LMFDB - Embedded newform 1890.2.r.b.89.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(89,1890)]

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([1, 3, 5]))

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

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

chi := DirichletCharacter("1890.89");

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.r (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.5
Character	$\chi$	$=$	1890.89
Dual form			1890.2.r.b.1529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.96632 + 1.06470i) q^{5} +(-0.733422 + 2.54206i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.96632 + 1.06470i) q^{5} +(-0.733422 + 2.54206i) q^{7} -1.00000 q^{8} +(-1.90522 - 1.17053i) q^{10} +1.30502i q^{11} +(-3.03357 - 5.25429i) q^{13} +(-2.56820 + 0.635870i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.502991 + 0.290402i) q^{17} +(-6.86424 - 3.96307i) q^{19} +(0.0611015 - 2.23523i) q^{20} +(-1.13018 + 0.652510i) q^{22} +6.57244 q^{23} +(2.73282 - 4.18708i) q^{25} +(3.03357 - 5.25429i) q^{26} +(-1.83478 - 1.90619i) q^{28} +(0.125548 + 0.0724850i) q^{29} +(-1.19742 - 0.691334i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.502991 - 0.290402i) q^{34} +(-1.26440 - 5.77939i) q^{35} +(-2.02863 - 1.17123i) q^{37} -7.92614i q^{38} +(1.96632 - 1.06470i) q^{40} +(3.16905 + 5.48896i) q^{41} +(10.0713 + 5.81466i) q^{43} +(-1.13018 - 0.652510i) q^{44} +(3.28622 + 5.69190i) q^{46} +(4.69056 - 2.70810i) q^{47} +(-5.92418 - 3.72881i) q^{49} +(4.99253 + 0.273152i) q^{50} +6.06713 q^{52} +(-4.19068 - 7.25846i) q^{53} +(-1.38946 - 2.56609i) q^{55} +(0.733422 - 2.54206i) q^{56} +0.144970i q^{58} +(1.54358 - 2.67356i) q^{59} +(1.83643 - 1.06026i) q^{61} -1.38267i q^{62} +1.00000 q^{64} +(11.5592 + 7.10177i) q^{65} +(-11.4291 - 6.59859i) q^{67} -0.580804i q^{68} +(4.37290 - 3.98469i) q^{70} +10.3545i q^{71} +(-3.84599 - 6.66144i) q^{73} -2.34246i q^{74} +(6.86424 - 3.96307i) q^{76} +(-3.31745 - 0.957131i) q^{77} +(3.54596 + 6.14179i) q^{79} +(1.90522 + 1.17053i) q^{80} +(-3.16905 + 5.48896i) q^{82} +(-4.32983 - 2.49983i) q^{83} +(0.679850 - 1.10656i) q^{85} +11.6293i q^{86} -1.30502i q^{88} +(1.35235 - 2.34234i) q^{89} +(15.5816 - 3.85791i) q^{91} +(-3.28622 + 5.69190i) q^{92} +(4.69056 + 2.70810i) q^{94} +(17.7168 + 0.484299i) q^{95} +(5.76032 - 9.97717i) q^{97} +(0.267153 - 6.99490i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8}+O(q^{10}) $ 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8	$ 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} - 3 q^{14} - 24 q^{16} + 6 q^{22} + 6 q^{23} - 3 q^{28} + 3 q^{29} + 24 q^{32} - 18 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} + 42 q^{55} - 9 q^{61} + 48 q^{64} + 33 q^{65} - 33 q^{67} - 6 q^{70} + 18 q^{73} - 6 q^{77} + 3 q^{82} + 9 q^{83} - 33 q^{85} - 33 q^{89} - 3 q^{92} - 33 q^{95} + 24 q^{97} - 3 q^{98}+O(q^{100}) $ 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8 - 3 * q^14 - 24 * q^16 + 6 * q^22 + 6 * q^23 - 3 * q^28 + 3 * q^29 + 24 * q^32 - 18 * q^35 - 3 * q^41 + 6 * q^44 + 3 * q^46 - 6 * q^49 + 18 * q^50 + 42 * q^55 - 9 * q^61 + 48 * q^64 + 33 * q^65 - 33 * q^67 - 6 * q^70 + 18 * q^73 - 6 * q^77 + 3 * q^82 + 9 * q^83 - 33 * q^85 - 33 * q^89 - 3 * q^92 - 33 * q^95 + 24 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.96632	+	1.06470i	−0.879365	+	0.476149i
$5$	−1.96632	+	1.06470i	−0.879365	+	0.476149i
$6$		0			0
$7$	−0.733422	+	2.54206i	−0.277207	+	0.960810i
$7$	−0.733422	+	2.54206i	−0.277207	+	0.960810i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.90522	−	1.17053i	−0.602483	−	0.370155i
$11$			1.30502i			0.393478i	0.980456	+	0.196739i	$0.0630352\pi$
$11$			1.30502i			0.393478i	−0.980456	+	0.196739i	$0.936965\pi$
$12$		0			0
$13$	−3.03357	−	5.25429i	−0.841360	−	1.45728i	−0.888745	−	0.458402i	$-0.848422\pi$
$13$	−3.03357	−	5.25429i	−0.841360	−	1.45728i	0.0473853	−	0.998877i	$-0.484911\pi$
$14$	−2.56820	+	0.635870i	−0.686381	+	0.169944i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.502991	+	0.290402i	−0.121993	+	0.0704328i	−0.559755	−	0.828658i	$-0.689105\pi$
$17$	−0.502991	+	0.290402i	−0.121993	+	0.0704328i	0.437762	+	0.899091i	$0.355771\pi$
$18$		0			0
$19$	−6.86424	−	3.96307i	−1.57476	−	0.909191i	−0.995572	−	0.0940001i	$-0.970035\pi$
$19$	−6.86424	−	3.96307i	−1.57476	−	0.909191i	−0.579193	−	0.815191i	$-0.696632\pi$
$20$	0.0611015	−	2.23523i	0.0136627	−	0.499813i
$21$		0			0
$22$	−1.13018	+	0.652510i	−0.240955	+	0.139116i
$23$	6.57244			1.37045			0.685224	−	0.728332i	$-0.259704\pi$
$23$	6.57244			1.37045			0.685224	+	0.728332i	$0.259704\pi$
$24$		0			0
$25$	2.73282	−	4.18708i	0.546565	−	0.837417i
$26$	3.03357	−	5.25429i	0.594931	−	1.03045i
$27$		0			0
$28$	−1.83478	−	1.90619i	−0.346741	−	0.360237i
$29$	0.125548	+	0.0724850i	0.0233136	+	0.0134601i	0.511612	−	0.859217i	$-0.329049\pi$
$29$	0.125548	+	0.0724850i	0.0233136	+	0.0134601i	−0.488298	+	0.872677i	$0.662382\pi$
$30$		0			0
$31$	−1.19742	−	0.691334i	−0.215064	−	0.124167i	0.388599	−	0.921407i	$-0.372959\pi$
$31$	−1.19742	−	0.691334i	−0.215064	−	0.124167i	−0.603663	+	0.797240i	$0.706293\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−0.502991	−	0.290402i	−0.0862622	−	0.0498035i
$35$	−1.26440	−	5.77939i	−0.213722	−	0.976894i
$36$		0			0
$37$	−2.02863	−	1.17123i	−0.333505	−	0.192549i	0.323891	−	0.946094i	$-0.395009\pi$
$37$	−2.02863	−	1.17123i	−0.333505	−	0.192549i	−0.657396	+	0.753545i	$0.728342\pi$
$38$		−	7.92614i		−	1.28579i
$39$		0			0
$40$	1.96632	−	1.06470i	0.310902	−	0.168344i
$41$	3.16905	+	5.48896i	0.494923	+	0.857232i	0.999983	−	0.00585232i	$-0.00186286\pi$
$41$	3.16905	+	5.48896i	0.494923	+	0.857232i	−0.505060	+	0.863084i	$0.668530\pi$
$42$		0			0
$43$	10.0713	+	5.81466i	1.53586	+	0.886728i	0.999075	+	0.0430080i	$0.0136941\pi$
$43$	10.0713	+	5.81466i	1.53586	+	0.886728i	0.536783	+	0.843720i	$0.319639\pi$
$44$	−1.13018	−	0.652510i	−0.170381	−	0.0983696i
$45$		0			0
$46$	3.28622	+	5.69190i	0.484527	+	0.839225i
$47$	4.69056	−	2.70810i	0.684188	−	0.395016i	−0.117243	−	0.993103i	$-0.537406\pi$
$47$	4.69056	−	2.70810i	0.684188	−	0.395016i	0.801431	+	0.598087i	$0.204072\pi$
$48$		0			0
$49$	−5.92418	−	3.72881i	−0.846312	−	0.532687i
$50$	4.99253	+	0.273152i	0.706051	+	0.0386295i
$51$		0			0
$52$	6.06713			0.841360
$53$	−4.19068	−	7.25846i	−0.575634	−	0.997027i	−0.995972	−	0.0896594i	$-0.971422\pi$
$53$	−4.19068	−	7.25846i	−0.575634	−	0.997027i	0.420339	−	0.907367i	$-0.361911\pi$
$54$		0			0
$55$	−1.38946	−	2.56609i	−0.187354	−	0.346011i
$56$	0.733422	−	2.54206i	0.0980076	−	0.339698i
$57$		0			0
$58$			0.144970i			0.0190355i
$59$	1.54358	−	2.67356i	0.200957	−	0.348067i	−0.747880	−	0.663834i	$-0.768928\pi$
$59$	1.54358	−	2.67356i	0.200957	−	0.348067i	0.948837	+	0.315766i	$0.102262\pi$
$60$		0			0
$61$	1.83643	−	1.06026i	0.235131	−	0.135753i	−0.377806	−	0.925885i	$-0.623321\pi$
$61$	1.83643	−	1.06026i	0.235131	−	0.135753i	0.612937	+	0.790132i	$0.289988\pi$
$62$		−	1.38267i		−	0.175599i
$63$		0			0
$64$	1.00000			0.125000
$65$	11.5592	+	7.10177i	1.43374	+	0.880867i
$66$		0			0
$67$	−11.4291	−	6.59859i	−1.39629	−	0.806146i	−0.402284	−	0.915515i	$-0.631784\pi$
$67$	−11.4291	−	6.59859i	−1.39629	−	0.806146i	−0.994001	+	0.109369i	$0.965117\pi$
$68$		−	0.580804i		−	0.0704328i
$69$		0			0
$70$	4.37290	−	3.98469i	0.522661	−	0.476262i
$71$			10.3545i			1.22885i	0.788975	+	0.614425i	$0.210612\pi$
