LMFDB - Embedded newform 189.4.h.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(37,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.h (of order $3$, degree $2$, not 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.03185 q^{2} +17.3195 q^{4} +(0.0751526 + 0.130168i) q^{5} +(12.4545 - 13.7072i) q^{7} -46.8942 q^{8} +O(q^{10})$	\(q-5.03185 q^{2} +17.3195 q^{4} +(0.0751526 + 0.130168i) q^{5} +(12.4545 - 13.7072i) q^{7} -46.8942 q^{8} +(-0.378156 - 0.654986i) q^{10} +(23.4910 - 40.6875i) q^{11} +(-8.75756 + 15.1685i) q^{13} +(-62.6689 + 68.9724i) q^{14} +97.4084 q^{16} +(35.7437 + 61.9098i) q^{17} +(-57.4382 + 99.4860i) q^{19} +(1.30160 + 2.25444i) q^{20} +(-118.203 + 204.733i) q^{22} +(-67.6463 - 117.167i) q^{23} +(62.4887 - 108.234i) q^{25} +(44.0667 - 76.3257i) q^{26} +(215.705 - 237.401i) q^{28} +(30.1444 + 52.2116i) q^{29} +10.2021 q^{31} -114.991 q^{32} +(-179.857 - 311.521i) q^{34} +(2.72022 + 0.591044i) q^{35} +(152.004 - 263.279i) q^{37} +(289.020 - 500.598i) q^{38} +(-3.52422 - 6.10413i) q^{40} +(142.917 - 247.540i) q^{41} +(-234.519 - 406.200i) q^{43} +(406.851 - 704.687i) q^{44} +(340.386 + 589.566i) q^{46} -337.945 q^{47} +(-32.7731 - 341.431i) q^{49} +(-314.434 + 544.615i) q^{50} +(-151.676 + 262.711i) q^{52} +(-13.1367 - 22.7535i) q^{53} +7.06163 q^{55} +(-584.041 + 642.786i) q^{56} +(-151.682 - 262.721i) q^{58} +579.352 q^{59} +807.201 q^{61} -51.3352 q^{62} -200.652 q^{64} -2.63261 q^{65} -121.252 q^{67} +(619.061 + 1072.25i) q^{68} +(-13.6877 - 2.97404i) q^{70} +26.5074 q^{71} +(-60.9077 - 105.495i) q^{73} +(-764.860 + 1324.78i) q^{74} +(-994.800 + 1723.04i) q^{76} +(-265.144 - 828.736i) q^{77} -58.6193 q^{79} +(7.32049 + 12.6795i) q^{80} +(-719.136 + 1245.58i) q^{82} +(-298.506 - 517.027i) q^{83} +(-5.37246 + 9.30537i) q^{85} +(1180.07 + 2043.93i) q^{86} +(-1101.59 + 1908.01i) q^{88} +(-286.291 + 495.870i) q^{89} +(98.8471 + 308.957i) q^{91} +(-1171.60 - 2029.27i) q^{92} +1700.49 q^{94} -17.2665 q^{95} +(-335.928 - 581.845i) q^{97} +(164.909 + 1718.03i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−5.03185			−1.77903			−0.889513	−	0.456910i	$-0.848956\pi$
$2$	−5.03185			−1.77903			−0.889513	+	0.456910i	$0.848956\pi$
$3$		0			0
$3$		0			0
$4$	17.3195			2.16493
$5$	0.0751526	+	0.130168i	0.00672186	+	0.0116426i	0.869367	−	0.494167i	$-0.164527\pi$
$5$	0.0751526	+	0.130168i	0.00672186	+	0.0116426i	−0.862645	+	0.505810i	$0.831194\pi$
$6$		0			0
$7$	12.4545	−	13.7072i	0.672477	−	0.740118i
$7$	12.4545	−	13.7072i	0.672477	−	0.740118i
$8$	−46.8942			−2.07245
$9$		0			0
$10$	−0.378156	−	0.654986i	−0.0119584	−	0.0207125i
$11$	23.4910	−	40.6875i	0.643890	−	1.11525i	−0.340666	−	0.940184i	$-0.610653\pi$
$11$	23.4910	−	40.6875i	0.643890	−	1.11525i	0.984557	−	0.175066i	$-0.0560140\pi$
$12$		0			0
$13$	−8.75756	+	15.1685i	−0.186839	+	0.323615i	−0.944195	−	0.329388i	$-0.893158\pi$
$13$	−8.75756	+	15.1685i	−0.186839	+	0.323615i	0.757356	+	0.653003i	$0.226491\pi$
$14$	−62.6689	+	68.9724i	−1.19635	+	1.31669i
$15$		0			0
$16$	97.4084			1.52201
$17$	35.7437	+	61.9098i	0.509948	+	0.883255i	0.999934	+	0.0115248i	$0.00366854\pi$
$17$	35.7437	+	61.9098i	0.509948	+	0.883255i	−0.489986	+	0.871730i	$0.662998\pi$
$18$		0			0
$19$	−57.4382	+	99.4860i	−0.693539	+	1.20124i	0.277132	+	0.960832i	$0.410616\pi$
$19$	−57.4382	+	99.4860i	−0.693539	+	1.20124i	−0.970671	+	0.240413i	$0.922717\pi$
$20$	1.30160	+	2.25444i	0.0145524	+	0.0252055i
$21$		0			0
$22$	−118.203	+	204.733i	−1.14550	+	1.98406i
$23$	−67.6463	−	117.167i	−0.613271	−	1.06222i	−0.990685	−	0.136172i	$-0.956520\pi$
$23$	−67.6463	−	117.167i	−0.613271	−	1.06222i	0.377414	−	0.926045i	$-0.376813\pi$
$24$		0			0
$25$	62.4887	−	108.234i	0.499910	−	0.865869i
$26$	44.0667	−	76.3257i	0.332392	−	0.575720i
$27$		0			0
$28$	215.705	−	237.401i	1.45587	−	1.60231i
$29$	30.1444	+	52.2116i	0.193023	+	0.334326i	0.946251	−	0.323434i	$-0.104837\pi$
$29$	30.1444	+	52.2116i	0.193023	+	0.334326i	−0.753227	+	0.657760i	$0.771504\pi$
$30$		0			0
$31$	10.2021			0.0591078			0.0295539	−	0.999563i	$-0.490591\pi$
$31$	10.2021			0.0591078			0.0295539	+	0.999563i	$0.490591\pi$
$32$	−114.991			−0.635240
$33$		0			0
$34$	−179.857	−	311.521i	−0.907210	−	1.57133i
$35$	2.72022	+	0.591044i	0.0131372	+	0.00285442i
$36$		0			0
$37$	152.004	−	263.279i	0.675386	−	1.16980i	−0.300970	−	0.953634i	$-0.597310\pi$
$37$	152.004	−	263.279i	0.675386	−	1.16980i	0.976356	−	0.216170i	$-0.0693564\pi$
$38$	289.020	−	500.598i	1.23382	−	2.13705i
$39$		0			0
$40$	−3.52422	−	6.10413i	−0.0139307	−	0.0241287i
$41$	142.917	−	247.540i	0.544388	−	0.942907i	−0.454258	−	0.890870i	$-0.650095\pi$
$41$	142.917	−	247.540i	0.544388	−	0.942907i	0.998645	−	0.0520365i	$-0.0165712\pi$
$42$		0			0
$43$	−234.519	−	406.200i	−0.831718	−	1.44058i	−0.896675	−	0.442690i	$-0.854024\pi$
$43$	−234.519	−	406.200i	−0.831718	−	1.44058i	0.0649564	−	0.997888i	$-0.479309\pi$
$44$	406.851	−	704.687i	1.39398	−	2.41444i
$45$		0			0
$46$	340.386	+	589.566i	1.09103	+	1.88971i
$47$	−337.945			−1.04882			−0.524408	−	0.851467i	$-0.675713\pi$
$47$	−337.945			−1.04882			−0.524408	+	0.851467i	$0.675713\pi$
$48$		0			0
$49$	−32.7731	−	341.431i	−0.0955484	−	0.995425i
$50$	−314.434	+	544.615i	−0.889352	+	1.54040i
$51$		0			0
$52$	−151.676	+	262.711i	−0.404495	+	0.700605i
$53$	−13.1367	−	22.7535i	−0.0340466	−	0.0589705i	0.848500	−	0.529195i	$-0.177506\pi$
$53$	−13.1367	−	22.7535i	−0.0340466	−	0.0589705i	−0.882547	+	0.470225i	$0.844173\pi$
$54$		0			0
$55$	7.06163			0.0173126
$56$	−584.041	+	642.786i	−1.39367	+	1.53386i
$57$		0			0
$58$	−151.682	−	262.721i	−0.343393	−	0.594775i
$59$	579.352			1.27839			0.639196	−	0.769044i	$-0.279267\pi$
$59$	579.352			1.27839			0.639196	+	0.769044i	$0.279267\pi$
$60$		0			0
$61$	807.201			1.69429			0.847144	−	0.531364i	$-0.178320\pi$
$61$	807.201			1.69429			0.847144	+	0.531364i	$0.178320\pi$
$62$	−51.3352			−0.105154
$63$		0			0
$64$	−200.652			−0.391898
$65$	−2.63261			−0.00502363
$66$		0			0
$67$	−121.252			−0.221095			−0.110547	−	0.993871i	$-0.535260\pi$
$67$	−121.252			−0.221095			−0.110547	+	0.993871i	$0.535260\pi$
$68$	619.061	+	1072.25i	1.10400	+	1.91219i
$69$		0			0
$70$	−13.6877	−	2.97404i	−0.0233714	−	0.00507808i
$71$	26.5074			0.0443077			0.0221538	−	0.999755i	$-0.492948\pi$
$71$	26.5074			0.0443077			0.0221538	+	0.999755i	$0.492948\pi$
$72$		0			0
$73$	−60.9077	−	105.495i	−0.0976534	−	0.169141i	0.813059	−	0.582181i	$-0.197800\pi$
$73$	−60.9077	−	105.495i	−0.0976534	−	0.169141i	−0.910713	+	0.413040i	$0.864467\pi$
$74$	−764.860	+	1324.78i	−1.20153	+	2.08111i
$75$		0			0
$76$	−994.800	+	1723.04i	−1.50147	+	2.60061i
$77$	−265.144	−	828.736i	−0.392415	−	1.22654i
$78$		0			0
$79$	−58.6193			−0.0834834			−0.0417417	−	0.999128i	$-0.513291\pi$
$79$	−58.6193			−0.0834834			−0.0417417	+	0.999128i	$0.513291\pi$
$80$	7.32049	+	12.6795i	0.0102307	+	0.0177201i
$81$		0			0
$82$	−719.136	+	1245.58i	−0.968480	+	1.67746i
$83$	−298.506	−	517.027i	−0.394762	−	0.683748i	0.598309	−	0.801266i	$-0.295840\pi$
