LMFDB - Embedded newform 162.4.e.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			19.3
Character	$\chi$	$=$	162.19
Dual form			162.4.e.b.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-0.127307 - 0.721992i) q^{5} +(1.18538 + 0.994655i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})$	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-0.127307 - 0.721992i) q^{5} +(1.18538 + 0.994655i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(0.733130 + 1.26982i) q^{10} +(4.18063 - 23.7095i) q^{11} +(26.9008 + 9.79111i) q^{13} +(-2.90818 - 1.05849i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-34.8695 - 60.3957i) q^{17} +(-14.7514 + 25.5501i) q^{19} +(-2.24644 - 1.88499i) q^{20} +(8.36126 + 47.4191i) q^{22} +(125.729 - 105.499i) q^{23} +(116.957 - 42.5687i) q^{25} -57.2546 q^{26} +6.18963 q^{28} +(197.138 - 71.7522i) q^{29} +(83.3328 - 69.9245i) q^{31} +(5.55674 + 31.5138i) q^{32} +(106.846 + 89.6547i) q^{34} +(0.567225 - 0.982463i) q^{35} +(63.3079 + 109.652i) q^{37} +(10.2462 - 58.1091i) q^{38} +(5.51133 + 2.00596i) q^{40} +(95.0553 + 34.5973i) q^{41} +(85.0002 - 482.060i) q^{43} +(-48.1506 - 83.3993i) q^{44} +(-164.128 + 284.278i) q^{46} +(223.532 + 187.565i) q^{47} +(-59.1455 - 335.431i) q^{49} +(-190.688 + 160.006i) q^{50} +(107.603 - 39.1644i) q^{52} -523.625 q^{53} -17.6503 q^{55} +(-11.6327 + 4.23396i) q^{56} +(-321.416 + 269.700i) q^{58} +(100.933 + 572.420i) q^{59} +(104.632 + 87.7968i) q^{61} +(-108.783 + 188.418i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(3.64444 - 20.6687i) q^{65} +(-822.330 - 299.304i) q^{67} +(-262.133 - 95.4086i) q^{68} +(-0.393991 + 2.23443i) q^{70} +(-265.726 - 460.252i) q^{71} +(-593.378 + 1027.76i) q^{73} +(-193.987 - 162.774i) q^{74} +(20.4924 + 116.218i) q^{76} +(28.5385 - 23.9466i) q^{77} +(-200.068 + 72.8188i) q^{79} -11.7301 q^{80} -202.311 q^{82} +(506.381 - 184.308i) q^{83} +(-39.1661 + 32.8643i) q^{85} +(170.000 + 964.120i) q^{86} +(147.542 + 123.802i) q^{88} +(-173.475 + 300.468i) q^{89} +(22.1490 + 38.3633i) q^{91} +(114.002 - 646.538i) q^{92} +(-548.405 - 199.603i) q^{94} +(20.3249 + 7.39767i) q^{95} +(-83.7836 + 475.160i) q^{97} +(340.606 + 589.946i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$3$		0			0
$3$		0			0
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	−0.127307	−	0.721992i	−0.0113867	−	0.0645769i	0.978585	−	0.205843i	$-0.0659937\pi$
$5$	−0.127307	−	0.721992i	−0.0113867	−	0.0645769i	−0.989972	+	0.141266i	$0.954883\pi$
$6$		0			0
$7$	1.18538	+	0.994655i	0.0640047	+	0.0537063i	0.674229	−	0.738523i	$-0.264476\pi$
$7$	1.18538	+	0.994655i	0.0640047	+	0.0537063i	−0.610224	+	0.792229i	$0.708921\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$		0			0
$10$	0.733130	+	1.26982i	0.0231836	+	0.0401552i
$11$	4.18063	−	23.7095i	0.114592	−	0.649881i	−0.872360	−	0.488864i	$-0.837411\pi$
$11$	4.18063	−	23.7095i	0.114592	−	0.649881i	0.986952	−	0.161017i	$-0.0514775\pi$
$12$		0			0
$13$	26.9008	+	9.79111i	0.573919	+	0.208890i	0.612642	−	0.790360i	$-0.290107\pi$
$13$	26.9008	+	9.79111i	0.573919	+	0.208890i	−0.0387227	+	0.999250i	$0.512329\pi$
$14$	−2.90818	−	1.05849i	−0.0555173	−	0.0202067i
$15$		0			0
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	−34.8695	−	60.3957i	−0.497476	−	0.861654i	0.502519	−	0.864566i	$-0.332407\pi$
$17$	−34.8695	−	60.3957i	−0.497476	−	0.861654i	−0.999996	+	0.00291171i	$0.999073\pi$
$18$		0			0
$19$	−14.7514	+	25.5501i	−0.178116	+	0.308505i	−0.941235	−	0.337752i	$-0.890333\pi$
$19$	−14.7514	+	25.5501i	−0.178116	+	0.308505i	0.763119	+	0.646257i	$0.223667\pi$
$20$	−2.24644	−	1.88499i	−0.0251160	−	0.0210748i
$21$		0			0
$22$	8.36126	+	47.4191i	0.0810285	+	0.459536i
$23$	125.729	−	105.499i	1.13984	−	0.956441i	0.140409	−	0.990094i	$-0.455158\pi$
$23$	125.729	−	105.499i	1.13984	−	0.956441i	0.999434	+	0.0336525i	$0.0107139\pi$
$24$		0			0
$25$	116.957	−	42.5687i	0.935652	−	0.340550i
$26$	−57.2546			−0.431867
$27$		0			0
$28$	6.18963			0.0417761
$29$	197.138	−	71.7522i	1.26233	−	0.459450i	0.377779	−	0.925896i	$-0.376688\pi$
$29$	197.138	−	71.7522i	1.26233	−	0.459450i	0.884550	+	0.466446i	$0.154466\pi$
$30$		0			0
$31$	83.3328	−	69.9245i	0.482807	−	0.405123i	−0.368633	−	0.929575i	$-0.620174\pi$
$31$	83.3328	−	69.9245i	0.482807	−	0.405123i	0.851440	+	0.524452i	$0.175730\pi$
$32$	5.55674	+	31.5138i	0.0306970	+	0.174091i
$33$		0			0
$34$	106.846	+	89.6547i	0.538941	+	0.452225i
$35$	0.567225	−	0.982463i	0.00273939	−	0.00474476i
$36$		0			0
$37$	63.3079	+	109.652i	0.281291	+	0.487210i	0.971703	−	0.236206i	$-0.0759042\pi$
$37$	63.3079	+	109.652i	0.281291	+	0.487210i	−0.690412	+	0.723416i	$0.742571\pi$
$38$	10.2462	−	58.1091i	0.0437409	−	0.248067i
$39$		0			0
$40$	5.51133	+	2.00596i	0.0217855	+	0.00792926i
$41$	95.0553	+	34.5973i	0.362077	+	0.131785i	0.516651	−	0.856196i	$-0.327178\pi$
$41$	95.0553	+	34.5973i	0.362077	+	0.131785i	−0.154574	+	0.987981i	$0.549401\pi$
$42$		0			0
$43$	85.0002	−	482.060i	0.301451	−	1.70962i	−0.338304	−	0.941037i	$-0.609853\pi$
$43$	85.0002	−	482.060i	0.301451	−	1.70962i	0.639755	−	0.768579i	$-0.279036\pi$
$44$	−48.1506	−	83.3993i	−0.164977	−	0.285748i
$45$		0			0
$46$	−164.128	+	284.278i	−0.526073	+	0.911185i
$47$	223.532	+	187.565i	0.693733	+	0.582111i	0.919983	−	0.391958i	$-0.128202\pi$
$47$	223.532	+	187.565i	0.693733	+	0.582111i	−0.226250	+	0.974069i	$0.572647\pi$
$48$		0			0
$49$	−59.1455	−	335.431i	−0.172436	−	0.977933i
$50$	−190.688	+	160.006i	−0.539346	+	0.452565i
$51$		0			0
$52$	107.603	−	39.1644i	0.286960	−	0.104445i
$53$	−523.625			−1.35708			−0.678542	−	0.734562i	$-0.737388\pi$
$53$	−523.625			−1.35708			−0.678542	+	0.734562i	$0.737388\pi$
$54$		0			0
$55$	−17.6503			−0.0432722
$56$	−11.6327	+	4.23396i	−0.0277587	+	0.0101033i
$57$		0			0
$58$	−321.416	+	269.700i	−0.727655	+	0.610575i
$59$	100.933	+	572.420i	0.222718	+	1.26310i	0.867000	+	0.498309i	$0.166045\pi$
$59$	100.933	+	572.420i	0.222718	+	1.26310i	−0.644282	+	0.764788i	$0.722843\pi$
$60$		0			0
$61$	104.632	+	87.7968i	0.219619	+	0.184282i	0.745959	−	0.665992i	$-0.231992\pi$
$61$	104.632	+	87.7968i	0.219619	+	0.184282i	−0.526340	+	0.850274i	$0.676436\pi$
$62$	−108.783	+	188.418i	−0.222830	+	0.385954i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	3.64444	−	20.6687i	0.00695442	−	0.0394405i
$66$		0			0
$67$	−822.330	−	299.304i	−1.49946	−	0.545758i	−0.543537	−	0.839385i	$-0.682915\pi$
$67$	−822.330	−	299.304i	−1.49946	−	0.545758i	−0.955920	+	0.293627i	$0.905138\pi$
$68$	−262.133	−	95.4086i	−0.467475	−	0.170147i
$69$		0			0
$70$	−0.393991	+	2.23443i	−0.000672727	+	0.00381522i
$71$	−265.726	−	460.252i	−0.444168	−	0.769322i	0.553826	−	0.832633i	$-0.313167\pi$
$71$	−265.726	−	460.252i	−0.444168	−	0.769322i	−0.997994	+	0.0633110i	$0.979834\pi$
$72$		0			0
$73$	−593.378	+	1027.76i	−0.951364	+	1.64781i	−0.208888	+	0.977940i	$0.566984\pi$
$73$	−593.378	+	1027.76i	−0.951364	+	1.64781i	−0.742477	+	0.669872i	$0.766349\pi$
$74$	−193.987	−	162.774i	−0.304736	−	0.255704i
$75$		0			0
$76$	20.4924	+	116.218i	0.0309295	+	0.175410i
$77$	28.5385	−	23.9466i	0.0422371	−	0.0354412i
$78$		0			0
$79$	−200.068	+	72.8188i	−0.284929	+	0.103706i	−0.480531	−	0.876978i	$-0.659556\pi$
$79$	−200.068	+	72.8188i	−0.284929	+	0.103706i	0.195602	+	0.980683i	$0.437334\pi$
$80$	−11.7301			−0.0163933
$81$		0			0
$82$	−202.311			−0.272458
$83$	506.381	−	184.308i	0.669670	−	0.243740i	0.0152640	−	0.999883i	$-0.495141\pi$
