LMFDB - Embedded newform 2100.2.ce.e.157.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(157,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("2100.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.6
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.e.1993.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{3} +(2.42120 - 1.06666i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{3} +(2.42120 - 1.06666i) q^{7} +(0.866025 - 0.500000i) q^{9} +(-1.81039 + 3.13569i) q^{11} +(-4.28466 - 4.28466i) q^{13} +(-1.60643 - 5.99526i) q^{17} +(0.974414 + 1.68773i) q^{19} +(2.06263 - 1.65697i) q^{21} +(5.55927 + 1.48960i) q^{23} +(0.707107 - 0.707107i) q^{27} -6.10032i q^{29} +(1.14260 + 0.659678i) q^{31} +(-0.937128 + 3.49741i) q^{33} +(3.08980 - 11.5313i) q^{37} +(-5.24762 - 3.02971i) q^{39} -4.50932i q^{41} +(6.04091 - 6.04091i) q^{43} +(-7.81202 - 2.09322i) q^{47} +(4.72446 - 5.16522i) q^{49} +(-3.10337 - 5.37520i) q^{51} +(2.59306 + 9.67743i) q^{53} +(1.37803 + 1.37803i) q^{57} +(-3.43249 + 5.94524i) q^{59} +(-5.74833 + 3.31880i) q^{61} +(1.56349 - 2.13436i) q^{63} +(3.08072 - 0.825476i) q^{67} +5.75538 q^{69} +1.00837 q^{71} +(2.86619 - 0.767993i) q^{73} +(-1.03861 + 9.52323i) q^{77} +(10.9434 - 6.31817i) q^{79} +(0.500000 - 0.866025i) q^{81} +(4.26779 + 4.26779i) q^{83} +(-1.57888 - 5.89246i) q^{87} +(5.82694 + 10.0926i) q^{89} +(-14.9443 - 5.80376i) q^{91} +(1.27440 + 0.341474i) q^{93} +(-8.89673 + 8.89673i) q^{97} +3.62079i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) $ 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.42120	−	1.06666i	0.915129	−	0.403160i
$7$	2.42120	−	1.06666i	0.915129	−	0.403160i
$8$		0			0
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	−1.81039	+	3.13569i	−0.545854	+	0.945447i	0.452699	+	0.891664i	$0.350461\pi$
$11$	−1.81039	+	3.13569i	−0.545854	+	0.945447i	−0.998553	+	0.0537833i	$0.982872\pi$
$12$		0			0
$13$	−4.28466	−	4.28466i	−1.18835	−	1.18835i	−0.977523	−	0.210829i	$-0.932384\pi$
$13$	−4.28466	−	4.28466i	−1.18835	−	1.18835i	−0.210829	−	0.977523i	$-0.567616\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.60643	−	5.99526i	−0.389615	−	1.45406i	−0.830761	−	0.556629i	$-0.812095\pi$
$17$	−1.60643	−	5.99526i	−0.389615	−	1.45406i	0.441146	−	0.897435i	$-0.354572\pi$
$18$		0			0
$19$	0.974414	+	1.68773i	0.223546	+	0.387193i	0.955882	−	0.293750i	$-0.0949034\pi$
$19$	0.974414	+	1.68773i	0.223546	+	0.387193i	−0.732336	+	0.680943i	$0.761570\pi$
$20$		0			0
$21$	2.06263	−	1.65697i	0.450103	−	0.361581i
$22$		0			0
$23$	5.55927	+	1.48960i	1.15919	+	0.310604i	0.786642	−	0.617410i	$-0.211818\pi$
$23$	5.55927	+	1.48960i	1.15919	+	0.310604i	0.372547	+	0.928013i	$0.378485\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	6.10032i		−	1.13280i	−0.824130	−	0.566401i	$-0.808336\pi$
$29$		−	6.10032i		−	1.13280i	0.824130	−	0.566401i	$-0.191664\pi$
$30$		0			0
$31$	1.14260	+	0.659678i	0.205216	+	0.118482i	0.599086	−	0.800685i	$-0.295531\pi$
$31$	1.14260	+	0.659678i	0.205216	+	0.118482i	−0.393870	+	0.919166i	$0.628864\pi$
$32$		0			0
$33$	−0.937128	+	3.49741i	−0.163133	+	0.608821i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.08980	−	11.5313i	0.507960	−	1.89573i	0.0680680	−	0.997681i	$-0.478317\pi$
$37$	3.08980	−	11.5313i	0.507960	−	1.89573i	0.439892	−	0.898051i	$-0.355017\pi$
$38$		0			0
$39$	−5.24762	−	3.02971i	−0.840292	−	0.485143i
$40$		0			0
$41$		−	4.50932i		−	0.704237i	−0.935955	−	0.352119i	$-0.885461\pi$
$41$		−	4.50932i		−	0.704237i	0.935955	−	0.352119i	$-0.114539\pi$
$42$		0			0
$43$	6.04091	−	6.04091i	0.921231	−	0.921231i	−0.0758859	−	0.997117i	$-0.524178\pi$
$43$	6.04091	−	6.04091i	0.921231	−	0.921231i	0.997117	+	0.0758859i	$0.0241785\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.81202	−	2.09322i	−1.13950	−	0.305328i	−0.360750	−	0.932662i	$-0.617479\pi$
$47$	−7.81202	−	2.09322i	−1.13950	−	0.305328i	−0.778750	+	0.627334i	$0.784146\pi$
$48$		0			0
$49$	4.72446	−	5.16522i	0.674923	−	0.737888i
$50$		0			0
$51$	−3.10337	−	5.37520i	−0.434559	−	0.752679i
$52$		0			0
$53$	2.59306	+	9.67743i	0.356184	+	1.32930i	0.878988	+	0.476844i	$0.158219\pi$
$53$	2.59306	+	9.67743i	0.356184	+	1.32930i	−0.522804	+	0.852453i	$0.675114\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.37803	+	1.37803i	0.182524	+	0.182524i
$58$		0			0
$59$	−3.43249	+	5.94524i	−0.446872	+	0.774005i	−0.998181	−	0.0602967i	$-0.980795\pi$
$59$	−3.43249	+	5.94524i	−0.446872	+	0.774005i	0.551309	+	0.834301i	$0.314129\pi$
$60$		0			0
$61$	−5.74833	+	3.31880i	−0.735998	+	0.424928i	−0.820612	−	0.571485i	$-0.806367\pi$
$61$	−5.74833	+	3.31880i	−0.735998	+	0.424928i	0.0846147	+	0.996414i	$0.473034\pi$
$62$		0			0
$63$	1.56349	−	2.13436i	0.196982	−	0.268904i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.08072	−	0.825476i	0.376369	−	0.100848i	−0.0656749	−	0.997841i	$-0.520920\pi$
$67$	3.08072	−	0.825476i	0.376369	−	0.100848i	0.442044	+	0.896993i	$0.354253\pi$
$68$		0			0
$69$	5.75538			0.692867
$70$		0			0
$71$	1.00837			0.119671			0.0598357	−	0.998208i	$-0.480942\pi$
$71$	1.00837			0.119671			0.0598357	+	0.998208i	$0.480942\pi$
$72$		0			0
$73$	2.86619	−	0.767993i	0.335462	−	0.0898867i	−0.0871561	−	0.996195i	$-0.527778\pi$
$73$	2.86619	−	0.767993i	0.335462	−	0.0898867i	0.422618	+	0.906308i	$0.361111\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.03861	+	9.52323i	−0.118360	+	1.08527i
$78$		0			0
$79$	10.9434	−	6.31817i	1.23123	−	0.710850i	0.263943	−	0.964538i	$-0.414977\pi$
$79$	10.9434	−	6.31817i	1.23123	−	0.710850i	0.967286	+	0.253688i	$0.0816437\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	4.26779	+	4.26779i	0.468451	+	0.468451i	0.901412	−	0.432961i	$-0.142531\pi$
$83$	4.26779	+	4.26779i	0.468451	+	0.468451i	−0.432961	+	0.901412i	$0.642531\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.57888	−	5.89246i	−0.169274	−	0.631738i
$88$		0			0
$89$	5.82694	+	10.0926i	0.617654	+	1.06981i	0.989913	+	0.141679i	$0.0452502\pi$
$89$	5.82694	+	10.0926i	0.617654	+	1.06981i	−0.372258	+	0.928129i	$0.621416\pi$
$90$		0			0
$91$	−14.9443	−	5.80376i	−1.56659	−	0.608399i
$92$		0			0
$93$	1.27440	+	0.341474i	0.132149	+	0.0354092i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−8.89673	+	8.89673i	−0.903327	+	0.903327i	−0.995722	−	0.0923958i	$-0.970547\pi$
