LMFDB - Embedded newform 63.6.p.b.17.1

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			17.1
Character	$\chi$	$=$	63.17
Dual form			63.6.p.b.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.49029 + 5.47922i) q^{2} +(44.0437 - 76.2859i) q^{4} +(-41.3063 - 71.5446i) q^{5} +(-18.0992 - 128.372i) q^{7} +614.630i q^{8} +O(q^{10})$	\(q+(-9.49029 + 5.47922i) q^{2} +(44.0437 - 76.2859i) q^{4} +(-41.3063 - 71.5446i) q^{5} +(-18.0992 - 128.372i) q^{7} +614.630i q^{8} +(784.017 + 452.652i) q^{10} +(-98.5671 - 56.9078i) q^{11} +329.288i q^{13} +(875.146 + 1119.12i) q^{14} +(-1958.30 - 3391.87i) q^{16} +(221.601 - 383.824i) q^{17} +(-1454.44 + 839.723i) q^{19} -7277.12 q^{20} +1247.24 q^{22} +(194.041 - 112.030i) q^{23} +(-1849.92 + 3204.15i) q^{25} +(-1804.24 - 3125.04i) q^{26} +(-10590.1 - 4273.27i) q^{28} -2982.54i q^{29} +(2924.18 + 1688.28i) q^{31} +(20136.4 + 11625.8i) q^{32} +4856.80i q^{34} +(-8436.72 + 6597.48i) q^{35} +(5858.99 + 10148.1i) q^{37} +(9202.05 - 15938.4i) q^{38} +(43973.5 - 25388.1i) q^{40} -14554.2 q^{41} -10531.9 q^{43} +(-8682.52 + 5012.86i) q^{44} +(-1227.67 + 2126.39i) q^{46} +(11046.1 + 19132.4i) q^{47} +(-16151.8 + 4646.86i) q^{49} -40544.4i q^{50} +(25120.0 + 14503.1i) q^{52} +(-3941.39 - 2275.56i) q^{53} +9402.59i q^{55} +(78901.4 - 11124.3i) q^{56} +(16342.0 + 28305.2i) q^{58} +(-6666.58 + 11546.9i) q^{59} +(-43971.6 + 25387.0i) q^{61} -37001.8 q^{62} -129470. q^{64} +(23558.8 - 13601.7i) q^{65} +(25659.4 - 44443.4i) q^{67} +(-19520.3 - 33810.1i) q^{68} +(43917.9 - 108839. i) q^{70} +1201.47i q^{71} +(7651.79 + 4417.76i) q^{73} +(-111207. - 64205.4i) q^{74} +147938. i q^{76} +(-5521.39 + 13683.3i) q^{77} +(-21780.4 - 37724.7i) q^{79} +(-161780. + 280211. i) q^{80} +(138123. - 79745.5i) q^{82} +58191.3 q^{83} -36614.0 q^{85} +(99950.5 - 57706.4i) q^{86} +(34977.2 - 60582.3i) q^{88} +(54255.1 + 93972.7i) q^{89} +(42271.4 - 5959.85i) q^{91} -19736.8i q^{92} +(-209661. - 121048. i) q^{94} +(120155. + 69371.6i) q^{95} -5444.51i q^{97} +(127824. - 132600. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) $ 24 * q + 304 * q^4 - 436 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−9.49029	+	5.47922i	−1.67766	+	0.968598i	−0.714515	+	0.699620i	$0.753353\pi$
$2$	−9.49029	+	5.47922i	−1.67766	+	0.968598i	−0.963146	+	0.268979i	$0.913314\pi$
$3$		0			0
$3$		0			0
$4$	44.0437	−	76.2859i	1.37637	−	2.38393i
$5$	−41.3063	−	71.5446i	−0.738909	−	1.27983i	−0.952987	−	0.303011i	$-0.902008\pi$
$5$	−41.3063	−	71.5446i	−0.738909	−	1.27983i	0.214078	−	0.976817i	$-0.431325\pi$
$6$		0			0
$7$	−18.0992	−	128.372i	−0.139609	−	0.990207i
$7$	−18.0992	−	128.372i	−0.139609	−	0.990207i
$8$			614.630i			3.39538i
$9$		0			0
$10$	784.017	+	452.652i	2.47928	+	1.43141i
$11$	−98.5671	−	56.9078i	−0.245613	−	0.141804i	0.372141	−	0.928176i	$-0.378624\pi$
$11$	−98.5671	−	56.9078i	−0.245613	−	0.141804i	−0.617754	+	0.786372i	$0.711957\pi$
$12$		0			0
$13$			329.288i			0.540403i	0.962804	+	0.270201i	$0.0870903\pi$
$13$			329.288i			0.540403i	−0.962804	+	0.270201i	$0.912910\pi$
$14$	875.146	+	1119.12i	1.19333	+	1.52601i
$15$		0			0
$16$	−1958.30	−	3391.87i	−1.91240	−	3.31237i
$17$	221.601	−	383.824i	0.185973	−	0.322114i	−0.757931	−	0.652335i	$-0.773790\pi$
$17$	221.601	−	383.824i	0.185973	−	0.322114i	0.943904	+	0.330220i	$0.107123\pi$
$18$		0			0
$19$	−1454.44	+	839.723i	−0.924299	+	0.533644i	−0.885004	−	0.465583i	$-0.845845\pi$
$19$	−1454.44	+	839.723i	−0.924299	+	0.533644i	−0.0392951	+	0.999228i	$0.512511\pi$
$20$	−7277.12			−4.06804
$21$		0			0
$22$	1247.24			0.549406
$23$	194.041	−	112.030i	0.0764847	−	0.0441584i	−0.461270	−	0.887260i	$-0.652606\pi$
$23$	194.041	−	112.030i	0.0764847	−	0.0441584i	0.537755	+	0.843101i	$0.319273\pi$
$24$		0			0
$25$	−1849.92	+	3204.15i	−0.591973	+	1.02533i
$26$	−1804.24	−	3125.04i	−0.523433	−	0.906613i
$27$		0			0
$28$	−10590.1	−	4273.27i	−2.55274	−	1.03007i
$29$		−	2982.54i		−	0.658554i	−0.944233	−	0.329277i	$-0.893195\pi$
$29$		−	2982.54i		−	0.658554i	0.944233	−	0.329277i	$-0.106805\pi$
$30$		0			0
$31$	2924.18	+	1688.28i	0.546512	+	0.315529i	0.747714	−	0.664021i	$-0.231151\pi$
$31$	2924.18	+	1688.28i	0.546512	+	0.315529i	−0.201202	+	0.979550i	$0.564485\pi$
$32$	20136.4	+	11625.8i	3.47622	+	2.00700i
$33$		0			0
$34$			4856.80i			0.720532i
$35$	−8436.72	+	6597.48i	−1.16414	+	0.910348i
$36$		0			0
$37$	5858.99	+	10148.1i	0.703588	+	1.21865i	0.967199	+	0.254021i	$0.0817532\pi$
$37$	5858.99	+	10148.1i	0.703588	+	1.21865i	−0.263611	+	0.964629i	$0.584913\pi$
$38$	9202.05	−	15938.4i	1.03377	−	1.79055i
$39$		0			0
$40$	43973.5	−	25388.1i	4.34551	−	2.50888i
$41$	−14554.2			−1.35216			−0.676079	−	0.736829i	$-0.736322\pi$
$41$	−14554.2			−1.35216			−0.676079	+	0.736829i	$0.736322\pi$
$42$		0			0
$43$	−10531.9			−0.868629			−0.434315	−	0.900761i	$-0.643009\pi$
$43$	−10531.9			−0.868629			−0.434315	+	0.900761i	$0.643009\pi$
$44$	−8682.52	+	5012.86i	−0.676105	+	0.390349i
$45$		0			0
$46$	−1227.67	+	2126.39i	−0.0855436	+	0.148166i
$47$	11046.1	+	19132.4i	0.729396	+	1.26335i	0.957139	+	0.289630i	$0.0935321\pi$
$47$	11046.1	+	19132.4i	0.729396	+	1.26335i	−0.227743	+	0.973721i	$0.573135\pi$
$48$		0			0
$49$	−16151.8	+	4646.86i	−0.961019	+	0.276484i
$50$		−	40544.4i		−	2.29354i
$51$		0			0
$52$	25120.0	+	14503.1i	1.28829	+	0.743792i
$53$	−3941.39	−	2275.56i	−0.192735	−	0.111275i	0.400527	−	0.916285i	$-0.368827\pi$
$53$	−3941.39	−	2275.56i	−0.192735	−	0.111275i	−0.593262	+	0.805009i	$0.702160\pi$
$54$		0			0
$55$			9402.59i			0.419122i
$56$	78901.4	−	11124.3i	3.36213	−	0.474027i
$57$		0			0
$58$	16342.0	+	28305.2i	0.637875	+	1.10483i
$59$	−6666.58	+	11546.9i	−0.249329	+	0.431851i	−0.963340	−	0.268284i	$-0.913543\pi$
$59$	−6666.58	+	11546.9i	−0.249329	+	0.431851i	0.714011	+	0.700135i	$0.246877\pi$
$60$		0			0
$61$	−43971.6	+	25387.0i	−1.51303	+	0.873548i	−0.513146	+	0.858301i	$0.671520\pi$
$61$	−43971.6	+	25387.0i	−1.51303	+	0.873548i	−0.999884	+	0.0152469i	$0.995147\pi$
$62$	−37001.8			−1.22248
$63$		0			0
$64$	−129470.			−3.95111
$65$	23558.8	−	13601.7i	0.691623	−	0.399309i
$66$		0			0
$67$	25659.4	−	44443.4i	0.698328	−	1.20954i	−0.270717	−	0.962659i	$-0.587261\pi$
$67$	25659.4	−	44443.4i	0.698328	−	1.20954i	0.969046	−	0.246881i	$-0.0794057\pi$
$68$	−19520.3	−	33810.1i	−0.511933	−	0.886694i
$69$		0			0
$70$	43917.9	−	108839.i	1.07126	−	2.65484i
$71$			1201.47i			0.0282858i	0.999900	+	0.0141429i	$0.00450198\pi$
$71$			1201.47i			0.0282858i	−0.999900	+	0.0141429i	$0.995498\pi$
$72$		0			0
$73$	7651.79	+	4417.76i	0.168057	+	0.0970276i	0.581669	−	0.813425i	$-0.302400\pi$
$73$	7651.79	+	4417.76i	0.168057	+	0.0970276i	−0.413613	+	0.910453i	$0.635733\pi$
$74$	−111207.	−	64205.4i	−2.36076	−	1.36299i
$75$		0			0
$76$			147938.i			2.93796i
$77$	−5521.39	+	13683.3i	−0.106126	+	0.263004i
$78$		0			0
$79$	−21780.4	−	37724.7i	−0.392642	−	0.680077i	0.600155	−	0.799884i	$-0.295106\pi$
$79$	−21780.4	−	37724.7i	−0.392642	−	0.680077i	−0.992797	+	0.119807i	$0.961772\pi$
$80$	−161780.	+	280211.i	−2.82618	+	4.89508i
$81$		0			0
$82$	138123.	−	79745.5i	2.26846	−	1.30970i
$83$	58191.3			0.927177			0.463589	−	0.886050i	$-0.346562\pi$
$83$	58191.3			0.927177			0.463589	+	0.886050i	$0.346562\pi$
$84$		0			0
$85$	−36614.0			−0.549668
$86$	99950.5	−	57706.4i	1.45727	−	0.841353i
