LMFDB - Embedded newform 162.4.e.b.37.3

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			37.3
Character	$\chi$	$=$	162.37
Dual form			162.4.e.b.127.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-3.40278 + 1.23851i) q^{5} +(-3.51598 - 19.9401i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-3.62116 + 6.27204i) q^{10} +(-49.0055 - 17.8366i) q^{11} +(20.2556 + 16.9964i) q^{13} +(-31.0213 - 26.0300i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(23.7547 - 41.1444i) q^{17} +(-61.3673 - 106.291i) q^{19} +(2.51523 + 14.2646i) q^{20} +(-98.0111 + 35.6731i) q^{22} +(17.4454 - 98.9375i) q^{23} +(-85.7106 + 71.9197i) q^{25} +52.8835 q^{26} -80.9910 q^{28} +(66.6543 - 55.9296i) q^{29} +(-39.5807 + 224.473i) q^{31} +(-30.0702 + 10.9446i) q^{32} +(-16.4999 - 93.5754i) q^{34} +(36.6602 + 63.4973i) q^{35} +(60.3294 - 104.494i) q^{37} +(-230.665 - 83.9554i) q^{38} +(22.1918 + 18.6211i) q^{40} +(24.5313 + 20.5842i) q^{41} +(267.140 + 97.2311i) q^{43} +(-104.301 + 180.655i) q^{44} +(-100.464 - 174.008i) q^{46} +(-43.5991 - 247.263i) q^{47} +(-62.9324 + 22.9055i) q^{49} +(-38.8580 + 220.375i) q^{50} +(81.0222 - 67.9857i) q^{52} +747.772 q^{53} +188.846 q^{55} +(-124.085 + 104.120i) q^{56} +(30.2186 - 171.378i) q^{58} +(-573.277 + 208.656i) q^{59} +(25.6145 + 145.267i) q^{61} +(227.936 + 394.797i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(-89.9755 - 32.7484i) q^{65} +(680.914 + 571.355i) q^{67} +(-145.577 - 122.154i) q^{68} +(137.797 + 50.1541i) q^{70} +(186.829 - 323.598i) q^{71} +(-315.996 - 547.321i) q^{73} +(-41.9043 - 237.651i) q^{74} +(-461.331 + 167.911i) q^{76} +(-183.361 + 1039.89i) q^{77} +(812.837 - 682.051i) q^{79} +57.9386 q^{80} +64.0467 q^{82} +(931.590 - 781.697i) q^{83} +(-29.8743 + 169.426i) q^{85} +(534.281 - 194.462i) q^{86} +(72.4469 + 410.867i) q^{88} +(150.809 + 261.208i) q^{89} +(267.693 - 463.658i) q^{91} +(-377.620 - 137.443i) q^{92} +(-384.673 - 322.779i) q^{94} +(340.462 + 285.682i) q^{95} +(424.244 + 154.412i) q^{97} +(-66.9712 + 115.998i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	1.53209	−	1.28558i	0.541675	−	0.454519i
$2$	1.53209	−	1.28558i	0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.694593	−	3.93923i	0.0868241	−	0.492404i
$5$	−3.40278	+	1.23851i	−0.304354	+	0.110776i	−0.489682	−	0.871901i	$-0.662887\pi$
$5$	−3.40278	+	1.23851i	−0.304354	+	0.110776i	0.185329	+	0.982677i	$0.440665\pi$
$6$		0			0
$7$	−3.51598	−	19.9401i	−0.189845	−	1.07667i	−0.919570	−	0.392925i	$-0.871463\pi$
$7$	−3.51598	−	19.9401i	−0.189845	−	1.07667i	0.729725	−	0.683741i	$-0.239648\pi$
$8$	−4.00000	−	6.92820i	−0.176777	−	0.306186i
$9$		0			0
$10$	−3.62116	+	6.27204i	−0.114511	+	0.198339i
$11$	−49.0055	−	17.8366i	−1.34325	−	0.488902i	−0.432414	−	0.901675i	$-0.642338\pi$
$11$	−49.0055	−	17.8366i	−1.34325	−	0.488902i	−0.910834	+	0.412773i	$0.864560\pi$
$12$		0			0
$13$	20.2556	+	16.9964i	0.432145	+	0.362613i	0.832760	−	0.553634i	$-0.186759\pi$
$13$	20.2556	+	16.9964i	0.432145	+	0.362613i	−0.400616	+	0.916246i	$0.631204\pi$
$14$	−31.0213	−	26.0300i	−0.592200	−	0.496915i
$15$		0			0
$16$	−15.0351	−	5.47232i	−0.234923	−	0.0855050i
$17$	23.7547	−	41.1444i	0.338904	−	0.586999i	−0.645323	−	0.763910i	$-0.723277\pi$
$17$	23.7547	−	41.1444i	0.338904	−	0.586999i	0.984227	+	0.176911i	$0.0566105\pi$
$18$		0			0
$19$	−61.3673	−	106.291i	−0.740980	−	1.28341i	−0.952050	−	0.305944i	$-0.901028\pi$
$19$	−61.3673	−	106.291i	−0.740980	−	1.28341i	0.211070	−	0.977471i	$-0.432305\pi$
$20$	2.51523	+	14.2646i	0.0281212	+	0.159483i
$21$		0			0
$22$	−98.0111	+	35.6731i	−0.949820	+	0.345706i
$23$	17.4454	−	98.9375i	0.158157	−	0.896952i	−0.797686	−	0.603073i	$-0.793943\pi$
$23$	17.4454	−	98.9375i	0.158157	−	0.896952i	0.955843	−	0.293879i	$-0.0949462\pi$
$24$		0			0
$25$	−85.7106	+	71.9197i	−0.685684	+	0.575358i
$26$	52.8835			0.398897
$27$		0			0
$28$	−80.9910			−0.546638
$29$	66.6543	−	55.9296i	0.426807	−	0.358133i	−0.403939	−	0.914786i	$-0.632359\pi$
$29$	66.6543	−	55.9296i	0.426807	−	0.358133i	0.830745	+	0.556653i	$0.187915\pi$
$30$		0			0
$31$	−39.5807	+	224.473i	−0.229319	+	1.30053i	0.624934	+	0.780677i	$0.285126\pi$
$31$	−39.5807	+	224.473i	−0.229319	+	1.30053i	−0.854253	+	0.519857i	$0.825985\pi$
$32$	−30.0702	+	10.9446i	−0.166116	+	0.0604612i
$33$		0			0
$34$	−16.4999	−	93.5754i	−0.0832266	−	0.472001i
$35$	36.6602	+	63.4973i	0.177049	+	0.306657i
$36$		0			0
$37$	60.3294	−	104.494i	0.268056	−	0.464287i	−0.700303	−	0.713845i	$-0.746952\pi$
$37$	60.3294	−	104.494i	0.268056	−	0.464287i	0.968360	+	0.249558i	$0.0802853\pi$
$38$	−230.665	−	83.9554i	−0.984707	−	0.358404i
$39$		0			0
$40$	22.1918	+	18.6211i	0.0877207	+	0.0736064i
$41$	24.5313	+	20.5842i	0.0934426	+	0.0784076i	0.688312	−	0.725415i	$-0.258352\pi$
$41$	24.5313	+	20.5842i	0.0934426	+	0.0784076i	−0.594870	+	0.803822i	$0.702796\pi$
$42$		0			0
$43$	267.140	+	97.2311i	0.947408	+	0.344828i	0.769087	−	0.639144i	$-0.220711\pi$
$43$	267.140	+	97.2311i	0.947408	+	0.344828i	0.178321	+	0.983972i	$0.442934\pi$
$44$	−104.301	+	180.655i	−0.357364	+	0.618972i
$45$		0			0
$46$	−100.464	−	174.008i	−0.322013	−	0.557742i
$47$	−43.5991	−	247.263i	−0.135310	−	0.767383i	−0.974643	−	0.223765i	$-0.928165\pi$
$47$	−43.5991	−	247.263i	−0.135310	−	0.767383i	0.839333	−	0.543618i	$-0.182946\pi$
$48$		0			0
$49$	−62.9324	+	22.9055i	−0.183476	+	0.0667799i
$50$	−38.8580	+	220.375i	−0.109907	+	0.623314i
$51$		0			0
$52$	81.0222	−	67.9857i	0.216072	−	0.181306i
$53$	747.772			1.93801			0.969004	−	0.247046i	$-0.0794600\pi$
$53$	747.772			1.93801			0.969004	+	0.247046i	$0.0794600\pi$
$54$		0			0
$55$	188.846			0.462981
$56$	−124.085	+	104.120i	−0.296100	+	0.248458i
$57$		0			0
$58$	30.2186	−	171.378i	0.0684120	−	0.387984i
$59$	−573.277	+	208.656i	−1.26499	+	0.460418i	−0.885440	−	0.464754i	$-0.846143\pi$
$59$	−573.277	+	208.656i	−1.26499	+	0.460418i	−0.379548	+	0.925172i	$0.623921\pi$
$60$		0			0
$61$	25.6145	+	145.267i	0.0537639	+	0.304910i	0.999818	−	0.0190996i	$-0.00607997\pi$
$61$	25.6145	+	145.267i	0.0537639	+	0.304910i	−0.946054	+	0.324010i	$0.894969\pi$
$62$	227.936	+	394.797i	0.466902	+	0.808697i
$63$		0			0
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−89.9755	−	32.7484i	−0.171694	−	0.0624914i
$66$		0			0
$67$	680.914	+	571.355i	1.24160	+	1.04182i	0.997398	+	0.0720968i	$0.0229690\pi$
$67$	680.914	+	571.355i	1.24160	+	1.04182i	0.244198	+	0.969725i	$0.421475\pi$
$68$	−145.577	−	122.154i	−0.259616	−	0.217843i
$69$		0			0
$70$	137.797	+	50.1541i	0.235285	+	0.0856366i
$71$	186.829	−	323.598i	0.312290	−	0.540902i	−0.666568	−	0.745444i	$-0.732237\pi$
$71$	186.829	−	323.598i	0.312290	−	0.540902i	0.978858	+	0.204543i	$0.0655707\pi$
$72$		0			0
$73$	−315.996	−	547.321i	−0.506637	−	0.877521i	−0.999971	−	0.00768107i	$-0.997555\pi$
$73$	−315.996	−	547.321i	−0.506637	−	0.877521i	0.493333	−	0.869840i	$-0.335778\pi$
$74$	−41.9043	−	237.651i	−0.0658281	−	0.373330i
$75$		0			0
$76$	−461.331	+	167.911i	−0.696293	+	0.253430i
$77$	−183.361	+	1039.89i	−0.271375	+	1.53905i
$78$		0			0
$79$	812.837	−	682.051i	1.15761	−	0.971351i	0.157741	−	0.987480i	$-0.449579\pi$
$79$	812.837	−	682.051i	1.15761	−	0.971351i	0.999870	+	0.0161293i	$0.00513434\pi$
$80$	57.9386			0.0809716
$81$		0			0
$82$	64.0467			0.0862533
$83$	931.590	−	781.697i	1.23199	−	1.03376i	0.233884	−	0.972264i	$-0.424856\pi$
