LMFDB - Embedded newform 63.6.p.b.26.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("63.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			26.9
Character	$\chi$	$=$	63.26
Dual form			63.6.p.b.17.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.81384 + 3.35662i) q^{2} +(6.53381 + 11.3169i) q^{4} +(-43.0174 + 74.5084i) q^{5} +(95.4202 + 87.7609i) q^{7} -127.098i q^{8} +O(q^{10})$	\(q+(5.81384 + 3.35662i) q^{2} +(6.53381 + 11.3169i) q^{4} +(-43.0174 + 74.5084i) q^{5} +(95.4202 + 87.7609i) q^{7} -127.098i q^{8} +(-500.193 + 288.786i) q^{10} +(-668.722 + 386.087i) q^{11} +273.772i q^{13} +(260.178 + 830.517i) q^{14} +(635.701 - 1101.07i) q^{16} +(563.078 + 975.279i) q^{17} +(-303.319 - 175.122i) q^{19} -1124.27 q^{20} -5183.79 q^{22} +(2841.21 + 1640.37i) q^{23} +(-2138.50 - 3703.99i) q^{25} +(-918.950 + 1591.67i) q^{26} +(-369.723 + 1653.27i) q^{28} -2053.84i q^{29} +(7393.97 - 4268.91i) q^{31} +(3869.49 - 2234.05i) q^{32} +7560.15i q^{34} +(-10643.7 + 3334.36i) q^{35} +(1120.07 - 1940.01i) q^{37} +(-1175.63 - 2036.26i) q^{38} +(9469.84 + 5467.41i) q^{40} +9767.49 q^{41} -5730.56 q^{43} +(-8738.61 - 5045.24i) q^{44} +(11012.2 + 19073.7i) q^{46} +(6590.66 - 11415.4i) q^{47} +(1403.04 + 16748.3i) q^{49} -28712.5i q^{50} +(-3098.25 + 1788.78i) q^{52} +(-18937.1 + 10933.3i) q^{53} -66433.8i q^{55} +(11154.2 - 12127.7i) q^{56} +(6893.97 - 11940.7i) q^{58} +(7840.61 + 13580.3i) q^{59} +(38560.9 + 22263.1i) q^{61} +57316.4 q^{62} -10689.4 q^{64} +(-20398.3 - 11777.0i) q^{65} +(-7452.90 - 12908.8i) q^{67} +(-7358.09 + 12744.6i) q^{68} +(-73072.7 - 16341.3i) q^{70} +37157.7i q^{71} +(-36977.1 + 21348.7i) q^{73} +(13023.8 - 7519.29i) q^{74} -4576.85i q^{76} +(-97692.9 - 21847.2i) q^{77} +(3853.63 - 6674.68i) q^{79} +(54692.4 + 94730.0i) q^{80} +(56786.6 + 32785.8i) q^{82} +2633.05 q^{83} -96888.6 q^{85} +(-33316.6 - 19235.3i) q^{86} +(49070.7 + 84992.9i) q^{88} +(-52132.1 + 90295.4i) q^{89} +(-24026.5 + 26123.4i) q^{91} +42871.6i q^{92} +(76634.0 - 44244.7i) q^{94} +(26096.0 - 15066.6i) q^{95} -6267.27i q^{97} +(-48060.8 + 102082. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	5.81384	+	3.35662i	1.02775	+	0.593372i	0.916340	−	0.400402i	$-0.131129\pi$
$2$	5.81384	+	3.35662i	1.02775	+	0.593372i	0.111412	+	0.993774i	$0.464463\pi$
$3$		0			0
$3$		0			0
$4$	6.53381	+	11.3169i	0.204182	+	0.353653i
$5$	−43.0174	+	74.5084i	−0.769519	+	1.33285i	0.168305	+	0.985735i	$0.446171\pi$
$5$	−43.0174	+	74.5084i	−0.769519	+	1.33285i	−0.937824	+	0.347111i	$0.887163\pi$
$6$		0			0
$7$	95.4202	+	87.7609i	0.736030	+	0.676949i
$7$	95.4202	+	87.7609i	0.736030	+	0.676949i
$8$		−	127.098i		−	0.702122i
$9$		0			0
$10$	−500.193	+	288.786i	−1.58175	+	0.913223i
$11$	−668.722	+	386.087i	−1.66634	+	0.962062i	−0.696755	+	0.717309i	$0.745374\pi$
$11$	−668.722	+	386.087i	−1.66634	+	0.962062i	−0.969585	+	0.244753i	$0.921293\pi$
$12$		0			0
$13$			273.772i			0.449295i	0.974440	+	0.224647i	$0.0721230\pi$
$13$			273.772i			0.449295i	−0.974440	+	0.224647i	$0.927877\pi$
$14$	260.178	+	830.517i	0.354773	+	1.13248i
$15$		0			0
$16$	635.701	−	1101.07i	0.620801	−	1.07526i
$17$	563.078	+	975.279i	0.472548	+	0.818477i	0.999506	−	0.0314138i	$-0.0100010\pi$
$17$	563.078	+	975.279i	0.472548	+	0.818477i	−0.526958	+	0.849891i	$0.676668\pi$
$18$		0			0
$19$	−303.319	−	175.122i	−0.192760	−	0.111290i	0.400514	−	0.916291i	$-0.368832\pi$
$19$	−303.319	−	175.122i	−0.192760	−	0.111290i	−0.593274	+	0.805001i	$0.702165\pi$
$20$	−1124.27			−0.628487
$21$		0			0
$22$	−5183.79			−2.28344
$23$	2841.21	+	1640.37i	1.11991	+	0.646581i	0.941378	−	0.337353i	$-0.109532\pi$
$23$	2841.21	+	1640.37i	1.11991	+	0.646581i	0.178533	+	0.983934i	$0.442865\pi$
$24$		0			0
$25$	−2138.50	−	3703.99i	−0.684319	−	1.18528i
$26$	−918.950	+	1591.67i	−0.266599	+	0.461763i
$27$		0			0
$28$	−369.723	+	1653.27i	−0.0891213	+	0.398520i
$29$		−	2053.84i		−	0.453495i	−0.973954	−	0.226747i	$-0.927191\pi$
$29$		−	2053.84i		−	0.453495i	0.973954	−	0.226747i	$-0.0728091\pi$
$30$		0			0
$31$	7393.97	−	4268.91i	1.38189	−	0.797834i	0.389506	−	0.921024i	$-0.372646\pi$
$31$	7393.97	−	4268.91i	1.38189	−	0.797834i	0.992383	+	0.123190i	$0.0393124\pi$
$32$	3869.49	−	2234.05i	0.668003	−	0.385672i
$33$		0			0
$34$			7560.15i			1.12159i
$35$	−10643.7	+	3334.36i	−1.46866	+	0.460089i
$36$		0			0
$37$	1120.07	−	1940.01i	0.134506	−	0.232970i	−0.790903	−	0.611942i	$-0.790389\pi$
$37$	1120.07	−	1940.01i	0.134506	−	0.232970i	0.925408	+	0.378971i	$0.123722\pi$
$38$	−1175.63	−	2036.26i	−0.132073	−	0.228757i
$39$		0			0
$40$	9469.84	+	5467.41i	0.935820	+	0.540296i
$41$	9767.49			0.907451			0.453725	−	0.891142i	$-0.350095\pi$
$41$	9767.49			0.907451			0.453725	+	0.891142i	$0.350095\pi$
$42$		0			0
$43$	−5730.56			−0.472635			−0.236318	−	0.971676i	$-0.575941\pi$
$43$	−5730.56			−0.472635			−0.236318	+	0.971676i	$0.575941\pi$
$44$	−8738.61	−	5045.24i	−0.680472	−	0.392871i
$45$		0			0
$46$	11012.2	+	19073.7i	0.767327	+	1.32905i
$47$	6590.66	−	11415.4i	0.435195	−	0.753780i	−0.562116	−	0.827058i	$-0.690013\pi$
$47$	6590.66	−	11415.4i	0.435195	−	0.753780i	0.997312	+	0.0732781i	$0.0233461\pi$
$48$		0			0
$49$	1403.04	+	16748.3i	0.0834797	+	0.996509i
$50$		−	28712.5i		−	1.62422i
$51$		0			0
$52$	−3098.25	+	1788.78i	−0.158894	+	0.0917377i
$53$	−18937.1	+	10933.3i	−0.926026	+	0.534641i	−0.885552	−	0.464539i	$-0.846220\pi$
$53$	−18937.1	+	10933.3i	−0.926026	+	0.534641i	−0.0404733	+	0.999181i	$0.512887\pi$
$54$		0			0
$55$		−	66433.8i		−	2.96130i
$56$	11154.2	−	12127.7i	0.475301	−	0.516783i
$57$		0			0
$58$	6893.97	−	11940.7i	0.269091	−	0.466080i
$59$	7840.61	+	13580.3i	0.293238	+	0.507902i	0.974573	−	0.224069i	$-0.0719340\pi$
$59$	7840.61	+	13580.3i	0.293238	+	0.507902i	−0.681336	+	0.731971i	$0.738601\pi$
$60$		0			0
$61$	38560.9	+	22263.1i	1.32685	+	0.766059i	0.984812	−	0.173627i	$-0.0555486\pi$
$61$	38560.9	+	22263.1i	1.32685	+	0.766059i	0.342041	+	0.939685i	$0.388882\pi$
$62$	57316.4			1.89365
$63$		0			0
$64$	−10689.4			−0.326214
$65$	−20398.3	−	11777.0i	−0.598840	−	0.345741i
$66$		0			0
$67$	−7452.90	−	12908.8i	−0.202833	−	0.351317i	0.746607	−	0.665265i	$-0.231681\pi$
$67$	−7452.90	−	12908.8i	−0.202833	−	0.351317i	−0.949440	+	0.313948i	$0.898348\pi$
$68$	−7358.09	+	12744.6i	−0.192971	+	0.334236i
$69$		0			0
$70$	−73072.7	−	16341.3i	−1.78242	−	0.398604i
$71$			37157.7i			0.874789i	0.899270	+	0.437394i	$0.144099\pi$
$71$			37157.7i			0.874789i	−0.899270	+	0.437394i	$0.855901\pi$
$72$		0			0
$73$	−36977.1	+	21348.7i	−0.812130	+	0.468884i	−0.847695	−	0.530484i	$-0.822010\pi$
$73$	−36977.1	+	21348.7i	−0.812130	+	0.468884i	0.0355647	+	0.999367i	$0.488677\pi$
$74$	13023.8	−	7519.29i	0.276476	−	0.159624i
$75$		0			0
$76$		−	4576.85i		−	0.0908934i
$77$	−97692.9	−	21847.2i	−1.87774	−	0.419921i
$78$		0			0
$79$	3853.63	−	6674.68i	0.0694708	−	0.120327i	−0.829198	−	0.558955i	$-0.811202\pi$
$79$	3853.63	−	6674.68i	0.0694708	−	0.120327i	0.898668	+	0.438629i	$0.144536\pi$
$80$	54692.4	+	94730.0i	0.955437	+	1.65487i
$81$		0			0
$82$	56786.6	+	32785.8i	0.932634	+	0.538456i
$83$	2633.05			0.0419531			0.0209765	−	0.999780i	$-0.493322\pi$
$83$	2633.05			0.0419531			0.0209765	+	0.999780i	$0.493322\pi$
$84$		0			0
$85$	−96888.6			−1.45454
