LMFDB - Embedded newform 162.4.e.b.73.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,4,Mod(19,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.19"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	162.73
Dual form			162.4.e.b.91.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.347296 - 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-0.657259 + 0.551505i) q^{5} +(-20.5288 + 7.47187i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(0.857990 + 1.48608i) q^{10} +(37.2066 + 31.2201i) q^{11} +(9.56100 + 54.2231i) q^{13} +(7.58714 + 43.0288i) q^{14} +(12.2567 + 10.2846i) q^{16} +(-39.6041 - 68.5963i) q^{17} +(-55.0156 + 95.2899i) q^{19} +(3.22499 - 1.17380i) q^{20} +(74.4132 - 62.4401i) q^{22} +(42.5012 + 15.4692i) q^{23} +(-21.5782 + 122.376i) q^{25} +110.119 q^{26} +87.3852 q^{28} +(-21.6890 + 123.004i) q^{29} +(125.635 + 45.7274i) q^{31} +(24.5134 - 20.5692i) q^{32} +(-148.863 + 54.1816i) q^{34} +(9.37195 - 16.2327i) q^{35} +(-84.1614 - 145.772i) q^{37} +(168.578 + 141.453i) q^{38} +(-1.19191 - 6.75964i) q^{40} +(3.71508 + 21.0693i) q^{41} +(-128.831 - 108.102i) q^{43} +(-97.1396 - 168.251i) q^{44} +(45.2289 - 78.3387i) q^{46} +(298.913 - 108.795i) q^{47} +(102.849 - 86.3009i) q^{49} +(233.540 + 85.0015i) q^{50} +(38.2440 - 216.893i) q^{52} -463.685 q^{53} -41.6724 q^{55} +(30.3485 - 172.115i) q^{56} +(234.739 + 85.4380i) q^{58} +(-415.527 + 348.668i) q^{59} +(-648.554 + 236.054i) q^{61} +(133.698 - 231.571i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-36.1884 - 30.3657i) q^{65} +(111.664 + 633.280i) q^{67} +(55.0174 + 312.019i) q^{68} +(-28.7173 - 24.0967i) q^{70} +(-524.772 - 908.932i) q^{71} +(480.157 - 831.656i) q^{73} +(-316.343 + 115.140i) q^{74} +(337.155 - 282.907i) q^{76} +(-997.080 - 362.907i) q^{77} +(39.7859 - 225.637i) q^{79} -13.7278 q^{80} +42.7886 q^{82} +(29.5416 - 167.539i) q^{83} +(63.8613 + 23.2436i) q^{85} +(-257.663 + 216.205i) q^{86} +(-365.125 + 132.895i) q^{88} +(-379.679 + 657.623i) q^{89} +(-601.424 - 1041.70i) q^{91} +(-138.589 - 116.290i) q^{92} +(-110.474 - 626.528i) q^{94} +(-16.3934 - 92.9715i) q^{95} +(1232.17 + 1033.92i) q^{97} +(-134.260 - 232.546i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31}+ \cdots - 4002 q^{98}+O(q^{100}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$3$		0			0
$3$		0			0
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	−0.657259	+	0.551505i	−0.0587870	+	0.0493282i	−0.671708	−	0.740816i	$-0.734439\pi$
$5$	−0.657259	+	0.551505i	−0.0587870	+	0.0493282i	0.612921	+	0.790144i	$0.289994\pi$
$6$		0			0
$7$	−20.5288	+	7.47187i	−1.10845	+	0.403443i	−0.830425	−	0.557130i	$-0.811902\pi$
$7$	−20.5288	+	7.47187i	−1.10845	+	0.403443i	−0.278026	+	0.960574i	$0.589680\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$		0			0
$10$	0.857990	+	1.48608i	0.0271320	+	0.0469941i
$11$	37.2066	+	31.2201i	1.01984	+	0.855746i	0.989607	−	0.143797i	$-0.0459313\pi$
$11$	37.2066	+	31.2201i	1.01984	+	0.855746i	0.0302309	+	0.999543i	$0.490376\pi$
$12$		0			0
$13$	9.56100	+	54.2231i	0.203980	+	1.15683i	0.899036	+	0.437874i	$0.144269\pi$
$13$	9.56100	+	54.2231i	0.203980	+	1.15683i	−0.695056	+	0.718956i	$0.744620\pi$
$14$	7.58714	+	43.0288i	0.144839	+	0.821423i
$15$		0			0
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	−39.6041	−	68.5963i	−0.565024	−	0.978649i	−0.997047	−	0.0767873i	$-0.975534\pi$
$17$	−39.6041	−	68.5963i	−0.565024	−	0.978649i	0.432024	−	0.901862i	$-0.357800\pi$
$18$		0			0
$19$	−55.0156	+	95.2899i	−0.664287	+	1.15058i	0.315191	+	0.949028i	$0.397931\pi$
$19$	−55.0156	+	95.2899i	−0.664287	+	1.15058i	−0.979478	+	0.201550i	$0.935402\pi$
$20$	3.22499	−	1.17380i	0.0360565	−	0.0131235i
$21$		0			0
$22$	74.4132	−	62.4401i	0.721134	−	0.605104i
$23$	42.5012	+	15.4692i	0.385310	+	0.140241i	0.527410	−	0.849611i	$-0.323163\pi$
$23$	42.5012	+	15.4692i	0.385310	+	0.140241i	−0.142100	+	0.989852i	$0.545386\pi$
$24$		0			0
$25$	−21.5782	+	122.376i	−0.172626	+	0.979008i
$26$	110.119			0.830621
$27$		0			0
$28$	87.3852			0.589794
$29$	−21.6890	+	123.004i	−0.138881	+	0.787633i	0.833197	+	0.552976i	$0.186508\pi$
$29$	−21.6890	+	123.004i	−0.138881	+	0.787633i	−0.972078	+	0.234657i	$0.924603\pi$
$30$		0			0
$31$	125.635	+	45.7274i	0.727893	+	0.264931i	0.679273	−	0.733886i	$-0.262295\pi$
$31$	125.635	+	45.7274i	0.727893	+	0.264931i	0.0486205	+	0.998817i	$0.484518\pi$
$32$	24.5134	−	20.5692i	0.135419	−	0.113630i
$33$		0			0
$34$	−148.863	+	54.1816i	−0.750874	+	0.273296i
$35$	9.37195	−	16.2327i	0.0452614	−	0.0783950i
$36$		0			0
$37$	−84.1614	−	145.772i	−0.373947	−	0.647696i	0.616222	−	0.787573i	$-0.288663\pi$
$37$	−84.1614	−	145.772i	−0.373947	−	0.647696i	−0.990169	+	0.139877i	$0.955329\pi$
$38$	168.578	+	141.453i	0.719655	+	0.603863i
$39$		0			0
$40$	−1.19191	−	6.75964i	−0.00471143	−	0.0267198i
$41$	3.71508	+	21.0693i	0.0141512	+	0.0802554i	0.991065	−	0.133376i	$-0.0425819\pi$
$41$	3.71508	+	21.0693i	0.0141512	+	0.0802554i	−0.976914	+	0.213632i	$0.931471\pi$
$42$		0			0
$43$	−128.831	−	108.102i	−0.456898	−	0.383383i	0.385090	−	0.922879i	$-0.374170\pi$
$43$	−128.831	−	108.102i	−0.456898	−	0.383383i	−0.841988	+	0.539496i	$0.818615\pi$
$44$	−97.1396	−	168.251i	−0.332826	−	0.576472i
$45$		0			0
$46$	45.2289	−	78.3387i	0.144970	−	0.251096i
$47$	298.913	−	108.795i	0.927680	−	0.337648i	0.166390	−	0.986060i	$-0.446789\pi$
$47$	298.913	−	108.795i	0.927680	−	0.337648i	0.761289	+	0.648412i	$0.224567\pi$
$48$		0			0
$49$	102.849	−	86.3009i	0.299853	−	0.251606i
$50$	233.540	+	85.0015i	0.660550	+	0.240420i
$51$		0			0
$52$	38.2440	−	216.893i	0.101990	−	0.578415i
$53$	−463.685			−1.20174			−0.600869	−	0.799348i	$-0.705178\pi$
$53$	−463.685			−1.20174			−0.600869	+	0.799348i	$0.705178\pi$
$54$		0			0
$55$	−41.6724			−0.102166
$56$	30.3485	−	172.115i	0.0724196	−	0.410712i
$57$		0			0
$58$	234.739	+	85.4380i	0.531427	+	0.193423i
$59$	−415.527	+	348.668i	−0.916898	+	0.769369i	−0.973419	−	0.229033i	$-0.926444\pi$
$59$	−415.527	+	348.668i	−0.916898	+	0.769369i	0.0565206	+	0.998401i	$0.481999\pi$
$60$		0			0
$61$	−648.554	+	236.054i	−1.36129	+	0.495470i	−0.916453	−	0.400141i	$-0.868961\pi$
$61$	−648.554	+	236.054i	−1.36129	+	0.495470i	−0.444838	+	0.895611i	$0.646739\pi$
$62$	133.698	−	231.571i	0.273865	−	0.474349i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−36.1884	−	30.3657i	−0.0690557	−	0.0579446i
$66$		0			0
$67$	111.664	+	633.280i	0.203611	+	1.15474i	0.899610	+	0.436695i	$0.143851\pi$
$67$	111.664	+	633.280i	0.203611	+	1.15474i	−0.695998	+	0.718043i	$0.745038\pi$
$68$	55.0174	+	312.019i	0.0981153	+	0.556440i
$69$		0			0
$70$	−28.7173	−	24.0967i	−0.0490340	−	0.0411444i
$71$	−524.772	−	908.932i	−0.877169	−	1.51930i	−0.854434	−	0.519560i	$-0.826096\pi$
$71$	−524.772	−	908.932i	−0.877169	−	1.51930i	−0.0227353	−	0.999742i	$-0.507237\pi$
$72$		0			0
$73$	480.157	−	831.656i	0.769837	−	1.33340i	−0.167814	−	0.985819i	$-0.553671\pi$
$73$	480.157	−	831.656i	0.769837	−	1.33340i	0.937651	−	0.347578i	$-0.112996\pi$
$74$	−316.343	+	115.140i	−0.496948	+	0.180874i
$75$		0			0
$76$	337.155	−	282.907i	0.508873	−	0.426995i
$77$	−997.080	−	362.907i	−1.47569	−	0.537105i
$78$		0			0
$79$	39.7859	−	225.637i	0.0566616	−	0.321344i	−0.943282	−	0.331993i	$-0.892279\pi$
$79$	39.7859	−	225.637i	0.0566616	−	0.321344i	0.999943	+	0.0106497i	$0.00338996\pi$
$80$	−13.7278			−0.0191852
$81$		0			0
$82$	42.7886			0.0576246
