LMFDB - Embedded newform 3150.2.bf.d.1601.6

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			1601.6
Character	$\chi$	$=$	3150.1601
Dual form			3150.2.bf.d.1151.6

$q$-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 $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.536419	−	0.843952i	$-0.319777\pi$
$11$	5.09272	−	2.94028i	1.53551	−	0.886529i	0.999093	−	0.0425771i	$-0.0135568\pi$
$12$		0			0
$13$		−	4.05674i		−	1.12514i	−0.826751	−	0.562569i	$-0.809813\pi$
$13$		−	4.05674i		−	1.12514i	0.826751	−	0.562569i	$-0.190187\pi$
$14$	−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	0.890865	−	0.454268i	$-0.150099\pi$
$17$	0.214504	+	0.371532i	0.0520249	+	0.0901098i	−0.838840	+	0.544378i	$0.816766\pi$
$18$		0			0
$19$	5.30761	+	3.06435i	1.21765	+	0.703010i	0.964414	−	0.264395i	$-0.0851723\pi$
$19$	5.30761	+	3.06435i	1.21765	+	0.703010i	0.253234	+	0.967405i	$0.418506\pi$
$20$		0			0
$21$		0			0
$22$	−5.88057			−1.25374
$23$	1.51729	+	0.876005i	0.316376	+	0.182660i	0.649776	−	0.760126i	$-0.274863\pi$
$23$	1.51729	+	0.876005i	0.316376	+	0.182660i	−0.333400	+	0.942785i	$0.608196\pi$
$24$		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	$-0.998761\pi$
$29$		−	0.0419065i		−	0.00778184i	0.999992	−	0.00389092i	$-0.00123852\pi$
$30$		0			0
$31$	7.92389	−	4.57486i	1.42317	−	0.821669i	0.426604	−	0.904439i	$-0.359710\pi$
$31$	7.92389	−	4.57486i	1.42317	−	0.821669i	0.996569	+	0.0827694i	$0.0263765\pi$
$32$	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	−0.818589	−	0.574379i	$-0.805243\pi$
$37$	0.536089	−	0.928534i	0.0881326	−	0.152650i	0.906722	+	0.421729i	$0.138577\pi$
$38$	−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	−0.828764	−	0.559598i	$-0.810956\pi$
$47$	0.481567	−	0.834099i	0.0702438	−	0.121666i	0.899008	+	0.437932i	$0.144289\pi$
$48$		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	−0.566965	+	0.823742i	$0.691883\pi$
$53$	−11.3848	+	6.57304i	−1.56383	+	0.902877i	−0.996864	+	0.0791353i	$0.974784\pi$
$54$		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	0.849345	+	0.527838i	$0.176997\pi$
$59$	6.77318	+	11.7315i	0.881793	+	1.52731i	0.0324481	+	0.999473i	$0.489670\pi$
$60$		0			0
$61$	1.05635	+	0.609885i	0.135252	+	0.0780878i	0.566099	−	0.824337i	$-0.308452\pi$
$61$	1.05635	+	0.609885i	0.135252	+	0.0780878i	−0.430847	+	0.902425i	$0.641785\pi$
$62$	−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	−0.936166	−	0.351558i	$-0.885652\pi$
$67$	−6.32352	−	10.9527i	−0.772541	−	1.33808i	0.163625	−	0.986523i	$-0.447681\pi$
$68$	−0.214504	+	0.371532i	−0.0260125	+	0.0450549i
$69$		0			0
$70$		0			0
$71$			2.54990i			0.302617i	0.988487	+	0.151308i	$0.0483487\pi$
$71$			2.54990i			0.302617i	−0.988487	+	0.151308i	$0.951651\pi$
$72$		0			0
$73$	8.08328	−	4.66689i	0.946077	−	0.546218i	0.0542168	−	0.998529i	$-0.482734\pi$
$73$	8.08328	−	4.66689i	0.946077	−	0.546218i	0.891860	+	0.452311i	$0.149400\pi$
$74$	−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	0.389360	+	0.921086i	$0.372696\pi$
$79$	−5.35961	+	9.28312i	−0.603003	+	1.04443i	−0.992364	+	0.123347i	$0.960637\pi$
$80$		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	−0.983403	−	0.181434i	$-0.941926\pi$
$89$	−3.15638	+	5.46700i	−0.334575	+	0.579501i	0.648828	+	0.760935i	$0.275259\pi$
$90$		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	$0.0419764\pi$