$83$	931.590	−	781.697i	1.23199	−	1.03376i	0.998107	−	0.0614992i	$-0.0195882\pi$
$84$		0			0
$85$	−29.8743	+	169.426i	−0.0381215	+	0.216198i
$86$	534.281	−	194.462i	0.669918	−	0.243830i
$87$		0			0
$88$	72.4469	+	410.867i	0.0877598	+	0.497710i
$89$	150.809	+	261.208i	0.179614	+	0.311101i	0.941749	−	0.336318i	$-0.109182\pi$
$89$	150.809	+	261.208i	0.179614	+	0.311101i	−0.762134	+	0.647419i	$0.775848\pi$
$90$		0			0
$91$	267.693	−	463.658i	0.308372	−	0.534116i
$92$	−377.620	−	137.443i	−0.427931	−	0.155754i
$93$		0			0
$94$	−384.673	−	322.779i	−0.422085	−	0.354171i
$95$	340.462	+	285.682i	0.367691	+	0.308530i
$96$		0			0
$97$	424.244	+	154.412i	0.444077	+	0.161631i	0.554373	−	0.832268i	$-0.312958\pi$
$97$	424.244	+	154.412i	0.444077	+	0.161631i	−0.110297	+	0.993899i	$0.535180\pi$
$98$	−66.9712	+	115.998i	−0.0690318	+	0.119567i
$99$		0			0
$100$	223.774	+	387.589i	0.223774	+	0.387589i
$101$	209.746	+	1189.53i	0.206639	+	1.17191i	0.894840	+	0.446387i	$0.147290\pi$
$101$	209.746	+	1189.53i	0.206639	+	1.17191i	−0.688201	+	0.725520i	$0.741599\pi$
$102$		0			0
$103$	−1166.41	+	424.538i	−1.11582	+	0.406126i	−0.833126	−	0.553083i	$-0.813451\pi$
$103$	−1166.41	+	424.538i	−1.11582	+	0.406126i	−0.282697	+	0.959209i	$0.591229\pi$
$104$	36.7325	−	208.320i	0.0346338	−	0.196418i
$105$		0			0
$106$	1145.65	−	961.317i	1.04977	−	0.880862i
$107$	−1309.46			−1.18309			−0.591543	−	0.806273i	$-0.701481\pi$
$107$	−1309.46			−1.18309			−0.591543	+	0.806273i	$0.701481\pi$
$108$		0			0
$109$	−1059.01			−0.930590			−0.465295	−	0.885156i	$-0.654052\pi$
$109$	−1059.01			−0.930590			−0.465295	+	0.885156i	$0.654052\pi$
$110$	289.329	−	242.775i	0.250785	−	0.210434i
$111$		0			0
$112$	−56.2557	+	319.042i	−0.0474613	+	0.269167i
$113$	−1301.72	+	473.787i	−1.08368	+	0.394426i	−0.821274	−	0.570533i	$-0.806737\pi$
$113$	−1301.72	+	473.787i	−1.08368	+	0.394426i	−0.262401	+	0.964959i	$0.584514\pi$
$114$		0			0
$115$	63.1725	+	358.269i	0.0512249	+	0.290511i
$116$	−174.022	−	301.415i	−0.139289	−	0.241256i
$117$		0			0
$118$	−610.068	+	1056.67i	−0.475944	+	0.824359i
$119$	−903.946	−	329.010i	−0.696341	−	0.253448i
$120$		0			0
$121$	1063.79	+	892.630i	0.799245	+	0.670646i
$122$	225.995	+	189.633i	0.167710	+	0.140726i
$123$		0			0
$124$	856.759	+	311.835i	0.620478	+	0.225835i
$125$	428.903	−	742.883i	0.306898	−	0.531563i
$126$		0			0
$127$	−595.134	−	1030.80i	−0.415824	−	0.720228i	0.579691	−	0.814837i	$-0.303173\pi$
$127$	−595.134	−	1030.80i	−0.415824	−	0.720228i	−0.995515	+	0.0946086i	$0.969840\pi$
$128$	22.2270	+	126.055i	0.0153485	+	0.0870455i
$129$		0			0
$130$	−179.951	+	65.4968i	−0.121406	+	0.0441881i
$131$	−59.7327	+	338.761i	−0.0398387	+	0.225936i	−0.998226	−	0.0595337i	$-0.981039\pi$
$131$	−59.7327	+	338.761i	−0.0398387	+	0.225936i	0.958388	+	0.285470i	$0.0921497\pi$
$132$		0			0
$133$	−1903.70	+	1597.39i	−1.24114	+	1.04144i
$134$	1777.74			1.14607
$135$		0			0
$136$	−380.076			−0.239641
$137$	1348.74	−	1131.73i	0.841102	−	0.705769i	−0.116709	−	0.993166i	$-0.537235\pi$
$137$	1348.74	−	1131.73i	0.841102	−	0.705769i	0.957811	+	0.287397i	$0.0927901\pi$
$138$		0			0
$139$	552.081	−	3131.01i	0.336884	−	1.91056i	−0.0708943	−	0.997484i	$-0.522585\pi$
$139$	552.081	−	3131.01i	0.336884	−	1.91056i	0.407778	−	0.913081i	$-0.366304\pi$
$140$	275.594	−	100.308i	0.166371	−	0.0605542i
$141$		0			0
$142$	−129.770	−	735.964i	−0.0766907	−	0.434935i
$143$	−689.477	−	1194.21i	−0.403195	−	0.698355i
$144$		0			0
$145$	−157.540	+	272.868i	−0.0902277	+	0.156279i
$146$	−1187.76	−	432.308i	−0.673283	−	0.245055i
$147$		0			0
$148$	−369.720	−	310.232i	−0.205343	−	0.172303i
$149$	−881.439	−	739.615i	−0.484633	−	0.406655i	0.367465	−	0.930037i	$-0.380226\pi$
$149$	−881.439	−	739.615i	−0.484633	−	0.406655i	−0.852098	+	0.523382i	$0.824670\pi$
$150$		0			0
$151$	−2690.31	−	979.193i	−1.44990	−	0.527719i	−0.507334	−	0.861749i	$-0.669369\pi$
$151$	−2690.31	−	979.193i	−1.44990	−	0.527719i	−0.942562	+	0.334030i	$0.891591\pi$
$152$	−490.938	+	850.330i	−0.261976	+	0.453756i
$153$		0			0
$154$	1055.93	+	1828.93i	0.552529	+	0.957008i
$155$	−143.328	−	812.854i	−0.0742734	−	0.421226i
$156$		0			0
$157$	−2794.04	+	1016.95i	−1.42031	+	0.516950i	−0.934138	−	0.356913i	$-0.883829\pi$
$157$	−2794.04	+	1016.95i	−1.42031	+	0.516950i	−0.486172	+	0.873863i	$0.661607\pi$
$158$	368.510	−	2089.93i	0.185551	−	1.05231i
$159$		0			0
$160$	88.7671	−	74.4844i	0.0438603	−	0.0368032i
$161$	−2034.17			−0.995743
$162$		0			0
$163$	−644.242			−0.309576			−0.154788	−	0.987948i	$-0.549469\pi$
$163$	−644.242			−0.309576			−0.154788	+	0.987948i	$0.549469\pi$
$164$	98.1252	−	82.3368i	0.0467213	−	0.0392038i
$165$		0			0
$166$	422.349	−	2395.26i	0.197474	−	1.11993i
$167$	1190.50	−	433.308i	0.551640	−	0.200781i	−0.0511350	−	0.998692i	$-0.516284\pi$
$167$	1190.50	−	433.308i	0.551640	−	0.200781i	0.602775	+	0.797911i	$0.294062\pi$
$168$		0			0
$169$	−260.096	−	1475.08i	−0.118387	−	0.671406i
$170$	172.039	+	297.981i	0.0776166	+	0.134436i
$171$		0			0
$172$	568.570	−	984.792i	0.252053	−	0.436568i
$173$	1292.05	+	470.269i	0.567821	+	0.206670i	0.609947	−	0.792443i	$-0.291191\pi$
$173$	1292.05	+	470.269i	0.567821	+	0.206670i	−0.0421260	+	0.999112i	$0.513413\pi$
$174$		0			0
$175$	1735.45	+	1456.21i	0.749642	+	0.629024i
$176$	639.195	+	536.348i	0.273756	+	0.229709i
$177$		0			0
$178$	566.855	+	206.318i	0.238694	+	0.0868776i
$179$	747.985	−	1295.55i	0.312330	−	0.540971i	−0.666536	−	0.745472i	$-0.732224\pi$
$179$	747.985	−	1295.55i	0.312330	−	0.540971i	0.978866	+	0.204501i	$0.0655573\pi$
$180$		0			0
$181$	1123.12	+	1945.30i	0.461219	+	0.798856i	0.999022	−	0.0442153i	$-0.0140787\pi$
$181$	1123.12	+	1945.30i	0.461219	+	0.798856i	−0.537803	+	0.843071i	$0.680745\pi$
$182$	−185.938	−	1054.50i	−0.0757286	−	0.429478i
$183$		0			0
$184$	−755.241	+	274.885i	−0.302593	+	0.110135i
$185$	−75.8712	+	430.287i	−0.0301522	+	0.171002i
$186$		0			0
$187$	−1897.99	+	1592.60i	−0.742217	+	0.622794i
$188$	−1004.31			−0.389610
$189$		0			0
$190$	888.883			0.339402
$191$	−3507.85	+	2943.44i	−1.32890	+	1.11508i	−0.344562	+	0.938764i	$0.611973\pi$
$191$	−3507.85	+	2943.44i	−1.32890	+	1.11508i	−0.984334	+	0.176313i	$0.943583\pi$
$192$		0			0
$193$	242.124	−	1373.15i	0.0903030	−	0.512134i	−0.905783	−	0.423742i	$-0.860716\pi$
$193$	242.124	−	1373.15i	0.0903030	−	0.512134i	0.996086	−	0.0883915i	$-0.0281727\pi$
$194$	848.487	−	308.824i	0.314010	−	0.114290i
$195$		0			0
$196$	46.5177	+	263.815i	0.0169525	+	0.0961425i
$197$	43.7108	+	75.7093i	0.0158085	+	0.0273810i	0.873821	−	0.486247i	$-0.161634\pi$
$197$	43.7108	+	75.7093i	0.0158085	+	0.0273810i	−0.858013	+	0.513628i	$0.828301\pi$
$198$		0			0
$199$	2068.38	−	3582.55i	0.736803	−	1.27618i	−0.217124	−	0.976144i	$-0.569668\pi$
$199$	2068.38	−	3582.55i	0.736803	−	1.27618i	0.953928	−	0.300037i	$-0.0969989\pi$
$200$	841.117	+	306.141i	0.297380	+	0.108237i
$201$		0			0
$202$	1850.58	+	1552.82i	0.644586	+	0.540872i
$203$	−1349.60	−	1132.45i	−0.466617	−	0.391538i
$204$		0			0
$205$	−108.968	−	39.6612i	−0.0371253	−	0.0135125i
$206$	−1241.27	+	2149.94i	−0.419821	+	0.727152i
$207$		0			0
$208$	−211.534	−	366.388i	−0.0705156	−	0.122137i
$209$	1111.47	+	6303.44i	0.367855	+	2.08621i
$210$		0			0
$211$	4114.80	−	1497.67i	1.34253	−	0.488642i	0.431924	−	0.901910i	$-0.357835\pi$
$211$	4114.80	−	1497.67i	1.34253	−	0.488642i	0.910610	+	0.413268i	$0.135613\pi$
$212$	519.397	−	2945.65i	0.168266	−	0.954282i
