LMFDB - Embedded newform 189.4.h.a.37.4

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			37.4
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.86663 q^{2} +6.95086 q^{4} +(-6.67810 - 11.5668i) q^{5} +(15.1080 + 10.7120i) q^{7} +4.05663 q^{8} +O(q^{10})$	\(q-3.86663 q^{2} +6.95086 q^{4} +(-6.67810 - 11.5668i) q^{5} +(15.1080 + 10.7120i) q^{7} +4.05663 q^{8} +(25.8218 + 44.7246i) q^{10} +(-14.3605 + 24.8730i) q^{11} +(2.75723 - 4.77566i) q^{13} +(-58.4172 - 41.4195i) q^{14} -71.2924 q^{16} +(8.48010 + 14.6880i) q^{17} +(31.6694 - 54.8530i) q^{19} +(-46.4185 - 80.3993i) q^{20} +(55.5266 - 96.1750i) q^{22} +(67.4183 + 116.772i) q^{23} +(-26.6939 + 46.2352i) q^{25} +(-10.6612 + 18.4657i) q^{26} +(105.014 + 74.4579i) q^{28} +(-118.224 - 204.770i) q^{29} +92.9315 q^{31} +243.209 q^{32} +(-32.7895 - 56.7930i) q^{34} +(23.0111 - 246.287i) q^{35} +(202.752 - 351.177i) q^{37} +(-122.454 + 212.097i) q^{38} +(-27.0905 - 46.9222i) q^{40} +(166.014 - 287.545i) q^{41} +(-173.016 - 299.673i) q^{43} +(-99.8176 + 172.889i) q^{44} +(-260.682 - 451.514i) q^{46} +304.957 q^{47} +(113.505 + 323.675i) q^{49} +(103.216 - 178.775i) q^{50} +(19.1651 - 33.1949i) q^{52} +(-332.075 - 575.170i) q^{53} +383.602 q^{55} +(61.2876 + 43.4547i) q^{56} +(457.129 + 791.770i) q^{58} +137.659 q^{59} -620.516 q^{61} -359.332 q^{62} -370.060 q^{64} -73.6521 q^{65} -587.763 q^{67} +(58.9440 + 102.094i) q^{68} +(-88.9755 + 952.304i) q^{70} +121.903 q^{71} +(143.624 + 248.763i) q^{73} +(-783.969 + 1357.87i) q^{74} +(220.130 - 381.276i) q^{76} +(-483.399 + 221.953i) q^{77} +977.500 q^{79} +(476.097 + 824.625i) q^{80} +(-641.917 + 1111.83i) q^{82} +(507.709 + 879.377i) q^{83} +(113.262 - 196.175i) q^{85} +(668.992 + 1158.73i) q^{86} +(-58.2550 + 100.901i) q^{88} +(258.781 - 448.222i) q^{89} +(92.8132 - 42.6152i) q^{91} +(468.616 + 811.666i) q^{92} -1179.16 q^{94} -845.965 q^{95} +(-823.870 - 1426.99i) q^{97} +(-438.882 - 1251.53i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.86663			−1.36706			−0.683531	−	0.729922i	$-0.739557\pi$
$2$	−3.86663			−1.36706			−0.683531	+	0.729922i	$0.739557\pi$
$3$		0			0
$3$		0			0
$4$	6.95086			0.868858
$5$	−6.67810	−	11.5668i	−0.597307	−	1.03457i	−0.993217	−	0.116277i	$-0.962904\pi$
$5$	−6.67810	−	11.5668i	−0.597307	−	1.03457i	0.395910	−	0.918289i	$-0.370429\pi$
$6$		0			0
$7$	15.1080	+	10.7120i	0.815757	+	0.578395i
$7$	15.1080	+	10.7120i	0.815757	+	0.578395i
$8$	4.05663			0.179279
$9$		0			0
$10$	25.8218	+	44.7246i	0.816556	+	1.41432i
$11$	−14.3605	+	24.8730i	−0.393622	+	0.681773i	−0.992924	−	0.118750i	$-0.962111\pi$
$11$	−14.3605	+	24.8730i	−0.393622	+	0.681773i	0.599302	+	0.800523i	$0.295445\pi$
$12$		0			0
$13$	2.75723	−	4.77566i	0.0588244	−	0.101887i	−0.835114	−	0.550078i	$-0.814598\pi$
$13$	2.75723	−	4.77566i	0.0588244	−	0.101887i	0.893938	+	0.448191i	$0.147931\pi$
$14$	−58.4172	−	41.4195i	−1.11519	−	0.790702i
$15$		0			0
$16$	−71.2924			−1.11394
$17$	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
$23$	67.4183	+	116.772i	0.611204	+	1.05864i	0.991038	+	0.133582i	$0.0426478\pi$
$23$	67.4183	+	116.772i	0.611204	+	1.05864i	−0.379834	+	0.925055i	$0.624019\pi$
$24$		0			0
$25$	−26.6939	+	46.2352i	−0.213551	+	0.369882i
$26$	−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	−0.944363	−	0.328905i	$-0.893320\pi$
$29$	−118.224	−	204.770i	−0.757022	−	1.31120i	0.187341	−	0.982295i	$-0.440013\pi$
$30$		0			0
$31$	92.9315			0.538419			0.269210	−	0.963082i	$-0.413238\pi$
$31$	92.9315			0.538419			0.269210	+	0.963082i	$0.413238\pi$
$32$	243.209			1.34355
$33$		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	$-0.190405\pi$
$38$	−122.454	+	212.097i	−0.522754	+	0.905437i
$39$		0			0
$40$	−27.0905	−	46.9222i	−0.107085	−	0.185476i
$41$	166.014	−	287.545i	0.632368	−	1.09529i	−0.354698	−	0.934981i	$-0.615416\pi$
$41$	166.014	−	287.545i	0.632368	−	1.09529i	0.987066	−	0.160313i	$-0.0512504\pi$
$42$		0			0
$43$	−173.016	−	299.673i	−0.613599	−	1.06279i	−0.990629	−	0.136584i	$-0.956388\pi$
$43$	−173.016	−	299.673i	−0.613599	−	1.06279i	0.377029	−	0.926201i	$-0.376946\pi$
$44$	−99.8176	+	172.889i	−0.342002	+	0.592364i
$45$		0			0
$46$	−260.682	−	451.514i	−0.835554	−	1.44722i
$47$	304.957			0.946437			0.473218	−	0.880945i	$-0.343092\pi$
$47$	304.957			0.946437			0.473218	+	0.880945i	$0.343092\pi$
$48$		0			0
$49$	113.505	+	323.675i	0.330918	+	0.943660i
$50$	103.216	−	178.775i	0.291938	−	0.505651i
$51$		0			0
$52$	19.1651	−	33.1949i	0.0511100	−	0.0885252i
$53$	−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
$56$	61.2876	+	43.4547i	0.146248	+	0.103694i
$57$		0			0
$58$	457.129	+	791.770i	1.03490	+	1.79249i
$59$	137.659			0.303757			0.151878	−	0.988399i	$-0.451468\pi$
$59$	137.659			0.303757			0.151878	+	0.988399i	$0.451468\pi$
$60$		0			0
$61$	−620.516			−1.30244			−0.651221	−	0.758888i	$-0.725743\pi$
$61$	−620.516			−1.30244			−0.651221	+	0.758888i	$0.725743\pi$
$62$	−359.332			−0.736052
$63$		0			0
$64$	−370.060			−0.722773
$65$	−73.6521			−0.140545
$66$		0			0
$67$	−587.763			−1.07174			−0.535871	−	0.844300i	$-0.680017\pi$
$67$	−587.763			−1.07174			−0.535871	+	0.844300i	$0.680017\pi$
$68$	58.9440	+	102.094i	0.105118	+	0.182069i
$69$		0			0
$70$	−88.9755	+	952.304i	−0.151923	+	1.62603i
$71$	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	$0.759372\pi$
