LMFDB - Embedded newform 637.2.e.m.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, 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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$-0.132804 + 0.230024i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.m.508.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.632804 + 1.09605i) q^{2} +(-1.31364 - 2.27529i) q^{3} +(0.199118 + 0.344882i) q^{4} +(-1.45130 + 2.51373i) q^{5} +3.32511 q^{6} -3.03523 q^{8} +(-1.95130 + 3.37975i) q^{9} +O(q^{10})$	\(q+(-0.632804 + 1.09605i) q^{2} +(-1.31364 - 2.27529i) q^{3} +(0.199118 + 0.344882i) q^{4} +(-1.45130 + 2.51373i) q^{5} +3.32511 q^{6} -3.03523 q^{8} +(-1.95130 + 3.37975i) q^{9} +(-1.83678 - 3.18139i) q^{10} +(-1.01828 - 1.76372i) q^{11} +(0.523138 - 0.906101i) q^{12} -1.00000 q^{13} +7.62594 q^{15} +(1.52247 - 2.63699i) q^{16} +(1.99933 + 3.46294i) q^{17} +(-2.46958 - 4.27744i) q^{18} +(3.48105 - 6.02935i) q^{19} -1.15592 q^{20} +2.57749 q^{22} +(0.313640 - 0.543240i) q^{23} +(3.98720 + 6.90602i) q^{24} +(-1.71254 - 2.96621i) q^{25} +(0.632804 - 1.09605i) q^{26} +2.37138 q^{27} +1.09606 q^{29} +(-4.82573 + 8.35841i) q^{30} +(-5.21624 - 9.03479i) q^{31} +(-1.10838 - 1.91977i) q^{32} +(-2.67531 + 4.63378i) q^{33} -5.06074 q^{34} -1.55415 q^{36} +(1.54268 - 2.67201i) q^{37} +(4.40565 + 7.63080i) q^{38} +(1.31364 + 2.27529i) q^{39} +(4.40502 - 7.62973i) q^{40} +0.521150 q^{41} +0.329024 q^{43} +(0.405516 - 0.702374i) q^{44} +(-5.66384 - 9.81006i) q^{45} +(0.396945 + 0.687530i) q^{46} +(5.27284 - 9.13283i) q^{47} -7.99991 q^{48} +4.33482 q^{50} +(5.25280 - 9.09812i) q^{51} +(-0.199118 - 0.344882i) q^{52} +(-3.55950 - 6.16523i) q^{53} +(-1.50062 + 2.59915i) q^{54} +5.91133 q^{55} -18.2914 q^{57} +(-0.693593 + 1.20134i) q^{58} +(1.01828 + 1.76372i) q^{59} +(1.51846 + 2.63005i) q^{60} +(1.20041 - 2.07917i) q^{61} +13.2034 q^{62} +8.89542 q^{64} +(1.45130 - 2.51373i) q^{65} +(-3.38590 - 5.86455i) q^{66} +(-7.34709 - 12.7255i) q^{67} +(-0.796204 + 1.37907i) q^{68} -1.64804 q^{69} +3.60141 q^{71} +(5.92264 - 10.2583i) q^{72} +(1.48786 + 2.57706i) q^{73} +(1.95243 + 3.38172i) q^{74} +(-4.49933 + 7.79307i) q^{75} +2.77255 q^{76} -3.32511 q^{78} +(4.38075 - 7.58769i) q^{79} +(4.41912 + 7.65414i) q^{80} +(2.73876 + 4.74367i) q^{81} +(-0.329786 + 0.571206i) q^{82} -12.8039 q^{83} -11.6065 q^{85} +(-0.208208 + 0.360627i) q^{86} +(-1.43983 - 2.49386i) q^{87} +(3.09072 + 5.35328i) q^{88} +(-1.34049 + 2.32180i) q^{89} +14.3364 q^{90} +0.249805 q^{92} +(-13.7045 + 23.7369i) q^{93} +(6.67335 + 11.5586i) q^{94} +(10.1041 + 17.5008i) q^{95} +(-2.91202 + 5.04376i) q^{96} +2.32902 q^{97} +7.94789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9	$ 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9} - 5 q^{10} - 11 q^{11} + 5 q^{12} - 10 q^{13} - 10 q^{16} - 5 q^{17} - 9 q^{18} + 9 q^{19} - 2 q^{20} + 16 q^{22} - 10 q^{23} - 9 q^{25} + 4 q^{26} - 6 q^{29} + 13 q^{30} - 6 q^{31} - 22 q^{32} + 8 q^{33} + 44 q^{34} + 14 q^{36} - 4 q^{37} - 10 q^{38} + 28 q^{40} - 28 q^{41} + 4 q^{43} - 32 q^{45} - 3 q^{46} + q^{47} + 46 q^{48} + 18 q^{50} + 8 q^{51} + 8 q^{52} - 17 q^{53} + 23 q^{54} - 32 q^{57} + 27 q^{58} + 11 q^{59} + 29 q^{60} - 11 q^{61} + 46 q^{62} + 18 q^{64} - 2 q^{65} + 21 q^{66} - 13 q^{67} - 32 q^{68} - 36 q^{69} + 30 q^{71} + 19 q^{72} + 33 q^{74} - 20 q^{75} - 16 q^{76} - 10 q^{78} - 2 q^{79} + 55 q^{80} + 19 q^{81} + 34 q^{82} - 12 q^{83} - 44 q^{85} - 28 q^{86} - 8 q^{87} + 3 q^{88} - 4 q^{89} + 68 q^{90} + 42 q^{92} - 18 q^{93} + 20 q^{94} + 12 q^{95} - 37 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) $ 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9 - 5 * q^10 - 11 * q^11 + 5 * q^12 - 10 * q^13 - 10 * q^16 - 5 * q^17 - 9 * q^18 + 9 * q^19 - 2 * q^20 + 16 * q^22 - 10 * q^23 - 9 * q^25 + 4 * q^26 - 6 * q^29 + 13 * q^30 - 6 * q^31 - 22 * q^32 + 8 * q^33 + 44 * q^34 + 14 * q^36 - 4 * q^37 - 10 * q^38 + 28 * q^40 - 28 * q^41 + 4 * q^43 - 32 * q^45 - 3 * q^46 + q^47 + 46 * q^48 + 18 * q^50 + 8 * q^51 + 8 * q^52 - 17 * q^53 + 23 * q^54 - 32 * q^57 + 27 * q^58 + 11 * q^59 + 29 * q^60 - 11 * q^61 + 46 * q^62 + 18 * q^64 - 2 * q^65 + 21 * q^66 - 13 * q^67 - 32 * q^68 - 36 * q^69 + 30 * q^71 + 19 * q^72 + 33 * q^74 - 20 * q^75 - 16 * q^76 - 10 * q^78 - 2 * q^79 + 55 * q^80 + 19 * q^81 + 34 * q^82 - 12 * q^83 - 44 * q^85 - 28 * q^86 - 8 * q^87 + 3 * q^88 - 4 * q^89 + 68 * q^90 + 42 * q^92 - 18 * q^93 + 20 * q^94 + 12 * q^95 - 37 * q^96 + 24 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.632804	+	1.09605i	−0.447460	+	0.775024i	−0.998220	−	0.0596401i	$-0.981005\pi$
$2$	−0.632804	+	1.09605i	−0.447460	+	0.775024i	0.550760	+	0.834664i	$0.314338\pi$
$3$	−1.31364	−	2.27529i	−0.758430	−	1.31364i	−0.943651	−	0.330943i	$-0.892633\pi$
$3$	−1.31364	−	2.27529i	−0.758430	−	1.31364i	0.185220	−	0.982697i	$-0.440700\pi$
$4$	0.199118	+	0.344882i	0.0995588	+	0.172441i
$5$	−1.45130	+	2.51373i	−0.649041	+	1.12417i	0.334311	+	0.942463i	$0.391496\pi$
$5$	−1.45130	+	2.51373i	−0.649041	+	1.12417i	−0.983352	+	0.181709i	$0.941837\pi$
$6$	3.32511			1.35747
$7$		0			0
$7$		0			0
$8$	−3.03523			−1.07311
$9$	−1.95130	+	3.37975i	−0.650433	+	1.12658i
$10$	−1.83678	−	3.18139i	−0.580840	−	1.00604i
$11$	−1.01828	−	1.76372i	−0.307024	−	0.531780i	0.670686	−	0.741741i	$-0.266000\pi$
$11$	−1.01828	−	1.76372i	−0.307024	−	0.531780i	−0.977710	+	0.209961i	$0.932666\pi$
$12$	0.523138	−	0.906101i	0.151017	−	0.261569i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	7.62594			1.96901
$16$	1.52247	−	2.63699i	0.380617	−	0.659249i
$17$	1.99933	+	3.46294i	0.484909	+	0.839887i	0.999850	−	0.0173386i	$-0.00551934\pi$
$17$	1.99933	+	3.46294i	0.484909	+	0.839887i	−0.514941	+	0.857226i	$0.672186\pi$
$18$	−2.46958	−	4.27744i	−0.582086	−	1.00820i
$19$	3.48105	−	6.02935i	0.798608	−	1.38323i	−0.121915	−	0.992540i	$-0.538904\pi$
$19$	3.48105	−	6.02935i	0.798608	−	1.38323i	0.920523	−	0.390688i	$-0.127763\pi$
$20$	−1.15592			−0.258471
$21$		0			0
$22$	2.57749			0.549523
$23$	0.313640	−	0.543240i	0.0653985	−	0.113273i	−0.831472	−	0.555566i	$-0.812501\pi$
$23$	0.313640	−	0.543240i	0.0653985	−	0.113273i	0.896871	+	0.442293i	$0.145835\pi$
$24$	3.98720	+	6.90602i	0.813883	+	1.40969i
$25$	−1.71254	−	2.96621i	−0.342509	−	0.593243i
$26$	0.632804	−	1.09605i	0.124103	−	0.214953i
$27$	2.37138			0.456373
$28$		0			0
$29$	1.09606			0.203534			0.101767	−	0.994808i	$-0.467550\pi$
$29$	1.09606			0.203534			0.101767	+	0.994808i	$0.467550\pi$
$30$	−4.82573	+	8.35841i	−0.881054	+	1.52603i
$31$	−5.21624	−	9.03479i	−0.936864	−	1.62270i	−0.771275	−	0.636502i	$-0.780381\pi$
$31$	−5.21624	−	9.03479i	−0.936864	−	1.62270i	−0.165589	−	0.986195i	$-0.552953\pi$
$32$	−1.10838	−	1.91977i	−0.195935	−	0.339370i
$33$	−2.67531	+	4.63378i	−0.465712	+	0.806637i
$34$	−5.06074			−0.867910
$35$		0			0
$36$	−1.55415			−0.259025
$37$	1.54268	−	2.67201i	0.253616	−	0.439275i	−0.710903	−	0.703290i	$-0.751713\pi$
$37$	1.54268	−	2.67201i	0.253616	−	0.439275i	0.964519	+	0.264015i	$0.0850468\pi$
$38$	4.40565	+	7.63080i	0.714690	+	1.23788i
$39$	1.31364	+	2.27529i	0.210351	+	0.364338i
$40$	4.40502	−	7.62973i	0.696496	−	1.20637i
$41$	0.521150			0.0813900			0.0406950	−	0.999172i	$-0.487043\pi$
$41$	0.521150			0.0813900			0.0406950	+	0.999172i	$0.487043\pi$
$42$		0			0
$43$	0.329024			0.0501757			0.0250879	−	0.999685i	$-0.492013\pi$
$43$	0.329024			0.0501757			0.0250879	+	0.999685i	$0.492013\pi$
$44$	0.405516	−	0.702374i	0.0611338	−	0.105887i
$45$	−5.66384	−	9.81006i	−0.844316	−	1.46240i
$46$	0.396945	+	0.687530i	0.0585264	+	0.101371i
$47$	5.27284	−	9.13283i	0.769123	−	1.33216i	−0.168916	−	0.985630i	$-0.554027\pi$
$47$	5.27284	−	9.13283i	0.769123	−	1.33216i	0.938039	−	0.346530i	$-0.112640\pi$
$48$	−7.99991			−1.15469
$49$		0			0
$50$	4.33482			0.613036
$51$	5.25280	−	9.09812i	0.735540	−	1.27399i
$52$	−0.199118	−	0.344882i	−0.0276126	−	0.0478265i
$53$	−3.55950	−	6.16523i	−0.488935	−	0.846860i	0.510984	−	0.859590i	$-0.329281\pi$
$53$	−3.55950	−	6.16523i	−0.488935	−	0.846860i	−0.999919	+	0.0127302i	$0.995948\pi$
$54$	−1.50062	+	2.59915i	−0.204209	+	0.353700i
$55$	5.91133			0.797084
$56$		0			0
$57$	−18.2914			−2.42275
