LMFDB - Embedded newform 3150.2.bp.g.899.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3150.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			899.11
Character	$\chi$	$=$	3150.899
Dual form			3150.2.bp.g.1349.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.61577 - 0.397202i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.61577 - 0.397202i) q^{7} +1.00000 q^{8} +(0.429853 + 0.248176i) q^{11} -2.74440 q^{13} +(-1.65187 - 2.06672i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.16952 + 1.82992i) q^{17} +(-3.12125 + 1.80205i) q^{19} -0.496352i q^{22} +(-3.21210 - 5.56351i) q^{23} +(1.37220 + 2.37672i) q^{26} +(-0.963896 + 2.46392i) q^{28} -8.87959i q^{29} +(-6.90736 - 3.98797i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.65984i q^{34} +(-1.98397 + 1.14545i) q^{37} +(3.12125 + 1.80205i) q^{38} -2.22816 q^{41} +2.22575i q^{43} +(-0.429853 + 0.248176i) q^{44} +(-3.21210 + 5.56351i) q^{46} +(5.66749 - 3.27213i) q^{47} +(6.68446 - 2.07798i) q^{49} +(1.37220 - 2.37672i) q^{52} +(3.88322 - 6.72594i) q^{53} +(2.61577 - 0.397202i) q^{56} +(-7.68995 + 4.43979i) q^{58} +(3.05194 - 5.28611i) q^{59} +(3.24271 - 1.87218i) q^{61} +7.97593i q^{62} +1.00000 q^{64} +(7.08216 + 4.08889i) q^{67} +(-3.16952 + 1.82992i) q^{68} -10.3761i q^{71} +(-6.53361 + 11.3165i) q^{73} +(1.98397 + 1.14545i) q^{74} -3.60411i q^{76} +(1.22297 + 0.478431i) q^{77} +(-4.44344 - 7.69627i) q^{79} +(1.11408 + 1.92964i) q^{82} -4.79091i q^{83} +(1.92756 - 1.11288i) q^{86} +(0.429853 + 0.248176i) q^{88} +(-0.743586 - 1.28793i) q^{89} +(-7.17871 + 1.09008i) q^{91} +6.42419 q^{92} +(-5.66749 - 3.27213i) q^{94} +9.05174 q^{97} +(-5.14181 - 4.74992i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 12 q^{16} + 24 q^{17} - 12 q^{19} - 8 q^{23} - 12 q^{32} + 12 q^{38} - 8 q^{46} - 24 q^{47} + 52 q^{49} - 32 q^{53} - 12 q^{61} + 24 q^{64} - 24 q^{68} - 16 q^{77} - 4 q^{79} + 68 q^{91} + 16 q^{92} + 24 q^{94} - 20 q^{98}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 12 * q^16 + 24 * q^17 - 12 * q^19 - 8 * q^23 - 12 * q^32 + 12 * q^38 - 8 * q^46 - 24 * q^47 + 52 * q^49 - 32 * q^53 - 12 * q^61 + 24 * q^64 - 24 * q^68 - 16 * q^77 - 4 * q^79 + 68 * q^91 + 16 * q^92 + 24 * q^94 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.61577	−	0.397202i	0.988667	−	0.150128i
$7$	2.61577	−	0.397202i	0.988667	−	0.150128i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	0.429853	+	0.248176i	0.129606	+	0.0748278i	0.563401	−	0.826184i	$-0.309493\pi$
$11$	0.429853	+	0.248176i	0.129606	+	0.0748278i	−0.433795	+	0.901011i	$0.642826\pi$
$12$		0			0
$13$	−2.74440			−0.761160			−0.380580	−	0.924748i	$-0.624276\pi$
$13$	−2.74440			−0.761160			−0.380580	+	0.924748i	$0.624276\pi$
$14$	−1.65187	−	2.06672i	−0.441481	−	0.552354i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.16952	+	1.82992i	0.768721	+	0.443821i	0.832418	−	0.554148i	$-0.186956\pi$
$17$	3.16952	+	1.82992i	0.768721	+	0.443821i	−0.0636974	+	0.997969i	$0.520289\pi$
$18$		0			0
$19$	−3.12125	+	1.80205i	−0.716064	+	0.413420i	−0.813302	−	0.581841i	$-0.802332\pi$
$19$	−3.12125	+	1.80205i	−0.716064	+	0.413420i	0.0972384	+	0.995261i	$0.468999\pi$
$20$		0			0
$21$		0			0
$22$		−	0.496352i		−	0.105823i
$23$	−3.21210	−	5.56351i	−0.669768	−	1.16007i	−0.977969	−	0.208751i	$-0.933060\pi$
$23$	−3.21210	−	5.56351i	−0.669768	−	1.16007i	0.308200	−	0.951321i	$-0.400273\pi$
$24$		0			0
$25$		0			0
$26$	1.37220	+	2.37672i	0.269111	+	0.466114i
$27$		0			0
$28$	−0.963896	+	2.46392i	−0.182159	+	0.465637i
$29$		−	8.87959i		−	1.64890i	−0.565937	−	0.824449i	$-0.691485\pi$
$29$		−	8.87959i		−	1.64890i	0.565937	−	0.824449i	$-0.308515\pi$
$30$		0			0
$31$	−6.90736	−	3.98797i	−1.24060	−	0.716260i	−0.271383	−	0.962472i	$-0.587481\pi$
$31$	−6.90736	−	3.98797i	−1.24060	−	0.716260i	−0.969216	+	0.246211i	$0.920814\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	3.65984i		−	0.627658i
$35$		0			0
$36$		0			0
$37$	−1.98397	+	1.14545i	−0.326163	+	0.188311i	−0.654136	−	0.756377i	$-0.726968\pi$
$37$	−1.98397	+	1.14545i	−0.326163	+	0.188311i	0.327973	+	0.944687i	$0.393634\pi$
$38$	3.12125	+	1.80205i	0.506334	+	0.292332i
$39$		0			0
$40$		0			0
$41$	−2.22816			−0.347980			−0.173990	−	0.984747i	$-0.555666\pi$
$41$	−2.22816			−0.347980			−0.173990	+	0.984747i	$0.555666\pi$
$42$		0			0
$43$			2.22575i			0.339424i	0.985494	+	0.169712i	$0.0542838\pi$
$43$			2.22575i			0.339424i	−0.985494	+	0.169712i	$0.945716\pi$
$44$	−0.429853	+	0.248176i	−0.0648028	+	0.0374139i
$45$		0			0
$46$	−3.21210	+	5.56351i	−0.473598	+	0.820295i
$47$	5.66749	−	3.27213i	0.826688	−	0.477289i	−0.0260292	−	0.999661i	$-0.508286\pi$
$47$	5.66749	−	3.27213i	0.826688	−	0.477289i	0.852717	+	0.522373i	$0.174953\pi$
$48$		0			0
$49$	6.68446	−	2.07798i	0.954923	−	0.296854i
$50$		0			0
$51$		0			0
$52$	1.37220	−	2.37672i	0.190290	−	0.329592i
$53$	3.88322	−	6.72594i	0.533402	−	0.923879i	−0.465837	−	0.884870i	$-0.654247\pi$
$53$	3.88322	−	6.72594i	0.533402	−	0.923879i	0.999239	−	0.0390085i	$-0.0124199\pi$
$54$		0			0
$55$		0			0
$56$	2.61577	−	0.397202i	0.349546	−	0.0530784i
$57$		0			0
$58$	−7.68995	+	4.43979i	−1.00974	+	0.582973i
$59$	3.05194	−	5.28611i	0.397328	−	0.688193i	−0.596067	−	0.802935i	$-0.703271\pi$
$59$	3.05194	−	5.28611i	0.397328	−	0.688193i	0.993395	+	0.114742i	$0.0366040\pi$
$60$		0			0
$61$	3.24271	−	1.87218i	0.415187	−	0.239708i	−0.277829	−	0.960630i	$-0.589615\pi$
$61$	3.24271	−	1.87218i	0.415187	−	0.239708i	0.693016	+	0.720922i	$0.256282\pi$
$62$			7.97593i			1.01294i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	7.08216	+	4.08889i	0.865224	+	0.499537i	0.865758	−	0.500463i	$-0.166837\pi$
$67$	7.08216	+	4.08889i	0.865224	+	0.499537i	−0.000534152		1.00000i	$0.500170\pi$
$68$	−3.16952	+	1.82992i	−0.384360	+	0.221911i
$69$		0			0
$70$		0			0
$71$		−	10.3761i		−	1.23141i	−0.787975	−	0.615707i	$-0.788871\pi$
$71$		−	10.3761i		−	1.23141i	0.787975	−	0.615707i	$-0.211129\pi$
$72$		0			0
$73$	−6.53361	+	11.3165i	−0.764701	+	1.32450i	0.175704	+	0.984443i	$0.443780\pi$
$73$	−6.53361	+	11.3165i	−0.764701	+	1.32450i	−0.940405	+	0.340058i	$0.889553\pi$
$74$	1.98397	+	1.14545i	0.230632	+	0.133156i
$75$		0			0
$76$		−	3.60411i		−	0.413420i
$77$	1.22297	+	0.478431i	0.139370	+	0.0545223i
$78$		0			0
$79$	−4.44344	−	7.69627i	−0.499926	−	0.865898i	0.500074	−	0.865983i	$-0.333306\pi$
$79$	−4.44344	−	7.69627i	−0.499926	−	0.865898i	−1.00000		8.52501e-5i	$0.999973\pi$
$80$		0			0
$81$		0			0
$82$	1.11408	+	1.92964i	0.123030	+	0.213093i
$83$		−	4.79091i		−	0.525871i	−0.964813	−	0.262935i	$-0.915309\pi$
