LMFDB - Embedded newform 3150.2.bp.g.899.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(899,3150)]

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, 3, 1]))

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

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

chi := DirichletCharacter("3150.899");

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.bp (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
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			899.3
Character	$\chi$	$=$	3150.899
Dual form			3150.2.bp.g.1349.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.54649 + 0.717905i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.54649 + 0.717905i) q^{7} +1.00000 q^{8} +(5.09272 + 2.94028i) q^{11} +4.05674 q^{13} +(1.89497 + 1.84637i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.371532 + 0.214504i) q^{17} +(-5.30761 + 3.06435i) q^{19} -5.88057i q^{22} +(-0.876005 - 1.51729i) q^{23} +(-2.02837 - 3.51324i) q^{26} +(0.651521 - 2.56428i) q^{28} -0.0419065i q^{29} +(7.92389 + 4.57486i) q^{31} +(-0.500000 + 0.866025i) q^{32} -0.429009i q^{34} +(-0.928534 + 0.536089i) q^{37} +(5.30761 + 3.06435i) q^{38} -8.61559 q^{41} -11.0724i q^{43} +(-5.09272 + 2.94028i) q^{44} +(-0.876005 + 1.51729i) q^{46} +(-0.834099 + 0.481567i) q^{47} +(5.96922 - 3.65628i) q^{49} +(-2.02837 + 3.51324i) q^{52} +(-6.57304 + 11.3848i) q^{53} +(-2.54649 + 0.717905i) q^{56} +(-0.0362921 + 0.0209532i) q^{58} +(-6.77318 + 11.7315i) q^{59} +(1.05635 - 0.609885i) q^{61} -9.14972i q^{62} +1.00000 q^{64} +(-10.9527 - 6.32352i) q^{67} +(-0.371532 + 0.214504i) q^{68} -2.54990i q^{71} +(4.66689 - 8.08328i) q^{73} +(0.928534 + 0.536089i) q^{74} -6.12870i q^{76} +(-15.0794 - 3.83131i) q^{77} +(5.35961 + 9.28312i) q^{79} +(4.30780 + 7.46132i) q^{82} +10.1027i q^{83} +(-9.58894 + 5.53618i) q^{86} +(5.09272 + 2.94028i) q^{88} +(3.15638 + 5.46700i) q^{89} +(-10.3304 + 2.91235i) q^{91} +1.75201 q^{92} +(0.834099 + 0.481567i) q^{94} +2.59007 q^{97} +(-6.15104 - 3.34136i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 12 q^{16} + 24 q^{17} - 12 q^{19} - 8 q^{23} - 12 q^{32} + 12 q^{38} - 8 q^{46} - 24 q^{47} + 52 q^{49} - 32 q^{53} - 12 q^{61} + 24 q^{64} - 24 q^{68} - 16 q^{77} - 4 q^{79} + 68 q^{91} + 16 q^{92} + 24 q^{94} - 20 q^{98}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 12 * q^16 + 24 * q^17 - 12 * q^19 - 8 * q^23 - 12 * q^32 + 12 * q^38 - 8 * q^46 - 24 * q^47 + 52 * q^49 - 32 * q^53 - 12 * q^61 + 24 * q^64 - 24 * q^68 - 16 * q^77 - 4 * q^79 + 68 * q^91 + 16 * q^92 + 24 * q^94 - 20 * q^98

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.54649	+	0.717905i	−0.962483	+	0.271343i
$7$	−2.54649	+	0.717905i	−0.962483	+	0.271343i
$8$	1.00000			0.353553
$9$		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
$13$	4.05674			1.12514			0.562569	−	0.826751i	$-0.309813\pi$
$13$	4.05674			1.12514			0.562569	+	0.826751i	$0.309813\pi$
$14$	1.89497	+	1.84637i	0.506452	+	0.493464i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.371532	+	0.214504i	0.0901098	+	0.0520249i	0.544378	−	0.838840i	$-0.316766\pi$
$17$	0.371532	+	0.214504i	0.0901098	+	0.0520249i	−0.454268	+	0.890865i	$0.650099\pi$
$18$		0			0
$19$	−5.30761	+	3.06435i	−1.21765	+	0.703010i	−0.964414	−	0.264395i	$-0.914828\pi$
$19$	−5.30761	+	3.06435i	−1.21765	+	0.703010i	−0.253234	+	0.967405i	$0.581494\pi$
$20$		0			0
$21$		0			0
$22$		−	5.88057i		−	1.25374i
$23$	−0.876005	−	1.51729i	−0.182660	−	0.316376i	0.760126	−	0.649776i	$-0.225137\pi$
$23$	−0.876005	−	1.51729i	−0.182660	−	0.316376i	−0.942785	+	0.333400i	$0.891804\pi$
$24$		0			0
$25$		0			0
$26$	−2.02837	−	3.51324i	−0.397796	−	0.689003i
$27$		0			0
$28$	0.651521	−	2.56428i	0.123126	−	0.484603i
$29$		−	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	0.996569	−	0.0827694i	$-0.0263765\pi$
$31$	7.92389	+	4.57486i	1.42317	+	0.821669i	0.426604	+	0.904439i	$0.359710\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	0.429009i		−	0.0735744i
$35$		0			0
$36$		0			0
$37$	−0.928534	+	0.536089i	−0.152650	+	0.0881326i	−0.574379	−	0.818589i	$-0.694757\pi$
$37$	−0.928534	+	0.536089i	−0.152650	+	0.0881326i	0.421729	+	0.906722i	$0.361423\pi$
$38$	5.30761	+	3.06435i	0.861008	+	0.497103i
$39$		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
$43$		−	11.0724i		−	1.68852i	−0.535935	−	0.844259i	$-0.680041\pi$
$43$		−	11.0724i		−	1.68852i	0.535935	−	0.844259i	$-0.319959\pi$
$44$	−5.09272	+	2.94028i	−0.767756	+	0.443264i
$45$		0			0
$46$	−0.876005	+	1.51729i	−0.129160	+	0.223712i
$47$	−0.834099	+	0.481567i	−0.121666	+	0.0702438i	−0.559598	−	0.828764i	$-0.689044\pi$
$47$	−0.834099	+	0.481567i	−0.121666	+	0.0702438i	0.437932	+	0.899008i	$0.355711\pi$
$48$		0			0
$49$	5.96922	−	3.65628i	0.852746	−	0.522325i
$50$		0			0
$51$		0			0
$52$	−2.02837	+	3.51324i	−0.281284	+	0.487199i
$53$	−6.57304	+	11.3848i	−0.902877	+	1.56383i	−0.0791353	+	0.996864i	$0.525216\pi$
$53$	−6.57304	+	11.3848i	−0.902877	+	1.56383i	−0.823742	+	0.566965i	$0.808117\pi$
$54$		0			0
$55$		0			0
$56$	−2.54649	+	0.717905i	−0.340289	+	0.0959341i
$57$		0			0
$58$	−0.0362921	+	0.0209532i	−0.00476538	+	0.00275129i
$59$	−6.77318	+	11.7315i	−0.881793	+	1.52731i	−0.0324481	+	0.999473i	$0.510330\pi$
$59$	−6.77318	+	11.7315i	−0.881793	+	1.52731i	−0.849345	+	0.527838i	$0.823003\pi$
$60$		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	$0.308452\pi$
$62$		−	9.14972i		−	1.16202i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−10.9527	−	6.32352i	−1.33808	−	0.772541i	−0.351558	−	0.936166i	$-0.614348\pi$
$67$	−10.9527	−	6.32352i	−1.33808	−	0.772541i	−0.986523	+	0.163625i	$0.947681\pi$
$68$	−0.371532	+	0.214504i	−0.0450549	+	0.0260125i
$69$		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
$73$	4.66689	−	8.08328i	0.546218	−	0.946077i	−0.452311	−	0.891860i	$-0.649400\pi$
$73$	4.66689	−	8.08328i	0.546218	−	0.946077i	0.998529	−	0.0542168i	$-0.0172662\pi$