$83$	29.5416	−	167.539i	0.0390676	−	0.221564i	−0.959023	−	0.283328i	$-0.908562\pi$
$83$	29.5416	−	167.539i	0.0390676	−	0.221564i	0.998091	+	0.0617642i	$0.0196727\pi$
$84$		0			0
$85$	63.8613	+	23.2436i	0.0814910	+	0.0296603i
$86$	−257.663	+	216.205i	−0.323075	+	0.271092i
$87$		0			0
$88$	−365.125	+	132.895i	−0.442301	+	0.160984i
$89$	−379.679	+	657.623i	−0.452201	+	0.783235i	−0.998522	−	0.0543405i	$-0.982694\pi$
$89$	−379.679	+	657.623i	−0.452201	+	0.783235i	0.546322	+	0.837576i	$0.316028\pi$
$90$		0			0
$91$	−601.424	−	1041.70i	−0.692817	−	1.19999i
$92$	−138.589	−	116.290i	−0.157054	−	0.131784i
$93$		0			0
$94$	−110.474	−	626.528i	−0.121218	−	0.687462i
$95$	−16.3934	−	92.9715i	−0.0177045	−	0.100407i
$96$		0			0
$97$	1232.17	+	1033.92i	1.28978	+	1.08225i	0.991816	+	0.127673i	$0.0407509\pi$
$97$	1232.17	+	1033.92i	1.28978	+	1.08225i	0.297961	+	0.954578i	$0.403694\pi$
$98$	−134.260	−	232.546i	−0.138391	−	0.239701i
$99$		0			0
$100$	248.528	−	430.463i	0.248528	−	0.430463i
$101$	1527.30	−	555.893i	1.50468	−	0.547657i	0.547410	−	0.836865i	$-0.315614\pi$
$101$	1527.30	−	555.893i	1.50468	−	0.547657i	0.957267	+	0.289207i	$0.0933916\pi$
$102$		0			0
$103$	−5.96157	+	5.00235i	−0.00570302	+	0.00478540i	−0.645635	−	0.763646i	$-0.723407\pi$
$103$	−5.96157	+	5.00235i	−0.00570302	+	0.00478540i	0.639932	+	0.768432i	$0.278963\pi$
$104$	−413.913	−	150.652i	−0.390264	−	0.142045i
$105$		0			0
$106$	−161.036	+	913.282i	−0.147559	+	0.836847i
$107$	1846.09			1.66792			0.833962	−	0.551822i	$-0.186067\pi$
$107$	1846.09			1.66792			0.833962	+	0.551822i	$0.186067\pi$
$108$		0			0
$109$	−1637.48			−1.43892			−0.719461	−	0.694532i	$-0.755611\pi$
$109$	−1637.48			−1.43892			−0.719461	+	0.694532i	$0.755611\pi$
$110$	−14.4727	+	82.0786i	−0.0125447	+	0.0711445i
$111$		0			0
$112$	−328.461	−	119.550i	−0.277113	−	0.100861i
$113$	−300.868	+	252.458i	−0.250471	+	0.210170i	−0.759375	−	0.650653i	$-0.774495\pi$
$113$	−300.868	+	252.458i	−0.250471	+	0.210170i	0.508904	+	0.860823i	$0.330051\pi$
$114$		0			0
$115$	−36.4656	+	13.2724i	−0.0295690	+	0.0107622i
$116$	249.804	−	432.673i	0.199946	−	0.346316i
$117$		0			0
$118$	542.432	+	939.519i	0.423177	+	0.732964i
$119$	1325.57	+	1112.28i	1.02113	+	0.856830i
$120$		0			0
$121$	178.515	+	1012.41i	0.134121	+	0.760637i
$122$	239.696	+	1359.38i	0.177877	+	1.00879i
$123$		0			0
$124$	−409.674	−	343.757i	−0.296692	−	0.248954i
$125$	−106.933	−	185.213i	−0.0765150	−	0.132528i
$126$		0			0
$127$	315.575	−	546.591i	0.220494	−	0.381907i	−0.734464	−	0.678647i	$-0.762566\pi$
$127$	315.575	−	546.591i	0.220494	−	0.381907i	0.954958	+	0.296741i	$0.0958998\pi$
$128$	−120.281	+	43.7786i	−0.0830579	+	0.0302306i
$129$		0			0
$130$	−72.3768	+	60.7314i	−0.0488297	+	0.0409730i
$131$	1695.44	+	617.090i	1.13077	+	0.411568i	0.838573	−	0.544789i	$-0.183390\pi$
$131$	1695.44	+	617.090i	1.13077	+	0.411568i	0.292200	+	0.956357i	$0.405613\pi$
$132$		0			0
$133$	417.411	−	2367.26i	0.272136	−	1.54336i
$134$	1286.10			0.829119
$135$		0			0
$136$	633.665			0.399532
$137$	39.3700	−	223.278i	0.0245518	−	0.139240i	−0.970068	−	0.242834i	$-0.921923\pi$
$137$	39.3700	−	223.278i	0.0245518	−	0.139240i	0.994620	+	0.103594i	$0.0330341\pi$
$138$		0			0
$139$	1267.23	+	461.235i	0.773275	+	0.281449i	0.698365	−	0.715741i	$-0.253911\pi$
$139$	1267.23	+	461.235i	0.773275	+	0.281449i	0.0749093	+	0.997190i	$0.476133\pi$
$140$	−57.4347	+	48.1934i	−0.0346722	+	0.0290935i
$141$		0			0
$142$	−1972.50	+	717.931i	−1.16569	+	0.424278i
$143$	−1337.12	+	2315.95i	−0.781926	+	1.35433i
$144$		0			0
$145$	−53.5824	−	92.8074i	−0.0306881	−	0.0531533i
$146$	−1471.29	−	1234.56i	−0.834003	−	0.699812i
$147$		0			0
$148$	116.916	+	663.062i	0.0649353	+	0.368266i
$149$	−300.894	−	1706.46i	−0.165438	−	0.938244i	−0.948612	−	0.316442i	$-0.897512\pi$
$149$	−300.894	−	1706.46i	−0.165438	−	0.938244i	0.783174	−	0.621802i	$-0.213599\pi$
$150$		0			0
$151$	2448.86	+	2054.84i	1.31977	+	1.10742i	0.986353	+	0.164642i	$0.0526468\pi$
$151$	2448.86	+	2054.84i	1.31977	+	1.10742i	0.333419	+	0.942779i	$0.391798\pi$
$152$	−440.125	−	762.319i	−0.234861	−	0.406791i
$153$		0			0
$154$	−1061.07	+	1837.83i	−0.555217	+	0.961664i
$155$	−107.794	+	39.2336i	−0.0558592	+	0.0203311i
$156$		0			0
$157$	−2697.72	+	2263.65i	−1.37134	+	1.15069i	−0.399052	+	0.916928i	$0.630661\pi$
$157$	−2697.72	+	2263.65i	−1.37134	+	1.15069i	−0.972293	+	0.233766i	$0.924895\pi$
$158$	−430.601	−	156.726i	−0.216815	−	0.0789142i
$159$		0			0
$160$	−4.76763	+	27.0386i	−0.00235571	+	0.0133599i
$161$	−988.083			−0.483676
$162$		0			0
$163$	3109.36			1.49414			0.747068	−	0.664747i	$-0.231461\pi$
$163$	3109.36			1.49414			0.747068	+	0.664747i	$0.231461\pi$
$164$	14.8603	−	84.2772i	0.00707559	−	0.0401277i
$165$		0			0
$166$	−319.727	−	116.371i	−0.149492	−	0.0544106i
$167$	354.144	−	297.162i	0.164099	−	0.137695i	−0.557041	−	0.830485i	$-0.688063\pi$
$167$	354.144	−	297.162i	0.164099	−	0.137695i	0.721139	+	0.692790i	$0.243619\pi$
$168$		0			0
$169$	−784.231	+	285.437i	−0.356955	+	0.129921i
$170$	67.9598	−	117.710i	0.0306605	−	0.0531055i
$171$		0			0
$172$	336.355	+	582.584i	0.149109	+	0.258265i
$173$	723.942	+	607.459i	0.318152	+	0.266961i	0.787852	−	0.615865i	$-0.211193\pi$
$173$	723.942	+	607.459i	0.318152	+	0.266961i	−0.469700	+	0.882826i	$0.655638\pi$
$174$		0			0
$175$	−471.403	−	2673.46i	−0.203627	−	1.15483i
$176$	134.945	+	765.311i	0.0577946	+	0.327770i
$177$		0			0
$178$	1163.40	+	976.212i	0.489892	+	0.411068i
$179$	2112.20	+	3658.44i	0.881974	+	1.52762i	0.849143	+	0.528164i	$0.177119\pi$
$179$	2112.20	+	3658.44i	0.881974	+	1.52762i	0.0328318	+	0.999461i	$0.489547\pi$
$180$		0			0
$181$	−1580.71	+	2737.87i	−0.649135	+	1.12433i	0.334195	+	0.942504i	$0.391535\pi$
$181$	−1580.71	+	2737.87i	−0.649135	+	1.12433i	−0.983330	+	0.181830i	$0.941798\pi$
$182$	−2260.62	+	822.797i	−0.920703	+	0.335109i
$183$		0			0
$184$	−277.179	+	232.580i	−0.111054	+	0.0931851i
$185$	135.710	+	49.3943i	0.0539329	+	0.0196300i
$186$		0			0
$187$	668.046	−	3788.68i	0.261243	−	1.48158i
$188$	−1272.39			−0.493608
$189$		0			0
$190$	−188.811			−0.0720938
$191$	101.947	−	578.168i	0.0386209	−	0.219030i	−0.959389	−	0.282086i	$-0.908974\pi$
$191$	101.947	−	578.168i	0.0386209	−	0.219030i	0.998010	+	0.0630561i	$0.0200847\pi$
$192$		0			0
$193$	−1246.84	−	453.811i	−0.465022	−	0.169254i	0.0988741	−	0.995100i	$-0.468476\pi$
$193$	−1246.84	−	453.811i	−0.465022	−	0.169254i	−0.563896	+	0.825846i	$0.690698\pi$
$194$	2464.35	−	2067.83i	0.912010	−	0.765267i
$195$		0			0
$196$	−504.654	+	183.679i	−0.183912	+	0.0669384i
$197$	1120.32	−	1940.45i	0.405174	−	0.701782i	−0.589168	−	0.808011i	$-0.700544\pi$
$197$	1120.32	−	1940.45i	0.405174	−	0.701782i	0.994342	+	0.106229i	$0.0338775\pi$
$198$		0			0
$199$	273.150	+	473.109i	0.0973019	+	0.168532i	0.910567	−	0.413362i	$-0.135645\pi$
$199$	273.150	+	473.109i	0.0973019	+	0.168532i	−0.813265	+	0.581893i	$0.802312\pi$
$200$	−761.533	−	639.002i	−0.269243	−	0.225921i
$201$		0			0
$202$	−564.468	−	3201.26i	−0.196613	−	1.11505i
$203$	−473.824	−	2687.19i	−0.163822	−	0.929083i
$204$		0			0
$205$	−14.0616	−	11.7991i	−0.00479075	−	0.00401992i
$206$	7.78227	+	13.4793i	0.00263212	+	0.00455896i
$207$		0			0
$208$	−440.477	+	762.928i	−0.146835	+	0.254325i
$209$	−5021.90	+	1827.82i	−1.66207	+	0.604943i
$210$		0			0
$211$	2303.93	−	1933.23i	0.751703	−	0.630754i	−0.184250	−	0.982879i	$-0.558985\pi$
