LMFDB - Embedded newform 3150.2.bf.e.1601.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1601.12
Character	$\chi$	$=$	3150.1601
Dual form			3150.2.bf.e.1151.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.52781 + 2.16005i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.52781 + 2.16005i) q^{7} +1.00000i q^{8} +(-4.29783 + 2.48135i) q^{11} -5.49388i q^{13} +(0.243099 + 2.63456i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.53712 + 2.66237i) q^{17} +(-2.68622 - 1.55089i) q^{19} -4.96270 q^{22} +(5.34875 + 3.08810i) q^{23} +(2.74694 - 4.75784i) q^{26} +(-1.10675 + 2.40314i) q^{28} +6.67885i q^{29} +(-1.01653 + 0.586893i) q^{31} +(-0.866025 + 0.500000i) q^{32} +3.07424i q^{34} +(-5.35400 + 9.27339i) q^{37} +(-1.55089 - 2.68622i) q^{38} +8.39427 q^{41} -8.81025 q^{43} +(-4.29783 - 2.48135i) q^{44} +(3.08810 + 5.34875i) q^{46} +(-2.07312 + 3.59075i) q^{47} +(-2.33160 + 6.60028i) q^{49} +(4.75784 - 2.74694i) q^{52} +(-3.85443 + 2.22536i) q^{53} +(-2.16005 + 1.52781i) q^{56} +(-3.33943 + 5.78405i) q^{58} +(-3.00381 - 5.20275i) q^{59} +(9.05018 + 5.22512i) q^{61} -1.17379 q^{62} -1.00000 q^{64} +(-5.97727 - 10.3529i) q^{67} +(-1.53712 + 2.66237i) q^{68} +0.973522i q^{71} +(-14.4612 + 8.34916i) q^{73} +(-9.27339 + 5.35400i) q^{74} -3.10178i q^{76} +(-11.9261 - 5.49247i) q^{77} +(2.12328 - 3.67763i) q^{79} +(7.26965 + 4.19713i) q^{82} +14.2841 q^{83} +(-7.62990 - 4.40513i) q^{86} +(-2.48135 - 4.29783i) q^{88} +(-7.38517 + 12.7915i) q^{89} +(11.8670 - 8.39360i) q^{91} +6.17620i q^{92} +(-3.59075 + 2.07312i) q^{94} +4.41643i q^{97} +(-5.31936 + 4.55021i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 4 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 4 * q^7	$ 24 q + 12 q^{4} + 4 q^{7} - 12 q^{16} + 12 q^{19} - 4 q^{28} - 28 q^{37} - 96 q^{43} - 8 q^{46} - 52 q^{49} + 12 q^{52} - 8 q^{58} - 12 q^{61} - 24 q^{64} + 4 q^{67} + 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 + 4 * q^7 - 12 * q^16 + 12 * q^19 - 4 * q^28 - 28 * q^37 - 96 * q^43 - 8 * q^46 - 52 * q^49 + 12 * q^52 - 8 * q^58 - 12 * q^61 - 24 * q^64 + 4 * q^67 + 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.52781	+	2.16005i	0.577458	+	0.816421i
$7$	1.52781	+	2.16005i	0.577458	+	0.816421i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	−4.29783	+	2.48135i	−1.29584	+	0.748156i	−0.979683	−	0.200550i	$-0.935727\pi$
$11$	−4.29783	+	2.48135i	−1.29584	+	0.748156i	−0.316160	+	0.948706i	$0.602394\pi$
$12$		0			0
$13$		−	5.49388i		−	1.52373i	−0.647737	−	0.761864i	$-0.724285\pi$
$13$		−	5.49388i		−	1.52373i	0.647737	−	0.761864i	$-0.275715\pi$
$14$	0.243099	+	2.63456i	0.0649709	+	0.704116i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.53712	+	2.66237i	0.372806	+	0.645719i	0.989996	−	0.141095i	$-0.0450623\pi$
$17$	1.53712	+	2.66237i	0.372806	+	0.645719i	−0.617190	+	0.786814i	$0.711729\pi$
$18$		0			0
$19$	−2.68622	−	1.55089i	−0.616261	−	0.355798i	0.159151	−	0.987254i	$-0.449124\pi$
$19$	−2.68622	−	1.55089i	−0.616261	−	0.355798i	−0.775412	+	0.631456i	$0.782458\pi$
$20$		0			0
$21$		0			0
$22$	−4.96270			−1.05805
$23$	5.34875	+	3.08810i	1.11529	+	0.643914i	0.940195	−	0.340638i	$-0.110643\pi$
$23$	5.34875	+	3.08810i	1.11529	+	0.643914i	0.175097	+	0.984551i	$0.443976\pi$
$24$		0			0
$25$		0			0
$26$	2.74694	−	4.75784i	0.538719	−	0.933089i
$27$		0			0
$28$	−1.10675	+	2.40314i	−0.209156	+	0.454152i
$29$			6.67885i			1.24023i	0.784510	+	0.620116i	$0.212914\pi$
$29$			6.67885i			1.24023i	−0.784510	+	0.620116i	$0.787086\pi$
$30$		0			0
$31$	−1.01653	+	0.586893i	−0.182574	+	0.105409i	−0.588501	−	0.808496i	$-0.700282\pi$
$31$	−1.01653	+	0.586893i	−0.182574	+	0.105409i	0.405928	+	0.913905i	$0.366949\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			3.07424i			0.527228i
$35$		0			0
$36$		0			0
$37$	−5.35400	+	9.27339i	−0.880192	+	1.52454i	−0.0290640	+	0.999578i	$0.509253\pi$
$37$	−5.35400	+	9.27339i	−0.880192	+	1.52454i	−0.851128	+	0.524959i	$0.824081\pi$
$38$	−1.55089	−	2.68622i	−0.251587	−	0.435762i
$39$		0			0
$40$		0			0
$41$	8.39427			1.31096			0.655482	−	0.755211i	$-0.272466\pi$
$41$	8.39427			1.31096			0.655482	+	0.755211i	$0.272466\pi$
$42$		0			0
$43$	−8.81025			−1.34355			−0.671776	−	0.740755i	$-0.734468\pi$
$43$	−8.81025			−1.34355			−0.671776	+	0.740755i	$0.734468\pi$
$44$	−4.29783	−	2.48135i	−0.647922	−	0.374078i
$45$		0			0
$46$	3.08810	+	5.34875i	0.455316	+	0.788630i
$47$	−2.07312	+	3.59075i	−0.302396	+	0.523765i	−0.976678	−	0.214709i	$-0.931120\pi$
$47$	−2.07312	+	3.59075i	−0.302396	+	0.523765i	0.674282	+	0.738474i	$0.264453\pi$
$48$		0			0
$49$	−2.33160	+	6.60028i	−0.333085	+	0.942897i
$50$		0			0
$51$		0			0
$52$	4.75784	−	2.74694i	0.659793	−	0.380932i
$53$	−3.85443	+	2.22536i	−0.529446	+	0.305676i	−0.740791	−	0.671736i	$-0.765549\pi$
$53$	−3.85443	+	2.22536i	−0.529446	+	0.305676i	0.211345	+	0.977412i	$0.432216\pi$
$54$		0			0
$55$		0			0
$56$	−2.16005	+	1.52781i	−0.288648	+	0.204162i
$57$		0			0
$58$	−3.33943	+	5.78405i	−0.438488	+	0.759484i
$59$	−3.00381	−	5.20275i	−0.391062	−	0.677340i	0.601528	−	0.798852i	$-0.294559\pi$
$59$	−3.00381	−	5.20275i	−0.391062	−	0.677340i	−0.992590	+	0.121512i	$0.961226\pi$
$60$		0			0
$61$	9.05018	+	5.22512i	1.15876	+	0.669008i	0.951006	−	0.309173i	$-0.100052\pi$
$61$	9.05018	+	5.22512i	1.15876	+	0.669008i	0.207751	+	0.978182i	$0.433386\pi$
$62$	−1.17379			−0.149071
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−5.97727	−	10.3529i	−0.730240	−	1.26481i	−0.956780	−	0.290811i	$-0.906075\pi$
$67$	−5.97727	−	10.3529i	−0.730240	−	1.26481i	0.226540	−	0.974002i	$-0.427259\pi$
$68$	−1.53712	+	2.66237i	−0.186403	+	0.322860i
$69$		0			0
$70$		0			0
$71$			0.973522i			0.115536i	0.998330	+	0.0577679i	$0.0183983\pi$
$71$			0.973522i			0.115536i	−0.998330	+	0.0577679i	$0.981602\pi$
$72$		0			0
$73$	−14.4612	+	8.34916i	−1.69255	+	0.977196i	−0.740106	+	0.672490i	$0.765225\pi$
$73$	−14.4612	+	8.34916i	−1.69255	+	0.977196i	−0.952446	+	0.304706i	$0.901442\pi$
$74$	−9.27339	+	5.35400i	−1.07801	+	0.622389i
$75$		0			0
$76$		−	3.10178i		−	0.355798i
$77$	−11.9261	−	5.49247i	−1.35910	−	0.625925i
$78$		0			0
$79$	2.12328	−	3.67763i	0.238887	−	0.413765i	−0.721508	−	0.692406i	$-0.756551\pi$
$79$	2.12328	−	3.67763i	0.238887	−	0.413765i	0.960395	+	0.278641i	$0.0898840\pi$
$80$		0			0
$81$		0			0
$82$	7.26965	+	4.19713i	0.802798	+	0.463496i
$83$	14.2841			1.56789			0.783944	−	0.620831i	$-0.213205\pi$
$83$	14.2841			1.56789			0.783944	+	0.620831i	$0.213205\pi$
$84$		0			0
$85$		0			0
