LMFDB - Embedded newform 1638.2.bj.h.1135.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 $ x^16 - 2x^15 + 2x^14 + 18x^13 + 143x^12 - 148x^11 + 172x^10 + 1612x^9 + 6655x^8 + 478x^7 + 1106x^6 + 11266x^5 + 55249x^4 + 8856x^3 + 288x^2 + 7488*x + 97344
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1135.7
Root			$2.48294 - 2.48294i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.h.127.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.145508i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.145508i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.0727538 - 0.126013i) q^{10} +(1.30736 + 0.754806i) q^{11} +(-2.95619 + 2.06420i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.160487 + 0.277972i) q^{17} +(-1.44811 + 0.836065i) q^{19} +(0.126013 - 0.0727538i) q^{20} +(0.754806 + 1.30736i) q^{22} +(-2.75250 + 4.76747i) q^{23} +4.97883 q^{25} +(-3.59224 + 0.309553i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(-4.59467 + 7.95821i) q^{29} -0.879471i q^{31} +(-0.866025 + 0.500000i) q^{32} +0.320974i q^{34} +(0.0727538 + 0.126013i) q^{35} +(3.14281 + 1.81450i) q^{37} -1.67213 q^{38} +0.145508 q^{40} +(1.12780 + 0.651136i) q^{41} +(0.499222 + 0.864677i) q^{43} +1.50961i q^{44} +(-4.76747 + 2.75250i) q^{46} +1.30183i q^{47} +(0.500000 - 0.866025i) q^{49} +(4.31179 + 2.48941i) q^{50} +(-3.26575 - 1.52804i) q^{52} -5.12731 q^{53} +(0.109830 - 0.190231i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-7.95821 + 4.59467i) q^{58} +(-2.78339 + 1.60699i) q^{59} +(1.63869 + 2.83829i) q^{61} +(0.439735 - 0.761644i) q^{62} -1.00000 q^{64} +(0.300357 + 0.430148i) q^{65} +(1.99785 + 1.15346i) q^{67} +(-0.160487 + 0.277972i) q^{68} +0.145508i q^{70} +(-6.10671 + 3.52571i) q^{71} -1.35714i q^{73} +(1.81450 + 3.14281i) q^{74} +(-1.44811 - 0.836065i) q^{76} -1.50961 q^{77} +8.66217 q^{79} +(0.126013 + 0.0727538i) q^{80} +(0.651136 + 1.12780i) q^{82} +0.148560i q^{83} +(0.0404470 - 0.0233521i) q^{85} +0.998443i q^{86} +(-0.754806 + 1.30736i) q^{88} +(-7.13132 - 4.11727i) q^{89} +(1.52804 - 3.26575i) q^{91} -5.50500 q^{92} +(-0.650914 + 1.12742i) q^{94} +(0.121654 + 0.210711i) q^{95} +(11.4206 - 6.59366i) q^{97} +(0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} - 24 q^{50} - 4 q^{52} - 40 q^{53} + 20 q^{55} - 8 q^{56} + 6 q^{58} + 6 q^{59} - 2 q^{61} - 14 q^{62} - 16 q^{64} - 52 q^{65} - 30 q^{67} + 6 q^{68} + 12 q^{71} + 24 q^{74} + 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} + 30 q^{89} + 4 q^{91} - 24 q^{92} - 8 q^{94} - 40 q^{95} - 24 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^10 - 12 * q^11 + 10 * q^13 - 16 * q^14 - 8 * q^16 - 6 * q^17 - 4 * q^22 - 12 * q^23 - 20 * q^25 - 2 * q^26 + 16 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^40 + 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 - 24 * q^50 - 4 * q^52 - 40 * q^53 + 20 * q^55 - 8 * q^56 + 6 * q^58 + 6 * q^59 - 2 * q^61 - 14 * q^62 - 16 * q^64 - 52 * q^65 - 30 * q^67 + 6 * q^68 + 12 * q^71 + 24 * q^74 + 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 + 30 * q^89 + 4 * q^91 - 24 * q^92 - 8 * q^94 - 40 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	0.145508i		−	0.0650729i	−0.999471	−	0.0325365i	$-0.989641\pi$
$5$		−	0.145508i		−	0.0650729i	0.999471	−	0.0325365i	$-0.0103585\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.0727538	−	0.126013i	0.0230068	−	0.0398489i
$11$	1.30736	+	0.754806i	0.394184	+	0.227582i	0.683972	−	0.729509i	$-0.260251\pi$
$11$	1.30736	+	0.754806i	0.394184	+	0.227582i	−0.289787	+	0.957091i	$0.593585\pi$
$12$		0			0
$13$	−2.95619	+	2.06420i	−0.819900	+	0.572506i
$13$	−2.95619	+	2.06420i	−0.819900	+	0.572506i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.160487	+	0.277972i	0.0389238	+	0.0674180i	0.884831	−	0.465912i	$-0.154274\pi$
$17$	0.160487	+	0.277972i	0.0389238	+	0.0674180i	−0.845907	+	0.533330i	$0.820940\pi$
$18$		0			0
$19$	−1.44811	+	0.836065i	−0.332219	+	0.191807i	−0.656826	−	0.754042i	$-0.728101\pi$
$19$	−1.44811	+	0.836065i	−0.332219	+	0.191807i	0.324607	+	0.945849i	$0.394768\pi$
$20$	0.126013	−	0.0727538i	0.0281774	−	0.0162682i
$21$		0			0
$22$	0.754806	+	1.30736i	0.160925	+	0.278730i
$23$	−2.75250	+	4.76747i	−0.573936	+	0.994087i	0.422220	+	0.906493i	$0.361251\pi$
$23$	−2.75250	+	4.76747i	−0.573936	+	0.994087i	−0.996156	+	0.0875933i	$0.972082\pi$
$24$		0			0
$25$	4.97883			0.995766
$26$	−3.59224	+	0.309553i	−0.704496	+	0.0607083i
$27$		0			0
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	−4.59467	+	7.95821i	−0.853209	+	1.47780i	0.0250870	+	0.999685i	$0.492014\pi$
$29$	−4.59467	+	7.95821i	−0.853209	+	1.47780i	−0.878296	+	0.478117i	$0.841320\pi$
$30$		0			0
$31$		−	0.879471i		−	0.157958i	−0.996876	−	0.0789788i	$-0.974834\pi$
$31$		−	0.879471i		−	0.157958i	0.996876	−	0.0789788i	$-0.0251659\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			0.320974i			0.0550466i
$35$	0.0727538	+	0.126013i	0.0122976	+	0.0213001i
$36$		0			0
$37$	3.14281	+	1.81450i	0.516674	+	0.298302i	0.735573	−	0.677446i	$-0.236913\pi$
$37$	3.14281	+	1.81450i	0.516674	+	0.298302i	−0.218899	+	0.975748i	$0.570246\pi$
$38$	−1.67213			−0.271255
$39$		0			0
$40$	0.145508			0.0230068
$41$	1.12780	+	0.651136i	0.176133	+	0.101690i	0.585474	−	0.810691i	$-0.300908\pi$
$41$	1.12780	+	0.651136i	0.176133	+	0.101690i	−0.409342	+	0.912381i	$0.634242\pi$
$42$		0			0
$43$	0.499222	+	0.864677i	0.0761306	+	0.131862i	0.901577	−	0.432618i	$-0.142410\pi$
$43$	0.499222	+	0.864677i	0.0761306	+	0.131862i	−0.825447	+	0.564480i	$0.809077\pi$
$44$			1.50961i			0.227582i
$45$		0			0
$46$	−4.76747	+	2.75250i	−0.702925	+	0.405834i
$47$			1.30183i			0.189891i	0.995482	+	0.0949455i	$0.0302677\pi$
$47$			1.30183i			0.189891i	−0.995482	+	0.0949455i	$0.969732\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	4.31179	+	2.48941i	0.609779	+	0.352056i
$51$		0			0
$52$	−3.26575	−	1.52804i	−0.452878	−	0.211901i
$53$	−5.12731			−0.704290			−0.352145	−	0.935945i	$-0.614548\pi$
$53$	−5.12731			−0.704290			−0.352145	+	0.935945i	$0.614548\pi$
$54$		0			0
$55$	0.109830	−	0.190231i	0.0148095	−	0.0256507i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	−7.95821	+	4.59467i	−1.04496	+	0.603310i
$59$	−2.78339	+	1.60699i	−0.362367	+	0.209213i	−0.670119	−	0.742254i	$-0.733757\pi$
$59$	−2.78339	+	1.60699i	−0.362367	+	0.209213i	0.307751	+	0.951467i	$0.400423\pi$
$60$		0			0
$61$	1.63869	+	2.83829i	0.209813	+	0.363406i	0.951655	−	0.307168i	$-0.0993813\pi$
$61$	1.63869	+	2.83829i	0.209813	+	0.363406i	−0.741843	+	0.670574i	$0.766048\pi$
$62$	0.439735	−	0.761644i	0.0558464	−	0.0967289i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.300357	+	0.430148i	0.0372546	+	0.0533533i
$66$		0			0
$67$	1.99785	+	1.15346i	0.244076	+	0.140917i	0.617049	−	0.786925i	$-0.288328\pi$
$67$	1.99785	+	1.15346i	0.244076	+	0.140917i	−0.372973	+	0.927842i	$0.621661\pi$
$68$	−0.160487	+	0.277972i	−0.0194619	+	0.0337090i
$69$		0			0
$70$			0.145508i			0.0173915i
$71$	−6.10671	+	3.52571i	−0.724733	+	0.418425i	−0.816492	−	0.577356i	$-0.804084\pi$
$71$	−6.10671	+	3.52571i	−0.724733	+	0.418425i	0.0917590	+	0.995781i	$0.470751\pi$
$72$		0			0
$73$		−	1.35714i		−	0.158841i	−0.996841	−	0.0794205i	$-0.974693\pi$
$73$		−	1.35714i		−	0.158841i	0.996841	−	0.0794205i	$-0.0253070\pi$
