	0.384844i	$-0.125745\pi$
$877$	2.04698	+	4.01742i	0.0691215	+	0.135659i	−0.853860	+	0.520502i	$0.825745\pi$
$878$		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
$883$	−6.15894	−	12.0876i	−0.207265	−	0.406780i	0.763850	−	0.645394i	$-0.223307\pi$
$883$	−6.15894	−	12.0876i	−0.207265	−	0.406780i	−0.971114	+	0.238614i	$0.923307\pi$
$884$		0			0
$885$	−19.5314	−	41.5151i	−0.656541	−	1.39551i
$886$		0			0
$887$	−22.8860	−	11.6610i	−0.768436	−	0.391538i	0.0253938	−	0.999678i	$-0.491916\pi$
$887$	−22.8860	−	11.6610i	−0.768436	−	0.391538i	−0.793830	+	0.608140i	$0.791916\pi$
$888$		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
$893$	−0.0763748	−	0.482211i	−0.00255578	−	0.0161366i
$894$		0			0
$895$	37.7957	+	29.3222i	1.26337	+	0.980134i
$896$		0			0
$897$	−1.71226	+	10.8108i	−0.0571707	+	0.360962i
$898$		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
$905$	15.6881	−	4.55643i	0.521490	−	0.151461i
$906$		0			0
$907$	−4.01859	−	0.636482i	−0.133435	−	0.0211340i	0.0893597	−	0.995999i	$-0.471518\pi$
$907$	−4.01859	−	0.636482i	−0.133435	−	0.0211340i	−0.222795	+	0.974865i	$0.571518\pi$
$908$		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	$0.00513075\pi$
$911$	39.9673	+	29.0380i	1.32418	+	0.962070i	0.324306	+	0.945952i	$0.394869\pi$
$912$		0			0
$913$	2.75907	+	40.9262i	0.0913118	+	1.35446i
$914$		0			0
$915$	57.3019	−	53.8013i	1.89434	−	1.77862i
$916$		0			0
$917$	5.62618	−	11.0420i	0.185793	−	0.364639i
$918$		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
$927$	24.7151	−	12.5930i	0.811750	−	0.413607i
$928$		0			0
$929$	−10.3144	−	14.1966i	−0.338404	−	0.465774i	0.605570	−	0.795792i	$-0.292945\pi$
$929$	−10.3144	−	14.1966i	−0.338404	−	0.465774i	−0.943975	+	0.330018i	$0.892945\pi$
$930$		0			0
$931$	−43.2993	+	14.0688i	−1.41908	+	0.461087i
$932$		0			0
$933$	−12.7815	+	2.02439i	−0.418447	+	0.0662755i
$934$		0			0
$935$	19.2614	+	5.50415i	0.629915	+	0.180005i
$936$		0			0
$937$	43.5848	−	6.90315i	1.42385	−	0.225516i	0.603495	−	0.797367i	$-0.293774\pi$
$937$	43.5848	−	6.90315i	1.42385	−	0.225516i	0.820357	+	0.571851i	$0.193774\pi$
$938$		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
$943$	−2.24430	+	1.14353i	−0.0730846	+	0.0372384i
$944$		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	$-0.144934\pi$
$947$	14.1055	+	14.1055i	0.458367	+	0.458367i	−0.439752	+	0.898119i	$0.644934\pi$
$948$		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
$953$	19.4856	−	38.2426i	0.631199	−	1.23880i	−0.324898	−	0.945749i	$-0.605330\pi$
$953$	19.4856	−	38.2426i	0.631199	−	1.23880i	0.956097	−	0.293050i	$-0.0946701\pi$
$954$		0			0
$955$	0.0263657	−	0.836810i	0.000853173	−	0.0270785i
$956$		0			0
$957$	10.9984	+	6.91086i	0.355528	+	0.223396i
$958$		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
$963$	−85.5884	−	13.5559i	−2.75805	−	0.436832i
$964$		0			0
$965$	26.5098	+	14.5767i	0.853382	+	0.469241i
$966$		0			0
$967$	−10.8777	+	10.8777i	−0.349803	+	0.349803i	−0.860036	−	0.510233i	$-0.829559\pi$
$967$	−10.8777	+	10.8777i	−0.349803	+	0.349803i	0.510233	+	0.860036i	$0.329559\pi$
$968$		0			0
$969$			57.3670i			1.84289i
$970$		0			0
$971$	−6.16511	+	18.9743i	−0.197848	+	0.608913i	0.802084	+	0.597212i	$0.203725\pi$
$971$	−6.16511	+	18.9743i	−0.197848	+	0.608913i	−0.999932	+	0.0117013i	$0.996275\pi$
$972$		0			0
$973$	0.270143	−	1.70561i	0.00866037	−	0.0546794i
$974$		0			0
$975$	−96.6735	−	6.09790i	−3.09603	−	0.195289i
$976$		0			0
$977$	3.88795	+	24.5475i	0.124386	+	0.785345i	0.968469	+	0.249133i	$0.0801455\pi$