$97$			2.59007i			0.262982i	−0.991317	+	0.131491i	$0.958024\pi$
$98$	3.34136	+	6.15104i	0.337529	+	0.621349i
$99$		0			0
$100$		0			0
$101$	5.21837	+	9.03849i	0.519248	+	0.899363i	0.999750	+	0.0223696i	$0.00712105\pi$
$101$	5.21837	+	9.03849i	0.519248	+	0.899363i	−0.480502	+	0.876993i	$0.659546\pi$
$102$		0			0
$103$	−4.28191	−	2.47216i	−0.421909	−	0.243589i	0.273985	−	0.961734i	$-0.411658\pi$
$103$	−4.28191	−	2.47216i	−0.421909	−	0.243589i	−0.695894	+	0.718145i	$0.744992\pi$
$104$	−4.05674			−0.397796
$105$		0			0
$106$	13.1461			1.27686
$107$	0.602588	+	0.347904i	0.0582544	+	0.0336332i	0.528844	−	0.848719i	$-0.322626\pi$
$107$	0.602588	+	0.347904i	0.0582544	+	0.0336332i	−0.470590	+	0.882352i	$0.655959\pi$
$108$		0			0
$109$	−2.98417	−	5.16874i	−0.285832	−	0.495076i	0.686979	−	0.726678i	$-0.258937\pi$
$109$	−2.98417	−	5.16874i	−0.285832	−	0.495076i	−0.972811	+	0.231602i	$0.925603\pi$
$110$		0			0
$111$		0			0
$112$	1.84637	+	1.89497i	0.174466	+	0.179058i
$113$			0.809894i			0.0761884i	0.999274	+	0.0380942i	$0.0121287\pi$
$113$			0.809894i			0.0761884i	−0.999274	+	0.0380942i	$0.987871\pi$
$114$		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	−0.0771893	−	0.997016i	$-0.524595\pi$
$131$	9.44080	−	16.3520i	0.824847	−	1.42868i	0.902036	−	0.431660i	$-0.142072\pi$
$132$		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	0.136970	−	0.990575i	$-0.456264\pi$
$137$	12.4458	−	7.18560i	1.06332	−	0.613907i	0.926348	+	0.376668i	$0.122930\pi$
$138$		0			0
$139$			16.7650i			1.42199i	0.703198	+	0.710994i	$0.251755\pi$
$139$			16.7650i			1.42199i	−0.703198	+	0.710994i	$0.748245\pi$
$140$		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	0.811446	−	0.584428i	$-0.198681\pi$
$149$	8.67934	+	5.01102i	0.711039	+	0.410519i	−0.100407	+	0.994946i	$0.532014\pi$
$150$		0			0
$151$	−7.20599	−	12.4811i	−0.586415	−	1.01570i	−0.994697	−	0.102845i	$-0.967206\pi$
$151$	−7.20599	−	12.4811i	−0.586415	−	1.01570i	0.408283	−	0.912856i	$-0.366128\pi$
$152$	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	−0.826189	−	0.563394i	$-0.809495\pi$
$157$	−9.41463	+	5.43554i	−0.751370	+	0.433803i	0.0748190	+	0.997197i	$0.476162\pi$
$158$	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	−0.579525	−	0.814955i	$-0.696762\pi$
$163$	5.31125	−	9.19935i	0.416009	−	0.720549i	0.995534	+	0.0944058i	$0.0300951\pi$
$164$	−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	−0.674271	−	0.738484i	$-0.735542\pi$
$173$	3.97759	−	6.88939i	0.302411	−	0.523790i	0.976681	+	0.214694i	$0.0688753\pi$
$174$		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	−0.586324	−	0.810077i	$-0.699425\pi$
$179$	−2.38066	+	1.37447i	−0.177939	+	0.102733i	0.408385	+	0.912810i	$0.366092\pi$
$180$		0			0
$181$		−	6.73202i		−	0.500387i	−0.968196	−	0.250194i	$-0.919506\pi$
$181$		−	6.73202i		−	0.500387i	0.968196	−	0.250194i	$-0.0804943\pi$
$182$	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	−0.998400	−	0.0565412i	$-0.981993\pi$
$191$	−21.3740	−	12.3403i	−1.54657	−	0.892911i	−0.548166	−	0.836369i	$-0.684674\pi$
$192$		0			0
$193$	−0.343610	−	0.595151i	−0.0247336	−	0.0428399i	0.853394	−	0.521267i	$-0.174540\pi$
$193$	−0.343610	−	0.595151i	−0.0247336	−	0.0428399i	−0.878127	+	0.478427i	$0.841207\pi$
$194$	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	$-0.998082\pi$
