LMFDB - Embedded newform 1008.2.q.k.625.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (of order $3$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.3
Character	$\chi$	$=$	1008.625
Dual form			1008.2.q.k.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34477 + 1.09160i) q^{3} +(0.918286 + 1.59052i) q^{5} +(0.361656 - 2.62092i) q^{7} +(0.616838 - 2.93590i) q^{9} +(-1.54860 + 2.68225i) q^{11} +(2.40225 - 4.16081i) q^{13} +(-2.97109 - 1.13649i) q^{15} +(1.87185 + 3.24214i) q^{17} +(2.71408 - 4.70093i) q^{19} +(2.37464 + 3.91932i) q^{21} +(-3.97914 - 6.89208i) q^{23} +(0.813503 - 1.40903i) q^{25} +(2.37531 + 4.62146i) q^{27} +(-0.325267 - 0.563379i) q^{29} -1.03668 q^{31} +(-0.845416 - 5.29746i) q^{33} +(4.50072 - 1.83153i) q^{35} +(0.873712 - 1.51331i) q^{37} +(1.31144 + 8.21764i) q^{39} +(2.52260 - 4.36927i) q^{41} +(6.09645 + 10.5594i) q^{43} +(5.23603 - 1.71490i) q^{45} +4.61383 q^{47} +(-6.73841 - 1.89574i) q^{49} +(-6.05632 - 2.31664i) q^{51} +(4.55082 + 7.88226i) q^{53} -5.68821 q^{55} +(1.48168 + 9.28438i) q^{57} +5.79727 q^{59} -4.81245 q^{61} +(-7.47167 - 2.67847i) q^{63} +8.82379 q^{65} +14.4774 q^{67} +(12.8744 + 4.92468i) q^{69} +5.00714 q^{71} +(-1.81364 - 3.14131i) q^{73} +(0.444111 + 2.78284i) q^{75} +(6.46989 + 5.02879i) q^{77} +14.3581 q^{79} +(-8.23902 - 3.62195i) q^{81} +(-3.83139 - 6.63616i) q^{83} +(-3.43778 + 5.95441i) q^{85} +(1.05239 + 0.402558i) q^{87} +(-5.76798 + 9.99043i) q^{89} +(-10.0364 - 7.80087i) q^{91} +(1.39411 - 1.13164i) q^{93} +9.96922 q^{95} +(-1.04480 - 1.80964i) q^{97} +(6.91957 + 6.20103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9} + 3 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 2 q^{23} - 10 q^{25} + 4 q^{27} + 9 q^{29} - 8 q^{31} + 29 q^{33} - 14 q^{35} + 2 q^{37} + 16 q^{39}+ \cdots + 56 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9 + 3 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 2 * q^23 - 10 * q^25 + 4 * q^27 + 9 * q^29 - 8 * q^31 + 29 * q^33 - 14 * q^35 + 2 * q^37 + 16 * q^39 + 16 * q^41 + q^45 + 10 * q^47 + 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 - 38 * q^59 + 26 * q^61 - 48 * q^63 - 26 * q^65 + 52 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 23 * q^75 + 17 * q^77 + 20 * q^79 - 38 * q^81 + 28 * q^83 - 20 * q^85 + 33 * q^87 + 6 * q^89 + 37 * q^91 + 19 * q^93 + 24 * q^95 - 29 * q^97 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.34477	+	1.09160i	−0.776406	+	0.630233i
$3$	−1.34477	+	1.09160i	−0.776406	+	0.630233i
$4$		0			0
$5$	0.918286	+	1.59052i	0.410670	+	0.711301i	0.994963	−	0.100242i	$-0.0319616\pi$
$5$	0.918286	+	1.59052i	0.410670	+	0.711301i	−0.584293	+	0.811543i	$0.698628\pi$
$6$		0			0
$7$	0.361656	−	2.62092i	0.136693	−	0.990613i
$7$	0.361656	−	2.62092i	0.136693	−	0.990613i
$8$		0			0
$9$	0.616838	−	2.93590i	0.205613	−	0.978633i
$10$		0			0
$11$	−1.54860	+	2.68225i	−0.466919	+	0.808728i	−0.999286	−	0.0377862i	$-0.987969\pi$
$11$	−1.54860	+	2.68225i	−0.466919	+	0.808728i	0.532367	+	0.846514i	$0.321303\pi$
$12$		0			0
$13$	2.40225	−	4.16081i	0.666263	−	1.15400i	−0.312678	−	0.949859i	$-0.601226\pi$
$13$	2.40225	−	4.16081i	0.666263	−	1.15400i	0.978941	−	0.204143i	$-0.0654406\pi$
$14$		0			0
$15$	−2.97109	−	1.13649i	−0.767132	−	0.293441i
$16$		0			0
$17$	1.87185	+	3.24214i	0.453990	+	0.786333i	0.998629	−	0.0523367i	$-0.0166669\pi$
$17$	1.87185	+	3.24214i	0.453990	+	0.786333i	−0.544640	+	0.838670i	$0.683334\pi$
$18$		0			0
$19$	2.71408	−	4.70093i	0.622654	−	1.07847i	−0.366336	−	0.930483i	$-0.619388\pi$
$19$	2.71408	−	4.70093i	0.622654	−	1.07847i	0.988990	−	0.147985i	$-0.0472788\pi$
$20$		0			0
$21$	2.37464	+	3.91932i	0.518188	+	0.855267i
$22$		0			0
$23$	−3.97914	−	6.89208i	−0.829709	−	1.43710i	−0.898267	−	0.439450i	$-0.855173\pi$
$23$	−3.97914	−	6.89208i	−0.829709	−	1.43710i	0.0685581	−	0.997647i	$-0.478160\pi$
$24$		0			0
$25$	0.813503	−	1.40903i	0.162701	−	0.281806i
$26$		0			0
$27$	2.37531	+	4.62146i	0.457128	+	0.889401i
$28$		0			0
$29$	−0.325267	−	0.563379i	−0.0604006	−	0.104617i	0.834244	−	0.551396i	$-0.185904\pi$
$29$	−0.325267	−	0.563379i	−0.0604006	−	0.104617i	−0.894645	+	0.446779i	$0.852571\pi$
$30$		0			0
$31$	−1.03668			−0.186194			−0.0930970	−	0.995657i	$-0.529677\pi$
$31$	−1.03668			−0.186194			−0.0930970	+	0.995657i	$0.529677\pi$
$32$		0			0
$33$	−0.845416	−	5.29746i	−0.147168	−	0.922169i
$34$		0			0
$35$	4.50072	−	1.83153i	0.760760	−	0.309585i
$36$		0			0
$37$	0.873712	−	1.51331i	0.143637	−	0.248787i	−0.785226	−	0.619209i	$-0.787453\pi$
$37$	0.873712	−	1.51331i	0.143637	−	0.248787i	0.928864	+	0.370422i	$0.120787\pi$
$38$		0			0
$39$	1.31144	+	8.21764i	0.209999	+	1.31588i
$40$		0			0
$41$	2.52260	−	4.36927i	0.393964	−	0.682365i	−0.599005	−	0.800745i	$-0.704437\pi$
$41$	2.52260	−	4.36927i	0.393964	−	0.682365i	0.992968	+	0.118381i	$0.0377703\pi$
$42$		0			0
$43$	6.09645	+	10.5594i	0.929699	+	1.61029i	0.783824	+	0.620984i	$0.213267\pi$
$43$	6.09645	+	10.5594i	0.929699	+	1.61029i	0.145876	+	0.989303i	$0.453400\pi$
$44$		0			0
$45$	5.23603	−	1.71490i	0.780542	−	0.255643i
$46$		0			0
$47$	4.61383			0.672996			0.336498	−	0.941684i	$-0.390757\pi$
$47$	4.61383			0.672996			0.336498	+	0.941684i	$0.390757\pi$
$48$		0			0
$49$	−6.73841	−	1.89574i	−0.962630	−	0.270820i
$50$		0			0
$51$	−6.05632	−	2.31664i	−0.848054	−	0.324395i
$52$		0			0
$53$	4.55082	+	7.88226i	0.625104	+	1.08271i	0.988521	+	0.151085i	$0.0482766\pi$
$53$	4.55082	+	7.88226i	0.625104	+	1.08271i	−0.363417	+	0.931626i	$0.618390\pi$
$54$		0			0
$55$	−5.68821			−0.766998
$56$		0			0
$57$	1.48168	+	9.28438i	0.196254	+	1.22975i
$58$		0			0
$59$	5.79727			0.754740			0.377370	−	0.926063i	$-0.376828\pi$
$59$	5.79727			0.754740			0.377370	+	0.926063i	$0.376828\pi$
$60$		0			0
$61$	−4.81245			−0.616172			−0.308086	−	0.951359i	$-0.599688\pi$
$61$	−4.81245			−0.616172			−0.308086	+	0.951359i	$0.599688\pi$
$62$		0			0
$63$	−7.47167	−	2.67847i	−0.941342	−	0.337455i
$64$		0			0
$65$	8.82379			1.09446
$66$		0			0
$67$	14.4774			1.76870			0.884348	−	0.466828i	$-0.154603\pi$
$67$	14.4774			1.76870			0.884348	+	0.466828i	$0.154603\pi$
$68$		0			0
$69$	12.8744	+	4.92468i	1.54990	+	0.592861i
$70$		0			0
$71$	5.00714			0.594238			0.297119	−	0.954840i	$-0.403974\pi$
$71$	5.00714			0.594238			0.297119	+	0.954840i	$0.403974\pi$
$72$		0			0
$73$	−1.81364	−	3.14131i	−0.212270	−	0.367662i	0.740155	−	0.672437i	$-0.234752\pi$
$73$	−1.81364	−	3.14131i	−0.212270	−	0.367662i	−0.952425	+	0.304774i	$0.901419\pi$
$74$		0			0
$75$	0.444111	+	2.78284i	0.0512816	+	0.321335i
$76$		0			0
$77$	6.46989	+	5.02879i	0.737312	+	0.573084i
$78$		0			0
$79$	14.3581			1.61541			0.807705	−	0.589587i	$-0.200710\pi$
