LMFDB - Embedded newform 63.6.p.b.26.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(17,63)]

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([3, 1]))

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

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

chi := DirichletCharacter("63.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.8
Character	$\chi$	$=$	63.26
Dual form			63.6.p.b.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.55322 + 2.62880i) q^{2} +(-2.17881 - 3.77381i) q^{4} +(11.2537 - 19.4920i) q^{5} +(-61.1173 - 114.331i) q^{7} -191.154i q^{8} +(102.481 - 59.1675i) q^{10} +(204.551 - 118.097i) q^{11} -74.9079i q^{13} +(22.2740 - 681.241i) q^{14} +(432.784 - 749.603i) q^{16} +(-706.376 - 1223.48i) q^{17} +(1900.03 + 1096.98i) q^{19} -98.0787 q^{20} +1241.82 q^{22} +(-1226.72 - 708.246i) q^{23} +(1309.21 + 2267.61i) q^{25} +(196.918 - 341.072i) q^{26} +(-298.302 + 479.751i) q^{28} -2670.05i q^{29} +(-18.6933 + 10.7926i) q^{31} +(-1356.30 + 783.058i) q^{32} -7427.69i q^{34} +(-2916.34 - 95.3534i) q^{35} +(-1561.94 + 2705.36i) q^{37} +(5767.51 + 9989.61i) q^{38} +(-3725.97 - 2151.19i) q^{40} +12756.7 q^{41} -16880.8 q^{43} +(-891.354 - 514.623i) q^{44} +(-3723.67 - 6449.59i) q^{46} +(-2895.03 + 5014.34i) q^{47} +(-9336.34 + 13975.3i) q^{49} +13766.6i q^{50} +(-282.688 + 163.210i) q^{52} +(2139.36 - 1235.16i) q^{53} -5316.14i q^{55} +(-21854.9 + 11682.8i) q^{56} +(7019.02 - 12157.3i) q^{58} +(11191.5 + 19384.3i) q^{59} +(44752.4 + 25837.8i) q^{61} -113.486 q^{62} -35932.2 q^{64} +(-1460.10 - 842.991i) q^{65} +(22828.0 + 39539.3i) q^{67} +(-3078.12 + 5331.46i) q^{68} +(-13028.1 - 8100.65i) q^{70} -77353.6i q^{71} +(6307.63 - 3641.71i) q^{73} +(-14223.7 + 8212.05i) q^{74} -9560.47i q^{76} +(-26003.8 - 16168.8i) q^{77} +(47785.0 - 82766.1i) q^{79} +(-9740.84 - 16871.6i) q^{80} +(58083.8 + 33534.7i) q^{82} +94774.5 q^{83} -31797.4 q^{85} +(-76861.9 - 44376.2i) q^{86} +(-22574.8 - 39100.7i) q^{88} +(66240.2 - 114731. i) q^{89} +(-8564.32 + 4578.17i) q^{91} +6172.53i q^{92} +(-26363.4 + 15220.9i) q^{94} +(42764.8 - 24690.3i) q^{95} -58525.4i q^{97} +(-79248.6 + 39089.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49}+ \cdots - 1481724 q^{94}+O(q^{100}) $ 24 * q + 304 * q^4 - 436 * q^7 + 1992 * q^10 - 3644 * q^16 + 3804 * q^19 - 5648 * q^22 - 18852 * q^25 - 39172 * q^28 + 38652 * q^31 + 20548 * q^37 + 132060 * q^40 + 2200 * q^43 - 25712 * q^46 - 125676 * q^49 - 2940 * q^52 + 154300 * q^58 + 48504 * q^61 - 327880 * q^64 + 156324 * q^67 - 9468 * q^70 - 703236 * q^73 + 165756 * q^79 + 1081020 * q^82 - 284448 * q^85 + 582308 * q^88 - 19812 * q^91 - 1481724 * q^94

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	4.55322	+	2.62880i	0.804903	+	0.464711i	0.845183	−	0.534478i	$-0.179492\pi$
$2$	4.55322	+	2.62880i	0.804903	+	0.464711i	−0.0402799	+	0.999188i	$0.512825\pi$
$3$		0			0
$3$		0			0
$4$	−2.17881	−	3.77381i	−0.0680878	−	0.117931i
$5$	11.2537	−	19.4920i	0.201312	−	0.348683i	−0.747639	−	0.664105i	$-0.768813\pi$
$5$	11.2537	−	19.4920i	0.201312	−	0.348683i	0.948952	+	0.315422i	$0.102146\pi$
$6$		0			0
$7$	−61.1173	−	114.331i	−0.471432	−	0.881902i
$7$	−61.1173	−	114.331i	−0.471432	−	0.881902i
$8$		−	191.154i		−	1.05599i
$9$		0			0
$10$	102.481	−	59.1675i	0.324074	−	0.187104i
$11$	204.551	−	118.097i	0.509706	−	0.294279i	−0.223007	−	0.974817i	$-0.571587\pi$
$11$	204.551	−	118.097i	0.509706	−	0.294279i	0.732713	+	0.680538i	$0.238254\pi$
$12$		0			0
$13$		−	74.9079i		−	0.122933i	−0.998109	−	0.0614666i	$-0.980422\pi$
$13$		−	74.9079i		−	0.122933i	0.998109	−	0.0614666i	$-0.0195778\pi$
$14$	22.2740	−	681.241i	0.0303723	−	0.928925i
$15$		0			0
$16$	432.784	−	749.603i	0.422640	−	0.732035i
$17$	−706.376	−	1223.48i	−0.592808	−	1.02677i	−0.993852	−	0.110714i	$-0.964686\pi$
$17$	−706.376	−	1223.48i	−0.592808	−	1.02677i	0.401045	−	0.916059i	$-0.368647\pi$
$18$		0			0
$19$	1900.03	+	1096.98i	1.20747	+	0.697134i	0.962206	−	0.272322i	$-0.0877916\pi$
$19$	1900.03	+	1096.98i	1.20747	+	0.697134i	0.245265	+	0.969456i	$0.421125\pi$
$20$	−98.0787			−0.0548277
$21$		0			0
$22$	1241.82			0.547018
$23$	−1226.72	−	708.246i	−0.483532	−	0.279167i	0.238355	−	0.971178i	$-0.423392\pi$
$23$	−1226.72	−	708.246i	−0.483532	−	0.279167i	−0.721887	+	0.692011i	$0.756725\pi$
$24$		0			0
$25$	1309.21	+	2267.61i	0.418947	+	0.725637i
$26$	196.918	−	341.072i	0.0571284	−	0.0989493i
$27$		0			0
$28$	−298.302	+	479.751i	−0.0719052	+	0.115643i
$29$		−	2670.05i		−	0.589555i	−0.955566	−	0.294777i	$-0.904755\pi$
$29$		−	2670.05i		−	0.589555i	0.955566	−	0.294777i	$-0.0952455\pi$
$30$		0			0
$31$	−18.6933	+	10.7926i	−0.00349367	+	0.00201707i	−0.501746	−	0.865015i	$-0.667309\pi$
$31$	−18.6933	+	10.7926i	−0.00349367	+	0.00201707i	0.498252	+	0.867032i	$0.333975\pi$
$32$	−1356.30	+	783.058i	−0.234142	+	0.135182i
$33$		0			0
$34$		−	7427.69i		−	1.10194i
$35$	−2916.34	−	95.3534i	−0.402410	−	0.0131573i
$36$		0			0
$37$	−1561.94	+	2705.36i	−0.187568	+	0.324878i	−0.944439	−	0.328687i	$-0.893394\pi$
$37$	−1561.94	+	2705.36i	−0.187568	+	0.324878i	0.756871	+	0.653565i	$0.226727\pi$
$38$	5767.51	+	9989.61i	0.647931	+	1.12225i
$39$		0			0
$40$	−3725.97	−	2151.19i	−0.368205	−	0.212583i
$41$	12756.7			1.18516			0.592580	−	0.805511i	$-0.298109\pi$
$41$	12756.7			1.18516			0.592580	+	0.805511i	$0.298109\pi$
$42$		0			0
$43$	−16880.8			−1.39226			−0.696132	−	0.717914i	$-0.745097\pi$
$43$	−16880.8			−1.39226			−0.696132	+	0.717914i	$0.745097\pi$
$44$	−891.354	−	514.623i	−0.0694094	−	0.0400736i
$45$		0			0
$46$	−3723.67	−	6449.59i	−0.259464	−	0.449405i
$47$	−2895.03	+	5014.34i	−0.191165	+	0.331108i	−0.945637	−	0.325225i	$-0.894560\pi$
$47$	−2895.03	+	5014.34i	−0.191165	+	0.331108i	0.754472	+	0.656333i	$0.227893\pi$
$48$		0			0
$49$	−9336.34	+	13975.3i	−0.555503	+	0.831514i
$50$			13766.6i			0.778756i
$51$		0			0
$52$	−282.688	+	163.210i	−0.0144977	+	0.00837025i
$53$	2139.36	−	1235.16i	0.104615	−	0.0603997i	−0.446779	−	0.894644i	$-0.647429\pi$
$53$	2139.36	−	1235.16i	0.104615	−	0.0603997i	0.551395	+	0.834244i	$0.314096\pi$
$54$		0			0
$55$		−	5316.14i		−	0.236968i
$56$	−21854.9	+	11682.8i	−0.931276	+	0.497826i
$57$		0			0
$58$	7019.02	−	12157.3i	0.273972	−	0.474534i
$59$	11191.5	+	19384.3i	0.418561	+	0.724968i	0.995795	−	0.0916102i	$-0.0292014\pi$
$59$	11191.5	+	19384.3i	0.418561	+	0.724968i	−0.577234	+	0.816579i	$0.695868\pi$
$60$		0			0
$61$	44752.4	+	25837.8i	1.53990	+	0.889060i	0.998844	+	0.0480720i	$0.0153077\pi$
$61$	44752.4	+	25837.8i	1.53990	+	0.889060i	0.541053	+	0.840988i	$0.318026\pi$
$62$	−113.486			−0.00374942
$63$		0			0
$64$	−35932.2			−1.09656
$65$	−1460.10	−	842.991i	−0.0428648	−	0.0247480i
$66$		0			0
$67$	22828.0	+	39539.3i	0.621271	+	1.07607i	0.989249	+	0.146239i	$0.0467169\pi$
$67$	22828.0	+	39539.3i	0.621271	+	1.07607i	−0.367978	+	0.929835i	$0.619950\pi$
$68$	−3078.12	+	5331.46i	−0.0807259	+	0.139821i
$69$		0			0
$70$	−13028.1	−	8100.65i	−0.317786	−	0.197595i
$71$		−	77353.6i		−	1.82110i	−0.413396	−	0.910551i	$-0.635657\pi$
$71$		−	77353.6i		−	1.82110i	0.413396	−	0.910551i	$-0.364343\pi$
$72$		0			0
$73$	6307.63	−	3641.71i	0.138535	−	0.0799831i	−0.429131	−	0.903242i	$-0.641180\pi$
$73$	6307.63	−	3641.71i	0.138535	−	0.0799831i	0.567666	+	0.823259i	$0.307847\pi$
$74$	−14223.7	+	8212.05i	−0.301948	+	0.174330i
$75$		0			0
$76$		−	9560.47i		−	0.189865i