$71$			10.3545i			1.22885i	−0.788975	+	0.614425i	$0.789388\pi$
$72$		0			0
$73$	−3.84599	−	6.66144i	−0.450139	−	0.779663i	0.548256	−	0.836311i	$-0.315292\pi$
$73$	−3.84599	−	6.66144i	−0.450139	−	0.779663i	−0.998394	+	0.0566478i	$0.981959\pi$
$74$		−	2.34246i		−	0.272306i
$75$		0			0
$76$	6.86424	−	3.96307i	0.787382	−	0.454595i
$77$	−3.31745	−	0.957131i	−0.378058	−	0.109075i
$78$		0			0
$79$	3.54596	+	6.14179i	0.398952	+	0.691005i	0.993597	−	0.112983i	$-0.0360407\pi$
$79$	3.54596	+	6.14179i	0.398952	+	0.691005i	−0.594645	+	0.803988i	$0.702707\pi$
$80$	1.90522	+	1.17053i	0.213010	+	0.130869i
$81$		0			0
$82$	−3.16905	+	5.48896i	−0.349964	+	0.606155i
$83$	−4.32983	−	2.49983i	−0.475261	−	0.274392i	0.243178	−	0.969982i	$-0.421810\pi$
$83$	−4.32983	−	2.49983i	−0.475261	−	0.274392i	−0.718439	+	0.695589i	$0.755143\pi$
$84$		0			0
$85$	0.679850	−	1.10656i	0.0737400	−	0.120023i
$86$			11.6293i			1.25402i
$87$		0			0
$88$		−	1.30502i		−	0.139116i
$89$	1.35235	−	2.34234i	0.143349	−	0.248288i	−0.785407	−	0.618980i	$-0.787546\pi$
$89$	1.35235	−	2.34234i	0.143349	−	0.248288i	0.928756	+	0.370692i	$0.120879\pi$
$90$		0			0
$91$	15.5816	−	3.85791i	1.63340	−	0.404419i
$92$	−3.28622	+	5.69190i	−0.342612	+	0.593422i
$93$		0			0
$94$	4.69056	+	2.70810i	0.483794	+	0.279319i
$95$	17.7168	+	0.484299i	1.81770	+	0.0496880i
$96$		0			0
$97$	5.76032	−	9.97717i	0.584872	−	1.01303i	−0.410019	−	0.912077i	$-0.634478\pi$
$97$	5.76032	−	9.97717i	0.584872	−	1.01303i	0.994891	−	0.100951i	$-0.0321887\pi$
$98$	0.267153	−	6.99490i	0.0269865	−	0.706592i
$99$		0			0
$100$	2.25971	+	4.46024i	0.225971	+	0.446024i
$101$	−14.3532			−1.42819			−0.714097	−	0.700047i	$-0.753162\pi$
$101$	−14.3532			−1.42819			−0.714097	+	0.700047i	$0.753162\pi$
$102$		0			0
$103$	−0.772004			−0.0760678			−0.0380339	−	0.999276i	$-0.512109\pi$
$103$	−0.772004			−0.0760678			−0.0380339	+	0.999276i	$0.512109\pi$
$104$	3.03357	+	5.25429i	0.297466	+	0.515226i
$105$		0			0
$106$	4.19068	−	7.25846i	0.407034	−	0.705004i
$107$	8.60622	−	14.9064i	0.831995	−	1.44106i	−0.0644590	−	0.997920i	$-0.520532\pi$
$107$	8.60622	−	14.9064i	0.831995	−	1.44106i	0.896454	−	0.443137i	$-0.146134\pi$
$108$		0			0
$109$	−6.30827	−	10.9262i	−0.604223	−	1.04654i	−0.992174	−	0.124864i	$-0.960150\pi$
$109$	−6.30827	−	10.9262i	−0.604223	−	1.04654i	0.387951	−	0.921680i	$-0.373183\pi$
$110$	1.52757	−	2.48635i	0.145648	−	0.237064i
$111$		0			0
$112$	2.56820	−	0.635870i	0.242672	−	0.0600841i
$113$	−6.02741	−	10.4398i	−0.567011	−	0.982092i	−0.996859	−	0.0791911i	$-0.974766\pi$
$113$	−6.02741	−	10.4398i	−0.567011	−	0.982092i	0.429848	−	0.902901i	$-0.358567\pi$
$114$		0			0
$115$	−12.9235	+	6.99768i	−1.20512	+	0.652537i
$116$	−0.125548	+	0.0724850i	−0.0116568	+	0.00673006i
$117$		0			0
$118$	3.08716			0.284196
$119$	−0.369316	−	1.49162i	−0.0338551	−	0.136737i
$120$		0			0
$121$	9.29692			0.845175
$122$	1.83643	+	1.06026i	0.166263	+	0.0959918i
$123$		0			0
$124$	1.19742	−	0.691334i	0.107532	−	0.0620836i
$125$	−0.915610	+	11.1428i	−0.0818946	+	0.996641i
$126$		0			0
$127$		−	14.7512i		−	1.30896i	−0.756079	−	0.654480i	$-0.772887\pi$
$127$		−	14.7512i		−	1.30896i	0.756079	−	0.654480i	$-0.227113\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.370711	+	13.5615i	−0.0325135	+	1.18942i
$131$	−15.6922			−1.37103			−0.685517	−	0.728057i	$-0.740424\pi$
$131$	−15.6922			−1.37103			−0.685517	+	0.728057i	$0.740424\pi$
$132$		0			0
$133$	15.1088	−	14.5427i	1.31010	−	1.26102i
$134$		−	13.1972i		−	1.14006i
$135$		0			0
$136$	0.502991	−	0.290402i	0.0431311	−	0.0249018i
$137$	−8.85857			−0.756839			−0.378419	−	0.925634i	$-0.623532\pi$
$137$	−8.85857			−0.756839			−0.378419	+	0.925634i	$0.623532\pi$
$138$		0			0
$139$	1.39913	−	0.807790i	0.118673	−	0.0685158i	−0.439489	−	0.898248i	$-0.644840\pi$
$139$	1.39913	−	0.807790i	0.118673	−	0.0685158i	0.558161	+	0.829732i	$0.311507\pi$
$140$	5.63729	+	1.79469i	0.476438	+	0.151679i
$141$		0			0
$142$	−8.96724	+	5.17724i	−0.752514	+	0.434464i
$143$	6.85696	−	3.95887i	0.573408	−	0.331057i
$144$		0			0
$145$	−0.324042	−	0.00885788i	−0.0269102	−	0.000735607i
$146$	3.84599	−	6.66144i	0.318296	−	0.551305i
$147$		0			0
$148$	2.02863	−	1.17123i	0.166753	−	0.0962746i
$149$			9.59314i			0.785901i	0.919560	+	0.392950i	$0.128546\pi$
$149$			9.59314i			0.785901i	−0.919560	+	0.392950i	$0.871454\pi$
$150$		0			0
$151$	−17.3655			−1.41318			−0.706592	−	0.707621i	$-0.749768\pi$
$151$	−17.3655			−1.41318			−0.706592	+	0.707621i	$0.749768\pi$
$152$	6.86424	+	3.96307i	0.556763	+	0.321448i
$153$		0			0
$154$	−0.829824	−	3.35156i	−0.0668691	−	0.270076i
$155$	3.09058	+	0.0844830i	0.248242	+	0.00678584i
$156$		0			0
$157$	−1.69869	+	2.94222i	−0.135570	+	0.234814i	−0.925815	−	0.377977i	$-0.876620\pi$
$157$	−1.69869	+	2.94222i	−0.135570	+	0.234814i	0.790245	+	0.612791i	$0.209953\pi$
$158$	−3.54596	+	6.14179i	−0.282102	+	0.488614i
$159$		0			0
$160$	−0.0611015	+	2.23523i	−0.00483050	+	0.176711i
$161$	−4.82037	+	16.7076i	−0.379898	+	1.31674i
$162$		0			0
$163$	−4.86586	−	2.80931i	−0.381124	−	0.220042i	0.297183	−	0.954820i	$-0.403953\pi$
$163$	−4.86586	−	2.80931i	−0.381124	−	0.220042i	−0.678307	+	0.734778i	$0.737286\pi$
$164$	−6.33811			−0.494923
$165$		0			0
$166$		−	4.99966i		−	0.388049i
$167$	−5.55272	+	3.20586i	−0.429682	+	0.248077i	−0.699211	−	0.714915i	$-0.746465\pi$
$167$	−5.55272	+	3.20586i	−0.429682	+	0.248077i	0.269529	+	0.962992i	$0.413132\pi$
$168$		0			0
$169$	−11.9051	+	20.6202i	−0.915773	+	1.58617i
$170$	1.29823	+	0.0354880i	0.0995699	+	0.00272180i
$171$		0			0
$172$	−10.0713	+	5.81466i	−0.767929	+	0.443364i
$173$	6.95118	−	4.01327i	0.528489	−	0.305123i	−0.211912	−	0.977289i	$-0.567969\pi$
$173$	6.95118	−	4.01327i	0.528489	−	0.305123i	0.740401	+	0.672166i	$0.234636\pi$
$174$		0			0
$175$	8.63953	+	10.0179i	0.653087	+	0.757283i
$176$	1.13018	−	0.652510i	0.0851906	−	0.0491848i
$177$		0			0
$178$	2.70471			0.202726
$179$	−14.3104	+	8.26209i	−1.06961	+	0.617538i	−0.928074	−	0.372396i	$-0.878536\pi$
$179$	−14.3104	+	8.26209i	−1.06961	+	0.617538i	−0.141533	+	0.989934i	$0.545203\pi$
$180$		0			0
$181$		−	6.84621i		−	0.508875i	−0.967089	−	0.254437i	$-0.918110\pi$
$181$		−	6.84621i		−	0.508875i	0.967089	−	0.254437i	$-0.0818903\pi$
$182$	11.1319	+	11.5651i	0.825149	+	0.857265i
$183$		0			0
$184$	−6.57244			−0.484527
$185$	5.23595	+	0.143128i	0.384955	+	0.0105230i
$186$		0			0
$187$	−0.378980	−	0.656413i	−0.0277138	−	0.0480017i
$188$			5.41619i			0.395016i
$189$		0			0
$190$	8.43897	+	15.5853i	0.612227	+	1.13068i
$191$	7.33287	−	4.23363i	0.530588	−	0.306335i	−0.210668	−	0.977558i	$-0.567564\pi$
$191$	7.33287	−	4.23363i	0.530588	−	0.306335i	0.741256	+	0.671223i	$0.234231\pi$
$192$		0			0
$193$	−1.96645	−	1.13533i	−0.141548	−	0.0817227i	0.427554	−	0.903990i	$-0.359376\pi$
$193$	−1.96645	−	1.13533i	−0.141548	−	0.0817227i	−0.569101	+	0.822267i	$0.692709\pi$
$194$	11.5206			0.827134
$195$		0			0
$196$	6.19134	−	3.26609i	0.442238	−	0.233292i
$197$	−13.0144			−0.927240			−0.463620	−	0.886034i	$-0.653450\pi$
$197$	−13.0144			−0.927240			−0.463620	+	0.886034i	$0.653450\pi$
$198$		0			0
$199$	−2.76888	+	1.59861i	−0.196280	+	0.113323i	−0.594919	−	0.803785i	$-0.702816\pi$
$199$	−2.76888	+	1.59861i	−0.196280	+	0.113323i	0.398639	+	0.917108i	$0.369483\pi$
$200$	−2.73282	+	4.18708i	−0.193240	+	0.296072i
$201$		0			0
$202$	−7.17658	−	12.4302i	−0.504943	−	0.874586i
$203$	−0.276341	+	0.265988i	−0.0193953	+	0.0186687i
$204$		0			0