$74$	−783.969	+	1357.87i	−1.23155	+	2.13310i
$75$		0			0
$76$	220.130	−	381.276i	0.332245	−	0.575465i
$77$	−483.399	+	221.953i	−0.715434	+	0.328492i
$78$		0			0
$79$	977.500			1.39212			0.696059	−	0.717984i	$-0.254935\pi$
$79$	977.500			1.39212			0.696059	+	0.717984i	$0.254935\pi$
$80$	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	0.977500	+	0.210934i	$0.0676507\pi$
$83$	507.709	+	879.377i	0.671425	+	1.16294i	−0.306075	+	0.952007i	$0.599016\pi$
$84$		0			0
$85$	113.262	−	196.175i	0.144529	−	0.250332i
$86$	668.992	+	1158.73i	0.838828	+	1.45289i
$87$		0			0
$88$	−58.2550	+	100.901i	−0.0705683	+	0.122228i
$89$	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
$94$	−1179.16			−1.29384
$95$	−845.965			−0.913623
$96$		0			0
$97$	−823.870	−	1426.99i	−0.862385	−	1.49369i	−0.869620	−	0.493721i	$-0.835636\pi$
$97$	−823.870	−	1426.99i	−0.862385	−	1.49369i	0.00723506	−	0.999974i	$-0.497697\pi$
$98$	−438.882	−	1251.53i	−0.452385	−	1.29004i
$99$		0			0
$100$	−185.546	+	321.375i	−0.185546	+	0.321375i
$101$	470.263	−	814.519i	0.463296	−	0.802452i	−0.535827	−	0.844328i	$-0.680000\pi$
$101$	470.263	−	814.519i	0.463296	−	0.802452i	0.999123	+	0.0418759i	$0.0133334\pi$
$102$		0			0
$103$	−50.1054	−	86.7851i	−0.0479323	−	0.0830212i	0.841064	−	0.540936i	$-0.181930\pi$
$103$	−50.1054	−	86.7851i	−0.0479323	−	0.0830212i	−0.888996	+	0.457915i	$0.848597\pi$
$104$	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	$0.897397\pi$
$110$	−1483.25			−1.28566
$111$		0			0
$112$	−1077.09	−	763.686i	−0.908707	−	0.644300i
$113$	443.068	−	767.417i	0.368853	−	0.638872i	−0.620534	−	0.784180i	$-0.713084\pi$
$113$	443.068	−	767.417i	0.368853	−	0.638872i	0.989386	+	0.145308i	$0.0464173\pi$
$114$		0			0
$115$	900.452	−	1559.63i	0.730153	−	1.26466i
$116$	−821.758	−	1423.33i	−0.657744	−	1.13925i
$117$		0			0
$118$	−532.276			−0.415254
$119$	−29.2204	+	312.745i	−0.0225095	+	0.240919i
$120$		0			0
$121$	253.054	+	438.303i	0.190124	+	0.329304i
$122$	2399.31			1.78052
$123$		0			0
$124$	645.954			0.467810
$125$	−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	$0.525130\pi$
$128$	−514.783			−0.355475
$129$		0			0
$130$	284.786			0.192134
$131$	258.667	+	448.024i	0.172518	+	0.298809i	0.939299	−	0.343098i	$-0.111476\pi$
$131$	258.667	+	448.024i	0.172518	+	0.298809i	−0.766782	+	0.641908i	$0.778143\pi$
$132$		0			0
$133$	1066.05	−	489.477i	0.695024	−	0.319121i
$134$	2272.66			1.46514
$135$		0			0
$136$	34.4006	+	59.5836i	0.0216899	+	0.0375680i
$137$	627.205	−	1086.35i	0.391137	−	0.677469i	−0.601463	−	0.798901i	$-0.705415\pi$
$137$	627.205	−	1086.35i	0.391137	−	0.677469i	0.992600	+	0.121432i	$0.0387486\pi$
$138$		0			0
$139$	−380.390	+	658.855i	−0.232117	+	0.402039i	−0.958431	−	0.285325i	$-0.907899\pi$
$139$	−380.390	+	658.855i	−0.232117	+	0.402039i	0.726314	+	0.687363i	$0.241232\pi$
$140$	159.947	−	1711.91i	0.0965571	−	1.03345i
$141$		0			0
$142$	−471.355			−0.278558
$143$	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
$149$	1281.40	+	2219.46i	0.704541	+	1.22030i	0.966857	+	0.255319i	$0.0821805\pi$
$149$	1281.40	+	2219.46i	0.704541	+	1.22030i	−0.262316	+	0.964982i	$0.584486\pi$
$150$		0			0
$151$	46.7419	−	80.9593i	0.0251907	−	0.0436316i	−0.853155	−	0.521657i	$-0.825314\pi$
$151$	46.7419	−	80.9593i	0.0251907	−	0.0436316i	0.878346	+	0.478026i	$0.158647\pi$
$152$	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
$157$	2822.48			1.43477			0.717384	−	0.696678i	$-0.245339\pi$
$157$	2822.48			1.43477			0.717384	+	0.696678i	$0.245339\pi$
$158$	−3779.64			−1.90311
$159$		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	$0.00740778\pi$
$164$	1153.94	−	1998.69i	0.549438	−	0.951655i
$165$		0			0
$166$	−1963.12	−	3400.23i	−0.917879	−	1.58981i
$167$	1551.97	−	2688.08i	0.719130	−	1.24557i	−0.242215	−	0.970223i	$-0.577874\pi$
$167$	1551.97	−	2688.08i	0.719130	−	1.24557i	0.961345	−	0.275347i	$-0.0887929\pi$
$168$		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
$173$	−320.396			−0.140805			−0.0704024	−	0.997519i	$-0.522428\pi$
$173$	−320.396			−0.140805			−0.0704024	+	0.997519i	$0.522428\pi$
$174$		0			0
$175$	−898.566	+	412.577i	−0.388144	+	0.178216i
$176$	1023.79	−	1773.26i	0.438473	−	0.759457i
$177$		0			0
$178$	−1000.61	+	1733.11i	−0.421343	+	0.729788i
$179$	−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	$0.347303\pi$
$182$	−358.875	+	164.778i	−0.146162	+	0.0671106i
$183$		0			0
$184$	273.491	+	473.700i	0.109576	+	0.189792i
$185$	−5415.99			−2.15239
$186$		0			0
$187$	−487.113			−0.190488
$188$	2119.71			0.822319
$189$		0			0
$190$	3271.04			1.24898
$191$	−141.725			−0.0536904			−0.0268452	−	0.999640i	$-0.508546\pi$
$191$	−141.725			−0.0536904			−0.0268452	+	0.999640i	$0.508546\pi$
$192$		0			0
$193$	609.033			0.227146			0.113573	−	0.993530i	$-0.463770\pi$
$193$	609.033			0.227146			0.113573	+	0.993530i	$0.463770\pi$
$194$	3185.61	+	5517.63i	1.17893	+	2.04197i
$195$		0			0
$196$	788.956	+	2249.82i	0.287521	+	0.819906i
$197$	−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	$0.680642\pi$
$200$	−108.287	+	187.559i	−0.0382853	+	0.0663122i
$201$		0			0
$202$	−1818.33	+	3149.45i	−0.633354	+	1.09700i
$203$	407.371	−	4360.08i	0.140846	−	1.50748i
$204$		0			0
$205$	−4434.64			−1.51087