$87$		0			0
$88$	34977.2	−	60582.3i	0.481481	−	0.833949i
$89$	54255.1	+	93972.7i	0.726049	+	1.25755i	0.958541	+	0.284955i	$0.0919788\pi$
$89$	54255.1	+	93972.7i	0.726049	+	1.25755i	−0.232492	+	0.972598i	$0.574688\pi$
$90$		0			0
$91$	42271.4	−	5959.85i	0.535111	−	0.0754452i
$92$		−	19736.8i		−	0.243113i
$93$		0			0
$94$	−209661.	−	121048.i	−2.44736	−	1.41298i
$95$	120155.	+	69371.6i	1.36595	+	0.788629i
$96$		0			0
$97$		−	5444.51i		−	0.0587529i	−0.999568	−	0.0293765i	$-0.990648\pi$
$97$		−	5444.51i		−	0.0587529i	0.999568	−	0.0293765i	$-0.00935217\pi$
$98$	127824.	−	132600.i	1.34446	−	1.39469i
$99$		0			0
$100$	162954.	+	282245.i	1.62954	+	2.82245i
$101$	−16535.2	+	28639.8i	−0.161289	+	0.279361i	−0.935331	−	0.353773i	$-0.884899\pi$
$101$	−16535.2	+	28639.8i	−0.161289	+	0.279361i	0.774042	+	0.633134i	$0.218232\pi$
$102$		0			0
$103$	33810.3	−	19520.4i	0.314019	−	0.181299i	−0.334704	−	0.942323i	$-0.608636\pi$
$103$	33810.3	−	19520.4i	0.314019	−	0.181299i	0.648724	+	0.761024i	$0.275303\pi$
$104$	−202390.			−1.83488
$105$		0			0
$106$	49873.2			0.431125
$107$	−109127.	+	63004.2i	−0.921448	+	0.531998i	−0.884097	−	0.467304i	$-0.845225\pi$
$107$	−109127.	+	63004.2i	−0.921448	+	0.531998i	−0.0373514	+	0.999302i	$0.511892\pi$
$108$		0			0
$109$	67351.1	−	116656.i	0.542974	−	0.940458i	−0.455758	−	0.890104i	$-0.650632\pi$
$109$	67351.1	−	116656.i	0.542974	−	0.940458i	0.998731	−	0.0503540i	$-0.0160350\pi$
$110$	−51518.9	−	89233.3i	−0.405961	−	0.703145i
$111$		0			0
$112$	−399978.	+	312781.i	−3.01294	+	2.35611i
$113$		−	22220.5i		−	0.163703i	−0.996645	−	0.0818517i	$-0.973917\pi$
$113$		−	22220.5i		−	0.163703i	0.996645	−	0.0818517i	$-0.0260834\pi$
$114$		0			0
$115$	−16030.2	−	9255.06i	−0.113030	−	0.0652582i
$116$	−227526.	−	131362.i	−1.56995	−	0.906412i
$117$		0			0
$118$		−	146111.i		−	0.966000i
$119$	−53283.1	−	21500.5i	−0.344923	−	0.139181i
$120$		0			0
$121$	−74048.5	−	128256.i	−0.459783	−	0.796368i
$122$	278202.	−	481860.i	1.69223	−	2.93104i
$123$		0			0
$124$	257584.	−	148716.i	1.50440	−	0.868567i
$125$	47488.4			0.271840
$126$		0			0
$127$	−167321.			−0.920537			−0.460268	−	0.887780i	$-0.652247\pi$
$127$	−167321.			−0.920537			−0.460268	+	0.887780i	$0.652247\pi$
$128$	584340.	−	337369.i	3.15240	−	1.82004i
$129$		0			0
$130$	−149053.	+	258167.i	−0.773539	+	1.33981i
$131$	−173655.	−	300780.i	−0.884117	−	1.53134i	−0.846723	−	0.532034i	$-0.821428\pi$
$131$	−173655.	−	300780.i	−0.884117	−	1.53134i	−0.0373940	−	0.999301i	$-0.511906\pi$
$132$		0			0
$133$	134121.	+	171512.i	0.657459	+	0.840746i
$134$			562374.i			2.70560i
$135$		0			0
$136$	235910.	+	136203.i	1.09370	+	0.631449i
$137$	319613.	+	184528.i	1.45486	+	0.839966i	0.998751	−	0.0499556i	$-0.0159080\pi$
$137$	319613.	+	184528.i	1.45486	+	0.839966i	0.456113	+	0.889922i	$0.349241\pi$
$138$		0			0
$139$			125256.i			0.549874i	0.961462	+	0.274937i	$0.0886570\pi$
$139$			125256.i			0.549874i	−0.961462	+	0.274937i	$0.911343\pi$
$140$	131710.	+	934180.i	0.567935	+	4.02820i
$141$		0			0
$142$	−6583.14	−	11402.3i	−0.0273976	−	0.0474540i
$143$	18739.1	−	32457.0i	0.0766315	−	0.132730i
$144$		0			0
$145$	−213385.	+	123198.i	−0.842837	+	0.486612i
$146$	−96823.6			−0.375923
$147$		0			0
$148$	1.03221e6			3.87358
$149$	−185494.	+	107095.i	−0.684485	+	0.395188i	−0.801543	−	0.597938i	$-0.795987\pi$
$149$	−185494.	+	107095.i	−0.684485	+	0.395188i	0.117058	+	0.993125i	$0.462654\pi$
$150$		0			0
$151$	−76373.6	+	132283.i	−0.272584	+	0.472130i	−0.969523	−	0.245001i	$-0.921212\pi$
$151$	−76373.6	+	132283.i	−0.272584	+	0.472130i	0.696938	+	0.717131i	$0.254545\pi$
$152$	−516119.	−	893944.i	−1.81193	−	3.13835i
$153$		0			0
$154$	−22574.0	−	160111.i	−0.0767021	−	0.544026i
$155$		−	278946.i		−	0.932589i
$156$		0			0
$157$	101208.	+	58432.5i	0.327692	+	0.189193i	0.654816	−	0.755788i	$-0.272746\pi$
$157$	101208.	+	58432.5i	0.327692	+	0.189193i	−0.327124	+	0.944981i	$0.606079\pi$
$158$	413404.	+	238679.i	1.31744	+	0.760626i
$159$		0			0
$160$		−	1.92087e6i		−	5.93196i
$161$	−17893.5	−	22881.9i	−0.0544040	−	0.0695707i
$162$		0			0
$163$	−39292.5	−	68056.6i	−0.115835	−	0.200632i	0.802278	−	0.596950i	$-0.203621\pi$
$163$	−39292.5	−	68056.6i	−0.115835	−	0.200632i	−0.918113	+	0.396318i	$0.870288\pi$
$164$	−641019.	+	1.11028e6i	−1.86106	+	3.22346i
$165$		0			0
$166$	−552252.	+	318843.i	−1.55549	+	0.898063i
$167$	−690721.			−1.91651			−0.958256	−	0.285911i	$-0.907704\pi$
$167$	−690721.			−1.91651			−0.958256	+	0.285911i	$0.907704\pi$
$168$		0			0
$169$	262862.			0.707965
$170$	347478.	−	200616.i	0.922157	−	0.532407i
$171$		0			0
$172$	−463862.	+	803433.i	−1.19555	+	2.07075i
$173$	−88564.4	−	153398.i	−0.224980	−	0.389677i	0.731333	−	0.682020i	$-0.238898\pi$
$173$	−88564.4	−	153398.i	−0.224980	−	0.389677i	−0.956313	+	0.292343i	$0.905565\pi$
$174$		0			0
$175$	444806.	+	179485.i	1.09793	+	0.443031i
$176$			445769.i			1.08475i
$177$		0			0
$178$	−1.02979e6	−	594552.i	−2.43613	−	1.40650i
$179$	−292398.	−	168816.i	−0.682091	−	0.393805i	0.118552	−	0.992948i	$-0.462175\pi$
$179$	−292398.	−	168816.i	−0.682091	−	0.393805i	−0.800642	+	0.599143i	$0.795508\pi$
$180$		0			0
$181$			514756.i			1.16790i	0.811790	+	0.583949i	$0.198493\pi$
$181$			514756.i			1.16790i	−0.811790	+	0.583949i	$0.801507\pi$
$182$	−368513.	+	288175.i	−0.824658	+	0.644879i
$183$		0			0
$184$	68856.9	+	119264.i	0.149935	+	0.259695i
$185$	484026.	−	838358.i	1.03977	−	1.80094i
$186$		0			0
$187$	−43685.2	+	25221.6i	−0.0913545	+	0.0527435i
$188$	1.94604e6			4.01566
$189$		0			0
$190$	−1.52041e6			−3.05546
$191$	−88502.5	+	51096.9i	−0.175538	+	0.101347i	−0.585195	−	0.810893i	$-0.698982\pi$
$191$	−88502.5	+	51096.9i	−0.175538	+	0.101347i	0.409656	+	0.912240i	$0.365649\pi$
$192$		0			0
$193$	354753.	−	614449.i	0.685539	−	1.18739i	−0.287728	−	0.957712i	$-0.592900\pi$
$193$	354753.	−	614449.i	0.685539	−	1.18739i	0.973267	−	0.229676i	$-0.0737668\pi$
$194$	29831.7	+	51670.0i	0.0569080	+	0.0985676i
$195$		0			0
$196$	−356896.	+	1.43682e6i	−0.663593	+	2.67155i
$197$			86388.0i			0.158594i	0.996851	+	0.0792972i	$0.0252676\pi$
$197$			86388.0i			0.158594i	−0.996851	+	0.0792972i	$0.974732\pi$
$198$		0			0
$199$	−624957.	−	360819.i	−1.11871	−	0.645888i	−0.177639	−	0.984096i	$-0.556846\pi$
$199$	−624957.	−	360819.i	−1.11871	−	0.645888i	−0.941071	+	0.338208i	$0.890179\pi$
$200$	−1.96937e6	−	1.13701e6i	−3.48138	−	2.00998i
$201$		0			0
$202$		−	362400.i		−	0.624898i
$203$	−382876.	+	53981.6i	−0.652105	+	0.0919403i
$204$		0			0
$205$	601178.	+	1.04127e6i	0.999122	+	1.73053i
$206$	−213913.	+	370508.i	−0.351212	+	0.608317i
$207$		0			0
$208$	1.11690e6	−	644843.i	1.79001	−	1.03347i
$209$	191147.			0.302693
$210$		0			0
$211$	381389.			0.589743			0.294871	−	0.955537i	$-0.404723\pi$
$211$	381389.			0.589743			0.294871	+	0.955537i	$0.404723\pi$
$212$	−347187.	+	200448.i	−0.530547	+	0.306311i
$213$		0			0
$214$	690428.	−	1.19586e6i	1.03059	−	1.78503i
$215$	435032.	+	753498.i	0.641838	+	1.11170i
$216$		0			0
$217$	163803.	−	405940.i	0.236141	−	0.585211i
$218$			1.47613e6i			2.10369i
$219$		0			0
$220$	717285.	+	414125.i	0.999160	+	0.576866i
$221$	126389.	+	72970.6i	0.174071	+	0.100500i
$222$		0			0
$223$		−	273465.i		−	0.368247i	−0.982903	−	0.184124i	$-0.941055\pi$
$223$		−	273465.i		−	0.368247i	0.982903	−	0.184124i	$-0.0589446\pi$