$58$	−0.693593	+	1.20134i	−0.0910733	+	0.157744i
$59$	1.01828	+	1.76372i	0.132569	+	0.229616i	0.924666	−	0.380779i	$-0.124344\pi$
$59$	1.01828	+	1.76372i	0.132569	+	0.229616i	−0.792097	+	0.610395i	$0.791011\pi$
$60$	1.51846	+	2.63005i	0.196032	+	0.339538i
$61$	1.20041	−	2.07917i	0.153696	−	0.266210i	−0.778887	−	0.627164i	$-0.784216\pi$
$61$	1.20041	−	2.07917i	0.153696	−	0.266210i	0.932584	+	0.360954i	$0.117549\pi$
$62$	13.2034			1.67684
$63$		0			0
$64$	8.89542			1.11193
$65$	1.45130	−	2.51373i	0.180012	−	0.311789i
$66$	−3.38590	−	5.86455i	−0.416775	−	0.721876i
$67$	−7.34709	−	12.7255i	−0.897589	−	1.55467i	−0.830567	−	0.556919i	$-0.811983\pi$
$67$	−7.34709	−	12.7255i	−0.897589	−	1.55467i	−0.0670226	−	0.997751i	$-0.521350\pi$
$68$	−0.796204	+	1.37907i	−0.0965539	+	0.167236i
$69$	−1.64804			−0.198401
$70$		0			0
$71$	3.60141			0.427409			0.213704	−	0.976898i	$-0.431447\pi$
$71$	3.60141			0.427409			0.213704	+	0.976898i	$0.431447\pi$
$72$	5.92264	−	10.2583i	0.697990	−	1.20895i
$73$	1.48786	+	2.57706i	0.174141	+	0.301622i	0.939864	−	0.341550i	$-0.110952\pi$
$73$	1.48786	+	2.57706i	0.174141	+	0.301622i	−0.765722	+	0.643171i	$0.777618\pi$
$74$	1.95243	+	3.38172i	0.226966	+	0.393117i
$75$	−4.49933	+	7.79307i	−0.519538	+	0.899866i
$76$	2.77255			0.318034
$77$		0			0
$78$	−3.32511			−0.376494
$79$	4.38075	−	7.58769i	0.492873	−	0.853681i	−0.507093	−	0.861891i	$-0.669280\pi$
$79$	4.38075	−	7.58769i	0.492873	−	0.853681i	0.999966	+	0.00820995i	$0.00261334\pi$
$80$	4.41912	+	7.65414i	0.494073	+	0.855759i
$81$	2.73876	+	4.74367i	0.304306	+	0.527074i
$82$	−0.329786	+	0.571206i	−0.0364188	+	0.0630792i
$83$	−12.8039			−1.40541			−0.702703	−	0.711483i	$-0.748024\pi$
$83$	−12.8039			−1.40541			−0.702703	+	0.711483i	$0.748024\pi$
$84$		0			0
$85$	−11.6065			−1.25890
$86$	−0.208208	+	0.360627i	−0.0224516	+	0.0388874i
$87$	−1.43983	−	2.49386i	−0.154366	−	0.267370i
$88$	3.09072	+	5.35328i	0.329471	+	0.570661i
$89$	−1.34049	+	2.32180i	−0.142092	+	0.246110i	−0.928284	−	0.371872i	$-0.878716\pi$
$89$	−1.34049	+	2.32180i	−0.142092	+	0.246110i	0.786192	+	0.617982i	$0.212050\pi$
$90$	14.3364			1.51119
$91$		0			0
$92$	0.249805			0.0260440
$93$	−13.7045	+	23.7369i	−1.42109	+	2.46141i
$94$	6.67335	+	11.5586i	0.688304	+	1.19218i
$95$	10.1041	+	17.5008i	1.03666	+	1.79554i
$96$	−2.91202	+	5.04376i	−0.297206	+	0.514777i
$97$	2.32902			0.236477			0.118238	−	0.992985i	$-0.462275\pi$
$97$	2.32902			0.236477			0.118238	+	0.992985i	$0.462275\pi$
$98$		0			0
$99$	7.94789			0.798793
$100$	0.681995	−	1.18125i	0.0681995	−	0.118125i
$101$	0.726620	+	1.25854i	0.0723014	+	0.125230i	0.899910	−	0.436077i	$-0.143632\pi$
$101$	0.726620	+	1.25854i	0.0723014	+	0.125230i	−0.827608	+	0.561306i	$0.810299\pi$
$102$	6.64799	+	11.5147i	0.658249	+	1.14012i
$103$	−5.81765	+	10.0765i	−0.573230	+	0.992864i	0.423001	+	0.906129i	$0.360977\pi$
$103$	−5.81765	+	10.0765i	−0.573230	+	0.992864i	−0.996231	+	0.0867346i	$0.972357\pi$
$104$	3.03523			0.297628
$105$		0			0
$106$	9.00987			0.875115
$107$	−9.81297	+	16.9966i	−0.948656	+	1.64312i	−0.200395	+	0.979715i	$0.564223\pi$
$107$	−9.81297	+	16.9966i	−0.948656	+	1.64312i	−0.748261	+	0.663405i	$0.769111\pi$
$108$	0.472184	+	0.817847i	0.0454359	+	0.0786973i
$109$	0.553378	+	0.958479i	0.0530040	+	0.0918057i	0.891310	−	0.453394i	$-0.149787\pi$
$109$	0.553378	+	0.958479i	0.0530040	+	0.0918057i	−0.838306	+	0.545200i	$0.816454\pi$
$110$	−3.74071	+	6.47911i	−0.356663	+	0.617759i
$111$	−8.10613			−0.769400
$112$		0			0
$113$	−1.09606			−0.103109			−0.0515545	−	0.998670i	$-0.516418\pi$
$113$	−1.09606			−0.103109			−0.0515545	+	0.998670i	$0.516418\pi$
$114$	11.5749	−	20.0483i	1.08409	−	1.87769i
$115$	0.910371	+	1.57681i	0.0848926	+	0.147038i
$116$	0.218245	+	0.378012i	0.0202636	+	0.0350975i
$117$	1.95130	−	3.37975i	0.180398	−	0.312458i
$118$	−2.57749			−0.237277
$119$		0			0
$120$	−23.1465			−2.11297
$121$	3.42620	−	5.93436i	0.311473	−	0.539487i
$122$	1.51925	+	2.63141i	0.137546	+	0.238237i
$123$	−0.684604	−	1.18577i	−0.0617286	−	0.106917i
$124$	2.07729	−	3.59797i	0.186546	−	0.323107i
$125$	−4.57134			−0.408873
$126$		0			0
$127$	5.18143			0.459778			0.229889	−	0.973217i	$-0.426164\pi$
$127$	5.18143			0.459778			0.229889	+	0.973217i	$0.426164\pi$
$128$	−3.41231	+	5.91029i	−0.301608	+	0.522400i
$129$	−0.432219	−	0.748626i	−0.0380548	−	0.0659128i
$130$	1.83678	+	3.18139i	0.161096	+	0.279027i
$131$	5.28335	−	9.15103i	0.461609	−	0.799530i	−0.537433	−	0.843307i	$-0.680606\pi$
$131$	5.28335	−	9.15103i	0.461609	−	0.799530i	0.999041	+	0.0437770i	$0.0139391\pi$
$132$	−2.13081			−0.185463
$133$		0			0
$134$	18.5971			1.60654
$135$	−3.44159	+	5.96101i	−0.296205	+	0.513042i
$136$	−6.06842	−	10.5108i	−0.520363	−	0.901295i
$137$	2.93589	+	5.08510i	0.250830	+	0.434450i	0.963754	−	0.266791i	$-0.0859632\pi$
$137$	2.93589	+	5.08510i	0.250830	+	0.434450i	−0.712925	+	0.701241i	$0.752630\pi$
$138$	1.04289	−	1.80633i	0.0887764	−	0.153765i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−27.7065			−2.33331
$142$	−2.27899	+	3.94732i	−0.191248	+	0.331252i
$143$	1.01828	+	1.76372i	0.0851530	+	0.147489i
$144$	5.94159	+	10.2911i	0.495132	+	0.857594i
$145$	−1.59072	+	2.75520i	−0.132102	+	0.228807i
$146$	−3.76611			−0.311685
$147$		0			0
$148$	1.22870			0.100999
$149$	5.05271	−	8.75155i	0.413934	−	0.716955i	−0.581382	−	0.813631i	$-0.697488\pi$
$149$	5.05271	−	8.75155i	0.413934	−	0.716955i	0.995316	+	0.0966760i	$0.0308211\pi$
$150$	−5.69439	−	9.86298i	−0.464945	−	0.805309i
$151$	0.0938631	+	0.162576i	0.00763847	+	0.0132302i	0.869819	−	0.493370i	$-0.164235\pi$
$151$	0.0938631	+	0.162576i	0.00763847	+	0.0132302i	−0.862181	+	0.506601i	$0.830902\pi$
$152$	−10.5658	+	18.3005i	−0.856998	+	1.48436i
$153$	−15.6052			−1.26160
$154$		0			0
$155$	30.2813			2.43225
$156$	−0.523138	+	0.906101i	−0.0418845	+	0.0725461i
$157$	−6.03590	−	10.4545i	−0.481717	−	0.834358i	0.518063	−	0.855343i	$-0.326653\pi$
$157$	−6.03590	−	10.4545i	−0.481717	−	0.834358i	−0.999780	+	0.0209844i	$0.993320\pi$
$158$	5.54432	+	9.60304i	0.441082	+	0.763977i
$159$	−9.35180	+	16.1978i	−0.741646	+	1.28457i
$160$	6.43435			0.508680
$161$		0			0
$162$	−6.93239			−0.544660
$163$	−7.45678	+	12.9155i	−0.584060	+	1.01162i	0.410932	+	0.911666i	$0.365203\pi$
$163$	−7.45678	+	12.9155i	−0.584060	+	1.01162i	−0.994992	+	0.0999554i	$0.968130\pi$
$164$	0.103770	+	0.179735i	0.00810309	+	0.0140350i
$165$	−7.76536	−	13.4500i	−0.604532	−	1.04708i
$166$	8.10234	−	14.0337i	0.628863	−	1.08922i
$167$	−5.05664			−0.391294			−0.195647	−	0.980674i	$-0.562681\pi$
$167$	−5.05664			−0.391294			−0.195647	+	0.980674i	$0.562681\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	7.34465	−	12.7213i	0.563309	−	0.975680i
$171$	13.5851	+	23.5302i	1.03888	+	1.79940i
$172$	0.0655145	+	0.113474i	0.00499543	+	0.00865235i
$173$	−0.297807	+	0.515817i	−0.0226419	+	0.0392169i	−0.877124	−	0.480263i	$-0.840541\pi$
$173$	−0.297807	+	0.515817i	−0.0226419	+	0.0392169i	0.854482	+	0.519480i	$0.173874\pi$
$174$	3.64453			0.276291
$175$		0			0
$176$	−6.20121			−0.467434
$177$	2.67531	−	4.63378i	0.201089	−	0.348296i
$178$	−1.69654	−	2.93849i	−0.127161	−	0.220249i
$179$	−4.03832	−	6.99458i	−0.301838	−	0.522799i	0.674714	−	0.738079i	$-0.264267\pi$
$179$	−4.03832	−	6.99458i	−0.301838	−	0.522799i	−0.976552	+	0.215280i	$0.930934\pi$
$180$	2.25554	−	3.90671i	0.168118	−	0.291189i
$181$	−1.89324			−0.140724			−0.0703618	−	0.997522i	$-0.522415\pi$
$181$	−1.89324			−0.140724			−0.0703618	+	0.997522i	$0.522415\pi$
$182$		0			0
$183$	−6.30761			−0.466272
$184$	−0.951968	+	1.64886i	−0.0701800	+	0.121555i
$185$	4.47780	+	7.75577i	0.329214	+	0.570216i
$186$	−17.3446	−	30.0417i	−1.27176	−	2.20276i
$187$	4.07177	−	7.05251i	0.297757	−	0.515730i
$188$	4.19966			0.306292
$189$		0			0
$190$	−25.5757			−1.85545
$191$	−1.85087	+	3.20580i	−0.133924	+	0.231964i	−0.925186	−	0.379514i	$-0.876091\pi$
$191$	−1.85087	+	3.20580i	−0.133924	+	0.231964i	0.791262	+	0.611478i	$0.209425\pi$
$192$	−11.6854	−	20.2397i	−0.843320	−	1.46067i
$193$	−6.79373	−	11.7671i	−0.489024	−	0.847014i	0.510897	−	0.859642i	$-0.329313\pi$
$193$	−6.79373	−	11.7671i	−0.489024	−	0.847014i	−0.999920	+	0.0126285i	$0.995980\pi$
$194$	−1.47382	+	2.55272i	−0.105814	+	0.183275i