$206$	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	−0.842114	−	0.539300i	$-0.818689\pi$
$211$	140.960	−	244.150i	0.0459910	−	0.0796588i	0.888105	+	0.459642i	$0.152022\pi$
$212$	−2308.21	−	3997.93i	−0.747775	−	1.29518i
$213$		0			0
$214$	897.872	−	1555.16i	0.286810	−	0.496769i
$215$	−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
$220$	2666.37			0.817120
$221$	93.5263			0.0284672
$222$		0			0
$223$	−803.773	−	1392.18i	−0.241366	−	0.418058i	0.719738	−	0.694246i	$-0.244262\pi$
$223$	−803.773	−	1392.18i	−0.241366	−	0.418058i	−0.961104	+	0.276188i	$0.910929\pi$
$224$	3674.40	+	2605.26i	1.09601	+	0.777103i
$225$		0			0
$226$	−1713.18	+	2967.32i	−0.504245	+	0.873377i
$227$	−2094.27	+	3627.38i	−0.612342	+	1.06061i	0.378503	+	0.925600i	$0.376439\pi$
$227$	−2094.27	+	3627.38i	−0.612342	+	1.06061i	−0.990845	+	0.135007i	$0.956894\pi$
$228$		0			0
$229$	1355.15	+	2347.19i	0.391052	+	0.677322i	0.992589	−	0.121523i	$-0.0387778\pi$
$229$	1355.15	+	2347.19i	0.391052	+	0.677322i	−0.601536	+	0.798845i	$0.705444\pi$
$230$	−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
$236$	956.847			0.263921
$237$		0			0
$238$	112.985	−	1209.27i	0.0307718	−	0.329351i
$239$	697.856	−	1208.72i	0.188873	−	0.327137i	−0.756002	−	0.654569i	$-0.772850\pi$
$239$	697.856	−	1208.72i	0.188873	−	0.327137i	0.944875	+	0.327432i	$0.106183\pi$
$240$		0			0
$241$	−1973.58	+	3418.33i	−0.527507	+	0.913669i	0.471979	+	0.881610i	$0.343540\pi$
$241$	−1973.58	+	3418.33i	−0.527507	+	0.913669i	−0.999486	+	0.0320590i	$0.989794\pi$
$242$	−978.469	−	1694.76i	−0.259911	−	0.450178i
$243$		0			0
$244$	−4313.12			−1.13164
$245$	2985.89	−	3474.42i	0.778619	−	0.906011i
$246$		0			0
$247$	−174.639	−	302.484i	−0.0449880	−	0.0779215i
$248$	376.989			0.0965274
$249$		0			0
$250$	3698.30			0.935605
$251$	−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
$254$	872.882			0.215628
$255$		0			0
$256$	4950.96			1.20873
$257$	1160.46	+	2009.98i	0.281664	+	0.487857i	0.971795	−	0.235828i	$-0.0757802\pi$
$257$	1160.46	+	2009.98i	0.281664	+	0.487857i	−0.690130	+	0.723685i	$0.742447\pi$
$258$		0			0
$259$	6825.00	−	3133.70i	1.63739	−	0.751810i
$260$	−511.946			−0.122114
$261$		0			0
$262$	−1000.17	−	1732.35i	−0.235842	−	0.408491i
$263$	1702.16	−	2948.22i	0.399086	−	0.691237i	−0.594528	−	0.804075i	$-0.702661\pi$
$263$	1702.16	−	2948.22i	0.399086	−	0.691237i	0.993613	+	0.112838i	$0.0359943\pi$
$264$		0			0
$265$	−4435.25	+	7682.08i	−1.02813	+	1.78078i
$266$	−4122.02	+	1892.63i	−0.950141	+	0.436258i
$267$		0			0
$268$	−4085.46			−0.931191
$269$	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
$275$	−766.674	−	1327.92i	−0.168117	−	0.291187i
$276$		0			0
$277$	−1053.04	+	1823.92i	−0.228415	+	0.395627i	−0.957339	−	0.288969i	$-0.906688\pi$
$277$	−1053.04	+	1823.92i	−0.228415	+	0.395627i	0.728923	+	0.684595i	$0.240021\pi$
$278$	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	0.744211	−	0.667945i	$-0.232826\pi$
$281$	−972.004	−	1683.56i	−0.206352	−	0.357412i	−0.950563	+	0.310533i	$0.899493\pi$
$282$		0			0
$283$	−9241.49			−1.94116			−0.970582	−	0.240771i	$-0.922600\pi$
$283$	−9241.49			−1.94116			−0.970582	+	0.240771i	$0.922600\pi$
$284$	847.332			0.177042
$285$		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
$290$	6105.50	−	10575.0i	1.23630	−	2.14134i
$291$		0			0
$292$	998.307	+	1729.12i	0.200074	+	0.346538i
$293$	−3079.42	+	5333.71i	−0.613998	+	1.06348i	0.376561	+	0.926392i	$0.377106\pi$
$293$	−3079.42	+	5333.71i	−0.613998	+	1.06348i	−0.990559	+	0.137084i	$0.956227\pi$
$294$		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
$299$	743.550			0.143815
$300$		0			0
$301$	596.173	−	6380.83i	0.114162	−	1.22188i
$302$	−180.734	+	313.040i	−0.0344373	+	0.0596471i
$303$		0			0
$304$	−2257.79	+	3910.60i	−0.425964	+	0.737791i
$305$	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	$0.380121\pi$
$308$	−3360.04	+	1542.76i	−0.621611	+	0.285413i
$309$		0			0
$310$	2399.65	+	4156.32i	0.439649	+	0.761495i
$311$	−5557.43			−1.01329			−0.506644	−	0.862155i	$-0.669114\pi$
$311$	−5557.43			−1.01329			−0.506644	+	0.862155i	$0.669114\pi$
$312$		0			0
$313$	−5348.55			−0.965873			−0.482936	−	0.875655i	$-0.660430\pi$
$313$	−5348.55			−0.965873			−0.482936	+	0.875655i	$0.660430\pi$
$314$	−10913.5			−1.96142
$315$		0			0
$316$	6794.47			1.20955
$317$	6418.11			1.13715			0.568576	−	0.822631i	$-0.307495\pi$
$317$	6418.11			1.13715			0.568576	+	0.822631i	$0.307495\pi$
$318$		0			0
$319$	6791.00			1.19192
$320$	2471.29	+	4280.41i	0.431717	+	0.747756i
$321$		0			0
$322$	898.247	−	9613.93i	0.155458	−	1.66386i
$323$	1074.24			0.185053
$324$		0			0
$325$	147.202	+	254.962i	0.0251241	+	0.0435161i
$326$	−3860.07	+	6685.84i	−0.655796	+	1.13587i
$327$		0			0
$328$	673.459	−	1166.46i	0.113371	−	0.196364i
$329$	4607.29	+	3266.71i	0.772062	+	0.547415i
$330$		0			0
$331$	−3261.47			−0.541590			−0.270795	−	0.962637i	$-0.587287\pi$
$331$	−3261.47			−0.541590			−0.270795	+	0.962637i	$0.587287\pi$
$332$	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	−0.784340	−	0.620332i	$-0.786998\pi$
$337$	897.370	−	1554.29i	0.145053	−	0.251239i	0.929393	+	0.369092i	$0.120331\pi$
$338$	−4188.71	−	7255.05i	−0.674070	−	1.16752i
$339$		0			0
$340$	787.268	−	1363.59i	0.125575	−	0.217503i
$341$	−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
$346$	1238.85			0.192489