$86$	−7.62990	−	4.40513i	−0.822754	−	0.475017i
$87$		0			0
$88$	−2.48135	−	4.29783i	−0.264513	−	0.458150i
$89$	−7.38517	+	12.7915i	−0.782826	+	1.35590i	0.147463	+	0.989068i	$0.452889\pi$
$89$	−7.38517	+	12.7915i	−0.782826	+	1.35590i	−0.930289	+	0.366827i	$0.880444\pi$
$90$		0			0
$91$	11.8670	−	8.39360i	1.24400	−	0.879888i
$92$			6.17620i			0.643914i
$93$		0			0
$94$	−3.59075	+	2.07312i	−0.370358	+	0.213826i
$95$		0			0
$96$		0			0
$97$			4.41643i			0.448420i	0.974541	+	0.224210i	$0.0719802\pi$
$97$			4.41643i			0.448420i	−0.974541	+	0.224210i	$0.928020\pi$
$98$	−5.31936	+	4.55021i	−0.537336	+	0.459641i
$99$		0			0
$100$		0			0
$101$	−5.19825	−	9.00364i	−0.517245	−	0.895895i	−0.999799	−	0.0200290i	$-0.993624\pi$
$101$	−5.19825	−	9.00364i	−0.517245	−	0.895895i	0.482554	−	0.875866i	$-0.339709\pi$
$102$		0			0
$103$	−8.86709	−	5.11942i	−0.873701	−	0.504431i	−0.00512447	−	0.999987i	$-0.501631\pi$
$103$	−8.86709	−	5.11942i	−0.873701	−	0.504431i	−0.868576	+	0.495556i	$0.834965\pi$
$104$	5.49388			0.538719
$105$		0			0
$106$	−4.45071			−0.432291
$107$	5.69797	+	3.28972i	0.550844	+	0.318030i	0.749462	−	0.662047i	$-0.230312\pi$
$107$	5.69797	+	3.28972i	0.550844	+	0.318030i	−0.198619	+	0.980077i	$0.563645\pi$
$108$		0			0
$109$	−1.34219	−	2.32474i	−0.128558	−	0.222669i	0.794560	−	0.607186i	$-0.207702\pi$
$109$	−1.34219	−	2.32474i	−0.128558	−	0.222669i	−0.923118	+	0.384516i	$0.874368\pi$
$110$		0			0
$111$		0			0
$112$	−2.63456	+	0.243099i	−0.248942	+	0.0229707i
$113$			3.55031i			0.333985i	0.985958	+	0.166992i	$0.0534056\pi$
$113$			3.55031i			0.333985i	−0.985958	+	0.166992i	$0.946594\pi$
$114$		0			0
$115$		0			0
$116$	−5.78405	+	3.33943i	−0.537036	+	0.310058i
$117$		0			0
$118$		−	6.00761i		−	0.553046i
$119$	−3.40241	+	7.38784i	−0.311899	+	0.677242i
$120$		0			0
$121$	6.81421	−	11.8026i	0.619474	−	1.07296i
$122$	5.22512	+	9.05018i	0.473060	+	0.819365i
$123$		0			0
$124$	−1.01653	−	0.586893i	−0.0912869	−	0.0527045i
$125$		0			0
$126$		0			0
$127$	5.51567			0.489437			0.244719	−	0.969594i	$-0.421304\pi$
$127$	5.51567			0.489437			0.244719	+	0.969594i	$0.421304\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	10.3068	−	17.8519i	0.900510	−	1.55973i	0.0736773	−	0.997282i	$-0.476527\pi$
$131$	10.3068	−	17.8519i	0.900510	−	1.55973i	0.826833	−	0.562447i	$-0.190140\pi$
$132$		0			0
$133$	−0.754039	−	8.17182i	−0.0653835	−	0.708586i
$134$		−	11.9545i		−	1.03272i
$135$		0			0
$136$	−2.66237	+	1.53712i	−0.228296	+	0.131807i
$137$	−9.92131	+	5.72807i	−0.847635	+	0.489382i	−0.859852	−	0.510543i	$-0.829444\pi$
$137$	−9.92131	+	5.72807i	−0.847635	+	0.489382i	0.0122175	+	0.999925i	$0.496111\pi$
$138$		0			0
$139$			1.16700i			0.0989840i	0.998775	+	0.0494920i	$0.0157602\pi$
$139$			1.16700i			0.0989840i	−0.998775	+	0.0494920i	$0.984240\pi$
$140$		0			0
$141$		0			0
$142$	−0.486761	+	0.843095i	−0.0408481	+	0.0707509i
$143$	13.6322	+	23.6117i	1.13999	+	1.97451i
$144$		0			0
$145$		0			0
$146$	−16.6983			−1.38196
$147$		0			0
$148$	−10.7080			−0.880192
$149$	13.3404	+	7.70205i	1.09288	+	0.630977i	0.934343	−	0.356375i	$-0.115988\pi$
$149$	13.3404	+	7.70205i	1.09288	+	0.630977i	0.158541	+	0.987352i	$0.449321\pi$
$150$		0			0
$151$	−0.511281	−	0.885565i	−0.0416075	−	0.0720663i	0.844472	−	0.535600i	$-0.179915\pi$
$151$	−0.511281	−	0.885565i	−0.0416075	−	0.0720663i	−0.886079	+	0.463534i	$0.846581\pi$
$152$	1.55089	−	2.68622i	0.125794	−	0.217881i
$153$		0			0
$154$	−7.58207	−	10.7197i	−0.610980	−	0.863815i
$155$		0			0
$156$		0			0
$157$	−4.64699	+	2.68294i	−0.370871	+	0.214122i	−0.673839	−	0.738878i	$-0.735356\pi$
$157$	−4.64699	+	2.68294i	−0.370871	+	0.214122i	0.302968	+	0.953001i	$0.402022\pi$
$158$	3.67763	−	2.12328i	0.292576	−	0.168919i
$159$		0			0
$160$		0			0
$161$	1.50143	+	16.2716i	0.118329	+	1.28238i
$162$		0			0
$163$	5.02108	−	8.69677i	0.393282	−	0.681184i	−0.599599	−	0.800301i	$-0.704673\pi$
$163$	5.02108	−	8.69677i	0.393282	−	0.681184i	0.992880	+	0.119117i	$0.0380064\pi$
$164$	4.19713	+	7.26965i	0.327741	+	0.567664i
$165$		0			0
$166$	12.3704	+	7.14207i	0.960131	+	0.554332i
$167$	−2.46005			−0.190364			−0.0951822	−	0.995460i	$-0.530343\pi$
$167$	−2.46005			−0.190364			−0.0951822	+	0.995460i	$0.530343\pi$
$168$		0			0
$169$	−17.1827			−1.32175
$170$		0			0
$171$		0			0
$172$	−4.40513	−	7.62990i	−0.335888	−	0.581775i
$173$	−1.50042	+	2.59880i	−0.114075	+	0.197583i	−0.917410	−	0.397944i	$-0.869724\pi$
$173$	−1.50042	+	2.59880i	−0.114075	+	0.197583i	0.803335	+	0.595528i	$0.203057\pi$
$174$		0			0
$175$		0			0
$176$		−	4.96270i		−	0.374078i
$177$		0			0
$178$	−12.7915	+	7.38517i	−0.958763	+	0.553542i
$179$	−3.18036	+	1.83618i	−0.237711	+	0.137243i	−0.614124	−	0.789209i	$-0.710491\pi$
$179$	−3.18036	+	1.83618i	−0.237711	+	0.137243i	0.376413	+	0.926452i	$0.377157\pi$
$180$		0			0
$181$			6.13560i			0.456056i	0.973655	+	0.228028i	$0.0732278\pi$
$181$			6.13560i			0.456056i	−0.973655	+	0.228028i	$0.926772\pi$
$182$	14.4739	−	1.33556i	1.07288	−	0.0989980i
$183$		0			0
$184$	−3.08810	+	5.34875i	−0.227658	+	0.394315i
$185$		0			0
$186$		0			0
$187$	−13.2125	−	7.62827i	−0.966197	−	0.557834i
$188$	−4.14624			−0.302396
$189$		0			0
$190$		0			0
$191$	4.95227	+	2.85920i	0.358334	+	0.206884i	0.668350	−	0.743847i	$-0.267001\pi$
$191$	4.95227	+	2.85920i	0.358334	+	0.206884i	−0.310016	+	0.950731i	$0.600334\pi$
$192$		0			0
$193$	3.11665	+	5.39819i	0.224341	+	0.388570i	0.956122	−	0.292970i	$-0.0946437\pi$
$193$	3.11665	+	5.39819i	0.224341	+	0.388570i	−0.731780	+	0.681541i	$0.761310\pi$
$194$	−2.20821	+	3.82474i	−0.158540	+	0.274600i
$195$		0			0
$196$	−6.88181	+	1.28092i	−0.491558	+	0.0914941i
$197$		−	1.32234i		−	0.0942128i	−0.998890	−	0.0471064i	$-0.985000\pi$
$197$		−	1.32234i		−	0.0942128i	0.998890	−	0.0471064i	$-0.0150000\pi$
$198$		0			0
$199$	−8.27163	+	4.77563i	−0.586360	+	0.338535i	−0.763657	−	0.645622i	$-0.776598\pi$
$199$	−8.27163	+	4.77563i	−0.586360	+	0.338535i	0.177297	+	0.984157i	$0.443265\pi$
$200$		0			0
$201$		0			0
$202$		−	10.3965i		−	0.731495i
$203$	−14.4266	+	10.2040i	−1.01255	+	0.716181i
$204$		0			0
$205$		0			0
$206$	−5.11942	−	8.86709i	−0.356687	−	0.617800i
$207$		0			0
$208$	4.75784	+	2.74694i	0.329897	+	0.190466i
$209$	15.3932			1.06477
$210$		0			0
$211$	26.0219			1.79142			0.895711	−	0.444636i	$-0.146667\pi$
$211$	26.0219			1.79142			0.895711	+	0.444636i	$0.146667\pi$
$212$	−3.85443	−	2.22536i	−0.264723	−	0.152838i
$213$		0			0
$214$	3.28972	+	5.69797i	0.224881	+	0.389505i
$215$		0			0
$216$		0			0
$217$	−2.82078	−	1.29909i	−0.191487	−	0.0881878i
