LMFDB - Embedded newform 63.6.e.d.37.2

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			37.2
Root			$1.77069 - 3.06693i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.6.e.d.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.54138 - 6.13385i) q^{2} +(-9.08276 - 15.7318i) q^{4} +(-39.9138 + 69.1328i) q^{5} +(43.1587 + 122.247i) q^{7} +97.9863 q^{8} +(282.700 + 489.651i) q^{10} +(175.952 + 304.757i) q^{11} -291.683 q^{13} +(902.686 + 168.194i) q^{14} +(637.655 - 1104.45i) q^{16} +(-185.038 - 320.495i) q^{17} +(-752.463 + 1303.30i) q^{19} +1450.11 q^{20} +2492.45 q^{22} +(-212.855 + 368.676i) q^{23} +(-1623.72 - 2812.37i) q^{25} +(-1032.96 + 1789.14i) q^{26} +(1531.17 - 1789.30i) q^{28} +7783.93 q^{29} +(1287.59 + 2230.17i) q^{31} +(-2948.58 - 5107.09i) q^{32} -2621.16 q^{34} +(-10173.9 - 1895.67i) q^{35} +(-369.809 + 640.528i) q^{37} +(5329.51 + 9230.99i) q^{38} +(-3911.01 + 6774.06i) q^{40} -7029.84 q^{41} +1835.23 q^{43} +(3196.26 - 5536.08i) q^{44} +(1507.60 + 2611.25i) q^{46} +(-766.342 + 1327.34i) q^{47} +(-13081.7 + 10552.0i) q^{49} -23000.9 q^{50} +(2649.28 + 4588.69i) q^{52} +(-4768.73 - 8259.68i) q^{53} -28091.6 q^{55} +(4228.96 + 11978.5i) q^{56} +(27565.9 - 47745.5i) q^{58} +(-14837.0 - 25698.5i) q^{59} +(23255.4 - 40279.5i) q^{61} +18239.4 q^{62} -958.246 q^{64} +(11642.2 - 20164.8i) q^{65} +(-13373.0 - 23162.8i) q^{67} +(-3361.31 + 5821.95i) q^{68} +(-47657.4 + 55691.9i) q^{70} +14388.8 q^{71} +(35047.6 + 60704.2i) q^{73} +(2619.27 + 4536.71i) q^{74} +27337.8 q^{76} +(-29661.8 + 34662.5i) q^{77} +(13542.9 - 23457.0i) q^{79} +(50902.5 + 88165.7i) q^{80} +(-24895.3 + 43120.0i) q^{82} +79755.4 q^{83} +29542.2 q^{85} +(6499.26 - 11257.0i) q^{86} +(17240.9 + 29862.1i) q^{88} +(21788.7 - 37739.1i) q^{89} +(-12588.6 - 35657.3i) q^{91} +7733.26 q^{92} +(5427.82 + 9401.25i) q^{94} +(-60067.3 - 104040. i) q^{95} +103374. q^{97} +(18397.5 + 117610. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8} + 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}+ \cdots - 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

Character values

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

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

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	−0.362306	−	0.932059i	$-0.618011\pi$
$2$	3.54138	−	6.13385i	0.626034	−	1.08432i	0.988340	−	0.152263i	$-0.0486561\pi$
$3$		0			0
$3$		0			0
$4$	−9.08276	−	15.7318i	−0.283836	−	0.491619i
$5$	−39.9138	+	69.1328i	−0.714000	+	1.23668i	0.249344	+	0.968415i	$0.419785\pi$
$5$	−39.9138	+	69.1328i	−0.714000	+	1.23668i	−0.963344	+	0.268269i	$0.913548\pi$
$6$		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	0.997570	−	0.0696781i	$-0.0221972\pi$
$11$	175.952	+	304.757i	0.438442	+	0.759403i	−0.559128	+	0.829082i	$0.688864\pi$
$12$		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	0.777876	−	0.628418i	$-0.216297\pi$
$17$	−185.038	−	320.495i	−0.155288	−	0.268967i	−0.933164	+	0.359451i	$0.882964\pi$
$18$		0			0
$19$	−752.463	+	1303.30i	−0.478190	+	0.828250i	−0.999687	−	0.0250030i	$-0.992040\pi$
$19$	−752.463	+	1303.30i	−0.478190	+	0.828250i	0.521497	+	0.853253i	$0.325374\pi$
$20$	1450.11			0.810637
$21$		0			0
$22$	2492.45			1.09792
$23$	−212.855	+	368.676i	−0.0839006	+	0.145320i	−0.904922	−	0.425577i	$-0.860071\pi$
$23$	−212.855	+	368.676i	−0.0839006	+	0.145320i	0.821022	+	0.570897i	$0.193404\pi$
$24$		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	0.960898	−	0.276904i	$-0.0893085\pi$
$31$	1287.59	+	2230.17i	0.240643	+	0.416805i	−0.720255	+	0.693710i	$0.755975\pi$
$32$	−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	−0.887376	−	0.461047i	$-0.847474\pi$
$37$	−369.809	+	640.528i	−0.0444092	+	0.0769190i	0.842966	+	0.537966i	$0.180807\pi$
$38$	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	−0.890217	−	0.455536i	$-0.849448\pi$
$47$	−766.342	+	1327.34i	−0.0506032	+	0.0876473i	0.839614	+	0.543183i	$0.182781\pi$
