LMFDB - Embedded newform 3150.2.bf.e.1151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.2
Character	$\chi$	$=$	3150.1151
Dual form			3150.2.bf.e.1601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.34325 - 1.22849i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.34325 - 1.22849i) q^{7} +1.00000i q^{8} +(2.03986 + 1.17771i) q^{11} +4.64698i q^{13} +(2.64356 - 0.107718i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.28109 - 3.95097i) q^{17} +(0.491268 - 0.283634i) q^{19} -2.35542 q^{22} +(-5.04588 + 2.91324i) q^{23} +(-2.32349 - 4.02440i) q^{26} +(-2.23553 + 1.41507i) q^{28} -2.55339i q^{29} +(-1.89659 - 1.09500i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.56218i q^{34} +(4.63355 + 8.02554i) q^{37} +(-0.283634 + 0.491268i) q^{38} +8.68451 q^{41} -6.57695 q^{43} +(2.03986 - 1.17771i) q^{44} +(2.91324 - 5.04588i) q^{46} +(-3.15616 - 5.46663i) q^{47} +(3.98161 + 5.75732i) q^{49} +(4.02440 + 2.32349i) q^{52} +(-10.5228 - 6.07533i) q^{53} +(1.22849 - 2.34325i) q^{56} +(1.27670 + 2.21130i) q^{58} +(1.67739 - 2.90532i) q^{59} +(-6.85523 + 3.95787i) q^{61} +2.18999 q^{62} -1.00000 q^{64} +(2.00143 - 3.46657i) q^{67} +(-2.28109 - 3.95097i) q^{68} -2.02720i q^{71} +(7.11528 + 4.10801i) q^{73} +(-8.02554 - 4.63355i) q^{74} -0.567267i q^{76} +(-3.33308 - 5.26562i) q^{77} +(4.13212 + 7.15704i) q^{79} +(-7.52101 + 4.34226i) q^{82} +0.171637 q^{83} +(5.69581 - 3.28848i) q^{86} +(-1.17771 + 2.03986i) q^{88} +(-2.72938 - 4.72742i) q^{89} +(5.70878 - 10.8890i) q^{91} +5.82648i q^{92} +(5.46663 + 3.15616i) q^{94} +10.8564i q^{97} +(-6.32684 - 2.99518i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 4 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 4 * q^7	$ 24 q + 12 q^{4} + 4 q^{7} - 12 q^{16} + 12 q^{19} - 4 q^{28} - 28 q^{37} - 96 q^{43} - 8 q^{46} - 52 q^{49} + 12 q^{52} - 8 q^{58} - 12 q^{61} - 24 q^{64} + 4 q^{67} + 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 + 4 * q^7 - 12 * q^16 + 12 * q^19 - 4 * q^28 - 28 * q^37 - 96 * q^43 - 8 * q^46 - 52 * q^49 + 12 * q^52 - 8 * q^58 - 12 * q^61 - 24 * q^64 + 4 * q^67 + 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.34325	−	1.22849i	−0.885664	−	0.464326i
$7$	−2.34325	−	1.22849i	−0.885664	−	0.464326i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	2.03986	+	1.17771i	0.615040	+	0.355093i	0.774935	−	0.632041i	$-0.217782\pi$
$11$	2.03986	+	1.17771i	0.615040	+	0.355093i	−0.159896	+	0.987134i	$0.551116\pi$
$12$		0			0
$13$			4.64698i			1.28884i	0.764672	+	0.644420i	$0.222901\pi$
$13$			4.64698i			1.28884i	−0.764672	+	0.644420i	$0.777099\pi$
$14$	2.64356	−	0.107718i	0.706520	−	0.0287888i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.28109	−	3.95097i	0.553246	−	0.958250i	−0.444792	−	0.895634i	$-0.646722\pi$
$17$	2.28109	−	3.95097i	0.553246	−	0.958250i	0.998038	−	0.0626158i	$-0.0199443\pi$
$18$		0			0
$19$	0.491268	−	0.283634i	0.112705	−	0.0650700i	−0.442588	−	0.896725i	$-0.645940\pi$
$19$	0.491268	−	0.283634i	0.112705	−	0.0650700i	0.555293	+	0.831655i	$0.312606\pi$
$20$		0			0
$21$		0			0
$22$	−2.35542			−0.502178
$23$	−5.04588	+	2.91324i	−1.05214	+	0.607453i	−0.923247	−	0.384206i	$-0.874475\pi$
$23$	−5.04588	+	2.91324i	−1.05214	+	0.607453i	−0.128891	+	0.991659i	$0.541142\pi$
$24$		0			0
$25$		0			0
$26$	−2.32349	−	4.02440i	−0.455674	−	0.789250i
$27$		0			0
$28$	−2.23553	+	1.41507i	−0.422475	+	0.267422i
$29$		−	2.55339i		−	0.474153i	−0.971491	−	0.237077i	$-0.923811\pi$
$29$		−	2.55339i		−	0.474153i	0.971491	−	0.237077i	$-0.0761893\pi$
$30$		0			0
$31$	−1.89659	−	1.09500i	−0.340638	−	0.196667i	0.319916	−	0.947446i	$-0.396345\pi$
$31$	−1.89659	−	1.09500i	−0.340638	−	0.196667i	−0.660554	+	0.750778i	$0.729679\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			4.56218i			0.782408i
$35$		0			0
$36$		0			0
$37$	4.63355	+	8.02554i	0.761750	+	1.31939i	0.941948	+	0.335760i	$0.108993\pi$
$37$	4.63355	+	8.02554i	0.761750	+	1.31939i	−0.180197	+	0.983630i	$0.557674\pi$
$38$	−0.283634	+	0.491268i	−0.0460114	+	0.0796942i
$39$		0			0
$40$		0			0
$41$	8.68451			1.35629			0.678147	−	0.734927i	$-0.262783\pi$
$41$	8.68451			1.35629			0.678147	+	0.734927i	$0.262783\pi$
$42$		0			0
$43$	−6.57695			−1.00298			−0.501488	−	0.865165i	$-0.667214\pi$
$43$	−6.57695			−1.00298			−0.501488	+	0.865165i	$0.667214\pi$
$44$	2.03986	−	1.17771i	0.307520	−	0.177547i
$45$		0			0
$46$	2.91324	−	5.04588i	0.429534	−	0.743975i
$47$	−3.15616	−	5.46663i	−0.460374	−	0.797391i	0.538606	−	0.842558i	$-0.318951\pi$
$47$	−3.15616	−	5.46663i	−0.460374	−	0.797391i	−0.998979	+	0.0451673i	$0.985618\pi$
$48$		0			0
$49$	3.98161	+	5.75732i	0.568802	+	0.822475i
$50$		0			0
$51$		0			0
$52$	4.02440	+	2.32349i	0.558084	+	0.322210i
$53$	−10.5228	−	6.07533i	−1.44542	−	0.834511i	−0.447212	−	0.894428i	$-0.647583\pi$
$53$	−10.5228	−	6.07533i	−1.44542	−	0.834511i	−0.998203	+	0.0599168i	$0.980916\pi$
$54$		0			0
$55$		0			0
$56$	1.22849	−	2.34325i	0.164164	−	0.313130i
$57$		0			0
$58$	1.27670	+	2.21130i	0.167639	+	0.290359i
$59$	1.67739	−	2.90532i	0.218377	−	0.378241i	−0.735935	−	0.677053i	$-0.763257\pi$
$59$	1.67739	−	2.90532i	0.218377	−	0.378241i	0.954312	+	0.298812i	$0.0965903\pi$
$60$		0			0
$61$	−6.85523	+	3.95787i	−0.877722	+	0.506753i	−0.869907	−	0.493216i	$-0.835821\pi$
$61$	−6.85523	+	3.95787i	−0.877722	+	0.506753i	−0.00781543	+	0.999969i	$0.502488\pi$
$62$	2.18999			0.278130
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	2.00143	−	3.46657i	0.244513	−	0.423509i	−0.717481	−	0.696578i	$-0.754705\pi$
$67$	2.00143	−	3.46657i	0.244513	−	0.423509i	0.961995	+	0.273068i	$0.0880385\pi$
$68$	−2.28109	−	3.95097i	−0.276623	−	0.479125i
$69$		0			0
$70$		0			0
$71$		−	2.02720i		−	0.240585i	−0.992738	−	0.120292i	$-0.961617\pi$
$71$		−	2.02720i		−	0.240585i	0.992738	−	0.120292i	$-0.0383832\pi$
$72$		0			0
$73$	7.11528	+	4.10801i	0.832780	+	0.480806i	0.854804	−	0.518952i	$-0.173678\pi$
$73$	7.11528	+	4.10801i	0.832780	+	0.480806i	−0.0220235	+	0.999757i	$0.507011\pi$
$74$	−8.02554	−	4.63355i	−0.932950	−	0.538639i
$75$		0			0
$76$		−	0.567267i		−	0.0650700i
$77$	−3.33308	−	5.26562i	−0.379839	−	0.600073i
$78$		0			0
$79$	4.13212	+	7.15704i	0.464900	+	0.805230i	0.999197	−	0.0400666i	$-0.0127570\pi$
$79$	4.13212	+	7.15704i	0.464900	+	0.805230i	−0.534297	+	0.845297i	$0.679424\pi$
$80$		0			0
$81$		0			0
$82$	−7.52101	+	4.34226i	−0.830556	+	0.479522i
$83$	0.171637			0.0188396			0.00941978	−	0.999956i	$-0.497002\pi$
$83$	0.171637			0.0188396			0.00941978	+	0.999956i	$0.497002\pi$
$84$		0			0
$85$		0			0
