LMFDB - Embedded newform 637.2.r.g.116.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("637.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.10
Character	$\chi$	$=$	637.116
Dual form			637.2.r.g.324.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.589067 - 0.340098i) q^{2} +(1.16706 - 2.02141i) q^{3} +(-0.768667 + 1.33137i) q^{4} +(-2.81123 + 1.62306i) q^{5} -1.58766i q^{6} +2.40608i q^{8} +(-1.22407 - 2.12016i) q^{9} +O(q^{10})$	\(q+(0.589067 - 0.340098i) q^{2} +(1.16706 - 2.02141i) q^{3} +(-0.768667 + 1.33137i) q^{4} +(-2.81123 + 1.62306i) q^{5} -1.58766i q^{6} +2.40608i q^{8} +(-1.22407 - 2.12016i) q^{9} +(-1.10400 + 1.91219i) q^{10} +(4.61728 + 2.66579i) q^{11} +(1.79417 + 3.10759i) q^{12} +(-1.47728 + 3.28902i) q^{13} +7.57687i q^{15} +(-0.719029 - 1.24540i) q^{16} +(1.33421 - 2.31092i) q^{17} +(-1.44212 - 0.832611i) q^{18} +(-0.603203 + 0.348259i) q^{19} -4.99038i q^{20} +3.62652 q^{22} +(4.48044 + 7.76035i) q^{23} +(4.86368 + 2.80805i) q^{24} +(2.76867 - 4.79547i) q^{25} +(0.248375 + 2.43987i) q^{26} +1.28809 q^{27} -5.28644 q^{29} +(2.57688 + 4.46329i) q^{30} +(4.72808 + 2.72976i) q^{31} +(-5.01457 - 2.89516i) q^{32} +(10.7773 - 6.22229i) q^{33} -1.81505i q^{34} +3.76362 q^{36} +(-5.79541 + 3.34598i) q^{37} +(-0.236885 + 0.410296i) q^{38} +(4.92440 + 6.82468i) q^{39} +(-3.90522 - 6.76404i) q^{40} -2.21339i q^{41} +2.39014 q^{43} +(-7.09829 + 4.09820i) q^{44} +(6.88231 + 3.97350i) q^{45} +(5.27856 + 3.04758i) q^{46} +(-5.01925 + 2.89787i) q^{47} -3.35661 q^{48} -3.76647i q^{50} +(-3.11421 - 5.39397i) q^{51} +(-3.24337 - 4.49496i) q^{52} +(2.35785 - 4.08392i) q^{53} +(0.758771 - 0.438077i) q^{54} -17.3070 q^{55} +1.62576i q^{57} +(-3.11407 + 1.79791i) q^{58} +(-2.58136 - 1.49035i) q^{59} +(-10.0876 - 5.82409i) q^{60} +(-1.09732 - 1.90062i) q^{61} +3.71354 q^{62} -1.06244 q^{64} +(-1.18533 - 11.6439i) q^{65} +(4.23238 - 7.33069i) q^{66} +(7.53957 + 4.35297i) q^{67} +(2.05112 + 3.55265i) q^{68} +20.9158 q^{69} -8.56190i q^{71} +(5.10128 - 2.94522i) q^{72} +(-5.09355 - 2.94076i) q^{73} +(-2.27593 + 3.94202i) q^{74} +(-6.46242 - 11.1932i) q^{75} -1.07078i q^{76} +(5.22186 + 2.34542i) q^{78} +(-0.455408 - 0.788790i) q^{79} +(4.04271 + 2.33406i) q^{80} +(5.17551 - 8.96424i) q^{81} +(-0.752769 - 1.30383i) q^{82} -11.7481i q^{83} +8.66202i q^{85} +(1.40795 - 0.812881i) q^{86} +(-6.16961 + 10.6861i) q^{87} +(-6.41410 + 11.1095i) q^{88} +(0.853918 - 0.493010i) q^{89} +5.40552 q^{90} -13.7758 q^{92} +(11.0359 - 6.37160i) q^{93} +(-1.97112 + 3.41408i) q^{94} +(1.13049 - 1.95807i) q^{95} +(-11.7046 + 6.75768i) q^{96} +15.3454i q^{97} -13.0525i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} - 16 q^{9}+O(q^{10}) $ 32 * q + 20 * q^4 - 16 * q^9	$ 32 q + 20 q^{4} - 16 q^{9} - 28 q^{16} - 16 q^{22} + 36 q^{23} + 44 q^{25} + 72 q^{29} + 104 q^{36} - 32 q^{39} - 72 q^{43} + 72 q^{51} - 12 q^{53} - 328 q^{64} + 24 q^{65} - 96 q^{74} + 48 q^{78} - 36 q^{79} - 16 q^{81} - 136 q^{88} + 48 q^{92} + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 - 16 * q^9 - 28 * q^16 - 16 * q^22 + 36 * q^23 + 44 * q^25 + 72 * q^29 + 104 * q^36 - 32 * q^39 - 72 * q^43 + 72 * q^51 - 12 * q^53 - 328 * q^64 + 24 * q^65 - 96 * q^74 + 48 * q^78 - 36 * q^79 - 16 * q^81 - 136 * q^88 + 48 * q^92 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.589067	−	0.340098i	0.416533	−	0.240486i	−0.277060	−	0.960853i	$-0.589360\pi$
$2$	0.589067	−	0.340098i	0.416533	−	0.240486i	0.693593	+	0.720367i	$0.256027\pi$
$3$	1.16706	−	2.02141i	0.673804	−	1.16706i	−0.303012	−	0.952987i	$-0.597992\pi$
$3$	1.16706	−	2.02141i	0.673804	−	1.16706i	0.976817	−	0.214077i	$-0.0686743\pi$
$4$	−0.768667	+	1.33137i	−0.384333	+	0.665685i
$5$	−2.81123	+	1.62306i	−1.25722	+	0.725856i	−0.972533	−	0.232765i	$-0.925223\pi$
$5$	−2.81123	+	1.62306i	−1.25722	+	0.725856i	−0.284686	+	0.958621i	$0.591889\pi$
$6$		−	1.58766i		−	0.648161i
$7$		0			0
$7$		0			0
$8$			2.40608i			0.850678i
$9$	−1.22407	−	2.12016i	−0.408025	−	0.706720i
$10$	−1.10400	+	1.91219i	−0.349116	+	0.604686i
$11$	4.61728	+	2.66579i	1.39216	+	0.803765i	0.993554	−	0.113357i	$-0.0361603\pi$
$11$	4.61728	+	2.66579i	1.39216	+	0.803765i	0.398607	+	0.917122i	$0.369494\pi$
$12$	1.79417	+	3.10759i	0.517931	+	0.897083i
$13$	−1.47728	+	3.28902i	−0.409723	+	0.912210i
$13$	−1.47728	+	3.28902i	−0.409723	+	0.912210i
$14$		0			0
$15$			7.57687i			1.95634i
$16$	−0.719029	−	1.24540i	−0.179757	−	0.311349i
$17$	1.33421	−	2.31092i	0.323593	−	0.560480i	−0.657633	−	0.753338i	$-0.728442\pi$
$17$	1.33421	−	2.31092i	0.323593	−	0.560480i	0.981227	+	0.192858i	$0.0617758\pi$
$18$	−1.44212	−	0.832611i	−0.339912	−	0.196248i
$19$	−0.603203	+	0.348259i	−0.138384	+	0.0798962i	−0.567594	−	0.823309i	$-0.692126\pi$
$19$	−0.603203	+	0.348259i	−0.138384	+	0.0798962i	0.429209	+	0.903205i	$0.358792\pi$
$20$		−	4.99038i		−	1.11588i
$21$		0			0
$22$	3.62652			0.773176
$23$	4.48044	+	7.76035i	0.934236	+	1.61814i	0.775991	+	0.630744i	$0.217250\pi$
$23$	4.48044	+	7.76035i	0.934236	+	1.61814i	0.158245	+	0.987400i	$0.449417\pi$
$24$	4.86368	+	2.80805i	0.992795	+	0.573191i
$25$	2.76867	−	4.79547i	0.553733	−	0.959094i
$26$	0.248375	+	2.43987i	0.0487103	+	0.478498i
$27$	1.28809			0.247893
$28$		0			0
$29$	−5.28644			−0.981667			−0.490833	−	0.871253i	$-0.663308\pi$
$29$	−5.28644			−0.981667			−0.490833	+	0.871253i	$0.663308\pi$
$30$	2.57688	+	4.46329i	0.470472	+	0.814881i
$31$	4.72808	+	2.72976i	0.849188	+	0.490279i	0.860377	−	0.509659i	$-0.170228\pi$
$31$	4.72808	+	2.72976i	0.849188	+	0.490279i	−0.0111891	+	0.999937i	$0.503562\pi$
$32$	−5.01457	−	2.89516i	−0.886459	−	0.511797i
$33$	10.7773	−	6.22229i	1.87609	−	1.08316i
$34$		−	1.81505i		−	0.311278i
$35$		0			0
$36$	3.76362			0.627270
$37$	−5.79541	+	3.34598i	−0.952760	+	0.550076i	−0.893937	−	0.448192i	$-0.852068\pi$
$37$	−5.79541	+	3.34598i	−0.952760	+	0.550076i	−0.0588228	+	0.998268i	$0.518735\pi$
$38$	−0.236885	+	0.410296i	−0.0384278	+	0.0665588i
$39$	4.92440	+	6.82468i	0.788534	+	1.09282i
$40$	−3.90522	−	6.76404i	−0.617470	−	1.06949i
$41$		−	2.21339i		−	0.345673i	−0.984951	−	0.172836i	$-0.944707\pi$
$41$		−	2.21339i		−	0.345673i	0.984951	−	0.172836i	$-0.0552932\pi$
$42$		0			0
$43$	2.39014			0.364493			0.182246	−	0.983253i	$-0.441663\pi$
$43$	2.39014			0.364493			0.182246	+	0.983253i	$0.441663\pi$
$44$	−7.09829	+	4.09820i	−1.07011	+	0.617827i
$45$	6.88231	+	3.97350i	1.02595	+	0.592335i
$46$	5.27856	+	3.04758i	0.778281	+	0.449341i
$47$	−5.01925	+	2.89787i	−0.732133	+	0.422697i	−0.819202	−	0.573505i	$-0.805583\pi$
$47$	−5.01925	+	2.89787i	−0.732133	+	0.422697i	0.0870689	+	0.996202i	$0.472250\pi$
$48$	−3.35661			−0.484485
$49$		0			0
$50$		−	3.76647i		−	0.532660i
$51$	−3.11421	−	5.39397i	−0.436077	−	0.755307i
$52$	−3.24337	−	4.49496i	−0.449774	−	0.623339i
$53$	2.35785	−	4.08392i	0.323876	−	0.560969i	−0.657409	−	0.753534i	$-0.728347\pi$
$53$	2.35785	−	4.08392i	0.323876	−	0.560969i	0.981284	+	0.192565i	$0.0616807\pi$
$54$	0.758771	−	0.438077i	0.103256	−	0.0596147i
$55$	−17.3070			−2.33367
$56$		0			0
$57$			1.62576i			0.215338i
$58$	−3.11407	+	1.79791i	−0.408897	+	0.236077i
$59$	−2.58136	−	1.49035i	−0.336065	−	0.194027i	0.322466	−	0.946581i	$-0.395488\pi$
$59$	−2.58136	−	1.49035i	−0.336065	−	0.194027i	−0.658531	+	0.752554i	$0.728822\pi$
$60$	−10.0876	−	5.82409i	−1.30231	−	0.751886i
$61$	−1.09732	−	1.90062i	−0.140498	−	0.243350i	0.787186	−	0.616715i	$-0.211537\pi$
$61$	−1.09732	−	1.90062i	−0.140498	−	0.243350i	−0.927684	+	0.373366i	$0.878204\pi$
$62$	3.71354			0.471620
$63$		0			0
$64$	−1.06244			−0.132805
$65$	−1.18533	−	11.6439i	−0.147022	−	1.44425i
$66$	4.23238	−	7.33069i	0.520969	−	0.902345i
$67$	7.53957	+	4.35297i	0.921105	+	0.531800i	0.883987	−	0.467511i	$-0.154849\pi$
$67$	7.53957	+	4.35297i	0.921105	+	0.531800i	0.0371174	+	0.999311i	$0.488182\pi$
$68$	2.05112	+	3.55265i	0.248735	+	0.430822i
$69$	20.9158			2.51797
$70$		0			0
$71$		−	8.56190i		−	1.01611i	−0.861325	−	0.508055i	$-0.830365\pi$
$71$		−	8.56190i		−	1.01611i	0.861325	−	0.508055i	$-0.169635\pi$
$72$	5.10128	−	2.94522i	0.601191	−	0.347098i