$48$		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	0.725554	−	0.688165i	$-0.241584\pi$
$53$	−4768.73	−	8259.68i	−0.233192	−	0.403900i	−0.958746	+	0.284265i	$0.908250\pi$
$54$		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	−0.997911	−	0.0646022i	$-0.979422\pi$
$59$	−14837.0	−	25698.5i	−0.554903	−	0.961120i	0.443008	−	0.896517i	$-0.353911\pi$
$60$		0			0
$61$	23255.4	−	40279.5i	0.800201	−	1.38599i	−0.119282	−	0.992860i	$-0.538059\pi$
$61$	23255.4	−	40279.5i	0.800201	−	1.38599i	0.919483	−	0.393129i	$-0.128607\pi$
$62$	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	0.624656	−	0.780900i	$-0.285239\pi$
$67$	−13373.0	−	23162.8i	−0.363951	−	0.630381i	−0.988607	+	0.150518i	$0.951906\pi$
$68$	−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	0.937697	+	0.347453i	$0.112953\pi$
$73$	35047.6	+	60704.2i	0.769752	+	1.33325i	−0.167946	+	0.985796i	$0.553713\pi$
$74$	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	−0.717748	−	0.696303i	$-0.754827\pi$
$79$	13542.9	−	23457.0i	0.244143	−	0.422868i	0.961890	+	0.273436i	$0.0881601\pi$
$80$	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	−0.682605	−	0.730788i	$-0.739153\pi$
$89$	21788.7	−	37739.1i	0.291579	−	0.505029i	0.974183	+	0.225759i	$0.0724862\pi$
$90$		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	0.927487	−	0.373855i	$-0.121964\pi$
$101$	14350.1	+	24855.1i	0.139975	+	0.242444i	−0.787512	+	0.616300i	$0.788631\pi$
$102$		0			0
$103$	−14614.0	+	25312.1i	−0.135730	+	0.235091i	−0.925876	−	0.377828i	$-0.876671\pi$
$103$	−14614.0	+	25312.1i	−0.135730	+	0.235091i	0.790146	+	0.612918i	$0.210005\pi$
$104$	−28580.9			−0.259115
$105$		0			0
$106$	−67551.6			−0.583944
$107$	43929.2	−	76087.6i	0.370932	−	0.642472i	−0.618778	−	0.785566i	$-0.712372\pi$
$107$	43929.2	−	76087.6i	0.370932	−	0.642472i	0.989709	+	0.143094i	$0.0457051\pi$
$108$		0			0
$109$	−110314.	−	191069.i	−0.889333	−	1.54037i	−0.840665	−	0.541555i	$-0.817836\pi$
$109$	−110314.	−	191069.i	−0.889333	−	1.54037i	−0.0486678	−	0.998815i	$-0.515498\pi$
$110$	−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	−0.996353	−	0.0853215i	$-0.972808\pi$
$131$	−83336.9	+	144344.i	−0.424286	+	0.734885i	0.572067	+	0.820207i	$0.306142\pi$
$132$		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	0.896391	−	0.443264i	$-0.146180\pi$
$137$	14129.7	+	24473.4i	0.0643178	+	0.111402i	−0.832073	+	0.554666i	$0.812846\pi$
$138$		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	0.326030	+	0.945360i	$0.394289\pi$
$149$	−177691.	+	307769.i	−0.655691	+	1.13569i	−0.981720	+	0.190330i	$0.939044\pi$
$150$		0			0
$151$	179399.	+	310727.i	0.640290	+	1.10901i	0.985368	+	0.170441i	$0.0545191\pi$
$151$	179399.	+	310727.i	0.640290	+	1.10901i	−0.345078	+	0.938574i	$0.612148\pi$
$152$	−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	−0.951155	−	0.308714i	$-0.900101\pi$
$157$	−229455.	−	397428.i	−0.742932	−	1.28680i	0.208223	−	0.978081i	$-0.433232\pi$
$158$	−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	0.211618	+	0.977353i	$0.432127\pi$
$163$	−251220.	+	435126.i	−0.740603	+	1.28276i	−0.952221	+	0.305410i	$0.901206\pi$
$164$	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	−0.979749	−	0.200230i	$-0.935831\pi$
$173$	−124580.	+	215779.i	−0.316470	+	0.548143i	0.663279	+	0.748373i	$0.269164\pi$
$174$		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	0.935738	−	0.352695i	$-0.114735\pi$
$179$	69628.9	+	120601.i	0.162427	+	0.281331i	−0.773312	+	0.634026i	$0.781401\pi$
$180$		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	−0.730893	−	0.682492i	$-0.760896\pi$
$191$	113747.	−	197015.i	0.225609	−	0.390766i	0.956502	+	0.291726i	$0.0942295\pi$
$192$		0			0
$193$	336187.	+	582293.i	0.649663	+	1.12525i	0.983203	+	0.182513i	$0.0584231\pi$
$193$	336187.	+	582293.i	0.649663	+	1.12525i	−0.333541	+	0.942736i	$0.608244\pi$
$194$	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	0.652371	−	0.757900i	$-0.273774\pi$