$224$	1.12797e6	−	2.79538e6i	1.50203	−	3.72238i
$225$		0			0
$226$	121751.	+	210879.i	0.158563	+	0.274639i
$227$	79769.7	−	138165.i	0.102748	−	0.177965i	−0.810068	−	0.586336i	$-0.800570\pi$
$227$	79769.7	−	138165.i	0.102748	−	0.177965i	0.912816	+	0.408371i	$0.133903\pi$
$228$		0			0
$229$	−889470.	+	513536.i	−1.12084	+	0.647116i	−0.941615	−	0.336693i	$-0.890692\pi$
$229$	−889470.	+	513536.i	−1.12084	+	0.647116i	−0.179223	+	0.983808i	$0.557358\pi$
$230$	202842.			0.252836
$231$		0			0
$232$	1.83316e6			2.23605
$233$	515764.	−	297777.i	0.622388	−	0.359336i	−0.155410	−	0.987850i	$-0.549670\pi$
$233$	515764.	−	297777.i	0.622388	−	0.359336i	0.777798	+	0.628514i	$0.216337\pi$
$234$		0			0
$235$	912544.	−	1.58057e6i	1.07791	−	1.86700i
$236$	587242.	+	1.01713e6i	0.686336	+	1.18877i
$237$		0			0
$238$	623478.	−	87904.2i	0.713475	−	0.100593i
$239$		−	1.34378e6i		−	1.52171i	−0.648921	−	0.760856i	$-0.724780\pi$
$239$		−	1.34378e6i		−	1.52171i	0.648921	−	0.760856i	$-0.275220\pi$
$240$		0			0
$241$	−1.39688e6	−	806487.i	−1.54923	−	0.894448i	−0.998201	−	0.0599611i	$-0.980902\pi$
$241$	−1.39688e6	−	806487.i	−1.54923	−	0.894448i	−0.551028	−	0.834487i	$-0.685764\pi$
$242$	1.40548e6	+	811456.i	1.54272	+	0.890690i
$243$		0			0
$244$			4.47255e6i			4.80929i
$245$	999630.	+	963632.i	1.06396	+	1.02564i
$246$		0			0
$247$	−276511.	−	478931.i	−0.288383	−	0.499494i
$248$	−1.03767e6	+	1.79729e6i	−1.07134	+	1.85562i
$249$		0			0
$250$	−450679.	+	260199.i	−0.456055	+	0.263303i
$251$	−1.19624e6			−1.19849			−0.599244	−	0.800567i	$-0.704532\pi$
$251$	−1.19624e6			−1.19849			−0.599244	+	0.800567i	$0.704532\pi$
$252$		0			0
$253$	−25501.5			−0.0250475
$254$	1.58792e6	−	916789.i	1.54435	−	0.891630i
$255$		0			0
$256$	−1.62552e6	+	2.81548e6i	−1.55022	+	2.68505i
$257$	−62945.9	−	109025.i	−0.0594476	−	0.102966i	0.834770	−	0.550599i	$-0.185601\pi$
$257$	−62945.9	−	109025.i	−0.0594476	−	0.102966i	−0.894218	+	0.447633i	$0.852267\pi$
$258$		0			0
$259$	1.19669e6	−	935803.i	1.10849	−	0.866832i
$260$		−	2.39627e6i		−	2.19838i
$261$		0			0
$262$	3.29608e6	+	1.90299e6i	2.96650	+	1.71271i
$263$	27103.4	+	15648.2i	0.0241621	+	0.0139500i	0.512032	−	0.858966i	$-0.328893\pi$
$263$	27103.4	+	15648.2i	0.0241621	+	0.0139500i	−0.487870	+	0.872916i	$0.662226\pi$
$264$		0			0
$265$			375980.i			0.328890i
$266$	−2.21260e6	−	892815.i	−1.91734	−	0.773673i
$267$		0			0
$268$	−2.26027e6	−	3.91490e6i	−1.92231	−	3.32954i
$269$	110072.	−	190650.i	0.0927459	−	0.160641i	−0.815920	−	0.578165i	$-0.803769\pi$
$269$	110072.	−	190650.i	0.0927459	−	0.160641i	0.908666	+	0.417525i	$0.137102\pi$
$270$		0			0
$271$	1.01098e6	−	583689.i	0.836217	−	0.482790i	−0.0197593	−	0.999805i	$-0.506290\pi$
$271$	1.01098e6	−	583689.i	0.836217	−	0.482790i	0.855977	+	0.517014i	$0.172957\pi$
$272$	−1.73584e6			−1.42262
$273$		0			0
$274$	−4.04429e6			−3.25436
$275$	364682.	−	210549.i	0.290792	−	0.167889i
$276$		0			0
$277$	−409580.	+	709413.i	−0.320730	+	0.555520i	−0.980639	−	0.195825i	$-0.937261\pi$
$277$	−409580.	+	709413.i	−0.320730	+	0.555520i	0.659909	+	0.751346i	$0.270595\pi$
$278$	−686308.	−	1.18872e6i	−0.532607	−	0.922502i
$279$		0			0
$280$	−4.05501e6	−	5.18546e6i	−3.09098	−	3.95269i
$281$			658409.i			0.497428i	0.968577	+	0.248714i	$0.0800079\pi$
$281$			658409.i			0.497428i	−0.968577	+	0.248714i	$0.919992\pi$
$282$		0			0
$283$	−1.54405e6	−	891457.i	−1.14603	−	0.661659i	−0.198111	−	0.980180i	$-0.563481\pi$
$283$	−1.54405e6	−	891457.i	−1.14603	−	0.661659i	−0.947916	+	0.318520i	$0.896814\pi$
$284$	91655.6	+	52917.4i	0.0674315	+	0.0389316i
$285$		0			0
$286$			410701.i			0.296901i
$287$	263419.	+	1.86835e6i	0.188774	+	1.33892i
$288$		0			0
$289$	611715.	+	1.05952e6i	0.430828	+	0.746216i
$290$	1.35005e6	−	2.33836e6i	0.942663	−	1.63274i
$291$		0			0
$292$	674026.	−	389149.i	0.462615	−	0.267091i
$293$	−693145.			−0.471689			−0.235844	−	0.971791i	$-0.575786\pi$
$293$	−693145.			−0.471689			−0.235844	+	0.971791i	$0.575786\pi$
$294$		0			0
$295$	1.10149e6			0.736927
$296$	−6.23731e6	+	3.60111e6i	−4.13779	+	2.38895i
$297$		0			0
$298$	1.17359e6	−	2.03272e6i	0.765556	−	1.32598i
$299$	36890.1	+	63895.5i	0.0238634	+	0.0413325i
$300$		0			0
$301$	190618.	+	1.35200e6i	0.121269	+	0.860122i
$302$		−	1.67387e6i		−	1.05610i
$303$		0			0
$304$	5.69646e6	+	3.28885e6i	3.53526	+	2.04108i
$305$	3.63260e6	+	2.09729e6i	2.23598	+	1.29095i
$306$		0			0
$307$			1.35379e6i			0.819793i	0.912132	+	0.409897i	$0.134435\pi$
$307$			1.35379e6i			0.819793i	−0.912132	+	0.409897i	$0.865565\pi$
$308$	800658.	+	1.02387e6i	0.480917	+	0.614987i
$309$		0			0
$310$	1.52840e6	+	2.64727e6i	0.903305	+	1.56457i
$311$	869759.	−	1.50647e6i	0.509915	−	0.883199i	−0.490019	−	0.871712i	$-0.663010\pi$
$311$	869759.	−	1.50647e6i	0.509915	−	0.883199i	0.999934	−	0.0114873i	$-0.00365659\pi$
$312$		0			0
$313$	−1.72330e6	+	994950.i	−0.994263	+	0.574038i	−0.906546	−	0.422108i	$-0.861290\pi$
$313$	−1.72330e6	+	994950.i	−0.994263	+	0.574038i	−0.0877169	+	0.996145i	$0.527957\pi$
$314$	−1.28066e6			−0.733008
$315$		0			0
$316$	−3.83715e6			−2.16168
$317$	−2.33882e6	+	1.35032e6i	−1.30722	+	0.754723i	−0.981631	−	0.190788i	$-0.938896\pi$
$317$	−2.33882e6	+	1.35032e6i	−1.30722	+	0.754723i	−0.325588	+	0.945512i	$0.605562\pi$
$318$		0			0
$319$	−169730.	+	293981.i	−0.0933860	+	0.161749i
$320$	5.34792e6	+	9.26287e6i	2.91951	+	5.05674i
$321$		0			0
$322$	295189.	+	119113.i	0.158657	+	0.0640205i
$323$			744334.i			0.396973i
$324$		0			0
$325$	−1.05509e6	−	609155.i	−0.554090	−	0.319904i
$326$	745794.	+	430584.i	0.388665	+	0.224396i
$327$		0			0
$328$		−	8.94543e6i		−	4.59110i
$329$	2.25614e6	−	1.76429e6i	1.14915	−	0.898628i
$330$		0			0
$331$	−279715.	−	484480.i	−0.140328	−	0.243056i	0.787292	−	0.616580i	$-0.211482\pi$
$331$	−279715.	−	484480.i	−0.140328	−	0.243056i	−0.927620	+	0.373525i	$0.878149\pi$
$332$	2.56296e6	−	4.43918e6i	1.27614	−	2.21033i
$333$		0			0
$334$	6.55514e6	−	3.78461e6i	3.21526	−	1.85633i
$335$	−4.23958e6			−2.06400
$336$		0			0
$337$	−967665.			−0.464141			−0.232071	−	0.972699i	$-0.574550\pi$
$337$	−967665.			−0.464141			−0.232071	+	0.972699i	$0.574550\pi$
$338$	−2.49464e6	+	1.44028e6i	−1.18773	+	0.685733i
$339$		0			0
$340$	−1.61262e6	+	2.79314e6i	−0.756544	+	1.31037i
$341$	−192152.	−	332817.i	−0.0894869	−	0.154996i
$342$		0			0
$343$	888863.	+	1.98934e6i	0.407943	+	0.913007i
$344$		−	6.47321e6i		−	2.94933i
$345$		0			0
$346$	1.68100e6	+	970528.i	0.754881	+	0.435831i
$347$	−1.92904e6	−	1.11373e6i	−0.860037	−	0.496543i	0.00398755	−	0.999992i	$-0.498731\pi$
$347$	−1.92904e6	−	1.11373e6i	−0.860037	−	0.496543i	−0.864025	+	0.503449i	$0.832064\pi$
$348$		0			0
$349$			1.98330e6i			0.871617i	0.900040	+	0.435808i	$0.143537\pi$
$349$			1.98330e6i			0.871617i	−0.900040	+	0.435808i	$0.856463\pi$
$350$	−5.20477e6	+	733821.i	−2.27108	+	0.320199i
$351$		0			0
$352$	−1.32319e6	−	2.29184e6i	−0.569203	−	0.985888i
$353$	−827602.	+	1.43345e6i	−0.353496	+	0.612273i	−0.986859	−	0.161581i	$-0.948341\pi$
$353$	−827602.	+	1.43345e6i	−0.353496	+	0.612273i	0.633363	+	0.773855i	$0.281674\pi$
$354$		0			0
$355$	85959.0	−	49628.4i	0.0362010	−	0.0209006i
$356$	9.55839e6			3.99723
$357$		0			0
$358$	3.69992e6			1.52576
$359$	−2.04413e6	+	1.18018e6i	−0.837089	+	0.483294i	−0.856274	−	0.516522i	$-0.827226\pi$