$83$	506.381	−	184.308i	0.669670	−	0.243740i	0.654406	+	0.756144i	$0.272919\pi$
$84$		0			0
$85$	−39.1661	+	32.8643i	−0.0499784	+	0.0419368i
$86$	170.000	+	964.120i	0.213158	+	1.20888i
$87$		0			0
$88$	147.542	+	123.802i	0.178728	+	0.149970i
$89$	−173.475	+	300.468i	−0.206611	+	0.357860i	−0.950645	−	0.310282i	$-0.899577\pi$
$89$	−173.475	+	300.468i	−0.206611	+	0.357860i	0.744034	+	0.668142i	$0.232910\pi$
$90$		0			0
$91$	22.1490	+	38.3633i	0.0255148	+	0.0441930i
$92$	114.002	−	646.538i	0.129191	−	0.732676i
$93$		0			0
$94$	−548.405	−	199.603i	−0.601741	−	0.219016i
$95$	20.3249	+	7.39767i	0.0219505	+	0.00798932i
$96$		0			0
$97$	−83.7836	+	475.160i	−0.0877004	+	0.497373i	0.909041	+	0.416707i	$0.136816\pi$
$97$	−83.7836	+	475.160i	−0.0877004	+	0.497373i	−0.996741	+	0.0806663i	$0.974295\pi$
$98$	340.606	+	589.946i	0.351085	+	0.608097i
$99$		0			0
$100$	248.925	−	431.151i	0.248925	−	0.431151i
$101$	−279.180	−	234.260i	−0.275044	−	0.230789i	0.494823	−	0.868994i	$-0.335233\pi$
$101$	−279.180	−	234.260i	−0.275044	−	0.230789i	−0.769867	+	0.638205i	$0.779677\pi$
$102$		0			0
$103$	−212.306	−	1204.05i	−0.203099	−	1.15183i	−0.900404	−	0.435055i	$-0.856729\pi$
$103$	−212.306	−	1204.05i	−0.203099	−	1.15183i	0.697305	−	0.716775i	$-0.254382\pi$
$104$	−175.438	+	147.210i	−0.165415	+	0.138799i
$105$		0			0
$106$	984.093	−	358.181i	0.901732	−	0.328203i
$107$	−762.846			−0.689226			−0.344613	−	0.938745i	$-0.611990\pi$
$107$	−762.846			−0.689226			−0.344613	+	0.938745i	$0.611990\pi$
$108$		0			0
$109$	2087.75			1.83459			0.917296	−	0.398206i	$-0.130367\pi$
$109$	2087.75			1.83459			0.917296	+	0.398206i	$0.130367\pi$
$110$	33.1718	−	12.0735i	0.0287527	−	0.0104651i
$111$		0			0
$112$	18.9661	−	15.9145i	0.0160012	−	0.0134266i
$113$	234.912	+	1332.25i	0.195563	+	1.10909i	0.911614	+	0.411046i	$0.134837\pi$
$113$	234.912	+	1332.25i	0.195563	+	1.10909i	−0.716051	+	0.698048i	$0.754052\pi$
$114$		0			0
$115$	−92.1759	−	77.3448i	−0.0747430	−	0.0627168i
$116$	419.579	−	726.732i	0.335836	−	0.581684i
$117$		0			0
$118$	−581.250	−	1006.76i	−0.453461	−	0.785418i
$119$	18.7392	−	106.275i	0.0144355	−	0.0818675i
$120$		0			0
$121$	706.066	+	256.987i	0.530478	+	0.193078i
$122$	−256.701	−	93.4314i	−0.190497	−	0.0693351i
$123$		0			0
$124$	75.5600	−	428.522i	0.0547217	−	0.310342i
$125$	−91.4442	−	158.386i	−0.0654321	−	0.113332i
$126$		0			0
$127$	−500.766	+	867.353i	−0.349888	+	0.606025i	−0.986229	−	0.165383i	$-0.947114\pi$
$127$	−500.766	+	867.353i	−0.349888	+	0.606025i	0.636341	+	0.771408i	$0.280447\pi$
$128$	98.0537	+	82.2768i	0.0677094	+	0.0568149i
$129$		0			0
$130$	7.28889	+	41.3373i	0.00491752	+	0.0278886i
$131$	1481.61	−	1243.22i	0.988157	−	0.829162i	0.00285684	−	0.999996i	$-0.499091\pi$
$131$	1481.61	−	1243.22i	0.988157	−	0.829162i	0.985300	+	0.170834i	$0.0546462\pi$
$132$		0			0
$133$	−42.8996	+	15.6142i	−0.0279689	+	0.0101799i
$134$	1750.21			1.12832
$135$		0			0
$136$	557.912			0.351769
$137$	−208.769	+	75.9858i	−0.130192	+	0.0473862i	−0.406295	−	0.913742i	$-0.633179\pi$
$137$	−208.769	+	75.9858i	−0.130192	+	0.0473862i	0.276102	+	0.961128i	$0.410957\pi$
$138$		0			0
$139$	741.480	−	622.175i	0.452457	−	0.379656i	−0.387890	−	0.921706i	$-0.626796\pi$
$139$	741.480	−	622.175i	0.452457	−	0.379656i	0.840347	+	0.542049i	$0.182351\pi$
$140$	−0.787981	−	4.46886i	−0.000475690	−	0.00269777i
$141$		0			0
$142$	814.233	+	683.223i	0.481190	+	0.403766i
$143$	344.605	−	596.874i	0.201520	−	0.349043i
$144$		0			0
$145$	−76.9015	−	133.197i	−0.0440436	−	0.0762857i
$146$	412.156	−	2337.45i	0.233632	−	1.32499i
$147$		0			0
$148$	475.920	+	173.221i	0.264327	+	0.0962071i
$149$	−1418.44	−	516.269i	−0.779886	−	0.283855i	−0.0787607	−	0.996894i	$-0.525096\pi$
$149$	−1418.44	−	516.269i	−0.779886	−	0.283855i	−0.701125	+	0.713038i	$0.747319\pi$
$150$		0			0
$151$	−272.728	+	1546.72i	−0.146982	+	0.833578i	0.818772	+	0.574119i	$0.194655\pi$
$151$	−272.728	+	1546.72i	−0.146982	+	0.833578i	−0.965754	+	0.259459i	$0.916456\pi$
$152$	−118.011	−	204.401i	−0.0629734	−	0.109073i
$153$		0			0
$154$	−37.2543	+	64.5264i	−0.0194938	+	0.0337642i
$155$	−61.0938	−	51.2638i	−0.0316592	−	0.0265652i
$156$		0			0
$157$	234.882	+	1332.08i	0.119399	+	0.677145i	0.984478	+	0.175509i	$0.0561571\pi$
$157$	234.882	+	1332.08i	0.119399	+	0.677145i	−0.865079	+	0.501636i	$0.832732\pi$
$158$	326.194	−	273.709i	0.164244	−	0.137817i
$159$		0			0
$160$	22.0453	−	8.02385i	0.0108927	−	0.00396463i
$161$	253.973			0.124322
$162$		0			0
$163$	2676.86			1.28630			0.643152	−	0.765739i	$-0.277626\pi$
$163$	2676.86			1.28630			0.643152	+	0.765739i	$0.277626\pi$
$164$	380.221	−	138.389i	0.181038	−	0.0658926i
$165$		0			0
$166$	−825.612	+	692.771i	−0.386024	+	0.323912i
$167$	−494.206	−	2802.78i	−0.228999	−	1.29872i	−0.854891	−	0.518807i	$-0.826376\pi$
$167$	−494.206	−	2802.78i	−0.228999	−	1.29872i	0.625893	−	0.779909i	$-0.284735\pi$
$168$		0			0
$169$	−1055.21	−	885.426i	−0.480296	−	0.403016i
$170$	51.1277	−	88.5558i	0.0230666	−	0.0399525i
$171$		0			0
$172$	−978.993	−	1695.67i	−0.433997	−	0.751705i
$173$	−740.549	+	4199.86i	−0.325450	+	1.84572i	0.181042	+	0.983475i	$0.442053\pi$
$173$	−740.549	+	4199.86i	−0.325450	+	1.84572i	−0.506493	+	0.862244i	$0.669058\pi$
$174$		0			0
$175$	180.979	+	65.8711i	0.0781758	+	0.0284537i
$176$	−361.974	−	131.748i	−0.155027	−	0.0564254i
$177$		0			0
$178$	120.495	−	683.359i	0.0507385	−	0.287752i
$179$	−771.476	−	1336.24i	−0.322139	−	0.557960i	0.658791	−	0.752326i	$-0.271068\pi$
$179$	−771.476	−	1336.24i	−0.322139	−	0.557960i	−0.980929	+	0.194366i	$0.937735\pi$
$180$		0			0
$181$	−1650.55	+	2858.83i	−0.677814	+	1.17401i	0.297824	+	0.954621i	$0.403739\pi$
$181$	−1650.55	+	2858.83i	−0.677814	+	1.17401i	−0.975638	+	0.219387i	$0.929594\pi$
$182$	−67.8686	−	56.9485i	−0.0276415	−	0.0231940i
$183$		0			0
$184$	228.004	+	1293.08i	0.0913516	+	0.518080i
$185$	71.1087	−	59.6673i	0.0282595	−	0.0237126i
$186$		0			0
$187$	−1577.73	+	574.248i	−0.616980	+	0.224562i
$188$	1167.20			0.452802
$189$		0			0
$190$	−43.2587			−0.0165175
$191$	−987.903	+	359.567i	−0.374252	+	0.136217i	−0.522296	−	0.852764i	$-0.674924\pi$
$191$	−987.903	+	359.567i	−0.374252	+	0.136217i	0.148044	+	0.988981i	$0.452702\pi$
$192$		0			0
$193$	999.507	−	838.686i	0.372778	−	0.312798i	−0.437082	−	0.899422i	$-0.643988\pi$
$193$	999.507	−	838.686i	0.372778	−	0.312798i	0.809859	+	0.586624i	$0.199543\pi$
$194$	−167.567	−	950.321i	−0.0620135	−	0.351696i
$195$		0			0
$196$	−1043.68	−	875.748i	−0.380348	−	0.319150i
$197$	−1223.38	+	2118.95i	−0.442447	+	0.766341i	−0.997870	−	0.0652268i	$-0.979223\pi$
$197$	−1223.38	+	2118.95i	−0.442447	+	0.766341i	0.555423	+	0.831568i	$0.312556\pi$
$198$		0			0
$199$	−2315.78	−	4011.05i	−0.824931	−	1.42882i	−0.901972	−	0.431794i	$-0.857881\pi$
$199$	−2315.78	−	4011.05i	−0.824931	−	1.42882i	0.0770413	−	0.997028i	$-0.475453\pi$
$200$	−172.902	+	980.573i	−0.0611299	+	0.346685i
$201$		0			0
$202$	684.929	+	249.294i	0.238572	+	0.0868329i
$203$	305.052	+	111.030i	0.105470	+	0.0383881i
$204$		0			0
$205$	12.8778	−	73.0336i	0.00438744	−	0.0248824i
$206$	1222.62	+	2117.65i	0.413516	+	0.716230i
$207$		0			0
$208$	229.018	−	396.671i	0.0763440	−	0.132232i
$209$	544.112	+	456.564i	0.180081	+	0.151106i
$210$		0			0
$211$	214.649	+	1217.34i	0.0700335	+	0.397180i	0.999594	+	0.0285090i	$0.00907592\pi$
$211$	214.649	+	1217.34i	0.0700335	+	0.397180i	−0.929560	+	0.368671i	$0.879813\pi$
$212$	−1604.48	+	1346.32i	−0.519793	+	0.436158i