$74$	0.928534	+	0.536089i	0.107940	+	0.0623191i
$75$		0			0
$76$		−	6.12870i		−	0.703010i
$77$	−15.0794	−	3.83131i	−1.71846	−	0.436619i
$78$		0			0
$79$	5.35961	+	9.28312i	0.603003	+	1.04443i	0.992364	+	0.123347i	$0.0393628\pi$
$79$	5.35961	+	9.28312i	0.603003	+	1.04443i	−0.389360	+	0.921086i	$0.627304\pi$
$80$		0			0
$81$		0			0
$82$	4.30780	+	7.46132i	0.475717	+	0.823965i
$83$			10.1027i			1.10891i	0.832212	+	0.554457i	$0.187074\pi$
$83$			10.1027i			1.10891i	−0.832212	+	0.554457i	$0.812926\pi$
$84$		0			0
$85$		0			0
$86$	−9.58894	+	5.53618i	−1.03400	+	0.596981i
$87$		0			0
$88$	5.09272	+	2.94028i	0.542886	+	0.313435i
$89$	3.15638	+	5.46700i	0.334575	+	0.579501i	0.983403	−	0.181434i	$-0.0580739\pi$
$89$	3.15638	+	5.46700i	0.334575	+	0.579501i	−0.648828	+	0.760935i	$0.724741\pi$
$90$		0			0
$91$	−10.3304	+	2.91235i	−1.08293	+	0.305298i
$92$	1.75201			0.182660
$93$		0			0
$94$	0.834099	+	0.481567i	0.0860307	+	0.0496698i
$95$		0			0
$96$		0			0
$97$	2.59007			0.262982			0.131491	−	0.991317i	$-0.458024\pi$
$97$	2.59007			0.262982			0.131491	+	0.991317i	$0.458024\pi$
$98$	−6.15104	−	3.34136i	−0.621349	−	0.337529i
$99$		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
$103$	2.47216	+	4.28191i	0.243589	+	0.421909i	0.961734	−	0.273985i	$-0.0883418\pi$
$103$	2.47216	+	4.28191i	0.243589	+	0.421909i	−0.718145	+	0.695894i	$0.755008\pi$
$104$	4.05674			0.397796
$105$		0			0
$106$	13.1461			1.27686
$107$	0.347904	+	0.602588i	0.0336332	+	0.0582544i	0.882352	−	0.470590i	$-0.155959\pi$
$107$	0.347904	+	0.602588i	0.0336332	+	0.0582544i	−0.848719	+	0.528844i	$0.822626\pi$
$108$		0			0
$109$	2.98417	−	5.16874i	0.285832	−	0.495076i	−0.686979	−	0.726678i	$-0.741063\pi$
$109$	2.98417	−	5.16874i	0.285832	−	0.495076i	0.972811	+	0.231602i	$0.0743967\pi$
$110$		0			0
$111$		0			0
$112$	1.89497	+	1.84637i	0.179058	+	0.174466i
$113$	−0.809894			−0.0761884			−0.0380942	−	0.999274i	$-0.512129\pi$
$113$	−0.809894			−0.0761884			−0.0380942	+	0.999274i	$0.512129\pi$
$114$		0			0
$115$		0			0
$116$	0.0362921	+	0.0209532i	0.00336963	+	0.00194546i
$117$		0			0
$118$	13.5464			1.24704
$119$	−1.10010	−	0.279508i	−0.100846	−	0.0256225i
$120$		0			0
$121$	11.7905	+	20.4218i	1.07187	+	1.85653i
$122$	−1.05635	−	0.609885i	−0.0956376	−	0.0552164i
$123$		0			0
$124$	−7.92389	+	4.57486i	−0.711586	+	0.410835i
$125$		0			0
$126$		0			0
$127$			11.0265i			0.978442i	0.872160	+	0.489221i	$0.162719\pi$
$127$			11.0265i			0.978442i	−0.872160	+	0.489221i	$0.837281\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		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
$133$	11.3159	−	11.6137i	0.981210	−	1.00704i
$134$			12.6470i			1.09254i
$135$		0			0
$136$	0.371532	+	0.214504i	0.0318586	+	0.0183936i
$137$	−7.18560	+	12.4458i	−0.613907	+	1.06332i	0.376668	+	0.926348i	$0.377070\pi$
$137$	−7.18560	+	12.4458i	−0.613907	+	1.06332i	−0.990575	+	0.136970i	$0.956264\pi$
$138$		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
$142$	−2.20827	+	1.27495i	−0.185314	+	0.106991i
$143$	20.6598	+	11.9280i	1.72766	+	0.997466i
$144$		0			0
$145$		0			0
$146$	−9.33377			−0.772469
$147$		0			0
$148$		−	1.07218i		−	0.0881326i
$149$	−8.67934	+	5.01102i	−0.711039	+	0.410519i	−0.811446	−	0.584428i	$-0.801319\pi$
$149$	−8.67934	+	5.01102i	−0.711039	+	0.410519i	0.100407	+	0.994946i	$0.467986\pi$
$150$		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	$0.967206\pi$
$152$	−5.30761	+	3.06435i	−0.430504	+	0.248552i
$153$		0			0
$154$	4.22169	+	14.9748i	0.340193	+	1.20670i
$155$		0			0
$156$		0			0
$157$	5.43554	−	9.41463i	0.433803	−	0.751370i	−0.563394	−	0.826189i	$-0.690505\pi$
$157$	5.43554	−	9.41463i	0.433803	−	0.751370i	0.997197	+	0.0748190i	$0.0238379\pi$
$158$	5.35961	−	9.28312i	0.426388	−	0.738525i
$159$		0			0
$160$		0			0
$161$	3.32001	+	3.23486i	0.261653	+	0.254943i
$162$		0			0
$163$	9.19935	−	5.31125i	0.720549	−	0.416009i	−0.0944058	−	0.995534i	$-0.530095\pi$
$163$	9.19935	−	5.31125i	0.720549	−	0.416009i	0.814955	+	0.579525i	$0.196762\pi$
$164$	4.30780	−	7.46132i	0.336382	−	0.582631i
$165$		0			0
$166$	8.74919	−	5.05134i	0.679068	−	0.392060i
$167$		−	3.45341i		−	0.267233i	−0.991033	−	0.133617i	$-0.957341\pi$
$167$		−	3.45341i		−	0.267233i	0.991033	−	0.133617i	$-0.0426591\pi$
$168$		0			0
$169$	3.45714			0.265934
$170$		0			0
$171$		0			0
$172$	9.58894	+	5.53618i	0.731150	+	0.422130i
$173$	6.88939	−	3.97759i	0.523790	−	0.302411i	−0.214694	−	0.976681i	$-0.568875\pi$
$173$	6.88939	−	3.97759i	0.523790	−	0.302411i	0.738484	+	0.674271i	$0.235542\pi$
$174$		0			0
$175$		0			0
$176$		−	5.88057i		−	0.443264i
$177$		0			0
$178$	3.15638	−	5.46700i	0.236580	−	0.409769i
$179$	2.38066	+	1.37447i	0.177939	+	0.102733i	0.586324	−	0.810077i	$-0.300575\pi$
$179$	2.38066	+	1.37447i	0.177939	+	0.102733i	−0.408385	+	0.912810i	$0.633908\pi$
$180$		0			0
$181$			6.73202i			0.500387i	0.968196	+	0.250194i	$0.0804943\pi$
$181$			6.73202i			0.500387i	−0.968196	+	0.250194i	$0.919506\pi$
$182$	7.68740	+	7.49025i	0.569828	+	0.555215i
$183$		0			0
$184$	−0.876005	−	1.51729i	−0.0645800	−	0.111856i
$185$		0			0
$186$		0			0
$187$	1.26141	+	2.18482i	0.0922432	+	0.159770i
$188$		−	0.963134i		−	0.0702438i
$189$		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
$193$	0.595151	+	0.343610i	0.0428399	+	0.0247336i	0.521267	−	0.853394i	$-0.325460\pi$
$193$	0.595151	+	0.343610i	0.0428399	+	0.0247336i	−0.478427	+	0.878127i	$0.658793\pi$
$194$	−1.29503	−	2.24306i	−0.0929780	−	0.161043i
$195$		0			0
$196$	0.181816	+	6.99764i	0.0129868	+	0.499831i
$197$	−0.169154			−0.0120517			−0.00602586	−	0.999982i	$-0.501918\pi$
$197$	−0.169154			−0.0120517			−0.00602586	+	0.999982i	$0.501918\pi$
$198$		0			0
$199$	0.359798	+	0.207730i	0.0255054	+	0.0147256i	0.512699	−	0.858569i	$-0.328646\pi$
$199$	0.359798	+	0.207730i	0.0255054	+	0.0147256i	−0.487193	+	0.873294i	$0.661979\pi$
$200$		0			0