$211$	2303.93	−	1933.23i	0.751703	−	0.630754i	0.935953	+	0.352126i	$0.114541\pi$
$212$	1742.89	+	634.359i	0.564632	+	0.205509i
$213$		0			0
$214$	641.139	−	3636.08i	0.204801	−	1.16148i
$215$	144.295			0.0457712
$216$		0			0
$217$	−2920.80			−0.913719
$218$	−568.692	+	3225.22i	−0.176682	+	1.00201i
$219$		0			0
$220$	156.637	+	57.0112i	0.0480021	+	0.0174713i
$221$	3340.85	−	2803.31i	1.01688	−	0.853261i
$222$		0			0
$223$	461.585	−	168.003i	0.138610	−	0.0504499i	−0.271784	−	0.962358i	$-0.587614\pi$
$223$	461.585	−	168.003i	0.138610	−	0.0504499i	0.410394	+	0.911908i	$0.365391\pi$
$224$	−349.541	+	605.422i	−0.104262	+	0.180587i
$225$		0			0
$226$	392.755	+	680.271i	0.115600	+	0.200225i
$227$	−2585.27	−	2169.30i	−0.755905	−	0.634280i	0.181152	−	0.983455i	$-0.442017\pi$
$227$	−2585.27	−	2169.30i	−0.755905	−	0.634280i	−0.937057	+	0.349175i	$0.886462\pi$
$228$		0			0
$229$	89.6481	+	508.420i	0.0258695	+	0.146713i	0.995007	−	0.0998092i	$-0.0318232\pi$
$229$	89.6481	+	508.420i	0.0258695	+	0.146713i	−0.969137	+	0.246522i	$0.920712\pi$
$230$	13.4772	+	76.4328i	0.00386373	+	0.0219123i
$231$		0			0
$232$	−765.444	−	642.284i	−0.216611	−	0.181759i
$233$	−659.917	−	1143.01i	−0.185548	−	0.321378i	0.758213	−	0.652007i	$-0.226073\pi$
$233$	−659.917	−	1143.01i	−0.185548	−	0.321378i	−0.943761	+	0.330629i	$0.892739\pi$
$234$		0			0
$235$	−136.462	+	236.359i	−0.0378800	+	0.0656100i
$236$	2038.88	−	742.090i	0.562371	−	0.204686i
$237$		0			0
$238$	2651.13	−	2224.56i	0.722048	−	0.605870i
$239$	−688.559	−	250.615i	−0.186357	−	0.0678282i	0.247156	−	0.968976i	$-0.420504\pi$
$239$	−688.559	−	250.615i	−0.186357	−	0.0678282i	−0.433513	+	0.901147i	$0.642726\pi$
$240$		0			0
$241$	678.306	−	3846.87i	0.181301	−	1.02821i	−0.749315	−	0.662213i	$-0.769617\pi$
$241$	678.306	−	3846.87i	0.181301	−	1.02821i	0.930616	−	0.365996i	$-0.119272\pi$
$242$	2056.05			0.546148
$243$		0			0
$244$	2760.71			0.724328
$245$	−20.0032	+	113.444i	−0.00521617	+	0.0295823i
$246$		0			0
$247$	−5692.92	−	2072.05i	−1.46653	−	0.533772i
$248$	−819.348	+	687.515i	−0.209793	+	0.176037i
$249$		0			0
$250$	−401.937	+	146.293i	−0.101683	+	0.0370095i
$251$	−1383.12	+	2395.63i	−0.347816	+	0.602435i	−0.985861	−	0.167564i	$-0.946410\pi$
$251$	−1383.12	+	2395.63i	−0.347816	+	0.602435i	0.638045	+	0.769999i	$0.279743\pi$
$252$		0			0
$253$	1098.38	+	1902.45i	0.272943	+	0.472750i
$254$	−966.977	−	811.390i	−0.238872	−	0.200438i
$255$		0			0
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	−811.001	−	4599.42i	−0.196844	−	1.11636i	−0.909768	−	0.415116i	$-0.863741\pi$
$257$	−811.001	−	4599.42i	−0.196844	−	1.11636i	0.712925	−	0.701241i	$-0.247370\pi$
$258$		0			0
$259$	2816.92	+	2363.68i	0.675811	+	0.567072i
$260$	94.4812	+	163.646i	0.0225364	+	0.0390343i
$261$		0			0
$262$	1804.25	−	3125.05i	0.425446	−	0.736895i
$263$	2955.79	−	1075.82i	0.693011	−	0.252236i	0.0285873	−	0.999591i	$-0.490899\pi$
$263$	2955.79	−	1075.82i	0.693011	−	0.252236i	0.664424	+	0.747356i	$0.268677\pi$
$264$		0			0
$265$	304.761	−	255.725i	0.0706465	−	0.0592795i
$266$	−4517.62	−	1644.28i	−1.04133	−	0.379012i
$267$		0			0
$268$	446.657	−	2533.12i	0.101806	−	0.577369i
$269$	−6454.02			−1.46286			−0.731428	−	0.681919i	$-0.761146\pi$
$269$	−6454.02			−1.46286			−0.731428	+	0.681919i	$0.761146\pi$
$270$		0			0
$271$	535.232			0.119974			0.0599871	−	0.998199i	$-0.480894\pi$
$271$	535.232			0.119974			0.0599871	+	0.998199i	$0.480894\pi$
$272$	220.070	−	1248.08i	0.0490577	−	0.278220i
$273$		0			0
$274$	−426.099	−	155.087i	−0.0939474	−	0.0341941i
$275$	−4623.44	+	3879.53i	−1.01383	+	0.850706i
$276$		0			0
$277$	−1257.77	+	457.791i	−0.272824	+	0.0992997i	−0.474809	−	0.880089i	$-0.657483\pi$
$277$	−1257.77	+	457.791i	−0.272824	+	0.0992997i	0.201985	+	0.979389i	$0.435261\pi$
$278$	1348.56	−	2335.77i	0.290940	−	0.503922i
$279$		0			0
$280$	74.9756	+	129.862i	0.0160023	+	0.0277168i
$281$	−1310.99	−	1100.05i	−0.278316	−	0.233535i	0.492935	−	0.870066i	$-0.335924\pi$
$281$	−1310.99	−	1100.05i	−0.278316	−	0.233535i	−0.771251	+	0.636531i	$0.780369\pi$
$282$		0			0
$283$	89.3278	+	506.603i	0.0187632	+	0.106411i	0.992751	−	0.120189i	$-0.0383500\pi$
$283$	89.3278	+	506.603i	0.0187632	+	0.106411i	−0.973988	+	0.226600i	$0.927239\pi$
$284$	729.006	+	4134.40i	0.152319	+	0.863843i
$285$		0			0
$286$	4097.16	+	3437.93i	0.847099	+	0.710801i
$287$	−233.693	−	404.769i	−0.0480644	−	0.0832499i
$288$		0			0
$289$	−680.466	+	1178.60i	−0.138503	+	0.239894i
$290$	−201.404	+	73.3050i	−0.0407822	+	0.0148435i
$291$		0			0
$292$	−2942.57	+	2469.11i	−0.589729	+	0.494842i
$293$	6134.57	+	2232.80i	1.22316	+	0.445193i	0.871249	−	0.490841i	$-0.163311\pi$
$293$	6134.57	+	2232.80i	1.22316	+	0.445193i	0.351909	+	0.936034i	$0.385533\pi$
$294$		0			0
$295$	80.8161	−	458.331i	0.0159501	−	0.0904578i
$296$	1346.58			0.264421
$297$		0			0
$298$	−3465.56			−0.673674
$299$	−432.433	+	2452.45i	−0.0836397	+	0.474344i
$300$		0			0
$301$	3452.48	+	1256.60i	0.661122	+	0.240629i
$302$	4897.73	−	4109.68i	0.933220	−	0.783065i
$303$		0			0
$304$	−1654.33	+	602.126i	−0.312113	+	0.113600i
$305$	296.082	−	512.830i	0.0555857	−	0.0962772i
$306$		0			0
$307$	2137.01	+	3701.42i	0.397283	+	0.688114i	0.993390	−	0.114791i	$-0.0366198\pi$
$307$	2137.01	+	3701.42i	0.397283	+	0.688114i	−0.596107	+	0.802905i	$0.703287\pi$
$308$	3251.31	+	2728.17i	0.601495	+	0.504714i
$309$		0			0
$310$	39.8389	+	225.937i	0.00729902	+	0.0413948i
$311$	−88.5028	−	501.924i	−0.0161368	−	0.0915161i	0.975676	−	0.219219i	$-0.0703508\pi$
$311$	−88.5028	−	501.924i	−0.0161368	−	0.0915161i	−0.991813	+	0.127703i	$0.959240\pi$
$312$		0			0
$313$	2293.96	+	1924.86i	0.414257	+	0.347603i	0.825973	−	0.563709i	$-0.190626\pi$
$313$	2293.96	+	1924.86i	0.414257	+	0.347603i	−0.411716	+	0.911312i	$0.635070\pi$
$314$	3521.62	+	6099.62i	0.632918	+	1.09625i
$315$		0			0
$316$	−458.236	+	793.687i	−0.0815752	+	0.141292i
$317$	−5173.58	+	1883.03i	−0.916648	+	0.333632i	−0.756904	−	0.653526i	$-0.773289\pi$
$317$	−5173.58	+	1883.03i	−0.916648	+	0.333632i	−0.159744	+	0.987159i	$0.551067\pi$
$318$		0			0
$319$	−4647.18	+	3899.45i	−0.815650	+	0.684411i
$320$	51.5998	+	18.7808i	0.00901412	+	0.00328087i
$321$		0			0
$322$	−343.158	+	1946.14i	−0.0593895	+	0.336815i
$323$	8715.37			1.50135
$324$		0			0
$325$	−6841.92			−1.16776
$326$	1079.87	−	6124.25i	0.183462	−	1.04046i
$327$		0			0
$328$	−160.833	−	58.5383i	−0.0270747	−	0.00985438i
$329$	−5323.42	+	4466.88i	−0.892066	+	0.748532i
$330$		0			0
$331$	−10127.9	+	3686.26i	−1.68182	+	0.612131i	−0.993557	−	0.113335i	$-0.963847\pi$
$331$	−10127.9	+	3686.26i	−1.68182	+	0.612131i	−0.688258	+	0.725466i	$0.741624\pi$
$332$	−340.247	+	589.325i	−0.0562454	+	0.0974198i
$333$		0			0
$334$	−462.302	−	800.731i	−0.0757367	−	0.131180i
$335$	−422.650	−	354.645i	−0.0689308	−	0.0578398i
$336$		0			0
$337$	834.960	+	4735.29i	0.134965	+	0.765424i	0.974884	+	0.222712i	$0.0714911\pi$
$337$	834.960	+	4735.29i	0.134965	+	0.765424i	−0.839919	+	0.542711i	$0.817398\pi$
$338$	289.840	+	1643.76i	0.0466427	+	0.264524i
$339$		0			0
$340$	−208.241	−	174.735i	−0.0332160	−	0.0278716i
$341$	3246.84	+	5623.69i	0.515619	+	0.893079i
$342$		0			0
$343$	2280.09	−	3949.24i	0.358931	−	0.621687i
$344$	1264.28	−	460.160i	0.198155	−	0.0721226i
$345$		0			0
$346$	1447.88	−	1214.92i	0.224967	−	0.188770i
$347$	322.471	+	117.370i	0.0498880	+	0.0181577i	0.366844	−	0.930283i	$-0.380438\pi$
$347$	322.471	+	117.370i	0.0498880	+	0.0181577i	−0.316956	+	0.948440i	$0.602661\pi$
