LMFDB - Embedded newform 312.4.m.a.181.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, 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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.52
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.800675 + 2.71273i) q^{2} +3.00000i q^{3} +(-6.71784 + 4.34403i) q^{4} -12.1272 q^{5} +(-8.13820 + 2.40203i) q^{6} -21.1519i q^{7} +(-17.1630 - 14.7455i) q^{8} -9.00000 q^{9} +(-9.70993 - 32.8978i) q^{10} -16.0069 q^{11} +(-13.0321 - 20.1535i) q^{12} +(36.8012 + 29.0288i) q^{13} +(57.3793 - 16.9358i) q^{14} -36.3815i q^{15} +(26.2587 - 58.3651i) q^{16} +45.8045 q^{17} +(-7.20608 - 24.4146i) q^{18} +117.007 q^{19} +(81.4684 - 52.6809i) q^{20} +63.4556 q^{21} +(-12.8163 - 43.4224i) q^{22} -97.3972 q^{23} +(44.2366 - 51.4890i) q^{24} +22.0685 q^{25} +(-49.2817 + 123.074i) q^{26} -27.0000i q^{27} +(91.8844 + 142.095i) q^{28} -90.0375i q^{29} +(98.6934 - 29.1298i) q^{30} -151.350i q^{31} +(179.354 + 24.5015i) q^{32} -48.0206i q^{33} +(36.6745 + 124.255i) q^{34} +256.512i q^{35} +(60.4606 - 39.0963i) q^{36} +66.3382 q^{37} +(93.6845 + 317.409i) q^{38} +(-87.0865 + 110.404i) q^{39} +(208.139 + 178.822i) q^{40} -112.250i q^{41} +(50.8073 + 172.138i) q^{42} +234.339i q^{43} +(107.532 - 69.5345i) q^{44} +109.145 q^{45} +(-77.9835 - 264.213i) q^{46} -580.433i q^{47} +(175.095 + 78.7762i) q^{48} -104.401 q^{49} +(17.6697 + 59.8660i) q^{50} +137.414i q^{51} +(-373.327 - 35.1454i) q^{52} -241.092i q^{53} +(73.2438 - 21.6182i) q^{54} +194.118 q^{55} +(-311.896 + 363.029i) q^{56} +351.021i q^{57} +(244.248 - 72.0908i) q^{58} -313.006 q^{59} +(158.043 + 244.405i) q^{60} -334.114i q^{61} +(410.572 - 121.182i) q^{62} +190.367i q^{63} +(77.1380 + 506.156i) q^{64} +(-446.295 - 352.038i) q^{65} +(130.267 - 38.4489i) q^{66} +315.258 q^{67} +(-307.707 + 198.976i) q^{68} -292.192i q^{69} +(-695.849 + 205.383i) q^{70} -503.306i q^{71} +(154.467 + 132.710i) q^{72} -757.602i q^{73} +(53.1154 + 179.958i) q^{74} +66.2055i q^{75} +(-786.034 + 508.282i) q^{76} +338.575i q^{77} +(-369.223 - 147.845i) q^{78} +1134.30 q^{79} +(-318.444 + 707.804i) q^{80} +81.0000 q^{81} +(304.503 - 89.8754i) q^{82} +822.684 q^{83} +(-426.284 + 275.653i) q^{84} -555.480 q^{85} +(-635.698 + 187.629i) q^{86} +270.113 q^{87} +(274.726 + 236.030i) q^{88} +803.525i q^{89} +(87.3894 + 296.080i) q^{90} +(614.014 - 778.413i) q^{91} +(654.299 - 423.097i) q^{92} +454.049 q^{93} +(1574.56 - 464.738i) q^{94} -1418.96 q^{95} +(-73.5044 + 538.061i) q^{96} -750.474i q^{97} +(-83.5911 - 283.211i) q^{98} +144.062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	0.800675	+	2.71273i	0.283081	+	0.959096i
$2$	0.800675	+	2.71273i	0.283081	+	0.959096i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−6.71784	+	4.34403i	−0.839730	+	0.543004i
$5$	−12.1272			−1.08469			−0.542344	−	0.840157i	$-0.682463\pi$
$5$	−12.1272			−1.08469			−0.542344	+	0.840157i	$0.682463\pi$
$6$	−8.13820	+	2.40203i	−0.553734	+	0.163437i
$7$		−	21.1519i		−	1.14209i	−0.820918	−	0.571046i	$-0.806538\pi$
$7$		−	21.1519i		−	1.14209i	0.820918	−	0.571046i	$-0.193462\pi$
$8$	−17.1630	−	14.7455i	−0.758505	−	0.651667i
$9$	−9.00000			−0.333333
$10$	−9.70993	−	32.8978i	−0.307055	−	1.04032i
$11$	−16.0069			−0.438751			−0.219375	−	0.975641i	$-0.570402\pi$
$11$	−16.0069			−0.438751			−0.219375	+	0.975641i	$0.570402\pi$
$12$	−13.0321	−	20.1535i	−0.313504	−	0.484818i
$13$	36.8012	+	29.0288i	0.785139	+	0.619319i
$13$	36.8012	+	29.0288i	0.785139	+	0.619319i
$14$	57.3793	−	16.9358i	1.09538	−	0.323305i
$15$		−	36.3815i		−	0.626245i
$16$	26.2587	−	58.3651i	0.410293	−	0.911954i
$17$	45.8045			0.653484			0.326742	−	0.945114i	$-0.394049\pi$
$17$	45.8045			0.653484			0.326742	+	0.945114i	$0.394049\pi$
$18$	−7.20608	−	24.4146i	−0.0943605	−	0.319699i
$19$	117.007			1.41280			0.706401	−	0.707812i	$-0.250318\pi$
$19$	117.007			1.41280			0.706401	+	0.707812i	$0.250318\pi$
$20$	81.4684	−	52.6809i	0.910845	−	0.588990i
$21$	63.4556			0.659387
$22$	−12.8163	−	43.4224i	−0.124202	−	0.420804i
$23$	−97.3972			−0.882988			−0.441494	−	0.897264i	$-0.645551\pi$
$23$	−97.3972			−0.882988			−0.441494	+	0.897264i	$0.645551\pi$
$24$	44.2366	−	51.4890i	0.376240	−	0.437923i
$25$	22.0685			0.176548
$26$	−49.2817	+	123.074i	−0.371728	+	0.928342i
$27$		−	27.0000i		−	0.192450i
$28$	91.8844	+	142.095i	0.620161	+	0.959049i
$29$		−	90.0375i		−	0.576536i	−0.957550	−	0.288268i	$-0.906921\pi$
$29$		−	90.0375i		−	0.576536i	0.957550	−	0.288268i	$-0.0930794\pi$
$30$	98.6934	−	29.1298i	0.600629	−	0.177278i
$31$		−	151.350i		−	0.876878i	−0.898761	−	0.438439i	$-0.855531\pi$
$31$		−	151.350i		−	0.876878i	0.898761	−	0.438439i	$-0.144469\pi$
$32$	179.354	+	24.5015i	0.990797	+	0.135353i
$33$		−	48.0206i		−	0.253313i
$34$	36.6745	+	124.255i	0.184989	+	0.626754i
$35$			256.512i			1.23881i
$36$	60.4606	−	39.0963i	0.279910	−	0.181001i
$37$	66.3382			0.294755			0.147378	−	0.989080i	$-0.452917\pi$
$37$	66.3382			0.294755			0.147378	+	0.989080i	$0.452917\pi$
$38$	93.6845	+	317.409i	0.399938	+	1.35501i
$39$	−87.0865	+	110.404i	−0.357564	+	0.453300i
$40$	208.139	+	178.822i	0.822741	+	0.706855i
$41$		−	112.250i		−	0.427572i	−0.976881	−	0.213786i	$-0.931421\pi$
$41$		−	112.250i		−	0.427572i	0.976881	−	0.213786i	$-0.0685795\pi$
$42$	50.8073	+	172.138i	0.186660	+	0.632416i
$43$			234.339i			0.831077i	0.909576	+	0.415538i	$0.136407\pi$
$43$			234.339i			0.831077i	−0.909576	+	0.415538i	$0.863593\pi$
