LMFDB - Embedded newform 1638.2.cm.a.341.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(269,1638)]

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([3, 1, 4]))

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

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

chi := DirichletCharacter("1638.269");

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.cm (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:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.33
Character	$\chi$	$=$	1638.341
Dual form			1638.2.cm.a.269.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(1.60938 - 2.78753i) q^{5} +(-2.28075 + 1.34096i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.60938 - 2.78753i) q^{5} +(-2.28075 + 1.34096i) q^{7} -1.00000i q^{8} +(2.78753 + 1.60938i) q^{10} +(-1.16231 - 0.671060i) q^{11} +(-3.22035 + 1.62153i) q^{13} +(-1.34096 - 2.28075i) q^{14} +1.00000 q^{16} +1.49181 q^{17} +(-2.36132 + 1.36331i) q^{19} +(-1.60938 + 2.78753i) q^{20} +(0.671060 - 1.16231i) q^{22} +6.73167i q^{23} +(-2.68020 - 4.64224i) q^{25} +(-1.62153 - 3.22035i) q^{26} +(2.28075 - 1.34096i) q^{28} +(-3.42023 + 1.97467i) q^{29} +(-1.51512 + 0.874756i) q^{31} +1.00000i q^{32} +1.49181i q^{34} +(0.0673645 + 8.51576i) q^{35} +7.43327 q^{37} +(-1.36331 - 2.36132i) q^{38} +(-2.78753 - 1.60938i) q^{40} +(1.92560 + 3.33523i) q^{41} +(0.103608 - 0.179454i) q^{43} +(1.16231 + 0.671060i) q^{44} -6.73167 q^{46} +(-5.95403 + 10.3127i) q^{47} +(3.40366 - 6.11679i) q^{49} +(4.64224 - 2.68020i) q^{50} +(3.22035 - 1.62153i) q^{52} +(-7.08304 + 4.08939i) q^{53} +(-3.74120 + 2.15998i) q^{55} +(1.34096 + 2.28075i) q^{56} +(-1.97467 - 3.42023i) q^{58} +9.70505 q^{59} +(-4.80221 + 2.77256i) q^{61} +(-0.874756 - 1.51512i) q^{62} -1.00000 q^{64} +(-0.662710 + 11.5865i) q^{65} +(-3.58306 + 6.20604i) q^{67} -1.49181 q^{68} +(-8.51576 + 0.0673645i) q^{70} +(10.2214 + 5.90134i) q^{71} +(-3.20058 + 1.84786i) q^{73} +7.43327i q^{74} +(2.36132 - 1.36331i) q^{76} +(3.55081 - 0.0280889i) q^{77} +(0.259931 - 0.450214i) q^{79} +(1.60938 - 2.78753i) q^{80} +(-3.33523 + 1.92560i) q^{82} -8.66968 q^{83} +(2.40088 - 4.15845i) q^{85} +(0.179454 + 0.103608i) q^{86} +(-0.671060 + 1.16231i) q^{88} +2.49327 q^{89} +(5.17041 - 8.01666i) q^{91} -6.73167i q^{92} +(-10.3127 - 5.95403i) q^{94} +8.77631i q^{95} +(-12.6787 - 7.32007i) q^{97} +(6.11679 + 3.40366i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) $ 72 * q - 72 * q^4 - 4 * q^7	$ 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) $ 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.60938	−	2.78753i	0.719736	−	1.24662i	−0.241368	−	0.970434i	$-0.577596\pi$
$5$	1.60938	−	2.78753i	0.719736	−	1.24662i	0.961104	−	0.276186i	$-0.0890704\pi$
$6$		0			0
$7$	−2.28075	+	1.34096i	−0.862043	+	0.506835i
$7$	−2.28075	+	1.34096i	−0.862043	+	0.506835i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.78753	+	1.60938i	0.881493	+	0.508930i
$11$	−1.16231	−	0.671060i	−0.350450	−	0.202332i	0.314434	−	0.949279i	$-0.398185\pi$
$11$	−1.16231	−	0.671060i	−0.350450	−	0.202332i	−0.664883	+	0.746947i	$0.731519\pi$
$12$		0			0
$13$	−3.22035	+	1.62153i	−0.893164	+	0.449731i
$13$	−3.22035	+	1.62153i	−0.893164	+	0.449731i
$14$	−1.34096	−	2.28075i	−0.358386	−	0.609557i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.49181			0.361817			0.180908	−	0.983500i	$-0.442096\pi$
$17$	1.49181			0.361817			0.180908	+	0.983500i	$0.442096\pi$
$18$		0			0
$19$	−2.36132	+	1.36331i	−0.541724	+	0.312764i	−0.745777	−	0.666195i	$-0.767922\pi$
$19$	−2.36132	+	1.36331i	−0.541724	+	0.312764i	0.204054	+	0.978960i	$0.434588\pi$
$20$	−1.60938	+	2.78753i	−0.359868	+	0.623310i
$21$		0			0
$22$	0.671060	−	1.16231i	0.143071	−	0.247805i
$23$			6.73167i			1.40365i	0.712349	+	0.701825i	$0.247631\pi$
$23$			6.73167i			1.40365i	−0.712349	+	0.701825i	$0.752369\pi$
$24$		0			0
$25$	−2.68020	−	4.64224i	−0.536040	−	0.928448i
$26$	−1.62153	−	3.22035i	−0.318008	−	0.631562i
$27$		0			0
$28$	2.28075	−	1.34096i	0.431022	−	0.253417i
$29$	−3.42023	+	1.97467i	−0.635121	+	0.366687i	−0.782733	−	0.622358i	$-0.786175\pi$
$29$	−3.42023	+	1.97467i	−0.635121	+	0.366687i	0.147612	+	0.989045i	$0.452841\pi$
$30$		0			0
$31$	−1.51512	+	0.874756i	−0.272124	+	0.157111i	−0.629852	−	0.776715i	$-0.716885\pi$
$31$	−1.51512	+	0.874756i	−0.272124	+	0.157111i	0.357728	+	0.933826i	$0.383551\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$			1.49181i			0.255843i
$35$	0.0673645	+	8.51576i	0.0113867	+	1.43943i
$36$		0			0
$37$	7.43327			1.22202			0.611011	−	0.791622i	$-0.290763\pi$
$37$	7.43327			1.22202			0.611011	+	0.791622i	$0.290763\pi$
$38$	−1.36331	−	2.36132i	−0.221158	−	0.383056i
$39$		0			0
$40$	−2.78753	−	1.60938i	−0.440746	−	0.254465i
$41$	1.92560	+	3.33523i	0.300728	+	0.520876i	0.976301	−	0.216417i	$-0.0694371\pi$
$41$	1.92560	+	3.33523i	0.300728	+	0.520876i	−0.675573	+	0.737293i	$0.736104\pi$
$42$		0			0
$43$	0.103608	−	0.179454i	0.0158000	−	0.0273664i	−0.858017	−	0.513621i	$-0.828304\pi$
$43$	0.103608	−	0.179454i	0.0158000	−	0.0273664i	0.873817	+	0.486254i	$0.161637\pi$
$44$	1.16231	+	0.671060i	0.175225	+	0.101166i
$45$		0			0
$46$	−6.73167			−0.992531
$47$	−5.95403	+	10.3127i	−0.868484	+	1.50426i	−0.00493797	+	0.999988i	$0.501572\pi$
$47$	−5.95403	+	10.3127i	−0.868484	+	1.50426i	−0.863546	+	0.504270i	$0.831762\pi$
$48$		0			0
$49$	3.40366	−	6.11679i	0.486237	−	0.873827i
$50$	4.64224	−	2.68020i	0.656512	−	0.379037i
$51$		0			0
$52$	3.22035	−	1.62153i	0.446582	−	0.224865i
$53$	−7.08304	+	4.08939i	−0.972930	+	0.561721i	−0.900128	−	0.435625i	$-0.856527\pi$
$53$	−7.08304	+	4.08939i	−0.972930	+	0.561721i	−0.0728016	+	0.997346i	$0.523194\pi$
$54$		0			0
$55$	−3.74120	+	2.15998i	−0.504463	+	0.291252i
$56$	1.34096	+	2.28075i	0.179193	+	0.304778i
$57$		0			0
$58$	−1.97467	−	3.42023i	−0.259287	−	0.449098i
$59$	9.70505			1.26349			0.631745	−	0.775176i	$-0.282339\pi$
$59$	9.70505			1.26349			0.631745	+	0.775176i	$0.282339\pi$
$60$		0			0
$61$	−4.80221	+	2.77256i	−0.614860	+	0.354990i	−0.774865	−	0.632126i	$-0.782182\pi$
$61$	−4.80221	+	2.77256i	−0.614860	+	0.354990i	0.160005	+	0.987116i	$0.448849\pi$
$62$	−0.874756	−	1.51512i	−0.111094	−	0.192421i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.662710	+	11.5865i	−0.0821991	+	1.43712i
$66$		0			0
$67$	−3.58306	+	6.20604i	−0.437740	+	0.758188i	−0.997515	−	0.0704565i	$-0.977554\pi$
$67$	−3.58306	+	6.20604i	−0.437740	+	0.758188i	0.559775	+	0.828645i	$0.310888\pi$
$68$	−1.49181			−0.180908
$69$		0			0
$70$	−8.51576	+	0.0673645i	−1.01783	+	0.00805160i
$71$	10.2214	+	5.90134i	1.21306	+	0.700361i	0.963425	−	0.267979i	$-0.0863558\pi$
$71$	10.2214	+	5.90134i	1.21306	+	0.700361i	0.249636	+	0.968340i	$0.419689\pi$
$72$		0			0
$73$	−3.20058	+	1.84786i	−0.374600	+	0.216275i	−0.675466	−	0.737391i	$-0.736058\pi$
$73$	−3.20058	+	1.84786i	−0.374600	+	0.216275i	0.300866	+	0.953666i	$0.402724\pi$
$74$			7.43327i			0.864100i
$75$		0			0
$76$	2.36132	−	1.36331i	0.270862	−	0.156382i
$77$	3.55081	−	0.0280889i	0.404652	−	0.00320102i
$78$		0			0
$79$	0.259931	−	0.450214i	0.0292445	−	0.0506530i	−0.851033	−	0.525113i	$-0.824023\pi$