$201$		0			0
$202$	−10.4367			−0.734327
$203$	0.0300849	+	0.106714i	0.00211154	+	0.00748988i
$204$		0			0
$205$		0			0
$206$	2.47216	−	4.28191i	0.172244	−	0.298335i
$207$		0			0
$208$	−2.02837	−	3.51324i	−0.140642	−	0.243599i
$209$	−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	$0.523044\pi$
$212$	−6.57304	−	11.3848i	−0.451439	−	0.781915i
$213$		0			0
$214$	0.347904	−	0.602588i	0.0237823	−	0.0411921i
$215$		0			0
$216$		0			0
$217$	−23.4624	−	5.96124i	−1.59273	−	0.404675i
$218$	−5.96835			−0.404227
$219$		0			0
$220$		0			0
$221$	1.50721	+	0.870188i	0.101386	+	0.0585352i
$222$		0			0
$223$	−25.9946			−1.74073			−0.870364	−	0.492409i	$-0.836117\pi$
$223$	−25.9946			−1.74073			−0.870364	+	0.492409i	$0.836117\pi$
$224$	0.651521	−	2.56428i	0.0435316	−	0.171333i
$225$		0			0
$226$	0.404947	+	0.701389i	0.0269367	+	0.0466557i
$227$	12.3905	+	7.15363i	0.822383	+	0.474803i	0.851238	−	0.524781i	$-0.175853\pi$
$227$	12.3905	+	7.15363i	0.822383	+	0.474803i	−0.0288545	+	0.999584i	$0.509186\pi$
$228$		0			0
$229$	1.36736	−	0.789445i	0.0903576	−	0.0521680i	−0.454140	−	0.890930i	$-0.650054\pi$
$229$	1.36736	−	0.789445i	0.0903576	−	0.0521680i	0.544498	+	0.838762i	$0.316720\pi$
$230$		0			0
$231$		0			0
$232$		−	0.0419065i		−	0.00275129i
$233$	9.13044	+	15.8144i	0.598155	+	1.03604i	0.993093	+	0.117327i	$0.0374327\pi$
$233$	9.13044	+	15.8144i	0.598155	+	1.03604i	−0.394938	+	0.918708i	$0.629234\pi$
$234$		0			0
$235$		0			0
$236$	−6.77318	−	11.7315i	−0.440897	−	0.763656i
$237$		0			0
$238$	0.307987	+	1.09247i	0.0199639	+	0.0708141i
$239$		−	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	0.0934660	−	0.995622i	$-0.470205\pi$
$241$	−11.2090	−	6.47152i	−0.722035	−	0.416867i	−0.815501	+	0.578755i	$0.803539\pi$
$242$	11.7905	−	20.4218i	0.757924	−	1.31276i
$243$		0			0
$244$			1.21977i			0.0780878i
$245$		0			0
$246$		0			0
$247$	−21.5316	+	12.4313i	−1.37002	+	0.790983i
$248$	7.92389	+	4.57486i	0.503168	+	0.290504i
$249$		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
$253$		−	10.3028i		−	0.647732i
$254$	9.54921	−	5.51324i	0.599171	−	0.345931i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.06331	+	3.50065i	−0.378219	+	0.218365i	−0.677043	−	0.735943i	$-0.736739\pi$
$257$	−6.06331	+	3.50065i	−0.378219	+	0.218365i	0.298824	+	0.954308i	$0.403406\pi$
$258$		0			0
$259$	1.97964	−	2.03175i	0.123009	−	0.126247i
$260$		0			0
$261$		0			0
$262$	9.44080	−	16.3520i	0.583255	−	1.01023i
$263$	−6.00972	+	10.4091i	−0.370575	+	0.641855i	−0.989654	−	0.143473i	$-0.954173\pi$
$263$	−6.00972	+	10.4091i	−0.370575	+	0.641855i	0.619079	+	0.785329i	$0.287506\pi$
$264$		0			0
$265$		0			0
$266$	−15.7157	−	3.99298i	−0.963590	−	0.244825i
$267$		0			0
$268$	10.9527	−	6.32352i	0.669040	−	0.386271i
$269$	0.611792	−	1.05966i	0.0373016	−	0.0646083i	−0.846772	−	0.531956i	$-0.821457\pi$
$269$	0.611792	−	1.05966i	0.0373016	−	0.0646083i	0.884074	+	0.467348i	$0.154790\pi$
$270$		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	$0.167540\pi$
$272$		−	0.429009i		−	0.0260125i
$273$		0			0
$274$	14.3712			0.868196
$275$		0			0
$276$		0			0
$277$	11.4092	+	6.58712i	0.685514	+	0.395781i	0.801929	−	0.597419i	$-0.203807\pi$
$277$	11.4092	+	6.58712i	0.685514	+	0.395781i	−0.116416	+	0.993201i	$0.537140\pi$
$278$	14.5189	−	8.38250i	0.870786	−	0.502749i
$279$		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
$283$	8.07354	−	13.9838i	0.479922	−	0.831249i	−0.519813	−	0.854280i	$-0.673998\pi$
$283$	8.07354	−	13.9838i	0.479922	−	0.831249i	0.999735	+	0.0230311i	$0.00733167\pi$
$284$	2.20827	+	1.27495i	0.131037	+	0.0756542i
$285$		0			0
$286$		−	23.8559i		−	1.41063i
$287$	21.9395	−	6.18518i	1.29505	−	0.365100i
$288$		0			0
$289$	−8.40798	−	14.5630i	−0.494587	−	0.856649i
$290$		0			0
$291$		0			0
$292$	4.66689	+	8.08328i	0.273109	+	0.473038i
$293$			24.2757i			1.41820i	0.705108	+	0.709100i	$0.250898\pi$
$293$			24.2757i			1.41820i	−0.705108	+	0.709100i	$0.749102\pi$
$294$		0			0
$295$		0			0
$296$	−0.928534	+	0.536089i	−0.0539699	+	0.0311596i
$297$		0			0
$298$	8.67934	+	5.01102i	0.502780	+	0.290280i
$299$	−3.55372	−	6.15523i	−0.205517	−	0.355966i
$300$		0			0
$301$	7.94890	+	28.1956i	0.458167	+	1.62517i
$302$	14.4120			0.829316
$303$		0			0
$304$	5.30761	+	3.06435i	0.304412	+	0.175752i
$305$		0			0
$306$		0			0
$307$	19.1856			1.09498			0.547490	−	0.836812i	$-0.315583\pi$
$307$	19.1856			1.09498			0.547490	+	0.836812i	$0.315583\pi$
$308$	10.8577	−	11.1435i	0.618676	−	0.634959i
$309$		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
$313$	9.76593	+	16.9151i	0.552003	+	0.956097i	0.998130	+	0.0611276i	$0.0194696\pi$
$313$	9.76593	+	16.9151i	0.552003	+	0.956097i	−0.446127	+	0.894970i	$0.647197\pi$
$314$	−10.8711			−0.613491
$315$		0			0
$316$	−10.7192			−0.603003
$317$	−7.28095	−	12.6110i	−0.408939	−	0.708303i	0.585832	−	0.810432i	$-0.300768\pi$
$317$	−7.28095	−	12.6110i	−0.408939	−	0.708303i	−0.994771	+	0.102129i	$0.967434\pi$
$318$		0			0
$319$	0.123217	−	0.213418i	0.00689882	−	0.0119491i
$320$		0			0
$321$		0			0
$322$	1.14147	−	4.49264i	0.0636117	−	0.250365i
$323$	−2.62926			−0.146296
$324$		0			0
$325$		0			0
$326$	−9.19935	−	5.31125i	−0.509505	−	0.294163i
$327$		0			0
$328$	−8.61559			−0.475717
$329$	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	$0.754709\pi$
$332$	−8.74919	−	5.05134i	−0.480174	−	0.277229i
$333$		0			0
$334$	−2.99074	+	1.72671i	−0.163646	+	0.0944812i
$335$		0			0
$336$		0			0
$337$			10.3636i			0.564543i	0.959335	+	0.282271i	$0.0910879\pi$
$337$			10.3636i			0.564543i	−0.959335	+	0.282271i	$0.908912\pi$
$338$	−1.72857	−	2.99397i	−0.0940217	−	0.162850i
$339$		0			0
$340$		0			0
$341$	26.9028	+	46.5970i	1.45687	+	2.52337i
$342$		0			0
$343$	−12.5757	+	13.5960i	−0.679025	+	0.734115i
$344$		−	11.0724i		−	0.596981i
$345$		0			0
$346$	−6.88939	−	3.97759i	−0.370376	−	0.213837i
$347$	−14.7440	+	25.5373i	−0.791497	+	1.37091i	0.133542	+	0.991043i	$0.457365\pi$
