LMFDB - Embedded newform 63.6.e.d.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{37})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 10x^{2} + 9x + 81 $ x^4 - x^3 + 10x^2 + 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.2
Root			$1.77069 + 3.06693i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.d.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.54138 + 6.13385i) q^{2} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +(43.1587 - 122.247i) q^{7} +97.9863 q^{8} +O(q^{10})$	\(q+(3.54138 + 6.13385i) q^{2} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +(43.1587 - 122.247i) q^{7} +97.9863 q^{8} +(282.700 - 489.651i) q^{10} +(175.952 - 304.757i) q^{11} -291.683 q^{13} +(902.686 - 168.194i) q^{14} +(637.655 + 1104.45i) q^{16} +(-185.038 + 320.495i) q^{17} +(-752.463 - 1303.30i) q^{19} +1450.11 q^{20} +2492.45 q^{22} +(-212.855 - 368.676i) q^{23} +(-1623.72 + 2812.37i) q^{25} +(-1032.96 - 1789.14i) q^{26} +(1531.17 + 1789.30i) q^{28} +7783.93 q^{29} +(1287.59 - 2230.17i) q^{31} +(-2948.58 + 5107.09i) q^{32} -2621.16 q^{34} +(-10173.9 + 1895.67i) q^{35} +(-369.809 - 640.528i) q^{37} +(5329.51 - 9230.99i) q^{38} +(-3911.01 - 6774.06i) q^{40} -7029.84 q^{41} +1835.23 q^{43} +(3196.26 + 5536.08i) q^{44} +(1507.60 - 2611.25i) q^{46} +(-766.342 - 1327.34i) q^{47} +(-13081.7 - 10552.0i) q^{49} -23000.9 q^{50} +(2649.28 - 4588.69i) q^{52} +(-4768.73 + 8259.68i) q^{53} -28091.6 q^{55} +(4228.96 - 11978.5i) q^{56} +(27565.9 + 47745.5i) q^{58} +(-14837.0 + 25698.5i) q^{59} +(23255.4 + 40279.5i) q^{61} +18239.4 q^{62} -958.246 q^{64} +(11642.2 + 20164.8i) q^{65} +(-13373.0 + 23162.8i) q^{67} +(-3361.31 - 5821.95i) q^{68} +(-47657.4 - 55691.9i) q^{70} +14388.8 q^{71} +(35047.6 - 60704.2i) q^{73} +(2619.27 - 4536.71i) q^{74} +27337.8 q^{76} +(-29661.8 - 34662.5i) q^{77} +(13542.9 + 23457.0i) q^{79} +(50902.5 - 88165.7i) q^{80} +(-24895.3 - 43120.0i) q^{82} +79755.4 q^{83} +29542.2 q^{85} +(6499.26 + 11257.0i) q^{86} +(17240.9 - 29862.1i) q^{88} +(21788.7 + 37739.1i) q^{89} +(-12588.6 + 35657.3i) q^{91} +7733.26 q^{92} +(5427.82 - 9401.25i) q^{94} +(-60067.3 + 104040. i) q^{95} +103374. q^{97} +(18397.5 - 117610. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8	$ 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8} + 778 q^{10} + 424 q^{11} - 1848 q^{13} + 2674 q^{14} + 2064 q^{16} - 2346 q^{17} + 360 q^{19} + 3416 q^{20} + 4252 q^{22} - 12 q^{23} - 1872 q^{25} + 1148 q^{26} + 2548 q^{28} + 14104 q^{29} - 3548 q^{31} - 8096 q^{32} + 14844 q^{34} - 27496 q^{35} - 11090 q^{37} + 20138 q^{38} - 15936 q^{40} - 7000 q^{41} - 25360 q^{43} + 5948 q^{44} + 5118 q^{46} - 22956 q^{47} + 4900 q^{49} - 59984 q^{50} + 1400 q^{52} + 3042 q^{53} - 50152 q^{55} + 57792 q^{56} + 58852 q^{58} - 65808 q^{59} + 42486 q^{61} + 98724 q^{62} + 70912 q^{64} - 3164 q^{65} - 42312 q^{67} + 5460 q^{68} - 113050 q^{70} + 4416 q^{71} + 50506 q^{73} - 47370 q^{74} + 77672 q^{76} - 65338 q^{77} - 9004 q^{79} + 68816 q^{80} - 67732 q^{82} + 208656 q^{83} - 106212 q^{85} + 86776 q^{86} + 20496 q^{88} - 26666 q^{89} + 135632 q^{91} + 20568 q^{92} - 98034 q^{94} - 198140 q^{95} + 418264 q^{97} - 98686 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8 + 778 * q^10 + 424 * q^11 - 1848 * q^13 + 2674 * q^14 + 2064 * q^16 - 2346 * q^17 + 360 * q^19 + 3416 * q^20 + 4252 * q^22 - 12 * q^23 - 1872 * q^25 + 1148 * q^26 + 2548 * q^28 + 14104 * q^29 - 3548 * q^31 - 8096 * q^32 + 14844 * q^34 - 27496 * q^35 - 11090 * q^37 + 20138 * q^38 - 15936 * q^40 - 7000 * q^41 - 25360 * q^43 + 5948 * q^44 + 5118 * q^46 - 22956 * q^47 + 4900 * q^49 - 59984 * q^50 + 1400 * q^52 + 3042 * q^53 - 50152 * q^55 + 57792 * q^56 + 58852 * q^58 - 65808 * q^59 + 42486 * q^61 + 98724 * q^62 + 70912 * q^64 - 3164 * q^65 - 42312 * q^67 + 5460 * q^68 - 113050 * q^70 + 4416 * q^71 + 50506 * q^73 - 47370 * q^74 + 77672 * q^76 - 65338 * q^77 - 9004 * q^79 + 68816 * q^80 - 67732 * q^82 + 208656 * q^83 - 106212 * q^85 + 86776 * q^86 + 20496 * q^88 - 26666 * q^89 + 135632 * q^91 + 20568 * q^92 - 98034 * q^94 - 198140 * q^95 + 418264 * q^97 - 98686 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	3.54138	+	6.13385i	0.626034	+	1.08432i	0.988340	+	0.152263i	$0.0486561\pi$
$2$	3.54138	+	6.13385i	0.626034	+	1.08432i	−0.362306	+	0.932059i	$0.618011\pi$
$3$		0			0
$3$		0			0
$4$	−9.08276	+	15.7318i	−0.283836	+	0.491619i
$5$	−39.9138	−	69.1328i	−0.714000	−	1.23668i	−0.963344	−	0.268269i	$-0.913548\pi$
$5$	−39.9138	−	69.1328i	−0.714000	−	1.23668i	0.249344	−	0.968415i	$-0.419785\pi$
$6$		0			0
$7$	43.1587	−	122.247i	0.332907	−	0.942960i
$7$	43.1587	−	122.247i	0.332907	−	0.942960i
$8$	97.9863			0.541303
$9$		0			0
$10$	282.700	−	489.651i	0.893976	−	1.54841i
$11$	175.952	−	304.757i	0.438442	−	0.759403i	−0.559128	−	0.829082i	$-0.688864\pi$
$11$	175.952	−	304.757i	0.438442	−	0.759403i	0.997570	+	0.0696781i	$0.0221972\pi$
$12$		0			0
$13$	−291.683			−0.478688			−0.239344	−	0.970935i	$-0.576932\pi$
$13$	−291.683			−0.478688			−0.239344	+	0.970935i	$0.576932\pi$
$14$	902.686	−	168.194i	1.23088	−	0.229346i
$15$		0			0
$16$	637.655	+	1104.45i	0.622710	+	1.07857i
$17$	−185.038	+	320.495i	−0.155288	+	0.268967i	−0.933164	−	0.359451i	$-0.882964\pi$
$17$	−185.038	+	320.495i	−0.155288	+	0.268967i	0.777876	+	0.628418i	$0.216297\pi$
$18$		0			0
$19$	−752.463	−	1303.30i	−0.478190	−	0.828250i	0.521497	−	0.853253i	$-0.325374\pi$
$19$	−752.463	−	1303.30i	−0.478190	−	0.828250i	−0.999687	+	0.0250030i	$0.992040\pi$
$20$	1450.11			0.810637
$21$		0			0
$22$	2492.45			1.09792
$23$	−212.855	−	368.676i	−0.0839006	−	0.145320i	0.821022	−	0.570897i	$-0.193404\pi$
$23$	−212.855	−	368.676i	−0.0839006	−	0.145320i	−0.904922	+	0.425577i	$0.860071\pi$
$24$		0			0
$25$	−1623.72	+	2812.37i	−0.519592	+	0.899960i
$26$	−1032.96	−	1789.14i	−0.299675	−	0.519052i
$27$		0			0
$28$	1531.17	+	1789.30i	0.369086	+	0.431310i
$29$	7783.93			1.71872			0.859358	−	0.511374i	$-0.170863\pi$
$29$	7783.93			1.71872			0.859358	+	0.511374i	$0.170863\pi$
$30$		0			0
$31$	1287.59	−	2230.17i	0.240643	−	0.416805i	−0.720255	−	0.693710i	$-0.755975\pi$
$31$	1287.59	−	2230.17i	0.240643	−	0.416805i	0.960898	+	0.276904i	$0.0893085\pi$
