LMFDB - Embedded newform 175.5.g.d.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,5,Mod(43,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("175.43");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	175.g (of order $4$, 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:	$18.0897435397$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	175.43
Dual form			175.5.g.d.57.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.62285 + 4.62285i) q^{2} +(6.85998 + 6.85998i) q^{3} -26.7415i q^{4} -63.4253 q^{6} +(13.0958 - 13.0958i) q^{7} +(49.6561 + 49.6561i) q^{8} +13.1187i q^{9} +O(q^{10})$	\(q+(-4.62285 + 4.62285i) q^{2} +(6.85998 + 6.85998i) q^{3} -26.7415i q^{4} -63.4253 q^{6} +(13.0958 - 13.0958i) q^{7} +(49.6561 + 49.6561i) q^{8} +13.1187i q^{9} -172.486 q^{11} +(183.446 - 183.446i) q^{12} +(26.0429 + 26.0429i) q^{13} +121.080i q^{14} -31.2422 q^{16} +(294.876 - 294.876i) q^{17} +(-60.6456 - 60.6456i) q^{18} -223.155i q^{19} +179.674 q^{21} +(797.376 - 797.376i) q^{22} +(-337.468 - 337.468i) q^{23} +681.280i q^{24} -240.785 q^{26} +(465.665 - 465.665i) q^{27} +(-350.201 - 350.201i) q^{28} -1228.04i q^{29} +1202.61 q^{31} +(-650.070 + 650.070i) q^{32} +(-1183.25 - 1183.25i) q^{33} +2726.33i q^{34} +350.812 q^{36} +(-481.756 + 481.756i) q^{37} +(1031.61 + 1031.61i) q^{38} +357.308i q^{39} -2145.36 q^{41} +(-830.605 + 830.605i) q^{42} +(1748.18 + 1748.18i) q^{43} +4612.53i q^{44} +3120.13 q^{46} +(2202.77 - 2202.77i) q^{47} +(-214.321 - 214.321i) q^{48} -343.000i q^{49} +4045.69 q^{51} +(696.426 - 696.426i) q^{52} +(3012.92 + 3012.92i) q^{53} +4305.39i q^{54} +1300.57 q^{56} +(1530.84 - 1530.84i) q^{57} +(5677.02 + 5677.02i) q^{58} -1080.84i q^{59} -1793.51 q^{61} +(-5559.50 + 5559.50i) q^{62} +(171.799 + 171.799i) q^{63} -6510.23i q^{64} +10940.0 q^{66} +(-1517.25 + 1517.25i) q^{67} +(-7885.41 - 7885.41i) q^{68} -4630.05i q^{69} -7861.02 q^{71} +(-651.422 + 651.422i) q^{72} +(654.271 + 654.271i) q^{73} -4454.17i q^{74} -5967.48 q^{76} +(-2258.84 + 2258.84i) q^{77} +(-1651.78 - 1651.78i) q^{78} +1243.55i q^{79} +7451.51 q^{81} +(9917.66 - 9917.66i) q^{82} +(-6982.20 - 6982.20i) q^{83} -4804.74i q^{84} -16163.1 q^{86} +(8424.30 - 8424.30i) q^{87} +(-8564.98 - 8564.98i) q^{88} -9246.50i q^{89} +682.106 q^{91} +(-9024.38 + 9024.38i) q^{92} +(8249.91 + 8249.91i) q^{93} +20366.1i q^{94} -8918.94 q^{96} +(8539.81 - 8539.81i) q^{97} +(1585.64 + 1585.64i) q^{98} -2262.79i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 248 q^{6}+O(q^{10}) $ 32 * q + 248 * q^6	$ 32 q + 248 q^{6} - 1008 q^{11} - 1732 q^{16} - 392 q^{21} - 4296 q^{26} + 9064 q^{31} - 14388 q^{36} + 1440 q^{41} + 26076 q^{46} + 11576 q^{51} + 12936 q^{56} - 6664 q^{61} + 20664 q^{66} - 11496 q^{71} - 78624 q^{76} - 24112 q^{81} - 17412 q^{86} + 25480 q^{91} + 144 q^{96}+O(q^{100}) $ 32 * q + 248 * q^6 - 1008 * q^11 - 1732 * q^16 - 392 * q^21 - 4296 * q^26 + 9064 * q^31 - 14388 * q^36 + 1440 * q^41 + 26076 * q^46 + 11576 * q^51 + 12936 * q^56 - 6664 * q^61 + 20664 * q^66 - 11496 * q^71 - 78624 * q^76 - 24112 * q^81 - 17412 * q^86 + 25480 * q^91 + 144 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−4.62285	+	4.62285i	−1.15571	+	1.15571i	−0.170324	+	0.985388i	$0.554481\pi$
$2$	−4.62285	+	4.62285i	−1.15571	+	1.15571i	−0.985388	+	0.170324i	$0.945519\pi$
$3$	6.85998	+	6.85998i	0.762220	+	0.762220i	0.976723	−	0.214503i	$-0.0688132\pi$
$3$	6.85998	+	6.85998i	0.762220	+	0.762220i	−0.214503	+	0.976723i	$0.568813\pi$
$4$		−	26.7415i		−	1.67134i
$5$		0			0
$5$		0			0
$6$	−63.4253			−1.76181
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$8$	49.6561	+	49.6561i	0.775877	+	0.775877i
$9$			13.1187i			0.161959i
$10$		0			0
$11$	−172.486			−1.42550			−0.712752	−	0.701416i	$-0.752551\pi$
$11$	−172.486			−1.42550			−0.712752	+	0.701416i	$0.752551\pi$
$12$	183.446	−	183.446i	1.27393	−	1.27393i
$13$	26.0429	+	26.0429i	0.154100	+	0.154100i	0.779946	−	0.625846i	$-0.215246\pi$
$13$	26.0429	+	26.0429i	0.154100	+	0.154100i	−0.625846	+	0.779946i	$0.715246\pi$
$14$			121.080i			0.617754i
$15$		0			0
$16$	−31.2422			−0.122040
$17$	294.876	−	294.876i	1.02033	−	1.02033i	0.0205430	−	0.999789i	$-0.493460\pi$
$17$	294.876	−	294.876i	1.02033	−	1.02033i	0.999789	−	0.0205430i	$-0.00653951\pi$
$18$	−60.6456	−	60.6456i	−0.187178	−	0.187178i
$19$		−	223.155i		−	0.618157i	−0.951037	−	0.309079i	$-0.899979\pi$
$19$		−	223.155i		−	0.618157i	0.951037	−	0.309079i	$-0.100021\pi$
$20$		0			0
$21$	179.674			0.407424
$22$	797.376	−	797.376i	1.64747	−	1.64747i
$23$	−337.468	−	337.468i	−0.637936	−	0.637936i	0.312110	−	0.950046i	$-0.398964\pi$
$23$	−337.468	−	337.468i	−0.637936	−	0.637936i	−0.950046	+	0.312110i	$0.898964\pi$
$24$			681.280i			1.18278i
$25$		0			0
$26$	−240.785			−0.356191
$27$	465.665	−	465.665i	0.638772	−	0.638772i
$28$	−350.201	−	350.201i	−0.446685	−	0.446685i
$29$		−	1228.04i		−	1.46021i	−0.683336	−	0.730104i	$-0.739472\pi$
$29$		−	1228.04i		−	1.46021i	0.683336	−	0.730104i	$-0.260528\pi$
$30$		0			0
$31$	1202.61			1.25142			0.625710	−	0.780056i	$-0.284809\pi$
$31$	1202.61			1.25142			0.625710	+	0.780056i	$0.284809\pi$
$32$	−650.070	+	650.070i	−0.634834	+	0.634834i
$33$	−1183.25	−	1183.25i	−1.08655	−	1.08655i
$34$			2726.33i			2.35842i
$35$		0			0
$36$	350.812			0.270688
$37$	−481.756	+	481.756i	−0.351904	+	0.351904i	−0.860817	−	0.508914i	$-0.830047\pi$
$37$	−481.756	+	481.756i	−0.351904	+	0.351904i	0.508914	+	0.860817i	$0.330047\pi$
$38$	1031.61	+	1031.61i	0.714412	+	0.714412i
$39$			357.308i			0.234916i
$40$		0			0
$41$	−2145.36			−1.27624			−0.638120	−	0.769937i	$-0.720287\pi$
$41$	−2145.36			−1.27624			−0.638120	+	0.769937i	$0.720287\pi$
$42$	−830.605	+	830.605i	−0.470865	+	0.470865i
$43$	1748.18	+	1748.18i	0.945471	+	0.945471i	0.998588	−	0.0531168i	$-0.0169156\pi$
$43$	1748.18	+	1748.18i	0.945471	+	0.945471i	−0.0531168	+	0.998588i	$0.516916\pi$
$44$			4612.53i			2.38250i
$45$		0			0
$46$	3120.13			1.47454
$47$	2202.77	−	2202.77i	0.997179	−	0.997179i	−0.00281662	−	0.999996i	$-0.500897\pi$
$47$	2202.77	−	2202.77i	0.997179	−	0.997179i	0.999996	+	0.00281662i	$0.000896559\pi$
$48$	−214.321	−	214.321i	−0.0930211	−	0.0930211i
$49$		−	343.000i		−	0.142857i
$50$		0			0
$51$	4045.69			1.55544
$52$	696.426	−	696.426i	0.257554	−	0.257554i
$53$	3012.92	+	3012.92i	1.07259	+	1.07259i	0.997150	+	0.0754442i	$0.0240375\pi$
$53$	3012.92	+	3012.92i	1.07259	+	1.07259i	0.0754442	+	0.997150i	$0.475963\pi$
$54$			4305.39i			1.47647i
$55$		0			0
$56$	1300.57			0.414724
$57$	1530.84	−	1530.84i	0.471172	−	0.471172i
$58$	5677.02	+	5677.02i	1.68758	+	1.68758i
$59$		−	1080.84i		−	0.310496i	−0.987876	−	0.155248i	$-0.950382\pi$
$59$		−	1080.84i		−	0.310496i	0.987876	−	0.155248i	$-0.0496177\pi$
$60$		0			0
$61$	−1793.51			−0.481997			−0.240998	−	0.970526i	$-0.577475\pi$
$61$	−1793.51			−0.481997			−0.240998	+	0.970526i	$0.577475\pi$
$62$	−5559.50	+	5559.50i	−1.44628	+	1.44628i
$63$	171.799	+	171.799i	0.0432853	+	0.0432853i
$64$		−	6510.23i		−	1.58941i
$65$		0			0
$66$	10940.0			2.51147
$67$	−1517.25	+	1517.25i	−0.337993	+	0.337993i	−0.855611	−	0.517619i	$-0.826819\pi$
$67$	−1517.25	+	1517.25i	−0.337993	+	0.337993i	0.517619	+	0.855611i	$0.326819\pi$