$218$		−	2.68437i		−	0.181809i
$219$		0			0
$220$		0			0
$221$	14.6267	−	8.44475i	0.983900	−	0.568055i
$222$		0			0
$223$			7.25222i			0.485644i	0.970071	+	0.242822i	$0.0780731\pi$
$223$			7.25222i			0.485644i	−0.970071	+	0.242822i	$0.921927\pi$
$224$	−2.40314	−	1.10675i	−0.160567	−	0.0739478i
$225$		0			0
$226$	−1.77515	+	3.07466i	−0.118081	+	0.204523i
$227$	−13.3604	−	23.1409i	−0.886762	−	1.53592i	−0.843680	−	0.536846i	$-0.819616\pi$
$227$	−13.3604	−	23.1409i	−0.886762	−	1.53592i	−0.0430820	−	0.999072i	$-0.513718\pi$
$228$		0			0
$229$	21.0473	+	12.1517i	1.39085	+	0.803006i	0.993409	−	0.114622i	$-0.0365658\pi$
$229$	21.0473	+	12.1517i	1.39085	+	0.803006i	0.397439	+	0.917629i	$0.369899\pi$
$230$		0			0
$231$		0			0
$232$	−6.67885			−0.438488
$233$	−8.01573	−	4.62788i	−0.525128	−	0.303183i	0.213902	−	0.976855i	$-0.431383\pi$
$233$	−8.01573	−	4.62788i	−0.525128	−	0.303183i	−0.739030	+	0.673672i	$0.764716\pi$
$234$		0			0
$235$		0			0
$236$	3.00381	−	5.20275i	0.195531	−	0.338670i
$237$		0			0
$238$	−6.64050	+	4.69685i	−0.430439	+	0.304452i
$239$		−	0.253367i		−	0.0163889i	−0.999966	−	0.00819446i	$-0.997392\pi$
$239$		−	0.253367i		−	0.0163889i	0.999966	−	0.00819446i	$-0.00260841\pi$
$240$		0			0
$241$	2.57538	−	1.48689i	0.165895	−	0.0957792i	−0.414754	−	0.909934i	$-0.636132\pi$
$241$	2.57538	−	1.48689i	0.165895	−	0.0957792i	0.580649	+	0.814154i	$0.302799\pi$
$242$	11.8026	−	6.81421i	0.758698	−	0.438034i
$243$		0			0
$244$			10.4502i			0.669008i
$245$		0			0
$246$		0			0
$247$	−8.52039	+	14.7578i	−0.542140	+	0.939013i
$248$	−0.586893	−	1.01653i	−0.0372677	−	0.0645496i
$249$		0			0
$250$		0			0
$251$	13.0800			0.825599			0.412800	−	0.910822i	$-0.364551\pi$
$251$	13.0800			0.825599			0.412800	+	0.910822i	$0.364551\pi$
$252$		0			0
$253$	−30.6507			−1.92699
$254$	4.77671	+	2.75784i	0.299718	+	0.173042i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.29797	+	10.9084i	−0.392856	+	0.680447i	−0.992825	−	0.119576i	$-0.961846\pi$
$257$	−6.29797	+	10.9084i	−0.392856	+	0.680447i	0.599969	+	0.800023i	$0.295180\pi$
$258$		0			0
$259$	−28.2108	+	2.60310i	−1.75294	+	0.161749i
$260$		0			0
$261$		0			0
$262$	17.8519	−	10.3068i	1.10290	−	0.636757i
$263$	−14.4383	+	8.33594i	−0.890302	+	0.514016i	−0.874041	−	0.485852i	$-0.838510\pi$
$263$	−14.4383	+	8.33594i	−0.890302	+	0.514016i	−0.0162609	+	0.999868i	$0.505176\pi$
$264$		0			0
$265$		0			0
$266$	3.43289	−	7.45402i	0.210484	−	0.457035i
$267$		0			0
$268$	5.97727	−	10.3529i	0.365120	−	0.632407i
$269$	10.0035	+	17.3265i	0.609923	+	1.05642i	0.991253	+	0.131978i	$0.0421328\pi$
$269$	10.0035	+	17.3265i	0.609923	+	1.05642i	−0.381330	+	0.924439i	$0.624534\pi$
$270$		0			0
$271$	−15.4684	−	8.93068i	−0.939638	−	0.542500i	−0.0497914	−	0.998760i	$-0.515856\pi$
$271$	−15.4684	−	8.93068i	−0.939638	−	0.542500i	−0.889847	+	0.456259i	$0.849189\pi$
$272$	−3.07424			−0.186403
$273$		0			0
$274$	−11.4561			−0.692091
$275$		0			0
$276$		0			0
$277$	9.07406	+	15.7167i	0.545207	+	0.944327i	0.998594	+	0.0530128i	$0.0168824\pi$
$277$	9.07406	+	15.7167i	0.545207	+	0.944327i	−0.453386	+	0.891314i	$0.649784\pi$
$278$	−0.583502	+	1.01066i	−0.0349961	+	0.0606151i
$279$		0			0
$280$		0			0
$281$			15.5129i			0.925425i	0.886508	+	0.462713i	$0.153124\pi$
$281$			15.5129i			0.925425i	−0.886508	+	0.462713i	$0.846876\pi$
$282$		0			0
$283$	15.2813	−	8.82268i	0.908381	−	0.524454i	0.0284708	−	0.999595i	$-0.490936\pi$
$283$	15.2813	−	8.82268i	0.908381	−	0.524454i	0.879910	+	0.475141i	$0.157603\pi$
$284$	−0.843095	+	0.486761i	−0.0500285	+	0.0288840i
$285$		0			0
$286$			27.2645i			1.61218i
$287$	12.8248	+	18.1320i	0.757026	+	1.07030i
$288$		0			0
$289$	3.77453	−	6.53767i	0.222031	−	0.384569i
$290$		0			0
$291$		0			0
$292$	−14.4612	−	8.34916i	−0.846276	−	0.488598i
$293$	10.4489			0.610432			0.305216	−	0.952283i	$-0.401271\pi$
$293$	10.4489			0.610432			0.305216	+	0.952283i	$0.401271\pi$
$294$		0			0
$295$		0			0
$296$	−9.27339	−	5.35400i	−0.539005	−	0.311195i
$297$		0			0
$298$	7.70205	+	13.3404i	0.446168	+	0.772786i
$299$	16.9657	−	29.3854i	0.981149	−	1.69940i
$300$		0			0
$301$	−13.4604	−	19.0306i	−0.775844	−	1.09690i
$302$		−	1.02256i		−	0.0588419i
$303$		0			0
$304$	2.68622	−	1.55089i	0.154065	−	0.0889496i
$305$		0			0
$306$		0			0
$307$		−	0.724648i		−	0.0413579i	−0.999786	−	0.0206789i	$-0.993417\pi$
$307$		−	0.724648i		−	0.0413579i	0.999786	−	0.0206789i	$-0.00658278\pi$
$308$	−1.20643	−	13.0745i	−0.0687426	−	0.744991i
$309$		0			0
$310$		0			0
$311$	14.1225	+	24.4609i	0.800813	+	1.38705i	0.919081	+	0.394068i	$0.128932\pi$
$311$	14.1225	+	24.4609i	0.800813	+	1.38705i	−0.118268	+	0.992982i	$0.537734\pi$
$312$		0			0
$313$	17.7797	+	10.2651i	1.00497	+	0.580218i	0.909714	−	0.415235i	$-0.136301\pi$
$313$	17.7797	+	10.2651i	1.00497	+	0.580218i	0.0952528	+	0.995453i	$0.469634\pi$
$314$	−5.36589			−0.302815
$315$		0			0
$316$	4.24656			0.238887
$317$	1.96890	+	1.13674i	0.110584	+	0.0638459i	0.554272	−	0.832336i	$-0.312997\pi$
$317$	1.96890	+	1.13674i	0.110584	+	0.0638459i	−0.443688	+	0.896181i	$0.646330\pi$
$318$		0			0
$319$	−16.5726	−	28.7045i	−0.927886	−	1.60715i
$320$		0			0
$321$		0			0
$322$	−6.83551	+	14.8423i	−0.380928	+	0.827130i
$323$		−	9.53560i		−	0.530575i
$324$		0			0
$325$		0			0
$326$	8.69677	−	5.02108i	0.481670	−	0.278092i
$327$		0			0
$328$			8.39427i			0.463496i
$329$	−10.9235	+	1.00795i	−0.602233	+	0.0555699i
$330$		0			0
$331$	18.0646	−	31.2889i	0.992922	−	1.71979i	0.393605	−	0.919280i	$-0.371228\pi$
$331$	18.0646	−	31.2889i	0.992922	−	1.71979i	0.599317	−	0.800512i	$-0.295439\pi$
$332$	7.14207	+	12.3704i	0.391972	+	0.678915i
$333$		0			0
$334$	−2.13047	−	1.23003i	−0.116574	−	0.0673040i
$335$		0			0
$336$		0			0
$337$	3.76361			0.205017			0.102508	−	0.994732i	$-0.467313\pi$
$337$	3.76361			0.205017			0.102508	+	0.994732i	$0.467313\pi$
$338$	−14.8806	−	8.59134i	−0.809400	−	0.467308i
$339$		0			0
$340$		0			0
$341$	2.91258	−	5.04473i	0.157725	−	0.273187i
$342$		0			0
$343$	−17.8191	+	5.04761i	−0.962143	+	0.272546i
$344$		−	8.81025i		−	0.475017i
$345$		0			0
$346$	−2.59880	+	1.50042i	−0.139713	+	0.0806631i
$347$	−3.50549	+	2.02389i	−0.188184	+	0.108648i	−0.591132	−	0.806575i	$-0.701319\pi$
$347$	−3.50549	+	2.02389i	−0.188184	+	0.108648i	0.402948	+	0.915223i	$0.367986\pi$
$348$		0			0
$349$		−	23.9364i		−	1.28129i	−0.767838	−	0.640644i	$-0.778667\pi$
$349$		−	23.9364i		−	1.28129i	0.767838	−	0.640644i	$-0.221333\pi$
$350$		0			0
$351$		0			0
$352$	2.48135	−	4.29783i	0.132256	−	0.229075i
