LMFDB - Embedded newform 3150.2.bf.d.1151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bf (of order $6$, degree $2$, 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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.6
Character	$\chi$	$=$	3150.1151
Dual form			3150.2.bf.d.1601.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.717905 + 2.54649i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.717905 + 2.54649i) q^{7} +1.00000i q^{8} +(5.09272 + 2.94028i) q^{11} +4.05674i q^{13} +(-1.89497 - 1.84637i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.214504 - 0.371532i) q^{17} +(5.30761 - 3.06435i) q^{19} -5.88057 q^{22} +(1.51729 - 0.876005i) q^{23} +(-2.02837 - 3.51324i) q^{26} +(2.56428 + 0.651521i) q^{28} +0.0419065i q^{29} +(7.92389 + 4.57486i) q^{31} +(0.866025 + 0.500000i) q^{32} +0.429009i q^{34} +(0.536089 + 0.928534i) q^{37} +(-3.06435 + 5.30761i) q^{38} -8.61559 q^{41} +11.0724 q^{43} +(5.09272 - 2.94028i) q^{44} +(-0.876005 + 1.51729i) q^{46} +(0.481567 + 0.834099i) q^{47} +(-5.96922 + 3.65628i) q^{49} +(3.51324 + 2.02837i) q^{52} +(-11.3848 - 6.57304i) q^{53} +(-2.54649 + 0.717905i) q^{56} +(-0.0209532 - 0.0362921i) q^{58} +(6.77318 - 11.7315i) q^{59} +(1.05635 - 0.609885i) q^{61} -9.14972 q^{62} -1.00000 q^{64} +(-6.32352 + 10.9527i) q^{67} +(-0.214504 - 0.371532i) q^{68} -2.54990i q^{71} +(8.08328 + 4.66689i) q^{73} +(-0.928534 - 0.536089i) q^{74} -6.12870i q^{76} +(-3.83131 + 15.0794i) q^{77} +(-5.35961 - 9.28312i) q^{79} +(7.46132 - 4.30780i) q^{82} -10.1027 q^{83} +(-9.58894 + 5.53618i) q^{86} +(-2.94028 + 5.09272i) q^{88} +(-3.15638 - 5.46700i) q^{89} +(-10.3304 + 2.91235i) q^{91} -1.75201i q^{92} +(-0.834099 - 0.481567i) q^{94} -2.59007i q^{97} +(3.34136 - 6.15104i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} - 4 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 - 4 * q^7	$ 24 q + 12 q^{4} - 4 q^{7} - 12 q^{16} + 12 q^{19} + 4 q^{28} + 28 q^{37} + 96 q^{43} - 8 q^{46} - 52 q^{49} - 12 q^{52} + 8 q^{58} - 12 q^{61} - 24 q^{64} - 4 q^{67} - 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 - 4 * q^7 - 12 * q^16 + 12 * q^19 + 4 * q^28 + 28 * q^37 + 96 * q^43 - 8 * q^46 - 52 * q^49 - 12 * q^52 + 8 * q^58 - 12 * q^61 - 24 * q^64 - 4 * q^67 - 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.717905	+	2.54649i	0.271343	+	0.962483i
$7$	0.717905	+	2.54649i	0.271343	+	0.962483i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	5.09272	+	2.94028i	1.53551	+	0.886529i	0.999093	+	0.0425771i	$0.0135568\pi$
$11$	5.09272	+	2.94028i	1.53551	+	0.886529i	0.536419	+	0.843952i	$0.319777\pi$
$12$		0			0
$13$			4.05674i			1.12514i	0.826751	+	0.562569i	$0.190187\pi$
$13$			4.05674i			1.12514i	−0.826751	+	0.562569i	$0.809813\pi$
$14$	−1.89497	−	1.84637i	−0.506452	−	0.493464i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.214504	−	0.371532i	0.0520249	−	0.0901098i	−0.838840	−	0.544378i	$-0.816766\pi$
$17$	0.214504	−	0.371532i	0.0520249	−	0.0901098i	0.890865	+	0.454268i	$0.150099\pi$
$18$		0			0
$19$	5.30761	−	3.06435i	1.21765	−	0.703010i	0.253234	−	0.967405i	$-0.418506\pi$
$19$	5.30761	−	3.06435i	1.21765	−	0.703010i	0.964414	+	0.264395i	$0.0851723\pi$
$20$		0			0
$21$		0			0
$22$	−5.88057			−1.25374
$23$	1.51729	−	0.876005i	0.316376	−	0.182660i	−0.333400	−	0.942785i	$-0.608196\pi$
$23$	1.51729	−	0.876005i	0.316376	−	0.182660i	0.649776	+	0.760126i	$0.274863\pi$
$24$		0			0
$25$		0			0
$26$	−2.02837	−	3.51324i	−0.397796	−	0.689003i
$27$		0			0
$28$	2.56428	+	0.651521i	0.484603	+	0.123126i
$29$			0.0419065i			0.00778184i	0.999992	+	0.00389092i	$0.00123852\pi$
$29$			0.0419065i			0.00778184i	−0.999992	+	0.00389092i	$0.998761\pi$
$30$		0			0
$31$	7.92389	+	4.57486i	1.42317	+	0.821669i	0.996569	−	0.0827694i	$-0.0263765\pi$
$31$	7.92389	+	4.57486i	1.42317	+	0.821669i	0.426604	+	0.904439i	$0.359710\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			0.429009i			0.0735744i
$35$		0			0
$36$		0			0
$37$	0.536089	+	0.928534i	0.0881326	+	0.152650i	0.906722	−	0.421729i	$-0.138577\pi$
$37$	0.536089	+	0.928534i	0.0881326	+	0.152650i	−0.818589	+	0.574379i	$0.805243\pi$
$38$	−3.06435	+	5.30761i	−0.497103	+	0.861008i
$39$		0			0
$40$		0			0
$41$	−8.61559			−1.34553			−0.672765	−	0.739856i	$-0.734893\pi$
$41$	−8.61559			−1.34553			−0.672765	+	0.739856i	$0.734893\pi$
$42$		0			0
$43$	11.0724			1.68852			0.844259	−	0.535935i	$-0.180041\pi$
$43$	11.0724			1.68852			0.844259	+	0.535935i	$0.180041\pi$
$44$	5.09272	−	2.94028i	0.767756	−	0.443264i
$45$		0			0
$46$	−0.876005	+	1.51729i	−0.129160	+	0.223712i
$47$	0.481567	+	0.834099i	0.0702438	+	0.121666i	0.899008	−	0.437932i	$-0.144289\pi$
$47$	0.481567	+	0.834099i	0.0702438	+	0.121666i	−0.828764	+	0.559598i	$0.810956\pi$
$48$		0			0
$49$	−5.96922	+	3.65628i	−0.852746	+	0.522325i
$50$		0			0
$51$		0			0
$52$	3.51324	+	2.02837i	0.487199	+	0.281284i
$53$	−11.3848	−	6.57304i	−1.56383	−	0.902877i	−0.996864	−	0.0791353i	$-0.974784\pi$
$53$	−11.3848	−	6.57304i	−1.56383	−	0.902877i	−0.566965	−	0.823742i	$-0.691883\pi$
$54$		0			0
$55$		0			0
$56$	−2.54649	+	0.717905i	−0.340289	+	0.0959341i
$57$		0			0
$58$	−0.0209532	−	0.0362921i	−0.00275129	−	0.00476538i
$59$	6.77318	−	11.7315i	0.881793	−	1.52731i	0.0324481	−	0.999473i	$-0.489670\pi$
$59$	6.77318	−	11.7315i	0.881793	−	1.52731i	0.849345	−	0.527838i	$-0.176997\pi$
$60$		0			0
$61$	1.05635	−	0.609885i	0.135252	−	0.0780878i	−0.430847	−	0.902425i	$-0.641785\pi$
$61$	1.05635	−	0.609885i	0.135252	−	0.0780878i	0.566099	+	0.824337i	$0.308452\pi$
$62$	−9.14972			−1.16202
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−6.32352	+	10.9527i	−0.772541	+	1.33808i	0.163625	+	0.986523i	$0.447681\pi$
$67$	−6.32352	+	10.9527i	−0.772541	+	1.33808i	−0.936166	+	0.351558i	$0.885652\pi$
$68$	−0.214504	−	0.371532i	−0.0260125	−	0.0450549i
$69$		0			0
$70$		0			0
$71$		−	2.54990i		−	0.302617i	−0.988487	−	0.151308i	$-0.951651\pi$
$71$		−	2.54990i		−	0.302617i	0.988487	−	0.151308i	$-0.0483487\pi$
$72$		0			0
$73$	8.08328	+	4.66689i	0.946077	+	0.546218i	0.891860	−	0.452311i	$-0.149400\pi$
$73$	8.08328	+	4.66689i	0.946077	+	0.546218i	0.0542168	+	0.998529i	$0.482734\pi$
$74$	−0.928534	−	0.536089i	−0.107940	−	0.0623191i
$75$		0			0
$76$		−	6.12870i		−	0.703010i
$77$	−3.83131	+	15.0794i	−0.436619	+	1.71846i
$78$		0			0
$79$	−5.35961	−	9.28312i	−0.603003	−	1.04443i	−0.992364	−	0.123347i	$-0.960637\pi$
$79$	−5.35961	−	9.28312i	−0.603003	−	1.04443i	0.389360	−	0.921086i	$-0.372696\pi$
$80$		0			0
$81$		0			0
$82$	7.46132	−	4.30780i	0.823965	−	0.475717i
$83$	−10.1027			−1.10891			−0.554457	−	0.832212i	$-0.687074\pi$
$83$	−10.1027			−1.10891			−0.554457	+	0.832212i	$0.687074\pi$
