LMFDB - Embedded newform 1100.2.q.b.221.9

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			221.9
Character	$\chi$	$=$	1100.221
Dual form			1100.2.q.b.881.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.921658 + 0.669624i) q^{3} +(-1.47725 + 1.67861i) q^{5} -4.58549 q^{7} +(-0.525993 - 1.61884i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(0.545520 + 1.67894i) q^{13} +(-2.48556 + 0.557910i) q^{15} +(5.64523 - 4.10150i) q^{17} +(0.225177 - 0.163601i) q^{19} +(-4.22626 - 3.07056i) q^{21} +(0.433073 - 1.33286i) q^{23} +(-0.635492 - 4.95945i) q^{25} +(1.65535 - 5.09466i) q^{27} +(-4.48401 - 3.25782i) q^{29} +(-1.75233 + 1.27315i) q^{31} +(-0.921658 + 0.669624i) q^{33} +(6.77390 - 7.69727i) q^{35} +(-3.20398 - 9.86084i) q^{37} +(-0.621474 + 1.91270i) q^{39} +(-0.479808 - 1.47670i) q^{41} -10.0846 q^{43} +(3.49443 + 1.50849i) q^{45} +(-8.19224 - 5.95201i) q^{47} +14.0267 q^{49} +7.94943 q^{51} +(-8.31392 - 6.04042i) q^{53} +(-1.13996 - 1.92366i) q^{55} +0.317087 q^{57} +(1.65927 + 5.10671i) q^{59} +(-0.419275 + 1.29039i) q^{61} +(2.41194 + 7.42318i) q^{63} +(-3.62416 - 1.56449i) q^{65} +(7.20492 - 5.23468i) q^{67} +(1.29166 - 0.938447i) q^{69} +(11.8891 + 8.63790i) q^{71} +(-2.82642 + 8.69883i) q^{73} +(2.73526 - 4.99646i) q^{75} +(1.41700 - 4.36106i) q^{77} +(-2.03346 - 1.47739i) q^{79} +(0.805971 - 0.585572i) q^{81} +(2.57741 - 1.87260i) q^{83} +(-1.45455 + 15.5351i) q^{85} +(-1.95121 - 6.00519i) q^{87} +(-3.18037 + 9.78818i) q^{89} +(-2.50148 - 7.69876i) q^{91} -2.46758 q^{93} +(-0.0580193 + 0.619664i) q^{95} +(13.8642 + 10.0729i) q^{97} +1.70215 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.921658	+	0.669624i	0.532120	+	0.386608i	0.821150	−	0.570712i	$-0.193333\pi$
$3$	0.921658	+	0.669624i	0.532120	+	0.386608i	−0.289030	+	0.957320i	$0.593333\pi$
$4$		0			0
$5$	−1.47725	+	1.67861i	−0.660644	+	0.750699i
$5$	−1.47725	+	1.67861i	−0.660644	+	0.750699i
$6$		0			0
$7$	−4.58549			−1.73315			−0.866577	−	0.499044i	$-0.833685\pi$
$7$	−4.58549			−1.73315			−0.866577	+	0.499044i	$0.833685\pi$
$8$		0			0
$9$	−0.525993	−	1.61884i	−0.175331	−	0.539614i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$		0			0
$13$	0.545520	+	1.67894i	0.151300	+	0.465654i	0.997767	−	0.0667872i	$-0.0212748\pi$
$13$	0.545520	+	1.67894i	0.151300	+	0.465654i	−0.846467	+	0.532441i	$0.821275\pi$
$14$		0			0
$15$	−2.48556	+	0.557910i	−0.641768	+	0.144052i
$16$		0			0
$17$	5.64523	−	4.10150i	1.36917	−	0.994759i	0.371367	−	0.928486i	$-0.378889\pi$
$17$	5.64523	−	4.10150i	1.36917	−	0.994759i	0.997802	−	0.0662726i	$-0.0211107\pi$
$18$		0			0
$19$	0.225177	−	0.163601i	0.0516592	−	0.0375326i	−0.561656	−	0.827371i	$-0.689836\pi$
$19$	0.225177	−	0.163601i	0.0516592	−	0.0375326i	0.613315	+	0.789838i	$0.289836\pi$
$20$		0			0
$21$	−4.22626	−	3.07056i	−0.922245	−	0.670050i
$22$		0			0
$23$	0.433073	−	1.33286i	0.0903020	−	0.277921i	−0.895699	−	0.444661i	$-0.853324\pi$
$23$	0.433073	−	1.33286i	0.0903020	−	0.277921i	0.986001	+	0.166740i	$0.0533241\pi$
$24$		0			0
$25$	−0.635492	−	4.95945i	−0.127098	−	0.991890i
$26$		0			0
$27$	1.65535	−	5.09466i	0.318573	−	0.980467i
$28$		0			0
$29$	−4.48401	−	3.25782i	−0.832659	−	0.604962i	0.0876513	−	0.996151i	$-0.472064\pi$
$29$	−4.48401	−	3.25782i	−0.832659	−	0.604962i	−0.920310	+	0.391189i	$0.872064\pi$
$30$		0			0
$31$	−1.75233	+	1.27315i	−0.314728	+	0.228664i	−0.733923	−	0.679233i	$-0.762313\pi$
$31$	−1.75233	+	1.27315i	−0.314728	+	0.228664i	0.419194	+	0.907897i	$0.362313\pi$
$32$		0			0
$33$	−0.921658	+	0.669624i	−0.160440	+	0.116567i
$34$		0			0
$35$	6.77390	−	7.69727i	1.14500	−	1.30108i
$36$		0			0
$37$	−3.20398	−	9.86084i	−0.526731	−	1.62111i	−0.760867	−	0.648908i	$-0.775226\pi$
$37$	−3.20398	−	9.86084i	−0.526731	−	1.62111i	0.234135	−	0.972204i	$-0.424774\pi$
$38$		0			0
$39$	−0.621474	+	1.91270i	−0.0995155	+	0.306277i
$40$		0			0
$41$	−0.479808	−	1.47670i	−0.0749334	−	0.230621i	0.906574	−	0.422048i	$-0.138689\pi$
$41$	−0.479808	−	1.47670i	−0.0749334	−	0.230621i	−0.981507	+	0.191427i	$0.938689\pi$
$42$		0			0
$43$	−10.0846			−1.53789			−0.768944	−	0.639316i	$-0.779218\pi$
$43$	−10.0846			−1.53789			−0.768944	+	0.639316i	$0.779218\pi$
$44$		0			0
$45$	3.49443	+	1.50849i	0.520919	+	0.224872i
$46$		0			0
$47$	−8.19224	−	5.95201i	−1.19496	−	0.868190i	−0.201181	−	0.979554i	$-0.564478\pi$
$47$	−8.19224	−	5.95201i	−1.19496	−	0.868190i	−0.993780	+	0.111364i	$0.964478\pi$
$48$		0			0
$49$	14.0267			2.00382
$50$		0			0
$51$	7.94943			1.11314
$52$		0			0
$53$	−8.31392	−	6.04042i	−1.14201	−	0.829715i	−0.154608	−	0.987976i	$-0.549411\pi$
$53$	−8.31392	−	6.04042i	−1.14201	−	0.829715i	−0.987397	+	0.158260i	$0.949411\pi$
$54$		0			0
$55$	−1.13996	−	1.92366i	−0.153713	−	0.259387i
$56$		0			0
$57$	0.317087			0.0419992
$58$		0			0
$59$	1.65927	+	5.10671i	0.216019	+	0.664837i	0.999080	+	0.0428920i	$0.0136571\pi$
$59$	1.65927	+	5.10671i	0.216019	+	0.664837i	−0.783061	+	0.621945i	$0.786343\pi$
$60$		0			0
$61$	−0.419275	+	1.29039i	−0.0536826	+	0.165218i	−0.974303	−	0.225240i	$-0.927683\pi$
$61$	−0.419275	+	1.29039i	−0.0536826	+	0.165218i	0.920621	+	0.390458i	$0.127683\pi$
$62$		0			0
$63$	2.41194	+	7.42318i	0.303876	+	0.935233i
$64$		0			0
$65$	−3.62416	−	1.56449i	−0.449521	−	0.194051i
$66$		0			0
$67$	7.20492	−	5.23468i	0.880221	−	0.639518i	−0.0530889	−	0.998590i	$-0.516907\pi$
$67$	7.20492	−	5.23468i	0.880221	−	0.639518i	0.933310	+	0.359072i	$0.116907\pi$
$68$		0			0
$69$	1.29166	−	0.938447i	0.155498	−	0.112976i
$70$		0			0
$71$	11.8891	+	8.63790i	1.41097	+	1.02513i	0.993180	+	0.116587i	$0.0371955\pi$
$71$	11.8891	+	8.63790i	1.41097	+	1.02513i	0.417791	+	0.908543i	$0.362805\pi$
$72$		0			0
$73$	−2.82642	+	8.69883i	−0.330808	+	1.01812i	0.637943	+	0.770084i	$0.279786\pi$
$73$	−2.82642	+	8.69883i	−0.330808	+	1.01812i	−0.968750	+	0.248038i	$0.920214\pi$
$74$		0			0
$75$	2.73526	−	4.99646i	0.315841	−	0.576941i
$76$		0			0
$77$	1.41700	−	4.36106i	0.161482	−	0.496989i
$78$		0			0
$79$	−2.03346	−	1.47739i	−0.228782	−	0.166220i	0.467489	−	0.883999i	$-0.345159\pi$
$79$	−2.03346	−	1.47739i	−0.228782	−	0.166220i	−0.696271	+	0.717779i	$0.745159\pi$
$80$		0			0
$81$	0.805971	−	0.585572i	0.0895523	−	0.0650636i
$82$		0			0
$83$	2.57741	−	1.87260i	0.282908	−	0.205545i	−0.437277	−	0.899327i	$-0.644057\pi$
$83$	2.57741	−	1.87260i	0.282908	−	0.205545i	0.720185	+	0.693782i	$0.244057\pi$
$84$		0			0
$85$	−1.45455	+	15.5351i	−0.157768	+	1.68502i
$86$		0			0