$86$	5.69581	−	3.28848i	0.614195	−	0.354606i
$87$		0			0
$88$	−1.17771	+	2.03986i	−0.125544	+	0.217449i
$89$	−2.72938	−	4.72742i	−0.289313	−	0.501105i	0.684333	−	0.729170i	$-0.260094\pi$
$89$	−2.72938	−	4.72742i	−0.289313	−	0.501105i	−0.973646	+	0.228065i	$0.926760\pi$
$90$		0			0
$91$	5.70878	−	10.8890i	0.598443	−	1.14148i
$92$			5.82648i			0.607453i
$93$		0			0
$94$	5.46663	+	3.15616i	0.563840	+	0.325533i
$95$		0			0
$96$		0			0
$97$			10.8564i			1.10230i	0.834406	+	0.551151i	$0.185811\pi$
$97$			10.8564i			1.10230i	−0.834406	+	0.551151i	$0.814189\pi$
$98$	−6.32684	−	2.99518i	−0.639107	−	0.302559i
$99$		0			0
$100$		0			0
$101$	−5.74827	+	9.95630i	−0.571975	+	0.990689i	0.424388	+	0.905480i	$0.360489\pi$
$101$	−5.74827	+	9.95630i	−0.571975	+	0.990689i	−0.996363	+	0.0852090i	$0.972844\pi$
$102$		0			0
$103$	−16.7782	+	9.68690i	−1.65320	+	0.954478i	−0.677462	+	0.735558i	$0.736920\pi$
$103$	−16.7782	+	9.68690i	−1.65320	+	0.954478i	−0.975743	+	0.218920i	$0.929747\pi$
$104$	−4.64698			−0.455674
$105$		0			0
$106$	12.1507			1.18018
$107$	−9.28430	+	5.36029i	−0.897547	+	0.518199i	−0.876404	−	0.481577i	$-0.840064\pi$
$107$	−9.28430	+	5.36029i	−0.897547	+	0.518199i	−0.0211436	+	0.999776i	$0.506731\pi$
$108$		0			0
$109$	−5.41186	+	9.37362i	−0.518363	+	0.897830i	0.481410	+	0.876496i	$0.340125\pi$
$109$	−5.41186	+	9.37362i	−0.518363	+	0.897830i	−0.999772	+	0.0213347i	$0.993208\pi$
$110$		0			0
$111$		0			0
$112$	0.107718	+	2.64356i	0.0101784	+	0.249793i
$113$			18.4343i			1.73415i	0.498176	+	0.867076i	$0.334003\pi$
$113$			18.4343i			1.73415i	−0.498176	+	0.867076i	$0.665997\pi$
$114$		0			0
$115$		0			0
$116$	−2.21130	−	1.27670i	−0.205314	−	0.118538i
$117$		0			0
$118$			3.35478i			0.308832i
$119$	−10.1989	+	6.45578i	−0.934931	+	0.591801i
$120$		0			0
$121$	−2.72599	−	4.72156i	−0.247817	−	0.429232i
$122$	3.95787	−	6.85523i	0.358329	−	0.620643i
$123$		0			0
$124$	−1.89659	+	1.09500i	−0.170319	+	0.0983337i
$125$		0			0
$126$		0			0
$127$	4.04880			0.359273			0.179637	−	0.983733i	$-0.442508\pi$
$127$	4.04880			0.359273			0.179637	+	0.983733i	$0.442508\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	7.14129	+	12.3691i	0.623937	+	1.08069i	0.988745	+	0.149608i	$0.0478012\pi$
$131$	7.14129	+	12.3691i	0.623937	+	1.08069i	−0.364808	+	0.931083i	$0.618866\pi$
$132$		0			0
$133$	−1.49960	+	0.0611049i	−0.130032	+	0.00529846i
$134$			4.00285i			0.345794i
$135$		0			0
$136$	3.95097	+	2.28109i	0.338792	+	0.195602i
$137$	4.52794	+	2.61421i	0.386848	+	0.223347i	0.680794	−	0.732475i	$-0.261635\pi$
$137$	4.52794	+	2.61421i	0.386848	+	0.223347i	−0.293945	+	0.955822i	$0.594968\pi$
$138$		0			0
$139$			19.4726i			1.65164i	0.563933	+	0.825820i	$0.309288\pi$
$139$			19.4726i			1.65164i	−0.563933	+	0.825820i	$0.690712\pi$
$140$		0			0
$141$		0			0
$142$	1.01360	+	1.75561i	0.0850596	+	0.147328i
$143$	−5.47280	+	9.47917i	−0.457659	+	0.792688i
$144$		0			0
$145$		0			0
$146$	−8.21601			−0.679962
$147$		0			0
$148$	9.26709			0.761750
$149$	4.79814	−	2.77021i	0.393079	−	0.226944i	−0.290414	−	0.956901i	$-0.593793\pi$
$149$	4.79814	−	2.77021i	0.393079	−	0.226944i	0.683493	+	0.729957i	$0.260460\pi$
$150$		0			0
$151$	4.23984	−	7.34362i	0.345033	−	0.597615i	−0.640327	−	0.768103i	$-0.721201\pi$
$151$	4.23984	−	7.34362i	0.345033	−	0.597615i	0.985360	+	0.170488i	$0.0545343\pi$
$152$	0.283634	+	0.491268i	0.0230057	+	0.0398471i
$153$		0			0
$154$	5.51934	+	2.89362i	0.444761	+	0.233174i
$155$		0			0
$156$		0			0
$157$	−0.970763	−	0.560470i	−0.0774753	−	0.0447304i	0.460762	−	0.887524i	$-0.347576\pi$
$157$	−0.970763	−	0.560470i	−0.0774753	−	0.0447304i	−0.538237	+	0.842793i	$0.680910\pi$
$158$	−7.15704	−	4.13212i	−0.569384	−	0.328734i
$159$		0			0
$160$		0			0
$161$	15.4026	−	0.627617i	1.21390	−	0.0494631i
$162$		0			0
$163$	3.35749	+	5.81534i	0.262979	+	0.455493i	0.967032	−	0.254654i	$-0.0819617\pi$
$163$	3.35749	+	5.81534i	0.262979	+	0.455493i	−0.704053	+	0.710147i	$0.748628\pi$
$164$	4.34226	−	7.52101i	0.339073	−	0.587292i
$165$		0			0
$166$	−0.148642	+	0.0858183i	−0.0115368	+	0.00666079i
$167$	−2.80110			−0.216756			−0.108378	−	0.994110i	$-0.534566\pi$
$167$	−2.80110			−0.216756			−0.108378	+	0.994110i	$0.534566\pi$
$168$		0			0
$169$	−8.59442			−0.661109
$170$		0			0
$171$		0			0
$172$	−3.28848	+	5.69581i	−0.250744	+	0.434301i
$173$	−6.90018	−	11.9515i	−0.524611	−	0.908653i	−0.999589	−	0.0286558i	$-0.990877\pi$
$173$	−6.90018	−	11.9515i	−0.524611	−	0.908653i	0.474978	−	0.879998i	$-0.342456\pi$
$174$		0			0
$175$		0			0
$176$		−	2.35542i		−	0.177547i
$177$		0			0
$178$	4.72742	+	2.72938i	0.354335	+	0.204575i
$179$	2.31980	+	1.33933i	0.173390	+	0.100107i	0.584183	−	0.811622i	$-0.301415\pi$
$179$	2.31980	+	1.33933i	0.173390	+	0.100107i	−0.410794	+	0.911728i	$0.634748\pi$
$180$		0			0
$181$		−	6.88082i		−	0.511447i	−0.966750	−	0.255724i	$-0.917686\pi$
$181$		−	6.88082i		−	0.511447i	0.966750	−	0.255724i	$-0.0823137\pi$
$182$	0.500563	+	12.2846i	0.0371042	+	0.910592i
$183$		0			0
$184$	−2.91324	−	5.04588i	−0.214767	−	0.371987i
$185$		0			0
$186$		0			0
$187$	9.30619	−	5.37293i	0.680536	−	0.392908i
$188$	−6.31233			−0.460374
$189$		0			0
$190$		0			0
$191$	8.65356	−	4.99614i	0.626150	−	0.361508i	−0.153110	−	0.988209i	$-0.548929\pi$
$191$	8.65356	−	4.99614i	0.626150	−	0.361508i	0.779260	+	0.626701i	$0.215595\pi$
$192$		0			0
$193$	−12.5643	+	21.7620i	−0.904398	+	1.56646i	−0.0826753	+	0.996577i	$0.526346\pi$
$193$	−12.5643	+	21.7620i	−0.904398	+	1.56646i	−0.821723	+	0.569887i	$0.806987\pi$
$194$	−5.42821	−	9.40193i	−0.389723	−	0.675019i
$195$		0			0
$196$	6.97679	−	0.569517i	0.498342	−	0.0406798i
$197$		−	20.0811i		−	1.43072i	−0.698757	−	0.715359i	$-0.746263\pi$
$197$		−	20.0811i		−	1.43072i	0.698757	−	0.715359i	$-0.253737\pi$
$198$		0			0
$199$	−10.3028	−	5.94834i	−0.730348	−	0.421667i	0.0882014	−	0.996103i	$-0.471888\pi$
$199$	−10.3028	−	5.94834i	−0.730348	−	0.421667i	−0.818550	+	0.574436i	$0.805221\pi$
$200$		0			0
$201$		0			0
$202$		−	11.4965i		−	0.808894i
$203$	−3.13683	+	5.98323i	−0.220162	+	0.419941i
$204$		0			0
$205$		0			0
$206$	9.68690	−	16.7782i	0.674918	−	1.16899i
$207$		0			0
$208$	4.02440	−	2.32349i	0.279042	−	0.161105i
$209$	1.33615			0.0924237
$210$		0			0
$211$	−6.78640			−0.467195			−0.233597	−	0.972333i	$-0.575050\pi$
$211$	−6.78640			−0.467195			−0.233597	+	0.972333i	$0.575050\pi$
$212$	−10.5228	+	6.07533i	−0.722708	+	0.417256i
$213$		0			0
$214$	5.36029	−	9.28430i	0.366422	−	0.634662i
$215$		0			0
$216$		0			0
$217$	3.09899	+	4.89580i	0.210373	+	0.332348i