$205$	−12.0755	−	7.41896i	−0.843388	−	0.518163i
$206$	−0.386002	−	0.668575i	−0.0268940	−	0.0465818i
$207$		0			0
$208$	−3.03357	+	5.25429i	−0.210340	+	0.364320i
$209$	5.17189	−	8.95797i	0.357747	−	0.619636i
$210$		0			0
$211$	−5.05309	−	8.75221i	−0.347869	−	0.602527i	0.638002	−	0.770035i	$-0.279761\pi$
$211$	−5.05309	−	8.75221i	−0.347869	−	0.602527i	−0.985871	+	0.167508i	$0.946428\pi$
$212$	8.38135			0.575634
$213$		0			0
$214$	17.2124			1.17662
$215$	−25.9943	−	0.710569i	−1.77279	−	0.0484604i
$216$		0			0
$217$	2.63563	−	2.53689i	0.178918	−	0.172215i
$218$	6.30827	−	10.9262i	0.427250	−	0.740019i
$219$		0			0
$220$	2.91702	+	0.0797387i	0.196666	+	0.00537598i
$221$	3.05171	+	1.76191i	0.205280	+	0.118519i
$222$		0			0
$223$	1.58167	−	2.73954i	0.105917	−	0.183453i	−0.808196	−	0.588914i	$-0.799556\pi$
$223$	1.58167	−	2.73954i	0.105917	−	0.183453i	0.914112	+	0.405461i	$0.132889\pi$
$224$	1.83478	+	1.90619i	0.122592	+	0.127363i
$225$		0			0
$226$	6.02741	−	10.4398i	0.400938	−	0.694444i
$227$			9.59332i			0.636731i	0.947968	+	0.318365i	$0.103134\pi$
$227$			9.59332i			0.636731i	−0.947968	+	0.318365i	$0.896866\pi$
$228$		0			0
$229$			3.59517i			0.237575i	0.992920	+	0.118788i	$0.0379008\pi$
$229$			3.59517i			0.237575i	−0.992920	+	0.118788i	$0.962099\pi$
$230$	−12.5219	−	7.69325i	−0.825672	−	0.507278i
$231$		0			0
$232$	−0.125548	−	0.0724850i	−0.00824261	−	0.00475887i
$233$	2.91309	−	5.04563i	0.190843	−	0.330550i	−0.754687	−	0.656085i	$-0.772211\pi$
$233$	2.91309	−	5.04563i	0.190843	−	0.330550i	0.945530	+	0.325535i	$0.105544\pi$
$234$		0			0
$235$	−6.33983	+	10.3190i	−0.413565	+	0.673139i
$236$	1.54358	+	2.67356i	0.100478	+	0.174034i
$237$		0			0
$238$	1.10713	−	1.06565i	0.0717643	−	0.0690757i
$239$	19.9340	−	11.5089i	1.28942	−	0.744448i	0.310870	−	0.950452i	$-0.399379\pi$
$239$	19.9340	−	11.5089i	1.28942	−	0.744448i	0.978551	+	0.206005i	$0.0660462\pi$
$240$		0			0
$241$			6.84601i			0.440990i	0.975388	+	0.220495i	$0.0707673\pi$
$241$			6.84601i			0.440990i	−0.975388	+	0.220495i	$0.929233\pi$
$242$	4.64846	+	8.05137i	0.298814	+	0.517562i
$243$		0			0
$244$			2.12053i			0.135753i
$245$	15.6189	+	1.02455i	0.997855	+	0.0654560i
$246$		0			0
$247$			48.0890i			3.05983i
$248$	1.19742	+	0.691334i	0.0760366	+	0.0438997i
$249$		0			0
$250$	−10.1077	+	4.77845i	−0.639270	+	0.302216i
$251$	−12.2160			−0.771068			−0.385534	−	0.922694i	$-0.625983\pi$
$251$	−12.2160			−0.771068			−0.385534	+	0.922694i	$0.625983\pi$
$252$		0			0
$253$			8.57717i			0.539242i
$254$	12.7749	−	7.37562i	0.801571	−	0.462788i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$			26.3720i			1.64504i	0.568737	+	0.822520i	$0.307432\pi$
$257$			26.3720i			1.64504i	−0.568737	+	0.822520i	$0.692568\pi$
$258$		0			0
$259$	4.46519	−	4.29791i	0.277453	−	0.267059i
$260$	−11.9299	+	6.45968i	−0.739862	+	0.400613i
$261$		0			0
$262$	−7.84610	−	13.5898i	−0.484734	−	0.839583i
$263$	−20.6961			−1.27618			−0.638088	−	0.769963i	$-0.720274\pi$
$263$	−20.6961			−1.27618			−0.638088	+	0.769963i	$0.720274\pi$
$264$		0			0
$265$	15.9683	+	9.81064i	0.980925	+	0.602663i
$266$	20.1488	+	5.81321i	1.23540	+	0.356431i
$267$		0			0
$268$	11.4291	−	6.59859i	0.698143	−	0.403073i
$269$	−4.69521	−	8.13233i	−0.286272	−	0.495837i	0.686645	−	0.726993i	$-0.259083\pi$
$269$	−4.69521	−	8.13233i	−0.286272	−	0.495837i	−0.972917	+	0.231156i	$0.925749\pi$
$270$		0			0
$271$	−2.94143	−	1.69824i	−0.178679	−	0.103161i	0.407993	−	0.912985i	$-0.366229\pi$
$271$	−2.94143	−	1.69824i	−0.178679	−	0.103161i	−0.586672	+	0.809825i	$0.699562\pi$
$272$	0.502991	+	0.290402i	0.0304983	+	0.0176082i
$273$		0			0
$274$	−4.42929	−	7.67175i	−0.267583	−	0.463467i
$275$	5.46423	+	3.56639i	0.329506	+	0.215061i
$276$		0			0
$277$			20.9520i			1.25888i	0.777047	+	0.629442i	$0.216717\pi$
$277$			20.9520i			1.25888i	−0.777047	+	0.629442i	$0.783283\pi$
$278$	1.39913	+	0.807790i	0.0839144	+	0.0484480i
$279$		0			0
$280$	1.26440	+	5.77939i	0.0755622	+	0.345384i
$281$	−0.919808	−	0.531051i	−0.0548712	−	0.0316799i	0.472313	−	0.881431i	$-0.343419\pi$
$281$	−0.919808	−	0.531051i	−0.0548712	−	0.0316799i	−0.527185	+	0.849751i	$0.676752\pi$
$282$		0			0
$283$	10.4824	−	18.1560i	0.623113	−	1.07926i	−0.365790	−	0.930697i	$-0.619201\pi$
$283$	10.4824	−	18.1560i	0.623113	−	1.07926i	0.988903	−	0.148565i	$-0.0474655\pi$
$284$	−8.96724	−	5.17724i	−0.532108	−	0.307213i
$285$		0			0
$286$	6.85696	+	3.95887i	0.405460	+	0.234093i
$287$	−16.2776	+	4.03022i	−0.960834	+	0.237896i
$288$		0			0
$289$	−8.33133	+	14.4303i	−0.490078	+	0.848841i
$290$	−0.154350	−	0.285057i	−0.00906373	−	0.0167391i
$291$		0			0
$292$	7.69197			0.450139
$293$	−19.5706	+	11.2991i	−1.14332	+	0.660099i	−0.947252	−	0.320491i	$-0.896152\pi$
$293$	−19.5706	+	11.2991i	−1.14332	+	0.660099i	−0.196073	+	0.980589i	$0.562819\pi$
$294$		0			0
$295$	−0.188630	+	6.90051i	−0.0109825	+	0.401763i
$296$	2.02863	+	1.17123i	0.117912	+	0.0680764i
$297$		0			0
$298$	−8.30790	+	4.79657i	−0.481264	+	0.277858i
$299$	−19.9379	−	34.5335i	−1.15304	−	1.99712i
$300$		0			0
$301$	−22.1678	+	21.3373i	−1.27773	+	1.22986i
$302$	−8.68275	−	15.0390i	−0.499636	−	0.865395i
$303$		0			0
$304$			7.92614i			0.454595i
$305$	−2.48214	+	4.04007i	−0.142127	+	0.231334i
$306$		0			0
$307$	29.2086			1.66702			0.833512	−	0.552501i	$-0.186326\pi$
$307$	29.2086			1.66702			0.833512	+	0.552501i	$0.186326\pi$
$308$	2.48762	−	2.39443i	0.141745	−	0.136435i
$309$		0			0
$310$	1.47213	+	2.71877i	0.0836112	+	0.154415i
$311$	6.50531	−	11.2675i	0.368882	−	0.638923i	−0.620509	−	0.784199i	$-0.713074\pi$
$311$	6.50531	−	11.2675i	0.368882	−	0.638923i	0.989391	+	0.145277i	$0.0464072\pi$
$312$		0			0
$313$	−3.62723	−	6.28255i	−0.205023	−	0.355111i	0.745117	−	0.666934i	$-0.232394\pi$
$313$	−3.62723	−	6.28255i	−0.205023	−	0.355111i	−0.950140	+	0.311823i	$0.899060\pi$
$314$	−3.39738			−0.191725
$315$		0			0
$316$	−7.09192			−0.398952
$317$	14.2603	+	24.6996i	0.800939	+	1.38727i	0.918999	+	0.394261i	$0.128999\pi$
$317$	14.2603	+	24.6996i	0.800939	+	1.38727i	−0.118059	+	0.993007i	$0.537667\pi$
$318$		0			0
$319$	−0.0945944	+	0.163842i	−0.00529627	+	0.00917341i
$320$	−1.96632	+	1.06470i	−0.109921	+	0.0595186i
$321$		0			0
$322$	−16.8794	+	4.17922i	−0.940650	+	0.232899i
$323$	4.60353			0.256147
$324$		0			0
$325$	−30.2904	−	1.65725i	−1.68021	−	0.0919277i
$326$		−	5.61862i		−	0.311186i
$327$		0			0
$328$	−3.16905	−	5.48896i	−0.174982	−	0.303077i
$329$	3.44400	+	13.9099i	0.189874	+	0.766877i
$330$		0			0
$331$	−12.3511	−	21.3927i	−0.678877	−	1.17585i	−0.975319	−	0.220798i	$-0.929134\pi$
$331$	−12.3511	−	21.3927i	−0.678877	−	1.17585i	0.296443	−	0.955051i	$-0.404200\pi$
$332$	4.32983	−	2.49983i	0.237631	−	0.137196i
$333$		0			0
$334$	−5.55272	−	3.20586i	−0.303831	−	0.175417i
$335$	29.4988	+	0.806367i	1.61169	+	0.0440565i
$336$		0			0
$337$	6.13756	−	3.54352i	0.334334	−	0.193028i	−0.323430	−	0.946252i	$-0.604836\pi$
$337$	6.13756	−	3.54352i	0.334334	−	0.193028i	0.657764	+	0.753224i	$0.271503\pi$
$338$	−23.8101			−1.29510
$339$		0			0
$340$	0.618383	+	1.14205i	0.0335365	+	0.0619361i
$341$	0.902204	−	1.56266i	0.0488571	−	0.0846230i
$342$		0			0
$343$	13.8238	−	12.3249i	0.746415	−	0.665480i
$344$	−10.0713	−	5.81466i	−0.543008	−	0.313506i
$345$		0			0
$346$	6.95118	+	4.01327i	0.373698	+	0.215755i
$347$	3.87822	−	6.71728i	0.208194	−	0.360603i	−0.742952	−	0.669345i	$-0.766575\pi$
$347$	3.87822	−	6.71728i	0.208194	−	0.360603i	0.951146	+	0.308743i	$0.0999081\pi$
$348$		0			0