$348$		0			0
$349$	−342.291	+	1941.23i	−0.0524997	+	0.297741i	−0.999740	−	0.0227823i	$-0.992748\pi$
$349$	−342.291	+	1941.23i	−0.0524997	+	0.297741i	0.947241	+	0.320523i	$0.103859\pi$
$350$	−5429.41			−0.829183
$351$		0			0
$352$	1554.23			0.235344
$353$	−132.796	+	753.122i	−0.0200227	+	0.113554i	−0.993181	−	0.116582i	$-0.962806\pi$
$353$	−132.796	+	753.122i	−0.0200227	+	0.113554i	0.973158	+	0.230136i	$0.0739172\pi$
$354$		0			0
$355$	846.192	+	307.989i	0.126510	+	0.0460460i
$356$	2326.81	−	1952.42i	0.346406	−	0.290669i
$357$		0			0
$358$	7939.28	−	2889.66i	1.17208	−	0.426602i
$359$	4076.65	−	7060.97i	0.599325	−	1.03806i	−0.393596	−	0.919283i	$-0.628769\pi$
$359$	4076.65	−	7060.97i	0.599325	−	1.03806i	0.992921	−	0.118777i	$-0.0378975\pi$
$360$		0			0
$361$	−2623.94	−	4544.79i	−0.382554	−	0.662603i
$362$	4843.58	+	4064.25i	0.703240	+	0.590089i
$363$		0			0
$364$	835.490	+	4738.30i	0.120306	+	0.682292i
$365$	143.076	+	811.422i	0.0205176	+	0.116361i
$366$		0			0
$367$	2251.99	+	1889.64i	0.320308	+	0.268770i	0.788737	−	0.614731i	$-0.210735\pi$
$367$	2251.99	+	1889.64i	0.320308	+	0.268770i	−0.468429	+	0.883501i	$0.655180\pi$
$368$	361.831	+	626.710i	0.0512547	+	0.0887758i
$369$		0			0
$370$	144.419	−	250.142i	0.0202919	−	0.0351466i
$371$	9518.90	−	3464.60i	1.33207	−	0.484833i
$372$		0			0
$373$	1766.21	−	1482.03i	0.245177	−	0.205728i	−0.511915	−	0.859036i	$-0.671064\pi$
$373$	1766.21	−	1482.03i	0.245177	−	0.205728i	0.757092	+	0.653308i	$0.226619\pi$
$374$	−7230.23	−	2631.59i	−0.999642	−	0.363840i
$375$		0			0
$376$	−441.895	+	2506.11i	−0.0606090	+	0.343731i
$377$	−6877.06			−0.939487
$378$		0			0
$379$	10193.5			1.38154			0.690769	−	0.723075i	$-0.257272\pi$
$379$	10193.5			1.38154			0.690769	+	0.723075i	$0.257272\pi$
$380$	−65.5735	+	371.886i	−0.00885224	+	0.0502036i
$381$		0			0
$382$	−1103.36	−	401.591i	−0.147783	−	0.0537885i
$383$	−4508.54	+	3783.11i	−0.601503	+	0.504721i	−0.891928	−	0.452177i	$-0.850648\pi$
$383$	−4508.54	+	3783.11i	−0.601503	+	0.504721i	0.290425	+	0.956898i	$0.406203\pi$
$384$		0			0
$385$	855.485	−	311.371i	0.113246	−	0.0412180i
$386$	−1326.86	+	2298.18i	−0.174962	+	0.303042i
$387$		0			0
$388$	−3216.98	−	5571.97i	−0.420921	−	0.729057i
$389$	2291.32	+	1922.65i	0.298649	+	0.250596i	0.779782	−	0.626051i	$-0.215330\pi$
$389$	2291.32	+	1922.65i	0.298649	+	0.250596i	−0.481133	+	0.876648i	$0.659774\pi$
$390$		0			0
$391$	−622.094	−	3528.07i	−0.0804620	−	0.456323i
$392$	186.513	+	1057.77i	0.0240314	+	0.136289i
$393$		0			0
$394$	−3432.85	−	2880.51i	−0.438946	−	0.368319i
$395$	98.2904	+	170.244i	0.0125203	+	0.0216858i
$396$		0			0
$397$	1459.68	−	2528.24i	0.184532	−	0.319619i	−0.758887	−	0.651223i	$-0.774256\pi$
$397$	1459.68	−	2528.24i	0.184532	−	0.319619i	0.943419	+	0.331604i	$0.107590\pi$
$398$	1026.71	−	373.691i	0.129307	−	0.0470639i
$399$		0			0
$400$	−1523.07	+	1278.00i	−0.190383	+	0.159751i
$401$	5558.14	+	2023.00i	0.692170	+	0.251929i	0.664064	−	0.747676i	$-0.268830\pi$
$401$	5558.14	+	2023.00i	0.692170	+	0.251929i	0.0281059	+	0.999605i	$0.491052\pi$
$402$		0			0
$403$	−1278.29	+	7249.52i	−0.158005	+	0.896090i
$404$	−6501.29			−0.800622
$405$		0			0
$406$	−5457.29			−0.667096
$407$	1419.64	−	8051.20i	0.172897	−	0.980549i
$408$		0			0
$409$	2898.68	+	1055.03i	0.350441	+	0.127550i	0.511242	−	0.859437i	$-0.329186\pi$
$409$	2898.68	+	1055.03i	0.350441	+	0.127550i	−0.160801	+	0.986987i	$0.551408\pi$
$410$	−28.1232	+	23.5982i	−0.00338757	+	0.00284251i
$411$		0			0
$412$	29.2518	−	10.6468i	0.00349789	−	0.00127313i
$413$	5925.06	−	10262.5i	0.705940	−	1.22272i
$414$		0			0
$415$	72.9821	+	126.409i	0.00863265	+	0.0149522i
$416$	1349.70	+	1132.53i	0.159073	+	0.133478i
$417$		0			0
$418$	1856.02	+	10526.0i	0.217179	+	1.23168i
$419$	2367.66	+	13427.7i	0.276056	+	1.56559i	0.735586	+	0.677431i	$0.236907\pi$
$419$	2367.66	+	13427.7i	0.276056	+	1.56559i	−0.459529	+	0.888163i	$0.651982\pi$
$420$		0			0
$421$	−4008.80	−	3363.78i	−0.464078	−	0.389408i	0.380551	−	0.924760i	$-0.375734\pi$
$421$	−4008.80	−	3363.78i	−0.464078	−	0.389408i	−0.844629	+	0.535352i	$0.820179\pi$
$422$	−3007.57	−	5209.27i	−0.346934	−	0.600908i
$423$		0			0
$424$	1854.74	−	3212.51i	0.212439	−	0.367955i
$425$	9249.12	−	3366.41i	1.05564	−	0.384223i
$426$		0			0
$427$	11550.3	−	9691.82i	1.30903	−	1.09841i
$428$	−6939.01	−	2525.59i	−0.783668	−	0.285232i
$429$		0			0
$430$	50.1130	−	284.205i	0.00562014	−	0.0318734i
$431$	−1533.38			−0.171370			−0.0856851	−	0.996322i	$-0.527308\pi$
$431$	−1533.38			−0.171370			−0.0856851	+	0.996322i	$0.527308\pi$
$432$		0			0
$433$	11955.1			1.32684			0.663422	−	0.748245i	$-0.269103\pi$
$433$	11955.1			1.32684			0.663422	+	0.748245i	$0.269103\pi$
$434$	−1014.38	+	5752.86i	−0.112194	+	0.636281i
$435$		0			0
$436$	6154.93	+	2240.21i	0.676073	+	0.246070i
$437$	−3812.29	+	3198.89i	−0.417315	+	0.350169i
$438$		0			0
$439$	−13930.3	+	5070.23i	−1.51449	+	0.551228i	−0.959764	−	0.280809i	$-0.909397\pi$
$439$	−13930.3	+	5070.23i	−1.51449	+	0.551228i	−0.554721	+	0.832036i	$0.687175\pi$
$440$	166.690	−	288.715i	0.0180605	−	0.0312817i
$441$		0			0
$442$	−4361.17	−	7553.77i	−0.469321	−	0.812887i
$443$	−7445.43	−	6247.46i	−0.798517	−	0.670035i	0.149321	−	0.988789i	$-0.452291\pi$
$443$	−7445.43	−	6247.46i	−0.798517	−	0.670035i	−0.947838	+	0.318754i	$0.896736\pi$
$444$		0			0
$445$	−113.136	−	641.624i	−0.0120520	−	0.0683503i
$446$	−170.595	−	967.492i	−0.0181119	−	0.102718i
$447$		0			0
$448$	1071.05	+	898.722i	0.112952	+	0.0947781i
$449$	−6100.99	−	10567.2i	−0.641255	−	1.11069i	−0.985153	−	0.171679i	$-0.945081\pi$
$449$	−6100.99	−	10567.2i	−0.641255	−	1.11069i	0.343898	−	0.939007i	$-0.388253\pi$
$450$		0			0
$451$	−519.559	+	899.902i	−0.0542463	+	0.0939573i
$452$	1476.27	−	537.320i	0.153624	−	0.0559146i
$453$		0			0
$454$	−5170.54	+	4338.60i	−0.534506	+	0.448504i
$455$	969.793	+	352.976i	0.0999222	+	0.0363687i
$456$		0			0
$457$	1221.09	−	6925.13i	0.124989	−	0.708849i	−0.856325	−	0.516437i	$-0.827258\pi$
$457$	1221.09	−	6925.13i	0.124989	−	0.708849i	0.981314	−	0.192412i	$-0.0616310\pi$
$458$	1032.53			0.105342
$459$		0			0
$460$	155.224			0.0157334
$461$	−1578.69	+	8953.18i	−0.159494	+	0.904536i	0.795067	+	0.606522i	$0.207436\pi$
$461$	−1578.69	+	8953.18i	−0.159494	+	0.904536i	−0.954561	+	0.298015i	$0.903676\pi$
$462$		0			0
$463$	931.412	+	339.006i	0.0934911	+	0.0340280i	0.388342	−	0.921515i	$-0.373048\pi$
$463$	931.412	+	339.006i	0.0934911	+	0.0340280i	−0.294851	+	0.955543i	$0.595270\pi$
$464$	−1530.89	+	1284.57i	−0.153167	+	0.128523i
$465$		0			0
$466$	−2480.48	+	902.820i	−0.246579	+	0.0897475i
$467$	3257.02	−	5641.32i	0.322734	−	0.558992i	−0.658317	−	0.752741i	$-0.728731\pi$
$467$	3257.02	−	5641.32i	0.322734	−	0.558992i	0.981051	+	0.193749i	$0.0620646\pi$
$468$		0			0
$469$	−7024.12	−	12166.1i	−0.691564	−	1.19782i
$470$	418.143	+	350.864i	0.0410373	+	0.0344344i
$471$		0			0
$472$	−753.538	−	4273.53i	−0.0734839	−	0.416748i
$473$	−1418.42	−	8044.25i	−0.137884	−	0.781976i
$474$		0			0
$475$	−10474.1	−	8788.78i	−1.01175	−	0.848961i
$476$	−3460.81	−	5994.30i	−0.333248	−	0.577202i
$477$		0			0
$478$	−732.750	+	1269.16i	−0.0701155	+	0.121444i
$479$	−17270.9	+	6286.09i	−1.64745	+	0.599622i	−0.988318	−	0.152407i	$-0.951298\pi$
$479$	−17270.9	+	6286.09i	−1.64745	+	0.599622i	−0.659130	+	0.752029i	$0.729075\pi$
$480$		0			0
$481$	7099.54	−	5957.22i	0.672996	−	0.564711i