$68$	−7885.41	−	7885.41i	−1.70532	−	1.70532i
$69$		−	4630.05i		−	0.972495i
$70$		0			0
$71$	−7861.02			−1.55942			−0.779708	−	0.626143i	$-0.784633\pi$
$71$	−7861.02			−1.55942			−0.779708	+	0.626143i	$0.784633\pi$
$72$	−651.422	+	651.422i	−0.125660	+	0.125660i
$73$	654.271	+	654.271i	0.122776	+	0.122776i	0.765825	−	0.643049i	$-0.222331\pi$
$73$	654.271	+	654.271i	0.122776	+	0.122776i	−0.643049	+	0.765825i	$0.722331\pi$
$74$		−	4454.17i		−	0.813398i
$75$		0			0
$76$	−5967.48			−1.03315
$77$	−2258.84	+	2258.84i	−0.380982	+	0.380982i
$78$	−1651.78	−	1651.78i	−0.271496	−	0.271496i
$79$			1243.55i			0.199255i	0.995025	+	0.0996275i	$0.0317651\pi$
$79$			1243.55i			0.199255i	−0.995025	+	0.0996275i	$0.968235\pi$
$80$		0			0
$81$	7451.51			1.13573
$82$	9917.66	−	9917.66i	1.47497	−	1.47497i
$83$	−6982.20	−	6982.20i	−1.01353	−	1.01353i	−0.999907	−	0.0136219i	$-0.995664\pi$
$83$	−6982.20	−	6982.20i	−1.01353	−	1.01353i	−0.0136219	−	0.999907i	$-0.504336\pi$
$84$		−	4804.74i		−	0.680944i
$85$		0			0
$86$	−16163.1			−2.18539
$87$	8424.30	−	8424.30i	1.11300	−	1.11300i
$88$	−8564.98	−	8564.98i	−1.10602	−	1.10602i
$89$		−	9246.50i		−	1.16734i	−0.811991	−	0.583670i	$-0.801616\pi$
$89$		−	9246.50i		−	1.16734i	0.811991	−	0.583670i	$-0.198384\pi$
$90$		0			0
$91$	682.106			0.0823700
$92$	−9024.38	+	9024.38i	−1.06621	+	1.06621i
$93$	8249.91	+	8249.91i	0.953857	+	0.953857i
$94$			20366.1i			2.30490i
$95$		0			0
$96$	−8918.94			−0.967767
$97$	8539.81	−	8539.81i	0.907621	−	0.907621i	−0.0884588	−	0.996080i	$-0.528194\pi$
$97$	8539.81	−	8539.81i	0.907621	−	0.907621i	0.996080	+	0.0884588i	$0.0281942\pi$
$98$	1585.64	+	1585.64i	0.165102	+	0.165102i
$99$		−	2262.79i		−	0.230873i
$100$		0			0
$101$	6421.19			0.629467			0.314734	−	0.949180i	$-0.398085\pi$
$101$	6421.19			0.629467			0.314734	+	0.949180i	$0.398085\pi$
$102$	−18702.6	+	18702.6i	−1.79764	+	1.79764i
$103$	6962.39	+	6962.39i	0.656272	+	0.656272i	0.954496	−	0.298224i	$-0.0963942\pi$
$103$	6962.39	+	6962.39i	0.656272	+	0.656272i	−0.298224	+	0.954496i	$0.596394\pi$
$104$			2586.38i			0.239125i
$105$		0			0
$106$	−27856.5			−2.47922
$107$	−775.586	+	775.586i	−0.0677427	+	0.0677427i	−0.740166	−	0.672424i	$-0.765253\pi$
$107$	−775.586	+	775.586i	−0.0677427	+	0.0677427i	0.672424	+	0.740166i	$0.265253\pi$
$108$	−12452.6	−	12452.6i	−1.06761	−	1.06761i
$109$		−	19331.6i		−	1.62710i	−0.581495	−	0.813550i	$-0.697532\pi$
$109$		−	19331.6i		−	1.62710i	0.581495	−	0.813550i	$-0.302468\pi$
$110$		0			0
$111$	−6609.67			−0.536456
$112$	−409.141	+	409.141i	−0.0326165	+	0.0326165i
$113$	−7047.82	−	7047.82i	−0.551947	−	0.551947i	0.375055	−	0.927003i	$-0.377624\pi$
$113$	−7047.82	−	7047.82i	−0.551947	−	0.551947i	−0.927003	+	0.375055i	$0.877624\pi$
$114$			14153.7i			1.08908i
$115$		0			0
$116$	−32839.5			−2.44051
$117$	−341.648	+	341.648i	−0.0249579	+	0.0249579i
$118$	4996.54	+	4996.54i	0.358844	+	0.358844i
$119$		−	7723.27i		−	0.545390i
$120$		0			0
$121$	15110.4			1.03206
$122$	8291.12	−	8291.12i	0.557049	−	0.557049i
$123$	−14717.1	−	14717.1i	−0.972775	−	0.972775i
$124$		−	32159.7i		−	2.09155i
$125$		0			0
$126$	−1588.41			−0.100051
$127$	−8849.78	+	8849.78i	−0.548688	+	0.548688i	−0.926061	−	0.377373i	$-0.876827\pi$
$127$	−8849.78	+	8849.78i	−0.548688	+	0.548688i	0.377373	+	0.926061i	$0.376827\pi$
$128$	19694.7	+	19694.7i	1.20207	+	1.20207i
$129$			23984.9i			1.44131i
$130$		0			0
$131$	29995.2			1.74787			0.873936	−	0.486040i	$-0.161559\pi$
$131$	29995.2			1.74787			0.873936	+	0.486040i	$0.161559\pi$
$132$	−31641.8	+	31641.8i	−1.81599	+	1.81599i
$133$	−2922.39	−	2922.39i	−0.165209	−	0.165209i
$134$		−	14028.0i		−	0.781244i
$135$		0			0
$136$	29284.8			1.58330
$137$	−20217.5	+	20217.5i	−1.07718	+	1.07718i	−0.0804160	+	0.996761i	$0.525625\pi$
$137$	−20217.5	+	20217.5i	−1.07718	+	1.07718i	−0.996761	+	0.0804160i	$0.974375\pi$
$138$	21404.0	+	21404.0i	1.12392	+	1.12392i
$139$		−	23970.9i		−	1.24067i	−0.784338	−	0.620333i	$-0.786997\pi$
$139$		−	23970.9i		−	1.24067i	0.784338	−	0.620333i	$-0.213003\pi$
$140$		0			0
$141$	30221.9			1.52014
$142$	36340.3	−	36340.3i	1.80224	−	1.80224i
$143$	−4492.04	−	4492.04i	−0.219670	−	0.219670i
$144$		−	409.855i		−	0.0197654i
$145$		0			0
$146$	−6049.19			−0.283787
$147$	2352.97	−	2352.97i	0.108889	−	0.108889i
$148$	12882.9	+	12882.9i	0.588151	+	0.588151i
$149$		−	4953.16i		−	0.223105i	−0.993759	−	0.111553i	$-0.964418\pi$
$149$		−	4953.16i		−	0.223105i	0.993759	−	0.111553i	$-0.0355824\pi$
$150$		0			0
$151$	18226.3			0.799366			0.399683	−	0.916653i	$-0.369120\pi$
$151$	18226.3			0.799366			0.399683	+	0.916653i	$0.369120\pi$
$152$	11081.0	−	11081.0i	0.479614	−	0.479614i
$153$	3868.38	+	3868.38i	0.165252	+	0.165252i
$154$		−	20884.6i		−	0.880611i
$155$		0			0
$156$	9554.93			0.392625
$157$	17966.9	−	17966.9i	0.728911	−	0.728911i	−0.241492	−	0.970403i	$-0.577637\pi$
$157$	17966.9	−	17966.9i	0.728911	−	0.728911i	0.970403	+	0.241492i	$0.0776366\pi$
$158$	−5748.74	−	5748.74i	−0.230281	−	0.230281i
$159$			41337.1i			1.63511i
$160$		0			0
$161$	−8838.82			−0.340991
$162$	−34447.2	+	34447.2i	−1.31257	+	1.31257i
$163$	−14457.8	−	14457.8i	−0.544160	−	0.544160i	0.380586	−	0.924746i	$-0.375722\pi$
$163$	−14457.8	−	14457.8i	−0.544160	−	0.544160i	−0.924746	+	0.380586i	$0.875722\pi$
$164$			57370.0i			2.13303i
$165$		0			0
$166$	64555.3			2.34270
$167$	−17249.0	+	17249.0i	−0.618488	+	0.618488i	−0.945144	−	0.326655i	$-0.894078\pi$
$167$	−17249.0	+	17249.0i	−0.618488	+	0.618488i	0.326655	+	0.945144i	$0.394078\pi$
$168$	8921.91	+	8921.91i	0.316111	+	0.316111i
$169$		−	27204.5i		−	0.952506i
$170$		0			0
$171$	2927.49			0.100116
$172$	46748.8	−	46748.8i	1.58021	−	1.58021i
$173$	12009.4	+	12009.4i	0.401262	+	0.401262i	0.878678	−	0.477416i	$-0.158426\pi$
$173$	12009.4	+	12009.4i	0.401262	+	0.401262i	−0.477416	+	0.878678i	$0.658426\pi$
$174$			77888.5i			2.57262i
$175$		0			0
$176$	5388.83			0.173968
$177$	7414.52	−	7414.52i	0.236666	−	0.236666i
$178$	42745.2	+	42745.2i	1.34911	+	1.34911i
$179$			41320.5i			1.28961i	0.764346	+	0.644807i	$0.223062\pi$
$179$			41320.5i			1.28961i	−0.764346	+	0.644807i	$0.776938\pi$
$180$		0			0
$181$	−37181.6			−1.13494			−0.567468	−	0.823396i	$-0.692077\pi$
$181$	−37181.6			−1.13494			−0.567468	+	0.823396i	$0.692077\pi$
$182$	−3153.27	+	3153.27i	−0.0951960	+	0.0951960i
$183$	−12303.4	−	12303.4i	−0.367387	−	0.367387i
$184$		−	33514.7i		−	0.989919i
$185$		0			0
$186$	−76276.2			−2.20477
$187$	−50862.0	+	50862.0i	−1.45449	+	1.45449i
$188$	−58905.3	−	58905.3i	−1.66663	−	1.66663i
$189$		−	12196.5i		−	0.341438i
$190$		0			0
$191$	1197.41			0.0328227			0.0164114	−	0.999865i	$-0.494776\pi$
$191$	1197.41			0.0328227			0.0164114	+	0.999865i	$0.494776\pi$
$192$	44660.0	−	44660.0i	1.21148	−	1.21148i
$193$	9123.80	+	9123.80i	0.244941	+	0.244941i	0.818891	−	0.573950i	$-0.194590\pi$
$193$	9123.80	+	9123.80i	0.244941	+	0.244941i	−0.573950	+	0.818891i	$0.694590\pi$
$194$			78956.5i			2.09790i
$195$		0			0
$196$	−9172.32			−0.238763
$197$	23440.8	−	23440.8i	0.604004	−	0.604004i	−0.337369	−	0.941373i	$-0.609537\pi$
$197$	23440.8	−	23440.8i	0.604004	−	0.604004i	0.941373	+	0.337369i	$0.109537\pi$
$198$	10460.5	+	10460.5i	0.266823	+	0.266823i
$199$			11182.0i			0.282367i	0.989983	+	0.141183i	$0.0450907\pi$