$84$		0			0
$85$		0			0
$86$	−9.58894	+	5.53618i	−1.03400	+	0.596981i
$87$		0			0
$88$	−2.94028	+	5.09272i	−0.313435	+	0.542886i
$89$	−3.15638	−	5.46700i	−0.334575	−	0.579501i	0.648828	−	0.760935i	$-0.275259\pi$
$89$	−3.15638	−	5.46700i	−0.334575	−	0.579501i	−0.983403	+	0.181434i	$0.941926\pi$
$90$		0			0
$91$	−10.3304	+	2.91235i	−1.08293	+	0.305298i
$92$		−	1.75201i		−	0.182660i
$93$		0			0
$94$	−0.834099	−	0.481567i	−0.0860307	−	0.0496698i
$95$		0			0
$96$		0			0
$97$		−	2.59007i		−	0.262982i	−0.991317	−	0.131491i	$-0.958024\pi$
$97$		−	2.59007i		−	0.262982i	0.991317	−	0.131491i	$-0.0419764\pi$
$98$	3.34136	−	6.15104i	0.337529	−	0.621349i
$99$		0			0
$100$		0			0
$101$	5.21837	−	9.03849i	0.519248	−	0.899363i	−0.480502	−	0.876993i	$-0.659546\pi$
$101$	5.21837	−	9.03849i	0.519248	−	0.899363i	0.999750	−	0.0223696i	$-0.00712105\pi$
$102$		0			0
$103$	−4.28191	+	2.47216i	−0.421909	+	0.243589i	−0.695894	−	0.718145i	$-0.744992\pi$
$103$	−4.28191	+	2.47216i	−0.421909	+	0.243589i	0.273985	+	0.961734i	$0.411658\pi$
$104$	−4.05674			−0.397796
$105$		0			0
$106$	13.1461			1.27686
$107$	0.602588	−	0.347904i	0.0582544	−	0.0336332i	−0.470590	−	0.882352i	$-0.655959\pi$
$107$	0.602588	−	0.347904i	0.0582544	−	0.0336332i	0.528844	+	0.848719i	$0.322626\pi$
$108$		0			0
$109$	−2.98417	+	5.16874i	−0.285832	+	0.495076i	−0.972811	−	0.231602i	$-0.925603\pi$
$109$	−2.98417	+	5.16874i	−0.285832	+	0.495076i	0.686979	+	0.726678i	$0.258937\pi$
$110$		0			0
$111$		0			0
$112$	1.84637	−	1.89497i	0.174466	−	0.179058i
$113$		−	0.809894i		−	0.0761884i	−0.999274	−	0.0380942i	$-0.987871\pi$
$113$		−	0.809894i		−	0.0761884i	0.999274	−	0.0380942i	$-0.0121287\pi$
$114$		0			0
$115$		0			0
$116$	0.0362921	+	0.0209532i	0.00336963	+	0.00194546i
$117$		0			0
$118$			13.5464i			1.24704i
$119$	1.10010	+	0.279508i	0.100846	+	0.0256225i
$120$		0			0
$121$	11.7905	+	20.4218i	1.07187	+	1.85653i
$122$	−0.609885	+	1.05635i	−0.0552164	+	0.0956376i
$123$		0			0
$124$	7.92389	−	4.57486i	0.711586	−	0.410835i
$125$		0			0
$126$		0			0
$127$	11.0265			0.978442			0.489221	−	0.872160i	$-0.337281\pi$
$127$	11.0265			0.978442			0.489221	+	0.872160i	$0.337281\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	9.44080	+	16.3520i	0.824847	+	1.42868i	0.902036	+	0.431660i	$0.142072\pi$
$131$	9.44080	+	16.3520i	0.824847	+	1.42868i	−0.0771893	+	0.997016i	$0.524595\pi$
$132$		0			0
$133$	11.6137	+	11.3159i	1.00704	+	0.981210i
$134$		−	12.6470i		−	1.09254i
$135$		0			0
$136$	0.371532	+	0.214504i	0.0318586	+	0.0183936i
$137$	12.4458	+	7.18560i	1.06332	+	0.613907i	0.926348	−	0.376668i	$-0.122930\pi$
$137$	12.4458	+	7.18560i	1.06332	+	0.613907i	0.136970	+	0.990575i	$0.456264\pi$
$138$		0			0
$139$		−	16.7650i		−	1.42199i	−0.703198	−	0.710994i	$-0.748245\pi$
$139$		−	16.7650i		−	1.42199i	0.703198	−	0.710994i	$-0.251755\pi$
$140$		0			0
$141$		0			0
$142$	1.27495	+	2.20827i	0.106991	+	0.185314i
$143$	−11.9280	+	20.6598i	−0.997466	+	1.72766i
$144$		0			0
$145$		0			0
$146$	−9.33377			−0.772469
$147$		0			0
$148$	1.07218			0.0881326
$149$	8.67934	−	5.01102i	0.711039	−	0.410519i	−0.100407	−	0.994946i	$-0.532014\pi$
$149$	8.67934	−	5.01102i	0.711039	−	0.410519i	0.811446	+	0.584428i	$0.198681\pi$
$150$		0			0
$151$	−7.20599	+	12.4811i	−0.586415	+	1.01570i	0.408283	+	0.912856i	$0.366128\pi$
$151$	−7.20599	+	12.4811i	−0.586415	+	1.01570i	−0.994697	+	0.102845i	$0.967206\pi$
$152$	3.06435	+	5.30761i	0.248552	+	0.430504i
$153$		0			0
$154$	−4.22169	−	14.9748i	−0.340193	−	1.20670i
$155$		0			0
$156$		0			0
$157$	−9.41463	−	5.43554i	−0.751370	−	0.433803i	0.0748190	−	0.997197i	$-0.476162\pi$
$157$	−9.41463	−	5.43554i	−0.751370	−	0.433803i	−0.826189	+	0.563394i	$0.809495\pi$
$158$	9.28312	+	5.35961i	0.738525	+	0.426388i
$159$		0			0
$160$		0			0
$161$	3.32001	+	3.23486i	0.261653	+	0.254943i
$162$		0			0
$163$	5.31125	+	9.19935i	0.416009	+	0.720549i	0.995534	−	0.0944058i	$-0.0300951\pi$
$163$	5.31125	+	9.19935i	0.416009	+	0.720549i	−0.579525	+	0.814955i	$0.696762\pi$
$164$	−4.30780	+	7.46132i	−0.336382	+	0.582631i
$165$		0			0
$166$	8.74919	−	5.05134i	0.679068	−	0.392060i
$167$	−3.45341			−0.267233			−0.133617	−	0.991033i	$-0.542659\pi$
$167$	−3.45341			−0.267233			−0.133617	+	0.991033i	$0.542659\pi$
$168$		0			0
$169$	−3.45714			−0.265934
$170$		0			0
$171$		0			0
$172$	5.53618	−	9.58894i	0.422130	−	0.731150i
$173$	3.97759	+	6.88939i	0.302411	+	0.523790i	0.976681	−	0.214694i	$-0.0688753\pi$
$173$	3.97759	+	6.88939i	0.302411	+	0.523790i	−0.674271	+	0.738484i	$0.735542\pi$
$174$		0			0
$175$		0			0
$176$		−	5.88057i		−	0.443264i
$177$		0			0
$178$	5.46700	+	3.15638i	0.409769	+	0.236580i
$179$	−2.38066	−	1.37447i	−0.177939	−	0.102733i	0.408385	−	0.912810i	$-0.366092\pi$
$179$	−2.38066	−	1.37447i	−0.177939	−	0.102733i	−0.586324	+	0.810077i	$0.699425\pi$
$180$		0			0
$181$			6.73202i			0.500387i	0.968196	+	0.250194i	$0.0804943\pi$
$181$			6.73202i			0.500387i	−0.968196	+	0.250194i	$0.919506\pi$
$182$	7.49025	−	7.68740i	0.555215	−	0.569828i
$183$		0			0
$184$	0.876005	+	1.51729i	0.0645800	+	0.111856i
$185$		0			0
$186$		0			0
$187$	2.18482	−	1.26141i	0.159770	−	0.0922432i
$188$	0.963134			0.0702438
$189$		0			0
$190$		0			0
$191$	−21.3740	+	12.3403i	−1.54657	+	0.892911i	−0.548166	+	0.836369i	$0.684674\pi$
$191$	−21.3740	+	12.3403i	−1.54657	+	0.892911i	−0.998400	+	0.0565412i	$0.981993\pi$
$192$		0			0
$193$	−0.343610	+	0.595151i	−0.0247336	+	0.0428399i	−0.878127	−	0.478427i	$-0.841207\pi$
$193$	−0.343610	+	0.595151i	−0.0247336	+	0.0428399i	0.853394	+	0.521267i	$0.174540\pi$
$194$	1.29503	+	2.24306i	0.0929780	+	0.161043i
$195$		0			0
$196$	0.181816	+	6.99764i	0.0129868	+	0.499831i
$197$			0.169154i			0.0120517i	0.999982	+	0.00602586i	$0.00191810\pi$
$197$			0.169154i			0.0120517i	−0.999982	+	0.00602586i	$0.998082\pi$
$198$		0			0
$199$	−0.359798	−	0.207730i	−0.0255054	−	0.0147256i	0.487193	−	0.873294i	$-0.338021\pi$
$199$	−0.359798	−	0.207730i	−0.0255054	−	0.0147256i	−0.512699	+	0.858569i	$0.671354\pi$
$200$		0			0
$201$		0			0
$202$			10.4367i			0.734327i
$203$	−0.106714	+	0.0300849i	−0.00748988	+	0.00211154i
$204$		0			0
$205$		0			0
$206$	2.47216	−	4.28191i	0.172244	−	0.298335i
$207$		0			0
$208$	3.51324	−	2.02837i	0.243599	−	0.140642i
$209$	36.0402			2.49295
$210$		0			0
$211$	−2.10135			−0.144663			−0.0723313	−	0.997381i	$-0.523044\pi$
$211$	−2.10135			−0.144663			−0.0723313	+	0.997381i	$0.523044\pi$
$212$	−11.3848	+	6.57304i	−0.781915	+	0.451439i
$213$		0			0
$214$	−0.347904	+	0.602588i	−0.0237823	+	0.0411921i
$215$		0			0
$216$		0			0
$217$	−5.96124	+	23.4624i	−0.404675	+	1.59273i
$218$		−	5.96835i		−	0.404227i
$219$		0			0