$74$	1.81450	+	3.14281i	0.210931	+	0.365344i
$75$		0			0
$76$	−1.44811	−	0.836065i	−0.166109	−	0.0959033i
$77$	−1.50961			−0.172036
$78$		0			0
$79$	8.66217			0.974570			0.487285	−	0.873243i	$-0.337987\pi$
$79$	8.66217			0.974570			0.487285	+	0.873243i	$0.337987\pi$
$80$	0.126013	+	0.0727538i	0.0140887	+	0.00813412i
$81$		0			0
$82$	0.651136	+	1.12780i	0.0719059	+	0.124545i
$83$			0.148560i			0.0163065i	0.999967	+	0.00815326i	$0.00259529\pi$
$83$			0.148560i			0.0163065i	−0.999967	+	0.00815326i	$0.997405\pi$
$84$		0			0
$85$	0.0404470	−	0.0233521i	0.00438709	−	0.00253289i
$86$			0.998443i			0.107665i
$87$		0			0
$88$	−0.754806	+	1.30736i	−0.0804626	+	0.139365i
$89$	−7.13132	−	4.11727i	−0.755918	−	0.436430i	0.0719100	−	0.997411i	$-0.477091\pi$
$89$	−7.13132	−	4.11727i	−0.755918	−	0.436430i	−0.827828	+	0.560981i	$0.810424\pi$
$90$		0			0
$91$	1.52804	−	3.26575i	0.160182	−	0.342343i
$92$	−5.50500			−0.573936
$93$		0			0
$94$	−0.650914	+	1.12742i	−0.0671366	+	0.116284i
$95$	0.121654	+	0.210711i	0.0124814	+	0.0216184i
$96$		0			0
$97$	11.4206	−	6.59366i	1.15958	−	0.669485i	0.208378	−	0.978048i	$-0.433182\pi$
$97$	11.4206	−	6.59366i	1.15958	−	0.669485i	0.951204	+	0.308564i	$0.0998483\pi$
$98$	0.866025	−	0.500000i	0.0874818	−	0.0505076i
$99$		0			0
$100$	2.48941	+	4.31179i	0.248941	+	0.431179i
$101$	−7.66821	+	13.2817i	−0.763015	+	1.32158i	0.178275	+	0.983981i	$0.442948\pi$
$101$	−7.66821	+	13.2817i	−0.763015	+	1.32158i	−0.941290	+	0.337600i	$0.890385\pi$
$102$		0			0
$103$	−2.10888			−0.207794			−0.103897	−	0.994588i	$-0.533131\pi$
$103$	−2.10888			−0.207794			−0.103897	+	0.994588i	$0.533131\pi$
$104$	−2.06420	−	2.95619i	−0.202411	−	0.289879i
$105$		0			0
$106$	−4.44038	−	2.56366i	−0.431288	−	0.249004i
$107$	2.43608	−	4.21941i	0.235505	−	0.407906i	−0.723915	−	0.689890i	$-0.757659\pi$
$107$	2.43608	−	4.21941i	0.235505	−	0.407906i	0.959419	+	0.281984i	$0.0909924\pi$
$108$		0			0
$109$			10.4010i			0.996235i	0.867110	+	0.498117i	$0.165975\pi$
$109$			10.4010i			0.996235i	−0.867110	+	0.498117i	$0.834025\pi$
$110$	0.190231	−	0.109830i	0.0181378	−	0.0104719i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	5.94751	+	10.3014i	0.559495	+	0.969073i	0.997539	+	0.0701196i	$0.0223381\pi$
$113$	5.94751	+	10.3014i	0.559495	+	0.969073i	−0.438044	+	0.898954i	$0.644329\pi$
$114$		0			0
$115$	0.693703	+	0.400510i	0.0646881	+	0.0373477i
$116$	−9.18935			−0.853209
$117$		0			0
$118$	−3.21399			−0.295872
$119$	−0.277972	−	0.160487i	−0.0254816	−	0.0147118i
$120$		0			0
$121$	−4.36054	−	7.55267i	−0.396412	−	0.686606i
$122$			3.27738i			0.296720i
$123$		0			0
$124$	0.761644	−	0.439735i	0.0683976	−	0.0394894i
$125$		−	1.45199i		−	0.129870i
$126$		0			0
$127$	3.08832	−	5.34913i	0.274044	−	0.474659i	−0.695849	−	0.718188i	$-0.744972\pi$
$127$	3.08832	−	5.34913i	0.274044	−	0.474659i	0.969894	+	0.243529i	$0.0783052\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	0.0450423	+	0.522698i	0.00395047	+	0.0458436i
$131$	3.61986			0.316269			0.158134	−	0.987418i	$-0.449452\pi$
$131$	3.61986			0.316269			0.158134	+	0.987418i	$0.449452\pi$
$132$		0			0
$133$	0.836065	−	1.44811i	0.0724961	−	0.125567i
$134$	1.15346	+	1.99785i	0.0996437	+	0.172588i
$135$		0			0
$136$	−0.277972	+	0.160487i	−0.0238359	+	0.0137617i
$137$	−0.721249	+	0.416413i	−0.0616205	+	0.0355766i	−0.530494	−	0.847689i	$-0.677993\pi$
$137$	−0.721249	+	0.416413i	−0.0616205	+	0.0355766i	0.468873	+	0.883265i	$0.344660\pi$
$138$		0			0
$139$	−10.2247	−	17.7098i	−0.867250	−	1.50212i	−0.864795	−	0.502125i	$-0.832552\pi$
$139$	−10.2247	−	17.7098i	−0.867250	−	1.50212i	−0.00245526	−	0.999997i	$-0.500782\pi$
$140$	−0.0727538	+	0.126013i	−0.00614881	+	0.0106501i
$141$		0			0
$142$	−7.05142			−0.591742
$143$	−5.42288	+	0.467305i	−0.453484	+	0.0390780i
$144$		0			0
$145$	1.15798	+	0.668559i	0.0961649	+	0.0555208i
$146$	0.678569	−	1.17532i	0.0561588	−	0.0972699i
$147$		0			0
$148$			3.62900i			0.298302i
$149$	11.8482	−	6.84056i	0.970642	−	0.560401i	0.0712103	−	0.997461i	$-0.477314\pi$
$149$	11.8482	−	6.84056i	0.970642	−	0.560401i	0.899432	+	0.437061i	$0.143981\pi$
$150$		0			0
$151$			0.670713i			0.0545819i	0.999628	+	0.0272909i	$0.00868806\pi$
$151$			0.670713i			0.0545819i	−0.999628	+	0.0272909i	$0.991312\pi$
$152$	−0.836065	−	1.44811i	−0.0678139	−	0.117457i
$153$		0			0
$154$	−1.30736	−	0.754806i	−0.105350	−	0.0608240i
$155$	−0.127970			−0.0102788
$156$		0			0
$157$	8.76914			0.699853			0.349927	−	0.936777i	$-0.386207\pi$
$157$	8.76914			0.699853			0.349927	+	0.936777i	$0.386207\pi$
$158$	7.50166	+	4.33108i	0.596800	+	0.344562i
$159$		0			0
$160$	0.0727538	+	0.126013i	0.00575169	+	0.00996222i
$161$		−	5.50500i		−	0.433855i
$162$		0			0
$163$	8.03647	−	4.63986i	0.629465	−	0.363422i	−0.151080	−	0.988522i	$-0.548275\pi$
$163$	8.03647	−	4.63986i	0.629465	−	0.363422i	0.780545	+	0.625100i	$0.214942\pi$
$164$			1.30227i			0.101690i
$165$		0			0
$166$	−0.0742798	+	0.128656i	−0.00576523	+	0.00998567i
$167$	4.05876	+	2.34332i	0.314076	+	0.181332i	0.648749	−	0.761002i	$-0.275293\pi$
$167$	4.05876	+	2.34332i	0.314076	+	0.181332i	−0.334673	+	0.942334i	$0.608626\pi$
$168$		0			0
$169$	4.47816	−	12.2043i	0.344474	−	0.938796i
$170$	0.0467041			0.00358204
$171$		0			0
$172$	−0.499222	+	0.864677i	−0.0380653	+	0.0659310i
$173$	−9.43684	−	16.3451i	−0.717470	−	1.24269i	−0.961999	−	0.273052i	$-0.911967\pi$
$173$	−9.43684	−	16.3451i	−0.717470	−	1.24269i	0.244530	−	0.969642i	$-0.421366\pi$
$174$		0			0
$175$	−4.31179	+	2.48941i	−0.325941	+	0.188182i
$176$	−1.30736	+	0.754806i	−0.0985461	+	0.0568956i
$177$		0			0
$178$	−4.11727	−	7.13132i	−0.308602	−	0.534515i
$179$	−8.97371	+	15.5429i	−0.670727	+	1.16173i	0.306972	+	0.951719i	$0.400684\pi$
$179$	−8.97371	+	15.5429i	−0.670727	+	1.16173i	−0.977698	+	0.210014i	$0.932649\pi$
$180$		0			0
$181$	10.0206			0.744825			0.372412	−	0.928067i	$-0.378531\pi$
$181$	10.0206			0.744825			0.372412	+	0.928067i	$0.378531\pi$
$182$	2.95619	−	2.06420i	0.219128	−	0.153009i
$183$		0			0
$184$	−4.76747	−	2.75250i	−0.351463	−	0.202917i
$185$	0.264023	−	0.457302i	0.0194114	−	0.0336215i
$186$		0			0
$187$			0.484546i			0.0354335i
$188$	−1.12742	+	0.650914i	−0.0822252	+	0.0474728i
$189$		0			0
$190$			0.243308i			0.0176514i
$191$	3.82269	+	6.62109i	0.276600	+	0.479085i	0.970538	−	0.240950i	$-0.0774590\pi$
$191$	3.82269	+	6.62109i	0.276600	+	0.479085i	−0.693938	+	0.720035i	$0.744126\pi$
$192$		0			0
$193$	15.8631	+	9.15855i	1.14185	+	0.659247i	0.946888	−	0.321564i	$-0.104209\pi$
$193$	15.8631	+	9.15855i	1.14185	+	0.659247i	0.194961	+	0.980811i	$0.437542\pi$
$194$	13.1873			0.946794
$195$		0			0
$196$	1.00000			0.0714286
$197$	13.9813	+	8.07212i	0.996128	+	0.575115i	0.907100	−	0.420915i	$-0.138291\pi$
$197$	13.9813	+	8.07212i	0.996128	+	0.575115i	0.0890273	+	0.996029i	$0.471624\pi$
$198$		0			0
$199$	−12.9703	−	22.4652i	−0.919438	−	1.59251i	−0.800270	−	0.599640i	$-0.795310\pi$
$199$	−12.9703	−	22.4652i	−0.919438	−	1.59251i	−0.119169	−	0.992874i	$-0.538023\pi$
$200$			4.97883i			0.352056i
$201$		0			0
$202$	−13.2817	+	7.66821i	−0.934499	+	0.539533i
$203$		−	9.18935i		−	0.644966i
$204$		0			0
$205$	0.0947452	−	0.164103i	0.00661729	−	0.0114615i