$347$	−1866.26			−0.288721			−0.144360	−	0.989525i	$-0.546112\pi$
$347$	−1866.26			−0.288721			−0.144360	+	0.989525i	$0.546112\pi$
$348$		0			0
$349$	2296.96	+	3978.45i	0.352302	+	0.610205i	0.986652	−	0.162841i	$-0.0520657\pi$
$349$	2296.96	+	3978.45i	0.352302	+	0.610205i	−0.634350	+	0.773046i	$0.718732\pi$
$350$	3474.42	−	1595.28i	0.530617	−	0.243633i
$351$		0			0
$352$	−3492.59	+	6049.34i	−0.528851	+	0.915997i
$353$	−3078.87	+	5332.76i	−0.464226	+	0.804062i	−0.999166	−	0.0408273i	$-0.987001\pi$
$353$	−3078.87	+	5332.76i	−0.464226	+	0.804062i	0.534941	+	0.844890i	$0.320334\pi$
$354$		0			0
$355$	−814.081	−	1410.03i	−0.121710	−	0.210807i
$356$	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
$362$	−8691.08			−1.26186
$363$		0			0
$364$	645.132	−	296.213i	0.0928959	−	0.0426532i
$365$	1918.26	−	3322.53i	0.275086	−	0.476463i
$366$		0			0
$367$	−3541.93	+	6134.81i	−0.503780	+	0.872573i	0.496210	+	0.868203i	$0.334725\pi$
$367$	−3541.93	+	6134.81i	−0.503780	+	0.872573i	−0.999990	+	0.00437080i	$0.998609\pi$
$368$	−4806.41	−	8324.95i	−0.680847	−	1.17926i
$369$		0			0
$370$	20941.7			2.94245
$371$	1144.25	−	12246.9i	0.160125	−	1.71382i
$372$		0			0
$373$	−6621.10	−	11468.1i	−0.919109	−	1.59194i	−0.800771	−	0.598970i	$-0.795577\pi$
$373$	−6621.10	−	11468.1i	−0.919109	−	1.59194i	−0.118338	−	0.992973i	$-0.537757\pi$
$374$	1883.49			0.260409
$375$		0			0
$376$	1237.10			0.169677
$377$	−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	$0.541440\pi$
$380$	−5880.19			−0.793809
$381$		0			0
$382$	547.999			0.0733981
$383$	−5821.11	−	10082.5i	−0.776618	−	1.34514i	−0.933881	−	0.357585i	$-0.883600\pi$
$383$	−5821.11	−	10082.5i	−0.776618	−	1.34514i	0.157262	−	0.987557i	$-0.449733\pi$
$384$		0			0
$385$	5795.47	+	4109.16i	0.767180	+	0.543953i
$386$	−2354.91			−0.310522
$387$		0			0
$388$	−5726.61	−	9918.78i	−0.749290	−	1.29781i
$389$	−2991.28	+	5181.06i	−0.389882	+	0.675296i	−0.992433	−	0.122785i	$-0.960818\pi$
$389$	−2991.28	+	5181.06i	−0.389882	+	0.675296i	0.602551	+	0.798080i	$0.294151\pi$
$390$		0			0
$391$	−1143.43	+	1980.48i	−0.147892	+	0.256156i
$392$	460.447	+	1313.03i	0.0593267	+	0.169179i
$393$		0			0
$394$	9461.61			1.20982
$395$	−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
$401$	−4173.68	−	7229.03i	−0.519760	−	0.900250i	−0.999736	−	0.0229689i	$-0.992688\pi$
$401$	−4173.68	−	7229.03i	−0.519760	−	0.900250i	0.479976	−	0.877281i	$-0.340645\pi$
$402$		0			0
$403$	256.233	−	443.809i	0.0316722	−	0.0548578i
$404$	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
$409$	11706.6			1.41530			0.707648	−	0.706565i	$-0.249756\pi$
$409$	11706.6			1.41530			0.707648	+	0.706565i	$0.249756\pi$
$410$	17147.1			2.06546
$411$		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
$416$	670.581	−	1161.48i	0.0790336	−	0.136890i
$417$		0			0
$418$	−3516.99	−	6091.61i	−0.411535	−	0.712800i
$419$	52.3192	−	90.6195i	0.00610015	−	0.0105658i	−0.862959	−	0.505274i	$-0.831392\pi$
$419$	52.3192	−	90.6195i	0.00610015	−	0.0105658i	0.869059	+	0.494708i	$0.164725\pi$
$420$		0			0
$421$	−5909.85	−	10236.2i	−0.684153	−	1.18499i	−0.973702	−	0.227824i	$-0.926839\pi$
$421$	−5909.85	−	10236.2i	−0.684153	−	1.18499i	0.289550	−	0.957163i	$-0.406494\pi$
$422$	−545.042	+	944.040i	−0.0628726	+	0.108898i
$423$		0			0
$424$	−1347.10	−	2333.25i	−0.154295	−	0.267247i
$425$	−905.469			−0.103345
$426$		0			0
$427$	−9374.78	−	6646.99i	−1.06248	−	0.753327i
$428$	−1614.06	+	2795.64i	−0.182287	+	0.315729i
$429$		0			0
$430$	8935.18	−	15476.2i	1.00208	−	1.73565i
$431$	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	$0.659557\pi$
$434$	−5428.80	−	3849.18i	−0.600439	−	0.425729i
$435$		0			0
$436$	−1581.27	−	2738.83i	−0.173690	−	0.300840i
$437$	8540.39			0.934879
$438$		0			0
$439$	14430.5			1.56886			0.784429	−	0.620219i	$-0.212956\pi$
$439$	14430.5			1.56886			0.784429	+	0.620219i	$0.212956\pi$
$440$	1556.13			0.168604
$441$		0			0
$442$	−361.632			−0.0389165
$443$	1747.73			0.187443			0.0937216	−	0.995598i	$-0.470124\pi$
$443$	1747.73			0.187443			0.0937216	+	0.995598i	$0.470124\pi$
$444$		0			0
$445$	−6912.66			−0.736386
$446$	3107.90	+	5383.03i	0.329962	+	0.571511i
$447$		0			0
$448$	−5590.87	−	3964.09i	−0.589607	−	0.418049i
$449$	−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
$452$	3079.71	−	5334.21i	0.320481	−	0.555089i
$453$		0			0
$454$	8097.78	−	14025.8i	0.837109	−	1.44992i
$455$	−1112.74	−	788.964i	−0.114650	−	0.0812905i
$456$		0			0
$457$	−2719.49			−0.278365			−0.139182	−	0.990267i	$-0.544447\pi$
$457$	−2719.49			−0.278365			−0.139182	+	0.990267i	$0.544447\pi$
$458$	−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	0.797082	−	0.603871i	$-0.206376\pi$
$461$	−1231.59	−	2133.18i	−0.124427	−	0.215514i	−0.921509	+	0.388357i	$0.873043\pi$
$462$		0			0
$463$	−488.238	+	845.653i	−0.0490072	+	0.0848830i	−0.889488	−	0.456958i	$-0.848939\pi$
$463$	−488.238	+	845.653i	−0.0490072	+	0.0848830i	0.840481	+	0.541841i	$0.182272\pi$
$464$	8428.47	+	14598.5i	0.843280	+	1.46060i
$465$		0			0
$466$	−5881.08	+	10186.3i	−0.584626	+	1.01260i
$467$	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
$472$	558.430			0.0544573
$473$	9938.38			0.966104
$474$		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
$479$	−489.544	+	847.916i	−0.0466970	+	0.0808815i	−0.888429	−	0.459014i	$-0.848203\pi$