$83$		−	4.79091i		−	0.525871i	0.964813	−	0.262935i	$-0.0846906\pi$
$84$		0			0
$85$		0			0
$86$	1.92756	−	1.11288i	0.207854	−	0.120005i
$87$		0			0
$88$	0.429853	+	0.248176i	0.0458225	+	0.0264556i
$89$	−0.743586	−	1.28793i	−0.0788199	−	0.136520i	0.823921	−	0.566704i	$-0.191782\pi$
$89$	−0.743586	−	1.28793i	−0.0788199	−	0.136520i	−0.902741	+	0.430184i	$0.858449\pi$
$90$		0			0
$91$	−7.17871	+	1.09008i	−0.752534	+	0.114272i
$92$	6.42419			0.669768
$93$		0			0
$94$	−5.66749	−	3.27213i	−0.584557	−	0.337494i
$95$		0			0
$96$		0			0
$97$	9.05174			0.919064			0.459532	−	0.888161i	$-0.348017\pi$
$97$	9.05174			0.919064			0.459532	+	0.888161i	$0.348017\pi$
$98$	−5.14181	−	4.74992i	−0.519401	−	0.479815i
$99$		0			0
$100$		0			0
$101$	1.50180	−	2.60119i	0.149434	−	0.258828i	−0.781584	−	0.623800i	$-0.785588\pi$
$101$	1.50180	−	2.60119i	0.149434	−	0.258828i	0.931019	+	0.364972i	$0.118921\pi$
$102$		0			0
$103$	7.18752	+	12.4491i	0.708207	+	1.22665i	0.965522	+	0.260323i	$0.0838291\pi$
$103$	7.18752	+	12.4491i	0.708207	+	1.22665i	−0.257314	+	0.966328i	$0.582838\pi$
$104$	−2.74440			−0.269111
$105$		0			0
$106$	−7.76645			−0.754344
$107$	1.06314	+	1.84141i	0.102778	+	0.178016i	0.912828	−	0.408344i	$-0.133894\pi$
$107$	1.06314	+	1.84141i	0.102778	+	0.178016i	−0.810050	+	0.586360i	$0.800560\pi$
$108$		0			0
$109$	3.95181	−	6.84474i	0.378515	−	0.655607i	−0.612331	−	0.790601i	$-0.709768\pi$
$109$	3.95181	−	6.84474i	0.378515	−	0.655607i	0.990846	+	0.134994i	$0.0431015\pi$
$110$		0			0
$111$		0			0
$112$	−1.65187	−	2.06672i	−0.156087	−	0.195287i
$113$	−12.2968			−1.15678			−0.578391	−	0.815760i	$-0.696319\pi$
$113$	−12.2968			−1.15678			−0.578391	+	0.815760i	$0.696319\pi$
$114$		0			0
$115$		0			0
$116$	7.68995	+	4.43979i	0.713994	+	0.412224i
$117$		0			0
$118$	−6.10388			−0.561907
$119$	9.01756	+	3.52771i	0.826638	+	0.323384i
$120$		0			0
$121$	−5.37682	−	9.31292i	−0.488802	−	0.846629i
$122$	−3.24271	−	1.87218i	−0.293581	−	0.169499i
$123$		0			0
$124$	6.90736	−	3.98797i	0.620299	−	0.358130i
$125$		0			0
$126$		0			0
$127$		−	0.753445i		−	0.0668574i	−0.999441	−	0.0334287i	$-0.989357\pi$
$127$		−	0.753445i		−	0.0668574i	0.999441	−	0.0334287i	$-0.0106427\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	6.35624	+	11.0093i	0.555347	+	0.961890i	0.997876	+	0.0651355i	$0.0207479\pi$
$131$	6.35624	+	11.0093i	0.555347	+	0.961890i	−0.442529	+	0.896754i	$0.645919\pi$
$132$		0			0
$133$	−7.44868	+	5.95352i	−0.645882	+	0.516236i
$134$		−	8.17778i		−	0.706452i
$135$		0			0
$136$	3.16952	+	1.82992i	0.271784	+	0.156914i
$137$	−2.15740	+	3.73673i	−0.184319	+	0.319250i	−0.943347	−	0.331808i	$-0.892341\pi$
$137$	−2.15740	+	3.73673i	−0.184319	+	0.319250i	0.759028	+	0.651058i	$0.225675\pi$
$138$		0			0
$139$		−	0.0681276i		−	0.00577851i	−0.999996	−	0.00288926i	$-0.999080\pi$
$139$		−	0.0681276i		−	0.00577851i	0.999996	−	0.00288926i	$-0.000919680\pi$
$140$		0			0
$141$		0			0
$142$	−8.98595	+	5.18804i	−0.754084	+	0.435371i
$143$	−1.17969	−	0.681094i	−0.0986507	−	0.0569560i
$144$		0			0
$145$		0			0
$146$	13.0672			1.08145
$147$		0			0
$148$		−	2.29090i		−	0.188311i
$149$	14.4611	−	8.34911i	1.18470	−	0.683986i	0.227602	−	0.973754i	$-0.426912\pi$
$149$	14.4611	−	8.34911i	1.18470	−	0.683986i	0.957097	+	0.289768i	$0.0935783\pi$
$150$		0			0
$151$	6.51016	−	11.2759i	0.529789	−	0.917622i	−0.469607	−	0.882876i	$-0.655604\pi$
$151$	6.51016	−	11.2759i	0.529789	−	0.917622i	0.999396	−	0.0347463i	$-0.0110623\pi$
$152$	−3.12125	+	1.80205i	−0.253167	+	0.146166i
$153$		0			0
$154$	−0.197152	−	1.29834i	−0.0158870	−	0.104623i
$155$		0			0
$156$		0			0
$157$	7.40408	−	12.8242i	0.590910	−	1.02349i	−0.403200	−	0.915112i	$-0.632102\pi$
$157$	7.40408	−	12.8242i	0.590910	−	1.02349i	0.994110	−	0.108374i	$-0.0345645\pi$
$158$	−4.44344	+	7.69627i	−0.353501	+	0.612282i
$159$		0			0
$160$		0			0
$161$	−10.6119	−	13.2770i	−0.836337	−	1.04637i
$162$		0			0
$163$	−13.3189	+	7.68966i	−1.04322	+	0.602301i	−0.920742	−	0.390171i	$-0.872416\pi$
$163$	−13.3189	+	7.68966i	−1.04322	+	0.602301i	−0.122473	+	0.992472i	$0.539082\pi$
$164$	1.11408	−	1.92964i	0.0869950	−	0.150680i
$165$		0			0
$166$	−4.14905	+	2.39546i	−0.322029	+	0.185923i
$167$		−	24.5161i		−	1.89712i	−0.316603	−	0.948558i	$-0.602542\pi$
$167$		−	24.5161i		−	1.89712i	0.316603	−	0.948558i	$-0.397458\pi$
$168$		0			0
$169$	−5.46825			−0.420635
$170$		0			0
$171$		0			0
$172$	−1.92756	−	1.11288i	−0.146975	−	0.0848561i
$173$	10.8463	−	6.26213i	0.824631	−	0.476101i	−0.0273795	−	0.999625i	$-0.508716\pi$
$173$	10.8463	−	6.26213i	0.824631	−	0.476101i	0.852011	+	0.523524i	$0.175383\pi$
$174$		0			0
$175$		0			0
$176$		−	0.496352i		−	0.0374139i
$177$		0			0
$178$	−0.743586	+	1.28793i	−0.0557341	+	0.0965343i
$179$	−1.58961	−	0.917762i	−0.118813	−	0.0685968i	0.439416	−	0.898284i	$-0.355186\pi$
$179$	−1.58961	−	0.917762i	−0.118813	−	0.0685968i	−0.558229	+	0.829687i	$0.688519\pi$
$180$		0			0
$181$		−	23.6564i		−	1.75837i	−0.476481	−	0.879185i	$-0.658088\pi$
$181$		−	23.6564i		−	1.75837i	0.476481	−	0.879185i	$-0.341912\pi$
$182$	4.53340	+	5.67191i	0.336038	+	0.420430i
$183$		0			0
$184$	−3.21210	−	5.56351i	−0.236799	−	0.410148i
$185$		0			0
$186$		0			0
$187$	0.908284	+	1.57319i	0.0664203	+	0.115043i
$188$			6.54425i			0.477289i
$189$		0			0
$190$		0			0
$191$	−7.02253	+	4.05446i	−0.508133	+	0.293371i	−0.732066	−	0.681234i	$-0.761444\pi$
$191$	−7.02253	+	4.05446i	−0.508133	+	0.293371i	0.223933	+	0.974605i	$0.428110\pi$
$192$		0			0
$193$	10.4356	+	6.02502i	0.751174	+	0.433691i	0.826118	−	0.563497i	$-0.190544\pi$
$193$	10.4356	+	6.02502i	0.751174	+	0.433691i	−0.0749438	+	0.997188i	$0.523878\pi$
$194$	−4.52587	−	7.83903i	−0.324938	−	0.562810i
$195$		0			0
$196$	−1.54265	+	6.82790i	−0.110189	+	0.487707i
$197$	12.7463			0.908137			0.454068	−	0.890967i	$-0.349972\pi$
$197$	12.7463			0.908137			0.454068	+	0.890967i	$0.349972\pi$
$198$		0			0
$199$	−16.4954	−	9.52361i	−1.16933	−	0.675111i	−0.215805	−	0.976436i	$-0.569238\pi$
$199$	−16.4954	−	9.52361i	−1.16933	−	0.675111i	−0.953521	+	0.301325i	$0.902571\pi$
$200$		0			0
$201$		0			0
$202$	−3.00359			−0.211332
$203$	−3.52699	−	23.2269i	−0.247546	−	1.63021i
$204$		0			0
$205$		0			0
$206$	7.18752	−	12.4491i	0.500778	−	0.867373i
$207$		0			0
$208$	1.37220	+	2.37672i	0.0951450	+	0.164796i
$209$	−1.78891			−0.123741
$210$		0			0
$211$	−8.92057			−0.614117			−0.307059	−	0.951691i	$-0.599345\pi$
$211$	−8.92057			−0.614117			−0.307059	+	0.951691i	$0.599345\pi$
$212$	3.88322	+	6.72594i	0.266701	+	0.461939i
$213$		0			0