$199$	−184449.	−	319475.i	−0.330175	−	0.571879i	−0.982546	+	0.186020i	$0.940441\pi$
$200$	−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	−0.994729	−	0.102542i	$-0.967302\pi$
$227$	−455079.	−	788220.i	−0.586168	−	1.01527i	0.408560	−	0.912731i	$-0.366031\pi$
$228$		0			0
$229$	−260962.	+	452000.i	−0.328843	+	0.569573i	−0.982283	−	0.187406i	$-0.939992\pi$
$229$	−260962.	+	452000.i	−0.328843	+	0.569573i	0.653439	+	0.756979i	$0.273325\pi$
$230$	−240697.			−0.300020
$231$		0			0
$232$	762719.			0.930346
$233$	−521394.	+	903081.i	−0.629182	+	1.08977i	0.358535	+	0.933516i	$0.383277\pi$
$233$	−521394.	+	903081.i	−0.629182	+	1.08977i	−0.987716	+	0.156258i	$0.950057\pi$
$234$		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	0.997602	+	0.0692059i	$0.0220465\pi$
$241$	503789.	+	872588.i	0.558735	+	0.967758i	−0.438867	+	0.898552i	$0.644620\pi$
$242$	−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	−0.963278	−	0.268505i	$-0.913470\pi$
$257$	−263766.	+	456856.i	−0.249107	+	0.431466i	0.714171	+	0.699971i	$0.246804\pi$
$258$		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	0.776825	−	0.629716i	$-0.216829\pi$
$263$	−176042.	−	304914.i	−0.156938	−	0.271824i	−0.933763	+	0.357892i	$0.883496\pi$
$264$		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	0.949182	−	0.314727i	$-0.101913\pi$
$269$	239770.	+	415294.i	0.202029	+	0.349925i	−0.747153	+	0.664652i	$0.768580\pi$
$270$		0			0
$271$	488805.	−	846636.i	0.404308	−	0.700283i	−0.589932	−	0.807453i	$-0.700846\pi$
$271$	488805.	−	846636.i	0.404308	−	0.700283i	0.994241	+	0.107170i	$0.0341789\pi$
$272$	−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	0.611670	−	0.791113i	$-0.290498\pi$
$277$	−484362.	−	838939.i	−0.379289	−	0.656948i	−0.990959	+	0.134165i	$0.957165\pi$
$278$	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	−0.981223	−	0.192875i	$-0.938219\pi$
$283$	−886051.	−	1.53468e6i	−0.657646	−	1.13908i	0.323577	−	0.946202i	$-0.395115\pi$
$284$	−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	−0.963093	−	0.269169i	$-0.913251\pi$
$311$	−1.21898e6	−	2.11134e6i	−0.714654	−	1.23782i	0.248439	−	0.968647i	$-0.420082\pi$
$312$		0			0
$313$	−1.21047e6	+	2.09659e6i	−0.698381	+	1.20963i	0.270646	+	0.962679i	$0.412763\pi$
$313$	−1.21047e6	+	2.09659e6i	−0.698381	+	1.20963i	−0.969028	+	0.246953i	$0.920571\pi$
$314$	−3.25035e6			−1.86040
$315$		0			0
$316$	−492028.			−0.277186
$317$	938057.	−	1.62476e6i	0.524301	−	0.908116i	−0.475298	−	0.879825i	$-0.657660\pi$
$317$	938057.	−	1.62476e6i	0.524301	−	0.908116i	0.999600	−	0.0282918i	$-0.00900675\pi$
$318$		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	−0.697607	−	0.716480i	$-0.745752\pi$
$331$	541549.	−	937990.i	0.271686	−	0.470575i	0.969294	+	0.245906i	$0.0790853\pi$
$332$	−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	0.578662	−	0.815568i	$-0.303575\pi$
$347$	−935255.	−	1.61991e6i	−0.416972	−	0.722216i	−0.995633	+	0.0933518i	$0.970242\pi$
$348$		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	0.797642	−	0.603132i	$-0.206081\pi$
$353$	−289153.	−	500827.i	−0.123507	−	0.213920i	−0.921148	+	0.389212i	$0.872747\pi$
$354$		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	−0.994086	−	0.108598i	$-0.965364\pi$
$359$	−984090.	+	1.70449e6i	−0.402994	+	0.698006i	0.591092	+	0.806604i	$0.298697\pi$
$360$		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	0.574700	−	0.818364i	$-0.305119\pi$
$367$	−1.08726e6	−	1.88319e6i	−0.421375	−	0.729842i	−0.996074	+	0.0885223i	$0.971786\pi$
$368$	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	−0.965619	−	0.259963i	$-0.916290\pi$
$373$	−692379.	+	1.19924e6i	−0.257675	+	0.446306i	0.707944	+	0.706269i	$0.249623\pi$
$374$	−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	−0.425043	−	0.905173i	$-0.639741\pi$
$383$	1.64030e6	−	2.84108e6i	0.571382	−	0.989662i	0.996424	−	0.0844886i	$-0.0269257\pi$
$384$		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	0.506077	−	0.862488i	$-0.331095\pi$