$479$	−489.544	+	847.916i	−0.0466970	+	0.0808815i	0.841732	+	0.539895i	$0.181536\pi$
$480$		0			0
$481$	−1118.07	−	1936.55i	−0.105986	−	0.183574i
$482$	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	$0.700027\pi$
$488$	−2517.20			−0.233501
$489$		0			0
$490$	−11545.4	+	13434.3i	−1.06442	+	1.23857i
$491$	6965.56	−	12064.7i	0.640226	−	1.10890i	−0.345156	−	0.938545i	$-0.612174\pi$
$491$	6965.56	−	12064.7i	0.640226	−	1.10890i	0.985382	−	0.170359i	$-0.0544928\pi$
$492$		0			0
$493$	2005.10	−	3472.94i	0.183175	−	0.317268i
$494$	675.267	+	1169.60i	0.0615014	+	0.106524i
$495$		0			0
$496$	−6625.31			−0.599769
$497$	1841.72	+	1305.83i	0.166222	+	0.117856i
$498$		0			0
$499$	4214.20	+	7299.21i	0.378063	+	0.654825i	0.990780	−	0.135477i	$-0.0432568\pi$
$499$	4214.20	+	7299.21i	0.378063	+	0.654825i	−0.612717	+	0.790302i	$0.709923\pi$
$500$	−6648.26			−0.594639
$501$		0			0
$502$	194.552			0.0172973
$503$	−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
$506$	14974.1			1.31557
$507$		0			0
$508$	−1569.14			−0.137046
$509$	5865.50	+	10159.3i	0.510773	+	0.884685i	0.999922	+	0.0124847i	$0.00397412\pi$
$509$	5865.50	+	10159.3i	0.510773	+	0.884685i	−0.489149	+	0.872200i	$0.662693\pi$
$510$		0			0
$511$	−494.892	+	5296.82i	−0.0428429	+	0.458547i
$512$	−15025.3			−1.29693
$513$		0			0
$514$	−4487.09	−	7771.87i	−0.385053	−	0.666931i
$515$	−669.217	+	1159.12i	−0.0572606	+	0.0991784i
$516$		0			0
$517$	−4379.32	+	7585.20i	−0.372538	+	0.645255i
$518$	−26389.8	+	12116.9i	−2.23842	+	1.02777i
$519$		0			0
$520$	−298.779			−0.0251968
$521$	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
$527$	788.069	+	1364.98i	0.0651401	+	0.112826i
$528$		0			0
$529$	−3006.96	+	5208.21i	−0.247141	+	0.428060i
$530$	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
$535$	6202.89			0.501260
$536$	−2384.34			−0.192141
$537$		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	$0.257240\pi$
$542$	−6976.20	+	12083.1i	−0.552866	+	0.957593i
$543$		0			0
$544$	2062.43	+	3572.24i	0.162548	+	0.281542i
$545$	−3038.43	+	5262.71i	−0.238811	+	0.413633i
$546$		0			0
$547$	5320.04	+	9214.58i	0.415847	+	0.720269i	0.995517	−	0.0945828i	$-0.0301517\pi$
$547$	5320.04	+	9214.58i	0.415847	+	0.720269i	−0.579670	+	0.814852i	$0.696818\pi$
$548$	4359.62	−	7551.08i	0.339842	−	0.588624i
$549$		0			0
$550$	2964.45	+	5134.57i	0.229826	+	0.398071i
$551$	−14976.3			−1.15792
$552$		0			0
$553$	14768.1	+	10471.0i	1.13563	+	0.805195i
$554$	4071.72	−	7052.42i	0.312258	−	0.540846i
$555$		0			0
$556$	−2644.04	+	4579.61i	−0.201677	+	0.349314i
$557$	−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
$560$	−1640.52	+	17558.4i	−0.123794	+	1.32496i
$561$		0			0
$562$	3758.38	+	6509.71i	0.282096	+	0.488604i
$563$	−15770.2			−1.18052			−0.590262	−	0.807212i	$-0.700976\pi$
$563$	−15770.2			−1.18052			−0.590262	+	0.807212i	$0.700976\pi$
$564$		0			0
$565$	−11835.4			−0.881274
$566$	35733.5			2.65369
$567$		0			0
$568$	494.516			0.0365307
$569$	−12175.2			−0.897029			−0.448514	−	0.893776i	$-0.648047\pi$
$569$	−12175.2			−0.897029			−0.448514	+	0.893776i	$0.648047\pi$
$570$		0			0
$571$	16568.3			1.21429			0.607147	−	0.794590i	$-0.292314\pi$
$571$	16568.3			1.21429			0.607147	+	0.794590i	$0.292314\pi$
$572$	550.439	+	953.389i	0.0402361	+	0.0696909i
$573$		0			0
$574$	−21608.1	+	9921.37i	−1.57126	+	0.721446i
$575$	−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	$0.841409\pi$
$578$	−8942.27	+	15488.5i	−0.643511	+	1.11459i
$579$		0			0
$580$	−10975.6	+	19010.2i	−0.785750	+	1.36096i
$581$	−1749.44	+	18724.2i	−0.124921	+	1.33703i
$582$		0			0
$583$	19075.0			1.35507
$584$	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	0.884680	−	0.466199i	$-0.154377\pi$
$587$	548.955	+	950.819i	0.0385993	+	0.0668560i	−0.846080	+	0.533055i	$0.821044\pi$
$588$		0			0
$589$	2943.09	−	5097.57i	0.205887	−	0.356608i
$590$	3554.59	+	6156.73i	0.248034	+	0.429608i
$591$		0			0
$592$	−14454.7	+	25036.3i	−1.00352	+	1.73815i
$593$	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
$598$	−2875.04			−0.196604
$599$	−11640.5			−0.794023			−0.397012	−	0.917814i	$-0.629953\pi$
$599$	−11640.5			−0.794023			−0.397012	+	0.917814i	$0.629953\pi$
$600$		0			0
$601$	970.960	+	1681.75i	0.0659007	+	0.114143i	0.897093	−	0.441841i	$-0.145675\pi$
$601$	970.960	+	1681.75i	0.0659007	+	0.114143i	−0.831192	+	0.555985i	$0.812341\pi$
$602$	−2305.18	+	24672.3i	−0.156067	+	1.67038i
$603$		0			0
$604$	324.896	−	562.737i	0.0218872	−	0.0379097i
$605$	3379.84	−	5854.06i	0.227124	−	0.393391i
$606$		0			0
$607$	6455.68	+	11181.6i	0.431677	+	0.747687i	0.997018	−	0.0771708i	$-0.0245887\pi$
$607$	6455.68	+	11181.6i	0.431677	+	0.747687i	−0.565341	+	0.824857i	$0.691255\pi$
$608$	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	$0.614340\pi$
$614$	−15298.5			−1.00553
$615$		0			0
$616$	−1960.97	+	900.380i	−0.128263	+	0.0588918i
$617$	779.062	−	1349.38i	0.0508329	−	0.0880451i	−0.839489	−	0.543376i	$-0.817146\pi$
$617$	779.062	−	1349.38i	0.0508329	−	0.0880451i	0.890322	+	0.455331i	$0.150479\pi$
$618$		0			0
$619$	−3522.77	+	6101.62i	−0.228743	+	0.396195i	−0.957436	−	0.288646i	$-0.906795\pi$
$619$	−3522.77	+	6101.62i	−0.228743	+	0.396195i	0.728693	+	0.684841i	$0.240128\pi$
$620$	−4313.74	−	7471.62i	−0.279426	−	0.483980i