$73$	−5.09355	−	2.94076i	−0.596155	−	0.344190i	0.171373	−	0.985206i	$-0.445180\pi$
$73$	−5.09355	−	2.94076i	−0.596155	−	0.344190i	−0.767527	+	0.641016i	$0.778513\pi$
$74$	−2.27593	+	3.94202i	−0.264571	+	0.458250i
$75$	−6.46242	−	11.1932i	−0.746216	−	1.29248i
$76$		−	1.07078i		−	0.122827i
$77$		0			0
$78$	5.22186	+	2.34542i	0.591259	+	0.265566i
$79$	−0.455408	−	0.788790i	−0.0512374	−	0.0887458i	0.839269	−	0.543716i	$-0.182983\pi$
$79$	−0.455408	−	0.788790i	−0.0512374	−	0.0887458i	−0.890507	+	0.454970i	$0.849650\pi$
$80$	4.04271	+	2.33406i	0.451989	+	0.260956i
$81$	5.17551	−	8.96424i	0.575056	−	0.996027i
$82$	−0.752769	−	1.30383i	−0.0831294	−	0.143984i
$83$		−	11.7481i		−	1.28952i	−0.764387	−	0.644758i	$-0.776958\pi$
$83$		−	11.7481i		−	1.28952i	0.764387	−	0.644758i	$-0.223042\pi$
$84$		0			0
$85$			8.66202i			0.939528i
$86$	1.40795	−	0.812881i	0.151823	−	0.0876553i
$87$	−6.16961	+	10.6861i	−0.661451	+	1.14567i
$88$	−6.41410	+	11.1095i	−0.683745	+	1.18428i
$89$	0.853918	−	0.493010i	0.0905151	−	0.0522589i	−0.454059	−	0.890971i	$-0.650025\pi$
$89$	0.853918	−	0.493010i	0.0905151	−	0.0522589i	0.544574	+	0.838713i	$0.316691\pi$
$90$	5.40552			0.569792
$91$		0			0
$92$	−13.7758			−1.43623
$93$	11.0359	−	6.37160i	1.14437	−	0.660704i
$94$	−1.97112	+	3.41408i	−0.203305	+	0.352135i
$95$	1.13049	−	1.95807i	0.115986	−	0.200894i
$96$	−11.7046	+	6.75768i	−1.19460	+	0.689702i
$97$			15.3454i			1.55809i	0.626969	+	0.779044i	$0.284295\pi$
$97$			15.3454i			1.55809i	−0.626969	+	0.779044i	$0.715705\pi$
$98$		0			0
$99$		−	13.0525i		−	1.31182i
$100$	4.25636	+	7.37224i	0.425636	+	0.737224i
$101$	−1.95463	+	3.38552i	−0.194493	+	0.336872i	−0.946734	−	0.322016i	$-0.895640\pi$
$101$	−1.95463	+	3.38552i	−0.194493	+	0.336872i	0.752241	+	0.658888i	$0.228973\pi$
$102$	−3.66896	−	2.11828i	−0.363281	−	0.209741i
$103$	9.28058	+	16.0744i	0.914443	+	1.58386i	0.807715	+	0.589573i	$0.200704\pi$
$103$	9.28058	+	16.0744i	0.914443	+	1.58386i	0.106728	+	0.994288i	$0.465963\pi$
$104$	−7.91365	−	3.55444i	−0.775997	−	0.348542i
$105$		0			0
$106$		−	3.20760i		−	0.311550i
$107$	−6.55292	−	11.3500i	−0.633495	−	1.09724i	−0.986832	−	0.161749i	$-0.948287\pi$
$107$	−6.55292	−	11.3500i	−0.633495	−	1.09724i	0.353337	−	0.935496i	$-0.385047\pi$
$108$	−0.990111	+	1.71492i	−0.0952735	+	0.165018i
$109$	−13.3350	−	7.69895i	−1.27726	−	0.737426i	−0.300916	−	0.953651i	$-0.597292\pi$
$109$	−13.3350	−	7.69895i	−1.27726	−	0.737426i	−0.976344	+	0.216225i	$0.930626\pi$
$110$	−10.1950	+	5.88606i	−0.972052	+	0.561214i
$111$			15.6199i			1.48258i
$112$		0			0
$113$	12.7346			1.19797			0.598985	−	0.800761i	$-0.295571\pi$
$113$	12.7346			1.19797			0.598985	+	0.800761i	$0.295571\pi$
$114$	0.552919	+	0.957684i	0.0517856	+	0.0896953i
$115$	−25.1911	−	14.5441i	−2.34908	−	1.35624i
$116$	4.06351	−	7.03820i	0.377287	−	0.653481i
$117$	8.78154	−	0.893946i	0.811854	−	0.0826454i
$118$	−2.02746			−0.186643
$119$		0			0
$120$	−18.2306			−1.66422
$121$	8.71284	+	15.0911i	0.792076	+	1.37192i
$122$	−1.29280	−	0.746396i	−0.117044	−	0.0675755i
$123$	−4.47417	−	2.58316i	−0.403422	−	0.232916i
$124$	−7.26863	+	4.19654i	−0.652742	+	0.376861i
$125$			1.74425i			0.156011i
$126$		0			0
$127$	10.2763			0.911878			0.455939	−	0.890011i	$-0.349303\pi$
$127$	10.2763			0.911878			0.455939	+	0.890011i	$0.349303\pi$
$128$	9.40329	−	5.42899i	0.831141	−	0.479859i
$129$	2.78944	−	4.83146i	0.245597	−	0.425386i
$130$	−4.65831	−	6.45591i	−0.408560	−	0.566221i
$131$	6.29063	+	10.8957i	0.549615	+	0.951961i	0.998301	+	0.0582718i	$0.0185590\pi$
$131$	6.29063	+	10.8957i	0.549615	+	0.951961i	−0.448686	+	0.893690i	$0.648108\pi$
$132$			19.1315i			1.66518i
$133$		0			0
$134$	5.92175			0.511561
$135$	−3.62111	+	2.09065i	−0.311656	+	0.179934i
$136$	5.56025	+	3.21021i	0.476788	+	0.275274i
$137$	1.49466	+	0.862942i	0.127697	+	0.0737261i	0.562488	−	0.826805i	$-0.309844\pi$
$137$	1.49466	+	0.862942i	0.127697	+	0.0737261i	−0.434791	+	0.900532i	$0.643178\pi$
$138$	12.3208	−	7.11343i	1.04882	−	0.605536i
$139$	2.93311			0.248783			0.124391	−	0.992233i	$-0.460302\pi$
$139$	2.93311			0.248783			0.124391	+	0.992233i	$0.460302\pi$
$140$		0			0
$141$			13.5280i			1.13926i
$142$	−2.91188	−	5.04353i	−0.244360	−	0.423244i
$143$	−15.5888	+	11.2482i	−1.30360	+	0.940623i
$144$	−1.76029	+	3.04891i	−0.146691	+	0.254076i
$145$	14.8614	−	8.58022i	1.23417	−	0.712548i
$146$	−4.00059			−0.331091
$147$		0			0
$148$		−	10.2878i		−	0.845650i
$149$	11.4661	−	6.61994i	0.939338	−	0.542327i	0.0495851	−	0.998770i	$-0.484210\pi$
$149$	11.4661	−	6.61994i	0.939338	−	0.542327i	0.889753	+	0.456443i	$0.150877\pi$
$150$	−7.61360	−	4.39571i	−0.621648	−	0.358909i
$151$	8.01838	+	4.62942i	0.652527	+	0.376736i	0.789424	−	0.613849i	$-0.210380\pi$
$151$	8.01838	+	4.62942i	0.652527	+	0.376736i	−0.136897	+	0.990585i	$0.543713\pi$
$152$	−0.837940	−	1.45135i	−0.0679659	−	0.117720i
$153$	−6.53268			−0.528136
$154$		0			0
$155$	−17.7223			−1.42349
$156$	−12.8714	+	1.31029i	−1.03054	+	0.104907i
$157$	−0.828132	+	1.43437i	−0.0660922	+	0.114475i	−0.897178	−	0.441669i	$-0.854386\pi$
$157$	−0.828132	+	1.43437i	−0.0660922	+	0.114475i	0.831086	+	0.556144i	$0.187720\pi$
$158$	−0.536532	−	0.309767i	−0.0426842	−	0.0246437i
$159$	−5.50352	−	9.53238i	−0.436458	−	0.755967i
$160$	18.7961			1.48596
$161$		0			0
$162$		−	7.04072i		−	0.553171i
$163$	8.57328	−	4.94978i	0.671511	−	0.387697i	−0.125138	−	0.992139i	$-0.539937\pi$
$163$	8.57328	−	4.94978i	0.671511	−	0.387697i	0.796649	+	0.604442i	$0.206604\pi$
$164$	2.94684	+	1.70136i	0.230109	+	0.132854i
$165$	−20.1983	+	34.9845i	−1.57244	+	2.72354i
$166$	−3.99549	−	6.92039i	−0.310110	−	0.537127i
$167$		−	6.10891i		−	0.472721i	−0.971665	−	0.236361i	$-0.924045\pi$
$167$		−	6.10891i		−	0.472721i	0.971665	−	0.236361i	$-0.0759547\pi$
$168$		0			0
$169$	−8.63531	−	9.71758i	−0.664255	−	0.747506i
$170$	2.94594	+	5.10251i	0.225943	+	0.391345i
$171$	1.47673	+	0.852591i	0.112928	+	0.0651992i
$172$	−1.83722	+	3.18216i	−0.140087	+	0.242637i
$173$	−9.36059	−	16.2130i	−0.711672	−	1.23265i	−0.964229	−	0.265070i	$-0.914605\pi$
$173$	−9.36059	−	16.2130i	−0.711672	−	1.23265i	0.252557	−	0.967582i	$-0.418729\pi$
$174$			8.39309i			0.636278i
$175$		0			0
$176$		−	7.66712i		−	0.577931i
$177$	−6.02523	+	3.47867i	−0.452884	+	0.261473i
$178$	0.335343	−	0.580832i	0.0251350	−	0.0435352i
$179$	−4.96878	+	8.60618i	−0.371384	+	0.643256i	−0.989779	−	0.142612i	$-0.954450\pi$
$179$	−4.96878	+	8.60618i	−0.371384	+	0.643256i	0.618395	+	0.785868i	$0.287783\pi$
$180$	−10.5804	+	6.10859i	−0.788616	+	0.455308i
$181$	22.6991			1.68721			0.843606	−	0.536962i	$-0.180428\pi$
$181$	22.6991			1.68721			0.843606	+	0.536962i	$0.180428\pi$
$182$		0			0
$183$	−5.12259			−0.378673
$184$	−18.6720	+	10.7803i	−1.37652	+	0.794734i
$185$	10.8615	−	18.8126i	0.798552	−	1.38313i
$186$	4.33394	−	7.50660i	0.317780	−	0.550411i
$187$	12.3208	−	7.11343i	0.900988	−	0.520186i
$188$		−	8.90997i		−	0.649827i
$189$		0			0
$190$		−	1.53791i		−	0.111572i
$191$	−2.71463	−	4.70188i	−0.196424	−	0.340216i	0.750943	−	0.660368i	$-0.229600\pi$
$191$	−2.71463	−	4.70188i	−0.196424	−	0.340216i	−0.947366	+	0.320152i	$0.896266\pi$
$192$	−1.23993	+	2.14763i	−0.0894845	+	0.154992i
$193$	−1.70611	−	0.985026i	−0.122809	−	0.0709037i	0.437337	−	0.899298i	$-0.355922\pi$
$193$	−1.70611	−	0.985026i	−0.122809	−	0.0709037i	−0.560146	+	0.828394i	$0.689255\pi$
$194$	5.21894	+	9.03947i	0.374698	+	0.648996i
$195$	−24.9205	−	11.1931i	−1.78459	−	0.801557i
$196$		0			0
$197$		−	19.1476i		−	1.36421i	−0.731253	−	0.682107i	$-0.761064\pi$
$197$		−	19.1476i		−	1.36421i	0.731253	−	0.682107i	$-0.238936\pi$
$198$	−4.43913	−	7.68879i	−0.315475	−	0.546419i
$199$	0.0974054	−	0.168711i	0.00690489	−	0.0119596i	−0.862552	−	0.505968i	$-0.831135\pi$
$199$	0.0974054	−	0.168711i	0.00690489	−	0.0119596i	0.869457	+	0.494008i	$0.164469\pi$
$200$	11.5383	+	6.66164i	0.815880	+	0.471049i
$201$	17.5983	−	10.1604i	1.24129	−	0.716659i
$202$			2.65907i			0.187091i
$203$		0			0
$204$	9.57516			0.670396
$205$	3.59247	+	6.22233i	0.250909	+	0.434587i