$83$	−298.506	−	517.027i	−0.394762	−	0.683748i	−0.993071	+	0.117517i	$0.962506\pi$
$84$		0			0
$85$	−5.37246	+	9.30537i	−0.00685559	+	0.0118742i
$86$	1180.07	+	2043.93i	1.47965	+	2.56283i
$87$		0			0
$88$	−1101.59	+	1908.01i	−1.33443	+	2.31130i
$89$	−286.291	+	495.870i	−0.340975	+	0.590586i	−0.984614	−	0.174743i	$-0.944090\pi$
$89$	−286.291	+	495.870i	−0.340975	+	0.590586i	0.643639	+	0.765329i	$0.277424\pi$
$90$		0			0
$91$	98.8471	+	308.957i	0.113868	+	0.355907i
$92$	−1171.60	−	2029.27i	−1.32769	−	2.29963i
$93$		0			0
$94$	1700.49			1.86587
$95$	−17.2665			−0.0186475
$96$		0			0
$97$	−335.928	−	581.845i	−0.351632	−	0.609045i	0.634903	−	0.772592i	$-0.281040\pi$
$97$	−335.928	−	581.845i	−0.351632	−	0.609045i	−0.986536	+	0.163547i	$0.947707\pi$
$98$	164.909	+	1718.03i	0.169983	+	1.77089i
$99$		0			0
$100$	1082.27	−	1874.55i	1.08227	−	1.87455i
$101$	404.599	−	700.785i	0.398605	−	0.690403i	−0.594949	−	0.803763i	$-0.702828\pi$
$101$	404.599	−	700.785i	0.398605	−	0.690403i	0.993554	+	0.113360i	$0.0361613\pi$
$102$		0			0
$103$	−259.355	−	449.217i	−0.248107	−	0.429734i	0.714893	−	0.699233i	$-0.246475\pi$
$103$	−259.355	−	449.217i	−0.248107	−	0.429734i	−0.963001	+	0.269499i	$0.913142\pi$
$104$	410.678	−	711.316i	0.387215	−	0.670675i
$105$		0			0
$106$	66.1021	+	114.492i	0.0605698	+	0.104910i
$107$	925.466	−	1602.95i	0.836152	−	1.44826i	−0.0569379	−	0.998378i	$-0.518134\pi$
$107$	925.466	−	1602.95i	0.836152	−	1.44826i	0.893089	−	0.449879i	$-0.148533\pi$
$108$		0			0
$109$	247.001	+	427.817i	0.217049	+	0.375940i	0.953905	−	0.300110i	$-0.0970235\pi$
$109$	247.001	+	427.817i	0.217049	+	0.375940i	−0.736855	+	0.676050i	$0.763690\pi$
$110$	−35.5330			−0.0307995
$111$		0			0
$112$	1213.17	−	1335.19i	1.02351	−	1.12646i
$113$	24.3606	−	42.1939i	0.0202801	−	0.0351262i	−0.855707	−	0.517460i	$-0.826878\pi$
$113$	24.3606	−	42.1939i	0.0202801	−	0.0351262i	0.875987	+	0.482334i	$0.160211\pi$
$114$		0			0
$115$	10.1676	−	17.6108i	0.00824464	−	0.0142801i
$116$	522.085	+	904.278i	0.417883	+	0.723794i
$117$		0			0
$118$	−2915.21			−2.27429
$119$	1293.78	+	281.109i	0.996641	+	0.216548i
$120$		0			0
$121$	−438.151	−	758.900i	−0.329189	−	0.570173i
$122$	−4061.71			−3.01418
$123$		0			0
$124$	176.694			0.127965
$125$	37.5729			0.0268850
$126$		0			0
$127$	1030.66			0.720128			0.360064	−	0.932928i	$-0.382755\pi$
$127$	1030.66			0.720128			0.360064	+	0.932928i	$0.382755\pi$
$128$	1929.57			1.33244
$129$		0			0
$130$	13.2469			0.00893716
$131$	−845.933	−	1465.20i	−0.564195	−	0.977214i	−0.997124	−	0.0757862i	$-0.975853\pi$
$131$	−845.933	−	1465.20i	−0.564195	−	0.977214i	0.432929	−	0.901428i	$-0.357480\pi$
$132$		0			0
$133$	648.309	+	2026.36i	0.422673	+	1.32111i
$134$	610.123			0.393333
$135$		0			0
$136$	−1676.17	−	2903.21i	−1.05684	−	1.83050i
$137$	−1209.64	+	2095.15i	−0.754352	+	1.30658i	0.191344	+	0.981523i	$0.438716\pi$
$137$	−1209.64	+	2095.15i	−0.754352	+	1.30658i	−0.945696	+	0.325053i	$0.894618\pi$
$138$		0			0
$139$	61.7931	−	107.029i	0.0377067	−	0.0653099i	−0.846556	−	0.532299i	$-0.821328\pi$
$139$	61.7931	−	107.029i	0.0377067	−	0.0653099i	0.884263	+	0.466989i	$0.154661\pi$
$140$	47.1128	+	10.2366i	0.0284411	+	0.00617963i
$141$		0			0
$142$	−133.381			−0.0788245
$143$	411.447	+	712.647i	0.240608	+	0.416745i
$144$		0			0
$145$	−4.53086	+	7.84768i	−0.00259495	+	0.00449458i
$146$	306.478	+	530.835i	0.173728	+	0.300906i
$147$		0			0
$148$	2632.63	−	4559.85i	1.46217	−	2.53255i
$149$	611.710	+	1059.51i	0.336330	+	0.582541i	0.983739	−	0.179601i	$-0.0574808\pi$
$149$	611.710	+	1059.51i	0.336330	+	0.582541i	−0.647409	+	0.762143i	$0.724147\pi$
$150$		0			0
$151$	589.079	−	1020.32i	0.317474	−	0.549881i	−0.662486	−	0.749074i	$-0.730499\pi$
$151$	589.079	−	1020.32i	0.317474	−	0.549881i	0.979960	+	0.199193i	$0.0638320\pi$
$152$	2693.52	−	4665.31i	1.43732	−	2.48952i
$153$		0			0
$154$	1334.16	+	4170.07i	0.698117	+	2.18204i
$155$	0.766711	+	1.32798i	0.000397314	+	0.000688169i
$156$		0			0
$157$	−3370.12			−1.71315			−0.856576	−	0.516021i	$-0.827413\pi$
$157$	−3370.12			−1.71315			−0.856576	+	0.516021i	$0.827413\pi$
$158$	294.963			0.148519
$159$		0			0
$160$	−8.64185	−	14.9681i	−0.00426999	−	0.00739584i
$161$	−2448.52	−	532.010i	−1.19858	−	0.260424i
$162$		0			0
$163$	−588.235	+	1018.85i	−0.282663	+	0.489587i	−0.972040	−	0.234816i	$-0.924551\pi$
$163$	−588.235	+	1018.85i	−0.282663	+	0.489587i	0.689377	+	0.724403i	$0.257885\pi$
$164$	2475.25	−	4287.25i	1.17856	−	2.04133i
$165$		0			0
$166$	1502.04	+	2601.60i	0.702292	+	1.21641i
$167$	−406.112	+	703.406i	−0.188179	+	0.325935i	−0.944643	−	0.328100i	$-0.893592\pi$
$167$	−406.112	+	703.406i	−0.188179	+	0.325935i	0.756464	+	0.654035i	$0.226925\pi$
$168$		0			0
$169$	945.110	+	1636.98i	0.430182	+	0.745097i
$170$	27.0334	−	46.8232i	0.0121963	−	0.0211246i
$171$		0			0
$172$	−4061.75	−	7035.16i	−1.80062	−	3.11876i
$173$	−1946.47			−0.855418			−0.427709	−	0.903916i	$-0.640679\pi$
$173$	−1946.47			−0.855418			−0.427709	+	0.903916i	$0.640679\pi$
$174$		0			0
$175$	−705.314	−	2204.53i	−0.304667	−	0.952269i
$176$	2288.22	−	3963.31i	0.980005	−	1.69742i
$177$		0			0
$178$	1440.57	−	2495.14i	0.606603	−	1.05067i
$179$	−536.432	−	929.128i	−0.223993	−	0.387968i	0.732024	−	0.681279i	$-0.238576\pi$
$179$	−536.432	−	929.128i	−0.223993	−	0.387968i	−0.956017	+	0.293311i	$0.905243\pi$
$180$		0			0
$181$	3177.73			1.30497			0.652483	−	0.757803i	$-0.273727\pi$
$181$	3177.73			1.30497			0.652483	+	0.757803i	$0.273727\pi$
$182$	−497.383	−	1554.63i	−0.202574	−	0.633167i
$183$		0			0
$184$	3172.22	+	5494.44i	1.27097	+	2.20139i
$185$	45.6940			0.0181594
$186$		0			0
$187$	3358.61			1.31340
$188$	−5853.02			−2.27062
$189$		0			0
$190$	86.8826			0.0331743
$191$	−2344.22			−0.888070			−0.444035	−	0.896009i	$-0.646454\pi$
$191$	−2344.22			−0.888070			−0.444035	+	0.896009i	$0.646454\pi$
$192$		0			0
$193$	2169.15			0.809008			0.404504	−	0.914536i	$-0.367444\pi$
$193$	2169.15			0.809008			0.404504	+	0.914536i	$0.367444\pi$
$194$	1690.34	+	2927.75i	0.625563	+	1.08351i
$195$		0			0
$196$	−567.613	−	5913.40i	−0.206856	−	2.15503i
$197$	−2081.90			−0.752941			−0.376470	−	0.926429i	$-0.622862\pi$
$197$	−2081.90			−0.752941			−0.376470	+	0.926429i	$0.622862\pi$
$198$		0			0
$199$	1309.24	+	2267.67i	0.466380	+	0.807795i	0.999263	−	0.0383949i	$-0.0122245\pi$
$199$	1309.24	+	2267.67i	0.466380	+	0.807795i	−0.532882	+	0.846189i	$0.678891\pi$
$200$	−2930.35	+	5075.52i	−1.03604	+	1.79447i
$201$		0			0
$202$	−2035.88	+	3526.24i	−0.709128	+	1.22825i
$203$	1091.11	+	237.073i	0.377244	+	0.0819668i
$204$		0			0
$205$	42.9624			0.0146372
$206$	1305.04	+	2260.39i	0.441389	+	0.764508i
$207$		0			0
$208$	−853.059	+	1477.54i	−0.284370	+	0.492544i
$209$	2698.56	+	4674.04i	0.893126	+	1.54694i
$210$		0			0
$211$	−2105.37	+	3646.61i	−0.686918	+	1.18978i	0.285913	+	0.958256i	$0.407703\pi$
$211$	−2105.37	+	3646.61i	−0.686918	+	1.18978i	−0.972830	+	0.231520i	$0.925630\pi$
$212$	−227.522	−	394.079i	−0.0737087	−	0.127667i
