LMFDB - Embedded newform 900.2.z.b.179.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(179,900)] 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("900.179"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [224] 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			179.3
Character	$\chi$	$=$	900.179
Dual form			900.2.z.b.719.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40055 + 0.196087i) q^{2} +(1.92310 - 0.549261i) q^{4} +(0.280394 - 2.21842i) q^{5} +3.98153 q^{7} +(-2.58570 + 1.14636i) q^{8} +(0.0422965 + 3.16199i) q^{10} +(1.92487 - 5.92413i) q^{11} +(-1.39956 + 0.454745i) q^{13} +(-5.57634 + 0.780726i) q^{14} +(3.39663 - 2.11257i) q^{16} +(1.80658 - 1.31256i) q^{17} +(-1.44762 - 1.99248i) q^{19} +(-0.679265 - 4.42025i) q^{20} +(-1.53423 + 8.67450i) q^{22} +(4.41714 + 1.43522i) q^{23} +(-4.84276 - 1.24406i) q^{25} +(1.87099 - 0.911330i) q^{26} +(7.65687 - 2.18690i) q^{28} +(-4.56115 + 6.27789i) q^{29} +(0.166237 + 0.228806i) q^{31} +(-4.34291 + 3.62480i) q^{32} +(-2.27284 + 2.19256i) q^{34} +(1.11640 - 8.83269i) q^{35} +(5.12410 - 1.66492i) q^{37} +(2.41817 + 2.50672i) q^{38} +(1.81810 + 6.05760i) q^{40} +(-11.8678 + 3.85608i) q^{41} -4.21998 q^{43} +(0.447819 - 12.4499i) q^{44} +(-6.46787 - 1.14395i) q^{46} +(-0.961595 + 1.32352i) q^{47} +8.85255 q^{49} +(7.02649 + 0.792773i) q^{50} +(-2.44172 + 1.64324i) q^{52} +(3.17072 + 2.30367i) q^{53} +(-12.6025 - 5.93125i) q^{55} +(-10.2950 + 4.56428i) q^{56} +(5.15712 - 9.68690i) q^{58} +(-3.30948 - 10.1855i) q^{59} +(1.88425 - 5.79911i) q^{61} +(-0.277690 - 0.287858i) q^{62} +(5.37170 - 5.92831i) q^{64} +(0.616386 + 3.23232i) q^{65} +(1.33759 - 0.971818i) q^{67} +(2.75330 - 3.51647i) q^{68} +(0.168404 + 12.5896i) q^{70} +(6.58294 + 4.78279i) q^{71} +(5.33053 + 1.73199i) q^{73} +(-6.85011 + 3.33658i) q^{74} +(-3.87832 - 3.03662i) q^{76} +(7.66391 - 23.5871i) q^{77} +(-1.28398 + 1.76724i) q^{79} +(-3.73416 - 8.12749i) q^{80} +(15.8654 - 7.72777i) q^{82} +(0.593962 + 0.817518i) q^{83} +(-2.40525 - 4.37579i) q^{85} +(5.91031 - 0.827484i) q^{86} +(1.81408 + 17.5246i) q^{88} +(10.7530 + 3.49386i) q^{89} +(-5.57239 + 1.81058i) q^{91} +(9.28292 + 0.333902i) q^{92} +(1.08724 - 2.04222i) q^{94} +(-4.82607 + 2.65276i) q^{95} +(8.79522 - 12.1056i) q^{97} +(-12.3985 + 1.73587i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 8 q^{4} - 12 q^{10} - 8 q^{16} - 8 q^{25} + 92 q^{34} + 40 q^{37} + 36 q^{40} - 40 q^{46} + 368 q^{49} - 100 q^{52} - 120 q^{58} + 48 q^{61} - 16 q^{64} - 40 q^{70} + 24 q^{76} - 120 q^{85} - 120 q^{88}+ \cdots + 200 q^{97}+O(q^{100}) $ 224 * q + 8 * q^4 - 12 * q^10 - 8 * q^16 - 8 * q^25 + 92 * q^34 + 40 * q^37 + 36 * q^40 - 40 * q^46 + 368 * q^49 - 100 * q^52 - 120 * q^58 + 48 * q^61 - 16 * q^64 - 40 * q^70 + 24 * q^76 - 120 * q^85 - 120 * q^88 - 4 * q^94 + 200 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.40055	+	0.196087i	−0.990341	+	0.138654i
$2$	−1.40055	+	0.196087i	−0.990341	+	0.138654i
$3$		0			0
$3$		0			0
$4$	1.92310	−	0.549261i	0.961550	−	0.274630i
$5$	0.280394	−	2.21842i	0.125396	−	0.992107i
$5$	0.280394	−	2.21842i	0.125396	−	0.992107i
$6$		0			0
$7$	3.98153			1.50488			0.752438	−	0.658663i	$-0.228878\pi$
$7$	3.98153			1.50488			0.752438	+	0.658663i	$0.228878\pi$
$8$	−2.58570	+	1.14636i	−0.914183	+	0.405301i
$9$		0			0
$10$	0.0422965	+	3.16199i	0.0133753	+	0.999911i
$11$	1.92487	−	5.92413i	0.580369	−	1.78619i	−0.0367516	−	0.999324i	$-0.511701\pi$
$11$	1.92487	−	5.92413i	0.580369	−	1.78619i	0.617121	−	0.786868i	$-0.288299\pi$
$12$		0			0
$13$	−1.39956	+	0.454745i	−0.388168	+	0.126124i	−0.496598	−	0.867981i	$-0.665418\pi$
$13$	−1.39956	+	0.454745i	−0.388168	+	0.126124i	0.108430	+	0.994104i	$0.465418\pi$
$14$	−5.57634	+	0.780726i	−1.49034	+	0.208658i
$15$		0			0
$16$	3.39663	−	2.11257i	0.849156	−	0.528142i
$17$	1.80658	−	1.31256i	0.438161	−	0.318343i	−0.346743	−	0.937960i	$-0.612712\pi$
$17$	1.80658	−	1.31256i	0.438161	−	0.318343i	0.784904	+	0.619618i	$0.212712\pi$
$18$		0			0
$19$	−1.44762	−	1.99248i	−0.332108	−	0.457107i	0.610008	−	0.792395i	$-0.291166\pi$
$19$	−1.44762	−	1.99248i	−0.332108	−	0.457107i	−0.942116	+	0.335288i	$0.891166\pi$
$20$	−0.679265	−	4.42025i	−0.151888	−	0.988398i
$21$		0			0
$22$	−1.53423	+	8.67450i	−0.327100	+	1.84941i
$23$	4.41714	+	1.43522i	0.921038	+	0.299264i	0.730893	−	0.682492i	$-0.239104\pi$
$23$	4.41714	+	1.43522i	0.921038	+	0.299264i	0.190146	+	0.981756i	$0.439104\pi$
$24$		0			0
$25$	−4.84276	−	1.24406i	−0.968552	−	0.248812i
$26$	1.87099	−	0.911330i	0.366931	−	0.178727i
$27$		0			0
$28$	7.65687	−	2.18690i	1.44701	−	0.413284i
$29$	−4.56115	+	6.27789i	−0.846984	+	1.16577i	0.137535	+	0.990497i	$0.456082\pi$
$29$	−4.56115	+	6.27789i	−0.846984	+	1.16577i	−0.984519	+	0.175277i	$0.943918\pi$
$30$		0			0
$31$	0.166237	+	0.228806i	0.0298571	+	0.0410948i	0.823685	−	0.567048i	$-0.191915\pi$
$31$	0.166237	+	0.228806i	0.0298571	+	0.0410948i	−0.793827	+	0.608143i	$0.791915\pi$
$32$	−4.34291	+	3.62480i	−0.767725	+	0.640779i
$33$		0			0
$34$	−2.27284	+	2.19256i	−0.389789	+	0.376021i
$35$	1.11640	−	8.83269i	0.188705	−	1.49300i
$36$		0			0
$37$	5.12410	−	1.66492i	0.842397	−	0.273712i	0.144139	−	0.989557i	$-0.453959\pi$
$37$	5.12410	−	1.66492i	0.842397	−	0.273712i	0.698258	+	0.715846i	$0.253959\pi$
$38$	2.41817	+	2.50672i	0.392280	+	0.406644i
$39$		0			0
$40$	1.81810	+	6.05760i	0.287467	+	0.957791i
$41$	−11.8678	+	3.85608i	−1.85344	+	0.602219i	−0.857260	+	0.514884i	$0.827835\pi$
$41$	−11.8678	+	3.85608i	−1.85344	+	0.602219i	−0.996179	+	0.0873354i	$0.972165\pi$
$42$		0			0
$43$	−4.21998			−0.643541			−0.321771	−	0.946818i	$-0.604278\pi$
$43$	−4.21998			−0.643541			−0.321771	+	0.946818i	$0.604278\pi$
$44$	0.447819	−	12.4499i	0.0675112	−	1.87690i
$45$		0			0
$46$	−6.46787	−	1.14395i	−0.953636	−	0.168667i
$47$	−0.961595	+	1.32352i	−0.140263	+	0.193055i	−0.873369	−	0.487059i	$-0.838070\pi$
$47$	−0.961595	+	1.32352i	−0.140263	+	0.193055i	0.733106	+	0.680114i	$0.238070\pi$
$48$		0			0
$49$	8.85255			1.26465
$50$	7.02649	+	0.792773i	0.993695	+	0.112115i
$51$		0			0
$52$	−2.44172	+	1.64324i	−0.338606	+	0.227877i
$53$	3.17072	+	2.30367i	0.435532	+	0.316433i	0.783857	−	0.620941i	$-0.213249\pi$
$53$	3.17072	+	2.30367i	0.435532	+	0.316433i	−0.348325	+	0.937374i	$0.613249\pi$
$54$		0			0
$55$	−12.6025	−	5.93125i	−1.69932	−	0.799770i
$56$	−10.2950	+	4.56428i	−1.37573	+	0.609927i
$57$		0			0
$58$	5.15712	−	9.68690i	0.677164	−	1.27195i
$59$	−3.30948	−	10.1855i	−0.430858	−	1.32604i	−0.897272	−	0.441478i	$-0.854454\pi$
$59$	−3.30948	−	10.1855i	−0.430858	−	1.32604i	0.466414	−	0.884566i	$-0.345546\pi$
$60$		0			0
$61$	1.88425	−	5.79911i	0.241253	−	0.742500i	−0.754977	−	0.655751i	$-0.772352\pi$
$61$	1.88425	−	5.79911i	0.241253	−	0.742500i	0.996230	−	0.0867491i	$-0.0276478\pi$
$62$	−0.277690	−	0.287858i	−0.0352667	−	0.0365580i
$63$		0			0
$64$	5.37170	−	5.92831i	0.671463	−	0.741039i
$65$	0.616386	+	3.23232i	0.0764533	+	0.400920i
$66$		0			0
$67$	1.33759	−	0.971818i	0.163413	−	0.118726i	−0.503073	−	0.864244i	$-0.667797\pi$
$67$	1.33759	−	0.971818i	0.163413	−	0.118726i	0.666486	+	0.745517i	$0.267797\pi$
$68$	2.75330	−	3.51647i	0.333887	−	0.426434i
$69$		0			0
$70$	0.168404	+	12.5896i	0.0201282	+	1.50474i
$71$	6.58294	+	4.78279i	0.781252	+	0.567613i	0.905354	−	0.424657i	$-0.139605\pi$
$71$	6.58294	+	4.78279i	0.781252	+	0.567613i	−0.124103	+	0.992269i	$0.539605\pi$
$72$		0			0
$73$	5.33053	+	1.73199i	0.623891	+	0.202714i	0.603867	−	0.797085i	$-0.293626\pi$
$73$	5.33053	+	1.73199i	0.623891	+	0.202714i	0.0200238	+	0.999800i	$0.493626\pi$
$74$	−6.85011	+	3.33658i	−0.796309	+	0.387870i
