LMFDB - Embedded newform 189.4.s.a.17.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(17,189)]

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([5, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.s (of order $6$, 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 $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.16
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.65116 + 1.53065i) q^{2} +(0.685763 + 1.18778i) q^{4} -5.50223 q^{5} +(-18.4916 - 1.02989i) q^{7} -20.2917i q^{8} +O(q^{10})$	\(q+(2.65116 + 1.53065i) q^{2} +(0.685763 + 1.18778i) q^{4} -5.50223 q^{5} +(-18.4916 - 1.02989i) q^{7} -20.2917i q^{8} +(-14.5873 - 8.42197i) q^{10} -59.4170i q^{11} +(12.7466 + 7.35927i) q^{13} +(-47.4478 - 31.0345i) q^{14} +(36.5456 - 63.2988i) q^{16} +(29.3070 - 50.7613i) q^{17} +(-66.1714 + 38.2041i) q^{19} +(-3.77322 - 6.53541i) q^{20} +(90.9465 - 157.524i) q^{22} -26.0925i q^{23} -94.7255 q^{25} +(22.5289 + 39.0212i) q^{26} +(-11.4576 - 22.6701i) q^{28} +(-217.541 + 125.597i) q^{29} +(190.447 - 109.955i) q^{31} +(53.1911 - 30.7099i) q^{32} +(155.395 - 89.7174i) q^{34} +(101.745 + 5.66667i) q^{35} +(-97.2240 - 168.397i) q^{37} -233.908 q^{38} +111.650i q^{40} +(-37.6465 + 65.2056i) q^{41} +(210.991 + 365.447i) q^{43} +(70.5741 - 40.7460i) q^{44} +(39.9385 - 69.1755i) q^{46} +(191.626 - 331.907i) q^{47} +(340.879 + 38.0885i) q^{49} +(-251.132 - 144.991i) q^{50} +20.1869i q^{52} +(-92.7384 - 53.5426i) q^{53} +326.926i q^{55} +(-20.8982 + 375.226i) q^{56} -768.979 q^{58} +(266.985 + 462.431i) q^{59} +(35.7367 + 20.6326i) q^{61} +673.209 q^{62} -396.705 q^{64} +(-70.1349 - 40.4924i) q^{65} +(-166.519 - 288.420i) q^{67} +80.3906 q^{68} +(261.069 + 170.759i) q^{70} -500.325i q^{71} +(351.906 + 203.173i) q^{73} -595.262i q^{74} +(-90.7557 - 52.3978i) q^{76} +(-61.1928 + 1098.72i) q^{77} +(-75.1067 + 130.089i) q^{79} +(-201.082 + 348.284i) q^{80} +(-199.614 + 115.247i) q^{82} +(-493.101 - 854.077i) q^{83} +(-161.254 + 279.300i) q^{85} +1291.81i q^{86} -1205.67 q^{88} +(-311.609 - 539.722i) q^{89} +(-228.126 - 149.212i) q^{91} +(30.9921 - 17.8933i) q^{92} +(1016.06 - 586.625i) q^{94} +(364.090 - 210.208i) q^{95} +(-407.846 + 235.470i) q^{97} +(845.423 + 622.744i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.65116	+	1.53065i	0.937326	+	0.541166i	0.889121	−	0.457672i	$-0.151317\pi$
$2$	2.65116	+	1.53065i	0.937326	+	0.541166i	0.0482051	+	0.998837i	$0.484650\pi$
$3$		0			0
$3$		0			0
$4$	0.685763	+	1.18778i	0.0857203	+	0.148472i
$5$	−5.50223			−0.492134			−0.246067	−	0.969253i	$-0.579138\pi$
$5$	−5.50223			−0.492134			−0.246067	+	0.969253i	$0.579138\pi$
$6$		0			0
$7$	−18.4916	−	1.02989i	−0.998453	−	0.0556087i
$7$	−18.4916	−	1.02989i	−0.998453	−	0.0556087i
$8$		−	20.2917i		−	0.896776i
$9$		0			0
$10$	−14.5873	−	8.42197i	−0.461290	−	0.266326i
$11$		−	59.4170i		−	1.62863i	−0.580425	−	0.814314i	$-0.697114\pi$
$11$		−	59.4170i		−	1.62863i	0.580425	−	0.814314i	$-0.302886\pi$
$12$		0			0
$13$	12.7466	+	7.35927i	0.271945	+	0.157007i	0.629771	−	0.776781i	$-0.283149\pi$
$13$	12.7466	+	7.35927i	0.271945	+	0.157007i	−0.357826	+	0.933788i	$0.616482\pi$
$14$	−47.4478	−	31.0345i	−0.905782	−	0.592452i
$15$		0			0
$16$	36.5456	−	63.2988i	0.571024	−	0.989043i
$17$	29.3070	−	50.7613i	0.418117	−	0.724201i	−0.577633	−	0.816297i	$-0.696023\pi$
$17$	29.3070	−	50.7613i	0.418117	−	0.724201i	0.995750	+	0.0920961i	$0.0293567\pi$
$18$		0			0
$19$	−66.1714	+	38.2041i	−0.798987	+	0.461296i	−0.843117	−	0.537730i	$-0.819282\pi$
$19$	−66.1714	+	38.2041i	−0.798987	+	0.461296i	0.0441297	+	0.999026i	$0.485949\pi$
$20$	−3.77322	−	6.53541i	−0.0421859	−	0.0730681i
$21$		0			0
$22$	90.9465	−	157.524i	0.881357	−	1.52656i
$23$		−	26.0925i		−	0.236551i	−0.992981	−	0.118275i	$-0.962263\pi$
$23$		−	26.0925i		−	0.236551i	0.992981	−	0.118275i	$-0.0377366\pi$
$24$		0			0
$25$	−94.7255			−0.757804
$26$	22.5289	+	39.0212i	0.169934	+	0.294334i
$27$		0			0
$28$	−11.4576	−	22.6701i	−0.0773314	−	0.153009i
$29$	−217.541	+	125.597i	−1.39297	+	0.804234i	−0.993643	−	0.112573i	$-0.964091\pi$
$29$	−217.541	+	125.597i	−1.39297	+	0.804234i	−0.399331	+	0.916807i	$0.630758\pi$
$30$		0			0
$31$	190.447	−	109.955i	1.10340	−	0.637048i	0.166287	−	0.986077i	$-0.446822\pi$
$31$	190.447	−	109.955i	1.10340	−	0.637048i	0.937112	+	0.349030i	$0.113489\pi$
$32$	53.1911	−	30.7099i	0.293842	−	0.169650i
$33$		0			0
$34$	155.395	−	89.7174i	0.783825	−	0.452542i
$35$	101.745	+	5.66667i	0.491373	+	0.0273669i
$36$		0			0
$37$	−97.2240	−	168.397i	−0.431987	−	0.748223i	0.565057	−	0.825052i	$-0.308854\pi$
$37$	−97.2240	−	168.397i	−0.431987	−	0.748223i	−0.997044	+	0.0768282i	$0.975521\pi$
$38$	−233.908			−0.998549
$39$		0			0
$40$			111.650i			0.441334i
$41$	−37.6465	+	65.2056i	−0.143400	+	0.248376i	−0.928775	−	0.370645i	$-0.879137\pi$
$41$	−37.6465	+	65.2056i	−0.143400	+	0.248376i	0.785375	+	0.619020i	$0.212470\pi$
$42$		0			0
$43$	210.991	+	365.447i	0.748275	+	1.29605i	0.948649	+	0.316330i	$0.102451\pi$
$43$	210.991	+	365.447i	0.748275	+	1.29605i	−0.200375	+	0.979719i	$0.564216\pi$
$44$	70.5741	−	40.7460i	0.241806	−	0.139606i
$45$		0			0
$46$	39.9385	−	69.1755i	0.128013	−	0.221725i
$47$	191.626	−	331.907i	0.594715	−	1.03008i	−0.398872	−	0.917006i	$-0.630598\pi$
$47$	191.626	−	331.907i	0.594715	−	1.03008i	0.993587	−	0.113070i	$-0.0360683\pi$
$48$		0			0
$49$	340.879	+	38.0885i	0.993815	+	0.111045i
$50$	−251.132	−	144.991i	−0.710309	−	0.410097i
$51$		0			0
$52$			20.1869i			0.0538349i
$53$	−92.7384	−	53.5426i	−0.240351	−	0.138767i	0.374987	−	0.927030i	$-0.377647\pi$
$53$	−92.7384	−	53.5426i	−0.240351	−	0.138767i	−0.615338	+	0.788263i	$0.710980\pi$
$54$		0			0
$55$			326.926i			0.801503i
$56$	−20.8982	+	375.226i	−0.0498685	+	0.895388i
$57$		0			0
$58$	−768.979			−1.74090
$59$	266.985	+	462.431i	0.589126	+	1.02040i	0.994347	+	0.106177i	$0.0338611\pi$
$59$	266.985	+	462.431i	0.589126	+	1.02040i	−0.405221	+	0.914219i	$0.632806\pi$
$60$		0			0
$61$	35.7367	+	20.6326i	0.0750101	+	0.0433071i	0.537036	−	0.843559i	$-0.319544\pi$
$61$	35.7367	+	20.6326i	0.0750101	+	0.0433071i	−0.462026	+	0.886866i	$0.652877\pi$
$62$	673.209			1.37899
$63$		0			0
$64$	−396.705			−0.774815
$65$	−70.1349	−	40.4924i	−0.133833	−	0.0772687i
$66$		0			0
$67$	−166.519	−	288.420i	−0.303636	−	0.525912i	0.673321	−	0.739350i	$-0.264867\pi$
$67$	−166.519	−	288.420i	−0.303636	−	0.525912i	−0.976957	+	0.213438i	$0.931534\pi$
$68$	80.3906			0.143365
$69$		0			0
$70$	261.069	+	170.759i	0.445767	+	0.291566i
$71$		−	500.325i		−	0.836305i	−0.908377	−	0.418153i	$-0.862678\pi$
$71$		−	500.325i		−	0.836305i	0.908377	−	0.418153i	$-0.137322\pi$
$72$		0			0
$73$	351.906	+	203.173i	0.564213	+	0.325748i	0.754835	−	0.655915i	$-0.227717\pi$
$73$	351.906	+	203.173i	0.564213	+	0.325748i	−0.190622	+	0.981664i	$0.561050\pi$
$74$		−	595.262i		−	0.935106i
$75$		0			0
$76$	−90.7557	−	52.3978i	−0.136979	−	0.0790848i
$77$	−61.1928	+	1098.72i	−0.0905658	+	1.62611i
$78$		0			0
$79$	−75.1067	+	130.089i	−0.106964	+	0.185267i	−0.914539	−	0.404498i	$-0.867446\pi$