$79$	0.259931	−	0.450214i	0.0292445	−	0.0506530i	0.880277	+	0.474460i	$0.157357\pi$
$80$	1.60938	−	2.78753i	0.179934	−	0.311655i
$81$		0			0
$82$	−3.33523	+	1.92560i	−0.368315	+	0.212647i
$83$	−8.66968			−0.951621			−0.475811	−	0.879548i	$-0.657845\pi$
$83$	−8.66968			−0.951621			−0.475811	+	0.879548i	$0.657845\pi$
$84$		0			0
$85$	2.40088	−	4.15845i	0.260412	−	0.451047i
$86$	0.179454	+	0.103608i	0.0193510	+	0.0111723i
$87$		0			0
$88$	−0.671060	+	1.16231i	−0.0715353	+	0.123903i
$89$	2.49327			0.264286			0.132143	−	0.991231i	$-0.457814\pi$
$89$	2.49327			0.264286			0.132143	+	0.991231i	$0.457814\pi$
$90$		0			0
$91$	5.17041	−	8.01666i	0.542007	−	0.840374i
$92$		−	6.73167i		−	0.701825i
$93$		0			0
$94$	−10.3127	−	5.95403i	−1.06367	−	0.614111i
$95$			8.77631i			0.900431i
$96$		0			0
$97$	−12.6787	−	7.32007i	−1.28733	−	0.743240i	−0.309153	−	0.951012i	$-0.600045\pi$
$97$	−12.6787	−	7.32007i	−1.28733	−	0.743240i	−0.978177	+	0.207772i	$0.933379\pi$
$98$	6.11679	+	3.40366i	0.617889	+	0.343821i
$99$		0			0
$100$	2.68020	+	4.64224i	0.268020	+	0.464224i
$101$	−2.09490	+	3.62848i	−0.208451	+	0.361047i	−0.951227	−	0.308493i	$-0.900175\pi$
$101$	−2.09490	+	3.62848i	−0.208451	+	0.361047i	0.742776	+	0.669540i	$0.233509\pi$
$102$		0			0
$103$	−6.77221	−	3.90993i	−0.667285	−	0.385257i	0.127762	−	0.991805i	$-0.459221\pi$
$103$	−6.77221	−	3.90993i	−0.667285	−	0.385257i	−0.795047	+	0.606548i	$0.792554\pi$
$104$	1.62153	+	3.22035i	0.159004	+	0.315781i
$105$		0			0
$106$	−4.08939	−	7.08304i	−0.397197	−	0.687965i
$107$			6.25037i			0.604246i	0.953269	+	0.302123i	$0.0976953\pi$
$107$			6.25037i			0.604246i	−0.953269	+	0.302123i	$0.902305\pi$
$108$		0			0
$109$	7.39015	+	12.8001i	0.707848	+	1.22603i	0.965654	+	0.259832i	$0.0836673\pi$
$109$	7.39015	+	12.8001i	0.707848	+	1.22603i	−0.257805	+	0.966197i	$0.582999\pi$
$110$	−2.15998	−	3.74120i	−0.205946	−	0.356709i
$111$		0			0
$112$	−2.28075	+	1.34096i	−0.215511	+	0.126709i
$113$	−6.02039	−	3.47587i	−0.566351	−	0.326983i	0.189340	−	0.981912i	$-0.439365\pi$
$113$	−6.02039	−	3.47587i	−0.566351	−	0.326983i	−0.755690	+	0.654929i	$0.772699\pi$
$114$		0			0
$115$	18.7647	+	10.8338i	1.74982	+	1.01026i
$116$	3.42023	−	1.97467i	0.317560	−	0.183344i
$117$		0			0
$118$			9.70505i			0.893422i
$119$	−3.40244	+	2.00045i	−0.311901	+	0.183381i
$120$		0			0
$121$	−4.59936	−	7.96632i	−0.418123	−	0.724211i
$122$	−2.77256	−	4.80221i	−0.251016	−	0.434772i
$123$		0			0
$124$	1.51512	−	0.874756i	0.136062	−	0.0785554i
$125$	−1.16002			−0.103756
$126$		0			0
$127$	4.93349	+	8.54505i	0.437776	+	0.758250i	0.997518	−	0.0704169i	$-0.0224330\pi$
$127$	4.93349	+	8.54505i	0.437776	+	0.758250i	−0.559742	+	0.828667i	$0.689100\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−11.5865	−	0.662710i	−1.01620	−	0.0581235i
$131$	−4.07756	+	7.06254i	−0.356258	+	0.617057i	−0.987332	−	0.158665i	$-0.949281\pi$
$131$	−4.07756	+	7.06254i	−0.356258	+	0.617057i	0.631074	+	0.775722i	$0.282614\pi$
$132$		0			0
$133$	3.55744	−	6.27580i	0.308469	−	0.544181i
$134$	−6.20604	−	3.58306i	−0.536120	−	0.309529i
$135$		0			0
$136$		−	1.49181i		−	0.127921i
$137$		−	13.5079i		−	1.15406i	−0.816723	−	0.577030i	$-0.804211\pi$
$137$		−	13.5079i		−	1.15406i	0.816723	−	0.577030i	$-0.195789\pi$
$138$		0			0
$139$	−14.5602	−	8.40631i	−1.23498	−	0.713014i	−0.266914	−	0.963720i	$-0.586004\pi$
$139$	−14.5602	−	8.40631i	−1.23498	−	0.713014i	−0.968063	+	0.250706i	$0.919337\pi$
$140$	−0.0673645	−	8.51576i	−0.00569334	−	0.719713i
$141$		0			0
$142$	−5.90134	+	10.2214i	−0.495230	+	0.857763i
$143$	4.83119	+	0.276329i	0.404004	+	0.0231078i
$144$		0			0
$145$			12.7120i			1.05567i
$146$	−1.84786	−	3.20058i	−0.152930	−	0.264882i
$147$		0			0
$148$	−7.43327			−0.611011
$149$	14.0135	−	8.09070i	1.14803	−	0.662816i	0.199624	−	0.979873i	$-0.436028\pi$
$149$	14.0135	−	8.09070i	1.14803	−	0.662816i	0.948407	+	0.317057i	$0.102695\pi$
$150$		0			0
$151$	−0.802559	−	1.39007i	−0.0653113	−	0.113123i	0.831521	−	0.555494i	$-0.187471\pi$
$151$	−0.802559	−	1.39007i	−0.0653113	−	0.113123i	−0.896832	+	0.442371i	$0.854137\pi$
$152$	1.36331	+	2.36132i	0.110579	+	0.191528i
$153$		0			0
$154$	0.0280889	+	3.55081i	0.00226347	+	0.286132i
$155$			5.63126i			0.452313i
$156$		0			0
$157$	−6.68846	+	3.86159i	−0.533797	+	0.308188i	−0.742561	−	0.669778i	$-0.766389\pi$
$157$	−6.68846	+	3.86159i	−0.533797	+	0.308188i	0.208764	+	0.977966i	$0.433056\pi$
$158$	0.450214	+	0.259931i	0.0358171	+	0.0206790i
$159$		0			0
$160$	2.78753	+	1.60938i	0.220373	+	0.127233i
$161$	−9.02690	−	15.3533i	−0.711419	−	1.21001i
$162$		0			0
$163$	−0.801640	−	1.38848i	−0.0627893	−	0.108754i	0.832922	−	0.553391i	$-0.186666\pi$
$163$	−0.801640	−	1.38848i	−0.0627893	−	0.108754i	−0.895711	+	0.444636i	$0.853333\pi$
$164$	−1.92560	−	3.33523i	−0.150364	−	0.260438i
$165$		0			0
$166$		−	8.66968i		−	0.672898i
$167$	−9.70418	−	16.8081i	−0.750932	−	1.30065i	−0.947371	−	0.320136i	$-0.896271\pi$
$167$	−9.70418	−	16.8081i	−0.750932	−	1.30065i	0.196440	−	0.980516i	$-0.437062\pi$
$168$		0			0
$169$	7.74129	−	10.4438i	0.595484	−	0.803367i
$170$	4.15845	+	2.40088i	0.318939	+	0.184139i
$171$		0			0
$172$	−0.103608	+	0.179454i	−0.00790001	+	0.0136832i
$173$	−10.8781	−	18.8414i	−0.827044	−	1.43248i	−0.900347	−	0.435172i	$-0.856688\pi$
$173$	−10.8781	−	18.8414i	−0.827044	−	1.43248i	0.0733036	−	0.997310i	$-0.476646\pi$
$174$		0			0
$175$	12.3379	+	6.99376i	0.932659	+	0.528678i
$176$	−1.16231	−	0.671060i	−0.0876125	−	0.0505831i
$177$		0			0
$178$			2.49327i			0.186879i
$179$	5.32092	+	3.07204i	0.397704	+	0.229615i	0.685493	−	0.728079i	$-0.259587\pi$
$179$	5.32092	+	3.07204i	0.397704	+	0.229615i	−0.287789	+	0.957694i	$0.592920\pi$
$180$		0			0
$181$		−	23.8659i		−	1.77394i	−0.461830	−	0.886968i	$-0.652807\pi$
$181$		−	23.8659i		−	1.77394i	0.461830	−	0.886968i	$-0.347193\pi$
$182$	8.01666	+	5.17041i	0.594234	+	0.383257i
$183$		0			0
$184$	6.73167			0.496265
$185$	11.9629	−	20.7204i	0.879533	−	1.52340i
$186$		0			0
$187$	−1.73394	−	1.00109i	−0.126799	−	0.0732072i
$188$	5.95403	−	10.3127i	0.434242	−	0.752129i
$189$		0			0
$190$	−8.77631			−0.636701
$191$	−20.1788	+	11.6502i	−1.46008	+	0.842980i	−0.999015	−	0.0443841i	$-0.985867\pi$
$191$	−20.1788	+	11.6502i	−1.46008	+	0.842980i	−0.461070	+	0.887364i	$0.652534\pi$
$192$		0			0
$193$	−9.27519	+	16.0651i	−0.667643	+	1.15639i	0.310918	+	0.950437i	$0.399363\pi$
$193$	−9.27519	+	16.0651i	−0.667643	+	1.15639i	−0.978561	+	0.205955i	$0.933970\pi$
$194$	7.32007	−	12.6787i	0.525550	−	0.910280i
$195$		0			0
$196$	−3.40366	+	6.11679i	−0.243118	+	0.436914i
$197$	−14.2984	+	8.25517i	−1.01872	+	0.588156i	−0.913732	−	0.406317i	$-0.866813\pi$
$197$	−14.2984	+	8.25517i	−1.01872	+	0.588156i	−0.104985	+	0.994474i	$0.533479\pi$
$198$		0			0
$199$			5.57525i			0.395219i	0.980281	+	0.197610i	$0.0633178\pi$
$199$			5.57525i			0.395219i	−0.980281	+	0.197610i	$0.936682\pi$
$200$	−4.64224	+	2.68020i	−0.328256	+	0.189519i
$201$		0			0
$202$	−3.62848	−	2.09490i	−0.255299	−	0.147397i
$203$	5.15274	−	9.09012i	0.361652	−	0.638002i
$204$		0			0
$205$	12.3961			0.865778
$206$	3.90993	−	6.77221i	0.272418	−	0.471842i
$207$		0			0