$206$	−1.82634	−	1.05444i	−0.127247	−	0.0734662i
$207$		0			0
$208$	−0.309553	−	3.59224i	−0.0214636	−	0.249077i
$209$	−2.52427			−0.174607
$210$		0			0
$211$	5.02188	−	8.69815i	0.345721	−	0.598806i	−0.639764	−	0.768572i	$-0.720968\pi$
$211$	5.02188	−	8.69815i	0.345721	−	0.598806i	0.985484	+	0.169766i	$0.0543012\pi$
$212$	−2.56366	−	4.44038i	−0.176073	−	0.304967i
$213$		0			0
$214$	4.21941	−	2.43608i	0.288433	−	0.166527i
$215$	0.125817	−	0.0726405i	0.00858065	−	0.00495404i
$216$		0			0
$217$	0.439735	+	0.761644i	0.0298512	+	0.0517038i
$218$	−5.20050	+	9.00753i	−0.352222	+	0.610067i
$219$		0			0
$220$	0.219660			0.0148095
$221$	−1.04822	−	0.490461i	−0.0705109	−	0.0329920i
$222$		0			0
$223$	−7.39252	−	4.26807i	−0.495040	−	0.285811i	0.231623	−	0.972806i	$-0.425596\pi$
$223$	−7.39252	−	4.26807i	−0.495040	−	0.285811i	−0.726663	+	0.686994i	$0.758930\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$			11.8950i			0.791245i
$227$	8.65098	−	4.99464i	0.574186	−	0.331506i	−0.184634	−	0.982807i	$-0.559110\pi$
$227$	8.65098	−	4.99464i	0.574186	−	0.331506i	0.758819	+	0.651301i	$0.225777\pi$
$228$		0			0
$229$			18.1455i			1.19909i	0.800341	+	0.599544i	$0.204652\pi$
$229$			18.1455i			1.19909i	−0.800341	+	0.599544i	$0.795348\pi$
$230$	0.400510	+	0.693703i	0.0264088	+	0.0457414i
$231$		0			0
$232$	−7.95821	−	4.59467i	−0.522482	−	0.301655i
$233$	−3.58850			−0.235091			−0.117545	−	0.993068i	$-0.537503\pi$
$233$	−3.58850			−0.235091			−0.117545	+	0.993068i	$0.537503\pi$
$234$		0			0
$235$	0.189426			0.0123568
$236$	−2.78339	−	1.60699i	−0.181184	−	0.104606i
$237$		0			0
$238$	−0.160487	−	0.277972i	−0.0104028	−	0.0180182i
$239$			12.0553i			0.779794i	0.920858	+	0.389897i	$0.127489\pi$
$239$			12.0553i			0.779794i	−0.920858	+	0.389897i	$0.872511\pi$
$240$		0			0
$241$	9.68612	−	5.59229i	0.623938	−	0.360231i	−0.154463	−	0.987999i	$-0.549365\pi$
$241$	9.68612	−	5.59229i	0.623938	−	0.360231i	0.778401	+	0.627768i	$0.216031\pi$
$242$		−	8.72107i		−	0.560612i
$243$		0			0
$244$	−1.63869	+	2.83829i	−0.104906	+	0.181703i
$245$	−0.126013	−	0.0727538i	−0.00805069	−	0.00464807i
$246$		0			0
$247$	2.55508	−	5.46076i	0.162576	−	0.347460i
$248$	0.879471			0.0558464
$249$		0			0
$250$	0.725997	−	1.25746i	0.0459161	−	0.0795290i
$251$	−8.28386	−	14.3481i	−0.522873	−	0.905642i	−0.999646	−	0.0266158i	$-0.991527\pi$
$251$	−8.28386	−	14.3481i	−0.522873	−	0.905642i	0.476773	−	0.879027i	$-0.341806\pi$
$252$		0			0
$253$	−7.19703	+	4.15521i	−0.452473	+	0.261236i
$254$	5.34913	−	3.08832i	0.335634	−	0.193779i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.63157	−	16.6824i	0.600801	−	1.04062i	−0.391899	−	0.920008i	$-0.628182\pi$
$257$	9.63157	−	16.6824i	0.600801	−	1.04062i	0.992700	−	0.120610i	$-0.0384849\pi$
$258$		0			0
$259$	−3.62900			−0.225495
$260$	−0.222341	+	0.475191i	−0.0137890	+	0.0294701i
$261$		0			0
$262$	3.13489	+	1.80993i	0.193674	+	0.111818i
$263$	8.66445	−	15.0073i	0.534273	−	0.925388i	−0.464925	−	0.885350i	$-0.653919\pi$
$263$	8.66445	−	15.0073i	0.534273	−	0.925388i	0.999198	−	0.0400377i	$-0.0127478\pi$
$264$		0			0
$265$			0.746062i			0.0458302i
$266$	1.44811	−	0.836065i	0.0887892	−	0.0512625i
$267$		0			0
$268$			2.30692i			0.140917i
$269$	5.13383	+	8.89206i	0.313015	+	0.542158i	0.979014	−	0.203795i	$-0.0653276\pi$
$269$	5.13383	+	8.89206i	0.313015	+	0.542158i	−0.665998	+	0.745953i	$0.731994\pi$
$270$		0			0
$271$	1.46333	+	0.844854i	0.0888909	+	0.0513212i	0.543787	−	0.839224i	$-0.316990\pi$
$271$	1.46333	+	0.844854i	0.0888909	+	0.0513212i	−0.454896	+	0.890545i	$0.650323\pi$
$272$	−0.320974			−0.0194619
$273$		0			0
$274$	−0.832827			−0.0503129
$275$	6.50913	+	3.75805i	0.392515	+	0.226619i
$276$		0			0
$277$	7.28198	+	12.6128i	0.437532	+	0.757827i	0.997498	−	0.0706879i	$-0.0225195\pi$
$277$	7.28198	+	12.6128i	0.437532	+	0.757827i	−0.559967	+	0.828515i	$0.689186\pi$
$278$		−	20.4495i		−	1.22648i
$279$		0			0
$280$	−0.126013	+	0.0727538i	−0.00753073	+	0.00434787i
$281$			21.9861i			1.31158i	0.754943	+	0.655790i	$0.227664\pi$
$281$			21.9861i			1.31158i	−0.754943	+	0.655790i	$0.772336\pi$
$282$		0			0
$283$	−10.5460	+	18.2662i	−0.626893	+	1.08581i	0.361278	+	0.932458i	$0.382341\pi$
$283$	−10.5460	+	18.2662i	−0.626893	+	1.08581i	−0.988171	+	0.153353i	$0.950993\pi$
$284$	−6.10671	−	3.52571i	−0.362367	−	0.209212i
$285$		0			0
$286$	−4.93001	−	2.30674i	−0.291517	−	0.136401i
$287$	−1.30227			−0.0768707
$288$		0			0
$289$	8.44849	−	14.6332i	0.496970	−	0.860777i
$290$	0.668559	+	1.15798i	0.0392592	+	0.0679989i
$291$		0			0
$292$	1.17532	−	0.678569i	0.0687802	−	0.0397103i
$293$	11.3293	−	6.54097i	0.661864	−	0.382128i	−0.131123	−	0.991366i	$-0.541858\pi$
$293$	11.3293	−	6.54097i	0.661864	−	0.382128i	0.792987	+	0.609239i	$0.208525\pi$
$294$		0			0
$295$	0.233830	+	0.405005i	0.0136141	+	0.0235803i
$296$	−1.81450	+	3.14281i	−0.105466	+	0.182672i
$297$		0			0
$298$	13.6811			0.792526
$299$	−1.70409	−	19.7753i	−0.0985501	−	1.14363i
$300$		0			0
$301$	−0.864677	−	0.499222i	−0.0498392	−	0.0287747i
$302$	−0.335357	+	0.580855i	−0.0192976	+	0.0334244i
$303$		0			0
$304$		−	1.67213i		−	0.0959033i
$305$	0.412993	−	0.238441i	0.0236479	−	0.0136531i
$306$		0			0
$307$		−	27.5551i		−	1.57266i	−0.617810	−	0.786328i	$-0.711980\pi$
$307$		−	27.5551i		−	1.57266i	0.617810	−	0.786328i	$-0.288020\pi$
$308$	−0.754806	−	1.30736i	−0.0430090	−	0.0744939i
$309$		0			0
$310$	−0.110825	−	0.0639848i	−0.00629443	−	0.00363409i
$311$	−9.19192			−0.521226			−0.260613	−	0.965443i	$-0.583925\pi$
$311$	−9.19192			−0.521226			−0.260613	+	0.965443i	$0.583925\pi$
$312$		0			0
$313$	25.4372			1.43779			0.718897	−	0.695117i	$-0.244647\pi$
$313$	25.4372			1.43779			0.718897	+	0.695117i	$0.244647\pi$
$314$	7.59429	+	4.38457i	0.428571	+	0.247435i
$315$		0			0
$316$	4.33108	+	7.50166i	0.243642	+	0.422001i
$317$		−	26.0786i		−	1.46472i	−0.680917	−	0.732361i	$-0.738418\pi$
$317$		−	26.0786i		−	1.46472i	0.680917	−	0.732361i	$-0.261582\pi$
$318$		0			0
$319$	−12.0138	+	6.93617i	−0.672644	+	0.388351i
$320$			0.145508i			0.00813412i
$321$		0			0
$322$	2.75250	−	4.76747i	0.153391	−	0.265681i
$323$	−0.464805	−	0.268355i	−0.0258624	−	0.0149317i
$324$		0			0
$325$	−14.7184	+	10.2773i	−0.816429	+	0.570082i
$326$	9.27972			0.513956
$327$		0			0
$328$	−0.651136	+	1.12780i	−0.0359530	+	0.0622724i
$329$	−0.650914	−	1.12742i	−0.0358860	−	0.0621564i
$330$		0			0
$331$	−3.80635	+	2.19759i	−0.209216	+	0.120791i	−0.600947	−	0.799289i	$-0.705210\pi$
$331$	−3.80635	+	2.19759i	−0.209216	+	0.120791i	0.391731	+	0.920080i	$0.371876\pi$
$332$	−0.128656	+	0.0742798i	−0.00706093	+	0.00407663i
$333$		0			0
$334$	2.34332	+	4.05876i	0.128221	+	0.222085i
$335$	0.167837	−	0.290702i	0.00916991	−	0.0158828i
$336$		0			0
$337$	−9.08845			−0.495080			−0.247540	−	0.968878i	$-0.579622\pi$
$337$	−9.08845			−0.495080			−0.247540	+	0.968878i	$0.579622\pi$
$338$	9.98037	−	8.33020i	0.542861	−	0.453103i
$339$		0			0
$340$	0.0404470	+	0.0233521i	0.00219355	+	0.00126644i
$341$	0.663829	−	1.14979i	0.0359484	−	0.0622644i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−0.864677	+	0.499222i	−0.0466203	+	0.0269162i
$345$		0			0
$346$		−	18.8737i		−	1.01466i
$347$	6.90968	+	11.9679i	0.370931	+	0.642471i	0.989709	−	0.143095i	$-0.0457053\pi$