$79$	−75.1067	+	130.089i	−0.106964	+	0.185267i	0.807575	+	0.589765i	$0.200780\pi$
$80$	−201.082	+	348.284i	−0.281021	+	0.486742i
$81$		0			0
$82$	−199.614	+	115.247i	−0.268825	+	0.155206i
$83$	−493.101	−	854.077i	−0.652107	−	1.12948i	−0.982611	−	0.185678i	$-0.940552\pi$
$83$	−493.101	−	854.077i	−0.652107	−	1.12948i	0.330503	−	0.943805i	$-0.392782\pi$
$84$		0			0
$85$	−161.254	+	279.300i	−0.205770	+	0.356404i
$86$			1291.81i			1.61976i
$87$		0			0
$88$	−1205.67			−1.46051
$89$	−311.609	−	539.722i	−0.371129	−	0.642814i	0.618611	−	0.785698i	$-0.287696\pi$
$89$	−311.609	−	539.722i	−0.371129	−	0.642814i	−0.989739	+	0.142884i	$0.954362\pi$
$90$		0			0
$91$	−228.126	−	149.212i	−0.262793	−	0.171887i
$92$	30.9921	−	17.8933i	0.0351212	−	0.0202772i
$93$		0			0
$94$	1016.06	−	586.625i	1.11488	−	0.643678i
$95$	364.090	−	210.208i	0.393209	−	0.227019i
$96$		0			0
$97$	−407.846	+	235.470i	−0.426912	+	0.246478i	−0.698030	−	0.716068i	$-0.745940\pi$
$97$	−407.846	+	235.470i	−0.426912	+	0.246478i	0.271118	+	0.962546i	$0.412607\pi$
$98$	845.423	+	622.744i	0.871435	+	0.641904i
$99$		0			0
$100$	−64.9592	−	112.513i	−0.0649592	−	0.112513i
$101$	1201.60			1.18380			0.591898	−	0.806013i	$-0.298379\pi$
$101$	1201.60			1.18380			0.591898	+	0.806013i	$0.298379\pi$
$102$		0			0
$103$			1020.81i			0.976539i	0.872693	+	0.488269i	$0.162372\pi$
$103$			1020.81i			0.976539i	−0.872693	+	0.488269i	$0.837628\pi$
$104$	149.332	−	258.651i	0.140800	−	0.243873i
$105$		0			0
$106$	−163.910	−	283.900i	−0.150192	−	0.260139i
$107$	−225.733	+	130.327i	−0.203948	+	0.117750i	−0.598496	−	0.801126i	$-0.704235\pi$
$107$	−225.733	+	130.327i	−0.203948	+	0.117750i	0.394548	+	0.918876i	$0.370901\pi$
$108$		0			0
$109$	1029.70	−	1783.50i	0.904840	−	1.56723i	0.0837089	−	0.996490i	$-0.473323\pi$
$109$	1029.70	−	1783.50i	0.904840	−	1.56723i	0.821131	−	0.570739i	$-0.193343\pi$
$110$	−500.408	+	866.733i	−0.433746	+	0.751270i
$111$		0			0
$112$	−740.977	+	1132.86i	−0.625140	+	0.955759i
$113$	141.454	+	81.6684i	0.117760	+	0.0679886i	0.557723	−	0.830027i	$-0.311675\pi$
$113$	141.454	+	81.6684i	0.117760	+	0.0679886i	−0.439963	+	0.898016i	$0.645009\pi$
$114$		0			0
$115$			143.567i			0.116415i
$116$	−298.362	−	172.260i	−0.238812	−	0.137878i
$117$		0			0
$118$			1634.64i			1.27526i
$119$	−594.212	+	908.474i	−0.457742	+	0.699829i
$120$		0			0
$121$	−2199.38			−1.65243
$122$	63.1625	+	109.401i	0.0468726	+	0.0811858i
$123$		0			0
$124$	261.203	+	150.806i	0.189167	+	0.109216i
$125$	1208.98			0.865075
$126$		0			0
$127$	2368.78			1.65508			0.827539	−	0.561408i	$-0.189740\pi$
$127$	2368.78			1.65508			0.827539	+	0.561408i	$0.189740\pi$
$128$	−1477.26	−	852.894i	−1.02010	−	0.588953i
$129$		0			0
$130$	−123.959	−	214.704i	−0.0836303	−	0.144852i
$131$	−881.350			−0.587816			−0.293908	−	0.955834i	$-0.594956\pi$
$131$	−881.350			−0.587816			−0.293908	+	0.955834i	$0.594956\pi$
$132$		0			0
$133$	1262.96	−	638.305i	0.823403	−	0.416151i
$134$		−	1019.53i		−	0.657269i
$135$		0			0
$136$	−1030.03	−	594.690i	−0.649446	−	0.374958i
$137$		−	1216.43i		−	0.758588i	−0.925276	−	0.379294i	$-0.876167\pi$
$137$		−	1216.43i		−	0.758588i	0.925276	−	0.379294i	$-0.123833\pi$
$138$		0			0
$139$	2303.79	+	1330.09i	1.40579	+	0.811634i	0.994979	−	0.100086i	$-0.0319119\pi$
$139$	2303.79	+	1330.09i	1.40579	+	0.811634i	0.410812	+	0.911720i	$0.365245\pi$
$140$	63.0422	+	124.736i	0.0380574	+	0.0753010i
$141$		0			0
$142$	765.821	−	1326.44i	0.452580	−	0.783891i
$143$	437.266	−	757.367i	0.255706	−	0.442896i
$144$		0			0
$145$	1196.96	−	691.064i	0.685530	−	0.395791i
$146$	621.973	+	1077.29i	0.352568	+	0.610665i
$147$		0			0
$148$	133.345	−	230.961i	0.0740601	−	0.128276i
$149$		−	989.826i		−	0.544226i	−0.962265	−	0.272113i	$-0.912277\pi$
$149$		−	989.826i		−	0.544226i	0.962265	−	0.272113i	$-0.0877225\pi$
$150$		0			0
$151$	982.760			0.529641			0.264821	−	0.964298i	$-0.414687\pi$
$151$	982.760			0.529641			0.264821	+	0.964298i	$0.414687\pi$
$152$	775.226	+	1342.73i	0.413679	+	0.716512i
$153$		0			0
$154$	−1843.98	+	2819.21i	−0.964883	+	1.47518i
$155$	−1047.89	+	604.997i	−0.543020	+	0.313513i
$156$		0			0
$157$	−576.402	+	332.786i	−0.293006	+	0.169167i	−0.639297	−	0.768960i	$-0.720774\pi$
$157$	−576.402	+	332.786i	−0.293006	+	0.169167i	0.346291	+	0.938127i	$0.387441\pi$
$158$	−398.240	+	229.924i	−0.200520	+	0.115771i
$159$		0			0
$160$	−292.669	+	168.973i	−0.144610	+	0.0834904i
$161$	−26.8724	+	482.493i	−0.0131543	+	0.236185i
$162$		0			0
$163$	462.170	+	800.502i	0.222086	+	0.384663i	0.955441	−	0.295182i	$-0.0953803\pi$
$163$	462.170	+	800.502i	0.222086	+	0.384663i	−0.733356	+	0.679845i	$0.762047\pi$
$164$	−103.266			−0.0491691
$165$		0			0
$166$		−	3019.06i		−	1.41159i
$167$	925.982	−	1603.85i	0.429070	−	0.743171i	−0.567721	−	0.823221i	$-0.692175\pi$
$167$	925.982	−	1603.85i	0.429070	−	0.743171i	0.996791	+	0.0800504i	$0.0255081\pi$
$168$		0			0
$169$	−990.182	−	1715.05i	−0.450697	−	0.780631i
$170$	−855.020	+	493.646i	−0.385747	+	0.222711i
$171$		0			0
$172$	−289.379	+	501.220i	−0.128285	+	0.222196i
$173$	738.631	−	1279.35i	0.324607	−	0.562236i	−0.656825	−	0.754043i	$-0.728101\pi$
$173$	738.631	−	1279.35i	0.324607	−	0.562236i	0.981433	+	0.191806i	$0.0614345\pi$
$174$		0			0
$175$	1751.63	+	97.5565i	0.756631	+	0.0421405i
$176$	−3761.02	−	2171.43i	−1.61078	−	0.929986i
$177$		0			0
$178$		−	1907.85i		−	0.803368i
$179$	−452.182	−	261.067i	−0.188814	−	0.109012i	0.402613	−	0.915370i	$-0.368102\pi$
$179$	−452.182	−	261.067i	−0.188814	−	0.109012i	−0.591427	+	0.806358i	$0.701435\pi$
$180$		0			0
$181$		−	3401.17i		−	1.39672i	−0.715745	−	0.698362i	$-0.753913\pi$
$181$		−	3401.17i		−	1.39672i	0.715745	−	0.698362i	$-0.246087\pi$
$182$	−376.408	−	744.767i	−0.153303	−	0.303328i
$183$		0			0
$184$	−529.462			−0.212133
$185$	534.948	+	926.558i	0.212596	+	0.368226i
$186$		0			0
$187$	−3016.08	−	1741.34i	−1.17945	−	0.680958i
$188$	525.641			0.203917
$189$		0			0
$190$	1287.01			0.491420
$191$	−2367.55	−	1366.91i	−0.896911	−	0.517832i	−0.0207146	−	0.999785i	$-0.506594\pi$
$191$	−2367.55	−	1366.91i	−0.896911	−	0.517832i	−0.876197	+	0.481953i	$0.839927\pi$
$192$		0			0
$193$	−1114.05	−	1929.59i	−0.415498	−	0.719663i	0.579983	−	0.814629i	$-0.303059\pi$
$193$	−1114.05	−	1929.59i	−0.415498	−	0.719663i	−0.995481	+	0.0949654i	$0.969726\pi$
$194$	−1441.68			−0.533541
$195$		0			0
$196$	188.521	+	431.007i	0.0687031	+	0.157073i
$197$		−	3184.20i		−	1.15160i	−0.817591	−	0.575800i	$-0.804691\pi$
$197$		−	3184.20i		−	1.15160i	0.817591	−	0.575800i	$-0.195309\pi$
$198$		0			0
$199$	−2236.98	−	1291.52i	−0.796860	−	0.460068i	0.0455118	−	0.998964i	$-0.485508\pi$
$199$	−2236.98	−	1291.52i	−0.796860	−	0.460068i	−0.842372	+	0.538896i	$0.818841\pi$
$200$			1922.14i			0.679580i
$201$		0			0
$202$	3185.62	+	1839.22i	1.10960	+	0.640629i
$203$	4152.02	−	2098.45i	1.43554	−	0.725528i
$204$		0			0
$205$	207.139	−	358.776i	0.0705719	−	0.122234i
$206$	−1562.50	+	2706.33i	−0.528469	+	0.915335i
$207$		0			0
$208$	931.666	−	537.897i	0.310574	−	0.179310i
$209$	2269.97	+	3931.71i	0.751279	+	1.30125i
