LMFDB - Embedded newform 1890.2.t.b.1151.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("1890.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.t (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.10
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.b.1601.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.53870 - 0.744985i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.53870 - 0.744985i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -0.441750i q^{11} +(3.17590 + 1.83361i) q^{13} +(2.57107 + 0.624174i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.136107 + 0.235743i) q^{17} +(-3.25564 + 1.87965i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.220875 - 0.382566i) q^{22} +2.59564i q^{23} +1.00000 q^{25} +(1.83361 + 3.17590i) q^{26} +(1.91453 + 1.82609i) q^{28} +(2.38822 - 1.37884i) q^{29} +(7.57702 - 4.37459i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.235743 + 0.136107i) q^{34} +(2.53870 - 0.744985i) q^{35} +(0.0597017 + 0.103406i) q^{37} -3.75929 q^{38} +1.00000i q^{40} +(-3.93435 + 6.81449i) q^{41} +(0.849825 + 1.47194i) q^{43} +(0.382566 - 0.220875i) q^{44} +(-1.29782 + 2.24789i) q^{46} +(3.94756 - 6.83738i) q^{47} +(5.89000 - 3.78259i) q^{49} +(0.866025 + 0.500000i) q^{50} +3.66721i q^{52} +(-0.0822585 - 0.0474920i) q^{53} -0.441750i q^{55} +(0.744985 + 2.53870i) q^{56} +2.75767 q^{58} +(-1.60532 - 2.78050i) q^{59} +(-11.2595 - 6.50065i) q^{61} +8.74919 q^{62} -1.00000 q^{64} +(3.17590 + 1.83361i) q^{65} +(0.268733 + 0.465460i) q^{67} -0.272213 q^{68} +(2.57107 + 0.624174i) q^{70} -3.75218i q^{71} +(9.64229 + 5.56698i) q^{73} +0.119403i q^{74} +(-3.25564 - 1.87965i) q^{76} +(-0.329097 - 1.12147i) q^{77} +(-1.51395 + 2.62224i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-6.81449 + 3.93435i) q^{82} +(4.29210 + 7.43413i) q^{83} +(-0.136107 + 0.235743i) q^{85} +1.69965i q^{86} +0.441750 q^{88} +(6.35119 + 11.0006i) q^{89} +(9.42867 + 2.28898i) q^{91} +(-2.24789 + 1.29782i) q^{92} +(6.83738 - 3.94756i) q^{94} +(-3.25564 + 1.87965i) q^{95} +(-12.9284 + 7.46424i) q^{97} +(6.99218 - 0.330818i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	2.53870	−	0.744985i	0.959538	−	0.281578i
$7$	2.53870	−	0.744985i	0.959538	−	0.281578i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	0.441750i		−	0.133193i	−0.997780	−	0.0665963i	$-0.978786\pi$
$11$		−	0.441750i		−	0.133193i	0.997780	−	0.0665963i	$-0.0212140\pi$
$12$		0			0
$13$	3.17590	+	1.83361i	0.880836	+	0.508551i	0.870934	−	0.491400i	$-0.163515\pi$
$13$	3.17590	+	1.83361i	0.880836	+	0.508551i	0.00990217	+	0.999951i	$0.496848\pi$
$14$	2.57107	+	0.624174i	0.687148	+	0.166818i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.136107	+	0.235743i	−0.0330107	+	0.0571762i	−0.882059	−	0.471139i	$-0.843843\pi$
$17$	−0.136107	+	0.235743i	−0.0330107	+	0.0571762i	0.849048	+	0.528316i	$0.177176\pi$
$18$		0			0
$19$	−3.25564	+	1.87965i	−0.746896	+	0.431221i	−0.824571	−	0.565758i	$-0.808584\pi$
$19$	−3.25564	+	1.87965i	−0.746896	+	0.431221i	0.0776753	+	0.996979i	$0.475250\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	0.220875	−	0.382566i	0.0470907	−	0.0815634i
$23$			2.59564i			0.541228i	0.962688	+	0.270614i	$0.0872267\pi$
$23$			2.59564i			0.541228i	−0.962688	+	0.270614i	$0.912773\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.83361	+	3.17590i	0.359600	+	0.622845i
$27$		0			0
$28$	1.91453	+	1.82609i	0.361811	+	0.345098i
$29$	2.38822	−	1.37884i	0.443481	−	0.256044i	−0.261592	−	0.965178i	$-0.584248\pi$
$29$	2.38822	−	1.37884i	0.443481	−	0.256044i	0.705073	+	0.709135i	$0.250914\pi$
$30$		0			0
$31$	7.57702	−	4.37459i	1.36087	−	0.785700i	0.371133	−	0.928580i	$-0.378970\pi$
$31$	7.57702	−	4.37459i	1.36087	−	0.785700i	0.989740	+	0.142880i	$0.0456362\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−0.235743	+	0.136107i	−0.0404297	+	0.0233421i
$35$	2.53870	−	0.744985i	0.429119	−	0.125925i
$36$		0			0
$37$	0.0597017	+	0.103406i	0.00981490	+	0.0169999i	0.870891	−	0.491476i	$-0.163542\pi$
$37$	0.0597017	+	0.103406i	0.00981490	+	0.0169999i	−0.861076	+	0.508476i	$0.830209\pi$
$38$	−3.75929			−0.609838
$39$		0			0
$40$			1.00000i			0.158114i
$41$	−3.93435	+	6.81449i	−0.614442	+	1.06424i	0.376041	+	0.926603i	$0.377285\pi$
$41$	−3.93435	+	6.81449i	−0.614442	+	1.06424i	−0.990482	+	0.137641i	$0.956048\pi$
$42$		0			0
$43$	0.849825	+	1.47194i	0.129597	+	0.224469i	0.923521	−	0.383549i	$-0.125298\pi$
$43$	0.849825	+	1.47194i	0.129597	+	0.224469i	−0.793923	+	0.608018i	$0.791965\pi$
$44$	0.382566	−	0.220875i	0.0576741	−	0.0332981i
$45$		0			0
$46$	−1.29782	+	2.24789i	−0.191353	+	0.331433i
$47$	3.94756	−	6.83738i	0.575811	−	0.997334i	−0.420142	−	0.907458i	$-0.638020\pi$
$47$	3.94756	−	6.83738i	0.575811	−	0.997334i	0.995953	−	0.0898756i	$-0.0286470\pi$
$48$		0			0
$49$	5.89000	−	3.78259i	0.841428	−	0.540369i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$			3.66721i			0.508551i
$53$	−0.0822585	−	0.0474920i	−0.0112991	−	0.00652352i	0.494340	−	0.869269i	$-0.335410\pi$
$53$	−0.0822585	−	0.0474920i	−0.0112991	−	0.00652352i	−0.505639	+	0.862745i	$0.668743\pi$
$54$		0			0
$55$		−	0.441750i		−	0.0595655i
$56$	0.744985	+	2.53870i	0.0995528	+	0.339248i
$57$		0			0
$58$	2.75767			0.362100
$59$	−1.60532	−	2.78050i	−0.208995	−	0.361990i	0.742403	−	0.669954i	$-0.233686\pi$
$59$	−1.60532	−	2.78050i	−0.208995	−	0.361990i	−0.951398	+	0.307963i	$0.900353\pi$
$60$		0			0
$61$	−11.2595	−	6.50065i	−1.44163	−	0.832323i	−0.443667	−	0.896192i	$-0.646323\pi$
$61$	−11.2595	−	6.50065i	−1.44163	−	0.832323i	−0.997958	+	0.0638687i	$0.979656\pi$
$62$	8.74919			1.11115
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.17590	+	1.83361i	0.393922	+	0.227431i
$66$		0			0
$67$	0.268733	+	0.465460i	0.0328310	+	0.0568650i	0.881974	−	0.471298i	$-0.156214\pi$
$67$	0.268733	+	0.465460i	0.0328310	+	0.0568650i	−0.849143	+	0.528163i	$0.822881\pi$
$68$	−0.272213			−0.0330107
$69$		0			0
$70$	2.57107	+	0.624174i	0.307302	+	0.0746031i
$71$		−	3.75218i		−	0.445302i	−0.974898	−	0.222651i	$-0.928529\pi$
$71$		−	3.75218i		−	0.445302i	0.974898	−	0.222651i	$-0.0714711\pi$
$72$		0			0
$73$	9.64229	+	5.56698i	1.12854	+	0.651565i	0.943568	−	0.331178i	$-0.107446\pi$
$73$	9.64229	+	5.56698i	1.12854	+	0.651565i	0.184976	+	0.982743i	$0.440779\pi$
$74$			0.119403i			0.0138804i
$75$		0			0
$76$	−3.25564	−	1.87965i	−0.373448	−	0.215610i
$77$	−0.329097	−	1.12147i	−0.0375041	−	0.127803i
$78$		0			0
$79$	−1.51395	+	2.62224i	−0.170333	+	0.295026i	−0.938536	−	0.345181i	$-0.887818\pi$
$79$	−1.51395	+	2.62224i	−0.170333	+	0.295026i	0.768203	+	0.640206i	$0.221151\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−6.81449	+	3.93435i	−0.752534	+	0.434476i
$83$	4.29210	+	7.43413i	0.471119	+	0.816002i	0.999454	−	0.0330340i	$-0.0105170\pi$
$83$	4.29210	+	7.43413i	0.471119	+	0.816002i	−0.528335	+	0.849036i	$0.677184\pi$
$84$		0			0
$85$	−0.136107	+	0.235743i	−0.0147628	+	0.0255700i
$86$			1.69965i			0.183278i
$87$		0			0
$88$	0.441750			0.0470907
