LMFDB - Embedded newform 630.2.be.b.341.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(341,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("630.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.be (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.2
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	630.341
Dual form			630.2.be.b.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.63896 + 0.189469i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.63896 + 0.189469i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +(1.32697 - 0.766125i) q^{11} +1.48236i q^{13} +(-2.19067 - 1.48356i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.21441 - 2.10342i) q^{17} +(4.21209 + 2.43185i) q^{19} +1.00000 q^{20} -1.53225 q^{22} +(-0.232051 - 0.133975i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.741181 - 1.28376i) q^{26} +(1.15539 + 2.38014i) q^{28} +0.898979i q^{29} +(-0.717439 + 0.414214i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.42883i q^{34} +(1.48356 - 2.19067i) q^{35} +(2.74118 - 4.74786i) q^{37} +(-2.43185 - 4.21209i) q^{38} +(-0.866025 - 0.500000i) q^{40} +8.76028 q^{41} +1.86370 q^{43} +(1.32697 + 0.766125i) q^{44} +(0.133975 + 0.232051i) q^{46} +(3.72973 - 6.46008i) q^{47} +(6.92820 + 1.00000i) q^{49} +1.00000i q^{50} +(-1.28376 + 0.741181i) q^{52} +(-3.00524 + 1.73508i) q^{53} -1.53225i q^{55} +(0.189469 - 2.63896i) q^{56} +(0.449490 - 0.778539i) q^{58} +(-3.12837 - 5.41849i) q^{59} +(5.73445 + 3.31079i) q^{61} +0.828427 q^{62} -1.00000 q^{64} +(1.28376 + 0.741181i) q^{65} +(-8.01702 - 13.8859i) q^{67} +(1.21441 - 2.10342i) q^{68} +(-2.38014 + 1.15539i) q^{70} +12.7627i q^{71} +(0.297173 - 0.171573i) q^{73} +(-4.74786 + 2.74118i) q^{74} +4.86370i q^{76} +(3.64697 - 1.77035i) q^{77} +(5.22438 - 9.04889i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-7.58662 - 4.38014i) q^{82} +5.45001 q^{83} -2.42883 q^{85} +(-1.61401 - 0.931852i) q^{86} +(-0.766125 - 1.32697i) q^{88} +(-7.98502 + 13.8305i) q^{89} +(-0.280861 + 3.91189i) q^{91} -0.267949i q^{92} +(-6.46008 + 3.72973i) q^{94} +(4.21209 - 2.43185i) q^{95} -14.9481i q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{5}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^5	$ 8 q + 4 q^{4} + 4 q^{5} + 24 q^{11} - 4 q^{16} + 8 q^{20} + 12 q^{23} - 4 q^{25} + 8 q^{26} + 24 q^{37} - 4 q^{38} + 32 q^{41} - 16 q^{43} + 24 q^{44} + 8 q^{46} - 8 q^{47} + 24 q^{53} - 16 q^{58} - 24 q^{59} - 16 q^{62} - 8 q^{64} - 24 q^{67} - 16 q^{77} - 24 q^{79} + 4 q^{80} - 16 q^{83} - 16 q^{89} - 20 q^{91} - 12 q^{94} - 44 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^5 + 24 * q^11 - 4 * q^16 + 8 * q^20 + 12 * q^23 - 4 * q^25 + 8 * q^26 + 24 * q^37 - 4 * q^38 + 32 * q^41 - 16 * q^43 + 24 * q^44 + 8 * q^46 - 8 * q^47 + 24 * q^53 - 16 * q^58 - 24 * q^59 - 16 * q^62 - 8 * q^64 - 24 * q^67 - 16 * q^77 - 24 * q^79 + 4 * q^80 - 16 * q^83 - 16 * q^89 - 20 * q^91 - 12 * q^94 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$	1.32697	−	0.766125i	0.400096	−	0.230995i	−0.286430	−	0.958101i	$-0.592468\pi$
$11$	1.32697	−	0.766125i	0.400096	−	0.230995i	0.686525	+	0.727106i	$0.259135\pi$
$12$		0			0
$13$			1.48236i			0.411133i	0.978643	+	0.205567i	$0.0659037\pi$
$13$			1.48236i			0.411133i	−0.978643	+	0.205567i	$0.934096\pi$
$14$	−2.19067	−	1.48356i	−0.585481	−	0.396499i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.21441	−	2.10342i	−0.294538	−	0.510155i	0.680339	−	0.732898i	$-0.261833\pi$
$17$	−1.21441	−	2.10342i	−0.294538	−	0.510155i	−0.974877	+	0.222742i	$0.928499\pi$
$18$		0			0
$19$	4.21209	+	2.43185i	0.966320	+	0.557905i	0.898112	−	0.439766i	$-0.144939\pi$
$19$	4.21209	+	2.43185i	0.966320	+	0.557905i	0.0682075	+	0.997671i	$0.478272\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−1.53225			−0.326677
$23$	−0.232051	−	0.133975i	−0.0483859	−	0.0279356i	0.475612	−	0.879655i	$-0.342227\pi$
$23$	−0.232051	−	0.133975i	−0.0483859	−	0.0279356i	−0.523998	+	0.851720i	$0.675560\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.741181	−	1.28376i	0.145358	−	0.251767i
$27$		0			0
$28$	1.15539	+	2.38014i	0.218349	+	0.449804i
$29$			0.898979i			0.166936i	0.996510	+	0.0834681i	$0.0265997\pi$
$29$			0.898979i			0.166936i	−0.996510	+	0.0834681i	$0.973400\pi$
$30$		0			0
$31$	−0.717439	+	0.414214i	−0.128856	+	0.0743950i	−0.563042	−	0.826428i	$-0.690369\pi$
$31$	−0.717439	+	0.414214i	−0.128856	+	0.0743950i	0.434187	+	0.900823i	$0.357036\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			2.42883i			0.416540i
$35$	1.48356	−	2.19067i	0.250768	−	0.370291i
$36$		0			0
$37$	2.74118	−	4.74786i	0.450647	−	0.780544i	−0.547779	−	0.836623i	$-0.684527\pi$
$37$	2.74118	−	4.74786i	0.450647	−	0.780544i	0.998426	+	0.0560790i	$0.0178599\pi$
$38$	−2.43185	−	4.21209i	−0.394498	−	0.683291i
$39$		0			0
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	8.76028			1.36813			0.684063	−	0.729423i	$-0.260211\pi$
$41$	8.76028			1.36813			0.684063	+	0.729423i	$0.260211\pi$
$42$		0			0
$43$	1.86370			0.284212			0.142106	−	0.989851i	$-0.454613\pi$
$43$	1.86370			0.284212			0.142106	+	0.989851i	$0.454613\pi$
$44$	1.32697	+	0.766125i	0.200048	+	0.115498i
$45$		0			0
$46$	0.133975	+	0.232051i	0.0197535	+	0.0342140i
$47$	3.72973	−	6.46008i	0.544037	−	0.942299i	−0.454630	−	0.890680i	$-0.650229\pi$
$47$	3.72973	−	6.46008i	0.544037	−	0.942299i	0.998667	−	0.0516191i	$-0.0164382\pi$
$48$		0			0
$49$	6.92820	+	1.00000i	0.989743	+	0.142857i
$50$			1.00000i			0.141421i
$51$		0			0
$52$	−1.28376	+	0.741181i	−0.178026	+	0.102783i
$53$	−3.00524	+	1.73508i	−0.412802	+	0.238331i	−0.691993	−	0.721904i	$-0.743267\pi$
$53$	−3.00524	+	1.73508i	−0.412802	+	0.238331i	0.279191	+	0.960236i	$0.409934\pi$
$54$		0			0
$55$		−	1.53225i		−	0.206609i
$56$	0.189469	−	2.63896i	0.0253188	−	0.352646i
$57$		0			0
$58$	0.449490	−	0.778539i	0.0590209	−	0.102227i
$59$	−3.12837	−	5.41849i	−0.407279	−	0.705428i	0.587305	−	0.809366i	$-0.300189\pi$
$59$	−3.12837	−	5.41849i	−0.407279	−	0.705428i	−0.994584	+	0.103938i	$0.966856\pi$
$60$		0			0
$61$	5.73445	+	3.31079i	0.734222	+	0.423903i	0.819965	−	0.572414i	$-0.193993\pi$
$61$	5.73445	+	3.31079i	0.734222	+	0.423903i	−0.0857429	+	0.996317i	$0.527326\pi$
$62$	0.828427			0.105210
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.28376	+	0.741181i	0.159231	+	0.0919322i
$66$		0			0
$67$	−8.01702	−	13.8859i	−0.979434	−	1.69643i	−0.664449	−	0.747334i	$-0.731334\pi$
$67$	−8.01702	−	13.8859i	−0.979434	−	1.69643i	−0.314985	−	0.949097i	$-0.602000\pi$
$68$	1.21441	−	2.10342i	0.147269	−	0.255078i
$69$		0			0
$70$	−2.38014	+	1.15539i	−0.284481	+	0.138096i
$71$			12.7627i			1.51465i	0.653037	+	0.757326i	$0.273495\pi$
$71$			12.7627i			1.51465i	−0.653037	+	0.757326i	$0.726505\pi$
$72$		0			0
$73$	0.297173	−	0.171573i	0.0347815	−	0.0200811i	−0.482508	−	0.875891i	$-0.660274\pi$
$73$	0.297173	−	0.171573i	0.0347815	−	0.0200811i	0.517290	+	0.855810i	$0.326941\pi$
$74$	−4.74786	+	2.74118i	−0.551928	+	0.318656i
$75$		0			0
$76$			4.86370i			0.557905i
$77$	3.64697	−	1.77035i	0.415611	−	0.201750i
$78$		0			0
$79$	5.22438	−	9.04889i	0.587789	−	1.01808i	−0.406733	−	0.913547i	$-0.633332\pi$
$79$	5.22438	−	9.04889i	0.587789	−	1.01808i	0.994521	−	0.104533i	$-0.0333347\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	−7.58662	−	4.38014i	−0.837802	−	0.483705i