$197$		−	0.169154i		−	0.0120517i	0.999982	−	0.00602586i	$-0.00191810\pi$
$198$		0			0
$199$	−0.359798	+	0.207730i	−0.0255054	+	0.0147256i	−0.512699	−	0.858569i	$-0.671354\pi$
$199$	−0.359798	+	0.207730i	−0.0255054	+	0.0147256i	0.487193	+	0.873294i	$0.338021\pi$
$200$		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	$0.336117\pi$
$223$			25.9946i			1.74073i	−0.492409	+	0.870364i	$0.663883\pi$
$224$	−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	0.999584	−	0.0288545i	$-0.00918594\pi$
$227$	7.15363	+	12.3905i	0.474803	+	0.822383i	−0.524781	+	0.851238i	$0.675853\pi$
$228$		0			0
$229$	−1.36736	−	0.789445i	−0.0903576	−	0.0521680i	0.454140	−	0.890930i	$-0.349946\pi$
$229$	−1.36736	−	0.789445i	−0.0903576	−	0.0521680i	−0.544498	+	0.838762i	$0.683280\pi$
$230$		0			0
$231$		0			0
$232$	−0.0419065			−0.00275129
$233$	−15.8144	−	9.13044i	−1.03604	−	0.598155i	−0.117327	−	0.993093i	$-0.537433\pi$
$233$	−15.8144	−	9.13044i	−1.03604	−	0.598155i	−0.918708	+	0.394938i	$0.870766\pi$
$234$		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	$-0.730198\pi$
$239$		−	23.1801i		−	1.49940i	0.661779	−	0.749699i	$-0.269802\pi$
$240$		0			0
$241$	−11.2090	+	6.47152i	−0.722035	+	0.416867i	−0.815501	−	0.578755i	$-0.803539\pi$
$241$	−11.2090	+	6.47152i	−0.722035	+	0.416867i	0.0934660	+	0.995622i	$0.470205\pi$
$242$	−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	−0.735943	−	0.677043i	$-0.763261\pi$
$257$	3.50065	−	6.06331i	0.218365	−	0.378219i	0.954308	+	0.298824i	$0.0965944\pi$
$258$		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	−0.785329	−	0.619079i	$-0.787506\pi$
$263$	−10.4091	+	6.00972i	−0.641855	+	0.370575i	0.143473	+	0.989654i	$0.454173\pi$
$264$		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	0.846772	−	0.531956i	$-0.178543\pi$
$269$	−0.611792	−	1.05966i	−0.0373016	−	0.0646083i	−0.884074	+	0.467348i	$0.845210\pi$
$270$		0			0
$271$	14.1888	+	8.19190i	0.861908	+	0.497623i	0.864651	−	0.502374i	$-0.167540\pi$
$271$	14.1888	+	8.19190i	0.861908	+	0.497623i	−0.00274289	+	0.999996i	$0.500873\pi$
$272$	−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	0.993201	−	0.116416i	$-0.0371404\pi$
$277$	6.58712	+	11.4092i	0.395781	+	0.685514i	−0.597419	+	0.801929i	$0.703807\pi$
$278$	8.38250	−	14.5189i	0.502749	−	0.870786i
$279$		0			0
$280$		0			0
$281$			5.72433i			0.341485i	0.985316	+	0.170742i	$0.0546166\pi$
$281$			5.72433i			0.341485i	−0.985316	+	0.170742i	$0.945383\pi$
$282$		0			0
$283$	13.9838	−	8.07354i	0.831249	−	0.479922i	−0.0230311	−	0.999735i	$-0.507332\pi$
$283$	13.9838	−	8.07354i	0.831249	−	0.479922i	0.854280	+	0.519813i	$0.173998\pi$
$284$	−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	$0.184417\pi$
$307$			19.1856i			1.09498i	−0.836812	+	0.547490i	$0.815583\pi$
$308$	11.1435	−	10.8577i	0.634959	−	0.618676i
$309$		0			0
$310$		0			0
$311$	−16.3473	−	28.3143i	−0.926969	−	1.60556i	−0.788363	−	0.615210i	$-0.789071\pi$
$311$	−16.3473	−	28.3143i	−0.926969	−	1.60556i	−0.138606	−	0.990348i	$-0.544262\pi$
$312$		0			0
$313$	−16.9151	−	9.76593i	−0.956097	−	0.552003i	−0.0611276	−	0.998130i	$-0.519470\pi$
$313$	−16.9151	−	9.76593i	−0.956097	−	0.552003i	−0.894970	+	0.446127i	$0.852803\pi$
$314$	10.8711			0.613491
$315$		0			0
$316$	−10.7192			−0.603003
$317$	−12.6110	−	7.28095i	−0.708303	−	0.408939i	0.102129	−	0.994771i	$-0.467434\pi$