$87$	−1.95121	−	6.00519i	−0.209191	−	0.643824i
$88$		0			0
$89$	−3.18037	+	9.78818i	−0.337119	+	1.03754i	0.628550	+	0.777769i	$0.283649\pi$
$89$	−3.18037	+	9.78818i	−0.337119	+	1.03754i	−0.965669	+	0.259776i	$0.916351\pi$
$90$		0			0
$91$	−2.50148	−	7.69876i	−0.262226	−	0.807049i
$92$		0			0
$93$	−2.46758			−0.255876
$94$		0			0
$95$	−0.0580193	+	0.619664i	−0.00595265	+	0.0635762i
$96$		0			0
$97$	13.8642	+	10.0729i	1.40770	+	1.02275i	0.993652	+	0.112497i	$0.0358850\pi$
$97$	13.8642	+	10.0729i	1.40770	+	1.02275i	0.414047	+	0.910256i	$0.364115\pi$
$98$		0			0
$99$	1.70215			0.171073
$100$		0			0
$101$	−10.6373			−1.05845			−0.529224	−	0.848482i	$-0.677517\pi$
$101$	−10.6373			−1.05845			−0.529224	+	0.848482i	$0.677517\pi$
$102$		0			0
$103$	2.75387	+	2.00080i	0.271346	+	0.197145i	0.715134	−	0.698987i	$-0.246366\pi$
$103$	2.75387	+	2.00080i	0.271346	+	0.197145i	−0.443788	+	0.896132i	$0.646366\pi$
$104$		0			0
$105$	11.3975	−	2.55829i	1.11228	−	0.249664i
$106$		0			0
$107$	−17.5843			−1.69994			−0.849968	−	0.526834i	$-0.823379\pi$
$107$	−17.5843			−1.69994			−0.849968	+	0.526834i	$0.823379\pi$
$108$		0			0
$109$	−4.60659	−	14.1776i	−0.441231	−	1.35797i	−0.886564	−	0.462605i	$-0.846915\pi$
$109$	−4.60659	−	14.1776i	−0.441231	−	1.35797i	0.445333	−	0.895365i	$-0.353085\pi$
$110$		0			0
$111$	3.65008	−	11.2338i	0.346450	−	1.06626i
$112$		0			0
$113$	1.52667	+	4.69861i	0.143617	+	0.442008i	0.996831	−	0.0795537i	$-0.0253495\pi$
$113$	1.52667	+	4.69861i	0.143617	+	0.442008i	−0.853213	+	0.521562i	$0.825350\pi$
$114$		0			0
$115$	1.59761	+	2.69593i	0.148978	+	0.251396i
$116$		0			0
$117$	2.43099	−	1.76622i	0.224746	−	0.163287i
$118$		0			0
$119$	−25.8861	+	18.8074i	−2.37298	+	1.72407i
$120$		0			0
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$		0			0
$123$	0.546613	−	1.68230i	0.0492864	−	0.151688i
$124$		0			0
$125$	9.26378	+	6.25958i	0.828578	+	0.559874i
$126$		0			0
$127$	−3.84281	+	11.8270i	−0.340994	+	1.04947i	0.622699	+	0.782462i	$0.286036\pi$
$127$	−3.84281	+	11.8270i	−0.340994	+	1.04947i	−0.963693	+	0.267011i	$0.913964\pi$
$128$		0			0
$129$	−9.29456	−	6.75289i	−0.818340	−	0.594559i
$130$		0			0
$131$	−0.0419436	+	0.0304738i	−0.00366463	+	0.00266251i	−0.589616	−	0.807684i	$-0.700721\pi$
$131$	−0.0419436	+	0.0304738i	−0.00366463	+	0.00266251i	0.585951	+	0.810346i	$0.300721\pi$
$132$		0			0
$133$	−1.03255	+	0.750190i	−0.0895332	+	0.0650497i
$134$		0			0
$135$	6.10660	+	10.3048i	0.525573	+	0.886893i
$136$		0			0
$137$	−5.54272	−	17.0587i	−0.473546	−	1.45743i	−0.847908	−	0.530143i	$-0.822138\pi$
$137$	−5.54272	−	17.0587i	−0.473546	−	1.45743i	0.374362	−	0.927283i	$-0.377862\pi$
$138$		0			0
$139$	−4.53157	+	13.9467i	−0.384362	+	1.18295i	0.552579	+	0.833460i	$0.313644\pi$
$139$	−4.53157	+	13.9467i	−0.384362	+	1.18295i	−0.936942	+	0.349486i	$0.886356\pi$
$140$		0			0
$141$	−3.56484	−	10.9714i	−0.300213	−	0.923962i
$142$		0			0
$143$	−1.76534			−0.147625
$144$		0			0
$145$	12.0926	−	2.71432i	1.00424	−	0.225412i
$146$		0			0
$147$	12.9279	+	9.39264i	1.06627	+	0.774692i
$148$		0			0
$149$	6.79887			0.556985			0.278492	−	0.960438i	$-0.410165\pi$
$149$	6.79887			0.556985			0.278492	+	0.960438i	$0.410165\pi$
$150$		0			0
$151$	2.83345			0.230583			0.115291	−	0.993332i	$-0.463220\pi$
$151$	2.83345			0.230583			0.115291	+	0.993332i	$0.463220\pi$
$152$		0			0
$153$	−9.60902	−	6.98136i	−0.776843	−	0.564410i
$154$		0			0
$155$	0.451508	−	4.82224i	0.0362660	−	0.387332i
$156$		0			0
$157$	−3.72445			−0.297244			−0.148622	−	0.988894i	$-0.547484\pi$
$157$	−3.72445			−0.297244			−0.148622	+	0.988894i	$0.547484\pi$
$158$		0			0
$159$	−3.61779	−	11.1344i	−0.286909	−	0.883016i
$160$		0			0
$161$	−1.98585	+	6.11183i	−0.156507	+	0.481680i
$162$		0			0
$163$	−7.65663	−	23.5647i	−0.599713	−	1.84573i	−0.529706	−	0.848181i	$-0.677698\pi$
$163$	−7.65663	−	23.5647i	−0.599713	−	1.84573i	−0.0700069	−	0.997547i	$-0.522302\pi$
$164$		0			0
$165$	0.237475	−	2.53631i	0.0184874	−	0.197451i
$166$		0			0
$167$	−13.3087	+	9.66933i	−1.02986	+	0.748235i	−0.968280	−	0.249867i	$-0.919613\pi$
$167$	−13.3087	+	9.66933i	−1.02986	+	0.748235i	−0.0615774	+	0.998102i	$0.519613\pi$
$168$		0			0
$169$	7.99598	−	5.80942i	0.615075	−	0.446878i
$170$		0			0
$171$	−0.383285	−	0.278473i	−0.0293105	−	0.0212954i
$172$		0			0
$173$	3.87771	−	11.9343i	0.294816	−	0.907352i	−0.688467	−	0.725268i	$-0.741716\pi$
$173$	3.87771	−	11.9343i	0.294816	−	0.907352i	0.983283	−	0.182084i	$-0.0582842\pi$
$174$		0			0
$175$	2.91404	+	22.7415i	0.220281	+	1.71910i
$176$		0			0
$177$	−1.89029	+	5.81773i	−0.142083	+	0.437287i
$178$		0			0
$179$	−3.89837	−	2.83233i	−0.291378	−	0.211698i	0.432487	−	0.901640i	$-0.357636\pi$
$179$	−3.89837	−	2.83233i	−0.291378	−	0.211698i	−0.723865	+	0.689942i	$0.757636\pi$
$180$		0			0
$181$	17.6958	−	12.8567i	1.31532	−	0.955633i	0.315338	−	0.948979i	$-0.397882\pi$
$181$	17.6958	−	12.8567i	1.31532	−	0.955633i	0.999978	−	0.00665351i	$-0.00211790\pi$
$182$		0			0
$183$	−1.25051	+	0.908547i	−0.0924401	+	0.0671617i
$184$		0			0
$185$	21.2856	+	9.18863i	1.56495	+	0.675562i
$186$		0			0
$187$	2.15628	+	6.63636i	0.157683	+	0.485299i
$188$		0			0
$189$	−7.59062	+	23.3615i	−0.552136	+	1.69930i
$190$		0			0
$191$	−0.110617	−	0.340443i	−0.00800394	−	0.0246336i	0.946975	−	0.321308i	$-0.104122\pi$
$191$	−0.110617	−	0.340443i	−0.00800394	−	0.0246336i	−0.954979	+	0.296674i	$0.904122\pi$
$192$		0			0
$193$	−8.83535			−0.635983			−0.317991	−	0.948094i	$-0.603008\pi$
$193$	−8.83535			−0.635983			−0.317991	+	0.948094i	$0.603008\pi$
$194$		0			0
$195$	−2.29262	−	3.86874i	−0.164178	−	0.277047i
$196$		0			0
$197$	−18.0192	−	13.0917i	−1.28381	−	0.932746i	−0.284154	−	0.958779i	$-0.591713\pi$
$197$	−18.0192	−	13.0917i	−1.28381	−	0.932746i	−0.999661	+	0.0260325i	$0.991713\pi$
$198$		0			0
$199$	−2.73266			−0.193713			−0.0968564	−	0.995298i	$-0.530879\pi$
$199$	−2.73266			−0.193713			−0.0968564	+	0.995298i	$0.530879\pi$
$200$		0			0
$201$	10.1457			0.715625
$202$		0			0
$203$	20.5614	+	14.9387i	1.44313	+	1.04849i
$204$		0			0
$205$	3.18760	+	1.37603i	0.222632	+	0.0961062i
$206$		0			0
$207$	−2.38549			−0.165803
$208$		0			0
$209$	0.0860100	+	0.264711i	0.00594943	+	0.0183105i
$210$		0			0
$211$	4.73541	−	14.5741i	0.325999	−	1.00332i	−0.644989	−	0.764192i	$-0.723138\pi$
$211$	4.73541	−	14.5741i	0.325999	−	1.00332i	0.970988	−	0.239129i	$-0.0768620\pi$
$212$		0			0
$213$	5.17350	+	15.9224i	0.354482	+	1.09098i
$214$		0			0
$215$	14.8974	−	16.9282i	1.01600	−	1.15449i