$44$	107.532	−	69.5345i	0.368432	−	0.238243i
$45$	109.145			0.361563
$46$	−77.9835	−	264.213i	−0.249957	−	0.846870i
$47$		−	580.433i		−	1.80138i	−0.434461	−	0.900690i	$-0.643061\pi$
$47$		−	580.433i		−	1.80138i	0.434461	−	0.900690i	$-0.356939\pi$
$48$	175.095	+	78.7762i	0.526517	+	0.236882i
$49$	−104.401			−0.304375
$50$	17.6697	+	59.8660i	0.0499775	+	0.169327i
$51$			137.414i			0.377289i
$52$	−373.327	−	35.1454i	−0.995598	−	0.0937269i
$53$		−	241.092i		−	0.624841i	−0.949944	−	0.312420i	$-0.898860\pi$
$53$		−	241.092i		−	0.624841i	0.949944	−	0.312420i	$-0.101140\pi$
$54$	73.2438	−	21.6182i	0.184578	−	0.0544790i
$55$	194.118			0.475908
$56$	−311.896	+	363.029i	−0.744264	+	0.866283i
$57$			351.021i			0.815681i
$58$	244.248	−	72.0908i	0.552954	−	0.163207i
$59$	−313.006			−0.690677			−0.345339	−	0.938478i	$-0.612236\pi$
$59$	−313.006			−0.690677			−0.345339	+	0.938478i	$0.612236\pi$
$60$	158.043	+	244.405i	0.340054	+	0.525877i
$61$		−	334.114i		−	0.701293i	−0.936508	−	0.350647i	$-0.885962\pi$
$61$		−	334.114i		−	0.701293i	0.936508	−	0.350647i	$-0.114038\pi$
$62$	410.572	−	121.182i	0.841011	−	0.248228i
$63$			190.367i			0.380698i
$64$	77.1380	+	506.156i	0.150660	+	0.988586i
$65$	−446.295	−	352.038i	−0.851631	−	0.671768i
$66$	130.267	−	38.4489i	0.242951	−	0.0717081i
$67$	315.258			0.574848			0.287424	−	0.957803i	$-0.407201\pi$
$67$	315.258			0.574848			0.287424	+	0.957803i	$0.407201\pi$
$68$	−307.707	+	198.976i	−0.548750	+	0.354845i
$69$		−	292.192i		−	0.509793i
$70$	−695.849	+	205.383i	−1.18814	+	0.350685i
$71$		−	503.306i		−	0.841288i	−0.907226	−	0.420644i	$-0.861804\pi$
$71$		−	503.306i		−	0.841288i	0.907226	−	0.420644i	$-0.138196\pi$
$72$	154.467	+	132.710i	0.252835	+	0.217222i
$73$		−	757.602i		−	1.21467i	−0.794447	−	0.607333i	$-0.792239\pi$
$73$		−	757.602i		−	1.21467i	0.794447	−	0.607333i	$-0.207761\pi$
$74$	53.1154	+	179.958i	0.0834397	+	0.282698i
$75$			66.2055i			0.101930i
$76$	−786.034	+	508.282i	−1.18637	+	0.767157i
$77$			338.575i			0.501094i
$78$	−369.223	−	147.845i	−0.535978	−	0.214617i
$79$	1134.30			1.61543			0.807717	−	0.589571i	$-0.200703\pi$
$79$	1134.30			1.61543			0.807717	+	0.589571i	$0.200703\pi$
$80$	−318.444	+	707.804i	−0.445039	+	0.989186i
$81$	81.0000			0.111111
$82$	304.503	−	89.8754i	0.410082	−	0.121038i
$83$	822.684			1.08797			0.543984	−	0.839096i	$-0.316915\pi$
$83$	822.684			1.08797			0.543984	+	0.839096i	$0.316915\pi$
$84$	−426.284	+	275.653i	−0.553707	+	0.358050i
$85$	−555.480			−0.708826
$86$	−635.698	+	187.629i	−0.797082	+	0.235262i
$87$	270.113			0.332863
$88$	274.726	+	236.030i	0.332795	+	0.285919i
$89$			803.525i			0.957005i	0.878086	+	0.478503i	$0.158820\pi$
$89$			803.525i			0.957005i	−0.878086	+	0.478503i	$0.841180\pi$
$90$	87.3894	+	296.080i	0.102352	+	0.346773i
$91$	614.014	−	778.413i	0.707320	−	0.896702i
$92$	654.299	−	423.097i	0.741471	−	0.479466i
$93$	454.049			0.506266
$94$	1574.56	−	464.738i	1.72770	−	0.509937i
$95$	−1418.96			−1.53245
$96$	−73.5044	+	538.061i	−0.0781459	+	0.572037i
$97$		−	750.474i		−	0.785557i	−0.919633	−	0.392779i	$-0.871514\pi$
$97$		−	750.474i		−	0.785557i	0.919633	−	0.392779i	$-0.128486\pi$
$98$	−83.5911	−	283.211i	−0.0861630	−	0.291925i
$99$	144.062			0.146250
$100$	−148.253	+	95.8664i	−0.148253	+	0.0958664i
$101$			460.391i			0.453570i	0.973945	+	0.226785i	$0.0728215\pi$
$101$			460.391i			0.453570i	−0.973945	+	0.226785i	$0.927178\pi$
$102$	−372.766	+	110.024i	−0.361857	+	0.106804i
$103$	1245.30			1.19129			0.595645	−	0.803248i	$-0.296897\pi$
$103$	1245.30			1.19129			0.595645	+	0.803248i	$0.296897\pi$
$104$	−203.573	−	1040.88i	−0.191942	−	0.981406i
$105$	−769.537			−0.715230
$106$	654.019	−	193.037i	0.599282	−	0.176881i
$107$		−	488.541i		−	0.441393i	−0.975343	−	0.220696i	$-0.929167\pi$
$107$		−	488.541i		−	0.441393i	0.975343	−	0.220696i	$-0.0708330\pi$
$108$	117.289	+	181.382i	0.104501	+	0.161606i
$109$	−703.953			−0.618591			−0.309296	−	0.950966i	$-0.600093\pi$
$109$	−703.953			−0.618591			−0.309296	+	0.950966i	$0.600093\pi$
$110$	155.426	+	526.591i	0.134721	+	0.456441i
$111$			199.015i			0.170177i
$112$	−1234.53	−	555.421i	−1.04154	−	0.468592i
$113$	−2263.50			−1.88435			−0.942177	−	0.335115i	$-0.891225\pi$
$113$	−2263.50			−1.88435			−0.942177	+	0.335115i	$0.891225\pi$
$114$	−952.226	+	281.054i	−0.782317	+	0.230904i
$115$	1181.15			0.957766
$116$	391.126	+	604.858i	0.313062	+	0.484135i
$117$	−331.211	−	261.260i	−0.261713	−	0.206440i
$118$	−250.616	−	849.102i	−0.195518	−	0.662426i
$119$		−	968.851i		−	0.746339i
$120$	−536.466	+	624.417i	−0.408103	+	0.475010i
$121$	−1074.78			−0.807498
$122$	906.361	−	267.516i	0.672607	−	0.198523i
$123$	336.749			0.246859
$124$	657.469	+	1016.74i	0.476149	+	0.736341i
$125$	1248.27			0.893188
$126$	−516.414	+	152.422i	−0.365125	+	0.107768i
$127$	−1539.77			−1.07585			−0.537923	−	0.842994i	$-0.680791\pi$
$127$	−1539.77			−1.07585			−0.537923	+	0.842994i	$0.680791\pi$
$128$	−1311.30	+	614.521i	−0.905499	+	0.424348i
$129$	−703.016			−0.479822
$130$	597.648	−	1492.55i	0.403209	−	1.00696i
$131$			833.576i			0.555953i	0.960588	+	0.277977i	$0.0896637\pi$
$131$			833.576i			0.555953i	−0.960588	+	0.277977i	$0.910336\pi$
$132$	208.603	+	322.595i	0.137550	+	0.212714i
$133$		−	2474.91i		−	1.61355i
$134$	252.419	+	855.210i	0.162729	+	0.551335i
$135$			327.434i			0.208748i
$136$	−786.144	−	675.413i	−0.495671	−	0.425854i
