LMFDB - Embedded newform 189.4.h.a.37.6

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			37.6
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.35315 q^{2} +3.24362 q^{4} +(-4.35326 - 7.54007i) q^{5} +(-2.88142 - 18.2947i) q^{7} +15.9489 q^{8} +O(q^{10})$	\(q-3.35315 q^{2} +3.24362 q^{4} +(-4.35326 - 7.54007i) q^{5} +(-2.88142 - 18.2947i) q^{7} +15.9489 q^{8} +(14.5971 + 25.2830i) q^{10} +(-5.89868 + 10.2168i) q^{11} +(26.5809 - 46.0395i) q^{13} +(9.66183 + 61.3450i) q^{14} -79.4279 q^{16} +(22.5463 + 39.0513i) q^{17} +(-13.0906 + 22.6736i) q^{19} +(-14.1203 - 24.4571i) q^{20} +(19.7792 - 34.2585i) q^{22} +(-29.0940 - 50.3923i) q^{23} +(24.5983 - 42.6055i) q^{25} +(-89.1298 + 154.377i) q^{26} +(-9.34621 - 59.3411i) q^{28} +(-36.7015 - 63.5688i) q^{29} -314.805 q^{31} +138.743 q^{32} +(-75.6011 - 130.945i) q^{34} +(-125.400 + 101.368i) q^{35} +(-189.337 + 327.941i) q^{37} +(43.8947 - 76.0279i) q^{38} +(-69.4296 - 120.256i) q^{40} +(-181.180 + 313.812i) q^{41} +(58.7824 + 101.814i) q^{43} +(-19.1331 + 33.1394i) q^{44} +(97.5565 + 168.973i) q^{46} -228.220 q^{47} +(-326.395 + 105.430i) q^{49} +(-82.4817 + 142.863i) q^{50} +(86.2183 - 149.334i) q^{52} +(-307.562 - 532.713i) q^{53} +102.714 q^{55} +(-45.9554 - 291.780i) q^{56} +(123.065 + 213.156i) q^{58} -576.660 q^{59} +446.281 q^{61} +1055.59 q^{62} +170.198 q^{64} -462.854 q^{65} +297.702 q^{67} +(73.1315 + 126.667i) q^{68} +(420.485 - 339.901i) q^{70} +866.428 q^{71} +(283.351 + 490.778i) q^{73} +(634.874 - 1099.63i) q^{74} +(-42.4608 + 73.5443i) q^{76} +(203.911 + 78.4759i) q^{77} -366.794 q^{79} +(345.770 + 598.891i) q^{80} +(607.523 - 1052.26i) q^{82} +(510.815 + 884.758i) q^{83} +(196.300 - 340.001i) q^{85} +(-197.106 - 341.398i) q^{86} +(-94.0773 + 162.947i) q^{88} +(247.021 - 427.852i) q^{89} +(-918.871 - 353.632i) q^{91} +(-94.3697 - 163.453i) q^{92} +765.257 q^{94} +227.947 q^{95} +(-76.3273 - 132.203i) q^{97} +(1094.45 - 353.521i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.35315			−1.18552			−0.592759	−	0.805380i	$-0.701961\pi$
$2$	−3.35315			−1.18552			−0.592759	+	0.805380i	$0.701961\pi$
$3$		0			0
$3$		0			0
$4$	3.24362			0.405452
$5$	−4.35326	−	7.54007i	−0.389367	−	0.674404i	0.602997	−	0.797743i	$-0.293973\pi$
$5$	−4.35326	−	7.54007i	−0.389367	−	0.674404i	−0.992365	+	0.123339i	$0.960640\pi$
$6$		0			0
$7$	−2.88142	−	18.2947i	−0.155582	−	0.987823i
$7$	−2.88142	−	18.2947i	−0.155582	−	0.987823i
$8$	15.9489			0.704847
$9$		0			0
$10$	14.5971	+	25.2830i	0.461602	+	0.799518i
$11$	−5.89868	+	10.2168i	−0.161684	+	0.280044i	−0.935473	−	0.353399i	$-0.885026\pi$
$11$	−5.89868	+	10.2168i	−0.161684	+	0.280044i	0.773789	+	0.633443i	$0.218359\pi$
$12$		0			0
$13$	26.5809	−	46.0395i	0.567094	−	0.982235i	−0.429758	−	0.902944i	$-0.641401\pi$
$13$	26.5809	−	46.0395i	0.567094	−	0.982235i	0.996852	−	0.0792910i	$-0.0252656\pi$
$14$	9.66183	+	61.3450i	0.184445	+	1.17108i
$15$		0			0
$16$	−79.4279			−1.24106
$17$	22.5463	+	39.0513i	0.321663	+	0.557137i	0.980831	−	0.194858i	$-0.0624248\pi$
$17$	22.5463	+	39.0513i	0.321663	+	0.557137i	−0.659168	+	0.751996i	$0.729091\pi$
$18$		0			0
$19$	−13.0906	+	22.6736i	−0.158062	+	0.273772i	−0.934170	−	0.356828i	$-0.883858\pi$
$19$	−13.0906	+	22.6736i	−0.158062	+	0.273772i	0.776107	+	0.630601i	$0.217191\pi$
$20$	−14.1203	−	24.4571i	−0.157870	−	0.273438i
$21$		0			0
$22$	19.7792	−	34.2585i	0.191679	−	0.331997i
$23$	−29.0940	−	50.3923i	−0.263762	−	0.456848i	0.703477	−	0.710718i	$-0.251630\pi$
$23$	−29.0940	−	50.3923i	−0.263762	−	0.456848i	−0.967238	+	0.253870i	$0.918297\pi$
$24$		0			0
$25$	24.5983	−	42.6055i	0.196786	−	0.340844i
$26$	−89.1298	+	154.377i	−0.672300	+	1.16446i
$27$		0			0
$28$	−9.34621	−	59.3411i	−0.0630810	−	0.400515i
$29$	−36.7015	−	63.5688i	−0.235010	−	0.407049i	0.724266	−	0.689521i	$-0.242179\pi$
$29$	−36.7015	−	63.5688i	−0.235010	−	0.407049i	−0.959276	+	0.282472i	$0.908846\pi$
$30$		0			0
$31$	−314.805			−1.82389			−0.911947	−	0.410308i	$-0.865421\pi$
$31$	−314.805			−1.82389			−0.911947	+	0.410308i	$0.865421\pi$
$32$	138.743			0.766452
$33$		0			0
$34$	−75.6011	−	130.945i	−0.381337	−	0.660496i
$35$	−125.400	+	101.368i	−0.605613	+	0.489551i
$36$		0			0
$37$	−189.337	+	327.941i	−0.841263	+	1.45711i	0.0475640	+	0.998868i	$0.484854\pi$
$37$	−189.337	+	327.941i	−0.841263	+	1.45711i	−0.888827	+	0.458242i	$0.848479\pi$
$38$	43.8947	−	76.0279i	0.187386	−	0.324562i
$39$		0			0
$40$	−69.4296	−	120.256i	−0.274444	−	0.475352i
$41$	−181.180	+	313.812i	−0.690134	+	1.19535i	0.281659	+	0.959515i	$0.409115\pi$
$41$	−181.180	+	313.812i	−0.690134	+	1.19535i	−0.971794	+	0.235833i	$0.924218\pi$
$42$		0			0
$43$	58.7824	+	101.814i	0.208470	+	0.361081i	0.951233	−	0.308474i	$-0.0998182\pi$
$43$	58.7824	+	101.814i	0.208470	+	0.361081i	−0.742762	+	0.669555i	$0.766485\pi$
$44$	−19.1331	+	33.1394i	−0.0655549	+	0.113544i
$45$		0			0
$46$	97.5565	+	168.973i	0.312694	+	0.541602i
$47$	−228.220			−0.708284			−0.354142	−	0.935192i	$-0.615227\pi$
$47$	−228.220			−0.708284			−0.354142	+	0.935192i	$0.615227\pi$
$48$		0			0
$49$	−326.395	+	105.430i	−0.951589	+	0.307375i
$50$	−82.4817	+	142.863i	−0.233293	+	0.404076i
$51$		0			0
$52$	86.2183	−	149.334i	0.229929	−	0.398249i
$53$	−307.562	−	532.713i	−0.797112	−	1.38064i	−0.921490	−	0.388403i	$-0.873027\pi$
$53$	−307.562	−	532.713i	−0.797112	−	1.38064i	0.124378	−	0.992235i	$-0.460306\pi$
$54$		0			0
$55$	102.714			0.251817
$56$	−45.9554	−	291.780i	−0.109661	−	0.696264i
$57$		0			0
$58$	123.065	+	213.156i	0.278608	+	0.482564i
$59$	−576.660			−1.27245			−0.636226	−	0.771502i	$-0.719506\pi$
$59$	−576.660			−1.27245			−0.636226	+	0.771502i	$0.719506\pi$
$60$		0			0
$61$	446.281			0.936729			0.468365	−	0.883535i	$-0.344843\pi$
$61$	446.281			0.936729			0.468365	+	0.883535i	$0.344843\pi$
$62$	1055.59			2.16226
$63$		0			0
$64$	170.198			0.332418
$65$	−462.854			−0.883231
$66$		0			0
$67$	297.702			0.542838			0.271419	−	0.962461i	$-0.412507\pi$
$67$	297.702			0.542838			0.271419	+	0.962461i	$0.412507\pi$
$68$	73.1315	+	126.667i	0.130419	+	0.225892i
$69$		0			0
$70$	420.485	−	339.901i	0.717965	−	0.580371i
$71$	866.428			1.44825			0.724127	−	0.689667i	$-0.242243\pi$
$71$	866.428			1.44825			0.724127	+	0.689667i	$0.242243\pi$
$72$		0			0
$73$	283.351	+	490.778i	0.454297	+	0.786866i	0.998648	−	0.0519920i	$-0.0165570\pi$
$73$	283.351	+	490.778i	0.454297	+	0.786866i	−0.544350	+	0.838858i	$0.683224\pi$
$74$	634.874	−	1099.63i	0.997332	−	1.72743i
$75$		0			0
$76$	−42.4608	+	73.5443i	−0.0640867	+	0.111001i
$77$	203.911	+	78.4759i	0.301789	+	0.116145i
$78$		0			0
$79$	−366.794			−0.522374			−0.261187	−	0.965288i	$-0.584114\pi$
$79$	−366.794			−0.522374			−0.261187	+	0.965288i	$0.584114\pi$
$80$	345.770	+	598.891i	0.483228	+	0.836976i
$81$		0			0
$82$	607.523	−	1052.26i	0.818166	−	1.41711i
$83$	510.815	+	884.758i	0.675533	+	1.17006i	0.976313	+	0.216364i	$0.0694199\pi$
$83$	510.815	+	884.758i	0.675533	+	1.17006i	−0.300779	+	0.953694i	$0.597247\pi$
