LMFDB - Embedded newform 162.4.e.b.37.5

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			37.5
Character	$\chi$	$=$	162.37
Dual form			162.4.e.b.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(17.2977 - 6.29584i) q^{5} +(6.03855 + 34.2463i) q^{7} +(-4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(17.2977 - 6.29584i) q^{5} +(6.03855 + 34.2463i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(18.4078 - 31.8832i) q^{10} +(27.3782 + 9.96484i) q^{11} +(-9.35152 - 7.84686i) q^{13} +(53.2778 + 44.7054i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(6.11689 - 10.5948i) q^{17} +(-38.8683 - 67.3218i) q^{19} +(-12.7859 - 72.5126i) q^{20} +(54.7563 - 19.9297i) q^{22} +(1.09835 - 6.22906i) q^{23} +(163.816 - 137.458i) q^{25} -24.4151 q^{26} +139.099 q^{28} +(102.565 - 86.0622i) q^{29} +(-26.2299 + 148.757i) q^{31} +(-30.0702 + 10.9446i) q^{32} +(-4.24875 - 24.0958i) q^{34} +(320.062 + 554.364i) q^{35} +(81.0251 - 140.340i) q^{37} +(-146.097 - 53.1749i) q^{38} +(-112.810 - 94.6584i) q^{40} +(-261.723 - 219.612i) q^{41} +(-326.265 - 118.751i) q^{43} +(58.2705 - 100.927i) q^{44} +(-6.32515 - 10.9555i) q^{46} +(26.2565 + 148.908i) q^{47} +(-814.032 + 296.283i) q^{49} +(74.2683 - 421.196i) q^{50} +(-37.4061 + 31.3874i) q^{52} -329.797 q^{53} +536.316 q^{55} +(213.111 - 178.822i) q^{56} +(46.4991 - 263.710i) q^{58} +(-215.891 + 78.5777i) q^{59} +(124.948 + 708.616i) q^{61} +(151.052 + 261.630i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(-211.162 - 76.8567i) q^{65} +(294.944 + 247.487i) q^{67} +(-37.4865 - 31.4549i) q^{68} +(1203.04 + 437.871i) q^{70} +(-62.9842 + 109.092i) q^{71} +(-184.783 - 320.053i) q^{73} +(-56.2794 - 319.177i) q^{74} +(-292.194 + 106.350i) q^{76} +(-175.935 + 997.775i) q^{77} +(-773.000 + 648.624i) q^{79} -294.525 q^{80} -683.310 q^{82} +(868.755 - 728.972i) q^{83} +(39.1050 - 221.776i) q^{85} +(-652.531 + 237.502i) q^{86} +(-40.4743 - 229.541i) q^{88} +(-325.306 - 563.446i) q^{89} +(212.256 - 367.639i) q^{91} +(-23.7748 - 8.65332i) q^{92} +(231.660 + 194.386i) q^{94} +(-1096.18 - 919.803i) q^{95} +(677.244 + 246.497i) q^{97} +(-866.275 + 1500.43i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

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

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
$5$	17.2977	−	6.29584i	1.54715	−	0.563117i	0.579404	−	0.815041i	$-0.303285\pi$
$5$	17.2977	−	6.29584i	1.54715	−	0.563117i	0.967747	+	0.251924i	$0.0810632\pi$
$6$		0			0
$7$	6.03855	+	34.2463i	0.326051	+	1.84913i	0.502184	+	0.864761i	$0.332530\pi$
$7$	6.03855	+	34.2463i	0.326051	+	1.84913i	−0.176132	+	0.984366i	$0.556359\pi$
$8$	−4.00000	−	6.92820i	−0.176777	−	0.306186i
$9$		0			0
$10$	18.4078	−	31.8832i	0.582106	−	1.00824i
$11$	27.3782	+	9.96484i	0.750439	+	0.273138i	0.688791	−	0.724960i	$-0.258142\pi$
$11$	27.3782	+	9.96484i	0.750439	+	0.273138i	0.0616486	+	0.998098i	$0.480364\pi$
$12$		0			0
$13$	−9.35152	−	7.84686i	−0.199511	−	0.167410i	0.537559	−	0.843226i	$-0.319347\pi$
$13$	−9.35152	−	7.84686i	−0.199511	−	0.167410i	−0.737070	+	0.675817i	$0.763791\pi$
$14$	53.2778	+	44.7054i	1.01708	+	0.853430i
$15$		0			0
$16$	−15.0351	−	5.47232i	−0.234923	−	0.0855050i
$17$	6.11689	−	10.5948i	0.0872684	−	0.151153i	−0.819087	−	0.573669i	$-0.805520\pi$
$17$	6.11689	−	10.5948i	0.0872684	−	0.151153i	0.906356	+	0.422516i	$0.138853\pi$
$18$		0			0
$19$	−38.8683	−	67.3218i	−0.469315	−	0.812878i	0.530069	−	0.847954i	$-0.322166\pi$
$19$	−38.8683	−	67.3218i	−0.469315	−	0.812878i	−0.999385	+	0.0350762i	$0.988833\pi$
$20$	−12.7859	−	72.5126i	−0.142951	−	0.810715i
$21$		0			0
$22$	54.7563	−	19.9297i	0.530641	−	0.193137i
$23$	1.09835	−	6.22906i	0.00995748	−	0.0564717i	−0.979424	−	0.201813i	$-0.935317\pi$
$23$	1.09835	−	6.22906i	0.00995748	−	0.0564717i	0.989382	+	0.145341i	$0.0464279\pi$
$24$		0			0
$25$	163.816	−	137.458i	1.31053	−	1.09967i
$26$	−24.4151			−0.184161
$27$		0			0
$28$	139.099			0.938827
$29$	102.565	−	86.0622i	0.656752	−	0.551081i	−0.252359	−	0.967634i	$-0.581206\pi$
$29$	102.565	−	86.0622i	0.656752	−	0.551081i	0.909111	+	0.416553i	$0.136762\pi$
$30$		0			0
$31$	−26.2299	+	148.757i	−0.151969	+	0.861859i	0.809536	+	0.587071i	$0.199719\pi$
$31$	−26.2299	+	148.757i	−0.151969	+	0.861859i	−0.961505	+	0.274788i	$0.911392\pi$
$32$	−30.0702	+	10.9446i	−0.166116	+	0.0604612i
$33$		0			0
$34$	−4.24875	−	24.0958i	−0.0214310	−	0.121541i
$35$	320.062	+	554.364i	1.54573	+	2.67727i
$36$		0			0
$37$	81.0251	−	140.340i	0.360012	−	0.623559i	−0.627950	−	0.778253i	$-0.716106\pi$
$37$	81.0251	−	140.340i	0.360012	−	0.623559i	0.987962	+	0.154694i	$0.0494392\pi$
$38$	−146.097	−	53.1749i	−0.623686	−	0.227003i
$39$		0			0
$40$	−112.810	−	94.6584i	−0.445919	−	0.374170i
$41$	−261.723	−	219.612i	−0.996933	−	0.836527i	−0.0103768	−	0.999946i	$-0.503303\pi$
$41$	−261.723	−	219.612i	−0.996933	−	0.836527i	−0.986557	+	0.163420i	$0.947748\pi$
$42$		0			0
$43$	−326.265	−	118.751i	−1.15709	−	0.421148i	−0.309035	−	0.951051i	$-0.600006\pi$
$43$	−326.265	−	118.751i	−1.15709	−	0.421148i	−0.848058	+	0.529903i	$0.822228\pi$
$44$	58.2705	−	100.927i	0.199650	−	0.345804i
$45$		0			0
$46$	−6.32515	−	10.9555i	−0.0202738	−	0.0351152i
$47$	26.2565	+	148.908i	0.0814875	+	0.462138i	0.998059	+	0.0622686i	$0.0198336\pi$
$47$	26.2565	+	148.908i	0.0814875	+	0.462138i	−0.916572	+	0.399870i	$0.869055\pi$
$48$		0			0
$49$	−814.032	+	296.283i	−2.37327	+	0.863800i
$50$	74.2683	−	421.196i	0.210062	−	1.19132i
$51$		0			0
$52$	−37.4061	+	31.3874i	−0.0997556	+	0.0837049i
$53$	−329.797			−0.854738			−0.427369	−	0.904077i	$-0.640559\pi$
$53$	−329.797			−0.854738			−0.427369	+	0.904077i	$0.640559\pi$
$54$		0			0
$55$	536.316			1.31485
$56$	213.111	−	178.822i	0.508539	−	0.426715i
$57$		0			0
$58$	46.4991	−	263.710i	0.105270	−	0.597014i
$59$	−215.891	+	78.5777i	−0.476382	+	0.173389i	−0.569041	−	0.822309i	$-0.692686\pi$
$59$	−215.891	+	78.5777i	−0.476382	+	0.173389i	0.0926590	+	0.995698i	$0.470463\pi$
$60$		0			0
$61$	124.948	+	708.616i	0.262262	+	1.48736i	0.776721	+	0.629845i	$0.216882\pi$
$61$	124.948	+	708.616i	0.262262	+	1.48736i	−0.514459	+	0.857515i	$0.672007\pi$
$62$	151.052	+	261.630i	0.309414	+	0.535920i
$63$		0			0
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−211.162	−	76.8567i	−0.402945	−	0.146660i
$66$		0			0
$67$	294.944	+	247.487i	0.537808	+	0.451274i	0.870787	−	0.491660i	$-0.163610\pi$
$67$	294.944	+	247.487i	0.537808	+	0.451274i	−0.332980	+	0.942934i	$0.608054\pi$
$68$	−37.4865	−	31.4549i	−0.0668515	−	0.0560951i
$69$		0			0
$70$	1203.04	+	437.871i	2.05415	+	0.747651i
$71$	−62.9842	+	109.092i	−0.105280	+	0.182350i	−0.913852	−	0.406047i	$-0.866907\pi$
$71$	−62.9842	+	109.092i	−0.105280	+	0.182350i	0.808573	+	0.588396i	$0.200240\pi$
$72$		0			0
$73$	−184.783	−	320.053i	−0.296263	−	0.513142i	0.679015	−	0.734124i	$-0.262407\pi$
$73$	−184.783	−	320.053i	−0.296263	−	0.513142i	−0.975278	+	0.220982i	$0.929074\pi$
$74$	−56.2794	−	319.177i	−0.0884102	−	0.501399i
$75$		0			0
$76$	−292.194	+	106.350i	−0.441012	+	0.160515i
$77$	−175.935	+	997.775i	−0.260385	+	1.47671i
$78$		0			0
$79$	−773.000	+	648.624i	−1.10088	+	0.923746i	−0.997484	−	0.0708943i	$-0.977415\pi$
$79$	−773.000	+	648.624i	−1.10088	+	0.923746i	−0.103394	+	0.994640i	$0.532970\pi$
$80$	−294.525			−0.411611
$81$		0			0
$82$	−683.310			−0.920232
$83$	868.755	−	728.972i	1.14889	−	0.964037i	0.149201	−	0.988807i	$-0.452330\pi$
