LMFDB - Embedded newform 162.4.e.a.73.4

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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	162.73
Dual form			162.4.e.a.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(12.8013 - 10.7416i) q^{5} +(-9.76778 + 3.55518i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(12.8013 - 10.7416i) q^{5} +(-9.76778 + 3.55518i) q^{7} +(4.00000 - 6.92820i) q^{8} +(16.7110 + 28.9442i) q^{10} +(-37.6631 - 31.6031i) q^{11} +(-5.86986 - 33.2897i) q^{13} +(-3.61003 - 20.4735i) q^{14} +(12.2567 + 10.2846i) q^{16} +(-55.3955 - 95.9478i) q^{17} +(6.99034 - 12.1076i) q^{19} +(-62.8126 + 22.8619i) q^{20} +(75.3263 - 63.2062i) q^{22} +(185.201 + 67.4078i) q^{23} +(26.7863 - 151.913i) q^{25} +67.6064 q^{26} +41.5786 q^{28} +(19.6811 - 111.617i) q^{29} +(67.6281 + 24.6146i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(208.219 - 75.7855i) q^{34} +(-86.8523 + 150.433i) q^{35} +(89.7337 + 155.423i) q^{37} +(21.4197 + 17.9732i) q^{38} +(-23.2146 - 131.657i) q^{40} +(-81.4849 - 462.124i) q^{41} +(14.3408 + 12.0333i) q^{43} +(98.3314 + 170.315i) q^{44} +(-197.087 + 341.365i) q^{46} +(-134.437 + 48.9312i) q^{47} +(-179.983 + 151.024i) q^{49} +(289.907 + 105.517i) q^{50} +(-23.4795 + 133.159i) q^{52} -99.0786 q^{53} -821.606 q^{55} +(-14.4401 + 81.8939i) q^{56} +(213.008 + 77.5284i) q^{58} +(106.415 - 89.2927i) q^{59} +(535.695 - 194.977i) q^{61} +(-71.9683 + 124.653i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-432.726 - 363.100i) q^{65} +(-122.797 - 696.417i) q^{67} +(76.9546 + 436.431i) q^{68} +(-266.131 - 223.310i) q^{70} +(189.267 + 327.820i) q^{71} +(-228.464 + 395.712i) q^{73} +(-337.288 + 122.763i) q^{74} +(-42.8393 + 35.9464i) q^{76} +(480.240 + 174.793i) q^{77} +(-180.088 + 1021.33i) q^{79} +267.375 q^{80} +938.505 q^{82} +(-105.632 + 599.067i) q^{83} +(-1739.77 - 633.224i) q^{85} +(-28.6815 + 24.0666i) q^{86} +(-369.605 + 134.525i) q^{88} +(-828.921 + 1435.73i) q^{89} +(175.686 + 304.298i) q^{91} +(-603.910 - 506.741i) q^{92} +(-49.6860 - 281.784i) q^{94} +(-40.5695 - 230.081i) q^{95} +(292.250 + 245.226i) q^{97} +(-234.951 - 406.947i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	12.8013	−	10.7416i	1.14499	−	0.960758i	0.145396	−	0.989374i	$-0.453554\pi$
$5$	12.8013	−	10.7416i	1.14499	−	0.960758i	0.999590	+	0.0286161i	$0.00911002\pi$
$6$		0			0
$7$	−9.76778	+	3.55518i	−0.527411	+	0.191962i	−0.591982	−	0.805951i	$-0.701654\pi$
$7$	−9.76778	+	3.55518i	−0.527411	+	0.191962i	0.0645711	+	0.997913i	$0.479432\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$		0			0
$10$	16.7110	+	28.9442i	0.528447	+	0.915297i
$11$	−37.6631	−	31.6031i	−1.03235	−	0.866245i	−0.0412221	−	0.999150i	$-0.513125\pi$
$11$	−37.6631	−	31.6031i	−1.03235	−	0.866245i	−0.991129	+	0.132905i	$0.957570\pi$
$12$		0			0
$13$	−5.86986	−	33.2897i	−0.125231	−	0.710222i	−0.981170	−	0.193145i	$-0.938131\pi$
$13$	−5.86986	−	33.2897i	−0.125231	−	0.710222i	0.855939	−	0.517077i	$-0.172980\pi$
$14$	−3.61003	−	20.4735i	−0.0689157	−	0.390841i
$15$		0			0
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	−55.3955	−	95.9478i	−0.790316	−	1.36887i	−0.925771	−	0.378084i	$-0.876583\pi$
$17$	−55.3955	−	95.9478i	−0.790316	−	1.36887i	0.135455	−	0.990783i	$-0.456750\pi$
$18$		0			0
$19$	6.99034	−	12.1076i	0.0844050	−	0.146194i	−0.820733	−	0.571313i	$-0.806434\pi$
$19$	6.99034	−	12.1076i	0.0844050	−	0.146194i	0.905138	+	0.425119i	$0.139768\pi$
$20$	−62.8126	+	22.8619i	−0.702267	+	0.255604i
$21$		0			0
$22$	75.3263	−	63.2062i	0.729982	−	0.612528i
$23$	185.201	+	67.4078i	1.67901	+	0.611108i	0.993173	−	0.116651i	$-0.0372159\pi$
$23$	185.201	+	67.4078i	1.67901	+	0.611108i	0.685833	+	0.727759i	$0.259438\pi$
$24$		0			0
$25$	26.7863	−	151.913i	0.214290	−	1.21530i
$26$	67.6064			0.509950
$27$		0			0
$28$	41.5786			0.280629
$29$	19.6811	−	111.617i	0.126024	−	0.714716i	−0.854671	−	0.519170i	$-0.826241\pi$
$29$	19.6811	−	111.617i	0.126024	−	0.714716i	0.980695	−	0.195546i	$-0.0626479\pi$
$30$		0			0
$31$	67.6281	+	24.6146i	0.391818	+	0.142610i	0.530414	−	0.847739i	$-0.322037\pi$
$31$	67.6281	+	24.6146i	0.391818	+	0.142610i	−0.138595	+	0.990349i	$0.544259\pi$
$32$	−24.5134	+	20.5692i	−0.135419	+	0.113630i
$33$		0			0
$34$	208.219	−	75.7855i	1.05027	−	0.382268i
$35$	−86.8523	+	150.433i	−0.419449	+	0.726507i
$36$		0			0
$37$	89.7337	+	155.423i	0.398706	+	0.690579i	0.993567	−	0.113250i	$-0.0361260\pi$
$37$	89.7337	+	155.423i	0.398706	+	0.690579i	−0.594860	+	0.803829i	$0.702793\pi$
$38$	21.4197	+	17.9732i	0.0914402	+	0.0767274i
$39$		0			0
$40$	−23.2146	−	131.657i	−0.0917638	−	0.520419i
$41$	−81.4849	−	462.124i	−0.310385	−	1.76028i	−0.597004	−	0.802238i	$-0.703642\pi$
$41$	−81.4849	−	462.124i	−0.310385	−	1.76028i	0.286619	−	0.958045i	$-0.407469\pi$
$42$		0			0
$43$	14.3408	+	12.0333i	0.0508592	+	0.0426759i	0.667863	−	0.744284i	$-0.267209\pi$
$43$	14.3408	+	12.0333i	0.0508592	+	0.0426759i	−0.617004	+	0.786960i	$0.711654\pi$
$44$	98.3314	+	170.315i	0.336910	+	0.583545i
$45$		0			0
$46$	−197.087	+	341.365i	−0.631715	+	1.09416i
$47$	−134.437	+	48.9312i	−0.417228	+	0.151858i	−0.542099	−	0.840314i	$-0.682370\pi$
$47$	−134.437	+	48.9312i	−0.417228	+	0.151858i	0.124872	+	0.992173i	$0.460148\pi$
$48$		0			0
$49$	−179.983	+	151.024i	−0.524732	+	0.440302i
$50$	289.907	+	105.517i	0.819980	+	0.298448i
$51$		0			0
$52$	−23.4795	+	133.159i	−0.0626157	+	0.355111i
$53$	−99.0786			−0.256783			−0.128391	−	0.991724i	$-0.540981\pi$
$53$	−99.0786			−0.256783			−0.128391	+	0.991724i	$0.540981\pi$
$54$		0			0
$55$	−821.606			−2.01428
$56$	−14.4401	+	81.8939i	−0.0344579	+	0.195420i
$57$		0			0
$58$	213.008	+	77.5284i	0.482229	+	0.175517i
$59$	106.415	−	89.2927i	0.234814	−	0.197032i	−0.517786	−	0.855510i	$-0.673244\pi$
$59$	106.415	−	89.2927i	0.234814	−	0.197032i	0.752600	+	0.658478i	$0.228799\pi$
$60$		0			0
$61$	535.695	−	194.977i	1.12440	−	0.409250i	0.288147	−	0.957586i	$-0.406961\pi$
$61$	535.695	−	194.977i	1.12440	−	0.409250i	0.836258	+	0.548337i	$0.184739\pi$
$62$	−71.9683	+	124.653i	−0.147419	+	0.255337i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−432.726	−	363.100i	−0.825739	−	0.692878i
$66$		0			0
$67$	−122.797	−	696.417i	−0.223911	−	1.26986i	−0.864755	−	0.502193i	$-0.832527\pi$
$67$	−122.797	−	696.417i	−0.223911	−	1.26986i	0.640844	−	0.767671i	$-0.278585\pi$
$68$	76.9546	+	436.431i	0.137237	+	0.778309i
$69$		0			0
$70$	−266.131	−	223.310i	−0.454411	−	0.381296i
$71$	189.267	+	327.820i	0.316365	+	0.547960i	0.979727	−	0.200339i	$-0.0642044\pi$
$71$	189.267	+	327.820i	0.316365	+	0.547960i	−0.663362	+	0.748299i	$0.730871\pi$
$72$		0			0
$73$	−228.464	+	395.712i	−0.366298	+	0.634446i	−0.988984	−	0.148026i	$-0.952708\pi$
$73$	−228.464	+	395.712i	−0.366298	+	0.634446i	0.622686	+	0.782472i	$0.286042\pi$
$74$	−337.288	+	122.763i	−0.529851	+	0.192850i
$75$		0			0
$76$	−42.8393	+	35.9464i	−0.0646580	+	0.0542545i
$77$	480.240	+	174.793i	0.710759	+	0.258695i
$78$		0			0
$79$	−180.088	+	1021.33i	−0.256475	+	1.45454i	0.535783	+	0.844356i	$0.320017\pi$
$79$	−180.088	+	1021.33i	−0.256475	+	1.45454i	−0.792258	+	0.610187i	$0.791094\pi$
$80$	267.375			0.373668
$81$		0			0
$82$	938.505			1.26391
$83$	−105.632	+	599.067i	−0.139694	+	0.792242i	0.831782	+	0.555103i	$0.187321\pi$
$83$	−105.632	+	599.067i	−0.139694	+	0.792242i	−0.971476	+	0.237140i	$0.923790\pi$