$218$		−	10.8237i		−	0.733075i
$219$		0			0
$220$		0			0
$221$	18.3601	+	10.6002i	1.23503	+	0.713045i
$222$		0			0
$223$			28.7684i			1.92648i	0.268646	+	0.963239i	$0.413424\pi$
$223$			28.7684i			1.92648i	−0.268646	+	0.963239i	$0.586576\pi$
$224$	−1.41507	−	2.23553i	−0.0945480	−	0.149368i
$225$		0			0
$226$	−9.21714	−	15.9646i	−0.613115	−	1.06195i
$227$	−1.05185	+	1.82186i	−0.0698140	+	0.120921i	−0.898819	−	0.438319i	$-0.855574\pi$
$227$	−1.05185	+	1.82186i	−0.0698140	+	0.120921i	0.829005	+	0.559241i	$0.188907\pi$
$228$		0			0
$229$	−14.0269	+	8.09841i	−0.926920	+	0.535158i	−0.885836	−	0.463998i	$-0.846415\pi$
$229$	−14.0269	+	8.09841i	−0.926920	+	0.535158i	−0.0410842	+	0.999156i	$0.513081\pi$
$230$		0			0
$231$		0			0
$232$	2.55339			0.167639
$233$	6.93805	−	4.00569i	0.454527	−	0.262421i	−0.255213	−	0.966885i	$-0.582146\pi$
$233$	6.93805	−	4.00569i	0.454527	−	0.262421i	0.709740	+	0.704464i	$0.248812\pi$
$234$		0			0
$235$		0			0
$236$	−1.67739	−	2.90532i	−0.109189	−	0.189120i
$237$		0			0
$238$	5.60460	−	10.6903i	0.363293	−	0.692950i
$239$			15.6233i			1.01059i	0.862947	+	0.505294i	$0.168616\pi$
$239$			15.6233i			1.01059i	−0.862947	+	0.505294i	$0.831384\pi$
$240$		0			0
$241$	−3.54491	−	2.04665i	−0.228348	−	0.131837i	0.381462	−	0.924385i	$-0.375421\pi$
$241$	−3.54491	−	2.04665i	−0.228348	−	0.131837i	−0.609809	+	0.792548i	$0.708754\pi$
$242$	4.72156	+	2.72599i	0.303513	+	0.175233i
$243$		0			0
$244$			7.91574i			0.506753i
$245$		0			0
$246$		0			0
$247$	1.31804	+	2.28291i	0.0838648	+	0.145258i
$248$	1.09500	−	1.89659i	0.0695324	−	0.120434i
$249$		0			0
$250$		0			0
$251$	−19.9413			−1.25869			−0.629343	−	0.777128i	$-0.716676\pi$
$251$	−19.9413			−1.25869			−0.629343	+	0.777128i	$0.716676\pi$
$252$		0			0
$253$	−13.7238			−0.862810
$254$	−3.50637	+	2.02440i	−0.220009	+	0.127022i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.1722	+	17.6188i	0.634527	+	1.09903i	0.986615	+	0.163067i	$0.0521385\pi$
$257$	10.1722	+	17.6188i	0.634527	+	1.09903i	−0.352088	+	0.935967i	$0.614528\pi$
$258$		0			0
$259$	−0.998233	−	24.4981i	−0.0620272	−	1.52224i
$260$		0			0
$261$		0			0
$262$	−12.3691	−	7.14129i	−0.764164	−	0.441190i
$263$	3.13156	+	1.80801i	0.193100	+	0.111487i	0.593433	−	0.804883i	$-0.297772\pi$
$263$	3.13156	+	1.80801i	0.193100	+	0.111487i	−0.400333	+	0.916370i	$0.631105\pi$
$264$		0			0
$265$		0			0
$266$	1.26814	−	0.802720i	0.0777548	−	0.0492179i
$267$		0			0
$268$	−2.00143	−	3.46657i	−0.122257	−	0.211755i
$269$	−10.6172	+	18.3896i	−0.647345	+	1.12123i	0.336410	+	0.941716i	$0.390787\pi$
$269$	−10.6172	+	18.3896i	−0.647345	+	1.12123i	−0.983755	+	0.179518i	$0.942546\pi$
$270$		0			0
$271$	−18.9957	+	10.9672i	−1.15390	+	0.666207i	−0.949836	−	0.312749i	$-0.898750\pi$
$271$	−18.9957	+	10.9672i	−1.15390	+	0.666207i	−0.204069	+	0.978956i	$0.565417\pi$
$272$	−4.56218			−0.276623
$273$		0			0
$274$	−5.22842			−0.315860
$275$		0			0
$276$		0			0
$277$	4.96452	−	8.59880i	0.298289	−	0.516652i	−0.677456	−	0.735564i	$-0.736917\pi$
$277$	4.96452	−	8.59880i	0.298289	−	0.516652i	0.975745	+	0.218912i	$0.0702508\pi$
$278$	−9.73628	−	16.8637i	−0.583943	−	1.01142i
$279$		0			0
$280$		0			0
$281$			11.0696i			0.660358i	0.943918	+	0.330179i	$0.107109\pi$
$281$			11.0696i			0.660358i	−0.943918	+	0.330179i	$0.892891\pi$
$282$		0			0
$283$	19.6392	+	11.3387i	1.16743	+	0.674014i	0.953072	−	0.302742i	$-0.0979021\pi$
$283$	19.6392	+	11.3387i	1.16743	+	0.674014i	0.214354	+	0.976756i	$0.431235\pi$
$284$	−1.75561	−	1.01360i	−0.104176	−	0.0601462i
$285$		0			0
$286$		−	10.9456i		−	0.647227i
$287$	−20.3500	−	10.6689i	−1.20122	−	0.629763i
$288$		0			0
$289$	−1.90675	−	3.30259i	−0.112162	−	0.194270i
$290$		0			0
$291$		0			0
$292$	7.11528	−	4.10801i	0.416390	−	0.240403i
$293$	12.3248			0.720020			0.360010	−	0.932949i	$-0.382773\pi$
$293$	12.3248			0.720020			0.360010	+	0.932949i	$0.382773\pi$
$294$		0			0
$295$		0			0
$296$	−8.02554	+	4.63355i	−0.466475	+	0.269319i
$297$		0			0
$298$	−2.77021	+	4.79814i	−0.160474	+	0.277949i
$299$	−13.5378	−	23.4481i	−0.782909	−	1.35604i
$300$		0			0
$301$	15.4114	+	8.07974i	0.888300	+	0.465708i
$302$			8.47968i			0.487951i
$303$		0			0
$304$	−0.491268	−	0.283634i	−0.0281761	−	0.0162675i
$305$		0			0
$306$		0			0
$307$			8.06274i			0.460165i	0.973171	+	0.230082i	$0.0738996\pi$
$307$			8.06274i			0.460165i	−0.973171	+	0.230082i	$0.926100\pi$
$308$	−6.22670	+	0.253721i	−0.354799	+	0.0144571i
$309$		0			0
$310$		0			0
$311$	−13.2215	+	22.9003i	−0.749721	+	1.29855i	0.198236	+	0.980154i	$0.436479\pi$
$311$	−13.2215	+	22.9003i	−0.749721	+	1.29855i	−0.947956	+	0.318400i	$0.896854\pi$
$312$		0			0
$313$	14.3180	−	8.26650i	0.809301	−	0.467250i	−0.0374122	−	0.999300i	$-0.511911\pi$
$313$	14.3180	−	8.26650i	0.809301	−	0.467250i	0.846713	+	0.532050i	$0.178578\pi$
$314$	1.12094			0.0632583
$315$		0			0
$316$	8.26424			0.464900
$317$	10.6181	−	6.13038i	0.596374	−	0.344317i	−0.171240	−	0.985229i	$-0.554777\pi$
$317$	10.6181	−	6.13038i	0.596374	−	0.344317i	0.767614	+	0.640913i	$0.221444\pi$
$318$		0			0
$319$	3.00716	−	5.20856i	0.168369	−	0.291623i
$320$		0			0
$321$		0			0
$322$	−13.0253	+	8.24485i	−0.725870	+	0.459468i
$323$		−	2.58798i		−	0.143999i
$324$		0			0
$325$		0			0
$326$	−5.81534	−	3.35749i	−0.322082	−	0.185954i
$327$		0			0
$328$			8.68451i			0.479522i
$329$	0.679951	+	16.6870i	0.0374869	+	0.919984i
$330$		0			0
$331$	−17.1942	−	29.7812i	−0.945077	−	1.63692i	−0.755598	−	0.655036i	$-0.772654\pi$
$331$	−17.1942	−	29.7812i	−0.945077	−	1.63692i	−0.189479	−	0.981885i	$-0.560680\pi$
$332$	0.0858183	−	0.148642i	0.00470989	−	0.00815777i
$333$		0			0
$334$	2.42583	−	1.40055i	0.132735	−	0.0766348i
$335$		0			0
$336$		0			0
$337$	−23.9536			−1.30484			−0.652418	−	0.757860i	$-0.726245\pi$
$337$	−23.9536			−1.30484			−0.652418	+	0.757860i	$0.726245\pi$
$338$	7.44298	−	4.29721i	0.404845	−	0.233737i
$339$		0			0
$340$		0			0
$341$	−2.57918	−	4.46727i	−0.139671	−	0.241916i
$342$		0			0
$343$	−2.25708	−	18.3822i	−0.121871	−	0.992546i
$344$		−	6.57695i		−	0.354606i
$345$		0			0
$346$	11.9515	+	6.90018i	0.642515	+	0.370956i
$347$	−24.8552	−	14.3501i	−1.33429	−	0.770355i	−0.348340	−	0.937368i	$-0.613254\pi$
$347$	−24.8552	−	14.3501i	−1.33429	−	0.770355i	−0.985955	+	0.167013i	$0.946588\pi$
$348$		0			0
$349$			3.57176i			0.191192i	0.995420	+	0.0955960i	$0.0304757\pi$
$349$			3.57176i			0.191192i	−0.995420	+	0.0955960i	$0.969524\pi$
$350$		0			0
$351$		0			0
$352$	1.17771	+	2.03986i	0.0627722	+	0.108725i