$75$		0			0
$76$	−3.87832	−	3.03662i	−0.444874	−	0.348324i
$77$	7.66391	−	23.5871i	0.873384	−	2.68800i
$78$		0			0
$79$	−1.28398	+	1.76724i	−0.144459	+	0.198830i	−0.875115	−	0.483915i	$-0.839214\pi$
$79$	−1.28398	+	1.76724i	−0.144459	+	0.198830i	0.730656	+	0.682746i	$0.239214\pi$
$80$	−3.73416	−	8.12749i	−0.417492	−	0.908681i
$81$		0			0
$82$	15.8654	−	7.72777i	1.75204	−	0.853390i
$83$	0.593962	+	0.817518i	0.0651957	+	0.0897343i	0.840370	−	0.542014i	$-0.182338\pi$
$83$	0.593962	+	0.817518i	0.0651957	+	0.0897343i	−0.775174	+	0.631748i	$0.782338\pi$
$84$		0			0
$85$	−2.40525	−	4.37579i	−0.260886	−	0.474621i
$86$	5.91031	−	0.827484i	0.637325	−	0.0892298i
$87$		0			0
$88$	1.81408	+	17.5246i	0.193381	+	1.86813i
$89$	10.7530	+	3.49386i	1.13981	+	0.370348i	0.817298	−	0.576216i	$-0.195471\pi$
$89$	10.7530	+	3.49386i	1.13981	+	0.370348i	0.322516	+	0.946564i	$0.395471\pi$
$90$		0			0
$91$	−5.57239	+	1.81058i	−0.584145	+	0.189800i
$92$	9.28292	+	0.333902i	0.967811	+	0.0348117i
$93$		0			0
$94$	1.08724	−	2.04222i	0.112140	−	0.210639i
$95$	−4.82607	+	2.65276i	−0.495144	+	0.272167i
$96$		0			0
$97$	8.79522	−	12.1056i	0.893019	−	1.22913i	−0.0796230	−	0.996825i	$-0.525372\pi$
$97$	8.79522	−	12.1056i	0.893019	−	1.22913i	0.972642	−	0.232310i	$-0.0746284\pi$
$98$	−12.3985	+	1.73587i	−1.25244	+	0.175349i
$99$		0			0
$100$	−9.99642	+	0.267482i	−0.999642	+	0.0267482i
$101$		−	8.06172i		−	0.802171i	−0.916041	−	0.401086i	$-0.868633\pi$
$101$		−	8.06172i		−	0.802171i	0.916041	−	0.401086i	$-0.131367\pi$
$102$		0			0
$103$	−2.81626	−	2.04613i	−0.277494	−	0.201611i	0.440330	−	0.897836i	$-0.354862\pi$
$103$	−2.81626	−	2.04613i	−0.277494	−	0.201611i	−0.717824	+	0.696225i	$0.754862\pi$
$104$	3.09754	−	2.78024i	0.303739	−	0.272625i
$105$		0			0
$106$	−4.89249	−	2.60467i	−0.475200	−	0.252988i
$107$			2.48092i			0.239839i	0.992784	+	0.119920i	$0.0382637\pi$
$107$			2.48092i			0.239839i	−0.992784	+	0.119920i	$0.961736\pi$
$108$		0			0
$109$	−0.509069	−	1.56675i	−0.0487599	−	0.150068i	0.923712	−	0.383088i	$-0.125139\pi$
$109$	−0.509069	−	1.56675i	−0.0487599	−	0.150068i	−0.972472	+	0.233020i	$0.925139\pi$
$110$	18.8135	+	5.83585i	1.79380	+	0.556426i
$111$		0			0
$112$	13.5238	−	8.41124i	1.27787	−	0.794787i
$113$	5.33399	+	16.4163i	0.501779	+	1.54432i	0.806119	+	0.591754i	$0.201564\pi$
$113$	5.33399	+	16.4163i	0.501779	+	1.54432i	−0.304340	+	0.952564i	$0.598436\pi$
$114$		0			0
$115$	4.42245	−	9.39665i	0.412396	−	0.876242i
$116$	−5.32335	+	14.5783i	−0.494261	+	1.35356i
$117$		0			0
$118$	6.63236	+	13.6164i	0.610558	+	1.25350i
$119$	7.19296	−	5.22599i	0.659378	−	0.479066i
$120$		0			0
$121$	−22.4910	−	16.3407i	−2.04464	−	1.48552i
$122$	−1.50186	+	8.49144i	−0.135972	+	0.768779i
$123$		0			0
$124$	0.445365	+	0.348709i	0.0399950	+	0.0313150i
$125$	−4.11773	+	10.3944i	−0.368301	+	0.929707i
$126$		0			0
$127$	3.89315	−	11.9819i	0.345461	−	1.06322i	−0.615875	−	0.787844i	$-0.711197\pi$
$127$	3.89315	−	11.9819i	0.345461	−	1.06322i	0.961336	−	0.275377i	$-0.0888026\pi$
$128$	−6.36089	+	9.35623i	−0.562228	+	0.826982i
$129$		0			0
$130$	−1.49710	−	4.40617i	−0.131304	−	0.386447i
$131$	12.6286	−	9.17523i	1.10337	−	0.801644i	0.121761	−	0.992559i	$-0.461146\pi$
$131$	12.6286	−	9.17523i	1.10337	−	0.801644i	0.981606	+	0.190916i	$0.0611458\pi$
$132$		0			0
$133$	−5.76375	−	7.93313i	−0.499781	−	0.687889i
$134$	−1.68281	+	1.62337i	−0.145373	+	0.140238i
$135$		0			0
$136$	−3.16661	+	5.46489i	−0.271535	+	0.468610i
$137$	4.09244	+	12.5952i	0.349641	+	1.07608i	0.959052	+	0.283230i	$0.0914058\pi$
$137$	4.09244	+	12.5952i	0.349641	+	1.07608i	−0.609411	+	0.792854i	$0.708594\pi$
$138$		0			0
$139$	−11.8408	−	3.84732i	−1.00433	−	0.326325i	−0.239733	−	0.970839i	$-0.577060\pi$
$139$	−11.8408	−	3.84732i	−1.00433	−	0.326325i	−0.764593	+	0.644514i	$0.777060\pi$
$140$	−2.70451	−	17.5993i	−0.228573	−	1.48742i
$141$		0			0
$142$	−10.1576	−	5.40772i	−0.852407	−	0.453806i
$143$			9.16650i			0.766542i
$144$		0			0
$145$	12.6481	+	11.8788i	1.05036	+	0.986482i
$146$	−7.80531	−	1.38050i	−0.645972	−	0.114251i
$147$		0			0
$148$	8.93969	−	6.01628i	0.734838	−	0.494535i
$149$		−	21.5535i		−	1.76573i	−0.469623	−	0.882867i	$-0.655610\pi$
$149$		−	21.5535i		−	1.76573i	0.469623	−	0.882867i	$-0.344390\pi$
$150$		0			0
$151$		−	7.66194i		−	0.623520i	−0.950161	−	0.311760i	$-0.899082\pi$
$151$		−	7.66194i		−	0.623520i	0.950161	−	0.311760i	$-0.100918\pi$
$152$	6.02723	+	3.49246i	0.488873	+	0.283276i
$153$		0			0
$154$	−6.10859	+	34.5378i	−0.492244	+	2.78313i
$155$	0.554199	−	0.304628i	0.0445144	−	0.0244683i
$156$		0			0
$157$			14.4576i			1.15384i	0.816801	+	0.576920i	$0.195746\pi$
$157$			14.4576i			1.15384i	−0.816801	+	0.576920i	$0.804254\pi$
$158$	1.45174	−	2.72689i	0.115495	−	0.216940i
$159$		0			0
$160$	6.82359	+	10.6508i	0.539452	+	0.842016i
$161$	17.5870	+	5.71436i	1.38605	+	0.450354i
$162$		0			0
$163$	7.06131	+	21.7325i	0.553084	+	1.70222i	0.700950	+	0.713210i	$0.252760\pi$
$163$	7.06131	+	21.7325i	0.553084	+	1.70222i	−0.147866	+	0.989007i	$0.547240\pi$
$164$	−20.7050	+	13.9341i	−1.61679	+	1.08807i
$165$		0			0
$166$	−0.992180	−	1.02851i	−0.0770081	−	0.0798278i
$167$	−13.7078	−	18.8672i	−1.06074	−	1.45998i	−0.879110	−	0.476618i	$-0.841862\pi$
$167$	−13.7078	−	18.8672i	−1.06074	−	1.45998i	−0.181631	−	0.983367i	$-0.558138\pi$
$168$		0			0
$169$	−8.76524	+	6.36832i	−0.674250	+	0.489871i
$170$	4.22672	+	5.65689i	0.324175	+	0.433864i
$171$		0			0
$172$	−8.11545	+	2.31787i	−0.618797	+	0.176736i
$173$	−2.61869	+	8.05949i	−0.199095	+	0.612752i	0.800809	+	0.598919i	$0.204403\pi$
$173$	−2.61869	+	8.05949i	−0.199095	+	0.612752i	−0.999904	+	0.0138322i	$0.995597\pi$
$174$		0			0
$175$	−19.2816	−	4.95326i	−1.45755	−	0.374432i
$176$	−5.97707	−	24.1885i	−0.450538	−	1.82327i
$177$		0			0
$178$	−15.7452	−	2.78481i	−1.18015	−	0.208730i
$179$	−11.4129	−	8.29193i	−0.853037	−	0.619768i	0.0729444	−	0.997336i	$-0.476760\pi$
$179$	−11.4129	−	8.29193i	−0.853037	−	0.619768i	−0.925982	+	0.377568i	$0.876760\pi$
$180$		0			0
$181$	−9.90763	+	7.19831i	−0.736428	+	0.535046i	−0.891590	−	0.452843i	$-0.850410\pi$
$181$	−9.90763	+	7.19831i	−0.736428	+	0.535046i	0.155162	+	0.987889i	$0.450410\pi$
$182$	7.44940	−	3.62848i	0.552186	−	0.268961i
$183$		0			0
$184$	−13.0667	+	1.35261i	−0.963290	+	0.0997159i
$185$	−2.25673	−	11.8342i	−0.165918	−	0.870071i
$186$		0			0
$187$	−4.29834	−	13.2289i	−0.314326	−	0.967396i
$188$	−1.12228	+	3.07343i	−0.0818510	+	0.224153i
$189$		0			0
$190$	6.23899	−	4.66165i	0.452624	−	0.338192i
$191$	6.30311	+	19.3990i	0.456077	+	1.40366i	0.869866	+	0.493288i	$0.164205\pi$
$191$	6.30311	+	19.3990i	0.456077	+	1.40366i	−0.413789	+	0.910373i	$0.635795\pi$
$192$		0			0
$193$		−	2.62559i		−	0.188994i	−0.995525	−	0.0944970i	$-0.969876\pi$
$193$		−	2.62559i		−	0.188994i	0.995525	−	0.0944970i	$-0.0301243\pi$
$194$	−9.94442	+	18.6791i	−0.713968	+	1.34108i
$195$		0			0
$196$	17.0243	−	4.86236i	1.21602	−	0.347311i
$197$	5.58063	+	4.05457i	0.397604	+	0.288876i	0.768564	−	0.639773i	$-0.220972\pi$
$197$	5.58063	+	4.05457i	0.397604	+	0.288876i	−0.370961	+	0.928649i	$0.620972\pi$
$198$		0			0
$199$			16.9856i			1.20407i	0.798468	+	0.602037i	$0.205644\pi$
$199$			16.9856i			1.20407i	−0.798468	+	0.602037i	$0.794356\pi$
$200$	13.9481	−	2.33479i	0.986278	−	0.165095i
$201$		0			0
$202$	1.58080	+	11.2909i	0.111225	+	0.794423i
$203$	−18.1603	+	24.9956i	−1.27461	+	1.75434i
$204$		0			0
$205$	5.22675	+	27.4090i	0.365052	+	1.91433i
$206$	4.34554	+	2.31348i	0.302768	+	0.161188i
$207$		0			0
$208$	−3.79310	+	4.50126i	−0.263004	+	0.312106i