$97$	−8.89673	+	8.89673i	−0.903327	+	0.903327i	0.0923958	+	0.995722i	$0.470547\pi$
$98$		0			0
$99$			3.62079i			0.363903i
$100$		0			0
$101$	−4.20228	−	2.42619i	−0.418142	−	0.241414i	0.276140	−	0.961117i	$-0.410945\pi$
$101$	−4.20228	−	2.42619i	−0.418142	−	0.241414i	−0.694282	+	0.719703i	$0.744278\pi$
$102$		0			0
$103$	−0.189067	+	0.705607i	−0.0186293	+	0.0695255i	−0.974615	−	0.223889i	$-0.928125\pi$
$103$	−0.189067	+	0.705607i	−0.0186293	+	0.0695255i	0.955985	+	0.293414i	$0.0947915\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.926512	−	3.45779i	0.0895693	−	0.334277i	−0.906571	−	0.422054i	$-0.861309\pi$
$107$	0.926512	−	3.45779i	0.0895693	−	0.334277i	0.996140	+	0.0877764i	$0.0279761\pi$
$108$		0			0
$109$	−4.45306	−	2.57098i	−0.426526	−	0.246255i	0.271339	−	0.962484i	$-0.412533\pi$
$109$	−4.45306	−	2.57098i	−0.426526	−	0.246255i	−0.697866	+	0.716229i	$0.745867\pi$
$110$		0			0
$111$		−	11.9381i		−	1.13311i
$112$		0			0
$113$	−0.711744	+	0.711744i	−0.0669552	+	0.0669552i	−0.739791	−	0.672836i	$-0.765076\pi$
$113$	−0.711744	+	0.711744i	−0.0669552	+	0.0669552i	0.672836	+	0.739791i	$0.265076\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.85296	−	1.56830i	−0.541106	−	0.144989i
$118$		0			0
$119$	−10.2844	−	12.8022i	−0.942770	−	1.17358i
$120$		0			0
$121$	−1.05505	−	1.82739i	−0.0959133	−	0.166127i
$122$		0			0
$123$	−1.16710	−	4.35567i	−0.105234	−	0.392737i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−4.20890	−	4.20890i	−0.373479	−	0.373479i	0.495264	−	0.868743i	$-0.335071\pi$
$127$	−4.20890	−	4.20890i	−0.373479	−	0.373479i	−0.868743	+	0.495264i	$0.835071\pi$
$128$		0			0
$129$	4.27157	−	7.39858i	0.376091	−	0.651408i
$130$		0			0
$131$	−1.37825	+	0.795736i	−0.120419	+	0.0695238i	−0.558999	−	0.829168i	$-0.688815\pi$
$131$	−1.37825	+	0.795736i	−0.120419	+	0.0695238i	0.438581	+	0.898692i	$0.355481\pi$
$132$		0			0
$133$	4.15950	+	3.04698i	0.360674	+	0.264207i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	22.2479	−	5.96131i	1.90077	−	0.509309i	0.904141	−	0.427234i	$-0.140512\pi$
$137$	22.2479	−	5.96131i	1.90077	−	0.509309i	0.996626	−	0.0820753i	$-0.0261548\pi$
$138$		0			0
$139$	−1.67374			−0.141964			−0.0709822	−	0.997478i	$-0.522613\pi$
$139$	−1.67374			−0.141964			−0.0709822	+	0.997478i	$0.522613\pi$
$140$		0			0
$141$	−8.08760			−0.681099
$142$		0			0
$143$	21.1923	−	5.67846i	1.77219	−	0.474857i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.22662	−	6.21200i	0.266128	−	0.512357i
$148$		0			0
$149$	0.512920	−	0.296135i	0.0420201	−	0.0242603i	−0.478843	−	0.877901i	$-0.658944\pi$
$149$	0.512920	−	0.296135i	0.0420201	−	0.0242603i	0.520863	+	0.853640i	$0.325610\pi$
$150$		0			0
$151$	6.90624	−	11.9620i	0.562022	−	0.973451i	−0.435298	−	0.900287i	$-0.643357\pi$
$151$	6.90624	−	11.9620i	0.562022	−	0.973451i	0.997320	−	0.0731644i	$-0.0233098\pi$
$152$		0			0
$153$	−4.38883	−	4.38883i	−0.354816	−	0.354816i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−6.04119	−	22.5460i	−0.482140	−	1.79937i	−0.592609	−	0.805490i	$-0.701902\pi$
$157$	−6.04119	−	22.5460i	−0.482140	−	1.79937i	0.110469	−	0.993880i	$-0.464765\pi$
$158$		0			0
$159$	5.00941	+	8.67655i	0.397272	+	0.688095i
$160$		0			0
$161$	15.0490	−	2.32323i	1.18603	−	0.183096i
$162$		0			0
$163$	−19.6665	−	5.26962i	−1.54040	−	0.412749i	−0.614005	−	0.789302i	$-0.710442\pi$
$163$	−19.6665	−	5.26962i	−1.54040	−	0.412749i	−0.926395	+	0.376554i	$0.877109\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.04294	+	6.04294i	−0.467617	+	0.467617i	−0.901142	−	0.433525i	$-0.857270\pi$
$167$	−6.04294	+	6.04294i	−0.467617	+	0.467617i	0.433525	+	0.901142i	$0.357270\pi$
$168$		0			0
$169$			23.7167i			1.82436i
$170$		0			0
$171$	1.68773	+	0.974414i	0.129064	+	0.0745153i
$172$		0			0
$173$	0.0594924	−	0.222029i	0.00452312	−	0.0168805i	−0.963627	−	0.267249i	$-0.913885\pi$
$173$	0.0594924	−	0.222029i	0.00452312	−	0.0168805i	0.968151	+	0.250369i	$0.0805519\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.77679	+	6.63106i	−0.133551	+	0.498421i
$178$		0			0
$179$	−2.94700	−	1.70145i	−0.220269	−	0.127173i	0.385806	−	0.922580i	$-0.373924\pi$
$179$	−2.94700	−	1.70145i	−0.220269	−	0.127173i	−0.606075	+	0.795408i	$0.707257\pi$
$180$		0			0
$181$		−	10.8261i		−	0.804698i	−0.915486	−	0.402349i	$-0.868194\pi$
$181$		−	10.8261i		−	0.804698i	0.915486	−	0.402349i	$-0.131806\pi$
$182$		0			0
$183$	−4.69349	+	4.69349i	−0.346953	+	0.346953i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	21.7076	+	5.81652i	1.58741	+	0.425346i
$188$		0			0
$189$	0.957806	−	2.46629i	0.0696701	−	0.179397i
$190$		0			0
$191$	7.19154	+	12.4561i	0.520361	+	0.901292i	0.999720	+	0.0236731i	$0.00753608\pi$
$191$	7.19154	+	12.4561i	0.520361	+	0.901292i	−0.479358	+	0.877619i	$0.659131\pi$
$192$		0			0
$193$	2.12512	+	7.93104i	0.152969	+	0.570889i	0.999271	+	0.0381846i	$0.0121575\pi$
$193$	2.12512	+	7.93104i	0.152969	+	0.570889i	−0.846301	+	0.532704i	$0.821176\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.73262	−	1.73262i	−0.123444	−	0.123444i	0.642686	−	0.766130i	$-0.277820\pi$
$197$	−1.73262	−	1.73262i	−0.123444	−	0.123444i	−0.766130	+	0.642686i	$0.777820\pi$
$198$		0			0
$199$	3.31553	−	5.74266i	0.235032	−	0.407087i	−0.724250	−	0.689537i	$-0.757814\pi$
$199$	3.31553	−	5.74266i	0.235032	−	0.407087i	0.959282	+	0.282451i	$0.0911473\pi$
$200$		0			0
$201$	2.76209	−	1.59470i	0.194823	−	0.112481i
$202$		0			0
$203$	−6.50698	−	14.7701i	−0.456701	−	1.03666i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	5.55927	−	1.48960i	0.386396	−	0.103535i
$208$		0			0
$209$	−7.05629			−0.488094
$210$		0			0
$211$	−13.7203			−0.944546			−0.472273	−	0.881452i	$-0.656566\pi$
$211$	−13.7203			−0.944546			−0.472273	+	0.881452i	$0.656566\pi$
$212$		0			0
$213$	0.974010	−	0.260985i	0.0667381	−	0.0178824i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.47011	+	0.378451i	0.235566	+	0.0256909i
$218$		0			0
$219$	2.56975	−	1.48365i	0.173648	−	0.100256i
$220$		0			0
$221$	−18.8047	+	32.5707i	−1.26494	+	2.19094i
$222$		0			0
$223$	9.72477	+	9.72477i	0.651219	+	0.651219i	0.953287	−	0.302068i	$-0.0976768\pi$