$347$	6.90968	+	11.9679i	0.370931	+	0.642471i	−0.618778	+	0.785566i	$0.712372\pi$
$348$		0			0
$349$	20.2260	+	11.6775i	1.08267	+	0.625082i	0.931616	−	0.363443i	$-0.118399\pi$
$349$	20.2260	+	11.6775i	1.08267	+	0.625082i	0.151057	+	0.988525i	$0.451732\pi$
$350$	−4.97883			−0.266130
$351$		0			0
$352$	−1.50961			−0.0804626
$353$	16.9040	+	9.75955i	0.899711	+	0.519448i	0.877106	−	0.480296i	$-0.159471\pi$
$353$	16.9040	+	9.75955i	0.899711	+	0.519448i	0.0226046	+	0.999744i	$0.492804\pi$
$354$		0			0
$355$	0.513017	+	0.888572i	0.0272281	+	0.0471605i
$356$		−	8.23454i		−	0.436430i
$357$		0			0
$358$	−15.5429	+	8.97371i	−0.821469	+	0.474275i
$359$		−	31.0158i		−	1.63695i	−0.574542	−	0.818475i	$-0.694820\pi$
$359$		−	31.0158i		−	1.63695i	0.574542	−	0.818475i	$-0.305180\pi$
$360$		0			0
$361$	−8.10199	+	14.0331i	−0.426420	+	0.738582i
$362$	8.67809	+	5.01030i	0.456110	+	0.263335i
$363$		0			0
$364$	3.59224	−	0.309553i	0.188284	−	0.0162250i
$365$	−0.197474			−0.0103363
$366$		0			0
$367$	0.155016	−	0.268496i	0.00809178	−	0.0140154i	−0.861951	−	0.506991i	$-0.830758\pi$
$367$	0.155016	−	0.268496i	0.00809178	−	0.0140154i	0.870043	+	0.492976i	$0.164091\pi$
$368$	−2.75250	−	4.76747i	−0.143484	−	0.248522i
$369$		0			0
$370$	0.457302	−	0.264023i	0.0237740	−	0.0137259i
$371$	4.44038	−	2.56366i	0.230533	−	0.133098i
$372$		0			0
$373$	4.99428	+	8.65035i	0.258594	+	0.447898i	0.965866	−	0.259044i	$-0.0834075\pi$
$373$	4.99428	+	8.65035i	0.258594	+	0.447898i	−0.707271	+	0.706942i	$0.750074\pi$
$374$	−0.242273	+	0.419629i	−0.0125276	+	0.0216985i
$375$		0			0
$376$	−1.30183			−0.0671366
$377$	−2.84459	−	33.0103i	−0.146504	−	1.70012i
$378$		0			0
$379$	−11.3451	−	6.55010i	−0.582759	−	0.336456i	0.179470	−	0.983763i	$-0.442562\pi$
$379$	−11.3451	−	6.55010i	−0.582759	−	0.336456i	−0.762229	+	0.647308i	$0.775895\pi$
$380$	−0.121654	+	0.210711i	−0.00624071	+	0.0108092i
$381$		0			0
$382$			7.64537i			0.391171i
$383$	26.9468	−	15.5577i	1.37692	−	0.794962i	0.385128	−	0.922863i	$-0.374157\pi$
$383$	26.9468	−	15.5577i	1.37692	−	0.794962i	0.991787	+	0.127901i	$0.0408239\pi$
$384$		0			0
$385$			0.219660i			0.0111949i
$386$	9.15855	+	15.8631i	0.466158	+	0.807409i
$387$		0			0
$388$	11.4206	+	6.59366i	0.579791	+	0.334742i
$389$	8.82237			0.447312			0.223656	−	0.974668i	$-0.428201\pi$
$389$	8.82237			0.447312			0.223656	+	0.974668i	$0.428201\pi$
$390$		0			0
$391$	−1.76696			−0.0893592
$392$	0.866025	+	0.500000i	0.0437409	+	0.0252538i
$393$		0			0
$394$	8.07212	+	13.9813i	0.406667	+	0.704369i
$395$		−	1.26041i		−	0.0634181i
$396$		0			0
$397$	7.41327	−	4.28006i	0.372062	−	0.214810i	−0.302297	−	0.953214i	$-0.597753\pi$
$397$	7.41327	−	4.28006i	0.372062	−	0.214810i	0.674359	+	0.738404i	$0.264420\pi$
$398$		−	25.9406i		−	1.30028i
$399$		0			0
$400$	−2.48941	+	4.31179i	−0.124471	+	0.215590i
$401$	−3.80943	−	2.19937i	−0.190234	−	0.109831i	0.401858	−	0.915702i	$-0.368364\pi$
$401$	−3.80943	−	2.19937i	−0.190234	−	0.109831i	−0.592092	+	0.805870i	$0.701698\pi$
$402$		0			0
$403$	1.81540	+	2.59989i	0.0904317	+	0.129510i
$404$	−15.3364			−0.763015
$405$		0			0
$406$	4.59467	−	7.95821i	0.228030	−	0.394959i
$407$	2.73919	+	4.74442i	0.135777	+	0.235172i
$408$		0			0
$409$	−14.3012	+	8.25679i	−0.707148	+	0.408272i	−0.810004	−	0.586424i	$-0.800535\pi$
$409$	−14.3012	+	8.25679i	−0.707148	+	0.408272i	0.102856	+	0.994696i	$0.467202\pi$
$410$	0.164103	−	0.0947452i	0.00810449	−	0.00467913i
$411$		0			0
$412$	−1.05444	−	1.82634i	−0.0519484	−	0.0899773i
$413$	1.60699	−	2.78339i	0.0790750	−	0.136962i
$414$		0			0
$415$	0.0216165			0.00106111
$416$	1.52804	−	3.26575i	0.0749182	−	0.160116i
$417$		0			0
$418$	−2.18608	−	1.26213i	−0.106925	−	0.0617330i
$419$	16.4980	−	28.5753i	0.805979	−	1.39600i	−0.109649	−	0.993970i	$-0.534973\pi$
$419$	16.4980	−	28.5753i	0.805979	−	1.39600i	0.915628	−	0.402027i	$-0.131694\pi$
$420$		0			0
$421$		−	1.67311i		−	0.0815425i	−0.999169	−	0.0407713i	$-0.987019\pi$
$421$		−	1.67311i		−	0.0815425i	0.999169	−	0.0407713i	$-0.0129815\pi$
$422$	8.69815	−	5.02188i	0.423419	−	0.244461i
$423$		0			0
$424$		−	5.12731i		−	0.249004i
$425$	0.799037	+	1.38397i	0.0387590	+	0.0671326i
$426$		0			0
$427$	−2.83829	−	1.63869i	−0.137355	−	0.0793017i
$428$	4.87216			0.235505
$429$		0			0
$430$	0.145281			0.00700607
$431$	5.64693	+	3.26026i	0.272003	+	0.157041i	0.629798	−	0.776759i	$-0.283138\pi$
$431$	5.64693	+	3.26026i	0.272003	+	0.157041i	−0.357794	+	0.933800i	$0.616471\pi$
$432$		0			0
$433$	−0.0128517	−	0.0222598i	−0.000617613	−	0.00106974i	0.865716	−	0.500535i	$-0.166863\pi$
$433$	−0.0128517	−	0.0222598i	−0.000617613	−	0.00106974i	−0.866334	+	0.499465i	$0.833530\pi$
$434$			0.879471i			0.0422159i
$435$		0			0
$436$	−9.00753	+	5.20050i	−0.431382	+	0.249059i
$437$		−	9.20508i		−	0.440339i
$438$		0			0
$439$	−15.0983	+	26.1509i	−0.720600	+	1.24812i	0.240159	+	0.970733i	$0.422800\pi$
$439$	−15.0983	+	26.1509i	−0.720600	+	1.24812i	−0.960760	+	0.277383i	$0.910533\pi$
$440$	0.190231	+	0.109830i	0.00906890	+	0.00523593i
$441$		0			0
$442$	−0.662555	−	0.948861i	−0.0315145	−	0.0451327i
$443$	−21.4059			−1.01703			−0.508513	−	0.861054i	$-0.669805\pi$
$443$	−21.4059			−1.01703			−0.508513	+	0.861054i	$0.669805\pi$
$444$		0			0
$445$	−0.599094	+	1.03766i	−0.0283998	+	0.0491898i
$446$	−4.26807	−	7.39252i	−0.202099	−	0.350046i
$447$		0			0
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	−26.3724	+	15.2261i	−1.24459	+	0.718565i	−0.970026	−	0.243003i	$-0.921867\pi$
$449$	−26.3724	+	15.2261i	−1.24459	+	0.718565i	−0.274566	+	0.961568i	$0.588534\pi$
$450$		0			0
$451$	0.982962	+	1.70254i	0.0462859	+	0.0801695i
$452$	−5.94751	+	10.3014i	−0.279747	+	0.484537i
$453$		0			0
$454$	9.98929			0.468821
$455$	−0.475191	−	0.222341i	−0.0222773	−	0.0104235i
$456$		0			0
$457$	10.9024	+	6.29450i	0.509992	+	0.294444i	0.732830	−	0.680411i	$-0.238199\pi$
$457$	10.9024	+	6.29450i	0.509992	+	0.294444i	−0.222838	+	0.974855i	$0.571532\pi$
$458$	−9.07275	+	15.7145i	−0.423942	+	0.734289i
$459$		0			0
$460$			0.801019i			0.0373477i
$461$	9.54400	−	5.51023i	0.444509	−	0.256637i	−0.261000	−	0.965339i	$-0.584052\pi$
$461$	9.54400	−	5.51023i	0.444509	−	0.256637i	0.705508	+	0.708702i	$0.250719\pi$
$462$		0			0
$463$			1.37834i			0.0640569i	0.999487	+	0.0320285i	$0.0101967\pi$
$463$			1.37834i			0.0640569i	−0.999487	+	0.0320285i	$0.989803\pi$
$464$	−4.59467	−	7.95821i	−0.213302	−	0.369450i
$465$		0			0
$466$	−3.10774	−	1.79425i	−0.143963	−	0.0831171i
$467$	−18.2967			−0.846672			−0.423336	−	0.905973i	$-0.639141\pi$
$467$	−18.2967			−0.846672			−0.423336	+	0.905973i	$0.639141\pi$
$468$		0			0
$469$	−2.30692			−0.106524
$470$	0.164047	+	0.0947128i	0.00756694	+	0.00436878i
$471$		0			0
$472$	−1.60699	−	2.78339i	−0.0739679	−	0.128116i
$473$			1.50726i			0.0693039i
$474$		0			0
$475$	−7.20988	+	4.16263i	−0.330812	+	0.190994i
$476$		−	0.320974i		−	0.0147118i
$477$		0			0
$478$	−6.02766	+	10.4402i	−0.275699	+	0.477524i
$479$	23.5123	+	13.5748i	1.07430	+	0.620249i	0.929354	−	0.369190i	$-0.120365\pi$
$479$	23.5123	+	13.5748i	1.07430	+	0.620249i	0.144949	+	0.989439i	$0.453698\pi$
$480$		0			0
$481$	−13.0362	+	1.12337i	−0.594401	+	0.0512212i
$482$	11.1846			0.509443
$483$		0			0
$484$	4.36054	−	7.55267i	0.198206	−	0.343303i