$353$	12.7409	+	22.0679i	0.678129	+	1.17455i	0.975544	+	0.219805i	$0.0705422\pi$
$353$	12.7409	+	22.0679i	0.678129	+	1.17455i	−0.297415	+	0.954748i	$0.596124\pi$
$354$		0			0
$355$		0			0
$356$	−14.7703			−0.782826
$357$		0			0
$358$	−3.67236			−0.194091
$359$	−15.4893	−	8.94277i	−0.817496	−	0.471981i	0.0320565	−	0.999486i	$-0.489794\pi$
$359$	−15.4893	−	8.94277i	−0.817496	−	0.471981i	−0.849552	+	0.527505i	$0.823128\pi$
$360$		0			0
$361$	−4.68949	−	8.12243i	−0.246815	−	0.427496i
$362$	−3.06780	+	5.31359i	−0.161240	+	0.279276i
$363$		0			0
$364$	13.2026	+	6.08035i	0.692003	+	0.318697i
$365$		0			0
$366$		0			0
$367$	4.57004	−	2.63851i	0.238554	−	0.137729i	−0.375958	−	0.926637i	$-0.622686\pi$
$367$	4.57004	−	2.63851i	0.238554	−	0.137729i	0.614512	+	0.788907i	$0.289353\pi$
$368$	−5.34875	+	3.08810i	−0.278823	+	0.160978i
$369$		0			0
$370$		0			0
$371$	−10.6957	−	4.92582i	−0.555293	−	0.255736i
$372$		0			0
$373$	7.27390	−	12.5988i	0.376628	−	0.652339i	−0.613941	−	0.789352i	$-0.710417\pi$
$373$	7.27390	−	12.5988i	0.376628	−	0.652339i	0.990569	+	0.137013i	$0.0437501\pi$
$374$	−7.62827	−	13.2125i	−0.394448	−	0.683205i
$375$		0			0
$376$	−3.59075	−	2.07312i	−0.185179	−	0.106913i
$377$	36.6928			1.88977
$378$		0			0
$379$	3.66669			0.188345			0.0941726	−	0.995556i	$-0.469979\pi$
$379$	3.66669			0.188345			0.0941726	+	0.995556i	$0.469979\pi$
$380$		0			0
$381$		0			0
$382$	2.85920	+	4.95227i	0.146289	+	0.253380i
$383$	−9.76247	+	16.9091i	−0.498839	+	0.864015i	−0.999999	−	0.00134002i	$-0.999573\pi$
$383$	−9.76247	+	16.9091i	−0.498839	+	0.864015i	0.501160	+	0.865355i	$0.332907\pi$
$384$		0			0
$385$		0			0
$386$			6.23330i			0.317266i
$387$		0			0
$388$	−3.82474	+	2.20821i	−0.194172	+	0.112105i
$389$	14.9711	−	8.64356i	0.759064	−	0.438246i	−0.0698956	−	0.997554i	$-0.522267\pi$
$389$	14.9711	−	8.64356i	0.759064	−	0.438246i	0.828960	+	0.559309i	$0.188933\pi$
$390$		0			0
$391$			18.9871i			0.960220i
$392$	−6.60028	−	2.33160i	−0.333364	−	0.117763i
$393$		0			0
$394$	0.661170	−	1.14518i	0.0333092	−	0.0576933i
$395$		0			0
$396$		0			0
$397$	−23.9755	−	13.8423i	−1.20330	−	0.694724i	−0.242011	−	0.970274i	$-0.577807\pi$
$397$	−23.9755	−	13.8423i	−1.20330	−	0.694724i	−0.961287	+	0.275549i	$0.911140\pi$
$398$	−9.55125			−0.478761
$399$		0			0
$400$		0			0
$401$	−32.7521	−	18.9095i	−1.63556	−	0.944293i	−0.982335	−	0.187132i	$-0.940081\pi$
$401$	−32.7521	−	18.9095i	−1.63556	−	0.944293i	−0.653229	−	0.757161i	$-0.726586\pi$
$402$		0			0
$403$	3.22432	+	5.58468i	0.160615	+	0.278193i
$404$	5.19825	−	9.00364i	0.258623	−	0.447948i
$405$		0			0
$406$	−17.5958	+	1.62362i	−0.873266	+	0.0805790i
$407$		−	53.1406i		−	2.63408i
$408$		0			0
$409$	31.6028	−	18.2459i	1.56266	−	0.902202i	0.565673	−	0.824630i	$-0.308617\pi$
$409$	31.6028	−	18.2459i	1.56266	−	0.902202i	0.996987	−	0.0775719i	$-0.0247167\pi$
$410$		0			0
$411$		0			0
$412$		−	10.2388i		−	0.504431i
$413$	6.64893	−	14.4372i	0.327172	−	0.710407i
$414$		0			0
$415$		0			0
$416$	2.74694	+	4.75784i	0.134680	+	0.233272i
$417$		0			0
$418$	13.3309	+	7.69660i	0.652036	+	0.376453i
$419$	21.6669			1.05850			0.529249	−	0.848466i	$-0.322474\pi$
$419$	21.6669			1.05850			0.529249	+	0.848466i	$0.322474\pi$
$420$		0			0
$421$	−8.84193			−0.430929			−0.215465	−	0.976512i	$-0.569127\pi$
$421$	−8.84193			−0.430929			−0.215465	+	0.976512i	$0.569127\pi$
$422$	22.5356	+	13.0110i	1.09702	+	0.633363i
$423$		0			0
$424$	−2.22536	−	3.85443i	−0.108073	−	0.187188i
$425$		0			0
$426$		0			0
$427$	2.54044	+	27.5318i	0.122941	+	1.33236i
$428$			6.57945i			0.318030i
$429$		0			0
$430$		0			0
$431$	25.7481	−	14.8656i	1.24024	−	0.716053i	0.271097	−	0.962552i	$-0.412614\pi$
$431$	25.7481	−	14.8656i	1.24024	−	0.716053i	0.969143	+	0.246499i	$0.0792802\pi$
$432$		0			0
$433$		−	26.5666i		−	1.27671i	−0.769741	−	0.638356i	$-0.779615\pi$
$433$		−	26.5666i		−	1.27671i	0.769741	−	0.638356i	$-0.220385\pi$
$434$	−1.79332	−	2.53543i	−0.0860822	−	0.121705i
$435$		0			0
$436$	1.34219	−	2.32474i	0.0642791	−	0.111335i
$437$	−9.57860	−	16.5906i	−0.458207	−	0.793637i
$438$		0			0
$439$	14.4067	+	8.31774i	0.687597	+	0.396984i	0.802711	−	0.596368i	$-0.203390\pi$
$439$	14.4067	+	8.31774i	0.687597	+	0.396984i	−0.115114	+	0.993352i	$0.536723\pi$
$440$		0			0
$441$		0			0
$442$	16.8895			0.803351
$443$	2.83428	+	1.63637i	0.134661	+	0.0777464i	0.565817	−	0.824531i	$-0.308561\pi$
$443$	2.83428	+	1.63637i	0.134661	+	0.0777464i	−0.431156	+	0.902277i	$0.641894\pi$
$444$		0			0
$445$		0			0
$446$	−3.62611	+	6.28060i	−0.171701	+	0.297395i
$447$		0			0
$448$	−1.52781	−	2.16005i	−0.0721822	−	0.102053i
$449$		−	10.4322i		−	0.492324i	−0.969229	−	0.246162i	$-0.920831\pi$
$449$		−	10.4322i		−	0.492324i	0.969229	−	0.246162i	$-0.0791695\pi$
$450$		0			0
$451$	−36.0771	+	20.8291i	−1.69880	+	0.980805i
$452$	−3.07466	+	1.77515i	−0.144620	+	0.0834962i
$453$		0			0
$454$		−	26.7208i		−	1.25407i
$455$		0			0
$456$		0			0
$457$	16.5394	−	28.6471i	0.773680	−	1.34005i	−0.161853	−	0.986815i	$-0.551747\pi$
$457$	16.5394	−	28.6471i	0.773680	−	1.34005i	0.935533	−	0.353238i	$-0.114920\pi$
$458$	12.1517	+	21.0473i	0.567811	+	0.983478i
$459$		0			0
$460$		0			0
$461$	11.5639			0.538585			0.269293	−	0.963058i	$-0.413210\pi$
$461$	11.5639			0.538585			0.269293	+	0.963058i	$0.413210\pi$
$462$		0			0
$463$	38.6061			1.79418			0.897090	−	0.441848i	$-0.145677\pi$
$463$	38.6061			1.79418			0.897090	+	0.441848i	$0.145677\pi$
$464$	−5.78405	−	3.33943i	−0.268518	−	0.155029i
$465$		0			0
$466$	−4.62788	−	8.01573i	−0.214383	−	0.371322i
$467$	−2.35692	+	4.08230i	−0.109065	+	0.188906i	−0.915392	−	0.402564i	$-0.868119\pi$
$467$	−2.35692	+	4.08230i	−0.109065	+	0.188906i	0.806327	+	0.591471i	$0.201452\pi$
$468$		0			0
$469$	13.2307	−	28.7285i	0.610937	−	1.32656i
$470$		0			0
$471$		0			0
$472$	5.20275	−	3.00381i	0.239476	−	0.138261i
$473$	37.8649	−	21.8613i	1.74103	−	1.00519i
$474$		0			0
$475$		0			0
$476$	−8.09926	+	0.747344i	−0.371229	+	0.0342545i
$477$		0			0
$478$	0.126683	−	0.219422i	0.00579436	−	0.0100361i
$479$	10.0096	+	17.3371i	0.457349	+	0.792152i	0.998820	−	0.0485678i	$-0.0154657\pi$
$479$	10.0096	+	17.3371i	0.457349	+	0.792152i	−0.541471	+	0.840720i	$0.682132\pi$
$480$		0			0
$481$	50.9469	+	29.4142i	2.32298	+	1.34117i
$482$	2.97379			0.135452
$483$		0			0
$484$	13.6284			0.619474
$485$		0			0
$486$		0			0
$487$	2.36544	+	4.09706i	0.107188	+	0.185656i	0.914630	−	0.404292i	$-0.132482\pi$
$487$	2.36544	+	4.09706i	0.107188	+	0.185656i	−0.807442	+	0.589947i	$0.799149\pi$
$488$	−5.22512	+	9.05018i	−0.236530	+	0.409682i
