LMFDB - Embedded newform 189.4.g.a.100.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(100,189)]

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([4, 2]))

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

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

chi := DirichletCharacter("189.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.g (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			100.19
Character	$\chi$	$=$	189.100
Dual form			189.4.g.a.172.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93332 + 3.34860i) q^{2} +(-3.47543 + 6.01962i) q^{4} +13.3562 q^{5} +(1.72288 - 18.4399i) q^{7} +4.05663 q^{8} +O(q^{10})$	\(q+(1.93332 + 3.34860i) q^{2} +(-3.47543 + 6.01962i) q^{4} +13.3562 q^{5} +(1.72288 - 18.4399i) q^{7} +4.05663 q^{8} +(25.8218 + 44.7246i) q^{10} +28.7209 q^{11} +(2.75723 + 4.77566i) q^{13} +(65.0790 - 29.8810i) q^{14} +(35.6462 + 61.7410i) q^{16} +(8.48010 + 14.6880i) q^{17} +(31.6694 - 54.8530i) q^{19} +(-46.4185 + 80.3993i) q^{20} +(55.5266 + 96.1750i) q^{22} -134.837 q^{23} +53.3878 q^{25} +(-10.6612 + 18.4657i) q^{26} +(105.014 + 74.4579i) q^{28} +(-118.224 + 204.770i) q^{29} +(-46.4658 + 80.4810i) q^{31} +(-121.604 + 210.625i) q^{32} +(-32.7895 + 56.7930i) q^{34} +(23.0111 - 246.287i) q^{35} +(202.752 - 351.177i) q^{37} +244.908 q^{38} +54.1811 q^{40} +(166.014 + 287.545i) q^{41} +(-173.016 + 299.673i) q^{43} +(-99.8176 + 172.889i) q^{44} +(-260.682 - 451.514i) q^{46} +(-152.478 - 264.100i) q^{47} +(-337.063 - 63.5396i) q^{49} +(103.216 + 178.775i) q^{50} -38.3302 q^{52} +(-332.075 - 575.170i) q^{53} +383.602 q^{55} +(6.98908 - 74.8040i) q^{56} -914.257 q^{58} +(-68.8294 + 119.216i) q^{59} +(310.258 + 537.383i) q^{61} -359.332 q^{62} -370.060 q^{64} +(36.8260 + 63.7846i) q^{65} +(293.882 - 509.018i) q^{67} -117.888 q^{68} +(869.207 - 399.097i) q^{70} +121.903 q^{71} +(143.624 + 248.763i) q^{73} +1567.94 q^{74} +(220.130 + 381.276i) q^{76} +(49.4827 - 529.612i) q^{77} +(-488.750 - 846.540i) q^{79} +(476.097 + 824.625i) q^{80} +(-641.917 + 1111.83i) q^{82} +(507.709 - 879.377i) q^{83} +(113.262 + 196.175i) q^{85} -1337.98 q^{86} +116.510 q^{88} +(258.781 - 448.222i) q^{89} +(92.8132 - 42.6152i) q^{91} +(468.616 - 811.666i) q^{92} +(589.578 - 1021.18i) q^{94} +(422.983 - 732.627i) q^{95} +(-823.870 + 1426.99i) q^{97} +(-438.882 - 1251.53i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.93332	+	3.34860i	0.683531	+	1.18391i	0.973896	+	0.226994i	$0.0728899\pi$
$2$	1.93332	+	3.34860i	0.683531	+	1.18391i	−0.290365	+	0.956916i	$0.593777\pi$
$3$		0			0
$3$		0			0
$4$	−3.47543	+	6.01962i	−0.434429	+	0.752453i
$5$	13.3562			1.19461			0.597307	−	0.802013i	$-0.296237\pi$
$5$	13.3562			1.19461			0.597307	+	0.802013i	$0.296237\pi$
$6$		0			0
$7$	1.72288	−	18.4399i	0.0930267	−	0.995664i
$7$	1.72288	−	18.4399i	0.0930267	−	0.995664i
$8$	4.05663			0.179279
$9$		0			0
$10$	25.8218	+	44.7246i	0.816556	+	1.41432i
$11$	28.7209			0.787244			0.393622	−	0.919272i	$-0.371222\pi$
$11$	28.7209			0.787244			0.393622	+	0.919272i	$0.371222\pi$
$12$		0			0
$13$	2.75723	+	4.77566i	0.0588244	+	0.101887i	0.893938	−	0.448191i	$-0.147931\pi$
$13$	2.75723	+	4.77566i	0.0588244	+	0.101887i	−0.835114	+	0.550078i	$0.814598\pi$
$14$	65.0790	−	29.8810i	1.24236	−	0.570432i
$15$		0			0
$16$	35.6462	+	61.7410i	0.556972	+	0.964704i
$17$	8.48010	+	14.6880i	0.120984	+	0.209550i	0.920156	−	0.391552i	$-0.128062\pi$
$17$	8.48010	+	14.6880i	0.120984	+	0.209550i	−0.799172	+	0.601102i	$0.794728\pi$
$18$		0			0
$19$	31.6694	−	54.8530i	0.382393	−	0.662323i	−0.609011	−	0.793162i	$-0.708434\pi$
$19$	31.6694	−	54.8530i	0.382393	−	0.662323i	0.991404	+	0.130838i	$0.0417669\pi$
$20$	−46.4185	+	80.3993i	−0.518975	+	0.898891i
$21$		0			0
$22$	55.5266	+	96.1750i	0.538106	+	0.932026i
$23$	−134.837			−1.22241			−0.611204	−	0.791473i	$-0.709314\pi$
$23$	−134.837			−1.22241			−0.611204	+	0.791473i	$0.709314\pi$
$24$		0			0
$25$	53.3878			0.427103
$26$	−10.6612	+	18.4657i	−0.0804166	+	0.139286i
$27$		0			0
$28$	105.014	+	74.4579i	0.708777	+	0.502543i
$29$	−118.224	+	204.770i	−0.757022	+	1.31120i	0.187341	+	0.982295i	$0.440013\pi$
$29$	−118.224	+	204.770i	−0.757022	+	1.31120i	−0.944363	+	0.328905i	$0.893320\pi$
$30$		0			0
$31$	−46.4658	+	80.4810i	−0.269210	+	0.466285i	−0.968658	−	0.248399i	$-0.920096\pi$
$31$	−46.4658	+	80.4810i	−0.269210	+	0.466285i	0.699448	+	0.714683i	$0.253429\pi$
$32$	−121.604	+	210.625i	−0.671775	+	1.16355i
$33$		0			0
$34$	−32.7895	+	56.7930i	−0.165393	+	0.286468i
$35$	23.0111	−	246.287i	0.111131	−	1.18943i
$36$		0			0
$37$	202.752	−	351.177i	0.900872	−	1.56036i	0.0745066	−	0.997221i	$-0.476262\pi$
$37$	202.752	−	351.177i	0.900872	−	1.56036i	0.826365	−	0.563135i	$-0.190405\pi$
$38$	244.908			1.04551
$39$		0			0
$40$	54.1811			0.214170
$41$	166.014	+	287.545i	0.632368	+	1.09529i	0.987066	+	0.160313i	$0.0512504\pi$
$41$	166.014	+	287.545i	0.632368	+	1.09529i	−0.354698	+	0.934981i	$0.615416\pi$
$42$		0			0
$43$	−173.016	+	299.673i	−0.613599	+	1.06279i	0.377029	+	0.926201i	$0.376946\pi$
$43$	−173.016	+	299.673i	−0.613599	+	1.06279i	−0.990629	+	0.136584i	$0.956388\pi$
$44$	−99.8176	+	172.889i	−0.342002	+	0.592364i
$45$		0			0
$46$	−260.682	−	451.514i	−0.835554	−	1.44722i
$47$	−152.478	−	264.100i	−0.473218	−	0.819638i	0.526312	−	0.850292i	$-0.323574\pi$
$47$	−152.478	−	264.100i	−0.473218	−	0.819638i	−0.999530	+	0.0306535i	$0.990241\pi$
$48$		0			0
$49$	−337.063	−	63.5396i	−0.982692	−	0.185247i
$50$	103.216	+	178.775i	0.291938	+	0.505651i
$51$		0			0
$52$	−38.3302			−0.102220
$53$	−332.075	−	575.170i	−0.860641	−	1.49067i	−0.871311	−	0.490730i	$-0.836730\pi$
$53$	−332.075	−	575.170i	−0.860641	−	1.49067i	0.0106707	−	0.999943i	$-0.496603\pi$
$54$		0			0
$55$	383.602			0.940453
$56$	6.98908	−	74.8040i	0.0166778	−	0.178502i
$57$		0			0
$58$	−914.257			−2.06979
$59$	−68.8294	+	119.216i	−0.151878	+	0.263061i	−0.931918	−	0.362669i	$-0.881866\pi$
$59$	−68.8294	+	119.216i	−0.151878	+	0.263061i	0.780040	+	0.625730i	$0.215199\pi$
$60$		0			0
$61$	310.258	+	537.383i	0.651221	+	1.12795i	0.982827	+	0.184530i	$0.0590763\pi$
$61$	310.258	+	537.383i	0.651221	+	1.12795i	−0.331606	+	0.943418i	$0.607590\pi$
$62$	−359.332			−0.736052
$63$		0			0
$64$	−370.060			−0.722773
$65$	36.8260	+	63.7846i	0.0702724	+	0.121715i
$66$		0			0
$67$	293.882	−	509.018i	0.535871	−	0.928155i	−0.463250	−	0.886228i	$-0.653317\pi$
$67$	293.882	−	509.018i	0.535871	−	0.928155i	0.999121	−	0.0419277i	$-0.0133499\pi$
$68$	−117.888			−0.210236
$69$		0			0
$70$	869.207	−	399.097i	1.48414	−	0.681446i
$71$	121.903			0.203764			0.101882	−	0.994796i	$-0.467514\pi$
$71$	121.903			0.203764			0.101882	+	0.994796i	$0.467514\pi$
$72$		0			0
$73$	143.624	+	248.763i	0.230272	+	0.398843i	0.957888	−	0.287142i	$-0.0927051\pi$
$73$	143.624	+	248.763i	0.230272	+	0.398843i	−0.727616	+	0.685985i	$0.759372\pi$
$74$	1567.94			2.46309
$75$		0			0
$76$	220.130	+	381.276i	0.332245	+	0.575465i
$77$	49.4827	−	529.612i	0.0732347	−	0.783830i
$78$		0			0
