LMFDB - Embedded newform 3150.2.bp.g.1349.5

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			1349.5
Character	$\chi$	$=$	3150.1349
Dual form			3150.2.bp.g.899.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.22849 - 2.34325i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.22849 - 2.34325i) q^{7} +1.00000 q^{8} +(-2.03986 + 1.17771i) q^{11} -4.64698 q^{13} +(2.64356 + 0.107718i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.95097 - 2.28109i) q^{17} +(-0.491268 - 0.283634i) q^{19} -2.35542i q^{22} +(2.91324 - 5.04588i) q^{23} +(2.32349 - 4.02440i) q^{26} +(-1.41507 + 2.23553i) q^{28} +2.55339i q^{29} +(-1.89659 + 1.09500i) q^{31} +(-0.500000 - 0.866025i) q^{32} +4.56218i q^{34} +(8.02554 + 4.63355i) q^{37} +(0.491268 - 0.283634i) q^{38} -8.68451 q^{41} +6.57695i q^{43} +(2.03986 + 1.17771i) q^{44} +(2.91324 + 5.04588i) q^{46} +(5.46663 + 3.15616i) q^{47} +(-3.98161 + 5.75732i) q^{49} +(2.32349 + 4.02440i) q^{52} +(-6.07533 - 10.5228i) q^{53} +(-1.22849 - 2.34325i) q^{56} +(-2.21130 - 1.27670i) q^{58} +(1.67739 + 2.90532i) q^{59} +(-6.85523 - 3.95787i) q^{61} -2.18999i q^{62} +1.00000 q^{64} +(-3.46657 + 2.00143i) q^{67} +(-3.95097 - 2.28109i) q^{68} -2.02720i q^{71} +(-4.10801 - 7.11528i) q^{73} +(-8.02554 + 4.63355i) q^{74} +0.567267i q^{76} +(5.26562 + 3.33308i) q^{77} +(-4.13212 + 7.15704i) q^{79} +(4.34226 - 7.52101i) q^{82} +0.171637i q^{83} +(-5.69581 - 3.28848i) q^{86} +(-2.03986 + 1.17771i) q^{88} +(-2.72938 + 4.72742i) q^{89} +(5.70878 + 10.8890i) q^{91} -5.82648 q^{92} +(-5.46663 + 3.15616i) q^{94} +10.8564 q^{97} +(-2.99518 - 6.32684i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	+	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
$7$	−1.22849	−	2.34325i	−0.464326	−	0.885664i
$7$	−1.22849	−	2.34325i	−0.464326	−	0.885664i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	−2.03986	+	1.17771i	−0.615040	+	0.355093i	−0.774935	−	0.632041i	$-0.782218\pi$
$11$	−2.03986	+	1.17771i	−0.615040	+	0.355093i	0.159896	+	0.987134i	$0.448884\pi$
$12$		0			0
$13$	−4.64698			−1.28884			−0.644420	−	0.764672i	$-0.722901\pi$
$13$	−4.64698			−1.28884			−0.644420	+	0.764672i	$0.722901\pi$
$14$	2.64356	+	0.107718i	0.706520	+	0.0287888i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.95097	−	2.28109i	0.958250	−	0.553246i	0.0626158	−	0.998038i	$-0.480056\pi$
$17$	3.95097	−	2.28109i	0.958250	−	0.553246i	0.895634	+	0.444792i	$0.146722\pi$
$18$		0			0
$19$	−0.491268	−	0.283634i	−0.112705	−	0.0650700i	0.442588	−	0.896725i	$-0.354060\pi$
$19$	−0.491268	−	0.283634i	−0.112705	−	0.0650700i	−0.555293	+	0.831655i	$0.687394\pi$
$20$		0			0
$21$		0			0
$22$		−	2.35542i		−	0.502178i
$23$	2.91324	−	5.04588i	0.607453	−	1.05214i	−0.384206	−	0.923247i	$-0.625525\pi$
$23$	2.91324	−	5.04588i	0.607453	−	1.05214i	0.991659	−	0.128891i	$-0.0411419\pi$
$24$		0			0
$25$		0			0
$26$	2.32349	−	4.02440i	0.455674	−	0.789250i
$27$		0			0
$28$	−1.41507	+	2.23553i	−0.267422	+	0.422475i
$29$			2.55339i			0.474153i	0.971491	+	0.237077i	$0.0761893\pi$
$29$			2.55339i			0.474153i	−0.971491	+	0.237077i	$0.923811\pi$
$30$		0			0
$31$	−1.89659	+	1.09500i	−0.340638	+	0.196667i	−0.660554	−	0.750778i	$-0.729679\pi$
$31$	−1.89659	+	1.09500i	−0.340638	+	0.196667i	0.319916	+	0.947446i	$0.396345\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$			4.56218i			0.782408i
$35$		0			0
$36$		0			0
$37$	8.02554	+	4.63355i	1.31939	+	0.761750i	0.983630	−	0.180197i	$-0.0576736\pi$
$37$	8.02554	+	4.63355i	1.31939	+	0.761750i	0.335760	+	0.941948i	$0.391007\pi$
$38$	0.491268	−	0.283634i	0.0796942	−	0.0460114i
$39$		0			0
$40$		0			0
$41$	−8.68451			−1.35629			−0.678147	−	0.734927i	$-0.737217\pi$
$41$	−8.68451			−1.35629			−0.678147	+	0.734927i	$0.737217\pi$
$42$		0			0
$43$			6.57695i			1.00298i	0.865165	+	0.501488i	$0.167214\pi$
$43$			6.57695i			1.00298i	−0.865165	+	0.501488i	$0.832786\pi$
$44$	2.03986	+	1.17771i	0.307520	+	0.177547i
$45$		0			0
$46$	2.91324	+	5.04588i	0.429534	+	0.743975i
$47$	5.46663	+	3.15616i	0.797391	+	0.460374i	0.842558	−	0.538606i	$-0.181049\pi$
$47$	5.46663	+	3.15616i	0.797391	+	0.460374i	−0.0451673	+	0.998979i	$0.514382\pi$
$48$		0			0
$49$	−3.98161	+	5.75732i	−0.568802	+	0.822475i
$50$		0			0
$51$		0			0
$52$	2.32349	+	4.02440i	0.322210	+	0.558084i
$53$	−6.07533	−	10.5228i	−0.834511	−	1.44542i	−0.894428	−	0.447212i	$-0.852417\pi$
$53$	−6.07533	−	10.5228i	−0.834511	−	1.44542i	0.0599168	−	0.998203i	$-0.480916\pi$
$54$		0			0
$55$		0			0
$56$	−1.22849	−	2.34325i	−0.164164	−	0.313130i
$57$		0			0
$58$	−2.21130	−	1.27670i	−0.290359	−	0.167639i
$59$	1.67739	+	2.90532i	0.218377	+	0.378241i	0.954312	−	0.298812i	$-0.0965903\pi$
$59$	1.67739	+	2.90532i	0.218377	+	0.378241i	−0.735935	+	0.677053i	$0.763257\pi$
$60$		0			0
$61$	−6.85523	−	3.95787i	−0.877722	−	0.506753i	−0.00781543	−	0.999969i	$-0.502488\pi$
$61$	−6.85523	−	3.95787i	−0.877722	−	0.506753i	−0.869907	+	0.493216i	$0.835821\pi$
$62$		−	2.18999i		−	0.278130i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−3.46657	+	2.00143i	−0.423509	+	0.244513i	−0.696578	−	0.717481i	$-0.745295\pi$
$67$	−3.46657	+	2.00143i	−0.423509	+	0.244513i	0.273068	+	0.961995i	$0.411961\pi$
$68$	−3.95097	−	2.28109i	−0.479125	−	0.276623i
$69$		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
$73$	−4.10801	−	7.11528i	−0.480806	−	0.832780i	0.518952	−	0.854804i	$-0.326322\pi$
$73$	−4.10801	−	7.11528i	−0.480806	−	0.832780i	−0.999757	+	0.0220235i	$0.992989\pi$
$74$	−8.02554	+	4.63355i	−0.932950	+	0.538639i
$75$		0			0
$76$			0.567267i			0.0650700i
$77$	5.26562	+	3.33308i	0.600073	+	0.379839i
$78$		0			0
$79$	−4.13212	+	7.15704i	−0.464900	+	0.805230i	−0.999197	−	0.0400666i	$-0.987243\pi$
$79$	−4.13212	+	7.15704i	−0.464900	+	0.805230i	0.534297	+	0.845297i	$0.320576\pi$
$80$		0			0
$81$		0			0
$82$	4.34226	−	7.52101i	0.479522	−	0.830556i
$83$			0.171637i			0.0188396i	0.999956	+	0.00941978i	$0.00299845\pi$
$83$			0.171637i			0.0188396i	−0.999956	+	0.00941978i	$0.997002\pi$
$84$		0			0
$85$		0			0
$86$	−5.69581	−	3.28848i	−0.614195	−	0.354606i
$87$		0			0
$88$	−2.03986	+	1.17771i	−0.217449	+	0.125544i