$489$		0			0
$490$		0			0
$491$			16.0027i			0.722190i	0.932529	+	0.361095i	$0.117597\pi$
$491$			16.0027i			0.722190i	−0.932529	+	0.361095i	$0.882403\pi$
$492$		0			0
$493$	−17.7816	+	10.2662i	−0.800841	+	0.462366i
$494$	−14.7578	+	8.52039i	−0.663983	+	0.383351i
$495$		0			0
$496$		−	1.17379i		−	0.0527045i
$497$	−2.10285	+	1.48736i	−0.0943258	+	0.0667170i
$498$		0			0
$499$	−3.18097	+	5.50961i	−0.142400	+	0.246644i	−0.928400	−	0.371583i	$-0.878815\pi$
$499$	−3.18097	+	5.50961i	−0.142400	+	0.246644i	0.786000	+	0.618227i	$0.212149\pi$
$500$		0			0
$501$		0			0
$502$	11.3276	+	6.53998i	0.505574	+	0.291893i
$503$	36.3826			1.62222			0.811109	−	0.584895i	$-0.198864\pi$
$503$	36.3826			1.62222			0.811109	+	0.584895i	$0.198864\pi$
$504$		0			0
$505$		0			0
$506$	−26.5443	−	15.3253i	−1.18004	−	0.681294i
$507$		0			0
$508$	2.75784	+	4.77671i	0.122359	+	0.211932i
$509$	−8.55353	+	14.8151i	−0.379128	+	0.656670i	−0.990936	−	0.134337i	$-0.957109\pi$
$509$	−8.55353	+	14.8151i	−0.379128	+	0.656670i	0.611807	+	0.791007i	$0.290443\pi$
$510$		0			0
$511$	−40.1285	−	18.4809i	−1.77518	−	0.817546i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−10.9084	+	6.29797i	−0.481149	+	0.277791i
$515$		0			0
$516$		0			0
$517$		−	20.5766i		−	0.904956i
$518$	−25.7329	−	11.8511i	−1.13064	−	0.520706i
$519$		0			0
$520$		0			0
$521$	20.2375	+	35.0524i	0.886622	+	1.53567i	0.843843	+	0.536590i	$0.180288\pi$
$521$	20.2375	+	35.0524i	0.886622	+	1.53567i	0.0427789	+	0.999085i	$0.486379\pi$
$522$		0			0
$523$	37.8314	+	21.8420i	1.65425	+	0.955083i	0.975295	+	0.220905i	$0.0709010\pi$
$523$	37.8314	+	21.8420i	1.65425	+	0.955083i	0.678957	+	0.734178i	$0.262432\pi$
$524$	20.6136			0.900510
$525$		0			0
$526$	−16.6719			−0.726929
$527$	−3.12505	−	1.80425i	−0.136129	−	0.0785943i
$528$		0			0
$529$	7.57274	+	13.1164i	0.329250	+	0.570277i
$530$		0			0
$531$		0			0
$532$	6.69998	−	4.73893i	0.290481	−	0.205458i
$533$		−	46.1171i		−	1.99755i
$534$		0			0
$535$		0			0
$536$	10.3529	−	5.97727i	0.447179	−	0.258179i
$537$		0			0
$538$			20.0069i			0.862561i
$539$	−6.35681	−	34.1524i	−0.273807	−	1.47105i
$540$		0			0
$541$	5.85601	−	10.1429i	0.251770	−	0.436078i	−0.712243	−	0.701933i	$-0.752321\pi$
$541$	5.85601	−	10.1429i	0.251770	−	0.436078i	0.964013	+	0.265855i	$0.0856541\pi$
$542$	−8.93068	−	15.4684i	−0.383606	−	0.664425i
$543$		0			0
$544$	−2.66237	−	1.53712i	−0.114148	−	0.0659035i
$545$		0			0
$546$		0			0
$547$	−34.6501			−1.48153			−0.740765	−	0.671764i	$-0.765537\pi$
$547$	−34.6501			−1.48153			−0.740765	+	0.671764i	$0.765537\pi$
$548$	−9.92131	−	5.72807i	−0.423817	−	0.244691i
$549$		0			0
$550$		0			0
$551$	10.3582	−	17.9409i	0.441272	−	0.764306i
$552$		0			0
$553$	11.1878	−	1.03233i	0.475754	−	0.0438993i
$554$			18.1481i			0.771040i
$555$		0			0
$556$	−1.01066	+	0.583502i	−0.0428613	+	0.0247460i
$557$	−30.5822	+	17.6567i	−1.29581	+	0.748137i	−0.979678	−	0.200578i	$-0.935718\pi$
$557$	−30.5822	+	17.6567i	−1.29581	+	0.748137i	−0.316134	+	0.948715i	$0.602385\pi$
$558$		0			0
$559$			48.4025i			2.04721i
$560$		0			0
$561$		0			0
$562$	−7.75647	+	13.4346i	−0.327187	+	0.566705i
$563$	−19.3495	−	33.5143i	−0.815483	−	1.41246i	−0.908981	−	0.416839i	$-0.863138\pi$
$563$	−19.3495	−	33.5143i	−0.815483	−	1.41246i	0.0934975	−	0.995620i	$-0.470195\pi$
$564$		0			0
$565$		0			0
$566$	17.6454			0.741690
$567$		0			0
$568$	−0.973522			−0.0408481
$569$	−6.20799	−	3.58419i	−0.260253	−	0.150257i	0.364197	−	0.931322i	$-0.381343\pi$
$569$	−6.20799	−	3.58419i	−0.260253	−	0.150257i	−0.624450	+	0.781065i	$0.714677\pi$
$570$		0			0
$571$	10.7717	+	18.6571i	0.450781	+	0.780776i	0.998435	−	0.0559290i	$-0.0178121\pi$
$571$	10.7717	+	18.6571i	0.450781	+	0.780776i	−0.547653	+	0.836705i	$0.684479\pi$
$572$	−13.6322	+	23.6117i	−0.569993	+	0.987256i
$573$		0			0
$574$	2.04064	+	22.1152i	0.0851746	+	0.923070i
$575$		0			0
$576$		0			0
$577$	13.6179	−	7.86230i	0.566921	−	0.327312i	−0.188998	−	0.981978i	$-0.560524\pi$
$577$	13.6179	−	7.86230i	0.566921	−	0.327312i	0.755919	+	0.654666i	$0.227191\pi$
$578$	6.53767	−	3.77453i	0.271931	−	0.157000i
$579$		0			0
$580$		0			0
$581$	21.8234	+	30.8544i	0.905389	+	1.28006i
$582$		0			0
$583$	11.0438	−	19.1284i	0.457387	−	0.792217i
$584$	−8.34916	−	14.4612i	−0.345491	−	0.598408i
$585$		0			0
$586$	9.04902	+	5.22446i	0.373812	+	0.215820i
$587$	4.59252			0.189554			0.0947769	−	0.995499i	$-0.469786\pi$
$587$	4.59252			0.189554			0.0947769	+	0.995499i	$0.469786\pi$
$588$		0			0
$589$	3.64082			0.150017
$590$		0			0
$591$		0			0
$592$	−5.35400	−	9.27339i	−0.220048	−	0.381134i
$593$	−1.91286	+	3.31317i	−0.0785516	+	0.136055i	−0.902625	−	0.430427i	$-0.858363\pi$
$593$	−1.91286	+	3.31317i	−0.0785516	+	0.136055i	0.824074	+	0.566483i	$0.191696\pi$
$594$		0			0
$595$		0			0
$596$			15.4041i			0.630977i
$597$		0			0
$598$	29.3854	−	16.9657i	1.20166	−	0.693777i
$599$	13.6589	−	7.88600i	0.558089	−	0.322213i	−0.194289	−	0.980944i	$-0.562240\pi$
$599$	13.6589	−	7.88600i	0.558089	−	0.322213i	0.752378	+	0.658731i	$0.228907\pi$
$600$		0			0
$601$			1.39673i			0.0569740i	0.999594	+	0.0284870i	$0.00906892\pi$
$601$			1.39673i			0.0569740i	−0.999594	+	0.0284870i	$0.990931\pi$
$602$	−2.14176	−	23.2111i	−0.0872918	−	0.946015i
$603$		0			0
$604$	0.511281	−	0.885565i	0.0208037	−	0.0360331i
$605$		0			0
$606$		0			0
$607$	8.94920	+	5.16682i	0.363237	+	0.209715i	0.670500	−	0.741910i	$-0.266080\pi$
$607$	8.94920	+	5.16682i	0.363237	+	0.209715i	−0.307263	+	0.951625i	$0.599413\pi$
$608$	3.10178			0.125794
$609$		0			0
$610$		0			0
$611$	19.7271	+	11.3895i	0.798075	+	0.460769i
$612$		0			0
$613$	6.14772	+	10.6482i	0.248304	+	0.430075i	0.963055	−	0.269303i	$-0.0867934\pi$
$613$	6.14772	+	10.6482i	0.248304	+	0.430075i	−0.714751	+	0.699379i	$0.753460\pi$
$614$	0.362324	−	0.627564i	0.0146222	−	0.0253264i
$615$		0			0
$616$	5.49247	−	11.9261i	0.221298	−	0.480516i
$617$			8.10935i			0.326470i	0.986587	+	0.163235i	$0.0521929\pi$
$617$			8.10935i			0.326470i	−0.986587	+	0.163235i	$0.947807\pi$
$618$		0			0
$619$	7.03506	−	4.06170i	0.282763	−	0.163253i	−0.351911	−	0.936034i	$-0.614468\pi$
$619$	7.03506	−	4.06170i	0.282763	−	0.163253i	0.634674	+	0.772780i	$0.281135\pi$
$620$		0			0
$621$		0			0
$622$			28.2450i			1.13252i
$623$	−38.9133	+	3.59065i	−1.55903	+	0.143857i
$624$		0			0
$625$		0			0
$626$	10.2651	+	17.7797i	0.410276	+	0.710619i
$627$		0			0
$628$	−4.64699	−	2.68294i	−0.185435	−	0.107061i
$629$	−32.9189			−1.31256
$630$		0			0
$631$	−40.6011			−1.61630			−0.808151	−	0.588975i	$-0.799532\pi$