$214$	1.06314	−	1.84141i	0.0726748	−	0.125876i
$215$		0			0
$216$		0			0
$217$	−19.6521	−	7.68797i	−1.33407	−	0.521893i
$218$	−7.90363			−0.535301
$219$		0			0
$220$		0			0
$221$	−8.69843	−	5.02204i	−0.585120	−	0.337819i
$222$		0			0
$223$	−23.5443			−1.57664			−0.788320	−	0.615265i	$-0.789049\pi$
$223$	−23.5443			−1.57664			−0.788320	+	0.615265i	$0.789049\pi$
$224$	−0.963896	+	2.46392i	−0.0644030	+	0.164628i
$225$		0			0
$226$	6.14838	+	10.6493i	0.408984	+	0.708382i
$227$	8.07522	+	4.66223i	0.535971	+	0.309443i	0.743445	−	0.668797i	$-0.233191\pi$
$227$	8.07522	+	4.66223i	0.535971	+	0.309443i	−0.207473	+	0.978241i	$0.566524\pi$
$228$		0			0
$229$	−20.1545	+	11.6362i	−1.33185	+	0.768944i	−0.985583	−	0.169193i	$-0.945884\pi$
$229$	−20.1545	+	11.6362i	−1.33185	+	0.768944i	−0.346266	+	0.938136i	$0.612551\pi$
$230$		0			0
$231$		0			0
$232$		−	8.87959i		−	0.582973i
$233$	−6.31017	−	10.9295i	−0.413393	−	0.716018i	0.581865	−	0.813285i	$-0.302323\pi$
$233$	−6.31017	−	10.9295i	−0.413393	−	0.716018i	−0.995258	+	0.0972676i	$0.968990\pi$
$234$		0			0
$235$		0			0
$236$	3.05194	+	5.28611i	0.198664	+	0.344097i
$237$		0			0
$238$	−1.45370	−	9.57329i	−0.0942292	−	0.620544i
$239$			16.1198i			1.04270i	0.853342	+	0.521351i	$0.174572\pi$
$239$			16.1198i			1.04270i	−0.853342	+	0.521351i	$0.825428\pi$
$240$		0			0
$241$	−18.3222	−	10.5783i	−1.18024	−	0.681411i	−0.224168	−	0.974550i	$-0.571966\pi$
$241$	−18.3222	−	10.5783i	−1.18024	−	0.681411i	−0.956070	+	0.293140i	$0.905300\pi$
$242$	−5.37682	+	9.31292i	−0.345635	+	0.598657i
$243$		0			0
$244$			3.74436i			0.239708i
$245$		0			0
$246$		0			0
$247$	8.56597	−	4.94556i	0.545039	−	0.314679i
$248$	−6.90736	−	3.98797i	−0.438618	−	0.253236i
$249$		0			0
$250$		0			0
$251$	−6.06317			−0.382704			−0.191352	−	0.981522i	$-0.561287\pi$
$251$	−6.06317			−0.382704			−0.191352	+	0.981522i	$0.561287\pi$
$252$		0			0
$253$		−	3.18866i		−	0.200469i
$254$	−0.652503	+	0.376723i	−0.0409416	+	0.0236377i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.51357	+	5.49266i	−0.593440	+	0.342623i	−0.766457	−	0.642296i	$-0.777982\pi$
$257$	−9.51357	+	5.49266i	−0.593440	+	0.342623i	0.173016	+	0.984919i	$0.444649\pi$
$258$		0			0
$259$	−4.73464	+	3.78426i	−0.294196	+	0.235143i
$260$		0			0
$261$		0			0
$262$	6.35624	−	11.0093i	0.392690	−	0.680159i
$263$	−0.669365	+	1.15937i	−0.0412748	+	0.0714901i	−0.885925	−	0.463829i	$-0.846475\pi$
$263$	−0.669365	+	1.15937i	−0.0412748	+	0.0714901i	0.844650	+	0.535319i	$0.179809\pi$
$264$		0			0
$265$		0			0
$266$	8.88024	+	3.47399i	0.544482	+	0.213004i
$267$		0			0
$268$	−7.08216	+	4.08889i	−0.432612	+	0.249769i
$269$	0.311161	−	0.538946i	0.0189718	−	0.0328601i	−0.856384	−	0.516340i	$-0.827294\pi$
$269$	0.311161	−	0.538946i	0.0189718	−	0.0328601i	0.875355	+	0.483480i	$0.160627\pi$
$270$		0			0
$271$	18.4634	−	10.6598i	1.12157	−	0.647539i	0.179769	−	0.983709i	$-0.442465\pi$
$271$	18.4634	−	10.6598i	1.12157	−	0.647539i	0.941801	+	0.336170i	$0.109132\pi$
$272$		−	3.65984i		−	0.221911i
$273$		0			0
$274$	4.31480			0.260667
$275$		0			0
$276$		0			0
$277$	1.02805	+	0.593544i	0.0617694	+	0.0356626i	0.530567	−	0.847643i	$-0.321979\pi$
$277$	1.02805	+	0.593544i	0.0617694	+	0.0356626i	−0.468797	+	0.883306i	$0.655312\pi$
$278$	−0.0590003	+	0.0340638i	−0.00353860	+	0.00204301i
$279$		0			0
$280$		0			0
$281$		−	1.97593i		−	0.117874i	−0.998262	−	0.0589370i	$-0.981229\pi$
$281$		−	1.97593i		−	0.117874i	0.998262	−	0.0589370i	$-0.0187711\pi$
$282$		0			0
$283$	13.5654	−	23.4960i	0.806382	−	1.39669i	−0.108972	−	0.994045i	$-0.534756\pi$
$283$	13.5654	−	23.4960i	0.806382	−	1.39669i	0.915354	−	0.402650i	$-0.131911\pi$
$284$	8.98595	+	5.18804i	0.533218	+	0.307853i
$285$		0			0
$286$			1.36219i			0.0805479i
$287$	−5.82835	+	0.885030i	−0.344036	+	0.0522417i
$288$		0			0
$289$	−1.80278	−	3.12250i	−0.106046	−	0.183677i
$290$		0			0
$291$		0			0
$292$	−6.53361	−	11.3165i	−0.382350	−	0.662250i
$293$			10.3808i			0.606456i	0.952918	+	0.303228i	$0.0980643\pi$
$293$			10.3808i			0.606456i	−0.952918	+	0.303228i	$0.901936\pi$
$294$		0			0
$295$		0			0
$296$	−1.98397	+	1.14545i	−0.115316	+	0.0665778i
$297$		0			0
$298$	−14.4611	−	8.34911i	−0.837708	−	0.483651i
$299$	8.81529	+	15.2685i	0.509801	+	0.883002i
$300$		0			0
$301$	0.884074	+	5.82205i	0.0509572	+	0.335577i
$302$	−13.0203			−0.749235
$303$		0			0
$304$	3.12125	+	1.80205i	0.179016	+	0.103355i
$305$		0			0
$306$		0			0
$307$	14.1364			0.806808			0.403404	−	0.915022i	$-0.367827\pi$
$307$	14.1364			0.806808			0.403404	+	0.915022i	$0.367827\pi$
$308$	−1.02582	+	0.819908i	−0.0584515	+	0.0467186i
$309$		0			0
$310$		0			0
$311$	3.32643	−	5.76155i	0.188625	−	0.326708i	−0.756167	−	0.654378i	$-0.772930\pi$
$311$	3.32643	−	5.76155i	0.188625	−	0.326708i	0.944792	+	0.327671i	$0.106264\pi$
$312$		0			0
$313$	6.07282	+	10.5184i	0.343256	+	0.594537i	0.985035	−	0.172352i	$-0.0551367\pi$
$313$	6.07282	+	10.5184i	0.343256	+	0.594537i	−0.641779	+	0.766890i	$0.721803\pi$
$314$	−14.8082			−0.835673
$315$		0			0
$316$	8.88688			0.499926
$317$	−15.3605	−	26.6051i	−0.862730	−	1.49429i	−0.869283	−	0.494314i	$-0.835419\pi$
$317$	−15.3605	−	26.6051i	−0.862730	−	1.49429i	0.00655283	−	0.999979i	$-0.497914\pi$
$318$		0			0
$319$	2.20370	−	3.81692i	0.123383	−	0.213706i
$320$		0			0
$321$		0			0
$322$	−6.19225	+	15.8287i	−0.345081	+	0.882099i
$323$	−13.1905			−0.733937
$324$		0			0
$325$		0			0
$326$	13.3189	+	7.68966i	0.737665	+	0.425891i
$327$		0			0
$328$	−2.22816			−0.123030
$329$	13.5251	−	10.8103i	0.745664	−	0.595989i
$330$		0			0
$331$	15.5140	+	26.8710i	0.852724	+	1.47696i	0.878741	+	0.477300i	$0.158384\pi$
$331$	15.5140	+	26.8710i	0.852724	+	1.47696i	−0.0260166	+	0.999662i	$0.508282\pi$
$332$	4.14905	+	2.39546i	0.227709	+	0.131468i
$333$		0			0
$334$	−21.2316	+	12.2581i	−1.16174	+	0.670732i
$335$		0			0
$336$		0			0
$337$			6.91470i			0.376668i	0.982105	+	0.188334i	$0.0603087\pi$
$337$			6.91470i			0.376668i	−0.982105	+	0.188334i	$0.939691\pi$
$338$	2.73413	+	4.73565i	0.148717	+	0.257585i
$339$		0			0
$340$		0			0
$341$	−1.97943	−	3.42848i	−0.107192	−	0.185663i
$342$		0			0
$343$	16.6596	−	8.09058i	0.899534	−	0.436850i
$344$			2.22575i			0.120005i
$345$		0			0
$346$	−10.8463	−	6.26213i	−0.583103	−	0.336654i
$347$	3.74704	−	6.49006i	0.201152	−	0.348405i	−0.747748	−	0.663982i	$-0.768865\pi$
$347$	3.74704	−	6.49006i	0.201152	−	0.348405i	0.948900	+	0.315578i	$0.102198\pi$
$348$		0			0
$349$			12.4552i			0.666714i	0.942801	+	0.333357i	$0.108181\pi$
$349$			12.4552i			0.666714i	−0.942801	+	0.333357i	$0.891819\pi$
$350$		0			0