$208$	−3.22035	+	1.62153i	−0.223291	+	0.112433i
$209$	3.65945			0.253129
$210$		0			0
$211$	−12.5054	−	21.6599i	−0.860905	−	1.49113i	−0.871057	−	0.491182i	$-0.836565\pi$
$211$	−12.5054	−	21.6599i	−0.860905	−	1.49113i	0.0101519	−	0.999948i	$-0.496769\pi$
$212$	7.08304	−	4.08939i	0.486465	−	0.280861i
$213$		0			0
$214$	−6.25037			−0.427266
$215$	−0.333488	−	0.577618i	−0.0227437	−	0.0393932i
$216$		0			0
$217$	2.28261	−	4.02682i	0.154953	−	0.273358i
$218$	−12.8001	+	7.39015i	−0.866934	+	0.500524i
$219$		0			0
$220$	3.74120	−	2.15998i	0.252231	−	0.145626i
$221$	−4.80414	+	2.41901i	−0.323162	+	0.162720i
$222$		0			0
$223$	1.20295	−	0.694525i	0.0805557	−	0.0465088i	−0.459181	−	0.888343i	$-0.651857\pi$
$223$	1.20295	−	0.694525i	0.0805557	−	0.0465088i	0.539737	+	0.841834i	$0.318524\pi$
$224$	−1.34096	−	2.28075i	−0.0895966	−	0.152389i
$225$		0			0
$226$	3.47587	−	6.02039i	0.231212	−	0.400470i
$227$	17.4434			1.15776			0.578881	−	0.815412i	$-0.303490\pi$
$227$	17.4434			1.15776			0.578881	+	0.815412i	$0.303490\pi$
$228$		0			0
$229$	6.54345	+	3.77786i	0.432403	+	0.249648i	0.700370	−	0.713780i	$-0.253018\pi$
$229$	6.54345	+	3.77786i	0.432403	+	0.249648i	−0.267967	+	0.963428i	$0.586352\pi$
$230$	−10.8338	+	18.7647i	−0.714360	+	1.23731i
$231$		0			0
$232$	1.97467	+	3.42023i	0.129644	+	0.224549i
$233$	13.2001	+	7.62108i	0.864767	+	0.499273i	0.865606	−	0.500726i	$-0.166934\pi$
$233$	13.2001	+	7.62108i	0.864767	+	0.499273i	−0.000838739		1.00000i	$0.500267\pi$
$234$		0			0
$235$	19.1646	+	33.1940i	1.25016	+	2.16534i
$236$	−9.70505			−0.631745
$237$		0			0
$238$	−2.00045	−	3.40244i	−0.129670	−	0.220548i
$239$			27.8312i			1.80025i	0.435631	+	0.900125i	$0.356525\pi$
$239$			27.8312i			1.80025i	−0.435631	+	0.900125i	$0.643475\pi$
$240$		0			0
$241$		−	3.34033i		−	0.215169i	−0.994196	−	0.107585i	$-0.965688\pi$
$241$		−	3.34033i		−	0.215169i	0.994196	−	0.107585i	$-0.0343117\pi$
$242$	7.96632	−	4.59936i	0.512094	−	0.295658i
$243$		0			0
$244$	4.80221	−	2.77256i	0.307430	−	0.177495i
$245$	−11.5729	−	19.3320i	−0.739368	−	1.23508i
$246$		0			0
$247$	5.39363	−	8.21927i	0.343188	−	0.522980i
$248$	0.874756	+	1.51512i	0.0555471	+	0.0962104i
$249$		0			0
$250$		−	1.16002i		−	0.0733664i
$251$	−3.67687	+	6.36852i	−0.232082	+	0.401977i	−0.958421	−	0.285359i	$-0.907887\pi$
$251$	−3.67687	+	6.36852i	−0.232082	+	0.401977i	0.726339	+	0.687337i	$0.241220\pi$
$252$		0			0
$253$	4.51736	−	7.82429i	0.284004	−	0.491909i
$254$	−8.54505	+	4.93349i	−0.536164	+	0.309554i
$255$		0			0
$256$	1.00000			0.0625000
$257$	19.8421			1.23771			0.618857	−	0.785504i	$-0.287596\pi$
$257$	19.8421			1.23771			0.618857	+	0.785504i	$0.287596\pi$
$258$		0			0
$259$	−16.9534	+	9.96771i	−1.05344	+	0.619363i
$260$	0.662710	−	11.5865i	0.0410996	−	0.718561i
$261$		0			0
$262$	−7.06254	−	4.07756i	−0.436325	−	0.251913i
$263$	9.27878	+	5.35711i	0.572154	+	0.330333i	0.758009	−	0.652244i	$-0.226172\pi$
$263$	9.27878	+	5.35711i	0.572154	+	0.330333i	−0.185855	+	0.982577i	$0.559505\pi$
$264$		0			0
$265$			26.3255i			1.61716i
$266$	6.27580	+	3.55744i	0.384794	+	0.218121i
$267$		0			0
$268$	3.58306	−	6.20604i	0.218870	−	0.379094i
$269$	13.9001			0.847506			0.423753	−	0.905778i	$-0.360712\pi$
$269$	13.9001			0.847506			0.423753	+	0.905778i	$0.360712\pi$
$270$		0			0
$271$		−	22.4093i		−	1.36127i	−0.732623	−	0.680635i	$-0.761704\pi$
$271$		−	22.4093i		−	1.36127i	0.732623	−	0.680635i	$-0.238296\pi$
$272$	1.49181			0.0904541
$273$		0			0
$274$	13.5079			0.816044
$275$			7.19430i			0.433832i
$276$		0			0
$277$	5.11989			0.307624			0.153812	−	0.988100i	$-0.450845\pi$
$277$	5.11989			0.307624			0.153812	+	0.988100i	$0.450845\pi$
$278$	8.40631	−	14.5602i	0.504177	−	0.873261i
$279$		0			0
$280$	8.51576	−	0.0673645i	0.508914	−	0.00402580i
$281$			5.14197i			0.306744i	0.988168	+	0.153372i	$0.0490134\pi$
$281$			5.14197i			0.306744i	−0.988168	+	0.153372i	$0.950987\pi$
$282$		0			0
$283$	18.8236	+	10.8678i	1.11895	+	0.646023i	0.941132	−	0.338041i	$-0.109764\pi$
$283$	18.8236	+	10.8678i	1.11895	+	0.646023i	0.177814	+	0.984064i	$0.443097\pi$
$284$	−10.2214	−	5.90134i	−0.606530	−	0.350180i
$285$		0			0
$286$	−0.276329	+	4.83119i	−0.0163397	+	0.285674i
$287$	−8.86422	−	5.02469i	−0.523238	−	0.296598i
$288$		0			0
$289$	−14.7745			−0.869089
$290$	−12.7120			−0.746473
$291$		0			0
$292$	3.20058	−	1.84786i	0.187300	−	0.108138i
$293$	1.37569	−	2.38277i	0.0803687	−	0.139203i	−0.823040	−	0.567984i	$-0.807724\pi$
$293$	1.37569	−	2.38277i	0.0803687	−	0.139203i	0.903408	+	0.428781i	$0.141057\pi$
$294$		0			0
$295$	15.6191	−	27.0531i	0.909379	−	1.57509i
$296$		−	7.43327i		−	0.432050i
$297$		0			0
$298$	8.09070	+	14.0135i	0.468682	+	0.811780i
$299$	−10.9156	−	21.6783i	−0.631265	−	1.25369i
$300$		0			0
$301$	0.00433675	+	0.548223i	0.000249966	+	0.0315991i
$302$	1.39007	−	0.802559i	0.0799897	−	0.0461821i
$303$		0			0
$304$	−2.36132	+	1.36331i	−0.135431	+	0.0781911i
$305$			17.8484i			1.02200i
$306$		0			0
$307$			10.6784i			0.609451i	0.952440	+	0.304725i	$0.0985647\pi$
$307$			10.6784i			0.609451i	−0.952440	+	0.304725i	$0.901435\pi$
$308$	−3.55081	+	0.0280889i	−0.202326	+	0.00160051i
$309$		0			0
$310$	−5.63126			−0.319834
$311$	−0.456858	−	0.791301i	−0.0259060	−	0.0448705i	0.852782	−	0.522267i	$-0.174914\pi$
$311$	−0.456858	−	0.791301i	−0.0259060	−	0.0448705i	−0.878688	+	0.477397i	$0.841580\pi$
$312$		0			0
$313$	−12.5098	−	7.22256i	−0.707098	−	0.408243i	0.102887	−	0.994693i	$-0.467192\pi$
$313$	−12.5098	−	7.22256i	−0.707098	−	0.408243i	−0.809986	+	0.586450i	$0.800525\pi$
$314$	−3.86159	−	6.68846i	−0.217922	−	0.377452i
$315$		0			0
$316$	−0.259931	+	0.450214i	−0.0146223	+	0.0253265i
$317$	15.9090	+	9.18507i	0.893539	+	0.515885i	0.875098	−	0.483945i	$-0.160797\pi$
$317$	15.9090	+	9.18507i	0.893539	+	0.515885i	0.0184403	+	0.999830i	$0.494130\pi$
$318$		0			0
$319$	5.30049			0.296771
$320$	−1.60938	+	2.78753i	−0.0899670	+	0.155827i
$321$		0			0
$322$	15.3533	−	9.02690i	0.855604	−	0.503049i
$323$	−3.52263	+	2.03379i	−0.196005	+	0.113163i
$324$		0			0
$325$	16.1587	+	10.6036i	0.896323	+	0.588183i
$326$	1.38848	−	0.801640i	0.0769009	−	0.0443988i
$327$		0			0
$328$	3.33523	−	1.92560i	0.184157	−	0.106323i
$329$	−0.249220	−	31.5048i	−0.0137400	−	1.73691i
$330$		0			0
$331$	−7.62878	−	13.2134i	−0.419316	−	0.726276i	0.576555	−	0.817058i	$-0.304397\pi$
$331$	−7.62878	−	13.2134i	−0.419316	−	0.726276i	−0.995871	+	0.0907821i	$0.971063\pi$
$332$	8.66968			0.475811
$333$		0			0
$334$	16.8081	−	9.70418i	0.919700	−	0.530989i
$335$	11.5330	+	19.9757i	0.630115	+	1.09139i
$336$		0			0
$337$	−9.23899			−0.503280			−0.251640	−	0.967821i	$-0.580970\pi$
$337$	−9.23899			−0.503280			−0.251640	+	0.967821i	$0.580970\pi$
$338$	10.4438	+	7.74129i	0.568066	+	0.421071i
$339$		0			0
$340$	−2.40088	+	4.15845i	−0.130206	+	0.225524i
$341$	2.34806			0.127154
$342$		0			0
$343$	0.439467	+	18.5150i	0.0237290	+	0.999718i
$344$	−0.179454	−	0.103608i	−0.00967550	−	0.00558615i
$345$		0			0
$346$	18.8414	−	10.8781i	1.01292	−	0.584808i
$347$		−	7.94366i		−	0.426438i	−0.977004	−	0.213219i	$-0.931605\pi$
$347$		−	7.94366i		−	0.426438i	0.977004	−	0.213219i	$-0.0683948\pi$
$348$		0			0