$210$		0			0
$211$	2235.20	−	3871.49i	0.729278	−	1.26315i	−0.227910	−	0.973682i	$-0.573189\pi$
$211$	2235.20	−	3871.49i	0.729278	−	1.26315i	0.957189	−	0.289465i	$-0.0934775\pi$
$212$		−	146.870i		−	0.0475805i
$213$		0			0
$214$	−797.940			−0.254888
$215$	−1160.92	−	2010.77i	−0.368252	−	0.637830i
$216$		0			0
$217$	−3634.92	+	1837.10i	−1.13712	+	0.574703i
$218$	5459.81	−	3152.22i	1.69626	−	0.979337i
$219$		0			0
$220$	−388.315	+	224.194i	−0.119001	+	0.0687051i
$221$	747.132	−	431.357i	0.227410	−	0.131295i
$222$		0			0
$223$	−1671.62	+	965.108i	−0.501972	+	0.289813i	−0.729527	−	0.683952i	$-0.760260\pi$
$223$	−1671.62	+	965.108i	−0.501972	+	0.289813i	0.227556	+	0.973765i	$0.426927\pi$
$224$	−1015.22	+	513.094i	−0.302821	+	0.153047i
$225$		0			0
$226$	250.011	+	433.032i	0.0735862	+	0.127455i
$227$	1092.70			0.319494			0.159747	−	0.987158i	$-0.448932\pi$
$227$	1092.70			0.319494			0.159747	+	0.987158i	$0.448932\pi$
$228$		0			0
$229$			3841.90i			1.10865i	0.832301	+	0.554324i	$0.187023\pi$
$229$			3841.90i			1.10865i	−0.832301	+	0.554324i	$0.812977\pi$
$230$	−219.751	+	380.619i	−0.0629997	+	0.109119i
$231$		0			0
$232$	2548.58	+	4414.27i	0.721218	+	1.24919i
$233$	−4219.38	+	2436.06i	−1.18636	+	0.684943i	−0.957476	−	0.288512i	$-0.906840\pi$
$233$	−4219.38	+	2436.06i	−1.18636	+	0.684943i	−0.228880	+	0.973455i	$0.573506\pi$
$234$		0			0
$235$	−1054.37	+	1826.23i	−0.292679	+	0.506936i
$236$	−366.176	+	634.236i	−0.101000	+	0.174937i
$237$		0			0
$238$	−2965.90	+	1498.98i	−0.807777	+	0.408254i
$239$	1383.42	+	798.720i	0.374419	+	0.216171i	0.675387	−	0.737463i	$-0.263976\pi$
$239$	1383.42	+	798.720i	0.374419	+	0.216171i	−0.300968	+	0.953634i	$0.597310\pi$
$240$		0			0
$241$			6885.74i			1.84045i	0.391385	+	0.920227i	$0.371996\pi$
$241$			6885.74i			1.84045i	−0.391385	+	0.920227i	$0.628004\pi$
$242$	−5830.91	−	3366.48i	−1.54886	−	0.894237i
$243$		0			0
$244$			56.5963i			0.0148492i
$245$	−1875.59	−	209.572i	−0.489091	−	0.0546492i
$246$		0			0
$247$	−1124.62			−0.289707
$248$	−2231.17	−	3864.50i	−0.571289	−	0.989501i
$249$		0			0
$250$	3205.20	+	1850.52i	0.810858	+	0.468149i
$251$	7468.24			1.87805			0.939026	−	0.343846i	$-0.111730\pi$
$251$	7468.24			1.87805			0.939026	+	0.343846i	$0.111730\pi$
$252$		0			0
$253$	−1550.34			−0.385253
$254$	6280.00	+	3625.76i	1.55135	+	0.895671i
$255$		0			0
$256$	−1024.14	−	1773.86i	−0.250034	−	0.433072i
$257$	−892.599			−0.216649			−0.108324	−	0.994116i	$-0.534549\pi$
$257$	−892.599			−0.216649			−0.108324	+	0.994116i	$0.534549\pi$
$258$		0			0
$259$	1624.40	+	3214.06i	0.389711	+	0.771088i
$260$		−	111.073i		−	0.0264940i
$261$		0			0
$262$	−2336.60	−	1349.04i	−0.550975	−	0.318106i
$263$			6421.39i			1.50555i	0.658277	+	0.752775i	$0.271285\pi$
$263$			6421.39i			1.50555i	−0.658277	+	0.752775i	$0.728715\pi$
$264$		0			0
$265$	510.268	+	294.603i	0.118285	+	0.0682918i
$266$	4325.33	+	240.899i	0.997004	+	0.0555280i
$267$		0			0
$268$	228.386	−	395.575i	0.0520555	−	0.0901628i
$269$	−3574.44	+	6191.12i	−0.810177	+	1.40327i	0.102562	+	0.994727i	$0.467296\pi$
$269$	−3574.44	+	6191.12i	−0.810177	+	1.40327i	−0.912740	+	0.408542i	$0.866037\pi$
$270$		0			0
$271$	4716.19	−	2722.90i	1.05715	−	0.610347i	0.132509	−	0.991182i	$-0.457697\pi$
$271$	4716.19	−	2722.90i	1.05715	−	0.610347i	0.924643	+	0.380835i	$0.124363\pi$
$272$	−2142.08	−	3710.20i	−0.477511	−	0.827073i
$273$		0			0
$274$	1861.92	−	3224.95i	0.410522	−	0.711044i
$275$			5628.31i			1.23418i
$276$		0			0
$277$	3155.80			0.684525			0.342262	−	0.939604i	$-0.388807\pi$
$277$	3155.80			0.684525			0.342262	+	0.939604i	$0.388807\pi$
$278$	4071.81	+	7052.58i	0.878456	+	1.52153i
$279$		0			0
$280$	114.987	−	2064.58i	0.0245420	−	0.440651i
$281$	−27.5066	+	15.8809i	−0.00583951	+	0.00337145i	−0.502917	−	0.864335i	$-0.667740\pi$
$281$	−27.5066	+	15.8809i	−0.00583951	+	0.00337145i	0.497077	+	0.867706i	$0.334406\pi$
$282$		0			0
$283$	−5043.64	+	2911.94i	−1.05941	+	0.611651i	−0.925269	−	0.379312i	$-0.876161\pi$
$283$	−5043.64	+	2911.94i	−1.05941	+	0.611651i	−0.134141	+	0.990962i	$0.542827\pi$
$284$	594.274	−	343.104i	0.124168	−	0.0716884i
$285$		0			0
$286$	2318.52	−	1338.60i	0.479361	−	0.276759i
$287$	763.298	−	1166.98i	0.156990	−	0.240017i
$288$		0			0
$289$	738.697	+	1279.46i	0.150356	+	0.260423i
$290$	4231.10			0.856754
$291$		0			0
$292$			557.314i			0.111693i
$293$	−177.914	+	308.157i	−0.0354739	+	0.0614427i	−0.883217	−	0.468964i	$-0.844627\pi$
$293$	−177.914	+	308.157i	−0.0354739	+	0.0614427i	0.847743	+	0.530407i	$0.177961\pi$
$294$		0			0
$295$	−1469.01	−	2544.40i	−0.289929	−	0.502172i
$296$	−3417.06	+	1972.84i	−0.670988	+	0.387395i
$297$		0			0
$298$	1515.08	−	2624.19i	0.294517	−	0.510118i
$299$	192.022	−	332.592i	0.0371402	−	0.0643287i
$300$		0			0
$301$	−3525.19	−	6975.00i	−0.675045	−	1.33565i
$302$	2605.45	+	1504.26i	0.496447	+	0.286624i
$303$		0			0
$304$			5584.76i			1.05364i
$305$	−196.632	−	113.525i	−0.0369150	−	0.0213129i
$306$		0			0
$307$			10085.9i			1.87502i	0.347955	+	0.937511i	$0.386876\pi$
$307$			10085.9i			1.87502i	−0.347955	+	0.937511i	$0.613124\pi$
$308$	−1346.99	+	680.775i	−0.249195	+	0.125944i
$309$		0			0
$310$	−3704.15			−0.678650
$311$	−2633.24	−	4560.90i	−0.480119	−	0.831591i	0.519621	−	0.854397i	$-0.326073\pi$
$311$	−2633.24	−	4560.90i	−0.480119	−	0.831591i	−0.999740	+	0.0228062i	$0.992740\pi$
$312$		0			0
$313$	−7509.58	−	4335.66i	−1.35612	−	0.782958i	−0.367024	−	0.930211i	$-0.619623\pi$
$313$	−7509.58	−	4335.66i	−1.35612	−	0.782958i	−0.989099	+	0.147253i	$0.952957\pi$
$314$	−2037.51			−0.366189
$315$		0			0
$316$	−206.021			−0.0366760
$317$	−3074.94	−	1775.32i	−0.544814	−	0.314548i	0.202214	−	0.979341i	$-0.435186\pi$
$317$	−3074.94	−	1775.32i	−0.544814	−	0.314548i	−0.747028	+	0.664793i	$0.768520\pi$
$318$		0			0
$319$	7462.60	+	12925.6i	1.30980	+	2.26864i
$320$	2182.76			0.381313
$321$		0			0
$322$	−809.769	+	1238.03i	−0.140145	+	0.214264i
$323$			4478.59i			0.771503i
$324$		0			0
$325$	−1207.43	−	697.111i	−0.206081	−	0.118981i
$326$			2829.68i			0.480740i
$327$		0			0
$328$	1323.13	+	763.911i	0.222737	+	0.128597i
$329$	−3885.31	+	5940.13i	−0.651076	+	0.995411i
$330$		0			0
$331$	1383.92	−	2397.03i	0.229811	−	0.398044i	−0.727941	−	0.685640i	$-0.759523\pi$
$331$	1383.92	−	2397.03i	0.229811	−	0.398044i	0.957752	+	0.287596i	$0.0928560\pi$
$332$	676.301	−	1171.39i	0.111798	−	0.193639i
$333$		0			0
$334$	4909.85	−	2834.70i	0.804357	−	0.464396i
$335$	916.228	+	1586.95i	0.149429	+	0.258819i
$336$		0			0
$337$	4541.71	−	7866.48i	0.734133	−	1.27156i	−0.220969	−	0.975281i	$-0.570922\pi$
$337$	4541.71	−	7866.48i	0.734133	−	1.27156i	0.955102	−	0.296276i	$-0.0957447\pi$
$338$		−	6062.48i		−	0.975608i
$339$		0			0
$340$	−442.328			−0.0705547
$341$	−6533.19	−	11315.8i	−1.03751	−	1.79703i
$342$		0			0
$343$	−6264.17	−	1055.38i	−0.986102	−	0.166138i
$344$	7415.54	−	4281.37i	1.16227	−	0.671034i
$345$		0			0
$346$	3916.46	−	2261.17i	0.608526	−	0.351333i
$347$	−1411.92	+	815.173i	−0.218432	+	0.126112i	−0.605224	−	0.796055i	$-0.706916\pi$