$213$		0			0
$214$	−4656.80	+	8065.82i	−1.48754	+	2.57649i
$215$	35.2495	−	61.0539i	0.0111814	−	0.0193667i
$216$		0			0
$217$	127.061	−	139.841i	0.0397487	−	0.0437468i
$218$	−1242.87	−	2152.71i	−0.386136	−	0.668807i
$219$		0			0
$220$	122.304			0.0374805
$221$	−1252.11			−0.381113
$222$		0			0
$223$	−437.287	−	757.403i	−0.131313	−	0.227442i	0.792870	−	0.609391i	$-0.208586\pi$
$223$	−437.287	−	757.403i	−0.131313	−	0.227442i	−0.924183	+	0.381950i	$0.875253\pi$
$224$	−1432.15	+	1576.20i	−0.427184	+	0.470152i
$225$		0			0
$226$	−122.579	+	212.313i	−0.0360789	+	0.0624905i
$227$	−252.915	+	438.062i	−0.0739496	+	0.128084i	−0.900629	−	0.434589i	$-0.856894\pi$
$227$	−252.915	+	438.062i	−0.0739496	+	0.128084i	0.826679	+	0.562673i	$0.190227\pi$
$228$		0			0
$229$	313.740	+	543.413i	0.0905350	+	0.156811i	0.907736	−	0.419541i	$-0.137809\pi$
$229$	313.740	+	543.413i	0.0905350	+	0.156811i	−0.817201	+	0.576352i	$0.804476\pi$
$230$	−51.1618	+	88.6148i	−0.0146674	+	0.0254047i
$231$		0			0
$232$	−1413.60	−	2448.42i	−0.400031	−	0.692874i
$233$	710.495	−	1230.61i	0.199769	−	0.346009i	−0.748685	−	0.662926i	$-0.769314\pi$
$233$	710.495	−	1230.61i	0.199769	−	0.346009i	0.948453	+	0.316917i	$0.102648\pi$
$234$		0			0
$235$	−25.3974	−	43.9897i	−0.00704998	−	0.0122109i
$236$	10034.1			2.76763
$237$		0			0
$238$	−6510.08	−	1414.50i	−1.77305	−	0.385244i
$239$	−325.023	+	562.956i	−0.0879665	+	0.152362i	−0.906651	−	0.421881i	$-0.861370\pi$
$239$	−325.023	+	562.956i	−0.0879665	+	0.152362i	0.818685	+	0.574243i	$0.194704\pi$
$240$		0			0
$241$	902.259	−	1562.76i	0.241160	−	0.417702i	−0.719885	−	0.694094i	$-0.755805\pi$
$241$	902.259	−	1562.76i	0.241160	−	0.417702i	0.961045	+	0.276392i	$0.0891387\pi$
$242$	2204.71	+	3818.67i	0.585637	+	1.01435i
$243$		0			0
$244$	13980.3			3.66802
$245$	41.9804	−	29.9254i	0.0109471	−	0.00780353i
$246$		0			0
$247$	−1006.04	−	1742.51i	−0.259160	−	0.448879i
$248$	−478.417			−0.122498
$249$		0			0
$250$	−189.061			−0.0478291
$251$	−405.653			−0.102010			−0.0510052	−	0.998698i	$-0.516242\pi$
$251$	−405.653			−0.102010			−0.0510052	+	0.998698i	$0.516242\pi$
$252$		0			0
$253$	−6356.31			−1.57952
$254$	−5186.12			−1.28113
$255$		0			0
$256$	−8104.10			−1.97854
$257$	1430.76	+	2478.14i	0.347269	+	0.601487i	0.985763	−	0.168139i	$-0.0537758\pi$
$257$	1430.76	+	2478.14i	0.347269	+	0.601487i	−0.638494	+	0.769626i	$0.720442\pi$
$258$		0			0
$259$	−1715.68	−	5362.53i	−0.411610	−	1.28653i
$260$	−45.5955			−0.0108758
$261$		0			0
$262$	4256.61	+	7372.66i	1.00372	+	1.73849i
$263$	2241.77	−	3882.86i	0.525603	−	0.910370i	−0.473953	−	0.880550i	$-0.657173\pi$
$263$	2241.77	−	3882.86i	0.525603	−	0.910370i	0.999555	−	0.0298201i	$-0.00949345\pi$
$264$		0			0
$265$	1.97452	−	3.41997i	0.000457713	−	0.000792782i
$266$	−3262.19	−	10196.3i	−0.751947	−	2.35029i
$267$		0			0
$268$	−2100.03			−0.478655
$269$	3638.36	+	6301.83i	0.824665	+	1.42836i	0.902175	+	0.431370i	$0.141970\pi$
$269$	3638.36	+	6301.83i	0.824665	+	1.42836i	−0.0775101	+	0.996992i	$0.524697\pi$
$270$		0			0
$271$	−1949.68	+	3376.94i	−0.437028	+	0.756954i	−0.997459	−	0.0712468i	$-0.977302\pi$
$271$	−1949.68	+	3376.94i	−0.437028	+	0.756954i	0.560431	+	0.828201i	$0.310636\pi$
$272$	3481.73	+	6030.53i	0.776143	+	1.34432i
$273$		0			0
$274$	6086.71	−	10542.5i	1.34201	−	2.32443i
$275$	−2935.84	−	5085.02i	−0.643774	−	1.11505i
$276$		0			0
$277$	349.169	−	604.779i	0.0757385	−	0.131183i	−0.825669	−	0.564155i	$-0.809202\pi$
$277$	349.169	−	604.779i	0.0757385	−	0.131183i	0.901407	+	0.432972i	$0.142535\pi$
$278$	−310.934	+	538.553i	−0.0670811	+	0.116188i
$279$		0			0
$280$	−127.563	−	27.7165i	−0.0272261	−	0.00591563i
$281$	1509.00	+	2613.67i	0.320354	+	0.554870i	0.980561	−	0.196214i	$-0.0628646\pi$
$281$	1509.00	+	2613.67i	0.320354	+	0.554870i	−0.660207	+	0.751084i	$0.729531\pi$
$282$		0			0
$283$	7812.42			1.64099			0.820495	−	0.571654i	$-0.193698\pi$
$283$	7812.42			1.64099			0.820495	+	0.571654i	$0.193698\pi$
$284$	459.094			0.0959232
$285$		0			0
$286$	−2070.34	−	3585.93i	−0.428048	−	0.741401i
$287$	−1613.11	−	5041.96i	−0.331774	−	1.03699i
$288$		0			0
$289$	−98.7172	+	170.983i	−0.0200931	+	0.0348022i
$290$	22.7986	−	39.4883i	0.00461648	−	0.00799598i
$291$		0			0
$292$	−1054.89	−	1827.12i	−0.211413	−	0.366179i
$293$	3904.99	−	6763.64i	0.778607	−	1.34859i	−0.154137	−	0.988049i	$-0.549260\pi$
$293$	3904.99	−	6763.64i	0.778607	−	1.34859i	0.932744	−	0.360538i	$-0.117407\pi$
$294$		0			0
$295$	43.5398	+	75.4131i	0.00859317	+	0.0148838i
$296$	−7128.09	+	12346.2i	−1.39970	+	2.42436i
$297$		0			0
$298$	−3078.03	−	5331.31i	−0.598341	−	1.03636i
$299$	2369.67			0.458332
$300$		0			0
$301$	−8488.66	−	1844.40i	−1.62551	−	0.353187i
$302$	−2964.16	+	5134.07i	−0.564795	+	0.978253i
$303$		0			0
$304$	−5594.96	+	9690.76i	−1.05557	+	1.82830i
$305$	60.6633	+	105.072i	0.0113888	+	0.0197259i
$306$		0			0
$307$	3185.56			0.592214			0.296107	−	0.955155i	$-0.404312\pi$
$307$	3185.56			0.592214			0.296107	+	0.955155i	$0.404312\pi$
$308$	−4592.15	−	14353.3i	−0.849553	−	2.65537i
$309$		0			0
$310$	−3.85797	−	6.68221i	−0.000706833	−	0.00122427i
$311$	7401.39			1.34950			0.674749	−	0.738047i	$-0.264252\pi$
$311$	7401.39			1.34950			0.674749	+	0.738047i	$0.264252\pi$
$312$		0			0
$313$	−594.828			−0.107417			−0.0537087	−	0.998557i	$-0.517104\pi$
$313$	−594.828			−0.107417			−0.0537087	+	0.998557i	$0.517104\pi$
$314$	16957.9			3.04774
$315$		0			0
$316$	−1015.26			−0.180736
$317$	4110.20			0.728238			0.364119	−	0.931352i	$-0.381370\pi$
$317$	4110.20			0.728238			0.364119	+	0.931352i	$0.381370\pi$
$318$		0			0
$319$	2832.48			0.497143
$320$	−15.0795	−	26.1185i	−0.00263428	−	0.00456271i
$321$		0			0
$322$	12320.6	+	2676.99i	2.13230	+	0.463301i
$323$	−8212.21			−1.41467
$324$		0			0
$325$	1094.50	+	1895.72i	0.186805	+	0.323557i
$326$	2959.91	−	5126.71i	0.502865	−	0.870988i
$327$		0			0
$328$	−6701.97	+	11608.2i	−1.12821	+	1.95413i
$329$	−4208.92	+	4632.27i	−0.705304	+	0.776247i
$330$		0			0
$331$	−9208.05			−1.52906			−0.764532	−	0.644586i	$-0.777030\pi$
$331$	−9208.05			−1.52906			−0.764532	+	0.644586i	$0.777030\pi$
$332$	−5169.96	−	8954.64i	−0.854634	−	1.48027i
$333$		0			0
$334$	2043.49	−	3539.43i	0.334775	−	0.579847i
$335$	−9.11244	−	15.7832i	−0.00148617	−	0.00257412i
$336$		0			0
$337$	−5091.35	+	8818.47i	−0.822977	+	1.42544i	0.0804782	+	0.996756i	$0.474355\pi$
$337$	−5091.35	+	8818.47i	−0.822977	+	1.42544i	−0.903455	+	0.428682i	$0.858978\pi$
$338$	−4755.65	−	8237.03i	−0.765305	−	1.32555i
$339$		0			0
$340$	−93.0482	+	161.164i	−0.0148419	+	0.0257069i
$341$	239.656	−	415.097i	0.0380590	−	0.0659201i
$342$		0			0
$343$	−5088.22	−	3803.11i	−0.800986	−	0.598684i
$344$	10997.6	+	19048.4i	1.72369	+	2.98552i
$345$		0			0
$346$	9794.34			1.52181
$347$	10025.9			1.55106			0.775528	−	0.631314i	$-0.217484\pi$
$347$	10025.9			1.55106			0.775528	+	0.631314i	$0.217484\pi$
$348$		0			0
$349$	−1707.59	−	2957.64i	−0.261907	−	0.453635i	0.704842	−	0.709364i	$-0.251018\pi$