$351$		0			0
$352$	−0.429853	+	0.248176i	−0.0229113	+	0.0132278i
$353$	16.4027	+	9.47011i	0.873028	+	0.504043i	0.868353	−	0.495946i	$-0.165179\pi$
$353$	16.4027	+	9.47011i	0.873028	+	0.504043i	0.00467471	+	0.999989i	$0.498512\pi$
$354$		0			0
$355$		0			0
$356$	1.48717			0.0788199
$357$		0			0
$358$			1.83552i			0.0970105i
$359$	−23.0590	+	13.3131i	−1.21701	+	0.702639i	−0.964277	−	0.264898i	$-0.914662\pi$
$359$	−23.0590	+	13.3131i	−1.21701	+	0.702639i	−0.252730	+	0.967537i	$0.581329\pi$
$360$		0			0
$361$	−3.00520	+	5.20516i	−0.158168	+	0.273956i
$362$	−20.4871	+	11.8282i	−1.07678	+	0.621677i
$363$		0			0
$364$	2.64532	−	6.76199i	0.138652	−	0.354425i
$365$		0			0
$366$		0			0
$367$	5.45606	−	9.45017i	0.284804	−	0.493295i	−0.687758	−	0.725940i	$-0.741405\pi$
$367$	5.45606	−	9.45017i	0.284804	−	0.493295i	0.972562	+	0.232646i	$0.0747382\pi$
$368$	−3.21210	+	5.56351i	−0.167442	+	0.290018i
$369$		0			0
$370$		0			0
$371$	7.48604	−	19.1359i	0.388656	−	0.993487i
$372$		0			0
$373$	−19.4924	+	11.2539i	−1.00928	+	0.582707i	−0.910980	−	0.412450i	$-0.864673\pi$
$373$	−19.4924	+	11.2539i	−1.00928	+	0.582707i	−0.0982976	+	0.995157i	$0.531340\pi$
$374$	0.908284	−	1.57319i	0.0469663	−	0.0813480i
$375$		0			0
$376$	5.66749	−	3.27213i	0.292278	−	0.168747i
$377$			24.3692i			1.25508i
$378$		0			0
$379$	3.25909			0.167408			0.0837040	−	0.996491i	$-0.473325\pi$
$379$	3.25909			0.167408			0.0837040	+	0.996491i	$0.473325\pi$
$380$		0			0
$381$		0			0
$382$	7.02253	+	4.05446i	0.359304	+	0.207444i
$383$	−15.0013	+	8.66098i	−0.766528	+	0.442555i	−0.831635	−	0.555323i	$-0.812595\pi$
$383$	−15.0013	+	8.66098i	−0.766528	+	0.442555i	0.0651064	+	0.997878i	$0.479261\pi$
$384$		0			0
$385$		0			0
$386$		−	12.0500i		−	0.613331i
$387$		0			0
$388$	−4.52587	+	7.83903i	−0.229766	+	0.397967i
$389$	27.4515	+	15.8491i	1.39185	+	0.803582i	0.993520	−	0.113662i	$-0.0362580\pi$
$389$	27.4515	+	15.8491i	1.39185	+	0.803582i	0.398326	+	0.917244i	$0.369591\pi$
$390$		0			0
$391$		−	23.5115i		−	1.18903i
$392$	6.68446	−	2.07798i	0.337616	−	0.104954i
$393$		0			0
$394$	−6.37315	−	11.0386i	−0.321075	−	0.556118i
$395$		0			0
$396$		0			0
$397$	16.7561	+	29.0224i	0.840964	+	1.45659i	0.889081	+	0.457750i	$0.151345\pi$
$397$	16.7561	+	29.0224i	0.840964	+	1.45659i	−0.0481170	+	0.998842i	$0.515322\pi$
$398$			19.0472i			0.954751i
$399$		0			0
$400$		0			0
$401$	−31.0404	+	17.9212i	−1.55008	+	0.894940i	−0.551947	+	0.833879i	$0.686115\pi$
$401$	−31.0404	+	17.9212i	−1.55008	+	0.894940i	−0.998134	+	0.0610611i	$0.980552\pi$
$402$		0			0
$403$	18.9566	+	10.9446i	0.944295	+	0.545189i
$404$	1.50180	+	2.60119i	0.0747171	+	0.129414i
$405$		0			0
$406$	−18.3516	+	14.6679i	−0.910775	+	0.727957i
$407$	−1.13709			−0.0563635
$408$		0			0
$409$	21.3474	+	12.3249i	1.05556	+	0.609429i	0.924201	−	0.381905i	$-0.124732\pi$
$409$	21.3474	+	12.3249i	1.05556	+	0.609429i	0.131361	+	0.991335i	$0.458065\pi$
$410$		0			0
$411$		0			0
$412$	−14.3750			−0.708207
$413$	5.88350	−	15.0395i	0.289508	−	0.740044i
$414$		0			0
$415$		0			0
$416$	1.37220	−	2.37672i	0.0672777	−	0.116528i
$417$		0			0
$418$	0.894453	+	1.54924i	0.0437491	+	0.0757757i
$419$	−10.6574			−0.520646			−0.260323	−	0.965522i	$-0.583829\pi$
$419$	−10.6574			−0.520646			−0.260323	+	0.965522i	$0.583829\pi$
$420$		0			0
$421$	22.6815			1.10543			0.552714	−	0.833371i	$-0.313592\pi$
$421$	22.6815			1.10543			0.552714	+	0.833371i	$0.313592\pi$
$422$	4.46028	+	7.72544i	0.217123	+	0.376068i
$423$		0			0
$424$	3.88322	−	6.72594i	0.188586	−	0.326641i
$425$		0			0
$426$		0			0
$427$	7.73854	−	6.18520i	0.374494	−	0.299323i
$428$	−2.12628			−0.102778
$429$		0			0
$430$		0			0
$431$	−26.0439	−	15.0364i	−1.25449	−	0.724279i	−0.282491	−	0.959270i	$-0.591161\pi$
$431$	−26.0439	−	15.0364i	−1.25449	−	0.724279i	−0.971998	+	0.234991i	$0.924494\pi$
$432$		0			0
$433$	14.9203			0.717025			0.358512	−	0.933525i	$-0.383284\pi$
$433$	14.9203			0.717025			0.358512	+	0.933525i	$0.383284\pi$
$434$	3.16806	+	20.8632i	0.152072	+	1.00146i
$435$		0			0
$436$	3.95181	+	6.84474i	0.189258	+	0.327804i
$437$	20.0515	+	11.5767i	0.959194	+	0.553791i
$438$		0			0
$439$	−11.1126	+	6.41586i	−0.530375	+	0.306212i	−0.741169	−	0.671318i	$-0.765728\pi$
$439$	−11.1126	+	6.41586i	−0.530375	+	0.306212i	0.210794	+	0.977530i	$0.432395\pi$
$440$		0			0
$441$		0			0
$442$			10.0441i			0.477748i
$443$	−10.2071	−	17.6792i	−0.484953	−	0.839963i	0.514898	−	0.857252i	$-0.327830\pi$
$443$	−10.2071	−	17.6792i	−0.484953	−	0.839963i	−0.999851	+	0.0172887i	$0.994497\pi$
$444$		0			0
$445$		0			0
$446$	11.7721	+	20.3899i	0.557426	+	0.965491i
$447$		0			0
$448$	2.61577	−	0.397202i	0.123583	−	0.0187660i
$449$		−	20.8404i		−	0.983519i	−0.870731	−	0.491760i	$-0.836354\pi$
$449$		−	20.8404i		−	0.983519i	0.870731	−	0.491760i	$-0.163646\pi$
$450$		0			0
$451$	−0.957782	−	0.552976i	−0.0451002	−	0.0260386i
$452$	6.14838	−	10.6493i	0.289196	−	0.500901i
$453$		0			0
$454$		−	9.32446i		−	0.437619i
$455$		0			0
$456$		0			0
$457$	−13.8811	+	8.01424i	−0.649329	+	0.374890i	−0.788199	−	0.615420i	$-0.788986\pi$
$457$	−13.8811	+	8.01424i	−0.649329	+	0.374890i	0.138870	+	0.990311i	$0.455653\pi$
$458$	20.1545	+	11.6362i	0.941760	+	0.543725i
$459$		0			0
$460$		0			0
$461$	−1.98400			−0.0924039			−0.0462020	−	0.998932i	$-0.514712\pi$
$461$	−1.98400			−0.0924039			−0.0462020	+	0.998932i	$0.514712\pi$
$462$		0			0
$463$		−	36.3987i		−	1.69159i	−0.533506	−	0.845796i	$-0.679126\pi$
$463$		−	36.3987i		−	1.69159i	0.533506	−	0.845796i	$-0.320874\pi$
$464$	−7.68995	+	4.43979i	−0.356997	+	0.206112i
$465$		0			0
$466$	−6.31017	+	10.9295i	−0.292313	+	0.506301i
$467$	−26.9113	+	15.5372i	−1.24530	+	0.718977i	−0.970169	−	0.242428i	$-0.922056\pi$
$467$	−26.9113	+	15.5372i	−1.24530	+	0.718977i	−0.275136	+	0.961405i	$0.588723\pi$
$468$		0			0
$469$	20.1494	+	7.88253i	0.930413	+	0.363981i
$470$		0			0
$471$		0			0
$472$	3.05194	−	5.28611i	0.140477	−	0.243313i
$473$	−0.552378	+	0.956747i	−0.0253984	+	0.0439913i
$474$		0			0
$475$		0			0
$476$	−7.56386	+	6.04558i	−0.346689	+	0.277099i
$477$		0			0
$478$	13.9601	−	8.05990i	0.638522	−	0.368651i
$479$	−18.2404	+	31.5933i	−0.833426	+	1.44354i	0.0618788	+	0.998084i	$0.480291\pi$
$479$	−18.2404	+	31.5933i	−0.833426	+	1.44354i	−0.895305	+	0.445453i	$0.853043\pi$
$480$		0			0
$481$	5.44483	−	3.14357i	0.248263	−	0.143335i
$482$			21.1567i			0.963660i
$483$		0			0
$484$	10.7536			0.488802
$485$		0			0
$486$		0			0
$487$	−12.2399	−	7.06672i	−0.554644	−	0.320224i	0.196349	−	0.980534i	$-0.437091\pi$