$89$	−2.72938	+	4.72742i	−0.289313	+	0.501105i	−0.973646	−	0.228065i	$-0.926760\pi$
$89$	−2.72938	+	4.72742i	−0.289313	+	0.501105i	0.684333	+	0.729170i	$0.260094\pi$
$90$		0			0
$91$	5.70878	+	10.8890i	0.598443	+	1.14148i
$92$	−5.82648			−0.607453
$93$		0			0
$94$	−5.46663	+	3.15616i	−0.563840	+	0.325533i
$95$		0			0
$96$		0			0
$97$	10.8564			1.10230			0.551151	−	0.834406i	$-0.314189\pi$
$97$	10.8564			1.10230			0.551151	+	0.834406i	$0.314189\pi$
$98$	−2.99518	−	6.32684i	−0.302559	−	0.639107i
$99$		0			0
$100$		0			0
$101$	5.74827	+	9.95630i	0.571975	+	0.990689i	0.996363	+	0.0852090i	$0.0271558\pi$
$101$	5.74827	+	9.95630i	0.571975	+	0.990689i	−0.424388	+	0.905480i	$0.639511\pi$
$102$		0			0
$103$	−9.68690	+	16.7782i	−0.954478	+	1.65320i	−0.218920	+	0.975743i	$0.570253\pi$
$103$	−9.68690	+	16.7782i	−0.954478	+	1.65320i	−0.735558	+	0.677462i	$0.763080\pi$
$104$	−4.64698			−0.455674
$105$		0			0
$106$	12.1507			1.18018
$107$	−5.36029	+	9.28430i	−0.518199	+	0.897547i	0.481577	+	0.876404i	$0.340064\pi$
$107$	−5.36029	+	9.28430i	−0.518199	+	0.897547i	−0.999776	+	0.0211436i	$0.993269\pi$
$108$		0			0
$109$	5.41186	+	9.37362i	0.518363	+	0.897830i	0.999772	+	0.0213347i	$0.00679157\pi$
$109$	5.41186	+	9.37362i	0.518363	+	0.897830i	−0.481410	+	0.876496i	$0.659875\pi$
$110$		0			0
$111$		0			0
$112$	2.64356	+	0.107718i	0.249793	+	0.0101784i
$113$	18.4343			1.73415			0.867076	−	0.498176i	$-0.165997\pi$
$113$	18.4343			1.73415			0.867076	+	0.498176i	$0.165997\pi$
$114$		0			0
$115$		0			0
$116$	2.21130	−	1.27670i	0.205314	−	0.118538i
$117$		0			0
$118$	−3.35478			−0.308832
$119$	−10.1989	−	6.45578i	−0.934931	−	0.591801i
$120$		0			0
$121$	−2.72599	+	4.72156i	−0.247817	+	0.429232i
$122$	6.85523	−	3.95787i	0.620643	−	0.358329i
$123$		0			0
$124$	1.89659	+	1.09500i	0.170319	+	0.0983337i
$125$		0			0
$126$		0			0
$127$			4.04880i			0.359273i	0.983733	+	0.179637i	$0.0574922\pi$
$127$			4.04880i			0.359273i	−0.983733	+	0.179637i	$0.942508\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−7.14129	+	12.3691i	−0.623937	+	1.08069i	0.364808	+	0.931083i	$0.381134\pi$
$131$	−7.14129	+	12.3691i	−0.623937	+	1.08069i	−0.988745	+	0.149608i	$0.952199\pi$
$132$		0			0
$133$	−0.0611049	+	1.49960i	−0.00529846	+	0.130032i
$134$		−	4.00285i		−	0.345794i
$135$		0			0
$136$	3.95097	−	2.28109i	0.338792	−	0.195602i
$137$	−2.61421	−	4.52794i	−0.223347	−	0.386848i	0.732475	−	0.680794i	$-0.238365\pi$
$137$	−2.61421	−	4.52794i	−0.223347	−	0.386848i	−0.955822	+	0.293945i	$0.905032\pi$
$138$		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
$142$	1.75561	+	1.01360i	0.147328	+	0.0850596i
$143$	9.47917	−	5.47280i	0.792688	−	0.457659i
$144$		0			0
$145$		0			0
$146$	8.21601			0.679962
$147$		0			0
$148$		−	9.26709i		−	0.761750i
$149$	4.79814	+	2.77021i	0.393079	+	0.226944i	0.683493	−	0.729957i	$-0.260460\pi$
$149$	4.79814	+	2.77021i	0.393079	+	0.226944i	−0.290414	+	0.956901i	$0.593793\pi$
$150$		0			0
$151$	4.23984	+	7.34362i	0.345033	+	0.597615i	0.985360	−	0.170488i	$-0.0545343\pi$
$151$	4.23984	+	7.34362i	0.345033	+	0.597615i	−0.640327	+	0.768103i	$0.721201\pi$
$152$	−0.491268	−	0.283634i	−0.0398471	−	0.0230057i
$153$		0			0
$154$	−5.51934	+	2.89362i	−0.444761	+	0.233174i
$155$		0			0
$156$		0			0
$157$	−0.560470	−	0.970763i	−0.0447304	−	0.0774753i	0.842793	−	0.538237i	$-0.180910\pi$
$157$	−0.560470	−	0.970763i	−0.0447304	−	0.0774753i	−0.887524	+	0.460762i	$0.847576\pi$
$158$	−4.13212	−	7.15704i	−0.328734	−	0.569384i
$159$		0			0
$160$		0			0
$161$	−15.4026	−	0.627617i	−1.21390	−	0.0494631i
$162$		0			0
$163$	−5.81534	−	3.35749i	−0.455493	−	0.262979i	0.254654	−	0.967032i	$-0.418038\pi$
$163$	−5.81534	−	3.35749i	−0.455493	−	0.262979i	−0.710147	+	0.704053i	$0.751372\pi$
$164$	4.34226	+	7.52101i	0.339073	+	0.587292i
$165$		0			0
$166$	−0.148642	−	0.0858183i	−0.0115368	−	0.00666079i
$167$			2.80110i			0.216756i	0.994110	+	0.108378i	$0.0345657\pi$
$167$			2.80110i			0.216756i	−0.994110	+	0.108378i	$0.965434\pi$
$168$		0			0
$169$	8.59442			0.661109
$170$		0			0
$171$		0			0
$172$	5.69581	−	3.28848i	0.434301	−	0.250744i
$173$	−11.9515	−	6.90018i	−0.908653	−	0.524611i	−0.0286558	−	0.999589i	$-0.509123\pi$
$173$	−11.9515	−	6.90018i	−0.908653	−	0.524611i	−0.879998	+	0.474978i	$0.842456\pi$
$174$		0			0
$175$		0			0
$176$		−	2.35542i		−	0.177547i
$177$		0			0
$178$	−2.72938	−	4.72742i	−0.204575	−	0.354335i
$179$	2.31980	−	1.33933i	0.173390	−	0.100107i	−0.410794	−	0.911728i	$-0.634748\pi$
$179$	2.31980	−	1.33933i	0.173390	−	0.100107i	0.584183	+	0.811622i	$0.301415\pi$
$180$		0			0
$181$			6.88082i			0.511447i	0.966750	+	0.255724i	$0.0823137\pi$
$181$			6.88082i			0.511447i	−0.966750	+	0.255724i	$0.917686\pi$
$182$	−12.2846	−	0.500563i	−0.910592	−	0.0371042i
$183$		0			0
$184$	2.91324	−	5.04588i	0.214767	−	0.371987i
$185$		0			0
$186$		0			0
$187$	−5.37293	+	9.30619i	−0.392908	+	0.680536i
$188$		−	6.31233i		−	0.460374i
$189$		0			0
$190$		0			0
$191$	−8.65356	−	4.99614i	−0.626150	−	0.361508i	0.153110	−	0.988209i	$-0.451071\pi$
$191$	−8.65356	−	4.99614i	−0.626150	−	0.361508i	−0.779260	+	0.626701i	$0.784405\pi$
$192$		0			0
$193$	−21.7620	+	12.5643i	−1.56646	+	0.904398i	−0.569887	+	0.821723i	$0.693013\pi$
$193$	−21.7620	+	12.5643i	−1.56646	+	0.904398i	−0.996577	+	0.0826753i	$0.973654\pi$
$194$	−5.42821	+	9.40193i	−0.389723	+	0.675019i
$195$		0			0
$196$	6.97679	+	0.569517i	0.498342	+	0.0406798i
$197$	20.0811			1.43072			0.715359	−	0.698757i	$-0.246263\pi$
$197$	20.0811			1.43072			0.715359	+	0.698757i	$0.246263\pi$
$198$		0			0
$199$	10.3028	−	5.94834i	0.730348	−	0.421667i	−0.0882014	−	0.996103i	$-0.528112\pi$
$199$	10.3028	−	5.94834i	0.730348	−	0.421667i	0.818550	+	0.574436i	$0.194779\pi$
$200$		0			0
$201$		0			0
$202$	−11.4965			−0.808894
$203$	5.98323	−	3.13683i	0.419941	−	0.220162i
$204$		0			0
$205$		0			0
$206$	−9.68690	−	16.7782i	−0.674918	−	1.16899i
$207$		0			0
$208$	2.32349	−	4.02440i	0.161105	−	0.279042i
$209$	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	$0.575050\pi$
$212$	−6.07533	+	10.5228i	−0.417256	+	0.722708i
$213$		0			0
$214$	−5.36029	−	9.28430i	−0.366422	−	0.634662i