$83$	5.45001			0.598216			0.299108	−	0.954219i	$-0.403311\pi$
$83$	5.45001			0.598216			0.299108	+	0.954219i	$0.403311\pi$
$84$		0			0
$85$	−2.42883			−0.263443
$86$	−1.61401	−	0.931852i	−0.174044	−	0.100484i
$87$		0			0
$88$	−0.766125	−	1.32697i	−0.0816692	−	0.141455i
$89$	−7.98502	+	13.8305i	−0.846411	+	1.46603i	0.0379795	+	0.999279i	$0.487908\pi$
$89$	−7.98502	+	13.8305i	−0.846411	+	1.46603i	−0.884390	+	0.466748i	$0.845426\pi$
$90$		0			0
$91$	−0.280861	+	3.91189i	−0.0294423	+	0.410078i
$92$		−	0.267949i		−	0.0279356i
$93$		0			0
$94$	−6.46008	+	3.72973i	−0.666306	+	0.384692i
$95$	4.21209	−	2.43185i	0.432151	−	0.249503i
$96$		0			0
$97$		−	14.9481i		−	1.51775i	−0.651234	−	0.758877i	$-0.725748\pi$
$97$		−	14.9481i		−	1.51775i	0.651234	−	0.758877i	$-0.274252\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	1.36773	+	2.36897i	0.136094	+	0.235721i	0.926015	−	0.377487i	$-0.123212\pi$
$101$	1.36773	+	2.36897i	0.136094	+	0.235721i	−0.789921	+	0.613209i	$0.789878\pi$
$102$		0			0
$103$	−5.34935	−	3.08845i	−0.527087	−	0.304314i	0.212742	−	0.977108i	$-0.431760\pi$
$103$	−5.34935	−	3.08845i	−0.527087	−	0.304314i	−0.739829	+	0.672794i	$0.765094\pi$
$104$	1.48236			0.145358
$105$		0			0
$106$	3.47015			0.337051
$107$	−3.95768	−	2.28497i	−0.382603	−	0.220896i	0.296347	−	0.955080i	$-0.404231\pi$
$107$	−3.95768	−	2.28497i	−0.382603	−	0.220896i	−0.678950	+	0.734184i	$0.737565\pi$
$108$		0			0
$109$	2.97934	+	5.16036i	0.285369	+	0.494273i	0.972699	−	0.232072i	$-0.0745506\pi$
$109$	2.97934	+	5.16036i	0.285369	+	0.494273i	−0.687330	+	0.726345i	$0.741217\pi$
$110$	−0.766125	+	1.32697i	−0.0730472	+	0.126521i
$111$		0			0
$112$	−1.48356	+	2.19067i	−0.140184	+	0.206999i
$113$			19.8977i			1.87182i	0.352237	+	0.935911i	$0.385421\pi$
$113$			19.8977i			1.87182i	−0.352237	+	0.935911i	$0.614579\pi$
$114$		0			0
$115$	−0.232051	+	0.133975i	−0.0216388	+	0.0124932i
$116$	−0.778539	+	0.449490i	−0.0722855	+	0.0417341i
$117$		0			0
$118$			6.25674i			0.575979i
$119$	−2.80625	−	5.78094i	−0.257249	−	0.529938i
$120$		0			0
$121$	−4.32611	+	7.49303i	−0.393282	+	0.681185i
$122$	−3.31079	−	5.73445i	−0.299745	−	0.519173i
$123$		0			0
$124$	−0.717439	−	0.414214i	−0.0644279	−	0.0371975i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−21.2025			−1.88142			−0.940708	−	0.339219i	$-0.889837\pi$
$127$	−21.2025			−1.88142			−0.940708	+	0.339219i	$0.889837\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−0.741181	−	1.28376i	−0.0650059	−	0.112593i
$131$	−3.73085	+	6.46202i	−0.325966	+	0.564589i	−0.981707	−	0.190396i	$-0.939023\pi$
$131$	−3.73085	+	6.46202i	−0.325966	+	0.564589i	0.655742	+	0.754985i	$0.272356\pi$
$132$		0			0
$133$	10.6548	+	7.21561i	0.923886	+	0.625673i
$134$			16.0340i			1.38513i
$135$		0			0
$136$	−2.10342	+	1.21441i	−0.180367	+	0.104135i
$137$	0.538302	−	0.310789i	0.0459903	−	0.0265525i	−0.476829	−	0.878996i	$-0.658214\pi$
$137$	0.538302	−	0.310789i	0.0459903	−	0.0265525i	0.522819	+	0.852444i	$0.324880\pi$
$138$		0			0
$139$			18.5334i			1.57198i	0.618237	+	0.785992i	$0.287847\pi$
$139$			18.5334i			1.57198i	−0.618237	+	0.785992i	$0.712153\pi$
$140$	2.63896	+	0.189469i	0.223033	+	0.0160130i
$141$		0			0
$142$	6.38134	−	11.0528i	0.535510	−	0.927531i
$143$	1.13567	+	1.96705i	0.0949699	+	0.164493i
$144$		0			0
$145$	0.778539	+	0.449490i	0.0646542	+	0.0373281i
$146$	−0.343146			−0.0283989
$147$		0			0
$148$	5.48236			0.450647
$149$	−12.1100	−	6.99171i	−0.992089	−	0.572783i	−0.0861911	−	0.996279i	$-0.527470\pi$
$149$	−12.1100	−	6.99171i	−0.992089	−	0.572783i	−0.905898	+	0.423496i	$0.860803\pi$
$150$		0			0
$151$	−9.83839	−	17.0406i	−0.800637	−	1.38674i	−0.919197	−	0.393797i	$-0.871161\pi$
$151$	−9.83839	−	17.0406i	−0.800637	−	1.38674i	0.118560	−	0.992947i	$-0.462172\pi$
$152$	2.43185	−	4.21209i	0.197249	−	0.341646i
$153$		0			0
$154$	−4.04354	−	0.290313i	−0.325838	−	0.0233941i
$155$			0.828427i			0.0665409i
$156$		0			0
$157$	−7.84628	+	4.53005i	−0.626201	+	0.361538i	−0.779279	−	0.626677i	$-0.784415\pi$
$157$	−7.84628	+	4.53005i	−0.626201	+	0.361538i	0.153078	+	0.988214i	$0.451081\pi$
$158$	−9.04889	+	5.22438i	−0.719891	+	0.415629i
$159$		0			0
$160$		−	1.00000i		−	0.0790569i
$161$	−0.586988	−	0.397520i	−0.0462612	−	0.0313289i
$162$		0			0
$163$	−5.91019	+	10.2368i	−0.462922	+	0.801804i	−0.999105	−	0.0422974i	$-0.986532\pi$
$163$	−5.91019	+	10.2368i	−0.462922	+	0.801804i	0.536183	+	0.844102i	$0.319866\pi$
$164$	4.38014	+	7.58662i	0.342031	+	0.592416i
$165$		0			0
$166$	−4.71984	−	2.72500i	−0.366331	−	0.211501i
$167$	15.7778			1.22092			0.610462	−	0.792046i	$-0.290984\pi$
$167$	15.7778			1.22092			0.610462	+	0.792046i	$0.290984\pi$
$168$		0			0
$169$	10.8026			0.830969
$170$	2.10342	+	1.21441i	0.161325	+	0.0931412i
$171$		0			0
$172$	0.931852	+	1.61401i	0.0710530	+	0.123067i
$173$	−10.1111	+	17.5129i	−0.768730	+	1.33148i	0.169521	+	0.985527i	$0.445778\pi$
$173$	−10.1111	+	17.5129i	−0.768730	+	1.33148i	−0.938252	+	0.345954i	$0.887555\pi$
$174$		0			0
$175$	−1.15539	−	2.38014i	−0.0873396	−	0.179922i
$176$			1.53225i			0.115498i
$177$		0			0
$178$	13.8305	−	7.98502i	1.03664	−	0.598503i
$179$	−5.94667	+	3.43331i	−0.444475	+	0.256618i	−0.705494	−	0.708716i	$-0.749275\pi$
$179$	−5.94667	+	3.43331i	−0.444475	+	0.256618i	0.261019	+	0.965334i	$0.415941\pi$
$180$		0			0
$181$			16.3066i			1.21206i	0.795441	+	0.606031i	$0.207239\pi$
$181$			16.3066i			1.21206i	−0.795441	+	0.606031i	$0.792761\pi$
$182$	2.19918	−	3.24737i	0.163014	−	0.240711i
$183$		0			0
$184$	−0.133975	+	0.232051i	−0.00987674	+	0.0171070i
$185$	−2.74118	−	4.74786i	−0.201536	−	0.349070i
$186$		0			0
$187$	−3.22297	−	1.86078i	−0.235687	−	0.136074i
$188$	7.45946			0.544037
$189$		0			0
$190$	−4.86370			−0.352850
$191$	−14.8630	−	8.58114i	−1.07545	−	0.620910i	−0.145782	−	0.989317i	$-0.546570\pi$
$191$	−14.8630	−	8.58114i	−1.07545	−	0.620910i	−0.929665	+	0.368407i	$0.879903\pi$
$192$		0			0
$193$	−4.52761	−	7.84204i	−0.325904	−	0.564483i	0.655791	−	0.754943i	$-0.272335\pi$
$193$	−4.52761	−	7.84204i	−0.325904	−	0.564483i	−0.981695	+	0.190460i	$0.939002\pi$
$194$	−7.47407	+	12.9455i	−0.536607	+	0.929430i
$195$		0			0
$196$	2.59808	+	6.50000i	0.185577	+	0.464286i
$197$			21.7379i			1.54876i	0.632720	+	0.774380i	$0.281938\pi$
$197$			21.7379i			1.54876i	−0.632720	+	0.774380i	$0.718062\pi$
$198$		0			0
$199$	−7.21101	+	4.16328i	−0.511175	+	0.295127i	−0.733317	−	0.679887i	$-0.762029\pi$
$199$	−7.21101	+	4.16328i	−0.511175	+	0.295127i	0.222141	+	0.975014i	$0.428695\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$		0			0
$202$		−	2.73545i		−	0.192466i
$203$	−0.170328	+	2.37237i	−0.0119547	+	0.166508i
$204$		0			0
$205$	4.38014	−	7.58662i	0.305922	−	0.529873i
$206$	3.08845	+	5.34935i	0.215182	+	0.372707i
$207$		0			0
$208$	−1.28376	−	0.741181i	−0.0890130	−	0.0513917i
$209$	7.45241			0.515494
$210$		0			0
$211$	−19.9330			−1.37225			−0.686123	−	0.727486i	$-0.740689\pi$
$211$	−19.9330			−1.37225			−0.686123	+	0.727486i	$0.740689\pi$
$212$	−3.00524	−	1.73508i	−0.206401	−	0.119166i
$213$		0			0
$214$	2.28497	+	3.95768i	0.156197	+	0.270541i
$215$	0.931852	−	1.61401i	0.0635518	−	0.110075i
$216$		0			0
$217$	−1.97177	+	0.957160i	−0.133853	+	0.0649763i