$89$	6.35119	+	11.0006i	0.673225	+	1.16606i	0.976984	+	0.213311i	$0.0684247\pi$
$89$	6.35119	+	11.0006i	0.673225	+	1.16606i	−0.303760	+	0.952749i	$0.598242\pi$
$90$		0			0
$91$	9.42867	+	2.28898i	0.988393	+	0.239950i
$92$	−2.24789	+	1.29782i	−0.234359	+	0.135307i
$93$		0			0
$94$	6.83738	−	3.94756i	0.705222	−	0.407160i
$95$	−3.25564	+	1.87965i	−0.334022	+	0.192848i
$96$		0			0
$97$	−12.9284	+	7.46424i	−1.31268	+	0.757879i	−0.982540	−	0.186052i	$-0.940431\pi$
$97$	−12.9284	+	7.46424i	−1.31268	+	0.757879i	−0.330144	+	0.943930i	$0.607097\pi$
$98$	6.99218	−	0.330818i	0.706317	−	0.0334176i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−4.57755			−0.455483			−0.227742	−	0.973722i	$-0.573134\pi$
$101$	−4.57755			−0.455483			−0.227742	+	0.973722i	$0.573134\pi$
$102$		0			0
$103$			4.60214i			0.453462i	0.973957	+	0.226731i	$0.0728039\pi$
$103$			4.60214i			0.453462i	−0.973957	+	0.226731i	$0.927196\pi$
$104$	−1.83361	+	3.17590i	−0.179800	+	0.311423i
$105$		0			0
$106$	−0.0474920	−	0.0822585i	−0.00461283	−	0.00798965i
$107$	14.0223	−	8.09579i	1.35559	−	0.782650i	0.366563	−	0.930393i	$-0.380534\pi$
$107$	14.0223	−	8.09579i	1.35559	−	0.782650i	0.989026	+	0.147743i	$0.0472010\pi$
$108$		0			0
$109$	−1.37107	+	2.37476i	−0.131325	+	0.227461i	−0.924187	−	0.381939i	$-0.875256\pi$
$109$	−1.37107	+	2.37476i	−0.131325	+	0.227461i	0.792863	+	0.609400i	$0.208590\pi$
$110$	0.220875	−	0.382566i	0.0210596	−	0.0364763i
$111$		0			0
$112$	−0.624174	+	2.57107i	−0.0589789	+	0.242943i
$113$	2.85536	+	1.64854i	0.268610	+	0.155082i	0.628256	−	0.778007i	$-0.283769\pi$
$113$	2.85536	+	1.64854i	0.268610	+	0.155082i	−0.359646	+	0.933089i	$0.617102\pi$
$114$		0			0
$115$			2.59564i			0.242045i
$116$	2.38822	+	1.37884i	0.221740	+	0.128022i
$117$		0			0
$118$		−	3.21065i		−	0.295564i
$119$	−0.169908	+	0.699879i	−0.0155755	+	0.0641578i
$120$		0			0
$121$	10.8049			0.982260
$122$	−6.50065	−	11.2595i	−0.588541	−	1.01938i
$123$		0			0
$124$	7.57702	+	4.37459i	0.680436	+	0.392850i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−21.1104			−1.87325			−0.936623	−	0.350339i	$-0.886066\pi$
$127$	−21.1104			−1.87325			−0.936623	+	0.350339i	$0.886066\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	1.83361	+	3.17590i	0.160818	+	0.278545i
$131$	−5.08532			−0.444307			−0.222153	−	0.975012i	$-0.571309\pi$
$131$	−5.08532			−0.444307			−0.222153	+	0.975012i	$0.571309\pi$
$132$		0			0
$133$	−6.86479	+	7.19726i	−0.595253	+	0.624082i
$134$			0.537467i			0.0464301i
$135$		0			0
$136$	−0.235743	−	0.136107i	−0.0202148	−	0.0116710i
$137$		−	13.6419i		−	1.16551i	−0.812649	−	0.582753i	$-0.801976\pi$
$137$		−	13.6419i		−	1.16551i	0.812649	−	0.582753i	$-0.198024\pi$
$138$		0			0
$139$	−8.22684	−	4.74977i	−0.697791	−	0.402870i	0.108733	−	0.994071i	$-0.465321\pi$
$139$	−8.22684	−	4.74977i	−0.697791	−	0.402870i	−0.806524	+	0.591201i	$0.798654\pi$
$140$	1.91453	+	1.82609i	0.161807	+	0.154332i
$141$		0			0
$142$	1.87609	−	3.24949i	0.157438	−	0.272691i
$143$	0.809995	−	1.40295i	0.0677352	−	0.117321i
$144$		0			0
$145$	2.38822	−	1.37884i	0.198331	−	0.114506i
$146$	5.56698	+	9.64229i	0.460726	+	0.798001i
$147$		0			0
$148$	−0.0597017	+	0.103406i	−0.00490745	+	0.00849995i
$149$		−	14.3445i		−	1.17515i	−0.809170	−	0.587574i	$-0.800083\pi$
$149$		−	14.3445i		−	1.17515i	0.809170	−	0.587574i	$-0.199917\pi$
$150$		0			0
$151$	0.679789			0.0553204			0.0276602	−	0.999617i	$-0.491194\pi$
$151$	0.679789			0.0553204			0.0276602	+	0.999617i	$0.491194\pi$
$152$	−1.87965	−	3.25564i	−0.152459	−	0.264068i
$153$		0			0
$154$	0.275729	−	1.13577i	0.0222189	−	0.0915229i
$155$	7.57702	−	4.37459i	0.608601	−	0.351376i
$156$		0			0
$157$	−20.6832	+	11.9414i	−1.65070	+	0.953030i	−0.673911	+	0.738812i	$0.735387\pi$
$157$	−20.6832	+	11.9414i	−1.65070	+	0.953030i	−0.976786	+	0.214218i	$0.931280\pi$
$158$	−2.62224	+	1.51395i	−0.208615	+	0.120444i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	1.93371	+	6.58955i	0.152398	+	0.519329i
$162$		0			0
$163$	−7.98983	−	13.8388i	−0.625812	−	1.08394i	−0.988383	−	0.151982i	$-0.951434\pi$
$163$	−7.98983	−	13.8388i	−0.625812	−	1.08394i	0.362571	−	0.931956i	$-0.381899\pi$
$164$	−7.86869			−0.614442
$165$		0			0
$166$			8.58419i			0.666263i
$167$	−2.36183	+	4.09080i	−0.182764	+	0.316556i	−0.942821	−	0.333300i	$-0.891838\pi$
$167$	−2.36183	+	4.09080i	−0.182764	+	0.316556i	0.760057	+	0.649856i	$0.225171\pi$
$168$		0			0
$169$	0.224227	+	0.388373i	0.0172483	+	0.0298749i
$170$	−0.235743	+	0.136107i	−0.0180807	+	0.0104389i
$171$		0			0
$172$	−0.849825	+	1.47194i	−0.0647985	+	0.112234i
$173$	10.1399	−	17.5629i	0.770925	−	1.33528i	−0.166132	−	0.986104i	$-0.553128\pi$
$173$	10.1399	−	17.5629i	0.770925	−	1.33528i	0.937057	−	0.349177i	$-0.113539\pi$
$174$		0			0
$175$	2.53870	−	0.744985i	0.191908	−	0.0563156i
$176$	0.382566	+	0.220875i	0.0288370	+	0.0166491i
$177$		0			0
$178$			12.7024i			0.952084i
$179$	13.2165	+	7.63053i	0.987846	+	0.570333i	0.904630	−	0.426199i	$-0.140148\pi$
$179$	13.2165	+	7.63053i	0.987846	+	0.570333i	0.0832159	+	0.996532i	$0.473481\pi$
$180$		0			0
$181$			24.7207i			1.83748i	0.394866	+	0.918739i	$0.370791\pi$
$181$			24.7207i			1.83748i	−0.394866	+	0.918739i	$0.629209\pi$
$182$	7.02097	+	6.69665i	0.520429	+	0.496389i
$183$		0			0
$184$	−2.59564			−0.191353
$185$	0.0597017	+	0.103406i	0.00438936	+	0.00760259i
$186$		0			0
$187$	0.104140	+	0.0601250i	0.00761544	+	0.00439678i
$188$	7.89512			0.575811
$189$		0			0
$190$	−3.75929			−0.272728
$191$	4.76721	+	2.75235i	0.344943	+	0.199153i	0.662456	−	0.749101i	$-0.269514\pi$
$191$	4.76721	+	2.75235i	0.344943	+	0.199153i	−0.317513	+	0.948254i	$0.602848\pi$
$192$		0			0
$193$	7.52344	+	13.0310i	0.541549	+	0.937991i	0.998815	+	0.0486607i	$0.0154953\pi$
$193$	7.52344	+	13.0310i	0.541549	+	0.937991i	−0.457266	+	0.889330i	$0.651171\pi$
$194$	−14.9285			−1.07180
$195$		0			0
$196$	6.22081	+	3.20959i	0.444344	+	0.229257i
$197$		−	19.6584i		−	1.40061i	−0.713846	−	0.700303i	$-0.753048\pi$
$197$		−	19.6584i		−	1.40061i	0.713846	−	0.700303i	$-0.246952\pi$
$198$		0			0
$199$	−9.23999	−	5.33471i	−0.655005	−	0.378168i	0.135366	−	0.990796i	$-0.456779\pi$
$199$	−9.23999	−	5.33471i	−0.655005	−	0.378168i	−0.790371	+	0.612628i	$0.790112\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−3.96428	−	2.28878i	−0.278926	−	0.161038i
$203$	5.03575	−	5.27964i	0.353440	−	0.370558i
$204$		0			0
$205$	−3.93435	+	6.81449i	−0.274787	+	0.475944i
$206$	−2.30107	+	3.98557i	−0.160323	+	0.277688i
$207$		0			0
$208$	−3.17590	+	1.83361i	−0.220209	+	0.127138i
$209$	0.830333	+	1.43818i	0.0574354	+	0.0994810i
$210$		0			0
$211$	−0.581500	+	1.00719i	−0.0400321	+	0.0693376i	−0.885347	−	0.464930i	$-0.846079\pi$
$211$	−0.581500	+	1.00719i	−0.0400321	+	0.0693376i	0.845315	+	0.534268i	$0.179413\pi$
$212$		−	0.0949840i		−	0.00652352i
$213$		0			0
$214$	16.1916			1.10683
$215$	0.849825	+	1.47194i	0.0579575	+	0.100385i
$216$		0			0
$217$	15.9768	−	16.7505i	1.08457	−	1.13710i
$218$	−2.37476	+	1.37107i	−0.160839	+	0.0928605i
$219$		0			0
$220$	0.382566	−	0.220875i	0.0257926	−	0.0148914i