$215$		0			0
$216$		0			0
$217$	4.89580	+	3.09899i	0.332348	+	0.210373i
$218$	−10.8237			−0.733075
$219$		0			0
$220$		0			0
$221$	−18.3601	+	10.6002i	−1.23503	+	0.713045i
$222$		0			0
$223$	−28.7684			−1.92648			−0.963239	−	0.268646i	$-0.913424\pi$
$223$	−28.7684			−1.92648			−0.963239	+	0.268646i	$0.913424\pi$
$224$	−1.41507	+	2.23553i	−0.0945480	+	0.149368i
$225$		0			0
$226$	−9.21714	+	15.9646i	−0.613115	+	1.06195i
$227$	−1.82186	+	1.05185i	−0.120921	+	0.0698140i	−0.559241	−	0.829005i	$-0.688907\pi$
$227$	−1.82186	+	1.05185i	−0.120921	+	0.0698140i	0.438319	+	0.898819i	$0.355574\pi$
$228$		0			0
$229$	14.0269	+	8.09841i	0.926920	+	0.535158i	0.885836	−	0.463998i	$-0.153585\pi$
$229$	14.0269	+	8.09841i	0.926920	+	0.535158i	0.0410842	+	0.999156i	$0.486919\pi$
$230$		0			0
$231$		0			0
$232$			2.55339i			0.167639i
$233$	−4.00569	+	6.93805i	−0.262421	+	0.454527i	−0.966885	−	0.255213i	$-0.917854\pi$
$233$	−4.00569	+	6.93805i	−0.262421	+	0.454527i	0.704464	+	0.709740i	$0.251188\pi$
$234$		0			0
$235$		0			0
$236$	1.67739	−	2.90532i	0.109189	−	0.189120i
$237$		0			0
$238$	10.6903	−	5.60460i	0.692950	−	0.363293i
$239$		−	15.6233i		−	1.01059i	−0.862947	−	0.505294i	$-0.831384\pi$
$239$		−	15.6233i		−	1.01059i	0.862947	−	0.505294i	$-0.168616\pi$
$240$		0			0
$241$	−3.54491	+	2.04665i	−0.228348	+	0.131837i	−0.609809	−	0.792548i	$-0.708754\pi$
$241$	−3.54491	+	2.04665i	−0.228348	+	0.131837i	0.381462	+	0.924385i	$0.375421\pi$
$242$	−2.72599	−	4.72156i	−0.175233	−	0.303513i
$243$		0			0
$244$			7.91574i			0.506753i
$245$		0			0
$246$		0			0
$247$	2.28291	+	1.31804i	0.145258	+	0.0838648i
$248$	−1.89659	+	1.09500i	−0.120434	+	0.0695324i
$249$		0			0
$250$		0			0
$251$	19.9413			1.25869			0.629343	−	0.777128i	$-0.283324\pi$
$251$	19.9413			1.25869			0.629343	+	0.777128i	$0.283324\pi$
$252$		0			0
$253$			13.7238i			0.862810i
$254$	−3.50637	−	2.02440i	−0.220009	−	0.127022i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−17.6188	−	10.1722i	−1.09903	−	0.634527i	−0.163067	−	0.986615i	$-0.552139\pi$
$257$	−17.6188	−	10.1722i	−1.09903	−	0.634527i	−0.935967	+	0.352088i	$0.885472\pi$
$258$		0			0
$259$	0.998233	−	24.4981i	0.0620272	−	1.52224i
$260$		0			0
$261$		0			0
$262$	−7.14129	−	12.3691i	−0.441190	−	0.764164i
$263$	1.80801	+	3.13156i	0.111487	+	0.193100i	0.916370	−	0.400333i	$-0.131105\pi$
$263$	1.80801	+	3.13156i	0.111487	+	0.193100i	−0.804883	+	0.593433i	$0.797772\pi$
$264$		0			0
$265$		0			0
$266$	−1.26814	−	0.802720i	−0.0777548	−	0.0492179i
$267$		0			0
$268$	3.46657	+	2.00143i	0.211755	+	0.122257i
$269$	−10.6172	−	18.3896i	−0.647345	−	1.12123i	−0.983755	−	0.179518i	$-0.942546\pi$
$269$	−10.6172	−	18.3896i	−0.647345	−	1.12123i	0.336410	−	0.941716i	$-0.390787\pi$
$270$		0			0
$271$	−18.9957	−	10.9672i	−1.15390	−	0.666207i	−0.204069	−	0.978956i	$-0.565417\pi$
$271$	−18.9957	−	10.9672i	−1.15390	−	0.666207i	−0.949836	+	0.312749i	$0.898750\pi$
$272$			4.56218i			0.276623i
$273$		0			0
$274$	5.22842			0.315860
$275$		0			0
$276$		0			0
$277$	−8.59880	+	4.96452i	−0.516652	+	0.298289i	−0.735564	−	0.677456i	$-0.763083\pi$
$277$	−8.59880	+	4.96452i	−0.516652	+	0.298289i	0.218912	+	0.975745i	$0.429749\pi$
$278$	−16.8637	−	9.73628i	−1.01142	−	0.583943i
$279$		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
$283$	−11.3387	−	19.6392i	−0.674014	−	1.16743i	−0.976756	−	0.214354i	$-0.931235\pi$
$283$	−11.3387	−	19.6392i	−0.674014	−	1.16743i	0.302742	−	0.953072i	$-0.402098\pi$
$284$	−1.75561	+	1.01360i	−0.104176	+	0.0601462i
$285$		0			0
$286$			10.9456i			0.647227i
$287$	10.6689	+	20.3500i	0.629763	+	1.20122i
$288$		0			0
$289$	1.90675	−	3.30259i	0.112162	−	0.194270i
$290$		0			0
$291$		0			0
$292$	−4.10801	+	7.11528i	−0.240403	+	0.416390i
$293$			12.3248i			0.720020i	0.932949	+	0.360010i	$0.117227\pi$
$293$			12.3248i			0.720020i	−0.932949	+	0.360010i	$0.882773\pi$
$294$		0			0
$295$		0			0
$296$	8.02554	+	4.63355i	0.466475	+	0.269319i
$297$		0			0
$298$	−4.79814	+	2.77021i	−0.277949	+	0.160474i
$299$	−13.5378	+	23.4481i	−0.782909	+	1.35604i
$300$		0			0
$301$	15.4114	−	8.07974i	0.888300	−	0.465708i
$302$	−8.47968			−0.487951
$303$		0			0
$304$	0.491268	−	0.283634i	0.0281761	−	0.0162675i
$305$		0			0
$306$		0			0
$307$	8.06274			0.460165			0.230082	−	0.973171i	$-0.426100\pi$
$307$	8.06274			0.460165			0.230082	+	0.973171i	$0.426100\pi$
$308$	0.253721	−	6.22670i	0.0144571	−	0.354799i
$309$		0			0
$310$		0			0
$311$	13.2215	+	22.9003i	0.749721	+	1.29855i	0.947956	+	0.318400i	$0.103146\pi$
$311$	13.2215	+	22.9003i	0.749721	+	1.29855i	−0.198236	+	0.980154i	$0.563521\pi$
$312$		0			0
$313$	8.26650	−	14.3180i	0.467250	−	0.809301i	−0.532050	−	0.846713i	$-0.678578\pi$
$313$	8.26650	−	14.3180i	0.467250	−	0.809301i	0.999300	+	0.0374122i	$0.0119114\pi$
$314$	1.12094			0.0632583
$315$		0			0
$316$	8.26424			0.464900
$317$	6.13038	−	10.6181i	0.344317	−	0.596374i	−0.640913	−	0.767614i	$-0.721444\pi$
$317$	6.13038	−	10.6181i	0.344317	−	0.596374i	0.985229	+	0.171240i	$0.0547773\pi$
$318$		0			0
$319$	−3.00716	−	5.20856i	−0.168369	−	0.291623i
$320$		0			0
$321$		0			0
$322$	8.24485	−	13.0253i	0.459468	−	0.725870i
$323$	−2.58798			−0.143999
$324$		0			0
$325$		0			0
$326$	5.81534	−	3.35749i	0.322082	−	0.185954i
$327$		0			0
$328$	−8.68451			−0.479522
$329$	0.679951	−	16.6870i	0.0374869	−	0.919984i
$330$		0			0
$331$	−17.1942	+	29.7812i	−0.945077	+	1.63692i	−0.189479	+	0.981885i	$0.560680\pi$
$331$	−17.1942	+	29.7812i	−0.945077	+	1.63692i	−0.755598	+	0.655036i	$0.772654\pi$
$332$	0.148642	−	0.0858183i	0.00815777	−	0.00470989i
$333$		0			0
$334$	−2.42583	−	1.40055i	−0.132735	−	0.0766348i
$335$		0			0
$336$		0			0
$337$		−	23.9536i		−	1.30484i	−0.757860	−	0.652418i	$-0.773755\pi$
$337$		−	23.9536i		−	1.30484i	0.757860	−	0.652418i	$-0.226245\pi$
$338$	−4.29721	+	7.44298i	−0.233737	+	0.404845i
$339$		0			0
$340$		0			0
$341$	2.57918	−	4.46727i	0.139671	−	0.241916i
$342$		0			0
$343$	18.3822	+	2.25708i	0.992546	+	0.121871i
$344$			6.57695i			0.354606i
$345$		0			0
$346$	11.9515	−	6.90018i	0.642515	−	0.370956i
$347$	14.3501	+	24.8552i	0.770355	+	1.33429i	0.937368	+	0.348340i	$0.113254\pi$