$77$	−26003.8	−	16168.8i	−0.499817	−	0.310778i
$78$		0			0
$79$	47785.0	−	82766.1i	0.861438	−	1.49205i	−0.00910243	−	0.999959i	$-0.502897\pi$
$79$	47785.0	−	82766.1i	0.861438	−	1.49205i	0.870541	−	0.492096i	$-0.163769\pi$
$80$	−9740.84	−	16871.6i	−0.170166	−	0.294735i
$81$		0			0
$82$	58083.8	+	33534.7i	0.953939	+	0.550757i
$83$	94774.5			1.51007			0.755034	−	0.655686i	$-0.227620\pi$
$83$	94774.5			1.51007			0.755034	+	0.655686i	$0.227620\pi$
$84$		0			0
$85$	−31797.4			−0.477358
$86$	−76861.9	−	44376.2i	−1.12064	−	0.647000i
$87$		0			0
$88$	−22574.8	−	39100.7i	−0.310754	−	0.538242i
$89$	66240.2	−	114731.i	0.886435	−	1.53535i	0.0423744	−	0.999102i	$-0.486508\pi$
$89$	66240.2	−	114731.i	0.886435	−	1.53535i	0.844060	−	0.536248i	$-0.180159\pi$
$90$		0			0
$91$	−8564.32	+	4578.17i	−0.108415	+	0.0579547i
$92$			6172.53i			0.0760315i
$93$		0			0
$94$	−26363.4	+	15220.9i	−0.307739	+	0.177673i
$95$	42764.8	−	24690.3i	0.486158	−	0.280684i
$96$		0			0
$97$		−	58525.4i		−	0.631560i	−0.948832	−	0.315780i	$-0.897734\pi$
$97$		−	58525.4i		−	0.631560i	0.948832	−	0.315780i	$-0.102266\pi$
$98$	−79248.6	+	39089.0i	−0.833540	+	0.411140i
$99$		0			0
$100$	5705.03	−	9881.40i	0.0570503	−	0.0988140i
$101$	59100.8	+	102366.i	0.576488	+	0.998506i	0.995878	+	0.0907003i	$0.0289105\pi$
$101$	59100.8	+	102366.i	0.576488	+	0.998506i	−0.419390	+	0.907806i	$0.637756\pi$
$102$		0			0
$103$	57902.2	+	33429.9i	0.537777	+	0.310486i	0.744178	−	0.667982i	$-0.232842\pi$
$103$	57902.2	+	33429.9i	0.537777	+	0.310486i	−0.206401	+	0.978468i	$0.566175\pi$
$104$	−14318.9			−0.129816
$105$		0			0
$106$	12988.0			0.112274
$107$	−103583.	−	59803.4i	−0.874635	−	0.504971i	−0.00574943	−	0.999983i	$-0.501830\pi$
$107$	−103583.	−	59803.4i	−0.874635	−	0.504971i	−0.868886	+	0.495013i	$0.835163\pi$
$108$		0			0
$109$	43105.3	+	74660.5i	0.347508	+	0.601901i	0.985806	−	0.167888i	$-0.0536948\pi$
$109$	43105.3	+	74660.5i	0.347508	+	0.601901i	−0.638298	+	0.769789i	$0.720361\pi$
$110$	13975.1	−	24205.5i	0.110122	−	0.190736i
$111$		0			0
$112$	−112154.	−	3667.01i	−0.844829	−	0.0276227i
$113$			156109.i			1.15009i	0.818122	+	0.575045i	$0.195016\pi$
$113$			156109.i			1.15009i	−0.818122	+	0.575045i	$0.804984\pi$
$114$		0			0
$115$	−27610.2	+	15940.8i	−0.194682	+	0.112400i
$116$	−10076.2	+	5817.52i	−0.0695270	+	0.0401414i
$117$		0			0
$118$			117681.i			0.778039i
$119$	−96710.3	+	155537.i	−0.626045	+	1.00685i
$120$		0			0
$121$	−52631.5	+	91160.4i	−0.326800	+	0.566034i
$122$	135845.	+	235290.i	0.826312	+	1.43121i
$123$		0			0
$124$	81.4583	+	47.0300i	0.000475753	+	0.000274676i
$125$	129269.			0.739982
$126$		0			0
$127$	−44114.5			−0.242702			−0.121351	−	0.992610i	$-0.538723\pi$
$127$	−44114.5			−0.242702			−0.121351	+	0.992610i	$0.538723\pi$
$128$	−120206.	−	69400.7i	−0.648484	−	0.374403i
$129$		0			0
$130$	−4432.11	−	7676.65i	−0.0230013	−	0.0398394i
$131$	56765.7	−	98321.1i	0.289007	−	0.500574i	−0.684566	−	0.728951i	$-0.740008\pi$
$131$	56765.7	−	98321.1i	0.289007	−	0.500574i	0.973573	+	0.228377i	$0.0733417\pi$
$132$		0			0
$133$	9294.82	−	284278.i	0.0455629	−	1.39352i
$134$			240041.i			1.15485i
$135$		0			0
$136$	−233873.	+	135027.i	−1.08426	+	0.625997i
$137$	−45729.4	+	26401.9i	−0.208158	+	0.120180i	−0.600455	−	0.799658i	$-0.705014\pi$
$137$	−45729.4	+	26401.9i	−0.208158	+	0.120180i	0.392297	+	0.919839i	$0.371681\pi$
$138$		0			0
$139$			225458.i			0.989758i	0.868962	+	0.494879i	$0.164788\pi$
$139$			225458.i			0.989758i	−0.868962	+	0.494879i	$0.835212\pi$
$140$	5994.31	+	11213.5i	0.0258475	+	0.0483526i
$141$		0			0
$142$	203347.	−	352208.i	0.846286	−	1.46581i
$143$	−8846.43	−	15322.5i	−0.0361766	−	0.0626597i
$144$		0			0
$145$	−52044.5	−	30047.9i	−0.205568	−	0.118685i
$146$	38293.4			0.148676
$147$		0			0
$148$	13612.7			0.0510844
$149$	−167621.	−	96776.2i	−0.618534	−	0.357111i	0.157764	−	0.987477i	$-0.449571\pi$
$149$	−167621.	−	96776.2i	−0.618534	−	0.357111i	−0.776298	+	0.630366i	$0.782905\pi$
$150$		0			0
$151$	−55732.4	−	96531.3i	−0.198914	−	0.344529i	0.749263	−	0.662273i	$-0.230408\pi$
$151$	−55732.4	−	96531.3i	−0.198914	−	0.344529i	−0.948177	+	0.317744i	$0.897075\pi$
$152$	209693.	−	363199.i	0.736164	−	1.27507i
$153$		0			0
$154$	−75896.7	−	141979.i	−0.257882	−	0.482416i
$155$			485.827i			0.00162425i
$156$		0			0
$157$	−482960.	+	278837.i	−1.56373	+	0.902821i	−0.566857	+	0.823816i	$0.691841\pi$
$157$	−482960.	+	278837.i	−1.56373	+	0.902821i	−0.996874	+	0.0790042i	$0.974826\pi$
$158$	435151.	−	251235.i	1.38675	−	0.800639i
$159$		0			0
$160$			35249.2i			0.108855i
$161$	−6001.01	+	183538.i	−0.0182457	+	0.558036i
$162$		0			0
$163$	170094.	−	294612.i	0.501442	−	0.868523i	−0.498556	−	0.866857i	$-0.666136\pi$
$163$	170094.	−	294612.i	0.501442	−	0.868523i	0.999999	−	0.00166607i	$-0.000530328\pi$
$164$	−27794.3	−	48141.2i	−0.0806949	−	0.139768i
$165$		0			0
$166$	431529.	+	249143.i	1.21546	+	0.701745i
$167$	−443163.			−1.22962			−0.614812	−	0.788674i	$-0.710768\pi$
$167$	−443163.			−1.22962			−0.614812	+	0.788674i	$0.710768\pi$
$168$		0			0
$169$	365682.			0.984887
$170$	−144781.	−	83589.1i	−0.384227	−	0.221834i
$171$		0			0
$172$	36780.0	+	63704.8i	0.0947961	+	0.164192i
$173$	240455.	−	416481.i	0.610829	−	1.05799i	−0.380272	−	0.924875i	$-0.624170\pi$
$173$	240455.	−	416481.i	0.610829	−	1.05799i	0.991101	−	0.133112i	$-0.0424969\pi$
$174$		0			0
$175$	179244.	−	288274.i	0.442436	−	0.711559i
$176$		−	204443.i		−	0.497496i
$177$		0			0
$178$	603212.	−	348265.i	1.42699	−	0.823872i
$179$	−362152.	+	209089.i	−0.844808	+	0.487750i	−0.858896	−	0.512150i	$-0.828849\pi$
$179$	−362152.	+	209089.i	−0.844808	+	0.487750i	0.0140874	+	0.999901i	$0.495516\pi$
$180$		0			0
$181$			559881.i			1.27028i	0.772397	+	0.635140i	$0.219058\pi$
$181$			559881.i			1.27028i	−0.772397	+	0.635140i	$0.780942\pi$
$182$	−51030.3	−	1668.50i	−0.114196	−	0.00373377i
$183$		0			0
$184$	−135384.	+	234492.i	−0.294797	+	0.510603i
$185$	35155.2	+	60890.6i	0.0755197	+	0.130804i
$186$		0			0
$187$	−288980.	−	166842.i	−0.604315	−	0.348901i
$188$	25230.9			0.0520640
$189$		0			0
$190$	259623.			0.521747
$191$	−625529.	−	361149.i	−1.24069	−	0.716314i	−0.271457	−	0.962451i	$-0.587506\pi$
$191$	−625529.	−	361149.i	−1.24069	−	0.716314i	−0.969235	+	0.246137i	$0.920839\pi$
$192$		0			0
$193$	98307.4	+	170273.i	0.189973	+	0.329044i	0.945241	−	0.326373i	$-0.105827\pi$
$193$	98307.4	+	170273.i	0.189973	+	0.329044i	−0.755268	+	0.655416i	$0.772493\pi$
$194$	153852.	−	266479.i	0.293493	−	0.508345i
$195$		0			0
$196$	73082.0	+	4784.13i	0.135885	+	0.00889534i
$197$			396596.i			0.728087i	0.931382	+	0.364043i	$0.118604\pi$
$197$			396596.i			0.728087i	−0.931382	+	0.364043i	$0.881396\pi$
$198$		0			0
$199$	−279066.	+	161119.i	−0.499544	+	0.288412i	−0.728525	−	0.685019i	$-0.759794\pi$
$199$	−279066.	+	161119.i	−0.499544	+	0.288412i	0.228981	+	0.973431i	$0.426461\pi$
$200$	433463.	−	250260.i	0.766262	−	0.442402i
$201$		0			0
$202$			621457.i			1.07160i
$203$	−305270.	+	163186.i	−0.519929	+	0.277935i
$204$		0			0
$205$	143560.	−	248653.i	0.238588	−	0.413246i
$206$	175761.	+	304427.i	0.288572	+	0.499821i
$207$		0			0
$208$	−56151.2	−	32418.9i	−0.0899913	−	0.0519565i
$209$	518204.			0.820607
$210$		0			0
$211$	−174621.			−0.270016			−0.135008	−	0.990844i	$-0.543106\pi$
$211$	−174621.			−0.270016			−0.135008	+	0.990844i	$0.543106\pi$