$195$	−7.62594			−0.546105
$196$		0			0
$197$	−9.70258			−0.691280			−0.345640	−	0.938367i	$-0.612338\pi$
$197$	−9.70258			−0.691280			−0.345640	+	0.938367i	$0.612338\pi$
$198$	−5.02946	+	8.71128i	−0.357428	+	0.619084i
$199$	13.1360	+	22.7522i	0.931185	+	1.61286i	0.781299	+	0.624156i	$0.214557\pi$
$199$	13.1360	+	22.7522i	0.931185	+	1.61286i	0.149885	+	0.988703i	$0.452109\pi$
$200$	5.19796	+	9.00313i	0.367551	+	0.636617i
$201$	−19.3029	+	33.4335i	−1.36152	+	2.35822i
$202$	−1.83923			−0.129408
$203$		0			0
$204$	4.18370			0.292918
$205$	−0.756345	+	1.31003i	−0.0528255	+	0.0914964i
$206$	−7.36287	−	12.7529i	−0.512995	−	0.888534i
$207$	1.22401	+	2.12005i	0.0850747	+	0.147354i
$208$	−1.52247	+	2.63699i	−0.105564	+	0.182843i
$209$	−14.1788			−0.980765
$210$		0			0
$211$	10.0338			0.690758			0.345379	−	0.938463i	$-0.387750\pi$
$211$	10.0338			0.690758			0.345379	+	0.938463i	$0.387750\pi$
$212$	1.41752	−	2.45521i	0.0973555	−	0.168625i
$213$	−4.73096	−	8.19426i	−0.324160	−	0.561461i
$214$	−12.4194	−	21.5110i	−0.848971	−	1.47046i
$215$	−0.477513	+	0.827077i	−0.0325661	+	0.0564062i
$216$	−7.19769			−0.489740
$217$		0			0
$218$	−1.40072			−0.0948688
$219$	3.90903	−	6.77065i	0.264148	−	0.457518i
$220$	1.17705	+	2.03871i	0.0793567	+	0.137450i
$221$	−1.99933	−	3.46294i	−0.134490	−	0.232943i
$222$	5.12959	−	8.88472i	0.344276	−	0.596303i
$223$	−17.4961			−1.17163			−0.585813	−	0.810446i	$-0.699225\pi$
$223$	−17.4961			−1.17163			−0.585813	+	0.810446i	$0.699225\pi$
$224$		0			0
$225$	13.3667			0.891116
$226$	0.693593	−	1.20134i	0.0461371	−	0.0799119i
$227$	−4.75815	−	8.24136i	−0.315810	−	0.546998i	0.663800	−	0.747910i	$-0.268943\pi$
$227$	−4.75815	−	8.24136i	−0.315810	−	0.546998i	−0.979609	+	0.200912i	$0.935609\pi$
$228$	−3.64214	−	6.30837i	−0.241206	−	0.417782i
$229$	10.5585	−	18.2878i	0.697725	−	1.20849i	−0.271529	−	0.962430i	$-0.587529\pi$
$229$	10.5585	−	18.2878i	0.697725	−	1.20849i	0.969254	−	0.246064i	$-0.0791374\pi$
$230$	−2.30435			−0.151944
$231$		0			0
$232$	−3.32680			−0.218415
$233$	−7.08938	+	12.2792i	−0.464441	+	0.804435i	−0.999176	−	0.0405847i	$-0.987078\pi$
$233$	−7.08938	+	12.2792i	−0.464441	+	0.804435i	0.534735	+	0.845020i	$0.320411\pi$
$234$	2.46958	+	4.27744i	0.161442	+	0.279625i
$235$	15.3050	+	26.5090i	0.998385	+	1.72925i
$236$	−0.405516	+	0.702374i	−0.0263968	+	0.0457206i
$237$	−23.0189			−1.49524
$238$		0			0
$239$	−16.5275			−1.06907			−0.534536	−	0.845145i	$-0.679514\pi$
$239$	−16.5275			−1.06907			−0.534536	+	0.845145i	$0.679514\pi$
$240$	11.6103	−	20.1096i	0.749439	−	1.29807i
$241$	−6.84450	−	11.8550i	−0.440893	−	0.763649i	0.556863	−	0.830604i	$-0.312005\pi$
$241$	−6.84450	−	11.8550i	−0.440893	−	0.763649i	−0.997756	+	0.0669552i	$0.978672\pi$
$242$	4.33623	+	7.51058i	0.278744	+	0.482798i
$243$	10.7526	−	18.6240i	0.689777	−	1.19473i
$244$	0.956089			0.0612073
$245$		0			0
$246$	1.73288			0.110484
$247$	−3.48105	+	6.02935i	−0.221494	+	0.383639i
$248$	15.8325	+	27.4226i	1.00536	+	1.74134i
$249$	16.8197	+	29.1325i	1.06590	+	1.84620i
$250$	2.89276	−	5.01042i	0.182954	−	0.316886i
$251$	14.6603			0.925349			0.462674	−	0.886528i	$-0.346890\pi$
$251$	14.6603			0.925349			0.462674	+	0.886528i	$0.346890\pi$
$252$		0			0
$253$	−1.27750			−0.0803155
$254$	−3.27883	+	5.67910i	−0.205732	+	0.356339i
$255$	15.2468	+	26.4082i	0.954791	+	1.65375i
$256$	4.57678	+	7.92721i	0.286049	+	0.495451i
$257$	−0.876387	+	1.51795i	−0.0546675	+	0.0946869i	−0.892064	−	0.451909i	$-0.850743\pi$
$257$	−0.876387	+	1.51795i	−0.0546675	+	0.0946869i	0.837397	+	0.546596i	$0.184077\pi$
$258$	1.09404			0.0681120
$259$		0			0
$260$	1.15592			0.0716870
$261$	−2.13875	+	3.70442i	−0.132385	+	0.229298i
$262$	6.68666	+	11.5816i	0.413103	+	0.715515i
$263$	−13.4708	−	23.3321i	−0.830645	−	1.43872i	−0.897527	−	0.440959i	$-0.854639\pi$
$263$	−13.4708	−	23.3321i	−0.830645	−	1.43872i	0.0668823	−	0.997761i	$-0.478695\pi$
$264$	8.12018	−	14.0646i	0.499762	−	0.865614i
$265$	20.6636			1.26936
$266$		0			0
$267$	7.04370			0.431067
$268$	2.92587	−	5.06775i	0.178726	−	0.309562i
$269$	−11.0346	−	19.1124i	−0.672789	−	1.16530i	−0.977110	−	0.212735i	$-0.931763\pi$
$269$	−11.0346	−	19.1124i	−0.672789	−	1.16530i	0.304321	−	0.952570i	$-0.401570\pi$
$270$	−4.35570	−	7.54430i	−0.265080	−	0.459131i
$271$	−4.48105	+	7.76141i	−0.272204	+	0.471472i	−0.969426	−	0.245384i	$-0.921086\pi$
$271$	−4.48105	+	7.76141i	−0.272204	+	0.471472i	0.697222	+	0.716856i	$0.254419\pi$
$272$	12.1757			0.738259
$273$		0			0
$274$	−7.43137			−0.448945
$275$	−3.48770	+	6.04088i	−0.210316	+	0.364279i
$276$	−0.328154	−	0.568379i	−0.0197525	−	0.0342124i
$277$	3.76463	+	6.52052i	0.226194	+	0.391780i	0.956677	−	0.291151i	$-0.0940382\pi$
$277$	3.76463	+	6.52052i	0.226194	+	0.391780i	−0.730483	+	0.682931i	$0.760705\pi$
$278$	−2.53122	+	4.38420i	−0.151812	+	0.262947i
$279$	40.7138			2.43747
$280$		0			0
$281$	29.7762			1.77630			0.888151	−	0.459553i	$-0.151990\pi$
$281$	29.7762			1.77630			0.888151	+	0.459553i	$0.151990\pi$
$282$	17.5328	−	30.3676i	1.04406	−	1.80837i
$283$	0.150726	+	0.261064i	0.00895970	+	0.0155187i	0.870470	−	0.492221i	$-0.163815\pi$
$283$	0.150726	+	0.261064i	0.00895970	+	0.0155187i	−0.861511	+	0.507739i	$0.830481\pi$
$284$	0.717104	+	1.24206i	0.0425523	+	0.0737027i
$285$	26.5463	−	45.9795i	1.57247	−	2.72359i
$286$	−2.57749			−0.152410
$287$		0			0
$288$	8.65110			0.509771
$289$	0.505347	−	0.875286i	0.0297263	−	0.0514874i
$290$	−2.01322	−	3.48701i	−0.118221	−	0.204764i
$291$	−3.05950	−	5.29921i	−0.179351	−	0.310645i
$292$	−0.592520	+	1.02627i	−0.0346746	+	0.0600582i
$293$	19.2471			1.12443			0.562214	−	0.826992i	$-0.309950\pi$
$293$	19.2471			1.12443			0.562214	+	0.826992i	$0.309950\pi$
$294$		0			0
$295$	−5.91133			−0.344171
$296$	−4.68240	+	8.11015i	−0.272159	+	0.471393i
$297$	−2.41474	−	4.18245i	−0.140117	−	0.242690i
$298$	6.39475	+	11.0760i	0.370438	+	0.641618i
$299$	−0.313640	+	0.543240i	−0.0181383	+	0.0314164i
$300$	−3.58358			−0.206898
$301$		0			0
$302$	−0.237588			−0.0136716
$303$	1.90903	−	3.30654i	0.109671	−	0.189956i
$304$	−10.5996	−	18.3590i	−0.607928	−	1.05296i
$305$	3.48430	+	6.03499i	0.199511	+	0.345562i
$306$	9.87503	−	17.1040i	0.564518	−	0.977773i
$307$	3.57779			0.204195			0.102098	−	0.994774i	$-0.467445\pi$
$307$	3.57779			0.204195			0.102098	+	0.994774i	$0.467445\pi$
$308$		0			0
$309$	30.5692			1.73902
$310$	−19.1621	+	33.1898i	−1.08834	+	1.88505i
$311$	−11.9153	−	20.6379i	−0.675655	−	1.17027i	−0.976277	−	0.216526i	$-0.930527\pi$
$311$	−11.9153	−	20.6379i	−0.675655	−	1.17027i	0.300622	−	0.953743i	$-0.402806\pi$
$312$	−3.98720	−	6.90602i	−0.225730	−	0.390977i
$313$	−9.04068	+	15.6589i	−0.511009	+	0.885094i	0.488909	+	0.872335i	$0.337395\pi$
$313$	−9.04068	+	15.6589i	−0.511009	+	0.885094i	−0.999919	+	0.0127596i	$0.995938\pi$
$314$	15.2782			0.862196
$315$		0			0
$316$	3.48914			0.196279
$317$	13.7741	−	23.8574i	0.773630	−	1.33997i	−0.161931	−	0.986802i	$-0.551772\pi$
$317$	13.7741	−	23.8574i	0.773630	−	1.33997i	0.935561	−	0.353164i	$-0.114894\pi$
$318$	−11.8357	−	20.5001i	−0.663714	−	1.14959i
$319$	−1.11610	−	1.93314i	−0.0624897	−	0.108235i
$320$	−12.9099	+	22.3606i	−0.721687	+	1.25000i
$321$	51.5628			2.87796
$322$		0			0
$323$	27.8391			1.54901
$324$	−1.09067	+	1.88909i	−0.0605927	+	0.104950i
$325$	1.71254	+	2.96621i	0.0949948	+	0.164536i
$326$	−9.43736	−	16.3460i	−0.522687	−	0.905321i
$327$	1.45388	−	2.51819i	0.0803997	−	0.139256i
$328$	−1.58181			−0.0873408
$329$		0			0
$330$	19.6558			1.08202
$331$	9.09069	−	15.7455i	0.499669	−	0.865453i	−0.500331	−	0.865834i	$-0.666788\pi$
$331$	9.09069	−	15.7455i	0.499669	−	0.865453i	1.00000		0.000381757i	$0.000121517\pi$
$332$	−2.54947	−	4.41582i	−0.139921	−	0.242350i
$333$	6.02048	+	10.4278i	0.329920	+	0.571439i
$334$	3.19986	−	5.54232i	0.175089	−	0.303262i
$335$	42.6513			2.33029
$336$		0			0
$337$	−17.1381			−0.933572			−0.466786	−	0.884370i	$-0.654588\pi$
$337$	−17.1381			−0.933572			−0.466786	+	0.884370i	$0.654588\pi$
$338$	−0.632804	+	1.09605i	−0.0344200	+	0.0596172i
$339$	1.43983	+	2.49386i	0.0782010	+	0.135448i
$340$	−2.31106	−	4.00288i	−0.125335	−	0.217086i
$341$	−10.6232	+	18.3999i	−0.575279	+	0.996412i
$342$	−34.3869			−1.85943