$631$	−40.6011			−1.61630			−0.808151	+	0.588975i	$0.799532\pi$
$632$	3.67763	+	2.12328i	0.146288	+	0.0844595i
$633$		0			0
$634$	1.13674	+	1.96890i	0.0451459	+	0.0781950i
$635$		0			0
$636$		0			0
$637$	36.2611	+	12.8095i	1.43672	+	0.507531i
$638$		−	33.1452i		−	1.31223i
$639$		0			0
$640$		0			0
$641$	−32.0260	+	18.4902i	−1.26495	+	0.730319i	−0.974028	−	0.226427i	$-0.927295\pi$
$641$	−32.0260	+	18.4902i	−1.26495	+	0.730319i	−0.290922	+	0.956747i	$0.593962\pi$
$642$		0			0
$643$		−	4.86696i		−	0.191934i	−0.995385	−	0.0959671i	$-0.969406\pi$
$643$		−	4.86696i		−	0.191934i	0.995385	−	0.0959671i	$-0.0305944\pi$
$644$	−13.3409	+	9.43606i	−0.525704	+	0.371833i
$645$		0			0
$646$	4.76780	−	8.25808i	0.187587	−	0.324910i
$647$	−12.4833	−	21.6217i	−0.490769	−	0.850037i	0.509175	−	0.860663i	$-0.329951\pi$
$647$	−12.4833	−	21.6217i	−0.490769	−	0.850037i	−0.999944	+	0.0106266i	$0.996617\pi$
$648$		0			0
$649$	25.8197	+	14.9070i	1.01351	+	0.585151i
$650$		0			0
$651$		0			0
$652$	10.0422			0.393282
$653$	−12.6352	−	7.29496i	−0.494455	−	0.285474i	0.231966	−	0.972724i	$-0.425484\pi$
$653$	−12.6352	−	7.29496i	−0.494455	−	0.285474i	−0.726421	+	0.687250i	$0.758818\pi$
$654$		0			0
$655$		0			0
$656$	−4.19713	+	7.26965i	−0.163870	+	0.283832i
$657$		0			0
$658$	−9.96402	−	4.58885i	−0.388438	−	0.178892i
$659$		−	33.8468i		−	1.31848i	−0.751931	−	0.659242i	$-0.770877\pi$
$659$		−	33.8468i		−	1.31848i	0.751931	−	0.659242i	$-0.229123\pi$
$660$		0			0
$661$	−14.9053	+	8.60557i	−0.579749	+	0.334718i	−0.761034	−	0.648713i	$-0.775308\pi$
$661$	−14.9053	+	8.60557i	−0.579749	+	0.334718i	0.181285	+	0.983431i	$0.441974\pi$
$662$	31.2889	−	18.0646i	1.21608	−	0.702102i
$663$		0			0
$664$			14.2841i			0.554332i
$665$		0			0
$666$		0			0
$667$	−20.6250	+	35.7235i	−0.798602	+	1.38322i
$668$	−1.23003	−	2.13047i	−0.0475911	−	0.0824302i
$669$		0			0
$670$		0			0
$671$	−51.8615			−2.00209
$672$		0			0
$673$	1.47971			0.0570387			0.0285193	−	0.999593i	$-0.490921\pi$
$673$	1.47971			0.0570387			0.0285193	+	0.999593i	$0.490921\pi$
$674$	3.25938	+	1.88181i	0.125547	+	0.0724844i
$675$		0			0
$676$	−8.59134	−	14.8806i	−0.330436	−	0.572333i
$677$	−5.92549	+	10.2632i	−0.227735	+	0.394448i	−0.957136	−	0.289637i	$-0.906465\pi$
$677$	−5.92549	+	10.2632i	−0.227735	+	0.394448i	0.729402	+	0.684086i	$0.239799\pi$
$678$		0			0
$679$	−9.53968	+	6.74746i	−0.366099	+	0.258944i
$680$		0			0
$681$		0			0
$682$	5.04473	−	2.91258i	0.193173	−	0.111528i
$683$	−9.11732	+	5.26389i	−0.348865	+	0.201417i	−0.664185	−	0.747568i	$-0.731221\pi$
$683$	−9.11732	+	5.26389i	−0.348865	+	0.201417i	0.315320	+	0.948985i	$0.397888\pi$
$684$		0			0
$685$		0			0
$686$	−17.9556	−	4.53821i	−0.685549	−	0.173270i
$687$		0			0
$688$	4.40513	−	7.62990i	0.167944	−	0.290887i
$689$	12.2258	+	21.1758i	0.465767	+	0.806732i
$690$		0			0
$691$	6.61628	+	3.81991i	0.251695	+	0.145316i	0.620540	−	0.784175i	$-0.286913\pi$
$691$	6.61628	+	3.81991i	0.251695	+	0.145316i	−0.368845	+	0.929491i	$0.620247\pi$
$692$	−3.00084			−0.114075
$693$		0			0
$694$	−4.04779			−0.153652
$695$		0			0
$696$		0			0
$697$	12.9030	+	22.3486i	0.488736	+	0.846515i
$698$	11.9682	−	20.7296i	0.453004	−	0.784626i
$699$		0			0
$700$		0			0
$701$			35.2007i			1.32951i	0.747060	+	0.664757i	$0.231465\pi$
$701$			35.2007i			1.32951i	−0.747060	+	0.664757i	$0.768535\pi$
$702$		0			0
$703$	28.7640	−	16.6069i	1.08485	−	0.626341i
$704$	4.29783	−	2.48135i	0.161980	−	0.0935195i
$705$		0			0
$706$			25.4818i			0.959019i
$707$	11.5063	−	24.9843i	0.432740	−	0.939631i
$708$		0			0
$709$	18.1846	−	31.4966i	0.682936	−	1.18288i	−0.291145	−	0.956679i	$-0.594036\pi$
$709$	18.1846	−	31.4966i	0.682936	−	1.18288i	0.974081	−	0.226201i	$-0.0726306\pi$
$710$		0			0
$711$		0			0
$712$	−12.7915	−	7.38517i	−0.479381	−	0.276771i
$713$	−7.24954			−0.271497
$714$		0			0
$715$		0			0
$716$	−3.18036	−	1.83618i	−0.118856	−	0.0686214i
$717$		0			0
$718$	−8.94277	−	15.4893i	−0.333741	−	0.578057i
$719$	−0.772550	+	1.33810i	−0.0288113	+	0.0499026i	−0.880072	−	0.474841i	$-0.842506\pi$
$719$	−0.772550	+	1.33810i	−0.0288113	+	0.0499026i	0.851260	+	0.524744i	$0.175839\pi$
$720$		0			0
$721$	−2.48905	−	26.9748i	−0.0926971	−	1.00460i
$722$		−	9.37898i		−	0.349049i
$723$		0			0
$724$	−5.31359	+	3.06780i	−0.197478	+	0.114014i
$725$		0			0
$726$		0			0
$727$		−	34.1857i		−	1.26788i	−0.773383	−	0.633939i	$-0.781437\pi$
$727$		−	34.1857i		−	1.26788i	0.773383	−	0.633939i	$-0.218563\pi$
$728$	8.39360	+	11.8670i	0.311087	+	0.439821i
$729$		0			0
$730$		0			0
$731$	−13.5424	−	23.4561i	−0.500884	−	0.867557i
$732$		0			0
$733$	37.9485	+	21.9095i	1.40166	+	0.809248i	0.994563	−	0.104138i	$-0.0332084\pi$
$733$	37.9485	+	21.9095i	1.40166	+	0.809248i	0.407095	+	0.913386i	$0.366542\pi$
$734$	5.27703			0.194779
$735$		0			0
$736$	−6.17620			−0.227658
$737$	51.3786	+	29.6634i	1.89255	+	1.09267i
$738$		0			0
$739$	6.86403	+	11.8888i	0.252497	+	0.437338i	0.964213	−	0.265130i	$-0.0854148\pi$
$739$	6.86403	+	11.8888i	0.252497	+	0.437338i	−0.711715	+	0.702468i	$0.752081\pi$
$740$		0			0
$741$		0			0
$742$	−6.79984	−	9.61374i	−0.249630	−	0.352931i
$743$			20.8393i			0.764520i	0.924055	+	0.382260i	$0.124854\pi$
$743$			20.8393i			0.764520i	−0.924055	+	0.382260i	$0.875146\pi$
$744$		0			0
$745$		0			0
$746$	12.5988	−	7.27390i	0.461274	−	0.266316i
$747$		0			0
$748$		−	15.2565i		−	0.557834i
$749$	1.59946	+	17.3339i	0.0584429	+	0.633369i
$750$		0			0
$751$	21.8346	−	37.8186i	0.796755	−	1.38002i	−0.124964	−	0.992161i	$-0.539881\pi$
$751$	21.8346	−	37.8186i	0.796755	−	1.38002i	0.921719	−	0.387859i	$-0.126785\pi$
$752$	−2.07312	−	3.59075i	−0.0755989	−	0.130941i
$753$		0			0
$754$	31.7769	+	18.3464i	1.15725	+	0.668136i
$755$		0			0
$756$		0			0
$757$	40.4115			1.46878			0.734391	−	0.678727i	$-0.237468\pi$
$757$	40.4115			1.46878			0.734391	+	0.678727i	$0.237468\pi$
$758$	3.17545	+	1.83335i	0.115337	+	0.0665901i
$759$		0			0
$760$		0			0
$761$	18.3292	−	31.7471i	0.664432	−	1.15083i	−0.315007	−	0.949089i	$-0.602007\pi$
$761$	18.3292	−	31.7471i	0.664432	−	1.15083i	0.979439	−	0.201741i	$-0.0646598\pi$
$762$		0			0
$763$	2.97093	−	6.45094i	0.107555	−	0.233540i
$764$			5.71839i			0.206884i
$765$		0			0
$766$	−16.9091	+	9.76247i	−0.610951	+	0.352732i
$767$	−28.5833	+	16.5025i	−1.03208	+	0.595872i
$768$		0			0
$769$			20.4304i			0.736738i	0.929680	+	0.368369i	$0.120084\pi$
$769$			20.4304i			0.736738i	−0.929680	+	0.368369i	$0.879916\pi$
$770$		0			0
$771$		0			0
$772$	−3.11665	+	5.39819i	−0.112171	+	0.194285i