$206$	10.9338	+	6.31262i	0.761792	+	0.439821i
$207$	10.9688	−	18.9985i	0.762383	−	1.32049i
$208$	5.15834	−	0.525110i	0.357666	−	0.0364098i
$209$	−3.71354			−0.256871
$210$		0			0
$211$	12.2618			0.844139			0.422070	−	0.906563i	$-0.361304\pi$
$211$	12.2618			0.844139			0.422070	+	0.906563i	$0.361304\pi$
$212$	3.62480	+	6.27834i	0.248952	+	0.431198i
$213$	−17.3071	−	9.99228i	−1.18587	−	0.684660i
$214$	−7.72022	−	4.45727i	−0.527743	−	0.304693i
$215$	−6.71922	+	3.87934i	−0.458247	+	0.264569i
$216$			3.09925i			0.210877i
$217$		0			0
$218$	−10.4736			−0.709362
$219$	−11.8890	+	6.86411i	−0.803383	+	0.463834i
$220$	13.3033	−	23.0420i	0.896907	−	1.55349i
$221$	5.62966	+	7.80210i	0.378692	+	0.524826i
$222$	5.31230	+	9.20117i	0.356538	+	0.617542i
$223$		−	27.1733i		−	1.81966i	−0.414981	−	0.909830i	$-0.636212\pi$
$223$		−	27.1733i		−	1.81966i	0.414981	−	0.909830i	$-0.363788\pi$
$224$		0			0
$225$	−13.5562			−0.903748
$226$	7.50153	−	4.33101i	0.498994	−	0.288094i
$227$	−6.24651	−	3.60642i	−0.414595	−	0.239367i	0.278167	−	0.960533i	$-0.410273\pi$
$227$	−6.24651	−	3.60642i	−0.414595	−	0.239367i	−0.692762	+	0.721166i	$0.743606\pi$
$228$	−2.16449	−	1.24967i	−0.143347	−	0.0827614i
$229$	−14.8200	+	8.55635i	−0.979335	+	0.565419i	−0.902069	−	0.431591i	$-0.857952\pi$
$229$	−14.8200	+	8.55635i	−0.979335	+	0.565419i	−0.0772656	+	0.997011i	$0.524619\pi$
$230$	−19.7856			−1.30463
$231$		0			0
$232$		−	12.7196i		−	0.835082i
$233$	−6.31766	−	10.9425i	−0.413883	−	0.716867i	0.581427	−	0.813599i	$-0.302495\pi$
$233$	−6.31766	−	10.9425i	−0.413883	−	0.716867i	−0.995311	+	0.0967314i	$0.969161\pi$
$234$	4.86889	−	3.51318i	0.318289	−	0.229664i
$235$	9.40684	−	16.2931i	0.613635	−	1.06285i
$236$	3.96842	−	2.29117i	0.258322	−	0.149142i
$237$	−2.12596			−0.138096
$238$		0			0
$239$		−	7.70807i		−	0.498594i	−0.968427	−	0.249297i	$-0.919801\pi$
$239$		−	7.70807i		−	0.498594i	0.968427	−	0.249297i	$-0.0801995\pi$
$240$	9.43620	−	5.44799i	0.609104	−	0.351666i
$241$	16.6296	+	9.60112i	1.07121	+	0.618463i	0.928512	−	0.371304i	$-0.121089\pi$
$241$	16.6296	+	9.60112i	1.07121	+	0.618463i	0.142697	+	0.989766i	$0.454422\pi$
$242$	10.2649	+	5.92644i	0.659853	+	0.380966i
$243$	−10.1482	−	17.5771i	−0.651005	−	1.12757i
$244$	3.37390			0.215992
$245$		0			0
$246$	−3.51412			−0.224052
$247$	−0.254335	−	2.49842i	−0.0161830	−	0.158971i
$248$	−6.56801	+	11.3761i	−0.417069	+	0.722385i
$249$	−23.7477	−	13.7107i	−1.50495	−	0.868882i
$250$	0.593216	+	1.02748i	0.0375183	+	0.0649836i
$251$	17.6761			1.11570			0.557851	−	0.829941i	$-0.311626\pi$
$251$	17.6761			1.11570			0.557851	+	0.829941i	$0.311626\pi$
$252$		0			0
$253$			47.7756i			3.00362i
$254$	6.05346	−	3.49497i	0.379828	−	0.219294i
$255$	17.5095	+	10.1091i	1.09649	+	0.633058i
$256$	4.75522	−	8.23628i	0.297201	−	0.514767i
$257$	1.30967	+	2.26842i	0.0816952	+	0.141500i	0.903978	−	0.427579i	$-0.140633\pi$
$257$	1.30967	+	2.26842i	0.0816952	+	0.141500i	−0.822283	+	0.569079i	$0.807300\pi$
$258$		−	3.79474i		−	0.236250i
$259$		0			0
$260$	16.4135	+	7.37216i	1.01792	+	0.457202i
$261$	6.47099	+	11.2081i	0.400544	+	0.693763i
$262$	7.41121	+	4.27887i	0.457866	+	0.264349i
$263$	−2.81437	+	4.87464i	−0.173542	+	0.300583i	−0.939656	−	0.342122i	$-0.888854\pi$
$263$	−2.81437	+	4.87464i	−0.173542	+	0.300583i	0.766114	+	0.642705i	$0.222188\pi$
$264$	14.9713	+	25.9311i	0.921421	+	1.59595i
$265$			15.3078i			0.940348i
$266$		0			0
$267$		−	2.30149i		−	0.140849i
$268$	−11.5908	+	6.69197i	−0.708022	+	0.408777i
$269$	−6.92905	+	12.0015i	−0.422472	+	0.731743i	−0.996181	−	0.0873166i	$-0.972171\pi$
$269$	−6.92905	+	12.0015i	−0.422472	+	0.731743i	0.573709	+	0.819059i	$0.305504\pi$
$270$	−1.42205	+	2.46307i	−0.0865433	+	0.149897i
$271$	−6.93575	+	4.00436i	−0.421317	+	0.243247i	−0.695641	−	0.718390i	$-0.744879\pi$
$271$	−6.93575	+	4.00436i	−0.421317	+	0.243247i	0.274324	+	0.961637i	$0.411546\pi$
$272$	−3.83734			−0.232673
$273$		0			0
$274$	1.17394			0.0709203
$275$	25.5674	−	14.7613i	1.54177	−	0.890143i
$276$	−16.0773	+	27.8467i	−0.967739	+	1.67617i
$277$	9.14650	−	15.8422i	0.549560	−	0.951866i	−0.448745	−	0.893660i	$-0.648129\pi$
$277$	9.14650	−	15.8422i	0.549560	−	0.951866i	0.998305	−	0.0582057i	$-0.0185379\pi$
$278$	1.72780	−	0.997544i	0.103626	−	0.0598287i
$279$		−	13.3657i		−	0.800184i
$280$		0			0
$281$			19.3790i			1.15605i	0.816018	+	0.578026i	$0.196177\pi$
$281$			19.3790i			1.15605i	−0.816018	+	0.578026i	$0.803823\pi$
$282$	4.60084	+	7.96889i	0.273976	+	0.474540i
$283$	−3.21864	+	5.57486i	−0.191329	+	0.331391i	−0.945691	−	0.325068i	$-0.894613\pi$
$283$	−3.21864	+	5.57486i	−0.191329	+	0.331391i	0.754362	+	0.656458i	$0.227946\pi$
$284$	11.3990	+	6.58124i	0.676409	+	0.390525i
$285$	−2.63872	−	4.57039i	−0.156304	−	0.270726i
$286$	−5.35737	+	11.9277i	−0.316788	+	0.705299i
$287$		0			0
$288$			14.1756i			0.835304i
$289$	4.93977	+	8.55594i	0.290575	+	0.503291i
$290$	5.83623	−	10.1087i	0.342715	−	0.593601i
$291$	31.0194	+	17.9090i	1.81839	+	1.04985i
$292$	7.83048	−	4.52093i	0.458244	−	0.264567i
$293$		−	7.66381i		−	0.447725i	−0.974621	−	0.223862i	$-0.928133\pi$
$293$		−	7.66381i		−	0.447725i	0.974621	−	0.223862i	$-0.0718666\pi$
$294$		0			0
$295$	9.67573			0.563343
$296$	−8.05071	−	13.9442i	−0.467938	−	0.810492i
$297$	5.94747	+	3.43377i	0.345107	+	0.199248i
$298$	4.50286	−	7.79918i	0.260844	−	0.451795i
$299$	−32.1428	+	3.27208i	−1.85886	+	0.189229i
$300$	19.8698			1.14718
$301$		0			0
$302$	6.29782			0.362399
$303$	4.56236	+	7.90224i	0.262101	+	0.453972i
$304$	0.867441	+	0.500817i	0.0497512	+	0.0287238i
$305$	6.16965	+	3.56205i	0.353273	+	0.203962i
$306$	−3.84819	+	2.22175i	−0.219986	+	0.127009i
$307$			0.312144i			0.0178150i	0.999960	+	0.00890751i	$0.00283539\pi$
$307$			0.312144i			0.0178150i	−0.999960	+	0.00890751i	$0.997165\pi$
$308$		0			0
$309$	43.3241			2.46462
$310$	−10.4396	+	6.02731i	−0.592930	+	0.342328i
$311$	1.40754	−	2.43792i	0.0798141	−	0.138242i	−0.823356	−	0.567526i	$-0.807901\pi$
$311$	1.40754	−	2.43792i	0.0798141	−	0.138242i	0.903170	+	0.429284i	$0.141234\pi$
$312$	−16.4207	+	11.8485i	−0.929641	+	0.670789i
$313$	−6.64651	−	11.5121i	−0.375683	−	0.650702i	0.614746	−	0.788725i	$-0.289258\pi$
$313$	−6.64651	−	11.5121i	−0.375683	−	0.650702i	−0.990429	+	0.138023i	$0.955925\pi$
$314$			1.12658i			0.0635769i
$315$		0			0
$316$	1.40023			0.0787690
$317$	−0.841932	+	0.486090i	−0.0472876	+	0.0273015i	−0.523457	−	0.852052i	$-0.675358\pi$
$317$	−0.841932	+	0.486090i	−0.0472876	+	0.0273015i	0.476170	+	0.879353i	$0.342025\pi$
$318$	−6.48389	−	3.74347i	−0.363598	−	0.209924i
$319$	−24.4090	−	14.0925i	−1.36664	−	0.789029i
$320$	2.98676	−	1.72440i	0.166965	−	0.0963972i
$321$	−30.5907			−1.70741
$322$		0			0
$323$			1.85860i			0.103415i
$324$	7.95648	+	13.7810i	0.442026	+	0.765612i
$325$	11.6823	+	16.1904i	0.648018	+	0.898084i
$326$	3.36682	−	5.83151i	0.186471	−	0.322978i
$327$	−31.1255	+	17.9703i	−1.72125	+	0.993762i
$328$	5.32559			0.294056
$329$		0			0
$330$			27.4776i			1.51259i
$331$	−6.68651	+	3.86046i	−0.367524	+	0.212190i	−0.672376	−	0.740210i	$-0.734726\pi$
$331$	−6.68651	+	3.86046i	−0.367524	+	0.212190i	0.304852	+	0.952400i	$0.401393\pi$
$332$	15.6410	+	9.03033i	0.858411	+	0.495604i
$333$	14.1880	+	8.19147i	0.777500	+	0.448890i
$334$	−2.07763	−	3.59856i	−0.113683	−	0.196904i
$335$	−28.2606			−1.54404
$336$		0			0
$337$	−27.4858			−1.49725			−0.748624	−	0.662995i	$-0.769285\pi$
$337$	−27.4858			−1.49725			−0.748624	+	0.662995i	$0.769285\pi$
$338$	−8.39171	−	2.78746i	−0.456449	−	0.151618i
$339$	14.8621	−	25.7419i	0.807197	−	1.39811i
$340$	−11.5323	−	6.65820i	−0.625429	−	0.361092i
$341$	14.5539	+	25.2081i	0.788138	+	1.36509i
$342$	1.15986			0.0627179
$343$		0			0
$344$			5.75086i			0.310066i
$345$	−58.7991	+	33.9477i	−3.16564	+	1.82768i
$346$	−11.0280	−	6.36704i	−0.592871	−	0.342294i
$347$	1.84773	−	3.20036i	0.0991914	−	0.171804i	−0.812159	−	0.583436i	$-0.801708\pi$
$347$	1.84773	−	3.20036i	0.0991914	−	0.171804i	0.911350	+	0.411632i	$0.135041\pi$
$348$	−9.48474	−	16.4281i	−0.508436	−	0.880636i
$349$			26.7513i			1.43197i	0.698118	+	0.715983i	$0.254021\pi$