$977$	3.88795	+	24.5475i	0.124386	+	0.785345i	−0.844083	+	0.536213i	$0.819854\pi$
$978$		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
$983$	−25.9317	−	13.2129i	−0.827092	−	0.421424i	−0.0114171	−	0.999935i	$-0.503634\pi$
$983$	−25.9317	−	13.2129i	−0.827092	−	0.421424i	−0.815675	+	0.578510i	$0.803634\pi$
$984$		0			0
$985$	51.7265	−	24.3355i	1.64814	−	0.775395i
$986$		0			0
$987$	−0.0689780	−	0.135377i	−0.00219560	−	0.00430910i
$988$		0			0
$989$	−1.47970			−0.0470516
$990$		0			0
$991$	48.5379			1.54186			0.770929	−	0.636921i	$-0.219792\pi$
$991$	48.5379			1.54186			0.770929	+	0.636921i	$0.219792\pi$
$992$		0			0
$993$	33.8060	+	66.3481i	1.07280	+	2.10549i
$994$		0			0
$995$	−1.19623	+	3.32180i	−0.0379229	+	0.105308i
$996$		0			0
$997$	23.1955	+	11.8187i	0.734610	+	0.374303i	0.780925	−	0.624624i	$-0.214748\pi$
$997$	23.1955	+	11.8187i	0.734610	+	0.374303i	−0.0463152	+	0.998927i	$0.514748\pi$
$998$		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	880.2.cm.b.337.1		48
4.3	odd	2		220.2.u.a.117.6	yes	48
5.3	odd	4	inner	880.2.cm.b.513.6		48
11.8	odd	10	inner	880.2.cm.b.657.6		48
20.3	even	4		220.2.u.a.73.1	✓	48
44.19	even	10		220.2.u.a.217.1	yes	48
55.8	even	20	inner	880.2.cm.b.833.1		48
220.63	odd	20		220.2.u.a.173.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.73.1	✓	48	20.3	even	4
220.2.u.a.117.6	yes	48	4.3	odd	2
220.2.u.a.173.6	yes	48	220.63	odd	20
220.2.u.a.217.1	yes	48	44.19	even	10
880.2.cm.b.337.1		48	1.1	even	1	trivial
880.2.cm.b.513.6		48	5.3	odd	4	inner
880.2.cm.b.657.6		48	11.8	odd	10	inner
880.2.cm.b.833.1		48	55.8	even	20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cm (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.37132 - 2.69137i) q^{3} +(2.10381 + 0.757611i) q^{5} +(0.645435 + 0.328865i) q^{7} +(-3.59960 + 4.95443i) q^{9} +(0.737999 + 3.23347i) q^{11} +(-1.00332 - 6.33471i) q^{13} +(-0.845991 - 6.70107i) q^{15} +(0.422556 - 2.66791i) q^{17} +(2.17270 - 6.68689i) q^{19} -2.18809i q^{21} +(0.399505 - 0.399505i) q^{23} +(3.85205 + 3.18774i) q^{25} +(9.32020 + 1.47617i) q^{27} +(0.400667 + 1.23312i) q^{29} +(-2.43127 - 1.76642i) q^{31} +(7.69045 - 6.42037i) q^{33} +(1.10872 + 1.18086i) q^{35} +(3.77284 - 7.40461i) q^{37} +(-15.6732 + 11.3872i) q^{39} +(-4.24004 - 1.37767i) q^{41} +(-1.85191 - 1.85191i) q^{43} +(-11.3264 + 7.69608i) q^{45} +(0.0618701 - 0.0315244i) q^{47} +(-3.80606 - 5.23860i) q^{49} +(-7.75981 + 2.52131i) q^{51} +(-8.11073 + 1.28461i) q^{53} +(-0.897106 + 7.36174i) q^{55} +(-20.9764 + 3.32233i) q^{57} +(6.46029 - 2.09908i) q^{59} +(6.84018 + 9.41470i) q^{61} +(-3.95265 + 2.01397i) q^{63} +(2.68845 - 14.0872i) q^{65} +(-2.17585 - 2.17585i) q^{67} +(-1.62307 - 0.527366i) q^{69} +(-5.64630 + 4.10228i) q^{71} +(2.20782 - 4.33309i) q^{73} +(3.29700 - 14.7387i) q^{75} +(-0.587048 + 2.32970i) q^{77} +(-3.49465 - 2.53901i) q^{79} +(-3.13079 - 9.63559i) q^{81} +(12.2155 + 1.93474i) q^{83} +(2.91022 - 5.29265i) q^{85} +(2.76935 - 2.76935i) q^{87} -7.03122i q^{89} +(1.43569 - 4.41860i) q^{91} +(-1.42004 + 8.96579i) q^{93} +(9.63702 - 12.4219i) q^{95} +(2.08736 + 13.1791i) q^{97} +(-18.6765 - 7.98286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} + 4 q^{5} - 10 q^{7} + 16 q^{15} + 10 q^{17} - 16 q^{23} - 26 q^{25} + 10 q^{27} - 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} + 2 q^{47} + 80 q^{51} + 6 q^{53} + 18 q^{55}+ \cdots + 6 q^{97}+O(q^{100}) \) 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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