$213$		0			0
$214$	1433.68	−	521.818i	0.457965	−	0.166686i
$215$	−358.865			−0.113834
$216$		0			0
$217$	168.332			0.0526596
$218$	−3923.69	+	1428.11i	−1.21902	+	0.443687i
$219$		0			0
$220$	−54.0837	+	45.3816i	−0.0165742	+	0.0139074i
$221$	−346.678	−	1966.11i	−0.105521	−	0.598438i
$222$		0			0
$223$	−3019.42	−	2533.59i	−0.906705	−	0.760816i	0.0647843	−	0.997899i	$-0.479364\pi$
$223$	−3019.42	−	2533.59i	−0.906705	−	0.760816i	−0.971489	+	0.237083i	$0.923809\pi$
$224$	−24.7585	+	42.8830i	−0.00738504	+	0.0127913i
$225$		0			0
$226$	−1352.80	−	2343.12i	−0.398173	−	0.689656i
$227$	−712.882	+	4042.96i	−0.208439	+	1.18212i	0.683496	+	0.729954i	$0.260458\pi$
$227$	−712.882	+	4042.96i	−0.208439	+	1.18212i	−0.891935	+	0.452163i	$0.850653\pi$
$228$		0			0
$229$	4707.41	+	1713.36i	1.35840	+	0.494419i	0.915560	−	0.402180i	$-0.131748\pi$
$229$	4707.41	+	1713.36i	1.35840	+	0.494419i	0.442843	+	0.896599i	$0.353970\pi$
$230$	226.141	+	82.3086i	0.0648317	+	0.0235968i
$231$		0			0
$232$	−291.436	+	1652.82i	−0.0824730	+	0.467728i
$233$	2225.37	+	3854.45i	0.625703	+	1.08375i	0.988405	+	0.151843i	$0.0485210\pi$
$233$	2225.37	+	3854.45i	0.625703	+	1.08375i	−0.362702	+	0.931905i	$0.618146\pi$
$234$		0			0
$235$	106.964	−	185.266i	0.0296917	−	0.0514275i
$236$	1781.05	+	1494.48i	0.491258	+	0.412214i
$237$		0			0
$238$	37.4784	+	212.550i	0.0102074	+	0.0578891i
$239$	3305.93	−	2774.01i	0.894740	−	0.750776i	−0.0744150	−	0.997227i	$-0.523709\pi$
$239$	3305.93	−	2774.01i	0.894740	−	0.750776i	0.969155	+	0.246451i	$0.0792645\pi$
$240$		0			0
$241$	−4277.35	+	1556.83i	−1.14327	+	0.416117i	−0.843094	−	0.537766i	$-0.819268\pi$
$241$	−4277.35	+	1556.83i	−1.14327	+	0.416117i	−0.300178	+	0.953883i	$0.597046\pi$
$242$	−1502.76			−0.399178
$243$		0			0
$244$	546.350			0.143346
$245$	−234.649	+	85.4052i	−0.0611884	+	0.0222708i
$246$		0			0
$247$	−646.989	+	542.888i	−0.166668	+	0.139851i
$248$	151.120	+	857.045i	0.0386941	+	0.219445i
$249$		0			0
$250$	280.201	+	235.117i	0.0708859	+	0.0594804i
$251$	1279.99	−	2217.00i	0.321880	−	0.557513i	−0.658996	−	0.752147i	$-0.729018\pi$
$251$	1279.99	−	2217.00i	0.321880	−	0.557513i	0.980876	+	0.194634i	$0.0623518\pi$
$252$		0			0
$253$	−1975.71	−	3422.04i	−0.490957	−	0.850362i
$254$	347.829	−	1972.63i	0.0859241	−	0.487300i
$255$		0			0
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	664.783	+	241.961i	0.161354	+	0.0587281i	0.421434	−	0.906859i	$-0.361527\pi$
$257$	664.783	+	241.961i	0.161354	+	0.0587281i	−0.260080	+	0.965587i	$0.583749\pi$
$258$		0			0
$259$	−34.0222	+	192.950i	−0.00816231	+	0.0462908i
$260$	−41.9750	−	72.7029i	−0.0100122	−	0.0173417i
$261$		0			0
$262$	−1934.10	+	3349.96i	−0.456065	+	0.789928i
$263$	−1392.56	−	1168.50i	−0.326498	−	0.273965i	0.464773	−	0.885430i	$-0.346136\pi$
$263$	−1392.56	−	1168.50i	−0.326498	−	0.273965i	−0.791271	+	0.611465i	$0.790580\pi$
$264$		0			0
$265$	66.6609	+	378.053i	0.0154526	+	0.0876363i
$266$	69.9442	−	58.6901i	0.0161224	−	0.0135283i
$267$		0			0
$268$	−3289.32	+	1197.22i	−0.749729	+	0.272879i
$269$	2704.39			0.612972			0.306486	−	0.951875i	$-0.400847\pi$
$269$	2704.39			0.612972			0.306486	+	0.951875i	$0.400847\pi$
$270$		0			0
$271$	3407.25			0.763747			0.381874	−	0.924215i	$-0.375279\pi$
$271$	3407.25			0.763747			0.381874	+	0.924215i	$0.375279\pi$
$272$	−1048.53	+	381.634i	−0.233737	+	0.0850735i
$273$		0			0
$274$	340.381	−	285.613i	0.0750480	−	0.0629727i
$275$	−520.332	−	2950.95i	−0.114099	−	0.647087i
$276$		0			0
$277$	1318.55	+	1106.40i	0.286008	+	0.239989i	0.774492	−	0.632584i	$-0.218006\pi$
$277$	1318.55	+	1106.40i	0.286008	+	0.239989i	−0.488484	+	0.872573i	$0.662450\pi$
$278$	−967.933	+	1676.51i	−0.208823	+	0.361692i
$279$		0			0
$280$	4.53780	+	7.85971i	0.000968520	+	0.00167753i
$281$	32.4048	−	183.777i	0.00687939	−	0.0390149i	−0.981175	−	0.193122i	$-0.938139\pi$
$281$	32.4048	−	183.777i	0.00687939	−	0.0390149i	0.988054	+	0.154107i	$0.0492499\pi$
$282$		0			0
$283$	−2224.17	−	809.532i	−0.467184	−	0.170041i	0.0976921	−	0.995217i	$-0.468854\pi$
$283$	−2224.17	−	809.532i	−0.467184	−	0.170041i	−0.564876	+	0.825175i	$0.691076\pi$
$284$	−1997.61	−	727.070i	−0.417381	−	0.151914i
$285$		0			0
$286$	−239.360	+	1357.48i	−0.0494884	+	0.280662i
$287$	78.2646	+	135.558i	0.0160969	+	0.0278807i
$288$		0			0
$289$	24.7357	−	42.8434i	0.00503474	−	0.00872042i
$290$	235.640	+	197.725i	0.0477146	+	0.0400373i
$291$		0			0
$292$	824.312	+	4674.90i	0.165203	+	0.936911i
$293$	−4350.54	+	3650.54i	−0.867445	+	0.727873i	−0.963558	−	0.267498i	$-0.913803\pi$
$293$	−4350.54	+	3650.54i	−0.867445	+	0.727873i	0.0961136	+	0.995370i	$0.469359\pi$
$294$		0			0
$295$	400.433	−	145.746i	0.0790309	−	0.0287649i
$296$	−1012.93			−0.198903
$297$		0			0
$298$	3018.94			0.586854
$299$	4415.18	−	1606.99i	0.853968	−	0.310819i
$300$		0			0
$301$	580.241	−	486.880i	0.111111	−	0.0932336i
$302$	−545.457	−	3093.44i	−0.103932	−	0.589428i
$303$		0			0
$304$	361.607	+	303.424i	0.0682223	+	0.0572453i
$305$	50.0682	−	86.7206i	0.00939966	−	0.0162807i
$306$		0			0
$307$	−2881.18	−	4990.36i	−0.535628	−	0.927735i	−0.999133	−	0.0416406i	$-0.986742\pi$
$307$	−2881.18	−	4990.36i	−0.535628	−	0.927735i	0.463505	−	0.886095i	$-0.346592\pi$
$308$	25.8766	−	146.753i	0.00478719	−	0.0271495i
$309$		0			0
$310$	149.885	+	54.5537i	0.0274610	+	0.00999498i
$311$	3837.77	+	1396.84i	0.699743	+	0.254686i	0.667301	−	0.744788i	$-0.267449\pi$
$311$	3837.77	+	1396.84i	0.699743	+	0.254686i	0.0324420	+	0.999474i	$0.489672\pi$
$312$		0			0
$313$	742.685	−	4211.98i	0.134118	−	0.760623i	−0.841351	−	0.540489i	$-0.818239\pi$
$313$	742.685	−	4211.98i	0.134118	−	0.760623i	0.975470	−	0.220134i	$-0.0706495\pi$
$314$	−1352.63	−	2342.83i	−0.243100	−	0.421062i
$315$		0			0
$316$	−425.816	+	737.534i	−0.0758038	+	0.131296i
$317$	−5951.52	−	4993.92i	−1.05448	−	0.884816i	−0.0609245	−	0.998142i	$-0.519405\pi$
$317$	−5951.52	−	4993.92i	−1.05448	−	0.884816i	−0.993558	+	0.113327i	$0.963849\pi$
$318$		0			0
$319$	−877.053	−	4974.01i	−0.153936	−	0.873013i
$320$	−35.9430	+	30.1598i	−0.00627899	+	0.00526870i
$321$		0			0
$322$	−477.313	+	173.728i	−0.0826075	+	0.0300667i
$323$	2057.49			0.354433
$324$		0			0
$325$	3563.02			0.608126
$326$	−5030.84	+	1831.08i	−0.854701	+	0.311086i
$327$		0			0
$328$	−619.918	+	520.173i	−0.104358	+	0.0875664i
$329$	78.4080	+	444.674i	0.0131391	+	0.0745157i
$330$		0			0
$331$	5920.82	+	4968.15i	0.983195	+	0.824998i	0.984568	−	0.175001i	$-0.0559928\pi$
$331$	5920.82	+	4968.15i	0.983195	+	0.824998i	−0.00137364	+	0.999999i	$0.500437\pi$
$332$	1077.76	−	1866.73i	0.178162	−	0.308585i
$333$		0			0
$334$	2846.02	+	4929.45i	0.466249	+	0.807567i
$335$	−111.407	+	631.819i	−0.0181696	+	0.103045i
$336$		0			0
$337$	−336.804	−	122.587i	−0.0544418	−	0.0198152i	0.314656	−	0.949206i	$-0.398111\pi$
$337$	−336.804	−	122.587i	−0.0544418	−	0.0198152i	−0.369097	+	0.929391i	$0.620333\pi$
$338$	2588.81	+	942.251i	0.416606	+	0.151632i
$339$		0			0
$340$	−35.5130	+	201.404i	−0.00566459	+	0.0321255i
$341$	−1309.49	−	2268.11i	−0.207956	−	0.360191i
$342$		0			0
$343$	528.908	−	916.096i	0.0832605	−	0.144211i
$344$	2999.81	+	2517.14i	0.470171	+	0.394521i
$345$		0			0
$346$	−1481.10	−	8399.72i	−0.230128	−	1.30512i
$347$	−4662.23	+	3912.07i	−0.721272	+	0.605219i	−0.927737	−	0.373235i	$-0.878249\pi$
$347$	−4662.23	+	3912.07i	−0.721272	+	0.605219i	0.206465	+	0.978454i	$0.433804\pi$
$348$		0			0
$349$	8660.80	−	3152.27i	1.32837	−	0.483488i	0.422241	−	0.906484i	$-0.361244\pi$