$482$	−7341.28	−	2672.01i	−0.693747	−	0.252503i
$483$		0			0
$484$	714.059	−	4049.63i	0.0670604	−	0.380318i
$485$	−1380.07			−0.129208
$486$		0			0
$487$	−13583.7			−1.26394			−0.631968	−	0.774994i	$-0.717753\pi$
$487$	−13583.7			−1.26394			−0.631968	+	0.774994i	$0.717753\pi$
$488$	958.783	−	5437.53i	0.0889387	−	0.504396i
$489$		0			0
$490$	216.494	+	78.7974i	0.0199596	+	0.00726470i
$491$	−6381.87	+	5355.02i	−0.586578	+	0.492197i	−0.887100	−	0.461578i	$-0.847284\pi$
$491$	−6381.87	+	5355.02i	−0.586578	+	0.492197i	0.300522	+	0.953775i	$0.402839\pi$
$492$		0			0
$493$	9296.62	−	3383.69i	0.849288	−	0.309115i
$494$	−6058.28	+	10493.2i	−0.551771	+	0.955695i
$495$		0			0
$496$	1069.58	+	1852.57i	0.0968260	+	0.167708i
$497$	17564.4	+	14738.3i	1.58525	+	1.33018i
$498$		0			0
$499$	−2896.15	−	16424.9i	−0.259818	−	1.47350i	−0.783395	−	0.621524i	$-0.786514\pi$
$499$	−2896.15	−	16424.9i	−0.259818	−	1.47350i	0.523577	−	0.851978i	$-0.324597\pi$
$500$	148.550	+	842.467i	0.0132867	+	0.0753526i
$501$		0			0
$502$	4238.12	+	3556.21i	0.376806	+	0.316178i
$503$	−5539.21	−	9594.19i	−0.491016	−	0.850464i	0.508931	−	0.860808i	$-0.330041\pi$
$503$	−5539.21	−	9594.19i	−0.491016	−	0.850464i	−0.999947	+	0.0103431i	$0.996708\pi$
$504$		0			0
$505$	−697.255	+	1207.68i	−0.0614405	+	0.106418i
$506$	4128.55	−	1502.67i	0.362721	−	0.132019i
$507$		0			0
$508$	−1933.95	+	1622.78i	−0.168908	+	0.141731i
$509$	8874.08	+	3229.90i	0.772764	+	0.281263i	0.698152	−	0.715950i	$-0.254006\pi$
$509$	8874.08	+	3229.90i	0.772764	+	0.281263i	0.0746117	+	0.997213i	$0.476228\pi$
$510$		0			0
$511$	−3643.02	+	20660.6i	−0.315377	+	1.78859i
$512$	512.000			0.0441942
$513$		0			0
$514$	−9340.74			−0.801561
$515$	1.15947	−	6.57567i	9.92083e−5	−	0.000562638i
$516$		0			0
$517$	14518.1	+	5284.17i	1.23502	+	0.449512i
$518$	5633.84	−	4727.35i	0.477870	−	0.400981i
$519$		0			0
$520$	355.133	−	129.258i	0.0299493	−	0.0109006i
$521$	−4490.89	+	7778.45i	−0.377638	+	0.654088i	−0.990718	−	0.135932i	$-0.956597\pi$
$521$	−4490.89	+	7778.45i	−0.377638	+	0.654088i	0.613080	+	0.790021i	$0.289930\pi$
$522$		0			0
$523$	5147.16	+	8915.14i	0.430343	+	0.745376i	0.996903	−	0.0786445i	$-0.0250592\pi$
$523$	5147.16	+	8915.14i	0.430343	+	0.745376i	−0.566560	+	0.824021i	$0.691726\pi$
$524$	−5528.54	−	4639.00i	−0.460907	−	0.386747i
$525$		0			0
$526$	−1092.42	−	6195.40i	−0.0905545	−	0.513560i
$527$	−1838.93	−	10429.1i	−0.152002	−	0.862045i
$528$		0			0
$529$	−7753.40	−	6505.88i	−0.637249	−	0.534715i
$530$	−397.837	−	689.075i	−0.0326056	−	0.0564745i
$531$		0			0
$532$	−4807.55	+	8326.92i	−0.391793	+	0.678605i
$533$	−1106.92	+	402.887i	−0.0899553	+	0.0327410i
$534$		0			0
$535$	−1213.36	+	1018.13i	−0.0980523	+	0.0822756i
$536$	−4834.15	−	1759.49i	−0.389559	−	0.141788i
$537$		0			0
$538$	−2241.46	+	12711.9i	−0.179621	+	1.01868i
$539$	6521.00			0.521112
$540$		0			0
$541$	11967.5			0.951059			0.475530	−	0.879700i	$-0.342256\pi$
$541$	11967.5			0.951059			0.475530	+	0.879700i	$0.342256\pi$
$542$	185.884	−	1054.20i	0.0147314	−	0.0835458i
$543$		0			0
$544$	−2381.80	−	866.905i	−0.187719	−	0.0683240i
$545$	1076.25	−	903.082i	0.0845900	−	0.0709794i
$546$		0			0
$547$	15758.3	−	5735.55i	1.23177	−	0.448326i	0.357564	−	0.933889i	$-0.383607\pi$
$547$	15758.3	−	5735.55i	1.23177	−	0.448326i	0.874202	+	0.485562i	$0.161385\pi$
$548$	−453.445	+	785.390i	−0.0353471	+	0.0612230i
$549$		0			0
$550$	6035.47	+	10453.7i	0.467915	+	0.810453i
$551$	−10527.8	−	8833.91i	−0.813977	−	0.683008i
$552$		0			0
$553$	869.174	+	4929.33i	0.0668373	+	0.379053i
$554$	464.853	+	2636.31i	0.0356493	+	0.202177i
$555$		0			0
$556$	−4132.23	−	3467.35i	−0.315190	−	0.264476i
$557$	−3779.27	−	6545.88i	−0.287491	−	0.497950i	0.685719	−	0.727866i	$-0.259488\pi$
$557$	−3779.27	−	6545.88i	−0.287491	−	0.497950i	−0.973210	+	0.229917i	$0.926155\pi$
$558$		0			0
$559$	4629.89	−	8019.21i	0.350310	−	0.606755i
$560$	281.816	−	102.573i	0.0212659	−	0.00774016i
$561$		0			0
$562$	−2621.97	+	2200.10i	−0.196799	+	0.165134i
$563$	8043.34	+	2927.54i	0.602107	+	0.219149i	0.625046	−	0.780588i	$-0.285080\pi$
$563$	8043.34	+	2927.54i	0.602107	+	0.219149i	−0.0229391	+	0.999737i	$0.507302\pi$
$564$		0			0
$565$	58.5159	−	331.860i	0.00435714	−	0.0247106i
$566$	1028.84			0.0764050
$567$		0			0
$568$	8396.36			0.620252
$569$	−1667.17	+	9454.99i	−0.122832	+	0.696615i	0.859740	+	0.510732i	$0.170626\pi$
$569$	−1667.17	+	9454.99i	−0.122832	+	0.696615i	−0.982572	+	0.185883i	$0.940486\pi$
$570$		0			0
$571$	1512.51	+	550.508i	0.110852	+	0.0403468i	0.396851	−	0.917883i	$-0.370103\pi$
$571$	1512.51	+	550.508i	0.110852	+	0.0403468i	−0.285999	+	0.958230i	$0.592325\pi$
$572$	8194.33	−	6875.86i	0.598990	−	0.502612i
$573$		0			0
$574$	−878.399	+	319.711i	−0.0638740	+	0.0232482i
$575$	−2810.16	+	4867.33i	−0.203812	+	0.353012i
$576$		0			0
$577$	6690.66	+	11588.6i	0.482731	+	0.836115i	0.999803	−	0.0198268i	$-0.00631146\pi$
$577$	6690.66	+	11588.6i	0.482731	+	0.836115i	−0.517072	+	0.855942i	$0.672978\pi$
$578$	2085.07	+	1749.58i	0.150047	+	0.125905i
$579$		0			0
$580$	74.4358	+	422.147i	0.00532893	+	0.0302219i
$581$	645.375	+	3660.10i	0.0460837	+	0.261354i
$582$		0			0
$583$	−17252.2	−	14476.3i	−1.22558	−	1.02838i
$584$	3841.25	+	6653.25i	0.272178	+	0.471427i
$585$		0			0
$586$	6528.27	−	11307.3i	0.460205	−	0.797099i
$587$	1415.97	−	515.370i	0.0995626	−	0.0362378i	−0.291759	−	0.956492i	$-0.594240\pi$
$587$	1415.97	−	515.370i	0.0995626	−	0.0362378i	0.391321	+	0.920254i	$0.372018\pi$
$588$		0			0
$589$	−11269.2	+	9456.01i	−0.788354	+	0.661508i
$590$	−874.668	−	318.353i	−0.0610331	−	0.0222142i
$591$		0			0
$592$	467.663	−	2652.25i	0.0324676	−	0.184133i
$593$	14995.5			1.03844			0.519218	−	0.854642i	$-0.326223\pi$
$593$	14995.5			1.03844			0.519218	+	0.854642i	$0.326223\pi$
$594$		0			0
$595$	−1484.67			−0.102295
$596$	−1203.58	+	6825.83i	−0.0827189	+	0.469122i
$597$		0			0
$598$	4680.20	+	1703.45i	0.320046	+	0.116487i
$599$	−2085.81	+	1750.20i	−0.142277	+	0.119384i	−0.711148	−	0.703042i	$-0.751825\pi$
$599$	−2085.81	+	1750.20i	−0.142277	+	0.119384i	0.568872	+	0.822426i	$0.307380\pi$
$600$		0			0
$601$	13275.2	−	4831.78i	0.901009	−	0.327941i	0.150352	−	0.988632i	$-0.451959\pi$
$601$	13275.2	−	4831.78i	0.901009	−	0.327941i	0.750657	+	0.660692i	$0.229737\pi$
$602$	3674.05	−	6363.64i	0.248743	−	0.430835i
$603$		0			0
$604$	−6393.53	−	11073.9i	−0.430710	−	0.746012i
$605$	−675.678	−	566.962i	−0.0454053	−	0.0380996i
$606$		0			0
$607$	1504.53	+	8532.61i	0.100605	+	0.570557i	0.992885	+	0.119076i	$0.0379931\pi$
$607$	1504.53	+	8532.61i	0.100605	+	0.570557i	−0.892281	+	0.451481i	$0.850896\pi$
$608$	611.415	+	3467.51i	0.0407832	+	0.231293i
$609$		0			0
$610$	−907.249	−	761.272i	−0.0602187	−	0.0505295i
$611$	8757.14	+	15167.8i	0.579830	+	1.00429i
$612$		0			0
$613$	−7949.88	+	13769.6i	−0.523805	+	0.907258i	0.475811	+	0.879548i	$0.342155\pi$
$613$	−7949.88	+	13769.6i	−0.523805	+	0.907258i	−0.999616	+	0.0277098i	$0.991179\pi$
$614$	8032.55	−	2923.61i	0.527960	−	0.192162i
$615$		0			0
$616$	6502.61	−	5456.34i	0.425321	−	0.356887i
$617$	25497.4	+	9280.31i	1.66368	+	0.605528i	0.990934	−	0.134349i	$-0.0428943\pi$
$617$	25497.4	+	9280.31i	1.66368	+	0.605528i	0.672742	+	0.739877i	$0.265117\pi$
$618$		0			0
$619$	−1712.87	+	9714.14i	−0.111221	+	0.630766i	0.877331	+	0.479886i	$0.159322\pi$
$619$	−1712.87	+	9714.14i	−0.111221	+	0.630766i	−0.988552	+	0.150880i	$0.951789\pi$