$221$	−0.864522	+	0.499132i	−0.0581540	+	0.0335752i
$222$		0			0
$223$	−2.45476	+	1.41726i	−0.164383	+	0.0949066i	−0.579935	−	0.814663i	$-0.696922\pi$
$223$	−2.45476	+	1.41726i	−0.164383	+	0.0949066i	0.415552	+	0.909570i	$0.363589\pi$
$224$	−1.82609	+	1.91453i	−0.122011	+	0.127920i
$225$		0			0
$226$	1.64854	+	2.85536i	0.109660	+	0.189936i
$227$	−11.2496			−0.746662			−0.373331	−	0.927698i	$-0.621784\pi$
$227$	−11.2496			−0.746662			−0.373331	+	0.927698i	$0.621784\pi$
$228$		0			0
$229$		−	16.1969i		−	1.07032i	−0.844751	−	0.535160i	$-0.820251\pi$
$229$		−	16.1969i		−	1.07032i	0.844751	−	0.535160i	$-0.179749\pi$
$230$	−1.29782	+	2.24789i	−0.0855757	+	0.148221i
$231$		0			0
$232$	1.37884	+	2.38822i	0.0905251	+	0.156794i
$233$	−3.21321	+	1.85515i	−0.210504	+	0.121535i	−0.601546	−	0.798838i	$-0.705448\pi$
$233$	−3.21321	+	1.85515i	−0.210504	+	0.121535i	0.391042	+	0.920373i	$0.372115\pi$
$234$		0			0
$235$	3.94756	−	6.83738i	0.257511	−	0.446021i
$236$	1.60532	−	2.78050i	0.104498	−	0.180995i
$237$		0			0
$238$	−0.497085	+	0.521159i	−0.0322212	+	0.0337817i
$239$	−7.04916	−	4.06984i	−0.455972	−	0.263256i	0.254377	−	0.967105i	$-0.418130\pi$
$239$	−7.04916	−	4.06984i	−0.455972	−	0.263256i	−0.710349	+	0.703849i	$0.751463\pi$
$240$		0			0
$241$		−	28.4731i		−	1.83412i	−0.398754	−	0.917058i	$-0.630557\pi$
$241$		−	28.4731i		−	1.83412i	0.398754	−	0.917058i	$-0.369443\pi$
$242$	9.35728	+	5.40243i	0.601509	+	0.347281i
$243$		0			0
$244$		−	13.0013i		−	0.832323i
$245$	5.89000	−	3.78259i	0.376298	−	0.241661i
$246$		0			0
$247$	−13.7861			−0.877191
$248$	4.37459	+	7.57702i	0.277787	+	0.481141i
$249$		0			0
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−4.61055			−0.291015			−0.145508	−	0.989357i	$-0.546482\pi$
$251$	−4.61055			−0.291015			−0.145508	+	0.989357i	$0.546482\pi$
$252$		0			0
$253$	1.14662			0.0720876
$254$	−18.2821	−	10.5552i	−1.14712	−	0.662292i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−27.2946			−1.70259			−0.851297	−	0.524685i	$-0.824183\pi$
$257$	−27.2946			−1.70259			−0.851297	+	0.524685i	$0.824183\pi$
$258$		0			0
$259$	0.228601	+	0.218041i	0.0142046	+	0.0135484i
$260$			3.66721i			0.227431i
$261$		0			0
$262$	−4.40402	−	2.54266i	−0.272081	−	0.157086i
$263$		−	29.9074i		−	1.84417i	−0.386985	−	0.922086i	$-0.626484\pi$
$263$		−	29.9074i		−	1.84417i	0.386985	−	0.922086i	$-0.373516\pi$
$264$		0			0
$265$	−0.0822585	−	0.0474920i	−0.00505310	−	0.00291741i
$266$	−9.54372	+	2.80062i	−0.585163	+	0.171717i
$267$		0			0
$268$	−0.268733	+	0.465460i	−0.0164155	+	0.0284325i
$269$	−6.84004	+	11.8473i	−0.417044	+	0.722342i	−0.995641	−	0.0932721i	$-0.970267\pi$
$269$	−6.84004	+	11.8473i	−0.417044	+	0.722342i	0.578596	+	0.815614i	$0.303601\pi$
$270$		0			0
$271$	−2.74454	+	1.58456i	−0.166719	+	0.0962551i	−0.581038	−	0.813877i	$-0.697353\pi$
$271$	−2.74454	+	1.58456i	−0.166719	+	0.0962551i	0.414319	+	0.910132i	$0.364020\pi$
$272$	−0.136107	−	0.235743i	−0.00825267	−	0.0142940i
$273$		0			0
$274$	6.82095	−	11.8142i	0.412068	−	0.713724i
$275$		−	0.441750i		−	0.0266385i
$276$		0			0
$277$	1.51760			0.0911837			0.0455919	−	0.998960i	$-0.485483\pi$
$277$	1.51760			0.0911837			0.0455919	+	0.998960i	$0.485483\pi$
$278$	−4.74977	−	8.22684i	−0.284872	−	0.493413i
$279$		0			0
$280$	0.744985	+	2.53870i	0.0445214	+	0.151716i
$281$	−3.08954	+	1.78375i	−0.184307	+	0.106409i	−0.589315	−	0.807904i	$-0.700602\pi$
$281$	−3.08954	+	1.78375i	−0.184307	+	0.106409i	0.405008	+	0.914313i	$0.367269\pi$
$282$		0			0
$283$	11.4290	−	6.59851i	0.679381	−	0.392241i	−0.120241	−	0.992745i	$-0.538367\pi$
$283$	11.4290	−	6.59851i	0.679381	−	0.392241i	0.799622	+	0.600504i	$0.205033\pi$
$284$	3.24949	−	1.87609i	0.192822	−	0.111326i
$285$		0			0
$286$	1.40295	−	0.809995i	0.0829583	−	0.0478960i
$287$	−4.91143	+	20.2310i	−0.289913	+	1.19420i
$288$		0			0
$289$	8.46295	+	14.6583i	0.497821	+	0.862251i
$290$	2.75767			0.161936
$291$		0			0
$292$			11.1340i			0.651565i
$293$	−11.0248	+	19.0955i	−0.644074	+	1.11557i	0.340440	+	0.940266i	$0.389424\pi$
$293$	−11.0248	+	19.0955i	−0.644074	+	1.11557i	−0.984515	+	0.175303i	$0.943910\pi$
$294$		0			0
$295$	−1.60532	−	2.78050i	−0.0934655	−	0.161887i
$296$	−0.103406	+	0.0597017i	−0.00601037	+	0.00347009i
$297$		0			0
$298$	7.17226	−	12.4227i	0.415478	−	0.719629i
$299$	−4.75938	+	8.24349i	−0.275242	+	0.476733i
$300$		0			0
$301$	3.25402	+	3.10371i	0.187559	+	0.178895i
$302$	0.588715	+	0.339894i	0.0338767	+	0.0195587i
$303$		0			0
$304$		−	3.75929i		−	0.215610i
$305$	−11.2595	−	6.50065i	−0.644715	−	0.372226i
$306$		0			0
$307$		−	29.2097i		−	1.66709i	−0.552453	−	0.833544i	$-0.686308\pi$
$307$		−	29.2097i		−	1.66709i	0.552453	−	0.833544i	$-0.313692\pi$
$308$	0.806673	−	0.845741i	0.0459645	−	0.0481906i
$309$		0			0
$310$	8.74919			0.496920
$311$	12.3964	+	21.4711i	0.702933	+	1.21752i	0.967432	+	0.253130i	$0.0814600\pi$
$311$	12.3964	+	21.4711i	0.702933	+	1.21752i	−0.264499	+	0.964386i	$0.585207\pi$
$312$		0			0
$313$	−29.3510	−	16.9458i	−1.65902	−	0.957835i	−0.973169	−	0.230092i	$-0.926097\pi$
$313$	−29.3510	−	16.9458i	−1.65902	−	0.957835i	−0.685850	−	0.727743i	$-0.740569\pi$
$314$	−23.8829			−1.34779
$315$		0			0
$316$	−3.02791			−0.170333
$317$	−29.5986	−	17.0887i	−1.66242	−	0.959799i	−0.971554	−	0.236818i	$-0.923895\pi$
$317$	−29.5986	−	17.0887i	−1.66242	−	0.959799i	−0.690867	−	0.722981i	$-0.742771\pi$
$318$		0			0
$319$	−0.609101	−	1.05499i	−0.0341031	−	0.0590683i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−1.62013	+	6.67357i	−0.0902864	+	0.371904i
$323$		−	1.02333i		−	0.0569395i
$324$		0			0
$325$	3.17590	+	1.83361i	0.176167	+	0.101710i
$326$		−	15.9797i		−	0.885032i
$327$		0			0
$328$	−6.81449	−	3.93435i	−0.376267	−	0.217238i
$329$	4.92793	−	20.2989i	0.271686	−	1.11912i
$330$		0			0
$331$	9.09408	−	15.7514i	0.499856	−	0.865776i	−0.500144	−	0.865942i	$-0.666720\pi$
$331$	9.09408	−	15.7514i	0.499856	−	0.865776i	1.00000		0.000166208i	$5.29056e-5\pi$
$332$	−4.29210	+	7.43413i	−0.235559	+	0.408001i
$333$		0			0
$334$	−4.09080	+	2.36183i	−0.223839	+	0.129233i
$335$	0.268733	+	0.465460i	0.0146825	+	0.0254308i
$336$		0			0
$337$	1.19477	−	2.06941i	0.0650834	−	0.112728i	−0.831648	−	0.555304i	$-0.812602\pi$
$337$	1.19477	−	2.06941i	0.0650834	−	0.112728i	0.896731	+	0.442576i	$0.145935\pi$
$338$			0.448455i			0.0243927i
$339$		0			0
$340$	−0.272213			−0.0147628
$341$	−1.93248	−	3.34715i	−0.104649	−	0.181258i
$342$		0			0
$343$	12.1350	−	13.9908i	0.655226	−	0.755433i
$344$	−1.47194	+	0.849825i	−0.0793616	+	0.0458195i
$345$		0			0
$346$	17.5629	−	10.1399i	0.944186	−	0.545126i
$347$	21.2317	−	12.2581i	1.13978	−	0.658052i	0.193403	−	0.981119i	$-0.438047\pi$
$347$	21.2317	−	12.2581i	1.13978	−	0.658052i	0.946376	+	0.323068i	$0.104714\pi$
$348$		0			0
$349$	−17.2041	+	9.93277i	−0.920912	+	0.531689i	−0.883926	−	0.467627i	$-0.845109\pi$
$349$	−17.2041	+	9.93277i	−0.920912	+	0.531689i	−0.0369861	+	0.999316i	$0.511776\pi$
$350$	2.57107	+	0.624174i	0.137430	+	0.0333635i
$351$		0			0