$359$	−2.04413e6	+	1.18018e6i	−0.837089	+	0.483294i	0.0191845	+	0.999816i	$0.493893\pi$
$360$		0			0
$361$	172219.	−	298293.i	0.0695527	−	0.120469i
$362$	−2.82046e6	−	4.88518e6i	−1.13122	−	1.95934i
$363$		0			0
$364$	1.40714e6	−	3.48721e6i	0.556651	−	1.37951i
$365$		−	729925.i		−	0.286778i
$366$		0			0
$367$	−3.12515e6	−	1.80430e6i	−1.21117	−	0.699269i	−0.248156	−	0.968720i	$-0.579825\pi$
$367$	−3.12515e6	−	1.80430e6i	−1.21117	−	0.699269i	−0.963014	+	0.269451i	$0.913158\pi$
$368$	−759980.	−	438775.i	−0.292538	−	0.168897i
$369$		0			0
$370$			1.06083e7i			4.02850i
$371$	−220783.	+	547151.i	−0.0832781	+	0.206382i
$372$		0			0
$373$	768104.	+	1.33040e6i	0.285856	+	0.495118i	0.972817	−	0.231577i	$-0.0743886\pi$
$373$	768104.	+	1.33040e6i	0.285856	+	0.495118i	−0.686960	+	0.726695i	$0.741055\pi$
$374$	276390.	−	478721.i	0.102175	−	0.176972i
$375$		0			0
$376$	−1.17593e7	+	6.78925e6i	−4.28956	+	2.47658i
$377$	982116.			0.355885
$378$		0			0
$379$	−4.61784e6			−1.65136			−0.825678	−	0.564141i	$-0.809207\pi$
$379$	−4.61784e6			−1.65136			−0.825678	+	0.564141i	$0.809207\pi$
$380$	1.05842e7	−	6.11077e6i	3.76008	−	2.17088i
$381$		0			0
$382$	559943.	−	969849.i	0.196329	−	0.340052i
$383$	−1.41514e6	−	2.45109e6i	−0.492948	−	0.853811i	0.507019	−	0.861935i	$-0.330747\pi$
$383$	−1.41514e6	−	2.45109e6i	−0.492948	−	0.853811i	−0.999967	+	0.00812384i	$0.997414\pi$
$384$		0			0
$385$	1.20703e6	−	170179.i	0.415018	−	0.0585133i
$386$			7.77507e6i			2.65605i
$387$		0			0
$388$	−415340.	−	239796.i	−0.140063	−	0.0808655i
$389$	4.37578e6	+	2.52636e6i	1.46616	+	0.846488i	0.999284	−	0.0378344i	$-0.0120459\pi$
$389$	4.37578e6	+	2.52636e6i	1.46616	+	0.846488i	0.466876	+	0.884323i	$0.345379\pi$
$390$		0			0
$391$		−	99303.6i		−	0.0328491i
$392$	−2.85610e6	−	9.92741e6i	−0.938769	−	3.26303i
$393$		0			0
$394$	−473339.	−	819846.i	−0.153614	−	0.266068i
$395$	−1.79933e6	+	3.11653e6i	−0.580254	+	1.00503i
$396$		0			0
$397$	−3.98853e6	+	2.30278e6i	−1.27009	+	0.733289i	−0.975006	−	0.222180i	$-0.928683\pi$
$397$	−3.98853e6	+	2.30278e6i	−1.27009	+	0.733289i	−0.295089	+	0.955470i	$0.595349\pi$
$398$	7.90803e6			2.50242
$399$		0			0
$400$	1.44907e7			4.52835
$401$	1.65943e6	−	958075.i	0.515346	−	0.297535i	−0.219682	−	0.975571i	$-0.570502\pi$
$401$	1.65943e6	−	958075.i	0.515346	−	0.297535i	0.735029	+	0.678036i	$0.237169\pi$
$402$		0			0
$403$	−555929.	+	962898.i	−0.170513	+	0.295337i
$404$	1.45654e6	+	2.52280e6i	0.443986	+	0.769007i
$405$		0			0
$406$	3.33782e6	−	2.61016e6i	1.00496	−	0.785872i
$407$		−	1.33369e6i		−	0.399088i
$408$		0			0
$409$	2.14820e6	+	1.24027e6i	0.634991	+	0.366612i	0.782682	−	0.622421i	$-0.213851\pi$
$409$	2.14820e6	+	1.24027e6i	0.634991	+	0.366612i	−0.147692	+	0.989033i	$0.547184\pi$
$410$	−1.14107e7	−	6.58798e6i	−3.35238	−	1.93550i
$411$		0			0
$412$		−	3.43900e6i		−	0.998135i
$413$	1.60296e6	+	646815.i	0.462430	+	0.186597i
$414$		0			0
$415$	−2.40367e6	−	4.16327e6i	−0.685100	−	1.18663i
$416$	−3.82823e6	+	6.63069e6i	−1.08459	+	1.87856i
$417$		0			0
$418$	−1.81404e6	+	1.04734e6i	−0.507816	+	0.293188i
$419$	−1.81159e6			−0.504110			−0.252055	−	0.967713i	$-0.581106\pi$
$419$	−1.81159e6			−0.504110			−0.252055	+	0.967713i	$0.581106\pi$
$420$		0			0
$421$	6.66082e6			1.83157			0.915783	−	0.401673i	$-0.131571\pi$
$421$	6.66082e6			1.83157			0.915783	+	0.401673i	$0.131571\pi$
$422$	−3.61950e6	+	2.08972e6i	−0.989389	+	0.571224i
$423$		0			0
$424$	1.39863e6	−	2.42250e6i	0.377823	−	0.654408i
$425$	819887.	+	1.42009e6i	0.220182	+	0.381366i
$426$		0			0
$427$	4.05484e6	+	5.18524e6i	1.07623	+	1.37626i
$428$			1.10998e7i			2.92890i
$429$		0			0
$430$	−8.25716e6	−	4.76727e6i	−2.15357	−	1.24337i
$431$	−1.30089e6	−	751070.i	−0.337325	−	0.194754i	0.321764	−	0.946820i	$-0.395724\pi$
$431$	−1.30089e6	−	751070.i	−0.337325	−	0.194754i	−0.659088	+	0.752066i	$0.729058\pi$
$432$		0			0
$433$		−	5.98390e6i		−	1.53379i	−0.641775	−	0.766893i	$-0.721802\pi$
$433$		−	5.98390e6i		−	1.53379i	0.641775	−	0.766893i	$-0.278198\pi$
$434$	669702.	+	4.75000e6i	0.170670	+	1.21051i
$435$		0			0
$436$	−5.93279e6	−	1.02759e7i	−1.49466	−	2.58883i
$437$	−188148.	+	325882.i	−0.0471298	+	0.0816312i
$438$		0			0
$439$	3.64522e6	−	2.10457e6i	0.902741	−	0.521198i	0.0246523	−	0.999696i	$-0.492152\pi$
$439$	3.64522e6	−	2.10457e6i	0.902741	−	0.521198i	0.878088	+	0.478498i	$0.158819\pi$
$440$	−5.77912e6			−1.42308
$441$		0			0
$442$	−1.59929e6			−0.389377
$443$	4.28649e6	−	2.47481e6i	1.03775	−	0.599146i	0.118555	−	0.992947i	$-0.462174\pi$
$443$	4.28649e6	−	2.47481e6i	1.03775	−	0.599146i	0.919195	+	0.393802i	$0.128840\pi$
$444$		0			0
$445$	4.48216e6	−	7.76332e6i	1.07297	−	1.85844i
$446$	1.49837e6	+	2.59526e6i	0.356683	+	0.617794i
$447$		0			0
$448$	2.34330e6	+	1.66203e7i	0.551611	+	3.91241i
$449$		−	4.75341e6i		−	1.11273i	−0.830939	−	0.556364i	$-0.812196\pi$
$449$		−	4.75341e6i		−	1.11273i	0.830939	−	0.556364i	$-0.187804\pi$
$450$		0			0
$451$	1.43456e6	+	828245.i	0.332107	+	0.191742i
$452$	−1.69511e6	−	978673.i	−0.390258	−	0.225316i
$453$		0			0
$454$			1.74830e6i			0.398086i
$455$	−2.17247e6	−	2.77811e6i	−0.491955	−	0.629102i
$456$		0			0
$457$	3.80847e6	+	6.59646e6i	0.853021	+	1.47748i	0.878469	+	0.477799i	$0.158565\pi$
$457$	3.80847e6	+	6.59646e6i	0.853021	+	1.47748i	−0.0254481	+	0.999676i	$0.508101\pi$
$458$	5.62755e6	−	9.74721e6i	1.25359	−	2.17128i
$459$		0			0
$460$	−1.41206e6	+	815254.i	−0.311142	+	0.179638i
$461$	376986.			0.0826176			0.0413088	−	0.999146i	$-0.486847\pi$
$461$	376986.			0.0826176			0.0413088	+	0.999146i	$0.486847\pi$
$462$		0			0
$463$	1.75954e6			0.381458			0.190729	−	0.981643i	$-0.438915\pi$
$463$	1.75954e6			0.381458			0.190729	+	0.981643i	$0.438915\pi$
$464$	−1.01164e7	+	5.84070e6i	−2.18138	+	1.25942i
$465$		0			0
$466$	−3.26317e6	+	5.65197e6i	−0.696105	+	1.20569i
$467$	4.19642e6	+	7.26842e6i	0.890404	+	1.54223i	0.839392	+	0.543527i	$0.182912\pi$
$467$	4.19642e6	+	7.26842e6i	0.890404	+	1.54223i	0.0510125	+	0.998698i	$0.483755\pi$
$468$		0			0
$469$	−6.16971e6	−	2.48957e6i	−1.29519	−	0.522626i
$470$			2.00001e7i			4.17627i
$471$		0			0
$472$	−7.09705e6	−	4.09748e6i	−1.46630	−	0.846569i
$473$	1.03810e6	+	599345.i	0.213346	+	0.123175i
$474$		0			0
$475$		−	6.21367e6i		−	1.26361i
$476$	−3.98697e6	+	3.11779e6i	−0.806540	+	0.630710i
$477$		0			0
$478$	7.36285e6	+	1.27528e7i	1.47393	+	2.55292i
$479$	686440.	−	1.18895e6i	0.136699	−	0.236769i	−0.789546	−	0.613691i	$-0.789684\pi$
$479$	686440.	−	1.18895e6i	0.136699	−	0.236769i	0.926245	+	0.376922i	$0.123017\pi$
$480$		0			0
$481$	−3.34164e6	+	1.92930e6i	−0.658562	+	0.380221i
$482$	1.76757e7			3.46544
$483$		0			0
$484$	−1.30455e7			−2.53132
$485$	−389525.	+	224893.i	−0.0751937	+	0.0434131i
$486$		0			0
$487$	897176.	−	1.55395e6i	0.171417	−	0.296904i	−0.767498	−	0.641051i	$-0.778499\pi$
$487$	897176.	−	1.55395e6i	0.171417	−	0.296904i	0.938916	+	0.344147i	$0.111832\pi$
$488$	−1.56036e7	−	2.70263e7i	−2.96603	−	5.13732i
$489$		0			0
$490$	−1.47667e7	−	3.66795e6i	−2.77840	−	0.690133i
$491$		−	1.00791e7i		−	1.88677i	−0.331698	−	0.943386i	$-0.607622\pi$
$491$		−	1.00791e7i		−	1.88677i	0.331698	−	0.943386i	$-0.392378\pi$
$492$		0			0
$493$	−1.14477e6	−	660934.i	−0.212130	−	0.122473i
$494$	5.24833e6	+	3.03013e6i	0.967618	+	0.558654i
$495$		0			0