$621$		0			0
$622$	21488.5			1.38523
$623$	8711.04	−	3999.68i	0.560193	−	0.257213i
$624$		0			0
$625$	9724.11	+	16842.7i	0.622343	+	1.07793i
$626$	20680.9			1.32041
$627$		0			0
$628$	19618.7			1.24661
$629$	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	$0.868887\pi$
$632$	3965.35			0.249578
$633$		0			0
$634$	−24816.5			−1.55456
$635$	1507.56	+	2611.17i	0.0942138	+	0.163183i
$636$		0			0
$637$	1858.72	+	350.386i	0.115613	+	0.0217940i
$638$	−26258.3			−1.62943
$639$		0			0
$640$	3437.77	+	5954.40i	0.212328	+	0.367763i
$641$	10141.5	−	17565.6i	0.624908	−	1.08237i	−0.363651	−	0.931535i	$-0.618470\pi$
$641$	10141.5	−	17565.6i	0.624908	−	1.08237i	0.988559	−	0.150836i	$-0.0481967\pi$
$642$		0			0
$643$	12393.5	−	21466.2i	0.760111	−	1.31655i	−0.182682	−	0.983172i	$-0.558478\pi$
$643$	12393.5	−	21466.2i	0.760111	−	1.31655i	0.942793	−	0.333379i	$-0.108189\pi$
$644$	−1614.74	+	17282.5i	−0.0988036	+	1.05749i
$645$		0			0
$646$	−4153.69			−0.252980
$647$	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
$653$	−5666.71	−	9815.03i	−0.339595	−	0.588196i	0.644761	−	0.764384i	$-0.276957\pi$
$653$	−5666.71	−	9815.03i	−0.339595	−	0.588196i	−0.984357	+	0.176188i	$0.943623\pi$
$654$		0			0
$655$	3454.80	−	5983.89i	0.206092	−	0.356962i
$656$	−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	0.819785	−	0.572672i	$-0.194093\pi$
$659$	−1455.83	−	2521.57i	−0.0860563	−	0.149054i	−0.905841	+	0.423618i	$0.860760\pi$
$660$		0			0
$661$	−26754.1			−1.57430			−0.787152	−	0.616759i	$-0.788445\pi$
$661$	−26754.1			−1.57430			−0.787152	+	0.616759i	$0.788445\pi$
$662$	12610.9			0.740387
$663$		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
$668$	10787.5	−	18684.5i	0.624822	−	1.08222i
$669$		0			0
$670$	−15177.1	−	26287.5i	−0.875137	−	1.51578i
$671$	8910.90	−	15434.1i	0.512670	−	0.887970i
$672$		0			0
$673$	−6830.55	−	11830.9i	−0.391231	−	0.677631i	0.601382	−	0.798962i	$-0.294617\pi$
$673$	−6830.55	−	11830.9i	−0.391231	−	0.677631i	−0.992612	+	0.121331i	$0.961284\pi$
$674$	−3469.80	+	6009.88i	−0.198296	+	0.343460i
$675$		0			0
$676$	7529.84	+	13042.1i	0.428416	+	0.742038i
$677$	8825.29			0.501009			0.250505	−	0.968115i	$-0.419403\pi$
$677$	8825.29			0.501009			0.250505	+	0.968115i	$0.419403\pi$
$678$		0			0
$679$	2838.86	−	30384.3i	0.160450	−	1.71729i
$680$	459.461	−	795.810i	0.0259111	−	0.0448793i
$681$		0			0
$682$	5160.18	−	8937.69i	0.289726	−	0.501821i
$683$	−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
$686$	6775.84	−	23609.5i	0.377118	−	1.31402i
$687$		0			0
$688$	12334.8	+	21364.4i	0.683515	+	1.18388i
$689$	−3662.42			−0.202507
$690$		0			0
$691$	−4571.67			−0.251685			−0.125843	−	0.992050i	$-0.540163\pi$
$691$	−4571.67			−0.251685			−0.125843	+	0.992050i	$0.540163\pi$
$692$	−2227.03			−0.122339
$693$		0			0
$694$	7216.15			0.394699
$695$	10161.1			0.554581
$696$		0			0
$697$	5631.28			0.306026
$698$	−8881.50	−	15383.2i	−0.481618	−	0.834188i
$699$		0			0
$700$	−6245.81	+	2867.77i	−0.337242	+	0.154845i
$701$	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
$704$	5314.23	−	9204.51i	0.284499	−	0.492767i
$705$		0			0
$706$	11904.9	−	20619.8i	0.634625	−	1.09920i
$707$	15829.9	−	7268.30i	0.842071	−	0.386637i
$708$		0			0
$709$	11662.4			0.617758			0.308879	−	0.951101i	$-0.400046\pi$
$709$	11662.4			0.617758			0.308879	+	0.951101i	$0.400046\pi$
$710$	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
$716$	−7309.82	−	12661.0i	−0.381537	−	0.660842i
$717$		0			0
$718$	7071.31	−	12247.9i	0.367547	−	0.636611i
$719$	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
$724$	15623.5			0.801995
$725$	12623.4			0.646652
$726$		0			0
$727$	−5157.33	−	8932.76i	−0.263102	−	0.455705i	0.703963	−	0.710237i	$-0.251412\pi$
$727$	−5157.33	−	8932.76i	−0.263102	−	0.455705i	−0.967064	+	0.254531i	$0.918079\pi$
$728$	376.509	−	172.874i	0.0191681	−	0.00880102i
$729$		0			0
$730$	−7417.22	+	12847.0i	−0.376060	+	0.651355i
$731$	2934.40	−	5082.52i	0.148471	−	0.257160i
$732$		0			0
$733$	−5418.34	−	9384.84i	−0.273030	−	0.472902i	0.696606	−	0.717454i	$-0.254692\pi$
$733$	−5418.34	−	9384.84i	−0.273030	−	0.472902i	−0.969636	+	0.244552i	$0.921359\pi$
$734$	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	$0.734257\pi$
$740$	−37645.8			−1.87012
$741$		0			0
$742$	−4424.39	+	47354.2i	−0.218901	+	2.34289i
$743$	−10676.9	+	18492.9i	−0.527182	+	0.913105i	0.472316	+	0.881429i	$0.343418\pi$
$743$	−10676.9	+	18492.9i	−0.527182	+	0.913105i	−0.999498	+	0.0316764i	$0.989915\pi$
$744$		0			0
$745$	17114.7	−	29643.5i	0.841655	−	1.45779i
$746$	25601.4	+	44342.9i	1.25648	+	2.17629i
$747$		0			0
$748$	−3385.85			−0.165507
$749$	−7816.62	+	3589.00i	−0.381326	+	0.175086i
$750$		0			0
$751$	−5214.18	−	9031.22i	−0.253353	−	0.438820i	0.711094	−	0.703097i	$-0.248200\pi$
$751$	−5214.18	−	9031.22i	−0.253353	−	0.438820i	−0.964447	+	0.264277i	$0.914867\pi$
$752$	−21741.1			−1.05428
$753$		0			0
$754$	5041.63			0.243508
$755$	−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	$0.115622\pi$
$758$	7407.43			0.354947
$759$		0			0
$760$	−3431.77			−0.163794
$761$	711.985	+	1233.19i	0.0339152	+	0.0587428i	0.882485	−	0.470341i	$-0.155869\pi$
$761$	711.985	+	1233.19i	0.0339152	+	0.0587428i	−0.848570	+	0.529084i	$0.822536\pi$
$762$		0			0
$763$	783.883	−	8389.89i	0.0371933	−	0.398079i