$79$	14.3581			1.61541			0.807705	+	0.589587i	$0.200710\pi$
$80$		0			0
$81$	−8.23902	−	3.62195i	−0.915447	−	0.402439i
$82$		0			0
$83$	−3.83139	−	6.63616i	−0.420550	−	0.728414i	0.575443	−	0.817842i	$-0.304829\pi$
$83$	−3.83139	−	6.63616i	−0.420550	−	0.728414i	−0.995993	+	0.0894279i	$0.971496\pi$
$84$		0			0
$85$	−3.43778	+	5.95441i	−0.372880	+	0.645847i
$86$		0			0
$87$	1.05239	+	0.402558i	0.112828	+	0.0431587i
$88$		0			0
$89$	−5.76798	+	9.99043i	−0.611405	+	1.05898i	0.379599	+	0.925151i	$0.376062\pi$
$89$	−5.76798	+	9.99043i	−0.611405	+	1.05898i	−0.991004	+	0.133833i	$0.957271\pi$
$90$		0			0
$91$	−10.0364	−	7.80087i	−1.05210	−	0.817753i
$92$		0			0
$93$	1.39411	−	1.13164i	0.144562	−	0.117346i
$94$		0			0
$95$	9.96922			1.02282
$96$		0			0
$97$	−1.04480	−	1.80964i	−0.106083	−	0.183741i	0.808097	−	0.589049i	$-0.200498\pi$
$97$	−1.04480	−	1.80964i	−0.106083	−	0.183741i	−0.914180	+	0.405308i	$0.867164\pi$
$98$		0			0
$99$	6.91957	+	6.20103i	0.695443	+	0.623227i
$100$		0			0
$101$	8.22661	−	14.2489i	0.818578	−	1.41782i	−0.0881520	−	0.996107i	$-0.528096\pi$
$101$	8.22661	−	14.2489i	0.818578	−	1.41782i	0.906730	−	0.421712i	$-0.138571\pi$
$102$		0			0
$103$	−3.87346	−	6.70903i	−0.381663	−	0.661060i	0.609637	−	0.792681i	$-0.291315\pi$
$103$	−3.87346	−	6.70903i	−0.381663	−	0.661060i	−0.991300	+	0.131621i	$0.957982\pi$
$104$		0			0
$105$	−4.05316	+	7.37596i	−0.395548	+	0.719820i
$106$		0			0
$107$	−3.74746	+	6.49080i	−0.362281	+	0.627489i	−0.988336	−	0.152290i	$-0.951335\pi$
$107$	−3.74746	+	6.49080i	−0.362281	+	0.627489i	0.626055	+	0.779779i	$0.284669\pi$
$108$		0			0
$109$	−4.30644	−	7.45897i	−0.412482	−	0.714440i	0.582678	−	0.812703i	$-0.302005\pi$
$109$	−4.30644	−	7.45897i	−0.412482	−	0.714440i	−0.995160	+	0.0982628i	$0.968671\pi$
$110$		0			0
$111$	0.476981	+	2.98881i	0.0452730	+	0.283685i
$112$		0			0
$113$	−1.55747	+	2.69762i	−0.146514	+	0.253771i	−0.929937	−	0.367719i	$-0.880139\pi$
$113$	−1.55747	+	2.69762i	−0.146514	+	0.253771i	0.783422	+	0.621490i	$0.213472\pi$
$114$		0			0
$115$	7.30798	−	12.6578i	0.681473	−	1.18035i
$116$		0			0
$117$	−10.7339	−	9.61930i	−0.992353	−	0.889305i
$118$		0			0
$119$	9.17433	−	3.73342i	0.841010	−	0.342242i
$120$		0			0
$121$	0.703704	+	1.21885i	0.0639731	+	0.110805i
$122$		0			0
$123$	1.37715	+	8.62934i	0.124173	+	0.778081i
$124$		0			0
$125$	12.1710			1.08860
$126$		0			0
$127$	−10.8866			−0.966033			−0.483017	−	0.875611i	$-0.660459\pi$
$127$	−10.8866			−0.966033			−0.483017	+	0.875611i	$0.660459\pi$
$128$		0			0
$129$	−19.7249	−	7.54510i	−1.73668	−	0.664309i
$130$		0			0
$131$	−8.02790	−	13.9047i	−0.701401	−	1.21486i	−0.967975	−	0.251048i	$-0.919225\pi$
$131$	−8.02790	−	13.9047i	−0.701401	−	1.21486i	0.266574	−	0.963815i	$-0.414108\pi$
$132$		0			0
$133$	−11.3392	−	8.81351i	−0.983232	−	0.764228i
$134$		0			0
$135$	−5.16930	+	8.02179i	−0.444903	+	0.690406i
$136$		0			0
$137$	−6.72031	+	11.6399i	−0.574155	+	0.994465i	0.421978	+	0.906606i	$0.361336\pi$
$137$	−6.72031	+	11.6399i	−0.574155	+	0.994465i	−0.996133	+	0.0878590i	$0.971998\pi$
$138$		0			0
$139$	4.06953	−	7.04863i	0.345173	−	0.597857i	−0.640212	−	0.768198i	$-0.721154\pi$
$139$	4.06953	−	7.04863i	0.345173	−	0.597857i	0.985385	+	0.170341i	$0.0544869\pi$
$140$		0			0
$141$	−6.20456	+	5.03644i	−0.522518	+	0.424144i
$142$		0			0
$143$	7.44022	+	12.8868i	0.622182	+	1.07765i
$144$		0			0
$145$	0.597376	−	1.03469i	0.0496094	−	0.0859260i
$146$		0			0
$147$	11.1310	−	4.80628i	0.918071	−	0.396415i
$148$		0			0
$149$	−3.76479	−	6.52081i	−0.308424	−	0.534205i	0.669594	−	0.742727i	$-0.266468\pi$
$149$	−3.76479	−	6.52081i	−0.308424	−	0.534205i	−0.978018	+	0.208522i	$0.933135\pi$
$150$		0			0
$151$	−2.83616	+	4.91237i	−0.230803	+	0.399763i	−0.958045	−	0.286619i	$-0.907469\pi$
$151$	−2.83616	+	4.91237i	−0.230803	+	0.399763i	0.727241	+	0.686382i	$0.240802\pi$
$152$		0			0
$153$	10.6732	−	3.49569i	0.862878	−	0.282610i
$154$		0			0
$155$	−0.951973	−	1.64886i	−0.0764643	−	0.132440i
$156$		0			0
$157$	0.436763			0.0348575			0.0174287	−	0.999848i	$-0.494452\pi$
$157$	0.436763			0.0348575			0.0174287	+	0.999848i	$0.494452\pi$
$158$		0			0
$159$	−14.7241	−	5.63220i	−1.16769	−	0.446663i
$160$		0			0
$161$	−19.5026	+	7.93644i	−1.53702	+	0.625479i
$162$		0			0
$163$	−9.12649	+	15.8076i	−0.714842	+	1.23814i	0.248178	+	0.968714i	$0.420168\pi$
$163$	−9.12649	+	15.8076i	−0.714842	+	1.23814i	−0.963020	+	0.269429i	$0.913165\pi$
$164$		0			0
$165$	7.64936	−	6.20923i	0.595502	−	0.483388i
$166$		0			0
$167$	−0.765108	+	1.32521i	−0.0592058	+	0.102548i	−0.894109	−	0.447849i	$-0.852190\pi$
$167$	−0.765108	+	1.32521i	−0.0592058	+	0.102548i	0.834903	+	0.550397i	$0.185523\pi$
$168$		0			0
$169$	−5.04157	−	8.73226i	−0.387813	−	0.671713i
$170$		0			0
$171$	−12.1273	−	10.8680i	−0.927399	−	0.831096i
$172$		0			0
$173$	2.16949			0.164943			0.0824716	−	0.996593i	$-0.473719\pi$
$173$	2.16949			0.164943			0.0824716	+	0.996593i	$0.473719\pi$
$174$		0			0
$175$	−3.39874	−	2.64171i	−0.256921	−	0.199694i
$176$		0			0
$177$	−7.79602	+	6.32827i	−0.585985	+	0.475662i
$178$		0			0
$179$	1.08263	+	1.87517i	0.0809195	+	0.140157i	0.903645	−	0.428282i	$-0.140881\pi$
$179$	1.08263	+	1.87517i	0.0809195	+	0.140157i	−0.822726	+	0.568439i	$0.807548\pi$
$180$		0			0
$181$	0.557838			0.0414638			0.0207319	−	0.999785i	$-0.493400\pi$
$181$	0.557838			0.0414638			0.0207319	+	0.999785i	$0.493400\pi$
$182$		0			0
$183$	6.47167	−	5.25325i	0.478399	−	0.388332i
$184$		0			0
$185$	3.20927			0.235950
$186$		0			0
$187$	−11.5949			−0.847906
$188$		0			0
$189$	12.9715	−	4.55411i	0.943539	−	0.331262i
$190$		0			0
$191$	23.9997			1.73655			0.868277	−	0.496079i	$-0.165227\pi$
$191$	23.9997			1.73655			0.868277	+	0.496079i	$0.165227\pi$
$192$		0			0
$193$	−21.2794			−1.53172			−0.765862	−	0.643005i	$-0.777687\pi$
$193$	−21.2794			−1.53172			−0.765862	+	0.643005i	$0.777687\pi$
$194$		0			0
$195$	−11.8660	+	9.63201i	−0.849743	+	0.689763i
$196$		0			0
$197$	−14.8768			−1.05993			−0.529964	−	0.848020i	$-0.677795\pi$
$197$	−14.8768			−1.05993			−0.529964	+	0.848020i	$0.677795\pi$
$198$		0			0
$199$	−6.17884	−	10.7021i	−0.438006	−	0.758649i	0.559530	−	0.828810i	$-0.310982\pi$
$199$	−6.17884	−	10.7021i	−0.438006	−	0.758649i	−0.997536	+	0.0701616i	$0.977649\pi$
$200$		0			0
$201$	−19.4688	+	15.8035i	−1.37323	+	1.11469i
$202$		0			0
$203$	−1.59420	+	0.648749i	−0.111891	+	0.0455332i
$204$		0			0
$205$	9.26586			0.647156
$206$		0			0
$207$	−22.6889	+	7.43107i	−1.57699	+	0.516495i
$208$		0			0
$209$	8.40604	+	14.5597i	0.581458	+	1.00711i
$210$		0			0
$211$	−8.65802	+	14.9961i	−0.596043	+	1.03238i	0.397356	+	0.917664i	$0.369928\pi$