$389$	−1.47405e6	−	2.55313e6i	−0.493899	−	0.855457i	−0.999975	+	0.00703108i	$0.997762\pi$
$390$		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	−0.860458	−	0.509521i	$-0.829823\pi$
$397$	34635.1	−	59989.7i	0.0110291	−	0.0191030i	0.871487	+	0.490418i	$0.163156\pi$
$398$	−2.61282e6			−0.826802
$399$		0			0
$400$	−4.14151e6			−1.29422
$401$	−1.67393e6	+	2.89933e6i	−0.519848	+	0.900404i	0.479886	+	0.877331i	$0.340678\pi$
$401$	−1.67393e6	+	2.89933e6i	−0.519848	+	0.900404i	−0.999734	+	0.0230725i	$0.992655\pi$
$402$		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	0.566502	−	0.824060i	$-0.308296\pi$
$409$	−1.45608e6	−	2.52201e6i	−0.430406	−	0.745485i	−0.996908	+	0.0785754i	$0.974963\pi$
$410$	−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	0.670592	+	0.741826i	$0.266040\pi$
$431$	3.77064e6	+	6.53094e6i	0.977736	+	1.69349i	0.307144	+	0.951663i	$0.400627\pi$
$432$		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	−0.876246	−	0.481865i	$-0.839960\pi$
$439$	−84051.9	+	145582.i	−0.0208155	+	0.0360535i	0.855430	+	0.517918i	$0.173293\pi$
$440$	−2.75259e6			−0.677814
$441$		0			0
$442$	764546.			0.186143
$443$	−1.42076e6	+	2.46082e6i	−0.343962	+	0.595760i	−0.985165	−	0.171612i	$-0.945102\pi$
$443$	−1.42076e6	+	2.46082e6i	−0.343962	+	0.595760i	0.641203	+	0.767372i	$0.278436\pi$
$444$		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	−0.939953	−	0.341303i	$-0.889132\pi$
$457$	−778637.	+	1.34864e6i	−0.174399	+	0.302068i	0.765554	+	0.643372i	$0.222465\pi$
$458$	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	−0.458800	−	0.888540i	$-0.651720\pi$
$467$	2.54545e6	−	4.40885e6i	0.540098	−	0.935477i	0.998898	−	0.0469376i	$-0.0149462\pi$
$468$		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	−0.900752	−	0.434334i	$-0.856984\pi$
$479$	−4.15042e6	−	7.18874e6i	−0.826521	−	1.43158i	0.0742312	−	0.997241i	$-0.476350\pi$
$480$		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	−0.902055	−	0.431621i	$-0.857942\pi$
$487$	−4.31701e6	−	7.47727e6i	−0.824822	−	1.42863i	0.0772330	−	0.997013i	$-0.475391\pi$
$488$	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	−0.946095	−	0.323890i	$-0.895009\pi$
$499$	−1.07102e6	+	1.85506e6i	−0.192551	+	0.333507i	0.753544	+	0.657397i	$0.228343\pi$
$500$	−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	−0.0859643	+	0.996298i	$0.527397\pi$
$509$	−5.29453e6	+	9.17040e6i	−0.905802	+	1.56889i	−0.819837	+	0.572596i	$0.805936\pi$
$510$		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	0.622301	−	0.782778i	$-0.286198\pi$
$521$	−2.27232e6	−	3.93578e6i	−0.366755	−	0.635238i	−0.989056	+	0.147540i	$0.952865\pi$
$522$		0			0
$523$	2.63599e6	−	4.56566e6i	0.421394	−	0.729877i	−0.574682	−	0.818377i	$-0.694874\pi$
$523$	2.63599e6	−	4.56566e6i	0.421394	−	0.729877i	0.996076	+	0.0885004i	$0.0282075\pi$
$524$	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	−0.997366	−	0.0725298i	$-0.976893\pi$
$541$	−2.96723e6	+	5.13939e6i	−0.435871	+	0.754950i	0.561496	+	0.827480i	$0.310226\pi$
$542$	−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	0.822833	−	0.568283i	$-0.192392\pi$
$557$	−591120.	−	1.02385e6i	−0.0807304	−	0.139829i	−0.903564	+	0.428453i	$0.859059\pi$
$558$		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	0.969136	−	0.246525i	$-0.0792888\pi$
$563$	2.03870e6	+	3.53114e6i	0.271071	+	0.469509i	−0.698065	+	0.716034i	$0.745955\pi$
$564$		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	−0.470070	−	0.882629i	$-0.655771\pi$
$569$	4.08807e6	−	7.08075e6i	0.529344	−	0.916851i	0.999414	−	0.0342216i	$-0.0108952\pi$
$570$		0			0
$571$	−1.65307e6	−	2.86321e6i	−0.212179	−	0.367504i	0.740217	−	0.672368i	$-0.234723\pi$
$571$	−1.65307e6	−	2.86321e6i	−0.212179	−	0.367504i	−0.952396	+	0.304863i	$0.901389\pi$
$572$	−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	0.998191	−	0.0601245i	$-0.0191498\pi$
$577$	3.57497e6	+	6.19203e6i	0.447026	+	0.774272i	−0.551165	+	0.834396i	$0.685816\pi$