$485$	−0.959427	−	1.66178i	−0.0435653	−	0.0754574i
$486$		0			0
$487$	−18.0511	+	10.4218i	−0.817973	+	0.472257i	−0.849717	−	0.527239i	$-0.823227\pi$
$487$	−18.0511	+	10.4218i	−0.817973	+	0.472257i	0.0317439	+	0.999496i	$0.489894\pi$
$488$	−2.83829	+	1.63869i	−0.128483	+	0.0741799i
$489$		0			0
$490$	−0.0727538	−	0.126013i	−0.00328668	−	0.00569270i
$491$	−12.3228	+	21.3438i	−0.556122	+	0.963232i	0.441693	+	0.897166i	$0.354378\pi$
$491$	−12.3228	+	21.3438i	−0.556122	+	0.963232i	−0.997815	+	0.0660655i	$0.978955\pi$
$492$		0			0
$493$	−2.94954			−0.132841
$494$	4.94314	−	3.45161i	0.222402	−	0.155295i
$495$		0			0
$496$	0.761644	+	0.439735i	0.0341988	+	0.0197447i
$497$	3.52571	−	6.10671i	0.158150	−	0.273923i
$498$		0			0
$499$			1.04444i			0.0467556i	0.999727	+	0.0233778i	$0.00744206\pi$
$499$			1.04444i			0.0467556i	−0.999727	+	0.0233778i	$0.992558\pi$
$500$	1.25746	−	0.725997i	0.0562355	−	0.0324676i
$501$		0			0
$502$		−	16.5677i		−	0.739454i
$503$	−10.2839	−	17.8123i	−0.458538	−	0.794212i	0.540346	−	0.841443i	$-0.318294\pi$
$503$	−10.2839	−	17.8123i	−0.458538	−	0.794212i	−0.998884	+	0.0472314i	$0.984960\pi$
$504$		0			0
$505$	1.93259	+	1.11578i	0.0859991	+	0.0496516i
$506$	−8.31041			−0.369443
$507$		0			0
$508$	6.17664			0.274044
$509$	29.5532	+	17.0625i	1.30992	+	0.756283i	0.982083	−	0.188451i	$-0.0603466\pi$
$509$	29.5532	+	17.0625i	1.30992	+	0.756283i	0.327838	+	0.944734i	$0.393680\pi$
$510$		0			0
$511$	0.678569	+	1.17532i	0.0300181	+	0.0519929i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	16.6824	−	9.63157i	0.735828	−	0.424830i
$515$			0.306857i			0.0135217i
$516$		0			0
$517$	−0.982627	+	1.70196i	−0.0432159	+	0.0748521i
$518$	−3.14281	−	1.81450i	−0.138087	−	0.0797246i
$519$		0			0
$520$	−0.430148	+	0.300357i	−0.0188633	+	0.0131715i
$521$	−26.5476			−1.16307			−0.581535	−	0.813521i	$-0.697548\pi$
$521$	−26.5476			−1.16307			−0.581535	+	0.813521i	$0.697548\pi$
$522$		0			0
$523$	−7.25999	+	12.5747i	−0.317457	+	0.549852i	−0.979957	−	0.199210i	$-0.936162\pi$
$523$	−7.25999	+	12.5747i	−0.317457	+	0.549852i	0.662500	+	0.749062i	$0.269496\pi$
$524$	1.80993	+	3.13489i	0.0790672	+	0.136948i
$525$		0			0
$526$	15.0073	−	8.66445i	0.654348	−	0.377788i
$527$	0.244468	−	0.141144i	0.0106492	−	0.00614831i
$528$		0			0
$529$	−3.65253	−	6.32636i	−0.158806	−	0.275059i
$530$	−0.373031	+	0.646109i	−0.0162034	+	0.0280652i
$531$		0			0
$532$	1.67213			0.0724961
$533$	−4.67807	+	0.403122i	−0.202630	+	0.0174612i
$534$		0			0
$535$	−0.613956	−	0.354468i	−0.0265436	−	0.0153250i
$536$	−1.15346	+	1.99785i	−0.0498219	+	0.0862940i
$537$		0			0
$538$			10.2677i			0.442670i
$539$	1.30736	−	0.754806i	0.0563121	−	0.0325118i
$540$		0			0
$541$		−	4.87496i		−	0.209591i	−0.994494	−	0.104795i	$-0.966581\pi$
$541$		−	4.87496i		−	0.209591i	0.994494	−	0.104795i	$-0.0334188\pi$
$542$	0.844854	+	1.46333i	0.0362896	+	0.0628554i
$543$		0			0
$544$	−0.277972	−	0.160487i	−0.0119179	−	0.00688083i
$545$	1.51342			0.0648279
$546$		0			0
$547$	33.4435			1.42994			0.714970	−	0.699155i	$-0.246440\pi$
$547$	33.4435			1.42994			0.714970	+	0.699155i	$0.246440\pi$
$548$	−0.721249	−	0.416413i	−0.0308102	−	0.0177883i
$549$		0			0
$550$	3.75805	+	6.50913i	0.160244	+	0.277550i
$551$		−	15.3658i		−	0.654605i
$552$		0			0
$553$	−7.50166	+	4.33108i	−0.319003	+	0.184176i
$554$			14.5640i			0.618763i
$555$		0			0
$556$	10.2247	−	17.7098i	0.433625	−	0.751061i
$557$	−0.462539	−	0.267047i	−0.0195984	−	0.0113151i	0.490169	−	0.871628i	$-0.336935\pi$
$557$	−0.462539	−	0.267047i	−0.0195984	−	0.0113151i	−0.509767	+	0.860312i	$0.670268\pi$
$558$		0			0
$559$	−3.26066	−	1.52566i	−0.137911	−	0.0645285i
$560$	−0.145508			−0.00614881
$561$		0			0
$562$	−10.9930	+	19.0405i	−0.463714	+	0.803176i
$563$	11.4298	+	19.7970i	0.481708	+	0.834343i	0.999780	−	0.0209944i	$-0.00668323\pi$
$563$	11.4298	+	19.7970i	0.481708	+	0.834343i	−0.518072	+	0.855337i	$0.673350\pi$
$564$		0			0
$565$	1.49893	−	0.865407i	0.0630604	−	0.0364080i
$566$	−18.2662	+	10.5460i	−0.767784	+	0.443281i
$567$		0			0
$568$	−3.52571	−	6.10671i	−0.147936	−	0.256232i
$569$	−2.23622	+	3.87326i	−0.0937474	+	0.162375i	−0.909085	−	0.416610i	$-0.863218\pi$
$569$	−2.23622	+	3.87326i	−0.0937474	+	0.162375i	0.815338	+	0.578986i	$0.196551\pi$
$570$		0			0
$571$	−10.3978			−0.435135			−0.217568	−	0.976045i	$-0.569812\pi$
$571$	−10.3978			−0.435135			−0.217568	+	0.976045i	$0.569812\pi$
$572$	−3.11614	−	4.46270i	−0.130292	−	0.186595i
$573$		0			0
$574$	−1.12780	−	0.651136i	−0.0470735	−	0.0271779i
$575$	−13.7042	+	23.7364i	−0.571506	+	0.989877i
$576$		0			0
$577$			16.4498i			0.684814i	0.939552	+	0.342407i	$0.111242\pi$
$577$			16.4498i			0.684814i	−0.939552	+	0.342407i	$0.888758\pi$
$578$	14.6332	−	8.44849i	0.608661	−	0.351411i
$579$		0			0
$580$			1.33712i			0.0555208i
$581$	−0.0742798	−	0.128656i	−0.00308164	−	0.00533756i
$582$		0			0
$583$	−6.70325	−	3.87012i	−0.277620	−	0.160284i
$584$	1.35714			0.0561588
$585$		0			0
$586$	13.0819			0.540410
$587$	2.63207	+	1.51963i	0.108637	+	0.0627218i	0.553334	−	0.832959i	$-0.313355\pi$
$587$	2.63207	+	1.51963i	0.108637	+	0.0627218i	−0.444697	+	0.895681i	$0.646689\pi$
$588$		0			0
$589$	0.735295	+	1.27357i	0.0302973	+	0.0524765i
$590$			0.467659i			0.0192532i
$591$		0			0
$592$	−3.14281	+	1.81450i	−0.129169	+	0.0745755i
$593$		−	14.4226i		−	0.592266i	−0.955147	−	0.296133i	$-0.904303\pi$
$593$		−	14.4226i		−	0.592266i	0.955147	−	0.296133i	$-0.0956972\pi$
$594$		0			0
$595$	−0.0233521	+	0.0404470i	−0.000957342	+	0.00165816i
$596$	11.8482	+	6.84056i	0.485321	+	0.280200i
$597$		0			0
$598$	8.41186	−	17.9779i	0.343986	−	0.735173i
$599$	9.47450			0.387118			0.193559	−	0.981089i	$-0.437997\pi$
$599$	9.47450			0.387118			0.193559	+	0.981089i	$0.437997\pi$
$600$		0			0
$601$	10.7733	−	18.6600i	0.439453	−	0.761156i	−0.558194	−	0.829710i	$-0.688506\pi$
$601$	10.7733	−	18.6600i	0.439453	−	0.761156i	0.997647	+	0.0685550i	$0.0218388\pi$
$602$	−0.499222	−	0.864677i	−0.0203468	−	0.0352416i
$603$		0			0
$604$	−0.580855	+	0.335357i	−0.0236347	+	0.0136455i
$605$	−1.09897	+	0.634491i	−0.0446795	+	0.0257957i
$606$		0			0
$607$	−11.5724	−	20.0439i	−0.469708	−	0.813558i	0.529692	−	0.848190i	$-0.322307\pi$
$607$	−11.5724	−	20.0439i	−0.469708	−	0.813558i	−0.999400	+	0.0346319i	$0.988974\pi$
$608$	0.836065	−	1.44811i	0.0339069	−	0.0587285i
$609$		0			0
$610$	0.476883			0.0193084
$611$	−2.68723	−	3.84845i	−0.108714	−	0.155692i
$612$		0			0
$613$	9.72308	+	5.61362i	0.392711	+	0.226732i	0.683334	−	0.730106i	$-0.260529\pi$
$613$	9.72308	+	5.61362i	0.392711	+	0.226732i	−0.290623	+	0.956838i	$0.593862\pi$
$614$	13.7776	−	23.8635i	0.556018	−	0.963051i
$615$		0			0
$616$		−	1.50961i		−	0.0608240i
$617$	14.8368	−	8.56601i	0.597305	−	0.344854i	−0.170675	−	0.985327i	$-0.554595\pi$
$617$	14.8368	−	8.56601i	0.597305	−	0.344854i	0.767981	+	0.640473i	$0.221262\pi$
$618$		0			0
$619$			4.05509i			0.162988i	0.996674	+	0.0814938i	$0.0259691\pi$
$619$			4.05509i			0.162988i	−0.996674	+	0.0814938i	$0.974031\pi$
$620$	−0.0639848	−	0.110825i	−0.00256969	−	0.00445084i
$621$		0			0
$622$	−7.96044	−	4.59596i	−0.319185	−	0.184281i
$623$	8.23454			0.329910
$624$		0			0
$625$	24.6829			0.987314
$626$	22.0292	+	12.7186i	0.880465	+	0.508337i