$349$	24.0932	−	13.9102i	1.28968	−	0.744598i	0.311084	−	0.950383i	$-0.399308\pi$
$349$	24.0932	−	13.9102i	1.28968	−	0.744598i	0.978597	+	0.205785i	$0.0659748\pi$
$350$	−6.99376	+	12.3379i	−0.373832	+	0.659489i
$351$		0			0
$352$	0.671060	−	1.16231i	0.0357676	−	0.0619514i
$353$	−13.4850	+	23.3566i	−0.717732	+	1.24315i	0.244165	+	0.969734i	$0.421486\pi$
$353$	−13.4850	+	23.3566i	−0.717732	+	1.24315i	−0.961897	+	0.273414i	$0.911847\pi$
$354$		0			0
$355$	32.9003	−	18.9950i	1.74617	−	1.00815i
$356$	−2.49327			−0.132143
$357$		0			0
$358$	−3.07204	+	5.32092i	−0.162362	+	0.281220i
$359$	−18.5888	−	10.7323i	−0.981080	−	0.566427i	−0.0784840	−	0.996915i	$-0.525008\pi$
$359$	−18.5888	−	10.7323i	−0.981080	−	0.566427i	−0.902596	+	0.430489i	$0.858341\pi$
$360$		0			0
$361$	−5.78278	+	10.0161i	−0.304357	+	0.527162i
$362$	23.8659			1.25436
$363$		0			0
$364$	−5.17041	+	8.01666i	−0.271003	+	0.420187i
$365$			11.8956i			0.622644i
$366$		0			0
$367$	21.6107	+	12.4769i	1.12807	+	0.651290i	0.943448	−	0.331520i	$-0.107562\pi$
$367$	21.6107	+	12.4769i	1.12807	+	0.651290i	0.184619	+	0.982810i	$0.440895\pi$
$368$			6.73167i			0.350913i
$369$		0			0
$370$	20.7204	+	11.9629i	1.07720	+	0.621924i
$371$	10.6709	−	18.8249i	0.554007	−	0.977343i
$372$		0			0
$373$	15.0885	+	26.1340i	0.781252	+	1.35317i	0.931213	+	0.364476i	$0.118752\pi$
$373$	15.0885	+	26.1340i	0.781252	+	1.35317i	−0.149961	+	0.988692i	$0.547915\pi$
$374$	1.00109	−	1.73394i	0.0517653	−	0.0896601i
$375$		0			0
$376$	10.3127	+	5.95403i	0.531836	+	0.307055i
$377$	7.81235	−	11.9051i	0.402357	−	0.613145i
$378$		0			0
$379$	1.30504	+	2.26040i	0.0670355	+	0.116109i	0.897595	−	0.440821i	$-0.145313\pi$
$379$	1.30504	+	2.26040i	0.0670355	+	0.116109i	−0.830560	+	0.556930i	$0.811979\pi$
$380$		−	8.77631i		−	0.450215i
$381$		0			0
$382$	−11.6502	−	20.1788i	−0.596077	−	1.03244i
$383$	9.04120	+	15.6598i	0.461984	+	0.800179i	0.999060	−	0.0433545i	$-0.0138045\pi$
$383$	9.04120	+	15.6598i	0.461984	+	0.800179i	−0.537076	+	0.843534i	$0.680471\pi$
$384$		0			0
$385$	5.63629	−	9.94317i	0.287252	−	0.506751i
$386$	−16.0651	−	9.27519i	−0.817692	−	0.472095i
$387$		0			0
$388$	12.6787	+	7.32007i	0.643665	+	0.371620i
$389$	16.9931	−	9.81095i	0.861583	−	0.497435i	−0.00295929	−	0.999996i	$-0.500942\pi$
$389$	16.9931	−	9.81095i	0.861583	−	0.497435i	0.864542	+	0.502561i	$0.167609\pi$
$390$		0			0
$391$			10.0424i			0.507864i
$392$	−6.11679	−	3.40366i	−0.308945	−	0.171911i
$393$		0			0
$394$	−8.25517	−	14.2984i	−0.415889	−	0.720342i
$395$	−0.836654	−	1.44913i	−0.0420966	−	0.0729135i
$396$		0			0
$397$	21.8071	−	12.5903i	1.09447	−	0.631891i	0.159705	−	0.987165i	$-0.448946\pi$
$397$	21.8071	−	12.5903i	1.09447	−	0.631891i	0.934762	+	0.355274i	$0.115612\pi$
$398$	−5.57525			−0.279462
$399$		0			0
$400$	−2.68020	−	4.64224i	−0.134010	−	0.232112i
$401$		−	9.85383i		−	0.492077i	−0.969260	−	0.246038i	$-0.920871\pi$
$401$		−	9.85383i		−	0.492077i	0.969260	−	0.246038i	$-0.0791289\pi$
$402$		0			0
$403$	3.46078	−	5.27383i	0.172394	−	0.262708i
$404$	2.09490	−	3.62848i	0.104225	−	0.180523i
$405$		0			0
$406$	9.09012	+	5.15274i	0.451135	+	0.255726i
$407$	−8.63977	−	4.98817i	−0.428257	−	0.247255i
$408$		0			0
$409$			27.5614i			1.36282i	0.731900	+	0.681412i	$0.238634\pi$
$409$			27.5614i			1.36282i	−0.731900	+	0.681412i	$0.761366\pi$
$410$			12.3961i			0.612198i
$411$		0			0
$412$	6.77221	+	3.90993i	0.333643	+	0.192629i
$413$	−22.1348	+	13.0141i	−1.08918	+	0.640381i
$414$		0			0
$415$	−13.9528	+	24.1670i	−0.684916	+	1.18631i
$416$	−1.62153	−	3.22035i	−0.0795019	−	0.157891i
$417$		0			0
$418$			3.65945i			0.178989i
$419$	11.1004	+	19.2264i	0.542288	+	0.939270i	0.998772	+	0.0495386i	$0.0157751\pi$
$419$	11.1004	+	19.2264i	0.542288	+	0.939270i	−0.456484	+	0.889731i	$0.650892\pi$
$420$		0			0
$421$	−16.2510			−0.792024			−0.396012	−	0.918245i	$-0.629606\pi$
$421$	−16.2510			−0.792024			−0.396012	+	0.918245i	$0.629606\pi$
$422$	21.6599	−	12.5054i	1.05439	−	0.608752i
$423$		0			0
$424$	4.08939	+	7.08304i	0.198598	+	0.343983i
$425$	−3.99834	−	6.92533i	−0.193948	−	0.335928i
$426$		0			0
$427$	7.23477	−	12.7631i	0.350115	−	0.617649i
$428$		−	6.25037i		−	0.302123i
$429$		0			0
$430$	0.577618	−	0.333488i	0.0278552	−	0.0160822i
$431$	14.1363	+	8.16162i	0.680923	+	0.393131i	0.800203	−	0.599729i	$-0.204725\pi$
$431$	14.1363	+	8.16162i	0.680923	+	0.393131i	−0.119280	+	0.992861i	$0.538058\pi$
$432$		0			0
$433$	−18.7695	−	10.8366i	−0.902003	−	0.520771i	−0.0241533	−	0.999708i	$-0.507689\pi$
$433$	−18.7695	−	10.8366i	−0.902003	−	0.520771i	−0.877849	+	0.478937i	$0.841022\pi$
$434$	4.02682	+	2.28261i	0.193294	+	0.109569i
$435$		0			0
$436$	−7.39015	−	12.8001i	−0.353924	−	0.613015i
$437$	−9.17734	−	15.8956i	−0.439012	−	0.760391i
$438$		0			0
$439$		−	5.48630i		−	0.261847i	−0.991392	−	0.130923i	$-0.958206\pi$
$439$		−	5.48630i		−	0.261847i	0.991392	−	0.130923i	$-0.0417942\pi$
$440$	2.15998	+	3.74120i	0.102973	+	0.178354i
$441$		0			0
$442$	−2.41901	−	4.80414i	−0.115060	−	0.228510i
$443$	23.5832	+	13.6158i	1.12047	+	0.646905i	0.941522	−	0.336953i	$-0.109396\pi$
$443$	23.5832	+	13.6158i	1.12047	+	0.646905i	0.178951	+	0.983858i	$0.442730\pi$
$444$		0			0
$445$	4.01262	−	6.95005i	0.190216	−	0.329464i
$446$	0.694525	+	1.20295i	0.0328867	+	0.0569615i
$447$		0			0
$448$	2.28075	−	1.34096i	0.107755	−	0.0633544i
$449$	−17.2760	−	9.97430i	−0.815304	−	0.470716i	0.0334901	−	0.999439i	$-0.489338\pi$
$449$	−17.2760	−	9.97430i	−0.815304	−	0.470716i	−0.848795	+	0.528723i	$0.822671\pi$
$450$		0			0
$451$		−	5.16877i		−	0.243388i
$452$	6.02039	+	3.47587i	0.283175	+	0.163491i
$453$		0			0
$454$			17.4434i			0.818662i
$455$	−14.0255	−	27.3145i	−0.657525	−	1.28052i
$456$		0			0
$457$	−36.5159			−1.70814			−0.854070	−	0.520158i	$-0.825873\pi$
$457$	−36.5159			−1.70814			−0.854070	+	0.520158i	$0.825873\pi$
$458$	−3.77786	+	6.54345i	−0.176528	+	0.305755i
$459$		0			0
$460$	−18.7647	−	10.8338i	−0.874909	−	0.505129i
$461$	0.395333	−	0.684736i	0.0184125	−	0.0318913i	−0.856672	−	0.515861i	$-0.827472\pi$
$461$	0.395333	−	0.684736i	0.0184125	−	0.0318913i	0.875085	+	0.483970i	$0.160805\pi$
$462$		0			0
$463$	9.97610			0.463629			0.231814	−	0.972760i	$-0.425534\pi$
$463$	9.97610			0.463629			0.231814	+	0.972760i	$0.425534\pi$
$464$	−3.42023	+	1.97467i	−0.158780	+	0.0916718i
$465$		0			0
$466$	−7.62108	+	13.2001i	−0.353040	+	0.611483i
$467$	1.65544	−	2.86731i	0.0766048	−	0.132683i	−0.825178	−	0.564872i	$-0.808925\pi$
$467$	1.65544	−	2.86731i	0.0766048	−	0.132683i	0.901783	+	0.432189i	$0.142259\pi$
$468$		0			0
$469$	−0.149978	−	18.9592i	−0.00692533	−	0.875453i
$470$	−33.1940	+	19.1646i	−1.53112	+	0.883995i
$471$		0			0
$472$		−	9.70505i		−	0.446711i
$473$	−0.240849	+	0.139054i	−0.0110742	+	0.00639371i
$474$		0			0
$475$	12.6576	+	7.30787i	0.580770	+	0.335308i
$476$	3.40244	−	2.00045i	0.155951	−	0.0916906i
$477$		0			0
$478$	−27.8312			−1.27297
$479$	−5.03807	+	8.72620i	−0.230195	+	0.398710i	−0.957865	−	0.287217i	$-0.907270\pi$
$479$	−5.03807	+	8.72620i	−0.230195	+	0.398710i	0.727670	+	0.685927i	$0.240603\pi$
$480$		0			0
$481$	−23.9377	+	12.0533i	−1.09147	+	0.549581i
$482$	3.34033			0.152148