$578$	−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	−0.604456	−	0.796639i	$-0.706609\pi$
$593$	3.31980e6	−	5.75006e6i	0.387682	−	0.671484i	0.992137	+	0.125154i	$0.0399426\pi$
$594$		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	0.758849	−	0.651266i	$-0.225762\pi$
$599$	−1.62096e6	−	2.80758e6i	−0.184588	−	0.319716i	−0.943438	+	0.331550i	$0.892428\pi$
$600$		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	−0.872443	−	0.488716i	$-0.837465\pi$
$607$	−117837.	+	204100.i	−0.0129811	+	0.0224839i	0.859462	+	0.511200i	$0.170799\pi$
$608$	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	0.844049	−	0.536267i	$-0.180166\pi$
$613$	−394438.	−	683187.i	−0.0423963	−	0.0734325i	−0.886445	+	0.462834i	$0.846833\pi$
$614$	−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	0.565691	−	0.824617i	$-0.308610\pi$
$619$	−4.11150e6	−	7.12132e6i	−0.431294	−	0.747023i	−0.996985	+	0.0775941i	$0.975276\pi$
$620$	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	−0.999884	−	0.0152411i	$-0.995148\pi$
$641$	−5.33804e6	−	9.24576e6i	−0.513141	−	0.888786i	0.486743	−	0.873545i	$-0.338185\pi$
$642$		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	0.726596	−	0.687065i	$-0.241101\pi$
$647$	−2.46728e6	−	4.27346e6i	−0.231717	−	0.401346i	−0.958314	+	0.285719i	$0.907768\pi$
$648$		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	−0.704351	−	0.709852i	$-0.748762\pi$
$653$	2.86112e6	−	4.95561e6i	0.262575	−	0.454793i	0.966925	+	0.255059i	$0.0820950\pi$
$654$		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	0.880220	+	0.474565i	$0.157395\pi$
$661$	9.56053e6	+	1.65593e7i	0.851096	+	1.47414i	−0.0291249	+	0.999576i	$0.509272\pi$
$662$	−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	−0.509790	−	0.860299i	$-0.670277\pi$
$677$	5.84516e6	−	1.01241e7i	0.490146	−	0.848957i	0.999936	+	0.0113419i	$0.00361030\pi$
$678$		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	0.946217	+	0.323534i	$0.104871\pi$
$683$	9.18370e6	+	1.59066e7i	0.753297	+	1.30475i	−0.192920	+	0.981214i	$0.561796\pi$
$684$		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	−0.170454	+	0.985366i	$0.554523\pi$
$691$	−1.17806e7	+	2.04045e7i	−0.938579	+	1.62567i	−0.768125	+	0.640300i	$0.778810\pi$
$692$	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	−0.709154	−	0.705053i	$-0.750923\pi$
$709$	3.42677e6	−	5.93533e6i	0.256017	−	0.443434i	0.965171	+	0.261619i	$0.0842564\pi$
$710$	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	0.232318	−	0.972640i	$-0.425369\pi$
$719$	1.32865e7	−	2.30128e7i	0.958490	−	1.66015i	0.726172	−	0.687513i	$-0.241298\pi$
$720$		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	−0.392447	−	0.919774i	$-0.628372\pi$
$733$	8.73265e6	−	1.51254e7i	0.600324	−	1.03979i	0.992772	−	0.120018i	$-0.0382951\pi$
$734$	−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	0.998939	−	0.0460536i	$-0.0146645\pi$
$739$	6.82304e6	+	1.18178e7i	0.459586	+	0.796026i	−0.539353	+	0.842080i	$0.681331\pi$
$740$	−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	−0.0857783	−	0.996314i	$-0.527338\pi$
$751$	1.26731e7	−	2.19505e7i	0.819944	−	1.42019i	0.905723	−	0.423871i	$-0.139329\pi$
$752$	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	−0.856809	−	0.515634i	$-0.827557\pi$
$761$	289914.	−	502146.i	0.0181471	−	0.0314318i	0.874956	+	0.484202i	$0.160890\pi$
$762$		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	−0.994666	−	0.103152i	$-0.967107\pi$
$773$	−9.74628e6	−	1.68810e7i	−0.586665	−	1.01613i	0.408001	−	0.912982i	$-0.366226\pi$
$774$		0			0
$775$	4.18138e6	−	7.24236e6i	0.250072	−	0.433137i
$776$	1.01292e7			0.603839
$777$		0			0
$778$	−2.08807e7			−1.23679
$779$	5.28969e6	−	9.16201e6i	0.312311	−	0.540938i
$780$		0			0
$781$	2.53173e6	+	4.38508e6i	0.148521	+	0.257247i
$782$	557927.	−	966358.i	0.0326257	−	0.0565094i
$783$		0			0
$784$	3.31262e6	+	2.11766e7i	0.192478	+	1.23046i
$785$	3.66337e7			2.12181
$786$		0			0
$787$	−6.81384e6	−	1.18019e7i	−0.392153	−	0.679228i	0.600580	−	0.799564i	$-0.294936\pi$