$86$	−33316.6	−	19235.3i	−0.485752	−	0.280449i
$87$		0			0
$88$	49070.7	+	84992.9i	0.675485	+	1.16997i
$89$	−52132.1	+	90295.4i	−0.697638	+	1.20834i	0.271646	+	0.962397i	$0.412432\pi$
$89$	−52132.1	+	90295.4i	−0.697638	+	1.20834i	−0.969283	+	0.245947i	$0.920901\pi$
$90$		0			0
$91$	−24026.5	+	26123.4i	−0.304150	+	0.330694i
$92$			42871.6i			0.528080i
$93$		0			0
$94$	76634.0	−	44244.7i	0.894545	−	0.516466i
$95$	26096.0	−	15066.6i	0.296665	−	0.171279i
$96$		0			0
$97$		−	6267.27i		−	0.0676316i	−0.999428	−	0.0338158i	$-0.989234\pi$
$97$		−	6267.27i		−	0.0676316i	0.999428	−	0.0338158i	$-0.0107659\pi$
$98$	−48060.8	+	102082.i	−0.505505	+	1.07370i
$99$		0			0
$100$	27945.1	−	48402.3i	0.279451	−	0.484023i
$101$	−12565.8	−	21764.7i	−0.122571	−	0.212299i	0.798210	−	0.602380i	$-0.205781\pi$
$101$	−12565.8	−	21764.7i	−0.122571	−	0.212299i	−0.920781	+	0.390080i	$0.872447\pi$
$102$		0			0
$103$	2363.04	+	1364.30i	0.0219471	+	0.0126712i	0.510933	−	0.859620i	$-0.329300\pi$
$103$	2363.04	+	1364.30i	0.0219471	+	0.0126712i	−0.488986	+	0.872291i	$0.662633\pi$
$104$	34795.8			0.315460
$105$		0			0
$106$	−146796.			−1.26897
$107$	−77454.3	−	44718.3i	−0.654012	−	0.377594i	0.135979	−	0.990712i	$-0.456582\pi$
$107$	−77454.3	−	44718.3i	−0.654012	−	0.377594i	−0.789992	+	0.613117i	$0.789915\pi$
$108$		0			0
$109$	−26633.0	−	46129.6i	−0.214710	−	0.371889i	0.738473	−	0.674284i	$-0.235547\pi$
$109$	−26633.0	−	46129.6i	−0.214710	−	0.371889i	−0.953183	+	0.302394i	$0.902214\pi$
$110$	222993.	−	386235.i	1.75715	−	3.04348i
$111$		0			0
$112$	157289.	−	49274.3i	1.18482	−	0.371172i
$113$		−	158001.i		−	1.16403i	−0.813179	−	0.582013i	$-0.802265\pi$
$113$		−	158001.i		−	1.16403i	0.813179	−	0.582013i	$-0.197735\pi$
$114$		0			0
$115$	−244443.	+	141129.i	−1.72359	+	0.995113i
$116$	23243.1	−	13419.4i	0.160380	−	0.0925953i
$117$		0			0
$118$			105272.i			0.695996i
$119$	−31862.4	+	142478.i	−0.206258	+	0.922315i
$120$		0			0
$121$	217600.	−	376895.i	1.35113	−	2.34022i
$122$	149458.	+	258869.i	0.909116	+	1.57464i
$123$		0			0
$124$	96621.6	+	55784.5i	0.564313	+	0.325806i
$125$	99111.7			0.567348
$126$		0			0
$127$	261759.			1.44010			0.720049	−	0.693924i	$-0.244119\pi$
$127$	261759.			1.44010			0.720049	+	0.693924i	$0.244119\pi$
$128$	−185970.	−	107370.i	−1.00327	−	0.579239i
$129$		0			0
$130$	−79061.7	−	136939.i	−0.410306	−	0.710671i
$131$	114351.	−	198062.i	0.582185	−	1.00837i	−0.413035	−	0.910715i	$-0.635531\pi$
$131$	114351.	−	198062.i	0.582185	−	1.00837i	0.995220	−	0.0976591i	$-0.0311355\pi$
$132$		0			0
$133$	−13574.0	−	43329.7i	−0.0665393	−	0.212401i
$134$		−	100066.i		−	0.481422i
$135$		0			0
$136$	123956.	−	71565.8i	0.574671	−	0.331786i
$137$	56953.1	−	32881.9i	0.259248	−	0.149677i	−0.364743	−	0.931108i	$-0.618843\pi$
$137$	56953.1	−	32881.9i	0.259248	−	0.149677i	0.623992	+	0.781431i	$0.285510\pi$
$138$		0			0
$139$			424407.i			1.86314i	0.363563	+	0.931570i	$0.381560\pi$
$139$			424407.i			1.86314i	−0.363563	+	0.931570i	$0.618440\pi$
$140$	−107278.	−	98667.1i	−0.462585	−	0.425454i
$141$		0			0
$142$	−124724.	+	216029.i	−0.519076	+	0.899065i
$143$	−105700.	−	183078.i	−0.432249	−	0.748678i
$144$		0			0
$145$	153028.	+	88351.0i	0.604438	+	0.348973i
$146$	−286639.			−1.11289
$147$		0			0
$148$	29273.3			0.109854
$149$	−91297.7	−	52710.8i	−0.336895	−	0.194506i	0.322003	−	0.946739i	$-0.395644\pi$
$149$	−91297.7	−	52710.8i	−0.336895	−	0.194506i	−0.658898	+	0.752232i	$0.728977\pi$
$150$		0			0
$151$	89946.5	+	155792.i	0.321027	+	0.556035i	0.980700	−	0.195517i	$-0.0626386\pi$
$151$	89946.5	+	155792.i	0.321027	+	0.556035i	−0.659673	+	0.751553i	$0.729305\pi$
$152$	−22257.5	+	38551.2i	−0.0781390	+	0.135341i
$153$		0			0
$154$	−494638.	−	454934.i	−1.68068	−	1.54578i
$155$			734550.i			2.45579i
$156$		0			0
$157$	−157408.	+	90879.3i	−0.509655	+	0.294250i	−0.732692	−	0.680560i	$-0.761736\pi$
$157$	−157408.	+	90879.3i	−0.509655	+	0.294250i	0.223037	+	0.974810i	$0.428403\pi$
$158$	44808.8	−	25870.3i	0.142797	−	0.0824441i
$159$		0			0
$160$			384412.i			1.18713i
$161$	127148.	+	405872.i	0.386586	+	1.23403i
$162$		0			0
$163$	−29654.6	+	51363.3i	−0.0874225	+	0.151420i	−0.906421	−	0.422376i	$-0.861196\pi$
$163$	−29654.6	+	51363.3i	−0.0874225	+	0.151420i	0.818998	+	0.573796i	$0.194530\pi$
$164$	63818.9	+	110538.i	0.185285	+	0.320923i
$165$		0			0
$166$	15308.1	+	8838.15i	0.0431173	+	0.0248938i
$167$	284486.			0.789349			0.394675	−	0.918821i	$-0.370857\pi$
$167$	284486.			0.789349			0.394675	+	0.918821i	$0.370857\pi$
$168$		0			0
$169$	296342.			0.798134
$170$	−563295.	−	325218.i	−1.49490	−	0.863083i
$171$		0			0
$172$	−37442.4	−	64852.2i	−0.0965035	−	0.167149i
$173$	238901.	−	413789.i	0.606880	−	1.05115i	−0.384871	−	0.922970i	$-0.625754\pi$
$173$	238901.	−	413789.i	0.606880	−	1.05115i	0.991751	−	0.128177i	$-0.0409126\pi$
$174$		0			0
$175$	121009.	−	541112.i	0.298692	−	1.33565i
$176$			981742.i			2.38900i
$177$		0			0
$178$	−606175.	+	349975.i	−1.43400	+	0.827918i
$179$	152770.	−	88201.6i	0.356373	−	0.205752i	−0.311116	−	0.950372i	$-0.600703\pi$
$179$	152770.	−	88201.6i	0.356373	−	0.205752i	0.667488	+	0.744620i	$0.267369\pi$
$180$		0			0
$181$		−	663555.i		−	1.50550i	−0.658307	−	0.752750i	$-0.728727\pi$
$181$		−	663555.i		−	1.50550i	0.658307	−	0.752750i	$-0.271273\pi$
$182$	−227373.	+	71229.4i	−0.508815	+	0.159397i
$183$		0			0
$184$	208487.	−	361111.i	0.453979	−	0.786314i
$185$	96364.9	+	166909.i	0.207009	+	0.358550i
$186$		0			0
$187$	−753085.	−	434794.i	−1.57485	−	0.909241i
$188$	172248.			0.355435
$189$		0			0
$190$	202291.			0.406530
$191$	251550.	+	145232.i	0.498931	+	0.288058i	0.728272	−	0.685288i	$-0.240324\pi$
$191$	251550.	+	145232.i	0.498931	+	0.288058i	−0.229341	+	0.973346i	$0.573657\pi$
$192$		0			0
$193$	79685.6	+	138020.i	0.153988	+	0.266715i	0.932690	−	0.360679i	$-0.117455\pi$
$193$	79685.6	+	138020.i	0.153988	+	0.266715i	−0.778702	+	0.627394i	$0.784122\pi$
$194$	21036.9	−	36436.9i	0.0401307	−	0.0695084i
$195$		0			0
$196$	−180372.	+	125309.i	−0.335374	+	0.232992i
$197$		−	663777.i		−	1.21859i	−0.792945	−	0.609294i	$-0.791453\pi$
$197$		−	663777.i		−	1.21859i	0.792945	−	0.609294i	$-0.208547\pi$
$198$		0			0
$199$	−507090.	+	292769.i	−0.907721	+	0.524073i	−0.879697	−	0.475534i	$-0.842255\pi$
$199$	−507090.	+	292769.i	−0.907721	+	0.524073i	−0.0280238	+	0.999607i	$0.508921\pi$
$200$	−470768.	+	271798.i	−0.832208	+	0.480475i
$201$		0			0
$202$		−	168715.i		−	0.290921i
$203$	180247.	−	195978.i	0.306993	−	0.333786i
$204$		0			0
$205$	−420172.	+	727759.i	−0.698301	+	1.20949i
$206$	9158.89	+	15863.7i	0.0150375	+	0.0260457i
$207$		0			0
$208$	301441.	+	174037.i	0.483108	+	0.278923i
$209$	270448.			0.428271
$210$		0			0
$211$	483496.			0.747630			0.373815	−	0.927503i	$-0.378049\pi$
$211$	483496.			0.747630			0.373815	+	0.927503i	$0.378049\pi$
$212$	−247463.	−	142873.i	−0.378155	−	0.218328i
$213$		0			0
$214$	−300204.	−	519969.i	−0.448108	−	0.776146i
$215$	246514.	−	426975.i	0.363702	−	0.629950i
$216$		0			0
$217$	1.08018e6	+	241561.i	1.55720	+	0.348239i
$218$		−	357587.i		−	0.509613i
$219$		0			0
$220$	751825.	−	434066.i	1.04727	−	0.604643i
$221$	−267004.	+	154155.i	−0.367737	+	0.212313i
$222$		0			0
$223$			1.19760e6i			1.61268i	0.591449	+	0.806342i	$0.298556\pi$