$216$		0			0
$217$	8.03531	−	5.83800i	0.545473	−	0.396309i
$218$		0			0
$219$	−8.42994	+	6.12471i	−0.569643	+	0.413870i
$220$		0			0
$221$	9.96574	+	7.24054i	0.670369	+	0.487051i
$222$		0			0
$223$	−4.53228	+	13.9489i	−0.303504	+	0.934090i	0.676727	+	0.736234i	$0.263398\pi$
$223$	−4.53228	+	13.9489i	−0.303504	+	0.934090i	−0.980231	+	0.197856i	$0.936602\pi$
$224$		0			0
$225$	−7.69430	+	3.63740i	−0.512953	+	0.242493i
$226$		0			0
$227$	0.260500	−	0.801738i	0.0172900	−	0.0532132i	−0.942039	−	0.335503i	$-0.891094\pi$
$227$	0.260500	−	0.801738i	0.0172900	−	0.0532132i	0.959329	+	0.282289i	$0.0910939\pi$
$228$		0			0
$229$	6.76463	+	4.91479i	0.447019	+	0.324778i	0.788418	−	0.615140i	$-0.210901\pi$
$229$	6.76463	+	4.91479i	0.447019	+	0.324778i	−0.341399	+	0.939919i	$0.610901\pi$
$230$		0			0
$231$	4.22626	−	3.07056i	0.278067	−	0.202028i
$232$		0			0
$233$	4.34638	−	3.15783i	0.284741	−	0.206876i	−0.436242	−	0.899829i	$-0.643691\pi$
$233$	4.34638	−	3.15783i	0.284741	−	0.206876i	0.720982	+	0.692953i	$0.243691\pi$
$234$		0			0
$235$	22.0931	−	4.95903i	1.44119	−	0.323492i
$236$		0			0
$237$	−0.884854	−	2.72330i	−0.0574775	−	0.176897i
$238$		0			0
$239$	−6.49070	+	19.9763i	−0.419849	+	1.29216i	0.487993	+	0.872848i	$0.337729\pi$
$239$	−6.49070	+	19.9763i	−0.419849	+	1.29216i	−0.907841	+	0.419314i	$0.862271\pi$
$240$		0			0
$241$	−4.00121	−	12.3145i	−0.257740	−	0.793244i	−0.993277	−	0.115759i	$-0.963070\pi$
$241$	−4.00121	−	12.3145i	−0.257740	−	0.793244i	0.735537	−	0.677485i	$-0.236930\pi$
$242$		0			0
$243$	−14.9356			−0.958118
$244$		0			0
$245$	−20.7209	+	23.5455i	−1.32381	+	1.50427i
$246$		0			0
$247$	0.397514	+	0.288811i	0.0252932	+	0.0183766i
$248$		0			0
$249$	3.62943			0.230006
$250$		0			0
$251$	−22.4497			−1.41701			−0.708507	−	0.705704i	$-0.750631\pi$
$251$	−22.4497			−1.41701			−0.708507	+	0.705704i	$0.750631\pi$
$252$		0			0
$253$	1.13380	+	0.823754i	0.0712814	+	0.0517890i
$254$		0			0
$255$	−11.7433	+	13.3440i	−0.735391	+	0.835635i
$256$		0			0
$257$	−7.47518			−0.466289			−0.233144	−	0.972442i	$-0.574901\pi$
$257$	−7.47518			−0.466289			−0.233144	+	0.972442i	$0.574901\pi$
$258$		0			0
$259$	14.6918	+	45.2168i	0.912906	+	2.80964i
$260$		0			0
$261$	−2.91534	+	8.97248i	−0.180455	+	0.555383i
$262$		0			0
$263$	9.89291	+	30.4472i	0.610023	+	1.87746i	0.457645	+	0.889135i	$0.348693\pi$
$263$	9.89291	+	30.4472i	0.610023	+	1.87746i	0.152378	+	0.988322i	$0.451307\pi$
$264$		0			0
$265$	22.4212	−	5.03269i	1.37733	−	0.309156i
$266$		0			0
$267$	−9.48561	+	6.89170i	−0.580510	+	0.421765i
$268$		0			0
$269$	−11.7758	+	8.55564i	−0.717985	+	0.521647i	−0.885740	−	0.464182i	$-0.846348\pi$
$269$	−11.7758	+	8.55564i	−0.717985	+	0.521647i	0.167755	+	0.985829i	$0.446348\pi$
$270$		0			0
$271$	−4.98543	−	3.62213i	−0.302843	−	0.220028i	0.425976	−	0.904734i	$-0.359931\pi$
$271$	−4.98543	−	3.62213i	−0.302843	−	0.220028i	−0.728820	+	0.684706i	$0.759931\pi$
$272$		0			0
$273$	2.84977	−	8.77068i	0.172476	−	0.530825i
$274$		0			0
$275$	4.91310	+	0.928165i	0.296271	+	0.0559705i
$276$		0			0
$277$	3.74157	−	11.5154i	0.224809	−	0.691891i	−0.773502	−	0.633794i	$-0.781497\pi$
$277$	3.74157	−	11.5154i	0.224809	−	0.691891i	0.998311	−	0.0580970i	$-0.0185033\pi$
$278$		0			0
$279$	2.98274	+	2.16708i	0.178572	+	0.129740i
$280$		0			0
$281$	−14.9792	+	10.8830i	−0.893582	+	0.649226i	−0.936810	−	0.349840i	$-0.886236\pi$
$281$	−14.9792	+	10.8830i	−0.893582	+	0.649226i	0.0432272	+	0.999065i	$0.486236\pi$
$282$		0			0
$283$	−8.00704	+	5.81746i	−0.475969	+	0.345812i	−0.799763	−	0.600316i	$-0.795042\pi$
$283$	−8.00704	+	5.81746i	−0.475969	+	0.345812i	0.323794	+	0.946128i	$0.395042\pi$
$284$		0			0
$285$	−0.468416	+	0.532267i	−0.0277465	+	0.0315288i
$286$		0			0
$287$	2.20016	+	6.77139i	0.129871	+	0.399702i
$288$		0			0
$289$	9.79301	−	30.1398i	0.576059	−	1.77293i
$290$		0			0
$291$	6.03299	+	18.5676i	0.353660	+	1.08845i
$292$		0			0
$293$	−21.8732			−1.27784			−0.638922	−	0.769272i	$-0.720619\pi$
$293$	−21.8732			−1.27784			−0.638922	+	0.769272i	$0.720619\pi$
$294$		0			0
$295$	−11.0233	−	4.75859i	−0.641804	−	0.277056i
$296$		0			0
$297$	4.33378	+	3.14867i	0.251471	+	0.182704i
$298$		0			0
$299$	2.47404			0.143078
$300$		0			0
$301$	46.2429			2.66540
$302$		0			0
$303$	−9.80393	−	7.12297i	−0.563221	−	0.409204i
$304$		0			0
$305$	−1.54670	−	2.61003i	−0.0885640	−	0.149450i
$306$		0			0
$307$	13.7714			0.785973			0.392987	−	0.919544i	$-0.371442\pi$
$307$	13.7714			0.785973			0.392987	+	0.919544i	$0.371442\pi$
$308$		0			0
$309$	1.19834	+	3.68811i	0.0681711	+	0.209809i
$310$		0			0
$311$	8.35233	−	25.7058i	0.473617	−	1.45764i	−0.374196	−	0.927350i	$-0.622081\pi$
$311$	8.35233	−	25.7058i	0.473617	−	1.45764i	0.847813	−	0.530295i	$-0.177919\pi$
$312$		0			0
$313$	−7.32139	−	22.5329i	−0.413829	−	1.27364i	−0.913294	−	0.407301i	$-0.866470\pi$
$313$	−7.32139	−	22.5329i	−0.413829	−	1.27364i	0.499464	−	0.866334i	$-0.333530\pi$
$314$		0			0
$315$	−16.0237	−	6.91715i	−0.902832	−	0.389737i
$316$		0			0
$317$	10.5954	−	7.69801i	0.595097	−	0.432363i	−0.249038	−	0.968494i	$-0.580114\pi$
$317$	10.5954	−	7.69801i	0.595097	−	0.432363i	0.844135	+	0.536130i	$0.180114\pi$
$318$		0			0
$319$	4.48401	−	3.25782i	0.251056	−	0.182403i
$320$		0			0
$321$	−16.2067	−	11.7749i	−0.904569	−	0.657208i
$322$		0			0
$323$	0.600167	−	1.84713i	0.0333942	−	0.102777i
$324$		0			0
$325$	7.97994	−	3.77243i	0.442647	−	0.209257i
$326$		0			0
$327$	5.24798	−	16.1516i	0.290214	−	0.893186i
$328$		0			0
$329$	37.5655	+	27.2929i	2.07105	+	1.50471i
$330$		0			0
$331$	1.33122	−	0.967189i	0.0731705	−	0.0531615i	−0.550599	−	0.834770i	$-0.685601\pi$
$331$	1.33122	−	0.967189i	0.0731705	−	0.0531615i	0.623769	+	0.781609i	$0.285601\pi$
$332$		0			0
$333$	−14.2779	+	10.3735i	−0.782422	+	0.568463i
$334$		0			0
$335$	−1.85642	+	19.8272i	−0.101427	+	1.08328i
$336$		0			0
$337$	−6.94397	−	21.3714i	−0.378262	−	1.16417i	−0.941251	−	0.337707i	$-0.890349\pi$
$337$	−6.94397	−	21.3714i	−0.378262	−	1.16417i	0.562989	−	0.826465i	$-0.309651\pi$
$338$		0			0
$339$	−1.73923	+	5.35281i	−0.0944622	+	0.290725i
$340$		0			0
$341$	−0.669332	−	2.05999i	−0.0362464	−	0.111555i
$342$		0			0
$343$	−32.2211			−1.73977
$344$		0			0
$345$	−0.332810	+	3.55452i	−0.0179179	+	0.191369i
$346$		0			0
$347$	5.08911	+	3.69745i	0.273198	+	0.198490i	0.715945	−	0.698157i	$-0.245996\pi$
$347$	5.08911	+	3.69745i	0.273198	+	0.198490i	−0.442747	+	0.896646i	$0.645996\pi$
$348$		0			0