$349$			26.7513i			1.43197i	−0.698118	+	0.715983i	$0.745979\pi$
$350$		0			0
$351$	−1.90286	+	4.23655i	−0.101567	+	0.226130i
$352$	−15.4358	−	26.7355i	−0.822729	−	1.42501i
$353$	−2.38444	−	1.37666i	−0.126911	−	0.0732722i	0.435200	−	0.900334i	$-0.356678\pi$
$353$	−2.38444	−	1.37666i	−0.126911	−	0.0732722i	−0.562112	+	0.827061i	$0.690011\pi$
$354$	−2.36618	+	4.09834i	−0.125761	+	0.217824i
$355$	13.8965	+	24.0694i	0.737549	+	1.27747i
$356$			1.51584i			0.0803394i
$357$		0			0
$358$			6.75949i			0.357250i
$359$	30.3581	−	17.5273i	1.60224	−	0.925053i	0.611201	−	0.791475i	$-0.290687\pi$
$359$	30.3581	−	17.5273i	1.60224	−	0.925053i	0.991038	−	0.133578i	$-0.0426466\pi$
$360$	−9.56056	+	16.5594i	−0.503886	+	0.872756i
$361$	−9.25743	+	16.0343i	−0.487233	+	0.843913i
$362$	13.3713	−	7.71993i	0.702781	−	0.405751i
$363$	40.6737			2.13482
$364$		0			0
$365$	19.0922			0.999329
$366$	−3.01755	+	1.74218i	−0.157730	+	0.0910653i
$367$	7.50027	−	12.9908i	0.391511	−	0.678117i	−0.601138	−	0.799145i	$-0.705286\pi$
$367$	7.50027	−	12.9908i	0.391511	−	0.678117i	0.992649	+	0.121028i	$0.0386192\pi$
$368$	6.44313	−	11.1598i	0.335872	−	0.581747i
$369$	−4.69273	+	2.70935i	−0.244294	+	0.141043i
$370$		−	14.7759i		−	0.768161i
$371$		0			0
$372$			19.5905i			1.01572i
$373$	−10.4971	−	18.1816i	−0.543521	−	0.941406i	−0.998698	−	0.0510055i	$-0.983757\pi$
$373$	−10.4971	−	18.1816i	−0.543521	−	0.941406i	0.455177	−	0.890401i	$-0.349576\pi$
$374$	4.83853	−	8.38058i	0.250194	−	0.433349i
$375$	3.52585	+	2.03565i	0.182074	+	0.105121i
$376$	−6.97250	−	12.0767i	−0.359579	−	0.622810i
$377$	7.80953	−	17.3872i	0.402211	−	0.895486i
$378$		0			0
$379$			15.2425i			0.782956i	0.920187	+	0.391478i	$0.128036\pi$
$379$			15.2425i			0.782956i	−0.920187	+	0.391478i	$0.871964\pi$
$380$	1.73794	+	3.01021i	0.0891547	+	0.154420i
$381$	11.9931	−	20.7727i	0.614428	−	1.06422i
$382$	−3.19820	−	1.84648i	−0.163634	−	0.0944742i
$383$	21.2834	−	12.2880i	1.08753	−	0.627887i	0.154613	−	0.987975i	$-0.450587\pi$
$383$	21.2834	−	12.2880i	1.08753	−	0.627887i	0.932918	+	0.360088i	$0.117253\pi$
$384$		−	25.3439i		−	1.29333i
$385$		0			0
$386$	−1.34002			−0.0682053
$387$	−2.92571	−	5.06747i	−0.148722	−	0.257594i
$388$	−20.4304	−	11.7955i	−1.03720	−	0.598825i
$389$	9.62037	−	16.6630i	0.487772	−	0.844846i	−0.512129	−	0.858909i	$-0.671143\pi$
$389$	9.62037	−	16.6630i	0.487772	−	0.844846i	0.999901	+	0.0140622i	$0.00447629\pi$
$390$	−18.4866	+	1.88190i	−0.936105	+	0.0952940i
$391$	23.9114			1.20925
$392$		0			0
$393$	29.3663			1.48133
$394$	−6.51208	−	11.2792i	−0.328074	−	0.568240i
$395$	2.56051	+	1.47831i	0.128833	+	0.0743820i
$396$	17.3777	+	10.0330i	0.873262	+	0.504178i
$397$	−0.516813	+	0.298382i	−0.0259381	+	0.0149754i	−0.512913	−	0.858441i	$-0.671434\pi$
$397$	−0.516813	+	0.298382i	−0.0259381	+	0.0149754i	0.486975	+	0.873416i	$0.338100\pi$
$398$		−	0.132510i		−	0.00664211i
$399$		0			0
$400$	−7.96301			−0.398151
$401$	−1.38104	+	0.797343i	−0.0689657	+	0.0398174i	−0.534086	−	0.845430i	$-0.679344\pi$
$401$	−1.38104	+	0.797343i	−0.0689657	+	0.0398174i	0.465121	+	0.885247i	$0.346011\pi$
$402$	6.91106	−	11.9703i	0.344692	−	0.597024i
$403$	−15.9629	+	11.5181i	−0.795169	+	0.573759i
$404$	−3.00492	−	5.20468i	−0.149500	−	0.258942i
$405$			33.6007i			1.66963i
$406$		0			0
$407$	−35.6787			−1.76853
$408$	12.9783	−	7.49305i	0.642523	−	0.370961i
$409$	25.1047	+	14.4942i	1.24135	+	0.716691i	0.969368	−	0.245612i	$-0.0789890\pi$
$409$	25.1047	+	14.4942i	1.24135	+	0.716691i	0.271978	+	0.962304i	$0.412322\pi$
$410$	4.23241	+	2.44358i	0.209024	+	0.120680i
$411$	3.48873	−	2.01422i	0.172086	−	0.0993540i
$412$	−28.5347			−1.40580
$413$		0			0
$414$		−	14.9218i		−	0.733369i
$415$	19.0678	+	33.0264i	0.936003	+	1.62120i
$416$	16.9301	−	12.2161i	0.830069	−	0.598942i
$417$	3.42312	−	5.92902i	0.167631	−	0.290345i
$418$	−2.18752	+	1.26297i	−0.106995	+	0.0617738i
$419$	5.18611			0.253358			0.126679	−	0.991944i	$-0.459568\pi$
$419$	5.18611			0.253358			0.126679	+	0.991944i	$0.459568\pi$
$420$		0			0
$421$		−	2.84363i		−	0.138590i	−0.997596	−	0.0692950i	$-0.977925\pi$
$421$		−	2.84363i		−	0.138590i	0.997596	−	0.0692950i	$-0.0220750\pi$
$422$	7.22304	−	4.17023i	0.351612	−	0.203003i
$423$	12.2879	+	7.09441i	0.597457	+	0.344942i
$424$	9.82623	+	5.67318i	0.477204	+	0.275514i
$425$	−7.38796	−	12.7963i	−0.358369	−	0.620713i
$426$	−13.5934			−0.658603
$427$		0			0
$428$	20.1480			0.973892
$429$	4.54416	+	44.6388i	0.219394	+	2.15518i
$430$	−2.63872	+	4.57039i	−0.127250	+	0.220404i
$431$	3.44770	+	1.99053i	0.166070	+	0.0958804i	0.580731	−	0.814095i	$-0.302767\pi$
$431$	3.44770	+	1.99053i	0.166070	+	0.0958804i	−0.414662	+	0.909976i	$0.636100\pi$
$432$	−0.926174	−	1.60418i	−0.0445606	−	0.0771812i
$433$	−7.42082			−0.356622			−0.178311	−	0.983974i	$-0.557063\pi$
$433$	−7.42082			−0.356622			−0.178311	+	0.983974i	$0.557063\pi$
$434$		0			0
$435$		−	40.0546i		−	1.92047i
$436$	20.5003	−	11.8359i	0.981787	−	0.566835i
$437$	−5.40522	−	3.12071i	−0.258567	−	0.149284i
$438$	−4.66894	+	8.08685i	−0.223091	+	0.386404i
$439$	15.2835	+	26.4718i	0.729442	+	1.26343i	0.957119	+	0.289694i	$0.0935534\pi$
$439$	15.2835	+	26.4718i	0.729442	+	1.26343i	−0.227678	+	0.973737i	$0.573113\pi$
$440$		−	41.6419i		−	1.98520i
$441$		0			0
$442$	5.96973	+	2.68133i	0.283951	+	0.127538i
$443$	2.15488	+	3.73235i	0.102381	+	0.177329i	0.912665	−	0.408708i	$-0.134021\pi$
$443$	2.15488	+	3.73235i	0.102381	+	0.177329i	−0.810284	+	0.586037i	$0.800687\pi$
$444$	−20.7959	−	12.0065i	−0.986928	−	0.569803i
$445$	−1.60037	+	2.77192i	−0.0758649	+	0.131402i
$446$	−9.24160	−	16.0069i	−0.437602	−	0.757949i
$447$		−	30.9036i		−	1.46169i
$448$		0			0
$449$		−	30.7830i		−	1.45274i	−0.687305	−	0.726369i	$-0.741206\pi$
$449$		−	30.7830i		−	1.45274i	0.687305	−	0.726369i	$-0.258794\pi$
$450$	−7.98552	+	4.61044i	−0.376441	+	0.217338i
$451$	5.90042	−	10.2198i	0.277840	−	0.481233i
$452$	−9.78865	+	16.9544i	−0.460419	+	0.797470i
$453$	18.7159	−	10.8056i	0.879351	−	0.507693i
$454$	−4.90615			−0.230257
$455$		0			0
$456$	−3.91172			−0.183183
$457$	−11.6873	+	6.74769i	−0.546711	+	0.315644i	−0.747794	−	0.663930i	$-0.768887\pi$
$457$	−11.6873	+	6.74769i	−0.546711	+	0.315644i	0.201083	+	0.979574i	$0.435554\pi$
$458$	−5.81999	+	10.0805i	−0.271950	+	0.471032i
$459$	1.71858	−	2.97667i	0.0802164	−	0.138939i
$460$	38.7270	−	22.3591i	1.80566	−	1.04250i
$461$			27.4778i			1.27977i	0.768471	+	0.639885i	$0.221018\pi$
$461$			27.4778i			1.27977i	−0.768471	+	0.639885i	$0.778982\pi$
$462$		0			0
$463$		−	8.06521i		−	0.374822i	−0.982282	−	0.187411i	$-0.939990\pi$
$463$		−	8.06521i		−	0.374822i	0.982282	−	0.187411i	$-0.0600096\pi$
$464$	3.80110	+	6.58371i	0.176462	+	0.305641i
$465$	−20.6830	+	35.8240i	−0.959152	+	1.66130i
$466$	−7.44305	−	4.29725i	−0.344793	−	0.199066i
$467$	6.31626	+	10.9401i	0.292282	+	0.506247i	0.974349	−	0.225043i	$-0.0722521\pi$
$467$	6.31626	+	10.9401i	0.292282	+	0.506247i	−0.682067	+	0.731290i	$0.738919\pi$
$468$	−5.55991	+	12.3786i	−0.257007	+	0.572202i
$469$		0			0
$470$		−	12.7970i		−	0.590281i
$471$	1.93297	+	3.34800i	0.0890664	+	0.154267i
$472$	3.58590	−	6.21097i	0.165055	−	0.285883i
$473$	11.0359	+	6.37160i	0.507433	+	0.292966i
$474$	−1.25233	+	0.723036i	−0.0575216	+	0.0332101i
$475$			3.85685i			0.176965i
$476$		0			0
$477$	−11.5447			−0.528597
$478$	−2.62150	−	4.54057i	−0.119905	−	0.207681i
$479$	27.3127	+	15.7690i	1.24795	+	0.720504i	0.970700	−	0.240295i	$-0.0772441\pi$
$479$	27.3127	+	15.7690i	1.24795	+	0.720504i	0.277249	+	0.960798i	$0.410577\pi$
$480$	21.9363	−	37.9947i	1.00125	−	1.73421i
$481$	−2.44358	−	24.0042i	−0.111418	−	1.09450i
$482$	13.0613			0.594926
$483$		0			0
$484$	−26.7891			−1.21769
$485$	−24.9065	−	43.1394i	−1.13095	−	1.95886i
$486$	−11.9559	−	6.90274i	−0.542330	−	0.313115i
$487$	36.4786	+	21.0609i	1.65300	+	0.954362i	0.975828	+	0.218539i	$0.0701292\pi$
$487$	36.4786	+	21.0609i	1.65300	+	0.954362i	0.677175	+	0.735822i	$0.263204\pi$
$488$	4.57305	−	2.64025i	0.207012	−	0.119519i
$489$		−	23.1068i		−	1.04493i
$490$		0			0