$223$	9.72477	+	9.72477i	0.651219	+	0.651219i	−0.302068	+	0.953287i	$0.597677\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.34390	+	5.01550i	0.0891978	+	0.332891i	0.996076	−	0.0885022i	$-0.0282080\pi$
$227$	1.34390	+	5.01550i	0.0891978	+	0.332891i	−0.906878	+	0.421393i	$0.861541\pi$
$228$		0			0
$229$	2.82068	+	4.88556i	0.186396	+	0.322847i	0.944046	−	0.329814i	$-0.106986\pi$
$229$	2.82068	+	4.88556i	0.186396	+	0.322847i	−0.757650	+	0.652661i	$0.773653\pi$
$230$		0			0
$231$	1.46158	+	9.46755i	0.0961647	+	0.622919i
$232$		0			0
$233$	3.31168	+	0.887361i	0.216955	+	0.0581329i	0.365659	−	0.930749i	$-0.380844\pi$
$233$	3.31168	+	0.887361i	0.216955	+	0.0581329i	−0.148704	+	0.988882i	$0.547510\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	8.93525	−	8.93525i	0.580407	−	0.580407i
$238$		0			0
$239$			15.8311i			1.02403i	0.858978	+	0.512013i	$0.171100\pi$
$239$			15.8311i			1.02403i	−0.858978	+	0.512013i	$0.828900\pi$
$240$		0			0
$241$	6.27425	+	3.62244i	0.404160	+	0.233342i	0.688277	−	0.725448i	$-0.258367\pi$
$241$	6.27425	+	3.62244i	0.404160	+	0.233342i	−0.284117	+	0.958789i	$0.591701\pi$
$242$		0			0
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.05634	−	11.4064i	0.194470	−	0.725772i
$248$		0			0
$249$	5.22696	+	3.01778i	0.331245	+	0.191244i
$250$		0			0
$251$			22.2337i			1.40338i	0.712484	+	0.701688i	$0.247570\pi$
$251$			22.2337i			1.40338i	−0.712484	+	0.701688i	$0.752430\pi$
$252$		0			0
$253$	−14.7354	+	14.7354i	−0.926407	+	0.926407i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−18.7823	−	5.03271i	−1.17161	−	0.313932i	−0.380016	−	0.924980i	$-0.624081\pi$
$257$	−18.7823	−	5.03271i	−1.17161	−	0.313932i	−0.791593	+	0.611048i	$0.790748\pi$
$258$		0			0
$259$	−4.81895	−	31.2154i	−0.299435	−	1.93963i
$260$		0			0
$261$	−3.05016	−	5.28303i	−0.188800	−	0.327012i
$262$		0			0
$263$	1.39511	+	5.20662i	0.0860262	+	0.321054i	0.995507	−	0.0946928i	$-0.0301869\pi$
$263$	1.39511	+	5.20662i	0.0860262	+	0.321054i	−0.909480	+	0.415747i	$0.863520\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	8.24053	+	8.24053i	0.504313	+	0.504313i
$268$		0			0
$269$	−5.48253	+	9.49601i	−0.334276	+	0.578982i	−0.983345	−	0.181747i	$-0.941825\pi$
$269$	−5.48253	+	9.49601i	−0.334276	+	0.578982i	0.649070	+	0.760729i	$0.275158\pi$
$270$		0			0
$271$	13.6426	−	7.87655i	0.828728	−	0.478466i	−0.0246891	−	0.999695i	$-0.507860\pi$
$271$	13.6426	−	7.87655i	0.828728	−	0.478466i	0.853417	+	0.521229i	$0.174526\pi$
$272$		0			0
$273$	−15.9372	−	1.73812i	−0.964566	−	0.105196i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−10.0804	+	2.70105i	−0.605675	+	0.162290i	−0.548607	−	0.836080i	$-0.684842\pi$
$277$	−10.0804	+	2.70105i	−0.605675	+	0.162290i	−0.0570679	+	0.998370i	$0.518175\pi$
$278$		0			0
$279$	1.31936			0.0789877
$280$		0			0
$281$	−10.3444			−0.617098			−0.308549	−	0.951208i	$-0.599843\pi$
$281$	−10.3444			−0.617098			−0.308549	+	0.951208i	$0.599843\pi$
$282$		0			0
$283$	3.26679	−	0.875333i	0.194190	−	0.0520332i	−0.160413	−	0.987050i	$-0.551283\pi$
$283$	3.26679	−	0.875333i	0.194190	−	0.0520332i	0.354603	+	0.935017i	$0.384616\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.80992	−	10.9180i	−0.283921	−	0.644468i
$288$		0			0
$289$	−18.6401	+	10.7619i	−1.09648	+	0.633051i
$290$		0			0
$291$	−6.29094	+	10.8962i	−0.368782	+	0.638748i
$292$		0			0
$293$	−0.204738	−	0.204738i	−0.0119609	−	0.0119609i	0.701101	−	0.713062i	$-0.252692\pi$
$293$	−0.204738	−	0.204738i	−0.0119609	−	0.0119609i	−0.713062	+	0.701101i	$0.752692\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.937128	+	3.49741i	0.0543777	+	0.202940i
$298$		0			0
$299$	−17.4372	−	30.2021i	−1.00842	−	1.74663i
$300$		0			0
$301$	8.18267	−	21.0699i	0.471641	−	1.21445i
$302$		0			0
$303$	−4.68703	−	1.25589i	−0.269263	−	0.0721488i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−20.2957	+	20.2957i	−1.15834	+	1.15834i	−0.173502	+	0.984833i	$0.555508\pi$
$307$	−20.2957	+	20.2957i	−1.15834	+	1.15834i	−0.984833	+	0.173502i	$0.944492\pi$
$308$		0			0
$309$			0.730498i			0.0415566i
$310$		0			0
$311$	20.6715	+	11.9347i	1.17217	+	0.676754i	0.954191	−	0.299198i	$-0.0967192\pi$
$311$	20.6715	+	11.9347i	1.17217	+	0.676754i	0.217982	+	0.975953i	$0.430053\pi$
$312$		0			0
$313$	0.0505981	−	0.188835i	0.00285997	−	0.0106736i	−0.964481	−	0.264152i	$-0.914908\pi$
$313$	0.0505981	−	0.188835i	0.00285997	−	0.0106736i	0.967341	+	0.253478i	$0.0815746\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.56465	+	20.7676i	−0.312542	+	1.16642i	0.613714	+	0.789528i	$0.289675\pi$
$317$	−5.56465	+	20.7676i	−0.312542	+	1.16642i	−0.926256	+	0.376895i	$0.876992\pi$
$318$		0			0
$319$	19.1287	+	11.0440i	1.07100	+	0.618344i
$320$		0			0
$321$		−	3.57977i		−	0.199803i
$322$		0			0
$323$	8.55308	−	8.55308i	0.475906	−	0.475906i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−4.96675	−	1.33084i	−0.274662	−	0.0735954i
$328$		0			0
$329$	−21.1473	+	3.26466i	−1.16589	+	0.179987i
$330$		0			0
$331$	7.85671	+	13.6082i	0.431844	+	0.747975i	0.997032	−	0.0769867i	$-0.0245299\pi$
$331$	7.85671	+	13.6082i	0.431844	+	0.747975i	−0.565189	+	0.824962i	$0.691197\pi$
$332$		0			0
$333$	−3.08980	−	11.5313i	−0.169320	−	0.631910i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.60208	+	2.60208i	0.141745	+	0.141745i	0.774418	−	0.632674i	$-0.218043\pi$
$337$	2.60208	+	2.60208i	0.141745	+	0.141745i	−0.632674	+	0.774418i	$0.718043\pi$
$338$		0			0
$339$	−0.503279	+	0.871705i	−0.0273344	+	0.0473445i
$340$		0			0
$341$	−4.13709	+	2.38855i	−0.224036	+	0.129347i
$342$		0			0
$343$	5.92935	−	17.5454i	0.320155	−	0.947365i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.1878	−	2.99777i	0.600593	−	0.160929i	0.0543033	−	0.998524i	$-0.482706\pi$
$347$	11.1878	−	2.99777i	0.600593	−	0.160929i	0.546290	+	0.837596i	$0.316040\pi$
$348$		0			0
$349$	3.30208			0.176756			0.0883781	−	0.996087i	$-0.471832\pi$
$349$	3.30208			0.176756			0.0883781	+	0.996087i	$0.471832\pi$
$350$		0			0
$351$	−6.05943			−0.323428
$352$		0			0
$353$	−3.19326	+	0.855632i	−0.169960	+	0.0455407i	−0.342796	−	0.939410i	$-0.611374\pi$
$353$	−3.19326	+	0.855632i	−0.169960	+	0.0455407i	0.172835	+	0.984951i	$0.444707\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−13.2474	−	9.70421i	−0.701128	−	0.513601i