$349$	−1707.59	−	2957.64i	−0.261907	−	0.453635i	−0.966749	+	0.255729i	$0.917685\pi$
$350$	3549.03	+	11092.9i	0.542011	+	1.69411i
$351$		0			0
$352$	−2701.24	+	4678.69i	−0.409025	+	0.708451i
$353$	−2379.63	+	4121.64i	−0.358796	+	0.621453i	−0.987760	−	0.155981i	$-0.950146\pi$
$353$	−2379.63	+	4121.64i	−0.358796	+	0.621453i	0.628964	+	0.777434i	$0.283479\pi$
$354$		0			0
$355$	1.99210	+	3.45042i	0.000297830	+	0.000515856i
$356$	−4958.40	+	8588.21i	−0.738188	+	1.27858i
$357$		0			0
$358$	2699.24	+	4675.23i	0.398490	+	0.690205i
$359$	−4207.68	+	7287.92i	−0.618588	+	1.07143i	0.371156	+	0.928571i	$0.378962\pi$
$359$	−4207.68	+	7287.92i	−0.618588	+	1.07143i	−0.989744	+	0.142855i	$0.954372\pi$
$360$		0			0
$361$	−3168.80	−	5488.53i	−0.461992	−	0.800194i
$362$	−15989.9			−2.32157
$363$		0			0
$364$	1711.98	+	5350.98i	0.246517	+	0.770515i
$365$	9.15474	−	15.8565i	0.00131282	−	0.00227388i
$366$		0			0
$367$	584.783	−	1012.87i	0.0831755	−	0.144064i	−0.821437	−	0.570300i	$-0.806827\pi$
$367$	584.783	−	1012.87i	0.0831755	−	0.144064i	0.904612	+	0.426235i	$0.140160\pi$
$368$	−6589.32	−	11413.0i	−0.933402	−	1.61670i
$369$		0			0
$370$	−229.925			−0.0323060
$371$	−475.497	−	103.315i	−0.0665407	−	0.0144578i
$372$		0			0
$373$	4188.69	+	7255.03i	0.581454	+	1.00711i	0.995307	+	0.0967638i	$0.0308492\pi$
$373$	4188.69	+	7255.03i	0.581454	+	1.00711i	−0.413854	+	0.910343i	$0.635818\pi$
$374$	−16900.0			−2.33658
$375$		0			0
$376$	15847.6			2.17361
$377$	−1055.97			−0.144257
$378$		0			0
$379$	3550.71			0.481234			0.240617	−	0.970620i	$-0.422650\pi$
$379$	3550.71			0.481234			0.240617	+	0.970620i	$0.422650\pi$
$380$	−299.047			−0.0403705
$381$		0			0
$382$	11795.7			1.57990
$383$	3601.65	+	6238.24i	0.480511	+	0.832269i	0.999750	−	0.0223601i	$-0.00711802\pi$
$383$	3601.65	+	6238.24i	0.480511	+	0.832269i	−0.519239	+	0.854629i	$0.673785\pi$
$384$		0			0
$385$	87.9488	−	96.7950i	0.0116423	−	0.0128133i
$386$	−10914.8			−1.43925
$387$		0			0
$388$	−5818.10	−	10077.2i	−0.761261	−	1.31854i
$389$	−1268.11	+	2196.43i	−0.165285	+	0.286281i	−0.936756	−	0.349982i	$-0.886188\pi$
$389$	−1268.11	+	2196.43i	−0.165285	+	0.286281i	0.771472	+	0.636264i	$0.219521\pi$
$390$		0			0
$391$	4835.85	−	8375.94i	0.625472	−	1.08335i
$392$	1536.87	+	16011.1i	0.198019	+	2.06297i
$393$		0			0
$394$	10475.8			1.33950
$395$	−4.40540	−	7.63037i	−0.000561164	−	0.000971964i
$396$		0			0
$397$	−4500.62	+	7795.31i	−0.568967	+	0.985479i	0.427702	+	0.903920i	$0.359323\pi$
$397$	−4500.62	+	7795.31i	−0.568967	+	0.985479i	−0.996668	+	0.0815593i	$0.974010\pi$
$398$	−6587.90	−	11410.6i	−0.829703	−	1.43709i
$399$		0			0
$400$	6086.92	−	10542.9i	0.760865	−	1.31786i
$401$	−1006.95	−	1744.09i	−0.125398	−	0.217196i	0.796490	−	0.604651i	$-0.206688\pi$
$401$	−1006.95	−	1744.09i	−0.125398	−	0.217196i	−0.921889	+	0.387455i	$0.873354\pi$
$402$		0			0
$403$	−89.3451	+	154.750i	−0.0110437	+	0.0191282i
$404$	7007.43	−	12137.2i	0.862953	−	1.49468i
$405$		0			0
$406$	−5490.28	−	1192.91i	−0.671128	−	0.145821i
$407$	−7141.44	−	12369.3i	−0.869749	−	1.50645i
$408$		0			0
$409$	2903.91			0.351074			0.175537	−	0.984473i	$-0.443834\pi$
$409$	2903.91			0.351074			0.175537	+	0.984473i	$0.443834\pi$
$410$	−216.180			−0.0260399
$411$		0			0
$412$	−4491.90	−	7780.19i	−0.537136	−	0.930346i
$413$	7215.51	−	7941.27i	0.859690	−	0.946161i
$414$		0			0
$415$	44.8670	−	77.7119i	0.00530707	−	0.00919212i
$416$	1007.04	−	1744.24i	0.118688	−	0.205573i
$417$		0			0
$418$	−13578.7	−	23519.1i	−1.58889	−	2.75205i
$419$	−1961.53	+	3397.47i	−0.228704	+	0.396127i	−0.957424	−	0.288684i	$-0.906782\pi$
$419$	−1961.53	+	3397.47i	−0.228704	+	0.396127i	0.728720	+	0.684812i	$0.240115\pi$
$420$		0			0
$421$	5680.15	+	9838.31i	0.657562	+	1.13893i	0.981245	+	0.192766i	$0.0617457\pi$
$421$	5680.15	+	9838.31i	0.657562	+	1.13893i	−0.323683	+	0.946166i	$0.604921\pi$
$422$	10593.9	−	18349.2i	1.22204	−	2.11664i
$423$		0			0
$424$	616.037	+	1067.01i	0.0705599	+	0.122213i
$425$	8934.30			1.01971
$426$		0			0
$427$	10053.3	−	11064.4i	1.13937	−	1.25397i
$428$	16028.6	−	27762.3i	1.81021	−	3.13538i
$429$		0			0
$430$	−177.370	+	307.214i	−0.0198920	+	0.0344539i
$431$	−5136.35	−	8896.43i	−0.574036	−	0.994259i	−0.996146	−	0.0877146i	$-0.972044\pi$
$431$	−5136.35	−	8896.43i	−0.574036	−	0.994259i	0.422110	−	0.906545i	$-0.361290\pi$
$432$		0			0
$433$	−6607.79			−0.733373			−0.366686	−	0.930345i	$-0.619508\pi$
$433$	−6607.79			−0.733373			−0.366686	+	0.930345i	$0.619508\pi$
$434$	−639.352	+	703.660i	−0.0707140	+	0.0778266i
$435$		0			0
$436$	4277.92	+	7409.57i	0.469897	+	0.813886i
$437$	15541.9			1.70131
$438$		0			0
$439$	1918.63			0.208591			0.104295	−	0.994546i	$-0.466741\pi$
$439$	1918.63			0.208591			0.104295	+	0.994546i	$0.466741\pi$
$440$	−331.149			−0.0358794
$441$		0			0
$442$	6300.42			0.678010
$443$	2277.97			0.244311			0.122156	−	0.992511i	$-0.461019\pi$
$443$	2277.97			0.244311			0.122156	+	0.992511i	$0.461019\pi$
$444$		0			0
$445$	−86.0620			−0.00916793
$446$	2200.36	+	3811.14i	0.233610	+	0.404625i
$447$		0			0
$448$	−2499.01	+	2750.37i	−0.263542	+	0.290051i
$449$	1177.62			0.123776			0.0618881	−	0.998083i	$-0.480288\pi$
$449$	1177.62			0.123776			0.0618881	+	0.998083i	$0.480288\pi$
$450$		0			0
$451$	−6714.52	−	11629.9i	−0.701052	−	1.21426i
$452$	421.913	−	730.776i	0.0439052	−	0.0760460i
$453$		0			0
$454$	1272.63	−	2204.26i	0.131558	−	0.227866i
$455$	−32.7878	+	36.0857i	−0.00337827	+	0.00371807i
$456$		0			0
$457$	−15642.0			−1.60110			−0.800548	−	0.599268i	$-0.795458\pi$
$457$	−15642.0			−1.60110			−0.800548	+	0.599268i	$0.795458\pi$
$458$	−1578.69	−	2734.37i	−0.161064	−	0.278971i
$459$		0			0
$460$	176.097	−	305.010i	0.0178491	−	0.0309156i
$461$	7323.78	+	12685.2i	0.739919	+	1.28158i	0.952531	+	0.304440i	$0.0984694\pi$
$461$	7323.78	+	12685.2i	0.739919	+	1.28158i	−0.212613	+	0.977137i	$0.568197\pi$
$462$		0			0
$463$	−1186.46	+	2055.01i	−0.119092	+	0.206274i	−0.919408	−	0.393305i	$-0.871332\pi$
$463$	−1186.46	+	2055.01i	−0.119092	+	0.206274i	0.800316	+	0.599578i	$0.204665\pi$
$464$	2936.32	+	5085.85i	0.293783	+	0.508846i
$465$		0			0
$466$	−3575.10	+	6192.26i	−0.355394	+	0.615560i
$467$	−2337.83	+	4049.24i	−0.231653	+	0.401234i	−0.958295	−	0.285782i	$-0.907747\pi$
$467$	−2337.83	+	4049.24i	−0.231653	+	0.401234i	0.726642	+	0.687016i	$0.241080\pi$
$468$		0			0
$469$	−1510.13	+	1662.03i	−0.148681	+	0.163636i
$470$	127.796	+	221.349i	0.0125421	+	0.0217236i
$471$		0			0
$472$	−27168.2			−2.64940
$473$	−22036.4			−2.14214
$474$		0			0
$475$	7178.48	+	12433.5i	0.693413	+	1.20103i
$476$	22407.5	+	4868.65i	2.15766	+	0.468812i
$477$		0			0
$478$	1635.47	−	2832.71i	0.156495	−	0.271057i
$479$	−9521.54	+	16491.8i	−0.908247	+	1.57313i	−0.0917491	+	0.995782i	$0.529246\pi$
$479$	−9521.54	+	16491.8i	−0.908247	+	1.57313i	−0.816498	+	0.577348i	$0.804088\pi$
$480$		0			0
$481$	2662.37	+	4611.35i	0.252377	+	0.437130i
$482$	−4540.03	+	7863.56i	−0.429030	+	0.743102i
$483$		0			0
$484$	−7588.55	−	13143.7i	−0.712673	−	1.23439i