$352$	0.220875	+	0.382566i	0.0117727	+	0.0203909i
$353$	−32.1481			−1.71107			−0.855535	−	0.517744i	$-0.826772\pi$
$353$	−32.1481			−1.71107			−0.855535	+	0.517744i	$0.826772\pi$
$354$		0			0
$355$		−	3.75218i		−	0.199145i
$356$	−6.35119	+	11.0006i	−0.336612	+	0.583030i
$357$		0			0
$358$	7.63053	+	13.2165i	0.403286	+	0.698512i
$359$	24.4812	−	14.1342i	1.29207	−	0.745976i	0.313048	−	0.949737i	$-0.398650\pi$
$359$	24.4812	−	14.1342i	1.29207	−	0.745976i	0.979021	+	0.203761i	$0.0653166\pi$
$360$		0			0
$361$	−2.43386	+	4.21556i	−0.128098	+	0.221872i
$362$	−12.3604	+	21.4088i	−0.649646	+	1.12522i
$363$		0			0
$364$	2.73202	+	9.30995i	0.143197	+	0.487974i
$365$	9.64229	+	5.56698i	0.504700	+	0.291389i
$366$		0			0
$367$		−	33.6602i		−	1.75705i	−0.477699	−	0.878524i	$-0.658529\pi$
$367$		−	33.6602i		−	1.75705i	0.477699	−	0.878524i	$-0.341471\pi$
$368$	−2.24789	−	1.29782i	−0.117179	−	0.0676535i
$369$		0			0
$370$			0.119403i			0.00620749i
$371$	−0.244210	−	0.0592865i	−0.0126788	−	0.00307800i
$372$		0			0
$373$	−11.9740			−0.619991			−0.309996	−	0.950738i	$-0.600328\pi$
$373$	−11.9740			−0.619991			−0.309996	+	0.950738i	$0.600328\pi$
$374$	0.0601250	+	0.104140i	0.00310899	+	0.00538493i
$375$		0			0
$376$	6.83738	+	3.94756i	0.352611	+	0.203580i
$377$	10.1130			0.520845
$378$		0			0
$379$	−10.9629			−0.563126			−0.281563	−	0.959543i	$-0.590853\pi$
$379$	−10.9629			−0.563126			−0.281563	+	0.959543i	$0.590853\pi$
$380$	−3.25564	−	1.87965i	−0.167011	−	0.0964238i
$381$		0			0
$382$	2.75235	+	4.76721i	0.140822	+	0.243912i
$383$	20.1252			1.02835			0.514174	−	0.857686i	$-0.328099\pi$
$383$	20.1252			1.02835			0.514174	+	0.857686i	$0.328099\pi$
$384$		0			0
$385$	−0.329097	−	1.12147i	−0.0167723	−	0.0571554i
$386$			15.0469i			0.765866i
$387$		0			0
$388$	−12.9284	−	7.46424i	−0.656342	−	0.378939i
$389$		−	27.3409i		−	1.38624i	−0.720823	−	0.693119i	$-0.756236\pi$
$389$		−	27.3409i		−	1.38624i	0.720823	−	0.693119i	$-0.243764\pi$
$390$		0			0
$391$	−0.611905	−	0.353283i	−0.0309454	−	0.0178663i
$392$	3.78259	+	5.89000i	0.191049	+	0.297490i
$393$		0			0
$394$	9.82922	−	17.0247i	0.495189	−	0.857692i
$395$	−1.51395	+	2.62224i	−0.0761753	+	0.131939i
$396$		0			0
$397$	13.5525	−	7.82456i	0.680182	−	0.392703i	−0.119742	−	0.992805i	$-0.538207\pi$
$397$	13.5525	−	7.82456i	0.680182	−	0.392703i	0.799924	+	0.600102i	$0.204873\pi$
$398$	−5.33471	−	9.23999i	−0.267405	−	0.463159i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			39.1525i			1.95518i	0.210509	+	0.977592i	$0.432488\pi$
$401$			39.1525i			1.95518i	−0.210509	+	0.977592i	$0.567512\pi$
$402$		0			0
$403$	32.0851			1.59827
$404$	−2.28878	−	3.96428i	−0.113871	−	0.197230i
$405$		0			0
$406$	7.00091	−	2.05443i	0.347449	−	0.101959i
$407$	0.0456797	−	0.0263732i	0.00226426	−	0.00130727i
$408$		0			0
$409$	−22.7149	+	13.1145i	−1.12318	+	0.648468i	−0.942211	−	0.335021i	$-0.891257\pi$
$409$	−22.7149	+	13.1145i	−1.12318	+	0.648468i	−0.180969	+	0.983489i	$0.557923\pi$
$410$	−6.81449	+	3.93435i	−0.336544	+	0.194303i
$411$		0			0
$412$	−3.98557	+	2.30107i	−0.196355	+	0.113366i
$413$	−6.14687	−	5.86292i	−0.302467	−	0.288495i
$414$		0			0
$415$	4.29210	+	7.43413i	0.210691	+	0.364927i
$416$	−3.66721			−0.179800
$417$		0			0
$418$			1.66067i			0.0812259i
$419$	−18.3795	+	31.8342i	−0.897897	+	1.55520i	−0.0677203	+	0.997704i	$0.521573\pi$
$419$	−18.3795	+	31.8342i	−0.897897	+	1.55520i	−0.830177	+	0.557500i	$0.811761\pi$
$420$		0			0
$421$	6.54747	+	11.3406i	0.319104	+	0.552705i	0.980301	−	0.197507i	$-0.0632847\pi$
$421$	6.54747	+	11.3406i	0.319104	+	0.552705i	−0.661197	+	0.750212i	$0.729951\pi$
$422$	−1.00719	+	0.581500i	−0.0490291	+	0.0283070i
$423$		0			0
$424$	0.0474920	−	0.0822585i	0.00230641	−	0.00399483i
$425$	−0.136107	+	0.235743i	−0.00660214	+	0.0114352i
$426$		0			0
$427$	−33.4273	−	8.11508i	−1.61766	−	0.392716i
$428$	14.0223	+	8.09579i	0.677795	+	0.391325i
$429$		0			0
$430$			1.69965i			0.0819644i
$431$	−17.9103	−	10.3405i	−0.862710	−	0.498086i	0.00220853	−	0.999998i	$-0.499297\pi$
$431$	−17.9103	−	10.3405i	−0.862710	−	0.498086i	−0.864919	+	0.501911i	$0.832630\pi$
$432$		0			0
$433$			5.36529i			0.257839i	0.991655	+	0.128920i	$0.0411509\pi$
$433$			5.36529i			0.257839i	−0.991655	+	0.128920i	$0.958849\pi$
$434$	22.2116	−	6.51801i	1.06619	−	0.312875i
$435$		0			0
$436$	−2.74214			−0.131325
$437$	−4.87888	−	8.45048i	−0.233389	−	0.404241i
$438$		0			0
$439$	−9.07559	−	5.23979i	−0.433154	−	0.250082i	0.267535	−	0.963548i	$-0.413791\pi$
$439$	−9.07559	−	5.23979i	−0.433154	−	0.250082i	−0.700689	+	0.713466i	$0.747124\pi$
$440$	0.441750			0.0210596
$441$		0			0
$442$	−0.998264			−0.0474826
$443$	6.73544	+	3.88871i	0.320010	+	0.184758i	0.651397	−	0.758737i	$-0.274183\pi$
$443$	6.73544	+	3.88871i	0.320010	+	0.184758i	−0.331387	+	0.943495i	$0.607516\pi$
$444$		0			0
$445$	6.35119	+	11.0006i	0.301075	+	0.521478i
$446$	−2.83452			−0.134218
$447$		0			0
$448$	−2.53870	+	0.744985i	−0.119942	+	0.0351972i
$449$			3.73404i			0.176220i	0.996111	+	0.0881102i	$0.0280828\pi$
$449$			3.73404i			0.176220i	−0.996111	+	0.0881102i	$0.971917\pi$
$450$		0			0
$451$	3.01030	+	1.73800i	0.141749	+	0.0818390i
$452$			3.29709i			0.155082i
$453$		0			0
$454$	−9.74244	−	5.62480i	−0.457235	−	0.263985i
$455$	9.42867	+	2.28898i	0.442023	+	0.107309i
$456$		0			0
$457$	−1.45393	+	2.51828i	−0.0680121	+	0.117800i	−0.898026	−	0.439942i	$-0.854999\pi$
$457$	−1.45393	+	2.51828i	−0.0680121	+	0.117800i	0.830014	+	0.557742i	$0.188332\pi$
$458$	8.09843	−	14.0269i	0.378415	−	0.655434i
$459$		0			0
$460$	−2.24789	+	1.29782i	−0.104808	+	0.0605111i
$461$	4.88443	+	8.46009i	0.227491	+	0.394026i	0.957064	−	0.289877i	$-0.0936145\pi$
$461$	4.88443	+	8.46009i	0.227491	+	0.394026i	−0.729573	+	0.683903i	$0.760281\pi$
$462$		0			0
$463$	1.43617	−	2.48752i	0.0667446	−	0.115605i	−0.830722	−	0.556688i	$-0.812072\pi$
$463$	1.43617	−	2.48752i	0.0667446	−	0.115605i	0.897467	+	0.441083i	$0.145405\pi$
$464$			2.75767i			0.128022i
$465$		0			0
$466$	−3.71029			−0.171876
$467$	−1.92955	−	3.34208i	−0.0892890	−	0.154653i	0.817922	−	0.575329i	$-0.195126\pi$
$467$	−1.92955	−	3.34208i	−0.0892890	−	0.154653i	−0.907211	+	0.420676i	$0.861793\pi$
$468$		0			0
$469$	1.02899	+	0.981461i	0.0475145	+	0.0453196i
$470$	6.83738	−	3.94756i	0.315385	−	0.182087i
$471$		0			0
$472$	2.78050	−	1.60532i	0.127983	−	0.0738910i
$473$	0.650229	−	0.375410i	0.0298975	−	0.0172614i
$474$		0			0
$475$	−3.25564	+	1.87965i	−0.149379	+	0.0862441i
$476$	−0.691067	+	0.202795i	−0.0316750	+	0.00929508i
$477$		0			0
$478$	−4.06984	−	7.04916i	−0.186150	−	0.322421i
$479$	16.3287			0.746079			0.373039	−	0.927815i	$-0.378316\pi$
$479$	16.3287			0.746079			0.373039	+	0.927815i	$0.378316\pi$
$480$		0			0
$481$			0.437878i			0.0199655i
$482$	14.2366	−	24.6585i	0.648458	−	1.12316i
$483$		0			0
$484$	5.40243	+	9.35728i	0.245565	+	0.425331i
$485$	−12.9284	+	7.46424i	−0.587050	+	0.338934i
$486$		0			0
$487$	7.05835	−	12.2254i	0.319844	−	0.553987i	−0.660611	−	0.750728i	$-0.729703\pi$
$487$	7.05835	−	12.2254i	0.319844	−	0.553987i	0.980455	+	0.196742i	$0.0630360\pi$
