LMFDB - Embedded newform 1350.2.q.g.1043.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(143,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("1350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.q (of order $12$, degree $4$, 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:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1043.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.1043
Dual form			1350.2.q.g.1007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(4.40508 + 1.18034i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(4.40508 + 1.18034i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.550510 - 0.317837i) q^{11} +(3.34607 - 0.896575i) q^{13} +(-2.28024 + 3.94949i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.317837 + 0.317837i) q^{17} -6.44949i q^{19} +(0.164525 + 0.614014i) q^{22} +(-0.258819 - 0.965926i) q^{23} +3.46410i q^{26} +(-3.22474 - 3.22474i) q^{28} +(0.158919 + 0.275255i) q^{29} +(-0.224745 + 0.389270i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.389270 + 0.224745i) q^{34} +(3.00000 - 3.00000i) q^{37} +(6.22973 + 1.66925i) q^{38} +(-6.39898 - 3.69445i) q^{41} +(0.896575 - 3.34607i) q^{43} -0.635674 q^{44} +1.00000 q^{46} +(-2.32937 + 8.69333i) q^{47} +(11.9494 + 6.89898i) q^{49} +(-3.34607 - 0.896575i) q^{52} +(3.78194 - 3.78194i) q^{53} +(3.94949 - 2.28024i) q^{56} +(-0.307007 + 0.0822623i) q^{58} +(4.48905 - 7.77526i) q^{59} +(0.275255 + 0.476756i) q^{61} +(-0.317837 - 0.317837i) q^{62} -1.00000i q^{64} +(1.71089 + 6.38512i) q^{67} +(-0.116337 - 0.434174i) q^{68} +6.29253i q^{71} +(6.89898 + 6.89898i) q^{73} +(2.12132 + 3.67423i) q^{74} +(-3.22474 + 5.58542i) q^{76} +(2.80020 - 0.750311i) q^{77} +(-2.12132 + 1.22474i) q^{79} +(5.22474 - 5.22474i) q^{82} +(5.26380 + 1.41043i) q^{83} +(3.00000 + 1.73205i) q^{86} +(0.164525 - 0.614014i) q^{88} +8.02458 q^{89} +15.7980 q^{91} +(-0.258819 + 0.965926i) q^{92} +(-7.79423 - 4.50000i) q^{94} +(2.59405 + 0.695075i) q^{97} +(-9.75663 + 9.75663i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^7	$ 8 q + 8 q^{7} + 24 q^{11} + 4 q^{16} + 8 q^{22} - 16 q^{28} + 8 q^{31} + 24 q^{37} + 12 q^{38} - 12 q^{41} + 8 q^{46} + 12 q^{56} + 4 q^{58} + 12 q^{61} - 4 q^{67} - 12 q^{68} + 16 q^{73} - 16 q^{76} + 24 q^{77} + 32 q^{82} + 12 q^{83} + 24 q^{86} + 8 q^{88} + 48 q^{91} - 12 q^{97}+O(q^{100}) $ 8 * q + 8 * q^7 + 24 * q^11 + 4 * q^16 + 8 * q^22 - 16 * q^28 + 8 * q^31 + 24 * q^37 + 12 * q^38 - 12 * q^41 + 8 * q^46 + 12 * q^56 + 4 * q^58 + 12 * q^61 - 4 * q^67 - 12 * q^68 + 16 * q^73 - 16 * q^76 + 24 * q^77 + 32 * q^82 + 12 * q^83 + 24 * q^86 + 8 * q^88 + 48 * q^91 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.40508	+	1.18034i	1.66497	+	0.446126i	0.963746	−	0.266820i	$-0.0859730\pi$
$7$	4.40508	+	1.18034i	1.66497	+	0.446126i	0.701219	+	0.712946i	$0.252640\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$	0.550510	−	0.317837i	0.165985	−	0.0958315i	−0.414706	−	0.909955i	$-0.636116\pi$
$11$	0.550510	−	0.317837i	0.165985	−	0.0958315i	0.580691	+	0.814124i	$0.302782\pi$
$12$		0			0
$13$	3.34607	−	0.896575i	0.928032	−	0.248665i	0.237016	−	0.971506i	$-0.423830\pi$
$13$	3.34607	−	0.896575i	0.928032	−	0.248665i	0.691015	+	0.722840i	$0.257164\pi$
$14$	−2.28024	+	3.94949i	−0.609419	+	1.05555i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.317837	+	0.317837i	0.0770869	+	0.0770869i	0.744599	−	0.667512i	$-0.232641\pi$
$17$	0.317837	+	0.317837i	0.0770869	+	0.0770869i	−0.667512	+	0.744599i	$0.732641\pi$
$18$		0			0
$19$		−	6.44949i		−	1.47961i	−0.672819	−	0.739807i	$-0.734917\pi$
$19$		−	6.44949i		−	1.47961i	0.672819	−	0.739807i	$-0.265083\pi$
$20$		0			0
$21$		0			0
$22$	0.164525	+	0.614014i	0.0350768	+	0.130908i
$23$	−0.258819	−	0.965926i	−0.0539675	−	0.201409i	0.933678	−	0.358113i	$-0.116580\pi$
$23$	−0.258819	−	0.965926i	−0.0539675	−	0.201409i	−0.987646	+	0.156704i	$0.949913\pi$
$24$		0			0
$25$		0			0
$26$			3.46410i			0.679366i
$27$		0			0
$28$	−3.22474	−	3.22474i	−0.609419	−	0.609419i
$29$	0.158919	+	0.275255i	0.0295104	+	0.0511136i	0.880403	−	0.474225i	$-0.157272\pi$
$29$	0.158919	+	0.275255i	0.0295104	+	0.0511136i	−0.850893	+	0.525339i	$0.823939\pi$
$30$		0			0
$31$	−0.224745	+	0.389270i	−0.0403654	+	0.0699149i	−0.885502	−	0.464635i	$-0.846186\pi$
$31$	−0.224745	+	0.389270i	−0.0403654	+	0.0699149i	0.845137	+	0.534550i	$0.179519\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	−0.389270	+	0.224745i	−0.0667592	+	0.0385434i
$35$		0			0
$36$		0			0
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$	6.22973	+	1.66925i	1.01060	+	0.270788i
$39$		0			0
$40$		0			0
$41$	−6.39898	−	3.69445i	−0.999353	−	0.576977i	−0.0912960	−	0.995824i	$-0.529101\pi$
$41$	−6.39898	−	3.69445i	−0.999353	−	0.576977i	−0.908057	+	0.418847i	$0.862434\pi$
$42$		0			0
$43$	0.896575	−	3.34607i	0.136726	−	0.510270i	−0.863258	−	0.504762i	$-0.831580\pi$
$43$	0.896575	−	3.34607i	0.136726	−	0.510270i	0.999985	−	0.00550783i	$-0.00175320\pi$
$44$	−0.635674			−0.0958315
$45$		0			0
$46$	1.00000			0.147442
$47$	−2.32937	+	8.69333i	−0.339774	+	1.26805i	0.558827	+	0.829285i	$0.311252\pi$
$47$	−2.32937	+	8.69333i	−0.339774	+	1.26805i	−0.898600	+	0.438768i	$0.855415\pi$
$48$		0			0
$49$	11.9494	+	6.89898i	1.70705	+	0.985568i
$50$		0			0
$51$		0			0
$52$	−3.34607	−	0.896575i	−0.464016	−	0.124333i
$53$	3.78194	−	3.78194i	0.519489	−	0.519489i	−0.397928	−	0.917417i	$-0.630270\pi$
$53$	3.78194	−	3.78194i	0.519489	−	0.519489i	0.917417	+	0.397928i	$0.130270\pi$
$54$		0			0
$55$		0			0
$56$	3.94949	−	2.28024i	0.527773	−	0.304710i
$57$		0			0
$58$	−0.307007	+	0.0822623i	−0.0403120	+	0.0108016i
$59$	4.48905	−	7.77526i	0.584424	−	1.01225i	−0.410523	−	0.911850i	$-0.634654\pi$
$59$	4.48905	−	7.77526i	0.584424	−	1.01225i	0.994947	−	0.100402i	$-0.0320128\pi$
$60$		0			0
$61$	0.275255	+	0.476756i	0.0352428	+	0.0610423i	0.883109	−	0.469168i	$-0.155446\pi$
$61$	0.275255	+	0.476756i	0.0352428	+	0.0610423i	−0.847866	+	0.530211i	$0.822113\pi$
$62$	−0.317837	−	0.317837i	−0.0403654	−	0.0403654i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	1.71089	+	6.38512i	0.209018	+	0.780067i	0.988187	+	0.153253i	$0.0489748\pi$
$67$	1.71089	+	6.38512i	0.209018	+	0.780067i	−0.779169	+	0.626814i	$0.784358\pi$
$68$	−0.116337	−	0.434174i	−0.0141079	−	0.0526513i
$69$		0			0
$70$		0			0
$71$			6.29253i			0.746786i	0.927673	+	0.373393i	$0.121806\pi$
$71$			6.29253i			0.746786i	−0.927673	+	0.373393i	$0.878194\pi$
$72$		0			0
$73$	6.89898	+	6.89898i	0.807464	+	0.807464i	0.984249	−	0.176785i	$-0.0565697\pi$
$73$	6.89898	+	6.89898i	0.807464	+	0.807464i	−0.176785	+	0.984249i	$0.556570\pi$
$74$	2.12132	+	3.67423i	0.246598	+	0.427121i
$75$		0			0
$76$	−3.22474	+	5.58542i	−0.369904	+	0.640692i
$77$	2.80020	−	0.750311i	0.319112	−	0.0855059i
$78$		0			0
$79$	−2.12132	+	1.22474i	−0.238667	+	0.137795i	−0.614564	−	0.788867i	$-0.710668\pi$
$79$	−2.12132	+	1.22474i	−0.238667	+	0.137795i	0.375897	+	0.926662i	$0.377335\pi$