$487$	−12.2399	−	7.06672i	−0.554644	−	0.320224i	−0.750993	+	0.660310i	$0.770425\pi$
$488$	3.24271	−	1.87218i	0.146791	−	0.0847496i
$489$		0			0
$490$		0			0
$491$		−	32.5466i		−	1.46881i	−0.678714	−	0.734403i	$-0.737462\pi$
$491$		−	32.5466i		−	1.46881i	0.678714	−	0.734403i	$-0.262538\pi$
$492$		0			0
$493$	16.2489	−	28.1440i	0.731815	−	1.26754i
$494$	−8.56597	−	4.94556i	−0.385401	−	0.222511i
$495$		0			0
$496$			7.97593i			0.358130i
$497$	−4.12140	−	27.1414i	−0.184870	−	1.21746i
$498$		0			0
$499$	5.87396	+	10.1740i	0.262955	+	0.455451i	0.967026	−	0.254679i	$-0.0819697\pi$
$499$	5.87396	+	10.1740i	0.262955	+	0.455451i	−0.704071	+	0.710130i	$0.748636\pi$
$500$		0			0
$501$		0			0
$502$	3.03158	+	5.25086i	0.135306	+	0.234357i
$503$			24.5250i			1.09352i	0.837291	+	0.546758i	$0.184138\pi$
$503$			24.5250i			1.09352i	−0.837291	+	0.546758i	$0.815862\pi$
$504$		0			0
$505$		0			0
$506$	−2.76146	+	1.59433i	−0.122762	+	0.0708766i
$507$		0			0
$508$	0.652503	+	0.376723i	0.0289501	+	0.0167144i
$509$	5.84634	+	10.1262i	0.259135	+	0.448834i	0.966010	−	0.258503i	$-0.0832293\pi$
$509$	5.84634	+	10.1262i	0.259135	+	0.448834i	−0.706876	+	0.707338i	$0.749896\pi$
$510$		0			0
$511$	−12.5954	+	32.1966i	−0.557189	+	1.42429i
$512$	1.00000			0.0441942
$513$		0			0
$514$	9.51357	+	5.49266i	0.419626	+	0.242271i
$515$		0			0
$516$		0			0
$517$	3.24825			0.142858
$518$	5.64459	+	2.20819i	0.248009	+	0.0970221i
$519$		0			0
$520$		0			0
$521$	−14.8674	+	25.7511i	−0.651354	+	1.12818i	0.331441	+	0.943476i	$0.392465\pi$
$521$	−14.8674	+	25.7511i	−0.651354	+	1.12818i	−0.982795	+	0.184702i	$0.940868\pi$
$522$		0			0
$523$	2.82915	+	4.90024i	0.123710	+	0.214272i	0.921228	−	0.389023i	$-0.127187\pi$
$523$	2.82915	+	4.90024i	0.123710	+	0.214272i	−0.797518	+	0.603295i	$0.793854\pi$
$524$	−12.7125			−0.555347
$525$		0			0
$526$	1.33873			0.0583714
$527$	−14.5953	−	25.2799i	−0.635783	−	1.10121i
$528$		0			0
$529$	−9.13513	+	15.8225i	−0.397179	+	0.687935i
$530$		0			0
$531$		0			0
$532$	−1.43156	−	9.42751i	−0.0620660	−	0.408734i
$533$	6.11497			0.264869
$534$		0			0
$535$		0			0
$536$	7.08216	+	4.08889i	0.305903	+	0.176613i
$537$		0			0
$538$	−0.622322			−0.0268302
$539$	3.38904	+	0.765697i	0.145976	+	0.0329809i
$540$		0			0
$541$	17.6742	+	30.6126i	0.759874	+	1.31614i	0.942915	+	0.333035i	$0.108073\pi$
$541$	17.6742	+	30.6126i	0.759874	+	1.31614i	−0.183041	+	0.983105i	$0.558594\pi$
$542$	−18.4634	−	10.6598i	−0.793070	−	0.457879i
$543$		0			0
$544$	−3.16952	+	1.82992i	−0.135892	+	0.0784572i
$545$		0			0
$546$		0			0
$547$		−	21.4806i		−	0.918445i	−0.888321	−	0.459223i	$-0.848128\pi$
$547$		−	21.4806i		−	0.918445i	0.888321	−	0.459223i	$-0.151872\pi$
$548$	−2.15740	−	3.73673i	−0.0921595	−	0.159625i
$549$		0			0
$550$		0			0
$551$	16.0015	+	27.7154i	0.681687	+	1.18072i
$552$		0			0
$553$	−14.6800	−	18.3667i	−0.624256	−	0.781031i
$554$		−	1.18709i		−	0.0504345i
$555$		0			0
$556$	0.0590003	+	0.0340638i	0.00250217	+	0.00144463i
$557$	−19.9150	+	34.4939i	−0.843828	+	1.46155i	0.0428076	+	0.999083i	$0.486370\pi$
$557$	−19.9150	+	34.4939i	−0.843828	+	1.46155i	−0.886635	+	0.462469i	$0.846964\pi$
$558$		0			0
$559$		−	6.10836i		−	0.258356i
$560$		0			0
$561$		0			0
$562$	−1.71120	+	0.987964i	−0.0721828	+	0.0416747i
$563$	8.95567	+	5.17056i	0.377437	+	0.217913i	0.676702	−	0.736257i	$-0.263408\pi$
$563$	8.95567	+	5.17056i	0.377437	+	0.217913i	−0.299266	+	0.954170i	$0.596742\pi$
$564$		0			0
$565$		0			0
$566$	−27.1309			−1.14040
$567$		0			0
$568$		−	10.3761i		−	0.435371i
$569$	24.3464	−	14.0564i	1.02065	−	0.589275i	0.106361	−	0.994328i	$-0.466080\pi$
$569$	24.3464	−	14.0564i	1.02065	−	0.589275i	0.914293	+	0.405053i	$0.132747\pi$
$570$		0			0
$571$	13.7146	−	23.7544i	0.573938	−	0.994090i	−0.422218	−	0.906494i	$-0.638748\pi$
$571$	13.7146	−	23.7544i	0.573938	−	0.994090i	0.996156	−	0.0875958i	$-0.0279184\pi$
$572$	1.17969	−	0.681094i	0.0493253	−	0.0284780i
$573$		0			0
$574$	3.68063	+	4.60498i	0.153627	+	0.192208i
$575$		0			0
$576$		0			0
$577$	−6.51910	+	11.2914i	−0.271394	+	0.470068i	−0.969219	−	0.246200i	$-0.920818\pi$
$577$	−6.51910	+	11.2914i	−0.271394	+	0.470068i	0.697825	+	0.716268i	$0.254151\pi$
$578$	−1.80278	+	3.12250i	−0.0749857	+	0.129879i
$579$		0			0
$580$		0			0
$581$	−1.90296	−	12.5319i	−0.0789481	−	0.519911i
$582$		0			0
$583$	3.33843	−	1.92744i	0.138264	−	0.0798266i
$584$	−6.53361	+	11.3165i	−0.270363	+	0.468282i
$585$		0			0
$586$	8.99008	−	5.19042i	0.371377	−	0.214414i
$587$		−	35.0223i		−	1.44553i	−0.691096	−	0.722763i	$-0.742872\pi$
$587$		−	35.0223i		−	1.44553i	0.691096	−	0.722763i	$-0.257128\pi$
$588$		0			0
$589$	28.7461			1.18446
$590$		0			0
$591$		0			0
$592$	1.98397	+	1.14545i	0.0815409	+	0.0470776i
$593$	14.1919	−	8.19370i	0.582792	−	0.336475i	−0.179450	−	0.983767i	$-0.557432\pi$
$593$	14.1919	−	8.19370i	0.582792	−	0.336475i	0.762242	+	0.647292i	$0.224099\pi$
$594$		0			0
$595$		0			0
$596$			16.6982i			0.683986i
$597$		0			0
$598$	8.81529	−	15.2685i	0.360484	−	0.624376i
$599$	−26.0718	−	15.0526i	−1.06527	−	0.615032i	−0.138382	−	0.990379i	$-0.544190\pi$
$599$	−26.0718	−	15.0526i	−1.06527	−	0.615032i	−0.926884	+	0.375347i	$0.877524\pi$
$600$		0			0
$601$		−	1.75569i		−	0.0716162i	−0.999359	−	0.0358081i	$-0.988599\pi$
$601$		−	1.75569i		−	0.0716162i	0.999359	−	0.0358081i	$-0.0114005\pi$
$602$	4.60001	−	3.67666i	0.187482	−	0.149849i
$603$		0			0
$604$	6.51016	+	11.2759i	0.264895	+	0.458811i
$605$		0			0
$606$		0			0
$607$	9.03616	+	15.6511i	0.366766	+	0.635258i	0.989058	−	0.147528i	$-0.0471315\pi$
$607$	9.03616	+	15.6511i	0.366766	+	0.635258i	−0.622292	+	0.782785i	$0.713798\pi$
$608$		−	3.60411i		−	0.146166i
$609$		0			0
$610$		0			0
$611$	−15.5539	+	8.98003i	−0.629242	+	0.363293i
$612$		0			0
$613$	11.1285	+	6.42507i	0.449478	+	0.259506i	0.707610	−	0.706604i	$-0.249774\pi$
$613$	11.1285	+	6.42507i	0.449478	+	0.259506i	−0.258132	+	0.966110i	$0.583107\pi$
$614$	−7.06821	−	12.2425i	−0.285250	−	0.494067i
$615$		0			0
$616$	1.22297	+	0.478431i	0.0492749	+	0.0192765i
$617$	37.3633			1.50419			0.752094	−	0.659055i	$-0.229044\pi$
$617$	37.3633			1.50419			0.752094	+	0.659055i	$0.229044\pi$
$618$		0			0
$619$	−23.7213	−	13.6955i	−0.953439	−	0.550468i	−0.0592911	−	0.998241i	$-0.518884\pi$
$619$	−23.7213	−	13.6955i	−0.953439	−	0.550468i	−0.894147	+	0.447773i	$0.852217\pi$
$620$		0			0
$621$		0			0
$622$	−6.65287			−0.266756
$623$	−2.45661	−	3.07356i	−0.0984222	−	0.123140i
$624$		0			0
$625$		0			0
$626$	6.07282	−	10.5184i	0.242719	−	0.420401i
$627$		0			0
$628$	7.40408	+	12.8242i	0.295455	+	0.511743i
$629$	−8.38432			−0.334305