$84$		0			0
$85$	−1739.77	−	633.224i	−2.22005	−	0.808032i
$86$	−28.6815	+	24.0666i	−0.0359629	+	0.0301764i
$87$		0			0
$88$	−369.605	+	134.525i	−0.447728	+	0.162960i
$89$	−828.921	+	1435.73i	−0.987252	+	1.70997i	−0.355786	+	0.934567i	$0.615787\pi$
$89$	−828.921	+	1435.73i	−0.987252	+	1.70997i	−0.631466	+	0.775403i	$0.717547\pi$
$90$		0			0
$91$	175.686	+	304.298i	0.202384	+	0.350539i
$92$	−603.910	−	506.741i	−0.684369	−	0.574254i
$93$		0			0
$94$	−49.6860	−	281.784i	−0.0545183	−	0.309189i
$95$	−40.5695	−	230.081i	−0.0438142	−	0.248482i
$96$		0			0
$97$	292.250	+	245.226i	0.305912	+	0.256690i	0.782800	−	0.622274i	$-0.213791\pi$
$97$	292.250	+	245.226i	0.305912	+	0.256690i	−0.476888	+	0.878964i	$0.658235\pi$
$98$	−234.951	−	406.947i	−0.242180	−	0.419468i
$99$		0			0
$100$	−308.512	+	534.359i	−0.308512	+	0.534359i
$101$	285.464	−	103.900i	0.281235	−	0.102361i	−0.197552	−	0.980293i	$-0.563299\pi$
$101$	285.464	−	103.900i	0.281235	−	0.102361i	0.478787	+	0.877931i	$0.341077\pi$
$102$		0			0
$103$	−390.931	+	328.030i	−0.373977	+	0.313804i	−0.810332	−	0.585971i	$-0.800713\pi$
$103$	−390.931	+	328.030i	−0.373977	+	0.313804i	0.436356	+	0.899774i	$0.356269\pi$
$104$	−254.117	−	92.4910i	−0.239598	−	0.0872066i
$105$		0			0
$106$	34.4096	−	195.147i	0.0315298	−	0.178814i
$107$	1024.68			0.925786			0.462893	−	0.886414i	$-0.346811\pi$
$107$	1024.68			0.925786			0.462893	+	0.886414i	$0.346811\pi$
$108$		0			0
$109$	209.195			0.183828			0.0919139	−	0.995767i	$-0.470702\pi$
$109$	209.195			0.183828			0.0919139	+	0.995767i	$0.470702\pi$
$110$	285.341	−	1618.25i	0.247329	−	1.40267i
$111$		0			0
$112$	−156.285	−	56.8829i	−0.131853	−	0.0479905i
$113$	1349.44	−	1132.32i	1.12341	−	0.942651i	0.124636	−	0.992203i	$-0.460224\pi$
$113$	1349.44	−	1132.32i	1.12341	−	0.942651i	0.998772	+	0.0495520i	$0.0157794\pi$
$114$		0			0
$115$	3094.89	−	1126.45i	2.50957	−	0.913407i
$116$	−226.678	+	392.618i	−0.181435	+	0.314255i
$117$		0			0
$118$	138.915	+	240.607i	0.108374	+	0.187709i
$119$	882.203	+	740.256i	0.679591	+	0.570245i
$120$		0			0
$121$	188.628	+	1069.77i	0.141719	+	0.803730i
$122$	197.985	+	1122.83i	0.146924	+	0.833246i
$123$		0			0
$124$	−220.524	−	185.041i	−0.159707	−	0.134010i
$125$	−244.448	−	423.397i	−0.174913	−	0.302958i
$126$		0			0
$127$	985.867	−	1707.57i	0.688831	−	1.19309i	−0.283385	−	0.959006i	$-0.591458\pi$
$127$	985.867	−	1707.57i	0.688831	−	1.19309i	0.972216	−	0.234084i	$-0.0752092\pi$
$128$	120.281	−	43.7786i	0.0830579	−	0.0302306i
$129$		0			0
$130$	865.452	−	726.201i	0.583886	−	0.489939i
$131$	−2257.77	−	821.762i	−1.50582	−	0.548074i	−0.548260	−	0.836308i	$-0.684710\pi$
$131$	−2257.77	−	821.762i	−1.50582	−	0.548074i	−0.957560	+	0.288234i	$0.906932\pi$
$132$		0			0
$133$	−25.2353	+	143.117i	−0.0164525	+	0.0933067i
$134$	1414.32			0.911782
$135$		0			0
$136$	−886.327			−0.558838
$137$	265.266	−	1504.40i	0.165425	−	0.938171i	−0.783200	−	0.621770i	$-0.786414\pi$
$137$	265.266	−	1504.40i	0.165425	−	0.938171i	0.948625	−	0.316402i	$-0.102475\pi$
$138$		0			0
$139$	2394.01	+	871.348i	1.46084	+	0.531703i	0.945597	−	0.325339i	$-0.105479\pi$
$139$	2394.01	+	871.348i	1.46084	+	0.531703i	0.515245	+	0.857043i	$0.327701\pi$
$140$	532.262	−	446.621i	0.321317	−	0.269617i
$141$		0			0
$142$	−711.412	+	258.933i	−0.420425	+	0.153022i
$143$	−830.979	+	1439.30i	−0.485944	+	0.841680i
$144$		0			0
$145$	−947.001	−	1640.25i	−0.542374	−	0.939419i
$146$	−700.056	−	587.416i	−0.396829	−	0.332979i
$147$		0			0
$148$	−124.657	−	706.963i	−0.0692346	−	0.392649i
$149$	−111.448	−	632.056i	−0.0612766	−	0.347517i	−0.999996	−	0.00283454i	$-0.999098\pi$
$149$	−111.448	−	632.056i	−0.0612766	−	0.347517i	0.938719	−	0.344682i	$-0.112013\pi$
$150$		0			0
$151$	−222.382	−	186.601i	−0.119849	−	0.100565i	0.580893	−	0.813980i	$-0.302703\pi$
$151$	−222.382	−	186.601i	−0.119849	−	0.100565i	−0.700742	+	0.713414i	$0.747148\pi$
$152$	−55.9227	−	96.8610i	−0.0298417	−	0.0516873i
$153$		0			0
$154$	−511.061	+	885.183i	−0.267419	+	0.463182i
$155$	1130.13	−	411.334i	0.585640	−	0.213156i
$156$		0			0
$157$	−319.862	+	268.396i	−0.162597	+	0.136435i	−0.720456	−	0.693501i	$-0.756067\pi$
$157$	−319.862	+	268.396i	−0.162597	+	0.136435i	0.557859	+	0.829936i	$0.311623\pi$
$158$	−1949.09	−	709.410i	−0.981399	−	0.357200i
$159$		0			0
$160$	−92.8585	+	526.627i	−0.0458819	+	0.260209i
$161$	−2048.65			−1.00284
$162$		0			0
$163$	737.562			0.354419			0.177209	−	0.984173i	$-0.443293\pi$
$163$	737.562			0.354419			0.177209	+	0.984173i	$0.443293\pi$
$164$	−325.939	+	1848.49i	−0.155193	+	0.880141i
$165$		0			0
$166$	−1143.25	−	416.107i	−0.534537	−	0.194555i
$167$	−1305.69	+	1095.61i	−0.605015	+	0.507668i	−0.893053	−	0.449951i	$-0.851441\pi$
$167$	−1305.69	+	1095.61i	−0.605015	+	0.507668i	0.288038	+	0.957619i	$0.406997\pi$
$168$		0			0
$169$	990.759	−	360.607i	0.450960	−	0.164136i
$170$	1851.42	−	3206.76i	0.835280	−	1.44675i
$171$		0			0
$172$	−37.4411	−	64.8498i	−0.0165980	−	0.0287486i
$173$	1640.65	+	1376.67i	0.721020	+	0.605007i	0.927667	−	0.373408i	$-0.121811\pi$
$173$	1640.65	+	1376.67i	0.721020	+	0.605007i	−0.206647	+	0.978415i	$0.566255\pi$
$174$		0			0
$175$	278.434	+	1579.08i	0.120272	+	0.682098i
$176$	−136.601	−	774.700i	−0.0585037	−	0.331791i
$177$		0			0
$178$	−2539.96	−	2131.28i	−1.06954	−	0.897451i
$179$	−1060.67	−	1837.13i	−0.442894	−	0.767115i	0.555009	−	0.831844i	$-0.312715\pi$
$179$	−1060.67	−	1837.13i	−0.442894	−	0.767115i	−0.997903	+	0.0647298i	$0.979381\pi$
$180$		0			0
$181$	1293.27	−	2240.01i	0.531095	−	0.919883i	−0.468247	−	0.883598i	$-0.655114\pi$
$181$	1293.27	−	2240.01i	0.531095	−	0.919883i	0.999341	−	0.0362852i	$-0.0115525\pi$
$182$	−660.365	+	240.353i	−0.268953	+	0.0978910i
$183$		0			0
$184$	1207.82	−	1013.48i	0.483922	−	0.406059i
$185$	2818.20	+	1025.74i	1.11999	+	0.407644i
$186$		0			0
$187$	−945.882	+	5364.36i	−0.369892	+	2.09776i
$188$	572.261			0.222002
$189$		0			0
$190$	467.261			0.178414
$191$	−450.269	+	2553.60i	−0.170577	+	0.967393i	0.772548	+	0.634956i	$0.218982\pi$
$191$	−450.269	+	2553.60i	−0.170577	+	0.967393i	−0.943126	+	0.332437i	$0.892129\pi$
$192$		0			0
$193$	−244.482	−	88.9841i	−0.0911823	−	0.0331876i	0.296026	−	0.955180i	$-0.404338\pi$
$193$	−244.482	−	88.9841i	−0.0911823	−	0.0331876i	−0.387209	+	0.921992i	$0.626561\pi$
$194$	−584.499	+	490.453i	−0.216312	+	0.181508i
$195$		0			0
$196$	883.127	−	321.432i	0.321839	−	0.117140i
$197$	2112.26	−	3658.55i	0.763921	−	1.32315i	−0.176893	−	0.984230i	$-0.556605\pi$
$197$	2112.26	−	3658.55i	0.763921	−	1.32315i	0.940815	−	0.338921i	$-0.110062\pi$
$198$		0			0
$199$	1038.31	+	1798.40i	0.369868	+	0.640630i	0.989545	−	0.144227i	$-0.0460696\pi$
$199$	1038.31	+	1798.40i	0.369868	+	0.640630i	−0.619677	+	0.784857i	$0.712736\pi$
$200$	−945.336	−	793.231i	−0.334227	−	0.280450i
$201$		0			0
$202$	105.503	+	598.339i	0.0367484	+	0.208411i
$203$	204.578	+	1160.22i	0.0707319	+	0.401141i
$204$		0			0
$205$	−6007.06	−	5040.52i	−2.04659	−	1.71729i
$206$	−510.324	−	883.908i	−0.172602	−	0.298955i
$207$		0			0
$208$	270.426	−	468.391i	0.0901473	−	0.156140i
$209$	−645.917	+	235.095i	−0.213775	+	0.0778078i
$210$		0			0
$211$	838.724	−	703.773i	0.273650	−	0.229620i	−0.495626	−	0.868536i	$-0.665061\pi$
$211$	838.724	−	703.773i	0.273650	−	0.229620i	0.769276	+	0.638916i	$0.220617\pi$
$212$	372.414	+	135.548i	0.120649	+	0.0439125i
$213$		0			0