$488$	6.50065	−	11.2595i	0.294271	−	0.509692i
$489$		0			0
$490$	6.99218	−	0.330818i	0.315874	−	0.0149448i
$491$	9.00388	+	5.19839i	0.406339	+	0.234600i	0.689216	−	0.724556i	$-0.257955\pi$
$491$	9.00388	+	5.19839i	0.406339	+	0.234600i	−0.282876	+	0.959156i	$0.591289\pi$
$492$		0			0
$493$			0.750675i			0.0338087i
$494$	−11.9391	−	6.89307i	−0.537167	−	0.310134i
$495$		0			0
$496$			8.74919i			0.392850i
$497$	−2.79532	−	9.52567i	−0.125387	−	0.427285i
$498$		0			0
$499$	−15.8790			−0.710840			−0.355420	−	0.934707i	$-0.615662\pi$
$499$	−15.8790			−0.710840			−0.355420	+	0.934707i	$0.615662\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−3.99285	−	2.30527i	−0.178210	−	0.102889i
$503$	0.0186342			0.000830858			0.000415429	−	1.00000i	$-0.499868\pi$
$503$	0.0186342			0.000830858			0.000415429		1.00000i	$0.499868\pi$
$504$		0			0
$505$	−4.57755			−0.203698
$506$	0.993004	+	0.573311i	0.0441444	+	0.0254868i
$507$		0			0
$508$	−10.5552	−	18.2821i	−0.468311	−	0.811139i
$509$	−32.9617			−1.46100			−0.730502	−	0.682911i	$-0.760714\pi$
$509$	−32.9617			−1.46100			−0.730502	+	0.682911i	$0.760714\pi$
$510$		0			0
$511$	28.6262	+	6.94953i	1.26635	+	0.307429i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−23.6379	−	13.6473i	−1.04262	−	0.601958i
$515$			4.60214i			0.202795i
$516$		0			0
$517$	−3.02041	−	1.74383i	−0.132837	−	0.0766937i
$518$	0.0889537	+	0.303129i	0.00390840	+	0.0133187i
$519$		0			0
$520$	−1.83361	+	3.17590i	−0.0804090	+	0.139272i
$521$	−3.94706	+	6.83651i	−0.172924	+	0.299513i	−0.939441	−	0.342711i	$-0.888655\pi$
$521$	−3.94706	+	6.83651i	−0.172924	+	0.299513i	0.766517	+	0.642224i	$0.221988\pi$
$522$		0			0
$523$	2.84277	−	1.64127i	0.124306	−	0.0717679i	−0.436558	−	0.899676i	$-0.643803\pi$
$523$	2.84277	−	1.64127i	0.124306	−	0.0717679i	0.560864	+	0.827908i	$0.310469\pi$
$524$	−2.54266	−	4.40402i	−0.111077	−	0.192390i
$525$		0			0
$526$	14.9537	−	25.9006i	0.652013	−	1.12932i
$527$			2.38164i			0.103746i
$528$		0			0
$529$	16.2627			0.707072
$530$	−0.0474920	−	0.0822585i	−0.00206292	−	0.00357308i
$531$		0			0
$532$	−9.66541	−	2.34645i	−0.419049	−	0.101732i
$533$	−24.9902	+	14.4281i	−1.08244	+	0.624950i
$534$		0			0
$535$	14.0223	−	8.09579i	0.606238	−	0.350012i
$536$	−0.465460	+	0.268733i	−0.0201048	+	0.0116075i
$537$		0			0
$538$	−11.8473	+	6.84004i	−0.510773	+	0.294895i
$539$	−1.67096	−	2.60190i	−0.0719732	−	0.112072i
$540$		0			0
$541$	7.89978	+	13.6828i	0.339638	+	0.588270i	0.984365	−	0.176143i	$-0.0563621\pi$
$541$	7.89978	+	13.6828i	0.339638	+	0.588270i	−0.644727	+	0.764413i	$0.723029\pi$
$542$	−3.16912			−0.136125
$543$		0			0
$544$		−	0.272213i		−	0.0116710i
$545$	−1.37107	+	2.37476i	−0.0587302	+	0.101724i
$546$		0			0
$547$	−8.85022	−	15.3290i	−0.378408	−	0.655422i	0.612423	−	0.790531i	$-0.290195\pi$
$547$	−8.85022	−	15.3290i	−0.378408	−	0.655422i	−0.990831	+	0.135108i	$0.956862\pi$
$548$	11.8142	−	6.82095i	0.504679	−	0.291376i
$549$		0			0
$550$	0.220875	−	0.382566i	0.00941814	−	0.0163127i
$551$	−5.18345	+	8.97800i	−0.220823	+	0.382476i
$552$		0			0
$553$	−1.88994	+	7.78496i	−0.0803685	+	0.331050i
$554$	1.31428	+	0.758800i	0.0558384	+	0.0322383i
$555$		0			0
$556$		−	9.49953i		−	0.402870i
$557$	−27.5064	−	15.8808i	−1.16548	−	0.672892i	−0.212871	−	0.977080i	$-0.568281\pi$
$557$	−27.5064	−	15.8808i	−1.16548	−	0.672892i	−0.952612	+	0.304188i	$0.901615\pi$
$558$		0			0
$559$			6.23298i			0.263627i
$560$	−0.624174	+	2.57107i	−0.0263762	+	0.108648i
$561$		0			0
$562$	−3.56750			−0.150486
$563$	−21.3085	−	36.9074i	−0.898046	−	1.55546i	−0.829989	−	0.557780i	$-0.811653\pi$
$563$	−21.3085	−	36.9074i	−0.898046	−	1.55546i	−0.0680571	−	0.997681i	$-0.521680\pi$
$564$		0			0
$565$	2.85536	+	1.64854i	0.120126	+	0.0693548i
$566$	13.1970			0.554712
$567$		0			0
$568$	3.75218			0.157438
$569$	14.8343	+	8.56459i	0.621886	+	0.359046i	0.777603	−	0.628756i	$-0.216435\pi$
$569$	14.8343	+	8.56459i	0.621886	+	0.359046i	−0.155717	+	0.987802i	$0.549769\pi$
$570$		0			0
$571$	−7.40719	−	12.8296i	−0.309981	−	0.536904i	0.668377	−	0.743823i	$-0.266989\pi$
$571$	−7.40719	−	12.8296i	−0.309981	−	0.536904i	−0.978358	+	0.206920i	$0.933656\pi$
$572$	1.61999			0.0677352
$573$		0			0
$574$	−14.3689	+	15.0648i	−0.599747	+	0.628793i
$575$			2.59564i			0.108246i
$576$		0			0
$577$	29.2079	+	16.8632i	1.21594	+	0.702025i	0.964048	−	0.265730i	$-0.0856129\pi$
$577$	29.2079	+	16.8632i	1.21594	+	0.702025i	0.251895	+	0.967755i	$0.418946\pi$
$578$			16.9259i			0.704025i
$579$		0			0
$580$	2.38822	+	1.37884i	0.0991653	+	0.0572531i
$581$	16.4347	+	15.6755i	0.681825	+	0.650328i
$582$		0			0
$583$	−0.0209796	+	0.0363377i	−0.000868885	+	0.00150495i
$584$	−5.56698	+	9.64229i	−0.230363	+	0.399001i
$585$		0			0
$586$	−19.0955	+	11.0248i	−0.788826	+	0.455429i
$587$	−5.76762	−	9.98982i	−0.238055	−	0.412324i	0.722101	−	0.691788i	$-0.243177\pi$
$587$	−5.76762	−	9.98982i	−0.238055	−	0.412324i	−0.960156	+	0.279464i	$0.909843\pi$
$588$		0			0
$589$	−16.4454	+	28.4842i	−0.677620	+	1.17367i
$590$		−	3.21065i		−	0.132180i
$591$		0			0
$592$	−0.119403			−0.00490745
$593$	11.7771	+	20.3985i	0.483627	+	0.837666i	0.999823	−	0.0188043i	$-0.00598596\pi$
$593$	11.7771	+	20.3985i	0.483627	+	0.837666i	−0.516197	+	0.856470i	$0.672653\pi$
$594$		0			0
$595$	−0.169908	+	0.699879i	−0.00696557	+	0.0286922i
$596$	12.4227	−	7.17226i	0.508854	−	0.293787i
$597$		0			0
$598$	−8.24349	+	4.75938i	−0.337101	+	0.194626i
$599$	31.9172	−	18.4274i	1.30410	−	0.752923i	0.322996	−	0.946400i	$-0.395310\pi$
$599$	31.9172	−	18.4274i	1.30410	−	0.752923i	0.981105	+	0.193477i	$0.0619765\pi$
$600$		0			0
$601$	−3.58818	+	2.07164i	−0.146365	+	0.0845039i	−0.571394	−	0.820676i	$-0.693597\pi$
$601$	−3.58818	+	2.07164i	−0.146365	+	0.0845039i	0.425029	+	0.905180i	$0.360264\pi$
$602$	1.26621	+	4.31490i	0.0516070	+	0.175862i
$603$		0			0
$604$	0.339894	+	0.588715i	0.0138301	+	0.0239545i
$605$	10.8049			0.439280
$606$		0			0
$607$		−	19.7232i		−	0.800540i	−0.916397	−	0.400270i	$-0.868916\pi$
$607$		−	19.7232i		−	0.800540i	0.916397	−	0.400270i	$-0.131084\pi$
$608$	1.87965	−	3.25564i	0.0762297	−	0.132034i
$609$		0			0
$610$	−6.50065	−	11.2595i	−0.263204	−	0.455882i
$611$	25.0741	−	14.4766i	1.01439	−	0.585659i
$612$		0			0
$613$	3.80772	−	6.59516i	0.153792	−	0.266376i	−0.778826	−	0.627240i	$-0.784185\pi$
$613$	3.80772	−	6.59516i	0.153792	−	0.266376i	0.932619	+	0.360864i	$0.117518\pi$
$614$	14.6049	−	25.2964i	0.589405	−	1.02088i
$615$		0			0
$616$	1.12147	−	0.329097i	0.0451853	−	0.0132597i
$617$	−32.0531	−	18.5058i	−1.29041	−	0.745017i	−0.311681	−	0.950187i	$-0.600892\pi$
$617$	−32.0531	−	18.5058i	−1.29041	−	0.745017i	−0.978726	+	0.205170i	$0.934225\pi$
$618$		0			0
$619$		−	21.0131i		−	0.844587i	−0.906459	−	0.422294i	$-0.861225\pi$
$619$		−	21.0131i		−	0.844587i	0.906459	−	0.422294i	$-0.138775\pi$
$620$	7.57702	+	4.37459i	0.304300	+	0.175688i
$621$		0			0
$622$			24.7927i			0.994097i
$623$	24.3190	+	23.1956i	0.974322	+	0.929314i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−16.9458	−	29.3510i	−0.677292	−	1.17310i