$32$	−2948.58	+	5107.09i	−0.509024	+	0.881655i
$33$		0			0
$34$	−2621.16			−0.388862
$35$	−10173.9	+	1895.67i	−1.40384	+	0.261572i
$36$		0			0
$37$	−369.809	−	640.528i	−0.0444092	−	0.0769190i	0.842966	−	0.537966i	$-0.180807\pi$
$37$	−369.809	−	640.528i	−0.0444092	−	0.0769190i	−0.887376	+	0.461047i	$0.847474\pi$
$38$	5329.51	−	9230.99i	0.598727	−	1.03703i
$39$		0			0
$40$	−3911.01	−	6774.06i	−0.386490	−	0.669421i
$41$	−7029.84			−0.653109			−0.326554	−	0.945178i	$-0.605888\pi$
$41$	−7029.84			−0.653109			−0.326554	+	0.945178i	$0.605888\pi$
$42$		0			0
$43$	1835.23			0.151363			0.0756816	−	0.997132i	$-0.475887\pi$
$43$	1835.23			0.151363			0.0756816	+	0.997132i	$0.475887\pi$
$44$	3196.26	+	5536.08i	0.248891	+	0.431093i
$45$		0			0
$46$	1507.60	−	2611.25i	0.105049	−	0.181950i
$47$	−766.342	−	1327.34i	−0.0506032	−	0.0876473i	0.839614	−	0.543183i	$-0.182781\pi$
$47$	−766.342	−	1327.34i	−0.0506032	−	0.0876473i	−0.890217	+	0.455536i	$0.849448\pi$
$48$		0			0
$49$	−13081.7	−	10552.0i	−0.778346	−	0.627836i
$50$	−23000.9			−1.30113
$51$		0			0
$52$	2649.28	−	4588.69i	0.135869	−	0.235332i
$53$	−4768.73	+	8259.68i	−0.233192	+	0.403900i	−0.958746	−	0.284265i	$-0.908250\pi$
$53$	−4768.73	+	8259.68i	−0.233192	+	0.403900i	0.725554	+	0.688165i	$0.241584\pi$
$54$		0			0
$55$	−28091.6			−1.25219
$56$	4228.96	−	11978.5i	0.180204	−	0.510427i
$57$		0			0
$58$	27565.9	+	47745.5i	1.07597	+	1.86364i
$59$	−14837.0	+	25698.5i	−0.554903	+	0.961120i	0.443008	+	0.896517i	$0.353911\pi$
$59$	−14837.0	+	25698.5i	−0.554903	+	0.961120i	−0.997911	+	0.0646022i	$0.979422\pi$
$60$		0			0
$61$	23255.4	+	40279.5i	0.800201	+	1.38599i	0.919483	+	0.393129i	$0.128607\pi$
$61$	23255.4	+	40279.5i	0.800201	+	1.38599i	−0.119282	+	0.992860i	$0.538059\pi$
$62$	18239.4			0.602602
$63$		0			0
$64$	−958.246			−0.0292434
$65$	11642.2	+	20164.8i	0.341783	+	0.591985i
$66$		0			0
$67$	−13373.0	+	23162.8i	−0.363951	+	0.630381i	−0.988607	−	0.150518i	$-0.951906\pi$
$67$	−13373.0	+	23162.8i	−0.363951	+	0.630381i	0.624656	+	0.780900i	$0.285239\pi$
$68$	−3361.31	−	5821.95i	−0.0881527	−	0.152685i
$69$		0			0
$70$	−47657.4	−	55691.9i	−1.16248	−	1.35846i
$71$	14388.8			0.338748			0.169374	−	0.985552i	$-0.445825\pi$
$71$	14388.8			0.338748			0.169374	+	0.985552i	$0.445825\pi$
$72$		0			0
$73$	35047.6	−	60704.2i	0.769752	−	1.33325i	−0.167946	−	0.985796i	$-0.553713\pi$
$73$	35047.6	−	60704.2i	0.769752	−	1.33325i	0.937697	−	0.347453i	$-0.112953\pi$
$74$	2619.27	−	4536.71i	0.0556033	−	0.0963078i
$75$		0			0
$76$	27337.8			0.542911
$77$	−29661.8	−	34662.5i	−0.570126	−	0.666244i
$78$		0			0
$79$	13542.9	+	23457.0i	0.244143	+	0.422868i	0.961890	−	0.273436i	$-0.0881601\pi$
$79$	13542.9	+	23457.0i	0.244143	+	0.422868i	−0.717748	+	0.696303i	$0.754827\pi$
$80$	50902.5	−	88165.7i	0.889230	−	1.54019i
$81$		0			0
$82$	−24895.3	−	43120.0i	−0.408868	−	0.708181i
$83$	79755.4			1.27076			0.635382	−	0.772198i	$-0.280843\pi$
$83$	79755.4			1.27076			0.635382	+	0.772198i	$0.280843\pi$
$84$		0			0
$85$	29542.2			0.443502
$86$	6499.26	+	11257.0i	0.0947584	+	0.164126i
$87$		0			0
$88$	17240.9	−	29862.1i	0.237330	−	0.411067i
$89$	21788.7	+	37739.1i	0.291579	+	0.505029i	0.974183	−	0.225759i	$-0.0724862\pi$
$89$	21788.7	+	37739.1i	0.291579	+	0.505029i	−0.682605	+	0.730788i	$0.739153\pi$
$90$		0			0
$91$	−12588.6	+	35657.3i	−0.159358	+	0.451383i
$92$	7733.26			0.0952561
$93$		0			0
$94$	5427.82	−	9401.25i	0.0633586	−	0.109740i
$95$	−60067.3	+	104040.i	−0.682856	+	1.18274i
$96$		0			0
$97$	103374.			1.11553			0.557765	−	0.829999i	$-0.311659\pi$
$97$	103374.			1.11553			0.557765	+	0.829999i	$0.311659\pi$
$98$	18397.5	−	117610.i	0.193506	−	1.23702i
$99$		0			0
$100$	−29495.8	−	51088.3i	−0.294958	−	0.510883i
$101$	14350.1	−	24855.1i	0.139975	−	0.242444i	−0.787512	−	0.616300i	$-0.788631\pi$
$101$	14350.1	−	24855.1i	0.139975	−	0.242444i	0.927487	+	0.373855i	$0.121964\pi$
$102$		0			0
$103$	−14614.0	−	25312.1i	−0.135730	−	0.235091i	0.790146	−	0.612918i	$-0.210005\pi$
$103$	−14614.0	−	25312.1i	−0.135730	−	0.235091i	−0.925876	+	0.377828i	$0.876671\pi$
$104$	−28580.9			−0.259115
$105$		0			0
$106$	−67551.6			−0.583944
$107$	43929.2	+	76087.6i	0.370932	+	0.642472i	0.989709	−	0.143094i	$-0.0457051\pi$
$107$	43929.2	+	76087.6i	0.370932	+	0.642472i	−0.618778	+	0.785566i	$0.712372\pi$
$108$		0			0
$109$	−110314.	+	191069.i	−0.889333	+	1.54037i	−0.0486678	+	0.998815i	$0.515498\pi$
$109$	−110314.	+	191069.i	−0.889333	+	1.54037i	−0.840665	+	0.541555i	$0.817836\pi$
$110$	−99483.2	−	172310.i	−0.783913	−	1.35778i
$111$		0			0
$112$	162536.	−	30284.8i	1.22435	−	0.228128i
$113$	−39665.6			−0.292225			−0.146113	−	0.989268i	$-0.546676\pi$
$113$	−39665.6			−0.292225			−0.146113	+	0.989268i	$0.546676\pi$
$114$		0			0
$115$	−16991.7	+	29430.5i	−0.119810	+	0.207517i
$116$	−70699.6	+	122455.i	−0.487834	+	0.844953i
$117$		0			0
$118$	−210174.			−1.38955
$119$	31193.5	+	36452.4i	0.201928	+	0.235971i
$120$		0			0
$121$	18607.4	+	32229.0i	0.115538	+	0.200117i
$122$	−164712.	+	285290.i	−1.00191	+	1.73535i
$123$		0			0
$124$	23389.7	+	40512.2i	0.136606	+	0.236609i
$125$	9774.87			0.0559546
$126$		0			0
$127$	51740.3			0.284655			0.142328	−	0.989820i	$-0.454541\pi$
$127$	51740.3			0.284655			0.142328	+	0.989820i	$0.454541\pi$
$128$	90961.0	+	157549.i	0.490716	+	0.849946i
$129$		0			0
$130$	−82458.7	+	142823.i	−0.427935	+	0.741206i
$131$	−83336.9	−	144344.i	−0.424286	−	0.734885i	0.572067	−	0.820207i	$-0.306142\pi$
$131$	−83336.9	−	144344.i	−0.424286	−	0.734885i	−0.996353	+	0.0853215i	$0.972808\pi$
$132$		0			0
$133$	−191800.	+	35737.4i	−0.940200	+	0.175184i
$134$	−189436.			−0.911382
$135$		0			0
$136$	−18131.2	+	31404.1i	−0.0840578	+	0.145592i
$137$	14129.7	−	24473.4i	0.0643178	−	0.111402i	−0.832073	−	0.554666i	$-0.812846\pi$
$137$	14129.7	−	24473.4i	0.0643178	−	0.111402i	0.896391	+	0.443264i	$0.146180\pi$
$138$		0			0
$139$	336393.			1.47676			0.738380	−	0.674384i	$-0.235591\pi$
$139$	336393.			1.47676			0.738380	+	0.674384i	$0.235591\pi$
$140$	62584.9	−	177272.i	0.269867	−	0.764398i
$141$		0			0
$142$	50956.1	+	88258.5i	0.212068	+	0.367312i
$143$	−51322.1	+	88892.4i	−0.209877	+	0.363517i