$214$	−355.866	+	2018.22i	−0.113675	+	0.644684i
$215$	312.838			0.0992343
$216$		0			0
$217$	−748.086			−0.234025
$218$	−72.6526	+	412.033i	−0.0225718	+	0.128011i
$219$		0			0
$220$	3088.23	+	1124.02i	0.946402	+	0.344462i
$221$	−2868.90	+	2407.30i	−0.873228	+	0.732725i
$222$		0			0
$223$	−2706.20	+	984.975i	−0.812648	+	0.295780i	−0.714717	−	0.699414i	$-0.753445\pi$
$223$	−2706.20	+	984.975i	−0.812648	+	0.295780i	−0.0979305	+	0.995193i	$0.531222\pi$
$224$	166.315	−	288.065i	0.0496087	−	0.0859248i
$225$		0			0
$226$	1761.57	+	3051.14i	0.518487	+	0.898047i
$227$	2912.77	+	2444.11i	0.851663	+	0.714630i	0.960155	−	0.279467i	$-0.0901578\pi$
$227$	2912.77	+	2444.11i	0.851663	+	0.714630i	−0.108492	+	0.994097i	$0.534602\pi$
$228$		0			0
$229$	723.744	+	4104.56i	0.208849	+	1.18444i	0.891267	+	0.453478i	$0.149817\pi$
$229$	723.744	+	4104.56i	0.208849	+	1.18444i	−0.682418	+	0.730962i	$0.739072\pi$
$230$	1143.83	+	6486.96i	0.327920	+	1.85973i
$231$		0			0
$232$	−694.581	−	582.823i	−0.196558	−	0.164932i
$233$	−918.106	−	1590.21i	−0.258142	−	0.447115i	0.707602	−	0.706611i	$-0.249777\pi$
$233$	−918.106	−	1590.21i	−0.258142	−	0.447115i	−0.965744	+	0.259496i	$0.916444\pi$
$234$		0			0
$235$	−1195.38	+	2070.46i	−0.331821	+	0.574731i
$236$	−522.149	+	190.047i	−0.144021	+	0.0524194i
$237$		0			0
$238$	−1764.41	+	1480.51i	−0.480544	+	0.403224i
$239$	2726.36	+	992.313i	0.737880	+	0.268567i	0.683497	−	0.729954i	$-0.260458\pi$
$239$	2726.36	+	992.313i	0.737880	+	0.268567i	0.0543837	+	0.998520i	$0.482681\pi$
$240$		0			0
$241$	−121.800	+	690.762i	−0.0325553	+	0.184630i	−0.996749	−	0.0805684i	$-0.974326\pi$
$241$	−121.800	+	690.762i	−0.0325553	+	0.184630i	0.964194	+	0.265199i	$0.0854376\pi$
$242$	−2172.54			−0.577090
$243$		0			0
$244$	−2280.30			−0.598283
$245$	−681.787	+	3866.61i	−0.177787	+	1.00828i
$246$		0			0
$247$	−444.091	−	161.636i	−0.114400	−	0.0416383i
$248$	441.048	−	370.083i	0.112930	−	0.0947592i
$249$		0			0
$250$	918.825	−	334.425i	0.232446	−	0.0846036i
$251$	−1048.09	+	1815.34i	−0.263564	+	0.456507i	−0.967186	−	0.254068i	$-0.918231\pi$
$251$	−1048.09	+	1815.34i	−0.263564	+	0.456507i	0.703622	+	0.710574i	$0.251565\pi$
$252$		0			0
$253$	−4844.96	−	8391.72i	−1.20395	−	2.08531i
$254$	3020.87	+	2534.81i	0.746245	+	0.626174i
$255$		0			0
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	−1273.57	−	7222.77i	−0.309117	−	1.75309i	−0.603464	−	0.797390i	$-0.706213\pi$
$257$	−1273.57	−	7222.77i	−0.309117	−	1.75309i	0.294347	−	0.955699i	$-0.404898\pi$
$258$		0			0
$259$	−1429.06	−	1199.12i	−0.342847	−	0.287683i
$260$	1129.77	+	1956.81i	0.269482	+	0.466756i
$261$		0			0
$262$	2402.67	−	4161.55i	0.566555	−	0.981302i
$263$	903.612	−	328.888i	0.211860	−	0.0771106i	−0.233910	−	0.972258i	$-0.575152\pi$
$263$	903.612	−	328.888i	0.211860	−	0.0771106i	0.445770	+	0.895148i	$0.352930\pi$
$264$		0			0
$265$	−1268.34	+	1064.26i	−0.294013	+	0.246706i
$266$	−273.121	−	99.4078i	−0.0629553	−	0.0229138i
$267$		0			0
$268$	−491.189	+	2785.67i	−0.111956	+	0.634932i
$269$	−533.148			−0.120842			−0.0604212	−	0.998173i	$-0.519244\pi$
$269$	−533.148			−0.120842			−0.0604212	+	0.998173i	$0.519244\pi$
$270$		0			0
$271$	5161.71			1.15702			0.578509	−	0.815676i	$-0.303635\pi$
$271$	5161.71			1.15702			0.578509	+	0.815676i	$0.303635\pi$
$272$	307.818	−	1745.72i	0.0686185	−	0.389155i
$273$		0			0
$274$	2870.96	+	1044.94i	0.632997	+	0.230392i
$275$	−5809.76	+	4874.97i	−1.27397	+	1.06899i
$276$		0			0
$277$	5584.45	−	2032.57i	1.21133	−	0.440886i	0.344162	−	0.938910i	$-0.388163\pi$
$277$	5584.45	−	2032.57i	1.21133	−	0.440886i	0.867163	+	0.498024i	$0.165941\pi$
$278$	−2547.65	+	4412.66i	−0.549633	+	0.951992i
$279$		0			0
$280$	694.819	+	1203.46i	0.148298	+	0.256859i
$281$	−802.484	−	673.364i	−0.170364	−	0.142952i	0.553619	−	0.832770i	$-0.313246\pi$
$281$	−802.484	−	673.364i	−0.170364	−	0.142952i	−0.723983	+	0.689818i	$0.757691\pi$
$282$		0			0
$283$	−581.586	−	3298.34i	−0.122161	−	0.692812i	−0.982953	−	0.183855i	$-0.941142\pi$
$283$	−581.586	−	3298.34i	−0.122161	−	0.692812i	0.860792	−	0.508957i	$-0.169969\pi$
$284$	−262.927	−	1491.13i	−0.0549361	−	0.311558i
$285$		0			0
$286$	−2546.27	−	2136.57i	−0.526448	−	0.441742i
$287$	2438.86	+	4224.23i	0.501608	+	0.868810i
$288$		0			0
$289$	−3680.81	+	6375.36i	−0.749199	+	1.29765i
$290$	3559.56	−	1295.57i	0.720774	−	0.262340i
$291$		0			0
$292$	1400.11	−	1174.83i	0.280600	−	0.235452i
$293$	−2033.85	−	740.260i	−0.405524	−	0.147599i	0.131201	−	0.991356i	$-0.458117\pi$
$293$	−2033.85	−	740.260i	−0.405524	−	0.147599i	−0.536725	+	0.843757i	$0.680339\pi$
$294$		0			0
$295$	403.106	−	2286.13i	0.0795585	−	0.451199i
$296$	1435.74			0.281928
$297$		0			0
$298$	1283.61			0.249522
$299$	1156.87	−	6560.96i	0.223758	−	1.26900i
$300$		0			0
$301$	−182.858	−	66.5549i	−0.0350158	−	0.0127447i
$302$	444.765	−	373.202i	0.0847462	−	0.0711105i
$303$		0			0
$304$	210.201	−	76.5068i	0.0396574	−	0.0144341i
$305$	4763.24	−	8250.18i	0.894238	−	1.54887i
$306$		0			0
$307$	336.985	+	583.675i	0.0626474	+	0.108509i	0.895648	−	0.444764i	$-0.146712\pi$
$307$	336.985	+	583.675i	0.0626474	+	0.108509i	−0.833001	+	0.553272i	$0.813379\pi$
$308$	−1565.98	−	1314.01i	−0.289708	−	0.243094i
$309$		0			0
$310$	417.679	+	2368.78i	0.0765245	+	0.433992i
$311$	−1538.42	−	8724.82i	−0.280501	−	1.59080i	−0.720926	−	0.693012i	$-0.756283\pi$
$311$	−1538.42	−	8724.82i	−0.280501	−	1.59080i	0.440425	−	0.897789i	$-0.354828\pi$
$312$		0			0
$313$	2920.45	+	2450.55i	0.527392	+	0.442535i	0.867200	−	0.497960i	$-0.165917\pi$
$313$	2920.45	+	2450.55i	0.527392	+	0.442535i	−0.339807	+	0.940495i	$0.610362\pi$
$314$	−417.550	−	723.218i	−0.0750437	−	0.129979i
$315$		0			0
$316$	2074.18	−	3592.58i	0.369245	−	0.639552i
$317$	1236.37	−	450.004i	0.219059	−	0.0797310i	−0.230159	−	0.973153i	$-0.573925\pi$
$317$	1236.37	−	450.004i	0.219059	−	0.0797310i	0.449218	+	0.893422i	$0.351703\pi$
$318$		0			0
$319$	−4268.70	+	3581.86i	−0.749220	+	0.628670i
$320$	−1005.00	−	365.791i	−0.175567	−	0.0639010i
$321$		0			0
$322$	711.490	−	4035.06i	0.123136	−	0.698339i
$323$	−1548.93			−0.266826
$324$		0			0
$325$	−5214.35			−0.889969
$326$	−256.152	+	1452.71i	−0.0435183	+	0.246805i
$327$		0			0
$328$	−3527.63	−	1283.95i	−0.593843	−	0.216141i
$329$	1139.20	−	955.899i	0.190899	−	0.160184i
$330$		0			0
$331$	−1642.75	+	597.910i	−0.272790	+	0.0992874i	−0.474793	−	0.880097i	$-0.657477\pi$
$331$	−1642.75	+	597.910i	−0.272790	+	0.0992874i	0.202003	+	0.979385i	$0.435255\pi$
$332$	1216.62	−	2107.24i	0.201116	−	0.348343i
$333$		0			0
$334$	−1704.46	−	2952.21i	−0.279233	−	0.483646i
$335$	−9052.60	−	7596.04i	−1.47641	−	1.23885i
$336$		0			0
$337$	−524.539	−	2974.81i	−0.0847876	−	0.480855i	−0.997402	−	0.0720336i	$-0.977051\pi$
$337$	−524.539	−	2974.81i	−0.0847876	−	0.480855i	0.912615	−	0.408821i	$-0.134060\pi$
$338$	366.170	+	2076.65i	0.0589261	+	0.334186i
$339$		0			0
$340$	5673.09	+	4760.29i	0.904901	+	0.759302i
$341$	−1769.19	−	3064.32i	−0.280959	−	0.486635i
$342$		0			0
$343$	3003.80	−	5202.74i	0.472857	−	0.819013i
$344$	140.732	−	51.2224i	0.0220575	−	0.00802827i
$345$		0			0
$346$	−3281.30	+	2753.34i	−0.509838	+	0.427805i
$347$	3695.36	+	1345.00i	0.571693	+	0.208079i	0.611658	−	0.791122i	$-0.290503\pi$
$347$	3695.36	+	1345.00i	0.571693	+	0.208079i	−0.0399658	+	0.999201i	$0.512725\pi$
$348$		0			0