$358$		0			0
$359$	16.2958	−	9.40841i	0.860061	−	0.496557i	−0.00397147	−	0.999992i	$-0.501264\pi$
$359$	16.2958	−	9.40841i	0.860061	−	0.496557i	0.864033	+	0.503435i	$0.167931\pi$
$360$		0			0
$361$	7.60104	−	13.1654i	0.400055	−	0.692915i
$362$		0			0
$363$	−1.49206	−	1.49206i	−0.0783129	−	0.0783129i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	9.29163	+	34.6768i	0.485019	+	1.81012i	0.579974	+	0.814635i	$0.303063\pi$
$367$	9.29163	+	34.6768i	0.485019	+	1.81012i	−0.0949552	+	0.995482i	$0.530271\pi$
$368$		0			0
$369$	−2.25466	−	3.90519i	−0.117373	−	0.203296i
$370$		0			0
$371$	16.6009	+	20.6651i	0.861875	+	1.07288i
$372$		0			0
$373$	19.2418	+	5.15582i	0.996303	+	0.266958i	0.719896	−	0.694082i	$-0.244190\pi$
$373$	19.2418	+	5.15582i	0.996303	+	0.266958i	0.276407	+	0.961041i	$0.410856\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−26.1378	+	26.1378i	−1.34617	+	1.34617i
$378$		0			0
$379$		−	10.2572i		−	0.526877i	−0.964676	−	0.263438i	$-0.915143\pi$
$379$		−	10.2572i		−	0.526877i	0.964676	−	0.263438i	$-0.0848565\pi$
$380$		0			0
$381$	−5.15482	−	2.97614i	−0.264090	−	0.152472i
$382$		0			0
$383$	−4.90072	+	18.2897i	−0.250415	+	0.934562i	0.720169	+	0.693799i	$0.244064\pi$
$383$	−4.90072	+	18.2897i	−0.250415	+	0.934562i	−0.970584	+	0.240763i	$0.922602\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.21113	−	8.25204i	0.112398	−	0.419475i
$388$		0			0
$389$	18.7017	+	10.7974i	0.948212	+	0.547451i	0.892525	−	0.450998i	$-0.148932\pi$
$389$	18.7017	+	10.7974i	0.948212	+	0.547451i	0.0556873	+	0.998448i	$0.482265\pi$
$390$		0			0
$391$		−	35.7222i		−	1.80655i
$392$		0			0
$393$	−1.12534	+	1.12534i	−0.0567659	+	0.0567659i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.49089	+	1.20333i	0.225391	+	0.0603935i	0.369747	−	0.929132i	$-0.379444\pi$
$397$	4.49089	+	1.20333i	0.225391	+	0.0603935i	−0.144356	+	0.989526i	$0.546111\pi$
$398$		0			0
$399$	4.80638	+	1.86660i	0.240620	+	0.0934468i
$400$		0			0
$401$	−2.93969	−	5.09170i	−0.146801	−	0.254267i	0.783242	−	0.621717i	$-0.213564\pi$
$401$	−2.93969	−	5.09170i	−0.146801	−	0.254267i	−0.930044	+	0.367449i	$0.880231\pi$
$402$		0			0
$403$	−2.06914	−	7.72213i	−0.103071	−	0.384667i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	30.5648	+	30.5648i	1.51504	+	1.51504i
$408$		0			0
$409$	1.71882	−	2.97708i	0.0849900	−	0.147207i	−0.820397	−	0.571794i	$-0.806248\pi$
$409$	1.71882	−	2.97708i	0.0849900	−	0.147207i	0.905387	+	0.424587i	$0.139581\pi$
$410$		0			0
$411$	19.9469	−	11.5164i	0.983910	−	0.568060i
$412$		0			0
$413$	−1.96919	+	18.0560i	−0.0968974	+	0.888475i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.61670	+	0.433195i	−0.0791704	+	0.0212136i
$418$		0			0
$419$	−27.8490			−1.36051			−0.680255	−	0.732975i	$-0.738131\pi$
$419$	−27.8490			−1.36051			−0.680255	+	0.732975i	$0.738131\pi$
$420$		0			0
$421$	16.3523			0.796961			0.398480	−	0.917177i	$-0.369538\pi$
$421$	16.3523			0.796961			0.398480	+	0.917177i	$0.369538\pi$
$422$		0			0
$423$	−7.81202	+	2.09322i	−0.379833	+	0.101776i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.3778	+	14.1670i	−0.502219	+	0.685590i
$428$		0			0
$429$	19.0005	−	10.9699i	0.917353	−	0.529634i
$430$		0			0
$431$	16.4853	−	28.5534i	0.794069	−	1.37537i	−0.129359	−	0.991598i	$-0.541292\pi$
$431$	16.4853	−	28.5534i	0.794069	−	1.37537i	0.923428	−	0.383771i	$-0.125375\pi$
$432$		0			0
$433$	−16.6251	−	16.6251i	−0.798952	−	0.798952i	0.183979	−	0.982930i	$-0.441102\pi$
$433$	−16.6251	−	16.6251i	−0.798952	−	0.798952i	−0.982930	+	0.183979i	$0.941102\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.90298	+	10.8341i	0.138868	+	0.518263i
$438$		0			0
$439$	3.02976	+	5.24771i	0.144603	+	0.250459i	0.929225	−	0.369515i	$-0.120476\pi$
$439$	3.02976	+	5.24771i	0.144603	+	0.250459i	−0.784622	+	0.619975i	$0.787143\pi$
$440$		0			0
$441$	1.50890	−	6.83544i	0.0718523	−	0.325497i
$442$		0			0
$443$	5.14893	+	1.37965i	0.244633	+	0.0655493i	0.379052	−	0.925375i	$-0.376250\pi$
$443$	5.14893	+	1.37965i	0.244633	+	0.0655493i	−0.134419	+	0.990925i	$0.542917\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.418798	−	0.418798i	0.0198084	−	0.0198084i
$448$		0			0
$449$			40.8974i			1.93007i	0.262121	+	0.965035i	$0.415578\pi$
$449$			40.8974i			1.93007i	−0.262121	+	0.965035i	$0.584422\pi$
$450$		0			0
$451$	14.1398	+	8.16364i	0.665819	+	0.384411i
$452$		0			0
$453$	3.57493	−	13.3418i	0.167965	−	0.626854i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.95465	−	22.2231i	0.278547	−	1.03955i	−0.674880	−	0.737927i	$-0.735805\pi$
$457$	5.95465	−	22.2231i	0.278547	−	1.03955i	0.953427	−	0.301624i	$-0.0975286\pi$
$458$		0			0
$459$	−5.37520	−	3.10337i	−0.250893	−	0.144853i
$460$		0			0
$461$			23.3880i			1.08929i	0.838667	+	0.544645i	$0.183336\pi$
$461$			23.3880i			1.08929i	−0.838667	+	0.544645i	$0.816664\pi$
$462$		0			0
$463$	−10.7736	+	10.7736i	−0.500691	+	0.500691i	−0.911653	−	0.410962i	$-0.865193\pi$
$463$	−10.7736	+	10.7736i	−0.500691	+	0.500691i	0.410962	+	0.911653i	$0.365193\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.31046	−	1.69088i	−0.292013	−	0.0782447i	0.109839	−	0.993949i	$-0.464967\pi$
$467$	−6.31046	−	1.69088i	−0.292013	−	0.0782447i	−0.401852	+	0.915705i	$0.631633\pi$
$468$		0			0
$469$	6.57854	−	5.28473i	0.303769	−	0.244026i
$470$		0			0
$471$	−11.6707	−	20.2142i	−0.537757	−	0.931422i
$472$		0			0
$473$	8.00602	+	29.8789i	0.368117	+	1.37383i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	7.08437	+	7.08437i	0.324371	+	0.324371i
$478$		0			0
$479$	17.0990	−	29.6164i	0.781275	−	1.35321i	−0.149924	−	0.988698i	$-0.547903\pi$
$479$	17.0990	−	29.6164i	0.781275	−	1.35321i	0.931199	−	0.364511i	$-0.118764\pi$
$480$		0			0
$481$	−62.6464	+	36.1689i	−2.85643	+	1.64916i
$482$		0			0
$483$	13.9350	−	6.13905i	0.634062	−	0.279336i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−22.9242	+	6.14252i	−1.03880	+	0.278344i	−0.737614	−	0.675223i	$-0.764048\pi$
$487$	−22.9242	+	6.14252i	−1.03880	+	0.278344i	−0.301181	+	0.953567i	$0.597381\pi$
$488$		0			0
$489$	−20.3603			−0.920723
$490$		0			0
$491$	−1.71849			−0.0775545			−0.0387773	−	0.999248i	$-0.512346\pi$
$491$	−1.71849			−0.0775545			−0.0387773	+	0.999248i	$0.512346\pi$
