LMFDB - Embedded newform 1100.2.q.b.441.2

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			441.2
Character	$\chi$	$=$	1100.441
Dual form			1100.2.q.b.661.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.885916 - 2.72657i) q^{3} +(-2.22917 - 0.175548i) q^{5} -1.14570 q^{7} +(-4.22229 + 3.06767i) q^{9} +(0.809017 + 0.587785i) q^{11} +(-1.78203 + 1.29472i) q^{13} +(1.49621 + 6.23350i) q^{15} +(-1.87765 + 5.77881i) q^{17} +(1.07976 - 3.32316i) q^{19} +(1.01500 + 3.12384i) q^{21} +(5.26216 + 3.82318i) q^{23} +(4.93837 + 0.782652i) q^{25} +(5.14673 + 3.73932i) q^{27} +(-0.266363 - 0.819782i) q^{29} +(1.73185 - 5.33009i) q^{31} +(0.885916 - 2.72657i) q^{33} +(2.55397 + 0.201126i) q^{35} +(-3.32291 + 2.41423i) q^{37} +(5.10888 + 3.71182i) q^{39} +(5.88665 - 4.27690i) q^{41} -10.6582 q^{43} +(9.95070 - 6.09713i) q^{45} +(1.58475 + 4.87737i) q^{47} -5.68736 q^{49} +17.4198 q^{51} +(-0.807722 - 2.48591i) q^{53} +(-1.70025 - 1.45229i) q^{55} -10.0174 q^{57} +(5.03977 - 3.66161i) q^{59} +(5.89852 + 4.28552i) q^{61} +(4.83749 - 3.51464i) q^{63} +(4.19973 - 2.57332i) q^{65} +(-4.55624 + 14.0227i) q^{67} +(5.76234 - 17.7347i) q^{69} +(2.11841 + 6.51980i) q^{71} +(7.89553 + 5.73644i) q^{73} +(-2.24102 - 14.1582i) q^{75} +(-0.926894 - 0.673428i) q^{77} +(3.62501 + 11.1566i) q^{79} +(0.797636 - 2.45487i) q^{81} +(2.82808 - 8.70393i) q^{83} +(5.20005 - 12.5523i) q^{85} +(-1.99922 + 1.45252i) q^{87} +(-7.48667 - 5.43939i) q^{89} +(2.04168 - 1.48337i) q^{91} -16.0671 q^{93} +(-2.99034 + 7.21833i) q^{95} +(-0.568337 - 1.74916i) q^{97} -5.21903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

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

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
$3$	−0.885916	−	2.72657i	−0.511484	−	1.57419i	−0.789589	−	0.613635i	$-0.789706\pi$
$3$	−0.885916	−	2.72657i	−0.511484	−	1.57419i	0.278105	−	0.960551i	$-0.410294\pi$
$4$		0			0
$5$	−2.22917	−	0.175548i	−0.996914	−	0.0785076i
$5$	−2.22917	−	0.175548i	−0.996914	−	0.0785076i
$6$		0			0
$7$	−1.14570			−0.433035			−0.216518	−	0.976279i	$-0.569470\pi$
$7$	−1.14570			−0.433035			−0.216518	+	0.976279i	$0.569470\pi$
$8$		0			0
$9$	−4.22229	+	3.06767i	−1.40743	+	1.02256i
$10$		0			0
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$12$		0			0
$13$	−1.78203	+	1.29472i	−0.494247	+	0.359091i	−0.806815	−	0.590804i	$-0.798811\pi$
$13$	−1.78203	+	1.29472i	−0.494247	+	0.359091i	0.312569	+	0.949895i	$0.398811\pi$
$14$		0			0
$15$	1.49621	+	6.23350i	0.386320	+	1.60948i
$16$		0			0
$17$	−1.87765	+	5.77881i	−0.455397	+	1.40157i	0.415271	+	0.909698i	$0.363687\pi$
$17$	−1.87765	+	5.77881i	−0.455397	+	1.40157i	−0.870668	+	0.491870i	$0.836313\pi$
$18$		0			0
$19$	1.07976	−	3.32316i	0.247714	−	0.762386i	−0.747464	−	0.664302i	$-0.768729\pi$
$19$	1.07976	−	3.32316i	0.247714	−	0.762386i	0.995178	−	0.0980835i	$-0.0312712\pi$
$20$		0			0
$21$	1.01500	+	3.12384i	0.221491	+	0.681678i
$22$		0			0
$23$	5.26216	+	3.82318i	1.09724	+	0.797189i	0.980607	−	0.195987i	$-0.0627910\pi$
$23$	5.26216	+	3.82318i	1.09724	+	0.797189i	0.116630	+	0.993175i	$0.462791\pi$
$24$		0			0
$25$	4.93837	+	0.782652i	0.987673	+	0.156530i
$26$		0			0
$27$	5.14673	+	3.73932i	0.990489	+	0.719633i
$28$		0			0
$29$	−0.266363	−	0.819782i	−0.0494624	−	0.152230i	0.923275	−	0.384141i	$-0.125502\pi$
$29$	−0.266363	−	0.819782i	−0.0494624	−	0.152230i	−0.972737	+	0.231911i	$0.925502\pi$
$30$		0			0
$31$	1.73185	−	5.33009i	0.311049	−	0.957312i	−0.666301	−	0.745683i	$-0.732123\pi$
$31$	1.73185	−	5.33009i	0.311049	−	0.957312i	0.977350	−	0.211628i	$-0.0678767\pi$
$32$		0			0
$33$	0.885916	−	2.72657i	0.154218	−	0.474635i
$34$		0			0
$35$	2.55397	+	0.201126i	0.431699	+	0.0339966i
$36$		0			0
$37$	−3.32291	+	2.41423i	−0.546283	+	0.396898i	−0.826413	−	0.563064i	$-0.809622\pi$
$37$	−3.32291	+	2.41423i	−0.546283	+	0.396898i	0.280130	+	0.959962i	$0.409622\pi$
$38$		0			0
$39$	5.10888	+	3.71182i	0.818075	+	0.594367i
$40$		0			0
$41$	5.88665	−	4.27690i	0.919340	−	0.667939i	−0.0240198	−	0.999711i	$-0.507646\pi$
$41$	5.88665	−	4.27690i	0.919340	−	0.667939i	0.943360	+	0.331772i	$0.107646\pi$
$42$		0			0
$43$	−10.6582			−1.62536			−0.812681	−	0.582709i	$-0.801993\pi$
$43$	−10.6582			−1.62536			−0.812681	+	0.582709i	$0.801993\pi$
$44$		0			0
$45$	9.95070	−	6.09713i	1.48336	−	0.908907i
$46$		0			0
$47$	1.58475	+	4.87737i	0.231160	+	0.711438i	0.997608	+	0.0691306i	$0.0220225\pi$
$47$	1.58475	+	4.87737i	0.231160	+	0.711438i	−0.766448	+	0.642307i	$0.777977\pi$
$48$		0			0
$49$	−5.68736			−0.812480
$50$		0			0
$51$	17.4198			2.43926
$52$		0			0
$53$	−0.807722	−	2.48591i	−0.110949	−	0.341466i	0.880132	−	0.474730i	$-0.157454\pi$
$53$	−0.807722	−	2.48591i	−0.110949	−	0.341466i	−0.991081	+	0.133264i	$0.957454\pi$
$54$		0			0
$55$	−1.70025	−	1.45229i	−0.229262	−	0.195827i
$56$		0			0
$57$	−10.0174			−1.32684
$58$		0			0
$59$	5.03977	−	3.66161i	0.656123	−	0.476701i	−0.209229	−	0.977867i	$-0.567095\pi$
$59$	5.03977	−	3.66161i	0.656123	−	0.476701i	0.865351	+	0.501166i	$0.167095\pi$
$60$		0			0
$61$	5.89852	+	4.28552i	0.755228	+	0.548705i	0.897443	−	0.441131i	$-0.145422\pi$
$61$	5.89852	+	4.28552i	0.755228	+	0.548705i	−0.142215	+	0.989836i	$0.545422\pi$
$62$		0			0
$63$	4.83749	−	3.51464i	0.609467	−	0.442803i
$64$		0			0
$65$	4.19973	−	2.57332i	0.520912	−	0.319181i
$66$		0			0
$67$	−4.55624	+	14.0227i	−0.556633	+	1.71314i	0.134959	+	0.990851i	$0.456910\pi$
$67$	−4.55624	+	14.0227i	−0.556633	+	1.71314i	−0.691592	+	0.722289i	$0.743090\pi$
$68$		0			0
$69$	5.76234	−	17.7347i	0.693705	−	2.13500i
$70$		0			0
$71$	2.11841	+	6.51980i	0.251409	+	0.773757i	0.994516	+	0.104585i	$0.0333513\pi$
$71$	2.11841	+	6.51980i	0.251409	+	0.773757i	−0.743107	+	0.669173i	$0.766649\pi$
$72$		0			0
$73$	7.89553	+	5.73644i	0.924102	+	0.671399i	0.944542	−	0.328392i	$-0.106507\pi$
$73$	7.89553	+	5.73644i	0.924102	+	0.671399i	−0.0204399	+	0.999791i	$0.506507\pi$
$74$		0			0
$75$	−2.24102	−	14.1582i	−0.258771	−	1.63484i
$76$		0			0
$77$	−0.926894	−	0.673428i	−0.105629	−	0.0767442i
$78$		0			0
$79$	3.62501	+	11.1566i	0.407845	+	1.25522i	0.918496	+	0.395430i	$0.129404\pi$
$79$	3.62501	+	11.1566i	0.407845	+	1.25522i	−0.510651	+	0.859788i	$0.670596\pi$
$80$		0			0
$81$	0.797636	−	2.45487i	0.0886262	−	0.272763i
$82$		0			0
$83$	2.82808	−	8.70393i	0.310422	−	0.955381i	−0.667176	−	0.744900i	$-0.732497\pi$
$83$	2.82808	−	8.70393i	0.310422	−	0.955381i	0.977598	−	0.210481i	$-0.0675029\pi$
$84$		0			0