$137$			1012.44i			0.631379i	0.948863	+	0.315689i	$0.102236\pi$
$137$			1012.44i			0.631379i	−0.948863	+	0.315689i	$0.897764\pi$
$138$	792.638	−	233.950i	0.488940	−	0.144313i
$139$		−	2463.08i		−	1.50299i	−0.659739	−	0.751495i	$-0.729333\pi$
$139$		−	2463.08i		−	1.50299i	0.659739	−	0.751495i	$-0.270667\pi$
$140$	−1114.30	−	1723.21i	−0.672681	−	1.04027i
$141$	1741.30			1.04003
$142$	1365.34	−	402.985i	0.806876	−	0.238153i
$143$	−589.072	−	464.661i	−0.344480	−	0.271727i
$144$	−236.328	+	525.285i	−0.136764	+	0.303985i
$145$			1091.90i			0.625362i
$146$	2055.17	−	606.593i	1.16498	−	0.343849i
$147$		−	313.202i		−	0.175731i
$148$	−445.650	+	288.176i	−0.247515	+	0.160053i
$149$	−2991.00			−1.64451			−0.822257	−	0.569117i	$-0.807285\pi$
$149$	−2991.00			−1.64451			−0.822257	+	0.569117i	$0.807285\pi$
$150$	−179.598	+	53.0091i	−0.0977607	+	0.0288545i
$151$		−	2307.79i		−	1.24374i	−0.783120	−	0.621871i	$-0.786373\pi$
$151$		−	2307.79i		−	1.24374i	0.783120	−	0.621871i	$-0.213627\pi$
$152$	−2008.19	−	1725.33i	−1.07162	−	0.920676i
$153$	−412.241			−0.217828
$154$	−918.464	+	271.089i	−0.480597	+	0.141850i
$155$			1835.45i			0.951140i
$156$	105.436	−	1119.98i	0.0541132	−	0.574809i
$157$		−	1097.78i		−	0.558042i	−0.960285	−	0.279021i	$-0.909990\pi$
$157$		−	1097.78i		−	0.558042i	0.960285	−	0.279021i	$-0.0900099\pi$
$158$	908.210	+	3077.07i	0.457299	+	1.54936i
$159$	723.277			0.360752
$160$	−2175.05	−	297.134i	−1.07471	−	0.146815i
$161$			2060.13i			1.00845i
$162$	64.8547	+	219.731i	0.0314535	+	0.106566i
$163$	−2138.86			−1.02778			−0.513891	−	0.857856i	$-0.671796\pi$
$163$	−2138.86			−1.02778			−0.513891	+	0.857856i	$0.671796\pi$
$164$	487.616	+	754.075i	0.232173	+	0.359045i
$165$			582.355i			0.274765i
$166$	658.703	+	2231.72i	0.307983	+	1.04347i
$167$		−	2341.22i		−	1.08484i	−0.840106	−	0.542422i	$-0.817507\pi$
$167$		−	2341.22i		−	1.08484i	0.840106	−	0.542422i	$-0.182493\pi$
$168$	−1089.09	−	935.687i	−0.500149	−	0.429701i
$169$	511.653	+	2136.59i	0.232887	+	0.972504i
$170$	−444.759	−	1506.87i	−0.200656	−	0.679832i
$171$	−1053.06			−0.470934
$172$	−1017.98	−	1574.25i	−0.451278	−	0.697880i
$173$			1655.20i			0.727413i	0.931514	+	0.363706i	$0.118489\pi$
$173$			1655.20i			0.727413i	−0.931514	+	0.363706i	$0.881511\pi$
$174$	216.272	+	732.743i	0.0942274	+	0.319248i
$175$		−	466.790i		−	0.201634i
$176$	−420.320	+	934.243i	−0.180016	+	0.400120i
$177$		−	939.019i		−	0.398763i
$178$	−2179.75	+	643.362i	−0.917860	+	0.270910i
$179$		−	2005.28i		−	0.837326i	−0.908142	−	0.418663i	$-0.862499\pi$
$179$		−	2005.28i		−	0.837326i	0.908142	−	0.418663i	$-0.137501\pi$
$180$	−733.216	+	474.128i	−0.303615	+	0.196330i
$181$		−	1629.54i		−	0.669184i	−0.942363	−	0.334592i	$-0.891401\pi$
$181$		−	1629.54i		−	0.669184i	0.942363	−	0.334592i	$-0.108599\pi$
$182$	2603.25	+	1042.40i	1.06025	+	0.424548i
$183$	1002.34			0.404892
$184$	1671.63	+	1436.17i	0.669751	+	0.575414i
$185$	−804.496			−0.319717
$186$	363.546	+	1231.71i	0.143314	+	0.485558i
$187$	−733.188			−0.286717
$188$	2521.42	+	3899.26i	0.978158	+	1.51267i
$189$	−571.100			−0.219796
$190$	−1136.13	−	3849.27i	−0.433808	−	1.46977i
$191$	4723.88			1.78957			0.894786	−	0.446495i	$-0.147328\pi$
$191$	4723.88			1.78957			0.894786	+	0.446495i	$0.147328\pi$
$192$	−1518.47	+	231.414i	−0.570760	+	0.0869837i
$193$			10.6845i			0.00398491i	0.999998	+	0.00199245i	$0.000634218\pi$
$193$			10.6845i			0.00398491i	−0.999998	+	0.00199245i	$0.999366\pi$
$194$	2035.83	−	600.886i	0.753425	−	0.222377i
$195$	1056.11	−	1338.88i	0.387846	−	0.491689i
$196$	701.348	−	453.521i	0.255593	−	0.165277i
$197$	−2024.67			−0.732244			−0.366122	−	0.930567i	$-0.619315\pi$
$197$	−2024.67			−0.732244			−0.366122	+	0.930567i	$0.619315\pi$
$198$	115.347	+	390.802i	0.0414007	+	0.140268i
$199$	1829.71			0.651782			0.325891	−	0.945407i	$-0.394336\pi$
$199$	1829.71			0.651782			0.325891	+	0.945407i	$0.394336\pi$
$200$	−378.762	−	325.412i	−0.133913	−	0.115051i
$201$			945.773i			0.331889i
$202$	−1248.92	+	368.623i	−0.435017	+	0.128397i
$203$	−1904.46			−0.658458
$204$	−596.929	−	923.122i	−0.204870	−	0.316821i
$205$			1361.27i			0.463782i
$206$	997.079	+	3378.16i	0.337232	+	1.14256i
$207$	876.575			0.294329
$208$	2660.62	−	1385.64i	0.886927	−	0.461909i
$209$	−1872.92			−0.619868
$210$	−616.149	−	2087.55i	−0.202468	−	0.685974i
$211$			2849.73i			0.929780i	0.885368	+	0.464890i	$0.153906\pi$
$211$			2849.73i			0.929780i	−0.885368	+	0.464890i	$0.846094\pi$
$212$	1047.31	+	1619.62i	0.339291	+	0.524698i
$213$	1509.92			0.485718
$214$	1325.28	−	391.162i	0.423338	−	0.124950i
$215$		−	2841.87i		−	0.901459i
$216$	−398.130	+	463.401i	−0.125413	+	0.145974i
$217$	−3201.33			−1.00148
$218$	−563.637	−	1909.64i	−0.175112	−	0.593288i
$219$	2272.81			0.701288
$220$	−1304.06	+	843.257i	−0.399634	+	0.258420i
$221$	1685.66	+	1329.65i	0.513076	+	0.404715i
$222$	−539.874	+	159.346i	−0.163216	+	0.0481739i
$223$		−	1372.76i		−	0.412228i	−0.978528	−	0.206114i	$-0.933918\pi$
$223$		−	1372.76i		−	0.412228i	0.978528	−	0.206114i	$-0.0660817\pi$
$224$	518.251	−	3793.66i	0.154585	−	1.13158i
$225$	−198.617			−0.0588494
$226$	−1812.33	−	6140.27i	−0.533426	−	1.80728i
$227$	−3957.76			−1.15720			−0.578602	−	0.815610i	$-0.696402\pi$
$227$	−3957.76			−1.15720			−0.578602	+	0.815610i	$0.696402\pi$
$228$	−1524.85	−	2358.10i	−0.442919	−	0.684952i
$229$	−1499.02			−0.432569			−0.216284	−	0.976330i	$-0.569394\pi$