$79$	−488.750	−	846.540i	−0.696059	−	1.20561i	−0.969822	−	0.243813i	$-0.921602\pi$
$79$	−488.750	−	846.540i	−0.696059	−	1.20561i	0.273763	−	0.961797i	$-0.411732\pi$
$80$	476.097	+	824.625i	0.665366	+	1.15245i
$81$		0			0
$82$	−641.917	+	1111.83i	−0.864487	+	1.49733i
$83$	507.709	−	879.377i	0.671425	−	1.16294i	−0.306075	−	0.952007i	$-0.599016\pi$
$83$	507.709	−	879.377i	0.671425	−	1.16294i	0.977500	−	0.210934i	$-0.0676507\pi$
$84$		0			0
$85$	113.262	+	196.175i	0.144529	+	0.250332i
$86$	−1337.98			−1.67766
$87$		0			0
$88$	116.510			0.141137
$89$	258.781	−	448.222i	0.308211	−	0.533837i	−0.669760	−	0.742577i	$-0.733603\pi$
$89$	258.781	−	448.222i	0.308211	−	0.533837i	0.977971	+	0.208741i	$0.0669365\pi$
$90$		0			0
$91$	92.8132	−	42.6152i	0.106917	−	0.0490911i
$92$	468.616	−	811.666i	0.531049	−	0.919805i
$93$		0			0
$94$	589.578	−	1021.18i	0.646919	−	1.12050i
$95$	422.983	−	732.627i	0.456812	−	0.791221i
$96$		0			0
$97$	−823.870	+	1426.99i	−0.862385	+	1.49369i	0.00723506	+	0.999974i	$0.497697\pi$
$97$	−823.870	+	1426.99i	−0.862385	+	1.49369i	−0.869620	+	0.493721i	$0.835636\pi$
$98$	−438.882	−	1251.53i	−0.452385	−	1.29004i
$99$		0			0
$100$	−185.546	+	321.375i	−0.185546	+	0.321375i
$101$	−940.525			−0.926592			−0.463296	−	0.886204i	$-0.653333\pi$
$101$	−940.525			−0.926592			−0.463296	+	0.886204i	$0.653333\pi$
$102$		0			0
$103$	100.211			0.0958647			0.0479323	−	0.998851i	$-0.484737\pi$
$103$	100.211			0.0958647			0.0479323	+	0.998851i	$0.484737\pi$
$104$	11.1850	+	19.3731i	0.0105460	+	0.0182662i
$105$		0			0
$106$	1284.01	−	2223.97i	1.17655	−	2.03784i
$107$	−232.210	+	402.200i	−0.209800	+	0.363384i	−0.951651	−	0.307180i	$-0.900615\pi$
$107$	−232.210	+	402.200i	−0.209800	+	0.363384i	0.741851	+	0.670564i	$0.233948\pi$
$108$		0			0
$109$	−227.492	−	394.028i	−0.199906	−	0.346248i	0.748591	−	0.663032i	$-0.230730\pi$
$109$	−227.492	−	394.028i	−0.199906	−	0.346248i	−0.948498	+	0.316783i	$0.897397\pi$
$110$	741.625	+	1284.53i	0.642828	+	1.11341i
$111$		0			0
$112$	1199.92	−	550.942i	1.01233	−	0.464813i
$113$	443.068	+	767.417i	0.368853	+	0.638872i	0.989386	−	0.145308i	$-0.0464173\pi$
$113$	443.068	+	767.417i	0.368853	+	0.638872i	−0.620534	+	0.784180i	$0.713084\pi$
$114$		0			0
$115$	−1800.90			−1.46031
$116$	−821.758	−	1423.33i	−0.657744	−	1.13925i
$117$		0			0
$118$	−532.276			−0.415254
$119$	285.456	−	131.067i	0.219896	−	0.100966i
$120$		0			0
$121$	−506.109			−0.380247
$122$	−1199.66	+	2077.86i	−0.890260	+	1.54197i
$123$		0			0
$124$	−322.977	−	559.413i	−0.233905	−	0.405135i
$125$	−956.466			−0.684391
$126$		0			0
$127$	−225.747			−0.157731			−0.0788655	−	0.996885i	$-0.525130\pi$
$127$	−225.747			−0.157731			−0.0788655	+	0.996885i	$0.525130\pi$
$128$	257.392	+	445.815i	0.177738	+	0.307851i
$129$		0			0
$130$	−142.393	+	246.632i	−0.0960668	+	0.166393i
$131$	−517.334			−0.345035			−0.172518	−	0.985006i	$-0.555190\pi$
$131$	−517.334			−0.345035			−0.172518	+	0.985006i	$0.555190\pi$
$132$		0			0
$133$	−956.924	−	678.487i	−0.623879	−	0.442348i
$134$	2272.66			1.46514
$135$		0			0
$136$	34.4006	+	59.5836i	0.0216899	+	0.0375680i
$137$	−1254.41			−0.782274			−0.391137	−	0.920333i	$-0.627918\pi$
$137$	−1254.41			−0.782274			−0.391137	+	0.920333i	$0.627918\pi$
$138$		0			0
$139$	−380.390	−	658.855i	−0.232117	−	0.402039i	0.726314	−	0.687363i	$-0.241232\pi$
$139$	−380.390	−	658.855i	−0.232117	−	0.402039i	−0.958431	+	0.285325i	$0.907899\pi$
$140$	1402.58	+	994.473i	0.846715	+	0.600345i
$141$		0			0
$142$	235.678	+	408.205i	0.139279	+	0.241238i
$143$	79.1901	+	137.161i	0.0463091	+	0.0802098i
$144$		0			0
$145$	−1579.02	+	2734.94i	−0.904349	+	1.56638i
$146$	−555.340	+	961.876i	−0.314796	+	0.545243i
$147$		0			0
$148$	1409.30	+	2440.98i	0.782729	+	1.35573i
$149$	−2562.81			−1.40908			−0.704541	−	0.709663i	$-0.748847\pi$
$149$	−2562.81			−1.40908			−0.704541	+	0.709663i	$0.748847\pi$
$150$		0			0
$151$	−93.4837			−0.0503815			−0.0251907	−	0.999683i	$-0.508019\pi$
$151$	−93.4837			−0.0503815			−0.0251907	+	0.999683i	$0.508019\pi$
$152$	128.471	−	222.518i	0.0685551	−	0.118741i
$153$		0			0
$154$	1869.13	−	858.211i	0.978043	−	0.449069i
$155$	−620.606	+	1074.92i	−0.321602	+	0.557030i
$156$		0			0
$157$	−1411.24	+	2444.34i	−0.717384	+	1.24255i	0.244649	+	0.969612i	$0.421327\pi$
$157$	−1411.24	+	2444.34i	−0.717384	+	1.24255i	−0.962033	+	0.272934i	$0.912006\pi$
$158$	1889.82	−	3273.26i	0.951556	−	1.64814i
$159$		0			0
$160$	−1624.17	+	2813.15i	−0.802512	+	1.38999i
$161$	−232.307	+	2486.38i	−0.113717	+	1.21711i
$162$		0			0
$163$	998.302	−	1729.11i	0.479712	−	0.830886i	−0.520017	−	0.854156i	$-0.674074\pi$
$163$	998.302	−	1729.11i	0.479712	−	0.830886i	0.999729	+	0.0232701i	$0.00740778\pi$
$164$	−2307.89			−1.09888
$165$		0			0
$166$	3926.25			1.83576
$167$	1551.97	+	2688.08i	0.719130	+	1.24557i	0.961345	+	0.275347i	$0.0887929\pi$
$167$	1551.97	+	2688.08i	0.719130	+	1.24557i	−0.242215	+	0.970223i	$0.577874\pi$
$168$		0			0
$169$	1083.30	−	1876.32i	0.493079	−	0.854039i
$170$	−437.942	+	758.538i	−0.197580	+	0.342219i
$171$		0			0
$172$	−1202.61	−	2082.99i	−0.533131	−	0.923409i
$173$	160.198	+	277.471i	0.0704024	+	0.121941i	0.899078	−	0.437789i	$-0.144238\pi$
$173$	160.198	+	277.471i	0.0704024	+	0.121941i	−0.828675	+	0.559730i	$0.810905\pi$
$174$		0			0
$175$	91.9808	−	984.469i	0.0397320	−	0.425251i
$176$	1023.79	+	1773.26i	0.438473	+	0.759457i
$177$		0			0
$178$	2001.22			0.842686
$179$	−1051.64	−	1821.50i	−0.439125	−	0.760587i	0.558497	−	0.829507i	$-0.311378\pi$
$179$	−1051.64	−	1821.50i	−0.439125	−	0.760587i	−0.997622	+	0.0689193i	$0.978045\pi$
$180$		0			0
$181$	2247.71			0.923045			0.461522	−	0.887129i	$-0.347303\pi$
$181$	2247.71			0.923045			0.461522	+	0.887129i	$0.347303\pi$
$182$	322.139	+	228.406i	0.131201	+	0.0930251i
$183$		0			0
$184$	−546.982			−0.219152
$185$	2708.00	−	4690.39i	1.07619	−	1.86402i
$186$		0			0
$187$	243.556	+	421.852i	0.0952439	+	0.164967i
$188$	2119.71			0.822319
$189$		0			0
$190$	3271.04			1.24898
$191$	70.8626	+	122.738i	0.0268452	+	0.0464973i	0.879136	−	0.476571i	$-0.158121\pi$
$191$	70.8626	+	122.738i	0.0268452	+	0.0464973i	−0.852291	+	0.523068i	$0.824787\pi$
$192$		0			0
$193$	−304.516	+	527.438i	−0.113573	+	0.196714i	−0.917208	−	0.398408i	$-0.869563\pi$
$193$	−304.516	+	527.438i	−0.113573	+	0.196714i	0.803635	+	0.595122i	$0.202896\pi$
$194$	−6371.21			−2.35787
$195$		0			0
$196$	1553.93	−	1808.17i	0.566299	−	0.658953i
$197$	−2446.99			−0.884978			−0.442489	−	0.896774i	$-0.645904\pi$
$197$	−2446.99			−0.884978			−0.442489	+	0.896774i	$0.645904\pi$
$198$		0			0
$199$	1295.56	+	2243.98i	0.461507	+	0.799354i	0.999036	−	0.0438910i	$-0.0139754\pi$
$199$	1295.56	+	2243.98i	0.461507	+	0.799354i	−0.537529	+	0.843245i	$0.680642\pi$
$200$	216.575			0.0765707
$201$		0			0
$202$	−1818.33	−	3149.45i	−0.633354	−	1.09700i
$203$	3572.26	+	2532.84i	1.23509	+	0.875715i
$204$		0			0
$205$	2217.32	+	3840.51i	0.755436	+	1.30845i
$206$	193.739	+	335.566i	0.0655265	+	0.113495i
$207$		0			0