$213$		0			0
$214$	−2006.21	+	1683.41i	−0.640849	+	0.537736i
$215$	−1029.44			−0.326546
$216$		0			0
$217$	4615.19			1.44378
$218$	−1622.49	+	1361.43i	−0.504078	+	0.422971i
$219$		0			0
$220$	131.171	−	743.907i	0.0401979	−	0.227974i
$221$	1180.47	−	429.657i	0.359309	−	0.130778i
$222$		0			0
$223$	198.433	+	1125.37i	0.0595878	+	0.337939i	0.999998	−	0.00210343i	$-0.000669543\pi$
$223$	198.433	+	1125.37i	0.0595878	+	0.337939i	−0.940410	+	0.340043i	$0.889558\pi$
$224$	323.964	+	561.122i	0.0966328	+	0.167373i
$225$		0			0
$226$	−1385.26	+	2399.34i	−0.407726	+	0.706202i
$227$	4929.32	+	1794.13i	1.44128	+	0.524583i	0.940141	−	0.340785i	$-0.110693\pi$
$227$	4929.32	+	1794.13i	1.44128	+	0.524583i	0.501138	+	0.865367i	$0.332915\pi$
$228$		0			0
$229$	2140.94	+	1796.46i	0.617804	+	0.518399i	0.897112	−	0.441802i	$-0.145661\pi$
$229$	2140.94	+	1796.46i	0.617804	+	0.518399i	−0.279308	+	0.960201i	$0.590105\pi$
$230$	557.367	+	467.687i	0.159790	+	0.134080i
$231$		0			0
$232$	−654.109	−	238.076i	−0.185105	−	0.0673727i
$233$	−460.424	+	797.478i	−0.129457	+	0.224225i	−0.923466	−	0.383680i	$-0.874657\pi$
$233$	−460.424	+	797.478i	−0.129457	+	0.224225i	0.794010	+	0.607905i	$0.207990\pi$
$234$		0			0
$235$	454.596	+	787.383i	0.126190	+	0.218567i
$236$	423.749	+	2403.20i	0.116880	+	0.662860i
$237$		0			0
$238$	−1807.89	+	658.019i	−0.492388	+	0.179214i
$239$	394.497	−	2237.31i	0.106770	−	0.605520i	−0.883729	−	0.467998i	$-0.844975\pi$
$239$	394.497	−	2237.31i	0.106770	−	0.605520i	0.990499	−	0.137521i	$-0.0439136\pi$
$240$		0			0
$241$	−389.454	+	326.791i	−0.104095	+	0.0873462i	−0.693350	−	0.720601i	$-0.743866\pi$
$241$	−389.454	+	326.791i	−0.104095	+	0.0873462i	0.589255	+	0.807947i	$0.299421\pi$
$242$	2777.37			0.737753
$243$		0			0
$244$	590.032			0.154807
$245$	185.776	−	155.885i	0.0484441	−	0.0406494i
$246$		0			0
$247$	563.543	−	3196.01i	0.145172	−	0.823309i
$248$	1713.52	−	623.670i	0.438744	−	0.159690i
$249$		0			0
$250$	−297.913	−	1689.55i	−0.0753667	−	0.427426i
$251$	1010.71	+	1750.60i	0.254165	+	0.440227i	0.964669	−	0.263467i	$-0.0848659\pi$
$251$	1010.71	+	1750.60i	0.254165	+	0.440227i	−0.710503	+	0.703694i	$0.751533\pi$
$252$		0			0
$253$	−2619.62	+	4537.32i	−0.650966	+	1.12751i
$254$	−2236.97	−	814.192i	−0.552599	−	0.201130i
$255$		0			0
$256$	196.107	+	164.554i	0.0478778	+	0.0401742i
$257$	3769.11	+	3162.66i	0.914827	+	0.767631i	0.973031	−	0.230674i	$-0.0740931\pi$
$257$	3769.11	+	3162.66i	0.914827	+	0.767631i	−0.0582044	+	0.998305i	$0.518538\pi$
$258$		0			0
$259$	−2295.73	−	835.578i	−0.550772	−	0.200464i
$260$	−191.500	+	331.687i	−0.0456781	+	0.0791168i
$261$		0			0
$262$	343.987	+	595.803i	0.0811129	+	0.140492i
$263$	−512.308	−	2905.44i	−0.120115	−	0.681206i	−0.984090	−	0.177671i	$-0.943144\pi$
$263$	−512.308	−	2905.44i	−0.120115	−	0.681206i	0.863975	−	0.503535i	$-0.167968\pi$
$264$		0			0
$265$	−2544.50	+	926.123i	−0.589840	+	0.214684i
$266$	−863.065	+	4894.69i	−0.198940	+	1.12824i
$267$		0			0
$268$	2723.66	−	2285.42i	0.620798	−	0.520911i
$269$	−1216.81			−0.275800			−0.137900	−	0.990446i	$-0.544035\pi$
$269$	−1216.81			−0.275800			−0.137900	+	0.990446i	$0.544035\pi$
$270$		0			0
$271$	746.032			0.167226			0.0836129	−	0.996498i	$-0.473354\pi$
$271$	746.032			0.167226			0.0836129	+	0.996498i	$0.473354\pi$
$272$	−582.310	+	488.616i	−0.129808	+	0.108922i
$273$		0			0
$274$	611.471	−	3467.83i	0.134819	−	0.764595i
$275$	5483.09	−	1995.68i	1.20234	−	0.437615i
$276$		0			0
$277$	251.081	+	1423.95i	0.0544620	+	0.308870i	0.999854	−	0.0170650i	$-0.00543222\pi$
$277$	251.081	+	1423.95i	0.0544620	+	0.308870i	−0.945392	+	0.325935i	$0.894321\pi$
$278$	−3179.31	−	5506.72i	−0.685907	−	1.18803i
$279$		0			0
$280$	293.281	−	507.978i	0.0625961	−	0.108420i
$281$	−1577.26	−	574.077i	−0.334846	−	0.121874i	0.169125	−	0.985595i	$-0.445906\pi$
$281$	−1577.26	−	574.077i	−0.334846	−	0.121874i	−0.503971	+	0.863721i	$0.668128\pi$
$282$		0			0
$283$	5310.00	+	4455.62i	1.11536	+	0.935898i	0.998361	−	0.0572342i	$-0.0182282\pi$
$283$	5310.00	+	4455.62i	1.11536	+	0.935898i	0.116999	+	0.993132i	$0.462673\pi$
$284$	−1144.96	−	960.733i	−0.239228	−	0.200736i
$285$		0			0
$286$	−2591.59	−	943.260i	−0.535817	−	0.195021i
$287$	324.200	−	561.531i	0.0666792	−	0.115492i
$288$		0			0
$289$	1327.93	+	2300.03i	0.270288	+	0.468153i
$290$	109.426	+	620.588i	0.0221577	+	0.125663i
$291$		0			0
$292$	−2375.51	+	864.616i	−0.476083	+	0.173280i
$293$	441.862	−	2505.92i	0.0881019	−	0.499651i	−0.908542	−	0.417793i	$-0.862804\pi$
$293$	441.862	−	2505.92i	0.0881019	−	0.499651i	0.996644	−	0.0818575i	$-0.0260852\pi$
$294$		0			0
$295$	1692.31	−	1420.02i	0.334001	−	0.280260i
$296$	−965.270			−0.189544
$297$		0			0
$298$	−2301.27			−0.447346
$299$	2034.95	−	1707.53i	0.393593	−	0.330264i
$300$		0			0
$301$	999.541	−	5668.68i	0.191404	−	1.08551i
$302$	−5380.62	+	1958.39i	−1.02523	+	0.373154i
$303$		0			0
$304$	341.002	+	1933.92i	0.0643349	+	0.364861i
$305$	−267.075	−	462.588i	−0.0501399	−	0.0868449i
$306$		0			0
$307$	893.701	−	1547.94i	0.166144	−	0.287770i	−0.770917	−	0.636936i	$-0.780202\pi$
$307$	893.701	−	1547.94i	0.166144	−	0.287770i	0.937061	+	0.349166i	$0.113535\pi$
$308$	3969.01	+	1444.60i	0.734270	+	0.267252i
$309$		0			0
$310$	−1264.58	−	1061.10i	−0.231687	−	0.194409i
$311$	−3486.59	−	2925.60i	−0.635713	−	0.533426i	0.266986	−	0.963701i	$-0.413972\pi$
$311$	−3486.59	−	2925.60i	−0.635713	−	0.533426i	−0.902698	+	0.430274i	$0.858417\pi$
$312$		0			0
$313$	−287.879	−	104.779i	−0.0519868	−	0.0189216i	0.315896	−	0.948794i	$-0.397695\pi$
$313$	−287.879	−	104.779i	−0.0519868	−	0.0189216i	−0.367883	+	0.929872i	$0.619917\pi$
$314$	−2973.35	+	5150.00i	−0.534382	+	0.925577i
$315$		0			0
$316$	−2122.17	−	3675.70i	−0.377789	−	0.654349i
$317$	−768.099	−	4356.11i	−0.136091	−	0.771809i	−0.974094	−	0.226143i	$-0.927388\pi$
$317$	−768.099	−	4356.11i	−0.136091	−	0.771809i	0.838003	−	0.545665i	$-0.183723\pi$
$318$		0			0
$319$	−4264.02	+	1551.98i	−0.748399	+	0.272395i
$320$	40.2437	−	228.234i	0.00703029	−	0.0398708i
$321$		0			0
$322$	−3116.52	+	2615.07i	−0.539370	+	0.452585i
$323$	−5831.05			−1.00448
$324$		0			0
$325$	−2958.49			−0.504947
$326$	−987.036	+	828.221i	−0.167690	+	0.140708i
$327$		0			0
$328$	44.4863	−	252.295i	0.00748886	−	0.0424715i
$329$	−4777.16	+	1738.74i	−0.800527	+	0.291368i
$330$		0			0
$331$	602.165	+	3415.05i	0.0999939	+	0.567094i	0.993102	+	0.117252i	$0.0374085\pi$
$331$	602.165	+	3415.05i	0.0999939	+	0.567094i	−0.893108	+	0.449842i	$0.851480\pi$
$332$	−2432.21	−	4212.71i	−0.402063	−	0.696393i
$333$		0			0
$334$	1266.91	−	2194.35i	0.207551	−	0.359489i
$335$	−3024.63	−	1100.87i	−0.493293	−	0.179544i
$336$		0			0
$337$	−4724.18	−	3964.05i	−0.763627	−	0.640759i	0.175441	−	0.984490i	$-0.443865\pi$
$337$	−4724.18	−	3964.05i	−0.763627	−	0.640759i	−0.939068	+	0.343731i	$0.888309\pi$
$338$	−2294.81	−	1925.58i	−0.369294	−	0.309875i
$339$		0			0
$340$	646.657	+	235.364i	0.103147	+	0.0375423i
$341$	5943.50	−	10294.4i	0.943867	−	1.63483i
$342$		0			0
$343$	−2794.48	−	4840.18i	−0.439906	−	0.761940i
$344$	−394.924	−	2239.73i	−0.0618980	−	0.351041i
$345$		0			0
$346$	2584.11	−	940.538i	0.401510	−	0.146138i
$347$	−150.663	+	854.453i	−0.0233084	+	0.132189i	−0.994242	−	0.107162i	$-0.965824\pi$
$347$	−150.663	+	854.453i	−0.0233084	+	0.132189i	0.970933	+	0.239351i	$0.0769347\pi$
$348$		0			0