$787$	−6.81384e6	−	1.18019e7i	−0.392153	−	0.679228i	−0.992733	+	0.120336i	$0.961603\pi$
$788$	−11651.0	−	20180.1i	−0.000668416	−	0.00115773i
$789$		0			0
$790$	1.53143e7			0.873031
$791$	−1.71192e6	−	4.84900e6i	−0.0972839	−	0.275557i
$792$		0			0
$793$	−6.78320e6	+	1.17488e7i	−0.383046	+	0.663456i
$794$	−245312.	−	424893.i	−0.0138092	−	0.0239182i
$795$		0			0
$796$	−3.35061e6	+	5.80343e6i	−0.187431	+	0.324640i
$797$	−3.62853e6			−0.202341			−0.101171	−	0.994869i	$-0.532259\pi$
$797$	−3.62853e6			−0.202341			−0.101171	+	0.994869i	$0.532259\pi$
$798$		0			0
$799$	567208.			0.0314323
$800$	−9.57537e6	+	1.65850e7i	−0.528969	+	0.916202i
$801$		0			0
$802$	1.18561e7	+	2.05353e7i	0.650885	+	1.12737i
$803$	−1.23334e7	+	2.13620e7i	−0.674983	+	1.16910i
$804$		0			0
$805$	2.86446e6	−	3.34737e6i	0.155795	−	0.182060i
$806$	−5.32010e6			−0.288458
$807$		0			0
$808$	1.40611e6	+	2.43546e6i	0.0757691	+	0.131236i
$809$	1.49390e7	+	2.58751e7i	0.802509	+	1.38999i	0.917960	+	0.396673i	$0.129835\pi$
$809$	1.49390e7	+	2.58751e7i	0.802509	+	1.38999i	−0.115451	+	0.993313i	$0.536831\pi$
$810$		0			0
$811$	−1.02643e6			−0.0547995			−0.0273998	−	0.999625i	$-0.508723\pi$
$811$	−1.02643e6			−0.0547995			−0.0273998	+	0.999625i	$0.508723\pi$
$812$	1.19185e7	−	1.39278e7i	0.634354	−	0.741299i
$813$		0			0
$814$	−921730.	+	1.59648e6i	−0.0487576	+	0.0844507i
$815$	−2.00543e7	−	3.47351e7i	−1.05758	−	1.83178i
$816$		0			0
$817$	−1.38094e6	+	2.39187e6i	−0.0723804	+	0.125367i
$818$	−2.06262e7			−1.07779
$819$		0			0
$820$	−1.01940e7			−0.529434
$821$	−5.75312e6	+	9.96470e6i	−0.297883	+	0.515948i	−0.975651	−	0.219327i	$-0.929614\pi$
$821$	−5.75312e6	+	9.96470e6i	−0.297883	+	0.515948i	0.677768	+	0.735275i	$0.262947\pi$
$822$		0			0
$823$	1.25605e7	+	2.17554e7i	0.646408	+	1.11961i	0.983974	+	0.178310i	$0.0570630\pi$
$823$	1.25605e7	+	2.17554e7i	0.646408	+	1.11961i	−0.337566	+	0.941302i	$0.609604\pi$
$824$	−1.43197e6	+	2.48024e6i	−0.0734708	+	0.127255i
$825$		0			0
$826$	−9.07084e6	−	2.56932e7i	−0.462591	−	1.31029i
$827$	2.14447e6			0.109032			0.0545162	−	0.998513i	$-0.482638\pi$
$827$	2.14447e6			0.109032			0.0545162	+	0.998513i	$0.482638\pi$
$828$		0			0
$829$	−409033.	−	708465.i	−0.0206715	−	0.0358041i	0.855505	−	0.517795i	$-0.173247\pi$
$829$	−409033.	−	708465.i	−0.0206715	−	0.0358041i	−0.876176	+	0.481991i	$0.839914\pi$
$830$	2.25469e7	+	3.90523e7i	1.13603	+	1.96767i
$831$		0			0
$832$	279504.			0.0139984
$833$	5.80247e6	+	2.24008e6i	0.289735	+	0.111854i
$834$		0			0
$835$	−2.70078e7	+	4.67788e7i	−1.34052	+	2.32184i
$836$	4.81013e6	+	8.33138e6i	0.238035	+	0.412289i
$837$		0			0
$838$	1.63740e7	−	2.83606e7i	0.805460	−	1.39510i
$839$	2.11279e7			1.03622			0.518110	−	0.855314i	$-0.326636\pi$
$839$	2.11279e7			1.03622			0.518110	+	0.855314i	$0.326636\pi$
$840$		0			0
$841$	4.00785e7			1.95398
$842$	−9.31533e6	+	1.61346e7i	−0.452812	+	0.784294i
$843$		0			0
$844$	−4.56107e6	−	7.90001e6i	−0.220400	−	0.381743i
$845$	1.14239e7	−	1.97868e7i	0.550393	−	0.953308i
$846$		0			0
$847$	4.74298e6	+	883742.i	0.227166	+	0.0423269i
$848$	−1.21632e7			−0.580844
$849$		0			0
$850$	4.25604e6	+	7.37167e6i	0.202050	+	0.349960i
$851$	−157432.	−	272679.i	−0.00745191	−	0.0129071i
$852$		0			0
$853$	−1.89000e7			−0.889386			−0.444693	−	0.895683i	$-0.646687\pi$
$853$	−1.89000e7			−0.889386			−0.444693	+	0.895683i	$0.646687\pi$
$854$	2.77671e7	−	3.24484e7i	1.30283	−	1.52247i
$855$		0			0
$856$	4.30446e6	−	7.45554e6i	0.200786	−	0.347772i
$857$	1.86143e7	+	3.22409e7i	0.865753	+	1.49953i	0.866297	+	0.499529i	$0.166493\pi$
$857$	1.86143e7	+	3.22409e7i	0.865753	+	1.49953i	−0.000544054		1.00000i	$0.500173\pi$
$858$		0			0
$859$	−1.51032e6	+	2.61595e6i	−0.0698371	+	0.120961i	−0.898829	−	0.438298i	$-0.855581\pi$
$859$	−1.51032e6	+	2.61595e6i	−0.0698371	+	0.120961i	0.828992	+	0.559260i	$0.188915\pi$
$860$	2.66129e6			0.122700
$861$		0			0
$862$	5.34131e7			2.44838
$863$	−1.35921e7	+	2.35423e7i	−0.621242	+	1.07602i	0.368013	+	0.929821i	$0.380038\pi$