$630$		0			0
$631$	−4.09420			−0.162987			−0.0814937	−	0.996674i	$-0.525969\pi$
$631$	−4.09420			−0.162987			−0.0814937	+	0.996674i	$0.525969\pi$
$632$	−4.44344	−	7.69627i	−0.176751	−	0.306141i
$633$		0			0
$634$	−15.3605	+	26.6051i	−0.610043	+	1.05662i
$635$		0			0
$636$		0			0
$637$	−18.3449	+	5.70280i	−0.726850	+	0.225953i
$638$	−4.40740			−0.174491
$639$		0			0
$640$		0			0
$641$	28.4700	+	16.4371i	1.12450	+	0.649228i	0.942545	−	0.334080i	$-0.108426\pi$
$641$	28.4700	+	16.4371i	1.12450	+	0.649228i	0.181951	+	0.983308i	$0.441759\pi$
$642$		0			0
$643$	48.1790			1.89999			0.949996	−	0.312261i	$-0.101086\pi$
$643$	48.1790			1.89999			0.949996	+	0.312261i	$0.101086\pi$
$644$	16.8042	−	2.55170i	0.662178	−	0.100551i
$645$		0			0
$646$	6.59524	+	11.4233i	0.259486	+	0.449443i
$647$	−4.58478	−	2.64703i	−0.180246	−	0.104065i	0.407162	−	0.913356i	$-0.366518\pi$
$647$	−4.58478	−	2.64703i	−0.180246	−	0.104065i	−0.587408	+	0.809291i	$0.699852\pi$
$648$		0			0
$649$	2.62377	−	1.51483i	0.102992	−	0.0594625i
$650$		0			0
$651$		0			0
$652$		−	15.3793i		−	0.602301i
$653$	25.0603	+	43.4057i	0.980686	+	1.69860i	0.659729	+	0.751503i	$0.270671\pi$
$653$	25.0603	+	43.4057i	0.980686	+	1.69860i	0.320956	+	0.947094i	$0.395996\pi$
$654$		0			0
$655$		0			0
$656$	1.11408	+	1.92964i	0.0434975	+	0.0753399i
$657$		0			0
$658$	−16.1245	−	6.30798i	−0.628599	−	0.245911i
$659$		−	2.20149i		−	0.0857579i	−0.999080	−	0.0428790i	$-0.986347\pi$
$659$		−	2.20149i		−	0.0857579i	0.999080	−	0.0428790i	$-0.0136530\pi$
$660$		0			0
$661$	−33.7612	−	19.4921i	−1.31316	−	0.758153i	−0.330542	−	0.943791i	$-0.607231\pi$
$661$	−33.7612	−	19.4921i	−1.31316	−	0.758153i	−0.982618	+	0.185638i	$0.940565\pi$
$662$	15.5140	−	26.8710i	0.602967	−	1.04437i
$663$		0			0
$664$		−	4.79091i		−	0.185923i
$665$		0			0
$666$		0			0
$667$	−49.4017	+	28.5221i	−1.91284	+	1.10438i
$668$	21.2316	+	12.2581i	0.821475	+	0.474279i
$669$		0			0
$670$		0			0
$671$	1.85852			0.0717473
$672$		0			0
$673$		−	43.4830i		−	1.67615i	−0.545556	−	0.838074i	$-0.683682\pi$
$673$		−	43.4830i		−	1.67615i	0.545556	−	0.838074i	$-0.316318\pi$
$674$	5.98830	−	3.45735i	0.230661	−	0.133172i
$675$		0			0
$676$	2.73413	−	4.73565i	0.105159	−	0.182140i
$677$	36.0802	−	20.8309i	1.38668	−	0.800597i	0.393736	−	0.919223i	$-0.371182\pi$
$677$	36.0802	−	20.8309i	1.38668	−	0.800597i	0.992939	+	0.118626i	$0.0378489\pi$
$678$		0			0
$679$	23.6772	−	3.59537i	0.908648	−	0.137978i
$680$		0			0
$681$		0			0
$682$	−1.97943	+	3.42848i	−0.0757965	+	0.131283i
$683$	23.8637	−	41.3332i	0.913120	−	1.58157i	0.103490	−	0.994631i	$-0.466999\pi$
$683$	23.8637	−	41.3332i	0.913120	−	1.58157i	0.809630	−	0.586940i	$-0.199668\pi$
$684$		0			0
$685$		0			0
$686$	−15.3365	−	10.3824i	−0.585548	−	0.396400i
$687$		0			0
$688$	1.92756	−	1.11288i	0.0734875	−	0.0424280i
$689$	−10.6571	+	18.4587i	−0.406004	+	0.703220i
$690$		0			0
$691$	33.6953	−	19.4540i	1.28183	−	0.740066i	0.304648	−	0.952465i	$-0.401461\pi$
$691$	33.6953	−	19.4540i	1.28183	−	0.740066i	0.977183	+	0.212399i	$0.0681277\pi$
$692$			12.5243i			0.476101i
$693$		0			0
$694$	−7.49408			−0.284471
$695$		0			0
$696$		0			0
$697$	−7.06219	−	4.07736i	−0.267500	−	0.154441i
$698$	10.7866	−	6.22762i	0.408277	−	0.235719i
$699$		0			0
$700$		0			0
$701$			8.73610i			0.329958i	0.986297	+	0.164979i	$0.0527556\pi$
$701$			8.73610i			0.329958i	−0.986297	+	0.164979i	$0.947244\pi$
$702$		0			0
$703$	4.12832	−	7.15046i	0.155703	−	0.269685i
$704$	0.429853	+	0.248176i	0.0162007	+	0.00935348i
$705$		0			0
$706$		−	18.9402i		−	0.712824i
$707$	2.89515	−	7.40061i	0.108883	−	0.278329i
$708$		0			0
$709$	8.25544	+	14.2988i	0.310039	+	0.537004i	0.978371	−	0.206860i	$-0.0663244\pi$
$709$	8.25544	+	14.2988i	0.310039	+	0.537004i	−0.668331	+	0.743864i	$0.732991\pi$
$710$		0			0
$711$		0			0
$712$	−0.743586	−	1.28793i	−0.0278671	−	0.0482671i
$713$			51.2389i			1.91891i
$714$		0			0
$715$		0			0
$716$	1.58961	−	0.917762i	0.0594066	−	0.0342984i
$717$		0			0
$718$	23.0590	+	13.3131i	0.860554	+	0.496841i
$719$	−22.5570	−	39.0699i	−0.841234	−	1.45706i	−0.888852	−	0.458195i	$-0.848496\pi$
$719$	−22.5570	−	39.0699i	−0.841234	−	1.45706i	0.0476171	−	0.998866i	$-0.484837\pi$
$720$		0			0
$721$	23.7457	+	29.7092i	0.884336	+	1.10643i
$722$	6.01040			0.223684
$723$		0			0
$724$	20.4871	+	11.8282i	0.761396	+	0.439592i
$725$		0			0
$726$		0			0
$727$	31.9760			1.18593			0.592963	−	0.805230i	$-0.297958\pi$
$727$	31.9760			1.18593			0.592963	+	0.805230i	$0.297958\pi$
$728$	−7.17871	+	1.09008i	−0.266061	+	0.0404012i
$729$		0			0
$730$		0			0
$731$	−4.07295	+	7.05456i	−0.150644	+	0.260922i
$732$		0			0
$733$	23.3606	+	40.4618i	0.862844	+	1.49449i	0.869172	+	0.494509i	$0.164652\pi$
$733$	23.3606	+	40.4618i	0.862844	+	1.49449i	−0.00632839	+	0.999980i	$0.502014\pi$
$734$	−10.9121			−0.402773
$735$		0			0
$736$	6.42419			0.236799
$737$	2.02953	+	3.51524i	0.0747586	+	0.129486i
$738$		0			0
$739$	−4.59353	+	7.95623i	−0.168976	+	0.292675i	−0.938060	−	0.346473i	$-0.887379\pi$
$739$	−4.59353	+	7.95623i	−0.168976	+	0.292675i	0.769084	+	0.639147i	$0.220713\pi$
$740$		0			0
$741$		0			0
$742$	−20.3152	+	3.08485i	−0.745795	+	0.113248i
$743$	28.5353			1.04686			0.523430	−	0.852069i	$-0.324652\pi$
$743$	28.5353			1.04686			0.523430	+	0.852069i	$0.324652\pi$
$744$		0			0
$745$		0			0
$746$	19.4924	+	11.2539i	0.713667	+	0.412036i
$747$		0			0
$748$	−1.81657			−0.0664203
$749$	3.51234	+	4.39442i	0.128338	+	0.160569i
$750$		0			0
$751$	21.4749	+	37.1956i	0.783629	+	1.35729i	0.929814	+	0.368029i	$0.119967\pi$
$751$	21.4749	+	37.1956i	0.783629	+	1.35729i	−0.146185	+	0.989257i	$0.546700\pi$
$752$	−5.66749	−	3.27213i	−0.206672	−	0.119322i
$753$		0			0
$754$	21.1043	−	12.1846i	0.768574	−	0.443736i
$755$		0			0
$756$		0			0
$757$			19.4415i			0.706612i	0.935508	+	0.353306i	$0.114943\pi$
$757$			19.4415i			0.706612i	−0.935508	+	0.353306i	$0.885057\pi$
$758$	−1.62954	−	2.82245i	−0.0591877	−	0.102516i
$759$		0			0
$760$		0			0
$761$	24.9154	+	43.1547i	0.903182	+	1.56436i	0.823339	+	0.567550i	$0.192109\pi$
$761$	24.9154	+	43.1547i	0.903182	+	1.56436i	0.0798434	+	0.996807i	$0.474558\pi$
$762$		0			0
$763$	7.61827	−	19.4739i	0.275800	−	0.705003i
$764$		−	8.10892i		−	0.293371i
$765$		0			0
$766$	15.0013	+	8.66098i	0.542017	+	0.312934i
$767$	−8.37575	+	14.5072i	−0.302431	+	0.523825i
$768$		0			0
$769$			29.5025i			1.06389i	0.846779	+	0.531944i	$0.178538\pi$
$769$			29.5025i			1.06389i	−0.846779	+	0.531944i	$0.821462\pi$
$770$		0			0
$771$		0			0
$772$	−10.4356	+	6.02502i	−0.375587	+	0.216845i