$496$		−	1.32246e7i		−	2.41367i
$497$	154236.	−	21745.7i	0.0280088	−	0.00394896i
$498$		0			0
$499$	−3.13155e6	−	5.42400e6i	−0.562999	−	0.975143i	−0.997233	−	0.0743428i	$-0.976314\pi$
$499$	−3.13155e6	−	5.42400e6i	−0.562999	−	0.975143i	0.434234	−	0.900800i	$-0.357019\pi$
$500$	2.09157e6	−	3.62270e6i	0.374151	−	0.648048i
$501$		0			0
$502$	1.13526e7	−	6.55445e6i	2.01066	−	1.16085i
$503$	598654.			0.105501			0.0527504	−	0.998608i	$-0.483201\pi$
$503$	598654.			0.105501			0.0527504	+	0.998608i	$0.483201\pi$
$504$		0			0
$505$	2.73203e6			0.476713
$506$	242016.	−	139728.i	0.0420212	−	0.0242609i
$507$		0			0
$508$	−7.36944e6	+	1.27642e7i	−1.26700	+	2.19450i
$509$	1.39878e6	+	2.42276e6i	0.239307	+	0.414492i	0.960516	−	0.278226i	$-0.0897465\pi$
$509$	1.39878e6	+	2.42276e6i	0.239307	+	0.414492i	−0.721209	+	0.692718i	$0.756413\pi$
$510$		0			0
$511$	428627.	−	1.06223e6i	0.0726151	−	0.179957i
$512$		−	1.40347e7i		−	2.36607i
$513$		0			0
$514$	1.19475e6	+	689789.i	0.199466	+	0.115162i
$515$	−2.79316e6	−	1.61263e6i	−0.464063	−	0.267927i
$516$		0			0
$517$		−	2.51443e6i		−	0.413726i
$518$	−6.22943e6	+	1.54379e7i	−1.02006	+	2.52793i
$519$		0			0
$520$	8.35999e6	+	1.44799e7i	1.35581	+	2.34833i
$521$	942575.	−	1.63259e6i	0.152132	−	0.263501i	−0.779879	−	0.625931i	$-0.784719\pi$
$521$	942575.	−	1.63259e6i	0.152132	−	0.263501i	0.932011	+	0.362430i	$0.118053\pi$
$522$		0			0
$523$	−1.31224e6	+	757625.i	−0.209778	+	0.121116i	−0.601208	−	0.799092i	$-0.705314\pi$
$523$	−1.31224e6	+	757625.i	−0.209778	+	0.121116i	0.391430	+	0.920208i	$0.371980\pi$
$524$	−3.05937e7			−4.86747
$525$		0			0
$526$	−342959.			−0.0540478
$527$	1.29600e6	−	748248.i	0.203273	−	0.117360i
$528$		0			0
$529$	−3.19307e6	+	5.53056e6i	−0.496100	+	0.859271i
$530$	−2.06008e6	−	3.56816e6i	−0.318562	−	0.551766i
$531$		0			0
$532$	1.89911e7	−	2.67756e6i	2.90919	−	0.410166i
$533$		−	4.79251e6i		−	0.730710i
$534$		0			0
$535$	9.01522e6	+	5.20494e6i	1.36173	+	0.786197i
$536$	2.73163e7	+	1.57710e7i	4.10685	+	2.37109i
$537$		0			0
$538$			2.41243e6i			0.359334i
$539$	1.85648e6	+	461137.i	0.275245	+	0.0683688i
$540$		0			0
$541$	−4.05078e6	−	7.01616e6i	−0.595040	−	1.03064i	−0.993541	−	0.113471i	$-0.963803\pi$
$541$	−4.05078e6	−	7.01616e6i	−0.595040	−	1.03064i	0.398502	−	0.917168i	$-0.369530\pi$
$542$	−6.39632e6	+	1.10788e7i	−0.935260	+	1.61992i
$543$		0			0
$544$	8.92451e6	−	5.15257e6i	1.29297	−	0.746494i
$545$	−1.11281e7			−1.60483
$546$		0			0
$547$	8.84662e6			1.26418			0.632091	−	0.774895i	$-0.282197\pi$
$547$	8.84662e6			1.26418			0.632091	+	0.774895i	$0.282197\pi$
$548$	2.81538e7	−	1.62546e7i	4.00485	−	2.31220i
$549$		0			0
$550$	−2.30729e6	+	3.99635e6i	−0.325234	+	0.563321i
$551$	2.50451e6	+	4.33794e6i	0.351434	+	0.608701i
$552$		0			0
$553$	−4.44859e6	+	3.47878e6i	−0.618600	+	0.483742i
$554$		−	8.97672e6i		−	1.24263i
$555$		0			0
$556$	9.55530e6	+	5.51676e6i	1.31086	+	0.756827i
$557$	−5.49401e6	−	3.17197e6i	−0.750328	−	0.433202i	0.0754841	−	0.997147i	$-0.475950\pi$
$557$	−5.49401e6	−	3.17197e6i	−0.750328	−	0.433202i	−0.825813	+	0.563945i	$0.809283\pi$
$558$		0			0
$559$		−	3.46802e6i		−	0.469410i
$560$	3.88994e7	+	1.56964e7i	5.24170	+	2.11510i
$561$		0			0
$562$	−3.60757e6	−	6.24849e6i	−0.481808	−	0.834516i
$563$	−1.24152e6	+	2.15038e6i	−0.165076	+	0.285920i	−0.936682	−	0.350181i	$-0.886120\pi$
$563$	−1.24152e6	+	2.15038e6i	−0.165076	+	0.285920i	0.771606	+	0.636100i	$0.219454\pi$
$564$		0			0
$565$	−1.58976e6	+	917846.i	−0.209512	+	0.120962i
$566$	1.95380e7			2.56353
$567$		0			0
$568$	−738462.			−0.0960412
$569$	−2.09432e6	+	1.20916e6i	−0.271183	+	0.156568i	−0.629425	−	0.777061i	$-0.716710\pi$
$569$	−2.09432e6	+	1.20916e6i	−0.271183	+	0.156568i	0.358242	+	0.933629i	$0.383376\pi$
$570$		0			0
$571$	−4.37744e6	+	7.58195e6i	−0.561862	+	0.973174i	0.435472	+	0.900202i	$0.356582\pi$
$571$	−4.37744e6	+	7.58195e6i	−0.561862	+	0.973174i	−0.997334	+	0.0729717i	$0.976752\pi$
$572$	−1.65067e6	−	2.85905e6i	−0.210946	−	0.365369i
$573$		0			0
$574$	−1.27370e7	−	1.62878e7i	−1.61357	−	2.06340i
$575$			828983.i			0.104562i
$576$		0			0
$577$	1.02899e7	+	5.94088e6i	1.28668	+	0.742868i	0.978061	−	0.208317i	$-0.0667985\pi$
$577$	1.02899e7	+	5.94088e6i	1.28668	+	0.742868i	0.308623	+	0.951184i	$0.400132\pi$
$578$	−1.16107e7	−	6.70344e6i	−1.44557	−	0.834599i
$579$		0			0
$580$			2.17043e7i			2.67902i
$581$	−1.05322e6	−	7.47015e6i	−0.129442	−	0.918097i
$582$		0			0
$583$	258994.	+	448592.i	0.0315587	+	0.0546613i
$584$	−2.71529e6	+	4.70302e6i	−0.329446	+	0.570617i
$585$		0			0
$586$	6.57815e6	−	3.79790e6i	0.791334	−	0.456877i
$587$	760681.			0.0911186			0.0455593	−	0.998962i	$-0.485493\pi$
$587$	760681.			0.0911186			0.0455593	+	0.998962i	$0.485493\pi$
$588$		0			0
$589$	−5.67074e6			−0.673521
$590$	−1.04534e7	+	6.03529e6i	−1.23631	+	0.713786i
$591$		0			0
$592$	2.29473e7	−	3.97458e7i	2.69108	−	4.66109i
$593$	−4.53856e6	−	7.86101e6i	−0.530006	−	0.917998i	−0.999387	−	0.0350019i	$-0.988856\pi$
$593$	−4.53856e6	−	7.86101e6i	−0.530006	−	0.917998i	0.469381	−	0.882996i	$-0.344477\pi$
$594$		0			0
$595$	662684.	+	4.70023e6i	0.0767387	+	0.544285i
$596$			1.88674e7i			2.17569i
$597$		0			0
$598$	−700195.	−	404258.i	−0.0800693	−	0.0462280i
$599$	2.99791e6	+	1.73084e6i	0.341390	+	0.197102i	0.660887	−	0.750486i	$-0.270180\pi$
$599$	2.99791e6	+	1.73084e6i	0.341390	+	0.197102i	−0.319497	+	0.947587i	$0.603514\pi$
$600$		0			0
$601$			3.99158e6i			0.450773i	0.974269	+	0.225387i	$0.0723646\pi$
$601$			3.99158e6i			0.450773i	−0.974269	+	0.225387i	$0.927635\pi$
$602$	−9.21692e6	−	1.17864e7i	−1.03656	−	1.32553i
$603$		0			0
$604$	6.72755e6	+	1.16525e7i	0.750352	+	1.29965i
$605$	−6.11734e6	+	1.05955e7i	−0.679476	+	1.17689i
$606$		0			0
$607$	−72399.6	+	41799.9i	−0.00797562	+	0.00460473i	−0.503983	−	0.863714i	$-0.668132\pi$
$607$	−72399.6	+	41799.9i	−0.00797562	+	0.00460473i	0.496007	+	0.868319i	$0.334799\pi$
$608$	−3.90497e7			−4.28410
$609$		0			0
$610$	−4.59659e7			−5.00163
$611$	−6.30006e6	+	3.63734e6i	−0.682718	+	0.394168i
$612$		0			0
$613$	−3.85894e6	+	6.68389e6i	−0.414779	+	0.718419i	−0.995405	−	0.0957514i	$-0.969475\pi$
$613$	−3.85894e6	+	6.68389e6i	−0.414779	+	0.718419i	0.580626	+	0.814171i	$0.302808\pi$
$614$	−7.41769e6	−	1.28478e7i	−0.794050	−	1.37534i
$615$		0			0
$616$	−8.41015e6	−	3.39361e6i	−0.893001	−	0.360338i
$617$			6.96962e6i			0.737049i	0.929618	+	0.368524i	$0.120137\pi$
$617$			6.96962e6i			0.737049i	−0.929618	+	0.368524i	$0.879863\pi$
$618$		0			0
$619$	−3.16726e6	−	1.82862e6i	−0.332244	−	0.191821i	0.324593	−	0.945854i	$-0.394773\pi$
$619$	−3.16726e6	−	1.82862e6i	−0.332244	−	0.191821i	−0.656837	+	0.754033i	$0.728106\pi$
$620$	−2.12796e7	−	1.22858e7i	−2.22323	−	1.28358i
$621$		0			0
$622$			1.90624e7i			1.97561i
$623$	1.10815e7	−	8.66568e6i	1.14387	−	0.894505i
$624$		0			0
$625$	3.81942e6	+	6.61543e6i	0.391109	+	0.677420i
$626$	1.09031e7	−	1.88847e7i	1.11202	−	1.92608i
$627$		0			0
$628$	8.91515e6	−	5.14716e6i	0.902047	−	0.520797i
$629$	5.19343e6			0.523393
$630$		0			0
$631$	−1.06183e6			−0.106165			−0.0530824	−	0.998590i	$-0.516905\pi$
$631$	−1.06183e6			−0.106165			−0.0530824	+	0.998590i	$0.516905\pi$
$632$	2.31867e7	−	1.33869e7i	2.30912	−	1.33317i
$633$		0			0
$634$	1.47974e7	−	2.56298e7i	1.46205	−	2.53234i