$208$	−196.569	+	340.468i	−0.0655271	+	0.113496i
$209$	909.574	−	1575.43i	0.301036	−	0.521410i
$210$		0			0
$211$	140.960	+	244.150i	0.0459910	+	0.0796588i	0.888105	−	0.459642i	$-0.152022\pi$
$211$	140.960	+	244.150i	0.0459910	+	0.0796588i	−0.842114	+	0.539300i	$0.818689\pi$
$212$	4616.41			1.49555
$213$		0			0
$214$	−1795.74			−0.573619
$215$	−2310.84	+	4002.49i	−0.733014	+	1.26962i
$216$		0			0
$217$	1404.01	+	995.485i	0.439219	+	0.311419i
$218$	879.629	−	1523.56i	0.273284	−	0.473342i
$219$		0			0
$220$	−1333.18	+	2309.14i	−0.408560	+	0.707646i
$221$	−46.7631	+	80.9961i	−0.0142336	+	0.0246533i
$222$		0			0
$223$	−803.773	+	1392.18i	−0.241366	+	0.418058i	−0.961104	−	0.276188i	$-0.910929\pi$
$223$	−803.773	+	1392.18i	−0.241366	+	0.418058i	0.719738	+	0.694246i	$0.244262\pi$
$224$	3674.40	+	2605.26i	1.09601	+	0.777103i
$225$		0			0
$226$	−1713.18	+	2967.32i	−0.504245	+	0.873377i
$227$	4188.54			1.22468			0.612342	−	0.790593i	$-0.290228\pi$
$227$	4188.54			1.22468			0.612342	+	0.790593i	$0.290228\pi$
$228$		0			0
$229$	−2710.30			−0.782105			−0.391052	−	0.920368i	$-0.627889\pi$
$229$	−2710.30			−0.782105			−0.391052	+	0.920368i	$0.627889\pi$
$230$	−3481.72	−	6030.51i	−0.998164	−	1.72887i
$231$		0			0
$232$	−479.590	+	830.675i	−0.135718	+	0.235071i
$233$	1520.98	−	2634.42i	0.427652	−	0.740715i	−0.569012	−	0.822329i	$-0.692674\pi$
$233$	1520.98	−	2634.42i	0.427652	−	0.740715i	0.996664	+	0.0816144i	$0.0260076\pi$
$234$		0			0
$235$	−2036.53	−	3527.37i	−0.565313	−	0.979151i
$236$	−478.423	−	828.654i	−0.131961	−	0.228563i
$237$		0			0
$238$	990.768	+	702.483i	0.269840	+	0.191325i
$239$	697.856	+	1208.72i	0.188873	+	0.327137i	0.944875	−	0.327432i	$-0.106183\pi$
$239$	697.856	+	1208.72i	0.188873	+	0.327137i	−0.756002	+	0.654569i	$0.772850\pi$
$240$		0			0
$241$	3947.15			1.05501			0.527507	−	0.849551i	$-0.323127\pi$
$241$	3947.15			1.05501			0.527507	+	0.849551i	$0.323127\pi$
$242$	−978.469	−	1694.76i	−0.259911	−	0.450178i
$243$		0			0
$244$	−4313.12			−1.13164
$245$	−4501.88	−	848.647i	−1.17394	−	0.221298i
$246$		0			0
$247$	349.279			0.0899760
$248$	−188.494	+	326.482i	−0.0482637	+	0.0835952i
$249$		0			0
$250$	−1849.15	−	3202.82i	−0.467802	−	0.810258i
$251$	−50.3155			−0.0126529			−0.00632646	−	0.999980i	$-0.502014\pi$
$251$	−50.3155			−0.0126529			−0.00632646	+	0.999980i	$0.502014\pi$
$252$		0			0
$253$	−3872.63			−0.962333
$254$	−436.441	−	755.938i	−0.107814	−	0.186739i
$255$		0			0
$256$	−2475.48	+	4287.65i	−0.604365	+	1.04679i
$257$	−2320.93			−0.563329			−0.281664	−	0.959513i	$-0.590886\pi$
$257$	−2320.93			−0.563329			−0.281664	+	0.959513i	$0.590886\pi$
$258$		0			0
$259$	−6126.37	−	4343.77i	−1.46978	−	1.04212i
$260$	−511.946			−0.122114
$261$		0			0
$262$	−1000.17	−	1732.35i	−0.235842	−	0.408491i
$263$	−3404.32			−0.798171			−0.399086	−	0.916914i	$-0.630672\pi$
$263$	−3404.32			−0.798171			−0.399086	+	0.916914i	$0.630672\pi$
$264$		0			0
$265$	−4435.25	−	7682.08i	−1.02813	−	1.78078i
$266$	421.947	−	4516.09i	0.0972602	−	1.04097i
$267$		0			0
$268$	2042.73	+	3538.11i	0.465596	+	0.806435i
$269$	3140.95	+	5440.28i	0.711922	+	1.23308i	0.964135	+	0.265413i	$0.0855082\pi$
$269$	3140.95	+	5440.28i	0.711922	+	1.23308i	−0.252213	+	0.967672i	$0.581158\pi$
$270$		0			0
$271$	1804.21	−	3124.98i	0.404419	−	0.700475i	−0.589834	−	0.807524i	$-0.700807\pi$
$271$	1804.21	−	3124.98i	0.404419	−	0.700475i	0.994254	+	0.107049i	$0.0341403\pi$
$272$	−604.567	+	1047.14i	−0.134769	+	0.233427i
$273$		0			0
$274$	−2425.17	−	4200.52i	−0.534708	−	0.926142i
$275$	1533.35			0.336234
$276$		0			0
$277$	2106.08			0.456830			0.228415	−	0.973564i	$-0.426646\pi$
$277$	2106.08			0.456830			0.228415	+	0.973564i	$0.426646\pi$
$278$	1470.83	−	2547.55i	0.317318	−	0.549612i
$279$		0			0
$280$	93.3475	−	999.097i	0.0199235	−	0.213241i
$281$	−972.004	+	1683.56i	−0.206352	+	0.357412i	−0.950563	−	0.310533i	$-0.899493\pi$
$281$	−972.004	+	1683.56i	−0.206352	+	0.357412i	0.744211	+	0.667945i	$0.232826\pi$
$282$		0			0
$283$	4620.74	−	8003.36i	0.970582	−	1.68110i	0.276777	−	0.960934i	$-0.410734\pi$
$283$	4620.74	−	8003.36i	0.970582	−	1.68110i	0.693805	−	0.720163i	$-0.255933\pi$
$284$	−423.666	+	733.811i	−0.0885210	+	0.153323i
$285$		0			0
$286$	−306.199	+	530.352i	−0.0633075	+	0.109652i
$287$	5588.35	−	2565.89i	1.14937	−	0.527735i
$288$		0			0
$289$	2312.68	−	4005.67i	0.470726	−	0.815321i
$290$	−12211.0			−2.47260
$291$		0			0
$292$	−1996.61			−0.400147
$293$	−3079.42	−	5333.71i	−0.613998	−	1.06348i	−0.990559	−	0.137084i	$-0.956227\pi$
$293$	−3079.42	−	5333.71i	−0.613998	−	1.06348i	0.376561	−	0.926392i	$-0.377106\pi$
$294$		0			0
$295$	−919.298	+	1592.27i	−0.181436	+	0.314256i
$296$	822.490	−	1424.59i	0.161508	−	0.279739i
$297$		0			0
$298$	−4954.72	−	8581.82i	−0.963151	−	1.66823i
$299$	−371.775	−	643.933i	−0.0719074	−	0.124547i
$300$		0			0
$301$	5227.87	+	3706.72i	1.00110	+	0.709806i
$302$	−180.734	−	313.040i	−0.0344373	−	0.0596471i
$303$		0			0
$304$	4515.58			0.851928
$305$	4143.87	+	7177.39i	0.777958	+	1.34746i
$306$		0			0
$307$	3956.54			0.735544			0.367772	−	0.929916i	$-0.380121\pi$
$307$	3956.54			0.735544			0.367772	+	0.929916i	$0.380121\pi$
$308$	3016.09	+	2138.50i	0.557980	+	0.395624i
$309$		0			0
$310$	−4799.31			−0.879298
$311$	2778.71	−	4812.87i	0.506644	−	0.877534i	−0.493326	−	0.869844i	$-0.664219\pi$
$311$	2778.71	−	4812.87i	0.506644	−	0.877534i	0.999970	−	0.00768915i	$-0.00244756\pi$
$312$		0			0
$313$	2674.28	+	4631.98i	0.482936	+	0.836470i	0.999808	−	0.0195925i	$-0.00623690\pi$
$313$	2674.28	+	4631.98i	0.482936	+	0.836470i	−0.516872	+	0.856063i	$0.672904\pi$
$314$	−10913.5			−1.96142
$315$		0			0
$316$	6794.47			1.20955
$317$	−3209.05	−	5558.25i	−0.568576	−	0.984802i	−0.996707	−	0.0810854i	$-0.974161\pi$
$317$	−3209.05	−	5558.25i	−0.568576	−	0.984802i	0.428132	−	0.903716i	$-0.359172\pi$
$318$		0			0
$319$	−3395.50	+	5881.18i	−0.595961	+	1.03223i
$320$	−4942.59			−0.863435
$321$		0			0
$322$	−8775.03	+	4029.06i	−1.51867	+	0.697300i
$323$	1074.24			0.185053
$324$		0			0
$325$	147.202	+	254.962i	0.0251241	+	0.0435161i
$326$	7720.14			1.31159
$327$		0			0
$328$	673.459	+	1166.46i	0.113371	+	0.196364i
$329$	−5132.70	+	2356.68i	−0.860106	+	0.394918i
$330$		0			0
$331$	1630.73	+	2824.51i	0.270795	+	0.469031i	0.969066	−	0.246803i	$-0.0793801\pi$
$331$	1630.73	+	2824.51i	0.270795	+	0.469031i	−0.698271	+	0.715834i	$0.746047\pi$
$332$	3529.01	+	6112.43i	0.583373	+	1.01043i
$333$		0			0
$334$	−6000.89	+	10393.8i	−0.983096	+	1.70277i
$335$	3925.14	−	6798.54i	0.640159	−	1.10879i
$336$		0			0
$337$	897.370	+	1554.29i	0.145053	+	0.251239i	0.929393	−	0.369092i	$-0.120331\pi$
$337$	897.370	+	1554.29i	0.145053	+	0.251239i	−0.784340	+	0.620332i	$0.786998\pi$
$338$	8377.42			1.34814
$339$		0			0
$340$	−1574.54			−0.251151
$341$	−1334.54	+	2311.49i	−0.211934	+	0.367080i
$342$		0			0
$343$	−1752.39	+	6105.96i	−0.275860	+	0.961198i
$344$	−701.863	+	1215.66i	−0.110006	+	0.190535i
$345$		0			0
$346$	−619.427	+	1072.88i	−0.0962445	+	0.166700i