$209$	−14.5902	+	4.74065i	−1.00923	+	0.327918i
$210$		0			0
$211$	10.9043	+	3.54302i	0.750683	+	0.243912i	0.659275	−	0.751902i	$-0.270863\pi$
$211$	10.9043	+	3.54302i	0.750683	+	0.243912i	0.0914079	+	0.995814i	$0.470863\pi$
$212$	7.36293	+	2.68863i	0.505688	+	0.184656i
$213$		0			0
$214$	−0.486476	−	3.47466i	−0.0332548	−	0.237523i
$215$	−1.18326	+	9.36168i	−0.0806974	+	0.638462i
$216$		0			0
$217$	0.661878	+	0.910997i	0.0449312	+	0.0618425i
$218$	1.02020	+	2.09450i	0.0690965	+	0.141857i
$219$		0			0
$220$	−27.4936	−	4.48434i	−1.85362	−	0.302334i
$221$	−1.93154	+	2.65854i	−0.129930	+	0.178833i
$222$		0			0
$223$	−3.27627	+	10.0833i	−0.219395	+	0.675229i	0.779417	+	0.626505i	$0.215515\pi$
$223$	−3.27627	+	10.0833i	−0.219395	+	0.675229i	−0.998812	+	0.0487237i	$0.984485\pi$
$224$	−17.2914	+	14.4322i	−1.15533	+	0.964293i
$225$		0			0
$226$	−10.6896	−	21.9460i	−0.711059	−	1.45983i
$227$	18.9895	+	6.17007i	1.26038	+	0.409522i	0.861629	−	0.507538i	$-0.169444\pi$
$227$	18.9895	+	6.17007i	1.26038	+	0.409522i	0.398750	+	0.917060i	$0.369444\pi$
$228$		0			0
$229$	11.7252	+	8.51885i	0.774822	+	0.562941i	0.903421	−	0.428755i	$-0.141048\pi$
$229$	11.7252	+	8.51885i	0.774822	+	0.562941i	−0.128598	+	0.991697i	$0.541048\pi$
$230$	−4.35132	+	14.0277i	−0.286918	+	0.924959i
$231$		0			0
$232$	4.59703	−	21.4615i	0.301810	−	1.40901i
$233$	−6.20563	+	4.50865i	−0.406544	+	0.295372i	−0.772201	−	0.635378i	$-0.780844\pi$
$233$	−6.20563	+	4.50865i	−0.406544	+	0.295372i	0.365657	+	0.930750i	$0.380844\pi$
$234$		0			0
$235$	2.66650	+	2.50433i	0.173943	+	0.163364i
$236$	−11.9590	−	17.7700i	−0.778463	−	1.15673i
$237$		0			0
$238$	−9.04938	+	8.72973i	−0.586584	+	0.565864i
$239$	2.00242	−	6.16283i	0.129526	−	0.398640i	−0.865172	−	0.501474i	$-0.832791\pi$
$239$	2.00242	−	6.16283i	0.129526	−	0.398640i	0.994699	+	0.102834i	$0.0327911\pi$
$240$		0			0
$241$	8.90333	+	27.4016i	0.573514	+	1.76509i	0.641184	+	0.767387i	$0.278443\pi$
$241$	8.90333	+	27.4016i	0.573514	+	1.76509i	−0.0676702	+	0.997708i	$0.521557\pi$
$242$	34.7041	+	18.4758i	2.23086	+	1.18767i
$243$		0			0
$244$	0.438368	−	12.1872i	0.0280637	−	0.780206i
$245$	2.48220	−	19.6387i	0.158582	−	1.25467i
$246$		0			0
$247$	2.93211	+	2.13030i	0.186566	+	0.135548i
$248$	−0.692135	−	0.401056i	−0.0439506	−	0.0254671i
$249$		0			0
$250$	3.72888	−	15.3654i	0.235835	−	0.971793i
$251$	20.6896			1.30592			0.652958	−	0.757394i	$-0.273528\pi$
$251$	20.6896			1.30592			0.652958	+	0.757394i	$0.273528\pi$
$252$		0			0
$253$	17.0048	−	23.4051i	1.06908	−	1.47147i
$254$	−3.10307	+	17.5447i	−0.194704	+	1.10085i
$255$		0			0
$256$	7.07413	−	14.3512i	0.442133	−	0.896949i
$257$	−1.04136			−0.0649582			−0.0324791	−	0.999472i	$-0.510340\pi$
$257$	−1.04136			−0.0649582			−0.0324791	+	0.999472i	$0.510340\pi$
$258$		0			0
$259$	20.4018	−	6.62893i	1.26770	−	0.411902i
$260$	2.96076	+	5.87751i	0.183618	+	0.364508i
$261$		0			0
$262$	−15.8879	+	15.3267i	−0.981559	+	0.946887i
$263$	20.3891	−	6.62481i	1.25724	−	0.408503i	0.396732	−	0.917934i	$-0.370144\pi$
$263$	20.3891	−	6.62481i	1.25724	−	0.408503i	0.860512	+	0.509431i	$0.170144\pi$
$264$		0			0
$265$	5.99955	−	6.38806i	0.368549	−	0.392415i
$266$	9.62803	+	9.98057i	0.590332	+	0.611948i
$267$		0			0
$268$	2.03854	−	2.60359i	0.124524	−	0.159040i
$269$	1.42745	+	1.96472i	0.0870331	+	0.119791i	0.850313	−	0.526277i	$-0.176412\pi$
$269$	1.42745	+	1.96472i	0.0870331	+	0.119791i	−0.763280	+	0.646068i	$0.776412\pi$
$270$		0			0
$271$	5.44104	−	7.48894i	0.330519	−	0.454921i	−0.611123	−	0.791536i	$-0.709282\pi$
$271$	5.44104	−	7.48894i	0.330519	−	0.454921i	0.941642	+	0.336615i	$0.109282\pi$
$272$	3.36342	−	8.27480i	0.203937	−	0.501734i
$273$		0			0
$274$	−8.20144	−	16.8378i	−0.495467	−	1.01721i
$275$	−16.6916	+	26.2945i	−1.00654	+	1.58562i
$276$		0			0
$277$	−12.5391	−	4.07419i	−0.753399	−	0.244794i	−0.0929560	−	0.995670i	$-0.529632\pi$
$277$	−12.5391	−	4.07419i	−0.753399	−	0.244794i	−0.660443	+	0.750876i	$0.729632\pi$
$278$	17.3381	+	3.06654i	1.03987	+	0.183919i
$279$		0			0
$280$	7.23881	+	24.1185i	0.432602	+	1.44136i
$281$	11.2165	+	15.4382i	0.669120	+	0.920965i	0.999740	−	0.0227988i	$-0.00725772\pi$
$281$	11.2165	+	15.4382i	0.669120	+	0.920965i	−0.330620	+	0.943764i	$0.607258\pi$
$282$		0			0
$283$	−17.1754	+	12.4786i	−1.02097	+	0.741777i	−0.966481	−	0.256737i	$-0.917353\pi$
$283$	−17.1754	+	12.4786i	−1.02097	+	0.741777i	−0.0544876	+	0.998514i	$0.517353\pi$
$284$	15.2867	+	5.58203i	0.907096	+	0.331232i
$285$		0			0
$286$	−1.79743	−	12.8382i	−0.106284	−	0.759137i
$287$	−47.2520	+	15.3531i	−2.78920	+	0.906265i
$288$		0			0
$289$	−3.71236	+	11.4255i	−0.218374	+	0.672086i
$290$	−20.0436	−	14.1568i	−1.17700	−	0.831316i
$291$		0			0
$292$	11.2024	+	0.402947i	0.655574	+	0.0235807i
$293$	−11.4622			−0.669628			−0.334814	−	0.942284i	$-0.608673\pi$
$293$	−11.4622			−0.669628			−0.334814	+	0.942284i	$0.608673\pi$
$294$		0			0
$295$	−23.5237	+	4.48585i	−1.36961	+	0.261177i
$296$	−11.3408	+	10.1791i	−0.659170	+	0.591647i
$297$		0			0
$298$	4.22637	+	30.1869i	0.244827	+	1.74868i
$299$	−6.83472			−0.395262
$300$		0			0
$301$	−16.8020			−0.968449
$302$	1.50241	+	10.7310i	0.0864538	+	0.617497i
$303$		0			0
$304$	−9.12629	−	3.70952i	−0.523429	−	0.212755i
$305$	−12.3365	−	5.80608i	−0.706387	−	0.332455i
$306$		0			0
$307$	22.5636			1.28777			0.643887	−	0.765120i	$-0.277321\pi$
$307$	22.5636			1.28777			0.643887	+	0.765120i	$0.277321\pi$
$308$	1.78300	−	49.5698i	0.101596	−	2.82450i
$309$		0			0
$310$	−0.716452	+	0.535319i	−0.0406918	+	0.0304041i
$311$	3.15404	−	9.70713i	0.178849	−	0.550441i	−0.820939	−	0.571016i	$-0.806550\pi$
$311$	3.15404	−	9.70713i	0.178849	−	0.550441i	0.999788	+	0.0205746i	$0.00654956\pi$
$312$		0			0
$313$	−9.52777	+	3.09576i	−0.538542	+	0.174983i	−0.565643	−	0.824650i	$-0.691372\pi$
$313$	−9.52777	+	3.09576i	−0.538542	+	0.174983i	0.0271018	+	0.999633i	$0.491372\pi$
$314$	−2.83494	−	20.2486i	−0.159985	−	1.14269i
$315$		0			0
$316$	−1.49854	+	4.10382i	−0.0842994	+	0.230858i
$317$	−4.44238	+	3.22758i	−0.249509	+	0.181279i	−0.705509	−	0.708701i	$-0.749282\pi$
$317$	−4.44238	+	3.22758i	−0.249509	+	0.181279i	0.456000	+	0.889980i	$0.349282\pi$
$318$		0			0
$319$	28.4114	+	39.1050i	1.59073	+	2.18946i
$320$	−11.6453	−	13.5789i	−0.650991	−	0.759086i
$321$		0			0
$322$	−25.7520	−	4.55468i	−1.43510	−	0.253823i
$323$	−5.23051	−	1.69949i	−0.291033	−	0.0945624i
$324$		0			0
$325$	7.34346	−	0.461080i	0.407342	−	0.0255761i
$326$	−14.1512	−	29.0528i	−0.783762	−	1.60909i
$327$		0			0
$328$	26.2661	−	23.5755i	1.45030	−	1.30174i
$329$	−3.82861	+	5.26964i	−0.211078	+	0.290524i
$330$		0			0
$331$	−10.9664	−	15.0939i	−0.602767	−	0.829637i	0.393191	−	0.919457i	$-0.371371\pi$
$331$	−10.9664	−	15.0939i	−0.602767	−	0.829637i	−0.995958	+	0.0898194i	$0.971371\pi$
$332$	1.59128	+	1.24593i	0.0873327	+	0.0683792i
$333$		0			0
$334$	22.8981	+	23.7365i	1.25293	+	1.29881i
$335$	−1.78085	−	3.23983i	−0.0972980	−	0.177011i
$336$		0			0
$337$	−24.6327	+	8.00366i	−1.34183	+	0.435987i	−0.889936	−	0.456085i	$-0.849251\pi$
$337$	−24.6327	+	8.00366i	−1.34183	+	0.435987i	−0.451894	+	0.892072i	$0.649251\pi$
$338$	11.0274	−	10.6379i	0.599814	−	0.578627i
$339$		0			0
$340$	−7.02899	−	7.09397i	−0.381200	−	0.384725i
$341$	1.67546	−	0.544391i	0.0907313	−	0.0294804i
$342$		0			0
$343$	7.37599			0.398266
$344$	10.9116	−	4.83763i	0.588315	−	0.260828i
$345$		0			0
$346$	2.08725	−	11.8012i	0.112211	−	0.634438i
$347$	−14.0199	+	19.2967i	−0.752626	+	1.03590i	0.245166	+	0.969481i	$0.421157\pi$
$347$	−14.0199	+	19.2967i	−0.752626	+	1.03590i	−0.997792	+	0.0664193i	$0.978843\pi$
$348$		0			0