$212$	−9322.53	−	5382.37i	−0.0142460	−	0.00822496i
$213$		0			0
$214$	−314422.	−	544596.i	−0.469331	−	0.812905i
$215$	−189971.	+	329040.i	−0.280280	+	0.485459i
$216$		0			0
$217$	2376.42	+	1477.62i	0.00342589	+	0.00213016i
$218$			453261.i			0.645962i
$219$		0			0
$220$	−20062.1	+	11582.8i	−0.0279460	+	0.0161346i
$221$	−91648.3	+	52913.2i	−0.126224	+	0.0728757i
$222$		0			0
$223$		−	1.43212e6i		−	1.92849i	−0.265018	−	0.964243i	$-0.585378\pi$
$223$		−	1.43212e6i		−	1.92849i	0.265018	−	0.964243i	$-0.414622\pi$
$224$	172421.	+	107209.i	0.229599	+	0.142761i
$225$		0			0
$226$	−410380.	+	710799.i	−0.534460	+	0.925711i
$227$	−64266.0	−	111312.i	−0.0827784	−	0.143376i	0.821664	−	0.569972i	$-0.193046\pi$
$227$	−64266.0	−	111312.i	−0.0827784	−	0.143376i	−0.904442	+	0.426596i	$0.859713\pi$
$228$		0			0
$229$	−580972.	−	335424.i	−0.732093	−	0.422674i	0.0870944	−	0.996200i	$-0.472242\pi$
$229$	−580972.	−	335424.i	−0.732093	−	0.422674i	−0.819187	+	0.573526i	$0.805575\pi$
$230$	−167621.			−0.208933
$231$		0			0
$232$	−510390.			−0.622561
$233$	1.29318e6	+	746617.i	1.56052	+	0.900966i	0.997204	+	0.0747225i	$0.0238071\pi$
$233$	1.29318e6	+	746617.i	1.56052	+	0.900966i	0.563314	+	0.826243i	$0.309526\pi$
$234$		0			0
$235$	65159.7	+	112860.i	0.0769678	+	0.133312i
$236$	48768.3	−	84469.2i	0.0569977	−	0.0987230i
$237$		0			0
$238$	−849218.	+	453961.i	−0.971800	+	0.519488i
$239$		−	296079.i		−	0.335284i	−0.985848	−	0.167642i	$-0.946385\pi$
$239$		−	296079.i		−	0.335284i	0.985848	−	0.167642i	$-0.0536153\pi$
$240$		0			0
$241$	−542160.	+	313016.i	−0.601291	+	0.347155i	−0.769549	−	0.638587i	$-0.779519\pi$
$241$	−542160.	+	313016.i	−0.601291	+	0.347155i	0.168258	+	0.985743i	$0.446186\pi$
$242$	−479285.	+	276715.i	−0.526085	+	0.303735i
$243$		0			0
$244$		−	225183.i		−	0.242136i
$245$	167337.	+	339257.i	0.178106	+	0.361089i
$246$		0			0
$247$	82172.7	−	142327.i	0.0857009	−	0.148438i
$248$	2063.05	+	3573.30i	0.00213000	+	0.00368927i
$249$		0			0
$250$	588592.	+	339824.i	0.595613	+	0.343877i
$251$	594368.			0.595486			0.297743	−	0.954646i	$-0.403766\pi$
$251$	594368.			0.595486			0.297743	+	0.954646i	$0.403766\pi$
$252$		0			0
$253$	−334568.			−0.328612
$254$	−200863.	−	115968.i	−0.195351	−	0.112786i
$255$		0			0
$256$	210033.	+	363789.i	0.200304	+	0.346936i
$257$	−900490.	+	1.55969e6i	−0.850445	+	1.47301i	0.0303625	+	0.999539i	$0.490334\pi$
$257$	−900490.	+	1.55969e6i	−0.850445	+	1.47301i	−0.880807	+	0.473475i	$0.843000\pi$
$258$		0			0
$259$	404769.	+	13234.4i	0.374936	+	0.0122590i
$260$			7346.87i			0.00674014i
$261$		0			0
$262$	516933.	−	298451.i	0.465244	−	0.268609i
$263$	−577447.	+	333389.i	−0.514781	+	0.297209i	−0.734797	−	0.678287i	$-0.762722\pi$
$263$	−577447.	+	333389.i	−0.514781	+	0.297209i	0.220016	+	0.975496i	$0.429389\pi$
$264$		0			0
$265$		−	55600.6i		−	0.0486368i
$266$	789632.	−	1.26995e6i	0.684259	−	1.10048i
$267$		0			0
$268$	99475.8	−	172297.i	0.0846020	−	0.146535i
$269$	−195297.	−	338265.i	−0.164557	−	0.285021i	0.771941	−	0.635694i	$-0.219286\pi$
$269$	−195297.	−	338265.i	−0.164557	−	0.285021i	−0.936498	+	0.350673i	$0.885953\pi$
$270$		0			0
$271$	811394.	+	468458.i	0.671133	+	0.387479i	0.796506	−	0.604631i	$-0.206679\pi$
$271$	811394.	+	468458.i	0.671133	+	0.387479i	−0.125373	+	0.992110i	$0.540013\pi$
$272$	−1.22283e6			−1.00218
$273$		0			0
$274$	−277621.			−0.223396
$275$	535599.	+	309228.i	0.427079	+	0.246574i
$276$		0			0
$277$	504635.	+	874053.i	0.395164	+	0.684445i	0.993122	−	0.117083i	$-0.0373543\pi$
$277$	504635.	+	874053.i	0.395164	+	0.684445i	−0.597958	+	0.801528i	$0.704021\pi$
$278$	−592685.	+	1.02656e6i	−0.459951	+	0.796659i
$279$		0			0
$280$	−18227.2	+	557470.i	−0.0138939	+	0.424939i
$281$		−	2.06576e6i		−	1.56068i	−0.625354	−	0.780341i	$-0.715045\pi$
$281$		−	2.06576e6i		−	1.56068i	0.625354	−	0.780341i	$-0.284955\pi$
$282$		0			0
$283$	1.17392e6	−	677761.i	0.871307	−	0.503049i	0.00352475	−	0.999994i	$-0.498878\pi$
$283$	1.17392e6	−	677761.i	0.871307	−	0.503049i	0.867782	+	0.496944i	$0.165545\pi$
$284$	−291917.	+	168539.i	−0.214765	+	0.123995i
$285$		0			0
$286$		−	93022.0i		−	0.0672467i
$287$	−779653.	−	1.45849e6i	−0.558723	−	1.04520i
$288$		0			0
$289$	−288006.	+	498842.i	−0.202842	+	0.351332i
$290$	−157980.	−	273630.i	−0.110308	−	0.191059i
$291$		0			0
$292$	−27486.2	−	15869.2i	−0.0188651	−	0.0108917i
$293$	2.10771e6			1.43431			0.717154	−	0.696915i	$-0.245445\pi$
$293$	2.10771e6			1.43431			0.717154	+	0.696915i	$0.245445\pi$
$294$		0			0
$295$	503784.			0.337046
$296$	517139.	+	298570.i	0.343066	+	0.198069i
$297$		0			0
$298$	−508811.	−	881286.i	−0.331906	−	0.574879i
$299$	−53053.2	+	91890.8i	−0.0343189	+	0.0594421i
$300$		0			0
$301$	1.03171e6	+	1.93000e6i	0.656358	+	1.22784i
$302$		−	586037.i		−	0.369750i
$303$		0			0
$304$	1.64461e6	−	949514.i	1.02065	−	0.589274i
$305$	1.00726e6	−	581542.i	0.620001	−	0.357958i
$306$		0			0
$307$		−	2.27569e6i		−	1.37806i	−0.724733	−	0.689029i	$-0.758037\pi$
$307$		−	2.27569e6i		−	1.37806i	0.724733	−	0.689029i	$-0.241963\pi$
$308$	−4360.44	+	133362.i	−0.00261911	+	0.0801043i
$309$		0			0
$310$	−1277.14	+	2212.08i	−0.000754805	+	0.00130736i
$311$	−1.41341e6	−	2.44810e6i	−0.828644	−	1.43525i	−0.899102	−	0.437739i	$-0.855779\pi$
$311$	−1.41341e6	−	2.44810e6i	−0.828644	−	1.43525i	0.0704576	−	0.997515i	$-0.477554\pi$
$312$		0			0
$313$	−672815.	−	388450.i	−0.388181	−	0.224117i	0.293191	−	0.956054i	$-0.405283\pi$
$313$	−672815.	−	388450.i	−0.388181	−	0.224117i	−0.681372	+	0.731937i	$0.738616\pi$
$314$	−2.93203e6			−1.67820
$315$		0			0
$316$	−416458.			−0.234614
$317$	1.01168e6	+	584096.i	0.565454	+	0.326465i	0.755332	−	0.655343i	$-0.227476\pi$
$317$	1.01168e6	+	584096.i	0.565454	+	0.326465i	−0.189878	+	0.981808i	$0.560809\pi$
$318$		0			0
$319$	−315326.	−	546160.i	−0.173493	−	0.300499i
$320$	−404370.	+	700390.i	−0.220752	+	0.382353i
$321$		0			0
$322$	−509810.	+	819915.i	−0.274011	+	0.440686i
$323$		−	3.09953e6i		−	1.65307i
$324$		0			0
$325$	169862.	−	98070.0i	0.0892048	−	0.0515024i
$326$	1.54895e6	−	894288.i	0.807224	−	0.466051i
$327$		0			0
$328$		−	2.43848e6i		−	1.25151i
$329$	750233.	+	24529.8i	0.382126	+	0.0124941i
$330$		0			0
$331$	−1.10539e6	+	1.91460e6i	−0.554558	+	0.960522i	0.443380	+	0.896334i	$0.353779\pi$
$331$	−1.10539e6	+	1.91460e6i	−0.554558	+	0.960522i	−0.997938	+	0.0641886i	$0.979554\pi$
$332$	−206496.	−	357661.i	−0.102817	−	0.178084i
$333$		0			0
$334$	−2.01782e6	−	1.16499e6i	−0.989728	−	0.571420i
$335$	1.02760e6			0.500279
$336$		0			0
$337$	−425609.			−0.204144			−0.102072	−	0.994777i	$-0.532547\pi$
$337$	−425609.			−0.204144			−0.102072	+	0.994777i	$0.532547\pi$
$338$	1.66503e6	+	961305.i	0.792739	+	0.457688i
$339$		0			0
$340$	69280.5	+	119997.i	0.0325023	+	0.0562956i
$341$	−2549.16	+	4415.27i	−0.00118716	+	0.00205623i
$342$		0			0
$343$	2.16842e6	+	213306.i	0.995197	+	0.0978967i
$344$			3.22683e6i			1.47021i
$345$		0			0
$346$	2.18969e6	−	1.26422e6i	0.983315	−	0.567717i
$347$	−3.01803e6	+	1.74246e6i	−1.34555	+	0.776854i	−0.987616	−	0.156892i	$-0.949853\pi$
$347$	−3.01803e6	+	1.74246e6i	−1.34555	+	0.776854i	−0.357935	+	0.933746i	$0.616519\pi$
$348$		0			0
$349$			2.41916e6i			1.06316i	0.847007	+	0.531582i	$0.178402\pi$
$349$			2.41916e6i			1.06316i	−0.847007	+	0.531582i	$0.821598\pi$
$350$	1.57395e6	−	841377.i	0.686787	−	0.367131i
$351$		0			0
$352$	−184954.	+	320350.i	−0.0795623	+	0.137806i