$317$	−12.6110	−	7.28095i	−0.708303	−	0.408939i	−0.810432	+	0.585832i	$0.800768\pi$
$318$		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	−0.717489	−	0.696569i	$-0.754709\pi$
$331$	4.44833	−	7.70473i	0.244502	−	0.423490i	0.961992	+	0.273079i	$0.0880422\pi$
$332$	−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	0.379870	−	0.925040i	$-0.375969\pi$
$347$	25.5373	−	14.7440i	1.37091	−	0.791497i	0.991043	+	0.133542i	$0.0426353\pi$
$348$		0			0
$349$			8.85764i			0.474138i	0.971493	+	0.237069i	$0.0761868\pi$
$349$			8.85764i			0.474138i	−0.971493	+	0.237069i	$0.923813\pi$
$350$		0			0
$351$		0			0
$352$	2.94028	−	5.09272i	0.156718	−	0.271443i
$353$	8.56472	+	14.8345i	0.455854	+	0.789562i	0.998737	−	0.0502461i	$-0.0160006\pi$
$353$	8.56472	+	14.8345i	0.455854	+	0.789562i	−0.542883	+	0.839808i	$0.682667\pi$
$354$		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	−0.0974241	−	0.995243i	$-0.531060\pi$
$359$	−19.0997	−	11.0272i	−1.00804	−	0.581993i	−0.910618	+	0.413250i	$0.864394\pi$
$360$		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	−0.424139	−	0.905597i	$-0.639423\pi$
$367$	2.83644	−	1.63762i	0.148061	−	0.0854831i	0.572200	+	0.820114i	$0.306090\pi$
$368$	−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	−0.271834	+	0.962344i	$0.587630\pi$
$373$	−18.7209	+	32.4255i	−0.969331	+	1.67893i	−0.697498	+	0.716587i	$0.745703\pi$
$374$	−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	−0.999272	−	0.0381579i	$-0.987851\pi$
$383$	−9.13135	+	15.8160i	−0.466590	+	0.808158i	0.532682	+	0.846316i	$0.321184\pi$
$384$		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	−0.442896	−	0.896573i	$-0.646049\pi$
$389$	2.21119	−	1.27663i	0.112112	−	0.0647278i	0.555007	+	0.831845i	$0.312715\pi$
$390$		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	−0.00147306	−	0.999999i	$-0.500469\pi$
$397$	−17.2994	−	9.98784i	−0.868234	−	0.501275i	−0.866761	+	0.498724i	$0.833802\pi$
$398$	0.415459			0.0208251
$399$		0			0
$400$		0			0
$401$	21.2087	+	12.2448i	1.05911	+	0.611477i	0.925186	−	0.379514i	$-0.123909\pi$
$401$	21.2087	+	12.2448i	1.05911	+	0.611477i	0.133924	+	0.990992i	$0.457242\pi$
$402$		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	−0.112140	−	0.993692i	$-0.535771\pi$
$409$	14.0020	−	8.08403i	0.692352	−	0.399730i	0.804493	+	0.593963i	$0.202437\pi$
$410$		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	−0.572371	−	0.819995i	$-0.693976\pi$
$431$	−3.08126	+	1.77897i	−0.148419	+	0.0856899i	0.423951	+	0.905685i	$0.360643\pi$
$432$		0			0
$433$		−	9.86329i		−	0.473999i	−0.971510	−	0.237000i	$-0.923836\pi$
$433$		−	9.86329i		−	0.473999i	0.971510	−	0.237000i	$-0.0761641\pi$
$434$	−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	0.180623	−	0.983552i	$-0.442189\pi$
$439$	−12.1701	−	7.02641i	−0.580847	−	0.335352i	−0.761470	+	0.648200i	$0.775522\pi$
$440$		0			0
$441$		0			0
$442$	−1.74038			−0.0827812
$443$	13.3752	+	7.72219i	0.635476	+	0.366892i	0.782870	−	0.622186i	$-0.213755\pi$
$443$	13.3752	+	7.72219i	0.635476	+	0.366892i	−0.147394	+	0.989078i	$0.547088\pi$
$444$		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	$0.00120064\pi$
$449$			0.159851i			0.00754383i	−0.999993	+	0.00377192i	$0.998799\pi$
$450$		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	−0.670026	−	0.742337i	$-0.733717\pi$
$457$	6.58150	−	11.3995i	0.307870	−	0.533246i	0.977896	+	0.209091i	$0.0670506\pi$