$85$	5.20005	−	12.5523i	0.564025	−	1.36149i
$86$		0			0
$87$	−1.99922	+	1.45252i	−0.214339	+	0.155726i
$88$		0			0
$89$	−7.48667	−	5.43939i	−0.793586	−	0.576574i	0.115440	−	0.993315i	$-0.463172\pi$
$89$	−7.48667	−	5.43939i	−0.793586	−	0.576574i	−0.909025	+	0.416741i	$0.863172\pi$
$90$		0			0
$91$	2.04168	−	1.48337i	0.214026	−	0.155499i
$92$		0			0
$93$	−16.0671			−1.66608
$94$		0			0
$95$	−2.99034	+	7.21833i	−0.306803	+	0.740585i
$96$		0			0
$97$	−0.568337	−	1.74916i	−0.0577059	−	0.177601i	0.918049	−	0.396467i	$-0.129764\pi$
$97$	−0.568337	−	1.74916i	−0.0577059	−	0.177601i	−0.975755	+	0.218867i	$0.929764\pi$
$98$		0			0
$99$	−5.21903			−0.524533
$100$		0			0
$101$	−0.385251			−0.0383339			−0.0191669	−	0.999816i	$-0.506101\pi$
$101$	−0.385251			−0.0383339			−0.0191669	+	0.999816i	$0.506101\pi$
$102$		0			0
$103$	4.60189	+	14.1632i	0.453438	+	1.39554i	0.872959	+	0.487793i	$0.162198\pi$
$103$	4.60189	+	14.1632i	0.453438	+	1.39554i	−0.419521	+	0.907746i	$0.637802\pi$
$104$		0			0
$105$	−1.71421	−	7.14175i	−0.167290	−	0.696963i
$106$		0			0
$107$	19.0190			1.83864			0.919320	−	0.393510i	$-0.128739\pi$
$107$	19.0190			1.83864			0.919320	+	0.393510i	$0.128739\pi$
$108$		0			0
$109$	0.465384	−	0.338121i	0.0445757	−	0.0323861i	−0.565274	−	0.824903i	$-0.691230\pi$
$109$	0.465384	−	0.338121i	0.0445757	−	0.0323861i	0.609850	+	0.792517i	$0.291230\pi$
$110$		0			0
$111$	9.52639	+	6.92133i	0.904205	+	0.656944i
$112$		0			0
$113$	−0.405512	+	0.294622i	−0.0381474	+	0.0277157i	−0.606696	−	0.794934i	$-0.707505\pi$
$113$	−0.405512	+	0.294622i	−0.0381474	+	0.0277157i	0.568548	+	0.822650i	$0.307505\pi$
$114$		0			0
$115$	−11.0591	−	9.44627i	−1.03126	−	0.880870i
$116$		0			0
$117$	3.55247	−	10.9334i	0.328426	−	1.01079i
$118$		0			0
$119$	2.15123	−	6.62081i	0.197203	−	0.606929i
$120$		0			0
$121$	0.309017	+	0.951057i	0.0280925	+	0.0864597i
$122$		0			0
$123$	−16.8763	−	12.2614i	−1.52169	−	1.10557i
$124$		0			0
$125$	−10.8710	−	2.61158i	−0.972336	−	0.233587i
$126$		0			0
$127$	15.3095	+	11.1230i	1.35850	+	0.987008i	0.998539	+	0.0540411i	$0.0172102\pi$
$127$	15.3095	+	11.1230i	1.35850	+	0.987008i	0.359962	+	0.932967i	$0.382790\pi$
$128$		0			0
$129$	9.44228	+	29.0604i	0.831347	+	2.55862i
$130$		0			0
$131$	−2.66663	+	8.20703i	−0.232984	+	0.717051i	0.764398	+	0.644744i	$0.223036\pi$
$131$	−2.66663	+	8.20703i	−0.232984	+	0.717051i	−0.997382	+	0.0723071i	$0.976964\pi$
$132$		0			0
$133$	−1.23709	+	3.80736i	−0.107269	+	0.330140i
$134$		0			0
$135$	−10.8165	−	9.23907i	−0.930936	−	0.795172i
$136$		0			0
$137$	0.197145	−	0.143234i	0.0168432	−	0.0122373i	−0.579332	−	0.815092i	$-0.696686\pi$
$137$	0.197145	−	0.143234i	0.0168432	−	0.0122373i	0.596175	+	0.802855i	$0.296686\pi$
$138$		0			0
$139$	−0.634738	−	0.461164i	−0.0538378	−	0.0391154i	0.560541	−	0.828127i	$-0.310593\pi$
$139$	−0.634738	−	0.461164i	−0.0538378	−	0.0391154i	−0.614379	+	0.789011i	$0.710593\pi$
$140$		0			0
$141$	11.8945	−	8.64188i	1.00170	−	0.727778i
$142$		0			0
$143$	−2.20271			−0.184200
$144$		0			0
$145$	0.449857	+	1.87419i	0.0373586	+	0.155643i
$146$		0			0
$147$	5.03853	+	15.5070i	0.415571	+	1.27900i
$148$		0			0
$149$	12.2267			1.00165			0.500827	−	0.865547i	$-0.333029\pi$
$149$	12.2267			1.00165			0.500827	+	0.865547i	$0.333029\pi$
$150$		0			0
$151$	−8.56670			−0.697148			−0.348574	−	0.937281i	$-0.613334\pi$
$151$	−8.56670			−0.697148			−0.348574	+	0.937281i	$0.613334\pi$
$152$		0			0
$153$	−9.79952	−	30.1598i	−0.792244	−	2.43828i
$154$		0			0
$155$	−4.79627	+	11.5776i	−0.385246	+	0.929937i
$156$		0			0
$157$	−22.6130			−1.80471			−0.902356	−	0.430992i	$-0.858164\pi$
$157$	−22.6130			−1.80471			−0.902356	+	0.430992i	$0.858164\pi$
$158$		0			0
$159$	−6.06244	+	4.40462i	−0.480783	+	0.349309i
$160$		0			0
$161$	−6.02888	−	4.38024i	−0.475142	−	0.345211i
$162$		0			0
$163$	−11.5939	+	8.42343i	−0.908101	+	0.659774i	−0.940534	−	0.339700i	$-0.889675\pi$
$163$	−11.5939	+	8.42343i	−0.908101	+	0.659774i	0.0324327	+	0.999474i	$0.489675\pi$
$164$		0			0
$165$	−2.45350	+	5.92246i	−0.191005	+	0.461063i
$166$		0			0
$167$	−4.19392	+	12.9075i	−0.324535	+	0.998816i	0.647115	+	0.762392i	$0.275975\pi$
$167$	−4.19392	+	12.9075i	−0.324535	+	0.998816i	−0.971650	+	0.236424i	$0.924025\pi$
$168$		0			0
$169$	−2.51789	+	7.74927i	−0.193684	+	0.596097i
$170$		0			0
$171$	5.63531	+	17.3437i	0.430943	+	1.32631i
$172$		0			0
$173$	5.16802	+	3.75479i	0.392917	+	0.285471i	0.766650	−	0.642065i	$-0.221922\pi$
$173$	5.16802	+	3.75479i	0.392917	+	0.285471i	−0.373733	+	0.927536i	$0.621922\pi$
$174$		0			0
$175$	−5.65791	−	0.896688i	−0.427697	−	0.0677832i
$176$		0			0
$177$	−14.4485	−	10.4974i	−1.08601	−	0.789034i
$178$		0			0
$179$	1.28678	+	3.96030i	0.0961785	+	0.296007i	0.987559	−	0.157249i	$-0.0502624\pi$
$179$	1.28678	+	3.96030i	0.0961785	+	0.296007i	−0.891381	+	0.453256i	$0.850262\pi$
$180$		0			0
$181$	−2.43270	+	7.48708i	−0.180821	+	0.556511i	−0.999851	−	0.0172400i	$-0.994512\pi$
$181$	−2.43270	+	7.48708i	−0.180821	+	0.556511i	0.819030	+	0.573750i	$0.194512\pi$
$182$		0			0
$183$	6.45919	−	19.8793i	0.477477	−	1.46952i
$184$		0			0
$185$	7.83113	−	4.79840i	0.575756	−	0.352785i
$186$		0			0
$187$	−4.91575	+	3.57150i	−0.359475	+	0.261174i
$188$		0			0
$189$	−5.89663	−	4.28416i	−0.428917	−	0.311626i
$190$		0			0
$191$	−9.26346	+	6.73030i	−0.670281	+	0.486987i	−0.870119	−	0.492842i	$-0.835958\pi$
$191$	−9.26346	+	6.73030i	−0.670281	+	0.486987i	0.199839	+	0.979829i	$0.435958\pi$
$192$		0			0
$193$	−22.9044			−1.64870			−0.824348	−	0.566084i	$-0.808458\pi$
$193$	−22.9044			−1.64870			−0.824348	+	0.566084i	$0.808458\pi$
$194$		0			0
$195$	−10.7369	−	9.17112i	−0.768888	−	0.656757i
$196$		0			0
$197$	−1.69924	−	5.22973i	−0.121066	−	0.372603i	0.872098	−	0.489331i	$-0.162759\pi$
$197$	−1.69924	−	5.22973i	−0.121066	−	0.372603i	−0.993164	+	0.116729i	$0.962759\pi$
$198$		0			0
$199$	−7.87973			−0.558579			−0.279289	−	0.960207i	$-0.590099\pi$
$199$	−7.87973			−0.558579			−0.279289	+	0.960207i	$0.590099\pi$
$200$		0			0
$201$	42.2702			2.98151
$202$		0			0
$203$	0.305173	+	0.939227i	0.0214190	+	0.0659208i
$204$		0			0
$205$	−13.8731	+	8.50053i	−0.968941	+	0.593703i
$206$		0			0
$207$	−33.9466			−2.35945
$208$		0			0
$209$	2.82685	−	2.05383i	0.195537	−	0.142066i
$210$		0			0
$211$	−9.42281	−	6.84607i	−0.648693	−	0.471303i	0.214133	−	0.976805i	$-0.431307\pi$
$211$	−9.42281	−	6.84607i	−0.648693	−	0.471303i	−0.862826	+	0.505502i	$0.831307\pi$
$212$		0			0