$347$	−14.7440	+	25.5373i	−0.791497	+	1.37091i	−0.925040	+	0.379870i	$0.875969\pi$
$348$		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
$352$	−5.09272	+	2.94028i	−0.271443	+	0.156718i
$353$	−14.8345	−	8.56472i	−0.789562	−	0.455854i	0.0502461	−	0.998737i	$-0.483999\pi$
$353$	−14.8345	−	8.56472i	−0.789562	−	0.455854i	−0.839808	+	0.542883i	$0.817333\pi$
$354$		0			0
$355$		0			0
$356$	−6.31275			−0.334575
$357$		0			0
$358$		−	2.74895i		−	0.145286i
$359$	19.0997	−	11.0272i	1.00804	−	0.581993i	0.0974241	−	0.995243i	$-0.468940\pi$
$359$	19.0997	−	11.0272i	1.00804	−	0.581993i	0.910618	+	0.413250i	$0.135606\pi$
$360$		0			0
$361$	9.28047	−	16.0743i	0.488446	−	0.846013i
$362$	5.83010	−	3.36601i	0.306423	−	0.176914i
$363$		0			0
$364$	2.64305	−	10.4026i	0.138534	−	0.545245i
$365$		0			0
$366$		0			0
$367$	−1.63762	+	2.83644i	−0.0854831	+	0.148061i	−0.905597	−	0.424139i	$-0.860577\pi$
$367$	−1.63762	+	2.83644i	−0.0854831	+	0.148061i	0.820114	+	0.572200i	$0.193910\pi$
$368$	−0.876005	+	1.51729i	−0.0456649	+	0.0790940i
$369$		0			0
$370$		0			0
$371$	8.56495	−	33.7102i	0.444670	−	1.75015i
$372$		0			0
$373$	−32.4255	+	18.7209i	−1.67893	+	0.969331i	−0.716587	+	0.697498i	$0.754297\pi$
$373$	−32.4255	+	18.7209i	−1.67893	+	0.969331i	−0.962344	+	0.271834i	$0.912370\pi$
$374$	1.26141	−	2.18482i	0.0652258	−	0.112974i
$375$		0			0
$376$	−0.834099	+	0.481567i	−0.0430154	+	0.0248349i
$377$		−	0.170004i		−	0.00875563i
$378$		0			0
$379$	37.2066			1.91117			0.955587	−	0.294708i	$-0.0952225\pi$
$379$	37.2066			1.91117			0.955587	+	0.294708i	$0.0952225\pi$
$380$		0			0
$381$		0			0
$382$	21.3740	+	12.3403i	1.09359	+	0.631383i
$383$	−15.8160	+	9.13135i	−0.808158	+	0.466590i	−0.846316	−	0.532682i	$-0.821184\pi$
$383$	−15.8160	+	9.13135i	−0.808158	+	0.466590i	0.0381579	+	0.999272i	$0.487851\pi$
$384$		0			0
$385$		0			0
$386$		−	0.687221i		−	0.0349786i
$387$		0			0
$388$	−1.29503	+	2.24306i	−0.0657454	+	0.113874i
$389$	−2.21119	−	1.27663i	−0.112112	−	0.0647278i	0.442896	−	0.896573i	$-0.353951\pi$
$389$	−2.21119	−	1.27663i	−0.112112	−	0.0647278i	−0.555007	+	0.831845i	$0.687285\pi$
$390$		0			0
$391$		−	0.751627i		−	0.0380114i
$392$	5.96922	−	3.65628i	0.301491	−	0.184670i
$393$		0			0
$394$	0.0845770	+	0.146492i	0.00426093	+	0.00738014i
$395$		0			0
$396$		0			0
$397$	−9.98784	−	17.2994i	−0.501275	−	0.868234i	−0.999999	−	0.00147306i	$-0.999531\pi$
$397$	−9.98784	−	17.2994i	−0.501275	−	0.868234i	0.498724	−	0.866761i	$-0.333802\pi$
$398$		−	0.415459i		−	0.0208251i
$399$		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
$403$	32.1452	+	18.5590i	1.60126	+	0.924490i
$404$	5.21837	+	9.03849i	0.259624	+	0.449682i
$405$		0			0
$406$	0.0773750	−	0.0794115i	0.00384006	−	0.00394113i
$407$	−6.30502			−0.312528
$408$		0			0
$409$	−14.0020	−	8.08403i	−0.692352	−	0.399730i	0.112140	−	0.993692i	$-0.464229\pi$
$409$	−14.0020	−	8.08403i	−0.692352	−	0.399730i	−0.804493	+	0.593963i	$0.797563\pi$
$410$		0			0
$411$		0			0
$412$	−4.94432			−0.243589
$413$	8.82575	−	34.7366i	0.434287	−	1.70928i
$414$		0			0
$415$		0			0
$416$	−2.02837	+	3.51324i	−0.0994490	+	0.172251i
$417$		0			0
$418$	18.0201	+	31.2117i	0.881392	+	1.52662i
$419$	14.1632			0.691920			0.345960	−	0.938249i	$-0.387553\pi$
$419$	14.1632			0.691920			0.345960	+	0.938249i	$0.387553\pi$
$420$		0			0
$421$	−21.7096			−1.05806			−0.529031	−	0.848603i	$-0.677444\pi$
$421$	−21.7096			−1.05806			−0.529031	+	0.848603i	$0.677444\pi$
$422$	1.05067	+	1.81982i	0.0511460	+	0.0885874i
$423$		0			0
$424$	−6.57304	+	11.3848i	−0.319215	+	0.552897i
$425$		0			0
$426$		0			0
$427$	−2.25215	+	2.31143i	−0.108989	+	0.111858i
$428$	−0.695809			−0.0336332
$429$		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
$433$	9.86329			0.473999			0.237000	−	0.971510i	$-0.423836\pi$
$433$	9.86329			0.473999			0.237000	+	0.971510i	$0.423836\pi$
$434$	6.56863	+	23.2997i	0.315304	+	1.11842i
$435$		0			0
$436$	2.98417	+	5.16874i	0.142916	+	0.247538i
$437$	9.29898	+	5.36877i	0.444831	+	0.256823i
$438$		0			0
$439$	12.1701	−	7.02641i	0.580847	−	0.335352i	−0.180623	−	0.983552i	$-0.557811\pi$
$439$	12.1701	−	7.02641i	0.580847	−	0.335352i	0.761470	+	0.648200i	$0.224478\pi$
$440$		0			0
$441$		0			0
$442$		−	1.74038i		−	0.0827812i
$443$	−7.72219	−	13.3752i	−0.366892	−	0.635476i	0.622186	−	0.782870i	$-0.286245\pi$
$443$	−7.72219	−	13.3752i	−0.366892	−	0.635476i	−0.989078	+	0.147394i	$0.952912\pi$
$444$		0			0
$445$		0			0
$446$	12.9973	+	22.5120i	0.615440	+	1.06597i
$447$		0			0
$448$	−2.54649	+	0.717905i	−0.120310	+	0.0339178i
$449$			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
$452$	0.404947	−	0.701389i	0.0190471	−	0.0329906i
$453$		0			0
$454$		−	14.3073i		−	0.671473i
$455$		0			0
$456$		0			0
$457$	−11.3995	+	6.58150i	−0.533246	+	0.307870i	−0.742337	−	0.670026i	$-0.766283\pi$
$457$	−11.3995	+	6.58150i	−0.533246	+	0.307870i	0.209091	+	0.977896i	$0.432949\pi$
$458$	−1.36736	−	0.789445i	−0.0638925	−	0.0368883i
$459$		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
$463$		−	17.7932i		−	0.826920i	−0.910522	−	0.413460i	$-0.864320\pi$
$463$		−	17.7932i		−	0.826920i	0.910522	−	0.413460i	$-0.135680\pi$
$464$	−0.0362921	+	0.0209532i	−0.00168482	+	0.000972730i
$465$		0			0
$466$	9.13044	−	15.8144i	0.422960	−	0.732587i
$467$	1.87225	−	1.08094i	0.0866373	−	0.0500201i	−0.456055	−	0.889951i	$-0.650738\pi$
$467$	1.87225	−	1.08094i	0.0866373	−	0.0500201i	0.542693	+	0.839931i	$0.317405\pi$
$468$		0			0
$469$	32.4305	+	8.23982i	1.49750	+	0.380479i
$470$		0			0
$471$		0			0
$472$	−6.77318	+	11.7315i	−0.311761	+	0.539986i
$473$	32.5559	−	56.3884i	1.49692	−	2.59274i
$474$		0			0
$475$		0			0
$476$	0.792110	−	0.812958i	0.0363063	−	0.0372619i
$477$		0			0
$478$	−20.0746	+	11.5901i	−0.918190	+	0.530117i
$479$	6.50176	−	11.2614i	0.297073	−	0.514546i	−0.678392	−	0.734700i	$-0.737323\pi$
