LMFDB - Embedded newform 162.4.e.b.37.2

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			37.2
Character	$\chi$	$=$	162.37
Dual form			162.4.e.b.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-11.4993 + 4.18541i) q^{5} +(3.15689 + 17.9036i) q^{7} +(-4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-11.4993 + 4.18541i) q^{5} +(3.15689 + 17.9036i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-12.2373 + 21.1956i) q^{10} +(-63.8609 - 23.2435i) q^{11} +(-28.0809 - 23.5627i) q^{13} +(27.8531 + 23.3715i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(-59.2567 + 102.636i) q^{17} +(51.9128 + 89.9156i) q^{19} +(8.49995 + 48.2056i) q^{20} +(-127.722 + 46.4869i) q^{22} +(2.68021 - 15.2003i) q^{23} +(18.9609 - 15.9101i) q^{25} -73.3141 q^{26} +72.7192 q^{28} +(113.444 - 95.1905i) q^{29} +(15.3207 - 86.8881i) q^{31} +(-30.0702 + 10.9446i) q^{32} +(41.1593 + 233.426i) q^{34} +(-111.236 - 192.666i) q^{35} +(-47.5646 + 82.3843i) q^{37} +(195.128 + 71.0209i) q^{38} +(74.9946 + 62.9279i) q^{40} +(-188.819 - 158.438i) q^{41} +(-94.8761 - 34.5321i) q^{43} +(-135.919 + 235.418i) q^{44} +(-15.4347 - 26.7338i) q^{46} +(24.8495 + 140.928i) q^{47} +(11.7417 - 4.27361i) q^{49} +(8.59619 - 48.7514i) q^{50} +(-112.324 + 94.2508i) q^{52} -213.760 q^{53} +831.639 q^{55} +(111.412 - 93.4860i) q^{56} +(51.4312 - 291.681i) q^{58} +(480.336 - 174.828i) q^{59} +(-75.9976 - 431.004i) q^{61} +(-88.2285 - 152.816i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(421.531 + 153.425i) q^{65} +(-680.267 - 570.811i) q^{67} +(363.146 + 304.716i) q^{68} +(-418.110 - 152.180i) q^{70} +(-202.613 + 350.936i) q^{71} +(37.3045 + 64.6133i) q^{73} +(33.0380 + 187.368i) q^{74} +(390.257 - 142.042i) q^{76} +(214.540 - 1216.72i) q^{77} +(-469.453 + 393.918i) q^{79} +195.797 q^{80} -492.972 q^{82} +(165.300 - 138.703i) q^{83} +(251.839 - 1428.25i) q^{85} +(-189.752 + 69.0641i) q^{86} +(94.4081 + 535.415i) q^{88} +(416.745 + 721.824i) q^{89} +(333.209 - 577.134i) q^{91} +(-58.0157 - 21.1160i) q^{92} +(219.246 + 183.969i) q^{94} +(-973.295 - 816.691i) q^{95} +(1132.55 + 412.213i) q^{97} +(12.4952 - 21.6423i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−11.4993	+	4.18541i	−1.02853	+	0.374354i	−0.800521	−	0.599305i	$-0.795444\pi$
$5$	−11.4993	+	4.18541i	−1.02853	+	0.374354i	−0.228009	+	0.973659i	$0.573221\pi$
$6$		0			0
$7$	3.15689	+	17.9036i	0.170456	+	0.966703i	0.943259	+	0.332058i	$0.107743\pi$
$7$	3.15689	+	17.9036i	0.170456	+	0.966703i	−0.772803	+	0.634646i	$0.781146\pi$
$8$	−4.00000	−	6.92820i	−0.176777	−	0.306186i
$9$		0			0
$10$	−12.2373	+	21.1956i	−0.386978	+	0.670265i
$11$	−63.8609	−	23.2435i	−1.75043	−	0.637106i	−0.750711	−	0.660631i	$-0.770289\pi$
$11$	−63.8609	−	23.2435i	−1.75043	−	0.637106i	−0.999723	+	0.0235245i	$0.992511\pi$
$12$		0			0
$13$	−28.0809	−	23.5627i	−0.599096	−	0.502701i	0.292059	−	0.956400i	$-0.405660\pi$
$13$	−28.0809	−	23.5627i	−0.599096	−	0.502701i	−0.891155	+	0.453699i	$0.850104\pi$
$14$	27.8531	+	23.3715i	0.531717	+	0.446164i
$15$		0			0
$16$	−15.0351	−	5.47232i	−0.234923	−	0.0855050i
$17$	−59.2567	+	102.636i	−0.845404	+	1.46428i	0.0398668	+	0.999205i	$0.487307\pi$
$17$	−59.2567	+	102.636i	−0.845404	+	1.46428i	−0.885270	+	0.465077i	$0.846027\pi$
$18$		0			0
$19$	51.9128	+	89.9156i	0.626822	+	1.08569i	0.988186	+	0.153262i	$0.0489779\pi$
$19$	51.9128	+	89.9156i	0.626822	+	1.08569i	−0.361364	+	0.932425i	$0.617689\pi$
$20$	8.49995	+	48.2056i	0.0950323	+	0.538955i
$21$		0			0
$22$	−127.722	+	46.4869i	−1.23774	+	0.450502i
$23$	2.68021	−	15.2003i	0.0242984	−	0.137803i	−0.970245	−	0.242124i	$-0.922156\pi$
$23$	2.68021	−	15.2003i	0.0242984	−	0.137803i	0.994544	+	0.104321i	$0.0332670\pi$
$24$		0			0
$25$	18.9609	−	15.9101i	0.151687	−	0.127281i
$26$	−73.3141			−0.553003
$27$		0			0
$28$	72.7192			0.490808
$29$	113.444	−	95.1905i	0.726412	−	0.609532i	−0.202739	−	0.979233i	$-0.564984\pi$
$29$	113.444	−	95.1905i	0.726412	−	0.609532i	0.929151	+	0.369700i	$0.120540\pi$
$30$		0			0
$31$	15.3207	−	86.8881i	0.0887639	−	0.503405i	−0.907717	−	0.419583i	$-0.862176\pi$
$31$	15.3207	−	86.8881i	0.0887639	−	0.503405i	0.996481	−	0.0838219i	$-0.0267127\pi$
$32$	−30.0702	+	10.9446i	−0.166116	+	0.0604612i
$33$		0			0
$34$	41.1593	+	233.426i	0.207610	+	1.17742i
$35$	−111.236	−	192.666i	−0.537208	−	0.930472i
$36$		0			0
$37$	−47.5646	+	82.3843i	−0.211340	+	0.366051i	−0.952134	−	0.305681i	$-0.901116\pi$
$37$	−47.5646	+	82.3843i	−0.211340	+	0.366051i	0.740794	+	0.671732i	$0.234449\pi$
$38$	195.128	+	71.0209i	0.833000	+	0.303187i
$39$		0			0
$40$	74.9946	+	62.9279i	0.296442	+	0.248744i
$41$	−188.819	−	158.438i	−0.719235	−	0.603510i	0.207939	−	0.978142i	$-0.433325\pi$
$41$	−188.819	−	158.438i	−0.719235	−	0.603510i	−0.927174	+	0.374632i	$0.877769\pi$
$42$		0			0
$43$	−94.8761	−	34.5321i	−0.336476	−	0.122467i	0.168256	−	0.985743i	$-0.446186\pi$
$43$	−94.8761	−	34.5321i	−0.336476	−	0.122467i	−0.504732	+	0.863276i	$0.668409\pi$
$44$	−135.919	+	235.418i	−0.465693	+	0.806605i
$45$		0			0
$46$	−15.4347	−	26.7338i	−0.0494724	−	0.0856886i
$47$	24.8495	+	140.928i	0.0771206	+	0.437372i	0.998780	+	0.0493735i	$0.0157225\pi$
$47$	24.8495	+	140.928i	0.0771206	+	0.437372i	−0.921660	+	0.387999i	$0.873166\pi$
$48$		0			0
$49$	11.7417	−	4.27361i	0.0342322	−	0.0124595i
$50$	8.59619	−	48.7514i	0.0243137	−	0.137890i
$51$		0			0
$52$	−112.324	+	94.2508i	−0.299548	+	0.251351i
$53$	−213.760			−0.554004			−0.277002	−	0.960869i	$-0.589341\pi$
$53$	−213.760			−0.554004			−0.277002	+	0.960869i	$0.589341\pi$
$54$		0			0
$55$	831.639			2.03888
$56$	111.412	−	93.4860i	0.265859	−	0.223082i
$57$		0			0
$58$	51.4312	−	291.681i	0.116435	−	0.660337i
$59$	480.336	−	174.828i	1.05991	−	0.385774i	0.247513	−	0.968885i	$-0.420387\pi$
$59$	480.336	−	174.828i	1.05991	−	0.385774i	0.812393	+	0.583110i	$0.198164\pi$
$60$		0			0
$61$	−75.9976	−	431.004i	−0.159516	−	0.904662i	−0.954540	−	0.298083i	$-0.903653\pi$
$61$	−75.9976	−	431.004i	−0.159516	−	0.904662i	0.795024	−	0.606578i	$-0.207458\pi$
$62$	−88.2285	−	152.816i	−0.180726	−	0.313027i
$63$		0			0
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	421.531	+	153.425i	0.804376	+	0.292769i
$66$		0			0
$67$	−680.267	−	570.811i	−1.24041	−	1.04083i	−0.997492	−	0.0707861i	$-0.977449\pi$
$67$	−680.267	−	570.811i	−1.24041	−	1.04083i	−0.242923	−	0.970046i	$-0.578106\pi$
$68$	363.146	+	304.716i	0.647617	+	0.543415i
$69$		0			0
$70$	−418.110	−	152.180i	−0.713910	−	0.259842i
$71$	−202.613	+	350.936i	−0.338672	+	0.586597i	−0.984183	−	0.177154i	$-0.943311\pi$
$71$	−202.613	+	350.936i	−0.338672	+	0.586597i	0.645511	+	0.763751i	$0.276644\pi$
$72$		0			0
$73$	37.3045	+	64.6133i	0.0598105	+	0.103595i	0.894380	−	0.447308i	$-0.147617\pi$
$73$	37.3045	+	64.6133i	0.0598105	+	0.103595i	−0.834570	+	0.550902i	$0.814284\pi$
$74$	33.0380	+	187.368i	0.0518999	+	0.294339i
$75$		0			0
$76$	390.257	−	142.042i	0.589020	−	0.214386i
$77$	214.540	−	1216.72i	0.317521	−	1.80075i
$78$		0			0
$79$	−469.453	+	393.918i	−0.668577	+	0.561003i	−0.912644	−	0.408756i	$-0.865963\pi$
$79$	−469.453	+	393.918i	−0.668577	+	0.561003i	0.244067	+	0.969758i	$0.421518\pi$
$80$	195.797			0.273635
$81$		0			0
$82$	−492.972			−0.663899
$83$	165.300	−	138.703i	0.218602	−	0.183429i	−0.526910	−	0.849921i	$-0.676649\pi$
$83$	165.300	−	138.703i	0.218602	−	0.183429i	0.745512	+	0.666492i	$0.232205\pi$
$84$		0			0
$85$	251.839	−	1428.25i	0.321363	−	1.82254i