$213$	15.8999	−	11.5520i	1.08945	−	0.791529i
$214$		0			0
$215$	23.7589	+	1.87103i	1.62035	+	0.127603i
$216$		0			0
$217$	−1.98419	+	6.10670i	−0.134695	+	0.414550i
$218$		0			0
$219$	8.64602	−	26.6097i	0.584244	−	1.79812i
$220$		0			0
$221$	−4.13592	−	12.7291i	−0.278212	−	0.856249i
$222$		0			0
$223$	−0.595513	−	0.432665i	−0.0398785	−	0.0289734i	0.567667	−	0.823258i	$-0.307846\pi$
$223$	−0.595513	−	0.432665i	−0.0398785	−	0.0289734i	−0.607546	+	0.794285i	$0.707846\pi$
$224$		0			0
$225$	−23.2521	+	11.8447i	−1.55014	+	0.789646i
$226$		0			0
$227$	2.58736	+	1.87983i	0.171729	+	0.124769i	0.670330	−	0.742063i	$-0.266153\pi$
$227$	2.58736	+	1.87983i	0.171729	+	0.124769i	−0.498601	+	0.866832i	$0.666153\pi$
$228$		0			0
$229$	6.24956	+	19.2342i	0.412983	+	1.27103i	0.914043	+	0.405618i	$0.132944\pi$
$229$	6.24956	+	19.2342i	0.412983	+	1.27103i	−0.501060	+	0.865412i	$0.667056\pi$
$230$		0			0
$231$	−1.01500	+	3.12384i	−0.0667820	+	0.205534i
$232$		0			0
$233$	−2.13183	+	6.56111i	−0.139661	+	0.429833i	−0.996286	−	0.0861073i	$-0.972557\pi$
$233$	−2.13183	+	6.56111i	−0.139661	+	0.429833i	0.856625	+	0.515940i	$0.172557\pi$
$234$		0			0
$235$	−2.67647	−	11.1507i	−0.174593	−	0.727390i
$236$		0			0
$237$	27.2079	−	19.7677i	1.76734	−	1.28405i
$238$		0			0
$239$	15.6995	+	11.4063i	1.01551	+	0.737815i	0.965359	−	0.260927i	$-0.0840280\pi$
$239$	15.6995	+	11.4063i	1.01551	+	0.737815i	0.0501563	+	0.998741i	$0.484028\pi$
$240$		0			0
$241$	−8.00198	+	5.81378i	−0.515453	+	0.374498i	−0.814888	−	0.579618i	$-0.803202\pi$
$241$	−8.00198	+	5.81378i	−0.515453	+	0.374498i	0.299435	+	0.954117i	$0.403202\pi$
$242$		0			0
$243$	11.6851			0.749601
$244$		0			0
$245$	12.6781	+	0.998406i	0.809973	+	0.0637858i
$246$		0			0
$247$	2.37840	+	7.31997i	0.151334	+	0.465758i
$248$		0			0
$249$	−26.2373			−1.66272
$250$		0			0
$251$	−12.9888			−0.819843			−0.409921	−	0.912121i	$-0.634444\pi$
$251$	−12.9888			−0.819843			−0.409921	+	0.912121i	$0.634444\pi$
$252$		0			0
$253$	2.00997	+	6.18604i	0.126365	+	0.388913i
$254$		0			0
$255$	−38.8316	−	3.05801i	−2.43173	−	0.191500i
$256$		0			0
$257$	−21.7299			−1.35548			−0.677739	−	0.735303i	$-0.737040\pi$
$257$	−21.7299			−1.35548			−0.677739	+	0.735303i	$0.737040\pi$
$258$		0			0
$259$	3.80707	−	2.76600i	0.236560	−	0.171871i
$260$		0			0
$261$	3.63948	+	2.64424i	0.225278	+	0.163674i
$262$		0			0
$263$	0.910004	−	0.661157i	0.0561133	−	0.0407687i	−0.559375	−	0.828915i	$-0.688959\pi$
$263$	0.910004	−	0.661157i	0.0561133	−	0.0407687i	0.615488	+	0.788146i	$0.288959\pi$
$264$		0			0
$265$	1.36415	+	5.68330i	0.0837990	+	0.349123i
$266$		0			0
$267$	−8.19830	+	25.2318i	−0.501728	+	1.54416i
$268$		0			0
$269$	−9.50703	+	29.2596i	−0.579654	+	1.78399i	0.0401019	+	0.999196i	$0.487232\pi$
$269$	−9.50703	+	29.2596i	−0.579654	+	1.78399i	−0.619756	+	0.784795i	$0.712768\pi$
$270$		0			0
$271$	−4.35540	−	13.4046i	−0.264572	−	0.814269i	−0.991792	−	0.127864i	$-0.959188\pi$
$271$	−4.35540	−	13.4046i	−0.264572	−	0.814269i	0.727220	−	0.686405i	$-0.240812\pi$
$272$		0			0
$273$	−5.85326	−	4.25265i	−0.354256	−	0.257382i
$274$		0			0
$275$	3.53519	+	3.53588i	0.213180	+	0.213221i
$276$		0			0
$277$	−15.9916	−	11.6186i	−0.960841	−	0.698092i	−0.00749505	−	0.999972i	$-0.502386\pi$
$277$	−15.9916	−	11.6186i	−0.960841	−	0.698092i	−0.953346	+	0.301880i	$0.902386\pi$
$278$		0			0
$279$	9.03858	+	27.8179i	0.541126	+	1.66541i
$280$		0			0
$281$	6.20825	−	19.1070i	0.370353	−	1.13983i	−0.576208	−	0.817303i	$-0.695468\pi$
$281$	6.20825	−	19.1070i	0.370353	−	1.13983i	0.946561	−	0.322526i	$-0.104532\pi$
$282$		0			0
$283$	7.55381	−	23.2482i	0.449027	−	1.38196i	−0.428979	−	0.903315i	$-0.641127\pi$
$283$	7.55381	−	23.2482i	0.449027	−	1.38196i	0.878006	−	0.478649i	$-0.158873\pi$
$284$		0			0
$285$	22.3305	+	1.75854i	1.32274	+	0.104167i
$286$		0			0
$287$	−6.74436	+	4.90006i	−0.398107	+	0.289241i
$288$		0			0
$289$	−16.1158	−	11.7088i	−0.947989	−	0.688754i
$290$		0			0
$291$	−4.26571	+	3.09922i	−0.250061	+	0.181680i
$292$		0			0
$293$	31.2441			1.82530			0.912649	−	0.408744i	$-0.134033\pi$
$293$	31.2441			1.82530			0.912649	+	0.408744i	$0.134033\pi$
$294$		0			0
$295$	−11.8773	+	7.27762i	−0.691522	+	0.423719i
$296$		0			0
$297$	1.96588	+	6.05035i	0.114072	+	0.351077i
$298$		0			0
$299$	−14.3273			−0.828569
$300$		0			0
$301$	12.2112			0.703839
$302$		0			0
$303$	0.341300	+	1.05041i	0.0196072	+	0.0603447i
$304$		0			0
$305$	−12.3965	−	10.5886i	−0.709819	−	0.606303i
$306$		0			0
$307$	−10.8429			−0.618837			−0.309418	−	0.950926i	$-0.600134\pi$
$307$	−10.8429			−0.618837			−0.309418	+	0.950926i	$0.600134\pi$
$308$		0			0
$309$	34.5400	−	25.0948i	1.96491	−	1.42759i
$310$		0			0
$311$	−6.80053	−	4.94087i	−0.385623	−	0.280171i	0.378037	−	0.925791i	$-0.376599\pi$
$311$	−6.80053	−	4.94087i	−0.385623	−	0.280171i	−0.763659	+	0.645619i	$0.776599\pi$
$312$		0			0
$313$	22.6032	−	16.4222i	1.27761	−	0.928236i	0.278130	−	0.960543i	$-0.410285\pi$
$313$	22.6032	−	16.4222i	1.27761	−	0.928236i	0.999478	+	0.0323070i	$0.0102854\pi$
$314$		0			0
$315$	−11.4006	+	6.98551i	−0.642349	+	0.393589i
$316$		0			0
$317$	−2.94087	+	9.05106i	−0.165176	+	0.508358i	−0.999049	−	0.0435973i	$-0.986118\pi$
$317$	−2.94087	+	9.05106i	−0.165176	+	0.508358i	0.833874	+	0.551955i	$0.186118\pi$
$318$		0			0
$319$	0.266363	−	0.819782i	0.0149135	−	0.0458990i
$320$		0			0
$321$	−16.8493	−	51.8568i	−0.940435	−	2.89436i
$322$		0			0
$323$	17.1765	+	12.4795i	0.955727	+	0.694376i
$324$		0			0
$325$	−9.81364	+	4.99910i	−0.544363	+	0.277300i
$326$		0			0
$327$	−1.33420	−	0.969354i	−0.0737815	−	0.0536054i
$328$		0			0
$329$	−1.81566	−	5.58802i	−0.100101	−	0.308078i
$330$		0			0
$331$	5.67928	−	17.4790i	0.312162	−	0.960735i	−0.664745	−	0.747070i	$-0.731460\pi$
$331$	5.67928	−	17.4790i	0.312162	−	0.960735i	0.976907	−	0.213665i	$-0.0685400\pi$
$332$		0			0
$333$	6.62419	−	20.3872i	0.363004	−	1.11721i
$334$		0			0
$335$	12.6183	−	30.4590i	0.689409	−	1.66415i
$336$		0			0
$337$	1.31164	−	0.952962i	0.0714496	−	0.0519112i	−0.551487	−	0.834183i	$-0.685939\pi$
$337$	1.31164	−	0.952962i	0.0714496	−	0.0519112i	0.622937	+	0.782272i	$0.285939\pi$
$338$		0			0
$339$	1.16256	+	0.844647i	0.0631414	+	0.0458749i
$340$		0			0
$341$	4.53404	−	3.29417i	0.245532	−	0.178390i
$342$		0			0
$343$	14.5360			0.784868
$344$		0			0
$345$	−15.9585	+	38.5220i	−0.859177	+	2.07395i
$346$		0			0
$347$	−1.27665	−	3.92913i	−0.0685342	−	0.210927i	0.910924	−	0.412575i	$-0.135370\pi$