$347$	933.130	−	1616.23i	0.144360	−	0.250039i	−0.784774	−	0.619782i	$-0.787221\pi$
$347$	933.130	−	1616.23i	0.144360	−	0.250039i	0.929134	+	0.369743i	$0.120554\pi$
$348$		0			0
$349$	2296.96	−	3978.45i	0.352302	−	0.610205i	−0.634350	−	0.773046i	$-0.718732\pi$
$349$	2296.96	−	3978.45i	0.352302	−	0.610205i	0.986652	+	0.162841i	$0.0520657\pi$
$350$	3474.42	−	1595.28i	0.530617	−	0.243633i
$351$		0			0
$352$	−3492.59	+	6049.34i	−0.528851	+	0.915997i
$353$	6157.74			0.928451			0.464226	−	0.885717i	$-0.346333\pi$
$353$	6157.74			0.928451			0.464226	+	0.885717i	$0.346333\pi$
$354$		0			0
$355$	1628.16			0.243419
$356$	1798.75	+	3115.53i	0.267791	+	0.463828i
$357$		0			0
$358$	4066.32	−	7043.07i	0.600311	−	1.03977i
$359$	−1828.80	+	3167.58i	−0.268859	+	0.465678i	−0.968568	−	0.248751i	$-0.919980\pi$
$359$	−1828.80	+	3167.58i	−0.268859	+	0.465678i	0.699708	+	0.714429i	$0.253313\pi$
$360$		0			0
$361$	1423.60	+	2465.74i	0.207552	+	0.359490i
$362$	4345.54	+	7526.69i	0.630929	+	1.09280i
$363$		0			0
$364$	−66.0383	+	706.807i	−0.00950920	+	0.101777i
$365$	1918.26	+	3322.53i	0.275086	+	0.476463i
$366$		0			0
$367$	7083.87			1.00756			0.503780	−	0.863832i	$-0.331942\pi$
$367$	7083.87			1.00756			0.503780	+	0.863832i	$0.331942\pi$
$368$	−4806.41	−	8324.95i	−0.680847	−	1.17926i
$369$		0			0
$370$	20941.7			2.94245
$371$	−11178.2	+	5132.49i	−1.56427	+	0.718236i
$372$		0			0
$373$	13242.2			1.83822			0.919109	−	0.394003i	$-0.128910\pi$
$373$	13242.2			1.83822			0.919109	+	0.394003i	$0.128910\pi$
$374$	−941.743	+	1631.15i	−0.130204	+	0.225520i
$375$		0			0
$376$	−618.548	−	1071.36i	−0.0848383	−	0.146944i
$377$	−1303.88			−0.178125
$378$		0			0
$379$	−1915.73			−0.259643			−0.129821	−	0.991537i	$-0.541440\pi$
$379$	−1915.73			−0.259643			−0.129821	+	0.991537i	$0.541440\pi$
$380$	2940.09	+	5092.39i	0.396904	+	0.687458i
$381$		0			0
$382$	−274.000	+	474.581i	−0.0366991	+	0.0635646i
$383$	11642.2			1.55324			0.776618	−	0.629972i	$-0.216934\pi$
$383$	11642.2			1.55324			0.776618	+	0.629972i	$0.216934\pi$
$384$		0			0
$385$	660.900	−	7073.60i	0.0874872	−	0.936374i
$386$	−2354.91			−0.310522
$387$		0			0
$388$	−5726.61	−	9918.78i	−0.749290	−	1.29781i
$389$	5982.57			0.779764			0.389882	−	0.920865i	$-0.372516\pi$
$389$	5982.57			0.779764			0.389882	+	0.920865i	$0.372516\pi$
$390$		0			0
$391$	−1143.43	−	1980.48i	−0.147892	−	0.256156i
$392$	−1367.34	−	257.756i	−0.176176	−	0.0332109i
$393$		0			0
$394$	−4730.80	−	8193.99i	−0.604910	−	1.04773i
$395$	−6527.84	−	11306.5i	−0.831522	−	1.44024i
$396$		0			0
$397$	−4543.74	+	7869.98i	−0.574417	+	0.994920i	0.421687	+	0.906741i	$0.361438\pi$
$397$	−4543.74	+	7869.98i	−0.574417	+	0.994920i	−0.996105	+	0.0881786i	$0.971895\pi$
$398$	−5009.47	+	8676.65i	−0.630909	+	1.09277i
$399$		0			0
$400$	1903.07	+	3296.22i	0.237884	+	0.412028i
$401$	8347.36			1.03952			0.519760	−	0.854312i	$-0.326021\pi$
$401$	8347.36			1.03952			0.519760	+	0.854312i	$0.326021\pi$
$402$		0			0
$403$	−512.466			−0.0633444
$404$	3268.73	−	5661.61i	0.402538	−	0.697217i
$405$		0			0
$406$	−1575.15	+	16858.9i	−0.192546	+	2.06082i
$407$	5823.23	−	10086.1i	0.709206	−	1.22838i
$408$		0			0
$409$	−5853.32	+	10138.2i	−0.707648	+	1.22568i	0.258079	+	0.966124i	$0.416910\pi$
$409$	−5853.32	+	10138.2i	−0.707648	+	1.22568i	−0.965727	+	0.259559i	$0.916423\pi$
$410$	−8573.57	+	14849.9i	−1.03273	+	1.78874i
$411$		0			0
$412$	−348.276	+	603.231i	−0.0416464	+	0.0721337i
$413$	2079.75	+	1474.60i	0.247791	+	0.175691i
$414$		0			0
$415$	6781.05	−	11745.1i	0.802093	−	1.38927i
$416$	−1341.16			−0.158067
$417$		0			0
$418$	7033.98			0.823070
$419$	52.3192	+	90.6195i	0.00610015	+	0.0105658i	0.869059	−	0.494708i	$-0.164725\pi$
$419$	52.3192	+	90.6195i	0.00610015	+	0.0105658i	−0.862959	+	0.505274i	$0.831392\pi$
$420$		0			0
$421$	−5909.85	+	10236.2i	−0.684153	+	1.18499i	0.289550	+	0.957163i	$0.406494\pi$
$421$	−5909.85	+	10236.2i	−0.684153	+	1.18499i	−0.973702	+	0.227824i	$0.926839\pi$
$422$	−545.042	+	944.040i	−0.0628726	+	0.108898i
$423$		0			0
$424$	−1347.10	−	2333.25i	−0.154295	−	0.267247i
$425$	452.734	+	784.159i	0.0516726	+	0.0894995i
$426$		0			0
$427$	10443.9	−	4795.30i	1.18364	−	0.543468i
$428$	−1614.06	−	2795.64i	−0.182287	−	0.315729i
$429$		0			0
$430$	−17870.4			−2.00415
$431$	3058.30	+	5297.12i	0.341793	+	0.592003i	0.984766	−	0.173886i	$-0.0556324\pi$
$431$	3058.30	+	5297.12i	0.341793	+	0.592003i	−0.642972	+	0.765889i	$0.722299\pi$
$432$		0			0
$433$	−8659.36			−0.961068			−0.480534	−	0.876976i	$-0.659557\pi$
$433$	−8659.36			−0.961068			−0.480534	+	0.876976i	$0.659557\pi$
$434$	−619.086	+	6626.07i	−0.0684725	+	0.732860i
$435$		0			0
$436$	3162.53			0.347381
$437$	−4270.20	+	7396.20i	−0.467440	+	0.809629i
$438$		0			0
$439$	−7215.23	−	12497.2i	−0.784429	−	1.35867i	−0.929340	−	0.369226i	$-0.879623\pi$
$439$	−7215.23	−	12497.2i	−0.784429	−	1.35867i	0.144911	−	0.989445i	$-0.453711\pi$
$440$	1556.13			0.168604
$441$		0			0
$442$	−361.632			−0.0389165
$443$	−873.867	−	1513.58i	−0.0937216	−	0.162331i	0.815353	−	0.578965i	$-0.196543\pi$
$443$	−873.867	−	1513.58i	−0.0937216	−	0.162331i	−0.909074	+	0.416634i	$0.863210\pi$
$444$		0			0
$445$	3456.33	−	5986.54i	0.368193	−	0.637729i
$446$	−6215.79			−0.659924
$447$		0			0
$448$	−637.568	+	6823.88i	−0.0672372	+	0.719639i
$449$	−6876.18			−0.722733			−0.361367	−	0.932424i	$-0.617690\pi$
$449$	−6876.18			−0.722733			−0.361367	+	0.932424i	$0.617690\pi$
$450$		0			0
$451$	4768.09	+	8258.57i	0.497828	+	0.862264i
$452$	−6159.42			−0.640961
$453$		0			0
$454$	8097.78	+	14025.8i	0.837109	+	1.44992i
$455$	1239.63	−	569.177i	0.127725	−	0.0586449i
$456$		0			0
$457$	1359.75	+	2355.15i	0.139182	+	0.241071i	0.927187	−	0.374598i	$-0.122219\pi$
$457$	1359.75	+	2355.15i	0.139182	+	0.241071i	−0.788005	+	0.615669i	$0.788886\pi$
$458$	−5239.88	−	9075.74i	−0.534593	−	0.925942i
$459$		0			0
$460$	6258.92	−	10840.8i	0.634399	−	1.09881i
$461$	−1231.59	+	2133.18i	−0.124427	+	0.215514i	−0.921509	−	0.388357i	$-0.873043\pi$
$461$	−1231.59	+	2133.18i	−0.124427	+	0.215514i	0.797082	+	0.603871i	$0.206376\pi$
$462$		0			0
$463$	−488.238	−	845.653i	−0.0490072	−	0.0848830i	0.840481	−	0.541841i	$-0.182272\pi$
$463$	−488.238	−	845.653i	−0.0490072	−	0.0848830i	−0.889488	+	0.456958i	$0.848939\pi$
$464$	−16856.9			−1.68656
$465$		0			0
$466$	11762.2			1.16925
$467$	5486.73	−	9503.29i	0.543673	−	0.941670i	−0.455016	−	0.890483i	$-0.650366\pi$
$467$	5486.73	−	9503.29i	0.543673	−	0.941670i	0.998689	−	0.0511862i	$-0.0163002\pi$
$468$		0			0
$469$	−8879.94	−	6296.14i	−0.874280	−	0.619890i
$470$	7874.52	−	13639.1i	0.772818	−	1.33856i
$471$		0			0
$472$	−279.215	+	483.615i	−0.0272286	+	0.0471614i
$473$	−4969.19	+	8606.89i	−0.483052	+	0.836671i
$474$		0			0
$475$	1690.76	−	2928.48i	0.163321	−	0.282880i
$476$	−203.107	+	2173.85i	−0.0195575	+	0.209324i
$477$		0			0
$478$	−2698.35	+	4673.68i	−0.258200	+	0.447216i
$479$	979.089			0.0933940			0.0466970	−	0.998909i	$-0.485130\pi$
$479$	979.089			0.0933940			0.0466970	+	0.998909i	$0.485130\pi$
$480$		0			0
