LMFDB - Embedded newform 1100.2.q.b.221.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(221,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.13
Character	$\chi$	$=$	1100.221
Dual form			1100.2.q.b.881.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.71414 + 1.97194i) q^{3} +(-1.74832 - 1.39405i) q^{5} +1.07366 q^{7} +(2.55096 + 7.85106i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(1.65608 + 5.09689i) q^{13} +(-1.99619 - 7.23123i) q^{15} +(4.84857 - 3.52269i) q^{17} +(-3.62641 + 2.63474i) q^{19} +(2.91406 + 2.11719i) q^{21} +(1.73036 - 5.32549i) q^{23} +(1.11323 + 4.87450i) q^{25} +(-5.44800 + 16.7672i) q^{27} +(-5.49403 - 3.99164i) q^{29} +(-1.09934 + 0.798716i) q^{31} +(-2.71414 + 1.97194i) q^{33} +(-1.87710 - 1.49674i) q^{35} +(1.00509 + 3.09334i) q^{37} +(-5.55592 + 17.0994i) q^{39} +(0.118510 + 0.364737i) q^{41} +8.63084 q^{43} +(6.48489 - 17.2823i) q^{45} +(-1.91181 - 1.38901i) q^{47} -5.84725 q^{49} +20.1062 q^{51} +(5.81123 + 4.22211i) q^{53} +(1.86608 - 1.23196i) q^{55} -15.0381 q^{57} +(4.57432 + 14.0783i) q^{59} +(3.20999 - 9.87933i) q^{61} +(2.73887 + 8.42937i) q^{63} +(4.20998 - 11.2196i) q^{65} +(2.19745 - 1.59654i) q^{67} +(15.1980 - 11.0420i) q^{69} +(-1.95143 - 1.41780i) q^{71} +(-2.18427 + 6.72250i) q^{73} +(-6.59073 + 15.4253i) q^{75} +(-0.331779 + 1.02111i) q^{77} +(0.876570 + 0.636866i) q^{79} +(-27.8150 + 20.2088i) q^{81} +(8.33222 - 6.05371i) q^{83} +(-13.3877 - 0.600377i) q^{85} +(-7.04028 - 21.6678i) q^{87} +(1.18992 - 3.66219i) q^{89} +(1.77807 + 5.47233i) q^{91} -4.55877 q^{93} +(10.0131 + 0.449042i) q^{95} +(-15.0546 - 10.9378i) q^{97} -8.25509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) $ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	2.71414	+	1.97194i	1.56701	+	1.13850i	0.929951	+	0.367682i	$0.119849\pi$
$3$	2.71414	+	1.97194i	1.56701	+	1.13850i	0.637057	+	0.770816i	$0.280151\pi$
$4$		0			0
$5$	−1.74832	−	1.39405i	−0.781872	−	0.623439i
$5$	−1.74832	−	1.39405i	−0.781872	−	0.623439i
$6$		0			0
$7$	1.07366			0.405806			0.202903	−	0.979199i	$-0.434962\pi$
$7$	1.07366			0.405806			0.202903	+	0.979199i	$0.434962\pi$
$8$		0			0
$9$	2.55096	+	7.85106i	0.850321	+	2.61702i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$		0			0
$13$	1.65608	+	5.09689i	0.459314	+	1.41362i	0.865995	+	0.500053i	$0.166686\pi$
$13$	1.65608	+	5.09689i	0.459314	+	1.41362i	−0.406681	+	0.913570i	$0.633314\pi$
$14$		0			0
$15$	−1.99619	−	7.23123i	−0.515415	−	1.86709i
$16$		0			0
$17$	4.84857	−	3.52269i	1.17595	−	0.854379i	0.184242	−	0.982881i	$-0.441017\pi$
$17$	4.84857	−	3.52269i	1.17595	−	0.854379i	0.991709	+	0.128502i	$0.0410169\pi$
$18$		0			0
$19$	−3.62641	+	2.63474i	−0.831955	+	0.604451i	−0.920112	−	0.391656i	$-0.871902\pi$
$19$	−3.62641	+	2.63474i	−0.831955	+	0.604451i	0.0881564	+	0.996107i	$0.471902\pi$
$20$		0			0
$21$	2.91406	+	2.11719i	0.635901	+	0.462009i
$22$		0			0
$23$	1.73036	−	5.32549i	0.360804	−	1.11044i	−0.591763	−	0.806112i	$-0.701568\pi$
$23$	1.73036	−	5.32549i	0.360804	−	1.11044i	0.952567	−	0.304329i	$-0.0984323\pi$
$24$		0			0
$25$	1.11323	+	4.87450i	0.222646	+	0.974899i
$26$		0			0
$27$	−5.44800	+	16.7672i	−1.04847	+	3.22685i
$28$		0			0
$29$	−5.49403	−	3.99164i	−1.02022	−	0.741230i	−0.0538884	−	0.998547i	$-0.517162\pi$
$29$	−5.49403	−	3.99164i	−1.02022	−	0.741230i	−0.966327	+	0.257317i	$0.917162\pi$
$30$		0			0
$31$	−1.09934	+	0.798716i	−0.197447	+	0.143454i	−0.682116	−	0.731244i	$-0.738940\pi$
$31$	−1.09934	+	0.798716i	−0.197447	+	0.143454i	0.484669	+	0.874698i	$0.338940\pi$
$32$		0			0
$33$	−2.71414	+	1.97194i	−0.472471	+	0.343270i
$34$		0			0
$35$	−1.87710	−	1.49674i	−0.317288	−	0.252995i
$36$		0			0
$37$	1.00509	+	3.09334i	0.165235	+	0.508542i	0.999054	−	0.0434972i	$-0.0138500\pi$
$37$	1.00509	+	3.09334i	0.165235	+	0.508542i	−0.833818	+	0.552039i	$0.813850\pi$
$38$		0			0
$39$	−5.55592	+	17.0994i	−0.889659	+	2.73809i
$40$		0			0
$41$	0.118510	+	0.364737i	0.0185082	+	0.0569624i	0.959884	−	0.280397i	$-0.0904662\pi$
$41$	0.118510	+	0.364737i	0.0185082	+	0.0569624i	−0.941376	+	0.337360i	$0.890466\pi$
$42$		0			0
$43$	8.63084			1.31619			0.658095	−	0.752935i	$-0.271362\pi$
$43$	8.63084			1.31619			0.658095	+	0.752935i	$0.271362\pi$
$44$		0			0
$45$	6.48489	−	17.2823i	0.966711	−	2.57630i
$46$		0			0
$47$	−1.91181	−	1.38901i	−0.278866	−	0.202608i	0.439557	−	0.898215i	$-0.355135\pi$
$47$	−1.91181	−	1.38901i	−0.278866	−	0.202608i	−0.718422	+	0.695607i	$0.755135\pi$
$48$		0			0
$49$	−5.84725			−0.835322
$50$		0			0
$51$	20.1062			2.81544
$52$		0			0
$53$	5.81123	+	4.22211i	0.798234	+	0.579951i	0.910396	−	0.413739i	$-0.135777\pi$
$53$	5.81123	+	4.22211i	0.798234	+	0.579951i	−0.112161	+	0.993690i	$0.535777\pi$
$54$		0			0
$55$	1.86608	−	1.23196i	0.251623	−	0.166118i
$56$		0			0
$57$	−15.0381			−1.99185
$58$		0			0
$59$	4.57432	+	14.0783i	0.595525	+	1.83284i	0.552094	+	0.833782i	$0.313829\pi$
$59$	4.57432	+	14.0783i	0.595525	+	1.83284i	0.0434308	+	0.999056i	$0.486171\pi$
$60$		0			0
$61$	3.20999	−	9.87933i	0.410997	−	1.26492i	−0.504785	−	0.863245i	$-0.668428\pi$
$61$	3.20999	−	9.87933i	0.410997	−	1.26492i	0.915783	−	0.401674i	$-0.131572\pi$
$62$		0			0
$63$	2.73887	+	8.42937i	0.345065	+	1.06200i
$64$		0			0
$65$	4.20998	−	11.2196i	0.522184	−	1.39163i
$66$		0			0
$67$	2.19745	−	1.59654i	0.268461	−	0.195048i	−0.445408	−	0.895328i	$-0.646941\pi$
$67$	2.19745	−	1.59654i	0.268461	−	0.195048i	0.713869	+	0.700280i	$0.246941\pi$
$68$		0			0
$69$	15.1980	−	11.0420i	1.82962	−	1.32930i
$70$		0			0
$71$	−1.95143	−	1.41780i	−0.231592	−	0.168262i	0.465937	−	0.884818i	$-0.345717\pi$
$71$	−1.95143	−	1.41780i	−0.231592	−	0.168262i	−0.697529	+	0.716556i	$0.745717\pi$
$72$		0			0
$73$	−2.18427	+	6.72250i	−0.255650	+	0.786809i	0.738051	+	0.674745i	$0.235746\pi$
$73$	−2.18427	+	6.72250i	−0.255650	+	0.786809i	−0.993701	+	0.112065i	$0.964254\pi$
$74$		0			0
$75$	−6.59073	+	15.4253i	−0.761032	+	1.78116i
$76$		0			0
$77$	−0.331779	+	1.02111i	−0.0378098	+	0.116367i
$78$		0			0
$79$	0.876570	+	0.636866i	0.0986219	+	0.0716530i	0.636003	−	0.771686i	$-0.280586\pi$
$79$	0.876570	+	0.636866i	0.0986219	+	0.0716530i	−0.537381	+	0.843339i	$0.680586\pi$
$80$		0			0
$81$	−27.8150	+	20.2088i	−3.09055	+	2.24542i
$82$		0			0
$83$	8.33222	−	6.05371i	0.914580	−	0.664481i	−0.0275890	−	0.999619i	$-0.508783\pi$
$83$	8.33222	−	6.05371i	0.914580	−	0.664481i	0.942169	+	0.335138i	$0.108783\pi$
$84$		0			0