$349$	8660.80	−	3152.27i	1.32837	−	0.483488i	0.906132	+	0.422995i	$0.139021\pi$
$350$	−385.189			−0.0588263
$351$		0			0
$352$	770.410			0.116656
$353$	8601.41	−	3130.66i	1.29690	−	0.472034i	0.400916	−	0.916115i	$-0.368692\pi$
$353$	8601.41	−	3130.66i	1.29690	−	0.472034i	0.895987	+	0.444081i	$0.146470\pi$
$354$		0			0
$355$	−298.469	+	250.445i	−0.0446228	+	0.0374430i
$356$	240.989	+	1366.72i	0.0358776	+	0.203472i
$357$		0			0
$358$	2363.94	+	1983.58i	0.348989	+	0.292836i
$359$	2699.19	−	4675.13i	0.396818	−	0.687309i	−0.596514	−	0.802603i	$-0.703448\pi$
$359$	2699.19	−	4675.13i	0.396818	−	0.687309i	0.993331	+	0.115294i	$0.0367812\pi$
$360$		0			0
$361$	2994.29	+	5186.27i	0.436550	+	0.756126i
$362$	1146.46	−	6501.89i	0.166455	−	0.944011i
$363$		0			0
$364$	166.506	+	60.6034i	0.0239761	+	0.00872659i
$365$	817.575	+	297.573i	0.117243	+	0.0426731i
$366$		0			0
$367$	−83.3632	+	472.776i	−0.0118570	+	0.0672445i	−0.990162	−	0.139925i	$-0.955314\pi$
$367$	−83.3632	+	472.776i	−0.0118570	+	0.0672445i	0.978305	+	0.207169i	$0.0664251\pi$
$368$	−1313.02	−	2274.22i	−0.185995	−	0.322152i
$369$		0			0
$370$	−92.8258	+	160.779i	−0.0130427	+	0.0225905i
$371$	−620.696	−	520.826i	−0.0868597	−	0.0728839i
$372$		0			0
$373$	580.895	+	3294.42i	0.0806369	+	0.457315i	0.998213	+	0.0597548i	$0.0190319\pi$
$373$	580.895	+	3294.42i	0.0806369	+	0.457315i	−0.917576	+	0.397560i	$0.869857\pi$
$374$	2572.36	−	2158.46i	0.355651	−	0.298427i
$375$		0			0
$376$	−2193.62	+	798.412i	−0.300870	+	0.109508i
$377$	6005.70			0.820449
$378$		0			0
$379$	6504.31			0.881541			0.440770	−	0.897620i	$-0.354705\pi$
$379$	6504.31			0.881541			0.440770	+	0.897620i	$0.354705\pi$
$380$	81.2998	−	29.5907i	0.0109752	−	0.00399466i
$381$		0			0
$382$	1610.69	−	1351.53i	0.215733	−	0.181022i
$383$	484.154	+	2745.77i	0.0645930	+	0.366325i	0.999921	+	0.0125441i	$0.00399302\pi$
$383$	484.154	+	2745.77i	0.0645930	+	0.366325i	−0.935328	+	0.353781i	$0.884896\pi$
$384$		0			0
$385$	−20.9224	−	17.5560i	−0.00276962	−	0.00232399i
$386$	−1304.76	+	2259.92i	−0.172049	+	0.297997i
$387$		0			0
$388$	964.981	+	1671.40i	0.126262	+	0.218691i
$389$	2374.56	−	13466.8i	0.309498	−	1.75525i	−0.292039	−	0.956407i	$-0.594334\pi$
$389$	2374.56	−	13466.8i	0.309498	−	1.75525i	0.601537	−	0.798845i	$-0.294555\pi$
$390$		0			0
$391$	−10755.8	−	3914.80i	−1.39117	−	0.506343i
$392$	2560.52	+	931.952i	0.329912	+	0.120078i
$393$		0			0
$394$	849.750	−	4819.17i	0.108654	−	0.616209i
$395$	78.0445	+	135.177i	0.00994138	+	0.0172190i
$396$		0			0
$397$	−5323.27	+	9220.17i	−0.672965	+	1.16561i	0.304094	+	0.952642i	$0.401646\pi$
$397$	−5323.27	+	9220.17i	−0.672965	+	1.16561i	−0.977059	+	0.212968i	$0.931687\pi$
$398$	7095.96	+	5954.22i	0.893689	+	0.749894i
$399$		0			0
$400$	−345.803	−	1961.15i	−0.0432254	−	0.245143i
$401$	−7854.20	+	6590.46i	−0.978105	+	0.820728i	−0.983802	−	0.179256i	$-0.942631\pi$
$401$	−7854.20	+	6590.46i	−0.978105	+	0.820728i	0.00569738	+	0.999984i	$0.498186\pi$
$402$		0			0
$403$	2926.36	−	1065.11i	0.361718	−	0.131655i
$404$	−1457.77			−0.179522
$405$		0			0
$406$	−649.260			−0.0793651
$407$	2864.48	−	1042.58i	0.348862	−	0.126975i
$408$		0			0
$409$	−2748.25	+	2306.06i	−0.332255	+	0.278795i	−0.793618	−	0.608416i	$-0.791805\pi$
$409$	−2748.25	+	2306.06i	−0.332255	+	0.278795i	0.461363	+	0.887212i	$0.347361\pi$
$410$	25.7556	+	146.067i	0.00310239	+	0.0175945i
$411$		0			0
$412$	−3746.34	−	3143.55i	−0.447982	−	0.375902i
$413$	−449.716	+	778.931i	−0.0535813	+	0.0928055i
$414$		0			0
$415$	−197.534	−	342.140i	−0.0233653	−	0.0404698i
$416$	−159.074	+	902.156i	−0.0187482	+	0.106327i
$417$		0			0
$418$	−1334.90	−	485.865i	−0.156202	−	0.0568528i
$419$	7085.05	+	2578.75i	0.826079	+	0.300668i	0.720249	−	0.693716i	$-0.244028\pi$
$419$	7085.05	+	2578.75i	0.826079	+	0.300668i	0.105830	+	0.994384i	$0.466250\pi$
$420$		0			0
$421$	−64.4943	+	365.765i	−0.00746617	+	0.0423428i	−0.988313	−	0.152437i	$-0.951288\pi$
$421$	−64.4943	+	365.765i	−0.00746617	+	0.0423428i	0.980847	+	0.194779i	$0.0623991\pi$
$422$	−1236.12	−	2141.02i	−0.142591	−	0.246974i
$423$		0			0
$424$	2094.50	−	3627.78i	0.239901	−	0.415520i
$425$	−6649.18	−	5579.33i	−0.758901	−	0.636793i
$426$		0			0
$427$	36.7017	+	208.146i	0.00415953	+	0.0235899i
$428$	−2337.50	+	1961.39i	−0.263989	+	0.221513i
$429$		0			0
$430$	674.445	−	245.478i	0.0756387	−	0.0275302i
$431$	−15830.9			−1.76925			−0.884624	−	0.466306i	$-0.845585\pi$
$431$	−15830.9			−1.76925			−0.884624	+	0.466306i	$0.845585\pi$
$432$		0			0
$433$	−15832.0			−1.75714			−0.878568	−	0.477618i	$-0.841500\pi$
$433$	−15832.0			−1.75714			−0.878568	+	0.477618i	$0.841500\pi$
$434$	−316.361	+	115.146i	−0.0349903	+	0.0127354i
$435$		0			0
$436$	6397.25	−	5367.93i	0.702690	−	0.589627i
$437$	840.844	+	4768.66i	0.0920435	+	0.522005i
$438$		0			0
$439$	7191.57	+	6034.45i	0.781857	+	0.656056i	0.943715	−	0.330758i	$-0.107305\pi$
$439$	7191.57	+	6034.45i	0.781857	+	0.656056i	−0.161859	+	0.986814i	$0.551749\pi$
$440$	70.6013	−	122.285i	0.00764951	−	0.0132493i
$441$		0			0
$442$	1996.44	+	3457.93i	0.214844	+	0.372120i
$443$	−2408.55	+	13659.5i	−0.258315	+	1.46498i	0.529104	+	0.848557i	$0.322528\pi$
$443$	−2408.55	+	13659.5i	−0.258315	+	1.46498i	−0.787418	+	0.616419i	$0.788583\pi$
$444$		0			0
$445$	239.020	+	86.9962i	0.0254621	+	0.00926745i
$446$	7407.73	+	2696.19i	0.786471	+	0.286252i
$447$		0			0
$448$	17.1971	−	97.5296i	0.00181359	−	0.0102854i
$449$	813.413	+	1408.87i	0.0854952	+	0.148082i	0.905602	−	0.424128i	$-0.139419\pi$
$449$	813.413	+	1408.87i	0.0854952	+	0.148082i	−0.820107	+	0.572210i	$0.806086\pi$
$450$		0			0
$451$	1217.68	−	2109.08i	0.127136	−	0.220205i
$452$	4145.23	+	3478.26i	0.431361	+	0.361955i
$453$		0			0
$454$	−1425.76	−	8085.91i	−0.147389	−	0.835883i
$455$	24.8783	−	20.8753i	0.00256332	−	0.00215088i
$456$		0			0
$457$	7249.59	−	2638.63i	0.742060	−	0.270088i	0.0567993	−	0.998386i	$-0.481910\pi$
$457$	7249.59	−	2638.63i	0.742060	−	0.270088i	0.685261	+	0.728298i	$0.259688\pi$
$458$	−10019.0			−1.02218
$459$		0			0
$460$	−481.308			−0.0487850
$461$	4106.01	−	1494.47i	0.414828	−	0.150985i	−0.126170	−	0.992009i	$-0.540269\pi$
$461$	4106.01	−	1494.47i	0.414828	−	0.150985i	0.540999	+	0.841023i	$0.318046\pi$
$462$		0			0
$463$	−13494.6	+	11323.3i	−1.35453	+	1.13658i	−0.376896	+	0.926256i	$0.623009\pi$
$463$	−13494.6	+	11323.3i	−1.35453	+	1.13658i	−0.977631	+	0.210327i	$0.932547\pi$
$464$	−582.873	−	3305.64i	−0.0583172	−	0.330733i
$465$		0			0
$466$	−6818.92	−	5721.76i	−0.677855	−	0.568788i
$467$	−8580.50	+	14861.9i	−0.850232	+	1.47264i	0.0307675	+	0.999527i	$0.490205\pi$
$467$	−8580.50	+	14861.9i	−0.850232	+	1.47264i	−0.880999	+	0.473118i	$0.843128\pi$
$468$		0			0
$469$	−677.073	−	1172.72i	−0.0666617	−	0.115461i
$470$	−74.2962	+	421.355i	−0.00729155	+	0.0413524i
$471$		0			0
$472$	−4369.57	−	1590.39i	−0.426114	−	0.155093i
$473$	−11074.1	−	4030.63i	−1.07650	−	0.391815i
$474$		0			0
$475$	−637.634	+	3616.20i	−0.0615930	+	0.349311i
$476$	−215.829	−	373.827i	−0.0207826	−	0.0359965i
$477$		0			0
$478$	−4315.59	+	7474.82i	−0.412950	+	0.715251i
$479$	−4996.09	−	4192.22i	−0.476570	−	0.399890i	0.372614	−	0.927986i	$-0.378462\pi$
$479$	−4996.09	−	4192.22i	−0.476570	−	0.399890i	−0.849184	+	0.528096i	$0.822906\pi$
$480$		0			0
$481$	629.417	+	3569.60i	0.0596651	+	0.338378i
$482$	6973.86	−	5851.76i	0.659026	−	0.552989i
$483$		0			0
$484$	2824.26	−	1027.95i	0.265239	−	0.0965391i