$479$	6.50176	−	11.2614i	0.297073	−	0.514546i	0.975465	+	0.220154i	$0.0706561\pi$
$480$		0			0
$481$	−3.76682	+	2.17478i	−0.171752	+	0.0991612i
$482$			12.9430i			0.589539i
$483$		0			0
$484$	−23.5811			−1.07187
$485$		0			0
$486$		0			0
$487$	−5.46224	−	3.15363i	−0.247518	−	0.142904i	0.371109	−	0.928589i	$-0.378978\pi$
$487$	−5.46224	−	3.15363i	−0.247518	−	0.142904i	−0.618627	+	0.785685i	$0.712311\pi$
$488$	1.05635	−	0.609885i	0.0478188	−	0.0276082i
$489$		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
$493$	0.00898912	−	0.0155696i	0.000404849	−	0.000701220i
$494$	21.5316	+	12.4313i	0.968752	+	0.559309i
$495$		0			0
$496$		−	9.14972i		−	0.410835i
$497$	1.83058	+	6.49328i	0.0821129	+	0.291264i
$498$		0			0
$499$	−12.1113	−	20.9774i	−0.542176	−	0.939076i	−0.998779	−	0.0494053i	$-0.984267\pi$
$499$	−12.1113	−	20.9774i	−0.542176	−	0.939076i	0.456603	−	0.889670i	$-0.349066\pi$
$500$		0			0
$501$		0			0
$502$	−11.3626	−	19.6806i	−0.507139	−	0.878390i
$503$			34.9707i			1.55927i	0.626237	+	0.779633i	$0.284594\pi$
$503$			34.9707i			1.55927i	−0.626237	+	0.779633i	$0.715406\pi$
$504$		0			0
$505$		0			0
$506$	−8.92250	+	5.15141i	−0.396653	+	0.229008i
$507$		0			0
$508$	−9.54921	−	5.51324i	−0.423678	−	0.244610i
$509$	−9.58793	−	16.6068i	−0.424978	−	0.736083i	0.571441	−	0.820643i	$-0.306385\pi$
$509$	−9.58793	−	16.6068i	−0.424978	−	0.736083i	−0.996418	+	0.0845605i	$0.973051\pi$
$510$		0			0
$511$	−6.08115	+	23.9344i	−0.269014	+	1.05879i
$512$	1.00000			0.0441942
$513$		0			0
$514$	6.06331	+	3.50065i	0.267441	+	0.154407i
$515$		0			0
$516$		0			0
$517$	−5.66377			−0.249092
$518$	−2.74936	−	0.698547i	−0.120800	−	0.0306924i
$519$		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
$523$	5.01992	+	8.69476i	0.219506	+	0.380195i	0.954657	−	0.297708i	$-0.0962222\pi$
$523$	5.01992	+	8.69476i	0.219506	+	0.380195i	−0.735151	+	0.677903i	$0.762889\pi$
$524$	−18.8816			−0.824847
$525$		0			0
$526$	12.0194			0.524073
$527$	1.96265	+	3.39942i	0.0854946	+	0.148081i
$528$		0			0
$529$	9.96523	−	17.2603i	0.433271	−	0.750447i
$530$		0			0
$531$		0			0
$532$	4.39982	+	15.6067i	0.190757	+	0.676635i
$533$	−34.9512			−1.51391
$534$		0			0
$535$		0			0
$536$	−10.9527	−	6.32352i	−0.473083	−	0.273135i
$537$		0			0
$538$	−1.22358			−0.0527525
$539$	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	$0.711466\pi$
$542$	−14.1888	−	8.19190i	−0.609461	−	0.351872i
$543$		0			0
$544$	−0.371532	+	0.214504i	−0.0159293	+	0.00919679i
$545$		0			0
$546$		0			0
$547$		−	32.6253i		−	1.39496i	−0.716606	−	0.697478i	$-0.754305\pi$
$547$		−	32.6253i		−	1.39496i	0.716606	−	0.697478i	$-0.245695\pi$
$548$	−7.18560	−	12.4458i	−0.306954	−	0.531659i
$549$		0			0
$550$		0			0
$551$	0.128416	+	0.222423i	0.00547071	+	0.00947555i
$552$		0			0
$553$	−20.3126	−	19.7917i	−0.863780	−	0.841628i
$554$		−	13.1742i		−	0.559720i
$555$		0			0
$556$	−14.5189	−	8.38250i	−0.615739	−	0.355497i
$557$	17.0656	−	29.5585i	0.723094	−	1.25243i	−0.236660	−	0.971592i	$-0.576053\pi$
$557$	17.0656	−	29.5585i	0.723094	−	1.25243i	0.959754	−	0.280842i	$-0.0906138\pi$
$558$		0			0
$559$		−	44.9177i		−	1.89981i
$560$		0			0
$561$		0			0
$562$	−4.95741	+	2.86216i	−0.209116	+	0.120733i
$563$	25.8012	+	14.8964i	1.08739	+	0.627806i	0.932881	−	0.360185i	$-0.117286\pi$
$563$	25.8012	+	14.8964i	1.08739	+	0.627806i	0.154512	+	0.987991i	$0.450620\pi$
$564$		0			0
$565$		0			0
$566$	−16.1471			−0.678712
$567$		0			0
$568$		−	2.54990i		−	0.106991i
$569$	−14.4586	+	8.34769i	−0.606137	+	0.349953i	−0.771452	−	0.636287i	$-0.780469\pi$
$569$	−14.4586	+	8.34769i	−0.606137	+	0.349953i	0.165315	+	0.986241i	$0.447136\pi$
$570$		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	$0.153552\pi$
$572$	−20.6598	+	11.9280i	−0.863831	+	0.498733i
$573$		0			0
$574$	−16.3263	−	15.9076i	−0.681446	−	0.663970i
$575$		0			0
$576$		0			0
$577$	19.9848	−	34.6146i	0.831977	−	1.44103i	−0.0644912	−	0.997918i	$-0.520542\pi$
$577$	19.9848	−	34.6146i	0.831977	−	1.44103i	0.896468	−	0.443108i	$-0.146124\pi$
$578$	−8.40798	+	14.5630i	−0.349726	+	0.605743i
$579$		0			0
$580$		0			0
$581$	−7.25277	−	25.7264i	−0.300896	−	1.06731i
$582$		0			0
$583$	−66.9493	+	38.6532i	−2.77276	+	1.60085i
$584$	4.66689	−	8.08328i	0.193117	−	0.334489i
$585$		0			0
$586$	21.0233	−	12.1378i	0.868466	−	0.501409i
$587$			25.5123i			1.05300i	0.850174	+	0.526502i	$0.176497\pi$
$587$			25.5123i			1.05300i	−0.850174	+	0.526502i	$0.823503\pi$
$588$		0			0
$589$	−56.0759			−2.31057
$590$		0			0
$591$		0			0
$592$	0.928534	+	0.536089i	0.0381625	+	0.0220331i
$593$	−34.9279	+	20.1656i	−1.43432	+	0.828103i	−0.997446	−	0.0714207i	$-0.977247\pi$
$593$	−34.9279	+	20.1656i	−1.43432	+	0.828103i	−0.436871	+	0.899524i	$0.643913\pi$
$594$		0			0
$595$		0			0
$596$		−	10.0220i		−	0.410519i
$597$		0			0
$598$	−3.55372	+	6.15523i	−0.145323	+	0.251706i
$599$	−19.9124	−	11.4964i	−0.813600	−	0.469732i	0.0346046	−	0.999401i	$-0.488983\pi$
$599$	−19.9124	−	11.4964i	−0.813600	−	0.469732i	−0.848204	+	0.529669i	$0.822316\pi$
$600$		0			0
$601$		−	25.9443i		−	1.05829i	−0.848532	−	0.529145i	$-0.822513\pi$
$601$		−	25.9443i		−	1.05829i	0.848532	−	0.529145i	$-0.177487\pi$
$602$	20.4437	−	20.9818i	0.833223	−	0.855153i
$603$		0			0
$604$	−7.20599	−	12.4811i	−0.293207	−	0.507850i
$605$		0			0
$606$		0			0
$607$	18.9551	+	32.8311i	0.769362	+	1.33257i	0.937909	+	0.346881i	$0.112759\pi$
$607$	18.9551	+	32.8311i	0.769362	+	1.33257i	−0.168547	+	0.985694i	$0.553908\pi$
$608$		−	6.12870i		−	0.248552i
$609$		0			0
$610$		0			0
$611$	−3.38372	+	1.95359i	−0.136891	+	0.0790339i
$612$		0			0
$613$	−18.0154	−	10.4012i	−0.727637	−	0.420101i	0.0899202	−	0.995949i	$-0.471339\pi$
$613$	−18.0154	−	10.4012i	−0.727637	−	0.420101i	−0.817557	+	0.575848i	$0.804672\pi$
$614$	−9.59280	−	16.6152i	−0.387134	−	0.670536i
$615$		0			0
$616$	−15.0794	−	3.83131i	−0.607566	−	0.154368i
$617$	40.9298			1.64777			0.823887	−	0.566755i	$-0.191801\pi$