$353$	−6.26984	+	10.8597i	−0.333710	+	0.578003i	−0.983236	−	0.182337i	$-0.941634\pi$
$353$	−6.26984	+	10.8597i	−0.333710	+	0.578003i	0.649526	+	0.760339i	$0.274967\pi$
$354$		0			0
$355$		0			0
$356$	−5.45875			−0.289313
$357$		0			0
$358$	−2.67867			−0.141572
$359$	−13.6940	+	7.90624i	−0.722742	+	0.417275i	−0.815761	−	0.578389i	$-0.803682\pi$
$359$	−13.6940	+	7.90624i	−0.722742	+	0.417275i	0.0930190	+	0.995664i	$0.470348\pi$
$360$		0			0
$361$	−9.33910	+	16.1758i	−0.491532	+	0.851358i
$362$	3.44041	+	5.95896i	0.180824	+	0.313196i
$363$		0			0
$364$	−6.57578	−	10.3885i	−0.344664	−	0.544503i
$365$		0			0
$366$		0			0
$367$	−30.8855	−	17.8317i	−1.61221	−	0.930809i	−0.988857	−	0.148867i	$-0.952437\pi$
$367$	−30.8855	−	17.8317i	−1.61221	−	0.930809i	−0.623351	−	0.781942i	$-0.714229\pi$
$368$	5.04588	+	2.91324i	0.263035	+	0.151863i
$369$		0			0
$370$		0			0
$371$	17.1940	+	27.1632i	0.892667	+	1.41024i
$372$		0			0
$373$	−11.5306	−	19.9717i	−0.597034	−	1.03409i	−0.993256	−	0.115939i	$-0.963012\pi$
$373$	−11.5306	−	19.9717i	−0.597034	−	1.03409i	0.396222	−	0.918155i	$-0.370321\pi$
$374$	−5.37293	+	9.30619i	−0.277828	+	0.481212i
$375$		0			0
$376$	5.46663	−	3.15616i	0.281920	−	0.162767i
$377$	11.8656			0.611108
$378$		0			0
$379$	8.20110			0.421262			0.210631	−	0.977566i	$-0.432448\pi$
$379$	8.20110			0.421262			0.210631	+	0.977566i	$0.432448\pi$
$380$		0			0
$381$		0			0
$382$	−4.99614	+	8.65356i	−0.255625	+	0.442755i
$383$	2.31637	+	4.01207i	0.118361	+	0.205007i	0.919118	−	0.393982i	$-0.128903\pi$
$383$	2.31637	+	4.01207i	0.118361	+	0.205007i	−0.800757	+	0.598989i	$0.795569\pi$
$384$		0			0
$385$		0			0
$386$		−	25.1286i		−	1.27901i
$387$		0			0
$388$	9.40193	+	5.42821i	0.477311	+	0.275575i
$389$	29.0194	+	16.7544i	1.47134	+	0.849480i	0.999482	−	0.0321938i	$-0.0102494\pi$
$389$	29.0194	+	16.7544i	1.47134	+	0.849480i	0.471860	+	0.881673i	$0.343583\pi$
$390$		0			0
$391$			26.5815i			1.34428i
$392$	−5.75732	+	3.98161i	−0.290789	+	0.201102i
$393$		0			0
$394$	10.0405	+	17.3907i	0.505835	+	0.876132i
$395$		0			0
$396$		0			0
$397$	16.0748	−	9.28081i	0.806772	−	0.465790i	−0.0390613	−	0.999237i	$-0.512437\pi$
$397$	16.0748	−	9.28081i	0.806772	−	0.465790i	0.845834	+	0.533447i	$0.179103\pi$
$398$	11.8967			0.596327
$399$		0			0
$400$		0			0
$401$	12.1377	−	7.00770i	0.606128	−	0.349948i	−0.165321	−	0.986240i	$-0.552866\pi$
$401$	12.1377	−	7.00770i	0.606128	−	0.349948i	0.771448	+	0.636292i	$0.219533\pi$
$402$		0			0
$403$	5.08843	−	8.81342i	0.253473	−	0.439028i
$404$	5.74827	+	9.95630i	0.285987	+	0.495345i
$405$		0			0
$406$	−0.275047	−	6.75005i	−0.0136503	−	0.334999i
$407$			21.8279i			1.08197i
$408$		0			0
$409$	20.6162	+	11.9028i	1.01941	+	0.588555i	0.913932	−	0.405868i	$-0.133031\pi$
$409$	20.6162	+	11.9028i	1.01941	+	0.588555i	0.105474	+	0.994422i	$0.466364\pi$
$410$		0			0
$411$		0			0
$412$			19.3738i			0.954478i
$413$	−7.49970	+	4.74723i	−0.369036	+	0.233596i
$414$		0			0
$415$		0			0
$416$	−2.32349	+	4.02440i	−0.113918	+	0.197313i
$417$		0			0
$418$	−1.15714	+	0.668077i	−0.0565977	+	0.0326767i
$419$	−18.1374			−0.886068			−0.443034	−	0.896505i	$-0.646098\pi$
$419$	−18.1374			−0.886068			−0.443034	+	0.896505i	$0.646098\pi$
$420$		0			0
$421$	7.98092			0.388966			0.194483	−	0.980906i	$-0.437697\pi$
$421$	7.98092			0.388966			0.194483	+	0.980906i	$0.437697\pi$
$422$	5.87719	−	3.39320i	0.286097	−	0.165178i
$423$		0			0
$424$	6.07533	−	10.5228i	0.295044	−	0.511032i
$425$		0			0
$426$		0			0
$427$	20.9257	−	0.852667i	1.01267	−	0.0412635i
$428$			10.7206i			0.518199i
$429$		0			0
$430$		0			0
$431$	−27.1353	−	15.6666i	−1.30706	−	0.754632i	−0.325456	−	0.945557i	$-0.605518\pi$
$431$	−27.1353	−	15.6666i	−1.30706	−	0.754632i	−0.981605	+	0.190925i	$0.938851\pi$
$432$		0			0
$433$		−	5.21564i		−	0.250648i	−0.992116	−	0.125324i	$-0.960003\pi$
$433$		−	5.21564i		−	0.250648i	0.992116	−	0.125324i	$-0.0399970\pi$
$434$	−5.13170	−	2.69039i	−0.246329	−	0.129143i
$435$		0			0
$436$	5.41186	+	9.37362i	0.259181	+	0.448915i
$437$	−1.65259	+	2.86236i	−0.0790539	+	0.136925i
$438$		0			0
$439$	−8.91887	+	5.14931i	−0.425675	+	0.245763i	−0.697502	−	0.716583i	$-0.745705\pi$
$439$	−8.91887	+	5.14931i	−0.425675	+	0.245763i	0.271828	+	0.962346i	$0.412372\pi$
$440$		0			0
$441$		0			0
$442$	−21.2004			−1.00840
$443$	35.9968	−	20.7828i	1.71026	−	0.987419i	0.776067	−	0.630651i	$-0.217212\pi$
$443$	35.9968	−	20.7828i	1.71026	−	0.987419i	0.934193	−	0.356768i	$-0.116121\pi$
$444$		0			0
$445$		0			0
$446$	−14.3842	−	24.9142i	−0.681113	−	1.17972i
$447$		0			0
$448$	2.34325	+	1.22849i	0.110708	+	0.0580408i
$449$			23.7838i			1.12242i	0.827672	+	0.561212i	$0.189665\pi$
$449$			23.7838i			1.12242i	−0.827672	+	0.561212i	$0.810335\pi$
$450$		0			0
$451$	17.7152	+	10.2279i	0.834174	+	0.481611i
$452$	15.9646	+	9.21714i	0.750910	+	0.433538i
$453$		0			0
$454$		−	2.10371i		−	0.0987319i
$455$		0			0
$456$		0			0
$457$	9.38745	+	16.2595i	0.439126	+	0.760589i	0.997622	−	0.0689182i	$-0.0219547\pi$
$457$	9.38745	+	16.2595i	0.439126	+	0.760589i	−0.558496	+	0.829507i	$0.688621\pi$
$458$	8.09841	−	14.0269i	0.378414	−	0.655432i
$459$		0			0
$460$		0			0
$461$	−17.4662			−0.813484			−0.406742	−	0.913543i	$-0.633335\pi$
$461$	−17.4662			−0.813484			−0.406742	+	0.913543i	$0.633335\pi$
$462$		0			0
$463$	−2.99345			−0.139117			−0.0695586	−	0.997578i	$-0.522159\pi$
$463$	−2.99345			−0.139117			−0.0695586	+	0.997578i	$0.522159\pi$
$464$	−2.21130	+	1.27670i	−0.102657	+	0.0592692i
$465$		0			0
$466$	−4.00569	+	6.93805i	−0.185560	+	0.321399i
$467$	−12.7050	−	22.0058i	−0.587920	−	1.01831i	−0.994505	−	0.104694i	$-0.966614\pi$
$467$	−12.7050	−	22.0058i	−0.587920	−	1.01831i	0.406585	−	0.913613i	$-0.366720\pi$
$468$		0			0
$469$	−8.94849	+	5.66430i	−0.413203	+	0.261553i
$470$		0			0
$471$		0			0
$472$	2.90532	+	1.67739i	0.133728	+	0.0772081i
$473$	−13.4160	−	7.74575i	−0.616870	−	0.356150i
$474$		0			0
$475$		0			0
$476$	0.491429	+	12.0604i	0.0225246	+	0.552787i
$477$		0			0
$478$	−7.81165	−	13.5302i	−0.357297	−	0.618856i
$479$	11.8516	−	20.5276i	0.541514	−	0.937929i	−0.457304	−	0.889311i	$-0.651185\pi$
$479$	11.8516	−	20.5276i	0.541514	−	0.937929i	0.998817	−	0.0486188i	$-0.0154819\pi$
$480$		0			0
$481$	−37.2945	+	21.5320i	−1.70048	+	0.981774i
$482$	4.09331			0.186445
$483$		0			0
$484$	−5.45198			−0.247817
$485$		0			0
$486$		0			0
$487$	5.10772	−	8.84683i	0.231453	−	0.400888i	−0.726783	−	0.686867i	$-0.758985\pi$
$487$	5.10772	−	8.84683i	0.231453	−	0.400888i	0.958236	+	0.285979i	$0.0923188\pi$
$488$	−3.95787	−	6.85523i	−0.179164	−	0.310322i