$211$	−8.65802	+	14.9961i	−0.596043	+	1.03238i	−0.993399	+	0.114712i	$0.963406\pi$
$212$		0			0
$213$	−6.73347	+	5.46577i	−0.461370	+	0.374508i
$214$		0			0
$215$	−11.1966	+	19.3930i	−0.763599	+	1.32259i
$216$		0			0
$217$	−0.374923	+	2.71706i	−0.0254514	+	0.184446i
$218$		0			0
$219$	5.86797	+	2.24460i	0.396521	+	0.151676i
$220$		0			0
$221$	17.9866			1.20991
$222$		0			0
$223$	−1.14489	−	1.98301i	−0.0766677	−	0.132792i	0.825143	−	0.564925i	$-0.191095\pi$
$223$	−1.14489	−	1.98301i	−0.0766677	−	0.132792i	−0.901810	+	0.432132i	$0.857761\pi$
$224$		0			0
$225$	−3.63497	−	3.25751i	−0.242331	−	0.217167i
$226$		0			0
$227$	−1.78013	+	3.08328i	−0.118152	+	0.204644i	−0.919035	−	0.394176i	$-0.871030\pi$
$227$	−1.78013	+	3.08328i	−0.118152	+	0.204644i	0.800884	+	0.598820i	$0.204364\pi$
$228$		0			0
$229$	13.4799	+	23.3478i	0.890775	+	1.54287i	0.838949	+	0.544211i	$0.183171\pi$
$229$	13.4799	+	23.3478i	0.890775	+	1.54287i	0.0518260	+	0.998656i	$0.483496\pi$
$230$		0			0
$231$	−14.1899	+	0.299909i	−0.933630	+	0.0197325i
$232$		0			0
$233$	10.7321	−	18.5885i	0.703081	−	1.21777i	−0.264298	−	0.964441i	$-0.585140\pi$
$233$	10.7321	−	18.5885i	0.703081	−	1.21777i	0.967380	−	0.253332i	$-0.0815264\pi$
$234$		0			0
$235$	4.23681	+	7.33837i	0.276379	+	0.478703i
$236$		0			0
$237$	−19.3084	+	15.6732i	−1.25421	+	1.01808i
$238$		0			0
$239$	−4.65970	+	8.07083i	−0.301411	+	0.522059i	−0.976456	−	0.215718i	$-0.930791\pi$
$239$	−4.65970	+	8.07083i	−0.301411	+	0.522059i	0.675045	+	0.737777i	$0.264124\pi$
$240$		0			0
$241$	10.1003	−	17.4943i	0.650620	−	1.12691i	−0.332353	−	0.943155i	$-0.607842\pi$
$241$	10.1003	−	17.4943i	0.650620	−	1.12691i	0.982973	−	0.183752i	$-0.0588242\pi$
$242$		0			0
$243$	15.0333	−	4.12297i	0.964389	−	0.264489i
$244$		0			0
$245$	−3.17258	−	12.4584i	−0.202689	−	0.795937i
$246$		0			0
$247$	−13.0398	−	22.5856i	−0.829702	−	1.43709i
$248$		0			0
$249$	12.3964	+	4.74182i	0.785588	+	0.300500i
$250$		0			0
$251$	−27.1837			−1.71582			−0.857910	−	0.513800i	$-0.828238\pi$
$251$	−27.1837			−1.71582			−0.857910	+	0.513800i	$0.828238\pi$
$252$		0			0
$253$	24.6483			1.54963
$254$		0			0
$255$	−1.87677	−	11.7600i	−0.117528	−	0.736441i
$256$		0			0
$257$	−14.2411	−	24.6662i	−0.888333	−	1.53864i	−0.841845	−	0.539719i	$-0.818531\pi$
$257$	−14.2411	−	24.6662i	−0.888333	−	1.53864i	−0.0464876	−	0.998919i	$-0.514803\pi$
$258$		0			0
$259$	−3.65028	−	2.83722i	−0.226818	−	0.176297i
$260$		0			0
$261$	−1.85466	+	0.607438i	−0.114801	+	0.0375995i
$262$		0			0
$263$	1.79907	−	3.11608i	0.110935	−	0.192146i	−0.805212	−	0.592987i	$-0.797949\pi$
$263$	1.79907	−	3.11608i	0.110935	−	0.192146i	0.916148	+	0.400841i	$0.131282\pi$
$264$		0			0
$265$	−8.35791	+	14.4763i	−0.513422	+	0.889274i
$266$		0			0
$267$	−3.14888	−	19.7312i	−0.192708	−	1.20753i
$268$		0			0
$269$	11.2261	+	19.4443i	0.684470	+	1.18554i	0.973603	+	0.228248i	$0.0732997\pi$
$269$	11.2261	+	19.4443i	0.684470	+	1.18554i	−0.289133	+	0.957289i	$0.593367\pi$
$270$		0			0
$271$	14.7935	−	25.6231i	0.898642	−	1.55649i	0.0694115	−	0.997588i	$-0.477888\pi$
$271$	14.7935	−	25.6231i	0.898642	−	1.55649i	0.829231	−	0.558906i	$-0.188779\pi$
$272$		0			0
$273$	22.0120	−	0.465231i	1.33223	−	0.0281570i
$274$		0			0
$275$	2.51958	+	4.36403i	0.151936	+	0.263161i
$276$		0			0
$277$	10.1933	−	17.6554i	0.612459	−	1.06081i	−0.378366	−	0.925656i	$-0.623514\pi$
$277$	10.1933	−	17.6554i	0.612459	−	1.06081i	0.990825	−	0.135153i	$-0.0431527\pi$
$278$		0			0
$279$	−0.639467	+	3.04360i	−0.0382839	+	0.182216i
$280$		0			0
$281$	−2.23968	−	3.87924i	−0.133608	−	0.231416i	0.791457	−	0.611225i	$-0.209323\pi$
$281$	−2.23968	−	3.87924i	−0.133608	−	0.231416i	−0.925065	+	0.379809i	$0.875990\pi$
$282$		0			0
$283$	−2.07680			−0.123453			−0.0617264	−	0.998093i	$-0.519661\pi$
$283$	−2.07680			−0.123453			−0.0617264	+	0.998093i	$0.519661\pi$
$284$		0			0
$285$	−13.4064	+	10.8824i	−0.794124	+	0.644615i
$286$		0			0
$287$	−10.5392	−	8.19169i	−0.622108	−	0.483540i
$288$		0			0
$289$	1.49237	−	2.58486i	0.0877865	−	0.152051i
$290$		0			0
$291$	3.38041	+	1.29306i	0.198163	+	0.0758007i
$292$		0			0
$293$	−0.887340	+	1.53692i	−0.0518389	+	0.0897877i	−0.890780	−	0.454434i	$-0.849842\pi$
$293$	−0.887340	+	1.53692i	−0.0518389	+	0.0897877i	0.838942	+	0.544222i	$0.183175\pi$
$294$		0			0
$295$	5.32355	+	9.22066i	0.309949	+	0.536847i
$296$		0			0
$297$	−16.0743	−	0.785616i	−0.932725	−	0.0455860i
$298$		0			0
$299$	−38.2355			−2.21122
$300$		0			0
$301$	29.8800	−	12.1594i	1.72225	−	0.700858i
$302$		0			0
$303$	4.49111	+	28.1417i	0.258007	+	1.61670i
$304$		0			0
$305$	−4.41921	−	7.65429i	−0.253043	−	0.438283i
$306$		0			0
$307$	−19.6315			−1.12043			−0.560215	−	0.828347i	$-0.689282\pi$
$307$	−19.6315			−1.12043			−0.560215	+	0.828347i	$0.689282\pi$
$308$		0			0
$309$	12.5325	+	4.79388i	0.712948	+	0.272714i
$310$		0			0
$311$	13.3159			0.755076			0.377538	−	0.925994i	$-0.376771\pi$
$311$	13.3159			0.755076			0.377538	+	0.925994i	$0.376771\pi$
$312$		0			0
$313$	4.65281			0.262992			0.131496	−	0.991317i	$-0.458022\pi$
$313$	4.65281			0.262992			0.131496	+	0.991317i	$0.458022\pi$
$314$		0			0
$315$	−2.60098	−	14.3434i	−0.146548	−	0.808160i
$316$		0			0
$317$	−4.12552			−0.231713			−0.115856	−	0.993266i	$-0.536961\pi$
$317$	−4.12552			−0.231713			−0.115856	+	0.993266i	$0.536961\pi$
$318$		0			0
$319$	2.01483			0.112809
$320$		0			0
$321$	−2.04583	−	12.8194i	−0.114187	−	0.715508i
$322$		0			0
$323$	20.3214			1.13071
$324$		0			0
$325$	−3.90847	−	6.76967i	−0.216803	−	0.375514i
$326$		0			0
$327$	13.9334	+	5.32975i	0.770517	+	0.294736i
$328$		0			0
$329$	1.66862	−	12.0925i	0.0919939	−	0.666679i
$330$		0			0
$331$	−0.0440594			−0.00242172			−0.00121086	−	0.999999i	$-0.500385\pi$
$331$	−0.0440594			−0.00242172			−0.00121086	+	0.999999i	$0.500385\pi$
$332$		0			0
$333$	−3.90400	−	3.49860i	−0.213938	−	0.191722i
$334$		0			0
$335$	13.2944	+	23.0266i	0.726350	+	1.25808i
$336$		0			0
$337$	−13.3351	+	23.0970i	−0.726407	+	1.25817i	0.231986	+	0.972719i	$0.425478\pi$
$337$	−13.3351	+	23.0970i	−0.726407	+	1.25817i	−0.958392	+	0.285454i	$0.907856\pi$
$338$		0			0
$339$	−0.850261	−	5.32782i	−0.0461798	−	0.289367i
$340$		0			0
$341$	1.60541	−	2.78064i	0.0869376	−	0.150580i
$342$		0			0
$343$	−7.40556	+	16.9752i	−0.399863	+	0.916575i
$344$		0			0
$345$	3.98960	+	24.9992i	0.214793	+	1.34591i
$346$		0			0
$347$	−10.8252			−0.581126			−0.290563	−	0.956856i	$-0.593843\pi$
$347$	−10.8252			−0.581126			−0.290563	+	0.956856i	$0.593843\pi$
$348$		0			0
$349$	−2.69555	−	4.66884i	−0.144290	−	0.249917i	0.784818	−	0.619726i	$-0.212756\pi$
$349$	−2.69555	−	4.66884i	−0.144290	−	0.249917i	−0.929108	+	0.369809i	$0.879423\pi$