$347$	14.3501	+	24.8552i	0.770355	+	1.33429i	−0.167013	+	0.985955i	$0.553412\pi$
$348$		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
$352$	2.03986	+	1.17771i	0.108725	+	0.0627722i
$353$	10.8597	−	6.26984i	0.578003	−	0.333710i	−0.182337	−	0.983236i	$-0.558366\pi$
$353$	10.8597	−	6.26984i	0.578003	−	0.333710i	0.760339	+	0.649526i	$0.225033\pi$
$354$		0			0
$355$		0			0
$356$	5.45875			0.289313
$357$		0			0
$358$			2.67867i			0.141572i
$359$	−13.6940	−	7.90624i	−0.722742	−	0.417275i	0.0930190	−	0.995664i	$-0.470348\pi$
$359$	−13.6940	−	7.90624i	−0.722742	−	0.417275i	−0.815761	+	0.578389i	$0.803682\pi$
$360$		0			0
$361$	−9.33910	−	16.1758i	−0.491532	−	0.851358i
$362$	−5.95896	−	3.44041i	−0.313196	−	0.180824i
$363$		0			0
$364$	6.57578	−	10.3885i	0.344664	−	0.544503i
$365$		0			0
$366$		0			0
$367$	−17.8317	−	30.8855i	−0.930809	−	1.61221i	−0.781942	−	0.623351i	$-0.785771\pi$
$367$	−17.8317	−	30.8855i	−0.930809	−	1.61221i	−0.148867	−	0.988857i	$-0.547563\pi$
$368$	2.91324	+	5.04588i	0.151863	+	0.263035i
$369$		0			0
$370$		0			0
$371$	−17.1940	+	27.1632i	−0.892667	+	1.41024i
$372$		0			0
$373$	19.9717	+	11.5306i	1.03409	+	0.597034i	0.918155	−	0.396222i	$-0.129679\pi$
$373$	19.9717	+	11.5306i	1.03409	+	0.597034i	0.115939	+	0.993256i	$0.463012\pi$
$374$	−5.37293	−	9.30619i	−0.277828	−	0.481212i
$375$		0			0
$376$	5.46663	+	3.15616i	0.281920	+	0.162767i
$377$		−	11.8656i		−	0.611108i
$378$		0			0
$379$	−8.20110			−0.421262			−0.210631	−	0.977566i	$-0.567552\pi$
$379$	−8.20110			−0.421262			−0.210631	+	0.977566i	$0.567552\pi$
$380$		0			0
$381$		0			0
$382$	8.65356	−	4.99614i	0.442755	−	0.255625i
$383$	4.01207	+	2.31637i	0.205007	+	0.118361i	0.598989	−	0.800757i	$-0.295569\pi$
$383$	4.01207	+	2.31637i	0.205007	+	0.118361i	−0.393982	+	0.919118i	$0.628903\pi$
$384$		0			0
$385$		0			0
$386$		−	25.1286i		−	1.27901i
$387$		0			0
$388$	−5.42821	−	9.40193i	−0.275575	−	0.477311i
$389$	29.0194	−	16.7544i	1.47134	−	0.849480i	0.471860	−	0.881673i	$-0.343583\pi$
$389$	29.0194	−	16.7544i	1.47134	−	0.849480i	0.999482	+	0.0321938i	$0.0102494\pi$
$390$		0			0
$391$		−	26.5815i		−	1.34428i
$392$	−3.98161	+	5.75732i	−0.201102	+	0.290789i
$393$		0			0
$394$	−10.0405	+	17.3907i	−0.505835	+	0.876132i
$395$		0			0
$396$		0			0
$397$	−9.28081	+	16.0748i	−0.465790	+	0.806772i	−0.999237	−	0.0390613i	$-0.987563\pi$
$397$	−9.28081	+	16.0748i	−0.465790	+	0.806772i	0.533447	+	0.845834i	$0.320897\pi$
$398$			11.8967i			0.596327i
$399$		0			0
$400$		0			0
$401$	−12.1377	−	7.00770i	−0.606128	−	0.349948i	0.165321	−	0.986240i	$-0.447134\pi$
$401$	−12.1377	−	7.00770i	−0.606128	−	0.349948i	−0.771448	+	0.636292i	$0.780467\pi$
$402$		0			0
$403$	8.81342	−	5.08843i	0.439028	−	0.253473i
$404$	5.74827	−	9.95630i	0.285987	−	0.495345i
$405$		0			0
$406$	−0.275047	+	6.75005i	−0.0136503	+	0.334999i
$407$	−21.8279			−1.08197
$408$		0			0
$409$	−20.6162	+	11.9028i	−1.01941	+	0.588555i	−0.913932	−	0.405868i	$-0.866969\pi$
$409$	−20.6162	+	11.9028i	−1.01941	+	0.588555i	−0.105474	+	0.994422i	$0.533636\pi$
$410$		0			0
$411$		0			0
$412$	19.3738			0.954478
$413$	4.74723	−	7.49970i	0.233596	−	0.369036i
$414$		0			0
$415$		0			0
$416$	2.32349	+	4.02440i	0.113918	+	0.197313i
$417$		0			0
$418$	−0.668077	+	1.15714i	−0.0326767	+	0.0565977i
$419$	−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	$0.437697\pi$
$422$	3.39320	−	5.87719i	0.165178	−	0.286097i
$423$		0			0
$424$	−6.07533	−	10.5228i	−0.295044	−	0.511032i
$425$		0			0
$426$		0			0
$427$	−0.852667	+	20.9257i	−0.0412635	+	1.01267i
$428$	10.7206			0.518199
$429$		0			0
$430$		0			0
$431$	27.1353	−	15.6666i	1.30706	−	0.754632i	0.325456	−	0.945557i	$-0.394482\pi$
$431$	27.1353	−	15.6666i	1.30706	−	0.754632i	0.981605	+	0.190925i	$0.0611488\pi$
$432$		0			0
$433$	5.21564			0.250648			0.125324	−	0.992116i	$-0.460003\pi$
$433$	5.21564			0.250648			0.125324	+	0.992116i	$0.460003\pi$
$434$	−5.13170	+	2.69039i	−0.246329	+	0.129143i
$435$		0			0
$436$	5.41186	−	9.37362i	0.259181	−	0.448915i
$437$	−2.86236	+	1.65259i	−0.136925	+	0.0790539i
$438$		0			0
$439$	8.91887	+	5.14931i	0.425675	+	0.245763i	0.697502	−	0.716583i	$-0.254295\pi$
$439$	8.91887	+	5.14931i	0.425675	+	0.245763i	−0.271828	+	0.962346i	$0.587628\pi$
$440$		0			0
$441$		0			0
$442$		−	21.2004i		−	1.00840i
$443$	−20.7828	+	35.9968i	−0.987419	+	1.71026i	−0.356768	+	0.934193i	$0.616121\pi$
$443$	−20.7828	+	35.9968i	−0.987419	+	1.71026i	−0.630651	+	0.776067i	$0.717212\pi$
$444$		0			0
$445$		0			0
$446$	14.3842	−	24.9142i	0.681113	−	1.17972i
$447$		0			0
$448$	−1.22849	−	2.34325i	−0.0580408	−	0.110708i
$449$		−	23.7838i		−	1.12242i	−0.827672	−	0.561212i	$-0.810335\pi$
$449$		−	23.7838i		−	1.12242i	0.827672	−	0.561212i	$-0.189665\pi$
$450$		0			0
$451$	17.7152	−	10.2279i	0.834174	−	0.481611i
$452$	−9.21714	−	15.9646i	−0.433538	−	0.750910i
$453$		0			0
$454$		−	2.10371i		−	0.0987319i
$455$		0			0
$456$		0			0
$457$	16.2595	+	9.38745i	0.760589	+	0.439126i	0.829507	−	0.558496i	$-0.188621\pi$
$457$	16.2595	+	9.38745i	0.760589	+	0.439126i	−0.0689182	+	0.997622i	$0.521955\pi$
$458$	−14.0269	+	8.09841i	−0.655432	+	0.378414i
$459$		0			0
$460$		0			0
$461$	17.4662			0.813484			0.406742	−	0.913543i	$-0.366665\pi$
$461$	17.4662			0.813484			0.406742	+	0.913543i	$0.366665\pi$
$462$		0			0
$463$			2.99345i			0.139117i	0.997578	+	0.0695586i	$0.0221591\pi$
$463$			2.99345i			0.139117i	−0.997578	+	0.0695586i	$0.977841\pi$
$464$	−2.21130	−	1.27670i	−0.102657	−	0.0592692i
$465$		0			0
$466$	−4.00569	−	6.93805i	−0.185560	−	0.321399i
$467$	22.0058	+	12.7050i	1.01831	+	0.587920i	0.913613	−	0.406585i	$-0.133280\pi$
$467$	22.0058	+	12.7050i	1.01831	+	0.587920i	0.104694	+	0.994505i	$0.466614\pi$
$468$		0			0
$469$	8.94849	+	5.66430i	0.413203	+	0.261553i
$470$		0			0
$471$		0			0
$472$	1.67739	+	2.90532i	0.0772081	+	0.133728i
$473$	−7.74575	−	13.4160i	−0.356150	−	0.616870i
$474$		0			0
$475$		0			0
$476$	−0.491429	+	12.0604i	−0.0225246	+	0.552787i
$477$		0			0
$478$	13.5302	+	7.81165i	0.618856	+	0.357297i
$479$	11.8516	+	20.5276i	0.541514	+	0.937929i	0.998817	+	0.0486188i	$0.0154819\pi$