$347$	−1411.92	+	815.173i	−0.218432	+	0.126112i	0.386792	+	0.922167i	$0.373583\pi$
$348$		0			0
$349$	−621.203	+	358.652i	−0.0952787	+	0.0550092i	−0.546882	−	0.837210i	$-0.684185\pi$
$349$	−621.203	+	358.652i	−0.0952787	+	0.0550092i	0.451604	+	0.892219i	$0.350852\pi$
$350$	4494.51	+	2939.76i	0.686405	+	0.448962i
$351$		0			0
$352$	−1824.69	−	3160.45i	−0.276296	−	0.478559i
$353$	−8387.64			−1.26467			−0.632336	−	0.774694i	$-0.717904\pi$
$353$	−8387.64			−1.26467			−0.632336	+	0.774694i	$0.717904\pi$
$354$		0			0
$355$			2752.90i			0.411574i
$356$	427.379	−	740.242i	0.0636265	−	0.110204i
$357$		0			0
$358$	−799.204	−	1384.26i	−0.117987	−	0.204359i
$359$	6043.86	−	3489.42i	0.888531	−	0.512994i	0.0150696	−	0.999886i	$-0.495203\pi$
$359$	6043.86	−	3489.42i	0.888531	−	0.512994i	0.873462	+	0.486893i	$0.161870\pi$
$360$		0			0
$361$	−510.398	+	884.036i	−0.0744129	+	0.128887i
$362$	5205.99	−	9017.04i	0.755858	−	1.30919i
$363$		0			0
$364$	20.7902	−	373.287i	0.00299369	−	0.0537516i
$365$	−1936.27	−	1117.91i	−0.277668	−	0.160312i
$366$		0			0
$367$		−	4329.87i		−	0.615851i	−0.951410	−	0.307926i	$-0.900365\pi$
$367$		−	4329.87i		−	0.615851i	0.951410	−	0.307926i	$-0.0996348\pi$
$368$	−1651.63	−	953.567i	−0.233959	−	0.135076i
$369$		0			0
$370$			3275.27i			0.460198i
$371$	1659.74	+	1085.60i	0.232262	+	0.151918i
$372$		0			0
$373$	−4667.41			−0.647907			−0.323954	−	0.946073i	$-0.605012\pi$
$373$	−4667.41			−0.647907			−0.323954	+	0.946073i	$0.605012\pi$
$374$	−5330.74	−	9233.12i	−0.737022	−	1.27656i
$375$		0			0
$376$	−6734.96	−	3888.43i	−0.923747	−	0.533326i
$377$	−3697.21			−0.505082
$378$		0			0
$379$	57.5316			0.00779736			0.00389868	−	0.999992i	$-0.498759\pi$
$379$	57.5316			0.00779736			0.00389868	+	0.999992i	$0.498759\pi$
$380$	499.359	+	288.305i	0.0674120	+	0.0389203i
$381$		0			0
$382$	−4184.51	−	7247.78i	−0.560466	−	0.970755i
$383$	3880.55			0.517720			0.258860	−	0.965915i	$-0.416653\pi$
$383$	3880.55			0.517720			0.258860	+	0.965915i	$0.416653\pi$
$384$		0			0
$385$	336.697	−	6045.38i	0.0445705	−	0.800263i
$386$		−	6820.87i		−	0.899412i
$387$		0			0
$388$	−559.370	−	322.953i	−0.0731900	−	0.0422563i
$389$			5277.43i			0.687856i	0.938996	+	0.343928i	$0.111758\pi$
$389$			5277.43i			0.687856i	−0.938996	+	0.343928i	$0.888242\pi$
$390$		0			0
$391$	−1324.49	−	764.695i	−0.171310	−	0.0989061i
$392$	772.881	−	6917.01i	0.0995827	−	0.891229i
$393$		0			0
$394$	4873.89	−	8441.83i	0.623206	−	1.07942i
$395$	413.254	−	715.777i	0.0526407	−	0.0911763i
$396$		0			0
$397$	−3252.23	+	1877.68i	−0.411146	+	0.237375i	−0.691282	−	0.722585i	$-0.742954\pi$
$397$	−3252.23	+	1877.68i	−0.411146	+	0.237375i	0.280136	+	0.959960i	$0.409620\pi$
$398$	−3953.72	−	6848.05i	−0.497945	−	0.862467i
$399$		0			0
$400$	−3461.80	+	5996.01i	−0.432724	+	0.749501i
$401$			3917.75i			0.487887i	0.969789	+	0.243944i	$0.0784412\pi$
$401$			3917.75i			0.487887i	−0.969789	+	0.243944i	$0.921559\pi$
$402$		0			0
$403$	3236.75			0.400084
$404$	824.010	+	1427.23i	0.101475	+	0.175760i
$405$		0			0
$406$	14219.7	+	791.962i	1.73820	+	0.0968089i
$407$	−10005.6	+	5776.76i	−1.21858	+	0.703546i
$408$		0			0
$409$	5560.57	−	3210.40i	0.672256	−	0.388127i	−0.124675	−	0.992198i	$-0.539789\pi$
$409$	5560.57	−	3210.40i	0.672256	−	0.388127i	0.796931	+	0.604071i	$0.206456\pi$
$410$	1098.32	−	634.115i	0.132298	−	0.0763822i
$411$		0			0
$412$	−1212.49	+	700.034i	−0.144989	+	0.0837092i
$413$	−4460.72	−	8826.05i	−0.531471	−	1.05158i
$414$		0			0
$415$	2713.16	+	4699.32i	0.320924	+	0.555857i
$416$	904.009			0.106545
$417$		0			0
$418$			13898.1i			1.62626i
$419$	−2427.93	+	4205.30i	−0.283084	+	0.490316i	−0.972143	−	0.234390i	$-0.924691\pi$
$419$	−2427.93	+	4205.30i	−0.283084	+	0.490316i	0.689059	+	0.724705i	$0.258024\pi$
$420$		0			0
$421$	1333.50	+	2309.69i	0.154372	+	0.267381i	0.932830	−	0.360316i	$-0.117331\pi$
$421$	1333.50	+	2309.69i	0.154372	+	0.267381i	−0.778458	+	0.627697i	$0.783998\pi$
$422$	11851.8	−	6842.62i	1.36714	−	0.789321i
$423$		0			0
$424$	−1086.47	+	1881.82i	−0.124443	+	0.215541i
$425$	−2776.12	+	4808.38i	−0.316851	+	0.548802i
$426$		0			0
$427$	−639.580	−	418.335i	−0.0724858	−	0.0474113i
$428$	−309.599	−	178.747i	−0.0349650	−	0.0201871i
$429$		0			0
$430$		−	7107.84i		−	0.797140i
$431$	1671.85	+	965.244i	0.186845	+	0.107875i	0.590505	−	0.807034i	$-0.298929\pi$
$431$	1671.85	+	965.244i	0.186845	+	0.107875i	−0.403660	+	0.914909i	$0.632262\pi$
$432$		0			0
$433$		−	14198.8i		−	1.57587i	−0.615761	−	0.787933i	$-0.711151\pi$
$433$		−	14198.8i		−	1.57587i	0.615761	−	0.787933i	$-0.288849\pi$
$434$	−12448.7	−	693.329i	−1.37686	−	0.0766840i
$435$		0			0
$436$	2824.53			0.310253
$437$	996.841	+	1726.58i	0.109120	+	0.189001i
$438$		0			0
$439$	−5176.07	−	2988.40i	−0.562734	−	0.324895i	0.191508	−	0.981491i	$-0.438662\pi$
$439$	−5176.07	−	2988.40i	−0.562734	−	0.324895i	−0.754242	+	0.656596i	$0.771995\pi$
$440$	6633.89			0.718769
$441$		0			0
$442$	2641.02			0.284209
$443$	1832.30	+	1057.88i	0.196513	+	0.113457i	0.595028	−	0.803705i	$-0.297141\pi$
$443$	1832.30	+	1057.88i	0.196513	+	0.113457i	−0.398515	+	0.917162i	$0.630474\pi$
$444$		0			0
$445$	1714.54	+	2969.67i	0.182645	+	0.316351i
$446$	−5908.96			−0.627348
$447$		0			0
$448$	7335.71	+	408.561i	0.773616	+	0.0430864i
$449$			7685.78i			0.807827i	0.914797	+	0.403913i	$0.132350\pi$
$449$			7685.78i			0.807827i	−0.914797	+	0.403913i	$0.867650\pi$
$450$		0			0
$451$	3874.32	+	2236.84i	0.404511	+	0.233545i
$452$			224.020i			0.0233120i
$453$		0			0
$454$	2896.92	+	1672.54i	0.299470	+	0.172899i
$455$	1255.20	+	821.000i	0.129329	+	0.0845914i
$456$		0			0
$457$	−2262.72	+	3919.14i	−0.231609	+	0.401159i	−0.958282	−	0.285825i	$-0.907732\pi$
$457$	−2262.72	+	3919.14i	−0.231609	+	0.401159i	0.726672	+	0.686984i	$0.241066\pi$
$458$	−5880.60	+	10185.5i	−0.599962	+	1.03916i
$459$		0			0
$460$	−170.526	+	98.4530i	−0.0172843	+	0.00997912i
$461$	−8067.99	−	13974.2i	−0.815106	−	1.41181i	−0.909252	−	0.416247i	$-0.863345\pi$
$461$	−8067.99	−	13974.2i	−0.815106	−	1.41181i	0.0941454	−	0.995558i	$-0.469988\pi$
$462$		0			0
$463$	−1572.22	+	2723.17i	−0.157813	+	0.273340i	−0.934080	−	0.357065i	$-0.883778\pi$
$463$	−1572.22	+	2723.17i	−0.157813	+	0.273340i	0.776267	+	0.630405i	$0.217111\pi$
$464$			18360.1i			1.83695i
$465$		0			0
$466$	−14915.0			−1.48267
$467$	7929.49	+	13734.3i	0.785724	+	1.36091i	0.928566	+	0.371168i	$0.121043\pi$
$467$	7929.49	+	13734.3i	0.785724	+	1.36091i	−0.142842	+	0.989746i	$0.545624\pi$
$468$		0			0
$469$	2782.17	+	5504.85i	0.273921	+	0.541983i
$470$	−5590.62	+	3227.75i	−0.548672	+	0.316776i
$471$		0			0
$472$	9383.51	−	5417.57i	0.915066	−	0.528314i
$473$	21713.8	−	12536.4i	2.11078	−	1.21866i
$474$		0			0
$475$	6268.12	−	3618.90i	0.605476	−	0.349572i
$476$	−1486.55	−	82.7933i	−0.143143	−	0.00797232i
$477$		0			0
$478$	2445.12	+	4235.07i	0.233969	+	0.405246i
$479$	10563.1			1.00760			0.503798	−	0.863821i	$-0.331935\pi$
$479$	10563.1			1.00760			0.503798	+	0.863821i	$0.331935\pi$
$480$		0			0
$481$		−	2861.99i		−	0.271300i
$482$	−10539.6	+	18255.2i	−0.995990	+	1.72511i