$635$	6.91141e6	+	1.19709e7i	0.680193	+	1.17813i
$636$		0			0
$637$	−1.53016e6	−	5.31861e6i	−0.149413	−	0.519337i
$638$		−	3.71995e6i		−	0.361814i
$639$		0			0
$640$	−4.82738e7	−	2.78709e7i	−4.65867	−	2.68968i
$641$	−6.37568e6	−	3.68100e6i	−0.612889	−	0.353851i	0.161207	−	0.986921i	$-0.448461\pi$
$641$	−6.37568e6	−	3.68100e6i	−0.612889	−	0.353851i	−0.774095	+	0.633069i	$0.781795\pi$
$642$		0			0
$643$		−	1.39847e6i		−	0.133391i	−0.997773	−	0.0666953i	$-0.978754\pi$
$643$		−	1.39847e6i		−	0.133391i	0.997773	−	0.0666953i	$-0.0212456\pi$
$644$	−2.53366e6	+	357220.i	−0.240732	+	0.0339408i
$645$		0			0
$646$	−4.07837e6	−	7.06394e6i	−0.384508	−	0.665987i
$647$	−5.88127e6	+	1.01867e7i	−0.552345	+	0.956690i	0.445759	+	0.895153i	$0.352934\pi$
$647$	−5.88127e6	+	1.01867e7i	−0.552345	+	0.956690i	−0.998105	+	0.0615374i	$0.980400\pi$
$648$		0			0
$649$	1.31421e6	−	758761.i	0.122477	−	0.0707120i
$650$	1.33508e7			1.23943
$651$		0			0
$652$	−6.92235e6			−0.637726
$653$	−1.32580e7	+	7.65451e6i	−1.21673	+	0.702481i	−0.964218	−	0.265112i	$-0.914591\pi$
$653$	−1.32580e7	+	7.65451e6i	−1.21673	+	0.702481i	−0.252515	+	0.967593i	$0.581258\pi$
$654$		0			0
$655$	−1.43461e7	+	2.48482e7i	−1.30656	+	2.26303i
$656$	2.85014e7	+	4.93658e7i	2.58587	+	4.47885i
$657$		0			0
$658$	−1.17445e7	+	2.91055e7i	−1.05747	+	2.62066i
$659$		−	6.80696e6i		−	0.610576i	−0.952260	−	0.305288i	$-0.901247\pi$
$659$		−	6.80696e6i		−	0.610576i	0.952260	−	0.305288i	$-0.0987527\pi$
$660$		0			0
$661$	−3.45537e6	−	1.99496e6i	−0.307603	−	0.177595i	0.338250	−	0.941056i	$-0.390165\pi$
$661$	−3.45537e6	−	1.99496e6i	−0.307603	−	0.177595i	−0.645854	+	0.763461i	$0.723498\pi$
$662$	5.30915e6	+	3.06524e6i	0.470847	+	0.271844i
$663$		0			0
$664$			3.57661e7i			3.14812i
$665$	6.73068e6	−	1.66802e7i	0.590207	−	1.46267i
$666$		0			0
$667$	−334134.	−	578736.i	−0.0290807	−	0.0503693i
$668$	−3.04219e7	+	5.26923e7i	−2.63782	+	4.56884i
$669$		0			0
$670$	4.02348e7	−	2.32296e7i	3.46270	−	1.99919i
$671$	5.77887e6			0.495492
$672$		0			0
$673$	1.33787e7			1.13861			0.569307	−	0.822125i	$-0.307212\pi$
$673$	1.33787e7			1.13861			0.569307	+	0.822125i	$0.307212\pi$
$674$	9.18342e6	−	5.30205e6i	0.778672	−	0.449566i
$675$		0			0
$676$	1.15774e7	−	2.00527e7i	0.974418	−	1.68774i
$677$	2.54641e6	+	4.41052e6i	0.213529	+	0.369843i	0.952817	−	0.303547i	$-0.0981708\pi$
$677$	2.54641e6	+	4.41052e6i	0.213529	+	0.369843i	−0.739287	+	0.673390i	$0.764837\pi$
$678$		0			0
$679$	−698924.	+	98541.2i	−0.0581776	+	0.00820245i
$680$		−	2.25041e7i		−	1.86633i
$681$		0			0
$682$	3.64716e6	+	2.10569e6i	0.300257	+	0.173354i
$683$	−2.07887e6	−	1.20024e6i	−0.170520	−	0.0984498i	0.412311	−	0.911043i	$-0.364722\pi$
$683$	−2.07887e6	−	1.20024e6i	−0.170520	−	0.0984498i	−0.582831	+	0.812593i	$0.698055\pi$
$684$		0			0
$685$		−	3.04887e7i		−	2.48264i
$686$	−1.93356e7	−	1.40092e7i	−1.56873	−	1.13658i
$687$		0			0
$688$	2.06245e7	+	3.57227e7i	1.66116	+	2.87722i
$689$	749316.	−	1.29785e6i	0.0601336	−	0.104154i
$690$		0			0
$691$	4.23945e6	−	2.44765e6i	0.337765	−	0.195009i	−0.321518	−	0.946903i	$-0.604193\pi$
$691$	4.23945e6	−	2.44765e6i	0.337765	−	0.195009i	0.659283	+	0.751895i	$0.270860\pi$
$692$	−1.56028e7			−1.23862
$693$		0			0
$694$	2.44095e7			1.92380
$695$	8.96142e6	−	5.17388e6i	0.703744	−	0.406307i
$696$		0			0
$697$	−3.22522e6	+	5.58624e6i	−0.251465	+	0.435550i
$698$	−1.08670e7	−	1.88221e7i	−0.844246	−	1.46228i
$699$		0			0
$700$	3.32831e7	−	2.60272e7i	2.56731	−	2.00762i
$701$		−	263433.i		−	0.0202477i	−0.999949	−	0.0101238i	$-0.996777\pi$
$701$		−	263433.i		−	0.0202477i	0.999949	−	0.0101238i	$-0.00322258\pi$
$702$		0			0
$703$	−1.70431e7	−	9.83985e6i	−1.30065	−	0.750931i
$704$	1.27615e7	+	7.36784e6i	0.970441	+	0.560285i
$705$		0			0
$706$		−	1.81384e7i		−	1.36958i
$707$	3.97583e6	+	1.60430e6i	0.299143	+	0.120708i
$708$		0			0
$709$	−1.06409e7	−	1.84306e7i	−0.794992	−	1.37697i	−0.922844	−	0.385173i	$-0.874142\pi$
$709$	−1.06409e7	−	1.84306e7i	−0.794992	−	1.37697i	0.127853	−	0.991793i	$-0.459191\pi$
$710$	−543850.	+	941976.i	−0.0404887	+	0.0701284i
$711$		0			0
$712$	−5.77584e7	+	3.33469e7i	−4.26988	+	2.46522i
$713$	756549.			0.0557331
$714$		0			0
$715$	−3.09616e6			−0.226495
$716$	−2.57566e7	+	1.48706e7i	−1.87761	+	1.08404i
$717$		0			0
$718$	1.29329e7	−	2.24004e7i	0.936235	−	1.62161i
$719$	5.08037e6	+	8.79946e6i	0.366499	+	0.634795i	0.989016	−	0.147812i	$-0.0472229\pi$
$719$	5.08037e6	+	8.79946e6i	0.366499	+	0.634795i	−0.622516	+	0.782607i	$0.713890\pi$
$720$		0			0
$721$	−3.11782e6	−	3.98700e6i	−0.223364	−	0.285633i
$722$			3.77451e6i			0.269475i
$723$		0			0
$724$	3.92686e7	+	2.26717e7i	2.78419	+	1.60745i
$725$	9.55651e6	+	5.51746e6i	0.675234	+	0.389847i
$726$		0			0
$727$			1.76047e7i			1.23536i	0.786431	+	0.617678i	$0.211926\pi$
$727$			1.76047e7i			1.23536i	−0.786431	+	0.617678i	$0.788074\pi$
$728$	3.66310e6	+	2.59813e7i	0.256165	+	1.81691i
$729$		0			0
$730$	3.99942e6	+	6.92720e6i	0.277773	+	0.481117i
$731$	−2.33387e6	+	4.04239e6i	−0.161541	+	0.279798i
$732$		0			0
$733$	1.05533e7	−	6.09294e6i	0.725484	−	0.418858i	−0.0912838	−	0.995825i	$-0.529097\pi$
$733$	1.05533e7	−	6.09294e6i	0.725484	−	0.418858i	0.816768	+	0.576967i	$0.195764\pi$
$734$	3.95447e7			2.70924
$735$		0			0
$736$	5.20973e6			0.354504
$737$	−5.05835e6	+	2.92044e6i	−0.343036	+	0.198052i
$738$		0			0
$739$	−3.19828e6	+	5.53959e6i	−0.215430	+	0.373136i	−0.953405	−	0.301692i	$-0.902449\pi$
$739$	−3.19828e6	+	5.53959e6i	−0.215430	+	0.373136i	0.737976	+	0.674827i	$0.235782\pi$
$740$	−4.26366e7	−	7.38487e7i	−2.86222	−	4.95751i
$741$		0			0
$742$	−902665.	−	6.40234e6i	−0.0601890	−	0.426903i
$743$			2.66345e7i			1.77000i	0.465592	+	0.885000i	$0.345842\pi$
$743$			2.66345e7i			1.77000i	−0.465592	+	0.885000i	$0.654158\pi$
$744$		0			0
$745$	1.53241e7	+	8.84738e6i	1.01154	+	0.584015i
$746$	−1.45791e7	−	8.41722e6i	−0.959141	−	0.553760i
$747$		0			0
$748$			4.44342e6i			0.290378i
$749$	1.00631e7	+	1.28685e7i	0.655431	+	0.838152i
$750$		0			0
$751$	−2.94887e6	−	5.10760e6i	−0.190790	−	0.330458i	0.754722	−	0.656045i	$-0.227772\pi$
$751$	−2.94887e6	−	5.10760e6i	−0.190790	−	0.330458i	−0.945512	+	0.325586i	$0.894438\pi$
$752$	4.32630e7	−	7.49337e7i	2.78979	−	4.83206i
$753$		0			0
$754$	−9.32056e6	+	5.38123e6i	−0.597054	+	0.344709i
$755$	1.26188e7			0.805660
$756$		0			0
$757$	1.22047e7			0.774082			0.387041	−	0.922063i	$-0.373497\pi$
$757$	1.22047e7			0.774082			0.387041	+	0.922063i	$0.373497\pi$
$758$	4.38246e7	−	2.53022e7i	2.77042	−	1.59950i
$759$		0			0
$760$	−4.26379e7	+	7.38510e7i	−2.67770	+	4.63791i
$761$	1.01564e7	+	1.75913e7i	0.635736	+	1.10113i	0.986359	+	0.164610i	$0.0526366\pi$
$761$	1.01564e7	+	1.75913e7i	0.635736	+	1.10113i	−0.350623	+	0.936517i	$0.614030\pi$
$762$		0			0
$763$	−1.61943e7	−	6.53464e6i	−1.00705	−	0.406360i
$764$			9.00199e6i			0.557963i
$765$		0			0
$766$	2.68601e7	+	1.55077e7i	1.65400	+	0.954937i
$767$	−3.80224e6	−	2.19523e6i	−0.233373	−	0.134738i
$768$		0			0
$769$		−	1.83510e7i		−	1.11904i	−0.828819	−	0.559518i	$-0.810986\pi$
$769$		−	1.83510e7i		−	1.11904i	0.828819	−	0.559518i	$-0.189014\pi$
$770$	−1.05226e7	+	8.22864e6i	−0.639583	+	0.500151i
$771$		0			0
$772$	−3.12492e7	−	5.41252e7i	−1.88710	−	3.26856i
$773$	−407127.	+	705165.i	−0.0245065	+	0.0424465i	−0.878019	−	0.478627i	$-0.841135\pi$