$84$		0			0
$85$	196.300	−	340.001i	0.250490	−	0.433862i
$86$	−197.106	−	341.398i	−0.247145	−	0.428068i
$87$		0			0
$88$	−94.0773	+	162.947i	−0.113962	+	0.197388i
$89$	247.021	−	427.852i	0.294204	−	0.509576i	−0.680596	−	0.732659i	$-0.738279\pi$
$89$	247.021	−	427.852i	0.294204	−	0.509576i	0.974799	+	0.223083i	$0.0716123\pi$
$90$		0			0
$91$	−918.871	−	353.632i	−1.05850	−	0.407370i
$92$	−94.3697	−	163.453i	−0.106943	−	0.185230i
$93$		0			0
$94$	765.257			0.839683
$95$	227.947			0.246177
$96$		0			0
$97$	−76.3273	−	132.203i	−0.0798955	−	0.138383i	0.823309	−	0.567593i	$-0.192125\pi$
$97$	−76.3273	−	132.203i	−0.0798955	−	0.138383i	−0.903205	+	0.429210i	$0.858792\pi$
$98$	1094.45	−	353.521i	1.12812	−	0.364398i
$99$		0			0
$100$	79.7874	−	138.196i	0.0797874	−	0.138196i
$101$	−84.5039	+	146.365i	−0.0832520	+	0.144197i	−0.904645	−	0.426166i	$-0.859864\pi$
$101$	−84.5039	+	146.365i	−0.0832520	+	0.144197i	0.821393	+	0.570363i	$0.193197\pi$
$102$		0			0
$103$	−512.502	−	887.679i	−0.490275	−	0.849181i	0.509663	−	0.860374i	$-0.329770\pi$
$103$	−512.502	−	887.679i	−0.490275	−	0.849181i	−0.999937	+	0.0111935i	$0.996437\pi$
$104$	423.936	−	734.278i	0.399714	−	0.692326i
$105$		0			0
$106$	1031.30	+	1786.27i	0.944990	+	1.63677i
$107$	−103.317	+	178.950i	−0.0933461	+	0.161680i	−0.908917	−	0.416977i	$-0.863090\pi$
$107$	−103.317	+	178.950i	−0.0933461	+	0.161680i	0.815571	+	0.578657i	$0.196423\pi$
$108$		0			0
$109$	−678.634	−	1175.43i	−0.596343	−	1.03290i	−0.993356	−	0.115083i	$-0.963286\pi$
$109$	−678.634	−	1175.43i	−0.596343	−	1.03290i	0.397013	−	0.917813i	$-0.370047\pi$
$110$	−344.415			−0.298534
$111$		0			0
$112$	228.865	+	1453.11i	0.193087	+	1.22595i
$113$	−851.436	+	1474.73i	−0.708817	+	1.22771i	0.256479	+	0.966550i	$0.417438\pi$
$113$	−851.436	+	1474.73i	−0.708817	+	1.22771i	−0.965296	+	0.261158i	$0.915896\pi$
$114$		0			0
$115$	−253.307	+	438.741i	−0.205400	+	0.355764i
$116$	−119.045	−	206.193i	−0.0952853	−	0.165039i
$117$		0			0
$118$	1933.63			1.50852
$119$	649.468	−	525.001i	0.500308	−	0.404427i
$120$		0			0
$121$	595.911	+	1032.15i	0.447717	+	0.775468i
$122$	−1496.45			−1.11051
$123$		0			0
$124$	−1021.11			−0.739501
$125$	−1516.65			−1.08522
$126$		0			0
$127$	−2478.87			−1.73200			−0.866001	−	0.500042i	$-0.833318\pi$
$127$	−2478.87			−1.73200			−0.866001	+	0.500042i	$0.833318\pi$
$128$	−1680.64			−1.16054
$129$		0			0
$130$	1552.02			1.04709
$131$	−87.2102	−	151.053i	−0.0581648	−	0.100744i	0.835477	−	0.549526i	$-0.185192\pi$
$131$	−87.2102	−	151.053i	−0.0581648	−	0.100744i	−0.893642	+	0.448781i	$0.851858\pi$
$132$		0			0
$133$	452.526	+	174.157i	0.295030	+	0.113544i
$134$	−998.241			−0.643544
$135$		0			0
$136$	359.588	+	622.824i	0.226723	+	0.392697i
$137$	1173.92	−	2033.30i	0.732081	−	1.26800i	−0.223911	−	0.974610i	$-0.571882\pi$
$137$	1173.92	−	2033.30i	0.732081	−	1.26800i	0.955992	−	0.293392i	$-0.0947842\pi$
$138$		0			0
$139$	218.286	−	378.082i	0.133200	−	0.230709i	−0.791709	−	0.610899i	$-0.790808\pi$
$139$	218.286	−	378.082i	0.133200	−	0.230709i	0.924908	+	0.380190i	$0.124141\pi$
$140$	−406.749	+	328.798i	−0.245547	+	0.198489i
$141$		0			0
$142$	−2905.26			−1.71693
$143$	313.585	+	543.145i	0.183380	+	0.317623i
$144$		0			0
$145$	−319.542	+	553.463i	−0.183010	+	0.316983i
$146$	−950.118	−	1645.65i	−0.538578	−	0.932844i
$147$		0			0
$148$	−614.135	+	1063.71i	−0.341092	+	0.590788i
$149$	373.432	+	646.803i	0.205320	+	0.355625i	0.950235	−	0.311535i	$-0.100843\pi$
$149$	373.432	+	646.803i	0.205320	+	0.355625i	−0.744914	+	0.667160i	$0.767510\pi$
$150$		0			0
$151$	633.434	−	1097.14i	0.341379	−	0.591285i	−0.643310	−	0.765605i	$-0.722440\pi$
$151$	633.434	−	1097.14i	0.341379	−	0.591285i	0.984689	+	0.174320i	$0.0557729\pi$
$152$	−208.780	+	361.618i	−0.111410	+	0.192968i
$153$		0			0
$154$	−683.743	−	263.142i	−0.357776	−	0.137692i
$155$	1370.43	+	2373.65i	0.710165	+	1.23004i
$156$		0			0
$157$	−1642.42			−0.834901			−0.417451	−	0.908700i	$-0.637076\pi$
$157$	−1642.42			−0.834901			−0.417451	+	0.908700i	$0.637076\pi$
$158$	1229.91			0.619283
$159$		0			0
$160$	−603.983	−	1046.13i	−0.298431	−	0.516898i
$161$	−838.081	+	677.468i	−0.410249	+	0.331627i
$162$		0			0
$163$	−248.421	+	430.277i	−0.119373	+	0.206760i	−0.919519	−	0.393045i	$-0.871422\pi$
$163$	−248.421	+	430.277i	−0.119373	+	0.206760i	0.800146	+	0.599805i	$0.204755\pi$
$164$	−587.677	+	1017.89i	−0.279816	+	0.484656i
$165$		0			0
$166$	−1712.84	−	2966.73i	−0.800857	−	1.38712i
$167$	−548.743	+	950.451i	−0.254270	+	0.440408i	−0.964697	−	0.263363i	$-0.915168\pi$
$167$	−548.743	+	950.451i	−0.254270	+	0.440408i	0.710427	+	0.703771i	$0.248502\pi$
$168$		0			0
$169$	−314.590	−	544.886i	−0.143191	−	0.248014i
$170$	−658.222	+	1140.07i	−0.296961	+	0.514351i
$171$		0			0
$172$	190.667	+	330.246i	0.0845248	+	0.146401i
$173$	−3413.84			−1.50029			−0.750143	−	0.661276i	$-0.770015\pi$
$173$	−3413.84			−1.50029			−0.750143	+	0.661276i	$0.770015\pi$
$174$		0			0
$175$	−850.334	−	327.255i	−0.367310	−	0.141361i
$176$	468.520	−	811.500i	0.200659	−	0.347552i
$177$		0			0
$178$	−828.297	+	1434.65i	−0.348784	+	0.604111i
$179$	134.237	+	232.506i	0.0560524	+	0.0970856i	0.892690	−	0.450671i	$-0.148815\pi$
$179$	134.237	+	232.506i	0.0560524	+	0.0970856i	−0.836638	+	0.547757i	$0.815482\pi$
$180$		0			0
$181$	3168.33			1.30110			0.650552	−	0.759462i	$-0.274538\pi$
$181$	3168.33			1.30110			0.650552	+	0.759462i	$0.274538\pi$
$182$	3081.11	+	1185.78i	1.25488	+	0.482945i
$183$		0			0
$184$	−464.016	−	803.700i	−0.185912	−	0.322008i
$185$	3296.92			1.31024
$186$		0			0
$187$	−531.973			−0.208031
$188$	−740.259			−0.287175
$189$		0			0
$190$	−764.340			−0.291848
$191$	−2643.74			−1.00154			−0.500770	−	0.865580i	$-0.666950\pi$
$191$	−2643.74			−1.00154			−0.500770	+	0.865580i	$0.666950\pi$
$192$		0			0
$193$	4176.77			1.55777			0.778887	−	0.627165i	$-0.215785\pi$
$193$	4176.77			1.55777			0.778887	+	0.627165i	$0.215785\pi$
$194$	255.937	+	443.296i	0.0947176	+	0.164056i
$195$		0			0
$196$	−1058.70	+	341.973i	−0.385823	+	0.124626i
$197$	1154.01			0.417360			0.208680	−	0.977984i	$-0.433083\pi$
$197$	1154.01			0.417360			0.208680	+	0.977984i	$0.433083\pi$
$198$		0			0
$199$	−2258.03	−	3911.02i	−0.804360	−	1.39319i	−0.916722	−	0.399525i	$-0.869175\pi$
$199$	−2258.03	−	3911.02i	−0.804360	−	1.39319i	0.112363	−	0.993667i	$-0.464158\pi$
$200$	392.315	−	679.509i	0.138704	−	0.240243i
$201$		0			0
$202$	283.354	−	490.784i	0.0986967	−	0.170948i
$203$	−1057.22	+	854.612i	−0.365529	+	0.295478i
$204$		0			0
$205$	3154.89			1.07486
$206$	1718.50	+	2976.52i	0.581229	+	1.00672i
$207$		0			0
$208$	−2111.27	+	3656.82i	−0.703798	+	1.21901i
$209$	−154.434	−	267.488i	−0.0511122	−	0.0885289i
$210$		0			0
$211$	139.232	−	241.157i	0.0454271	−	0.0786820i	−0.842418	−	0.538825i	$-0.818868\pi$
$211$	139.232	−	241.157i	0.0454271	−	0.0786820i	0.887845	+	0.460143i	$0.152202\pi$
$212$	−997.614	−	1727.92i	−0.323191	−	0.559782i
$213$		0			0
$214$	346.438	−	600.048i	0.110664	−	0.191675i