$492$		0			0
$493$	−36.5730	+	9.79971i	−1.64717	+	0.441357i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.44147	−	1.07559i	0.109515	−	0.0482468i
$498$		0			0
$499$	5.85939	−	3.38292i	0.262302	−	0.151440i	−0.363082	−	0.931757i	$-0.618276\pi$
$499$	5.85939	−	3.38292i	0.262302	−	0.151440i	0.625384	+	0.780317i	$0.284942\pi$
$500$		0			0
$501$	−4.27301	+	7.40106i	−0.190904	+	0.330655i
$502$		0			0
$503$	−28.8714	−	28.8714i	−1.28731	−	1.28731i	−0.936415	−	0.350895i	$-0.885877\pi$
$503$	−28.8714	−	28.8714i	−1.28731	−	1.28731i	−0.350895	−	0.936415i	$-0.614123\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.13833	+	22.9086i	0.272613	+	1.01740i
$508$		0			0
$509$	19.2679	+	33.3729i	0.854033	+	1.47923i	0.877540	+	0.479504i	$0.159183\pi$
$509$	19.2679	+	33.3729i	0.854033	+	1.47923i	−0.0235070	+	0.999724i	$0.507483\pi$
$510$		0			0
$511$	6.12044	−	4.91672i	0.270752	−	0.217503i
$512$		0			0
$513$	1.88242	+	0.504394i	0.0831110	+	0.0222695i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	20.7065	−	20.7065i	0.910672	−	0.910672i
$518$		0			0
$519$		−	0.229861i		−	0.0100898i
$520$		0			0
$521$	−1.88362	−	1.08751i	−0.0825227	−	0.0476445i	0.458171	−	0.888864i	$-0.348505\pi$
$521$	−1.88362	−	1.08751i	−0.0825227	−	0.0476445i	−0.540694	+	0.841220i	$0.681838\pi$
$522$		0			0
$523$	−0.803907	+	3.00022i	−0.0351524	+	0.131190i	−0.981272	−	0.192626i	$-0.938299\pi$
$523$	−0.803907	+	3.00022i	−0.0351524	+	0.131190i	0.946120	+	0.323817i	$0.104966\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.11945	−	7.90988i	0.0923245	−	0.344560i
$528$		0			0
$529$	8.76800	+	5.06221i	0.381217	+	0.220096i
$530$		0			0
$531$			6.86498i			0.297915i
$532$		0			0
$533$	−19.3209	+	19.3209i	−0.836882	+	0.836882i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.28695	−	0.880737i	−0.141843	−	0.0380066i
$538$		0			0
$539$	7.64339	+	24.1655i	0.329224	+	1.04088i
$540$		0			0
$541$	18.8967	+	32.7300i	0.812432	+	1.40717i	0.911157	+	0.412059i	$0.135190\pi$
$541$	18.8967	+	32.7300i	0.812432	+	1.40717i	−0.0987246	+	0.995115i	$0.531476\pi$
$542$		0			0
$543$	−2.80200	−	10.4572i	−0.120245	−	0.448762i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	10.7083	+	10.7083i	0.457854	+	0.457854i	0.897950	−	0.440097i	$-0.145056\pi$
$547$	10.7083	+	10.7083i	0.457854	+	0.457854i	−0.440097	+	0.897950i	$0.645056\pi$
$548$		0			0
$549$	−3.31880	+	5.74833i	−0.141643	+	0.245333i
$550$		0			0
$551$	10.2957	−	5.94424i	0.438612	−	0.253233i
$552$		0			0
$553$	19.7569	−	26.9705i	0.840147	−	1.14690i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−21.5540	+	5.77537i	−0.913272	+	0.244710i	−0.684707	−	0.728818i	$-0.740070\pi$
$557$	−21.5540	+	5.77537i	−0.913272	+	0.244710i	−0.228564	+	0.973529i	$0.573403\pi$
$558$		0			0
$559$	−51.7666			−2.18949
$560$		0			0
$561$	22.4733			0.948824
$562$		0			0
$563$	15.8325	−	4.24232i	0.667262	−	0.178792i	0.0907410	−	0.995875i	$-0.471076\pi$
$563$	15.8325	−	4.24232i	0.667262	−	0.178792i	0.576521	+	0.817082i	$0.304410\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.286846	−	2.63016i	0.0120464	−	0.110456i
$568$		0			0
$569$	−17.5745	+	10.1466i	−0.736760	+	0.425368i	−0.820890	−	0.571086i	$-0.806522\pi$
$569$	−17.5745	+	10.1466i	−0.736760	+	0.425368i	0.0841304	+	0.996455i	$0.473189\pi$
$570$		0			0
$571$	−14.4488	+	25.0260i	−0.604663	+	1.04731i	0.387442	+	0.921894i	$0.373359\pi$
$571$	−14.4488	+	25.0260i	−0.604663	+	1.04731i	−0.992105	+	0.125412i	$0.959975\pi$
$572$		0			0
$573$	10.1704	+	10.1704i	0.424873	+	0.424873i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.799860	+	2.98512i	0.0332986	+	0.124272i	0.980575	−	0.196147i	$-0.0628429\pi$
$577$	0.799860	+	2.98512i	0.0332986	+	0.124272i	−0.947276	+	0.320419i	$0.896176\pi$
$578$		0			0
$579$	4.10541	+	7.11078i	0.170615	+	0.295514i
$580$		0			0
$581$	14.8855	+	5.78090i	0.617554	+	0.239832i
$582$		0			0
$583$	−35.0399	−	9.38891i	−1.45120	−	0.388849i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.2202	+	18.2202i	−0.752029	+	0.752029i	−0.974858	−	0.222828i	$-0.928471\pi$
$587$	−18.2202	+	18.2202i	−0.752029	+	0.752029i	0.222828	+	0.974858i	$0.428471\pi$
$588$		0			0
$589$			2.57120i			0.105944i
$590$		0			0
$591$	−2.12202	−	1.22515i	−0.0872881	−	0.0503958i
$592$		0			0
$593$	−0.504523	+	1.88290i	−0.0207183	+	0.0773216i	−0.975511	−	0.219951i	$-0.929410\pi$
$593$	−0.504523	+	1.88290i	−0.0207183	+	0.0773216i	0.954793	+	0.297272i	$0.0960770\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.71624	−	6.40511i	0.0702412	−	0.262144i
$598$		0			0
$599$	−6.10854	−	3.52676i	−0.249588	−	0.144100i	0.369988	−	0.929037i	$-0.379362\pi$
$599$	−6.10854	−	3.52676i	−0.249588	−	0.144100i	−0.619576	+	0.784937i	$0.712695\pi$
$600$		0			0
$601$			10.0063i			0.408165i	0.978954	+	0.204083i	$0.0654211\pi$
$601$			10.0063i			0.408165i	−0.978954	+	0.204083i	$0.934579\pi$
$602$		0			0
$603$	2.25524	−	2.25524i	0.0918405	−	0.0918405i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	42.8539	+	11.4827i	1.73939	+	0.466067i	0.982310	−	0.187261i	$-0.0599610\pi$
$607$	42.8539	+	11.4827i	1.73939	+	0.466067i	0.757075	+	0.653328i	$0.226628\pi$
$608$		0			0
$609$	−10.1081	−	12.5827i	−0.409599	−	0.509877i
$610$		0			0
$611$	24.5031	+	42.4406i	0.991290	+	1.71696i
$612$		0			0
$613$	−2.07575	−	7.74681i	−0.0838388	−	0.312891i	0.911253	−	0.411847i	$-0.135116\pi$
$613$	−2.07575	−	7.74681i	−0.0838388	−	0.312891i	−0.995092	+	0.0989564i	$0.968450\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.4760	+	15.4760i	0.623042	+	0.623042i	0.946308	−	0.323266i	$-0.104781\pi$
$617$	15.4760	+	15.4760i	0.623042	+	0.623042i	−0.323266	+	0.946308i	$0.604781\pi$
$618$		0			0
$619$	−9.99537	+	17.3125i	−0.401748	+	0.695848i	−0.993937	−	0.109951i	$-0.964931\pi$
$619$	−9.99537	+	17.3125i	−0.401748	+	0.695848i	0.592189	+	0.805799i	$0.298264\pi$
$620$		0			0
$621$	4.98431	−	2.87769i	0.200013	−	0.115478i
$622$		0			0
$623$	24.8736	+	18.2208i	0.996538	+	0.729999i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−6.81585	+	1.82630i	−0.272199	+	0.0729354i
$628$		0			0
$629$	−74.0966			−2.95442
$630$		0			0
$631$	−13.7976			−0.549272			−0.274636	−	0.961548i	$-0.588557\pi$
$631$	−13.7976			−0.549272			−0.274636	+	0.961548i	$0.588557\pi$
$632$		0			0