$458$	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	−0.889951	−	0.456055i	$-0.849262\pi$
$467$	−1.08094	+	1.87225i	−0.0500201	+	0.0866373i	0.839931	+	0.542693i	$0.182595\pi$
$468$		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	0.678392	−	0.734700i	$-0.262677\pi$
$479$	−6.50176	−	11.2614i	−0.297073	−	0.514546i	−0.975465	+	0.220154i	$0.929344\pi$
$480$		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	0.785685	−	0.618627i	$-0.212311\pi$
$487$	−3.15363	−	5.46224i	−0.142904	−	0.247518i	−0.928589	+	0.371109i	$0.878978\pi$
$488$	0.609885	−	1.05635i	0.0276082	−	0.0478188i
$489$		0			0
$490$		0			0
$491$			14.6640i			0.661776i	0.943670	+	0.330888i	$0.107348\pi$
$491$			14.6640i			0.661776i	−0.943670	+	0.330888i	$0.892652\pi$
$492$		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	−0.456603	−	0.889670i	$-0.650934\pi$
$499$	12.1113	−	20.9774i	0.542176	−	0.939076i	0.998779	−	0.0494053i	$-0.0157326\pi$
$500$		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	−0.571441	−	0.820643i	$-0.693615\pi$
$509$	9.58793	−	16.6068i	0.424978	−	0.736083i	0.996418	+	0.0845605i	$0.0269486\pi$
$510$		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	0.997858	−	0.0654110i	$-0.0208358\pi$
$521$	10.0953	+	17.4855i	0.442282	+	0.766054i	−0.555577	+	0.831465i	$0.687503\pi$
$522$		0			0
$523$	−8.69476	−	5.01992i	−0.380195	−	0.219506i	0.297708	−	0.954657i	$-0.403778\pi$
$523$	−8.69476	−	5.01992i	−0.380195	−	0.219506i	−0.677903	+	0.735151i	$0.737111\pi$
$524$	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	−0.616540	−	0.787324i	$-0.711466\pi$
$541$	8.68907	−	15.0499i	0.373572	−	0.647046i	0.990112	+	0.140277i	$0.0447994\pi$
$542$	−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	−0.971592	−	0.236660i	$-0.923947\pi$
$557$	−29.5585	+	17.0656i	−1.25243	+	0.723094i	−0.280842	+	0.959754i	$0.590614\pi$
$558$		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	−0.987991	−	0.154512i	$-0.950620\pi$
$563$	−14.8964	−	25.8012i	−0.627806	−	1.08739i	0.360185	−	0.932881i	$-0.382714\pi$
$564$		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	0.771452	−	0.636287i	$-0.219531\pi$
$569$	14.4586	+	8.34769i	0.606137	+	0.349953i	−0.165315	+	0.986241i	$0.552864\pi$
$570$		0			0
$571$	0.984264	+	1.70480i	0.0411902	+	0.0713435i	0.885886	−	0.463904i	$-0.153552\pi$
$571$	0.984264	+	1.70480i	0.0411902	+	0.0713435i	−0.844695	+	0.535247i	$0.820218\pi$
$572$	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	−0.997918	−	0.0644912i	$-0.979458\pi$
$577$	−34.6146	+	19.9848i	−1.44103	+	0.831977i	−0.443108	+	0.896468i	$0.646124\pi$
$578$	−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	0.0714207	+	0.997446i	$0.477247\pi$
$593$	−20.1656	+	34.9279i	−0.828103	+	1.43432i	−0.899524	+	0.436871i	$0.856087\pi$
$594$		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	−0.0346046	−	0.999401i	$-0.511017\pi$
$599$	19.9124	−	11.4964i	0.813600	−	0.469732i	0.848204	+	0.529669i	$0.177684\pi$
$600$		0			0
$601$			25.9443i			1.05829i	0.848532	+	0.529145i	$0.177487\pi$
$601$			25.9443i			1.05829i	−0.848532	+	0.529145i	$0.822513\pi$
$602$	−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	0.985694	−	0.168547i	$-0.0539076\pi$
$607$	32.8311	+	18.9551i	1.33257	+	0.769362i	0.346881	+	0.937909i	$0.387241\pi$
$608$	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	0.995949	−	0.0899202i	$-0.0286612\pi$