$85$	−13.3877	−	0.600377i	−1.45210	−	0.0651200i
$86$		0			0
$87$	−7.04028	−	21.6678i	−0.754797	−	2.32303i
$88$		0			0
$89$	1.18992	−	3.66219i	0.126131	−	0.388191i	−0.867974	−	0.496609i	$-0.834578\pi$
$89$	1.18992	−	3.66219i	0.126131	−	0.388191i	0.994105	+	0.108418i	$0.0345783\pi$
$90$		0			0
$91$	1.77807	+	5.47233i	0.186392	+	0.573656i
$92$		0			0
$93$	−4.55877			−0.472723
$94$		0			0
$95$	10.0131	+	0.449042i	1.02732	+	0.0460708i
$96$		0			0
$97$	−15.0546	−	10.9378i	−1.52856	−	1.11056i	−0.957033	−	0.289978i	$-0.906352\pi$
$97$	−15.0546	−	10.9378i	−1.52856	−	1.11056i	−0.571525	−	0.820585i	$-0.693648\pi$
$98$		0			0
$99$	−8.25509			−0.829668
$100$		0			0
$101$	3.98933			0.396953			0.198477	−	0.980106i	$-0.436401\pi$
$101$	3.98933			0.396953			0.198477	+	0.980106i	$0.436401\pi$
$102$		0			0
$103$	−15.5912	−	11.3276i	−1.53624	−	1.11615i	−0.952638	−	0.304108i	$-0.901642\pi$
$103$	−15.5912	−	11.3276i	−1.53624	−	1.11615i	−0.583605	−	0.812038i	$-0.698358\pi$
$104$		0			0
$105$	−2.14323	−	7.76389i	−0.209158	−	0.757678i
$106$		0			0
$107$	3.79357			0.366739			0.183369	−	0.983044i	$-0.441300\pi$
$107$	3.79357			0.366739			0.183369	+	0.983044i	$0.441300\pi$
$108$		0			0
$109$	−5.11364	−	15.7382i	−0.489798	−	1.50744i	−0.824910	−	0.565264i	$-0.808774\pi$
$109$	−5.11364	−	15.7382i	−0.489798	−	1.50744i	0.335113	−	0.942178i	$-0.391226\pi$
$110$		0			0
$111$	−3.37193	+	10.3777i	−0.320049	+	0.985010i
$112$		0			0
$113$	−2.20506	−	6.78647i	−0.207435	−	0.638418i	−0.999605	−	0.0281175i	$-0.991049\pi$
$113$	−2.20506	−	6.78647i	−0.207435	−	0.638418i	0.792170	−	0.610300i	$-0.208951\pi$
$114$		0			0
$115$	−10.4492	+	6.89844i	−0.974396	+	0.643283i
$116$		0			0
$117$	−35.7914	+	26.0040i	−3.30891	+	2.40407i
$118$		0			0
$119$	5.20572	−	3.78218i	0.477208	−	0.346712i
$120$		0			0
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$		0			0
$123$	−0.397585	+	1.22364i	−0.0358491	+	0.110332i
$124$		0			0
$125$	4.84902	−	10.0741i	0.433710	−	0.901053i
$126$		0			0
$127$	2.86728	−	8.82458i	0.254430	−	0.783055i	−0.739511	−	0.673144i	$-0.764943\pi$
$127$	2.86728	−	8.82458i	0.254430	−	0.783055i	0.993941	−	0.109911i	$-0.0350566\pi$
$128$		0			0
$129$	23.4253	+	17.0195i	2.06248	+	1.49848i
$130$		0			0
$131$	−5.62360	+	4.08579i	−0.491337	+	0.356977i	−0.805698	−	0.592326i	$-0.798210\pi$
$131$	−5.62360	+	4.08579i	−0.491337	+	0.356977i	0.314362	+	0.949303i	$0.398210\pi$
$132$		0			0
$133$	−3.89353	+	2.82882i	−0.337612	+	0.245290i
$134$		0			0
$135$	32.8992	−	21.7196i	2.83151	−	1.86933i
$136$		0			0
$137$	−3.69483	−	11.3715i	−0.315671	−	0.971534i	−0.975478	−	0.220099i	$-0.929362\pi$
$137$	−3.69483	−	11.3715i	−0.315671	−	0.971534i	0.659807	−	0.751435i	$-0.270638\pi$
$138$		0			0
$139$	5.82661	−	17.9325i	0.494207	−	1.52101i	−0.323983	−	0.946063i	$-0.605022\pi$
$139$	5.82661	−	17.9325i	0.494207	−	1.52101i	0.818189	−	0.574949i	$-0.194978\pi$
$140$		0			0
$141$	−2.44987	−	7.53992i	−0.206316	−	0.634976i
$142$		0			0
$143$	−5.35919			−0.448158
$144$		0			0
$145$	4.04074	+	14.6376i	0.335566	+	1.21559i
$146$		0			0
$147$	−15.8703	−	11.5304i	−1.30896	−	0.951013i
$148$		0			0
$149$	20.5937			1.68710			0.843550	−	0.537050i	$-0.180461\pi$
$149$	20.5937			1.68710			0.843550	+	0.537050i	$0.180461\pi$
$150$		0			0
$151$	6.19641			0.504257			0.252128	−	0.967694i	$-0.418869\pi$
$151$	6.19641			0.504257			0.252128	+	0.967694i	$0.418869\pi$
$152$		0			0
$153$	40.0254	+	29.0801i	3.23586	+	2.35099i
$154$		0			0
$155$	3.03545	+	0.136126i	0.243813	+	0.0109339i
$156$		0			0
$157$	−1.23210			−0.0983326			−0.0491663	−	0.998791i	$-0.515656\pi$
$157$	−1.23210			−0.0983326			−0.0491663	+	0.998791i	$0.515656\pi$
$158$		0			0
$159$	7.44676	+	22.9188i	0.590567	+	1.81758i
$160$		0			0
$161$	1.85782	−	5.71777i	0.146416	−	0.450623i
$162$		0			0
$163$	−0.575857	−	1.77231i	−0.0451046	−	0.138818i	0.925968	−	0.377602i	$-0.123251\pi$
$163$	−0.575857	−	1.77231i	−0.0451046	−	0.138818i	−0.971073	+	0.238784i	$0.923251\pi$
$164$		0			0
$165$	7.49416	+	0.336080i	0.583420	+	0.0261638i
$166$		0			0
$167$	1.18431	−	0.860452i	0.0916447	−	0.0665837i	−0.541019	−	0.841010i	$-0.681961\pi$
$167$	1.18431	−	0.860452i	0.0916447	−	0.0665837i	0.632664	+	0.774426i	$0.281961\pi$
$168$		0			0
$169$	−12.7185	+	9.24051i	−0.978344	+	0.710809i
$170$		0			0
$171$	−29.9363	−	21.7500i	−2.28929	−	1.66327i
$172$		0			0
$173$	4.06811	−	12.5204i	0.309293	−	0.951905i	−0.668748	−	0.743490i	$-0.733169\pi$
$173$	4.06811	−	12.5204i	0.309293	−	0.951905i	0.978040	−	0.208416i	$-0.0668307\pi$
$174$		0			0
$175$	1.19523	+	5.23356i	0.0903512	+	0.395620i
$176$		0			0
$177$	−15.3462	+	47.2307i	−1.15349	+	3.55008i
$178$		0			0
$179$	−5.48191	−	3.98284i	−0.409737	−	0.297691i	0.363758	−	0.931493i	$-0.381493\pi$
$179$	−5.48191	−	3.98284i	−0.409737	−	0.297691i	−0.773495	+	0.633802i	$0.781493\pi$
$180$		0			0
$181$	−1.30652	+	0.949239i	−0.0971125	+	0.0705564i	−0.635282	−	0.772280i	$-0.719116\pi$
$181$	−1.30652	+	0.949239i	−0.0971125	+	0.0705564i	0.538169	+	0.842837i	$0.319116\pi$
$182$		0			0
$183$	28.1938	−	20.4840i	2.08414	−	1.51422i
$184$		0			0
$185$	2.55507	−	6.80928i	0.187852	−	0.500629i
$186$		0			0
$187$	1.85199	+	5.69984i	0.135431	+	0.416813i
$188$		0			0
$189$	−5.84930	+	18.0023i	−0.425474	+	1.30947i
$190$		0			0
$191$	−1.09017	−	3.35518i	−0.0788816	−	0.242773i	0.903837	−	0.427876i	$-0.140738\pi$
$191$	−1.09017	−	3.35518i	−0.0788816	−	0.242773i	−0.982719	+	0.185103i	$0.940738\pi$
$192$		0			0
$193$	15.2987			1.10122			0.550612	−	0.834761i	$-0.314394\pi$
$193$	15.2987			1.10122			0.550612	+	0.834761i	$0.314394\pi$
$194$		0			0
$195$	33.5509	−	22.1499i	2.40263	−	1.58619i
$196$		0			0
$197$	3.58061	+	2.60147i	0.255108	+	0.185347i	0.707988	−	0.706225i	$-0.249603\pi$
$197$	3.58061	+	2.60147i	0.255108	+	0.185347i	−0.452880	+	0.891572i	$0.649603\pi$
$198$		0			0
$199$	11.7582			0.833514			0.416757	−	0.909018i	$-0.363167\pi$
$199$	11.7582			0.833514			0.416757	+	0.909018i	$0.363167\pi$
$200$		0			0
$201$	9.11244			0.642742
$202$		0			0
$203$	−5.89872	−	4.28567i	−0.414009	−	0.300795i
$204$		0			0
$205$	0.301269	−	0.802886i	0.0210416	−	0.0560760i
$206$		0			0
$207$	46.2248			3.21285
$208$		0			0
$209$	−1.38517	−	4.26310i	−0.0958139	−	0.294885i
$210$		0			0
$211$	1.76322	−	5.42664i	0.121385	−	0.373585i	−0.871840	−	0.489791i	$-0.837073\pi$
$211$	1.76322	−	5.42664i	0.121385	−	0.373585i	0.993225	+	0.116206i	$0.0370732\pi$
$212$		0			0
$213$	−2.50065	−	7.69620i	−0.171341	−	0.527335i