$83$	868.755	−	728.972i	1.14889	−	0.964037i	0.999693	+	0.0247704i	$0.00788547\pi$
$84$		0			0
$85$	39.1050	−	221.776i	0.0499004	−	0.282999i
$86$	−652.531	+	237.502i	−0.818189	+	0.297796i
$87$		0			0
$88$	−40.4743	−	229.541i	−0.0490292	−	0.278058i
$89$	−325.306	−	563.446i	−0.387442	−	0.671069i	0.604663	−	0.796482i	$-0.293308\pi$
$89$	−325.306	−	563.446i	−0.387442	−	0.671069i	−0.992105	+	0.125412i	$0.959975\pi$
$90$		0			0
$91$	212.256	−	367.639i	0.244511	−	0.423506i
$92$	−23.7748	−	8.65332i	−0.0269423	−	0.00980620i
$93$		0			0
$94$	231.660	+	194.386i	0.254191	+	0.213291i
$95$	−1096.18	−	919.803i	−1.18385	−	0.993366i
$96$		0			0
$97$	677.244	+	246.497i	0.708905	+	0.258020i	0.671208	−	0.741269i	$-0.265776\pi$
$97$	677.244	+	246.497i	0.708905	+	0.258020i	0.0376966	+	0.999289i	$0.487998\pi$
$98$	−866.275	+	1500.43i	−0.892928	+	1.54660i
$99$		0			0
$100$	−427.694	−	740.788i	−0.427694	−	0.740788i
$101$	113.833	+	645.580i	0.112147	+	0.636016i	0.988123	+	0.153662i	$0.0491069\pi$
$101$	113.833	+	645.580i	0.112147	+	0.636016i	−0.875977	+	0.482354i	$0.839782\pi$
$102$		0			0
$103$	−515.030	+	187.456i	−0.492693	+	0.179326i	−0.576405	−	0.817164i	$-0.695545\pi$
$103$	−515.030	+	187.456i	−0.492693	+	0.179326i	0.0837115	+	0.996490i	$0.473323\pi$
$104$	−16.9585	+	96.1767i	−0.0159896	+	0.0906817i
$105$		0			0
$106$	−505.278	+	423.979i	−0.462990	+	0.388495i
$107$	1872.22			1.69154			0.845769	−	0.533549i	$-0.179142\pi$
$107$	1872.22			1.69154			0.845769	+	0.533549i	$0.179142\pi$
$108$		0			0
$109$	−360.413			−0.316709			−0.158354	−	0.987382i	$-0.550619\pi$
$109$	−360.413			−0.316709			−0.158354	+	0.987382i	$0.550619\pi$
$110$	821.683	−	689.474i	0.712222	−	0.597625i
$111$		0			0
$112$	96.6168	−	547.941i	0.0815128	−	0.462282i
$113$	−1065.80	+	387.920i	−0.887276	+	0.322942i	−0.745142	−	0.666906i	$-0.767618\pi$
$113$	−1065.80	+	387.920i	−0.887276	+	0.322942i	−0.142133	+	0.989848i	$0.545396\pi$
$114$		0			0
$115$	−20.2182	−	114.663i	−0.0163944	−	0.0929774i
$116$	−267.778	−	463.805i	−0.214332	−	0.371235i
$117$		0			0
$118$	−229.746	+	397.932i	−0.179236	+	0.310446i
$119$	399.769	+	145.504i	0.307956	+	0.112087i
$120$		0			0
$121$	−369.339	−	309.912i	−0.277490	−	0.232841i
$122$	1102.41	+	925.033i	0.818095	+	0.686463i
$123$		0			0
$124$	567.771	+	206.652i	0.411188	+	0.149660i
$125$	817.739	−	1416.37i	0.585126	−	1.01347i
$126$		0			0
$127$	149.809	+	259.476i	0.104672	+	0.181297i	0.913604	−	0.406605i	$-0.133287\pi$
$127$	149.809	+	259.476i	0.104672	+	0.181297i	−0.808932	+	0.587902i	$0.799954\pi$
$128$	22.2270	+	126.055i	0.0153485	+	0.0870455i
$129$		0			0
$130$	−422.324	+	153.713i	−0.284925	+	0.103704i
$131$	301.829	−	1711.76i	0.201305	−	1.14166i	−0.701845	−	0.712330i	$-0.747640\pi$
$131$	301.829	−	1711.76i	0.201305	−	1.14166i	0.903150	−	0.429326i	$-0.141249\pi$
$132$		0			0
$133$	2070.82	−	1737.62i	1.35009	−	1.13286i
$134$	770.043			0.496430
$135$		0			0
$136$	−97.8702			−0.0617081
$137$	−1115.90	+	936.348i	−0.695894	+	0.583924i	−0.920602	−	0.390502i	$-0.872302\pi$
$137$	−1115.90	+	936.348i	−0.695894	+	0.583924i	0.224708	+	0.974426i	$0.427857\pi$
$138$		0			0
$139$	217.884	−	1235.68i	0.132954	−	0.754022i	−0.843308	−	0.537431i	$-0.819395\pi$
$139$	217.884	−	1235.68i	0.132954	−	0.754022i	0.976262	−	0.216591i	$-0.0694939\pi$
$140$	2406.08	−	875.742i	1.45251	−	0.528669i
$141$		0			0
$142$	43.7484	+	248.109i	0.0258541	+	0.146626i
$143$	−177.835	−	308.019i	−0.103995	−	0.180125i
$144$		0			0
$145$	1232.30	−	2134.41i	0.705772	−	1.22243i
$146$	−694.556	−	252.798i	−0.393711	−	0.143299i
$147$		0			0
$148$	−496.551	−	416.655i	−0.275785	−	0.231411i
$149$	153.503	+	128.804i	0.0843990	+	0.0708191i	0.684011	−	0.729472i	$-0.260234\pi$
$149$	153.503	+	128.804i	0.0843990	+	0.0708191i	−0.599612	+	0.800291i	$0.704678\pi$
$150$		0			0
$151$	−1533.68	−	558.214i	−0.826550	−	0.300840i	−0.106108	−	0.994355i	$-0.533839\pi$
$151$	−1533.68	−	558.214i	−0.826550	−	0.300840i	−0.720442	+	0.693515i	$0.756061\pi$
$152$	−310.946	+	538.575i	−0.165928	+	0.287396i
$153$		0			0
$154$	1013.17	+	1754.86i	0.530152	+	0.918249i
$155$	482.836	+	2738.30i	0.250208	+	1.41900i
$156$		0			0
$157$	−611.620	+	222.611i	−0.310908	+	0.113161i	−0.492762	−	0.870164i	$-0.664013\pi$
$157$	−611.620	+	222.611i	−0.310908	+	0.113161i	0.181854	+	0.983326i	$0.441790\pi$
$158$	−350.450	+	1987.50i	−0.176458	+	1.00074i
$159$		0			0
$160$	−451.238	+	378.634i	−0.222959	+	0.187085i
$161$	219.955			0.107670
$162$		0			0
$163$	2696.10			1.29555			0.647776	−	0.761831i	$-0.275699\pi$
$163$	2696.10			1.29555			0.647776	+	0.761831i	$0.275699\pi$
$164$	−1046.89	+	878.447i	−0.498467	+	0.418263i
$165$		0			0
$166$	393.861	−	2233.70i	0.184154	−	1.04439i
$167$	−335.174	+	121.993i	−0.155309	+	0.0565278i	−0.418505	−	0.908215i	$-0.637446\pi$
$167$	−335.174	+	121.993i	−0.155309	+	0.0565278i	0.263196	+	0.964742i	$0.415223\pi$
$168$		0			0
$169$	−355.627	−	2016.86i	−0.161869	−	0.918007i
$170$	−225.197	−	390.052i	−0.101599	−	0.175974i
$171$		0			0
$172$	−694.409	+	1202.75i	−0.307838	+	0.533192i
$173$	304.282	+	110.750i	0.133723	+	0.0486713i	0.408015	−	0.912975i	$-0.366221\pi$
$173$	304.282	+	110.750i	0.133723	+	0.0486713i	−0.274292	+	0.961647i	$0.588443\pi$
$174$		0			0
$175$	5696.65	+	4780.06i	2.46072	+	2.06479i
$176$	−357.102	−	299.644i	−0.152941	−	0.128333i
$177$		0			0
$178$	−1222.75	−	445.044i	−0.514882	−	0.187402i
$179$	−41.0735	+	71.1414i	−0.0171507	+	0.0297059i	−0.874473	−	0.485073i	$-0.838793\pi$
$179$	−41.0735	+	71.1414i	−0.0171507	+	0.0297059i	0.857323	+	0.514779i	$0.172126\pi$
$180$		0			0
$181$	177.362	+	307.201i	0.0728356	+	0.126155i	0.900143	−	0.435594i	$-0.143462\pi$
$181$	177.362	+	307.201i	0.0728356	+	0.126155i	−0.827307	+	0.561749i	$0.810128\pi$
$182$	−147.432	−	836.127i	−0.0600460	−	0.340538i
$183$		0			0
$184$	−47.5496	+	17.3066i	−0.0190511	+	0.00693403i
$185$	517.990	−	2937.67i	0.205856	−	1.16747i
$186$		0			0
$187$	273.044	−	229.111i	0.106775	−	0.0895951i
$188$	604.822			0.234634
$189$		0			0
$190$	−2861.92			−1.09276
$191$	4009.13	−	3364.06i	1.51880	−	1.27442i	0.674923	−	0.737889i	$-0.264177\pi$
$191$	4009.13	−	3364.06i	1.51880	−	1.27442i	0.843877	−	0.536536i	$-0.180267\pi$
$192$		0			0
$193$	352.398	−	1998.55i	0.131431	−	0.745381i	−0.845848	−	0.533424i	$-0.820905\pi$
$193$	352.398	−	1998.55i	0.131431	−	0.745381i	0.977279	−	0.211957i	$-0.0679837\pi$
$194$	1354.49	−	492.994i	0.501271	−	0.182448i
$195$		0			0
$196$	601.708	+	3412.46i	0.219281	+	1.24361i
$197$	−282.221	−	488.821i	−0.102068	−	0.176787i	0.810468	−	0.585782i	$-0.199213\pi$
$197$	−282.221	−	488.821i	−0.102068	−	0.176787i	−0.912537	+	0.408995i	$0.865879\pi$
$198$		0			0
$199$	−1488.72	+	2578.54i	−0.530314	+	0.918531i	0.469060	+	0.883166i	$0.344593\pi$
$199$	−1488.72	+	2578.54i	−0.530314	+	0.918531i	−0.999374	+	0.0353651i	$0.988741\pi$
$200$	−1607.60	−	585.120i	−0.568374	−	0.206871i
$201$		0			0
$202$	1004.34	+	842.745i	0.349829	+	0.293541i
$203$	3566.66	+	2992.78i	1.23315	+	1.03474i
$204$		0			0
$205$	−5909.84	−	2151.01i	−2.01347	−	0.732843i
$206$	−548.083	+	949.308i	−0.185373	+	0.321075i
$207$		0			0
$208$	97.6604	+	169.153i	0.0325554	+	0.0563877i
$209$	−393.291	−	2230.46i	−0.130165	−	0.738203i
$210$		0			0
$211$	−2776.49	+	1010.56i	−0.905883	+	0.329714i	−0.752608	−	0.658469i	$-0.771204\pi$
$211$	−2776.49	+	1010.56i	−0.905883	+	0.329714i	−0.153275	+	0.988184i	$0.548982\pi$