$223$			1.19760e6i			1.61268i	−0.591449	+	0.806342i	$0.701444\pi$
$224$	565290.	+	126416.i	0.752751	+	0.168338i
$225$		0			0
$226$	530348.	−	918590.i	0.690701	−	1.19633i
$227$	509169.	+	881906.i	0.655839	+	1.13595i	0.981683	+	0.190523i	$0.0610183\pi$
$227$	509169.	+	881906.i	0.655839	+	1.13595i	−0.325844	+	0.945424i	$0.605648\pi$
$228$		0			0
$229$	643594.	+	371579.i	0.811005	+	0.468234i	0.847305	−	0.531107i	$-0.178224\pi$
$229$	643594.	+	371579.i	0.811005	+	0.468234i	−0.0363000	+	0.999341i	$0.511557\pi$
$230$	−1.89487e6			−2.36189
$231$		0			0
$232$	−261038.			−0.318408
$233$	−773154.	−	446381.i	−0.932988	−	0.538661i	−0.0452327	−	0.998976i	$-0.514403\pi$
$233$	−773154.	−	446381.i	−0.932988	−	0.538661i	−0.887755	+	0.460316i	$0.847736\pi$
$234$		0			0
$235$	567026.	+	982118.i	0.669782	+	1.16010i
$236$	−102458.	+	177463.i	−0.119747	+	0.207409i
$237$		0			0
$238$	−663486.	+	721392.i	−0.759258	+	0.825522i
$239$		−	770982.i		−	0.873071i	−0.899687	−	0.436535i	$-0.856205\pi$
$239$		−	770982.i		−	0.873071i	0.899687	−	0.436535i	$-0.143795\pi$
$240$		0			0
$241$	610067.	−	352222.i	0.676604	−	0.390638i	−0.121970	−	0.992534i	$-0.538921\pi$
$241$	610067.	−	352222.i	0.676604	−	0.390638i	0.798574	+	0.601896i	$0.205588\pi$
$242$	2.53019e6	−	1.46080e6i	2.77724	−	1.60344i
$243$		0			0
$244$			581853.i			0.625660i
$245$	−1.30825e6	−	615932.i	−1.39243	−	0.655567i
$246$		0			0
$247$	47943.4	−	83040.5i	0.0500019	−	0.0866059i
$248$	−542568.	−	939756.i	−0.560177	−	0.970255i
$249$		0			0
$250$	576219.	+	332680.i	0.583093	+	0.336649i
$251$	471518.			0.472404			0.236202	−	0.971704i	$-0.424097\pi$
$251$	471518.			0.472404			0.236202	+	0.971704i	$0.424097\pi$
$252$		0			0
$253$	−2.53330e6			−2.48820
$254$	1.52182e6	+	878625.i	1.48006	+	0.854514i
$255$		0			0
$256$	−549770.	−	952229.i	−0.524301	−	0.908116i
$257$	−333663.	+	577921.i	−0.315119	+	0.545803i	−0.979463	−	0.201625i	$-0.935378\pi$
$257$	−333663.	+	577921.i	−0.315119	+	0.545803i	0.664343	+	0.747427i	$0.268711\pi$
$258$		0			0
$259$	277135.	−	86818.5i	0.256709	−	0.0804197i
$260$		−	307794.i		−	0.282376i
$261$		0			0
$262$	1.32963e6	−	767665.i	1.19668	−	0.690905i
$263$	−1.41359e6	+	816138.i	−1.26019	+	0.727569i	−0.973111	−	0.230339i	$-0.926017\pi$
$263$	−1.41359e6	+	816138.i	−1.26019	+	0.727569i	−0.287076	+	0.957908i	$0.592683\pi$
$264$		0			0
$265$		−	1.88129e6i		−	1.64567i
$266$	66524.6	−	297475.i	0.0576472	−	0.257778i
$267$		0			0
$268$	97391.7	−	168687.i	0.0828295	−	0.143465i
$269$	−958193.	−	1.65964e6i	−0.807369	−	1.39840i	−0.914680	−	0.404179i	$-0.867557\pi$
$269$	−958193.	−	1.65964e6i	−0.807369	−	1.39840i	0.107311	−	0.994226i	$-0.465776\pi$
$270$		0			0
$271$	−1.19495e6	−	689904.i	−0.988385	−	0.570644i	−0.0835940	−	0.996500i	$-0.526640\pi$
$271$	−1.19495e6	−	689904.i	−0.988385	−	0.570644i	−0.904791	+	0.425855i	$0.859973\pi$
$272$	1.43180e6			1.17343
$273$		0			0
$274$	441488.			0.355257
$275$	2.86012e6	+	1.65129e6i	2.28062	+	1.31672i
$276$		0			0
$277$	416099.	+	720704.i	0.325834	+	0.564362i	0.981681	−	0.190533i	$-0.0610215\pi$
$277$	416099.	+	720704.i	0.325834	+	0.564362i	−0.655847	+	0.754894i	$0.727688\pi$
$278$	−1.42457e6	+	2.46743e6i	−1.10554	+	1.91484i
$279$		0			0
$280$	423789.	+	1.35278e6i	0.323039	+	1.03118i
$281$		−	1.63211e6i		−	1.23306i	−0.787331	−	0.616531i	$-0.788538\pi$
$281$		−	1.63211e6i		−	1.23306i	0.787331	−	0.616531i	$-0.211462\pi$
$282$		0			0
$283$	−768392.	+	443631.i	−0.570318	+	0.329273i	−0.757276	−	0.653095i	$-0.773470\pi$
$283$	−768392.	+	443631.i	−0.570318	+	0.329273i	0.186958	+	0.982368i	$0.440137\pi$
$284$	−420510.	+	242782.i	−0.309372	+	0.178616i
$285$		0			0
$286$		−	1.41918e6i		−	1.02594i
$287$	932016.	+	857204.i	0.667911	+	0.614298i
$288$		0			0
$289$	75815.5	−	131316.i	0.0533966	−	0.0924856i
$290$	593122.	+	1.02732e6i	0.414142	+	0.717314i
$291$		0			0
$292$	−483203.	−	278977.i	−0.331644	−	0.191475i
$293$	882663.			0.600656			0.300328	−	0.953836i	$-0.402904\pi$
$293$	882663.			0.600656			0.300328	+	0.953836i	$0.402904\pi$
$294$		0			0
$295$	−1.34913e6			−0.902608
$296$	−246571.	−	142358.i	−0.163574	−	0.0944393i
$297$		0			0
$298$	−353860.	−	612904.i	−0.230829	−	0.399808i
$299$	−449089.	+	777844.i	−0.290505	+	0.503170i
$300$		0			0
$301$	−546812.	−	502920.i	−0.347874	−	0.319950i
$302$			1.20767e6i			0.761955i
$303$		0			0
$304$	−385641.	+	222650.i	−0.239331	+	0.138178i
$305$	−3.31758e6	+	1.91541e6i	−2.04208	+	1.17899i
$306$		0			0
$307$		−	1.86696e6i		−	1.13055i	−0.824903	−	0.565275i	$-0.808770\pi$
$307$		−	1.86696e6i		−	1.13055i	0.824903	−	0.565275i	$-0.191230\pi$
$308$	−391065.	−	1.24833e6i	−0.234894	−	0.749810i
$309$		0			0
$310$	−2.46561e6	+	4.27055e6i	−1.45720	+	2.52395i
$311$	917.319	+	1588.84i	0.000537798	+	0.000931494i	0.866294	−	0.499534i	$-0.166495\pi$
$311$	917.319	+	1588.84i	0.000537798	+	0.000931494i	−0.865756	+	0.500466i	$0.833162\pi$
$312$		0			0
$313$	357850.	+	206605.i	0.206462	+	0.119201i	0.599666	−	0.800250i	$-0.295300\pi$
$313$	357850.	+	206605.i	0.206462	+	0.119201i	−0.393204	+	0.919451i	$0.628633\pi$
$314$	−1.22019e6			−0.698399
$315$		0			0
$316$	100716.			0.0567386
$317$	−1.94382e6	−	1.12226e6i	−1.08645	−	0.627259i	−0.153817	−	0.988099i	$-0.549157\pi$
$317$	−1.94382e6	−	1.12226e6i	−1.08645	−	0.627259i	−0.932628	+	0.360840i	$0.882490\pi$
$318$		0			0
$319$	792961.	+	1.37345e6i	0.436290	+	0.755676i
$320$	459830.	−	796449.i	0.251028	−	0.434794i
$321$		0			0
$322$	−623139.	+	2.78646e6i	−0.334923	+	1.49766i
$323$		−	394428.i		−	0.210359i
$324$		0			0
$325$	1.01405e6	−	585461.i	0.532538	−	0.307461i
$326$	−344814.	+	199079.i	−0.179697	+	0.103748i
$327$		0			0
$328$		−	1.24142e6i		−	0.637141i
$329$	1.63070e6	−	510853.i	0.830587	−	0.260200i
$330$		0			0
$331$	697950.	−	1.20888e6i	0.350150	−	0.606478i	−0.636125	−	0.771586i	$-0.719464\pi$
$331$	697950.	−	1.20888e6i	0.350150	−	0.606478i	0.986275	+	0.165108i	$0.0527973\pi$
$332$	17203.9	+	29798.0i	0.00856605	+	0.0148368i
$333$		0			0
$334$	1.65395e6	+	954911.i	0.811255	+	0.468378i
$335$	1.28242e6			0.624335
$336$		0			0
$337$	3.48937e6			1.67368			0.836841	−	0.547446i	$-0.184400\pi$
$337$	3.48937e6			1.67368			0.836841	+	0.547446i	$0.184400\pi$
$338$	1.72288e6	+	994707.i	0.820284	+	0.473591i
$339$		0			0
$340$	−633052.	−	1.09648e6i	−0.296990	−	0.514402i
$341$	−3.29634e6	+	5.70942e6i	−1.53513	+	2.65893i
$342$		0			0
$343$	−1.33597e6	+	1.72126e6i	−0.613143	+	0.789972i
$344$			728341.i			0.331848i
$345$		0			0
$346$	2.77787e6	−	1.60380e6i	1.24744	−	0.720212i
$347$	154630.	−	89275.4i	0.0689396	−	0.0398023i	−0.465134	−	0.885240i	$-0.653994\pi$
$347$	154630.	−	89275.4i	0.0689396	−	0.0398023i	0.534074	+	0.845438i	$0.320661\pi$
$348$		0			0
$349$		−	1.07517e6i		−	0.472512i	−0.971691	−	0.236256i	$-0.924080\pi$
$349$		−	1.07517e6i		−	0.472512i	0.971691	−	0.236256i	$-0.0759205\pi$
$350$	2.51984e6	−	2.73975e6i	1.09952	−	1.19548i
$351$		0			0
$352$	−1.72507e6	+	2.98792e6i	−0.742081	+	1.28532i
$353$	−949110.	−	1.64391e6i	−0.405396	−	0.702167i	0.588971	−	0.808154i	$-0.299533\pi$
$353$	−949110.	−	1.64391e6i	−0.405396	−	0.702167i	−0.994367	+	0.105987i	$0.966200\pi$
$354$		0			0
$355$	−2.76856e6	−	1.59843e6i	−1.16596	−	0.673167i
$356$	−1.36248e6			−0.569779
$357$		0			0
$358$	1.18424e6			0.488350