$229$	−1499.02			−0.432569			−0.216284	+	0.976330i	$0.569394\pi$
$230$	945.720	+	3204.15i	0.271126	+	0.918590i
$231$	−1015.73			−0.289307
$232$	−1327.65	+	1545.32i	−0.375710	+	0.437306i
$233$	3777.11			1.06200			0.531001	−	0.847371i	$-0.321816\pi$
$233$	3777.11			1.06200			0.531001	+	0.847371i	$0.321816\pi$
$234$	443.535	−	1107.67i	0.123909	−	0.309447i
$235$			7039.02i			1.95394i
$236$	2102.73	−	1359.71i	0.579982	−	0.375041i
$237$			3402.91i			0.932671i
$238$	2628.23	−	775.734i	0.715811	−	0.211275i
$239$			4920.95i			1.33184i	0.746023	+	0.665920i	$0.231961\pi$
$239$			4920.95i			1.33184i	−0.746023	+	0.665920i	$0.768039\pi$
$240$	−2123.41	−	955.333i	−0.571107	−	0.256944i
$241$			1467.06i			0.392123i	0.980592	+	0.196061i	$0.0628152\pi$
$241$			1467.06i			0.392123i	−0.980592	+	0.196061i	$0.937185\pi$
$242$	−860.549	−	2915.59i	−0.228588	−	0.774468i
$243$			243.000i			0.0641500i
$244$	1451.40	+	2244.52i	0.380805	+	0.588897i
$245$	1266.09			0.330152
$246$	269.626	+	913.509i	0.0698811	+	0.236761i
$247$	4305.99	+	3396.57i	1.10925	+	0.874975i
$248$	−2231.74	+	2597.62i	−0.571433	+	0.665117i
$249$			2468.05i			0.628138i
$250$	999.458	+	3386.22i	0.252845	+	0.856653i
$251$			4882.12i			1.22772i	0.789416	+	0.613858i	$0.210383\pi$
$251$			4882.12i			1.22772i	−0.789416	+	0.613858i	$0.789617\pi$
$252$	−826.959	−	1278.85i	−0.206720	−	0.319683i
$253$	1559.03			0.387411
$254$	−1232.85	−	4176.98i	−0.304552	−	1.03184i
$255$		−	1666.44i		−	0.409241i
$256$	−2716.96	−	3065.18i	−0.663320	−	0.748336i
$257$	−1903.23			−0.461946			−0.230973	−	0.972960i	$-0.574191\pi$
$257$	−1903.23			−0.461946			−0.230973	+	0.972960i	$0.574191\pi$
$258$	−562.887	−	1907.09i	−0.135829	−	0.460196i
$259$		−	1403.18i		−	0.336638i
$260$	4527.40	+	426.215i	1.07991	+	0.101664i
$261$			810.338i			0.192179i
$262$	−2261.27	+	667.423i	−0.533212	+	0.157380i
$263$	5914.88			1.38680			0.693398	−	0.720555i	$-0.256113\pi$
$263$	5914.88			1.38680			0.693398	+	0.720555i	$0.256113\pi$
$264$	−708.090	+	824.179i	−0.165076	+	0.192139i
$265$			2923.77i			0.677757i
$266$	6713.78	−	1981.60i	1.54755	−	0.456766i
$267$	−2410.57			−0.552527
$268$	−2117.85	+	1369.49i	−0.482717	+	0.312145i
$269$			4203.72i			0.952808i	0.879226	+	0.476404i	$0.158060\pi$
$269$			4203.72i			0.952808i	−0.879226	+	0.476404i	$0.841940\pi$
$270$	−888.241	+	262.168i	−0.200210	+	0.0590928i
$271$			2759.47i			0.618545i	0.950974	+	0.309272i	$0.100085\pi$
$271$			2759.47i			0.618545i	−0.950974	+	0.309272i	$0.899915\pi$
$272$	1202.77	−	2673.38i	0.268120	−	0.595947i
$273$	2335.24	+	1842.04i	0.517711	+	0.408371i
$274$	−2746.49	+	810.638i	−0.605553	+	0.178732i
$275$	−353.248			−0.0774606
$276$	1269.29	+	1962.90i	0.276820	+	0.428089i
$277$		−	8888.17i		−	1.92794i	−0.266019	−	0.963968i	$-0.585708\pi$
$277$		−	8888.17i		−	1.92794i	0.266019	−	0.963968i	$-0.414292\pi$
$278$	6681.67	−	1972.12i	1.44151	−	0.425468i
$279$			1362.15i			0.292293i
$280$	3782.41	−	4402.52i	0.807294	−	0.939647i
$281$		−	4050.83i		−	0.859972i	−0.902835	−	0.429986i	$-0.858518\pi$
$281$		−	4050.83i		−	0.859972i	0.902835	−	0.429986i	$-0.141482\pi$
$282$	1394.22	+	4723.68i	0.294412	+	0.997486i
$283$			4078.29i			0.856640i	0.903627	+	0.428320i	$0.140894\pi$
$283$			4078.29i			0.856640i	−0.903627	+	0.428320i	$0.859106\pi$
$284$	2186.38	+	3381.13i	0.456823	+	0.706455i
$285$		−	4256.89i		−	0.884760i
$286$	788.846	−	1970.04i	0.163096	−	0.407310i
$287$	−2374.29			−0.488326
$288$	−1614.18	−	220.513i	−0.330266	−	0.0451176i
$289$	−2814.95			−0.572959
$290$	−2962.04	+	874.258i	−0.599782	+	0.177028i
$291$	2251.42			0.453542
$292$	3291.05	+	5089.45i	0.659569	+	1.01999i
$293$	−1590.21			−0.317069			−0.158535	−	0.987353i	$-0.550677\pi$
$293$	−1590.21			−0.317069			−0.158535	+	0.987353i	$0.550677\pi$
$294$	849.634	−	250.773i	0.168543	−	0.0497463i
$295$	3795.88			0.749169
$296$	−1138.56	−	978.193i	−0.223573	−	0.192082i
$297$			432.186i			0.0844376i
$298$	−2394.82	−	8113.79i	−0.465531	−	1.57725i
$299$	−3584.33	−	2827.33i	−0.693268	−	0.546851i
$300$	−287.599	−	444.758i	−0.0553485	−	0.0855937i
$301$	4956.70			0.949167
$302$	6260.41	−	1847.79i	1.19287	−	0.352080i
$303$	−1381.17			−0.261869
$304$	3072.45	−	6829.12i	0.579662	−	1.28841i
$305$			4051.86i			0.760684i
$306$	−330.071	−	1118.30i	−0.0616631	−	0.208918i
$307$	6423.44			1.19415			0.597077	−	0.802184i	$-0.296329\pi$
$307$	6423.44			1.19415			0.597077	+	0.802184i	$0.296329\pi$
$308$	−1470.78	−	2274.49i	−0.272096	−	0.420783i
$309$			3735.89i			0.687791i
$310$	−4979.08	+	1469.60i	−0.912234	+	0.269250i
$311$	3419.21			0.623427			0.311713	−	0.950176i	$-0.399097\pi$
$311$	3419.21			0.623427			0.311713	+	0.950176i	$0.399097\pi$
$312$	3122.63	−	610.719i	0.566615	−	0.110818i
$313$	8831.43			1.59483			0.797415	−	0.603431i	$-0.206200\pi$
$313$	8831.43			1.59483			0.797415	+	0.603431i	$0.206200\pi$
$314$	2977.99	−	878.967i	0.535216	−	0.157971i
$315$		−	2308.61i		−	0.412938i
$316$	−7620.08	+	4927.46i	−1.35653	+	0.877188i
$317$	−6479.78			−1.14808			−0.574039	−	0.818828i	$-0.694624\pi$
$317$	−6479.78			−1.14808			−0.574039	+	0.818828i	$0.694624\pi$
$318$	579.110	+	1962.06i	0.102122	+	0.345996i
$319$			1441.22i			0.252956i
$320$	−935.466	−	6138.24i	−0.163419	−	1.07231i
$321$	1465.62			0.254838
$322$	−5588.58	+	1649.50i	−0.967204	+	0.285474i
$323$	5359.45			0.923243
$324$	−544.145	+	351.867i	−0.0933033	+	0.0603338i
$325$	812.147	+	640.623i	0.138615	+	0.109340i