$218$		−	5.95867i		−	0.403572i
$219$		0			0
$220$	1.32697	−	0.766125i	0.0894641	−	0.0516521i
$221$	3.11804	−	1.80020i	0.209742	−	0.121094i
$222$		0			0
$223$			7.16604i			0.479873i	0.970789	+	0.239937i	$0.0771267\pi$
$223$			7.16604i			0.479873i	−0.970789	+	0.239937i	$0.922873\pi$
$224$	2.38014	−	1.15539i	0.159030	−	0.0771980i
$225$		0			0
$226$	9.94887	−	17.2319i	0.661789	−	1.14625i
$227$	−7.92721	−	13.7303i	−0.526147	−	0.911314i	−0.999536	−	0.0304601i	$-0.990303\pi$
$227$	−7.92721	−	13.7303i	−0.526147	−	0.911314i	0.473389	−	0.880854i	$-0.343031\pi$
$228$		0			0
$229$	24.4371	+	14.1087i	1.61485	+	0.932332i	0.988225	+	0.153009i	$0.0488964\pi$
$229$	24.4371	+	14.1087i	1.61485	+	0.932332i	0.626622	+	0.779323i	$0.284437\pi$
$230$	0.267949			0.0176680
$231$		0			0
$232$	0.898979			0.0590209
$233$	−21.0421	−	12.1487i	−1.37851	−	0.795886i	−0.386534	−	0.922275i	$-0.626328\pi$
$233$	−21.0421	−	12.1487i	−1.37851	−	0.795886i	−0.991981	+	0.126390i	$0.959661\pi$
$234$		0			0
$235$	−3.72973	−	6.46008i	−0.243301	−	0.421409i
$236$	3.12837	−	5.41849i	0.203639	−	0.352714i
$237$		0			0
$238$	−0.460186	+	6.40957i	−0.0298295	+	0.415471i
$239$		−	19.9081i		−	1.28774i	−0.765133	−	0.643872i	$-0.777327\pi$
$239$		−	19.9081i		−	1.28774i	0.765133	−	0.643872i	$-0.222673\pi$
$240$		0			0
$241$	17.7755	−	10.2627i	1.14502	−	0.661078i	0.197351	−	0.980333i	$-0.436766\pi$
$241$	17.7755	−	10.2627i	1.14502	−	0.661078i	0.947669	+	0.319255i	$0.103433\pi$
$242$	7.49303	−	4.32611i	0.481670	−	0.278093i
$243$		0			0
$244$			6.62158i			0.423903i
$245$	4.33013	−	5.50000i	0.276642	−	0.351382i
$246$		0			0
$247$	−3.60488	+	6.24384i	−0.229373	+	0.397286i
$248$	0.414214	+	0.717439i	0.0263026	+	0.0455574i
$249$		0			0
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	5.86787			0.370376			0.185188	−	0.982703i	$-0.440711\pi$
$251$	5.86787			0.370376			0.185188	+	0.982703i	$0.440711\pi$
$252$		0			0
$253$	−0.410565			−0.0258120
$254$	18.3619	+	10.6012i	1.15213	+	0.665181i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.83083	−	6.63519i	0.238961	−	0.413892i	−0.721456	−	0.692461i	$-0.756527\pi$
$257$	3.83083	−	6.63519i	0.238961	−	0.413892i	0.960416	+	0.278569i	$0.0898600\pi$
$258$		0			0
$259$	8.13343	−	12.0100i	0.505387	−	0.746268i
$260$			1.48236i			0.0919322i
$261$		0			0
$262$	6.46202	−	3.73085i	0.399225	−	0.230493i
$263$	7.32905	−	4.23143i	0.451929	−	0.260921i	−0.256716	−	0.966487i	$-0.582640\pi$
$263$	7.32905	−	4.23143i	0.451929	−	0.260921i	0.708644	+	0.705566i	$0.249307\pi$
$264$		0			0
$265$			3.47015i			0.213170i
$266$	−5.61950	−	11.5763i	−0.344553	−	0.709788i
$267$		0			0
$268$	8.01702	−	13.8859i	0.489717	−	0.848215i
$269$	−8.52155	−	14.7598i	−0.519568	−	0.899919i	−0.999741	−	0.0227449i	$-0.992759\pi$
$269$	−8.52155	−	14.7598i	−0.519568	−	0.899919i	0.480173	−	0.877174i	$-0.340574\pi$
$270$		0			0
$271$	−9.12436	−	5.26795i	−0.554265	−	0.320005i	0.196575	−	0.980489i	$-0.437018\pi$
$271$	−9.12436	−	5.26795i	−0.554265	−	0.320005i	−0.750840	+	0.660484i	$0.770351\pi$
$272$	2.42883			0.147269
$273$		0			0
$274$	−0.621578			−0.0375509
$275$	−1.32697	−	0.766125i	−0.0800191	−	0.0461991i
$276$		0			0
$277$	4.04561	+	7.00720i	0.243077	+	0.421022i	0.961589	−	0.274493i	$-0.0885099\pi$
$277$	4.04561	+	7.00720i	0.243077	+	0.421022i	−0.718512	+	0.695514i	$0.755177\pi$
$278$	9.26670	−	16.0504i	0.555780	−	0.962639i
$279$		0			0
$280$	−2.19067	−	1.48356i	−0.130918	−	0.0886599i
$281$		−	11.1684i		−	0.666253i	−0.942882	−	0.333127i	$-0.891896\pi$
$281$		−	11.1684i		−	0.666253i	0.942882	−	0.333127i	$-0.108104\pi$
$282$		0			0
$283$	−6.24917	+	3.60796i	−0.371475	+	0.214471i	−0.674103	−	0.738638i	$-0.735469\pi$
$283$	−6.24917	+	3.60796i	−0.371475	+	0.214471i	0.302628	+	0.953109i	$0.402136\pi$
$284$	−11.0528	+	6.38134i	−0.655863	+	0.378663i
$285$		0			0
$286$		−	2.27135i		−	0.134308i
$287$	23.1180	+	1.65980i	1.36461	+	0.0979748i
$288$		0			0
$289$	5.55040	−	9.61358i	0.326494	−	0.565505i
$290$	−0.449490	−	0.778539i	−0.0263949	−	0.0457174i
$291$		0			0
$292$	0.297173	+	0.171573i	0.0173907	+	0.0100405i
$293$	18.2573			1.06660			0.533300	−	0.845926i	$-0.320952\pi$
$293$	18.2573			1.06660			0.533300	+	0.845926i	$0.320952\pi$
$294$		0			0
$295$	−6.25674			−0.364281
$296$	−4.74786	−	2.74118i	−0.275964	−	0.159328i
$297$		0			0
$298$	6.99171	+	12.1100i	0.405019	+	0.701513i
$299$	0.198599	−	0.343983i	0.0114853	−	0.0198931i
$300$		0			0
$301$	4.91824	+	0.353113i	0.283482	+	0.0203531i
$302$			19.6768i			1.13227i
$303$		0			0
$304$	−4.21209	+	2.43185i	−0.241580	+	0.139476i
$305$	5.73445	−	3.31079i	0.328354	−	0.189575i
$306$		0			0
$307$			3.42078i			0.195234i	0.995224	+	0.0976172i	$0.0311221\pi$
$307$			3.42078i			0.195234i	−0.995224	+	0.0976172i	$0.968878\pi$
$308$	3.35666	+	2.27319i	0.191263	+	0.129527i
$309$		0			0
$310$	0.414214	−	0.717439i	0.0235257	−	0.0407478i
$311$	−2.84544	−	4.92845i	−0.161350	−	0.279467i	0.774003	−	0.633182i	$-0.218252\pi$
$311$	−2.84544	−	4.92845i	−0.161350	−	0.279467i	−0.935353	+	0.353715i	$0.884918\pi$
$312$		0			0
$313$	−11.5586	−	6.67335i	−0.653330	−	0.377200i	0.136401	−	0.990654i	$-0.456447\pi$
$313$	−11.5586	−	6.67335i	−0.653330	−	0.377200i	−0.789731	+	0.613453i	$0.789780\pi$
$314$	9.06010			0.511291
$315$		0			0
$316$	10.4488			0.587789
$317$	−10.8484	−	6.26330i	−0.609305	−	0.351782i	0.163389	−	0.986562i	$-0.447758\pi$
$317$	−10.8484	−	6.26330i	−0.609305	−	0.351782i	−0.772693	+	0.634780i	$0.781091\pi$
$318$		0			0
$319$	0.688731	+	1.19292i	0.0385615	+	0.0667905i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	0.309587	+	0.637756i	0.0172526	+	0.0355408i
$323$		−	11.8131i		−	0.657298i
$324$		0			0
$325$	1.28376	−	0.741181i	0.0712104	−	0.0411133i
$326$	10.2368	−	5.91019i	0.566961	−	0.327335i
$327$		0			0
$328$		−	8.76028i		−	0.483705i
$329$	11.0666	−	16.3412i	0.610120	−	0.900920i
$330$		0			0
$331$	0.640916	−	1.11010i	0.0352279	−	0.0610166i	−0.847874	−	0.530198i	$-0.822118\pi$
$331$	0.640916	−	1.11010i	0.0352279	−	0.0610166i	0.883102	+	0.469181i	$0.155451\pi$
$332$	2.72500	+	4.71984i	0.149554	+	0.259035i
$333$		0			0
$334$	−13.6640	−	7.88891i	−0.747660	−	0.431662i
$335$	−16.0340			−0.876033
$336$		0			0
$337$	−13.1058			−0.713920			−0.356960	−	0.934120i	$-0.616187\pi$
$337$	−13.1058			−0.713920			−0.356960	+	0.934120i	$0.616187\pi$
$338$	−9.35533	−	5.40130i	−0.508863	−	0.293792i
$339$		0			0
$340$	−1.21441	−	2.10342i	−0.0658608	−	0.114074i
$341$	−0.634679	+	1.09930i	−0.0343698	+	0.0595302i
$342$		0			0
$343$	18.0938	+	3.95164i	0.976972	+	0.213368i
$344$		−	1.86370i		−	0.100484i
$345$		0			0
$346$	17.5129	−	10.1111i	0.941499	−	0.543574i
$347$	12.3714	−	7.14262i	0.664130	−	0.383436i	−0.129719	−	0.991551i	$-0.541407\pi$
$347$	12.3714	−	7.14262i	0.664130	−	0.383436i	0.793849	+	0.608115i	$0.208074\pi$
$348$		0			0
$349$			13.2713i			0.710399i	0.934791	+	0.355200i	$0.115587\pi$
$349$			13.2713i			0.710399i	−0.934791	+	0.355200i	$0.884413\pi$
$350$	−0.189469	+	2.63896i	−0.0101275	+	0.141058i
$351$		0			0
$352$	0.766125	−	1.32697i	0.0408346	−	0.0707276i
$353$	16.3232	+	28.2725i	0.868794	+	1.50480i	0.863230	+	0.504811i	$0.168438\pi$
$353$	16.3232	+	28.2725i	0.868794	+	1.50480i	0.00556437	+	0.999985i	$0.498229\pi$
$354$		0			0
$355$	11.0528	+	6.38134i	0.586622	+	0.338686i