$349$	−1922.23	+	10901.5i	−0.294828	+	1.67205i	0.373074	+	0.927802i	$0.378304\pi$
$349$	−1922.23	+	10901.5i	−0.294828	+	1.67205i	−0.667902	+	0.744249i	$0.732807\pi$
$350$	−3206.88			−0.489757
$351$		0			0
$352$	1573.30			0.238231
$353$	26.0278	−	147.611i	0.00392443	−	0.0222565i	−0.982783	−	0.184765i	$-0.940847\pi$
$353$	26.0278	−	147.611i	0.00392443	−	0.0222565i	0.986707	+	0.162509i	$0.0519586\pi$
$354$		0			0
$355$	5944.19	+	2163.51i	0.888690	+	0.323457i
$356$	5079.92	−	4262.56i	0.756279	−	0.634593i
$357$		0			0
$358$	3986.80	−	1451.08i	0.588573	−	0.214223i
$359$	−101.333	+	175.513i	−0.0148973	+	0.0258029i	−0.873378	−	0.487043i	$-0.838075\pi$
$359$	−101.333	+	175.513i	−0.0148973	+	0.0258029i	0.858481	+	0.512846i	$0.171409\pi$
$360$		0			0
$361$	3331.77	+	5770.80i	0.485752	+	0.841346i
$362$	3962.81	+	3325.20i	0.575362	+	0.482786i
$363$		0			0
$364$	−244.061	−	1384.14i	−0.0351436	−	0.199309i
$365$	1325.93	+	7519.72i	0.190143	+	1.07836i
$366$		0			0
$367$	−4676.88	−	3924.37i	−0.665207	−	0.558175i	0.246435	−	0.969159i	$-0.420741\pi$
$367$	−4676.88	−	3924.37i	−0.665207	−	0.558175i	−0.911643	+	0.410984i	$0.865185\pi$
$368$	1576.70	+	2730.92i	0.223345	+	0.386845i
$369$		0			0
$370$	−2999.07	+	5194.54i	−0.421390	+	0.729869i
$371$	967.779	−	352.243i	0.135430	−	0.0492925i
$372$		0			0
$373$	9760.64	−	8190.15i	1.35492	−	1.13692i	0.377411	−	0.926046i	$-0.376815\pi$
$373$	9760.64	−	8190.15i	1.35492	−	1.13692i	0.977514	−	0.210871i	$-0.0676299\pi$
$374$	−10237.2	−	3726.05i	−1.41539	−	0.515158i
$375$		0			0
$376$	−198.744	+	1127.13i	−0.0272592	+	0.154594i
$377$	−3831.22			−0.523389
$378$		0			0
$379$	9435.34			1.27879			0.639394	−	0.768879i	$-0.279185\pi$
$379$	9435.34			1.27879			0.639394	+	0.768879i	$0.279185\pi$
$380$	−162.278	+	920.325i	−0.0219071	+	0.124241i
$381$		0			0
$382$	−4873.23	−	1773.71i	−0.652713	−	0.237568i
$383$	2696.23	−	2262.41i	0.359716	−	0.301837i	−0.444962	−	0.895550i	$-0.646783\pi$
$383$	2696.23	−	2262.41i	0.359716	−	0.301837i	0.804677	+	0.593712i	$0.202338\pi$
$384$		0			0
$385$	8025.27	−	2920.96i	1.06235	−	0.386665i
$386$	260.172	−	450.631i	0.0343068	−	0.0594210i
$387$		0			0
$388$	−763.009	−	1321.57i	−0.0998349	−	0.172919i
$389$	2731.65	+	2292.13i	0.356042	+	0.298755i	0.803211	−	0.595695i	$-0.203123\pi$
$389$	2731.65	+	2292.13i	0.356042	+	0.298755i	−0.447169	+	0.894450i	$0.647568\pi$
$390$		0			0
$391$	−3791.69	−	21503.7i	−0.490419	−	2.78131i
$392$	326.391	+	1851.05i	0.0420541	+	0.238501i
$393$		0			0
$394$	6472.35	+	5430.95i	0.827595	+	0.694434i
$395$	8665.37	+	15008.9i	1.10380	+	1.91184i
$396$		0			0
$397$	2426.31	−	4202.48i	0.306732	−	0.531276i	−0.670913	−	0.741536i	$-0.734098\pi$
$397$	2426.31	−	4202.48i	0.306732	−	0.531276i	0.977646	+	0.210260i	$0.0674310\pi$
$398$	−3902.76	+	1420.49i	−0.491527	+	0.178901i
$399$		0			0
$400$	1890.67	−	1586.46i	0.236334	−	0.198308i
$401$	4670.79	+	1700.03i	0.581666	+	0.211709i	0.616060	−	0.787699i	$-0.288728\pi$
$401$	4670.79	+	1700.03i	0.581666	+	0.211709i	−0.0343937	+	0.999408i	$0.510950\pi$
$402$		0			0
$403$	422.444	−	2395.80i	0.0522170	−	0.296137i
$404$	−1215.14			−0.149642
$405$		0			0
$406$	−2356.24			−0.288025
$407$	1532.21	−	8689.59i	0.186606	−	1.05830i
$408$		0			0
$409$	−9146.79	−	3329.16i	−1.10582	−	0.402485i	−0.276360	−	0.961054i	$-0.589128\pi$
$409$	−9146.79	−	3329.16i	−1.10582	−	0.402485i	−0.829458	+	0.558569i	$0.811350\pi$
$410$	12014.1	−	10081.0i	1.44716	−	1.21431i
$411$		0			0
$412$	1918.19	−	698.165i	0.229375	−	0.0834857i
$413$	−721.985	+	1250.52i	−0.0860208	+	0.148992i
$414$		0			0
$415$	5082.71	+	8803.51i	0.601205	+	1.04132i
$416$	828.632	+	695.305i	0.0976611	+	0.0819474i
$417$		0			0
$418$	−238.721	−	1353.86i	−0.0279336	−	0.158419i
$419$	1803.86	+	10230.2i	0.210320	+	1.19279i	0.888845	+	0.458208i	$0.151509\pi$
$419$	1803.86	+	10230.2i	0.210320	+	1.19279i	−0.678524	+	0.734578i	$0.737380\pi$
$420$		0			0
$421$	−564.242	−	473.455i	−0.0653194	−	0.0548095i	0.609543	−	0.792753i	$-0.291353\pi$
$421$	−564.242	−	473.455i	−0.0653194	−	0.0548095i	−0.674863	+	0.737943i	$0.735797\pi$
$422$	1094.88	+	1896.38i	0.126298	+	0.218755i
$423$		0			0
$424$	−396.315	+	686.437i	−0.0453932	+	0.0786234i
$425$	−16059.5	+	5845.18i	−1.83294	+	0.667136i
$426$		0			0
$427$	−4539.37	+	3808.98i	−0.514463	+	0.431685i
$428$	−3851.52	−	1401.84i	−0.434977	−	0.158319i
$429$		0			0
$430$	−108.647	+	616.170i	−0.0121848	+	0.0691032i
$431$	3271.16			0.365583			0.182791	−	0.983152i	$-0.441487\pi$
$431$	3271.16			0.365583			0.182791	+	0.983152i	$0.441487\pi$
$432$		0			0
$433$	−6955.94			−0.772012			−0.386006	−	0.922496i	$-0.626146\pi$
$433$	−6955.94			−0.772012			−0.386006	+	0.922496i	$0.626146\pi$
$434$	259.808	−	1473.44i	0.0287354	−	0.162967i
$435$		0			0
$436$	−786.315	−	286.195i	−0.0863708	−	0.0314364i
$437$	2110.77	−	1771.14i	0.231057	−	0.193880i
$438$		0			0
$439$	93.3375	−	33.9721i	0.0101475	−	0.00369339i	−0.336941	−	0.941526i	$-0.609392\pi$
$439$	93.3375	−	33.9721i	0.0101475	−	0.00369339i	0.347089	+	0.937832i	$0.387170\pi$
$440$	−3286.42	+	5692.25i	−0.356078	+	0.616745i
$441$		0			0
$442$	−3745.09	−	6486.68i	−0.403022	−	0.698054i
$443$	−8097.69	−	6794.77i	−0.868471	−	0.728734i	0.0953043	−	0.995448i	$-0.469618\pi$
$443$	−8097.69	−	6794.77i	−0.868471	−	0.728734i	−0.963776	+	0.266714i	$0.914062\pi$
$444$		0			0
$445$	4810.77	+	27283.2i	0.512477	+	2.90640i
$446$	−1000.17	−	5672.25i	−0.106187	−	0.602217i
$447$		0			0
$448$	509.617	+	427.620i	0.0537436	+	0.0450963i
$449$	4357.21	+	7546.91i	0.457972	+	0.793231i	0.998854	−	0.0478675i	$-0.0152425\pi$
$449$	4357.21	+	7546.91i	0.457972	+	0.793231i	−0.540881	+	0.841099i	$0.681909\pi$
$450$		0			0
$451$	−11535.6	+	19980.2i	−1.20441	+	2.08610i
$452$	−6621.35	+	2409.98i	−0.689031	+	0.250787i
$453$		0			0
$454$	−5825.55	+	4888.21i	−0.602217	+	0.505320i
$455$	5517.66	+	2008.26i	0.568510	+	0.206921i
$456$		0			0
$457$	1796.41	−	10187.9i	0.183878	−	1.04282i	−0.743510	−	0.668725i	$-0.766841\pi$
$457$	1796.41	−	10187.9i	0.183878	−	1.04282i	0.927388	−	0.374100i	$-0.122048\pi$
$458$	−8335.75			−0.850446
$459$		0			0
$460$	−13174.1			−1.33531
$461$	−1068.03	+	6057.09i	−0.107903	+	0.611946i	0.882119	+	0.471027i	$0.156117\pi$
$461$	−1068.03	+	6057.09i	−0.107903	+	0.611946i	−0.990021	+	0.140918i	$0.954994\pi$
$462$		0			0
$463$	−3194.35	−	1162.65i	−0.320635	−	0.116702i	0.176688	−	0.984267i	$-0.443462\pi$
$463$	−3194.35	−	1162.65i	−0.320635	−	0.116702i	−0.497324	+	0.867565i	$0.665684\pi$
$464$	1389.16	−	1165.65i	0.138988	−	0.116624i
$465$		0			0
$466$	3450.95	−	1256.04i	0.343052	−	0.124861i
$467$	−4666.42	+	8082.47i	−0.462390	+	0.800883i	−0.999079	−	0.0428971i	$-0.986341\pi$
$467$	−4666.42	+	8082.47i	−0.462390	+	0.800883i	0.536690	+	0.843780i	$0.319675\pi$
$468$		0			0
$469$	3675.35	+	6365.89i	0.361859	+	0.626758i
$470$	−3662.85	−	3073.50i	−0.359478	−	0.301638i
$471$		0			0
$472$	−192.978	−	1094.43i	−0.0188190	−	0.106728i
$473$	−159.827	−	906.425i	−0.0155367	−	0.0881131i
$474$		0			0
$475$	−1652.06	−	1386.24i	−0.159582	−	0.133905i
$476$	−2303.27	−	3989.38i	−0.221786	−	0.384144i
$477$		0			0
$478$	−2901.33	+	5025.25i	−0.277623	+	0.480857i
$479$	14932.8	−	5435.09i	1.42442	−	0.518446i	0.489091	−	0.872233i	$-0.337328\pi$
$479$	14932.8	−	5435.09i	1.42442	−	0.518446i	0.935326	+	0.353787i	$0.115106\pi$
$480$		0			0
$481$	4647.26	−	3899.52i	0.440534	−	0.369652i
$482$	−1318.24	−	479.798i	−0.124573	−	0.0453407i