$491$	−30.2284			−1.36419			−0.682095	−	0.731264i	$-0.738931\pi$
$491$	−30.2284			−1.36419			−0.682095	+	0.731264i	$0.738931\pi$
$492$	6.87829	−	3.97118i	0.310097	−	0.179035i
$493$	−7.05321	+	12.2165i	−0.317661	+	0.550204i
$494$	−0.999529	−	1.38524i	−0.0449709	−	0.0623249i
$495$	21.1850	+	36.6935i	0.952196	+	1.64925i
$496$		−	7.85110i		−	0.352525i
$497$		0			0
$498$	−18.6520			−0.835815
$499$	3.03799	−	1.75398i	0.135999	−	0.0785191i	−0.430457	−	0.902611i	$-0.641648\pi$
$499$	3.03799	−	1.75398i	0.135999	−	0.0785191i	0.566456	+	0.824092i	$0.308314\pi$
$500$	−2.32224	−	1.34075i	−0.103854	−	0.0599600i
$501$	−12.3486	−	7.12948i	−0.551696	−	0.318522i
$502$	10.4124	−	6.01159i	0.464727	−	0.268310i
$503$	−22.8622			−1.01937			−0.509687	−	0.860360i	$-0.670239\pi$
$503$	−22.8622			−1.01937			−0.509687	+	0.860360i	$0.670239\pi$
$504$		0			0
$505$		−	12.6900i		−	0.564696i
$506$	16.2484	+	28.1430i	0.722329	+	1.25111i
$507$	−29.7212	+	6.11450i	−1.31997	+	0.271555i
$508$	−7.89908	+	13.6816i	−0.350465	+	0.607023i
$509$	−18.8582	+	10.8878i	−0.835873	+	0.482592i	−0.855859	−	0.517209i	$-0.826971\pi$
$509$	−18.8582	+	10.8878i	−0.835873	+	0.482592i	0.0199862	+	0.999800i	$0.493638\pi$
$510$	13.7524			0.608966
$511$		0			0
$512$			15.2470i			0.673829i
$513$	−0.776979	+	0.448589i	−0.0343045	+	0.0198057i
$514$	1.54297	+	0.890835i	0.0680575	+	0.0392930i
$515$	−52.1797	−	30.1259i	−2.29931	−	1.32751i
$516$	4.28830	+	7.42756i	0.188782	+	0.326980i
$517$	−30.9004			−1.35900
$518$		0			0
$519$	−43.6976			−1.91811
$520$	28.0162	−	2.85200i	1.22859	−	0.125068i
$521$	−7.26177	+	12.5777i	−0.318144	+	0.551041i	−0.980101	−	0.198501i	$-0.936393\pi$
$521$	−7.26177	+	12.5777i	−0.318144	+	0.551041i	0.661957	+	0.749542i	$0.269726\pi$
$522$	7.62370	+	4.40155i	0.333680	+	0.192650i
$523$	−8.20941	−	14.2191i	−0.358973	−	0.621759i	0.628817	−	0.777553i	$-0.283539\pi$
$523$	−8.20941	−	14.2191i	−0.358973	−	0.621759i	−0.987789	+	0.155795i	$0.950206\pi$
$524$	−19.3416			−0.844942
$525$		0			0
$526$			3.82865i			0.166937i
$527$	12.6165	−	7.28413i	0.549583	−	0.317302i
$528$	−15.4984	−	8.94801i	−0.674482	−	0.389412i
$529$	−28.6486	+	49.6209i	−1.24559	+	2.15743i
$530$	5.20614	+	9.01730i	0.226140	+	0.391686i
$531$			7.29720i			0.316672i
$532$		0			0
$533$	7.27987	+	3.26978i	0.315326	+	0.141630i
$534$	−0.782734	−	1.35573i	−0.0338722	−	0.0586684i
$535$	36.8435	+	21.2716i	1.59288	+	0.919651i
$536$	−10.4736	+	18.1408i	−0.452391	+	0.783564i
$537$	11.5978	+	20.0879i	0.500481	+	0.866858i
$538$			9.42623i			0.406394i
$539$		0			0
$540$		−	6.42805i		−	0.276619i
$541$	−11.6873	+	6.74769i	−0.502478	+	0.290106i	−0.729736	−	0.683729i	$-0.760357\pi$
$541$	−11.6873	+	6.74769i	−0.502478	+	0.290106i	0.227258	+	0.973835i	$0.427024\pi$
$542$	−2.72375	+	4.71767i	−0.116995	+	0.202641i
$543$	26.4913	−	45.8843i	1.13685	−	1.96908i
$544$	−13.3810	+	7.72550i	−0.573704	+	0.331228i
$545$	49.9835			2.14106
$546$		0			0
$547$	13.5615			0.579847			0.289924	−	0.957050i	$-0.406370\pi$
$547$	13.5615			0.579847			0.289924	+	0.957050i	$0.406370\pi$
$548$	−2.29779	+	1.32663i	−0.0981567	+	0.0566708i
$549$	−2.68641	+	4.65300i	−0.114653	+	0.198585i
$550$	10.0406	−	17.3909i	0.428133	−	0.741549i
$551$	3.18879	−	1.84105i	0.135847	−	0.0784314i
$552$			50.3252i			2.14198i
$553$		0			0
$554$		−	12.4428i		−	0.528645i
$555$	−25.3521	−	43.9111i	−1.07614	−	1.86392i
$556$	−2.25458	+	3.90505i	−0.0956155	+	0.165611i
$557$	−30.5478	−	17.6368i	−1.29435	−	0.747294i	−0.314929	−	0.949115i	$-0.601981\pi$
$557$	−30.5478	−	17.6368i	−1.29435	−	0.747294i	−0.979422	+	0.201821i	$0.935314\pi$
$558$	−4.54565	−	7.87330i	−0.192433	−	0.333303i
$559$	−3.53089	+	7.86121i	−0.149341	+	0.332494i
$560$		0			0
$561$		−	33.2073i		−	1.40201i
$562$	6.59075	+	11.4155i	0.278014	+	0.481534i
$563$	18.0551	−	31.2723i	0.760931	−	1.31797i	−0.181440	−	0.983402i	$-0.558076\pi$
$563$	18.0551	−	31.2723i	0.760931	−	1.31797i	0.942371	−	0.334569i	$-0.108591\pi$
$564$	−18.0107	−	10.3985i	−0.758389	−	0.437856i
$565$	−35.7998	+	20.6690i	−1.50611	+	0.869553i
$566$			4.37862i			0.184047i
$567$		0			0
$568$	20.6006			0.864383
$569$	5.91808	+	10.2504i	0.248099	+	0.429719i	0.962998	−	0.269508i	$-0.0868610\pi$
$569$	5.91808	+	10.2504i	0.248099	+	0.429719i	−0.714900	+	0.699227i	$0.753528\pi$
$570$	−3.10876	−	1.79484i	−0.130212	−	0.0751778i
$571$	−22.9707	+	39.7864i	−0.961294	+	1.66501i	−0.242034	+	0.970268i	$0.577815\pi$
$571$	−22.9707	+	39.7864i	−0.961294	+	1.66501i	−0.719260	+	0.694741i	$0.755519\pi$
$572$	−2.99293	−	29.4006i	−0.125141	−	1.22930i
$573$	−12.6726			−0.529405
$574$		0			0
$575$	49.6193			2.06927
$576$	1.30050	+	2.25254i	0.0541877	+	0.0938558i
$577$	−25.7617	−	14.8735i	−1.07247	−	0.619192i	−0.143616	−	0.989633i	$-0.545873\pi$
$577$	−25.7617	−	14.8735i	−1.07247	−	0.619192i	−0.928856	+	0.370441i	$0.879206\pi$
$578$	5.81972	+	3.36002i	0.242068	+	0.139758i
$579$	−3.98229	+	2.29918i	−0.165498	+	0.0955505i
$580$			26.3813i			1.09542i
$581$		0			0
$582$	24.3633			1.00989
$583$	21.7737	−	12.5711i	0.901774	−	0.520640i
$584$	7.07571	−	12.2555i	0.292795	−	0.507136i
$585$	−23.2360	+	16.7661i	−0.960690	+	0.693192i
$586$	−2.60645	−	4.51450i	−0.107671	−	0.186492i
$587$			11.3406i			0.468078i	0.972227	+	0.234039i	$0.0751943\pi$
$587$			11.3406i			0.468078i	−0.972227	+	0.234039i	$0.924806\pi$
$588$		0			0
$589$	−3.80265			−0.156686
$590$	5.69966	−	3.29070i	0.234651	−	0.135476i
$591$	−38.7053	−	22.3465i	−1.59212	−	0.919213i
$592$	8.33415	+	4.81172i	0.342531	+	0.197761i
$593$	−2.48622	+	1.43542i	−0.102097	+	0.0589455i	−0.550179	−	0.835047i	$-0.685440\pi$
$593$	−2.48622	+	1.43542i	−0.102097	+	0.0589455i	0.448082	+	0.893992i	$0.352107\pi$
$594$	4.67128			0.191665
$595$		0			0
$596$			20.3541i			0.833737i
$597$	−0.227357	−	0.393793i	−0.00930509	−	0.0161169i
$598$	−17.8214	+	12.8592i	−0.728772	+	0.525851i
$599$	2.70779	−	4.69004i	0.110637	−	0.191630i	−0.805390	−	0.592745i	$-0.798044\pi$
$599$	2.70779	−	4.69004i	0.110637	−	0.191630i	0.916027	+	0.401116i	$0.131377\pi$
$600$	26.9318	−	15.5491i	1.09949	−	0.634789i
$601$	34.1648			1.39361			0.696805	−	0.717261i	$-0.254604\pi$
$601$	34.1648			1.39361			0.696805	+	0.717261i	$0.254604\pi$
$602$		0			0
$603$		−	21.3134i		−	0.867951i
$604$	−12.3269	+	7.11695i	−0.501575	+	0.289585i
$605$	−48.9875	−	28.2830i	−1.99163	−	1.14987i
$606$	5.37508	+	3.10330i	0.218348	+	0.126063i
$607$	−11.0215	−	19.0898i	−0.447349	−	0.774830i	0.550864	−	0.834595i	$-0.314298\pi$
$607$	−11.0215	−	19.0898i	−0.447349	−	0.774830i	−0.998212	+	0.0597646i	$0.980965\pi$
$608$	4.03307			0.163562
$609$		0			0
$610$	4.84579			0.196200
$611$	−2.11632	−	20.7894i	−0.0856173	−	0.841048i
$612$	5.02146	−	8.69742i	0.202980	−	0.351572i
$613$	21.4294	+	12.3723i	0.865527	+	0.499712i	0.865859	−	0.500288i	$-0.166772\pi$
$613$	21.4294	+	12.3723i	0.865527	+	0.499712i	−0.000332251		1.00000i	$0.500106\pi$
$614$	0.106160	+	0.183874i	0.00428426	+	0.00742055i
$615$	16.7705			0.676254
$616$		0			0
$617$		−	19.9659i		−	0.803797i	−0.915684	−	0.401898i	$-0.868350\pi$
$617$		−	19.9659i		−	0.803797i	0.915684	−	0.401898i	$-0.131650\pi$
$618$	25.5208	−	14.7345i	1.02660	−	0.592707i
$619$	−8.72521	−	5.03750i	−0.350696	−	0.202474i	0.314296	−	0.949325i	$-0.398232\pi$
$619$	−8.72521	−	5.03750i	−0.350696	−	0.202474i	−0.664992	+	0.746851i	$0.731565\pi$
$620$	13.6225	−	23.5949i	0.547093	−	0.947593i
$621$	5.77120	+	9.99602i	0.231590	+	0.401126i
$622$		−	1.91480i		−	0.0767766i
$623$		0			0
$624$	4.95864	−	11.0400i	0.198505	−	0.441952i
$625$	11.0123	+	19.0739i	0.440492	+	0.762955i
$626$	−7.83048	−	4.52093i	−0.312969	−	0.180693i
$627$	−4.33394	+	7.50660i	−0.173081	+	0.299785i
$628$	−1.27312	−	2.20510i	−0.0508028	−	0.0879931i
$629$			17.8570i			0.712004i
$630$		0			0
$631$			26.2386i			1.04454i	0.852780	+	0.522271i	$0.174915\pi$
$631$			26.2386i			1.04454i	−0.852780	+	0.522271i	$0.825085\pi$
$632$	1.89789	−	1.09575i	0.0754941	−	0.0435866i
$633$	14.3103	−	24.7862i	0.568785	−	0.985164i
$634$	−0.330636	+	0.572679i	−0.0131312	+	0.0227440i
$635$	−28.8891	+	16.6792i	−1.14643	+	0.661892i
$636$	16.9215			0.670981
$637$		0			0