$86$	−189.752	+	69.0641i	−0.237924	+	0.0865974i
$87$		0			0
$88$	94.4081	+	535.415i	0.114363	+	0.648584i
$89$	416.745	+	721.824i	0.496347	+	0.859699i	0.999991	−	0.00421251i	$-0.00134089\pi$
$89$	416.745	+	721.824i	0.496347	+	0.859699i	−0.503644	+	0.863911i	$0.668008\pi$
$90$		0			0
$91$	333.209	−	577.134i	0.383844	−	0.664837i
$92$	−58.0157	−	21.1160i	−0.0657451	−	0.0239293i
$93$		0			0
$94$	219.246	+	183.969i	0.240569	+	0.201861i
$95$	−973.295	−	816.691i	−1.05114	−	0.882008i
$96$		0			0
$97$	1132.55	+	412.213i	1.18549	+	0.431483i	0.858138	−	0.513419i	$-0.171621\pi$
$97$	1132.55	+	412.213i	1.18549	+	0.431483i	0.327353	+	0.944902i	$0.393844\pi$
$98$	12.4952	−	21.6423i	0.0128797	−	0.0223082i
$99$		0			0
$100$	−49.5035	−	85.7425i	−0.0495035	−	0.0857425i
$101$	331.728	+	1881.32i	0.326814	+	1.85345i	0.496610	+	0.867974i	$0.334578\pi$
$101$	331.728	+	1881.32i	0.326814	+	1.85345i	−0.169796	+	0.985479i	$0.554311\pi$
$102$		0			0
$103$	−1814.49	+	660.421i	−1.73580	+	0.631779i	−0.999016	−	0.0443502i	$-0.985878\pi$
$103$	−1814.49	+	660.421i	−1.73580	+	0.631779i	−0.736783	+	0.676129i	$0.763656\pi$
$104$	−50.9234	+	288.801i	−0.0480140	+	0.272301i
$105$		0			0
$106$	−327.500	+	274.805i	−0.300090	+	0.251806i
$107$	−130.274			−0.117702			−0.0588509	−	0.998267i	$-0.518744\pi$
$107$	−130.274			−0.117702			−0.0588509	+	0.998267i	$0.518744\pi$
$108$		0			0
$109$	515.662			0.453133			0.226566	−	0.973996i	$-0.427250\pi$
$109$	515.662			0.453133			0.226566	+	0.973996i	$0.427250\pi$
$110$	1274.15	−	1069.13i	1.10441	−	0.926709i
$111$		0			0
$112$	50.5102	−	286.458i	0.0426140	−	0.241676i
$113$	694.631	−	252.825i	0.578277	−	0.210476i	−0.0362883	−	0.999341i	$-0.511553\pi$
$113$	694.631	−	252.825i	0.578277	−	0.210476i	0.614566	+	0.788866i	$0.289331\pi$
$114$		0			0
$115$	32.7986	+	186.010i	0.0265955	+	0.150831i
$116$	−296.180	−	512.999i	−0.237066	−	0.410610i
$117$		0			0
$118$	511.163	−	885.361i	0.398783	−	0.690712i
$119$	−2024.61	−	736.899i	−1.55963	−	0.567659i
$120$		0			0
$121$	2518.35	+	2113.15i	1.89207	+	1.58764i
$122$	−670.523	−	562.635i	−0.497592	−	0.417530i
$123$		0			0
$124$	−331.631	−	120.704i	−0.240172	−	0.0874154i
$125$	613.385	−	1062.41i	0.438902	−	0.760201i
$126$		0			0
$127$	693.825	+	1201.74i	0.484780	+	0.839663i	0.999847	−	0.0174867i	$-0.00556646\pi$
$127$	693.825	+	1201.74i	0.484780	+	0.839663i	−0.515067	+	0.857150i	$0.672233\pi$
$128$	22.2270	+	126.055i	0.0153485	+	0.0870455i
$129$		0			0
$130$	843.062	−	306.849i	0.568780	−	0.207019i
$131$	−64.0493	+	363.242i	−0.0427177	+	0.242264i	−0.998689	−	0.0511977i	$-0.983696\pi$
$131$	−64.0493	+	363.242i	−0.0427177	+	0.242264i	0.955971	+	0.293462i	$0.0948073\pi$
$132$		0			0
$133$	−1445.93	+	1213.28i	−0.942692	+	0.791012i
$134$	−1776.05			−1.14498
$135$		0			0
$136$	948.107			0.597791
$137$	−737.591	+	618.912i	−0.459975	+	0.385965i	−0.843122	−	0.537722i	$-0.819285\pi$
$137$	−737.591	+	618.912i	−0.459975	+	0.385965i	0.383147	+	0.923688i	$0.374840\pi$
$138$		0			0
$139$	98.0862	−	556.275i	0.0598530	−	0.339443i	−0.940146	−	0.340772i	$-0.889312\pi$
$139$	98.0862	−	556.275i	0.0598530	−	0.339443i	0.999999	+	0.00132838i	$0.000422836\pi$
$140$	−836.220	+	304.359i	−0.504811	+	0.183736i
$141$		0			0
$142$	140.733	+	798.139i	0.0831696	+	0.471678i
$143$	1245.59	+	2157.43i	0.728404	+	1.26163i
$144$		0			0
$145$	−906.113	+	1569.43i	−0.518956	+	0.898858i
$146$	140.219	+	51.0356i	0.0794837	+	0.0289297i
$147$		0			0
$148$	291.493	+	244.592i	0.161896	+	0.135847i
$149$	908.485	+	762.309i	0.499503	+	0.419133i	0.857417	−	0.514622i	$-0.172068\pi$
$149$	908.485	+	762.309i	0.499503	+	0.419133i	−0.357914	+	0.933754i	$0.616512\pi$
$150$		0			0
$151$	−2454.71	−	893.442i	−1.32293	−	0.481505i	−0.418531	−	0.908203i	$-0.637455\pi$
$151$	−2454.71	−	893.442i	−1.32293	−	0.481505i	−0.904394	+	0.426697i	$0.859677\pi$
$152$	415.302	−	719.325i	0.221615	−	0.383848i
$153$		0			0
$154$	−1235.49	−	2139.93i	−0.646483	−	1.11974i
$155$	187.484	+	1063.28i	0.0971555	+	0.550996i
$156$		0			0
$157$	−3080.94	+	1121.37i	−1.56615	+	0.570033i	−0.972135	−	0.234420i	$-0.924681\pi$
$157$	−3080.94	+	1121.37i	−1.56615	+	0.570033i	−0.594017	+	0.804453i	$0.702459\pi$
$158$	−212.833	+	1207.03i	−0.107165	+	0.607763i
$159$		0			0
$160$	299.978	−	251.712i	0.148221	−	0.124372i
$161$	280.600			0.137357
$162$		0			0
$163$	−3215.05			−1.54492			−0.772460	−	0.635064i	$-0.780974\pi$
$163$	−3215.05			−1.54492			−0.772460	+	0.635064i	$0.780974\pi$
$164$	−755.278	+	633.753i	−0.359618	+	0.301755i
$165$		0			0
$166$	74.9407	−	425.010i	0.0350393	−	0.198718i
$167$	−3545.57	+	1290.48i	−1.64290	+	0.597968i	−0.987543	−	0.157349i	$-0.949705\pi$
$167$	−3545.57	+	1290.48i	−1.64290	+	0.597968i	−0.655360	+	0.755317i	$0.727483\pi$
$168$		0			0
$169$	−148.167	−	840.298i	−0.0674407	−	0.382475i
$170$	−1450.29	−	2511.97i	−0.654305	−	1.13329i
$171$		0			0
$172$	−201.930	+	349.753i	−0.0895176	+	0.155049i
$173$	−178.813	−	65.0826i	−0.0785832	−	0.0286020i	0.302429	−	0.953172i	$-0.402202\pi$
$173$	−178.813	−	65.0826i	−0.0785832	−	0.0286020i	−0.381013	+	0.924570i	$0.624425\pi$
$174$		0			0
$175$	344.706	+	289.242i	0.148899	+	0.124941i
$176$	832.958	+	698.935i	0.356742	+	0.299342i
$177$		0			0
$178$	1566.45	+	570.141i	0.659609	+	0.240078i
$179$	425.982	−	737.822i	0.177874	−	0.308086i	−0.763278	−	0.646070i	$-0.776412\pi$
$179$	425.982	−	737.822i	0.177874	−	0.308086i	0.941152	+	0.337984i	$0.109745\pi$
$180$		0			0
$181$	878.518	+	1521.64i	0.360772	+	0.624875i	0.988088	−	0.153889i	$-0.0491800\pi$
$181$	878.518	+	1521.64i	0.360772	+	0.624875i	−0.627316	+	0.778765i	$0.715847\pi$
$182$	−231.444	−	1312.59i	−0.0942626	−	0.534590i
$183$		0			0
$184$	−116.031	+	42.2319i	−0.0464888	+	0.0169205i
$185$	202.148	−	1146.44i	0.0803364	−	0.455610i
$186$		0			0
$187$	6169.79	−	5177.07i	2.41273	−	2.02452i
$188$	572.409			0.222060
$189$		0			0
$190$	−2541.09			−0.970264
$191$	−168.192	+	141.130i	−0.0637171	+	0.0534650i	−0.674090	−	0.738649i	$-0.735464\pi$
$191$	−168.192	+	141.130i	−0.0637171	+	0.0534650i	0.610373	+	0.792114i	$0.291020\pi$
$192$		0			0
$193$	−190.033	+	1077.73i	−0.0708750	+	0.401952i	0.928645	+	0.370970i	$0.120975\pi$
$193$	−190.033	+	1077.73i	−0.0708750	+	0.401952i	−0.999520	+	0.0309822i	$0.990136\pi$
$194$	2265.09	−	824.426i	0.838269	−	0.305105i
$195$		0			0
$196$	−8.67908	−	49.2215i	−0.00316293	−	0.0179379i
$197$	1098.62	+	1902.86i	0.397327	+	0.688190i	0.993395	−	0.114744i	$-0.0366047\pi$
$197$	1098.62	+	1902.86i	0.397327	+	0.688190i	−0.596069	+	0.802934i	$0.703271\pi$
$198$		0			0
$199$	69.9985	−	121.241i	0.0249350	−	0.0431887i	−0.853289	−	0.521439i	$-0.825395\pi$
$199$	69.9985	−	121.241i	0.0249350	−	0.0431887i	0.878224	+	0.478250i	$0.158729\pi$
$200$	−186.072	−	67.7247i	−0.0657864	−	0.0239443i
$201$		0			0
$202$	2926.82	+	2455.89i	1.01946	+	0.855426i
$203$	2062.38	+	1730.54i	0.713058	+	0.598327i
$204$		0			0
$205$	2834.42	+	1031.64i	0.965681	+	0.351479i
$206$	−1930.94	+	3344.49i	−0.653083	+	1.13117i
$207$		0			0
$208$	293.256	+	507.935i	0.0977580	+	0.169322i
$209$	−1225.25	−	6948.72i	−0.405513	−	2.29978i
$210$		0			0
$211$	−2609.50	+	949.780i	−0.851400	+	0.309884i	−0.730611	−	0.682794i	$-0.760765\pi$
$211$	−2609.50	+	949.780i	−0.851400	+	0.309884i	−0.120789	+	0.992678i	$0.538542\pi$
$212$	−148.476	+	842.051i	−0.0481009	+	0.272794i
$213$		0			0
$214$	−199.592	+	167.477i	−0.0637562	+	0.0534978i
$215$	1235.54			0.391922