$347$	−1.27665	−	3.92913i	−0.0685342	−	0.210927i	−0.979458	+	0.201648i	$0.935370\pi$
$348$		0			0
$349$	10.9081			0.583896			0.291948	−	0.956434i	$-0.405697\pi$
$349$	10.9081			0.583896			0.291948	+	0.956434i	$0.405697\pi$
$350$		0			0
$351$	−14.0130			−0.747960
$352$		0			0
$353$	−2.09441	−	6.44593i	−0.111474	−	0.343082i	0.879721	−	0.475490i	$-0.157729\pi$
$353$	−2.09441	−	6.44593i	−0.111474	−	0.343082i	−0.991195	+	0.132408i	$0.957729\pi$
$354$		0			0
$355$	−3.57775	−	14.9056i	−0.189887	−	0.791107i
$356$		0			0
$357$	−19.9579			−1.05628
$358$		0			0
$359$	−0.00346936	+	0.00252064i	−0.000183106	+	0.000133034i	−0.587877	−	0.808950i	$-0.700036\pi$
$359$	−0.00346936	+	0.00252064i	−0.000183106	+	0.000133034i	0.587694	+	0.809084i	$0.300036\pi$
$360$		0			0
$361$	5.49380	+	3.99148i	0.289147	+	0.210078i
$362$		0			0
$363$	2.31936	−	1.68511i	0.121735	−	0.0884455i
$364$		0			0
$365$	−16.5934	−	14.1735i	−0.868540	−	0.741876i
$366$		0			0
$367$	9.24858	−	28.4642i	0.482772	−	1.48582i	−0.352410	−	0.935846i	$-0.614638\pi$
$367$	9.24858	−	28.4642i	0.482772	−	1.48582i	0.835182	−	0.549973i	$-0.185362\pi$
$368$		0			0
$369$	−11.7350	+	36.1166i	−0.610899	+	1.88015i
$370$		0			0
$371$	0.925410	+	2.84812i	0.0480449	+	0.147867i
$372$		0			0
$373$	−14.3585	−	10.4320i	−0.743453	−	0.540150i	0.150338	−	0.988635i	$-0.451964\pi$
$373$	−14.3585	−	10.4320i	−0.743453	−	0.540150i	−0.893791	+	0.448485i	$0.851964\pi$
$374$		0			0
$375$	2.51017	+	31.9543i	0.129625	+	1.65011i
$376$		0			0
$377$	1.53606	+	1.11601i	0.0791109	+	0.0574775i
$378$		0			0
$379$	−3.02187	−	9.30037i	−0.155223	−	0.477728i	0.842960	−	0.537976i	$-0.180811\pi$
$379$	−3.02187	−	9.30037i	−0.155223	−	0.477728i	−0.998183	+	0.0602481i	$0.980811\pi$
$380$		0			0
$381$	16.7647	−	51.5965i	0.858883	−	2.64337i
$382$		0			0
$383$	8.84080	−	27.2092i	0.451744	−	1.39032i	−0.423172	−	0.906049i	$-0.639083\pi$
$383$	8.84080	−	27.2092i	0.451744	−	1.39032i	0.874916	−	0.484275i	$-0.160917\pi$
$384$		0			0
$385$	1.94798	+	1.66390i	0.0992784	+	0.0848001i
$386$		0			0
$387$	45.0020	−	32.6959i	2.28758	−	1.66202i
$388$		0			0
$389$	31.1008	+	22.5961i	1.57687	+	1.14567i	0.920171	+	0.391518i	$0.128050\pi$
$389$	31.1008	+	22.5961i	1.57687	+	1.14567i	0.656704	+	0.754149i	$0.271950\pi$
$390$		0			0
$391$	−31.9740	+	23.2304i	−1.61699	+	1.17481i
$392$		0			0
$393$	24.7394			1.24794
$394$		0			0
$395$	−6.12222	−	25.5063i	−0.308042	−	1.28336i
$396$		0			0
$397$	2.43464	+	7.49304i	0.122191	+	0.376065i	0.993379	−	0.114885i	$-0.0366499\pi$
$397$	2.43464	+	7.49304i	0.122191	+	0.376065i	−0.871188	+	0.490950i	$0.836650\pi$
$398$		0			0
$399$	11.4770			0.574568
$400$		0			0
$401$	−14.5423			−0.726207			−0.363104	−	0.931749i	$-0.618283\pi$
$401$	−14.5423			−0.726207			−0.363104	+	0.931749i	$0.618283\pi$
$402$		0			0
$403$	3.81477	+	11.7406i	0.190027	+	0.584843i
$404$		0			0
$405$	−2.20901	+	5.33229i	−0.109767	+	0.264964i
$406$		0			0
$407$	−4.10734			−0.203593
$408$		0			0
$409$	−1.80046	+	1.30811i	−0.0890272	+	0.0646821i	−0.631408	−	0.775450i	$-0.717523\pi$
$409$	−1.80046	+	1.30811i	−0.0890272	+	0.0646821i	0.542381	+	0.840132i	$0.317523\pi$
$410$		0			0
$411$	−0.565192	−	0.410636i	−0.0278788	−	0.0202552i
$412$		0			0
$413$	−5.77409	+	4.19512i	−0.284124	+	0.206428i
$414$		0			0
$415$	−7.83222	+	18.9060i	−0.384468	+	0.928061i
$416$		0			0
$417$	−0.695072	+	2.13921i	−0.0340378	+	0.104758i
$418$		0			0
$419$	−1.16950	+	3.59934i	−0.0571336	+	0.175839i	−0.975551	−	0.219774i	$-0.929468\pi$
$419$	−1.16950	+	3.59934i	−0.0571336	+	0.175839i	0.918417	+	0.395613i	$0.129468\pi$
$420$		0			0
$421$	6.06471	+	18.6653i	0.295576	+	0.909689i	0.983027	+	0.183459i	$0.0587294\pi$
$421$	6.06471	+	18.6653i	0.295576	+	0.909689i	−0.687451	+	0.726230i	$0.741271\pi$
$422$		0			0
$423$	−21.6534	−	15.7321i	−1.05283	−	0.764923i
$424$		0			0
$425$	−13.7953	+	27.0683i	−0.669171	+	1.31301i
$426$		0			0
$427$	−6.75796	−	4.90994i	−0.327040	−	0.237609i
$428$		0			0
$429$	1.95142	+	6.00585i	0.0942154	+	0.289965i
$430$		0			0
$431$	0.457170	−	1.40702i	0.0220211	−	0.0677740i	−0.939442	−	0.342708i	$-0.888656\pi$
$431$	0.457170	−	1.40702i	0.0220211	−	0.0677740i	0.961463	+	0.274934i	$0.0886559\pi$
$432$		0			0
$433$	−7.91905	+	24.3723i	−0.380565	+	1.17126i	0.559081	+	0.829113i	$0.311154\pi$
$433$	−7.91905	+	24.3723i	−0.380565	+	1.17126i	−0.939647	+	0.342147i	$0.888846\pi$
$434$		0			0
$435$	4.71157	−	2.88694i	0.225903	−	0.138418i
$436$		0			0
$437$	18.3869	−	13.3589i	0.879566	−	0.639042i
$438$		0			0
$439$	29.8617	+	21.6958i	1.42522	+	1.03549i	0.990881	+	0.134737i	$0.0430190\pi$
$439$	29.8617	+	21.6958i	1.42522	+	1.03549i	0.434342	+	0.900748i	$0.356981\pi$
$440$		0			0
$441$	24.0137	−	17.4470i	1.14351	−	0.830807i
$442$		0			0
$443$	−10.4666			−0.497281			−0.248641	−	0.968596i	$-0.579984\pi$
$443$	−10.4666			−0.497281			−0.248641	+	0.968596i	$0.579984\pi$
$444$		0			0
$445$	15.7342	+	13.4396i	0.745871	+	0.637097i
$446$		0			0
$447$	−10.8319	−	33.3371i	−0.512330	−	1.57679i
$448$		0			0
$449$	−15.9779			−0.754043			−0.377021	−	0.926205i	$-0.623052\pi$
$449$	−15.9779			−0.754043			−0.377021	+	0.926205i	$0.623052\pi$
$450$		0			0
$451$	7.27630			0.342627
$452$		0			0
$453$	7.58938	+	23.3577i	0.356580	+	1.09744i
$454$		0			0
$455$	−4.81165	+	2.94826i	−0.225574	+	0.138217i
$456$		0			0
$457$	5.71945			0.267545			0.133772	−	0.991012i	$-0.457291\pi$
$457$	5.71945			0.267545			0.133772	+	0.991012i	$0.457291\pi$
$458$		0			0
$459$	−31.2726	+	22.7209i	−1.45968	+	1.06052i
$460$		0			0
$461$	0.903540	+	0.656460i	0.0420821	+	0.0305744i	0.608627	−	0.793456i	$-0.291720\pi$
$461$	0.903540	+	0.656460i	0.0420821	+	0.0305744i	−0.566545	+	0.824031i	$0.691720\pi$
$462$		0			0
$463$	−5.30960	+	3.85765i	−0.246758	+	0.179280i	−0.704289	−	0.709914i	$-0.748734\pi$
$463$	−5.30960	+	3.85765i	−0.246758	+	0.179280i	0.457531	+	0.889194i	$0.348734\pi$
$464$		0			0
$465$	35.8163	+	2.82056i	1.66094	+	0.130800i
$466$		0			0
$467$	−3.60567	+	11.0971i	−0.166851	+	0.513514i	−0.999168	−	0.0407860i	$-0.987014\pi$
$467$	−3.60567	+	11.0971i	−0.166851	+	0.513514i	0.832317	+	0.554300i	$0.187014\pi$
$468$		0			0
$469$	5.22010	−	16.0658i	0.241042	−	0.741850i
$470$		0			0
$471$	20.0332	+	61.6559i	0.923081	+	2.84095i
$472$		0			0
$473$	−8.62267	−	6.26474i	−0.396471	−	0.288053i
$474$		0			0
$475$	7.93314	−	15.5659i	0.363997	−	0.714213i
$476$		0			0
$477$	11.0364	+	8.01841i	0.505322	+	0.367138i
$478$		0			0
$479$	12.3839	+	38.1137i	0.565834	+	1.74146i	0.665460	+	0.746434i	$0.268236\pi$