$214$		0			0
$215$	−15.0895	−	12.0318i	−1.02909	−	0.820565i
$216$		0			0
$217$	−1.18032	+	0.857550i	−0.0801251	+	0.0582143i
$218$		0			0
$219$	−19.1848	+	13.9386i	−1.29639	+	0.941880i
$220$		0			0
$221$	25.9844	+	18.8788i	1.74790	+	1.26992i
$222$		0			0
$223$	−5.87573	+	18.0836i	−0.393468	+	1.21097i	0.536680	+	0.843786i	$0.319678\pi$
$223$	−5.87573	+	18.0836i	−0.393468	+	1.21097i	−0.930148	+	0.367184i	$0.880322\pi$
$224$		0			0
$225$	−35.4301	+	21.1747i	−2.36201	+	1.41165i
$226$		0			0
$227$	−1.71135	+	5.26700i	−0.113586	+	0.349583i	−0.991650	−	0.128962i	$-0.958836\pi$
$227$	−1.71135	+	5.26700i	−0.113586	+	0.349583i	0.878063	+	0.478545i	$0.158836\pi$
$228$		0			0
$229$	−0.00833282	−	0.00605415i	−0.000550648	−	0.000400069i	0.587510	−	0.809217i	$-0.300108\pi$
$229$	−0.00833282	−	0.00605415i	−0.000550648	−	0.000400069i	−0.588061	+	0.808817i	$0.700108\pi$
$230$		0			0
$231$	−2.91406	+	2.11719i	−0.191731	+	0.139301i
$232$		0			0
$233$	−0.946404	+	0.687603i	−0.0620010	+	0.0450463i	−0.618354	−	0.785900i	$-0.712200\pi$
$233$	−0.946404	+	0.687603i	−0.0620010	+	0.0450463i	0.556353	+	0.830946i	$0.312200\pi$
$234$		0			0
$235$	1.40609	+	5.09359i	0.0917234	+	0.332269i
$236$		0			0
$237$	1.12327	+	3.45708i	0.0729645	+	0.224562i
$238$		0			0
$239$	6.52800	−	20.0911i	0.422262	−	1.29959i	−0.483331	−	0.875438i	$-0.660573\pi$
$239$	6.52800	−	20.0911i	0.422262	−	1.29959i	0.905592	−	0.424149i	$-0.139427\pi$
$240$		0			0
$241$	−2.96012	−	9.11030i	−0.190678	−	0.586846i	0.809322	−	0.587365i	$-0.199835\pi$
$241$	−2.96012	−	9.11030i	−0.190678	−	0.586846i	−1.00000		0.000519021i	$0.999835\pi$
$242$		0			0
$243$	−62.4539			−4.00642
$244$		0			0
$245$	10.2229	+	8.15138i	0.653114	+	0.520773i
$246$		0			0
$247$	−19.4346	−	14.1201i	−1.23659	−	0.898439i
$248$		0			0
$249$	34.5523			2.18967
$250$		0			0
$251$	−5.31728			−0.335624			−0.167812	−	0.985819i	$-0.553670\pi$
$251$	−5.31728			−0.335624			−0.167812	+	0.985819i	$0.553670\pi$
$252$		0			0
$253$	4.53013	+	3.29133i	0.284807	+	0.206924i
$254$		0			0
$255$	−35.1521	−	28.0291i	−2.20131	−	1.75525i
$256$		0			0
$257$	−13.3865			−0.835026			−0.417513	−	0.908671i	$-0.637098\pi$
$257$	−13.3865			−0.835026			−0.417513	+	0.908671i	$0.637098\pi$
$258$		0			0
$259$	1.07912	+	3.32120i	0.0670534	+	0.206369i
$260$		0			0
$261$	17.3236	−	53.3165i	1.07230	−	3.30021i
$262$		0			0
$263$	4.96941	+	15.2943i	0.306427	+	0.943084i	0.979141	+	0.203182i	$0.0651283\pi$
$263$	4.96941	+	15.2943i	0.306427	+	0.943084i	−0.672714	+	0.739902i	$0.734872\pi$
$264$		0			0
$265$	−4.27404	−	15.4828i	−0.262552	−	0.951098i
$266$		0			0
$267$	10.4512	−	7.59325i	0.639604	−	0.464699i
$268$		0			0
$269$	−1.86456	+	1.35469i	−0.113685	+	0.0825966i	−0.643175	−	0.765719i	$-0.722383\pi$
$269$	−1.86456	+	1.35469i	−0.113685	+	0.0825966i	0.529490	+	0.848316i	$0.322383\pi$
$270$		0			0
$271$	9.01948	+	6.55304i	0.547894	+	0.398069i	0.827009	−	0.562189i	$-0.190041\pi$
$271$	9.01948	+	6.55304i	0.547894	+	0.398069i	−0.279114	+	0.960258i	$0.590041\pi$
$272$		0			0
$273$	−5.96517	+	18.3589i	−0.361029	+	1.11113i
$274$		0			0
$275$	−4.97993	−	0.447555i	−0.300301	−	0.0269886i
$276$		0			0
$277$	−3.82881	+	11.7839i	−0.230051	+	0.708023i	0.767689	+	0.640823i	$0.221407\pi$
$277$	−3.82881	+	11.7839i	−0.230051	+	0.708023i	−0.997740	+	0.0672004i	$0.978593\pi$
$278$		0			0
$279$	−9.07513	−	6.59347i	−0.543314	−	0.394741i
$280$		0			0
$281$	−13.5046	+	9.81163i	−0.805614	+	0.585313i	−0.912556	−	0.408952i	$-0.865894\pi$
$281$	−13.5046	+	9.81163i	−0.805614	+	0.585313i	0.106942	+	0.994265i	$0.465894\pi$
$282$		0			0
$283$	12.6186	−	9.16798i	0.750101	−	0.544980i	−0.145757	−	0.989320i	$-0.546562\pi$
$283$	12.6186	−	9.16798i	0.750101	−	0.544980i	0.895858	+	0.444340i	$0.146562\pi$
$284$		0			0
$285$	26.2914	+	20.9639i	1.55737	+	1.24180i
$286$		0			0
$287$	0.127240	+	0.391604i	0.00751073	+	0.0231157i
$288$		0			0
$289$	5.84599	−	17.9921i	0.343882	−	1.05836i
$290$		0			0
$291$	−19.2915	−	59.3733i	−1.13089	−	3.48052i
$292$		0			0
$293$	−27.8267			−1.62565			−0.812827	−	0.582506i	$-0.802072\pi$
$293$	−27.8267			−1.62565			−0.812827	+	0.582506i	$0.802072\pi$
$294$		0			0
$295$	11.6285	−	30.9902i	0.677039	−	1.80432i
$296$		0			0
$297$	−14.2630	−	10.3627i	−0.827625	−	0.601305i
$298$		0			0
$299$	30.0091			1.73547
$300$		0			0
$301$	9.26659			0.534118
$302$		0			0
$303$	10.8276	+	7.86671i	0.622029	+	0.451931i
$304$		0			0
$305$	−19.3844	+	12.7973i	−1.10995	+	0.732773i
$306$		0			0
$307$	14.2381			0.812609			0.406304	−	0.913738i	$-0.366817\pi$
$307$	14.2381			0.812609			0.406304	+	0.913738i	$0.366817\pi$
$308$		0			0
$309$	−19.9792	−	61.4896i	−1.13658	−	3.49802i
$310$		0			0
$311$	3.77819	−	11.6281i	0.214242	−	0.659368i	−0.784965	−	0.619540i	$-0.787319\pi$
$311$	3.77819	−	11.6281i	0.214242	−	0.659368i	0.999207	−	0.0398276i	$-0.0126809\pi$
$312$		0			0
$313$	9.23171	+	28.4123i	0.521807	+	1.60596i	0.770545	+	0.637386i	$0.219984\pi$
$313$	9.23171	+	28.4123i	0.521807	+	1.60596i	−0.248738	+	0.968571i	$0.580016\pi$
$314$		0			0
$315$	6.96258	−	18.5553i	0.392297	−	1.04548i
$316$		0			0
$317$	−7.86726	+	5.71590i	−0.441870	+	0.321037i	−0.786377	−	0.617746i	$-0.788046\pi$
$317$	−7.86726	+	5.71590i	−0.441870	+	0.321037i	0.344508	+	0.938783i	$0.388046\pi$
$318$		0			0
$319$	5.49403	−	3.99164i	0.307607	−	0.223489i
$320$		0			0
$321$	10.2963	+	7.48069i	0.574683	+	0.417531i
$322$		0			0
$323$	−8.30152	+	25.5495i	−0.461909	+	1.42161i
$324$		0			0
$325$	−23.0012	+	13.7466i	−1.27588	+	0.762523i
$326$		0			0
$327$	17.1555	−	52.7993i	0.948703	−	2.91981i
$328$		0			0
$329$	−2.05263	−	1.49132i	−0.113165	−	0.0822193i
$330$		0			0
$331$	−17.1593	+	12.4669i	−0.943159	+	0.685245i	−0.949179	−	0.314737i	$-0.898084\pi$
$331$	−17.1593	+	12.4669i	−0.943159	+	0.685245i	0.00602033	+	0.999982i	$0.498084\pi$
$332$		0			0
$333$	−21.7220	+	15.7820i	−1.19036	+	0.864847i
$334$		0			0
$335$	−6.06749	−	0.272100i	−0.331502	−	0.0148664i
$336$		0			0
$337$	0.870156	+	2.67807i	0.0474004	+	0.145883i	0.971955	−	0.235165i	$-0.0755631\pi$
$337$	0.870156	+	2.67807i	0.0474004	+	0.145883i	−0.924555	+	0.381049i	$0.875563\pi$
$338$		0			0
$339$	7.39767	−	22.7677i	0.401786	−	1.23657i
$340$		0			0
$341$	−0.419910	−	1.29235i	−0.0227394	−	0.0699847i
$342$		0			0
$343$	−13.7936			−0.744784
$344$		0			0
$345$	−41.9640	−	1.88190i	−2.25926	−	0.101318i
$346$		0			0
$347$	2.96493	+	2.15415i	0.159166	+	0.115641i	0.664517	−	0.747273i	$-0.268637\pi$