$353$	1.30391e6	+	2.25843e6i	0.556942	+	0.964652i	0.997750	+	0.0670505i	$0.0213589\pi$
$353$	1.30391e6	+	2.25843e6i	0.556942	+	0.964652i	−0.440807	+	0.897602i	$0.645308\pi$
$354$		0			0
$355$	−1.50778e6	−	870514.i	−0.634988	−	0.366611i
$356$	−577299.			−0.241421
$357$		0			0
$358$	−2.19861e6			−0.906651
$359$	1.03254e6	+	596139.i	0.422836	+	0.244125i	0.696290	−	0.717761i	$-0.254833\pi$
$359$	1.03254e6	+	596139.i	0.422836	+	0.244125i	−0.273454	+	0.961885i	$0.588166\pi$
$360$		0			0
$361$	1.16870e6	+	2.02424e6i	0.471992	+	0.817514i
$362$	−1.47182e6	+	2.54926e6i	−0.590313	+	1.02245i
$363$		0			0
$364$	35937.1	+	22345.1i	0.0142164	+	0.00883954i
$365$		−	163931.i		−	0.0644064i
$366$		0			0
$367$	−2.79577e6	+	1.61414e6i	−1.08352	+	0.625570i	−0.931844	−	0.362860i	$-0.881800\pi$
$367$	−2.79577e6	+	1.61414e6i	−1.08352	+	0.625570i	−0.151676	+	0.988430i	$0.548467\pi$
$368$	−1.06181e6	+	613034.i	−0.408720	+	0.235975i
$369$		0			0
$370$			369664.i			0.140379i
$371$	−271970.	−	169107.i	−0.102586	−	0.0637861i
$372$		0			0
$373$	−626843.	+	1.08572e6i	−0.233285	+	0.404062i	−0.958773	−	0.284173i	$-0.908281\pi$
$373$	−626843.	+	1.08572e6i	−0.233285	+	0.404062i	0.725488	+	0.688235i	$0.241614\pi$
$374$	−877191.	−	1.51934e6i	−0.324276	−	0.561663i
$375$		0			0
$376$	958511.	+	553396.i	0.349645	+	0.201868i
$377$	−200008.			−0.0724758
$378$		0			0
$379$	3.09861e6			1.10808			0.554038	−	0.832492i	$-0.313086\pi$
$379$	3.09861e6			1.10808			0.554038	+	0.832492i	$0.313086\pi$
$380$	−186353.	−	107591.i	−0.0662028	−	0.0382222i
$381$		0			0
$382$	−1.89878e6	−	3.28878e6i	−0.665758	−	1.15313i
$383$	−2.21038e6	+	3.82848e6i	−0.769962	+	1.33361i	0.167621	+	0.985852i	$0.446392\pi$
$383$	−2.21038e6	+	3.82848e6i	−0.769962	+	1.33361i	−0.937583	+	0.347762i	$0.886942\pi$
$384$		0			0
$385$	−607801.	+	324908.i	−0.208982	+	0.111714i
$386$			1.03372e6i			0.353131i
$387$		0			0
$388$	−220863.	+	127516.i	−0.0744808	+	0.0430015i
$389$	−654412.	+	377825.i	−0.219269	+	0.126595i	−0.605612	−	0.795760i	$-0.707072\pi$
$389$	−654412.	+	377825.i	−0.219269	+	0.126595i	0.386343	+	0.922355i	$0.373738\pi$
$390$		0			0
$391$			2.00115e6i			0.661970i
$392$	2.67143e6	+	1.78468e6i	0.878068	+	0.586604i
$393$		0			0
$394$	−1.04257e6	+	1.80579e6i	−0.338350	+	0.586039i
$395$	−1.07552e6	−	1.86285e6i	−0.346837	−	0.600738i
$396$		0			0
$397$	−2.54728e6	−	1.47067e6i	−0.811150	−	0.468317i	0.0362054	−	0.999344i	$-0.488473\pi$
$397$	−2.54728e6	−	1.47067e6i	−0.811150	−	0.468317i	−0.847355	+	0.531027i	$0.821806\pi$
$398$	−1.69420e6			−0.536113
$399$		0			0
$400$	2.26642e6			0.708255
$401$	4.90714e6	+	2.83314e6i	1.52394	+	0.879847i	0.999598	+	0.0283388i	$0.00902172\pi$
$401$	4.90714e6	+	2.83314e6i	1.52394	+	0.879847i	0.524341	+	0.851508i	$0.324312\pi$
$402$		0			0
$403$	808.450	+	1400.28i	0.000247965	+	0.000429488i
$404$	257539.	−	446070.i	0.0785035	−	0.135972i
$405$		0			0
$406$	−1.81895e6	−	59472.7i	−0.547652	−	0.0179062i
$407$			737843.i			0.220789i
$408$		0			0
$409$	−273655.	+	157995.i	−0.0808899	+	0.0467018i	−0.539899	−	0.841730i	$-0.681538\pi$
$409$	−273655.	+	157995.i	−0.0808899	+	0.0467018i	0.459009	+	0.888431i	$0.348204\pi$
$410$	1.30732e6	−	754780.i	0.384080	−	0.221748i
$411$		0			0
$412$		−	291349.i		−	0.0845611i
$413$	1.53223e6	−	2.46425e6i	0.442028	−	0.710903i
$414$		0			0
$415$	1.06656e6	−	1.84734e6i	0.303995	−	0.526536i
$416$	58657.2	+	101597.i	0.0166183	+	0.0287838i
$417$		0			0
$418$	2.35950e6	+	1.36226e6i	0.660509	+	0.381345i
$419$	−2.99225e6			−0.832651			−0.416325	−	0.909216i	$-0.636682\pi$
$419$	−2.99225e6			−0.832651			−0.416325	+	0.909216i	$0.636682\pi$
$420$		0			0
$421$	2.64469e6			0.727227			0.363613	−	0.931550i	$-0.381543\pi$
$421$	2.64469e6			0.727227			0.363613	+	0.931550i	$0.381543\pi$
$422$	−795087.	−	459044.i	−0.217337	−	0.125480i
$423$		0			0
$424$	−236106.	−	408948.i	−0.0637812	−	0.110472i
$425$	1.84959e6	−	3.20358e6i	0.496710	−	0.860326i
$426$		0			0
$427$	218926.	−	6.69574e6i	0.0581068	−	1.77717i
$428$			521200.i			0.137529i
$429$		0			0
$430$	−1.72996e6	+	998794.i	−0.451196	+	0.260498i
$431$	3.22483e6	−	1.86186e6i	0.836207	−	0.482784i	−0.0197662	−	0.999805i	$-0.506292\pi$
$431$	3.22483e6	−	1.86186e6i	0.836207	−	0.482784i	0.855973	+	0.517020i	$0.172959\pi$
$432$		0			0
$433$			646932.i			0.165821i	0.996557	+	0.0829104i	$0.0264215\pi$
$433$			646932.i			0.165821i	−0.996557	+	0.0829104i	$0.973578\pi$
$434$	6935.98	+	12975.1i	0.00176760	+	0.00330662i
$435$		0			0
$436$	187836.	−	325342.i	0.0473220	−	0.0819642i
$437$	−1.55387e6	−	2.69138e6i	−0.389234	−	0.674173i
$438$		0			0
$439$	−4.07186e6	−	2.35089e6i	−1.00840	−	0.582198i	−0.0976753	−	0.995218i	$-0.531141\pi$
$439$	−4.07186e6	−	2.35089e6i	−1.00840	−	0.582198i	−0.910722	+	0.413020i	$0.864474\pi$
$440$	−1.01620e6			−0.250235
$441$		0			0
$442$	−556393.			−0.135465
$443$	−6.32445e6	−	3.65143e6i	−1.53114	−	0.884002i	−0.999310	−	0.0371482i	$-0.988173\pi$
$443$	−6.32445e6	−	3.65143e6i	−1.53114	−	0.884002i	−0.531826	−	0.846854i	$-0.678494\pi$
$444$		0			0
$445$	−1.49090e6	−	2.58231e6i	−0.356901	−	0.618170i
$446$	3.76475e6	−	6.52074e6i	0.896189	−	1.55224i
$447$		0			0
$448$	2.19608e6	+	4.10818e6i	0.516955	+	0.967061i
$449$			511884.i			0.119827i	0.998204	+	0.0599136i	$0.0190825\pi$
$449$			511884.i			0.119827i	−0.998204	+	0.0599136i	$0.980917\pi$
$450$		0			0
$451$	2.60938e6	−	1.50653e6i	0.604083	−	0.348768i
$452$	589125.	−	340132.i	0.135632	−	0.0783071i
$453$		0			0
$454$		−	675771.i		−	0.153872i
$455$	−7142.72	+	218457.i	−0.00161747	+	0.0494695i
$456$		0			0
$457$	−1.05991e6	+	1.83582e6i	−0.237399	+	0.411186i	−0.959967	−	0.280113i	$-0.909628\pi$
$457$	−1.05991e6	+	1.83582e6i	−0.237399	+	0.411186i	0.722568	+	0.691299i	$0.242961\pi$
$458$	−1.76353e6	−	3.05452e6i	−0.392842	−	0.680423i
$459$		0			0
$460$	120315.	+	69463.8i	0.0265109	+	0.0153061i
$461$	5.89721e6			1.29239			0.646197	−	0.763171i	$-0.276359\pi$
$461$	5.89721e6			1.29239			0.646197	+	0.763171i	$0.276359\pi$
$462$		0			0
$463$	3.96682e6			0.859982			0.429991	−	0.902833i	$-0.358517\pi$
$463$	3.96682e6			0.859982			0.429991	+	0.902833i	$0.358517\pi$
$464$	−2.00148e6	−	1.15555e6i	−0.431574	−	0.249170i
$465$		0			0
$466$	3.92542e6	+	6.79902e6i	0.837377	+	1.45038i
$467$	−1.85318e6	+	3.20980e6i	−0.393210	+	0.681060i	−0.992871	−	0.119194i	$-0.961969\pi$
$467$	−1.85318e6	+	3.20980e6i	−0.393210	+	0.681060i	0.599661	+	0.800254i	$0.295302\pi$
$468$		0			0
$469$	3.12540e6	−	5.02650e6i	0.656104	−	1.05520i
$470$			685167.i			0.143071i
$471$		0			0
$472$	3.70538e6	−	2.13930e6i	0.765557	−	0.441994i
$473$	−3.45298e6	+	1.99358e6i	−0.709644	+	0.409713i
$474$		0			0
$475$			5.74472e6i			1.16825i
$476$	797679.	+	26081.1i	0.161366	+	0.00527604i
$477$		0			0
$478$	778333.	−	1.34811e6i	0.155810	−	0.269871i
$479$	2.97998e6	+	5.16147e6i	0.593436	+	1.02786i	0.993766	+	0.111490i	$0.0355624\pi$
$479$	2.97998e6	+	5.16147e6i	0.593436	+	1.02786i	−0.400329	+	0.916371i	$0.631104\pi$
$480$		0			0
$481$	202652.	+	117001.i	0.0399383	+	0.0230584i
$482$	−3.29143e6			−0.645308
$483$		0			0
$484$	458696.			0.0890043
$485$	−1.14078e6	−	658627.i	−0.220215	−	0.127141i
$486$		0			0
$487$	−1.35647e6	−	2.34948e6i	−0.259172	−	0.448900i	0.706848	−	0.707365i	$-0.250116\pi$
$487$	−1.35647e6	−	2.34948e6i	−0.259172	−	0.448900i	−0.966020	+	0.258466i	$0.916783\pi$
$488$	4.93900e6	−	8.55460e6i	0.938835	−	1.62611i