$479$	11.8516	+	20.5276i	0.541514	+	0.937929i	−0.457304	+	0.889311i	$0.651185\pi$
$480$		0			0
$481$	−37.2945	−	21.5320i	−1.70048	−	0.981774i
$482$		−	4.09331i		−	0.186445i
$483$		0			0
$484$	5.45198			0.247817
$485$		0			0
$486$		0			0
$487$	−8.84683	+	5.10772i	−0.400888	+	0.231453i	−0.686867	−	0.726783i	$-0.741015\pi$
$487$	−8.84683	+	5.10772i	−0.400888	+	0.231453i	0.285979	+	0.958236i	$0.407681\pi$
$488$	−6.85523	−	3.95787i	−0.310322	−	0.179164i
$489$		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
$493$	5.82452	+	10.0884i	0.262323	+	0.454357i
$494$	−2.28291	+	1.31804i	−0.102713	+	0.0593014i
$495$		0			0
$496$		−	2.18999i		−	0.0983337i
$497$	−4.75024	+	2.49041i	−0.213077	+	0.111710i
$498$		0			0
$499$	17.6811	−	30.6246i	0.791517	−	1.37095i	−0.133511	−	0.991047i	$-0.542625\pi$
$499$	17.6811	−	30.6246i	0.791517	−	1.37095i	0.925028	−	0.379900i	$-0.124042\pi$
$500$		0			0
$501$		0			0
$502$	−9.97066	+	17.2697i	−0.445012	+	0.770784i
$503$			30.7297i			1.37017i	0.728464	+	0.685084i	$0.240234\pi$
$503$			30.7297i			1.37017i	−0.728464	+	0.685084i	$0.759766\pi$
$504$		0			0
$505$		0			0
$506$	−11.8852	−	6.86191i	−0.528361	−	0.305049i
$507$		0			0
$508$	3.50637	−	2.02440i	0.155570	−	0.0898183i
$509$	−1.03925	+	1.80003i	−0.0460637	+	0.0797847i	−0.888138	−	0.459577i	$-0.848001\pi$
$509$	−1.03925	+	1.80003i	−0.0460637	+	0.0797847i	0.842074	+	0.539362i	$0.181334\pi$
$510$		0			0
$511$	−11.6262	+	18.3671i	−0.514313	+	0.812514i
$512$	1.00000			0.0441942
$513$		0			0
$514$	17.6188	−	10.1722i	0.777134	−	0.448679i
$515$		0			0
$516$		0			0
$517$	−14.8682			−0.653903
$518$	20.7169	+	13.1135i	0.910246	+	0.576176i
$519$		0			0
$520$		0			0
$521$	4.86182	+	8.42093i	0.213000	+	0.368927i	0.952652	−	0.304062i	$-0.0983431\pi$
$521$	4.86182	+	8.42093i	0.213000	+	0.368927i	−0.739652	+	0.672990i	$0.765010\pi$
$522$		0			0
$523$	0.695001	−	1.20378i	0.0303903	−	0.0526375i	−0.850430	−	0.526088i	$-0.823658\pi$
$523$	0.695001	−	1.20378i	0.0303903	−	0.0526375i	0.880821	+	0.473450i	$0.156992\pi$
$524$	14.2826			0.623937
$525$		0			0
$526$	−3.61602			−0.157666
$527$	−4.99558	+	8.65259i	−0.217611	+	0.376913i
$528$		0			0
$529$	−5.47394	−	9.48114i	−0.237997	−	0.412224i
$530$		0			0
$531$		0			0
$532$	1.32925	−	0.696883i	0.0576302	−	0.0302137i
$533$	40.3568			1.74805
$534$		0			0
$535$		0			0
$536$	−3.46657	+	2.00143i	−0.149733	+	0.0864485i
$537$		0			0
$538$	21.2345			0.915484
$539$	1.34145	−	16.4333i	0.0577805	−	0.707832i
$540$		0			0
$541$	−22.5510	+	39.0594i	−0.969541	+	1.67930i	−0.272658	+	0.962111i	$0.587903\pi$
$541$	−22.5510	+	39.0594i	−0.969541	+	1.67930i	−0.696884	+	0.717184i	$0.745431\pi$
$542$	18.9957	−	10.9672i	0.815934	−	0.471080i
$543$		0			0
$544$	−3.95097	−	2.28109i	−0.169396	−	0.0978010i
$545$		0			0
$546$		0			0
$547$		−	11.1372i		−	0.476193i	−0.971242	−	0.238096i	$-0.923477\pi$
$547$		−	11.1372i		−	0.476193i	0.971242	−	0.238096i	$-0.0765234\pi$
$548$	−2.61421	+	4.52794i	−0.111673	+	0.193424i
$549$		0			0
$550$		0			0
$551$	0.724228	−	1.25440i	0.0308532	−	0.0534393i
$552$		0			0
$553$	21.8470	+	0.890207i	0.929029	+	0.0378555i
$554$		−	9.92903i		−	0.421844i
$555$		0			0
$556$	16.8637	−	9.73628i	0.715181	−	0.412910i
$557$	13.7214	+	23.7662i	0.581395	+	1.00701i	0.995314	+	0.0966925i	$0.0308263\pi$
$557$	13.7214	+	23.7662i	0.581395	+	1.00701i	−0.413919	+	0.910314i	$0.635840\pi$
$558$		0			0
$559$		−	30.5630i		−	1.29268i
$560$		0			0
$561$		0			0
$562$	−9.58656	−	5.53481i	−0.404385	−	0.233472i
$563$	−28.8238	+	16.6414i	−1.21478	+	0.701352i	−0.963796	−	0.266640i	$-0.914086\pi$
$563$	−28.8238	+	16.6414i	−1.21478	+	0.701352i	−0.250981	+	0.967992i	$0.580753\pi$
$564$		0			0
$565$		0			0
$566$	22.6773			0.953200
$567$		0			0
$568$		−	2.02720i		−	0.0850596i
$569$	24.6215	+	14.2152i	1.03219	+	0.595932i	0.917610	−	0.397482i	$-0.130116\pi$
$569$	24.6215	+	14.2152i	1.03219	+	0.595932i	0.114575	+	0.993415i	$0.463449\pi$
$570$		0			0
$571$	−14.0784	−	24.3845i	−0.589162	−	1.02046i	−0.994343	−	0.106221i	$-0.966125\pi$
$571$	−14.0784	−	24.3845i	−0.589162	−	1.02046i	0.405181	−	0.914237i	$-0.367209\pi$
$572$	−9.47917	−	5.47280i	−0.396344	−	0.228829i
$573$		0			0
$574$	−22.9580	−	0.935478i	−0.958249	−	0.0390461i
$575$		0			0
$576$		0			0
$577$	−1.02540	−	1.77604i	−0.0426879	−	0.0739377i	0.843892	−	0.536513i	$-0.180259\pi$
$577$	−1.02540	−	1.77604i	−0.0426879	−	0.0739377i	−0.886580	+	0.462575i	$0.846925\pi$
$578$	1.90675	+	3.30259i	0.0793103	+	0.137370i
$579$		0			0
$580$		0			0
$581$	0.402187	−	0.210854i	0.0166855	−	0.00874771i
$582$		0			0
$583$	24.7856	+	14.3100i	1.02652	+	0.592659i
$584$	−4.10801	−	7.11528i	−0.169991	−	0.294432i
$585$		0			0
$586$	−10.6735	−	6.16238i	−0.440920	−	0.254565i
$587$		−	36.2336i		−	1.49552i	−0.663968	−	0.747761i	$-0.731129\pi$
$587$		−	36.2336i		−	1.49552i	0.663968	−	0.747761i	$-0.268871\pi$
$588$		0			0
$589$	1.24231			0.0511886
$590$		0			0
$591$		0			0
$592$	−8.02554	+	4.63355i	−0.329848	+	0.190438i
$593$	−30.1239	−	17.3920i	−1.23704	−	0.714205i	−0.268551	−	0.963265i	$-0.586545\pi$
$593$	−30.1239	−	17.3920i	−1.23704	−	0.714205i	−0.968488	+	0.249061i	$0.919878\pi$
$594$		0			0
$595$		0			0
$596$		−	5.54041i		−	0.226944i
$597$		0			0
$598$	−13.5378	−	23.4481i	−0.553601	−	0.958864i
$599$	−31.6459	+	18.2708i	−1.29302	+	0.746524i	−0.979188	−	0.202956i	$-0.934945\pi$
$599$	−31.6459	+	18.2708i	−1.29302	+	0.746524i	−0.313829	+	0.949479i	$0.601612\pi$
$600$		0			0
$601$		−	45.5137i		−	1.85654i	−0.371902	−	0.928272i	$-0.621294\pi$
$601$		−	45.5137i		−	1.85654i	0.371902	−	0.928272i	$-0.378706\pi$
$602$	−0.708456	+	17.3866i	−0.0288745	+	0.708623i
$603$		0			0
$604$	4.23984	−	7.34362i	0.172517	−	0.298807i
$605$		0			0
$606$		0			0
$607$	−18.3836	+	31.8414i	−0.746169	+	1.29240i	0.203478	+	0.979080i	$0.434776\pi$
$607$	−18.3836	+	31.8414i	−0.746169	+	1.29240i	−0.949647	+	0.313323i	$0.898558\pi$
$608$			0.567267i			0.0230057i
$609$		0			0
$610$		0			0
$611$	−25.4033	−	14.6666i	−1.02771	−	0.593348i
$612$		0			0
$613$	28.3288	−	16.3557i	1.14419	−	0.660599i	0.196726	−	0.980459i	$-0.436969\pi$