$144$		0			0
$145$	−310686.	−	538125.i	−1.22716	−	2.12551i
$146$	496467.			1.92756
$147$		0			0
$148$	13435.5			0.0504198
$149$	−177691.	−	307769.i	−0.655691	−	1.13569i	−0.981720	−	0.190330i	$-0.939044\pi$
$149$	−177691.	−	307769.i	−0.655691	−	1.13569i	0.326030	−	0.945360i	$-0.394289\pi$
$150$		0			0
$151$	179399.	−	310727.i	0.640290	−	1.10901i	−0.345078	−	0.938574i	$-0.612148\pi$
$151$	179399.	−	310727.i	0.640290	−	1.10901i	0.985368	−	0.170441i	$-0.0545191\pi$
$152$	−73731.0	−	127706.i	−0.258846	−	0.448334i
$153$		0			0
$154$	107571.	−	304694.i	0.365504	−	1.03529i
$155$	−205570.			−0.687275
$156$		0			0
$157$	−229455.	+	397428.i	−0.742932	+	1.28680i	0.208223	+	0.978081i	$0.433232\pi$
$157$	−229455.	+	397428.i	−0.742932	+	1.28680i	−0.951155	+	0.308714i	$0.900101\pi$
$158$	−95921.1	+	166140.i	−0.305683	+	0.529459i
$159$		0			0
$160$	470756.			1.45377
$161$	−54256.1	+	10109.3i	−0.164962	+	0.0307368i
$162$		0			0
$163$	−251220.	−	435126.i	−0.740603	−	1.28276i	−0.952221	−	0.305410i	$-0.901206\pi$
$163$	−251220.	−	435126.i	−0.740603	−	1.28276i	0.211618	−	0.977353i	$-0.432127\pi$
$164$	63850.3	−	110592.i	0.185376	−	0.321081i
$165$		0			0
$166$	282444.	+	489208.i	0.795541	+	1.37792i
$167$	676652.			1.87748			0.938738	−	0.344632i	$-0.111996\pi$
$167$	676652.			1.87748			0.938738	+	0.344632i	$0.111996\pi$
$168$		0			0
$169$	−286214.			−0.770858
$170$	104620.	+	181208.i	0.277647	+	0.480900i
$171$		0			0
$172$	−16669.0	+	28871.5i	−0.0429623	+	0.0744130i
$173$	−124580.	−	215779.i	−0.316470	−	0.548143i	0.663279	−	0.748373i	$-0.269164\pi$
$173$	−124580.	−	215779.i	−0.316470	−	0.548143i	−0.979749	+	0.200230i	$0.935831\pi$
$174$		0			0
$175$	273726.	+	319874.i	0.675650	+	0.789557i
$176$	448786.			1.09209
$177$		0			0
$178$	−154324.	+	267297.i	−0.365076	+	0.632330i
$179$	69628.9	−	120601.i	0.162427	−	0.281331i	−0.773312	−	0.634026i	$-0.781401\pi$
$179$	69628.9	−	120601.i	0.162427	−	0.281331i	0.935738	+	0.352695i	$0.114735\pi$
$180$		0			0
$181$	306246.			0.694823			0.347412	−	0.937713i	$-0.387061\pi$
$181$	306246.			0.694823			0.347412	+	0.937713i	$0.387061\pi$
$182$	−263298.	+	49059.4i	−0.589209	+	0.109785i
$183$		0			0
$184$	−20856.9	−	36125.2i	−0.0454156	−	0.0786622i
$185$	−29521.0	+	51131.8i	−0.0634163	+	0.109840i
$186$		0			0
$187$	65115.4	+	112783.i	0.136169	+	0.235852i
$188$	27842.0			0.0574521
$189$		0			0
$190$	−850885.			−1.70996
$191$	113747.	+	197015.i	0.225609	+	0.390766i	0.956502	−	0.291726i	$-0.0942295\pi$
$191$	113747.	+	197015.i	0.225609	+	0.390766i	−0.730893	+	0.682492i	$0.760896\pi$
$192$		0			0
$193$	336187.	−	582293.i	0.649663	−	1.12525i	−0.333541	−	0.942736i	$-0.608244\pi$
$193$	336187.	−	582293.i	0.649663	−	1.12525i	0.983203	−	0.182513i	$-0.0584231\pi$
$194$	366086.	+	634079.i	0.698359	+	1.20959i
$195$		0			0
$196$	284820.	−	109956.i	0.529579	−	0.204447i
$197$	1282.76			0.00235493			0.00117747	−	0.999999i	$-0.499625\pi$
$197$	1282.76			0.00235493			0.00117747	+	0.999999i	$0.499625\pi$
$198$		0			0
$199$	−184449.	+	319475.i	−0.330175	+	0.571879i	−0.982546	−	0.186020i	$-0.940441\pi$
$199$	−184449.	+	319475.i	−0.330175	+	0.571879i	0.652371	+	0.757900i	$0.273774\pi$
$200$	−159103.	+	275574.i	−0.281257	+	0.487151i
$201$		0			0
$202$	203277.			0.350517
$203$	335944.	−	951563.i	0.572173	−	1.62068i
$204$		0			0
$205$	280588.	+	485992.i	0.466320	+	0.807690i
$206$	103507.	−	179280.i	0.169943	−	0.294349i
$207$		0			0
$208$	−185993.	−	322149.i	−0.298084	−	0.516296i
$209$	−529589.			−0.838635
$210$		0			0
$211$	502168.			0.776503			0.388251	−	0.921553i	$-0.373079\pi$
$211$	502168.			0.776503			0.388251	+	0.921553i	$0.373079\pi$
$212$	−86626.5	−	150042.i	−0.132377	−	0.229283i
$213$		0			0
$214$	−311140.	+	538910.i	−0.464431	+	0.804419i
$215$	−73251.1	−	126875.i	−0.108073	−	0.187188i
$216$		0			0
$217$	−217061.	−	253655.i	−0.312919	−	0.365674i
$218$	−1.56266e6			−2.22701
$219$		0			0
$220$	255150.	−	441932.i	0.355417	−	0.615600i
$221$	53972.3	−	93482.7i	0.0743344	−	0.128751i
$222$		0			0
$223$	−1.17328e6			−1.57993			−0.789967	−	0.613149i	$-0.789902\pi$
$223$	−1.17328e6			−1.57993			−0.789967	+	0.613149i	$0.789902\pi$
$224$	497070.	+	580870.i	0.661907	+	0.773498i
$225$		0			0
$226$	−140471.	−	243303.i	−0.182943	−	0.316867i
$227$	−455079.	+	788220.i	−0.586168	+	1.01527i	0.408560	+	0.912731i	$0.366031\pi$
$227$	−455079.	+	788220.i	−0.586168	+	1.01527i	−0.994729	+	0.102542i	$0.967302\pi$
$228$		0			0
$229$	−260962.	−	452000.i	−0.328843	−	0.569573i	0.653439	−	0.756979i	$-0.273325\pi$
$229$	−260962.	−	452000.i	−0.328843	−	0.569573i	−0.982283	+	0.187406i	$0.939992\pi$
$230$	−240697.			−0.300020
$231$		0			0
$232$	762719.			0.930346
$233$	−521394.	−	903081.i	−0.629182	−	1.08977i	−0.987716	−	0.156258i	$-0.950057\pi$
$233$	−521394.	−	903081.i	−0.629182	−	1.08977i	0.358535	−	0.933516i	$-0.383277\pi$
$234$		0			0
$235$	−61175.2	+	105959.i	−0.0722613	+	0.125160i
$236$	−269522.	−	466826.i	−0.315003	−	0.545601i
$237$		0			0
$238$	−113126.	+	320428.i	−0.129455	+	0.366681i
$239$	1.53447e6			1.73766			0.868830	−	0.495110i	$-0.164872\pi$
$239$	1.53447e6			1.73766			0.868830	+	0.495110i	$0.164872\pi$
$240$		0			0
$241$	503789.	−	872588.i	0.558735	−	0.967758i	−0.438867	−	0.898552i	$-0.644620\pi$
$241$	503789.	−	872588.i	0.558735	−	0.967758i	0.997602	−	0.0692059i	$-0.0220465\pi$
$242$	−131792.	+	228271.i	−0.144661	+	0.250560i
$243$		0			0
$244$	−844893.			−0.908505
$245$	−207353.	+	1.32554e6i	−0.220696	+	1.41084i
$246$		0			0
$247$	219480.	+	380151.i	0.228904	+	0.396473i
$248$	126166.	−	218526.i	0.130261	−	0.225618i
$249$		0			0
$250$	34616.6	+	59957.6i	0.0350295	+	0.0606729i
$251$	−8511.89			−0.00852789			−0.00426394	−	0.999991i	$-0.501357\pi$
$251$	−8511.89			−0.00852789			−0.00426394	+	0.999991i	$0.501357\pi$
$252$		0			0
$253$	−149809.			−0.147142
$254$	183232.	+	317367.i	0.178204	+	0.308658i
$255$		0			0
$256$	−659587.	+	1.14244e6i	−0.629032	+	1.08951i
$257$	−263766.	−	456856.i	−0.249107	−	0.431466i	0.714171	−	0.699971i	$-0.246804\pi$
$257$	−263766.	−	456856.i	−0.249107	−	0.431466i	−0.963278	+	0.268505i	$0.913470\pi$
$258$		0			0
$259$	−94263.0	+	17563.7i	−0.0873156	+	0.0162692i
$260$	−422972.			−0.388042