$343$		0			0
$344$	−0.998663			−0.0538443
$345$	2.39180	−	4.14272i	0.128770	−	0.223037i
$346$	−0.376907	−	0.652823i	−0.0202627	−	0.0350960i
$347$	−11.1344	−	19.2853i	−0.597725	−	1.03529i	−0.993156	−	0.116794i	$-0.962738\pi$
$347$	−11.1344	−	19.2853i	−0.597725	−	1.03529i	0.395431	−	0.918496i	$-0.370595\pi$
$348$	0.573392	−	0.993144i	0.0307370	−	0.0532381i
$349$	−19.9368			−1.06719			−0.533595	−	0.845740i	$-0.679159\pi$
$349$	−19.9368			−1.06719			−0.533595	+	0.845740i	$0.679159\pi$
$350$		0			0
$351$	−2.37138			−0.126575
$352$	−2.25728	+	3.90972i	−0.120313	+	0.208389i
$353$	11.4576	+	19.8451i	0.609825	+	1.05625i	0.991269	+	0.131856i	$0.0420937\pi$
$353$	11.4576	+	19.8451i	0.609825	+	1.05625i	−0.381444	+	0.924392i	$0.624573\pi$
$354$	3.38590	+	5.86455i	0.179958	+	0.311697i
$355$	−5.22673	+	9.05296i	−0.277406	+	0.480481i
$356$	−1.06766			−0.0565860
$357$		0			0
$358$	10.2219			0.540242
$359$	−13.6157	+	23.5831i	−0.718610	+	1.24467i	0.242940	+	0.970041i	$0.421888\pi$
$359$	−13.6157	+	23.5831i	−0.718610	+	1.24467i	−0.961551	+	0.274628i	$0.911445\pi$
$360$	17.1910	+	29.7758i	0.906048	+	1.56932i
$361$	−14.7354	−	25.5225i	−0.775548	−	1.34329i
$362$	1.19805	−	2.07509i	0.0629682	−	0.109064i
$363$	−18.0032			−0.944923
$364$		0			0
$365$	−8.63735			−0.452099
$366$	3.99148	−	6.91345i	0.208638	−	0.361372i
$367$	−5.42822	−	9.40195i	−0.283351	−	0.490778i	0.688857	−	0.724897i	$-0.258113\pi$
$367$	−5.42822	−	9.40195i	−0.283351	−	0.490778i	−0.972208	+	0.234119i	$0.924779\pi$
$368$	−0.955014	−	1.65413i	−0.0497836	−	0.0862277i
$369$	−1.01692	+	1.76136i	−0.0529388	+	0.0916926i
$370$	−11.3343			−0.589241
$371$		0			0
$372$	−10.9152			−0.565929
$373$	1.18572	−	2.05373i	0.0613943	−	0.106338i	−0.833695	−	0.552226i	$-0.813779\pi$
$373$	1.18572	−	2.05373i	0.0613943	−	0.106338i	0.895089	+	0.445888i	$0.147112\pi$
$374$	5.15326	+	8.92571i	0.266469	+	0.461538i
$375$	6.00510	+	10.4011i	0.310102	+	0.537112i
$376$	−16.0043	+	27.7202i	−0.825357	+	1.42956i
$377$	−1.09606			−0.0564501
$378$		0			0
$379$	−29.2197			−1.50092			−0.750458	−	0.660918i	$-0.770167\pi$
$379$	−29.2197			−1.50092			−0.750458	+	0.660918i	$0.770167\pi$
$380$	−4.02381	+	6.96944i	−0.206417	+	0.357525i
$381$	−6.80654	−	11.7893i	−0.348709	−	0.603982i
$382$	−2.34248	−	4.05729i	−0.119852	−	0.207589i
$383$	−1.53297	+	2.65519i	−0.0783313	+	0.135674i	−0.902530	−	0.430627i	$-0.858293\pi$
$383$	−1.53297	+	2.65519i	−0.0783313	+	0.135674i	0.824199	+	0.566301i	$0.191626\pi$
$384$	17.9302			0.914995
$385$		0			0
$386$	17.1964			0.875274
$387$	−0.642025	+	1.11202i	−0.0326360	+	0.0565271i
$388$	0.463750	+	0.803238i	0.0235433	+	0.0407782i
$389$	−13.8705	−	24.0244i	−0.703261	−	1.21808i	−0.967315	−	0.253576i	$-0.918393\pi$
$389$	−13.8705	−	24.0244i	−0.703261	−	1.21808i	0.264054	−	0.964508i	$-0.414940\pi$
$390$	4.82573	−	8.35841i	0.244360	−	0.423244i
$391$	2.50828			0.126849
$392$		0			0
$393$	−27.7617			−1.40039
$394$	6.13984	−	10.6345i	0.309320	−	0.535759i
$395$	12.7156	+	22.0240i	0.639790	+	1.10815i
$396$	1.58257	+	2.74108i	0.0795269	+	0.137745i
$397$	8.61559	−	14.9226i	0.432404	−	0.748946i	−0.564676	−	0.825313i	$-0.690999\pi$
$397$	8.61559	−	14.9226i	0.432404	−	0.748946i	0.997080	+	0.0763669i	$0.0243320\pi$
$398$	−33.2500			−1.66667
$399$		0			0
$400$	−10.4292			−0.521459
$401$	−8.32201	+	14.4142i	−0.415582	+	0.719808i	−0.995489	−	0.0948737i	$-0.969755\pi$
$401$	−8.32201	+	14.4142i	−0.415582	+	0.719808i	0.579908	+	0.814682i	$0.303089\pi$
$402$	−24.4299	−	42.3137i	−1.21845	−	2.11042i
$403$	5.21624	+	9.03479i	0.259839	+	0.450055i
$404$	−0.289366	+	0.501196i	−0.0143965	+	0.0249354i
$405$	−15.8990			−0.790029
$406$		0			0
$407$	−6.28355			−0.311464
$408$	−15.9435	+	27.6149i	−0.789318	+	1.36714i
$409$	−6.81689	−	11.8072i	−0.337073	−	0.583828i	0.646807	−	0.762653i	$-0.276104\pi$
$409$	−6.81689	−	11.8072i	−0.337073	−	0.583828i	−0.983881	+	0.178825i	$0.942770\pi$
$410$	−0.957237	−	1.65798i	−0.0472746	−	0.0818820i
$411$	7.71340	−	13.3600i	0.380474	−	0.659000i
$412$	−4.63359			−0.228280
$413$		0			0
$414$	−3.09824			−0.152270
$415$	18.5822	−	32.1854i	0.912167	−	1.57992i
$416$	1.10838	+	1.91977i	0.0543426	+	0.0941242i
$417$	−5.25456	−	9.10116i	−0.257317	−	0.445686i
$418$	8.97238	−	15.5406i	0.438853	−	0.760116i
$419$	10.8502			0.530066			0.265033	−	0.964239i	$-0.414617\pi$
$419$	10.8502			0.530066			0.265033	+	0.964239i	$0.414617\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−6.34946	+	10.9976i	−0.309087	+	0.535354i
$423$	20.5778	+	35.6418i	1.00053	+	1.73296i
$424$	10.8039	+	18.7129i	0.524683	+	0.908778i
$425$	6.84788	−	11.8609i	0.332171	−	0.575337i
$426$	11.9751			0.580194
$427$		0			0
$428$	−7.81574			−0.377788
$429$	2.67531	−	4.63378i	0.129165	−	0.223721i
$430$	−0.604344	−	1.04676i	−0.0291441	−	0.0504790i
$431$	−0.604764	−	1.04748i	−0.0291304	−	0.0504554i	0.851093	−	0.525016i	$-0.175940\pi$
$431$	−0.604764	−	1.04748i	−0.0291304	−	0.0504554i	−0.880223	+	0.474560i	$0.842607\pi$
$432$	3.61036	−	6.25332i	0.173703	−	0.300863i
$433$	5.56422			0.267399			0.133700	−	0.991022i	$-0.457314\pi$
$433$	5.56422			0.267399			0.133700	+	0.991022i	$0.457314\pi$
$434$		0			0
$435$	8.35851			0.400760
$436$	−0.220375	+	0.381700i	−0.0105540	+	0.0182801i
$437$	−2.18359	−	3.78209i	−0.104455	−	0.180922i
$438$	4.94731	+	8.56899i	0.236391	+	0.409442i
$439$	−9.85960	+	17.0773i	−0.470573	+	0.815057i	−0.999434	−	0.0336522i	$-0.989286\pi$
$439$	−9.85960	+	17.0773i	−0.470573	+	0.815057i	0.528860	+	0.848709i	$0.322619\pi$
$440$	−17.9422			−0.855362
$441$		0			0
$442$	5.06074			0.240715
$443$	−11.1155	+	19.2526i	−0.528113	+	0.914719i	0.471350	+	0.881946i	$0.343767\pi$
$443$	−11.1155	+	19.2526i	−0.528113	+	0.914719i	−0.999463	+	0.0327726i	$0.989566\pi$
$444$	−1.61407	−	2.79566i	−0.0766005	−	0.132676i
$445$	−3.89091	−	6.73926i	−0.184447	−	0.319471i
$446$	11.0716	−	19.1766i	0.524256	−	0.908039i
$447$	−26.5498			−1.25576
$448$		0			0
$449$	18.4579			0.871082			0.435541	−	0.900169i	$-0.356557\pi$
$449$	18.4579			0.871082			0.435541	+	0.900169i	$0.356557\pi$
$450$	−8.45853	+	14.6506i	−0.398739	+	0.690636i
$451$	−0.530678	−	0.919161i	−0.0249886	−	0.0432816i
$452$	−0.218245	−	0.378012i	−0.0102654	−	0.0177802i
$453$	0.246605	−	0.427132i	0.0115865	−	0.0200684i
$454$	12.0439			0.565249
$455$		0			0
$456$	55.5185			2.59989
$457$	14.9910	−	25.9651i	0.701248	−	1.21460i	−0.266781	−	0.963757i	$-0.585960\pi$
$457$	14.9910	−	25.9651i	0.701248	−	1.21460i	0.968029	−	0.250840i	$-0.0807067\pi$
$458$	13.3629	+	23.1452i	0.624408	+	1.08151i
$459$	4.74118	+	8.21197i	0.221299	+	0.383302i
$460$	−0.362542	+	0.627941i	−0.0169036	+	0.0292779i
$461$	−29.1498			−1.35764			−0.678821	−	0.734304i	$-0.737509\pi$
$461$	−29.1498			−1.35764			−0.678821	+	0.734304i	$0.737509\pi$
$462$		0			0
$463$	1.55900			0.0724530			0.0362265	−	0.999344i	$-0.488466\pi$
$463$	1.55900			0.0724530			0.0362265	+	0.999344i	$0.488466\pi$
$464$	1.66872	−	2.89031i	0.0774685	−	0.134179i
$465$	−39.7787	−	68.8988i	−1.84470	−	3.19511i
$466$	−8.97238	−	15.5406i	−0.415637	−	0.719905i
$467$	6.21156	−	10.7587i	0.287437	−	0.497855i	−0.685760	−	0.727827i	$-0.740530\pi$
$467$	6.21156	−	10.7587i	0.287437	−	0.497855i	0.973197	+	0.229972i	$0.0738635\pi$
$468$	1.55415			0.0718407
$469$		0			0
$470$	−38.7402			−1.78695
$471$	−15.8580	+	27.4668i	−0.730697	+	1.26561i
$472$	−3.09072	−	5.35328i	−0.142262	−	0.246405i
$473$	−0.335039	−	0.580305i	−0.0154051	−	0.0266825i
$474$	14.5665	−	25.2299i	0.669060	−	1.15885i
$475$	−23.8458			−1.09412
$476$		0			0
$477$	27.7826			1.27208
$478$	10.4587	−	18.1149i	0.478368	−	0.828557i
$479$	18.0279	+	31.2252i	0.823716	+	1.42672i	0.902897	+	0.429857i	$0.141436\pi$
$479$	18.0279	+	31.2252i	0.823716	+	1.42672i	−0.0791811	+	0.996860i	$0.525231\pi$
$480$	−8.45242	−	14.6400i	−0.385798	−	0.668222i
$481$	−1.54268	+	2.67201i	−0.0703404	+	0.121833i
$482$	17.3249			0.789128
$483$		0			0
$484$	2.72887			0.124040
$485$	−3.38011	+	5.85453i	−0.153483	+	0.265840i
$486$	13.6085	+	23.5707i	0.617295	+	1.06919i
$487$	−3.65002	−	6.32202i	−0.165398	−	0.286478i	0.771398	−	0.636352i	$-0.219558\pi$
$487$	−3.65002	−	6.32202i	−0.165398	−	0.286478i	−0.936797	+	0.349874i	$0.886224\pi$
$488$	−3.64351	+	6.31074i	−0.164934	+	0.285674i