$199$			11182.0i			0.282367i	−0.989983	+	0.141183i	$0.954909\pi$
$200$		0			0
$201$	−20816.6			−0.515250
$202$	−29684.2	+	29684.2i	−0.727483	+	0.727483i
$203$	−16082.1	−	16082.1i	−0.390257	−	0.390257i
$204$		−	108188.i		−	2.59966i
$205$		0			0
$206$	−64372.1			−1.51692
$207$	4427.13	−	4427.13i	0.103319	−	0.103319i
$208$	−813.637	−	813.637i	−0.0188063	−	0.0188063i
$209$			38491.0i			0.881185i
$210$		0			0
$211$	−15642.1			−0.351341			−0.175670	−	0.984449i	$-0.556209\pi$
$211$	−15642.1			−0.351341			−0.175670	+	0.984449i	$0.556209\pi$
$212$	80569.8	−	80569.8i	1.79267	−	1.79267i
$213$	−53926.4	−	53926.4i	−1.18862	−	1.18862i
$214$		−	7170.84i		−	0.156582i
$215$		0			0
$216$	46246.2			0.991217
$217$	15749.2	−	15749.2i	0.334456	−	0.334456i
$218$	89366.9	+	89366.9i	1.88046	+	1.88046i
$219$			8976.58i			0.187164i
$220$		0			0
$221$	15358.9			0.314467
$222$	30555.5	−	30555.5i	0.619989	−	0.619989i
$223$	−55429.7	−	55429.7i	−1.11464	−	1.11464i	−0.992515	−	0.122120i	$-0.961031\pi$
$223$	−55429.7	−	55429.7i	−1.11464	−	1.11464i	−0.122120	−	0.992515i	$-0.538969\pi$
$224$			17026.4i			0.339333i
$225$		0			0
$226$	65162.0			1.27578
$227$	46119.3	−	46119.3i	0.895017	−	0.895017i	−0.0999730	−	0.994990i	$-0.531876\pi$
$227$	46119.3	−	46119.3i	0.895017	−	0.895017i	0.994990	+	0.0999730i	$0.0318757\pi$
$228$	−40936.8	−	40936.8i	−0.787489	−	0.787489i
$229$		−	35036.6i		−	0.668114i	−0.942553	−	0.334057i	$-0.891582\pi$
$229$		−	35036.6i		−	0.668114i	0.942553	−	0.334057i	$-0.108418\pi$
$230$		0			0
$231$	−30991.2			−0.580784
$232$	60979.5	−	60979.5i	1.13294	−	1.13294i
$233$	−49452.5	−	49452.5i	−0.910912	−	0.910912i	0.0854321	−	0.996344i	$-0.472773\pi$
$233$	−49452.5	−	49452.5i	−0.910912	−	0.910912i	−0.996344	+	0.0854321i	$0.972773\pi$
$234$		−	3158.78i		−	0.0576882i
$235$		0			0
$236$	−28903.1			−0.518945
$237$	−8530.73	+	8530.73i	−0.151876	+	0.151876i
$238$	35703.5	+	35703.5i	0.630314	+	0.630314i
$239$			82663.3i			1.44716i	0.690240	+	0.723581i	$0.257505\pi$
$239$			82663.3i			1.44716i	−0.690240	+	0.723581i	$0.742495\pi$
$240$		0			0
$241$	49073.7			0.844918			0.422459	−	0.906382i	$-0.361167\pi$
$241$	49073.7			0.844918			0.422459	+	0.906382i	$0.361167\pi$
$242$	−69853.1	+	69853.1i	−1.19277	+	1.19277i
$243$	13398.4	+	13398.4i	0.226903	+	0.226903i
$244$			47961.0i			0.805581i
$245$		0			0
$246$	136070.			2.24850
$247$	5811.60	−	5811.60i	0.0952581	−	0.0952581i
$248$	59717.2	+	59717.2i	0.970948	+	0.970948i
$249$		−	95795.5i		−	1.54506i
$250$		0			0
$251$	26692.3			0.423680			0.211840	−	0.977304i	$-0.432054\pi$
$251$	26692.3			0.423680			0.211840	+	0.977304i	$0.432054\pi$
$252$	4594.17	−	4594.17i	0.0723445	−	0.0723445i
$253$	58208.5	+	58208.5i	0.909379	+	0.909379i
$254$		−	81822.4i		−	1.26825i
$255$		0			0
$256$	−77927.3			−1.18908
$257$	−29469.9	+	29469.9i	−0.446183	+	0.446183i	−0.894083	−	0.447901i	$-0.852172\pi$
$257$	−29469.9	+	29469.9i	−0.446183	+	0.446183i	0.447901	+	0.894083i	$0.352172\pi$
$258$	−110879.	−	110879.i	−1.66574	−	1.66574i
$259$			12618.0i			0.188100i
$260$		0			0
$261$	16110.2			0.236494
$262$	−138663.	+	138663.i	−2.02004	+	2.02004i
$263$	−19630.8	−	19630.8i	−0.283809	−	0.283809i	0.550817	−	0.834626i	$-0.314316\pi$
$263$	−19630.8	−	19630.8i	−0.283809	−	0.283809i	−0.834626	+	0.550817i	$0.814316\pi$
$264$		−	117511.i		−	1.68605i
$265$		0			0
$266$	27019.5			0.381869
$267$	63430.8	−	63430.8i	0.889770	−	0.889770i
$268$	40573.4	+	40573.4i	0.564901	+	0.564901i
$269$		−	31695.7i		−	0.438021i	−0.975722	−	0.219011i	$-0.929717\pi$
$269$		−	31695.7i		−	0.438021i	0.975722	−	0.219011i	$-0.0702830\pi$
$270$		0			0
$271$	−77598.0			−1.05660			−0.528301	−	0.849057i	$-0.677171\pi$
$271$	−77598.0			−1.05660			−0.528301	+	0.849057i	$0.677171\pi$
$272$	−9212.56	+	9212.56i	−0.124521	+	0.124521i
$273$	4679.23	+	4679.23i	0.0627841	+	0.0627841i
$274$		−	186925.i		−	2.48981i
$275$		0			0
$276$	−123814.			−1.62537
$277$	−33166.3	+	33166.3i	−0.432252	+	0.432252i	−0.889394	−	0.457142i	$-0.848873\pi$
$277$	−33166.3	+	33166.3i	−0.432252	+	0.432252i	0.457142	+	0.889394i	$0.348873\pi$
$278$	110814.	+	110814.i	1.43385	+	1.43385i
$279$			15776.7i			0.202678i
$280$		0			0
$281$	−124135.			−1.57211			−0.786053	−	0.618160i	$-0.787879\pi$
$281$	−124135.			−1.57211			−0.786053	+	0.618160i	$0.787879\pi$
$282$	−139711.	+	139711.i	−1.75684	+	1.75684i
$283$	21549.5	+	21549.5i	0.269069	+	0.269069i	0.828725	−	0.559656i	$-0.189067\pi$
$283$	21549.5	+	21549.5i	0.269069	+	0.269069i	−0.559656	+	0.828725i	$0.689067\pi$
$284$			210215.i			2.60632i
$285$		0			0
$286$	41532.0			0.507751
$287$	−28095.2	+	28095.2i	−0.341089	+	0.341089i
$288$	−8528.05	−	8528.05i	−0.102817	−	0.102817i
$289$		−	90382.7i		−	1.08215i
$290$		0			0
$291$	117166.			1.38361
$292$	17496.2	−	17496.2i	0.205200	−	0.205200i
$293$	18857.8	+	18857.8i	0.219663	+	0.219663i	0.808356	−	0.588694i	$-0.200358\pi$
$293$	18857.8	+	18857.8i	0.219663	+	0.219663i	−0.588694	+	0.808356i	$0.700358\pi$
$294$			21754.9i			0.251688i
$295$		0			0
$296$	−47844.3			−0.546068
$297$	−80320.6	+	80320.6i	−0.910572	+	0.910572i
$298$	22897.7	+	22897.7i	0.257846	+	0.257846i
$299$		−	17577.3i		−	0.196612i
$300$		0			0
$301$	45787.5			0.505376
$302$	−84257.6	+	84257.6i	−0.923837	+	0.923837i
$303$	44049.3	+	44049.3i	0.479792	+	0.479792i
$304$			6971.84i			0.0754397i
$305$		0			0
$306$	−35765.9			−0.381967
$307$	−23749.9	+	23749.9i	−0.251991	+	0.251991i	−0.821786	−	0.569796i	$-0.807022\pi$
$307$	−23749.9	+	23749.9i	−0.251991	+	0.251991i	0.569796	+	0.821786i	$0.307022\pi$
$308$	60404.7	+	60404.7i	0.636751	+	0.636751i
$309$			95523.7i			1.00045i
$310$		0			0
$311$	20548.8			0.212454			0.106227	−	0.994342i	$-0.466123\pi$
$311$	20548.8			0.212454			0.106227	+	0.994342i	$0.466123\pi$
$312$	−17742.5	+	17742.5i	−0.182266	+	0.182266i
$313$	−5019.39	−	5019.39i	−0.0512345	−	0.0512345i	0.681025	−	0.732260i	$-0.261534\pi$
$313$	−5019.39	−	5019.39i	−0.0512345	−	0.0512345i	−0.732260	+	0.681025i	$0.761534\pi$
$314$			166117.i			1.68482i
$315$		0			0
$316$	33254.3			0.333023
$317$	−66659.0	+	66659.0i	−0.663346	+	0.663346i	−0.956167	−	0.292821i	$-0.905406\pi$
$317$	−66659.0	+	66659.0i	−0.663346	+	0.663346i	0.292821	+	0.956167i	$0.405406\pi$
$318$	−191095.	−	191095.i	−1.88971	−	1.88971i
$319$			211819.i			2.08153i
$320$		0			0
$321$	−10641.0			−0.103270
$322$	40860.5	−	40860.5i	0.394087	−	0.394087i
$323$	−65802.9	−	65802.9i	−0.630725	−	0.630725i
$324$		−	199264.i		−	1.89819i
$325$		0			0
$326$	133672.			1.25778
$327$	132614.	−	132614.i	1.24021	−	1.24021i
$328$	−106530.	−	106530.i	−0.990204	−	0.990204i
$329$		−	57694.1i		−	0.533015i
$330$		0			0
$331$	97809.4			0.892739			0.446369	−	0.894849i	$-0.352717\pi$
$331$	97809.4			0.892739			0.446369	+	0.894849i	$0.352717\pi$
$332$	−186714.	+	186714.i	−1.69395	+	1.69395i
$333$	−6319.99	−	6319.99i	−0.0569939	−	0.0569939i
$334$		−	159479.i		−	1.42959i
$335$		0			0
$336$	−5613.40			−0.0497219
$337$	81259.9	−	81259.9i	0.715511	−	0.715511i	−0.252172	−	0.967683i	$-0.581145\pi$
$337$	81259.9	−	81259.9i	0.715511	−	0.715511i	0.967683	+	0.252172i	$0.0811447\pi$
$338$	125762.	+	125762.i	1.10082	+	1.10082i
$339$		−	96695.8i		−	0.841411i
$340$		0			0
$341$	−207434.			−1.78390
$342$	−13533.3	+	13533.3i	−0.115705	+	0.115705i