$620$	458.846			0.0297221
$621$		0			0
$622$	−1019.33			−0.0657099
$623$	2880.68	−	16337.1i	0.185252	−	1.05061i
$624$		0			0
$625$	−14423.8	−	5249.83i	−0.923123	−	0.335989i
$626$	4587.93	−	3849.73i	0.292924	−	0.245793i
$627$		0			0
$628$	13237.0	−	4817.86i	0.841102	−	0.306136i
$629$	−6666.27	+	11546.3i	−0.422578	+	0.731927i
$630$		0			0
$631$	8889.21	+	15396.6i	0.560814	+	0.971359i	0.997426	+	0.0717088i	$0.0228452\pi$
$631$	8889.21	+	15396.6i	0.560814	+	0.971359i	−0.436611	+	0.899650i	$0.643821\pi$
$632$	1404.12	+	1178.19i	0.0883746	+	0.0741551i
$633$		0			0
$634$	1912.08	+	10843.9i	0.119777	+	0.679287i
$635$	94.0340	+	533.293i	0.00587657	+	0.0333277i
$636$		0			0
$637$	5662.85	+	4751.70i	0.352230	+	0.295556i
$638$	6066.47	+	10507.4i	0.376448	+	0.652027i
$639$		0			0
$640$	54.9114	−	95.1093i	0.00339150	−	0.00587426i
$641$	−7457.28	+	2714.23i	−0.459508	+	0.167247i	−0.561394	−	0.827549i	$-0.689735\pi$
$641$	−7457.28	+	2714.23i	−0.459508	+	0.167247i	0.101885	+	0.994796i	$0.467512\pi$
$642$		0			0
$643$	−13696.9	+	11493.0i	−0.840050	+	0.704886i	−0.957575	−	0.288184i	$-0.906948\pi$
$643$	−13696.9	+	11493.0i	−0.840050	+	0.704886i	0.117525	+	0.993070i	$0.462504\pi$
$644$	3713.98	+	1351.78i	0.227253	+	0.0827135i
$645$		0			0
$646$	3026.82	−	17165.9i	0.184348	−	1.04549i
$647$	−2356.45			−0.143186			−0.0715931	−	0.997434i	$-0.522808\pi$
$647$	−2356.45			−0.143186			−0.0715931	+	0.997434i	$0.522808\pi$
$648$		0			0
$649$	−26345.8			−1.59347
$650$	−2376.17	+	13476.0i	−0.143386	+	0.813185i
$651$		0			0
$652$	−11687.4	−	4253.86i	−0.702014	−	0.255512i
$653$	20131.3	−	16892.2i	1.20643	−	1.01232i	0.207008	−	0.978339i	$-0.433627\pi$
$653$	20131.3	−	16892.2i	1.20643	−	1.01232i	0.999423	−	0.0339767i	$-0.0108172\pi$
$654$		0			0
$655$	−1454.67	+	529.457i	−0.0867766	+	0.0315841i
$656$	−171.155	+	296.448i	−0.0101867	+	0.0176438i
$657$		0			0
$658$	6949.23	+	12036.4i	0.411716	+	0.713113i
$659$	−4826.44	−	4049.86i	−0.285298	−	0.239393i	0.488896	−	0.872342i	$-0.337400\pi$
$659$	−4826.44	−	4049.86i	−0.285298	−	0.239393i	−0.774194	+	0.632949i	$0.781844\pi$
$660$		0			0
$661$	−1279.64	−	7257.19i	−0.0752983	−	0.427038i	−0.999031	−	0.0440013i	$-0.985989\pi$
$661$	−1279.64	−	7257.19i	−0.0752983	−	0.427038i	0.923733	−	0.383037i	$-0.125122\pi$
$662$	3743.13	+	21228.3i	0.219760	+	1.24632i
$663$		0			0
$664$	1042.58	+	874.825i	0.0609334	+	0.0511292i
$665$	1031.21	+	1786.10i	0.0601331	+	0.104154i
$666$		0			0
$667$	−2824.59	+	4892.33i	−0.163971	+	0.284006i
$668$	−1737.69	+	632.467i	−0.100648	+	0.0366330i
$669$		0			0
$670$	−845.299	+	709.290i	−0.0487414	+	0.0408989i
$671$	−31500.1	−	11465.1i	−1.81229	−	0.659621i
$672$		0			0
$673$	−3374.45	+	19137.4i	−0.193277	+	1.09613i	0.721574	+	0.692337i	$0.243419\pi$
$673$	−3374.45	+	19137.4i	−0.193277	+	1.09613i	−0.914851	+	0.403791i	$0.867692\pi$
$674$	9616.68			0.549586
$675$		0			0
$676$	3338.24			0.189932
$677$	3076.42	−	17447.3i	0.174648	−	0.990477i	−0.763902	−	0.645333i	$-0.776719\pi$
$677$	3076.42	−	17447.3i	0.174648	−	0.990477i	0.938550	−	0.345144i	$-0.112170\pi$
$678$		0			0
$679$	−33020.4	−	12018.4i	−1.86628	−	0.679271i
$680$	−416.482	+	349.470i	−0.0234873	+	0.0197082i
$681$		0			0
$682$	12204.1	−	4441.94i	0.685220	−	0.249400i
$683$	−3496.02	+	6055.29i	−0.195859	+	0.339238i	−0.947182	−	0.320697i	$-0.896083\pi$
$683$	−3496.02	+	6055.29i	−0.195859	+	0.339238i	0.751323	+	0.659935i	$0.229416\pi$
$684$		0			0
$685$	97.2629	+	168.464i	0.00542514	+	0.00939662i
$686$	−6986.61	−	5862.46i	−0.388848	−	0.326283i
$687$		0			0
$688$	−467.259	−	2649.96i	−0.0258926	−	0.146844i
$689$	−4433.30	−	25142.5i	−0.245131	−	1.39021i
$690$		0			0
$691$	12868.3	+	10797.8i	0.708441	+	0.594453i	0.924161	−	0.382003i	$-0.124765\pi$
$691$	12868.3	+	10797.8i	0.708441	+	0.594453i	−0.215720	+	0.976455i	$0.569210\pi$
$692$	−1890.08	−	3273.71i	−0.103829	−	0.179838i
$693$		0			0
$694$	343.166	−	594.381i	0.0187700	−	0.0325107i
$695$	−1087.27	+	395.735i	−0.0593419	+	0.0215987i
$696$		0			0
$697$	1298.14	−	1089.27i	0.0705461	−	0.0591952i
$698$	3704.60	+	1348.36i	0.200890	+	0.0731179i
$699$		0			0
$700$	−1885.61	+	10693.8i	−0.101814	+	0.577413i
$701$	18157.5			0.978315			0.489158	−	0.872195i	$-0.337304\pi$
$701$	18157.5			0.978315			0.489158	+	0.872195i	$0.337304\pi$
$702$		0			0
$703$	18520.8			0.993633
$704$	539.780	−	3061.24i	0.0288973	−	0.163885i
$705$		0			0
$706$	1437.24	+	523.113i	0.0766165	+	0.0278861i
$707$	−27200.1	+	22823.6i	−1.44691	+	1.21410i
$708$		0			0
$709$	23930.9	−	8710.13i	1.26762	−	0.461376i	0.381302	−	0.924451i	$-0.375476\pi$
$709$	23930.9	−	8710.13i	1.26762	−	0.461376i	0.886320	+	0.463074i	$0.153254\pi$
$710$	900.499	−	1559.71i	0.0475988	−	0.0824435i
$711$		0			0
$712$	−3037.43	−	5260.99i	−0.159877	−	0.276915i
$713$	4632.27	+	3886.94i	0.243310	+	0.204161i
$714$		0			0
$715$	−398.430	−	2259.61i	−0.0208398	−	0.118188i
$716$	−2934.24	−	16640.9i	−0.153153	−	0.868575i
$717$		0			0
$718$	−12491.6	−	10481.7i	−0.649279	−	0.544809i
$719$	15455.2	+	26769.1i	0.801642	+	1.38848i	0.918535	+	0.395340i	$0.129373\pi$
$719$	15455.2	+	26769.1i	0.801642	+	1.38848i	−0.116893	+	0.993145i	$0.537293\pi$
$720$		0			0
$721$	85.0069	−	147.236i	0.00439088	−	0.00760522i
$722$	−9862.78	+	3589.76i	−0.508386	+	0.185037i
$723$		0			0
$724$	9687.16	−	8128.49i	0.497266	−	0.417256i
$725$	−14584.8	−	5308.43i	−0.747125	−	0.271931i
$726$		0			0
$727$	−2502.44	+	14192.0i	−0.127662	+	0.724007i	0.852029	+	0.523494i	$0.175372\pi$
$727$	−2502.44	+	14192.0i	−0.127662	+	0.724007i	−0.979691	+	0.200513i	$0.935739\pi$
$728$	9622.79			0.489896
$729$		0			0
$730$	1647.88			0.0835490
$731$	−2313.17	+	13118.6i	−0.117039	+	0.663763i
$732$		0			0
$733$	9569.46	+	3483.00i	0.482205	+	0.175508i	0.571673	−	0.820482i	$-0.306295\pi$
$733$	9569.46	+	3483.00i	0.482205	+	0.175508i	−0.0894684	+	0.995990i	$0.528517\pi$
$734$	4503.98	−	3779.29i	0.226492	−	0.190049i
$735$		0			0
$736$	1360.04	−	495.014i	0.0681138	−	0.0247914i
$737$	−15616.4	+	27048.4i	−0.780511	+	1.35189i
$738$		0			0
$739$	−4804.30	−	8321.29i	−0.239146	−	0.414213i	0.721323	−	0.692598i	$-0.243534\pi$
$739$	−4804.30	−	8321.29i	−0.239146	−	0.414213i	−0.960469	+	0.278385i	$0.910201\pi$
$740$	−442.527	−	371.324i	−0.0219832	−	0.0184461i
$741$		0			0
$742$	−3518.04	−	19951.8i	−0.174059	−	0.987135i
$743$	−4955.96	−	28106.6i	−0.244706	−	1.38780i	−0.821175	−	0.570677i	$-0.806681\pi$
$743$	−4955.96	−	28106.6i	−0.244706	−	1.38780i	0.576469	−	0.817119i	$-0.304430\pi$
$744$		0			0
$745$	1138.89	+	955.639i	0.0560074	+	0.0469958i
$746$	−2305.63	−	3993.47i	−0.113157	−	0.195994i
$747$		0			0
$748$	−7694.25	+	13326.8i	−0.376109	+	0.651440i
$749$	−37897.9	+	13793.7i	−1.84881	+	0.672913i
$750$		0			0
$751$	−2949.90	+	2475.26i	−0.143333	+	0.120271i	−0.711635	−	0.702549i	$-0.752045\pi$
$751$	−2949.90	+	2475.26i	−0.143333	+	0.120271i	0.568302	+	0.822820i	$0.307601\pi$
$752$	4782.61	+	1740.73i	0.231920	+	0.0844119i
$753$		0			0
$754$	−2388.38	+	13545.2i	−0.115357	+	0.654225i
$755$	−2742.79			−0.132212
$756$		0			0
$757$	−22515.6			−1.08104			−0.540518	−	0.841332i	$-0.681772\pi$
$757$	−22515.6			−1.08104			−0.540518	+	0.841332i	$0.681772\pi$
$758$	3540.15	−	20077.2i	0.169636	−	0.962054i
$759$		0			0
$760$	709.699	+	258.309i	0.0338730	+	0.0123288i
$761$	15419.0	−	12938.1i	0.734479	−	0.616301i	−0.196869	−	0.980430i	$-0.563078\pi$
$761$	15419.0	−	12938.1i	0.734479	−	0.616301i	0.931349	+	0.364128i	$0.118633\pi$