$481$	2236.13			0.211973
$482$	7631.10	+	13217.4i	0.721135	+	1.24904i
$483$		0			0
$484$	1758.95	−	3046.59i	0.165190	−	0.286118i
$485$	−11003.8	+	19059.1i	−1.03022	+	1.78439i
$486$		0			0
$487$	4370.44	+	7569.83i	0.406660	+	0.704357i	0.994513	−	0.104611i	$-0.0333599\pi$
$487$	4370.44	+	7569.83i	0.406660	+	0.704357i	−0.587853	+	0.808968i	$0.700027\pi$
$488$	1258.60	+	2179.96i	0.116750	+	0.202218i
$489$		0			0
$490$	−5861.79	−	16715.7i	−0.540425	−	1.54110i
$491$	6965.56	+	12064.7i	0.640226	+	1.10890i	0.985382	+	0.170359i	$0.0544928\pi$
$491$	6965.56	+	12064.7i	0.640226	+	1.10890i	−0.345156	+	0.938545i	$0.612174\pi$
$492$		0			0
$493$	−4010.20			−0.366350
$494$	675.267	+	1169.60i	0.0615014	+	0.106524i
$495$		0			0
$496$	−6625.31			−0.599769
$497$	210.024	−	2247.89i	0.0189555	−	0.202880i
$498$		0			0
$499$	−8428.41			−0.756127			−0.378063	−	0.925780i	$-0.623410\pi$
$499$	−8428.41			−0.756127			−0.378063	+	0.925780i	$0.623410\pi$
$500$	3324.13	−	5757.56i	0.297319	−	0.514972i
$501$		0			0
$502$	−97.2758	−	168.487i	−0.00864867	−	0.0149799i
$503$	−2009.66			−0.178144			−0.0890719	−	0.996025i	$-0.528390\pi$
$503$	−2009.66			−0.178144			−0.0890719	+	0.996025i	$0.528390\pi$
$504$		0			0
$505$	−12561.8			−1.10692
$506$	−7487.03	−	12967.9i	−0.657784	−	1.13932i
$507$		0			0
$508$	784.569	−	1358.91i	0.0685229	−	0.118685i
$509$	−11731.0			−1.02155			−0.510773	−	0.859716i	$-0.670641\pi$
$509$	−11731.0			−1.02155			−0.510773	+	0.859716i	$0.670641\pi$
$510$		0			0
$511$	4834.63	−	2219.82i	0.418535	−	0.192170i
$512$	−15025.3			−1.29693
$513$		0			0
$514$	−4487.09	−	7771.87i	−0.385053	−	0.666931i
$515$	1338.43			0.114521
$516$		0			0
$517$	−4379.32	−	7585.20i	−0.372538	−	0.645255i
$518$	2701.37	−	28912.7i	0.229134	−	2.45241i
$519$		0			0
$520$	149.390	+	258.750i	0.0125984	+	0.0218211i
$521$	4418.73	+	7653.46i	0.371570	+	0.643578i	0.989807	−	0.142413i	$-0.0454862\pi$
$521$	4418.73	+	7653.46i	0.371570	+	0.643578i	−0.618237	+	0.785992i	$0.712153\pi$
$522$		0			0
$523$	5711.81	−	9893.14i	0.477552	−	0.827145i	−0.522117	−	0.852874i	$-0.674857\pi$
$523$	5711.81	−	9893.14i	0.477552	−	0.827145i	0.999669	+	0.0257292i	$0.00819077\pi$
$524$	1797.96	−	3114.15i	0.149893	−	0.259623i
$525$		0			0
$526$	−6581.62	−	11399.7i	−0.545575	−	0.944963i
$527$	−1576.14			−0.130280
$528$		0			0
$529$	6013.92			0.494281
$530$	17149.5	−	29703.8i	1.40552	−	2.43444i
$531$		0			0
$532$	7409.96	−	3402.29i	0.603877	−	0.277270i
$533$	−915.479	+	1585.66i	−0.0743974	+	0.128860i
$534$		0			0
$535$	−3101.44	+	5371.86i	−0.250630	+	0.434104i
$536$	1192.17	−	2064.90i	0.0960705	−	0.166399i
$537$		0			0
$538$	−12144.9	+	21035.6i	−0.973241	+	1.68570i
$539$	−9680.77	−	1824.92i	−0.773618	−	0.145834i
$540$		0			0
$541$	−3532.39	+	6118.28i	−0.280719	+	0.486220i	−0.971562	−	0.236785i	$-0.923906\pi$
$541$	−3532.39	+	6118.28i	−0.280719	+	0.486220i	0.690843	+	0.723005i	$0.257240\pi$
$542$	13952.4			1.10573
$543$		0			0
$544$	−4124.87			−0.325096
$545$	−3038.43	−	5262.71i	−0.238811	−	0.413633i
$546$		0			0
$547$	5320.04	−	9214.58i	0.415847	−	0.720269i	−0.579670	−	0.814852i	$-0.696818\pi$
$547$	5320.04	−	9214.58i	0.415847	−	0.720269i	0.995517	+	0.0945828i	$0.0301517\pi$
$548$	4359.62	−	7551.08i	0.339842	−	0.588624i
$549$		0			0
$550$	2964.45	+	5134.57i	0.229826	+	0.398071i
$551$	7488.16	+	12969.9i	0.578959	+	1.00279i
$552$		0			0
$553$	−16452.2	+	7554.04i	−1.26513	+	0.580887i
$554$	4071.72	+	7052.42i	0.312258	+	0.540846i
$555$		0			0
$556$	5288.08			0.403354
$557$	−3260.15	−	5646.75i	−0.248002	−	0.429552i	0.714969	−	0.699156i	$-0.246441\pi$
$557$	−3260.15	−	5646.75i	−0.248002	−	0.429552i	−0.962971	+	0.269604i	$0.913107\pi$
$558$		0			0
$559$	−1908.18			−0.144378
$560$	16026.3	−	7358.48i	1.20935	−	0.555273i
$561$		0			0
$562$	−7516.77			−0.564192
$563$	7885.11	−	13657.4i	0.590262	−	1.02236i	−0.403935	−	0.914788i	$-0.632358\pi$
$563$	7885.11	−	13657.4i	0.590262	−	1.02236i	0.994197	−	0.107576i	$-0.0343090\pi$
$564$		0			0
$565$	5917.71	+	10249.8i	0.440637	+	0.763205i
$566$	35733.5			2.65369
$567$		0			0
$568$	494.516			0.0365307
$569$	6087.58	+	10544.0i	0.448514	+	0.776850i	0.998290	−	0.0584630i	$-0.0186200\pi$
$569$	6087.58	+	10544.0i	0.448514	+	0.776850i	−0.549775	+	0.835313i	$0.685287\pi$
$570$		0			0
$571$	−8284.15	+	14348.6i	−0.607147	+	1.05161i	0.384562	+	0.923099i	$0.374353\pi$
$571$	−8284.15	+	14348.6i	−0.607147	+	1.05161i	−0.991708	+	0.128510i	$0.958981\pi$
$572$	−1100.88			−0.0804721
$573$		0			0
$574$	19396.2	+	13752.5i	1.41042	+	1.00003i
$575$	−7198.64			−0.522094
$576$		0			0
$577$	−351.578	−	608.951i	−0.0253664	−	0.0439358i	0.853064	−	0.521807i	$-0.174742\pi$
$577$	−351.578	−	608.951i	−0.0253664	−	0.0439358i	−0.878430	+	0.477871i	$0.841409\pi$
$578$	17884.5			1.28702
$579$		0			0
$580$	−10975.6	−	19010.2i	−0.785750	−	1.36096i
$581$	−15340.9	−	10877.2i	−1.09544	−	0.776698i
$582$		0			0
$583$	−9537.49	−	16519.4i	−0.677534	−	1.17352i
$584$	582.627	+	1009.14i	0.0412830	+	0.0715043i
$585$		0			0
$586$	11907.0	−	20623.5i	0.839374	−	1.45384i
$587$	548.955	−	950.819i	0.0385993	−	0.0668560i	−0.846080	−	0.533055i	$-0.821044\pi$
$587$	548.955	−	950.819i	0.0385993	−	0.0668560i	0.884680	+	0.466199i	$0.154377\pi$
$588$		0			0
$589$	2943.09	+	5097.57i	0.205887	+	0.356608i
$590$	−7109.18			−0.496068
$591$		0			0
$592$	28909.4			2.00704
$593$	5626.37	−	9745.16i	0.389625	−	0.674850i	−0.602774	−	0.797912i	$-0.705938\pi$
$593$	5626.37	−	9745.16i	0.389625	−	0.674850i	0.992399	+	0.123062i	$0.0392714\pi$
$594$		0			0
$595$	3812.60	−	1750.56i	0.262691	−	0.120615i
$596$	8906.86	−	15427.1i	0.612146	−	1.06027i
$597$		0			0
$598$	1437.52	−	2489.86i	0.0983019	−	0.170264i
$599$	5820.27	−	10081.0i	0.397012	−	0.687644i	−0.596344	−	0.802729i	$-0.703381\pi$
$599$	5820.27	−	10081.0i	0.397012	−	0.687644i	0.993356	+	0.115085i	$0.0367139\pi$
$600$		0			0
$601$	970.960	−	1681.75i	0.0659007	−	0.114143i	−0.831192	−	0.555985i	$-0.812341\pi$
$601$	970.960	−	1681.75i	0.0659007	−	0.114143i	0.897093	+	0.441841i	$0.145675\pi$
$602$	−2305.18	+	24672.3i	−0.156067	+	1.67038i
$603$		0			0
$604$	324.896	−	562.737i	0.0218872	−	0.0379097i
$605$	−6759.69			−0.454249
$606$		0			0
$607$	−12911.4			−0.863354			−0.431677	−	0.902028i	$-0.642078\pi$
$607$	−12911.4			−0.863354			−0.431677	+	0.902028i	$0.642078\pi$
$608$	7702.27	+	13340.7i	0.513764	+	0.889865i
$609$		0			0
$610$	−16022.8	+	27752.3i	−1.06352	+	1.84206i
$611$	840.835	−	1456.37i	0.0556736	−	0.0964294i
$612$		0			0
$613$	9637.25	+	16692.2i	0.634984	+	1.09982i	0.986519	+	0.163649i	$0.0523265\pi$
$613$	9637.25	+	16692.2i	0.634984	+	1.09982i	−0.351535	+	0.936175i	$0.614340\pi$
$614$	7649.26	+	13248.9i	0.502767	+	0.870818i
$615$		0			0
$616$	200.733	−	2148.44i	0.0131295	−	0.140525i
$617$	779.062	+	1349.38i	0.0508329	+	0.0880451i	0.890322	−	0.455331i	$-0.150479\pi$
$617$	779.062	+	1349.38i	0.0508329	+	0.0880451i	−0.839489	+	0.543376i	$0.817146\pi$
$618$		0			0
$619$	7045.54			0.457486			0.228743	−	0.973487i	$-0.426538\pi$