$80$		0			0
$81$		0			0
$82$	5.22474	−	5.22474i	0.576977	−	0.576977i
$83$	5.26380	+	1.41043i	0.577777	+	0.154815i	0.535861	−	0.844306i	$-0.319987\pi$
$83$	5.26380	+	1.41043i	0.577777	+	0.154815i	0.0419163	+	0.999121i	$0.486654\pi$
$84$		0			0
$85$		0			0
$86$	3.00000	+	1.73205i	0.323498	+	0.186772i
$87$		0			0
$88$	0.164525	−	0.614014i	0.0175384	−	0.0654542i
$89$	8.02458			0.850604			0.425302	−	0.905052i	$-0.360168\pi$
$89$	8.02458			0.850604			0.425302	+	0.905052i	$0.360168\pi$
$90$		0			0
$91$	15.7980			1.65608
$92$	−0.258819	+	0.965926i	−0.0269838	+	0.100705i
$93$		0			0
$94$	−7.79423	−	4.50000i	−0.803913	−	0.464140i
$95$		0			0
$96$		0			0
$97$	2.59405	+	0.695075i	0.263386	+	0.0705741i	0.388095	−	0.921619i	$-0.373133\pi$
$97$	2.59405	+	0.695075i	0.263386	+	0.0705741i	−0.124709	+	0.992193i	$0.539800\pi$
$98$	−9.75663	+	9.75663i	−0.985568	+	0.985568i
$99$		0			0
$100$		0			0
$101$	−10.8990	+	6.29253i	−1.08449	+	0.626130i	−0.932104	−	0.362191i	$-0.882029\pi$
$101$	−10.8990	+	6.29253i	−1.08449	+	0.626130i	−0.152385	+	0.988321i	$0.548695\pi$
$102$		0			0
$103$	−9.42418	+	2.52520i	−0.928592	+	0.248816i	−0.691254	−	0.722612i	$-0.742942\pi$
$103$	−9.42418	+	2.52520i	−0.928592	+	0.248816i	−0.237338	+	0.971427i	$0.576275\pi$
$104$	1.73205	−	3.00000i	0.169842	−	0.294174i
$105$		0			0
$106$	2.67423	+	4.63191i	0.259745	+	0.449891i
$107$	13.6100	+	13.6100i	1.31573	+	1.31573i	0.917122	+	0.398606i	$0.130506\pi$
$107$	13.6100	+	13.6100i	1.31573	+	1.31573i	0.398606	+	0.917122i	$0.369494\pi$
$108$		0			0
$109$			5.65153i			0.541318i	0.962675	+	0.270659i	$0.0872417\pi$
$109$			5.65153i			0.541318i	−0.962675	+	0.270659i	$0.912758\pi$
$110$		0			0
$111$		0			0
$112$	1.18034	+	4.40508i	0.111532	+	0.416241i
$113$	−1.50062	−	5.60040i	−0.141167	−	0.526841i	−0.999896	−	0.0144120i	$-0.995412\pi$
$113$	−1.50062	−	5.60040i	−0.141167	−	0.526841i	0.858729	−	0.512429i	$-0.171254\pi$
$114$		0			0
$115$		0			0
$116$		−	0.317837i		−	0.0295104i
$117$		0			0
$118$	6.34847	+	6.34847i	0.584424	+	0.584424i
$119$	1.02494	+	1.77526i	0.0939565	+	0.162737i
$120$		0			0
$121$	−5.29796	+	9.17633i	−0.481633	+	0.834212i
$122$	−0.531752	+	0.142483i	−0.0481426	+	0.0128998i
$123$		0			0
$124$	0.389270	−	0.224745i	0.0349574	−	0.0201827i
$125$		0			0
$126$		0			0
$127$	−1.87628	+	1.87628i	−0.166493	+	0.166493i	−0.785436	−	0.618943i	$-0.787561\pi$
$127$	−1.87628	+	1.87628i	−0.166493	+	0.166493i	0.618943	+	0.785436i	$0.287561\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$		0			0
$131$	3.12372	+	1.80348i	0.272921	+	0.157571i	0.630214	−	0.776421i	$-0.282967\pi$
$131$	3.12372	+	1.80348i	0.272921	+	0.157571i	−0.357293	+	0.933992i	$0.616300\pi$
$132$		0			0
$133$	7.61258	−	28.4105i	0.660095	−	2.46351i
$134$	−6.61037			−0.571049
$135$		0			0
$136$	0.449490			0.0385434
$137$	5.64173	−	21.0552i	0.482005	−	1.79887i	−0.111178	−	0.993801i	$-0.535462\pi$
$137$	5.64173	−	21.0552i	0.482005	−	1.79887i	0.593183	−	0.805068i	$-0.297871\pi$
$138$		0			0
$139$	2.68556	+	1.55051i	0.227786	+	0.131513i	0.609550	−	0.792747i	$-0.291350\pi$
$139$	2.68556	+	1.55051i	0.227786	+	0.131513i	−0.381764	+	0.924260i	$0.624683\pi$
$140$		0			0
$141$		0			0
$142$	−6.07812	−	1.62863i	−0.510064	−	0.136671i
$143$	1.55708	−	1.55708i	0.130209	−	0.130209i
$144$		0			0
$145$		0			0
$146$	−8.44949	+	4.87832i	−0.699285	+	0.403732i
$147$		0			0
$148$	−4.09808	+	1.09808i	−0.336860	+	0.0902613i
$149$	−2.20881	+	3.82577i	−0.180952	+	0.313419i	−0.942205	−	0.335036i	$-0.891251\pi$
$149$	−2.20881	+	3.82577i	−0.180952	+	0.313419i	0.761253	+	0.648455i	$0.224585\pi$
$150$		0			0
$151$	−8.79796	−	15.2385i	−0.715968	−	1.24009i	−0.962585	−	0.270980i	$-0.912652\pi$
$151$	−8.79796	−	15.2385i	−0.715968	−	1.24009i	0.246617	−	0.969113i	$-0.420681\pi$
$152$	−4.56048	−	4.56048i	−0.369904	−	0.369904i
$153$		0			0
$154$			2.89898i			0.233606i
$155$		0			0
$156$		0			0
$157$	3.78780	+	14.1363i	0.302300	+	1.12820i	0.935245	+	0.354001i	$0.115179\pi$
$157$	3.78780	+	14.1363i	0.302300	+	1.12820i	−0.632945	+	0.774196i	$0.718154\pi$
$158$	−0.633975	−	2.36603i	−0.0504363	−	0.188231i
$159$		0			0
$160$		0			0
$161$		−	4.56048i		−	0.359416i
$162$		0			0
$163$	−4.44949	−	4.44949i	−0.348511	−	0.348511i	0.511044	−	0.859555i	$-0.329259\pi$
$163$	−4.44949	−	4.44949i	−0.348511	−	0.348511i	−0.859555	+	0.511044i	$0.829259\pi$
$164$	3.69445	+	6.39898i	0.288488	+	0.499676i
$165$		0			0
$166$	−2.72474	+	4.71940i	−0.211481	+	0.366296i
$167$	−8.49818	+	2.27708i	−0.657609	+	0.176206i	−0.572167	−	0.820137i	$-0.693897\pi$
$167$	−8.49818	+	2.27708i	−0.657609	+	0.176206i	−0.0854420	+	0.996343i	$0.527230\pi$
$168$		0			0
$169$	−0.866025	+	0.500000i	−0.0666173	+	0.0384615i
$170$		0			0
$171$		0			0
$172$	−2.44949	+	2.44949i	−0.186772	+	0.186772i
$173$	−12.4595	−	3.33850i	−0.947275	−	0.253822i	−0.248069	−	0.968742i	$-0.579796\pi$
$173$	−12.4595	−	3.33850i	−0.947275	−	0.253822i	−0.699206	+	0.714921i	$0.746463\pi$
$174$		0			0
$175$		0			0
$176$	0.550510	+	0.317837i	0.0414963	+	0.0239579i
$177$		0			0
$178$	−2.07691	+	7.75115i	−0.155671	+	0.580973i
$179$	−10.6780			−0.798114			−0.399057	−	0.916926i	$-0.630662\pi$
$179$	−10.6780			−0.798114			−0.399057	+	0.916926i	$0.630662\pi$
$180$		0			0
$181$	−15.4495			−1.14835			−0.574176	−	0.818732i	$-0.694677\pi$
$181$	−15.4495			−1.14835			−0.574176	+	0.818732i	$0.694677\pi$
$182$	−4.08881	+	15.2597i	−0.303083	+	1.13112i
$183$		0			0
$184$	−0.866025	−	0.500000i	−0.0638442	−	0.0368605i
$185$		0			0
$186$		0			0
$187$	0.275993	+	0.0739521i	0.0201826	+	0.00540792i
$188$	6.36396	−	6.36396i	0.464140	−	0.464140i
$189$		0			0
$190$		0			0
$191$	15.1237	−	8.73169i	1.09431	−	0.631803i	0.159593	−	0.987183i	$-0.448982\pi$
$191$	15.1237	−	8.73169i	1.09431	−	0.631803i	0.934722	+	0.355380i	$0.115649\pi$
$192$		0			0
$193$	−16.7303	+	4.48288i	−1.20428	+	0.322685i	−0.804513	−	0.593934i	$-0.797574\pi$
$193$	−16.7303	+	4.48288i	−1.20428	+	0.322685i	−0.399762	+	0.916619i	$0.630907\pi$
$194$	−1.34278	+	2.32577i	−0.0964061	+	0.166980i
$195$		0			0
$196$	−6.89898	−	11.9494i	−0.492784	−	0.853527i
$197$	6.92820	+	6.92820i	0.493614	+	0.493614i	0.909443	−	0.415829i	$-0.136508\pi$
$197$	6.92820	+	6.92820i	0.493614	+	0.493614i	−0.415829	+	0.909443i	$0.636508\pi$
$198$		0			0
$199$		−	8.44949i		−	0.598968i	−0.954101	−	0.299484i	$-0.903185\pi$
$199$		−	8.44949i		−	0.598968i	0.954101	−	0.299484i	$-0.0968146\pi$
$200$		0			0
$201$		0			0
$202$	−3.25725	−	12.1562i	−0.229179	−	0.855310i
$203$	0.375156	+	1.40010i	0.0263308	+	0.0982677i
$204$		0			0
$205$		0			0
$206$		−	9.75663i		−	0.679777i
$207$		0			0
$208$	2.44949	+	2.44949i	0.169842	+	0.169842i
$209$	−2.04989	−	3.55051i	−0.141794	−	0.245594i
$210$		0			0
$211$	−4.55051	+	7.88171i	−0.313270	+	0.542600i	−0.979068	−	0.203532i	$-0.934758\pi$
$211$	−4.55051	+	7.88171i	−0.313270	+	0.542600i	0.665798	+	0.746132i	$0.268091\pi$
$212$	−5.16622	+	1.38429i	−0.354818	+	0.0950731i
$213$		0			0
$214$	−16.6688	+	9.62372i	−1.13945	+	0.657864i