$483$		0			0
$484$	−1508.25	−	2612.37i	−0.141647	−	0.245339i
$485$	2244.06	−	1295.61i	0.210098	−	0.121300i
$486$		0			0
$487$	4915.35	−	8513.63i	0.457363	−	0.792175i	−0.541458	−	0.840728i	$-0.682127\pi$
$487$	4915.35	−	8513.63i	0.457363	−	0.792175i	0.998821	+	0.0485525i	$0.0154608\pi$
$488$	418.671	−	725.159i	0.0388368	−	0.0672672i
$489$		0			0
$490$	−4651.71	−	3426.48i	−0.428863	−	0.315903i
$491$	−4775.18	−	2756.95i	−0.438902	−	0.253400i	0.264230	−	0.964460i	$-0.414882\pi$
$491$	−4775.18	−	2756.95i	−0.438902	−	0.253400i	−0.703132	+	0.711060i	$0.748216\pi$
$492$		0			0
$493$			14723.5i			1.34506i
$494$	−2981.54	−	1721.39i	−0.271550	−	0.156779i
$495$		0			0
$496$		−	16073.4i		−	1.45508i
$497$	−515.278	+	9251.81i	−0.0465058	+	0.835011i
$498$		0			0
$499$	3718.10			0.333557			0.166779	−	0.985994i	$-0.446663\pi$
$499$	3718.10			0.333557			0.166779	+	0.985994i	$0.446663\pi$
$500$	829.073	+	1436.00i	0.0741546	+	0.128439i
$501$		0			0
$502$	19799.5	+	11431.2i	1.76035	+	1.01634i
$503$	16413.0			1.45491			0.727453	−	0.686158i	$-0.240704\pi$
$503$	16413.0			1.45491			0.727453	+	0.686158i	$0.240704\pi$
$504$		0			0
$505$	−6611.46			−0.582586
$506$	−4110.20	−	2373.03i	−0.361108	−	0.208486i
$507$		0			0
$508$	1624.42	+	2813.58i	0.141874	+	0.245733i
$509$	−5482.62			−0.477432			−0.238716	−	0.971089i	$-0.576726\pi$
$509$	−5482.62			−0.477432			−0.238716	+	0.971089i	$0.576726\pi$
$510$		0			0
$511$	−6298.07	−	4119.42i	−0.545225	−	0.356619i
$512$			7375.92i			0.636665i
$513$		0			0
$514$	−2366.42	−	1366.25i	−0.203071	−	0.117243i
$515$		−	5616.73i		−	0.480588i
$516$		0			0
$517$	−19720.9	−	11385.9i	−1.67761	−	0.968569i
$518$	−613.053	+	11007.4i	−0.0520000	+	0.933659i
$519$		0			0
$520$	−821.660	+	1423.16i	−0.0692926	+	0.120018i
$521$	4450.46	−	7708.43i	0.374238	−	0.648200i	−0.615974	−	0.787766i	$-0.711237\pi$
$521$	4450.46	−	7708.43i	0.374238	−	0.648200i	0.990213	+	0.139566i	$0.0445708\pi$
$522$		0			0
$523$	−15123.5	+	8731.55i	−1.26444	+	0.730026i	−0.973931	−	0.226845i	$-0.927159\pi$
$523$	−15123.5	+	8731.55i	−1.26444	+	0.730026i	−0.290512	+	0.956871i	$0.593826\pi$
$524$	−604.397	−	1046.85i	−0.0503878	−	0.0872742i
$525$		0			0
$526$	−9828.88	+	17024.1i	−0.814752	+	1.41119i
$527$		−	12889.8i		−	1.06544i
$528$		0			0
$529$	11486.2			0.944044
$530$	901.868	+	1562.08i	0.0739144	+	0.128023i
$531$		0			0
$532$	1624.26	+	1062.39i	0.132369	+	0.0865796i
$533$	−959.731	+	554.101i	−0.0779936	+	0.0450296i
$534$		0			0
$535$	1242.04	−	717.090i	0.100370	−	0.0579486i
$536$	−5852.54	+	3378.96i	−0.471625	+	0.272293i
$537$		0			0
$538$	−18952.8	+	10942.4i	−1.51880	+	0.876880i
$539$	2263.11	−	20254.0i	0.180851	−	1.61856i
$540$		0			0
$541$	3242.17	+	5615.60i	0.257656	+	0.446273i	0.965613	−	0.259982i	$-0.0837167\pi$
$541$	3242.17	+	5615.60i	0.257656	+	0.446273i	−0.707958	+	0.706255i	$0.750383\pi$
$542$	16671.2			1.32120
$543$		0			0
$544$		−	3600.06i		−	0.283734i
$545$	−5665.66	+	9813.21i	−0.445303	+	0.771287i
$546$		0			0
$547$	7429.77	+	12868.7i	0.580757	+	1.00590i	0.995390	+	0.0959117i	$0.0305766\pi$
$547$	7429.77	+	12868.7i	0.580757	+	1.00590i	−0.414633	+	0.909989i	$0.636090\pi$
$548$	1444.84	−	834.181i	0.112629	−	0.0650264i
$549$		0			0
$550$	−8614.95	+	14921.5i	−0.667896	+	1.15683i
$551$	9596.64	−	16621.9i	0.741979	−	1.28515i
$552$		0			0
$553$	1522.82	−	2328.20i	0.117101	−	0.179032i
$554$	8366.52	+	4830.41i	0.641623	+	0.370441i
$555$		0			0
$556$			3648.51i			0.278294i
$557$	−10822.7	−	6248.49i	−0.823290	−	0.475327i	0.0282599	−	0.999601i	$-0.491003\pi$
$557$	−10822.7	−	6248.49i	−0.823290	−	0.475327i	−0.851550	+	0.524274i	$0.824337\pi$
$558$		0			0
$559$			6210.96i			0.469938i
$560$	4077.02	−	6233.24i	0.307653	−	0.470362i
$561$		0			0
$562$	−97.2323			−0.00729804
$563$	12205.3	+	21140.2i	0.913664	+	1.58251i	0.808846	+	0.588021i	$0.200093\pi$
$563$	12205.3	+	21140.2i	0.913664	+	1.58251i	0.104818	+	0.994491i	$0.466574\pi$
$564$		0			0
$565$	−778.311	−	449.358i	−0.0579536	−	0.0334595i
$566$	−17828.6			−1.32402
$567$		0			0
$568$	−10152.5			−0.749978
$569$	−13128.1	−	7579.50i	−0.967237	−	0.558434i	−0.0688439	−	0.997627i	$-0.521931\pi$
$569$	−13128.1	−	7579.50i	−0.967237	−	0.558434i	−0.898393	+	0.439193i	$0.855264\pi$
$570$		0			0
$571$	−5144.94	−	8911.30i	−0.377074	−	0.653111i	0.613562	−	0.789647i	$-0.289736\pi$
$571$	−5144.94	−	8911.30i	−0.377074	−	0.653111i	−0.990635	+	0.136536i	$0.956403\pi$
$572$	1199.44			0.0876769
$573$		0			0
$574$	3809.87	−	1925.52i	0.277040	−	0.140017i
$575$			2471.63i			0.179259i
$576$		0			0
$577$	−3545.65	−	2047.08i	−0.255818	−	0.147697i	0.366607	−	0.930376i	$-0.380519\pi$
$577$	−3545.65	−	2047.08i	−0.255818	−	0.147697i	−0.622426	+	0.782679i	$0.713853\pi$
$578$			4522.74i			0.325469i
$579$		0			0
$580$	1641.66	+	947.811i	0.117528	+	0.0678547i
$581$	8238.63	+	16301.1i	0.588289	+	1.16400i
$582$		0			0
$583$	−3181.34	+	5510.24i	−0.225999	+	0.391442i
$584$	4122.73	−	7140.78i	0.292123	−	0.505972i
$585$		0			0
$586$	−943.358	+	544.648i	−0.0665013	+	0.0383945i
$587$	−4131.33	−	7155.67i	−0.290491	−	0.503145i	0.683435	−	0.730011i	$-0.260485\pi$
$587$	−4131.33	−	7155.67i	−0.290491	−	0.503145i	−0.973926	+	0.226866i	$0.927152\pi$
$588$		0			0
$589$	−8401.45	+	14551.7i	−0.587734	+	1.01799i
$590$		−	8994.14i		−	0.627598i
$591$		0			0
$592$	−14212.4			−0.986700
$593$	2857.34	+	4949.05i	0.197870	+	0.342721i	0.947838	−	0.318754i	$-0.103264\pi$
$593$	2857.34	+	4949.05i	0.197870	+	0.342721i	−0.749968	+	0.661474i	$0.769931\pi$
$594$		0			0
$595$	3269.49	−	4998.63i	0.225271	−	0.344410i
$596$	1175.69	−	678.786i	0.0808024	−	0.0466513i
$597$		0			0
$598$	1018.16	−	587.836i	0.0696250	−	0.0401980i
$599$	9639.02	−	5565.09i	0.657495	−	0.379605i	−0.133827	−	0.991005i	$-0.542727\pi$
$599$	9639.02	−	5565.09i	0.657495	−	0.379605i	0.791322	+	0.611400i	$0.209393\pi$
$600$		0			0
$601$	12690.8	−	7327.05i	0.861347	−	0.497299i	−0.00311588	−	0.999995i	$-0.500992\pi$
$601$	12690.8	−	7327.05i	0.861347	−	0.497299i	0.864463	+	0.502696i	$0.167658\pi$
$602$	1330.42	−	23887.6i	0.0900728	−	1.61726i
$603$		0			0
$604$	673.940	+	1167.30i	0.0454010	+	0.0786369i
$605$	12101.5			0.813216
$606$		0			0
$607$		−	23920.2i		−	1.59949i	−0.600340	−	0.799745i	$-0.704968\pi$
$607$		−	23920.2i		−	1.59949i	0.600340	−	0.799745i	$-0.295032\pi$
$608$	−2346.48	+	4064.23i	−0.156517	+	0.271096i
$609$		0			0
$610$	−347.534	−	601.947i	−0.0230676	−	0.0399543i
$611$	4885.18	−	2820.46i	0.323459	−	0.186749i
$612$		0			0
$613$	2063.73	−	3574.48i	0.135976	−	0.235517i	−0.789994	−	0.613115i	$-0.789916\pi$
$613$	2063.73	−	3574.48i	0.135976	−	0.235517i	0.925970	+	0.377598i	$0.123250\pi$
$614$	−15437.9	+	26739.3i	−1.01470	+	1.75751i
$615$		0			0
$616$	22294.8	+	1241.71i	1.45825	+	0.0812172i
$617$	3577.34	+	2065.38i	0.233417	+	0.134763i	0.612147	−	0.790744i	$-0.290306\pi$
$617$	3577.34	+	2065.38i	0.233417	+	0.134763i	−0.378731	+	0.925507i	$0.623639\pi$
$618$		0			0
$619$		−	4035.79i		−	0.262055i	−0.991379	−	0.131028i	$-0.958172\pi$
$619$		−	4035.79i		−	0.262055i	0.991379	−	0.131028i	$-0.0418276\pi$