$619$	7045.54			0.457486			0.228743	+	0.973487i	$0.426538\pi$
$620$	−4313.74	−	7471.62i	−0.279426	−	0.483980i
$621$		0			0
$622$	21488.5			1.38523
$623$	−7819.34	−	5544.14i	−0.502850	−	0.356535i
$624$		0			0
$625$	−19448.2			−1.24469
$626$	−10340.5	+	17910.2i	−0.660204	+	1.14351i
$627$		0			0
$628$	−9809.34	−	16990.3i	−0.623305	−	1.07960i
$629$	6877.44			0.435964
$630$		0			0
$631$	−29049.6			−1.83272			−0.916361	−	0.400354i	$-0.868887\pi$
$631$	−29049.6			−1.83272			−0.916361	+	0.400354i	$0.868887\pi$
$632$	−1982.68	−	3434.10i	−0.124789	−	0.216141i
$633$		0			0
$634$	12408.2	−	21491.7i	0.777278	−	1.34628i
$635$	−3015.12			−0.188428
$636$		0			0
$637$	−625.917	−	1784.89i	−0.0389321	−	0.111020i
$638$	−26258.3			−1.62943
$639$		0			0
$640$	3437.77	+	5954.40i	0.212328	+	0.367763i
$641$	−20283.0			−1.24982			−0.624908	−	0.780699i	$-0.714863\pi$
$641$	−20283.0			−1.24982			−0.624908	+	0.780699i	$0.714863\pi$
$642$		0			0
$643$	12393.5	+	21466.2i	0.760111	+	1.31655i	0.942793	+	0.333379i	$0.108189\pi$
$643$	12393.5	+	21466.2i	0.760111	+	1.31655i	−0.182682	+	0.983172i	$0.558478\pi$
$644$	−14159.7	−	10039.6i	−0.866414	−	0.614313i
$645$		0			0
$646$	2076.85	+	3597.20i	0.126490	+	0.219087i
$647$	5412.76	+	9375.17i	0.328899	+	0.569669i	0.982294	−	0.187348i	$-0.0599892\pi$
$647$	5412.76	+	9375.17i	0.328899	+	0.569669i	−0.653395	+	0.757017i	$0.726656\pi$
$648$		0			0
$649$	−1976.84	+	3423.99i	−0.119565	+	0.207093i
$650$	−569.178	+	985.845i	−0.0343461	+	0.0594893i
$651$		0			0
$652$	6939.06	+	12018.8i	0.416802	+	0.721922i
$653$	11333.4			0.679190			0.339595	−	0.940572i	$-0.389710\pi$
$653$	11333.4			0.679190			0.339595	+	0.940572i	$0.389710\pi$
$654$		0			0
$655$	−6909.61			−0.412184
$656$	−11835.6	+	20499.8i	−0.704423	+	1.22010i
$657$		0			0
$658$	−17814.7	−	12631.2i	−1.05546	−	0.748349i
$659$	−1455.83	+	2521.57i	−0.0860563	+	0.149054i	−0.905841	−	0.423618i	$-0.860760\pi$
$659$	−1455.83	+	2521.57i	−0.0860563	+	0.149054i	0.819785	+	0.572672i	$0.194093\pi$
$660$		0			0
$661$	13377.1	−	23169.8i	0.787152	−	1.36339i	−0.140553	−	0.990073i	$-0.544888\pi$
$661$	13377.1	−	23169.8i	0.787152	−	1.36339i	0.927705	−	0.373314i	$-0.121779\pi$
$662$	−6305.45	+	10921.4i	−0.370194	+	0.641194i
$663$		0			0
$664$	2059.58	−	3567.31i	0.120373	−	0.208491i
$665$	−12780.9	−	9062.01i	−0.745294	−	0.528435i
$666$		0			0
$667$	15940.9	−	27610.5i	0.925389	−	1.60282i
$668$	−21575.0			−1.24964
$669$		0			0
$670$	30354.1			1.75027
$671$	8910.90	+	15434.1i	0.512670	+	0.887970i
$672$		0			0
$673$	−6830.55	+	11830.9i	−0.391231	+	0.677631i	−0.992612	−	0.121331i	$-0.961284\pi$
$673$	−6830.55	+	11830.9i	−0.391231	+	0.677631i	0.601382	+	0.798962i	$0.294617\pi$
$674$	−3469.80	+	6009.88i	−0.198296	+	0.343460i
$675$		0			0
$676$	7529.84	+	13042.1i	0.428416	+	0.742038i
$677$	−4412.64	−	7642.92i	−0.250505	−	0.433887i	0.713160	−	0.701001i	$-0.247263\pi$
$677$	−4412.64	−	7642.92i	−0.250505	−	0.433887i	−0.963665	+	0.267114i	$0.913930\pi$
$678$		0			0
$679$	24894.1	+	17650.7i	1.40699	+	0.997599i
$680$	459.461	+	795.810i	0.0259111	+	0.0448793i
$681$		0			0
$682$	−10320.4			−0.579453
$683$	−7312.23	−	12665.2i	−0.409655	−	0.709544i	0.585196	−	0.810892i	$-0.301018\pi$
$683$	−7312.23	−	12665.2i	−0.409655	−	0.709544i	−0.994851	+	0.101348i	$0.967684\pi$
$684$		0			0
$685$	−16754.1			−0.934515
$686$	−23834.4	+	5936.71i	−1.32653	+	0.330415i
$687$		0			0
$688$	−24669.5			−1.36703
$689$	1831.21	−	3171.75i	0.101253	−	0.175376i
$690$		0			0
$691$	2285.84	+	3959.18i	0.125843	+	0.217966i	0.922062	−	0.387042i	$-0.126503\pi$
$691$	2285.84	+	3959.18i	0.125843	+	0.217966i	−0.796219	+	0.605008i	$0.793170\pi$
$692$	−2227.03			−0.122339
$693$		0			0
$694$	7216.15			0.394699
$695$	−5080.56	−	8799.80i	−0.277290	−	0.480281i
$696$		0			0
$697$	−2815.64	+	4876.83i	−0.153013	+	0.265026i
$698$	17763.0			0.963237
$699$		0			0
$700$	5606.46	+	3975.14i	0.302720	+	0.214638i
$701$	1521.50			0.0819773			0.0409886	−	0.999160i	$-0.486949\pi$
$701$	1521.50			0.0819773			0.0409886	+	0.999160i	$0.486949\pi$
$702$		0			0
$703$	−12842.1	−	22243.1i	−0.688973	−	1.19334i
$704$	−10628.5			−0.568999
$705$		0			0
$706$	11904.9	+	20619.8i	0.634625	+	1.09920i
$707$	−1620.41	+	17343.2i	−0.0861978	+	0.922574i
$708$		0			0
$709$	−5831.20	−	10099.9i	−0.308879	−	0.534994i	0.669238	−	0.743048i	$-0.266621\pi$
$709$	−5831.20	−	10099.9i	−0.308879	−	0.534994i	−0.978117	+	0.208053i	$0.933287\pi$
$710$	3147.75	+	5452.07i	0.166385	+	0.288187i
$711$		0			0
$712$	1049.78	−	1818.27i	0.0552558	−	0.0957058i
$713$	6265.29	−	10851.8i	0.329084	−	0.569990i
$714$		0			0
$715$	1057.68	+	1831.95i	0.0553216	+	0.0958197i
$716$	14619.6			0.763075
$717$		0			0
$718$	−14142.6			−0.735094
$719$	6176.82	−	10698.6i	0.320384	−	0.554922i	−0.660183	−	0.751105i	$-0.729521\pi$
$719$	6176.82	−	10698.6i	0.320384	−	0.554922i	0.980567	+	0.196183i	$0.0628546\pi$
$720$		0			0
$721$	172.651	−	1847.88i	0.00891798	−	0.0954490i
$722$	−5504.53	+	9534.13i	−0.283736	+	0.491445i
$723$		0			0
$724$	−7811.77	+	13530.4i	−0.400997	+	0.694548i
$725$	−6311.72	+	10932.2i	−0.323326	+	0.560017i
$726$		0			0
$727$	−5157.33	+	8932.76i	−0.263102	+	0.455705i	−0.967064	−	0.254531i	$-0.918079\pi$
$727$	−5157.33	+	8932.76i	−0.263102	+	0.455705i	0.703963	+	0.710237i	$0.251412\pi$
$728$	376.509	−	172.874i	0.0191681	−	0.00880102i
$729$		0			0
$730$	−7417.22	+	12847.0i	−0.376060	+	0.651355i
$731$	−5868.79			−0.296943
$732$		0			0
$733$	10836.7			0.546060			0.273030	−	0.962006i	$-0.411974\pi$
$733$	10836.7			0.546060			0.273030	+	0.962006i	$0.411974\pi$
$734$	13695.4	+	23721.1i	0.688699	+	1.19286i
$735$		0			0
$736$	16396.7	−	28399.9i	0.821184	−	1.42233i
$737$	8440.55	−	14619.5i	0.421861	−	0.730685i
$738$		0			0
$739$	6152.50	+	10656.4i	0.306256	+	0.530451i	0.977540	−	0.210749i	$-0.0675902\pi$
$739$	6152.50	+	10656.4i	0.306256	+	0.530451i	−0.671284	+	0.741200i	$0.734257\pi$
$740$	18822.9	+	32602.2i	0.935060	+	1.61957i
$741$		0			0
$742$	−38797.7	−	27508.7i	−1.91956	−	1.36102i
$743$	−10676.9	−	18492.9i	−0.527182	−	0.913105i	−0.999498	−	0.0316764i	$-0.989915\pi$
$743$	−10676.9	−	18492.9i	−0.527182	−	0.913105i	0.472316	−	0.881429i	$-0.343418\pi$
$744$		0			0
$745$	−34229.3			−1.68331
$746$	25601.4	+	44342.9i	1.25648	+	2.17629i
$747$		0			0
$748$	−3385.85			−0.165507
$749$	7016.48	+	4974.89i	0.342292	+	0.242695i
$750$		0			0
$751$	10428.4			0.506706			0.253353	−	0.967374i	$-0.418467\pi$
$751$	10428.4			0.506706			0.253353	+	0.967374i	$0.418467\pi$
$752$	10870.6	−	18828.3i	0.527139	−	0.913031i
$753$		0			0
$754$	−2520.81	−	4366.18i	−0.121754	−	0.210884i
$755$	−1248.59			−0.0601864
$756$		0			0
$757$	38937.7			1.86950			0.934751	−	0.355303i	$-0.115622\pi$
$757$	38937.7			1.86950			0.934751	+	0.355303i	$0.115622\pi$
$758$	−3703.72	−	6415.03i	−0.177474	−	0.307393i
$759$		0			0
$760$	1715.88	−	2972.00i	0.0818969	−	0.141850i
$761$	−1423.97			−0.0678303			−0.0339152	−	0.999425i	$-0.510798\pi$
$761$	−1423.97			−0.0678303			−0.0339152	+	0.999425i	$0.510798\pi$
$762$		0			0
$763$	−7657.80	+	3516.08i	−0.363343	+	0.166829i