$483$		0			0
$484$	4.59936	+	7.96632i	0.209062	+	0.362105i
$485$	−40.8098	+	23.5615i	−1.85308	+	1.06987i
$486$		0			0
$487$	5.47656			0.248167			0.124083	−	0.992272i	$-0.460401\pi$
$487$	5.47656			0.248167			0.124083	+	0.992272i	$0.460401\pi$
$488$	2.77256	+	4.80221i	0.125508	+	0.217386i
$489$		0			0
$490$	19.3320	−	11.5729i	0.873331	−	0.522812i
$491$	11.6094	−	6.70268i	0.523924	−	0.302488i	−0.214615	−	0.976699i	$-0.568850\pi$
$491$	11.6094	−	6.70268i	0.523924	−	0.302488i	0.738539	+	0.674211i	$0.235516\pi$
$492$		0			0
$493$	−5.10233	+	2.94583i	−0.229797	+	0.132674i
$494$	8.21927	+	5.39363i	0.369802	+	0.242671i
$495$		0			0
$496$	−1.51512	+	0.874756i	−0.0680310	+	0.0392777i
$497$	−31.2260	+	0.247015i	−1.40068	+	0.0110802i
$498$		0			0
$499$	−7.81563	+	13.5371i	−0.349876	+	0.606003i	−0.986227	−	0.165397i	$-0.947110\pi$
$499$	−7.81563	+	13.5371i	−0.349876	+	0.606003i	0.636351	+	0.771399i	$0.280443\pi$
$500$	1.16002			0.0518779
$501$		0			0
$502$	−6.36852	−	3.67687i	−0.284241	−	0.164107i
$503$	5.47356	−	9.48048i	0.244054	−	0.422714i	−0.717811	−	0.696238i	$-0.754856\pi$
$503$	5.47356	−	9.48048i	0.244054	−	0.422714i	0.961865	+	0.273524i	$0.0881893\pi$
$504$		0			0
$505$	6.74298	+	11.6792i	0.300059	+	0.519717i
$506$	7.82429	+	4.51736i	0.347832	+	0.200821i
$507$		0			0
$508$	−4.93349	−	8.54505i	−0.218888	−	0.379125i
$509$	15.3451			0.680160			0.340080	−	0.940396i	$-0.389546\pi$
$509$	15.3451			0.680160			0.340080	+	0.940396i	$0.389546\pi$
$510$		0			0
$511$	4.82183	−	8.50635i	0.213305	−	0.376299i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$			19.8421i			0.875196i
$515$	−21.7981	+	12.5851i	−0.960538	+	0.554567i
$516$		0			0
$517$	13.8409	−	7.99102i	0.608720	−	0.351445i
$518$	−9.96771	−	16.9534i	−0.437956	−	0.744892i
$519$		0			0
$520$	11.5865	+	0.662710i	0.508100	+	0.0290618i
$521$	−7.99209	−	13.8427i	−0.350140	−	0.606460i	0.636134	−	0.771579i	$-0.280533\pi$
$521$	−7.99209	−	13.8427i	−0.350140	−	0.606460i	−0.986274	+	0.165119i	$0.947199\pi$
$522$		0			0
$523$		−	14.2248i		−	0.622007i	−0.950409	−	0.311004i	$-0.899335\pi$
$523$		−	14.2248i		−	0.622007i	0.950409	−	0.311004i	$-0.100665\pi$
$524$	4.07756	−	7.06254i	0.178129	−	0.308529i
$525$		0			0
$526$	−5.35711	+	9.27878i	−0.233581	+	0.404574i
$527$	−2.26027	+	1.30497i	−0.0984590	+	0.0568453i
$528$		0			0
$529$	−22.3154			−0.970235
$530$	−26.3255			−1.14351
$531$		0			0
$532$	−3.55744	+	6.27580i	−0.154235	+	0.272090i
$533$	−11.6093	−	7.61820i	−0.502853	−	0.329981i
$534$		0			0
$535$	17.4231	+	10.0592i	0.753265	+	0.434898i
$536$	6.20604	+	3.58306i	0.268060	+	0.154765i
$537$		0			0
$538$			13.9001i			0.599277i
$539$	−8.06084	+	4.82555i	−0.347205	+	0.207851i
$540$		0			0
$541$	15.1077	−	26.1673i	0.649530	−	1.12502i	−0.333706	−	0.942677i	$-0.608299\pi$
$541$	15.1077	−	26.1673i	0.649530	−	1.12502i	0.983235	−	0.182341i	$-0.0583675\pi$
$542$	22.4093			0.962563
$543$		0			0
$544$			1.49181i			0.0639607i
$545$	47.5742			2.03786
$546$		0			0
$547$	−19.6208			−0.838926			−0.419463	−	0.907772i	$-0.637782\pi$
$547$	−19.6208			−0.838926			−0.419463	+	0.907772i	$0.637782\pi$
$548$			13.5079i			0.577030i
$549$		0			0
$550$	−7.19430			−0.306766
$551$	5.38417	−	9.32565i	0.229373	−	0.397286i
$552$		0			0
$553$	0.0108800	+	1.37538i	0.000462667	+	0.0584872i
$554$			5.11989i			0.217523i
$555$		0			0
$556$	14.5602	+	8.40631i	0.617488	+	0.356507i
$557$	16.2778	+	9.39800i	0.689713	+	0.398206i	0.803504	−	0.595299i	$-0.202966\pi$
$557$	16.2778	+	9.39800i	0.689713	+	0.398206i	−0.113792	+	0.993505i	$0.536300\pi$
$558$		0			0
$559$	−0.0426636	+	0.745906i	−0.00180448	+	0.0315485i
$560$	0.0673645	+	8.51576i	0.00284667	+	0.359857i
$561$		0			0
$562$	−5.14197			−0.216901
$563$	−34.4080			−1.45013			−0.725063	−	0.688683i	$-0.758189\pi$
$563$	−34.4080			−1.45013			−0.725063	+	0.688683i	$0.758189\pi$
$564$		0			0
$565$	−19.3782	+	11.1880i	−0.815246	+	0.470682i
$566$	−10.8678	+	18.8236i	−0.456808	+	0.791214i
$567$		0			0
$568$	5.90134	−	10.2214i	0.247615	−	0.428882i
$569$		−	16.9241i		−	0.709497i	−0.934962	−	0.354748i	$-0.884567\pi$
$569$		−	16.9241i		−	0.709497i	0.934962	−	0.354748i	$-0.115433\pi$
$570$		0			0
$571$	−19.8382	−	34.3608i	−0.830204	−	1.43796i	−0.897876	−	0.440248i	$-0.854891\pi$
$571$	−19.8382	−	34.3608i	−0.830204	−	1.43796i	0.0676723	−	0.997708i	$-0.478443\pi$
$572$	−4.83119	−	0.276329i	−0.202002	−	0.0115539i
$573$		0			0
$574$	5.02469	−	8.86422i	0.209726	−	0.369985i
$575$	31.2500	−	18.0422i	1.30322	−	0.752412i
$576$		0			0
$577$	−21.2390	+	12.2623i	−0.884189	+	0.510487i	−0.872037	−	0.489439i	$-0.837201\pi$
$577$	−21.2390	+	12.2623i	−0.884189	+	0.510487i	−0.0121519	+	0.999926i	$0.503868\pi$
$578$		−	14.7745i		−	0.614539i
$579$		0			0
$580$		−	12.7120i		−	0.527836i
$581$	19.7734	−	11.6257i	0.820339	−	0.482315i
$582$		0			0
$583$	10.9769			0.454617
$584$	1.84786	+	3.20058i	0.0764649	+	0.132441i
$585$		0			0
$586$	2.38277	+	1.37569i	0.0984311	+	0.0568292i
$587$	−14.6169	−	25.3172i	−0.603304	−	1.04495i	−0.992317	−	0.123721i	$-0.960517\pi$
$587$	−14.6169	−	25.3172i	−0.603304	−	1.04495i	0.389013	−	0.921232i	$-0.372816\pi$
$588$		0			0
$589$	2.38512	−	4.13116i	0.0982773	−	0.170221i
$590$	27.0531	+	15.6191i	1.11376	+	0.643028i
$591$		0			0
$592$	7.43327			0.305506
$593$	−3.66429	+	6.34673i	−0.150474	+	0.260629i	−0.931402	−	0.363992i	$-0.881413\pi$
$593$	−3.66429	+	6.34673i	−0.150474	+	0.260629i	0.780928	+	0.624621i	$0.214747\pi$
$594$		0			0
$595$	0.100495	+	12.7039i	0.00411989	+	0.520808i
$596$	−14.0135	+	8.09070i	−0.574015	+	0.331408i
$597$		0			0
$598$	21.6783	−	10.9156i	0.886493	−	0.446372i
$599$	−6.58328	+	3.80086i	−0.268985	+	0.155299i	−0.628426	−	0.777869i	$-0.716301\pi$
$599$	−6.58328	+	3.80086i	−0.268985	+	0.155299i	0.359441	+	0.933168i	$0.382967\pi$
$600$		0			0
$601$	−36.0046	+	20.7873i	−1.46866	+	0.847930i	−0.999383	−	0.0351224i	$-0.988818\pi$
$601$	−36.0046	+	20.7873i	−1.46866	+	0.847930i	−0.469275	+	0.883052i	$0.655485\pi$
$602$	−0.548223	+	0.00433675i	−0.0223439	+	0.000176753i
$603$		0			0
$604$	0.802559	+	1.39007i	0.0326557	+	0.0565613i
$605$	−29.6084			−1.20375
$606$		0			0
$607$	20.8904	−	12.0611i	0.847914	−	0.489543i	−0.0120324	−	0.999928i	$-0.503830\pi$
$607$	20.8904	−	12.0611i	0.847914	−	0.489543i	0.859947	+	0.510384i	$0.170497\pi$
$608$	−1.36331	−	2.36132i	−0.0552894	−	0.0957641i
$609$		0			0
$610$	−17.8484			−0.722660
$611$	2.45175	−	42.8650i	0.0991872	−	1.73413i
$612$		0			0
$613$	−17.3185	+	29.9965i	−0.699488	+	1.21155i	0.269156	+	0.963097i	$0.413255\pi$
$613$	−17.3185	+	29.9965i	−0.699488	+	1.21155i	−0.968644	+	0.248452i	$0.920078\pi$
$614$	−10.6784			−0.430947
$615$		0			0
$616$	−0.0280889	−	3.55081i	−0.00113173	−	0.143066i
$617$	16.4923	+	9.52185i	0.663956	+	0.383335i	0.793783	−	0.608202i	$-0.208109\pi$
$617$	16.4923	+	9.52185i	0.663956	+	0.383335i	−0.129827	+	0.991537i	$0.541442\pi$
$618$		0			0
$619$	26.3413	−	15.2082i	1.05875	−	0.611268i	0.133662	−	0.991027i	$-0.457326\pi$
$619$	26.3413	−	15.2082i	1.05875	−	0.611268i	0.925086	+	0.379759i	$0.123993\pi$
$620$		−	5.63126i		−	0.226157i
$621$		0			0
$622$	0.791301	−	0.456858i	0.0317283	−	0.0183183i