$485$	50.4918	−	87.4543i	0.00472724	−	0.00818783i
$486$		0			0
$487$	2864.85	+	4962.07i	0.266569	+	0.461710i	0.967973	−	0.251053i	$-0.0807768\pi$
$487$	2864.85	+	4962.07i	0.266569	+	0.461710i	−0.701405	+	0.712763i	$0.747443\pi$
$488$	−37853.0			−3.51132
$489$		0			0
$490$	−211.239	+	150.580i	−0.0194751	+	0.0138827i
$491$	1143.99	−	1981.45i	0.105148	−	0.182121i	−0.808651	−	0.588289i	$-0.799802\pi$
$491$	1143.99	−	1981.45i	0.105148	−	0.182121i	0.913798	+	0.406168i	$0.133135\pi$
$492$		0			0
$493$	−2154.94	+	3732.47i	−0.196864	+	0.340978i
$494$	5062.23	+	8768.03i	0.461053	+	0.798568i
$495$		0			0
$496$	993.765			0.0899625
$497$	330.135	−	363.341i	0.0297959	−	0.0327929i
$498$		0			0
$499$	39.8748	+	69.0652i	0.00357724	+	0.00619595i	0.867808	−	0.496899i	$-0.165528\pi$
$499$	39.8748	+	69.0652i	0.00357724	+	0.00619595i	−0.864231	+	0.503095i	$0.832195\pi$
$500$	650.743			0.0582042
$501$		0			0
$502$	2041.18			0.181479
$503$	7215.65			0.639622			0.319811	−	0.947481i	$-0.396381\pi$
$503$	7215.65			0.639622			0.319811	+	0.947481i	$0.396381\pi$
$504$		0			0
$505$	121.627			0.0107174
$506$	31984.0			2.81000
$507$		0			0
$508$	17850.5			1.55903
$509$	−5003.04	−	8665.53i	−0.435670	−	0.754603i	0.561680	−	0.827355i	$-0.310155\pi$
$509$	−5003.04	−	8665.53i	−0.435670	−	0.754603i	−0.997350	+	0.0727519i	$0.976822\pi$
$510$		0			0
$511$	−2204.61	−	479.013i	−0.190854	−	0.0414683i
$512$	25342.0			2.18744
$513$		0			0
$514$	−7199.34	−	12469.6i	−0.617800	−	1.07006i
$515$	38.9825	−	67.5196i	0.00333548	−	0.00577722i
$516$		0			0
$517$	−7938.65	+	13750.1i	−0.675322	+	1.16969i
$518$	8633.03	+	26983.4i	0.732265	+	2.28877i
$519$		0			0
$520$	123.454			0.0104112
$521$	283.660	+	491.314i	0.0238529	+	0.0413145i	0.877705	−	0.479200i	$-0.159073\pi$
$521$	283.660	+	491.314i	0.0238529	+	0.0413145i	−0.853853	+	0.520515i	$0.825740\pi$
$522$		0			0
$523$	7144.87	−	12375.3i	0.597368	−	1.03467i	−0.395840	−	0.918320i	$-0.629546\pi$
$523$	7144.87	−	12375.3i	0.597368	−	1.03467i	0.993208	−	0.116352i	$-0.0371202\pi$
$524$	−14651.1	−	25376.5i	−1.22144	−	2.11560i
$525$		0			0
$526$	−11280.2	+	19538.0i	−0.935061	+	1.61957i
$527$	364.659	+	631.607i	0.0301419	+	0.0522073i
$528$		0			0
$529$	−3068.55	+	5314.89i	−0.252203	+	0.436828i
$530$	−9.93549	+	17.2088i	−0.000814283	+	0.00141038i
$531$		0			0
$532$	11228.4	+	35095.5i	0.915059	+	2.86012i
$533$	2503.21	+	4335.68i	0.203426	+	0.352344i
$534$		0			0
$535$	278.205			0.0224820
$536$	5686.03			0.458207
$537$		0			0
$538$	−18307.7	−	31709.8i	−1.46710	−	2.54109i
$539$	−14661.9	−	6687.08i	−1.17167	−	0.534384i
$540$		0			0
$541$	8571.74	−	14846.7i	0.681198	−	1.17987i	−0.293418	−	0.955984i	$-0.594793\pi$
$541$	8571.74	−	14846.7i	0.681198	−	1.17987i	0.974616	−	0.223885i	$-0.0718739\pi$
$542$	9810.48	−	16992.3i	0.777484	−	1.34664i
$543$		0			0
$544$	−4110.19	−	7119.05i	−0.323939	−	0.561079i
$545$	−37.1255	+	64.3032i	−0.00291795	+	0.00505403i
$546$		0			0
$547$	1277.70	+	2213.05i	0.0998733	+	0.172986i	0.911632	−	0.411007i	$-0.134823\pi$
$547$	1277.70	+	2213.05i	0.0998733	+	0.172986i	−0.811759	+	0.583993i	$0.801490\pi$
$548$	−20950.3	+	36286.9i	−1.63312	+	2.82865i
$549$		0			0
$550$	14772.7	+	25587.1i	1.14529	+	1.98370i
$551$	−6925.77			−0.535477
$552$		0			0
$553$	−730.072	+	803.505i	−0.0561407	+	0.0617876i
$554$	−1756.97	+	3043.16i	−0.134741	+	0.233378i
$555$		0			0
$556$	1070.22	−	1853.68i	0.0816324	−	0.141392i
$557$	6867.52	+	11894.9i	0.522417	+	0.904852i	0.999660	+	0.0260810i	$0.00830277\pi$
$557$	6867.52	+	11894.9i	0.522417	+	0.904852i	−0.477243	+	0.878771i	$0.658364\pi$
$558$		0			0
$559$	8215.27			0.621590
$560$	264.972	+	57.5726i	0.0199949	+	0.00434444i
$561$		0			0
$562$	−7593.07	−	13151.6i	−0.569919	−	0.987129i
$563$	−8276.51			−0.619562			−0.309781	−	0.950808i	$-0.600256\pi$
$563$	−8276.51			−0.619562			−0.309781	+	0.950808i	$0.600256\pi$
$564$		0			0
$565$	7.32307			0.000545281
$566$	−39310.9			−2.91936
$567$		0			0
$568$	−1243.04			−0.0918254
$569$	−981.628			−0.0723233			−0.0361617	−	0.999346i	$-0.511513\pi$
$569$	−981.628			−0.0723233			−0.0361617	+	0.999346i	$0.511513\pi$
$570$		0			0
$571$	11041.8			0.809259			0.404629	−	0.914481i	$-0.367401\pi$
$571$	11041.8			0.809259			0.404629	+	0.914481i	$0.367401\pi$
$572$	7126.05	+	12342.7i	0.520900	+	0.902226i
$573$		0			0
$574$	8116.94	+	25370.4i	0.590234	+	1.84484i
$575$	−16908.5			−1.22632
$576$		0			0
$577$	12110.6	+	20976.2i	0.873780	+	1.51343i	0.858057	+	0.513554i	$0.171672\pi$
$577$	12110.6	+	20976.2i	0.873780	+	1.51343i	0.0157228	+	0.999876i	$0.494995\pi$
$578$	496.730	−	860.361i	0.0357461	−	0.0619140i
$579$		0			0
$580$	−78.4722	+	135.918i	−0.00561789	+	0.00973048i
$581$	−10804.7	−	2347.62i	−0.771523	−	0.167635i
$582$		0			0
$583$	−1234.38			−0.0876892
$584$	2856.21	+	4947.11i	0.202382	+	0.350535i
$585$		0			0
$586$	−19649.3	+	34033.6i	−1.38516	+	2.39917i
$587$	−11452.6	−	19836.5i	−0.805280	−	1.39479i	−0.916102	−	0.400945i	$-0.868682\pi$
$587$	−11452.6	−	19836.5i	−0.805280	−	1.39479i	0.110822	−	0.993840i	$-0.464652\pi$
$588$		0			0
$589$	−585.988	+	1014.96i	−0.0409936	+	0.0710030i
$590$	−219.086	−	379.467i	−0.0152875	−	0.0264787i
$591$		0			0
$592$	14806.5	−	25645.5i	1.02794	−	1.78045i
$593$	−4993.20	+	8648.48i	−0.345778	+	0.598905i	−0.985495	−	0.169706i	$-0.945718\pi$
$593$	−4993.20	+	8648.48i	−0.345778	+	0.598905i	0.639717	+	0.768611i	$0.279052\pi$
$594$		0			0
$595$	60.6393	+	189.535i	0.00417810	+	0.0130591i
$596$	10594.5	+	18350.2i	0.728133	+	1.26116i
$597$		0			0
$598$	−11923.8			−0.815385
$599$	11593.7			0.790828			0.395414	−	0.918503i	$-0.370601\pi$
$599$	11593.7			0.790828			0.395414	+	0.918503i	$0.370601\pi$
$600$		0			0
$601$	4948.59	+	8571.22i	0.335869	+	0.581742i	0.983651	−	0.180083i	$-0.0576367\pi$
$601$	4948.59	+	8571.22i	0.335869	+	0.581742i	−0.647782	+	0.761826i	$0.724303\pi$
$602$	42713.6	+	9280.72i	2.89182	+	0.628329i
$603$		0			0
$604$	10202.5	−	17671.3i	0.687311	−	1.19046i
$605$	65.8564	−	114.067i	0.00442553	−	0.00766524i
$606$		0			0
$607$	7703.14	+	13342.2i	0.515092	+	0.892165i	0.999847	+	0.0175150i	$0.00557548\pi$
$607$	7703.14	+	13342.2i	0.515092	+	0.892165i	−0.484755	+	0.874650i	$0.661091\pi$
$608$	6604.86	−	11440.0i	0.440563	−	0.763078i
$609$		0			0
$610$	−305.248	−	528.706i	−0.0202609	−	0.0350929i
$611$	2959.57	−	5126.13i	0.195960	−	0.339412i
$612$		0			0
$613$	−10363.9	−	17950.8i	−0.682863	−	1.18275i	−0.974103	−	0.226104i	$-0.927401\pi$
$613$	−10363.9	−	17950.8i	−0.682863	−	1.18275i	0.291240	−	0.956650i	$-0.405932\pi$
$614$	−16029.3			−1.05356
$615$		0			0
$616$	12433.7	+	38862.9i	0.813260	+	2.54193i
$617$	−11842.4	+	20511.7i	−0.772704	+	1.33836i	0.163371	+	0.986565i	$0.447763\pi$
$617$	−11842.4	+	20511.7i	−0.772704	+	1.33836i	−0.936076	+	0.351799i	$0.885570\pi$
$618$		0			0
$619$	11606.3	−	20102.7i	0.753630	−	1.30532i	−0.192423	−	0.981312i	$-0.561635\pi$
$619$	11606.3	−	20102.7i	0.753630	−	1.30532i	0.946053	−	0.324013i	$-0.105032\pi$
$620$	13.2790	+	23.0000i	0.000860160	+	0.00148984i