$220$		0			0
$221$	1.50721	+	0.870188i	0.101386	+	0.0585352i
$222$		0			0
$223$		−	25.9946i		−	1.74073i	−0.492409	−	0.870364i	$-0.663883\pi$
$223$		−	25.9946i		−	1.74073i	0.492409	−	0.870364i	$-0.336117\pi$
$224$	−0.651521	+	2.56428i	−0.0435316	+	0.171333i
$225$		0			0
$226$	0.404947	+	0.701389i	0.0269367	+	0.0466557i
$227$	7.15363	−	12.3905i	0.474803	−	0.822383i	−0.524781	−	0.851238i	$-0.675853\pi$
$227$	7.15363	−	12.3905i	0.474803	−	0.822383i	0.999584	+	0.0288545i	$0.00918594\pi$
$228$		0			0
$229$	−1.36736	+	0.789445i	−0.0903576	+	0.0521680i	−0.544498	−	0.838762i	$-0.683280\pi$
$229$	−1.36736	+	0.789445i	−0.0903576	+	0.0521680i	0.454140	+	0.890930i	$0.349946\pi$
$230$		0			0
$231$		0			0
$232$	−0.0419065			−0.00275129
$233$	−15.8144	+	9.13044i	−1.03604	+	0.598155i	−0.918708	−	0.394938i	$-0.870766\pi$
$233$	−15.8144	+	9.13044i	−1.03604	+	0.598155i	−0.117327	+	0.993093i	$0.537433\pi$
$234$		0			0
$235$		0			0
$236$	−6.77318	−	11.7315i	−0.440897	−	0.763656i
$237$		0			0
$238$	−1.09247	+	0.307987i	−0.0708141	+	0.0199639i
$239$			23.1801i			1.49940i	0.661779	+	0.749699i	$0.269802\pi$
$239$			23.1801i			1.49940i	−0.661779	+	0.749699i	$0.730198\pi$
$240$		0			0
$241$	−11.2090	−	6.47152i	−0.722035	−	0.416867i	0.0934660	−	0.995622i	$-0.470205\pi$
$241$	−11.2090	−	6.47152i	−0.722035	−	0.416867i	−0.815501	+	0.578755i	$0.803539\pi$
$242$	−20.4218	−	11.7905i	−1.31276	−	0.757924i
$243$		0			0
$244$		−	1.21977i		−	0.0780878i
$245$		0			0
$246$		0			0
$247$	12.4313	+	21.5316i	0.790983	+	1.37002i
$248$	−4.57486	+	7.92389i	−0.290504	+	0.503168i
$249$		0			0
$250$		0			0
$251$	22.7253			1.43441			0.717203	−	0.696865i	$-0.245422\pi$
$251$	22.7253			1.43441			0.717203	+	0.696865i	$0.245422\pi$
$252$		0			0
$253$	10.3028			0.647732
$254$	−9.54921	+	5.51324i	−0.599171	+	0.345931i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.50065	+	6.06331i	0.218365	+	0.378219i	0.954308	−	0.298824i	$-0.0965944\pi$
$257$	3.50065	+	6.06331i	0.218365	+	0.378219i	−0.735943	+	0.677043i	$0.763261\pi$
$258$		0			0
$259$	−1.97964	+	2.03175i	−0.123009	+	0.126247i
$260$		0			0
$261$		0			0
$262$	−16.3520	−	9.44080i	−1.01023	−	0.583255i
$263$	−10.4091	−	6.00972i	−0.641855	−	0.370575i	0.143473	−	0.989654i	$-0.454173\pi$
$263$	−10.4091	−	6.00972i	−0.641855	−	0.370575i	−0.785329	+	0.619079i	$0.787506\pi$
$264$		0			0
$265$		0			0
$266$	−15.7157	−	3.99298i	−0.963590	−	0.244825i
$267$		0			0
$268$	6.32352	+	10.9527i	0.386271	+	0.669040i
$269$	−0.611792	+	1.05966i	−0.0373016	+	0.0646083i	−0.884074	−	0.467348i	$-0.845210\pi$
$269$	−0.611792	+	1.05966i	−0.0373016	+	0.0646083i	0.846772	+	0.531956i	$0.178543\pi$
$270$		0			0
$271$	14.1888	−	8.19190i	0.861908	−	0.497623i	−0.00274289	−	0.999996i	$-0.500873\pi$
$271$	14.1888	−	8.19190i	0.861908	−	0.497623i	0.864651	+	0.502374i	$0.167540\pi$
$272$	−0.429009			−0.0260125
$273$		0			0
$274$	−14.3712			−0.868196
$275$		0			0
$276$		0			0
$277$	6.58712	−	11.4092i	0.395781	−	0.685514i	−0.597419	−	0.801929i	$-0.703807\pi$
$277$	6.58712	−	11.4092i	0.395781	−	0.685514i	0.993201	+	0.116416i	$0.0371404\pi$
$278$	8.38250	+	14.5189i	0.502749	+	0.870786i
$279$		0			0
$280$		0			0
$281$		−	5.72433i		−	0.341485i	−0.985316	−	0.170742i	$-0.945383\pi$
$281$		−	5.72433i		−	0.341485i	0.985316	−	0.170742i	$-0.0546166\pi$
$282$		0			0
$283$	13.9838	+	8.07354i	0.831249	+	0.479922i	0.854280	−	0.519813i	$-0.173998\pi$
$283$	13.9838	+	8.07354i	0.831249	+	0.479922i	−0.0230311	+	0.999735i	$0.507332\pi$
$284$	−2.20827	−	1.27495i	−0.131037	−	0.0756542i
$285$		0			0
$286$		−	23.8559i		−	1.41063i
$287$	−6.18518	−	21.9395i	−0.365100	−	1.29505i
$288$		0			0
$289$	8.40798	+	14.5630i	0.494587	+	0.856649i
$290$		0			0
$291$		0			0
$292$	8.08328	−	4.66689i	0.473038	−	0.273109i
$293$	−24.2757			−1.41820			−0.709100	−	0.705108i	$-0.750898\pi$
$293$	−24.2757			−1.41820			−0.709100	+	0.705108i	$0.750898\pi$
$294$		0			0
$295$		0			0
$296$	−0.928534	+	0.536089i	−0.0539699	+	0.0311596i
$297$		0			0
$298$	−5.01102	+	8.67934i	−0.290280	+	0.502780i
$299$	3.55372	+	6.15523i	0.205517	+	0.355966i
$300$		0			0
$301$	7.94890	+	28.1956i	0.458167	+	1.62517i
$302$		−	14.4120i		−	0.829316i
$303$		0			0
$304$	−5.30761	−	3.06435i	−0.304412	−	0.175752i
$305$		0			0
$306$		0			0
$307$		−	19.1856i		−	1.09498i	−0.836812	−	0.547490i	$-0.815583\pi$
$307$		−	19.1856i		−	1.09498i	0.836812	−	0.547490i	$-0.184417\pi$
$308$	11.1435	+	10.8577i	0.634959	+	0.618676i
$309$		0			0
$310$		0			0
$311$	−16.3473	+	28.3143i	−0.926969	+	1.60556i	−0.138606	+	0.990348i	$0.544262\pi$
$311$	−16.3473	+	28.3143i	−0.926969	+	1.60556i	−0.788363	+	0.615210i	$0.789071\pi$
$312$		0			0
$313$	−16.9151	+	9.76593i	−0.956097	+	0.552003i	−0.894970	−	0.446127i	$-0.852803\pi$
$313$	−16.9151	+	9.76593i	−0.956097	+	0.552003i	−0.0611276	+	0.998130i	$0.519470\pi$
$314$	10.8711			0.613491
$315$		0			0
$316$	−10.7192			−0.603003
$317$	−12.6110	+	7.28095i	−0.708303	+	0.408939i	−0.810432	−	0.585832i	$-0.800768\pi$
$317$	−12.6110	+	7.28095i	−0.708303	+	0.408939i	0.102129	+	0.994771i	$0.467434\pi$
$318$		0			0
$319$	−0.123217	+	0.213418i	−0.00689882	+	0.0119491i
$320$		0			0
$321$		0			0
$322$	−4.49264	−	1.14147i	−0.250365	−	0.0636117i
$323$		−	2.62926i		−	0.146296i
$324$		0			0
$325$		0			0
$326$	−9.19935	−	5.31125i	−0.509505	−	0.294163i
$327$		0			0
$328$		−	8.61559i		−	0.475717i
$329$	−1.77830	+	1.82511i	−0.0980411	+	0.100622i
$330$		0			0
$331$	4.44833	+	7.70473i	0.244502	+	0.423490i	0.961992	−	0.273079i	$-0.0880422\pi$
$331$	4.44833	+	7.70473i	0.244502	+	0.423490i	−0.717489	+	0.696569i	$0.754709\pi$
$332$	−5.05134	+	8.74919i	−0.277229	+	0.480174i
$333$		0			0
$334$	2.99074	−	1.72671i	0.163646	−	0.0944812i
$335$		0			0
$336$		0			0
$337$	10.3636			0.564543			0.282271	−	0.959335i	$-0.408912\pi$
$337$	10.3636			0.564543			0.282271	+	0.959335i	$0.408912\pi$
$338$	2.99397	−	1.72857i	0.162850	−	0.0940217i
$339$		0			0
$340$		0			0
$341$	26.9028	+	46.5970i	1.45687	+	2.52337i
$342$		0			0
$343$	−13.5960	−	12.5757i	−0.734115	−	0.679025i
$344$			11.0724i			0.596981i
$345$		0			0
$346$	−6.88939	−	3.97759i	−0.370376	−	0.213837i
$347$	25.5373	+	14.7440i	1.37091	+	0.791497i	0.991043	−	0.133542i	$-0.0426353\pi$
$347$	25.5373	+	14.7440i	1.37091	+	0.791497i	0.379870	+	0.925040i	$0.375969\pi$
$348$		0			0
$349$		−	8.85764i		−	0.474138i	−0.971493	−	0.237069i	$-0.923813\pi$
$349$		−	8.85764i		−	0.474138i	0.971493	−	0.237069i	$-0.0761868\pi$
$350$		0			0
$351$		0			0
$352$	2.94028	+	5.09272i	0.156718	+	0.271443i
$353$	8.56472	−	14.8345i	0.455854	−	0.789562i	−0.542883	−	0.839808i	$-0.682667\pi$
$353$	8.56472	−	14.8345i	0.455854	−	0.789562i	0.998737	+	0.0502461i	$0.0160006\pi$