$215$	511.790	−	886.446i	0.162343	−	0.281187i
$216$		0			0
$217$	907.086	+	5759.28i	0.283765	+	1.80168i
$218$	2275.56	+	3941.39i	0.706975	+	1.22452i
$219$		0			0
$220$	333.165			0.102100
$221$	2397.20			0.729653
$222$		0			0
$223$	−1453.32	−	2517.23i	−0.436420	−	0.755902i	0.560990	−	0.827822i	$-0.310421\pi$
$223$	−1453.32	−	2517.23i	−0.436420	−	0.755902i	−0.997410	+	0.0719205i	$0.977087\pi$
$224$	−399.776	−	2538.26i	−0.119246	−	0.757119i
$225$		0			0
$226$	2854.99	−	4944.99i	0.840315	−	1.45547i
$227$	457.588	−	792.566i	0.133794	−	0.231738i	−0.791342	−	0.611373i	$-0.790617\pi$
$227$	457.588	−	792.566i	0.133794	−	0.231738i	0.925136	+	0.379636i	$0.123951\pi$
$228$		0			0
$229$	−1572.89	−	2724.33i	−0.453885	−	0.786151i	0.544739	−	0.838606i	$-0.316629\pi$
$229$	−1572.89	−	2724.33i	−0.453885	−	0.786151i	−0.998623	+	0.0524545i	$0.983296\pi$
$230$	849.377	−	1471.16i	0.243506	−	0.421764i
$231$		0			0
$232$	−585.347	−	1013.85i	−0.165646	−	0.286907i
$233$	1606.54	−	2782.60i	0.451707	−	0.782379i	−0.546786	−	0.837273i	$-0.684149\pi$
$233$	1606.54	−	2782.60i	0.451707	−	0.782379i	0.998492	+	0.0548940i	$0.0174821\pi$
$234$		0			0
$235$	993.502	+	1720.80i	0.275783	+	0.477669i
$236$	−1870.46			−0.515918
$237$		0			0
$238$	−2177.76	+	1760.41i	−0.593124	+	0.479455i
$239$	3206.85	−	5554.43i	0.867925	−	1.50329i	0.00381177	−	0.999993i	$-0.498787\pi$
$239$	3206.85	−	5554.43i	0.867925	−	1.50329i	0.864113	−	0.503297i	$-0.167880\pi$
$240$		0			0
$241$	688.272	−	1192.12i	0.183965	−	0.318636i	−0.759262	−	0.650785i	$-0.774440\pi$
$241$	688.272	−	1192.12i	0.183965	−	0.318636i	0.943227	+	0.332148i	$0.107773\pi$
$242$	−1998.18	−	3460.95i	−0.530776	−	0.919331i
$243$		0			0
$244$	1447.57			0.379799
$245$	2215.83	+	2002.08i	0.577812	+	0.522073i
$246$		0			0
$247$	695.920	+	1205.37i	0.179272	+	0.310509i
$248$	−5020.79			−1.28557
$249$		0			0
$250$	5085.54			1.28655
$251$	−7148.55			−1.79766			−0.898830	−	0.438298i	$-0.855582\pi$
$251$	−7148.55			−1.79766			−0.898830	+	0.438298i	$0.855582\pi$
$252$		0			0
$253$	686.465			0.170584
$254$	8312.03			2.05332
$255$		0			0
$256$	4273.86			1.04342
$257$	−334.190	−	578.834i	−0.0811137	−	0.140493i	0.822615	−	0.568599i	$-0.192514\pi$
$257$	−334.190	−	578.834i	−0.0811137	−	0.140493i	−0.903729	+	0.428106i	$0.859181\pi$
$258$		0			0
$259$	6545.14	+	2518.93i	1.57025	+	0.604319i
$260$	−1501.32			−0.358108
$261$		0			0
$262$	292.429	+	506.502i	0.0689554	+	0.119434i
$263$	−3896.06	+	6748.17i	−0.913464	+	1.58217i	−0.104330	+	0.994543i	$0.533270\pi$
$263$	−3896.06	+	6748.17i	−0.913464	+	1.58217i	−0.809135	+	0.587623i	$0.800064\pi$
$264$		0			0
$265$	−2677.80	+	4638.08i	−0.620738	+	1.07515i
$266$	−1517.39	−	583.974i	−0.349763	−	0.134608i
$267$		0			0
$268$	965.632			0.220095
$269$	−3360.58	−	5820.69i	−0.761703	−	1.31931i	−0.941972	−	0.335690i	$-0.891030\pi$
$269$	−3360.58	−	5820.69i	−0.761703	−	1.31931i	0.180270	−	0.983617i	$-0.442303\pi$
$270$		0			0
$271$	−321.852	+	557.464i	−0.0721444	+	0.124958i	−0.899841	−	0.436218i	$-0.856318\pi$
$271$	−321.852	+	557.464i	−0.0721444	+	0.124958i	0.827697	+	0.561176i	$0.189651\pi$
$272$	−1790.80	−	3101.76i	−0.399204	−	0.691441i
$273$		0			0
$274$	−3936.34	+	6817.95i	−0.867895	+	1.50324i
$275$	290.195	+	502.632i	0.0636342	+	0.110218i
$276$		0			0
$277$	−1588.33	+	2751.06i	−0.344525	+	0.596734i	−0.985267	−	0.171022i	$-0.945293\pi$
$277$	−1588.33	+	2751.06i	−0.344525	+	0.596734i	0.640743	+	0.767756i	$0.278627\pi$
$278$	−731.946	+	1267.77i	−0.157911	+	0.273509i
$279$		0			0
$280$	−1999.99	+	1616.70i	−0.426865	+	0.345059i
$281$	750.228	+	1299.43i	0.159270	+	0.275863i	0.934606	−	0.355686i	$-0.115753\pi$
$281$	750.228	+	1299.43i	0.159270	+	0.275863i	−0.775336	+	0.631549i	$0.782419\pi$
$282$		0			0
$283$	−6590.70			−1.38437			−0.692184	−	0.721721i	$-0.743352\pi$
$283$	−6590.70			−1.38437			−0.692184	+	0.721721i	$0.743352\pi$
$284$	2810.36			0.587197
$285$		0			0
$286$	−1051.50	−	1821.25i	−0.217400	−	0.376547i
$287$	6263.17	+	2410.41i	1.28816	+	0.495756i
$288$		0			0
$289$	1439.83	−	2493.86i	0.293065	−	0.507604i
$290$	1071.47	−	1855.84i	0.216962	−	0.375789i
$291$		0			0
$292$	919.081	+	1591.90i	0.184196	+	0.319036i
$293$	3933.62	−	6813.23i	0.784316	−	1.35848i	−0.145090	−	0.989418i	$-0.546347\pi$
$293$	3933.62	−	6813.23i	0.784316	−	1.35848i	0.929407	−	0.369057i	$-0.120319\pi$
$294$		0			0
$295$	2510.35	+	4348.05i	0.495451	+	0.858147i
$296$	−3019.70	+	5230.28i	−0.592962	+	1.02704i
$297$		0			0
$298$	−1252.17	−	2168.83i	−0.243411	−	0.421600i
$299$	−3093.38			−0.598310
$300$		0			0
$301$	1693.29	−	1368.78i	0.324250	−	0.262110i
$302$	−2124.00	+	3678.88i	−0.404710	+	0.700979i
$303$		0			0
$304$	1039.76	−	1800.91i	0.196165	−	0.339768i
$305$	−1942.78	−	3364.99i	−0.364732	−	0.631734i
$306$		0			0
$307$	862.229			0.160293			0.0801466	−	0.996783i	$-0.474461\pi$
$307$	862.229			0.160293			0.0801466	+	0.996783i	$0.474461\pi$
$308$	661.408	+	254.546i	0.122361	+	0.0470912i
$309$		0			0
$310$	−4595.25	−	7959.22i	−0.841913	−	1.45824i
$311$	−1815.86			−0.331086			−0.165543	−	0.986203i	$-0.552938\pi$
$311$	−1815.86			−0.331086			−0.165543	+	0.986203i	$0.552938\pi$
$312$		0			0
$313$	−1154.60			−0.208504			−0.104252	−	0.994551i	$-0.533245\pi$
$313$	−1154.60			−0.208504			−0.104252	+	0.994551i	$0.533245\pi$
$314$	5507.29			0.989790
$315$		0			0
$316$	−1189.74			−0.211797
$317$	7933.67			1.40568			0.702838	−	0.711350i	$-0.251916\pi$
$317$	7933.67			1.40568			0.702838	+	0.711350i	$0.251916\pi$
$318$		0			0
$319$	865.961			0.151989
$320$	−740.916	−	1283.30i	−0.129433	−	0.224184i
$321$		0			0
$322$	2810.21	−	2271.65i	0.486357	−	0.393150i
$323$	−1180.58			−0.203372
$324$		0			0
$325$	−1307.69	−	2264.98i	−0.223192	−	0.386581i
$326$	832.992	−	1442.78i	0.141519	−	0.245118i
$327$		0			0
$328$	−2889.61	+	5004.95i	−0.486439	+	0.842538i
$329$	657.598	+	4175.23i	0.110196	+	0.699659i
$330$		0			0
$331$	−3227.64			−0.535974			−0.267987	−	0.963423i	$-0.586358\pi$
$331$	−3227.64			−0.535974			−0.267987	+	0.963423i	$0.586358\pi$
$332$	1656.89	+	2869.82i	0.273896	+	0.474402i
$333$		0			0
$334$	1840.02	−	3187.01i	0.301441	−	0.522111i
$335$	−1295.98	−	2244.70i	−0.211363	−	0.366092i
$336$		0			0
$337$	5569.87	−	9647.30i	0.900327	−	1.55941i	0.0732572	−	0.997313i	$-0.476661\pi$
$337$	5569.87	−	9647.30i	0.900327	−	1.55941i	0.827070	−	0.562099i	$-0.190006\pi$
$338$	1054.87	+	1827.08i	0.169755	+	0.294025i
$339$		0			0
$340$	636.720	−	1102.83i	0.101562	−	0.175910i
$341$	1856.94	−	3216.31i	0.294894	−	0.510771i
$342$		0			0
$343$	2869.29	+	5667.52i	0.451682	+	0.892179i
$344$	937.513	+	1623.82i	0.146940	+	0.254507i
$345$		0			0
$346$	11447.1			1.77861
$347$	3413.43			0.528077			0.264039	−	0.964512i	$-0.414945\pi$
$347$	3413.43			0.528077			0.264039	+	0.964512i	$0.414945\pi$
$348$		0			0
$349$	−4013.28	−	6951.20i	−0.615547	−	1.06616i	−0.990288	−	0.139029i	$-0.955602\pi$
$349$	−4013.28	−	6951.20i	−0.615547	−	1.06616i	0.374741	−	0.927129i	$-0.377732\pi$