$356$	−15.9700			−0.846411
$357$		0			0
$358$	6.86662			0.362912
$359$	5.40692	+	3.12168i	0.285366	+	0.164756i	0.635850	−	0.771812i	$-0.280650\pi$
$359$	5.40692	+	3.12168i	0.285366	+	0.164756i	−0.350484	+	0.936569i	$0.613983\pi$
$360$		0			0
$361$	2.32780	+	4.03188i	0.122516	+	0.212204i
$362$	8.15331	−	14.1220i	0.428529	−	0.742233i
$363$		0			0
$364$	−3.52823	+	1.71271i	−0.184929	+	0.0897705i
$365$		−	0.343146i		−	0.0179611i
$366$		0			0
$367$	10.9026	−	6.29461i	0.569110	−	0.328576i	−0.187684	−	0.982230i	$-0.560098\pi$
$367$	10.9026	−	6.29461i	0.569110	−	0.328576i	0.756794	+	0.653654i	$0.226765\pi$
$368$	0.232051	−	0.133975i	0.0120965	−	0.00698391i
$369$		0			0
$370$			5.48236i			0.285014i
$371$	−8.25945	+	4.00940i	−0.428809	+	0.208158i
$372$		0			0
$373$	−17.9791	+	31.1408i	−0.930924	+	1.61241i	−0.149179	+	0.988810i	$0.547663\pi$
$373$	−17.9791	+	31.1408i	−0.930924	+	1.61241i	−0.781745	+	0.623598i	$0.785670\pi$
$374$	1.86078	+	3.22297i	0.0962188	+	0.166656i
$375$		0			0
$376$	−6.46008	−	3.72973i	−0.333153	−	0.192346i
$377$	−1.33261			−0.0686331
$378$		0			0
$379$	−11.5899			−0.595331			−0.297666	−	0.954670i	$-0.596208\pi$
$379$	−11.5899			−0.595331			−0.297666	+	0.954670i	$0.596208\pi$
$380$	4.21209	+	2.43185i	0.216076	+	0.124751i
$381$		0			0
$382$	8.58114	+	14.8630i	0.439049	+	0.760456i
$383$	2.23375	−	3.86897i	0.114139	−	0.197695i	−0.803296	−	0.595580i	$-0.796922\pi$
$383$	2.23375	−	3.86897i	0.114139	−	0.197695i	0.917435	+	0.397885i	$0.130256\pi$
$384$		0			0
$385$	0.290313	−	4.04354i	0.0147957	−	0.206078i
$386$			9.05521i			0.460898i
$387$		0			0
$388$	12.9455	−	7.47407i	0.657207	−	0.379438i
$389$	−11.2197	+	6.47772i	−0.568863	+	0.328433i	−0.756695	−	0.653768i	$-0.773187\pi$
$389$	−11.2197	+	6.47772i	−0.568863	+	0.328433i	0.187832	+	0.982201i	$0.439854\pi$
$390$		0			0
$391$			0.650802i			0.0329125i
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$		0			0
$394$	10.8689	−	18.8256i	0.547570	−	0.948418i
$395$	−5.22438	−	9.04889i	−0.262867	−	0.455299i
$396$		0			0
$397$	8.03664	+	4.63995i	0.403347	+	0.232873i	0.687927	−	0.725780i	$-0.258521\pi$
$397$	8.03664	+	4.63995i	0.403347	+	0.232873i	−0.284580	+	0.958652i	$0.591854\pi$
$398$	8.32656			0.417373
$399$		0			0
$400$	1.00000			0.0500000
$401$	−6.44260	−	3.71964i	−0.321728	−	0.185750i	0.330434	−	0.943829i	$-0.392805\pi$
$401$	−6.44260	−	3.71964i	−0.321728	−	0.185750i	−0.652163	+	0.758079i	$0.726138\pi$
$402$		0			0
$403$	−0.614014	−	1.06350i	−0.0305862	−	0.0529769i
$404$	−1.36773	+	2.36897i	−0.0680469	+	0.117861i
$405$		0			0
$406$	1.33369	−	1.96937i	0.0661901	−	0.0977381i
$407$		−	8.40035i		−	0.416390i
$408$		0			0
$409$	−13.8647	+	8.00481i	−0.685567	+	0.395812i	−0.801949	−	0.597392i	$-0.796204\pi$
$409$	−13.8647	+	8.00481i	−0.685567	+	0.395812i	0.116382	+	0.993204i	$0.462870\pi$
$410$	−7.58662	+	4.38014i	−0.374677	+	0.216320i
$411$		0			0
$412$		−	6.17690i		−	0.304314i
$413$	−7.22900	−	14.8919i	−0.355716	−	0.732783i
$414$		0			0
$415$	2.72500	−	4.71984i	0.133765	−	0.231688i
$416$	0.741181	+	1.28376i	0.0363394	+	0.0629417i
$417$		0			0
$418$	−6.45398	−	3.72620i	−0.315674	−	0.182255i
$419$	28.4419			1.38948			0.694738	−	0.719263i	$-0.255520\pi$
$419$	28.4419			1.38948			0.694738	+	0.719263i	$0.255520\pi$
$420$		0			0
$421$	17.8345			0.869199			0.434600	−	0.900624i	$-0.356890\pi$
$421$	17.8345			0.869199			0.434600	+	0.900624i	$0.356890\pi$
$422$	17.2625	+	9.96651i	0.840325	+	0.485162i
$423$		0			0
$424$	1.73508	+	3.00524i	0.0842628	+	0.145947i
$425$	−1.21441	+	2.10342i	−0.0589077	+	0.102031i
$426$		0			0
$427$	14.5057	+	9.82353i	0.701980	+	0.475394i
$428$		−	4.56993i		−	0.220896i
$429$		0			0
$430$	−1.61401	+	0.931852i	−0.0778347	+	0.0449379i
$431$	−26.7539	+	15.4464i	−1.28869	+	0.744025i	−0.978420	−	0.206624i	$-0.933752\pi$
$431$	−26.7539	+	15.4464i	−1.28869	+	0.744025i	−0.310268	+	0.950649i	$0.600419\pi$
$432$		0			0
$433$		−	15.2207i		−	0.731462i	−0.930721	−	0.365731i	$-0.880819\pi$
$433$		−	15.2207i		−	0.731462i	0.930721	−	0.365731i	$-0.119181\pi$
$434$	2.18618	+	0.156961i	0.104940	+	0.00753437i
$435$		0			0
$436$	−2.97934	+	5.16036i	−0.142684	+	0.247136i
$437$	−0.651613	−	1.12863i	−0.0311709	−	0.0539895i
$438$		0			0
$439$	12.4054	+	7.16228i	0.592079	+	0.341837i	0.765919	−	0.642937i	$-0.222284\pi$
$439$	12.4054	+	7.16228i	0.592079	+	0.341837i	−0.173840	+	0.984774i	$0.555618\pi$
$440$	−1.53225			−0.0730472
$441$		0			0
$442$	−3.60040			−0.171253
$443$	−4.46651	−	2.57874i	−0.212210	−	0.122520i	0.390128	−	0.920761i	$-0.372431\pi$
$443$	−4.46651	−	2.57874i	−0.212210	−	0.122520i	−0.602338	+	0.798241i	$0.705764\pi$
$444$		0			0
$445$	7.98502	+	13.8305i	0.378526	+	0.655627i
$446$	3.58302	−	6.20597i	0.169661	−	0.293861i
$447$		0			0
$448$	−2.63896	−	0.189469i	−0.124679	−	0.00895155i
$449$		−	19.9377i		−	0.940918i	−0.882422	−	0.470459i	$-0.844088\pi$
$449$		−	19.9377i		−	0.940918i	0.882422	−	0.470459i	$-0.155912\pi$
$450$		0			0
$451$	11.6246	−	6.71147i	0.547381	−	0.316031i
$452$	−17.2319	+	9.94887i	−0.810522	+	0.467955i
$453$		0			0
$454$			15.8544i			0.744085i
$455$	3.24737	+	2.19918i	0.152239	+	0.103099i
$456$		0			0
$457$	−5.66995	+	9.82065i	−0.265229	+	0.459391i	−0.967624	−	0.252397i	$-0.918781\pi$
$457$	−5.66995	+	9.82065i	−0.265229	+	0.459391i	0.702394	+	0.711788i	$0.252114\pi$
$458$	−14.1087	−	24.4371i	−0.659258	−	1.14187i
$459$		0			0
$460$	−0.232051	−	0.133975i	−0.0108194	−	0.00624660i
$461$	2.01890			0.0940298			0.0470149	−	0.998894i	$-0.485029\pi$
$461$	2.01890			0.0940298			0.0470149	+	0.998894i	$0.485029\pi$
$462$		0			0
$463$	−27.2844			−1.26801			−0.634007	−	0.773327i	$-0.718591\pi$
$463$	−27.2844			−1.26801			−0.634007	+	0.773327i	$0.718591\pi$
$464$	−0.778539	−	0.449490i	−0.0361428	−	0.0208670i
$465$		0			0
$466$	12.1487	+	21.0421i	0.562776	+	0.974757i
$467$	−0.346065	+	0.599403i	−0.0160140	+	0.0277370i	−0.873921	−	0.486067i	$-0.838431\pi$
$467$	−0.346065	+	0.599403i	−0.0160140	+	0.0277370i	0.857907	+	0.513804i	$0.171764\pi$
$468$		0			0
$469$	−18.5256	−	38.1632i	−0.855434	−	1.76221i
$470$			7.45946i			0.344079i
$471$		0			0
$472$	−5.41849	+	3.12837i	−0.249406	+	0.143995i
$473$	2.47307	−	1.42783i	0.113712	−	0.0656517i
$474$		0			0
$475$		−	4.86370i		−	0.223162i
$476$	3.60332	−	5.32076i	0.165158	−	0.243876i
$477$		0			0
$478$	−9.95403	+	17.2409i	−0.455287	+	0.788580i
$479$	−7.95403	−	13.7768i	−0.363429	−	0.629477i	0.625094	−	0.780550i	$-0.285061\pi$
$479$	−7.95403	−	13.7768i	−0.363429	−	0.629477i	−0.988523	+	0.151072i	$0.951727\pi$
$480$		0			0
$481$	7.03805	+	4.06342i	0.320908	+	0.185276i
$482$	−20.5254			−0.934905
$483$		0			0
$484$	−8.65221			−0.393282
$485$	−12.9455	−	7.47407i	−0.587823	−	0.339380i
$486$		0			0
$487$	14.3749	+	24.8981i	0.651390	+	1.12824i	0.982786	+	0.184749i	$0.0591471\pi$
$487$	14.3749	+	24.8981i	0.651390	+	1.12824i	−0.331396	+	0.943492i	$0.607520\pi$
$488$	3.31079	−	5.73445i	0.149872	−	0.259587i
$489$		0			0
$490$	−6.50000	+	2.59808i	−0.293640	+	0.117369i
$491$			5.45753i			0.246295i	0.992388	+	0.123148i	$0.0392988\pi$
$491$			5.45753i			0.246295i	−0.992388	+	0.123148i	$0.960701\pi$
$492$		0			0
$493$	1.89094	−	1.09173i	0.0851635	−	0.0491691i
$494$	6.24384	−	3.60488i	0.280924	−	0.162191i
$495$		0			0
$496$		−	0.828427i		−	0.0371975i