$343$	−4491.86	−	4491.86i	−0.0381802	−	0.0381802i
$344$			173615.i			1.46714i
$345$		0			0
$346$	−111035.			−0.927487
$347$	71853.6	−	71853.6i	0.596746	−	0.596746i	−0.342699	−	0.939445i	$-0.611341\pi$
$347$	71853.6	−	71853.6i	0.596746	−	0.596746i	0.939445	+	0.342699i	$0.111341\pi$
$348$	−225278.	−	225278.i	−1.86020	−	1.86020i
$349$		−	134969.i		−	1.10811i	−0.832481	−	0.554054i	$-0.813080\pi$
$349$		−	134969.i		−	1.10811i	0.832481	−	0.554054i	$-0.186920\pi$
$350$		0			0
$351$	24254.5			0.196870
$352$	112128.	−	112128.i	0.904958	−	0.904958i
$353$	126341.	+	126341.i	1.01390	+	1.01390i	0.999902	+	0.0139944i	$0.00445469\pi$
$353$	126341.	+	126341.i	1.01390	+	1.01390i	0.0139944	+	0.999902i	$0.495545\pi$
$354$			68552.4i			0.547036i
$355$		0			0
$356$	−247265.			−1.95102
$357$	52981.5	−	52981.5i	0.415708	−	0.415708i
$358$	−191018.	−	191018.i	−1.49042	−	1.49042i
$359$		−	172842.i		−	1.34110i	−0.741864	−	0.670550i	$-0.766058\pi$
$359$		−	172842.i		−	1.34110i	0.741864	−	0.670550i	$-0.233942\pi$
$360$		0			0
$361$	80523.0			0.617882
$362$	171885.	−	171885.i	1.31166	−	1.31166i
$363$	103657.	+	103657.i	0.786657	+	0.786657i
$364$		−	18240.5i		−	0.137668i
$365$		0			0
$366$	113754.			0.849188
$367$	−130065.	+	130065.i	−0.965671	+	0.965671i	−0.999430	−	0.0337588i	$-0.989252\pi$
$367$	−130065.	+	130065.i	−0.965671	+	0.965671i	0.0337588	+	0.999430i	$0.489252\pi$
$368$	10543.2	+	10543.2i	0.0778535	+	0.0778535i
$369$		−	28144.2i		−	0.206698i
$370$		0			0
$371$	78913.1			0.573326
$372$	220615.	−	220615.i	1.59422	−	1.59422i
$373$	−47428.3	−	47428.3i	−0.340894	−	0.340894i	0.515809	−	0.856704i	$-0.327491\pi$
$373$	−47428.3	−	47428.3i	−0.340894	−	0.340894i	−0.856704	+	0.515809i	$0.827491\pi$
$374$		−	470254.i		−	3.36194i
$375$		0			0
$376$	218762.			1.54738
$377$	31981.6	−	31981.6i	0.225018	−	0.225018i
$378$	56382.6	+	56382.6i	0.394604	+	0.394604i
$379$			165306.i			1.15083i	0.817861	+	0.575415i	$0.195160\pi$
$379$			165306.i			1.15083i	−0.817861	+	0.575415i	$0.804840\pi$
$380$		0			0
$381$	−121419.			−0.836442
$382$	−5535.42	+	5535.42i	−0.0379336	+	0.0379336i
$383$	169294.	+	169294.i	1.15410	+	1.15410i	0.985722	+	0.168380i	$0.0538536\pi$
$383$	169294.	+	169294.i	1.15410	+	1.15410i	0.168380	+	0.985722i	$0.446146\pi$
$384$			270210.i			1.83248i
$385$		0			0
$386$	−84355.9			−0.566162
$387$	−22933.7	+	22933.7i	−0.153127	+	0.153127i
$388$	−228367.	−	228367.i	−1.51694	−	1.51694i
$389$		−	81630.3i		−	0.539452i	−0.962937	−	0.269726i	$-0.913067\pi$
$389$		−	81630.3i		−	0.539452i	0.962937	−	0.269726i	$-0.0869331\pi$
$390$		0			0
$391$	−199022.			−1.30181
$392$	17032.0	−	17032.0i	0.110840	−	0.110840i
$393$	205767.	+	205767.i	1.33226	+	1.33226i
$394$			216726.i			1.39611i
$395$		0			0
$396$	−60510.2			−0.385867
$397$	−151107.	+	151107.i	−0.958744	+	0.958744i	−0.999182	−	0.0404377i	$-0.987125\pi$
$397$	−151107.	+	151107.i	−0.958744	+	0.958744i	0.0404377	+	0.999182i	$0.487125\pi$
$398$	−51692.7	−	51692.7i	−0.326335	−	0.326335i
$399$		−	40095.1i		−	0.251852i
$400$		0			0
$401$	−166443.			−1.03509			−0.517543	−	0.855657i	$-0.673153\pi$
$401$	−166443.			−1.03509			−0.517543	+	0.855657i	$0.673153\pi$
$402$	96232.0	−	96232.0i	0.595480	−	0.595480i
$403$	31319.6	+	31319.6i	0.192844	+	0.192844i
$404$		−	171712.i		−	1.05205i
$405$		0			0
$406$	148690.			0.902050
$407$	83096.1	−	83096.1i	0.501640	−	0.501640i
$408$	200893.	+	200893.i	1.20683	+	1.20683i
$409$			194400.i			1.16212i	0.813861	+	0.581059i	$0.197361\pi$
$409$			194400.i			1.16212i	−0.813861	+	0.581059i	$0.802639\pi$
$410$		0			0
$411$	−277384.			−1.64209
$412$	186184.	−	186184.i	1.09685	−	1.09685i
$413$	−14154.4	−	14154.4i	−0.0829836	−	0.0829836i
$414$			40931.9i			0.238815i
$415$		0			0
$416$	−33859.5			−0.195656
$417$	164440.	−	164440.i	0.945661	−	0.945661i
$418$	−177938.	−	177938.i	−1.01840	−	1.01840i
$419$			261923.i			1.49192i	0.665991	+	0.745959i	$0.268009\pi$
$419$			261923.i			1.49192i	−0.665991	+	0.745959i	$0.731991\pi$
$420$		0			0
$421$	217041.			1.22455			0.612275	−	0.790645i	$-0.290254\pi$
$421$	217041.			1.22455			0.612275	+	0.790645i	$0.290254\pi$
$422$	72310.8	−	72310.8i	0.406049	−	0.406049i
$423$	28897.4	+	28897.4i	0.161502	+	0.161502i
$424$			299220.i			1.66440i
$425$		0			0
$426$	498588.			2.74740
$427$	−23487.4	+	23487.4i	−0.128819	+	0.128819i
$428$	20740.3	+	20740.3i	0.113221	+	0.113221i
$429$		−	61630.6i		−	0.334874i
$430$		0			0
$431$	−98525.8			−0.530390			−0.265195	−	0.964195i	$-0.585436\pi$
$431$	−98525.8			−0.530390			−0.265195	+	0.964195i	$0.585436\pi$
$432$	−14548.4	+	14548.4i	−0.0779555	+	0.0779555i
$433$	124989.	+	124989.i	0.666647	+	0.666647i	0.956938	−	0.290291i	$-0.0937521\pi$
$433$	124989.	+	124989.i	0.666647	+	0.666647i	−0.290291	+	0.956938i	$0.593752\pi$
$434$			145612.i			0.773070i
$435$		0			0
$436$	−516954.			−2.71944
$437$	−75307.5	+	75307.5i	−0.394344	+	0.394344i
$438$	−41497.4	−	41497.4i	−0.216308	−	0.216308i
$439$			111878.i			0.580520i	0.956948	+	0.290260i	$0.0937419\pi$
$439$			111878.i			0.580520i	−0.956948	+	0.290260i	$0.906258\pi$
$440$		0			0
$441$	4499.70			0.0231370
$442$	−71001.7	+	71001.7i	−0.363433	+	0.363433i
$443$	143058.	+	143058.i	0.728963	+	0.728963i	0.970413	−	0.241450i	$-0.0776230\pi$
$443$	143058.	+	143058.i	0.728963	+	0.728963i	−0.241450	+	0.970413i	$0.577623\pi$
$444$			176752.i			0.896601i
$445$		0			0
$446$	512486.			2.57640
$447$	33978.6	−	33978.6i	0.170055	−	0.170055i
$448$	−85256.6	−	85256.6i	−0.424788	−	0.424788i
$449$			95250.7i			0.472471i	0.971696	+	0.236236i	$0.0759137\pi$
$449$			95250.7i			0.472471i	−0.971696	+	0.236236i	$0.924086\pi$
$450$		0			0
$451$	370044.			1.81928
$452$	−188469.	+	188469.i	−0.922492	+	0.922492i
$453$	125032.	+	125032.i	0.609293	+	0.609293i
$454$			426405.i			2.06876i
$455$		0			0
$456$	152031.			0.731142
$457$	−155248.	+	155248.i	−0.743350	+	0.743350i	−0.973221	−	0.229871i	$-0.926169\pi$
$457$	−155248.	+	155248.i	−0.743350	+	0.743350i	0.229871	+	0.973221i	$0.426169\pi$
$458$	161969.	+	161969.i	0.772148	+	0.772148i
$459$		−	274627.i		−	1.30352i
$460$		0			0
$461$	18536.5			0.0872217			0.0436109	−	0.999049i	$-0.486114\pi$
$461$	18536.5			0.0872217			0.0436109	+	0.999049i	$0.486114\pi$
$462$	143268.	−	143268.i	0.671219	−	0.671219i
$463$	189728.	+	189728.i	0.885055	+	0.885055i	0.994043	−	0.108988i	$-0.0347611\pi$
$463$	189728.	+	189728.i	0.885055	+	0.885055i	−0.108988	+	0.994043i	$0.534761\pi$
$464$			38366.5i			0.178203i
$465$		0			0
$466$	457223.			2.10550
$467$	−136538.	+	136538.i	−0.626064	+	0.626064i	−0.947075	−	0.321011i	$-0.895977\pi$
$467$	−136538.	+	136538.i	−0.626064	+	0.626064i	0.321011	+	0.947075i	$0.395977\pi$
$468$	9136.18	+	9136.18i	0.0417131	+	0.0417131i
$469$			39739.2i			0.180665i
$470$		0			0
$471$	246506.			1.11118
$472$	53670.2	−	53670.2i	0.240907	−	0.240907i
$473$	−301536.	−	301536.i	−1.34777	−	1.34777i
$474$		−	78872.5i		−	0.351050i
$475$		0			0
$476$	−206532.			−0.911533
$477$	−39525.5	+	39525.5i	−0.173716	+	0.173716i
$478$	−382140.	−	382140.i	−1.67250	−	1.67250i
$479$		−	296151.i		−	1.29075i	−0.763867	−	0.645374i	$-0.776701\pi$
$479$		−	296151.i		−	1.29075i	0.763867	−	0.645374i	$-0.223299\pi$
$480$		0			0
$481$	−25092.7			−0.108457