$216$		0			0
$217$	1603.97			0.501774
$218$	790.040	−	662.922i	0.245451	−	0.205958i
$219$		0			0
$220$	577.651	−	3276.02i	0.177024	−	1.00395i
$221$	4082.35	−	1485.86i	1.24257	−	0.452260i
$222$		0			0
$223$	−533.402	−	3025.07i	−0.160176	−	0.908403i	−0.953900	−	0.300125i	$-0.902972\pi$
$223$	−533.402	−	3025.07i	−0.160176	−	0.908403i	0.793724	−	0.608278i	$-0.208139\pi$
$224$	−290.877	−	503.813i	−0.0867635	−	0.150279i
$225$		0			0
$226$	739.210	−	1280.35i	0.217573	−	0.376848i
$227$	−1701.79	−	619.399i	−0.497583	−	0.181106i	0.0810233	−	0.996712i	$-0.474181\pi$
$227$	−1701.79	−	619.399i	−0.497583	−	0.181106i	−0.578607	+	0.815607i	$0.696403\pi$
$228$		0			0
$229$	904.380	+	758.865i	0.260974	+	0.218983i	0.763881	−	0.645357i	$-0.223292\pi$
$229$	904.380	+	758.865i	0.260974	+	0.218983i	−0.502906	+	0.864341i	$0.667736\pi$
$230$	289.381	+	242.819i	0.0829617	+	0.0696131i
$231$		0			0
$232$	−1113.27	−	405.199i	−0.315043	−	0.114666i
$233$	1317.16	−	2281.38i	0.370342	−	0.641452i	−0.619276	−	0.785174i	$-0.712574\pi$
$233$	1317.16	−	2281.38i	0.370342	−	0.641452i	0.989618	+	0.143722i	$0.0459070\pi$
$234$		0			0
$235$	−875.594	−	1516.57i	−0.243053	−	0.420980i
$236$	−355.050	−	2013.59i	−0.0979314	−	0.555397i
$237$		0			0
$238$	−4049.23	+	1473.80i	−1.10283	+	0.401396i
$239$	−867.607	+	4920.45i	−0.234815	+	1.33170i	0.608187	+	0.793794i	$0.291897\pi$
$239$	−867.607	+	4920.45i	−0.234815	+	1.33170i	−0.843002	+	0.537910i	$0.819214\pi$
$240$		0			0
$241$	2961.05	−	2484.62i	0.791445	−	0.664101i	−0.154658	−	0.987968i	$-0.549428\pi$
$241$	2961.05	−	2484.62i	0.791445	−	0.664101i	0.946103	+	0.323867i	$0.104983\pi$
$242$	6574.94			1.74650
$243$		0			0
$244$	−1750.61			−0.459309
$245$	−117.134	+	98.2872i	−0.0305446	+	0.0256300i
$246$		0			0
$247$	660.895	−	3748.12i	0.170250	−	0.965535i
$248$	−663.261	+	241.407i	−0.169827	+	0.0618120i
$249$		0			0
$250$	−426.052	−	2416.26i	−0.107784	−	0.611272i
$251$	−2690.61	−	4660.27i	−0.676613	−	1.17193i	−0.975995	−	0.217794i	$-0.930114\pi$
$251$	−2690.61	−	4660.27i	−0.676613	−	1.17193i	0.299382	−	0.954133i	$-0.403219\pi$
$252$		0			0
$253$	−524.467	+	908.404i	−0.130328	+	0.225735i
$254$	2607.93	+	949.209i	0.644236	+	0.234483i
$255$		0			0
$256$	196.107	+	164.554i	0.0478778	+	0.0401742i
$257$	345.203	+	289.659i	0.0837866	+	0.0703053i	0.683719	−	0.729745i	$-0.260361\pi$
$257$	345.203	+	289.659i	0.0837866	+	0.0703053i	−0.599932	+	0.800051i	$0.704806\pi$
$258$		0			0
$259$	−1625.13	−	591.500i	−0.389887	−	0.141907i
$260$	897.167	−	1553.94i	0.214000	−	0.370659i
$261$		0			0
$262$	368.845	+	638.859i	0.0869746	+	0.150644i
$263$	700.062	+	3970.25i	0.164136	+	0.930859i	0.949951	+	0.312398i	$0.101132\pi$
$263$	700.062	+	3970.25i	0.164136	+	0.930859i	−0.785816	+	0.618461i	$0.787757\pi$
$264$		0			0
$265$	2458.09	−	894.673i	0.569810	−	0.207394i
$266$	−655.531	+	3717.70i	−0.151102	+	0.856944i
$267$		0			0
$268$	−2721.07	+	2283.25i	−0.620207	+	0.520416i
$269$	3636.53			0.824250			0.412125	−	0.911127i	$-0.364787\pi$
$269$	3636.53			0.824250			0.412125	+	0.911127i	$0.364787\pi$
$270$		0			0
$271$	441.873			0.0990474			0.0495237	−	0.998773i	$-0.484230\pi$
$271$	441.873			0.0990474			0.0495237	+	0.998773i	$0.484230\pi$
$272$	1452.58	−	1218.86i	0.323808	−	0.271707i
$273$		0			0
$274$	−334.397	+	1896.46i	−0.0737286	+	0.418136i
$275$	−1580.67	+	575.316i	−0.346610	+	0.126156i
$276$		0			0
$277$	256.912	+	1457.02i	0.0557269	+	0.316043i	0.999911	−	0.0133766i	$-0.00425802\pi$
$277$	256.912	+	1457.02i	0.0557269	+	0.316043i	−0.944184	+	0.329420i	$0.893147\pi$
$278$	−564.856	−	978.360i	−0.121863	−	0.211072i
$279$		0			0
$280$	−889.887	+	1541.33i	−0.189932	+	0.328972i
$281$	−3006.77	−	1094.38i	−0.638324	−	0.232331i	0.00252641	−	0.999997i	$-0.499196\pi$
$281$	−3006.77	−	1094.38i	−0.638324	−	0.232331i	−0.640850	+	0.767666i	$0.721418\pi$
$282$		0			0
$283$	4475.59	+	3755.46i	0.940092	+	0.788831i	0.977601	−	0.210465i	$-0.0674979\pi$
$283$	4475.59	+	3755.46i	0.940092	+	0.788831i	−0.0375091	+	0.999296i	$0.511942\pi$
$284$	1241.68	+	1041.90i	0.259438	+	0.217694i
$285$		0			0
$286$	4681.90	+	1704.07i	0.967996	+	0.352322i
$287$	2240.53	−	3880.72i	0.460817	−	0.798159i
$288$		0			0
$289$	−4566.21	−	7908.91i	−0.929414	−	1.60979i
$290$	629.379	+	3569.39i	0.127443	+	0.722764i
$291$		0			0
$292$	280.438	−	102.071i	0.0562034	−	0.0204564i
$293$	416.122	−	2359.95i	0.0829697	−	0.470545i	−0.914807	−	0.403892i	$-0.867657\pi$
$293$	416.122	−	2359.95i	0.0829697	−	0.470545i	0.997776	−	0.0666523i	$-0.0212318\pi$
$294$		0			0
$295$	−4791.81	+	4020.81i	−0.945729	+	0.793561i
$296$	761.034			0.149440
$297$		0			0
$298$	2371.88			0.461072
$299$	−433.422	+	363.684i	−0.0838309	+	0.0703425i
$300$		0			0
$301$	318.735	−	1807.64i	0.0610352	−	0.346148i
$302$	−4909.43	+	1786.88i	−0.935449	+	0.340476i
$303$		0			0
$304$	−288.466	−	1635.97i	−0.0544232	−	0.308649i
$305$	2677.84	+	4638.16i	0.502731	+	0.870756i
$306$		0			0
$307$	2402.93	−	4162.00i	0.446718	−	0.773738i	−0.551452	−	0.834207i	$-0.685926\pi$
$307$	2402.93	−	4162.00i	0.446718	−	0.773738i	0.998170	+	0.0604683i	$0.0192594\pi$
$308$	−4643.91	−	1690.24i	−0.859128	−	0.312697i
$309$		0			0
$310$	1654.16	+	1388.01i	0.303065	+	0.254302i
$311$	−4652.21	−	3903.66i	−0.848239	−	0.711757i	0.111162	−	0.993802i	$-0.464543\pi$
$311$	−4652.21	−	3903.66i	−0.848239	−	0.711757i	−0.959401	+	0.282045i	$0.908987\pi$
$312$		0			0
$313$	367.487	+	133.754i	0.0663630	+	0.0241541i	0.374988	−	0.927030i	$-0.377647\pi$
$313$	367.487	+	133.754i	0.0663630	+	0.0241541i	−0.308625	+	0.951184i	$0.599869\pi$
$314$	−3278.67	+	5678.82i	−0.589255	+	1.02062i
$315$		0			0
$316$	1225.65	+	2122.90i	0.218191	+	0.377918i
$317$	−783.029	−	4440.78i	−0.138736	−	0.786810i	−0.972185	−	0.234214i	$-0.924748\pi$
$317$	−783.029	−	4440.78i	−0.138736	−	0.786810i	0.833449	−	0.552596i	$-0.186363\pi$
$318$		0			0
$319$	−9457.17	+	3442.13i	−1.65987	+	0.604145i
$320$	135.999	−	771.289i	0.0237581	−	0.134739i
$321$		0			0
$322$	429.905	−	360.733i	0.0744027	−	0.0624312i
$323$	−12304.7			−2.11967
$324$		0			0
$325$	−907.326			−0.154860
$326$	−4925.74	+	4133.18i	−0.836845	+	0.702196i
$327$		0			0
$328$	−342.415	+	1941.93i	−0.0576424	+	0.326906i
$329$	−2444.68	+	889.790i	−0.409664	+	0.149105i
$330$		0			0
$331$	383.382	+	2174.27i	0.0636635	+	0.361053i	0.999952	+	0.00982105i	$0.00312619\pi$
$331$	383.382	+	2174.27i	0.0636635	+	0.361053i	−0.936288	+	0.351232i	$0.885763\pi$
$332$	−431.567	−	747.495i	−0.0713412	−	0.123567i
$333$		0			0
$334$	−3773.12	+	6535.24i	−0.618132	+	1.07064i
$335$	10211.7	+	3716.75i	1.66544	+	0.606172i
$336$		0			0
$337$	3584.75	+	3007.97i	0.579448	+	0.486215i	0.884766	−	0.466036i	$-0.154318\pi$
$337$	3584.75	+	3007.97i	0.579448	+	0.486215i	−0.305318	+	0.952251i	$0.598763\pi$
$338$	−1307.27	−	1096.93i	−0.210373	−	0.176524i
$339$		0			0
$340$	−5451.29	−	1984.11i	−0.869522	−	0.316480i
$341$	−2997.97	+	5192.64i	−0.476098	+	0.824626i
$342$		0			0
$343$	3231.41	+	5596.97i	0.508688	+	0.881073i
$344$	140.259	+	795.449i	0.0219833	+	0.124674i
$345$		0			0
$346$	−357.626	+	130.165i	−0.0555667	+	0.0202246i
$347$	976.820	−	5539.82i	0.151119	−	0.857041i	−0.811129	−	0.584867i	$-0.801147\pi$
$347$	976.820	−	5539.82i	0.151119	−	0.857041i	0.962248	−	0.272173i	$-0.0877423\pi$
$348$		0			0
$349$	−3739.14	+	3137.51i	−0.573500	+	0.481223i	−0.882805	−	0.469739i	$-0.844348\pi$
$349$	−3739.14	+	3137.51i	−0.573500	+	0.481223i	0.309306	+	0.950963i	$0.399903\pi$