$773$	−6.84657	−	11.8586i	−0.246254	−	0.426525i	0.716229	−	0.697865i	$-0.245866\pi$
$773$	−6.84657	−	11.8586i	−0.246254	−	0.426525i	−0.962483	+	0.271340i	$0.912533\pi$
$774$		0			0
$775$		0			0
$776$	−4.41643			−0.158540
$777$		0			0
$778$	17.2871			0.619773
$779$	−22.5488	−	13.0186i	−0.807896	−	0.466439i
$780$		0			0
$781$	−2.41565	−	4.18403i	−0.0864388	−	0.149716i
$782$	−9.49356	+	16.4433i	−0.339489	+	0.588012i
$783$		0			0
$784$	−4.55021	−	5.31936i	−0.162507	−	0.189977i
$785$		0			0
$786$		0			0
$787$	11.6169	−	6.70701i	0.414097	−	0.239079i	−0.278451	−	0.960450i	$-0.589821\pi$
$787$	11.6169	−	6.70701i	0.414097	−	0.239079i	0.692549	+	0.721371i	$0.256488\pi$
$788$	1.14518	−	0.661170i	0.0407953	−	0.0235532i
$789$		0			0
$790$		0			0
$791$	−7.66883	+	5.42419i	−0.272672	+	0.192862i
$792$		0			0
$793$	28.7062	−	49.7206i	1.01939	−	1.76563i
$794$	−13.8423	−	23.9755i	−0.491244	−	0.850860i
$795$		0			0
$796$	−8.27163	−	4.77563i	−0.293180	−	0.169268i
$797$	−53.8858			−1.90873			−0.954367	−	0.298636i	$-0.903468\pi$
$797$	−53.8858			−1.90873			−0.954367	+	0.298636i	$0.903468\pi$
$798$		0			0
$799$	−12.7465			−0.450940
$800$		0			0
$801$		0			0
$802$	−18.9095	−	32.7521i	−0.667716	−	1.15652i
$803$	41.4344	−	71.7665i	1.46219	−	2.53259i
$804$		0			0
$805$		0			0
$806$			6.44864i			0.227144i
$807$		0			0
$808$	9.00364	−	5.19825i	0.316747	−	0.182874i
$809$	−10.1762	+	5.87522i	−0.357775	+	0.206562i	−0.668104	−	0.744068i	$-0.732894\pi$
$809$	−10.1762	+	5.87522i	−0.357775	+	0.206562i	0.310329	+	0.950629i	$0.399561\pi$
$810$		0			0
$811$			22.8579i			0.802649i	0.915936	+	0.401325i	$0.131450\pi$
$811$			22.8579i			0.802649i	−0.915936	+	0.401325i	$0.868550\pi$
$812$	−16.0502	−	7.39182i	−0.563253	−	0.259402i
$813$		0			0
$814$	26.5703	−	46.0211i	0.931288	−	1.61304i
$815$		0			0
$816$		0			0
$817$	23.6663	+	13.6637i	0.827978	+	0.478033i
$818$	36.4918			1.27591
$819$		0			0
$820$		0			0
$821$	−9.58876	−	5.53607i	−0.334650	−	0.193210i	0.323254	−	0.946312i	$-0.395223\pi$
$821$	−9.58876	−	5.53607i	−0.334650	−	0.193210i	−0.657904	+	0.753102i	$0.728557\pi$
$822$		0			0
$823$	−0.353401	−	0.612108i	−0.0123188	−	0.0213368i	0.859800	−	0.510630i	$-0.170588\pi$
$823$	−0.353401	−	0.612108i	−0.0123188	−	0.0213368i	−0.872119	+	0.489294i	$0.837255\pi$
$824$	5.11942	−	8.86709i	0.178343	−	0.308900i
$825$		0			0
$826$	12.9767	−	9.17849i	0.451518	−	0.319361i
$827$			18.8230i			0.654540i	0.944931	+	0.327270i	$0.106129\pi$
$827$			18.8230i			0.654540i	−0.944931	+	0.327270i	$0.893871\pi$
$828$		0			0
$829$	−26.7423	+	15.4397i	−0.928800	+	0.536243i	−0.886432	−	0.462859i	$-0.846824\pi$
$829$	−26.7423	+	15.4397i	−0.928800	+	0.536243i	−0.0423683	+	0.999102i	$0.513490\pi$
$830$		0			0
$831$		0			0
$832$			5.49388i			0.190466i
$833$	−21.1563	+	3.93785i	−0.733023	+	0.136438i
$834$		0			0
$835$		0			0
$836$	7.69660	+	13.3309i	0.266193	+	0.461059i
$837$		0			0
$838$	18.7641	+	10.8335i	0.648195	+	0.374236i
$839$	20.9932			0.724766			0.362383	−	0.932029i	$-0.381963\pi$
$839$	20.9932			0.724766			0.362383	+	0.932029i	$0.381963\pi$
$840$		0			0
$841$	−15.6071			−0.538174
$842$	−7.65733	−	4.42096i	−0.263889	−	0.152356i
$843$		0			0
$844$	13.0110	+	22.5356i	0.447856	+	0.775709i
$845$		0			0
$846$		0			0
$847$	35.9049	−	3.31306i	1.23371	−	0.113838i
$848$		−	4.45071i		−	0.152838i
$849$		0			0
$850$		0			0
$851$	−57.2744	+	33.0674i	−1.96334	+	1.13353i
$852$		0			0
$853$		−	18.2167i		−	0.623729i	−0.950127	−	0.311864i	$-0.899047\pi$
$853$		−	18.2167i		−	0.623729i	0.950127	−	0.311864i	$-0.100953\pi$
$854$	−11.5658	+	25.1135i	−0.395774	+	0.859365i
$855$		0			0
$856$	−3.28972	+	5.69797i	−0.112440	+	0.194753i
$857$	−6.19973	−	10.7382i	−0.211779	−	0.366812i	0.740493	−	0.672065i	$-0.234592\pi$
$857$	−6.19973	−	10.7382i	−0.211779	−	0.366812i	−0.952271	+	0.305253i	$0.901259\pi$
$858$		0			0
$859$	6.67438	+	3.85345i	0.227727	+	0.131478i	0.609523	−	0.792768i	$-0.291361\pi$
$859$	6.67438	+	3.85345i	0.227727	+	0.131478i	−0.381796	+	0.924247i	$0.624694\pi$
$860$		0			0
$861$		0			0
$862$	29.7313			1.01265
$863$	6.54406	+	3.77821i	0.222762	+	0.128612i	0.607229	−	0.794527i	$-0.292281\pi$
$863$	6.54406	+	3.77821i	0.222762	+	0.128612i	−0.384466	+	0.923139i	$0.625615\pi$
$864$		0			0
$865$		0			0
$866$	13.2833	−	23.0074i	0.451386	−	0.781823i
$867$		0			0
$868$	−0.285346	−	3.09241i	−0.00968528	−	0.104963i
$869$			21.0744i			0.714900i
$870$		0			0
$871$	−56.8778	+	32.8384i	−1.92723	+	1.11269i
$872$	2.32474	−	1.34219i	0.0787255	−	0.0454522i
$873$		0			0
$874$		−	19.1572i		−	0.648002i
$875$		0			0
$876$		0			0
$877$	−15.0598	+	26.0843i	−0.508532	+	0.880803i	0.491420	+	0.870923i	$0.336478\pi$
$877$	−15.0598	+	26.0843i	−0.508532	+	0.880803i	−0.999951	+	0.00987971i	$0.996855\pi$
$878$	8.31774	+	14.4067i	0.280710	+	0.486204i
$879$		0			0
$880$		0			0
$881$	29.6642			0.999411			0.499706	−	0.866195i	$-0.333442\pi$
$881$	29.6642			0.999411			0.499706	+	0.866195i	$0.333442\pi$
$882$		0			0
$883$	−38.9643			−1.31125			−0.655626	−	0.755086i	$-0.727595\pi$
$883$	−38.9643			−1.31125			−0.655626	+	0.755086i	$0.727595\pi$
$884$	14.6267	+	8.44475i	0.491950	+	0.284028i
$885$		0			0
$886$	1.63637	+	2.83428i	0.0549750	+	0.0952195i
$887$	10.3423	−	17.9134i	0.347260	−	0.601472i	−0.638502	−	0.769620i	$-0.720446\pi$
$887$	10.3423	−	17.9134i	0.347260	−	0.601472i	0.985762	+	0.168149i	$0.0537789\pi$
$888$		0			0
$889$	8.42690	+	11.9141i	0.282629	+	0.399586i
$890$		0			0
$891$		0			0
$892$	−6.28060	+	3.62611i	−0.210290	+	0.121411i
$893$	11.1377	−	6.43036i	0.372709	−	0.215184i
$894$		0			0
$895$		0			0
$896$	−0.243099	−	2.63456i	−0.00812137	−	0.0880144i
$897$		0			0
$898$	5.21608	−	9.03451i	0.174063	−	0.301485i
$899$	−3.91977	−	6.78924i	−0.130732	−	0.226434i
$900$		0			0
$901$	−11.8494	−	6.84127i	−0.394762	−	0.227916i
$902$	−41.6583			−1.38707
$903$		0			0
$904$	−3.55031			−0.118081
$905$		0			0
$906$		0			0
$907$	−6.06658	−	10.5076i	−0.201437	−	0.348900i	0.747554	−	0.664201i	$-0.231228\pi$
$907$	−6.06658	−	10.5076i	−0.201437	−	0.348900i	−0.948992	+	0.315301i	$0.897895\pi$
$908$	13.3604	−	23.1409i	0.443381	−	0.767959i
$909$		0			0
$910$		0			0
$911$		−	24.5869i		−	0.814600i	−0.913294	−	0.407300i	$-0.866470\pi$
$911$		−	24.5869i		−	0.814600i	0.913294	−	0.407300i	$-0.133530\pi$
$912$		0			0
$913$	−61.3908	+	35.4440i	−2.03174	+	1.17302i
$914$	28.6471	−	16.5394i	0.947561	−	0.547074i
$915$		0			0
$916$			24.3034i			0.803006i
$917$	54.3078	−	5.01115i	1.79340	−	0.165483i
$918$		0			0
$919$	11.5230	−	19.9585i	0.380110	−	0.658369i	−0.610968	−	0.791655i	$-0.709220\pi$