$482$	−226860.	+	226860.i	−0.976482	+	0.976482i
$483$	−60634.2	−	60634.2i	−0.259910	−	0.259910i
$484$		−	404074.i		−	1.72493i
$485$		0			0
$486$	−123878.			−0.524469
$487$	269739.	−	269739.i	1.13733	−	1.13733i	0.148401	−	0.988927i	$-0.452587\pi$
$487$	269739.	−	269739.i	1.13733	−	1.13733i	0.988927	−	0.148401i	$-0.0474127\pi$
$488$	−89058.7	−	89058.7i	−0.373970	−	0.373970i
$489$		−	198360.i		−	0.829539i
$490$		0			0
$491$	27623.0			0.114580			0.0572899	−	0.998358i	$-0.481754\pi$
$491$	27623.0			0.114580			0.0572899	+	0.998358i	$0.481754\pi$
$492$	−393557.	+	393557.i	−1.62584	+	1.62584i
$493$	−362118.	−	362118.i	−1.48990	−	1.48990i
$494$			53732.3i			0.220182i
$495$		0			0
$496$	−37572.3			−0.152723
$497$	−102946.	+	102946.i	−0.416772	+	0.416772i
$498$	442848.	+	442848.i	1.78565	+	1.78565i
$499$			194010.i			0.779153i	0.920994	+	0.389577i	$0.127379\pi$
$499$			194010.i			0.779153i	−0.920994	+	0.389577i	$0.872621\pi$
$500$		0			0
$501$	−236656.			−0.942848
$502$	−123394.	+	123394.i	−0.489653	+	0.489653i
$503$	−217646.	−	217646.i	−0.860230	−	0.860230i	0.131135	−	0.991365i	$-0.458138\pi$
$503$	−217646.	−	217646.i	−0.860230	−	0.860230i	−0.991365	+	0.131135i	$0.958138\pi$
$504$			17061.8i			0.0671682i
$505$		0			0
$506$	−538178.			−2.10196
$507$	186623.	−	186623.i	0.726019	−	0.726019i
$508$	236656.	+	236656.i	0.917044	+	0.917044i
$509$			269020.i			1.03836i	0.854664	+	0.519182i	$0.173763\pi$
$509$			269020.i			1.03836i	−0.854664	+	0.519182i	$0.826237\pi$
$510$		0			0
$511$	17136.4			0.0656263
$512$	45131.4	−	45131.4i	0.172163	−	0.172163i
$513$	−103915.	−	103915.i	−0.394861	−	0.394861i
$514$		−	272470.i		−	1.03132i
$515$		0			0
$516$	641392.			2.40893
$517$	−379947.	+	379947.i	−1.42148	+	1.42148i
$518$	−58330.9	−	58330.9i	−0.217390	−	0.217390i
$519$			164768.i			0.611700i
$520$		0			0
$521$	287409.			1.05883			0.529413	−	0.848364i	$-0.322412\pi$
$521$	287409.			1.05883			0.529413	+	0.848364i	$0.322412\pi$
$522$	−74474.9	+	74474.9i	−0.273319	+	0.273319i
$523$	291190.	+	291190.i	1.06457	+	1.06457i	0.997766	+	0.0667989i	$0.0212786\pi$
$523$	291190.	+	291190.i	1.06457	+	1.06457i	0.0667989	+	0.997766i	$0.478721\pi$
$524$		−	802117.i		−	2.92129i
$525$		0			0
$526$	181500.			0.656003
$527$	354622.	−	354622.i	1.27686	−	1.27686i
$528$	36967.3	+	36967.3i	0.132602	+	0.132602i
$529$		−	52071.8i		−	0.186076i
$530$		0			0
$531$	14179.1			0.0502876
$532$	−78148.9	+	78148.9i	−0.276121	+	0.276121i
$533$	−55871.4	−	55871.4i	−0.196669	−	0.196669i
$534$			586462.i			2.05664i
$535$		0			0
$536$	−150681.			−0.524481
$537$	−283458.	+	283458.i	−0.982969	+	0.982969i
$538$	146524.	+	146524.i	0.506227	+	0.506227i
$539$			59162.7i			0.203643i
$540$		0			0
$541$	2540.09			0.00867871			0.00433936	−	0.999991i	$-0.498619\pi$
$541$	2540.09			0.00867871			0.00433936	+	0.999991i	$0.498619\pi$
$542$	358724.	−	358724.i	1.22113	−	1.22113i
$543$	−255065.	−	255065.i	−0.865071	−	0.865071i
$544$			383380.i			1.29548i
$545$		0			0
$546$	−43262.8			−0.145121
$547$	−78242.0	+	78242.0i	−0.261496	+	0.261496i	−0.825662	−	0.564166i	$-0.809198\pi$
$547$	−78242.0	+	78242.0i	−0.261496	+	0.261496i	0.564166	+	0.825662i	$0.309198\pi$
$548$	540647.	+	540647.i	1.80033	+	1.80033i
$549$		−	23528.4i		−	0.0780636i
$550$		0			0
$551$	−274042.			−0.902638
$552$	229910.	−	229910.i	0.754536	−	0.754536i
$553$	16285.3	+	16285.3i	0.0532531	+	0.0532531i
$554$		−	306645.i		−	0.999118i
$555$		0			0
$556$	−641017.			−2.07358
$557$	334567.	−	334567.i	1.07838	−	1.07838i	0.0817273	−	0.996655i	$-0.473956\pi$
$557$	334567.	−	334567.i	1.07838	−	1.07838i	0.996655	−	0.0817273i	$-0.0260436\pi$
$558$	−72933.3	−	72933.3i	−0.234238	−	0.234238i
$559$			91055.3i			0.291395i
$560$		0			0
$561$	−697824.			−2.21728
$562$	573857.	−	573857.i	1.81690	−	1.81690i
$563$	350328.	+	350328.i	1.10524	+	1.10524i	0.993767	+	0.111476i	$0.0355577\pi$
$563$	350328.	+	350328.i	1.10524	+	1.10524i	0.111476	+	0.993767i	$0.464442\pi$
$564$		−	808178.i		−	2.54067i
$565$		0			0
$566$	−199240.			−0.621932
$567$	97583.5	−	97583.5i	0.303536	−	0.303536i
$568$	−390348.	−	390348.i	−1.20992	−	1.20992i
$569$		−	52610.6i		−	0.162498i	−0.996694	−	0.0812492i	$-0.974109\pi$
$569$		−	52610.6i		−	0.162498i	0.996694	−	0.0812492i	$-0.0258910\pi$
$570$		0			0
$571$	−318898.			−0.978093			−0.489047	−	0.872258i	$-0.662655\pi$
$571$	−318898.			−0.978093			−0.489047	+	0.872258i	$0.662655\pi$
$572$	−120124.	+	120124.i	−0.367144	+	0.367144i
$573$	8214.18	+	8214.18i	0.0250181	+	0.0250181i
$574$		−	259760.i		−	0.788402i
$575$		0			0
$576$	85405.5			0.257419
$577$	−228263.	+	228263.i	−0.685621	+	0.685621i	−0.961261	−	0.275640i	$-0.911110\pi$
$577$	−228263.	+	228263.i	−0.685621	+	0.685621i	0.275640	+	0.961261i	$0.411110\pi$
$578$	417825.	+	417825.i	1.25066	+	1.25066i
$579$			125178.i			0.373398i
$580$		0			0
$581$	−182875.			−0.541754
$582$	−541640.	+	541640.i	−1.59906	+	1.59906i
$583$	−519686.	−	519686.i	−1.52899	−	1.52899i
$584$			64977.1i			0.190518i
$585$		0			0
$586$	−174354.			−0.507733
$587$	244137.	−	244137.i	0.708529	−	0.708529i	−0.257697	−	0.966226i	$-0.582964\pi$
$587$	244137.	−	244137.i	0.708529	−	0.708529i	0.966226	+	0.257697i	$0.0829636\pi$
$588$	−62921.9	−	62921.9i	−0.181990	−	0.181990i
$589$		−	268369.i		−	0.773574i
$590$		0			0
$591$	321607.			0.920768
$592$	15051.1	−	15051.1i	0.0429462	−	0.0429462i
$593$	−98281.5	−	98281.5i	−0.279488	−	0.279488i	0.553417	−	0.832904i	$-0.313324\pi$
$593$	−98281.5	−	98281.5i	−0.279488	−	0.279488i	−0.832904	+	0.553417i	$0.813324\pi$
$594$		−	742620.i		−	2.10472i
$595$		0			0
$596$	−132455.			−0.372885
$597$	−76708.4	+	76708.4i	−0.215226	+	0.215226i
$598$	81257.2	+	81257.2i	0.227227	+	0.227227i
$599$			279180.i			0.778092i	0.921218	+	0.389046i	$0.127195\pi$
$599$			279180.i			0.778092i	−0.921218	+	0.389046i	$0.872805\pi$
$600$		0			0
$601$	−640601.			−1.77353			−0.886766	−	0.462219i	$-0.847053\pi$
$601$	−640601.			−1.77353			−0.886766	+	0.462219i	$0.847053\pi$
$602$	−211669.	+	211669.i	−0.584069	+	0.584069i
$603$	−19904.3	−	19904.3i	−0.0547409	−	0.0547409i
$604$		−	487399.i		−	1.33601i
$605$		0			0
$606$	−407266.			−1.10900
$607$	115131.	−	115131.i	0.312475	−	0.312475i	−0.533393	−	0.845868i	$-0.679083\pi$
$607$	115131.	−	115131.i	0.312475	−	0.312475i	0.845868	+	0.533393i	$0.179083\pi$
$608$	145066.	+	145066.i	0.392427	+	0.392427i
$609$		−	220646.i		−	0.594924i
$610$		0			0
$611$	114733.			0.307331
$612$	103446.	−	103446.i	0.276192	−	0.276192i
$613$	−260483.	−	260483.i	−0.693200	−	0.693200i	0.269734	−	0.962935i	$-0.413064\pi$
$613$	−260483.	−	260483.i	−0.693200	−	0.693200i	−0.962935	+	0.269734i	$0.913064\pi$
$614$		−	219584.i		−	0.582457i
$615$		0			0
$616$	−224331.			−0.591190
$617$	−265228.	+	265228.i	−0.696706	+	0.696706i	−0.963699	−	0.266992i	$-0.913970\pi$
$617$	−265228.	+	265228.i	−0.696706	+	0.696706i	0.266992	+	0.963699i	$0.413970\pi$
$618$	−441592.	−	441592.i	−1.15623	−	1.15623i
$619$			653363.i			1.70519i	0.522571	+	0.852595i	$0.324973\pi$
$619$			653363.i			1.70519i	−0.522571	+	0.852595i	$0.675027\pi$
$620$		0			0
$621$	−314294.			−0.814990
$622$	−94993.9	+	94993.9i	−0.245536	+	0.245536i
$623$	−121090.	−	121090.i	−0.311985	−	0.311985i
$624$		−	11163.1i		−	0.0286691i
$625$		0			0
$626$	46407.8			0.118425
