LMFDB - Embedded newform 63.6.p.b.17.12

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			17.12
Character	$\chi$	$=$	63.17
Dual form			63.6.p.b.26.12

$q$-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	$-0.246647\pi$
$2$	9.49029	−	5.47922i	1.67766	−	0.968598i	0.963146	−	0.268979i	$-0.0866861\pi$
$3$		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	$0.0979921\pi$
$5$	41.3063	+	71.5446i	0.738909	+	1.27983i	−0.214078	+	0.976817i	$0.568675\pi$
$6$		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	0.617754	−	0.786372i	$-0.288043\pi$
$11$	98.5671	+	56.9078i	0.245613	+	0.141804i	−0.372141	+	0.928176i	$0.621376\pi$
$12$		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	−0.943904	−	0.330220i	$-0.892877\pi$
$17$	−221.601	+	383.824i	−0.185973	+	0.322114i	0.757931	+	0.652335i	$0.226210\pi$
$18$		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	−0.537755	−	0.843101i	$-0.680727\pi$
$23$	−194.041	+	112.030i	−0.0764847	+	0.0441584i	0.461270	+	0.887260i	$0.347394\pi$
$24$		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	$0.106805\pi$
$29$			2982.54i			0.658554i	−0.944233	+	0.329277i	$0.893195\pi$
$30$		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	$-0.263678\pi$
$41$	14554.2			1.35216			0.676079	+	0.736829i	$0.263678\pi$
$42$		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	$-0.906468\pi$
$47$	−11046.1	−	19132.4i	−0.729396	−	1.26335i	0.227743	−	0.973721i	$-0.426865\pi$
$48$		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	0.593262	−	0.805009i	$-0.297840\pi$
$53$	3941.39	+	2275.56i	0.192735	+	0.111275i	−0.400527	+	0.916285i	$0.631173\pi$
$54$		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	−0.714011	−	0.700135i	$-0.753123\pi$
$59$	6666.58	−	11546.9i	0.249329	−	0.431851i	0.963340	+	0.268284i	$0.0864565\pi$
$60$		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	$-0.995498\pi$
$71$		−	1201.47i		−	0.0282858i	0.999900	−	0.0141429i	$-0.00450198\pi$
$72$		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	$-0.653438\pi$
$83$	−58191.3			−0.927177			−0.463589	+	0.886050i	$0.653438\pi$
$84$		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	$-0.908021\pi$
$89$	−54255.1	−	93972.7i	−0.726049	−	1.25755i	0.232492	−	0.972598i	$-0.425312\pi$
$90$		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	−0.774042	−	0.633134i	$-0.781768\pi$
$101$	16535.2	−	28639.8i	0.161289	−	0.279361i	0.935331	+	0.353773i	$0.115101\pi$
$102$		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	0.0373514	−	0.999302i	$-0.488108\pi$
$107$	109127.	−	63004.2i	0.921448	−	0.531998i	0.884097	+	0.467304i	$0.154775\pi$
$108$		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	$0.0260834\pi$
$113$			22220.5i			0.163703i	−0.996645	+	0.0818517i	$0.973917\pi$
$114$		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	$0.178572\pi$
$131$	173655.	+	300780.i	0.884117	+	1.53134i	0.0373940	+	0.999301i	$0.488094\pi$
$132$		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	−0.456113	−	0.889922i	$-0.650759\pi$
$137$	−319613.	−	184528.i	−1.45486	−	0.839966i	−0.998751	+	0.0499556i	$0.984092\pi$
$138$		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	−0.117058	−	0.993125i	$-0.537346\pi$
$149$	185494.	−	107095.i	0.684485	−	0.395188i	0.801543	+	0.597938i	$0.204013\pi$
$150$		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	$-0.0922961\pi$
$167$	690721.			1.91651			0.958256	+	0.285911i	$0.0922961\pi$
$168$		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	0.956313	−	0.292343i	$-0.0944349\pi$
$173$	88564.4	+	153398.i	0.224980	+	0.389677i	−0.731333	+	0.682020i	$0.761102\pi$
$174$		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	0.800642	−	0.599143i	$-0.204492\pi$
$179$	292398.	+	168816.i	0.682091	+	0.393805i	−0.118552	+	0.992948i	$0.537825\pi$