$359$	2.33923e6	+	1.35056e6i	0.957938	+	0.553065i	0.895538	−	0.444986i	$-0.146791\pi$
$359$	2.33923e6	+	1.35056e6i	0.957938	+	0.553065i	0.0623999	+	0.998051i	$0.480125\pi$
$360$		0			0
$361$	−1.17671e6	−	2.03813e6i	−0.475229	−	0.823121i
$362$	2.22730e6	−	3.85780e6i	0.893322	−	1.54728i
$363$		0			0
$364$	−452621.	−	101220.i	−0.179053	−	0.0400417i
$365$		−	3.67347e6i		−	1.44326i
$366$		0			0
$367$	1.12965e6	−	652203.i	0.437803	−	0.252766i	−0.264862	−	0.964286i	$-0.585327\pi$
$367$	1.12965e6	−	652203.i	0.437803	−	0.252766i	0.702665	+	0.711521i	$0.251993\pi$
$368$	3.61232e6	−	2.08557e6i	1.39048	−	0.802797i
$369$		0			0
$370$			1.29384e6i			0.491334i
$371$	−2.76650e6	−	618674.i	−1.04351	−	0.233360i
$372$		0			0
$373$	−213324.	+	369489.i	−0.0793905	+	0.137508i	−0.902987	−	0.429668i	$-0.858631\pi$
$373$	−213324.	+	369489.i	−0.0793905	+	0.137508i	0.823597	+	0.567176i	$0.191964\pi$
$374$	−2.91887e6	−	5.05564e6i	−1.07904	−	1.86895i
$375$		0			0
$376$	−1.45086e6	−	837657.i	−0.529245	−	0.305560i
$377$	562285.			0.203753
$378$		0			0
$379$	1.26860e6			0.453655			0.226827	−	0.973935i	$-0.427165\pi$
$379$	1.26860e6			0.453655			0.226827	+	0.973935i	$0.427165\pi$
$380$	341013.	+	196884.i	0.121147	+	0.0699442i
$381$		0			0
$382$	974979.	+	1.68871e6i	0.341851	+	0.592104i
$383$	−687864.	+	1.19141e6i	−0.239610	+	0.415017i	−0.960602	−	0.277926i	$-0.910353\pi$
$383$	−687864.	+	1.19141e6i	−0.239610	+	0.415017i	0.720992	+	0.692943i	$0.243686\pi$
$384$		0			0
$385$	5.83029e6	−	6.33913e6i	2.00465	−	2.17961i
$386$			1.06990e6i			0.365489i
$387$		0			0
$388$	70926.1	−	40949.2i	0.0239181	−	0.0138091i
$389$	4.50972e6	−	2.60369e6i	1.51104	−	0.872398i	0.511120	−	0.859509i	$-0.329231\pi$
$389$	4.50972e6	−	2.60369e6i	1.51104	−	0.872398i	0.999917	−	0.0128886i	$-0.00410268\pi$
$390$		0			0
$391$			3.69463e6i			1.22216i
$392$	2.12867e6	−	178323.i	0.699671	−	0.0586129i
$393$		0			0
$394$	2.22805e6	−	3.85909e6i	0.723076	−	1.25240i
$395$	331546.	+	574255.i	0.106918	+	0.185188i
$396$		0			0
$397$	−1.55770e6	−	899340.i	−0.496031	−	0.286383i	0.231042	−	0.972944i	$-0.425786\pi$
$397$	−1.55770e6	−	899340.i	−0.496031	−	0.286383i	−0.727073	+	0.686560i	$0.759120\pi$
$398$	−3.93085e6			−1.24388
$399$		0			0
$400$	−5.43778e6			−1.69930
$401$	906599.	+	523425.i	0.281549	+	0.162553i	0.634125	−	0.773231i	$-0.281361\pi$
$401$	906599.	+	523425.i	0.281549	+	0.162553i	−0.352575	+	0.935783i	$0.614694\pi$
$402$		0			0
$403$	1.16871e6	+	2.02426e6i	0.358463	+	0.620875i
$404$	164206.	−	284413.i	0.0500535	−	0.0866953i
$405$		0			0
$406$	1.70575e6	−	534364.i	0.513571	−	0.160887i
$407$			1.72977e6i			0.517611i
$408$		0			0
$409$	−5.11918e6	+	2.95556e6i	−1.51319	+	0.873638i	−0.513305	+	0.858206i	$0.671579\pi$
$409$	−5.11918e6	+	2.95556e6i	−1.51319	+	0.873638i	−0.999881	+	0.0154319i	$0.995088\pi$
$410$	−4.88563e6	+	2.82072e6i	−1.43536	+	0.828705i
$411$		0			0
$412$			35656.4i			0.0103489i
$413$	−443670.	+	1.98394e6i	−0.127992	+	0.572338i
$414$		0			0
$415$	−113267.	+	196184.i	−0.0322837	+	0.0559170i
$416$	611621.	+	1.05936e6i	0.173280	+	0.300130i
$417$		0			0
$418$	1.57234e6	+	907793.i	0.440156	+	0.254124i
$419$	−1.02962e6			−0.286512			−0.143256	−	0.989686i	$-0.545757\pi$
$419$	−1.02962e6			−0.286512			−0.143256	+	0.989686i	$0.545757\pi$
$420$		0			0
$421$	4.77306e6			1.31248			0.656239	−	0.754553i	$-0.272146\pi$
$421$	4.77306e6			1.31248			0.656239	+	0.754553i	$0.272146\pi$
$422$	2.81097e6	+	1.62291e6i	0.768378	+	0.443623i
$423$		0			0
$424$	1.38960e6	+	2.40686e6i	0.375383	+	0.650183i
$425$	2.40828e6	−	4.17126e6i	0.646747	−	1.12020i
$426$		0			0
$427$	1.72566e6	+	5.50849e6i	0.458020	+	1.46205i
$428$		−	1.16872e6i		−	0.308391i
$429$		0			0
$430$	2.86639e6	−	1.65491e6i	0.747590	−	0.431621i
$431$	−3.53021e6	+	2.03817e6i	−0.915393	+	0.528502i	−0.882162	−	0.470945i	$-0.843913\pi$
$431$	−3.53021e6	+	2.03817e6i	−0.915393	+	0.528502i	−0.0332307	+	0.999448i	$0.510580\pi$
$432$		0			0
$433$			3.49364e6i			0.895486i	0.894162	+	0.447743i	$0.147772\pi$
$433$			3.49364e6i			0.895486i	−0.894162	+	0.447743i	$0.852228\pi$
$434$	5.46915e6	+	5.03014e6i	1.39378	+	1.28191i
$435$		0			0
$436$	348030.	−	602805.i	0.0876799	−	0.151866i
$437$	−574529.	−	995114.i	−0.143916	−	0.249270i
$438$		0			0
$439$	−4.79681e6	−	2.76944e6i	−1.18793	−	0.685853i	−0.230095	−	0.973168i	$-0.573904\pi$
$439$	−4.79681e6	−	2.76944e6i	−1.18793	−	0.685853i	−0.957836	+	0.287315i	$0.907237\pi$
$440$	−8.44358e6			−2.07919
$441$		0			0
$442$	−2.06976e6			−0.503923
$443$	−2.45834e6	−	1.41932e6i	−0.595158	−	0.343615i	0.171976	−	0.985101i	$-0.444985\pi$
$443$	−2.45834e6	−	1.41932e6i	−0.595158	−	0.343615i	−0.767134	+	0.641486i	$0.778318\pi$
$444$		0			0
$445$	−4.48517e6	−	7.76855e6i	−1.07369	−	1.85969i
$446$	−4.01989e6	+	6.96265e6i	−0.956923	+	1.65744i
$447$		0			0
$448$	−1.01998e6	−	938111.i	−0.240104	−	0.220831i
$449$			1.78776e6i			0.418497i	0.977862	+	0.209249i	$0.0671018\pi$
$449$			1.78776e6i			0.418497i	−0.977862	+	0.209249i	$0.932898\pi$
$450$		0			0
$451$	−6.53173e6	+	3.77110e6i	−1.51212	+	0.873024i
$452$	1.78808e6	−	1.03235e6i	0.411661	−	0.237673i
$453$		0			0
$454$			6.83635e6i			1.55663i
$455$	−912855.	−	2.91394e6i	−0.206716	−	0.659860i
$456$		0			0
$457$	−2.63202e6	+	4.55879e6i	−0.589521	+	1.02108i	0.404775	+	0.914416i	$0.367350\pi$
$457$	−2.63202e6	+	4.55879e6i	−0.589521	+	1.02108i	−0.994295	+	0.106663i	$0.965983\pi$
$458$	2.49450e6	+	4.32060e6i	0.555674	+	0.962455i
$459$		0			0
$460$	−3.19429e6	−	1.84422e6i	−0.703849	−	0.406368i
$461$	−1.95230e6			−0.427853			−0.213926	−	0.976850i	$-0.568625\pi$
$461$	−1.95230e6			−0.427853			−0.213926	+	0.976850i	$0.568625\pi$
$462$		0			0
$463$	3.51480e6			0.761988			0.380994	−	0.924578i	$-0.375582\pi$
$463$	3.51480e6			0.761988			0.380994	+	0.924578i	$0.375582\pi$
$464$	−2.26142e6	−	1.30563e6i	−0.487624	−	0.281530i
$465$		0			0
$466$	−2.99666e6	−	5.19037e6i	−0.639253	−	1.10722i
$467$	2.62952e6	−	4.55446e6i	0.557935	−	0.966372i	−0.439733	−	0.898128i	$-0.644927\pi$
$467$	2.62952e6	−	4.55446e6i	0.557935	−	0.966372i	0.997669	−	0.0682439i	$-0.0217396\pi$
$468$		0			0
$469$	421731.	−	1.88583e6i	0.0885326	−	0.395887i
$470$			7.61317e6i			1.58972i
$471$		0			0
$472$	1.72603e6	−	996522.i	0.356609	−	0.205888i
$473$	3.83215e6	−	2.21249e6i	0.787572	−	0.454705i
$474$		0			0
$475$			1.49799e6i			0.304631i
$476$	−1.82059e6	+	570339.i	−0.368293	+	0.115376i
$477$		0			0
$478$	2.58789e6	−	4.48236e6i	0.518056	−	0.897299i
$479$	3.97217e6	+	6.87999e6i	0.791022	+	1.37009i	0.925335	+	0.379151i	$0.123784\pi$
$479$	3.97217e6	+	6.87999e6i	0.791022	+	1.37009i	−0.134313	+	0.990939i	$0.542883\pi$
$480$		0			0
$481$	531122.	+	306644.i	0.104672	+	0.0604326i
$482$	4.72911e6			0.927175
$483$		0			0
$484$	5.68704e6			1.10350
$485$	466964.	+	269602.i	0.0901425	+	0.0520438i
$486$		0			0
$487$	226271.	+	391912.i	0.0432321	+	0.0748801i	0.886832	−	0.462092i	$-0.152901\pi$
$487$	226271.	+	391912.i	0.0432321	+	0.0748801i	−0.843600	+	0.536973i	$0.819568\pi$
$488$	2.82959e6	−	4.90100e6i	0.537866	−	0.931612i
$489$		0			0
$490$	−5.53848e6	−	7.97222e6i	−1.04208	−	1.49999i
$491$		−	344870.i		−	0.0645582i	−0.999479	−	0.0322791i	$-0.989723\pi$
$491$		−	344870.i		−	0.0645582i	0.999479	−	0.0322791i	$-0.0102765\pi$
$492$		0			0