$489$	39.1821			1.77188
$490$		0			0
$491$	4.49178			0.202711			0.101356	−	0.994850i	$-0.467682\pi$
$491$	4.49178			0.202711			0.101356	+	0.994850i	$0.467682\pi$
$492$	0.272633	−	0.472215i	0.0122913	−	0.0212891i
$493$	2.19139	+	3.79560i	0.0986954	+	0.170945i
$494$	−4.40565	−	7.63080i	−0.198219	−	0.343326i
$495$	−11.5348	+	19.9788i	−0.518450	+	0.897981i
$496$	−31.7663			−1.42635
$497$		0			0
$498$	−42.5742			−1.90780
$499$	−5.68369	+	9.84443i	−0.254437	+	0.440697i	−0.964742	−	0.263196i	$-0.915223\pi$
$499$	−5.68369	+	9.84443i	−0.254437	+	0.440697i	0.710306	+	0.703893i	$0.248557\pi$
$500$	−0.910235	−	1.57657i	−0.0407069	−	0.0705065i
$501$	6.64260	+	11.5053i	0.296770	+	0.514020i
$502$	−9.27709	+	16.0684i	−0.414057	+	0.717167i
$503$	−17.1080			−0.762806			−0.381403	−	0.924409i	$-0.624559\pi$
$503$	−17.1080			−0.762806			−0.381403	+	0.924409i	$0.624559\pi$
$504$		0			0
$505$	−4.21818			−0.187706
$506$	0.808405	−	1.40020i	0.0359380	−	0.0622464i
$507$	−1.31364	−	2.27529i	−0.0583408	−	0.101049i
$508$	1.03171	+	1.78698i	0.0457749	+	0.0792845i
$509$	1.64142	−	2.84303i	0.0727547	−	0.126015i	−0.827353	−	0.561682i	$-0.810154\pi$
$509$	1.64142	−	2.84303i	0.0727547	−	0.126015i	0.900108	+	0.435667i	$0.143488\pi$
$510$	−38.5929			−1.70892
$511$		0			0
$512$	−25.2340			−1.11520
$513$	8.25490	−	14.2979i	0.364463	−	0.631268i
$514$	−1.10916	−	1.92113i	−0.0489231	−	0.0847373i
$515$	−16.8863	−	29.2479i	−0.744100	−	1.28882i
$516$	0.172125	−	0.298129i	0.00757738	−	0.0131244i
$517$	−21.4770			−0.944555
$518$		0			0
$519$	1.56485			0.0686891
$520$	−4.40502	+	7.62973i	−0.193173	+	0.334586i
$521$	−2.38530	−	4.13147i	−0.104502	−	0.181003i	0.809033	−	0.587764i	$-0.199992\pi$
$521$	−2.38530	−	4.13147i	−0.104502	−	0.181003i	−0.913535	+	0.406761i	$0.866658\pi$
$522$	−2.70682	−	4.68835i	−0.118474	−	0.205203i
$523$	12.7562	−	22.0944i	0.557789	−	0.966119i	−0.439892	−	0.898051i	$-0.644983\pi$
$523$	12.7562	−	22.0944i	0.557789	−	0.966119i	0.997681	−	0.0680682i	$-0.0216835\pi$
$524$	4.20803			0.183829
$525$		0			0
$526$	34.0975			1.48672
$527$	20.8580	−	36.1271i	0.908588	−	1.57372i
$528$	8.14616	+	14.1096i	0.354516	+	0.614040i
$529$	11.3033	+	19.5778i	0.491446	+	0.851210i
$530$	−13.0760	+	22.6483i	−0.567986	+	0.983780i
$531$	−7.94789			−0.344909
$532$		0			0
$533$	−0.521150			−0.0225735
$534$	−4.45728	+	7.72024i	−0.192885	+	0.334087i
$535$	−28.4831	−	49.3342i	−1.23143	−	2.13290i
$536$	22.3001	+	38.6249i	0.963216	+	1.66834i
$537$	−10.6098	+	18.3767i	−0.457847	+	0.793013i
$538$	27.9309			1.20418
$539$		0			0
$540$	−2.74112			−0.117959
$541$	8.25784	−	14.3030i	0.355032	−	0.614934i	−0.632091	−	0.774894i	$-0.717803\pi$
$541$	8.25784	−	14.3030i	0.355032	−	0.614934i	0.987123	+	0.159960i	$0.0511366\pi$
$542$	−5.67125	−	9.82290i	−0.243601	−	0.421930i
$543$	2.48704	+	4.30768i	0.106729	+	0.184860i
$544$	4.43203	−	7.67649i	0.190022	−	0.329127i
$545$	−3.21247			−0.137607
$546$		0			0
$547$	23.3317			0.997591			0.498796	−	0.866720i	$-0.333776\pi$
$547$	23.3317			0.997591			0.498796	+	0.866720i	$0.333776\pi$
$548$	−1.16917	+	2.02507i	−0.0499446	+	0.0865066i
$549$	4.68471	+	8.11416i	0.199939	+	0.346304i
$550$	−4.41407	−	7.64539i	−0.188216	−	0.326001i
$551$	3.81545	−	6.60855i	0.162544	−	0.281534i
$552$	5.00218			0.212907
$553$		0			0
$554$	−9.52909			−0.404852
$555$	11.7644	−	20.3766i	0.499372	−	0.864938i
$556$	0.796470	+	1.37953i	0.0337779	+	0.0585050i
$557$	10.0235	+	17.3613i	0.424711	+	0.735621i	0.996393	−	0.0848540i	$-0.0270424\pi$
$557$	10.0235	+	17.3613i	0.424711	+	0.735621i	−0.571682	+	0.820475i	$0.693709\pi$
$558$	−25.7639	+	44.6243i	−1.09067	+	1.88910i
$559$	−0.329024			−0.0139162
$560$		0			0
$561$	−21.3953			−0.903312
$562$	−18.8425	+	32.6362i	−0.794824	+	1.37668i
$563$	−20.2642	−	35.0986i	−0.854034	−	1.47923i	−0.877539	−	0.479506i	$-0.840816\pi$
$563$	−20.2642	−	35.0986i	−0.854034	−	1.47923i	0.0235047	−	0.999724i	$-0.492518\pi$
$564$	−5.51684	−	9.55545i	−0.232301	−	0.402357i
$565$	1.59072	−	2.75520i	0.0669219	−	0.115912i
$566$	−0.381519			−0.0160364
$567$		0			0
$568$	−10.9311			−0.458659
$569$	10.7252	−	18.5766i	0.449623	−	0.778770i	−0.548739	−	0.835994i	$-0.684892\pi$
$569$	10.7252	−	18.5766i	0.449623	−	0.778770i	0.998361	+	0.0572245i	$0.0182251\pi$
$570$	33.5972	+	58.1921i	1.40723	+	2.43740i
$571$	5.47793	+	9.48806i	0.229244	+	0.397063i	0.957584	−	0.288153i	$-0.0930412\pi$
$571$	5.47793	+	9.48806i	0.229244	+	0.397063i	−0.728340	+	0.685216i	$0.759708\pi$
$572$	−0.405516	+	0.702374i	−0.0169555	+	0.0293677i
$573$	9.72552			0.406289
$574$		0			0
$575$	−2.14849			−0.0895982
$576$	−17.3576	+	30.0643i	−0.723235	+	1.25268i
$577$	17.3708	+	30.0870i	0.723154	+	1.25254i	0.959729	+	0.280927i	$0.0906418\pi$
$577$	17.3708	+	30.0870i	0.723154	+	1.25254i	−0.236575	+	0.971613i	$0.576025\pi$
$578$	0.639571	+	1.10777i	0.0266027	+	0.0460771i
$579$	−17.8490	+	30.9154i	−0.741781	+	1.28480i
$580$	−1.26696			−0.0526076
$581$		0			0
$582$	7.74426			0.321010
$583$	−7.24915	+	12.5559i	−0.300229	+	0.520012i
$584$	−4.51600	−	7.82195i	−0.186874	−	0.323675i
$585$	5.66384	+	9.81006i	0.234171	+	0.405596i
$586$	−12.1796	+	21.0958i	−0.503136	+	0.871458i
$587$	22.8463			0.942967			0.471483	−	0.881875i	$-0.343719\pi$
$587$	22.8463			0.942967			0.471483	+	0.881875i	$0.343719\pi$
$588$		0			0
$589$	−72.6320			−2.99275
$590$	3.74071	−	6.47911i	0.154003	−	0.266741i
$591$	12.7457	+	22.0762i	0.524288	+	0.908094i
$592$	−4.69738	−	8.13610i	−0.193061	−	0.334392i
$593$	8.79676	−	15.2364i	0.361240	−	0.625686i	−0.626925	−	0.779079i	$-0.715687\pi$
$593$	8.79676	−	15.2364i	0.361240	−	0.625686i	0.988165	+	0.153394i	$0.0490202\pi$
$594$	6.11222			0.250787
$595$		0			0
$596$	4.02433			0.164843
$597$	34.5119	−	59.7764i	1.41248	−	2.44648i
$598$	−0.396945	−	0.687530i	−0.0162323	−	0.0281152i
$599$	−15.5036	−	26.8531i	−0.633461	−	1.09719i	−0.986839	−	0.161706i	$-0.948300\pi$
$599$	−15.5036	−	26.8531i	−0.633461	−	1.09719i	0.353378	−	0.935481i	$-0.385033\pi$
$600$	13.6565	−	23.6537i	0.557524	−	0.965660i
$601$	1.43754			0.0586385			0.0293193	−	0.999570i	$-0.490666\pi$
$601$	1.43754			0.0586385			0.0293193	+	0.999570i	$0.490666\pi$
$602$		0			0
$603$	57.3455			2.33529
$604$	−0.0373796	+	0.0647433i	−0.00152095	+	0.00263437i
$605$	9.94490	+	17.2251i	0.404318	+	0.700299i
$606$	2.41609	+	4.18479i	0.0981470	+	0.169996i
$607$	−16.5085	+	28.5936i	−0.670061	+	1.16058i	0.307826	+	0.951443i	$0.400399\pi$
$607$	−16.5085	+	28.5936i	−0.670061	+	1.16058i	−0.977887	+	0.209136i	$0.932935\pi$
$608$	−15.4333			−0.625901
$609$		0			0
$610$	−8.81953			−0.357092
$611$	−5.27284	+	9.13283i	−0.213316	+	0.369475i
$612$	−3.10727	−	5.38194i	−0.125604	−	0.217552i
$613$	21.5829	+	37.3826i	0.871723	+	1.50987i	0.860213	+	0.509935i	$0.170331\pi$
$613$	21.5829	+	37.3826i	0.871723	+	1.50987i	0.0115102	+	0.999934i	$0.496336\pi$
$614$	−2.26404	+	3.92143i	−0.0913692	+	0.158256i
$615$	3.97426			0.160258
$616$		0			0
$617$	2.45772			0.0989441			0.0494721	−	0.998776i	$-0.484246\pi$
$617$	2.45772			0.0989441			0.0494721	+	0.998776i	$0.484246\pi$
$618$	−19.3443	+	33.5053i	−0.778142	+	1.34778i
$619$	18.8894	+	32.7175i	0.759231	+	1.31503i	0.943243	+	0.332102i	$0.107758\pi$
$619$	18.8894	+	32.7175i	0.759231	+	1.31503i	−0.184013	+	0.982924i	$0.558909\pi$
$620$	6.02954	+	10.4435i	0.242152	+	0.419420i
$621$	0.743761	−	1.28823i	0.0298461	−	0.0516949i
$622$	30.1602			1.20932
$623$		0			0
$624$	7.99991			0.320253
$625$	15.1971	−	26.3222i	0.607884	−	1.05289i
$626$	−11.4420	−	19.8181i	−0.457313	−	0.792089i
$627$	18.6258	+	32.2608i	0.743842	+	1.28837i
$628$	2.40371	−	4.16334i	0.0959183	−	0.166135i
$629$	12.3374			0.491922
$630$		0			0
$631$	−28.4828			−1.13388			−0.566942	−	0.823758i	$-0.691874\pi$
$631$	−28.4828			−1.13388			−0.566942	+	0.823758i	$0.691874\pi$
$632$	−13.2966	+	23.0303i	−0.528909	+	0.916098i
$633$	−13.1809	−	22.8299i	−0.523892	−	0.907407i
$634$	17.4326	+	30.1942i	0.692337	+	1.19916i
$635$	−7.51981	+	13.0247i	−0.298415	+	0.516869i
$636$	−7.44843			−0.295350
$637$		0			0
$638$	2.82509			0.111847
$639$	−7.02743	+	12.1719i	−0.278001	+	0.481512i
$640$	−9.90456	−	17.1552i	−0.391512	−	0.678119i
$641$	13.5961	+	23.5492i	0.537014	+	0.930136i	0.999063	+	0.0432812i	$0.0137811\pi$