$349$	8.20147			0.439015			0.219507	−	0.975611i	$-0.429555\pi$
$349$	8.20147			0.439015			0.219507	+	0.975611i	$0.429555\pi$
$350$	27.9761	+	3.15645i	1.49539	+	0.168719i
$351$		0			0
$352$	13.1142	+	32.7052i	0.698992	+	1.74319i
$353$	−13.8300	−	10.0481i	−0.736094	−	0.534804i	0.155391	−	0.987853i	$-0.450336\pi$
$353$	−13.8300	−	10.0481i	−0.736094	−	0.534804i	−0.891486	+	0.453049i	$0.850336\pi$
$354$		0			0
$355$	12.4560	−	13.2627i	0.661098	−	0.703909i
$356$	22.5981	+	0.812843i	1.19770	+	0.0430806i
$357$		0			0
$358$	17.6103	+	9.37538i	0.930731	+	0.495504i
$359$	−8.56831	−	26.3706i	−0.452218	−	1.39178i	−0.874370	−	0.485260i	$-0.838725\pi$
$359$	−8.56831	−	26.3706i	−0.452218	−	1.39178i	0.422152	−	0.906525i	$-0.361275\pi$
$360$		0			0
$361$	3.99695	−	12.3013i	0.210366	−	0.647439i
$362$	12.4647	−	12.0244i	0.655128	−	0.631987i
$363$		0			0
$364$	−9.72178	+	6.54262i	−0.509560	+	0.342926i
$365$	5.33693	−	11.3397i	0.279348	−	0.593547i
$366$		0			0
$367$	13.6288	−	9.90188i	0.711416	−	0.516874i	−0.172214	−	0.985060i	$-0.555092\pi$
$367$	13.6288	−	9.90188i	0.711416	−	0.516874i	0.883630	+	0.468186i	$0.155092\pi$
$368$	18.0354	−	4.45661i	0.940159	−	0.232317i
$369$		0			0
$370$	5.48121	+	16.1320i	0.284954	+	0.838661i
$371$	12.6243	+	9.17211i	0.655422	+	0.476192i
$372$		0			0
$373$	4.22785	+	1.37371i	0.218910	+	0.0711280i	0.416418	−	0.909173i	$-0.363285\pi$
$373$	4.22785	+	1.37371i	0.218910	+	0.0711280i	−0.197509	+	0.980301i	$0.563285\pi$
$374$	8.61408	+	17.6850i	0.445424	+	0.914469i
$375$		0			0
$376$	0.969159	−	4.52457i	0.0499806	−	0.233337i
$377$	3.52877	−	10.8604i	0.181741	−	0.559341i
$378$		0			0
$379$	4.42329	−	6.08814i	0.227209	−	0.312727i	−0.680158	−	0.733066i	$-0.738089\pi$
$379$	4.42329	−	6.08814i	0.227209	−	0.312727i	0.907367	+	0.420339i	$0.138089\pi$
$380$	−7.82395	+	7.75228i	−0.401360	+	0.397684i
$381$		0			0
$382$	−12.6317	−	25.9333i	−0.646295	−	1.32687i
$383$	−3.61636	−	4.97749i	−0.184787	−	0.254338i	0.706566	−	0.707647i	$-0.250243\pi$
$383$	−3.61636	−	4.97749i	−0.184787	−	0.254338i	−0.891353	+	0.453309i	$0.850243\pi$
$384$		0			0
$385$	−50.1771	−	23.6154i	−2.55726	−	1.20355i
$386$	0.514844	+	3.67728i	0.0262049	+	0.187168i
$387$		0			0
$388$	10.2650	−	28.1111i	0.521124	−	1.42712i
$389$	19.4653	+	6.32466i	0.986929	+	0.320673i	0.757631	−	0.652683i	$-0.226357\pi$
$389$	19.4653	+	6.32466i	0.986929	+	0.320673i	0.229298	+	0.973356i	$0.426357\pi$
$390$		0			0
$391$	9.86375	−	3.20493i	0.498831	−	0.162080i
$392$	−22.8901	+	10.1482i	−1.15612	+	0.512564i
$393$		0			0
$394$	−8.61102	−	4.58435i	−0.433817	−	0.230956i
$395$	3.56046	+	3.34392i	0.179146	+	0.168251i
$396$		0			0
$397$	15.9886	−	22.0064i	0.802443	−	1.10447i	−0.190003	−	0.981783i	$-0.560850\pi$
$397$	15.9886	−	22.0064i	0.802443	−	1.10447i	0.992446	−	0.122684i	$-0.0391502\pi$
$398$	−3.33065	−	23.7892i	−0.166950	−	1.19244i
$399$		0			0
$400$	−19.0772	+	6.00504i	−0.953860	+	0.300252i
$401$		−	5.46509i		−	0.272914i	−0.990646	−	0.136457i	$-0.956429\pi$
$401$		−	5.46509i		−	0.272914i	0.990646	−	0.136457i	$-0.0435715\pi$
$402$		0			0
$403$	−0.336708	−	0.244632i	−0.0167726	−	0.0121860i
$404$	−4.42799	−	15.5035i	−0.220301	−	0.771328i
$405$		0			0
$406$	20.5332	−	38.5686i	1.01905	−	1.91413i
$407$		−	33.5606i		−	1.66354i
$408$		0			0
$409$	5.80568	+	17.8681i	0.287073	+	0.883519i	0.985770	+	0.168101i	$0.0537635\pi$
$409$	5.80568	+	17.8681i	0.287073	+	0.883519i	−0.698697	+	0.715418i	$0.746236\pi$
$410$	−12.6949	−	37.3628i	−0.626955	−	1.84522i
$411$		0			0
$412$	−6.53980	−	2.38805i	−0.322193	−	0.117651i
$413$	−13.1768	−	40.5540i	−0.648388	−	1.99553i
$414$		0			0
$415$	1.98014	−	1.08843i	0.0972012	−	0.0534288i
$416$	4.42981	−	7.04804i	0.217189	−	0.345558i
$417$		0			0
$418$	19.5048	−	9.50048i	0.954011	−	0.464684i
$419$	3.73967	−	2.71703i	0.182695	−	0.132736i	−0.492679	−	0.870211i	$-0.663982\pi$
$419$	3.73967	−	2.71703i	0.182695	−	0.132736i	0.675374	+	0.737476i	$0.263982\pi$
$420$		0			0
$421$	10.6813	+	7.76039i	0.520573	+	0.378218i	0.816820	−	0.576893i	$-0.195735\pi$
$421$	10.6813	+	7.76039i	0.520573	+	0.378218i	−0.296247	+	0.955111i	$0.595735\pi$
$422$	−15.9668	−	2.82400i	−0.777251	−	0.137470i
$423$		0			0
$424$	−10.8394	−	2.32179i	−0.526407	−	0.112756i
$425$	−10.3818	+	4.10891i	−0.503589	+	0.199311i
$426$		0			0
$427$	7.50217	−	23.0893i	0.363056	−	1.11737i
$428$	1.36267	+	4.77105i	0.0658672	+	0.230618i
$429$		0			0
$430$	−0.178490	−	13.3436i	−0.00860757	−	0.643484i
$431$	−0.707053	+	0.513704i	−0.0340575	+	0.0247442i	−0.604684	−	0.796466i	$-0.706701\pi$
$431$	−0.707053	+	0.513704i	−0.0340575	+	0.0247442i	0.570626	+	0.821210i	$0.306701\pi$
$432$		0			0
$433$	−7.92436	−	10.9069i	−0.380820	−	0.524154i	0.574981	−	0.818167i	$-0.305009\pi$
$433$	−7.92436	−	10.9069i	−0.380820	−	0.524154i	−0.955802	+	0.294012i	$0.905009\pi$
$434$	−1.10563	−	1.14611i	−0.0530720	−	0.0550153i
$435$		0			0
$436$	−1.83955	−	2.73341i	−0.0880983	−	0.130907i
$437$	−3.53472	−	10.8787i	−0.169088	−	0.520401i
$438$		0			0
$439$	1.45064	+	0.471340i	0.0692351	+	0.0224958i	0.343430	−	0.939178i	$-0.388411\pi$
$439$	1.45064	+	0.471340i	0.0692351	+	0.0224958i	−0.274195	+	0.961674i	$0.588411\pi$
$440$	39.3856	+	0.889412i	1.87764	+	0.0424011i
$441$		0			0
$442$	2.18392	−	4.10218i	0.103879	−	0.195121i
$443$			40.9585i			1.94600i	0.230807	+	0.973000i	$0.425863\pi$
$443$			40.9585i			1.94600i	−0.230807	+	0.973000i	$0.574137\pi$
$444$		0			0
$445$	10.7659	−	22.8750i	0.510353	−	1.08438i
$446$	2.61138	−	14.7647i	0.123653	−	0.699127i
$447$		0			0
$448$	21.3876	−	23.6037i	1.01047	−	1.11517i
$449$			23.7668i			1.12163i	0.827942	+	0.560813i	$0.189511\pi$
$449$			23.7668i			1.12163i	−0.827942	+	0.560813i	$0.810489\pi$
$450$		0			0
$451$			77.7289i			3.66011i
$452$	19.2746	+	28.6405i	0.906602	+	1.34713i
$453$		0			0
$454$	−27.8057	−	4.91791i	−1.30499	−	0.230809i
$455$	2.45416	+	12.8696i	0.115053	+	0.603334i
$456$		0			0
$457$		−	22.6396i		−	1.05903i	−0.848299	−	0.529517i	$-0.822373\pi$
$457$		−	22.6396i		−	1.05903i	0.848299	−	0.529517i	$-0.177627\pi$
$458$	−18.0922	−	9.63194i	−0.845392	−	0.450071i
$459$		0			0
$460$	3.34361	−	20.4998i	0.155897	−	0.955807i
$461$	−11.5797	−	3.76246i	−0.539319	−	0.175235i	0.0266760	−	0.999644i	$-0.491508\pi$
$461$	−11.5797	−	3.76246i	−0.539319	−	0.175235i	−0.565995	+	0.824409i	$0.691508\pi$
$462$		0			0
$463$	−2.18172	−	6.71465i	−0.101393	−	0.312056i	0.887474	−	0.460858i	$-0.152458\pi$
$463$	−2.18172	−	6.71465i	−0.101393	−	0.312056i	−0.988867	+	0.148802i	$0.952458\pi$
$464$	−2.23007	+	30.9594i	−0.103529	+	1.43725i
$465$		0			0
$466$	7.80722	−	7.53145i	0.361663	−	0.348888i
$467$	1.97492	+	2.71824i	0.0913883	+	0.125785i	0.852263	−	0.523114i	$-0.175230\pi$
$467$	1.97492	+	2.71824i	0.0913883	+	0.125785i	−0.760874	+	0.648899i	$0.775230\pi$
$468$		0			0
$469$	5.32566	−	3.86932i	0.245916	−	0.178668i
$470$	−4.22564	−	2.98458i	−0.194914	−	0.137668i
$471$		0			0
$472$	20.2337	+	22.5429i	0.931330	+	1.03762i
$473$	−8.12290	+	24.9997i	−0.373491	+	1.14949i
$474$		0			0
$475$	4.53172	+	11.4500i	0.207930	+	0.525364i
$476$	10.9623	−	14.0009i	0.502458	−	0.641731i
$477$		0			0
$478$	−1.59605	+	9.02402i	−0.0730017	+	0.412749i
$479$	28.0221	+	20.3593i	1.28036	+	0.930239i	0.999564	−	0.0295273i	$-0.00940019\pi$
$479$	28.0221	+	20.3593i	1.28036	+	0.930239i	0.280800	+	0.959766i	$0.409400\pi$
$480$		0			0
$481$	−6.41438	+	4.66032i	−0.292470	+	0.212492i
$482$	−17.8427	−	36.6316i	−0.812713	−	1.66853i
$483$		0			0
$484$	−52.2278	−	19.0713i	−2.37399	−	0.866879i
$485$	−24.3891	−	22.9058i	−1.10745	−	1.04010i
$486$		0			0
$487$	9.18033	+	28.2541i	0.416000	+	1.28032i	0.911353	+	0.411625i	$0.135039\pi$