$261$		0			0
$262$	590255.	−	1.02235e6i	0.531235	−	0.920126i
$263$	−176042.	+	304914.i	−0.156938	+	0.271824i	−0.933763	−	0.357892i	$-0.883496\pi$
$263$	−176042.	+	304914.i	−0.156938	+	0.271824i	0.776825	+	0.629716i	$0.216829\pi$
$264$		0			0
$265$	761353.			0.665996
$266$	−898446.	−	1.04991e6i	−0.778552	−	0.909808i
$267$		0			0
$268$	−242928.	−	420764.i	−0.206605	−	0.357850i
$269$	239770.	−	415294.i	0.202029	−	0.349925i	−0.747153	−	0.664652i	$-0.768580\pi$
$269$	239770.	−	415294.i	0.202029	−	0.349925i	0.949182	+	0.314727i	$0.101913\pi$
$270$		0			0
$271$	488805.	+	846636.i	0.404308	+	0.700283i	0.994241	−	0.107170i	$-0.0341789\pi$
$271$	488805.	+	846636.i	0.404308	+	0.700283i	−0.589932	+	0.807453i	$0.700846\pi$
$272$	−471961.			−0.386798
$273$		0			0
$274$	200155.			0.161061
$275$	571395.	+	989684.i	0.455622	+	0.789160i
$276$		0			0
$277$	−484362.	+	838939.i	−0.379289	+	0.656948i	−0.990959	−	0.134165i	$-0.957165\pi$
$277$	−484362.	+	838939.i	−0.379289	+	0.656948i	0.611670	+	0.791113i	$0.290498\pi$
$278$	1.19130e6	+	2.06339e6i	0.924502	+	1.60128i
$279$		0			0
$280$	−996903.	+	185749.i	−0.759902	+	0.141590i
$281$	318333.			0.240501			0.120250	−	0.992744i	$-0.461630\pi$
$281$	318333.			0.240501			0.120250	+	0.992744i	$0.461630\pi$
$282$		0			0
$283$	−886051.	+	1.53468e6i	−0.657646	+	1.13908i	0.323577	+	0.946202i	$0.395115\pi$
$283$	−886051.	+	1.53468e6i	−0.657646	+	1.13908i	−0.981223	+	0.192875i	$0.938219\pi$
$284$	−130690.	+	226361.i	−0.0961491	+	0.166535i
$285$		0			0
$286$	−727004.			−0.525559
$287$	−303398.	+	859377.i	−0.217425	+	0.615855i
$288$		0			0
$289$	641451.	+	1.11103e6i	0.451771	+	0.782491i
$290$	2.20052e6	−	3.81141e6i	1.53649	−	2.66128i
$291$		0			0
$292$	636657.	+	1.10272e6i	0.436967	+	0.756849i
$293$	−1.64148e6			−1.11703			−0.558516	−	0.829494i	$-0.688629\pi$
$293$	−1.64148e6			−1.11703			−0.558516	+	0.829494i	$0.688629\pi$
$294$		0			0
$295$	2.36881e6			1.58480
$296$	−36236.2	−	62762.9i	−0.0240388	−	0.0416365i
$297$		0			0
$298$	1.25854e6	−	2.17986e6i	0.820969	−	1.42196i
$299$	62086.2	+	107536.i	0.0401622	+	0.0695629i
$300$		0			0
$301$	79206.2	−	224352.i	0.0503898	−	0.142729i
$302$	2.54128e6			1.60337
$303$		0			0
$304$	959623.	−	1.66212e6i	0.595548	−	1.03152i
$305$	1.85642e6	−	3.21542e6i	1.14269	−	1.97919i
$306$		0			0
$307$	−466930.			−0.282752			−0.141376	−	0.989956i	$-0.545153\pi$
$307$	−466930.			−0.282752			−0.141376	+	0.989956i	$0.545153\pi$
$308$	814715.	−	151803.i	0.489361	−	0.0911808i
$309$		0			0
$310$	−728002.	−	1.26094e6i	−0.430257	−	0.745228i
$311$	−1.21898e6	+	2.11134e6i	−0.714654	+	1.23782i	0.248439	+	0.968647i	$0.420082\pi$
$311$	−1.21898e6	+	2.11134e6i	−0.714654	+	1.23782i	−0.963093	+	0.269169i	$0.913251\pi$
$312$		0			0
$313$	−1.21047e6	−	2.09659e6i	−0.698381	−	1.20963i	−0.969028	−	0.246953i	$-0.920571\pi$
$313$	−1.21047e6	−	2.09659e6i	−0.698381	−	1.20963i	0.270646	−	0.962679i	$-0.412763\pi$
$314$	−3.25035e6			−1.86040
$315$		0			0
$316$	−492028.			−0.277186
$317$	938057.	+	1.62476e6i	0.524301	+	0.908116i	0.999600	+	0.0282918i	$0.00900675\pi$
$317$	938057.	+	1.62476e6i	0.524301	+	0.908116i	−0.475298	+	0.879825i	$0.657660\pi$
$318$		0			0
$319$	1.36960e6	−	2.37221e6i	0.753557	−	1.30520i
$320$	38247.3	+	66246.2i	0.0208798	+	0.0361648i
$321$		0			0
$322$	−254151.	−	296998.i	−0.136600	−	0.159630i
$323$	556936.			0.297029
$324$		0			0
$325$	473612.	−	820321.i	0.248722	−	0.430800i
$326$	1.77933e6	−	3.08190e6i	0.927285	−	1.60611i
$327$		0			0
$328$	−688828.			−0.353530
$329$	−195338.	+	36396.6i	−0.0994940	+	0.0185384i
$330$		0			0
$331$	541549.	+	937990.i	0.271686	+	0.470575i	0.969294	−	0.245906i	$-0.0790853\pi$
$331$	541549.	+	937990.i	0.271686	+	0.470575i	−0.697607	+	0.716480i	$0.745752\pi$
$332$	−724399.	+	1.25470e6i	−0.360689	+	0.624732i
$333$		0			0
$334$	2.39628e6	+	4.15048e6i	1.17536	+	2.03579i
$335$	2.13507e6			1.03944
$336$		0			0
$337$	−2.59465e6			−1.24453			−0.622263	−	0.782809i	$-0.713786\pi$
$337$	−2.59465e6			−1.24453			−0.622263	+	0.782809i	$0.713786\pi$
$338$	−1.01359e6	−	1.75560e6i	−0.482583	−	0.835859i
$339$		0			0
$340$	−268325.	+	464753.i	−0.125882	+	0.218034i
$341$	−453107.	−	784804.i	−0.211016	−	0.365490i
$342$		0			0
$343$	−1.85454e6	+	1.14378e6i	−0.851141	+	0.524938i
$344$	179828.			0.0819333
$345$		0			0
$346$	882371.	−	1.52831e6i	0.396242	−	0.686312i
$347$	−935255.	+	1.61991e6i	−0.416972	+	0.722216i	−0.995633	−	0.0933518i	$-0.970242\pi$
$347$	−935255.	+	1.61991e6i	−0.416972	+	0.722216i	0.578662	+	0.815568i	$0.303575\pi$
$348$		0			0
$349$	−1.61685e6			−0.710568			−0.355284	−	0.934758i	$-0.615616\pi$
$349$	−1.61685e6			−0.710568			−0.355284	+	0.934758i	$0.615616\pi$
$350$	−992689.	+	2.81179e6i	−0.433155	+	1.22691i
$351$		0			0
$352$	1.03762e6	+	1.79720e6i	0.446354	+	0.773109i
$353$	−289153.	+	500827.i	−0.123507	+	0.213920i	−0.921148	−	0.389212i	$-0.872747\pi$
$353$	−289153.	+	500827.i	−0.123507	+	0.213920i	0.797642	+	0.603132i	$0.206081\pi$
$354$		0			0
$355$	−574310.	−	994734.i	−0.241866	−	0.418925i
$356$	−791605.			−0.331042
$357$		0			0
$358$	986330.			0.406738
$359$	−984090.	−	1.70449e6i	−0.402994	−	0.698006i	0.591092	−	0.806604i	$-0.298697\pi$
$359$	−984090.	−	1.70449e6i	−0.402994	−	0.698006i	−0.994086	+	0.108598i	$0.965364\pi$
$360$		0			0
$361$	105650.	−	182990.i	0.0426677	−	0.0739027i
$362$	1.08453e6	+	1.87847e6i	0.434983	+	0.753412i
$363$		0			0
$364$	−446615.	−	521909.i	−0.176677	−	0.206463i
$365$	−5.59553e6			−2.19841
$366$		0			0
$367$	−1.08726e6	+	1.88319e6i	−0.421375	+	0.729842i	−0.996074	−	0.0885223i	$-0.971786\pi$
$367$	−1.08726e6	+	1.88319e6i	−0.421375	+	0.729842i	0.574700	+	0.818364i	$0.305119\pi$
$368$	271457.	−	470177.i	0.104491	−	0.180985i
$369$		0			0
$370$	−418180.			−0.158803
$371$	803910.	+	939440.i	0.303230	+	0.354352i
$372$		0			0
$373$	−692379.	−	1.19924e6i	−0.257675	−	0.446306i	0.707944	−	0.706269i	$-0.249623\pi$
$373$	−692379.	−	1.19924e6i	−0.257675	−	0.446306i	−0.965619	+	0.259963i	$0.916290\pi$
$374$	−461197.	+	798817.i	−0.170493	+	0.295303i
$375$		0			0
$376$	−75091.0	−	130061.i	−0.0273916	−	0.0474437i
$377$	−2.27044e6			−0.822728
$378$		0			0
$379$	3.37190e6			1.20580			0.602902	−	0.797815i	$-0.294011\pi$