$350$	2851.30	+	1097.33i	0.435452	+	0.167586i
$351$		0			0
$352$	−818.399	+	1417.51i	−0.123923	+	0.214640i
$353$	−187.723	+	325.145i	−0.0283045	+	0.0490248i	−0.879831	−	0.475287i	$-0.842344\pi$
$353$	−187.723	+	325.145i	−0.0283045	+	0.0490248i	0.851526	+	0.524312i	$0.175677\pi$
$354$		0			0
$355$	−3771.78	−	6532.92i	−0.563903	−	0.976708i
$356$	801.240	−	1387.79i	0.119285	−	0.206609i
$357$		0			0
$358$	−450.118	−	779.628i	−0.0664511	−	0.115097i
$359$	1475.85	−	2556.25i	0.216970	−	0.375804i	−0.736910	−	0.675991i	$-0.763716\pi$
$359$	1475.85	−	2556.25i	0.216970	−	0.375804i	0.953880	+	0.300187i	$0.0970491\pi$
$360$		0			0
$361$	3086.77	+	5346.45i	0.450033	+	0.779479i
$362$	−10623.9			−1.54248
$363$		0			0
$364$	−2980.47	−	1147.05i	−0.429173	−	0.165169i
$365$	2467.00	−	4272.97i	0.353777	−	0.612760i
$366$		0			0
$367$	−3475.47	+	6019.68i	−0.494326	+	0.856199i	−0.999979	−	0.00653891i	$-0.997919\pi$
$367$	−3475.47	+	6019.68i	−0.494326	+	0.856199i	0.505652	+	0.862737i	$0.331252\pi$
$368$	2310.87	+	4002.55i	0.327344	+	0.566976i
$369$		0			0
$370$	−11055.1			−1.55331
$371$	−8859.64	+	7161.74i	−1.23981	+	1.00221i
$372$		0			0
$373$	5496.02	+	9519.39i	0.762931	+	1.32143i	0.941334	+	0.337477i	$0.109574\pi$
$373$	5496.02	+	9519.39i	0.762931	+	1.32143i	−0.178403	+	0.983958i	$0.557093\pi$
$374$	1783.79			0.246624
$375$		0			0
$376$	−3639.85			−0.499232
$377$	−3902.23			−0.533091
$378$		0			0
$379$	3498.29			0.474130			0.237065	−	0.971494i	$-0.423815\pi$
$379$	3498.29			0.474130			0.237065	+	0.971494i	$0.423815\pi$
$380$	739.372			0.0998131
$381$		0			0
$382$	8864.85			1.18734
$383$	3056.68	+	5294.33i	0.407805	+	0.706339i	0.994643	−	0.103365i	$-0.0329610\pi$
$383$	3056.68	+	5294.33i	0.407805	+	0.706339i	−0.586839	+	0.809704i	$0.699628\pi$
$384$		0			0
$385$	−295.962	−	1879.13i	−0.0391782	−	0.248751i
$386$	−14005.3			−1.84677
$387$		0			0
$388$	−247.577	−	428.815i	−0.0323938	−	0.0561077i
$389$	2683.00	−	4647.10i	0.349701	−	0.605700i	−0.636495	−	0.771280i	$-0.719617\pi$
$389$	2683.00	−	4647.10i	0.349701	−	0.605700i	0.986196	+	0.165581i	$0.0529499\pi$
$390$		0			0
$391$	1311.92	−	2272.32i	0.169685	−	0.293903i
$392$	−5205.63	+	1681.48i	−0.670724	+	0.216652i
$393$		0			0
$394$	−3869.58			−0.494788
$395$	1596.75	+	2765.65i	0.203395	+	0.352291i
$396$		0			0
$397$	−221.151	+	383.045i	−0.0279578	+	0.0484243i	−0.879666	−	0.475592i	$-0.842234\pi$
$397$	−221.151	+	383.045i	−0.0279578	+	0.0484243i	0.851708	+	0.524017i	$0.175567\pi$
$398$	7571.52	+	13114.3i	0.953583	+	1.65165i
$399$		0			0
$400$	−1953.79	+	3384.06i	−0.244224	+	0.423008i
$401$	−2643.70	−	4579.02i	−0.329227	−	0.570237i	0.653132	−	0.757244i	$-0.273455\pi$
$401$	−2643.70	−	4579.02i	−0.329227	−	0.570237i	−0.982359	+	0.187007i	$0.940121\pi$
$402$		0			0
$403$	−8367.81	+	14493.5i	−1.03432	+	1.79149i
$404$	−274.098	+	474.752i	−0.0337547	+	0.0584649i
$405$		0			0
$406$	3545.02	−	2865.64i	0.433341	−	0.350294i
$407$	−2233.67	−	3868.83i	−0.272037	−	0.471182i
$408$		0			0
$409$	5365.46			0.648667			0.324334	−	0.945943i	$-0.394860\pi$
$409$	5365.46			0.648667			0.324334	+	0.945943i	$0.394860\pi$
$410$	−10578.8			−1.27427
$411$		0			0
$412$	−1662.36	−	2879.29i	−0.198783	−	0.344302i
$413$	1661.60	+	10549.8i	0.197971	+	1.25696i
$414$		0			0
$415$	4447.42	−	7703.16i	0.526061	−	0.911165i
$416$	3687.91	−	6387.64i	0.434650	−	0.752836i
$417$		0			0
$418$	517.842	+	896.928i	0.0605944	+	0.104953i
$419$	−3399.92	+	5888.83i	−0.396413	+	0.686607i	−0.993280	−	0.115733i	$-0.963078\pi$
$419$	−3399.92	+	5888.83i	−0.396413	+	0.686607i	0.596868	+	0.802340i	$0.296412\pi$
$420$		0			0
$421$	−1937.13	−	3355.21i	−0.224252	−	0.388415i	0.731843	−	0.681473i	$-0.238660\pi$
$421$	−1937.13	−	3355.21i	−0.224252	−	0.388415i	−0.956095	+	0.293058i	$0.905327\pi$
$422$	−466.865	+	808.635i	−0.0538546	+	0.0932789i
$423$		0			0
$424$	−4905.27	−	8496.18i	−0.561842	−	0.973139i
$425$	2218.40			0.253196
$426$		0			0
$427$	−1285.92	−	8164.60i	−0.145738	−	0.925322i
$428$	−335.121	+	580.446i	−0.0378474	+	0.0655536i
$429$		0			0
$430$	−1716.11	+	2972.39i	−0.192461	+	0.333352i
$431$	−2486.59	−	4306.90i	−0.277900	−	0.481337i	0.692963	−	0.720974i	$-0.256305\pi$
$431$	−2486.59	−	4306.90i	−0.277900	−	0.481337i	−0.970863	+	0.239636i	$0.922972\pi$
$432$		0			0
$433$	−4522.66			−0.501952			−0.250976	−	0.967993i	$-0.580752\pi$
$433$	−4522.66			−0.501952			−0.250976	+	0.967993i	$0.580752\pi$
$434$	−3041.59	−	19311.7i	−0.336408	−	2.13593i
$435$		0			0
$436$	−2201.23	−	3812.64i	−0.241788	−	0.418790i
$437$	1523.43			0.166763
$438$		0			0
$439$	−8458.79			−0.919626			−0.459813	−	0.888016i	$-0.652084\pi$
$439$	−8458.79			−0.919626			−0.459813	+	0.888016i	$0.652084\pi$
$440$	1638.17			0.177493
$441$		0			0
$442$	−8038.18			−0.865016
$443$	−10043.7			−1.07718			−0.538589	−	0.842569i	$-0.681042\pi$
$443$	−10043.7			−1.07718			−0.538589	+	0.842569i	$0.681042\pi$
$444$		0			0
$445$	−4301.38			−0.458213
$446$	4873.21	+	8440.65i	0.517384	+	0.896135i
$447$		0			0
$448$	−490.412	−	3113.73i	−0.0517183	−	0.328370i
$449$	3746.19			0.393750			0.196875	−	0.980429i	$-0.436921\pi$
$449$	3746.19			0.393750			0.196875	+	0.980429i	$0.436921\pi$
$450$		0			0
$451$	−2137.44	−	3702.16i	−0.223167	−	0.386536i
$452$	−2761.73	+	4783.46i	−0.287391	+	0.497776i
$453$		0			0
$454$	−1534.36	+	2657.59i	−0.158615	+	0.274729i
$455$	1333.68	+	8467.80i	0.137415	+	0.872476i
$456$		0			0
$457$	6991.75			0.715668			0.357834	−	0.933785i	$-0.383515\pi$
$457$	6991.75			0.715668			0.357834	+	0.933785i	$0.383515\pi$
$458$	5274.14	+	9135.08i	0.538088	+	0.931996i
$459$		0			0
$460$	−821.632	+	1423.11i	−0.0832799	+	0.144245i
$461$	−2826.32	−	4895.34i	−0.285542	−	0.494574i	0.687198	−	0.726470i	$-0.258840\pi$
$461$	−2826.32	−	4895.34i	−0.285542	−	0.494574i	−0.972741	+	0.231896i	$0.925507\pi$
$462$		0			0
$463$	−4524.54	+	7836.73i	−0.454154	+	0.786617i	−0.998639	−	0.0521531i	$-0.983392\pi$
$463$	−4524.54	+	7836.73i	−0.454154	+	0.786617i	0.544485	+	0.838770i	$0.316725\pi$
$464$	2915.12	+	5049.13i	0.291662	+	0.505173i
$465$		0			0
$466$	−5386.95	+	9330.48i	−0.535506	+	0.927524i
$467$	3169.20	−	5489.22i	0.314033	−	0.543921i	−0.665199	−	0.746666i	$-0.731653\pi$
$467$	3169.20	−	5489.22i	0.314033	−	0.543921i	0.979231	+	0.202746i	$0.0649865\pi$
$468$		0			0
$469$	−857.805	−	5446.39i	−0.0844557	−	0.536228i
$470$	−3331.36	−	5770.08i	−0.326945	−	0.566285i
$471$		0			0
$472$	−9197.07			−0.896885
$473$	−1386.95			−0.134825
$474$		0			0
$475$	644.012	+	1115.46i	0.0622090	+	0.107749i
$476$	2106.62	−	1702.90i	0.202851	−	0.163976i
$477$		0			0
$478$	−10753.1	+	18624.8i	−1.02894	+	1.78218i
$479$	2336.85	−	4047.54i	0.222909	−	0.386089i	−0.732781	−	0.680464i	$-0.761778\pi$
$479$	2336.85	−	4047.54i	0.222909	−	0.386089i	0.955690	+	0.294375i	$0.0951115\pi$
$480$		0			0
$481$	10065.5	+	17433.9i	0.954150	+	1.65264i
$482$	−2307.88	+	3997.36i	−0.218093	+	0.377749i
$483$		0			0
$484$	1932.91	+	3347.89i	0.181528	+	0.314415i
$485$	−664.545	+	1151.03i	−0.0622174	+	0.107764i