$489$		0			0
$490$		0			0
$491$			2.25910i			0.101952i	0.998700	+	0.0509758i	$0.0162331\pi$
$491$			2.25910i			0.101952i	−0.998700	+	0.0509758i	$0.983767\pi$
$492$		0			0
$493$	−10.0884	−	5.82452i	−0.454357	−	0.262323i
$494$	−2.28291	−	1.31804i	−0.102713	−	0.0593014i
$495$		0			0
$496$			2.18999i			0.0983337i
$497$	−2.49041	+	4.75024i	−0.111710	+	0.213077i
$498$		0			0
$499$	−17.6811	−	30.6246i	−0.791517	−	1.37095i	−0.925028	−	0.379900i	$-0.875958\pi$
$499$	−17.6811	−	30.6246i	−0.791517	−	1.37095i	0.133511	−	0.991047i	$-0.457375\pi$
$500$		0			0
$501$		0			0
$502$	17.2697	−	9.97066i	0.770784	−	0.445012i
$503$	30.7297			1.37017			0.685084	−	0.728464i	$-0.259766\pi$
$503$	30.7297			1.37017			0.685084	+	0.728464i	$0.259766\pi$
$504$		0			0
$505$		0			0
$506$	11.8852	−	6.86191i	0.528361	−	0.305049i
$507$		0			0
$508$	2.02440	−	3.50637i	0.0898183	−	0.155570i
$509$	−1.03925	−	1.80003i	−0.0460637	−	0.0797847i	0.842074	−	0.539362i	$-0.181334\pi$
$509$	−1.03925	−	1.80003i	−0.0460637	−	0.0797847i	−0.888138	+	0.459577i	$0.848001\pi$
$510$		0			0
$511$	−11.6262	−	18.3671i	−0.514313	−	0.812514i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−17.6188	−	10.1722i	−0.777134	−	0.448679i
$515$		0			0
$516$		0			0
$517$		−	14.8682i		−	0.653903i
$518$	13.1135	+	20.7169i	0.576176	+	0.910246i
$519$		0			0
$520$		0			0
$521$	−4.86182	+	8.42093i	−0.213000	+	0.368927i	−0.952652	−	0.304062i	$-0.901657\pi$
$521$	−4.86182	+	8.42093i	−0.213000	+	0.368927i	0.739652	+	0.672990i	$0.234990\pi$
$522$		0			0
$523$	1.20378	−	0.695001i	0.0526375	−	0.0303903i	−0.473450	−	0.880821i	$-0.656992\pi$
$523$	1.20378	−	0.695001i	0.0526375	−	0.0303903i	0.526088	+	0.850430i	$0.323658\pi$
$524$	14.2826			0.623937
$525$		0			0
$526$	−3.61602			−0.157666
$527$	−8.65259	+	4.99558i	−0.376913	+	0.217611i
$528$		0			0
$529$	5.47394	−	9.48114i	0.237997	−	0.412224i
$530$		0			0
$531$		0			0
$532$	−0.696883	+	1.32925i	−0.0302137	+	0.0576302i
$533$			40.3568i			1.74805i
$534$		0			0
$535$		0			0
$536$	3.46657	+	2.00143i	0.149733	+	0.0864485i
$537$		0			0
$538$		−	21.2345i		−	0.915484i
$539$	1.34145	+	16.4333i	0.0577805	+	0.707832i
$540$		0			0
$541$	−22.5510	−	39.0594i	−0.969541	−	1.67930i	−0.696884	−	0.717184i	$-0.745431\pi$
$541$	−22.5510	−	39.0594i	−0.969541	−	1.67930i	−0.272658	−	0.962111i	$-0.587903\pi$
$542$	10.9672	−	18.9957i	0.471080	−	0.815934i
$543$		0			0
$544$	3.95097	−	2.28109i	0.169396	−	0.0978010i
$545$		0			0
$546$		0			0
$547$	−11.1372			−0.476193			−0.238096	−	0.971242i	$-0.576523\pi$
$547$	−11.1372			−0.476193			−0.238096	+	0.971242i	$0.576523\pi$
$548$	4.52794	−	2.61421i	0.193424	−	0.111673i
$549$		0			0
$550$		0			0
$551$	−0.724228	−	1.25440i	−0.0308532	−	0.0534393i
$552$		0			0
$553$	−0.890207	−	21.8470i	−0.0378555	−	0.929029i
$554$			9.92903i			0.421844i
$555$		0			0
$556$	16.8637	+	9.73628i	0.715181	+	0.412910i
$557$	−23.7662	−	13.7214i	−1.00701	−	0.581395i	−0.0966925	−	0.995314i	$-0.530826\pi$
$557$	−23.7662	−	13.7214i	−1.00701	−	0.581395i	−0.910314	+	0.413919i	$0.864160\pi$
$558$		0			0
$559$		−	30.5630i		−	1.29268i
$560$		0			0
$561$		0			0
$562$	−5.53481	−	9.58656i	−0.233472	−	0.404385i
$563$	16.6414	−	28.8238i	0.701352	−	1.21478i	−0.266640	−	0.963796i	$-0.585914\pi$
$563$	16.6414	−	28.8238i	0.701352	−	1.21478i	0.967992	−	0.250981i	$-0.0807531\pi$
$564$		0			0
$565$		0			0
$566$	−22.6773			−0.953200
$567$		0			0
$568$	2.02720			0.0850596
$569$	24.6215	−	14.2152i	1.03219	−	0.595932i	0.114575	−	0.993415i	$-0.463449\pi$
$569$	24.6215	−	14.2152i	1.03219	−	0.595932i	0.917610	+	0.397482i	$0.130116\pi$
$570$		0			0
$571$	−14.0784	+	24.3845i	−0.589162	+	1.02046i	0.405181	+	0.914237i	$0.367209\pi$
$571$	−14.0784	+	24.3845i	−0.589162	+	1.02046i	−0.994343	+	0.106221i	$0.966125\pi$
$572$	5.47280	+	9.47917i	0.228829	+	0.396344i
$573$		0			0
$574$	22.9580	−	0.935478i	0.958249	−	0.0390461i
$575$		0			0
$576$		0			0
$577$	−1.77604	−	1.02540i	−0.0739377	−	0.0426879i	0.462575	−	0.886580i	$-0.346925\pi$
$577$	−1.77604	−	1.02540i	−0.0739377	−	0.0426879i	−0.536513	+	0.843892i	$0.680259\pi$
$578$	3.30259	+	1.90675i	0.137370	+	0.0793103i
$579$		0			0
$580$		0			0
$581$	−0.402187	−	0.210854i	−0.0166855	−	0.00874771i
$582$		0			0
$583$	−14.3100	−	24.7856i	−0.592659	−	1.02652i
$584$	−4.10801	+	7.11528i	−0.169991	+	0.294432i
$585$		0			0
$586$	−10.6735	+	6.16238i	−0.440920	+	0.254565i
$587$	36.2336			1.49552			0.747761	−	0.663968i	$-0.231129\pi$
$587$	36.2336			1.49552			0.747761	+	0.663968i	$0.231129\pi$
$588$		0			0
$589$	−1.24231			−0.0511886
$590$		0			0
$591$		0			0
$592$	4.63355	−	8.02554i	0.190438	−	0.329848i
$593$	−17.3920	−	30.1239i	−0.714205	−	1.23704i	−0.963265	−	0.268551i	$-0.913455\pi$
$593$	−17.3920	−	30.1239i	−0.714205	−	1.23704i	0.249061	−	0.968488i	$-0.419878\pi$
$594$		0			0
$595$		0			0
$596$		−	5.54041i		−	0.226944i
$597$		0			0
$598$	23.4481	+	13.5378i	0.958864	+	0.553601i
$599$	−31.6459	−	18.2708i	−1.29302	−	0.746524i	−0.313829	−	0.949479i	$-0.601612\pi$
$599$	−31.6459	−	18.2708i	−1.29302	−	0.746524i	−0.979188	+	0.202956i	$0.934945\pi$
$600$		0			0
$601$			45.5137i			1.85654i	0.371902	+	0.928272i	$0.378706\pi$
$601$			45.5137i			1.85654i	−0.371902	+	0.928272i	$0.621294\pi$
$602$	−17.3866	+	0.708456i	−0.708623	+	0.0288745i
$603$		0			0
$604$	−4.23984	−	7.34362i	−0.172517	−	0.298807i
$605$		0			0
$606$		0			0
$607$	31.8414	−	18.3836i	1.29240	−	0.746169i	0.313323	−	0.949647i	$-0.398558\pi$
$607$	31.8414	−	18.3836i	1.29240	−	0.746169i	0.979080	+	0.203478i	$0.0652245\pi$
$608$	0.567267			0.0230057
$609$		0			0
$610$		0			0
$611$	25.4033	−	14.6666i	1.02771	−	0.593348i
$612$		0			0
$613$	16.3557	−	28.3288i	0.660599	−	1.14419i	−0.319860	−	0.947465i	$-0.603636\pi$
$613$	16.3557	−	28.3288i	0.660599	−	1.14419i	0.980459	−	0.196726i	$-0.0630309\pi$
$614$	−4.03137	−	6.98254i	−0.162693	−	0.281792i
$615$		0			0
$616$	5.26562	−	3.33308i	0.212158	−	0.134294i
$617$			20.5530i			0.827435i	0.910405	+	0.413717i	$0.135770\pi$
$617$			20.5530i			0.827435i	−0.910405	+	0.413717i	$0.864230\pi$
$618$		0			0
$619$	14.9593	+	8.63675i	0.601265	+	0.347140i	0.769539	−	0.638600i	$-0.220486\pi$
$619$	14.9593	+	8.63675i	0.601265	+	0.347140i	−0.168274	+	0.985740i	$0.553819\pi$
$620$		0			0
$621$		0			0
$622$		−	26.4429i		−	1.06027i
$623$	0.588006	+	14.4305i	0.0235580	+	0.578147i
$624$		0			0
$625$		0			0
$626$	−8.26650	+	14.3180i	−0.330396	+	0.572262i
$627$		0			0
$628$	−0.970763	+	0.560470i	−0.0387377	+	0.0223652i
$629$	42.2782			1.68574
$630$		0			0