$349$	8.89557	+	5.13586i	0.476169	+	0.274916i	0.718819	−	0.695198i	$-0.244683\pi$
$349$	8.89557	+	5.13586i	0.476169	+	0.274916i	−0.242650	+	0.970114i	$0.578017\pi$
$350$	−4.35600	+	12.4910i	−0.232838	+	0.667672i
$351$		0			0
$352$	1.13018	+	0.652510i	0.0602388	+	0.0347789i
$353$		−	21.0732i		−	1.12161i	−0.827947	−	0.560807i	$-0.810491\pi$
$353$		−	21.0732i		−	1.12161i	0.827947	−	0.560807i	$-0.189509\pi$
$354$		0			0
$355$	−11.0244	−	20.3602i	−0.585116	−	1.08061i
$356$	1.35235	+	2.34234i	0.0716746	+	0.124144i
$357$		0			0
$358$	−14.3104	−	8.26209i	−0.756326	−	0.436665i
$359$	15.0004	+	8.66050i	0.791692	+	0.457084i	0.840558	−	0.541722i	$-0.182227\pi$
$359$	15.0004	+	8.66050i	0.791692	+	0.457084i	−0.0488656	+	0.998805i	$0.515561\pi$
$360$		0			0
$361$	21.9119	+	37.9525i	1.15326	+	1.99750i
$362$	5.92899	−	3.42310i	0.311621	−	0.179914i
$363$		0			0
$364$	−4.44977	+	15.4230i	−0.233231	+	0.808387i
$365$	14.6549	+	9.00370i	0.767072	+	0.471275i
$366$		0			0
$367$	−6.99660			−0.365220			−0.182610	−	0.983185i	$-0.558454\pi$
$367$	−6.99660			−0.365220			−0.182610	+	0.983185i	$0.558454\pi$
$368$	−3.28622	−	5.69190i	−0.171306	−	0.296711i
$369$		0			0
$370$	2.49402	+	4.60603i	0.129658	+	0.239456i
$371$	21.5250	−	5.32945i	1.11752	−	0.276691i
$372$		0			0
$373$		−	14.9568i		−	0.774432i	−0.921989	−	0.387216i	$-0.873437\pi$
$373$		−	14.9568i		−	0.774432i	0.921989	−	0.387216i	$-0.126563\pi$
$374$	0.378980	−	0.656413i	0.0195966	−	0.0339423i
$375$		0			0
$376$	−4.69056	+	2.70810i	−0.241897	+	0.139659i
$377$		−	0.879552i		−	0.0452992i
$378$		0			0
$379$	1.81688			0.0933268			0.0466634	−	0.998911i	$-0.485141\pi$
$379$	1.81688			0.0933268			0.0466634	+	0.998911i	$0.485141\pi$
$380$	−9.27780	+	15.1010i	−0.475941	+	0.774666i
$381$		0			0
$382$	7.33287	+	4.23363i	0.375182	+	0.216611i
$383$			4.60201i			0.235152i	0.993064	+	0.117576i	$0.0375123\pi$
$383$			4.60201i			0.235152i	−0.993064	+	0.117576i	$0.962488\pi$
$384$		0			0
$385$	7.54222	−	1.65006i	0.384387	−	0.0840951i
$386$		−	2.27066i		−	0.115573i
$387$		0			0
$388$	5.76032	+	9.97717i	0.292436	+	0.506514i
$389$			17.1177i			0.867902i	0.900936	+	0.433951i	$0.142881\pi$
$389$			17.1177i			0.867902i	−0.900936	+	0.433951i	$0.857119\pi$
$390$		0			0
$391$	−3.30588	+	1.90865i	−0.167185	+	0.0965245i
$392$	5.92418	+	3.72881i	0.299217	+	0.188333i
$393$		0			0
$394$	−6.50721	−	11.2708i	−0.327829	−	0.567816i
$395$	−13.5117	−	8.30132i	−0.679845	−	0.417685i
$396$		0			0
$397$	−7.42358	+	12.8580i	−0.372579	+	0.645325i	−0.989961	−	0.141338i	$-0.954860\pi$
$397$	−7.42358	+	12.8580i	−0.372579	+	0.645325i	0.617383	+	0.786663i	$0.288193\pi$
$398$	−2.76888	−	1.59861i	−0.138791	−	0.0801312i
$399$		0			0
$400$	−4.99253	−	0.273152i	−0.249627	−	0.0136576i
$401$		−	9.57306i		−	0.478056i	−0.971013	−	0.239028i	$-0.923171\pi$
$401$		−	9.57306i		−	0.478056i	0.971013	−	0.239028i	$-0.0768287\pi$
$402$		0			0
$403$			8.38883i			0.417877i
$404$	7.17658	−	12.4302i	0.357048	−	0.618426i
$405$		0			0
$406$	−0.368523	−	0.106324i	−0.0182895	−	0.00527678i
$407$	1.52848	−	2.64741i	0.0757640	−	0.131227i
$408$		0			0
$409$	−33.4503	−	19.3125i	−1.65401	−	0.954944i	−0.975399	−	0.220446i	$-0.929249\pi$
$409$	−33.4503	−	19.3125i	−1.65401	−	0.954944i	−0.678612	−	0.734497i	$-0.737418\pi$
$410$	0.387268	−	14.1672i	0.0191258	−	0.699666i
$411$		0			0
$412$	0.386002	−	0.668575i	0.0190169	−	0.0329383i
$413$	5.66426	+	5.88472i	0.278720	+	0.289568i
$414$		0			0
$415$	11.1754	+	0.305487i	0.548579	+	0.0149958i
$416$	−6.06713			−0.297466
$417$		0			0
$418$	10.3438			0.505931
$419$	−6.88512	−	11.9254i	−0.336360	−	0.582593i	0.647385	−	0.762163i	$-0.275863\pi$
$419$	−6.88512	−	11.9254i	−0.336360	−	0.582593i	−0.983745	+	0.179570i	$0.942529\pi$
$420$		0			0
$421$	−9.44758	+	16.3637i	−0.460447	+	0.797517i	−0.998983	−	0.0450850i	$-0.985644\pi$
$421$	−9.44758	+	16.3637i	−0.460447	+	0.797517i	0.538536	+	0.842602i	$0.318977\pi$
$422$	5.05309	−	8.75221i	0.245981	−	0.426051i
$423$		0			0
$424$	4.19068	+	7.25846i	0.203517	+	0.352502i
$425$	−0.158648	+	2.89968i	−0.00769555	+	0.140655i
$426$		0			0
$427$	1.34838	+	5.44595i	0.0652527	+	0.263548i
$428$	8.60622	+	14.9064i	0.415997	+	0.720529i
$429$		0			0
$430$	−12.3818	−	22.8670i	−0.597101	−	1.10274i
$431$	−29.2156	+	16.8676i	−1.40726	+	0.812485i	−0.995124	−	0.0986352i	$-0.968552\pi$
$431$	−29.2156	+	16.8676i	−1.40726	+	0.812485i	−0.412141	+	0.911120i	$0.635219\pi$
$432$		0			0
$433$	7.29213			0.350437			0.175219	−	0.984530i	$-0.443937\pi$
$433$	7.29213			0.350437			0.175219	+	0.984530i	$0.443937\pi$
$434$	3.51483	+	1.01408i	0.168717	+	0.0486773i
$435$		0			0
$436$	12.6165			0.604223
$437$	−45.1148	−	26.0470i	−2.15813	−	1.24600i
$438$		0			0
$439$	2.29308	−	1.32391i	0.109443	−	0.0631868i	−0.444279	−	0.895888i	$-0.646540\pi$
$439$	2.29308	−	1.32391i	0.109443	−	0.0631868i	0.553722	+	0.832701i	$0.313207\pi$
$440$	1.38946	+	2.56609i	0.0662397	+	0.122333i
$441$		0			0
$442$			3.52381i			0.167611i
$443$	−12.9543	−	22.4376i	−0.615480	−	1.06604i	−0.990300	−	0.138945i	$-0.955629\pi$
$443$	−12.9543	−	22.4376i	−0.615480	−	1.06604i	0.374821	−	0.927097i	$-0.377704\pi$
$444$		0			0
$445$	−0.165262	+	6.04565i	−0.00783415	+	0.286591i
$446$	3.16334			0.149789
$447$		0			0
$448$	−0.733422	+	2.54206i	−0.0346509	+	0.120101i
$449$		−	11.3781i		−	0.536965i	−0.963285	−	0.268482i	$-0.913478\pi$
$449$		−	11.3781i		−	0.536965i	0.963285	−	0.268482i	$-0.0865221\pi$
$450$		0			0
$451$	−7.16321	+	4.13568i	−0.337302	+	0.194742i
$452$	12.0548			0.567011
$453$		0			0
$454$	−8.30806	+	4.79666i	−0.389916	+	0.225118i
$455$	−26.5309	+	24.1757i	−1.24379	+	1.13337i
$456$		0			0
$457$	9.95317	−	5.74647i	0.465590	−	0.268808i	−0.248802	−	0.968554i	$-0.580037\pi$
$457$	9.95317	−	5.74647i	0.465590	−	0.268808i	0.714392	+	0.699746i	$0.246704\pi$
$458$	−3.11351	+	1.79758i	−0.145485	+	0.0839956i
$459$		0			0
$460$	0.401586	−	14.6909i	0.0187240	−	0.684968i
$461$	−0.576578	+	0.998663i	−0.0268539	+	0.0465124i	−0.879140	−	0.476564i	$-0.841882\pi$
$461$	−0.576578	+	0.998663i	−0.0268539	+	0.0465124i	0.852286	+	0.523076i	$0.175216\pi$
$462$		0			0
$463$	15.2816	−	8.82285i	0.710197	−	0.410033i	−0.100937	−	0.994893i	$-0.532184\pi$
$463$	15.2816	−	8.82285i	0.710197	−	0.410033i	0.811134	+	0.584860i	$0.198851\pi$
$464$		−	0.144970i		−	0.00673006i
$465$		0			0
$466$	5.82619			0.269893
$467$	16.2441	+	9.37851i	0.751685	+	0.433986i	0.826302	−	0.563227i	$-0.190440\pi$
$467$	16.2441	+	9.37851i	0.751685	+	0.433986i	−0.0746173	+	0.997212i	$0.523774\pi$
$468$		0			0
$469$	25.1564	−	24.2139i	1.16161	−	1.11810i
$470$	−12.1065	−	0.330937i	−0.558429	−	0.0152650i
$471$		0			0
$472$	−1.54358	+	2.67356i	−0.0710489	+	0.123060i
$473$	−7.58826	+	13.1432i	−0.348908	+	0.604327i
$474$		0			0
$475$	−35.3525	+	17.9108i	−1.62208	+	0.821803i
$476$	1.47644	+	0.425974i	0.0676726	+	0.0195245i
$477$		0			0
$478$	19.9340	+	11.5089i	0.911759	+	0.526404i
$479$	0.124194			0.00567456			0.00283728	−	0.999996i	$-0.499097\pi$
$479$	0.124194			0.00567456			0.00283728	+	0.999996i	$0.499097\pi$
$480$		0			0
$481$			14.2120i			0.648013i
$482$	−5.92882	+	3.42300i	−0.270050	+	0.155914i
$483$		0			0
$484$	−4.64846	+	8.05137i	−0.211294	+	0.365971i
$485$	−0.703929	+	25.7513i	−0.0319638	+	1.16931i
$486$		0			0
$487$	22.4789	−	12.9782i	1.01862	−	0.588099i	0.104914	−	0.994481i	$-0.466543\pi$
$487$	22.4789	−	12.9782i	1.01862	−	0.588099i	0.913703	+	0.406382i	$0.133210\pi$
$488$	−1.83643	+	1.06026i	−0.0831313	+	0.0479959i