$180$		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	−0.409656	−	0.912240i	$-0.634351\pi$
$191$	88502.5	−	51096.9i	0.175538	−	0.101347i	0.585195	+	0.810893i	$0.301018\pi$
$192$		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	$-0.974732\pi$
$197$		−	86388.0i		−	0.158594i	0.996851	−	0.0792972i	$-0.0252676\pi$
$198$		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	−0.912816	−	0.408371i	$-0.866097\pi$
$227$	−79769.7	+	138165.i	−0.102748	+	0.177965i	0.810068	+	0.586336i	$0.199430\pi$
$228$		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	−0.777798	−	0.628514i	$-0.783663\pi$
$233$	−515764.	+	297777.i	−0.622388	+	0.359336i	0.155410	+	0.987850i	$0.450330\pi$
$234$		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	$0.275220\pi$
$239$			1.34378e6i			1.52171i	−0.648921	+	0.760856i	$0.724780\pi$
$240$		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	$-0.295468\pi$
$251$	1.19624e6			1.19849			0.599244	+	0.800567i	$0.295468\pi$
$252$		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	0.894218	−	0.447633i	$-0.147733\pi$
$257$	62945.9	+	109025.i	0.0594476	+	0.102966i	−0.834770	+	0.550599i	$0.814399\pi$
$258$		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	0.487870	−	0.872916i	$-0.337774\pi$
$263$	−27103.4	−	15648.2i	−0.0241621	−	0.0139500i	−0.512032	+	0.858966i	$0.671107\pi$
$264$		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	−0.908666	−	0.417525i	$-0.862898\pi$
$269$	−110072.	+	190650.i	−0.0927459	+	0.160641i	0.815920	+	0.578165i	$0.196231\pi$
$270$		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	$-0.919992\pi$
$281$		−	658409.i		−	0.497428i	0.968577	−	0.248714i	$-0.0800079\pi$
$282$		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	$-0.424214\pi$
$293$	693145.			0.471689			0.235844	+	0.971791i	$0.424214\pi$
$294$		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	$0.336990\pi$
$311$	−869759.	+	1.50647e6i	−0.509915	+	0.883199i	−0.999934	+	0.0114873i	$0.996343\pi$
$312$		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	0.325588	−	0.945512i	$-0.394438\pi$
$317$	2.33882e6	−	1.35032e6i	1.30722	−	0.754723i	0.981631	+	0.190788i	$0.0611044\pi$
$318$		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	0.864025	−	0.503449i	$-0.167936\pi$
$347$	1.92904e6	+	1.11373e6i	0.860037	+	0.496543i	−0.00398755	+	0.999992i	$0.501269\pi$
$348$		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	−0.633363	−	0.773855i	$-0.718326\pi$
$353$	827602.	−	1.43345e6i	0.353496	−	0.612273i	0.986859	+	0.161581i	$0.0516594\pi$
$354$		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	−0.0191845	−	0.999816i	$-0.506107\pi$
$359$	2.04413e6	−	1.18018e6i	0.837089	−	0.483294i	0.856274	+	0.516522i	$0.172774\pi$
$360$		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	0.999967	−	0.00812384i	$-0.00258593\pi$
$383$	1.41514e6	+	2.45109e6i	0.492948	+	0.853811i	−0.507019	+	0.861935i	$0.669253\pi$
$384$		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	−0.466876	−	0.884323i	$-0.654621\pi$
$389$	−4.37578e6	−	2.52636e6i	−1.46616	−	0.846488i	−0.999284	+	0.0378344i	$0.987954\pi$
$390$		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	−0.735029	−	0.678036i	$-0.762831\pi$
$401$	−1.65943e6	+	958075.i	−0.515346	+	0.297535i	0.219682	+	0.975571i	$0.429498\pi$
$402$		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	$-0.418894\pi$
$419$	1.81159e6			0.504110			0.252055	+	0.967713i	$0.418894\pi$
$420$		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	0.659088	−	0.752066i	$-0.270942\pi$
$431$	1.30089e6	+	751070.i	0.337325	+	0.194754i	−0.321764	+	0.946820i	$0.604276\pi$
$432$		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	−0.919195	−	0.393802i	$-0.871160\pi$
$443$	−4.28649e6	+	2.47481e6i	−1.03775	+	0.599146i	−0.118555	+	0.992947i	$0.537826\pi$