$379$	3.37190e6			1.20580			0.602902	+	0.797815i	$0.294011\pi$
$380$	−1.09115e6	−	1.88993e6i	−0.387639	−	0.671410i
$381$		0			0
$382$	−805642.	+	1.39541e6i	−0.282478	+	0.489265i
$383$	1.64030e6	+	2.84108e6i	0.571382	+	0.989662i	0.996424	+	0.0844886i	$0.0269257\pi$
$383$	1.64030e6	+	2.84108e6i	0.571382	+	0.989662i	−0.425043	+	0.905173i	$0.639741\pi$
$384$		0			0
$385$	−1.21240e6	+	3.43412e6i	−0.416863	+	1.18076i
$386$	4.76227e6			1.62684
$387$		0			0
$388$	−938919.	+	1.62626e6i	−0.316628	+	0.548415i
$389$	−1.47405e6	+	2.55313e6i	−0.493899	+	0.855457i	−0.999975	−	0.00703108i	$-0.997762\pi$
$389$	−1.47405e6	+	2.55313e6i	−0.493899	+	0.855457i	0.506077	+	0.862488i	$0.331095\pi$
$390$		0			0
$391$	157545.			0.0521150
$392$	−1.28182e6	−	1.03396e6i	−0.421321	−	0.339849i
$393$		0			0
$394$	4542.73	+	7868.24i	0.00147427	+	0.00255351i
$395$	1.08110e6	−	1.87251e6i	0.348636	−	0.603855i
$396$		0			0
$397$	34635.1	+	59989.7i	0.0110291	+	0.0191030i	0.871487	−	0.490418i	$-0.163156\pi$
$397$	34635.1	+	59989.7i	0.0110291	+	0.0191030i	−0.860458	+	0.509521i	$0.829823\pi$
$398$	−2.61282e6			−0.826802
$399$		0			0
$400$	−4.14151e6			−1.29422
$401$	−1.67393e6	−	2.89933e6i	−0.519848	−	0.900404i	−0.999734	−	0.0230725i	$-0.992655\pi$
$401$	−1.67393e6	−	2.89933e6i	−0.519848	−	0.900404i	0.479886	−	0.877331i	$-0.340678\pi$
$402$		0			0
$403$	−375567.	+	650501.i	−0.115193	+	0.199520i
$404$	260677.	+	451506.i	0.0794602	+	0.137629i
$405$		0			0
$406$	7.02645e6	−	1.30921e6i	2.11554	−	0.394181i
$407$	−260274.			−0.0778834
$408$		0			0
$409$	−1.45608e6	+	2.52201e6i	−0.430406	+	0.745485i	−0.996908	−	0.0785754i	$-0.974963\pi$
$409$	−1.45608e6	+	2.52201e6i	−0.430406	+	0.745485i	0.566502	+	0.824060i	$0.308296\pi$
$410$	−1.98734e6	+	3.44217e6i	−0.583864	+	1.01128i
$411$		0			0
$412$	530940.			0.154100
$413$	2.50122e6	+	2.92289e6i	0.721566	+	0.843214i
$414$		0			0
$415$	−3.18334e6	−	5.51371e6i	−0.907326	−	1.57153i
$416$	860050.	−	1.48965e6i	0.243663	−	0.422037i
$417$		0			0
$418$	−1.87547e6	−	3.24842e6i	−0.525014	−	0.909350i
$419$	4.62361e6			1.28661			0.643304	−	0.765611i	$-0.277563\pi$
$419$	4.62361e6			1.28661			0.643304	+	0.765611i	$0.277563\pi$
$420$		0			0
$421$	−2.63042e6			−0.723303			−0.361652	−	0.932313i	$-0.617787\pi$
$421$	−2.63042e6			−0.723303			−0.361652	+	0.932313i	$0.617787\pi$
$422$	1.77837e6	+	3.08023e6i	0.486117	+	0.841979i
$423$		0			0
$424$	−467270.	+	809336.i	−0.126227	+	0.218632i
$425$	−600901.	−	1.04079e6i	−0.161373	−	0.279506i
$426$		0			0
$427$	5.92772e6	−	1.10449e6i	1.57332	−	0.293152i
$428$	−1.59599e6			−0.421135
$429$		0			0
$430$	518820.	−	898623.i	0.135315	−	0.234372i
$431$	3.77064e6	−	6.53094e6i	0.977736	−	1.69349i	0.307144	−	0.951663i	$-0.400627\pi$
$431$	3.77064e6	−	6.53094e6i	0.977736	−	1.69349i	0.670592	−	0.741826i	$-0.266040\pi$
$432$		0			0
$433$	5.83558e6			1.49577			0.747883	−	0.663830i	$-0.231070\pi$
$433$	5.83558e6			1.49577			0.747883	+	0.663830i	$0.231070\pi$
$434$	787186.	−	2.22971e6i	0.200610	−	0.568229i
$435$		0			0
$436$	−2.00391e6	−	3.47088e6i	−0.504850	−	0.874426i
$437$	−320331.	+	554830.i	−0.0802409	+	0.138981i
$438$		0			0
$439$	−84051.9	−	145582.i	−0.0208155	−	0.0360535i	0.855430	−	0.517918i	$-0.173293\pi$
$439$	−84051.9	−	145582.i	−0.0208155	−	0.0360535i	−0.876246	+	0.481865i	$0.839960\pi$
$440$	−2.75259e6			−0.677814
$441$		0			0
$442$	764546.			0.186143
$443$	−1.42076e6	−	2.46082e6i	−0.343962	−	0.595760i	0.641203	−	0.767372i	$-0.278436\pi$
$443$	−1.42076e6	−	2.46082e6i	−0.343962	−	0.595760i	−0.985165	+	0.171612i	$0.945102\pi$
$444$		0			0
$445$	1.73934e6	−	3.01262e6i	0.416374	−	0.721181i
$446$	−4.15503e6	−	7.19672e6i	−0.989092	−	1.71316i
$447$		0			0
$448$	−41356.6	+	117143.i	−0.00973532	+	0.0275753i
$449$	1.41567e6			0.331396			0.165698	−	0.986177i	$-0.447012\pi$
$449$	1.41567e6			0.331396			0.165698	+	0.986177i	$0.447012\pi$
$450$		0			0
$451$	−1.23691e6	+	2.14240e6i	−0.286350	+	0.495973i
$452$	360273.	−	624012.i	0.0829442	−	0.143664i
$453$		0			0
$454$	−6.44644e6			−1.46784
$455$	2.96755e6	−	552933.i	0.672000	−	0.125211i
$456$		0			0
$457$	−778637.	−	1.34864e6i	−0.174399	−	0.302068i	0.765554	−	0.643372i	$-0.222465\pi$
$457$	−778637.	−	1.34864e6i	−0.174399	−	0.302068i	−0.939953	+	0.341303i	$0.889132\pi$
$458$	1.84833e6	−	3.20141e6i	0.411734	−	0.713144i
$459$		0			0
$460$	−308664.	−	534621.i	−0.0680129	−	0.117802i
$461$	4.45345e6			0.975987			0.487994	−	0.872847i	$-0.337729\pi$
$461$	4.45345e6			0.975987			0.487994	+	0.872847i	$0.337729\pi$
$462$		0			0
$463$	4.92263e6			1.06720			0.533599	−	0.845738i	$-0.320839\pi$
$463$	4.92263e6			1.06720			0.533599	+	0.845738i	$0.320839\pi$
$464$	4.96347e6	+	8.59698e6i	1.07026	+	1.85375i
$465$		0			0
$466$	3.69291e6	−	6.39631e6i	0.787778	−	1.36447i
$467$	2.54545e6	+	4.40885e6i	0.540098	+	0.935477i	0.998898	+	0.0469376i	$0.0149462\pi$
$467$	2.54545e6	+	4.40885e6i	0.540098	+	0.935477i	−0.458800	+	0.888540i	$0.651720\pi$
$468$		0			0
$469$	2.25442e6	+	2.63449e6i	0.473262	+	0.553049i
$470$	−866579.			−0.180952
$471$		0			0
$472$	−1.45383e6	+	2.51810e6i	−0.300370	+	0.520257i
$473$	322912.	−	559301.i	0.0663639	−	0.114946i
$474$		0			0
$475$	4.88717e6			0.993856
$476$	−856786.	+	159642.i	−0.173322	+	0.0322946i
$477$		0			0
$478$	5.43416e6	+	9.41224e6i	1.08783	+	1.88418i
$479$	−4.15042e6	+	7.18874e6i	−0.826521	+	1.43158i	0.0742312	+	0.997241i	$0.476350\pi$
$479$	−4.15042e6	+	7.18874e6i	−0.826521	+	1.43158i	−0.900752	+	0.434334i	$0.856984\pi$
$480$		0			0
$481$	107867.	+	186831.i	0.0212581	+	0.0368202i
$482$	7.13644e6			1.39915
$483$		0			0
$484$	−676028.			−0.131175
$485$	−4.12604e6	−	7.14651e6i	−0.796488	−	1.37956i
$486$		0			0
$487$	−4.31701e6	+	7.47727e6i	−0.824822	+	1.42863i	0.0772330	+	0.997013i	$0.475391\pi$
$487$	−4.31701e6	+	7.47727e6i	−0.824822	+	1.42863i	−0.902055	+	0.431621i	$0.857942\pi$
$488$	2.27871e6	+	3.94684e6i	0.433151	+	0.750240i
$489$		0			0
$490$	−8.86500e6	+	3.42238e6i	−1.66797	+	0.643930i
$491$	−95039.5			−0.0177910			−0.00889550	−	0.999960i	$-0.502832\pi$
$491$	−95039.5			−0.0177910			−0.00889550	+	0.999960i	$0.502832\pi$
$492$		0			0
$493$	−1.44032e6	+	2.49471e6i	−0.266896	+	0.462277i