$349$	29.5658			1.58262			0.791310	−	0.611415i	$-0.209399\pi$
$349$	29.5658			1.58262			0.791310	+	0.611415i	$0.209399\pi$
$350$		0			0
$351$	9.45665			0.504759
$352$		0			0
$353$	12.4799	+	9.06715i	0.664236	+	0.482596i	0.868091	−	0.496405i	$-0.165347\pi$
$353$	12.4799	+	9.06715i	0.664236	+	0.482596i	−0.203855	+	0.979001i	$0.565347\pi$
$354$		0			0
$355$	−32.0628	+	7.19683i	−1.70171	+	0.381968i
$356$		0			0
$357$	−36.4520			−1.92925
$358$		0			0
$359$	4.02855	+	12.3986i	0.212619	+	0.654374i	0.999314	+	0.0370321i	$0.0117904\pi$
$359$	4.02855	+	12.3986i	0.212619	+	0.654374i	−0.786695	+	0.617342i	$0.788210\pi$
$360$		0			0
$361$	−5.84738	+	17.9964i	−0.307757	+	0.947179i
$362$		0			0
$363$	−0.352042	−	1.08347i	−0.0184774	−	0.0568676i
$364$		0			0
$365$	−10.4267	−	17.5948i	−0.545757	−	0.920953i
$366$		0			0
$367$	10.7106	−	7.78171i	0.559089	−	0.406202i	−0.272036	−	0.962287i	$-0.587697\pi$
$367$	10.7106	−	7.78171i	0.559089	−	0.406202i	0.831126	+	0.556085i	$0.187697\pi$
$368$		0			0
$369$	−2.13816	+	1.55347i	−0.111308	+	0.0808702i
$370$		0			0
$371$	38.1234	+	27.6983i	1.97927	+	1.43802i
$372$		0			0
$373$	−1.39598	+	4.29638i	−0.0722811	+	0.222458i	−0.980670	−	0.195667i	$-0.937313\pi$
$373$	−1.39598	+	4.29638i	−0.0722811	+	0.222458i	0.908389	+	0.418126i	$0.137313\pi$
$374$		0			0
$375$	4.34648	+	11.9724i	0.224451	+	0.618254i
$376$		0			0
$377$	3.02357	−	9.30558i	0.155722	−	0.479262i
$378$		0			0
$379$	−6.97127	−	5.06492i	−0.358090	−	0.260168i	0.394165	−	0.919040i	$-0.371034\pi$
$379$	−6.97127	−	5.06492i	−0.358090	−	0.260168i	−0.752255	+	0.658872i	$0.771034\pi$
$380$		0			0
$381$	−11.4614	+	8.32718i	−0.587184	+	0.426614i
$382$		0			0
$383$	4.31988	−	3.13857i	0.220735	−	0.160374i	−0.471922	−	0.881640i	$-0.656440\pi$
$383$	4.31988	−	3.13857i	0.220735	−	0.160374i	0.692658	+	0.721267i	$0.256440\pi$
$384$		0			0
$385$	5.22729	+	8.82095i	0.266408	+	0.449557i
$386$		0			0
$387$	5.30444	+	16.3254i	0.269640	+	0.829865i
$388$		0			0
$389$	4.92524	−	15.1583i	0.249720	−	0.768559i	−0.745104	−	0.666948i	$-0.767600\pi$
$389$	4.92524	−	15.1583i	0.249720	−	0.768559i	0.994824	−	0.101611i	$-0.0323996\pi$
$390$		0			0
$391$	−3.02193	−	9.30055i	−0.152826	−	0.470349i
$392$		0			0
$393$	−0.0590637			−0.00297937
$394$		0			0
$395$	5.48389	−	1.23092i	0.275924	−	0.0619342i
$396$		0			0
$397$	−8.58441	−	6.23694i	−0.430839	−	0.313023i	0.351145	−	0.936321i	$-0.385792\pi$
$397$	−8.58441	−	6.23694i	−0.430839	−	0.313023i	−0.781984	+	0.623298i	$0.785792\pi$
$398$		0			0
$399$	−1.45400			−0.0727911
$400$		0			0
$401$	2.39723			0.119712			0.0598561	−	0.998207i	$-0.480936\pi$
$401$	2.39723			0.119712			0.0598561	+	0.998207i	$0.480936\pi$
$402$		0			0
$403$	−3.09347	−	2.24753i	−0.154097	−	0.111958i
$404$		0			0
$405$	−0.207667	+	2.21795i	−0.0103191	+	0.110211i
$406$		0			0
$407$	10.3683			0.513938
$408$		0			0
$409$	3.81628	+	11.7453i	0.188703	+	0.580768i	0.999992	−	0.00387685i	$-0.00123404\pi$
$409$	3.81628	+	11.7453i	0.188703	+	0.580768i	−0.811290	+	0.584644i	$0.801234\pi$
$410$		0			0
$411$	6.31444	−	19.4339i	0.311469	−	0.958602i
$412$		0			0
$413$	−7.60857	−	23.4168i	−0.374393	−	1.15226i
$414$		0			0
$415$	−0.664098	+	7.09277i	−0.0325993	+	0.348171i
$416$		0			0
$417$	−13.5156	+	9.81967i	−0.661863	+	0.480871i
$418$		0			0
$419$	−11.9035	+	8.64837i	−0.581522	+	0.422500i	−0.839272	−	0.543711i	$-0.817019\pi$
$419$	−11.9035	+	8.64837i	−0.581522	+	0.422500i	0.257751	+	0.966211i	$0.417019\pi$
$420$		0			0
$421$	25.6588	+	18.6422i	1.25054	+	0.908567i	0.998253	−	0.0590866i	$-0.0188188\pi$
$421$	25.6588	+	18.6422i	1.25054	+	0.908567i	0.252282	+	0.967654i	$0.418819\pi$
$422$		0			0
$423$	−5.32630	+	16.3927i	−0.258973	+	0.797038i
$424$		0			0
$425$	−23.9287	−	25.3907i	−1.16071	−	1.23163i
$426$		0			0
$427$	1.92258	−	5.91710i	0.0930402	−	0.286348i
$428$		0			0
$429$	−1.62704	−	1.18211i	−0.0785543	−	0.0570730i
$430$		0			0
$431$	−4.27343	+	3.10483i	−0.205844	+	0.149554i	−0.685931	−	0.727666i	$-0.740605\pi$
$431$	−4.27343	+	3.10483i	−0.205844	+	0.149554i	0.480087	+	0.877221i	$0.340605\pi$
$432$		0			0
$433$	22.2601	−	16.1729i	1.06975	−	0.777221i	0.0938847	−	0.995583i	$-0.470072\pi$
$433$	22.2601	−	16.1729i	1.06975	−	0.777221i	0.975868	+	0.218362i	$0.0700715\pi$
$434$		0			0
$435$	12.9628	+	5.59582i	0.621519	+	0.268299i
$436$		0			0
$437$	−0.120539	−	0.370981i	−0.00576616	−	0.0177464i
$438$		0			0
$439$	10.8600	−	33.4237i	0.518320	−	1.59523i	−0.258838	−	0.965921i	$-0.583340\pi$
$439$	10.8600	−	33.4237i	0.518320	−	1.59523i	0.777159	−	0.629305i	$-0.216660\pi$
$440$		0			0
$441$	−7.37797	−	22.7071i	−0.351332	−	1.08129i
$442$		0			0
$443$	−19.1930			−0.911889			−0.455944	−	0.890008i	$-0.650698\pi$
$443$	−19.1930			−0.911889			−0.455944	+	0.890008i	$0.650698\pi$
$444$		0			0
$445$	−11.7324	−	19.7982i	−0.556168	−	0.938523i
$446$		0			0
$447$	6.26623	+	4.55268i	0.296383	+	0.215335i
$448$		0			0
$449$	4.97256			0.234670			0.117335	−	0.993092i	$-0.462565\pi$
$449$	4.97256			0.234670			0.117335	+	0.993092i	$0.462565\pi$
$450$		0			0
$451$	1.55269			0.0731134
$452$		0			0
$453$	2.61147	+	1.89735i	0.122698	+	0.0891451i
$454$		0			0
$455$	16.6185	+	7.17394i	0.779090	+	0.336319i
$456$		0			0
$457$	32.8864			1.53836			0.769181	−	0.639031i	$-0.220664\pi$
$457$	32.8864			1.53836			0.769181	+	0.639031i	$0.220664\pi$
$458$		0			0
$459$	−11.5509	−	35.5499i	−0.539148	−	1.65933i
$460$		0			0
$461$	2.33973	−	7.20094i	0.108972	−	0.335381i	−0.881670	−	0.471866i	$-0.843581\pi$
$461$	2.33973	−	7.20094i	0.108972	−	0.335381i	0.990642	+	0.136485i	$0.0435805\pi$
$462$		0			0
$463$	5.06969	+	15.6029i	0.235608	+	0.725128i	0.997040	+	0.0768831i	$0.0244968\pi$
$463$	5.06969	+	15.6029i	0.235608	+	0.725128i	−0.761432	+	0.648245i	$0.775503\pi$
$464$		0			0
$465$	3.64522	−	4.14212i	0.169043	−	0.192086i
$466$		0			0
$467$	6.05684	−	4.40055i	0.280277	−	0.203633i	−0.438761	−	0.898604i	$-0.644583\pi$
$467$	6.05684	−	4.40055i	0.280277	−	0.203633i	0.719038	+	0.694971i	$0.244583\pi$
$468$		0			0
$469$	−33.0381	+	24.0036i	−1.52556	+	1.10838i
$470$		0			0
$471$	−3.43267	−	2.49398i	−0.158169	−	0.114917i
$472$		0			0
$473$	3.11631	−	9.59103i	0.143288	−	0.440996i
$474$		0			0
$475$	−0.954468	−	1.01279i	−0.0437940	−	0.0464699i
$476$		0			0
$477$	−5.40541	+	16.6361i	−0.247497	+	0.761717i
$478$		0			0
$479$	13.7560	+	9.99436i	0.628530	+	0.456654i	0.855891	−	0.517157i	$-0.173010\pi$
$479$	13.7560	+	9.99436i	0.628530	+	0.456654i	−0.227361	+	0.973811i	$0.573010\pi$