$354$		0			0
$355$		0			0
$356$	−6.31275			−0.334575
$357$		0			0
$358$	2.74895			0.145286
$359$	−19.0997	+	11.0272i	−1.00804	+	0.581993i	−0.910618	−	0.413250i	$-0.864394\pi$
$359$	−19.0997	+	11.0272i	−1.00804	+	0.581993i	−0.0974241	+	0.995243i	$0.531060\pi$
$360$		0			0
$361$	9.28047	−	16.0743i	0.488446	−	0.846013i
$362$	−3.36601	−	5.83010i	−0.176914	−	0.306423i
$363$		0			0
$364$	−2.64305	+	10.4026i	−0.138534	+	0.545245i
$365$		0			0
$366$		0			0
$367$	2.83644	+	1.63762i	0.148061	+	0.0854831i	0.572200	−	0.820114i	$-0.306090\pi$
$367$	2.83644	+	1.63762i	0.148061	+	0.0854831i	−0.424139	+	0.905597i	$0.639423\pi$
$368$	−1.51729	−	0.876005i	−0.0790940	−	0.0456649i
$369$		0			0
$370$		0			0
$371$	8.56495	−	33.7102i	0.444670	−	1.75015i
$372$		0			0
$373$	−18.7209	−	32.4255i	−0.969331	−	1.67893i	−0.697498	−	0.716587i	$-0.745703\pi$
$373$	−18.7209	−	32.4255i	−0.969331	−	1.67893i	−0.271834	−	0.962344i	$-0.587630\pi$
$374$	−1.26141	+	2.18482i	−0.0652258	+	0.112974i
$375$		0			0
$376$	−0.834099	+	0.481567i	−0.0430154	+	0.0248349i
$377$	−0.170004			−0.00875563
$378$		0			0
$379$	−37.2066			−1.91117			−0.955587	−	0.294708i	$-0.904777\pi$
$379$	−37.2066			−1.91117			−0.955587	+	0.294708i	$0.904777\pi$
$380$		0			0
$381$		0			0
$382$	12.3403	−	21.3740i	0.631383	−	1.09359i
$383$	−9.13135	−	15.8160i	−0.466590	−	0.808158i	0.532682	−	0.846316i	$-0.321184\pi$
$383$	−9.13135	−	15.8160i	−0.466590	−	0.808158i	−0.999272	+	0.0381579i	$0.987851\pi$
$384$		0			0
$385$		0			0
$386$		−	0.687221i		−	0.0349786i
$387$		0			0
$388$	−2.24306	−	1.29503i	−0.113874	−	0.0657454i
$389$	2.21119	+	1.27663i	0.112112	+	0.0647278i	0.555007	−	0.831845i	$-0.312715\pi$
$389$	2.21119	+	1.27663i	0.112112	+	0.0647278i	−0.442896	+	0.896573i	$0.646049\pi$
$390$		0			0
$391$		−	0.751627i		−	0.0380114i
$392$	−3.65628	−	5.96922i	−0.184670	−	0.301491i
$393$		0			0
$394$	−0.0845770	−	0.146492i	−0.00426093	−	0.00738014i
$395$		0			0
$396$		0			0
$397$	−17.2994	+	9.98784i	−0.868234	+	0.501275i	−0.866761	−	0.498724i	$-0.833802\pi$
$397$	−17.2994	+	9.98784i	−0.868234	+	0.501275i	−0.00147306	+	0.999999i	$0.500469\pi$
$398$	0.415459			0.0208251
$399$		0			0
$400$		0			0
$401$	21.2087	−	12.2448i	1.05911	−	0.611477i	0.133924	−	0.990992i	$-0.457242\pi$
$401$	21.2087	−	12.2448i	1.05911	−	0.611477i	0.925186	+	0.379514i	$0.123909\pi$
$402$		0			0
$403$	−18.5590	+	32.1452i	−0.924490	+	1.60126i
$404$	−5.21837	−	9.03849i	−0.259624	−	0.449682i
$405$		0			0
$406$	0.0773750	−	0.0794115i	0.00384006	−	0.00394113i
$407$			6.30502i			0.312528i
$408$		0			0
$409$	14.0020	+	8.08403i	0.692352	+	0.399730i	0.804493	−	0.593963i	$-0.202437\pi$
$409$	14.0020	+	8.08403i	0.692352	+	0.399730i	−0.112140	+	0.993692i	$0.535771\pi$
$410$		0			0
$411$		0			0
$412$			4.94432i			0.243589i
$413$	34.7366	+	8.82575i	1.70928	+	0.434287i
$414$		0			0
$415$		0			0
$416$	−2.02837	+	3.51324i	−0.0994490	+	0.172251i
$417$		0			0
$418$	−31.2117	+	18.0201i	−1.52662	+	0.881392i
$419$	−14.1632			−0.691920			−0.345960	−	0.938249i	$-0.612447\pi$
$419$	−14.1632			−0.691920			−0.345960	+	0.938249i	$0.612447\pi$
$420$		0			0
$421$	−21.7096			−1.05806			−0.529031	−	0.848603i	$-0.677444\pi$
$421$	−21.7096			−1.05806			−0.529031	+	0.848603i	$0.677444\pi$
$422$	1.81982	−	1.05067i	0.0885874	−	0.0511460i
$423$		0			0
$424$	6.57304	−	11.3848i	0.319215	−	0.552897i
$425$		0			0
$426$		0			0
$427$	2.31143	+	2.25215i	0.111858	+	0.108989i
$428$		−	0.695809i		−	0.0336332i
$429$		0			0
$430$		0			0
$431$	−3.08126	−	1.77897i	−0.148419	−	0.0856899i	0.423951	−	0.905685i	$-0.360643\pi$
$431$	−3.08126	−	1.77897i	−0.148419	−	0.0856899i	−0.572371	+	0.819995i	$0.693976\pi$
$432$		0			0
$433$			9.86329i			0.473999i	0.971510	+	0.237000i	$0.0761641\pi$
$433$			9.86329i			0.473999i	−0.971510	+	0.237000i	$0.923836\pi$
$434$	−6.56863	−	23.2997i	−0.315304	−	1.11842i
$435$		0			0
$436$	2.98417	+	5.16874i	0.142916	+	0.247538i
$437$	5.36877	−	9.29898i	0.256823	−	0.444831i
$438$		0			0
$439$	−12.1701	+	7.02641i	−0.580847	+	0.335352i	−0.761470	−	0.648200i	$-0.775522\pi$
$439$	−12.1701	+	7.02641i	−0.580847	+	0.335352i	0.180623	+	0.983552i	$0.442189\pi$
$440$		0			0
$441$		0			0
$442$	−1.74038			−0.0827812
$443$	13.3752	−	7.72219i	0.635476	−	0.366892i	−0.147394	−	0.989078i	$-0.547088\pi$
$443$	13.3752	−	7.72219i	0.635476	−	0.366892i	0.782870	+	0.622186i	$0.213755\pi$
$444$		0			0
$445$		0			0
$446$	12.9973	+	22.5120i	0.615440	+	1.06597i
$447$		0			0
$448$	−0.717905	−	2.54649i	−0.0339178	−	0.120310i
$449$		−	0.159851i		−	0.00754383i	−0.999993	−	0.00377192i	$-0.998799\pi$
$449$		−	0.159851i		−	0.00754383i	0.999993	−	0.00377192i	$-0.00120064\pi$
$450$		0			0
$451$	−43.8768	−	25.3323i	−2.06608	−	1.19285i
$452$	−0.701389	−	0.404947i	−0.0329906	−	0.0190471i
$453$		0			0
$454$			14.3073i			0.671473i
$455$		0			0
$456$		0			0
$457$	6.58150	+	11.3995i	0.307870	+	0.533246i	0.977896	−	0.209091i	$-0.0670506\pi$
$457$	6.58150	+	11.3995i	0.307870	+	0.533246i	−0.670026	+	0.742337i	$0.733717\pi$
$458$	0.789445	−	1.36736i	0.0368883	−	0.0638925i
$459$		0			0
$460$		0			0
$461$	20.7565			0.966725			0.483363	−	0.875420i	$-0.339415\pi$
$461$	20.7565			0.966725			0.483363	+	0.875420i	$0.339415\pi$
$462$		0			0
$463$	17.7932			0.826920			0.413460	−	0.910522i	$-0.364320\pi$
$463$	17.7932			0.826920			0.413460	+	0.910522i	$0.364320\pi$
$464$	0.0362921	−	0.0209532i	0.00168482	−	0.000972730i
$465$		0			0
$466$	9.13044	−	15.8144i	0.422960	−	0.732587i
$467$	−1.08094	−	1.87225i	−0.0500201	−	0.0866373i	0.839931	−	0.542693i	$-0.182595\pi$
$467$	−1.08094	−	1.87225i	−0.0500201	−	0.0866373i	−0.889951	+	0.456055i	$0.849262\pi$
$468$		0			0
$469$	−32.4305	−	8.23982i	−1.49750	−	0.380479i
$470$		0			0
$471$		0			0
$472$	11.7315	+	6.77318i	0.539986	+	0.311761i
$473$	56.3884	+	32.5559i	2.59274	+	1.49692i
$474$		0			0
$475$		0			0
$476$	0.792110	−	0.812958i	0.0363063	−	0.0372619i
$477$		0			0
$478$	−11.5901	−	20.0746i	−0.530117	−	0.918190i
$479$	−6.50176	+	11.2614i	−0.297073	+	0.514546i	−0.975465	−	0.220154i	$-0.929344\pi$
$479$	−6.50176	+	11.2614i	−0.297073	+	0.514546i	0.678392	+	0.734700i	$0.262677\pi$
$480$		0			0
$481$	−3.76682	+	2.17478i	−0.171752	+	0.0991612i
$482$	12.9430			0.589539
$483$		0			0
$484$	23.5811			1.07187
$485$		0			0
$486$		0			0
$487$	−3.15363	+	5.46224i	−0.142904	+	0.247518i	−0.928589	−	0.371109i	$-0.878978\pi$
$487$	−3.15363	+	5.46224i	−0.142904	+	0.247518i	0.785685	+	0.618627i	$0.212311\pi$
$488$	0.609885	+	1.05635i	0.0276082	+	0.0478188i
$489$		0			0
$490$		0			0
$491$		−	14.6640i		−	0.661776i	−0.943670	−	0.330888i	$-0.892652\pi$
$491$		−	14.6640i		−	0.661776i	0.943670	−	0.330888i	$-0.107348\pi$
$492$		0			0