$494$	−1.55453e6	+	2.69252e6i	−0.286603	+	0.496411i
$495$		0			0
$496$	3.28415e6			0.599402
$497$	621000.	−	1.75898e6i	0.112772	−	0.319426i
$498$		0			0
$499$	−1.07102e6	−	1.85506e6i	−0.192551	−	0.333507i	0.753544	−	0.657397i	$-0.228343\pi$
$499$	−1.07102e6	−	1.85506e6i	−0.192551	−	0.333507i	−0.946095	+	0.323890i	$0.895009\pi$
$500$	−88782.9	+	153776.i	−0.0158820	+	0.0275084i
$501$		0			0
$502$	−30143.8	−	52210.7i	−0.00533875	−	0.00924698i
$503$	−5.24794e6			−0.924844			−0.462422	−	0.886660i	$-0.653019\pi$
$503$	−5.24794e6			−0.924844			−0.462422	+	0.886660i	$0.653019\pi$
$504$		0			0
$505$	−2.29107e6			−0.399769
$506$	−530531.	−	918907.i	−0.0921159	−	0.159549i
$507$		0			0
$508$	−469945.	+	813968.i	−0.0807956	+	0.139942i
$509$	−5.29453e6	−	9.17040e6i	−0.905802	−	1.56889i	−0.819837	−	0.572596i	$-0.805936\pi$
$509$	−5.29453e6	−	9.17040e6i	−0.905802	−	1.56889i	−0.0859643	−	0.996298i	$-0.527397\pi$
$510$		0			0
$511$	−5.90829e6	−	6.90437e6i	−1.00094	−	1.16969i
$512$	−3.52190e6			−0.593747
$513$		0			0
$514$	1.86819e6	−	3.23580e6i	0.311899	−	0.540225i
$515$	−1.16660e6	+	2.02061e6i	−0.193822	+	0.335709i
$516$		0			0
$517$	−539357.			−0.0887462
$518$	−441554.	−	515996.i	−0.0723036	−	0.0844932i
$519$		0			0
$520$	1.14077e6	+	1.97588e6i	0.185008	+	0.320443i
$521$	−2.27232e6	+	3.93578e6i	−0.366755	+	0.635238i	−0.989056	−	0.147540i	$-0.952865\pi$
$521$	−2.27232e6	+	3.93578e6i	−0.366755	+	0.635238i	0.622301	+	0.782778i	$0.286198\pi$
$522$		0			0
$523$	2.63599e6	+	4.56566e6i	0.421394	+	0.729877i	0.996076	−	0.0885004i	$-0.0282075\pi$
$523$	2.63599e6	+	4.56566e6i	0.421394	+	0.729877i	−0.574682	+	0.818377i	$0.694874\pi$
$524$	3.02772e6			0.481711
$525$		0			0
$526$	−2.49373e6			−0.392993
$527$	476504.	+	825330.i	0.0747378	+	0.129450i
$528$		0			0
$529$	3.12756e6	−	5.41709e6i	0.485921	−	0.841641i
$530$	2.69624e6	+	4.67003e6i	0.416936	+	0.722154i
$531$		0			0
$532$	1.17986e6	−	3.34196e6i	0.180739	−	0.511943i
$533$	2.05048e6			0.312635
$534$		0			0
$535$	3.50676e6	−	6.07389e6i	0.529690	−	0.917451i
$536$	−1.31037e6	+	2.26963e6i	−0.197008	+	0.341227i
$537$		0			0
$538$	3.39647e6			0.505908
$539$	−5.51755e6	+	2.13008e6i	−0.818040	+	0.315809i
$540$		0			0
$541$	−2.96723e6	−	5.13939e6i	−0.435871	−	0.754950i	0.561496	−	0.827480i	$-0.310226\pi$
$541$	−2.96723e6	−	5.13939e6i	−0.435871	−	0.754950i	−0.997366	+	0.0725298i	$0.976893\pi$
$542$	−3.46209e6	+	5.99652e6i	−0.506221	+	0.876801i
$543$		0			0
$544$	−1.09120e6	−	1.89001e6i	−0.158091	−	0.273821i
$545$	1.76122e7			2.53994
$546$		0			0
$547$	−8.82017e6			−1.26040			−0.630200	−	0.776433i	$-0.717027\pi$
$547$	−8.82017e6			−1.26040			−0.630200	+	0.776433i	$0.717027\pi$
$548$	256673.	+	444571.i	0.0365115	+	0.0632397i
$549$		0			0
$550$	−4.04705e6	+	7.00970e6i	−0.570469	+	0.988081i
$551$	−5.85712e6	−	1.01448e7i	−0.821874	−	1.42353i
$552$		0			0
$553$	3.45204e6	−	643206.i	0.480024	−	0.0894411i
$554$	−6.86124e6			−0.949791
$555$		0			0
$556$	−3.05538e6	+	5.29207e6i	−0.419158	+	0.726004i
$557$	−591120.	+	1.02385e6i	−0.0807304	+	0.139829i	−0.903564	−	0.428453i	$-0.859059\pi$
$557$	−591120.	+	1.02385e6i	−0.0807304	+	0.139829i	0.822833	+	0.568283i	$0.192392\pi$
$558$		0			0
$559$	−535306.			−0.0724556
$560$	−8.58111e6	−	1.00278e7i	−1.15631	−	1.35125i
$561$		0			0
$562$	1.12734e6	+	1.95261e6i	0.150561	+	0.260780i
$563$	2.03870e6	−	3.53114e6i	0.271071	−	0.469509i	−0.698065	−	0.716034i	$-0.745955\pi$
$563$	2.03870e6	−	3.53114e6i	0.271071	−	0.469509i	0.969136	+	0.246525i	$0.0792888\pi$
$564$		0			0
$565$	1.58321e6	+	2.74219e6i	0.208649	+	0.361391i
$566$	−1.25514e7			−1.64684
$567$		0			0
$568$	1.40990e6			0.183366
$569$	4.08807e6	+	7.08075e6i	0.529344	+	0.916851i	0.999414	+	0.0342216i	$0.0108952\pi$
$569$	4.08807e6	+	7.08075e6i	0.529344	+	0.916851i	−0.470070	+	0.882629i	$0.655771\pi$
$570$		0			0
$571$	−1.65307e6	+	2.86321e6i	−0.212179	+	0.367504i	−0.952396	−	0.304863i	$-0.901389\pi$
$571$	−1.65307e6	+	2.86321e6i	−0.212179	+	0.367504i	0.740217	+	0.672368i	$0.234723\pi$
$572$	−932292.	−	1.61478e6i	−0.119141	−	0.206359i
$573$		0			0
$574$	−6.34574e6	+	1.18238e6i	−0.803901	+	0.149788i
$575$	1.38247e6			0.174376
$576$		0			0
$577$	3.57497e6	−	6.19203e6i	0.447026	−	0.774272i	−0.551165	−	0.834396i	$-0.685816\pi$
$577$	3.57497e6	−	6.19203e6i	0.447026	−	0.774272i	0.998191	+	0.0601245i	$0.0191498\pi$
$578$	−4.54324e6	+	7.86913e6i	−0.565648	+	0.979731i
$579$		0			0
$580$	1.12876e7			1.39325
$581$	3.44214e6	−	9.74986e6i	0.423046	−	1.19828i
$582$		0			0
$583$	1.67813e6	+	2.90661e6i	0.204482	+	0.354173i
$584$	3.43418e6	−	5.94818e6i	0.416669	−	0.721692i
$585$		0			0
$586$	−5.81309e6	−	1.00686e7i	−0.699300	−	1.21122i
$587$	−9.69191e6			−1.16095			−0.580476	−	0.814277i	$-0.697133\pi$
$587$	−9.69191e6			−1.16095			−0.580476	+	0.814277i	$0.697133\pi$
$588$		0			0
$589$	−3.87545e6			−0.460292
$590$	8.38886e6	+	1.45299e7i	0.992139	+	1.71844i
$591$		0			0
$592$	471621.	−	816872.i	0.0553081	−	0.0957965i
$593$	3.31980e6	+	5.75006e6i	0.387682	+	0.671484i	0.992137	−	0.125154i	$-0.0399426\pi$
$593$	3.31980e6	+	5.75006e6i	0.387682	+	0.671484i	−0.604456	+	0.796639i	$0.706609\pi$
$594$		0			0
$595$	1.27500e6	−	3.61145e6i	0.147645	−	0.418205i
$596$	6.45569e6			0.744435
$597$		0			0
$598$	−439742.	+	761655.i	−0.0502857	+	0.0870974i
$599$	−1.62096e6	+	2.80758e6i	−0.184588	+	0.319716i	−0.943438	−	0.331550i	$-0.892428\pi$
$599$	−1.62096e6	+	2.80758e6i	−0.184588	+	0.319716i	0.758849	+	0.651266i	$0.225762\pi$
$600$		0			0
$601$	−5.65076e6			−0.638147			−0.319074	−	0.947730i	$-0.603372\pi$
$601$	−5.65076e6			−0.638147			−0.319074	+	0.947730i	$0.603372\pi$
$602$	1.65664e6	−	308676.i	0.186310	−	0.0347145i
$603$		0			0
$604$	3.25887e6	+	5.64453e6i	0.363475	+	0.629557i
$605$	1.48539e6	−	2.57277e6i	0.164988	−	0.285767i
$606$		0			0
$607$	−117837.	−	204100.i	−0.0129811	−	0.0224839i	0.859462	−	0.511200i	$-0.170799\pi$
$607$	−117837.	−	204100.i	−0.0129811	−	0.0224839i	−0.872443	+	0.488716i	$0.837465\pi$
$608$	8.87478e6			0.973641
$609$		0			0
$610$	2.62972e7			2.86144
$611$	223529.	+	387163.i	0.0242231	+	0.0419557i
$612$		0			0
$613$	−394438.	+	683187.i	−0.0423963	+	0.0734325i	−0.886445	−	0.462834i	$-0.846833\pi$