$326$	−1712.53	−	5802.15i	−0.290946	−	0.985741i
$327$		−	2111.86i		−	0.357144i
$328$	−1655.18	+	1926.54i	−0.278634	+	0.324315i
$329$	−12277.2			−2.05734
$330$	−1579.77	+	466.277i	−0.263526	+	0.0777809i
$331$	8657.99			1.43772			0.718861	−	0.695154i	$-0.244664\pi$
$331$	8657.99			1.43772			0.718861	+	0.695154i	$0.244664\pi$
$332$	−5526.66	+	3573.77i	−0.913599	+	0.590771i
$333$	−597.044			−0.0982517
$334$	6351.11	−	1874.56i	1.04047	−	0.307099i
$335$	−3823.19			−0.623531
$336$	1666.26	−	3703.59i	0.270542	−	0.601331i
$337$	8924.60			1.44259			0.721297	−	0.692626i	$-0.243546\pi$
$337$	8924.60			1.44259			0.721297	+	0.692626i	$0.243546\pi$
$338$	−5386.33	+	3098.69i	−0.866798	+	0.498659i
$339$		−	6790.50i		−	1.08793i
$340$	3731.62	−	2413.02i	0.595223	−	0.384896i
$341$			2422.64i			0.384731i
$342$	−843.161	−	2856.68i	−0.133313	−	0.451671i
$343$		−	5046.81i		−	0.794468i
$344$	3455.45	−	4021.96i	0.541585	−	0.630376i
$345$			3543.46i			0.552966i
$346$	−4490.11	+	1325.28i	−0.697659	+	0.205917i
$347$			1537.77i			0.237901i	0.992900	+	0.118951i	$0.0379531\pi$
$347$			1537.77i			0.237901i	−0.992900	+	0.118951i	$0.962047\pi$
$348$	−1814.57	+	1173.38i	−0.279515	+	0.180746i
$349$	−8471.05			−1.29927			−0.649634	−	0.760247i	$-0.725078\pi$
$349$	−8471.05			−1.29927			−0.649634	+	0.760247i	$0.725078\pi$
$350$	1266.28	−	373.747i	0.193387	−	0.0570789i
$351$	783.779	−	993.632i	0.119188	−	0.151100i
$352$	−2870.89	−	392.192i	−0.434713	−	0.0593861i
$353$		−	6922.13i		−	1.04370i	−0.853036	−	0.521852i	$-0.825241\pi$
$353$		−	6922.13i		−	1.04370i	0.853036	−	0.521852i	$-0.174759\pi$
$354$	2547.31	−	751.849i	0.382452	−	0.112882i
$355$			6103.68i			0.912535i
$356$	−3490.54	−	5397.95i	−0.519658	−	0.803626i
$357$	2906.55			0.430899
$358$	5439.78	−	1605.57i	0.803076	−	0.237031i
$359$		−	4046.73i		−	0.594925i	−0.954733	−	0.297463i	$-0.903860\pi$
$359$		−	4046.73i		−	0.594925i	0.954733	−	0.297463i	$-0.0961404\pi$
$360$	−1873.25	−	1609.40i	−0.274247	−	0.235618i
$361$	6831.62			0.996008
$362$	4420.49	−	1304.73i	0.641812	−	0.189434i
$363$		−	3224.34i		−	0.466209i
$364$	−743.391	+	7896.55i	−0.107045	+	1.13707i
$365$			9187.58i			1.31753i
$366$	802.549	+	2719.08i	0.114617	+	0.388330i
$367$	−567.928			−0.0807783			−0.0403891	−	0.999184i	$-0.512860\pi$
$367$	−567.928			−0.0807783			−0.0403891	+	0.999184i	$0.512860\pi$
$368$	−2557.53	+	5684.59i	−0.362283	+	0.805244i
$369$			1010.25i			0.142524i
$370$	−644.140	−	2182.38i	−0.0905060	−	0.306640i
$371$	−5099.55			−0.713626
$372$	−3050.23	+	1972.41i	−0.425127	+	0.274905i
$373$			4632.74i			0.643094i	0.946894	+	0.321547i	$0.104203\pi$
$373$			4632.74i			0.643094i	−0.946894	+	0.321547i	$0.895797\pi$
$374$	−587.045	−	1988.94i	−0.0811641	−	0.274989i
$375$			3744.81i			0.515683i
$376$	−8558.80	+	9961.98i	−1.17390	+	1.36636i
$377$	2613.68	−	3313.49i	0.357060	−	0.452661i
$378$	−457.265	−	1549.24i	−0.0622201	−	0.210805i
$379$	8005.02			1.08494			0.542468	−	0.840077i	$-0.317490\pi$
$379$	8005.02			1.08494			0.542468	+	0.840077i	$0.317490\pi$
$380$	9532.37	−	6164.03i	1.28684	−	0.832126i
$381$		−	4619.31i		−	0.621140i
$382$	3782.30	+	12814.6i	0.506595	+	1.71637i
$383$			9120.11i			1.21675i	0.793649	+	0.608376i	$0.208179\pi$
$383$			9120.11i			1.21675i	−0.793649	+	0.608376i	$0.791821\pi$
$384$	−1843.56	−	3933.91i	−0.244997	−	0.522790i
$385$		−	4105.96i		−	0.543530i
$386$	−28.9842	+	8.55481i	−0.00382191	+	0.00112805i
$387$		−	2109.05i		−	0.277026i
$388$	3260.08	+	5041.56i	0.426561	+	0.659656i
$389$		−	13700.5i		−	1.78571i	−0.450339	−	0.892857i	$-0.648697\pi$
$389$		−	13700.5i		−	1.78571i	0.450339	−	0.892857i	$-0.351303\pi$
$390$	4477.64	+	1792.94i	0.581369	+	0.232793i
$391$	−4461.23			−0.577018
$392$	1791.83	+	1539.45i	0.230870	+	0.198351i
$393$	−2500.73			−0.320980
$394$	−1621.11	−	5492.40i	−0.207285	−	0.702292i
$395$	−13755.9			−1.75224
$396$	−967.785	+	625.810i	−0.122811	+	0.0794145i
$397$	−6204.37			−0.784354			−0.392177	−	0.919890i	$-0.628278\pi$
$397$	−6204.37			−0.784354			−0.392177	+	0.919890i	$0.628278\pi$
$398$	1465.00	+	4963.51i	0.184507	+	0.625122i
$399$	7424.74			0.931584
$400$	579.491	−	1288.03i	0.0724364	−	0.161004i
$401$			3377.04i			0.420552i	0.977642	+	0.210276i	$0.0674363\pi$
$401$			3377.04i			0.420552i	−0.977642	+	0.210276i	$0.932564\pi$
$402$	−2565.63	+	757.257i	−0.318313	+	0.0939516i
$403$	4393.51	−	5569.85i	0.543068	−	0.688472i
$404$	−1999.95	−	3092.83i	−0.246291	−	0.380876i
$405$	−982.302			−0.120521
$406$	−1524.85	−	5166.29i	−0.186397	−	0.631524i
$407$	−1061.87			−0.129324
$408$	2026.24	−	2358.43i	0.245867	−	0.286176i
$409$			5434.16i			0.656973i	0.944509	+	0.328486i	$0.106539\pi$
$409$			5434.16i			0.656973i	−0.944509	+	0.328486i	$0.893461\pi$
$410$	−3692.76	+	1089.94i	−0.444811	+	0.131288i
$411$	−3037.33			−0.364527
$412$	−8365.71	+	5409.62i	−1.00036	+	0.646875i
$413$			6620.66i			0.788817i
$414$	701.851	+	2377.91i	0.0833191	+	0.282290i
$415$	−9976.84			−1.18011
$416$	5889.17	+	6108.11i	0.694087	+	0.719891i
$417$	7389.23			0.867751
$418$	−1499.60	−	5080.72i	−0.175473	−	0.594512i
$419$		−	3615.54i		−	0.421553i	−0.977534	−	0.210776i	$-0.932401\pi$
$419$		−	3615.54i		−	0.421553i	0.977534	−	0.210776i	$-0.0675992\pi$
$420$	5169.63	−	3342.90i	0.600600	−	0.388373i
$421$	−9792.46			−1.13362			−0.566811	−	0.823848i	$-0.691823\pi$
$421$	−9792.46			−1.13362			−0.566811	+	0.823848i	$0.691823\pi$
$422$	−7730.56	+	2281.71i	−0.891748	+	0.263203i