$638$	−19.1714			−0.759001
$639$	−18.1526	+	10.4804i	−0.718105	+	0.414598i
$640$	−17.6232	+	30.5243i	−0.696618	+	1.20658i
$641$	18.6107	−	32.2346i	0.735077	−	1.27319i	−0.219613	−	0.975587i	$-0.570479\pi$
$641$	18.6107	−	32.2346i	0.735077	−	1.27319i	0.954690	−	0.297603i	$-0.0961872\pi$
$642$	−18.0200	+	10.4038i	−0.711192	+	0.410607i
$643$		−	10.8569i		−	0.428155i	−0.976817	−	0.214077i	$-0.931326\pi$
$643$		−	10.8569i		−	0.428155i	0.976817	−	0.214077i	$-0.0686744\pi$
$644$		0			0
$645$			18.1098i			0.713071i
$646$	0.632107	+	1.09484i	0.0248699	+	0.0430760i
$647$	5.61938	−	9.73305i	0.220921	−	0.382646i	−0.734167	−	0.678969i	$-0.762427\pi$
$647$	5.61938	−	9.73305i	0.220921	−	0.382646i	0.955088	+	0.296323i	$0.0957605\pi$
$648$	21.5687	+	12.4527i	0.847298	+	0.489188i
$649$	−7.94592	−	13.7627i	−0.311904	−	0.540234i
$650$	12.3880	+	5.56412i	0.485898	+	0.218243i
$651$		0			0
$652$			15.2189i			0.596019i
$653$	7.91231	+	13.7045i	0.309632	+	0.536299i	0.978282	−	0.207279i	$-0.0664607\pi$
$653$	7.91231	+	13.7045i	0.309632	+	0.536299i	−0.668649	+	0.743578i	$0.733127\pi$
$654$	−12.2234	+	21.1715i	−0.477971	+	0.827870i
$655$	−35.3688	−	20.4202i	−1.38197	−	0.797883i
$656$	−2.75654	+	1.59149i	−0.107625	+	0.0621372i
$657$			14.3988i			0.561753i
$658$		0			0
$659$	−27.8237			−1.08386			−0.541928	−	0.840425i	$-0.682306\pi$
$659$	−27.8237			−1.08386			−0.541928	+	0.840425i	$0.682306\pi$
$660$	−31.0515	−	53.7829i	−1.20868	−	2.09349i
$661$	−15.1140	−	8.72604i	−0.587865	−	0.339404i	0.176388	−	0.984321i	$-0.443559\pi$
$661$	−15.1140	−	8.72604i	−0.587865	−	0.339404i	−0.764253	+	0.644917i	$0.776892\pi$
$662$	−2.62587	+	4.54814i	−0.102057	+	0.176768i
$663$	22.3414	−	2.27432i	0.867670	−	0.0883273i
$664$	28.2668			1.09696
$665$		0			0
$666$	11.1436			0.431806
$667$	−23.6855	−	41.0246i	−0.917108	−	1.58848i
$668$	8.13321	+	4.69571i	0.314683	+	0.181683i
$669$	−54.9285	−	31.7130i	−2.12366	−	1.22610i
$670$	−16.6474	+	9.61137i	−0.643145	+	0.371320i
$671$		−	11.7009i		−	0.451709i
$672$		0			0
$673$	−30.6883			−1.18295			−0.591474	−	0.806324i	$-0.701454\pi$
$673$	−30.6883			−1.18295			−0.591474	+	0.806324i	$0.701454\pi$
$674$	−16.1910	+	9.34788i	−0.623654	+	0.360067i
$675$	3.56629	−	6.17699i	0.137267	−	0.237753i
$676$	19.5754	−	4.02721i	0.752899	−	0.154893i
$677$	1.73778	+	3.00992i	0.0667883	+	0.115681i	0.897486	−	0.441043i	$-0.145391\pi$
$677$	1.73778	+	3.00992i	0.0667883	+	0.115681i	−0.830698	+	0.556724i	$0.812058\pi$
$678$		−	20.2183i		−	0.776477i
$679$		0			0
$680$	−20.8415			−0.799236
$681$	−14.5801	+	8.41785i	−0.558712	+	0.322573i
$682$	17.1464	+	9.89951i	0.656571	+	0.379072i
$683$	2.58740	+	1.49384i	0.0990042	+	0.0571601i	0.548685	−	0.836029i	$-0.315129\pi$
$683$	2.58740	+	1.49384i	0.0990042	+	0.0571601i	−0.449680	+	0.893190i	$0.648462\pi$
$684$	−2.27023	+	1.31072i	−0.0868043	+	0.0501165i
$685$	−5.60244			−0.214058
$686$		0			0
$687$			39.9432i			1.52393i
$688$	−1.71858	−	2.97667i	−0.0655202	−	0.113484i
$689$	9.94889	+	13.7881i	0.379022	+	0.525284i
$690$	−23.0911	+	39.9949i	−0.879063	+	1.52258i
$691$	9.95176	−	5.74565i	0.378583	−	0.218575i	−0.298619	−	0.954373i	$-0.596526\pi$
$691$	9.95176	−	5.74565i	0.378583	−	0.218575i	0.677202	+	0.735798i	$0.263193\pi$
$692$	28.7807			1.09408
$693$		0			0
$694$		−	2.51364i		−	0.0954164i
$695$	−8.24563	+	4.76061i	−0.312774	+	0.180580i
$696$	−25.7116	−	14.8446i	−0.974594	−	0.562682i
$697$	−5.11495	−	2.95312i	−0.193743	−	0.111857i
$698$	9.09807	+	15.7583i	0.344367	+	0.596461i
$699$	−29.4924			−1.11551
$700$		0			0
$701$	−0.977624			−0.0369244			−0.0184622	−	0.999830i	$-0.505877\pi$
$701$	−0.977624			−0.0369244			−0.0184622	+	0.999830i	$0.505877\pi$
$702$	0.319929	+	3.14277i	0.0120749	+	0.118616i
$703$	2.33054	−	4.03661i	0.0878979	−	0.152244i
$704$	−4.90557	−	2.83223i	−0.184886	−	0.106744i
$705$	−21.9568	−	38.0302i	−0.826939	−	1.43230i
$706$	−1.87280			−0.0704836
$707$		0			0
$708$		−	10.6957i		−	0.401971i
$709$	−8.53524	+	4.92782i	−0.320548	+	0.185068i	−0.651637	−	0.758531i	$-0.725917\pi$
$709$	−8.53524	+	4.92782i	−0.320548	+	0.185068i	0.331089	+	0.943600i	$0.392584\pi$
$710$	16.3719	+	9.45235i	0.614428	+	0.354740i
$711$	−1.11491	+	1.93108i	−0.0418123	+	0.0724210i
$712$	1.18622	+	2.05460i	0.0444555	+	0.0769992i
$713$			48.9220i			1.83214i
$714$		0			0
$715$	25.5672	−	56.9229i	0.956157	−	2.12880i
$716$	−7.63867	−	13.2306i	−0.285471	−	0.494449i
$717$	−15.5812	−	8.99581i	−0.581890	−	0.335955i
$718$	11.9220	−	20.6495i	0.444924	−	0.770631i
$719$	9.76729	+	16.9174i	0.364258	+	0.630914i	0.988657	−	0.150192i	$-0.0479892\pi$
$719$	9.76729	+	16.9174i	0.364258	+	0.630914i	−0.624398	+	0.781106i	$0.714656\pi$
$720$		−	11.4283i		−	0.425906i
$721$		0			0
$722$			12.5937i			0.468690i
$723$	38.8157	−	22.4102i	1.44357	−	0.833446i
$724$	−17.4481	+	30.2209i	−0.648452	+	1.12315i
$725$	−14.6364	+	25.3510i	−0.543582	+	0.941511i
$726$	23.9596	−	13.8331i	0.889223	−	0.513393i
$727$	−24.4958			−0.908498			−0.454249	−	0.890875i	$-0.650092\pi$
$727$	−24.4958			−0.908498			−0.454249	+	0.890875i	$0.650092\pi$
$728$		0			0
$729$	−16.3211			−0.604486
$730$	11.2466	−	6.49321i	0.416254	−	0.240324i
$731$	3.18894	−	5.52341i	0.117947	−	0.204291i
$732$	3.93756	−	6.82006i	0.145536	−	0.252077i
$733$	−26.6977	+	15.4140i	−0.986104	+	0.569327i	−0.904107	−	0.427305i	$-0.859463\pi$
$733$	−26.6977	+	15.4140i	−0.986104	+	0.569327i	−0.0819964	+	0.996633i	$0.526130\pi$
$734$		−	10.2033i		−	0.376611i
$735$		0			0
$736$		−	51.8864i		−	1.91256i
$737$	23.2082	+	40.1978i	0.854885	+	1.48070i
$738$	−1.84289	+	3.19198i	−0.0678377	+	0.117498i
$739$	2.33709	+	1.34932i	0.0859712	+	0.0496355i	0.542369	−	0.840140i	$-0.317527\pi$
$739$	2.33709	+	1.34932i	0.0859712	+	0.0496355i	−0.456398	+	0.889776i	$0.650861\pi$
$740$	16.6977	+	28.9213i	0.613820	+	1.06317i
$741$	−5.34717	−	2.40170i	−0.196433	−	0.0882287i
$742$		0			0
$743$			15.2204i			0.558382i	0.960236	+	0.279191i	$0.0900662\pi$
$743$			15.2204i			0.558382i	−0.960236	+	0.279191i	$0.909934\pi$
$744$	15.3306	+	26.5533i	0.562046	+	0.973493i
$745$	−21.4892	+	37.2203i	−0.787302	+	1.36365i
$746$	−12.3670	−	7.14011i	−0.452790	−	0.261418i
$747$	−24.9077	+	14.3805i	−0.911327	+	0.526155i
$748$			21.8714i			0.799699i
$749$		0			0
$750$	2.76929			0.101120
$751$	−12.2741	−	21.2594i	−0.447888	−	0.775765i	0.550360	−	0.834927i	$-0.314490\pi$
$751$	−12.2741	−	21.2594i	−0.447888	−	0.775765i	−0.998248	+	0.0591620i	$0.981157\pi$
$752$	7.21798	+	4.16730i	0.263213	+	0.151966i
$753$	20.6291	−	35.7306i	0.751765	−	1.30210i
$754$	−1.31302	−	12.8982i	−0.0478173	−	0.469726i
$755$	−30.0553			−1.09383
$756$		0			0
$757$	11.0892			0.403043			0.201522	−	0.979484i	$-0.435411\pi$
$757$	11.0892			0.403043			0.201522	+	0.979484i	$0.435411\pi$
$758$	5.18396	+	8.97888i	0.188290	+	0.326128i
$759$	96.5742	+	55.7571i	3.50542	+	2.02386i
$760$	4.71128	+	2.72006i	0.170896	+	0.0986669i
$761$	14.6802	−	8.47561i	0.532157	−	0.307241i	−0.209738	−	0.977758i	$-0.567261\pi$
$761$	14.6802	−	8.47561i	0.532157	−	0.307241i	0.741894	+	0.670517i	$0.233928\pi$
$762$		−	16.3154i		−	0.591044i
$763$		0			0
$764$	8.34659			0.301969
$765$	18.3649	−	10.6030i	0.663983	−	0.383351i
$766$	8.35824	−	14.4769i	0.301996	−	0.523072i
$767$	8.71518	−	6.28850i	0.314687	−	0.227064i
$768$	−11.0993	−	19.2245i	−0.400511	−	0.693705i
$769$		−	50.7371i		−	1.82962i	−0.403879	−	0.914812i	$-0.632338\pi$
$769$		−	50.7371i		−	1.82962i	0.403879	−	0.914812i	$-0.367662\pi$
$770$		0			0
$771$	6.11389			0.220186
$772$	2.62287	−	1.51431i	0.0943990	−	0.0545013i
$773$	−26.7221	−	15.4280i	−0.961128	−	0.554907i	−0.0646079	−	0.997911i	$-0.520580\pi$
$773$	−26.7221	−	15.4280i	−0.961128	−	0.554907i	−0.896520	+	0.443003i	$0.853913\pi$
$774$	−3.44688	−	1.99006i	−0.123895	−	0.0715311i
$775$	26.1809	−	15.1156i	0.940447	−	0.542967i
$776$	−36.9223			−1.32543
$777$		0			0
$778$		−	13.0875i		−	0.469209i
$779$	0.770832	+	1.33512i	0.0276179	+	0.0478357i
$780$	34.0577	−	24.5746i	1.21946	−	0.879911i
$781$	22.8242	−	39.5327i	0.816714	−	1.41459i
$782$	14.0854	−	8.13221i	0.503693	−	0.290807i
$783$	−6.80940			−0.243348
$784$		0			0