$480$		0			0
$481$	14.8079	−	10.7586i	0.675183	−	0.490549i
$482$		0			0
$483$	−5.92291	+	4.30324i	−0.269502	+	0.195804i
$484$		0			0
$485$	−37.3895	+	8.39247i	−1.69777	+	0.381082i
$486$		0			0
$487$	0.709421	+	2.18337i	0.0321470	+	0.0989381i	0.965843	−	0.259130i	$-0.0834357\pi$
$487$	0.709421	+	2.18337i	0.0321470	+	0.0989381i	−0.933696	+	0.358068i	$0.883436\pi$
$488$		0			0
$489$	8.72268	−	26.8456i	0.394453	−	1.21400i
$490$		0			0
$491$	−0.814069	−	2.50545i	−0.0367384	−	0.113069i	0.931006	−	0.365005i	$-0.118933\pi$
$491$	−0.814069	−	2.50545i	−0.0367384	−	0.113069i	−0.967744	+	0.251936i	$0.918933\pi$
$492$		0			0
$493$	−38.6752			−1.74184
$494$		0			0
$495$	−2.51449	+	2.85725i	−0.113018	+	0.128424i
$496$		0			0
$497$	−54.5172	−	39.6090i	−2.44543	−	1.77671i
$498$		0			0
$499$	−13.3532			−0.597773			−0.298887	−	0.954289i	$-0.596615\pi$
$499$	−13.3532			−0.597773			−0.298887	+	0.954289i	$0.596615\pi$
$500$		0			0
$501$	−18.7409			−0.837281
$502$		0			0
$503$	−5.51952	−	4.01016i	−0.246103	−	0.178804i	0.457895	−	0.889006i	$-0.348604\pi$
$503$	−5.51952	−	4.01016i	−0.246103	−	0.178804i	−0.703998	+	0.710202i	$0.748604\pi$
$504$		0			0
$505$	15.7139	−	17.8559i	0.699258	−	0.794576i
$506$		0			0
$507$	11.2597			0.500060
$508$		0			0
$509$	3.74714	+	11.5325i	0.166089	+	0.511170i	0.999115	−	0.0420645i	$-0.0133935\pi$
$509$	3.74714	+	11.5325i	0.166089	+	0.511170i	−0.833026	+	0.553234i	$0.813394\pi$
$510$		0			0
$511$	12.9605	−	39.8884i	0.573340	−	1.76456i
$512$		0			0
$513$	−0.460742	−	1.41802i	−0.0203422	−	0.0626070i
$514$		0			0
$515$	−7.42671	+	1.66701i	−0.327260	+	0.0734570i
$516$		0			0
$517$	8.19224	−	5.95201i	0.360294	−	0.261769i
$518$		0			0
$519$	11.5654	−	8.40279i	0.507667	−	0.368841i
$520$		0			0
$521$	13.6406	+	9.91051i	0.597607	+	0.434187i	0.845029	−	0.534721i	$-0.179583\pi$
$521$	13.6406	+	9.91051i	0.597607	+	0.434187i	−0.247421	+	0.968908i	$0.579583\pi$
$522$		0			0
$523$	6.52443	−	20.0801i	0.285294	−	0.878043i	−0.701017	−	0.713145i	$-0.747270\pi$
$523$	6.52443	−	20.0801i	0.285294	−	0.878043i	0.986311	−	0.164899i	$-0.0527297\pi$
$524$		0			0
$525$	−12.5425	+	22.9112i	−0.547400	+	0.999928i
$526$		0			0
$527$	−4.67052	+	14.3744i	−0.203451	+	0.626158i
$528$		0			0
$529$	17.0184	+	12.3646i	0.739931	+	0.537592i
$530$		0			0
$531$	7.39418	−	5.37219i	0.320880	−	0.233133i
$532$		0			0
$533$	2.21754	−	1.61114i	0.0960523	−	0.0697861i
$534$		0			0
$535$	25.9763	−	29.5172i	1.12305	−	1.27614i
$536$		0			0
$537$	−1.69637	−	5.22088i	−0.0732037	−	0.225298i
$538$		0			0
$539$	−4.33450	+	13.3402i	−0.186700	+	0.574604i
$540$		0			0
$541$	5.55390	+	17.0931i	0.238781	+	0.734891i	0.996597	+	0.0824238i	$0.0262661\pi$
$541$	5.55390	+	17.0931i	0.238781	+	0.734891i	−0.757817	+	0.652468i	$0.773734\pi$
$542$		0			0
$543$	24.9186			1.06936
$544$		0			0
$545$	30.6038	+	13.2111i	1.31092	+	0.565903i
$546$		0			0
$547$	−20.8191	−	15.1259i	−0.890159	−	0.646739i	0.0457603	−	0.998952i	$-0.485429\pi$
$547$	−20.8191	−	15.1259i	−0.890159	−	0.646739i	−0.935920	+	0.352214i	$0.885429\pi$
$548$		0			0
$549$	2.30948			0.0985662
$550$		0			0
$551$	−1.54268			−0.0657202
$552$		0			0
$553$	9.32440	+	6.77457i	0.396514	+	0.288084i
$554$		0			0
$555$	13.4651	+	22.7221i	0.571563	+	0.964501i
$556$		0			0
$557$	−8.80469			−0.373067			−0.186533	−	0.982449i	$-0.559725\pi$
$557$	−8.80469			−0.373067			−0.186533	+	0.982449i	$0.559725\pi$
$558$		0			0
$559$	−5.50136	−	16.9314i	−0.232683	−	0.716123i
$560$		0			0
$561$	−2.45651	+	7.56035i	−0.103714	+	0.319198i
$562$		0			0
$563$	−5.16793	−	15.9053i	−0.217802	−	0.670326i	−0.998943	−	0.0459712i	$-0.985362\pi$
$563$	−5.16793	−	15.9053i	−0.217802	−	0.670326i	0.781140	−	0.624355i	$-0.214638\pi$
$564$		0			0
$565$	−10.1424	−	4.37831i	−0.426695	−	0.184197i
$566$		0			0
$567$	−3.69577	+	2.68514i	−0.155208	+	0.112765i
$568$		0			0
$569$	1.65776	−	1.20443i	0.0694967	−	0.0504923i	−0.552494	−	0.833517i	$-0.686324\pi$
$569$	1.65776	−	1.20443i	0.0694967	−	0.0504923i	0.621991	+	0.783024i	$0.286324\pi$
$570$		0			0
$571$	−31.0693	−	22.5731i	−1.30021	−	0.944657i	−0.300251	−	0.953860i	$-0.597070\pi$
$571$	−31.0693	−	22.5731i	−1.30021	−	0.944657i	−0.999958	+	0.00920359i	$0.997070\pi$
$572$		0			0
$573$	0.126018	−	0.387843i	0.00526448	−	0.0162024i
$574$		0			0
$575$	−6.88548	−	1.30078i	−0.287144	−	0.0542463i
$576$		0			0
$577$	−2.90734	+	8.94789i	−0.121034	+	0.372505i	−0.993158	−	0.116781i	$-0.962743\pi$
$577$	−2.90734	+	8.94789i	−0.121034	+	0.372505i	0.872123	+	0.489286i	$0.162743\pi$
$578$		0			0
$579$	−8.14318	−	5.91636i	−0.338419	−	0.245876i
$580$		0			0
$581$	−11.8187	+	8.58679i	−0.490323	+	0.356240i
$582$		0			0
$583$	8.31392	−	6.04042i	0.344328	−	0.250169i
$584$		0			0
$585$	−0.626372	+	6.68984i	−0.0258973	+	0.276591i
$586$		0			0
$587$	−10.7447	−	33.0687i	−0.443480	−	1.36489i	−0.884142	−	0.467217i	$-0.845257\pi$
$587$	−10.7447	−	33.0687i	−0.443480	−	1.36489i	0.440663	−	0.897673i	$-0.354743\pi$
$588$		0			0
$589$	−0.186298	+	0.573366i	−0.00767627	+	0.0236251i
$590$		0			0
$591$	−7.84102	−	24.1322i	−0.322536	−	0.992665i
$592$		0			0
$593$	−40.7019			−1.67143			−0.835713	−	0.549166i	$-0.814945\pi$
$593$	−40.7019			−1.67143			−0.835713	+	0.549166i	$0.814945\pi$
$594$		0			0
$595$	6.66984	−	71.2360i	0.273437	−	2.92039i
$596$		0			0
$597$	−2.51858	−	1.82985i	−0.103078	−	0.0748909i
$598$		0			0
$599$	−6.80611			−0.278090			−0.139045	−	0.990286i	$-0.544403\pi$
$599$	−6.80611			−0.278090			−0.139045	+	0.990286i	$0.544403\pi$
$600$		0			0
$601$	−12.3566			−0.504036			−0.252018	−	0.967722i	$-0.581094\pi$
$601$	−12.3566			−0.504036			−0.252018	+	0.967722i	$0.581094\pi$
$602$		0			0
$603$	−12.2639	−	8.91021i	−0.499423	−	0.362852i
$604$		0			0
$605$	2.18178	−	0.489724i	0.0887020	−	0.0199101i
$606$		0			0
$607$	−7.11226			−0.288678			−0.144339	−	0.989528i	$-0.546106\pi$
$607$	−7.11226			−0.288678			−0.144339	+	0.989528i	$0.546106\pi$
$608$		0			0
$609$	8.94724	+	27.5368i	0.362561	+	1.11585i
$610$		0			0
$611$	5.52403	−	17.0012i	0.223478	−	0.687795i
$612$		0			0
$613$	8.05789	+	24.7996i	0.325455	+	1.00165i	0.971235	+	0.238124i	$0.0765325\pi$
$613$	8.05789	+	24.7996i	0.325455	+	1.00165i	−0.645779	+	0.763524i	$0.723467\pi$
$614$		0			0
$615$	2.01645	+	3.40272i	0.0813113	+	0.137211i
$616$		0			0
$617$	−18.3156	+	13.3071i	−0.737359	+	0.535723i	−0.891883	−	0.452266i	$-0.850616\pi$
$617$	−18.3156	+	13.3071i	−0.737359	+	0.535723i	0.154524	+	0.987989i	$0.450616\pi$
$618$		0			0