$764$	−985.112			−0.0466494
$765$		0			0
$766$	22508.1	+	38985.2i	1.06168	+	1.83889i
$767$	−759.113			−0.0357366
$768$		0			0
$769$	7436.72	+	12880.8i	0.348732	+	0.604022i	0.986025	−	0.166600i	$-0.0532790\pi$
$769$	7436.72	+	12880.8i	0.348732	+	0.604022i	−0.637292	+	0.770622i	$0.719946\pi$
$770$	24964.4	−	11462.4i	1.16838	−	0.536464i
$771$		0			0
$772$	−2116.65	−	3666.15i	−0.0986787	−	0.170917i
$773$	13639.2	+	23623.8i	0.634630	+	1.09921i	0.986593	+	0.163197i	$0.0521807\pi$
$773$	13639.2	+	23623.8i	0.634630	+	1.09921i	−0.351964	+	0.936014i	$0.614486\pi$
$774$		0			0
$775$	−2480.71	+	4296.71i	−0.114980	+	0.199151i
$776$	−3342.14	+	5788.75i	−0.154608	+	0.267789i
$777$		0			0
$778$	11566.2	+	20033.3i	0.532993	+	0.923171i
$779$	21030.3			0.967252
$780$		0			0
$781$	3501.17			0.160412
$782$	4421.22	−	7657.78i	0.202177	−	0.350181i
$783$		0			0
$784$	−8092.03	−	23075.6i	−0.368624	−	1.05118i
$785$	−18848.8	+	32647.1i	−0.856997	+	1.48436i
$786$		0			0
$787$	11259.4	−	19501.9i	0.509981	−	0.883313i	−0.489952	−	0.871749i	$-0.662986\pi$
$787$	11259.4	−	19501.9i	0.509981	−	0.883313i	0.999933	−	0.0115637i	$-0.00368093\pi$
$788$	8504.34	−	14730.0i	0.384460	−	0.665905i
$789$		0			0
$790$	25240.8	−	43718.3i	1.13674	−	1.96890i
$791$	14914.5	−	6847.99i	0.670415	−	0.307821i
$792$		0			0
$793$	−1710.90	+	2963.37i	−0.0766154	+	0.132702i
$794$	−35137.9			−1.57053
$795$		0			0
$796$	−18010.6			−0.801969
$797$	−14101.5	−	24424.5i	−0.626727	−	1.08552i	−0.988204	−	0.153142i	$-0.951061\pi$
$797$	−14101.5	−	24424.5i	−0.626727	−	1.08552i	0.361478	−	0.932381i	$-0.382272\pi$
$798$		0			0
$799$	2586.07	−	4479.20i	0.114504	−	0.198326i
$800$	−6492.19	+	11244.8i	−0.286917	+	0.496955i
$801$		0			0
$802$	16138.1	+	27952.0i	0.710544	+	1.23070i
$803$	4125.00	+	7144.71i	0.181280	+	0.313987i
$804$		0			0
$805$	−3102.74	+	33208.6i	−0.135847	+	1.45397i
$806$	−990.760	−	1716.05i	−0.0432978	−	0.0749940i
$807$		0			0
$808$	−3815.36			−0.166119
$809$	−7209.83	−	12487.8i	−0.313330	−	0.542704i	0.665751	−	0.746174i	$-0.268111\pi$
$809$	−7209.83	−	12487.8i	−0.313330	−	0.542704i	−0.979081	+	0.203470i	$0.934778\pi$
$810$		0			0
$811$	−22959.6			−0.994106			−0.497053	−	0.867720i	$-0.665585\pi$
$811$	−22959.6			−0.994106			−0.497053	+	0.867720i	$0.665585\pi$
$812$	−27661.9	+	12701.0i	−1.19549	+	0.548912i
$813$		0			0
$814$	45032.6			1.93906
$815$	13333.5	−	23094.3i	0.573071	−	0.992588i
$816$		0			0
$817$	10958.7	+	18981.0i	0.469272	+	0.812802i
$818$	−45265.3			−1.93480
$819$		0			0
$820$	−30824.6			−1.31273
$821$	−1719.95	−	2979.05i	−0.0731143	−	0.126638i	0.827150	−	0.561981i	$-0.189960\pi$
$821$	−1719.95	−	2979.05i	−0.0731143	−	0.126638i	−0.900265	+	0.435343i	$0.856627\pi$
$822$		0			0
$823$	9781.08	−	16941.3i	0.414273	−	0.717542i	−0.581079	−	0.813847i	$-0.697369\pi$
$823$	9781.08	−	16941.3i	0.414273	−	0.717542i	0.995352	+	0.0963050i	$0.0307024\pi$
$824$	406.518			0.0171866
$825$		0			0
$826$	−917.047	+	9815.14i	−0.0386297	+	0.413453i
$827$	10120.5			0.425544			0.212772	−	0.977102i	$-0.431751\pi$
$827$	10120.5			0.425544			0.212772	+	0.977102i	$0.431751\pi$
$828$		0			0
$829$	6005.06	+	10401.1i	0.251586	+	0.435759i	0.963963	−	0.266038i	$-0.0857147\pi$
$829$	6005.06	+	10401.1i	0.251586	+	0.435759i	−0.712377	+	0.701797i	$0.752381\pi$
$830$	52439.7			2.19302
$831$		0			0
$832$	−1020.34	−	1767.28i	−0.0425167	−	0.0736411i
$833$	−1925.06	−	5489.60i	−0.0800715	−	0.228335i
$834$		0			0
$835$	20728.4	+	35902.6i	0.859083	+	1.48798i
$836$	6322.33	+	10950.6i	0.261558	+	0.453031i
$837$		0			0
$838$	−202.299	+	350.393i	−0.00833928	+	0.0144440i
$839$	15824.0	−	27407.9i	0.651136	−	1.12780i	−0.331711	−	0.943381i	$-0.607626\pi$
$839$	15824.0	−	27407.9i	0.651136	−	1.12780i	0.982847	−	0.184420i	$-0.0590408\pi$
$840$		0			0
$841$	−15759.3	−	27295.9i	−0.646163	−	1.11919i
$842$	−45702.4			−1.87056
$843$		0			0
$844$	−1959.59			−0.0799193
$845$	14468.7	−	25060.5i	0.589040	−	1.02025i
$846$		0			0
$847$	−871.964	+	9332.62i	−0.0353731	+	0.378598i
$848$	23674.4	−	41005.3i	0.958705	−	1.66053i
$849$		0			0
$850$	−1750.56	+	3032.06i	−0.0706396	+	0.122351i
$851$	−27338.4	+	47351.5i	−1.10123	+	1.90739i
$852$		0			0
$853$	20475.4	−	35464.4i	0.821880	−	1.42354i	−0.0824005	−	0.996599i	$-0.526259\pi$
$853$	20475.4	−	35464.4i	0.821880	−	1.42354i	0.904281	−	0.426939i	$-0.140408\pi$
$854$	36248.8	+	25701.5i	1.45247	+	1.02984i
$855$		0			0
$856$	−941.991	+	1631.58i	−0.0376128	+	0.0651473i
$857$	19171.0			0.764142			0.382071	−	0.924133i	$-0.375211\pi$
$857$	19171.0			0.764142			0.382071	+	0.924133i	$0.375211\pi$
$858$		0			0
$859$	−30524.7			−1.21244			−0.606222	−	0.795295i	$-0.707316\pi$
$859$	−30524.7			−1.21244			−0.606222	+	0.795295i	$0.707316\pi$
$860$	−16062.3	−	27820.8i	−0.636885	−	1.10312i
$861$		0			0
$862$	−11825.3	+	20482.0i	−0.467253	+	0.809305i
$863$	−7085.52	+	12272.5i	−0.279483	+	0.484079i	−0.971256	−	0.238036i	$-0.923496\pi$
$863$	−7085.52	+	12272.5i	−0.279483	+	0.484079i	0.691773	+	0.722115i	$0.256830\pi$
$864$		0			0
$865$	2139.63	+	3705.95i	0.0841037	+	0.145672i
$866$	−16741.3	−	28996.8i	−0.656919	−	1.13782i
$867$		0			0
$868$	−10872.0	+	4991.88i	−0.425138	+	0.195202i
$869$	−14037.4	−	24313.4i	−0.547968	−	0.949109i
$870$		0			0
$871$	3241.19			0.126089
$872$	−922.851	−	1598.42i	−0.0358391	−	0.0620751i
$873$		0			0
$874$	−33022.6			−1.27804
$875$	−1647.87	+	17637.2i	−0.0636667	+	0.681423i
$876$		0			0
$877$	36262.7			1.39624			0.698121	−	0.715980i	$-0.254020\pi$
$877$	36262.7			1.39624			0.698121	+	0.715980i	$0.254020\pi$
$878$	27898.7	−	48321.9i	1.07236	−	1.85739i
$879$		0			0
$880$	13674.0	+	23684.0i	0.523806	+	0.907258i
$881$	2958.35			0.113132			0.0565660	−	0.998399i	$-0.481985\pi$
$881$	2958.35			0.113132			0.0565660	+	0.998399i	$0.481985\pi$
$882$		0			0
$883$	23107.6			0.880671			0.440335	−	0.897833i	$-0.354860\pi$
$883$	23107.6			0.880671			0.440335	+	0.897833i	$0.354860\pi$
$884$	−325.044	−	562.993i	−0.0123670	−	0.0214203i
$885$		0			0
$886$	3378.92	−	5852.47i	0.128123	−	0.221916i
$887$	−24734.0			−0.936285			−0.468143	−	0.883653i	$-0.655077\pi$
$887$	−24734.0			−0.936285			−0.468143	+	0.883653i	$0.655077\pi$
$888$		0			0
$889$	−388.935	+	4162.77i	−0.0146732	+	0.157047i
$890$	26728.7			1.00668
$891$		0			0
$892$	−5586.92	−	9676.82i	−0.209713	−	0.363233i
$893$	−19315.6			−0.723821
$894$		0			0
$895$	−14045.9	−	24328.3i	−0.524585	−	0.908608i
$896$	8664.27	−	3978.20i	0.323050	−	0.148329i
$897$		0			0
$898$	−13293.8	−	23025.6i	−0.494010	−	0.855651i
$899$	−10986.7	−	19029.6i	−0.407595	−	0.705975i
$900$		0			0
$901$	5632.05	−	9755.00i	0.208247	−	0.360695i
$902$	−18436.5	+	31932.9i	−0.680562	+	1.17877i
$903$		0			0
$904$	1797.36	+	3113.12i	0.0661277	+	0.114536i
$905$	30020.9			1.10268
$906$		0			0
$907$	−50574.9			−1.85150			−0.925751	−	0.378133i	$-0.876566\pi$
$907$	−50574.9			−1.85150			−0.925751	+	0.378133i	$0.876566\pi$
$908$	−14557.0	+	25213.4i	−0.532038	+	0.921517i
$909$		0			0
$910$	4302.55	+	3050.63i	0.156734	+	0.111129i