$631$	32.7501			1.30376			0.651880	−	0.758322i	$-0.273981\pi$
$631$	32.7501			1.30376			0.651880	+	0.758322i	$0.273981\pi$
$632$	−7.15704	+	4.13212i	−0.284692	+	0.164367i
$633$		0			0
$634$	−6.13038	+	10.6181i	−0.243469	+	0.421700i
$635$		0			0
$636$		0			0
$637$	−26.7542	+	18.5025i	−1.06004	+	0.733095i
$638$			6.01432i			0.238109i
$639$		0			0
$640$		0			0
$641$	18.9300	+	10.9292i	0.747688	+	0.431678i	0.824858	−	0.565340i	$-0.191255\pi$
$641$	18.9300	+	10.9292i	0.747688	+	0.431678i	−0.0771698	+	0.997018i	$0.524588\pi$
$642$		0			0
$643$			4.13643i			0.163125i	0.996668	+	0.0815624i	$0.0259910\pi$
$643$			4.13643i			0.163125i	−0.996668	+	0.0815624i	$0.974009\pi$
$644$	7.15779	−	13.6529i	0.282056	−	0.537999i
$645$		0			0
$646$	1.29399	+	2.24125i	0.0509113	+	0.0881809i
$647$	15.4046	−	26.6816i	0.605618	−	1.04896i	−0.386335	−	0.922358i	$-0.626259\pi$
$647$	15.4046	−	26.6816i	0.605618	−	1.04896i	0.991953	−	0.126603i	$-0.0404075\pi$
$648$		0			0
$649$	6.84327	−	3.95096i	0.268622	−	0.155089i
$650$		0			0
$651$		0			0
$652$	6.71498			0.262979
$653$	−5.97747	+	3.45110i	−0.233917	+	0.135052i	−0.612378	−	0.790565i	$-0.709787\pi$
$653$	−5.97747	+	3.45110i	−0.233917	+	0.135052i	0.378461	+	0.925617i	$0.376453\pi$
$654$		0			0
$655$		0			0
$656$	−4.34226	−	7.52101i	−0.169537	−	0.293646i
$657$		0			0
$658$	−8.93235	−	14.1114i	−0.348219	−	0.550119i
$659$		−	11.0895i		−	0.431985i	−0.976395	−	0.215992i	$-0.930701\pi$
$659$		−	11.0895i		−	0.431985i	0.976395	−	0.215992i	$-0.0692986\pi$
$660$		0			0
$661$	13.7077	+	7.91416i	0.533169	+	0.307825i	0.742306	−	0.670061i	$-0.233732\pi$
$661$	13.7077	+	7.91416i	0.533169	+	0.307825i	−0.209137	+	0.977886i	$0.567065\pi$
$662$	29.7812	+	17.1942i	1.15748	+	0.668270i
$663$		0			0
$664$			0.171637i			0.00666079i
$665$		0			0
$666$		0			0
$667$	7.43865	+	12.8841i	0.288026	+	0.498875i
$668$	−1.40055	+	2.42583i	−0.0541890	+	0.0938581i
$669$		0			0
$670$		0			0
$671$	−18.6449			−0.719779
$672$		0			0
$673$	27.8980			1.07539			0.537695	−	0.843139i	$-0.319295\pi$
$673$	27.8980			1.07539			0.537695	+	0.843139i	$0.319295\pi$
$674$	20.7444	−	11.9768i	0.799045	−	0.461329i
$675$		0			0
$676$	−4.29721	+	7.44298i	−0.165277	+	0.286269i
$677$	15.5739	+	26.9749i	0.598555	+	1.03673i	0.993035	+	0.117823i	$0.0375916\pi$
$677$	15.5739	+	26.9749i	0.598555	+	1.03673i	−0.394479	+	0.918905i	$0.629075\pi$
$678$		0			0
$679$	13.3370	−	25.4393i	0.511828	−	0.976269i
$680$		0			0
$681$		0			0
$682$	4.46727	+	2.57918i	0.171061	+	0.0987620i
$683$	21.8168	+	12.5960i	0.834798	+	0.481971i	0.855493	−	0.517815i	$-0.173254\pi$
$683$	21.8168	+	12.5960i	0.834798	+	0.481971i	−0.0206948	+	0.999786i	$0.506588\pi$
$684$		0			0
$685$		0			0
$686$	11.1458	+	14.7909i	0.425548	+	0.564720i
$687$		0			0
$688$	3.28848	+	5.69581i	0.125372	+	0.217151i
$689$	28.2319	−	48.8992i	1.07555	−	1.86291i
$690$		0			0
$691$	−27.2549	+	15.7356i	−1.03683	+	0.598612i	−0.918933	−	0.394414i	$-0.870948\pi$
$691$	−27.2549	+	15.7356i	−1.03683	+	0.598612i	−0.117894	+	0.993026i	$0.537614\pi$
$692$	−13.8004			−0.524611
$693$		0			0
$694$	28.7003			1.08945
$695$		0			0
$696$		0			0
$697$	19.8102	−	34.3122i	0.750363	−	1.29967i
$698$	−1.78588	−	3.09324i	−0.0675966	−	0.117081i
$699$		0			0
$700$		0			0
$701$			5.19395i			0.196173i	0.995178	+	0.0980864i	$0.0312721\pi$
$701$			5.19395i			0.196173i	−0.995178	+	0.0980864i	$0.968728\pi$
$702$		0			0
$703$	4.55262	+	2.62846i	0.171705	+	0.0991342i
$704$	−2.03986	−	1.17771i	−0.0768800	−	0.0443867i
$705$		0			0
$706$		−	12.5397i		−	0.471937i
$707$	25.7009	−	16.2684i	0.966581	−	0.611835i
$708$		0			0
$709$	−17.9440	−	31.0800i	−0.673903	−	1.16723i	−0.976788	−	0.214207i	$-0.931283\pi$
$709$	−17.9440	−	31.0800i	−0.673903	−	1.16723i	0.302885	−	0.953027i	$-0.402050\pi$
$710$		0			0
$711$		0			0
$712$	4.72742	−	2.72938i	0.177167	−	0.102288i
$713$	12.7600			0.477864
$714$		0			0
$715$		0			0
$716$	2.31980	−	1.33933i	0.0866948	−	0.0500533i
$717$		0			0
$718$	7.90624	−	13.6940i	0.295058	−	0.511056i
$719$	13.0548	+	22.6115i	0.486861	+	0.843268i	0.999886	−	0.0151058i	$-0.00480851\pi$
$719$	13.0548	+	22.6115i	0.486861	+	0.843268i	−0.513025	+	0.858374i	$0.671475\pi$
$720$		0			0
$721$	51.2157	−	2.08691i	1.90737	−	0.0777204i
$722$		−	18.6782i		−	0.695131i
$723$		0			0
$724$	−5.95896	−	3.44041i	−0.221463	−	0.127862i
$725$		0			0
$726$		0			0
$727$		−	19.0193i		−	0.705386i	−0.935739	−	0.352693i	$-0.885266\pi$
$727$		−	19.0193i		−	0.705386i	0.935739	−	0.352693i	$-0.114734\pi$
$728$	10.8890	+	5.70878i	0.403574	+	0.211581i
$729$		0			0
$730$		0			0
$731$	−15.0026	+	25.9853i	−0.554892	+	0.961101i
$732$		0			0
$733$	−7.65553	+	4.41992i	−0.282763	+	0.163254i	−0.634674	−	0.772780i	$-0.718866\pi$
$733$	−7.65553	+	4.41992i	−0.282763	+	0.163254i	0.351910	+	0.936034i	$0.385532\pi$
$734$	35.6635			1.31636
$735$		0			0
$736$	−5.82648			−0.214767
$737$	8.16524	−	4.71421i	0.300771	−	0.173650i
$738$		0			0
$739$	8.20546	−	14.2123i	0.301843	−	0.522807i	−0.674711	−	0.738082i	$-0.735732\pi$
$739$	8.20546	−	14.2123i	0.301843	−	0.522807i	0.976553	+	0.215276i	$0.0690650\pi$
$740$		0			0
$741$		0			0
$742$	−28.4720	−	14.9270i	−1.04524	−	0.547987i
$743$			47.4829i			1.74198i	0.491302	+	0.870989i	$0.336521\pi$
$743$			47.4829i			1.74198i	−0.491302	+	0.870989i	$0.663479\pi$
$744$		0			0
$745$		0			0
$746$	19.9717	+	11.5306i	0.731214	+	0.422167i
$747$		0			0
$748$		−	10.7459i		−	0.392908i
$749$	28.3405	−	1.15480i	1.03554	−	0.0421955i
$750$		0			0
$751$	17.4048	+	30.1459i	0.635109	+	1.10004i	0.986492	+	0.163809i	$0.0523781\pi$
$751$	17.4048	+	30.1459i	0.635109	+	1.10004i	−0.351383	+	0.936232i	$0.614289\pi$
$752$	−3.15616	+	5.46663i	−0.115093	+	0.199348i
$753$		0			0
$754$	−10.2759	+	5.93279i	−0.374226	+	0.216059i
$755$		0			0
$756$		0			0
$757$	9.68581			0.352037			0.176018	−	0.984387i	$-0.443678\pi$
$757$	9.68581			0.352037			0.176018	+	0.984387i	$0.443678\pi$
$758$	−7.10236	+	4.10055i	−0.257969	+	0.148939i
$759$		0			0
$760$		0			0
$761$	−22.2236	−	38.4924i	−0.805605	−	1.39535i	−0.915882	−	0.401448i	$-0.868507\pi$
$761$	−22.2236	−	38.4924i	−0.805605	−	1.39535i	0.110277	−	0.993901i	$-0.464826\pi$
$762$		0			0
$763$	24.1968	−	15.3163i	0.875982	−	0.554487i
$764$		−	9.99228i		−	0.361508i
$765$		0			0
$766$	−4.01207	−	2.31637i	−0.144962	−	0.0836939i
$767$	13.5010	+	7.79479i	0.487492	+	0.281454i
$768$		0			0
$769$			41.0290i			1.47954i	0.672858	+	0.739771i	$0.265066\pi$
$769$			41.0290i			1.47954i	−0.672858	+	0.739771i	$0.734934\pi$
$770$		0			0
$771$		0			0
$772$	12.5643	+	21.7620i	0.452199	+	0.783232i