$444$		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	$0.187804\pi$
$449$			4.75341e6i			1.11273i	−0.830939	+	0.556364i	$0.812196\pi$
$450$		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	$-0.513153\pi$
$461$	−376986.			−0.0826176			−0.0413088	+	0.999146i	$0.513153\pi$
$462$		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	$-0.817088\pi$
$467$	−4.19642e6	−	7.26842e6i	−0.890404	−	1.54223i	−0.0510125	−	0.998698i	$-0.516245\pi$
$468$		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	−0.926245	−	0.376922i	$-0.876983\pi$
$479$	−686440.	+	1.18895e6i	−0.136699	+	0.236769i	0.789546	+	0.613691i	$0.210316\pi$
$480$		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	$0.392378\pi$
$491$			1.00791e7i			1.88677i	−0.331698	+	0.943386i	$0.607622\pi$
$492$		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	$-0.516799\pi$
$503$	−598654.			−0.105501			−0.0527504	+	0.998608i	$0.516799\pi$
$504$		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	0.721209	−	0.692718i	$-0.243587\pi$
$509$	−1.39878e6	−	2.42276e6i	−0.239307	−	0.414492i	−0.960516	+	0.278226i	$0.910254\pi$
$510$		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	−0.932011	−	0.362430i	$-0.881947\pi$
$521$	−942575.	+	1.63259e6i	−0.152132	+	0.263501i	0.779879	+	0.625931i	$0.215281\pi$
$522$		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	0.825813	−	0.563945i	$-0.190717\pi$
$557$	5.49401e6	+	3.17197e6i	0.750328	+	0.433202i	−0.0754841	+	0.997147i	$0.524050\pi$
$558$		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	−0.771606	−	0.636100i	$-0.780546\pi$
$563$	1.24152e6	−	2.15038e6i	0.165076	−	0.285920i	0.936682	+	0.350181i	$0.113880\pi$
$564$		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	−0.358242	−	0.933629i	$-0.616624\pi$
$569$	2.09432e6	−	1.20916e6i	0.271183	−	0.156568i	0.629425	+	0.777061i	$0.283290\pi$
$570$		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	$-0.514507\pi$
$587$	−760681.			−0.0911186			−0.0455593	+	0.998962i	$0.514507\pi$
$588$		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	$0.0111437\pi$
$593$	4.53856e6	+	7.86101e6i	0.530006	+	0.917998i	−0.469381	+	0.882996i	$0.655523\pi$
$594$		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	0.319497	−	0.947587i	$-0.396486\pi$
$599$	−2.99791e6	−	1.73084e6i	−0.341390	−	0.197102i	−0.660887	+	0.750486i	$0.729820\pi$
$600$		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	$-0.879863\pi$
$617$		−	6.96962e6i		−	0.737049i	0.929618	−	0.368524i	$-0.120137\pi$
$618$		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	0.774095	−	0.633069i	$-0.218205\pi$
$641$	6.37568e6	+	3.68100e6i	0.612889	+	0.353851i	−0.161207	+	0.986921i	$0.551539\pi$
$642$		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	$-0.647066\pi$
$647$	5.88127e6	−	1.01867e7i	0.552345	−	0.956690i	0.998105	−	0.0615374i	$-0.0196003\pi$
$648$		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	0.252515	−	0.967593i	$-0.418742\pi$
$653$	1.32580e7	−	7.65451e6i	1.21673	−	0.702481i	0.964218	+	0.265112i	$0.0854091\pi$
$654$		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	$0.0987527\pi$
$659$			6.80696e6i			0.610576i	−0.952260	+	0.305288i	$0.901247\pi$
$660$		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	0.739287	−	0.673390i	$-0.235163\pi$
$677$	−2.54641e6	−	4.41052e6i	−0.213529	−	0.369843i	−0.952817	+	0.303547i	$0.901829\pi$
$678$		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	0.582831	−	0.812593i	$-0.301945\pi$
$683$	2.07887e6	+	1.20024e6i	0.170520	+	0.0984498i	−0.412311	+	0.911043i	$0.635278\pi$
$684$		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	$0.00322258\pi$
$701$			263433.i			0.0202477i	−0.999949	+	0.0101238i	$0.996777\pi$
$702$		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	0.622516	−	0.782607i	$-0.286110\pi$
$719$	−5.08037e6	−	8.79946e6i	−0.366499	−	0.634795i	−0.989016	+	0.147812i	$0.952777\pi$