$617$	40.9298			1.64777			0.823887	+	0.566755i	$0.191801\pi$
$618$		0			0
$619$	23.2122	+	13.4016i	0.932976	+	0.538654i	0.887752	−	0.460323i	$-0.152266\pi$
$619$	23.2122	+	13.4016i	0.932976	+	0.538654i	0.0452247	+	0.998977i	$0.485600\pi$
$620$		0			0
$621$		0			0
$622$	32.6946			1.31093
$623$	−11.9625	−	11.6557i	−0.479266	−	0.466975i
$624$		0			0
$625$		0			0
$626$	9.76593	−	16.9151i	0.390325	−	0.676063i
$627$		0			0
$628$	5.43554	+	9.41463i	0.216902	+	0.375685i
$629$	−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	$0.514498\pi$
$632$	5.35961	+	9.28312i	0.213194	+	0.369263i
$633$		0			0
$634$	−7.28095	+	12.6110i	−0.289164	+	0.500846i
$635$		0			0
$636$		0			0
$637$	24.2156	−	14.8326i	0.959457	−	0.587687i
$638$	−0.246434			−0.00975641
$639$		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
$643$	−44.2035			−1.74322			−0.871608	−	0.490203i	$-0.836923\pi$
$643$	−44.2035			−1.74322			−0.871608	+	0.490203i	$0.836923\pi$
$644$	−4.46148	+	1.25778i	−0.175807	+	0.0495634i
$645$		0			0
$646$	1.31463	+	2.27701i	0.0517235	+	0.0895877i
$647$	17.9336	+	10.3540i	0.705044	+	0.407058i	0.809223	−	0.587501i	$-0.199888\pi$
$647$	17.9336	+	10.3540i	0.705044	+	0.407058i	−0.104179	+	0.994559i	$0.533221\pi$
$648$		0			0
$649$	−68.9878	+	39.8302i	−2.70801	+	1.56347i
$650$		0			0
$651$		0			0
$652$			10.6225i			0.416009i
$653$	−13.5019	−	23.3860i	−0.528370	−	0.915164i	−0.999453	−	0.0330748i	$-0.989470\pi$
$653$	−13.5019	−	23.3860i	−0.528370	−	0.915164i	0.471083	−	0.882089i	$-0.343863\pi$
$654$		0			0
$655$		0			0
$656$	4.30780	+	7.46132i	0.168191	+	0.291316i
$657$		0			0
$658$	−2.46974	−	0.627502i	−0.0962806	−	0.0244626i
$659$		−	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	−0.401176	−	0.916001i	$-0.631398\pi$
$661$	−35.8665	−	20.7075i	−1.39504	−	0.805429i	−0.993868	+	0.110572i	$0.964732\pi$
$662$	4.44833	−	7.70473i	0.172889	−	0.299453i
$663$		0			0
$664$			10.1027i			0.392060i
$665$		0			0
$666$		0			0
$667$	−0.0635841	+	0.0367103i	−0.00246199	+	0.00142143i
$668$	2.99074	+	1.72671i	0.115715	+	0.0668083i
$669$		0			0
$670$		0			0
$671$	7.17294			0.276908
$672$		0			0
$673$		−	15.2809i		−	0.589037i	−0.955646	−	0.294518i	$-0.904841\pi$
$673$		−	15.2809i		−	0.589037i	0.955646	−	0.294518i	$-0.0951592\pi$
$674$	8.97517	−	5.18182i	0.345711	−	0.199596i
$675$		0			0
$676$	−1.72857	+	2.99397i	−0.0664834	+	0.115153i
$677$	−42.0596	+	24.2831i	−1.61648	+	0.933277i	−0.628662	+	0.777679i	$0.716397\pi$
$677$	−42.0596	+	24.2831i	−1.61648	+	0.933277i	−0.987820	+	0.155598i	$0.950270\pi$
$678$		0			0
$679$	−6.59558	+	1.85942i	−0.253115	+	0.0713581i
$680$		0			0
$681$		0			0
$682$	26.9028	−	46.5970i	1.03016	−	1.78429i
$683$	−6.15706	+	10.6643i	−0.235593	+	0.408059i	−0.959445	−	0.281896i	$-0.909037\pi$
$683$	−6.15706	+	10.6643i	−0.235593	+	0.408059i	0.723852	+	0.689956i	$0.242370\pi$
$684$		0			0
$685$		0			0
$686$	18.0623	+	4.09288i	0.689624	+	0.156267i
$687$		0			0
$688$	−9.58894	+	5.53618i	−0.365575	+	0.211065i
$689$	−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	$0.0334134\pi$
$692$			7.95518i			0.302411i
$693$		0			0
$694$	29.4879			1.11935
$695$		0			0
$696$		0			0
$697$	−3.20097	−	1.84808i	−0.121245	−	0.0700011i
$698$	7.67094	−	4.42882i	0.290349	−	0.167633i
$699$		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
$703$	3.28553	−	5.69071i	0.123916	−	0.214629i
$704$	5.09272	+	2.94028i	0.191939	+	0.110816i
$705$		0			0
$706$			17.1294i			0.644675i
$707$	−6.79976	+	26.7627i	−0.255731	+	1.00652i
$708$		0			0
$709$	−10.4912	−	18.1712i	−0.394004	−	0.682435i	0.598969	−	0.800772i	$-0.295577\pi$
$709$	−10.4912	−	18.1712i	−0.394004	−	0.682435i	−0.992974	+	0.118337i	$0.962244\pi$
$710$		0			0
$711$		0			0
$712$	3.15638	+	5.46700i	0.118290	+	0.204885i
$713$		−	16.0304i		−	0.600343i
$714$		0			0
$715$		0			0
$716$	−2.38066	+	1.37447i	−0.0889694	+	0.0513665i
$717$		0			0
$718$	−19.0997	−	11.0272i	−0.712793	−	0.411531i
$719$	8.73253	+	15.1252i	0.325668	+	0.564074i	0.981647	−	0.190705i	$-0.0610773\pi$
$719$	8.73253	+	15.1252i	0.325668	+	0.564074i	−0.655979	+	0.754779i	$0.727744\pi$
$720$		0			0
$721$	−9.36934	−	9.12906i	−0.348932	−	0.339984i
$722$	−18.5609			−0.690767
$723$		0			0
$724$	−5.83010	−	3.36601i	−0.216674	−	0.125097i
$725$		0			0
$726$		0			0
$727$	12.4470			0.461633			0.230816	−	0.972997i	$-0.425860\pi$
$727$	12.4470			0.461633			0.230816	+	0.972997i	$0.425860\pi$
$728$	−10.3304	+	2.91235i	−0.382872	+	0.107939i
$729$		0			0
$730$		0			0
$731$	2.37507	−	4.11374i	0.0878450	−	0.152152i
$732$		0			0
$733$	11.1806	+	19.3654i	0.412966	+	0.715279i	0.995213	−	0.0977339i	$-0.0311594\pi$
$733$	11.1806	+	19.3654i	0.412966	+	0.715279i	−0.582246	+	0.813012i	$0.697826\pi$
$734$	3.27524			0.120891
$735$		0			0
$736$	1.75201			0.0645800
$737$	−37.1859	−	64.4079i	−1.36976	−	2.37249i
$738$		0			0
$739$	−15.9125	+	27.5613i	−0.585351	+	1.01386i	0.409481	+	0.912319i	$0.365710\pi$
$739$	−15.9125	+	27.5613i	−0.585351	+	1.01386i	−0.994832	+	0.101539i	$0.967623\pi$
$740$		0			0
$741$		0			0
$742$	−33.4764	+	9.43764i	−1.22896	+	0.346467i
$743$	−15.1736			−0.556667			−0.278333	−	0.960485i	$-0.589782\pi$
$743$	−15.1736			−0.556667			−0.278333	+	0.960485i	$0.589782\pi$
$744$		0			0
$745$		0			0
$746$	32.4255	+	18.7209i	1.18718	+	0.685421i
$747$		0			0
$748$	−2.52281			−0.0922432
$749$	−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	$0.708227\pi$
$752$	0.834099	+	0.481567i	0.0304164	+	0.0175609i
$753$		0			0
$754$	−0.147227	+	0.0850018i	−0.00536171	+	0.00309558i
$755$		0			0
$756$		0			0
$757$		−	17.0421i		−	0.619407i	−0.950833	−	0.309704i	$-0.899770\pi$
$757$		−	17.0421i		−	0.619407i	0.950833	−	0.309704i	$-0.100230\pi$
$758$	−18.6033	−	32.2219i	−0.675702	−	1.17035i
$759$		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
$763$	−3.88850	+	15.3045i	−0.140773	+	0.554060i
$764$		−	24.6805i		−	0.892911i
$765$		0			0