$627$	−264048.	+	264048.i	−0.671657	+	0.671657i
$628$	−480462.	−	480462.i	−1.21826	−	1.21826i
$629$			284116.i			0.718117i
$630$		0			0
$631$	98543.0			0.247495			0.123748	−	0.992314i	$-0.460509\pi$
$631$	98543.0			0.247495			0.123748	+	0.992314i	$0.460509\pi$
$632$	−61749.9	+	61749.9i	−0.154597	+	0.154597i
$633$	−107304.	−	107304.i	−0.267799	−	0.267799i
$634$		−	616308.i		−	1.53327i
$635$		0			0
$636$	1.10541e6			2.73282
$637$	8932.72	−	8932.72i	0.0220143	−	0.0220143i
$638$	−979206.	−	979206.i	−2.40565	−	2.40565i
$639$		−	103126.i		−	0.252561i
$640$		0			0
$641$	390699.			0.950882			0.475441	−	0.879748i	$-0.342289\pi$
$641$	390699.			0.950882			0.475441	+	0.879748i	$0.342289\pi$
$642$	49191.8	−	49191.8i	0.119350	−	0.119350i
$643$	526218.	+	526218.i	1.27275	+	1.27275i	0.944638	+	0.328115i	$0.106413\pi$
$643$	526218.	+	526218.i	1.27275	+	1.27275i	0.328115	+	0.944638i	$0.393587\pi$
$644$			236363.i			0.569912i
$645$		0			0
$646$	608394.			1.45787
$647$	386057.	−	386057.i	0.922238	−	0.922238i	−0.0749495	−	0.997187i	$-0.523880\pi$
$647$	386057.	−	386057.i	0.922238	−	0.922238i	0.997187	+	0.0749495i	$0.0238796\pi$
$648$	370013.	+	370013.i	0.881185	+	0.881185i
$649$			186429.i			0.442613i
$650$		0			0
$651$	216078.			0.509858
$652$	−386622.	+	386622.i	−0.909476	+	0.909476i
$653$	−122162.	−	122162.i	−0.286491	−	0.286491i	0.549200	−	0.835691i	$-0.314933\pi$
$653$	−122162.	−	122162.i	−0.286491	−	0.286491i	−0.835691	+	0.549200i	$0.814933\pi$
$654$			1.22611e6i			2.86665i
$655$		0			0
$656$	67025.6			0.155752
$657$	−8583.17	+	8583.17i	−0.0198846	+	0.0198846i
$658$	266711.	+	266711.i	0.616012	+	0.616012i
$659$			570740.i			1.31422i	0.753795	+	0.657110i	$0.228221\pi$
$659$			570740.i			1.31422i	−0.753795	+	0.657110i	$0.771779\pi$
$660$		0			0
$661$	130218.			0.298035			0.149017	−	0.988835i	$-0.452389\pi$
$661$	130218.			0.298035			0.149017	+	0.988835i	$0.452389\pi$
$662$	−452158.	+	452158.i	−1.03175	+	1.03175i
$663$	105362.	+	105362.i	0.239693	+	0.239693i
$664$		−	693418.i		−	1.57275i
$665$		0			0
$666$	58432.8			0.131737
$667$	−414422.	+	414422.i	−0.931519	+	0.931519i
$668$	461264.	+	461264.i	1.03370	+	1.03370i
$669$		−	760493.i		−	1.69919i
$670$		0			0
$671$	309355.			0.687088
$672$	−116801.	+	116801.i	−0.258647	+	0.258647i
$673$	−299201.	−	299201.i	−0.660591	−	0.660591i	0.294928	−	0.955519i	$-0.404704\pi$
$673$	−299201.	−	299201.i	−0.660591	−	0.660591i	−0.955519	+	0.294928i	$0.904704\pi$
$674$			751304.i			1.65385i
$675$		0			0
$676$	−727489.			−1.59196
$677$	308222.	−	308222.i	0.672492	−	0.672492i	−0.285798	−	0.958290i	$-0.592259\pi$
$677$	308222.	−	308222.i	0.672492	−	0.672492i	0.958290	+	0.285798i	$0.0922587\pi$
$678$	447010.	+	447010.i	0.972429	+	0.972429i
$679$		−	223671.i		−	0.485144i
$680$		0			0
$681$	632755.			1.36440
$682$	958936.	−	958936.i	2.06168	−	2.06168i
$683$	−122960.	−	122960.i	−0.263585	−	0.263585i	0.562924	−	0.826509i	$-0.309677\pi$
$683$	−122960.	−	122960.i	−0.263585	−	0.263585i	−0.826509	+	0.562924i	$0.809677\pi$
$684$		−	78285.4i		−	0.167328i
$685$		0			0
$686$	41530.4			0.0882506
$687$	240350.	−	240350.i	0.509250	−	0.509250i
$688$	−54616.8	−	54616.8i	−0.115385	−	0.115385i
$689$			156930.i			0.330574i
$690$		0			0
$691$	511145.			1.07050			0.535251	−	0.844693i	$-0.320217\pi$
$691$	511145.			1.07050			0.535251	+	0.844693i	$0.320217\pi$
$692$	321148.	−	321148.i	0.670646	−	0.670646i
$693$	−29633.0	−	29633.0i	−0.0617034	−	0.0617034i
$694$			664336.i			1.37933i
$695$		0			0
$696$	836636.			1.72710
$697$	−632614.	+	632614.i	−1.30219	+	1.30219i
$698$	623939.	+	623939.i	1.28065	+	1.28065i
$699$		−	678486.i		−	1.38863i
$700$		0			0
$701$	−624118.			−1.27008			−0.635039	−	0.772480i	$-0.719016\pi$
$701$	−624118.			−1.27008			−0.635039	+	0.772480i	$0.719016\pi$
$702$	−112125.	+	112125.i	−0.227525	+	0.227525i
$703$	107506.	+	107506.i	0.217532	+	0.217532i
$704$			1.12292e6i			2.26571i
$705$		0			0
$706$	−1.16811e6			−2.34354
$707$	84090.7	−	84090.7i	0.168232	−	0.168232i
$708$	−198275.	−	198275.i	−0.395550	−	0.395550i
$709$		−	148682.i		−	0.295779i	−0.989004	−	0.147889i	$-0.952752\pi$
$709$		−	148682.i		−	0.295779i	0.989004	−	0.147889i	$-0.0472480\pi$
$710$		0			0
$711$	−16313.7			−0.0322711
$712$	459146.	−	459146.i	0.905713	−	0.905713i
$713$	−405844.	−	405844.i	−0.798325	−	0.798325i
$714$			489851.i			0.960876i
$715$		0			0
$716$	1.10497e6			2.15538
$717$	−567069.	+	567069.i	−1.10306	+	1.10306i
$718$	799024.	+	799024.i	1.54993	+	1.54993i
$719$			259924.i			0.502792i	0.967884	+	0.251396i	$0.0808897\pi$
$719$			259924.i			0.502792i	−0.967884	+	0.251396i	$0.919110\pi$
$720$		0			0
$721$	182356.			0.350792
$722$	−372246.	+	372246.i	−0.714094	+	0.714094i
$723$	336645.	+	336645.i	0.644014	+	0.644014i
$724$			994291.i			1.89686i
$725$		0			0
$726$	−958382.			−1.81830
$727$	188187.	−	188187.i	0.356058	−	0.356058i	−0.506300	−	0.862358i	$-0.668987\pi$
$727$	188187.	−	188187.i	0.356058	−	0.356058i	0.862358	+	0.506300i	$0.168987\pi$
$728$	33870.7	+	33870.7i	0.0639090	+	0.0639090i
$729$		−	419747.i		−	0.789828i
$730$		0			0
$731$	1.03099e6			1.92939
$732$	−329012.	+	329012.i	−0.614030	+	0.614030i
$733$	279698.	+	279698.i	0.520573	+	0.520573i	0.917745	−	0.397171i	$-0.130008\pi$
$733$	279698.	+	279698.i	0.520573	+	0.520573i	−0.397171	+	0.917745i	$0.630008\pi$
$734$		−	1.20254e6i		−	2.23208i
$735$		0			0
$736$	438756.			0.809967
$737$	261704.	−	261704.i	0.481810	−	0.481810i
$738$	130107.	+	130107.i	0.238884	+	0.238884i
$739$		−	390065.i		−	0.714246i	−0.934057	−	0.357123i	$-0.883758\pi$
$739$		−	390065.i		−	0.714246i	0.934057	−	0.357123i	$-0.116242\pi$
$740$		0			0
$741$	79734.9			0.145215
$742$	−364803.	+	364803.i	−0.662599	+	0.662599i
$743$	−76893.6	−	76893.6i	−0.139288	−	0.139288i	0.634025	−	0.773313i	$-0.281402\pi$
$743$	−76893.6	−	76893.6i	−0.139288	−	0.139288i	−0.773313	+	0.634025i	$0.781402\pi$
$744$			819317.i			1.48015i
$745$		0			0
$746$	438508.			0.787951
$747$	91597.2	−	91597.2i	0.164150	−	0.164150i
$748$	1.36012e6	+	1.36012e6i	2.43094	+	2.43094i
$749$			20313.8i			0.0362100i
$750$		0			0
$751$	691655.			1.22634			0.613168	−	0.789952i	$-0.289895\pi$
$751$	691655.			1.22634			0.613168	+	0.789952i	$0.289895\pi$
$752$	−68819.3	+	68819.3i	−0.121695	+	0.121695i
$753$	183109.	+	183109.i	0.322938	+	0.322938i
$754$			295692.i			0.520113i
$755$		0			0
$756$	−326152.			−0.570659
$757$	176521.	−	176521.i	0.308039	−	0.308039i	−0.536110	−	0.844148i	$-0.680107\pi$
$757$	176521.	−	176521.i	0.308039	−	0.308039i	0.844148	+	0.536110i	$0.180107\pi$
$758$	−764187.	−	764187.i	−1.33003	−	1.33003i
$759$			798618.i			1.38629i
$760$		0			0
$761$	−873004.			−1.50746			−0.753732	−	0.657182i	$-0.771748\pi$
$761$	−873004.			−1.50746			−0.753732	+	0.657182i	$0.771748\pi$
$762$	561300.	−	561300.i	0.966686	−	0.966686i
$763$	−253162.	−	253162.i	−0.434861	−	0.434861i
$764$		−	32020.4i		−	0.0548580i
$765$		0			0
$766$	−1.56524e6			−2.66762
$767$	28148.1	−	28148.1i	0.0478475	−	0.0478475i
$768$	−534580.	−	534580.i	−0.906338	−	0.906338i
$769$		−	184914.i		−	0.312692i	−0.987702	−	0.156346i	$-0.950028\pi$
$769$		−	184914.i		−	0.312692i	0.987702	−	0.156346i	$-0.0499715\pi$
$770$		0			0
$771$	−404326.			−0.680179