$489$		0			0
$490$	6.92217	+	14.0386i	0.312712	+	0.634201i
$491$	−17.4877	+	10.0965i	−0.789210	+	0.455651i	−0.839684	−	0.543075i	$-0.817260\pi$
$491$	−17.4877	+	10.0965i	−0.789210	+	0.455651i	0.0504742	+	0.998725i	$0.483927\pi$
$492$		0			0
$493$	−0.0841991			−0.00379214
$494$	−41.6463	+	24.0445i	−1.87375	+	1.08181i
$495$		0			0
$496$			1.38267i			0.0620836i
$497$	−26.3218	−	7.59420i	−1.18069	−	0.340646i
$498$		0			0
$499$	−7.61998			−0.341117			−0.170559	−	0.985348i	$-0.554557\pi$
$499$	−7.61998			−0.341117			−0.170559	+	0.985348i	$0.554557\pi$
$500$	−9.19213	−	6.36433i	−0.411085	−	0.284622i
$501$		0			0
$502$	−6.10801	−	10.5794i	−0.272614	−	0.472181i
$503$			20.5824i			0.917723i	0.888508	+	0.458861i	$0.151743\pi$
$503$			20.5824i			0.917723i	−0.888508	+	0.458861i	$0.848257\pi$
$504$		0			0
$505$	28.2229	−	15.2818i	1.25590	−	0.680032i
$506$	−7.42805	+	4.28858i	−0.330217	+	0.190651i
$507$		0			0
$508$	12.7749	+	7.37562i	0.566797	+	0.327240i
$509$	−2.57903			−0.114313			−0.0571567	−	0.998365i	$-0.518203\pi$
$509$	−2.57903			−0.114313			−0.0571567	+	0.998365i	$0.518203\pi$
$510$		0			0
$511$	19.7546	−	4.89110i	0.873890	−	0.216369i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−22.8388	+	13.1860i	−1.00738	+	0.581609i
$515$	1.51801	−	0.821953i	0.0668913	−	0.0362196i
$516$		0			0
$517$	3.53412	+	6.12128i	0.155430	+	0.269213i
$518$	5.95469	+	1.71801i	0.261634	+	0.0754852i
$519$		0			0
$520$	−11.5592	−	7.10177i	−0.506905	−	0.311433i
$521$	−16.7954	−	29.0904i	−0.735818	−	1.27447i	−0.954363	−	0.298648i	$-0.903464\pi$
$521$	−16.7954	−	29.0904i	−0.735818	−	1.27447i	0.218545	−	0.975827i	$-0.429869\pi$
$522$		0			0
$523$	1.28600	−	2.22742i	0.0562330	−	0.0973984i	−0.836539	−	0.547908i	$-0.815424\pi$
$523$	1.28600	−	2.22742i	0.0562330	−	0.0973984i	0.892772	+	0.450510i	$0.148758\pi$
$524$	7.84610	−	13.5898i	0.342758	−	0.593675i
$525$		0			0
$526$	−10.3480	−	17.9233i	−0.451196	−	0.781495i
$527$	0.803058			0.0349818
$528$		0			0
$529$	20.1970			0.878129
$530$	−0.512113	+	18.7343i	−0.0222448	+	0.813765i
$531$		0			0
$532$	5.04000	+	20.3559i	0.218512	+	0.882542i
$533$	19.2271	−	33.3023i	0.832817	−	1.44248i
$534$		0			0
$535$	−1.05171	+	38.4738i	−0.0454692	+	1.66337i
$536$	11.4291	+	6.59859i	0.493661	+	0.285016i
$537$		0			0
$538$	4.69521	−	8.13233i	0.202425	−	0.350610i
$539$	4.86618	−	7.73118i	0.209601	−	0.333006i
$540$		0			0
$541$	−15.6121	+	27.0410i	−0.671218	+	1.16258i	0.306341	+	0.951922i	$0.400895\pi$
$541$	−15.6121	+	27.0410i	−0.671218	+	1.16258i	−0.977559	+	0.210662i	$0.932438\pi$
$542$		−	3.39647i		−	0.145891i
$543$		0			0
$544$			0.580804i			0.0249018i
$545$	24.0373	+	14.7681i	1.02964	+	0.632594i
$546$		0			0
$547$	18.7975	+	10.8527i	0.803721	+	0.464029i	0.844771	−	0.535128i	$-0.179737\pi$
$547$	18.7975	+	10.8527i	0.803721	+	0.464029i	−0.0410494	+	0.999157i	$0.513070\pi$
$548$	4.42929	−	7.67175i	0.189210	−	0.327721i
$549$		0			0
$550$	−0.356469	+	6.51536i	−0.0151999	+	0.277816i
$551$	−0.574526	−	0.995109i	−0.0244756	−	0.0423931i
$552$		0			0
$553$	−18.2135	+	4.50954i	−0.774517	+	0.191765i
$554$	−18.1450	+	10.4760i	−0.770906	+	0.445083i
$555$		0			0
$556$			1.61558i			0.0685158i
$557$	6.54619	+	11.3383i	0.277371	+	0.480421i	0.970731	−	0.240171i	$-0.0772035\pi$
$557$	6.54619	+	11.3383i	0.277371	+	0.480421i	−0.693360	+	0.720592i	$0.743870\pi$
$558$		0			0
$559$		−	70.5567i		−	2.98423i
$560$	−4.37290	+	3.98469i	−0.184789	+	0.168384i
$561$		0			0
$562$		−	1.06210i		−	0.0448021i
$563$	−4.96871	−	2.86869i	−0.209406	−	0.120901i	0.391629	−	0.920123i	$-0.371912\pi$
$563$	−4.96871	−	2.86869i	−0.209406	−	0.120901i	−0.601035	+	0.799222i	$0.705245\pi$
$564$		0			0
$565$	22.9671	+	14.1106i	0.966232	+	0.593636i
$566$	20.9648			0.881214
$567$		0			0
$568$		−	10.3545i		−	0.434464i
$569$	−36.9166	+	21.3138i	−1.54762	+	0.893521i	−0.549301	+	0.835624i	$0.685106\pi$
$569$	−36.9166	+	21.3138i	−1.54762	+	0.893521i	−0.998323	+	0.0578969i	$0.981561\pi$
$570$		0			0
$571$	16.9274	−	29.3191i	0.708390	−	1.22697i	−0.257064	−	0.966394i	$-0.582755\pi$
$571$	16.9274	−	29.3191i	0.708390	−	1.22697i	0.965454	−	0.260573i	$-0.0839116\pi$
$572$			7.91773i			0.331057i
$573$		0			0
$574$	−11.6290	−	12.0817i	−0.485387	−	0.504279i
$575$	17.9613	−	27.5194i	0.749039	−	1.14764i
$576$		0			0
$577$	−6.51191	−	11.2790i	−0.271095	−	0.469549i	0.698048	−	0.716051i	$-0.254052\pi$
$577$	−6.51191	−	11.2790i	−0.271095	−	0.469549i	−0.969142	+	0.246502i	$0.920719\pi$
$578$	−16.6627			−0.693076
$579$		0			0
$580$	0.169692	−	0.276199i	0.00704608	−	0.0114686i
$581$	9.53033	−	9.17329i	0.395385	−	0.380572i
$582$		0			0
$583$	9.47244	−	5.46892i	0.392309	−	0.226499i
$584$	3.84599	+	6.66144i	0.159148	+	0.275653i
$585$		0			0
$586$	−19.5706	−	11.2991i	−0.808452	−	0.466760i
$587$	33.7149	+	19.4653i	1.39156	+	0.803419i	0.993488	−	0.113934i	$-0.0363451\pi$
$587$	33.7149	+	19.4653i	1.39156	+	0.803419i	0.398075	+	0.917353i	$0.369678\pi$
$588$		0			0
$589$	5.47961	+	9.49096i	0.225783	+	0.391068i
$590$	−6.07033	+	3.28690i	−0.249912	+	0.135319i
$591$		0			0
$592$			2.34246i			0.0962746i
$593$	−22.4867	−	12.9827i	−0.923419	−	0.533136i	−0.0386950	−	0.999251i	$-0.512320\pi$
$593$	−22.4867	−	12.9827i	−0.923419	−	0.533136i	−0.884724	+	0.466115i	$0.845653\pi$
$594$		0			0
$595$	2.31433	+	2.53980i	0.0948781	+	0.104121i
$596$	−8.30790	−	4.79657i	−0.340305	−	0.196475i
$597$		0			0
$598$	19.9379	−	34.5335i	0.815323	−	1.41218i
$599$	22.1583	+	12.7931i	0.905364	+	0.522712i	0.878937	−	0.476938i	$-0.158253\pi$
$599$	22.1583	+	12.7931i	0.905364	+	0.522712i	0.0264277	+	0.999651i	$0.491587\pi$
$600$		0			0
$601$	−29.1769	−	16.8453i	−1.19015	−	0.687133i	−0.231809	−	0.972761i	$-0.574464\pi$
$601$	−29.1769	−	16.8453i	−1.19015	−	0.687133i	−0.958340	+	0.285629i	$0.907798\pi$
$602$	−29.5625	−	8.52920i	−1.20488	−	0.347624i
$603$		0			0
$604$	8.68275	−	15.0390i	0.353296	−	0.611927i
$605$	−18.2807	+	9.89844i	−0.743217	+	0.402429i
$606$		0			0
$607$	−27.8164			−1.12903			−0.564517	−	0.825422i	$-0.690937\pi$
$607$	−27.8164			−1.12903			−0.564517	+	0.825422i	$0.690937\pi$
$608$	−6.86424	+	3.96307i	−0.278382	+	0.160724i
$609$		0			0
$610$	−4.73987	−	0.129567i	−0.191912	−	0.00524603i
$611$	−28.4582	−	16.4304i	−1.15130	−	0.664702i
$612$		0			0
$613$	−24.9598	+	14.4106i	−1.00812	+	0.582037i	−0.910640	−	0.413201i	$-0.864411\pi$
$613$	−24.9598	+	14.4106i	−1.00812	+	0.582037i	−0.0974774	+	0.995238i	$0.531077\pi$
$614$	14.6043	+	25.2954i	0.589382	+	1.02084i
$615$		0			0
$616$	3.31745	+	0.957131i	0.133664	+	0.0385639i
$617$	5.31220	+	9.20099i	0.213861	+	0.370418i	0.952920	−	0.303223i	$-0.0980627\pi$
$617$	5.31220	+	9.20099i	0.213861	+	0.370418i	−0.739059	+	0.673641i	$0.764729\pi$
$618$		0			0
$619$		−	34.6381i		−	1.39222i	−0.717934	−	0.696111i	$-0.754912\pi$
$619$		−	34.6381i		−	1.39222i	0.717934	−	0.696111i	$-0.245088\pi$
$620$	−1.61846	+	2.63428i	−0.0649988	+	0.105795i
$621$		0			0
$622$	13.0106			0.521678
$623$	4.96254	+	5.15569i	0.198820	+	0.206559i
$624$		0			0
$625$	−10.0634	−	22.8851i	−0.402534	−	0.915405i
$626$	3.62723	−	6.28255i	0.144973	−	0.251101i
$627$		0			0
$628$	−1.69869	−	2.94222i	−0.0677851	−	0.117407i
$629$	1.36051			0.0542471
$630$		0			0
$631$	−17.6726			−0.703534			−0.351767	−	0.936088i	$-0.614419\pi$
$631$	−17.6726			−0.703534			−0.351767	+	0.936088i	$0.614419\pi$
$632$	−3.54596	−	6.14179i	−0.141051	−	0.244307i
$633$		0			0
$634$	−14.2603	+	24.6996i	−0.566350	+	0.980946i