$215$		0			0
$216$		0			0
$217$	−1.44949	+	1.44949i	−0.0983978	+	0.0983978i
$218$	−5.45896	−	1.46272i	−0.369727	−	0.0990682i
$219$		0			0
$220$		0			0
$221$	1.34847	+	0.778539i	0.0907079	+	0.0523702i
$222$		0			0
$223$	−6.63374	+	24.7575i	−0.444228	+	1.65788i	0.273738	+	0.961804i	$0.411740\pi$
$223$	−6.63374	+	24.7575i	−0.444228	+	1.65788i	−0.717966	+	0.696078i	$0.754927\pi$
$224$	−4.56048			−0.304710
$225$		0			0
$226$	5.79796			0.385674
$227$	6.44433	−	24.0506i	0.427725	−	1.59629i	−0.330174	−	0.943920i	$-0.607107\pi$
$227$	6.44433	−	24.0506i	0.427725	−	1.59629i	0.757899	−	0.652372i	$-0.226226\pi$
$228$		0			0
$229$	−1.43027	−	0.825765i	−0.0945147	−	0.0545681i	0.451998	−	0.892019i	$-0.350712\pi$
$229$	−1.43027	−	0.825765i	−0.0945147	−	0.0545681i	−0.546512	+	0.837451i	$0.684045\pi$
$230$		0			0
$231$		0			0
$232$	0.307007	+	0.0822623i	0.0201560	+	0.00540079i
$233$	−14.4600	+	14.4600i	−0.947304	+	0.947304i	−0.998679	−	0.0513751i	$-0.983640\pi$
$233$	−14.4600	+	14.4600i	−0.947304	+	0.947304i	0.0513751	+	0.998679i	$0.483640\pi$
$234$		0			0
$235$		0			0
$236$	−7.77526	+	4.48905i	−0.506126	+	0.292212i
$237$		0			0
$238$	−1.98004	+	0.530550i	−0.128347	+	0.0343905i
$239$	8.48528	−	14.6969i	0.548867	−	0.950666i	−0.449485	−	0.893288i	$-0.648393\pi$
$239$	8.48528	−	14.6969i	0.548867	−	0.950666i	0.998353	−	0.0573782i	$-0.0182741\pi$
$240$		0			0
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$	−7.49245	−	7.49245i	−0.481633	−	0.481633i
$243$		0			0
$244$		−	0.550510i		−	0.0352428i
$245$		0			0
$246$		0			0
$247$	−5.78245	−	21.5804i	−0.367929	−	1.37313i
$248$	0.116337	+	0.434174i	0.00738738	+	0.0275701i
$249$		0			0
$250$		0			0
$251$			2.68556i			0.169511i	0.996402	+	0.0847556i	$0.0270110\pi$
$251$			2.68556i			0.169511i	−0.996402	+	0.0847556i	$0.972989\pi$
$252$		0			0
$253$	−0.449490	−	0.449490i	−0.0282592	−	0.0282592i
$254$	−1.32673	−	2.29796i	−0.0832463	−	0.144187i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−17.4305	+	4.67050i	−1.08729	+	0.291337i	−0.757578	−	0.652745i	$-0.773617\pi$
$257$	−17.4305	+	4.67050i	−1.08729	+	0.291337i	−0.329709	+	0.944083i	$0.606951\pi$
$258$		0			0
$259$	16.7563	−	9.67423i	1.04118	−	0.601128i
$260$		0			0
$261$		0			0
$262$	−2.55051	+	2.55051i	−0.157571	+	0.157571i
$263$	16.1280	+	4.32149i	0.994495	+	0.266474i	0.719138	−	0.694868i	$-0.244537\pi$
$263$	16.1280	+	4.32149i	0.994495	+	0.266474i	0.275358	+	0.961342i	$0.411204\pi$
$264$		0			0
$265$		0			0
$266$	25.4722	+	14.7064i	1.56180	+	0.901706i
$267$		0			0
$268$	1.71089	−	6.38512i	0.104509	−	0.390033i
$269$	15.0956			0.920398			0.460199	−	0.887816i	$-0.347778\pi$
$269$	15.0956			0.920398			0.460199	+	0.887816i	$0.347778\pi$
$270$		0			0
$271$	28.0454			1.70364			0.851819	−	0.523837i	$-0.175500\pi$
$271$	28.0454			1.70364			0.851819	+	0.523837i	$0.175500\pi$
$272$	−0.116337	+	0.434174i	−0.00705394	+	0.0263257i
$273$		0			0
$274$	18.8776	+	10.8990i	1.14044	+	0.658431i
$275$		0			0
$276$		0			0
$277$	−27.1825	−	7.28353i	−1.63324	−	0.437625i	−0.678386	−	0.734705i	$-0.737320\pi$
$277$	−27.1825	−	7.28353i	−1.63324	−	0.437625i	−0.954852	+	0.297080i	$0.903987\pi$
$278$	−2.19275	+	2.19275i	−0.131513	+	0.131513i
$279$		0			0
$280$		0			0
$281$	14.8485	−	8.57277i	0.885785	−	0.511408i	0.0132238	−	0.999913i	$-0.495791\pi$
$281$	14.8485	−	8.57277i	0.885785	−	0.511408i	0.872562	+	0.488504i	$0.162457\pi$
$282$		0			0
$283$	23.3914	−	6.26772i	1.39048	−	0.372577i	0.515561	−	0.856853i	$-0.327583\pi$
$283$	23.3914	−	6.26772i	1.39048	−	0.372577i	0.874916	+	0.484275i	$0.160917\pi$
$284$	3.14626	−	5.44949i	0.186696	−	0.323368i
$285$		0			0
$286$	1.10102	+	1.90702i	0.0651047	+	0.112765i
$287$	−23.8273	−	23.8273i	−1.40648	−	1.40648i
$288$		0			0
$289$		−	16.7980i		−	0.988115i
$290$		0			0
$291$		0			0
$292$	−2.52520	−	9.42418i	−0.147776	−	0.551508i
$293$	5.70577	+	21.2942i	0.333335	+	1.24402i	0.905663	+	0.423998i	$0.139374\pi$
$293$	5.70577	+	21.2942i	0.333335	+	1.24402i	−0.572329	+	0.820024i	$0.693960\pi$
$294$		0			0
$295$		0			0
$296$		−	4.24264i		−	0.246598i
$297$		0			0
$298$	−3.12372	−	3.12372i	−0.180952	−	0.180952i
$299$	−1.73205	−	3.00000i	−0.100167	−	0.173494i
$300$		0			0
$301$	7.89898	−	13.6814i	0.455290	−	0.788585i
$302$	16.9964	−	4.55416i	0.978030	−	0.262062i
$303$		0			0
$304$	5.58542	−	3.22474i	0.320346	−	0.184952i
$305$		0			0
$306$		0			0
$307$	6.67423	−	6.67423i	0.380919	−	0.380919i	−0.490514	−	0.871433i	$-0.663191\pi$
$307$	6.67423	−	6.67423i	0.380919	−	0.380919i	0.871433	+	0.490514i	$0.163191\pi$
$308$	−2.80020	−	0.750311i	−0.159556	−	0.0427529i
$309$		0			0
$310$		0			0
$311$	−23.8207	−	13.7529i	−1.35075	−	0.779853i	−0.362392	−	0.932026i	$-0.618040\pi$
$311$	−23.8207	−	13.7529i	−1.35075	−	0.779853i	−0.988354	+	0.152172i	$0.951373\pi$
$312$		0			0
$313$	−3.09273	+	11.5422i	−0.174811	+	0.652405i	0.821772	+	0.569816i	$0.192985\pi$
$313$	−3.09273	+	11.5422i	−0.174811	+	0.652405i	−0.996584	+	0.0825888i	$0.973681\pi$
$314$	−14.6349			−0.825898
$315$		0			0
$316$	2.44949			0.137795
$317$	−2.82086	+	10.5276i	−0.158435	+	0.591289i	0.840351	+	0.542042i	$0.182349\pi$
$317$	−2.82086	+	10.5276i	−0.158435	+	0.591289i	−0.998787	+	0.0492469i	$0.984318\pi$
$318$		0			0
$319$	0.174973	+	0.101021i	0.00979659	+	0.00565606i
$320$		0			0
$321$		0			0
$322$	4.40508	+	1.18034i	0.245486	+	0.0657777i
$323$	2.04989	−	2.04989i	0.114059	−	0.114059i
$324$		0			0
$325$		0			0
$326$	5.44949	−	3.14626i	0.301819	−	0.174255i
$327$		0			0
$328$	−7.13713	+	1.91239i	−0.394082	+	0.105594i
$329$	−20.5222	+	35.5454i	−1.13142	+	1.95968i
$330$		0			0
$331$	−0.224745	−	0.389270i	−0.0123531	−	0.0213962i	0.859783	−	0.510660i	$-0.170599\pi$
$331$	−0.224745	−	0.389270i	−0.0123531	−	0.0213962i	−0.872136	+	0.489264i	$0.837266\pi$
$332$	−3.85337	−	3.85337i	−0.211481	−	0.211481i
$333$		0			0
$334$		−	8.79796i		−	0.481403i
$335$		0			0
$336$		0			0
$337$	0.806003	+	3.00804i	0.0439058	+	0.163859i	0.984398	−	0.175957i	$-0.0563020\pi$
$337$	0.806003	+	3.00804i	0.0439058	+	0.163859i	−0.940492	+	0.339816i	$0.889635\pi$
$338$	−0.258819	−	0.965926i	−0.0140779	−	0.0525394i
$339$		0			0
$340$		0			0
$341$			0.285729i			0.0154731i
$342$		0			0
$343$	21.9217	+	21.9217i	1.18366	+	1.18366i
$344$	−1.73205	−	3.00000i	−0.0933859	−	0.161749i
$345$		0			0
$346$	6.44949	−	11.1708i	0.346727	−	0.600548i
$347$	22.9871	−	6.15937i	1.23401	−	0.330652i	0.417870	−	0.908507i	$-0.362777\pi$
$347$	22.9871	−	6.15937i	1.23401	−	0.330652i	0.816140	+	0.577855i	$0.196110\pi$
$348$		0			0
$349$	−25.1541	+	14.5227i	−1.34647	+	0.777383i	−0.987747	−	0.156063i	$-0.950120\pi$
$349$	−25.1541	+	14.5227i	−1.34647	+	0.777383i	−0.358719	+	0.933446i	$0.616786\pi$
$350$		0			0
$351$		0			0
$352$	−0.449490	+	0.449490i	−0.0239579	+	0.0239579i
$353$	−33.1244	−	8.87564i	−1.76303	−	0.472403i	−0.775704	−	0.631097i	$-0.782605\pi$
$353$	−33.1244	−	8.87564i	−1.76303	−	0.472403i	−0.987328	+	0.158694i	$0.949272\pi$
$354$		0			0
$355$		0			0
$356$	−6.94949	−	4.01229i	−0.368322	−	0.212651i