$493$	0.0155696	+	0.00898912i	0.000701220	+	0.000404849i
$494$	−21.5316	−	12.4313i	−0.968752	−	0.559309i
$495$		0			0
$496$		−	9.14972i		−	0.410835i
$497$	6.49328	−	1.83058i	0.291264	−	0.0821129i
$498$		0			0
$499$	12.1113	+	20.9774i	0.542176	+	0.939076i	0.998779	+	0.0494053i	$0.0157326\pi$
$499$	12.1113	+	20.9774i	0.542176	+	0.939076i	−0.456603	+	0.889670i	$0.650934\pi$
$500$		0			0
$501$		0			0
$502$	−19.6806	+	11.3626i	−0.878390	+	0.507139i
$503$	−34.9707			−1.55927			−0.779633	−	0.626237i	$-0.784594\pi$
$503$	−34.9707			−1.55927			−0.779633	+	0.626237i	$0.784594\pi$
$504$		0			0
$505$		0			0
$506$	−8.92250	+	5.15141i	−0.396653	+	0.229008i
$507$		0			0
$508$	5.51324	−	9.54921i	0.244610	−	0.423678i
$509$	9.58793	+	16.6068i	0.424978	+	0.736083i	0.996418	−	0.0845605i	$-0.0269486\pi$
$509$	9.58793	+	16.6068i	0.424978	+	0.736083i	−0.571441	+	0.820643i	$0.693615\pi$
$510$		0			0
$511$	−6.08115	+	23.9344i	−0.269014	+	1.05879i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−6.06331	−	3.50065i	−0.267441	−	0.154407i
$515$		0			0
$516$		0			0
$517$			5.66377i			0.249092i
$518$	0.698547	−	2.74936i	0.0306924	−	0.120800i
$519$		0			0
$520$		0			0
$521$	10.0953	−	17.4855i	0.442282	−	0.766054i	−0.555577	−	0.831465i	$-0.687503\pi$
$521$	10.0953	−	17.4855i	0.442282	−	0.766054i	0.997858	+	0.0654110i	$0.0208358\pi$
$522$		0			0
$523$	−8.69476	+	5.01992i	−0.380195	+	0.219506i	−0.677903	−	0.735151i	$-0.737111\pi$
$523$	−8.69476	+	5.01992i	−0.380195	+	0.219506i	0.297708	+	0.954657i	$0.403778\pi$
$524$	18.8816			0.824847
$525$		0			0
$526$	12.0194			0.524073
$527$	3.39942	−	1.96265i	0.148081	−	0.0854946i
$528$		0			0
$529$	−9.96523	+	17.2603i	−0.433271	+	0.750447i
$530$		0			0
$531$		0			0
$532$	15.6067	−	4.39982i	0.676635	−	0.190757i
$533$		−	34.9512i		−	1.51391i
$534$		0			0
$535$		0			0
$536$	−10.9527	−	6.32352i	−0.473083	−	0.273135i
$537$		0			0
$538$		−	1.22358i		−	0.0527525i
$539$	−41.1501	+	1.06918i	−1.77246	+	0.0460528i
$540$		0			0
$541$	8.68907	+	15.0499i	0.373572	+	0.647046i	0.990112	−	0.140277i	$-0.0447994\pi$
$541$	8.68907	+	15.0499i	0.373572	+	0.647046i	−0.616540	+	0.787324i	$0.711466\pi$
$542$	−8.19190	+	14.1888i	−0.351872	+	0.609461i
$543$		0			0
$544$	0.371532	−	0.214504i	0.0159293	−	0.00919679i
$545$		0			0
$546$		0			0
$547$	−32.6253			−1.39496			−0.697478	−	0.716606i	$-0.745695\pi$
$547$	−32.6253			−1.39496			−0.697478	+	0.716606i	$0.745695\pi$
$548$	12.4458	−	7.18560i	0.531659	−	0.306954i
$549$		0			0
$550$		0			0
$551$	0.128416	+	0.222423i	0.00547071	+	0.00947555i
$552$		0			0
$553$	19.7917	−	20.3126i	0.841628	−	0.863780i
$554$			13.1742i			0.559720i
$555$		0			0
$556$	−14.5189	−	8.38250i	−0.615739	−	0.355497i
$557$	−29.5585	−	17.0656i	−1.25243	−	0.723094i	−0.280842	−	0.959754i	$-0.590614\pi$
$557$	−29.5585	−	17.0656i	−1.25243	−	0.723094i	−0.971592	+	0.236660i	$0.923947\pi$
$558$		0			0
$559$			44.9177i			1.89981i
$560$		0			0
$561$		0			0
$562$	2.86216	+	4.95741i	0.120733	+	0.209116i
$563$	−14.8964	+	25.8012i	−0.627806	+	1.08739i	0.360185	+	0.932881i	$0.382714\pi$
$563$	−14.8964	+	25.8012i	−0.627806	+	1.08739i	−0.987991	+	0.154512i	$0.950620\pi$
$564$		0			0
$565$		0			0
$566$	−16.1471			−0.678712
$567$		0			0
$568$	2.54990			0.106991
$569$	14.4586	−	8.34769i	0.606137	−	0.349953i	−0.165315	−	0.986241i	$-0.552864\pi$
$569$	14.4586	−	8.34769i	0.606137	−	0.349953i	0.771452	+	0.636287i	$0.219531\pi$
$570$		0			0
$571$	0.984264	−	1.70480i	0.0411902	−	0.0713435i	−0.844695	−	0.535247i	$-0.820218\pi$
$571$	0.984264	−	1.70480i	0.0411902	−	0.0713435i	0.885886	+	0.463904i	$0.153552\pi$
$572$	11.9280	+	20.6598i	0.498733	+	0.863831i
$573$		0			0
$574$	16.3263	+	15.9076i	0.681446	+	0.663970i
$575$		0			0
$576$		0			0
$577$	−34.6146	−	19.9848i	−1.44103	−	0.831977i	−0.443108	−	0.896468i	$-0.646124\pi$
$577$	−34.6146	−	19.9848i	−1.44103	−	0.831977i	−0.997918	+	0.0644912i	$0.979458\pi$
$578$	−14.5630	−	8.40798i	−0.605743	−	0.349726i
$579$		0			0
$580$		0			0
$581$	−7.25277	−	25.7264i	−0.300896	−	1.06731i
$582$		0			0
$583$	−38.6532	−	66.9493i	−1.60085	−	2.77276i
$584$	−4.66689	+	8.08328i	−0.193117	+	0.334489i
$585$		0			0
$586$	21.0233	−	12.1378i	0.868466	−	0.501409i
$587$	25.5123			1.05300			0.526502	−	0.850174i	$-0.323503\pi$
$587$	25.5123			1.05300			0.526502	+	0.850174i	$0.323503\pi$
$588$		0			0
$589$	56.0759			2.31057
$590$		0			0
$591$		0			0
$592$	0.536089	−	0.928534i	0.0220331	−	0.0381625i
$593$	−20.1656	−	34.9279i	−0.828103	−	1.43432i	−0.899524	−	0.436871i	$-0.856087\pi$
$593$	−20.1656	−	34.9279i	−0.828103	−	1.43432i	0.0714207	−	0.997446i	$-0.477247\pi$
$594$		0			0
$595$		0			0
$596$		−	10.0220i		−	0.410519i
$597$		0			0
$598$	−6.15523	−	3.55372i	−0.251706	−	0.145323i
$599$	19.9124	+	11.4964i	0.813600	+	0.469732i	0.848204	−	0.529669i	$-0.177684\pi$
$599$	19.9124	+	11.4964i	0.813600	+	0.469732i	−0.0346046	+	0.999401i	$0.511017\pi$
$600$		0			0
$601$		−	25.9443i		−	1.05829i	−0.848532	−	0.529145i	$-0.822513\pi$
$601$		−	25.9443i		−	1.05829i	0.848532	−	0.529145i	$-0.177487\pi$
$602$	−20.9818	−	20.4437i	−0.855153	−	0.833223i
$603$		0			0
$604$	7.20599	+	12.4811i	0.293207	+	0.507850i
$605$		0			0
$606$		0			0
$607$	32.8311	−	18.9551i	1.33257	−	0.769362i	0.346881	−	0.937909i	$-0.387241\pi$
$607$	32.8311	−	18.9551i	1.33257	−	0.769362i	0.985694	+	0.168547i	$0.0539076\pi$
$608$	6.12870			0.248552
$609$		0			0
$610$		0			0
$611$	−3.38372	+	1.95359i	−0.136891	+	0.0790339i
$612$		0			0
$613$	10.4012	−	18.0154i	0.420101	−	0.727637i	−0.575848	−	0.817557i	$-0.695328\pi$
$613$	10.4012	−	18.0154i	0.420101	−	0.727637i	0.995949	+	0.0899202i	$0.0286612\pi$
$614$	9.59280	+	16.6152i	0.387134	+	0.670536i
$615$		0			0
$616$	−15.0794	−	3.83131i	−0.607566	−	0.154368i
$617$		−	40.9298i		−	1.64777i	−0.566755	−	0.823887i	$-0.691801\pi$
$617$		−	40.9298i		−	1.64777i	0.566755	−	0.823887i	$-0.308199\pi$
$618$		0			0
$619$	−23.2122	−	13.4016i	−0.932976	−	0.538654i	−0.0452247	−	0.998977i	$-0.514400\pi$
$619$	−23.2122	−	13.4016i	−0.932976	−	0.538654i	−0.887752	+	0.460323i	$0.847734\pi$
$620$		0			0
$621$		0			0
$622$		−	32.6946i		−	1.31093i
$623$	11.6557	−	11.9625i	0.466975	−	0.479266i
$624$		0			0
$625$		0			0
$626$	9.76593	−	16.9151i	0.390325	−	0.676063i
$627$		0			0
$628$	−9.41463	+	5.43554i	−0.375685	+	0.216902i
$629$	0.459974			0.0183404
$630$		0			0
$631$	−2.28749			−0.0910636			−0.0455318	−	0.998963i	$-0.514498\pi$
$631$	−2.28749			−0.0910636			−0.0455318	+	0.998963i	$0.514498\pi$
$632$	9.28312	−	5.35961i	0.369263	−	0.213194i
$633$		0			0
$634$	7.28095	−	12.6110i	0.289164	−	0.500846i
$635$		0			0
$636$		0			0
$637$	−14.8326	−	24.2156i	−0.587687	−	0.959457i
$638$		−	0.246434i		−	0.00975641i