$633$	−13.2528	+	3.55108i	−0.526752	+	0.141143i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−42.3739	+	1.88847i	−1.67892	+	0.0748241i
$638$		0			0
$639$	0.873274	−	0.504185i	0.0345462	−	0.0199452i
$640$		0			0
$641$	−4.05520	+	7.02382i	−0.160171	+	0.277424i	−0.934930	−	0.354833i	$-0.884538\pi$
$641$	−4.05520	+	7.02382i	−0.160171	+	0.277424i	0.774759	+	0.632257i	$0.217871\pi$
$642$		0			0
$643$	−20.0083	−	20.0083i	−0.789051	−	0.789051i	0.192288	−	0.981339i	$-0.438409\pi$
$643$	−20.0083	−	20.0083i	−0.789051	−	0.789051i	−0.981339	+	0.192288i	$0.938409\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.55765	−	31.9376i	−0.336436	−	1.25560i	−0.902304	−	0.431100i	$-0.858126\pi$
$647$	−8.55765	−	31.9376i	−0.336436	−	1.25560i	0.565868	−	0.824496i	$-0.308541\pi$
$648$		0			0
$649$	−12.4283	−	21.5265i	−0.487854	−	0.844987i
$650$		0			0
$651$	3.44982	−	0.532575i	0.135209	−	0.0208732i
$652$		0			0
$653$	7.29469	+	1.95461i	0.285463	+	0.0764896i	0.398709	−	0.917077i	$-0.369458\pi$
$653$	7.29469	+	1.95461i	0.285463	+	0.0764896i	−0.113246	+	0.993567i	$0.536125\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.09819	−	2.09819i	0.0818584	−	0.0818584i
$658$		0			0
$659$		−	27.9181i		−	1.08753i	−0.839236	−	0.543767i	$-0.816997\pi$
$659$		−	27.9181i		−	1.08753i	0.839236	−	0.543767i	$-0.183003\pi$
$660$		0			0
$661$	11.6168	+	6.70694i	0.451840	+	0.260870i	0.708607	−	0.705603i	$-0.249324\pi$
$661$	11.6168	+	6.70694i	0.451840	+	0.260870i	−0.256767	+	0.966473i	$0.582657\pi$
$662$		0			0
$663$	−9.73402	+	36.3279i	−0.378038	+	1.41086i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.08705	−	33.9133i	0.351852	−	1.31313i
$668$		0			0
$669$	11.9104	+	6.87645i	0.460481	+	0.265859i
$670$		0			0
$671$		−	24.0333i		−	0.927796i
$672$		0			0
$673$	−15.0304	+	15.0304i	−0.579381	+	0.579381i	−0.934733	−	0.355351i	$-0.884361\pi$
$673$	−15.0304	+	15.0304i	−0.579381	+	0.579381i	0.355351	+	0.934733i	$0.384361\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.3276	+	5.17882i	0.742821	+	0.199038i	0.610332	−	0.792146i	$-0.291036\pi$
$677$	19.3276	+	5.17882i	0.742821	+	0.199038i	0.132490	+	0.991184i	$0.457703\pi$
$678$		0			0
$679$	−12.0510	+	31.0306i	−0.462475	+	1.19085i
$680$		0			0
$681$	2.59622	+	4.49678i	0.0994872	+	0.172317i
$682$		0			0
$683$	−10.5542	−	39.3888i	−0.403845	−	1.50717i	−0.806175	−	0.591677i	$-0.798466\pi$
$683$	−10.5542	−	39.3888i	−0.403845	−	1.50717i	0.402330	−	0.915495i	$-0.368201\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	3.98904	+	3.98904i	0.152191	+	0.152191i
$688$		0			0
$689$	30.3541	−	52.5749i	1.15640	−	2.00294i
$690$		0			0
$691$	−11.1389	+	6.43106i	−0.423745	+	0.244649i	−0.696678	−	0.717384i	$-0.745339\pi$
$691$	−11.1389	+	6.43106i	−0.423745	+	0.244649i	0.272934	+	0.962033i	$0.412006\pi$
$692$		0			0
$693$	3.86216	+	8.76666i	0.146711	+	0.333018i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−27.0345	+	7.24389i	−1.02401	+	0.274382i
$698$		0			0
$699$	3.42850			0.129678
$700$		0			0
$701$	−24.4875			−0.924879			−0.462439	−	0.886651i	$-0.653026\pi$
$701$	−24.4875			−0.924879			−0.462439	+	0.886651i	$0.653026\pi$
$702$		0			0
$703$	22.4725	−	6.02148i	0.847566	−	0.227105i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−12.7625	−	1.39188i	−0.479983	−	0.0523471i
$708$		0			0
$709$	18.0554	−	10.4243i	0.678086	−	0.391493i	−0.121047	−	0.992647i	$-0.538625\pi$
$709$	18.0554	−	10.4243i	0.678086	−	0.391493i	0.799134	+	0.601153i	$0.205292\pi$
$710$		0			0
$711$	6.31817	−	10.9434i	0.236950	−	0.410410i
$712$		0			0
$713$	5.36934	+	5.36934i	0.201083	+	0.201083i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.09738	+	15.2916i	0.153019	+	0.571076i
$718$		0			0
$719$	10.0687	+	17.4396i	0.375501	+	0.650387i	0.990402	−	0.138218i	$-0.0441373\pi$
$719$	10.0687	+	17.4396i	0.375501	+	0.650387i	−0.614901	+	0.788604i	$0.710804\pi$
$720$		0			0
$721$	0.294875	+	1.91009i	0.0109817	+	0.0711354i
$722$		0			0
$723$	6.99802	+	1.87511i	0.260259	+	0.0697362i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	25.7043	−	25.7043i	0.953318	−	0.953318i	−0.0456398	−	0.998958i	$-0.514533\pi$
$727$	25.7043	−	25.7043i	0.953318	−	0.953318i	0.998958	+	0.0456398i	$0.0145326\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−45.9211	−	26.5126i	−1.69845	−	0.980603i
$732$		0			0
$733$	0.781774	−	2.91762i	0.0288755	−	0.107765i	−0.949984	−	0.312298i	$-0.898901\pi$
$733$	0.781774	−	2.91762i	0.0288755	−	0.107765i	0.978860	+	0.204534i	$0.0655678\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.98887	+	11.1546i	−0.110096	+	0.410886i
$738$		0			0
$739$	35.6209	+	20.5657i	1.31033	+	0.756522i	0.982151	−	0.188092i	$-0.0602303\pi$
$739$	35.6209	+	20.5657i	1.31033	+	0.756522i	0.328183	+	0.944614i	$0.393564\pi$
$740$		0			0
$741$		−	11.8088i		−	0.433806i
$742$		0			0
$743$	9.93640	−	9.93640i	0.364531	−	0.364531i	−0.500947	−	0.865478i	$-0.667015\pi$
$743$	9.93640	−	9.93640i	0.364531	−	0.364531i	0.865478	+	0.500947i	$0.167015\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.82991	+	1.56212i	0.213305	+	0.0571550i
$748$		0			0
$749$	−1.44502	−	9.36029i	−0.0527998	−	0.342018i
$750$		0			0
$751$	18.5207	+	32.0789i	0.675832	+	1.17057i	0.976225	+	0.216759i	$0.0695487\pi$
$751$	18.5207	+	32.0789i	0.675832	+	1.17057i	−0.300393	+	0.953815i	$0.597118\pi$
$752$		0			0
$753$	5.75450	+	21.4761i	0.209706	+	0.782632i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	24.2819	+	24.2819i	0.882542	+	0.882542i	0.993792	−	0.111250i	$-0.0354856\pi$
$757$	24.2819	+	24.2819i	0.882542	+	0.882542i	−0.111250	+	0.993792i	$0.535486\pi$
$758$		0			0
$759$	−10.4195	+	18.0471i	−0.378204	+	0.655069i
$760$		0			0
$761$	−5.51706	+	3.18527i	−0.199993	+	0.115466i	−0.596652	−	0.802500i	$-0.703503\pi$
$761$	−5.51706	+	3.18527i	−0.199993	+	0.115466i	0.396659	+	0.917966i	$0.370169\pi$
$762$		0			0
$763$	−13.5241	−	1.47495i	−0.489607	−	0.0533967i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	40.1804	−	10.7663i	1.45083	−	0.388749i
$768$		0			0
$769$	42.2841			1.52480			0.762402	−	0.647103i	$-0.224020\pi$
$769$	42.2841			1.52480			0.762402	+	0.647103i	$0.224020\pi$
$770$		0			0
$771$	−19.4449			−0.700291
$772$		0			0
$773$	−20.3095	+	5.44191i	−0.730482	+	0.195732i	−0.604844	−	0.796344i	$-0.706764\pi$