$627$		0			0
$628$	−20.6832	−	11.9414i	−0.825349	−	0.476515i
$629$	−0.0325032			−0.00129599
$630$		0			0
$631$	24.9229			0.992166			0.496083	−	0.868275i	$-0.334771\pi$
$631$	24.9229			0.992166			0.496083	+	0.868275i	$0.334771\pi$
$632$	−2.62224	−	1.51395i	−0.104307	−	0.0602218i
$633$		0			0
$634$	−17.0887	−	29.5986i	−0.678681	−	1.17551i
$635$	−21.1104			−0.837741
$636$		0			0
$637$	25.6418	−	1.21318i	1.01597	−	0.0480679i
$638$		−	1.21820i		−	0.0482291i
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$		−	6.42378i		−	0.253724i	−0.991920	−	0.126862i	$-0.959509\pi$
$641$		−	6.42378i		−	0.253724i	0.991920	−	0.126862i	$-0.0404905\pi$
$642$		0			0
$643$	34.0574	+	19.6630i	1.34309	+	0.775434i	0.987260	−	0.159116i	$-0.0508642\pi$
$643$	34.0574	+	19.6630i	1.34309	+	0.775434i	0.355832	+	0.934550i	$0.384198\pi$
$644$	−4.73986	+	4.96942i	−0.186777	+	0.195822i
$645$		0			0
$646$	0.511664	−	0.886229i	0.0201312	−	0.0348682i
$647$	−13.4151	+	23.2356i	−0.527401	+	0.913486i	0.472089	+	0.881551i	$0.343500\pi$
$647$	−13.4151	+	23.2356i	−0.527401	+	0.913486i	−0.999490	+	0.0319349i	$0.989833\pi$
$648$		0			0
$649$	−1.22829	+	0.709151i	−0.0482144	+	0.0278366i
$650$	1.83361	+	3.17590i	0.0719200	+	0.124569i
$651$		0			0
$652$	7.98983	−	13.8388i	0.312906	−	0.541969i
$653$			40.2139i			1.57369i	0.617149	+	0.786846i	$0.288288\pi$
$653$			40.2139i			1.57369i	−0.617149	+	0.786846i	$0.711712\pi$
$654$		0			0
$655$	−5.08532			−0.198700
$656$	−3.93435	−	6.81449i	−0.153610	−	0.266061i
$657$		0			0
$658$	14.4172	−	15.1154i	0.562040	−	0.589260i
$659$	−18.2869	+	10.5580i	−0.712357	+	0.411280i	−0.811933	−	0.583750i	$-0.801585\pi$
$659$	−18.2869	+	10.5580i	−0.712357	+	0.411280i	0.0995760	+	0.995030i	$0.468251\pi$
$660$		0			0
$661$	22.9592	−	13.2555i	0.893010	−	0.515580i	0.0180841	−	0.999836i	$-0.494243\pi$
$661$	22.9592	−	13.2555i	0.893010	−	0.515580i	0.874926	+	0.484257i	$0.160910\pi$
$662$	15.7514	−	9.09408i	0.612196	−	0.353452i
$663$		0			0
$664$	−7.43413	+	4.29210i	−0.288500	+	0.166566i
$665$	−6.86479	+	7.19726i	−0.266205	+	0.279098i
$666$		0			0
$667$	3.57896	+	6.19895i	0.138578	+	0.240024i
$668$	−4.72365			−0.182764
$669$		0			0
$670$			0.537467i			0.0207642i
$671$	−2.87166	+	4.97386i	−0.110859	+	0.192014i
$672$		0			0
$673$	17.0764	+	29.5771i	0.658245	+	1.14011i	0.981070	+	0.193655i	$0.0620344\pi$
$673$	17.0764	+	29.5771i	0.658245	+	1.14011i	−0.322824	+	0.946459i	$0.604632\pi$
$674$	2.06941	−	1.19477i	0.0797105	−	0.0460209i
$675$		0			0
$676$	−0.224227	+	0.388373i	−0.00862413	+	0.0149374i
$677$	3.73419	−	6.46780i	0.143516	−	0.248578i	−0.785302	−	0.619113i	$-0.787492\pi$
$677$	3.73419	−	6.46780i	0.143516	−	0.248578i	0.928818	+	0.370535i	$0.120826\pi$
$678$		0			0
$679$	−27.2607	+	28.5810i	−1.04617	+	1.09684i
$680$	−0.235743	−	0.136107i	−0.00904035	−	0.00521945i
$681$		0			0
$682$		−	3.86495i		−	0.147997i
$683$	20.4287	+	11.7945i	0.781681	+	0.451304i	0.837026	−	0.547163i	$-0.184292\pi$
$683$	20.4287	+	11.7945i	0.781681	+	0.451304i	−0.0553445	+	0.998467i	$0.517626\pi$
$684$		0			0
$685$		−	13.6419i		−	0.521230i
$686$	17.5046	−	6.04891i	0.668328	−	0.230949i
$687$		0			0
$688$	−1.69965			−0.0647985
$689$	−0.174163	−	0.301660i	−0.00663509	−	0.0114923i
$690$		0			0
$691$	14.1003	+	8.14082i	0.536401	+	0.309692i	0.743619	−	0.668603i	$-0.233108\pi$
$691$	14.1003	+	8.14082i	0.536401	+	0.309692i	−0.207218	+	0.978295i	$0.566441\pi$
$692$	20.2799			0.770925
$693$		0			0
$694$	24.5163			0.930626
$695$	−8.22684	−	4.74977i	−0.312062	−	0.180169i
$696$		0			0
$697$	−1.07098	−	1.85499i	−0.0405663	−	0.0702629i
$698$	−19.8655			−0.751921
$699$		0			0
$700$	1.91453	+	1.82609i	0.0723623	+	0.0690196i
$701$			4.22872i			0.159717i	0.996806	+	0.0798583i	$0.0254468\pi$
$701$			4.22872i			0.159717i	−0.996806	+	0.0798583i	$0.974553\pi$
$702$		0			0
$703$	−0.388735	−	0.224436i	−0.0146614	−	0.00846477i
$704$			0.441750i			0.0166491i
$705$		0			0
$706$	−27.8411	−	16.0741i	−1.04781	−	0.604955i
$707$	−11.6210	+	3.41021i	−0.437054	+	0.128254i
$708$		0			0
$709$	2.89202	−	5.00912i	0.108612	−	0.188121i	−0.806596	−	0.591103i	$-0.798693\pi$
$709$	2.89202	−	5.00912i	0.108612	−	0.188121i	0.915208	+	0.402981i	$0.132026\pi$
$710$	1.87609	−	3.24949i	0.0704085	−	0.121951i
$711$		0			0
$712$	−11.0006	+	6.35119i	−0.412264	+	0.238021i
$713$	11.3549	+	19.6672i	0.425243	+	0.736543i
$714$		0			0
$715$	0.809995	−	1.40295i	0.0302921	−	0.0524675i
$716$			15.2611i			0.570333i
$717$		0			0
$718$	28.2685			1.05497
$719$	7.58926	+	13.1450i	0.283032	+	0.490225i	0.972130	−	0.234443i	$-0.0753265\pi$
$719$	7.58926	+	13.1450i	0.283032	+	0.490225i	−0.689098	+	0.724668i	$0.741993\pi$
$720$		0			0
$721$	3.42852	+	11.6835i	0.127685	+	0.435115i
$722$	−4.21556	+	2.43386i	−0.156887	+	0.0905787i
$723$		0			0
$724$	−21.4088	+	12.3604i	−0.795651	+	0.459369i
$725$	2.38822	−	1.37884i	0.0886961	−	0.0512087i
$726$		0			0
$727$	23.3867	−	13.5023i	0.867364	−	0.500773i	0.000892806	−	1.00000i	$-0.499716\pi$
$727$	23.3867	−	13.5023i	0.867364	−	0.500773i	0.866471	+	0.499227i	$0.166382\pi$
$728$	−2.28898	+	9.42867i	−0.0848353	+	0.349450i
$729$		0			0
$730$	5.56698	+	9.64229i	0.206043	+	0.356877i
$731$	−0.462667			−0.0171123
$732$		0			0
$733$			18.1508i			0.670416i	0.942144	+	0.335208i	$0.108807\pi$
$733$			18.1508i			0.670416i	−0.942144	+	0.335208i	$0.891193\pi$
$734$	16.8301	−	29.1506i	0.621210	−	1.07597i
$735$		0			0
$736$	−1.29782	−	2.24789i	−0.0478383	−	0.0828583i
$737$	0.205617	−	0.118713i	0.00757399	−	0.00437285i
$738$		0			0
$739$	2.83491	−	4.91021i	0.104284	−	0.180625i	−0.809162	−	0.587586i	$-0.800078\pi$
$739$	2.83491	−	4.91021i	0.104284	−	0.180625i	0.913445	+	0.406961i	$0.133412\pi$
$740$	−0.0597017	+	0.103406i	−0.00219468	+	0.00380129i
$741$		0			0
$742$	−0.181849	−	0.173449i	−0.00667590	−	0.00636751i
$743$	−14.9685	−	8.64209i	−0.549142	−	0.317047i	0.199634	−	0.979871i	$-0.436025\pi$
$743$	−14.9685	−	8.64209i	−0.549142	−	0.317047i	−0.748776	+	0.662823i	$0.769358\pi$
$744$		0			0
$745$		−	14.3445i		−	0.525543i
$746$	−10.3698	−	5.98701i	−0.379665	−	0.219200i
$747$		0			0
$748$			0.120250i			0.00439678i
$749$	29.5672	−	30.9992i	1.08036	−	1.13269i
$750$		0			0
$751$	−38.8281			−1.41686			−0.708429	−	0.705782i	$-0.750596\pi$
$751$	−38.8281			−1.41686			−0.708429	+	0.705782i	$0.750596\pi$
$752$	3.94756	+	6.83738i	0.143953	+	0.249334i
$753$		0			0
$754$	8.75810	+	5.05649i	0.318951	+	0.184146i
$755$	0.679789			0.0247401
$756$		0			0
$757$	−33.5417			−1.21910			−0.609548	−	0.792749i	$-0.708649\pi$
$757$	−33.5417			−1.21910			−0.609548	+	0.792749i	$0.708649\pi$
$758$	−9.49414	−	5.48144i	−0.344843	−	0.199095i
$759$		0			0
$760$	−1.87965	−	3.25564i	−0.0681820	−	0.118095i
$761$	26.6928			0.967612			0.483806	−	0.875175i	$-0.339254\pi$
$761$	26.6928			0.967612			0.483806	+	0.875175i	$0.339254\pi$
$762$		0			0
$763$	−1.71157	+	7.05023i	−0.0619631	+	0.255236i
$764$			5.50470i			0.199153i
$765$		0			0
$766$	17.4289	+	10.0626i	0.629732	+	0.363576i
$767$		−	11.7741i		−	0.425139i