$350$		0			0
$351$	24.9351	+	1.21868i	1.33094	+	0.0650483i
$352$		0			0
$353$	4.47307	−	7.74759i	0.238078	−	0.412362i	−0.722085	−	0.691804i	$-0.756816\pi$
$353$	4.47307	−	7.74759i	0.238078	−	0.412362i	0.960163	+	0.279442i	$0.0901494\pi$
$354$		0			0
$355$	4.59798	+	7.96394i	0.244036	+	0.422682i
$356$		0			0
$357$	−8.26203	+	15.0353i	−0.437273	+	0.795751i
$358$		0			0
$359$	−1.84157	+	3.18969i	−0.0971942	+	0.168345i	−0.910522	−	0.413460i	$-0.864320\pi$
$359$	−1.84157	+	3.18969i	−0.0971942	+	0.168345i	0.813328	+	0.581805i	$0.197653\pi$
$360$		0			0
$361$	−5.23251	−	9.06297i	−0.275395	−	0.476998i
$362$		0			0
$363$	−2.27682	−	0.870920i	−0.119502	−	0.0457114i
$364$		0			0
$365$	3.33087	−	5.76924i	0.174346	−	0.301976i
$366$		0			0
$367$	−3.74988	+	6.49498i	−0.195742	+	0.339035i	−0.947144	−	0.320810i	$-0.896045\pi$
$367$	−3.74988	+	6.49498i	−0.195742	+	0.339035i	0.751401	+	0.659845i	$0.229378\pi$
$368$		0			0
$369$	−11.2717	−	10.1012i	−0.586781	−	0.525849i
$370$		0			0
$371$	22.3046	−	9.07666i	1.15800	−	0.471237i
$372$		0			0
$373$	−4.11917	−	7.13461i	−0.213282	−	0.369416i	0.739458	−	0.673203i	$-0.235082\pi$
$373$	−4.11917	−	7.13461i	−0.213282	−	0.369416i	−0.952740	+	0.303787i	$0.901749\pi$
$374$		0			0
$375$	−16.3672	+	13.2858i	−0.845199	+	0.686075i
$376$		0			0
$377$	−3.12549			−0.160971
$378$		0			0
$379$	3.92853			0.201795			0.100897	−	0.994897i	$-0.467829\pi$
$379$	3.92853			0.201795			0.100897	+	0.994897i	$0.467829\pi$
$380$		0			0
$381$	14.6401	−	11.8838i	0.750034	−	0.608826i
$382$		0			0
$383$	11.9632	+	20.7210i	0.611293	+	1.05879i	0.991023	+	0.133694i	$0.0426838\pi$
$383$	11.9632	+	20.7210i	0.611293	+	1.05879i	−0.379729	+	0.925098i	$0.623983\pi$
$384$		0			0
$385$	−2.05718	+	14.9083i	−0.104843	+	0.759799i
$386$		0			0
$387$	34.7617	−	11.3851i	1.76704	−	0.578740i
$388$		0			0
$389$	−6.32875	+	10.9617i	−0.320881	+	0.555781i	−0.980670	−	0.195669i	$-0.937312\pi$
$389$	−6.32875	+	10.9617i	−0.320881	+	0.555781i	0.659789	+	0.751451i	$0.270645\pi$
$390$		0			0
$391$	14.8967	−	25.8018i	0.753359	−	1.30486i
$392$		0			0
$393$	25.9741	+	9.93551i	1.31022	+	0.501180i
$394$		0			0
$395$	13.1848	+	22.8368i	0.663400	+	1.14904i
$396$		0			0
$397$	−17.7703	+	30.7791i	−0.891866	+	1.54476i	−0.0542297	+	0.998528i	$0.517270\pi$
$397$	−17.7703	+	30.7791i	−0.891866	+	1.54476i	−0.837636	+	0.546229i	$0.816063\pi$
$398$		0			0
$399$	24.8694	−	0.525623i	1.24503	−	0.0263141i
$400$		0			0
$401$	1.66166	+	2.87808i	0.0829794	+	0.143724i	0.904528	−	0.426413i	$-0.140223\pi$
$401$	1.66166	+	2.87808i	0.0829794	+	0.143724i	−0.821549	+	0.570138i	$0.806890\pi$
$402$		0			0
$403$	−2.49037	+	4.31345i	−0.124054	+	0.214868i
$404$		0			0
$405$	−1.80500	−	16.4303i	−0.0896912	−	0.816428i
$406$		0			0
$407$	2.70605	+	4.68702i	0.134134	+	0.232327i
$408$		0			0
$409$	22.5129			1.11319			0.556595	−	0.830784i	$-0.312107\pi$
$409$	22.5129			1.11319			0.556595	+	0.830784i	$0.312107\pi$
$410$		0			0
$411$	−3.66878	−	22.9889i	−0.180968	−	1.13396i
$412$		0			0
$413$	2.09662	−	15.1942i	0.103168	−	0.747656i
$414$		0			0
$415$	7.03662	−	12.1878i	0.345414	−	0.598275i
$416$		0			0
$417$	2.22165	+	13.9211i	0.108795	+	0.681719i
$418$		0			0
$419$	3.59772	−	6.23144i	0.175760	−	0.304426i	−0.764664	−	0.644429i	$-0.777095\pi$
$419$	3.59772	−	6.23144i	0.175760	−	0.304426i	0.940424	+	0.340004i	$0.110428\pi$
$420$		0			0
$421$	16.8121	+	29.1193i	0.819370	+	1.41919i	0.906147	+	0.422962i	$0.139010\pi$
$421$	16.8121	+	29.1193i	0.819370	+	1.41919i	−0.0867773	+	0.996228i	$0.527657\pi$
$422$		0			0
$423$	2.84599	−	13.5457i	0.138377	−	0.658616i
$424$		0			0
$425$	6.09102			0.295458
$426$		0			0
$427$	−1.74045	+	12.6130i	−0.0842264	+	0.610388i
$428$		0			0
$429$	−24.0726	−	9.20818i	−1.16224	−	0.444575i
$430$		0			0
$431$	−16.4871	−	28.5565i	−0.794156	−	1.37552i	−0.923373	−	0.383903i	$-0.874580\pi$
$431$	−16.4871	−	28.5565i	−0.794156	−	1.37552i	0.129217	−	0.991616i	$-0.458754\pi$
$432$		0			0
$433$	19.8977			0.956221			0.478110	−	0.878300i	$-0.341322\pi$
$433$	19.8977			0.956221			0.478110	+	0.878300i	$0.341322\pi$
$434$		0			0
$435$	0.326122	+	2.04351i	0.0156364	+	0.0979789i
$436$		0			0
$437$	−43.1989			−2.06648
$438$		0			0
$439$	−29.1268			−1.39015			−0.695074	−	0.718938i	$-0.744628\pi$
$439$	−29.1268			−1.39015			−0.695074	+	0.718938i	$0.744628\pi$
$440$		0			0
$441$	−9.72221	+	18.6139i	−0.462962	+	0.886378i
$442$		0			0
$443$	−13.7663			−0.654058			−0.327029	−	0.945014i	$-0.606048\pi$
$443$	−13.7663			−0.654058			−0.327029	+	0.945014i	$0.606048\pi$
$444$		0			0
$445$	−21.1866			−1.00434
$446$		0			0
$447$	12.1809	+	4.65939i	0.576136	+	0.220382i
$448$		0			0
$449$	−12.0958			−0.570838			−0.285419	−	0.958403i	$-0.592133\pi$
$449$	−12.0958			−0.570838			−0.285419	+	0.958403i	$0.592133\pi$
$450$		0			0
$451$	7.81297	+	13.5325i	0.367898	+	0.637218i
$452$		0			0
$453$	−1.54833	−	9.70197i	−0.0727468	−	0.455838i
$454$		0			0
$455$	3.19118	−	23.1264i	0.149605	−	1.08418i
$456$		0			0
$457$	−8.35476			−0.390819			−0.195410	−	0.980722i	$-0.562604\pi$
$457$	−8.35476			−0.390819			−0.195410	+	0.980722i	$0.562604\pi$
$458$		0			0
$459$	−10.5372	+	16.3517i	−0.491834	+	0.763234i
$460$		0			0
$461$	11.1673	+	19.3423i	0.520112	+	0.900860i	0.999727	+	0.0233807i	$0.00744299\pi$
$461$	11.1673	+	19.3423i	0.520112	+	0.900860i	−0.479615	+	0.877479i	$0.659224\pi$
$462$		0			0
$463$	0.0370790	−	0.0642228i	0.00172321	−	0.00298469i	−0.865163	−	0.501492i	$-0.832785\pi$
$463$	0.0370790	−	0.0642228i	0.00172321	−	0.00298469i	0.866886	+	0.498507i	$0.166118\pi$
$464$		0			0
$465$	3.08008	+	1.17818i	0.142835	+	0.0546369i
$466$		0			0
$467$	−14.5828	+	25.2581i	−0.674810	+	1.16880i	0.301715	+	0.953398i	$0.402441\pi$
$467$	−14.5828	+	25.2581i	−0.674810	+	1.16880i	−0.976524	+	0.215407i	$0.930892\pi$
$468$		0			0
$469$	5.23584	−	37.9441i	0.241769	−	1.75209i
$470$		0			0
$471$	−0.587348	+	0.476768i	−0.0270635	+	0.0219683i
$472$		0			0
$473$	−37.7637			−1.73638
$474$		0			0
$475$	−4.41583	−	7.64845i	−0.202612	−	0.350935i
$476$		0			0
$477$	25.9486	−	8.49869i	1.18811	−	0.389128i
$478$		0			0
$479$	13.9551	−	24.1710i	0.637626	−	1.10440i	−0.348326	−	0.937373i	$-0.613250\pi$
$479$	13.9551	−	24.1710i	0.637626	−	1.10440i	0.985952	−	0.167027i	$-0.0534168\pi$
$480$		0			0
$481$	−4.19774	−	7.27070i	−0.191401	−	0.331515i
$482$		0			0
$483$	17.5633	−	31.9617i	0.799157	−	1.45431i
$484$		0			0
$485$	1.91884	−	3.32353i	0.0871301	−	0.150914i
$486$		0			0
$487$	2.14409	+	3.71367i	0.0971580	+	0.168283i	0.910507	−	0.413493i	$-0.135691\pi$
$487$	2.14409	+	3.71367i	0.0971580	+	0.168283i	−0.813349	+	0.581776i	$0.802358\pi$
$488$		0			0