$613$	28.3288	−	16.3557i	1.14419	−	0.660599i	0.947465	+	0.319860i	$0.103636\pi$
$614$	−4.03137	+	6.98254i	−0.162693	+	0.281792i
$615$		0			0
$616$	5.26562	+	3.33308i	0.212158	+	0.134294i
$617$	−20.5530			−0.827435			−0.413717	−	0.910405i	$-0.635770\pi$
$617$	−20.5530			−0.827435			−0.413717	+	0.910405i	$0.635770\pi$
$618$		0			0
$619$	−14.9593	+	8.63675i	−0.601265	+	0.347140i	−0.769539	−	0.638600i	$-0.779514\pi$
$619$	−14.9593	+	8.63675i	−0.601265	+	0.347140i	0.168274	+	0.985740i	$0.446181\pi$
$620$		0			0
$621$		0			0
$622$	−26.4429			−1.06027
$623$	14.4305	+	0.588006i	0.578147	+	0.0235580i
$624$		0			0
$625$		0			0
$626$	8.26650	+	14.3180i	0.330396	+	0.572262i
$627$		0			0
$628$	−0.560470	+	0.970763i	−0.0223652	+	0.0387377i
$629$	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	$0.273981\pi$
$632$	−4.13212	+	7.15704i	−0.164367	+	0.284692i
$633$		0			0
$634$	6.13038	+	10.6181i	0.243469	+	0.421700i
$635$		0			0
$636$		0			0
$637$	18.5025	−	26.7542i	0.733095	−	1.06004i
$638$	6.01432			0.238109
$639$		0			0
$640$		0			0
$641$	−18.9300	+	10.9292i	−0.747688	+	0.431678i	−0.824858	−	0.565340i	$-0.808745\pi$
$641$	−18.9300	+	10.9292i	−0.747688	+	0.431678i	0.0771698	+	0.997018i	$0.475412\pi$
$642$		0			0
$643$	−4.13643			−0.163125			−0.0815624	−	0.996668i	$-0.525991\pi$
$643$	−4.13643			−0.163125			−0.0815624	+	0.996668i	$0.525991\pi$
$644$	7.15779	+	13.6529i	0.282056	+	0.537999i
$645$		0			0
$646$	1.29399	−	2.24125i	0.0509113	−	0.0881809i
$647$	26.6816	−	15.4046i	1.04896	−	0.605618i	0.126603	−	0.991953i	$-0.459593\pi$
$647$	26.6816	−	15.4046i	1.04896	−	0.605618i	0.922358	+	0.386335i	$0.126259\pi$
$648$		0			0
$649$	−6.84327	−	3.95096i	−0.268622	−	0.155089i
$650$		0			0
$651$		0			0
$652$			6.71498i			0.262979i
$653$	3.45110	−	5.97747i	0.135052	−	0.233917i	−0.790565	−	0.612378i	$-0.790213\pi$
$653$	3.45110	−	5.97747i	0.135052	−	0.233917i	0.925617	+	0.378461i	$0.123547\pi$
$654$		0			0
$655$		0			0
$656$	4.34226	−	7.52101i	0.169537	−	0.293646i
$657$		0			0
$658$	14.1114	+	8.93235i	0.550119	+	0.348219i
$659$			11.0895i			0.431985i	0.976395	+	0.215992i	$0.0692986\pi$
$659$			11.0895i			0.431985i	−0.976395	+	0.215992i	$0.930701\pi$
$660$		0			0
$661$	13.7077	−	7.91416i	0.533169	−	0.307825i	−0.209137	−	0.977886i	$-0.567065\pi$
$661$	13.7077	−	7.91416i	0.533169	−	0.307825i	0.742306	+	0.670061i	$0.233732\pi$
$662$	−17.1942	−	29.7812i	−0.668270	−	1.15748i
$663$		0			0
$664$			0.171637i			0.00666079i
$665$		0			0
$666$		0			0
$667$	12.8841	+	7.43865i	0.498875	+	0.288026i
$668$	2.42583	−	1.40055i	0.0938581	−	0.0541890i
$669$		0			0
$670$		0			0
$671$	18.6449			0.719779
$672$		0			0
$673$		−	27.8980i		−	1.07539i	−0.843139	−	0.537695i	$-0.819295\pi$
$673$		−	27.8980i		−	1.07539i	0.843139	−	0.537695i	$-0.180705\pi$
$674$	20.7444	+	11.9768i	0.799045	+	0.461329i
$675$		0			0
$676$	−4.29721	−	7.44298i	−0.165277	−	0.286269i
$677$	−26.9749	−	15.5739i	−1.03673	−	0.598555i	−0.117823	−	0.993035i	$-0.537592\pi$
$677$	−26.9749	−	15.5739i	−1.03673	−	0.598555i	−0.918905	+	0.394479i	$0.870925\pi$
$678$		0			0
$679$	−13.3370	−	25.4393i	−0.511828	−	0.976269i
$680$		0			0
$681$		0			0
$682$	2.57918	+	4.46727i	0.0987620	+	0.171061i
$683$	12.5960	+	21.8168i	0.481971	+	0.834798i	0.999786	−	0.0206948i	$-0.00658782\pi$
$683$	12.5960	+	21.8168i	0.481971	+	0.834798i	−0.517815	+	0.855493i	$0.673254\pi$
$684$		0			0
$685$		0			0
$686$	−11.1458	+	14.7909i	−0.425548	+	0.564720i
$687$		0			0
$688$	−5.69581	−	3.28848i	−0.217151	−	0.125372i
$689$	28.2319	+	48.8992i	1.07555	+	1.86291i
$690$		0			0
$691$	−27.2549	−	15.7356i	−1.03683	−	0.598612i	−0.117894	−	0.993026i	$-0.537614\pi$
$691$	−27.2549	−	15.7356i	−1.03683	−	0.598612i	−0.918933	+	0.394414i	$0.870948\pi$
$692$			13.8004i			0.524611i
$693$		0			0
$694$	−28.7003			−1.08945
$695$		0			0
$696$		0			0
$697$	−34.3122	+	19.8102i	−1.29967	+	0.750363i
$698$	−3.09324	−	1.78588i	−0.117081	−	0.0675966i
$699$		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
$703$	−2.62846	−	4.55262i	−0.0991342	−	0.171705i
$704$	−2.03986	+	1.17771i	−0.0768800	+	0.0443867i
$705$		0			0
$706$			12.5397i			0.471937i
$707$	16.2684	−	25.7009i	0.611835	−	0.966581i
$708$		0			0
$709$	17.9440	−	31.0800i	0.673903	−	1.16723i	−0.302885	−	0.953027i	$-0.597950\pi$
$709$	17.9440	−	31.0800i	0.673903	−	1.16723i	0.976788	−	0.214207i	$-0.0687167\pi$
$710$		0			0
$711$		0			0
$712$	−2.72938	+	4.72742i	−0.102288	+	0.177167i
$713$			12.7600i			0.477864i
$714$		0			0
$715$		0			0
$716$	−2.31980	−	1.33933i	−0.0866948	−	0.0500533i
$717$		0			0
$718$	13.6940	−	7.90624i	0.511056	−	0.295058i
$719$	13.0548	−	22.6115i	0.486861	−	0.843268i	−0.513025	−	0.858374i	$-0.671475\pi$
$719$	13.0548	−	22.6115i	0.486861	−	0.843268i	0.999886	+	0.0151058i	$0.00480851\pi$
$720$		0			0
$721$	51.2157	+	2.08691i	1.90737	+	0.0777204i
$722$	18.6782			0.695131
$723$		0			0
$724$	5.95896	−	3.44041i	0.221463	−	0.127862i
$725$		0			0
$726$		0			0
$727$	−19.0193			−0.705386			−0.352693	−	0.935739i	$-0.614734\pi$
$727$	−19.0193			−0.705386			−0.352693	+	0.935739i	$0.614734\pi$
$728$	5.70878	+	10.8890i	0.211581	+	0.403574i
$729$		0			0
$730$		0			0
$731$	15.0026	+	25.9853i	0.554892	+	0.961101i
$732$		0			0
$733$	−4.41992	+	7.65553i	−0.163254	+	0.282763i	−0.936034	−	0.351910i	$-0.885532\pi$
$733$	−4.41992	+	7.65553i	−0.163254	+	0.282763i	0.772780	+	0.634674i	$0.218866\pi$
$734$	35.6635			1.31636
$735$		0			0
$736$	−5.82648			−0.214767
$737$	4.71421	−	8.16524i	0.173650	−	0.300771i
$738$		0			0
$739$	−8.20546	−	14.2123i	−0.301843	−	0.522807i	0.674711	−	0.738082i	$-0.264268\pi$
$739$	−8.20546	−	14.2123i	−0.301843	−	0.522807i	−0.976553	+	0.215276i	$0.930935\pi$
$740$		0			0
$741$		0			0
$742$	−14.9270	−	28.4720i	−0.547987	−	1.04524i
$743$	47.4829			1.74198			0.870989	−	0.491302i	$-0.163479\pi$
$743$	47.4829			1.74198			0.870989	+	0.491302i	$0.163479\pi$
$744$		0			0
$745$		0			0
$746$	−19.9717	+	11.5306i	−0.731214	+	0.422167i
$747$		0			0
$748$	10.7459			0.392908
$749$	28.3405	+	1.15480i	1.03554	+	0.0421955i
$750$		0			0
$751$	17.4048	−	30.1459i	0.635109	−	1.10004i	−0.351383	−	0.936232i	$-0.614289\pi$