$497$	−2.41813	+	33.6802i	−0.108468	+	1.51076i
$498$		0			0
$499$	4.43148	−	7.67555i	0.198380	−	0.343605i	−0.749623	−	0.661865i	$-0.769765\pi$
$499$	4.43148	−	7.67555i	0.198380	−	0.343605i	0.948003	+	0.318260i	$0.103099\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−5.08172	−	2.93393i	−0.226808	−	0.130948i
$503$	−9.36536			−0.417581			−0.208790	−	0.977960i	$-0.566953\pi$
$503$	−9.36536			−0.417581			−0.208790	+	0.977960i	$0.566953\pi$
$504$		0			0
$505$	2.73545			0.121726
$506$	0.355560	+	0.205283i	0.0158066	+	0.00912592i
$507$		0			0
$508$	−10.6012	−	18.3619i	−0.470354	−	0.814677i
$509$	−17.5164	+	30.3393i	−0.776400	+	1.34477i	0.157603	+	0.987502i	$0.449623\pi$
$509$	−17.5164	+	30.3393i	−0.776400	+	1.34477i	−0.934004	+	0.357263i	$0.883710\pi$
$510$		0			0
$511$	0.816735	−	0.396469i	0.0361302	−	0.0175387i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−6.63519	+	3.83083i	−0.292666	+	0.168971i
$515$	−5.34935	+	3.08845i	−0.235720	+	0.136093i
$516$		0			0
$517$		−	11.4298i		−	0.502680i
$518$	−13.0488	+	6.33429i	−0.573331	+	0.278313i
$519$		0			0
$520$	0.741181	−	1.28376i	0.0325029	−	0.0562967i
$521$	9.99807	+	17.3172i	0.438023	+	0.758679i	0.997537	−	0.0701424i	$-0.0223454\pi$
$521$	9.99807	+	17.3172i	0.438023	+	0.758679i	−0.559514	+	0.828821i	$0.689012\pi$
$522$		0			0
$523$	−29.0144	−	16.7515i	−1.26871	−	0.732491i	−0.293967	−	0.955816i	$-0.594976\pi$
$523$	−29.0144	−	16.7515i	−1.26871	−	0.732491i	−0.974744	+	0.223325i	$0.928309\pi$
$524$	−7.46170			−0.325966
$525$		0			0
$526$	−8.46286			−0.368998
$527$	1.74253	+	1.00605i	0.0759060	+	0.0438243i
$528$		0			0
$529$	−11.4641	−	19.8564i	−0.498439	−	0.863322i
$530$	1.73508	−	3.00524i	0.0753669	−	0.130539i
$531$		0			0
$532$	−0.921519	+	12.8351i	−0.0399529	+	0.556473i
$533$			12.9859i			0.562482i
$534$		0			0
$535$	−3.95768	+	2.28497i	−0.171105	+	0.0987877i
$536$	−13.8859	+	8.01702i	−0.599779	+	0.346282i
$537$		0			0
$538$			17.0431i			0.734781i
$539$	9.95962	−	3.98090i	0.428991	−	0.171470i
$540$		0			0
$541$	−18.8766	+	32.6952i	−0.811568	+	1.40568i	0.100198	+	0.994967i	$0.468052\pi$
$541$	−18.8766	+	32.6952i	−0.811568	+	1.40568i	−0.911766	+	0.410710i	$0.865281\pi$
$542$	5.26795	+	9.12436i	0.226278	+	0.391925i
$543$		0			0
$544$	−2.10342	−	1.21441i	−0.0901836	−	0.0520675i
$545$	5.95867			0.255241
$546$		0			0
$547$	5.07130			0.216833			0.108417	−	0.994106i	$-0.465422\pi$
$547$	5.07130			0.216833			0.108417	+	0.994106i	$0.465422\pi$
$548$	0.538302	+	0.310789i	0.0229951	+	0.0132762i
$549$		0			0
$550$	0.766125	+	1.32697i	0.0326677	+	0.0565821i
$551$	−2.18618	+	3.78658i	−0.0931346	+	0.161314i
$552$		0			0
$553$	15.5014	−	22.8898i	0.659187	−	0.973373i
$554$		−	8.09122i		−	0.343763i
$555$		0			0
$556$	−16.0504	+	9.26670i	−0.680689	+	0.392996i
$557$	−29.7528	+	17.1778i	−1.26067	+	0.727846i	−0.973203	−	0.229946i	$-0.926145\pi$
$557$	−29.7528	+	17.1778i	−1.26067	+	0.727846i	−0.287463	+	0.957792i	$0.592812\pi$
$558$		0			0
$559$			2.76268i			0.116849i
$560$	1.15539	+	2.38014i	0.0488243	+	0.100579i
$561$		0			0
$562$	−5.58422	+	9.67215i	−0.235556	+	0.407995i
$563$	23.5293	+	40.7539i	0.991641	+	1.71757i	0.607562	+	0.794272i	$0.292148\pi$
$563$	23.5293	+	40.7539i	0.991641	+	1.71757i	0.384079	+	0.923300i	$0.374519\pi$
$564$		0			0
$565$	17.2319	+	9.94887i	0.724953	+	0.418552i
$566$	7.21592			0.303308
$567$		0			0
$568$	12.7627			0.535510
$569$	38.2670	+	22.0934i	1.60424	+	0.926206i	0.990627	+	0.136595i	$0.0436159\pi$
$569$	38.2670	+	22.0934i	1.60424	+	0.926206i	0.613608	+	0.789611i	$0.289717\pi$
$570$		0			0
$571$	−20.5804	−	35.6463i	−0.861263	−	1.49175i	−0.870710	−	0.491797i	$-0.836340\pi$
$571$	−20.5804	−	35.6463i	−0.861263	−	1.49175i	0.00944654	−	0.999955i	$-0.496993\pi$
$572$	−1.13567	+	1.96705i	−0.0474849	+	0.0822463i
$573$		0			0
$574$	−19.1909	−	12.9964i	−0.801012	−	0.542461i
$575$			0.267949i			0.0111743i
$576$		0			0
$577$	12.2293	−	7.06058i	0.509112	−	0.293936i	−0.223357	−	0.974737i	$-0.571701\pi$
$577$	12.2293	−	7.06058i	0.509112	−	0.293936i	0.732469	+	0.680801i	$0.238368\pi$
$578$	−9.61358	+	5.55040i	−0.399872	+	0.230866i
$579$		0			0
$580$			0.898979i			0.0373281i
$581$	14.3823	+	1.03261i	0.596680	+	0.0428397i
$582$		0			0
$583$	−2.65857	+	4.60478i	−0.110107	+	0.190711i
$584$	−0.171573	−	0.297173i	−0.00709974	−	0.0122971i
$585$		0			0
$586$	−15.8112	−	9.12863i	−0.653156	−	0.377100i
$587$	−37.7819			−1.55942			−0.779712	−	0.626138i	$-0.784635\pi$
$587$	−37.7819			−1.55942			−0.779712	+	0.626138i	$0.784635\pi$
$588$		0			0
$589$	−4.02922			−0.166021
$590$	5.41849	+	3.12837i	0.223076	+	0.128793i
$591$		0			0
$592$	2.74118	+	4.74786i	0.112662	+	0.195136i
$593$	13.0981	−	22.6865i	0.537873	−	0.931623i	−0.461146	−	0.887324i	$-0.652562\pi$
$593$	13.0981	−	22.6865i	0.537873	−	0.931623i	0.999018	−	0.0442982i	$-0.0141052\pi$
$594$		0			0
$595$	−6.40957	−	0.460186i	−0.262767	−	0.0188658i
$596$		−	13.9834i		−	0.572783i
$597$		0			0
$598$	−0.343983	+	0.198599i	−0.0140665	+	0.00812131i
$599$	4.15712	−	2.40012i	0.169856	−	0.0980661i	−0.412662	−	0.910884i	$-0.635401\pi$
$599$	4.15712	−	2.40012i	0.169856	−	0.0980661i	0.582518	+	0.812818i	$0.302068\pi$
$600$		0			0
$601$		−	37.3722i		−	1.52444i	−0.647317	−	0.762221i	$-0.724109\pi$
$601$		−	37.3722i		−	1.52444i	0.647317	−	0.762221i	$-0.275891\pi$
$602$	−4.08276	−	2.76492i	−0.166401	−	0.112690i
$603$		0			0
$604$	9.83839	−	17.0406i	0.400319	−	0.693372i
$605$	4.32611	+	7.49303i	0.175881	+	0.304635i
$606$		0			0
$607$	32.2499	+	18.6195i	1.30898	+	0.755742i	0.981927	−	0.189263i	$-0.0606097\pi$
$607$	32.2499	+	18.6195i	1.30898	+	0.755742i	0.327057	+	0.945005i	$0.393943\pi$
$608$	4.86370			0.197249
$609$		0			0
$610$	−6.62158			−0.268100
$611$	9.57618	+	5.52881i	0.387411	+	0.223672i
$612$		0			0
$613$	4.92977	+	8.53861i	0.199112	+	0.344871i	0.948241	−	0.317553i	$-0.102861\pi$
$613$	4.92977	+	8.53861i	0.199112	+	0.344871i	−0.749129	+	0.662424i	$0.769528\pi$
$614$	1.71039	−	2.96248i	0.0690258	−	0.119556i
$615$		0			0
$616$	−1.77035	−	3.64697i	−0.0713296	−	0.146941i
$617$			31.3545i			1.26229i	0.775666	+	0.631143i	$0.217414\pi$
$617$			31.3545i			1.26229i	−0.775666	+	0.631143i	$0.782586\pi$
$618$		0			0
$619$	−13.1943	+	7.61774i	−0.530325	+	0.306183i	−0.741149	−	0.671341i	$-0.765719\pi$
$619$	−13.1943	+	7.61774i	−0.530325	+	0.306183i	0.210824	+	0.977524i	$0.432385\pi$
$620$	−0.717439	+	0.414214i	−0.0288130	+	0.0166352i
$621$		0			0
$622$			5.69089i			0.228184i
$623$	−23.6926	+	34.9851i	−0.949223	+	1.40165i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.67335	+	11.5586i	0.266721	+	0.461974i
$627$		0			0
$628$	−7.84628	−	4.53005i	−0.313101	−	0.180769i
$629$	−13.3157			−0.530932
$630$		0			0
$631$	−1.00406			−0.0399710			−0.0199855	−	0.999800i	$-0.506362\pi$
$631$	−1.00406			−0.0399710			−0.0199855	+	0.999800i	$0.506362\pi$
$632$	−9.04889	−	5.22438i	−0.359946	−	0.207815i
$633$		0			0
$634$	6.26330	+	10.8484i	0.248748	+	0.430844i
$635$	−10.6012	+	18.3619i	−0.420697	+	0.728669i
$636$		0			0
$637$	−1.48236	+	10.2701i	−0.0587333	+	0.406916i
$638$		−	1.37746i		−	0.0545342i
$639$		0			0
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	20.2689	−	11.7023i	0.800574	−	0.462211i	−0.0430981	−	0.999071i	$-0.513723\pi$
$641$	20.2689	−	11.7023i	0.800574	−	0.462211i	0.843672	+	0.536860i	$0.180389\pi$