$635$	15.7057	+	29.0056i	0.623260	+	1.15105i
$636$		0			0
$637$	−1.62085	+	42.4390i	−0.0642205	+	1.68149i
$638$	−0.189189			−0.00749006
$639$		0			0
$640$	−1.90522	−	1.17053i	−0.0753103	−	0.0462693i
$641$		−	13.7317i		−	0.542369i	−0.962527	−	0.271185i	$-0.912585\pi$
$641$		−	13.7317i		−	0.542369i	0.962527	−	0.271185i	$-0.0874154\pi$
$642$		0			0
$643$	−7.15031	−	12.3847i	−0.281981	−	0.488405i	0.689892	−	0.723912i	$-0.257658\pi$
$643$	−7.15031	−	12.3847i	−0.281981	−	0.488405i	−0.971872	+	0.235508i	$0.924325\pi$
$644$	−12.0590	−	12.5283i	−0.475191	−	0.493686i
$645$		0			0
$646$	2.30177	+	3.98678i	0.0905618	+	0.156858i
$647$	18.0964	−	10.4480i	0.711443	−	0.410752i	−0.100152	−	0.994972i	$-0.531933\pi$
$647$	18.0964	−	10.4480i	0.711443	−	0.410752i	0.811595	+	0.584220i	$0.198600\pi$
$648$		0			0
$649$	3.48904	+	2.01440i	0.136957	+	0.0790721i
$650$	−13.7100	−	27.0608i	−0.537749	−	1.06141i
$651$		0			0
$652$	4.86586	−	2.80931i	0.190562	−	0.110021i
$653$	−1.28292			−0.0502046			−0.0251023	−	0.999685i	$-0.507991\pi$
$653$	−1.28292			−0.0502046			−0.0251023	+	0.999685i	$0.507991\pi$
$654$		0			0
$655$	30.8559	−	16.7075i	1.20564	−	0.652816i
$656$	3.16905	−	5.48896i	0.123731	−	0.214308i
$657$		0			0
$658$	−10.3243	+	9.93753i	−0.402484	+	0.387405i
$659$	4.33134	+	2.50070i	0.168725	+	0.0974136i	0.581985	−	0.813200i	$-0.302276\pi$
$659$	4.33134	+	2.50070i	0.168725	+	0.0974136i	−0.413259	+	0.910613i	$0.635610\pi$
$660$		0			0
$661$	−8.66549	−	5.00302i	−0.337049	−	0.194595i	0.321918	−	0.946768i	$-0.395673\pi$
$661$	−8.66549	−	5.00302i	−0.337049	−	0.194595i	−0.658966	+	0.752173i	$0.729006\pi$
$662$	12.3511	−	21.3927i	0.480038	−	0.831451i
$663$		0			0
$664$	4.32983	+	2.49983i	0.168030	+	0.0970123i
$665$	−14.2250	+	44.6820i	−0.551621	+	1.73269i
$666$		0			0
$667$	0.825155	+	0.476403i	0.0319501	+	0.0184464i
$668$		−	6.41173i		−	0.248077i
$669$		0			0
$670$	14.0510	+	25.9499i	0.542839	+	1.00253i
$671$	1.38367	+	2.39658i	0.0534158	+	0.0925189i
$672$		0			0
$673$	−2.63843	−	1.52330i	−0.101704	−	0.0587189i	0.448285	−	0.893891i	$-0.352035\pi$
$673$	−2.63843	−	1.52330i	−0.101704	−	0.0587189i	−0.549989	+	0.835172i	$0.685368\pi$
$674$	6.13756	+	3.54352i	0.236410	+	0.136491i
$675$		0			0
$676$	−11.9051	−	20.6202i	−0.457887	−	0.793083i
$677$	7.77071	−	4.48642i	0.298653	−	0.172427i	−0.343185	−	0.939268i	$-0.611506\pi$
$677$	7.77071	−	4.48642i	0.298653	−	0.172427i	0.641838	+	0.766841i	$0.278172\pi$
$678$		0			0
$679$	21.1379	+	21.9606i	0.811197	+	0.842770i
$680$	−0.679850	+	1.10656i	−0.0260710	+	0.0424346i
$681$		0			0
$682$	1.80441			0.0690944
$683$	0.499734	+	0.865564i	0.0191218	+	0.0331199i	0.875428	−	0.483349i	$-0.160580\pi$
$683$	0.499734	+	0.865564i	0.0191218	+	0.0331199i	−0.856306	+	0.516469i	$0.827246\pi$
$684$		0			0
$685$	17.4188	−	9.43173i	0.665537	−	0.360368i
$686$	17.5856	+	5.80933i	0.671420	+	0.221801i
$687$		0			0
$688$		−	11.6293i		−	0.443364i
$689$	−25.4254	+	44.0381i	−0.968630	+	1.67772i
$690$		0			0
$691$	−14.7899	+	8.53893i	−0.562633	+	0.324836i	−0.754202	−	0.656643i	$-0.771976\pi$
$691$	−14.7899	+	8.53893i	−0.562633	+	0.324836i	0.191569	+	0.981479i	$0.438643\pi$
$692$			8.02653i			0.305123i
$693$		0			0
$694$	7.75645			0.294431
$695$	−1.89109	+	3.07803i	−0.0717331	+	0.116756i
$696$		0			0
$697$	−3.18801	−	1.84060i	−0.120755	−	0.0697177i
$698$			10.2717i			0.388790i
$699$		0			0
$700$	−12.9955	+	2.47309i	−0.491185	+	0.0934742i
$701$			10.9031i			0.411803i	0.978573	+	0.205902i	$0.0660127\pi$
$701$			10.9031i			0.411803i	−0.978573	+	0.205902i	$0.933987\pi$
$702$		0			0
$703$	9.28334	+	16.0792i	0.350128	+	0.606439i
$704$			1.30502i			0.0491848i
$705$		0			0
$706$	18.2499	−	10.5366i	0.686845	−	0.396550i
$707$	10.5269	−	36.4867i	0.395906	−	1.37222i
$708$		0			0
$709$	23.2624	+	40.2917i	0.873638	+	1.51318i	0.858207	+	0.513304i	$0.171579\pi$
$709$	23.2624	+	40.2917i	0.873638	+	1.51318i	0.0154309	+	0.999881i	$0.495088\pi$
$710$	12.1202	−	19.7275i	0.454865	−	0.740361i
$711$		0			0
$712$	−1.35235	+	2.34234i	−0.0506816	+	0.0877830i
$713$	−7.87000	−	4.54375i	−0.294734	−	0.170165i
$714$		0			0
$715$	−9.26796	+	15.0850i	−0.346602	+	0.564147i
$716$		−	16.5242i		−	0.617538i
$717$		0			0
$718$			17.3210i			0.646414i
$719$	−8.48584	+	14.6979i	−0.316468	+	0.548139i	−0.979749	−	0.200232i	$-0.935830\pi$
$719$	−8.48584	+	14.6979i	−0.316468	+	0.548139i	0.663280	+	0.748371i	$0.269164\pi$
$720$		0			0
$721$	0.566204	−	1.96248i	0.0210865	−	0.0730867i
$722$	−21.9119	+	37.9525i	−0.815475	+	1.41244i
$723$		0			0
$724$	5.92899	+	3.42310i	0.220349	+	0.127219i
$725$	0.646600	−	0.327590i	0.0240141	−	0.0121664i
$726$		0			0
$727$	−19.9409	+	34.5386i	−0.739567	+	1.28097i	0.213124	+	0.977025i	$0.431636\pi$
$727$	−19.9409	+	34.5386i	−0.739567	+	1.28097i	−0.952691	+	0.303942i	$0.901697\pi$
$728$	−15.5816	+	3.85791i	−0.577494	+	0.142984i
$729$		0			0
$730$	−0.469991	+	17.1934i	−0.0173951	+	0.636355i
$731$	−6.75436			−0.249819
$732$		0			0
$733$	−14.2054			−0.524689			−0.262345	−	0.964974i	$-0.584496\pi$
$733$	−14.2054			−0.524689			−0.262345	+	0.964974i	$0.584496\pi$
$734$	−3.49830	−	6.05923i	−0.129125	−	0.223650i
$735$		0			0
$736$	3.28622	−	5.69190i	0.121132	−	0.209806i
$737$	8.61129	−	14.9152i	0.317201	−	0.549408i
$738$		0			0
$739$	15.4922	+	26.8333i	0.569891	+	0.987080i	0.996576	+	0.0826801i	$0.0263480\pi$
$739$	15.4922	+	26.8333i	0.569891	+	0.987080i	−0.426685	+	0.904400i	$0.640319\pi$
$740$	−2.74193	+	4.46290i	−0.100795	+	0.164059i
$741$		0			0
$742$	15.3779	+	15.9765i	0.564542	+	0.586515i
$743$	−25.1293	−	43.5252i	−0.921904	−	1.59678i	−0.796467	−	0.604682i	$-0.793300\pi$
$743$	−25.1293	−	43.5252i	−0.921904	−	1.59678i	−0.125437	−	0.992102i	$-0.540033\pi$
$744$		0			0
$745$	−10.2138	−	18.8632i	−0.374206	−	0.691093i
$746$	12.9529	−	7.47838i	0.474241	−	0.273803i
$747$		0			0
$748$	0.757961			0.0277138
$749$	31.5811	+	32.8103i	1.15395	+	1.19886i
$750$		0			0
$751$	27.9926			1.02146			0.510732	−	0.859740i	$-0.329375\pi$
$751$	27.9926			1.02146			0.510732	+	0.859740i	$0.329375\pi$
$752$	−4.69056	−	2.70810i	−0.171047	−	0.0987541i
$753$		0			0
$754$	0.761715	−	0.439776i	0.0277400	−	0.0160157i
$755$	34.1461	−	18.4891i	1.24270	−	0.672886i
$756$		0			0
$757$			17.6703i			0.642238i	0.947039	+	0.321119i	$0.104059\pi$
$757$			17.6703i			0.642238i	−0.947039	+	0.321119i	$0.895941\pi$
$758$	0.908439	+	1.57346i	0.0329960	+	0.0571507i
$759$		0			0
$760$	−17.7168	−	0.484299i	−0.642655	−	0.0175674i
$761$	−2.05727			−0.0745758			−0.0372879	−	0.999305i	$-0.511872\pi$
$761$	−2.05727			−0.0745758			−0.0372879	+	0.999305i	$0.511872\pi$
$762$		0			0
$763$	32.4018	−	8.02248i	1.17303	−	0.290433i
$764$			8.46726i			0.306335i
$765$		0			0
$766$	−3.98546	+	2.30101i	−0.144000	+	0.0831387i
$767$	−18.7302			−0.676308
$768$		0			0
$769$	−12.1169	+	6.99571i	−0.436947	+	0.252272i	−0.702302	−	0.711879i	$-0.747844\pi$
$769$	−12.1169	+	6.99571i	−0.436947	+	0.252272i	0.265355	+	0.964151i	$0.414511\pi$
$770$	5.20011	+	5.70672i	0.187399	+	0.205656i
$771$		0			0
$772$	1.96645	−	1.13533i	0.0707739	−	0.0408613i
$773$	36.5855	−	21.1226i	1.31589	−	0.759728i	0.332824	−	0.942989i	$-0.391999\pi$
$773$	36.5855	−	21.1226i	1.31589	−	0.759728i	0.983064	+	0.183261i	$0.0586652\pi$
$774$		0			0
$775$	−6.16702	+	3.12443i	−0.221526	+	0.112233i
$776$	−5.76032	+	9.97717i	−0.206784	+	0.358160i
$777$		0			0
$778$	−14.8244	+	8.55885i	−0.531479	+	0.306850i
$779$		−	50.2368i		−	1.79992i
$780$		0			0
$781$	−13.5128			−0.483526