$863$	−1.35921e7	+	2.35423e7i	−0.621242	+	1.07602i	−0.989255	+	0.146202i	$0.953295\pi$
$864$		0			0
$865$	−9.94493e6	−	1.72251e7i	−0.451920	−	0.782748i
$866$	2.06660e7	−	3.57946e7i	0.936400	−	1.62189i
$867$		0			0
$868$	5.96196e6	+	1.11087e6i	0.268590	+	0.0500454i
$869$	9.53158e6			0.428169
$870$		0			0
$871$	3.90068e6	+	6.75618e6i	0.174219	+	0.301756i
$872$	−1.08093e7	−	1.87222e7i	−0.481399	−	0.833807i
$873$		0			0
$874$	−4.53766e6			−0.200934
$875$	421871.	+	1.19495e6i	0.0186277	+	0.0527630i
$876$		0			0
$877$	−8.69339e6	+	1.50574e7i	−0.381672	+	0.661075i	−0.991301	−	0.131611i	$-0.957985\pi$
$877$	−8.69339e6	+	1.50574e7i	−0.381672	+	0.661075i	0.609629	+	0.792687i	$0.291318\pi$
$878$	595320.	+	1.03112e6i	0.0260624	+	0.0451414i
$879$		0			0
$880$	−1.79128e7	+	3.10258e7i	−0.779751	+	1.35057i
$881$	8.14472e6			0.353538			0.176769	−	0.984252i	$-0.443435\pi$
$881$	8.14472e6			0.353538			0.176769	+	0.984252i	$0.443435\pi$
$882$		0			0
$883$	−3.10298e7			−1.33930			−0.669649	−	0.742678i	$-0.733555\pi$
$883$	−3.10298e7			−1.33930			−0.669649	+	0.742678i	$0.733555\pi$
$884$	980435.	−	1.69816e6i	0.0421976	−	0.0730884i
$885$		0			0
$886$	1.00629e7	+	1.74294e7i	0.430664	+	0.745931i
$887$	−7.35138e6	+	1.27330e7i	−0.313733	+	0.543401i	−0.979167	−	0.203055i	$-0.934913\pi$
$887$	−7.35138e6	+	1.27330e7i	−0.313733	+	0.543401i	0.665435	+	0.746456i	$0.268246\pi$
$888$		0			0
$889$	2.23304e6	+	6.32509e6i	0.0947638	+	0.268419i
$890$	2.46386e7			1.04266
$891$		0			0
$892$	1.06566e7	+	1.84578e7i	0.448443	+	0.776726i
$893$	−1.15329e6	−	1.99755e6i	−0.0483959	−	0.0838242i
$894$		0			0
$895$	−1.11166e7			−0.463890
$896$	2.31857e7	+	4.32010e6i	0.964827	+	0.179773i
$897$		0			0
$898$	5.01344e6	−	8.68354e6i	0.207465	−	0.359340i
$899$	1.00225e7	+	1.73595e7i	0.413596	+	0.716370i
$900$		0			0
$901$	−1.76479e6	+	3.05671e6i	−0.0724238	+	0.125442i
$902$	−1.75215e7			−0.717060
$903$		0			0
$904$	−3.88669e6			−0.158183
$905$	−1.22235e7	+	2.11716e7i	−0.496104	+	0.859277i
$906$		0			0
$907$	−6.54701e6	−	1.13398e7i	−0.264256	−	0.457705i	0.703112	−	0.711079i	$-0.251793\pi$
$907$	−6.54701e6	−	1.13398e7i	−0.264256	−	0.457705i	−0.967368	+	0.253374i	$0.918460\pi$
$908$	−8.26675e6	+	1.43184e7i	−0.332752	+	0.576343i
$909$		0			0
$910$	1.39008e7	−	1.62444e7i	0.556464	−	0.650278i
$911$	−2.68695e7			−1.07266			−0.536332	−	0.844007i	$-0.680191\pi$
$911$	−2.68695e7			−1.07266			−0.536332	+	0.844007i	$0.680191\pi$
$912$		0			0
$913$	1.40331e7	+	2.43061e7i	0.557156	+	0.965023i
$914$	5.51490e6	+	9.55209e6i	0.218360	+	0.378210i
$915$		0			0
$916$	9.48103e6			0.373351
$917$	−2.12423e7	−	3.95800e6i	−0.834215	−	0.155436i
$918$		0			0
$919$	−636586.	+	1.10260e6i	−0.0248638	+	0.0430654i	−0.878190	−	0.478313i	$-0.841249\pi$
$919$	−636586.	+	1.10260e6i	−0.0248638	+	0.0430654i	0.853326	+	0.521378i	$0.174582\pi$
$920$	−1.66496e6	−	2.88379e6i	−0.0648535	−	0.112330i
$921$		0			0
$922$	1.57714e7	−	2.73168e7i	0.611001	−	1.05828i
$923$	−4.19695e6			−0.162155
$924$		0			0
$925$	2.40187e6			0.0922986
$926$	1.74329e7	−	3.01947e7i	0.668102	−	1.15719i
$927$		0			0
$928$	−2.29516e7	−	3.97533e7i	−0.874867	−	1.51531i
$929$	−4.65852e6	+	8.06880e6i	−0.177096	+	0.306740i	−0.940885	−	0.338727i	$-0.890004\pi$
$929$	−4.65852e6	+	8.06880e6i	−0.177096	+	0.306740i	0.763789	+	0.645467i	$0.223337\pi$
$930$		0			0
$931$	−3.90905e6	−	2.49894e7i	−0.147808	−	0.944890i
$932$	1.89428e7			0.714338
$933$		0			0
$934$	−1.80288e7	−	3.12268e7i	−0.676239	−	1.17128i
$935$	5.19801e6	+	9.00322e6i	0.194450	+	0.336797i
$936$		0			0
$937$	1.18158e7			0.439657			0.219829	−	0.975539i	$-0.429450\pi$
$937$	1.18158e7			0.439657			0.219829	+	0.975539i	$0.429450\pi$
$938$	−8.17581e6	−	2.31580e7i	−0.303406	−	0.859397i
$939$		0			0
$940$	−1.11128e6	+	1.92479e6i	−0.0410208	+	0.0710501i
$941$	−1.26765e7	−	2.19563e7i	−0.466685	−	0.808323i	0.532591	−	0.846373i	$-0.321219\pi$
$941$	−1.26765e7	−	2.19563e7i	−0.466685	−	0.808323i	−0.999276	+	0.0380504i	$0.987885\pi$