$773$	−20.3095	+	5.44191i	−0.730482	+	0.195732i	−0.125638	+	0.992076i	$0.540098\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−12.7339	−	28.9045i	−0.456825	−	1.03694i
$778$		0			0
$779$	7.61053	−	4.39394i	0.272676	−	0.157429i
$780$		0			0
$781$	−1.82555	+	3.16194i	−0.0653231	+	0.113143i
$782$		0			0
$783$	−4.31358	−	4.31358i	−0.154155	−	0.154155i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	6.24021	+	23.2888i	0.222439	+	0.830155i	0.983414	+	0.181374i	$0.0580544\pi$
$787$	6.24021	+	23.2888i	0.222439	+	0.830155i	−0.760975	+	0.648781i	$0.775279\pi$
$788$		0			0
$789$	2.69515	+	4.66813i	0.0959497	+	0.166190i
$790$		0			0
$791$	−0.964087	+	2.48247i	−0.0342790	+	0.0882664i
$792$		0			0
$793$	38.8496	+	10.4097i	1.37959	+	0.369660i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.1406	−	12.1406i	0.430044	−	0.430044i	−0.458599	−	0.888643i	$-0.651649\pi$
$797$	12.1406	−	12.1406i	0.430044	−	0.430044i	0.888643	+	0.458599i	$0.151649\pi$
$798$		0			0
$799$			50.1977i			1.77587i
$800$		0			0
$801$	10.0926	+	5.82694i	0.356603	+	0.205885i
$802$		0			0
$803$	−2.78074	+	10.3779i	−0.0981301	+	0.366226i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.83796	+	10.5914i	−0.0999011	+	0.372836i
$808$		0			0
$809$	5.26597	+	3.04031i	0.185142	+	0.106892i	0.589706	−	0.807618i	$-0.299244\pi$
$809$	5.26597	+	3.04031i	0.185142	+	0.106892i	−0.404565	+	0.914509i	$0.632577\pi$
$810$		0			0
$811$		−	35.9716i		−	1.26313i	−0.775321	−	0.631567i	$-0.782412\pi$
$811$		−	35.9716i		−	1.26313i	0.775321	−	0.631567i	$-0.217588\pi$
$812$		0			0
$813$	11.1391	−	11.1391i	0.390666	−	0.390666i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	16.0818	+	4.30911i	0.562631	+	0.150757i
$818$		0			0
$819$	−15.8441	+	2.44597i	−0.553636	+	0.0854690i
$820$		0			0
$821$	−15.4504	−	26.7609i	−0.539224	−	0.933963i	−0.998946	−	0.0459000i	$-0.985384\pi$
$821$	−15.4504	−	26.7609i	−0.539224	−	0.933963i	0.459722	−	0.888063i	$-0.347949\pi$
$822$		0			0
$823$	5.27876	+	19.7006i	0.184006	+	0.686720i	0.994841	+	0.101445i	$0.0323467\pi$
$823$	5.27876	+	19.7006i	0.184006	+	0.686720i	−0.810835	+	0.585275i	$0.800987\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−32.6523	−	32.6523i	−1.13543	−	1.13543i	−0.989259	−	0.146171i	$-0.953305\pi$
$827$	−32.6523	−	32.6523i	−1.13543	−	1.13543i	−0.146171	−	0.989259i	$-0.546695\pi$
$828$		0			0
$829$	22.7431	−	39.3921i	0.789899	−	1.36815i	−0.136129	−	0.990691i	$-0.543466\pi$
$829$	22.7431	−	39.3921i	0.789899	−	1.36815i	0.926028	−	0.377455i	$-0.123201\pi$
$830$		0			0
$831$	−9.03788	+	5.21802i	−0.313521	+	0.181011i
$832$		0			0
$833$	−38.5563	−	20.0269i	−1.33590	−	0.693889i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.27440	−	0.341474i	0.0440497	−	0.0118031i
$838$		0			0
$839$	−23.4000			−0.807857			−0.403929	−	0.914790i	$-0.632356\pi$
$839$	−23.4000			−0.807857			−0.403929	+	0.914790i	$0.632356\pi$
$840$		0			0
$841$	−8.21392			−0.283239
$842$		0			0
$843$	−9.99197	+	2.67734i	−0.344142	+	0.0922125i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−4.50369	−	3.29911i	−0.154749	−	0.113359i
$848$		0			0
$849$	2.92892	−	1.69101i	0.100520	−	0.0580355i
$850$		0			0
$851$	34.3541	−	59.5030i	1.17764	−	2.03974i
$852$		0			0
$853$	22.4233	+	22.4233i	0.767759	+	0.767759i	0.977712	−	0.209953i	$-0.0673310\pi$
$853$	22.4233	+	22.4233i	0.767759	+	0.767759i	−0.209953	+	0.977712i	$0.567331\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.0734	−	37.5945i	−0.344101	−	1.28420i	−0.893659	−	0.448747i	$-0.851870\pi$
$857$	−10.0734	−	37.5945i	−0.344101	−	1.28420i	0.549557	−	0.835456i	$-0.314796\pi$
$858$		0			0
$859$	−5.01890	−	8.69298i	−0.171243	−	0.296601i	0.767612	−	0.640915i	$-0.221445\pi$
$859$	−5.01890	−	8.69298i	−0.171243	−	0.296601i	−0.938855	+	0.344314i	$0.888112\pi$
$860$		0			0
$861$	−7.47181	−	9.30107i	−0.254639	−	0.316979i
$862$		0			0
$863$	40.1781	+	10.7657i	1.36768	+	0.366468i	0.866630	−	0.498951i	$-0.166281\pi$
$863$	40.1781	+	10.7657i	1.36768	+	0.366468i	0.501048	+	0.865419i	$0.332948\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−15.2196	+	15.2196i	−0.516884	+	0.516884i
$868$		0			0
$869$			45.7535i			1.55208i
$870$		0			0
$871$	−16.7367	−	9.66295i	−0.567102	−	0.327417i
$872$		0			0
$873$	−3.25643	+	12.1532i	−0.110213	+	0.411322i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.50464	+	5.61540i	−0.0508082	+	0.189619i	−0.986666	−	0.162760i	$-0.947960\pi$
$877$	−1.50464	+	5.61540i	−0.0508082	+	0.189619i	0.935858	+	0.352379i	$0.114627\pi$
$878$		0			0
$879$	−0.250751	−	0.144771i	−0.00845763	−	0.00488302i
$880$		0			0
$881$		−	16.9009i		−	0.569404i	−0.958616	−	0.284702i	$-0.908105\pi$
$881$		−	16.9009i		−	0.569404i	0.958616	−	0.284702i	$-0.0918947\pi$
$882$		0			0
$883$	26.0789	−	26.0789i	0.877625	−	0.877625i	−0.115663	−	0.993288i	$-0.536899\pi$
$883$	26.0789	−	26.0789i	0.877625	−	0.877625i	0.993288	+	0.115663i	$0.0368994\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.15499	+	0.309478i	0.0387807	+	0.0103913i	0.278157	−	0.960536i	$-0.410276\pi$
$887$	1.15499	+	0.309478i	0.0387807	+	0.0103913i	−0.239377	+	0.970927i	$0.576943\pi$
$888$		0			0
$889$	−14.6801	−	5.70113i	−0.492354	−	0.191210i
$890$		0			0
$891$	1.81039	+	3.13569i	0.0606504	+	0.105050i
$892$		0			0
$893$	−4.07933	−	15.2243i	−0.136510	−	0.509461i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−24.6599	−	24.6599i	−0.823369	−	0.823369i
$898$		0			0
$899$	4.02424	−	6.97020i	0.134216	−	0.232469i
$900$		0			0
$901$	53.8532	−	31.0921i	1.79411	−	1.03583i
$902$		0			0
$903$	2.45056	−	22.4698i	0.0815496	−	0.747748i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−6.74360	+	1.80694i	−0.223918	+	0.0599985i	−0.369033	−	0.929416i	$-0.620311\pi$
$907$	−6.74360	+	1.80694i	−0.223918	+	0.0599985i	0.145116	+	0.989415i	$0.453645\pi$
$908$		0			0
$909$	−4.85237			−0.160943
$910$		0			0
$911$	−29.7513			−0.985704			−0.492852	−	0.870113i	$-0.664046\pi$
$911$	−29.7513			−0.985704			−0.492852	+	0.870113i	$0.664046\pi$
$912$		0			0
$913$	−21.1089	+	5.65610i	−0.698601	+	0.187190i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.48826	+	3.39677i	−0.0821694	+	0.112171i
$918$		0			0
$919$	32.8025	−	18.9386i	1.08206	−	0.624725i	0.150606	−	0.988594i	$-0.451878\pi$