$766$	15.8160	+	9.13135i	0.571454	+	0.329929i
$767$	−27.4770	+	47.5916i	−0.992139	+	1.71843i
$768$		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
$772$	−0.595151	+	0.343610i	−0.0214199	+	0.0123668i
$773$	−38.5322	−	22.2466i	−1.38591	−	0.800153i	−0.393055	−	0.919515i	$-0.628582\pi$
$773$	−38.5322	−	22.2466i	−1.38591	−	0.800153i	−0.992851	+	0.119361i	$0.961915\pi$
$774$		0			0
$775$		0			0
$776$	2.59007			0.0929780
$777$		0			0
$778$			2.55326i			0.0915390i
$779$	45.7282	−	26.4012i	1.63838	−	0.945921i
$780$		0			0
$781$	7.49741	−	12.9859i	0.268279	−	0.464672i
$782$	−0.650928	+	0.375814i	−0.0232771	+	0.0134391i
$783$		0			0
$784$	−6.15104	−	3.34136i	−0.219680	−	0.119334i
$785$		0			0
$786$		0			0
$787$	−7.68522	+	13.3112i	−0.273948	+	0.474493i	−0.969869	−	0.243626i	$-0.921663\pi$
$787$	−7.68522	+	13.3112i	−0.273948	+	0.474493i	0.695921	+	0.718118i	$0.254996\pi$
$788$	0.0845770	−	0.146492i	0.00301293	−	0.00521855i
$789$		0			0
$790$		0			0
$791$	2.06239	−	0.581427i	0.0733301	−	0.0206732i
$792$		0			0
$793$	4.28535	−	2.47415i	0.152177	−	0.0878595i
$794$	−9.98784	+	17.2994i	−0.354455	+	0.613934i
$795$		0			0
$796$	−0.359798	+	0.207730i	−0.0127527	+	0.00736278i
$797$		−	28.8285i		−	1.02116i	−0.859830	−	0.510580i	$-0.829431\pi$
$797$		−	28.8285i		−	1.02116i	0.859830	−	0.510580i	$-0.170569\pi$
$798$		0			0
$799$	−0.413193			−0.0146177
$800$		0			0
$801$		0			0
$802$	−21.2087	−	12.2448i	−0.748904	−	0.432380i
$803$	47.5343	−	27.4439i	1.67745	−	0.968475i
$804$		0			0
$805$		0			0
$806$		−	37.1180i		−	1.30743i
$807$		0			0
$808$	5.21837	−	9.03849i	0.183582	−	0.317973i
$809$	15.9209	+	9.19196i	0.559751	+	0.323172i	0.753045	−	0.657968i	$-0.228584\pi$
$809$	15.9209	+	9.19196i	0.559751	+	0.323172i	−0.193295	+	0.981141i	$0.561917\pi$
$810$		0			0
$811$		−	47.0100i		−	1.65074i	−0.564589	−	0.825372i	$-0.690965\pi$
$811$		−	47.0100i		−	1.65074i	0.564589	−	0.825372i	$-0.309035\pi$
$812$	−0.107460	−	0.0273030i	−0.00377110	−	0.000958146i
$813$		0			0
$814$	3.15251	+	5.46031i	0.110495	+	0.191384i
$815$		0			0
$816$		0			0
$817$	33.9296	+	58.7677i	1.18705	+	2.05602i
$818$			16.1681i			0.565303i
$819$		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
$823$	0.620733	+	0.358380i	0.0216374	+	0.0124924i	0.510780	−	0.859712i	$-0.329357\pi$
$823$	0.620733	+	0.358380i	0.0216374	+	0.0124924i	−0.489142	+	0.872204i	$0.662690\pi$
$824$	2.47216	+	4.28191i	0.0861218	+	0.149167i
$825$		0			0
$826$	−34.4957	+	9.72501i	−1.20026	+	0.338376i
$827$	32.8584			1.14260			0.571299	−	0.820742i	$-0.306440\pi$
$827$	32.8584			1.14260			0.571299	+	0.820742i	$0.306440\pi$
$828$		0			0
$829$	−43.6845	−	25.2212i	−1.51722	−	0.875970i	−0.999795	−	0.0202442i	$-0.993556\pi$
$829$	−43.6845	−	25.2212i	−1.51722	−	0.875970i	−0.517429	−	0.855726i	$-0.673111\pi$
$830$		0			0
$831$		0			0
$832$	4.05674			0.140642
$833$	3.00205	−	0.0780005i	0.104015	−	0.00270256i
$834$		0			0
$835$		0			0
$836$	18.0201	−	31.2117i	0.623238	−	1.07948i
$837$		0			0
$838$	−7.08162	−	12.2657i	−0.244631	−	0.423713i
$839$	21.6729			0.748233			0.374116	−	0.927382i	$-0.377946\pi$
$839$	21.6729			0.748233			0.374116	+	0.927382i	$0.377946\pi$
$840$		0			0
$841$	28.9982			0.999939
$842$	10.8548	+	18.8011i	0.374081	+	0.647928i
$843$		0			0
$844$	1.05067	−	1.81982i	0.0361657	−	0.0626408i
$845$		0			0
$846$		0			0
$847$	−44.6854	−	43.5394i	−1.53541	−	1.49603i
$848$	13.1461			0.451439
$849$		0			0
$850$		0			0
$851$	1.62680	+	0.939234i	0.0557660	+	0.0321965i
$852$		0			0
$853$	25.1282			0.860372			0.430186	−	0.902740i	$-0.358448\pi$
$853$	25.1282			0.860372			0.430186	+	0.902740i	$0.358448\pi$
$854$	3.12783	+	0.794706i	0.107032	+	0.0271943i
$855$		0			0
$856$	0.347904	+	0.602588i	0.0118911	+	0.0205960i
$857$	39.1591	+	22.6085i	1.33765	+	0.772293i	0.986459	−	0.164011i	$-0.0524433\pi$
$857$	39.1591	+	22.6085i	1.33765	+	0.772293i	0.351192	+	0.936304i	$0.385777\pi$
$858$		0			0
$859$	−24.3260	+	14.0446i	−0.829992	+	0.479196i	−0.853850	−	0.520519i	$-0.825738\pi$
$859$	−24.3260	+	14.0446i	−0.829992	+	0.479196i	0.0238577	+	0.999715i	$0.492405\pi$
$860$		0			0
$861$		0			0
$862$			3.55794i			0.121184i
$863$	−14.5140	−	25.1390i	−0.494062	−	0.855740i	0.505915	−	0.862583i	$-0.331155\pi$
$863$	−14.5140	−	25.1390i	−0.494062	−	0.855740i	−0.999977	+	0.00684347i	$0.997822\pi$
$864$		0			0
$865$		0			0
$866$	−4.93164	−	8.54186i	−0.167584	−	0.290264i
$867$		0			0
$868$	16.8938	−	17.3384i	0.573413	−	0.588505i
$869$			63.0351i			2.13832i
$870$		0			0
$871$	−44.4321	−	25.6529i	−1.50552	−	0.869215i
$872$	2.98417	−	5.16874i	0.101057	−	0.175036i
$873$		0			0
$874$		−	10.7375i		−	0.363203i
$875$		0			0
$876$		0			0
$877$	31.0400	−	17.9210i	1.04815	−	0.605148i	0.126017	−	0.992028i	$-0.459780\pi$
$877$	31.0400	−	17.9210i	1.04815	−	0.605148i	0.922130	+	0.386880i	$0.126447\pi$
$878$	−12.1701	−	7.02641i	−0.410721	−	0.237130i
$879$		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
$883$			43.5609i			1.46594i	0.680260	+	0.732971i	$0.261867\pi$
$883$			43.5609i			1.46594i	−0.680260	+	0.732971i	$0.738133\pi$
$884$	−1.50721	+	0.870188i	−0.0506930	+	0.0292676i
$885$		0			0
$886$	−7.72219	+	13.3752i	−0.259432	+	0.449350i
$887$	−33.2119	+	19.1749i	−1.11515	+	0.643831i	−0.940158	−	0.340739i	$-0.889323\pi$
$887$	−33.2119	+	19.1749i	−1.11515	+	0.643831i	−0.174990	+	0.984570i	$0.555989\pi$
$888$		0			0
$889$	−7.91596	−	28.0788i	−0.265493	−	0.941733i
$890$		0			0
$891$		0			0
$892$	12.9973	−	22.5120i	0.435182	−	0.753757i
$893$	2.95138	−	5.11194i	0.0987641	−	0.171065i
$894$		0			0
$895$		0			0
$896$	1.89497	+	1.84637i	0.0633065	+	0.0616830i
$897$		0			0
$898$	0.138435	−	0.0799255i	0.00461964	−	0.00266715i
$899$	0.191716	−	0.332062i	0.00639409	−	0.0110749i
$900$		0			0
$901$	−4.88420	+	2.81989i	−0.162716	+	0.0939442i
$902$			50.6646i			1.68695i
$903$		0			0
$904$	−0.809894			−0.0269367
$905$		0			0
$906$		0			0