$347$	2.96493	+	2.15415i	0.159166	+	0.115641i	−0.505352	+	0.862914i	$0.668637\pi$
$348$		0			0
$349$	−35.2158			−1.88506			−0.942530	−	0.334122i	$-0.891560\pi$
$349$	−35.2158			−1.88506			−0.942530	+	0.334122i	$0.891560\pi$
$350$		0			0
$351$	−94.4829			−5.04313
$352$		0			0
$353$	1.34081	+	0.974154i	0.0713640	+	0.0518490i	0.622895	−	0.782305i	$-0.285956\pi$
$353$	1.34081	+	0.974154i	0.0713640	+	0.0518490i	−0.551531	+	0.834154i	$0.685956\pi$
$354$		0			0
$355$	1.43524	+	5.19916i	0.0761744	+	0.275943i
$356$		0			0
$357$	21.5873			1.14252
$358$		0			0
$359$	3.13298	+	9.64233i	0.165352	+	0.508903i	0.999062	−	0.0433005i	$-0.0137873\pi$
$359$	3.13298	+	9.64233i	0.165352	+	0.508903i	−0.833710	+	0.552203i	$0.813787\pi$
$360$		0			0
$361$	0.337665	−	1.03923i	0.0177718	−	0.0546961i
$362$		0			0
$363$	−1.03671	−	3.19066i	−0.0544131	−	0.167466i
$364$		0			0
$365$	13.1903	−	8.70808i	0.690413	−	0.455802i
$366$		0			0
$367$	−12.4386	+	9.03717i	−0.649290	+	0.471737i	−0.863029	−	0.505154i	$-0.831436\pi$
$367$	−12.4386	+	9.03717i	−0.649290	+	0.471737i	0.213739	+	0.976891i	$0.431436\pi$
$368$		0			0
$369$	−2.56126	+	1.86086i	−0.133334	+	0.0968726i
$370$		0			0
$371$	6.23929	+	4.53311i	0.323928	+	0.235347i
$372$		0			0
$373$	−10.8666	+	33.4439i	−0.562650	+	1.73166i	0.112181	+	0.993688i	$0.464216\pi$
$373$	−10.8666	+	33.4439i	−0.562650	+	1.73166i	−0.674831	+	0.737972i	$0.735784\pi$
$374$		0			0
$375$	33.0264	−	17.7805i	1.70547	−	0.918180i
$376$		0			0
$377$	11.2464	−	34.6129i	0.579220	−	1.78266i
$378$		0			0
$379$	26.9470	+	19.5781i	1.38417	+	1.00566i	0.996476	+	0.0838758i	$0.0267299\pi$
$379$	26.9470	+	19.5781i	1.38417	+	1.00566i	0.387699	+	0.921786i	$0.373270\pi$
$380$		0			0
$381$	25.1837	−	18.2970i	1.29020	−	0.937386i
$382$		0			0
$383$	10.3603	−	7.52721i	0.529387	−	0.384622i	−0.290741	−	0.956802i	$-0.593902\pi$
$383$	10.3603	−	7.52721i	0.529387	−	0.384622i	0.820128	+	0.572179i	$0.193902\pi$
$384$		0			0
$385$	2.00354	−	1.32271i	0.102110	−	0.0674116i
$386$		0			0
$387$	22.0169	+	67.7612i	1.11918	+	3.44450i
$388$		0			0
$389$	9.14904	−	28.1578i	0.463875	−	1.42766i	−0.396518	−	0.918027i	$-0.629781\pi$
$389$	9.14904	−	28.1578i	0.463875	−	1.42766i	0.860392	−	0.509632i	$-0.170219\pi$
$390$		0			0
$391$	−10.3703	−	31.9165i	−0.524449	−	1.61409i
$392$		0			0
$393$	−23.3202			−1.17635
$394$		0			0
$395$	−0.644699	−	2.33543i	−0.0324383	−	0.117508i
$396$		0			0
$397$	12.7455	+	9.26013i	0.639677	+	0.464753i	0.859739	−	0.510733i	$-0.170626\pi$
$397$	12.7455	+	9.26013i	0.639677	+	0.464753i	−0.220062	+	0.975486i	$0.570626\pi$
$398$		0			0
$399$	−16.1458			−0.808303
$400$		0			0
$401$	−32.8107			−1.63849			−0.819244	−	0.573446i	$-0.805606\pi$
$401$	−32.8107			−1.63849			−0.819244	+	0.573446i	$0.805606\pi$
$402$		0			0
$403$	−5.89156	−	4.28047i	−0.293480	−	0.213225i
$404$		0			0
$405$	76.8015	+	3.44421i	3.81630	+	0.171144i
$406$		0			0
$407$	−3.25253			−0.161222
$408$		0			0
$409$	4.06025	+	12.4962i	0.200766	+	0.617895i	0.999861	+	0.0166898i	$0.00531277\pi$
$409$	4.06025	+	12.4962i	0.200766	+	0.617895i	−0.799094	+	0.601206i	$0.794687\pi$
$410$		0			0
$411$	12.3956	−	38.1498i	0.611432	−	1.88179i
$412$		0			0
$413$	4.91126	+	15.1153i	0.241667	+	0.743776i
$414$		0			0
$415$	−23.0066	−	1.03174i	−1.12935	−	0.0506462i
$416$		0			0
$417$	51.1759	−	37.1815i	2.50610	−	1.82079i
$418$		0			0
$419$	8.93830	−	6.49405i	0.436665	−	0.317255i	−0.347644	−	0.937627i	$-0.613018\pi$
$419$	8.93830	−	6.49405i	0.436665	−	0.317255i	0.784308	+	0.620371i	$0.213018\pi$
$420$		0			0
$421$	−7.72748	−	5.61435i	−0.376614	−	0.273626i	0.383334	−	0.923610i	$-0.374776\pi$
$421$	−7.72748	−	5.61435i	−0.376614	−	0.273626i	−0.759948	+	0.649983i	$0.774776\pi$
$422$		0			0
$423$	6.02824	−	18.5530i	0.293103	−	0.902078i
$424$		0			0
$425$	22.5689	+	19.7128i	1.09475	+	0.956210i
$426$		0			0
$427$	3.44644	−	10.6071i	0.166785	−	0.513311i
$428$		0			0
$429$	−14.5456	−	10.5680i	−0.702267	−	0.510227i
$430$		0			0
$431$	−1.57973	+	1.14774i	−0.0760929	+	0.0552848i	−0.625181	−	0.780479i	$-0.714975\pi$
$431$	−1.57973	+	1.14774i	−0.0760929	+	0.0552848i	0.549088	+	0.835764i	$0.314975\pi$
$432$		0			0
$433$	−7.42271	+	5.39291i	−0.356713	+	0.259167i	−0.751680	−	0.659528i	$-0.770756\pi$
$433$	−7.42271	+	5.39291i	−0.356713	+	0.259167i	0.394967	+	0.918695i	$0.370756\pi$
$434$		0			0
$435$	−17.8974	+	47.6967i	−0.858112	+	2.28688i
$436$		0			0
$437$	7.75631	+	23.8715i	0.371034	+	1.14193i
$438$		0			0
$439$	−1.50998	+	4.64725i	−0.0720676	+	0.221801i	−0.980602	−	0.196008i	$-0.937202\pi$
$439$	−1.50998	+	4.64725i	−0.0720676	+	0.221801i	0.908535	+	0.417810i	$0.137202\pi$
$440$		0			0
$441$	−14.9161	−	45.9071i	−0.710291	−	2.18605i
$442$		0			0
$443$	−5.41164			−0.257115			−0.128557	−	0.991702i	$-0.541035\pi$
$443$	−5.41164			−0.257115			−0.128557	+	0.991702i	$0.541035\pi$
$444$		0			0
$445$	−7.18564	+	4.74387i	−0.340632	+	0.224881i
$446$		0			0
$447$	55.8941	+	40.6095i	2.64370	+	1.92076i
$448$		0			0
$449$	−30.3853			−1.43397			−0.716986	−	0.697088i	$-0.754479\pi$
$449$	−30.3853			−1.43397			−0.716986	+	0.697088i	$0.754479\pi$
$450$		0			0
$451$	−0.383507			−0.0180587
$452$		0			0
$453$	16.8179	+	12.2189i	0.790175	+	0.574095i
$454$		0			0
$455$	4.52009	−	12.0461i	0.211905	−	0.564730i
$456$		0			0
$457$	−36.1890			−1.69285			−0.846424	−	0.532509i	$-0.821249\pi$
$457$	−36.1890			−1.69285			−0.846424	+	0.532509i	$0.821249\pi$
$458$		0			0
$459$	32.6507	+	100.489i	1.52401	+	4.69041i
$460$		0			0
$461$	−4.87601	+	15.0068i	−0.227099	+	0.698938i	0.770973	+	0.636868i	$0.219770\pi$
$461$	−4.87601	+	15.0068i	−0.227099	+	0.698938i	−0.998072	+	0.0620701i	$0.980230\pi$
$462$		0			0
$463$	6.85866	+	21.1088i	0.318749	+	0.981009i	0.974184	+	0.225757i	$0.0724855\pi$
$463$	6.85866	+	21.1088i	0.318749	+	0.981009i	−0.655435	+	0.755252i	$0.727515\pi$
$464$		0			0
$465$	7.97019	+	6.35517i	0.369609	+	0.294714i
$466$		0			0
$467$	10.0098	−	7.27256i	0.463199	−	0.336534i	−0.331586	−	0.943425i	$-0.607584\pi$
$467$	10.0098	−	7.27256i	0.463199	−	0.336534i	0.794785	+	0.606891i	$0.207584\pi$
$468$		0			0
$469$	2.35931	−	1.71414i	0.108943	−	0.0791516i
$470$		0			0
$471$	−3.34410	−	2.42963i	−0.154088	−	0.111952i
$472$		0			0
$473$	−2.66708	+	8.20842i	−0.122632	+	0.377423i
$474$		0			0
$475$	−16.8801	−	14.7438i	−0.774511	−	0.676494i
$476$		0			0
$477$	−18.3238	+	56.3948i	−0.838988	+	2.58214i
$478$		0			0
$479$	−22.9008	−	16.6384i	−1.04637	−	0.760229i	−0.0748476	−	0.997195i	$-0.523847\pi$