$212$	−229.075	+	1299.15i	−0.0742118	+	0.420876i
$213$		0			0
$214$	2868.41	−	2406.88i	0.916264	−	0.768837i
$215$	−6391.27			−2.02735
$216$		0			0
$217$	−5252.79			−1.64324
$218$	−552.184	+	463.338i	−0.171553	+	0.143950i
$219$		0			0
$220$	372.521	−	2112.67i	0.114161	−	0.647438i
$221$	−140.338	+	51.0788i	−0.0427156	+	0.0155472i
$222$		0			0
$223$	−256.880	−	1456.84i	−0.0771389	−	0.437476i	−0.998778	−	0.0494275i	$-0.984260\pi$
$223$	−256.880	−	1456.84i	−0.0771389	−	0.437476i	0.921639	−	0.388049i	$-0.126851\pi$
$224$	−556.394	−	963.703i	−0.165963	−	0.287456i
$225$		0			0
$226$	−1134.20	+	1964.50i	−0.333832	+	0.578214i
$227$	−4635.06	−	1687.03i	−1.35524	−	0.493268i	−0.440662	−	0.897673i	$-0.645256\pi$
$227$	−4635.06	−	1687.03i	−1.35524	−	0.493268i	−0.914580	+	0.404405i	$0.867479\pi$
$228$		0			0
$229$	3672.63	+	3081.70i	1.05980	+	0.889277i	0.994090	−	0.108562i	$-0.0346246\pi$
$229$	3672.63	+	3081.70i	1.05980	+	0.889277i	0.0657091	+	0.997839i	$0.479069\pi$
$230$	−178.384	−	149.682i	−0.0511405	−	0.0429120i
$231$		0			0
$232$	−1006.52	−	366.342i	−0.284832	−	0.103670i
$233$	1872.47	−	3243.21i	0.526478	−	0.911887i	−0.473046	−	0.881038i	$-0.656846\pi$
$233$	1872.47	−	3243.21i	0.526478	−	0.911887i	0.999524	−	0.0308492i	$-0.00982115\pi$
$234$		0			0
$235$	1391.68	+	2410.46i	0.386311	+	0.669111i
$236$	159.580	+	905.022i	0.0440160	+	0.249627i
$237$		0			0
$238$	799.537	−	291.008i	0.217758	−	0.0792573i
$239$	−927.559	+	5260.45i	−0.251041	+	1.42372i	0.554993	+	0.831855i	$0.312721\pi$
$239$	−927.559	+	5260.45i	−0.251041	+	1.42372i	−0.806034	+	0.591869i	$0.798390\pi$
$240$		0			0
$241$	−5230.74	+	4389.11i	−1.39810	+	1.17314i	−0.436160	+	0.899869i	$0.643662\pi$
$241$	−5230.74	+	4389.11i	−1.39810	+	1.17314i	−0.961936	+	0.273273i	$0.911894\pi$
$242$	−964.275			−0.256140
$243$		0			0
$244$	2878.19			0.755153
$245$	−12215.5	+	10250.0i	−3.18539	+	2.67286i
$246$		0			0
$247$	−164.787	+	934.556i	−0.0424501	+	0.240746i
$248$	1135.54	−	413.303i	0.290754	−	0.105826i
$249$		0			0
$250$	−567.996	−	3221.26i	−0.143693	−	0.814922i
$251$	285.502	+	494.503i	0.0717956	+	0.124354i	0.899688	−	0.436533i	$-0.143794\pi$
$251$	285.502	+	494.503i	0.0717956	+	0.124354i	−0.827893	+	0.560887i	$0.810460\pi$
$252$		0			0
$253$	92.1424	−	159.595i	0.0228970	−	0.0396588i
$254$	563.096	+	204.950i	0.139101	+	0.0506288i
$255$		0			0
$256$	196.107	+	164.554i	0.0478778	+	0.0401742i
$257$	−1913.91	−	1605.96i	−0.464538	−	0.389794i	0.380260	−	0.924880i	$-0.375835\pi$
$257$	−1913.91	−	1605.96i	−0.464538	−	0.389794i	−0.844797	+	0.535086i	$0.820279\pi$
$258$		0			0
$259$	5295.39	+	1927.36i	1.27042	+	0.462396i
$260$	−449.428	+	778.432i	−0.107201	+	0.185678i
$261$		0			0
$262$	−1738.16	−	3010.59i	−0.409863	−	0.709903i
$263$	545.473	+	3093.53i	0.127891	+	0.725305i	0.979549	+	0.201207i	$0.0644863\pi$
$263$	545.473	+	3093.53i	0.127891	+	0.725305i	−0.851658	+	0.524098i	$0.824403\pi$
$264$		0			0
$265$	−5704.72	+	2076.35i	−1.32241	+	0.481317i
$266$	938.832	−	5324.38i	0.216404	−	1.22729i
$267$		0			0
$268$	1179.77	−	989.949i	0.268904	−	0.225637i
$269$	−1573.50			−0.356647			−0.178324	−	0.983972i	$-0.557067\pi$
$269$	−1573.50			−0.356647			−0.178324	+	0.983972i	$0.557067\pi$
$270$		0			0
$271$	5646.06			1.26558			0.632792	−	0.774322i	$-0.281909\pi$
$271$	5646.06			1.26558			0.632792	+	0.774322i	$0.281909\pi$
$272$	−149.946	+	125.819i	−0.0334257	+	0.0280475i
$273$		0			0
$274$	−505.906	+	2869.14i	−0.111543	+	0.632595i
$275$	5854.74	−	2130.95i	1.28383	−	0.467277i
$276$		0			0
$277$	−1044.60	−	5924.21i	−0.226584	−	1.28502i	−0.859634	−	0.510911i	$-0.829308\pi$
$277$	−1044.60	−	5924.21i	−0.226584	−	1.28502i	0.633050	−	0.774111i	$-0.281803\pi$
$278$	−1254.74	−	2173.28i	−0.270700	−	0.468865i
$279$		0			0
$280$	2560.50	−	4434.91i	0.546496	−	0.946559i
$281$	5031.60	+	1831.35i	1.06819	+	0.388788i	0.815498	−	0.578760i	$-0.196463\pi$
$281$	5031.60	+	1831.35i	1.06819	+	0.388788i	0.252688	+	0.967548i	$0.418686\pi$
$282$		0			0
$283$	−2242.33	−	1881.54i	−0.470998	−	0.395214i	0.376160	−	0.926555i	$-0.377244\pi$
$283$	−2242.33	−	1881.54i	−0.470998	−	0.395214i	−0.847159	+	0.531340i	$0.821689\pi$
$284$	385.990	+	323.884i	0.0806489	+	0.0676724i
$285$		0			0
$286$	−668.441	−	243.293i	−0.138202	−	0.0503014i
$287$	5940.47	−	10289.2i	1.22179	−	2.11621i
$288$		0			0
$289$	2381.67	+	4125.17i	0.484768	+	0.839644i
$290$	−855.947	−	4854.32i	−0.173320	−	0.982949i
$291$		0			0
$292$	−1389.11	+	505.596i	−0.278396	+	0.101328i
$293$	659.784	−	3741.82i	0.131553	−	0.746073i	−0.845646	−	0.533745i	$-0.820784\pi$
$293$	659.784	−	3741.82i	0.131553	−	0.746073i	0.977198	−	0.212328i	$-0.0681046\pi$
$294$		0			0
$295$	−3239.69	+	2718.42i	−0.639397	+	0.536518i
$296$	−1296.40			−0.254567
$297$		0			0
$298$	400.768			0.0779055
$299$	−59.1498	+	49.6326i	−0.0114405	+	0.00959975i
$300$		0			0
$301$	2096.61	−	11890.5i	0.401484	−	2.27693i
$302$	−3067.36	+	1116.43i	−0.584459	+	0.212726i
$303$		0			0
$304$	215.981	+	1224.89i	0.0407479	+	0.231093i
$305$	6622.64	+	11470.8i	1.24332	+	2.15349i
$306$		0			0
$307$	−4227.04	+	7321.45i	−0.785831	+	1.36110i	0.142671	+	0.989770i	$0.454431\pi$
$307$	−4227.04	+	7321.45i	−0.785831	+	1.36110i	−0.928501	+	0.371329i	$0.878902\pi$
$308$	3808.26	+	1386.09i	0.704532	+	0.256429i
$309$		0			0
$310$	4260.03	+	3574.59i	0.780496	+	0.654914i
$311$	3228.28	+	2708.84i	0.588613	+	0.493905i	0.887763	−	0.460301i	$-0.152259\pi$
$311$	3228.28	+	2708.84i	0.588613	+	0.493905i	−0.299150	+	0.954206i	$0.596703\pi$
$312$		0			0
$313$	8018.11	+	2918.35i	1.44796	+	0.527013i	0.942020	−	0.335558i	$-0.108925\pi$
$313$	8018.11	+	2918.35i	1.44796	+	0.527013i	0.505937	+	0.862571i	$0.331147\pi$
$314$	−650.872	+	1127.34i	−0.116977	+	0.202610i
$315$		0			0
$316$	2018.16	+	3495.56i	0.359273	+	0.622280i
$317$	−342.280	−	1941.16i	−0.0606446	−	0.343933i	−1.00000		0.000986087i	$-0.999686\pi$
$317$	−342.280	−	1941.16i	−0.0606446	−	0.343933i	0.939355	−	0.342947i	$-0.111425\pi$
$318$		0			0
$319$	3665.63	−	1334.18i	0.643374	−	0.234169i
$320$	−204.575	+	1160.20i	−0.0357377	+	0.202679i
$321$		0			0
$322$	336.990	−	282.768i	0.0583222	−	0.0489381i
$323$	−951.011			−0.163826
$324$		0			0
$325$	−2610.55			−0.445560
$326$	4130.67	−	3466.04i	0.701769	−	0.588854i
$327$		0			0
$328$	−474.622	+	2691.72i	−0.0798983	+	0.453126i
$329$	−4941.01	+	1798.38i	−0.827984	+	0.301361i
$330$		0			0
$331$	−394.770	−	2238.85i	−0.0655545	−	0.371778i	−0.999882	−	0.0153624i	$-0.995110\pi$
$331$	−394.770	−	2238.85i	−0.0655545	−	0.371778i	0.934327	−	0.356416i	$-0.116001\pi$
$332$	−2268.16	−	3928.56i	−0.374944	−	0.649421i
$333$		0			0
$334$	−356.685	+	617.797i	−0.0584340	+	0.101211i
$335$	6659.98	+	2424.03i	1.08619	+	0.395341i
$336$		0			0
$337$	−1081.51	−	907.493i	−0.174817	−	0.146689i	0.551181	−	0.834386i	$-0.314177\pi$
$337$	−1081.51	−	907.493i	−0.174817	−	0.146689i	−0.725998	+	0.687697i	$0.758622\pi$
$338$	−3137.68	−	2632.83i	−0.504933	−	0.423689i
$339$		0			0
$340$	−846.463	−	308.087i	−0.135017	−	0.0491423i
$341$	−2200.47	+	3811.33i	−0.349449	+	0.605264i
$342$		0			0
$343$	−9098.34	−	15758.8i	−1.43226	−	2.48074i
$344$	482.331	+	2735.44i	0.0755976	+	0.428735i
$345$		0			0
$346$	608.564	−	221.499i	0.0945566	−	0.0344158i
$347$	−1677.69	+	9514.68i	−0.259549	+	1.47197i	0.524573	+	0.851366i	$0.324225\pi$
$347$	−1677.69	+	9514.68i	−0.259549	+	1.47197i	−0.784121	+	0.620608i	$0.786886\pi$
$348$		0			0