$639$		0			0
$640$		0			0
$641$	1.82398	+	1.05307i	0.0720428	+	0.0415939i	0.535589	−	0.844479i	$-0.320090\pi$
$641$	1.82398	+	1.05307i	0.0720428	+	0.0415939i	−0.463546	+	0.886073i	$0.653423\pi$
$642$		0			0
$643$		−	44.2035i		−	1.74322i	−0.490203	−	0.871608i	$-0.663077\pi$
$643$		−	44.2035i		−	1.74322i	0.490203	−	0.871608i	$-0.336923\pi$
$644$	4.46148	−	1.25778i	0.175807	−	0.0495634i
$645$		0			0
$646$	1.31463	+	2.27701i	0.0517235	+	0.0895877i
$647$	10.3540	−	17.9336i	0.407058	−	0.705044i	−0.587501	−	0.809223i	$-0.699888\pi$
$647$	10.3540	−	17.9336i	0.407058	−	0.705044i	0.994559	+	0.104179i	$0.0332215\pi$
$648$		0			0
$649$	68.9878	−	39.8302i	2.70801	−	1.56347i
$650$		0			0
$651$		0			0
$652$	10.6225			0.416009
$653$	23.3860	−	13.5019i	0.915164	−	0.528370i	0.0330748	−	0.999453i	$-0.489470\pi$
$653$	23.3860	−	13.5019i	0.915164	−	0.528370i	0.882089	+	0.471083i	$0.156137\pi$
$654$		0			0
$655$		0			0
$656$	4.30780	+	7.46132i	0.168191	+	0.291316i
$657$		0			0
$658$	0.627502	−	2.46974i	0.0244626	−	0.0962806i
$659$			15.2065i			0.592363i	0.955132	+	0.296181i	$0.0957133\pi$
$659$			15.2065i			0.592363i	−0.955132	+	0.296181i	$0.904287\pi$
$660$		0			0
$661$	−35.8665	−	20.7075i	−1.39504	−	0.805429i	−0.401176	−	0.916001i	$-0.631398\pi$
$661$	−35.8665	−	20.7075i	−1.39504	−	0.805429i	−0.993868	+	0.110572i	$0.964732\pi$
$662$	−7.70473	−	4.44833i	−0.299453	−	0.172889i
$663$		0			0
$664$		−	10.1027i		−	0.392060i
$665$		0			0
$666$		0			0
$667$	0.0367103	+	0.0635841i	0.00142143	+	0.00246199i
$668$	−1.72671	+	2.99074i	−0.0668083	+	0.115715i
$669$		0			0
$670$		0			0
$671$	7.17294			0.276908
$672$		0			0
$673$	15.2809			0.589037			0.294518	−	0.955646i	$-0.404841\pi$
$673$	15.2809			0.589037			0.294518	+	0.955646i	$0.404841\pi$
$674$	−8.97517	+	5.18182i	−0.345711	+	0.199596i
$675$		0			0
$676$	−1.72857	+	2.99397i	−0.0664834	+	0.115153i
$677$	24.2831	+	42.0596i	0.933277	+	1.61648i	0.777679	+	0.628662i	$0.216397\pi$
$677$	24.2831	+	42.0596i	0.933277	+	1.61648i	0.155598	+	0.987820i	$0.450270\pi$
$678$		0			0
$679$	6.59558	−	1.85942i	0.253115	−	0.0713581i
$680$		0			0
$681$		0			0
$682$	−46.5970	−	26.9028i	−1.78429	−	1.03016i
$683$	−10.6643	−	6.15706i	−0.408059	−	0.235593i	0.281896	−	0.959445i	$-0.409037\pi$
$683$	−10.6643	−	6.15706i	−0.408059	−	0.235593i	−0.689956	+	0.723852i	$0.742370\pi$
$684$		0			0
$685$		0			0
$686$	18.0623	+	4.09288i	0.689624	+	0.156267i
$687$		0			0
$688$	−5.53618	−	9.58894i	−0.211065	−	0.365575i
$689$	26.6651	−	46.1854i	1.01586	−	1.75952i
$690$		0			0
$691$	36.8280	−	21.2626i	1.40100	−	0.808869i	0.406507	−	0.913648i	$-0.366747\pi$
$691$	36.8280	−	21.2626i	1.40100	−	0.808869i	0.994496	+	0.104779i	$0.0334134\pi$
$692$	7.95518			0.302411
$693$		0			0
$694$	−29.4879			−1.11935
$695$		0			0
$696$		0			0
$697$	−1.84808	+	3.20097i	−0.0700011	+	0.121245i
$698$	4.42882	+	7.67094i	0.167633	+	0.290349i
$699$		0			0
$700$		0			0
$701$		−	2.16278i		−	0.0816870i	−0.999166	−	0.0408435i	$-0.986995\pi$
$701$		−	2.16278i		−	0.0816870i	0.999166	−	0.0408435i	$-0.0130045\pi$
$702$		0			0
$703$	5.69071	+	3.28553i	0.214629	+	0.123916i
$704$	−5.09272	−	2.94028i	−0.191939	−	0.110816i
$705$		0			0
$706$			17.1294i			0.644675i
$707$	26.7627	+	6.79976i	1.00652	+	0.255731i
$708$		0			0
$709$	10.4912	+	18.1712i	0.394004	+	0.682435i	0.992974	−	0.118337i	$-0.0377562\pi$
$709$	10.4912	+	18.1712i	0.394004	+	0.682435i	−0.598969	+	0.800772i	$0.704423\pi$
$710$		0			0
$711$		0			0
$712$	5.46700	−	3.15638i	0.204885	−	0.118290i
$713$	16.0304			0.600343
$714$		0			0
$715$		0			0
$716$	−2.38066	+	1.37447i	−0.0889694	+	0.0513665i
$717$		0			0
$718$	11.0272	−	19.0997i	0.411531	−	0.712793i
$719$	−8.73253	−	15.1252i	−0.325668	−	0.564074i	0.655979	−	0.754779i	$-0.272256\pi$
$719$	−8.73253	−	15.1252i	−0.325668	−	0.564074i	−0.981647	+	0.190705i	$0.938923\pi$
$720$		0			0
$721$	−9.36934	−	9.12906i	−0.348932	−	0.339984i
$722$			18.5609i			0.690767i
$723$		0			0
$724$	5.83010	+	3.36601i	0.216674	+	0.125097i
$725$		0			0
$726$		0			0
$727$		−	12.4470i		−	0.461633i	−0.972997	−	0.230816i	$-0.925860\pi$
$727$		−	12.4470i		−	0.461633i	0.972997	−	0.230816i	$-0.0741397\pi$
$728$	−2.91235	−	10.3304i	−0.107939	−	0.382872i
$729$		0			0
$730$		0			0
$731$	2.37507	−	4.11374i	0.0878450	−	0.152152i
$732$		0			0
$733$	−19.3654	+	11.1806i	−0.715279	+	0.412966i	−0.813012	−	0.582246i	$-0.802174\pi$
$733$	−19.3654	+	11.1806i	−0.715279	+	0.412966i	0.0977339	+	0.995213i	$0.468841\pi$
$734$	−3.27524			−0.120891
$735$		0			0
$736$	1.75201			0.0645800
$737$	−64.4079	+	37.1859i	−2.37249	+	1.36976i
$738$		0			0
$739$	15.9125	−	27.5613i	0.585351	−	1.01386i	−0.409481	−	0.912319i	$-0.634290\pi$
$739$	15.9125	−	27.5613i	0.585351	−	1.01386i	0.994832	−	0.101539i	$-0.0323765\pi$
$740$		0			0
$741$		0			0
$742$	9.43764	+	33.4764i	0.346467	+	1.22896i
$743$		−	15.1736i		−	0.556667i	−0.960485	−	0.278333i	$-0.910218\pi$
$743$		−	15.1736i		−	0.556667i	0.960485	−	0.278333i	$-0.0897820\pi$
$744$		0			0
$745$		0			0
$746$	32.4255	+	18.7209i	1.18718	+	0.685421i
$747$		0			0
$748$		−	2.52281i		−	0.0922432i
$749$	1.31854	+	1.28472i	0.0481783	+	0.0469427i
$750$		0			0
$751$	10.4956	+	18.1790i	0.382991	+	0.663360i	0.991488	−	0.130196i	$-0.0415607\pi$
$751$	10.4956	+	18.1790i	0.382991	+	0.663360i	−0.608497	+	0.793556i	$0.708227\pi$
$752$	0.481567	−	0.834099i	0.0175609	−	0.0304164i
$753$		0			0
$754$	0.147227	−	0.0850018i	0.00536171	−	0.00309558i
$755$		0			0
$756$		0			0
$757$	−17.0421			−0.619407			−0.309704	−	0.950833i	$-0.600230\pi$
$757$	−17.0421			−0.619407			−0.309704	+	0.950833i	$0.600230\pi$
$758$	32.2219	−	18.6033i	1.17035	−	0.675702i
$759$		0			0
$760$		0			0
$761$	3.13659	+	5.43274i	0.113701	+	0.196937i	0.917260	−	0.398289i	$-0.130396\pi$
$761$	3.13659	+	5.43274i	0.113701	+	0.196937i	−0.803559	+	0.595226i	$0.797063\pi$
$762$		0			0
$763$	−15.3045	−	3.88850i	−0.554060	−	0.140773i
$764$			24.6805i			0.892911i
$765$		0			0
$766$	15.8160	+	9.13135i	0.571454	+	0.329929i
$767$	47.5916	+	27.4770i	1.71843	+	0.992139i
$768$		0			0
$769$			20.7852i			0.749534i	0.927119	+	0.374767i	$0.122277\pi$
$769$			20.7852i			0.749534i	−0.927119	+	0.374767i	$0.877723\pi$
$770$		0			0
$771$		0			0
$772$	0.343610	+	0.595151i	0.0123668	+	0.0214199i
$773$	22.2466	−	38.5322i	0.800153	−	1.38591i	−0.119361	−	0.992851i	$-0.538085\pi$
$773$	22.2466	−	38.5322i	0.800153	−	1.38591i	0.919515	−	0.393055i	$-0.128582\pi$
$774$		0			0
$775$		0			0
$776$	2.59007			0.0929780
$777$		0			0
$778$	−2.55326			−0.0915390
$779$	−45.7282	+	26.4012i	−1.63838	+	0.945921i
$780$		0			0
$781$	7.49741	−	12.9859i	0.268279	−	0.464672i
$782$	0.375814	+	0.650928i	0.0134391	+	0.0232771i