$487$	9.18033	+	28.2541i	0.416000	+	1.28032i	−0.495353	+	0.868692i	$0.664961\pi$
$488$	1.77580	+	17.1548i	0.0803865	+	0.776561i
$489$		0			0
$490$	0.374432	+	27.9917i	0.0169151	+	1.26454i
$491$	−9.73980	−	29.9760i	−0.439551	−	1.35280i	−0.888350	−	0.459166i	$-0.848148\pi$
$491$	−9.73980	−	29.9760i	−0.439551	−	1.35280i	0.448799	−	0.893633i	$-0.351852\pi$
$492$		0			0
$493$			17.3283i			0.780428i
$494$	−4.52430	−	2.40865i	−0.203558	−	0.108370i
$495$		0			0
$496$	1.04801	+	0.425981i	0.0470572	+	0.0191271i
$497$	26.2102	+	19.0428i	1.17569	+	0.854186i
$498$		0			0
$499$			3.25610i			0.145763i	0.997341	+	0.0728815i	$0.0232195\pi$
$499$			3.25610i			0.145763i	−0.997341	+	0.0728815i	$0.976781\pi$
$500$	−2.20955	+	22.2512i	−0.0988140	+	0.995106i
$501$		0			0
$502$	−28.9769	+	4.05696i	−1.29330	+	0.181071i
$503$	6.62006	−	9.11172i	0.295174	−	0.406272i	−0.635512	−	0.772091i	$-0.719211\pi$
$503$	6.62006	−	9.11172i	0.295174	−	0.406272i	0.930686	+	0.365819i	$0.119211\pi$
$504$		0			0
$505$	−17.8843	−	2.26046i	−0.795840	−	0.100589i
$506$	−19.2267	+	36.1146i	−0.854732	+	1.60549i
$507$		0			0
$508$	0.905739	−	25.1807i	0.0401857	−	1.11721i
$509$	30.6303	−	9.95238i	1.35766	−	0.441132i	0.462401	−	0.886671i	$-0.346988\pi$
$509$	30.6303	−	9.95238i	1.35766	−	0.441132i	0.895262	+	0.445539i	$0.146988\pi$
$510$		0			0
$511$	21.2236	+	6.89598i	0.938878	+	0.305060i
$512$	−7.09361	+	21.4868i	−0.313496	+	0.949589i
$513$		0			0
$514$	1.45848	−	0.204197i	0.0643308	−	0.00900675i
$515$	−5.32883	+	5.67391i	−0.234816	+	0.250022i
$516$		0			0
$517$	5.98977	+	8.24422i	0.263430	+	0.362580i
$518$	−27.2739	+	13.2847i	−1.19835	+	0.583696i
$519$		0			0
$520$	−5.29920	−	7.65121i	−0.232385	−	0.335528i
$521$	2.03518	−	2.80119i	0.0891630	−	0.122722i	−0.762105	−	0.647453i	$-0.775834\pi$
$521$	2.03518	−	2.80119i	0.0891630	−	0.122722i	0.851268	+	0.524731i	$0.175834\pi$
$522$		0			0
$523$	−2.27198	+	6.99243i	−0.0993467	+	0.305758i	−0.988362	−	0.152120i	$-0.951390\pi$
$523$	−2.27198	+	6.99243i	−0.0993467	+	0.305758i	0.889015	+	0.457877i	$0.151390\pi$
$524$	19.2465	−	24.5813i	0.840787	−	1.07384i
$525$		0			0
$526$	−27.2569	+	13.2764i	−1.18846	+	0.578880i
$527$	0.600643	+	0.195161i	0.0261644	+	0.00850134i
$528$		0			0
$529$	−1.15607	−	0.839935i	−0.0502640	−	0.0365189i
$530$	−7.15007	+	10.1233i	−0.310579	+	0.439726i
$531$		0			0
$532$	−15.4416	−	12.0904i	−0.669479	−	0.524185i
$533$	14.8562	−	10.7936i	0.643492	−	0.467524i
$534$		0			0
$535$	5.50371	+	0.695634i	0.237946	+	0.0300749i
$536$	−2.34456	+	4.04620i	−0.101269	+	0.174769i
$537$		0			0
$538$	−2.38447	−	2.47179i	−0.102802	−	0.106566i
$539$	17.0400	−	52.4437i	0.733964	−	2.25891i
$540$		0			0
$541$	11.9639	+	36.8212i	0.514370	+	1.58307i	0.784426	+	0.620222i	$0.212958\pi$
$541$	11.9639	+	36.8212i	0.514370	+	1.58307i	−0.270057	+	0.962844i	$0.587042\pi$
$542$	−6.15198	+	11.5556i	−0.264250	+	0.496355i
$543$		0			0
$544$	−3.08807	+	12.2488i	−0.132400	+	0.525164i
$545$	−3.61845	+	0.690020i	−0.154997	+	0.0295572i
$546$		0			0
$547$	4.12325	+	2.99572i	0.176298	+	0.128088i	0.672435	−	0.740157i	$-0.265249\pi$
$547$	4.12325	+	2.99572i	0.176298	+	0.128088i	−0.496137	+	0.868244i	$0.665249\pi$
$548$	14.7882	+	21.9741i	0.631722	+	0.938686i
$549$		0			0
$550$	18.2215	−	40.0998i	0.776969	−	1.70986i
$551$	19.1114			0.814174
$552$		0			0
$553$	−5.11219	+	7.03632i	−0.217392	+	0.299215i
$554$	18.3605	+	3.24737i	0.780064	+	0.137968i
$555$		0			0
$556$	−24.8843	−	0.895075i	−1.05533	−	0.0379596i
$557$	−38.9120			−1.64875			−0.824377	−	0.566041i	$-0.808475\pi$
$557$	−38.9120			−1.64875			−0.824377	+	0.566041i	$0.808475\pi$
$558$		0			0
$559$	5.90612	−	1.91901i	0.249802	−	0.0811657i
$560$	−14.8677	−	32.3598i	−0.628274	−	1.36745i
$561$		0			0
$562$	−18.7365	−	19.4226i	−0.790353	−	0.819293i
$563$	−14.7711	+	4.79943i	−0.622529	+	0.202272i	−0.603263	−	0.797543i	$-0.706133\pi$
$563$	−14.7711	+	4.79943i	−0.622529	+	0.202272i	−0.0192660	+	0.999814i	$0.506133\pi$
$564$		0			0
$565$	37.9139	−	7.22998i	1.59505	−	0.304167i
$566$	21.6081	−	20.8448i	0.908256	−	0.876174i
$567$		0			0
$568$	−22.5043	−	4.82041i	−0.944261	−	0.202260i
$569$	8.73697	+	12.0254i	0.366273	+	0.504131i	0.951883	−	0.306462i	$-0.0991451\pi$
$569$	8.73697	+	12.0254i	0.366273	+	0.504131i	−0.585610	+	0.810593i	$0.699145\pi$
$570$		0			0
$571$	1.65944	−	2.28402i	0.0694454	−	0.0955834i	−0.772881	−	0.634550i	$-0.781185\pi$
$571$	1.65944	−	2.28402i	0.0694454	−	0.0955834i	0.842327	+	0.538967i	$0.181185\pi$
$572$	5.03480	+	17.6281i	0.210516	+	0.737068i
$573$		0			0
$574$	63.1684	−	30.7683i	2.63660	−	1.28425i
$575$	−19.6057	−	12.4456i	−0.817613	−	0.519018i
$576$		0			0
$577$	35.1778	+	11.4300i	1.46447	+	0.475836i	0.929433	−	0.368992i	$-0.120297\pi$
$577$	35.1778	+	11.4300i	1.46447	+	0.475836i	0.535039	+	0.844827i	$0.320297\pi$
$578$	2.95897	−	16.7299i	0.123077	−	0.695873i
$579$		0			0
$580$	30.8480	+	15.8971i	1.28090	+	0.660090i
$581$	2.36487	+	3.25497i	0.0981115	+	0.135039i
$582$		0			0
$583$	19.7504	−	14.3495i	0.817980	−	0.594297i
$584$	−15.7686	+	1.63231i	−0.652511	+	0.0675453i
$585$		0			0
$586$	16.0534	−	2.24759i	0.663160	−	0.0928469i
$587$	−7.04928	+	2.29045i	−0.290955	+	0.0945370i	−0.450858	−	0.892596i	$-0.648882\pi$
$587$	−7.04928	+	2.29045i	−0.290955	+	0.0945370i	0.159903	+	0.987133i	$0.448882\pi$
$588$		0			0
$589$	0.215243	−	0.662450i	0.00886894	−	0.0272958i
$590$	32.0666	−	10.8954i	1.32016	−	0.448556i
$591$		0			0
$592$	13.8874	−	16.4801i	0.570769	−	0.677329i
$593$	−23.8333			−0.978716			−0.489358	−	0.872083i	$-0.662769\pi$
$593$	−23.8333			−0.978716			−0.489358	+	0.872083i	$0.662769\pi$
$594$		0			0
$595$	−9.57657	−	17.4223i	−0.392601	−	0.714246i
$596$	−11.8385	−	41.4496i	−0.484924	−	1.69784i
$597$		0			0
$598$	9.57239	−	1.34020i	0.391444	−	0.0548048i
$599$	−26.8670			−1.09775			−0.548877	−	0.835903i	$-0.684945\pi$
$599$	−26.8670			−1.09775			−0.548877	+	0.835903i	$0.684945\pi$
$600$		0			0
$601$	−22.7927			−0.929732			−0.464866	−	0.885381i	$-0.653897\pi$
$601$	−22.7927			−0.929732			−0.464866	+	0.885381i	$0.653897\pi$
$602$	23.5321	−	3.29465i	0.959095	−	0.134280i
$603$		0			0
$604$	−4.20840	−	14.7347i	−0.171238	−	0.599546i
$605$	−42.5568	+	45.3127i	−1.73018	+	1.84222i
$606$		0			0
$607$	14.9310			0.606032			0.303016	−	0.952985i	$-0.402006\pi$
$607$	14.9310			0.606032			0.303016	+	0.952985i	$0.402006\pi$
$608$	13.5092	+	3.40583i	0.547872	+	0.138125i
$609$		0			0
$610$	18.4165	+	5.71269i	0.745660	+	0.231300i
$611$	0.743945	−	2.28963i	0.0300968	−	0.0926284i
$612$		0			0
$613$	−5.49599	+	1.78576i	−0.221981	+	0.0721260i	−0.417896	−	0.908495i	$-0.637232\pi$
$613$	−5.49599	+	1.78576i	−0.221981	+	0.0721260i	0.195915	+	0.980621i	$0.437232\pi$
$614$	−31.6016	+	4.42443i	−1.27534	+	0.178556i
$615$		0			0
$616$	7.22280	+	69.7748i	0.291015	+	2.81131i
$617$	−0.751237	+	0.545805i	−0.0302436	+	0.0219733i	−0.602804	−	0.797889i	$-0.705950\pi$
$617$	−0.751237	+	0.545805i	−0.0302436	+	0.0219733i	0.572561	+	0.819862i	$0.305950\pi$
$618$		0			0
$619$	−8.54010	−	11.7544i	−0.343256	−	0.472451i	0.602133	−	0.798396i	$-0.294318\pi$
$619$	−8.54010	−	11.7544i	−0.343256	−	0.472451i	−0.945389	+	0.325945i	$0.894318\pi$
$620$	0.898460	−	0.890230i	0.0360830	−	0.0357525i
$621$		0			0
$622$	−2.51396	+	14.2138i	−0.100800	+	0.569922i
$623$	42.8133	+	13.9109i	1.71528	+	0.557328i
$624$		0			0
$625$	21.9046	+	12.0494i	0.876185	+	0.481975i
$626$	12.7371	−	6.20405i	0.509078	−	0.247964i
$627$		0			0
$628$	7.94098	+	27.8034i	0.316879	+	1.10947i
$629$	7.07181	−	9.73351i	0.281972	−	0.388101i
$630$		0			0