$623$	−5.68653	+	3.34337i	−0.227826	+	0.133949i
$624$		0			0
$625$	11.5341	−	19.9776i	0.461363	−	0.799104i
$626$	7.22256	−	12.5098i	0.288672	−	0.499994i
$627$		0			0
$628$	6.68846	−	3.86159i	0.266899	−	0.154094i
$629$	11.0890			0.442148
$630$		0			0
$631$	23.1363	−	40.0732i	0.921040	−	1.59529i	0.123230	−	0.992378i	$-0.460675\pi$
$631$	23.1363	−	40.0732i	0.921040	−	1.59529i	0.797810	−	0.602910i	$-0.205992\pi$
$632$	−0.450214	−	0.259931i	−0.0179085	−	0.0103395i
$633$		0			0
$634$	−9.18507	+	15.9090i	−0.364786	+	0.631827i
$635$	31.7594			1.26033
$636$		0			0
$637$	−1.04242	+	25.2173i	−0.0413022	+	0.999147i
$638$			5.30049i			0.209849i
$639$		0			0
$640$	−2.78753	−	1.60938i	−0.110187	−	0.0636163i
$641$			27.5815i			1.08941i	0.838629	+	0.544703i	$0.183357\pi$
$641$			27.5815i			1.08941i	−0.838629	+	0.544703i	$0.816643\pi$
$642$		0			0
$643$	26.6935	+	15.4115i	1.05269	+	0.607769i	0.923400	−	0.383838i	$-0.125398\pi$
$643$	26.6935	+	15.4115i	1.05269	+	0.607769i	0.129287	+	0.991607i	$0.458731\pi$
$644$	9.02690	+	15.3533i	0.355710	+	0.605004i
$645$		0			0
$646$	−2.03379	−	3.52263i	−0.0800185	−	0.138596i
$647$	16.0939	−	27.8754i	0.632716	−	1.09590i	−0.354278	−	0.935140i	$-0.615273\pi$
$647$	16.0939	−	27.8754i	0.632716	−	1.09590i	0.986994	−	0.160757i	$-0.0513934\pi$
$648$		0			0
$649$	−11.2803	−	6.51267i	−0.442790	−	0.255645i
$650$	−10.6036	+	16.1587i	−0.415908	+	0.633796i
$651$		0			0
$652$	0.801640	+	1.38848i	0.0313947	+	0.0543771i
$653$		−	45.5132i		−	1.78107i	−0.454914	−	0.890535i	$-0.650330\pi$
$653$		−	45.5132i		−	1.78107i	0.454914	−	0.890535i	$-0.349670\pi$
$654$		0			0
$655$	13.1247	+	22.7326i	0.512824	+	0.888236i
$656$	1.92560	+	3.33523i	0.0751819	+	0.130219i
$657$		0			0
$658$	31.5048	−	0.249220i	1.22818	−	0.00971562i
$659$	9.03365	+	5.21558i	0.351901	+	0.203170i	0.665522	−	0.746378i	$-0.268209\pi$
$659$	9.03365	+	5.21558i	0.351901	+	0.203170i	−0.313621	+	0.949548i	$0.601542\pi$
$660$		0			0
$661$	31.8555	+	18.3918i	1.23904	+	0.715358i	0.968897	−	0.247463i	$-0.0795969\pi$
$661$	31.8555	+	18.3918i	1.23904	+	0.715358i	0.270139	+	0.962821i	$0.412930\pi$
$662$	13.2134	−	7.62878i	0.513555	−	0.296501i
$663$		0			0
$664$			8.66968i			0.336449i
$665$	−11.7687	−	20.0166i	−0.456370	−	0.776210i
$666$		0			0
$667$	−13.2928	−	23.0239i	−0.514701	−	0.891488i
$668$	9.70418	+	16.8081i	0.375466	+	0.650326i
$669$		0			0
$670$	−19.9757	+	11.5330i	−0.771730	+	0.445558i
$671$	7.44222			0.287304
$672$		0			0
$673$	4.40213	+	7.62472i	0.169690	+	0.293911i	0.938311	−	0.345793i	$-0.112390\pi$
$673$	4.40213	+	7.62472i	0.169690	+	0.293911i	−0.768621	+	0.639704i	$0.779057\pi$
$674$		−	9.23899i		−	0.355873i
$675$		0			0
$676$	−7.74129	+	10.4438i	−0.297742	+	0.401683i
$677$	−5.62065	+	9.73525i	−0.216019	+	0.374156i	−0.953587	−	0.301117i	$-0.902641\pi$
$677$	−5.62065	+	9.73525i	−0.216019	+	0.374156i	0.737568	+	0.675273i	$0.235974\pi$
$678$		0			0
$679$	38.7330	−	0.306399i	1.48643	−	0.0117585i
$680$	−4.15845	−	2.40088i	−0.159469	−	0.0920697i
$681$		0			0
$682$			2.34806i			0.0899117i
$683$		−	4.44740i		−	0.170175i	−0.996373	−	0.0850875i	$-0.972883\pi$
$683$		−	4.44740i		−	0.170175i	0.996373	−	0.0850875i	$-0.0271170\pi$
$684$		0			0
$685$	−37.6537	−	21.7394i	−1.43867	−	0.830619i
$686$	−18.5150	+	0.439467i	−0.706908	+	0.0167789i
$687$		0			0
$688$	0.103608	−	0.179454i	0.00395001	−	0.00684161i
$689$	16.1788	−	24.6546i	0.616362	−	0.939266i
$690$		0			0
$691$		−	40.8273i		−	1.55314i	−0.630029	−	0.776572i	$-0.716957\pi$
$691$		−	40.8273i		−	1.55314i	0.630029	−	0.776572i	$-0.283043\pi$
$692$	10.8781	+	18.8414i	0.413522	+	0.716241i
$693$		0			0
$694$	7.94366			0.301537
$695$	−46.8656	+	27.0579i	−1.77771	+	1.02636i
$696$		0			0
$697$	2.87262	+	4.97552i	0.108808	+	0.188461i
$698$	13.9102	+	24.0932i	0.526510	+	0.911942i
$699$		0			0
$700$	−12.3379	−	6.99376i	−0.466329	−	0.264339i
$701$		−	23.3768i		−	0.882929i	−0.897279	−	0.441465i	$-0.854459\pi$
$701$		−	23.3768i		−	0.882929i	0.897279	−	0.441465i	$-0.145541\pi$
$702$		0			0
$703$	−17.5523	+	10.1338i	−0.661998	+	0.382205i
$704$	1.16231	+	0.671060i	0.0438062	+	0.0252915i
$705$		0			0
$706$	−23.3566	−	13.4850i	−0.879038	−	0.507513i
$707$	−0.0876873	−	11.0848i	−0.00329782	−	0.416888i
$708$		0			0
$709$	13.7077	+	23.7424i	0.514803	+	0.891665i	0.999852	+	0.0171780i	$0.00546819\pi$
$709$	13.7077	+	23.7424i	0.514803	+	0.891665i	−0.485050	+	0.874487i	$0.661198\pi$
$710$	18.9950	+	32.9003i	0.712869	+	1.23473i
$711$		0			0
$712$		−	2.49327i		−	0.0934393i
$713$	−5.88857	−	10.1993i	−0.220529	−	0.381967i
$714$		0			0
$715$	8.54549	−	13.0223i	0.319583	−	0.487008i
$716$	−5.32092	−	3.07204i	−0.198852	−	0.114807i
$717$		0			0
$718$	10.7323	−	18.5888i	0.400524	−	0.693728i
$719$	10.6095	+	18.3762i	0.395667	+	0.685315i	0.993186	−	0.116540i	$-0.0371802\pi$
$719$	10.6095	+	18.3762i	0.395667	+	0.685315i	−0.597519	+	0.801855i	$0.703847\pi$
$720$		0			0
$721$	20.6888	−	0.163660i	0.770491	−	0.00609501i
$722$	−10.0161	−	5.78278i	−0.372760	−	0.215213i
$723$		0			0
$724$			23.8659i			0.886968i
$725$	18.3338	+	10.5850i	0.680900	+	0.393118i
$726$		0			0
$727$			26.9627i			0.999991i	0.866028	+	0.499995i	$0.166665\pi$
$727$			26.9627i			0.999991i	−0.866028	+	0.499995i	$0.833335\pi$
$728$	−8.01666	−	5.17041i	−0.297117	−	0.191628i
$729$		0			0
$730$	−11.8956			−0.440276
$731$	0.154563	−	0.267711i	0.00571671	−	0.00990163i
$732$		0			0
$733$	−34.7781	−	20.0791i	−1.28456	−	0.741640i	−0.306880	−	0.951748i	$-0.599285\pi$
$733$	−34.7781	−	20.0791i	−1.28456	−	0.741640i	−0.977678	+	0.210108i	$0.932618\pi$
$734$	−12.4769	+	21.6107i	−0.460532	+	0.797664i
$735$		0			0
$736$	−6.73167			−0.248133
$737$	8.32925	−	4.80890i	0.306812	−	0.177138i
$738$		0			0
$739$	−24.7860	+	42.9306i	−0.911767	+	1.57923i	−0.100199	+	0.994967i	$0.531948\pi$
$739$	−24.7860	+	42.9306i	−0.911767	+	1.57923i	−0.811568	+	0.584259i	$0.801385\pi$
$740$	−11.9629	+	20.7204i	−0.439767	+	0.761698i
$741$		0			0
$742$	18.8249	+	10.6709i	0.691086	+	0.391742i
$743$	−10.4827	+	6.05220i	−0.384574	+	0.222034i	−0.679806	−	0.733392i	$-0.737936\pi$
$743$	−10.4827	+	6.05220i	−0.384574	+	0.222034i	0.295233	+	0.955425i	$0.404603\pi$
$744$		0			0
$745$		−	52.0840i		−	1.90821i
$746$	−26.1340	+	15.0885i	−0.956834	+	0.552428i
$747$		0			0
$748$	1.73394	+	1.00109i	0.0633993	+	0.0366036i
$749$	−8.38149	−	14.2555i	−0.306253	−	0.520886i
$750$		0			0
$751$	−53.1982			−1.94123			−0.970614	−	0.240641i	$-0.922642\pi$
$751$	−53.1982			−1.94123			−0.970614	+	0.240641i	$0.922642\pi$
$752$	−5.95403	+	10.3127i	−0.217121	+	0.376065i
$753$		0			0
$754$	11.9051	+	7.81235i	0.433559	+	0.284509i
$755$	−5.16648			−0.188028
$756$		0			0
$757$	−16.2705	−	28.1814i	−0.591362	−	1.02427i	−0.994049	−	0.108931i	$-0.965257\pi$
$757$	−16.2705	−	28.1814i	−0.591362	−	1.02427i	0.402687	−	0.915338i	$-0.368076\pi$
$758$	−2.26040	+	1.30504i	−0.0821014	+	0.0474013i
$759$		0			0
$760$	8.77631			0.318350
$761$	15.3913	+	26.6585i	0.557933	+	0.966369i	0.997669	+	0.0682415i	$0.0217388\pi$
$761$	15.3913	+	26.6585i	0.557933	+	0.966369i	−0.439736	+	0.898127i	$0.644928\pi$
$762$		0			0
$763$	−34.0195	−	19.2840i	−1.23159	−	0.698128i
$764$	20.1788	−	11.6502i	0.730042	−	0.421490i