$489$	−4.98238	−	31.2200i	−0.225311	−	1.41182i
$490$		0			0
$491$	5.22215	−	9.04503i	0.235672	−	0.408196i	−0.723796	−	0.690015i	$-0.757604\pi$
$491$	5.22215	−	9.04503i	0.235672	−	0.408196i	0.959468	+	0.281818i	$0.0909375\pi$
$492$		0			0
$493$	1.21770	−	2.10912i	0.0548425	−	0.0949900i
$494$		0			0
$495$	−3.50871	+	16.7000i	−0.157705	+	0.750610i
$496$		0			0
$497$	1.81086	−	13.1233i	0.0812282	−	0.588660i
$498$		0			0
$499$	−3.06312	−	5.30548i	−0.137124	−	0.237506i	0.789283	−	0.614030i	$-0.210453\pi$
$499$	−3.06312	−	5.30548i	−0.137124	−	0.237506i	−0.926407	+	0.376524i	$0.877119\pi$
$500$		0			0
$501$	−0.417691	−	2.61729i	−0.0186611	−	0.116932i
$502$		0			0
$503$	12.4469			0.554982			0.277491	−	0.960728i	$-0.410497\pi$
$503$	12.4469			0.554982			0.277491	+	0.960728i	$0.410497\pi$
$504$		0			0
$505$	30.2175			1.34466
$506$		0			0
$507$	16.3119	+	6.23957i	0.724436	+	0.277109i
$508$		0			0
$509$	−5.90450	−	10.2269i	−0.261712	−	0.453299i	0.704985	−	0.709222i	$-0.250954\pi$
$509$	−5.90450	−	10.2269i	−0.261712	−	0.453299i	−0.966697	+	0.255923i	$0.917620\pi$
$510$		0			0
$511$	−8.88902	+	3.61731i	−0.393227	+	0.160021i
$512$		0			0
$513$	28.1720	+	1.37688i	1.24382	+	0.0607906i
$514$		0			0
$515$	7.11388	−	12.3216i	0.313475	−	0.542955i
$516$		0			0
$517$	−7.14495	+	12.3754i	−0.314235	+	0.544271i
$518$		0			0
$519$	−2.91748	+	2.36821i	−0.128063	+	0.103953i
$520$		0			0
$521$	5.54828	+	9.60991i	0.243075	+	0.421018i	0.961589	−	0.274495i	$-0.0885107\pi$
$521$	5.54828	+	9.60991i	0.243075	+	0.421018i	−0.718514	+	0.695513i	$0.755177\pi$
$522$		0			0
$523$	−10.6209	+	18.3960i	−0.464421	+	0.804401i	−0.999175	−	0.0406065i	$-0.987071\pi$
$523$	−10.6209	+	18.3960i	−0.464421	+	0.804401i	0.534754	+	0.845008i	$0.320404\pi$
$524$		0			0
$525$	7.45422	−	0.157547i	0.325329	−	0.00687592i
$526$		0			0
$527$	−1.94052	−	3.36107i	−0.0845302	−	0.146411i
$528$		0			0
$529$	−20.1672	+	34.9305i	−0.876833	+	1.51872i
$530$		0			0
$531$	3.57598	−	17.0202i	0.155184	−	0.738614i
$532$		0			0
$533$	−12.1198	−	20.9921i	−0.524967	−	0.909269i
$534$		0			0
$535$	−13.7650			−0.595111
$536$		0			0
$537$	−3.50282	−	1.33989i	−0.151158	−	0.0578204i
$538$		0			0
$539$	15.5199	−	15.1383i	0.668490	−	0.652054i
$540$		0			0
$541$	−6.33567	+	10.9737i	−0.272392	+	0.471796i	−0.969474	−	0.245195i	$-0.921148\pi$
$541$	−6.33567	+	10.9737i	−0.272392	+	0.471796i	0.697082	+	0.716991i	$0.254481\pi$
$542$		0			0
$543$	−0.750167	+	0.608934i	−0.0321928	+	0.0261319i
$544$		0			0
$545$	7.90908	−	13.6989i	0.338788	−	0.586798i
$546$		0			0
$547$	21.4805	+	37.2053i	0.918438	+	1.59078i	0.801788	+	0.597609i	$0.203883\pi$
$547$	21.4805	+	37.2053i	0.918438	+	1.59078i	0.116651	+	0.993173i	$0.462784\pi$
$548$		0			0
$549$	−2.96850	+	14.1289i	−0.126693	+	0.603006i
$550$		0			0
$551$	−3.53121			−0.150435
$552$		0			0
$553$	5.19268	−	37.6313i	0.220815	−	1.60025i
$554$		0			0
$555$	−4.31574	+	3.50322i	−0.183193	+	0.148704i
$556$		0			0
$557$	16.5129	+	28.6012i	0.699673	+	1.21187i	0.968580	+	0.248703i	$0.0800044\pi$
$557$	16.5129	+	28.6012i	0.699673	+	1.21187i	−0.268906	+	0.963166i	$0.586662\pi$
$558$		0			0
$559$	58.5807			2.47770
$560$		0			0
$561$	15.5926	−	12.6570i	0.658319	−	0.534378i
$562$		0			0
$563$	−36.8132			−1.55149			−0.775746	−	0.631046i	$-0.782626\pi$
$563$	−36.8132			−1.55149			−0.775746	+	0.631046i	$0.782626\pi$
$564$		0			0
$565$	−5.72081			−0.240676
$566$		0			0
$567$	−12.4725	+	20.2839i	−0.523797	+	0.851843i
$568$		0			0
$569$	44.3571			1.85955			0.929774	−	0.368132i	$-0.120002\pi$
$569$	44.3571			1.85955			0.929774	+	0.368132i	$0.120002\pi$
$570$		0			0
$571$	42.5872			1.78222			0.891110	−	0.453787i	$-0.149927\pi$
$571$	42.5872			1.78222			0.891110	+	0.453787i	$0.149927\pi$
$572$		0			0
$573$	−32.2741	+	26.1979i	−1.34827	+	1.09443i
$574$		0			0
$575$	−12.9482			−0.539977
$576$		0			0
$577$	16.3209	+	28.2687i	0.679450	+	1.17684i	0.975147	+	0.221559i	$0.0711147\pi$
$577$	16.3209	+	28.2687i	0.679450	+	1.17684i	−0.295697	+	0.955282i	$0.595552\pi$
$578$		0			0
$579$	28.6160	−	23.2285i	1.18924	−	0.965343i
$580$		0			0
$581$	−18.7785	+	7.64175i	−0.779063	+	0.317033i
$582$		0			0
$583$	−28.1895			−1.16749
$584$		0			0
$585$	5.44285	−	25.9058i	0.225034	−	1.07107i
$586$		0			0
$587$	13.1270	+	22.7366i	0.541809	+	0.938441i	0.998800	+	0.0489701i	$0.0155939\pi$
$587$	13.1270	+	22.7366i	0.541809	+	0.938441i	−0.456991	+	0.889471i	$0.651073\pi$
$588$		0			0
$589$	−2.81365	+	4.87338i	−0.115934	+	0.200804i
$590$		0			0
$591$	20.0059	−	16.2394i	0.822934	−	0.668002i
$592$		0			0
$593$	−2.59998	+	4.50330i	−0.106768	+	0.184928i	−0.914459	−	0.404678i	$-0.867384\pi$
$593$	−2.59998	+	4.50330i	−0.106768	+	0.184928i	0.807691	+	0.589606i	$0.200717\pi$
$594$		0			0
$595$	14.3627	+	11.1636i	0.588814	+	0.457663i
$596$		0			0
$597$	19.9915	+	7.64707i	0.818196	+	0.312974i
$598$		0			0
$599$	−26.3675			−1.07735			−0.538673	−	0.842515i	$-0.681074\pi$
$599$	−26.3675			−1.07735			−0.538673	+	0.842515i	$0.681074\pi$
$600$		0			0
$601$	−15.4505	−	26.7611i	−0.630239	−	1.09161i	−0.987503	−	0.157603i	$-0.949623\pi$
$601$	−15.4505	−	26.7611i	−0.630239	−	1.09161i	0.357263	−	0.934004i	$-0.383710\pi$
$602$		0			0
$603$	8.93021	−	42.5042i	0.363666	−	1.73091i
$604$		0			0
$605$	−1.29240	+	2.23851i	−0.0525436	+	0.0910082i
$606$		0			0
$607$	3.83661	+	6.64519i	0.155723	+	0.269720i	0.933322	−	0.359040i	$-0.116896\pi$
$607$	3.83661	+	6.64519i	0.155723	+	0.269720i	−0.777599	+	0.628760i	$0.783563\pi$
$608$		0			0
$609$	1.43568	−	2.61265i	0.0581765	−	0.105870i
$610$		0			0
$611$	11.0836	−	19.1973i	0.448393	−	0.776639i
$612$		0			0
$613$	7.97498	+	13.8131i	0.322106	+	0.557905i	0.980922	−	0.194399i	$-0.0622758\pi$
$613$	7.97498	+	13.8131i	0.322106	+	0.557905i	−0.658816	+	0.752304i	$0.728942\pi$
$614$		0			0
$615$	−12.4605	+	10.1146i	−0.502456	+	0.407859i
$616$		0			0
$617$	−3.67011	+	6.35682i	−0.147753	+	0.255916i	−0.930397	−	0.366554i	$-0.880537\pi$
$617$	−3.67011	+	6.35682i	−0.147753	+	0.255916i	0.782644	+	0.622470i	$0.213871\pi$
$618$		0			0
$619$	10.2842	−	17.8127i	0.413357	−	0.715955i	−0.581898	−	0.813262i	$-0.697690\pi$
$619$	10.2842	−	17.8127i	0.413357	−	0.715955i	0.995254	+	0.0973072i	$0.0310229\pi$
$620$		0			0
$621$	22.3998	−	34.7603i	0.898873	−	1.39488i
$622$		0			0
$623$	24.0981	+	18.7305i	0.965469	+	0.750421i
$624$		0			0
$625$	7.10891	+	12.3130i	0.284356	+	0.492520i
$626$		0			0
$627$	−27.1975	−	10.4035i	−1.08616	−	0.415476i
$628$		0			0
$629$	6.54182			0.260840
$630$		0			0
$631$	5.09394			0.202787			0.101393	−	0.994846i	$-0.467670\pi$
$631$	5.09394			0.202787			0.101393	+	0.994846i	$0.467670\pi$
$632$		0			0
$633$	−4.72662	−	29.6175i	−0.187866	−	1.17719i
$634$		0			0