$773$	21.9349	+	12.6641i	0.788945	+	0.455498i	0.839591	−	0.543219i	$-0.182795\pi$
$773$	21.9349	+	12.6641i	0.788945	+	0.455498i	−0.0506458	+	0.998717i	$0.516128\pi$
$774$		0			0
$775$		0			0
$776$	9.05174			0.324938
$777$		0			0
$778$		−	31.6982i		−	1.13644i
$779$	6.95465	−	4.01527i	0.249176	−	0.143862i
$780$		0			0
$781$	2.57509	−	4.46019i	0.0921440	−	0.159598i
$782$	−20.3616	+	11.7558i	−0.728129	+	0.420385i
$783$		0			0
$784$	−5.14181	−	4.74992i	−0.183636	−	0.169640i
$785$		0			0
$786$		0			0
$787$	3.40220	−	5.89278i	0.121275	−	0.210055i	−0.798996	−	0.601337i	$-0.794635\pi$
$787$	3.40220	−	5.89278i	0.121275	−	0.210055i	0.920271	+	0.391282i	$0.127968\pi$
$788$	−6.37315	+	11.0386i	−0.227034	+	0.393235i
$789$		0			0
$790$		0			0
$791$	−32.1655	+	4.88430i	−1.14367	+	0.173666i
$792$		0			0
$793$	−8.89931	+	5.13802i	−0.316024	+	0.182456i
$794$	16.7561	−	29.0224i	0.594651	−	1.02997i
$795$		0			0
$796$	16.4954	−	9.52361i	0.584663	−	0.337556i
$797$		−	31.6373i		−	1.12065i	−0.828272	−	0.560326i	$-0.810676\pi$
$797$		−	31.6373i		−	1.12065i	0.828272	−	0.560326i	$-0.189324\pi$
$798$		0			0
$799$	23.9509			0.847323
$800$		0			0
$801$		0			0
$802$	31.0404	+	17.9212i	1.09607	+	0.632818i
$803$	−5.61698	+	3.24297i	−0.198219	+	0.114442i
$804$		0			0
$805$		0			0
$806$		−	21.8892i		−	0.771013i
$807$		0			0
$808$	1.50180	−	2.60119i	0.0528330	−	0.0915094i
$809$	−22.9302	−	13.2388i	−0.806183	−	0.465450i	0.0394457	−	0.999222i	$-0.487441\pi$
$809$	−22.9302	−	13.2388i	−0.806183	−	0.465450i	−0.845629	+	0.533772i	$0.820774\pi$
$810$		0			0
$811$			25.4799i			0.894720i	0.894354	+	0.447360i	$0.147636\pi$
$811$			25.4799i			0.894720i	−0.894354	+	0.447360i	$0.852364\pi$
$812$	21.8786	+	8.55899i	0.767788	+	0.300362i
$813$		0			0
$814$	0.568545	+	0.984749i	0.0199275	+	0.0345154i
$815$		0			0
$816$		0			0
$817$	−4.01093	−	6.94713i	−0.140325	−	0.243049i
$818$		−	24.6499i		−	0.861863i
$819$		0			0
$820$		0			0
$821$	−32.9335	+	19.0141i	−1.14939	+	0.663598i	−0.948738	−	0.316065i	$-0.897638\pi$
$821$	−32.9335	+	19.0141i	−1.14939	+	0.663598i	−0.200649	+	0.979663i	$0.564305\pi$
$822$		0			0
$823$	3.09676	+	1.78791i	0.107946	+	0.0623228i	0.553001	−	0.833181i	$-0.313483\pi$
$823$	3.09676	+	1.78791i	0.107946	+	0.0623228i	−0.445055	+	0.895503i	$0.646816\pi$
$824$	7.18752	+	12.4491i	0.250389	+	0.433687i
$825$		0			0
$826$	−15.9663	+	2.42447i	−0.555539	+	0.0843582i
$827$	−15.0648			−0.523855			−0.261927	−	0.965088i	$-0.584358\pi$
$827$	−15.0648			−0.523855			−0.261927	+	0.965088i	$0.584358\pi$
$828$		0			0
$829$	27.5046	+	15.8798i	0.955273	+	0.551527i	0.894715	−	0.446637i	$-0.147379\pi$
$829$	27.5046	+	15.8798i	0.955273	+	0.551527i	0.0605582	+	0.998165i	$0.480712\pi$
$830$		0			0
$831$		0			0
$832$	−2.74440			−0.0951450
$833$	24.9890	+	5.64586i	0.865819	+	0.195617i
$834$		0			0
$835$		0			0
$836$	0.894453	−	1.54924i	0.0309353	−	0.0535815i
$837$		0			0
$838$	5.32868	+	9.22954i	0.184076	+	0.318829i
$839$	−15.1305			−0.522362			−0.261181	−	0.965290i	$-0.584112\pi$
$839$	−15.1305			−0.522362			−0.261181	+	0.965290i	$0.584112\pi$
$840$		0			0
$841$	−49.8470			−1.71886
$842$	−11.3407	−	19.6427i	−0.390828	−	0.676933i
$843$		0			0
$844$	4.46028	−	7.72544i	0.153529	−	0.265920i
$845$		0			0
$846$		0			0
$847$	−17.7636	−	22.2247i	−0.610365	−	0.763651i
$848$	−7.76645			−0.266701
$849$		0			0
$850$		0			0
$851$	12.7454	+	7.35858i	0.436908	+	0.252249i
$852$		0			0
$853$	−12.1586			−0.416302			−0.208151	−	0.978097i	$-0.566745\pi$
$853$	−12.1586			−0.416302			−0.208151	+	0.978097i	$0.566745\pi$
$854$	−9.22581	−	3.60917i	−0.315701	−	0.123503i
$855$		0			0
$856$	1.06314	+	1.84141i	0.0363374	+	0.0629382i
$857$	27.1356	+	15.6668i	0.926936	+	0.535167i	0.885841	−	0.463989i	$-0.153582\pi$
$857$	27.1356	+	15.6668i	0.926936	+	0.535167i	0.0410947	+	0.999155i	$0.486915\pi$
$858$		0			0
$859$	12.7872	−	7.38268i	0.436293	−	0.251894i	−0.265731	−	0.964047i	$-0.585613\pi$
$859$	12.7872	−	7.38268i	0.436293	−	0.251894i	0.702024	+	0.712153i	$0.252280\pi$
$860$		0			0
$861$		0			0
$862$			30.0728i			1.02429i
$863$	−7.21398	−	12.4950i	−0.245567	−	0.425334i	0.716724	−	0.697357i	$-0.245641\pi$
$863$	−7.21398	−	12.4950i	−0.245567	−	0.425334i	−0.962291	+	0.272023i	$0.912307\pi$
$864$		0			0
$865$		0			0
$866$	−7.46016	−	12.9214i	−0.253507	−	0.439086i
$867$		0			0
$868$	16.4840	−	13.1752i	0.559504	−	0.447196i
$869$		−	4.41102i		−	0.149634i
$870$		0			0
$871$	−19.4363	−	11.2216i	−0.658574	−	0.380228i
$872$	3.95181	−	6.84474i	0.133825	−	0.231792i
$873$		0			0
$874$		−	23.1535i		−	0.783179i
$875$		0			0
$876$		0			0
$877$	−9.14788	+	5.28153i	−0.308902	+	0.178345i	−0.646435	−	0.762969i	$-0.723741\pi$
$877$	−9.14788	+	5.28153i	−0.308902	+	0.178345i	0.337533	+	0.941314i	$0.390408\pi$
$878$	11.1126	+	6.41586i	0.375032	+	0.216525i
$879$		0			0
$880$		0			0
$881$	13.4300			0.452469			0.226234	−	0.974073i	$-0.427358\pi$
$881$	13.4300			0.452469			0.226234	+	0.974073i	$0.427358\pi$
$882$		0			0
$883$			4.06019i			0.136636i	0.997664	+	0.0683181i	$0.0217633\pi$
$883$			4.06019i			0.136636i	−0.997664	+	0.0683181i	$0.978237\pi$
$884$	8.69843	−	5.02204i	0.292560	−	0.168909i
$885$		0			0
$886$	−10.2071	+	17.6792i	−0.342913	+	0.593943i
$887$	−28.6095	+	16.5177i	−0.960614	+	0.554611i	−0.896362	−	0.443323i	$-0.853799\pi$
$887$	−28.6095	+	16.5177i	−0.960614	+	0.554611i	−0.0642519	+	0.997934i	$0.520466\pi$
$888$		0			0
$889$	−0.299270	−	1.97084i	−0.0100372	−	0.0660997i
$890$		0			0
$891$		0			0
$892$	11.7721	−	20.3899i	0.394160	−	0.682705i
$893$	−11.7931	+	20.4262i	−0.394641	+	0.683538i
$894$		0			0
$895$		0			0
$896$	−1.65187	−	2.06672i	−0.0551851	−	0.0690442i
$897$		0			0
$898$	−18.0483	+	10.4202i	−0.602280	+	0.347727i
$899$	−35.4115	+	61.3345i	−1.18104	+	2.04562i
$900$		0			0
$901$	24.6159	−	14.2120i	0.820074	−	0.473470i
$902$			1.10595i			0.0368241i
$903$		0			0
$904$	−12.2968			−0.408984
$905$		0			0
$906$		0			0
$907$	−23.6700	−	13.6659i	−0.785949	−	0.453768i	0.0525853	−	0.998616i	$-0.483254\pi$
$907$	−23.6700	−	13.6659i	−0.785949	−	0.453768i	−0.838535	+	0.544848i	$0.816587\pi$
$908$	−8.07522	+	4.66223i	−0.267986	+	0.154722i
$909$		0			0
$910$		0			0
$911$			1.06838i			0.0353972i	0.999843	+	0.0176986i	$0.00563393\pi$
$911$			1.06838i			0.0353972i	−0.999843	+	0.0176986i	$0.994366\pi$
$912$		0			0
$913$	1.18899	−	2.05939i	0.0393498	−	0.0681558i
$914$	13.8811	+	8.01424i	0.459145	+	0.265087i
$915$		0			0
$916$		−	23.2725i		−	0.768944i
$917$	20.9994	+	26.2731i	0.693460	+	0.867615i
$918$		0			0
$919$	−26.8653	−	46.5320i	−0.886203	−	1.53495i	−0.844329	−	0.535826i	$-0.820000\pi$