$486$		0			0
$487$	−4782.59	−	8283.70i	−0.445010	−	0.770781i	0.553043	−	0.833153i	$-0.313467\pi$
$487$	−4782.59	−	8283.70i	−0.445010	−	0.770781i	−0.998053	+	0.0623725i	$0.980133\pi$
$488$	7117.68			0.660251
$489$		0			0
$490$	−7430.00	−	6713.26i	−0.685007	−	0.618927i
$491$	2518.90	−	4362.87i	0.231520	−	0.401005i	−0.726735	−	0.686917i	$-0.758963\pi$
$491$	2518.90	−	4362.87i	0.231520	−	0.401005i	0.958256	+	0.285913i	$0.0922967\pi$
$492$		0			0
$493$	1654.96	−	2866.48i	0.151188	−	0.261866i
$494$	−2333.52	−	4041.78i	−0.212531	−	0.368114i
$495$		0			0
$496$	25004.3			2.26356
$497$	−2496.54	−	15851.1i	−0.225322	−	1.43062i
$498$		0			0
$499$	5896.41	+	10212.9i	0.528977	+	0.916216i	0.999429	+	0.0337898i	$0.0107577\pi$
$499$	5896.41	+	10212.9i	0.528977	+	0.916216i	−0.470452	+	0.882426i	$0.655909\pi$
$500$	−4919.41			−0.440006
$501$		0			0
$502$	23970.2			2.13116
$503$	11275.8			0.999525			0.499762	−	0.866163i	$-0.333421\pi$
$503$	11275.8			0.999525			0.499762	+	0.866163i	$0.333421\pi$
$504$		0			0
$505$	1471.47			0.129662
$506$	−2301.82			−0.202230
$507$		0			0
$508$	−8040.51			−0.702244
$509$	5813.97	+	10070.1i	0.506286	+	0.876913i	0.999974	+	0.00727395i	$0.00231539\pi$
$509$	5813.97	+	10070.1i	0.506286	+	0.876913i	−0.493687	+	0.869639i	$0.664351\pi$
$510$		0			0
$511$	8162.20	−	6597.97i	0.706604	−	0.571188i
$512$	−885.756			−0.0764556
$513$		0			0
$514$	1120.59	+	1940.92i	0.0961617	+	0.166557i
$515$	−4462.11	+	7728.60i	−0.381794	+	0.661287i
$516$		0			0
$517$	1346.20	−	2331.68i	0.114518	−	0.198351i
$518$	−21946.9	−	8446.35i	−1.86156	−	0.716431i
$519$		0			0
$520$	−7382.00			−0.622543
$521$	−2028.63	−	3513.69i	−0.170587	−	0.295465i	0.768038	−	0.640404i	$-0.221233\pi$
$521$	−2028.63	−	3513.69i	−0.170587	−	0.295465i	−0.938625	+	0.344939i	$0.887900\pi$
$522$		0			0
$523$	2546.76	−	4411.11i	0.212929	−	0.368804i	−0.739701	−	0.672936i	$-0.765033\pi$
$523$	2546.76	−	4411.11i	0.212929	−	0.368804i	0.952630	+	0.304132i	$0.0983663\pi$
$524$	−282.876	−	489.956i	−0.0235830	−	0.0408470i
$525$		0			0
$526$	13064.1	−	22627.6i	1.08293	−	1.87569i
$527$	−7097.69	−	12293.6i	−0.586680	−	1.01616i
$528$		0			0
$529$	4390.58	−	7604.71i	0.360860	−	0.625027i
$530$	8979.05	−	15552.2i	0.735896	−	1.27461i
$531$		0			0
$532$	1467.82	+	564.898i	0.119621	+	0.0460365i
$533$	9631.84	+	16682.8i	0.782742	+	1.35575i
$534$		0			0
$535$	1799.06			0.145384
$536$	4748.02			0.382618
$537$		0			0
$538$	11268.5	+	19517.6i	0.903012	+	1.56406i
$539$	848.145	−	3956.61i	0.0677777	−	0.316184i
$540$		0			0
$541$	−1284.83	+	2225.38i	−0.102105	+	0.176852i	−0.912552	−	0.408961i	$-0.865891\pi$
$541$	−1284.83	+	2225.38i	−0.102105	+	0.176852i	0.810447	+	0.585813i	$0.199225\pi$
$542$	1079.22	−	1869.26i	0.0855284	−	0.148140i
$543$		0			0
$544$	3128.13	+	5418.08i	0.246540	+	0.427019i
$545$	−5908.54	+	10233.9i	−0.464393	+	0.804352i
$546$		0			0
$547$	−5096.80	−	8827.92i	−0.398398	−	0.690045i	0.595131	−	0.803629i	$-0.297100\pi$
$547$	−5096.80	−	8827.92i	−0.398398	−	0.690045i	−0.993528	+	0.113584i	$0.963767\pi$
$548$	3807.76	−	6595.23i	0.296824	−	0.514114i
$549$		0			0
$550$	−973.067	−	1685.40i	−0.0754395	−	0.130665i
$551$	1921.77			0.148585
$552$		0			0
$553$	1056.89	+	6710.39i	0.0812719	+	0.516013i
$554$	5325.90	−	9224.73i	0.408440	−	0.707439i
$555$		0			0
$556$	708.036	−	1226.35i	0.0540061	−	0.0935414i
$557$	8941.40	+	15487.0i	0.680178	+	1.17810i	0.974926	+	0.222529i	$0.0714311\pi$
$557$	8941.40	+	15487.0i	0.680178	+	1.17810i	−0.294748	+	0.955575i	$0.595236\pi$
$558$		0			0
$559$	6249.96			0.472889
$560$	9960.25	−	8051.43i	0.751603	−	0.607563i
$561$		0			0
$562$	−2515.63	−	4357.19i	−0.188817	−	0.327041i
$563$	−10376.2			−0.776740			−0.388370	−	0.921504i	$-0.626962\pi$
$563$	−10376.2			−0.776740			−0.388370	+	0.921504i	$0.626962\pi$
$564$		0			0
$565$	14826.1			1.10396
$566$	22099.6			1.64119
$567$		0			0
$568$	13818.5			1.02080
$569$	10224.8			0.753335			0.376667	−	0.926349i	$-0.377070\pi$
$569$	10224.8			0.753335			0.376667	+	0.926349i	$0.377070\pi$
$570$		0			0
$571$	−16342.6			−1.19775			−0.598877	−	0.800841i	$-0.704386\pi$
$571$	−16342.6			−1.19775			−0.598877	+	0.800841i	$0.704386\pi$
$572$	1017.15	+	1761.75i	0.0743516	+	0.128781i
$573$		0			0
$574$	−21001.3	−	8082.47i	−1.52714	−	0.587728i
$575$	−2862.65			−0.207618
$576$		0			0
$577$	10787.0	+	18683.7i	0.778285	+	1.34803i	0.932930	+	0.360058i	$0.117243\pi$
$577$	10787.0	+	18683.7i	0.778285	+	1.34803i	−0.154645	+	0.987970i	$0.549423\pi$
$578$	−4827.97	+	8362.29i	−0.347434	+	0.601774i
$579$		0			0
$580$	−1036.47	+	1795.22i	−0.0742019	+	0.128522i
$581$	14714.5	−	11894.6i	1.05071	−	0.849347i
$582$		0			0
$583$	7256.85			0.515520
$584$	4519.13	+	7827.36i	0.320210	+	0.554620i
$585$		0			0
$586$	−13190.0	+	22845.8i	−0.929821	+	1.61050i
$587$	1860.80	+	3223.00i	0.130840	+	0.226622i	0.924001	−	0.382391i	$-0.124899\pi$
$587$	1860.80	+	3223.00i	0.130840	+	0.226622i	−0.793160	+	0.609013i	$0.791566\pi$
$588$		0			0
$589$	4120.99	−	7137.76i	0.288289	−	0.499331i
$590$	−8417.58	−	14579.7i	−0.587366	−	1.01735i
$591$		0			0
$592$	15038.6	−	26047.6i	1.04406	−	1.80836i
$593$	6561.64	−	11365.1i	0.454392	−	0.787029i	−0.544261	−	0.838916i	$-0.683190\pi$
$593$	6561.64	−	11365.1i	0.454392	−	0.787029i	0.998653	+	0.0518863i	$0.0165233\pi$
$594$		0			0
$595$	−6785.85	−	2611.56i	−0.467551	−	0.179939i
$596$	1211.27	+	2097.98i	0.0832475	+	0.144189i
$597$		0			0
$598$	10372.6			0.709307
$599$	−3168.55			−0.216133			−0.108066	−	0.994144i	$-0.534466\pi$
$599$	−3168.55			−0.216133			−0.108066	+	0.994144i	$0.534466\pi$
$600$		0			0
$601$	−3617.13	−	6265.05i	−0.245500	−	0.425219i	0.716772	−	0.697308i	$-0.245619\pi$
$601$	−3617.13	−	6265.05i	−0.245500	−	0.425219i	−0.962272	+	0.272089i	$0.912286\pi$
$602$	−5677.84	+	4589.72i	−0.384404	+	0.310736i
$603$		0			0
$604$	2054.62	−	3558.70i	0.138413	−	0.239738i
$605$	5188.31	−	8986.42i	0.348653	−	0.603884i
$606$		0			0
$607$	−7388.40	−	12797.1i	−0.494046	−	0.855713i	0.505931	−	0.862574i	$-0.331149\pi$
$607$	−7388.40	−	12797.1i	−0.494046	−	0.855713i	−0.999976	+	0.00686160i	$0.997816\pi$
$608$	−1816.22	+	3145.79i	−0.121147	+	0.209833i
$609$		0			0
$610$	6514.43	+	11283.3i	0.432396	+	0.748932i
$611$	−6066.30	+	10507.1i	−0.401663	+	0.695701i
$612$		0			0
$613$	−6363.75	−	11022.3i	−0.419298	−	0.726245i	0.576571	−	0.817047i	$-0.304390\pi$
$613$	−6363.75	−	11022.3i	−0.419298	−	0.726245i	−0.995869	+	0.0908021i	$0.971057\pi$
$614$	−2891.18			−0.190030
$615$		0			0
$616$	3252.14	+	1251.60i	0.212715	+	0.0818644i
$617$	6853.94	−	11871.4i	0.447211	−	0.774593i	−0.550992	−	0.834510i	$-0.685751\pi$
$617$	6853.94	−	11871.4i	0.447211	−	0.774593i	0.998203	+	0.0599179i	$0.0190839\pi$
$618$		0			0
$619$	10086.4	−	17470.1i	0.654937	−	1.13438i	−0.326973	−	0.945034i	$-0.606029\pi$
$619$	10086.4	−	17470.1i	0.654937	−	1.13438i	0.981910	−	0.189350i	$-0.0606381\pi$
$620$	4445.15	+	7699.22i	0.287938	+	0.498723i
$621$		0			0
$622$	6088.84			0.392509