$423$			5223.90i			0.600460i
$424$	−3555.04	+	4137.87i	−0.407188	+	0.473945i
$425$	1010.84			0.115371
$426$	1208.95	+	4096.01i	0.137498	+	0.465850i
$427$	−7067.12			−0.800942
$428$	2122.24	+	3281.94i	0.239678	+	0.370651i
$429$	1393.98	−	1767.22i	0.156881	−	0.198886i
$430$	7709.23	−	2275.41i	0.864586	−	0.255186i
$431$		−	8176.94i		−	0.913850i	−0.889505	−	0.456925i	$-0.848951\pi$
$431$		−	8176.94i		−	0.913850i	0.889505	−	0.456925i	$-0.151049\pi$
$432$	−1575.86	−	708.985i	−0.175506	−	0.0789608i
$433$	−14447.6			−1.60348			−0.801740	−	0.597673i	$-0.796092\pi$
$433$	−14447.6			−1.60348			−0.801740	+	0.597673i	$0.796092\pi$
$434$	−2563.22	−	8684.35i	−0.283499	−	0.960512i
$435$	−3275.70			−0.361053
$436$	4729.04	−	3058.00i	0.519450	−	0.335898i
$437$	−11396.1			−1.24749
$438$	1819.78	+	6165.52i	0.198521	+	0.672602i
$439$	−14823.9			−1.61163			−0.805816	−	0.592166i	$-0.798273\pi$
$439$	−14823.9			−1.61163			−0.805816	+	0.592166i	$0.798273\pi$
$440$	−3331.66	−	2862.38i	−0.360978	−	0.310133i
$441$	939.607			0.101458
$442$	−2257.32	+	5637.37i	−0.242919	+	0.606656i
$443$			6678.46i			0.716260i	0.933672	+	0.358130i	$0.116586\pi$
$443$			6678.46i			0.716260i	−0.933672	+	0.358130i	$0.883414\pi$
$444$	−864.527	−	1336.95i	−0.0924068	−	0.142903i
$445$		−	9744.49i		−	1.03805i
$446$	3723.93	−	1099.13i	0.395366	−	0.116694i
$447$		−	8973.01i		−	0.949460i
$448$	10706.1	−	1631.61i	1.12906	−	0.172068i
$449$		−	13672.9i		−	1.43712i	−0.695467	−	0.718558i	$-0.744802\pi$
$449$		−	13672.9i		−	1.43712i	0.695467	−	0.718558i	$-0.255198\pi$
$450$	−159.027	−	538.794i	−0.0166592	−	0.0564422i
$451$			1796.77i			0.187597i
$452$	15205.8	−	9832.72i	1.58235	−	1.02321i
$453$	6923.36			0.718075
$454$	−3168.88	−	10736.3i	−0.327583	−	1.10987i
$455$	−7446.25	+	9439.96i	−0.767221	+	0.972642i
$456$	5175.99	−	6024.57i	0.531553	−	0.618698i
$457$			8454.03i			0.865345i	0.901551	+	0.432672i	$0.142429\pi$
$457$			8454.03i			0.865345i	−0.901551	+	0.432672i	$0.857571\pi$
$458$	−1200.23	−	4066.45i	−0.122452	−	0.414875i
$459$		−	1236.72i		−	0.125763i
$460$	−7934.80	+	5130.97i	−0.804265	+	0.520071i
$461$	12560.1			1.26895			0.634473	−	0.772945i	$-0.281217\pi$
$461$	12560.1			1.26895			0.634473	+	0.772945i	$0.281217\pi$
$462$	−813.266	−	2755.39i	−0.0818973	−	0.277473i
$463$			14540.8i			1.45954i	0.683690	+	0.729772i	$0.260374\pi$
$463$			14540.8i			1.45954i	−0.683690	+	0.729772i	$0.739626\pi$
$464$	−5255.05	−	2364.27i	−0.525774	−	0.236548i
$465$	−5506.34			−0.549141
$466$	3024.24	+	10246.3i	0.300633	+	1.01856i
$467$			10533.0i			1.04370i	0.853038	+	0.521849i	$0.174758\pi$
$467$			10533.0i			1.04370i	−0.853038	+	0.521849i	$0.825242\pi$
$468$	3359.94	+	316.309i	0.331866	+	0.0312423i
$469$		−	6668.28i		−	0.656530i
$470$	−19095.0	+	5635.97i	−1.87401	+	0.553123i
$471$	3293.35			0.322186
$472$	5372.13	+	4615.45i	0.523882	+	0.450092i
$473$		−	3751.03i		−	0.364635i
$474$	−9231.20	+	2724.63i	−0.894521	+	0.264022i
$475$	2582.17			0.249427
$476$	4208.72	+	6508.58i	0.405266	+	0.626723i
$477$			2169.83i			0.208280i
$478$	−13349.2	+	3940.08i	−1.27736	+	0.377019i
$479$		−	9522.04i		−	0.908295i	−0.890927	−	0.454147i	$-0.849944\pi$
$479$		−	9522.04i		−	0.908295i	0.890927	−	0.454147i	$-0.150056\pi$
$480$	891.401	−	6525.16i	0.0847639	−	0.620482i
$481$	2441.33	+	1925.72i	0.231424	+	0.182548i
$482$	−3979.74	+	1174.64i	−0.376083	+	0.111003i
$483$	−6180.39			−0.582231
$484$	7220.20	−	4668.88i	0.678080	−	0.438475i
$485$			9101.13i			0.852085i
$486$	−659.194	+	194.564i	−0.0615260	+	0.0181597i
$487$			15094.0i			1.40446i	0.711950	+	0.702230i	$0.247812\pi$
$487$			15094.0i			1.40446i	−0.711950	+	0.702230i	$0.752188\pi$
$488$	−4926.69	+	5734.40i	−0.457010	+	0.531934i
$489$		−	6416.58i		−	0.593390i
$490$	1013.72	+	3434.56i	0.0934600	+	0.316648i
$491$		−	21589.6i		−	1.98437i	−0.124791	−	0.992183i	$-0.539826\pi$
$491$		−	21589.6i		−	1.98437i	0.124791	−	0.992183i	$-0.460174\pi$
$492$	−2262.22	+	1462.85i	−0.207295	+	0.134045i
$493$		−	4124.13i		−	0.376757i
$494$	−5766.30	+	14400.6i	−0.525178	+	1.31156i
$495$	−1747.07			−0.158636
$496$	−8833.54	−	3974.25i	−0.799673	−	0.359777i
$497$	−10645.9			−0.960829
$498$	−6695.17	+	1976.11i	−0.602445	+	0.177814i
$499$	17274.5			1.54973			0.774863	−	0.632130i	$-0.217819\pi$
$499$	17274.5			1.54973			0.774863	+	0.632130i	$0.217819\pi$
$500$	−8385.67	+	5422.52i	−0.750037	+	0.485005i
$501$	7023.66			0.626335
$502$	−13243.9	+	3908.99i	−1.17750	+	0.347544i
$503$	−5755.02			−0.510146			−0.255073	−	0.966922i	$-0.582100\pi$
$503$	−5755.02			−0.510146			−0.255073	+	0.966922i	$0.582100\pi$
$504$	2807.06	−	3267.27i	0.248088	−	0.288761i
$505$		−	5583.24i		−	0.491982i
$506$	1248.27	+	4229.22i	0.109669	+	0.371565i
$507$	−6409.77	+	1534.96i	−0.561475	+	0.134458i
$508$	10343.9	−	6688.81i	0.903420	−	0.584189i
$509$	8760.81			0.762900			0.381450	−	0.924389i	$-0.375425\pi$
$509$	8760.81			0.762900			0.381450	+	0.924389i	$0.375425\pi$
$510$	4520.60	−	1334.28i	0.392501	−	0.115849i
$511$	−16024.7			−1.38726
$512$	6139.62	−	9824.60i	0.529952	−	0.848028i
$513$		−	3159.19i		−	0.271894i
$514$	−1523.87	−	5162.95i	−0.130768	−	0.443050i
$515$	−15101.9			−1.29218
$516$	4722.75	−	3053.93i	0.402921	−	0.260546i
$517$			9290.93i			0.790357i
$518$	3806.44	−	1123.49i	0.322868	−	0.0952958i
$519$	−4965.60			−0.419972
$520$	2468.77	+	12622.9i	0.208197	+	1.06452i
$521$	16422.2			1.38094			0.690468	−	0.723363i	$-0.257405\pi$