$489$		0			0
$490$	−129917.	+	1.98461e6i	−0.0244443	+	0.373409i
$491$		−	3.15074e6i		−	0.589806i	−0.955527	−	0.294903i	$-0.904713\pi$
$491$		−	3.15074e6i		−	0.589806i	0.955527	−	0.294903i	$-0.0952873\pi$
$492$		0			0
$493$	−3.26675e6	+	1.88606e6i	−0.605339	+	0.349492i
$494$	748301.	−	432032.i	0.137962	−	0.0796523i
$495$		0			0
$496$			18683.4i			0.00340999i
$497$	−8.84394e6	+	4.72764e6i	−1.60603	+	0.858527i
$498$		0			0
$499$	883993.	−	1.53112e6i	0.158927	−	0.275270i	−0.775555	−	0.631280i	$-0.782530\pi$
$499$	883993.	−	1.53112e6i	0.158927	−	0.275270i	0.934482	+	0.356010i	$0.115863\pi$
$500$	−281653.	−	487838.i	−0.0503837	−	0.0872671i
$501$		0			0
$502$	2.70629e6	+	1.56248e6i	0.479308	+	0.276729i
$503$	−696922.			−0.122819			−0.0614093	−	0.998113i	$-0.519560\pi$
$503$	−696922.			−0.122819			−0.0614093	+	0.998113i	$0.519560\pi$
$504$		0			0
$505$	2.66041e6			0.464217
$506$	−1.52336e6	−	879513.i	−0.264501	−	0.152709i
$507$		0			0
$508$	96117.1	+	166480.i	0.0165250	+	0.0286221i
$509$	−2.44284e6	+	4.23113e6i	−0.417928	+	0.723872i	−0.995731	−	0.0923040i	$-0.970577\pi$
$509$	−2.44284e6	+	4.23113e6i	−0.417928	+	0.723872i	0.577803	+	0.816176i	$0.303910\pi$
$510$		0			0
$511$	−801868.	−	498589.i	−0.135847	−	0.0844676i
$512$			6.65019e6i			1.12114i
$513$		0			0
$514$	−8.20025e6	+	4.73442e6i	−1.36905	+	0.790422i
$515$	1.30323e6	−	752420.i	0.216522	−	0.125009i
$516$		0			0
$517$			1.36758e6i			0.225023i
$518$	1.80821e6	+	1.12432e6i	0.296090	+	0.184104i
$519$		0			0
$520$	−161141.	+	279105.i	−0.0261335	+	0.0452646i
$521$	4.50674e6	+	7.80591e6i	0.727392	+	1.25988i	0.957982	+	0.286829i	$0.0926012\pi$
$521$	4.50674e6	+	7.80591e6i	0.727392	+	1.25988i	−0.230590	+	0.973051i	$0.574065\pi$
$522$		0			0
$523$	1.30249e6	+	751996.i	0.208220	+	0.120216i	0.600484	−	0.799637i	$-0.294975\pi$
$523$	1.30249e6	+	751996.i	0.208220	+	0.120216i	−0.392264	+	0.919853i	$0.628308\pi$
$524$	−494726.			−0.0787112
$525$		0			0
$526$	−3.50565e6			−0.552465
$527$	26409.0	+	15247.3i	0.00414215	+	0.00239147i
$528$		0			0
$529$	−2.21495e6	−	3.83640e6i	−0.344131	−	0.596053i
$530$	146163.	−	253162.i	0.0226021	−	0.0391479i
$531$		0			0
$532$	−1.09306e6	+	584311.i	−0.167443	+	0.0895086i
$533$		−	955574.i		−	0.145696i
$534$		0			0
$535$	−2.33137e6	+	1.34602e6i	−0.352150	+	0.203314i
$536$	7.55809e6	−	4.36367e6i	1.13632	−	0.656054i
$537$		0			0
$538$		−	2.05359e6i		−	0.305885i
$539$	−259313.	+	3.96125e6i	−0.0384461	+	0.587300i
$540$		0			0
$541$	3.09265e6	−	5.35663e6i	0.454295	−	0.786862i	−0.544352	−	0.838857i	$-0.683224\pi$
$541$	3.09265e6	−	5.35663e6i	0.454295	−	0.786862i	0.998647	+	0.0519944i	$0.0165578\pi$
$542$	2.46297e6	+	4.26599e6i	0.360131	+	0.623765i
$543$		0			0
$544$	1.91611e6	+	1.10627e6i	0.277602	+	0.160274i
$545$	1.94038e6			0.279830
$546$		0			0
$547$	−1.09172e7			−1.56007			−0.780034	−	0.625737i	$-0.784798\pi$
$547$	−1.09172e7			−1.56007			−0.780034	+	0.625737i	$0.784798\pi$
$548$	199271.	+	115049.i	0.0283461	+	0.0163656i
$549$		0			0
$550$	1.62580e6	+	2.81597e6i	0.229171	+	0.396936i
$551$	2.92900e6	−	5.07318e6i	0.410999	−	0.711870i
$552$		0			0
$553$	−1.23833e7	−	404886.i	−1.72196	−	0.0563015i
$554$			5.30634e6i			0.734549i
$555$		0			0
$556$	850836.	−	491230.i	0.116724	−	0.0673904i
$557$	−7.04997e6	+	4.07030e6i	−0.962829	+	0.555890i	−0.897043	−	0.441944i	$-0.854289\pi$
$557$	−7.04997e6	+	4.07030e6i	−0.962829	+	0.555890i	−0.0657868	+	0.997834i	$0.520956\pi$
$558$		0			0
$559$			1.26450e6i			0.171155i
$560$	−1.33362e6	+	2.14483e6i	−0.179706	+	0.289017i
$561$		0			0
$562$	5.43048e6	−	9.40587e6i	0.725266	−	1.25620i
$563$	4.11593e6	+	7.12900e6i	0.547264	+	0.947890i	0.998461	+	0.0554648i	$0.0176641\pi$
$563$	4.11593e6	+	7.12900e6i	0.547264	+	0.947890i	−0.451196	+	0.892425i	$0.649003\pi$
$564$		0			0
$565$	3.04288e6	+	1.75681e6i	0.401017	+	0.231528i
$566$	7.12680e6			0.935090
$567$		0			0
$568$	−1.47864e7			−1.92306
$569$	−7.87402e6	−	4.54607e6i	−1.01957	−	0.588648i	−0.105589	−	0.994410i	$-0.533673\pi$
$569$	−7.87402e6	−	4.54607e6i	−1.01957	−	0.588648i	−0.913979	+	0.405762i	$0.867006\pi$
$570$		0			0
$571$	−1.05695e6	−	1.83070e6i	−0.135664	−	0.234977i	0.790187	−	0.612866i	$-0.209983\pi$
$571$	−1.05695e6	−	1.83070e6i	−0.135664	−	0.234977i	−0.925851	+	0.377889i	$0.876650\pi$
$572$	−38549.4	+	66769.4i	−0.00492637	+	0.00853272i
$573$		0			0
$574$	284142.	−	8.69036e6i	0.0359961	−	1.10093i
$575$		−	3.70896e6i		−	0.467825i
$576$		0			0
$577$	−348444.	+	201174.i	−0.0435706	+	0.0251555i	−0.521627	−	0.853174i	$-0.674675\pi$
$577$	−348444.	+	201174.i	−0.0435706	+	0.0251555i	0.478056	+	0.878329i	$0.341341\pi$
$578$	−2.62271e6	+	1.51422e6i	−0.326536	+	0.188526i
$579$		0			0
$580$			261875.i			0.0323239i
$581$	−5.79237e6	−	1.08357e7i	−0.711895	−	1.33173i
$582$		0			0
$583$	291739.	−	505307.i	0.0355487	−	0.0615721i
$584$	−696128.	−	1.20573e6i	−0.0844611	−	0.146291i
$585$		0			0
$586$	9.59687e6	+	5.54076e6i	1.15448	+	0.666538i
$587$	1.06195e7			1.27207			0.636034	−	0.771661i	$-0.280574\pi$
$587$	1.06195e7			1.27207			0.636034	+	0.771661i	$0.280574\pi$
$588$		0			0
$589$	−47357.2			−0.00562468
$590$	2.29384e6	+	1.32435e6i	0.271289	+	0.156629i
$591$		0			0
$592$	1.35196e6	+	2.34167e6i	0.158548	+	0.274613i
$593$	−3.22876e6	+	5.59238e6i	−0.377050	+	0.653070i	−0.990632	−	0.136561i	$-0.956395\pi$
$593$	−3.22876e6	+	5.59238e6i	−0.377050	+	0.653070i	0.613581	+	0.789632i	$0.289728\pi$
$594$		0			0
$595$	1.94337e6	+	3.63544e6i	0.225042	+	0.420983i
$596$			843427.i			0.0972594i
$597$		0			0
$598$	−483125.	+	278933.i	−0.0552468	+	0.0318967i
$599$	2.43380e6	−	1.40515e6i	0.277152	−	0.160014i	−0.354982	−	0.934873i	$-0.615513\pi$
$599$	2.43380e6	−	1.40515e6i	0.277152	−	0.160014i	0.632133	+	0.774860i	$0.282180\pi$
$600$		0			0
$601$			33651.1i			0.00380025i	0.999998	+	0.00190013i	$0.000604829\pi$
$601$			33651.1i			0.00380025i	−0.999998	+	0.00190013i	$0.999395\pi$
$602$	−376003.	+	1.14999e7i	−0.0422863	+	1.29331i
$603$		0			0
$604$	−242860.	+	420647.i	−0.0270872	+	0.0469164i
$605$	1.18460e6	+	2.05179e6i	0.131578	+	0.227900i
$606$		0			0
$607$	5.91614e6	+	3.41569e6i	0.651729	+	0.376276i	0.789118	−	0.614241i	$-0.210538\pi$
$607$	5.91614e6	+	3.41569e6i	0.651729	+	0.376276i	−0.137389	+	0.990517i	$0.543871\pi$
$608$	−3.43601e6			−0.376960
$609$		0			0
$610$	6.11504e6			0.665387
$611$	375614.	+	216861.i	0.0407041	+	0.0235005i
$612$		0			0
$613$	5.24247e6	+	9.08022e6i	0.563488	+	0.975990i	0.997189	+	0.0749326i	$0.0238742\pi$
$613$	5.24247e6	+	9.08022e6i	0.563488	+	0.975990i	−0.433701	+	0.901057i	$0.642793\pi$
$614$	5.98235e6	−	1.03617e7i	0.640399	−	1.10920i
$615$		0			0
$616$	−3.09072e6	+	4.97074e6i	−0.328177	+	0.527800i
$617$		−	8.92914e6i		−	0.944272i	−0.881526	−	0.472136i	$-0.843483\pi$
$617$		−	8.92914e6i		−	0.944272i	0.881526	−	0.472136i	$-0.156517\pi$
$618$		0			0
$619$	−1.18670e6	+	685140.i	−0.124484	+	0.0718708i	−0.560949	−	0.827850i	$-0.689564\pi$
$619$	−1.18670e6	+	685140.i	−0.124484	+	0.0718708i	0.436465	+	0.899721i	$0.356230\pi$
$620$	1833.42	−	1058.52i	0.000191550	−	0.000110591i
$621$		0			0
$622$		−	1.48623e7i		−	1.54032i
$623$	−1.71658e7	−	561258.i	−1.77192	−	0.0579352i
$624$		0			0
$625$	−2.63651e6	+	4.56658e6i	−0.269979	+	0.467618i
$626$	−2.04231e6	−	3.53739e6i	−0.208299	−	0.360784i
$627$		0			0
$628$	2.10455e6	+	1.21507e6i	0.212942	+	0.122942i
$629$	4.41326e6			0.444768
$630$		0			0