$357$		0			0
$358$	2.76368	−	10.3142i	0.146065	−	0.545122i
$359$	−3.32124			−0.175288			−0.0876441	−	0.996152i	$-0.527934\pi$
$359$	−3.32124			−0.175288			−0.0876441	+	0.996152i	$0.527934\pi$
$360$		0			0
$361$	−22.5959			−1.18926
$362$	3.99862	−	14.9231i	0.210163	−	0.784339i
$363$		0			0
$364$	−13.6814	−	7.89898i	−0.717102	−	0.414019i
$365$		0			0
$366$		0			0
$367$	−3.96008	−	1.06110i	−0.206714	−	0.0553890i	0.153976	−	0.988075i	$-0.450792\pi$
$367$	−3.96008	−	1.06110i	−0.206714	−	0.0553890i	−0.360690	+	0.932686i	$0.617459\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$		0			0
$370$		0			0
$371$	21.1237	−	12.1958i	1.09669	−	0.633174i
$372$		0			0
$373$	−0.476018	+	0.127549i	−0.0246473	+	0.00660422i	−0.271122	−	0.962545i	$-0.587395\pi$
$373$	−0.476018	+	0.127549i	−0.0246473	+	0.00660422i	0.246474	+	0.969149i	$0.420728\pi$
$374$	−0.142865	+	0.247449i	−0.00738735	+	0.0127953i
$375$		0			0
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$	0.778539	+	0.778539i	0.0400968	+	0.0400968i
$378$		0			0
$379$			21.3485i			1.09660i	0.836283	+	0.548299i	$0.184724\pi$
$379$			21.3485i			1.09660i	−0.836283	+	0.548299i	$0.815276\pi$
$380$		0			0
$381$		0			0
$382$	4.51985	+	16.8683i	0.231256	+	0.863058i
$383$	−2.12284	−	7.92256i	−0.108472	−	0.404824i	0.890244	−	0.455485i	$-0.150534\pi$
$383$	−2.12284	−	7.92256i	−0.108472	−	0.404824i	−0.998716	+	0.0506606i	$0.983867\pi$
$384$		0			0
$385$		0			0
$386$		−	17.3205i		−	0.881591i
$387$		0			0
$388$	−1.89898	−	1.89898i	−0.0964061	−	0.0964061i
$389$	−18.4008	−	31.8712i	−0.932959	−	1.61593i	−0.778233	−	0.627975i	$-0.783884\pi$
$389$	−18.4008	−	31.8712i	−0.932959	−	1.61593i	−0.154726	−	0.987957i	$-0.549449\pi$
$390$		0			0
$391$	0.224745	−	0.389270i	0.0113658	−	0.0196862i
$392$	13.3278	−	3.57117i	0.673156	−	0.180372i
$393$		0			0
$394$	−8.48528	+	4.89898i	−0.427482	+	0.246807i
$395$		0			0
$396$		0			0
$397$	−10.5505	+	10.5505i	−0.529515	+	0.529515i	−0.920428	−	0.390913i	$-0.872159\pi$
$397$	−10.5505	+	10.5505i	−0.529515	+	0.529515i	0.390913	+	0.920428i	$0.372159\pi$
$398$	8.16158	+	2.18689i	0.409103	+	0.109619i
$399$		0			0
$400$		0			0
$401$	−7.65153	−	4.41761i	−0.382099	−	0.220605i	0.296632	−	0.954992i	$-0.404137\pi$
$401$	−7.65153	−	4.41761i	−0.382099	−	0.220605i	−0.678731	+	0.734387i	$0.737470\pi$
$402$		0			0
$403$	−0.403001	+	1.50402i	−0.0200749	+	0.0749207i
$404$	12.5851			0.626130
$405$		0			0
$406$	−1.44949			−0.0719370
$407$	0.698019	−	2.60504i	0.0345995	−	0.129127i
$408$		0			0
$409$	−25.0273	−	14.4495i	−1.23752	−	0.714481i	−0.268932	−	0.963159i	$-0.586671\pi$
$409$	−25.0273	−	14.4495i	−1.23752	−	0.714481i	−0.968586	+	0.248678i	$0.920004\pi$
$410$		0			0
$411$		0			0
$412$	9.42418	+	2.52520i	0.464296	+	0.124408i
$413$	28.9521	−	28.9521i	1.42464	−	1.42464i
$414$		0			0
$415$		0			0
$416$	−3.00000	+	1.73205i	−0.147087	+	0.0849208i
$417$		0			0
$418$	3.96008	−	1.06110i	0.193694	−	0.0519001i
$419$	−2.51059	+	4.34847i	−0.122650	+	0.212437i	−0.920812	−	0.390007i	$-0.872473\pi$
$419$	−2.51059	+	4.34847i	−0.122650	+	0.212437i	0.798162	+	0.602443i	$0.205806\pi$
$420$		0			0
$421$	2.55051	+	4.41761i	0.124304	+	0.215301i	0.921461	−	0.388471i	$-0.126997\pi$
$421$	2.55051	+	4.41761i	0.124304	+	0.215301i	−0.797157	+	0.603773i	$0.793663\pi$
$422$	−6.43539	−	6.43539i	−0.313270	−	0.313270i
$423$		0			0
$424$		−	5.34847i		−	0.259745i
$425$		0			0
$426$		0			0
$427$	0.649788	+	2.42504i	0.0314455	+	0.117356i
$428$	−4.98161	−	18.5916i	−0.240795	−	0.898659i
$429$		0			0
$430$		0			0
$431$		−	15.5563i		−	0.749323i	−0.927162	−	0.374661i	$-0.877759\pi$
$431$		−	15.5563i		−	0.749323i	0.927162	−	0.374661i	$-0.122241\pi$
$432$		0			0
$433$	−13.4495	−	13.4495i	−0.646341	−	0.646341i	0.305766	−	0.952107i	$-0.401088\pi$
$433$	−13.4495	−	13.4495i	−0.646341	−	0.646341i	−0.952107	+	0.305766i	$0.901088\pi$
$434$	−1.02494	−	1.77526i	−0.0491989	−	0.0852150i
$435$		0			0
$436$	2.82577	−	4.89437i	0.135330	−	0.234398i
$437$	−6.22973	+	1.66925i	−0.298008	+	0.0798511i
$438$		0			0
$439$	−25.8058	+	14.8990i	−1.23164	+	0.711089i	−0.967372	−	0.253359i	$-0.918465\pi$
$439$	−25.8058	+	14.8990i	−1.23164	+	0.711089i	−0.264271	+	0.964449i	$0.585131\pi$
$440$		0			0
$441$		0			0
$442$	−1.10102	+	1.10102i	−0.0523702	+	0.0523702i
$443$	−5.26380	−	1.41043i	−0.250091	−	0.0670116i	0.131596	−	0.991303i	$-0.457990\pi$
$443$	−5.26380	−	1.41043i	−0.250091	−	0.0670116i	−0.381687	+	0.924292i	$0.624657\pi$
$444$		0			0
$445$		0			0
$446$	−22.1969	−	12.8154i	−1.05106	−	0.606827i
$447$		0			0
$448$	1.18034	−	4.40508i	0.0557658	−	0.208121i
$449$	−0.921404			−0.0434837			−0.0217419	−	0.999764i	$-0.506921\pi$
$449$	−0.921404			−0.0434837			−0.0217419	+	0.999764i	$0.506921\pi$
$450$		0			0
$451$	−4.69694			−0.221170
$452$	−1.50062	+	5.60040i	−0.0705833	+	0.263421i
$453$		0			0
$454$	21.5631	+	12.4495i	1.01201	+	0.584284i
$455$		0			0
$456$		0			0
$457$	−14.1363	−	3.78780i	−0.661267	−	0.177186i	−0.0874492	−	0.996169i	$-0.527872\pi$
$457$	−14.1363	−	3.78780i	−0.661267	−	0.177186i	−0.573818	+	0.818983i	$0.694538\pi$
$458$	1.16781	−	1.16781i	0.0545681	−	0.0545681i
$459$		0			0
$460$		0			0
$461$	−28.6237	+	16.5259i	−1.33314	+	0.769689i	−0.985780	−	0.168043i	$-0.946255\pi$
$461$	−28.6237	+	16.5259i	−1.33314	+	0.769689i	−0.347360	+	0.937732i	$0.612922\pi$
$462$		0			0
$463$	−11.8182	+	3.16668i	−0.549239	+	0.147168i	−0.522758	−	0.852481i	$-0.675097\pi$
$463$	−11.8182	+	3.16668i	−0.549239	+	0.147168i	−0.0264810	+	0.999649i	$0.508430\pi$
$464$	−0.158919	+	0.275255i	−0.00737761	+	0.0127784i
$465$		0			0
$466$	−10.2247	−	17.7098i	−0.473652	−	0.820390i
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	0.769514	−	0.638630i	$-0.220499\pi$
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	−0.638630	+	0.769514i	$0.720499\pi$
$468$		0			0
$469$			30.1464i			1.39203i
$470$		0			0
$471$		0			0
$472$	−2.32370	−	8.67217i	−0.106957	−	0.399169i
$473$	−0.569930	−	2.12701i	−0.0262054	−	0.0977999i
$474$		0			0
$475$		0			0
$476$		−	2.04989i		−	0.0939565i
$477$		0			0
$478$	12.0000	+	12.0000i	0.548867	+	0.548867i
$479$	3.53553	+	6.12372i	0.161543	+	0.279800i	0.935422	−	0.353533i	$-0.115020\pi$
$479$	3.53553	+	6.12372i	0.161543	+	0.279800i	−0.773879	+	0.633333i	$0.781686\pi$
$480$		0			0
$481$	7.34847	−	12.7279i	0.335061	−	0.580343i
$482$	18.3526	−	4.91756i	0.835938	−	0.223989i
$483$		0			0
$484$	9.17633	−	5.29796i	0.417106	−	0.240816i
$485$		0			0
$486$		0			0
$487$	12.0000	−	12.0000i	0.543772	−	0.543772i	−0.380861	−	0.924632i	$-0.624372\pi$
$487$	12.0000	−	12.0000i	0.543772	−	0.543772i	0.924632	+	0.380861i	$0.124372\pi$
$488$	0.531752	+	0.142483i	0.0240713	+	0.00644988i
$489$		0			0
$490$		0			0
$491$	24.2474	+	13.9993i	1.09427	+	0.631778i	0.934711	−	0.355410i	$-0.115659\pi$
$491$	24.2474	+	13.9993i	1.09427	+	0.631778i	0.159561	+	0.987188i	$0.448992\pi$
$492$		0			0
$493$	−0.0369761	+	0.137997i	−0.00166532	+	0.00621505i
$494$	22.3417			1.00520