$768$		0			0
$769$	36.2335	+	20.9194i	1.30661	+	0.754373i	0.981529	−	0.191313i	$-0.0612744\pi$
$769$	36.2335	+	20.9194i	1.30661	+	0.754373i	0.325083	+	0.945685i	$0.394608\pi$
$770$	0.275729	−	1.13577i	0.00993658	−	0.0409303i
$771$		0			0
$772$	−7.52344	+	13.0310i	−0.270775	+	0.468995i
$773$	−0.0374243	+	0.0648208i	−0.00134606	+	0.00233144i	−0.866698	−	0.498834i	$-0.833762\pi$
$773$	−0.0374243	+	0.0648208i	−0.00134606	+	0.00233144i	0.865352	+	0.501165i	$0.167095\pi$
$774$		0			0
$775$	7.57702	−	4.37459i	0.272175	−	0.157140i
$776$	−7.46424	−	12.9284i	−0.267951	−	0.464104i
$777$		0			0
$778$	13.6704	−	23.6779i	0.490109	−	0.848894i
$779$		−	29.5807i		−	1.05984i
$780$		0			0
$781$	−1.65753			−0.0593110
$782$	−0.353283	−	0.611905i	−0.0126334	−	0.0218817i
$783$		0			0
$784$	0.330818	+	6.99218i	0.0118149	+	0.249721i
$785$	−20.6832	+	11.9414i	−0.738214	+	0.426208i
$786$		0			0
$787$	−28.9107	+	16.6916i	−1.03055	+	0.594991i	−0.917143	−	0.398557i	$-0.869511\pi$
$787$	−28.9107	+	16.6916i	−1.03055	+	0.594991i	−0.113411	+	0.993548i	$0.536178\pi$
$788$	17.0247	−	9.82922i	0.606480	−	0.350151i
$789$		0			0
$790$	−2.62224	+	1.51395i	−0.0932953	+	0.0538640i
$791$	8.47705	+	2.05796i	0.301409	+	0.0731726i
$792$		0			0
$793$	−23.8393	−	41.2908i	−0.846557	−	1.46628i
$794$	15.6491			0.555366
$795$		0			0
$796$		−	10.6694i		−	0.378168i
$797$	15.3572	−	26.5995i	0.543980	−	0.942201i	−0.454690	−	0.890650i	$-0.650250\pi$
$797$	15.3572	−	26.5995i	0.543980	−	0.942201i	0.998670	−	0.0515514i	$-0.0164166\pi$
$798$		0			0
$799$	1.07458	+	1.86122i	0.0380158	+	0.0658454i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−19.5763	+	33.9071i	−0.691262	+	1.19730i
$803$	2.45921	−	4.25948i	0.0867837	−	0.150314i
$804$		0			0
$805$	1.93371	+	6.58955i	0.0681544	+	0.232251i
$806$	27.7865	+	16.0426i	0.978739	+	0.565075i
$807$		0			0
$808$		−	4.57755i		−	0.161038i
$809$	8.63831	+	4.98733i	0.303707	+	0.175345i	0.644107	−	0.764936i	$-0.277229\pi$
$809$	8.63831	+	4.98733i	0.303707	+	0.175345i	−0.340400	+	0.940281i	$0.610563\pi$
$810$		0			0
$811$			56.5329i			1.98514i	0.121685	+	0.992569i	$0.461170\pi$
$811$			56.5329i			1.98514i	−0.121685	+	0.992569i	$0.538830\pi$
$812$	7.09018	+	1.72127i	0.248816	+	0.0604047i
$813$		0			0
$814$	0.0527464			0.00184876
$815$	−7.98983	−	13.8388i	−0.279872	−	0.484752i
$816$		0			0
$817$	−5.53345	−	3.19474i	−0.193591	−	0.111770i
$818$	−26.2289			−0.917072
$819$		0			0
$820$	−7.86869			−0.274787
$821$	35.7881	+	20.6622i	1.24901	+	0.721117i	0.970912	−	0.239435i	$-0.0769622\pi$
$821$	35.7881	+	20.6622i	1.24901	+	0.721117i	0.278099	+	0.960552i	$0.410296\pi$
$822$		0			0
$823$	13.5798	+	23.5209i	0.473363	+	0.819888i	0.999535	−	0.0304896i	$-0.00970664\pi$
$823$	13.5798	+	23.5209i	0.473363	+	0.819888i	−0.526172	+	0.850378i	$0.676373\pi$
$824$	−4.60214			−0.160323
$825$		0			0
$826$	−2.39188	−	8.15087i	−0.0832242	−	0.283605i
$827$		−	5.74951i		−	0.199930i	−0.994991	−	0.0999650i	$-0.968127\pi$
$827$		−	5.74951i		−	0.199930i	0.994991	−	0.0999650i	$-0.0318731\pi$
$828$		0			0
$829$	−26.3765	−	15.2285i	−0.916093	−	0.528907i	−0.0337068	−	0.999432i	$-0.510731\pi$
$829$	−26.3765	−	15.2285i	−0.916093	−	0.528907i	−0.882387	+	0.470525i	$0.844065\pi$
$830$			8.58419i			0.297962i
$831$		0			0
$832$	−3.17590	−	1.83361i	−0.110105	−	0.0635689i
$833$	0.0900529	+	1.90336i	0.00312015	+	0.0659476i
$834$		0			0
$835$	−2.36183	+	4.09080i	−0.0817344	+	0.141568i
$836$	−0.830333	+	1.43818i	−0.0287177	+	0.0497405i
$837$		0			0
$838$	−31.8342	+	18.3795i	−1.09970	+	0.634909i
$839$	15.5311	+	26.9006i	0.536193	+	0.928713i	0.999105	+	0.0423086i	$0.0134713\pi$
$839$	15.5311	+	26.9006i	0.536193	+	0.928713i	−0.462912	+	0.886404i	$0.653195\pi$
$840$		0			0
$841$	−10.6976	+	18.5288i	−0.368883	+	0.638925i
$842$			13.0949i			0.451282i
$843$		0			0
$844$	−1.16300			−0.0400321
$845$	0.224227	+	0.388373i	0.00771366	+	0.0133605i
$846$		0			0
$847$	27.4303	−	8.04945i	0.942516	−	0.276583i
$848$	0.0822585	−	0.0474920i	0.00282477	−	0.00163088i
$849$		0			0
$850$	−0.235743	+	0.136107i	−0.00808593	+	0.00466842i
$851$	−0.268406	+	0.154964i	−0.00920083	+	0.00531210i
$852$		0			0
$853$	−44.5942	+	25.7465i	−1.52688	+	0.881542i	−0.527385	+	0.849626i	$0.676827\pi$
$853$	−44.5942	+	25.7465i	−1.52688	+	0.881542i	−0.999491	+	0.0319155i	$0.989839\pi$
$854$	−24.8913	−	23.7415i	−0.851764	−	0.812417i
$855$		0			0
$856$	8.09579	+	14.0223i	0.276708	+	0.479273i
$857$	−17.8647			−0.610247			−0.305123	−	0.952313i	$-0.598698\pi$
$857$	−17.8647			−0.610247			−0.305123	+	0.952313i	$0.598698\pi$
$858$		0			0
$859$		−	1.26629i		−	0.0432054i	−0.999767	−	0.0216027i	$-0.993123\pi$
$859$		−	1.26629i		−	0.0432054i	0.999767	−	0.0216027i	$-0.00687689\pi$
$860$	−0.849825	+	1.47194i	−0.0289788	+	0.0501927i
$861$		0			0
$862$	−10.3405	−	17.9103i	−0.352200	−	0.610028i
$863$	35.3845	−	20.4293i	1.20450	−	0.695420i	0.242949	−	0.970039i	$-0.421885\pi$
$863$	35.3845	−	20.4293i	1.20450	−	0.695420i	0.961553	+	0.274619i	$0.0885518\pi$
$864$		0			0
$865$	10.1399	−	17.5629i	0.344768	−	0.597156i
$866$	−2.68264	+	4.64647i	−0.0911599	+	0.157894i
$867$		0			0
$868$	22.4948	+	5.46102i	0.763523	+	0.185359i
$869$	1.15838	+	0.668788i	0.0392952	+	0.0226871i
$870$		0			0
$871$			1.97101i			0.0667850i
$872$	−2.37476	−	1.37107i	−0.0804196	−	0.0464303i
$873$		0			0
$874$		−	9.75777i		−	0.330061i
$875$	2.53870	−	0.744985i	0.0858237	−	0.0251851i
$876$		0			0
$877$	20.0847			0.678213			0.339107	−	0.940748i	$-0.389875\pi$
$877$	20.0847			0.678213			0.339107	+	0.940748i	$0.389875\pi$
$878$	−5.23979	−	9.07559i	−0.176834	−	0.306286i
$879$		0			0
$880$	0.382566	+	0.220875i	0.0128963	+	0.00744569i
$881$	−26.6064			−0.896393			−0.448196	−	0.893935i	$-0.647933\pi$
$881$	−26.6064			−0.896393			−0.448196	+	0.893935i	$0.647933\pi$
$882$		0			0
$883$	−27.6319			−0.929887			−0.464943	−	0.885340i	$-0.653925\pi$
$883$	−27.6319			−0.929887			−0.464943	+	0.885340i	$0.653925\pi$
$884$	−0.864522	−	0.499132i	−0.0290770	−	0.0167876i
$885$		0			0
$886$	3.88871	+	6.73544i	0.130644	+	0.226282i
$887$	−8.98710			−0.301757			−0.150879	−	0.988552i	$-0.548210\pi$
$887$	−8.98710			−0.301757			−0.150879	+	0.988552i	$0.548210\pi$
$888$		0			0
$889$	−53.5930	+	15.7269i	−1.79745	+	0.527464i
$890$			12.7024i			0.425785i
$891$		0			0
$892$	−2.45476	−	1.41726i	−0.0821915	−	0.0474533i
$893$			29.6801i			0.993206i
$894$		0			0
$895$	13.2165	+	7.63053i	0.441778	+	0.255061i
$896$	−2.57107	−	0.624174i	−0.0858935	−	0.0208522i
$897$		0			0
$898$	−1.86702	+	3.23378i	−0.0623033	+	0.107912i
$899$	12.0637	−	20.8949i	0.402347	−	0.696885i
$900$		0			0
$901$	0.0223918	−	0.0129279i	0.000745981	−	0.000430692i
$902$	1.73800	+	3.01030i	0.0578689	+	0.100232i
$903$		0			0
$904$	−1.64854	+	2.85536i	−0.0548298	+	0.0949680i
$905$			24.7207i			0.821745i
$906$		0			0
$907$	30.2147			1.00326			0.501631	−	0.865081i	$-0.332733\pi$
$907$	30.2147			1.00326			0.501631	+	0.865081i	$0.332733\pi$
$908$	−5.62480	−	9.74244i	−0.186666	−	0.323314i
$909$		0			0
$910$	7.02097	+	6.69665i	0.232743	+	0.221992i