$762$		0			0
$763$	33615.6	−	12235.1i	1.59498	−	0.580524i
$764$	−1174.17	+	2033.73i	−0.0556023	+	0.0963059i
$765$		0			0
$766$	5885.48	+	10194.0i	0.277612	+	0.480839i
$767$	−22878.7	−	19197.6i	−1.07706	−	0.903759i
$768$		0			0
$769$	5018.25	+	28459.9i	0.235322	+	1.33458i	0.841935	+	0.539579i	$0.181417\pi$
$769$	5018.25	+	28459.9i	0.235322	+	1.33458i	−0.606613	+	0.794997i	$0.707472\pi$
$770$	−316.174	−	1793.11i	−0.0147976	−	0.0839212i
$771$		0			0
$772$	4065.72	+	3411.54i	0.189545	+	0.159047i
$773$	−20093.2	−	34802.5i	−0.934932	−	1.61935i	−0.774755	−	0.632261i	$-0.782127\pi$
$773$	−20093.2	−	34802.5i	−0.934932	−	1.61935i	−0.160177	−	0.987088i	$-0.551206\pi$
$774$		0			0
$775$	−8306.91	+	14388.0i	−0.385023	+	0.666879i
$776$	−12091.9	+	4401.09i	−0.559373	+	0.203595i
$777$		0			0
$778$	4582.64	−	3845.29i	0.211177	−	0.177198i
$779$	−2212.08	−	805.130i	−0.101741	−	0.0370305i
$780$		0			0
$781$	8851.92	−	50201.7i	0.405565	−	2.30008i
$782$	−7164.99			−0.327647
$783$		0			0
$784$	2148.17			0.0978574
$785$	524.680	−	2975.61i	0.0238556	−	0.135292i
$786$		0			0
$787$	−12441.4	−	4528.31i	−0.563518	−	0.205104i	0.0445242	−	0.999008i	$-0.485823\pi$
$787$	−12441.4	−	4528.31i	−0.563518	−	0.205104i	−0.608043	+	0.793904i	$0.708045\pi$
$788$	−6865.70	+	5761.01i	−0.310381	+	0.260441i
$789$		0			0
$790$	369.451	−	134.469i	0.0166386	−	0.00605595i
$791$	4290.12	−	7430.70i	0.192843	−	0.334014i
$792$		0			0
$793$	−19000.4	−	32909.7i	−0.850851	−	1.47372i
$794$	−4472.72	−	3753.06i	−0.199913	−	0.167747i
$795$		0			0
$796$	−379.456	−	2152.00i	−0.0168963	−	0.0958236i
$797$	4406.01	+	24987.7i	0.195820	+	1.11055i	0.911245	+	0.411864i	$0.135122\pi$
$797$	4406.01	+	24987.7i	0.195820	+	1.11055i	−0.715425	+	0.698690i	$0.753767\pi$
$798$		0			0
$799$	−19301.1	−	16195.6i	−0.854600	−	0.717094i
$800$	1988.22	+	3443.70i	0.0878678	+	0.152192i
$801$		0			0
$802$	5914.85	−	10244.8i	0.260425	−	0.451069i
$803$	43829.4	−	15952.6i	1.92616	−	0.701064i
$804$		0			0
$805$	649.426	−	544.933i	0.0284339	−	0.0238589i
$806$	13834.8	+	5035.46i	0.604604	+	0.220058i
$807$		0			0
$808$	−2257.87	+	12805.0i	−0.0983066	+	0.557524i
$809$	−13345.4			−0.579976			−0.289988	−	0.957030i	$-0.593651\pi$
$809$	−13345.4			−0.579976			−0.289988	+	0.957030i	$0.593651\pi$
$810$		0			0
$811$	33175.7			1.43644			0.718222	−	0.695815i	$-0.244956\pi$
$811$	33175.7			1.43644			0.718222	+	0.695815i	$0.244956\pi$
$812$	−1895.30	+	10748.8i	−0.0819112	+	0.464542i
$813$		0			0
$814$	−15364.7	−	5592.31i	−0.661589	−	0.240799i
$815$	−2043.66	+	1714.83i	−0.0878358	+	0.0737030i
$816$		0			0
$817$	17388.8	−	6329.00i	0.744623	−	0.271021i
$818$	3084.71	−	5342.87i	0.131851	−	0.228373i
$819$		0			0
$820$	36.7122	+	63.5874i	0.00156347	+	0.00270801i
$821$	13847.4	+	11619.4i	0.588646	+	0.493933i	0.887774	−	0.460280i	$-0.152251\pi$
$821$	13847.4	+	11619.4i	0.588646	+	0.493933i	−0.299127	+	0.954213i	$0.596696\pi$
$822$		0			0
$823$	−4271.08	−	24222.5i	−0.180900	−	1.02593i	−0.931111	−	0.364735i	$-0.881159\pi$
$823$	−4271.08	−	24222.5i	−0.180900	−	1.02593i	0.750212	−	0.661198i	$-0.229952\pi$
$824$	−10.8110	−	61.3123i	−0.000457063	−	0.00259213i
$825$		0			0
$826$	−18155.4	−	15234.2i	−0.764780	−	0.641727i
$827$	−3860.28	−	6686.21i	−0.162316	−	0.281139i	0.773383	−	0.633939i	$-0.218563\pi$
$827$	−3860.28	−	6686.21i	−0.162316	−	0.281139i	−0.935699	+	0.352800i	$0.885230\pi$
$828$		0			0
$829$	6380.71	−	11051.7i	0.267323	−	0.463018i	−0.700846	−	0.713312i	$-0.747194\pi$
$829$	6380.71	−	11051.7i	0.267323	−	0.463018i	0.968170	+	0.250295i	$0.0805275\pi$
$830$	274.323	−	99.8454i	0.0114722	−	0.00417552i
$831$		0			0
$832$	2699.40	−	2265.06i	0.112482	−	0.0943834i
$833$	−9993.18	−	3637.22i	−0.415658	−	0.151287i
$834$		0			0
$835$	−68.8777	+	390.625i	−0.00285462	+	0.0161894i
$836$	21376.8			0.884368
$837$		0			0
$838$	27269.6			1.12412
$839$	−310.479	+	1760.81i	−0.0127758	+	0.0724553i	−0.990529	−	0.137303i	$-0.956157\pi$
$839$	−310.479	+	1760.81i	−0.0127758	+	0.0724553i	0.977753	+	0.209758i	$0.0672677\pi$
$840$		0			0
$841$	8258.48	+	3005.84i	0.338615	+	0.123246i
$842$	−8017.60	+	6727.56i	−0.328153	+	0.275353i
$843$		0			0
$844$	−11304.8	+	4114.60i	−0.461050	+	0.167809i
$845$	358.023	−	620.113i	0.0145756	−	0.0252456i
$846$		0			0
$847$	−11229.3	−	19449.7i	−0.455540	−	0.789018i
$848$	−5683.26	−	4768.82i	−0.230146	−	0.193115i
$849$		0			0
$850$	−3418.34	−	19386.4i	−0.137939	−	0.782290i
$851$	−1321.99	−	7497.39i	−0.0532518	−	0.302006i
$852$		0			0
$853$	−17839.3	−	14968.9i	−0.716067	−	0.600852i	0.210227	−	0.977653i	$-0.432580\pi$
$853$	−17839.3	−	14968.9i	−0.716067	−	0.600852i	−0.926294	+	0.376801i	$0.877024\pi$
$854$	−15077.8	−	26115.5i	−0.604159	−	1.04643i
$855$		0			0
$856$	−7384.34	+	12790.1i	−0.294850	+	0.510695i
$857$	9309.08	−	3388.23i	0.371053	−	0.135052i	−0.149762	−	0.988722i	$-0.547851\pi$
$857$	9309.08	−	3388.23i	0.371053	−	0.135052i	0.520814	+	0.853670i	$0.325628\pi$
$858$		0			0
$859$	5179.55	−	4346.16i	0.205732	−	0.172630i	−0.534100	−	0.845421i	$-0.679349\pi$
$859$	5179.55	−	4346.16i	0.205732	−	0.172630i	0.739832	+	0.672791i	$0.234905\pi$
$860$	−542.370	−	197.407i	−0.0215054	−	0.00782733i
$861$		0			0
$862$	−532.539	+	3020.18i	−0.0210422	+	0.119336i
$863$	−6733.15			−0.265584			−0.132792	−	0.991144i	$-0.542394\pi$
$863$	−6733.15			−0.265584			−0.132792	+	0.991144i	$0.542394\pi$
$864$		0			0
$865$	−810.834			−0.0318719
$866$	4151.95	−	23546.9i	0.162920	−	0.923967i
$867$		0			0
$868$	10978.6	+	3995.89i	0.429307	+	0.156255i
$869$	8524.70	−	7153.07i	0.332774	−	0.279231i
$870$		0			0
$871$	−33270.8	+	12109.6i	−1.29430	+	0.471088i
$872$	6549.94	−	11344.8i	0.254368	−	0.440578i
$873$		0			0
$874$	4976.59	+	8619.71i	0.192604	+	0.333599i
$875$	3579.10	+	3003.22i	0.138281	+	0.116031i
$876$		0			0
$877$	3348.73	+	18991.6i	0.128938	+	0.731244i	0.978891	+	0.204385i	$0.0655193\pi$
$877$	3348.73	+	18991.6i	0.128938	+	0.731244i	−0.849953	+	0.526859i	$0.823370\pi$
$878$	5148.45	+	29198.3i	0.197895	+	1.12232i
$879$		0			0
$880$	−510.767	−	428.584i	−0.0195658	−	0.0164177i
$881$	19079.7	+	33047.0i	0.729638	+	1.26377i	0.957036	+	0.289969i	$0.0936448\pi$
$881$	19079.7	+	33047.0i	0.729638	+	1.26377i	−0.227398	+	0.973802i	$0.573022\pi$
$882$		0			0
$883$	7602.93	−	13168.7i	0.289761	−	0.501881i	−0.683992	−	0.729490i	$-0.739758\pi$
$883$	7602.93	−	13168.7i	0.289761	−	0.501881i	0.973753	+	0.227609i	$0.0730909\pi$
$884$	−16392.6	+	5966.43i	−0.623692	+	0.227005i
$885$		0			0
$886$	−14890.9	+	12494.9i	−0.564637	+	0.473786i
$887$	31508.2	+	11468.1i	1.19272	+	0.434115i	0.860678	−	0.509149i	$-0.170040\pi$
$887$	31508.2	+	11468.1i	1.19272	+	0.434115i	0.332043	+	0.943264i	$0.392262\pi$
$888$		0			0
$889$	−2394.31	+	13578.8i	−0.0903290	+	0.512281i
$890$	−1303.04			−0.0490765
$891$		0			0
$892$	−1964.83			−0.0737528
$893$	−6077.78	+	34468.8i	−0.227755	+	1.29166i
$894$		0			0
$895$	−3405.91	−	1239.65i	−0.127204	−	0.0462983i
$896$	2142.11	−	1797.44i	0.0798693	−	0.0670183i
$897$		0			0
$898$	−22932.2	+	8346.64i	−0.852180	+	0.310168i
$899$	−8349.57	+	14461.9i	−0.309759	+	0.536519i
$900$		0			0
$901$	18363.8	+	31807.1i	0.679010	+	1.17608i
$902$	1592.02	+	1335.86i	0.0587677	+	0.0493120i
$903$		0			0
$904$	−545.609	−	3094.30i	−0.0200738	−	0.113844i
$905$	−471.015	−	2671.26i	−0.0173006	−	0.0981168i
$906$		0			0
$907$	35183.3	+	29522.3i	1.28803	+	1.08078i	0.992084	+	0.125578i	$0.0400785\pi$