$765$		0			0
$766$	−15.6598	+	9.04120i	−0.565812	+	0.326672i
$767$	−31.2536	+	15.7370i	−1.12850	+	0.568230i
$768$		0			0
$769$	−23.8288	+	13.7576i	−0.859288	+	0.496110i	−0.863774	−	0.503880i	$-0.831906\pi$
$769$	−23.8288	+	13.7576i	−0.859288	+	0.496110i	0.00448562	+	0.999990i	$0.498572\pi$
$770$	9.94317	+	5.63629i	0.358327	+	0.203118i
$771$		0			0
$772$	9.27519	−	16.0651i	0.333822	−	0.578196i
$773$	46.6451			1.67771			0.838855	−	0.544355i	$-0.183226\pi$
$773$	46.6451			1.67771			0.838855	+	0.544355i	$0.183226\pi$
$774$		0			0
$775$	8.12165	+	4.68904i	0.291738	+	0.168435i
$776$	−7.32007	+	12.6787i	−0.262775	+	0.455140i
$777$		0			0
$778$	9.81095	+	16.9931i	0.351740	+	0.609231i
$779$	−9.09389	−	5.25036i	−0.325823	−	0.188114i
$780$		0			0
$781$	−7.92032	−	13.7184i	−0.283411	−	0.490883i
$782$	−10.0424			−0.359114
$783$		0			0
$784$	3.40366	−	6.11679i	0.121559	−	0.218457i
$785$			24.8590i			0.887256i
$786$		0			0
$787$			42.4104i			1.51177i	0.654706	+	0.755884i	$0.272793\pi$
$787$			42.4104i			1.51177i	−0.654706	+	0.755884i	$0.727207\pi$
$788$	14.2984	−	8.25517i	0.509358	−	0.294078i
$789$		0			0
$790$	1.44913	−	0.836654i	0.0515577	−	0.0297668i
$791$	18.3920	−	0.145491i	0.653945	−	0.00517307i
$792$		0			0
$793$	10.9690	−	16.7155i	0.389521	−	0.593586i
$794$	12.5903	+	21.8071i	0.446814	+	0.773905i
$795$		0			0
$796$		−	5.57525i		−	0.197610i
$797$	1.81183	−	3.13818i	0.0641784	−	0.111160i	−0.832151	−	0.554549i	$-0.812891\pi$
$797$	1.81183	−	3.13818i	0.0641784	−	0.111160i	0.896329	+	0.443389i	$0.146224\pi$
$798$		0			0
$799$	−8.88226	+	15.3845i	−0.314232	+	0.544265i
$800$	4.64224	−	2.68020i	0.164128	−	0.0947593i
$801$		0			0
$802$	9.85383			0.347951
$803$	4.96009			0.175038
$804$		0			0
$805$	−57.3253	+	0.453476i	−2.02045	+	0.0159829i
$806$	5.27383	+	3.46078i	0.185763	+	0.121901i
$807$		0			0
$808$	3.62848	+	2.09490i	0.127649	+	0.0736984i
$809$	44.7535	+	25.8385i	1.57345	+	0.908432i	0.995742	+	0.0921887i	$0.0293863\pi$
$809$	44.7535	+	25.8385i	1.57345	+	0.908432i	0.577709	+	0.816243i	$0.303947\pi$
$810$		0			0
$811$		−	51.9560i		−	1.82442i	−0.409722	−	0.912210i	$-0.634374\pi$
$811$		−	51.9560i		−	1.82442i	0.409722	−	0.912210i	$-0.365626\pi$
$812$	−5.15274	+	9.09012i	−0.180826	+	0.319001i
$813$		0			0
$814$	4.98817	−	8.63977i	0.174835	−	0.302824i
$815$	−5.16057			−0.180767
$816$		0			0
$817$			0.564997i			0.0197667i
$818$	−27.5614			−0.963662
$819$		0			0
$820$	−12.3961			−0.432889
$821$			32.3551i			1.12920i	0.825365	+	0.564600i	$0.190969\pi$
$821$			32.3551i			1.12920i	−0.825365	+	0.564600i	$0.809031\pi$
$822$		0			0
$823$	−51.0598			−1.77983			−0.889916	−	0.456124i	$-0.849237\pi$
$823$	−51.0598			−1.77983			−0.889916	+	0.456124i	$0.849237\pi$
$824$	−3.90993	+	6.77221i	−0.136209	+	0.235921i
$825$		0			0
$826$	−13.0141	−	22.1348i	−0.452818	−	0.770169i
$827$			31.8257i			1.10669i	0.832952	+	0.553345i	$0.186649\pi$
$827$			31.8257i			1.10669i	−0.832952	+	0.553345i	$0.813351\pi$
$828$		0			0
$829$	−36.3424	−	20.9823i	−1.26222	−	0.728745i	−0.288719	−	0.957414i	$-0.593229\pi$
$829$	−36.3424	−	20.9823i	−1.26222	−	0.728745i	−0.973504	+	0.228669i	$0.926563\pi$
$830$	−24.1670	−	13.9528i	−0.838847	−	0.484309i
$831$		0			0
$832$	3.22035	−	1.62153i	0.111646	−	0.0562164i
$833$	5.07760	−	9.12507i	0.175929	−	0.316165i
$834$		0			0
$835$	−62.4708			−2.16189
$836$	−3.65945			−0.126565
$837$		0			0
$838$	−19.2264	+	11.1004i	−0.664164	+	0.383455i
$839$	6.66139	−	11.5379i	0.229977	−	0.398331i	−0.727824	−	0.685764i	$-0.759468\pi$
$839$	6.66139	−	11.5379i	0.229977	−	0.398331i	0.957801	+	0.287432i	$0.0928017\pi$
$840$		0			0
$841$	−6.70135	+	11.6071i	−0.231081	+	0.400244i
$842$		−	16.2510i		−	0.560045i
$843$		0			0
$844$	12.5054	+	21.6599i	0.430452	+	0.745565i
$845$	−16.6536	−	38.3870i	−0.572901	−	1.32055i
$846$		0			0
$847$	21.1725	+	12.0016i	0.727496	+	0.412381i
$848$	−7.08304	+	4.08939i	−0.243232	+	0.140430i
$849$		0			0
$850$	6.92533	−	3.99834i	0.237537	−	0.137142i
$851$			50.0383i			1.71529i
$852$		0			0
$853$		−	10.3527i		−	0.354471i	−0.984168	−	0.177235i	$-0.943285\pi$
$853$		−	10.3527i		−	0.354471i	0.984168	−	0.177235i	$-0.0567154\pi$
$854$	12.7631	+	7.23477i	0.436744	+	0.247569i
$855$		0			0
$856$	6.25037			0.213633
$857$	7.44723	+	12.8990i	0.254392	+	0.440621i	0.964730	−	0.263240i	$-0.0847912\pi$
$857$	7.44723	+	12.8990i	0.254392	+	0.440621i	−0.710338	+	0.703861i	$0.751458\pi$
$858$		0			0
$859$	27.4019	+	15.8205i	0.934940	+	0.539788i	0.888371	−	0.459127i	$-0.151838\pi$
$859$	27.4019	+	15.8205i	0.934940	+	0.539788i	0.0465697	+	0.998915i	$0.485171\pi$
$860$	0.333488	+	0.577618i	0.0113718	+	0.0196966i
$861$		0			0
$862$	−8.16162	+	14.1363i	−0.277986	+	0.481485i
$863$	34.3421	+	19.8274i	1.16902	+	0.674933i	0.953448	−	0.301556i	$-0.0975060\pi$
$863$	34.3421	+	19.8274i	1.16902	+	0.674933i	0.215569	+	0.976489i	$0.430839\pi$
$864$		0			0
$865$	−70.0277			−2.38101
$866$	10.8366	−	18.7695i	0.368241	−	0.637812i
$867$		0			0
$868$	−2.28261	+	4.02682i	−0.0774767	+	0.136679i
$869$	−0.604241	+	0.348859i	−0.0204975	+	0.0118342i
$870$		0			0
$871$	1.47543	−	25.7956i	0.0499931	−	0.874052i
$872$	12.8001	−	7.39015i	0.433467	−	0.250262i
$873$		0			0
$874$	15.8956	−	9.17734i	0.537677	−	0.310428i
$875$	2.64573	−	1.55554i	0.0894419	−	0.0525870i
$876$		0			0
$877$	22.2380	+	38.5173i	0.750923	+	1.30064i	0.947376	+	0.320123i	$0.103724\pi$
$877$	22.2380	+	38.5173i	0.750923	+	1.30064i	−0.196453	+	0.980513i	$0.562942\pi$
$878$	5.48630			0.185154
$879$		0			0
$880$	−3.74120	+	2.15998i	−0.126116	+	0.0728129i
$881$	−27.5125	−	47.6530i	−0.926918	−	1.60547i	−0.788447	−	0.615103i	$-0.789115\pi$
$881$	−27.5125	−	47.6530i	−0.926918	−	1.60547i	−0.138471	−	0.990366i	$-0.544219\pi$
$882$		0			0
$883$	−44.5081			−1.49782			−0.748909	−	0.662673i	$-0.769422\pi$
$883$	−44.5081			−1.49782			−0.748909	+	0.662673i	$0.769422\pi$
$884$	4.80414	−	2.41901i	0.161581	−	0.0813600i
$885$		0			0
$886$	−13.6158	+	23.5832i	−0.457431	+	0.792294i
$887$	−40.6124			−1.36363			−0.681815	−	0.731525i	$-0.738809\pi$
$887$	−40.6124			−1.36363			−0.681815	+	0.731525i	$0.738809\pi$
$888$		0			0
$889$	−22.7106	−	12.8735i	−0.761690	−	0.431764i
$890$	6.95005	+	4.01262i	0.232966	+	0.134503i
$891$		0			0
$892$	−1.20295	+	0.694525i	−0.0402778	+	0.0232544i
$893$		−	32.4687i		−	1.08652i
$894$		0			0
$895$	17.1268	−	9.88814i	0.572484	−	0.330524i
$896$	1.34096	+	2.28075i	0.0447983	+	0.0761946i
$897$		0			0
$898$	9.97430	−	17.2760i	0.332847	−	0.576507i
$899$	3.45471	−	5.98374i	0.115221	−	0.199569i
$900$		0			0
$901$	−10.5665	+	6.10059i	−0.352022	+	0.203240i
$902$	5.16877			0.172101
$903$		0			0
$904$	−3.47587	+	6.02039i	−0.115606	+	0.200235i
$905$	−66.5267	−	38.4092i	−2.21142	−	1.27677i
$906$		0			0
$907$	1.24557	−	2.15739i	0.0413584	−	0.0716348i	−0.844605	−	0.535390i	$-0.820165\pi$
$907$	1.24557	−	2.15739i	0.0413584	−	0.0716348i	0.885964	+	0.463755i	$0.153498\pi$
$908$	−17.4434			−0.578881
$909$		0			0
$910$	27.3145	−	14.0255i	0.905467	−	0.464940i
$911$			7.57945i			0.251118i	0.992086	+	0.125559i	$0.0400725\pi$
$911$			7.57945i			0.251118i	−0.992086	+	0.125559i	$0.959928\pi$
$912$		0			0