$483$		0			0
$484$	754.514	−	4279.06i	0.0708597	−	0.401865i
$485$	6375.31			0.596882
$486$		0			0
$487$	−14534.5			−1.35240			−0.676201	−	0.736717i	$-0.736375\pi$
$487$	−14534.5			−1.35240			−0.676201	+	0.736717i	$0.736375\pi$
$488$	791.939	−	4491.31i	0.0734619	−	0.416623i
$489$		0			0
$490$	−7378.95	−	2685.72i	−0.680300	−	0.247609i
$491$	−10316.8	+	8656.83i	−0.948251	+	0.795677i	−0.979002	−	0.203850i	$-0.934654\pi$
$491$	−10316.8	+	8656.83i	−0.948251	+	0.795677i	0.0307514	+	0.999527i	$0.490210\pi$
$492$		0			0
$493$	−11799.7	+	4294.72i	−1.07795	+	0.392342i
$494$	472.592	−	818.553i	0.0430423	−	0.0745515i
$495$		0			0
$496$	575.747	+	997.223i	0.0521205	+	0.0902754i
$497$	−3014.18	−	2529.20i	−0.272041	−	0.228270i
$498$		0			0
$499$	−1211.59	−	6871.28i	−0.108694	−	0.616434i	−0.989680	−	0.143293i	$-0.954231\pi$
$499$	−1211.59	−	6871.28i	−0.108694	−	0.616434i	0.880986	−	0.473142i	$-0.156880\pi$
$500$	339.584	+	1925.88i	0.0303733	+	0.172256i
$501$		0			0
$502$	−3211.52	−	2694.79i	−0.285532	−	0.239590i
$503$	−6433.86	−	11143.8i	−0.570321	−	0.987825i	−0.996533	−	0.0832017i	$-0.973485\pi$
$503$	−6433.86	−	11143.8i	−0.570321	−	0.987825i	0.426212	−	0.904624i	$-0.359848\pi$
$504$		0			0
$505$	2538.27	−	4396.40i	0.223666	−	0.387401i
$506$	18211.1	−	6628.30i	1.59997	−	0.582340i
$507$		0			0
$508$	−6041.74	+	5069.62i	−0.527675	+	0.442772i
$509$	17844.5	+	6494.88i	1.55392	+	0.565580i	0.969333	−	0.245752i	$-0.0790348\pi$
$509$	17844.5	+	6494.88i	1.55392	+	0.565580i	0.584586	+	0.811332i	$0.301257\pi$
$510$		0			0
$511$	824.763	−	4677.46i	0.0713999	−	0.404929i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	14668.4			1.25874
$515$	−1480.87	+	8398.45i	−0.126709	+	0.718602i
$516$		0			0
$517$	6609.71	+	2405.74i	0.562272	+	0.204650i
$518$	2858.11	−	2398.24i	0.242429	−	0.203422i
$519$		0			0
$520$	−4246.54	+	1545.61i	−0.358121	+	0.130345i
$521$	−9451.91	+	16371.2i	−0.794810	+	1.37665i	0.128150	+	0.991755i	$0.459096\pi$
$521$	−9451.91	+	16371.2i	−0.794810	+	1.37665i	−0.922960	+	0.384896i	$0.874237\pi$
$522$		0			0
$523$	4210.95	+	7293.58i	0.352069	+	0.609801i	0.986612	−	0.163087i	$-0.0521450\pi$
$523$	4210.95	+	7293.58i	0.352069	+	0.609801i	−0.634543	+	0.772888i	$0.718812\pi$
$524$	7362.21	+	6177.63i	0.613778	+	0.515021i
$525$		0			0
$526$	333.961	+	1893.99i	0.0276833	+	0.157000i
$527$	−1384.57	−	7852.30i	−0.114446	−	0.649055i
$528$		0			0
$529$	20435.2	+	17147.2i	1.67956	+	1.40932i
$530$	−1655.70	−	2867.75i	−0.135696	−	0.235033i
$531$		0			0
$532$	290.649	−	503.419i	0.0236865	−	0.0410262i
$533$	−14905.6	+	5425.21i	−1.21132	+	0.440885i
$534$		0			0
$535$	13117.2	−	11006.6i	1.06001	−	0.889456i
$536$	−5316.11	−	1934.91i	−0.428397	−	0.155924i
$537$		0			0
$538$	185.160	−	1050.10i	0.0148380	−	0.0841503i
$539$	11551.5			0.923117
$540$		0			0
$541$	−2619.21			−0.208149			−0.104074	−	0.994570i	$-0.533188\pi$
$541$	−2619.21			−0.208149			−0.104074	+	0.994570i	$0.533188\pi$
$542$	−1792.64	+	10166.6i	−0.142068	+	0.805706i
$543$		0			0
$544$	3331.50	+	1212.57i	0.262568	+	0.0955669i
$545$	2677.97	−	2247.09i	0.210480	−	0.176614i
$546$		0			0
$547$	−14294.2	+	5202.68i	−1.11733	+	0.406674i	−0.833676	−	0.552254i	$-0.813768\pi$
$547$	−14294.2	+	5202.68i	−1.11733	+	0.406674i	−0.283651	+	0.958928i	$0.591546\pi$
$548$	−3055.21	+	5291.79i	−0.238161	+	0.412507i
$549$		0			0
$550$	−7584.11	−	13136.1i	−0.587977	−	1.01841i
$551$	−1213.84	−	1018.53i	−0.0938500	−	0.0787495i
$552$		0			0
$553$	−1871.96	−	10616.4i	−0.143949	−	0.816375i
$554$	2063.93	+	11705.1i	0.158282	+	0.897659i
$555$		0			0
$556$	−7806.45	−	6550.39i	−0.595445	−	0.499638i
$557$	−11440.0	−	19814.7i	−0.870250	−	1.50732i	−0.861738	−	0.507354i	$-0.830624\pi$
$557$	−11440.0	−	19814.7i	−0.870250	−	1.50732i	−0.00851217	−	0.999964i	$-0.502710\pi$
$558$		0			0
$559$	316.407	−	548.033i	0.0239402	−	0.0414657i
$560$	−2611.66	+	950.568i	−0.197077	+	0.0717300i
$561$		0			0
$562$	1604.97	−	1346.73i	0.120465	−	0.101082i
$563$	−8845.48	−	3219.49i	−0.662154	−	0.241004i	−0.0109879	−	0.999940i	$-0.503498\pi$
$563$	−8845.48	−	3219.49i	−0.662154	−	0.241004i	−0.651166	+	0.758935i	$0.725720\pi$
$564$		0			0
$565$	5111.78	−	28990.4i	0.380627	−	2.15864i
$566$	6698.44			0.497449
$567$		0			0
$568$	3028.28			0.223704
$569$	−805.311	+	4567.14i	−0.0593328	+	0.336493i	−0.999996	−	0.00284866i	$-0.999093\pi$
$569$	−805.311	+	4567.14i	−0.0593328	+	0.336493i	0.940663	+	0.339342i	$0.110204\pi$
$570$		0			0
$571$	−2498.07	−	909.222i	−0.183084	−	0.0666371i	0.248851	−	0.968542i	$-0.419947\pi$
$571$	−2498.07	−	909.222i	−0.183084	−	0.0666371i	−0.431935	+	0.901905i	$0.642169\pi$
$572$	5092.54	−	4273.15i	0.372255	−	0.312359i
$573$		0			0
$574$	−9167.12	+	3336.56i	−0.666599	+	0.242622i
$575$	15200.9	−	26328.8i	1.10247	−	1.90954i
$576$		0			0
$577$	4452.00	+	7711.10i	0.321212	+	0.556355i	0.980738	−	0.195326i	$-0.0625765\pi$
$577$	4452.00	+	7711.10i	0.321212	+	0.556355i	−0.659526	+	0.751681i	$0.729243\pi$
$578$	−11278.7	−	9463.93i	−0.811645	−	0.681051i
$579$		0			0
$580$	1315.56	+	7460.91i	0.0941822	+	0.534134i
$581$	−1098.00	−	6227.09i	−0.0784043	−	0.444653i
$582$		0			0
$583$	3731.61	+	3131.19i	0.265090	+	0.222437i
$584$	1827.72	+	3165.70i	0.129506	+	0.224311i
$585$		0			0
$586$	2164.37	−	3748.81i	0.152576	−	0.264269i
$587$	−16770.1	+	6103.82i	−1.17918	+	0.429185i	−0.855911	−	0.517124i	$-0.827003\pi$
$587$	−16770.1	+	6103.82i	−1.17918	+	0.429185i	−0.323265	+	0.946308i	$0.604781\pi$
$588$		0			0
$589$	770.768	−	646.751i	0.0539201	−	0.0452444i
$590$	4362.80	+	1587.93i	0.304430	+	0.110803i
$591$		0			0
$592$	−498.627	+	2827.85i	−0.0346173	+	0.196324i
$593$	−1536.73			−0.106418			−0.0532090	−	0.998583i	$-0.516945\pi$
$593$	−1536.73			−0.106418			−0.0532090	+	0.998583i	$0.516945\pi$
$594$		0			0
$595$	19244.9			1.32599
$596$	−445.794	+	2528.22i	−0.0306383	+	0.173758i
$597$		0			0
$598$	12520.8	+	4557.20i	0.856209	+	0.311635i
$599$	−14115.0	+	11843.9i	−0.962812	+	0.807896i	−0.981408	−	0.191931i	$-0.938525\pi$
$599$	−14115.0	+	11843.9i	−0.962812	+	0.807896i	0.0185958	+	0.999827i	$0.494080\pi$
$600$		0			0
$601$	66.4645	−	24.1911i	0.00451106	−	0.00164189i	−0.339764	−	0.940511i	$-0.610347\pi$
$601$	66.4645	−	24.1911i	0.00451106	−	0.00164189i	0.344275	+	0.938869i	$0.388125\pi$
$602$	194.593	−	337.046i	0.0131745	−	0.0228189i
$603$		0			0
$604$	580.599	+	1005.63i	0.0391130	+	0.0677457i
$605$	13905.7	+	11668.3i	0.934457	+	0.784102i
$606$		0			0
$607$	−1058.85	−	6005.03i	−0.0708028	−	0.401543i	−0.999526	−	0.0307702i	$-0.990204\pi$
$607$	−1058.85	−	6005.03i	−0.0708028	−	0.401543i	0.928724	−	0.370773i	$-0.120907\pi$
$608$	77.6871	+	440.585i	0.00518195	+	0.0293883i
$609$		0			0
$610$	14595.4	+	12247.0i	0.968773	+	0.812897i
$611$	2418.03	+	4188.15i	0.160103	+	0.277307i
$612$		0			0
$613$	4937.90	−	8552.70i	0.325351	−	0.563524i	−0.656232	−	0.754559i	$-0.727851\pi$
$613$	4937.90	−	8552.70i	0.325351	−	0.563524i	0.981583	+	0.191035i	$0.0611843\pi$
$614$	−1266.65	+	461.023i	−0.0832538	+	0.0303019i
$615$		0			0
$616$	3131.96	−	2628.03i	0.204854	−	0.171893i
$617$	22389.7	+	8149.19i	1.46090	+	0.531725i	0.945613	−	0.325292i	$-0.105463\pi$
$617$	22389.7	+	8149.19i	1.46090	+	0.531725i	0.515288	+	0.857017i	$0.327685\pi$
$618$		0			0
$619$	−2005.76	+	11375.2i	−0.130240	+	0.738627i	0.847817	+	0.530289i	$0.177916\pi$
$619$	−2005.76	+	11375.2i	−0.130240	+	0.738627i	−0.978057	+	0.208338i	$0.933195\pi$