$479$	12.3839	+	38.1137i	0.565834	+	1.74146i	−0.0996254	+	0.995025i	$0.531764\pi$
$480$		0			0
$481$	2.79576	−	8.60448i	0.127476	−	0.392330i
$482$		0			0
$483$	−6.60194	+	20.3187i	−0.300399	+	0.924532i
$484$		0			0
$485$	0.959856	+	3.99894i	0.0435848	+	0.181583i
$486$		0			0
$487$	−21.4808	+	15.6067i	−0.973386	+	0.707207i	−0.956221	−	0.292646i	$-0.905464\pi$
$487$	−21.4808	+	15.6067i	−0.973386	+	0.707207i	−0.0171656	+	0.999853i	$0.505464\pi$
$488$		0			0
$489$	33.2383	+	24.1490i	1.50309	+	1.09206i
$490$		0			0
$491$	2.75659	−	2.00278i	0.124403	−	0.0903842i	−0.523844	−	0.851814i	$-0.675502\pi$
$491$	2.75659	−	2.00278i	0.124403	−	0.0903842i	0.648247	+	0.761430i	$0.275502\pi$
$492$		0			0
$493$	5.23750			0.235885
$494$		0			0
$495$	11.6341	+	0.916192i	0.522914	+	0.0411798i
$496$		0			0
$497$	−2.42707	−	7.46976i	−0.108869	−	0.335064i
$498$		0			0
$499$	−22.3349			−0.999850			−0.499925	−	0.866069i	$-0.666639\pi$
$499$	−22.3349			−0.999850			−0.499925	+	0.866069i	$0.666639\pi$
$500$		0			0
$501$	38.9088			1.73832
$502$		0			0
$503$	−1.44176	−	4.43729i	−0.0642851	−	0.197849i	0.913755	−	0.406265i	$-0.133169\pi$
$503$	−1.44176	−	4.43729i	−0.0642851	−	0.197849i	−0.978040	+	0.208416i	$0.933169\pi$
$504$		0			0
$505$	0.858788	+	0.0676301i	0.0382156	+	0.00300950i
$506$		0			0
$507$	23.3596			1.03743
$508$		0			0
$509$	17.0878	−	12.4150i	0.757401	−	0.550284i	−0.140711	−	0.990051i	$-0.544939\pi$
$509$	17.0878	−	12.4150i	0.757401	−	0.550284i	0.898112	+	0.439766i	$0.144939\pi$
$510$		0			0
$511$	−9.04594	−	6.57226i	−0.400169	−	0.290740i
$512$		0			0
$513$	17.9836	−	13.0659i	0.793996	−	0.576872i
$514$		0			0
$515$	−7.77207	−	32.3799i	−0.342478	−	1.42683i
$516$		0			0
$517$	−1.58475	+	4.87737i	−0.0696974	+	0.214506i
$518$		0			0
$519$	5.65926	−	17.4174i	0.248414	−	0.764539i
$520$		0			0
$521$	−8.43065	−	25.9469i	−0.369353	−	1.13675i	−0.947210	−	0.320614i	$-0.896111\pi$
$521$	−8.43065	−	25.9469i	−0.369353	−	1.13675i	0.577856	−	0.816138i	$-0.303889\pi$
$522$		0			0
$523$	7.20179	+	5.23241i	0.314912	+	0.228797i	0.734001	−	0.679148i	$-0.237651\pi$
$523$	7.20179	+	5.23241i	0.314912	+	0.228797i	−0.419089	+	0.907945i	$0.637651\pi$
$524$		0			0
$525$	2.56755	+	16.2211i	0.112057	+	0.707945i
$526$		0			0
$527$	27.5498	+	20.0161i	1.20009	+	0.871914i
$528$		0			0
$529$	5.96621	+	18.3621i	0.259400	+	0.798352i
$530$		0			0
$531$	−10.0468	+	30.9207i	−0.435992	+	1.34185i
$532$		0			0
$533$	−4.95280	+	15.2431i	−0.214529	+	0.660254i
$534$		0			0
$535$	−42.3966	−	3.33876i	−1.83297	−	0.144347i
$536$		0			0
$537$	9.65807	−	7.01700i	0.416776	−	0.302806i
$538$		0			0
$539$	−4.60117	−	3.34295i	−0.198187	−	0.143991i
$540$		0			0
$541$	−32.3528	+	23.5057i	−1.39095	+	1.01059i	−0.395194	+	0.918598i	$0.629323\pi$
$541$	−32.3528	+	23.5057i	−1.39095	+	1.01059i	−0.995760	+	0.0919897i	$0.970677\pi$
$542$		0			0
$543$	22.5692			0.968538
$544$		0			0
$545$	−1.09677	+	0.672031i	−0.0469806	+	0.0287866i
$546$		0			0
$547$	−10.5424	−	32.4462i	−0.450761	−	1.38730i	−0.876040	−	0.482239i	$-0.839824\pi$
$547$	−10.5424	−	32.4462i	−0.450761	−	1.38730i	0.425278	−	0.905063i	$-0.360176\pi$
$548$		0			0
$549$	−38.0518			−1.62401
$550$		0			0
$551$	−3.01188			−0.128310
$552$		0			0
$553$	−4.15318	−	12.7822i	−0.176611	−	0.543554i
$554$		0			0
$555$	−20.0209	−	17.1011i	−0.849840	−	0.725903i
$556$		0			0
$557$	−13.6163			−0.576942			−0.288471	−	0.957489i	$-0.593147\pi$
$557$	−13.6163			−0.576942			−0.288471	+	0.957489i	$0.593147\pi$
$558$		0			0
$559$	18.9933	−	13.7994i	0.803329	−	0.583653i
$560$		0			0
$561$	14.0929	+	10.2391i	0.595003	+	0.432295i
$562$		0			0
$563$	23.5645	−	17.1206i	0.993125	−	0.721548i	0.0325218	−	0.999471i	$-0.489646\pi$
$563$	23.5645	−	17.1206i	0.993125	−	0.721548i	0.960603	+	0.277923i	$0.0896462\pi$
$564$		0			0
$565$	0.955674	−	0.585574i	0.0402055	−	0.0246353i
$566$		0			0
$567$	−0.913855	+	2.81256i	−0.0383783	+	0.118116i
$568$		0			0
$569$	0.614153	−	1.89017i	0.0257467	−	0.0792400i	−0.937358	−	0.348369i	$-0.886736\pi$
$569$	0.614153	−	1.89017i	0.0257467	−	0.0792400i	0.963104	+	0.269129i	$0.0867357\pi$
$570$		0			0
$571$	7.15967	+	22.0352i	0.299623	+	0.922144i	0.981629	+	0.190798i	$0.0611076\pi$
$571$	7.15967	+	22.0352i	0.299623	+	0.922144i	−0.682006	+	0.731346i	$0.738892\pi$
$572$		0			0
$573$	26.5573	+	19.2950i	1.10945	+	0.806060i
$574$		0			0
$575$	22.9942	+	22.9987i	0.958926	+	0.959113i
$576$		0			0
$577$	2.19342	+	1.59361i	0.0913132	+	0.0663429i	0.632505	−	0.774556i	$-0.282027\pi$
$577$	2.19342	+	1.59361i	0.0913132	+	0.0663429i	−0.541192	+	0.840899i	$0.682027\pi$
$578$		0			0
$579$	20.2914	+	62.4505i	0.843281	+	2.59535i
$580$		0			0
$581$	−3.24014	+	9.97213i	−0.134424	+	0.413714i
$582$		0			0
$583$	0.807722	−	2.48591i	0.0334524	−	0.102956i
$584$		0			0
$585$	−9.83837	+	23.7487i	−0.406767	+	0.981887i
$586$		0			0
$587$	30.1267	−	21.8883i	1.24346	−	0.903428i	0.245638	−	0.969362i	$-0.421002\pi$
$587$	30.1267	−	21.8883i	1.24346	−	0.903428i	0.997824	+	0.0659332i	$0.0210024\pi$
$588$		0			0
$589$	−15.8428	−	11.5104i	−0.652789	−	0.474279i
$590$		0			0
$591$	−12.7538	+	9.26620i	−0.524622	+	0.381161i
$592$		0			0
$593$	−34.2608			−1.40692			−0.703461	−	0.710734i	$-0.748363\pi$
$593$	−34.2608			−1.40692			−0.703461	+	0.710734i	$0.748363\pi$
$594$		0			0
$595$	−5.95772	+	14.3812i	−0.244243	+	0.589573i
$596$		0			0
$597$	6.98078	+	21.4846i	0.285704	+	0.879307i
$598$		0			0
$599$	17.3407			0.708521			0.354260	−	0.935147i	$-0.384733\pi$
$599$	17.3407			0.708521			0.354260	+	0.935147i	$0.384733\pi$
$600$		0			0
$601$	−36.2671			−1.47937			−0.739684	−	0.672955i	$-0.765025\pi$
$601$	−36.2671			−1.47937			−0.739684	+	0.672955i	$0.765025\pi$
$602$		0			0
$603$	−23.7791	−	73.1847i	−0.968362	−	2.98031i
$604$		0			0
$605$	−0.521894	−	2.17431i	−0.0212180	−	0.0883983i
$606$		0			0
$607$	−7.89311			−0.320371			−0.160186	−	0.987087i	$-0.551209\pi$
$607$	−7.89311			−0.320371			−0.160186	+	0.987087i	$0.551209\pi$
$608$		0			0
$609$	2.29051	−	1.66415i	0.0928162	−	0.0674349i
$610$		0			0
$611$	−9.13892	−	6.63981i	−0.369721	−	0.268618i
$612$		0			0
$613$	−25.3840	+	18.4425i	−1.02525	+	0.744886i	−0.967352	−	0.253436i	$-0.918439\pi$
$613$	−25.3840	+	18.4425i	−1.02525	+	0.744886i	−0.0578960	+	0.998323i	$0.518439\pi$
$614$		0			0
$615$	35.4677	+	30.2953i	1.43020	+	1.22162i
$616$		0			0
$617$	−10.0521	+	30.9372i	−0.404683	+	1.24549i	0.516477	+	0.856301i	$0.327243\pi$
$617$	−10.0521	+	30.9372i	−0.404683	+	1.24549i	−0.921160	+	0.389185i	$0.872757\pi$