$623$	−8539.21	−	3286.36i	−0.549143	−	0.211340i
$624$		0			0
$625$	3527.57	+	6109.92i	0.225764	+	0.391035i
$626$	3871.53			0.247185
$627$		0			0
$628$	−5327.38			−0.338512
$629$	−17075.3			−1.08241
$630$		0			0
$631$	8153.08			0.514373			0.257186	−	0.966362i	$-0.417205\pi$
$631$	8153.08			0.514373			0.257186	+	0.966362i	$0.417205\pi$
$632$	−5849.95			−0.368194
$633$		0			0
$634$	−26602.8			−1.66645
$635$	10791.2	+	18690.9i	0.674385	+	1.16807i
$636$		0			0
$637$	−3821.95	+	17829.5i	−0.237726	+	1.10899i
$638$	−2903.70			−0.180186
$639$		0			0
$640$	7316.27	+	12672.1i	0.451876	+	0.782673i
$641$	−1315.11	+	2277.84i	−0.0810357	+	0.140358i	−0.903695	−	0.428177i	$-0.859156\pi$
$641$	−1315.11	+	2277.84i	−0.0810357	+	0.140358i	0.822659	+	0.568535i	$0.192489\pi$
$642$		0			0
$643$	−5342.55	+	9253.56i	−0.327666	+	0.567535i	−0.982048	−	0.188629i	$-0.939595\pi$
$643$	−5342.55	+	9253.56i	−0.327666	+	0.567535i	0.654382	+	0.756164i	$0.272929\pi$
$644$	−2718.41	+	2197.45i	−0.166336	+	0.134459i
$645$		0			0
$646$	3958.65			0.241101
$647$	−9243.79	−	16010.7i	−0.561686	−	0.972869i	−0.997350	−	0.0727595i	$-0.976819\pi$
$647$	−9243.79	−	16010.7i	−0.561686	−	0.972869i	0.435663	−	0.900110i	$-0.356514\pi$
$648$		0			0
$649$	3401.53	−	5891.63i	0.205735	−	0.356343i
$650$	4384.88	+	7594.83i	0.264599	+	0.458298i
$651$		0			0
$652$	−805.781	+	1395.65i	−0.0484000	+	0.0838313i
$653$	9443.31	+	16356.3i	0.565919	+	0.980201i	0.996964	+	0.0778702i	$0.0248120\pi$
$653$	9443.31	+	16356.3i	0.565919	+	0.980201i	−0.431044	+	0.902331i	$0.641855\pi$
$654$		0			0
$655$	−759.297	+	1315.14i	−0.0452950	+	0.0784532i
$656$	14390.7	−	24925.5i	0.856499	−	1.48350i
$657$		0			0
$658$	−2205.02	−	14000.2i	−0.130639	−	0.829458i
$659$	−1649.50	−	2857.01i	−0.0975043	−	0.168882i	0.813147	−	0.582059i	$-0.197753\pi$
$659$	−1649.50	−	2857.01i	−0.0975043	−	0.168882i	−0.910651	+	0.413176i	$0.864419\pi$
$660$		0			0
$661$	−7120.51			−0.418995			−0.209498	−	0.977809i	$-0.567183\pi$
$661$	−7120.51			−0.418995			−0.209498	+	0.977809i	$0.567183\pi$
$662$	10822.8			0.635406
$663$		0			0
$664$	8146.93	+	14110.9i	0.476148	+	0.824712i
$665$	−656.810	−	4170.23i	−0.0383008	−	0.243180i
$666$		0			0
$667$	−2135.58	+	3698.94i	−0.123973	+	0.214728i
$668$	−1779.91	+	3082.90i	−0.103094	+	0.178564i
$669$		0			0
$670$	4345.60	+	7526.80i	0.250575	+	0.434008i
$671$	−2632.47	+	4559.57i	−0.151454	+	0.262326i
$672$		0			0
$673$	−6950.81	−	12039.2i	−0.398119	−	0.689562i	0.595375	−	0.803448i	$-0.297003\pi$
$673$	−6950.81	−	12039.2i	−0.398119	−	0.689562i	−0.993494	+	0.113886i	$0.963670\pi$
$674$	−18676.6	+	32348.8i	−1.06735	+	1.84871i
$675$		0			0
$676$	−1020.41	−	1767.40i	−0.0580570	−	0.100558i
$677$	−6770.68			−0.384370			−0.192185	−	0.981359i	$-0.561557\pi$
$677$	−6770.68			−0.384370			−0.192185	+	0.981359i	$0.561557\pi$
$678$		0			0
$679$	−2198.69	+	1777.32i	−0.124268	+	0.100453i
$680$	3130.76	−	5422.63i	0.176557	−	0.305806i
$681$		0			0
$682$	−6226.59	+	10784.8i	−0.349602	+	0.605528i
$683$	2459.98	+	4260.81i	0.137816	+	0.238705i	0.926670	−	0.375877i	$-0.122658\pi$
$683$	2459.98	+	4260.81i	0.137816	+	0.238705i	−0.788854	+	0.614581i	$0.789325\pi$
$684$		0			0
$685$	−20441.6			−1.14019
$686$	−9621.15	−	19004.1i	−0.535477	−	1.05769i
$687$		0			0
$688$	−4668.96	−	8086.88i	−0.258724	−	0.448124i
$689$	−32701.1			−1.80815
$690$		0			0
$691$	−29784.8			−1.63975			−0.819874	−	0.572545i	$-0.805956\pi$
$691$	−29784.8			−1.63975			−0.819874	+	0.572545i	$0.805956\pi$
$692$	−11073.2			−0.608294
$693$		0			0
$694$	−11445.8			−0.626045
$695$	−3801.02			−0.207455
$696$		0			0
$697$	−16339.7			−0.887964
$698$	13457.1	+	23308.4i	0.729742	+	1.26395i
$699$		0			0
$700$	−2758.16	−	1061.49i	−0.148926	−	0.0573150i
$701$	−26420.4			−1.42352			−0.711758	−	0.702425i	$-0.752101\pi$
$701$	−26420.4			−1.42352			−0.711758	+	0.702425i	$0.752101\pi$
$702$		0			0
$703$	−4957.05	−	8585.87i	−0.265944	−	0.460629i
$704$	−1003.94	+	1738.88i	−0.0537466	+	0.0930918i
$705$		0			0
$706$	629.463	−	1090.26i	0.0335554	−	0.0581197i
$707$	2921.20	+	1124.24i	0.155393	+	0.0598039i
$708$		0			0
$709$	−26470.9			−1.40217			−0.701083	−	0.713080i	$-0.747300\pi$
$709$	−26470.9			−1.40217			−0.701083	+	0.713080i	$0.747300\pi$
$710$	12647.4	+	21905.9i	0.668517	+	1.15790i
$711$		0			0
$712$	3939.70	−	6823.76i	0.207369	−	0.359173i
$713$	9158.94	+	15863.8i	0.481073	+	0.833243i
$714$		0			0
$715$	2730.23	−	4728.90i	0.142804	−	0.247344i
$716$	435.415	+	754.161i	0.0227266	+	0.0393636i
$717$		0			0
$718$	−4948.75	+	8571.48i	−0.257222	+	0.445522i
$719$	−901.859	+	1562.06i	−0.0467784	+	0.0810225i	−0.888467	−	0.458941i	$-0.848229\pi$
$719$	−901.859	+	1562.06i	−0.0467784	+	0.0810225i	0.841688	+	0.539964i	$0.181562\pi$
$720$		0			0
$721$	−14763.1	+	11933.9i	−0.762563	+	0.616422i
$722$	−10350.4	−	17927.4i	−0.533521	−	0.924086i
$723$		0			0
$724$	10276.8			0.527535
$725$	−3611.17			−0.184987
$726$		0			0
$727$	5340.34	+	9249.74i	0.272438	+	0.471876i	0.969485	−	0.245149i	$-0.0788368\pi$
$727$	5340.34	+	9249.74i	0.272438	+	0.471876i	−0.697048	+	0.717025i	$0.745503\pi$
$728$	−14655.0	−	5640.03i	−0.746084	−	0.287134i
$729$		0			0
$730$	−8272.22	+	14327.9i	−0.419409	+	0.726438i
$731$	−2650.65	+	4591.06i	−0.134115	+	0.232293i
$732$		0			0
$733$	8936.47	+	15478.4i	0.450308	+	0.779957i	0.998405	−	0.0564583i	$-0.0179808\pi$
$733$	8936.47	+	15478.4i	0.450308	+	0.779957i	−0.548097	+	0.836415i	$0.684647\pi$
$734$	11653.8	−	20184.9i	0.586033	−	1.01504i
$735$		0			0
$736$	−4036.58	−	6991.56i	−0.202161	−	0.350152i
$737$	−1756.05	+	3041.57i	−0.0877680	+	0.152019i
$738$		0			0
$739$	2136.60	+	3700.70i	0.106355	+	0.184212i	0.914291	−	0.405058i	$-0.132749\pi$
$739$	2136.60	+	3700.70i	0.106355	+	0.184212i	−0.807936	+	0.589270i	$0.799415\pi$
$740$	10694.0			0.531240
$741$		0			0
$742$	29707.7	−	24014.4i	1.46982	−	1.18813i
$743$	−14303.0	+	24773.5i	−0.706227	+	1.22322i	0.260020	+	0.965603i	$0.416271\pi$
$743$	−14303.0	+	24773.5i	−0.706227	+	1.22322i	−0.966247	+	0.257618i	$0.917062\pi$
$744$		0			0
$745$	3251.29	−	5631.40i	0.159890	−	0.276938i
$746$	−18429.0	−	31919.9i	−0.904468	−	1.56658i
$747$		0			0
$748$	−1725.52			−0.0843465
$749$	3571.55	+	1374.53i	0.174234	+	0.0670549i
$750$		0			0
$751$	6745.45	+	11683.5i	0.327756	+	0.567691i	0.982066	−	0.188536i	$-0.0603741\pi$
$751$	6745.45	+	11683.5i	0.327756	+	0.567691i	−0.654310	+	0.756227i	$0.727041\pi$
$752$	18127.0			0.879023
$753$		0			0
$754$	13084.8			0.631988
$755$	−11030.0			−0.531687
$756$		0			0
$757$	3429.25			0.164648			0.0823239	−	0.996606i	$-0.473766\pi$
$757$	3429.25			0.164648			0.0823239	+	0.996606i	$0.473766\pi$
$758$	−11730.3			−0.562089
$759$		0			0
$760$	3635.49			0.173517
$761$	−11218.9	−	19431.7i	−0.534408	−	0.925622i	−0.999192	−	0.0401976i	$-0.987201\pi$
$761$	−11218.9	−	19431.7i	−0.534408	−	0.925622i	0.464784	−	0.885424i	$-0.346132\pi$
$762$		0			0
$763$	−19548.7	+	15802.3i	−0.927539	+	0.749781i
$764$	−8575.27			−0.406077
$765$		0			0
$766$	−10249.5	−	17752.7i	−0.483460	−	0.837377i