$620$	−4810.64			−0.311613
$621$		0			0
$622$	17718.8			1.14222
$623$	2992.43	−	16970.9i	0.192438	−	1.09137i
$624$		0			0
$625$	10441.9	+	3800.55i	0.668284	+	0.243235i
$626$	−5840.91	+	4901.10i	−0.372923	+	0.312919i
$627$		0			0
$628$	1569.47	−	571.242i	0.0997275	−	0.0362978i
$629$	9941.68	−	17219.5i	0.630208	−	1.09155i
$630$		0			0
$631$	−10910.2	−	18897.0i	−0.688318	−	1.19220i	−0.972382	−	0.233397i	$-0.925016\pi$
$631$	−10910.2	−	18897.0i	−0.688318	−	1.19220i	0.284063	−	0.958805i	$-0.408317\pi$
$632$	6355.64	+	5333.02i	0.400022	+	0.335658i
$633$		0			0
$634$	456.946	+	2591.47i	0.0286240	+	0.162335i
$635$	−5721.63	−	32449.0i	−0.357568	−	2.02787i
$636$		0			0
$637$	6084.00	+	5105.08i	0.378425	+	0.317536i
$638$	−5572.39	−	9651.66i	−0.345789	−	0.598923i
$639$		0			0
$640$	1069.50	−	1852.43i	0.0660559	−	0.114412i
$641$	17403.0	−	6334.18i	1.07235	−	0.390304i	0.255296	−	0.966863i	$-0.417827\pi$
$641$	17403.0	−	6334.18i	1.07235	−	0.390304i	0.817056	+	0.576559i	$0.195605\pi$
$642$		0			0
$643$	2026.77	−	1700.66i	0.124305	−	0.104304i	−0.578516	−	0.815671i	$-0.696368\pi$
$643$	2026.77	−	1700.66i	0.124305	−	0.104304i	0.702821	+	0.711367i	$0.251924\pi$
$644$	7700.42	+	2802.72i	0.471178	+	0.171495i
$645$		0			0
$646$	537.939	−	3050.80i	0.0327630	−	0.185808i
$647$	15048.2			0.914383			0.457192	−	0.889368i	$-0.348855\pi$
$647$	15048.2			0.914383			0.457192	+	0.889368i	$0.348855\pi$
$648$		0			0
$649$	−6829.84			−0.413089
$650$	1810.92	−	10270.3i	0.109277	−	0.619743i
$651$		0			0
$652$	−2772.32	−	1009.04i	−0.166522	−	0.0606092i
$653$	−15907.9	+	13348.3i	−0.953330	+	0.799939i	−0.979855	−	0.199709i	$-0.936000\pi$
$653$	−15907.9	+	13348.3i	−0.953330	+	0.799939i	0.0265252	+	0.999648i	$0.491556\pi$
$654$		0			0
$655$	−37729.5	+	13732.4i	−2.25071	+	0.819191i
$656$	3754.02	−	6502.16i	0.223430	−	0.386992i
$657$		0			0
$658$	1487.11	+	2575.76i	0.0881060	+	0.152604i
$659$	2631.22	+	2207.85i	0.155535	+	0.130509i	0.717234	−	0.696832i	$-0.245408\pi$
$659$	2631.22	+	2207.85i	0.155535	+	0.130509i	−0.561699	+	0.827342i	$0.689852\pi$
$660$		0			0
$661$	2927.61	+	16603.3i	0.172271	+	0.976995i	0.941247	+	0.337718i	$0.109655\pi$
$661$	2927.61	+	16603.3i	0.172271	+	0.976995i	−0.768977	+	0.639277i	$0.779234\pi$
$662$	−607.134	−	3443.23i	−0.0356449	−	0.202152i
$663$		0			0
$664$	3727.93	+	3128.10i	0.217879	+	0.182822i
$665$	1214.26	+	2103.15i	0.0708072	+	0.122642i
$666$		0			0
$667$	11168.8	−	19345.0i	0.648364	−	1.12300i
$668$	6406.67	−	2331.84i	0.371080	−	0.135062i
$669$		0			0
$670$	18105.2	−	15192.1i	1.04398	−	0.876001i
$671$	−26337.8	−	9586.18i	−1.51529	−	0.551521i
$672$		0			0
$673$	1226.68	−	6956.83i	0.0702599	−	0.398464i	−0.929314	−	0.369289i	$-0.879601\pi$
$673$	1226.68	−	6956.83i	0.0702599	−	0.398464i	0.999574	−	0.0291743i	$-0.00928779\pi$
$674$	6041.39			0.345261
$675$		0			0
$676$	−4217.37			−0.239951
$677$	1101.90	−	6249.17i	0.0625544	−	0.354764i	−0.937424	−	0.348190i	$-0.886796\pi$
$677$	1101.90	−	6249.17i	0.0625544	−	0.354764i	0.999978	−	0.00657376i	$-0.00209251\pi$
$678$		0			0
$679$	−3726.46	−	1356.32i	−0.210616	−	0.0766579i
$680$	−11346.2	+	9520.57i	−0.639862	+	0.536908i
$681$		0			0
$682$	6649.97	−	2420.39i	0.373373	−	0.135897i
$683$	−5523.64	+	9567.23i	−0.309453	+	0.535988i	−0.978243	−	0.207463i	$-0.933479\pi$
$683$	−5523.64	+	9567.23i	−0.309453	+	0.535988i	0.668790	+	0.743451i	$0.266813\pi$
$684$		0			0
$685$	−12763.9	−	22107.7i	−0.711946	−	1.23313i
$686$	9204.18	+	7723.23i	0.512270	+	0.429846i
$687$		0			0
$688$	52.0126	+	294.978i	0.00288221	+	0.0163458i
$689$	581.578	+	3298.29i	0.0321573	+	0.182373i
$690$		0			0
$691$	−6989.78	−	5865.12i	−0.384810	−	0.322894i	0.429777	−	0.902935i	$-0.358592\pi$
$691$	−6989.78	−	5865.12i	−0.384810	−	0.322894i	−0.814587	+	0.580041i	$0.803037\pi$
$692$	−4283.44	−	7419.13i	−0.235306	−	0.407562i
$693$		0			0
$694$	−3932.52	+	6811.33i	−0.215096	+	0.372557i
$695$	40006.2	−	14561.1i	2.18348	−	0.794723i
$696$		0			0
$697$	−39825.8	+	33417.8i	−2.16429	+	1.81606i
$698$	−20804.2	−	7572.13i	−1.12816	−	0.410615i
$699$		0			0
$700$	1113.74	−	6316.32i	0.0601361	−	0.341049i
$701$	−23630.0			−1.27317			−0.636587	−	0.771205i	$-0.719654\pi$
$701$	−23630.0			−1.27317			−0.636587	+	0.771205i	$0.719654\pi$
$702$		0			0
$703$	2509.08			0.134611
$704$	−546.402	+	3098.80i	−0.0292519	+	0.165896i
$705$		0			0
$706$	281.698	+	102.530i	0.0150168	+	0.00546566i
$707$	−2418.97	+	2029.75i	−0.128677	+	0.107973i
$708$		0			0
$709$	3714.21	−	1351.86i	0.196742	−	0.0716082i	−0.241770	−	0.970334i	$-0.577728\pi$
$709$	3714.21	−	1351.86i	0.196742	−	0.0716082i	0.438512	+	0.898725i	$0.355506\pi$
$710$	−6325.67	+	10956.4i	−0.334364	+	0.579135i
$711$		0			0
$712$	6631.37	+	11485.9i	0.349046	+	0.604566i
$713$	10865.6	+	9117.32i	0.570715	+	0.478887i
$714$		0			0
$715$	4822.72	+	27351.0i	0.252251	+	1.43059i
$716$	1473.46	+	8356.43i	0.0769077	+	0.436165i
$717$		0			0
$718$	−310.501	−	260.541i	−0.0161390	−	0.0135422i
$719$	−11181.4	−	19366.8i	−0.579968	−	1.00453i	−0.995482	−	0.0949479i	$-0.969732\pi$
$719$	−11181.4	−	19366.8i	−0.579968	−	1.00453i	0.415514	−	0.909587i	$-0.363602\pi$
$720$		0			0
$721$	2652.32	−	4593.96i	0.137001	−	0.237293i
$722$	−12523.4	+	4558.13i	−0.645528	+	0.234953i
$723$		0			0
$724$	−7925.63	+	6650.39i	−0.406842	+	0.341381i
$725$	−16428.9	−	5979.61i	−0.841589	−	0.306313i
$726$		0			0
$727$	−256.810	+	1456.44i	−0.0131012	+	0.0743004i	−0.990657	−	0.136374i	$-0.956455\pi$
$727$	−256.810	+	1456.44i	−0.0131012	+	0.0743004i	0.977556	+	0.210675i	$0.0675661\pi$
$728$	2810.98			0.143107
$729$		0			0
$730$	−15271.4			−0.774276
$731$	360.158	−	2042.55i	0.0182229	−	0.103347i
$732$		0			0
$733$	313.357	+	114.053i	0.0157901	+	0.00574711i	0.349903	−	0.936786i	$-0.386215\pi$
$733$	313.357	+	114.053i	0.0157901	+	0.00574711i	−0.334113	+	0.942533i	$0.608437\pi$
$734$	9353.76	−	7848.73i	0.470373	−	0.394689i
$735$		0			0
$736$	−5926.44	+	2157.05i	−0.296809	+	0.108030i
$737$	−17384.0	+	30110.0i	−0.868859	+	1.50491i
$738$		0			0
$739$	−831.311	−	1439.87i	−0.0413806	−	0.0716733i	0.844593	−	0.535408i	$-0.179842\pi$
$739$	−831.311	−	1439.87i	−0.0413806	−	0.0716733i	−0.885974	+	0.463735i	$0.846509\pi$
$740$	−9189.69	−	7711.06i	−0.456513	−	0.383060i
$741$		0			0
$742$	357.676	+	2028.48i	0.0176964	+	0.100361i
$743$	−611.291	−	3466.80i	−0.0301832	−	0.171177i	0.965990	−	0.258580i	$-0.0832545\pi$
$743$	−611.291	−	3466.80i	−0.0301832	−	0.171177i	−0.996173	+	0.0874025i	$0.972143\pi$
$744$		0			0
$745$	−8215.98	−	6894.02i	−0.404040	−	0.339030i
$746$	12741.6	+	22069.1i	0.625340	+	1.08312i
$747$		0			0
$748$	10894.2	−	18869.4i	0.532530	−	0.922369i
$749$	−10008.8	+	3642.91i	−0.488269	+	0.177716i
$750$		0			0
$751$	6386.22	−	5358.67i	0.310301	−	0.260374i	−0.474315	−	0.880355i	$-0.657304\pi$
$751$	6386.22	−	5358.67i	0.310301	−	0.260374i	0.784617	+	0.619981i	$0.212860\pi$
$752$	−2151.00	−	782.899i	−0.104307	−	0.0379646i
$753$		0			0
$754$	1330.57	−	7546.03i	0.0642658	−	0.364470i
$755$	−4851.19			−0.233845
$756$		0			0
$757$	9160.30			0.439811			0.219905	−	0.975521i	$-0.429425\pi$
$757$	9160.30			0.439811			0.219905	+	0.975521i	$0.429425\pi$
$758$	−3276.86	+	18584.0i	−0.157020	+	0.890502i
$759$		0			0
$760$	−1756.33	−	639.251i	−0.0838272	−	0.0305106i
$761$	176.231	−	147.876i	0.00839472	−	0.00704401i	−0.638581	−	0.769555i	$-0.720478\pi$