$641$	13.5961	+	23.5492i	0.537014	+	0.930136i	−0.462049	+	0.886854i	$0.652886\pi$
$642$	−32.6292	+	56.5154i	−1.28777	+	2.23049i
$643$	37.1664			1.46570			0.732849	−	0.680391i	$-0.238190\pi$
$643$	37.1664			1.46570			0.732849	+	0.680391i	$0.238190\pi$
$644$		0			0
$645$	2.50912			0.0987965
$646$	−17.6167	+	30.5130i	−0.693120	+	1.20052i
$647$	9.41593	+	16.3089i	0.370178	+	0.641168i	0.989593	−	0.143896i	$-0.0459632\pi$
$647$	9.41593	+	16.3089i	0.370178	+	0.641168i	−0.619414	+	0.785064i	$0.712630\pi$
$648$	−8.31275	−	14.3981i	−0.326556	−	0.565611i
$649$	2.07380	−	3.59192i	0.0814036	−	0.140995i
$650$	−4.33482			−0.170026
$651$		0			0
$652$	−5.93910			−0.232593
$653$	13.0092	−	22.5326i	0.509090	−	0.881770i	−0.490854	−	0.871242i	$-0.663315\pi$
$653$	13.0092	−	22.5326i	0.509090	−	0.881770i	0.999945	−	0.0105286i	$-0.00335143\pi$
$654$	1.84004	+	3.18705i	0.0719513	+	0.124623i
$655$	15.3355	+	26.5618i	0.599206	+	1.03786i
$656$	0.793435	−	1.37427i	0.0309784	−	0.0536562i
$657$	−11.6131			−0.453069
$658$		0			0
$659$	−33.3339			−1.29851			−0.649253	−	0.760573i	$-0.724918\pi$
$659$	−33.3339			−1.29851			−0.649253	+	0.760573i	$0.724918\pi$
$660$	3.09244	−	5.35626i	0.120373	−	0.208492i
$661$	3.14920	+	5.45458i	0.122490	+	0.212159i	0.920749	−	0.390156i	$-0.127579\pi$
$661$	3.14920	+	5.45458i	0.122490	+	0.212159i	−0.798259	+	0.602314i	$0.794245\pi$
$662$	11.5053	+	19.9277i	0.447164	+	0.774511i
$663$	−5.25280	+	9.09812i	−0.204002	+	0.353342i
$664$	38.8626			1.50816
$665$		0			0
$666$	−15.2391			−0.590505
$667$	0.343769	−	0.595426i	0.0133108	−	0.0230550i
$668$	−1.00687	−	1.74394i	−0.0389568	−	0.0674752i
$669$	22.9836	+	39.8088i	0.888597	+	1.53910i
$670$	−26.9899	+	46.7479i	−1.04271	+	1.80603i
$671$	−4.88941			−0.188754
$672$		0			0
$673$	18.3188			0.706137			0.353068	−	0.935598i	$-0.385138\pi$
$673$	18.3188			0.706137			0.353068	+	0.935598i	$0.385138\pi$
$674$	10.8451	−	18.7842i	0.417736	−	0.723541i
$675$	−4.06110	−	7.03403i	−0.156312	−	0.270740i
$676$	0.199118	+	0.344882i	0.00765837	+	0.0132647i
$677$	12.1696	−	21.0783i	0.467715	−	0.810106i	−0.531604	−	0.846993i	$-0.678411\pi$
$677$	12.1696	−	21.0783i	0.467715	−	0.810106i	0.999319	+	0.0368866i	$0.0117440\pi$
$678$	−3.64453			−0.139967
$679$		0			0
$680$	35.2284			1.35095
$681$	−12.5010	+	21.6524i	−0.479039	+	0.829720i
$682$	−13.4448	−	23.2871i	−0.514829	−	0.891709i
$683$	−5.88409	−	10.1916i	−0.225149	−	0.389969i	0.731215	−	0.682147i	$-0.238953\pi$
$683$	−5.88409	−	10.1916i	−0.225149	−	0.389969i	−0.956364	+	0.292178i	$0.905620\pi$
$684$	−5.41008	+	9.37054i	−0.206860	+	0.358291i
$685$	−17.0434			−0.651195
$686$		0			0
$687$	−55.4802			−2.11670
$688$	0.500929	−	0.867635i	0.0190977	−	0.0330783i
$689$	3.55950	+	6.16523i	0.135606	+	0.234877i
$690$	3.02708	+	5.24306i	0.115239	+	0.199600i
$691$	0.588923	−	1.02004i	0.0224037	−	0.0388043i	−0.854606	−	0.519277i	$-0.826201\pi$
$691$	0.588923	−	1.02004i	0.0224037	−	0.0388043i	0.877010	+	0.480472i	$0.159535\pi$
$692$	−0.237195			−0.00901679
$693$		0			0
$694$	28.1835			1.06983
$695$	−5.80520	+	10.0549i	−0.220204	+	0.381404i
$696$	4.37022	+	7.56944i	0.165653	+	0.286919i
$697$	1.04195	+	1.80471i	0.0394668	+	0.0683584i
$698$	12.6161	−	21.8517i	0.477525	−	0.827097i
$699$	37.2516			1.40898
$700$		0			0
$701$	−31.2867			−1.18168			−0.590841	−	0.806788i	$-0.701204\pi$
$701$	−31.2867			−1.18168			−0.590841	+	0.806788i	$0.701204\pi$
$702$	1.50062	−	2.59915i	0.0566373	−	0.0980987i
$703$	−10.7403	−	18.6028i	−0.405079	−	0.701617i
$704$	−9.05804	−	15.6890i	−0.341388	−	0.591301i
$705$	40.2104	−	69.6464i	1.51441	−	2.62304i
$706$	−29.0016			−1.09149
$707$		0			0
$708$	2.13081			0.0800806
$709$	−7.68738	+	13.3149i	−0.288706	+	0.500053i	−0.973501	−	0.228682i	$-0.926558\pi$
$709$	−7.68738	+	13.3149i	−0.288706	+	0.500053i	0.684795	+	0.728735i	$0.259892\pi$
$710$	−6.61499	−	11.4575i	−0.248256	−	0.429992i
$711$	17.0963	+	29.6117i	0.641162	+	1.11053i
$712$	4.06870	−	7.04719i	0.152481	−	0.264105i
$713$	−6.54409			−0.245078
$714$		0			0
$715$	−5.91133			−0.221071
$716$	1.60820	−	2.78549i	0.0601013	−	0.104098i
$717$	21.7111	+	37.6048i	0.810817	+	1.40438i
$718$	−17.2322	−	29.8470i	−0.643099	−	1.11388i
$719$	−5.57087	+	9.64904i	−0.207759	+	0.359848i	−0.951008	−	0.309166i	$-0.899950\pi$
$719$	−5.57087	+	9.64904i	−0.207759	+	0.359848i	0.743250	+	0.669014i	$0.233283\pi$
$720$	−34.4921			−1.28545
$721$		0			0
$722$	37.2985			1.38811
$723$	−17.9824	+	31.1465i	−0.668773	+	1.15835i
$724$	−0.376978	−	0.652945i	−0.0140103	−	0.0242665i
$725$	−1.87706	−	3.25116i	−0.0697121	−	0.120745i
$726$	11.3925	−	19.7324i	0.422815	−	0.732338i
$727$	6.24735			0.231702			0.115851	−	0.993267i	$-0.463041\pi$
$727$	6.24735			0.231702			0.115851	+	0.993267i	$0.463041\pi$
$728$		0			0
$729$	−40.0674			−1.48398
$730$	5.46575	−	9.46696i	0.202296	−	0.350388i
$731$	0.657828	+	1.13939i	0.0243307	+	0.0421419i
$732$	−1.25596	−	2.17538i	−0.0464215	−	0.0804044i
$733$	15.4834	−	26.8181i	0.571894	−	0.990550i	−0.424477	−	0.905439i	$-0.639542\pi$
$733$	15.4834	−	26.8181i	0.571894	−	0.990550i	0.996371	−	0.0851111i	$-0.0271245\pi$
$734$	13.7400			0.507153
$735$		0			0
$736$	−1.39053			−0.0512554
$737$	−14.9628	+	25.9163i	−0.551162	+	0.954641i
$738$	−1.28702	−	2.22919i	−0.0473760	−	0.0820576i
$739$	−1.16872	−	2.02429i	−0.0429921	−	0.0744646i	0.843729	−	0.536770i	$-0.180356\pi$
$739$	−1.16872	−	2.02429i	−0.0429921	−	0.0744646i	−0.886721	+	0.462305i	$0.847022\pi$
$740$	−1.78322	+	3.08862i	−0.0655523	+	0.113540i
$741$	18.2914			0.671951
$742$		0			0
$743$	24.3612			0.893726			0.446863	−	0.894603i	$-0.352541\pi$
$743$	24.3612			0.893726			0.446863	+	0.894603i	$0.352541\pi$
$744$	41.5963	−	72.0470i	1.52500	−	2.64137i
$745$	14.6660	+	25.4022i	0.537321	+	0.930666i
$746$	1.50066	+	2.59922i	0.0549430	+	0.0951641i
$747$	24.9842	−	43.2739i	0.914123	−	1.58331i
$748$	3.24304			0.118577
$749$		0			0
$750$	−15.2002			−0.555033
$751$	6.01266	−	10.4142i	0.219405	−	0.380021i	−0.735221	−	0.677827i	$-0.762922\pi$
$751$	6.01266	−	10.4142i	0.219405	−	0.380021i	0.954626	+	0.297806i	$0.0962550\pi$
$752$	−16.0555	−	27.8089i	−0.585483	−	1.01409i
$753$	−19.2583	−	33.3564i	−0.701813	−	1.21558i
$754$	0.693593	−	1.20134i	0.0252592	−	0.0437502i
$755$	−0.544894			−0.0198307
$756$		0			0
$757$	25.9905			0.944641			0.472321	−	0.881427i	$-0.343416\pi$
$757$	25.9905			0.944641			0.472321	+	0.881427i	$0.343416\pi$
$758$	18.4904	−	32.0263i	0.671600	−	1.16325i
$759$	1.67817	+	2.90667i	0.0609137	+	0.105506i
$760$	−30.6682	−	53.1189i	−1.11245	−	1.92683i
$761$	6.66350	−	11.5415i	0.241552	−	0.418380i	−0.719605	−	0.694384i	$-0.755677\pi$
$761$	6.66350	−	11.5415i	0.241552	−	0.418380i	0.961156	+	0.276004i	$0.0890103\pi$
$762$	17.2288			0.624134
$763$		0			0
$764$	−1.47416			−0.0533334
$765$	22.6478	−	39.2271i	0.818833	−	1.41826i
$766$	−1.94014	−	3.36043i	−0.0701002	−	0.121417i
$767$	−1.01828	−	1.76372i	−0.0367680	−	0.0636841i
$768$	12.0245	−	20.8270i	0.433896	−	0.751530i
$769$	−9.24486			−0.333378			−0.166689	−	0.986010i	$-0.553308\pi$
$769$	−9.24486			−0.333378			−0.166689	+	0.986010i	$0.553308\pi$
$770$		0			0
$771$	4.60503			0.165846
$772$	2.70550	−	4.68607i	0.0973732	−	0.168655i
$773$	−5.07097	−	8.78317i	−0.182390	−	0.315909i	0.760304	−	0.649568i	$-0.225050\pi$
$773$	−5.07097	−	8.78317i	−0.182390	−	0.315909i	−0.942694	+	0.333659i	$0.891717\pi$
$774$	−0.812552	−	1.40738i	−0.0292066	−	0.0505873i
$775$	−17.8661	+	30.9450i	−0.641768	+	1.11158i
$776$	−7.06912			−0.253766
$777$		0			0
$778$	35.1092			1.25873
$779$	1.81415	−	3.14220i	0.0649987	−	0.112581i
$780$	−1.51846	−	2.63005i	−0.0543696	−	0.0941709i
$781$	−3.66725	−	6.35186i	−0.131225	−	0.227288i
$782$	−1.58725	+	2.74920i	−0.0567600	+	0.0983112i
$783$	2.59919			0.0928873
$784$		0			0
$785$	35.0396			1.25062
$786$	17.5677	−	30.4282i	0.626620	−	1.08534i
$787$	22.6411	+	39.2156i	0.807070	+	1.39789i	0.914885	+	0.403715i	$0.132281\pi$
$787$	22.6411	+	39.2156i	0.807070	+	1.39789i	−0.107815	+	0.994171i	$0.534386\pi$
$788$	−1.93195	−	3.34624i	−0.0688230	−	0.119205i
$789$	−35.3916	+	61.3000i	−1.25997	+	2.18234i
$790$	−32.1859			−1.14512
$791$		0			0
$792$	−24.1237			−0.857197
$793$	−1.20041	+	2.07917i	−0.0426277	+	0.0738334i