$631$	11.4007	+	15.6917i	0.453855	+	0.624677i	0.973220	−	0.229875i	$-0.0738317\pi$
$631$	11.4007	+	15.6917i	0.453855	+	0.624677i	−0.519366	+	0.854552i	$0.673832\pi$
$632$	1.29408	−	6.04146i	0.0514756	−	0.240317i
$633$		0			0
$634$	5.58891	−	5.39149i	0.221964	−	0.214124i
$635$	−25.4892	−	11.9963i	−1.01151	−	0.476058i
$636$		0			0
$637$	−12.3897	+	4.02565i	−0.490897	+	0.159502i
$638$	−47.4597	−	49.1975i	−1.87895	−	1.94775i
$639$		0			0
$640$	18.9725	+	16.7345i	0.749953	+	0.661491i
$641$	6.27677	−	2.03945i	0.247917	−	0.0805533i	−0.182422	−	0.983220i	$-0.558394\pi$
$641$	6.27677	−	2.03945i	0.247917	−	0.0805533i	0.430340	+	0.902667i	$0.358394\pi$
$642$		0			0
$643$	−25.6404			−1.01116			−0.505580	−	0.862780i	$-0.668721\pi$
$643$	−25.6404			−1.01116			−0.505580	+	0.862780i	$0.668721\pi$
$644$	36.9602	+	1.32944i	1.45644	+	0.0523873i
$645$		0			0
$646$	7.65885	+	1.35460i	0.301334	+	0.0532960i
$647$	9.37903	−	12.9091i	0.368728	−	0.507510i	−0.583827	−	0.811878i	$-0.698445\pi$
$647$	9.37903	−	12.9091i	0.368728	−	0.507510i	0.952555	+	0.304368i	$0.0984453\pi$
$648$		0			0
$649$	−66.7108			−2.61863
$650$	−10.1945	+	2.08572i	−0.399861	+	0.0818089i
$651$		0			0
$652$	25.5164	+	37.9152i	0.999299	+	1.48487i
$653$	26.5939	+	19.3216i	1.04070	+	0.756112i	0.970422	−	0.241415i	$-0.0776117\pi$
$653$	26.5939	+	19.3216i	1.04070	+	0.756112i	0.0702771	+	0.997528i	$0.477612\pi$
$654$		0			0
$655$	−16.8135	−	30.5882i	−0.656958	−	1.19518i
$656$	−32.1642	+	38.1692i	−1.25580	+	1.49026i
$657$		0			0
$658$	4.32887	−	8.13115i	0.168757	−	0.316985i
$659$	0.231908	+	0.713739i	0.00903385	+	0.0278033i	0.955472	−	0.295082i	$-0.0953471\pi$
$659$	0.231908	+	0.713739i	0.00903385	+	0.0278033i	−0.946438	+	0.322886i	$0.895347\pi$
$660$		0			0
$661$	5.85500	−	18.0198i	0.227733	−	0.700890i	−0.770270	−	0.637718i	$-0.779878\pi$
$661$	5.85500	−	18.0198i	0.227733	−	0.700890i	0.998003	−	0.0631719i	$-0.0201216\pi$
$662$	18.3187	+	18.9895i	0.711978	+	0.738047i
$663$		0			0
$664$	−2.47298	−	1.43296i	−0.0959702	−	0.0556097i
$665$	−19.2151	+	10.5620i	−0.745130	+	0.409577i
$666$		0			0
$667$	−29.1574	+	21.1841i	−1.12898	+	0.820251i
$668$	−36.7244	−	28.7543i	−1.42091	−	1.11254i
$669$		0			0
$670$	3.12946	+	4.18835i	0.120901	+	0.161810i
$671$	−30.7278	−	22.3250i	−1.18623	−	0.861848i
$672$		0			0
$673$	19.2318	+	6.24879i	0.741331	+	0.240873i	0.655247	−	0.755415i	$-0.272565\pi$
$673$	19.2318	+	6.24879i	0.741331	+	0.240873i	0.0860843	+	0.996288i	$0.472565\pi$
$674$	32.9300	−	16.0397i	1.26842	−	0.617827i
$675$		0			0
$676$	−13.3586	+	17.0613i	−0.513791	+	0.656205i
$677$	7.07923	−	21.7876i	0.272077	−	0.837366i	−0.717901	−	0.696145i	$-0.754897\pi$
$677$	7.07923	−	21.7876i	0.272077	−	0.837366i	0.989978	−	0.141221i	$-0.0451029\pi$
$678$		0			0
$679$	35.0184	−	48.1987i	1.34388	−	1.84970i
$680$	11.2355	+	8.55720i	0.430862	+	0.328153i
$681$		0			0
$682$	−2.23983	+	1.09098i	−0.0857674	+	0.0417759i
$683$	23.4871	+	32.3272i	0.898708	+	1.23697i	0.970878	+	0.239573i	$0.0770074\pi$
$683$	23.4871	+	32.3272i	0.898708	+	1.23697i	−0.0721706	+	0.997392i	$0.522993\pi$
$684$		0			0
$685$	29.0890	−	5.54712i	1.11143	−	0.211945i
$686$	−10.3305	+	1.44634i	−0.394419	+	0.0552214i
$687$		0			0
$688$	−14.3337	+	8.91499i	−0.546467	+	0.339881i
$689$	−5.48520	−	1.78225i	−0.208970	−	0.0678983i
$690$		0			0
$691$	−26.0849	+	8.47550i	−0.992316	+	0.322423i	−0.759791	−	0.650167i	$-0.774699\pi$
$691$	−26.0849	+	8.47550i	−0.992316	+	0.322423i	−0.232525	+	0.972590i	$0.574699\pi$
$692$	−0.609236	+	16.9375i	−0.0231597	+	0.643869i
$693$		0			0
$694$	15.8517	−	29.7752i	0.601724	−	1.13025i
$695$	−11.8550	+	25.1891i	−0.449688	+	0.955478i
$696$		0			0
$697$	−16.3788	+	22.5435i	−0.620393	+	0.853897i
$698$	−11.4866	+	1.60820i	−0.434774	+	0.0608713i
$699$		0			0
$700$	−39.8010	+	1.06499i	−1.50434	+	0.0402528i
$701$		−	9.82186i		−	0.370967i	−0.982647	−	0.185483i	$-0.940615\pi$
$701$		−	9.82186i		−	0.370967i	0.982647	−	0.185483i	$-0.0593850\pi$
$702$		0			0
$703$	−10.7351	−	7.79951i	−0.404882	−	0.294164i
$704$	−24.7803	−	43.2339i	−0.933941	−	1.62944i
$705$		0			0
$706$	21.3399	+	11.3610i	0.803137	+	0.427575i
$707$		−	32.0980i		−	1.20717i
$708$		0			0
$709$	−0.828371	−	2.54947i	−0.0311101	−	0.0957472i	0.934296	−	0.356499i	$-0.116030\pi$
$709$	−0.828371	−	2.54947i	−0.0311101	−	0.0957472i	−0.965406	+	0.260752i	$0.916030\pi$
$710$	−14.8447	+	21.0175i	−0.557112	+	0.788774i
$711$		0			0
$712$	−31.8092	+	3.29276i	−1.19210	+	0.123402i
$713$	0.405908	+	1.24926i	0.0152014	+	0.0467850i
$714$		0			0
$715$	20.3351	+	2.57023i	0.760491	+	0.0961212i
$716$	−26.5025	−	9.67757i	−0.990445	−	0.361668i
$717$		0			0
$718$	17.1713	+	35.2532i	0.640827	+	1.31564i
$719$	−17.4787	+	12.6990i	−0.651846	+	0.473594i	−0.863899	−	0.503664i	$-0.831985\pi$
$719$	−17.4787	+	12.6990i	−0.651846	+	0.473594i	0.212054	+	0.977258i	$0.431985\pi$
$720$		0			0
$721$	−11.2130	−	8.14672i	−0.417594	−	0.303400i
$722$	−3.18581	+	18.0124i	−0.118563	+	0.670353i
$723$		0			0
$724$	−15.0996	+	19.2849i	−0.561172	+	0.716719i
$725$	29.8986	−	24.7279i	1.11041	−	0.918372i
$726$		0			0
$727$	−8.79498	+	27.0682i	−0.326188	+	1.00390i	0.644714	+	0.764424i	$0.276976\pi$
$727$	−8.79498	+	27.0682i	−0.326188	+	1.00390i	−0.970902	+	0.239478i	$0.923024\pi$
$728$	12.3329	−	11.0696i	0.457089	−	0.410267i
$729$		0			0
$730$	−5.25109	+	16.9284i	−0.194352	+	0.626546i
$731$	−7.62375	+	5.53898i	−0.281975	+	0.204867i
$732$		0			0
$733$	3.56517	+	4.90703i	0.131682	+	0.181245i	0.869767	−	0.493463i	$-0.164269\pi$
$733$	3.56517	+	4.90703i	0.131682	+	0.181245i	−0.738084	+	0.674709i	$0.764269\pi$
$734$	−17.1462	+	16.5405i	−0.632877	+	0.610522i
$735$		0			0
$736$	−24.3856	+	9.77823i	−0.898866	+	0.360430i
$737$	−3.18249	−	9.79469i	−0.117228	−	0.360792i
$738$		0			0
$739$	−25.5699	−	8.30817i	−0.940604	−	0.305621i	−0.201712	−	0.979445i	$-0.564651\pi$
$739$	−25.5699	−	8.30817i	−0.940604	−	0.305621i	−0.738892	+	0.673824i	$0.764651\pi$
$740$	−10.8400	−	21.5189i	−0.398486	−	0.791050i
$741$		0			0
$742$	−19.4796	−	10.3706i	−0.715118	−	0.380715i
$743$			2.03025i			0.0744827i	0.999306	+	0.0372414i	$0.0118570\pi$
$743$			2.03025i			0.0744827i	−0.999306	+	0.0372414i	$0.988143\pi$
$744$		0			0
$745$	−47.8147	−	6.04348i	−1.75180	−	0.221416i
$746$	−6.19069	−	1.09493i	−0.226657	−	0.0400882i
$747$		0			0
$748$	−15.5323	−	23.0797i	−0.567916	−	0.843876i
$749$			9.87784i			0.360928i
$750$		0			0
$751$		−	9.20535i		−	0.335908i	−0.985795	−	0.167954i	$-0.946284\pi$
$751$		−	9.20535i		−	0.335908i	0.985795	−	0.167954i	$-0.0537160\pi$
$752$	−0.470150	+	6.52694i	−0.0171446	+	0.238013i
$753$		0			0
$754$	−2.81264	+	15.9026i	−0.102430	+	0.579138i
$755$	−16.9974	−	2.14836i	−0.618598	−	0.0781869i
$756$		0			0
$757$			28.0053i			1.01787i	0.860805	+	0.508936i	$0.169961\pi$
$757$			28.0053i			1.01787i	−0.860805	+	0.508936i	$0.830039\pi$
$758$	−5.00125	+	9.39411i	−0.181654	+	0.341209i
$759$		0			0
$760$	9.43774	−	12.3917i	0.342343	−	0.449493i
$761$	−6.54953	−	2.12807i	−0.237420	−	0.0771425i	0.187890	−	0.982190i	$-0.439835\pi$
$761$	−6.54953	−	2.12807i	−0.237420	−	0.0771425i	−0.425310	+	0.905048i	$0.639835\pi$
$762$		0			0
$763$	−2.02687	−	6.23807i	−0.0733777	−	0.225833i
$764$	22.7766	+	33.8441i	0.824028	+	1.22444i
$765$		0			0
$766$	6.04093	+	6.26212i	0.218268	+	0.226260i
$767$	9.26364	+	12.7503i	0.334491	+	0.460387i
$768$		0			0
$769$	−26.4792	+	19.2383i	−0.954866	+	0.693751i	−0.951953	−	0.306245i	$-0.900927\pi$
$769$	−26.4792	+	19.2383i	−0.954866	+	0.693751i	−0.00291302	+	0.999996i	$0.500927\pi$
$770$	74.9064	+	23.2356i	2.69944	+	0.837353i
$771$		0			0
$772$	−1.44213	−	5.04927i	−0.0519035	−	0.181727i