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	−7.42731	+	27.7191i	−0.333161	+	1.24337i
$498$		0			0
$499$	0.778539	+	0.449490i	0.0348522	+	0.0201219i	0.517325	−	0.855789i	$-0.326928\pi$
$499$	0.778539	+	0.449490i	0.0348522	+	0.0201219i	−0.482473	+	0.875911i	$0.660261\pi$
$500$		0			0
$501$		0			0
$502$	−2.59405	−	0.695075i	−0.115778	−	0.0310227i
$503$	4.02834	−	4.02834i	0.179615	−	0.179615i	−0.611573	−	0.791188i	$-0.709463\pi$
$503$	4.02834	−	4.02834i	0.179615	−	0.179615i	0.791188	+	0.611573i	$0.209463\pi$
$504$		0			0
$505$		0			0
$506$	0.550510	−	0.317837i	0.0244732	−	0.0141296i
$507$		0			0
$508$	2.56304	−	0.686765i	0.113717	−	0.0304702i
$509$	4.22659	−	7.32066i	0.187340	−	0.324483i	−0.757022	−	0.653389i	$-0.773347\pi$
$509$	4.22659	−	7.32066i	0.187340	−	0.324483i	0.944363	+	0.328906i	$0.106680\pi$
$510$		0			0
$511$	22.2474	+	38.5337i	0.984169	+	1.70463i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	18.0454i		−	0.795949i
$515$		0			0
$516$		0			0
$517$	1.48072	+	5.52613i	0.0651221	+	0.243039i
$518$	5.00775	+	18.6892i	0.220028	+	0.821156i
$519$		0			0
$520$		0			0
$521$			29.4449i			1.29000i	0.764181	+	0.645001i	$0.223143\pi$
$521$			29.4449i			1.29000i	−0.764181	+	0.645001i	$0.776857\pi$
$522$		0			0
$523$	−4.22474	−	4.22474i	−0.184735	−	0.184735i	0.608680	−	0.793416i	$-0.291699\pi$
$523$	−4.22474	−	4.22474i	−0.184735	−	0.184735i	−0.793416	+	0.608680i	$0.791699\pi$
$524$	−1.80348	−	3.12372i	−0.0787855	−	0.136461i
$525$		0			0
$526$	−8.34847	+	14.4600i	−0.364011	+	0.630485i
$527$	−0.195157	+	0.0522921i	−0.00850116	+	0.00227788i
$528$		0			0
$529$	19.0526	−	11.0000i	0.828372	−	0.478261i
$530$		0			0
$531$		0			0
$532$	−20.7980	+	20.7980i	−0.901706	+	0.901706i
$533$	−24.7238	−	6.62471i	−1.07090	−	0.286948i
$534$		0			0
$535$		0			0
$536$	5.72474	+	3.30518i	0.247271	+	0.142762i
$537$		0			0
$538$	−3.90704	+	14.5813i	−0.168444	+	0.628643i
$539$	8.77101			0.377794
$540$		0			0
$541$	27.9444			1.20142			0.600712	−	0.799466i	$-0.294884\pi$
$541$	27.9444			1.20142			0.600712	+	0.799466i	$0.294884\pi$
$542$	−7.25869	+	27.0898i	−0.311787	+	1.16361i
$543$		0			0
$544$	−0.389270	−	0.224745i	−0.0166898	−	0.00963586i
$545$		0			0
$546$		0			0
$547$	−3.92907	−	1.05279i	−0.167995	−	0.0450140i	0.173841	−	0.984774i	$-0.444382\pi$
$547$	−3.92907	−	1.05279i	−0.167995	−	0.0450140i	−0.341836	+	0.939760i	$0.611049\pi$
$548$	−15.4135	+	15.4135i	−0.658431	+	0.658431i
$549$		0			0
$550$		0			0
$551$	1.77526	−	1.02494i	0.0756284	−	0.0436641i
$552$		0			0
$553$	−10.7902	+	2.89123i	−0.458846	+	0.122947i
$554$	14.0707	−	24.3712i	0.597807	−	1.03543i
$555$		0			0
$556$	−1.55051	−	2.68556i	−0.0657563	−	0.113893i
$557$	−7.88171	−	7.88171i	−0.333959	−	0.333959i	0.520129	−	0.854088i	$-0.325884\pi$
$557$	−7.88171	−	7.88171i	−0.333959	−	0.333959i	−0.854088	+	0.520129i	$0.825884\pi$
$558$		0			0
$559$		−	12.0000i		−	0.507546i
$560$		0			0
$561$		0			0
$562$	4.43759	+	16.5613i	0.187188	+	0.698597i
$563$	5.08619	+	18.9819i	0.214357	+	0.799993i	0.986392	+	0.164412i	$0.0525726\pi$
$563$	5.08619	+	18.9819i	0.214357	+	0.799993i	−0.772034	+	0.635581i	$0.780761\pi$
$564$		0			0
$565$		0			0
$566$			24.2166i			1.01790i
$567$		0			0
$568$	4.44949	+	4.44949i	0.186696	+	0.186696i
$569$	9.58166	+	16.5959i	0.401684	+	0.695737i	0.993929	−	0.110021i	$-0.0350917\pi$
$569$	9.58166	+	16.5959i	0.401684	+	0.695737i	−0.592245	+	0.805758i	$0.701758\pi$
$570$		0			0
$571$	−18.4495	+	31.9555i	−0.772087	+	1.33729i	0.164330	+	0.986405i	$0.447454\pi$
$571$	−18.4495	+	31.9555i	−0.772087	+	1.33729i	−0.936417	+	0.350889i	$0.885880\pi$
$572$	−2.12701	+	0.569930i	−0.0889347	+	0.0238300i
$573$		0			0
$574$	29.1824	−	16.8485i	1.21805	−	0.703242i
$575$		0			0
$576$		0			0
$577$	17.0000	−	17.0000i	0.707719	−	0.707719i	−0.258336	−	0.966055i	$-0.583174\pi$
$577$	17.0000	−	17.0000i	0.707719	−	0.707719i	0.966055	+	0.258336i	$0.0831741\pi$
$578$	16.2256	+	4.34763i	0.674895	+	0.180838i
$579$		0			0
$580$		0			0
$581$	21.5227	+	12.4261i	0.892912	+	0.515523i
$582$		0			0
$583$	0.879955	−	3.28404i	0.0364440	−	0.136011i
$584$	9.75663			0.403732
$585$		0			0
$586$	−22.0454			−0.910687
$587$	3.37640	−	12.6009i	0.139359	−	0.520095i	−0.860583	−	0.509310i	$-0.829901\pi$
$587$	3.37640	−	12.6009i	0.139359	−	0.520095i	0.999942	−	0.0107843i	$-0.00343281\pi$
$588$		0			0
$589$	2.51059	+	1.44949i	0.103447	+	0.0597252i
$590$		0			0
$591$		0			0
$592$	4.09808	+	1.09808i	0.168430	+	0.0451307i
$593$	−7.24604	+	7.24604i	−0.297559	+	0.297559i	−0.840057	−	0.542498i	$-0.817479\pi$
$593$	−7.24604	+	7.24604i	−0.297559	+	0.297559i	0.542498	+	0.840057i	$0.317479\pi$
$594$		0			0
$595$		0			0
$596$	3.82577	−	2.20881i	0.156709	−	0.0904762i
$597$		0			0
$598$	3.34607	−	0.896575i	0.136831	−	0.0366637i
$599$	−9.97093	+	17.2702i	−0.407401	+	0.705639i	−0.994598	−	0.103805i	$-0.966898\pi$
$599$	−9.97093	+	17.2702i	−0.407401	+	0.705639i	0.587197	+	0.809444i	$0.300232\pi$
$600$		0			0
$601$	−2.65153	−	4.59259i	−0.108158	−	0.187335i	0.806866	−	0.590735i	$-0.201162\pi$
$601$	−2.65153	−	4.59259i	−0.108158	−	0.187335i	−0.915024	+	0.403399i	$0.867829\pi$
$602$	11.1708	+	11.1708i	0.455290	+	0.455290i
$603$		0			0
$604$			17.5959i			0.715968i
$605$		0			0
$606$		0			0
$607$	−3.04744	−	11.3732i	−0.123692	−	0.461624i	0.876098	−	0.482133i	$-0.160138\pi$
$607$	−3.04744	−	11.3732i	−0.123692	−	0.461624i	−0.999790	+	0.0205092i	$0.993471\pi$
$608$	1.66925	+	6.22973i	0.0676971	+	0.252649i
$609$		0			0
$610$		0			0
$611$			31.1769i			1.26128i
$612$		0			0
$613$	−6.79796	−	6.79796i	−0.274567	−	0.274567i	0.556369	−	0.830936i	$-0.312194\pi$
$613$	−6.79796	−	6.79796i	−0.274567	−	0.274567i	−0.830936	+	0.556369i	$0.812194\pi$
$614$	4.71940	+	8.17423i	0.190459	+	0.329885i
$615$		0			0
$616$	1.44949	−	2.51059i	0.0584016	−	0.101155i
$617$	−16.3232	+	4.37378i	−0.657146	+	0.176082i	−0.571958	−	0.820283i	$-0.693816\pi$
$617$	−16.3232	+	4.37378i	−0.657146	+	0.176082i	−0.0851882	+	0.996365i	$0.527149\pi$
$618$		0			0
$619$	42.2121	−	24.3712i	1.69665	−	0.979560i	0.747748	−	0.663982i	$-0.231135\pi$
$619$	42.2121	−	24.3712i	1.69665	−	0.979560i	0.948900	−	0.315578i	$-0.102198\pi$
$620$		0			0
$621$		0			0
$622$	19.4495	−	19.4495i	0.779853	−	0.779853i
$623$	35.3489	+	9.47172i	1.41623	+	0.379476i
$624$		0			0
$625$		0			0
$626$	−10.3485	−	5.97469i	−0.413608	−	0.238797i
$627$		0			0
$628$	3.78780	−	14.1363i	0.151150	−	0.564099i
$629$	1.90702			0.0760380
$630$		0			0
$631$	−3.10102			−0.123450			−0.0617248	−	0.998093i	$-0.519660\pi$
$631$	−3.10102			−0.123450			−0.0617248	+	0.998093i	$0.519660\pi$
$632$	−0.633975	+	2.36603i	−0.0252182	+	0.0941154i
$633$		0			0
$634$	−9.43879	−	5.44949i	−0.374862	−	0.216427i
$635$		0			0
$636$		0			0
$637$	46.1689	+	12.3709i	1.82928	+	0.490153i
$638$	−0.142865	+	0.142865i	−0.00565606	+	0.00565606i
$639$		0			0
$640$		0			0
$641$	−16.7474	+	9.66914i	−0.661484	+	0.381908i	−0.792842	−	0.609427i	$-0.791400\pi$
$641$	−16.7474	+	9.66914i	−0.661484	+	0.381908i	0.131358	+	0.991335i	$0.458066\pi$