$782$	−3.30588	−	1.90865i	−0.118218	−	0.0682532i
$783$		0			0
$784$	−0.267153	+	6.99490i	−0.00954118	+	0.249818i
$785$	0.207585	−	7.59393i	0.00740902	−	0.271039i
$786$		0			0
$787$	22.4107	−	38.8164i	0.798854	−	1.38366i	−0.121509	−	0.992590i	$-0.538773\pi$
$787$	22.4107	−	38.8164i	0.798854	−	1.38366i	0.920363	−	0.391065i	$-0.127893\pi$
$788$	6.50721	−	11.2708i	0.231810	−	0.401507i
$789$		0			0
$790$	0.433327	−	15.8521i	0.0154171	−	0.563993i
$791$	30.9592	−	7.66531i	1.10078	−	0.272547i
$792$		0			0
$793$	−11.1419	−	6.43276i	−0.395659	−	0.228434i
$794$	−14.8472			−0.526906
$795$		0			0
$796$		−	3.19722i		−	0.113323i
$797$	33.4229	−	19.2967i	1.18390	−	0.683524i	0.226986	−	0.973898i	$-0.427113\pi$
$797$	33.4229	−	19.2967i	1.18390	−	0.683524i	0.956913	+	0.290374i	$0.0937796\pi$
$798$		0			0
$799$	−1.57287	+	2.72430i	−0.0556442	+	0.0963786i
$800$	−2.25971	−	4.46024i	−0.0798928	−	0.157693i
$801$		0			0
$802$	8.29051	−	4.78653i	0.292748	−	0.169018i
$803$	8.69332	−	5.01909i	0.306781	−	0.177120i
$804$		0			0
$805$	−8.31017	−	37.9847i	−0.292895	−	1.33878i
$806$	−7.26494	+	4.19441i	−0.255896	+	0.147742i
$807$		0			0
$808$	14.3532			0.504943
$809$	12.0653	−	6.96590i	0.424193	−	0.244908i	−0.272677	−	0.962106i	$-0.587909\pi$
$809$	12.0653	−	6.96590i	0.424193	−	0.244908i	0.696870	+	0.717198i	$0.254576\pi$
$810$		0			0
$811$			50.7243i			1.78117i	0.454815	+	0.890586i	$0.349705\pi$
$811$			50.7243i			1.78117i	−0.454815	+	0.890586i	$0.650295\pi$
$812$	−0.0921821	−	0.372312i	−0.00323496	−	0.0130656i
$813$		0			0
$814$	3.05696			0.107146
$815$	12.5589	+	0.343306i	0.439920	+	0.0120255i
$816$		0			0
$817$	−46.0879	−	79.8265i	−1.61241	−	2.79278i
$818$		−	38.6251i		−	1.35049i
$819$		0			0
$820$	12.4627	−	6.74819i	0.435218	−	0.235657i
$821$	21.4858	−	12.4048i	0.749860	−	0.432932i	−0.0757835	−	0.997124i	$-0.524146\pi$
$821$	21.4858	−	12.4048i	0.749860	−	0.432932i	0.825643	+	0.564193i	$0.190812\pi$
$822$		0			0
$823$	−8.62872	−	4.98179i	−0.300778	−	0.173654i	0.342014	−	0.939695i	$-0.388891\pi$
$823$	−8.62872	−	4.98179i	−0.300778	−	0.173654i	−0.642792	+	0.766040i	$0.722224\pi$
$824$	0.772004			0.0268940
$825$		0			0
$826$	−2.26419	+	7.84775i	−0.0787812	+	0.273058i
$827$	36.2819			1.26165			0.630823	−	0.775926i	$-0.282717\pi$
$827$	36.2819			1.26165			0.630823	+	0.775926i	$0.282717\pi$
$828$		0			0
$829$	−16.8402	+	9.72267i	−0.584883	+	0.337682i	−0.763071	−	0.646314i	$-0.776310\pi$
$829$	−16.8402	+	9.72267i	−0.584883	+	0.337682i	0.178189	+	0.983996i	$0.442976\pi$
$830$	5.32315	+	9.83093i	0.184769	+	0.341237i
$831$		0			0
$832$	−3.03357	−	5.25429i	−0.105170	−	0.182160i
$833$	4.06267	+	0.155163i	0.140763	+	0.00537610i
$834$		0			0
$835$	7.50513	−	12.2157i	0.259726	−	0.422743i
$836$	5.17189	+	8.95797i	0.178874	+	0.309818i
$837$		0			0
$838$	6.88512	−	11.9254i	0.237843	−	0.411956i
$839$	21.1582	−	36.6471i	0.730463	−	1.26520i	−0.226223	−	0.974075i	$-0.572638\pi$
$839$	21.1582	−	36.6471i	0.730463	−	1.26520i	0.956686	−	0.291123i	$-0.0940288\pi$
$840$		0			0
$841$	−14.4895	−	25.0965i	−0.499638	−	0.865398i
$842$	−18.8952			−0.651170
$843$		0			0
$844$	10.1062			0.347869
$845$	1.45483	−	53.2211i	0.0500478	−	1.83086i
$846$		0			0
$847$	−6.81857	+	23.6334i	−0.234289	+	0.812052i
$848$	−4.19068	+	7.25846i	−0.143908	+	0.249257i
$849$		0			0
$850$	−2.59052	+	1.31245i	−0.0888542	+	0.0450166i
$851$	−13.3331	−	7.69785i	−0.457051	−	0.263879i
$852$		0			0
$853$	−4.70765	+	8.15389i	−0.161187	+	0.279184i	−0.935295	−	0.353870i	$-0.884866\pi$
$853$	−4.70765	+	8.15389i	−0.161187	+	0.279184i	0.774108	+	0.633054i	$0.218199\pi$
$854$	−4.04214	+	3.89070i	−0.138319	+	0.133137i
$855$		0			0
$856$	−8.60622	+	14.9064i	−0.294155	+	0.509491i
$857$			36.5321i			1.24791i	0.781459	+	0.623956i	$0.214476\pi$
$857$			36.5321i			1.24791i	−0.781459	+	0.623956i	$0.785524\pi$
$858$		0			0
$859$		−	25.9238i		−	0.884509i	−0.896890	−	0.442254i	$-0.854179\pi$
$859$		−	25.9238i		−	0.884509i	0.896890	−	0.442254i	$-0.145821\pi$
$860$	13.6125	−	22.1564i	0.464182	−	0.755527i
$861$		0			0
$862$	−29.2156	−	16.8676i	−0.995087	−	0.574513i
$863$	−11.4281	+	19.7941i	−0.389018	+	0.673800i	−0.992318	−	0.123715i	$-0.960519\pi$
$863$	−11.4281	+	19.7941i	−0.389018	+	0.673800i	0.603299	+	0.797515i	$0.293852\pi$
$864$		0			0
$865$	−9.39531	+	15.2923i	−0.319450	+	0.519954i
$866$	3.64607	+	6.31517i	0.123898	+	0.214598i
$867$		0			0
$868$	0.879197	+	3.55097i	0.0298419	+	0.120528i
$869$	−8.01516	+	4.62755i	−0.271896	+	0.156979i
$870$		0			0
$871$			80.0690i			2.71304i
$872$	6.30827	+	10.9262i	0.213625	+	0.370009i
$873$		0			0
$874$		−	52.0941i		−	1.76211i
$875$	−27.6542	−	10.4999i	−0.934881	−	0.354961i
$876$		0			0
$877$			4.90352i			0.165580i	0.996567	+	0.0827901i	$0.0263831\pi$
$877$			4.90352i			0.165580i	−0.996567	+	0.0827901i	$0.973617\pi$
$878$	2.29308	+	1.32391i	0.0773877	+	0.0446798i
$879$		0			0
$880$	−1.52757	+	2.48635i	−0.0514943	+	0.0838148i
$881$	42.9169			1.44591			0.722953	−	0.690897i	$-0.242784\pi$
$881$	42.9169			1.44591			0.722953	+	0.690897i	$0.242784\pi$
$882$		0			0
$883$		−	39.4640i		−	1.32807i	−0.747701	−	0.664035i	$-0.768843\pi$
$883$		−	39.4640i		−	1.32807i	0.747701	−	0.664035i	$-0.231157\pi$
$884$	−3.05171	+	1.76191i	−0.102640	+	0.0592594i
$885$		0			0
$886$	12.9543	−	22.4376i	0.435210	−	0.753805i
$887$			27.7389i			0.931380i	0.884948	+	0.465690i	$0.154194\pi$
$887$			27.7389i			0.931380i	−0.884948	+	0.465690i	$0.845806\pi$
$888$		0			0
$889$	37.4986	+	10.8189i	1.25766	+	0.362854i
$890$	−5.31832	+	2.87970i	−0.178270	+	0.0965279i
$891$		0			0
$892$	1.58167	+	2.73954i	0.0529583	+	0.0917264i
$893$	−42.9295			−1.43658
$894$		0			0
$895$	19.3421	−	31.4822i	0.646535	−	1.05233i
$896$	−2.56820	+	0.635870i	−0.0857977	+	0.0212429i
$897$		0			0
$898$	9.85371	−	5.68904i	0.328822	−	0.189846i
$899$	−0.100223	−	0.173591i	−0.00334261	−	0.00578957i
$900$		0			0
$901$	4.21574	+	2.43396i	0.140447	+	0.0810870i
$902$	−7.16321	−	4.13568i	−0.238509	−	0.137703i
$903$		0			0
$904$	6.02741	+	10.4398i	0.200469	+	0.347222i
$905$	7.28916	+	13.4618i	0.242300	+	0.447486i
$906$		0			0
$907$		−	44.6436i		−	1.48237i	−0.671303	−	0.741183i	$-0.734265\pi$
$907$		−	44.6436i		−	1.48237i	0.671303	−	0.741183i	$-0.265735\pi$
$908$	−8.30806	−	4.79666i	−0.275713	−	0.159183i
$909$		0			0
$910$	−34.2022	−	10.8886i	−1.13379	−	0.360955i
$911$	14.1534	+	8.17148i	0.468924	+	0.270733i	0.715789	−	0.698317i	$-0.246067\pi$
$911$	14.1534	+	8.17148i	0.468924	+	0.270733i	−0.246865	+	0.969050i	$0.579401\pi$
$912$		0			0
$913$	3.26233	−	5.65052i	0.107967	−	0.187005i
$914$	9.95317	+	5.74647i	0.329222	+	0.190076i
$915$		0			0
$916$	−3.11351	−	1.79758i	−0.102873	−	0.0593939i
$917$	11.5090	−	39.8906i	0.380061	−	1.31730i
$918$		0			0
$919$	19.1208	−	33.1181i	0.630736	−	1.09247i	−0.356666	−	0.934232i	$-0.616087\pi$
$919$	19.1208	−	33.1181i	0.630736	−	1.09247i	0.987402	−	0.158234i	$-0.0505801\pi$
$920$	12.9235	−	6.99768i	0.426076	−	0.230707i
$921$		0			0
$922$	−1.15316			−0.0379772
$923$	54.4054	−	31.4110i	1.79078	−	1.03391i
$924$		0			0
$925$	−10.4479	+	5.29329i	−0.343526	+	0.174042i
$926$	15.2816	+	8.82285i	0.502185	+	0.289937i
$927$		0			0
$928$	0.125548	−	0.0724850i	0.00412131	−	0.00237944i
$929$	1.29878	+	2.24955i	0.0426115	+	0.0738053i	0.886545	−	0.462643i	$-0.153099\pi$
$929$	1.29878	+	2.24955i	0.0426115	+	0.0738053i	−0.843933	+	0.536449i	$0.819766\pi$
$930$		0			0
$931$	25.8875	+	49.0734i	0.848428	+	1.60832i
$932$	2.91309	+	5.04563i	0.0954215	+	0.165275i