$631$	8.20153e6			0.820014			0.410007	−	0.912082i	$-0.365526\pi$
$631$	8.20153e6			0.820014			0.410007	+	0.912082i	$0.365526\pi$
$632$	−1.58211e7	−	9.13430e6i	−1.57559	−	0.909667i
$633$		0			0
$634$	3.07095e6	+	5.31904e6i	0.303423	+	0.525545i
$635$	−496452.	+	859880.i	−0.0488588	+	0.0846260i
$636$		0			0
$637$	1.04686e6	+	699366.i	0.102221	+	0.0682898i
$638$		−	3.31572e6i		−	0.322497i
$639$		0			0
$640$	−2.70552e6	+	1.56203e6i	−0.261096	+	0.150744i
$641$	6.39812e6	−	3.69396e6i	0.615046	−	0.355097i	−0.159892	−	0.987135i	$-0.551115\pi$
$641$	6.39812e6	−	3.69396e6i	0.615046	−	0.355097i	0.774938	+	0.632038i	$0.217781\pi$
$642$		0			0
$643$			8.80653e6i			0.839996i	0.907525	+	0.419998i	$0.137969\pi$
$643$			8.80653e6i			0.839996i	−0.907525	+	0.419998i	$0.862031\pi$
$644$	705714.	−	377248.i	0.0670523	−	0.0358437i
$645$		0			0
$646$	8.14806e6	−	1.41129e7i	0.768197	−	1.33056i
$647$	1.75481e6	+	3.03942e6i	0.164805	+	0.285450i	0.936586	−	0.350438i	$-0.113967\pi$
$647$	1.75481e6	+	3.03942e6i	0.164805	+	0.285450i	−0.771781	+	0.635888i	$0.780634\pi$
$648$		0			0
$649$	4.57846e6	+	2.64338e6i	0.426686	+	0.246347i
$650$	1.03123e6			0.0957350
$651$		0			0
$652$	−1.48241e6			−0.136568
$653$	−5.91843e6	−	3.41700e6i	−0.543154	−	0.313590i	0.203202	−	0.979137i	$-0.434865\pi$
$653$	−5.91843e6	−	3.41700e6i	−0.543154	−	0.313590i	−0.746356	+	0.665547i	$0.768199\pi$
$654$		0			0
$655$	−1.27765e6	−	2.21295e6i	−0.116361	−	0.201544i
$656$	5.52087e6	−	9.56243e6i	0.500897	−	0.867579i
$657$		0			0
$658$	3.35149e6	+	2.08390e6i	0.301768	+	0.187635i
$659$		−	65765.0i		−	0.00589904i	−0.999996	−	0.00294952i	$-0.999061\pi$
$659$		−	65765.0i		−	0.00589904i	0.999996	−	0.00294952i	$-0.000938862\pi$
$660$		0			0
$661$	1.51037e7	−	8.72015e6i	1.34456	−	0.776283i	0.357089	−	0.934070i	$-0.383769\pi$
$661$	1.51037e7	−	8.72015e6i	1.34456	−	0.776283i	0.987473	+	0.157787i	$0.0504359\pi$
$662$	−1.00662e7	+	5.81172e6i	−0.892730	+	0.515418i
$663$		0			0
$664$		−	1.81165e7i		−	1.59461i
$665$	−5.43655e6	−	3.38036e6i	−0.476726	−	0.296421i
$666$		0			0
$667$	−1.89105e6	+	3.27539e6i	−0.164584	+	0.285068i
$668$	965567.	+	1.67241e6i	0.0837224	+	0.145011i
$669$		0			0
$670$	4.67889e6	+	2.70136e6i	0.402676	+	0.232485i
$671$	1.22055e7			1.04653
$672$		0			0
$673$	474954.			0.0404216			0.0202108	−	0.999796i	$-0.493566\pi$
$673$	474954.			0.0404216			0.0202108	+	0.999796i	$0.493566\pi$
$674$	−1.93789e6	−	1.11884e6i	−0.164316	−	0.0948678i
$675$		0			0
$676$	−796751.	−	1.38001e6i	−0.0670588	−	0.116149i
$677$	6.61186e6	−	1.14521e7i	0.554437	−	0.960313i	−0.443510	−	0.896269i	$-0.646267\pi$
$677$	6.61186e6	−	1.14521e7i	0.554437	−	0.960313i	0.997947	−	0.0640437i	$-0.0203997\pi$
$678$		0			0
$679$	−6.69129e6	+	3.57691e6i	−0.556974	+	0.297738i
$680$			6.07820e6i			0.504084i
$681$		0			0
$682$	−23213.7	+	13402.4i	−0.00191110	+	0.00110338i
$683$	8.64660e6	−	4.99212e6i	0.709241	−	0.409480i	−0.101539	−	0.994832i	$-0.532377\pi$
$683$	8.64660e6	−	4.99212e6i	0.709241	−	0.409480i	0.810780	+	0.585351i	$0.199043\pi$
$684$		0			0
$685$			1.18848e6i			0.0967752i
$686$	9.31257e6	+	6.67158e6i	0.755543	+	0.541276i
$687$		0			0
$688$	−7.30573e6	+	1.26539e7i	−0.588427	+	1.01918i
$689$	−92523.4	−	160255.i	−0.00742512	−	0.0128607i
$690$		0			0
$691$	2.45061e6	+	1.41486e6i	0.195244	+	0.112724i	0.594435	−	0.804143i	$-0.297376\pi$
$691$	2.45061e6	+	1.41486e6i	0.195244	+	0.112724i	−0.399191	+	0.916868i	$0.630709\pi$
$692$	−2.09563e6			−0.166360
$693$		0			0
$694$	−1.83223e7			−1.44405
$695$	4.39463e6	+	2.53724e6i	0.345112	+	0.199251i
$696$		0			0
$697$	−9.01100e6	−	1.56075e7i	−0.702572	−	1.21689i
$698$	−6.35948e6	+	1.10149e7i	−0.494064	+	0.855744i
$699$		0			0
$700$	−1.47843e6	−	48339.1i	−0.114040	−	0.00372866i
$701$		−	1.27474e7i		−	0.979772i	−0.871787	−	0.489886i	$-0.837038\pi$
$701$		−	1.27474e7i		−	0.979772i	0.871787	−	0.489886i	$-0.162962\pi$
$702$		0			0
$703$	−5.93546e6	+	3.42684e6i	−0.452967	+	0.261520i
$704$	−7.34995e6	+	4.24350e6i	−0.558924	+	0.322695i
$705$		0			0
$706$			1.37109e7i			1.03527i
$707$	8.09152e6	−	1.30134e7i	0.608810	−	0.979134i
$708$		0			0
$709$	8.48126e6	−	1.46900e7i	0.633643	−	1.09750i	−0.353157	−	0.935564i	$-0.614892\pi$
$709$	8.48126e6	−	1.46900e7i	0.633643	−	1.09750i	0.986801	−	0.161939i	$-0.0517747\pi$
$710$	−4.57682e6	−	7.92728e6i	−0.340736	−	0.590172i
$711$		0			0
$712$	−2.19314e7	−	1.26621e7i	−1.62131	−	0.936063i
$713$	30575.2			0.00225240
$714$		0			0
$715$	−398221.			−0.0291312
$716$	1.57812e6	+	911128.i	0.115042	+	0.0664197i
$717$		0			0
$718$	3.13426e6	+	5.42870e6i	0.226895	+	0.392993i
$719$	−4.90177e6	+	8.49011e6i	−0.353615	+	0.612479i	−0.986880	−	0.161456i	$-0.948381\pi$
$719$	−4.90177e6	+	8.49011e6i	−0.353615	+	0.612479i	0.633265	+	0.773935i	$0.281714\pi$
$720$		0			0
$721$	283253.	−	8.66319e6i	0.0202926	−	0.620640i
$722$			1.22891e7i			0.877359i
$723$		0			0
$724$	2.11288e6	−	1.21987e6i	0.149806	−	0.0864905i
$725$	6.05464e6	−	3.49565e6i	0.427802	−	0.246992i
$726$		0			0
$727$			146850.i			0.0103047i	0.999987	+	0.00515236i	$0.00164006\pi$
$727$			146850.i			0.0103047i	−0.999987	+	0.00515236i	$0.998360\pi$
$728$	875135.	+	1.63710e6i	0.0611993	+	0.114485i
$729$		0			0
$730$	430942.	−	746414.i	0.0299304	−	0.0518409i
$731$	1.19242e7	+	2.06533e7i	0.825344	+	1.42954i
$732$		0			0
$733$	738680.	+	426477.i	0.0507804	+	0.0293181i	0.525175	−	0.850994i	$-0.324000\pi$
$733$	738680.	+	426477.i	0.0507804	+	0.0293181i	−0.474395	+	0.880312i	$0.657333\pi$
$734$	−1.69730e7			−1.16284
$735$		0			0
$736$	2.21839e6			0.150953
$737$	9.33898e6	+	5.39186e6i	0.633331	+	0.365654i
$738$		0			0
$739$	5.08111e6	+	8.80073e6i	0.342253	+	0.592799i	0.984851	−	0.173404i	$-0.0554767\pi$
$739$	5.08111e6	+	8.80073e6i	0.342253	+	0.592799i	−0.642598	+	0.766204i	$0.722143\pi$
$740$	153193.	−	265338.i	0.0102839	−	0.0178123i
$741$		0			0
$742$	−793791.	−	1.48494e6i	−0.0529294	−	0.0990143i
$743$			3.62229e6i			0.240719i	0.992730	+	0.120360i	$0.0384048\pi$
$743$			3.62229e6i			0.240719i	−0.992730	+	0.120360i	$0.961595\pi$
$744$		0			0
$745$	−3.77272e6	+	2.17818e6i	−0.249037	+	0.143782i
$746$	−5.70831e6	+	3.29569e6i	−0.375544	+	0.216820i
$747$		0			0
$748$			1.45407e6i			0.0950236i
$749$	−506718.	+	1.54978e7i	−0.0330036	+	1.00940i
$750$		0			0
$751$	−1.08320e7	+	1.87616e7i	−0.700824	+	1.21386i	0.267354	+	0.963598i	$0.413851\pi$
$751$	−1.08320e7	+	1.87616e7i	−0.700824	+	1.21386i	−0.968178	+	0.250264i	$0.919483\pi$
$752$	2.50584e6	+	4.34025e6i	0.161588	+	0.279879i
$753$		0			0
$754$	−910678.	−	525780.i	−0.0583360	−	0.0336803i
$755$	−2.50878e6			−0.160175
$756$		0			0
$757$	1.93250e7			1.22569			0.612845	−	0.790204i	$-0.290025\pi$
$757$	1.93250e7			1.22569			0.612845	+	0.790204i	$0.290025\pi$
$758$	1.41087e7	+	8.14564e6i	0.891893	+	0.514934i
$759$		0			0
$760$	−4.71964e6	−	8.17466e6i	−0.296398	−	0.513376i
$761$	−1.07353e7	+	1.85941e7i	−0.671974	+	1.16389i	0.305370	+	0.952234i	$0.401220\pi$
$761$	−1.07353e7	+	1.85941e7i	−0.671974	+	1.16389i	−0.977344	+	0.211659i	$0.932114\pi$
$762$		0			0
$763$	5.90156e6	−	9.49134e6i	0.366991	−	0.590223i
$764$			3.14750e6i			0.195089i
$765$		0			0
$766$	−2.01287e7	+	1.16213e7i	−1.23949	+	0.715619i
$767$	1.45203e6	−	838332.i	0.0891227	−	0.0514550i
$768$		0			0
$769$			2.72925e7i			1.66428i	0.554562	+	0.832142i	$0.312886\pi$
$769$			2.72925e7i			1.66428i	−0.554562	+	0.832142i	$0.687114\pi$