$485$	353.728			0.0331175
$486$		0			0
$487$	−10552.3			−0.981868			−0.490934	−	0.871197i	$-0.663344\pi$
$487$	−10552.3			−0.981868			−0.490934	+	0.871197i	$0.663344\pi$
$488$	−1026.80	+	373.725i	−0.0952483	+	0.0346675i
$489$		0			0
$490$	382.575	−	321.019i	0.0352714	−	0.0295962i
$491$	3078.62	+	17459.7i	0.282965	+	1.60478i	0.712464	+	0.701708i	$0.247579\pi$
$491$	3078.62	+	17459.7i	0.282965	+	1.60478i	−0.429499	+	0.903067i	$0.641310\pi$
$492$		0			0
$493$	−11207.6	−	9404.31i	−1.02387	−	0.859125i
$494$	844.584	−	1462.86i	0.0769223	−	0.133233i
$495$		0			0
$496$	−870.266	−	1507.34i	−0.0787824	−	0.136455i
$497$	142.804	−	809.881i	0.0128886	−	0.0730948i
$498$		0			0
$499$	1748.04	+	636.234i	0.156819	+	0.0570776i	0.419237	−	0.907877i	$-0.362298\pi$
$499$	1748.04	+	636.234i	0.156819	+	0.0570776i	−0.262418	+	0.964954i	$0.584520\pi$
$500$	−687.436	−	250.206i	−0.0614861	−	0.0223791i
$501$		0			0
$502$	−889.068	+	5042.16i	−0.0790459	+	0.448292i
$503$	−3332.34	−	5771.79i	−0.295391	−	0.511633i	0.679684	−	0.733505i	$-0.262117\pi$
$503$	−3332.34	−	5771.79i	−0.295391	−	0.511633i	−0.975076	+	0.221872i	$0.928783\pi$
$504$		0			0
$505$	−133.592	+	231.388i	−0.0117718	+	0.0203894i
$506$	6053.94	+	5079.86i	0.531878	+	0.446299i
$507$		0			0
$508$	695.657	+	3945.27i	0.0607575	+	0.344573i
$509$	−3833.32	+	3216.53i	−0.333809	+	0.280099i	−0.794250	−	0.607591i	$-0.792136\pi$
$509$	−3833.32	+	3216.53i	−0.333809	+	0.280099i	0.460441	+	0.887690i	$0.347691\pi$
$510$		0			0
$511$	−1725.65	+	628.084i	−0.149390	+	0.0543734i
$512$	512.000			0.0441942
$513$		0			0
$514$	−1414.90			−0.121417
$515$	−842.286	+	306.567i	−0.0720690	+	0.0262310i
$516$		0			0
$517$	5381.59	−	4515.69i	0.457799	−	0.384139i
$518$	−68.0445	−	385.899i	−0.00577163	−	0.0327325i
$519$		0			0
$520$	128.619	+	107.924i	0.0108468	+	0.00910151i
$521$	−1193.72	+	2067.58i	−0.100380	+	0.173863i	−0.911841	−	0.410543i	$-0.865339\pi$
$521$	−1193.72	+	2067.58i	−0.100380	+	0.173863i	0.811461	+	0.584406i	$0.198672\pi$
$522$		0			0
$523$	9418.72	+	16313.7i	0.787479	+	1.36395i	0.927507	+	0.373807i	$0.121948\pi$
$523$	9418.72	+	16313.7i	0.787479	+	1.36395i	−0.140027	+	0.990148i	$0.544719\pi$
$524$	1343.41	−	7618.86i	0.111998	−	0.635175i
$525$		0			0
$526$	3416.46	+	1243.49i	0.283203	+	0.103077i
$527$	−7128.92	−	2594.71i	−0.589261	−	0.214473i
$528$		0			0
$529$	2564.95	−	14546.6i	0.210812	−	1.19558i
$530$	−383.885	−	664.908i	−0.0314621	−	0.0544939i
$531$		0			0
$532$	−91.3056	+	158.146i	−0.00744098	+	0.0128882i
$533$	2218.32	+	1861.39i	0.180274	+	0.151268i
$534$		0			0
$535$	97.1154	+	550.769i	0.00784797	+	0.0445081i
$536$	5362.96	−	4500.06i	0.432173	−	0.362636i
$537$		0			0
$538$	−5082.59	+	1849.91i	−0.407297	+	0.148244i
$539$	−8200.18			−0.655300
$540$		0			0
$541$	−17185.2			−1.36571			−0.682854	−	0.730555i	$-0.739262\pi$
$541$	−17185.2			−1.36571			−0.682854	+	0.730555i	$0.739262\pi$
$542$	−6403.53	+	2330.69i	−0.507482	+	0.184708i
$543$		0			0
$544$	1709.54	−	1434.48i	0.134735	−	0.113056i
$545$	−265.785	−	1507.34i	−0.0208899	−	0.118472i
$546$		0			0
$547$	9869.20	+	8281.24i	0.771438	+	0.647313i	0.941077	−	0.338193i	$-0.109816\pi$
$547$	9869.20	+	8281.24i	0.771438	+	0.647313i	−0.169639	+	0.985506i	$0.554260\pi$
$548$	−444.335	+	769.611i	−0.0346370	+	0.0599930i
$549$		0			0
$550$	2996.47	+	5190.04i	0.232309	+	0.402371i
$551$	−1074.77	+	6095.34i	−0.0830977	+	0.471271i
$552$		0			0
$553$	−309.587	−	112.680i	−0.0238064	−	0.00866484i
$554$	−3234.89	−	1177.40i	−0.248082	−	0.0902943i
$555$		0			0
$556$	672.319	−	3812.91i	0.0512818	−	0.290834i
$557$	3360.10	+	5819.87i	0.255605	+	0.442721i	0.965060	−	0.262030i	$-0.0843919\pi$
$557$	3360.10	+	5819.87i	0.255605	+	0.442721i	−0.709455	+	0.704751i	$0.751059\pi$
$558$		0			0
$559$	7006.48	−	12135.6i	0.530130	−	0.918212i
$560$	−13.9046	−	11.6674i	−0.00104925	−	0.000880423i
$561$		0			0
$562$	64.8096	+	367.553i	0.00486446	+	0.0275877i
$563$	11598.0	−	9731.85i	0.868199	−	0.728505i	−0.0955194	−	0.995428i	$-0.530451\pi$
$563$	11598.0	−	9731.85i	0.868199	−	0.728505i	0.963718	+	0.266922i	$0.0860067\pi$
$564$		0			0
$565$	931.969	−	339.209i	0.0693951	−	0.0252577i
$566$	4733.82			0.351550
$567$		0			0
$568$	4251.62			0.314074
$569$	11394.8	−	4147.37i	0.839534	−	0.305565i	0.113768	−	0.993507i	$-0.463708\pi$
$569$	11394.8	−	4147.37i	0.839534	−	0.305565i	0.725766	+	0.687942i	$0.241486\pi$
$570$		0			0
$571$	1326.70	−	1113.23i	0.0972341	−	0.0815891i	−0.592875	−	0.805295i	$-0.702007\pi$
$571$	1326.70	−	1113.23i	0.0972341	−	0.0815891i	0.690109	+	0.723706i	$0.257563\pi$
$572$	−478.721	−	2714.96i	−0.0349936	−	0.198458i
$573$		0			0
$574$	−239.817	−	201.230i	−0.0174386	−	0.0146327i
$575$	10213.9	−	17691.0i	0.740780	−	1.28307i
$576$		0			0
$577$	−887.429	−	1537.07i	−0.0640280	−	0.110900i	0.832234	−	0.554424i	$-0.187061\pi$
$577$	−887.429	−	1537.07i	−0.0640280	−	0.110900i	−0.896262	+	0.443524i	$0.853728\pi$
$578$	−17.1812	+	97.4395i	−0.00123641	+	0.00701202i
$579$		0			0
$580$	−578.110	−	210.415i	−0.0413874	−	0.0150638i
$581$	783.579	+	285.199i	0.0559524	+	0.0203650i
$582$		0			0
$583$	−2189.08	+	12414.9i	−0.155510	+	0.881943i
$584$	−4747.02	−	8222.08i	−0.336358	−	0.582589i
$585$		0			0
$586$	5679.23	−	9836.71i	0.400353	−	0.693431i
$587$	1355.86	+	1137.70i	0.0953359	+	0.0799963i	0.689210	−	0.724562i	$-0.257958\pi$
$587$	1355.86	+	1137.70i	0.0953359	+	0.0799963i	−0.593874	+	0.804558i	$0.702402\pi$
$588$		0			0
$589$	557.307	+	3160.65i	0.0389872	+	0.221107i
$590$	−652.872	+	547.825i	−0.0455565	+	0.0382264i
$591$		0			0
$592$	1903.68	−	692.882i	0.132163	−	0.0481035i
$593$	23108.7			1.60027			0.800137	−	0.599818i	$-0.204760\pi$
$593$	23108.7			1.60027			0.800137	+	0.599818i	$0.204760\pi$
$594$		0			0
$595$	−79.1155			−0.00545112
$596$	−5673.75	+	2065.08i	−0.389943	+	0.141928i
$597$		0			0
$598$	−7198.58	+	6040.32i	−0.492260	+	0.413055i
$599$	−3108.53	−	17629.3i	−0.212038	−	1.20253i	−0.885973	−	0.463738i	$-0.846508\pi$
$599$	−3108.53	−	17629.3i	−0.212038	−	1.20253i	0.673934	−	0.738791i	$-0.264603\pi$
$600$		0			0
$601$	−5028.11	−	4219.09i	−0.341266	−	0.286356i	0.456005	−	0.889977i	$-0.349280\pi$
$601$	−5028.11	−	4219.09i	−0.341266	−	0.286356i	−0.797272	+	0.603621i	$0.793724\pi$
$602$	−757.451	+	1311.94i	−0.0512814	+	0.0888220i
$603$		0			0
$604$	3141.16	+	5440.65i	0.211609	+	0.366518i
$605$	95.6557	−	542.490i	0.00642803	−	0.0364551i
$606$		0			0
$607$	12464.6	+	4536.76i	0.833483	+	0.303363i	0.723288	−	0.690547i	$-0.242630\pi$
$607$	12464.6	+	4536.76i	0.833483	+	0.303363i	0.110195	+	0.993910i	$0.464852\pi$
$608$	−887.153	−	322.897i	−0.0591756	−	0.0215382i
$609$		0			0
$610$	−34.7770	+	197.230i	−0.00230833	+	0.0130912i
$611$	4176.72	+	7234.29i	0.276550	+	0.478999i
$612$		0			0
$613$	10092.8	−	17481.3i	0.665001	−	1.15182i	−0.314284	−	0.949329i	$-0.601765\pi$
$613$	10092.8	−	17481.3i	0.665001	−	1.15182i	0.979285	−	0.202486i	$-0.0649021\pi$
$614$	8828.46	+	7407.96i	0.580273	+	0.486907i
$615$		0			0
$616$	51.7532	+	293.507i	0.00338505	+	0.0191976i
$617$	7820.48	−	6562.17i	0.510277	−	0.428173i	−0.350950	−	0.936394i	$-0.614141\pi$
$617$	7820.48	−	6562.17i	0.510277	−	0.428173i	0.861227	+	0.508221i	$0.169697\pi$
$618$		0			0
$619$	15688.1	−	5710.00i	1.01867	−	0.370767i	0.221915	−	0.975066i	$-0.428769\pi$
$619$	15688.1	−	5710.00i	1.01867	−	0.370767i	0.796757	+	0.604299i	$0.206547\pi$
$620$	−319.009			−0.0206640
$621$		0			0
$622$	−8168.15			−0.526548