$907$	−21.6272	−	12.4865i	−0.718120	−	0.414607i	0.0959402	−	0.995387i	$-0.469414\pi$
$907$	−21.6272	−	12.4865i	−0.718120	−	0.414607i	−0.814060	+	0.580780i	$0.802748\pi$
$908$	−12.3905	+	7.15363i	−0.411192	+	0.237402i
$909$		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
$913$	−29.7048	+	51.4502i	−0.983084	+	1.70275i
$914$	11.3995	+	6.58150i	0.377062	+	0.217697i
$915$		0			0
$916$			1.57889i			0.0521680i
$917$	−35.7801	−	34.8625i	−1.18156	−	1.15126i
$918$		0			0
$919$	5.76087	+	9.97811i	0.190033	+	0.329148i	0.945261	−	0.326315i	$-0.105807\pi$
$919$	5.76087	+	9.97811i	0.190033	+	0.329148i	−0.755228	+	0.655463i	$0.772474\pi$
$920$		0			0
$921$		0			0
$922$	−10.3782	−	17.9756i	−0.341789	−	0.591996i
$923$		−	10.3443i		−	0.340486i
$924$		0			0
$925$		0			0
$926$	−15.4094	+	8.89659i	−0.506383	+	0.292360i
$927$		0			0
$928$	0.0362921	+	0.0209532i	0.00119135	+	0.000687824i
$929$	9.55386	+	16.5478i	0.313452	+	0.542915i	0.979107	−	0.203345i	$-0.0651812\pi$
$929$	9.55386	+	16.5478i	0.313452	+	0.542915i	−0.665655	+	0.746259i	$0.731848\pi$
$930$		0			0
$931$	−20.4782	+	37.6979i	−0.671146	+	1.23550i
$932$	−18.2609			−0.598155
$933$		0			0
$934$	−1.87225	−	1.08094i	−0.0612618	−	0.0353695i
$935$		0			0
$936$		0			0
$937$	49.5320			1.61814			0.809070	−	0.587713i	$-0.199972\pi$
$937$	49.5320			1.61814			0.809070	+	0.587713i	$0.199972\pi$
$938$	−9.07938	−	32.2056i	−0.296452	−	1.05155i
$939$		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
$943$	7.54730	+	13.0723i	0.245774	+	0.425693i
$944$	13.5464			0.440897
$945$		0			0
$946$	−65.1117			−2.11696
$947$	1.32786	+	2.29992i	0.0431496	+	0.0747373i	0.886794	−	0.462166i	$-0.152927\pi$
$947$	1.32786	+	2.29992i	0.0431496	+	0.0747373i	−0.843644	+	0.536903i	$0.819594\pi$
$948$		0			0
$949$	18.9323	−	32.7918i	0.614570	−	1.06447i
$950$		0			0
$951$		0			0
$952$	−1.10010	−	0.279508i	−0.0356543	−	0.00905891i
$953$	−36.5346			−1.18347			−0.591735	−	0.806132i	$-0.701557\pi$
$953$	−36.5346			−1.18347			−0.591735	+	0.806132i	$0.701557\pi$
$954$		0			0
$955$		0			0
$956$	20.0746	+	11.5901i	0.649258	+	0.374850i
$957$		0			0
$958$	−13.0035			−0.420125
$959$	9.36314	−	36.8517i	0.302351	−	1.19000i
$960$		0			0
$961$	26.3587	+	45.6546i	0.850280	+	1.47273i
$962$	3.76682	+	2.17478i	0.121447	+	0.0701176i
$963$		0			0
$964$	11.2090	−	6.47152i	0.361018	−	0.208434i
$965$		0			0
$966$		0			0
$967$		−	22.6175i		−	0.727330i	−0.931530	−	0.363665i	$-0.881525\pi$
$967$		−	22.6175i		−	0.727330i	0.931530	−	0.363665i	$-0.118475\pi$
$968$	11.7905	+	20.4218i	0.378962	+	0.656381i
$969$		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
$973$	−12.0357	−	42.6919i	−0.385846	−	1.36864i
$974$			6.30725i			0.202097i
$975$		0			0
$976$	−1.05635	−	0.609885i	−0.0338130	−	0.0195220i
$977$	−21.6323	+	37.4682i	−0.692078	+	1.19871i	0.279077	+	0.960269i	$0.409971\pi$
$977$	−21.6323	+	37.4682i	−0.692078	+	1.19871i	−0.971156	+	0.238446i	$0.923362\pi$
$978$		0			0
$979$			37.1225i			1.18644i
$980$		0			0
$981$		0			0
$982$	−12.6994	+	7.33199i	−0.405253	+	0.233973i
$983$	31.1460	+	17.9821i	0.993402	+	0.573541i	0.906289	−	0.422658i	$-0.138903\pi$
$983$	31.1460	+	17.9821i	0.993402	+	0.573541i	0.0871125	+	0.996198i	$0.472236\pi$
$984$		0			0
$985$		0			0
$986$	−0.0179782			−0.000572544
$987$		0			0
$988$		−	24.8625i		−	0.790983i
$989$	−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	$0.0405448\pi$
$992$	−7.92389	+	4.57486i	−0.251584	+	0.145252i
$993$		0			0
$994$	4.70806	−	4.83197i	0.149331	−	0.153261i
$995$		0			0
$996$		0			0
$997$	−26.8764	+	46.5513i	−0.851184	+	1.47429i	0.0289572	+	0.999581i	$0.490781\pi$
$997$	−26.8764	+	46.5513i	−0.851184	+	1.47429i	−0.880141	+	0.474713i	$0.842552\pi$
$998$	−12.1113	+	20.9774i	−0.383376	+	0.664027i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.54649 + 0.717905i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.54649 + 0.717905i) q^{7} +1.00000 q^{8} +(5.09272 + 2.94028i) q^{11} +4.05674 q^{13} +(1.89497 + 1.84637i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.371532 + 0.214504i) q^{17} +(-5.30761 + 3.06435i) q^{19} -5.88057i q^{22} +(-0.876005 - 1.51729i) q^{23} +(-2.02837 - 3.51324i) q^{26} +(0.651521 - 2.56428i) q^{28} -0.0419065i q^{29} +(7.92389 + 4.57486i) q^{31} +(-0.500000 + 0.866025i) q^{32} -0.429009i q^{34} +(-0.928534 + 0.536089i) q^{37} +(5.30761 + 3.06435i) q^{38} -8.61559 q^{41} -11.0724i q^{43} +(-5.09272 + 2.94028i) q^{44} +(-0.876005 + 1.51729i) q^{46} +(-0.834099 + 0.481567i) q^{47} +(5.96922 - 3.65628i) q^{49} +(-2.02837 + 3.51324i) q^{52} +(-6.57304 + 11.3848i) q^{53} +(-2.54649 + 0.717905i) q^{56} +(-0.0362921 + 0.0209532i) q^{58} +(-6.77318 + 11.7315i) q^{59} +(1.05635 - 0.609885i) q^{61} -9.14972i q^{62} +1.00000 q^{64} +(-10.9527 - 6.32352i) q^{67} +(-0.371532 + 0.214504i) q^{68} -2.54990i q^{71} +(4.66689 - 8.08328i) q^{73} +(0.928534 + 0.536089i) q^{74} -6.12870i q^{76} +(-15.0794 - 3.83131i) q^{77} +(5.35961 + 9.28312i) q^{79} +(4.30780 + 7.46132i) q^{82} +10.1027i q^{83} +(-9.58894 + 5.53618i) q^{86} +(5.09272 + 2.94028i) q^{88} +(3.15638 + 5.46700i) q^{89} +(-10.3304 + 2.91235i) q^{91} +1.75201 q^{92} +(0.834099 + 0.481567i) q^{94} +2.59007 q^{97} +(-6.15104 - 3.34136i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 12 q^{16} + 24 q^{17} - 12 q^{19} - 8 q^{23} - 12 q^{32} + 12 q^{38} - 8 q^{46} - 24 q^{47} + 52 q^{49} - 32 q^{53} - 12 q^{61} + 24 q^{64} - 24 q^{68} - 16 q^{77} - 4 q^{79} + 68 q^{91} + 16 q^{92} + 24 q^{94} - 20 q^{98}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 12 * q^16 + 24 * q^17 - 12 * q^19 - 8 * q^23 - 12 * q^32 + 12 * q^38 - 8 * q^46 - 24 * q^47 + 52 * q^49 - 32 * q^53 - 12 * q^61 + 24 * q^64 - 24 * q^68 - 16 * q^77 - 4 * q^79 + 68 * q^91 + 16 * q^92 + 24 * q^94 - 20 * q^98

Introduction

L-functions

Modular forms

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Database

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