$618$		0			0
$619$	12.8307	−	39.4888i	0.515709	−	1.58719i	−0.266279	−	0.963896i	$-0.585794\pi$
$619$	12.8307	−	39.4888i	0.515709	−	1.58719i	0.781988	−	0.623293i	$-0.214206\pi$
$620$		0			0
$621$	12.7868	+	39.3538i	0.513118	+	1.57921i
$622$		0			0
$623$	8.57751	+	6.23193i	0.343651	+	0.249677i
$624$		0			0
$625$	23.7749	+	7.73005i	0.950996	+	0.309202i
$626$		0			0
$627$	−8.10426	−	5.88809i	−0.323653	−	0.235148i
$628$		0			0
$629$	−7.71215	−	23.7355i	−0.307503	−	0.946398i
$630$		0			0
$631$	−1.09871	+	3.38149i	−0.0437390	+	0.134615i	−0.970541	−	0.240935i	$-0.922546\pi$
$631$	−1.09871	+	3.38149i	−0.0437390	+	0.134615i	0.926802	+	0.375550i	$0.122546\pi$
$632$		0			0
$633$	−10.3185	+	31.7570i	−0.410122	+	1.26223i
$634$		0			0
$635$	−32.1748	−	27.4826i	−1.27682	−	1.09061i
$636$		0			0
$637$	10.1351	−	7.36355i	0.401566	−	0.291754i
$638$		0			0
$639$	−28.9451	−	21.0299i	−1.14505	−	0.831928i
$640$		0			0
$641$	−33.5781	+	24.3959i	−1.32625	+	0.963580i	−0.326422	+	0.945224i	$0.605843\pi$
$641$	−33.5781	+	24.3959i	−1.32625	+	0.963580i	−0.999832	+	0.0183556i	$0.994157\pi$
$642$		0			0
$643$	35.5532			1.40208			0.701041	−	0.713121i	$-0.252719\pi$
$643$	35.5532			1.40208			0.701041	+	0.713121i	$0.252719\pi$
$644$		0			0
$645$	−15.9469	−	66.4379i	−0.627910	−	2.61599i
$646$		0			0
$647$	1.39755	+	4.30122i	0.0549433	+	0.169098i	0.974763	−	0.223244i	$-0.0716648\pi$
$647$	1.39755	+	4.30122i	0.0549433	+	0.169098i	−0.919819	+	0.392343i	$0.871665\pi$
$648$		0			0
$649$	6.22950			0.244529
$650$		0			0
$651$	18.4082			0.721473
$652$		0			0
$653$	−2.50557	−	7.71136i	−0.0980507	−	0.301769i	0.889986	−	0.455988i	$-0.150714\pi$
$653$	−2.50557	−	7.71136i	−0.0980507	−	0.301769i	−0.988037	+	0.154219i	$0.950714\pi$
$654$		0			0
$655$	7.38508	−	17.8267i	0.288559	−	0.696547i
$656$		0			0
$657$	−50.9347			−1.98715
$658$		0			0
$659$	21.8026	−	15.8405i	0.849310	−	0.617060i	−0.0756454	−	0.997135i	$-0.524102\pi$
$659$	21.8026	−	15.8405i	0.849310	−	0.617060i	0.924956	+	0.380075i	$0.124102\pi$
$660$		0			0
$661$	−1.32987	−	0.966204i	−0.0517258	−	0.0375810i	0.561622	−	0.827394i	$-0.310178\pi$
$661$	−1.32987	−	0.966204i	−0.0517258	−	0.0375810i	−0.613348	+	0.789813i	$0.710178\pi$
$662$		0			0
$663$	−31.0426	+	22.5538i	−1.20559	+	0.875916i
$664$		0			0
$665$	3.42605	−	8.27007i	0.132856	−	0.320700i
$666$		0			0
$667$	1.73253	−	5.33218i	0.0670838	−	0.206463i
$668$		0			0
$669$	−0.652118	+	2.00701i	−0.0252123	+	0.0775956i
$670$		0			0
$671$	2.25303	+	6.93412i	0.0869774	+	0.267689i
$672$		0			0
$673$	−14.2804	−	10.3753i	−0.550469	−	0.399939i	0.277489	−	0.960729i	$-0.410498\pi$
$673$	−14.2804	−	10.3753i	−0.550469	−	0.399939i	−0.827958	+	0.560789i	$0.810498\pi$
$674$		0			0
$675$	22.4899	+	22.4942i	0.865635	+	0.865804i
$676$		0			0
$677$	−3.52148	−	2.55850i	−0.135341	−	0.0983313i	0.518055	−	0.855348i	$-0.326656\pi$
$677$	−3.52148	−	2.55850i	−0.135341	−	0.0983313i	−0.653396	+	0.757016i	$0.726656\pi$
$678$		0			0
$679$	0.651146	+	2.00402i	0.0249887	+	0.0769073i
$680$		0			0
$681$	2.83330	−	8.71999i	0.108572	−	0.334151i
$682$		0			0
$683$	−15.0109	+	46.1988i	−0.574376	+	1.76775i	0.0639170	+	0.997955i	$0.479641\pi$
$683$	−15.0109	+	46.1988i	−0.574376	+	1.76775i	−0.638293	+	0.769793i	$0.720359\pi$
$684$		0			0
$685$	−0.464613	+	0.284684i	−0.0177520	+	0.0108772i
$686$		0			0
$687$	46.9067	−	34.0797i	1.78960	−	1.30022i
$688$		0			0
$689$	4.65795	+	3.38420i	0.177454	+	0.128928i
$690$		0			0
$691$	30.2107	−	21.9493i	1.14927	−	0.834992i	0.160884	−	0.986973i	$-0.448565\pi$
$691$	30.2107	−	21.9493i	1.14927	−	0.834992i	0.988383	+	0.151981i	$0.0485653\pi$
$692$		0			0
$693$	5.97947			0.227141
$694$		0			0
$695$	1.33398	+	1.13944i	0.0506008	+	0.0432214i
$696$		0			0
$697$	13.6623	+	42.0483i	0.517498	+	1.59269i
$698$		0			0
$699$	19.7780			0.748071
$700$		0			0
$701$	15.4319			0.582853			0.291427	−	0.956593i	$-0.405870\pi$
$701$	15.4319			0.582853			0.291427	+	0.956593i	$0.405870\pi$
$702$		0			0
$703$	4.43494	+	13.6494i	0.167267	+	0.514795i
$704$		0			0
$705$	−28.0320	+	17.1761i	−1.05574	+	0.646891i
$706$		0			0
$707$	0.441383			0.0165999
$708$		0			0
$709$	31.5693	−	22.9364i	1.18561	−	0.861396i	0.192817	−	0.981235i	$-0.438238\pi$
$709$	31.5693	−	22.9364i	1.18561	−	0.861396i	0.992793	+	0.119839i	$0.0382377\pi$
$710$		0			0
$711$	−49.5306	−	35.9861i	−1.85754	−	1.34958i
$712$		0			0
$713$	29.4912	−	21.4266i	1.10445	−	0.802432i
$714$		0			0
$715$	4.91021	+	0.386682i	0.183631	+	0.0144611i
$716$		0			0
$717$	17.1918	−	52.9108i	0.642038	−	1.97599i
$718$		0			0
$719$	−12.3310	+	37.9508i	−0.459867	+	1.41533i	0.405458	+	0.914114i	$0.367112\pi$
$719$	−12.3310	+	37.9508i	−0.459867	+	1.41533i	−0.865325	+	0.501211i	$0.832888\pi$
$720$		0			0
$721$	−5.27241	−	16.2268i	−0.196355	−	0.604318i
$722$		0			0
$723$	22.9408	+	16.6674i	0.853176	+	0.619869i
$724$		0			0
$725$	−0.673795	−	4.25685i	−0.0250241	−	0.158095i
$726$		0			0
$727$	−7.75974	−	5.63778i	−0.287793	−	0.209094i	0.434516	−	0.900664i	$-0.356919\pi$
$727$	−7.75974	−	5.63778i	−0.287793	−	0.209094i	−0.722309	+	0.691570i	$0.756919\pi$
$728$		0			0
$729$	−12.7449	−	39.2249i	−0.472035	−	1.45277i
$730$		0			0
$731$	20.0124	−	61.5918i	0.740185	−	2.27805i
$732$		0			0
$733$	−7.76020	+	23.8834i	−0.286629	+	0.882154i	0.699276	+	0.714852i	$0.253506\pi$
$733$	−7.76020	+	23.8834i	−0.286629	+	0.882154i	−0.985906	+	0.167303i	$0.946494\pi$
$734$		0			0
$735$	−8.50949	−	35.4522i	−0.313877	−	1.30767i
$736$		0			0
$737$	−11.9284	+	8.66648i	−0.439388	+	0.319234i
$738$		0			0
$739$	37.3834	+	27.1606i	1.37517	+	0.999120i	0.997313	+	0.0732569i	$0.0233393\pi$
$739$	37.3834	+	27.1606i	1.37517	+	0.999120i	0.377858	+	0.925863i	$0.376661\pi$
$740$		0			0
$741$	17.8513	−	12.9698i	0.655786	−	0.476456i
$742$		0			0
$743$	41.3622			1.51743			0.758716	−	0.651422i	$-0.225827\pi$
$743$	41.3622			1.51743			0.758716	+	0.651422i	$0.225827\pi$
$744$		0			0
$745$	−27.2555	−	2.14638i	−0.998563	−	0.0786374i
$746$		0			0
$747$	14.7598	+	45.4261i	0.540034	+	1.66205i
$748$		0			0
$749$	−21.7902			−0.796196
$750$		0			0
$751$	12.1336			0.442763			0.221382	−	0.975187i	$-0.428943\pi$
$751$	12.1336			0.442763			0.221382	+	0.975187i	$0.428943\pi$
$752$		0			0
$753$	11.5069	+	35.4147i	0.419336	+	1.29058i
$754$		0			0
$755$	19.0966	+	1.50387i	0.694996	+	0.0547314i
$756$		0			0
$757$	−45.2951			−1.64628			−0.823139	−	0.567841i	$-0.807779\pi$
$757$	−45.2951			−1.64628			−0.823139	+	0.567841i	$0.807779\pi$