$350$	899.963			0.137443
$351$		0			0
$352$	2174.70			0.329295
$353$	−8196.80	+	6877.93i	−1.23590	+	1.03704i	−0.238064	+	0.971250i	$0.576513\pi$
$353$	−8196.80	+	6877.93i	−1.23590	+	1.03704i	−0.997833	+	0.0657914i	$0.979043\pi$
$354$		0			0
$355$	861.099	−	4883.53i	0.128739	−	0.730116i
$356$	3132.90	−	1140.28i	0.466414	−	0.169761i
$357$		0			0
$358$	−295.884	−	1678.04i	−0.0436814	−	0.247729i
$359$	−430.342	−	745.374i	−0.0632662	−	0.109580i	0.832657	−	0.553788i	$-0.186818\pi$
$359$	−430.342	−	745.374i	−0.0632662	−	0.109580i	−0.895924	+	0.444208i	$0.853485\pi$
$360$		0			0
$361$	−1960.38	+	3395.47i	−0.285811	+	0.495039i
$362$	3302.15	+	1201.88i	0.479439	+	0.174502i
$363$		0			0
$364$	−2042.02	−	1713.46i	−0.294041	−	0.246730i
$365$	−699.409	−	586.874i	−0.100298	−	0.0841600i
$366$		0			0
$367$	2259.70	+	822.465i	0.321405	+	0.116982i	0.497684	−	0.867358i	$-0.334184\pi$
$367$	2259.70	+	822.465i	0.321405	+	0.116982i	−0.176279	+	0.984340i	$0.556406\pi$
$368$	−123.478	+	213.870i	−0.0174911	+	0.0302955i
$369$		0			0
$370$	−1164.13	−	2016.32i	−0.163568	−	0.283307i
$371$	−674.817	−	3827.08i	−0.0944333	−	0.535558i
$372$		0			0
$373$	7411.12	−	2697.43i	1.02878	−	0.374444i	0.228161	−	0.973623i	$-0.426729\pi$
$373$	7411.12	−	2697.43i	1.02878	−	0.374444i	0.800614	+	0.599180i	$0.204507\pi$
$374$	2797.16	−	15863.5i	0.386731	−	2.19326i
$375$		0			0
$376$	876.982	−	735.875i	0.120284	−	0.100931i
$377$	−5428.55			−0.741604
$378$		0			0
$379$	−1352.50			−0.183307			−0.0916534	−	0.995791i	$-0.529215\pi$
$379$	−1352.50			−0.183307			−0.0916534	+	0.995791i	$0.529215\pi$
$380$	−3893.18	+	3266.76i	−0.525568	+	0.441004i
$381$		0			0
$382$	−76.2522	+	432.448i	−0.0102131	+	0.0579213i
$383$	2405.55	−	875.549i	0.320934	−	0.116811i	−0.176529	−	0.984295i	$-0.556487\pi$
$383$	2405.55	−	875.549i	0.320934	−	0.116811i	0.497464	+	0.867485i	$0.334265\pi$
$384$		0			0
$385$	2625.39	+	14889.3i	0.347539	+	1.97099i
$386$	1094.36	+	1895.48i	0.144304	+	0.249941i
$387$		0			0
$388$	2410.46	−	4175.04i	0.315393	−	0.546277i
$389$	9007.01	+	3278.28i	1.17397	+	0.427289i	0.854068	−	0.520162i	$-0.174128\pi$
$389$	9007.01	+	3278.28i	1.17397	+	0.427289i	0.319900	+	0.947451i	$0.396351\pi$
$390$		0			0
$391$	1401.27	+	1175.80i	0.181241	+	0.152079i
$392$	−76.5751	−	64.2541i	−0.00986639	−	0.00827889i
$393$		0			0
$394$	4129.45	+	1503.00i	0.528018	+	0.192183i
$395$	3749.68	−	6494.63i	0.477637	−	0.827292i
$396$		0			0
$397$	−1661.86	−	2878.43i	−0.210092	−	0.363890i	0.741651	−	0.670786i	$-0.234043\pi$
$397$	−1661.86	−	2878.43i	−0.210092	−	0.363890i	−0.951743	+	0.306896i	$0.900710\pi$
$398$	−48.6204	−	275.740i	−0.00612342	−	0.0347277i
$399$		0			0
$400$	−372.144	+	135.449i	−0.0465180	+	0.0169312i
$401$	−1483.86	+	8415.37i	−0.184789	+	1.04799i	0.741438	+	0.671021i	$0.234144\pi$
$401$	−1483.86	+	8415.37i	−0.184789	+	1.04799i	−0.926227	+	0.376967i	$0.876967\pi$
$402$		0			0
$403$	−2477.54	+	2078.90i	−0.306240	+	0.256966i
$404$	7641.39			0.941023
$405$		0			0
$406$	5384.50			0.658197
$407$	4952.41	−	4155.57i	0.603150	−	0.506103i
$408$		0			0
$409$	1794.12	−	10174.9i	0.216903	−	1.23012i	−0.660670	−	0.750676i	$-0.729728\pi$
$409$	1794.12	−	10174.9i	0.216903	−	1.23012i	0.877573	−	0.479443i	$-0.159161\pi$
$410$	5668.84	−	2063.29i	0.682839	−	0.248533i
$411$		0			0
$412$	1341.22	+	7606.43i	0.160381	+	0.909568i
$413$	4646.42	+	8047.84i	0.553597	+	0.958858i
$414$		0			0
$415$	−1320.30	+	2286.83i	−0.156171	+	0.270497i
$416$	1102.28	+	401.198i	0.129913	+	0.0472845i
$417$		0			0
$418$	−10810.3	−	9070.91i	−1.26495	−	1.06142i
$419$	−1085.25	−	910.631i	−0.126534	−	0.106175i	0.577325	−	0.816515i	$-0.304097\pi$
$419$	−1085.25	−	910.631i	−0.126534	−	0.106175i	−0.703859	+	0.710340i	$0.748541\pi$
$420$		0			0
$421$	−13521.6	−	4921.45i	−1.56532	−	0.569731i	−0.593375	−	0.804926i	$-0.702205\pi$
$421$	−13521.6	−	4921.45i	−1.56532	−	0.569731i	−0.971948	+	0.235195i	$0.924427\pi$
$422$	−2776.97	+	4809.85i	−0.320334	+	0.554834i
$423$		0			0
$424$	855.041	+	1480.97i	0.0979350	+	0.169628i
$425$	509.382	+	2888.85i	0.0581380	+	0.329717i
$426$		0			0
$427$	7476.60	−	2721.26i	0.847349	−	0.308410i
$428$	−90.4876	+	513.181i	−0.0102194	+	0.0579568i
$429$		0			0
$430$	1892.96	−	1588.38i	0.212294	−	0.178136i
$431$	−10938.5			−1.22248			−0.611238	−	0.791447i	$-0.709328\pi$
$431$	−10938.5			−1.22248			−0.611238	+	0.791447i	$0.709328\pi$
$432$		0			0
$433$	8967.48			0.995265			0.497633	−	0.867388i	$-0.334203\pi$
$433$	8967.48			0.995265			0.497633	+	0.867388i	$0.334203\pi$
$434$	2457.43	−	2062.03i	0.271798	−	0.228066i
$435$		0			0
$436$	358.175	−	2031.31i	0.0393428	−	0.223124i
$437$	1505.88	−	548.095i	0.164842	−	0.0599975i
$438$		0			0
$439$	−2714.55	−	15395.0i	−0.295122	−	1.67372i	−0.666708	−	0.745319i	$-0.732297\pi$
$439$	−2714.55	−	15395.0i	−0.295122	−	1.67372i	0.371586	−	0.928398i	$-0.378814\pi$
$440$	−3326.56	−	5761.77i	−0.360426	−	0.624276i
$441$		0			0
$442$	4344.35	−	7524.64i	0.467511	−	0.809752i
$443$	5592.34	+	2035.45i	0.599774	+	0.218300i	0.624023	−	0.781406i	$-0.285497\pi$
$443$	5592.34	+	2035.45i	0.599774	+	0.218300i	−0.0242487	+	0.999706i	$0.507719\pi$
$444$		0			0
$445$	−7813.41	−	6556.23i	−0.832340	−	0.698416i
$446$	−4706.18	−	3948.95i	−0.499650	−	0.419256i
$447$		0			0
$448$	−1093.34	−	397.943i	−0.115302	−	0.0419666i
$449$	4929.18	−	8537.58i	0.518090	−	0.897357i	−0.481690	−	0.876342i	$-0.659977\pi$
$449$	4929.18	−	8537.58i	0.518090	−	0.897357i	0.999779	−	0.0210156i	$-0.00668995\pi$
$450$		0			0
$451$	8375.52	+	14506.8i	0.874474	+	1.51463i
$452$	−513.450	−	2911.92i	−0.0534307	−	0.303020i
$453$		0			0
$454$	−3403.57	+	1238.80i	−0.351845	+	0.128061i
$455$	−1416.13	+	8031.26i	−0.145910	+	0.827497i
$456$		0			0
$457$	−8054.49	+	6758.52i	−0.824449	+	0.691795i	−0.954009	−	0.299777i	$-0.903088\pi$
$457$	−8054.49	+	6758.52i	−0.824449	+	0.691795i	0.129561	+	0.991572i	$0.458643\pi$
$458$	2361.17			0.240896
$459$		0			0
$460$	755.519			0.0765788
$461$	8936.16	−	7498.33i	0.902816	−	0.757553i	−0.0679225	−	0.997691i	$-0.521637\pi$
$461$	8936.16	−	7498.33i	0.902816	−	0.757553i	0.970739	+	0.240138i	$0.0771926\pi$
$462$		0			0
$463$	−2638.58	+	14964.1i	−0.264849	+	1.50203i	0.504616	+	0.863344i	$0.331634\pi$
$463$	−2638.58	+	14964.1i	−0.264849	+	1.50203i	−0.769465	+	0.638689i	$0.779477\pi$
$464$	−2226.55	+	810.397i	−0.222769	+	0.0810814i
$465$		0			0
$466$	−914.887	−	5188.58i	−0.0909471	−	0.515787i
$467$	3786.69	+	6558.74i	0.375219	+	0.649898i	0.990360	−	0.138519i	$-0.0442342\pi$
$467$	3786.69	+	6558.74i	0.375219	+	0.649898i	−0.615141	+	0.788417i	$0.710901\pi$
$468$		0			0
$469$	8072.05	−	13981.2i	0.794739	−	1.37653i
$470$	−3291.16	−	1197.88i	−0.322999	−	0.117562i
$471$		0			0
$472$	−3132.59	−	2628.56i	−0.305486	−	0.256333i
$473$	5256.23	+	4410.50i	0.510955	+	0.428742i
$474$		0			0
$475$	2414.88	+	878.945i	0.233268	+	0.0849027i
$476$	−4309.10	+	7463.58i	−0.414931	+	0.718682i
$477$		0			0
$478$	4996.35	+	8653.94i	0.478092	+	0.828079i
$479$	1747.95	+	9913.12i	0.166735	+	0.945599i	0.947258	+	0.320472i	$0.103842\pi$
$479$	1747.95	+	9913.12i	0.166735	+	0.945599i	−0.780523	+	0.625127i	$0.785047\pi$
$480$		0			0
$481$	3276.85	−	1192.68i	0.310627	−	0.113059i
$482$	1342.43	−	7613.31i	0.126859	−	0.719454i
$483$		0			0
$484$	10073.4	−	8452.58i	0.946036	−	0.793819i
$485$	−14748.8			−1.38084
$486$		0			0
$487$	38.1375			0.00354862			0.00177431	−	0.999998i	$-0.499435\pi$