$785$		−	5.37644i		−	0.191893i
$786$	17.2987	−	9.98742i	0.617025	−	0.356239i
$787$	3.46788	+	2.00218i	0.123616	+	0.0713700i	0.560533	−	0.828132i	$-0.310596\pi$
$787$	3.46788	+	2.00218i	0.123616	+	0.0713700i	−0.436917	+	0.899502i	$0.643930\pi$
$788$	25.4926	+	14.7182i	0.908136	+	0.524312i
$789$	6.56911	+	11.3780i	0.233866	+	0.405069i
$790$	2.01109			0.0715512
$791$		0			0
$792$	31.4053			1.11594
$793$	7.87223	−	0.801380i	0.279551	−	0.0284578i
$794$	−0.202958	+	0.351534i	−0.00720272	+	0.0124755i
$795$	30.9433	+	17.8651i	1.09745	+	0.633611i
$796$	0.149745	+	0.259365i	0.00530756	+	0.00919296i
$797$	−17.3993			−0.616316			−0.308158	−	0.951335i	$-0.599713\pi$
$797$	−17.3993			−0.616316			−0.308158	+	0.951335i	$0.599713\pi$
$798$		0			0
$799$			15.4654i			0.547128i
$800$	−27.7673	+	16.0315i	−0.981723	+	0.566798i
$801$	−2.09052	−	1.20696i	−0.0738648	−	0.0426459i
$802$	−0.542349	+	0.939377i	−0.0191510	+	0.0331705i
$803$	−15.6789	−	27.1566i	−0.553296	−	0.958337i
$804$			31.2398i			1.10174i
$805$		0			0
$806$	−5.48592	+	12.2139i	−0.193233	+	0.430217i
$807$	16.1733	+	28.0130i	0.569327	+	0.986103i
$808$	−8.14584	−	4.70300i	−0.286570	−	0.165451i
$809$	−22.6592	+	39.2469i	−0.796656	+	1.37985i	0.125126	+	0.992141i	$0.460066\pi$
$809$	−22.6592	+	39.2469i	−0.796656	+	1.37985i	−0.921782	+	0.387708i	$0.873267\pi$
$810$	11.4275	+	19.7931i	0.401523	+	0.695457i
$811$		−	3.47248i		−	0.121935i	−0.998140	−	0.0609676i	$-0.980581\pi$
$811$		−	3.47248i		−	0.121935i	0.998140	−	0.0609676i	$-0.0194186\pi$
$812$		0			0
$813$			18.6934i			0.655605i
$814$	−21.0172	+	12.1343i	−0.736651	+	0.425306i
$815$	−16.0676	+	27.8299i	−0.562824	+	0.974840i
$816$	−4.47842	+	7.75685i	−0.156776	+	0.271544i
$817$	−1.44174	+	0.832388i	−0.0504400	+	0.0291216i
$818$	19.7178			0.689416
$819$		0			0
$820$	−11.0456			−0.385730
$821$	−10.4883	+	6.05541i	−0.366043	+	0.211335i	−0.671728	−	0.740797i	$-0.734448\pi$
$821$	−10.4883	+	6.05541i	−0.366043	+	0.211335i	0.305685	+	0.952133i	$0.401114\pi$
$822$	1.37006	−	2.37302i	0.0477864	−	0.0827685i
$823$	6.17222	−	10.6906i	0.215150	−	0.372651i	−0.738169	−	0.674616i	$-0.764309\pi$
$823$	6.17222	−	10.6906i	0.215150	−	0.372651i	0.953319	+	0.301965i	$0.0976426\pi$
$824$	−38.6764	+	22.3298i	−1.34736	+	0.777896i
$825$		−	68.9097i		−	2.39913i
$826$		0			0
$827$		−	33.0214i		−	1.14827i	−0.818762	−	0.574133i	$-0.805339\pi$
$827$		−	33.0214i		−	1.14827i	0.818762	−	0.574133i	$-0.194661\pi$
$828$	16.8627	+	29.2070i	0.586018	+	1.01501i
$829$	12.9259	−	22.3883i	0.448935	−	0.777578i	−0.549382	−	0.835571i	$-0.685137\pi$
$829$	12.9259	−	22.3883i	0.448935	−	0.777578i	0.998317	+	0.0579933i	$0.0184702\pi$
$830$	22.4645	+	12.9699i	0.779753	+	0.450191i
$831$	−21.3491	−	36.9777i	−0.740592	−	1.28274i
$832$	1.56951	−	3.49438i	0.0544131	−	0.121146i
$833$		0			0
$834$		−	4.65679i		−	0.161251i
$835$	9.91514	+	17.1735i	0.343127	+	0.594314i
$836$	2.85447	−	4.94409i	0.0987240	−	0.170995i
$837$	6.09018	+	3.51617i	0.210508	+	0.121537i
$838$	3.05497	−	1.76379i	0.105532	−	0.0609290i
$839$		−	24.3723i		−	0.841424i	−0.907194	−	0.420712i	$-0.861780\pi$
$839$		−	24.3723i		−	0.841424i	0.907194	−	0.420712i	$-0.138220\pi$
$840$		0			0
$841$	−1.05359			−0.0363305
$842$	−0.967113	−	1.67509i	−0.0333289	−	0.0577273i
$843$	39.1729	+	22.6165i	1.34919	+	0.778953i
$844$	−9.42526	+	16.3250i	−0.324431	+	0.561931i
$845$	40.0481	+	13.3027i	1.37770	+	0.457626i
$846$	9.65118			0.331815
$847$		0			0
$848$	−6.78145			−0.232876
$849$	7.51273	+	13.0124i	0.257836	+	0.446585i
$850$	−8.70401	−	5.02526i	−0.298545	−	0.172365i
$851$	−51.9320	−	29.9829i	−1.78020	−	1.02780i
$852$	26.6068	−	15.3615i	0.911535	−	0.526275i
$853$			16.2919i			0.557825i	0.960316	+	0.278913i	$0.0899740\pi$
$853$			16.2919i			0.557825i	−0.960316	+	0.278913i	$0.910026\pi$
$854$		0			0
$855$	−5.53523			−0.189301
$856$	27.3090	−	15.7669i	0.933402	−	0.538900i
$857$	−14.1483	+	24.5056i	−0.483296	+	0.837094i	−0.999816	−	0.0191815i	$-0.993894\pi$
$857$	−14.1483	+	24.5056i	−0.483296	+	0.837094i	0.516520	+	0.856275i	$0.327227\pi$
$858$	17.8584	+	24.7498i	0.609676	+	0.844945i
$859$	2.65355	+	4.59609i	0.0905380	+	0.156816i	0.907738	−	0.419538i	$-0.137808\pi$
$859$	2.65355	+	4.59609i	0.0905380	+	0.156816i	−0.817200	+	0.576355i	$0.804475\pi$
$860$		−	11.9277i		−	0.406731i
$861$		0			0
$862$	2.70790			0.0922314
$863$	−30.7323	+	17.7433i	−1.04614	+	0.603990i	−0.921567	−	0.388220i	$-0.873090\pi$
$863$	−30.7323	+	17.7433i	−1.04614	+	0.603990i	−0.124575	+	0.992210i	$0.539757\pi$
$864$	−6.45921	−	3.72923i	−0.219747	−	0.126871i
$865$	52.6295	+	30.3856i	1.78946	+	1.03314i
$866$	−4.37136	+	2.52381i	−0.148545	+	0.0857624i
$867$	23.0601			0.783163
$868$		0			0
$869$		−	4.85609i		−	0.164731i
$870$	−13.6225	−	23.5949i	−0.461846	−	0.799941i
$871$	−25.4550	+	18.3673i	−0.862511	+	0.622351i
$872$	18.5243	−	32.0850i	0.627312	−	1.08654i
$873$	32.5347	−	18.7839i	1.10113	−	0.635739i
$874$	−4.24539			−0.143602
$875$		0			0
$876$		−	21.1048i		−	0.713067i
$877$	−36.7183	+	21.1993i	−1.23989	+	0.715850i	−0.969071	−	0.246781i	$-0.920627\pi$
$877$	−36.7183	+	21.1993i	−1.23989	+	0.715850i	−0.270817	+	0.962631i	$0.587294\pi$
$878$	18.0060	+	10.3958i	0.607674	+	0.350841i
$879$	−15.4917	−	8.94416i	−0.522523	−	0.301679i
$880$	12.4442	+	21.5540i	0.419494	+	0.726586i
$881$	−33.1997			−1.11853			−0.559263	−	0.828990i	$-0.688916\pi$
$881$	−33.1997			−1.11853			−0.559263	+	0.828990i	$0.688916\pi$
$882$		0			0
$883$	−11.9618			−0.402546			−0.201273	−	0.979535i	$-0.564508\pi$
$883$	−11.9618			−0.402546			−0.201273	+	0.979535i	$0.564508\pi$
$884$	−14.7148	+	1.49794i	−0.494913	+	0.0503813i
$885$	11.2922	−	19.5587i	0.379583	−	0.657457i
$886$	2.53873	+	1.46574i	0.0852904	+	0.0492424i
$887$	−3.16331	−	5.47902i	−0.106214	−	0.183967i	0.808020	−	0.589155i	$-0.200539\pi$
$887$	−3.16331	−	5.47902i	−0.106214	−	0.183967i	−0.914233	+	0.405188i	$0.867206\pi$
$888$	−37.5827			−1.26119
$889$		0			0
$890$			2.17713i			0.0729777i
$891$	47.7935	−	27.5936i	1.60114	−	0.924420i
$892$	36.1777	+	20.8872i	1.21132	+	0.699356i
$893$	2.01842	−	3.49600i	0.0675438	−	0.116989i
$894$	−10.5102	−	18.2043i	−0.351515	−	0.608842i
$895$		−	32.2586i		−	1.07829i
$896$		0			0
$897$	−30.8984	+	68.7926i	−1.03167	+	2.29692i
$898$	−10.4692	−	18.1332i	−0.349363	−	0.605114i
$899$	−24.9947	−	14.4307i	−0.833619	−	0.481290i
$900$	10.4202	−	18.0483i	0.347340	−	0.601611i
$901$	−6.29173	−	10.8976i	−0.209608	−	0.363051i
$902$		−	8.02688i		−	0.267266i
$903$		0			0
$904$			30.6404i			1.01909i
$905$	−63.8124	+	36.8421i	−2.12120	+	1.22467i
$906$	7.34996	−	12.7305i	0.244186	−	0.422943i
$907$	4.65667	−	8.06558i	0.154622	−	0.267813i	−0.778299	−	0.627894i	$-0.783917\pi$
$907$	4.65667	−	8.06558i	0.154622	−	0.267813i	0.932921	+	0.360080i	$0.117251\pi$
$908$	9.60296	−	5.54427i	0.318686	−	0.183993i
$909$	9.57047			0.317432
$910$		0			0
$911$	28.4873			0.943826			0.471913	−	0.881645i	$-0.343564\pi$
$911$	28.4873			0.943826			0.471913	+	0.881645i	$0.343564\pi$
$912$	2.02472	−	1.16897i	0.0670451	−	0.0387085i
$913$	31.3178	−	54.2440i	1.03647	−	1.79522i
$914$	−4.58975	+	7.94969i	−0.151816	+	0.262952i
$915$	14.4008	−	8.31428i	0.476074	−	0.274862i
$916$		−	26.3079i		−	0.869238i
$917$		0			0
$918$		−	2.33794i		−	0.0771636i
$919$	−27.3916	−	47.4437i	−0.903566	−	1.56502i	−0.822830	−	0.568287i	$-0.807606\pi$
$919$	−27.3916	−	47.4437i	−0.903566	−	1.56502i	−0.0807363	−	0.996735i	$-0.525727\pi$
$920$	34.9942	−	60.6117i	1.15372	−	1.99831i
$921$	0.630973	+	0.364292i	0.0207913	+	0.0120038i
$922$	9.34515	+	16.1863i	0.307766	+	0.533067i
$923$	28.1603	+	12.6483i	0.926906	+	0.416323i
$924$		0			0
$925$			37.0556i			1.21838i
$926$	−2.74296	−	4.75095i	−0.0901393	−	0.156126i
$927$	22.7203	−	39.3526i	0.746231	−	1.29251i
$928$	26.5092	+	15.3051i	0.870207	+	0.502414i
$929$	11.5496	−	6.66817i	0.378930	−	0.218776i	−0.298422	−	0.954434i	$-0.596460\pi$
$929$	11.5496	−	6.66817i	0.378930	−	0.218776i	0.677353	+	0.735658i	$0.263127\pi$
$930$			28.1370i			0.922649i
$931$		0			0
$932$	19.4247			0.636277
$933$	−3.28537	−	5.69043i	−0.107558	−	0.186296i