$761$	176.231	−	147.876i	0.00839472	−	0.00704401i	0.646975	+	0.762511i	$0.276034\pi$
$762$		0			0
$763$	−2043.37	+	743.726i	−0.0969527	+	0.0352879i
$764$	5185.99	−	8982.39i	0.245579	−	0.425356i
$765$		0			0
$766$	3519.68	+	6096.27i	0.166020	+	0.287555i
$767$	−3597.16	−	3018.38i	−0.169343	−	0.142096i
$768$		0			0
$769$	−296.877	−	1683.67i	−0.0139215	−	0.0789529i	0.977055	−	0.212985i	$-0.0683186\pi$
$769$	−296.877	−	1683.67i	−0.0139215	−	0.0789529i	−0.990977	+	0.134032i	$0.957207\pi$
$770$	2966.02	+	16821.1i	0.138816	+	0.787262i
$771$		0			0
$772$	797.213	+	668.941i	0.0371662	+	0.0311862i
$773$	−3392.27	−	5875.59i	−0.157842	−	0.273390i	0.776248	−	0.630427i	$-0.217120\pi$
$773$	−3392.27	−	5875.59i	−0.157842	−	0.273390i	−0.934090	+	0.357037i	$0.883787\pi$
$774$		0			0
$775$	5550.78	−	9614.23i	0.257277	−	0.445617i
$776$	2867.98	−	1043.86i	0.132673	−	0.0482891i
$777$		0			0
$778$	−5463.31	+	4584.26i	−0.251760	+	0.211251i
$779$	−6164.83	−	2243.81i	−0.283540	−	0.103200i
$780$		0			0
$781$	3231.75	−	18328.2i	0.148068	−	0.839736i
$782$	43670.9			1.99702
$783$		0			0
$784$	−3759.22			−0.171247
$785$	−1211.66	+	6871.65i	−0.0550903	+	0.312433i
$786$		0			0
$787$	6055.42	+	2203.99i	0.274273	+	0.0998271i	0.475495	−	0.879719i	$-0.342269\pi$
$787$	6055.42	+	2203.99i	0.274273	+	0.0998271i	−0.201222	+	0.979546i	$0.564491\pi$
$788$	−12944.7	+	10861.9i	−0.585198	+	0.491039i
$789$		0			0
$790$	−32571.1	+	11854.9i	−1.46687	+	0.533898i
$791$	−9155.48	+	15857.8i	−0.411544	+	0.712815i
$792$		0			0
$793$	−9635.17	−	16688.6i	−0.431469	−	0.747326i
$794$	7434.63	+	6238.40i	0.332299	+	0.278832i
$795$		0			0
$796$	−1442.40	−	8180.27i	−0.0642269	−	0.364249i
$797$	5046.55	+	28620.4i	0.224289	+	1.27200i	0.864040	+	0.503423i	$0.167926\pi$
$797$	5046.55	+	28620.4i	0.224289	+	1.27200i	−0.639752	+	0.768582i	$0.720963\pi$
$798$		0			0
$799$	12142.1	+	10188.4i	0.537616	+	0.451113i
$800$	2468.10	+	4274.87i	0.109075	+	0.188924i
$801$		0			0
$802$	−4970.55	+	8609.25i	−0.218848	+	0.379056i
$803$	21110.4	−	7683.56i	0.927734	−	0.337668i
$804$		0			0
$805$	−26225.5	+	22005.8i	−1.14823	+	0.963481i
$806$	4572.09	+	1664.11i	0.199808	+	0.0727241i
$807$		0			0
$808$	422.013	−	2393.36i	0.0183742	−	0.104205i
$809$	11537.5			0.501405			0.250703	−	0.968064i	$-0.419338\pi$
$809$	11537.5			0.501405			0.250703	+	0.968064i	$0.419338\pi$
$810$		0			0
$811$	−7010.58			−0.303545			−0.151772	−	0.988415i	$-0.548498\pi$
$811$	−7010.58			−0.303545			−0.151772	+	0.988415i	$0.548498\pi$
$812$	818.313	−	4640.89i	0.0353660	−	0.200570i
$813$		0			0
$814$	16583.0	+	6035.73i	0.714047	+	0.259892i
$815$	9441.77	−	7922.59i	0.405805	−	0.340511i
$816$		0			0
$817$	245.942	−	89.5155i	0.0105317	−	0.00383323i
$818$	9733.81	−	16859.4i	0.416057	−	0.720632i
$819$		0			0
$820$	15683.3	+	27164.3i	0.667909	+	1.15685i
$821$	7775.34	+	6524.29i	0.330525	+	0.277344i	0.792914	−	0.609334i	$-0.208563\pi$
$821$	7775.34	+	6524.29i	0.330525	+	0.277344i	−0.462389	+	0.886677i	$0.653007\pi$
$822$		0			0
$823$	−4928.30	−	27949.8i	−0.208736	−	1.18380i	−0.891451	−	0.453116i	$-0.850312\pi$
$823$	−4928.30	−	27949.8i	−0.208736	−	1.18380i	0.682715	−	0.730684i	$-0.260799\pi$
$824$	708.935	+	4020.57i	0.0299720	+	0.169980i
$825$		0			0
$826$	−2212.29	−	1856.33i	−0.0931906	−	0.0781962i
$827$	3291.01	+	5700.20i	0.138379	+	0.239680i	0.926883	−	0.375350i	$-0.122477\pi$
$827$	3291.01	+	5700.20i	0.138379	+	0.239680i	−0.788504	+	0.615030i	$0.789144\pi$
$828$		0			0
$829$	−19065.3	+	33022.0i	−0.798750	+	1.38348i	0.121681	+	0.992569i	$0.461172\pi$
$829$	−19065.3	+	33022.0i	−0.798750	+	1.38348i	−0.920431	+	0.390906i	$0.872162\pi$
$830$	−19104.7	+	6953.55i	−0.798958	+	0.290797i
$831$		0			0
$832$	−1657.26	+	1390.61i	−0.0690569	+	0.0579456i
$833$	24460.6	+	8902.94i	1.01742	+	0.370310i
$834$		0			0
$835$	−4946.05	+	28050.4i	−0.204988	+	1.16254i
$836$	2749.48			0.113747
$837$		0			0
$838$	−20776.0			−0.856438
$839$	−6098.85	+	34588.3i	−0.250960	+	1.42327i	0.555272	+	0.831669i	$0.312614\pi$
$839$	−6098.85	+	34588.3i	−0.250960	+	1.42327i	−0.806233	+	0.591598i	$0.798497\pi$
$840$		0			0
$841$	10847.1	+	3948.04i	0.444755	+	0.161878i
$842$	1128.48	−	946.910i	0.0461878	−	0.0387561i
$843$		0			0
$844$	−4115.39	+	1497.88i	−0.167841	+	0.0610890i
$845$	8809.55	−	15258.6i	0.358648	−	0.621197i
$846$		0			0
$847$	−5645.69	−	9778.62i	−0.229030	−	0.396691i
$848$	−1214.38	−	1018.98i	−0.0491768	−	0.0412642i
$849$		0			0
$850$	−5935.35	−	33661.1i	−0.239507	−	1.35831i
$851$	6142.06	+	34833.3i	0.247411	+	1.40314i
$852$		0			0
$853$	24999.6	+	20977.1i	1.00348	+	0.842020i	0.987463	−	0.157852i	$-0.0504568\pi$
$853$	24999.6	+	20977.1i	1.00348	+	0.842020i	0.0160176	+	0.999872i	$0.494901\pi$
$854$	−5925.73	−	10263.7i	−0.237441	−	0.411259i
$855$		0			0
$856$	4098.70	−	7099.16i	0.163657	−	0.283463i
$857$	−41239.8	+	15010.1i	−1.64379	+	0.598289i	−0.987695	−	0.156392i	$-0.950014\pi$
$857$	−41239.8	+	15010.1i	−1.64379	+	0.598289i	−0.656092	+	0.754681i	$0.727792\pi$
$858$		0			0
$859$	22054.0	−	18505.5i	0.875989	−	0.735042i	−0.0893614	−	0.995999i	$-0.528483\pi$
$859$	22054.0	−	18505.5i	0.875989	−	0.735042i	0.965350	+	0.260957i	$0.0840382\pi$
$860$	−1175.89	−	427.987i	−0.0466249	−	0.0169701i
$861$		0			0
$862$	−1136.06	+	6442.92i	−0.0448891	+	0.254579i
$863$	−19441.4			−0.766853			−0.383427	−	0.923571i	$-0.625256\pi$
$863$	−19441.4			−0.766853			−0.383427	+	0.923571i	$0.625256\pi$
$864$		0			0
$865$	35790.2			1.40682
$866$	2415.77	−	13700.5i	0.0947937	−	0.537602i
$867$		0			0
$868$	2811.88	+	1023.44i	0.109956	+	0.0400206i
$869$	39060.0	−	32775.2i	1.52476	−	1.27943i
$870$		0			0
$871$	−22462.7	+	8175.75i	−0.873845	+	0.318054i
$872$	836.779	−	1449.34i	0.0324965	−	0.0562855i
$873$		0			0
$874$	2755.41	+	4772.51i	0.106640	+	0.184706i
$875$	3892.97	+	3266.59i	0.150407	+	0.126207i
$876$		0			0
$877$	6180.82	+	35053.2i	0.237983	+	1.34967i	0.836239	+	0.548365i	$0.184750\pi$
$877$	6180.82	+	35053.2i	0.237983	+	1.34967i	−0.598256	+	0.801305i	$0.704139\pi$
$878$	34.4962	+	195.637i	0.00132596	+	0.00751987i
$879$		0			0
$880$	−10070.2	−	8449.89i	−0.385757	−	0.323688i
$881$	−17804.1	−	30837.7i	−0.680859	−	1.17928i	−0.974719	−	0.223434i	$-0.928273\pi$
$881$	−17804.1	−	30837.7i	−0.680859	−	1.17928i	0.293860	−	0.955848i	$-0.405060\pi$
$882$		0			0
$883$	5881.79	−	10187.6i	0.224165	−	0.388266i	−0.731903	−	0.681408i	$-0.761368\pi$
$883$	5881.79	−	10187.6i	0.224165	−	0.388266i	0.956069	+	0.293143i	$0.0947011\pi$
$884$	14076.9	−	5123.58i	0.535586	−	0.194937i
$885$		0			0
$886$	16195.4	−	13589.5i	0.614102	−	0.515293i
$887$	−22315.4	−	8122.13i	−0.844731	−	0.307457i	−0.116841	−	0.993151i	$-0.537277\pi$
$887$	−22315.4	−	8122.13i	−0.844731	−	0.307457i	−0.727890	+	0.685694i	$0.759499\pi$
$888$		0			0
$889$	−3559.01	+	20184.1i	−0.134269	+	0.761478i
$890$	−55408.2			−2.08684
$891$		0			0
$892$	11519.5			0.432401
$893$	−347.322	+	1969.76i	−0.0130153	+	0.0738137i
$894$		0			0
$895$	−33311.7	−	12124.5i	−1.24412	−	0.452822i
$896$	−1019.23	+	855.239i	−0.0380025	+	0.0318879i
$897$		0			0
$898$	−16377.8	+	5961.02i	−0.608611	+	0.221516i
$899$	4078.41	−	7064.01i	0.151304	−	0.262067i
$900$		0			0
$901$	5488.51	+	9506.37i	0.202940	+	0.351502i
$902$	−35347.0	−	29659.7i	−1.30480	−	1.09486i
$903$		0			0
$904$	−2447.15	−	13878.5i	−0.0900344	−	0.510610i
$905$	−7505.70	−	42566.9i	−0.275688	−	1.56351i
$906$		0			0