$627$		0			0
$628$	4.38457	+	7.59429i	0.174963	+	0.303045i
$629$			1.16482i			0.0464442i
$630$		0			0
$631$	−3.27784	+	1.89246i	−0.130489	+	0.0753378i	−0.563823	−	0.825895i	$-0.690670\pi$
$631$	−3.27784	+	1.89246i	−0.130489	+	0.0753378i	0.433335	+	0.901233i	$0.357337\pi$
$632$			8.66217i			0.344562i
$633$		0			0
$634$	13.0393	−	22.5848i	0.517857	−	0.896955i
$635$	−0.778339	−	0.449374i	−0.0308874	−	0.0178329i
$636$		0			0
$637$	0.309553	+	3.59224i	0.0122649	+	0.142330i
$638$	−13.8723			−0.549211
$639$		0			0
$640$	−0.0727538	+	0.126013i	−0.00287584	+	0.00498111i
$641$	4.17476	+	7.23090i	0.164893	+	0.285604i	0.936617	−	0.350354i	$-0.113939\pi$
$641$	4.17476	+	7.23090i	0.164893	+	0.285604i	−0.771724	+	0.635957i	$0.780605\pi$
$642$		0			0
$643$	−27.2735	+	15.7464i	−1.07556	+	0.620976i	−0.929696	−	0.368328i	$-0.879930\pi$
$643$	−27.2735	+	15.7464i	−1.07556	+	0.620976i	−0.145866	+	0.989304i	$0.546597\pi$
$644$	4.76747	−	2.75250i	0.187865	−	0.108464i
$645$		0			0
$646$	−0.268355	−	0.464805i	−0.0105583	−	0.0182875i
$647$	−21.3575	+	36.9922i	−0.839649	+	1.45432i	0.0505387	+	0.998722i	$0.483906\pi$
$647$	−21.3575	+	36.9922i	−0.839649	+	1.45432i	−0.890188	+	0.455593i	$0.849427\pi$
$648$		0			0
$649$	−4.85187			−0.190453
$650$	−17.8851	+	1.54121i	−0.701513	+	0.0604513i
$651$		0			0
$652$	8.03647	+	4.63986i	0.314732	+	0.181711i
$653$	4.55714	−	7.89321i	0.178335	−	0.308885i	−0.762975	−	0.646427i	$-0.776262\pi$
$653$	4.55714	−	7.89321i	0.178335	−	0.308885i	0.941310	+	0.337542i	$0.109596\pi$
$654$		0			0
$655$		−	0.526717i		−	0.0205805i
$656$	−1.12780	+	0.651136i	−0.0440332	+	0.0254226i
$657$		0			0
$658$		−	1.30183i		−	0.0507505i
$659$	23.9967	+	41.5635i	0.934778	+	1.61908i	0.775030	+	0.631924i	$0.217735\pi$
$659$	23.9967	+	41.5635i	0.934778	+	1.61908i	0.159748	+	0.987158i	$0.448932\pi$
$660$		0			0
$661$	−12.1581	−	7.01949i	−0.472896	−	0.273026i	0.244556	−	0.969635i	$-0.421358\pi$
$661$	−12.1581	−	7.01949i	−0.472896	−	0.273026i	−0.717451	+	0.696609i	$0.754691\pi$
$662$	−4.39519			−0.170824
$663$		0			0
$664$	−0.148560			−0.00576523
$665$	−0.210711	−	0.121654i	−0.00817100	−	0.00471753i
$666$		0			0
$667$	−25.2937	−	43.8099i	−0.979375	−	1.69633i
$668$			4.68665i			0.181332i
$669$		0			0
$670$	0.290702	−	0.167837i	0.0112308	−	0.00648411i
$671$			4.94757i			0.190999i
$672$		0			0
$673$	−4.01666	+	6.95706i	−0.154831	+	0.268175i	−0.932997	−	0.359883i	$-0.882817\pi$
$673$	−4.01666	+	6.95706i	−0.154831	+	0.268175i	0.778167	+	0.628058i	$0.216150\pi$
$674$	−7.87083	−	4.54423i	−0.303173	−	0.175037i
$675$		0			0
$676$	12.8084	−	2.22398i	0.492629	−	0.0855376i
$677$	−5.93746			−0.228195			−0.114098	−	0.993470i	$-0.536398\pi$
$677$	−5.93746			−0.228195			−0.114098	+	0.993470i	$0.536398\pi$
$678$		0			0
$679$	−6.59366	+	11.4206i	−0.253041	+	0.438281i
$680$	0.0233521	+	0.0404470i	0.000895511	+	0.00155107i
$681$		0			0
$682$	1.14979	−	0.663829i	0.0440276	−	0.0254193i
$683$	−26.7857	+	15.4648i	−1.02493	+	0.591742i	−0.915527	−	0.402255i	$-0.868226\pi$
$683$	−26.7857	+	15.4648i	−1.02493	+	0.591742i	−0.109400	+	0.993998i	$0.534893\pi$
$684$		0			0
$685$	0.0605913	+	0.104947i	0.00231507	+	0.00400982i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	−0.998443			−0.0380653
$689$	15.1573	−	10.5838i	0.577448	−	0.403210i
$690$		0			0
$691$	−28.7071	−	16.5741i	−1.09207	−	0.630507i	−0.157943	−	0.987448i	$-0.550486\pi$
$691$	−28.7071	−	16.5741i	−1.09207	−	0.630507i	−0.934127	+	0.356941i	$0.883820\pi$
$692$	9.43684	−	16.3451i	0.358735	−	0.621347i
$693$		0			0
$694$			13.8194i			0.524576i
$695$	−2.57690	+	1.48778i	−0.0977475	+	0.0564345i
$696$		0			0
$697$			0.417995i			0.0158327i
$698$	11.6775	+	20.2260i	0.442000	+	0.765566i
$699$		0			0
$700$	−4.31179	−	2.48941i	−0.162970	−	0.0940910i
$701$	−39.6504			−1.49758			−0.748788	−	0.662810i	$-0.769364\pi$
$701$	−39.6504			−1.49758			−0.748788	+	0.662810i	$0.769364\pi$
$702$		0			0
$703$	−6.06816			−0.228865
$704$	−1.30736	−	0.754806i	−0.0492731	−	0.0284478i
$705$		0			0
$706$	9.75955	+	16.9040i	0.367305	+	0.636192i
$707$		−	15.3364i		−	0.576785i
$708$		0			0
$709$	27.3063	−	15.7653i	1.02551	−	0.592078i	0.109814	−	0.993952i	$-0.464975\pi$
$709$	27.3063	−	15.7653i	1.02551	−	0.592078i	0.915695	+	0.401875i	$0.131641\pi$
$710$			1.02603i			0.0385064i
$711$		0			0
$712$	4.11727	−	7.13132i	0.154301	−	0.267257i
$713$	4.19285	+	2.42074i	0.157024	+	0.0906576i
$714$		0			0
$715$	0.0679963	+	0.789070i	0.00254292	+	0.0295096i
$716$	−17.9474			−0.670727
$717$		0			0
$718$	15.5079	−	26.8604i	0.578749	−	1.00242i
$719$	−11.4839	−	19.8908i	−0.428279	−	0.741800i	0.568442	−	0.822723i	$-0.307546\pi$
$719$	−11.4839	−	19.8908i	−0.428279	−	0.741800i	−0.996720	+	0.0809233i	$0.974213\pi$
$720$		0			0
$721$	1.82634	−	1.05444i	0.0680164	−	0.0392693i
$722$	−14.0331	+	8.10199i	−0.522256	+	0.301525i
$723$		0			0
$724$	5.01030	+	8.67809i	0.186206	+	0.322519i
$725$	−22.8761	+	39.6225i	−0.849596	+	1.47154i
$726$		0			0
$727$	−15.0527			−0.558275			−0.279138	−	0.960251i	$-0.590049\pi$
$727$	−15.0527			−0.558275			−0.279138	+	0.960251i	$0.590049\pi$
$728$	3.26575	+	1.52804i	0.121037	+	0.0566329i
$729$		0			0
$730$	−0.171017	−	0.0987369i	−0.00632964	−	0.00365442i
$731$	−0.160237	+	0.277539i	−0.00592659	+	0.0102651i
$732$		0			0
$733$			39.9321i			1.47493i	0.675388	+	0.737463i	$0.263976\pi$
$733$			39.9321i			1.47493i	−0.675388	+	0.737463i	$0.736024\pi$
$734$	0.268496	−	0.155016i	0.00991036	−	0.00572175i
$735$		0			0
$736$		−	5.50500i		−	0.202917i
$737$	1.74128	+	3.01598i	0.0641407	+	0.111095i
$738$		0			0
$739$	5.84273	+	3.37330i	0.214928	+	0.124089i	0.603600	−	0.797287i	$-0.293733\pi$
$739$	5.84273	+	3.37330i	0.214928	+	0.124089i	−0.388671	+	0.921376i	$0.627066\pi$
$740$	0.528047			0.0194114
$741$		0			0
$742$	5.12731			0.188229
$743$	37.6905	+	21.7606i	1.38273	+	0.798319i	0.992482	−	0.122390i	$-0.0390560\pi$
$743$	37.6905	+	21.7606i	1.38273	+	0.798319i	0.390248	+	0.920710i	$0.372389\pi$
$744$		0			0
$745$	−0.995353	−	1.72400i	−0.0364669	−	0.0631625i
$746$			9.98856i			0.365707i
$747$		0			0
$748$	−0.419629	+	0.242273i	−0.0153432	+	0.00885838i
$749$			4.87216i			0.178025i
$750$		0			0
$751$	−1.52891	+	2.64814i	−0.0557906	+	0.0966322i	−0.892572	−	0.450905i	$-0.851101\pi$
$751$	−1.52891	+	2.64814i	−0.0557906	+	0.0966322i	0.836781	+	0.547537i	$0.184435\pi$
$752$	−1.12742	−	0.650914i	−0.0411126	−	0.0237364i
$753$		0			0
$754$	14.0417	−	30.0101i	0.511368	−	1.09290i
$755$	0.0975938			0.00355180
$756$		0			0
$757$	−8.76691	+	15.1847i	−0.318639	+	0.551899i	−0.980204	−	0.197989i	$-0.936559\pi$
$757$	−8.76691	+	15.1847i	−0.318639	+	0.551899i	0.661565	+	0.749887i	$0.269892\pi$
$758$	−6.55010	−	11.3451i	−0.237910	−	0.412073i
$759$		0			0
$760$	−0.210711	+	0.121654i	−0.00764328	+	0.00441285i
$761$	−26.7397	+	15.4382i	−0.969313	+	0.559633i	−0.899027	−	0.437894i	$-0.855725\pi$
$761$	−26.7397	+	15.4382i	−0.969313	+	0.559633i	−0.0702864	+	0.997527i	$0.522391\pi$
$762$		0			0
$763$	−5.20050	−	9.00753i	−0.188271	−	0.326094i
$764$	−3.82269	+	6.62109i	−0.138300	+	0.239543i
$765$		0			0
$766$	31.1154			1.12425
$767$	4.91110	−	10.4961i	0.177329	−	0.378991i
$768$		0			0
$769$	6.29237	+	3.63290i	0.226909	+	0.131006i	0.609145	−	0.793059i	$-0.291513\pi$