$934$	7.44141	+	4.29630i	0.243490	+	0.140579i
$935$	−23.0911	+	39.9949i	−0.755160	+	1.30797i
$936$	2.15091	+	21.1291i	0.0703046	+	0.690626i
$937$	−15.4989			−0.506327			−0.253164	−	0.967423i	$-0.581471\pi$
$937$	−15.4989			−0.506327			−0.253164	+	0.967423i	$0.581471\pi$
$938$		0			0
$939$	−31.0276			−1.01255
$940$	14.4614	+	25.0480i	0.471680	+	0.816974i
$941$	18.8503	+	10.8832i	0.614502	+	0.354783i	0.774725	−	0.632298i	$-0.217888\pi$
$941$	18.8503	+	10.8832i	0.614502	+	0.354783i	−0.160223	+	0.987081i	$0.551221\pi$
$942$	2.27729	+	1.31480i	0.0741982	+	0.0428384i
$943$	17.1766	−	9.91694i	0.559348	−	0.322940i
$944$			4.28642i			0.139511i
$945$		0			0
$946$	8.66787			0.281817
$947$	−14.0527	+	8.11331i	−0.456650	+	0.263647i	−0.710635	−	0.703561i	$-0.751592\pi$
$947$	−14.0527	+	8.11331i	−0.456650	+	0.263647i	0.253985	+	0.967208i	$0.418259\pi$
$948$	1.63416	−	2.83044i	0.0530749	−	0.0919284i
$949$	17.1968	−	12.4085i	0.558232	−	0.402796i
$950$	1.31171	+	2.27195i	0.0425575	+	0.0737117i
$951$			2.26919i			0.0735835i
$952$		0			0
$953$	25.2125			0.816712			0.408356	−	0.912823i	$-0.366102\pi$
$953$	25.2125			0.816712			0.408356	+	0.912823i	$0.366102\pi$
$954$	−6.80063	+	3.92634i	−0.220178	+	0.127120i
$955$	15.2629	+	8.81204i	0.493896	+	0.285151i
$956$	10.2623	+	5.92494i	0.331906	+	0.191626i
$957$	−56.9736	+	32.8937i	−1.84169	+	1.06330i
$958$	21.4520			0.693083
$959$		0			0
$960$		−	8.04996i		−	0.259811i
$961$	−0.596863	−	1.03380i	−0.0192537	−	0.0333483i
$962$	−9.60321	−	13.3090i	−0.309620	−	0.429100i
$963$	−16.0425	+	27.7865i	−0.516963	+	0.895406i
$964$	−25.5653	+	14.7601i	−0.823402	+	0.475392i
$965$	6.39504			0.205863
$966$		0			0
$967$			32.6302i			1.04932i	0.851313	+	0.524658i	$0.175807\pi$
$967$			32.6302i			1.04932i	−0.851313	+	0.524658i	$0.824193\pi$
$968$	−36.3104	+	20.9638i	−1.16706	+	0.673802i
$969$	3.75700	+	2.16911i	0.120692	+	0.0696817i
$970$	−29.3433	−	16.9413i	−0.942155	−	0.543953i
$971$	−17.0162	−	29.4730i	−0.546077	−	0.945832i	−0.998538	−	0.0540486i	$-0.982787\pi$
$971$	−17.0162	−	29.4730i	−0.546077	−	0.945832i	0.452462	−	0.891784i	$-0.350546\pi$
$972$	31.2022			1.00081
$973$		0			0
$974$	28.6511			0.918041
$975$	46.3616	−	4.71953i	1.48476	−	0.151146i
$976$	−1.57802	+	2.73320i	−0.0505111	+	0.0874878i
$977$	4.20500	+	2.42776i	0.134530	+	0.0776708i	0.565754	−	0.824574i	$-0.308585\pi$
$977$	4.20500	+	2.42776i	0.134530	+	0.0776708i	−0.431225	+	0.902245i	$0.641918\pi$
$978$	−7.85860	−	13.6115i	−0.251290	−	0.435247i
$979$	5.25703			0.168016
$980$		0			0
$981$			37.6964i			1.20355i
$982$	−17.8066	+	10.2806i	−0.568231	+	0.328068i
$983$	−23.8899	−	13.7928i	−0.761968	−	0.439922i	0.0680339	−	0.997683i	$-0.478327\pi$
$983$	−23.8899	−	13.7928i	−0.761968	−	0.439922i	−0.830002	+	0.557761i	$0.811661\pi$
$984$	6.21530	−	10.7652i	0.198136	−	0.343182i
$985$	31.0778	+	53.8284i	0.990222	+	1.71511i
$986$			9.59513i			0.305571i
$987$		0			0
$988$	3.52182	+	1.58184i	0.112044	+	0.0503250i
$989$	10.7089	+	18.5483i	0.340522	+	0.589801i
$990$	24.9588	+	14.4100i	0.793243	+	0.457979i
$991$	0.996052	−	1.72521i	0.0316406	−	0.0548032i	−0.849771	−	0.527151i	$-0.823260\pi$
$991$	0.996052	−	1.72521i	0.0316406	−	0.0548032i	0.881412	+	0.472348i	$0.156593\pi$
$992$	−15.8062	−	27.3771i	−0.501846	−	0.869224i
$993$			18.0216i			0.571898i
$994$		0			0
$995$			0.632380i			0.0200478i
$996$	36.5081	−	21.0779i	1.15680	−	0.667880i
$997$	15.7800	−	27.3318i	0.499758	−	0.865607i	−0.500242	−	0.865886i	$-0.666756\pi$
$997$	15.7800	−	27.3318i	0.499758	−	0.865607i	1.00000		0.000279244i	$8.88862e-5\pi$
$998$	1.19305	−	2.06643i	0.0377654	−	0.0654116i
$999$	−7.46501	+	4.30992i	−0.236182	+	0.136360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.g.116.10		32
7.2	even	3	inner	637.2.r.g.324.8		32
7.3	odd	6		637.2.c.g.246.10	yes	16
7.4	even	3		637.2.c.g.246.9	yes	16
7.5	odd	6	inner	637.2.r.g.324.7		32
7.6	odd	2	inner	637.2.r.g.116.9		32
13.12	even	2	inner	637.2.r.g.116.8		32
91.12	odd	6	inner	637.2.r.g.324.9		32
91.18	odd	12		8281.2.a.cs.1.9		16
91.25	even	6		637.2.c.g.246.7	✓	16
91.31	even	12		8281.2.a.cs.1.10		16
91.38	odd	6		637.2.c.g.246.8	yes	16
91.51	even	6	inner	637.2.r.g.324.10		32
91.60	odd	12		8281.2.a.cs.1.7		16
91.73	even	12		8281.2.a.cs.1.8		16
91.90	odd	2	inner	637.2.r.g.116.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.7	✓	16	91.25	even	6
637.2.c.g.246.8	yes	16	91.38	odd	6
637.2.c.g.246.9	yes	16	7.4	even	3
637.2.c.g.246.10	yes	16	7.3	odd	6
637.2.r.g.116.7		32	91.90	odd	2	inner
637.2.r.g.116.8		32	13.12	even	2	inner
637.2.r.g.116.9		32	7.6	odd	2	inner
637.2.r.g.116.10		32	1.1	even	1	trivial
637.2.r.g.324.7		32	7.5	odd	6	inner
637.2.r.g.324.8		32	7.2	even	3	inner
637.2.r.g.324.9		32	91.12	odd	6	inner
637.2.r.g.324.10		32	91.51	even	6	inner
8281.2.a.cs.1.7		16	91.60	odd	12
8281.2.a.cs.1.8		16	91.73	even	12
8281.2.a.cs.1.9		16	91.18	odd	12
8281.2.a.cs.1.10		16	91.31	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.589067 - 0.340098i) q^{2} +(1.16706 - 2.02141i) q^{3} +(-0.768667 + 1.33137i) q^{4} +(-2.81123 + 1.62306i) q^{5} -1.58766i q^{6} +2.40608i q^{8} +(-1.22407 - 2.12016i) q^{9} +O(q^{10})\)	\(q+(0.589067 - 0.340098i) q^{2} +(1.16706 - 2.02141i) q^{3} +(-0.768667 + 1.33137i) q^{4} +(-2.81123 + 1.62306i) q^{5} -1.58766i q^{6} +2.40608i q^{8} +(-1.22407 - 2.12016i) q^{9} +(-1.10400 + 1.91219i) q^{10} +(4.61728 + 2.66579i) q^{11} +(1.79417 + 3.10759i) q^{12} +(-1.47728 + 3.28902i) q^{13} +7.57687i q^{15} +(-0.719029 - 1.24540i) q^{16} +(1.33421 - 2.31092i) q^{17} +(-1.44212 - 0.832611i) q^{18} +(-0.603203 + 0.348259i) q^{19} -4.99038i q^{20} +3.62652 q^{22} +(4.48044 + 7.76035i) q^{23} +(4.86368 + 2.80805i) q^{24} +(2.76867 - 4.79547i) q^{25} +(0.248375 + 2.43987i) q^{26} +1.28809 q^{27} -5.28644 q^{29} +(2.57688 + 4.46329i) q^{30} +(4.72808 + 2.72976i) q^{31} +(-5.01457 - 2.89516i) q^{32} +(10.7773 - 6.22229i) q^{33} -1.81505i q^{34} +3.76362 q^{36} +(-5.79541 + 3.34598i) q^{37} +(-0.236885 + 0.410296i) q^{38} +(4.92440 + 6.82468i) q^{39} +(-3.90522 - 6.76404i) q^{40} -2.21339i q^{41} +2.39014 q^{43} +(-7.09829 + 4.09820i) q^{44} +(6.88231 + 3.97350i) q^{45} +(5.27856 + 3.04758i) q^{46} +(-5.01925 + 2.89787i) q^{47} -3.35661 q^{48} -3.76647i q^{50} +(-3.11421 - 5.39397i) q^{51} +(-3.24337 - 4.49496i) q^{52} +(2.35785 - 4.08392i) q^{53} +(0.758771 - 0.438077i) q^{54} -17.3070 q^{55} +1.62576i q^{57} +(-3.11407 + 1.79791i) q^{58} +(-2.58136 - 1.49035i) q^{59} +(-10.0876 - 5.82409i) q^{60} +(-1.09732 - 1.90062i) q^{61} +3.71354 q^{62} -1.06244 q^{64} +(-1.18533 - 11.6439i) q^{65} +(4.23238 - 7.33069i) q^{66} +(7.53957 + 4.35297i) q^{67} +(2.05112 + 3.55265i) q^{68} +20.9158 q^{69} -8.56190i q^{71} +(5.10128 - 2.94522i) q^{72} +(-5.09355 - 2.94076i) q^{73} +(-2.27593 + 3.94202i) q^{74} +(-6.46242 - 11.1932i) q^{75} -1.07078i q^{76} +(5.22186 + 2.34542i) q^{78} +(-0.455408 - 0.788790i) q^{79} +(4.04271 + 2.33406i) q^{80} +(5.17551 - 8.96424i) q^{81} +(-0.752769 - 1.30383i) q^{82} -11.7481i q^{83} +8.66202i q^{85} +(1.40795 - 0.812881i) q^{86} +(-6.16961 + 10.6861i) q^{87} +(-6.41410 + 11.1095i) q^{88} +(0.853918 - 0.493010i) q^{89} +5.40552 q^{90} -13.7758 q^{92} +(11.0359 - 6.37160i) q^{93} +(-1.97112 + 3.41408i) q^{94} +(1.13049 - 1.95807i) q^{95} +(-11.7046 + 6.75768i) q^{96} +15.3454i q^{97} -13.0525i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 16 q^{9}+O(q^{10}) \) 32 * q + 20 * q^4 - 16 * q^9	\( 32 q + 20 q^{4} - 16 q^{9} - 28 q^{16} - 16 q^{22} + 36 q^{23} + 44 q^{25} + 72 q^{29} + 104 q^{36} - 32 q^{39} - 72 q^{43} + 72 q^{51} - 12 q^{53} - 328 q^{64} + 24 q^{65} - 96 q^{74} + 48 q^{78} - 36 q^{79} - 16 q^{81} - 136 q^{88} + 48 q^{92} + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 - 16 * q^9 - 28 * q^16 - 16 * q^22 + 36 * q^23 + 44 * q^25 + 72 * q^29 + 104 * q^36 - 32 * q^39 - 72 * q^43 + 72 * q^51 - 12 * q^53 - 328 * q^64 + 24 * q^65 - 96 * q^74 + 48 * q^78 - 36 * q^79 - 16 * q^81 - 136 * q^88 + 48 * q^92 + 84 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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