$623$	−504.497	+	183.622i	−0.0324434	+	0.0118084i
$624$		0			0
$625$	11815.3	−	9914.19i	0.756177	−	0.634508i
$626$	1485.37	+	8423.95i	0.0948360	+	0.537842i
$627$		0			0
$628$	4144.70	+	3477.82i	0.263363	+	0.220987i
$629$	4415.03	−	7647.05i	0.279871	−	0.484750i
$630$		0			0
$631$	3922.35	+	6793.72i	0.247459	+	0.428611i	0.962820	−	0.270144i	$-0.0870712\pi$
$631$	3922.35	+	6793.72i	0.247459	+	0.428611i	−0.715361	+	0.698755i	$0.753738\pi$
$632$	295.768	−	1677.39i	0.0186156	−	0.105574i
$633$		0			0
$634$	14601.2	+	5314.42i	0.914652	+	0.332906i
$635$	689.973	+	251.129i	0.0431193	+	0.0156941i
$636$		0			0
$637$	1693.18	−	9602.48i	0.105316	−	0.597275i
$638$	5050.74	+	8748.15i	0.313418	+	0.542856i
$639$		0			0
$640$	46.9203	−	81.2684i	0.00289795	−	0.00501940i
$641$	−13949.6	−	11705.1i	−0.859560	−	0.721256i	0.102313	−	0.994752i	$-0.467376\pi$
$641$	−13949.6	−	11705.1i	−0.859560	−	0.721256i	−0.961873	+	0.273496i	$0.911820\pi$
$642$		0			0
$643$	1619.12	+	9182.50i	0.0993032	+	0.563177i	0.993343	+	0.115190i	$0.0367477\pi$
$643$	1619.12	+	9182.50i	0.0993032	+	0.563177i	−0.894040	+	0.447987i	$0.852141\pi$
$644$	778.218	−	653.003i	0.0476182	−	0.0399564i
$645$		0			0
$646$	−3866.82	+	1407.41i	−0.235508	+	0.0857178i
$647$	657.535			0.0399542			0.0199771	−	0.999800i	$-0.493641\pi$
$647$	657.535			0.0399542			0.0199771	+	0.999800i	$0.493641\pi$
$648$		0			0
$649$	13993.8			0.846385
$650$	−6696.29	+	2437.25i	−0.404077	+	0.147072i
$651$		0			0
$652$	8202.36	−	6882.60i	0.492683	−	0.413410i
$653$	−383.096	−	2172.65i	−0.0229582	−	0.130203i	0.971175	−	0.238370i	$-0.0766130\pi$
$653$	−383.096	−	2172.65i	−0.0229582	−	0.130203i	−0.994133	+	0.108167i	$0.965502\pi$
$654$		0			0
$655$	−1086.21	−	911.438i	−0.0647965	−	0.0543707i
$656$	809.246	−	1401.66i	0.0481642	−	0.0834229i
$657$		0			0
$658$	−451.534	−	782.079i	−0.0267517	−	0.0463353i
$659$	−3376.22	+	19147.5i	−0.199573	+	1.13184i	0.706180	+	0.708032i	$0.250417\pi$
$659$	−3376.22	+	19147.5i	−0.199573	+	1.13184i	−0.905754	+	0.423805i	$0.860694\pi$
$660$		0			0
$661$	−413.572	−	150.528i	−0.0243360	−	0.00885757i	0.329823	−	0.944043i	$-0.393011\pi$
$661$	−413.572	−	150.528i	−0.0243360	−	0.00885757i	−0.354159	+	0.935185i	$0.615233\pi$
$662$	−14525.9	−	5287.00i	−0.852818	−	0.310400i
$663$		0			0
$664$	−748.604	+	4245.54i	−0.0437522	+	0.248131i
$665$	16.7347	+	28.9854i	0.000975856	+	0.00169023i
$666$		0			0
$667$	17216.2	−	29819.3i	0.999419	−	1.73104i
$668$	−8720.70	−	7317.54i	−0.505111	−	0.423838i
$669$		0			0
$670$	−222.814	−	1263.64i	−0.0128478	−	0.0728636i
$671$	2519.05	−	2113.73i	0.144928	−	0.121609i
$672$		0			0
$673$	−22211.4	+	8084.29i	−1.27219	+	0.463041i	−0.887843	−	0.460146i	$-0.847797\pi$
$673$	−22211.4	+	8084.29i	−1.27219	+	0.463041i	−0.384351	+	0.923187i	$0.625575\pi$
$674$	716.838			0.0409667
$675$		0			0
$676$	−5509.91			−0.313491
$677$	4570.60	−	1663.56i	0.259472	−	0.0944400i	−0.209009	−	0.977914i	$-0.567024\pi$
$677$	4570.60	−	1663.56i	0.259472	−	0.0944400i	0.468481	+	0.883474i	$0.344802\pi$
$678$		0			0
$679$	−571.936	+	479.911i	−0.0323253	+	0.0271242i
$680$	−71.0259	−	402.808i	−0.00400547	−	0.0227161i
$681$		0			0
$682$	4012.52	+	3366.91i	0.225290	+	0.189040i
$683$	1470.06	−	2546.21i	0.0823575	−	0.142647i	−0.821905	−	0.569625i	$-0.807088\pi$
$683$	1470.06	−	2546.21i	0.0823575	−	0.142647i	0.904262	+	0.426978i	$0.140422\pi$
$684$		0			0
$685$	81.4389	+	141.056i	0.00454251	+	0.00786786i
$686$	−367.376	+	2083.49i	−0.0204468	+	0.115959i
$687$		0			0
$688$	−7359.62	−	2678.68i	−0.407824	−	0.148436i
$689$	−14086.0	−	5126.87i	−0.778857	−	0.283481i
$690$		0			0
$691$	−5409.49	+	30678.7i	−0.297810	+	1.68896i	0.357748	+	0.933818i	$0.383545\pi$
$691$	−5409.49	+	30678.7i	−0.297810	+	1.68896i	−0.655558	+	0.755145i	$0.727567\pi$
$692$	8529.30	+	14773.2i	0.468548	+	0.811549i
$693$		0			0
$694$	6086.11	−	10541.4i	0.332890	−	0.576582i
$695$	−543.601	−	456.135i	−0.0296690	−	0.0248953i
$696$		0			0
$697$	−1225.00	−	6947.33i	−0.0665713	−	0.377545i
$698$	−14120.7	+	11848.7i	−0.765725	+	0.642520i
$699$		0			0
$700$	723.918	−	263.485i	0.0390879	−	0.0142268i
$701$	28257.6			1.52250			0.761252	−	0.648456i	$-0.224585\pi$
$701$	28257.6			1.52250			0.761252	+	0.648456i	$0.224585\pi$
$702$		0			0
$703$	−3735.51			−0.200409
$704$	−1447.90	+	526.991i	−0.0775137	+	0.0282127i
$705$		0			0
$706$	−14023.9	+	11767.4i	−0.747585	+	0.627298i
$707$	−97.9276	−	555.375i	−0.00520926	−	0.0295432i
$708$		0			0
$709$	−14734.3	−	12363.6i	−0.780479	−	0.654899i	0.162891	−	0.986644i	$-0.447918\pi$
$709$	−14734.3	−	12363.6i	−0.780479	−	0.654899i	−0.943369	+	0.331745i	$0.892363\pi$
$710$	389.624	−	674.849i	0.0205948	−	0.0356713i
$711$		0			0
$712$	−1387.80	−	2403.74i	−0.0730479	−	0.126523i
$713$	3100.38	−	17583.1i	0.162847	−	0.923553i
$714$		0			0
$715$	−474.809	−	172.816i	−0.0248347	−	0.00903910i
$716$	−5799.60	−	2110.88i	−0.302711	−	0.110178i
$717$		0			0
$718$	−1874.83	+	10632.7i	−0.0974488	+	0.552659i
$719$	−3841.21	−	6653.16i	−0.199239	−	0.345092i	0.749043	−	0.662521i	$-0.230514\pi$
$719$	−3841.21	−	6653.16i	−0.199239	−	0.345092i	−0.948282	+	0.317429i	$0.897180\pi$
$720$		0			0
$721$	945.949	−	1638.43i	0.0488613	−	0.0846302i
$722$	−9175.05	−	7698.78i	−0.472936	−	0.396841i
$723$		0			0
$724$	2292.92	+	13003.8i	0.117701	+	0.667516i
$725$	20002.1	−	16783.8i	1.02464	−	0.859771i
$726$		0			0
$727$	−33936.8	+	12352.0i	−1.73129	+	0.630137i	−0.998721	−	0.0505574i	$-0.983900\pi$
$727$	−33936.8	+	12352.0i	−1.73129	+	0.630137i	−0.732567	+	0.680695i	$0.761678\pi$
$728$	−354.385			−0.0180417
$729$		0			0
$730$	−1740.09			−0.0882242
$731$	−32078.3	+	11675.5i	−1.62306	+	0.590746i
$732$		0			0
$733$	−3422.22	+	2871.58i	−0.172446	+	0.144699i	−0.724926	−	0.688827i	$-0.758126\pi$
$733$	−3422.22	+	2871.58i	−0.172446	+	0.144699i	0.552480	+	0.833526i	$0.313682\pi$
$734$	−166.726	−	945.553i	−0.00838418	−	0.0475490i
$735$		0			0
$736$	4023.34	+	3375.98i	0.201498	+	0.169077i
$737$	−10534.2	+	18245.8i	−0.526503	+	0.911930i
$738$		0			0
$739$	4318.02	+	7479.04i	0.214941	+	0.372288i	0.953254	−	0.302170i	$-0.0977109\pi$
$739$	4318.02	+	7479.04i	0.214941	+	0.372288i	−0.738314	+	0.674458i	$0.764378\pi$
$740$	64.4761	−	365.662i	0.00320296	−	0.0181649i
$741$		0			0
$742$	1522.79	+	554.251i	0.0753417	+	0.0274221i
$743$	3771.96	+	1372.88i	0.186245	+	0.0677876i	0.433459	−	0.901173i	$-0.357293\pi$
$743$	3771.96	+	1372.88i	0.186245	+	0.0677876i	−0.247214	+	0.968961i	$0.579515\pi$
$744$		0			0
$745$	−192.166	+	1089.83i	−0.00945021	+	0.0535948i
$746$	−3345.24	−	5794.12i	−0.164179	−	0.284367i
$747$		0			0
$748$	−3357.97	+	5816.18i	−0.164144	+	0.284306i
$749$	−904.265	−	758.769i	−0.0441137	−	0.0370158i
$750$		0			0
$751$	−3272.96	−	18561.9i	−0.159030	−	0.901906i	−0.955008	−	0.296580i	$-0.904154\pi$
$751$	−3272.96	−	18561.9i	−0.159030	−	0.901906i	0.795978	−	0.605326i	$-0.206957\pi$
$752$	3576.51	−	3001.05i	0.173433	−	0.145528i
$753$		0			0
$754$	−11287.0	+	4108.14i	−0.545158	+	0.198421i
$755$	1151.44			0.0555035
$756$		0			0
$757$	−40760.5			−1.95702			−0.978511	−	0.206195i	$-0.933892\pi$
$757$	−40760.5			−1.95702			−0.978511	+	0.206195i	$0.933892\pi$
$758$	−12224.1	+	4449.21i	−0.585751	+	0.213196i
$759$		0			0
$760$	−132.552	+	111.225i	−0.00632655	+	0.00530861i
$761$	907.661	+	5147.60i	0.0432361	+	0.245204i	0.998764	−	0.0496952i	$-0.0158250\pi$
$761$	907.661	+	5147.60i	0.0432361	+	0.245204i	−0.955528	+	0.294899i	$0.904714\pi$
$762$		0			0
$763$	2474.79	+	2076.59i	0.117423	+	0.0985292i