$349$	7807.22	−	6551.04i	1.19745	−	1.00478i	0.197754	−	0.980252i	$-0.436635\pi$
$349$	7807.22	−	6551.04i	1.19745	−	1.00478i	0.999699	−	0.0245303i	$-0.00780902\pi$
$350$	4530.93			0.691966
$351$		0			0
$352$	1668.82			0.252694
$353$	−1505.43	+	1263.20i	−0.226985	+	0.190463i	−0.749187	−	0.662359i	$-0.769555\pi$
$353$	−1505.43	+	1263.20i	−0.226985	+	0.190463i	0.522201	+	0.852822i	$0.325111\pi$
$354$		0			0
$355$	−234.960	+	1332.52i	−0.0351278	+	0.199220i
$356$	1133.71	−	412.637i	0.168782	−	0.0614318i
$357$		0			0
$358$	−519.545	−	2946.49i	−0.0767006	−	0.434991i
$359$	3334.17	+	5774.96i	0.490170	+	0.848999i	0.999936	−	0.0113142i	$-0.00360149\pi$
$359$	3334.17	+	5774.96i	0.490170	+	0.848999i	−0.509766	+	0.860313i	$0.670268\pi$
$360$		0			0
$361$	−4102.38	+	7105.54i	−0.598102	+	1.03594i
$362$	4221.54	+	1536.52i	0.612927	+	0.223087i
$363$		0			0
$364$	−1640.52	−	1376.56i	−0.236227	−	0.198218i
$365$	1753.13	+	1471.05i	0.251405	+	0.210954i
$366$		0			0
$367$	7550.57	+	2748.18i	1.07394	+	0.390883i	0.817649	−	0.575717i	$-0.195277\pi$
$367$	7550.57	+	2748.18i	1.07394	+	0.390883i	0.256292	+	0.966599i	$0.417499\pi$
$368$	−803.710	+	1392.07i	−0.113849	+	0.197192i
$369$		0			0
$370$	436.925	+	756.776i	0.0613909	+	0.106332i
$371$	−2629.15	−	14910.7i	−0.367922	−	2.08659i
$372$		0			0
$373$	−12082.4	+	4397.64i	−1.67722	+	0.610459i	−0.992925	−	0.118744i	$-0.962113\pi$
$373$	−12082.4	+	4397.64i	−1.67722	+	0.610459i	−0.684298	+	0.729203i	$0.739891\pi$
$374$	−860.478	+	4880.01i	−0.118969	+	0.674704i
$375$		0			0
$376$	−1538.69	+	1291.11i	−0.211042	+	0.177085i
$377$	2300.72			0.314306
$378$		0			0
$379$	−2336.31			−0.316644			−0.158322	−	0.987388i	$-0.550608\pi$
$379$	−2336.31			−0.316644			−0.158322	+	0.987388i	$0.550608\pi$
$380$	1361.85	−	1142.73i	0.183846	−	0.154265i
$381$		0			0
$382$	−1590.33	+	9019.21i	−0.213006	+	1.20802i
$383$	−4384.77	+	1595.92i	−0.584990	+	0.212919i	−0.617524	−	0.786552i	$-0.711864\pi$
$383$	−4384.77	+	1595.92i	−0.584990	+	0.212919i	0.0325346	+	0.999471i	$0.489642\pi$
$384$		0			0
$385$	−663.979	−	3765.61i	−0.0878948	−	0.498476i
$386$	−1394.34	−	2415.06i	−0.183860	−	0.318455i
$387$		0			0
$388$	902.942	−	1563.94i	0.118144	−	0.204632i
$389$	9058.55	+	3297.04i	1.18069	+	0.429735i	0.856444	−	0.516240i	$-0.172669\pi$
$389$	9058.55	+	3297.04i	1.18069	+	0.429735i	0.324242	+	0.945974i	$0.394891\pi$
$390$		0			0
$391$	−3656.32	−	3068.01i	−0.472910	−	0.396819i
$392$	410.423	+	344.386i	0.0528814	+	0.0443728i
$393$		0			0
$394$	164.299	+	59.7999i	0.0210083	+	0.00764638i
$395$	−1921.18	+	3327.58i	−0.244721	+	0.423870i
$396$		0			0
$397$	442.781	+	766.920i	0.0559762	+	0.0969537i	0.892656	−	0.450739i	$-0.148840\pi$
$397$	442.781	+	766.920i	0.0559762	+	0.0969537i	−0.836679	+	0.547693i	$0.815506\pi$
$398$	−1436.68	−	8147.84i	−0.180941	−	1.02617i
$399$		0			0
$400$	1682.23	−	612.283i	0.210279	−	0.0765353i
$401$	−283.003	+	1604.99i	−0.0352431	+	0.199874i	−0.997345	−	0.0728149i	$-0.976802\pi$
$401$	−283.003	+	1604.99i	−0.0352431	+	0.199874i	0.962102	+	0.272689i	$0.0879129\pi$
$402$		0			0
$403$	−4616.97	+	3874.10i	−0.570689	+	0.478865i
$404$	4831.52			0.594993
$405$		0			0
$406$	−3523.55			−0.430717
$407$	−4820.28	+	4044.69i	−0.587057	+	0.492599i
$408$		0			0
$409$	−483.047	+	2739.49i	−0.0583988	+	0.331196i	−0.999984	−	0.00557746i	$-0.998225\pi$
$409$	−483.047	+	2739.49i	−0.0583988	+	0.331196i	0.941586	+	0.336774i	$0.109336\pi$
$410$	−217.937	+	79.3225i	−0.0262515	+	0.00955477i
$411$		0			0
$412$	862.175	+	4889.64i	0.103098	+	0.584697i
$413$	6176.26	+	10697.6i	0.735868	+	1.27456i
$414$		0			0
$415$	−2201.86	+	3813.73i	−0.260445	+	0.451105i
$416$	−795.108	−	289.396i	−0.0937100	−	0.0341077i
$417$		0			0
$418$	9806.41	+	8228.56i	1.14748	+	0.962851i
$419$	8333.06	+	6992.27i	0.971591	+	0.815261i	0.982799	−	0.184676i	$-0.0591235\pi$
$419$	8333.06	+	6992.27i	0.971591	+	0.815261i	−0.0112088	+	0.999937i	$0.503568\pi$
$420$		0			0
$421$	4945.40	+	1799.98i	0.572504	+	0.208374i	0.612017	−	0.790845i	$-0.290358\pi$
$421$	4945.40	+	1799.98i	0.572504	+	0.208374i	−0.0395130	+	0.999219i	$0.512581\pi$
$422$	4378.88	−	7584.44i	0.505120	−	0.874893i
$423$		0			0
$424$	−2991.09	−	5180.72i	−0.342595	−	0.593391i
$425$	923.062	+	5234.94i	0.105353	+	0.597487i
$426$		0			0
$427$	2806.58	−	1021.51i	0.318080	−	0.115772i
$428$	−909.541	+	5158.27i	−0.102720	+	0.582556i
$429$		0			0
$430$	−1577.20	+	1323.42i	−0.176882	+	0.148421i
$431$	507.234			0.0566881			0.0283441	−	0.999598i	$-0.490977\pi$
$431$	507.234			0.0566881			0.0283441	+	0.999598i	$0.490977\pi$
$432$		0			0
$433$	1544.74			0.171444			0.0857222	−	0.996319i	$-0.472680\pi$
$433$	1544.74			0.171444			0.0857222	+	0.996319i	$0.472680\pi$
$434$	7070.88	−	5933.17i	0.782058	−	0.656225i
$435$		0			0
$436$	−735.578	+	4171.67i	−0.0807977	+	0.458226i
$437$	−11586.8	+	4217.24i	−1.26835	+	0.461643i
$438$		0			0
$439$	−1435.70	−	8142.25i	−0.156087	−	0.885212i	−0.957785	−	0.287484i	$-0.907181\pi$
$439$	−1435.70	−	8142.25i	−0.156087	−	0.885212i	0.801699	−	0.597728i	$-0.203930\pi$
$440$	−755.383	−	1308.36i	−0.0818443	−	0.141758i
$441$		0			0
$442$	1256.23	−	2175.86i	0.135188	−	0.234152i
$443$	−14556.8	−	5298.22i	−1.56120	−	0.568231i	−0.590190	−	0.807264i	$-0.700947\pi$
$443$	−14556.8	−	5298.22i	−1.56120	−	0.568231i	−0.971011	+	0.239034i	$0.923169\pi$
$444$		0			0
$445$	−836.678	−	702.056i	−0.0891288	−	0.0747880i
$446$	1750.77	+	1469.07i	0.185877	+	0.155970i
$447$		0			0
$448$	1217.71	+	443.209i	0.128418	+	0.0467403i
$449$	1863.55	−	3227.76i	0.195871	−	0.339259i	−0.751314	−	0.659944i	$-0.770580\pi$
$449$	1863.55	−	3227.76i	0.195871	−	0.339259i	0.947186	+	0.320685i	$0.103913\pi$
$450$		0			0
$451$	−835.018	−	1446.29i	−0.0871828	−	0.151005i
$452$	962.191	+	5456.86i	0.100128	+	0.567852i
$453$		0			0
$454$	9858.64	−	3588.25i	1.01914	−	0.370936i
$455$	−336.655	+	1909.27i	−0.0346871	+	0.196720i
$456$		0			0
$457$	12152.4	−	10197.1i	1.24391	−	1.04377i	0.246704	−	0.969091i	$-0.420653\pi$
$457$	12152.4	−	10197.1i	1.24391	−	1.04377i	0.997208	−	0.0746748i	$-0.0237919\pi$
$458$	5589.59			0.570272
$459$		0			0
$460$	1455.18			0.147496
$461$	−5397.46	+	4529.01i	−0.545303	+	0.457564i	−0.873347	−	0.487099i	$-0.838055\pi$
$461$	−5397.46	+	4529.01i	−0.545303	+	0.457564i	0.328043	+	0.944663i	$0.393611\pi$
$462$		0			0
$463$	−801.375	+	4544.82i	−0.0804385	+	0.456190i	0.917809	+	0.397021i	$0.129956\pi$
$463$	−801.375	+	4544.82i	−0.0804385	+	0.456190i	−0.998248	+	0.0591685i	$0.981155\pi$
$464$	−1308.22	+	476.152i	−0.130889	+	0.0476397i
$465$		0			0
$466$	319.807	+	1813.72i	0.0317914	+	0.180298i
$467$	8295.62	+	14368.4i	0.822003	+	1.42375i	0.904188	+	0.427134i	$0.140477\pi$
$467$	8295.62	+	14368.4i	0.822003	+	1.42375i	−0.0821852	+	0.996617i	$0.526190\pi$
$468$		0			0
$469$	8998.81	−	15586.4i	0.885984	−	1.53457i
$470$	1708.72	+	621.923i	0.167697	+	0.0610366i
$471$		0			0
$472$	3738.72	+	3137.16i	0.364594	+	0.305931i
$473$	−11357.1	−	9529.73i	−1.10402	−	0.926379i
$474$		0			0
$475$	12904.3	+	4696.76i	1.24650	+	0.453689i
$476$	−1923.92	+	3332.33i	−0.185258	+	0.320876i
$477$		0			0
$478$	−2271.82	−	3934.91i	−0.217386	−	0.376524i
$479$	−135.944	−	770.976i	−0.0129675	−	0.0735423i	0.977637	−	0.210298i	$-0.0674435\pi$
$479$	−135.944	−	770.976i	−0.0129675	−	0.0735423i	−0.990605	+	0.136756i	$0.956332\pi$
$480$		0			0
$481$	2998.02	−	1091.19i	0.284196	−	0.103439i
$482$	−176.564	+	1001.35i	−0.0166852	+	0.0946266i