$635$	−9.99705	−	17.3154i	−0.396721	−	0.687141i
$636$		0			0
$637$	−24.0751	+	23.4832i	−0.953892	+	0.930439i
$638$		0			0
$639$	3.08859	−	14.7005i	0.122183	−	0.581541i
$640$		0			0
$641$	−6.31861	+	10.9442i	−0.249570	+	0.432268i	−0.963407	−	0.268044i	$-0.913623\pi$
$641$	−6.31861	+	10.9442i	−0.249570	+	0.432268i	0.713836	+	0.700312i	$0.246956\pi$
$642$		0			0
$643$	−12.4329	+	21.5344i	−0.490306	+	0.849235i	−0.999938	−	0.0111579i	$-0.996448\pi$
$643$	−12.4329	+	21.5344i	−0.490306	+	0.849235i	0.509632	+	0.860393i	$0.329782\pi$
$644$		0			0
$645$	−6.11247	−	38.3013i	−0.240678	−	1.50811i
$646$		0			0
$647$	−1.12339	−	1.94577i	−0.0441650	−	0.0764960i	0.843098	−	0.537760i	$-0.180729\pi$
$647$	−1.12339	−	1.94577i	−0.0441650	−	0.0764960i	−0.887263	+	0.461264i	$0.847396\pi$
$648$		0			0
$649$	−8.97762	+	15.5497i	−0.352403	+	0.610379i
$650$		0			0
$651$	−2.46175	−	4.06310i	−0.0964835	−	0.159246i
$652$		0			0
$653$	−1.02881	−	1.78195i	−0.0402604	−	0.0697330i	0.845193	−	0.534461i	$-0.179485\pi$
$653$	−1.02881	−	1.78195i	−0.0402604	−	0.0697330i	−0.885453	+	0.464728i	$0.846152\pi$
$654$		0			0
$655$	14.7438	−	25.5370i	0.576088	−	0.997815i
$656$		0			0
$657$	−10.3413	+	3.38697i	−0.403452	+	0.132138i
$658$		0			0
$659$	4.16599	+	7.21571i	0.162284	+	0.281084i	0.935687	−	0.352830i	$-0.114781\pi$
$659$	4.16599	+	7.21571i	0.162284	+	0.281084i	−0.773403	+	0.633914i	$0.781447\pi$
$660$		0			0
$661$	34.0926			1.32605			0.663024	−	0.748598i	$-0.269273\pi$
$661$	34.0926			1.32605			0.663024	+	0.748598i	$0.269273\pi$
$662$		0			0
$663$	−24.1879	+	19.6341i	−0.939379	+	0.762523i
$664$		0			0
$665$	3.60543	−	26.1285i	0.139812	−	1.01322i
$666$		0			0
$667$	−2.58857	+	4.48353i	−0.100230	+	0.173603i
$668$		0			0
$669$	3.70427	+	1.41694i	0.143215	+	0.0547823i
$670$		0			0
$671$	7.45255	−	12.9082i	0.287702	−	0.498315i
$672$		0			0
$673$	0.571008	+	0.989016i	0.0220108	+	0.0381237i	0.876821	−	0.480817i	$-0.159660\pi$
$673$	0.571008	+	0.989016i	0.0220108	+	0.0381237i	−0.854810	+	0.518941i	$0.826327\pi$
$674$		0			0
$675$	8.44410	+	0.412697i	0.325013	+	0.0158847i
$676$		0			0
$677$	36.3812			1.39824			0.699121	−	0.715004i	$-0.253575\pi$
$677$	36.3812			1.39824			0.699121	+	0.715004i	$0.253575\pi$
$678$		0			0
$679$	−5.12077	+	2.08386i	−0.196517	+	0.0799711i
$680$		0			0
$681$	−0.971817	−	6.08950i	−0.0372401	−	0.233350i
$682$		0			0
$683$	−3.11274	−	5.39142i	−0.119106	−	0.206297i	0.800308	−	0.599589i	$-0.204669\pi$
$683$	−3.11274	−	5.39142i	−0.119106	−	0.206297i	−0.919414	+	0.393292i	$0.871336\pi$
$684$		0			0
$685$	−24.6846			−0.943152
$686$		0			0
$687$	−43.6138	−	16.6830i	−1.66397	−	0.636496i
$688$		0			0
$689$	43.7288			1.66593
$690$		0			0
$691$	39.8259			1.51505			0.757525	−	0.652806i	$-0.226408\pi$
$691$	39.8259			1.51505			0.757525	+	0.652806i	$0.226408\pi$
$692$		0			0
$693$	18.7549	−	15.8930i	0.712440	−	0.603725i
$694$		0			0
$695$	14.9480			0.567008
$696$		0			0
$697$	18.8877			0.715422
$698$		0			0
$699$	5.85890	+	36.7124i	0.221604	+	1.38859i
$700$		0			0
$701$	−48.3337			−1.82554			−0.912769	−	0.408477i	$-0.866060\pi$
$701$	−48.3337			−1.82554			−0.912769	+	0.408477i	$0.866060\pi$
$702$		0			0
$703$	−4.74265	−	8.21452i	−0.178873	−	0.309816i
$704$		0			0
$705$	−13.7081	−	5.24357i	−0.516277	−	0.197484i
$706$		0			0
$707$	−34.3700	−	26.7145i	−1.29262	−	1.00470i
$708$		0			0
$709$	−16.0840			−0.604046			−0.302023	−	0.953301i	$-0.597662\pi$
$709$	−16.0840			−0.604046			−0.302023	+	0.953301i	$0.597662\pi$
$710$		0			0
$711$	8.85660	−	42.1539i	0.332149	−	1.58089i
$712$		0			0
$713$	4.12512	+	7.14491i	0.154487	+	0.267579i
$714$		0			0
$715$	−13.6645	+	23.6676i	−0.511023	+	0.885117i
$716$		0			0
$717$	−2.54384	−	15.9400i	−0.0950015	−	0.595288i
$718$		0			0
$719$	−21.0734	+	36.5002i	−0.785906	+	1.36123i	0.142550	+	0.989788i	$0.454470\pi$
$719$	−21.0734	+	36.5002i	−0.785906	+	1.36123i	−0.928456	+	0.371442i	$0.878864\pi$
$720$		0			0
$721$	−18.9847	+	7.72566i	−0.707026	+	0.287718i
$722$		0			0
$723$	5.51402	+	34.5514i	0.205069	+	1.28498i
$724$		0			0
$725$	−1.05842			−0.0393089
$726$		0			0
$727$	12.9548	+	22.4384i	0.480467	+	0.832192i	0.999749	−	0.0224103i	$-0.00713401\pi$
$727$	12.9548	+	22.4384i	0.480467	+	0.832192i	−0.519282	+	0.854603i	$0.673801\pi$
$728$		0			0
$729$	−15.7158	+	21.9548i	−0.582068	+	0.813140i
$730$		0			0
$731$	−22.8232	+	39.5310i	−0.844148	+	1.46211i
$732$		0			0
$733$	−10.2027	−	17.6716i	−0.376846	−	0.652716i	0.613756	−	0.789496i	$-0.289658\pi$
$733$	−10.2027	−	17.6716i	−0.376846	−	0.652716i	−0.990601	+	0.136780i	$0.956325\pi$
$734$		0			0
$735$	17.8659	+	13.2906i	0.658994	+	0.490229i
$736$		0			0
$737$	−22.4196	+	38.8320i	−0.825838	+	1.43039i
$738$		0			0
$739$	11.8953	+	20.6033i	0.437576	+	0.757903i	0.997502	−	0.0706392i	$-0.0225039\pi$
$739$	11.8953	+	20.6033i	0.437576	+	0.757903i	−0.559926	+	0.828542i	$0.689171\pi$
$740$		0			0
$741$	42.1899	+	16.1383i	1.54989	+	0.592857i
$742$		0			0
$743$	−21.6320	+	37.4678i	−0.793603	+	1.37456i	0.130120	+	0.991498i	$0.458464\pi$
$743$	−21.6320	+	37.4678i	−0.793603	+	1.37456i	−0.923723	+	0.383062i	$0.874870\pi$
$744$		0			0
$745$	6.91430	−	11.9759i	0.253321	−	0.438764i
$746$		0			0
$747$	−21.8465	+	7.15515i	−0.799320	+	0.261793i
$748$		0			0
$749$	15.6565	+	12.1692i	0.572078	+	0.444654i
$750$		0			0
$751$	−7.18465	−	12.4442i	−0.262172	−	0.454095i	0.704647	−	0.709558i	$-0.251105\pi$
$751$	−7.18465	−	12.4442i	−0.262172	−	0.454095i	−0.966819	+	0.255463i	$0.917772\pi$
$752$		0			0
$753$	36.5560	−	29.6736i	1.33217	−	1.08137i
$754$		0			0
$755$	−10.4176			−0.379136
$756$		0			0
$757$	39.7854			1.44603			0.723013	−	0.690835i	$-0.242757\pi$
$757$	39.7854			1.44603			0.723013	+	0.690835i	$0.242757\pi$
$758$		0			0
$759$	−33.1465	+	26.9060i	−1.20314	+	0.976626i
$760$		0			0
$761$	11.1966	+	19.3932i	0.405878	+	0.703002i	0.994423	−	0.105463i	$-0.0336324\pi$
$761$	11.1966	+	19.3932i	0.405878	+	0.703002i	−0.588545	+	0.808464i	$0.700299\pi$
$762$		0			0
$763$	−21.1068	+	8.58924i	−0.764117	+	0.310951i
$764$		0			0
$765$	15.3610	+	13.7659i	0.555378	+	0.497707i
$766$		0			0
$767$	13.9265	−	24.1213i	0.502856	−	0.870971i
$768$		0			0
$769$	−1.45546	+	2.52093i	−0.0524853	+	0.0909071i	−0.891074	−	0.453857i	$-0.850048\pi$
$769$	−1.45546	+	2.52093i	−0.0524853	+	0.0909071i	0.838589	+	0.544764i	$0.183381\pi$
$770$		0			0
$771$	46.0766	+	17.6251i	1.65941	+	0.634751i
$772$		0			0
$773$	−6.68612	−	11.5807i	−0.240483	−	0.416529i	0.720369	−	0.693591i	$-0.243972\pi$
$773$	−6.68612	−	11.5807i	−0.240483	−	0.416529i	−0.960852	+	0.277062i	$0.910639\pi$
$774$		0			0
$775$	−0.843347	+	1.46072i	−0.0302939	+	0.0524706i
$776$		0			0