$613$	−394438.	+	683187.i	−0.0423963	+	0.0734325i	0.844049	+	0.536267i	$0.180166\pi$
$614$	−1.65358e6	−	2.86408e6i	−0.177012	−	0.306595i
$615$		0			0
$616$	−2.90645e6	−	3.39645e6i	−0.308611	−	0.360640i
$617$	−1.67739e7			−1.77387			−0.886935	−	0.461894i	$-0.847170\pi$
$617$	−1.67739e7			−1.77387			−0.886935	+	0.461894i	$0.847170\pi$
$618$		0			0
$619$	−4.11150e6	+	7.12132e6i	−0.431294	+	0.747023i	−0.996985	−	0.0775941i	$-0.975276\pi$
$619$	−4.11150e6	+	7.12132e6i	−0.431294	+	0.747023i	0.565691	+	0.824617i	$0.308610\pi$
$620$	1.86714e6	−	3.23399e6i	0.195074	−	0.337878i
$621$		0			0
$622$	−1.72675e7			−1.78959
$623$	5.55386e6	−	1.03483e6i	0.573290	−	0.106819i
$624$		0			0
$625$	4.68399e6	+	8.11290e6i	0.479640	+	0.830761i
$626$	8.57346e6	−	1.48497e7i	0.874420	−	1.51454i
$627$		0			0
$628$	−4.16818e6	−	7.21949e6i	−0.421742	−	0.730479i
$629$	273714.			0.0275849
$630$		0			0
$631$	−5.94507e6			−0.594406			−0.297203	−	0.954814i	$-0.596054\pi$
$631$	−5.94507e6			−0.594406			−0.297203	+	0.954814i	$0.596054\pi$
$632$	1.32702e6	+	2.29846e6i	0.132155	+	0.228899i
$633$		0			0
$634$	−6.64403e6	+	1.15078e7i	−0.656460	+	1.13702i
$635$	−2.06515e6	−	3.57695e6i	−0.203244	−	0.352029i
$636$		0			0
$637$	3.81569e6	+	3.07785e6i	0.372585	+	0.300537i
$638$	1.94011e7			1.88701
$639$		0			0
$640$	7.26120e6	−	1.25768e7i	0.700743	−	1.21372i
$641$	−5.33804e6	+	9.24576e6i	−0.513141	+	0.888786i	0.486743	+	0.873545i	$0.338185\pi$
$641$	−5.33804e6	+	9.24576e6i	−0.513141	+	0.888786i	−0.999884	+	0.0152411i	$0.995148\pi$
$642$		0			0
$643$	−3.13159e6			−0.298701			−0.149351	−	0.988784i	$-0.547718\pi$
$643$	−3.13159e6			−0.298701			−0.149351	+	0.988784i	$0.547718\pi$
$644$	333757.	−	945367.i	0.0317114	−	0.0898227i
$645$		0			0
$646$	1.97232e6	+	3.41616e6i	0.185950	+	0.322075i
$647$	−2.46728e6	+	4.27346e6i	−0.231717	+	0.401346i	−0.958314	−	0.285719i	$-0.907768\pi$
$647$	−2.46728e6	+	4.27346e6i	−0.231717	+	0.401346i	0.726596	+	0.687065i	$0.241101\pi$
$648$		0			0
$649$	5.22120e6	+	9.04339e6i	0.486585	+	0.842790i
$650$	6.70897e6			0.622834
$651$		0			0
$652$	9.12710e6			0.840841
$653$	2.86112e6	+	4.95561e6i	0.262575	+	0.454793i	0.966925	−	0.255059i	$-0.0820950\pi$
$653$	2.86112e6	+	4.95561e6i	0.262575	+	0.454793i	−0.704351	+	0.709852i	$0.748762\pi$
$654$		0			0
$655$	−6.65258e6	+	1.15226e7i	−0.605881	+	1.04942i
$656$	−4.48261e6	−	7.76411e6i	−0.406698	−	0.704421i
$657$		0			0
$658$	−915018.	−	1.06928e6i	−0.0823881	−	0.0962779i
$659$	−362477.			−0.0325137			−0.0162569	−	0.999868i	$-0.505175\pi$
$659$	−362477.			−0.0325137			−0.0162569	+	0.999868i	$0.505175\pi$
$660$		0			0
$661$	9.56053e6	−	1.65593e7i	0.851096	−	1.47414i	−0.0291249	−	0.999576i	$-0.509272\pi$
$661$	9.56053e6	−	1.65593e7i	0.851096	−	1.47414i	0.880220	−	0.474565i	$-0.157395\pi$
$662$	−3.83566e6	+	6.64356e6i	−0.340170	+	0.589191i
$663$		0			0
$664$	7.81494e6			0.687868
$665$	1.01261e7	+	1.18333e7i	0.887950	+	1.03765i
$666$		0			0
$667$	−1.65685e6	−	2.86975e6i	−0.144201	−	0.249764i
$668$	−6.14587e6	+	1.06450e7i	−0.532896	+	0.923003i
$669$		0			0
$670$	7.56111e6	+	1.30962e7i	0.650727	+	1.12709i
$671$	1.63673e7			1.40337
$672$		0			0
$673$	−573374.			−0.0487978			−0.0243989	−	0.999702i	$-0.507767\pi$
$673$	−573374.			−0.0487978			−0.0243989	+	0.999702i	$0.507767\pi$
$674$	−9.18864e6	−	1.59152e7i	−0.779115	−	1.34947i
$675$		0			0
$676$	2.59962e6	−	4.50267e6i	0.218798	−	0.378968i
$677$	5.84516e6	+	1.01241e7i	0.490146	+	0.848957i	0.999936	−	0.0113419i	$-0.00361030\pi$
$677$	5.84516e6	+	1.01241e7i	0.490146	+	0.848957i	−0.509790	+	0.860299i	$0.670277\pi$
$678$		0			0
$679$	4.46148e6	−	1.26371e7i	0.371368	−	1.05190i
$680$	2.89473e6			0.240069
$681$		0			0
$682$	3.20925e6	−	5.55858e6i	0.264206	−	0.457618i
$683$	9.18370e6	−	1.59066e7i	0.753297	−	1.30475i	−0.192920	−	0.981214i	$-0.561796\pi$
$683$	9.18370e6	−	1.59066e7i	0.753297	−	1.30475i	0.946217	−	0.323534i	$-0.104871\pi$
$684$		0			0
$685$	−2.25588e6			−0.183692
$686$	−1.35834e7	−	7.32492e6i	−1.10204	−	0.594282i
$687$		0			0
$688$	1.17025e6	+	2.02693e6i	0.0942554	+	0.163255i
$689$	1.39096e6	−	2.40921e6i	0.111626	−	0.193342i
$690$		0			0
$691$	−1.17806e7	−	2.04045e7i	−0.938579	−	1.62567i	−0.768125	−	0.640300i	$-0.778810\pi$
$691$	−1.17806e7	−	2.04045e7i	−0.938579	−	1.62567i	−0.170454	−	0.985366i	$-0.554523\pi$
$692$	4.52612e6			0.359303
$693$		0			0
$694$	−1.32484e7			−1.04415
$695$	−1.34267e7	−	2.32558e7i	−1.05441	−	1.82629i
$696$		0			0
$697$	1.30078e6	−	2.25303e6i	0.101420	−	0.175665i
$698$	−5.72587e6	−	9.91750e6i	−0.444839	−	0.770484i
$699$		0			0
$700$	−7.51839e6	+	1.40087e6i	−0.579935	+	0.108057i
$701$	−1.32980e7			−1.02210			−0.511048	−	0.859552i	$-0.670743\pi$
$701$	−1.32980e7			−1.02210			−0.511048	+	0.859552i	$0.670743\pi$
$702$		0			0
$703$	−556535.	+	963946.i	−0.0424721	+	0.0735639i
$704$	−168605.	+	292033.i	−0.0128215	+	0.0222075i
$705$		0			0
$706$	−4.09600e6			−0.309277
$707$	−2.41913e6	−	2.82697e6i	−0.182016	−	0.212703i
$708$		0			0
$709$	3.42677e6	+	5.93533e6i	0.256017	+	0.443434i	0.965171	−	0.261619i	$-0.0842564\pi$
$709$	3.42677e6	+	5.93533e6i	0.256017	+	0.443434i	−0.709154	+	0.705053i	$0.750923\pi$
$710$	4.06770e6	−	7.04547e6i	0.302833	−	0.524522i
$711$		0			0
$712$	2.13499e6	+	3.69791e6i	0.157832	+	0.273374i
$713$	−1.09628e6			−0.0807602
$714$		0			0
$715$	8.19384e6			0.599408
$716$	1.26485e6	+	2.19078e6i	0.0922051	+	0.159704i
$717$		0			0
$718$	6.97008e6	−	1.20725e7i	0.504576	−	0.873951i
$719$	1.32865e7	+	2.30128e7i	0.958490	+	1.66015i	0.726172	+	0.687513i	$0.241298\pi$
$719$	1.32865e7	+	2.30128e7i	0.958490	+	1.66015i	0.232318	+	0.972640i	$0.425369\pi$
$720$		0			0
$721$	−3.72505e6	+	694075.i	−0.266866	+	0.0497242i
$722$	1.49658e6			0.106846
$723$		0			0
$724$	−2.78156e6	+	4.81781e6i	−0.197216	+	0.341588i
$725$	−1.26390e7	+	2.18913e7i	−0.893031	+	1.54678i
$726$		0			0
$727$	2.16991e6			0.152267			0.0761335	−	0.997098i	$-0.475742\pi$
$727$	2.16991e6			0.152267			0.0761335	+	0.997098i	$0.475742\pi$
$728$	−1.23351e6	+	3.49393e6i	−0.0862612	+	0.244335i
$729$		0			0
$730$	−1.98159e7	−	3.43221e7i	−1.37628	−	2.38379i
$731$	−339587.	+	588182.i	−0.0235049	+	0.0407116i
$732$		0			0
$733$	8.73265e6	+	1.51254e7i	0.600324	+	1.03979i	0.992772	+	0.120018i	$0.0382951\pi$