$349$	3602.40	−	3022.77i	0.552527	−	0.463625i	−0.323269	−	0.946307i	$-0.604782\pi$
$349$	3602.40	−	3022.77i	0.552527	−	0.463625i	0.875796	+	0.482682i	$0.160337\pi$
$350$	14872.9			2.27140
$351$		0			0
$352$	−932.328			−0.141174
$353$	10012.5	−	8401.53i	1.50967	−	1.26677i	0.645280	−	0.763946i	$-0.276741\pi$
$353$	10012.5	−	8401.53i	1.50967	−	1.26677i	0.864392	−	0.502819i	$-0.167704\pi$
$354$		0			0
$355$	−402.656	+	2283.57i	−0.0601993	+	0.341407i
$356$	−2445.50	+	890.089i	−0.364076	+	0.132513i
$357$		0			0
$358$	28.5294	+	161.798i	0.00421180	+	0.0238863i
$359$	−929.092	−	1609.23i	−0.136589	−	0.236580i	0.789614	−	0.613604i	$-0.210281\pi$
$359$	−929.092	−	1609.23i	−0.136589	−	0.236580i	−0.926203	+	0.377024i	$0.876947\pi$
$360$		0			0
$361$	408.014	−	706.702i	0.0594860	−	0.103033i
$362$	666.665	+	242.646i	0.0967931	+	0.0352298i
$363$		0			0
$364$	−1300.78	−	1091.49i	−0.187306	−	0.157169i
$365$	−5211.32	−	4372.81i	−0.747323	−	0.627078i
$366$		0			0
$367$	−1533.65	−	558.203i	−0.218136	−	0.0793950i	0.230640	−	0.973039i	$-0.425918\pi$
$367$	−1533.65	−	558.203i	−0.218136	−	0.0793950i	−0.448777	+	0.893644i	$0.648140\pi$
$368$	−50.6012	+	87.6439i	−0.00716786	+	0.0124151i
$369$		0			0
$370$	−2982.99	−	5166.69i	−0.419130	−	0.725955i
$371$	−1991.50	−	11294.3i	−0.278688	−	1.58052i
$372$		0			0
$373$	9930.35	−	3614.35i	1.37848	−	0.501727i	0.456765	−	0.889587i	$-0.349008\pi$
$373$	9930.35	−	3614.35i	1.37848	−	0.501727i	0.921718	+	0.387861i	$0.126786\pi$
$374$	123.788	−	702.038i	0.0171148	−	0.0970629i
$375$		0			0
$376$	926.641	−	777.544i	0.127095	−	0.106646i
$377$	−1634.46			−0.223286
$378$		0			0
$379$	−4209.91			−0.570576			−0.285288	−	0.958442i	$-0.592089\pi$
$379$	−4209.91			−0.570576			−0.285288	+	0.958442i	$0.592089\pi$
$380$	−4384.71	+	3679.21i	−0.591924	+	0.496683i
$381$		0			0
$382$	1817.59	−	10308.1i	0.243446	−	1.38065i
$383$	3042.30	−	1107.31i	0.405885	−	0.147730i	−0.131006	−	0.991382i	$-0.541821\pi$
$383$	3042.30	−	1107.31i	0.405885	−	0.147730i	0.536891	+	0.843651i	$0.319599\pi$
$384$		0			0
$385$	3238.57	+	18366.8i	0.428709	+	2.43133i
$386$	−2029.38	−	3514.98i	−0.267597	−	0.463492i
$387$		0			0
$388$	1441.42	−	2496.61i	0.188600	−	0.326665i
$389$	3289.34	+	1197.22i	0.428730	+	0.156045i	0.547367	−	0.836893i	$-0.315630\pi$
$389$	3289.34	+	1197.22i	0.428730	+	0.156045i	−0.118637	+	0.992938i	$0.537852\pi$
$390$		0			0
$391$	−59.2769	−	49.7392i	−0.00766691	−	0.00643330i
$392$	5308.84	+	4454.64i	0.684023	+	0.573963i
$393$		0			0
$394$	−1060.80	−	386.101i	−0.135641	−	0.0493693i
$395$	−9287.47	+	16086.4i	−1.18305	+	2.04910i
$396$		0			0
$397$	4480.40	+	7760.28i	0.566410	+	0.981051i	0.996917	+	0.0784638i	$0.0250015\pi$
$397$	4480.40	+	7760.28i	0.566410	+	0.981051i	−0.430507	+	0.902587i	$0.641665\pi$
$398$	1034.05	+	5864.41i	0.130232	+	0.738584i
$399$		0			0
$400$	−3215.21	+	1170.24i	−0.401901	+	0.146280i
$401$	182.594	−	1035.54i	0.0227389	−	0.128959i	−0.971325	−	0.237755i	$-0.923589\pi$
$401$	182.594	−	1035.54i	0.0227389	−	0.128959i	0.994064	+	0.108796i	$0.0346996\pi$
$402$		0			0
$403$	1412.57	−	1185.29i	0.174603	−	0.146509i
$404$	2622.16			0.322914
$405$		0			0
$406$	9311.88			1.13828
$407$	3616.78	−	3034.84i	0.440485	−	0.369610i
$408$		0			0
$409$	−15.3475	+	87.0400i	−0.00185546	+	0.0105229i	−0.985721	−	0.168384i	$-0.946145\pi$
$409$	−15.3475	+	87.0400i	−0.00185546	+	0.0105229i	0.983866	+	0.178907i	$0.0572562\pi$
$410$	−11819.7	+	4302.01i	−1.42374	+	0.518198i
$411$		0			0
$412$	380.695	+	2159.03i	0.0455230	+	0.258174i
$413$	−3994.66	−	6918.96i	−0.475943	−	0.824358i
$414$		0			0
$415$	10437.9	−	18079.0i	1.23465	−	2.13847i
$416$	367.083	+	133.607i	0.0432638	+	0.0157467i
$417$		0			0
$418$	−3469.99	−	2911.67i	−0.406035	−	0.340704i
$419$	−2132.04	−	1788.99i	−0.248584	−	0.208587i	0.509978	−	0.860187i	$-0.329653\pi$
$419$	−2132.04	−	1788.99i	−0.248584	−	0.208587i	−0.758562	+	0.651600i	$0.774098\pi$
$420$		0			0
$421$	9001.90	+	3276.42i	1.04210	+	0.379295i	0.805678	−	0.592354i	$-0.201801\pi$
$421$	9001.90	+	3276.42i	1.04210	+	0.379295i	0.236427	+	0.971649i	$0.424024\pi$
$422$	−2954.68	+	5117.65i	−0.340833	+	0.590339i
$423$		0			0
$424$	1319.19	+	2284.90i	0.151098	+	0.261709i
$425$	−454.291	−	2576.41i	−0.0518502	−	0.294057i
$426$		0			0
$427$	−23513.0	+	8558.03i	−2.66481	+	0.969911i
$428$	1300.43	−	7375.12i	0.146866	−	0.832920i
$429$		0			0
$430$	−9791.99	+	8216.46i	−1.09817	+	0.921472i
$431$	−6818.04			−0.761980			−0.380990	−	0.924579i	$-0.624417\pi$
$431$	−6818.04			−0.761980			−0.380990	+	0.924579i	$0.624417\pi$
$432$		0			0
$433$	−4810.43			−0.533891			−0.266945	−	0.963712i	$-0.586014\pi$
$433$	−4810.43			−0.533891			−0.266945	+	0.963712i	$0.586014\pi$
$434$	−8047.73	+	6752.85i	−0.890100	+	0.746883i
$435$		0			0
$436$	−250.340	+	1419.75i	−0.0274980	+	0.155949i
$437$	−462.043	+	168.170i	−0.0505778	+	0.0184088i
$438$		0			0
$439$	2116.25	+	12001.9i	0.230076	+	1.30482i	0.852740	+	0.522335i	$0.174939\pi$
$439$	2116.25	+	12001.9i	0.230076	+	1.30482i	−0.622665	+	0.782489i	$0.713950\pi$
$440$	−2145.26	−	3715.70i	−0.232435	−	0.402589i
$441$		0			0
$442$	−149.344	+	258.672i	−0.0160715	+	0.0278366i
$443$	−9078.69	−	3304.37i	−0.973683	−	0.354392i	−0.194302	−	0.980942i	$-0.562244\pi$
$443$	−9078.69	−	3304.37i	−0.973683	−	0.354392i	−0.779381	+	0.626550i	$0.784466\pi$
$444$		0			0
$445$	−9174.40	−	7698.23i	−0.977322	−	0.820070i
$446$	−2266.44	−	1901.77i	−0.240626	−	0.201909i
$447$		0			0
$448$	−2091.36	−	761.192i	−0.220552	−	0.0802744i
$449$	−253.436	+	438.963i	−0.0266378	+	0.0461380i	−0.879037	−	0.476754i	$-0.841813\pi$
$449$	−253.436	+	438.963i	−0.0266378	+	0.0461380i	0.852399	+	0.522892i	$0.175147\pi$
$450$		0			0
$451$	−4977.10	−	8620.60i	−0.519651	−	0.900062i
$452$	787.808	+	4467.88i	0.0819809	+	0.464937i
$453$		0			0
$454$	−9270.13	+	3374.05i	−0.958301	+	0.348793i
$455$	1356.95	−	7695.63i	0.139812	−	0.792916i
$456$		0			0
$457$	12733.3	−	10684.5i	1.30337	−	1.09366i	0.313819	−	0.949483i	$-0.398391\pi$
$457$	12733.3	−	10684.5i	1.30337	−	1.09366i	0.989552	−	0.144175i	$-0.0460530\pi$
$458$	9588.54			0.978260
$459$		0			0
$460$	−465.729			−0.0472059
$461$	1624.97	−	1363.51i	0.164170	−	0.137755i	−0.557001	−	0.830512i	$-0.688048\pi$
$461$	1624.97	−	1363.51i	0.164170	−	0.137755i	0.721172	+	0.692756i	$0.243604\pi$
$462$		0			0
$463$	−1442.64	+	8181.63i	−0.144806	+	0.821237i	0.822716	+	0.568452i	$0.192458\pi$
$463$	−1442.64	+	8181.63i	−0.144806	+	0.821237i	−0.967523	+	0.252785i	$0.918654\pi$
$464$	−2013.03	+	732.683i	−0.201407	+	0.0733060i
$465$		0			0
$466$	−1300.60	−	7376.08i	−0.129290	−	0.733241i
$467$	6898.77	+	11949.0i	0.683591	+	1.18401i	0.973877	+	0.227074i	$0.0729161\pi$
$467$	6898.77	+	11949.0i	0.683591	+	1.18401i	−0.290286	+	0.956940i	$0.593751\pi$
$468$		0			0
$469$	−6694.49	+	11595.2i	−0.659111	+	1.14161i
$470$	5231.00	+	1903.93i	0.513379	+	0.186855i
$471$		0			0
$472$	1407.96	+	1181.42i	0.137303	+	0.115211i
$473$	−7749.22	−	6502.37i	−0.753297	−	0.632091i
$474$		0			0
$475$	−15621.2	−	5685.65i	−1.50895	−	0.549212i
$476$	850.850	−	1473.72i	0.0819299	−	0.141907i
$477$		0			0
$478$	5341.60	+	9251.92i	0.511128	+	0.885299i
$479$	−2610.42	−	14804.4i	−0.249005	−	1.41217i	−0.811006	−	0.585038i	$-0.801079\pi$
$479$	−2610.42	−	14804.4i	−0.249005	−	1.41217i	0.562001	−	0.827137i	$-0.310032\pi$
$480$		0			0
$481$	−1858.93	+	676.596i	−0.176216	+	0.0641375i
$482$	−2371.42	+	13449.0i	−0.224098	+	1.27092i