$620$	−1437.20	−	829.768i	−0.0930958	−	0.0537489i
$621$		0			0
$622$		−	16122.2i		−	1.03930i
$623$	5206.29	+	10301.2i	0.334808	+	0.662457i
$624$		0			0
$625$	5188.60			0.332071
$626$	−13272.7	−	22989.0i	−0.847420	−	1.46777i
$627$		0			0
$628$	−790.550	−	456.424i	−0.0502331	−	0.0290021i
$629$	−11397.4			−0.722485
$630$		0			0
$631$	−19836.6			−1.25147			−0.625737	−	0.780034i	$-0.715202\pi$
$631$	−19836.6			−1.25147			−0.625737	+	0.780034i	$0.715202\pi$
$632$	2639.72	+	1524.04i	0.166143	+	0.0959228i
$633$		0			0
$634$	−5434.77	−	9413.30i	−0.340445	−	0.589669i
$635$	−13033.5			−0.814521
$636$		0			0
$637$	4064.75	+	2994.12i	0.252828	+	0.186234i
$638$			45690.5i			2.83527i
$639$		0			0
$640$	8128.20	+	4692.82i	0.502024	+	0.289844i
$641$		−	1990.63i		−	0.122660i	−0.998118	−	0.0613302i	$-0.980466\pi$
$641$		−	1990.63i		−	0.122660i	0.998118	−	0.0613302i	$-0.0195343\pi$
$642$		0			0
$643$	3590.95	+	2073.23i	0.220238	+	0.127155i	0.606061	−	0.795419i	$-0.292749\pi$
$643$	3590.95	+	2073.23i	0.220238	+	0.127155i	−0.385822	+	0.922573i	$0.626082\pi$
$644$	−591.521	+	298.957i	−0.0361944	+	0.0182928i
$645$		0			0
$646$	−6855.14	+	11873.5i	−0.417511	+	0.723150i
$647$	−7896.88	+	13677.8i	−0.479843	+	0.831112i	−0.999733	−	0.0231210i	$-0.992640\pi$
$647$	−7896.88	+	13677.8i	−0.479843	+	0.831112i	0.519890	+	0.854233i	$0.325973\pi$
$648$		0			0
$649$	27476.3	−	15863.4i	1.66185	−	0.959467i
$650$	−2134.06	−	3696.30i	−0.128777	−	0.223048i
$651$		0			0
$652$	−633.878	+	1097.91i	−0.0380745	+	0.0659469i
$653$		−	13416.5i		−	0.804023i	−0.915635	−	0.402012i	$-0.868311\pi$
$653$		−	13416.5i		−	0.804023i	0.915635	−	0.402012i	$-0.131689\pi$
$654$		0			0
$655$	4849.39			0.289284
$656$	2751.62	+	4765.95i	0.163770	+	0.283657i
$657$		0			0
$658$	−19392.8	+	9801.21i	−1.14895	+	0.580685i
$659$	−382.577	+	220.881i	−0.0226147	+	0.0130566i	−0.511265	−	0.859423i	$-0.670823\pi$
$659$	−382.577	+	220.881i	−0.0226147	+	0.0130566i	0.488650	+	0.872480i	$0.337489\pi$
$660$		0			0
$661$	−3170.86	+	1830.70i	−0.186584	+	0.107724i	−0.590383	−	0.807124i	$-0.701023\pi$
$661$	−3170.86	+	1830.70i	−0.186584	+	0.107724i	0.403798	+	0.914848i	$0.367690\pi$
$662$	7338.00	−	4236.60i	0.430815	−	0.248731i
$663$		0			0
$664$	−17330.7	+	10005.9i	−1.01289	+	0.584794i
$665$	−6949.10	+	3512.10i	−0.405225	+	0.204802i
$666$		0			0
$667$	3277.15	+	5676.19i	0.190242	+	0.329509i
$668$	2540.02			0.147120
$669$		0			0
$670$			5609.69i			0.323464i
$671$	1225.93	−	2123.37i	0.0705312	−	0.122164i
$672$		0			0
$673$	−2370.91	−	4106.54i	−0.135798	−	0.235209i	0.790104	−	0.612973i	$-0.210026\pi$
$673$	−2370.91	−	4106.54i	−0.135798	−	0.235209i	−0.925902	+	0.377764i	$0.876693\pi$
$674$	24081.6	−	13903.5i	1.37625	−	0.794575i
$675$		0			0
$676$	1358.06	−	2352.23i	0.0772679	−	0.133832i
$677$	−4086.07	+	7077.29i	−0.231965	+	0.401776i	−0.958386	−	0.285474i	$-0.907849\pi$
$677$	−4086.07	+	7077.29i	−0.231965	+	0.401776i	0.726421	+	0.687250i	$0.241182\pi$
$678$		0			0
$679$	7784.22	−	3934.18i	0.439957	−	0.222356i
$680$	5667.48	+	3272.12i	0.319614	+	0.184529i
$681$		0			0
$682$		−	40000.0i		−	2.24587i
$683$	18929.2	+	10928.8i	1.06048	+	0.612266i	0.925564	−	0.378592i	$-0.123592\pi$
$683$	18929.2	+	10928.8i	1.06048	+	0.612266i	0.134912	+	0.990858i	$0.456925\pi$
$684$		0			0
$685$			6693.07i			0.373327i
$686$	−14991.9	−	12386.2i	−0.834391	−	0.689370i
$687$		0			0
$688$	30843.1			1.70913
$689$	−788.068	−	1364.97i	−0.0435748	−	0.0754737i
$690$		0			0
$691$	22416.7	+	12942.3i	1.23411	+	0.712516i	0.967885	−	0.251394i	$-0.0808891\pi$
$691$	22416.7	+	12942.3i	1.23411	+	0.712516i	0.266228	+	0.963910i	$0.414222\pi$
$692$	2026.10			0.111302
$693$		0			0
$694$	−4990.97			−0.272989
$695$	−12676.0	−	7318.48i	−0.691838	−	0.399433i
$696$		0			0
$697$	2206.61	+	3821.96i	0.119916	+	0.207700i
$698$	−2195.88			−0.119076
$699$		0			0
$700$	1085.32	+	2147.44i	0.0586020	+	0.115951i
$701$		−	24745.4i		−	1.33327i	−0.745385	−	0.666634i	$-0.767734\pi$
$701$		−	24745.4i		−	1.33327i	0.745385	−	0.666634i	$-0.232266\pi$
$702$		0			0
$703$	12866.9	+	7428.70i	0.690304	+	0.398547i
$704$			23571.0i			1.26188i
$705$		0			0
$706$	−22237.0	−	12838.5i	−1.18541	−	0.684397i
$707$	−22219.4	−	1237.51i	−1.18196	−	0.0658293i
$708$		0			0
$709$	7953.44	−	13775.8i	0.421294	−	0.729703i	−0.574772	−	0.818314i	$-0.694909\pi$
$709$	7953.44	−	13775.8i	0.421294	−	0.729703i	0.996066	+	0.0886105i	$0.0282426\pi$
$710$	−4213.72	+	7298.38i	−0.222730	+	0.385780i
$711$		0			0
$712$	−10951.9	+	6323.07i	−0.576460	+	0.332819i
$713$	−2869.00	−	4969.26i	−0.150694	−	0.261010i
$714$		0			0
$715$	−2405.94	+	4167.20i	−0.125842	+	0.217965i
$716$		−	716.121i		−	0.0373781i
$717$		0			0
$718$	21364.3			1.11046
$719$	−3347.21	−	5797.53i	−0.173616	−	0.300711i	0.766066	−	0.642762i	$-0.222212\pi$
$719$	−3347.21	−	5797.53i	−0.173616	−	0.300711i	−0.939681	+	0.342051i	$0.888878\pi$
$720$		0			0
$721$	1051.32	−	18876.4i	0.0543040	−	0.975028i
$722$	−2706.29	+	1562.48i	−0.139498	+	0.0805394i
$723$		0			0
$724$	4039.83	−	2332.39i	0.207374	−	0.119728i
$725$	20606.6	−	11897.2i	1.05560	−	0.609452i
$726$		0			0
$727$	17642.6	−	10186.0i	0.900041	−	0.519639i	0.0228273	−	0.999739i	$-0.492733\pi$
$727$	17642.6	−	10186.0i	0.900041	−	0.519639i	0.877213	+	0.480101i	$0.159400\pi$
$728$	−3027.77	+	4629.08i	−0.154144	+	0.235666i
$729$		0			0
$730$	−3422.24	−	5927.49i	−0.173511	−	0.300529i
$731$	24734.1			1.25147
$732$		0			0
$733$			12531.3i			0.631453i	0.948850	+	0.315727i	$0.102248\pi$
$733$			12531.3i			0.631453i	−0.948850	+	0.315727i	$0.897752\pi$
$734$	6627.51	−	11479.2i	0.333278	−	0.577254i
$735$		0			0
$736$	−801.299	−	1387.89i	−0.0401308	−	0.0695086i
$737$	−17137.1	+	9894.09i	−0.856515	+	0.494509i
$738$		0			0
$739$	3311.99	−	5736.53i	0.164863	−	0.285550i	−0.771744	−	0.635933i	$-0.780615\pi$
$739$	3311.99	−	5736.53i	0.164863	−	0.285550i	0.936606	+	0.350383i	$0.113949\pi$
$740$	−733.695	+	1270.80i	−0.0364475	+	0.0631290i
$741$		0			0
$742$	2738.57	+	5418.57i	0.135493	+	0.268089i
$743$	−23846.9	−	13768.0i	−1.17747	−	0.679811i	−0.222039	−	0.975038i	$-0.571271\pi$
$743$	−23846.9	−	13768.0i	−1.17747	−	0.679811i	−0.955427	+	0.295227i	$0.904605\pi$
$744$		0			0
$745$			5446.25i			0.267832i
$746$	−12374.1	−	7144.16i	−0.607301	−	0.350625i
$747$		0			0
$748$		−	4776.57i		−	0.233488i
$749$	4308.39	−	2177.48i	0.210180	−	0.106226i
$750$		0			0
$751$	27525.1			1.33742			0.668712	−	0.743522i	$-0.266846\pi$
$751$	27525.1			1.33742			0.668712	+	0.743522i	$0.266846\pi$
$752$	−14006.2	−	24259.4i	−0.679193	−	1.17640i
$753$		0			0
$754$	−9801.90	−	5659.13i	−0.473427	−	0.273333i
$755$	−5407.37			−0.260655
$756$		0			0
$757$	15056.0			0.722877			0.361439	−	0.932396i	$-0.382286\pi$
$757$	15056.0			0.722877			0.361439	+	0.932396i	$0.382286\pi$
$758$	152.525	+	88.0605i	0.00730867	+	0.00421966i
$759$		0			0
$760$	−4265.47	−	7388.01i	−0.203585	−	0.352620i
$761$	−9883.03			−0.470775			−0.235387	−	0.971902i	$-0.575636\pi$
$761$	−9883.03			−0.470775			−0.235387	+	0.971902i	$0.575636\pi$
$762$		0			0
$763$	−20877.6	+	31919.2i	−0.990592	+	1.51449i