$769$	6.29237	+	3.63290i	0.226909	+	0.131006i	−0.382236	+	0.924065i	$0.624846\pi$
$770$	−0.109830	+	0.190231i	−0.00395799	+	0.00685545i
$771$		0			0
$772$			18.3171i			0.659247i
$773$	−30.8223	+	17.7953i	−1.10860	+	0.640051i	−0.938467	−	0.345370i	$-0.887754\pi$
$773$	−30.8223	+	17.7953i	−1.10860	+	0.640051i	−0.170134	+	0.985421i	$0.554420\pi$
$774$		0			0
$775$		−	4.37873i		−	0.157289i
$776$	6.59366	+	11.4206i	0.236699	+	0.409974i
$777$		0			0
$778$	7.64039	+	4.41118i	0.273921	+	0.158149i
$779$	−2.17757			−0.0780195
$780$		0			0
$781$	−10.6449			−0.380905
$782$	−1.53024	−	0.883482i	−0.0547211	−	0.0315932i
$783$		0			0
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$		−	1.27597i		−	0.0455415i
$786$		0			0
$787$	2.07853	−	1.20004i	0.0740914	−	0.0427767i	−0.462497	−	0.886621i	$-0.653046\pi$
$787$	2.07853	−	1.20004i	0.0740914	−	0.0427767i	0.536588	+	0.843844i	$0.319713\pi$
$788$			16.1442i			0.575115i
$789$		0			0
$790$	0.630205	−	1.09155i	0.0224217	−	0.0388355i
$791$	−10.3014	−	5.94751i	−0.366275	−	0.211469i
$792$		0			0
$793$	−10.7031	−	5.00796i	−0.380078	−	0.177838i
$794$	8.56011			0.303787
$795$		0			0
$796$	12.9703	−	22.4652i	0.459719	−	0.796257i
$797$	−13.0250	−	22.5600i	−0.461370	−	0.799117i	0.537659	−	0.843162i	$-0.319309\pi$
$797$	−13.0250	−	22.5600i	−0.461370	−	0.799117i	−0.999030	+	0.0440456i	$0.985975\pi$
$798$		0			0
$799$	−0.361871	+	0.208926i	−0.0128021	+	0.00739129i
$800$	−4.31179	+	2.48941i	−0.152445	+	0.0880141i
$801$		0			0
$802$	−2.19937	−	3.80943i	−0.0776626	−	0.134516i
$803$	1.02438	−	1.77427i	0.0361494	−	0.0626127i
$804$		0			0
$805$	−0.801019			−0.0282322
$806$	0.272243	+	3.15927i	0.00958934	+	0.111280i
$807$		0			0
$808$	−13.2817	−	7.66821i	−0.467249	−	0.269767i
$809$	−2.83859	+	4.91659i	−0.0997996	+	0.172858i	−0.911602	−	0.411075i	$-0.865154\pi$
$809$	−2.83859	+	4.91659i	−0.0997996	+	0.172858i	0.811802	+	0.583933i	$0.198487\pi$
$810$		0			0
$811$		−	41.2139i		−	1.44722i	−0.690211	−	0.723608i	$-0.742482\pi$
$811$		−	41.2139i		−	1.44722i	0.690211	−	0.723608i	$-0.257518\pi$
$812$	7.95821	−	4.59467i	0.279278	−	0.161241i
$813$		0			0
$814$			5.47838i			0.192017i
$815$	−0.675134	−	1.16937i	−0.0236489	−	0.0409611i
$816$		0			0
$817$	−1.44585	−	0.834764i	−0.0505840	−	0.0292047i
$818$	−16.5136			−0.577384
$819$		0			0
$820$	0.189490			0.00661729
$821$	16.7269	+	9.65729i	0.583774	+	0.337042i	0.762632	−	0.646833i	$-0.223907\pi$
$821$	16.7269	+	9.65729i	0.583774	+	0.337042i	−0.178858	+	0.983875i	$0.557240\pi$
$822$		0			0
$823$	−18.2714	−	31.6470i	−0.636901	−	1.10314i	−0.986109	−	0.166099i	$-0.946883\pi$
$823$	−18.2714	−	31.6470i	−0.636901	−	1.10314i	0.349208	−	0.937045i	$-0.386451\pi$
$824$		−	2.10888i		−	0.0734662i
$825$		0			0
$826$	2.78339	−	1.60699i	0.0968467	−	0.0559145i
$827$			10.4134i			0.362108i	0.983473	+	0.181054i	$0.0579509\pi$
$827$			10.4134i			0.362108i	−0.983473	+	0.181054i	$0.942049\pi$
$828$		0			0
$829$	−20.2110	+	35.0066i	−0.701959	+	1.21583i	0.265819	+	0.964023i	$0.414358\pi$
$829$	−20.2110	+	35.0066i	−0.701959	+	1.21583i	−0.967778	+	0.251805i	$0.918976\pi$
$830$	0.0187205	+	0.0108083i	0.000649797	+	0.000375160i
$831$		0			0
$832$	2.95619	−	2.06420i	0.102488	−	0.0715633i
$833$	0.320974			0.0111211
$834$		0			0
$835$	0.340971	−	0.590580i	0.0117998	−	0.0204378i
$836$	−1.26213	−	2.18608i	−0.0436518	−	0.0756072i
$837$		0			0
$838$	28.5753	−	16.4980i	0.987119	−	0.569913i
$839$	−45.3995	+	26.2114i	−1.56736	+	0.904918i	−0.570888	+	0.821028i	$0.693401\pi$
$839$	−45.3995	+	26.2114i	−1.56736	+	0.904918i	−0.996475	+	0.0838897i	$0.973266\pi$
$840$		0			0
$841$	−27.7220	−	48.0160i	−0.955932	−	1.65572i
$842$	0.836556	−	1.44896i	0.0288296	−	0.0499344i
$843$		0			0
$844$	10.0438			0.345721
$845$	−1.77582	−	0.651605i	−0.0610902	−	0.0224159i
$846$		0			0
$847$	7.55267	+	4.36054i	0.259513	+	0.149830i
$848$	2.56366	−	4.44038i	0.0880363	−	0.152483i
$849$		0			0
$850$			1.59807i			0.0548135i
$851$	−17.3012	+	9.98883i	−0.593076	+	0.342413i
$852$		0			0
$853$			33.2052i			1.13692i	0.822709	+	0.568462i	$0.192461\pi$
$853$			33.2052i			1.13692i	−0.822709	+	0.568462i	$0.807539\pi$
$854$	−1.63869	−	2.83829i	−0.0560748	−	0.0971243i
$855$		0			0
$856$	4.21941	+	2.43608i	0.144217	+	0.0832635i
$857$	7.65504			0.261491			0.130746	−	0.991416i	$-0.458263\pi$
$857$	7.65504			0.261491			0.130746	+	0.991416i	$0.458263\pi$
$858$		0			0
$859$	−17.1318			−0.584528			−0.292264	−	0.956338i	$-0.594409\pi$
$859$	−17.1318			−0.584528			−0.292264	+	0.956338i	$0.594409\pi$
$860$	0.125817	+	0.0726405i	0.00429032	+	0.00247702i
$861$		0			0
$862$	3.26026	+	5.64693i	0.111045	+	0.192335i
$863$		−	35.0912i		−	1.19452i	−0.802049	−	0.597259i	$-0.796257\pi$
$863$		−	35.0912i		−	1.19452i	0.802049	−	0.597259i	$-0.203743\pi$
$864$		0			0
$865$	−2.37833	+	1.37313i	−0.0808657	+	0.0466878i
$866$		−	0.0257034i		−	0.000873437i
$867$		0			0
$868$	−0.439735	+	0.761644i	−0.0149256	+	0.0258519i
$869$	11.3246	+	6.53825i	0.384160	+	0.221795i
$870$		0			0
$871$	−8.28700	+	0.714114i	−0.280794	+	0.0241968i
$872$	−10.4010			−0.352222
$873$		0			0
$874$	4.60254	−	7.97184i	0.155683	−	0.269651i
$875$	0.725997	+	1.25746i	0.0245432	+	0.0425100i
$876$		0			0
$877$	23.0035	−	13.2811i	0.776773	−	0.448470i	−0.0585126	−	0.998287i	$-0.518636\pi$
$877$	23.0035	−	13.2811i	0.776773	−	0.448470i	0.835285	+	0.549817i	$0.185302\pi$
$878$	−26.1509	+	15.0983i	−0.882551	+	0.509541i
$879$		0			0
$880$	0.109830	+	0.190231i	0.00370236	+	0.00641268i
$881$	−25.3323	+	43.8768i	−0.853466	+	1.47825i	0.0245942	+	0.999698i	$0.492171\pi$
$881$	−25.3323	+	43.8768i	−0.853466	+	1.47825i	−0.878061	+	0.478550i	$0.841163\pi$
$882$		0			0
$883$	−10.9125			−0.367235			−0.183618	−	0.982998i	$-0.558781\pi$
$883$	−10.9125			−0.367235			−0.183618	+	0.982998i	$0.558781\pi$
$884$	−0.0993585	−	1.15302i	−0.00334179	−	0.0387801i
$885$		0			0
$886$	−18.5381	−	10.7030i	−0.622799	−	0.359573i
$887$	7.49249	−	12.9774i	0.251573	−	0.435738i	−0.712386	−	0.701788i	$-0.752385\pi$
$887$	7.49249	−	12.9774i	0.251573	−	0.435738i	0.963959	+	0.266050i	$0.0857187\pi$
$888$		0			0
$889$			6.17664i			0.207158i
$890$	−1.03766	+	0.599094i	−0.0347825	+	0.0200817i
$891$		0			0
$892$		−	8.53615i		−	0.285811i
$893$	−1.08841	−	1.88519i	−0.0364224	−	0.0630854i
$894$		0			0
$895$	2.26161	+	1.30574i	0.0755974	+	0.0436462i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−30.4522			−1.01620
$899$	6.99901	+	4.04088i	0.233430	+	0.134771i
$900$		0			0
$901$	−0.822867	−	1.42525i	−0.0274137	−	0.0474819i
$902$			1.96592i			0.0654581i
$903$		0			0
$904$	−10.3014	+	5.94751i	−0.342619	+	0.197811i
$905$		−	1.45807i		−	0.0484679i
$906$		0			0
$907$	2.89845	−	5.02027i	0.0962415	−	0.166695i	−0.813885	−	0.581027i	$-0.802651\pi$
$907$	2.89845	−	5.02027i	0.0962415	−	0.166695i	0.910126	+	0.414331i	$0.135985\pi$
$908$	8.65098	+	4.99464i	0.287093	+	0.165753i
$909$		0			0
$910$	−0.300357	−	0.430148i	−0.00995672	−	0.0142593i
$911$	−45.1175			−1.49481			−0.747405	−	0.664369i	$-0.768700\pi$
$911$	−45.1175			−1.49481			−0.747405	+	0.664369i	$0.768700\pi$
$912$		0			0
$913$	−0.112134	+	0.194221i	−0.00371108	+	0.00642778i
$914$	6.29450	+	10.9024i	0.208203	+	0.360619i
$915$		0			0
$916$	−15.7145	+	9.07275i	−0.519221	+	0.299772i
$917$	−3.13489	+	1.80993i	−0.103523	+	0.0597691i