$487$	38.1375			0.00354862			0.00177431	+	0.999998i	$0.499435\pi$
$488$	−2682.09	+	2250.54i	−0.248796	+	0.208765i
$489$		0			0
$490$	−53.1043	+	301.170i	−0.00489594	+	0.0277662i
$491$	3565.97	−	1297.91i	0.327760	−	0.119295i	−0.172899	−	0.984940i	$-0.555313\pi$
$491$	3565.97	−	1297.91i	0.327760	−	0.119295i	0.500659	+	0.865645i	$0.333091\pi$
$492$		0			0
$493$	3047.64	+	17284.0i	0.278416	+	1.57897i
$494$	−3805.94	−	6592.08i	−0.346634	−	0.600388i
$495$		0			0
$496$	−705.828	+	1222.53i	−0.0638964	+	0.110672i
$497$	−6922.64	−	2519.63i	−0.624794	−	0.227406i
$498$		0			0
$499$	−9633.47	−	8083.44i	−0.864236	−	0.725180i	0.0986407	−	0.995123i	$-0.468551\pi$
$499$	−9633.47	−	8083.44i	−0.864236	−	0.725180i	−0.962876	+	0.269943i	$0.912995\pi$
$500$	−3759.04	−	3154.21i	−0.336219	−	0.282121i
$501$		0			0
$502$	−10113.4	−	3680.97i	−0.899168	−	0.327270i
$503$	1624.75	−	2814.16i	0.144024	−	0.249457i	−0.784984	−	0.619516i	$-0.787329\pi$
$503$	1624.75	−	2814.16i	0.144024	−	0.249457i	0.929008	+	0.370058i	$0.120662\pi$
$504$		0			0
$505$	−11688.8	−	20245.5i	−1.02999	−	1.78399i
$506$	364.291	+	2066.00i	0.0320054	+	0.181512i
$507$		0			0
$508$	5215.86	−	1898.42i	0.455544	−	0.165804i
$509$	3340.96	−	18947.5i	0.290934	−	1.64997i	−0.392351	−	0.919816i	$-0.628338\pi$
$509$	3340.96	−	18947.5i	0.290934	−	1.64997i	0.683285	−	0.730152i	$-0.260551\pi$
$510$		0			0
$511$	−1039.04	+	871.862i	−0.0899504	+	0.0754773i
$512$	512.000			0.0441942
$513$		0			0
$514$	901.260			0.0773402
$515$	18101.3	−	15188.8i	1.54881	−	1.29961i
$516$		0			0
$517$	1688.75	−	9577.39i	0.143658	−	0.814726i
$518$	−3250.26	+	1183.00i	−0.275692	+	0.100344i
$519$		0			0
$520$	−623.166	−	3534.15i	−0.0525531	−	0.298044i
$521$	−2291.42	−	3968.86i	−0.192685	−	0.333741i	0.753454	−	0.657501i	$-0.228386\pi$
$521$	−2291.42	−	3968.86i	−0.192685	−	0.333741i	−0.946139	+	0.323760i	$0.895053\pi$
$522$		0			0
$523$	−95.9940	+	166.267i	−0.00802586	+	0.0139012i	−0.870010	−	0.493033i	$-0.835888\pi$
$523$	−95.9940	+	166.267i	−0.00802586	+	0.0139012i	0.861985	+	0.506934i	$0.169221\pi$
$524$	1386.40	+	504.610i	0.115583	+	0.0420687i
$525$		0			0
$526$	6176.61	+	5182.79i	0.512002	+	0.429620i
$527$	8009.96	+	6721.15i	0.662086	+	0.555556i
$528$		0			0
$529$	11209.4	+	4079.88i	0.921293	+	0.335323i
$530$	2615.85	−	4530.78i	0.214387	−	0.371330i
$531$		0			0
$532$	3775.05	+	6538.59i	0.307649	+	0.532864i
$533$	1568.99	+	8898.19i	0.127506	+	0.723121i
$534$		0			0
$535$	1498.07	−	545.251i	0.121060	−	0.0440622i
$536$	−1233.63	+	6996.27i	−0.0994119	+	0.563793i
$537$		0			0
$538$	5571.49	−	4675.04i	0.446476	−	0.374638i
$539$	−849.166			−0.0678593
$540$		0			0
$541$	−20037.8			−1.59241			−0.796203	−	0.605030i	$-0.793161\pi$
$541$	−20037.8			−1.59241			−0.796203	+	0.605030i	$0.793161\pi$
$542$	676.988	−	568.061i	0.0536515	−	0.0450190i
$543$		0			0
$544$	658.548	−	3734.81i	0.0519026	−	0.294354i
$545$	−5929.76	+	2158.26i	−0.466060	+	0.169632i
$546$		0			0
$547$	−915.647	−	5192.89i	−0.0715726	−	0.405908i	−0.999454	−	0.0330336i	$-0.989483\pi$
$547$	−915.647	−	5192.89i	−0.0715726	−	0.405908i	0.927882	−	0.372875i	$-0.121628\pi$
$548$	1925.71	+	3335.43i	0.150114	+	0.260005i
$549$		0			0
$550$	−1682.11	+	2913.50i	−0.130410	+	0.225877i
$551$	14448.3	+	5258.75i	1.11709	+	0.406588i
$552$		0			0
$553$	−8534.56	−	7161.34i	−0.656286	−	0.550689i
$554$	2266.72	+	1902.01i	0.173834	+	0.145864i
$555$		0			0
$556$	−2123.16	−	772.769i	−0.161946	−	0.0589437i
$557$	−12241.6	+	21203.1i	−0.931228	+	1.61293i	−0.150002	+	0.988686i	$0.547928\pi$
$557$	−12241.6	+	21203.1i	−0.931228	+	1.61293i	−0.781226	+	0.624248i	$0.785405\pi$
$558$		0			0
$559$	1850.54	+	3205.23i	0.140017	+	0.242517i
$560$	618.109	+	3505.47i	0.0466426	+	0.264523i
$561$		0			0
$562$	−6013.54	+	2188.75i	−0.451363	+	0.164283i
$563$	−3416.79	+	19377.6i	−0.255774	+	1.45057i	0.538305	+	0.842750i	$0.319065\pi$
$563$	−3416.79	+	19377.6i	−0.255774	+	1.45057i	−0.794079	+	0.607815i	$0.792046\pi$
$564$		0			0
$565$	−6929.60	+	5814.62i	−0.515983	+	0.432961i
$566$	11684.9			0.867764
$567$		0			0
$568$	3241.80			0.239477
$569$	−7025.05	+	5894.72i	−0.517584	+	0.434305i	−0.863789	−	0.503854i	$-0.831915\pi$
$569$	−7025.05	+	5894.72i	−0.517584	+	0.434305i	0.346204	+	0.938159i	$0.387470\pi$
$570$		0			0
$571$	−4419.78	+	25065.8i	−0.323926	+	1.83708i	0.193188	+	0.981162i	$0.438117\pi$
$571$	−4419.78	+	25065.8i	−0.323926	+	1.83708i	−0.517114	+	0.855917i	$0.672994\pi$
$572$	9363.81	−	3408.15i	0.684476	−	0.249129i
$573$		0			0
$574$	−1556.26	−	8825.98i	−0.113165	−	0.641793i
$575$	−191.018	−	330.853i	−0.0138539	−	0.0239957i
$576$		0			0
$577$	−12967.3	+	22460.0i	−0.935591	+	1.62049i	−0.162015	+	0.986788i	$0.551799\pi$
$577$	−12967.3	+	22460.0i	−0.935591	+	1.62049i	−0.773576	+	0.633703i	$0.781534\pi$
$578$	−17163.3	−	6246.95i	−1.23512	−	0.449548i
$579$		0			0
$580$	5552.98	+	4659.50i	0.397543	+	0.333578i
$581$	3005.11	+	2521.59i	0.214584	+	0.180057i
$582$		0			0
$583$	13650.9	+	4968.53i	0.969748	+	0.352959i
$584$	298.436	−	516.907i	0.0211462	−	0.0366263i
$585$		0			0
$586$	−2396.35	−	4150.60i	−0.168929	−	0.292594i
$587$	−2210.91	−	12538.7i	−0.155458	−	0.881647i	−0.958366	−	0.285543i	$-0.907826\pi$
$587$	−2210.91	−	12538.7i	−0.155458	−	0.881647i	0.802908	−	0.596103i	$-0.203285\pi$
$588$		0			0
$589$	8607.93	−	3133.03i	0.602180	−	0.219175i
$590$	−2172.43	+	12320.5i	−0.151589	+	0.859704i
$591$		0			0
$592$	1165.97	−	978.366i	0.0809478	−	0.0679233i
$593$	4950.53			0.342823			0.171411	−	0.985200i	$-0.445167\pi$
$593$	4950.53			0.342823			0.171411	+	0.985200i	$0.445167\pi$
$594$		0			0
$595$	26365.9			1.81663
$596$	3633.94	−	3049.24i	0.249752	−	0.209566i
$597$		0			0
$598$	−196.498	+	1114.39i	−0.0134371	+	0.0762055i
$599$	5023.42	−	1828.38i	0.342657	−	0.124717i	−0.164959	−	0.986300i	$-0.552749\pi$
$599$	5023.42	−	1828.38i	0.342657	−	0.124717i	0.507616	+	0.861584i	$0.330527\pi$
$600$		0			0
$601$	−2454.17	−	13918.3i	−0.166569	−	0.944657i	−0.947432	−	0.319956i	$-0.896332\pi$
$601$	−2454.17	−	13918.3i	−0.166569	−	0.944657i	0.780864	−	0.624701i	$-0.214779\pi$
$602$	−1835.52	−	3179.22i	−0.124270	−	0.215241i
$603$		0			0
$604$	−5224.50	+	9049.10i	−0.351957	+	0.609607i
$605$	−37803.6	−	13759.4i	−2.54039	−	0.924627i
$606$		0			0
$607$	−2999.82	−	2517.15i	−0.200591	−	0.168316i	0.536959	−	0.843608i	$-0.319573\pi$
$607$	−2999.82	−	2517.15i	−0.200591	−	0.168316i	−0.737550	+	0.675292i	$0.764017\pi$
$608$	−2545.12	−	2135.61i	−0.169767	−	0.142451i
$609$		0			0
$610$	10065.4	+	3663.51i	0.668092	+	0.243166i
$611$	2622.85	−	4542.92i	0.173665	−	0.300797i
$612$		0			0
$613$	8062.31	+	13964.3i	0.531213	+	0.920089i	0.999336	+	0.0364252i	$0.0115971\pi$
$613$	8062.31	+	13964.3i	0.531213	+	0.920089i	−0.468123	+	0.883663i	$0.655070\pi$
$614$	−1669.06	−	9465.69i	−0.109703	−	0.622157i
$615$		0			0
$616$	−9287.82	+	3380.49i	−0.607495	+	0.221110i
$617$	3782.49	−	21451.6i	0.246803	−	1.39969i	−0.569465	−	0.822016i	$-0.692849\pi$
$617$	3782.49	−	21451.6i	0.246803	−	1.39969i	0.816268	−	0.577674i	$-0.196039\pi$
$618$		0			0
$619$	8641.39	−	7250.99i	0.561110	−	0.470827i	−0.317573	−	0.948234i	$-0.602868\pi$
$619$	8641.39	−	7250.99i	0.561110	−	0.470827i	0.878682	+	0.477407i	$0.158423\pi$
$620$	4318.72			0.279748
$621$		0			0
$622$	−12146.0			−0.782978
$623$	−11607.6	+	9739.96i	−0.746469	+	0.626362i
$624$		0			0
$625$	−3144.13	+	17831.2i	−0.201224	+	1.14120i