$758$		0			0
$759$	15.0860	−	10.9606i	0.547587	−	0.397846i
$760$		0			0
$761$	−12.3392	−	8.96492i	−0.447294	−	0.324978i	0.341233	−	0.939979i	$-0.389156\pi$
$761$	−12.3392	−	8.96492i	−0.447294	−	0.324978i	−0.788526	+	0.615001i	$0.789156\pi$
$762$		0			0
$763$	−0.533192	+	0.387387i	−0.0193028	+	0.0140243i
$764$		0			0
$765$	16.5503	+	68.9515i	0.598376	+	2.49295i
$766$		0			0
$767$	−4.24027	+	13.0502i	−0.153107	+	0.471216i
$768$		0			0
$769$	15.6548	−	48.1806i	0.564527	−	1.73744i	−0.104825	−	0.994491i	$-0.533428\pi$
$769$	15.6548	−	48.1806i	0.564527	−	1.73744i	0.669352	−	0.742945i	$-0.266572\pi$
$770$		0			0
$771$	19.2509	+	59.2482i	0.693305	+	2.13377i
$772$		0			0
$773$	−20.5056	−	14.8982i	−0.737535	−	0.535850i	0.154403	−	0.988008i	$-0.450654\pi$
$773$	−20.5056	−	14.8982i	−0.737535	−	0.535850i	−0.891938	+	0.452158i	$0.850654\pi$
$774$		0			0
$775$	12.7241	−	24.9665i	0.457064	−	0.896822i
$776$		0			0
$777$	−10.9144	−	7.92980i	−0.391553	−	0.284480i
$778$		0			0
$779$	−7.85666	−	24.1803i	−0.281494	−	0.866350i
$780$		0			0
$781$	−2.11841	+	6.51980i	−0.0758027	+	0.233297i
$782$		0			0
$783$	1.69453	−	5.21522i	0.0605574	−	0.186377i
$784$		0			0
$785$	50.4081	+	3.96967i	1.79914	+	0.141684i
$786$		0			0
$787$	−3.20191	+	2.32632i	−0.114136	+	0.0829245i	−0.643389	−	0.765539i	$-0.722472\pi$
$787$	−3.20191	+	2.32632i	−0.114136	+	0.0829245i	0.529253	+	0.848464i	$0.322472\pi$
$788$		0			0
$789$	−2.60888	−	1.89546i	−0.0928785	−	0.0674802i
$790$		0			0
$791$	0.464597	−	0.337549i	0.0165192	−	0.0120019i
$792$		0			0
$793$	−16.0599			−0.570304
$794$		0			0
$795$	14.2874	−	8.75438i	0.506722	−	0.310486i
$796$		0			0
$797$	1.43960	+	4.43062i	0.0509931	+	0.156941i	0.973310	−	0.229493i	$-0.0737068\pi$
$797$	1.43960	+	4.43062i	0.0509931	+	0.156941i	−0.922317	+	0.386434i	$0.873707\pi$
$798$		0			0
$799$	−31.1610			−1.10240
$800$		0			0
$801$	48.2971			1.70650
$802$		0			0
$803$	3.01582	+	9.28175i	0.106426	+	0.327546i
$804$		0			0
$805$	12.6704	+	10.8226i	0.446574	+	0.381448i
$806$		0			0
$807$	88.2008			3.10482
$808$		0			0
$809$	−6.68555	+	4.85734i	−0.235051	+	0.170775i	−0.699076	−	0.715048i	$-0.746405\pi$
$809$	−6.68555	+	4.85734i	−0.235051	+	0.170775i	0.464024	+	0.885822i	$0.346405\pi$
$810$		0			0
$811$	−36.7056	−	26.6682i	−1.28891	−	0.936448i	−0.289127	−	0.957291i	$-0.593365\pi$
$811$	−36.7056	−	26.6682i	−1.28891	−	0.936448i	−0.999783	+	0.0208433i	$0.993365\pi$
$812$		0			0
$813$	−32.6899	+	23.7506i	−1.14649	+	0.832971i
$814$		0			0
$815$	27.3234	−	16.7420i	0.957096	−	0.586445i
$816$		0			0
$817$	−11.5083	+	35.4190i	−0.402625	+	1.23915i
$818$		0			0
$819$	−4.07008	+	12.5264i	−0.142220	+	0.437708i
$820$		0			0
$821$	−8.73911	−	26.8962i	−0.304997	−	0.938684i	−0.979678	−	0.200575i	$-0.935719\pi$
$821$	−8.73911	−	26.8962i	−0.304997	−	0.938684i	0.674681	−	0.738109i	$-0.264281\pi$
$822$		0			0
$823$	−35.9883	−	26.1470i	−1.25447	−	0.911428i	−0.256001	−	0.966677i	$-0.582405\pi$
$823$	−35.9883	−	26.1470i	−1.25447	−	0.911428i	−0.998473	+	0.0552481i	$0.982405\pi$
$824$		0			0
$825$	6.50894	−	12.7714i	0.226612	−	0.444644i
$826$		0			0
$827$	42.7382	+	31.0511i	1.48615	+	1.07975i	0.975508	+	0.219963i	$0.0705937\pi$
$827$	42.7382	+	31.0511i	1.48615	+	1.07975i	0.510646	+	0.859791i	$0.329406\pi$
$828$		0			0
$829$	2.81172	+	8.65359i	0.0976551	+	0.300552i	0.987937	−	0.154859i	$-0.0494924\pi$
$829$	2.81172	+	8.65359i	0.0976551	+	0.300552i	−0.890281	+	0.455411i	$0.849492\pi$
$830$		0			0
$831$	−17.5116	+	53.8952i	−0.607472	+	1.86961i
$832$		0			0
$833$	10.6789	−	32.8662i	0.370001	−	1.13875i
$834$		0			0
$835$	11.6148	−	28.0368i	0.401948	−	0.970255i
$836$		0			0
$837$	28.8443	−	20.9566i	0.997004	−	0.724366i
$838$		0			0
$839$	−9.59816	−	6.97347i	−0.331365	−	0.240751i	0.409644	−	0.912245i	$-0.365653\pi$
$839$	−9.59816	−	6.97347i	−0.331365	−	0.240751i	−0.741010	+	0.671494i	$0.765653\pi$
$840$		0			0
$841$	22.8604	−	16.6091i	0.788290	−	0.572726i
$842$		0			0
$843$	−57.5966			−1.98373
$844$		0			0
$845$	6.97316	−	16.8324i	0.239884	−	0.579052i
$846$		0			0
$847$	−0.354042	−	1.08963i	−0.0121650	−	0.0374401i
$848$		0			0
$849$	−70.0800			−2.40514
$850$		0			0
$851$	−26.7157			−0.915803
$852$		0			0
$853$	−5.67703	−	17.4721i	−0.194378	−	0.598233i	−0.999983	−	0.00578107i	$-0.998160\pi$
$853$	−5.67703	−	17.4721i	−0.194378	−	0.598233i	0.805605	−	0.592452i	$-0.201840\pi$
$854$		0			0
$855$	−9.51738	−	39.6512i	−0.325488	−	1.35604i
$856$		0			0
$857$	−46.7933			−1.59843			−0.799214	−	0.601046i	$-0.794751\pi$
$857$	−46.7933			−1.59843			−0.799214	+	0.601046i	$0.794751\pi$
$858$		0			0
$859$	−15.5455	+	11.2944i	−0.530405	+	0.385361i	−0.820509	−	0.571634i	$-0.806310\pi$
$859$	−15.5455	+	11.2944i	−0.530405	+	0.385361i	0.290105	+	0.956995i	$0.406310\pi$
$860$		0			0
$861$	19.3353	+	14.0479i	0.658945	+	0.478752i
$862$		0			0
$863$	24.8576	−	18.0601i	0.846161	−	0.614772i	−0.0779238	−	0.996959i	$-0.524829\pi$
$863$	24.8576	−	18.0601i	0.846161	−	0.614772i	0.924085	+	0.382187i	$0.124829\pi$
$864$		0			0
$865$	−10.8612	−	9.27728i	−0.369293	−	0.315437i
$866$		0			0
$867$	−17.6477	+	54.3139i	−0.599346	+	1.84460i
$868$		0			0
$869$	−3.62501	+	11.1566i	−0.122970	+	0.378462i
$870$		0			0
$871$	−10.0361	−	30.8879i	−0.340059	−	1.04660i
$872$		0			0
$873$	7.76554	+	5.64199i	0.262824	+	0.190953i
$874$		0			0
$875$	12.4550	+	2.99210i	0.421056	+	0.101152i
$876$		0			0
$877$	−10.0938	−	7.33356i	−0.340843	−	0.247637i	0.404175	−	0.914682i	$-0.367559\pi$
$877$	−10.0938	−	7.33356i	−0.340843	−	0.247637i	−0.745017	+	0.667045i	$0.767559\pi$
$878$		0			0
$879$	−27.6796	−	85.1891i	−0.933611	−	2.87336i
$880$		0			0
$881$	3.99053	−	12.2816i	0.134444	−	0.413777i	−0.861059	−	0.508505i	$-0.830198\pi$
$881$	3.99053	−	12.2816i	0.134444	−	0.413777i	0.995503	+	0.0947282i	$0.0301982\pi$
$882$		0			0
$883$	−0.708403	+	2.18024i	−0.0238397	+	0.0733709i	−0.962269	−	0.272102i	$-0.912281\pi$
$883$	−0.708403	+	2.18024i	−0.0238397	+	0.0733709i	0.938429	+	0.345472i	$0.112281\pi$
$884$		0			0
$885$	30.3652	+	25.9369i	1.02072	+	0.871859i
$886$		0			0
$887$	38.6429	−	28.0757i	1.29750	−	0.942689i	0.297572	−	0.954699i	$-0.403823\pi$
$887$	38.6429	−	28.0757i	1.29750	−	0.942689i	0.999928	+	0.0120102i	$0.00382305\pi$
$888$		0			0
$889$	−17.5402	−	12.7437i	−0.588279	−	0.427410i
$890$		0			0
$891$	2.08824	−	1.51719i	0.0699586	−	0.0508279i
$892$		0			0
$893$	17.9194			0.599651
$894$		0			0
$895$	−2.17322	−	9.05407i	−0.0726429	−	0.302644i
$896$		0			0