$907$	35183.3	+	29522.3i	1.28803	+	1.08078i	0.295944	+	0.955205i	$0.404366\pi$
$908$	6749.67	+	11690.8i	0.246691	+	0.427281i
$909$		0			0
$910$	1032.03	−	1787.53i	0.0375951	−	0.0651166i
$911$	42041.8	−	15302.0i	1.52899	−	0.556506i	0.565615	−	0.824670i	$-0.308639\pi$
$911$	42041.8	−	15302.0i	1.52899	−	0.556506i	0.963373	+	0.268163i	$0.0864167\pi$
$912$		0			0
$913$	6329.72	−	5311.26i	0.229445	−	0.192527i
$914$	−13215.8	−	4810.15i	−0.478270	−	0.174076i
$915$		0			0
$916$	358.592	−	2033.68i	0.0129347	−	0.0733566i
$917$	−39416.2			−1.41945
$918$		0			0
$919$	−24618.1			−0.883651			−0.441826	−	0.897101i	$-0.645669\pi$
$919$	−24618.1			−0.883651			−0.441826	+	0.897101i	$0.645669\pi$
$920$	53.9086	−	305.731i	0.00193186	−	0.0109561i
$921$		0			0
$922$	17086.1	+	6218.82i	0.610303	+	0.222132i
$923$	44267.8	−	37145.1i	1.57865	−	1.32464i
$924$		0			0
$925$	19655.0	−	7153.84i	0.698652	−	0.254289i
$926$	991.188	−	1716.79i	0.0351754	−	0.0609257i
$927$		0			0
$928$	1998.43	+	3461.39i	0.0706915	+	0.122441i
$929$	13710.8	+	11504.7i	0.484214	+	0.406304i	0.851947	−	0.523627i	$-0.175422\pi$
$929$	13710.8	+	11504.7i	0.484214	+	0.406304i	−0.367733	+	0.929931i	$0.619866\pi$
$930$		0			0
$931$	2565.28	+	14548.4i	0.0903046	+	0.512143i
$932$	916.748	+	5199.13i	0.0322200	+	0.182729i
$933$		0			0
$934$	−9980.09	−	8374.29i	−0.349634	−	0.293378i
$935$	1650.40	+	2858.57i	0.0577260	+	0.0999843i
$936$		0			0
$937$	5441.89	−	9425.63i	0.189732	−	0.328625i	−0.755429	−	0.655231i	$-0.772571\pi$
$937$	5441.89	−	9425.63i	0.189732	−	0.328625i	0.945161	+	0.326605i	$0.105905\pi$
$938$	−26402.0	+	9609.56i	−0.919038	+	0.334502i
$939$		0			0
$940$	836.287	−	701.728i	0.0290177	−	0.0243488i
$941$	−13465.7	−	4901.12i	−0.466493	−	0.169789i	0.0980702	−	0.995179i	$-0.468733\pi$
$941$	−13465.7	−	4901.12i	−0.466493	−	0.169789i	−0.564563	+	0.825390i	$0.690955\pi$
$942$		0			0
$943$	−168.029	+	952.940i	−0.00580252	+	0.0329077i
$944$	−8678.91			−0.299231
$945$		0			0
$946$	−16336.7			−0.561471
$947$	−5576.29	+	31624.7i	−0.191346	+	1.08518i	0.726180	+	0.687505i	$0.241294\pi$
$947$	−5576.29	+	31624.7i	−0.191346	+	1.08518i	−0.917526	+	0.397675i	$0.869817\pi$
$948$		0			0
$949$	49685.8	+	18084.1i	1.69955	+	0.618584i
$950$	−20948.1	+	17577.6i	−0.715417	+	0.600306i
$951$		0			0
$952$	−13008.4	+	4734.67i	−0.442862	+	0.161188i
$953$	23715.8	−	41077.0i	0.806118	−	1.39624i	−0.109417	−	0.993996i	$-0.534898\pi$
$953$	23715.8	−	41077.0i	0.806118	−	1.39624i	0.915534	−	0.402241i	$-0.131768\pi$
$954$		0			0
$955$	251.857	+	436.230i	0.00853394	+	0.0147812i
$956$	2245.28	+	1884.01i	0.0759596	+	0.0637377i
$957$		0			0
$958$	6383.07	+	36200.2i	0.215269	+	1.22085i
$959$	860.088	+	4877.80i	0.0289611	+	0.164246i
$960$		0			0
$961$	−9128.10	−	7659.38i	−0.306404	−	0.257104i
$962$	−9267.79	−	16052.3i	−0.310609	−	0.537990i
$963$		0			0
$964$	−7812.42	+	13531.5i	−0.261018	+	0.452096i
$965$	1069.77	−	389.366i	0.0356862	−	0.0129887i
$966$		0			0
$967$	−616.492	+	517.298i	−0.0205016	+	0.0172029i	−0.652981	−	0.757374i	$-0.726482\pi$
$967$	−616.492	+	517.298i	−0.0205016	+	0.0172029i	0.632479	+	0.774577i	$0.282037\pi$
$968$	−7728.22	−	2812.84i	−0.256606	−	0.0933969i
$969$		0			0
$970$	−479.293	+	2718.20i	−0.0158651	+	0.0899755i
$971$	−5884.04			−0.194467			−0.0972337	−	0.995262i	$-0.530999\pi$
$971$	−5884.04			−0.194467			−0.0972337	+	0.995262i	$0.530999\pi$
$972$		0			0
$973$	−29461.0			−0.970686
$974$	−4717.58	+	26754.7i	−0.155196	+	0.880160i
$975$		0			0
$976$	−10376.9	−	3776.87i	−0.340323	−	0.123867i
$977$	−27422.2	+	23009.9i	−0.897966	+	0.753483i	−0.969792	−	0.243934i	$-0.921562\pi$
$977$	−27422.2	+	23009.9i	−0.897966	+	0.753483i	0.0718255	+	0.997417i	$0.477118\pi$
$978$		0			0
$979$	−34657.6	+	12614.3i	−1.13142	+	0.411804i
$980$	230.388	−	399.044i	0.00750968	−	0.0130071i
$981$		0			0
$982$	8330.94	+	14429.6i	0.270724	+	0.468908i
$983$	3166.54	+	2657.04i	0.102744	+	0.0862121i	0.692712	−	0.721214i	$-0.256416\pi$
$983$	3166.54	+	2657.04i	0.102744	+	0.0862121i	−0.589969	+	0.807426i	$0.700860\pi$
$984$		0			0
$985$	333.829	+	1893.24i	0.0107986	+	0.0612422i
$986$	−3435.89	−	19485.9i	−0.110975	−	0.629369i
$987$		0			0
$988$	18563.6	+	15576.7i	0.597761	+	0.501581i
$989$	−3803.24	−	6587.40i	−0.122281	−	0.211797i
$990$		0			0
$991$	−4653.74	+	8060.52i	−0.149174	+	0.258376i	−0.930922	−	0.365217i	$-0.880995\pi$
$991$	−4653.74	+	8060.52i	−0.149174	+	0.258376i	0.781749	+	0.623594i	$0.214328\pi$
$992$	4020.32	−	1463.28i	0.128675	−	0.0468337i
$993$		0			0
$994$	35128.7	−	29476.5i	1.12094	−	0.940582i
$995$	−440.452	−	160.312i	−0.0140334	−	0.00510776i
$996$		0			0
$997$	−4637.89	+	26302.8i	−0.147325	+	0.835524i	0.818145	+	0.575012i	$0.195003\pi$
$997$	−4637.89	+	26302.8i	−0.147325	+	0.835524i	−0.965471	+	0.260512i	$0.916109\pi$
$998$	−33356.5			−1.05800
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.73.3		30
3.2	odd	2		54.4.e.b.25.2	yes	30
27.11	odd	18		1458.4.a.i.1.9		15
27.13	even	9	inner	162.4.e.b.91.3		30
27.14	odd	18		54.4.e.b.13.2	✓	30
27.16	even	9		1458.4.a.j.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.13.2	✓	30	27.14	odd	18
54.4.e.b.25.2	yes	30	3.2	odd	2
162.4.e.b.73.3		30	1.1	even	1	trivial
162.4.e.b.91.3		30	27.13	even	9	inner
1458.4.a.i.1.9		15	27.11	odd	18
1458.4.a.j.1.7		15	27.16	even	9

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.347296 - 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-0.657259 + 0.551505i) q^{5} +(-20.5288 + 7.47187i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(0.857990 + 1.48608i) q^{10} +(37.2066 + 31.2201i) q^{11} +(9.56100 + 54.2231i) q^{13} +(7.58714 + 43.0288i) q^{14} +(12.2567 + 10.2846i) q^{16} +(-39.6041 - 68.5963i) q^{17} +(-55.0156 + 95.2899i) q^{19} +(3.22499 - 1.17380i) q^{20} +(74.4132 - 62.4401i) q^{22} +(42.5012 + 15.4692i) q^{23} +(-21.5782 + 122.376i) q^{25} +110.119 q^{26} +87.3852 q^{28} +(-21.6890 + 123.004i) q^{29} +(125.635 + 45.7274i) q^{31} +(24.5134 - 20.5692i) q^{32} +(-148.863 + 54.1816i) q^{34} +(9.37195 - 16.2327i) q^{35} +(-84.1614 - 145.772i) q^{37} +(168.578 + 141.453i) q^{38} +(-1.19191 - 6.75964i) q^{40} +(3.71508 + 21.0693i) q^{41} +(-128.831 - 108.102i) q^{43} +(-97.1396 - 168.251i) q^{44} +(45.2289 - 78.3387i) q^{46} +(298.913 - 108.795i) q^{47} +(102.849 - 86.3009i) q^{49} +(233.540 + 85.0015i) q^{50} +(38.2440 - 216.893i) q^{52} -463.685 q^{53} -41.6724 q^{55} +(30.3485 - 172.115i) q^{56} +(234.739 + 85.4380i) q^{58} +(-415.527 + 348.668i) q^{59} +(-648.554 + 236.054i) q^{61} +(133.698 - 231.571i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-36.1884 - 30.3657i) q^{65} +(111.664 + 633.280i) q^{67} +(55.0174 + 312.019i) q^{68} +(-28.7173 - 24.0967i) q^{70} +(-524.772 - 908.932i) q^{71} +(480.157 - 831.656i) q^{73} +(-316.343 + 115.140i) q^{74} +(337.155 - 282.907i) q^{76} +(-997.080 - 362.907i) q^{77} +(39.7859 - 225.637i) q^{79} -13.7278 q^{80} +42.7886 q^{82} +(29.5416 - 167.539i) q^{83} +(63.8613 + 23.2436i) q^{85} +(-257.663 + 216.205i) q^{86} +(-365.125 + 132.895i) q^{88} +(-379.679 + 657.623i) q^{89} +(-601.424 - 1041.70i) q^{91} +(-138.589 - 116.290i) q^{92} +(-110.474 - 626.528i) q^{94} +(-16.3934 - 92.9715i) q^{95} +(1232.17 + 1033.92i) q^{97} +(-134.260 - 232.546i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31}+ \cdots - 4002 q^{98}+O(q^{100}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

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