$619$	−0.445488	+	0.323666i	−0.0179057	+	0.0130092i	−0.596702	−	0.802463i	$-0.703523\pi$
$619$	−0.445488	+	0.323666i	−0.0179057	+	0.0130092i	0.578796	+	0.815472i	$0.303523\pi$
$620$		0			0
$621$	−6.07359	−	4.41272i	−0.243725	−	0.177076i
$622$		0			0
$623$	14.5836	−	44.8836i	0.584278	−	1.79822i
$624$		0			0
$625$	−24.1923	+	6.30338i	−0.967692	+	0.252135i
$626$		0			0
$627$	−0.0979853	+	0.301568i	−0.00391316	+	0.0120435i
$628$		0			0
$629$	−58.5314	−	42.5256i	−2.33380	−	1.69560i
$630$		0			0
$631$	2.23979	−	1.62730i	0.0891646	−	0.0647819i	−0.542310	−	0.840179i	$-0.682450\pi$
$631$	2.23979	−	1.62730i	0.0891646	−	0.0647819i	0.631474	+	0.775397i	$0.282450\pi$
$632$		0			0
$633$	14.1236	−	10.2614i	0.561362	−	0.407853i
$634$		0			0
$635$	−14.1761	−	23.9219i	−0.562562	−	0.949312i
$636$		0			0
$637$	7.65187	+	23.5500i	0.303178	+	0.933087i
$638$		0			0
$639$	7.72983	−	23.7900i	0.305787	−	0.941117i
$640$		0			0
$641$	−0.307565	−	0.946588i	−0.0121481	−	0.0373880i	0.944799	−	0.327651i	$-0.106257\pi$
$641$	−0.307565	−	0.946588i	−0.0121481	−	0.0373880i	−0.956947	+	0.290263i	$0.906257\pi$
$642$		0			0
$643$	15.0690			0.594264			0.297132	−	0.954836i	$-0.403970\pi$
$643$	15.0690			0.594264			0.297132	+	0.954836i	$0.403970\pi$
$644$		0			0
$645$	25.0658	−	5.62630i	0.986967	−	0.221535i
$646$		0			0
$647$	32.4314	+	23.5628i	1.27501	+	0.926348i	0.999390	−	0.0349197i	$-0.0111175\pi$
$647$	32.4314	+	23.5628i	1.27501	+	0.926348i	0.275618	+	0.961267i	$0.411118\pi$
$648$		0			0
$649$	−5.36951			−0.210772
$650$		0			0
$651$	11.3151			0.443473
$652$		0			0
$653$	6.17534	+	4.48664i	0.241660	+	0.175576i	0.702022	−	0.712155i	$-0.252281\pi$
$653$	6.17534	+	4.48664i	0.241660	+	0.175576i	−0.460363	+	0.887731i	$0.652281\pi$
$654$		0			0
$655$	0.0108072	−	0.115425i	0.000422273	−	0.00451001i
$656$		0			0
$657$	15.5687			0.607393
$658$		0			0
$659$	9.38662	+	28.8891i	0.365651	+	1.12536i	0.949572	+	0.313548i	$0.101518\pi$
$659$	9.38662	+	28.8891i	0.365651	+	1.12536i	−0.583922	+	0.811810i	$0.698482\pi$
$660$		0			0
$661$	0.602895	−	1.85552i	0.0234499	−	0.0721714i	−0.938647	−	0.344880i	$-0.887920\pi$
$661$	0.602895	−	1.85552i	0.0234499	−	0.0721714i	0.962097	+	0.272709i	$0.0879196\pi$
$662$		0			0
$663$	4.33657	+	13.3466i	0.168419	+	0.518339i
$664$		0			0
$665$	0.266047	−	2.84146i	0.0103169	−	0.110187i
$666$		0			0
$667$	−6.28413	+	4.56569i	−0.243322	+	0.176784i
$668$		0			0
$669$	−13.5178	+	9.82123i	−0.522627	+	0.379711i
$670$		0			0
$671$	−1.09768	−	0.797508i	−0.0423753	−	0.0307874i
$672$		0			0
$673$	−5.86346	+	18.0459i	−0.226020	+	0.695617i	0.772167	+	0.635420i	$0.219173\pi$
$673$	−5.86346	+	18.0459i	−0.226020	+	0.695617i	−0.998186	+	0.0601973i	$0.980827\pi$
$674$		0			0
$675$	−26.3187	−	4.97203i	−1.01301	−	0.191374i
$676$		0			0
$677$	8.84693	−	27.2280i	0.340015	−	1.04646i	−0.624184	−	0.781278i	$-0.714568\pi$
$677$	8.84693	−	27.2280i	0.340015	−	1.04646i	0.964199	−	0.265181i	$-0.0854317\pi$
$678$		0			0
$679$	−63.5743	−	46.1894i	−2.43976	−	1.77259i
$680$		0			0
$681$	0.776955	−	0.564491i	0.0297730	−	0.0216313i
$682$		0			0
$683$	−3.99716	+	2.90411i	−0.152947	+	0.111123i	−0.661627	−	0.749833i	$-0.730134\pi$
$683$	−3.99716	+	2.90411i	−0.152947	+	0.111123i	0.508680	+	0.860956i	$0.330134\pi$
$684$		0			0
$685$	36.8230	+	15.8958i	1.40693	+	0.607349i
$686$		0			0
$687$	2.94361	+	9.05951i	0.112306	+	0.345642i
$688$		0			0
$689$	5.60608	−	17.2537i	0.213575	−	0.657315i
$690$		0			0
$691$	12.1626	+	37.4325i	0.462685	+	1.42400i	0.861870	+	0.507129i	$0.169293\pi$
$691$	12.1626	+	37.4325i	0.462685	+	1.42400i	−0.399185	+	0.916871i	$0.630707\pi$
$692$		0			0
$693$	−7.80520			−0.296495
$694$		0			0
$695$	−16.7169	−	28.2095i	−0.634110	−	1.07005i
$696$		0			0
$697$	−8.76529	−	6.36836i	−0.332009	−	0.241219i
$698$		0			0
$699$	6.12043			0.231496
$700$		0			0
$701$	2.25152			0.0850387			0.0425194	−	0.999096i	$-0.486462\pi$
$701$	2.25152			0.0850387			0.0425194	+	0.999096i	$0.486462\pi$
$702$		0			0
$703$	−2.33470	−	1.69626i	−0.0880550	−	0.0639757i
$704$		0			0
$705$	23.6830	+	10.2235i	0.891952	+	0.385040i
$706$		0			0
$707$	48.7772			1.83445
$708$		0			0
$709$	7.33541	+	22.5761i	0.275487	+	0.847863i	0.989090	+	0.147312i	$0.0470622\pi$
$709$	7.33541	+	22.5761i	0.275487	+	0.847863i	−0.713603	+	0.700551i	$0.752938\pi$
$710$		0			0
$711$	−1.32208	+	4.06894i	−0.0495818	+	0.152597i
$712$		0			0
$713$	0.938038	+	2.88698i	0.0351298	+	0.108118i
$714$		0			0
$715$	2.60784	−	2.96333i	0.0975277	−	0.110822i
$716$		0			0
$717$	−19.3588	+	14.0650i	−0.722969	+	0.525268i
$718$		0			0
$719$	24.5662	−	17.8484i	0.916163	−	0.665631i	−0.0264030	−	0.999651i	$-0.508405\pi$
$719$	24.5662	−	17.8484i	0.916163	−	0.665631i	0.942566	+	0.334020i	$0.108405\pi$
$720$		0			0
$721$	−12.6278	−	9.17466i	−0.470285	−	0.341682i
$722$		0			0
$723$	4.55830	−	14.0290i	0.169525	−	0.521745i
$724$		0			0
$725$	−13.3075	+	24.3085i	−0.494226	+	0.902796i
$726$		0			0
$727$	1.43839	−	4.42691i	0.0533470	−	0.164185i	−0.920833	−	0.389956i	$-0.872490\pi$
$727$	1.43839	−	4.42691i	0.0533470	−	0.164185i	0.974180	+	0.225771i	$0.0724901\pi$
$728$		0			0
$729$	−16.1834	−	11.7579i	−0.599386	−	0.435479i
$730$		0			0
$731$	−56.9299	+	41.3620i	−2.10563	+	1.52983i
$732$		0			0
$733$	30.9322	−	22.4735i	1.14251	−	0.830079i	0.155039	−	0.987908i	$-0.450450\pi$
$733$	30.9322	−	22.4735i	1.14251	−	0.830079i	0.987466	+	0.157830i	$0.0504497\pi$
$734$		0			0
$735$	−34.8642	+	7.82566i	−1.28599	+	0.288654i
$736$		0			0
$737$	2.75203	+	8.46989i	0.101372	+	0.311992i
$738$		0			0
$739$	−5.73319	+	17.6450i	−0.210899	+	0.649080i	0.788520	+	0.615008i	$0.210847\pi$
$739$	−5.73319	+	17.6450i	−0.210899	+	0.649080i	−0.999419	+	0.0340716i	$0.989153\pi$
$740$		0			0
$741$	0.172977	+	0.532370i	0.00635449	+	0.0195571i
$742$		0			0
$743$	28.1558			1.03294			0.516469	−	0.856306i	$-0.327246\pi$
$743$	28.1558			1.03294			0.516469	+	0.856306i	$0.327246\pi$
$744$		0			0
$745$	−10.0436	+	11.4127i	−0.367969	+	0.418128i
$746$		0			0
$747$	−4.38714	−	3.18745i	−0.160517	−	0.116623i
$748$		0			0
$749$	80.6326			2.94625
$750$		0			0
$751$	−1.68076			−0.0613319			−0.0306660	−	0.999530i	$-0.509763\pi$
$751$	−1.68076			−0.0613319			−0.0306660	+	0.999530i	$0.509763\pi$
$752$		0			0
$753$	−20.6910	−	15.0329i	−0.754020	−	0.547828i
$754$		0			0
$755$	−4.18570	+	4.75627i	−0.152333	+	0.173098i
$756$		0			0
$757$	11.4300			0.415430			0.207715	−	0.978189i	$-0.433397\pi$
$757$	11.4300			0.415430			0.207715	+	0.978189i	$0.433397\pi$