$483$		0			0
$484$	4255.18	−	3570.52i	0.399622	−	0.335323i
$485$	−1634.85			−0.153061
$486$		0			0
$487$	−6863.12			−0.638599			−0.319300	−	0.947654i	$-0.603448\pi$
$487$	−6863.12			−0.638599			−0.319300	+	0.947654i	$0.603448\pi$
$488$	903.981	−	758.530i	0.0838551	−	0.0703628i
$489$		0			0
$490$	84.2241	−	477.659i	0.00776501	−	0.0440376i
$491$	17841.5	−	6493.78i	1.63987	−	0.596864i	0.652854	−	0.757484i	$-0.273572\pi$
$491$	17841.5	−	6493.78i	1.63987	−	0.596864i	0.987016	+	0.160620i	$0.0513494\pi$
$492$		0			0
$493$	−717.835	−	4071.04i	−0.0655774	−	0.371908i
$494$	−3245.32	−	5621.05i	−0.295574	−	0.511950i
$495$		0			0
$496$	1823.49	−	3158.37i	0.165075	−	0.285918i
$497$	−7109.48	−	2587.64i	−0.641657	−	0.233544i
$498$		0			0
$499$	1447.67	+	1214.74i	0.129873	+	0.108976i	0.705410	−	0.708799i	$-0.250763\pi$
$499$	1447.67	+	1214.74i	0.129873	+	0.108976i	−0.575538	+	0.817775i	$0.695207\pi$
$500$	−2628.47	−	2205.55i	−0.235098	−	0.197270i
$501$		0			0
$502$	3799.03	+	1382.73i	0.337767	+	0.122937i
$503$	−7100.04	+	12297.6i	−0.629374	+	1.09011i	0.358303	+	0.933605i	$0.383355\pi$
$503$	−7100.04	+	12297.6i	−0.629374	+	1.09011i	−0.987677	+	0.156503i	$0.949978\pi$
$504$		0			0
$505$	−2186.97	−	3787.94i	−0.192710	−	0.333784i
$506$	1819.57	+	10319.3i	0.159861	+	0.906619i
$507$		0			0
$508$	−4473.95	+	1628.38i	−0.390747	+	0.142220i
$509$	661.736	−	3752.89i	0.0576246	−	0.326805i	−0.942345	−	0.334644i	$-0.891384\pi$
$509$	661.736	−	3752.89i	0.0576246	−	0.326805i	0.999969	+	0.00783851i	$0.00249510\pi$
$510$		0			0
$511$	−9802.62	+	8225.37i	−0.848615	+	0.712073i
$512$	512.000			0.0441942
$513$		0			0
$514$	9840.44			0.844442
$515$	3443.24	−	2889.22i	0.294616	−	0.247212i
$516$		0			0
$517$	−2273.72	+	12894.9i	−0.193420	+	1.09694i
$518$	−4591.46	+	1671.16i	−0.389454	+	0.141750i
$519$		0			0
$520$	133.014	+	754.362i	0.0112174	+	0.0636172i
$521$	−1428.45	−	2474.15i	−0.120118	−	0.208051i	0.799696	−	0.600405i	$-0.204994\pi$
$521$	−1428.45	−	2474.15i	−0.120118	−	0.208051i	−0.919814	+	0.392355i	$0.871661\pi$
$522$		0			0
$523$	2147.81	−	3720.12i	0.179574	−	0.311032i	−0.762161	−	0.647388i	$-0.775861\pi$
$523$	2147.81	−	3720.12i	0.179574	−	0.311032i	0.941735	+	0.336356i	$0.109195\pi$
$524$	1292.97	+	470.602i	0.107793	+	0.0392334i
$525$		0			0
$526$	−4520.07	−	3792.79i	−0.374685	−	0.314398i
$527$	8295.58	+	6960.82i	0.685695	+	0.575366i
$528$		0			0
$529$	1948.95	+	709.359i	0.160183	+	0.0583019i
$530$	−2707.80	+	4690.05i	−0.221924	+	0.384383i
$531$		0			0
$532$	4970.20	+	8608.63i	0.405048	+	0.701563i
$533$	147.037	+	833.889i	0.0119491	+	0.0677669i
$534$		0			0
$535$	4455.80	−	1621.78i	0.360077	−	0.131057i
$536$	1234.81	−	7002.93i	0.0995065	−	0.564329i
$537$		0			0
$538$	−1864.26	+	1564.30i	−0.149394	+	0.125357i
$539$	3492.59			0.279103
$540$		0			0
$541$	−10906.1			−0.866713			−0.433357	−	0.901223i	$-0.642671\pi$
$541$	−10906.1			−0.866713			−0.433357	+	0.901223i	$0.642671\pi$
$542$	1142.99	−	959.080i	0.0905821	−	0.0760074i
$543$		0			0
$544$	−263.998	+	1497.21i	−0.0208066	+	0.118000i
$545$	3603.56	−	1311.59i	0.283229	−	0.103087i
$546$		0			0
$547$	1522.32	+	8633.51i	0.118994	+	0.674849i	0.984695	+	0.174287i	$0.0557621\pi$
$547$	1522.32	+	8633.51i	0.118994	+	0.674849i	−0.865701	+	0.500562i	$0.833127\pi$
$548$	−3521.32	−	6099.11i	−0.274495	−	0.475440i
$549$		0			0
$550$	5834.98	−	10106.5i	0.452372	−	0.783531i
$551$	−10035.2	−	3652.52i	−0.775888	−	0.282400i
$552$		0			0
$553$	−16458.1	−	13810.0i	−1.26559	−	1.06195i
$554$	2215.27	+	1858.83i	0.169888	+	0.142553i
$555$		0			0
$556$	−11950.3	−	4349.55i	−0.911520	−	0.331766i
$557$	8736.12	−	15131.4i	0.664562	−	1.15106i	−0.314842	−	0.949144i	$-0.601951\pi$
$557$	8736.12	−	15131.4i	0.664562	−	1.15106i	0.979404	−	0.201911i	$-0.0647153\pi$
$558$		0			0
$559$	3758.50	+	6509.91i	0.284378	+	0.492558i
$560$	−203.711	−	1155.30i	−0.0153721	−	0.0871794i
$561$		0			0
$562$	−3154.53	+	1148.15i	−0.236772	+	0.0861779i
$563$	−1779.76	+	10093.5i	−0.133229	+	0.755580i	0.842848	+	0.538152i	$0.180878\pi$
$563$	−1779.76	+	10093.5i	−0.133229	+	0.755580i	−0.976077	+	0.217427i	$0.930234\pi$
$564$		0			0
$565$	3842.67	−	3224.38i	0.286128	−	0.240090i
$566$	13863.4			1.02955
$567$		0			0
$568$	−2989.27			−0.220822
$569$	7176.89	−	6022.12i	0.528771	−	0.443692i	−0.338906	−	0.940820i	$-0.610057\pi$
$569$	7176.89	−	6022.12i	0.528771	−	0.443692i	0.867677	+	0.497129i	$0.165612\pi$
$570$		0			0
$571$	−3564.71	+	20216.4i	−0.261258	+	1.48167i	0.518225	+	0.855244i	$0.326593\pi$
$571$	−3564.71	+	20216.4i	−0.261258	+	1.48167i	−0.779483	+	0.626423i	$0.784518\pi$
$572$	−5183.17	+	1886.52i	−0.378880	+	0.137901i
$573$		0			0
$574$	−225.187	−	1277.10i	−0.0163748	−	0.0928660i
$575$	5620.31	+	9734.65i	0.407623	+	0.706023i
$576$		0			0
$577$	−9397.75	+	16277.4i	−0.678047	+	1.17441i	0.297521	+	0.954715i	$0.403840\pi$
$577$	−9397.75	+	16277.4i	−0.678047	+	1.17441i	−0.975568	+	0.219697i	$0.929493\pi$
$578$	4991.37	+	1816.71i	0.359193	+	0.130736i
$579$		0			0
$580$	965.464	+	810.120i	0.0691185	+	0.0579973i
$581$	−18862.6	−	15827.6i	−1.34691	−	1.13019i
$582$		0			0
$583$	−36645.0	−	13337.7i	−2.60322	−	0.947496i
$584$	−2527.97	+	4378.57i	−0.179123	+	0.310251i
$585$		0			0
$586$	−2544.58	−	4407.35i	−0.179378	−	0.310692i
$587$	2215.12	+	12562.6i	0.155755	+	0.883328i	0.958093	+	0.286458i	$0.0924780\pi$
$587$	2215.12	+	12562.6i	0.155755	+	0.883328i	−0.802338	+	0.596870i	$0.796411\pi$
$588$		0			0
$589$	26288.5	−	9568.22i	1.83905	−	0.669358i
$590$	767.232	−	4351.19i	0.0535364	−	0.303620i
$591$		0			0
$592$	−1478.88	+	1240.93i	−0.102672	+	0.0861517i
$593$	−4347.81			−0.301085			−0.150542	−	0.988604i	$-0.548102\pi$
$593$	−4347.81			−0.301085			−0.150542	+	0.988604i	$0.548102\pi$
$594$		0			0
$595$	3483.41			0.240010
$596$	−3525.76	+	2958.46i	−0.242316	+	0.203328i
$597$		0			0
$598$	922.572	−	5232.16i	0.0630882	−	0.357791i
$599$	7264.20	−	2643.95i	0.495505	−	0.180349i	−0.0821664	−	0.996619i	$-0.526184\pi$
$599$	7264.20	−	2643.95i	0.495505	−	0.180349i	0.577671	+	0.816270i	$0.303962\pi$
$600$		0			0
$601$	1040.21	+	5899.33i	0.0706008	+	0.400397i	0.999545	+	0.0301763i	$0.00960689\pi$
$601$	1040.21	+	5899.33i	0.0706008	+	0.400397i	−0.928944	+	0.370221i	$0.879282\pi$
$602$	−5756.13	−	9969.91i	−0.389705	−	0.674988i
$603$		0			0
$604$	−5725.94	+	9917.62i	−0.385737	+	0.668116i
$605$	−4725.39	−	1719.90i	−0.317545	−	0.115577i
$606$		0			0
$607$	−6621.09	−	5555.76i	−0.442738	−	0.371501i	0.393995	−	0.919113i	$-0.371093\pi$
$607$	−6621.09	−	5555.76i	−0.442738	−	0.371501i	−0.836733	+	0.547612i	$0.815537\pi$
$608$	3008.64	+	2524.55i	0.200685	+	0.168395i
$609$		0			0
$610$	−1003.87	−	365.380i	−0.0666322	−	0.0242522i
$611$	3319.46	−	5749.48i	0.219789	−	0.380686i
$612$		0			0
$613$	7951.11	+	13771.7i	0.523887	+	0.907398i	0.999613	+	0.0278051i	$0.00885177\pi$
$613$	7951.11	+	13771.7i	0.523887	+	0.907398i	−0.475727	+	0.879593i	$0.657815\pi$
$614$	−620.759	−	3520.50i	−0.0408009	−	0.231394i
$615$		0			0
$616$	7938.01	−	2889.20i	0.519207	−	0.188976i
$617$	2929.32	−	16613.0i	0.191134	−	1.08398i	−0.726682	−	0.686974i	$-0.758939\pi$
$617$	2929.32	−	16613.0i	0.191134	−	1.08398i	0.917817	−	0.397004i	$-0.129950\pi$
$618$		0			0
$619$	−8684.02	+	7286.75i	−0.563877	+	0.473149i	−0.879608	−	0.475700i	$-0.842195\pi$
$619$	−8684.02	+	7286.75i	−0.563877	+	0.473149i	0.315730	+	0.948849i	$0.397750\pi$