$907$	21002.4	+	17623.1i	0.768880	+	0.645167i	0.940422	−	0.340010i	$-0.110430\pi$
$907$	21002.4	+	17623.1i	0.768880	+	0.645167i	−0.171542	+	0.985177i	$0.554875\pi$
$908$	−7604.71	−	13171.7i	−0.277942	−	0.481409i
$909$		0			0
$910$	−5871.77	+	10170.2i	−0.213898	+	0.370483i
$911$	−1837.95	+	668.959i	−0.0668430	+	0.0243289i	−0.375225	−	0.926934i	$-0.622435\pi$
$911$	−1837.95	+	668.959i	−0.0668430	+	0.0243289i	0.308382	+	0.951263i	$0.400212\pi$
$912$		0			0
$913$	22910.8	−	19224.4i	0.830489	−	0.696863i
$914$	19442.4	+	7076.46i	0.703608	+	0.256092i
$915$		0			0
$916$	2894.98	−	16418.2i	0.104424	−	0.592220i
$917$	24974.9			0.899395
$918$		0			0
$919$	−31146.3			−1.11798			−0.558988	−	0.829175i	$-0.688810\pi$
$919$	−31146.3			−1.11798			−0.558988	+	0.829175i	$0.688810\pi$
$920$	4575.30	−	25947.8i	0.163960	−	0.929863i
$921$		0			0
$922$	−11559.2	−	4207.21i	−0.412888	−	0.150279i
$923$	9802.06	−	8224.90i	0.349554	−	0.293311i
$924$		0			0
$925$	26014.4	−	9468.46i	0.924700	−	0.336563i
$926$	3399.36	−	5887.86i	0.120637	−	0.208949i
$927$		0			0
$928$	1813.42	+	3140.94i	0.0641471	+	0.111106i
$929$	19927.1	+	16720.8i	0.703753	+	0.590519i	0.922839	−	0.385186i	$-0.125863\pi$
$929$	19927.1	+	16720.8i	0.703753	+	0.590519i	−0.219085	+	0.975706i	$0.570307\pi$
$930$		0			0
$931$	570.396	+	3234.87i	0.0200794	+	0.113876i
$932$	1275.42	+	7233.26i	0.0448259	+	0.254220i
$933$		0			0
$934$	−14298.7	−	11998.1i	−0.500930	−	0.420330i
$935$	45513.3	+	78831.3i	1.59192	+	2.75728i
$936$		0			0
$937$	1054.25	−	1826.02i	0.0367567	−	0.0636644i	−0.847062	−	0.531494i	$-0.821631\pi$
$937$	1054.25	−	1826.02i	0.0367567	−	0.0636644i	0.883819	+	0.467830i	$0.154964\pi$
$938$	−13814.8	+	5028.17i	−0.480884	+	0.175027i
$939$		0			0
$940$	7325.71	−	6147.00i	0.254190	−	0.213290i
$941$	−25109.9	−	9139.26i	−0.869883	−	0.316611i	−0.131763	−	0.991281i	$-0.542064\pi$
$941$	−25109.9	−	9139.26i	−0.869883	−	0.316611i	−0.738120	+	0.674670i	$0.764286\pi$
$942$		0			0
$943$	16059.6	−	91078.6i	0.554584	−	3.14520i
$944$	2222.64			0.0766320
$945$		0			0
$946$	1840.82			0.0632665
$947$	−3630.50	+	20589.6i	−0.124578	+	0.706516i	0.856980	+	0.515350i	$0.172338\pi$
$947$	−3630.50	+	20589.6i	−0.124578	+	0.706516i	−0.981558	+	0.191166i	$0.938773\pi$
$948$		0			0
$949$	14514.2	+	5282.73i	0.496470	+	0.180700i
$950$	3304.11	−	2772.48i	0.112842	−	0.0946853i
$951$		0			0
$952$	8657.45	−	3151.06i	0.294737	−	0.107276i
$953$	5193.70	−	8995.75i	0.176538	−	0.305772i	−0.764155	−	0.645033i	$-0.776844\pi$
$953$	5193.70	−	8995.75i	0.176538	−	0.305772i	0.940692	+	0.339261i	$0.110177\pi$
$954$		0			0
$955$	21665.7	+	37526.1i	0.734121	+	1.27154i
$956$	−8890.19	−	7459.75i	−0.300763	−	0.252370i
$957$		0			0
$958$	5518.93	+	31299.4i	0.186126	+	1.05557i
$959$	2757.35	+	15637.7i	0.0928462	+	0.526557i
$960$		0			0
$961$	−18853.5	−	15820.0i	−0.632860	−	0.531033i
$962$	6066.57	+	10507.6i	0.203320	+	0.352161i
$963$		0			0
$964$	1402.84	−	2429.78i	0.0468696	−	0.0811806i
$965$	−4085.52	+	1487.01i	−0.136288	+	0.0496047i
$966$		0			0
$967$	−15858.8	+	13307.1i	−0.527388	+	0.442531i	−0.867198	−	0.497963i	$-0.834082\pi$
$967$	−15858.8	+	13307.1i	−0.527388	+	0.442531i	0.339810	+	0.940494i	$0.389637\pi$
$968$	8166.06	+	2972.20i	0.271144	+	0.0986883i
$969$		0			0
$970$	−2214.12	+	12556.9i	−0.0732898	+	0.415647i
$971$	−27154.0			−0.897441			−0.448720	−	0.893672i	$-0.648120\pi$
$971$	−27154.0			−0.897441			−0.448720	+	0.893672i	$0.648120\pi$
$972$		0			0
$973$	−26482.0			−0.872531
$974$	5047.77	−	28627.3i	0.166059	−	0.941765i
$975$		0			0
$976$	8571.11	+	3119.63i	0.281101	+	0.102312i
$977$	8375.07	−	7027.52i	0.274250	−	0.230123i	−0.495281	−	0.868733i	$-0.664935\pi$
$977$	8375.07	−	7027.52i	0.274250	−	0.230123i	0.769531	+	0.638610i	$0.220490\pi$
$978$		0			0
$979$	76593.4	−	27877.7i	2.50044	−	0.910087i
$980$	7852.51	−	13601.0i	0.255959	−	0.443333i
$981$		0			0
$982$	−13467.6	−	23326.6i	−0.437647	−	0.758027i
$983$	−23118.2	−	19398.5i	−0.750109	−	0.629416i	0.185423	−	0.982659i	$-0.440634\pi$
$983$	−23118.2	−	19398.5i	−0.750109	−	0.629416i	−0.935532	+	0.353243i	$0.885079\pi$
$984$		0			0
$985$	−12258.8	−	69523.4i	−0.396548	−	2.24893i
$986$	−4360.98	−	24732.3i	−0.140854	−	0.798821i
$987$		0			0
$988$	1448.11	+	1215.10i	0.0466299	+	0.0391272i
$989$	1844.79	+	3195.27i	0.0593133	+	0.102734i
$990$		0			0
$991$	−25409.9	+	44011.2i	−0.814501	+	1.41076i	0.0951843	+	0.995460i	$0.469656\pi$
$991$	−25409.9	+	44011.2i	−0.814501	+	1.41076i	−0.909686	+	0.415298i	$0.863677\pi$
$992$	−2164.10	+	787.668i	−0.0692644	+	0.0252102i
$993$		0			0
$994$	6028.37	−	5058.40i	0.192362	−	0.161411i
$995$	32609.4	+	11868.9i	1.03898	+	0.378159i
$996$		0			0
$997$	1911.07	−	10838.2i	0.0607062	−	0.344282i	−0.939293	−	0.343116i	$-0.888518\pi$
$997$	1911.07	−	10838.2i	0.0607062	−	0.344282i	0.999999	−	0.00116621i	$-0.000371217\pi$
$998$	13954.6			0.442609
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.73.4		24
3.2	odd	2		54.4.e.a.25.2	yes	24
27.11	odd	18		1458.4.a.h.1.2		12
27.13	even	9	inner	162.4.e.a.91.4		24
27.14	odd	18		54.4.e.a.13.2	✓	24
27.16	even	9		1458.4.a.e.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.13.2	✓	24	27.14	odd	18
54.4.e.a.25.2	yes	24	3.2	odd	2
162.4.e.a.73.4		24	1.1	even	1	trivial
162.4.e.a.91.4		24	27.13	even	9	inner
1458.4.a.e.1.11		12	27.16	even	9
1458.4.a.h.1.2		12	27.11	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(12.8013 - 10.7416i) q^{5} +(-9.76778 + 3.55518i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(12.8013 - 10.7416i) q^{5} +(-9.76778 + 3.55518i) q^{7} +(4.00000 - 6.92820i) q^{8} +(16.7110 + 28.9442i) q^{10} +(-37.6631 - 31.6031i) q^{11} +(-5.86986 - 33.2897i) q^{13} +(-3.61003 - 20.4735i) q^{14} +(12.2567 + 10.2846i) q^{16} +(-55.3955 - 95.9478i) q^{17} +(6.99034 - 12.1076i) q^{19} +(-62.8126 + 22.8619i) q^{20} +(75.3263 - 63.2062i) q^{22} +(185.201 + 67.4078i) q^{23} +(26.7863 - 151.913i) q^{25} +67.6064 q^{26} +41.5786 q^{28} +(19.6811 - 111.617i) q^{29} +(67.6281 + 24.6146i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(208.219 - 75.7855i) q^{34} +(-86.8523 + 150.433i) q^{35} +(89.7337 + 155.423i) q^{37} +(21.4197 + 17.9732i) q^{38} +(-23.2146 - 131.657i) q^{40} +(-81.4849 - 462.124i) q^{41} +(14.3408 + 12.0333i) q^{43} +(98.3314 + 170.315i) q^{44} +(-197.087 + 341.365i) q^{46} +(-134.437 + 48.9312i) q^{47} +(-179.983 + 151.024i) q^{49} +(289.907 + 105.517i) q^{50} +(-23.4795 + 133.159i) q^{52} -99.0786 q^{53} -821.606 q^{55} +(-14.4401 + 81.8939i) q^{56} +(213.008 + 77.5284i) q^{58} +(106.415 - 89.2927i) q^{59} +(535.695 - 194.977i) q^{61} +(-71.9683 + 124.653i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-432.726 - 363.100i) q^{65} +(-122.797 - 696.417i) q^{67} +(76.9546 + 436.431i) q^{68} +(-266.131 - 223.310i) q^{70} +(189.267 + 327.820i) q^{71} +(-228.464 + 395.712i) q^{73} +(-337.288 + 122.763i) q^{74} +(-42.8393 + 35.9464i) q^{76} +(480.240 + 174.793i) q^{77} +(-180.088 + 1021.33i) q^{79} +267.375 q^{80} +938.505 q^{82} +(-105.632 + 599.067i) q^{83} +(-1739.77 - 633.224i) q^{85} +(-28.6815 + 24.0666i) q^{86} +(-369.605 + 134.525i) q^{88} +(-828.921 + 1435.73i) q^{89} +(175.686 + 304.298i) q^{91} +(-603.910 - 506.741i) q^{92} +(-49.6860 - 281.784i) q^{94} +(-40.5695 - 230.081i) q^{95} +(292.250 + 245.226i) q^{97} +(-234.951 - 406.947i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more