$783$		0			0
$784$	6.15104	+	3.34136i	0.219680	+	0.119334i
$785$		0			0
$786$		0			0
$787$	13.3112	+	7.68522i	0.474493	+	0.273948i	0.718118	−	0.695921i	$-0.245004\pi$
$787$	13.3112	+	7.68522i	0.474493	+	0.273948i	−0.243626	+	0.969869i	$0.578337\pi$
$788$	0.146492	+	0.0845770i	0.00521855	+	0.00301293i
$789$		0			0
$790$		0			0
$791$	2.06239	−	0.581427i	0.0733301	−	0.0206732i
$792$		0			0
$793$	2.47415	+	4.28535i	0.0878595	+	0.152177i
$794$	9.98784	−	17.2994i	0.354455	−	0.613934i
$795$		0			0
$796$	−0.359798	+	0.207730i	−0.0127527	+	0.00736278i
$797$	−28.8285			−1.02116			−0.510580	−	0.859830i	$-0.670569\pi$
$797$	−28.8285			−1.02116			−0.510580	+	0.859830i	$0.670569\pi$
$798$		0			0
$799$	0.413193			0.0146177
$800$		0			0
$801$		0			0
$802$	−12.2448	+	21.2087i	−0.432380	+	0.748904i
$803$	27.4439	+	47.5343i	0.968475	+	1.67745i
$804$		0			0
$805$		0			0
$806$		−	37.1180i		−	1.30743i
$807$		0			0
$808$	9.03849	+	5.21837i	0.317973	+	0.183582i
$809$	−15.9209	−	9.19196i	−0.559751	−	0.323172i	0.193295	−	0.981141i	$-0.438083\pi$
$809$	−15.9209	−	9.19196i	−0.559751	−	0.323172i	−0.753045	+	0.657968i	$0.771416\pi$
$810$		0			0
$811$		−	47.0100i		−	1.65074i	−0.564589	−	0.825372i	$-0.690965\pi$
$811$		−	47.0100i		−	1.65074i	0.564589	−	0.825372i	$-0.309035\pi$
$812$	−0.0273030	+	0.107460i	−0.000958146	+	0.00377110i
$813$		0			0
$814$	−3.15251	−	5.46031i	−0.110495	−	0.191384i
$815$		0			0
$816$		0			0
$817$	58.7677	−	33.9296i	2.05602	−	1.18705i
$818$	−16.1681			−0.565303
$819$		0			0
$820$		0			0
$821$	−47.2833	+	27.2990i	−1.65020	+	0.952742i	−0.673209	+	0.739452i	$0.735085\pi$
$821$	−47.2833	+	27.2990i	−1.65020	+	0.952742i	−0.976989	+	0.213290i	$0.931582\pi$
$822$		0			0
$823$	−0.358380	+	0.620733i	−0.0124924	+	0.0216374i	−0.872204	−	0.489142i	$-0.837310\pi$
$823$	−0.358380	+	0.620733i	−0.0124924	+	0.0216374i	0.859712	+	0.510780i	$0.170643\pi$
$824$	−2.47216	−	4.28191i	−0.0861218	−	0.149167i
$825$		0			0
$826$	−34.4957	+	9.72501i	−1.20026	+	0.338376i
$827$		−	32.8584i		−	1.14260i	−0.820742	−	0.571299i	$-0.806440\pi$
$827$		−	32.8584i		−	1.14260i	0.820742	−	0.571299i	$-0.193560\pi$
$828$		0			0
$829$	43.6845	+	25.2212i	1.51722	+	0.875970i	0.999795	+	0.0202442i	$0.00644436\pi$
$829$	43.6845	+	25.2212i	1.51722	+	0.875970i	0.517429	+	0.855726i	$0.326889\pi$
$830$		0			0
$831$		0			0
$832$		−	4.05674i		−	0.140642i
$833$	0.0780005	+	3.00205i	0.00270256	+	0.104015i
$834$		0			0
$835$		0			0
$836$	18.0201	−	31.2117i	0.623238	−	1.07948i
$837$		0			0
$838$	12.2657	−	7.08162i	0.423713	−	0.244631i
$839$	−21.6729			−0.748233			−0.374116	−	0.927382i	$-0.622054\pi$
$839$	−21.6729			−0.748233			−0.374116	+	0.927382i	$0.622054\pi$
$840$		0			0
$841$	28.9982			0.999939
$842$	18.8011	−	10.8548i	0.647928	−	0.374081i
$843$		0			0
$844$	−1.05067	+	1.81982i	−0.0361657	+	0.0626408i
$845$		0			0
$846$		0			0
$847$	−43.5394	+	44.6854i	−1.49603	+	1.53541i
$848$			13.1461i			0.451439i
$849$		0			0
$850$		0			0
$851$	1.62680	+	0.939234i	0.0557660	+	0.0321965i
$852$		0			0
$853$			25.1282i			0.860372i	0.902740	+	0.430186i	$0.141552\pi$
$853$			25.1282i			0.860372i	−0.902740	+	0.430186i	$0.858448\pi$
$854$	−3.12783	−	0.794706i	−0.107032	−	0.0271943i
$855$		0			0
$856$	0.347904	+	0.602588i	0.0118911	+	0.0205960i
$857$	22.6085	−	39.1591i	0.772293	−	1.33765i	−0.164011	−	0.986459i	$-0.552443\pi$
$857$	22.6085	−	39.1591i	0.772293	−	1.33765i	0.936304	−	0.351192i	$-0.114223\pi$
$858$		0			0
$859$	24.3260	−	14.0446i	0.829992	−	0.479196i	−0.0238577	−	0.999715i	$-0.507595\pi$
$859$	24.3260	−	14.0446i	0.829992	−	0.479196i	0.853850	+	0.520519i	$0.174262\pi$
$860$		0			0
$861$		0			0
$862$	3.55794			0.121184
$863$	25.1390	−	14.5140i	0.855740	−	0.494062i	−0.00684347	−	0.999977i	$-0.502178\pi$
$863$	25.1390	−	14.5140i	0.855740	−	0.494062i	0.862583	+	0.505915i	$0.168845\pi$
$864$		0			0
$865$		0			0
$866$	−4.93164	−	8.54186i	−0.167584	−	0.290264i
$867$		0			0
$868$	17.3384	+	16.8938i	0.588505	+	0.573413i
$869$		−	63.0351i		−	2.13832i
$870$		0			0
$871$	−44.4321	−	25.6529i	−1.50552	−	0.869215i
$872$	−5.16874	−	2.98417i	−0.175036	−	0.101057i
$873$		0			0
$874$			10.7375i			0.363203i
$875$		0			0
$876$		0			0
$877$	−17.9210	−	31.0400i	−0.605148	−	1.04815i	−0.992028	−	0.126017i	$-0.959780\pi$
$877$	−17.9210	−	31.0400i	−0.605148	−	1.04815i	0.386880	−	0.922130i	$-0.373553\pi$
$878$	7.02641	−	12.1701i	0.237130	−	0.410721i
$879$		0			0
$880$		0			0
$881$	16.4620			0.554619			0.277309	−	0.960781i	$-0.410557\pi$
$881$	16.4620			0.554619			0.277309	+	0.960781i	$0.410557\pi$
$882$		0			0
$883$	−43.5609			−1.46594			−0.732971	−	0.680260i	$-0.761867\pi$
$883$	−43.5609			−1.46594			−0.732971	+	0.680260i	$0.761867\pi$
$884$	1.50721	−	0.870188i	0.0506930	−	0.0292676i
$885$		0			0
$886$	−7.72219	+	13.3752i	−0.259432	+	0.449350i
$887$	19.1749	+	33.2119i	0.643831	+	1.11515i	0.984570	+	0.174990i	$0.0559894\pi$
$887$	19.1749	+	33.2119i	0.643831	+	1.11515i	−0.340739	+	0.940158i	$0.610677\pi$
$888$		0			0
$889$	7.91596	+	28.0788i	0.265493	+	0.941733i
$890$		0			0
$891$		0			0
$892$	−22.5120	−	12.9973i	−0.753757	−	0.435182i
$893$	5.11194	+	2.95138i	0.171065	+	0.0987641i
$894$		0			0
$895$		0			0
$896$	1.89497	+	1.84637i	0.0633065	+	0.0616830i
$897$		0			0
$898$	0.0799255	+	0.138435i	0.00266715	+	0.00461964i
$899$	−0.191716	+	0.332062i	−0.00639409	+	0.0110749i
$900$		0			0
$901$	−4.88420	+	2.81989i	−0.162716	+	0.0939442i
$902$	50.6646			1.68695
$903$		0			0
$904$	0.809894			0.0269367
$905$		0			0
$906$		0			0
$907$	−12.4865	+	21.6272i	−0.414607	+	0.718120i	−0.995387	−	0.0959402i	$-0.969414\pi$
$907$	−12.4865	+	21.6272i	−0.414607	+	0.718120i	0.580780	+	0.814060i	$0.302748\pi$
$908$	−7.15363	−	12.3905i	−0.237402	−	0.411192i
$909$		0			0
$910$		0			0
$911$		−	5.02786i		−	0.166580i	−0.996525	−	0.0832902i	$-0.973457\pi$
$911$		−	5.02786i		−	0.166580i	0.996525	−	0.0832902i	$-0.0265428\pi$
$912$		0			0
$913$	−51.4502	−	29.7048i	−1.70275	−	0.983084i
$914$	−11.3995	−	6.58150i	−0.377062	−	0.217697i
$915$		0			0
$916$			1.57889i			0.0521680i
$917$	−34.8625	+	35.7801i	−1.15126	+	1.18156i
$918$		0			0
$919$	−5.76087	−	9.97811i	−0.190033	−	0.329148i	0.755228	−	0.655463i	$-0.227526\pi$
$919$	−5.76087	−	9.97811i	−0.190033	−	0.329148i	−0.945261	+	0.326315i	$0.894193\pi$
$920$		0			0
$921$		0			0
$922$	−17.9756	+	10.3782i	−0.591996	+	0.341789i
$923$	10.3443			0.340486
$924$		0			0
$925$		0			0
$926$	−15.4094	+	8.89659i	−0.506383	+	0.292360i
$927$		0			0
$928$	−0.0209532	+	0.0362921i	−0.000687824	+	0.00119135i
$929$	−9.55386	−	16.5478i	−0.313452	−	0.542915i	0.665655	−	0.746259i	$-0.268152\pi$
$929$	−9.55386	−	16.5478i	−0.313452	−	0.542915i	−0.979107	+	0.203345i	$0.934819\pi$