$483$		0			0
$484$	−1477.36	+	1239.65i	−0.138745	+	0.116421i
$485$	13266.7			1.24208
$486$		0			0
$487$	17512.1			1.62946			0.814732	−	0.579838i	$-0.196884\pi$
$487$	17512.1			1.62946			0.814732	+	0.579838i	$0.196884\pi$
$488$	4409.64	−	3700.13i	0.409047	−	0.343232i
$489$		0			0
$490$	−5538.06	+	31407.9i	−0.510580	+	2.89564i
$491$	3839.54	−	1397.48i	0.352904	−	0.128447i	−0.159484	−	0.987201i	$-0.550983\pi$
$491$	3839.54	−	1397.48i	0.352904	−	0.128447i	0.512388	+	0.858754i	$0.328761\pi$
$492$		0			0
$493$	−284.430	−	1613.08i	−0.0259839	−	0.147362i
$494$	948.973	+	1643.67i	0.0864298	+	0.149701i
$495$		0			0
$496$	1208.42	−	2093.04i	0.109394	−	0.189476i
$497$	−4116.33	−	1498.22i	−0.371514	−	0.135220i
$498$		0			0
$499$	7650.20	+	6419.28i	0.686313	+	0.575885i	0.917843	−	0.396943i	$-0.129929\pi$
$499$	7650.20	+	6419.28i	0.686313	+	0.575885i	−0.231531	+	0.972828i	$0.574373\pi$
$500$	−5011.40	−	4205.06i	−0.448233	−	0.376112i
$501$		0			0
$502$	1073.14	+	390.589i	0.0954111	+	0.0347268i
$503$	3217.25	−	5572.44i	0.285189	−	0.493962i	−0.687466	−	0.726217i	$-0.741277\pi$
$503$	3217.25	−	5572.44i	0.285189	−	0.493962i	0.972655	+	0.232255i	$0.0746103\pi$
$504$		0			0
$505$	6033.52	+	10450.4i	0.531659	+	0.920861i
$506$	−64.0015	−	362.970i	−0.00562295	−	0.0318893i
$507$		0			0
$508$	1126.19	−	409.900i	0.0983596	−	0.0358000i
$509$	624.488	−	3541.65i	0.0543811	−	0.308410i	−0.945469	−	0.325711i	$-0.894396\pi$
$509$	624.488	−	3541.65i	0.0543811	−	0.308410i	0.999850	+	0.0173010i	$0.00550736\pi$
$510$		0			0
$511$	9844.82	−	8260.79i	0.852269	−	0.715139i
$512$	512.000			0.0441942
$513$		0			0
$514$	−4996.86			−0.428797
$515$	−7728.63	+	6485.09i	−0.661289	+	0.554888i
$516$		0			0
$517$	−764.991	+	4338.48i	−0.0650759	+	0.369064i
$518$	10590.8	−	3854.73i	0.898325	−	0.326963i
$519$		0			0
$520$	312.170	+	1770.40i	0.0263260	+	0.149302i
$521$	10026.5	+	17366.3i	0.843123	+	1.46033i	0.887242	+	0.461305i	$0.152619\pi$
$521$	10026.5	+	17366.3i	0.843123	+	1.46033i	−0.0441187	+	0.999026i	$0.514048\pi$
$522$		0			0
$523$	−197.838	+	342.665i	−0.0165408	+	0.0286495i	−0.874177	−	0.485607i	$-0.838599\pi$
$523$	−197.838	+	342.665i	−0.0165408	+	0.0286495i	0.857637	+	0.514256i	$0.171932\pi$
$524$	−6533.35	−	2377.95i	−0.544677	−	0.198246i
$525$		0			0
$526$	4812.68	+	4038.31i	0.398940	+	0.334751i
$527$	1415.60	+	1187.83i	0.117011	+	0.0981837i
$528$		0			0
$529$	11395.6	+	4147.68i	0.936603	+	0.340896i
$530$	−6070.84	+	10515.0i	−0.497548	+	0.861778i
$531$		0			0
$532$	−5406.52	−	9364.37i	−0.440606	−	0.763152i
$533$	724.247	+	4107.41i	0.0588567	+	0.333793i
$534$		0			0
$535$	32385.1	−	11787.2i	2.61706	−	0.952534i
$536$	534.867	−	3033.38i	0.0431021	−	0.244444i
$537$		0			0
$538$	−2410.75	+	2022.86i	−0.193187	+	0.162103i
$539$	−25239.1			−2.01693
$540$		0			0
$541$	−19391.5			−1.54105			−0.770525	−	0.637410i	$-0.780006\pi$
$541$	−19391.5			−1.54105			−0.770525	+	0.637410i	$0.780006\pi$
$542$	8650.26	−	7258.43i	0.685536	−	0.575233i
$543$		0			0
$544$	−67.9799	+	385.533i	−0.00535775	+	0.0303853i
$545$	−6234.30	+	2269.10i	−0.489996	+	0.178344i
$546$		0			0
$547$	243.157	+	1379.01i	0.0190067	+	0.107792i	0.992835	−	0.119492i	$-0.0381265\pi$
$547$	243.157	+	1379.01i	0.0190067	+	0.107792i	−0.973829	+	0.227284i	$0.927015\pi$
$548$	2913.40	+	5046.15i	0.227106	+	0.393360i
$549$		0			0
$550$	6230.49	−	10791.5i	0.483034	−	0.836640i
$551$	−9780.38	−	3559.77i	−0.756186	−	0.275229i
$552$		0			0
$553$	−26880.8	−	22555.7i	−2.06707	−	1.73448i
$554$	−9216.43	−	7733.50i	−0.706803	−	0.593078i
$555$		0			0
$556$	−4716.29	−	1716.59i	−0.359740	−	0.130935i
$557$	7495.73	−	12983.0i	0.570205	−	0.987625i	−0.426339	−	0.904563i	$-0.640197\pi$
$557$	7495.73	−	12983.0i	0.570205	−	0.987625i	0.996544	−	0.0830613i	$-0.0264697\pi$
$558$		0			0
$559$	2119.26	+	3670.66i	0.160349	+	0.277732i
$560$	−1778.50	−	10086.4i	−0.134206	−	0.761121i
$561$		0			0
$562$	10063.2	−	3662.70i	0.755321	−	0.274914i
$563$	171.864	−	974.687i	0.0128653	−	0.0729630i	−0.977699	−	0.210010i	$-0.932650\pi$
$563$	171.864	−	974.687i	0.0128653	−	0.0729630i	0.990564	+	0.137048i	$0.0437613\pi$
$564$		0			0
$565$	−15993.6	+	13420.2i	−1.19090	+	0.999280i
$566$	−5854.30			−0.434761
$567$		0			0
$568$	1007.75			0.0744439
$569$	3229.08	−	2709.52i	0.237908	−	0.199629i	−0.516036	−	0.856567i	$-0.672593\pi$
$569$	3229.08	−	2709.52i	0.237908	−	0.199629i	0.753945	+	0.656938i	$0.228149\pi$
$570$		0			0
$571$	538.608	−	3054.60i	0.0394747	−	0.223872i	−0.958688	−	0.284459i	$-0.908186\pi$
$571$	538.608	−	3054.60i	0.0394747	−	0.223872i	0.998163	+	0.0605868i	$0.0192972\pi$
$572$	−1336.88	+	486.585i	−0.0977235	+	0.0355684i
$573$		0			0
$574$	−4126.20	−	23400.9i	−0.300043	−	1.70163i
$575$	−676.308	−	1171.40i	−0.0490504	−	0.0849578i
$576$		0			0
$577$	3363.56	−	5825.86i	0.242681	−	0.420336i	−0.718796	−	0.695221i	$-0.755307\pi$
$577$	3363.56	−	5825.86i	0.242681	−	0.420336i	0.961477	+	0.274885i	$0.0886399\pi$
$578$	8952.14	+	3258.31i	0.644221	+	0.234477i
$579$		0			0
$580$	−7551.97	−	6336.86i	−0.540653	−	0.453662i
$581$	30210.6	+	25349.7i	2.15722	+	1.81013i
$582$		0			0
$583$	−9029.24	−	3286.38i	−0.641429	−	0.233461i
$584$	−1478.26	+	2560.43i	−0.104745	+	0.181423i
$585$		0			0
$586$	−3799.54	−	6581.00i	−0.267846	−	0.463923i
$587$	2856.30	+	16198.9i	0.200839	+	1.13901i	0.903855	+	0.427839i	$0.140725\pi$
$587$	2856.30	+	16198.9i	0.200839	+	1.13901i	−0.703016	+	0.711174i	$0.748164\pi$
$588$		0			0
$589$	11034.1	−	4016.10i	0.771908	−	0.280951i
$590$	−1468.76	+	8329.73i	−0.102488	+	0.581237i
$591$		0			0
$592$	−1986.20	+	1666.62i	−0.137893	+	0.115706i
$593$	−18525.6			−1.28289			−0.641446	−	0.767168i	$-0.721665\pi$
$593$	−18525.6			−1.28289			−0.641446	+	0.767168i	$0.721665\pi$
$594$		0			0
$595$	7831.14			0.539572
$596$	614.011	−	515.217i	0.0421995	−	0.0354096i
$597$		0			0
$598$	−26.8163	+	152.083i	−0.00183378	+	0.0103999i
$599$	−4260.11	+	1550.55i	−0.290590	+	0.105766i	−0.483202	−	0.875509i	$-0.660526\pi$
$599$	−4260.11	+	1550.55i	−0.290590	+	0.105766i	0.192612	+	0.981275i	$0.438304\pi$
$600$		0			0
$601$	−502.080	−	2847.44i	−0.0340770	−	0.193260i	0.963017	−	0.269440i	$-0.0868387\pi$
$601$	−502.080	−	2847.44i	−0.0340770	−	0.193260i	−0.997094	+	0.0761802i	$0.975728\pi$
$602$	−12073.9	−	20912.6i	−0.817435	−	1.41584i
$603$		0			0
$604$	−3264.22	+	5653.79i	−0.219899	+	0.380876i
$605$	−8339.86	−	3035.46i	−0.560435	−	0.203982i
$606$		0			0
$607$	−8842.78	−	7419.97i	−0.591297	−	0.496157i	0.297338	−	0.954772i	$-0.403901\pi$
$607$	−8842.78	−	7419.97i	−0.591297	−	0.496157i	−0.888635	+	0.458615i	$0.848346\pi$
$608$	1905.59	+	1598.98i	0.127108	+	0.106657i
$609$		0			0
$610$	24893.0	+	9060.31i	1.65228	+	0.601379i
$611$	922.924	−	1598.55i	0.0611088	−	0.105844i
$612$		0			0
$613$	1813.16	+	3140.48i	0.119466	+	0.206922i	0.919556	−	0.392958i	$-0.128548\pi$
$613$	1813.16	+	3140.48i	0.119466	+	0.206922i	−0.800090	+	0.599880i	$0.795215\pi$
$614$	2936.07	+	16651.3i	0.192981	+	1.09445i
$615$		0			0
$616$	7616.53	−	2772.19i	0.498180	−	0.181323i
$617$	903.616	−	5124.66i	0.0589598	−	0.334378i	−0.941032	−	0.338316i	$-0.890143\pi$
$617$	903.616	−	5124.66i	0.0589598	−	0.334378i	0.999992	+	0.00393856i	$0.00125369\pi$
$618$		0			0
$619$	−19408.4	+	16285.6i	−1.26024	+	1.05747i	−0.264585	+	0.964362i	$0.585235\pi$
$619$	−19408.4	+	16285.6i	−1.26024	+	1.05747i	−0.995656	+	0.0931052i	$0.970321\pi$
$620$	11122.2			0.720446