$770$	−3.62157e6	−	118412.i	−0.220125	−	0.00719727i
$771$		0			0
$772$	428386.	−	741986.i	0.0258697	−	0.0448077i
$773$	−1.48969e7	−	2.58021e7i	−0.896698	−	1.55313i	−0.831689	−	0.555242i	$-0.812626\pi$
$773$	−1.48969e7	−	2.58021e7i	−0.896698	−	1.55313i	−0.0650088	−	0.997885i	$-0.520708\pi$
$774$		0			0
$775$	−48946.9	−	28259.5i	−0.00292732	−	0.00169009i
$776$	−1.11874e7			−0.666919
$777$		0			0
$778$	−3.97290e6			−0.235320
$779$	2.42381e7	+	1.39938e7i	1.43105	+	0.826216i
$780$		0			0
$781$	−9.13526e6	−	1.58227e7i	−0.535912	−	0.928226i
$782$	−5.26063e6	+	9.11168e6i	−0.307624	+	0.532821i
$783$		0			0
$784$	6.43529e6	+	1.30468e7i	0.373919	+	0.758079i
$785$			1.25518e7i			0.726996i
$786$		0			0
$787$	−6.44578e6	+	3.72147e6i	−0.370970	+	0.214180i	−0.673882	−	0.738839i	$-0.735374\pi$
$787$	−6.44578e6	+	3.72147e6i	−0.370970	+	0.214180i	0.302912	+	0.953018i	$0.402041\pi$
$788$	1.49668e6	−	864107.i	0.0858643	−	0.0495738i
$789$		0			0
$790$		−	1.13093e7i		−	0.644715i
$791$	1.78482e7	−	9.54097e6i	1.01427	−	0.542190i
$792$		0			0
$793$	1.93546e6	−	3.35231e6i	0.109295	−	0.189304i
$794$	−7.73222e6	−	1.33926e7i	−0.435264	−	0.753900i
$795$		0			0
$796$	1.21606e6	+	702094.i	0.0680257	+	0.0392747i
$797$	−1.32098e7			−0.736632			−0.368316	−	0.929701i	$-0.620066\pi$
$797$	−1.32098e7			−0.736632			−0.368316	+	0.929701i	$0.620066\pi$
$798$		0			0
$799$	8.17993e6			0.453297
$800$	−3.55135e6	−	2.05037e6i	−0.196186	−	0.113268i
$801$		0			0
$802$	1.48955e7	+	2.57998e7i	0.817749	+	1.41638i
$803$	860154.	−	1.48983e6i	0.0470747	−	0.0815357i
$804$		0			0
$805$	3.51000e6	+	2.18246e6i	0.190905	+	0.118702i
$806$			8501.02i			0.000460928i
$807$		0			0
$808$	1.95676e7	−	1.12974e7i	1.05441	−	0.608763i
$809$	−1.03698e7	+	5.98700e6i	−0.557055	+	0.321616i	−0.751963	−	0.659206i	$-0.770893\pi$
$809$	−1.03698e7	+	5.98700e6i	−0.557055	+	0.321616i	0.194907	+	0.980822i	$0.437559\pi$
$810$		0			0
$811$			4.67363e6i			0.249518i	0.992187	+	0.124759i	$0.0398158\pi$
$811$			4.67363e6i			0.249518i	−0.992187	+	0.124759i	$0.960184\pi$
$812$	1.28096e6	+	796480.i	0.0681781	+	0.0423921i
$813$		0			0
$814$	−1.93964e6	+	3.35956e6i	−0.102603	+	0.177714i
$815$	−3.82838e6	−	6.63096e6i	−0.201893	−	0.349689i
$816$		0			0
$817$	−3.20740e7	−	1.85179e7i	−1.68112	−	0.970594i
$818$	−1.66134e6			−0.0868114
$819$		0			0
$820$	−1.25116e6			−0.0649796
$821$	−2.13773e7	−	1.23422e7i	−1.10687	−	0.639049i	−0.168850	−	0.985642i	$-0.554005\pi$
$821$	−2.13773e7	−	1.23422e7i	−1.10687	−	0.639049i	−0.938016	+	0.346593i	$0.887339\pi$
$822$		0			0
$823$	−6.46757e6	−	1.12022e7i	−0.332845	−	0.576504i	0.650224	−	0.759743i	$-0.274675\pi$
$823$	−6.46757e6	−	1.12022e7i	−0.332845	−	0.576504i	−0.983068	+	0.183239i	$0.941342\pi$
$824$	6.39025e6	−	1.10682e7i	0.327869	−	0.567885i
$825$		0			0
$826$	1.34546e7	−	7.19235e6i	0.686154	−	0.366793i
$827$		−	3.64047e6i		−	0.185095i	−0.995708	−	0.0925473i	$-0.970499\pi$
$827$		−	3.64047e6i		−	0.185095i	0.995708	−	0.0925473i	$-0.0295009\pi$
$828$		0			0
$829$	1.41343e7	−	8.16042e6i	0.714310	−	0.412407i	−0.0983449	−	0.995152i	$-0.531355\pi$
$829$	1.41343e7	−	8.16042e6i	0.714310	−	0.412407i	0.812655	+	0.582745i	$0.198022\pi$
$830$	9.71260e6	−	5.60757e6i	0.489373	−	0.282540i
$831$		0			0
$832$			2.69160e6i			0.134804i
$833$	2.36934e7	+	1.55103e6i	1.18308	+	0.0774475i
$834$		0			0
$835$	−4.98723e6	+	8.63813e6i	−0.247539	+	0.428750i
$836$	−1.12907e6	−	1.95560e6i	−0.0558733	−	0.0967754i
$837$		0			0
$838$	−1.36244e7	−	7.86603e6i	−0.670203	−	0.386942i
$839$	−997803.			−0.0489373			−0.0244687	−	0.999701i	$-0.507789\pi$
$839$	−997803.			−0.0489373			−0.0244687	+	0.999701i	$0.507789\pi$
$840$		0			0
$841$	1.33820e7			0.652425
$842$	1.20419e7	+	6.95237e6i	0.585347	+	0.337950i
$843$		0			0
$844$	380466.	+	658986.i	0.0183848	+	0.0318434i
$845$	4.11528e6	−	7.12787e6i	0.198270	−	0.343414i
$846$		0			0
$847$	1.36392e7	+	445950.i	0.653251	+	0.0213588i
$848$		−	2.13823e6i		−	0.102109i
$849$		0			0
$850$	1.68431e7	−	9.72439e6i	0.799606	−	0.461653i
$851$	3.83211e6	−	2.21247e6i	0.181390	−	0.104726i
$852$		0			0
$853$		−	1.11746e7i		−	0.525846i	−0.964817	−	0.262923i	$-0.915313\pi$
$853$		−	1.11746e7i		−	0.525846i	0.964817	−	0.262923i	$-0.0846865\pi$
$854$	1.85986e7	−	2.99117e7i	0.872641	−	1.40345i
$855$		0			0
$856$	−1.14317e7	+	1.98002e7i	−0.533242	+	0.923603i
$857$	−4.97509e6	−	8.61711e6i	−0.231392	−	0.400783i	0.726826	−	0.686822i	$-0.240995\pi$
$857$	−4.97509e6	−	8.61711e6i	−0.231392	−	0.400783i	−0.958218	+	0.286039i	$0.907661\pi$
$858$		0			0
$859$	−1.48609e7	−	8.57994e6i	−0.687166	−	0.396736i	0.115383	−	0.993321i	$-0.463190\pi$
$859$	−1.48609e7	−	8.57994e6i	−0.687166	−	0.396736i	−0.802550	+	0.596585i	$0.796524\pi$
$860$	1.65564e6			0.0763345
$861$		0			0
$862$	1.95778e7			0.897420
$863$	2.93859e6	+	1.69660e6i	0.134311	+	0.0775446i	0.565650	−	0.824645i	$-0.308625\pi$
$863$	2.93859e6	+	1.69660e6i	0.134311	+	0.0775446i	−0.431339	+	0.902190i	$0.641959\pi$
$864$		0			0
$865$	−5.41203e6	−	9.37391e6i	−0.245935	−	0.425972i
$866$	−1.70066e6	+	2.94562e6i	−0.0770587	+	0.133470i
$867$		0			0
$868$	398.488	−	12187.6i	1.79521e−5	−	0.000549059i
$869$		−	2.25732e7i		−	1.01401i
$870$		0			0
$871$	2.96181e6	−	1.71000e6i	0.132285	−	0.0763749i
$872$	1.42717e7	−	8.23974e6i	0.635599	−	0.366963i
$873$		0			0
$874$		−	1.63392e7i		−	0.723525i
$875$	−7.90061e6	−	1.47796e7i	−0.348851	−	0.652591i
$876$		0			0
$877$	−8.50176e6	+	1.47255e7i	−0.373259	+	0.646503i	−0.990065	−	0.140612i	$-0.955093\pi$
$877$	−8.50176e6	+	1.47255e7i	−0.373259	+	0.646503i	0.616806	+	0.787115i	$0.288426\pi$
$878$	−1.23600e7	−	2.14082e7i	−0.541108	−	0.937226i
$879$		0			0
$880$	−3.98499e6	−	2.30074e6i	−0.173469	−	0.100152i
$881$	−3.88085e7			−1.68456			−0.842281	−	0.539038i	$-0.818788\pi$
$881$	−3.88085e7			−1.68456			−0.842281	+	0.539038i	$0.818788\pi$
$882$		0			0
$883$	2.10286e7			0.907628			0.453814	−	0.891096i	$-0.350063\pi$
$883$	2.10286e7			0.907628			0.453814	+	0.891096i	$0.350063\pi$
$884$	399368.	+	230575.i	0.0171887	+	0.00992389i
$885$		0			0
$886$	−1.91977e7	−	3.32515e7i	−0.821610	−	1.42307i
$887$	−2.76468e6	+	4.78856e6i	−0.117987	+	0.204360i	−0.918970	−	0.394327i	$-0.870978\pi$
$887$	−2.76468e6	+	4.78856e6i	−0.117987	+	0.204360i	0.800983	+	0.598688i	$0.204311\pi$
$888$		0			0
$889$	2.69616e6	+	5.04368e6i	0.114417	+	0.214039i
$890$		−	1.56771e7i		−	0.663422i
$891$		0			0
$892$	−5.40454e6	+	3.12031e6i	−0.227429	+	0.131306i
$893$	−1.10013e7	+	6.35161e6i	−0.461653	+	0.266535i
$894$		0			0
$895$			9.41208e6i			0.392761i
$896$	−588037.	+	1.79849e7i	−0.0244700	+	0.748405i
$897$		0			0
$898$	−1.34564e6	+	2.33072e6i	−0.0556850	+	0.0964493i
$899$	28816.7	+	49912.1i	0.00118917	+	0.00205971i
$900$		0			0
$901$	−3.02239e6	−	1.74498e6i	−0.124033	−	0.0716108i
$902$	1.58415e7			0.648304
$903$		0			0
$904$	2.98409e7			1.21448
$905$	1.09132e7	+	6.30074e6i	0.442926	+	0.255723i
$906$		0			0
$907$	1.80754e7	+	3.13074e7i	0.729573	+	1.26366i	0.957064	+	0.289877i	$0.0936146\pi$
$907$	1.80754e7	+	3.13074e7i	0.729573	+	1.26366i	−0.227491	+	0.973780i	$0.573052\pi$
$908$	−280047.	+	485055.i	−0.0112724	+	0.0195243i
$909$		0			0
$910$	−606803.	+	975906.i	−0.0242909	+	0.0390665i
$911$			1.01876e7i			0.406701i	0.979106	+	0.203350i	$0.0651831\pi$
$911$			1.01876e7i			0.406701i	−0.979106	+	0.203350i	$0.934817\pi$
$912$		0			0
$913$	1.93862e7	−	1.11926e7i	0.769690	−	0.444381i