$720$		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	$-0.654158\pi$
$743$		−	2.66345e7i		−	1.77000i	0.465592	−	0.885000i	$-0.345842\pi$
$744$		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	$-0.947363\pi$
$761$	−1.01564e7	−	1.75913e7i	−0.635736	−	1.10113i	0.350623	−	0.936517i	$-0.385970\pi$
$762$		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	−0.853512	−	0.521073i	$-0.825532\pi$
$773$	407127.	−	705165.i	0.0245065	−	0.0424465i	0.878019	+	0.478627i	$0.158865\pi$
$774$		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	$-0.109621\pi$
$797$	3.37595e7			1.88257			0.941284	+	0.337616i	$0.109621\pi$
$798$		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	0.866352	−	0.499434i	$-0.166459\pi$
$809$	1.61396e7	+	9.31820e6i	0.867005	+	0.500565i	0.000653062		1.00000i	$0.499792\pi$
$810$		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	−0.255694	−	0.966758i	$-0.582304\pi$
$821$	8.76240e6	−	5.05897e6i	0.453696	−	0.261942i	0.709390	+	0.704816i	$0.248971\pi$
$822$		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	$0.152780\pi$
$827$			1.81637e7i			0.923509i	−0.887008	+	0.461754i	$0.847220\pi$
$828$		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	$-0.585954\pi$
$839$	−1.08782e7			−0.533523			−0.266761	+	0.963763i	$0.585954\pi$
$840$		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	−0.976319	−	0.216338i	$-0.930589\pi$
$857$	−6.46752e6	+	1.12021e7i	−0.300805	+	0.521010i	0.675513	+	0.737348i	$0.263922\pi$
$858$		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	−0.793764	−	0.608226i	$-0.791881\pi$
$863$	−1.45256e7	+	8.38636e6i	−0.663906	+	0.383307i	0.129857	+	0.991533i	$0.458548\pi$
$864$		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	$-0.576594\pi$
$881$	−1.09803e7			−0.476621			−0.238311	+	0.971189i	$0.576594\pi$
$882$		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	0.684833	−	0.728700i	$-0.259875\pi$
$887$	−6.76380e6	−	1.17152e7i	−0.288657	−	0.499968i	−0.973489	+	0.228732i	$0.926542\pi$
$888$		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	$0.146322\pi$
$911$			2.22270e7i			0.887329i	−0.896193	+	0.443665i	$0.853678\pi$
$912$		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	$0.0178635\pi$
$929$	1.44096e7	+	2.49582e7i	0.547788	+	0.948797i	−0.450637	+	0.892707i	$0.648803\pi$
$930$		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	$-0.632113\pi$
$941$	1.60500e7	−	2.77994e7i	0.590881	−	1.02344i	0.994114	−	0.108339i	$-0.0345532\pi$
$942$		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	0.356690	−	0.934223i	$-0.383905\pi$
$947$	3.70941e7	−	2.14163e7i	1.34410	−	0.776014i	0.987406	+	0.158209i	$0.0505720\pi$
$948$		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	$0.345638\pi$
$953$			4.96089e7i			1.76940i	−0.466156	+	0.884702i	$0.654362\pi$
$954$		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	$0.0911016\pi$
$971$	2.12754e7	+	3.68500e7i	0.724151	+	1.25427i	−0.235171	+	0.971954i	$0.575565\pi$
$972$		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	0.0313109	−	0.999510i	$-0.490032\pi$
$977$	−2.44245e7	−	1.41015e7i	−0.818635	−	0.472639i	−0.849945	+	0.526871i	$0.823365\pi$
$978$		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	−0.548730	−	0.836000i	$-0.684888\pi$
$983$	1.36220e7	−	2.35940e7i	0.449632	−	0.778786i	0.998362	+	0.0572142i	$0.0182218\pi$
$984$		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.17.12	yes	24
3.2	odd	2	inner	63.6.p.b.17.1	✓	24
7.3	odd	6		441.6.c.b.440.22		24
7.4	even	3		441.6.c.b.440.4		24
7.5	odd	6	inner	63.6.p.b.26.1	yes	24
21.5	even	6	inner	63.6.p.b.26.12	yes	24
21.11	odd	6		441.6.c.b.440.21		24
21.17	even	6		441.6.c.b.440.3		24

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

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