$621$		0			0
$622$	−37242.6			−2.40079
$623$	3231.38	+	10100.0i	0.207805	+	0.649517i
$624$		0			0
$625$	−7808.26	−	13524.3i	−0.499729	−	0.865556i
$626$	2993.08			0.191098
$627$		0			0
$628$	−58368.7			−3.70886
$629$	21732.7			1.37765
$630$		0			0
$631$	12646.4			0.797855			0.398928	−	0.916982i	$-0.369382\pi$
$631$	12646.4			0.797855			0.398928	+	0.916982i	$0.369382\pi$
$632$	2748.90			0.173015
$633$		0			0
$634$	−20681.9			−1.29556
$635$	77.4568	+	134.159i	0.00484060	+	0.00838416i
$636$		0			0
$637$	5466.02	+	2492.98i	0.339987	+	0.155063i
$638$	−14252.6			−0.884431
$639$		0			0
$640$	145.013	+	251.169i	0.00895644	+	0.0155130i
$641$	1507.04	−	2610.27i	0.0928619	−	0.160842i	−0.815852	−	0.578260i	$-0.803732\pi$
$641$	1507.04	−	2610.27i	0.0928619	−	0.160842i	0.908714	+	0.417419i	$0.137065\pi$
$642$		0			0
$643$	4295.52	−	7440.06i	0.263451	−	0.456310i	−0.703706	−	0.710491i	$-0.748473\pi$
$643$	4295.52	−	7440.06i	0.263451	−	0.456310i	0.967157	+	0.254182i	$0.0818061\pi$
$644$	−42407.2	−	9214.13i	−2.59484	−	0.563801i
$645$		0			0
$646$	41322.6			2.51674
$647$	−268.558	−	465.157i	−0.0163186	−	0.0282646i	0.857751	−	0.514066i	$-0.171861\pi$
$647$	−268.558	−	465.157i	−0.0163186	−	0.0282646i	−0.874069	+	0.485801i	$0.838528\pi$
$648$		0			0
$649$	13609.5	−	23572.4i	0.823144	−	1.42573i
$650$	−5507.34	−	9538.99i	−0.332332	−	0.575616i
$651$		0			0
$652$	−10187.9	+	17646.0i	−0.611947	+	1.05992i
$653$	1445.19	+	2503.14i	0.0866075	+	0.150009i	0.906075	−	0.423117i	$-0.139064\pi$
$653$	1445.19	+	2503.14i	0.0866075	+	0.150009i	−0.819468	+	0.573126i	$0.805731\pi$
$654$		0			0
$655$	127.148	−	220.227i	0.00758487	−	0.0131374i
$656$	13921.3	−	24112.4i	0.828561	−	1.43511i
$657$		0			0
$658$	21178.6	−	23308.9i	1.25475	−	1.38096i
$659$	6891.76	+	11936.9i	0.407382	+	0.705607i	0.994596	−	0.103826i	$-0.0331084\pi$
$659$	6891.76	+	11936.9i	0.407382	+	0.705607i	−0.587213	+	0.809432i	$0.699775\pi$
$660$		0			0
$661$	−17867.0			−1.05136			−0.525678	−	0.850684i	$-0.676188\pi$
$661$	−17867.0			−1.05136			−0.525678	+	0.850684i	$0.676188\pi$
$662$	46333.5			2.72024
$663$		0			0
$664$	13998.2	+	24245.6i	0.818124	+	1.41703i
$665$	−215.045	+	236.675i	−0.0125400	+	0.0138013i
$666$		0			0
$667$	4078.32	−	7063.85i	0.236751	−	0.410065i
$668$	−7033.64	+	12182.6i	−0.407395	+	0.705628i
$669$		0			0
$670$	45.8524	+	79.4186i	0.00264393	+	0.00457942i
$671$	18961.9	−	32843.0i	1.09094	−	1.88956i
$672$		0			0
$673$	535.840	+	928.102i	0.0306911	+	0.0531585i	0.880963	−	0.473185i	$-0.156896\pi$
$673$	535.840	+	928.102i	0.0306911	+	0.0531585i	−0.850272	+	0.526344i	$0.823563\pi$
$674$	25618.9	−	44373.2i	1.46410	−	2.53589i
$675$		0			0
$676$	16368.8	+	28351.6i	0.931316	+	1.61309i
$677$	−7803.00			−0.442974			−0.221487	−	0.975163i	$-0.571091\pi$
$677$	−7803.00			−0.442974			−0.221487	+	0.975163i	$0.571091\pi$
$678$		0			0
$679$	−12159.2	−	2641.93i	−0.687230	−	0.149320i
$680$	251.937	−	436.368i	0.0142079	−	0.0246087i
$681$		0			0
$682$	−1205.91	+	2088.70i	−0.0677079	+	0.117274i
$683$	−7390.06	−	12800.0i	−0.414016	−	0.717097i	0.581309	−	0.813683i	$-0.302541\pi$
$683$	−7390.06	−	12800.0i	−0.414016	−	0.717097i	−0.995325	+	0.0965864i	$0.969208\pi$
$684$		0			0
$685$	−363.630			−0.0202826
$686$	25603.1	+	19136.6i	1.42497	+	1.06507i
$687$		0			0
$688$	−22844.2	−	39567.2i	−1.26588	−	2.19257i
$689$	460.183			0.0254450
$690$		0			0
$691$	−27122.3			−1.49317			−0.746585	−	0.665290i	$-0.768308\pi$
$691$	−27122.3			−1.49317			−0.746585	+	0.665290i	$0.768308\pi$
$692$	−33711.8			−1.85192
$693$		0			0
$694$	−50448.6			−2.75937
$695$	18.5757			0.00101384
$696$		0			0
$697$	20433.5			1.11044
$698$	8592.35	+	14882.4i	0.465939	+	0.807029i
$699$		0			0
$700$	−12215.7	−	38181.4i	−0.659584	−	2.06160i
$701$	273.255			0.0147228			0.00736142	−	0.999973i	$-0.497657\pi$
$701$	273.255			0.0147228			0.00736142	+	0.999973i	$0.497657\pi$
$702$		0			0
$703$	17461.7	+	30244.5i	0.936813	+	1.62261i
$704$	−4713.50	+	8164.03i	−0.252339	+	0.437064i
$705$		0			0
$706$	11973.9	−	20739.5i	0.638308	−	1.10558i
$707$	−4566.73	−	14273.8i	−0.242927	−	0.759295i
$708$		0			0
$709$	−23559.8			−1.24796			−0.623981	−	0.781439i	$-0.714486\pi$
$709$	−23559.8			−1.24796			−0.623981	+	0.781439i	$0.714486\pi$
$710$	−10.0239	−	17.3620i	−0.000529847	−	0.000917722i
$711$		0			0
$712$	13425.4	−	23253.4i	0.706653	−	1.22396i
$713$	−690.132	−	1195.34i	−0.0362491	−	0.0627853i
$714$		0			0
$715$	−61.8427	+	107.115i	−0.00323466	+	0.00560260i
$716$	−9290.72	−	16092.0i	−0.484931	−	0.839925i
$717$		0			0
$718$	21172.4	−	36671.7i	1.10048	−	1.90609i
$719$	12946.1	−	22423.3i	0.671499	−	1.16307i	−0.305980	−	0.952038i	$-0.598984\pi$
$719$	12946.1	−	22423.3i	0.671499	−	1.16307i	0.977479	−	0.211032i	$-0.0676824\pi$
$720$		0			0
$721$	−9387.62	−	2039.72i	−0.484900	−	0.105358i
$722$	15944.9	+	27617.4i	0.821896	+	1.42357i
$723$		0			0
$724$	55036.6			2.82517
$725$	7534.74			0.385977
$726$		0			0
$727$	2348.92	+	4068.44i	0.119830	+	0.207552i	0.919700	−	0.392621i	$-0.128432\pi$
$727$	2348.92	+	4068.44i	0.119830	+	0.207552i	−0.799870	+	0.600173i	$0.795098\pi$
$728$	−4635.35	−	14488.3i	−0.235986	−	0.737598i
$729$		0			0
$730$	−46.0652	+	79.7873i	−0.00233555	+	0.00404529i
$731$	16765.2	−	29038.1i	0.848265	−	1.46924i
$732$		0			0
$733$	5671.52	+	9823.35i	0.285788	+	0.494998i	0.972800	−	0.231647i	$-0.0744115\pi$
$733$	5671.52	+	9823.35i	0.285788	+	0.494998i	−0.687012	+	0.726646i	$0.741078\pi$
$734$	−2942.54	+	5096.62i	−0.147971	+	0.256294i
$735$		0			0
$736$	7778.69	+	13473.1i	0.389574	+	0.674762i
$737$	−2848.34	+	4933.46i	−0.142361	+	0.246576i
$738$		0			0
$739$	−4193.51	−	7263.36i	−0.208742	−	0.361552i	0.742576	−	0.669762i	$-0.233604\pi$
$739$	−4193.51	−	7263.36i	−0.208742	−	0.361552i	−0.951319	+	0.308209i	$0.900270\pi$
$740$	791.396			0.0393139
$741$		0			0
$742$	2392.63	+	519.865i	0.118378	+	0.0257208i
$743$	11445.1	−	19823.6i	0.565116	−	0.978810i	−0.431923	−	0.901911i	$-0.642165\pi$
$743$	11445.1	−	19823.6i	0.565116	−	0.978810i	0.997039	−	0.0768995i	$-0.0245021\pi$
$744$		0			0
$745$	−91.9432	+	159.250i	−0.00452153	+	0.00783152i
$746$	−21076.8	−	36506.2i	−1.03442	−	1.79167i
$747$		0			0
$748$	58169.4			2.84343
$749$	−10445.8	−	32649.5i	−0.509588	−	1.59277i
$750$		0			0
$751$	−6923.06	−	11991.1i	−0.336386	−	0.582638i	0.647364	−	0.762181i	$-0.275871\pi$
$751$	−6923.06	−	11991.1i	−0.336386	−	0.582638i	−0.983750	+	0.179543i	$0.942538\pi$
$752$	−32918.6			−1.59630
$753$		0			0
$754$	5313.46			0.256637
$755$	177.083			0.00853606
$756$		0			0
$757$	−33857.4			−1.62558			−0.812792	−	0.582554i	$-0.802053\pi$
$757$	−33857.4			−1.62558			−0.812792	+	0.582554i	$0.802053\pi$
$758$	−17866.6			−0.856127
$759$		0			0
$760$	809.700			0.0386459
$761$	−11204.3	−	19406.5i	−0.533715	−	0.924422i	−0.999224	−	0.0393788i	$-0.987462\pi$
$761$	−11204.3	−	19406.5i	−0.533715	−	0.924422i	0.465509	−	0.885043i	$-0.345871\pi$
$762$		0			0
$763$	8940.42	+	1942.55i	0.424201	+	0.0921693i
$764$	−40600.6			−1.92261
$765$		0			0