$626$	734.975	−	267.509i	0.0469257	−	0.0170796i
$627$		0			0
$628$	2277.34	+	12915.4i	0.144707	+	0.820672i
$629$	−5637.04	−	9763.64i	−0.357335	−	0.618922i
$630$		0			0
$631$	7928.45	−	13732.5i	0.500201	−	0.866373i	−0.499799	−	0.866141i	$-0.666593\pi$
$631$	7928.45	−	13732.5i	0.500201	−	0.866373i	1.00000		0.000231688i	$-7.37485e-5\pi$
$632$	4606.95	+	1676.79i	0.289960	+	0.105537i
$633$		0			0
$634$	−6908.62	−	5797.02i	−0.432770	−	0.363138i
$635$	−13008.3	−	10915.2i	−0.812941	−	0.682139i
$636$		0			0
$637$	−430.415	−	156.658i	−0.0267718	−	0.00974414i
$638$	−10064.1	+	17431.5i	−0.624517	+	1.08170i
$639$		0			0
$640$	−783.188	−	1356.52i	−0.0483722	−	0.0837831i
$641$	−1045.71	−	5930.49i	−0.0644351	−	0.365430i	−0.999927	−	0.0120815i	$-0.996154\pi$
$641$	−1045.71	−	5930.49i	−0.0644351	−	0.365430i	0.935492	−	0.353348i	$-0.114957\pi$
$642$		0			0
$643$	19404.4	−	7062.62i	1.19010	−	0.433161i	0.330341	−	0.943862i	$-0.392836\pi$
$643$	19404.4	−	7062.62i	1.19010	−	0.433161i	0.859759	+	0.510701i	$0.170614\pi$
$644$	194.903	−	1105.35i	0.0119259	−	0.0676349i
$645$		0			0
$646$	−18851.9	+	15818.6i	−1.14817	+	0.963431i
$647$	15438.8			0.938120			0.469060	−	0.883166i	$-0.344593\pi$
$647$	15438.8			0.938120			0.469060	+	0.883166i	$0.344593\pi$
$648$		0			0
$649$	−34738.3			−2.10108
$650$	−1390.10	+	1166.44i	−0.0838836	+	0.0703867i
$651$		0			0
$652$	−2233.15	+	12664.8i	−0.134136	+	0.760724i
$653$	−7078.57	+	2576.39i	−0.424205	+	0.154398i	−0.545296	−	0.838243i	$-0.683583\pi$
$653$	−7078.57	+	2576.39i	−0.424205	+	0.154398i	0.121091	+	0.992641i	$0.461361\pi$
$654$		0			0
$655$	−783.791	−	4445.10i	−0.0467561	−	0.265167i
$656$	1971.89	+	3415.41i	0.117362	+	0.203277i
$657$		0			0
$658$	−2601.57	+	4506.05i	−0.154133	+	0.266967i
$659$	−4114.07	−	1497.40i	−0.243189	−	0.0885136i	0.217550	−	0.976049i	$-0.430193\pi$
$659$	−4114.07	−	1497.40i	−0.243189	−	0.0885136i	−0.460739	+	0.887536i	$0.652416\pi$
$660$		0			0
$661$	15787.7	+	13247.4i	0.929002	+	0.779525i	0.975638	−	0.219387i	$-0.0704057\pi$
$661$	15787.7	+	13247.4i	0.929002	+	0.779525i	−0.0466363	+	0.998912i	$0.514850\pi$
$662$	3382.56	+	2838.31i	0.198591	+	0.166637i
$663$		0			0
$664$	−1622.16	−	590.418i	−0.0948072	−	0.0345070i
$665$	11549.1	−	20003.7i	0.673468	−	1.16648i
$666$		0			0
$667$	−1142.87	−	1979.50i	−0.0663448	−	0.114913i
$668$	2620.78	+	14863.2i	0.151798	+	0.860890i
$669$		0			0
$670$	20423.3	−	7433.49i	1.17765	−	0.428628i
$671$	−5164.74	+	29290.7i	−0.297143	+	1.68518i
$672$		0			0
$673$	13707.7	−	11502.1i	0.785128	−	0.658801i	−0.159406	−	0.987213i	$-0.550958\pi$
$673$	13707.7	−	11502.1i	0.785128	−	0.658801i	0.944534	+	0.328412i	$0.106514\pi$
$674$	9359.13			0.534867
$675$		0			0
$676$	−3413.04			−0.194188
$677$	−15418.8	+	12937.9i	−0.875320	+	0.734480i	−0.965211	−	0.261471i	$-0.915792\pi$
$677$	−15418.8	+	12937.9i	−0.875320	+	0.734480i	0.0898917	+	0.995952i	$0.471348\pi$
$678$		0			0
$679$	−3804.78	+	21578.0i	−0.215043	+	1.21957i
$680$	−10902.6	+	3968.21i	−0.614845	+	0.223785i
$681$		0			0
$682$	2082.37	+	11809.7i	0.116918	+	0.663075i
$683$	−12856.6	−	22268.3i	−0.720268	−	1.24754i	−0.960892	−	0.276923i	$-0.910685\pi$
$683$	−12856.6	−	22268.3i	−0.720268	−	1.24754i	0.240624	−	0.970619i	$-0.422648\pi$
$684$		0			0
$685$	5891.39	−	10204.2i	0.328611	−	0.569170i
$686$	12146.1	+	4420.84i	0.676009	+	0.246047i
$687$		0			0
$688$	1237.50	+	1038.39i	0.0685744	+	0.0575408i
$689$	6002.58	+	5036.77i	0.331902	+	0.278499i
$690$		0			0
$691$	−3686.75	−	1341.87i	−0.202967	−	0.0738741i	0.238536	−	0.971134i	$-0.423332\pi$
$691$	−3686.75	−	1341.87i	−0.202967	−	0.0738741i	−0.441503	+	0.897260i	$0.645555\pi$
$692$	−380.578	+	659.180i	−0.0209066	+	0.0362114i
$693$		0			0
$694$	−5625.28	−	9743.27i	−0.307684	−	0.532924i
$695$	1200.31	+	6807.31i	0.0655114	+	0.371534i
$696$		0			0
$697$	27450.2	−	9991.06i	1.49175	−	0.542953i
$698$	−1695.19	+	9613.88i	−0.0919252	+	0.521333i
$699$		0			0
$700$	1378.82	−	1156.97i	0.0744494	−	0.0624705i
$701$	−616.064			−0.0331932			−0.0165966	−	0.999862i	$-0.505283\pi$
$701$	−616.064			−0.0331932			−0.0165966	+	0.999862i	$0.505283\pi$
$702$		0			0
$703$	−9876.85			−0.529889
$704$	3331.83	−	2795.74i	0.178371	−	0.149671i
$705$		0			0
$706$	−3716.13	+	21075.2i	−0.198100	+	1.12348i
$707$	−32635.2	+	11878.3i	−1.73603	+	0.631864i
$708$		0			0
$709$	−2272.28	−	12886.7i	−0.120363	−	0.682612i	−0.983954	−	0.178420i	$-0.942901\pi$
$709$	−2272.28	−	12886.7i	−0.120363	−	0.682612i	0.863592	−	0.504192i	$-0.168210\pi$
$710$	−4958.87	−	8589.02i	−0.262117	−	0.454000i
$711$		0			0
$712$	3333.96	−	5774.59i	0.175485	−	0.303949i
$713$	−1279.66	−	465.757i	−0.0672140	−	0.0244639i
$714$		0			0
$715$	−23353.2	−	19595.7i	−1.22148	−	1.02495i
$716$	−2610.57	−	2190.53i	−0.136259	−	0.114335i
$717$		0			0
$718$	−1617.56	−	588.742i	−0.0840761	−	0.0306012i
$719$	14913.4	−	25830.8i	0.773543	−	1.33982i	−0.162067	−	0.986780i	$-0.551816\pi$
$719$	14913.4	−	25830.8i	0.773543	−	1.33982i	0.935610	−	0.353036i	$-0.114851\pi$
$720$		0			0
$721$	−17552.1	−	30401.1i	−0.906620	−	1.57031i
$722$	1361.66	+	7722.38i	0.0701882	+	0.398057i
$723$		0			0
$724$	6604.29	−	2403.77i	0.339015	−	0.123391i
$725$	636.506	−	3609.80i	0.0326058	−	0.184917i
$726$		0			0
$727$	−1841.80	+	1545.46i	−0.0939596	+	0.0788415i	−0.688557	−	0.725182i	$-0.741756\pi$
$727$	−1841.80	+	1545.46i	−0.0939596	+	0.0788415i	0.594598	+	0.804023i	$0.297311\pi$
$728$	−5331.34			−0.271418
$729$		0			0
$730$	−1826.03			−0.0925812
$731$	9166.26	−	7691.41i	0.463785	−	0.389161i
$732$		0			0
$733$	−2986.40	+	16936.7i	−0.150485	+	0.853440i	0.812314	+	0.583220i	$0.198208\pi$
$733$	−2986.40	+	16936.7i	−0.150485	+	0.853440i	−0.962799	+	0.270220i	$0.912904\pi$
$734$	4519.41	−	1644.93i	0.227268	−	0.0827186i
$735$		0			0
$736$	85.7669	+	486.408i	0.00429539	+	0.0243604i
$737$	30174.8	+	52264.3i	1.50814	+	2.61218i
$738$		0			0
$739$	3236.87	−	5606.42i	0.161123	−	0.279074i	−0.774149	−	0.633004i	$-0.781822\pi$
$739$	3236.87	−	5606.42i	0.161123	−	0.279074i	0.935272	+	0.353930i	$0.115155\pi$
$740$	−4375.68	−	1592.62i	−0.217369	−	0.0791159i
$741$		0			0
$742$	−5953.87	−	4995.89i	−0.294574	−	0.247177i
$743$	−1398.40	−	1173.40i	−0.0690476	−	0.0579378i	0.607611	−	0.794235i	$-0.292128\pi$
$743$	−1398.40	−	1173.40i	−0.0690476	−	0.0579378i	−0.676658	+	0.736297i	$0.736573\pi$
$744$		0			0
$745$	−13637.5	−	4963.65i	−0.670658	−	0.244099i
$746$	7886.75	−	13660.2i	0.387070	−	0.670425i
$747$		0			0
$748$	−16108.2	−	27900.2i	−0.787398	−	1.36381i
$749$	−411.262	−	2332.38i	−0.0200630	−	0.113783i
$750$		0			0
$751$	−29316.2	+	10670.2i	−1.42445	+	0.518457i	−0.935335	−	0.353762i	$-0.884902\pi$
$751$	−29316.2	+	10670.2i	−1.42445	+	0.518457i	−0.489114	+	0.872220i	$0.662680\pi$
$752$	397.591	−	2254.85i	0.0192801	−	0.109343i
$753$		0			0
$754$	−8317.02	+	6978.81i	−0.401708	+	0.337073i
$755$	31966.9			1.54092
$756$		0			0
$757$	14678.8			0.704770			0.352385	−	0.935855i	$-0.385371\pi$
$757$	14678.8			0.704770			0.352385	+	0.935855i	$0.385371\pi$
$758$	−2072.15	+	1738.74i	−0.0992927	+	0.0833165i
$759$		0			0
$760$	−1765.02	+	10009.9i	−0.0842423	+	0.477762i
$761$	−300.061	+	109.213i	−0.0142933	+	0.00520233i	−0.349157	−	0.937064i	$-0.613532\pi$
$761$	−300.061	+	109.213i	−0.0142933	+	0.00520233i	0.334864	+	0.942267i	$0.391310\pi$
$762$		0			0
$763$	1627.89	+	9232.21i	0.0772392	+	0.438045i
$764$	439.119	+	760.576i	0.0207942	+	0.0360166i
$765$		0			0