$758$		0			0
$759$	0.493371	+	1.51844i	0.0179082	+	0.0551159i
$760$		0			0
$761$	−6.66007	+	20.4976i	−0.241427	+	0.743037i	0.754776	+	0.655982i	$0.227745\pi$
$761$	−6.66007	+	20.4976i	−0.241427	+	0.743037i	−0.996204	+	0.0870547i	$0.972255\pi$
$762$		0			0
$763$	21.1235	+	65.0114i	0.764722	+	2.35357i
$764$		0			0
$765$	25.9139	−	5.81665i	0.936919	−	0.210302i
$766$		0			0
$767$	−7.66868	+	5.57162i	−0.276900	+	0.201180i
$768$		0			0
$769$	10.7228	−	7.79053i	0.386672	−	0.280934i	−0.377418	−	0.926043i	$-0.623188\pi$
$769$	10.7228	−	7.79053i	0.386672	−	0.280934i	0.764091	+	0.645109i	$0.223188\pi$
$770$		0			0
$771$	−6.88956	−	5.00556i	−0.248121	−	0.180271i
$772$		0			0
$773$	2.52496	−	7.77103i	0.0908165	−	0.279505i	−0.895324	−	0.445415i	$-0.853056\pi$
$773$	2.52496	−	7.77103i	0.0908165	−	0.279505i	0.986141	+	0.165910i	$0.0530562\pi$
$774$		0			0
$775$	7.42769	+	7.88154i	0.266811	+	0.283113i
$776$		0			0
$777$	−16.7374	+	51.5125i	−0.600451	+	1.84800i
$778$		0			0
$779$	−0.349631	−	0.254021i	−0.0125268	−	0.00910126i
$780$		0			0
$781$	−11.8891	+	8.63790i	−0.425424	+	0.309089i
$782$		0			0
$783$	−24.0201	+	17.4516i	−0.858409	+	0.623670i
$784$		0			0
$785$	5.50193	−	6.25192i	0.196372	−	0.223141i
$786$		0			0
$787$	14.5311	+	44.7220i	0.517976	+	1.59417i	0.777800	+	0.628511i	$0.216335\pi$
$787$	14.5311	+	44.7220i	0.517976	+	1.59417i	−0.259824	+	0.965656i	$0.583665\pi$
$788$		0			0
$789$	−11.2703	+	34.6865i	−0.401234	+	1.23487i
$790$		0			0
$791$	−7.00054	−	21.5455i	−0.248911	−	0.766068i
$792$		0			0
$793$	−2.39522			−0.0850566
$794$		0			0
$795$	24.0347	+	10.3754i	0.852424	+	0.367977i
$796$		0			0
$797$	34.8436	+	25.3154i	1.23422	+	0.896716i	0.997199	−	0.0747878i	$-0.0238279\pi$
$797$	34.8436	+	25.3154i	1.23422	+	0.896716i	0.237024	+	0.971504i	$0.423828\pi$
$798$		0			0
$799$	−70.6592			−2.49974
$800$		0			0
$801$	17.5184			0.618981
$802$		0			0
$803$	−7.39967	−	5.37617i	−0.261129	−	0.189721i
$804$		0			0
$805$	−7.32581	−	12.3622i	−0.258201	−	0.435709i
$806$		0			0
$807$	−16.5824			−0.583727
$808$		0			0
$809$	7.56461	+	23.2815i	0.265958	+	0.818534i	0.991471	+	0.130326i	$0.0416023\pi$
$809$	7.56461	+	23.2815i	0.265958	+	0.818534i	−0.725514	+	0.688208i	$0.758398\pi$
$810$		0			0
$811$	−9.79588	+	30.1486i	−0.343980	+	1.05866i	0.618148	+	0.786062i	$0.287883\pi$
$811$	−9.79588	+	30.1486i	−0.343980	+	1.05866i	−0.962128	+	0.272599i	$0.912117\pi$
$812$		0			0
$813$	−2.16940	−	6.67672i	−0.0760841	−	0.234163i
$814$		0			0
$815$	50.8667	+	21.9583i	1.78178	+	0.769165i
$816$		0			0
$817$	−2.27082	+	1.64985i	−0.0794460	+	0.0577209i
$818$		0			0
$819$	−11.1473	+	8.09899i	−0.389518	+	0.283002i
$820$		0			0
$821$	−8.15139	−	5.92233i	−0.284485	−	0.206691i	0.436386	−	0.899760i	$-0.356258\pi$
$821$	−8.15139	−	5.92233i	−0.284485	−	0.206691i	−0.720871	+	0.693069i	$0.756258\pi$
$822$		0			0
$823$	2.79584	−	8.60472i	0.0974569	−	0.299942i	−0.890429	−	0.455122i	$-0.849596\pi$
$823$	2.79584	−	8.60472i	0.0974569	−	0.299942i	0.987886	+	0.155180i	$0.0495958\pi$
$824$		0			0
$825$	3.90667	+	4.14538i	0.136013	+	0.144324i
$826$		0			0
$827$	11.1649	−	34.3619i	0.388240	−	1.19488i	−0.545862	−	0.837875i	$-0.683798\pi$
$827$	11.1649	−	34.3619i	0.388240	−	1.19488i	0.934102	−	0.357006i	$-0.116202\pi$
$828$		0			0
$829$	16.9324	+	12.3021i	0.588085	+	0.427269i	0.841630	−	0.540055i	$-0.181596\pi$
$829$	16.9324	+	12.3021i	0.588085	+	0.427269i	−0.253545	+	0.967324i	$0.581596\pi$
$830$		0			0
$831$	11.1594	−	8.10778i	0.387115	−	0.281256i
$832$		0			0
$833$	79.1841	−	57.5306i	2.74357	−	1.99332i
$834$		0			0
$835$	3.42913	−	36.6241i	0.118670	−	1.26743i
$836$		0			0
$837$	3.58550	+	11.0350i	0.123933	+	0.381427i
$838$		0			0
$839$	16.3818	−	50.4181i	0.565564	−	1.74063i	−0.100706	−	0.994916i	$-0.532110\pi$
$839$	16.3818	−	50.4181i	0.565564	−	1.74063i	0.666270	−	0.745710i	$-0.267890\pi$
$840$		0			0
$841$	0.531419	+	1.63554i	0.0183248	+	0.0563979i
$842$		0			0
$843$	−21.0932			−0.726488
$844$		0			0
$845$	−2.06025	+	22.0041i	−0.0708747	+	0.756964i
$846$		0			0
$847$	3.70974	+	2.69528i	0.127468	+	0.0926111i
$848$		0			0
$849$	−11.2753			−0.386966
$850$		0			0
$851$	−14.5307			−0.498106
$852$		0			0
$853$	24.2281	+	17.6027i	0.829553	+	0.602705i	0.919433	−	0.393247i	$-0.128648\pi$
$853$	24.2281	+	17.6027i	0.829553	+	0.602705i	−0.0898799	+	0.995953i	$0.528648\pi$
$854$		0			0
$855$	1.03365	−	0.232015i	0.0353502	−	0.00793475i
$856$		0			0
$857$	−45.4353			−1.55204			−0.776020	−	0.630708i	$-0.782764\pi$
$857$	−45.4353			−1.55204			−0.776020	+	0.630708i	$0.782764\pi$
$858$		0			0
$859$	−6.39177	−	19.6719i	−0.218084	−	0.671195i	−0.998920	−	0.0464586i	$-0.985206\pi$
$859$	−6.39177	−	19.6719i	−0.218084	−	0.671195i	0.780836	−	0.624736i	$-0.214794\pi$
$860$		0			0
$861$	−2.50649	+	7.71418i	−0.0854209	+	0.262899i
$862$		0			0
$863$	9.67666	+	29.7817i	0.329397	+	1.01378i	0.969416	+	0.245422i	$0.0789265\pi$
$863$	9.67666	+	29.7817i	0.329397	+	1.01378i	−0.640019	+	0.768359i	$0.721074\pi$
$864$		0			0
$865$	14.3048	+	24.1391i	0.486379	+	0.820755i
$866$		0			0
$867$	29.2081	−	21.2209i	0.991960	−	0.720701i
$868$		0			0
$869$	2.03346	−	1.47739i	0.0689803	−	0.0501171i
$870$		0			0
$871$	12.7191	+	9.24099i	0.430972	+	0.313119i
$872$		0			0
$873$	9.01401	−	27.7423i	0.305078	−	0.938934i
$874$		0			0
$875$	−42.4790	−	28.7033i	−1.43605	−	0.970347i
$876$		0			0
$877$	3.55277	−	10.9343i	0.119968	−	0.369225i	−0.872982	−	0.487752i	$-0.837817\pi$
$877$	3.55277	−	10.9343i	0.119968	−	0.369225i	0.992951	+	0.118527i	$0.0378171\pi$
$878$		0			0
$879$	−20.1596	−	14.6468i	−0.679966	−	0.494024i
$880$		0			0
$881$	14.9835	−	10.8862i	0.504809	−	0.366765i	−0.306042	−	0.952018i	$-0.599005\pi$
$881$	14.9835	−	10.8862i	0.504809	−	0.366765i	0.810851	+	0.585253i	$0.199005\pi$
$882$		0			0
$883$	14.4200	−	10.4767i	0.485271	−	0.352570i	−0.318092	−	0.948060i	$-0.603042\pi$
$883$	14.4200	−	10.4767i	0.485271	−	0.352570i	0.803363	+	0.595490i	$0.203042\pi$
$884$		0			0
$885$	−6.97329	−	11.7673i	−0.234405	−	0.395553i
$886$		0			0
$887$	−4.86199	−	14.9637i	−0.163250	−	0.502431i	0.835653	−	0.549257i	$-0.185089\pi$
$887$	−4.86199	−	14.9637i	−0.163250	−	0.502431i	−0.998903	+	0.0468263i	$0.985089\pi$
$888$		0			0
$889$	17.6212	−	54.2324i	0.590996	−	1.81890i
$890$		0			0
$891$	0.307854	+	0.947476i	0.0103135	+	0.0317416i
$892$		0			0
$893$	−2.81846			−0.0943161
$894$		0			0
$895$	10.5132	−	2.35981i	0.351419	−	0.0788798i
$896$		0			0
$897$	2.28022	+	1.65668i	0.0761344	+	0.0553149i