$794$	10.9040	+	18.8862i	0.386967	+	0.670247i
$795$	−27.1445	−	47.0157i	−0.962718	−	1.66748i
$796$	−5.23121	+	9.06072i	−0.185415	+	0.321149i
$797$	−27.0784			−0.959165			−0.479583	−	0.877497i	$-0.659212\pi$
$797$	−27.0784			−0.959165			−0.479583	+	0.877497i	$0.659212\pi$
$798$		0			0
$799$	42.1686			1.49182
$800$	−3.79629	+	6.57536i	−0.134219	+	0.232474i
$801$	−5.23140	−	9.06106i	−0.184843	−	0.320157i
$802$	−10.5324	−	18.2427i	−0.371912	−	0.644171i
$803$	3.03013	−	5.24834i	0.106931	−	0.185210i
$804$	−15.3741			−0.542204
$805$		0			0
$806$	−13.2034			−0.465071
$807$	−28.9909	+	50.2137i	−1.02053	+	1.76760i
$808$	−2.20546	−	3.81996i	−0.0775877	−	0.134386i
$809$	12.8899	+	22.3260i	0.453185	+	0.784939i	0.998582	−	0.0532388i	$-0.0169544\pi$
$809$	12.8899	+	22.3260i	0.453185	+	0.784939i	−0.545397	+	0.838178i	$0.683621\pi$
$810$	10.0610	−	17.4261i	0.353507	−	0.612291i
$811$	25.7829			0.905362			0.452681	−	0.891673i	$-0.350468\pi$
$811$	25.7829			0.905362			0.452681	+	0.891673i	$0.350468\pi$
$812$		0			0
$813$	23.5459			0.825792
$814$	3.97626	−	6.88708i	0.139368	−	0.241392i
$815$	−21.6440	−	37.4886i	−0.758158	−	1.31317i
$816$	−15.9945	−	27.7032i	−0.559918	−	0.969807i
$817$	1.14535	−	1.98380i	0.0400707	−	0.0694045i
$818$	17.2550			0.603308
$819$		0			0
$820$	−0.602407			−0.0210370
$821$	0.855366	−	1.48154i	0.0298525	−	0.0517060i	−0.850713	−	0.525630i	$-0.823830\pi$
$821$	0.855366	−	1.48154i	0.0298525	−	0.0517060i	0.880566	+	0.473924i	$0.157163\pi$
$822$	9.76214	+	16.9085i	0.340494	+	0.589752i
$823$	20.1887	+	34.9678i	0.703733	+	1.21890i	0.967147	+	0.254218i	$0.0818181\pi$
$823$	20.1887	+	34.9678i	0.703733	+	1.21890i	−0.263414	+	0.964683i	$0.584849\pi$
$824$	17.6579	−	30.5844i	0.615142	−	1.06546i
$825$	18.3264			0.638042
$826$		0			0
$827$	19.5698			0.680509			0.340254	−	0.940333i	$-0.389487\pi$
$827$	19.5698			0.680509			0.340254	+	0.940333i	$0.389487\pi$
$828$	−0.487444	+	0.844278i	−0.0169399	+	0.0293407i
$829$	20.7871	+	36.0043i	0.721966	+	1.25048i	0.960211	+	0.279277i	$0.0900948\pi$
$829$	20.7871	+	36.0043i	0.721966	+	1.25048i	−0.238244	+	0.971205i	$0.576572\pi$
$830$	23.5178	+	40.7341i	0.816316	+	1.41390i
$831$	9.89073	−	17.1312i	0.343106	−	0.594276i
$832$	−8.89542			−0.308393
$833$		0			0
$834$	13.3004			0.460556
$835$	7.33870	−	12.7110i	0.253966	−	0.439882i
$836$	−2.82324	−	4.89000i	−0.0976438	−	0.169124i
$837$	−12.3697	−	21.4250i	−0.427560	−	0.740555i
$838$	−6.86604	+	11.8923i	−0.237183	+	0.410814i
$839$	−45.8480			−1.58285			−0.791425	−	0.611266i	$-0.790660\pi$
$839$	−45.8480			−1.58285			−0.791425	+	0.611266i	$0.790660\pi$
$840$		0			0
$841$	−27.7986			−0.958574
$842$	6.32804	−	10.9605i	0.218079	−	0.377723i
$843$	−39.1152	−	67.7496i	−1.34720	−	2.33342i
$844$	1.99791	+	3.46049i	0.0687710	+	0.119115i
$845$	−1.45130	+	2.51373i	−0.0499262	+	0.0864748i
$846$	−52.0869			−1.79078
$847$		0			0
$848$	−21.6769			−0.744388
$849$	0.395998	−	0.685889i	0.0135906	−	0.0235397i
$850$	8.66674	+	15.0112i	0.297267	+	0.514881i
$851$	−0.967695	−	1.67610i	−0.0331722	−	0.0574559i
$852$	1.88403	−	3.26324i	0.0645459	−	0.111797i
$853$	−40.0236			−1.37038			−0.685191	−	0.728364i	$-0.740281\pi$
$853$	−40.0236			−1.37038			−0.685191	+	0.728364i	$0.740281\pi$
$854$		0			0
$855$	−78.8645			−2.69711
$856$	29.7846	−	51.5884i	1.01802	−	1.76326i
$857$	16.4351	+	28.4664i	0.561412	+	0.972395i	0.997374	+	0.0724294i	$0.0230752\pi$
$857$	16.4351	+	28.4664i	0.561412	+	0.972395i	−0.435961	+	0.899966i	$0.643591\pi$
$858$	3.38590	+	5.86455i	0.115593	+	0.200212i
$859$	−17.0252	+	29.4885i	−0.580891	+	1.00613i	0.414483	+	0.910057i	$0.363963\pi$
$859$	−17.0252	+	29.4885i	−0.580891	+	1.00613i	−0.995374	+	0.0960762i	$0.969371\pi$
$860$	−0.380325			−0.0129690
$861$		0			0
$862$	1.53079			0.0521388
$863$	7.03208	−	12.1799i	0.239375	−	0.414609i	−0.721160	−	0.692768i	$-0.756391\pi$
$863$	7.03208	−	12.1799i	0.239375	−	0.414609i	0.960535	+	0.278159i	$0.0897243\pi$
$864$	−2.62839	−	4.55250i	−0.0894195	−	0.154879i
$865$	−0.864415	−	1.49721i	−0.0293910	−	0.0509067i
$866$	−3.52106	+	6.09866i	−0.119651	+	0.207241i
$867$	−2.65537			−0.0901813
$868$		0			0
$869$	−17.8434			−0.605295
$870$	−5.28930	+	9.16134i	−0.179324	+	0.310599i
$871$	7.34709	+	12.7255i	0.248947	+	0.431188i
$872$	−1.67963	−	2.90920i	−0.0568794	−	0.0985180i
$873$	−4.54463	+	7.87152i	−0.153812	+	0.266411i
$874$	5.52715			0.186959
$875$		0			0
$876$	3.11343			0.105193
$877$	−25.5335	+	44.2252i	−0.862204	+	1.49338i	0.00759373	+	0.999971i	$0.497583\pi$
$877$	−25.5335	+	44.2252i	−0.862204	+	1.49338i	−0.869797	+	0.493409i	$0.835751\pi$
$878$	−12.4784	−	21.6132i	−0.421125	−	0.729411i
$879$	−25.2838	−	43.7927i	−0.852800	−	1.47709i
$880$	8.99982	−	15.5881i	0.303384	−	0.525476i
$881$	18.4203			0.620597			0.310298	−	0.950639i	$-0.399571\pi$
$881$	18.4203			0.620597			0.310298	+	0.950639i	$0.399571\pi$
$882$		0			0
$883$	0.126678			0.00426305			0.00213153	−	0.999998i	$-0.499322\pi$
$883$	0.126678			0.00426305			0.00213153	+	0.999998i	$0.499322\pi$
$884$	0.796204	−	1.37907i	0.0267792	−	0.0463830i
$885$	7.76536	+	13.4500i	0.261030	+	0.452117i
$886$	−14.0679	−	24.3663i	−0.472619	−	0.818601i
$887$	1.93735	−	3.35559i	0.0650498	−	0.112670i	−0.831666	−	0.555276i	$-0.812613\pi$
$887$	1.93735	−	3.35559i	0.0650498	−	0.112670i	0.896716	+	0.442606i	$0.145946\pi$
$888$	24.6039			0.825654
$889$		0			0
$890$	9.84874			0.330131
$891$	5.57765	−	9.66078i	0.186858	−	0.323648i
$892$	−3.48378	−	6.03409i	−0.116646	−	0.202036i
$893$	−36.7100	−	63.5837i	−1.22845	−	2.12775i
$894$	16.8008	−	29.0998i	0.561903	−	0.973244i
$895$	23.4433			0.783622
$896$		0			0
$897$	1.64804			0.0550265
$898$	−11.6802	+	20.2308i	−0.389775	+	0.675109i
$899$	−5.71733	−	9.90270i	−0.190684	−	0.330274i
$900$	2.66155	+	4.60995i	0.0887185	+	0.153665i
$901$	14.2332	−	24.6527i	0.474178	−	0.821300i
$902$	1.34326			0.0447257
$903$		0			0
$904$	3.32680			0.110648
$905$	2.74766	−	4.75909i	0.0913355	−	0.158198i
$906$	0.312105	+	0.540581i	0.0103690	+	0.0179596i
$907$	23.3871	+	40.5076i	0.776555	+	1.34503i	0.933916	+	0.357491i	$0.116368\pi$
$907$	23.3871	+	40.5076i	0.776555	+	1.34503i	−0.157362	+	0.987541i	$0.550299\pi$
$908$	1.89486	−	3.28200i	0.0628832	−	0.108917i
$909$	−5.67142			−0.188109
$910$		0			0
$911$	5.93675			0.196693			0.0983467	−	0.995152i	$-0.468645\pi$
$911$	5.93675			0.196693			0.0983467	+	0.995152i	$0.468645\pi$
$912$	−27.8481	+	48.2343i	−0.922142	+	1.59720i
$913$	13.0379	+	22.5824i	0.431493	+	0.747368i
$914$	18.9727	+	32.8617i	0.627561	+	1.08697i
$915$	9.15424	−	15.8556i	0.302630	−	0.524170i
$916$	8.40952			0.277858
$917$		0			0
$918$	−12.0010			−0.396091
$919$	4.29351	−	7.43657i	0.141630	−	0.245310i	−0.786481	−	0.617615i	$-0.788099\pi$
$919$	4.29351	−	7.43657i	0.141630	−	0.245310i	0.928110	+	0.372305i	$0.121432\pi$
$920$	−2.76318	−	4.78597i	−0.0910995	−	0.157789i
$921$	−4.69993	−	8.14051i	−0.154868	−	0.268239i
$922$	18.4461	−	31.9496i	0.607490	−	1.05220i
$923$	−3.60141			−0.118542
$924$		0			0
$925$	−10.5677			−0.347463
$926$	−0.986543	+	1.70874i	−0.0324198	+	0.0561528i
$927$	−22.7040	−	39.3244i	−0.745696	−	1.29158i
$928$	−1.21485	−	2.10418i	−0.0398794	−	0.0690732i
$929$	−4.22972	+	7.32610i	−0.138773	+	0.240361i	−0.927032	−	0.374981i	$-0.877649\pi$
$929$	−4.22972	+	7.32610i	−0.138773	+	0.240361i	0.788260	+	0.615343i	$0.210982\pi$
$930$	100.689			3.30171
$931$		0			0
$932$	−5.64648			−0.184957
$933$	−31.3049	+	54.2216i	−1.02487	+	1.77514i
$934$	7.86141	+	13.6164i	0.257233	+	0.445541i
$935$	11.8187	+	20.4706i	0.386513	+	0.669460i
$936$	−5.92264	+	10.2583i	−0.193587	+	0.335303i
$937$	33.3596			1.08981			0.544905	−	0.838498i	$-0.316566\pi$
$937$	33.3596			1.08981			0.544905	+	0.838498i	$0.316566\pi$
$938$		0			0
$939$	47.5048			1.55026
$940$	−6.09497	+	10.5568i	−0.198796	+	0.344325i
$941$	−6.70187	−	11.6080i	−0.218475	−	0.378409i	0.735867	−	0.677126i	$-0.236775\pi$
$941$	−6.70187	−	11.6080i	−0.218475	−	0.378409i	−0.954342	+	0.298717i	$0.903441\pi$
$942$	−20.0700	−	34.7623i	−0.653916	−	1.13262i
$943$	0.163454	−	0.283110i	0.00532278	−	0.00921933i
$944$	6.20121			0.201832
$945$		0			0
$946$	0.848057			0.0275727
$947$	−21.5397	+	37.3078i	−0.699946	+	1.21234i	0.268539	+	0.963269i	$0.413459\pi$