$479$	−22.9008	−	16.6384i	−1.04637	−	0.760229i	−0.971518	+	0.236966i	$0.923847\pi$
$480$		0			0
$481$	−14.1019	+	10.2456i	−0.642992	+	0.467161i
$482$		0			0
$483$	16.3175	−	11.8553i	0.742470	−	0.539436i
$484$		0			0
$485$	11.0723	+	40.1095i	0.502768	+	1.82128i
$486$		0			0
$487$	1.55503	+	4.78590i	0.0704653	+	0.216870i	0.980087	−	0.198567i	$-0.0636287\pi$
$487$	1.55503	+	4.78590i	0.0704653	+	0.216870i	−0.909622	+	0.415437i	$0.863629\pi$
$488$		0			0
$489$	1.93192	−	5.94584i	0.0873644	−	0.268880i
$490$		0			0
$491$	5.03466	+	15.4951i	0.227211	+	0.699283i	0.998060	+	0.0622650i	$0.0198324\pi$
$491$	5.03466	+	15.4951i	0.227211	+	0.699283i	−0.770849	+	0.637018i	$0.780168\pi$
$492$		0			0
$493$	−40.6995			−1.83301
$494$		0			0
$495$	14.4325	+	11.5080i	0.648694	+	0.517247i
$496$		0			0
$497$	−2.09517	−	1.52223i	−0.0939814	−	0.0682815i
$498$		0			0
$499$	22.6354			1.01330			0.506650	−	0.862152i	$-0.330884\pi$
$499$	22.6354			1.01330			0.506650	+	0.862152i	$0.330884\pi$
$500$		0			0
$501$	4.91114			0.219413
$502$		0			0
$503$	24.7028	+	17.9476i	1.10144	+	0.800245i	0.981295	−	0.192511i	$-0.0616630\pi$
$503$	24.7028	+	17.9476i	1.10144	+	0.800245i	0.120148	+	0.992756i	$0.461663\pi$
$504$		0			0
$505$	−6.97462	−	5.56134i	−0.310366	−	0.247476i
$506$		0			0
$507$	−52.7414			−2.34233
$508$		0			0
$509$	−3.97475	−	12.2330i	−0.176177	−	0.542219i	0.823508	−	0.567305i	$-0.192014\pi$
$509$	−3.97475	−	12.2330i	−0.176177	−	0.542219i	−0.999685	+	0.0250864i	$0.992014\pi$
$510$		0			0
$511$	−2.34517	+	7.21769i	−0.103744	+	0.319292i
$512$		0			0
$513$	−24.4206	−	75.1588i	−1.07820	−	3.31834i
$514$		0			0
$515$	11.4670	+	41.5392i	0.505295	+	1.83044i
$516$		0			0
$517$	1.91181	−	1.38901i	0.0840811	−	0.0610885i
$518$		0			0
$519$	35.7308	−	25.9599i	1.56841	−	1.13951i
$520$		0			0
$521$	33.9978	+	24.7008i	1.48947	+	1.08216i	0.974348	+	0.225047i	$0.0722535\pi$
$521$	33.9978	+	24.7008i	1.48947	+	1.08216i	0.515122	+	0.857117i	$0.327747\pi$
$522$		0			0
$523$	−1.72812	+	5.31860i	−0.0755654	+	0.232566i	−0.981704	−	0.190415i	$-0.939017\pi$
$523$	−1.72812	+	5.31860i	−0.0755654	+	0.232566i	0.906138	+	0.422982i	$0.139017\pi$
$524$		0			0
$525$	−7.07621	+	16.5615i	−0.308831	+	0.722804i
$526$		0			0
$527$	−2.51659	+	7.74526i	−0.109624	+	0.337389i
$528$		0			0
$529$	−6.75933	−	4.91094i	−0.293884	−	0.213519i
$530$		0			0
$531$	−98.8606	+	71.8264i	−4.29018	+	3.11700i
$532$		0			0
$533$	−1.66276	+	1.20807i	−0.0720223	+	0.0523272i
$534$		0			0
$535$	−6.63237	−	5.28844i	−0.286743	−	0.228639i
$536$		0			0
$537$	−7.02475	−	21.6200i	−0.303140	−	0.932970i
$538$		0			0
$539$	1.80690	−	5.56107i	0.0778287	−	0.239532i
$540$		0			0
$541$	−0.0878298	−	0.270312i	−0.00377610	−	0.0116216i	0.949151	−	0.314822i	$-0.101945\pi$
$541$	−0.0878298	−	0.270312i	−0.00377610	−	0.0116216i	−0.952927	+	0.303200i	$0.901945\pi$
$542$		0			0
$543$	−5.41790			−0.232504
$544$		0			0
$545$	−12.9996	+	34.6440i	−0.556840	+	1.48399i
$546$		0			0
$547$	5.80660	+	4.21874i	0.248272	+	0.180380i	0.704961	−	0.709246i	$-0.250965\pi$
$547$	5.80660	+	4.21874i	0.248272	+	0.180380i	−0.456688	+	0.889627i	$0.650965\pi$
$548$		0			0
$549$	85.7518			3.65980
$550$		0			0
$551$	30.4405			1.29681
$552$		0			0
$553$	0.941139	+	0.683778i	0.0400213	+	0.0290772i
$554$		0			0
$555$	20.3623	−	13.4429i	0.864331	−	0.570620i
$556$		0			0
$557$	−19.8118			−0.839454			−0.419727	−	0.907650i	$-0.637874\pi$
$557$	−19.8118			−0.839454			−0.419727	+	0.907650i	$0.637874\pi$
$558$		0			0
$559$	14.2934	+	43.9904i	0.604545	+	1.86060i
$560$		0			0
$561$	−6.21317	+	19.1222i	−0.262320	+	0.807338i
$562$		0			0
$563$	−13.0683	−	40.2202i	−0.550764	−	1.69508i	−0.706874	−	0.707339i	$-0.749895\pi$
$563$	−13.0683	−	40.2202i	−0.550764	−	1.69508i	0.156110	−	0.987740i	$-0.450105\pi$
$564$		0			0
$565$	−5.60556	+	14.9389i	−0.235828	+	0.628484i
$566$		0			0
$567$	−29.8639	+	21.6974i	−1.25416	+	0.911204i
$568$		0			0
$569$	33.0182	−	23.9891i	1.38419	−	1.00568i	0.387719	−	0.921778i	$-0.373263\pi$
$569$	33.0182	−	23.9891i	1.38419	−	1.00568i	0.996474	−	0.0838976i	$-0.0267369\pi$
$570$		0			0
$571$	16.2945	+	11.8386i	0.681902	+	0.495431i	0.873988	−	0.485947i	$-0.161525\pi$
$571$	16.2945	+	11.8386i	0.681902	+	0.495431i	−0.192086	+	0.981378i	$0.561525\pi$
$572$		0			0
$573$	3.65735	−	11.2562i	0.152788	−	0.470233i
$574$		0			0
$575$	27.8854	+	2.50611i	1.16290	+	0.104512i
$576$		0			0
$577$	1.05622	−	3.25071i	0.0439710	−	0.135329i	−0.926661	−	0.375898i	$-0.877334\pi$
$577$	1.05622	−	3.25071i	0.0439710	−	0.135329i	0.970632	+	0.240570i	$0.0773342\pi$
$578$		0			0
$579$	41.5228	+	30.1681i	1.72563	+	1.25374i
$580$		0			0
$581$	8.94598	−	6.49963i	0.371142	−	0.269650i
$582$		0			0
$583$	−5.81123	+	4.22211i	−0.240677	+	0.174862i
$584$		0			0
$585$	98.8256	+	4.43189i	4.08594	+	0.183236i
$586$		0			0
$587$	−7.67379	−	23.6175i	−0.316731	−	0.974798i	−0.975036	−	0.222047i	$-0.928726\pi$
$587$	−7.67379	−	23.6175i	−0.316731	−	0.974798i	0.658305	−	0.752751i	$-0.271274\pi$
$588$		0			0
$589$	1.88224	−	5.79294i	0.0775564	−	0.238694i
$590$		0			0
$591$	4.58835	+	14.1215i	0.188739	+	0.580880i
$592$		0			0
$593$	−6.30461			−0.258899			−0.129450	−	0.991586i	$-0.541321\pi$
$593$	−6.30461			−0.258899			−0.129450	+	0.991586i	$0.541321\pi$
$594$		0			0
$595$	−14.3738	−	0.644601i	−0.589269	−	0.0264261i
$596$		0			0
$597$	31.9133	+	23.1864i	1.30612	+	0.948955i
$598$		0			0
$599$	−13.3617			−0.545943			−0.272971	−	0.962022i	$-0.588006\pi$
$599$	−13.3617			−0.545943			−0.272971	+	0.962022i	$0.588006\pi$
$600$		0			0
$601$	35.5089			1.44844			0.724220	−	0.689569i	$-0.242200\pi$
$601$	35.5089			1.44844			0.724220	+	0.689569i	$0.242200\pi$
$602$		0			0
$603$	18.1401	+	13.1796i	0.738722	+	0.536713i
$604$		0			0
$605$	0.595015	+	2.15545i	0.0241908	+	0.0876314i
$606$		0			0
$607$	17.1840			0.697476			0.348738	−	0.937220i	$-0.386610\pi$
$607$	17.1840			0.697476			0.348738	+	0.937220i	$0.386610\pi$
$608$		0			0
$609$	−7.55887	−	23.2638i	−0.306301	−	0.942698i
$610$		0			0
$611$	3.91352	−	12.0446i	0.158324	−	0.487271i
$612$		0			0
$613$	−7.36762	−	22.6752i	−0.297575	−	0.915843i	−0.982344	−	0.187083i	$-0.940097\pi$
$613$	−7.36762	−	22.6752i	−0.297575	−	0.915843i	0.684769	−	0.728760i	$-0.259903\pi$
$614$		0			0
$615$	2.40093	−	1.58506i	0.0968148	−	0.0639158i
$616$		0			0
$617$	−11.2616	+	8.18204i	−0.453375	+	0.329396i	−0.790927	−	0.611911i	$-0.790401\pi$