$766$	2559.93	−	4433.93i	0.120750	−	0.209144i
$767$	−17607.7	−	6408.68i	−0.828915	−	0.301700i
$768$		0			0
$769$	10193.2	+	8553.09i	0.477991	+	0.401082i	0.849699	−	0.527267i	$-0.176783\pi$
$769$	10193.2	+	8553.09i	0.477991	+	0.401082i	−0.371708	+	0.928350i	$0.621228\pi$
$770$	23163.7	+	19436.6i	1.08411	+	0.909673i
$771$		0			0
$772$	4113.43	+	1497.17i	0.191769	+	0.0697982i
$773$	−7564.08	+	13101.4i	−0.351955	+	0.609604i	−0.986592	−	0.163207i	$-0.947816\pi$
$773$	−7564.08	+	13101.4i	−0.351955	+	0.609604i	0.634637	+	0.772810i	$0.281150\pi$
$774$		0			0
$775$	−1091.90	−	1891.23i	−0.0506095	−	0.0876582i
$776$	−1674.29	−	9495.36i	−0.0774529	−	0.439257i
$777$		0			0
$778$	18014.0	−	6556.57i	0.830121	−	0.302139i
$779$	4443.93	−	25202.8i	0.204391	−	1.15916i
$780$		0			0
$781$	21096.0	−	17701.6i	0.966548	−	0.811030i
$782$	3658.45			0.167296
$783$		0			0
$784$	−199.923			−0.00910730
$785$	30735.3	−	25790.0i	1.39744	−	1.17259i
$786$		0			0
$787$	5993.37	−	33990.1i	0.271462	−	1.53954i	−0.478519	−	0.878077i	$-0.658826\pi$
$787$	5993.37	−	33990.1i	0.271462	−	1.53954i	0.749981	−	0.661460i	$-0.230063\pi$
$788$	8258.91	−	3006.00i	0.373365	−	0.135894i
$789$		0			0
$790$	−2604.50	−	14770.9i	−0.117296	−	0.665219i
$791$	6719.35	+	11638.2i	0.302038	+	0.523146i
$792$		0			0
$793$	−8021.53	+	13893.7i	−0.359209	+	0.622168i
$794$	−6246.56	−	2273.56i	−0.279197	−	0.101619i
$795$		0			0
$796$	−428.976	−	359.953i	−0.0191013	−	0.0160279i
$797$	−1317.62	−	1105.61i	−0.0585600	−	0.0491377i	0.613038	−	0.790054i	$-0.289947\pi$
$797$	−1317.62	−	1105.61i	−0.0585600	−	0.0491377i	−0.671598	+	0.740916i	$0.734392\pi$
$798$		0			0
$799$	−15936.8	−	5800.51i	−0.705635	−	0.256830i
$800$	−396.028	+	685.940i	−0.0175021	+	0.0303146i
$801$		0			0
$802$	8545.19	+	14800.7i	0.376236	+	0.651659i
$803$	−880.462	−	4993.35i	−0.0386934	−	0.219441i
$804$		0			0
$805$	−3226.71	+	1174.43i	−0.141275	+	0.0514200i
$806$	−1123.22	+	6370.12i	−0.0490867	+	0.278385i
$807$		0			0
$808$	11707.3	−	9823.58i	0.509729	−	0.427713i
$809$	1016.73			0.0441860			0.0220930	−	0.999756i	$-0.492967\pi$
$809$	1016.73			0.0441860			0.0220930	+	0.999756i	$0.492967\pi$
$810$		0			0
$811$	34010.6			1.47259			0.736297	−	0.676658i	$-0.236573\pi$
$811$	34010.6			1.47259			0.736297	+	0.676658i	$0.236573\pi$
$812$	8249.53	−	6922.18i	0.356529	−	0.299164i
$813$		0			0
$814$	2245.24	−	12733.4i	0.0966778	−	0.548287i
$815$	36970.8	−	13456.3i	1.58900	−	0.578347i
$816$		0			0
$817$	−1820.31	−	10323.5i	−0.0779493	−	0.442073i
$818$	−10331.9	−	17895.4i	−0.441622	−	0.764912i
$819$		0			0
$820$	6032.66	−	10448.9i	0.256914	−	0.444988i
$821$	−26614.8	−	9687.00i	−1.13138	−	0.411789i	−0.292588	−	0.956239i	$-0.594516\pi$
$821$	−26614.8	−	9687.00i	−1.13138	−	0.411789i	−0.838793	+	0.544450i	$0.816739\pi$
$822$		0			0
$823$	5343.72	+	4483.92i	0.226331	+	0.189914i	0.748901	−	0.662682i	$-0.230582\pi$
$823$	5343.72	+	4483.92i	0.226331	+	0.189914i	−0.522569	+	0.852597i	$0.675026\pi$
$824$	11833.5	+	9929.49i	0.500291	+	0.419794i
$825$		0			0
$826$	17464.8	+	6356.68i	0.735689	+	0.267769i
$827$	21052.7	−	36464.3i	0.885215	−	1.53324i	0.0397473	−	0.999210i	$-0.487345\pi$
$827$	21052.7	−	36464.3i	0.885215	−	1.53324i	0.845467	−	0.534027i	$-0.179322\pi$
$828$		0			0
$829$	4310.19	+	7465.47i	0.180578	+	0.312770i	0.942077	−	0.335395i	$-0.108870\pi$
$829$	4310.19	+	7465.47i	0.180578	+	0.312770i	−0.761500	+	0.648165i	$0.775537\pi$
$830$	917.073	+	5200.98i	0.0383519	+	0.217504i
$831$		0			0
$832$	2204.57	−	802.397i	0.0918625	−	0.0334352i
$833$	−257.147	+	1458.35i	−0.0106958	+	0.0606590i
$834$		0			0
$835$	35370.5	−	29679.3i	1.46592	−	1.23005i
$836$	−28223.7			−1.16763
$837$		0			0
$838$	−2833.38			−0.116799
$839$	−19852.3	+	16658.1i	−0.816900	+	0.685460i	−0.952244	−	0.305338i	$-0.901230\pi$
$839$	−19852.3	+	16658.1i	−0.816900	+	0.685460i	0.135344	+	0.990799i	$0.456786\pi$
$840$		0			0
$841$	−426.878	+	2420.95i	−0.0175029	+	0.0992639i
$842$	−27043.2	+	9842.90i	−1.10685	+	0.402861i
$843$		0			0
$844$	1928.86	+	10939.1i	0.0786661	+	0.446138i
$845$	5220.81	+	9042.70i	0.212546	+	0.368140i
$846$		0			0
$847$	−29882.8	+	51758.5i	−1.21226	+	2.09969i
$848$	3213.90	+	1169.76i	0.130148	+	0.0473701i
$849$		0			0
$850$	4494.25	+	3771.12i	0.181355	+	0.152175i
$851$	1124.78	+	943.802i	0.0453078	+	0.0380178i
$852$		0			0
$853$	7248.34	+	2638.18i	0.290948	+	0.105896i	0.483371	−	0.875416i	$-0.339412\pi$
$853$	7248.34	+	2638.18i	0.290948	+	0.105896i	−0.192423	+	0.981312i	$0.561635\pi$
$854$	7956.43	−	13780.9i	0.318810	−	0.552195i
$855$		0			0
$856$	521.097	+	902.567i	0.0208069	+	0.0360387i
$857$	4374.98	+	24811.7i	0.174383	+	0.988977i	0.938853	+	0.344318i	$0.111890\pi$
$857$	4374.98	+	24811.7i	0.174383	+	0.988977i	−0.764470	+	0.644659i	$0.776999\pi$
$858$		0			0
$859$	11000.9	−	4004.01i	0.436958	−	0.159040i	−0.114168	−	0.993461i	$-0.536420\pi$
$859$	11000.9	−	4004.01i	0.436958	−	0.159040i	0.551127	+	0.834422i	$0.314198\pi$
$860$	858.197	−	4867.08i	0.0340282	−	0.192984i
$861$		0			0
$862$	−16758.7	+	14062.2i	−0.662185	+	0.555639i
$863$	−17818.3			−0.702831			−0.351415	−	0.936220i	$-0.614299\pi$
$863$	−17818.3			−0.702831			−0.351415	+	0.936220i	$0.614299\pi$
$864$		0			0
$865$	2328.62			0.0915324
$866$	13739.0	−	11528.4i	0.539110	−	0.452367i
$867$		0			0
$868$	1114.11	−	6318.43i	0.0435661	−	0.247075i
$869$	39135.7	−	14244.2i	1.52772	−	0.556044i
$870$		0			0
$871$	5652.66	+	32057.8i	0.219900	+	1.24712i
$872$	−2062.65	−	3572.61i	−0.0801033	−	0.138743i
$873$		0			0
$874$	1602.52	−	2775.65i	0.0620207	−	0.107423i
$875$	20957.4	+	7627.87i	0.809702	+	0.294708i
$876$		0			0
$877$	−34469.7	−	28923.5i	−1.32720	−	1.11366i	−0.984722	−	0.174132i	$-0.944288\pi$
$877$	−34469.7	−	28923.5i	−1.32720	−	1.11366i	−0.342482	−	0.939524i	$-0.611268\pi$
$878$	−23950.3	−	20096.7i	−0.920597	−	0.772473i
$879$		0			0
$880$	−12503.8	−	4551.00i	−0.478979	−	0.174334i
$881$	−8051.59	+	13945.8i	−0.307906	+	0.533308i	−0.977904	−	0.209054i	$-0.932961\pi$
$881$	−8051.59	+	13945.8i	−0.307906	+	0.533308i	0.669998	+	0.742363i	$0.266295\pi$
$882$		0			0
$883$	8025.93	+	13901.3i	0.305882	+	0.529804i	0.977457	−	0.211133i	$-0.0677153\pi$
$883$	8025.93	+	13901.3i	0.305882	+	0.529804i	−0.671575	+	0.740936i	$0.734382\pi$
$884$	−3017.55	−	17113.4i	−0.114809	−	0.651115i
$885$		0			0
$886$	11184.7	−	4070.89i	0.424105	−	0.154361i
$887$	−3691.32	+	20934.5i	−0.139732	+	0.792460i	0.831715	+	0.555203i	$0.187359\pi$
$887$	−3691.32	+	20934.5i	−0.139732	+	0.792460i	−0.971447	+	0.237257i	$0.923752\pi$
$888$		0			0
$889$	−19325.1	+	16215.7i	−0.729072	+	0.611764i
$890$	−20399.4			−0.768302
$891$		0			0
$892$	−12287.0			−0.461208
$893$	−11381.6	+	9550.34i	−0.426509	+	0.357883i
$894$		0			0
$895$	−1810.41	+	10267.3i	−0.0676149	+	0.383463i
$896$	−2186.68	+	795.885i	−0.0815310	+	0.0296748i
$897$		0			0
$898$	−3423.77	−	19417.2i	−0.127230	−	0.721558i
$899$	−6532.89	−	11315.3i	−0.242363	−	0.419784i
$900$		0			0
$901$	12666.7	−	21939.4i	0.468357	−	0.811218i
$902$	31481.7	+	11458.4i	1.16211	+	0.422974i
$903$		0			0
$904$	−4530.14	−	3801.24i	−0.166671	−	0.139853i
$905$	−16471.0	−	13820.8i	−0.604989	−	0.507646i
$906$		0			0
$907$	−3656.62	−	1330.90i	−0.133865	−	0.0487230i	0.274219	−	0.961667i	$-0.411581\pi$
$907$	−3656.62	−	1330.90i	−0.133865	−	0.0487230i	−0.408084	+	0.912944i	$0.633803\pi$
$908$	−3622.00	+	6273.49i	−0.132379	+	0.229288i
$909$		0			0
$910$	8155.16	+	14125.1i	0.297078	+	0.514554i