$764$	−2102.61	+	3641.83i	−0.0995677	+	0.172456i
$765$		0			0
$766$	−2788.13	−	4829.19i	−0.131513	−	0.227788i
$767$	−2889.44	+	16386.8i	−0.136026	+	0.771440i
$768$		0			0
$769$	26469.7	+	9634.18i	1.24125	+	0.451778i	0.877436	−	0.479693i	$-0.159252\pi$
$769$	26469.7	+	9634.18i	1.24125	+	0.451778i	0.363814	+	0.931472i	$0.381474\pi$
$770$	51.3302	+	18.6827i	0.00240235	+	0.000874386i
$771$		0			0
$772$	906.279	−	5139.77i	0.0422509	−	0.239617i
$773$	4978.93	+	8623.75i	0.231668	+	0.401261i	0.958299	−	0.285767i	$-0.0922483\pi$
$773$	4978.93	+	8623.75i	0.231668	+	0.401261i	−0.726631	+	0.687028i	$0.758915\pi$
$774$		0			0
$775$	6769.72	−	11725.5i	0.313775	−	0.543474i
$776$	−2956.87	−	2481.11i	−0.136786	−	0.114777i
$777$		0			0
$778$	4749.11	+	26933.6i	0.218848	+	1.24115i
$779$	−2286.16	+	1918.32i	−0.105148	+	0.0882296i
$780$		0			0
$781$	−12023.3	+	4376.11i	−0.550866	+	0.200499i
$782$	22892.2			1.04683
$783$		0			0
$784$	−5449.69			−0.248255
$785$	931.850	−	339.166i	0.0423684	−	0.0154208i
$786$		0			0
$787$	4270.10	−	3583.04i	0.193409	−	0.162289i	−0.540941	−	0.841061i	$-0.681932\pi$
$787$	4270.10	−	3583.04i	0.193409	−	0.162289i	0.734350	+	0.678771i	$0.237487\pi$
$788$	1699.50	+	9638.34i	0.0768301	+	0.435725i
$789$		0			0
$790$	−239.142	−	200.664i	−0.0107700	−	0.00903710i
$791$	−1046.67	+	1812.88i	−0.0470484	+	0.0814902i
$792$		0			0
$793$	1955.06	+	3386.27i	0.0875490	+	0.151639i
$794$	3697.50	−	20969.6i	0.165264	−	0.937258i
$795$		0			0
$796$	−17409.0	−	6336.35i	−0.775181	−	0.282143i
$797$	−11821.7	−	4302.75i	−0.525403	−	0.191231i	0.0656815	−	0.997841i	$-0.479078\pi$
$797$	−11821.7	−	4302.75i	−0.525403	−	0.191231i	−0.591085	+	0.806610i	$0.701300\pi$
$798$		0			0
$799$	3533.71	−	20040.7i	0.156463	−	0.887345i
$800$	1991.40	+	3449.21i	0.0880083	+	0.152435i
$801$		0			0
$802$	10252.9	−	17758.6i	0.451426	−	0.781893i
$803$	21887.0	+	18365.4i	0.961864	+	0.807099i
$804$		0			0
$805$	−32.3324	−	183.366i	−0.00141561	−	0.00802834i
$806$	−4771.18	+	4003.50i	−0.208508	+	0.174959i
$807$		0			0
$808$	2739.72	−	997.175i	0.119286	−	0.0434165i
$809$	−17237.7			−0.749129			−0.374564	−	0.927201i	$-0.622208\pi$
$809$	−17237.7			−0.749129			−0.374564	+	0.927201i	$0.622208\pi$
$810$		0			0
$811$	22420.5			0.970763			0.485382	−	0.874302i	$-0.338681\pi$
$811$	22420.5			0.970763			0.485382	+	0.874302i	$0.338681\pi$
$812$	1220.21	−	444.120i	0.0527352	−	0.0191940i
$813$		0			0
$814$	−4670.29	+	3918.84i	−0.201098	+	0.168741i
$815$	−340.782	−	1932.67i	−0.0146467	−	0.0830655i
$816$		0			0
$817$	11062.8	+	9282.82i	0.473733	+	0.397509i
$818$	3587.59	−	6213.89i	0.153346	−	0.265603i
$819$		0			0
$820$	−148.321	−	256.899i	−0.00631656	−	0.0109406i
$821$	−6480.94	+	36755.2i	−0.275501	+	1.56244i	0.461865	+	0.886950i	$0.347181\pi$
$821$	−6480.94	+	36755.2i	−0.275501	+	1.56244i	−0.737366	+	0.675494i	$0.763931\pi$
$822$		0			0
$823$	−40979.0	−	14915.1i	−1.73565	−	0.631724i	−0.736640	−	0.676285i	$-0.763589\pi$
$823$	−40979.0	−	14915.1i	−1.73565	−	0.631724i	−0.999007	+	0.0445610i	$0.985811\pi$
$824$	9191.12	+	3345.29i	0.388578	+	0.141431i
$825$		0			0
$826$	312.369	−	1771.53i	0.0131583	−	0.0746242i
$827$	8190.08	+	14185.6i	0.344374	+	0.596473i	0.985240	−	0.171180i	$-0.0547579\pi$
$827$	8190.08	+	14185.6i	0.344374	+	0.596473i	−0.640866	+	0.767653i	$0.721425\pi$
$828$		0			0
$829$	−1459.28	+	2527.55i	−0.0611375	+	0.105893i	−0.894974	−	0.446118i	$-0.852806\pi$
$829$	−1459.28	+	2527.55i	−0.0611375	+	0.105893i	0.833837	+	0.552011i	$0.186139\pi$
$830$	605.281	+	507.891i	0.0253128	+	0.0212399i
$831$		0			0
$832$	−318.149	−	1804.31i	−0.0132570	−	0.0751842i
$833$	−18196.2	+	15268.4i	−0.756857	+	0.635079i
$834$		0			0
$835$	−1960.67	+	713.625i	−0.0812596	+	0.0295761i
$836$	2841.15			0.117540
$837$		0			0
$838$	−15079.5			−0.621614
$839$	5190.18	−	1889.07i	0.213570	−	0.0777330i	−0.233020	−	0.972472i	$-0.574861\pi$
$839$	5190.18	−	1889.07i	0.213570	−	0.0777330i	0.446589	+	0.894739i	$0.352638\pi$
$840$		0			0
$841$	15031.8	−	12613.2i	0.616335	−	0.517167i
$842$	−128.989	−	731.531i	−0.00527938	−	0.0299409i
$843$		0			0
$844$	3787.68	+	3178.24i	0.154476	+	0.129620i
$845$	−504.935	+	874.574i	−0.0205566	+	0.0356050i
$846$		0			0
$847$	581.346	+	1006.92i	0.0235836	+	0.0408479i
$848$	−1454.82	+	8250.72i	−0.0589138	+	0.334117i
$849$		0			0
$850$	16312.9	+	5937.40i	0.658267	+	0.239589i
$851$	19527.9	+	7107.58i	0.786614	+	0.286304i
$852$		0			0
$853$	3389.52	−	19223.0i	0.136055	−	0.771608i	−0.838064	−	0.545572i	$-0.816312\pi$
$853$	3389.52	−	19223.0i	0.136055	−	0.771608i	0.974119	−	0.226035i	$-0.0725765\pi$
$854$	−211.357	−	366.080i	−0.00846894	−	0.0146686i
$855$		0			0
$856$	3051.39	−	5285.15i	0.121839	−	0.211031i
$857$	3314.13	+	2780.89i	0.132099	+	0.110844i	0.706443	−	0.707770i	$-0.250299\pi$
$857$	3314.13	+	2780.89i	0.132099	+	0.110844i	−0.574345	+	0.818614i	$0.694743\pi$
$858$		0			0
$859$	2186.38	+	12399.6i	0.0868433	+	0.492513i	0.996944	+	0.0781247i	$0.0248932\pi$
$859$	2186.38	+	12399.6i	0.0868433	+	0.492513i	−0.910100	+	0.414388i	$0.863996\pi$
$860$	−1099.63	+	922.695i	−0.0436010	+	0.0365856i
$861$		0			0
$862$	29752.3	−	10828.9i	1.17560	−	0.427883i
$863$	−47955.5			−1.89157			−0.945785	−	0.324794i	$-0.894705\pi$
$863$	−47955.5			−1.89157			−0.945785	+	0.324794i	$0.894705\pi$
$864$		0			0
$865$	3126.54			0.122897
$866$	29754.5	−	10829.8i	1.16755	−	0.424954i
$867$		0			0
$868$	515.799	−	432.807i	0.0201698	−	0.0169245i
$869$	890.089	+	5047.95i	0.0347459	+	0.197054i
$870$		0			0
$871$	−19190.9	−	16103.1i	−0.746565	−	0.626442i
$872$	−8351.02	+	14464.4i	−0.324313	+	0.561727i
$873$		0			0
$874$	−4842.23	−	8386.98i	−0.187404	−	0.324593i
$875$	49.1430	−	278.704i	0.00189867	−	0.0107679i
$876$		0			0
$877$	16259.6	+	5918.02i	0.626053	+	0.227865i	0.635513	−	0.772091i	$-0.280789\pi$
$877$	16259.6	+	5918.02i	0.626053	+	0.227865i	−0.00945936	+	0.999955i	$0.503011\pi$
$878$	−17643.5	−	6421.72i	−0.678178	−	0.246837i
$879$		0			0
$880$	−49.0391	+	278.115i	−0.00187853	+	0.0106537i
$881$	−13900.2	−	24075.9i	−0.531567	−	0.920701i	−0.999321	−	0.0368423i	$-0.988270\pi$
$881$	−13900.2	−	24075.9i	−0.531567	−	0.920701i	0.467754	−	0.883859i	$-0.345063\pi$
$882$		0			0
$883$	−13801.9	+	23905.6i	−0.526014	+	0.911083i	0.473527	+	0.880779i	$0.342981\pi$
$883$	−13801.9	+	23905.6i	−0.526014	+	0.911083i	−0.999541	+	0.0303037i	$0.990353\pi$
$884$	−6117.44	−	5133.14i	−0.232751	−	0.195301i
$885$		0			0
$886$	−4817.09	−	27319.1i	−0.182656	−	1.03589i
$887$	26155.1	−	21946.7i	0.990080	−	0.830776i	0.00450057	−	0.999990i	$-0.498567\pi$
$887$	26155.1	−	21946.7i	0.990080	−	0.830776i	0.985579	+	0.169214i	$0.0541230\pi$
$888$		0			0
$889$	−1456.32	+	530.056i	−0.0549418	+	0.0199972i
$890$	−508.720			−0.0191599
$891$		0			0
$892$	−15766.3			−0.591810
$893$	−8089.72	+	2944.42i	−0.303149	+	0.110337i
$894$		0			0
$895$	−866.537	+	727.111i	−0.0323633	+	0.0271560i
$896$	34.3942	+	195.059i	0.00128240	+	0.00727284i
$897$		0			0
$898$	−2492.44	−	2091.41i	−0.0926213	−	0.0777185i
$899$	11410.8	−	19764.1i	0.423327	−	0.733224i
$900$		0			0
$901$	18258.5	+	31624.7i	0.675117	+	1.16934i
$902$	−845.790	+	4796.71i	−0.0312214	+	0.177065i
$903$		0			0
$904$	−10169.8	−	3701.49i	−0.374160	−	0.136183i
$905$	2274.18	+	827.734i	0.0835319	+	0.0304031i
$906$		0			0
$907$	−1190.68	+	6752.68i	−0.0435897	+	0.247209i	−0.998815	−	0.0486702i	$-0.984502\pi$
$907$	−1190.68	+	6752.68i	−0.0435897	+	0.247209i	0.955225	+	0.295880i	$0.0956128\pi$