$617$	−11.2616	+	8.18204i	−0.453375	+	0.329396i	0.337552	+	0.941307i	$0.390401\pi$
$618$		0			0
$619$	−10.6409	+	7.73105i	−0.427693	+	0.310737i	−0.780726	−	0.624874i	$-0.785150\pi$
$619$	−10.6409	+	7.73105i	−0.427693	+	0.310737i	0.353033	+	0.935611i	$0.385150\pi$
$620$		0			0
$621$	79.8666	+	58.0265i	3.20494	+	2.32852i
$622$		0			0
$623$	1.27757	−	3.93195i	0.0511847	−	0.157530i
$624$		0			0
$625$	−22.5214	+	10.8529i	−0.900857	+	0.434116i
$626$		0			0
$627$	4.64704	−	14.3021i	0.185585	−	0.571171i
$628$		0			0
$629$	15.7701	+	11.4577i	0.628796	+	0.456847i
$630$		0			0
$631$	20.1369	−	14.6303i	0.801635	−	0.582422i	−0.109758	−	0.993958i	$-0.535008\pi$
$631$	20.1369	−	14.6303i	0.801635	−	0.582422i	0.911393	+	0.411536i	$0.135008\pi$
$632$		0			0
$633$	15.4866	−	11.2517i	0.615538	−	0.447214i
$634$		0			0
$635$	−17.3149	+	11.4310i	−0.687119	+	0.453627i
$636$		0			0
$637$	−9.68352	−	29.8028i	−0.383675	−	1.18083i
$638$		0			0
$639$	6.15318	−	18.9375i	0.243416	−	0.749157i
$640$		0			0
$641$	2.12546	+	6.54149i	0.0839505	+	0.258373i	0.984217	−	0.176966i	$-0.0566284\pi$
$641$	2.12546	+	6.54149i	0.0839505	+	0.258373i	−0.900266	+	0.435339i	$0.856628\pi$
$642$		0			0
$643$	4.69018			0.184963			0.0924814	−	0.995714i	$-0.470520\pi$
$643$	4.69018			0.184963			0.0924814	+	0.995714i	$0.470520\pi$
$644$		0			0
$645$	−17.2288	−	62.4116i	−0.678384	−	2.45745i
$646$		0			0
$647$	−22.9192	−	16.6518i	−0.901047	−	0.654649i	0.0376879	−	0.999290i	$-0.488001\pi$
$647$	−22.9192	−	16.6518i	−0.901047	−	0.654649i	−0.938735	+	0.344641i	$0.888001\pi$
$648$		0			0
$649$	−14.8028			−0.581061
$650$		0			0
$651$	−4.89458			−0.191834
$652$		0			0
$653$	16.4711	+	11.9670i	0.644564	+	0.468303i	0.861415	−	0.507901i	$-0.169579\pi$
$653$	16.4711	+	11.9670i	0.644564	+	0.468303i	−0.216851	+	0.976205i	$0.569579\pi$
$654$		0			0
$655$	15.5277	+	0.696346i	0.606716	+	0.0272085i
$656$		0			0
$657$	−58.3507			−2.27648
$658$		0			0
$659$	−13.2389	−	40.7453i	−0.515716	−	1.58721i	−0.781975	−	0.623309i	$-0.785788\pi$
$659$	−13.2389	−	40.7453i	−0.515716	−	1.58721i	0.266259	−	0.963901i	$-0.414212\pi$
$660$		0			0
$661$	−15.1168	+	46.5249i	−0.587977	+	1.80961i	−0.00100678	+	0.999999i	$0.500320\pi$
$661$	−15.1168	+	46.5249i	−0.587977	+	1.80961i	−0.586970	+	0.809608i	$0.699680\pi$
$662$		0			0
$663$	33.2975	+	102.479i	1.29317	+	3.97996i
$664$		0			0
$665$	10.7507	+	0.482119i	0.416893	+	0.0186958i
$666$		0			0
$667$	−30.7641	+	22.3514i	−1.19119	+	0.865451i
$668$		0			0
$669$	−51.6074	+	37.4949i	−1.99526	+	1.44964i
$670$		0			0
$671$	8.40386	+	6.10576i	0.324428	+	0.235710i
$672$		0			0
$673$	11.0907	−	34.1337i	0.427515	−	1.31576i	−0.473050	−	0.881036i	$-0.656847\pi$
$673$	11.0907	−	34.1337i	0.427515	−	1.31576i	0.900565	−	0.434721i	$-0.143153\pi$
$674$		0			0
$675$	−87.7966	−	7.89044i	−3.37929	−	0.303703i
$676$		0			0
$677$	13.3259	−	41.0128i	0.512155	−	1.57625i	−0.276244	−	0.961087i	$-0.589090\pi$
$677$	13.3259	−	41.0128i	0.512155	−	1.57625i	0.788399	−	0.615164i	$-0.210910\pi$
$678$		0			0
$679$	−16.1635	−	11.7435i	−0.620298	−	0.450673i
$680$		0			0
$681$	−15.0310	+	10.9207i	−0.575991	+	0.418482i
$682$		0			0
$683$	1.75104	−	1.27221i	0.0670017	−	0.0486796i	−0.553780	−	0.832663i	$-0.686815\pi$
$683$	1.75104	−	1.27221i	0.0670017	−	0.0486796i	0.620782	+	0.783983i	$0.286815\pi$
$684$		0			0
$685$	−9.39276	+	25.0318i	−0.358879	+	0.956417i
$686$		0			0
$687$	−0.0106780	−	0.0328636i	−0.000407392	−	0.00125382i
$688$		0			0
$689$	−11.8958	+	36.6114i	−0.453192	+	1.39478i
$690$		0			0
$691$	10.2197	+	31.4530i	0.388775	+	1.19653i	0.933704	+	0.358045i	$0.116556\pi$
$691$	10.2197	+	31.4530i	0.388775	+	1.19653i	−0.544929	+	0.838482i	$0.683444\pi$
$692$		0			0
$693$	−8.86316			−0.336684
$694$		0			0
$695$	−35.1856	+	23.2290i	−1.33467	+	0.881128i
$696$		0			0
$697$	1.85946	+	1.35098i	0.0704322	+	0.0511720i
$698$		0			0
$699$	−3.92458			−0.148441
$700$		0			0
$701$	−0.658770			−0.0248814			−0.0124407	−	0.999923i	$-0.503960\pi$
$701$	−0.658770			−0.0248814			−0.0124407	+	0.999923i	$0.503960\pi$
$702$		0			0
$703$	−11.7950	−	8.56957i	−0.444857	−	0.323207i
$704$		0			0
$705$	−6.22790	+	16.5974i	−0.234556	+	0.625095i
$706$		0			0
$707$	4.28319			0.161086
$708$		0			0
$709$	−0.793010	−	2.44063i	−0.0297821	−	0.0916599i	0.935061	−	0.354488i	$-0.115345\pi$
$709$	−0.793010	−	2.44063i	−0.0297821	−	0.0916599i	−0.964843	+	0.262828i	$0.915345\pi$
$710$		0			0
$711$	−2.76397	+	8.50662i	−0.103657	+	0.319023i
$712$		0			0
$713$	2.35131	+	7.23658i	0.0880571	+	0.271012i
$714$		0			0
$715$	9.36957	+	7.47099i	0.350402	+	0.279399i
$716$		0			0
$717$	57.3364	−	41.6573i	2.14127	−	1.55572i
$718$		0			0
$719$	−5.40714	+	3.92852i	−0.201652	+	0.146509i	−0.684029	−	0.729455i	$-0.739774\pi$
$719$	−5.40714	+	3.92852i	−0.201652	+	0.146509i	0.482376	+	0.875964i	$0.339774\pi$
$720$		0			0
$721$	−16.7396	−	12.1620i	−0.623416	−	0.452938i
$722$		0			0
$723$	9.93078	−	30.5638i	0.369330	−	1.13668i
$724$		0			0
$725$	13.3411	−	31.2242i	0.495477	−	1.15964i
$726$		0			0
$727$	9.07007	−	27.9148i	0.336390	−	1.03530i	−0.629643	−	0.776885i	$-0.716799\pi$
$727$	9.07007	−	27.9148i	0.336390	−	1.03530i	0.966033	−	0.258418i	$-0.0832012\pi$
$728$		0			0
$729$	−86.0636	−	62.5289i	−3.18754	−	2.31588i
$730$		0			0
$731$	41.8472	−	30.4038i	1.54778	−	1.12453i
$732$		0			0
$733$	−12.8402	+	9.32897i	−0.474265	+	0.344573i	−0.799101	−	0.601197i	$-0.794691\pi$
$733$	−12.8402	+	9.32897i	−0.474265	+	0.344573i	0.324836	+	0.945770i	$0.394691\pi$
$734$		0			0
$735$	11.6722	+	42.2828i	0.430537	+	1.55963i
$736$		0			0
$737$	0.839349	+	2.58325i	0.0309178	+	0.0951553i
$738$		0			0
$739$	1.12280	−	3.45563i	0.0413030	−	0.127117i	−0.928279	−	0.371885i	$-0.878712\pi$
$739$	1.12280	−	3.45563i	0.0413030	−	0.127117i	0.969582	+	0.244767i	$0.0787116\pi$
$740$		0			0
$741$	−24.9043	−	76.6477i	−0.914884	−	2.81572i
$742$		0			0
$743$	−37.9148			−1.39096			−0.695480	−	0.718546i	$-0.744808\pi$
$743$	−37.9148			−1.39096			−0.695480	+	0.718546i	$0.744808\pi$
$744$		0			0
$745$	−36.0043	−	28.7087i	−1.31910	−	1.05181i
$746$		0			0
$747$	68.7832	+	49.9739i	2.51665	+	1.82845i
$748$		0			0
$749$	4.07301			0.148825
$750$		0			0
$751$	−19.2197			−0.701337			−0.350668	−	0.936500i	$-0.614046\pi$
$751$	−19.2197			−0.701337			−0.350668	+	0.936500i	$0.614046\pi$
$752$		0			0
$753$	−14.4318	−	10.4853i	−0.525926	−	0.382107i
$754$		0			0
$755$	−10.8333	−	8.63812i	−0.394264	−	0.314373i
$756$		0			0
$757$	−19.0214			−0.691344			−0.345672	−	0.938355i	$-0.612349\pi$