$493$	2.00307e6	−	1.15647e6i	0.371175	−	0.214298i
$494$	557471.	−	321856.i	0.102779	−	0.0593395i
$495$		0			0
$496$		−	1.08550e7i		−	1.98119i
$497$	−3.26100e6	+	3.54560e6i	−0.592188	+	0.643871i
$498$		0			0
$499$	−254248.	+	440371.i	−0.0457095	+	0.0791712i	−0.887975	−	0.459892i	$-0.847888\pi$
$499$	−254248.	+	440371.i	−0.0457095	+	0.0791712i	0.842265	+	0.539063i	$0.181222\pi$
$500$	647577.	+	1.12164e6i	0.115842	+	0.200644i
$501$		0			0
$502$	2.74133e6	+	1.58271e6i	0.485514	+	0.280312i
$503$	1.11246e7			1.96049			0.980245	−	0.197788i	$-0.0633758\pi$
$503$	1.11246e7			1.96049			0.980245	+	0.197788i	$0.0633758\pi$
$504$		0			0
$505$	2.16220e6			0.377283
$506$	−1.47282e7	−	8.50334e6i	−2.55726	−	1.47643i
$507$		0			0
$508$	1.71028e6	+	2.96230e6i	0.294041	+	0.509295i
$509$	−1.07449e6	+	1.86108e6i	−0.183827	+	0.318397i	−0.943181	−	0.332281i	$-0.892182\pi$
$509$	−1.07449e6	+	1.86108e6i	−0.183827	+	0.318397i	0.759354	+	0.650678i	$0.225515\pi$
$510$		0			0
$511$	−5.40195e6	−	1.20804e6i	−0.915163	−	0.204659i
$512$		−	509802.i		−	0.0859462i
$513$		0			0
$514$	−3.87972e6	+	2.23996e6i	−0.647729	+	0.373966i
$515$	−203304.	+	117377.i	−0.0337775	+	0.0195014i
$516$		0			0
$517$			1.01783e7i			1.67474i
$518$	1.90263e6	+	425487.i	0.311552	+	0.0696727i
$519$		0			0
$520$	−1.49683e6	+	2.59258e6i	−0.242752	+	0.420459i
$521$	−5.45660e6	−	9.45110e6i	−0.880699	−	1.52542i	−0.850565	−	0.525869i	$-0.823740\pi$
$521$	−5.45660e6	−	9.45110e6i	−0.880699	−	1.52542i	−0.0301335	−	0.999546i	$-0.509593\pi$
$522$		0			0
$523$	5.30113e6	+	3.06061e6i	0.847450	+	0.489276i	0.859790	−	0.510648i	$-0.170595\pi$
$523$	5.30113e6	+	3.06061e6i	0.847450	+	0.489276i	−0.0123395	+	0.999924i	$0.503928\pi$
$524$	2.98859e6			0.475486
$525$		0			0
$526$	−1.09579e7			−1.72688
$527$	8.32676e6	+	4.80745e6i	1.30602	+	0.754030i
$528$		0			0
$529$	2.16347e6	+	3.74725e6i	0.336134	+	0.582201i
$530$	6.31479e6	−	1.09375e7i	0.976493	−	1.69134i
$531$		0			0
$532$	401668.	−	436724.i	0.0615302	−	0.0669002i
$533$			2.67407e6i			0.407713i
$534$		0			0
$535$	6.66377e6	−	3.84733e6i	1.00655	−	0.581132i
$536$	−1.64068e6	+	947246.i	−0.246667	+	0.142413i
$537$		0			0
$538$		−	1.28652e7i		−	1.91628i
$539$	−7.40455e6	−	1.06583e7i	−1.09781	−	1.58021i
$540$		0			0
$541$	−1.93414e6	+	3.35002e6i	−0.284115	+	0.492101i	−0.972394	−	0.233345i	$-0.925033\pi$
$541$	−1.93414e6	+	3.35002e6i	−0.284115	+	0.492101i	0.688279	+	0.725446i	$0.258366\pi$
$542$	−4.63149e6	−	8.02198e6i	−0.677209	−	1.17296i
$543$		0			0
$544$	4.35765e6	+	2.51589e6i	0.631327	+	0.364497i
$545$	4.58273e6			0.660895
$546$		0			0
$547$	5.03881e6			0.720045			0.360022	−	0.932944i	$-0.382769\pi$
$547$	5.03881e6			0.720045			0.360022	+	0.932944i	$0.382769\pi$
$548$	744242.	+	429688.i	0.105867	+	0.0611226i
$549$		0			0
$550$	1.10855e7	+	1.92007e7i	1.56260	+	2.70651i
$551$	−359672.	+	622970.i	−0.0504694	+	0.0874155i
$552$		0			0
$553$	953490.	−	298702.i	0.132588	−	0.0415360i
$554$			5.58674e6i			0.773364i
$555$		0			0
$556$	−4.80297e6	+	2.77299e6i	−0.658905	+	0.380419i
$557$	−2.84824e6	+	1.64443e6i	−0.388990	+	0.224584i	−0.681723	−	0.731611i	$-0.738769\pi$
$557$	−2.84824e6	+	1.64443e6i	−0.388990	+	0.224584i	0.292732	+	0.956194i	$0.405436\pi$
$558$		0			0
$559$		−	1.56887e6i		−	0.212353i
$560$	−3.09483e6	+	1.38390e7i	−0.417030	+	1.86481i
$561$		0			0
$562$	5.47839e6	−	9.48885e6i	0.731665	−	1.26728i
$563$	1.57992e6	+	2.73650e6i	0.210070	+	0.363852i	0.951736	−	0.306917i	$-0.0992974\pi$
$563$	1.57992e6	+	2.73650e6i	0.210070	+	0.363852i	−0.741666	+	0.670769i	$0.765964\pi$
$564$		0			0
$565$	1.17724e7	+	6.79678e6i	1.55147	+	0.895740i
$566$	−5.95641e6			−0.781526
$567$		0			0
$568$	4.72266e6			0.614208
$569$	−1.18613e7	−	6.84815e6i	−1.53587	−	0.886732i	−0.999074	−	0.0430169i	$-0.986303\pi$
$569$	−1.18613e7	−	6.84815e6i	−1.53587	−	0.886732i	−0.536791	−	0.843715i	$-0.680364\pi$
$570$		0			0
$571$	−3.28821e6	−	5.69534e6i	−0.422055	−	0.731021i	0.574085	−	0.818795i	$-0.305358\pi$
$571$	−3.28821e6	−	5.69534e6i	−0.422055	−	0.731021i	−0.996140	+	0.0877749i	$0.972024\pi$
$572$	1.38125e6	−	2.39239e6i	0.176515	−	0.305732i
$573$		0			0
$574$	2.54128e6	+	8.11207e6i	0.321939	+	1.02767i
$575$		−	1.40317e7i		−	1.76987i
$576$		0			0
$577$	−8.94955e6	+	5.16703e6i	−1.11908	+	0.646102i	−0.941166	−	0.337944i	$-0.890269\pi$
$577$	−8.94955e6	+	5.16703e6i	−1.11908	+	0.646102i	−0.177915	+	0.984046i	$0.556935\pi$
$578$	881559.	−	508968.i	0.109757	−	0.0633681i
$579$		0			0
$580$			2.30908e6i			0.285015i
$581$	251246.	+	231079.i	0.0308787	+	0.0284001i
$582$		0			0
$583$	8.44242e6	−	1.46227e7i	1.02872	−	1.78179i
$584$	2.71337e6	+	4.69970e6i	0.329213	+	0.570215i
$585$		0			0
$586$	5.13166e6	+	2.96277e6i	0.617325	+	0.356413i
$587$	1.38382e7			1.65762			0.828808	−	0.559533i	$-0.189020\pi$
$587$	1.38382e7			1.65762			0.828808	+	0.559533i	$0.189020\pi$
$588$		0			0
$589$	−2.99031e6			−0.355163
$590$	−7.84363e6	−	4.52852e6i	−0.927656	−	0.535582i
$591$		0			0
$592$	−1.42406e6	−	2.46654e6i	−0.167002	−	0.289257i
$593$	−1.57760e6	+	2.73249e6i	−0.184230	+	0.319096i	−0.943317	−	0.331894i	$-0.892313\pi$
$593$	−1.57760e6	+	2.73249e6i	−0.184230	+	0.319096i	0.759087	+	0.650990i	$0.225646\pi$
$594$		0			0
$595$	−9.24513e6	−	8.50303e6i	−1.07058	−	0.984649i
$596$		−	1.37761e6i		−	0.158858i
$597$		0			0
$598$	−5.22186e6	+	3.01484e6i	−0.597134	+	0.344756i
$599$	5.19533e6	−	2.99953e6i	0.591625	−	0.341575i	−0.174115	−	0.984725i	$-0.555706\pi$
$599$	5.19533e6	−	2.99953e6i	0.591625	−	0.341575i	0.765740	+	0.643151i	$0.222373\pi$
$600$		0			0
$601$			3.13040e6i			0.353520i	0.984254	+	0.176760i	$0.0565616\pi$
$601$			3.13040e6i			0.353520i	−0.984254	+	0.176760i	$0.943438\pi$
$602$	−1.49097e6	−	4.75933e6i	−0.167678	−	0.535248i
$603$		0			0
$604$	−1.17539e6	+	2.03583e6i	−0.131096	+	0.227064i
$605$	1.87212e7	+	3.24261e7i	2.07944	+	3.60169i
$606$		0			0
$607$	4.33625e6	+	2.50354e6i	0.477687	+	0.275792i	0.719452	−	0.694542i	$-0.244393\pi$
$607$	4.33625e6	+	2.50354e6i	0.477687	+	0.275792i	−0.241765	+	0.970335i	$0.577726\pi$
$608$	−1.56492e6			−0.171686
$609$		0			0
$610$	−2.57172e7			−2.79833
$611$	3.12521e6	+	1.80434e6i	0.338669	+	0.195531i
$612$		0			0
$613$	−7.80212e6	−	1.35137e7i	−0.838613	−	1.45252i	−0.891055	−	0.453896i	$-0.850034\pi$
$613$	−7.80212e6	−	1.35137e7i	−0.838613	−	1.45252i	0.0524417	−	0.998624i	$-0.483300\pi$
$614$	6.26669e6	−	1.08542e7i	0.670837	−	1.16192i
$615$		0			0
$616$	−2.77672e6	+	1.24165e7i	−0.294836	+	1.31840i
$617$		−	1.63258e7i		−	1.72648i	−0.504793	−	0.863241i	$-0.668431\pi$
$617$		−	1.63258e7i		−	1.72648i	0.504793	−	0.863241i	$-0.331569\pi$
$618$		0			0
$619$	3.89827e6	−	2.25066e6i	0.408926	−	0.236094i	−0.281402	−	0.959590i	$-0.590799\pi$
$619$	3.89827e6	−	2.25066e6i	0.408926	−	0.236094i	0.690328	+	0.723496i	$0.257466\pi$
$620$	−8.31282e6	+	4.79941e6i	−0.868499	+	0.501428i
$621$		0			0
$622$			12316.4i			0.00127646i
$623$	−1.28989e7	+	4.04085e6i	−1.33147	+	0.417112i
$624$		0			0
$625$	2.41928e6	−	4.19031e6i	0.247734	−	0.429087i
$626$	1.38699e6	+	2.40233e6i	0.141461	+	0.245018i
$627$		0			0
$628$	−2.05694e6	−	1.18758e6i	−0.208125	−	0.120161i
$629$	2.52274e6			0.254241
$630$		0			0
$631$	−1.03793e7			−1.03776			−0.518879	−	0.854848i	$-0.673650\pi$