$773$	8.39317	−	25.8315i	0.301881	−	0.929096i	−0.678941	−	0.734193i	$-0.737561\pi$
$773$	8.39317	−	25.8315i	0.301881	−	0.929096i	0.980823	−	0.194903i	$-0.0624392\pi$
$774$		0			0
$775$	−0.520398	−	1.31486i	−0.0186933	−	0.0472312i
$776$	−8.86440	+	41.3839i	−0.318214	+	1.48560i
$777$		0			0
$778$	−28.5024	−	5.04113i	−1.02186	−	0.180733i
$779$	24.8633	+	18.0642i	0.890820	+	0.647219i
$780$		0			0
$781$	41.0052	−	29.7920i	1.46728	−	1.06604i
$782$	−13.1863	+	6.42282i	−0.471540	+	0.229680i
$783$		0			0
$784$	30.0688	−	18.7016i	1.07389	−	0.667915i
$785$	32.0729	+	4.05381i	1.14473	+	0.144687i
$786$		0			0
$787$	−16.4331	−	50.5758i	−0.585776	−	1.80283i	−0.596132	−	0.802886i	$-0.703297\pi$
$787$	−16.4331	−	50.5758i	−0.585776	−	1.80283i	0.0103566	−	0.999946i	$-0.496703\pi$
$788$	12.9591	+	4.73211i	0.461650	+	0.168575i
$789$		0			0
$790$	−5.64232	−	3.98518i	−0.200745	−	0.141786i
$791$	21.2374	+	65.3620i	0.755115	+	2.32401i
$792$		0			0
$793$			8.97306i			0.318643i
$794$	−18.0777	+	33.9562i	−0.641552	+	1.20506i
$795$		0			0
$796$	9.32950	+	32.6649i	0.330675	+	1.15778i
$797$	4.84653	+	3.52121i	0.171673	+	0.124728i	0.670304	−	0.742087i	$-0.266164\pi$
$797$	4.84653	+	3.52121i	0.171673	+	0.124728i	−0.498631	+	0.866814i	$0.666164\pi$
$798$		0			0
$799$			3.65320i			0.129241i
$800$	25.5411	−	12.1512i	0.903015	−	0.429609i
$801$		0			0
$802$	1.07163	+	7.65415i	0.0378407	+	0.270277i
$803$	20.5211	−	28.2449i	0.724174	−	0.996740i
$804$		0			0
$805$	17.6081	−	37.4130i	0.620604	−	1.31864i
$806$	0.519546	+	0.276597i	0.0183002	+	0.00974270i
$807$		0			0
$808$	9.24167	+	20.8452i	0.325121	+	0.733332i
$809$	18.2954	−	5.94453i	0.643231	−	0.208999i	0.0308041	−	0.999525i	$-0.490193\pi$
$809$	18.2954	−	5.94453i	0.643231	−	0.208999i	0.612427	+	0.790527i	$0.290193\pi$
$810$		0			0
$811$	0.268631	+	0.0872835i	0.00943291	+	0.00306494i	0.313730	−	0.949512i	$-0.398421\pi$
$811$	0.268631	+	0.0872835i	0.00943291	+	0.00306494i	−0.304297	+	0.952577i	$0.598421\pi$
$812$	−21.1951	+	58.0437i	−0.743801	+	2.03694i
$813$		0			0
$814$	6.58080	+	47.0034i	0.230657	+	1.64747i
$815$	50.1916	−	9.57128i	1.75814	−	0.335267i
$816$		0			0
$817$	6.10895	+	8.40824i	0.213725	+	0.294167i
$818$	−11.6349	−	23.8868i	−0.406804	−	0.835181i
$819$		0			0
$820$	25.1062	+	49.8393i	0.876747	+	1.74047i
$821$	−6.88565	+	9.47729i	−0.240311	+	0.330760i	−0.912089	−	0.409993i	$-0.865531\pi$
$821$	−6.88565	+	9.47729i	−0.240311	+	0.330760i	0.671778	+	0.740753i	$0.265531\pi$
$822$		0			0
$823$	0.720149	−	2.21639i	0.0251028	−	0.0772585i	−0.937720	−	0.347391i	$-0.887068\pi$
$823$	0.720149	−	2.21639i	0.0251028	−	0.0772585i	0.962823	+	0.270133i	$0.0870676\pi$
$824$	9.62761	+	2.06223i	0.335394	+	0.0718411i
$825$		0			0
$826$	26.4069	+	54.2142i	0.918814	+	1.88635i
$827$	10.5090	+	3.41457i	0.365433	+	0.118736i	0.485977	−	0.873972i	$-0.338464\pi$
$827$	10.5090	+	3.41457i	0.365433	+	0.118736i	−0.120544	+	0.992708i	$0.538464\pi$
$828$		0			0
$829$	4.37850	+	3.18116i	0.152071	+	0.110486i	0.661219	−	0.750193i	$-0.270039\pi$
$829$	4.37850	+	3.18116i	0.152071	+	0.110486i	−0.509148	+	0.860679i	$0.670039\pi$
$830$	−2.55986	+	1.91268i	−0.0888542	+	0.0663901i
$831$		0			0
$832$	−4.82215	+	10.7398i	−0.167178	+	0.372335i
$833$	15.9929	−	11.6195i	0.554120	−	0.402592i
$834$		0			0
$835$	−45.6988	+	25.1194i	−1.58147	+	0.869292i
$836$	−25.4546	+	17.1306i	−0.880365	+	0.592473i
$837$		0			0
$838$	−4.70483	+	4.53865i	−0.162526	+	0.156785i
$839$	6.51456	−	20.0498i	0.224908	−	0.692195i	−0.773393	−	0.633927i	$-0.781442\pi$
$839$	6.51456	−	20.0498i	0.224908	−	0.692195i	0.998301	−	0.0582682i	$-0.0185579\pi$
$840$		0			0
$841$	−9.64626	−	29.6881i	−0.332630	−	1.02373i
$842$	−16.4814	−	8.77439i	−0.567986	−	0.302385i
$843$		0			0
$844$	22.9161	+	0.824281i	0.788805	+	0.0283729i
$845$	11.6699	+	21.2306i	0.401456	+	0.730355i
$846$		0			0
$847$	−89.5486	−	65.0609i	−3.07693	−	2.23552i
$848$	15.6364	+	1.12633i	0.536957	+	0.0386782i
$849$		0			0
$850$	13.7345	−	7.79047i	0.471089	−	0.267211i
$851$	25.0234			0.857792
$852$		0			0
$853$	5.75060	−	7.91502i	0.196897	−	0.271005i	−0.699140	−	0.714985i	$-0.746434\pi$
$853$	5.75060	−	7.91502i	0.196897	−	0.271005i	0.896037	+	0.443979i	$0.146434\pi$
$854$	−5.97968	+	33.8089i	−0.204620	+	1.15692i
$855$		0			0
$856$	−2.84403	−	6.41491i	−0.0972071	−	0.219257i
$857$	−50.9698			−1.74110			−0.870548	−	0.492083i	$-0.836236\pi$
$857$	−50.9698			−1.74110			−0.870548	+	0.492083i	$0.836236\pi$
$858$		0			0
$859$	−13.7432	+	4.46544i	−0.468912	+	0.152359i	−0.533936	−	0.845525i	$-0.679288\pi$
$859$	−13.7432	+	4.46544i	−0.468912	+	0.152359i	0.0650240	+	0.997884i	$0.479288\pi$
$860$	2.86648	+	18.6534i	0.0977463	+	0.636075i
$861$		0			0
$862$	0.889534	−	0.858113i	0.0302977	−	0.0292275i
$863$	−35.1006	+	11.4049i	−1.19484	+	0.388226i	−0.837859	−	0.545886i	$-0.816193\pi$
$863$	−35.1006	+	11.4049i	−1.19484	+	0.388226i	−0.356978	+	0.934113i	$0.616193\pi$
$864$		0			0
$865$	17.1451	+	8.06917i	0.582949	+	0.274360i
$866$	13.2372	+	13.7219i	0.449818	+	0.466289i
$867$		0			0
$868$	1.77323	+	1.38839i	0.0601874	+	0.0471252i
$869$	7.99789	+	11.0082i	0.271310	+	0.373426i
$870$		0			0
$871$	−1.43011	+	1.96838i	−0.0484575	+	0.0666960i
$872$	3.11237	+	3.46758i	0.105398	+	0.117427i
$873$		0			0
$874$	7.08374	+	14.5431i	0.239611	+	0.491929i
$875$	−16.3948	+	41.3857i	−0.554247	+	1.39909i
$876$		0			0
$877$	32.0025	+	10.3982i	1.08065	+	0.351124i	0.794626	−	0.607100i	$-0.207667\pi$
$877$	32.0025	+	10.3982i	1.08065	+	0.351124i	0.286021	+	0.958223i	$0.407667\pi$
$878$	−2.12412	−	0.375686i	−0.0716855	−	0.0126788i
$879$		0			0
$880$	−55.3361	+	6.47734i	−1.86538	+	0.218351i
$881$	22.0911	+	30.4057i	0.744267	+	1.02440i	0.998362	+	0.0572164i	$0.0182225\pi$
$881$	22.0911	+	30.4057i	0.744267	+	1.02440i	−0.254095	+	0.967179i	$0.581778\pi$
$882$		0			0
$883$	−3.92579	+	2.85225i	−0.132113	+	0.0959859i	−0.651879	−	0.758323i	$-0.726019\pi$
$883$	−3.92579	+	2.85225i	−0.132113	+	0.0959859i	0.519766	+	0.854309i	$0.326019\pi$
$884$	−2.25432	+	6.17356i	−0.0758209	+	0.207639i
$885$		0			0
$886$	−8.03144	−	57.3646i	−0.269821	−	1.92720i
$887$	−31.1009	+	10.1053i	−1.04426	+	0.339302i	−0.780415	−	0.625262i	$-0.784992\pi$
$887$	−31.1009	+	10.1053i	−1.04426	+	0.339302i	−0.263850	+	0.964564i	$0.584992\pi$
$888$		0			0
$889$	15.5007	−	47.7062i	0.519876	−	1.60002i
$890$	−10.5927	+	34.1487i	−0.355070	+	1.14467i
$891$		0			0
$892$	−0.762222	+	21.1908i	−0.0255211	+	0.709519i
$893$	4.02912			0.134829
$894$		0			0
$895$	−21.5951	+	22.9935i	−0.721843	+	0.768588i
$896$	−25.3260	+	37.2521i	−0.846084	+	1.24450i
$897$		0			0
$898$	−4.66037	−	33.2867i	−0.155518	−	1.11079i
$899$	−2.19465			−0.0731957
$900$		0			0
$901$	8.75188			0.291567
$902$	−15.2416	−	108.863i	−0.507490	−	3.62476i
$903$		0			0
$904$	−32.6112	−	36.3330i	−1.08463	−	1.20842i
$905$	13.1908	+	23.9976i	0.438478	+	0.797708i
$906$		0			0
$907$	40.0352			1.32935			0.664674	−	0.747133i	$-0.268570\pi$
$907$	40.0352			1.32935			0.664674	+	0.747133i	$0.268570\pi$
$908$	39.9077	+	1.43546i	1.32438	+	0.0476375i
$909$		0			0
$910$	−5.96073	−	17.5433i	−0.197596	−	0.581554i
$911$	14.0839	−	43.3459i	0.466621	−	1.43611i	−0.390311	−	0.920683i	$-0.627632\pi$
$911$	14.0839	−	43.3459i	0.466621	−	1.43611i	0.856932	−	0.515430i	$-0.172368\pi$
$912$		0			0
$913$	5.98638	−	1.94509i	0.198120	−	0.0643732i
$914$	4.43932	+	31.7079i	0.146840	+	1.04880i
$915$		0			0
$916$	27.2278	+	9.94241i	0.899631	+	0.328506i
$917$	50.2812	−	36.5314i	1.66043	−	1.20637i
$918$		0			0
$919$	−0.148831	−	0.204849i	−0.00490949	−	0.00675733i	0.806555	−	0.591159i	$-0.201329\pi$