$733$	8.73265e6	+	1.51254e7i	0.600324	+	1.03979i	−0.392447	+	0.919774i	$0.628372\pi$
$734$	−1.54016e7			−1.05518
$735$		0			0
$736$	2.51048e6			0.170829
$737$	4.70602e6	+	8.15106e6i	0.319143	+	0.552771i
$738$		0			0
$739$	6.82304e6	−	1.18178e7i	0.459586	−	0.796026i	−0.539353	−	0.842080i	$-0.681331\pi$
$739$	6.82304e6	−	1.18178e7i	0.459586	−	0.796026i	0.998939	+	0.0460536i	$0.0146645\pi$
$740$	−536264.	−	928836.i	−0.0359997	−	0.0623533i
$741$		0			0
$742$	−2.91544e6	+	8.25798e6i	−0.194399	+	0.550635i
$743$	−1.48965e7			−0.989944			−0.494972	−	0.868909i	$-0.664822\pi$
$743$	−1.48965e7			−0.989944			−0.494972	+	0.868909i	$0.664822\pi$
$744$		0			0
$745$	−1.41846e7	+	2.45685e7i	−0.936326	+	1.62176i
$746$	4.90396e6	−	8.49390e6i	0.322626	−	0.558805i
$747$		0			0
$748$	−2.36571e6			−0.154599
$749$	1.11974e7	−	2.08637e6i	0.729311	−	0.135890i
$750$		0			0
$751$	1.26731e7	+	2.19505e7i	0.819944	+	1.42019i	0.905723	+	0.423871i	$0.139329\pi$
$751$	1.26731e7	+	2.19505e7i	0.819944	+	1.42019i	−0.0857783	+	0.996314i	$0.527338\pi$
$752$	977324.	−	1.69277e6i	0.0630222	−	0.109158i
$753$		0			0
$754$	−8.04049e6	−	1.39265e7i	−0.515056	−	0.892102i
$755$	−2.86419e7			−1.82867
$756$		0			0
$757$	−2.66725e7			−1.69170			−0.845852	−	0.533417i	$-0.820908\pi$
$757$	−2.66725e7			−1.69170			−0.845852	+	0.533417i	$0.820908\pi$
$758$	1.19412e7	+	2.06828e7i	0.754875	+	1.30748i
$759$		0			0
$760$	−5.88577e6	+	1.01945e7i	−0.369632	+	0.640221i
$761$	289914.	+	502146.i	0.0181471	+	0.0314318i	0.874956	−	0.484202i	$-0.160890\pi$
$761$	289914.	+	502146.i	0.0181471	+	0.0314318i	−0.856809	+	0.515634i	$0.827557\pi$
$762$		0			0
$763$	1.85967e7	+	2.17319e7i	1.15644	+	1.35141i
$764$	−4.13255e6			−0.256144
$765$		0			0
$766$	−1.16179e7	+	2.01227e7i	−0.715408	+	1.23912i
$767$	4.32770e6	−	7.49580e6i	0.265625	−	0.460076i
$768$		0			0
$769$	1.52438e7			0.929562			0.464781	−	0.885426i	$-0.346133\pi$
$769$	1.52438e7			0.929562			0.464781	+	0.885426i	$0.346133\pi$
$770$	−2.53579e7	+	4.72485e6i	−1.54130	+	0.287185i
$771$		0			0
$772$	6.10702e6	+	1.05777e7i	0.368796	+	0.638773i
$773$	−9.74628e6	+	1.68810e7i	−0.586665	+	1.01613i	0.408001	+	0.912982i	$0.366226\pi$
$773$	−9.74628e6	+	1.68810e7i	−0.586665	+	1.01613i	−0.994666	+	0.103152i	$0.967107\pi$
$774$		0			0

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.54138 + 6.13385i) q^{2} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +(43.1587 - 122.247i) q^{7} +97.9863 q^{8} +O(q^{10})\)	\(q+(3.54138 + 6.13385i) q^{2} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +(43.1587 - 122.247i) q^{7} +97.9863 q^{8} +(282.700 - 489.651i) q^{10} +(175.952 - 304.757i) q^{11} -291.683 q^{13} +(902.686 - 168.194i) q^{14} +(637.655 + 1104.45i) q^{16} +(-185.038 + 320.495i) q^{17} +(-752.463 - 1303.30i) q^{19} +1450.11 q^{20} +2492.45 q^{22} +(-212.855 - 368.676i) q^{23} +(-1623.72 + 2812.37i) q^{25} +(-1032.96 - 1789.14i) q^{26} +(1531.17 + 1789.30i) q^{28} +7783.93 q^{29} +(1287.59 - 2230.17i) q^{31} +(-2948.58 + 5107.09i) q^{32} -2621.16 q^{34} +(-10173.9 + 1895.67i) q^{35} +(-369.809 - 640.528i) q^{37} +(5329.51 - 9230.99i) q^{38} +(-3911.01 - 6774.06i) q^{40} -7029.84 q^{41} +1835.23 q^{43} +(3196.26 + 5536.08i) q^{44} +(1507.60 - 2611.25i) q^{46} +(-766.342 - 1327.34i) q^{47} +(-13081.7 - 10552.0i) q^{49} -23000.9 q^{50} +(2649.28 - 4588.69i) q^{52} +(-4768.73 + 8259.68i) q^{53} -28091.6 q^{55} +(4228.96 - 11978.5i) q^{56} +(27565.9 + 47745.5i) q^{58} +(-14837.0 + 25698.5i) q^{59} +(23255.4 + 40279.5i) q^{61} +18239.4 q^{62} -958.246 q^{64} +(11642.2 + 20164.8i) q^{65} +(-13373.0 + 23162.8i) q^{67} +(-3361.31 - 5821.95i) q^{68} +(-47657.4 - 55691.9i) q^{70} +14388.8 q^{71} +(35047.6 - 60704.2i) q^{73} +(2619.27 - 4536.71i) q^{74} +27337.8 q^{76} +(-29661.8 - 34662.5i) q^{77} +(13542.9 + 23457.0i) q^{79} +(50902.5 - 88165.7i) q^{80} +(-24895.3 - 43120.0i) q^{82} +79755.4 q^{83} +29542.2 q^{85} +(6499.26 + 11257.0i) q^{86} +(17240.9 - 29862.1i) q^{88} +(21788.7 + 37739.1i) q^{89} +(-12588.6 + 35657.3i) q^{91} +7733.26 q^{92} +(5427.82 - 9401.25i) q^{94} +(-60067.3 + 104040. i) q^{95} +103374. q^{97} +(18397.5 - 117610. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8	\( 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8} + 778 q^{10} + 424 q^{11} - 1848 q^{13} + 2674 q^{14} + 2064 q^{16} - 2346 q^{17} + 360 q^{19} + 3416 q^{20} + 4252 q^{22} - 12 q^{23} - 1872 q^{25} + 1148 q^{26} + 2548 q^{28} + 14104 q^{29} - 3548 q^{31} - 8096 q^{32} + 14844 q^{34} - 27496 q^{35} - 11090 q^{37} + 20138 q^{38} - 15936 q^{40} - 7000 q^{41} - 25360 q^{43} + 5948 q^{44} + 5118 q^{46} - 22956 q^{47} + 4900 q^{49} - 59984 q^{50} + 1400 q^{52} + 3042 q^{53} - 50152 q^{55} + 57792 q^{56} + 58852 q^{58} - 65808 q^{59} + 42486 q^{61} + 98724 q^{62} + 70912 q^{64} - 3164 q^{65} - 42312 q^{67} + 5460 q^{68} - 113050 q^{70} + 4416 q^{71} + 50506 q^{73} - 47370 q^{74} + 77672 q^{76} - 65338 q^{77} - 9004 q^{79} + 68816 q^{80} - 67732 q^{82} + 208656 q^{83} - 106212 q^{85} + 86776 q^{86} + 20496 q^{88} - 26666 q^{89} + 135632 q^{91} + 20568 q^{92} - 98034 q^{94} - 198140 q^{95} + 418264 q^{97} - 98686 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8 + 778 * q^10 + 424 * q^11 - 1848 * q^13 + 2674 * q^14 + 2064 * q^16 - 2346 * q^17 + 360 * q^19 + 3416 * q^20 + 4252 * q^22 - 12 * q^23 - 1872 * q^25 + 1148 * q^26 + 2548 * q^28 + 14104 * q^29 - 3548 * q^31 - 8096 * q^32 + 14844 * q^34 - 27496 * q^35 - 11090 * q^37 + 20138 * q^38 - 15936 * q^40 - 7000 * q^41 - 25360 * q^43 + 5948 * q^44 + 5118 * q^46 - 22956 * q^47 + 4900 * q^49 - 59984 * q^50 + 1400 * q^52 + 3042 * q^53 - 50152 * q^55 + 57792 * q^56 + 58852 * q^58 - 65808 * q^59 + 42486 * q^61 + 98724 * q^62 + 70912 * q^64 - 3164 * q^65 - 42312 * q^67 + 5460 * q^68 - 113050 * q^70 + 4416 * q^71 + 50506 * q^73 - 47370 * q^74 + 77672 * q^76 - 65338 * q^77 - 9004 * q^79 + 68816 * q^80 - 67732 * q^82 + 208656 * q^83 - 106212 * q^85 + 86776 * q^86 + 20496 * q^88 - 26666 * q^89 + 135632 * q^91 + 20568 * q^92 - 98034 * q^94 - 198140 * q^95 + 418264 * q^97 - 98686 * q^98

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