$631$	−1.03793e7			−1.03776			−0.518879	+	0.854848i	$0.673650\pi$
$632$	−848336.	−	489787.i	−0.0844842	−	0.0487770i
$633$		0			0
$634$	−7.53404e6	−	1.30493e7i	−0.744397	−	1.28933i
$635$	−1.12602e7	+	1.95032e7i	−1.10818	+	1.91943i
$636$		0			0
$637$	−4.58523e6	+	384114.i	−0.447726	+	0.0375070i
$638$			1.06467e7i			1.03553i
$639$		0			0
$640$	1.59999e7	−	9.23755e6i	1.54407	−	0.891470i
$641$	5.17921e6	−	2.99022e6i	0.497873	−	0.287447i	−0.229962	−	0.973200i	$-0.573860\pi$
$641$	5.17921e6	−	2.99022e6i	0.497873	−	0.287447i	0.727835	+	0.685752i	$0.240527\pi$
$642$		0			0
$643$		−	4.70802e6i		−	0.449067i	−0.974466	−	0.224534i	$-0.927914\pi$
$643$		−	4.70802e6i		−	0.449067i	0.974466	−	0.224534i	$-0.0720858\pi$
$644$	−3.76245e6	+	4.09081e6i	−0.357483	+	0.388683i
$645$		0			0
$646$	1.32395e6	−	2.29314e6i	0.124821	−	0.216197i
$647$	1.08894e6	+	1.88609e6i	0.102269	+	0.177134i	0.912619	−	0.408811i	$-0.134057\pi$
$647$	1.08894e6	+	1.88609e6i	0.102269	+	0.177134i	−0.810350	+	0.585946i	$0.800723\pi$
$648$		0			0
$649$	−1.04864e7	−	6.05431e6i	−0.977267	−	0.564226i
$650$	7.86069e6			0.729755
$651$		0			0
$652$	−775030.			−0.0714003
$653$	3.31679e6	+	1.91495e6i	0.304393	+	0.175742i	0.644415	−	0.764676i	$-0.277101\pi$
$653$	3.31679e6	+	1.91495e6i	0.304393	+	0.175742i	−0.340022	+	0.940418i	$0.610434\pi$
$654$		0			0
$655$	9.83816e6	+	1.70402e7i	0.896005	+	1.55193i
$656$	6.20920e6	−	1.07546e7i	0.563347	−	0.975745i
$657$		0			0
$658$	1.11954e7	+	2.50363e6i	1.00803	+	0.225427i
$659$		−	1.55697e6i		−	0.139659i	−0.997559	−	0.0698293i	$-0.977755\pi$
$659$		−	1.55697e6i		−	0.139659i	0.997559	−	0.0698293i	$-0.0222455\pi$
$660$		0			0
$661$	1.71638e7	−	9.90952e6i	1.52795	−	0.882163i	0.528503	−	0.848931i	$-0.322753\pi$
$661$	1.71638e7	−	9.90952e6i	1.52795	−	0.882163i	0.999448	−	0.0332319i	$-0.0105800\pi$
$662$	8.11553e6	−	4.68551e6i	0.719734	−	0.415539i
$663$		0			0
$664$		−	334654.i		−	0.0294562i
$665$	3.81235e6	+	852558.i	0.334301	+	0.0747601i
$666$		0			0
$667$	3.36907e6	−	5.83540e6i	0.293221	−	0.507874i
$668$	1.85878e6	+	3.21949e6i	0.161171	+	0.279156i
$669$		0			0
$670$	7.45577e6	+	4.30459e6i	0.641661	+	0.370463i
$671$	−3.43820e7			−2.94798
$672$		0			0
$673$	−1.76794e7			−1.50463			−0.752313	−	0.658806i	$-0.771062\pi$
$673$	−1.76794e7			−1.50463			−0.752313	+	0.658806i	$0.771062\pi$
$674$	2.02867e7	+	1.17125e7i	1.72013	+	0.993116i
$675$		0			0
$676$	1.93624e6	+	3.35367e6i	0.162964	+	0.282263i
$677$	−4.71045e6	+	8.15874e6i	−0.394994	+	0.684150i	−0.993100	−	0.117267i	$-0.962587\pi$
$677$	−4.71045e6	+	8.15874e6i	−0.394994	+	0.684150i	0.598106	+	0.801417i	$0.295920\pi$
$678$		0			0
$679$	550022.	−	598025.i	0.0457831	−	0.0497788i
$680$			1.23143e7i			1.02126i
$681$		0			0
$682$	−3.83287e7	+	2.21291e7i	−3.15547	+	1.82181i
$683$	−5.07780e6	+	2.93167e6i	−0.416508	+	0.240471i	−0.693582	−	0.720377i	$-0.743969\pi$
$683$	−5.07780e6	+	2.93167e6i	−0.416508	+	0.240471i	0.277074	+	0.960849i	$0.410635\pi$
$684$		0			0
$685$			5.65798e6i			0.460717i
$686$	−1.35447e7	+	5.52279e6i	−1.09891	+	0.448073i
$687$		0			0
$688$	−3.64292e6	+	6.30973e6i	−0.293413	+	0.508206i
$689$	−2.99324e6	−	5.18445e6i	−0.240211	−	0.416058i
$690$		0			0
$691$	−4.42871e6	−	2.55692e6i	−0.352844	−	0.203714i	0.313093	−	0.949722i	$-0.398635\pi$
$691$	−4.42871e6	−	2.55692e6i	−0.352844	−	0.203714i	−0.665937	+	0.746008i	$0.731968\pi$
$692$	6.24374e6			0.495655
$693$		0			0
$694$	1.19865e6			0.0944703
$695$	−3.16219e7	−	1.82569e7i	−2.48328	−	1.43372i
$696$		0			0
$697$	5.49985e6	+	9.52603e6i	0.428814	+	0.742728i
$698$	3.60894e6	−	6.25086e6i	0.280376	−	0.485625i
$699$		0			0
$700$	6.91436e6	−	2.16607e6i	0.533343	−	0.167081i
$701$			1.41229e7i			1.08550i	0.839894	+	0.542750i	$0.182617\pi$
$701$			1.41229e7i			1.08550i	−0.839894	+	0.542750i	$0.817383\pi$
$702$		0			0
$703$	−679477.	+	392296.i	−0.0518545	+	0.0299382i
$704$	7.14823e6	−	4.12703e6i	0.543584	−	0.313839i
$705$		0			0
$706$		−	1.27432e7i		−	0.962204i
$707$	711052.	−	3.17958e6i	0.0534999	−	0.239233i
$708$		0			0
$709$	−8.98261e6	+	1.55583e7i	−0.671099	+	1.16238i	0.306493	+	0.951873i	$0.400844\pi$
$709$	−8.98261e6	+	1.55583e7i	−0.671099	+	1.16238i	−0.977593	+	0.210506i	$0.932489\pi$
$710$	−1.07306e7	−	1.85860e7i	−0.798877	−	1.38370i
$711$		0			0
$712$	1.14763e7	+	6.62586e6i	0.848405	+	0.489827i
$713$	2.80104e7			2.06346
$714$		0			0
$715$	1.81877e7			1.33050
$716$	1.99634e6	+	1.15259e6i	0.145530	+	0.0840215i
$717$		0			0
$718$	9.06661e6	+	1.57038e7i	0.656348	+	1.13683i
$719$	3.50151e6	−	6.06479e6i	0.252600	−	0.437516i	−0.711641	−	0.702543i	$-0.752048\pi$
$719$	3.50151e6	−	6.06479e6i	0.252600	−	0.437516i	0.964241	+	0.265027i	$0.0853810\pi$
$720$		0			0
$721$	105749.	+	337564.i	0.00757600	+	0.0241835i
$722$		−	1.57991e7i		−	1.12795i
$723$		0			0
$724$	7.50939e6	−	4.33555e6i	0.532425	−	0.307395i
$725$	−7.60740e6	+	4.39214e6i	−0.537516	+	0.310335i
$726$		0			0
$727$			1.11429e7i			0.781923i	0.920407	+	0.390961i	$0.127857\pi$
$727$			1.11429e7i			0.781923i	−0.920407	+	0.390961i	$0.872143\pi$
$728$	3.32022e6	+	3.05371e6i	0.232188	+	0.213550i
$729$		0			0
$730$	1.23305e7	−	2.13570e7i	0.856391	−	1.48331i
$731$	−3.22675e6	−	5.58890e6i	−0.223343	−	0.386841i
$732$		0			0
$733$	1.44593e6	+	834808.i	0.0994003	+	0.0573888i	0.548876	−	0.835904i	$-0.315056\pi$
$733$	1.44593e6	+	834808.i	0.0994003	+	0.0573888i	−0.449476	+	0.893292i	$0.648389\pi$
$734$	8.75680e6			0.599936
$735$		0			0
$736$	1.46587e7			0.997473
$737$	9.96783e6	+	5.75493e6i	0.675977	+	0.390276i
$738$		0			0
$739$	−5.60248e6	−	9.70379e6i	−0.377372	−	0.653627i	0.613307	−	0.789845i	$-0.289839\pi$
$739$	−5.60248e6	−	9.70379e6i	−0.377372	−	0.653627i	−0.990679	+	0.136217i	$0.956505\pi$
$740$	−1.25926e6	+	2.18110e6i	−0.0845349	+	0.146419i
$741$		0			0
$742$	−1.40073e7	−	1.28830e7i	−0.933996	−	0.859025i
$743$		−	1.17351e7i		−	0.779855i	−0.920846	−	0.389927i	$-0.872500\pi$
$743$		−	1.17351e7i		−	0.779855i	0.920846	−	0.389927i	$-0.127500\pi$
$744$		0			0
$745$	7.85479e6	−	4.53496e6i	0.518494	−	0.299353i
$746$	−2.48047e6	+	1.43210e6i	−0.163187	+	0.0942162i
$747$		0			0
$748$		−	1.13634e7i		−	0.742601i
$749$	−3.46619e6	−	1.10645e7i	−0.225761	−	0.720654i
$750$		0			0
$751$	−9.36574e6	+	1.62219e7i	−0.605958	+	1.04955i	0.385941	+	0.922523i	$0.373877\pi$
$751$	−9.36574e6	+	1.62219e7i	−0.605958	+	1.04955i	−0.991899	+	0.127027i	$0.959457\pi$
$752$	−8.37937e6	−	1.45135e7i	−0.540339	−	0.935895i
$753$		0			0
$754$	3.26904e6	+	1.88738e6i	0.209407	+	0.120901i
$755$	−1.54771e7			−0.988146
$756$		0			0
$757$	1.51170e7			0.958793			0.479396	−	0.877598i	$-0.340856\pi$
$757$	1.51170e7			0.958793			0.479396	+	0.877598i	$0.340856\pi$
$758$	7.37541e6	+	4.25820e6i	0.466244	+	0.269186i
$759$		0			0
$760$	−1.91492e6	−	3.31675e6i	−0.120259	−	0.208295i
$761$	591158.	−	1.02392e6i	0.0370034	−	0.0640918i	−0.846931	−	0.531703i	$-0.821552\pi$
$761$	591158.	−	1.02392e6i	0.0370034	−	0.0640918i	0.883934	+	0.467612i	$0.154885\pi$
$762$		0			0
$763$	1.50706e6	−	6.73903e6i	0.0937169	−	0.419070i
$764$			3.79568e6i			0.235265i
$765$		0			0
$766$	−7.99826e6	+	4.61780e6i	−0.492520	+	0.284356i
$767$	−3.71792e6	+	2.14654e6i	−0.228198	+	0.131750i
$768$		0			0
$769$		−	2.26016e6i		−	0.137823i	−0.997623	−	0.0689117i	$-0.978047\pi$
$769$		−	2.26016e6i		−	0.137823i	0.997623	−	0.0689117i	$-0.0219527\pi$