$919$	32.8025	−	18.9386i	1.08206	−	0.624725i	0.931450	+	0.363869i	$0.118544\pi$
$920$		0			0
$921$	−14.3512	+	24.8570i	−0.472889	+	0.819067i
$922$		0			0
$923$	−4.32052	−	4.32052i	−0.142212	−	0.142212i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.189067	+	0.705607i	0.00620977	+	0.0231752i
$928$		0			0
$929$	−12.7873	−	22.1482i	−0.419537	−	0.726659i	0.576356	−	0.817199i	$-0.304474\pi$
$929$	−12.7873	−	22.1482i	−0.419537	−	0.726659i	−0.995893	+	0.0905394i	$0.971141\pi$
$930$		0			0
$931$	13.3211	+	2.94058i	0.436581	+	0.0963736i
$932$		0			0
$933$	23.0561	+	6.17785i	0.754821	+	0.202254i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−19.3602	+	19.3602i	−0.632471	+	0.632471i	−0.948687	−	0.316216i	$-0.897588\pi$
$937$	−19.3602	+	19.3602i	−0.632471	+	0.632471i	0.316216	+	0.948687i	$0.397588\pi$
$938$		0			0
$939$		−	0.195496i		−	0.00637977i
$940$		0			0
$941$	−8.41099	−	4.85609i	−0.274191	−	0.158304i	0.356600	−	0.934257i	$-0.383936\pi$
$941$	−8.41099	−	4.85609i	−0.274191	−	0.158304i	−0.630791	+	0.775953i	$0.717269\pi$
$942$		0			0
$943$	6.71709	−	25.0685i	0.218739	−	0.816344i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.57642	+	17.0794i	−0.148714	+	0.555007i	0.850848	+	0.525411i	$0.176089\pi$
$947$	−4.57642	+	17.0794i	−0.148714	+	0.555007i	−0.999562	+	0.0295954i	$0.990578\pi$
$948$		0			0
$949$	−15.5712	−	8.99006i	−0.505464	−	0.291830i
$950$		0			0
$951$			21.5002i			0.697191i
$952$		0			0
$953$	−0.496791	+	0.496791i	−0.0160926	+	0.0160926i	−0.715107	−	0.699015i	$-0.753622\pi$
$953$	−0.496791	+	0.496791i	−0.0160926	+	0.0160926i	0.699015	+	0.715107i	$0.253622\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	21.3353	+	5.71678i	0.689673	+	0.184797i
$958$		0			0
$959$	47.5080	−	38.1646i	1.53411	−	1.23240i
$960$		0			0
$961$	−14.6297	−	25.3393i	−0.471924	−	0.817397i
$962$		0			0
$963$	−0.926512	−	3.45779i	−0.0298564	−	0.111426i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−16.2692	−	16.2692i	−0.523182	−	0.523182i	0.395349	−	0.918531i	$-0.370624\pi$
$967$	−16.2692	−	16.2692i	−0.523182	−	0.523182i	−0.918531	+	0.395349i	$0.870624\pi$
$968$		0			0
$969$	6.04794	−	10.4753i	0.194288	−	0.336516i
$970$		0			0
$971$	−3.41442	+	1.97132i	−0.109574	+	0.0632626i	−0.553785	−	0.832659i	$-0.686817\pi$
$971$	−3.41442	+	1.97132i	−0.109574	+	0.0632626i	0.444211	+	0.895922i	$0.353484\pi$
$972$		0			0
$973$	−4.05246	+	1.78531i	−0.129916	+	0.0572344i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.26980	−	1.41204i	0.168596	−	0.0451751i	−0.173534	−	0.984828i	$-0.555519\pi$
$977$	5.26980	−	1.41204i	0.168596	−	0.0451751i	0.342129	+	0.939653i	$0.388852\pi$
$978$		0			0
$979$	−42.1962			−1.34860
$980$		0			0
$981$	−5.14195			−0.164170
$982$		0			0
$983$	43.8273	−	11.7435i	1.39787	−	0.374559i	0.520292	−	0.853988i	$-0.325823\pi$
$983$	43.8273	−	11.7435i	1.39787	−	0.374559i	0.877580	+	0.479429i	$0.159156\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−19.5817	+	8.62674i	−0.623293	+	0.274592i
$988$		0			0
$989$	42.5816	−	24.5845i	1.35402	−	0.781742i
$990$		0			0
$991$	−9.48726	+	16.4324i	−0.301373	+	0.521993i	−0.976447	−	0.215757i	$-0.930778\pi$
$991$	−9.48726	+	16.4324i	−0.301373	+	0.521993i	0.675075	+	0.737750i	$0.264111\pi$
$992$		0			0
$993$	11.1111	+	11.1111i	0.352599	+	0.352599i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−8.25751	−	30.8174i	−0.261518	−	0.975998i	−0.964347	−	0.264640i	$-0.914747\pi$
$997$	−8.25751	−	30.8174i	−0.261518	−	0.975998i	0.702830	−	0.711358i	$-0.251920\pi$
$998$		0			0
$999$	−5.96903	−	10.3387i	−0.188852	−	0.327101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.e.157.6		32
5.2	odd	4		420.2.bo.a.73.4	✓	32
5.3	odd	4	inner	2100.2.ce.e.493.8		32
5.4	even	2		420.2.bo.a.157.3	yes	32
7.5	odd	6	inner	2100.2.ce.e.1657.8		32
15.2	even	4		1260.2.dq.c.73.2		32
15.14	odd	2		1260.2.dq.c.577.5		32
35.4	even	6		2940.2.x.c.97.9		32
35.12	even	12		420.2.bo.a.313.3	yes	32
35.17	even	12		2940.2.x.c.1273.9		32
35.19	odd	6		420.2.bo.a.397.4	yes	32
35.24	odd	6		2940.2.x.c.97.6		32
35.32	odd	12		2940.2.x.c.1273.6		32
35.33	even	12	inner	2100.2.ce.e.1993.6		32
105.47	odd	12		1260.2.dq.c.1153.5		32
105.89	even	6		1260.2.dq.c.397.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.4	✓	32	5.2	odd	4
420.2.bo.a.157.3	yes	32	5.4	even	2
420.2.bo.a.313.3	yes	32	35.12	even	12
420.2.bo.a.397.4	yes	32	35.19	odd	6
1260.2.dq.c.73.2		32	15.2	even	4
1260.2.dq.c.397.2		32	105.89	even	6
1260.2.dq.c.577.5		32	15.14	odd	2
1260.2.dq.c.1153.5		32	105.47	odd	12
2100.2.ce.e.157.6		32	1.1	even	1	trivial
2100.2.ce.e.493.8		32	5.3	odd	4	inner
2100.2.ce.e.1657.8		32	7.5	odd	6	inner
2100.2.ce.e.1993.6		32	35.33	even	12	inner
2940.2.x.c.97.6		32	35.24	odd	6
2940.2.x.c.97.9		32	35.4	even	6
2940.2.x.c.1273.6		32	35.32	odd	12
2940.2.x.c.1273.9		32	35.17	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{3} +(2.42120 - 1.06666i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{3} +(2.42120 - 1.06666i) q^{7} +(0.866025 - 0.500000i) q^{9} +(-1.81039 + 3.13569i) q^{11} +(-4.28466 - 4.28466i) q^{13} +(-1.60643 - 5.99526i) q^{17} +(0.974414 + 1.68773i) q^{19} +(2.06263 - 1.65697i) q^{21} +(5.55927 + 1.48960i) q^{23} +(0.707107 - 0.707107i) q^{27} -6.10032i q^{29} +(1.14260 + 0.659678i) q^{31} +(-0.937128 + 3.49741i) q^{33} +(3.08980 - 11.5313i) q^{37} +(-5.24762 - 3.02971i) q^{39} -4.50932i q^{41} +(6.04091 - 6.04091i) q^{43} +(-7.81202 - 2.09322i) q^{47} +(4.72446 - 5.16522i) q^{49} +(-3.10337 - 5.37520i) q^{51} +(2.59306 + 9.67743i) q^{53} +(1.37803 + 1.37803i) q^{57} +(-3.43249 + 5.94524i) q^{59} +(-5.74833 + 3.31880i) q^{61} +(1.56349 - 2.13436i) q^{63} +(3.08072 - 0.825476i) q^{67} +5.75538 q^{69} +1.00837 q^{71} +(2.86619 - 0.767993i) q^{73} +(-1.03861 + 9.52323i) q^{77} +(10.9434 - 6.31817i) q^{79} +(0.500000 - 0.866025i) q^{81} +(4.26779 + 4.26779i) q^{83} +(-1.57888 - 5.89246i) q^{87} +(5.82694 + 10.0926i) q^{89} +(-14.9443 - 5.80376i) q^{91} +(1.27440 + 0.341474i) q^{93} +(-8.89673 + 8.89673i) q^{97} +3.62079i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) \) 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Introduction

L-functions

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