$521$	16422.2			1.38094			0.690468	+	0.723363i	$0.257405\pi$
$522$	−2198.23	+	648.817i	−0.184318	+	0.0544022i
$523$			15056.8i			1.25887i	0.777054	+	0.629434i	$0.216713\pi$
$523$			15056.8i			1.25887i	−0.777054	+	0.629434i	$0.783287\pi$
$524$	−3621.08	−	5599.83i	−0.301885	−	0.466850i
$525$	1400.37			0.116414
$526$	4735.90	+	16045.5i	0.392576	+	1.33007i
$527$		−	6932.51i		−	0.573026i
$528$	−2802.73	−	1260.96i	−0.231010	−	0.103932i
$529$	−2680.79			−0.220333
$530$	−7931.41	+	2340.99i	−0.650034	+	0.191861i
$531$	2817.06			0.230226
$532$	10751.1	+	16626.1i	0.876165	+	1.35495i
$533$	3258.47	−	4130.92i	0.264803	−	0.335703i
$534$	−1930.09	−	6539.24i	−0.156410	−	0.529926i
$535$			5924.62i			0.478773i
$536$	−5410.77	−	4648.64i	−0.436026	−	0.374610i
$537$	6015.83			0.483430
$538$	−11403.6	+	3365.81i	−0.913835	+	0.269722i
$539$	1671.13			0.133545
$540$	−1422.38	−	2199.65i	−0.113351	−	0.175292i
$541$	−2634.99			−0.209403			−0.104702	−	0.994504i	$-0.533389\pi$
$541$	−2634.99			−0.209403			−0.104702	+	0.994504i	$0.533389\pi$
$542$	−7485.69	+	2209.43i	−0.593244	+	0.175098i
$543$	4888.61			0.386354
$544$	8215.20	+	1122.28i	0.647470	+	0.0884508i
$545$	8536.96			0.670978
$546$	−3127.20	+	7809.76i	−0.245113	+	0.612137i
$547$		−	2007.56i		−	0.156923i	−0.996917	−	0.0784616i	$-0.974999\pi$
$547$		−	2007.56i		−	0.156923i	0.996917	−	0.0784616i	$-0.0250008\pi$
$548$	−4398.09	−	6801.43i	−0.342841	−	0.530187i
$549$			3007.02i			0.233764i
$550$	−282.837	−	958.268i	−0.0219276	−	0.0742921i
$551$		−	10535.0i		−	0.814531i
$552$	−4308.52	+	5014.89i	−0.332215	+	0.386681i
$553$		−	23992.6i		−	1.84497i
$554$	24111.2	−	7116.53i	1.84907	−	0.545763i
$555$		−	2413.49i		−	0.184589i
$556$	10699.7	+	16546.6i	0.816130	+	1.26211i
$557$	15077.3			1.14694			0.573468	−	0.819228i	$-0.305598\pi$
$557$	15077.3			1.14694			0.573468	+	0.819228i	$0.305598\pi$
$558$	−3695.14	+	1090.64i	−0.280337	+	0.0827427i
$559$	−6802.58	+	8623.94i	−0.514702	+	0.652511i
$560$	14971.4	+	6735.69i	1.12974	+	0.508276i
$561$		−	2199.56i		−	0.165536i
$562$	10988.8	−	3243.40i	0.824796	−	0.243442i
$563$		−	14038.8i		−	1.05091i	−0.850821	−	0.525455i	$-0.823895\pi$
$563$		−	14038.8i		−	1.05091i	0.850821	−	0.525455i	$-0.176105\pi$
$564$	−11697.8	+	7564.27i	−0.873342	+	0.564740i
$565$	27449.9			2.04394
$566$	−11063.3	+	3265.39i	−0.821600	+	0.242499i
$567$		−	1713.30i		−	0.126899i
$568$	−7421.52	+	8638.25i	−0.548240	+	0.638121i
$569$	5607.45			0.413140			0.206570	−	0.978432i	$-0.433770\pi$
$569$	5607.45			0.413140			0.206570	+	0.978432i	$0.433770\pi$
$570$	11547.8	−	3408.39i	0.848569	−	0.250459i
$571$		−	6820.92i		−	0.499906i	−0.968258	−	0.249953i	$-0.919585\pi$
$571$		−	6820.92i		−	0.499906i	0.968258	−	0.249953i	$-0.0804152\pi$
$572$	5975.80	+	562.569i	0.436819	+	0.0411227i
$573$			14171.7i			1.03321i
$574$	−1901.03	−	6440.80i	−0.138236	−	0.468352i
$575$	−2149.41			−0.155890
$576$	−694.242	−	4555.40i	−0.0502200	−	0.329529i
$577$		−	23328.9i		−	1.68318i	−0.540117	−	0.841590i	$-0.681620\pi$
$577$		−	23328.9i		−	1.68318i	0.540117	−	0.841590i	$-0.318380\pi$
$578$	−2253.86	−	7636.19i	−0.162194	−	0.549522i
$579$	−32.0535			−0.00230069
$580$	−4743.26	−	7335.22i	−0.339574	−	0.525135i
$581$		−	17401.3i		−	1.24256i
$582$	1802.66	+	6107.50i	0.128389	+	0.434990i
$583$			3859.14i			0.274149i
$584$	−11171.3	+	13002.7i	−0.791558	+	0.921330i
$585$	4016.65	+	3168.34i	0.283877	+	0.223923i
$586$	−1273.24	−	4313.82i	−0.0897564	−	0.304100i
$587$	−11535.3			−0.811093			−0.405547	−	0.914074i	$-0.632919\pi$
$587$	−11535.3			−0.811093			−0.405547	+	0.914074i	$0.632919\pi$
$588$	1360.56	+	2104.04i	0.0954228	+	0.147567i
$589$		−	17709.0i		−	1.23886i
$590$	3039.27	+	10297.2i	0.212076	+	0.718525i
$591$		−	6074.02i		−	0.422761i
$592$	1741.96	−	3871.83i	0.120936	−	0.268803i
$593$		−	17605.5i		−	1.21917i	−0.792720	−	0.609586i	$-0.791336\pi$
$593$		−	17605.5i		−	1.21917i	0.792720	−	0.609586i	$-0.208664\pi$
$594$	−1172.40	+	346.040i	−0.0809837	+	0.0239027i
$595$			11749.4i			0.809545i
$596$	20093.1	−	12993.0i	1.38095	−	0.892978i
$597$			5489.13i			0.376307i
$598$	4799.90	−	11987.1i	0.328231	−	0.819714i
$599$	−23660.0			−1.61389			−0.806945	−	0.590627i	$-0.798881\pi$
$599$	−23660.0			−1.61389			−0.806945	+	0.590627i	$0.798881\pi$
$600$	976.237	−	1136.29i	0.0664245	−	0.0773145i
$601$	−408.208			−0.0277057			−0.0138529	−	0.999904i	$-0.504410\pi$
$601$	−408.208			−0.0277057			−0.0138529	+	0.999904i	$0.504410\pi$
$602$	3968.70	+	13446.2i	0.268691	+	0.910342i
$603$	−2837.32			−0.191616
$604$	10025.1	+	15503.3i	0.675357	+	1.04441i
$605$	13034.0			0.875883
$606$	−1105.87	−	3746.75i	−0.0741302	−	0.251157i
$607$	19900.9			1.33073			0.665363	−	0.746520i	$-0.268277\pi$
$607$	19900.9			1.33073			0.665363	+	0.746520i	$0.268277\pi$
$608$	20985.6	+	2866.84i	1.39980	+	0.191226i
$609$		−	5713.38i		−	0.380161i
$610$	−10991.6	+	3244.22i	−0.729569	+	0.215336i
$611$	16849.3	−	21360.6i	1.11563	−	1.41433i
$612$	2769.37	−	1790.79i	0.182917	−	0.118282i
$613$	−710.858			−0.0468373			−0.0234187	−	0.999726i	$-0.507455\pi$
$613$	−710.858			−0.0468373			−0.0234187	+	0.999726i	$0.507455\pi$
$614$	5143.09	+	17425.1i	0.338043	+	1.14531i
$615$	−4083.81			−0.267765
$616$	4992.47	−	5810.97i	0.326546	−	0.380082i
$617$			16609.5i			1.08375i	0.840459	+	0.541875i	$0.182286\pi$
$617$			16609.5i			1.08375i	−0.840459	+	0.541875i	$0.817714\pi$
$618$	−10134.5	+	2991.24i	−0.659658	+	0.194701i
$619$	−19446.3			−1.26270			−0.631351	−	0.775497i	$-0.717499\pi$