$751$	17.4048	−	30.1459i	0.635109	−	1.10004i	0.986492	−	0.163809i	$-0.0523781\pi$
$752$	−5.46663	+	3.15616i	−0.199348	+	0.115093i
$753$		0			0
$754$	10.2759	+	5.93279i	0.374226	+	0.216059i
$755$		0			0
$756$		0			0
$757$			9.68581i			0.352037i	0.984387	+	0.176018i	$0.0563218\pi$
$757$			9.68581i			0.352037i	−0.984387	+	0.176018i	$0.943678\pi$
$758$	4.10055	−	7.10236i	0.148939	−	0.257969i
$759$		0			0
$760$		0			0
$761$	22.2236	−	38.4924i	0.805605	−	1.39535i	−0.110277	−	0.993901i	$-0.535174\pi$
$761$	22.2236	−	38.4924i	0.805605	−	1.39535i	0.915882	−	0.401448i	$-0.131493\pi$
$762$		0			0
$763$	15.3163	−	24.1968i	0.554487	−	0.875982i
$764$			9.99228i			0.361508i
$765$		0			0
$766$	−4.01207	+	2.31637i	−0.144962	+	0.0836939i
$767$	−7.79479	−	13.5010i	−0.281454	−	0.487492i
$768$		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
$772$	21.7620	+	12.5643i	0.783232	+	0.452199i
$773$	30.3059	−	17.4971i	1.09003	−	0.629327i	0.156443	−	0.987687i	$-0.449997\pi$
$773$	30.3059	−	17.4971i	1.09003	−	0.629327i	0.933583	+	0.358360i	$0.116664\pi$
$774$		0			0
$775$		0			0
$776$	10.8564			0.389723
$777$		0			0
$778$			33.5087i			1.20135i
$779$	4.26642	+	2.46322i	0.152860	+	0.0882540i
$780$		0			0
$781$	2.38746	+	4.13521i	0.0854301	+	0.147969i
$782$	23.0202	+	13.2907i	0.823201	+	0.475276i
$783$		0			0
$784$	−2.99518	−	6.32684i	−0.106971	−	0.225959i
$785$		0			0
$786$		0			0
$787$	−11.1509	−	19.3139i	−0.397485	−	0.688465i	0.595930	−	0.803037i	$-0.296784\pi$
$787$	−11.1509	−	19.3139i	−0.397485	−	0.688465i	−0.993415	+	0.114572i	$0.963450\pi$
$788$	−10.0405	−	17.3907i	−0.357679	−	0.619519i
$789$		0			0
$790$		0			0
$791$	−22.6464	−	43.1961i	−0.805212	−	1.53588i
$792$		0			0
$793$	31.8561	+	18.3921i	1.13124	+	0.653124i
$794$	−9.28081	−	16.0748i	−0.329363	−	0.570474i
$795$		0			0
$796$	−10.3028	−	5.94834i	−0.365174	−	0.210833i
$797$		−	49.1382i		−	1.74057i	−0.492553	−	0.870283i	$-0.663936\pi$
$797$		−	49.1382i		−	1.74057i	0.492553	−	0.870283i	$-0.336064\pi$
$798$		0			0
$799$	28.7980			1.01880
$800$		0			0
$801$		0			0
$802$	12.1377	−	7.00770i	0.428597	−	0.247451i
$803$	16.7595	+	9.67609i	0.591429	+	0.341462i
$804$		0			0
$805$		0			0
$806$			10.1769i			0.358465i
$807$		0			0
$808$	5.74827	+	9.95630i	0.202224	+	0.350262i
$809$	32.5217	−	18.7764i	1.14340	−	0.660144i	0.196132	−	0.980578i	$-0.437162\pi$
$809$	32.5217	−	18.7764i	1.14340	−	0.660144i	0.947271	+	0.320434i	$0.103829\pi$
$810$		0			0
$811$			32.3972i			1.13762i	0.822469	+	0.568810i	$0.192596\pi$
$811$			32.3972i			1.13762i	−0.822469	+	0.568810i	$0.807404\pi$
$812$	−5.70819	−	3.61322i	−0.200318	−	0.126799i
$813$		0			0
$814$	10.9140	−	18.9035i	0.382534	−	0.662569i
$815$		0			0
$816$		0			0
$817$	1.86544	−	3.23104i	0.0652636	−	0.113040i
$818$		−	23.8056i		−	0.832342i
$819$		0			0
$820$		0			0
$821$	16.8756	+	9.74316i	0.588964	+	0.340039i	0.764688	−	0.644401i	$-0.222893\pi$
$821$	16.8756	+	9.74316i	0.588964	+	0.340039i	−0.175724	+	0.984440i	$0.556227\pi$
$822$		0			0
$823$	24.9370	−	14.3974i	0.869250	−	0.501861i	0.00215079	−	0.999998i	$-0.499315\pi$
$823$	24.9370	−	14.3974i	0.869250	−	0.501861i	0.867099	+	0.498136i	$0.165982\pi$
$824$	−9.68690	+	16.7782i	−0.337459	+	0.584496i
$825$		0			0
$826$	4.12132	+	7.86107i	0.143399	+	0.273522i
$827$	32.2720			1.12221			0.561104	−	0.827745i	$-0.310377\pi$
$827$	32.2720			1.12221			0.561104	+	0.827745i	$0.310377\pi$
$828$		0			0
$829$	−47.2675	+	27.2899i	−1.64167	+	0.947817i	−0.661426	+	0.750011i	$0.730048\pi$
$829$	−47.2675	+	27.2899i	−1.64167	+	0.947817i	−0.980241	+	0.197806i	$0.936618\pi$
$830$		0			0
$831$		0			0
$832$	−4.64698			−0.161105
$833$	−2.59824	+	31.8294i	−0.0900237	+	1.10282i
$834$		0			0
$835$		0			0
$836$	−0.668077	−	1.15714i	−0.0231059	−	0.0400206i
$837$		0			0
$838$	9.06868	−	15.7074i	0.313272	−	0.542604i
$839$	−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
$842$	−3.99046	+	6.91168i	−0.137520	+	0.238192i
$843$		0			0
$844$	3.39320	+	5.87719i	0.116799	+	0.202301i
$845$		0			0
$846$		0			0
$847$	14.4126	+	0.587277i	0.495224	+	0.0201791i
$848$	12.1507			0.417256
$849$		0			0
$850$		0			0
$851$	46.7606	−	26.9973i	1.60293	−	0.925455i
$852$		0			0
$853$	10.9274			0.374148			0.187074	−	0.982346i	$-0.440100\pi$
$853$	10.9274			0.374148			0.187074	+	0.982346i	$0.440100\pi$
$854$	−17.6959	−	11.2013i	−0.605540	−	0.383300i
$855$		0			0
$856$	−5.36029	+	9.28430i	−0.183211	+	0.317331i
$857$	−19.3778	+	11.1878i	−0.661932	+	0.382167i	−0.793013	−	0.609205i	$-0.791489\pi$
$857$	−19.3778	+	11.1878i	−0.661932	+	0.382167i	0.131081	+	0.991372i	$0.458155\pi$
$858$		0			0
$859$	−28.2119	−	16.2881i	−0.962577	−	0.555744i	−0.0656116	−	0.997845i	$-0.520900\pi$
$859$	−28.2119	−	16.2881i	−0.962577	−	0.555744i	−0.896965	+	0.442101i	$0.854233\pi$
$860$		0			0
$861$		0			0
$862$			31.3331i			1.06721i
$863$	−20.9504	+	36.2871i	−0.713160	+	1.23523i	0.250506	+	0.968115i	$0.419403\pi$
$863$	−20.9504	+	36.2871i	−0.713160	+	1.23523i	−0.963665	+	0.267113i	$0.913930\pi$
$864$		0			0
$865$		0			0
$866$	−2.60782	+	4.51688i	−0.0886174	+	0.153490i
$867$		0			0
$868$	0.235902	−	5.78938i	0.00800703	−	0.196504i
$869$		−	19.4658i		−	0.660331i
$870$		0			0
$871$	16.1091	−	9.30059i	0.545836	−	0.315138i
$872$	5.41186	+	9.37362i	0.183269	+	0.317431i
$873$		0			0
$874$		−	3.30517i		−	0.111799i
$875$		0			0
$876$		0			0
$877$	50.7637	+	29.3084i	1.71417	+	0.989675i	0.928749	+	0.370710i	$0.120886\pi$
$877$	50.7637	+	29.3084i	1.71417	+	0.989675i	0.785419	+	0.618965i	$0.212448\pi$
$878$	−8.91887	+	5.14931i	−0.300997	+	0.173781i
$879$		0			0
$880$		0			0
$881$	−4.97791			−0.167710			−0.0838550	−	0.996478i	$-0.526723\pi$
$881$	−4.97791			−0.167710			−0.0838550	+	0.996478i	$0.526723\pi$
$882$		0			0
$883$			20.8600i			0.701995i	0.936376	+	0.350998i	$0.114157\pi$
$883$			20.8600i			0.701995i	−0.936376	+	0.350998i	$0.885843\pi$
$884$	18.3601	+	10.6002i	0.617515	+	0.356523i
$885$		0			0
$886$	−20.7828	−	35.9968i	−0.698211	−	1.20934i
$887$	−43.1470	−	24.9109i	−1.44873	−	0.836427i	−0.450327	−	0.892864i	$-0.648693\pi$
$887$	−43.1470	−	24.9109i	−1.44873	−	0.836427i	−0.998406	+	0.0564371i	$0.982026\pi$
$888$		0			0