$764$		−	3749.50i		−	0.177555i
$765$		0			0
$766$	10287.9	+	5939.75i	0.485272	+	0.280172i
$767$			7859.25i			0.369988i
$768$		0			0
$769$	−6460.28	−	3729.84i	−0.302944	−	0.174905i	0.340821	−	0.940128i	$-0.389295\pi$
$769$	−6460.28	−	3729.84i	−0.302944	−	0.174905i	−0.643765	+	0.765224i	$0.722628\pi$
$770$	10146.0	−	15511.9i	0.474852	−	0.725988i
$771$		0			0
$772$	1527.95	−	2646.48i	0.0712332	−	0.123380i
$773$	1435.39	−	2486.18i	0.0667886	−	0.115681i	−0.830697	−	0.556724i	$-0.812058\pi$
$773$	1435.39	−	2486.18i	0.0667886	−	0.115681i	0.897486	+	0.441043i	$0.145391\pi$
$774$		0			0
$775$	−18040.2	+	10415.5i	−0.836160	+	0.482757i
$776$	4778.08	+	8275.88i	0.221035	+	0.382844i
$777$		0			0
$778$	−8077.88	+	13991.3i	−0.372244	+	0.644746i
$779$		−	5752.99i		−	0.264599i
$780$		0			0
$781$	−29727.8			−1.36203
$782$	−2340.96	−	4054.65i	−0.107049	−	0.185415i
$783$		0			0
$784$	14868.6	−	20185.2i	0.677321	−	0.919517i
$785$	3171.50	−	1831.06i	0.144198	−	0.0832528i
$786$		0			0
$787$	−11631.6	+	6715.53i	−0.526840	+	0.304171i	−0.739729	−	0.672905i	$-0.765046\pi$
$787$	−11631.6	+	6715.53i	−0.526840	+	0.304171i	0.212889	+	0.977076i	$0.431713\pi$
$788$	3782.12	−	2183.61i	0.170980	−	0.0987155i
$789$		0			0
$790$	2191.20	−	1265.09i	0.0986830	−	0.0569747i
$791$	−2531.60	−	1655.86i	−0.113797	−	0.0744319i
$792$		0			0
$793$	303.682	+	525.992i	0.0135991	+	0.0235543i
$794$	−11496.2			−0.513837
$795$		0			0
$796$		−	3542.71i		−	0.157749i
$797$	−12211.0	+	21150.1i	−0.542707	+	0.939996i	0.456041	+	0.889959i	$0.349267\pi$
$797$	−12211.0	+	21150.1i	−0.542707	+	0.939996i	−0.998747	+	0.0500368i	$0.984066\pi$
$798$		0			0
$799$	−11232.0	−	19454.4i	−0.497321	−	0.861386i
$800$	−5038.55	+	2909.01i	−0.222675	+	0.128561i
$801$		0			0
$802$	−5996.69	+	10386.6i	−0.264028	+	0.457310i
$803$	12071.9	−	20909.2i	0.530523	−	0.918892i
$804$		0			0
$805$	147.858	−	2654.79i	0.00647367	−	0.116235i
$806$	8581.14	+	4954.32i	0.375010	+	0.216512i
$807$		0			0
$808$		−	24382.5i		−	1.06160i
$809$	−15783.5	−	9112.60i	−0.685931	−	0.396022i	0.116155	−	0.993231i	$-0.462943\pi$
$809$	−15783.5	−	9112.60i	−0.685931	−	0.396022i	−0.802086	+	0.597209i	$0.796276\pi$
$810$		0			0
$811$			9023.87i			0.390716i	0.980732	+	0.195358i	$0.0625870\pi$
$811$			9023.87i			0.390716i	−0.980732	+	0.195358i	$0.937413\pi$
$812$	5339.79	+	3492.63i	0.230776	+	0.150945i
$813$		0			0
$814$	−35368.7			−1.52294
$815$	−2542.96	−	4404.54i	−0.109296	−	0.189306i
$816$		0			0
$817$	−27923.1	−	16121.4i	−1.19572	−	0.690351i
$818$	19655.9			0.840164
$819$		0			0
$820$	568.194			0.0241978
$821$	37336.3	+	21556.1i	1.58714	+	0.916337i	0.993775	+	0.111406i	$0.0355354\pi$
$821$	37336.3	+	21556.1i	1.58714	+	0.916337i	0.593368	+	0.804931i	$0.297798\pi$
$822$		0			0
$823$	20544.3	+	35583.8i	0.870146	+	1.50714i	0.861845	+	0.507171i	$0.169309\pi$
$823$	20544.3	+	35583.8i	0.870146	+	1.50714i	0.00830039	+	0.999966i	$0.497358\pi$
$824$	20714.0			0.875736
$825$		0			0
$826$	1683.49	−	30227.1i	0.0709154	−	1.27329i
$827$		−	5668.45i		−	0.238345i	−0.992874	−	0.119173i	$-0.961976\pi$
$827$		−	5668.45i		−	0.238345i	0.992874	−	0.119173i	$-0.0380242\pi$
$828$		0			0
$829$	3922.78	+	2264.82i	0.164347	+	0.0948858i	0.579918	−	0.814675i	$-0.303085\pi$
$829$	3922.78	+	2264.82i	0.164347	+	0.0948858i	−0.415571	+	0.909561i	$0.636418\pi$
$830$			16611.5i			0.694693i
$831$		0			0
$832$	−5056.65	−	2919.46i	−0.210707	−	0.121652i
$833$	11923.6	−	16187.2i	0.495951	−	0.673292i
$834$		0			0
$835$	−5094.96	+	8824.74i	−0.211160	+	0.365740i
$836$	−3113.32	+	5392.43i	−0.128800	+	0.223088i
$837$		0			0
$838$	−12873.7	+	7432.61i	−0.530684	+	0.306390i
$839$	−7887.26	−	13661.1i	−0.324551	−	0.562139i	0.656870	−	0.754004i	$-0.271880\pi$
$839$	−7887.26	−	13661.1i	−0.324551	−	0.562139i	−0.981421	+	0.191865i	$0.938547\pi$
$840$		0			0
$841$	19354.7	−	33523.4i	0.793585	−	1.37453i
$842$			8164.47i			0.334164i
$843$		0			0
$844$	6131.28			0.250056
$845$	5448.21	+	9436.57i	0.221804	+	0.384175i
$846$		0			0
$847$	40670.1	+	2265.11i	1.64987	+	0.0918893i
$848$	−6778.36	+	3913.49i	−0.274493	+	0.158478i
$849$		0			0
$850$	−14719.9	+	8498.53i	−0.593986	+	0.342938i
$851$	−4393.90	+	2536.82i	−0.176993	+	0.102187i
$852$		0			0
$853$	23201.4	−	13395.3i	0.931301	−	0.537687i	0.0440783	−	0.999028i	$-0.485965\pi$
$853$	23201.4	−	13395.3i	0.931301	−	0.537687i	0.887223	+	0.461341i	$0.152632\pi$
$854$	−1055.30	−	2088.04i	−0.0422855	−	0.0836667i
$855$		0			0
$856$	2644.56	+	4580.51i	0.105595	+	0.182896i
$857$	13696.0			0.545914			0.272957	−	0.962026i	$-0.411998\pi$
$857$	13696.0			0.545914			0.272957	+	0.962026i	$0.411998\pi$
$858$		0			0
$859$			3353.32i			0.133194i	0.997780	+	0.0665970i	$0.0212142\pi$
$859$			3353.32i			0.133194i	−0.997780	+	0.0665970i	$0.978786\pi$
$860$	1592.23	−	2757.82i	0.0631333	−	0.109350i
$861$		0			0
$862$	2954.90	+	5118.03i	0.116757	+	0.202228i
$863$	−7661.03	+	4423.10i	−0.302184	+	0.174466i	−0.643423	−	0.765510i	$-0.722487\pi$
$863$	−7661.03	+	4423.10i	−0.302184	+	0.174466i	0.341240	+	0.939976i	$0.389153\pi$
$864$		0			0
$865$	−4064.12	+	7039.26i	−0.159750	+	0.276696i
$866$	21733.3	−	37643.2i	0.852805	−	1.47710i
$867$		0			0
$868$	−4674.76	−	3057.65i	−0.182801	−	0.119566i
$869$	7729.48	+	4462.62i	0.301731	+	0.174205i
$870$		0			0
$871$		−	4901.85i		−	0.190692i
$872$	−36190.2	−	20894.4i	−1.40545	−	0.811439i
$873$		0			0
$874$			6103.25i			0.236208i
$875$	−22356.0	−	1245.11i	−0.863737	−	0.0481057i
$876$		0			0
$877$	−14339.3			−0.552115			−0.276057	−	0.961141i	$-0.589028\pi$
$877$	−14339.3			−0.552115			−0.276057	+	0.961141i	$0.589028\pi$
$878$	−9148.38	−	15845.5i	−0.351643	−	0.609064i
$879$		0			0
$880$	20694.0	+	11947.7i	0.792721	+	0.457678i
$881$	−31099.9			−1.18931			−0.594654	−	0.803982i	$-0.702711\pi$
$881$	−31099.9			−1.18931			−0.594654	+	0.803982i	$0.702711\pi$
$882$		0			0
$883$	−3877.74			−0.147788			−0.0738938	−	0.997266i	$-0.523543\pi$
$883$	−3877.74			−0.147788			−0.0738938	+	0.997266i	$0.523543\pi$
$884$	1024.71	+	591.617i	0.0389872	+	0.0225093i
$885$		0			0
$886$	3238.48	+	5609.21i	0.122798	+	0.212692i
$887$	6654.64			0.251906			0.125953	−	0.992036i	$-0.459801\pi$
$887$	6654.64			0.251906			0.125953	+	0.992036i	$0.459801\pi$
$888$		0			0
$889$	−43802.5	−	2439.57i	−1.65252	−	0.0920367i
$890$			10497.4i			0.395365i
$891$		0			0
$892$	−2292.66	−	1323.67i	−0.0860584	−	0.0496858i
$893$			29283.6i			1.09736i
$894$		0			0
$895$	2488.01	+	1436.45i	0.0929217	+	0.0536484i
$896$	26438.5	+	17292.8i	0.985767	+	0.644767i
$897$		0			0
$898$	−11764.2	+	20376.2i	−0.437168	+	0.757197i
$899$	−27620.0	+	47839.3i	−1.02467	+	1.77478i
$900$		0			0
$901$	−5435.77	+	3138.35i	−0.200990	+	0.116042i
$902$	6847.63	+	11860.4i	0.252773	+	0.437815i
$903$		0			0
$904$	1657.19	−	2870.34i	0.0609705	−	0.105604i
$905$			18714.0i			0.687375i
$906$		0			0
$907$	31281.4			1.14519			0.572593	−	0.819840i	$-0.305938\pi$
$907$	31281.4			1.14519			0.572593	+	0.819840i	$0.305938\pi$
$908$	749.333	+	1297.88i	0.0273871	+	0.0474359i
$909$		0			0
$910$	2071.08	+	4097.88i	0.0754458	+	0.149278i