$766$	−18122.9	−	31389.8i	−0.854841	−	1.48063i
$767$	−5073.70	+	8787.91i	−0.238854	+	0.413707i
$768$		0			0
$769$	15146.3	−	26234.1i	0.710258	−	1.23020i	−0.254502	−	0.967072i	$-0.581912\pi$
$769$	15146.3	−	26234.1i	0.710258	−	1.23020i	0.964760	−	0.263131i	$-0.0847551\pi$
$770$	−442.545	+	487.058i	−0.0207120	+	0.0227952i
$771$		0			0
$772$	37568.5			1.75145
$773$	9079.91	+	15726.9i	0.422486	+	0.731767i	0.996182	−	0.0873013i	$-0.0278243\pi$
$773$	9079.91	+	15726.9i	0.422486	+	0.731767i	−0.573696	+	0.819068i	$0.694491\pi$
$774$		0			0
$775$	637.513	−	1104.21i	0.0295486	−	0.0511796i
$776$	15753.1	+	27285.1i	0.728740	+	1.26221i
$777$		0			0
$778$	6380.93	−	11052.1i	0.294045	−	0.509302i
$779$	16417.8	+	28436.5i	0.755108	+	1.30788i
$780$		0			0
$781$	622.684	−	1078.52i	0.0285293	−	0.0494142i
$782$	−24333.3	+	42146.5i	−1.11273	+	1.92731i
$783$		0			0
$784$	−3192.38	−	33258.2i	−0.145425	−	1.51504i
$785$	−253.273	−	438.682i	−0.0115156	−	0.0199455i
$786$		0			0
$787$	−3400.43			−0.154018			−0.0770091	−	0.997030i	$-0.524537\pi$
$787$	−3400.43			−0.154018			−0.0770091	+	0.997030i	$0.524537\pi$
$788$	−36057.4			−1.63007
$789$		0			0
$790$	22.1673	+	38.3949i	0.000998325	+	0.00172915i
$791$	−274.960	−	859.417i	−0.0123596	−	0.0386313i
$792$		0			0
$793$	−7069.11	+	12244.1i	−0.316559	+	0.548297i
$794$	22646.4	−	39224.8i	1.01221	−	1.75319i
$795$		0			0
$796$	22675.4	+	39274.9i	1.00968	+	1.74882i
$797$	−5166.74	+	8949.06i	−0.229630	+	0.397731i	−0.957699	−	0.287773i	$-0.907085\pi$
$797$	−5166.74	+	8949.06i	−0.229630	+	0.397731i	0.728068	+	0.685505i	$0.240418\pi$
$798$		0			0
$799$	−12079.4	−	20922.1i	−0.534841	−	0.926371i
$800$	−7185.62	+	12445.9i	−0.317562	+	0.550034i
$801$		0			0
$802$	5066.82	+	8775.99i	0.223087	+	0.386398i
$803$	−5723.12			−0.251512
$804$		0			0
$805$	−114.762	−	358.702i	−0.00502465	−	0.0157051i
$806$	449.571	−	778.679i	0.0196470	−	0.0340295i
$807$		0			0
$808$	−18973.3	+	32862.7i	−0.826087	+	1.43083i
$809$	8311.05	+	14395.2i	0.361188	+	0.625596i	0.988157	−	0.153449i	$-0.0490380\pi$
$809$	8311.05	+	14395.2i	0.361188	+	0.625596i	−0.626969	+	0.779044i	$0.715705\pi$
$810$		0			0
$811$	−42626.7			−1.84565			−0.922827	−	0.385215i	$-0.874127\pi$
$811$	−42626.7			−1.84565			−0.922827	+	0.385215i	$0.874127\pi$
$812$	18897.4	+	4105.98i	0.816709	+	0.177453i
$813$		0			0
$814$	35934.6	+	62240.6i	1.54731	+	2.68001i
$815$	−176.830			−0.00760009
$816$		0			0
$817$	53881.5			2.30732
$818$	−14612.1			−0.624570
$819$		0			0
$820$	744.085			0.0316885
$821$	−7153.20			−0.304078			−0.152039	−	0.988374i	$-0.548584\pi$
$821$	−7153.20			−0.304078			−0.152039	+	0.988374i	$0.548584\pi$
$822$		0			0
$823$	−19831.0			−0.839936			−0.419968	−	0.907539i	$-0.637959\pi$
$823$	−19831.0			−0.839936			−0.419968	+	0.907539i	$0.637959\pi$
$824$	12162.2	+	21065.6i	0.514189	+	0.890602i
$825$		0			0
$826$	−36307.3	+	39959.2i	−1.52941	+	1.68324i
$827$	39271.8			1.65129			0.825643	−	0.564193i	$-0.190813\pi$
$827$	39271.8			1.65129			0.825643	+	0.564193i	$0.190813\pi$
$828$		0			0
$829$	2520.01	+	4364.79i	0.105577	+	0.182865i	0.913974	−	0.405773i	$-0.132998\pi$
$829$	2520.01	+	4364.79i	0.105577	+	0.182865i	−0.808397	+	0.588638i	$0.799664\pi$
$830$	−225.764	+	391.034i	−0.00944142	+	0.0163530i
$831$		0			0
$832$	1757.22	−	3043.59i	0.0732219	−	0.126824i
$833$	19966.5	−	14233.0i	0.830489	−	0.592008i
$834$		0			0
$835$	−122.081			−0.00505964
$836$	46737.6	+	80952.0i	1.93356	+	3.34902i
$837$		0			0
$838$	9870.12	−	17095.5i	0.406871	−	0.704721i
$839$	17615.0	+	30510.1i	0.724838	+	1.25546i	0.959041	+	0.283268i	$0.0914186\pi$
$839$	17615.0	+	30510.1i	0.724838	+	1.25546i	−0.234203	+	0.972188i	$0.575248\pi$
$840$		0			0
$841$	10377.1	−	17973.7i	0.425484	−	0.736960i
$842$	−28581.7	−	49504.9i	−1.16982	−	2.02619i
$843$		0			0
$844$	−36463.9	+	63157.3i	−1.48713	+	2.57579i
$845$	−142.055	+	246.047i	−0.00578325	+	0.0100169i
$846$		0			0
$847$	−15859.3	−	3445.87i	−0.643367	−	0.139789i
$848$	−1279.63	−	2216.38i	−0.0518192	−	0.0897534i
$849$		0			0
$850$	−44956.0			−1.81409
$851$	−41130.0			−1.65678
$852$		0			0
$853$	18218.4	+	31555.2i	0.731286	+	1.26662i	0.956334	+	0.292276i	$0.0944127\pi$
$853$	18218.4	+	31555.2i	0.731286	+	1.26662i	−0.225048	+	0.974348i	$0.572254\pi$
$854$	−50586.4	+	55674.6i	−2.02697	+	2.23085i
$855$		0			0
$856$	−43399.0	+	75169.2i	−1.73288	+	3.00144i
$857$	7067.32	−	12241.0i	0.281698	−	0.487915i	−0.690105	−	0.723709i	$-0.742436\pi$
$857$	7067.32	−	12241.0i	0.281698	−	0.487915i	0.971803	+	0.235794i	$0.0757691\pi$
$858$		0			0
$859$	−3241.12	−	5613.78i	−0.128738	−	0.222980i	0.794450	−	0.607329i	$-0.207759\pi$
$859$	−3241.12	−	5613.78i	−0.128738	−	0.222980i	−0.923188	+	0.384349i	$0.874426\pi$
$860$	610.503	−	1057.42i	0.0242070	−	0.0419277i
$861$		0			0
$862$	25845.3	+	44765.4i	1.02122	+	1.76881i
$863$	−13029.5	+	22567.7i	−0.513938	+	0.890167i	0.485931	+	0.873997i	$0.338481\pi$
$863$	−13029.5	+	22567.7i	−0.513938	+	0.890167i	−0.999869	+	0.0161701i	$0.994853\pi$
$864$		0			0
$865$	−146.282	−	253.368i	−0.00575000	−	0.00995929i
$866$	33249.4			1.30469
$867$		0			0
$868$	2200.63	−	2421.98i	0.0860533	−	0.0947089i
$869$	−1377.02	+	2385.08i	−0.0537542	+	0.0931049i
$870$		0			0
$871$	1061.87	−	1839.22i	0.0413091	−	0.0715495i
$872$	−11582.9	−	20062.1i	−0.449823	−	0.779117i
$873$		0			0
$874$	−78204.7			−3.02667
$875$	467.950	−	515.018i	0.0180795	−	0.0198981i
$876$		0			0
$877$	−4520.01	−	7828.88i	−0.174036	−	0.301440i	0.765791	−	0.643089i	$-0.222348\pi$
$877$	−4520.01	−	7828.88i	−0.174036	−	0.301440i	−0.939827	+	0.341650i	$0.889014\pi$
$878$	−9654.27			−0.371089
$879$		0			0
$880$	687.862			0.0263498
$881$	−3778.64			−0.144501			−0.0722507	−	0.997387i	$-0.523018\pi$
$881$	−3778.64			−0.144501			−0.0722507	+	0.997387i	$0.523018\pi$
$882$		0			0
$883$	42444.2			1.61762			0.808812	−	0.588067i	$-0.200111\pi$
$883$	42444.2			1.61762			0.808812	+	0.588067i	$0.200111\pi$
$884$	−21685.9			−0.825084
$885$		0			0
$886$	−11462.4			−0.434636
$887$	17422.1	+	30175.9i	0.659500	+	1.14229i	0.980745	+	0.195291i	$0.0625651\pi$
$887$	17422.1	+	30175.9i	0.659500	+	1.14229i	−0.321246	+	0.946996i	$0.604102\pi$
$888$		0			0
$889$	12836.3	−	14127.4i	0.484270	−	0.532980i
$890$	433.051			0.0163100
$891$		0			0
$892$	−7573.58	−	13117.8i	−0.284285	−	0.492396i
$893$	19411.0	−	33620.8i	0.727394	−	1.25988i
$894$		0			0
$895$	80.6286	−	139.653i	0.00301130	−	0.00521573i
$896$	24031.8	−	26449.0i	0.896033	−	0.986160i
$897$		0			0
$898$	−5925.62			−0.220201
$899$	307.535	+	532.666i	0.0114092	+	0.0197613i
$900$		0			0
$901$	939.111	−	1626.59i	0.0347240	−	0.0601437i
$902$	33786.4	+	58519.8i	1.24719	+	2.16020i
$903$		0			0
$904$	−1142.37	+	1978.65i	−0.0420296	+	0.0727973i
$905$	238.815	+	413.640i	0.00877180	+	0.0151932i
$906$		0			0
$907$	25897.7	−	44856.1i	0.948091	−	1.64214i	0.198650	−	0.980070i	$-0.436344\pi$
$907$	25897.7	−	44856.1i	0.948091	−	1.64214i	0.749441	−	0.662072i	$-0.230323\pi$
$908$	−4380.35	+	7587.00i	−0.160096	+	0.277294i
$909$		0			0