$889$	9.48735	−	4.97392i	0.318195	−	0.166820i
$890$		0			0
$891$		0			0
$892$	14.3842	+	24.9142i	0.481619	+	0.834189i
$893$	−1.79039	−	3.10104i	−0.0599130	−	0.103772i
$894$		0			0
$895$		0			0
$896$	2.64356	+	0.107718i	0.0883151	+	0.00359861i
$897$		0			0
$898$	20.5973	+	11.8919i	0.687342	+	0.396837i
$899$	−2.79596	−	4.84275i	−0.0932505	−	0.161515i
$900$		0			0
$901$	−48.0069	−	27.7168i	−1.59934	−	0.923379i
$902$			20.4557i			0.681100i
$903$		0			0
$904$	18.4343			0.613115
$905$		0			0
$906$		0			0
$907$	−31.3149	+	18.0797i	−1.03980	+	0.600326i	−0.919775	−	0.392445i	$-0.871629\pi$
$907$	−31.3149	+	18.0797i	−1.03980	+	0.600326i	−0.120020	+	0.992771i	$0.538296\pi$
$908$	1.82186	+	1.05185i	0.0604607	+	0.0349070i
$909$		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
$913$	−0.202138	−	0.350114i	−0.00668980	−	0.0115871i
$914$	−16.2595	+	9.38745i	−0.537818	+	0.310509i
$915$		0			0
$916$		−	16.1968i		−	0.535158i
$917$	37.7568	+	1.53849i	1.24684	+	0.0508054i
$918$		0			0
$919$	0.696500	−	1.20637i	0.0229754	−	0.0397946i	−0.854309	−	0.519765i	$-0.826019\pi$
$919$	0.696500	−	1.20637i	0.0229754	−	0.0397946i	0.877285	+	0.479971i	$0.159353\pi$
$920$		0			0
$921$		0			0
$922$	−8.73312	+	15.1262i	−0.287610	+	0.498155i
$923$			9.42038i			0.310076i
$924$		0			0
$925$		0			0
$926$	−2.59240	−	1.49672i	−0.0851916	−	0.0491854i
$927$		0			0
$928$	2.21130	−	1.27670i	0.0725896	−	0.0419096i
$929$	−16.5276	+	28.6266i	−0.542252	+	0.939208i	0.456522	+	0.889712i	$0.349095\pi$
$929$	−16.5276	+	28.6266i	−0.542252	+	0.939208i	−0.998774	+	0.0494960i	$0.984238\pi$
$930$		0			0
$931$	3.58901	−	1.69907i	0.117625	−	0.0556847i
$932$	8.01137			0.262421
$933$		0			0
$934$	−22.0058	+	12.7050i	−0.720051	+	0.415722i
$935$		0			0
$936$		0			0
$937$	2.53551			0.0828314			0.0414157	−	0.999142i	$-0.486813\pi$
$937$	2.53551			0.0828314			0.0414157	+	0.999142i	$0.486813\pi$
$938$	−9.37967	+	4.91747i	−0.306257	+	0.160561i
$939$		0			0
$940$		0			0
$941$	18.8858	+	32.7112i	0.615659	+	1.06635i	0.990268	+	0.139171i	$0.0444436\pi$
$941$	18.8858	+	32.7112i	0.615659	+	1.06635i	−0.374609	+	0.927183i	$0.622223\pi$
$942$		0			0
$943$	−25.3001	+	43.8210i	−0.823884	+	1.42701i
$944$	−3.35478			−0.109189
$945$		0			0
$946$	15.4915			0.503672
$947$	−28.2981	+	49.0138i	−0.919566	+	1.59274i	−0.119491	+	0.992835i	$0.538126\pi$
$947$	−28.2981	+	49.0138i	−0.919566	+	1.59274i	−0.800075	+	0.599900i	$0.795207\pi$
$948$		0			0
$949$	19.0898	+	33.0645i	0.619682	+	1.07332i
$950$		0			0
$951$		0			0
$952$	−10.1989	−	6.45578i	−0.330548	−	0.209233i
$953$	−34.3234			−1.11184			−0.555922	−	0.831234i	$-0.687635\pi$
$953$	−34.3234			−1.11184			−0.555922	+	0.831234i	$0.687635\pi$
$954$		0			0
$955$		0			0
$956$	−13.5302	+	7.81165i	−0.437597	+	0.252647i
$957$		0			0
$958$	−23.7032			−0.765816
$959$	−7.39855	+	11.6883i	−0.238912	+	0.377434i
$960$		0			0
$961$	−13.1020	+	22.6933i	−0.422644	+	0.732041i
$962$	37.2945	−	21.5320i	1.20242	−	0.694219i
$963$		0			0
$964$	3.54491	+	2.04665i	0.114174	+	0.0659183i
$965$		0			0
$966$		0			0
$967$			0.903990i			0.0290703i	0.999894	+	0.0145352i	$0.00462685\pi$
$967$			0.903990i			0.0290703i	−0.999894	+	0.0145352i	$0.995373\pi$
$968$	−2.72599	+	4.72156i	−0.0876167	+	0.151757i
$969$		0			0
$970$		0			0
$971$	21.2293	−	36.7703i	0.681282	−	1.18001i	−0.293308	−	0.956018i	$-0.594756\pi$
$971$	21.2293	−	36.7703i	0.681282	−	1.18001i	0.974590	−	0.223997i	$-0.0719105\pi$
$972$		0			0
$973$	45.6290	−	23.9219i	1.46280	−	0.766901i
$974$		−	10.2154i		−	0.327324i
$975$		0			0
$976$	6.85523	−	3.95787i	0.219431	−	0.126688i
$977$	−3.07196	−	5.32079i	−0.0982807	−	0.170227i	0.812692	−	0.582693i	$-0.198001\pi$
$977$	−3.07196	−	5.32079i	−0.0982807	−	0.170227i	−0.910973	+	0.412466i	$0.864668\pi$
$978$		0			0
$979$		−	12.8577i		−	0.410933i
$980$		0			0
$981$		0			0
$982$	−1.95643	−	1.12955i	−0.0624323	−	0.0360453i
$983$	34.2830	−	19.7933i	1.09346	−	0.631309i	0.158964	−	0.987284i	$-0.449185\pi$
$983$	34.2830	−	19.7933i	1.09346	−	0.631309i	0.934495	+	0.355976i	$0.115851\pi$
$984$		0			0
$985$		0			0
$986$	−11.6490			−0.370981
$987$		0			0
$988$		−	2.63608i		−	0.0838648i
$989$	33.1865	+	19.1602i	1.05527	+	0.609260i
$990$		0			0
$991$	19.4602	+	33.7060i	0.618172	+	1.07071i	0.989819	+	0.142331i	$0.0454599\pi$
$991$	19.4602	+	33.7060i	0.618172	+	1.07071i	−0.371647	+	0.928374i	$0.621207\pi$
$992$	1.89659	+	1.09500i	0.0602168	+	0.0347662i
$993$		0			0
$994$	0.218366	−	5.35903i	0.00692616	−	0.169978i
$995$		0			0
$996$		0			0
$997$	−10.7111	−	18.5522i	−0.339225	−	0.587555i	0.645062	−	0.764130i	$-0.276832\pi$
$997$	−10.7111	−	18.5522i	−0.339225	−	0.587555i	−0.984287	+	0.176575i	$0.943498\pi$
$998$	17.6811	+	30.6246i	0.559687	+	0.969406i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bp.g.1349.5		24
3.2	odd	2		3150.2.bp.h.1349.5		24
5.2	odd	4		3150.2.bf.d.1601.2	yes	24
5.3	odd	4		3150.2.bf.e.1601.11	yes	24
5.4	even	2		3150.2.bp.h.1349.8		24
7.3	odd	6	inner	3150.2.bp.g.899.8		24
15.2	even	4		3150.2.bf.d.1601.11	yes	24
15.8	even	4		3150.2.bf.e.1601.2	yes	24
15.14	odd	2	inner	3150.2.bp.g.1349.8		24
21.17	even	6		3150.2.bp.h.899.8		24
35.3	even	12		3150.2.bf.e.1151.2	yes	24
35.17	even	12		3150.2.bf.d.1151.11	yes	24
35.24	odd	6		3150.2.bp.h.899.5		24
105.17	odd	12		3150.2.bf.d.1151.2	✓	24
105.38	odd	12		3150.2.bf.e.1151.11	yes	24
105.59	even	6	inner	3150.2.bp.g.899.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.2	✓	24	105.17	odd	12
3150.2.bf.d.1151.11	yes	24	35.17	even	12
3150.2.bf.d.1601.2	yes	24	5.2	odd	4
3150.2.bf.d.1601.11	yes	24	15.2	even	4
3150.2.bf.e.1151.2	yes	24	35.3	even	12
3150.2.bf.e.1151.11	yes	24	105.38	odd	12
3150.2.bf.e.1601.2	yes	24	15.8	even	4
3150.2.bf.e.1601.11	yes	24	5.3	odd	4
3150.2.bp.g.899.5		24	105.59	even	6	inner
3150.2.bp.g.899.8		24	7.3	odd	6	inner
3150.2.bp.g.1349.5		24	1.1	even	1	trivial
3150.2.bp.g.1349.8		24	15.14	odd	2	inner
3150.2.bp.h.899.5		24	35.24	odd	6
3150.2.bp.h.899.8		24	21.17	even	6
3150.2.bp.h.1349.5		24	3.2	odd	2
3150.2.bp.h.1349.8		24	5.4	even	2

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)

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more