$919$	−0.148831	−	0.204849i	−0.00490949	−	0.00675733i	−0.811465	+	0.584401i	$0.801329\pi$
$920$	−0.663163	+	29.3667i	−0.0218638	+	0.968190i
$921$		0			0
$922$	16.9557	+	2.99891i	0.558407	+	0.0987637i
$923$	−11.3882	−	3.70024i	−0.374846	−	0.121795i
$924$		0			0
$925$	−26.8861	+	1.68812i	−0.884008	+	0.0555049i
$926$	4.37227	+	8.97642i	0.143682	+	0.294983i
$927$		0			0
$928$	−2.94739	−	43.7975i	−0.0967529	−	1.43772i
$929$	12.9198	−	17.7826i	0.423886	−	0.583430i	−0.542650	−	0.839959i	$-0.682579\pi$
$929$	12.9198	−	17.7826i	0.423886	−	0.583430i	0.966536	+	0.256529i	$0.0825790\pi$
$930$		0			0
$931$	−12.8152	−	17.6386i	−0.420000	−	0.578081i
$932$	−9.45761	+	12.0791i	−0.309794	+	0.395664i
$933$		0			0
$934$	−3.29899	−	3.41979i	−0.107946	−	0.111899i
$935$	−30.5526	+	5.82621i	−0.999175	+	0.190537i
$936$		0			0
$937$	27.0812	−	8.79921i	0.884704	−	0.287458i	0.168795	−	0.985651i	$-0.446012\pi$
$937$	27.0812	−	8.79921i	0.884704	−	0.287458i	0.715909	+	0.698193i	$0.246012\pi$
$938$	−6.70015	+	6.46348i	−0.218768	+	0.211040i
$939$		0			0
$940$	6.50347	+	3.35147i	0.212120	+	0.109313i
$941$	−7.93480	+	2.57817i	−0.258667	+	0.0840461i	−0.435480	−	0.900198i	$-0.643421\pi$
$941$	−7.93480	+	2.57817i	−0.258667	+	0.0840461i	0.176813	+	0.984245i	$0.443421\pi$
$942$		0			0
$943$	−57.9561			−1.88731
$944$	−32.7587	−	27.6050i	−1.06620	−	0.898465i
$945$		0			0
$946$	6.47444	−	36.6062i	0.210502	−	1.19017i
$947$	−1.00236	+	1.37963i	−0.0325724	+	0.0448321i	−0.824993	−	0.565144i	$-0.808821\pi$
$947$	−1.00236	+	1.37963i	−0.0325724	+	0.0448321i	0.792420	+	0.609976i	$0.208821\pi$
$948$		0			0
$949$	−8.24801			−0.267742
$950$	−8.59212	−	15.1478i	−0.278765	−	0.491459i
$951$		0			0
$952$	−12.6080	+	21.7586i	−0.408626	+	0.705200i
$953$	22.8082	+	16.5712i	0.738831	+	0.536792i	0.892345	−	0.451354i	$-0.149059\pi$
$953$	22.8082	+	16.5712i	0.738831	+	0.536792i	−0.153513	+	0.988147i	$0.549059\pi$
$954$		0			0
$955$	44.8024	−	8.54358i	1.44977	−	0.276464i
$956$	0.465862	−	12.9516i	0.0150671	−	0.418884i
$957$		0			0
$958$	−43.2387	−	23.0195i	−1.39698	−	0.743725i
$959$	16.2942	+	50.1483i	0.526166	+	1.61937i
$960$		0			0
$961$	9.55481	−	29.4067i	0.308220	−	0.948603i
$962$	8.06985	−	7.78480i	0.260182	−	0.250992i
$963$		0			0
$964$	32.1726	+	47.8058i	1.03621	+	1.53972i
$965$	−5.82465	−	0.736199i	−0.187502	−	0.0236991i
$966$		0			0
$967$	−37.8384	+	27.4912i	−1.21680	+	0.884058i	−0.995831	−	0.0912226i	$-0.970923\pi$
$967$	−37.8384	+	27.4912i	−1.21680	+	0.884058i	−0.220971	+	0.975280i	$0.570923\pi$
$968$	76.8875	+	16.4692i	2.47126	+	0.529341i
$969$		0			0
$970$	38.6498	+	27.2984i	1.24097	+	0.876499i
$971$	−31.2706	−	22.7195i	−1.00352	−	0.729102i	−0.0406821	−	0.999172i	$-0.512953\pi$
$971$	−31.2706	−	22.7195i	−1.00352	−	0.729102i	−0.962841	+	0.270070i	$0.912953\pi$
$972$		0			0
$973$	−47.1445	−	15.3182i	−1.51138	−	0.491079i
$974$	−18.3978	−	37.7713i	−0.589504	−	1.21027i
$975$		0			0
$976$	−5.85093	−	23.6780i	−0.187284	−	0.757914i
$977$	−14.7310	+	45.3374i	−0.471287	+	1.45047i	0.379613	+	0.925145i	$0.376057\pi$
$977$	−14.7310	+	45.3374i	−0.471287	+	1.45047i	−0.850900	+	0.525328i	$0.823943\pi$
$978$		0			0
$979$	41.3961	−	56.9769i	1.32303	−	1.82099i
$980$	−6.01323	−	39.1305i	−0.192085	−	1.24998i
$981$		0			0
$982$	19.5190	+	40.0732i	0.622877	+	1.27879i
$983$	−2.01932	−	2.77936i	−0.0644064	−	0.0886477i	0.775599	−	0.631226i	$-0.217448\pi$
$983$	−2.01932	−	2.77936i	−0.0644064	−	0.0886477i	−0.840005	+	0.542579i	$0.817448\pi$
$984$		0			0
$985$	10.5595	−	11.2433i	0.336454	−	0.358241i
$986$	−3.39786	−	24.2692i	−0.108210	−	0.772889i
$987$		0			0
$988$	6.80883	+	2.48629i	0.216618	+	0.0790994i
$989$	−18.6403	−	6.05659i	−0.592726	−	0.192588i
$990$		0			0
$991$	−14.8841	+	4.83615i	−0.472810	+	0.153625i	−0.535723	−	0.844394i	$-0.679961\pi$
$991$	−14.8841	+	4.83615i	−0.472810	+	0.153625i	0.0629132	+	0.998019i	$0.479961\pi$
$992$	−1.55133	−	0.391107i	−0.0492547	−	0.0124177i
$993$		0			0
$994$	−40.4428	−	21.5310i	−1.28277	−	0.682921i
$995$	37.6811	+	4.76264i	1.19457	+	0.150986i
$996$		0			0
$997$	−32.5660	+	44.8233i	−1.03138	+	1.41957i	−0.127469	+	0.991843i	$0.540685\pi$
$997$	−32.5660	+	44.8233i	−1.03138	+	1.41957i	−0.903908	+	0.427726i	$0.859315\pi$
$998$	−0.638479	−	4.56034i	−0.0202107	−	0.144355i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.z.b.179.3	✓	224
3.2	odd	2	inner	900.2.z.b.179.54	yes	224
4.3	odd	2	inner	900.2.z.b.179.42	yes	224
12.11	even	2	inner	900.2.z.b.179.15	yes	224
25.19	even	10	inner	900.2.z.b.719.15	yes	224
75.44	odd	10	inner	900.2.z.b.719.42	yes	224
100.19	odd	10	inner	900.2.z.b.719.54	yes	224
300.119	even	10	inner	900.2.z.b.719.3	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.z.b.179.3	✓	224	1.1	even	1	trivial
900.2.z.b.179.15	yes	224	12.11	even	2	inner
900.2.z.b.179.42	yes	224	4.3	odd	2	inner
900.2.z.b.179.54	yes	224	3.2	odd	2	inner
900.2.z.b.719.3	yes	224	300.119	even	10	inner
900.2.z.b.719.15	yes	224	25.19	even	10	inner
900.2.z.b.719.42	yes	224	75.44	odd	10	inner
900.2.z.b.719.54	yes	224	100.19	odd	10	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40055 + 0.196087i) q^{2} +(1.92310 - 0.549261i) q^{4} +(0.280394 - 2.21842i) q^{5} +3.98153 q^{7} +(-2.58570 + 1.14636i) q^{8} +(0.0422965 + 3.16199i) q^{10} +(1.92487 - 5.92413i) q^{11} +(-1.39956 + 0.454745i) q^{13} +(-5.57634 + 0.780726i) q^{14} +(3.39663 - 2.11257i) q^{16} +(1.80658 - 1.31256i) q^{17} +(-1.44762 - 1.99248i) q^{19} +(-0.679265 - 4.42025i) q^{20} +(-1.53423 + 8.67450i) q^{22} +(4.41714 + 1.43522i) q^{23} +(-4.84276 - 1.24406i) q^{25} +(1.87099 - 0.911330i) q^{26} +(7.65687 - 2.18690i) q^{28} +(-4.56115 + 6.27789i) q^{29} +(0.166237 + 0.228806i) q^{31} +(-4.34291 + 3.62480i) q^{32} +(-2.27284 + 2.19256i) q^{34} +(1.11640 - 8.83269i) q^{35} +(5.12410 - 1.66492i) q^{37} +(2.41817 + 2.50672i) q^{38} +(1.81810 + 6.05760i) q^{40} +(-11.8678 + 3.85608i) q^{41} -4.21998 q^{43} +(0.447819 - 12.4499i) q^{44} +(-6.46787 - 1.14395i) q^{46} +(-0.961595 + 1.32352i) q^{47} +8.85255 q^{49} +(7.02649 + 0.792773i) q^{50} +(-2.44172 + 1.64324i) q^{52} +(3.17072 + 2.30367i) q^{53} +(-12.6025 - 5.93125i) q^{55} +(-10.2950 + 4.56428i) q^{56} +(5.15712 - 9.68690i) q^{58} +(-3.30948 - 10.1855i) q^{59} +(1.88425 - 5.79911i) q^{61} +(-0.277690 - 0.287858i) q^{62} +(5.37170 - 5.92831i) q^{64} +(0.616386 + 3.23232i) q^{65} +(1.33759 - 0.971818i) q^{67} +(2.75330 - 3.51647i) q^{68} +(0.168404 + 12.5896i) q^{70} +(6.58294 + 4.78279i) q^{71} +(5.33053 + 1.73199i) q^{73} +(-6.85011 + 3.33658i) q^{74} +(-3.87832 - 3.03662i) q^{76} +(7.66391 - 23.5871i) q^{77} +(-1.28398 + 1.76724i) q^{79} +(-3.73416 - 8.12749i) q^{80} +(15.8654 - 7.72777i) q^{82} +(0.593962 + 0.817518i) q^{83} +(-2.40525 - 4.37579i) q^{85} +(5.91031 - 0.827484i) q^{86} +(1.81408 + 17.5246i) q^{88} +(10.7530 + 3.49386i) q^{89} +(-5.57239 + 1.81058i) q^{91} +(9.28292 + 0.333902i) q^{92} +(1.08724 - 2.04222i) q^{94} +(-4.82607 + 2.65276i) q^{95} +(8.79522 - 12.1056i) q^{97} +(-12.3985 + 1.73587i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 8 q^{4} - 12 q^{10} - 8 q^{16} - 8 q^{25} + 92 q^{34} + 40 q^{37} + 36 q^{40} - 40 q^{46} + 368 q^{49} - 100 q^{52} - 120 q^{58} + 48 q^{61} - 16 q^{64} - 40 q^{70} + 24 q^{76} - 120 q^{85} - 120 q^{88}+ \cdots + 200 q^{97}+O(q^{100}) \) 224 * q + 8 * q^4 - 12 * q^10 - 8 * q^16 - 8 * q^25 + 92 * q^34 + 40 * q^37 + 36 * q^40 - 40 * q^46 + 368 * q^49 - 100 * q^52 - 120 * q^58 + 48 * q^61 - 16 * q^64 - 40 * q^70 + 24 * q^76 - 120 * q^85 - 120 * q^88 - 4 * q^94 + 200 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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