$918$		0			0
$919$	−18.1331	−	31.4075i	−0.598157	−	1.03604i	−0.993093	−	0.117329i	$-0.962567\pi$
$919$	−18.1331	−	31.4075i	−0.598157	−	1.03604i	0.394936	−	0.918708i	$-0.370767\pi$
$920$	−0.400510	+	0.693703i	−0.0132044	+	0.0228707i
$921$		0			0
$922$	11.0205			0.362940
$923$	10.7748	−	23.0282i	0.354658	−	0.757981i
$924$		0			0
$925$	15.6475	+	9.03409i	0.514486	+	0.297039i
$926$	−0.689170	+	1.19368i	−0.0226475	+	0.0392267i
$927$		0			0
$928$		−	9.18935i		−	0.301655i
$929$	35.1857	−	20.3145i	1.15440	−	0.666496i	0.204448	−	0.978877i	$-0.434460\pi$
$929$	35.1857	−	20.3145i	1.15440	−	0.666496i	0.949957	+	0.312381i	$0.101127\pi$
$930$		0			0
$931$			1.67213i			0.0548019i
$932$	−1.79425	−	3.10774i	−0.0587727	−	0.101797i
$933$		0			0
$934$	−15.8454	−	9.14837i	−0.518478	−	0.299344i
$935$	0.0705051			0.00230576
$936$		0			0
$937$	42.0408			1.37341			0.686707	−	0.726934i	$-0.259056\pi$
$937$	42.0408			1.37341			0.686707	+	0.726934i	$0.259056\pi$
$938$	−1.99785	−	1.15346i	−0.0652321	−	0.0376618i
$939$		0			0
$940$	0.0947128	+	0.164047i	0.00308919	+	0.00535064i
$941$			31.8484i			1.03823i	0.854705	+	0.519114i	$0.173738\pi$
$941$			31.8484i			1.03823i	−0.854705	+	0.519114i	$0.826262\pi$
$942$		0			0
$943$	−6.20854	+	3.58450i	−0.202178	+	0.116728i
$944$		−	3.21399i		−	0.104606i
$945$		0			0
$946$	−0.753631	+	1.30533i	−0.0245026	+	0.0424398i
$947$	−23.8646	−	13.7782i	−0.775495	−	0.447732i	0.0593364	−	0.998238i	$-0.481102\pi$
$947$	−23.8646	−	13.7782i	−0.775495	−	0.447732i	−0.834831	+	0.550506i	$0.814435\pi$
$948$		0			0
$949$	2.80141	+	4.01196i	0.0909375	+	0.130234i
$950$	−8.32525			−0.270107
$951$		0			0
$952$	0.160487	−	0.277972i	0.00520142	−	0.00900912i
$953$	14.2985	+	24.7658i	0.463175	+	0.802243i	0.999117	−	0.0420117i	$-0.0133767\pi$
$953$	14.2985	+	24.7658i	0.463175	+	0.802243i	−0.535942	+	0.844255i	$0.680043\pi$
$954$		0			0
$955$	0.963418	−	0.556230i	0.0311755	−	0.0179992i
$956$	−10.4402	+	6.02766i	−0.337661	+	0.194949i
$957$		0			0
$958$	13.5748	+	23.5123i	0.438582	+	0.759647i
$959$	0.416413	−	0.721249i	0.0134467	−	0.0232903i
$960$		0			0
$961$	30.2265			0.975049
$962$	−11.8514	−	5.54525i	−0.382104	−	0.178786i
$963$		0			0
$964$	9.68612	+	5.59229i	0.311969	+	0.180115i
$965$	1.33264	−	2.30820i	0.0428991	−	0.0743034i
$966$		0			0
$967$		−	17.4799i		−	0.562115i	−0.959691	−	0.281057i	$-0.909315\pi$
$967$		−	17.4799i		−	0.562115i	0.959691	−	0.281057i	$-0.0906851\pi$
$968$	7.55267	−	4.36054i	0.242752	−	0.140153i
$969$		0			0
$970$		−	1.91885i		−	0.0616107i
$971$	14.5288	+	25.1646i	0.466251	+	0.807570i	0.999257	−	0.0385416i	$-0.0122712\pi$
$971$	14.5288	+	25.1646i	0.466251	+	0.807570i	−0.533006	+	0.846111i	$0.678938\pi$
$972$		0			0
$973$	17.7098	+	10.2247i	0.567749	+	0.327790i
$974$	−20.8436			−0.667872
$975$		0			0
$976$	−3.27738			−0.104906
$977$	22.6162	+	13.0575i	0.723556	+	0.417745i	0.816060	−	0.577967i	$-0.196154\pi$
$977$	22.6162	+	13.0575i	0.723556	+	0.417745i	−0.0925039	+	0.995712i	$0.529487\pi$
$978$		0			0
$979$	−6.21548	−	10.7655i	−0.198647	−	0.344068i
$980$		−	0.145508i		−	0.00464807i
$981$		0			0
$982$	−21.3438	+	12.3228i	−0.681108	+	0.393238i
$983$			10.0398i			0.320219i	0.987099	+	0.160109i	$0.0511847\pi$
$983$			10.0398i			0.320219i	−0.987099	+	0.160109i	$0.948815\pi$
$984$		0			0
$985$	1.17455	−	2.03439i	0.0374244	−	0.0648209i
$986$	−2.55438	−	1.47477i	−0.0813480	−	0.0469663i
$987$		0			0
$988$	6.00669	−	0.517613i	0.191098	−	0.0164675i
$989$	−5.49643			−0.174776
$990$		0			0
$991$	6.78355	−	11.7494i	0.215486	−	0.373234i	−0.737936	−	0.674870i	$-0.764200\pi$
$991$	6.78355	−	11.7494i	0.215486	−	0.373234i	0.953423	+	0.301637i	$0.0975329\pi$
$992$	0.439735	+	0.761644i	0.0139616	+	0.0241822i
$993$		0			0
$994$	6.10671	−	3.52571i	0.193693	−	0.111829i
$995$	−3.26885	+	1.88727i	−0.103630	+	0.0598306i
$996$		0			0
$997$	30.7329	+	53.2310i	0.973321	+	1.68584i	0.685368	+	0.728196i	$0.259641\pi$
$997$	30.7329	+	53.2310i	0.973321	+	1.68584i	0.287952	+	0.957645i	$0.407026\pi$
$998$	−0.522220	+	0.904512i	−0.0165306	+	0.0286318i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.h.1135.7	yes	16
3.2	odd	2		1638.2.bj.i.1135.2	yes	16
13.10	even	6	inner	1638.2.bj.h.127.6	✓	16
39.23	odd	6		1638.2.bj.i.127.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bj.h.127.6	✓	16	13.10	even	6	inner
1638.2.bj.h.1135.7	yes	16	1.1	even	1	trivial
1638.2.bj.i.127.3	yes	16	39.23	odd	6
1638.2.bj.i.1135.2	yes	16	3.2	odd	2

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.145508i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.145508i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.0727538 - 0.126013i) q^{10} +(1.30736 + 0.754806i) q^{11} +(-2.95619 + 2.06420i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.160487 + 0.277972i) q^{17} +(-1.44811 + 0.836065i) q^{19} +(0.126013 - 0.0727538i) q^{20} +(0.754806 + 1.30736i) q^{22} +(-2.75250 + 4.76747i) q^{23} +4.97883 q^{25} +(-3.59224 + 0.309553i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(-4.59467 + 7.95821i) q^{29} -0.879471i q^{31} +(-0.866025 + 0.500000i) q^{32} +0.320974i q^{34} +(0.0727538 + 0.126013i) q^{35} +(3.14281 + 1.81450i) q^{37} -1.67213 q^{38} +0.145508 q^{40} +(1.12780 + 0.651136i) q^{41} +(0.499222 + 0.864677i) q^{43} +1.50961i q^{44} +(-4.76747 + 2.75250i) q^{46} +1.30183i q^{47} +(0.500000 - 0.866025i) q^{49} +(4.31179 + 2.48941i) q^{50} +(-3.26575 - 1.52804i) q^{52} -5.12731 q^{53} +(0.109830 - 0.190231i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-7.95821 + 4.59467i) q^{58} +(-2.78339 + 1.60699i) q^{59} +(1.63869 + 2.83829i) q^{61} +(0.439735 - 0.761644i) q^{62} -1.00000 q^{64} +(0.300357 + 0.430148i) q^{65} +(1.99785 + 1.15346i) q^{67} +(-0.160487 + 0.277972i) q^{68} +0.145508i q^{70} +(-6.10671 + 3.52571i) q^{71} -1.35714i q^{73} +(1.81450 + 3.14281i) q^{74} +(-1.44811 - 0.836065i) q^{76} -1.50961 q^{77} +8.66217 q^{79} +(0.126013 + 0.0727538i) q^{80} +(0.651136 + 1.12780i) q^{82} +0.148560i q^{83} +(0.0404470 - 0.0233521i) q^{85} +0.998443i q^{86} +(-0.754806 + 1.30736i) q^{88} +(-7.13132 - 4.11727i) q^{89} +(1.52804 - 3.26575i) q^{91} -5.50500 q^{92} +(-0.650914 + 1.12742i) q^{94} +(0.121654 + 0.210711i) q^{95} +(11.4206 - 6.59366i) q^{97} +(0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} - 24 q^{50} - 4 q^{52} - 40 q^{53} + 20 q^{55} - 8 q^{56} + 6 q^{58} + 6 q^{59} - 2 q^{61} - 14 q^{62} - 16 q^{64} - 52 q^{65} - 30 q^{67} + 6 q^{68} + 12 q^{71} + 24 q^{74} + 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} + 30 q^{89} + 4 q^{91} - 24 q^{92} - 8 q^{94} - 40 q^{95} - 24 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^10 - 12 * q^11 + 10 * q^13 - 16 * q^14 - 8 * q^16 - 6 * q^17 - 4 * q^22 - 12 * q^23 - 20 * q^25 - 2 * q^26 + 16 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^40 + 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 - 24 * q^50 - 4 * q^52 - 40 * q^53 + 20 * q^55 - 8 * q^56 + 6 * q^58 + 6 * q^59 - 2 * q^61 - 14 * q^62 - 16 * q^64 - 52 * q^65 - 30 * q^67 + 6 * q^68 + 12 * q^71 + 24 * q^74 + 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 + 30 * q^89 + 4 * q^91 - 24 * q^92 - 8 * q^94 - 40 * q^95 - 24 * q^97

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