$919$	11.5230	−	19.9585i	0.380110	−	0.658369i	0.991078	+	0.133286i	$0.0425529\pi$
$920$		0			0
$921$		0			0
$922$	10.0146	+	5.78196i	0.329815	+	0.190419i
$923$	5.34841			0.176045
$924$		0			0
$925$		0			0
$926$	33.4339	+	19.3031i	1.09871	+	0.634338i
$927$		0			0
$928$	−3.33943	−	5.78405i	−0.109622	−	0.189871i
$929$	−20.1685	+	34.9328i	−0.661706	+	1.14611i	0.318461	+	0.947936i	$0.396834\pi$
$929$	−20.1685	+	34.9328i	−0.661706	+	1.14611i	−0.980167	+	0.198173i	$0.936499\pi$
$930$		0			0
$931$	16.4995	−	14.1137i	0.540748	−	0.462559i
$932$		−	9.25577i		−	0.303183i
$933$		0			0
$934$	−4.08230	+	2.35692i	−0.133577	+	0.0771207i
$935$		0			0
$936$		0			0
$937$		−	41.4861i		−	1.35529i	−0.735389	−	0.677646i	$-0.763000\pi$
$937$		−	41.4861i		−	1.35529i	0.735389	−	0.677646i	$-0.237000\pi$
$938$	25.8224	−	18.2643i	0.843130	−	0.596350i
$939$		0			0
$940$		0			0
$941$	−9.37786	−	16.2429i	−0.305710	−	0.529505i	0.671709	−	0.740815i	$-0.265560\pi$
$941$	−9.37786	−	16.2429i	−0.305710	−	0.529505i	−0.977419	+	0.211310i	$0.932227\pi$
$942$		0			0
$943$	44.8988	+	25.9223i	1.46211	+	0.844148i
$944$	6.00761			0.195531
$945$		0			0
$946$	43.7227			1.42155
$947$	−37.5699	−	21.6910i	−1.22086	−	0.704862i	−0.255756	−	0.966741i	$-0.582324\pi$
$947$	−37.5699	−	21.6910i	−1.22086	−	0.704862i	−0.965101	+	0.261879i	$0.915658\pi$
$948$		0			0
$949$	45.8693	+	79.4479i	1.48898	+	2.57899i
$950$		0			0
$951$		0			0
$952$	−7.38784	−	3.40241i	−0.239441	−	0.110273i
$953$		−	18.1672i		−	0.588492i	−0.955730	−	0.294246i	$-0.904931\pi$
$953$		−	18.1672i		−	0.588492i	0.955730	−	0.294246i	$-0.0950685\pi$
$954$		0			0
$955$		0			0
$956$	0.219422	−	0.126683i	0.00709661	−	0.00409723i
$957$		0			0
$958$			20.0191i			0.646789i
$959$	−27.5308	−	12.6791i	−0.889015	−	0.409429i
$960$		0			0
$961$	−14.8111	+	25.6536i	−0.477778	+	0.827536i
$962$	29.4142	+	50.9469i	0.948352	+	1.64259i
$963$		0			0
$964$	2.57538	+	1.48689i	0.0829473	+	0.0478896i
$965$		0			0
$966$		0			0
$967$	−29.7712			−0.957378			−0.478689	−	0.877985i	$-0.658888\pi$
$967$	−29.7712			−0.957378			−0.478689	+	0.877985i	$0.658888\pi$
$968$	11.8026	+	6.81421i	0.379349	+	0.219017i
$969$		0			0
$970$		0			0
$971$	18.5472	−	32.1247i	0.595209	−	1.03093i	−0.398309	−	0.917251i	$-0.630403\pi$
$971$	18.5472	−	32.1247i	0.595209	−	1.03093i	0.993517	−	0.113680i	$-0.0362640\pi$
$972$		0			0
$973$	−2.52078	+	1.78296i	−0.0808126	+	0.0571591i
$974$			4.73088i			0.151587i
$975$		0			0
$976$	−9.05018	+	5.22512i	−0.289689	+	0.167252i
$977$	0.874971	−	0.505165i	0.0279928	−	0.0161617i	−0.485938	−	0.873993i	$-0.661522\pi$
$977$	0.874971	−	0.505165i	0.0279928	−	0.0161617i	0.513931	+	0.857831i	$0.328189\pi$
$978$		0			0
$979$		−	73.3008i		−	2.34270i
$980$		0			0
$981$		0			0
$982$	−8.00133	+	13.8587i	−0.255333	+	0.442249i
$983$	12.6799	+	21.9623i	0.404427	+	0.700487i	0.994255	−	0.107042i	$-0.0341378\pi$
$983$	12.6799	+	21.9623i	0.404427	+	0.700487i	−0.589828	+	0.807529i	$0.700804\pi$
$984$		0			0
$985$		0			0
$986$	−20.5324			−0.653884
$987$		0			0
$988$	−17.0408			−0.542140
$989$	−47.1238	−	27.2070i	−1.49845	−	0.865131i
$990$		0			0
$991$	21.3875	+	37.0442i	0.679396	+	1.17675i	0.975163	+	0.221488i	$0.0710914\pi$
$991$	21.3875	+	37.0442i	0.679396	+	1.17675i	−0.295767	+	0.955260i	$0.595575\pi$
$992$	0.586893	−	1.01653i	0.0186339	−	0.0322748i
$993$		0			0
$994$	−2.56480	+	0.236662i	−0.0813506	+	0.00750647i
$995$		0			0
$996$		0			0
$997$	21.9808	−	12.6906i	0.696139	−	0.401916i	−0.109769	−	0.993957i	$-0.535011\pi$
$997$	21.9808	−	12.6906i	0.696139	−	0.401916i	0.805908	+	0.592041i	$0.201678\pi$
$998$	−5.50961	+	3.18097i	−0.174404	+	0.100692i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.e.1601.12	yes	24
3.2	odd	2	inner	3150.2.bf.e.1601.1	yes	24
5.2	odd	4		3150.2.bp.g.1349.4		24
5.3	odd	4		3150.2.bp.h.1349.9		24
5.4	even	2		3150.2.bf.d.1601.1	yes	24
7.3	odd	6	inner	3150.2.bf.e.1151.1	yes	24
15.2	even	4		3150.2.bp.h.1349.4		24
15.8	even	4		3150.2.bp.g.1349.9		24
15.14	odd	2		3150.2.bf.d.1601.12	yes	24
21.17	even	6	inner	3150.2.bf.e.1151.12	yes	24
35.3	even	12		3150.2.bp.h.899.4		24
35.17	even	12		3150.2.bp.g.899.9		24
35.24	odd	6		3150.2.bf.d.1151.12	yes	24
105.17	odd	12		3150.2.bp.h.899.9		24
105.38	odd	12		3150.2.bp.g.899.4		24
105.59	even	6		3150.2.bf.d.1151.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.1	✓	24	105.59	even	6
3150.2.bf.d.1151.12	yes	24	35.24	odd	6
3150.2.bf.d.1601.1	yes	24	5.4	even	2
3150.2.bf.d.1601.12	yes	24	15.14	odd	2
3150.2.bf.e.1151.1	yes	24	7.3	odd	6	inner
3150.2.bf.e.1151.12	yes	24	21.17	even	6	inner
3150.2.bf.e.1601.1	yes	24	3.2	odd	2	inner
3150.2.bf.e.1601.12	yes	24	1.1	even	1	trivial
3150.2.bp.g.899.4		24	105.38	odd	12
3150.2.bp.g.899.9		24	35.17	even	12
3150.2.bp.g.1349.4		24	5.2	odd	4
3150.2.bp.g.1349.9		24	15.8	even	4
3150.2.bp.h.899.4		24	35.3	even	12
3150.2.bp.h.899.9		24	105.17	odd	12
3150.2.bp.h.1349.4		24	15.2	even	4
3150.2.bp.h.1349.9		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.52781 + 2.16005i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.52781 + 2.16005i) q^{7} +1.00000i q^{8} +(-4.29783 + 2.48135i) q^{11} -5.49388i q^{13} +(0.243099 + 2.63456i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.53712 + 2.66237i) q^{17} +(-2.68622 - 1.55089i) q^{19} -4.96270 q^{22} +(5.34875 + 3.08810i) q^{23} +(2.74694 - 4.75784i) q^{26} +(-1.10675 + 2.40314i) q^{28} +6.67885i q^{29} +(-1.01653 + 0.586893i) q^{31} +(-0.866025 + 0.500000i) q^{32} +3.07424i q^{34} +(-5.35400 + 9.27339i) q^{37} +(-1.55089 - 2.68622i) q^{38} +8.39427 q^{41} -8.81025 q^{43} +(-4.29783 - 2.48135i) q^{44} +(3.08810 + 5.34875i) q^{46} +(-2.07312 + 3.59075i) q^{47} +(-2.33160 + 6.60028i) q^{49} +(4.75784 - 2.74694i) q^{52} +(-3.85443 + 2.22536i) q^{53} +(-2.16005 + 1.52781i) q^{56} +(-3.33943 + 5.78405i) q^{58} +(-3.00381 - 5.20275i) q^{59} +(9.05018 + 5.22512i) q^{61} -1.17379 q^{62} -1.00000 q^{64} +(-5.97727 - 10.3529i) q^{67} +(-1.53712 + 2.66237i) q^{68} +0.973522i q^{71} +(-14.4612 + 8.34916i) q^{73} +(-9.27339 + 5.35400i) q^{74} -3.10178i q^{76} +(-11.9261 - 5.49247i) q^{77} +(2.12328 - 3.67763i) q^{79} +(7.26965 + 4.19713i) q^{82} +14.2841 q^{83} +(-7.62990 - 4.40513i) q^{86} +(-2.48135 - 4.29783i) q^{88} +(-7.38517 + 12.7915i) q^{89} +(11.8670 - 8.39360i) q^{91} +6.17620i q^{92} +(-3.59075 + 2.07312i) q^{94} +4.41643i q^{97} +(-5.31936 + 4.55021i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 4 q^{7}+O(q^{10}) \) 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