$642$		0			0
$643$		−	33.4475i		−	1.31904i	−0.751686	−	0.659521i	$-0.770759\pi$
$643$		−	33.4475i		−	1.31904i	0.751686	−	0.659521i	$-0.229241\pi$
$644$	0.0507680	−	0.707107i	0.00200054	−	0.0278639i
$645$		0			0
$646$	−5.90654	+	10.2304i	−0.232390	+	0.402511i
$647$	8.28540	+	14.3507i	0.325733	+	0.564185i	0.981660	−	0.190638i	$-0.0610557\pi$
$647$	8.28540	+	14.3507i	0.325733	+	0.564185i	−0.655928	+	0.754824i	$0.727722\pi$
$648$		0			0
$649$	−8.30249	−	4.79344i	−0.325901	−	0.188159i
$650$	−1.48236			−0.0581430
$651$		0			0
$652$	−11.8204			−0.462922
$653$	−5.22132	−	3.01453i	−0.204326	−	0.117968i	0.394346	−	0.918962i	$-0.370971\pi$
$653$	−5.22132	−	3.01453i	−0.204326	−	0.117968i	−0.598672	+	0.800994i	$0.704305\pi$
$654$		0			0
$655$	3.73085	+	6.46202i	0.145776	+	0.252492i
$656$	−4.38014	+	7.58662i	−0.171016	+	0.296208i
$657$		0			0
$658$	−17.7545	+	8.61862i	−0.692144	+	0.335989i
$659$		−	36.3672i		−	1.41666i	−0.705880	−	0.708332i	$-0.749448\pi$
$659$		−	36.3672i		−	1.41666i	0.705880	−	0.708332i	$-0.250552\pi$
$660$		0			0
$661$	−9.90289	+	5.71744i	−0.385178	+	0.222383i	−0.680069	−	0.733148i	$-0.738050\pi$
$661$	−9.90289	+	5.71744i	−0.385178	+	0.222383i	0.294891	+	0.955531i	$0.404717\pi$
$662$	−1.11010	+	0.640916i	−0.0431452	+	0.0249099i
$663$		0			0
$664$		−	5.45001i		−	0.211501i
$665$	11.5763	−	5.61950i	0.448909	−	0.217915i
$666$		0			0
$667$	0.120440	−	0.208609i	0.00466347	−	0.00807737i
$668$	7.88891	+	13.6640i	0.305231	+	0.528675i
$669$		0			0
$670$	13.8859	+	8.01702i	0.536458	+	0.309724i
$671$	10.1459			0.391679
$672$		0			0
$673$	10.8070			0.416581			0.208290	−	0.978067i	$-0.433210\pi$
$673$	10.8070			0.416581			0.208290	+	0.978067i	$0.433210\pi$
$674$	11.3500	+	6.55291i	0.437185	+	0.252409i
$675$		0			0
$676$	5.40130	+	9.35533i	0.207742	+	0.359820i
$677$	−7.02280	+	12.1638i	−0.269908	+	0.467494i	−0.968838	−	0.247696i	$-0.920327\pi$
$677$	−7.02280	+	12.1638i	−0.269908	+	0.467494i	0.698930	+	0.715190i	$0.253660\pi$
$678$		0			0
$679$	2.83220	−	39.4475i	0.108690	−	1.51386i
$680$			2.42883i			0.0931412i
$681$		0			0
$682$	1.09930	−	0.634679i	0.0420942	−	0.0243031i
$683$	31.5900	−	18.2385i	1.20876	−	0.697877i	0.246271	−	0.969201i	$-0.420795\pi$
$683$	31.5900	−	18.2385i	1.20876	−	0.697877i	0.962488	+	0.271324i	$0.0874614\pi$
$684$		0			0
$685$		−	0.621578i		−	0.0237493i
$686$	−13.6938	−	12.4691i	−0.522834	−	0.476073i
$687$		0			0
$688$	−0.931852	+	1.61401i	−0.0355265	+	0.0615337i
$689$	−2.57201	−	4.45486i	−0.0979859	−	0.169716i
$690$		0			0
$691$	−20.5831	−	11.8836i	−0.783017	−	0.452075i	0.0544816	−	0.998515i	$-0.482649\pi$
$691$	−20.5831	−	11.8836i	−0.783017	−	0.452075i	−0.837498	+	0.546440i	$0.815983\pi$
$692$	−20.2221			−0.768730
$693$		0			0
$694$	−14.2852			−0.542260
$695$	16.0504	+	9.26670i	0.608827	+	0.351506i
$696$		0			0
$697$	−10.6386	−	18.4266i	−0.402965	−	0.697957i
$698$	6.63567	−	11.4933i	0.251164	−	0.435029i
$699$		0			0
$700$	1.48356	−	2.19067i	0.0560734	−	0.0827996i
$701$			1.74502i			0.0659086i	0.999457	+	0.0329543i	$0.0104916\pi$
$701$			1.74502i			0.0659086i	−0.999457	+	0.0329543i	$0.989508\pi$
$702$		0			0
$703$	23.0922	−	13.3323i	0.870939	−	0.502837i
$704$	−1.32697	+	0.766125i	−0.0500120	+	0.0288744i
$705$		0			0
$706$		−	32.6463i		−	1.22866i
$707$	3.16052	+	6.51075i	0.118864	+	0.244862i
$708$		0			0
$709$	6.06162	−	10.4990i	0.227649	−	0.394299i	−0.729462	−	0.684021i	$-0.760230\pi$
$709$	6.06162	−	10.4990i	0.227649	−	0.394299i	0.957111	+	0.289722i	$0.0935629\pi$
$710$	−6.38134	−	11.0528i	−0.239487	−	0.414804i
$711$		0			0
$712$	13.8305	+	7.98502i	0.518319	+	0.299251i
$713$	0.221976			0.00831308
$714$		0			0
$715$	2.27135			0.0849436
$716$	−5.94667	−	3.43331i	−0.222237	−	0.128309i
$717$		0			0
$718$	−3.12168	−	5.40692i	−0.116500	−	0.201784i
$719$	0.893176	−	1.54703i	0.0333098	−	0.0576943i	−0.848890	−	0.528570i	$-0.822729\pi$
$719$	0.893176	−	1.54703i	0.0333098	−	0.0576943i	0.882200	+	0.470875i	$0.156062\pi$
$720$		0			0
$721$	−13.5315	−	9.16382i	−0.503941	−	0.341279i
$722$		−	4.65561i		−	0.173264i
$723$		0			0
$724$	−14.1220	+	8.15331i	−0.524838	+	0.303015i
$725$	0.778539	−	0.449490i	0.0289142	−	0.0166936i
$726$		0			0
$727$			29.8785i			1.10813i	0.832472	+	0.554066i	$0.186925\pi$
$727$			29.8785i			1.10813i	−0.832472	+	0.554066i	$0.813075\pi$
$728$	3.91189	+	0.280861i	0.144984	+	0.0104094i
$729$		0			0
$730$	−0.171573	+	0.297173i	−0.00635020	+	0.0109989i
$731$	−2.26330	−	3.92016i	−0.0837114	−	0.144992i
$732$		0			0
$733$	−11.9434	−	6.89554i	−0.441140	−	0.254692i	0.262941	−	0.964812i	$-0.415308\pi$
$733$	−11.9434	−	6.89554i	−0.441140	−	0.254692i	−0.704081	+	0.710119i	$0.748641\pi$
$734$	−12.5892			−0.464677
$735$		0			0
$736$	−0.267949			−0.00987674
$737$	−21.2766	−	12.2841i	−0.783735	−	0.452490i
$738$		0			0
$739$	−3.68349	−	6.37999i	−0.135499	−	0.234692i	0.790289	−	0.612735i	$-0.209931\pi$
$739$	−3.68349	−	6.37999i	−0.135499	−	0.234692i	−0.925788	+	0.378043i	$0.876597\pi$
$740$	2.74118	−	4.74786i	0.100768	−	0.174535i
$741$		0			0
$742$	9.15759	+	0.657486i	0.336186	+	0.0241371i
$743$		−	11.0774i		−	0.406389i	−0.979138	−	0.203194i	$-0.934868\pi$
$743$		−	11.0774i		−	0.406389i	0.979138	−	0.203194i	$-0.0651323\pi$
$744$		0			0
$745$	−12.1100	+	6.99171i	−0.443676	+	0.256156i
$746$	31.1408	−	17.9791i	1.14014	−	0.658263i
$747$		0			0
$748$		−	3.72157i		−	0.136074i
$749$	−10.0112	−	6.77978i	−0.365802	−	0.247728i
$750$		0			0
$751$	−12.1879	+	21.1100i	−0.444741	+	0.770315i	−0.998034	−	0.0626722i	$-0.980038\pi$
$751$	−12.1879	+	21.1100i	−0.444741	+	0.770315i	0.553293	+	0.832987i	$0.313371\pi$
$752$	3.72973	+	6.46008i	0.136009	+	0.235575i
$753$		0			0
$754$	1.15408	+	0.666306i	0.0420290	+	0.0242655i
$755$	−19.6768			−0.716112
$756$		0			0
$757$	19.6761			0.715139			0.357569	−	0.933887i	$-0.383606\pi$
$757$	19.6761			0.715139			0.357569	+	0.933887i	$0.383606\pi$
$758$	10.0371	+	5.79493i	0.364565	+	0.210481i
$759$		0			0
$760$	−2.43185	−	4.21209i	−0.0882125	−	0.152789i
$761$	24.9168	−	43.1572i	0.903234	−	1.56445i	0.0799647	−	0.996798i	$-0.474519\pi$
$761$	24.9168	−	43.1572i	0.903234	−	1.56445i	0.823270	−	0.567650i	$-0.192147\pi$
$762$		0			0
$763$	6.88462	+	14.1825i	0.249240	+	0.513440i
$764$		−	17.1623i		−	0.620910i
$765$		0			0
$766$	−3.86897	+	2.23375i	−0.139792	+	0.0807087i
$767$	8.03217	−	4.63737i	0.290025	−	0.167446i
$768$		0			0
$769$		−	31.0584i		−	1.12000i	−0.828494	−	0.559998i	$-0.810802\pi$
$769$		−	31.0584i		−	1.12000i	0.828494	−	0.559998i	$-0.189198\pi$
$770$	−2.27319	+	3.35666i	−0.0819201	+	0.120965i
$771$		0			0
$772$	4.52761	−	7.84204i	0.162952	−	0.282241i
$773$	1.98525	+	3.43855i	0.0714043	+	0.123676i	0.899517	−	0.436886i	$-0.143919\pi$
$773$	1.98525	+	3.43855i	0.0714043	+	0.123676i	−0.828113	+	0.560562i	$0.810585\pi$
$774$		0			0
$775$	0.717439	+	0.414214i	0.0257712	+	0.0148790i
$776$	−14.9481			−0.536607
$777$		0			0
$778$	12.9554			0.464475
$779$	36.8991	+	21.3037i	1.32205	+	0.763284i
$780$		0			0
$781$	9.77781	+	16.9357i	0.349878	+	0.606006i
$782$	0.325401	−	0.563611i	0.0116363	−	0.0201547i
$783$		0			0
$784$	−4.33013	+	5.50000i	−0.154647	+	0.196429i
$785$			9.06010i			0.323369i
$786$		0			0
$787$	38.8001	−	22.4013i	1.38308	−	0.798519i	0.390553	−	0.920580i	$-0.372284\pi$