$898$		0			0
$899$	12.0052			0.400394
$900$		0			0
$901$	−71.7087			−2.38896
$902$		0			0
$903$	42.6201	+	30.9653i	1.41831	+	1.03046i
$904$		0			0
$905$	−4.55950	+	48.6969i	−0.151563	+	1.61874i
$906$		0			0
$907$	41.9377			1.39252			0.696260	−	0.717790i	$-0.254846\pi$
$907$	41.9377			1.39252			0.696260	+	0.717790i	$0.254846\pi$
$908$		0			0
$909$	5.59514	+	17.2201i	0.185579	+	0.571153i
$910$		0			0
$911$	−1.31596	+	4.05011i	−0.0435997	+	0.134186i	−0.970487	−	0.241154i	$-0.922474\pi$
$911$	−1.31596	+	4.05011i	−0.0435997	+	0.134186i	0.926887	+	0.375340i	$0.122474\pi$
$912$		0			0
$913$	0.984484	+	3.02993i	0.0325817	+	0.100276i
$914$		0			0
$915$	0.322206	−	3.44127i	0.0106518	−	0.113765i
$916$		0			0
$917$	0.192332	−	0.139738i	0.00635137	−	0.00461454i
$918$		0			0
$919$	18.0413	−	13.1078i	0.595129	−	0.432386i	−0.249018	−	0.968499i	$-0.580108\pi$
$919$	18.0413	−	13.1078i	0.595129	−	0.432386i	0.844146	+	0.536113i	$0.180108\pi$
$920$		0			0
$921$	12.6925	+	9.22164i	0.418232	+	0.303863i
$922$		0			0
$923$	−8.01679	+	24.6731i	−0.263876	+	0.812126i
$924$		0			0
$925$	−46.8683	+	22.1565i	−1.54102	+	0.728500i
$926$		0			0
$927$	1.79046	−	5.51048i	0.0588065	−	0.180988i
$928$		0			0
$929$	−8.98659	−	6.52914i	−0.294841	−	0.214214i	0.430524	−	0.902579i	$-0.358329\pi$
$929$	−8.98659	−	6.52914i	−0.294841	−	0.214214i	−0.725365	+	0.688365i	$0.758329\pi$
$930$		0			0
$931$	3.15850	−	2.29478i	0.103516	−	0.0752085i
$932$		0			0
$933$	24.9112	−	18.0991i	0.815557	−	0.592537i
$934$		0			0
$935$	−14.3253	−	6.18396i	−0.468486	−	0.202237i
$936$		0			0
$937$	−1.55456	−	4.78445i	−0.0507854	−	0.156301i	0.922447	−	0.386123i	$-0.126186\pi$
$937$	−1.55456	−	4.78445i	−0.0507854	−	0.156301i	−0.973233	+	0.229821i	$0.926186\pi$
$938$		0			0
$939$	8.34076	−	25.6702i	0.272190	−	0.837716i
$940$		0			0
$941$	0.681989	+	2.09894i	0.0222322	+	0.0684236i	0.961557	−	0.274605i	$-0.0885471\pi$
$941$	0.681989	+	2.09894i	0.0222322	+	0.0684236i	−0.939325	+	0.343029i	$0.888547\pi$
$942$		0			0
$943$	−2.17603			−0.0708612
$944$		0			0
$945$	−28.0018	−	47.2524i	−0.910898	−	1.53712i
$946$		0			0
$947$	−5.33110	−	3.87327i	−0.173238	−	0.125864i	0.497788	−	0.867299i	$-0.334146\pi$
$947$	−5.33110	−	3.87327i	−0.173238	−	0.125864i	−0.671025	+	0.741434i	$0.734146\pi$
$948$		0			0
$949$	−16.1467			−0.524143
$950$		0			0
$951$	14.9201			0.483818
$952$		0			0
$953$	28.2142	+	20.4988i	0.913948	+	0.664022i	0.942010	−	0.335584i	$-0.108934\pi$
$953$	28.2142	+	20.4988i	0.913948	+	0.664022i	−0.0280620	+	0.999606i	$0.508934\pi$
$954$		0			0
$955$	0.734880	+	0.317235i	0.0237802	+	0.0102655i
$956$		0			0
$957$	6.31424			0.204110
$958$		0			0
$959$	25.4161	+	78.2227i	0.820729	+	2.52594i
$960$		0			0
$961$	−8.12975	+	25.0208i	−0.262250	+	0.807123i
$962$		0			0
$963$	9.24921	+	28.4661i	0.298052	+	0.917309i
$964$		0			0
$965$	13.0520	−	14.8312i	0.420158	−	0.477432i
$966$		0			0
$967$	−10.4451	+	7.58878i	−0.335891	+	0.244039i	−0.742926	−	0.669374i	$-0.766563\pi$
$967$	−10.4451	+	7.58878i	−0.335891	+	0.244039i	0.407035	+	0.913412i	$0.366563\pi$
$968$		0			0
$969$	1.79003	−	1.30053i	0.0575040	−	0.0417791i
$970$		0			0
$971$	−35.8313	−	26.0330i	−1.14988	−	0.835437i	−0.161416	−	0.986887i	$-0.551606\pi$
$971$	−35.8313	−	26.0330i	−1.14988	−	0.835437i	−0.988465	+	0.151449i	$0.951606\pi$
$972$		0			0
$973$	20.7795	−	63.9526i	0.666159	−	2.05023i
$974$		0			0
$975$	9.88089	+	1.86666i	0.316442	+	0.0597811i
$976$		0			0
$977$	−12.8772	+	39.6321i	−0.411980	+	1.26794i	0.502945	+	0.864318i	$0.332250\pi$
$977$	−12.8772	+	39.6321i	−0.411980	+	1.26794i	−0.914925	+	0.403624i	$0.867750\pi$
$978$		0			0
$979$	−8.32632	−	6.04943i	−0.266110	−	0.193341i
$980$		0			0
$981$	−20.5283	+	14.9147i	−0.655418	+	0.476189i
$982$		0			0
$983$	−12.4536	+	9.04806i	−0.397208	+	0.288588i	−0.768403	−	0.639967i	$-0.778948\pi$
$983$	−12.4536	+	9.04806i	−0.397208	+	0.288588i	0.371195	+	0.928555i	$0.378948\pi$
$984$		0			0
$985$	48.5947	−	10.9076i	1.54836	−	0.347545i
$986$		0			0
$987$	16.3465	+	50.3095i	0.520316	+	1.60137i
$988$		0			0
$989$	−4.36737	+	13.4414i	−0.138874	+	0.427411i
$990$		0			0
$991$	−6.62847	−	20.4003i	−0.210560	−	0.648038i	−0.999439	−	0.0334889i	$-0.989338\pi$
$991$	−6.62847	−	20.4003i	−0.210560	−	0.648038i	0.788879	−	0.614549i	$-0.210662\pi$
$992$		0			0
$993$	1.87458			0.0594881
$994$		0			0
$995$	4.03680	−	4.58708i	0.127975	−	0.145420i
$996$		0			0
$997$	2.25047	+	1.63506i	0.0712730	+	0.0517829i	0.622851	−	0.782340i	$-0.285974\pi$
$997$	2.25047	+	1.63506i	0.0712730	+	0.0517829i	−0.551578	+	0.834123i	$0.685974\pi$
$998$		0			0
$999$	−55.5413			−1.75725

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.221.9	✓	52
25.6	even	5	inner	1100.2.q.b.881.9	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.9	✓	52	1.1	even	1	trivial
1100.2.q.b.881.9	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)

\(f(q)\)	\(=\)	\(q+(0.921658 + 0.669624i) q^{3} +(-1.47725 + 1.67861i) q^{5} -4.58549 q^{7} +(-0.525993 - 1.61884i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(0.545520 + 1.67894i) q^{13} +(-2.48556 + 0.557910i) q^{15} +(5.64523 - 4.10150i) q^{17} +(0.225177 - 0.163601i) q^{19} +(-4.22626 - 3.07056i) q^{21} +(0.433073 - 1.33286i) q^{23} +(-0.635492 - 4.95945i) q^{25} +(1.65535 - 5.09466i) q^{27} +(-4.48401 - 3.25782i) q^{29} +(-1.75233 + 1.27315i) q^{31} +(-0.921658 + 0.669624i) q^{33} +(6.77390 - 7.69727i) q^{35} +(-3.20398 - 9.86084i) q^{37} +(-0.621474 + 1.91270i) q^{39} +(-0.479808 - 1.47670i) q^{41} -10.0846 q^{43} +(3.49443 + 1.50849i) q^{45} +(-8.19224 - 5.95201i) q^{47} +14.0267 q^{49} +7.94943 q^{51} +(-8.31392 - 6.04042i) q^{53} +(-1.13996 - 1.92366i) q^{55} +0.317087 q^{57} +(1.65927 + 5.10671i) q^{59} +(-0.419275 + 1.29039i) q^{61} +(2.41194 + 7.42318i) q^{63} +(-3.62416 - 1.56449i) q^{65} +(7.20492 - 5.23468i) q^{67} +(1.29166 - 0.938447i) q^{69} +(11.8891 + 8.63790i) q^{71} +(-2.82642 + 8.69883i) q^{73} +(2.73526 - 4.99646i) q^{75} +(1.41700 - 4.36106i) q^{77} +(-2.03346 - 1.47739i) q^{79} +(0.805971 - 0.585572i) q^{81} +(2.57741 - 1.87260i) q^{83} +(-1.45455 + 15.5351i) q^{85} +(-1.95121 - 6.00519i) q^{87} +(-3.18037 + 9.78818i) q^{89} +(-2.50148 - 7.69876i) q^{91} -2.46758 q^{93} +(-0.0580193 + 0.619664i) q^{95} +(13.8642 + 10.0729i) q^{97} +1.70215 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 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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