$770$	5.51744e7	−	1.72846e7i	3.35360	−	1.05059i
$771$		0			0
$772$	−1.04130e6	+	1.80359e6i	−0.0628830	+	0.108917i
$773$	7.76280e6	+	1.34456e7i	0.467272	+	0.809338i	0.999301	−	0.0373878i	$-0.0119037\pi$
$773$	7.76280e6	+	1.34456e7i	0.467272	+	0.809338i	−0.532029	+	0.846726i	$0.678570\pi$
$774$		0			0
$775$	−3.16240e7	−	1.82581e7i	−1.89131	−	1.09195i
$776$	−796556.			−0.0474856
$777$		0			0
$778$	3.49583e7			2.07063
$779$	−2.96267e6	−	1.71050e6i	−0.174920	−	0.100990i
$780$		0			0
$781$	−1.43461e7	−	2.48482e7i	−0.841601	−	1.45770i
$782$	−1.24015e7	+	2.14800e7i	−0.725198	+	1.25608i
$783$		0			0
$784$	1.93329e7	+	9.10208e6i	1.12333	+	0.528872i
$785$		−	1.56376e7i		−	0.905723i
$786$		0			0
$787$	1.33376e7	−	7.70048e6i	0.767612	−	0.443181i	−0.0644100	−	0.997924i	$-0.520517\pi$
$787$	1.33376e7	−	7.70048e6i	0.767612	−	0.443181i	0.832022	+	0.554742i	$0.187183\pi$
$788$	7.51189e6	−	4.33699e6i	0.430957	−	0.248813i
$789$		0			0
$790$			4.45150e6i			0.253769i
$791$	1.38663e7	−	1.50765e7i	0.787987	−	0.856758i
$792$		0			0
$793$	−6.09503e6	+	1.05569e7i	−0.344186	+	0.596147i
$794$	−6.03749e6	−	1.04572e7i	−0.339864	−	0.588662i
$795$		0			0
$796$	−6.62646e6	−	3.82579e6i	−0.370680	−	0.214012i
$797$	−5.69605e6			−0.317635			−0.158817	−	0.987308i	$-0.550768\pi$
$797$	−5.69605e6			−0.317635			−0.158817	+	0.987308i	$0.550768\pi$
$798$		0			0
$799$	1.48442e7			0.822602
$800$	−1.65498e7	−	9.55502e6i	−0.914255	−	0.527845i
$801$		0			0
$802$	3.51388e6	+	6.08622e6i	0.192908	+	0.334127i
$803$	1.64849e7	−	2.85527e7i	0.902191	−	1.56264i
$804$		0			0
$805$	−3.57104e7	−	7.98596e6i	−1.94225	−	0.434347i
$806$			1.56917e7i			0.850807i
$807$		0			0
$808$	−2.76624e6	+	1.59709e6i	−0.149060	+	0.0860599i
$809$	−1.04229e7	+	6.01767e6i	−0.559909	+	0.323264i	−0.753109	−	0.657896i	$-0.771447\pi$
$809$	−1.04229e7	+	6.01767e6i	−0.559909	+	0.323264i	0.193200	+	0.981159i	$0.438113\pi$
$810$		0			0
$811$			2.38612e7i			1.27392i	0.770899	+	0.636958i	$0.219807\pi$
$811$			2.38612e7i			1.27392i	−0.770899	+	0.636958i	$0.780193\pi$
$812$	3.39556e6	+	759353.i	0.180727	+	0.0404160i
$813$		0			0
$814$	−5.80619e6	+	1.00566e7i	−0.307136	+	0.531975i
$815$	−2.55133e6	−	4.41903e6i	−0.134547	−	0.233041i
$816$		0			0
$817$	1.73819e6	+	1.00355e6i	0.0911051	+	0.0525995i
$818$	−3.96828e7			−2.07357
$819$		0			0
$820$	−1.09813e7			−0.570321
$821$	2.00407e7	+	1.15705e7i	1.03766	+	0.599092i	0.919169	−	0.393864i	$-0.128862\pi$
$821$	2.00407e7	+	1.15705e7i	1.03766	+	0.599092i	0.118489	+	0.992955i	$0.462195\pi$
$822$		0			0
$823$	−1.83302e7	−	3.17489e7i	−0.943340	−	1.63391i	−0.759042	−	0.651041i	$-0.774332\pi$
$823$	−1.83302e7	−	3.17489e7i	−0.943340	−	1.63391i	−0.184297	−	0.982871i	$-0.559001\pi$
$824$	173399.	−	300337.i	0.00889672	−	0.0154096i
$825$		0			0
$826$	−9.23875e6	+	1.00451e7i	−0.471154	+	0.512274i
$827$			3.37794e7i			1.71747i	0.512421	+	0.858734i	$0.328749\pi$
$827$			3.37794e7i			1.71747i	−0.512421	+	0.858734i	$0.671251\pi$
$828$		0			0
$829$	−1.65060e7	+	9.52975e6i	−0.834173	+	0.481610i	−0.855279	−	0.518167i	$-0.826614\pi$
$829$	−1.65060e7	+	9.52975e6i	−0.834173	+	0.481610i	0.0211066	+	0.999777i	$0.493281\pi$
$830$	−1.31703e6	+	760389.i	−0.0663592	+	0.0383125i
$831$		0			0
$832$		−	2.92646e6i		−	0.146566i
$833$	−1.55443e7	+	1.07990e7i	−0.776172	+	0.539225i
$834$		0			0
$835$	−1.22378e7	+	2.11966e7i	−0.607419	+	1.05208i
$836$	1.76706e6	+	3.06064e6i	0.0874451	+	0.151459i
$837$		0			0
$838$	−5.98607e6	−	3.45606e6i	−0.294463	−	0.170009i
$839$	−8.70075e6			−0.426728			−0.213364	−	0.976973i	$-0.568442\pi$
$839$	−8.70075e6			−0.426728			−0.213364	+	0.976973i	$0.568442\pi$
$840$		0			0
$841$	1.62929e7			0.794343
$842$	2.77498e7	+	1.60214e7i	1.34890	+	0.778788i
$843$		0			0
$844$	3.15907e6	+	5.47168e6i	0.152652	+	0.264402i
$845$	−1.27479e7	+	2.20799e7i	−0.614180	+	1.06379i
$846$		0			0
$847$	5.38401e7	−	1.68666e7i	2.57868	−	0.807828i
$848$			2.78013e7i			1.32762i
$849$		0			0
$850$	2.80027e7	−	1.61674e7i	1.32939	−	0.767524i
$851$	6.36469e6	−	3.67466e6i	0.301268	−	0.173937i
$852$		0			0
$853$			1.74812e7i			0.822617i	0.911496	+	0.411309i	$0.134928\pi$
$853$			1.74812e7i			0.822617i	−0.911496	+	0.411309i	$0.865072\pi$
$854$	−8.45724e6	+	3.78179e7i	−0.396811	+	1.77440i
$855$		0			0
$856$	−5.68358e6	+	9.84426e6i	−0.265117	+	0.459196i
$857$	−9.59728e6	−	1.66230e7i	−0.446371	−	0.773138i	0.551775	−	0.833993i	$-0.313951\pi$
$857$	−9.59728e6	−	1.66230e7i	−0.446371	−	0.773138i	−0.998147	+	0.0608551i	$0.980617\pi$
$858$		0			0
$859$	8.90816e6	+	5.14313e6i	0.411912	+	0.237818i	0.691611	−	0.722270i	$-0.256901\pi$
$859$	8.90816e6	+	5.14313e6i	0.411912	+	0.237818i	−0.279699	+	0.960088i	$0.590235\pi$
$860$	6.44271e6			0.297045
$861$		0			0
$862$	−2.73654e7			−1.25440
$863$	2.21894e6	+	1.28110e6i	0.101419	+	0.0585541i	0.549851	−	0.835262i	$-0.314684\pi$
$863$	2.21894e6	+	1.28110e6i	0.101419	+	0.0585541i	−0.448433	+	0.893817i	$0.648018\pi$
$864$		0			0
$865$	2.05538e7	+	3.56003e7i	0.934012	+	1.61776i
$866$	−1.17268e7	+	2.03115e7i	−0.531356	+	0.920336i
$867$		0			0
$868$	4.32396e6	+	1.38026e7i	0.194797	+	0.621814i
$869$			5.95134e6i			0.267341i
$870$		0			0
$871$	3.53407e6	−	2.04040e6i	0.157845	−	0.0911317i
$872$	−5.86297e6	+	3.38499e6i	−0.261112	+	0.150753i
$873$		0			0
$874$		−	7.71391e6i		−	0.341583i
$875$	9.45726e6	+	8.69813e6i	0.417585	+	0.384066i
$876$		0			0
$877$	4.01808e6	−	6.95952e6i	0.176409	−	0.305549i	−0.764239	−	0.644933i	$-0.776885\pi$
$877$	4.01808e6	−	6.95952e6i	0.176409	−	0.305549i	0.940648	+	0.339384i	$0.110219\pi$
$878$	−1.85919e7	−	3.22022e7i	−0.813932	−	1.40977i
$879$		0			0
$880$	−7.31480e7	−	4.22320e7i	−3.18417	−	1.83838i
$881$	1.67424e7			0.726740			0.363370	−	0.931645i	$-0.381626\pi$
$881$	1.67424e7			0.726740			0.363370	+	0.931645i	$0.381626\pi$
$882$		0			0
$883$	−4.37874e6			−0.188994			−0.0944970	−	0.995525i	$-0.530124\pi$
$883$	−4.37874e6			−0.188994			−0.0944970	+	0.995525i	$0.530124\pi$
$884$	−3.48911e6	−	2.01444e6i	−0.150170	−	0.0867009i
$885$		0			0
$886$	−9.52825e6	−	1.65034e7i	−0.407783	−	0.706301i
$887$	−1.47795e7	+	2.55988e7i	−0.630739	+	1.09247i	0.356662	+	0.934234i	$0.383915\pi$
$887$	−1.47795e7	+	2.55988e7i	−0.630739	+	1.09247i	−0.987401	+	0.158239i	$0.949419\pi$
$888$		0			0
$889$	2.49771e7	+	2.29722e7i	1.05995	+	0.974873i
$890$		−	6.02201e7i		−	2.54839i
$891$		0			0
$892$	−1.35531e7	+	7.82489e6i	−0.570331	+	0.329281i
$893$	−3.99815e6	+	2.30833e6i	−0.167776	+	0.0968656i
$894$		0			0
$895$			1.51768e7i			0.633320i
$896$	−8.32243e6	−	2.65662e7i	−0.346322	−	1.10550i
$897$		0			0
$898$	−6.00082e6	+	1.03937e7i	−0.248325	+	0.430111i
$899$	−8.76767e6	−	1.51860e7i	−0.361813	−	0.626679i
$900$		0			0
$901$	−2.13261e7	−	1.23126e7i	−0.875183	−	0.505287i
$902$	−5.06326e7			−2.07211
$903$		0			0
$904$	−2.00815e7			−0.817288
$905$	4.94404e7	+	2.85444e7i	2.00660	+	1.15851i
$906$		0			0
$907$	2.01888e6	+	3.49681e6i	0.0814878	+	0.141141i	0.903889	−	0.427767i	$-0.140699\pi$
$907$	2.01888e6	+	3.49681e6i	0.0814878	+	0.141141i	−0.822401	+	0.568908i	$0.807366\pi$
$908$	−6.65363e6	+	1.15244e7i	−0.267821	+	0.463879i
$909$		0			0
$910$	4.47380e6	−	2.00053e7i	0.179091	−	0.800831i
$911$			4.80884e6i			0.191975i	0.995383	+	0.0959874i	$0.0306009\pi$