$642$		0			0
$643$	6.10913	−	1.63694i	0.240921	−	0.0645545i	−0.136338	−	0.990662i	$-0.543533\pi$
$643$	6.10913	−	1.63694i	0.240921	−	0.0645545i	0.377259	+	0.926108i	$0.376867\pi$
$644$	−2.28024	+	3.94949i	−0.0898540	+	0.155632i
$645$		0			0
$646$	1.44949	+	2.51059i	0.0570294	+	0.0987778i
$647$	23.5416	+	23.5416i	0.925516	+	0.925516i	0.997412	−	0.0718961i	$-0.0229050\pi$
$647$	23.5416	+	23.5416i	0.925516	+	0.925516i	−0.0718961	+	0.997412i	$0.522905\pi$
$648$		0			0
$649$		−	5.70714i		−	0.224025i
$650$		0			0
$651$		0			0
$652$	1.62863	+	6.07812i	0.0637819	+	0.238037i
$653$	6.84563	+	25.5482i	0.267890	+	0.999780i	0.960457	+	0.278427i	$0.0898129\pi$
$653$	6.84563	+	25.5482i	0.267890	+	0.999780i	−0.692567	+	0.721353i	$0.743520\pi$
$654$		0			0
$655$		0			0
$656$		−	7.38891i		−	0.288488i
$657$		0			0
$658$	−29.0227	−	29.0227i	−1.13142	−	1.13142i
$659$	−5.65685	−	9.79796i	−0.220360	−	0.381674i	0.734557	−	0.678546i	$-0.237390\pi$
$659$	−5.65685	−	9.79796i	−0.220360	−	0.381674i	−0.954917	+	0.296872i	$0.904056\pi$
$660$		0			0
$661$	0.651531	−	1.12848i	0.0253416	−	0.0438930i	−0.853076	−	0.521786i	$-0.825266\pi$
$661$	0.651531	−	1.12848i	0.0253416	−	0.0438930i	0.878418	+	0.477893i	$0.158599\pi$
$662$	0.434174	−	0.116337i	0.0168746	−	0.00452155i
$663$		0			0
$664$	4.71940	−	2.72474i	0.183148	−	0.105741i
$665$		0			0
$666$		0			0
$667$	0.224745	−	0.224745i	0.00870216	−	0.00870216i
$668$	8.49818	+	2.27708i	0.328804	+	0.0881028i
$669$		0			0
$670$		0			0
$671$	0.303062	+	0.174973i	0.0116996	+	0.00675474i
$672$		0			0
$673$	6.02093	−	22.4704i	0.232090	−	0.866171i	−0.747349	−	0.664431i	$-0.768674\pi$
$673$	6.02093	−	22.4704i	0.232090	−	0.866171i	0.979439	−	0.201740i	$-0.0646595\pi$
$674$	−3.11416			−0.119953
$675$		0			0
$676$	1.00000			0.0384615
$677$	−11.8011	+	44.0423i	−0.453553	+	1.69268i	0.238755	+	0.971080i	$0.423261\pi$
$677$	−11.8011	+	44.0423i	−0.453553	+	1.69268i	−0.692308	+	0.721602i	$0.743406\pi$
$678$		0			0
$679$	10.6066	+	6.12372i	0.407044	+	0.235007i
$680$		0			0
$681$		0			0
$682$	−0.275993	−	0.0739521i	−0.0105683	−	0.00283177i
$683$	−13.8564	+	13.8564i	−0.530201	+	0.530201i	−0.920632	−	0.390431i	$-0.872326\pi$
$683$	−13.8564	+	13.8564i	−0.530201	+	0.530201i	0.390431	+	0.920632i	$0.372326\pi$
$684$		0			0
$685$		0			0
$686$	−26.8485	+	15.5010i	−1.02508	+	0.591830i
$687$		0			0
$688$	3.34607	−	0.896575i	0.127568	−	0.0341816i
$689$	9.26382	−	16.0454i	0.352923	−	0.611281i
$690$		0			0
$691$	10.4722	+	18.1384i	0.398381	+	0.690016i	0.993526	−	0.113602i	$-0.0362388\pi$
$691$	10.4722	+	18.1384i	0.398381	+	0.690016i	−0.595145	+	0.803618i	$0.702906\pi$
$692$	9.12096	+	9.12096i	0.346727	+	0.346727i
$693$		0			0
$694$			23.7980i			0.903358i
$695$		0			0
$696$		0			0
$697$	−0.859599	−	3.20807i	−0.0325596	−	0.121514i
$698$	−7.51750	−	28.0557i	−0.284542	−	1.06192i
$699$		0			0
$700$		0			0
$701$		−	21.1024i		−	0.797028i	−0.917162	−	0.398514i	$-0.869526\pi$
$701$		−	21.1024i		−	0.797028i	0.917162	−	0.398514i	$-0.130474\pi$
$702$		0			0
$703$	−19.3485	−	19.3485i	−0.729741	−	0.729741i
$704$	−0.317837	−	0.550510i	−0.0119789	−	0.0207481i
$705$		0			0
$706$	17.1464	−	29.6985i	0.645314	−	1.11772i
$707$	−55.4382	+	14.8546i	−2.08497	+	0.558666i
$708$		0			0
$709$	−25.6790	+	14.8258i	−0.964394	+	0.556793i	−0.897523	−	0.440968i	$-0.854635\pi$
$709$	−25.6790	+	14.8258i	−0.964394	+	0.556793i	−0.0668716	+	0.997762i	$0.521302\pi$
$710$		0			0
$711$		0			0
$712$	5.67423	−	5.67423i	0.212651	−	0.212651i
$713$	0.434174	+	0.116337i	0.0162599	+	0.00435684i
$714$		0			0
$715$		0			0
$716$	9.24745	+	5.33902i	0.345593	+	0.199528i
$717$		0			0
$718$	0.859599	−	3.20807i	0.0320800	−	0.119724i
$719$	−32.5269			−1.21305			−0.606525	−	0.795065i	$-0.707437\pi$
$719$	−32.5269			−1.21305			−0.606525	+	0.795065i	$0.707437\pi$
$720$		0			0
$721$	−44.4949			−1.65708
$722$	5.84825	−	21.8260i	0.217649	−	0.812279i
$723$		0			0
$724$	13.3797	+	7.72474i	0.497251	+	0.287088i
$725$		0			0
$726$		0			0
$727$	46.6759	+	12.5068i	1.73111	+	0.463850i	0.980439	−	0.196822i	$-0.0630622\pi$
$727$	46.6759	+	12.5068i	1.73111	+	0.463850i	0.750674	+	0.660673i	$0.229729\pi$
$728$	11.1708	−	11.1708i	0.414019	−	0.414019i
$729$		0			0
$730$		0			0
$731$	1.34847	−	0.778539i	0.0498749	−	0.0287953i
$732$		0			0
$733$	32.9846	−	8.83821i	1.21832	−	0.326447i	0.408296	−	0.912850i	$-0.366123\pi$
$733$	32.9846	−	8.83821i	1.21832	−	0.326447i	0.810019	+	0.586403i	$0.199457\pi$
$734$	2.04989	−	3.55051i	0.0756627	−	0.131052i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	2.97129	+	2.97129i	0.109449	+	0.109449i
$738$		0			0
$739$		−	28.9444i		−	1.06474i	−0.846513	−	0.532368i	$-0.821302\pi$
$739$		−	28.9444i		−	1.06474i	0.846513	−	0.532368i	$-0.178698\pi$
$740$		0			0
$741$		0			0
$742$	6.31300	+	23.5605i	0.231758	+	0.864931i
$743$	−2.56204	−	9.56168i	−0.0939923	−	0.350784i	0.902872	−	0.429909i	$-0.141454\pi$
$743$	−2.56204	−	9.56168i	−0.0939923	−	0.350784i	−0.996865	+	0.0791245i	$0.974788\pi$
$744$		0			0
$745$		0			0
$746$		−	0.492810i		−	0.0180431i
$747$		0			0
$748$	−0.202041	−	0.202041i	−0.00738735	−	0.00738735i
$749$	43.8888	+	76.0176i	1.60366	+	2.77762i
$750$		0			0
$751$	−10.3485	+	17.9241i	−0.377621	+	0.654059i	−0.990716	−	0.135951i	$-0.956591\pi$
$751$	−10.3485	+	17.9241i	−0.377621	+	0.654059i	0.613095	+	0.790010i	$0.289924\pi$
$752$	−8.69333	+	2.32937i	−0.317013	+	0.0849434i
$753$		0			0
$754$	−0.953512	+	0.550510i	−0.0347248	+	0.0200484i
$755$		0			0
$756$		0			0
$757$	−22.0454	+	22.0454i	−0.801254	+	0.801254i	−0.983292	−	0.182038i	$-0.941731\pi$
$757$	−22.0454	+	22.0454i	−0.801254	+	0.801254i	0.182038	+	0.983292i	$0.441731\pi$
$758$	−20.6210	−	5.52539i	−0.748990	−	0.200691i
$759$		0			0
$760$		0			0
$761$	5.60102	+	3.23375i	0.203037	+	0.117223i	0.598071	−	0.801443i	$-0.295934\pi$
$761$	5.60102	+	3.23375i	0.203037	+	0.117223i	−0.395034	+	0.918666i	$0.629267\pi$
$762$		0			0
$763$	−6.67072	+	24.8955i	−0.241496	+	0.901276i
$764$	−17.4634			−0.631803
$765$		0			0
$766$	8.20204			0.296352
$767$	8.04954	−	30.0413i	0.290652	−	1.08473i
$768$		0			0
$769$	−8.39780	−	4.84847i	−0.302832	−	0.174840i	0.340882	−	0.940106i	$-0.389274\pi$
$769$	−8.39780	−	4.84847i	−0.302832	−	0.174840i	−0.643715	+	0.765266i	$0.722608\pi$
$770$		0			0
$771$		0			0
$772$	16.7303	+	4.48288i	0.602138	+	0.161342i
$773$	30.8270	−	30.8270i	1.10877	−	1.10877i	0.115456	−	0.993313i	$-0.463167\pi$
$773$	30.8270	−	30.8270i	1.10877	−	1.10877i	0.993313	−	0.115456i	$-0.0368331\pi$
$774$		0			0
$775$		0			0
$776$	2.32577	−	1.34278i	0.0834901	−	0.0482030i
$777$		0			0
$778$	35.5477	−	9.52497i	1.27445	−	0.341487i
$779$	−23.8273	+	41.2702i	−0.853703	+	1.47866i
$780$		0			0
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	0.317837	+	0.317837i	0.0113658	+	0.0113658i
$783$		0			0
$784$			13.7980i			0.492784i
$785$		0			0
$786$		0			0
$787$	2.52520	+	9.42418i	0.0900137	+	0.335936i	0.996216	−	0.0869079i	$-0.0276986\pi$