$773$	−407127.	+	705165.i	−0.0245065	+	0.0424465i	0.853512	+	0.521073i	$0.174468\pi$
$774$		0			0
$775$	−1.08190e7	+	6.24634e6i	−0.647042	+	0.373570i
$776$	3.34636e6			0.199489
$777$		0			0
$778$	−5.53699e7			−3.27963
$779$	2.11682e7	−	1.22215e7i	1.24980	−	0.721572i
$780$		0			0
$781$	68373.2	−	118426.i	0.00401105	−	0.00694735i
$782$	544106.	+	942420.i	0.0318176	+	0.0551096i
$783$		0			0
$784$	4.73916e7	+	4.56850e7i	2.75367	+	2.65450i
$785$		−	9.65451e6i		−	0.559186i
$786$		0			0
$787$	1.63487e7	+	9.43895e6i	0.940908	+	0.543234i	0.890245	−	0.455482i	$-0.150533\pi$
$787$	1.63487e7	+	9.43895e6i	0.940908	+	0.543234i	0.0506634	+	0.998716i	$0.483866\pi$
$788$	6.59018e6	+	3.80484e6i	0.378079	+	0.218284i
$789$		0			0
$790$		−	3.94357e7i		−	2.24813i
$791$	−2.85249e6	+	402173.i	−0.162100	+	0.0228545i
$792$		0			0
$793$	−8.35964e6	−	1.44793e7i	−0.472068	−	0.817646i
$794$	2.52348e7	−	4.37080e7i	1.42053	−	2.46042i
$795$		0			0
$796$	−5.50509e7	+	3.17836e7i	−3.07951	+	1.77795i
$797$	−3.37595e7			−1.88257			−0.941284	−	0.337616i	$-0.890379\pi$
$797$	−3.37595e7			−1.88257			−0.941284	+	0.337616i	$0.890379\pi$
$798$		0			0
$799$	9.79128e6			0.542591
$800$	−7.45015e7	+	4.30134e7i	−4.11566	+	2.37618i
$801$		0			0
$802$	−1.04990e7	+	1.81848e7i	−0.576384	+	0.998327i
$803$	−502810.	−	870892.i	−0.0275179	−	0.0476624i
$804$		0			0
$805$	−897959.	+	2.22535e6i	−0.0488390	+	0.121034i
$806$		−	1.21842e7i		−	0.660634i
$807$		0			0
$808$	−1.76029e7	−	1.01630e7i	−0.948539	−	0.547639i
$809$	−1.61396e7	−	9.31820e6i	−0.867005	−	0.500565i	−0.000653062	−	1.00000i	$-0.500208\pi$
$809$	−1.61396e7	−	9.31820e6i	−0.867005	−	0.500565i	−0.866352	+	0.499434i	$0.833541\pi$
$810$		0			0
$811$		−	2.29132e7i		−	1.22330i	−0.791128	−	0.611651i	$-0.790506\pi$
$811$		−	2.29132e7i		−	1.22330i	0.791128	−	0.611651i	$-0.209494\pi$
$812$	−1.27452e7	+	3.15856e7i	−0.678355	+	1.68112i
$813$		0			0
$814$	7.30757e6	+	1.26571e7i	0.386556	+	0.669534i
$815$	−3.24605e6	+	5.62233e6i	−0.171183	+	0.296498i
$816$		0			0
$817$	1.53180e7	−	8.84385e6i	0.802873	−	0.463539i
$818$	−2.71828e7			−1.42040
$819$		0			0
$820$	1.05912e8			5.50063
$821$	−8.76240e6	+	5.05897e6i	−0.453696	+	0.261942i	−0.709390	−	0.704816i	$-0.751029\pi$
$821$	−8.76240e6	+	5.05897e6i	−0.453696	+	0.261942i	0.255694	+	0.966758i	$0.417696\pi$
$822$		0			0
$823$	1.09742e7	−	1.90078e7i	0.564771	−	0.978212i	−0.432300	−	0.901730i	$-0.642298\pi$
$823$	1.09742e7	−	1.90078e7i	0.564771	−	0.978212i	0.997071	−	0.0764824i	$-0.0243689\pi$
$824$	1.19978e7	+	2.07809e7i	0.615580	+	1.06622i
$825$		0			0
$826$	−1.87565e7	+	2.64448e6i	−0.956539	+	0.134862i
$827$		−	1.81637e7i		−	0.923509i	−0.887008	−	0.461754i	$-0.847220\pi$
$827$		−	1.81637e7i		−	0.923509i	0.887008	−	0.461754i	$-0.152780\pi$
$828$		0			0
$829$	−1.93856e7	−	1.11923e7i	−0.979699	−	0.565629i	−0.0775195	−	0.996991i	$-0.524700\pi$
$829$	−1.93856e7	−	1.11923e7i	−0.979699	−	0.565629i	−0.902179	+	0.431362i	$0.858033\pi$
$830$	4.56230e7	+	2.63404e7i	2.29873	+	1.32717i
$831$		0			0
$832$		−	4.26329e7i		−	2.13519i
$833$	−1.79568e6	+	7.22922e6i	−0.0896639	+	0.360976i
$834$		0			0
$835$	2.85311e7	+	4.94174e7i	1.41613	+	2.45281i
$836$	8.41882e6	−	1.45818e7i	0.416616	−	0.721599i
$837$		0			0
$838$	1.71925e7	−	9.92611e6i	0.845726	−	0.488280i
$839$	1.08782e7			0.533523			0.266761	−	0.963763i	$-0.414046\pi$
$839$	1.08782e7			0.533523			0.266761	+	0.963763i	$0.414046\pi$
$840$		0			0
$841$	1.16156e7			0.566306
$842$	−6.32131e7	+	3.64961e7i	−3.07275	+	1.77405i
$843$		0			0
$844$	1.67978e7	−	2.90946e7i	0.811701	−	1.40591i
$845$	−1.08579e7	−	1.88064e7i	−0.523122	−	0.906073i
$846$		0			0
$847$	−1.51243e7	+	1.18271e7i	−0.724379	+	0.566460i
$848$			1.78249e7i			0.851212i
$849$		0			0
$850$	−1.55619e7	−	8.98468e6i	−0.738781	−	0.426536i
$851$	2.27377e6	+	1.31276e6i	0.107627	+	0.0621387i
$852$		0			0
$853$		−	1.14153e7i		−	0.537172i	−0.963256	−	0.268586i	$-0.913444\pi$
$853$		−	1.14153e7i		−	0.537172i	0.963256	−	0.268586i	$-0.0865564\pi$
$854$	−6.68926e7	−	2.69921e7i	−3.13858	−	1.26646i
$855$		0			0
$856$	−3.87243e7	−	6.70725e7i	−1.80634	−	3.12867i
$857$	6.46752e6	−	1.12021e7i	0.300805	−	0.521010i	−0.675513	−	0.737348i	$-0.736078\pi$
$857$	6.46752e6	−	1.12021e7i	0.300805	−	0.521010i	0.976319	+	0.216338i	$0.0694112\pi$
$858$		0			0
$859$	−2.39231e7	+	1.38120e7i	−1.10620	+	0.638666i	−0.937843	−	0.347060i	$-0.887180\pi$
$859$	−2.39231e7	+	1.38120e7i	−1.10620	+	0.638666i	−0.168359	+	0.985726i	$0.553847\pi$
$860$	7.66417e7			3.53361
$861$		0			0
$862$	1.64611e7			0.754555
$863$	1.45256e7	−	8.38636e6i	0.663906	−	0.383307i	−0.129857	−	0.991533i	$-0.541452\pi$
$863$	1.45256e7	−	8.38636e6i	0.663906	−	0.383307i	0.793764	+	0.608226i	$0.208119\pi$
$864$		0			0
$865$	−7.31653e6	+	1.26726e7i	−0.332480	+	0.575872i
$866$	3.27871e7	+	5.67889e7i	1.48562	+	2.57317i
$867$		0			0
$868$	−2.37530e7	−	3.03749e7i	−1.07009	−	1.36841i
$869$			4.95789e6i			0.222714i
$870$		0			0
$871$	1.46347e7	+	8.44934e6i	0.653639	+	0.377379i
$872$	7.17000e7	+	4.13960e7i	3.19322	+	1.84360i
$873$		0			0
$874$		−	4.12361e6i		−	0.182599i
$875$	−859502.	−	6.09619e6i	−0.0379513	−	0.269177i
$876$		0			0
$877$	9.43408e6	+	1.63403e7i	0.414191	+	0.717400i	0.995343	−	0.0963952i	$-0.0307313\pi$
$877$	9.43408e6	+	1.63403e7i	0.414191	+	0.717400i	−0.581152	+	0.813795i	$0.697398\pi$
$878$	−2.30628e7	+	3.99460e7i	−1.00966	+	1.74879i
$879$		0			0
$880$	3.18923e7	−	1.84131e7i	1.38829	−	0.801529i
$881$	1.09803e7			0.476621			0.238311	−	0.971189i	$-0.423406\pi$
$881$	1.09803e7			0.476621			0.238311	+	0.971189i	$0.423406\pi$
$882$		0			0
$883$	−1.31516e7			−0.567645			−0.283822	−	0.958877i	$-0.591603\pi$
$883$	−1.31516e7			−0.567645			−0.283822	+	0.958877i	$0.591603\pi$
$884$	1.11333e7	−	6.42779e6i	0.479172	−	0.276650i
$885$		0			0
$886$	−2.71200e7	+	4.69733e7i	−1.16066	+	2.01033i
$887$	6.76380e6	+	1.17152e7i	0.288657	+	0.499968i	0.973489	−	0.228732i	$-0.0734581\pi$
$887$	6.76380e6	+	1.17152e7i	0.288657	+	0.499968i	−0.684833	+	0.728700i	$0.740125\pi$
$888$		0			0
$889$	3.02837e6	+	2.14794e7i	0.128515	+	0.911522i
$890$			9.82349e7i			4.15710i
$891$		0			0
$892$	−2.08615e7	−	1.20444e7i	−0.877877	−	0.506843i
$893$	−3.21318e7	−	1.85513e7i	−1.34836	−	0.778476i
$894$		0			0
$895$			2.78927e7i			1.16395i
$896$	−5.38849e7	−	6.89069e7i	−2.24232	−	2.86743i
$897$		0			0
$898$	2.60450e7	+	4.51112e7i	1.07779	+	1.86678i
$899$	5.03536e6	−	8.72150e6i	0.207793	−	0.359908i
$900$		0			0
$901$	−1.74683e6	+	1.00853e6i	−0.0716868	+	0.0413884i
$902$	−1.81525e7			−0.742884
$903$		0			0
$904$	1.36574e7			0.555836
$905$	3.68280e7	−	2.12626e7i	1.49471	−	0.862970i
$906$		0			0
$907$	6.54068e6	−	1.13288e7i	0.264001	−	0.457262i	−0.703301	−	0.710892i	$-0.748291\pi$
$907$	6.54068e6	−	1.13288e7i	0.264001	−	0.457262i	0.967301	+	0.253630i	$0.0816246\pi$
$908$	−7.02670e6	−	1.21706e7i	−0.282837	−	0.489889i
$909$		0			0
$910$	3.58392e7	+	1.44616e7i	1.43468	+	0.578914i
$911$		−	2.22270e7i		−	0.887329i	−0.896193	−	0.443665i	$-0.853678\pi$
$911$		−	2.22270e7i		−	0.887329i	0.896193	−	0.443665i	$-0.146322\pi$
$912$		0			0
$913$	−5.73575e6	−	3.31154e6i	−0.227726	−	0.131478i
$914$	−7.22869e7	−	4.17349e7i	−2.86216	−	1.65247i
$915$		0			0
$916$			9.04721e7i			3.56267i
$917$	−3.54687e7	+	2.77364e7i	−1.39291	+	1.08925i
$918$		0			0