$919$	−26.8653	−	46.5320i	−0.886203	−	1.53495i	−0.0418743	−	0.999123i	$-0.513333\pi$
$920$		0			0
$921$		0			0
$922$	0.991998	+	1.71819i	0.0326697	+	0.0565856i
$923$			28.4761i			0.937303i
$924$		0			0
$925$		0			0
$926$	−31.5222	+	18.1994i	−1.03588	+	0.598068i
$927$		0			0
$928$	7.68995	+	4.43979i	0.252435	+	0.145743i
$929$	−4.80716	−	8.32625i	−0.157718	−	0.273175i	0.776327	−	0.630330i	$-0.217080\pi$
$929$	−4.80716	−	8.32625i	−0.157718	−	0.273175i	−0.934045	+	0.357154i	$0.883747\pi$
$930$		0			0
$931$	−17.1192	+	18.5316i	−0.561061	+	0.607350i
$932$	12.6203			0.413393
$933$		0			0
$934$	26.9113	+	15.5372i	0.880563	+	0.508394i
$935$		0			0
$936$		0			0
$937$	12.8030			0.418256			0.209128	−	0.977888i	$-0.432937\pi$
$937$	12.8030			0.418256			0.209128	+	0.977888i	$0.432937\pi$
$938$	−3.24823	−	21.3912i	−0.106059	−	0.698446i
$939$		0			0
$940$		0			0
$941$	24.2221	−	41.9538i	0.789616	−	1.36766i	−0.136586	−	0.990628i	$-0.543613\pi$
$941$	24.2221	−	41.9538i	0.789616	−	1.36766i	0.926202	−	0.377028i	$-0.123054\pi$
$942$		0			0
$943$	7.15707	+	12.3964i	0.233066	+	0.403682i
$944$	−6.10388			−0.198664
$945$		0			0
$946$	1.10476			0.0359187
$947$	−18.9980	−	32.9055i	−0.617353	−	1.06929i	−0.989967	−	0.141300i	$-0.954872\pi$
$947$	−18.9980	−	32.9055i	−0.617353	−	1.06929i	0.372614	−	0.927986i	$-0.378461\pi$
$948$		0			0
$949$	17.9308	−	31.0571i	0.582060	−	1.00816i
$950$		0			0
$951$		0			0
$952$	9.01756	+	3.52771i	0.292261	+	0.114334i
$953$	−15.2394			−0.493652			−0.246826	−	0.969060i	$-0.579388\pi$
$953$	−15.2394			−0.493652			−0.246826	+	0.969060i	$0.579388\pi$
$954$		0			0
$955$		0			0
$956$	−13.9601	−	8.05990i	−0.451503	−	0.260676i
$957$		0			0
$958$	36.4809			1.17864
$959$	−4.15902	+	10.6313i	−0.134302	+	0.343303i
$960$		0			0
$961$	16.3078	+	28.2459i	0.526057	+	0.911157i
$962$	−5.44483	−	3.14357i	−0.175548	−	0.101353i
$963$		0			0
$964$	18.3222	−	10.5783i	0.590119	−	0.340705i
$965$		0			0
$966$		0			0
$967$			27.7458i			0.892244i	0.894972	+	0.446122i	$0.147195\pi$
$967$			27.7458i			0.892244i	−0.894972	+	0.446122i	$0.852805\pi$
$968$	−5.37682	−	9.31292i	−0.172817	−	0.299329i
$969$		0			0
$970$		0			0
$971$	10.2730	+	17.7934i	0.329677	+	0.571018i	0.982448	−	0.186538i	$-0.0597268\pi$
$971$	10.2730	+	17.7934i	0.329677	+	0.571018i	−0.652771	+	0.757556i	$0.726393\pi$
$972$		0			0
$973$	−0.0270604	−	0.178206i	−0.000867518	−	0.00571302i
$974$			14.1334i			0.452865i
$975$		0			0
$976$	−3.24271	−	1.87218i	−0.103797	−	0.0599270i
$977$	−3.81400	+	6.60604i	−0.122021	+	0.211346i	−0.920564	−	0.390591i	$-0.872271\pi$
$977$	−3.81400	+	6.60604i	−0.122021	+	0.211346i	0.798544	+	0.601937i	$0.205604\pi$
$978$		0			0
$979$		−	0.738160i		−	0.0235917i
$980$		0			0
$981$		0			0
$982$	−28.1861	+	16.2733i	−0.899456	+	0.519301i
$983$	20.4984	+	11.8347i	0.653797	+	0.377470i	0.789909	−	0.613224i	$-0.210128\pi$
$983$	20.4984	+	11.8347i	0.653797	+	0.377470i	−0.136113	+	0.990693i	$0.543461\pi$
$984$		0			0
$985$		0			0
$986$	−32.4979			−1.03494
$987$		0			0
$988$			9.89113i			0.314679i
$989$	12.3830	−	7.14933i	0.393757	−	0.227336i
$990$		0			0
$991$	−13.3947	+	23.2003i	−0.425497	+	0.736982i	−0.996467	−	0.0839887i	$-0.973234\pi$
$991$	−13.3947	+	23.2003i	−0.425497	+	0.736982i	0.570970	+	0.820971i	$0.306567\pi$
$992$	6.90736	−	3.98797i	0.219309	−	0.126618i
$993$		0			0
$994$	−21.4444	+	17.1399i	−0.680176	+	0.543646i
$995$		0			0
$996$		0			0
$997$	−21.1111	+	36.5656i	−0.668596	+	1.15804i	0.309700	+	0.950834i	$0.399771\pi$
$997$	−21.1111	+	36.5656i	−0.668596	+	1.15804i	−0.978297	+	0.207209i	$0.933562\pi$
$998$	5.87396	−	10.1740i	0.185937	−	0.322053i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bp.g.899.11		24
3.2	odd	2		3150.2.bp.h.899.11		24
5.2	odd	4		3150.2.bf.e.1151.9	yes	24
5.3	odd	4		3150.2.bf.d.1151.4	✓	24
5.4	even	2		3150.2.bp.h.899.2		24
7.5	odd	6	inner	3150.2.bp.g.1349.2		24
15.2	even	4		3150.2.bf.e.1151.4	yes	24
15.8	even	4		3150.2.bf.d.1151.9	yes	24
15.14	odd	2	inner	3150.2.bp.g.899.2		24
21.5	even	6		3150.2.bp.h.1349.2		24
35.12	even	12		3150.2.bf.e.1601.4	yes	24
35.19	odd	6		3150.2.bp.h.1349.11		24
35.33	even	12		3150.2.bf.d.1601.9	yes	24
105.47	odd	12		3150.2.bf.e.1601.9	yes	24
105.68	odd	12		3150.2.bf.d.1601.4	yes	24
105.89	even	6	inner	3150.2.bp.g.1349.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.4	✓	24	5.3	odd	4
3150.2.bf.d.1151.9	yes	24	15.8	even	4
3150.2.bf.d.1601.4	yes	24	105.68	odd	12
3150.2.bf.d.1601.9	yes	24	35.33	even	12
3150.2.bf.e.1151.4	yes	24	15.2	even	4
3150.2.bf.e.1151.9	yes	24	5.2	odd	4
3150.2.bf.e.1601.4	yes	24	35.12	even	12
3150.2.bf.e.1601.9	yes	24	105.47	odd	12
3150.2.bp.g.899.2		24	15.14	odd	2	inner
3150.2.bp.g.899.11		24	1.1	even	1	trivial
3150.2.bp.g.1349.2		24	7.5	odd	6	inner
3150.2.bp.g.1349.11		24	105.89	even	6	inner
3150.2.bp.h.899.2		24	5.4	even	2
3150.2.bp.h.899.11		24	3.2	odd	2
3150.2.bp.h.1349.2		24	21.5	even	6
3150.2.bp.h.1349.11		24	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.61577 - 0.397202i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.61577 - 0.397202i) q^{7} +1.00000 q^{8} +(0.429853 + 0.248176i) q^{11} -2.74440 q^{13} +(-1.65187 - 2.06672i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.16952 + 1.82992i) q^{17} +(-3.12125 + 1.80205i) q^{19} -0.496352i q^{22} +(-3.21210 - 5.56351i) q^{23} +(1.37220 + 2.37672i) q^{26} +(-0.963896 + 2.46392i) q^{28} -8.87959i q^{29} +(-6.90736 - 3.98797i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.65984i q^{34} +(-1.98397 + 1.14545i) q^{37} +(3.12125 + 1.80205i) q^{38} -2.22816 q^{41} +2.22575i q^{43} +(-0.429853 + 0.248176i) q^{44} +(-3.21210 + 5.56351i) q^{46} +(5.66749 - 3.27213i) q^{47} +(6.68446 - 2.07798i) q^{49} +(1.37220 - 2.37672i) q^{52} +(3.88322 - 6.72594i) q^{53} +(2.61577 - 0.397202i) q^{56} +(-7.68995 + 4.43979i) q^{58} +(3.05194 - 5.28611i) q^{59} +(3.24271 - 1.87218i) q^{61} +7.97593i q^{62} +1.00000 q^{64} +(7.08216 + 4.08889i) q^{67} +(-3.16952 + 1.82992i) q^{68} -10.3761i q^{71} +(-6.53361 + 11.3165i) q^{73} +(1.98397 + 1.14545i) q^{74} -3.60411i q^{76} +(1.22297 + 0.478431i) q^{77} +(-4.44344 - 7.69627i) q^{79} +(1.11408 + 1.92964i) q^{82} -4.79091i q^{83} +(1.92756 - 1.11288i) q^{86} +(0.429853 + 0.248176i) q^{88} +(-0.743586 - 1.28793i) q^{89} +(-7.17871 + 1.09008i) q^{91} +6.42419 q^{92} +(-5.66749 - 3.27213i) q^{94} +9.05174 q^{97} +(-5.14181 - 4.74992i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 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

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