$910$	164.983	−	181.578i	0.00601004	−	0.00661455i
$911$	−24407.4	−	42274.8i	−0.887653	−	1.53746i	−0.842642	−	0.538474i	$-0.819001\pi$
$911$	−24407.4	−	42274.8i	−0.887653	−	1.53746i	−0.0450114	−	0.998986i	$-0.514332\pi$
$912$		0			0
$913$	−28048.8			−1.01673
$914$	78708.0			2.84839
$915$		0			0
$916$	5433.81	+	9411.63i	0.196002	+	0.339486i
$917$	−30619.4	−	6652.91i	−1.10266	−	0.239584i
$918$		0			0
$919$	−17989.4	+	31158.6i	−0.645720	+	1.11842i	0.338415	+	0.940997i	$0.390109\pi$
$919$	−17989.4	+	31158.6i	−0.645720	+	1.11842i	−0.984135	+	0.177423i	$0.943224\pi$
$920$	−476.801	+	825.843i	−0.0170866	+	0.0295948i
$921$		0			0
$922$	−36852.1	−	63829.8i	−1.31633	−	2.27996i
$923$	−232.140	+	402.078i	−0.00827841	+	0.0143386i
$924$		0			0
$925$	−18997.1	−	32903.9i	−0.675264	−	1.16959i
$926$	5970.10	−	10340.5i	0.211868	−	0.366966i
$927$		0			0
$928$	−3466.32	−	6003.85i	−0.122616	−	0.212377i
$929$	−13422.6			−0.474038			−0.237019	−	0.971505i	$-0.576170\pi$
$929$	−13422.6			−0.474038			−0.237019	+	0.971505i	$0.576170\pi$
$930$		0			0
$931$	35850.0	+	16350.7i	1.26201	+	0.575589i
$932$	12305.4	−	21313.6i	0.432486	−	0.749088i
$933$		0			0
$934$	11763.6	−	20375.1i	0.412116	−	0.713806i
$935$	252.409	+	437.184i	0.00882849	+	0.0152914i
$936$		0			0
$937$	35672.1			1.24371			0.621855	−	0.783132i	$-0.286379\pi$
$937$	35672.1			1.24371			0.621855	+	0.783132i	$0.286379\pi$
$938$	7598.75	−	8363.07i	0.264508	−	0.291113i
$939$		0			0
$940$	−439.870	−	761.878i	−0.0152627	−	0.0264359i
$941$	−53820.9			−1.86452			−0.932260	−	0.361790i	$-0.882166\pi$
$941$	−53820.9			−1.86452			−0.932260	+	0.361790i	$0.882166\pi$
$942$		0			0
$943$	−38671.2			−1.33543
$944$	56433.7			1.94572
$945$		0			0
$946$	110884.			3.81093
$947$	−35477.0			−1.21737			−0.608683	−	0.793413i	$-0.708302\pi$
$947$	−35477.0			−1.21737			−0.608683	+	0.793413i	$0.708302\pi$
$948$		0			0
$949$	2133.61			0.0729820
$950$	−36121.0	−	62563.4i	−1.23360	−	2.13666i
$951$		0			0
$952$	−60670.5	−	13182.4i	−2.06549	−	0.448784i
$953$	45890.3			1.55985			0.779923	−	0.625875i	$-0.215258\pi$
$953$	45890.3			1.55985			0.779923	+	0.625875i	$0.215258\pi$
$954$		0			0
$955$	−176.174	−	305.142i	−0.00596948	−	0.0103394i
$956$	−5629.23	+	9750.11i	−0.190442	+	0.329855i
$957$		0			0
$958$	47910.9	−	82984.2i	1.61580	−	2.79864i
$959$	13653.2	+	42674.7i	0.459735	+	1.43695i
$960$		0			0
$961$	−29686.9			−0.996506
$962$	−13396.6	−	23203.6i	−0.448986	−	0.777666i
$963$		0			0
$964$	15626.6	−	27066.1i	0.522096	−	0.904297i
$965$	163.017	+	282.354i	0.00543804	+	0.00941896i
$966$		0			0
$967$	−10452.6	+	18104.5i	−0.347605	+	0.602069i	−0.985823	−	0.167786i	$-0.946338\pi$
$967$	−10452.6	+	18104.5i	−0.347605	+	0.602069i	0.638219	+	0.769855i	$0.279672\pi$
$968$	20546.7	+	35588.0i	0.682228	+	1.18165i
$969$		0			0
$970$	−254.067	+	440.057i	−0.00840989	+	0.0145664i
$971$	25647.4	−	44422.5i	0.847644	−	1.46816i	−0.0356605	−	0.999364i	$-0.511353\pi$
$971$	25647.4	−	44422.5i	0.847644	−	1.46816i	0.883305	−	0.468799i	$-0.155313\pi$
$972$		0			0
$973$	−697.463	−	2180.00i	−0.0229801	−	0.0718268i
$974$	−14415.5	−	24968.4i	−0.474233	−	0.821395i
$975$		0			0
$976$	78628.2			2.57872
$977$	−7619.67			−0.249514			−0.124757	−	0.992187i	$-0.539815\pi$
$977$	−7619.67			−0.249514			−0.124757	+	0.992187i	$0.539815\pi$
$978$		0			0
$979$	13450.5	+	23296.9i	0.439101	+	0.760545i
$980$	727.079	−	518.293i	0.0236997	−	0.0168941i
$981$		0			0
$982$	−5756.37	+	9970.33i	−0.187060	+	0.323998i
$983$	−27790.8	+	48135.2i	−0.901719	+	1.56182i	−0.0764581	+	0.997073i	$0.524361\pi$
$983$	−27790.8	+	48135.2i	−0.901719	+	1.56182i	−0.825261	+	0.564751i	$0.808972\pi$
$984$		0			0
$985$	−156.460	−	270.997i	−0.00506116	−	0.00876618i
$986$	10843.3	−	18781.2i	0.350225	−	0.606608i
$987$		0			0
$988$	−17424.0	−	30179.3i	−0.561065	−	0.971794i
$989$	−31728.8	+	54955.8i	−1.02014	+	1.76693i
$990$		0			0
$991$	1200.45	+	2079.25i	0.0384800	+	0.0666493i	0.884624	−	0.466305i	$-0.154415\pi$
$991$	1200.45	+	2079.25i	0.0384800	+	0.0666493i	−0.846144	+	0.532954i	$0.821082\pi$
$992$	−1173.14			−0.0375476
$993$		0			0
$994$	−1661.19	+	1828.28i	−0.0530077	+	0.0583394i
$995$	−196.786	+	340.843i	−0.00626988	+	0.0108598i
$996$		0			0
$997$	1087.00	−	1882.74i	0.0345293	−	0.0598065i	−0.848244	−	0.529605i	$-0.822340\pi$
$997$	1087.00	−	1882.74i	0.0345293	−	0.0598065i	0.882774	+	0.469799i	$0.155673\pi$
$998$	−200.644	−	347.525i	−0.00636400	−	0.0110228i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.h.a.37.2		44
3.2	odd	2		63.4.h.a.58.21	yes	44
7.4	even	3		189.4.g.a.172.21		44
9.2	odd	6		63.4.g.a.16.2	yes	44
9.7	even	3		189.4.g.a.100.21		44
21.11	odd	6		63.4.g.a.4.2	✓	44
63.11	odd	6		63.4.h.a.25.21	yes	44
63.25	even	3	inner	189.4.h.a.46.2		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.2	✓	44	21.11	odd	6
63.4.g.a.16.2	yes	44	9.2	odd	6
63.4.h.a.25.21	yes	44	63.11	odd	6
63.4.h.a.58.21	yes	44	3.2	odd	2
189.4.g.a.100.21		44	9.7	even	3
189.4.g.a.172.21		44	7.4	even	3
189.4.h.a.37.2		44	1.1	even	1	trivial
189.4.h.a.46.2		44	63.25	even	3	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-5.03185 q^{2} +17.3195 q^{4} +(0.0751526 + 0.130168i) q^{5} +(12.4545 - 13.7072i) q^{7} -46.8942 q^{8} +O(q^{10})\)	\(q-5.03185 q^{2} +17.3195 q^{4} +(0.0751526 + 0.130168i) q^{5} +(12.4545 - 13.7072i) q^{7} -46.8942 q^{8} +(-0.378156 - 0.654986i) q^{10} +(23.4910 - 40.6875i) q^{11} +(-8.75756 + 15.1685i) q^{13} +(-62.6689 + 68.9724i) q^{14} +97.4084 q^{16} +(35.7437 + 61.9098i) q^{17} +(-57.4382 + 99.4860i) q^{19} +(1.30160 + 2.25444i) q^{20} +(-118.203 + 204.733i) q^{22} +(-67.6463 - 117.167i) q^{23} +(62.4887 - 108.234i) q^{25} +(44.0667 - 76.3257i) q^{26} +(215.705 - 237.401i) q^{28} +(30.1444 + 52.2116i) q^{29} +10.2021 q^{31} -114.991 q^{32} +(-179.857 - 311.521i) q^{34} +(2.72022 + 0.591044i) q^{35} +(152.004 - 263.279i) q^{37} +(289.020 - 500.598i) q^{38} +(-3.52422 - 6.10413i) q^{40} +(142.917 - 247.540i) q^{41} +(-234.519 - 406.200i) q^{43} +(406.851 - 704.687i) q^{44} +(340.386 + 589.566i) q^{46} -337.945 q^{47} +(-32.7731 - 341.431i) q^{49} +(-314.434 + 544.615i) q^{50} +(-151.676 + 262.711i) q^{52} +(-13.1367 - 22.7535i) q^{53} +7.06163 q^{55} +(-584.041 + 642.786i) q^{56} +(-151.682 - 262.721i) q^{58} +579.352 q^{59} +807.201 q^{61} -51.3352 q^{62} -200.652 q^{64} -2.63261 q^{65} -121.252 q^{67} +(619.061 + 1072.25i) q^{68} +(-13.6877 - 2.97404i) q^{70} +26.5074 q^{71} +(-60.9077 - 105.495i) q^{73} +(-764.860 + 1324.78i) q^{74} +(-994.800 + 1723.04i) q^{76} +(-265.144 - 828.736i) q^{77} -58.6193 q^{79} +(7.32049 + 12.6795i) q^{80} +(-719.136 + 1245.58i) q^{82} +(-298.506 - 517.027i) q^{83} +(-5.37246 + 9.30537i) q^{85} +(1180.07 + 2043.93i) q^{86} +(-1101.59 + 1908.01i) q^{88} +(-286.291 + 495.870i) q^{89} +(98.8471 + 308.957i) q^{91} +(-1171.60 - 2029.27i) q^{92} +1700.49 q^{94} -17.2665 q^{95} +(-335.928 - 581.845i) q^{97} +(164.909 + 1718.03i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

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