$897$	12.6928	+	39.0644i	0.423800	+	1.30432i
$898$		0			0
$899$	−4.83081			−0.161116
$900$		0			0
$901$	15.8822			0.529114
$902$		0			0
$903$	−10.8181	−	33.2946i	−0.360003	−	1.10797i
$904$		0			0
$905$	6.73724	−	16.2629i	0.223953	−	0.540597i
$906$		0			0
$907$	−33.9338			−1.12675			−0.563376	−	0.826201i	$-0.690498\pi$
$907$	−33.9338			−1.12675			−0.563376	+	0.826201i	$0.690498\pi$
$908$		0			0
$909$	1.62664	−	1.18182i	0.0539522	−	0.0391986i
$910$		0			0
$911$	−8.04283	−	5.84346i	−0.266471	−	0.193602i	0.446524	−	0.894772i	$-0.352662\pi$
$911$	−8.04283	−	5.84346i	−0.266471	−	0.193602i	−0.712995	+	0.701169i	$0.752662\pi$
$912$		0			0
$913$	7.40401	−	5.37933i	0.245037	−	0.178030i
$914$		0			0
$915$	−17.8884	+	43.1805i	−0.591372	+	1.42750i
$916$		0			0
$917$	3.05516	−	9.40283i	0.100890	−	0.310509i
$918$		0			0
$919$	14.4326	−	44.4191i	0.476089	−	1.46525i	−0.368395	−	0.929669i	$-0.620093\pi$
$919$	14.4326	−	44.4191i	0.476089	−	1.46525i	0.844484	−	0.535581i	$-0.179907\pi$
$920$		0			0
$921$	9.60590	+	29.5639i	0.316525	+	0.974164i
$922$		0			0
$923$	−12.2164	−	8.87573i	−0.402107	−	0.292148i
$924$		0			0
$925$	−18.2992	+	9.32169i	−0.601675	+	0.306495i
$926$		0			0
$927$	−62.8785	−	45.6839i	−2.06520	−	1.50046i
$928$		0			0
$929$	−7.04266	−	21.6751i	−0.231062	−	0.711137i	−0.997619	−	0.0689605i	$-0.978032\pi$
$929$	−7.04266	−	21.6751i	−0.231062	−	0.711137i	0.766557	−	0.642176i	$-0.221968\pi$
$930$		0			0
$931$	−6.14099	+	18.9000i	−0.201263	+	0.619423i
$932$		0			0
$933$	−7.44694	+	22.9193i	−0.243802	+	0.750345i
$934$		0			0
$935$	11.5850	−	7.09852i	0.378870	−	0.232146i
$936$		0			0
$937$	28.3654	−	20.6087i	0.926658	−	0.673256i	−0.0185144	−	0.999829i	$-0.505894\pi$
$937$	28.3654	−	20.6087i	0.926658	−	0.673256i	0.945172	+	0.326572i	$0.105894\pi$
$938$		0			0
$939$	−64.8008	−	47.0805i	−2.11469	−	1.53641i
$940$		0			0
$941$	−6.26330	+	4.55056i	−0.204178	+	0.148344i	−0.685176	−	0.728378i	$-0.740275\pi$
$941$	−6.26330	+	4.55056i	−0.204178	+	0.148344i	0.480998	+	0.876722i	$0.340275\pi$
$942$		0			0
$943$	47.3278			1.54121
$944$		0			0
$945$	12.3925	+	10.5852i	0.403128	+	0.344338i
$946$		0			0
$947$	10.5141	+	32.3592i	0.341664	+	1.05153i	0.963346	+	0.268263i	$0.0864495\pi$
$947$	10.5141	+	32.3592i	0.341664	+	1.05153i	−0.621682	+	0.783270i	$0.713550\pi$
$948$		0			0
$949$	−21.4972			−0.697828
$950$		0			0
$951$	27.2837			0.884735
$952$		0			0
$953$	8.96937	+	27.6049i	0.290546	+	0.894210i	0.984681	+	0.174365i	$0.0557872\pi$
$953$	8.96937	+	27.6049i	0.290546	+	0.894210i	−0.694135	+	0.719845i	$0.744213\pi$
$954$		0			0
$955$	21.8313	−	13.3768i	0.706444	−	0.432862i
$956$		0			0
$957$	−2.47117			−0.0798815
$958$		0			0
$959$	−0.225870	+	0.164104i	−0.00729371	+	0.00529919i
$960$		0			0
$961$	−0.330977	−	0.240469i	−0.0106767	−	0.00775706i
$962$		0			0
$963$	−80.3038	+	58.3442i	−2.58776	+	1.88011i
$964$		0			0
$965$	51.0577	+	4.02083i	1.64361	+	0.129435i
$966$		0			0
$967$	0.0423965	−	0.130483i	0.00136338	−	0.00419606i	−0.950373	−	0.311114i	$-0.899298\pi$
$967$	0.0423965	−	0.130483i	0.00136338	−	0.00419606i	0.951736	+	0.306918i	$0.0992978\pi$
$968$		0			0
$969$	18.8092	−	57.8888i	0.604238	−	1.85965i
$970$		0			0
$971$	11.2672	+	34.6769i	0.361582	+	1.11283i	0.952094	+	0.305805i	$0.0989256\pi$
$971$	11.2672	+	34.6769i	0.361582	+	1.11283i	−0.590513	+	0.807028i	$0.701074\pi$
$972$		0			0
$973$	0.727222	+	0.528358i	0.0233137	+	0.0169384i
$974$		0			0
$975$	22.3245	+	22.3288i	0.714955	+	0.715094i
$976$		0			0
$977$	−4.07988	−	2.96421i	−0.130527	−	0.0948335i	0.520606	−	0.853797i	$-0.325706\pi$
$977$	−4.07988	−	2.96421i	−0.130527	−	0.0948335i	−0.651133	+	0.758964i	$0.725706\pi$
$978$		0			0
$979$	−2.85966	−	8.80111i	−0.0913950	−	0.281285i
$980$		0			0
$981$	−0.927739	+	2.85529i	−0.0296204	+	0.0911623i
$982$		0			0
$983$	−5.09901	+	15.6931i	−0.162633	+	0.500533i	−0.998854	−	0.0478595i	$-0.984760\pi$
$983$	−5.09901	+	15.6931i	−0.162633	+	0.500533i	0.836221	+	0.548393i	$0.184760\pi$
$984$		0			0
$985$	2.86982	+	11.9562i	0.0914401	+	0.380957i
$986$		0			0
$987$	−13.6276	+	9.90104i	−0.433772	+	0.315154i
$988$		0			0
$989$	−56.0852	−	40.7483i	−1.78341	−	1.29572i
$990$		0			0
$991$	−37.1515	+	26.9921i	−1.18016	+	0.857433i	−0.992189	−	0.124742i	$-0.960190\pi$
$991$	−37.1515	+	26.9921i	−1.18016	+	0.857433i	−0.187967	+	0.982175i	$0.560190\pi$
$992$		0			0
$993$	−52.6892			−1.67204
$994$		0			0
$995$	17.5652	+	1.38327i	0.556855	+	0.0438527i
$996$		0			0
$997$	0.364823	+	1.12281i	0.0115541	+	0.0355597i	0.956667	−	0.291183i	$-0.0940489\pi$
$997$	0.364823	+	1.12281i	0.0115541	+	0.0355597i	−0.945113	+	0.326743i	$0.894049\pi$
$998$		0			0
$999$	−26.1297			−0.826708

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.441.2	✓	52
25.11	even	5	inner	1100.2.q.b.661.2	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.441.2	✓	52	1.1	even	1	trivial
1100.2.q.b.661.2	yes	52	25.11	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)

\(f(q)\)	\(=\)	\(q+(-0.885916 - 2.72657i) q^{3} +(-2.22917 - 0.175548i) q^{5} -1.14570 q^{7} +(-4.22229 + 3.06767i) q^{9} +(0.809017 + 0.587785i) q^{11} +(-1.78203 + 1.29472i) q^{13} +(1.49621 + 6.23350i) q^{15} +(-1.87765 + 5.77881i) q^{17} +(1.07976 - 3.32316i) q^{19} +(1.01500 + 3.12384i) q^{21} +(5.26216 + 3.82318i) q^{23} +(4.93837 + 0.782652i) q^{25} +(5.14673 + 3.73932i) q^{27} +(-0.266363 - 0.819782i) q^{29} +(1.73185 - 5.33009i) q^{31} +(0.885916 - 2.72657i) q^{33} +(2.55397 + 0.201126i) q^{35} +(-3.32291 + 2.41423i) q^{37} +(5.10888 + 3.71182i) q^{39} +(5.88665 - 4.27690i) q^{41} -10.6582 q^{43} +(9.95070 - 6.09713i) q^{45} +(1.58475 + 4.87737i) q^{47} -5.68736 q^{49} +17.4198 q^{51} +(-0.807722 - 2.48591i) q^{53} +(-1.70025 - 1.45229i) q^{55} -10.0174 q^{57} +(5.03977 - 3.66161i) q^{59} +(5.89852 + 4.28552i) q^{61} +(4.83749 - 3.51464i) q^{63} +(4.19973 - 2.57332i) q^{65} +(-4.55624 + 14.0227i) q^{67} +(5.76234 - 17.7347i) q^{69} +(2.11841 + 6.51980i) q^{71} +(7.89553 + 5.73644i) q^{73} +(-2.24102 - 14.1582i) q^{75} +(-0.926894 - 0.673428i) q^{77} +(3.62501 + 11.1566i) q^{79} +(0.797636 - 2.45487i) q^{81} +(2.82808 - 8.70393i) q^{83} +(5.20005 - 12.5523i) q^{85} +(-1.99922 + 1.45252i) q^{87} +(-7.48667 - 5.43939i) q^{89} +(2.04168 - 1.48337i) q^{91} -16.0671 q^{93} +(-2.99034 + 7.21833i) q^{95} +(-0.568337 - 1.74916i) q^{97} -5.21903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 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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