$787$	38.8001	−	22.4013i	1.38308	−	0.798519i	0.992523	+	0.122061i	$0.0389504\pi$
$788$	−18.8256	+	10.8689i	−0.670633	+	0.387190i
$789$		0			0
$790$			10.4488i			0.371750i
$791$	−3.77000	+	52.5093i	−0.134046	+	1.86702i
$792$		0			0
$793$	−4.90779	+	8.50054i	−0.174281	+	0.301863i
$794$	−4.63995	−	8.03664i	−0.164666	−	0.285210i
$795$		0			0
$796$	−7.21101	−	4.16328i	−0.255588	−	0.147564i
$797$	−38.4813			−1.36308			−0.681539	−	0.731781i	$-0.738689\pi$
$797$	−38.4813			−1.36308			−0.681539	+	0.731781i	$0.738689\pi$
$798$		0			0
$799$	−18.1177			−0.640959
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		0			0
$802$	3.71964	+	6.44260i	0.131345	+	0.227496i
$803$	0.262893	−	0.455343i	0.00927728	−	0.0160687i
$804$		0			0
$805$	−0.637756	+	0.309587i	−0.0224780	+	0.0109115i
$806$			1.22803i			0.0432555i
$807$		0			0
$808$	2.36897	−	1.36773i	0.0833401	−	0.0481164i
$809$	15.0298	−	8.67748i	0.528421	−	0.305084i	−0.211952	−	0.977280i	$-0.567982\pi$
$809$	15.0298	−	8.67748i	0.528421	−	0.305084i	0.740373	+	0.672196i	$0.234649\pi$
$810$		0			0
$811$			32.7270i			1.14920i	0.818434	+	0.574601i	$0.194843\pi$
$811$			32.7270i			1.14920i	−0.818434	+	0.574601i	$0.805157\pi$
$812$	−2.13970	+	1.03868i	−0.0750886	+	0.0364504i
$813$		0			0
$814$	−4.20017	+	7.27492i	−0.147216	+	0.254986i
$815$	5.91019	+	10.2368i	0.207025	+	0.358578i
$816$		0			0
$817$	7.85009	+	4.53225i	0.274640	+	0.158563i
$818$	16.0096			0.559763
$819$		0			0
$820$	8.76028			0.305922
$821$	15.4093	+	8.89658i	0.537789	+	0.310493i	0.744182	−	0.667976i	$-0.232839\pi$
$821$	15.4093	+	8.89658i	0.537789	+	0.310493i	−0.206393	+	0.978469i	$0.566173\pi$
$822$		0			0
$823$	−4.91082	−	8.50579i	−0.171181	−	0.296493i	0.767652	−	0.640867i	$-0.221425\pi$
$823$	−4.91082	−	8.50579i	−0.171181	−	0.296493i	−0.938833	+	0.344373i	$0.888091\pi$
$824$	−3.08845	+	5.34935i	−0.107591	+	0.186353i
$825$		0			0
$826$	−1.18546	+	16.5113i	−0.0412473	+	0.574501i
$827$		−	7.78482i		−	0.270705i	−0.990798	−	0.135352i	$-0.956783\pi$
$827$		−	7.78482i		−	0.270705i	0.990798	−	0.135352i	$-0.0432167\pi$
$828$		0			0
$829$	−13.1015	+	7.56413i	−0.455032	+	0.262713i	−0.709953	−	0.704249i	$-0.751284\pi$
$829$	−13.1015	+	7.56413i	−0.455032	+	0.262713i	0.254921	+	0.966962i	$0.417951\pi$
$830$	−4.71984	+	2.72500i	−0.163828	+	0.0945862i
$831$		0			0
$832$		−	1.48236i		−	0.0513917i
$833$	−6.31027	−	15.7874i	−0.218638	−	0.547000i
$834$		0			0
$835$	7.88891	−	13.6640i	0.273007	−	0.472862i
$836$	3.72620	+	6.45398i	0.128873	+	0.223215i
$837$		0			0
$838$	−24.6314	−	14.2209i	−0.850877	−	0.491254i
$839$	−25.2077			−0.870265			−0.435133	−	0.900366i	$-0.643299\pi$
$839$	−25.2077			−0.870265			−0.435133	+	0.900366i	$0.643299\pi$
$840$		0			0
$841$	28.1918			0.972132
$842$	−15.4451	−	8.91724i	−0.532274	−	0.307308i
$843$		0			0
$844$	−9.96651	−	17.2625i	−0.343061	−	0.594200i
$845$	5.40130	−	9.35533i	0.185810	−	0.321833i
$846$		0			0
$847$	−12.8361	+	18.9541i	−0.441054	+	0.651272i
$848$		−	3.47015i		−	0.119166i
$849$		0			0
$850$	2.10342	−	1.21441i	0.0721469	−	0.0416540i
$851$	−1.27219	+	0.734497i	−0.0436100	+	0.0251782i
$852$		0			0
$853$		−	23.3020i		−	0.797846i	−0.916984	−	0.398923i	$-0.869384\pi$
$853$		−	23.3020i		−	0.797846i	0.916984	−	0.398923i	$-0.130616\pi$
$854$	−7.65053	−	15.7603i	−0.261796	−	0.539306i
$855$		0			0
$856$	−2.28497	+	3.95768i	−0.0780985	+	0.135271i
$857$	−13.3030	−	23.0414i	−0.454421	−	0.787080i	0.544234	−	0.838934i	$-0.316820\pi$
$857$	−13.3030	−	23.0414i	−0.454421	−	0.787080i	−0.998655	+	0.0518534i	$0.983487\pi$
$858$		0			0
$859$	49.0044	+	28.2927i	1.67201	+	0.965334i	0.966512	+	0.256620i	$0.0826088\pi$
$859$	49.0044	+	28.2927i	1.67201	+	0.965334i	0.705495	+	0.708714i	$0.250725\pi$
$860$	1.86370			0.0635518
$861$		0			0
$862$	30.8927			1.05221
$863$	−29.4939	−	17.0283i	−1.00398	−	0.579650i	−0.0945593	−	0.995519i	$-0.530144\pi$
$863$	−29.4939	−	17.0283i	−1.00398	−	0.579650i	−0.909425	+	0.415869i	$0.863478\pi$
$864$		0			0
$865$	10.1111	+	17.5129i	0.343787	+	0.595456i
$866$	−7.61037	+	13.1815i	−0.258611	+	0.447927i
$867$		0			0
$868$	−1.81481	−	1.22902i	−0.0615987	−	0.0417158i
$869$		−	16.0101i		−	0.543106i
$870$		0			0
$871$	20.5839	−	11.8841i	0.697459	−	0.402678i
$872$	5.16036	−	2.97934i	0.174752	−	0.100893i
$873$		0			0
$874$			1.30323i			0.0440823i
$875$	−2.63896	−	0.189469i	−0.0892131	−	0.00640521i
$876$		0			0
$877$	−12.0691	+	20.9043i	−0.407545	+	0.705888i	−0.994614	−	0.103649i	$-0.966948\pi$
$877$	−12.0691	+	20.9043i	−0.407545	+	0.705888i	0.587069	+	0.809537i	$0.300282\pi$
$878$	−7.16228	−	12.4054i	−0.241715	−	0.418663i
$879$		0			0
$880$	1.32697	+	0.766125i	0.0447321	+	0.0258261i
$881$	37.2609			1.25535			0.627676	−	0.778475i	$-0.284006\pi$
$881$	37.2609			1.25535			0.627676	+	0.778475i	$0.284006\pi$
$882$		0			0
$883$	48.5544			1.63398			0.816992	−	0.576648i	$-0.195640\pi$
$883$	48.5544			1.63398			0.816992	+	0.576648i	$0.195640\pi$
$884$	3.11804	+	1.80020i	0.104871	+	0.0605472i
$885$		0			0
$886$	2.57874	+	4.46651i	0.0866344	+	0.150055i
$887$	8.73545	−	15.1302i	0.293308	−	0.508024i	−0.681282	−	0.732021i	$-0.738577\pi$
$887$	8.73545	−	15.1302i	0.293308	−	0.508024i	0.974590	+	0.223997i	$0.0719106\pi$
$888$		0			0
$889$	−55.9524	−	4.01720i	−1.87658	−	0.134733i
$890$		−	15.9700i		−	0.535317i
$891$		0			0
$892$	−6.20597	+	3.58302i	−0.207791	+	0.119968i
$893$	31.4199	−	18.1403i	1.05143	−	0.607042i
$894$		0			0
$895$			6.86662i			0.229526i
$896$	2.19067	+	1.48356i	0.0731852	+	0.0495624i
$897$		0			0
$898$	−9.96885	+	17.2665i	−0.332665	+	0.576192i
$899$	−0.372369	−	0.644963i	−0.0124192	−	0.0215107i
$900$		0			0
$901$	7.29921	+	4.21420i	0.243172	+	0.140395i
$902$	−13.4229			−0.446935
$903$		0			0
$904$	19.8977			0.661789
$905$	14.1220	+	8.15331i	0.469430	+	0.271025i
$906$		0			0
$907$	10.7260	+	18.5780i	0.356151	+	0.616872i	0.987314	−	0.158778i	$-0.0507556\pi$
$907$	10.7260	+	18.5780i	0.356151	+	0.616872i	−0.631163	+	0.775650i	$0.717422\pi$
$908$	7.92721	−	13.7303i	0.263074	−	0.455657i
$909$		0			0
$910$	−1.71271	−	3.52823i	−0.0567759	−	0.116960i
$911$		−	42.2281i		−	1.39908i	−0.714593	−	0.699540i	$-0.753388\pi$
$911$		−	42.2281i		−	1.39908i	0.714593	−	0.699540i	$-0.246612\pi$
$912$		0			0
$913$	7.23198	−	4.17539i	0.239344	−	0.138185i
$914$	9.82065	−	5.66995i	0.324838	−	0.187545i
$915$		0			0
$916$			28.2175i			0.932332i
$917$	−11.0699	+	16.3461i	−0.365560	+	0.539797i
$918$		0			0
$919$	28.0816	−	48.6387i	0.926325	−	1.60444i	0.136908	−	0.990584i	$-0.456283\pi$
$919$	28.0816	−	48.6387i	0.926325	−	1.60444i	0.789416	−	0.613858i	$-0.210383\pi$
$920$	0.133975	+	0.232051i	0.00441701	+	0.00765049i
$921$		0			0
$922$	−1.74842	−	1.00945i	−0.0575812	−	0.0332445i
$923$	−18.9189			−0.622724
$924$		0			0
$925$	−5.48236			−0.180259
$926$	23.6290	+	13.6422i	0.776497	+	0.448311i
$927$		0			0
$928$	0.449490	+	0.778539i	0.0147552	+	0.0255568i
$929$	−9.26942	+	16.0551i	−0.304120	+	0.526751i	−0.977065	−	0.212941i	$-0.931696\pi$
$929$	−9.26942	+	16.0551i	−0.304120	+	0.526751i	0.672945	+	0.739692i	$0.265029\pi$
$930$		0			0
$931$	26.7504	+	21.0605i	0.876708	+	0.690228i
$932$		−	24.2973i		−	0.795886i
$933$		0			0
$934$	0.599403	−	0.346065i	0.0196131	−	0.0113236i
$935$	−3.22297	+	1.86078i	−0.105402	+	0.0608541i
$936$		0			0
$937$		−	39.5337i		−	1.29151i	−0.763545	−	0.645755i	$-0.776543\pi$