$613$	10.4012	+	18.0154i	0.420101	+	0.727637i	−0.575848	+	0.817557i	$0.695328\pi$
$614$	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	$0.308199\pi$
$617$			40.9298i			1.64777i	−0.566755	+	0.823887i	$0.691801\pi$
$618$		0			0
$619$	−23.2122	+	13.4016i	−0.932976	+	0.538654i	−0.887752	−	0.460323i	$-0.847734\pi$
$619$	−23.2122	+	13.4016i	−0.932976	+	0.538654i	−0.0452247	+	0.998977i	$0.514400\pi$
$620$		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	−0.463546	−	0.886073i	$-0.653423\pi$
$641$	1.82398	−	1.05307i	0.0720428	−	0.0415939i	0.535589	+	0.844479i	$0.320090\pi$
$642$		0			0
$643$			44.2035i			1.74322i	0.490203	+	0.871608i	$0.336923\pi$
$643$			44.2035i			1.74322i	−0.490203	+	0.871608i	$0.663077\pi$
$644$	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	0.994559	−	0.104179i	$-0.0332215\pi$
$647$	10.3540	+	17.9336i	0.407058	+	0.705044i	−0.587501	+	0.809223i	$0.699888\pi$
$648$		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	0.882089	−	0.471083i	$-0.156137\pi$
$653$	23.3860	+	13.5019i	0.915164	+	0.528370i	0.0330748	+	0.999453i	$0.489470\pi$
$654$		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	$-0.904287\pi$
$659$		−	15.2065i		−	0.592363i	0.955132	−	0.296181i	$-0.0957133\pi$
$660$		0			0
$661$	−35.8665	+	20.7075i	−1.39504	+	0.805429i	−0.993868	−	0.110572i	$-0.964732\pi$
$661$	−35.8665	+	20.7075i	−1.39504	+	0.805429i	−0.401176	+	0.916001i	$0.631398\pi$
$662$	−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	0.155598	−	0.987820i	$-0.450270\pi$
$677$	24.2831	−	42.0596i	0.933277	−	1.61648i	0.777679	−	0.628662i	$-0.216397\pi$
$678$		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	−0.689956	−	0.723852i	$-0.742370\pi$
$683$	−10.6643	+	6.15706i	−0.408059	+	0.235593i	0.281896	+	0.959445i	$0.409037\pi$
$684$		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	0.994496	−	0.104779i	$-0.0334134\pi$
$691$	36.8280	+	21.2626i	1.40100	+	0.808869i	0.406507	+	0.913648i	$0.366747\pi$
$692$	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	$0.0130045\pi$
$701$			2.16278i			0.0816870i	−0.999166	+	0.0408435i	$0.986995\pi$
$702$		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	−0.598969	−	0.800772i	$-0.704423\pi$
$709$	10.4912	−	18.1712i	0.394004	−	0.682435i	0.992974	+	0.118337i	$0.0377562\pi$
$710$		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	−0.981647	−	0.190705i	$-0.938923\pi$
$719$	−8.73253	+	15.1252i	−0.325668	+	0.564074i	0.655979	+	0.754779i	$0.272256\pi$
$720$		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	$0.0741397\pi$
$727$			12.4470i			0.461633i	−0.972997	+	0.230816i	$0.925860\pi$
$728$	−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	0.0977339	−	0.995213i	$-0.468841\pi$
$733$	−19.3654	−	11.1806i	−0.715279	−	0.412966i	−0.813012	+	0.582246i	$0.802174\pi$
$734$	−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	0.994832	+	0.101539i	$0.0323765\pi$
$739$	15.9125	+	27.5613i	0.585351	+	1.01386i	−0.409481	+	0.912319i	$0.634290\pi$
$740$		0			0
$741$		0			0
$742$	9.43764	−	33.4764i	0.346467	−	1.22896i
$743$			15.1736i			0.556667i	0.960485	+	0.278333i	$0.0897820\pi$
$743$			15.1736i			0.556667i	−0.960485	+	0.278333i	$0.910218\pi$
$744$		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	−0.608497	−	0.793556i	$-0.708227\pi$