$911$	18448.5	−	31953.7i	0.670939	−	1.16210i	−0.306699	−	0.951807i	$-0.599224\pi$
$911$	18448.5	−	31953.7i	0.670939	−	1.16210i	0.977638	−	0.210295i	$-0.0674423\pi$
$912$		0			0
$913$	14581.9	−	25256.5i	0.528575	−	0.915519i
$914$	−5257.65	+	9106.51i	−0.190271	+	0.329559i
$915$		0			0
$916$	9419.48	−	16315.0i	0.339769	−	0.588497i
$917$	−891.303	+	9539.60i	−0.0320975	+	0.343539i
$918$		0			0
$919$	−5914.26	+	10243.8i	−0.212289	+	0.367695i	−0.952431	−	0.304756i	$-0.901425\pi$
$919$	−5914.26	+	10243.8i	−0.212289	+	0.367695i	0.740142	+	0.672451i	$0.234758\pi$
$920$	−7305.60			−0.261803
$921$		0			0
$922$	−9524.23			−0.340199
$923$	336.115	+	582.168i	0.0119863	+	0.0207609i
$924$		0			0
$925$	10824.5	−	18748.6i	0.384765	−	0.666432i
$926$	1887.84	−	3269.83i	0.0669959	−	0.116040i
$927$		0			0
$928$	−28753.1	−	49801.8i	−1.01710	−	1.76166i
$929$	−7751.49	−	13426.0i	−0.273755	−	0.474157i	0.696065	−	0.717978i	$-0.254932\pi$
$929$	−7751.49	−	13426.0i	−0.273755	−	0.474157i	−0.969820	+	0.243821i	$0.921599\pi$
$930$		0			0
$931$	−14159.9	+	16476.7i	−0.498467	+	0.580023i
$932$	10572.1	+	18311.5i	0.371569	+	0.643576i
$933$		0			0
$934$	42430.3			1.48647
$935$	3252.99	+	5634.34i	0.113780	+	0.197072i
$936$		0			0
$937$	45491.1			1.58605			0.793026	−	0.609188i	$-0.208505\pi$
$937$	45491.1			1.58605			0.793026	+	0.609188i	$0.208505\pi$
$938$	3915.53	−	41907.8i	0.136297	−	1.45878i
$939$		0			0
$940$	28311.3			0.982354
$941$	−1746.83	+	3025.60i	−0.0605154	+	0.104816i	−0.894696	−	0.446676i	$-0.852608\pi$
$941$	−1746.83	+	3025.60i	−0.0605154	+	0.104816i	0.834180	+	0.551492i	$0.185941\pi$
$942$		0			0
$943$	−22384.8	−	38771.7i	−0.773012	−	1.33890i
$944$	−9814.02			−0.338368
$945$		0			0
$946$	−38428.1			−1.32072
$947$	20884.9	+	36173.7i	0.716651	+	1.24128i	0.962319	+	0.271921i	$0.0876591\pi$
$947$	20884.9	+	36173.7i	0.716651	+	1.24128i	−0.245669	+	0.969354i	$0.579008\pi$
$948$		0			0
$949$	−792.005	+	1371.79i	−0.0270912	+	0.0469234i
$950$	13075.1			0.446540
$951$		0			0
$952$	1157.99	−	531.690i	0.0394229	−	0.0181010i
$953$	7119.73			0.242005			0.121002	−	0.992652i	$-0.461389\pi$
$953$	7119.73			0.242005			0.121002	+	0.992652i	$0.461389\pi$
$954$		0			0
$955$	946.454	+	1639.31i	0.0320697	+	0.0555463i
$956$	−9701.40			−0.328207
$957$		0			0
$958$	1892.89	+	3278.58i	0.0638377	+	0.110570i
$959$	−2161.20	+	23131.3i	−0.0727724	+	0.778882i
$960$		0			0
$961$	10577.4	+	18320.5i	0.355052	+	0.614969i
$962$	4323.16	+	7487.93i	0.144890	+	0.250957i
$963$		0			0
$964$	−13718.1	+	23760.4i	−0.458329	+	0.793848i
$965$	−4067.18	+	7044.56i	−0.135676	+	0.234997i
$966$		0			0
$967$	−27441.1	−	47529.4i	−0.912562	−	1.58060i	−0.810433	−	0.585832i	$-0.800768\pi$
$967$	−27441.1	−	47529.4i	−0.912562	−	1.58060i	−0.102129	−	0.994771i	$-0.532565\pi$
$968$	−2053.10			−0.0681704
$969$		0			0
$970$	−85095.1			−2.81674
$971$	−19341.9	+	33501.1i	−0.639248	+	1.10721i	0.346350	+	0.938105i	$0.387421\pi$
$971$	−19341.9	+	33501.1i	−0.639248	+	1.10721i	−0.985598	+	0.169105i	$0.945912\pi$
$972$		0			0
$973$	−12804.6	+	5879.25i	−0.421888	+	0.193710i
$974$	−16898.9	+	29269.8i	−0.555930	+	0.962899i
$975$		0			0
$976$	−22119.1	+	38311.3i	−0.725424	+	1.25647i
$977$	19052.5	−	32999.8i	0.623892	−	1.08061i	−0.364862	−	0.931062i	$-0.618884\pi$
$977$	19052.5	−	32999.8i	0.623892	−	1.08061i	0.988754	−	0.149551i	$-0.0477828\pi$
$978$		0			0
$979$	7432.43	−	12873.4i	0.242637	−	0.420260i
$980$	20754.5	−	24150.2i	0.676509	−	0.787195i
$981$		0			0
$982$	−26933.3	+	46649.8i	−0.875229	+	1.51594i
$983$	−55354.0			−1.79605			−0.898026	−	0.439942i	$-0.854999\pi$
$983$	−55354.0			−1.79605			−0.898026	+	0.439942i	$0.854999\pi$
$984$		0			0
$985$	−32682.4			−1.05721
$986$	−7753.00	−	13428.6i	−0.250411	−	0.433725i
$987$		0			0
$988$	−1213.89	+	2102.53i	−0.0390882	+	0.0677028i
$989$	23329.0	−	40406.9i	0.750069	−	1.29916i
$990$		0			0
$991$	−21782.9	−	37729.0i	−0.698239	−	1.20939i	−0.969076	−	0.246761i	$-0.920634\pi$
$991$	−21782.9	−	37729.0i	−0.698239	−	1.20939i	0.270837	−	0.962625i	$-0.412700\pi$
$992$	−11300.9	−	19573.7i	−0.361697	−	0.626477i
$993$		0			0
$994$	7933.33	−	3642.59i	0.253149	−	0.116233i
$995$	17303.8	+	29971.0i	0.551323	+	0.954920i
$996$		0			0
$997$	−37202.5			−1.18176			−0.590881	−	0.806759i	$-0.701220\pi$
$997$	−37202.5			−1.18176			−0.590881	+	0.806759i	$0.701220\pi$
$998$	−16294.8	−	28223.4i	−0.516836	−	0.895186i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.g.a.100.19		44
3.2	odd	2		63.4.g.a.16.4	yes	44
7.4	even	3		189.4.h.a.46.4		44
9.4	even	3		189.4.h.a.37.4		44
9.5	odd	6		63.4.h.a.58.19	yes	44
21.11	odd	6		63.4.h.a.25.19	yes	44
63.4	even	3	inner	189.4.g.a.172.19		44
63.32	odd	6		63.4.g.a.4.4	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.4	✓	44	63.32	odd	6
63.4.g.a.16.4	yes	44	3.2	odd	2
63.4.h.a.25.19	yes	44	21.11	odd	6
63.4.h.a.58.19	yes	44	9.5	odd	6
189.4.g.a.100.19		44	1.1	even	1	trivial
189.4.g.a.172.19		44	63.4	even	3	inner
189.4.h.a.37.4		44	9.4	even	3
189.4.h.a.46.4		44	7.4	even	3

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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93332 + 3.34860i) q^{2} +(-3.47543 + 6.01962i) q^{4} +13.3562 q^{5} +(1.72288 - 18.4399i) q^{7} +4.05663 q^{8} +O(q^{10})\)	\(q+(1.93332 + 3.34860i) q^{2} +(-3.47543 + 6.01962i) q^{4} +13.3562 q^{5} +(1.72288 - 18.4399i) q^{7} +4.05663 q^{8} +(25.8218 + 44.7246i) q^{10} +28.7209 q^{11} +(2.75723 + 4.77566i) q^{13} +(65.0790 - 29.8810i) q^{14} +(35.6462 + 61.7410i) q^{16} +(8.48010 + 14.6880i) q^{17} +(31.6694 - 54.8530i) q^{19} +(-46.4185 + 80.3993i) q^{20} +(55.5266 + 96.1750i) q^{22} -134.837 q^{23} +53.3878 q^{25} +(-10.6612 + 18.4657i) q^{26} +(105.014 + 74.4579i) q^{28} +(-118.224 + 204.770i) q^{29} +(-46.4658 + 80.4810i) q^{31} +(-121.604 + 210.625i) q^{32} +(-32.7895 + 56.7930i) q^{34} +(23.0111 - 246.287i) q^{35} +(202.752 - 351.177i) q^{37} +244.908 q^{38} +54.1811 q^{40} +(166.014 + 287.545i) q^{41} +(-173.016 + 299.673i) q^{43} +(-99.8176 + 172.889i) q^{44} +(-260.682 - 451.514i) q^{46} +(-152.478 - 264.100i) q^{47} +(-337.063 - 63.5396i) q^{49} +(103.216 + 178.775i) q^{50} -38.3302 q^{52} +(-332.075 - 575.170i) q^{53} +383.602 q^{55} +(6.98908 - 74.8040i) q^{56} -914.257 q^{58} +(-68.8294 + 119.216i) q^{59} +(310.258 + 537.383i) q^{61} -359.332 q^{62} -370.060 q^{64} +(36.8260 + 63.7846i) q^{65} +(293.882 - 509.018i) q^{67} -117.888 q^{68} +(869.207 - 399.097i) q^{70} +121.903 q^{71} +(143.624 + 248.763i) q^{73} +1567.94 q^{74} +(220.130 + 381.276i) q^{76} +(49.4827 - 529.612i) q^{77} +(-488.750 - 846.540i) q^{79} +(476.097 + 824.625i) q^{80} +(-641.917 + 1111.83i) q^{82} +(507.709 - 879.377i) q^{83} +(113.262 + 196.175i) q^{85} -1337.98 q^{86} +116.510 q^{88} +(258.781 - 448.222i) q^{89} +(92.8132 - 42.6152i) q^{91} +(468.616 - 811.666i) q^{92} +(589.578 - 1021.18i) q^{94} +(422.983 - 732.627i) q^{95} +(-823.870 + 1426.99i) q^{97} +(-438.882 - 1251.53i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

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