$772$	243984.	−	243984.i	0.409380	−	0.409380i
$773$	528554.	+	528554.i	0.884566	+	0.884566i	0.993995	−	0.109429i	$-0.0349021\pi$
$773$	528554.	+	528554.i	0.884566	+	0.884566i	−0.109429	+	0.993995i	$0.534902\pi$
$774$		−	212038.i		−	0.353943i
$775$		0			0
$776$	848107.			1.40840
$777$	−86559.0	+	86559.0i	−0.143374	+	0.143374i
$778$	377365.	+	377365.i	0.623451	+	0.623451i
$779$			478747.i			0.788916i
$780$		0			0
$781$	1.35592e6			2.22295
$782$	920050.	−	920050.i	1.50452	−	1.50452i
$783$	−571853.	−	571853.i	−0.932740	−	0.932740i
$784$			10716.1i			0.0174342i
$785$		0			0
$786$	−1.90246e6			−3.07943
$787$	−460572.	+	460572.i	−0.743614	+	0.743614i	−0.973272	−	0.229657i	$-0.926239\pi$
$787$	−460572.	+	460572.i	−0.743614	+	0.743614i	0.229657	+	0.973272i	$0.426239\pi$
$788$	−626841.	−	626841.i	−1.00950	−	1.00950i
$789$		−	269333.i		−	0.432650i
$790$		0			0
$791$	−184594.			−0.295028
$792$	112361.	−	112361.i	0.179129	−	0.179129i
$793$	−46708.2	−	46708.2i	−0.0742757	−	0.0742757i
$794$		−	1.39709e6i		−	2.21606i
$795$		0			0
$796$	299023.			0.471931
$797$	35127.1	−	35127.1i	0.0553001	−	0.0553001i	−0.678916	−	0.734216i	$-0.737550\pi$
$797$	35127.1	−	35127.1i	0.0553001	−	0.0553001i	0.734216	+	0.678916i	$0.237550\pi$
$798$	185353.	+	185353.i	0.291068	+	0.291068i
$799$		−	1.29909e6i		−	2.03491i
$800$		0			0
$801$	121302.			0.189061
$802$	769441.	−	769441.i	1.19626	−	1.19626i
$803$	−112853.	−	112853.i	−0.175017	−	0.175017i
$804$			556666.i			0.861158i
$805$		0			0
$806$	−289571.			−0.445744
$807$	217432.	−	217432.i	0.333869	−	0.333869i
$808$	318852.	+	318852.i	0.488389	+	0.488389i
$809$		−	293002.i		−	0.447687i	−0.974625	−	0.223843i	$-0.928140\pi$
$809$		−	293002.i		−	0.447687i	0.974625	−	0.223843i	$-0.0718604\pi$
$810$		0			0
$811$	928790.			1.41213			0.706067	−	0.708145i	$-0.250468\pi$
$811$	928790.			1.41213			0.706067	+	0.708145i	$0.250468\pi$
$812$	−430059.	+	430059.i	−0.652253	+	0.652253i
$813$	−532321.	−	532321.i	−0.805364	−	0.805364i
$814$			768282.i			1.15950i
$815$		0			0
$816$	−126396.			−0.189825
$817$	390114.	−	390114.i	0.584450	−	0.584450i
$818$	−898683.	−	898683.i	−1.34307	−	1.34307i
$819$			8948.32i			0.0133405i
$820$		0			0
$821$	1.04744e6			1.55397			0.776985	−	0.629519i	$-0.216748\pi$
$821$	1.04744e6			1.55397			0.776985	+	0.629519i	$0.216748\pi$
$822$	1.28230e6	−	1.28230e6i	1.89779	−	1.89779i
$823$	553267.	+	553267.i	0.816836	+	0.816836i	0.985648	−	0.168812i	$-0.0539932\pi$
$823$	553267.	+	553267.i	0.816836	+	0.816836i	−0.168812	+	0.985648i	$0.553993\pi$
$824$			691451.i			1.01837i
$825$		0			0
$826$	130867.			0.191810
$827$	240884.	−	240884.i	0.352206	−	0.352206i	−0.508724	−	0.860930i	$-0.669883\pi$
$827$	240884.	−	240884.i	0.352206	−	0.352206i	0.860930	+	0.508724i	$0.169883\pi$
$828$	−118388.	−	118388.i	−0.172682	−	0.172682i
$829$		−	1.27420e6i		−	1.85409i	−0.374956	−	0.927043i	$-0.622342\pi$
$829$		−	1.27420e6i		−	1.85409i	0.374956	−	0.927043i	$-0.377658\pi$
$830$		0			0
$831$	−455040.			−0.658943
$832$	169545.	−	169545.i	0.244928	−	0.244928i
$833$	−101142.	−	101142.i	−0.145762	−	0.145762i
$834$			1.52036e6i			2.18582i
$835$		0			0
$836$	1.02931e6			1.47276
$837$	560015.	−	560015.i	0.799371	−	0.799371i
$838$	−1.21083e6	−	1.21083e6i	−1.72423	−	1.72423i
$839$		−	26951.6i		−	0.0382878i	−0.999817	−	0.0191439i	$-0.993906\pi$
$839$		−	26951.6i		−	0.0382878i	0.999817	−	0.0191439i	$-0.00609407\pi$
$840$		0			0
$841$	−800790.			−1.13221
$842$	−1.00335e6	+	1.00335e6i	−1.41523	+	1.41523i
$843$	−851564.	−	851564.i	−1.19829	−	1.19829i
$844$			418291.i			0.587211i
$845$		0			0
$846$	−267177.			−0.373300
$847$	197883.	−	197883.i	0.275830	−	0.275830i
$848$	−94130.1	−	94130.1i	−0.130899	−	0.130899i
$849$			295658.i			0.410179i
$850$		0			0
$851$	325154.			0.448984
$852$	−1.44207e6	+	1.44207e6i	−1.98659	+	1.98659i
$853$	546317.	+	546317.i	0.750838	+	0.750838i	0.974636	−	0.223798i	$-0.0718454\pi$
$853$	546317.	+	546317.i	0.750838	+	0.750838i	−0.223798	+	0.974636i	$0.571845\pi$
$854$		−	217158.i		−	0.297755i
$855$		0			0
$856$	−77025.2			−0.105120
$857$	223047.	−	223047.i	0.303692	−	0.303692i	−0.538764	−	0.842457i	$-0.681109\pi$
$857$	223047.	−	223047.i	0.303692	−	0.303692i	0.842457	+	0.538764i	$0.181109\pi$
$858$	284909.	+	284909.i	0.387018	+	0.387018i
$859$			737032.i			0.998849i	0.866357	+	0.499425i	$0.166455\pi$
$859$			737032.i			0.998849i	−0.866357	+	0.499425i	$0.833545\pi$
$860$		0			0
$861$	−385465.			−0.519970
$862$	455470.	−	455470.i	0.612978	−	0.612978i
$863$	352024.	+	352024.i	0.472662	+	0.472662i	0.902775	−	0.430113i	$-0.141526\pi$
$863$	352024.	+	352024.i	0.472662	+	0.472662i	−0.430113	+	0.902775i	$0.641526\pi$
$864$			605429.i			0.811028i
$865$		0			0
$866$	−1.15561e6			−1.54090
$867$	620023.	−	620023.i	0.824840	−	0.824840i
$868$	−421156.	−	421156.i	−0.558990	−	0.558990i
$869$		−	214495.i		−	0.284039i
$870$		0			0
$871$	−79027.2			−0.104169
$872$	959931.	−	959931.i	1.26243	−	1.26243i
$873$	112031.	+	112031.i	0.146997	+	0.146997i
$874$		−	696271.i		−	0.911497i
$875$		0			0
$876$	240047.			0.312815
$877$	−409187.	+	409187.i	−0.532014	+	0.532014i	−0.921171	−	0.389157i	$-0.872766\pi$
$877$	−409187.	+	409187.i	−0.532014	+	0.532014i	0.389157	+	0.921171i	$0.372766\pi$
$878$	−517197.	−	517197.i	−0.670914	−	0.670914i
$879$			258728.i			0.334862i
$880$		0			0
$881$	−640306.			−0.824966			−0.412483	−	0.910965i	$-0.635338\pi$
$881$	−640306.			−0.824966			−0.412483	+	0.910965i	$0.635338\pi$
$882$	−20801.4	+	20801.4i	−0.0267397	+	0.0267397i
$883$	399939.	+	399939.i	0.512947	+	0.512947i	0.915428	−	0.402481i	$-0.131852\pi$
$883$	399939.	+	399939.i	0.512947	+	0.512947i	−0.402481	+	0.915428i	$0.631852\pi$
$884$		−	410718.i		−	0.525581i
$885$		0			0
$886$	−1.32267e6			−1.68494
$887$	−509945.	+	509945.i	−0.648150	+	0.648150i	−0.952546	−	0.304395i	$-0.901546\pi$
$887$	−509945.	+	509945.i	−0.648150	+	0.648150i	0.304395	+	0.952546i	$0.401546\pi$
$888$	−328211.	−	328211.i	−0.416224	−	0.416224i
$889$			231790.i			0.293286i
$890$		0			0
$891$	−1.28528e6			−1.61898
$892$	−1.48227e6	+	1.48227e6i	−1.86294	+	1.86294i
$893$	−491558.	−	491558.i	−0.616413	−	0.616413i
$894$			314156.i			0.393070i
$895$		0			0
$896$	515835.			0.642532
$897$	120580.	−	120580.i	0.149862	−	0.149862i
$898$	−440329.	−	440329.i	−0.546041	−	0.546041i
$899$		−	1.47685e6i		−	1.82733i
$900$		0			0
$901$	1.77687e6			2.18880
$902$	−1.71066e6	+	1.71066e6i	−2.10257	+	2.10257i
$903$	314102.	+	314102.i	0.385208	+	0.385208i
$904$		−	699934.i		−	0.856486i
$905$		0			0
$906$	−1.15601e6			−1.40833
$907$	−207779.	+	207779.i	−0.252573	+	0.252573i	−0.822025	−	0.569452i	$-0.807155\pi$
$907$	−207779.	+	207779.i	−0.252573	+	0.252573i	0.569452	+	0.822025i	$0.307155\pi$
$908$	−1.23330e6	−	1.23330e6i	−1.49588	−	1.49588i
$909$			84237.5i			0.101948i
$910$		0			0
$911$	−398980.			−0.480745			−0.240372	−	0.970681i	$-0.577270\pi$
$911$	−398980.			−0.480745			−0.240372	+	0.970681i	$0.577270\pi$
$912$	−47826.7	+	47826.7i	−0.0575017	+	0.0575017i
$913$	1.20433e6	+	1.20433e6i	1.44479	+	1.44479i
$914$		−	1.43537e6i		−	1.71820i
$915$		0			0
$916$	−936929.			−1.11665
$917$	392812.	−	392812.i	0.467139	−	0.467139i
$918$	1.26956e6	+	1.26956e6i	1.50649	+	1.50649i
$919$		−	547724.i		−	0.648531i	−0.945966	−	0.324265i	$-0.894883\pi$