$911$			4.80884e6i			0.191975i	−0.995383	+	0.0959874i	$0.969399\pi$
$912$		0			0
$913$	−1.76078e6	+	1.01659e6i	−0.0699081	+	0.0403615i
$914$	−3.06043e7	+	1.76694e7i	−1.21176	+	0.699610i
$915$		0			0
$916$			9.71132e6i			0.382419i
$917$	2.82934e7	−	8.86354e6i	1.11112	−	0.348084i
$918$		0			0
$919$	1.15250e7	−	1.99618e7i	0.450144	−	0.779672i	−0.548251	−	0.836314i	$-0.684706\pi$
$919$	1.15250e7	−	1.99618e7i	0.450144	−	0.779672i	0.998395	+	0.0566422i	$0.0180394\pi$
$920$	1.79372e7	+	3.10681e7i	0.698690	+	1.21017i
$921$		0			0
$922$	−1.13504e7	−	6.55313e6i	−0.439726	−	0.253876i
$923$	−1.01728e7			−0.393038
$924$		0			0
$925$	−9.58105e6			−0.368179
$926$	2.04345e7	+	1.17978e7i	0.783134	+	0.452142i
$927$		0			0
$928$	−4.58839e6	−	7.94732e6i	−0.174900	−	0.302936i
$929$	1.71299e7	−	2.96699e7i	0.651204	−	1.12792i	−0.331628	−	0.943410i	$-0.607598\pi$
$929$	1.71299e7	−	2.96699e7i	0.651204	−	1.12792i	0.982831	−	0.184507i	$-0.0590690\pi$
$930$		0			0
$931$	2.50742e6	−	5.32580e6i	0.0948099	−	0.201377i
$932$		−	1.16663e7i		−	0.439939i
$933$		0			0
$934$	3.05752e7	−	1.76526e7i	1.14684	−	0.662127i
$935$	6.47915e7	−	3.74074e7i	2.42376	−	1.39936i
$936$		0			0
$937$		−	4.56579e7i		−	1.69890i	−0.527671	−	0.849449i	$-0.676935\pi$
$937$		−	4.56579e7i		−	1.69890i	0.527671	−	0.849449i	$-0.323065\pi$
$938$	8.78191e6	−	9.54834e6i	0.325898	−	0.354341i
$939$		0			0
$940$	−7.40968e6	+	1.28339e7i	−0.273514	+	0.473741i
$941$	2.67827e6	+	4.63890e6i	0.0986008	+	0.170782i	0.911106	−	0.412173i	$-0.135230\pi$
$941$	2.67827e6	+	4.63890e6i	0.0986008	+	0.170782i	−0.812505	+	0.582954i	$0.801897\pi$
$942$		0			0
$943$	2.77515e7	+	1.60223e7i	1.01626	+	0.586741i
$944$	1.99371e7			0.728169
$945$		0			0
$946$	2.97060e7			1.07924
$947$	6.21217e6	+	3.58660e6i	0.225096	+	0.129959i	0.608308	−	0.793701i	$-0.291849\pi$
$947$	6.21217e6	+	3.58660e6i	0.225096	+	0.129959i	−0.383211	+	0.923661i	$0.625182\pi$
$948$		0			0
$949$	−5.84469e6	−	1.01233e7i	−0.210667	−	0.364886i
$950$	−5.02818e6	+	8.70906e6i	−0.180760	+	0.313085i
$951$		0			0
$952$	1.81086e7	+	4.04963e6i	0.647577	+	0.144818i
$953$		−	1.77506e7i		−	0.633113i	−0.948574	−	0.316556i	$-0.897473\pi$
$953$		−	1.77506e7i		−	0.633113i	0.948574	−	0.316556i	$-0.102527\pi$
$954$		0			0
$955$	−2.16420e7	+	1.24950e7i	−0.767874	+	0.443332i
$956$	8.72512e6	−	5.03745e6i	0.308764	−	0.178265i
$957$		0			0
$958$			5.33322e7i			1.87748i
$959$	8.32022e6	+	1.86066e6i	0.292138	+	0.0653311i
$960$		0			0
$961$	2.21326e7	−	3.83348e7i	0.773079	−	1.33901i
$962$	2.05857e6	+	3.56555e6i	0.0717181	+	0.124219i
$963$		0			0
$964$	7.97213e6	+	4.60271e6i	0.276300	+	0.159522i
$965$	−1.37115e7			−0.473986
$966$		0			0
$967$	−8.41461e6			−0.289380			−0.144690	−	0.989477i	$-0.546218\pi$
$967$	−8.41461e6			−0.289380			−0.144690	+	0.989477i	$0.546218\pi$
$968$	−4.79024e7	−	2.76565e7i	−1.64312	−	0.948656i
$969$		0			0
$970$	1.80990e6	+	3.13485e6i	0.0617627	+	0.106976i
$971$	−1.21819e7	+	2.10997e7i	−0.414636	+	0.718170i	−0.995390	−	0.0959087i	$-0.969424\pi$
$971$	−1.21819e7	+	2.10997e7i	−0.414636	+	0.718170i	0.580754	+	0.814079i	$0.302758\pi$
$972$		0			0
$973$	−3.72463e7	+	4.04970e7i	−1.26125	+	1.37133i
$974$			3.03802e6i			0.102611i
$975$		0			0
$976$	4.90264e7	−	2.83054e7i	1.64742	−	0.951140i
$977$	−2.43018e7	+	1.40307e7i	−0.814522	+	0.470265i	−0.848524	−	0.529157i	$-0.822508\pi$
$977$	−2.43018e7	+	1.40307e7i	−0.814522	+	0.470265i	0.0340016	+	0.999422i	$0.489175\pi$
$978$		0			0
$979$		−	8.05100e7i		−	2.68468i
$980$	−1.57740e6	−	1.88297e7i	−0.0524659	−	0.626293i
$981$		0			0
$982$	1.15760e6	−	2.00502e6i	0.0383070	−	0.0663497i
$983$	−676213.	−	1.17123e6i	−0.0223203	−	0.0386599i	0.854650	−	0.519205i	$-0.173772\pi$
$983$	−676213.	−	1.17123e6i	−0.0223203	−	0.0386599i	−0.876970	+	0.480546i	$0.840439\pi$
$984$		0			0
$985$	4.94569e7	+	2.85540e7i	1.62419	+	0.937726i
$986$	1.55274e7			0.508634
$987$		0			0
$988$	1.25301e6			0.0408379
$989$	−1.62817e7	−	9.40026e6i	−0.529310	−	0.305597i
$990$		0			0
$991$	−1.76598e6	−	3.05877e6i	−0.0571219	−	0.0989381i	0.836050	−	0.548653i	$-0.184859\pi$
$991$	−1.76598e6	−	3.05877e6i	−0.0571219	−	0.0989381i	−0.893172	+	0.449715i	$0.851526\pi$
$992$	1.90739e7	−	3.30370e7i	0.615404	−	1.06591i
$993$		0			0
$994$	−3.08601e7	+	9.66761e6i	−0.990677	+	0.310351i
$995$		−	5.03766e7i		−	1.61314i
$996$		0			0
$997$	−1.10995e7	+	6.40832e6i	−0.353644	+	0.204177i	−0.666289	−	0.745693i	$-0.732118\pi$
$997$	−1.10995e7	+	6.40832e6i	−0.353644	+	0.204177i	0.312645	+	0.949870i	$0.398785\pi$
$998$	−2.95631e6	+	1.70683e6i	−0.0939560	+	0.0542455i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.p.b.26.9	yes	24
3.2	odd	2	inner	63.6.p.b.26.4	yes	24
7.2	even	3		441.6.c.b.440.5		24
7.3	odd	6	inner	63.6.p.b.17.4	✓	24
7.5	odd	6		441.6.c.b.440.19		24
21.2	odd	6		441.6.c.b.440.20		24
21.5	even	6		441.6.c.b.440.6		24
21.17	even	6	inner	63.6.p.b.17.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.p.b.17.4	✓	24	7.3	odd	6	inner
63.6.p.b.17.9	yes	24	21.17	even	6	inner
63.6.p.b.26.4	yes	24	3.2	odd	2	inner
63.6.p.b.26.9	yes	24	1.1	even	1	trivial
441.6.c.b.440.5		24	7.2	even	3
441.6.c.b.440.6		24	21.5	even	6
441.6.c.b.440.19		24	7.5	odd	6
441.6.c.b.440.20		24	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(5.81384 + 3.35662i) q^{2} +(6.53381 + 11.3169i) q^{4} +(-43.0174 + 74.5084i) q^{5} +(95.4202 + 87.7609i) q^{7} -127.098i q^{8} +O(q^{10})\)	\(q+(5.81384 + 3.35662i) q^{2} +(6.53381 + 11.3169i) q^{4} +(-43.0174 + 74.5084i) q^{5} +(95.4202 + 87.7609i) q^{7} -127.098i q^{8} +(-500.193 + 288.786i) q^{10} +(-668.722 + 386.087i) q^{11} +273.772i q^{13} +(260.178 + 830.517i) q^{14} +(635.701 - 1101.07i) q^{16} +(563.078 + 975.279i) q^{17} +(-303.319 - 175.122i) q^{19} -1124.27 q^{20} -5183.79 q^{22} +(2841.21 + 1640.37i) q^{23} +(-2138.50 - 3703.99i) q^{25} +(-918.950 + 1591.67i) q^{26} +(-369.723 + 1653.27i) q^{28} -2053.84i q^{29} +(7393.97 - 4268.91i) q^{31} +(3869.49 - 2234.05i) q^{32} +7560.15i q^{34} +(-10643.7 + 3334.36i) q^{35} +(1120.07 - 1940.01i) q^{37} +(-1175.63 - 2036.26i) q^{38} +(9469.84 + 5467.41i) q^{40} +9767.49 q^{41} -5730.56 q^{43} +(-8738.61 - 5045.24i) q^{44} +(11012.2 + 19073.7i) q^{46} +(6590.66 - 11415.4i) q^{47} +(1403.04 + 16748.3i) q^{49} -28712.5i q^{50} +(-3098.25 + 1788.78i) q^{52} +(-18937.1 + 10933.3i) q^{53} -66433.8i q^{55} +(11154.2 - 12127.7i) q^{56} +(6893.97 - 11940.7i) q^{58} +(7840.61 + 13580.3i) q^{59} +(38560.9 + 22263.1i) q^{61} +57316.4 q^{62} -10689.4 q^{64} +(-20398.3 - 11777.0i) q^{65} +(-7452.90 - 12908.8i) q^{67} +(-7358.09 + 12744.6i) q^{68} +(-73072.7 - 16341.3i) q^{70} +37157.7i q^{71} +(-36977.1 + 21348.7i) q^{73} +(13023.8 - 7519.29i) q^{74} -4576.85i q^{76} +(-97692.9 - 21847.2i) q^{77} +(3853.63 - 6674.68i) q^{79} +(54692.4 + 94730.0i) q^{80} +(56786.6 + 32785.8i) q^{82} +2633.05 q^{83} -96888.6 q^{85} +(-33316.6 - 19235.3i) q^{86} +(49070.7 + 84992.9i) q^{88} +(-52132.1 + 90295.4i) q^{89} +(-24026.5 + 26123.4i) q^{91} +42871.6i q^{92} +(76634.0 - 44244.7i) q^{94} +(26096.0 - 15066.6i) q^{95} -6267.27i q^{97} +(-48060.8 + 102082. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) \) 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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