$621$		0			0
$622$	8428.43			0.543327
$623$	17331.6	−	14542.9i	1.11457	−	0.935232i
$624$		0			0
$625$	586.006	−	3323.41i	0.0375044	−	0.212698i
$626$	16036.2	−	5836.71i	1.02386	−	0.372654i
$627$		0			0
$628$	452.091	+	2563.94i	0.0287267	+	0.162917i
$629$	−991.243	−	1716.88i	−0.0628354	−	0.108834i
$630$		0			0
$631$	981.328	−	1699.71i	0.0619113	−	0.107234i	−0.833408	−	0.552658i	$-0.813614\pi$
$631$	981.328	−	1699.71i	0.0619113	−	0.107234i	0.895320	+	0.445424i	$0.146947\pi$
$632$	7585.80	+	2761.01i	0.477448	+	0.173777i
$633$		0			0
$634$	−3019.92	−	2534.01i	−0.189174	−	0.158736i
$635$	4224.96	+	3545.16i	0.264035	+	0.221552i
$636$		0			0
$637$	9937.33	+	3616.89i	0.618103	+	0.224971i
$638$	3900.89	−	6756.53i	0.242065	−	0.419269i
$639$		0			0
$640$	1178.10	+	2040.53i	0.0727632	+	0.126030i
$641$	4546.99	+	25787.3i	0.280180	+	1.58898i	0.722011	+	0.691881i	$0.243218\pi$
$641$	4546.99	+	25787.3i	0.280180	+	1.58898i	−0.441831	+	0.897098i	$0.645671\pi$
$642$		0			0
$643$	14388.6	−	5237.03i	0.882476	−	0.321195i	0.139267	−	0.990255i	$-0.455525\pi$
$643$	14388.6	−	5237.03i	0.882476	−	0.321195i	0.743208	+	0.669060i	$0.233303\pi$
$644$	152.779	−	866.453i	0.00934835	−	0.0530171i
$645$		0			0
$646$	−1457.03	+	1222.60i	−0.0887403	+	0.0744620i
$647$	−2663.26			−0.161829			−0.0809146	−	0.996721i	$-0.525784\pi$
$647$	−2663.26			−0.161829			−0.0809146	+	0.996721i	$0.525784\pi$
$648$		0			0
$649$	−6693.70			−0.404855
$650$	−3999.59	+	3356.06i	−0.241349	+	0.202516i
$651$		0			0
$652$	1872.69	−	10620.6i	0.112485	−	0.637935i
$653$	26737.9	−	9731.79i	1.60235	−	0.583207i	0.622442	−	0.782666i	$-0.286141\pi$
$653$	26737.9	−	9731.79i	1.60235	−	0.583207i	0.979906	+	0.199459i	$0.0639184\pi$
$654$		0			0
$655$	−5556.00	−	31509.7i	−0.331437	−	1.87967i
$656$	2733.24	+	4734.11i	0.162676	+	0.281762i
$657$		0			0
$658$	−5258.11	+	9107.32i	−0.311524	+	0.539575i
$659$	13219.3	+	4811.43i	0.781412	+	0.284411i	0.701761	−	0.712412i	$-0.252397\pi$
$659$	13219.3	+	4811.43i	0.781412	+	0.284411i	0.0796509	+	0.996823i	$0.474619\pi$
$660$		0			0
$661$	23359.4	+	19600.8i	1.37455	+	1.15338i	0.971182	+	0.238341i	$0.0766035\pi$
$661$	23359.4	+	19600.8i	1.37455	+	1.15338i	0.403364	+	0.915040i	$0.367841\pi$
$662$	−3483.04	−	2922.62i	−0.204490	−	0.171587i
$663$		0			0
$664$	−8525.48	−	3103.02i	−0.498272	−	0.181356i
$665$	24880.5	−	43094.3i	1.45087	−	2.51297i
$666$		0			0
$667$	−423.434	−	733.409i	−0.0245809	−	0.0425753i
$668$	247.751	+	1405.07i	0.0143500	+	0.0813826i
$669$		0			0
$670$	13320.0	−	4848.07i	0.768052	−	0.279548i
$671$	−3640.39	+	20645.7i	−0.209442	+	1.18781i
$672$		0			0
$673$	20306.5	−	17039.2i	1.16309	−	0.975947i	0.163145	−	0.986602i	$-0.447836\pi$
$673$	20306.5	−	17039.2i	1.16309	−	0.975947i	0.999943	+	0.0106548i	$0.00339161\pi$
$674$	−2823.62			−0.161367
$675$		0			0
$676$	−8191.90			−0.466085
$677$	−15044.4	+	12623.7i	−0.854064	+	0.716645i	−0.960681	−	0.277655i	$-0.910443\pi$
$677$	−15044.4	+	12623.7i	−0.854064	+	0.716645i	0.106617	+	0.994300i	$0.465998\pi$
$678$		0			0
$679$	−4352.03	+	24681.6i	−0.245973	+	1.39498i
$680$	−1692.93	+	616.175i	−0.0954717	+	0.0347489i
$681$		0			0
$682$	1528.43	+	8668.17i	0.0858163	+	0.486688i
$683$	−2676.25	−	4635.41i	−0.149933	−	0.259691i	0.781270	−	0.624194i	$-0.214572\pi$
$683$	−2676.25	−	4635.41i	−0.149933	−	0.259691i	−0.931202	+	0.364503i	$0.881239\pi$
$684$		0			0
$685$	−13407.3	+	23222.1i	−0.747835	+	1.29529i
$686$	−34198.6	−	12447.3i	−1.90336	−	0.692768i
$687$		0			0
$688$	4255.59	+	3570.86i	0.235818	+	0.197875i
$689$	3084.11	+	2587.87i	0.170530	+	0.143092i
$690$		0			0
$691$	−26778.2	−	9746.48i	−1.47423	−	0.536576i	−0.524984	−	0.851112i	$-0.675929\pi$
$691$	−26778.2	−	9746.48i	−1.47423	−	0.536576i	−0.949245	+	0.314537i	$0.898151\pi$
$692$	647.620	−	1121.71i	0.0355763	−	0.0616200i
$693$		0			0
$694$	9661.46	+	16734.1i	0.528449	+	0.915301i
$695$	−4010.76	−	22746.2i	−0.218902	−	1.24145i
$696$		0			0
$697$	−3927.66	+	1429.55i	−0.213445	+	0.0776875i
$698$	1633.19	−	9262.30i	0.0885635	−	0.502268i
$699$		0			0
$700$	22786.6	−	19120.2i	1.23036	−	1.03240i
$701$	32930.0			1.77425			0.887125	−	0.461530i	$-0.152699\pi$
$701$	32930.0			1.77425			0.887125	+	0.461530i	$0.152699\pi$
$702$		0			0
$703$	−12597.2			−0.675837
$704$	−1428.41	+	1198.58i	−0.0764704	+	0.0641663i
$705$		0			0
$706$	4539.32	−	25743.8i	0.241982	−	1.37235i
$707$	−21421.4	+	7796.74i	−1.13951	+	0.414747i
$708$		0			0
$709$	763.361	+	4329.24i	0.0404353	+	0.229320i	0.998328	−	0.0578072i	$-0.0184109\pi$
$709$	763.361	+	4329.24i	0.0404353	+	0.229320i	−0.957892	+	0.287127i	$0.907300\pi$
$710$	2318.80	+	4016.28i	0.122568	+	0.212293i
$711$		0			0
$712$	−2602.45	+	4507.57i	−0.136981	+	0.237259i
$713$	897.809	+	326.776i	0.0471574	+	0.0171639i
$714$		0			0
$715$	−5015.37	−	4208.39i	−0.262328	−	0.220119i
$716$	251.713	+	211.212i	0.0131382	+	0.0110243i
$717$		0			0
$718$	−3492.24	−	1271.07i	−0.181517	−	0.0660669i
$719$	−12425.5	+	21521.7i	−0.644499	+	1.11630i	0.339918	+	0.940455i	$0.389601\pi$
$719$	−12425.5	+	21521.7i	−0.644499	+	1.11630i	−0.984417	+	0.175850i	$0.943733\pi$
$720$		0			0
$721$	−9529.69	−	16505.9i	−0.492239	−	0.852583i
$722$	−283.404	−	1607.26i	−0.0146083	−	0.0828478i
$723$		0			0
$724$	1333.33	−	485.292i	0.0684431	−	0.0249112i
$725$	4971.85	−	28196.8i	0.254690	−	1.44442i
$726$		0			0
$727$	−2713.68	+	2277.04i	−0.138438	+	0.116164i	−0.709377	−	0.704829i	$-0.751024\pi$
$727$	−2713.68	+	2277.04i	−0.138438	+	0.116164i	0.570939	+	0.820993i	$0.306579\pi$
$728$	−3396.10			−0.172896
$729$		0			0
$730$	−13605.8			−0.689825
$731$	−3253.87	+	2730.32i	−0.164636	+	0.138146i
$732$		0			0
$733$	−5600.23	+	31760.5i	−0.282196	+	1.60041i	0.432939	+	0.901423i	$0.357477\pi$
$733$	−5600.23	+	31760.5i	−0.282196	+	1.60041i	−0.715134	+	0.698987i	$0.753635\pi$
$734$	−3067.30	+	1116.41i	−0.154246	+	0.0561408i
$735$		0			0
$736$	35.1472	+	199.330i	0.00176025	+	0.00998288i
$737$	5608.85	+	9714.81i	0.280332	+	0.485549i
$738$		0			0
$739$	−11899.3	+	20610.1i	−0.592316	+	1.02592i	0.401604	+	0.915813i	$0.368453\pi$
$739$	−11899.3	+	20610.1i	−0.592316	+	1.02592i	−0.993920	+	0.110107i	$0.964881\pi$
$740$	−11212.4	−	4080.97i	−0.556993	−	0.202729i
$741$		0			0
$742$	−17570.9	−	14743.7i	−0.869335	−	0.729459i
$743$	−12061.7	−	10121.0i	−0.595560	−	0.499734i	0.294455	−	0.955665i	$-0.404862\pi$
$743$	−12061.7	−	10121.0i	−0.595560	−	0.499734i	−0.890015	+	0.455931i	$0.849306\pi$
$744$		0			0
$745$	3466.17	+	1261.58i	0.170457	+	0.0620414i
$746$	10567.7	−	18303.7i	0.518645	−	0.898320i
$747$		0			0
$748$	−712.868	−	1234.72i	−0.0348463	−	0.0603556i
$749$	11305.5	+	64116.7i	0.551528	+	3.12787i
$750$		0			0
$751$	15119.4	−	5503.01i	0.734641	−	0.267387i	0.0525127	−	0.998620i	$-0.483277\pi$
$751$	15119.4	−	5503.01i	0.734641	−	0.267387i	0.682128	+	0.731233i	$0.261055\pi$
$752$	420.105	−	2382.53i	0.0203719	−	0.115535i
$753$		0			0
$754$	−2504.13	+	2101.22i	−0.120948	+	0.101488i
$755$	−30043.5			−1.44821
$756$		0			0
$757$	28643.2			1.37524			0.687620	−	0.726071i	$-0.258656\pi$
$757$	28643.2			1.37524			0.687620	+	0.726071i	$0.258656\pi$
$758$	−6449.95	+	5412.15i	−0.309067	+	0.259338i
$759$		0			0
$760$	−1987.87	+	11273.8i	−0.0948783	+	0.538082i
$761$	−26202.8	+	9537.04i	−1.24816	+	0.454294i	−0.879780	−	0.475381i	$-0.842310\pi$
$761$	−26202.8	+	9537.04i	−1.24816	+	0.454294i	−0.368381	+	0.929675i	$0.620088\pi$
$762$		0			0
$763$	−2176.37	−	12342.8i	−0.103263	−	0.585635i