$913$	10.0769	+	5.81788i	0.333496	+	0.192544i
$914$		−	36.5159i		−	1.20784i
$915$		0			0
$916$	−6.54345	−	3.77786i	−0.216202	−	0.124824i
$917$	−0.170676	−	21.5757i	−0.00563623	−	0.712494i
$918$		0			0
$919$	−0.965287	−	1.67193i	−0.0318419	−	0.0551517i	0.849665	−	0.527322i	$-0.176804\pi$
$919$	−0.965287	−	1.67193i	−0.0318419	−	0.0551517i	−0.881507	+	0.472171i	$0.843471\pi$
$920$	10.8338	−	18.7647i	0.357180	−	0.618654i
$921$		0			0
$922$	0.684736	+	0.395333i	0.0225506	+	0.0130196i
$923$	−42.4858	−	2.43006i	−1.39844	−	0.0799863i
$924$		0			0
$925$	−19.9226	−	34.5070i	−0.655052	−	1.13458i
$926$			9.97610i			0.327835i
$927$		0			0
$928$	−1.97467	−	3.42023i	−0.0648218	−	0.112275i
$929$	−9.92992	−	17.1991i	−0.325790	−	0.564285i	0.655882	−	0.754864i	$-0.272297\pi$
$929$	−9.92992	−	17.1991i	−0.325790	−	0.564285i	−0.981672	+	0.190579i	$0.938964\pi$
$930$		0			0
$931$	0.301948	+	19.0839i	0.00989595	+	0.625450i
$932$	−13.2001	−	7.62108i	−0.432383	−	0.249637i
$933$		0			0
$934$	2.86731	+	1.65544i	0.0938214	+	0.0541678i
$935$	−5.58114	+	3.22228i	−0.182523	+	0.105380i
$936$		0			0
$937$		−	9.21014i		−	0.300882i	−0.988619	−	0.150441i	$-0.951931\pi$
$937$		−	9.21014i		−	0.300882i	0.988619	−	0.150441i	$-0.0480694\pi$
$938$	18.9592	−	0.149978i	0.619039	−	0.00489695i
$939$		0			0
$940$	−19.1646	−	33.1940i	−0.625079	−	1.08267i
$941$	−15.5975	−	27.0157i	−0.508465	−	0.880687i	−0.999952	−	0.00980186i	$-0.996880\pi$
$941$	−15.5975	−	27.0157i	−0.508465	−	0.880687i	0.491487	−	0.870885i	$-0.336453\pi$
$942$		0			0
$943$	−22.4517	+	12.9625i	−0.731127	+	0.422117i
$944$	9.70505			0.315872
$945$		0			0
$946$	−0.139054	−	0.240849i	−0.00452104	−	0.00783066i
$947$			47.9790i			1.55911i	0.626335	+	0.779554i	$0.284554\pi$
$947$			47.9790i			1.55911i	−0.626335	+	0.779554i	$0.715446\pi$
$948$		0			0
$949$	7.31064	−	11.1406i	0.237313	−	0.361638i
$950$	−7.30787	+	12.6576i	−0.237099	+	0.410667i
$951$		0			0
$952$	2.00045	+	3.40244i	0.0648351	+	0.110274i
$953$	12.4088	+	7.16424i	0.401962	+	0.232073i	0.687330	−	0.726345i	$-0.258783\pi$
$953$	12.4088	+	7.16424i	0.401962	+	0.232073i	−0.285368	+	0.958418i	$0.592116\pi$
$954$		0			0
$955$			74.9984i			2.42689i
$956$		−	27.8312i		−	0.900125i
$957$		0			0
$958$	−8.72620	−	5.03807i	−0.281931	−	0.162773i
$959$	18.1136	+	30.8082i	0.584918	+	0.994850i
$960$		0			0
$961$	−13.9696	+	24.1961i	−0.450632	+	0.780518i
$962$	−12.0533	−	23.9377i	−0.388613	−	0.771783i
$963$		0			0
$964$			3.34033i			0.107585i
$965$	29.8546	+	51.7097i	0.961053	+	1.66459i
$966$		0			0
$967$	−1.62832			−0.0523632			−0.0261816	−	0.999657i	$-0.508335\pi$
$967$	−1.62832			−0.0523632			−0.0261816	+	0.999657i	$0.508335\pi$
$968$	−7.96632	+	4.59936i	−0.256047	+	0.147829i
$969$		0			0
$970$	−23.5615	−	40.8098i	−0.756515	−	1.31032i
$971$	12.5028	+	21.6555i	0.401235	+	0.694959i	0.993875	−	0.110508i	$-0.0352478\pi$
$971$	12.5028	+	21.6555i	0.401235	+	0.694959i	−0.592641	+	0.805467i	$0.701915\pi$
$972$		0			0
$973$	44.4806	−	0.351867i	1.42598	−	0.0112803i
$974$			5.47656i			0.175480i
$975$		0			0
$976$	−4.80221	+	2.77256i	−0.153715	+	0.0887474i
$977$	6.95475	+	4.01533i	0.222502	+	0.128462i	0.607108	−	0.794619i	$-0.292329\pi$
$977$	6.95475	+	4.01533i	0.222502	+	0.128462i	−0.384606	+	0.923081i	$0.625663\pi$
$978$		0			0
$979$	−2.89795	−	1.67313i	−0.0926190	−	0.0534736i
$980$	11.5729	+	19.3320i	0.369684	+	0.617538i
$981$		0			0
$982$	6.70268	+	11.6094i	0.213891	+	0.370470i
$983$	−12.1347	−	21.0180i	−0.387038	−	0.670369i	0.605012	−	0.796216i	$-0.293168\pi$
$983$	−12.1347	−	21.0180i	−0.387038	−	0.670369i	−0.992050	+	0.125848i	$0.959835\pi$
$984$		0			0
$985$			53.1428i			1.69327i
$986$	−2.94583	−	5.10233i	−0.0938143	−	0.162491i
$987$		0			0
$988$	−5.39363	+	8.21927i	−0.171594	+	0.261490i
$989$	1.20802	+	0.697453i	0.0384129	+	0.0221777i
$990$		0			0
$991$	15.4327	−	26.7302i	0.490236	−	0.849113i	−0.509701	−	0.860351i	$-0.670244\pi$
$991$	15.4327	−	26.7302i	0.490236	−	0.849113i	0.999937	+	0.0112385i	$0.00357739\pi$
$992$	−0.874756	−	1.51512i	−0.0277735	−	0.0481052i
$993$		0			0
$994$	−0.247015	−	31.2260i	−0.00783485	−	0.990429i
$995$	15.5412	+	8.97269i	0.492688	+	0.284453i
$996$		0			0
$997$		−	2.84369i		−	0.0900605i	−0.998986	−	0.0450302i	$-0.985662\pi$
$997$		−	2.84369i		−	0.0900605i	0.998986	−	0.0450302i	$-0.0143384\pi$
$998$	−13.5371	−	7.81563i	−0.428509	−	0.247400i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.cm.a.341.33	yes	72
3.2	odd	2	inner	1638.2.cm.a.341.4	yes	72
7.3	odd	6		1638.2.bq.a.1277.1	yes	72
13.9	even	3		1638.2.bq.a.971.36	yes	72
21.17	even	6		1638.2.bq.a.1277.36	yes	72
39.35	odd	6		1638.2.bq.a.971.1	✓	72
91.87	odd	6	inner	1638.2.cm.a.269.4	yes	72
273.269	even	6	inner	1638.2.cm.a.269.33	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bq.a.971.1	✓	72	39.35	odd	6
1638.2.bq.a.971.36	yes	72	13.9	even	3
1638.2.bq.a.1277.1	yes	72	7.3	odd	6
1638.2.bq.a.1277.36	yes	72	21.17	even	6
1638.2.cm.a.269.4	yes	72	91.87	odd	6	inner
1638.2.cm.a.269.33	yes	72	273.269	even	6	inner
1638.2.cm.a.341.4	yes	72	3.2	odd	2	inner
1638.2.cm.a.341.33	yes	72	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.60938 - 2.78753i) q^{5} +(-2.28075 + 1.34096i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.60938 - 2.78753i) q^{5} +(-2.28075 + 1.34096i) q^{7} -1.00000i q^{8} +(2.78753 + 1.60938i) q^{10} +(-1.16231 - 0.671060i) q^{11} +(-3.22035 + 1.62153i) q^{13} +(-1.34096 - 2.28075i) q^{14} +1.00000 q^{16} +1.49181 q^{17} +(-2.36132 + 1.36331i) q^{19} +(-1.60938 + 2.78753i) q^{20} +(0.671060 - 1.16231i) q^{22} +6.73167i q^{23} +(-2.68020 - 4.64224i) q^{25} +(-1.62153 - 3.22035i) q^{26} +(2.28075 - 1.34096i) q^{28} +(-3.42023 + 1.97467i) q^{29} +(-1.51512 + 0.874756i) q^{31} +1.00000i q^{32} +1.49181i q^{34} +(0.0673645 + 8.51576i) q^{35} +7.43327 q^{37} +(-1.36331 - 2.36132i) q^{38} +(-2.78753 - 1.60938i) q^{40} +(1.92560 + 3.33523i) q^{41} +(0.103608 - 0.179454i) q^{43} +(1.16231 + 0.671060i) q^{44} -6.73167 q^{46} +(-5.95403 + 10.3127i) q^{47} +(3.40366 - 6.11679i) q^{49} +(4.64224 - 2.68020i) q^{50} +(3.22035 - 1.62153i) q^{52} +(-7.08304 + 4.08939i) q^{53} +(-3.74120 + 2.15998i) q^{55} +(1.34096 + 2.28075i) q^{56} +(-1.97467 - 3.42023i) q^{58} +9.70505 q^{59} +(-4.80221 + 2.77256i) q^{61} +(-0.874756 - 1.51512i) q^{62} -1.00000 q^{64} +(-0.662710 + 11.5865i) q^{65} +(-3.58306 + 6.20604i) q^{67} -1.49181 q^{68} +(-8.51576 + 0.0673645i) q^{70} +(10.2214 + 5.90134i) q^{71} +(-3.20058 + 1.84786i) q^{73} +7.43327i q^{74} +(2.36132 - 1.36331i) q^{76} +(3.55081 - 0.0280889i) q^{77} +(0.259931 - 0.450214i) q^{79} +(1.60938 - 2.78753i) q^{80} +(-3.33523 + 1.92560i) q^{82} -8.66968 q^{83} +(2.40088 - 4.15845i) q^{85} +(0.179454 + 0.103608i) q^{86} +(-0.671060 + 1.16231i) q^{88} +2.49327 q^{89} +(5.17041 - 8.01666i) q^{91} -6.73167i q^{92} +(-10.3127 - 5.95403i) q^{94} +8.77631i q^{95} +(-12.6787 - 7.32007i) q^{97} +(6.11679 + 3.40366i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) \) 72 * q - 72 * q^4 - 4 * q^7	\( 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) \) 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

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