$751$	10.4956	−	18.1790i	0.382991	−	0.663360i	0.991488	+	0.130196i	$0.0415607\pi$
$752$	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	−0.803559	−	0.595226i	$-0.797063\pi$
$761$	3.13659	−	5.43274i	0.113701	−	0.196937i	0.917260	+	0.398289i	$0.130396\pi$
$762$		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	$-0.877723\pi$
$769$		−	20.7852i		−	0.749534i	0.927119	−	0.374767i	$-0.122277\pi$
$770$		0			0
$771$		0			0
$772$	0.343610	−	0.595151i	0.0123668	−	0.0214199i
$773$	22.2466	+	38.5322i	0.800153	+	1.38591i	0.919515	+	0.393055i	$0.128582\pi$
$773$	22.2466	+	38.5322i	0.800153	+	1.38591i	−0.119361	+	0.992851i	$0.538085\pi$
$774$		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	−0.243626	−	0.969869i	$-0.578337\pi$
$787$	13.3112	−	7.68522i	0.474493	−	0.273948i	0.718118	+	0.695921i	$0.245004\pi$
$788$	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	−0.753045	−	0.657968i	$-0.771416\pi$
$809$	−15.9209	+	9.19196i	−0.559751	+	0.323172i	0.193295	+	0.981141i	$0.438083\pi$
$810$		0			0
$811$			47.0100i			1.65074i	0.564589	+	0.825372i	$0.309035\pi$
$811$			47.0100i			1.65074i	−0.564589	+	0.825372i	$0.690965\pi$
$812$	−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	−0.976989	−	0.213290i	$-0.931582\pi$
$821$	−47.2833	−	27.2990i	−1.65020	−	0.952742i	−0.673209	−	0.739452i	$-0.735085\pi$
$822$		0			0
$823$	−0.358380	−	0.620733i	−0.0124924	−	0.0216374i	0.859712	−	0.510780i	$-0.170643\pi$
$823$	−0.358380	−	0.620733i	−0.0124924	−	0.0216374i	−0.872204	+	0.489142i	$0.837310\pi$
$824$	−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	$0.193560\pi$
$827$			32.8584i			1.14260i	−0.820742	+	0.571299i	$0.806440\pi$
$828$		0			0
$829$	43.6845	−	25.2212i	1.51722	−	0.875970i	0.517429	−	0.855726i	$-0.326889\pi$
$829$	43.6845	−	25.2212i	1.51722	−	0.875970i	0.999795	−	0.0202442i	$-0.00644436\pi$
$830$		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	$-0.858448\pi$
$853$		−	25.1282i		−	0.860372i	0.902740	−	0.430186i	$-0.141552\pi$
$854$	−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	0.936304	+	0.351192i	$0.114223\pi$
$857$	22.6085	+	39.1591i	0.772293	+	1.33765i	−0.164011	+	0.986459i	$0.552443\pi$
$858$		0			0
$859$	24.3260	+	14.0446i	0.829992	+	0.479196i	0.853850	−	0.520519i	$-0.174262\pi$
$859$	24.3260	+	14.0446i	0.829992	+	0.479196i	−0.0238577	+	0.999715i	$0.507595\pi$
$860$		0			0
$861$		0			0
$862$	3.55794			0.121184
$863$	25.1390	+	14.5140i	0.855740	+	0.494062i	0.862583	−	0.505915i	$-0.168845\pi$
$863$	25.1390	+	14.5140i	0.855740	+	0.494062i	−0.00684347	+	0.999977i	$0.502178\pi$
$864$		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	0.386880	+	0.922130i	$0.373553\pi$
$877$	−17.9210	+	31.0400i	−0.605148	+	1.04815i	−0.992028	+	0.126017i	$0.959780\pi$
$878$	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	−0.340739	−	0.940158i	$-0.610677\pi$
$887$	19.1749	−	33.2119i	0.643831	−	1.11515i	0.984570	−	0.174990i	$-0.0559894\pi$
$888$		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	0.580780	−	0.814060i	$-0.302748\pi$
$907$	−12.4865	−	21.6272i	−0.414607	−	0.718120i	−0.995387	+	0.0959402i	$0.969414\pi$
$908$	−7.15363	+	12.3905i	−0.237402	+	0.411192i
$909$		0			0
$910$		0			0
$911$			5.02786i			0.166580i	0.996525	+	0.0832902i	$0.0265428\pi$
$911$			5.02786i			0.166580i	−0.996525	+	0.0832902i	$0.973457\pi$