$764$	−985.112			−0.0466494
$765$		0			0
$766$	22508.1	+	38985.2i	1.06168	+	1.83889i
$767$	379.556	−	657.411i	0.0178683	−	0.0309488i
$768$		0			0
$769$	7436.72	−	12880.8i	0.348732	−	0.604022i	−0.637292	−	0.770622i	$-0.719946\pi$
$769$	7436.72	−	12880.8i	0.348732	−	0.604022i	0.986025	+	0.166600i	$0.0532790\pi$
$770$	−22409.0	−	15888.6i	−1.04878	−	0.743618i
$771$		0			0
$772$	4233.30			0.197357
$773$	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
$779$	−10515.2	−	18212.8i	−0.483626	−	0.837665i
$780$		0			0
$781$	−1750.59	+	3032.10i	−0.0802060	+	0.138921i
$782$	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
$787$	−22518.8			−1.01996			−0.509981	−	0.860186i	$-0.670348\pi$
$787$	−22518.8			−1.01996			−0.509981	+	0.860186i	$0.670348\pi$
$788$	−17008.7			−0.768920
$789$		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
$794$	17569.0	−	30430.4i	0.785264	−	1.36012i
$795$		0			0
$796$	9005.28	+	15597.6i	0.400984	+	0.694525i
$797$	−14101.5	+	24424.5i	−0.626727	+	1.08552i	0.361478	+	0.932381i	$0.382272\pi$
$797$	−14101.5	+	24424.5i	−0.626727	+	1.08552i	−0.988204	+	0.153142i	$0.951061\pi$
$798$		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
$803$	−8250.00			−0.362561
$804$		0			0
$805$	30310.8	−	13917.2i	1.32710	−	0.609339i
$806$	−990.760	+	1716.05i	−0.0432978	+	0.0749940i
$807$		0			0
$808$	1907.68	−	3304.20i	0.0830593	−	0.143863i
$809$	−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	$0.665585\pi$
$812$	2831.58	−	30306.4i	0.122376	−	1.30978i
$813$		0			0
$814$	−22516.3	−	38999.4i	−0.969528	−	1.67927i
$815$	−26667.0			−1.14614
$816$		0			0
$817$	−21917.3			−0.938543
$818$	−45265.3			−1.93480
$819$		0			0
$820$	−30824.6			−1.31273
$821$	3439.91			0.146229			0.0731143	−	0.997324i	$-0.476706\pi$
$821$	3439.91			0.146229			0.0731143	+	0.997324i	$0.476706\pi$
$822$		0			0
$823$	−19562.2			−0.828547			−0.414273	−	0.910153i	$-0.635964\pi$
$823$	−19562.2			−0.828547			−0.414273	+	0.910153i	$0.635964\pi$
$824$	−203.259	−	352.055i	−0.00859328	−	0.0148840i
$825$		0			0
$826$	−8041.64	−	5701.76i	−0.338746	−	0.240181i
$827$	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	$0.752381\pi$
$830$	−26219.9	+	45414.1i	−1.09651	+	1.89921i
$831$		0			0
$832$	−1020.34	+	1767.28i	−0.0425167	+	0.0736411i
$833$	−3791.60	+	4411.95i	−0.157708	+	0.183512i
$834$		0			0
$835$	−41456.7			−1.71817
$836$	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	0.982847	+	0.184420i	$0.0590408\pi$
$839$	15824.0	+	27407.9i	0.651136	+	1.12780i	−0.331711	+	0.943381i	$0.607626\pi$
$840$		0			0
$841$	−15759.3	+	27295.9i	−0.646163	+	1.11919i
$842$	22851.2	+	39579.5i	0.935279	+	1.61995i
$843$		0			0
$844$	979.796	−	1697.06i	0.0399597	−	0.0692122i
$845$	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
$850$	3501.12			0.141279
$851$	54676.8			2.20247
$852$		0			0
$853$	20475.4	+	35464.4i	0.821880	+	1.42354i	0.904281	+	0.426939i	$0.140408\pi$
$853$	20475.4	+	35464.4i	0.821880	+	1.42354i	−0.0824005	+	0.996599i	$0.526259\pi$
$854$	36248.8	+	25701.5i	1.45247	+	1.02984i
$855$		0			0
$856$	−941.991	+	1631.58i	−0.0376128	+	0.0651473i
$857$	−9585.51	+	16602.6i	−0.382071	+	0.661766i	−0.991358	−	0.131183i	$-0.958122\pi$
$857$	−9585.51	+	16602.6i	−0.382071	+	0.661766i	0.609287	+	0.792950i	$0.291456\pi$
$858$		0			0
$859$	15262.4	+	26435.2i	0.606222	+	1.05001i	0.991857	+	0.127356i	$0.0406491\pi$
$859$	15262.4	+	26435.2i	0.606222	+	1.05001i	−0.385635	+	0.922651i	$0.626018\pi$
$860$	−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
$866$	33482.6			1.31384
$867$		0			0
$868$	9759.09	+	6919.48i	0.381619	+	0.270579i
$869$	−14037.4	+	24313.4i	−0.547968	+	0.949109i
$870$		0			0
$871$	−1620.60	+	2806.95i	−0.0630445	+	0.109196i
$872$	−922.851	−	1598.42i	−0.0358391	−	0.0620751i
$873$		0			0
$874$	−33022.6			−1.27804
$875$	−14450.3	−	10245.7i	−0.558297	−	0.395849i
$876$		0			0
$877$	−18131.3	−	31404.4i	−0.698121	−	1.20918i	−0.969117	−	0.246600i	$-0.920687\pi$
$877$	−18131.3	−	31404.4i	−0.698121	−	1.20918i	0.270997	−	0.962580i	$-0.412647\pi$
$878$	−55797.3			−2.14473
$879$		0			0
$880$	−27347.9			−1.04761
$881$	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	$0.354860\pi$
$884$	650.088			0.0247340
$885$		0			0
$886$	−6757.85			−0.256246
$887$	12367.0	+	21420.2i	0.468143	+	0.810847i	0.999337	−	0.0364031i	$-0.0115900\pi$
$887$	12367.0	+	21420.2i	0.468143	+	0.810847i	−0.531195	+	0.847250i	$0.678257\pi$
$888$		0			0
$889$	−3410.60	−	2418.21i	−0.128670	−	0.0912309i
$890$	26728.7			1.00668
$891$		0			0
$892$	−5586.92	−	9676.82i	−0.209713	−	0.363233i
$893$	9657.80	−	16727.8i	0.361910	−	0.626847i
$894$		0			0
$895$	−14045.9	+	24328.3i	−0.524585	+	0.908608i
$896$	−7777.36	−	5514.37i	−0.289981	−	0.205605i
$897$		0			0
$898$	26587.7			0.988021
$899$	−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
$905$	−15010.4	−	25998.8i	−0.551341	−	0.954951i
$906$		0			0
$907$	25287.5	−	43799.2i	0.925751	−	1.60345i	0.135403	−	0.990791i	$-0.456767\pi$
$907$	25287.5	−	43799.2i	0.925751	−	1.60345i	0.790348	−	0.612658i	$-0.209900\pi$
$908$	−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	0.977638	+	0.210295i	$0.0674423\pi$
$911$	18448.5	+	31953.7i	0.670939	+	1.16210i	−0.306699	+	0.951807i	$0.599224\pi$
$912$		0			0
$913$	−29163.7			−1.05715
$914$	10515.3			0.380542