$773$	−17.4971	+	30.3059i	−0.629327	+	1.09003i	0.358360	+	0.933583i	$0.383336\pi$
$773$	−17.4971	+	30.3059i	−0.629327	+	1.09003i	−0.987687	+	0.156443i	$0.949997\pi$
$774$		0			0
$775$		0			0
$776$	−10.8564			−0.389723
$777$		0			0
$778$	−33.5087			−1.20135
$779$	4.26642	−	2.46322i	0.152860	−	0.0882540i
$780$		0			0
$781$	2.38746	−	4.13521i	0.0854301	−	0.147969i
$782$	−13.2907	−	23.0202i	−0.475276	−	0.823201i
$783$		0			0
$784$	2.99518	−	6.32684i	0.106971	−	0.225959i
$785$		0			0
$786$		0			0
$787$	−19.3139	−	11.1509i	−0.688465	−	0.397485i	0.114572	−	0.993415i	$-0.463450\pi$
$787$	−19.3139	−	11.1509i	−0.688465	−	0.397485i	−0.803037	+	0.595930i	$0.796784\pi$
$788$	−17.3907	−	10.0405i	−0.619519	−	0.357679i
$789$		0			0
$790$		0			0
$791$	22.6464	−	43.1961i	0.805212	−	1.53588i
$792$		0			0
$793$	−18.3921	−	31.8561i	−0.653124	−	1.13124i
$794$	−9.28081	+	16.0748i	−0.329363	+	0.570474i
$795$		0			0
$796$	−10.3028	+	5.94834i	−0.365174	+	0.210833i
$797$	49.1382			1.74057			0.870283	−	0.492553i	$-0.163936\pi$
$797$	49.1382			1.74057			0.870283	+	0.492553i	$0.163936\pi$
$798$		0			0
$799$	−28.7980			−1.01880
$800$		0			0
$801$		0			0
$802$	−7.00770	+	12.1377i	−0.247451	+	0.428597i
$803$	9.67609	+	16.7595i	0.341462	+	0.591429i
$804$		0			0
$805$		0			0
$806$			10.1769i			0.358465i
$807$		0			0
$808$	−9.95630	−	5.74827i	−0.350262	−	0.202224i
$809$	32.5217	+	18.7764i	1.14340	+	0.660144i	0.947271	−	0.320434i	$-0.103829\pi$
$809$	32.5217	+	18.7764i	1.14340	+	0.660144i	0.196132	+	0.980578i	$0.437162\pi$
$810$		0			0
$811$		−	32.3972i		−	1.13762i	−0.822469	−	0.568810i	$-0.807404\pi$
$811$		−	32.3972i		−	1.13762i	0.822469	−	0.568810i	$-0.192596\pi$
$812$	3.61322	+	5.70819i	0.126799	+	0.200318i
$813$		0			0
$814$	−10.9140	−	18.9035i	−0.382534	−	0.662569i
$815$		0			0
$816$		0			0
$817$	−3.23104	+	1.86544i	−0.113040	+	0.0652636i
$818$	−23.8056			−0.832342
$819$		0			0
$820$		0			0
$821$	−16.8756	+	9.74316i	−0.588964	+	0.340039i	−0.764688	−	0.644401i	$-0.777107\pi$
$821$	−16.8756	+	9.74316i	−0.588964	+	0.340039i	0.175724	+	0.984440i	$0.443773\pi$
$822$		0			0
$823$	14.3974	−	24.9370i	0.501861	−	0.869250i	−0.498136	−	0.867099i	$-0.665982\pi$
$823$	14.3974	−	24.9370i	0.501861	−	0.869250i	0.999998	−	0.00215079i	$-0.000684617\pi$
$824$	−9.68690	−	16.7782i	−0.337459	−	0.584496i
$825$		0			0
$826$	4.12132	−	7.86107i	0.143399	−	0.273522i
$827$		−	32.2720i		−	1.12221i	−0.827745	−	0.561104i	$-0.810377\pi$
$827$		−	32.2720i		−	1.12221i	0.827745	−	0.561104i	$-0.189623\pi$
$828$		0			0
$829$	47.2675	+	27.2899i	1.64167	+	0.947817i	0.980241	+	0.197806i	$0.0633816\pi$
$829$	47.2675	+	27.2899i	1.64167	+	0.947817i	0.661426	+	0.750011i	$0.269952\pi$
$830$		0			0
$831$		0			0
$832$		−	4.64698i		−	0.161105i
$833$	31.8294	−	2.59824i	1.10282	−	0.0900237i
$834$		0			0
$835$		0			0
$836$	0.668077	−	1.15714i	0.0231059	−	0.0400206i
$837$		0			0
$838$	15.7074	−	9.06868i	0.542604	−	0.313272i
$839$	−47.8295			−1.65126			−0.825629	−	0.564213i	$-0.809180\pi$
$839$	−47.8295			−1.65126			−0.825629	+	0.564213i	$0.809180\pi$
$840$		0			0
$841$	22.4802			0.775179
$842$	−6.91168	+	3.99046i	−0.238192	+	0.137520i
$843$		0			0
$844$	−3.39320	+	5.87719i	−0.116799	+	0.202301i
$845$		0			0
$846$		0			0
$847$	0.587277	+	14.4126i	0.0201791	+	0.495224i
$848$			12.1507i			0.417256i
$849$		0			0
$850$		0			0
$851$	−46.7606	−	26.9973i	−1.60293	−	0.925455i
$852$		0			0
$853$		−	10.9274i		−	0.374148i	−0.982346	−	0.187074i	$-0.940100\pi$
$853$		−	10.9274i		−	0.374148i	0.982346	−	0.187074i	$-0.0599004\pi$
$854$	−17.6959	+	11.2013i	−0.605540	+	0.383300i
$855$		0			0
$856$	−5.36029	−	9.28430i	−0.183211	−	0.317331i
$857$	−11.1878	+	19.3778i	−0.382167	+	0.661932i	−0.991372	−	0.131081i	$-0.958155\pi$
$857$	−11.1878	+	19.3778i	−0.382167	+	0.661932i	0.609205	+	0.793013i	$0.291489\pi$
$858$		0			0
$859$	28.2119	−	16.2881i	0.962577	−	0.555744i	0.0656116	−	0.997845i	$-0.479100\pi$
$859$	28.2119	−	16.2881i	0.962577	−	0.555744i	0.896965	+	0.442101i	$0.145767\pi$
$860$		0			0
$861$		0			0
$862$	31.3331			1.06721
$863$	36.2871	−	20.9504i	1.23523	−	0.713160i	0.267113	−	0.963665i	$-0.413930\pi$
$863$	36.2871	−	20.9504i	1.23523	−	0.713160i	0.968115	+	0.250506i	$0.0805969\pi$
$864$		0			0
$865$		0			0
$866$	2.60782	+	4.51688i	0.0886174	+	0.153490i
$867$		0			0
$868$	5.78938	−	0.235902i	0.196504	−	0.00800703i
$869$			19.4658i			0.660331i
$870$		0			0
$871$	16.1091	+	9.30059i	0.545836	+	0.315138i
$872$	−9.37362	−	5.41186i	−0.317431	−	0.183269i
$873$		0			0
$874$		−	3.30517i		−	0.111799i
$875$		0			0
$876$		0			0
$877$	29.3084	+	50.7637i	0.989675	+	1.71417i	0.618965	+	0.785419i	$0.287552\pi$
$877$	29.3084	+	50.7637i	0.989675	+	1.71417i	0.370710	+	0.928749i	$0.379114\pi$
$878$	5.14931	−	8.91887i	0.173781	−	0.300997i
$879$		0			0
$880$		0			0
$881$	4.97791			0.167710			0.0838550	−	0.996478i	$-0.473277\pi$
$881$	4.97791			0.167710			0.0838550	+	0.996478i	$0.473277\pi$
$882$		0			0
$883$	−20.8600			−0.701995			−0.350998	−	0.936376i	$-0.614157\pi$
$883$	−20.8600			−0.701995			−0.350998	+	0.936376i	$0.614157\pi$
$884$	18.3601	−	10.6002i	0.617515	−	0.356523i
$885$		0			0
$886$	−20.7828	+	35.9968i	−0.698211	+	1.20934i
$887$	24.9109	+	43.1470i	0.836427	+	1.44873i	0.892864	+	0.450327i	$0.148693\pi$
$887$	24.9109	+	43.1470i	0.836427	+	1.44873i	−0.0564371	+	0.998406i	$0.517974\pi$
$888$		0			0
$889$	−9.48735	−	4.97392i	−0.318195	−	0.166820i
$890$		0			0
$891$		0			0
$892$	24.9142	+	14.3842i	0.834189	+	0.481619i
$893$	−3.10104	−	1.79039i	−0.103772	−	0.0599130i
$894$		0			0
$895$		0			0
$896$	−2.64356	+	0.107718i	−0.0883151	+	0.00359861i
$897$		0			0
$898$	−11.8919	−	20.5973i	−0.396837	−	0.687342i
$899$	−2.79596	+	4.84275i	−0.0932505	+	0.161515i
$900$		0			0
$901$	−48.0069	+	27.7168i	−1.59934	+	0.923379i
$902$	−20.4557			−0.681100
$903$		0			0
$904$	−18.4343			−0.613115
$905$		0			0
$906$		0			0
$907$	18.0797	−	31.3149i	0.600326	−	1.03980i	−0.392445	−	0.919775i	$-0.628371\pi$
$907$	18.0797	−	31.3149i	0.600326	−	1.03980i	0.992771	−	0.120020i	$-0.0382960\pi$
$908$	1.05185	+	1.82186i	0.0349070	+	0.0604607i
$909$		0			0
$910$		0			0
$911$		−	2.05205i		−	0.0679873i	−0.999422	−	0.0339937i	$-0.989177\pi$
$911$		−	2.05205i		−	0.0679873i	0.999422	−	0.0339937i	$-0.0108226\pi$
$912$		0			0
$913$	0.350114	+	0.202138i	0.0115871	+	0.00668980i
$914$	−16.2595	−	9.38745i	−0.537818	−	0.310509i
$915$		0			0
$916$			16.1968i			0.535158i
$917$	−1.53849	−	37.7568i	−0.0508054	−	1.24684i
$918$		0			0
$919$	−0.696500	−	1.20637i	−0.0229754	−	0.0397946i	0.854309	−	0.519765i	$-0.173981\pi$