$620$	−3301.57			−0.213862
$621$		0			0
$622$	−9102.85			−0.586802
$623$	4678.29	−	3925.55i	0.300853	−	0.252446i
$624$		0			0
$625$	1889.23	−	10714.4i	0.120911	−	0.685719i
$626$	−575.757	+	209.558i	−0.0367602	+	0.0133796i
$627$		0			0
$628$	2065.27	+	11712.7i	0.131231	+	0.744250i
$629$	−2866.22	−	4964.43i	−0.181691	−	0.314698i
$630$		0			0
$631$	2248.78	−	3895.00i	0.141874	−	0.245733i	−0.786328	−	0.617809i	$-0.788021\pi$
$631$	2248.78	−	3895.00i	0.141874	−	0.245733i	0.928202	+	0.372076i	$0.121354\pi$
$632$	−7976.74	−	2903.29i	−0.502053	−	0.182732i
$633$		0			0
$634$	−6776.90	−	5686.49i	−0.424519	−	0.356214i
$635$	3301.77	+	2770.51i	0.206341	+	0.173141i
$636$		0			0
$637$	−1664.04	−	605.662i	−0.103504	−	0.0376722i
$638$	−4537.68	+	7859.48i	−0.281580	+	0.487712i
$639$		0			0
$640$	−231.754	−	401.410i	−0.0143139	−	0.0247924i
$641$	−317.582	−	1801.10i	−0.0195690	−	0.110981i	0.973459	−	0.228863i	$-0.0735008\pi$
$641$	−317.582	−	1801.10i	−0.0195690	−	0.110981i	−0.993028	+	0.117882i	$0.962390\pi$
$642$		0			0
$643$	6742.00	−	2453.89i	0.413497	−	0.150501i	−0.126891	−	0.991917i	$-0.540500\pi$
$643$	6742.00	−	2453.89i	0.413497	−	0.150501i	0.540388	+	0.841416i	$0.318278\pi$
$644$	−1412.92	+	8013.05i	−0.0864545	+	0.490308i
$645$		0			0
$646$	−8933.69	+	7496.26i	−0.544104	+	0.456558i
$647$	−25129.0			−1.52693			−0.763465	−	0.645849i	$-0.776504\pi$
$647$	−25129.0			−1.52693			−0.763465	+	0.645849i	$0.776504\pi$
$648$		0			0
$649$	31815.4			1.92429
$650$	−4532.68	+	3803.37i	−0.273517	+	0.229508i
$651$		0			0
$652$	−447.486	+	2537.82i	−0.0268787	+	0.152437i
$653$	−11093.4	+	4037.68i	−0.664809	+	0.241971i	−0.652311	−	0.757951i	$-0.726200\pi$
$653$	−11093.4	+	4037.68i	−0.664809	+	0.241971i	−0.0124975	+	0.999922i	$0.503978\pi$
$654$		0			0
$655$	−216.302	−	1226.71i	−0.0129032	−	0.0731778i
$656$	−256.187	−	443.728i	−0.0152476	−	0.0264096i
$657$		0			0
$658$	−5083.75	+	8805.31i	−0.301193	+	0.521682i
$659$	21199.9	+	7716.13i	1.25316	+	0.456112i	0.881467	−	0.472245i	$-0.156556\pi$
$659$	21199.9	+	7716.13i	1.25316	+	0.456112i	0.371689	+	0.928357i	$0.378779\pi$
$660$		0			0
$661$	−18615.9	−	15620.6i	−1.09542	−	0.919170i	−0.0983153	−	0.995155i	$-0.531345\pi$
$661$	−18615.9	−	15620.6i	−1.09542	−	0.919170i	−0.997109	+	0.0759852i	$0.975790\pi$
$662$	5312.87	+	4458.03i	0.311919	+	0.261731i
$663$		0			0
$664$	−9142.11	−	3327.46i	−0.534312	−	0.194473i
$665$	4499.47	−	7793.31i	0.262379	−	0.454454i
$666$		0			0
$667$	−4370.73	−	7570.32i	−0.253726	−	0.439466i
$668$	−879.984	−	4990.64i	−0.0509695	−	0.289062i
$669$		0			0
$670$	−6049.26	+	2201.75i	−0.348811	+	0.126957i
$671$	1335.81	−	7575.76i	0.0768531	−	0.435855i
$672$		0			0
$673$	10578.6	−	8876.52i	0.605908	−	0.508417i	−0.287431	−	0.957801i	$-0.592801\pi$
$673$	10578.6	−	8876.52i	0.605908	−	0.508417i	0.893338	+	0.449385i	$0.148357\pi$
$674$	−12333.9			−0.704875
$675$		0			0
$676$	−5991.33			−0.340882
$677$	−1444.99	+	1212.49i	−0.0820316	+	0.0688327i	−0.682881	−	0.730529i	$-0.739273\pi$
$677$	−1444.99	+	1212.49i	−0.0820316	+	0.0688327i	0.600850	+	0.799362i	$0.294829\pi$
$678$		0			0
$679$	1587.36	−	9002.39i	0.0897164	−	0.508807i
$680$	1293.31	−	470.728i	0.0729358	−	0.0265464i
$681$		0			0
$682$	−4128.31	−	23412.8i	−0.231791	−	1.31455i
$683$	−9978.38	−	17283.1i	−0.559022	−	0.968255i	−0.997578	−	0.0695513i	$-0.977843\pi$
$683$	−9978.38	−	17283.1i	−0.559022	−	0.968255i	0.438556	−	0.898704i	$-0.355490\pi$
$684$		0			0
$685$	−3187.82	+	5521.47i	−0.177811	+	0.307977i
$686$	−10503.8	−	3823.07i	−0.584603	−	0.212778i
$687$		0			0
$688$	−3484.40	−	2923.76i	−0.193083	−	0.162016i
$689$	15146.5	+	12709.5i	0.837500	+	0.702746i
$690$		0			0
$691$	18467.4	+	6721.59i	1.01669	+	0.370045i	0.795999	−	0.605298i	$-0.206946\pi$
$691$	18467.4	+	6721.59i	1.01669	+	0.370045i	0.220692	+	0.975343i	$0.429168\pi$
$692$	2749.95	−	4763.05i	0.151066	−	0.261653i
$693$		0			0
$694$	867.635	+	1502.79i	0.0474567	+	0.0821974i
$695$	1999.17	+	11337.9i	0.109112	+	0.618806i
$696$		0			0
$697$	1429.66	−	520.353i	0.0776932	−	0.0282780i
$698$	3539.51	−	20073.5i	0.191937	−	1.08853i
$699$		0			0
$700$	6941.78	−	5824.85i	0.374821	−	0.314512i
$701$	−18729.0			−1.00911			−0.504554	−	0.863380i	$-0.668343\pi$
$701$	−18729.0			−1.00911			−0.504554	+	0.863380i	$0.668343\pi$
$702$		0			0
$703$	−14809.0			−0.794497
$704$	2556.78	−	2145.39i	0.136878	−	0.114854i
$705$		0			0
$706$	−682.505	+	3870.68i	−0.0363830	+	0.206338i
$707$	22981.9	−	8364.74i	1.22252	−	0.444962i
$708$		0			0
$709$	−1329.31	−	7538.90i	−0.0704138	−	0.399336i	−0.999561	−	0.0296265i	$-0.990568\pi$
$709$	−1329.31	−	7538.90i	−0.0704138	−	0.399336i	0.929147	−	0.369710i	$-0.120543\pi$
$710$	1353.08	+	2343.60i	0.0715214	+	0.123879i
$711$		0			0
$712$	1206.47	−	2089.67i	0.0635033	−	0.109991i
$713$	21518.3	+	7832.03i	1.13025	+	0.411377i
$714$		0			0
$715$	3825.18	+	3209.70i	0.200075	+	0.167883i
$716$	−4583.92	−	3846.37i	−0.239259	−	0.200762i
$717$		0			0
$718$	12532.4	+	4561.42i	0.651399	+	0.237090i
$719$	−9064.45	+	15700.1i	−0.470163	+	0.814346i	−0.999418	−	0.0341168i	$-0.989138\pi$
$719$	−9064.45	+	15700.1i	−0.470163	+	0.814346i	0.529255	+	0.848463i	$0.322471\pi$
$720$		0			0
$721$	12566.4	+	21765.7i	0.649096	+	1.12427i
$722$	2849.49	+	16160.2i	0.146879	+	0.832994i
$723$		0			0
$724$	8443.09	−	3073.03i	0.433405	−	0.157746i
$725$	−1690.54	+	9587.51i	−0.0866000	+	0.491133i
$726$		0			0
$727$	−9807.85	+	8229.76i	−0.500348	+	0.419842i	−0.857718	−	0.514121i	$-0.828118\pi$
$727$	−9807.85	+	8229.76i	−0.500348	+	0.419842i	0.357369	+	0.933963i	$0.383674\pi$
$728$	−4283.09			−0.218052
$729$		0			0
$730$	4577.09			0.232063
$731$	10346.4	−	8681.63i	0.523494	−	0.439264i
$732$		0			0
$733$	−58.9879	+	334.537i	−0.00297240	+	0.0168573i	−0.986258	−	0.165213i	$-0.947169\pi$
$733$	−58.9879	+	334.537i	−0.00297240	+	0.0168573i	0.983285	+	0.182070i	$0.0582799\pi$
$734$	15101.1	−	5496.37i	0.759391	−	0.276396i
$735$		0			0
$736$	558.251	+	3166.00i	0.0279584	+	0.158560i
$737$	−23177.6	−	40144.7i	−1.15842	−	2.00644i
$738$		0			0
$739$	−6213.47	+	10762.0i	−0.309291	+	0.535708i	−0.978208	−	0.207630i	$-0.933425\pi$
$739$	−6213.47	+	10762.0i	−0.309291	+	0.535708i	0.668916	+	0.743338i	$0.266758\pi$
$740$	1642.30	+	597.748i	0.0815840	+	0.0296941i
$741$		0			0
$742$	−23196.9	−	19464.5i	−1.14769	−	0.963025i
$743$	−11505.4	−	9654.19i	−0.568093	−	0.476686i	0.312920	−	0.949780i	$-0.398693\pi$
$743$	−11505.4	−	9654.19i	−0.568093	−	0.476686i	−0.881012	+	0.473093i	$0.843137\pi$
$744$		0			0
$745$	3915.36	+	1425.08i	0.192547	+	0.0700815i
$746$	−12857.8	+	22270.4i	−0.631044	+	1.09300i
$747$		0			0
$748$	4955.29	+	8582.82i	0.242224	+	0.419544i
$749$	4604.04	+	26110.8i	0.224603	+	1.27379i
$750$		0			0
$751$	28556.0	−	10393.5i	1.38751	−	0.505014i	0.463066	−	0.886324i	$-0.346749\pi$
$751$	28556.0	−	10393.5i	1.38751	−	0.505014i	0.924447	+	0.381310i	$0.124527\pi$
$752$	−697.586	+	3956.20i	−0.0338276	+	0.191846i
$753$		0			0
$754$	3524.91	−	2957.75i	0.170252	−	0.142858i
$755$	10367.3			0.499740
$756$		0			0
$757$	19500.3			0.936262			0.468131	−	0.883659i	$-0.344928\pi$
$757$	19500.3			0.936262			0.468131	+	0.883659i	$0.344928\pi$
$758$	−3579.43	+	3003.50i	−0.171518	+	0.143921i
$759$		0			0
$760$	617.412	−	3501.52i	0.0294683	−	0.167123i
$761$	−3246.71	+	1181.71i	−0.154656	+	0.0562902i	−0.418188	−	0.908360i	$-0.637335\pi$
$761$	−3246.71	+	1181.71i	−0.154656	+	0.0562902i	0.263532	+	0.964651i	$0.415112\pi$