$787$	2.52520	+	9.42418i	0.0900137	+	0.335936i	−0.906203	+	0.422844i	$0.861032\pi$
$788$	−2.53590	−	9.46410i	−0.0903376	−	0.337145i
$789$		0			0
$790$		0			0
$791$		−	26.4415i		−	0.940150i
$792$		0			0
$793$	1.34847	+	1.34847i	0.0478855	+	0.0478855i
$794$	−7.46034	−	12.9217i	−0.264757	−	0.458573i
$795$		0			0
$796$	−4.22474	+	7.31747i	−0.149742	+	0.259361i
$797$	38.4419	−	10.3005i	1.36168	−	0.364861i	0.497248	−	0.867609i	$-0.334344\pi$
$797$	38.4419	−	10.3005i	1.36168	−	0.364861i	0.864433	+	0.502747i	$0.167677\pi$
$798$		0			0
$799$	−3.50343	+	2.02270i	−0.123942	+	0.0715581i
$800$		0			0
$801$		0			0
$802$	6.24745	−	6.24745i	0.220605	−	0.220605i
$803$	5.99071	+	1.60521i	0.211408	+	0.0566465i
$804$		0			0
$805$		0			0
$806$	−1.34847	−	0.778539i	−0.0474978	−	0.0274229i
$807$		0			0
$808$	−3.25725	+	12.1562i	−0.114590	+	0.427655i
$809$	19.4490			0.683792			0.341896	−	0.939738i	$-0.388931\pi$
$809$	19.4490			0.683792			0.341896	+	0.939738i	$0.388931\pi$
$810$		0			0
$811$	−39.6413			−1.39200			−0.695998	−	0.718044i	$-0.745038\pi$
$811$	−39.6413			−1.39200			−0.695998	+	0.718044i	$0.745038\pi$
$812$	0.375156	−	1.40010i	0.0131654	−	0.0491339i
$813$		0			0
$814$	2.33562	+	1.34847i	0.0818633	+	0.0472638i
$815$		0			0
$816$		0			0
$817$	−21.5804	−	5.78245i	−0.755003	−	0.202302i
$818$	20.4347	−	20.4347i	0.714481	−	0.714481i
$819$		0			0
$820$		0			0
$821$	−19.3207	+	11.1548i	−0.674296	+	0.389305i	−0.797702	−	0.603051i	$-0.793951\pi$
$821$	−19.3207	+	11.1548i	−0.674296	+	0.389305i	0.123407	+	0.992356i	$0.460618\pi$
$822$		0			0
$823$	3.23908	−	0.867910i	0.112907	−	0.0302534i	−0.201923	−	0.979401i	$-0.564719\pi$
$823$	3.23908	−	0.867910i	0.112907	−	0.0302534i	0.314830	+	0.949148i	$0.398052\pi$
$824$	−4.87832	+	8.44949i	−0.169944	+	0.294352i
$825$		0			0
$826$	20.4722	+	35.4589i	0.712319	+	1.23377i
$827$	31.5662	+	31.5662i	1.09766	+	1.09766i	0.994683	+	0.102980i	$0.0328379\pi$
$827$	31.5662	+	31.5662i	1.09766	+	1.09766i	0.102980	+	0.994683i	$0.467162\pi$
$828$		0			0
$829$			10.5505i			0.366434i	0.983072	+	0.183217i	$0.0586512\pi$
$829$			10.5505i			0.366434i	−0.983072	+	0.183217i	$0.941349\pi$
$830$		0			0
$831$		0			0
$832$	−0.896575	−	3.34607i	−0.0310832	−	0.116004i
$833$	1.60521	+	5.99071i	0.0556171	+	0.207566i
$834$		0			0
$835$		0			0
$836$			4.09978i			0.141794i
$837$		0			0
$838$	−3.55051	−	3.55051i	−0.122650	−	0.122650i
$839$	−0.246405	−	0.426786i	−0.00850684	−	0.0147343i	0.861741	−	0.507349i	$-0.169375\pi$
$839$	−0.246405	−	0.426786i	−0.00850684	−	0.0147343i	−0.870247	+	0.492615i	$0.836041\pi$
$840$		0			0
$841$	14.4495	−	25.0273i	0.498258	−	0.863009i
$842$	−4.92721	+	1.32024i	−0.169803	+	0.0454985i
$843$		0			0
$844$	7.88171	−	4.55051i	0.271300	−	0.156635i
$845$		0			0
$846$		0			0
$847$	−34.1691	+	34.1691i	−1.17407	+	1.17407i
$848$	5.16622	+	1.38429i	0.177409	+	0.0475366i
$849$		0			0
$850$		0			0
$851$	−3.67423	−	2.12132i	−0.125951	−	0.0727179i
$852$		0			0
$853$	0.641478	−	2.39403i	0.0219638	−	0.0819700i	−0.954074	−	0.299571i	$-0.903156\pi$
$853$	0.641478	−	2.39403i	0.0219638	−	0.0819700i	0.976038	+	0.217601i	$0.0698231\pi$
$854$	−2.51059			−0.0859106
$855$		0			0
$856$	19.2474			0.657864
$857$	4.08881	−	15.2597i	0.139671	−	0.521260i	−0.860264	−	0.509849i	$-0.829701\pi$
$857$	4.08881	−	15.2597i	0.139671	−	0.521260i	0.999935	−	0.0114106i	$-0.00363219\pi$
$858$		0			0
$859$	−40.2658	−	23.2474i	−1.37385	−	0.793193i	−0.382440	−	0.923980i	$-0.624916\pi$
$859$	−40.2658	−	23.2474i	−1.37385	−	0.793193i	−0.991410	+	0.130788i	$0.958249\pi$
$860$		0			0
$861$		0			0
$862$	15.0263	+	4.02628i	0.511797	+	0.137136i
$863$	−20.7132	+	20.7132i	−0.705085	+	0.705085i	−0.965497	−	0.260413i	$-0.916141\pi$
$863$	−20.7132	+	20.7132i	−0.705085	+	0.705085i	0.260413	+	0.965497i	$0.416141\pi$
$864$		0			0
$865$		0			0
$866$	16.4722	−	9.51023i	0.559748	−	0.323171i
$867$		0			0
$868$	1.98004	−	0.530550i	0.0672069	−	0.0180080i
$869$	−0.778539	+	1.34847i	−0.0264101	+	0.0457437i
$870$		0			0
$871$	11.4495	+	19.8311i	0.387951	+	0.671951i
$872$	3.99624	+	3.99624i	0.135330	+	0.135330i
$873$		0			0
$874$		−	6.44949i		−	0.218157i
$875$		0			0
$876$		0			0
$877$	−11.0713	−	41.3188i	−0.373852	−	1.39524i	−0.855014	−	0.518604i	$-0.826452\pi$
$877$	−11.0713	−	41.3188i	−0.373852	−	1.39524i	0.481162	−	0.876632i	$-0.340215\pi$
$878$	−7.71228	−	28.7826i	−0.260277	−	0.971366i
$879$		0			0
$880$		0			0
$881$			54.8365i			1.84749i	0.383010	+	0.923744i	$0.374887\pi$
$881$			54.8365i			1.84749i	−0.383010	+	0.923744i	$0.625113\pi$
$882$		0			0
$883$	−6.27015	−	6.27015i	−0.211007	−	0.211007i	0.593688	−	0.804695i	$-0.297671\pi$
$883$	−6.27015	−	6.27015i	−0.211007	−	0.211007i	−0.804695	+	0.593688i	$0.797671\pi$
$884$	−0.778539	−	1.34847i	−0.0261851	−	0.0453539i
$885$		0			0
$886$	2.72474	−	4.71940i	0.0915396	−	0.158551i
$887$	−7.92256	+	2.12284i	−0.266014	+	0.0712781i	−0.389360	−	0.921085i	$-0.627304\pi$
$887$	−7.92256	+	2.12284i	−0.266014	+	0.0712781i	0.123347	+	0.992364i	$0.460637\pi$
$888$		0			0
$889$	−10.4798	+	6.05051i	−0.351481	+	0.202928i
$890$		0			0
$891$		0			0
$892$	18.1237	−	18.1237i	0.606827	−	0.606827i
$893$	56.0676	+	15.0233i	1.87623	+	0.502734i
$894$		0			0
$895$		0			0
$896$	3.94949	+	2.28024i	0.131943	+	0.0761774i
$897$		0			0
$898$	0.238477	−	0.890008i	0.00795807	−	0.0296999i
$899$	−0.142865			−0.00476480
$900$		0			0
$901$	2.40408			0.0800916
$902$	1.21566	−	4.53689i	0.0404770	−	0.151062i
$903$		0			0
$904$	−5.02118	−	2.89898i	−0.167002	−	0.0964186i
$905$		0			0
$906$		0			0
$907$	−3.65307	−	0.978838i	−0.121298	−	0.0325018i	0.197659	−	0.980271i	$-0.436666\pi$
$907$	−3.65307	−	0.978838i	−0.121298	−	0.0325018i	−0.318957	+	0.947769i	$0.603333\pi$
$908$	−17.6062	+	17.6062i	−0.584284	+	0.584284i
$909$		0			0
$910$		0			0
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	−0.395114	−	0.918632i	$-0.629295\pi$
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	0.598002	+	0.801495i	$0.295962\pi$
$912$		0			0
$913$	3.34607	−	0.896575i	0.110739	−	0.0296723i
$914$	7.31747	−	12.6742i	0.242040	−	0.419226i
$915$		0			0
$916$	0.825765	+	1.43027i	0.0272841	+	0.0472574i
$917$	11.6315	+	11.6315i	0.384107	+	0.384107i
$918$		0			0
$919$		−	12.6515i		−	0.417335i	−0.977987	−	0.208668i	$-0.933087\pi$
$919$		−	12.6515i		−	0.417335i	0.977987	−	0.208668i	$-0.0669127\pi$
$920$		0			0
$921$		0			0
$922$	−8.55444	−	31.9256i	−0.281726	−	1.05141i
$923$	5.64173	+	21.0552i	0.185700	+	0.693041i
$924$		0			0
$925$		0			0
$926$		−	12.2351i		−	0.402071i
$927$		0			0
$928$	−0.224745	−	0.224745i	−0.00737761	−	0.00737761i
$929$	−21.1024	−	36.5505i	−0.692349	−	1.19918i	−0.971066	−	0.238810i	$-0.923243\pi$
$929$	−21.1024	−	36.5505i	−0.692349	−	1.19918i	0.278717	−	0.960373i	$-0.410091\pi$
$930$		0			0
$931$	44.4949	−	77.0674i	1.45826	−	2.52578i
$932$	19.7527	−	5.29272i	0.647021	−	0.173369i
$933$		0			0
$934$	−3.46410	+	2.00000i	−0.113349	+	0.0654420i
$935$		0			0
$936$		0			0
$937$	3.10102	−	3.10102i	0.101306	−	0.101306i	−0.654637	−	0.755943i	$-0.727179\pi$