$757$	−19.0214			−0.691344			−0.345672	+	0.938355i	$0.612349\pi$
$758$		0			0
$759$	5.80511	+	17.8663i	0.210712	+	0.648505i
$760$		0			0
$761$	3.91374	−	12.0452i	0.141873	−	0.436640i	−0.854723	−	0.519085i	$-0.826273\pi$
$761$	3.91374	−	12.0452i	0.141873	−	0.436640i	0.996596	+	0.0824449i	$0.0262729\pi$
$762$		0			0
$763$	−5.49031	−	16.8974i	−0.198763	−	0.611728i
$764$		0			0
$765$	−29.4378	−	106.639i	−1.06433	−	3.85554i
$766$		0			0
$767$	−64.1801	+	46.6296i	−2.31741	+	1.68370i
$768$		0			0
$769$	−10.7581	+	7.81622i	−0.387947	+	0.281860i	−0.764614	−	0.644489i	$-0.777070\pi$
$769$	−10.7581	+	7.81622i	−0.387947	+	0.281860i	0.376667	+	0.926349i	$0.377070\pi$
$770$		0			0
$771$	−36.3328	−	26.3973i	−1.30849	−	0.950676i
$772$		0			0
$773$	−11.2985	+	34.7731i	−0.406378	+	1.25070i	0.513361	+	0.858173i	$0.328400\pi$
$773$	−11.2985	+	34.7731i	−0.406378	+	1.25070i	−0.919739	+	0.392530i	$0.871600\pi$
$774$		0			0
$775$	−5.11716	−	4.46956i	−0.183814	−	0.160551i
$776$		0			0
$777$	−3.62030	+	11.1422i	−0.129878	+	0.399722i
$778$		0			0
$779$	−1.39075	−	1.01044i	−0.0498290	−	0.0362029i
$780$		0			0
$781$	1.95143	−	1.41780i	0.0698277	−	0.0507328i
$782$		0			0
$783$	96.8602	−	70.3730i	3.46150	−	2.51493i
$784$		0			0
$785$	2.15411	+	1.71762i	0.0768835	+	0.0613044i
$786$		0			0
$787$	−7.46727	−	22.9819i	−0.266179	−	0.819216i	−0.991419	−	0.130720i	$-0.958271\pi$
$787$	−7.46727	−	22.9819i	−0.266179	−	0.819216i	0.725240	−	0.688496i	$-0.241729\pi$
$788$		0			0
$789$	−16.6717	+	51.3101i	−0.593527	+	1.82669i
$790$		0			0
$791$	−2.36749	−	7.28637i	−0.0841781	−	0.259074i
$792$		0			0
$793$	55.6699			1.97690
$794$		0			0
$795$	18.9307	−	50.4505i	0.671402	−	1.78929i
$796$		0			0
$797$	−35.5702	−	25.8433i	−1.25996	−	0.915415i	−0.261205	−	0.965283i	$-0.584120\pi$
$797$	−35.5702	−	25.8433i	−1.25996	−	0.915415i	−0.998756	+	0.0498681i	$0.984120\pi$
$798$		0			0
$799$	−14.1626			−0.501036
$800$		0			0
$801$	31.7875			1.12316
$802$		0			0
$803$	−5.71850	−	4.15473i	−0.201802	−	0.146617i
$804$		0			0
$805$	−11.2189	+	7.40659i	−0.395415	+	0.261048i
$806$		0			0
$807$	−7.73204			−0.272181
$808$		0			0
$809$	−10.1028	−	31.0931i	−0.355194	−	1.09318i	−0.955897	−	0.293703i	$-0.905112\pi$
$809$	−10.1028	−	31.0931i	−0.355194	−	1.09318i	0.600702	−	0.799473i	$-0.294888\pi$
$810$		0			0
$811$	3.68775	−	11.3497i	0.129494	−	0.398543i	−0.865199	−	0.501429i	$-0.832808\pi$
$811$	3.68775	−	11.3497i	0.129494	−	0.398543i	0.994693	+	0.102886i	$0.0328078\pi$
$812$		0			0
$813$	11.5579	+	35.5717i	0.405355	+	1.24755i
$814$		0			0
$815$	−1.46391	+	3.90133i	−0.0512784	+	0.136658i
$816$		0			0
$817$	−31.2990	+	22.7400i	−1.09501	+	0.795573i
$818$		0			0
$819$	−38.4278	+	27.9194i	−1.34278	+	0.975584i
$820$		0			0
$821$	19.7598	+	14.3563i	0.689621	+	0.501039i	0.876536	−	0.481337i	$-0.159849\pi$
$821$	19.7598	+	14.3563i	0.689621	+	0.501039i	−0.186914	+	0.982376i	$0.559849\pi$
$822$		0			0
$823$	−11.3929	+	35.0639i	−0.397133	+	1.22225i	0.530155	+	0.847901i	$0.322134\pi$
$823$	−11.3929	+	35.0639i	−0.397133	+	1.22225i	−0.927288	+	0.374349i	$0.877866\pi$
$824$		0			0
$825$	−12.6337	−	11.0348i	−0.439848	−	0.384184i
$826$		0			0
$827$	−12.5223	+	38.5396i	−0.435442	+	1.34015i	0.457192	+	0.889368i	$0.348855\pi$
$827$	−12.5223	+	38.5396i	−0.435442	+	1.34015i	−0.892633	+	0.450784i	$0.851145\pi$
$828$		0			0
$829$	3.27924	+	2.38251i	0.113893	+	0.0827480i	0.643274	−	0.765636i	$-0.277576\pi$
$829$	3.27924	+	2.38251i	0.113893	+	0.0827480i	−0.529381	+	0.848384i	$0.677576\pi$
$830$		0			0
$831$	−33.6289	+	24.4329i	−1.16657	+	0.847566i
$832$		0			0
$833$	−28.3508	+	20.5981i	−0.982298	+	0.713681i
$834$		0			0
$835$	−3.27007	−	0.146648i	−0.113165	−	0.00507496i
$836$		0			0
$837$	−7.40305	−	22.7842i	−0.255887	−	0.787538i
$838$		0			0
$839$	2.77448	−	8.53896i	0.0957856	−	0.294798i	−0.891672	−	0.452682i	$-0.850467\pi$
$839$	2.77448	−	8.53896i	0.0957856	−	0.294798i	0.987458	+	0.157884i	$0.0504673\pi$
$840$		0			0
$841$	5.28962	+	16.2798i	0.182401	+	0.561372i
$842$		0			0
$843$	−56.0012			−1.92878
$844$		0			0
$845$	35.1177	+	1.57487i	1.20809	+	0.0541772i
$846$		0			0
$847$	−0.868610	−	0.631082i	−0.0298458	−	0.0216842i
$848$		0			0
$849$	52.3274			1.79587
$850$		0			0
$851$	18.2127			0.624324
$852$		0			0
$853$	−14.0446	−	10.2040i	−0.480877	−	0.349378i	0.320788	−	0.947151i	$-0.396052\pi$
$853$	−14.0446	−	10.2040i	−0.480877	−	0.349378i	−0.801665	+	0.597773i	$0.796052\pi$
$854$		0			0
$855$	22.0176	+	79.7588i	0.752984	+	2.72769i
$856$		0			0
$857$	−27.0908			−0.925405			−0.462702	−	0.886514i	$-0.653120\pi$
$857$	−27.0908			−0.925405			−0.462702	+	0.886514i	$0.653120\pi$
$858$		0			0
$859$	4.79492	+	14.7572i	0.163601	+	0.503511i	0.998930	−	0.0462384i	$-0.0147234\pi$
$859$	4.79492	+	14.7572i	0.163601	+	0.503511i	−0.835330	+	0.549749i	$0.814723\pi$
$860$		0			0
$861$	−0.426872	+	1.31378i	−0.0145478	+	0.0447734i
$862$		0			0
$863$	−3.92660	−	12.0848i	−0.133663	−	0.411373i	0.861717	−	0.507390i	$-0.169390\pi$
$863$	−3.92660	−	12.0848i	−0.133663	−	0.411373i	−0.995380	+	0.0960172i	$0.969390\pi$
$864$		0			0
$865$	−24.5664	+	16.2184i	−0.835283	+	0.551442i
$866$		0			0
$867$	51.3461	−	37.3052i	1.74381	−	1.26695i
$868$		0			0
$869$	−0.876570	+	0.636866i	−0.0297356	+	0.0216042i
$870$		0			0
$871$	11.7765	+	8.55614i	0.399032	+	0.289914i
$872$		0			0
$873$	47.4695	−	146.096i	1.60660	−	4.94460i
$874$		0			0
$875$	5.20620	−	10.8161i	0.176002	−	0.365652i
$876$		0			0
$877$	5.34528	−	16.4511i	0.180497	−	0.555513i	−0.819345	−	0.573301i	$-0.805662\pi$
$877$	5.34528	−	16.4511i	0.180497	−	0.555513i	0.999842	+	0.0177880i	$0.00566240\pi$
$878$		0			0
$879$	−75.5255	−	54.8725i	−2.54741	−	1.85080i
$880$		0			0
$881$	−17.8537	+	12.9715i	−0.601507	+	0.437020i	−0.846413	−	0.532526i	$-0.821243\pi$
$881$	−17.8537	+	12.9715i	−0.601507	+	0.437020i	0.244907	+	0.969547i	$0.421243\pi$
$882$		0			0
$883$	34.3330	−	24.9444i	1.15540	−	0.839446i	0.166209	−	0.986091i	$-0.446847\pi$
$883$	34.3330	−	24.9444i	1.15540	−	0.839446i	0.989189	+	0.146645i	$0.0468474\pi$
$884$		0			0
$885$	92.6721	−	61.1809i	3.11514	−	2.05657i
$886$		0			0
$887$	10.9365	+	33.6590i	0.367211	+	1.13016i	0.948585	+	0.316523i	$0.102515\pi$
$887$	10.9365	+	33.6590i	0.367211	+	1.13016i	−0.581374	+	0.813636i	$0.697485\pi$
$888$		0			0
$889$	3.07849	−	9.47461i	0.103249	−	0.317768i
$890$		0			0
$891$	−10.6244	−	32.6985i	−0.355930	−	1.09544i
$892$		0			0