$947$	−21.5397	+	37.3078i	−0.699946	+	1.21234i	−0.968485	+	0.249073i	$0.919874\pi$
$948$	−4.58347	−	7.93881i	−0.148864	−	0.257840i
$949$	−1.48786	−	2.57706i	−0.0482981	−	0.0836548i
$950$	15.0897	−	26.1362i	0.489575	−	0.847969i
$951$	−72.3768			−2.34698
$952$		0			0
$953$	16.7332			0.542040			0.271020	−	0.962574i	$-0.412639\pi$
$953$	16.7332			0.542040			0.271020	+	0.962574i	$0.412639\pi$
$954$	−17.5810	+	30.4511i	−0.569204	+	0.985891i
$955$	−5.37234	−	9.30517i	−0.173845	−	0.301108i
$956$	−3.29091	−	5.70002i	−0.106436	−	0.184352i
$957$	−2.93231	+	5.07891i	−0.0947881	+	0.164178i
$958$	−45.6325			−1.47432
$959$		0			0
$960$	67.8360			2.18940
$961$	−38.9183	+	67.4085i	−1.25543	+	2.17447i
$962$	−1.95243	−	3.38172i	−0.0629490	−	0.109031i
$963$	−38.2961	−	66.3308i	−1.23407	−	2.13748i
$964$	2.72572	−	4.72109i	0.0877896	−	0.152056i
$965$	39.4390			1.26959
$966$		0			0
$967$	44.7594			1.43937			0.719683	−	0.694303i	$-0.244287\pi$
$967$	44.7594			1.43937			0.719683	+	0.694303i	$0.244287\pi$
$968$	−10.3993	+	18.0121i	−0.334246	+	0.578932i
$969$	−36.5705	−	63.3420i	−1.17482	−	2.03484i
$970$	−4.27790	−	7.40954i	−0.137355	−	0.237906i
$971$	−2.10129	+	3.63955i	−0.0674337	+	0.116799i	−0.897771	−	0.440463i	$-0.854814\pi$
$971$	−2.10129	+	3.63955i	−0.0674337	+	0.116799i	0.830337	+	0.557261i	$0.188148\pi$
$972$	8.56409			0.274693
$973$		0			0
$974$	9.23899			0.296036
$975$	4.49933	−	7.79307i	0.144094	−	0.249578i
$976$	−3.65517	−	6.33093i	−0.116999	−	0.202648i
$977$	12.8449	+	22.2481i	0.410946	+	0.711779i	0.994993	−	0.0999403i	$-0.0318652\pi$
$977$	12.8449	+	22.2481i	0.410946	+	0.711779i	−0.584048	+	0.811719i	$0.698532\pi$
$978$	−24.7946	+	42.9455i	−0.792843	+	1.37325i
$979$	5.45999			0.174502
$980$		0			0
$981$	−4.31923			−0.137902
$982$	−2.84242	+	4.92321i	−0.0907051	+	0.157106i
$983$	−15.9122	−	27.5607i	−0.507520	−	0.879051i	−0.999962	−	0.00870538i	$-0.997229\pi$
$983$	−15.9122	−	27.5607i	−0.507520	−	0.879051i	0.492442	−	0.870345i	$-0.336104\pi$
$984$	2.07793	+	3.59908i	0.0662419	+	0.114734i
$985$	14.0814	−	24.3896i	0.448669	−	0.777118i
$986$	−5.54689			−0.176649
$987$		0			0
$988$	−2.77255			−0.0882067
$989$	0.103195	−	0.178739i	0.00328141	−	0.00568358i
$990$	−14.5985	−	25.2854i	−0.463971	−	0.803622i
$991$	−4.73739	−	8.20540i	−0.150488	−	0.260653i	0.780919	−	0.624632i	$-0.214751\pi$
$991$	−4.73739	−	8.20540i	−0.150488	−	0.260653i	−0.931407	+	0.363979i	$0.881418\pi$
$992$	−11.5631	+	20.0279i	−0.367129	+	0.635887i
$993$	−47.7676			−1.51586
$994$		0			0
$995$	−76.2570			−2.41751
$996$	−6.69818	+	11.6016i	−0.212240	+	0.367611i
$997$	10.9755	+	19.0102i	0.347599	+	0.602059i	0.985822	−	0.167792i	$-0.0536638\pi$
$997$	10.9755	+	19.0102i	0.347599	+	0.602059i	−0.638224	+	0.769851i	$0.720330\pi$
$998$	−7.19332	−	12.4592i	−0.227701	−	0.394389i
$999$	3.65830	−	6.33636i	0.115743	−	0.200473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.m.79.3		10
7.2	even	3		637.2.a.k.1.3		5
7.3	odd	6		91.2.e.c.53.3	✓	10
7.4	even	3	inner	637.2.e.m.508.3		10
7.5	odd	6		637.2.a.l.1.3		5
7.6	odd	2		91.2.e.c.79.3	yes	10
21.2	odd	6		5733.2.a.bm.1.3		5
21.5	even	6		5733.2.a.bl.1.3		5
21.17	even	6		819.2.j.h.235.3		10
21.20	even	2		819.2.j.h.352.3		10
28.3	even	6		1456.2.r.p.417.1		10
28.27	even	2		1456.2.r.p.625.1		10
91.12	odd	6		8281.2.a.bw.1.3		5
91.38	odd	6		1183.2.e.f.508.3		10
91.51	even	6		8281.2.a.bx.1.3		5
91.90	odd	2		1183.2.e.f.170.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.3	✓	10	7.3	odd	6
91.2.e.c.79.3	yes	10	7.6	odd	2
637.2.a.k.1.3		5	7.2	even	3
637.2.a.l.1.3		5	7.5	odd	6
637.2.e.m.79.3		10	1.1	even	1	trivial
637.2.e.m.508.3		10	7.4	even	3	inner
819.2.j.h.235.3		10	21.17	even	6
819.2.j.h.352.3		10	21.20	even	2
1183.2.e.f.170.3		10	91.90	odd	2
1183.2.e.f.508.3		10	91.38	odd	6
1456.2.r.p.417.1		10	28.3	even	6
1456.2.r.p.625.1		10	28.27	even	2
5733.2.a.bl.1.3		5	21.5	even	6
5733.2.a.bm.1.3		5	21.2	odd	6
8281.2.a.bw.1.3		5	91.12	odd	6
8281.2.a.bx.1.3		5	91.51	even	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.632804 + 1.09605i) q^{2} +(-1.31364 - 2.27529i) q^{3} +(0.199118 + 0.344882i) q^{4} +(-1.45130 + 2.51373i) q^{5} +3.32511 q^{6} -3.03523 q^{8} +(-1.95130 + 3.37975i) q^{9} +O(q^{10})\)	\(q+(-0.632804 + 1.09605i) q^{2} +(-1.31364 - 2.27529i) q^{3} +(0.199118 + 0.344882i) q^{4} +(-1.45130 + 2.51373i) q^{5} +3.32511 q^{6} -3.03523 q^{8} +(-1.95130 + 3.37975i) q^{9} +(-1.83678 - 3.18139i) q^{10} +(-1.01828 - 1.76372i) q^{11} +(0.523138 - 0.906101i) q^{12} -1.00000 q^{13} +7.62594 q^{15} +(1.52247 - 2.63699i) q^{16} +(1.99933 + 3.46294i) q^{17} +(-2.46958 - 4.27744i) q^{18} +(3.48105 - 6.02935i) q^{19} -1.15592 q^{20} +2.57749 q^{22} +(0.313640 - 0.543240i) q^{23} +(3.98720 + 6.90602i) q^{24} +(-1.71254 - 2.96621i) q^{25} +(0.632804 - 1.09605i) q^{26} +2.37138 q^{27} +1.09606 q^{29} +(-4.82573 + 8.35841i) q^{30} +(-5.21624 - 9.03479i) q^{31} +(-1.10838 - 1.91977i) q^{32} +(-2.67531 + 4.63378i) q^{33} -5.06074 q^{34} -1.55415 q^{36} +(1.54268 - 2.67201i) q^{37} +(4.40565 + 7.63080i) q^{38} +(1.31364 + 2.27529i) q^{39} +(4.40502 - 7.62973i) q^{40} +0.521150 q^{41} +0.329024 q^{43} +(0.405516 - 0.702374i) q^{44} +(-5.66384 - 9.81006i) q^{45} +(0.396945 + 0.687530i) q^{46} +(5.27284 - 9.13283i) q^{47} -7.99991 q^{48} +4.33482 q^{50} +(5.25280 - 9.09812i) q^{51} +(-0.199118 - 0.344882i) q^{52} +(-3.55950 - 6.16523i) q^{53} +(-1.50062 + 2.59915i) q^{54} +5.91133 q^{55} -18.2914 q^{57} +(-0.693593 + 1.20134i) q^{58} +(1.01828 + 1.76372i) q^{59} +(1.51846 + 2.63005i) q^{60} +(1.20041 - 2.07917i) q^{61} +13.2034 q^{62} +8.89542 q^{64} +(1.45130 - 2.51373i) q^{65} +(-3.38590 - 5.86455i) q^{66} +(-7.34709 - 12.7255i) q^{67} +(-0.796204 + 1.37907i) q^{68} -1.64804 q^{69} +3.60141 q^{71} +(5.92264 - 10.2583i) q^{72} +(1.48786 + 2.57706i) q^{73} +(1.95243 + 3.38172i) q^{74} +(-4.49933 + 7.79307i) q^{75} +2.77255 q^{76} -3.32511 q^{78} +(4.38075 - 7.58769i) q^{79} +(4.41912 + 7.65414i) q^{80} +(2.73876 + 4.74367i) q^{81} +(-0.329786 + 0.571206i) q^{82} -12.8039 q^{83} -11.6065 q^{85} +(-0.208208 + 0.360627i) q^{86} +(-1.43983 - 2.49386i) q^{87} +(3.09072 + 5.35328i) q^{88} +(-1.34049 + 2.32180i) q^{89} +14.3364 q^{90} +0.249805 q^{92} +(-13.7045 + 23.7369i) q^{93} +(6.67335 + 11.5586i) q^{94} +(10.1041 + 17.5008i) q^{95} +(-2.91202 + 5.04376i) q^{96} +2.32902 q^{97} +7.94789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9	\( 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9} - 5 q^{10} - 11 q^{11} + 5 q^{12} - 10 q^{13} - 10 q^{16} - 5 q^{17} - 9 q^{18} + 9 q^{19} - 2 q^{20} + 16 q^{22} - 10 q^{23} - 9 q^{25} + 4 q^{26} - 6 q^{29} + 13 q^{30} - 6 q^{31} - 22 q^{32} + 8 q^{33} + 44 q^{34} + 14 q^{36} - 4 q^{37} - 10 q^{38} + 28 q^{40} - 28 q^{41} + 4 q^{43} - 32 q^{45} - 3 q^{46} + q^{47} + 46 q^{48} + 18 q^{50} + 8 q^{51} + 8 q^{52} - 17 q^{53} + 23 q^{54} - 32 q^{57} + 27 q^{58} + 11 q^{59} + 29 q^{60} - 11 q^{61} + 46 q^{62} + 18 q^{64} - 2 q^{65} + 21 q^{66} - 13 q^{67} - 32 q^{68} - 36 q^{69} + 30 q^{71} + 19 q^{72} + 33 q^{74} - 20 q^{75} - 16 q^{76} - 10 q^{78} - 2 q^{79} + 55 q^{80} + 19 q^{81} + 34 q^{82} - 12 q^{83} - 44 q^{85} - 28 q^{86} - 8 q^{87} + 3 q^{88} - 4 q^{89} + 68 q^{90} + 42 q^{92} - 18 q^{93} + 20 q^{94} + 12 q^{95} - 37 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9 - 5 * q^10 - 11 * q^11 + 5 * q^12 - 10 * q^13 - 10 * q^16 - 5 * q^17 - 9 * q^18 + 9 * q^19 - 2 * q^20 + 16 * q^22 - 10 * q^23 - 9 * q^25 + 4 * q^26 - 6 * q^29 + 13 * q^30 - 6 * q^31 - 22 * q^32 + 8 * q^33 + 44 * q^34 + 14 * q^36 - 4 * q^37 - 10 * q^38 + 28 * q^40 - 28 * q^41 + 4 * q^43 - 32 * q^45 - 3 * q^46 + q^47 + 46 * q^48 + 18 * q^50 + 8 * q^51 + 8 * q^52 - 17 * q^53 + 23 * q^54 - 32 * q^57 + 27 * q^58 + 11 * q^59 + 29 * q^60 - 11 * q^61 + 46 * q^62 + 18 * q^64 - 2 * q^65 + 21 * q^66 - 13 * q^67 - 32 * q^68 - 36 * q^69 + 30 * q^71 + 19 * q^72 + 33 * q^74 - 20 * q^75 - 16 * q^76 - 10 * q^78 - 2 * q^79 + 55 * q^80 + 19 * q^81 + 34 * q^82 - 12 * q^83 - 44 * q^85 - 28 * q^86 - 8 * q^87 + 3 * q^88 - 4 * q^89 + 68 * q^90 + 42 * q^92 - 18 * q^93 + 20 * q^94 + 12 * q^95 - 37 * q^96 + 24 * q^97 + 22 * q^99

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