$919$		−	547724.i		−	0.648531i	0.945966	−	0.324265i	$-0.105117\pi$
$920$		0			0
$921$	−325847.			−0.384144
$922$	−85691.2	+	85691.2i	−0.100803	+	0.100803i
$923$	−204724.	−	204724.i	−0.240306	−	0.240306i
$924$			828750.i			0.970688i
$925$		0			0
$926$	−1.75417e6			−2.04574
$927$	−91337.3	+	91337.3i	−0.106289	+	0.106289i
$928$	798309.	+	798309.i	0.926990	+	0.926990i
$929$			163754.i			0.189740i	0.995490	+	0.0948701i	$0.0302436\pi$
$929$			163754.i			0.189740i	−0.995490	+	0.0948701i	$0.969756\pi$
$930$		0			0
$931$	−76542.1			−0.0883081
$932$	−1.32243e6	+	1.32243e6i	−1.52244	+	1.52244i
$933$	140964.	+	140964.i	0.161937	+	0.161937i
$934$		−	1.26239e6i		−	1.44710i
$935$		0			0
$936$	−33929.9			−0.0387285
$937$	208041.	−	208041.i	0.236958	−	0.236958i	−0.578632	−	0.815589i	$-0.696413\pi$
$937$	208041.	−	208041.i	0.236958	−	0.236958i	0.815589	+	0.578632i	$0.196413\pi$
$938$	−183708.	−	183708.i	−0.208796	−	0.208796i
$939$		−	68865.9i		−	0.0781039i
$940$		0			0
$941$	−224861.			−0.253942			−0.126971	−	0.991906i	$-0.540525\pi$
$941$	−224861.			−0.253942			−0.126971	+	0.991906i	$0.540525\pi$
$942$	−1.13956e6	+	1.13956e6i	−1.28421	+	1.28421i
$943$	723989.	+	723989.i	0.814158	+	0.814158i
$944$			33767.7i			0.0378928i
$945$		0			0
$946$	2.78791e6			3.11528
$947$	−215253.	+	215253.i	−0.240021	+	0.240021i	−0.816859	−	0.576838i	$-0.804286\pi$
$947$	−215253.	+	215253.i	−0.240021	+	0.240021i	0.576838	+	0.816859i	$0.304286\pi$
$948$	228124.	+	228124.i	0.253837	+	0.253837i
$949$			34078.3i			0.0378395i
$950$		0			0
$951$	−914558.			−1.01123
$952$	383508.	−	383508.i	0.423156	−	0.423156i
$953$	579508.	+	579508.i	0.638078	+	0.638078i	0.950081	−	0.312003i	$-0.101000\pi$
$953$	579508.	+	579508.i	0.638078	+	0.638078i	−0.312003	+	0.950081i	$0.601000\pi$
$954$		−	365440.i		−	0.401532i
$955$		0			0
$956$	2.21054e6			2.41870
$957$	−1.45307e6	+	1.45307e6i	−1.58659	+	1.58659i
$958$	1.36906e6	+	1.36906e6i	1.49173	+	1.49173i
$959$			529530.i			0.575776i
$960$		0			0
$961$	522760.			0.566051
$962$	116000.	−	116000.i	0.125345	−	0.125345i
$963$	−10174.7	−	10174.7i	−0.0109715	−	0.0109715i
$964$		−	1.31230e6i		−	1.41215i
$965$		0			0
$966$	560605.			0.600763
$967$	630473.	−	630473.i	0.674239	−	0.674239i	−0.284452	−	0.958690i	$-0.591812\pi$
$967$	630473.	−	630473.i	0.674239	−	0.674239i	0.958690	+	0.284452i	$0.0918115\pi$
$968$	750324.	+	750324.i	0.800752	+	0.800752i
$969$		−	902814.i		−	0.961503i
$970$		0			0
$971$	964569.			1.02304			0.511522	−	0.859270i	$-0.329082\pi$
$971$	964569.			1.02304			0.511522	+	0.859270i	$0.329082\pi$
$972$	358293.	−	358293.i	0.379232	−	0.379232i
$973$	−313918.	−	313918.i	−0.331582	−	0.331582i
$974$			2.49393e6i			2.62885i
$975$		0			0
$976$	56033.1			0.0588227
$977$	−284782.	+	284782.i	−0.298348	+	0.298348i	−0.840367	−	0.542018i	$-0.817660\pi$
$977$	−284782.	+	284782.i	−0.298348	+	0.298348i	0.542018	+	0.840367i	$0.317660\pi$
$978$	916989.	+	916989.i	0.958708	+	0.958708i
$979$			1.59489e6i			1.66405i
$980$		0			0
$981$	253604.			0.263523
$982$	−127697.	+	127697.i	−0.132421	+	0.132421i
$983$	−973234.	−	973234.i	−1.00719	−	1.00719i	−0.999974	−	0.00721380i	$-0.997704\pi$
$983$	−973234.	−	973234.i	−1.00719	−	1.00719i	−0.00721380	−	0.999974i	$-0.502296\pi$
$984$		−	1.46159e6i		−	1.50951i
$985$		0			0
$986$	3.34803e6			3.44378
$987$	395780.	−	395780.i	0.406275	−	0.406275i
$988$	−155411.	−	155411.i	−0.159209	−	0.159209i
$989$		−	1.17991e6i		−	1.20630i
$990$		0			0
$991$	−1.59169e6			−1.62073			−0.810364	−	0.585926i	$-0.800731\pi$
$991$	−1.59169e6			−1.62073			−0.810364	+	0.585926i	$0.800731\pi$
$992$	−781784.	+	781784.i	−0.794444	+	0.794444i
$993$	670970.	+	670970.i	0.680464	+	0.680464i
$994$		−	951811.i		−	0.963336i
$995$		0			0
$996$	−2.56171e6			−2.58233
$997$	−247611.	+	247611.i	−0.249104	+	0.249104i	−0.820603	−	0.571499i	$-0.806362\pi$
$997$	−247611.	+	247611.i	−0.249104	+	0.249104i	0.571499	+	0.820603i	$0.306362\pi$
$998$	−896879.	−	896879.i	−0.900477	−	0.900477i
$999$			448673.i			0.449572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.g.d.43.2	✓	32
5.2	odd	4	inner	175.5.g.d.57.2	yes	32
5.3	odd	4	inner	175.5.g.d.57.15	yes	32
5.4	even	2	inner	175.5.g.d.43.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.5.g.d.43.2	✓	32	1.1	even	1	trivial
175.5.g.d.43.15	yes	32	5.4	even	2	inner
175.5.g.d.57.2	yes	32	5.2	odd	4	inner
175.5.g.d.57.15	yes	32	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.62285 + 4.62285i) q^{2} +(6.85998 + 6.85998i) q^{3} -26.7415i q^{4} -63.4253 q^{6} +(13.0958 - 13.0958i) q^{7} +(49.6561 + 49.6561i) q^{8} +13.1187i q^{9} +O(q^{10})\)	\(q+(-4.62285 + 4.62285i) q^{2} +(6.85998 + 6.85998i) q^{3} -26.7415i q^{4} -63.4253 q^{6} +(13.0958 - 13.0958i) q^{7} +(49.6561 + 49.6561i) q^{8} +13.1187i q^{9} -172.486 q^{11} +(183.446 - 183.446i) q^{12} +(26.0429 + 26.0429i) q^{13} +121.080i q^{14} -31.2422 q^{16} +(294.876 - 294.876i) q^{17} +(-60.6456 - 60.6456i) q^{18} -223.155i q^{19} +179.674 q^{21} +(797.376 - 797.376i) q^{22} +(-337.468 - 337.468i) q^{23} +681.280i q^{24} -240.785 q^{26} +(465.665 - 465.665i) q^{27} +(-350.201 - 350.201i) q^{28} -1228.04i q^{29} +1202.61 q^{31} +(-650.070 + 650.070i) q^{32} +(-1183.25 - 1183.25i) q^{33} +2726.33i q^{34} +350.812 q^{36} +(-481.756 + 481.756i) q^{37} +(1031.61 + 1031.61i) q^{38} +357.308i q^{39} -2145.36 q^{41} +(-830.605 + 830.605i) q^{42} +(1748.18 + 1748.18i) q^{43} +4612.53i q^{44} +3120.13 q^{46} +(2202.77 - 2202.77i) q^{47} +(-214.321 - 214.321i) q^{48} -343.000i q^{49} +4045.69 q^{51} +(696.426 - 696.426i) q^{52} +(3012.92 + 3012.92i) q^{53} +4305.39i q^{54} +1300.57 q^{56} +(1530.84 - 1530.84i) q^{57} +(5677.02 + 5677.02i) q^{58} -1080.84i q^{59} -1793.51 q^{61} +(-5559.50 + 5559.50i) q^{62} +(171.799 + 171.799i) q^{63} -6510.23i q^{64} +10940.0 q^{66} +(-1517.25 + 1517.25i) q^{67} +(-7885.41 - 7885.41i) q^{68} -4630.05i q^{69} -7861.02 q^{71} +(-651.422 + 651.422i) q^{72} +(654.271 + 654.271i) q^{73} -4454.17i q^{74} -5967.48 q^{76} +(-2258.84 + 2258.84i) q^{77} +(-1651.78 - 1651.78i) q^{78} +1243.55i q^{79} +7451.51 q^{81} +(9917.66 - 9917.66i) q^{82} +(-6982.20 - 6982.20i) q^{83} -4804.74i q^{84} -16163.1 q^{86} +(8424.30 - 8424.30i) q^{87} +(-8564.98 - 8564.98i) q^{88} -9246.50i q^{89} +682.106 q^{91} +(-9024.38 + 9024.38i) q^{92} +(8249.91 + 8249.91i) q^{93} +20366.1i q^{94} -8918.94 q^{96} +(8539.81 - 8539.81i) q^{97} +(1585.64 + 1585.64i) q^{98} -2262.79i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 248 q^{6}+O(q^{10}) \) 32 * q + 248 * q^6	\( 32 q + 248 q^{6} - 1008 q^{11} - 1732 q^{16} - 392 q^{21} - 4296 q^{26} + 9064 q^{31} - 14388 q^{36} + 1440 q^{41} + 26076 q^{46} + 11576 q^{51} + 12936 q^{56} - 6664 q^{61} + 20664 q^{66} - 11496 q^{71} - 78624 q^{76} - 24112 q^{81} - 17412 q^{86} + 25480 q^{91} + 144 q^{96}+O(q^{100}) \) 32 * q + 248 * q^6 - 1008 * q^11 - 1732 * q^16 - 392 * q^21 - 4296 * q^26 + 9064 * q^31 - 14388 * q^36 + 1440 * q^41 + 26076 * q^46 + 11576 * q^51 + 12936 * q^56 - 6664 * q^61 + 20664 * q^66 - 11496 * q^71 - 78624 * q^76 - 24112 * q^81 - 17412 * q^86 + 25480 * q^91 + 144 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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