$762$		0			0
$763$	3723.45	+	21116.7i	0.176668	+	1.00194i
$764$	9158.35	+	15862.7i	0.433688	+	0.751169i
$765$		0			0
$766$	−4666.17	+	8082.04i	−0.220099	+	0.381222i
$767$	−15158.4	−	5517.22i	−0.713611	−	0.259733i
$768$		0			0
$769$	3745.14	+	3142.54i	0.175622	+	0.147364i	0.726361	−	0.687313i	$-0.241210\pi$
$769$	3745.14	+	3142.54i	0.175622	+	0.147364i	−0.550740	+	0.834677i	$0.685654\pi$
$770$	−5858.25	−	4915.66i	−0.274178	−	0.230062i
$771$		0			0
$772$	−5240.99	−	1907.57i	−0.244336	−	0.0889311i
$773$	4341.80	−	7520.22i	0.202023	−	0.349914i	−0.747157	−	0.664647i	$-0.768582\pi$
$773$	4341.80	−	7520.22i	0.202023	−	0.349914i	0.949180	+	0.314733i	$0.101915\pi$
$774$		0			0
$775$	−12751.6	−	22086.3i	−0.591032	−	1.02370i
$776$	−627.177	−	3556.90i	−0.0290133	−	0.164543i
$777$		0			0
$778$	18117.1	−	6594.09i	0.834871	−	0.303868i
$779$	682.501	−	3870.66i	0.0313904	−	0.178024i
$780$		0			0
$781$	−14927.6	+	12525.7i	−0.683931	+	0.573886i
$782$	−9545.96			−0.436525
$783$		0			0
$784$	1071.54			0.0488128
$785$	8248.00	−	6920.89i	0.375011	−	0.314672i
$786$		0			0
$787$	−2575.24	+	14604.9i	−0.116642	+	0.661512i	0.869282	+	0.494317i	$0.164582\pi$
$787$	−2575.24	+	14604.9i	−0.116642	+	0.661512i	−0.985924	+	0.167194i	$0.946529\pi$
$788$	328.598	−	119.600i	0.0148551	−	0.00540681i
$789$		0			0
$790$	1334.44	+	7567.96i	0.0600976	+	0.340830i
$791$	14024.2	+	24290.6i	0.630395	+	1.09188i
$792$		0			0
$793$	−1950.18	+	3377.82i	−0.0873305	+	0.151261i
$794$	1664.31	+	605.761i	0.0743883	+	0.0270751i
$795$		0			0
$796$	−12675.8	−	10636.3i	−0.564424	−	0.473608i
$797$	29340.0	+	24619.2i	1.30399	+	1.09417i	0.989442	+	0.144931i	$0.0462960\pi$
$797$	29340.0	+	24619.2i	1.30399	+	1.09417i	0.314544	+	0.949243i	$0.398148\pi$
$798$		0			0
$799$	−11209.2	−	4079.80i	−0.496310	−	0.180642i
$800$	1790.19	−	3100.71i	0.0791162	−	0.137033i
$801$		0			0
$802$	1629.75	+	2822.81i	0.0717561	+	0.124285i
$803$	5723.23	+	32458.0i	0.251517	+	1.42642i
$804$		0			0
$805$	6921.82	−	2519.33i	0.303058	−	0.110304i
$806$	−2093.16	+	11870.9i	−0.0914747	+	0.518779i
$807$		0			0
$808$	7402.32	−	6211.28i	0.322293	−	0.270436i
$809$	28776.2			1.25058			0.625290	−	0.780393i	$-0.284981\pi$
$809$	28776.2			1.25058			0.625290	+	0.780393i	$0.284981\pi$
$810$		0			0
$811$	4006.85			0.173489			0.0867444	−	0.996231i	$-0.472354\pi$
$811$	4006.85			0.173489			0.0867444	+	0.996231i	$0.472354\pi$
$812$	−5398.40	+	4529.79i	−0.233309	+	0.195769i
$813$		0			0
$814$	−2185.34	+	12393.7i	−0.0940983	+	0.533658i
$815$	2192.21	−	797.900i	0.0942207	−	0.0342935i
$816$		0			0
$817$	−6058.86	−	34361.5i	−0.259452	−	1.47143i
$818$	2781.76	+	4818.14i	0.118902	+	0.205944i
$819$		0			0
$820$	−231.923	+	401.703i	−0.00987697	+	0.0171074i
$821$	11460.9	+	4171.43i	0.487197	+	0.177325i	0.573927	−	0.818907i	$-0.305419\pi$
$821$	11460.9	+	4171.43i	0.487197	+	0.177325i	−0.0867299	+	0.996232i	$0.527642\pi$
$822$		0			0
$823$	19247.4	+	16150.5i	0.815214	+	0.684046i	0.951846	−	0.306576i	$-0.0991833\pi$
$823$	19247.4	+	16150.5i	0.815214	+	0.684046i	−0.136632	+	0.990622i	$0.543628\pi$
$824$	7606.93	+	6382.97i	0.321602	+	0.269856i
$825$		0			0
$826$	23215.1	+	8449.62i	0.977915	+	0.355932i
$827$	10796.1	−	18699.5i	0.453952	−	0.786268i	−0.544675	−	0.838647i	$-0.683347\pi$
$827$	10796.1	−	18699.5i	0.453952	−	0.786268i	0.998627	+	0.0523790i	$0.0166804\pi$
$828$		0			0
$829$	2249.44	+	3896.14i	0.0942414	+	0.163231i	0.909292	−	0.416159i	$-0.136624\pi$
$829$	2249.44	+	3896.14i	0.0942414	+	0.163231i	−0.815050	+	0.579390i	$0.803291\pi$
$830$	1529.39	+	8673.62i	0.0639590	+	0.362730i
$831$		0			0
$832$	−1590.22	+	578.791i	−0.0662630	+	0.0241178i
$833$	−552.508	+	3133.43i	−0.0229811	+	0.130332i
$834$		0			0
$835$	−3514.36	+	2948.90i	−0.145652	+	0.122217i
$836$	25602.7			1.05920
$837$		0			0
$838$	21756.1			0.896839
$839$	3563.35	−	2990.01i	0.146628	−	0.123035i	−0.566523	−	0.824046i	$-0.691712\pi$
$839$	3563.35	−	2990.01i	0.146628	−	0.123035i	0.713151	+	0.701011i	$0.247267\pi$
$840$		0			0
$841$	−2920.43	+	16562.6i	−0.119744	+	0.679101i
$842$	9890.80	−	3599.96i	0.404821	−	0.147343i
$843$		0			0
$844$	−3041.54	−	17249.4i	−0.124045	−	0.703495i
$845$	2711.95	+	4697.23i	0.110407	+	0.191230i
$846$		0			0
$847$	14058.9	−	24350.7i	0.570329	−	0.987839i
$848$	−11242.8	−	4092.05i	−0.455283	−	0.165709i
$849$		0			0
$850$	8144.12	+	6833.73i	0.328637	+	0.275759i
$851$	−9285.86	−	7791.76i	−0.374048	−	0.313864i
$852$		0			0
$853$	494.887	+	180.124i	0.0198647	+	0.00723017i	0.351933	−	0.936025i	$-0.385524\pi$
$853$	494.887	+	180.124i	0.0198647	+	0.00723017i	−0.332069	+	0.943255i	$0.607747\pi$
$854$	2986.70	−	5173.12i	0.119676	−	0.207284i
$855$		0			0
$856$	5237.84	+	9072.21i	0.209142	+	0.362245i
$857$	−5888.40	−	33394.8i	−0.234707	−	1.33109i	−0.843230	−	0.537554i	$-0.819349\pi$
$857$	−5888.40	−	33394.8i	−0.234707	−	1.33109i	0.608523	−	0.793537i	$-0.291763\pi$
$858$		0			0
$859$	32960.8	−	11996.7i	1.30921	−	0.476512i	0.409221	−	0.912435i	$-0.365800\pi$
$859$	32960.8	−	11996.7i	1.30921	−	0.476512i	0.899984	+	0.435923i	$0.143578\pi$
$860$	−715.043	+	4055.21i	−0.0283520	+	0.160792i
$861$		0			0
$862$	777.127	−	652.087i	0.0307065	−	0.0257659i
$863$	−41934.5			−1.65408			−0.827039	−	0.562145i	$-0.809976\pi$
$863$	−41934.5			−1.65408			−0.827039	+	0.562145i	$0.809976\pi$
$864$		0			0
$865$	−4979.00			−0.195712
$866$	2366.68	−	1985.88i	0.0928672	−	0.0779248i
$867$		0			0
$868$	3205.68	−	18180.3i	0.125355	−	0.710921i
$869$	−51998.9	+	18926.1i	−2.02985	+	0.738807i
$870$		0			0
$871$	4081.30	+	23146.2i	0.158771	+	0.900436i
$872$	4236.02	+	7337.01i	0.164507	+	0.284934i
$873$		0			0
$874$	−12330.4	+	21356.8i	−0.477210	+	0.826551i
$875$	−16321.2	−	5940.43i	−0.630580	−	0.229512i
$876$		0			0
$877$	−4161.69	−	3492.07i	−0.160240	−	0.134457i	0.559142	−	0.829072i	$-0.311131\pi$
$877$	−4161.69	−	3492.07i	−0.160240	−	0.134457i	−0.719382	+	0.694615i	$0.755575\pi$
$878$	−12667.1	−	10628.9i	−0.486895	−	0.408553i
$879$		0			0
$880$	−2839.31	−	1033.43i	−0.108765	−	0.0395872i
$881$	−15147.7	+	26236.6i	−0.579272	+	1.00333i	0.416291	+	0.909232i	$0.363330\pi$
$881$	−15147.7	+	26236.6i	−0.579272	+	1.00333i	−0.995563	+	0.0940975i	$0.970003\pi$
$882$		0			0
$883$	491.486	+	851.279i	0.0187314	+	0.0324437i	0.875239	−	0.483690i	$-0.160704\pi$
$883$	491.486	+	851.279i	0.0187314	+	0.0324437i	−0.856508	+	0.516134i	$0.827371\pi$
$884$	−872.571	−	4948.59i	−0.0331988	−	0.188280i
$885$		0			0
$886$	−29113.5	+	10596.4i	−1.10394	+	0.401800i
$887$	−7619.45	+	43212.0i	−0.288428	+	1.63576i	0.404347	+	0.914606i	$0.367499\pi$
$887$	−7619.45	+	43212.0i	−0.288428	+	1.63576i	−0.692776	+	0.721153i	$0.743612\pi$
$888$		0			0
$889$	−18461.9	+	15491.3i	−0.696503	+	0.584435i
$890$	−2184.41			−0.0822715
$891$		0			0
$892$	4570.93			0.171576
$893$	−23606.3	+	19808.0i	−0.884608	+	0.742274i
$894$		0			0
$895$	−940.679	+	5334.85i	−0.0351323	+	0.199245i
$896$	2435.41	−	886.418i	0.0908051	−	0.0330504i
$897$		0			0
$898$	−1294.41	−	7340.95i	−0.0481013	−	0.272796i
$899$	9916.47	+	17175.8i	0.367890	+	0.637203i
$900$		0			0
$901$	17763.1	−	30766.6i	0.656798	−	1.13761i
$902$	−3138.64	−	1142.37i	−0.115860	−	0.0421694i
$903$		0			0
$904$	8489.36	+	7123.42i	0.312336	+	0.262081i
$905$	−6231.00	−	5228.43i	−0.228868	−	0.192043i
$906$		0			0
$907$	−24439.5	−	8895.25i	−0.894708	−	0.325647i	−0.146578	−	0.989199i	$-0.546826\pi$