$767$	−15328.1	+	26549.1i	−0.721600	+	1.24985i
$768$		0			0
$769$	14767.0	−	25577.2i	0.692473	−	1.19940i	−0.278552	−	0.960421i	$-0.589854\pi$
$769$	14767.0	−	25577.2i	0.692473	−	1.19940i	0.971025	−	0.238978i	$-0.0768123\pi$
$770$	992.405	+	6300.99i	0.0464465	+	0.294899i
$771$		0			0
$772$	13547.8			0.631602
$773$	4375.97	+	7579.41i	0.203613	+	0.352668i	0.949690	−	0.313192i	$-0.101398\pi$
$773$	4375.97	+	7579.41i	0.203613	+	0.352668i	−0.746077	+	0.665860i	$0.768065\pi$
$774$		0			0
$775$	−7743.67	+	13412.4i	−0.358917	+	0.621663i
$776$	−1217.33	−	2108.49i	−0.0563141	−	0.0975390i
$777$		0			0
$778$	−8996.51	+	15582.4i	−0.414576	+	0.718067i
$779$	−4743.50	−	8215.98i	−0.218169	−	0.377879i
$780$		0			0
$781$	−5110.78	+	8852.13i	−0.234159	+	0.405575i
$782$	−4399.07	+	7619.42i	−0.201164	+	0.348427i
$783$		0			0
$784$	25924.9	−	8374.05i	1.18098	−	0.381471i
$785$	7149.89	+	12384.0i	0.325083	+	0.563061i
$786$		0			0
$787$	−2046.89			−0.0927114			−0.0463557	−	0.998925i	$-0.514761\pi$
$787$	−2046.89			−0.0927114			−0.0463557	+	0.998925i	$0.514761\pi$
$788$	3743.17			0.169220
$789$		0			0
$790$	−5354.14	−	9273.64i	−0.241129	−	0.417647i
$791$	29433.1	+	11327.5i	1.32304	+	0.509177i
$792$		0			0
$793$	11862.6	−	20546.6i	0.531213	−	0.920088i
$794$	741.552	−	1284.41i	0.0331445	−	0.0574079i
$795$		0			0
$796$	−7324.19	−	12685.9i	−0.326129	−	0.564872i
$797$	3863.18	−	6691.23i	0.171695	−	0.297385i	−0.767317	−	0.641267i	$-0.778409\pi$
$797$	3863.18	−	6691.23i	0.171695	−	0.297385i	0.939013	+	0.343883i	$0.111742\pi$
$798$		0			0
$799$	−5145.52	−	8912.29i	−0.227829	−	0.394611i
$800$	3412.83	−	5911.19i	0.150827	−	0.261240i
$801$		0			0
$802$	8864.71	+	15354.1i	0.390304	+	0.676026i
$803$	−6685.59			−0.293810
$804$		0			0
$805$	8756.54	+	3369.99i	0.383388	+	0.147549i
$806$	28058.5	−	48598.8i	1.22620	−	2.12385i
$807$		0			0
$808$	−1347.74	+	2334.36i	−0.0586799	+	0.101637i
$809$	2509.49	+	4346.56i	0.109059	+	0.188896i	0.915389	−	0.402570i	$-0.131883\pi$
$809$	2509.49	+	4346.56i	0.109059	+	0.188896i	−0.806330	+	0.591466i	$0.798550\pi$
$810$		0			0
$811$	−26696.2			−1.15589			−0.577947	−	0.816074i	$-0.696146\pi$
$811$	−26696.2			−1.15589			−0.577947	+	0.816074i	$0.696146\pi$
$812$	−3429.22	+	2772.03i	−0.148205	+	0.119802i
$813$		0			0
$814$	7489.84	+	12972.8i	0.322505	+	0.558594i
$815$	4325.76			0.185920
$816$		0			0
$817$	−3077.98			−0.131805
$818$	−17991.2			−0.769006
$819$		0			0
$820$	10233.2			0.435805
$821$	42056.0			1.78778			0.893889	−	0.448288i	$-0.147966\pi$
$821$	42056.0			1.78778			0.893889	+	0.448288i	$0.147966\pi$
$822$		0			0
$823$	−15456.8			−0.654668			−0.327334	−	0.944909i	$-0.606150\pi$
$823$	−15456.8			−0.654668			−0.327334	+	0.944909i	$0.606150\pi$
$824$	−8173.83	−	14157.5i	−0.345569	−	0.598543i
$825$		0			0
$826$	−5571.59	−	35375.2i	−0.234698	−	1.49015i
$827$	−7902.10			−0.332265			−0.166132	−	0.986103i	$-0.553128\pi$
$827$	−7902.10			−0.332265			−0.166132	+	0.986103i	$0.553128\pi$
$828$		0			0
$829$	4549.18	+	7879.41i	0.190591	+	0.330113i	0.945446	−	0.325779i	$-0.105626\pi$
$829$	4549.18	+	7879.41i	0.190591	+	0.330113i	−0.754856	+	0.655891i	$0.772293\pi$
$830$	−14912.9	+	25829.9i	−0.623655	+	1.08020i
$831$		0			0
$832$	4524.02	−	7835.83i	0.188512	−	0.326513i
$833$	−11476.2	−	10369.1i	−0.477341	−	0.431294i
$834$		0			0
$835$	9555.29			0.396017
$836$	−500.926	−	867.629i	−0.0207235	−	0.0358942i
$837$		0			0
$838$	11400.4	−	19746.1i	0.469954	−	0.813985i
$839$	6085.37	+	10540.2i	0.250406	+	0.433715i	0.963638	−	0.267213i	$-0.0861026\pi$
$839$	6085.37	+	10540.2i	0.250406	+	0.433715i	−0.713232	+	0.700928i	$0.752769\pi$
$840$		0			0
$841$	9500.51	−	16455.4i	0.389541	−	0.674704i
$842$	6495.49	+	11250.5i	0.265854	+	0.460473i
$843$		0			0
$844$	451.615	−	782.220i	0.0184185	−	0.0319018i
$845$	−2738.98	+	4744.06i	−0.111508	+	0.193137i
$846$		0			0
$847$	17165.8	−	13876.1i	0.696369	−	0.562914i
$848$	24429.0	+	42312.3i	0.989264	+	1.71346i
$849$		0			0
$850$	−7438.62			−0.300168
$851$	22034.2			0.887571
$852$		0			0
$853$	6487.96	+	11237.5i	0.260426	+	0.451071i	0.966355	−	0.257211i	$-0.0828037\pi$
$853$	6487.96	+	11237.5i	0.260426	+	0.451071i	−0.705929	+	0.708282i	$0.749470\pi$
$854$	4311.89	+	27377.1i	0.172775	+	1.09699i
$855$		0			0
$856$	−1647.79	+	2854.06i	−0.0657948	+	0.113960i
$857$	22576.8	−	39104.2i	0.899895	−	1.55866i	0.0722684	−	0.997385i	$-0.476976\pi$
$857$	22576.8	−	39104.2i	0.899895	−	1.55866i	0.827627	−	0.561279i	$-0.189690\pi$
$858$		0			0
$859$	9001.57	+	15591.2i	0.357543	+	0.619283i	0.987550	−	0.157307i	$-0.0502812\pi$
$859$	9001.57	+	15591.2i	0.357543	+	0.619283i	−0.630007	+	0.776590i	$0.716948\pi$
$860$	1660.05	−	2875.29i	0.0658224	−	0.114008i
$861$		0			0
$862$	8337.92	+	14441.7i	0.329455	+	0.570634i
$863$	24467.7	−	42379.3i	0.965110	−	1.67162i	0.255792	−	0.966732i	$-0.417664\pi$
$863$	24467.7	−	42379.3i	0.965110	−	1.67162i	0.709318	−	0.704888i	$-0.249003\pi$
$864$		0			0
$865$	14861.3	+	25740.6i	0.584162	+	1.01180i
$866$	15165.2			0.595073
$867$		0			0
$868$	2942.24	+	18680.9i	0.115053	+	0.730496i
$869$	2163.60	−	3747.46i	0.0844592	−	0.146288i
$870$		0			0
$871$	7913.20	−	13706.1i	0.307840	−	0.533194i
$872$	−10823.5	−	18746.8i	−0.420331	−	0.728034i
$873$		0			0
$874$	−5108.29			−0.197701
$875$	4370.09	+	27746.6i	0.168841	+	1.07201i
$876$		0			0
$877$	−16521.8	−	28616.6i	−0.636148	−	1.10184i	−0.986271	−	0.165137i	$-0.947193\pi$
$877$	−16521.8	−	28616.6i	−0.636148	−	1.10184i	0.350123	−	0.936704i	$-0.386140\pi$
$878$	28363.6			1.09023
$879$		0			0
$880$	−8158.35			−0.312520
$881$	−31827.5			−1.21713			−0.608567	−	0.793502i	$-0.708255\pi$
$881$	−31827.5			−1.21713			−0.608567	+	0.793502i	$0.708255\pi$
$882$		0			0
$883$	−24000.9			−0.914716			−0.457358	−	0.889283i	$-0.651204\pi$
$883$	−24000.9			−0.914716			−0.457358	+	0.889283i	$0.651204\pi$
$884$	7775.61			0.295839
$885$		0			0
$886$	33678.0			1.27701
$887$	6874.62	+	11907.2i	0.260233	+	0.450738i	0.966304	−	0.257404i	$-0.0828671\pi$
$887$	6874.62	+	11907.2i	0.260233	+	0.450738i	−0.706070	+	0.708142i	$0.749534\pi$
$888$		0			0
$889$	7142.67	+	45350.3i	0.269468	+	1.71091i
$890$	14423.2			0.543220
$891$		0			0
$892$	−4714.02	−	8164.93i	−0.176947	−	0.306482i
$893$	2987.54	−	5174.56i	0.111953	−	0.193908i
$894$		0			0
$895$	1168.74	−	2024.32i	0.0436499	−	0.0756039i
$896$	4842.63	+	30746.9i	0.180559	+	1.14641i
$897$		0			0
$898$	−12561.5			−0.466797
$899$	11553.8	+	20011.8i	0.428633	+	0.742415i
$900$		0			0
$901$	13868.8	−	24021.4i	0.512803	−	0.888201i
$902$	7167.17	+	12413.9i	0.264568	+	0.458246i
$903$		0			0
$904$	−13579.4	+	23520.3i	−0.499608	+	0.865346i
$905$	−13792.5	−	23889.4i	−0.506608	−	0.877470i
$906$		0			0
$907$	4173.10	−	7228.03i	0.152774	−	0.264612i	−0.779473	−	0.626436i	$-0.784513\pi$
$907$	4173.10	−	7228.03i	0.152774	−	0.264612i	0.932246	+	0.361825i	$0.117846\pi$
$908$	1484.24	−	2570.78i	0.0542470	−	0.0939586i
$909$		0			0
$910$	−4472.02	−	28393.8i	−0.162908	−	1.03434i