$930$		0			0
$931$	−20.4782	+	37.6979i	−0.671146	+	1.23550i
$932$			18.2609i			0.598155i
$933$		0			0
$934$	1.87225	+	1.08094i	0.0612618	+	0.0353695i
$935$		0			0
$936$		0			0
$937$		−	49.5320i		−	1.61814i	−0.587713	−	0.809070i	$-0.699972\pi$
$937$		−	49.5320i		−	1.61814i	0.587713	−	0.809070i	$-0.300028\pi$
$938$	32.2056	−	9.07938i	1.05155	−	0.296452i
$939$		0			0
$940$		0			0
$941$	22.4564	−	38.8957i	0.732059	−	1.26796i	−0.223942	−	0.974602i	$-0.571893\pi$
$941$	22.4564	−	38.8957i	0.732059	−	1.26796i	0.956002	−	0.293361i	$-0.0947739\pi$
$942$		0			0
$943$	−13.0723	+	7.54730i	−0.425693	+	0.245774i
$944$	−13.5464			−0.440897
$945$		0			0
$946$	−65.1117			−2.11696
$947$	2.29992	−	1.32786i	0.0747373	−	0.0431496i	−0.462166	−	0.886794i	$-0.652927\pi$
$947$	2.29992	−	1.32786i	0.0747373	−	0.0431496i	0.536903	+	0.843644i	$0.319594\pi$
$948$		0			0
$949$	−18.9323	+	32.7918i	−0.614570	+	1.06447i
$950$		0			0
$951$		0			0
$952$	−0.279508	+	1.10010i	−0.00905891	+	0.0356543i
$953$		−	36.5346i		−	1.18347i	−0.806132	−	0.591735i	$-0.798443\pi$
$953$		−	36.5346i		−	1.18347i	0.806132	−	0.591735i	$-0.201557\pi$
$954$		0			0
$955$		0			0
$956$	20.0746	+	11.5901i	0.649258	+	0.374850i
$957$		0			0
$958$		−	13.0035i		−	0.420125i
$959$	−9.36314	+	36.8517i	−0.302351	+	1.19000i
$960$		0			0
$961$	26.3587	+	45.6546i	0.850280	+	1.47273i
$962$	2.17478	−	3.76682i	0.0701176	−	0.121447i
$963$		0			0
$964$	−11.2090	+	6.47152i	−0.361018	+	0.208434i
$965$		0			0
$966$		0			0
$967$	−22.6175			−0.727330			−0.363665	−	0.931530i	$-0.618475\pi$
$967$	−22.6175			−0.727330			−0.363665	+	0.931530i	$0.618475\pi$
$968$	−20.4218	+	11.7905i	−0.656381	+	0.378962i
$969$		0			0
$970$		0			0
$971$	−4.86871	−	8.43286i	−0.156244	−	0.270623i	0.777267	−	0.629171i	$-0.216605\pi$
$971$	−4.86871	−	8.43286i	−0.156244	−	0.270623i	−0.933511	+	0.358548i	$0.883272\pi$
$972$		0			0
$973$	42.6919	−	12.0357i	1.36864	−	0.385846i
$974$		−	6.30725i		−	0.202097i
$975$		0			0
$976$	−1.05635	−	0.609885i	−0.0338130	−	0.0195220i
$977$	37.4682	+	21.6323i	1.19871	+	0.692078i	0.960269	−	0.279077i	$-0.0900286\pi$
$977$	37.4682	+	21.6323i	1.19871	+	0.692078i	0.238446	+	0.971156i	$0.423362\pi$
$978$		0			0
$979$		−	37.1225i		−	1.18644i
$980$		0			0
$981$		0			0
$982$	7.33199	+	12.6994i	0.233973	+	0.405253i
$983$	−17.9821	+	31.1460i	−0.573541	+	0.993402i	0.422658	+	0.906289i	$0.361097\pi$
$983$	−17.9821	+	31.1460i	−0.573541	+	0.993402i	−0.996198	+	0.0871125i	$0.972236\pi$
$984$		0			0
$985$		0			0
$986$	−0.0179782			−0.000572544
$987$		0			0
$988$	24.8625			0.790983
$989$	16.7999	−	9.69944i	0.534206	−	0.308424i
$990$		0			0
$991$	12.1494	−	21.0433i	0.385937	−	0.668463i	−0.605962	−	0.795494i	$-0.707212\pi$
$991$	12.1494	−	21.0433i	0.385937	−	0.668463i	0.991899	+	0.127031i	$0.0405448\pi$
$992$	4.57486	+	7.92389i	0.145252	+	0.251584i
$993$		0			0
$994$	−4.70806	+	4.83197i	−0.149331	+	0.153261i
$995$		0			0
$996$		0			0
$997$	46.5513	+	26.8764i	1.47429	+	0.851184i	0.999581	−	0.0289572i	$-0.00921865\pi$
$997$	46.5513	+	26.8764i	1.47429	+	0.851184i	0.474713	+	0.880141i	$0.342552\pi$
$998$	−20.9774	−	12.1113i	−0.664027	−	0.383376i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.d.1151.6	✓	24
3.2	odd	2	inner	3150.2.bf.d.1151.7	yes	24
5.2	odd	4		3150.2.bp.g.899.3		24
5.3	odd	4		3150.2.bp.h.899.10		24
5.4	even	2		3150.2.bf.e.1151.7	yes	24
7.5	odd	6	inner	3150.2.bf.d.1601.7	yes	24
15.2	even	4		3150.2.bp.h.899.3		24
15.8	even	4		3150.2.bp.g.899.10		24
15.14	odd	2		3150.2.bf.e.1151.6	yes	24
21.5	even	6	inner	3150.2.bf.d.1601.6	yes	24
35.12	even	12		3150.2.bp.g.1349.10		24
35.19	odd	6		3150.2.bf.e.1601.6	yes	24
35.33	even	12		3150.2.bp.h.1349.3		24
105.47	odd	12		3150.2.bp.h.1349.10		24
105.68	odd	12		3150.2.bp.g.1349.3		24
105.89	even	6		3150.2.bf.e.1601.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.6	✓	24	1.1	even	1	trivial
3150.2.bf.d.1151.7	yes	24	3.2	odd	2	inner
3150.2.bf.d.1601.6	yes	24	21.5	even	6	inner
3150.2.bf.d.1601.7	yes	24	7.5	odd	6	inner
3150.2.bf.e.1151.6	yes	24	15.14	odd	2
3150.2.bf.e.1151.7	yes	24	5.4	even	2
3150.2.bf.e.1601.6	yes	24	35.19	odd	6
3150.2.bf.e.1601.7	yes	24	105.89	even	6
3150.2.bp.g.899.3		24	5.2	odd	4
3150.2.bp.g.899.10		24	15.8	even	4
3150.2.bp.g.1349.3		24	105.68	odd	12
3150.2.bp.g.1349.10		24	35.12	even	12
3150.2.bp.h.899.3		24	15.2	even	4
3150.2.bp.h.899.10		24	5.3	odd	4
3150.2.bp.h.1349.3		24	35.33	even	12
3150.2.bp.h.1349.10		24	105.47	odd	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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.717905 + 2.54649i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.717905 + 2.54649i) q^{7} +1.00000i q^{8} +(5.09272 + 2.94028i) q^{11} +4.05674i q^{13} +(-1.89497 - 1.84637i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.214504 - 0.371532i) q^{17} +(5.30761 - 3.06435i) q^{19} -5.88057 q^{22} +(1.51729 - 0.876005i) q^{23} +(-2.02837 - 3.51324i) q^{26} +(2.56428 + 0.651521i) q^{28} +0.0419065i q^{29} +(7.92389 + 4.57486i) q^{31} +(0.866025 + 0.500000i) q^{32} +0.429009i q^{34} +(0.536089 + 0.928534i) q^{37} +(-3.06435 + 5.30761i) q^{38} -8.61559 q^{41} +11.0724 q^{43} +(5.09272 - 2.94028i) q^{44} +(-0.876005 + 1.51729i) q^{46} +(0.481567 + 0.834099i) q^{47} +(-5.96922 + 3.65628i) q^{49} +(3.51324 + 2.02837i) q^{52} +(-11.3848 - 6.57304i) q^{53} +(-2.54649 + 0.717905i) q^{56} +(-0.0209532 - 0.0362921i) q^{58} +(6.77318 - 11.7315i) q^{59} +(1.05635 - 0.609885i) q^{61} -9.14972 q^{62} -1.00000 q^{64} +(-6.32352 + 10.9527i) q^{67} +(-0.214504 - 0.371532i) q^{68} -2.54990i q^{71} +(8.08328 + 4.66689i) q^{73} +(-0.928534 - 0.536089i) q^{74} -6.12870i q^{76} +(-3.83131 + 15.0794i) q^{77} +(-5.35961 - 9.28312i) q^{79} +(7.46132 - 4.30780i) q^{82} -10.1027 q^{83} +(-9.58894 + 5.53618i) q^{86} +(-2.94028 + 5.09272i) q^{88} +(-3.15638 - 5.46700i) q^{89} +(-10.3304 + 2.91235i) q^{91} -1.75201i q^{92} +(-0.834099 - 0.481567i) q^{94} -2.59007i q^{97} +(3.34136 - 6.15104i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} - 4 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 - 4 * q^7	\( 24 q + 12 q^{4} - 4 q^{7} - 12 q^{16} + 12 q^{19} + 4 q^{28} + 28 q^{37} + 96 q^{43} - 8 q^{46} - 52 q^{49} - 12 q^{52} + 8 q^{58} - 12 q^{61} - 24 q^{64} - 4 q^{67} - 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) \) 24 * q + 12 * q^4 - 4 * q^7 - 12 * q^16 + 12 * q^19 + 4 * q^28 + 28 * q^37 + 96 * q^43 - 8 * q^46 - 52 * q^49 - 12 * q^52 + 8 * q^58 - 12 * q^61 - 24 * q^64 - 4 * q^67 - 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

Introduction

L-functions

Modular forms

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