$914$	−9.65199e6	+	5.57258e6i	−0.382165	+	0.220643i
$915$		0			0
$916$			2.92330e6i			0.115116i
$917$	−1.47106e7	−	480980.i	−0.577704	−	0.0188888i
$918$		0			0
$919$	459542.	−	795949.i	0.0179488	−	0.0310883i	−0.856911	−	0.515464i	$-0.827620\pi$
$919$	459542.	−	795949.i	0.0179488	−	0.0310883i	0.874860	+	0.484375i	$0.160953\pi$
$920$	3.04714e6	+	5.27780e6i	0.118692	+	0.205581i
$921$		0			0
$922$	2.68513e7	+	1.55026e7i	1.04025	+	0.600589i
$923$	−5.79439e6			−0.223874
$924$		0			0
$925$	−8.17961e6			−0.314324
$926$	1.80618e7	+	1.04280e7i	0.692202	+	0.399643i
$927$		0			0
$928$	2.09080e6	+	3.62137e6i	0.0796971	+	0.138039i
$929$	−1.63800e7	+	2.83710e7i	−0.622695	+	1.07854i	0.366287	+	0.930502i	$0.380629\pi$
$929$	−1.63800e7	+	2.83710e7i	−0.622695	+	1.07854i	−0.988982	+	0.148037i	$0.952704\pi$
$930$		0			0
$931$	−3.30700e7	+	1.63116e7i	−1.25043	+	0.616770i
$932$		−	6.50694e6i		−	0.245379i
$933$		0			0
$934$	−1.68758e7	+	9.74327e6i	−0.632992	+	0.365458i
$935$	−6.50419e6	+	3.75519e6i	−0.243312	+	0.140476i
$936$		0			0
$937$		−	1.54558e7i		−	0.575101i	−0.957766	−	0.287550i	$-0.907159\pi$
$937$		−	1.54558e7i		−	0.575101i	0.957766	−	0.287550i	$-0.0928409\pi$
$938$	2.74443e7	−	1.46707e7i	1.01846	−	0.544432i
$939$		0			0
$940$	283941.	−	491800.i	0.0104811	−	0.0181539i
$941$	−1.38446e7	−	2.39796e7i	−0.509691	−	0.882811i	−0.999937	−	0.0112266i	$-0.996426\pi$
$941$	−1.38446e7	−	2.39796e7i	−0.509691	−	0.882811i	0.490246	−	0.871584i	$-0.336907\pi$
$942$		0			0
$943$	−1.56488e7	−	9.03485e6i	−0.573063	−	0.330858i
$944$	1.93740e7			0.707603
$945$		0			0
$946$	−2.09629e7			−0.761593
$947$	5.18682e6	+	2.99461e6i	0.187943	+	0.108509i	0.591019	−	0.806658i	$-0.298726\pi$
$947$	5.18682e6	+	2.99461e6i	0.187943	+	0.108509i	−0.403076	+	0.915166i	$0.632059\pi$
$948$		0			0
$949$	−272793.	−	472491.i	−0.00983258	−	0.0170305i
$950$	−1.51017e7	+	2.61570e7i	−0.542897	+	0.940326i
$951$		0			0
$952$	2.97315e7	+	1.84866e7i	1.06322	+	0.661095i
$953$			4.28775e7i			1.52932i	0.644436	+	0.764658i	$0.277092\pi$
$953$			4.28775e7i			1.52932i	−0.644436	+	0.764658i	$0.722908\pi$
$954$		0			0
$955$	−1.40790e7	+	8.12854e6i	−0.499534	+	0.288406i
$956$	−1.11734e6	+	645099.i	−0.0395405	+	0.0228287i
$957$		0			0
$958$			3.13351e7i			1.10310i
$959$	5.81342e6	+	3.61469e6i	0.204120	+	0.126919i
$960$		0			0
$961$	−1.43143e7	+	2.47932e7i	−0.499992	+	0.866011i
$962$	615147.	+	1.06547e6i	0.0214309	+	0.0371195i
$963$		0			0
$964$	2.36252e6	+	1.36400e6i	0.0818811	+	0.0472741i
$965$	4.42529e6			0.152976
$966$		0			0
$967$	−3.89106e7			−1.33814			−0.669071	−	0.743199i	$-0.733308\pi$
$967$	−3.89106e7			−1.33814			−0.669071	+	0.743199i	$0.733308\pi$
$968$	1.74257e7	+	1.00607e7i	0.597724	+	0.345096i
$969$		0			0
$970$	−3.46280e6	−	5.99775e6i	−0.118168	−	0.204672i
$971$	−1.92911e7	+	3.34132e7i	−0.656612	+	1.13729i	0.324875	+	0.945757i	$0.394678\pi$
$971$	−1.92911e7	+	3.34132e7i	−0.656612	+	1.13729i	−0.981487	+	0.191529i	$0.938656\pi$
$972$		0			0
$973$	2.57770e7	−	1.37794e7i	0.872870	−	0.466604i
$974$		−	1.42636e7i		−	0.481761i
$975$		0			0
$976$	3.87362e7	−	2.23644e7i	1.30165	−	0.751505i
$977$	−3.07761e7	+	1.77686e7i	−1.03152	+	0.595547i	−0.917419	−	0.397922i	$-0.869732\pi$
$977$	−3.07761e7	+	1.77686e7i	−1.03152	+	0.595547i	−0.114099	+	0.993469i	$0.536398\pi$
$978$		0			0
$979$		−	3.12912e7i		−	1.04344i
$980$	915696.	−	1.37068e6i	0.0304569	−	0.0455900i
$981$		0			0
$982$	8.28267e6	−	1.43460e7i	0.274089	−	0.474736i
$983$	5.77902e6	+	1.00096e7i	0.190753	+	0.330393i	0.945500	−	0.325623i	$-0.105574\pi$
$983$	5.77902e6	+	1.00096e7i	0.190753	+	0.330393i	−0.754747	+	0.656016i	$0.772241\pi$
$984$		0			0
$985$	7.73045e6	+	4.46318e6i	0.253872	+	0.146573i
$986$	−1.98323e7			−0.649652
$987$		0			0
$988$	−716155.			−0.0233407
$989$	2.07079e7	+	1.19557e7i	0.673203	+	0.388674i
$990$		0			0
$991$	9.26292e6	+	1.60438e7i	0.299615	+	0.518948i	0.976048	−	0.217556i	$-0.0698084\pi$
$991$	9.26292e6	+	1.60438e7i	0.299615	+	0.518948i	−0.676433	+	0.736504i	$0.736475\pi$
$992$	16902.4	−	29275.9i	0.000545344	−	0.000944563i
$993$		0			0
$994$	−5.26964e7	−	1.72297e6i	−1.69167	−	0.0553112i
$995$			7.25273e6i			0.232244i
$996$		0			0
$997$	−2.74542e7	+	1.58507e7i	−0.874723	+	0.505022i	−0.868915	−	0.494962i	$-0.835182\pi$
$997$	−2.74542e7	+	1.58507e7i	−0.874723	+	0.505022i	−0.00580815	+	0.999983i	$0.501849\pi$
$998$	8.05003e6	−	4.64769e6i	0.255841	−	0.147710i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.p.b.26.8	yes	24
3.2	odd	2	inner	63.6.p.b.26.5	yes	24
7.2	even	3		441.6.c.b.440.9		24
7.3	odd	6	inner	63.6.p.b.17.5	✓	24
7.5	odd	6		441.6.c.b.440.15		24
21.2	odd	6		441.6.c.b.440.16		24
21.5	even	6		441.6.c.b.440.10		24
21.17	even	6	inner	63.6.p.b.17.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.p.b.17.5	✓	24	7.3	odd	6	inner
63.6.p.b.17.8	yes	24	21.17	even	6	inner
63.6.p.b.26.5	yes	24	3.2	odd	2	inner
63.6.p.b.26.8	yes	24	1.1	even	1	trivial
441.6.c.b.440.9		24	7.2	even	3
441.6.c.b.440.10		24	21.5	even	6
441.6.c.b.440.15		24	7.5	odd	6
441.6.c.b.440.16		24	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4.55322 + 2.62880i) q^{2} +(-2.17881 - 3.77381i) q^{4} +(11.2537 - 19.4920i) q^{5} +(-61.1173 - 114.331i) q^{7} -191.154i q^{8} +(102.481 - 59.1675i) q^{10} +(204.551 - 118.097i) q^{11} -74.9079i q^{13} +(22.2740 - 681.241i) q^{14} +(432.784 - 749.603i) q^{16} +(-706.376 - 1223.48i) q^{17} +(1900.03 + 1096.98i) q^{19} -98.0787 q^{20} +1241.82 q^{22} +(-1226.72 - 708.246i) q^{23} +(1309.21 + 2267.61i) q^{25} +(196.918 - 341.072i) q^{26} +(-298.302 + 479.751i) q^{28} -2670.05i q^{29} +(-18.6933 + 10.7926i) q^{31} +(-1356.30 + 783.058i) q^{32} -7427.69i q^{34} +(-2916.34 - 95.3534i) q^{35} +(-1561.94 + 2705.36i) q^{37} +(5767.51 + 9989.61i) q^{38} +(-3725.97 - 2151.19i) q^{40} +12756.7 q^{41} -16880.8 q^{43} +(-891.354 - 514.623i) q^{44} +(-3723.67 - 6449.59i) q^{46} +(-2895.03 + 5014.34i) q^{47} +(-9336.34 + 13975.3i) q^{49} +13766.6i q^{50} +(-282.688 + 163.210i) q^{52} +(2139.36 - 1235.16i) q^{53} -5316.14i q^{55} +(-21854.9 + 11682.8i) q^{56} +(7019.02 - 12157.3i) q^{58} +(11191.5 + 19384.3i) q^{59} +(44752.4 + 25837.8i) q^{61} -113.486 q^{62} -35932.2 q^{64} +(-1460.10 - 842.991i) q^{65} +(22828.0 + 39539.3i) q^{67} +(-3078.12 + 5331.46i) q^{68} +(-13028.1 - 8100.65i) q^{70} -77353.6i q^{71} +(6307.63 - 3641.71i) q^{73} +(-14223.7 + 8212.05i) q^{74} -9560.47i q^{76} +(-26003.8 - 16168.8i) q^{77} +(47785.0 - 82766.1i) q^{79} +(-9740.84 - 16871.6i) q^{80} +(58083.8 + 33534.7i) q^{82} +94774.5 q^{83} -31797.4 q^{85} +(-76861.9 - 44376.2i) q^{86} +(-22574.8 - 39100.7i) q^{88} +(66240.2 - 114731. i) q^{89} +(-8564.32 + 4578.17i) q^{91} +6172.53i q^{92} +(-26363.4 + 15220.9i) q^{94} +(42764.8 - 24690.3i) q^{95} -58525.4i q^{97} +(-79248.6 + 39089.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49}+ \cdots - 1481724 q^{94}+O(q^{100}) \) 24 * q + 304 * q^4 - 436 * q^7 + 1992 * q^10 - 3644 * q^16 + 3804 * q^19 - 5648 * q^22 - 18852 * q^25 - 39172 * q^28 + 38652 * q^31 + 20548 * q^37 + 132060 * q^40 + 2200 * q^43 - 25712 * q^46 - 125676 * q^49 - 2940 * q^52 + 154300 * q^58 + 48504 * q^61 - 327880 * q^64 + 156324 * q^67 - 9468 * q^70 - 703236 * q^73 + 165756 * q^79 + 1081020 * q^82 - 284448 * q^85 + 582308 * q^88 - 19812 * q^91 - 1481724 * q^94

Introduction

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