$919$	−6.55565e6	−	1.13547e7i	−0.256051	−	0.443494i	0.709129	−	0.705079i	$-0.249088\pi$
$919$	−6.55565e6	−	1.13547e7i	−0.256051	−	0.443494i	−0.965181	+	0.261585i	$0.915755\pi$
$920$	5.68844e6	−	9.85267e6i	0.221577	−	0.383782i
$921$		0			0
$922$	−3.57770e6	+	2.06559e6i	−0.138604	+	0.0800232i
$923$	−395631.			−0.0152857
$924$		0			0
$925$	−4.33546e7			−1.66602
$926$	−1.66986e7	+	9.64091e6i	−0.639958	+	0.369480i
$927$		0			0
$928$	3.46744e7	−	6.00578e7i	1.32172	−	2.28928i
$929$	−1.44096e7	−	2.49582e7i	−0.547788	−	0.948797i	−0.998426	−	0.0560903i	$-0.982137\pi$
$929$	−1.44096e7	−	2.49582e7i	−0.547788	−	0.948797i	0.450637	−	0.892707i	$-0.351197\pi$
$930$		0			0
$931$	1.95898e7	−	2.03217e7i	0.740725	−	0.768396i
$932$		−	5.24607e7i		−	1.97831i
$933$		0			0
$934$	−7.96505e7	−	4.59863e7i	−2.98759	−	1.72489i
$935$	3.60894e6	+	2.08362e6i	0.135005	+	0.0779454i
$936$		0			0
$937$			3.33706e7i			1.24170i	0.783931	+	0.620848i	$0.213212\pi$
$937$			3.33706e7i			1.24170i	−0.783931	+	0.620848i	$0.786788\pi$
$938$	7.21932e7	−	1.01785e7i	2.67910	−	0.377726i
$939$		0			0
$940$	−8.03837e7	−	1.39229e8i	−2.96721	−	5.13936i
$941$	−1.60500e7	+	2.77994e7i	−0.590881	+	1.02344i	0.403233	+	0.915098i	$0.367887\pi$
$941$	−1.60500e7	+	2.77994e7i	−0.590881	+	1.02344i	−0.994114	+	0.108339i	$0.965447\pi$
$942$		0			0
$943$	−2.82411e6	+	1.63050e6i	−0.103419	+	0.0597092i
$944$	5.22206e7			1.90727
$945$		0			0
$946$	−1.31358e7			−0.477230
$947$	−3.70941e7	+	2.14163e7i	−1.34410	+	0.776014i	−0.987406	−	0.158209i	$-0.949428\pi$
$947$	−3.70941e7	+	2.14163e7i	−1.34410	+	0.776014i	−0.356690	+	0.934223i	$0.616095\pi$
$948$		0			0
$949$	−1.45472e6	+	2.51964e6i	−0.0524340	+	0.0908183i
$950$	3.40461e7	+	5.89695e7i	1.22393	+	2.11991i
$951$		0			0
$952$	1.32149e7	−	3.27494e7i	0.472574	−	1.17115i
$953$		−	4.96089e7i		−	1.76940i	−0.466156	−	0.884702i	$-0.654362\pi$
$953$		−	4.96089e7i		−	1.76940i	0.466156	−	0.884702i	$-0.345638\pi$
$954$		0			0
$955$	7.31141e6	+	4.22125e6i	0.259414	+	0.149773i
$956$	−1.02511e8	−	5.91849e7i	−3.62766	−	2.09443i
$957$		0			0
$958$			1.50446e7i			0.529624i
$959$	1.79036e7	−	4.43692e7i	0.628628	−	1.55788i
$960$		0			0
$961$	−8.61402e6	−	1.49199e7i	−0.300883	−	0.521144i
$962$	2.11421e7	−	3.66191e7i	0.736563	−	1.27576i
$963$		0			0
$964$	−1.23047e8	+	7.10414e7i	−4.26461	+	2.46217i
$965$	−5.86140e7			−2.02620
$966$		0			0
$967$	3.78348e7			1.30114			0.650572	−	0.759445i	$-0.274529\pi$
$967$	3.78348e7			1.30114			0.650572	+	0.759445i	$0.274529\pi$
$968$	7.88299e7	−	4.55125e7i	2.70397	−	1.56114i
$969$		0			0
$970$	2.46447e6	−	4.26859e6i	0.0840997	−	0.145665i
$971$	−2.12754e7	−	3.68500e7i	−0.724151	−	1.25427i	−0.959322	−	0.282313i	$-0.908898\pi$
$971$	−2.12754e7	−	3.68500e7i	−0.724151	−	1.25427i	0.235171	−	0.971954i	$-0.424435\pi$
$972$		0			0
$973$	1.60794e7	−	2.26704e6i	0.544489	−	0.0767674i
$974$			1.96633e7i			0.664139i
$975$		0			0
$976$	1.72219e8	+	9.94305e7i	5.78703	+	3.34114i
$977$	2.44245e7	+	1.41015e7i	0.818635	+	0.472639i	0.849945	−	0.526871i	$-0.176635\pi$
$977$	2.44245e7	+	1.41015e7i	0.818635	+	0.472639i	−0.0313109	+	0.999510i	$0.509968\pi$
$978$		0			0
$979$		−	1.23502e7i		−	0.411828i
$980$	1.17539e8	−	3.38158e7i	3.90946	−	1.12475i
$981$		0			0
$982$	5.52258e7	+	9.56538e7i	1.82752	+	3.16536i
$983$	−1.36220e7	+	2.35940e7i	−0.449632	+	0.778786i	−0.998362	−	0.0572142i	$-0.981778\pi$
$983$	−1.36220e7	+	2.35940e7i	−0.449632	+	0.778786i	0.548730	+	0.836000i	$0.315112\pi$
$984$		0			0
$985$	6.18059e6	−	3.56836e6i	0.202973	−	0.117187i
$986$	1.44856e7			0.474509
$987$		0			0
$988$	−4.87142e7			−1.58768
$989$	−2.04362e6	+	1.17988e6i	−0.0664368	+	0.0383573i
$990$		0			0
$991$	1.97068e7	−	3.41333e7i	0.637431	−	1.10406i	−0.348564	−	0.937285i	$-0.613331\pi$
$991$	1.97068e7	−	3.41333e7i	0.637431	−	1.10406i	0.985995	−	0.166777i	$-0.0533361\pi$
$992$	3.92551e7	+	6.79918e7i	1.26653	+	2.19370i
$993$		0			0
$994$	−1.34459e6	+	1.05147e6i	−0.0431643	+	0.0337543i
$995$			5.96164e7i			1.90901i
$996$		0			0
$997$	2.60819e7	+	1.50584e7i	0.831001	+	0.479779i	0.854195	−	0.519952i	$-0.174050\pi$
$997$	2.60819e7	+	1.50584e7i	0.831001	+	0.479779i	−0.0231943	+	0.999731i	$0.507384\pi$
$998$	5.94386e7	+	3.43169e7i	1.88904	+	1.09064i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.p.b.17.1	✓	24
3.2	odd	2	inner	63.6.p.b.17.12	yes	24
7.3	odd	6		441.6.c.b.440.3		24
7.4	even	3		441.6.c.b.440.21		24
7.5	odd	6	inner	63.6.p.b.26.12	yes	24
21.5	even	6	inner	63.6.p.b.26.1	yes	24
21.11	odd	6		441.6.c.b.440.4		24
21.17	even	6		441.6.c.b.440.22		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.p.b.17.1	✓	24	1.1	even	1	trivial
63.6.p.b.17.12	yes	24	3.2	odd	2	inner
63.6.p.b.26.1	yes	24	21.5	even	6	inner
63.6.p.b.26.12	yes	24	7.5	odd	6	inner
441.6.c.b.440.3		24	7.3	odd	6
441.6.c.b.440.4		24	21.11	odd	6
441.6.c.b.440.21		24	7.4	even	3
441.6.c.b.440.22		24	21.17	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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.49029 + 5.47922i) q^{2} +(44.0437 - 76.2859i) q^{4} +(-41.3063 - 71.5446i) q^{5} +(-18.0992 - 128.372i) q^{7} +614.630i q^{8} +O(q^{10})\)	\(q+(-9.49029 + 5.47922i) q^{2} +(44.0437 - 76.2859i) q^{4} +(-41.3063 - 71.5446i) q^{5} +(-18.0992 - 128.372i) q^{7} +614.630i q^{8} +(784.017 + 452.652i) q^{10} +(-98.5671 - 56.9078i) q^{11} +329.288i q^{13} +(875.146 + 1119.12i) q^{14} +(-1958.30 - 3391.87i) q^{16} +(221.601 - 383.824i) q^{17} +(-1454.44 + 839.723i) q^{19} -7277.12 q^{20} +1247.24 q^{22} +(194.041 - 112.030i) q^{23} +(-1849.92 + 3204.15i) q^{25} +(-1804.24 - 3125.04i) q^{26} +(-10590.1 - 4273.27i) q^{28} -2982.54i q^{29} +(2924.18 + 1688.28i) q^{31} +(20136.4 + 11625.8i) q^{32} +4856.80i q^{34} +(-8436.72 + 6597.48i) q^{35} +(5858.99 + 10148.1i) q^{37} +(9202.05 - 15938.4i) q^{38} +(43973.5 - 25388.1i) q^{40} -14554.2 q^{41} -10531.9 q^{43} +(-8682.52 + 5012.86i) q^{44} +(-1227.67 + 2126.39i) q^{46} +(11046.1 + 19132.4i) q^{47} +(-16151.8 + 4646.86i) q^{49} -40544.4i q^{50} +(25120.0 + 14503.1i) q^{52} +(-3941.39 - 2275.56i) q^{53} +9402.59i q^{55} +(78901.4 - 11124.3i) q^{56} +(16342.0 + 28305.2i) q^{58} +(-6666.58 + 11546.9i) q^{59} +(-43971.6 + 25387.0i) q^{61} -37001.8 q^{62} -129470. q^{64} +(23558.8 - 13601.7i) q^{65} +(25659.4 - 44443.4i) q^{67} +(-19520.3 - 33810.1i) q^{68} +(43917.9 - 108839. i) q^{70} +1201.47i q^{71} +(7651.79 + 4417.76i) q^{73} +(-111207. - 64205.4i) q^{74} +147938. i q^{76} +(-5521.39 + 13683.3i) q^{77} +(-21780.4 - 37724.7i) q^{79} +(-161780. + 280211. i) q^{80} +(138123. - 79745.5i) q^{82} +58191.3 q^{83} -36614.0 q^{85} +(99950.5 - 57706.4i) q^{86} +(34977.2 - 60582.3i) q^{88} +(54255.1 + 93972.7i) q^{89} +(42271.4 - 5959.85i) q^{91} -19736.8i q^{92} +(-209661. - 121048. i) q^{94} +(120155. + 69371.6i) q^{95} -5444.51i q^{97} +(127824. - 132600. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) \) 24 * q + 304 * q^4 - 436 * q^7	\( 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49} - 2940 q^{52} + 154300 q^{58} + 48504 q^{61} - 327880 q^{64} + 156324 q^{67} - 9468 q^{70} - 703236 q^{73} + 165756 q^{79} + 1081020 q^{82} - 284448 q^{85} + 582308 q^{88} - 19812 q^{91} - 1481724 q^{94}+O(q^{100}) \) 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

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