$933$		0			0
$934$			18.7570i			0.613748i
$935$	1.44408	+	0.887218i	0.0472265	+	0.0290151i
$936$		0			0
$937$	−55.8623			−1.82494			−0.912472	−	0.409140i	$-0.865829\pi$
$937$	−55.8623			−1.82494			−0.912472	+	0.409140i	$0.865829\pi$
$938$	33.5481	+	9.67910i	1.09538	+	0.316034i
$939$		0			0
$940$	−5.76663	−	10.6500i	−0.188087	−	0.347363i
$941$	10.7190	−	18.5659i	0.349430	−	0.605231i	−0.636718	−	0.771097i	$-0.719709\pi$
$941$	10.7190	−	18.5659i	0.349430	−	0.605231i	0.986148	+	0.165866i	$0.0530419\pi$
$942$		0			0
$943$	20.8284	+	36.0759i	0.678267	+	1.17479i
$944$	−3.08716			−0.100478
$945$		0			0
$946$	−15.1765			−0.493431
$947$	10.2729	+	17.7933i	0.333826	+	0.578203i	0.983259	−	0.182216i	$-0.0583269\pi$
$947$	10.2729	+	17.7933i	0.333826	+	0.578203i	−0.649433	+	0.760419i	$0.724994\pi$
$948$		0			0
$949$	−23.3341	+	40.4159i	−0.757457	+	1.31195i
$950$	−33.1874	−	21.6607i	−1.07674	−	0.702767i
$951$		0			0
$952$	0.369316	+	1.49162i	0.0119696	+	0.0483438i
$953$	47.6780			1.54444			0.772220	−	0.635355i	$-0.219146\pi$
$953$	47.6780			1.54444			0.772220	+	0.635355i	$0.219146\pi$
$954$		0			0
$955$	−9.91120	+	16.1320i	−0.320719	+	0.522019i
$956$			23.0178i			0.744448i
$957$		0			0
$958$	0.0620969	+	0.107555i	0.00200626	+	0.00347495i
$959$	6.49707	−	22.5191i	0.209801	−	0.727178i
$960$		0			0
$961$	−14.5441	−	25.1911i	−0.469165	−	0.812618i
$962$	−12.3080	+	7.10601i	−0.396825	+	0.229107i
$963$		0			0
$964$	−5.92882	−	3.42300i	−0.190954	−	0.110248i
$965$	5.07544	+	0.138740i	0.163384	+	0.00446621i
$966$		0			0
$967$	8.54536	−	4.93367i	0.274800	−	0.158656i	−0.356267	−	0.934384i	$-0.615951\pi$
$967$	8.54536	−	4.93367i	0.274800	−	0.158656i	0.631067	+	0.775728i	$0.282617\pi$
$968$	−9.29692			−0.298814
$969$		0			0
$970$	−22.6533	+	12.2660i	−0.727353	+	0.393839i
$971$	25.6986	−	44.5114i	0.824709	−	1.42844i	−0.0774332	−	0.996998i	$-0.524672\pi$
$971$	25.6986	−	44.5114i	0.824709	−	1.42844i	0.902142	−	0.431440i	$-0.141994\pi$
$972$		0			0
$973$	1.02730	+	4.14914i	0.0329337	+	0.133015i
$974$	22.4789	+	12.9782i	0.720271	+	0.415849i
$975$		0			0
$976$	−1.83643	−	1.06026i	−0.0587827	−	0.0339382i
$977$	−5.62485	+	9.74253i	−0.179955	+	0.311691i	−0.941865	−	0.335992i	$-0.890929\pi$
$977$	−5.62485	+	9.74253i	−0.179955	+	0.311691i	0.761910	+	0.647683i	$0.224262\pi$
$978$		0			0
$979$	3.05681	+	1.76485i	0.0976960	+	0.0564048i
$980$	−8.69674	+	13.0141i	−0.277807	+	0.415720i
$981$		0			0
$982$	−17.4877	−	10.0965i	−0.558056	−	0.322194i
$983$			47.4181i			1.51240i	0.654338	+	0.756202i	$0.272947\pi$
$983$			47.4181i			1.51240i	−0.654338	+	0.756202i	$0.727053\pi$
$984$		0			0
$985$	25.5905	−	13.8565i	0.815382	−	0.441504i
$986$	−0.0420996	−	0.0729186i	−0.00134072	−	0.00232220i
$987$		0			0
$988$	−41.6463	−	24.0445i	−1.32494	−	0.764957i
$989$	66.1930	+	38.2165i	2.10481	+	1.21522i
$990$		0			0
$991$	16.8939	+	29.2611i	0.536653	+	0.929511i	0.999081	+	0.0428538i	$0.0136450\pi$
$991$	16.8939	+	29.2611i	0.536653	+	0.929511i	−0.462428	+	0.886657i	$0.653022\pi$
$992$	−1.19742	+	0.691334i	−0.0380183	+	0.0219499i
$993$		0			0
$994$	−6.58411	−	26.5924i	−0.208835	−	0.843460i
$995$	3.74245	−	6.09141i	0.118644	−	0.193111i
$996$		0			0
$997$	16.7948			0.531898			0.265949	−	0.963987i	$-0.414315\pi$
$997$	16.7948			0.531898			0.265949	+	0.963987i	$0.414315\pi$
$998$	−3.80999	−	6.59910i	−0.120603	−	0.208891i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.r.b.89.5		48
3.2	odd	2		630.2.r.a.299.8	yes	48
5.4	even	2		1890.2.r.a.89.5		48
7.3	odd	6		1890.2.bi.a.899.13		48
9.4	even	3		630.2.bi.a.509.10	yes	48
9.5	odd	6		1890.2.bi.b.719.5		48
15.14	odd	2		630.2.r.b.299.17	yes	48
21.17	even	6		630.2.bi.b.479.15	yes	48
35.24	odd	6		1890.2.bi.b.899.5		48
45.4	even	6		630.2.bi.b.509.15	yes	48
45.14	odd	6		1890.2.bi.a.719.13		48
63.31	odd	6		630.2.r.b.59.17	yes	48
63.59	even	6		1890.2.r.a.1529.5		48
105.59	even	6		630.2.bi.a.479.10	yes	48
315.59	even	6	inner	1890.2.r.b.1529.5		48
315.94	odd	6		630.2.r.a.59.8	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.8	✓	48	315.94	odd	6
630.2.r.a.299.8	yes	48	3.2	odd	2
630.2.r.b.59.17	yes	48	63.31	odd	6
630.2.r.b.299.17	yes	48	15.14	odd	2
630.2.bi.a.479.10	yes	48	105.59	even	6
630.2.bi.a.509.10	yes	48	9.4	even	3
630.2.bi.b.479.15	yes	48	21.17	even	6
630.2.bi.b.509.15	yes	48	45.4	even	6
1890.2.r.a.89.5		48	5.4	even	2
1890.2.r.a.1529.5		48	63.59	even	6
1890.2.r.b.89.5		48	1.1	even	1	trivial
1890.2.r.b.1529.5		48	315.59	even	6	inner
1890.2.bi.a.719.13		48	45.14	odd	6
1890.2.bi.a.899.13		48	7.3	odd	6
1890.2.bi.b.719.5		48	9.5	odd	6
1890.2.bi.b.899.5		48	35.24	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.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.96632 + 1.06470i) q^{5} +(-0.733422 + 2.54206i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.96632 + 1.06470i) q^{5} +(-0.733422 + 2.54206i) q^{7} -1.00000 q^{8} +(-1.90522 - 1.17053i) q^{10} +1.30502i q^{11} +(-3.03357 - 5.25429i) q^{13} +(-2.56820 + 0.635870i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.502991 + 0.290402i) q^{17} +(-6.86424 - 3.96307i) q^{19} +(0.0611015 - 2.23523i) q^{20} +(-1.13018 + 0.652510i) q^{22} +6.57244 q^{23} +(2.73282 - 4.18708i) q^{25} +(3.03357 - 5.25429i) q^{26} +(-1.83478 - 1.90619i) q^{28} +(0.125548 + 0.0724850i) q^{29} +(-1.19742 - 0.691334i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.502991 - 0.290402i) q^{34} +(-1.26440 - 5.77939i) q^{35} +(-2.02863 - 1.17123i) q^{37} -7.92614i q^{38} +(1.96632 - 1.06470i) q^{40} +(3.16905 + 5.48896i) q^{41} +(10.0713 + 5.81466i) q^{43} +(-1.13018 - 0.652510i) q^{44} +(3.28622 + 5.69190i) q^{46} +(4.69056 - 2.70810i) q^{47} +(-5.92418 - 3.72881i) q^{49} +(4.99253 + 0.273152i) q^{50} +6.06713 q^{52} +(-4.19068 - 7.25846i) q^{53} +(-1.38946 - 2.56609i) q^{55} +(0.733422 - 2.54206i) q^{56} +0.144970i q^{58} +(1.54358 - 2.67356i) q^{59} +(1.83643 - 1.06026i) q^{61} -1.38267i q^{62} +1.00000 q^{64} +(11.5592 + 7.10177i) q^{65} +(-11.4291 - 6.59859i) q^{67} -0.580804i q^{68} +(4.37290 - 3.98469i) q^{70} +10.3545i q^{71} +(-3.84599 - 6.66144i) q^{73} -2.34246i q^{74} +(6.86424 - 3.96307i) q^{76} +(-3.31745 - 0.957131i) q^{77} +(3.54596 + 6.14179i) q^{79} +(1.90522 + 1.17053i) q^{80} +(-3.16905 + 5.48896i) q^{82} +(-4.32983 - 2.49983i) q^{83} +(0.679850 - 1.10656i) q^{85} +11.6293i q^{86} -1.30502i q^{88} +(1.35235 - 2.34234i) q^{89} +(15.5816 - 3.85791i) q^{91} +(-3.28622 + 5.69190i) q^{92} +(4.69056 + 2.70810i) q^{94} +(17.7168 + 0.484299i) q^{95} +(5.76032 - 9.97717i) q^{97} +(0.267153 - 6.99490i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8}+O(q^{10}) \) 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} - 3 q^{14} - 24 q^{16} + 6 q^{22} + 6 q^{23} - 3 q^{28} + 3 q^{29} + 24 q^{32} - 18 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} + 42 q^{55} - 9 q^{61} + 48 q^{64} + 33 q^{65} - 33 q^{67} - 6 q^{70} + 18 q^{73} - 6 q^{77} + 3 q^{82} + 9 q^{83} - 33 q^{85} - 33 q^{89} - 3 q^{92} - 33 q^{95} + 24 q^{97} - 3 q^{98}+O(q^{100}) \) 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8 - 3 * q^14 - 24 * q^16 + 6 * q^22 + 6 * q^23 - 3 * q^28 + 3 * q^29 + 24 * q^32 - 18 * q^35 - 3 * q^41 + 6 * q^44 + 3 * q^46 - 6 * q^49 + 18 * q^50 + 42 * q^55 - 9 * q^61 + 48 * q^64 + 33 * q^65 - 33 * q^67 - 6 * q^70 + 18 * q^73 - 6 * q^77 + 3 * q^82 + 9 * q^83 - 33 * q^85 - 33 * q^89 - 3 * q^92 - 33 * q^95 + 24 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more