$911$	11285.5	−	6515.71i	0.410436	−	0.236965i	−0.280541	−	0.959842i	$-0.590514\pi$
$911$	11285.5	−	6515.71i	0.410436	−	0.236965i	0.690977	+	0.722877i	$0.257181\pi$
$912$		0			0
$913$	−50746.7	+	29298.6i	−1.83951	+	1.06204i
$914$	−11997.7	+	6926.85i	−0.434187	+	0.250678i
$915$		0			0
$916$	−4563.32	+	2634.63i	−0.164603	+	0.0950336i
$917$	16297.6	+	907.691i	0.586906	+	0.0326877i
$918$		0			0
$919$	−23820.0	−	41257.4i	−0.855003	−	1.48091i	−0.876642	−	0.481143i	$-0.840222\pi$
$919$	−23820.0	−	41257.4i	−0.855003	−	1.48091i	0.0216393	−	0.999766i	$-0.493111\pi$
$920$	2913.22			0.104398
$921$		0			0
$922$		−	49397.0i		−	1.76443i
$923$	3682.03	−	6377.46i	0.131306	−	0.227429i
$924$		0			0
$925$	9209.59	+	15951.5i	0.327361	+	0.567007i
$926$	−8336.42	+	4813.04i	−0.295844	+	0.170806i
$927$		0			0
$928$	−7714.14	+	13361.3i	−0.272876	+	0.472635i
$929$	−375.384	+	650.184i	−0.0132572	+	0.0229622i	−0.872578	−	0.488475i	$-0.837553\pi$
$929$	−375.384	+	650.184i	−0.0132572	+	0.0229622i	0.859321	+	0.511437i	$0.170887\pi$
$930$		0			0
$931$	−24011.6	+	10502.6i	−0.845270	+	0.369719i
$932$	−5786.99	−	3341.12i	−0.203390	−	0.117427i
$933$		0			0
$934$			48549.0i			1.70083i
$935$	16595.2	+	9581.23i	0.580449	+	0.335123i
$936$		0			0
$937$			27064.0i			0.943589i	0.881709	+	0.471794i	$0.156394\pi$
$937$			27064.0i			0.943589i	−0.881709	+	0.471794i	$0.843606\pi$
$938$	−1050.00	+	18852.7i	−0.0365498	+	0.656252i
$939$		0			0
$940$	−2892.20			−0.100354
$941$	−14965.8	−	25921.5i	−0.518459	−	0.897998i	−0.999770	−	0.0214477i	$-0.993172\pi$
$941$	−14965.8	−	25921.5i	−0.518459	−	0.897998i	0.481311	−	0.876550i	$-0.340161\pi$
$942$		0			0
$943$	1701.38	+	982.292i	0.0587535	+	0.0339213i
$944$	39028.4			1.34562
$945$		0			0
$946$	76755.5			2.63799
$947$	20049.8	+	11575.8i	0.687995	+	0.397214i	0.802861	−	0.596167i	$-0.203310\pi$
$947$	20049.8	+	11575.8i	0.687995	+	0.397214i	−0.114865	+	0.993381i	$0.536644\pi$
$948$		0			0
$949$	2990.41	+	5179.55i	0.102290	+	0.177171i
$950$	22157.0			0.756704
$951$		0			0
$952$	18434.5	+	12057.6i	0.627590	+	0.410492i
$953$			16312.5i			0.554472i	0.960802	+	0.277236i	$0.0894184\pi$
$953$			16312.5i			0.554472i	−0.960802	+	0.277236i	$0.910582\pi$
$954$		0			0
$955$	13026.8	+	7521.03i	0.441401	+	0.254843i
$956$			2190.93i			0.0741210i
$957$		0			0
$958$	28004.4	+	16168.3i	0.944447	+	0.545277i
$959$	−1252.78	+	22493.7i	−0.0421841	+	0.757414i
$960$		0			0
$961$	9284.65	−	16081.5i	0.311659	−	0.539810i
$962$	4380.70	−	7587.59i	0.146818	−	0.254297i
$963$		0			0
$964$	−8178.71	+	4721.98i	−0.273256	+	0.157764i
$965$	6129.76	+	10617.1i	0.204481	+	0.354171i
$966$		0			0
$967$	2542.55	−	4403.83i	0.0845533	−	0.146451i	−0.820647	−	0.571435i	$-0.806387\pi$
$967$	2542.55	−	4403.83i	0.0845533	−	0.146451i	0.905201	+	0.424984i	$0.139720\pi$
$968$			44629.2i			1.48186i
$969$		0			0
$970$	7932.48			0.262574
$971$	18128.7	+	31399.9i	0.599155	+	1.03777i	0.992946	+	0.118567i	$0.0378299\pi$
$971$	18128.7	+	31399.9i	0.599155	+	1.03777i	−0.393791	+	0.919200i	$0.628837\pi$
$972$		0			0
$973$	−41230.9	−	26968.2i	−1.35848	−	0.888552i
$974$	26062.7	−	15047.3i	0.857396	−	0.495018i
$975$		0			0
$976$	2612.04	−	1508.06i	0.0856652	−	0.0494588i
$977$	1344.95	−	776.507i	0.0440417	−	0.0254275i	−0.477817	−	0.878459i	$-0.658572\pi$
$977$	1344.95	−	776.507i	0.0440417	−	0.0254275i	0.521859	+	0.853032i	$0.325239\pi$
$978$		0			0
$979$	−32068.7	+	18514.9i	−1.04690	+	0.604430i
$980$	−1037.29	−	2371.50i	−0.0338111	−	0.0773008i
$981$		0			0
$982$	−8439.84	−	14618.2i	−0.274263	−	0.475037i
$983$	−29218.9			−0.948054			−0.474027	−	0.880510i	$-0.657200\pi$
$983$	−29218.9			−0.948054			−0.474027	+	0.880510i	$0.657200\pi$
$984$		0			0
$985$			17520.2i			0.566741i
$986$	−22536.5	+	39034.4i	−0.727899	+	1.26076i
$987$		0			0
$988$	−771.220	−	1335.79i	−0.0248338	−	0.0430134i
$989$	9535.44	−	5505.29i	0.306582	−	0.177005i
$990$		0			0
$991$	2491.34	−	4315.12i	0.0798586	−	0.138319i	−0.823330	−	0.567563i	$-0.807886\pi$
$991$	2491.34	−	4315.12i	0.0798586	−	0.138319i	0.903189	+	0.429244i	$0.141220\pi$
$992$	6753.40	−	11697.2i	0.216150	−	0.374383i
$993$		0			0
$994$	−15527.4	+	23739.3i	−0.495470	+	0.757511i
$995$	12308.4	+	7106.24i	0.392162	+	0.226415i
$996$		0			0
$997$			32768.7i			1.04092i	0.853887	+	0.520459i	$0.174239\pi$
$997$			32768.7i			1.04092i	−0.853887	+	0.520459i	$0.825761\pi$
$998$	9857.28	+	5691.11i	0.312652	+	0.180510i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.s.a.17.16		44
3.2	odd	2		63.4.s.a.59.7	yes	44
7.5	odd	6		189.4.i.a.152.7		44
9.2	odd	6		189.4.i.a.143.16		44
9.7	even	3		63.4.i.a.38.7	yes	44
21.5	even	6		63.4.i.a.5.16	✓	44
63.47	even	6	inner	189.4.s.a.89.16		44
63.61	odd	6		63.4.s.a.47.7	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.16	✓	44	21.5	even	6
63.4.i.a.38.7	yes	44	9.7	even	3
63.4.s.a.47.7	yes	44	63.61	odd	6
63.4.s.a.59.7	yes	44	3.2	odd	2
189.4.i.a.143.16		44	9.2	odd	6
189.4.i.a.152.7		44	7.5	odd	6
189.4.s.a.17.16		44	1.1	even	1	trivial
189.4.s.a.89.16		44	63.47	even	6	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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.65116 + 1.53065i) q^{2} +(0.685763 + 1.18778i) q^{4} -5.50223 q^{5} +(-18.4916 - 1.02989i) q^{7} -20.2917i q^{8} +O(q^{10})\)	\(q+(2.65116 + 1.53065i) q^{2} +(0.685763 + 1.18778i) q^{4} -5.50223 q^{5} +(-18.4916 - 1.02989i) q^{7} -20.2917i q^{8} +(-14.5873 - 8.42197i) q^{10} -59.4170i q^{11} +(12.7466 + 7.35927i) q^{13} +(-47.4478 - 31.0345i) q^{14} +(36.5456 - 63.2988i) q^{16} +(29.3070 - 50.7613i) q^{17} +(-66.1714 + 38.2041i) q^{19} +(-3.77322 - 6.53541i) q^{20} +(90.9465 - 157.524i) q^{22} -26.0925i q^{23} -94.7255 q^{25} +(22.5289 + 39.0212i) q^{26} +(-11.4576 - 22.6701i) q^{28} +(-217.541 + 125.597i) q^{29} +(190.447 - 109.955i) q^{31} +(53.1911 - 30.7099i) q^{32} +(155.395 - 89.7174i) q^{34} +(101.745 + 5.66667i) q^{35} +(-97.2240 - 168.397i) q^{37} -233.908 q^{38} +111.650i q^{40} +(-37.6465 + 65.2056i) q^{41} +(210.991 + 365.447i) q^{43} +(70.5741 - 40.7460i) q^{44} +(39.9385 - 69.1755i) q^{46} +(191.626 - 331.907i) q^{47} +(340.879 + 38.0885i) q^{49} +(-251.132 - 144.991i) q^{50} +20.1869i q^{52} +(-92.7384 - 53.5426i) q^{53} +326.926i q^{55} +(-20.8982 + 375.226i) q^{56} -768.979 q^{58} +(266.985 + 462.431i) q^{59} +(35.7367 + 20.6326i) q^{61} +673.209 q^{62} -396.705 q^{64} +(-70.1349 - 40.4924i) q^{65} +(-166.519 - 288.420i) q^{67} +80.3906 q^{68} +(261.069 + 170.759i) q^{70} -500.325i q^{71} +(351.906 + 203.173i) q^{73} -595.262i q^{74} +(-90.7557 - 52.3978i) q^{76} +(-61.1928 + 1098.72i) q^{77} +(-75.1067 + 130.089i) q^{79} +(-201.082 + 348.284i) q^{80} +(-199.614 + 115.247i) q^{82} +(-493.101 - 854.077i) q^{83} +(-161.254 + 279.300i) q^{85} +1291.81i q^{86} -1205.67 q^{88} +(-311.609 - 539.722i) q^{89} +(-228.126 - 149.212i) q^{91} +(30.9921 - 17.8933i) q^{92} +(1016.06 - 586.625i) q^{94} +(364.090 - 210.208i) q^{95} +(-407.846 + 235.470i) q^{97} +(845.423 + 622.744i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

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