$764$	−10467.1	−	18129.6i	−0.495663	−	0.858514i
$765$		0			0
$766$	3237.54	−	5607.59i	0.152712	−	0.264505i
$767$	2635.49	+	959.242i	0.124071	+	0.0451580i
$768$		0			0
$769$	6348.77	+	5327.25i	0.297715	+	0.249812i	0.779392	−	0.626536i	$-0.215528\pi$
$769$	6348.77	+	5327.25i	0.297715	+	0.249812i	−0.481678	+	0.876348i	$0.659972\pi$
$770$	28573.7	+	23976.2i	1.33731	+	1.12213i
$771$		0			0
$772$	−7627.96	−	2776.35i	−0.355617	−	0.129434i
$773$	−6513.50	+	11281.7i	−0.303072	+	0.524935i	−0.976830	−	0.214016i	$-0.931345\pi$
$773$	−6513.50	+	11281.7i	−0.303072	+	0.524935i	0.673759	+	0.738952i	$0.264679\pi$
$774$		0			0
$775$	16151.0	+	27974.4i	0.748597	+	1.29661i
$776$	−1001.20	−	5678.07i	−0.0463156	−	0.262669i
$777$		0			0
$778$	6578.68	−	2394.44i	0.303158	−	0.110341i
$779$	−4611.94	+	26155.6i	−0.212118	+	1.20298i
$780$		0			0
$781$	−2811.48	+	2359.11i	−0.128812	+	0.108086i
$782$	−154.761			−0.00707703
$783$		0			0
$784$	13860.4			0.631395
$785$	−9178.07	+	7701.32i	−0.417299	+	0.350155i
$786$		0			0
$787$	−598.294	+	3393.09i	−0.0270989	+	0.153686i	−0.995355	−	0.0962759i	$-0.969307\pi$
$787$	−598.294	+	3393.09i	−0.0270989	+	0.153686i	0.968256	+	0.249962i	$0.0804180\pi$
$788$	−2121.61	+	772.202i	−0.0959126	+	0.0349093i
$789$		0			0
$790$	6451.01	+	36585.5i	0.290527	+	1.64766i
$791$	−19720.7	−	34157.3i	−0.886458	−	1.53539i
$792$		0			0
$793$	4391.96	−	7607.09i	0.196675	−	0.340650i
$794$	16840.8	+	6129.55i	0.752717	+	0.273967i
$795$		0			0
$796$	9123.40	+	7655.45i	0.406244	+	0.340879i
$797$	−26755.6	−	22450.6i	−1.18912	−	0.997792i	−0.999874	−	0.0158628i	$-0.994950\pi$
$797$	−26755.6	−	22450.6i	−1.18912	−	0.997792i	−0.189248	−	0.981929i	$-0.560605\pi$
$798$		0			0
$799$	1738.26	+	632.673i	0.0769650	+	0.0280130i
$800$	−3421.55	+	5926.30i	−0.151213	+	0.261908i
$801$		0			0
$802$	−1051.51	−	1821.28i	−0.0462971	−	0.0801889i
$803$	−1869.74	−	10603.8i	−0.0821688	−	0.466003i
$804$		0			0
$805$	3804.71	−	1384.80i	0.166582	−	0.0606308i
$806$	640.407	−	3631.93i	0.0279868	−	0.158721i
$807$		0			0
$808$	4017.38	−	3370.98i	0.174914	−	0.146771i
$809$	2065.17			0.0897498			0.0448749	−	0.998993i	$-0.485711\pi$
$809$	2065.17			0.0897498			0.0448749	+	0.998993i	$0.485711\pi$
$810$		0			0
$811$	−26833.1			−1.16182			−0.580911	−	0.813967i	$-0.697304\pi$
$811$	−26833.1			−1.16182			−0.580911	+	0.813967i	$0.697304\pi$
$812$	14266.6	−	11971.1i	0.616577	−	0.517369i
$813$		0			0
$814$	1639.72	−	9299.29i	0.0706044	−	0.400418i
$815$	46636.3	−	16974.2i	2.00442	−	0.729548i
$816$		0			0
$817$	4686.85	+	26580.4i	0.200700	+	1.13823i
$818$	88.3827	+	153.083i	0.00377779	+	0.00654332i
$819$		0			0
$820$	−12578.2	+	21786.1i	−0.535672	+	0.927811i
$821$	−31911.2	−	11614.7i	−1.35653	−	0.493736i	−0.441549	−	0.897237i	$-0.645571\pi$
$821$	−31911.2	−	11614.7i	−1.35653	−	0.493736i	−0.914979	+	0.403501i	$0.867793\pi$
$822$		0			0
$823$	−25930.6	−	21758.4i	−1.09828	−	0.921567i	−0.100973	−	0.994889i	$-0.532195\pi$
$823$	−25930.6	−	21758.4i	−1.09828	−	0.921567i	−0.997308	+	0.0733220i	$0.976640\pi$
$824$	3358.85	+	2818.41i	0.142004	+	0.119155i
$825$		0			0
$826$	−15015.0	−	5465.02i	−0.632494	−	0.230209i
$827$	8456.66	−	14647.4i	0.355583	−	0.615887i	−0.631635	−	0.775266i	$-0.717616\pi$
$827$	8456.66	−	14647.4i	0.355583	−	0.615887i	0.987217	+	0.159379i	$0.0509492\pi$
$828$		0			0
$829$	−13539.3	−	23450.7i	−0.567235	−	0.982480i	−0.996838	−	0.0794620i	$-0.974680\pi$
$829$	−13539.3	−	23450.7i	−0.567235	−	0.982480i	0.429603	−	0.903018i	$-0.358654\pi$
$830$	−7250.12	−	41117.5i	−0.303199	−	1.71953i
$831$		0			0
$832$	734.166	−	267.215i	0.0305921	−	0.0111346i
$833$	−1840.29	+	10436.8i	−0.0765453	+	0.434110i
$834$		0			0
$835$	−5029.69	+	4220.41i	−0.208454	+	0.174914i
$836$	−9059.49			−0.374796
$837$		0			0
$838$	−5566.35			−0.229459
$839$	−17687.5	+	14841.6i	−0.727818	+	0.610712i	−0.929536	−	0.368732i	$-0.879792\pi$
$839$	−17687.5	+	14841.6i	−0.727818	+	0.610712i	0.201718	+	0.979444i	$0.435348\pi$
$840$		0			0
$841$	−1122.24	+	6364.57i	−0.0460144	+	0.260961i
$842$	18003.8	−	6552.85i	0.736879	−	0.268202i
$843$		0			0
$844$	2052.30	+	11639.1i	0.0837002	+	0.474687i
$845$	−18849.4	−	32648.1i	−0.767382	−	1.32914i
$846$		0			0
$847$	8383.08	−	14519.9i	0.340078	−	0.589032i
$848$	4958.53	+	1804.76i	0.200798	+	0.0730844i
$849$		0			0
$850$	−4008.18	−	3363.27i	−0.161741	−	0.135717i
$851$	−785.190	−	658.852i	−0.0316286	−	0.0265396i
$852$		0			0
$853$	−16220.4	−	5903.74i	−0.651085	−	0.236976i	−0.00470255	−	0.999989i	$-0.501497\pi$
$853$	−16220.4	−	5903.74i	−0.651085	−	0.236976i	−0.646383	+	0.763013i	$0.723719\pi$
$854$	−25022.0	+	43339.4i	−1.00262	+	1.73658i
$855$		0			0
$856$	−7488.89	−	12971.1i	−0.299025	−	0.517926i
$857$	−1490.25	−	8451.61i	−0.0594001	−	0.336874i	0.940596	−	0.339527i	$-0.110267\pi$
$857$	−1490.25	−	8451.61i	−0.0594001	−	0.336874i	−0.999996	+	0.00265221i	$0.999156\pi$
$858$		0			0
$859$	−2167.81	+	789.017i	−0.0861055	+	0.0313398i	−0.384714	−	0.923036i	$-0.625700\pi$
$859$	−2167.81	+	789.017i	−0.0861055	+	0.0313398i	0.298608	+	0.954376i	$0.403478\pi$
$860$	−4439.33	+	25176.7i	−0.176023	+	0.998277i
$861$		0			0
$862$	−10445.8	+	8765.10i	−0.412746	+	0.346335i
$863$	23551.9			0.928988			0.464494	−	0.885576i	$-0.346236\pi$
$863$	23551.9			0.928988			0.464494	+	0.885576i	$0.346236\pi$
$864$		0			0
$865$	5960.63			0.234298
$866$	−7370.01	+	6184.17i	−0.289195	+	0.242664i
$867$		0			0
$868$	−3648.55	+	20691.9i	−0.142673	+	0.809136i
$869$	−27626.8	+	10055.3i	−1.07845	+	0.392524i
$870$		0			0
$871$	−816.176	−	4628.76i	−0.0317509	−	0.180069i
$872$	1441.65	+	2497.01i	0.0559868	+	0.0969719i
$873$		0			0
$874$	−491.696	+	851.642i	−0.0190296	+	0.0329602i
$875$	53443.3	+	19451.8i	2.06481	+	0.751531i
$876$		0			0
$877$	−26106.7	−	21906.1i	−1.00520	−	0.843464i	−0.0175048	−	0.999847i	$-0.505572\pi$
$877$	−26106.7	−	21906.1i	−1.00520	−	0.843464i	−0.987697	+	0.156383i	$0.950017\pi$
$878$	18671.6	+	15667.3i	0.717694	+	0.602217i
$879$		0			0
$880$	−8063.55	−	2934.89i	−0.308889	−	0.112426i
$881$	−18402.0	+	31873.2i	−0.703721	+	1.21888i	0.263430	+	0.964679i	$0.415146\pi$
$881$	−18402.0	+	31873.2i	−0.703721	+	1.21888i	−0.967151	+	0.254203i	$0.918187\pi$
$882$		0			0
$883$	−4552.15	−	7884.56i	−0.173490	−	0.300494i	0.766147	−	0.642665i	$-0.222171\pi$
$883$	−4552.15	−	7884.56i	−0.173490	−	0.300494i	−0.939638	+	0.342171i	$0.888838\pi$
$884$	103.734	+	588.302i	0.00394676	+	0.0223832i
$885$		0			0
$886$	−18157.4	+	6608.75i	−0.688498	+	0.250593i
$887$	−1149.27	+	6517.85i	−0.0435049	+	0.246728i	−0.998803	−	0.0489161i	$-0.984423\pi$
$887$	−1149.27	+	6517.85i	−0.0435049	+	0.246728i	0.955298	+	0.295645i	$0.0955344\pi$
$888$		0			0
$889$	−7981.47	+	6697.25i	−0.301114	+	0.252664i
$890$	−23952.6			−0.902129
$891$		0			0
$892$	−5917.26			−0.222113
$893$	9004.23	−	7555.45i	0.337419	−	0.283128i
$894$		0			0
$895$	−262.581	+	1489.17i	−0.00980685	+	0.0556174i
$896$	−4182.71	+	1522.38i	−0.155954	+	0.0567626i
$897$		0			0
$898$	176.035	+	998.341i	0.00654159	+	0.0370992i
$899$	10112.1	+	17514.7i	0.375148	+	0.649775i
$900$		0			0
$901$	−2017.33	+	3494.12i	−0.0745916	+	0.129196i
$902$	−18707.8	−	6809.08i	−0.690578	−	0.251350i
$903$		0			0
$904$	6950.79	+	5832.41i	0.255730	+	0.214583i
$905$	5002.04	+	4197.21i	0.183728	+	0.154166i
$906$		0			0
$907$	3051.76	+	1110.75i	0.111722	+	0.0406635i	0.397276	−	0.917699i	$-0.369955\pi$