$942$		0			0
$943$	1.49634e6	−	2.59173e6i	0.0547962	−	0.0949098i
$944$	−3.78436e7			−1.38217
$945$		0			0
$946$	4.57422e6			0.166184
$947$	1.32471e7	−	2.29446e7i	0.480004	−	0.831391i	−0.519733	−	0.854329i	$-0.673969\pi$
$947$	1.32471e7	−	2.29446e7i	0.480004	−	0.831391i	0.999737	+	0.0229375i	$0.00730187\pi$
$948$		0			0
$949$	−1.02228e7	−	1.77063e7i	−0.368471	−	0.638210i
$950$	1.73073e7	−	2.99772e7i	0.622187	−	1.07766i
$951$		0			0
$952$	3.05654e6	−	3.57184e6i	0.109304	−	0.127732i
$953$	1.88335e7			0.671735			0.335868	−	0.941909i	$-0.390970\pi$
$953$	1.88335e7			0.671735			0.335868	+	0.941909i	$0.390970\pi$
$954$		0			0
$955$	9.08015e6	+	1.57273e7i	0.322170	+	0.558014i
$956$	−1.39373e7	−	2.41401e7i	−0.493211	−	0.854267i
$957$		0			0
$958$	−5.87929e7			−2.06972
$959$	−2.38198e6	+	2.78355e6i	−0.0836355	+	0.0977356i
$960$		0			0
$961$	1.09988e7	−	1.90505e7i	0.384182	−	0.665423i
$962$	−763995.	−	1.32328e6i	−0.0266166	−	0.0461013i
$963$		0			0
$964$	9.15159e6	−	1.58510e7i	0.317179	−	0.549370i
$965$	−5.36740e7			−1.85544
$966$		0			0
$967$	−3.14956e7			−1.08314			−0.541569	−	0.840656i	$-0.682169\pi$
$967$	−3.14956e7			−1.08314			−0.541569	+	0.840656i	$0.682169\pi$
$968$	1.82328e6	−	3.15801e6i	0.0625409	−	0.108324i
$969$		0			0
$970$	2.92238e7	+	5.06171e7i	0.997257	+	1.72730i
$971$	−3.42834e6	+	5.93806e6i	−0.116691	+	0.202114i	−0.918454	−	0.395527i	$-0.870562\pi$
$971$	−3.42834e6	+	5.93806e6i	−0.116691	+	0.202114i	0.801764	+	0.597641i	$0.203895\pi$
$972$		0			0
$973$	1.45183e7	+	4.11231e7i	0.491624	+	1.39253i
$974$	−6.11527e7			−2.06547
$975$		0			0
$976$	−2.96579e7	−	5.13689e7i	−0.996587	−	1.72614i
$977$	1.40735e7	+	2.43761e7i	0.471701	+	0.817010i	0.999476	−	0.0323741i	$-0.0103068\pi$
$977$	1.40735e7	+	2.43761e7i	0.471701	+	0.817010i	−0.527775	+	0.849384i	$0.676973\pi$
$978$		0			0
$979$	1.53350e7			0.511361
$980$	−1.89699e7	+	1.53016e7i	−0.630956	+	0.508947i
$981$		0			0
$982$	−336571.	+	582958.i	−0.0111378	+	0.0192912i
$983$	1.17458e7	+	2.03443e7i	0.387703	+	0.671521i	0.992140	−	0.125132i	$-0.0399354\pi$
$983$	1.17458e7	+	2.03443e7i	0.387703	+	0.671521i	−0.604437	+	0.796653i	$0.706602\pi$
$984$		0			0
$985$	−51199.7	+	88680.5i	−0.00168142	+	0.00291231i
$986$	−2.04029e7			−0.668343
$987$		0			0
$988$	−7.97395e6			−0.259885
$989$	−390639.	+	676607.i	−0.0126995	+	0.0219961i
$990$		0			0
$991$	1.07206e6	+	1.85686e6i	0.0346765	+	0.0600615i	0.882843	−	0.469669i	$-0.155627\pi$
$991$	1.07206e6	+	1.85686e6i	0.0346765	+	0.0600615i	−0.848166	+	0.529730i	$0.822293\pi$
$992$	7.59311e6	−	1.31517e7i	0.244986	−	0.424327i
$993$		0			0
$994$	1.29885e7	+	2.42011e6i	0.416960	+	0.0776906i
$995$	2.94483e7			0.942979
$996$		0			0
$997$	−1.25436e7	−	2.17261e7i	−0.399654	−	0.692220i	0.594029	−	0.804443i	$-0.297536\pi$
$997$	−1.25436e7	−	2.17261e7i	−0.399654	−	0.692220i	−0.993683	+	0.112223i	$0.964203\pi$
$998$	7.58576e6	+	1.31389e7i	0.241086	+	0.417574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.e.d.37.2		4
3.2	odd	2		7.6.c.a.2.1	✓	4
7.2	even	3		441.6.a.n.1.1		2
7.4	even	3	inner	63.6.e.d.46.2		4
7.5	odd	6		441.6.a.m.1.1		2
12.11	even	2		112.6.i.c.65.1		4
21.2	odd	6		49.6.a.d.1.2		2
21.5	even	6		49.6.a.e.1.2		2
21.11	odd	6		7.6.c.a.4.1	yes	4
21.17	even	6		49.6.c.f.18.1		4
21.20	even	2		49.6.c.f.30.1		4
84.11	even	6		112.6.i.c.81.1		4
84.23	even	6		784.6.a.ba.1.2		2
84.47	odd	6		784.6.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.c.a.2.1	✓	4	3.2	odd	2
7.6.c.a.4.1	yes	4	21.11	odd	6
49.6.a.d.1.2		2	21.2	odd	6
49.6.a.e.1.2		2	21.5	even	6
49.6.c.f.18.1		4	21.17	even	6
49.6.c.f.30.1		4	21.20	even	2
63.6.e.d.37.2		4	1.1	even	1	trivial
63.6.e.d.46.2		4	7.4	even	3	inner
112.6.i.c.65.1		4	12.11	even	2
112.6.i.c.81.1		4	84.11	even	6
441.6.a.m.1.1		2	7.5	odd	6
441.6.a.n.1.1		2	7.2	even	3
784.6.a.t.1.1		2	84.47	odd	6
784.6.a.ba.1.2		2	84.23	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

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