$908$	8210.65	+	14221.3i	0.300088	+	0.519768i
$909$		0			0
$910$	−32.4763	+	56.2505i	−0.00118305	+	0.00204911i
$911$	7563.92	+	6346.88i	0.275086	+	0.230825i	0.769885	−	0.638183i	$-0.220314\pi$
$911$	7563.92	+	6346.88i	0.275086	+	0.230825i	−0.494798	+	0.869008i	$0.664758\pi$
$912$		0			0
$913$	−2252.86	−	12776.6i	−0.0816635	−	0.463136i
$914$	−11819.8	+	9918.02i	−0.427752	+	0.358927i
$915$		0			0
$916$	18829.6	−	6853.43i	0.679202	−	0.247209i
$917$	2992.84			0.107778
$918$		0			0
$919$	−4520.13			−0.162247			−0.0811237	−	0.996704i	$-0.525851\pi$
$919$	−4520.13			−0.162247			−0.0811237	+	0.996704i	$0.525851\pi$
$920$	904.564	−	329.234i	0.0324159	−	0.0117984i
$921$		0			0
$922$	−6694.50	+	5617.35i	−0.239123	+	0.200648i
$923$	−2641.89	−	14982.9i	−0.0942134	−	0.534311i
$924$		0			0
$925$	12072.0	+	10129.6i	0.429109	+	0.360065i
$926$	17615.9	−	30511.7i	0.625156	−	1.08280i
$927$		0			0
$928$	3356.63	+	5813.86i	0.118736	+	0.205656i
$929$	4600.64	−	26091.5i	0.162478	−	0.921458i	−0.789149	−	0.614202i	$-0.789478\pi$
$929$	4600.64	−	26091.5i	0.162478	−	0.921458i	0.951627	−	0.307256i	$-0.0994109\pi$
$930$		0			0
$931$	9442.79	+	3436.89i	0.332411	+	0.120988i
$932$	16729.3	+	6088.97i	0.587968	+	0.214003i
$933$		0			0
$934$	5959.95	−	33800.6i	0.208796	−	1.18414i
$935$	615.458	+	1066.00i	0.0215269	+	0.0372856i
$936$		0			0
$937$	−20545.5	+	35585.8i	−0.716320	+	1.24070i	0.246129	+	0.969237i	$0.420841\pi$
$937$	−20545.5	+	35585.8i	−0.716320	+	1.24070i	−0.962448	+	0.271465i	$0.912492\pi$
$938$	2074.67	+	1740.86i	0.0722179	+	0.0605981i
$939$		0			0
$940$	−148.592	−	842.709i	−0.00515590	−	0.0292406i
$941$	−10086.2	+	8463.31i	−0.349416	+	0.293195i	−0.800555	−	0.599259i	$-0.795462\pi$
$941$	−10086.2	+	8463.31i	−0.349416	+	0.293195i	0.451140	+	0.892453i	$0.351018\pi$
$942$		0			0
$943$	15601.2	−	5678.38i	0.538755	−	0.196091i
$944$	9300.01			0.320646
$945$		0			0
$946$	23569.6			0.810056
$947$	16313.0	−	5937.44i	0.559768	−	0.203739i	−0.0466129	−	0.998913i	$-0.514843\pi$
$947$	16313.0	−	5937.44i	0.559768	−	0.203739i	0.606381	+	0.795174i	$0.292620\pi$
$948$		0			0
$949$	−26025.3	+	21837.8i	−0.890217	+	0.746981i
$950$	−1275.27	−	7232.40i	−0.0435528	−	0.247000i
$951$		0			0
$952$	661.340	+	554.930i	0.0225149	+	0.0188922i
$953$	−15169.6	+	26274.6i	−0.515628	+	0.893093i	0.484208	+	0.874953i	$0.339108\pi$
$953$	−15169.6	+	26274.6i	−0.515628	+	0.893093i	−0.999835	+	0.0181401i	$0.994226\pi$
$954$		0			0
$955$	385.371	+	667.483i	0.0130579	+	0.0226170i
$956$	2997.57	−	17000.1i	0.101411	−	0.575128i
$957$		0			0
$958$	12257.2	+	4461.27i	0.413375	+	0.150456i
$959$	−323.051	−	117.581i	−0.0108779	−	0.00395922i
$960$		0			0
$961$	−3118.24	+	17684.4i	−0.104670	+	0.593615i
$962$	−3624.67	−	6278.11i	−0.121480	−	0.210410i
$963$		0			0
$964$	−9103.73	+	15768.1i	−0.304161	+	0.526823i
$965$	−732.768	−	614.866i	−0.0244442	−	0.0205111i
$966$		0			0
$967$	282.202	+	1600.45i	0.00938470	+	0.0532233i	0.989140	−	0.146973i	$-0.0469531\pi$
$967$	282.202	+	1600.45i	0.00938470	+	0.0532233i	−0.979756	+	0.200196i	$0.935842\pi$
$968$	−4604.72	+	3863.82i	−0.152894	+	0.128293i
$969$		0			0
$970$	−664.791	+	241.964i	−0.0220053	+	0.00800928i
$971$	−48316.1			−1.59684			−0.798422	−	0.602098i	$-0.794332\pi$
$971$	−48316.1			−1.59684			−0.798422	+	0.602098i	$0.794332\pi$
$972$		0			0
$973$	1497.79			0.0493493
$974$	19831.8	−	7218.19i	0.652415	−	0.237460i
$975$		0			0
$976$	1674.11	−	1404.75i	0.0549048	−	0.0460706i
$977$	−5343.32	−	30303.5i	−0.174972	−	0.992318i	−0.938176	−	0.346159i	$-0.887486\pi$
$977$	−5343.32	−	30303.5i	−0.174972	−	0.992318i	0.763203	−	0.646158i	$-0.223625\pi$
$978$		0			0
$979$	6398.72	+	5369.17i	0.208891	+	0.175280i
$980$	−499.416	+	865.014i	−0.0162788	+	0.0281958i
$981$		0			0
$982$	−17729.0	−	30707.6i	−0.576127	−	0.997881i
$983$	5884.20	−	33371.0i	0.190923	−	1.08278i	−0.727184	−	0.686442i	$-0.759171\pi$
$983$	5884.20	−	33371.0i	0.190923	−	1.08278i	0.918107	−	0.396333i	$-0.129717\pi$
$984$		0			0
$985$	1685.61	+	613.512i	0.0545259	+	0.0198458i
$986$	27496.4	+	10007.9i	0.888096	+	0.323240i
$987$		0			0
$988$	−586.642	+	3327.01i	−0.0188902	+	0.107132i
$989$	−40170.0	−	69576.6i	−1.29154	−	2.23701i
$990$		0			0
$991$	−10533.8	+	18245.0i	−0.337656	+	0.584837i	−0.983991	−	0.178217i	$-0.942967\pi$
$991$	−10533.8	+	18245.0i	−0.337656	+	0.584837i	0.646336	+	0.763053i	$0.276301\pi$
$992$	2666.65	+	2237.58i	0.0853490	+	0.0716163i
$993$		0			0
$994$	285.608	+	1619.76i	0.00911361	+	0.0516858i
$995$	−2601.13	+	2182.61i	−0.0828757	+	0.0695410i
$996$		0			0
$997$	52839.6	−	19232.0i	1.67848	−	0.610917i	0.685381	−	0.728185i	$-0.259636\pi$
$997$	52839.6	−	19232.0i	1.67848	−	0.610917i	0.993100	+	0.117267i	$0.0374134\pi$
$998$	−3720.45			−0.118005
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.19.3		30
3.2	odd	2		54.4.e.b.7.3	✓	30
27.2	odd	18		1458.4.a.i.1.8		15
27.4	even	9	inner	162.4.e.b.145.3		30
27.23	odd	18		54.4.e.b.31.3	yes	30
27.25	even	9		1458.4.a.j.1.8		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.7.3	✓	30	3.2	odd	2
54.4.e.b.31.3	yes	30	27.23	odd	18
162.4.e.b.19.3		30	1.1	even	1	trivial
162.4.e.b.145.3		30	27.4	even	9	inner
1458.4.a.i.1.8		15	27.2	odd	18
1458.4.a.j.1.8		15	27.25	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-0.127307 - 0.721992i) q^{5} +(1.18538 + 0.994655i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})\)	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-0.127307 - 0.721992i) q^{5} +(1.18538 + 0.994655i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(0.733130 + 1.26982i) q^{10} +(4.18063 - 23.7095i) q^{11} +(26.9008 + 9.79111i) q^{13} +(-2.90818 - 1.05849i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-34.8695 - 60.3957i) q^{17} +(-14.7514 + 25.5501i) q^{19} +(-2.24644 - 1.88499i) q^{20} +(8.36126 + 47.4191i) q^{22} +(125.729 - 105.499i) q^{23} +(116.957 - 42.5687i) q^{25} -57.2546 q^{26} +6.18963 q^{28} +(197.138 - 71.7522i) q^{29} +(83.3328 - 69.9245i) q^{31} +(5.55674 + 31.5138i) q^{32} +(106.846 + 89.6547i) q^{34} +(0.567225 - 0.982463i) q^{35} +(63.3079 + 109.652i) q^{37} +(10.2462 - 58.1091i) q^{38} +(5.51133 + 2.00596i) q^{40} +(95.0553 + 34.5973i) q^{41} +(85.0002 - 482.060i) q^{43} +(-48.1506 - 83.3993i) q^{44} +(-164.128 + 284.278i) q^{46} +(223.532 + 187.565i) q^{47} +(-59.1455 - 335.431i) q^{49} +(-190.688 + 160.006i) q^{50} +(107.603 - 39.1644i) q^{52} -523.625 q^{53} -17.6503 q^{55} +(-11.6327 + 4.23396i) q^{56} +(-321.416 + 269.700i) q^{58} +(100.933 + 572.420i) q^{59} +(104.632 + 87.7968i) q^{61} +(-108.783 + 188.418i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(3.64444 - 20.6687i) q^{65} +(-822.330 - 299.304i) q^{67} +(-262.133 - 95.4086i) q^{68} +(-0.393991 + 2.23443i) q^{70} +(-265.726 - 460.252i) q^{71} +(-593.378 + 1027.76i) q^{73} +(-193.987 - 162.774i) q^{74} +(20.4924 + 116.218i) q^{76} +(28.5385 - 23.9466i) q^{77} +(-200.068 + 72.8188i) q^{79} -11.7301 q^{80} -202.311 q^{82} +(506.381 - 184.308i) q^{83} +(-39.1661 + 32.8643i) q^{85} +(170.000 + 964.120i) q^{86} +(147.542 + 123.802i) q^{88} +(-173.475 + 300.468i) q^{89} +(22.1490 + 38.3633i) q^{91} +(114.002 - 646.538i) q^{92} +(-548.405 - 199.603i) q^{94} +(20.3249 + 7.39767i) q^{95} +(-83.7836 + 475.160i) q^{97} +(340.606 + 589.946i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

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Database

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