$907$	3051.76	+	1110.75i	0.111722	+	0.0406635i	−0.285554	+	0.958363i	$0.592178\pi$
$908$	−9865.06	+	17086.8i	−0.360555	+	0.624499i
$909$		0			0
$910$	−7814.35	−	13534.8i	−0.284663	−	0.493050i
$911$	−5990.86	−	33975.8i	−0.217877	−	1.23564i	−0.875844	−	0.482595i	$-0.839694\pi$
$911$	−5990.86	−	33975.8i	−0.217877	−	1.23564i	0.657967	−	0.753047i	$-0.271417\pi$
$912$		0			0
$913$	31049.0	−	11300.9i	1.12549	−	0.409645i
$914$	5772.83	−	32739.3i	0.208915	−	1.18482i
$915$		0			0
$916$	14690.5	−	12326.8i	0.529899	−	0.444638i
$917$	60444.0			2.17670
$918$		0			0
$919$	42888.3			1.53945			0.769724	−	0.638376i	$-0.220394\pi$
$919$	42888.3			1.53945			0.769724	+	0.638376i	$0.220394\pi$
$920$	−713.538	+	598.729i	−0.0255703	+	0.0214560i
$921$		0			0
$922$	736.703	−	4178.05i	0.0263146	−	0.149237i
$923$	1445.03	−	525.947i	0.0515316	−	0.0187560i
$924$		0			0
$925$	−6017.60	−	34127.5i	−0.213900	−	1.21309i
$926$	8307.85	+	14389.6i	0.294830	+	0.510661i
$927$		0			0
$928$	−2142.22	+	3710.44i	−0.0757779	+	0.131251i
$929$	−13916.3	−	5065.12i	−0.491473	−	0.178882i	0.0843816	−	0.996434i	$-0.473109\pi$
$929$	−13916.3	−	5065.12i	−0.491473	−	0.178882i	−0.575855	+	0.817552i	$0.695331\pi$
$930$		0			0
$931$	51586.4	+	43286.1i	1.81598	+	1.52379i
$932$	−11475.1	−	9628.79i	−0.403306	−	0.338414i
$933$		0			0
$934$	25930.9	+	9438.07i	0.908442	+	0.330646i
$935$	3280.58	−	5682.14i	0.114745	−	0.198744i
$936$		0			0
$937$	11756.8	+	20363.3i	0.409900	+	0.709968i	0.994878	−	0.101081i	$-0.0322302\pi$
$937$	11756.8	+	20363.3i	0.409900	+	0.709968i	−0.584978	+	0.811049i	$0.698897\pi$
$938$	4649.95	+	26371.2i	0.161862	+	0.917962i
$939$		0			0
$940$	10462.0	−	3807.86i	0.363014	−	0.132126i
$941$	9822.20	−	55704.5i	0.340271	−	1.92977i	−0.0269506	−	0.999637i	$-0.508580\pi$
$941$	9822.20	−	55704.5i	0.340271	−	1.92977i	0.367221	−	0.930134i	$-0.380309\pi$
$942$		0			0
$943$	−1655.44	+	1389.08i	−0.0571670	+	0.0479688i
$944$	3675.94			0.126739
$945$		0			0
$946$	−20231.8			−0.695340
$947$	28200.4	−	23662.9i	0.967676	−	0.811976i	−0.0145088	−	0.999895i	$-0.504618\pi$
$947$	28200.4	−	23662.9i	0.967676	−	0.811976i	0.982185	+	0.187918i	$0.0601740\pi$
$948$		0			0
$949$	−783.412	+	4442.95i	−0.0267973	+	0.151975i
$950$	−31242.4	+	11371.3i	−1.06699	+	0.388351i
$951$		0			0
$952$	−590.994	−	3351.69i	−0.0201200	−	0.114106i
$953$	2900.39	+	5023.62i	0.0985863	+	0.170756i	0.911100	−	0.412186i	$-0.135235\pi$
$953$	2900.39	+	5023.62i	0.0985863	+	0.170756i	−0.812513	+	0.582942i	$0.801901\pi$
$954$		0			0
$955$	48169.1	−	83431.3i	1.63216	−	2.82699i
$956$	20077.9	+	7307.74i	0.679251	+	0.247227i
$957$		0			0
$958$	−23031.6	−	19325.8i	−0.776741	−	0.651763i
$959$	−38804.9	−	32561.2i	−1.30665	−	1.09641i
$960$		0			0
$961$	6553.62	+	2385.32i	0.219987	+	0.0800686i
$962$	−1978.24	+	3426.40i	−0.0663003	+	0.114835i
$963$		0			0
$964$	13656.5	+	23653.7i	0.456271	+	0.790285i
$965$	−6486.86	−	36788.8i	−0.216393	−	1.22723i
$966$		0			0
$967$	−44676.5	+	16260.9i	−1.48573	+	0.540761i	−0.952321	−	0.305098i	$-0.901311\pi$
$967$	−44676.5	+	16260.9i	−1.48573	+	0.540761i	−0.533407	+	0.845859i	$0.679089\pi$
$968$	−669.778	+	3798.50i	−0.0222391	+	0.126124i
$969$		0			0
$970$	20325.7	−	17055.3i	0.672803	−	0.564549i
$971$	51826.6			1.71287			0.856434	−	0.516257i	$-0.172675\pi$
$971$	51826.6			1.71287			0.856434	+	0.516257i	$0.172675\pi$
$972$		0			0
$973$	43633.2			1.43763
$974$	26830.1	−	22513.1i	0.882640	−	0.740623i
$975$		0			0
$976$	1999.17	−	11337.9i	0.0655654	−	0.371840i
$977$	9808.90	−	3570.15i	0.321202	−	0.116908i	−0.176387	−	0.984321i	$-0.556441\pi$
$977$	9808.90	−	3570.15i	0.321202	−	0.116908i	0.497589	+	0.867413i	$0.334219\pi$
$978$		0			0
$979$	−3291.63	−	18667.7i	−0.107457	−	0.609422i
$980$	31892.4	+	55239.3i	1.03956	+	1.80057i
$981$		0			0
$982$	4085.95	−	7077.08i	0.132778	−	0.229978i
$983$	2938.25	+	1069.44i	0.0953365	+	0.0346996i	0.389248	−	0.921133i	$-0.372735\pi$
$983$	2938.25	+	1069.44i	0.0953365	+	0.0346996i	−0.293912	+	0.955833i	$0.594957\pi$
$984$		0			0
$985$	−7959.30	−	6678.65i	−0.257467	−	0.216040i
$986$	−2509.51	−	2105.73i	−0.0810539	−	0.0680123i
$987$		0			0
$988$	3566.97	+	1298.27i	0.114859	+	0.0418052i
$989$	−1098.06	+	1901.90i	−0.0353046	+	0.0611494i
$990$		0			0
$991$	13315.7	+	23063.5i	0.426829	+	0.739289i	0.996589	−	0.0825218i	$-0.0262974\pi$
$991$	13315.7	+	23063.5i	0.426829	+	0.739289i	−0.569761	+	0.821811i	$0.692964\pi$
$992$	−839.358	−	4760.24i	−0.0268646	−	0.152357i
$993$		0			0
$994$	−8232.66	+	2996.44i	−0.262700	+	0.0956151i
$995$	−9517.33	+	53975.4i	−0.303236	+	1.71974i
$996$		0			0
$997$	−1492.48	+	1252.34i	−0.0474097	+	0.0397814i	−0.666185	−	0.745787i	$-0.732074\pi$
$997$	−1492.48	+	1252.34i	−0.0474097	+	0.0397814i	0.618775	+	0.785568i	$0.287629\pi$
$998$	19973.3			0.633509
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.37.5		30
3.2	odd	2		54.4.e.b.49.3	yes	30
27.4	even	9		1458.4.a.j.1.1		15
27.11	odd	18		54.4.e.b.43.3	✓	30
27.16	even	9	inner	162.4.e.b.127.5		30
27.23	odd	18		1458.4.a.i.1.15		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.43.3	✓	30	27.11	odd	18
54.4.e.b.49.3	yes	30	3.2	odd	2
162.4.e.b.37.5		30	1.1	even	1	trivial
162.4.e.b.127.5		30	27.16	even	9	inner
1458.4.a.i.1.15		15	27.23	odd	18
1458.4.a.j.1.1		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(17.2977 - 6.29584i) q^{5} +(6.03855 + 34.2463i) q^{7} +(-4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(17.2977 - 6.29584i) q^{5} +(6.03855 + 34.2463i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(18.4078 - 31.8832i) q^{10} +(27.3782 + 9.96484i) q^{11} +(-9.35152 - 7.84686i) q^{13} +(53.2778 + 44.7054i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(6.11689 - 10.5948i) q^{17} +(-38.8683 - 67.3218i) q^{19} +(-12.7859 - 72.5126i) q^{20} +(54.7563 - 19.9297i) q^{22} +(1.09835 - 6.22906i) q^{23} +(163.816 - 137.458i) q^{25} -24.4151 q^{26} +139.099 q^{28} +(102.565 - 86.0622i) q^{29} +(-26.2299 + 148.757i) q^{31} +(-30.0702 + 10.9446i) q^{32} +(-4.24875 - 24.0958i) q^{34} +(320.062 + 554.364i) q^{35} +(81.0251 - 140.340i) q^{37} +(-146.097 - 53.1749i) q^{38} +(-112.810 - 94.6584i) q^{40} +(-261.723 - 219.612i) q^{41} +(-326.265 - 118.751i) q^{43} +(58.2705 - 100.927i) q^{44} +(-6.32515 - 10.9555i) q^{46} +(26.2565 + 148.908i) q^{47} +(-814.032 + 296.283i) q^{49} +(74.2683 - 421.196i) q^{50} +(-37.4061 + 31.3874i) q^{52} -329.797 q^{53} +536.316 q^{55} +(213.111 - 178.822i) q^{56} +(46.4991 - 263.710i) q^{58} +(-215.891 + 78.5777i) q^{59} +(124.948 + 708.616i) q^{61} +(151.052 + 261.630i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(-211.162 - 76.8567i) q^{65} +(294.944 + 247.487i) q^{67} +(-37.4865 - 31.4549i) q^{68} +(1203.04 + 437.871i) q^{70} +(-62.9842 + 109.092i) q^{71} +(-184.783 - 320.053i) q^{73} +(-56.2794 - 319.177i) q^{74} +(-292.194 + 106.350i) q^{76} +(-175.935 + 997.775i) q^{77} +(-773.000 + 648.624i) q^{79} -294.525 q^{80} -683.310 q^{82} +(868.755 - 728.972i) q^{83} +(39.1050 - 221.776i) q^{85} +(-652.531 + 237.502i) q^{86} +(-40.4743 - 229.541i) q^{88} +(-325.306 - 563.446i) q^{89} +(212.256 - 367.639i) q^{91} +(-23.7748 - 8.65332i) q^{92} +(231.660 + 194.386i) q^{94} +(-1096.18 - 919.803i) q^{95} +(677.244 + 246.497i) q^{97} +(-866.275 + 1500.43i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) 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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