$915$		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	$0.234758\pi$
$920$	3652.80	−	6326.83i	0.130901	−	0.226728i
$921$		0			0
$922$	4762.11	+	8248.22i	0.170100	+	0.294621i
$923$	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
$929$	15503.0			0.547510			0.273755	−	0.961800i	$-0.411734\pi$
$929$	15503.0			0.547510			0.273755	+	0.961800i	$0.411734\pi$
$930$		0			0
$931$	21349.2	+	4024.52i	0.751548	+	0.141674i
$932$	10572.1	−	18311.5i	0.371569	−	0.643576i
$933$		0			0
$934$	−21215.2	+	36745.7i	−0.743235	+	1.28732i
$935$	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	$0.208505\pi$
$938$	34335.5	+	24344.9i	1.19520	+	0.847428i
$939$		0			0
$940$	−14155.6	−	24518.3i	−0.491177	−	0.850743i
$941$	3493.66			0.121031			0.0605154	−	0.998167i	$-0.480726\pi$
$941$	3493.66			0.121031			0.0605154	+	0.998167i	$0.480726\pi$
$942$		0			0
$943$	44769.7			1.54602
$944$	−9814.02			−0.338368
$945$		0			0
$946$	−38428.1			−1.32072
$947$	−41769.8			−1.43330			−0.716651	−	0.697432i	$-0.754326\pi$
$947$	−41769.8			−1.43330			−0.716651	+	0.697432i	$0.754326\pi$
$948$		0			0
$949$	1584.01			0.0541825
$950$	−6537.56	−	11323.4i	−0.223270	−	0.386715i
$951$		0			0
$952$	−118.536	+	1268.69i	−0.00403548	+	0.0431917i
$953$	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
$956$	4850.70	−	8401.66i	0.164103	−	0.284235i
$957$		0			0
$958$	1892.89	−	3278.58i	0.0638377	−	0.110570i
$959$	21112.9	−	9693.98i	0.710917	−	0.326418i
$960$		0			0
$961$	−21154.7			−0.710105
$962$	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	−0.102129	+	0.994771i	$0.532565\pi$
$967$	−27441.1	+	47529.4i	−0.912562	+	1.58060i	−0.810433	+	0.585832i	$0.800768\pi$
$968$	1026.55	+	1778.03i	0.0340852	+	0.0590373i
$969$		0			0
$970$	42547.6	−	73694.5i	1.40837	−	2.43937i
$971$	−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
$976$	44238.1			1.45085
$977$	−38104.9			−1.24778			−0.623892	−	0.781511i	$-0.714449\pi$
$977$	−38104.9			−1.24778			−0.623892	+	0.781511i	$0.714449\pi$
$978$		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
$983$	27677.0	−	47938.0i	0.898026	−	1.55543i	0.0680127	−	0.997684i	$-0.478334\pi$
$983$	27677.0	−	47938.0i	0.898026	−	1.55543i	0.830014	−	0.557743i	$-0.188332\pi$
$984$		0			0
$985$	16341.2	+	28303.8i	0.528604	+	0.915568i
$986$	−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	$-0.412700\pi$
$992$	22601.7			0.723393
$993$		0			0
$994$	−7121.24	−	5049.17i	−0.227236	−	0.161117i
$995$	17303.8	−	29971.0i	0.551323	−	0.954920i
$996$		0			0
$997$	18601.3	−	32218.3i	0.590881	−	1.02344i	−0.403233	−	0.915097i	$-0.632114\pi$
$997$	18601.3	−	32218.3i	0.590881	−	1.02344i	0.994114	−	0.108338i	$-0.0345529\pi$
$998$	−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.h.a.37.4		44
3.2	odd	2		63.4.h.a.58.19	yes	44
7.4	even	3		189.4.g.a.172.19		44
9.2	odd	6		63.4.g.a.16.4	yes	44
9.7	even	3		189.4.g.a.100.19		44
21.11	odd	6		63.4.g.a.4.4	✓	44
63.11	odd	6		63.4.h.a.25.19	yes	44
63.25	even	3	inner	189.4.h.a.46.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.4	✓	44	21.11	odd	6
63.4.g.a.16.4	yes	44	9.2	odd	6
63.4.h.a.25.19	yes	44	63.11	odd	6
63.4.h.a.58.19	yes	44	3.2	odd	2
189.4.g.a.100.19		44	9.7	even	3
189.4.g.a.172.19		44	7.4	even	3
189.4.h.a.37.4		44	1.1	even	1	trivial
189.4.h.a.46.4		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)

\(f(q)\)	\(=\)	\(q-3.86663 q^{2} +6.95086 q^{4} +(-6.67810 - 11.5668i) q^{5} +(15.1080 + 10.7120i) q^{7} +4.05663 q^{8} +O(q^{10})\)	\(q-3.86663 q^{2} +6.95086 q^{4} +(-6.67810 - 11.5668i) q^{5} +(15.1080 + 10.7120i) q^{7} +4.05663 q^{8} +(25.8218 + 44.7246i) q^{10} +(-14.3605 + 24.8730i) q^{11} +(2.75723 - 4.77566i) q^{13} +(-58.4172 - 41.4195i) q^{14} -71.2924 q^{16} +(8.48010 + 14.6880i) q^{17} +(31.6694 - 54.8530i) q^{19} +(-46.4185 - 80.3993i) q^{20} +(55.5266 - 96.1750i) q^{22} +(67.4183 + 116.772i) q^{23} +(-26.6939 + 46.2352i) q^{25} +(-10.6612 + 18.4657i) q^{26} +(105.014 + 74.4579i) q^{28} +(-118.224 - 204.770i) q^{29} +92.9315 q^{31} +243.209 q^{32} +(-32.7895 - 56.7930i) q^{34} +(23.0111 - 246.287i) q^{35} +(202.752 - 351.177i) q^{37} +(-122.454 + 212.097i) q^{38} +(-27.0905 - 46.9222i) q^{40} +(166.014 - 287.545i) q^{41} +(-173.016 - 299.673i) q^{43} +(-99.8176 + 172.889i) q^{44} +(-260.682 - 451.514i) q^{46} +304.957 q^{47} +(113.505 + 323.675i) q^{49} +(103.216 - 178.775i) q^{50} +(19.1651 - 33.1949i) q^{52} +(-332.075 - 575.170i) q^{53} +383.602 q^{55} +(61.2876 + 43.4547i) q^{56} +(457.129 + 791.770i) q^{58} +137.659 q^{59} -620.516 q^{61} -359.332 q^{62} -370.060 q^{64} -73.6521 q^{65} -587.763 q^{67} +(58.9440 + 102.094i) q^{68} +(-88.9755 + 952.304i) q^{70} +121.903 q^{71} +(143.624 + 248.763i) q^{73} +(-783.969 + 1357.87i) q^{74} +(220.130 - 381.276i) q^{76} +(-483.399 + 221.953i) q^{77} +977.500 q^{79} +(476.097 + 824.625i) q^{80} +(-641.917 + 1111.83i) q^{82} +(507.709 + 879.377i) q^{83} +(113.262 - 196.175i) q^{85} +(668.992 + 1158.73i) q^{86} +(-58.2550 + 100.901i) q^{88} +(258.781 - 448.222i) q^{89} +(92.8132 - 42.6152i) q^{91} +(468.616 + 811.666i) q^{92} -1179.16 q^{94} -845.965 q^{95} +(-823.870 - 1426.99i) q^{97} +(-438.882 - 1251.53i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 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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