$912$		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	−0.945261	−	0.326315i	$-0.894193\pi$
$919$	−5.76087	+	9.97811i	−0.190033	+	0.329148i	0.755228	+	0.655463i	$0.227526\pi$
$920$		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	−0.979107	−	0.203345i	$-0.934819\pi$
$929$	−9.55386	+	16.5478i	−0.313452	+	0.542915i	0.665655	+	0.746259i	$0.268152\pi$
$930$		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	$0.300028\pi$
$937$			49.5320i			1.61814i	−0.587713	+	0.809070i	$0.699972\pi$
$938$	32.2056	+	9.07938i	1.05155	+	0.296452i
$939$		0			0
$940$		0			0
$941$	22.4564	+	38.8957i	0.732059	+	1.26796i	0.956002	+	0.293361i	$0.0947739\pi$
$941$	22.4564	+	38.8957i	0.732059	+	1.26796i	−0.223942	+	0.974602i	$0.571893\pi$
$942$		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	0.536903	−	0.843644i	$-0.319594\pi$
$947$	2.29992	+	1.32786i	0.0747373	+	0.0431496i	−0.462166	+	0.886794i	$0.652927\pi$
$948$		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	$0.201557\pi$
$953$			36.5346i			1.18347i	−0.806132	+	0.591735i	$0.798443\pi$
$954$		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	−0.933511	−	0.358548i	$-0.883272\pi$
$971$	−4.86871	+	8.43286i	−0.156244	+	0.270623i	0.777267	+	0.629171i	$0.216605\pi$
$972$		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	0.238446	−	0.971156i	$-0.423362\pi$
$977$	37.4682	−	21.6323i	1.19871	−	0.692078i	0.960269	+	0.279077i	$0.0900286\pi$
$978$		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	−0.996198	−	0.0871125i	$-0.972236\pi$
$983$	−17.9821	−	31.1460i	−0.573541	−	0.993402i	0.422658	−	0.906289i	$-0.361097\pi$
$984$		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	0.991899	−	0.127031i	$-0.0405448\pi$
$991$	12.1494	+	21.0433i	0.385937	+	0.668463i	−0.605962	+	0.795494i	$0.707212\pi$
$992$	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	0.474713	−	0.880141i	$-0.342552\pi$
$997$	46.5513	−	26.8764i	1.47429	−	0.851184i	0.999581	+	0.0289572i	$0.00921865\pi$
$998$	−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.1601.6	yes	24
3.2	odd	2	inner	3150.2.bf.d.1601.7	yes	24
5.2	odd	4		3150.2.bp.h.1349.10		24
5.3	odd	4		3150.2.bp.g.1349.3		24
5.4	even	2		3150.2.bf.e.1601.7	yes	24
7.3	odd	6	inner	3150.2.bf.d.1151.7	yes	24
15.2	even	4		3150.2.bp.g.1349.10		24
15.8	even	4		3150.2.bp.h.1349.3		24
15.14	odd	2		3150.2.bf.e.1601.6	yes	24
21.17	even	6	inner	3150.2.bf.d.1151.6	✓	24
35.3	even	12		3150.2.bp.g.899.10		24
35.17	even	12		3150.2.bp.h.899.3		24
35.24	odd	6		3150.2.bf.e.1151.6	yes	24
105.17	odd	12		3150.2.bp.g.899.3		24
105.38	odd	12		3150.2.bp.h.899.10		24
105.59	even	6		3150.2.bf.e.1151.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.6	✓	24	21.17	even	6	inner
3150.2.bf.d.1151.7	yes	24	7.3	odd	6	inner
3150.2.bf.d.1601.6	yes	24	1.1	even	1	trivial
3150.2.bf.d.1601.7	yes	24	3.2	odd	2	inner
3150.2.bf.e.1151.6	yes	24	35.24	odd	6
3150.2.bf.e.1151.7	yes	24	105.59	even	6
3150.2.bf.e.1601.6	yes	24	15.14	odd	2
3150.2.bf.e.1601.7	yes	24	5.4	even	2
3150.2.bp.g.899.3		24	105.17	odd	12
3150.2.bp.g.899.10		24	35.3	even	12
3150.2.bp.g.1349.3		24	5.3	odd	4
3150.2.bp.g.1349.10		24	15.2	even	4
3150.2.bp.h.899.3		24	35.17	even	12
3150.2.bp.h.899.10		24	105.38	odd	12
3150.2.bp.h.1349.3		24	15.8	even	4
3150.2.bp.h.1349.10		24	5.2	odd	4

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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