$911$	−25.4482	+	14.6925i	−0.843135	+	0.486784i	−0.858329	−	0.513100i	$-0.828497\pi$
$911$	−25.4482	+	14.6925i	−0.843135	+	0.486784i	0.0151935	+	0.999885i	$0.495164\pi$
$912$		0			0
$913$	3.28402	−	1.89603i	0.108685	−	0.0627495i
$914$	−2.51828	+	1.45393i	−0.0832974	+	0.0480918i
$915$		0			0
$916$	14.0269	−	8.09843i	0.463462	−	0.267580i
$917$	−12.9101	+	3.78849i	−0.426329	+	0.125107i
$918$		0			0
$919$	15.7829	+	27.3368i	0.520630	+	0.901758i	0.999712	+	0.0239876i	$0.00763621\pi$
$919$	15.7829	+	27.3368i	0.520630	+	0.901758i	−0.479082	+	0.877770i	$0.659030\pi$
$920$	−2.59564			−0.0855757
$921$		0			0
$922$			9.76887i			0.321721i
$923$	6.88003	−	11.9166i	0.226459	−	0.392238i
$924$		0			0
$925$	0.0597017	+	0.103406i	0.00196298	+	0.00339998i
$926$	2.48752	−	1.43617i	0.0817451	−	0.0471956i
$927$		0			0
$928$	−1.37884	+	2.38822i	−0.0452625	+	0.0783970i
$929$	−25.4122	+	44.0152i	−0.833747	+	1.44409i	0.0613000	+	0.998119i	$0.480475\pi$
$929$	−25.4122	+	44.0152i	−0.833747	+	1.44409i	−0.895047	+	0.445972i	$0.852858\pi$
$930$		0			0
$931$	−12.0658	+	23.3859i	−0.395441	+	0.766441i
$932$	−3.21321	−	1.85515i	−0.105252	−	0.0607673i
$933$		0			0
$934$		−	3.85910i		−	0.126274i
$935$	0.104140	+	0.0601250i	0.00340573	+	0.00196630i
$936$		0			0
$937$			19.6915i			0.643294i	0.946860	+	0.321647i	$0.104236\pi$
$937$			19.6915i			0.643294i	−0.946860	+	0.321647i	$0.895764\pi$
$938$	0.400405	+	1.36447i	0.0130737	+	0.0445514i
$939$		0			0
$940$	7.89512			0.257511
$941$	−13.5916	−	23.5413i	−0.443072	−	0.767424i	0.554843	−	0.831955i	$-0.312778\pi$
$941$	−13.5916	−	23.5413i	−0.443072	−	0.767424i	−0.997916	+	0.0645309i	$0.979445\pi$
$942$		0			0
$943$	−17.6879	−	10.2121i	−0.575999	−	0.332553i
$944$	3.21065			0.104498
$945$		0			0
$946$	0.750819			0.0244112
$947$	6.80067	+	3.92637i	0.220992	+	0.127590i	0.606409	−	0.795153i	$-0.292609\pi$
$947$	6.80067	+	3.92637i	0.220992	+	0.127590i	−0.385418	+	0.922742i	$0.625943\pi$
$948$		0			0
$949$	20.4153	+	35.3603i	0.662709	+	1.14784i
$950$	−3.75929			−0.121968
$951$		0			0
$952$	−0.699879	−	0.169908i	−0.0226832	−	0.00550676i
$953$		−	14.7756i		−	0.478628i	−0.970942	−	0.239314i	$-0.923078\pi$
$953$		−	14.7756i		−	0.478628i	0.970942	−	0.239314i	$-0.0769225\pi$
$954$		0			0
$955$	4.76721	+	2.75235i	0.154263	+	0.0890639i
$956$		−	8.13967i		−	0.263256i
$957$		0			0
$958$	14.1411	+	8.16437i	0.456878	+	0.263779i
$959$	−10.1630	−	34.6327i	−0.328181	−	1.11835i
$960$		0			0
$961$	22.7741	−	39.4460i	0.734649	−	1.27245i
$962$	−0.218939	+	0.379213i	−0.00705887	+	0.0122263i
$963$		0			0
$964$	24.6585	−	14.2366i	0.794195	−	0.458529i
$965$	7.52344	+	13.0310i	0.242188	+	0.419482i
$966$		0			0
$967$	11.9085	−	20.6261i	0.382950	−	0.663290i	−0.608532	−	0.793529i	$-0.708241\pi$
$967$	11.9085	−	20.6261i	0.382950	−	0.663290i	0.991483	+	0.130240i	$0.0415747\pi$
$968$			10.8049i			0.347281i
$969$		0			0
$970$	−14.9285			−0.479324
$971$	14.5985	+	25.2854i	0.468489	+	0.811446i	0.999351	−	0.0360115i	$-0.0114653\pi$
$971$	14.5985	+	25.2854i	0.468489	+	0.811446i	−0.530863	+	0.847458i	$0.678132\pi$
$972$		0			0
$973$	−24.4240	−	5.92936i	−0.782997	−	0.190087i
$974$	12.2254	−	7.05835i	0.391728	−	0.226164i
$975$		0			0
$976$	11.2595	−	6.50065i	0.360406	−	0.208081i
$977$	26.9080	−	15.5354i	0.860864	−	0.497020i	−0.00343741	−	0.999994i	$-0.501094\pi$
$977$	26.9080	−	15.5354i	0.860864	−	0.497020i	0.864302	+	0.502974i	$0.167761\pi$
$978$		0			0
$979$	4.85950	−	2.80564i	0.155310	−	0.0896685i
$980$	6.22081	+	3.20959i	0.198717	+	0.102527i
$981$		0			0
$982$	5.19839	+	9.00388i	0.165887	+	0.287325i
$983$	−30.3387			−0.967654			−0.483827	−	0.875164i	$-0.660754\pi$
$983$	−30.3387			−0.967654			−0.483827	+	0.875164i	$0.660754\pi$
$984$		0			0
$985$		−	19.6584i		−	0.626370i
$986$	−0.375337	+	0.650104i	−0.0119532	+	0.0207035i
$987$		0			0
$988$	−6.89307	−	11.9391i	−0.219298	−	0.379835i
$989$	−3.82062	+	2.20584i	−0.121489	+	0.0701416i
$990$		0			0
$991$	14.0266	−	24.2947i	0.445568	−	0.771747i	−0.552523	−	0.833497i	$-0.686335\pi$
$991$	14.0266	−	24.2947i	0.445568	−	0.771747i	0.998092	+	0.0617506i	$0.0196683\pi$
$992$	−4.37459	+	7.57702i	−0.138893	+	0.240571i
$993$		0			0
$994$	2.34202	−	9.64713i	0.0742843	−	0.305989i
$995$	−9.23999	−	5.33471i	−0.292927	−	0.169122i
$996$		0			0
$997$			30.1817i			0.955863i	0.878397	+	0.477931i	$0.158613\pi$
$997$			30.1817i			0.955863i	−0.878397	+	0.477931i	$0.841387\pi$
$998$	−13.7516	−	7.93948i	−0.435299	−	0.251320i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1151.10		28
3.2	odd	2		630.2.t.b.311.7	✓	28
7.5	odd	6		1890.2.bk.b.341.8		28
9.2	odd	6		1890.2.bk.b.521.8		28
9.7	even	3		630.2.bk.b.101.4	yes	28
21.5	even	6		630.2.bk.b.131.11	yes	28
63.47	even	6	inner	1890.2.t.b.1601.10		28
63.61	odd	6		630.2.t.b.551.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.7	✓	28	3.2	odd	2
630.2.t.b.551.7	yes	28	63.61	odd	6
630.2.bk.b.101.4	yes	28	9.7	even	3
630.2.bk.b.131.11	yes	28	21.5	even	6
1890.2.t.b.1151.10		28	1.1	even	1	trivial
1890.2.t.b.1601.10		28	63.47	even	6	inner
1890.2.bk.b.341.8		28	7.5	odd	6
1890.2.bk.b.521.8		28	9.2	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.53870 - 0.744985i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.53870 - 0.744985i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -0.441750i q^{11} +(3.17590 + 1.83361i) q^{13} +(2.57107 + 0.624174i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.136107 + 0.235743i) q^{17} +(-3.25564 + 1.87965i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.220875 - 0.382566i) q^{22} +2.59564i q^{23} +1.00000 q^{25} +(1.83361 + 3.17590i) q^{26} +(1.91453 + 1.82609i) q^{28} +(2.38822 - 1.37884i) q^{29} +(7.57702 - 4.37459i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.235743 + 0.136107i) q^{34} +(2.53870 - 0.744985i) q^{35} +(0.0597017 + 0.103406i) q^{37} -3.75929 q^{38} +1.00000i q^{40} +(-3.93435 + 6.81449i) q^{41} +(0.849825 + 1.47194i) q^{43} +(0.382566 - 0.220875i) q^{44} +(-1.29782 + 2.24789i) q^{46} +(3.94756 - 6.83738i) q^{47} +(5.89000 - 3.78259i) q^{49} +(0.866025 + 0.500000i) q^{50} +3.66721i q^{52} +(-0.0822585 - 0.0474920i) q^{53} -0.441750i q^{55} +(0.744985 + 2.53870i) q^{56} +2.75767 q^{58} +(-1.60532 - 2.78050i) q^{59} +(-11.2595 - 6.50065i) q^{61} +8.74919 q^{62} -1.00000 q^{64} +(3.17590 + 1.83361i) q^{65} +(0.268733 + 0.465460i) q^{67} -0.272213 q^{68} +(2.57107 + 0.624174i) q^{70} -3.75218i q^{71} +(9.64229 + 5.56698i) q^{73} +0.119403i q^{74} +(-3.25564 - 1.87965i) q^{76} +(-0.329097 - 1.12147i) q^{77} +(-1.51395 + 2.62224i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-6.81449 + 3.93435i) q^{82} +(4.29210 + 7.43413i) q^{83} +(-0.136107 + 0.235743i) q^{85} +1.69965i q^{86} +0.441750 q^{88} +(6.35119 + 11.0006i) q^{89} +(9.42867 + 2.28898i) q^{91} +(-2.24789 + 1.29782i) q^{92} +(6.83738 - 3.94756i) q^{94} +(-3.25564 + 1.87965i) q^{95} +(-12.9284 + 7.46424i) q^{97} +(6.99218 - 0.330818i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

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