$911$	−277.594	−	1574.31i	−0.0100956	−	0.0572550i	0.979344	−	0.202202i	$-0.0648098\pi$
$911$	−277.594	−	1574.31i	−0.0100956	−	0.0572550i	−0.989439	+	0.144947i	$0.953699\pi$
$912$		0			0
$913$	−13780.1	+	5015.55i	−0.499513	+	0.181808i
$914$	−3651.61	+	20709.3i	−0.132149	+	0.749456i
$915$		0			0
$916$	3617.52	−	3035.46i	0.130487	−	0.109492i
$917$	−6705.53			−0.241479
$918$		0			0
$919$	−18234.3			−0.654510			−0.327255	−	0.944936i	$-0.606124\pi$
$919$	−18234.3			−0.654510			−0.327255	+	0.944936i	$0.606124\pi$
$920$	1157.52	−	971.276i	0.0414808	−	0.0348066i
$921$		0			0
$922$	4051.32	−	22976.2i	0.144711	−	0.820695i
$923$	13958.5	−	5080.50i	0.497780	−	0.181177i
$924$		0			0
$925$	408.874	+	2318.84i	0.0145337	+	0.0824249i
$926$	15195.0	+	26318.4i	0.539241	+	0.933993i
$927$		0			0
$928$	−2369.44	+	4104.00i	−0.0838155	+	0.145173i
$929$	13265.6	+	4828.29i	0.468494	+	0.170518i	0.565470	−	0.824769i	$-0.308695\pi$
$929$	13265.6	+	4828.29i	0.468494	+	0.170518i	−0.0969762	+	0.995287i	$0.530917\pi$
$930$		0			0
$931$	993.807	+	833.903i	0.0349846	+	0.0293556i
$932$	−8072.00	−	6773.22i	−0.283699	−	0.238052i
$933$		0			0
$934$	14233.3	+	5180.50i	0.498638	+	0.181489i
$935$	−49280.2	+	85355.8i	−1.72367	+	2.98549i
$936$		0			0
$937$	14978.8	+	25944.1i	0.522237	+	0.904542i	0.999665	+	0.0258707i	$0.00823583\pi$
$937$	14978.8	+	25944.1i	0.522237	+	0.904542i	−0.477428	+	0.878671i	$0.658431\pi$
$938$	−5606.79	−	31797.7i	−0.195169	−	1.10686i
$939$		0			0
$940$	−6582.31	+	2395.77i	−0.228395	+	0.0831290i
$941$	3761.10	−	21330.2i	0.130296	−	0.738944i	−0.847725	−	0.530436i	$-0.822028\pi$
$941$	3761.10	−	21330.2i	0.130296	−	0.738944i	0.978021	−	0.208508i	$-0.0668607\pi$
$942$		0			0
$943$	−2914.38	+	2445.45i	−0.100642	+	0.0844485i
$944$	−8178.61			−0.281982
$945$		0			0
$946$	13723.0			0.471643
$947$	−20706.2	+	17374.6i	−0.710520	+	0.596197i	−0.924745	−	0.380588i	$-0.875722\pi$
$947$	−20706.2	+	17374.6i	−0.710520	+	0.596197i	0.214225	+	0.976784i	$0.431277\pi$
$948$		0			0
$949$	474.919	−	2693.40i	0.0162450	−	0.0921300i
$950$	4829.76	−	1757.89i	0.164945	−	0.0600352i
$951$		0			0
$952$	2993.07	+	16974.5i	0.101897	+	0.577886i
$953$	−4869.58	−	8434.35i	−0.165520	−	0.286690i	0.771320	−	0.636448i	$-0.219597\pi$
$953$	−4869.58	−	8434.35i	−0.165520	−	0.286690i	−0.936840	+	0.349758i	$0.886264\pi$
$954$		0			0
$955$	1343.41	−	2326.85i	0.0455201	−	0.0788431i
$956$	18780.1	+	6835.41i	0.635349	+	0.231248i
$957$		0			0
$958$	15422.1	+	12940.7i	0.520109	+	0.436423i
$959$	−13409.2	−	11251.7i	−0.451519	−	0.378870i
$960$		0			0
$961$	20679.6	+	7526.75i	0.694155	+	0.252652i
$962$	3487.16	−	6039.93i	0.116872	−	0.202427i
$963$		0			0
$964$	−7730.76	−	13390.1i	−0.258289	−	0.447370i
$965$	−2325.49	−	13188.5i	−0.0775754	−	0.439952i
$966$		0			0
$967$	−45725.3	+	16642.6i	−1.52061	+	0.553455i	−0.961299	−	0.275506i	$-0.911155\pi$
$967$	−45725.3	+	16642.6i	−1.52061	+	0.553455i	−0.559306	+	0.828961i	$0.688932\pi$
$968$	4566.91	−	25900.2i	0.151638	−	0.859984i
$969$		0			0
$970$	−22596.4	+	18960.7i	−0.747967	+	0.627619i
$971$	−23327.1			−0.770960			−0.385480	−	0.922716i	$-0.625964\pi$
$971$	−23327.1			−0.770960			−0.385480	+	0.922716i	$0.625964\pi$
$972$		0			0
$973$	10269.0			0.338343
$974$	58.4301	−	49.0287i	0.00192220	−	0.00161292i
$975$		0			0
$976$	−1215.96	+	6896.06i	−0.0398791	+	0.226165i
$977$	−23961.5	+	8721.29i	−0.784645	+	0.285587i	−0.703108	−	0.711083i	$-0.748205\pi$
$977$	−23961.5	+	8721.29i	−0.784645	+	0.285587i	−0.0815366	+	0.996670i	$0.525983\pi$
$978$		0			0
$979$	−9836.04	−	55782.9i	−0.321104	−	1.82107i
$980$	305.816	+	529.688i	0.00996828	+	0.0172656i
$981$		0			0
$982$	3794.83	−	6572.83i	0.123317	−	0.213592i
$983$	56679.3	+	20629.6i	1.83905	+	0.669360i	0.990003	+	0.141046i	$0.0450465\pi$
$983$	56679.3	+	20629.6i	1.83905	+	0.669360i	0.849049	+	0.528314i	$0.177176\pi$
$984$		0			0
$985$	−20597.6	−	17283.4i	−0.666289	−	0.559083i
$986$	26889.2	+	22562.7i	0.868485	+	0.728745i
$987$		0			0
$988$	−14305.7	−	5206.83i	−0.460651	−	0.167663i
$989$	−779.185	+	1349.59i	−0.0250522	+	0.0433917i
$990$		0			0
$991$	11326.9	+	19618.9i	0.363080	+	0.628873i	0.988466	−	0.151442i	$-0.0483918\pi$
$991$	11326.9	+	19618.9i	0.363080	+	0.628873i	−0.625386	+	0.780316i	$0.715058\pi$
$992$	490.263	+	2780.42i	0.0156914	+	0.0889903i
$993$		0			0
$994$	−13845.3	+	5039.27i	−0.441796	+	0.160801i
$995$	−297.492	+	1687.16i	−0.00947851	+	0.0537553i
$996$		0			0
$997$	−35805.8	+	30044.7i	−1.13739	+	0.954387i	−0.999350	−	0.0360388i	$-0.988526\pi$
$997$	−35805.8	+	30044.7i	−1.13739	+	0.954387i	−0.138044	+	0.990426i	$0.544082\pi$
$998$	−25151.2			−0.797743
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.37.2		30
3.2	odd	2		54.4.e.b.49.1	yes	30
27.4	even	9		1458.4.a.j.1.10		15
27.11	odd	18		54.4.e.b.43.1	✓	30
27.16	even	9	inner	162.4.e.b.127.2		30
27.23	odd	18		1458.4.a.i.1.6		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.43.1	✓	30	27.11	odd	18
54.4.e.b.49.1	yes	30	3.2	odd	2
162.4.e.b.37.2		30	1.1	even	1	trivial
162.4.e.b.127.2		30	27.16	even	9	inner
1458.4.a.i.1.6		15	27.23	odd	18
1458.4.a.j.1.10		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)

\(f(q)\)	\(=\)	\(q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-11.4993 + 4.18541i) q^{5} +(3.15689 + 17.9036i) q^{7} +(-4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(1.53209 - 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-11.4993 + 4.18541i) q^{5} +(3.15689 + 17.9036i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-12.2373 + 21.1956i) q^{10} +(-63.8609 - 23.2435i) q^{11} +(-28.0809 - 23.5627i) q^{13} +(27.8531 + 23.3715i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(-59.2567 + 102.636i) q^{17} +(51.9128 + 89.9156i) q^{19} +(8.49995 + 48.2056i) q^{20} +(-127.722 + 46.4869i) q^{22} +(2.68021 - 15.2003i) q^{23} +(18.9609 - 15.9101i) q^{25} -73.3141 q^{26} +72.7192 q^{28} +(113.444 - 95.1905i) q^{29} +(15.3207 - 86.8881i) q^{31} +(-30.0702 + 10.9446i) q^{32} +(41.1593 + 233.426i) q^{34} +(-111.236 - 192.666i) q^{35} +(-47.5646 + 82.3843i) q^{37} +(195.128 + 71.0209i) q^{38} +(74.9946 + 62.9279i) q^{40} +(-188.819 - 158.438i) q^{41} +(-94.8761 - 34.5321i) q^{43} +(-135.919 + 235.418i) q^{44} +(-15.4347 - 26.7338i) q^{46} +(24.8495 + 140.928i) q^{47} +(11.7417 - 4.27361i) q^{49} +(8.59619 - 48.7514i) q^{50} +(-112.324 + 94.2508i) q^{52} -213.760 q^{53} +831.639 q^{55} +(111.412 - 93.4860i) q^{56} +(51.4312 - 291.681i) q^{58} +(480.336 - 174.828i) q^{59} +(-75.9976 - 431.004i) q^{61} +(-88.2285 - 152.816i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(421.531 + 153.425i) q^{65} +(-680.267 - 570.811i) q^{67} +(363.146 + 304.716i) q^{68} +(-418.110 - 152.180i) q^{70} +(-202.613 + 350.936i) q^{71} +(37.3045 + 64.6133i) q^{73} +(33.0380 + 187.368i) q^{74} +(390.257 - 142.042i) q^{76} +(214.540 - 1216.72i) q^{77} +(-469.453 + 393.918i) q^{79} +195.797 q^{80} -492.972 q^{82} +(165.300 - 138.703i) q^{83} +(251.839 - 1428.25i) q^{85} +(-189.752 + 69.0641i) q^{86} +(94.4081 + 535.415i) q^{88} +(416.745 + 721.824i) q^{89} +(333.209 - 577.134i) q^{91} +(-58.0157 - 21.1160i) q^{92} +(219.246 + 183.969i) q^{94} +(-973.295 - 816.691i) q^{95} +(1132.55 + 412.213i) q^{97} +(12.4952 - 21.6423i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) 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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