$937$		−	39.5337i		−	1.29151i	0.763545	−	0.645755i	$-0.223457\pi$
$938$	−3.03795	+	42.3131i	−0.0991925	+	1.38157i
$939$		0			0
$940$	3.72973	−	6.46008i	0.121650	−	0.210705i
$941$	−25.2474	−	43.7299i	−0.823043	−	1.42555i	−0.903406	−	0.428787i	$-0.858941\pi$
$941$	−25.2474	−	43.7299i	−0.823043	−	1.42555i	0.0803623	−	0.996766i	$-0.474392\pi$
$942$		0			0
$943$	−2.03283	−	1.17365i	−0.0661980	−	0.0382195i
$944$	6.25674			0.203639
$945$		0			0
$946$	−2.85566			−0.0928455
$947$	33.9160	+	19.5814i	1.10212	+	0.636310i	0.936777	−	0.349926i	$-0.113793\pi$
$947$	33.9160	+	19.5814i	1.10212	+	0.636310i	0.165344	+	0.986236i	$0.447126\pi$
$948$		0			0
$949$	0.254333	+	0.440518i	0.00825600	+	0.0142998i
$950$	−2.43185	+	4.21209i	−0.0788997	+	0.136658i
$951$		0			0
$952$	−5.78094	+	2.80625i	−0.187361	+	0.0909511i
$953$		−	52.9933i		−	1.71662i	−0.513130	−	0.858311i	$-0.671514\pi$
$953$		−	52.9933i		−	1.71662i	0.513130	−	0.858311i	$-0.328486\pi$
$954$		0			0
$955$	−14.8630	+	8.58114i	−0.480955	+	0.277679i
$956$	17.2409	−	9.95403i	0.557610	−	0.321936i
$957$		0			0
$958$			15.9081i			0.513966i
$959$	1.47944	−	0.718168i	0.0477737	−	0.0231909i
$960$		0			0
$961$	−15.1569	+	26.2524i	−0.488931	+	0.846853i
$962$	−4.06342	−	7.03805i	−0.131010	−	0.226916i
$963$		0			0
$964$	17.7755	+	10.2627i	0.572510	+	0.330539i
$965$	−9.05521			−0.291498
$966$		0			0
$967$	30.6208			0.984700			0.492350	−	0.870397i	$-0.336138\pi$
$967$	30.6208			0.984700			0.492350	+	0.870397i	$0.336138\pi$
$968$	7.49303	+	4.32611i	0.240835	+	0.139046i
$969$		0			0
$970$	7.47407	+	12.9455i	0.239978	+	0.415654i
$971$	−6.03548	+	10.4538i	−0.193688	+	0.335477i	−0.946470	−	0.322793i	$-0.895378\pi$
$971$	−6.03548	+	10.4538i	−0.193688	+	0.335477i	0.752782	+	0.658270i	$0.228712\pi$
$972$		0			0
$973$	−3.51150	+	48.9089i	−0.112574	+	1.56795i
$974$		−	28.7498i		−	0.921205i
$975$		0			0
$976$	−5.73445	+	3.31079i	−0.183555	+	0.105976i
$977$	9.72792	−	5.61642i	0.311224	−	0.179685i	−0.336250	−	0.941773i	$-0.609159\pi$
$977$	9.72792	−	5.61642i	0.311224	−	0.179685i	0.647474	+	0.762088i	$0.275825\pi$
$978$		0			0
$979$			24.4701i			0.782068i
$980$	6.92820	+	1.00000i	0.221313	+	0.0319438i
$981$		0			0
$982$	2.72877	−	4.72636i	0.0870784	−	0.150824i
$983$	11.3960	+	19.7385i	0.363477	+	0.629561i	0.988531	−	0.151021i	$-0.0482562\pi$
$983$	11.3960	+	19.7385i	0.363477	+	0.629561i	−0.625053	+	0.780582i	$0.714923\pi$
$984$		0			0
$985$	18.8256	+	10.8689i	0.599832	+	0.346313i
$986$	−2.18346			−0.0695357
$987$		0			0
$988$	−7.20977			−0.229373
$989$	−0.432474	−	0.249689i	−0.0137519	−	0.00793965i
$990$		0			0
$991$	4.41057	+	7.63932i	0.140106	+	0.242671i	0.927536	−	0.373733i	$-0.121922\pi$
$991$	4.41057	+	7.63932i	0.140106	+	0.242671i	−0.787430	+	0.616404i	$0.788589\pi$
$992$	−0.414214	+	0.717439i	−0.0131513	+	0.0227787i
$993$		0			0
$994$	18.9343	−	27.9588i	0.600558	−	0.886800i
$995$			8.32656i			0.263970i
$996$		0			0
$997$	−40.2497	+	23.2381i	−1.27472	+	0.735960i	−0.975872	−	0.218342i	$-0.929935\pi$
$997$	−40.2497	+	23.2381i	−1.27472	+	0.735960i	−0.298847	+	0.954301i	$0.596602\pi$
$998$	−7.67555	+	4.43148i	−0.242965	+	0.140276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.be.b.341.2	yes	8
3.2	odd	2		630.2.be.a.341.4	✓	8
5.2	odd	4		3150.2.bp.f.1349.2		8
5.3	odd	4		3150.2.bp.c.1349.3		8
5.4	even	2		3150.2.bf.c.1601.3		8
7.2	even	3		4410.2.b.b.881.7		8
7.3	odd	6		630.2.be.a.521.4	yes	8
7.5	odd	6		4410.2.b.e.881.7		8
15.2	even	4		3150.2.bp.a.1349.2		8
15.8	even	4		3150.2.bp.d.1349.3		8
15.14	odd	2		3150.2.bf.b.1601.1		8
21.2	odd	6		4410.2.b.e.881.2		8
21.5	even	6		4410.2.b.b.881.2		8
21.17	even	6	inner	630.2.be.b.521.2	yes	8
35.3	even	12		3150.2.bp.a.899.2		8
35.17	even	12		3150.2.bp.d.899.3		8
35.24	odd	6		3150.2.bf.b.1151.1		8
105.17	odd	12		3150.2.bp.c.899.3		8
105.38	odd	12		3150.2.bp.f.899.2		8
105.59	even	6		3150.2.bf.c.1151.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.4	✓	8	3.2	odd	2
630.2.be.a.521.4	yes	8	7.3	odd	6
630.2.be.b.341.2	yes	8	1.1	even	1	trivial
630.2.be.b.521.2	yes	8	21.17	even	6	inner
3150.2.bf.b.1151.1		8	35.24	odd	6
3150.2.bf.b.1601.1		8	15.14	odd	2
3150.2.bf.c.1151.3		8	105.59	even	6
3150.2.bf.c.1601.3		8	5.4	even	2
3150.2.bp.a.899.2		8	35.3	even	12
3150.2.bp.a.1349.2		8	15.2	even	4
3150.2.bp.c.899.3		8	105.17	odd	12
3150.2.bp.c.1349.3		8	5.3	odd	4
3150.2.bp.d.899.3		8	35.17	even	12
3150.2.bp.d.1349.3		8	15.8	even	4
3150.2.bp.f.899.2		8	105.38	odd	12
3150.2.bp.f.1349.2		8	5.2	odd	4
4410.2.b.b.881.2		8	21.5	even	6
4410.2.b.b.881.7		8	7.2	even	3
4410.2.b.e.881.2		8	21.2	odd	6
4410.2.b.e.881.7		8	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.63896 + 0.189469i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.63896 + 0.189469i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +(1.32697 - 0.766125i) q^{11} +1.48236i q^{13} +(-2.19067 - 1.48356i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.21441 - 2.10342i) q^{17} +(4.21209 + 2.43185i) q^{19} +1.00000 q^{20} -1.53225 q^{22} +(-0.232051 - 0.133975i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.741181 - 1.28376i) q^{26} +(1.15539 + 2.38014i) q^{28} +0.898979i q^{29} +(-0.717439 + 0.414214i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.42883i q^{34} +(1.48356 - 2.19067i) q^{35} +(2.74118 - 4.74786i) q^{37} +(-2.43185 - 4.21209i) q^{38} +(-0.866025 - 0.500000i) q^{40} +8.76028 q^{41} +1.86370 q^{43} +(1.32697 + 0.766125i) q^{44} +(0.133975 + 0.232051i) q^{46} +(3.72973 - 6.46008i) q^{47} +(6.92820 + 1.00000i) q^{49} +1.00000i q^{50} +(-1.28376 + 0.741181i) q^{52} +(-3.00524 + 1.73508i) q^{53} -1.53225i q^{55} +(0.189469 - 2.63896i) q^{56} +(0.449490 - 0.778539i) q^{58} +(-3.12837 - 5.41849i) q^{59} +(5.73445 + 3.31079i) q^{61} +0.828427 q^{62} -1.00000 q^{64} +(1.28376 + 0.741181i) q^{65} +(-8.01702 - 13.8859i) q^{67} +(1.21441 - 2.10342i) q^{68} +(-2.38014 + 1.15539i) q^{70} +12.7627i q^{71} +(0.297173 - 0.171573i) q^{73} +(-4.74786 + 2.74118i) q^{74} +4.86370i q^{76} +(3.64697 - 1.77035i) q^{77} +(5.22438 - 9.04889i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-7.58662 - 4.38014i) q^{82} +5.45001 q^{83} -2.42883 q^{85} +(-1.61401 - 0.931852i) q^{86} +(-0.766125 - 1.32697i) q^{88} +(-7.98502 + 13.8305i) q^{89} +(-0.280861 + 3.91189i) q^{91} -0.267949i q^{92} +(-6.46008 + 3.72973i) q^{94} +(4.21209 - 2.43185i) q^{95} -14.9481i q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{5}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^5	\( 8 q + 4 q^{4} + 4 q^{5} + 24 q^{11} - 4 q^{16} + 8 q^{20} + 12 q^{23} - 4 q^{25} + 8 q^{26} + 24 q^{37} - 4 q^{38} + 32 q^{41} - 16 q^{43} + 24 q^{44} + 8 q^{46} - 8 q^{47} + 24 q^{53} - 16 q^{58} - 24 q^{59} - 16 q^{62} - 8 q^{64} - 24 q^{67} - 16 q^{77} - 24 q^{79} + 4 q^{80} - 16 q^{83} - 16 q^{89} - 20 q^{91} - 12 q^{94} - 44 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^5 + 24 * q^11 - 4 * q^16 + 8 * q^20 + 12 * q^23 - 4 * q^25 + 8 * q^26 + 24 * q^37 - 4 * q^38 + 32 * q^41 - 16 * q^43 + 24 * q^44 + 8 * q^46 - 8 * q^47 + 24 * q^53 - 16 * q^58 - 24 * q^59 - 16 * q^62 - 8 * q^64 - 24 * q^67 - 16 * q^77 - 24 * q^79 + 4 * q^80 - 16 * q^83 - 16 * q^89 - 20 * q^91 - 12 * q^94 - 44 * q^98

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