$937$	3.10102	−	3.10102i	0.101306	−	0.101306i	0.755943	+	0.654637i	$0.227179\pi$
$938$	−29.1192	−	7.80247i	−0.950776	−	0.254760i
$939$		0			0
$940$		0			0
$941$	−27.5227	−	15.8902i	−0.897215	−	0.518007i	−0.0209191	−	0.999781i	$-0.506659\pi$
$941$	−27.5227	−	15.8902i	−0.897215	−	0.518007i	−0.876295	+	0.481774i	$0.839993\pi$
$942$		0			0
$943$	−1.91239	+	7.13713i	−0.0622760	+	0.232417i
$944$	8.97809			0.292212
$945$		0			0
$946$	2.20204			0.0715945
$947$	0.788210	−	2.94164i	0.0256134	−	0.0955904i	−0.951936	−	0.306297i	$-0.900910\pi$
$947$	0.788210	−	2.94164i	0.0256134	−	0.0955904i	0.977549	+	0.210707i	$0.0675765\pi$
$948$		0			0
$949$	29.2699	+	16.8990i	0.950141	+	0.548564i
$950$		0			0
$951$		0			0
$952$	1.98004	+	0.530550i	0.0641735	+	0.0171952i
$953$	−5.79972	+	5.79972i	−0.187871	+	0.187871i	−0.794775	−	0.606904i	$-0.792411\pi$
$953$	−5.79972	+	5.79972i	−0.187871	+	0.187871i	0.606904	+	0.794775i	$0.292411\pi$
$954$		0			0
$955$		0			0
$956$	−14.6969	+	8.48528i	−0.475333	+	0.274434i
$957$		0			0
$958$	−6.83013	+	1.83013i	−0.220671	+	0.0591287i
$959$	49.7046	−	86.0908i	1.60504	−	2.78002i
$960$		0			0
$961$	15.3990	+	26.6718i	0.496741	+	0.860381i
$962$	10.3923	+	10.3923i	0.335061	+	0.335061i
$963$		0			0
$964$			19.0000i			0.611949i
$965$		0			0
$966$		0			0
$967$	10.3679	+	38.6937i	0.333411	+	1.24431i	0.905582	+	0.424172i	$0.139435\pi$
$967$	10.3679	+	38.6937i	0.333411	+	1.24431i	−0.572171	+	0.820134i	$0.693899\pi$
$968$	2.74243	+	10.2349i	0.0881449	+	0.328961i
$969$		0			0
$970$		0			0
$971$		−	21.4989i		−	0.689934i	−0.938615	−	0.344967i	$-0.887890\pi$
$971$		−	21.4989i		−	0.689934i	0.938615	−	0.344967i	$-0.112110\pi$
$972$		0			0
$973$	10.0000	+	10.0000i	0.320585	+	0.320585i
$974$	8.48528	+	14.6969i	0.271886	+	0.470920i
$975$		0			0
$976$	−0.275255	+	0.476756i	−0.00881070	+	0.0152606i
$977$	6.27359	−	1.68100i	0.200710	−	0.0537801i	−0.157063	−	0.987589i	$-0.550203\pi$
$977$	6.27359	−	1.68100i	0.200710	−	0.0537801i	0.357773	+	0.933808i	$0.383536\pi$
$978$		0			0
$979$	4.41761	−	2.55051i	0.141188	−	0.0815147i
$980$		0			0
$981$		0			0
$982$	−19.7980	+	19.7980i	−0.631778	+	0.631778i
$983$	−26.2752	−	7.04041i	−0.838047	−	0.224554i	−0.185826	−	0.982583i	$-0.559496\pi$
$983$	−26.2752	−	7.04041i	−0.838047	−	0.224554i	−0.652221	+	0.758029i	$0.726163\pi$
$984$		0			0
$985$		0			0
$986$	−0.123724	−	0.0714323i	−0.00394019	−	0.00227487i
$987$		0			0
$988$	−5.78245	+	21.5804i	−0.183964	+	0.686564i
$989$	−3.46410			−0.110152
$990$		0			0
$991$	16.7423			0.531838			0.265919	−	0.963995i	$-0.414325\pi$
$991$	16.7423			0.531838			0.265919	+	0.963995i	$0.414325\pi$
$992$	0.116337	−	0.434174i	0.00369369	−	0.0137850i
$993$		0			0
$994$	−24.8523	−	14.3485i	−0.788266	−	0.455106i
$995$		0			0
$996$		0			0
$997$	−6.49211	−	1.73955i	−0.205607	−	0.0550922i	0.154545	−	0.987986i	$-0.450609\pi$
$997$	−6.49211	−	1.73955i	−0.205607	−	0.0550922i	−0.360153	+	0.932893i	$0.617275\pi$
$998$	−0.635674	+	0.635674i	−0.0201219	+	0.0201219i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.q.g.1043.1		8
3.2	odd	2		450.2.p.a.293.2		8
5.2	odd	4	inner	1350.2.q.g.557.1		8
5.3	odd	4		270.2.m.a.17.2		8
5.4	even	2		270.2.m.a.233.2		8
9.2	odd	6	inner	1350.2.q.g.143.1		8
9.7	even	3		450.2.p.a.443.2		8
15.2	even	4		450.2.p.a.257.2		8
15.8	even	4		90.2.l.a.77.1	yes	8
15.14	odd	2		90.2.l.a.23.1	✓	8
45.2	even	12	inner	1350.2.q.g.1007.1		8
45.4	even	6		810.2.f.b.323.4		8
45.7	odd	12		450.2.p.a.407.2		8
45.13	odd	12		810.2.f.b.647.2		8
45.14	odd	6		810.2.f.b.323.1		8
45.23	even	12		810.2.f.b.647.3		8
45.29	odd	6		270.2.m.a.143.2		8
45.34	even	6		90.2.l.a.83.1	yes	8
45.38	even	12		270.2.m.a.197.2		8
45.43	odd	12		90.2.l.a.47.1	yes	8
60.23	odd	4		720.2.cu.a.257.1		8
60.59	even	2		720.2.cu.a.113.1		8
180.43	even	12		720.2.cu.a.497.1		8
180.79	odd	6		720.2.cu.a.353.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.1	✓	8	15.14	odd	2
90.2.l.a.47.1	yes	8	45.43	odd	12
90.2.l.a.77.1	yes	8	15.8	even	4
90.2.l.a.83.1	yes	8	45.34	even	6
270.2.m.a.17.2		8	5.3	odd	4
270.2.m.a.143.2		8	45.29	odd	6
270.2.m.a.197.2		8	45.38	even	12
270.2.m.a.233.2		8	5.4	even	2
450.2.p.a.257.2		8	15.2	even	4
450.2.p.a.293.2		8	3.2	odd	2
450.2.p.a.407.2		8	45.7	odd	12
450.2.p.a.443.2		8	9.7	even	3
720.2.cu.a.113.1		8	60.59	even	2
720.2.cu.a.257.1		8	60.23	odd	4
720.2.cu.a.353.1		8	180.79	odd	6
720.2.cu.a.497.1		8	180.43	even	12
810.2.f.b.323.1		8	45.14	odd	6
810.2.f.b.323.4		8	45.4	even	6
810.2.f.b.647.2		8	45.13	odd	12
810.2.f.b.647.3		8	45.23	even	12
1350.2.q.g.143.1		8	9.2	odd	6	inner
1350.2.q.g.557.1		8	5.2	odd	4	inner
1350.2.q.g.1007.1		8	45.2	even	12	inner
1350.2.q.g.1043.1		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(4.40508 + 1.18034i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(4.40508 + 1.18034i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.550510 - 0.317837i) q^{11} +(3.34607 - 0.896575i) q^{13} +(-2.28024 + 3.94949i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.317837 + 0.317837i) q^{17} -6.44949i q^{19} +(0.164525 + 0.614014i) q^{22} +(-0.258819 - 0.965926i) q^{23} +3.46410i q^{26} +(-3.22474 - 3.22474i) q^{28} +(0.158919 + 0.275255i) q^{29} +(-0.224745 + 0.389270i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.389270 + 0.224745i) q^{34} +(3.00000 - 3.00000i) q^{37} +(6.22973 + 1.66925i) q^{38} +(-6.39898 - 3.69445i) q^{41} +(0.896575 - 3.34607i) q^{43} -0.635674 q^{44} +1.00000 q^{46} +(-2.32937 + 8.69333i) q^{47} +(11.9494 + 6.89898i) q^{49} +(-3.34607 - 0.896575i) q^{52} +(3.78194 - 3.78194i) q^{53} +(3.94949 - 2.28024i) q^{56} +(-0.307007 + 0.0822623i) q^{58} +(4.48905 - 7.77526i) q^{59} +(0.275255 + 0.476756i) q^{61} +(-0.317837 - 0.317837i) q^{62} -1.00000i q^{64} +(1.71089 + 6.38512i) q^{67} +(-0.116337 - 0.434174i) q^{68} +6.29253i q^{71} +(6.89898 + 6.89898i) q^{73} +(2.12132 + 3.67423i) q^{74} +(-3.22474 + 5.58542i) q^{76} +(2.80020 - 0.750311i) q^{77} +(-2.12132 + 1.22474i) q^{79} +(5.22474 - 5.22474i) q^{82} +(5.26380 + 1.41043i) q^{83} +(3.00000 + 1.73205i) q^{86} +(0.164525 - 0.614014i) q^{88} +8.02458 q^{89} +15.7980 q^{91} +(-0.258819 + 0.965926i) q^{92} +(-7.79423 - 4.50000i) q^{94} +(2.59405 + 0.695075i) q^{97} +(-9.75663 + 9.75663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^7	\( 8 q + 8 q^{7} + 24 q^{11} + 4 q^{16} + 8 q^{22} - 16 q^{28} + 8 q^{31} + 24 q^{37} + 12 q^{38} - 12 q^{41} + 8 q^{46} + 12 q^{56} + 4 q^{58} + 12 q^{61} - 4 q^{67} - 12 q^{68} + 16 q^{73} - 16 q^{76} + 24 q^{77} + 32 q^{82} + 12 q^{83} + 24 q^{86} + 8 q^{88} + 48 q^{91} - 12 q^{97}+O(q^{100}) \) 8 * q + 8 * q^7 + 24 * q^11 + 4 * q^16 + 8 * q^22 - 16 * q^28 + 8 * q^31 + 24 * q^37 + 12 * q^38 - 12 * q^41 + 8 * q^46 + 12 * q^56 + 4 * q^58 + 12 * q^61 - 4 * q^67 - 12 * q^68 + 16 * q^73 - 16 * q^76 + 24 * q^77 + 32 * q^82 + 12 * q^83 + 24 * q^86 + 8 * q^88 + 48 * q^91 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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