$777$	8.00591	−	0.169207i	0.287211	−	0.00607028i
$778$		0			0
$779$	−13.6931	−	23.7171i	−0.490606	−	0.849754i
$780$		0			0
$781$	−7.75403	+	13.4304i	−0.277461	+	0.480577i
$782$		0			0
$783$	1.83103	−	2.84141i	0.0654355	−	0.101544i
$784$		0			0
$785$	0.401073	+	0.694679i	0.0143149	+	0.0247941i
$786$		0			0
$787$	23.8528			0.850260			0.425130	−	0.905132i	$-0.360228\pi$
$787$	23.8528			0.850260			0.425130	+	0.905132i	$0.360228\pi$
$788$		0			0
$789$	0.982156	+	6.15428i	0.0349657	+	0.219098i
$790$		0			0
$791$	6.50696	+	5.05761i	0.231361	+	0.179828i
$792$		0			0
$793$	−11.5607	+	20.0237i	−0.410533	+	0.711063i
$794$		0			0
$795$	−4.56279	−	28.5909i	−0.161825	−	1.01401i
$796$		0			0
$797$	−6.10559	+	10.5752i	−0.216271	+	0.374593i	−0.953665	−	0.300870i	$-0.902723\pi$
$797$	−6.10559	+	10.5752i	−0.216271	+	0.374593i	0.737394	+	0.675463i	$0.236056\pi$
$798$		0			0
$799$	8.63639	+	14.9587i	0.305533	+	0.529199i
$800$		0			0
$801$	25.7730	+	23.0967i	0.910645	+	0.816082i
$802$		0			0
$803$	11.2344			0.396452
$804$		0			0
$805$	−30.5320	−	23.7314i	−1.07611	−	0.836421i
$806$		0			0
$807$	−36.3219	−	13.8937i	−1.27859	−	0.489082i
$808$		0			0
$809$	26.7838	+	46.3910i	0.941669	+	1.63102i	0.762287	+	0.647240i	$0.224077\pi$
$809$	26.7838	+	46.3910i	0.941669	+	1.63102i	0.179383	+	0.983779i	$0.442590\pi$
$810$		0			0
$811$	−1.81310			−0.0636667			−0.0318334	−	0.999493i	$-0.510135\pi$
$811$	−1.81310			−0.0636667			−0.0318334	+	0.999493i	$0.510135\pi$
$812$		0			0
$813$	8.07614	+	50.6059i	0.283243	+	1.77483i
$814$		0			0
$815$	−33.5229			−1.17426
$816$		0			0
$817$	66.1851			2.31552
$818$		0			0
$819$	−29.0934	+	24.6539i	−1.01661	+	0.861476i
$820$		0			0
$821$	−39.6743			−1.38464			−0.692321	−	0.721590i	$-0.743412\pi$
$821$	−39.6743			−1.38464			−0.692321	+	0.721590i	$0.743412\pi$
$822$		0			0
$823$	−16.8131			−0.586069			−0.293034	−	0.956102i	$-0.594665\pi$
$823$	−16.8131			−0.586069			−0.293034	+	0.956102i	$0.594665\pi$
$824$		0			0
$825$	−8.15202	−	3.11828i	−0.283817	−	0.108565i
$826$		0			0
$827$	−37.2198			−1.29426			−0.647130	−	0.762379i	$-0.724031\pi$
$827$	−37.2198			−1.29426			−0.647130	+	0.762379i	$0.724031\pi$
$828$		0			0
$829$	−11.4365	−	19.8086i	−0.397206	−	0.687981i	0.596174	−	0.802855i	$-0.296687\pi$
$829$	−11.4365	−	19.8086i	−0.397206	−	0.687981i	−0.993380	+	0.114874i	$0.963354\pi$
$830$		0			0
$831$	5.56479	+	34.8695i	0.193041	+	1.20961i
$832$		0			0
$833$	−6.46703	−	25.3954i	−0.224069	−	0.879898i
$834$		0			0
$835$	−2.81035			−0.0972562
$836$		0			0
$837$	−2.46245	−	4.79100i	−0.0851146	−	0.165601i
$838$		0			0
$839$	−18.4071	−	31.8820i	−0.635484	−	1.10069i	−0.986412	−	0.164288i	$-0.947467\pi$
$839$	−18.4071	−	31.8820i	−0.635484	−	1.10069i	0.350929	−	0.936402i	$-0.385866\pi$
$840$		0			0
$841$	14.2884	−	24.7482i	0.492704	−	0.853388i
$842$		0			0
$843$	7.24643	+	2.77188i	0.249580	+	0.0954686i
$844$		0			0
$845$	9.25921	−	16.0374i	0.318527	−	0.551704i
$846$		0			0
$847$	3.44901	−	1.40354i	0.118509	−	0.0482264i
$848$		0			0
$849$	2.79282	−	2.26702i	0.0958495	−	0.0778040i
$850$		0			0
$851$	−13.9065			−0.476709
$852$		0			0
$853$	6.98355	+	12.0959i	0.239112	+	0.414155i	0.960460	−	0.278419i	$-0.0898102\pi$
$853$	6.98355	+	12.0959i	0.239112	+	0.414155i	−0.721347	+	0.692573i	$0.756477\pi$
$854$		0			0
$855$	6.14939	−	29.2686i	0.210305	−	1.00097i
$856$		0			0
$857$	−8.78386	+	15.2141i	−0.300051	+	0.519703i	−0.976147	−	0.217110i	$-0.930337\pi$
$857$	−8.78386	+	15.2141i	−0.300051	+	0.519703i	0.676096	+	0.736813i	$0.263670\pi$
$858$		0			0
$859$	1.42288	+	2.46451i	0.0485482	+	0.0840879i	0.889278	−	0.457366i	$-0.151207\pi$
$859$	1.42288	+	2.46451i	0.0485482	+	0.0840879i	−0.840730	+	0.541454i	$0.817874\pi$
$860$		0			0
$861$	23.1148	−	0.488539i	0.787751	−	0.0166493i
$862$		0			0
$863$	27.7115	−	47.9977i	0.943310	−	1.63386i	0.184210	−	0.982887i	$-0.441027\pi$
$863$	27.7115	−	47.9977i	0.943310	−	1.63386i	0.759100	−	0.650974i	$-0.225639\pi$
$864$		0			0
$865$	1.99221	+	3.45061i	0.0677372	+	0.117324i
$866$		0			0
$867$	0.814721	+	5.10512i	0.0276694	+	0.173379i
$868$		0			0
$869$	−22.2348	+	38.5119i	−0.754265	+	1.30643i
$870$		0			0
$871$	34.7783	−	60.2378i	1.17842	−	2.04108i
$872$		0			0
$873$	−5.95739	+	1.95116i	−0.201627	+	0.0660368i
$874$		0			0
$875$	4.40170	−	31.8991i	0.148805	−	1.07839i
$876$		0			0
$877$	−27.4345	−	47.5179i	−0.926396	−	1.60456i	−0.789301	−	0.614006i	$-0.789557\pi$
$877$	−27.4345	−	47.5179i	−0.926396	−	1.60456i	−0.137095	−	0.990558i	$-0.543776\pi$
$878$		0			0
$879$	−0.484420	−	3.03542i	−0.0163391	−	0.102382i
$880$		0			0
$881$	−51.1572			−1.72353			−0.861765	−	0.507307i	$-0.830641\pi$
$881$	−51.1572			−1.72353			−0.861765	+	0.507307i	$0.830641\pi$
$882$		0			0
$883$	−38.6438			−1.30047			−0.650234	−	0.759734i	$-0.725329\pi$
$883$	−38.6438			−1.30047			−0.650234	+	0.759734i	$0.725329\pi$
$884$		0			0
$885$	−17.2242	−	6.58854i	−0.578985	−	0.221471i
$886$		0			0
$887$	−8.92626	−	15.4607i	−0.299714	−	0.519121i	0.676356	−	0.736575i	$-0.263558\pi$
$887$	−8.92626	−	15.4607i	−0.299714	−	0.519121i	−0.976071	+	0.217454i	$0.930225\pi$
$888$		0			0
$889$	−3.93722	+	28.5330i	−0.132050	+	0.956966i
$890$		0			0
$891$	22.4739	−	16.4901i	0.752903	−	0.552441i
$892$		0			0
$893$	12.5223	−	21.6893i	0.419043	−	0.725805i
$894$		0			0
$895$	−1.98833	+	3.44388i	−0.0664624	+	0.115116i
$896$		0			0
$897$	51.4182	−	41.7377i	1.71680	−	1.39358i
$898$		0			0
$899$	0.337199	+	0.584047i	0.0112462	+	0.0194790i
$900$		0			0
$901$	−17.0369	+	29.5088i	−0.567581	+	0.983080i
$902$		0			0
$903$	−26.9087	+	48.9686i	−0.895465	+	1.62957i
$904$		0			0
$905$	0.512255	+	0.887252i	0.0170279	+	0.0294932i
$906$		0			0
$907$	−18.2332	+	31.5807i	−0.605422	+	1.04862i	0.386563	+	0.922263i	$0.373662\pi$
$907$	−18.2332	+	31.5807i	−0.605422	+	1.04862i	−0.991985	+	0.126358i	$0.959671\pi$
$908$		0			0
$909$	−36.7589	−	32.9418i	−1.21921	−	1.09261i
$910$		0			0
$911$	−18.9847	−	32.8825i	−0.628993	−	1.08945i	−0.987754	−	0.156018i	$-0.950134\pi$
$911$	−18.9847	−	32.8825i	−0.628993	−	1.08945i	0.358762	−	0.933429i	$-0.383199\pi$
$912$		0			0
$913$	23.7331			0.785451
$914$		0			0
$915$	14.2982	+	5.46931i	0.472685	+	0.180810i
$916$		0			0
$917$	−39.3465	+	16.0117i	−1.29934	+	0.528754i
$918$		0			0
$919$	1.21770	−	2.10911i	0.0401681	−	0.0695732i	−0.845242	−	0.534383i	$-0.820544\pi$
$919$	1.21770	−	2.10911i	0.0401681	−	0.0695732i	0.885411	+	0.464810i	$0.153877\pi$
$920$		0			0
$921$	26.4000	−	21.4297i	0.869909	−	0.706132i
$922$		0			0
$923$	12.0284	−	20.8338i	0.395919	−	0.685752i
$924$		0			0
$925$	−1.42153	−	2.46217i	−0.0467398	−	0.0809557i
$926$		0			0
$927$	−22.0863	+	7.23371i	−0.725410	+	0.237586i
$928$		0			0