$893$	10.5927			0.354470
$894$		0			0
$895$	4.03183	+	14.6053i	0.134769	+	0.488203i
$896$		0			0
$897$	81.4487	+	59.1760i	2.71949	+	1.97583i
$898$		0			0
$899$	9.22799			0.307771
$900$		0			0
$901$	43.0494			1.43418
$902$		0			0
$903$	25.1508	+	18.2731i	0.836967	+	0.608092i
$904$		0			0
$905$	3.60749	+	0.161780i	0.119917	+	0.00537775i
$906$		0			0
$907$	55.9405			1.85747			0.928736	−	0.370741i	$-0.120896\pi$
$907$	55.9405			1.85747			0.928736	+	0.370741i	$0.120896\pi$
$908$		0			0
$909$	10.1766	+	31.3205i	0.337538	+	1.03883i
$910$		0			0
$911$	1.25520	−	3.86310i	0.0415865	−	0.127990i	−0.928108	−	0.372312i	$-0.878565\pi$
$911$	1.25520	−	3.86310i	0.0415865	−	0.127990i	0.969694	+	0.244322i	$0.0785653\pi$
$912$		0			0
$913$	3.18262	+	9.79511i	0.105330	+	0.324171i
$914$		0			0
$915$	−77.8475	−	3.49111i	−2.57356	−	0.115413i
$916$		0			0
$917$	−6.03784	+	4.38675i	−0.199387	+	0.144863i
$918$		0			0
$919$	−30.6559	+	22.2728i	−1.01125	+	0.734713i	−0.964470	−	0.264192i	$-0.914895\pi$
$919$	−30.6559	+	22.2728i	−1.01125	+	0.734713i	−0.0467760	+	0.998905i	$0.514895\pi$
$920$		0			0
$921$	38.6441	+	28.0765i	1.27336	+	0.925154i
$922$		0			0
$923$	3.99463	−	12.2942i	0.131485	−	0.404669i
$924$		0			0
$925$	−13.9596	+	8.34290i	−0.458988	+	0.274313i
$926$		0			0
$927$	49.1615	−	151.303i	1.61467	−	4.96946i
$928$		0			0
$929$	16.6169	+	12.0729i	0.545182	+	0.396098i	0.826006	−	0.563661i	$-0.190608\pi$
$929$	16.6169	+	12.0729i	0.545182	+	0.396098i	−0.280824	+	0.959759i	$0.590608\pi$
$930$		0			0
$931$	21.2045	−	15.4060i	0.694950	−	0.504911i
$932$		0			0
$933$	33.1844	−	24.1099i	1.08641	−	0.789321i
$934$		0			0
$935$	4.70801	−	12.5469i	0.153968	−	0.410328i
$936$		0			0
$937$	7.79889	+	24.0025i	0.254779	+	0.784128i	0.993873	+	0.110526i	$0.0352536\pi$
$937$	7.79889	+	24.0025i	0.254779	+	0.784128i	−0.739095	+	0.673602i	$0.764746\pi$
$938$		0			0
$939$	−30.9711	+	95.3192i	−1.01070	+	3.11062i
$940$		0			0
$941$	16.3499	+	50.3199i	0.532992	+	1.64038i	0.747948	+	0.663757i	$0.231039\pi$
$941$	16.3499	+	50.3199i	0.532992	+	1.64038i	−0.214956	+	0.976624i	$0.568961\pi$
$942$		0			0
$943$	2.14747			0.0699312
$944$		0			0
$945$	35.3226	−	23.3195i	1.14904	−	0.758583i
$946$		0			0
$947$	5.60383	+	4.07142i	0.182100	+	0.132303i	0.675101	−	0.737725i	$-0.264100\pi$
$947$	5.60383	+	4.07142i	0.182100	+	0.132303i	−0.493001	+	0.870029i	$0.664100\pi$
$948$		0			0
$949$	−37.8812			−1.22968
$950$		0			0
$951$	−32.6242			−1.05791
$952$		0			0
$953$	48.7024	+	35.3844i	1.57762	+	1.14621i	0.919355	+	0.393430i	$0.128712\pi$
$953$	48.7024	+	35.3844i	1.57762	+	1.14621i	0.658270	+	0.752782i	$0.271288\pi$
$954$		0			0
$955$	−2.77135	+	7.38568i	−0.0896787	+	0.238995i
$956$		0			0
$957$	22.7828			0.736464
$958$		0			0
$959$	−3.96699	−	12.2092i	−0.128101	−	0.394254i
$960$		0			0
$961$	−9.00893	+	27.7266i	−0.290611	+	0.894408i
$962$		0			0
$963$	9.67727	+	29.7836i	0.311846	+	0.959762i
$964$		0			0
$965$	−26.7470	−	21.3272i	−0.861016	−	0.686547i
$966$		0			0
$967$	−11.5825	+	8.41516i	−0.372467	+	0.270613i	−0.758233	−	0.651983i	$-0.773937\pi$
$967$	−11.5825	+	8.41516i	−0.372467	+	0.270613i	0.385766	+	0.922597i	$0.373937\pi$
$968$		0			0
$969$	−72.9134	+	52.9747i	−2.34232	+	1.70179i
$970$		0			0
$971$	29.3031	+	21.2899i	0.940381	+	0.683227i	0.948512	−	0.316740i	$-0.102588\pi$
$971$	29.3031	+	21.2899i	0.940381	+	0.683227i	−0.00813162	+	0.999967i	$0.502588\pi$
$972$		0			0
$973$	6.25580	−	19.2534i	0.200552	−	0.617235i
$974$		0			0
$975$	−89.5358	−	8.04674i	−2.86744	−	0.257702i
$976$		0			0
$977$	12.7621	−	39.2776i	0.408294	−	1.25660i	−0.509819	−	0.860282i	$-0.670287\pi$
$977$	12.7621	−	39.2776i	0.408294	−	1.25660i	0.918113	−	0.396319i	$-0.129713\pi$
$978$		0			0
$979$	3.11525	+	2.26336i	0.0995637	+	0.0723372i
$980$		0			0
$981$	110.516	−	80.2949i	3.52852	−	2.56362i
$982$		0			0
$983$	−32.0068	+	23.2543i	−1.02086	+	0.741697i	−0.966459	−	0.256822i	$-0.917325\pi$
$983$	−32.0068	+	23.2543i	−1.02086	+	0.741697i	−0.0544001	+	0.998519i	$0.517325\pi$
$984$		0			0
$985$	−2.63347	−	9.53975i	−0.0839092	−	0.303962i
$986$		0			0
$987$	−2.63033	−	8.09532i	−0.0837243	−	0.257677i
$988$		0			0
$989$	14.9344	−	45.9635i	0.474887	−	1.46155i
$990$		0			0
$991$	5.24461	+	16.1413i	0.166601	+	0.512744i	0.999151	−	0.0412058i	$-0.0131199\pi$
$991$	5.24461	+	16.1413i	0.166601	+	0.512744i	−0.832550	+	0.553950i	$0.813120\pi$
$992$		0			0
$993$	−71.1567			−2.25809
$994$		0			0
$995$	−20.5570	−	16.3915i	−0.651701	−	0.519646i
$996$		0			0
$997$	−8.45689	−	6.14429i	−0.267832	−	0.194592i	0.445760	−	0.895152i	$-0.352933\pi$
$997$	−8.45689	−	6.14429i	−0.267832	−	0.194592i	−0.713593	+	0.700561i	$0.752933\pi$
$998$		0			0
$999$	−57.3424			−1.81423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.221.13	✓	52
25.6	even	5	inner	1100.2.q.b.881.13	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.13	✓	52	1.1	even	1	trivial
1100.2.q.b.881.13	yes	52	25.6	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.71414 + 1.97194i) q^{3} +(-1.74832 - 1.39405i) q^{5} +1.07366 q^{7} +(2.55096 + 7.85106i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(1.65608 + 5.09689i) q^{13} +(-1.99619 - 7.23123i) q^{15} +(4.84857 - 3.52269i) q^{17} +(-3.62641 + 2.63474i) q^{19} +(2.91406 + 2.11719i) q^{21} +(1.73036 - 5.32549i) q^{23} +(1.11323 + 4.87450i) q^{25} +(-5.44800 + 16.7672i) q^{27} +(-5.49403 - 3.99164i) q^{29} +(-1.09934 + 0.798716i) q^{31} +(-2.71414 + 1.97194i) q^{33} +(-1.87710 - 1.49674i) q^{35} +(1.00509 + 3.09334i) q^{37} +(-5.55592 + 17.0994i) q^{39} +(0.118510 + 0.364737i) q^{41} +8.63084 q^{43} +(6.48489 - 17.2823i) q^{45} +(-1.91181 - 1.38901i) q^{47} -5.84725 q^{49} +20.1062 q^{51} +(5.81123 + 4.22211i) q^{53} +(1.86608 - 1.23196i) q^{55} -15.0381 q^{57} +(4.57432 + 14.0783i) q^{59} +(3.20999 - 9.87933i) q^{61} +(2.73887 + 8.42937i) q^{63} +(4.20998 - 11.2196i) q^{65} +(2.19745 - 1.59654i) q^{67} +(15.1980 - 11.0420i) q^{69} +(-1.95143 - 1.41780i) q^{71} +(-2.18427 + 6.72250i) q^{73} +(-6.59073 + 15.4253i) q^{75} +(-0.331779 + 1.02111i) q^{77} +(0.876570 + 0.636866i) q^{79} +(-27.8150 + 20.2088i) q^{81} +(8.33222 - 6.05371i) q^{83} +(-13.3877 - 0.600377i) q^{85} +(-7.04028 - 21.6678i) q^{87} +(1.18992 - 3.66219i) q^{89} +(1.77807 + 5.47233i) q^{91} -4.55877 q^{93} +(10.0131 + 0.449042i) q^{95} +(-15.0546 - 10.9378i) q^{97} -8.25509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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