$911$	−23902.6	−	41400.5i	−0.869296	−	1.50567i	−0.862717	−	0.505687i	$-0.831239\pi$
$911$	−23902.6	−	41400.5i	−0.869296	−	1.50567i	−0.00657938	−	0.999978i	$-0.502094\pi$
$912$		0			0
$913$	−12052.5			−0.436891
$914$	−23444.4			−0.848436
$915$		0			0
$916$	−5101.86	−	8836.67i	−0.184028	−	0.318747i
$917$	−2512.18	+	2030.73i	−0.0904683	+	0.0731306i
$918$		0			0
$919$	13868.9	−	24021.6i	0.497815	−	0.862241i	−0.502182	−	0.864762i	$-0.667469\pi$
$919$	13868.9	−	24021.6i	0.497815	−	0.862241i	0.999997	+	0.00252097i	$0.000802450\pi$
$920$	−4039.96	+	6997.42i	−0.144776	+	0.250759i
$921$		0			0
$922$	9477.09	+	16414.8i	0.338516	+	0.586326i
$923$	23030.4	−	39889.9i	0.821296	−	1.42253i
$924$		0			0
$925$	9314.71	+	16133.5i	0.331098	+	0.573479i
$926$	15171.5	−	26277.7i	0.538407	−	0.932548i
$927$		0			0
$928$	−5092.06	−	8819.70i	−0.180124	−	0.311984i
$929$	−47047.7			−1.66156			−0.830778	−	0.556604i	$-0.812104\pi$
$929$	−47047.7			−1.66156			−0.830778	+	0.556604i	$0.812104\pi$
$930$		0			0
$931$	1882.24	−	8780.67i	0.0662597	−	0.309103i
$932$	5210.98	−	9025.69i	0.183145	−	0.317217i
$933$		0			0
$934$	−10626.8	+	18406.2i	−0.372291	+	0.644828i
$935$	2315.82	+	4011.11i	0.0810004	+	0.140297i
$936$		0			0
$937$	−39433.8			−1.37486			−0.687431	−	0.726250i	$-0.741262\pi$
$937$	−39433.8			−1.37486			−0.687431	+	0.726250i	$0.741262\pi$
$938$	2876.35	+	18262.5i	0.100124	+	0.635707i
$939$		0			0
$940$	3222.54	+	5581.60i	0.111817	+	0.193672i
$941$	−17203.5			−0.595980			−0.297990	−	0.954569i	$-0.596316\pi$
$941$	−17203.5			−0.595980			−0.297990	+	0.954569i	$0.596316\pi$
$942$		0			0
$943$	21085.0			0.728124
$944$	45802.9			1.57919
$945$		0			0
$946$	4650.67			0.159837
$947$	14674.6			0.503549			0.251774	−	0.967786i	$-0.418986\pi$
$947$	14674.6			0.503549			0.251774	+	0.967786i	$0.418986\pi$
$948$		0			0
$949$	30126.9			1.03052
$950$	−2159.47	−	3740.31i	−0.0737499	−	0.127739i
$951$		0			0
$952$	10358.3	−	8373.18i	0.352641	−	0.285059i
$953$	−9270.99			−0.315128			−0.157564	−	0.987509i	$-0.550364\pi$
$953$	−9270.99			−0.315128			−0.157564	+	0.987509i	$0.550364\pi$
$954$		0			0
$955$	11508.9	+	19934.0i	0.389967	+	0.675443i
$956$	10401.8	−	18016.4i	0.351902	−	0.609512i
$957$		0			0
$958$	−7835.80	+	13572.0i	−0.264262	+	0.457715i
$959$	−40581.2	−	15617.9i	−1.36646	−	0.525888i
$960$		0			0
$961$	69311.4			2.32659
$962$	−33751.1	−	58458.6i	−1.13116	−	1.95923i
$963$		0			0
$964$	2232.49	−	3866.79i	0.0745888	−	0.129192i
$965$	−18182.5	−	31493.1i	−0.606546	−	1.05057i
$966$		0			0
$967$	−16803.5	+	29104.6i	−0.558806	+	0.967880i	0.438791	+	0.898589i	$0.355407\pi$
$967$	−16803.5	+	29104.6i	−0.558806	+	0.967880i	−0.997596	+	0.0692909i	$0.977926\pi$
$968$	9504.11	+	16461.6i	0.315572	+	0.546587i
$969$		0			0
$970$	2228.32	−	3859.56i	0.0737599	−	0.127756i
$971$	−7193.08	+	12458.8i	−0.237731	+	0.411763i	−0.960063	−	0.279784i	$-0.909737\pi$
$971$	−7193.08	+	12458.8i	−0.237731	+	0.411763i	0.722332	+	0.691547i	$0.243070\pi$
$972$		0			0
$973$	−7545.89	−	2904.07i	−0.248623	−	0.0956837i
$974$	16036.8	+	27776.5i	0.527568	+	0.913774i
$975$		0			0
$976$	−35447.2			−1.16254
$977$	−9092.67			−0.297749			−0.148874	−	0.988856i	$-0.547565\pi$
$977$	−9092.67			−0.297749			−0.148874	+	0.988856i	$0.547565\pi$
$978$		0			0
$979$	2914.19	+	5047.53i	0.0951358	+	0.164780i
$980$	7187.29	+	6493.97i	0.234275	+	0.211676i
$981$		0			0
$982$	−8446.26	+	14629.3i	−0.274471	+	0.475398i
$983$	5804.46	−	10053.6i	0.188335	−	0.326206i	−0.756360	−	0.654155i	$-0.773024\pi$
$983$	5804.46	−	10053.6i	0.188335	−	0.326206i	0.944695	+	0.327949i	$0.106358\pi$
$984$		0			0
$985$	−5023.72	−	8701.33i	−0.162507	−	0.281470i
$986$	−5549.34	+	9611.73i	−0.179236	+	0.310446i
$987$		0			0
$988$	2257.30	+	3909.75i	0.0726864	+	0.125897i
$989$	3420.43	−	5924.35i	0.109973	−	0.190479i
$990$		0			0
$991$	27469.9	+	47579.2i	0.880534	+	1.52513i	0.850749	+	0.525573i	$0.176149\pi$
$991$	27469.9	+	47579.2i	0.880534	+	1.52513i	0.0297852	+	0.999556i	$0.490518\pi$
$992$	−43676.9			−1.39793
$993$		0			0
$994$	8371.27	+	53151.0i	0.267123	+	1.69602i
$995$	−19659.6	+	34051.4i	−0.626383	+	1.08493i
$996$		0			0
$997$	4572.73	−	7920.20i	0.145255	−	0.251590i	−0.784213	−	0.620492i	$-0.786933\pi$
$997$	4572.73	−	7920.20i	0.145255	−	0.251590i	0.929468	+	0.368902i	$0.120266\pi$
$998$	−19771.6	−	34245.3i	−0.627112	−	1.08619i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.h.a.37.6		44
3.2	odd	2		63.4.h.a.58.17	yes	44
7.4	even	3		189.4.g.a.172.17		44
9.2	odd	6		63.4.g.a.16.6	yes	44
9.7	even	3		189.4.g.a.100.17		44
21.11	odd	6		63.4.g.a.4.6	✓	44
63.11	odd	6		63.4.h.a.25.17	yes	44
63.25	even	3	inner	189.4.h.a.46.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.6	✓	44	21.11	odd	6
63.4.g.a.16.6	yes	44	9.2	odd	6
63.4.h.a.25.17	yes	44	63.11	odd	6
63.4.h.a.58.17	yes	44	3.2	odd	2
189.4.g.a.100.17		44	9.7	even	3
189.4.g.a.172.17		44	7.4	even	3
189.4.h.a.37.6		44	1.1	even	1	trivial
189.4.h.a.46.6		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)

\(f(q)\)	\(=\)	\(q-3.35315 q^{2} +3.24362 q^{4} +(-4.35326 - 7.54007i) q^{5} +(-2.88142 - 18.2947i) q^{7} +15.9489 q^{8} +O(q^{10})\)	\(q-3.35315 q^{2} +3.24362 q^{4} +(-4.35326 - 7.54007i) q^{5} +(-2.88142 - 18.2947i) q^{7} +15.9489 q^{8} +(14.5971 + 25.2830i) q^{10} +(-5.89868 + 10.2168i) q^{11} +(26.5809 - 46.0395i) q^{13} +(9.66183 + 61.3450i) q^{14} -79.4279 q^{16} +(22.5463 + 39.0513i) q^{17} +(-13.0906 + 22.6736i) q^{19} +(-14.1203 - 24.4571i) q^{20} +(19.7792 - 34.2585i) q^{22} +(-29.0940 - 50.3923i) q^{23} +(24.5983 - 42.6055i) q^{25} +(-89.1298 + 154.377i) q^{26} +(-9.34621 - 59.3411i) q^{28} +(-36.7015 - 63.5688i) q^{29} -314.805 q^{31} +138.743 q^{32} +(-75.6011 - 130.945i) q^{34} +(-125.400 + 101.368i) q^{35} +(-189.337 + 327.941i) q^{37} +(43.8947 - 76.0279i) q^{38} +(-69.4296 - 120.256i) q^{40} +(-181.180 + 313.812i) q^{41} +(58.7824 + 101.814i) q^{43} +(-19.1331 + 33.1394i) q^{44} +(97.5565 + 168.973i) q^{46} -228.220 q^{47} +(-326.395 + 105.430i) q^{49} +(-82.4817 + 142.863i) q^{50} +(86.2183 - 149.334i) q^{52} +(-307.562 - 532.713i) q^{53} +102.714 q^{55} +(-45.9554 - 291.780i) q^{56} +(123.065 + 213.156i) q^{58} -576.660 q^{59} +446.281 q^{61} +1055.59 q^{62} +170.198 q^{64} -462.854 q^{65} +297.702 q^{67} +(73.1315 + 126.667i) q^{68} +(420.485 - 339.901i) q^{70} +866.428 q^{71} +(283.351 + 490.778i) q^{73} +(634.874 - 1099.63i) q^{74} +(-42.4608 + 73.5443i) q^{76} +(203.911 + 78.4759i) q^{77} -366.794 q^{79} +(345.770 + 598.891i) q^{80} +(607.523 - 1052.26i) q^{82} +(510.815 + 884.758i) q^{83} +(196.300 - 340.001i) q^{85} +(-197.106 - 341.398i) q^{86} +(-94.0773 + 162.947i) q^{88} +(247.021 - 427.852i) q^{89} +(-918.871 - 353.632i) q^{91} +(-94.3697 - 163.453i) q^{92} +765.257 q^{94} +227.947 q^{95} +(-76.3273 - 132.203i) q^{97} +(1094.45 - 353.521i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 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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