$929$	−35.4808			−1.16409			−0.582044	−	0.813157i	$-0.697747\pi$
$929$	−35.4808			−1.16409			−0.582044	+	0.813157i	$0.697747\pi$
$930$		0			0
$931$	−27.2004	+	26.5316i	−0.891456	+	0.869538i
$932$		0			0
$933$	−17.9069	+	14.5356i	−0.586245	+	0.475874i
$934$		0			0
$935$	−10.6475	−	18.4420i	−0.348209	−	0.603116i
$936$		0			0
$937$	−30.0427			−0.981452			−0.490726	−	0.871314i	$-0.663268\pi$
$937$	−30.0427			−0.981452			−0.490726	+	0.871314i	$0.663268\pi$
$938$		0			0
$939$	−6.25698	+	5.07899i	−0.204189	+	0.165746i
$940$		0			0
$941$	−30.2499			−0.986119			−0.493060	−	0.869996i	$-0.664122\pi$
$941$	−30.2499			−0.986119			−0.493060	+	0.869996i	$0.664122\pi$
$942$		0			0
$943$	−40.1511			−1.30750
$944$		0			0
$945$	19.1549	+	16.4494i	0.623110	+	0.535100i
$946$		0			0
$947$	−33.9889			−1.10449			−0.552245	−	0.833682i	$-0.686229\pi$
$947$	−33.9889			−1.10449			−0.552245	+	0.833682i	$0.686229\pi$
$948$		0			0
$949$	−17.4272			−0.565711
$950$		0			0
$951$	5.54790	−	4.50340i	0.179903	−	0.146033i
$952$		0			0
$953$	−21.4324			−0.694265			−0.347132	−	0.937816i	$-0.612845\pi$
$953$	−21.4324			−0.694265			−0.347132	+	0.937816i	$0.612845\pi$
$954$		0			0
$955$	22.0385	+	38.1719i	0.713151	+	1.23521i
$956$		0			0
$957$	−2.70949	+	2.19938i	−0.0875854	+	0.0710958i
$958$		0			0
$959$	28.0768	+	21.8230i	0.906647	+	0.704702i
$960$		0			0
$961$	−29.9253			−0.965332
$962$		0			0
$963$	16.7448	+	15.0060i	0.539592	+	0.483560i
$964$		0			0
$965$	−19.5406	−	33.8452i	−0.629033	−	1.08952i
$966$		0			0
$967$	−12.4095	+	21.4938i	−0.399061	+	0.691194i	−0.993610	−	0.112865i	$-0.963997\pi$
$967$	−12.4095	+	21.4938i	−0.399061	+	0.691194i	0.594549	+	0.804059i	$0.297331\pi$
$968$		0			0
$969$	−27.3277	+	22.1828i	−0.877893	+	0.712613i
$970$		0			0
$971$	13.9437	−	24.1512i	0.447475	−	0.775050i	−0.550746	−	0.834673i	$-0.685657\pi$
$971$	13.9437	−	24.1512i	0.447475	−	0.775050i	0.998221	+	0.0596234i	$0.0189900\pi$
$972$		0			0
$973$	−17.0021	−	13.2151i	−0.545062	−	0.423656i
$974$		0			0
$975$	12.6458	+	4.83721i	0.404988	+	0.154915i
$976$		0			0
$977$	27.2473			0.871719			0.435859	−	0.900015i	$-0.356445\pi$
$977$	27.2473			0.871719			0.435859	+	0.900015i	$0.356445\pi$
$978$		0			0
$979$	−17.8645	−	30.9423i	−0.570953	−	0.988920i
$980$		0			0
$981$	−24.5552	+	8.04230i	−0.783986	+	0.256771i
$982$		0			0
$983$	−6.94539	+	12.0298i	−0.221523	+	0.383690i	−0.955271	−	0.295733i	$-0.904436\pi$
$983$	−6.94539	+	12.0298i	−0.221523	+	0.383690i	0.733747	+	0.679422i	$0.237770\pi$
$984$		0			0
$985$	−13.6611	−	23.6618i	−0.435280	−	0.753928i
$986$		0			0
$987$	10.9562	+	18.0831i	0.348738	+	0.575591i
$988$		0			0
$989$	48.5173	−	84.0344i	1.54276	−	2.67214i
$990$		0			0
$991$	−21.3271	−	36.9397i	−0.677479	−	1.17343i	−0.975738	−	0.218942i	$-0.929739\pi$
$991$	−21.3271	−	36.9397i	−0.677479	−	1.17343i	0.298259	−	0.954485i	$-0.403594\pi$
$992$		0			0
$993$	0.0592500	−	0.0480950i	0.00188024	−	0.00152625i
$994$		0			0
$995$	11.3479	−	19.6551i	0.359752	−	0.623108i
$996$		0			0
$997$	−21.5905	+	37.3959i	−0.683779	+	1.18434i	0.290040	+	0.957014i	$0.406331\pi$
$997$	−21.5905	+	37.3959i	−0.683779	+	1.18434i	−0.973819	+	0.227325i	$0.927002\pi$
$998$		0			0
$999$	9.06905	+	0.443241i	0.286932	+	0.0140235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.k.625.3		22
3.2	odd	2		3024.2.q.k.2305.4		22
4.3	odd	2		504.2.q.d.121.9	yes	22
7.4	even	3		1008.2.t.k.193.11		22
9.2	odd	6		3024.2.t.l.289.8		22
9.7	even	3		1008.2.t.k.961.11		22
12.11	even	2		1512.2.q.c.793.4		22
21.11	odd	6		3024.2.t.l.1873.8		22
28.11	odd	6		504.2.t.d.193.1	yes	22
36.7	odd	6		504.2.t.d.457.1	yes	22
36.11	even	6		1512.2.t.d.289.8		22
63.11	odd	6		3024.2.q.k.2881.4		22
63.25	even	3	inner	1008.2.q.k.529.3		22
84.11	even	6		1512.2.t.d.361.8		22
252.11	even	6		1512.2.q.c.1369.4		22
252.151	odd	6		504.2.q.d.25.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.9	✓	22	252.151	odd	6
504.2.q.d.121.9	yes	22	4.3	odd	2
504.2.t.d.193.1	yes	22	28.11	odd	6
504.2.t.d.457.1	yes	22	36.7	odd	6
1008.2.q.k.529.3		22	63.25	even	3	inner
1008.2.q.k.625.3		22	1.1	even	1	trivial
1008.2.t.k.193.11		22	7.4	even	3
1008.2.t.k.961.11		22	9.7	even	3
1512.2.q.c.793.4		22	12.11	even	2
1512.2.q.c.1369.4		22	252.11	even	6
1512.2.t.d.289.8		22	36.11	even	6
1512.2.t.d.361.8		22	84.11	even	6
3024.2.q.k.2305.4		22	3.2	odd	2
3024.2.q.k.2881.4		22	63.11	odd	6
3024.2.t.l.289.8		22	9.2	odd	6
3024.2.t.l.1873.8		22	21.11	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34477 + 1.09160i) q^{3} +(0.918286 + 1.59052i) q^{5} +(0.361656 - 2.62092i) q^{7} +(0.616838 - 2.93590i) q^{9} +(-1.54860 + 2.68225i) q^{11} +(2.40225 - 4.16081i) q^{13} +(-2.97109 - 1.13649i) q^{15} +(1.87185 + 3.24214i) q^{17} +(2.71408 - 4.70093i) q^{19} +(2.37464 + 3.91932i) q^{21} +(-3.97914 - 6.89208i) q^{23} +(0.813503 - 1.40903i) q^{25} +(2.37531 + 4.62146i) q^{27} +(-0.325267 - 0.563379i) q^{29} -1.03668 q^{31} +(-0.845416 - 5.29746i) q^{33} +(4.50072 - 1.83153i) q^{35} +(0.873712 - 1.51331i) q^{37} +(1.31144 + 8.21764i) q^{39} +(2.52260 - 4.36927i) q^{41} +(6.09645 + 10.5594i) q^{43} +(5.23603 - 1.71490i) q^{45} +4.61383 q^{47} +(-6.73841 - 1.89574i) q^{49} +(-6.05632 - 2.31664i) q^{51} +(4.55082 + 7.88226i) q^{53} -5.68821 q^{55} +(1.48168 + 9.28438i) q^{57} +5.79727 q^{59} -4.81245 q^{61} +(-7.47167 - 2.67847i) q^{63} +8.82379 q^{65} +14.4774 q^{67} +(12.8744 + 4.92468i) q^{69} +5.00714 q^{71} +(-1.81364 - 3.14131i) q^{73} +(0.444111 + 2.78284i) q^{75} +(6.46989 + 5.02879i) q^{77} +14.3581 q^{79} +(-8.23902 - 3.62195i) q^{81} +(-3.83139 - 6.63616i) q^{83} +(-3.43778 + 5.95441i) q^{85} +(1.05239 + 0.402558i) q^{87} +(-5.76798 + 9.99043i) q^{89} +(-10.0364 - 7.80087i) q^{91} +(1.39411 - 1.13164i) q^{93} +9.96922 q^{95} +(-1.04480 - 1.80964i) q^{97} +(6.91957 + 6.20103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9} + 3 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 2 q^{23} - 10 q^{25} + 4 q^{27} + 9 q^{29} - 8 q^{31} + 29 q^{33} - 14 q^{35} + 2 q^{37} + 16 q^{39}+ \cdots + 56 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9 + 3 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 2 * q^23 - 10 * q^25 + 4 * q^27 + 9 * q^29 - 8 * q^31 + 29 * q^33 - 14 * q^35 + 2 * q^37 + 16 * q^39 + 16 * q^41 + q^45 + 10 * q^47 + 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 - 38 * q^59 + 26 * q^61 - 48 * q^63 - 26 * q^65 + 52 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 23 * q^75 + 17 * q^77 + 20 * q^79 - 38 * q^81 + 28 * q^83 - 20 * q^85 + 33 * q^87 + 6 * q^89 + 37 * q^91 + 19 * q^93 + 24 * q^95 - 29 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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