$907$	−24439.5	−	8895.25i	−0.894708	−	0.325647i	−0.748130	+	0.663552i	$0.769048\pi$
$908$	10491.3	−	18171.5i	0.383444	−	0.664145i
$909$		0			0
$910$	1938.72	+	3357.96i	0.0706241	+	0.122325i
$911$	−6850.83	−	38853.0i	−0.249153	−	1.41302i	−0.810647	−	0.585535i	$-0.800884\pi$
$911$	−6850.83	−	38853.0i	−0.249153	−	1.41302i	0.561494	−	0.827481i	$-0.310227\pi$
$912$		0			0
$913$	−59595.9	+	21691.1i	−2.16028	+	0.786277i
$914$	5509.47	−	31245.8i	0.199384	−	1.13076i
$915$		0			0
$916$	8563.75	−	7185.84i	0.308902	−	0.259200i
$917$	6964.96			0.250821
$918$		0			0
$919$	1286.40			0.0461745			0.0230872	−	0.999733i	$-0.492650\pi$
$919$	1286.40			0.0461745			0.0230872	+	0.999733i	$0.492650\pi$
$920$	2229.47	−	1870.75i	0.0798950	−	0.0670399i
$921$		0			0
$922$	−2447.01	+	13877.7i	−0.0874057	+	0.495702i
$923$	9284.35	−	3379.23i	0.331092	−	0.120508i
$924$		0			0
$925$	2344.28	+	13295.1i	0.0833291	+	0.472583i
$926$	4614.93	+	7993.30i	0.163775	+	0.283667i
$927$		0			0
$928$	−1392.18	+	2411.32i	−0.0492461	+	0.0852968i
$929$	33256.4	+	12104.3i	1.17450	+	0.427482i	0.854255	−	0.519854i	$-0.174014\pi$
$929$	33256.4	+	12104.3i	1.17450	+	0.427482i	0.320242	+	0.947336i	$0.396236\pi$
$930$		0			0
$931$	6296.64	+	5283.51i	0.221659	+	0.185994i
$932$	2821.64	+	2367.64i	0.0991695	+	0.0832131i
$933$		0			0
$934$	31181.3	+	11349.1i	1.09238	+	0.397594i
$935$	4485.98	−	7769.95i	0.156906	−	0.271769i
$936$		0			0
$937$	−21641.7	−	37484.6i	−0.754541	−	1.30690i	−0.945602	−	0.325325i	$-0.894526\pi$
$937$	−21641.7	−	37484.6i	−0.754541	−	1.30690i	0.191062	−	0.981578i	$-0.438807\pi$
$938$	−6250.51	−	35448.4i	−0.217576	−	1.23393i
$939$		0			0
$940$	3417.44	−	1243.85i	0.118579	−	0.0431594i
$941$	8547.15	−	48473.3i	0.296099	−	1.67926i	−0.366603	−	0.930377i	$-0.619479\pi$
$941$	8547.15	−	48473.3i	0.296099	−	1.67926i	0.662702	−	0.748883i	$-0.269410\pi$
$942$		0			0
$943$	2464.51	−	2067.97i	0.0851065	−	0.0714128i
$944$	9761.10			0.336543
$945$		0			0
$946$	−29651.3			−1.01908
$947$	−4023.43	+	3376.06i	−0.138061	+	0.115847i	−0.709203	−	0.705004i	$-0.750945\pi$
$947$	−4023.43	+	3376.06i	−0.138061	+	0.115847i	0.571142	+	0.820851i	$0.306501\pi$
$948$		0			0
$949$	2901.83	−	16457.1i	0.0992596	−	0.562929i
$950$	25808.5	−	9393.53i	0.881409	−	0.320807i
$951$		0			0
$952$	1336.34	+	7578.76i	0.0454948	+	0.258014i
$953$	12379.8	+	21442.5i	0.420800	+	0.728846i	0.996018	−	0.0891537i	$-0.0284162\pi$
$953$	12379.8	+	21442.5i	0.420800	+	0.728846i	−0.575218	+	0.818000i	$0.695083\pi$
$954$		0			0
$955$	8290.96	−	14360.4i	0.280931	−	0.486587i
$956$	−8539.25	−	3108.03i	−0.288890	−	0.105147i
$957$		0			0
$958$	−1199.43	−	1006.44i	−0.0404506	−	0.0339421i
$959$	−27309.0	−	22915.0i	−0.919557	−	0.771600i
$960$		0			0
$961$	−20827.2	−	7580.47i	−0.699109	−	0.254455i
$962$	3190.43	−	5525.98i	0.106927	−	0.185203i
$963$		0			0
$964$	1016.79	+	1761.14i	0.0339717	+	0.0588406i
$965$	876.771	+	4972.41i	0.0292479	+	0.165873i
$966$		0			0
$967$	−23090.8	+	8404.36i	−0.767890	+	0.279489i	−0.696114	−	0.717932i	$-0.745089\pi$
$967$	−23090.8	+	8404.36i	−0.767890	+	0.279489i	−0.0717763	+	0.997421i	$0.522867\pi$
$968$	1929.14	−	10940.7i	0.0640547	−	0.363272i
$969$		0			0
$970$	−2504.73	+	2101.72i	−0.0829094	+	0.0695693i
$971$	48144.1			1.59116			0.795580	−	0.605849i	$-0.207166\pi$
$971$	48144.1			1.59116			0.795580	+	0.605849i	$0.207166\pi$
$972$		0			0
$973$	−64373.8			−2.12100
$974$	−10514.9	+	8823.06i	−0.345913	+	0.290256i
$975$		0			0
$976$	409.832	−	2324.27i	0.0134410	−	0.0762276i
$977$	−26696.9	+	9716.89i	−0.874218	+	0.318189i	−0.739874	−	0.672746i	$-0.765115\pi$
$977$	−26696.9	+	9716.89i	−0.874218	+	0.318189i	−0.134344	+	0.990935i	$0.542893\pi$
$978$		0			0
$979$	−2731.40	−	15490.6i	−0.0891686	−	0.505700i
$980$	−485.027	−	840.092i	−0.0158098	−	0.0273834i
$981$		0			0
$982$	18986.5	−	32885.7i	0.616991	−	1.06866i
$983$	−8144.66	−	2964.41i	−0.264267	−	0.0961852i	0.206489	−	0.978449i	$-0.433796\pi$
$983$	−8144.66	−	2964.41i	−0.264267	−	0.0961852i	−0.470755	+	0.882264i	$0.656019\pi$
$984$		0			0
$985$	−242.505	−	203.486i	−0.00784452	−	0.00658233i
$986$	−6333.42	−	5314.37i	−0.204561	−	0.171647i
$987$		0			0
$988$	−12198.4	−	4439.85i	−0.392796	−	0.142966i
$989$	14280.2	−	24734.0i	0.459133	−	0.795242i
$990$		0			0
$991$	−25482.4	−	44136.8i	−0.816826	−	1.41478i	−0.908009	−	0.418950i	$-0.862398\pi$
$991$	−25482.4	−	44136.8i	−0.816826	−	1.41478i	0.0911833	−	0.995834i	$-0.470935\pi$
$992$	−1266.58	−	7183.14i	−0.0405383	−	0.229904i
$993$		0			0
$994$	−14219.0	+	5175.28i	−0.453720	+	0.165141i
$995$	−2601.23	+	14752.3i	−0.0828790	+	0.470030i
$996$		0			0
$997$	27937.3	−	23442.1i	0.887444	−	0.744654i	−0.0802518	−	0.996775i	$-0.525572\pi$
$997$	27937.3	−	23442.1i	0.887444	−	0.744654i	0.967696	+	0.252121i	$0.0811280\pi$
$998$	3779.60			0.119881
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.37.3		30
3.2	odd	2		54.4.e.b.49.5	yes	30
27.4	even	9		1458.4.a.j.1.9		15
27.11	odd	18		54.4.e.b.43.5	✓	30
27.16	even	9	inner	162.4.e.b.127.3		30
27.23	odd	18		1458.4.a.i.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.43.5	✓	30	27.11	odd	18
54.4.e.b.49.5	yes	30	3.2	odd	2
162.4.e.b.37.3		30	1.1	even	1	trivial
162.4.e.b.127.3		30	27.16	even	9	inner
1458.4.a.i.1.7		15	27.23	odd	18
1458.4.a.j.1.9		15	27.4	even	9

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-3.40278 + 1.23851i) q^{5} +(-3.51598 - 19.9401i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-3.62116 + 6.27204i) q^{10} +(-49.0055 - 17.8366i) q^{11} +(20.2556 + 16.9964i) q^{13} +(-31.0213 - 26.0300i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(23.7547 - 41.1444i) q^{17} +(-61.3673 - 106.291i) q^{19} +(2.51523 + 14.2646i) q^{20} +(-98.0111 + 35.6731i) q^{22} +(17.4454 - 98.9375i) q^{23} +(-85.7106 + 71.9197i) q^{25} +52.8835 q^{26} -80.9910 q^{28} +(66.6543 - 55.9296i) q^{29} +(-39.5807 + 224.473i) q^{31} +(-30.0702 + 10.9446i) q^{32} +(-16.4999 - 93.5754i) q^{34} +(36.6602 + 63.4973i) q^{35} +(60.3294 - 104.494i) q^{37} +(-230.665 - 83.9554i) q^{38} +(22.1918 + 18.6211i) q^{40} +(24.5313 + 20.5842i) q^{41} +(267.140 + 97.2311i) q^{43} +(-104.301 + 180.655i) q^{44} +(-100.464 - 174.008i) q^{46} +(-43.5991 - 247.263i) q^{47} +(-62.9324 + 22.9055i) q^{49} +(-38.8580 + 220.375i) q^{50} +(81.0222 - 67.9857i) q^{52} +747.772 q^{53} +188.846 q^{55} +(-124.085 + 104.120i) q^{56} +(30.2186 - 171.378i) q^{58} +(-573.277 + 208.656i) q^{59} +(25.6145 + 145.267i) q^{61} +(227.936 + 394.797i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(-89.9755 - 32.7484i) q^{65} +(680.914 + 571.355i) q^{67} +(-145.577 - 122.154i) q^{68} +(137.797 + 50.1541i) q^{70} +(186.829 - 323.598i) q^{71} +(-315.996 - 547.321i) q^{73} +(-41.9043 - 237.651i) q^{74} +(-461.331 + 167.911i) q^{76} +(-183.361 + 1039.89i) q^{77} +(812.837 - 682.051i) q^{79} +57.9386 q^{80} +64.0467 q^{82} +(931.590 - 781.697i) q^{83} +(-29.8743 + 169.426i) q^{85} +(534.281 - 194.462i) q^{86} +(72.4469 + 410.867i) q^{88} +(150.809 + 261.208i) q^{89} +(267.693 - 463.658i) q^{91} +(-377.620 - 137.443i) q^{92} +(-384.673 - 322.779i) q^{94} +(340.462 + 285.682i) q^{95} +(424.244 + 154.412i) q^{97} +(-66.9712 + 115.998i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31}+ \cdots - 4002 q^{98}+O(q^{100}) \) 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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