$919$	−0.696500	−	1.20637i	−0.0229754	−	0.0397946i	−0.877285	+	0.479971i	$0.840647\pi$
$920$		0			0
$921$		0			0
$922$	15.1262	−	8.73312i	0.498155	−	0.287610i
$923$	9.42038			0.310076
$924$		0			0
$925$		0			0
$926$	2.59240	−	1.49672i	0.0851916	−	0.0491854i
$927$		0			0
$928$	1.27670	−	2.21130i	0.0419096	−	0.0725896i
$929$	−16.5276	−	28.6266i	−0.542252	−	0.939208i	−0.998774	−	0.0494960i	$-0.984238\pi$
$929$	−16.5276	−	28.6266i	−0.542252	−	0.939208i	0.456522	−	0.889712i	$-0.349095\pi$
$930$		0			0
$931$	3.58901	+	1.69907i	0.117625	+	0.0556847i
$932$		−	8.01137i		−	0.262421i
$933$		0			0
$934$	22.0058	+	12.7050i	0.720051	+	0.415722i
$935$		0			0
$936$		0			0
$937$			2.53551i			0.0828314i	0.999142	+	0.0414157i	$0.0131868\pi$
$937$			2.53551i			0.0828314i	−0.999142	+	0.0414157i	$0.986813\pi$
$938$	4.91747	−	9.37967i	0.160561	−	0.306257i
$939$		0			0
$940$		0			0
$941$	−18.8858	+	32.7112i	−0.615659	+	1.06635i	0.374609	+	0.927183i	$0.377777\pi$
$941$	−18.8858	+	32.7112i	−0.615659	+	1.06635i	−0.990268	+	0.139171i	$0.955556\pi$
$942$		0			0
$943$	−43.8210	+	25.3001i	−1.42701	+	0.823884i
$944$	−3.35478			−0.109189
$945$		0			0
$946$	15.4915			0.503672
$947$	−49.0138	+	28.2981i	−1.59274	+	0.919566i	−0.599900	+	0.800075i	$0.704793\pi$
$947$	−49.0138	+	28.2981i	−1.59274	+	0.919566i	−0.992835	+	0.119491i	$0.961874\pi$
$948$		0			0
$949$	−19.0898	+	33.0645i	−0.619682	+	1.07332i
$950$		0			0
$951$		0			0
$952$	−6.45578	−	10.1989i	−0.209233	−	0.330548i
$953$		−	34.3234i		−	1.11184i	−0.831234	−	0.555922i	$-0.812365\pi$
$953$		−	34.3234i		−	1.11184i	0.831234	−	0.555922i	$-0.187635\pi$
$954$		0			0
$955$		0			0
$956$	13.5302	+	7.81165i	0.437597	+	0.252647i
$957$		0			0
$958$			23.7032i			0.765816i
$959$	−7.39855	−	11.6883i	−0.238912	−	0.377434i
$960$		0			0
$961$	−13.1020	−	22.6933i	−0.422644	−	0.732041i
$962$	21.5320	−	37.2945i	0.694219	−	1.20242i
$963$		0			0
$964$	−3.54491	+	2.04665i	−0.114174	+	0.0659183i
$965$		0			0
$966$		0			0
$967$	0.903990			0.0290703			0.0145352	−	0.999894i	$-0.495373\pi$
$967$	0.903990			0.0290703			0.0145352	+	0.999894i	$0.495373\pi$
$968$	4.72156	−	2.72599i	0.151757	−	0.0876167i
$969$		0			0
$970$		0			0
$971$	−21.2293	−	36.7703i	−0.681282	−	1.18001i	−0.974590	−	0.223997i	$-0.928089\pi$
$971$	−21.2293	−	36.7703i	−0.681282	−	1.18001i	0.293308	−	0.956018i	$-0.405244\pi$
$972$		0			0
$973$	23.9219	−	45.6290i	0.766901	−	1.46280i
$974$			10.2154i			0.327324i
$975$		0			0
$976$	6.85523	+	3.95787i	0.219431	+	0.126688i
$977$	5.32079	+	3.07196i	0.170227	+	0.0982807i	0.582693	−	0.812692i	$-0.301999\pi$
$977$	5.32079	+	3.07196i	0.170227	+	0.0982807i	−0.412466	+	0.910973i	$0.635332\pi$
$978$		0			0
$979$		−	12.8577i		−	0.410933i
$980$		0			0
$981$		0			0
$982$	−1.12955	−	1.95643i	−0.0360453	−	0.0624323i
$983$	−19.7933	+	34.2830i	−0.631309	+	1.09346i	0.355976	+	0.934495i	$0.384149\pi$
$983$	−19.7933	+	34.2830i	−0.631309	+	1.09346i	−0.987284	+	0.158964i	$0.949185\pi$
$984$		0			0
$985$		0			0
$986$	11.6490			0.370981
$987$		0			0
$988$	2.63608			0.0838648
$989$	33.1865	−	19.1602i	1.05527	−	0.609260i
$990$		0			0
$991$	19.4602	−	33.7060i	0.618172	−	1.07071i	−0.371647	−	0.928374i	$-0.621207\pi$
$991$	19.4602	−	33.7060i	0.618172	−	1.07071i	0.989819	−	0.142331i	$-0.0454599\pi$
$992$	−1.09500	−	1.89659i	−0.0347662	−	0.0602168i
$993$		0			0
$994$	−0.218366	−	5.35903i	−0.00692616	−	0.169978i
$995$		0			0
$996$		0			0
$997$	−18.5522	−	10.7111i	−0.587555	−	0.339225i	0.176575	−	0.984287i	$-0.443498\pi$
$997$	−18.5522	−	10.7111i	−0.587555	−	0.339225i	−0.764130	+	0.645062i	$0.776832\pi$
$998$	30.6246	+	17.6811i	0.969406	+	0.559687i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.e.1151.2	yes	24
3.2	odd	2	inner	3150.2.bf.e.1151.11	yes	24
5.2	odd	4		3150.2.bp.g.899.8		24
5.3	odd	4		3150.2.bp.h.899.5		24
5.4	even	2		3150.2.bf.d.1151.11	yes	24
7.5	odd	6	inner	3150.2.bf.e.1601.11	yes	24
15.2	even	4		3150.2.bp.h.899.8		24
15.8	even	4		3150.2.bp.g.899.5		24
15.14	odd	2		3150.2.bf.d.1151.2	✓	24
21.5	even	6	inner	3150.2.bf.e.1601.2	yes	24
35.12	even	12		3150.2.bp.g.1349.5		24
35.19	odd	6		3150.2.bf.d.1601.2	yes	24
35.33	even	12		3150.2.bp.h.1349.8		24
105.47	odd	12		3150.2.bp.h.1349.5		24
105.68	odd	12		3150.2.bp.g.1349.8		24
105.89	even	6		3150.2.bf.d.1601.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.2	✓	24	15.14	odd	2
3150.2.bf.d.1151.11	yes	24	5.4	even	2
3150.2.bf.d.1601.2	yes	24	35.19	odd	6
3150.2.bf.d.1601.11	yes	24	105.89	even	6
3150.2.bf.e.1151.2	yes	24	1.1	even	1	trivial
3150.2.bf.e.1151.11	yes	24	3.2	odd	2	inner
3150.2.bf.e.1601.2	yes	24	21.5	even	6	inner
3150.2.bf.e.1601.11	yes	24	7.5	odd	6	inner
3150.2.bp.g.899.5		24	15.8	even	4
3150.2.bp.g.899.8		24	5.2	odd	4
3150.2.bp.g.1349.5		24	35.12	even	12
3150.2.bp.g.1349.8		24	105.68	odd	12
3150.2.bp.h.899.5		24	5.3	odd	4
3150.2.bp.h.899.8		24	15.2	even	4
3150.2.bp.h.1349.5		24	105.47	odd	12
3150.2.bp.h.1349.8		24	35.33	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.34325 - 1.22849i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.34325 - 1.22849i) q^{7} +1.00000i q^{8} +(2.03986 + 1.17771i) q^{11} +4.64698i q^{13} +(2.64356 - 0.107718i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.28109 - 3.95097i) q^{17} +(0.491268 - 0.283634i) q^{19} -2.35542 q^{22} +(-5.04588 + 2.91324i) q^{23} +(-2.32349 - 4.02440i) q^{26} +(-2.23553 + 1.41507i) q^{28} -2.55339i q^{29} +(-1.89659 - 1.09500i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.56218i q^{34} +(4.63355 + 8.02554i) q^{37} +(-0.283634 + 0.491268i) q^{38} +8.68451 q^{41} -6.57695 q^{43} +(2.03986 - 1.17771i) q^{44} +(2.91324 - 5.04588i) q^{46} +(-3.15616 - 5.46663i) q^{47} +(3.98161 + 5.75732i) q^{49} +(4.02440 + 2.32349i) q^{52} +(-10.5228 - 6.07533i) q^{53} +(1.22849 - 2.34325i) q^{56} +(1.27670 + 2.21130i) q^{58} +(1.67739 - 2.90532i) q^{59} +(-6.85523 + 3.95787i) q^{61} +2.18999 q^{62} -1.00000 q^{64} +(2.00143 - 3.46657i) q^{67} +(-2.28109 - 3.95097i) q^{68} -2.02720i q^{71} +(7.11528 + 4.10801i) q^{73} +(-8.02554 - 4.63355i) q^{74} -0.567267i q^{76} +(-3.33308 - 5.26562i) q^{77} +(4.13212 + 7.15704i) q^{79} +(-7.52101 + 4.34226i) q^{82} +0.171637 q^{83} +(5.69581 - 3.28848i) q^{86} +(-1.17771 + 2.03986i) q^{88} +(-2.72938 - 4.72742i) q^{89} +(5.70878 - 10.8890i) q^{91} +5.82648i q^{92} +(5.46663 + 3.15616i) q^{94} +10.8564i q^{97} +(-6.32684 - 2.99518i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 4 q^{7}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more