$619$	−19446.3			−1.26270			−0.631351	+	0.775497i	$0.717499\pi$
$620$	−7973.24	−	12330.2i	−0.516473	−	0.798700i
$621$			2629.72i			0.169931i
$622$	2737.68	+	9275.41i	0.176481	+	0.597926i
$623$	16996.0			1.09299
$624$	4156.93	+	7981.86i	0.266683	+	0.512068i
$625$	−17896.5			−1.14538
$626$	7071.10	+	23957.3i	0.451467	+	1.52960i
$627$		−	5618.75i		−	0.357881i
$628$	4768.81	+	7374.73i	0.303019	+	0.468605i
$629$	3038.59			0.192618
$630$	6262.64	−	1848.45i	0.396047	−	0.116895i
$631$		−	25295.7i		−	1.59589i	−0.602733	−	0.797943i	$-0.705922\pi$
$631$		−	25295.7i		−	1.59589i	0.602733	−	0.797943i	$-0.294078\pi$
$632$	−19468.1	−	16725.9i	−1.22531	−	1.05272i
$633$	−8549.20			−0.536809
$634$	−5188.20	−	17577.9i	−0.325000	−	1.10112i
$635$	18673.1			1.16696
$636$	−4858.86	+	3141.94i	−0.302934	+	0.195890i
$637$	−3842.07	−	3030.63i	−0.238977	−	0.188506i
$638$	−3909.65	+	1153.95i	−0.242609	+	0.0716070i
$639$			4529.76i			0.280429i
$640$	15902.4	−	7452.41i	0.982184	−	0.460285i
$641$	25718.1			1.58471			0.792357	−	0.610057i	$-0.208854\pi$
$641$	25718.1			1.58471			0.792357	+	0.610057i	$0.208854\pi$
$642$	1173.49	+	3975.84i	0.0721399	+	0.244414i
$643$	12820.0			0.786268			0.393134	−	0.919481i	$-0.371391\pi$
$643$	12820.0			0.786268			0.393134	+	0.919481i	$0.371391\pi$
$644$	−8949.28	−	13839.6i	−0.547595	−	0.846829i
$645$	8525.60			0.520458
$646$	4291.18	+	14538.7i	0.261353	+	0.885479i
$647$	−5429.39			−0.329910			−0.164955	−	0.986301i	$-0.552748\pi$
$647$	−5429.39			−0.329910			−0.164955	+	0.986301i	$0.552748\pi$
$648$	−1390.20	−	1194.39i	−0.0842783	−	0.0724074i
$649$	5010.25			0.303035
$650$	−1087.57	+	2716.07i	−0.0656279	+	0.163897i
$651$		−	9603.99i		−	0.578203i
$652$	14368.5	−	9291.28i	0.863058	−	0.558090i
$653$			23782.4i			1.42523i	0.701553	+	0.712617i	$0.252490\pi$
$653$			23782.4i			1.42523i	−0.701553	+	0.712617i	$0.747510\pi$
$654$	5728.91	−	1690.91i	0.342535	−	0.101101i
$655$		−	10108.9i		−	0.603036i
$656$	−6551.45	−	2947.53i	−0.389926	−	0.175429i
$657$			6818.42i			0.404889i
$658$	−9830.08	−	33304.9i	−0.582396	−	1.97319i
$659$		−	27296.5i		−	1.61354i	−0.590868	−	0.806768i	$-0.701215\pi$
$659$		−	27296.5i		−	1.61354i	0.590868	−	0.806768i	$-0.298785\pi$
$660$	−2529.77	−	3912.17i	−0.149199	−	0.230729i
$661$	−27338.9			−1.60871			−0.804357	−	0.594147i	$-0.797490\pi$
$661$	−27338.9			−1.60871			−0.804357	+	0.594147i	$0.797490\pi$
$662$	6932.24	+	23486.8i	0.406992	+	1.37891i
$663$	−3988.96	+	5056.98i	−0.233662	+	0.296225i
$664$	−14119.7	−	12130.9i	−0.825229	−	0.708993i
$665$			30013.7i			1.75020i
$666$	−478.038	−	1619.62i	−0.0278132	−	0.0942328i
$667$			8769.40i			0.509074i
$668$	10170.3	+	15727.9i	0.589076	+	0.910977i
$669$	4118.28			0.238000
$670$	−3061.13	−	10371.3i	−0.176510	−	0.598026i
$671$			5348.12i			0.307693i
$672$	11381.0	+	1554.75i	0.653319	+	0.0892499i
$673$	26689.5			1.52868			0.764342	−	0.644811i	$-0.223064\pi$
$673$	26689.5			1.52868			0.764342	+	0.644811i	$0.223064\pi$
$674$	7145.70	+	24210.1i	0.408371	+	1.38359i
$675$		−	595.850i		−	0.0339767i
$676$	−12718.6	−	12130.6i	−0.723636	−	0.690182i
$677$			12731.9i			0.722787i	0.932413	+	0.361393i	$0.117699\pi$
$677$			12731.9i			0.722787i	−0.932413	+	0.361393i	$0.882301\pi$
$678$	18420.8	−	5436.98i	1.04343	−	0.307973i
$679$	−15873.9			−0.897179
$680$	9533.71	+	8190.85i	0.537648	+	0.461919i
$681$		−	11873.3i		−	0.668112i
$682$	−6571.97	+	1939.75i	−0.368994	+	0.108910i
$683$	10423.4			0.583955			0.291977	−	0.956425i	$-0.405687\pi$
$683$	10423.4			0.583955			0.291977	+	0.956425i	$0.405687\pi$
$684$	7074.30	−	4574.54i	0.395457	−	0.255719i
$685$		−	12278.1i		−	0.684849i
$686$	13690.7	−	4040.86i	0.761971	−	0.224899i
$687$		−	4497.07i		−	0.249744i
$688$	13677.2	+	6153.43i	0.757904	+	0.340985i
$689$	6998.63	−	8872.48i	0.386976	−	0.490587i
$690$	−9612.46	+	2837.16i	−0.530348	+	0.156535i
$691$	12008.8			0.661124			0.330562	−	0.943784i	$-0.392762\pi$
$691$	12008.8			0.661124			0.330562	+	0.943784i	$0.392762\pi$
$692$	−7190.24	−	11119.4i	−0.394988	−	0.610830i
$693$		−	3047.18i		−	0.167031i
$694$	−4171.56	+	1231.25i	−0.228170	+	0.0673455i
$695$			29870.2i			1.63027i
$696$	−4635.95	−	3982.96i	−0.252479	−	0.216916i
$697$		−	5141.54i		−	0.279411i
$698$	−6782.56	−	22979.7i	−0.367799	−	1.24612i
$699$			11331.3i			0.613147i
$700$	2027.75	+	3135.82i	0.109488	+	0.169318i
$701$			10284.3i			0.554114i	0.960853	+	0.277057i	$0.0893591\pi$
$701$			10284.3i			0.554114i	−0.960853	+	0.277057i	$0.910641\pi$
$702$	3323.01	+	1330.61i	0.178659	+	0.0715391i
$703$	7762.03			0.416430
$704$	−1234.74	−	8101.98i	−0.0661022	−	0.433743i
$705$	−21117.1			−1.12811
$706$	18777.9	−	5542.38i	1.00101	−	0.295453i
$707$	9738.12			0.518019
$708$	4079.13	+	6308.18i	0.216530	+	0.334853i
$709$	−16944.0			−0.897524			−0.448762	−	0.893651i	$-0.648135\pi$
$709$	−16944.0			−0.897524			−0.448762	+	0.893651i	$0.648135\pi$
$710$	−16557.7	+	4887.07i	−0.875209	+	0.258322i
$711$	−10208.7			−0.538478
$712$	11848.4	−	13790.9i	0.623649	−	0.725893i
$713$			14741.0i			0.774273i
$714$	2327.20	+	7884.70i	0.121980	+	0.413274i
$715$	7143.78	+	5635.03i	0.373654	+	0.294739i
$716$	8710.99	+	13471.1i	0.454672	+	0.703128i
$717$	−14762.9			−0.768939
$718$	10977.7	−	3240.12i	0.570590	−	0.168412i
$719$	14267.6			0.740041			0.370021	−	0.929023i	$-0.379351\pi$
$719$	14267.6			0.740041			0.370021	+	0.929023i	$0.379351\pi$
$720$	2866.00	−	6370.23i	0.148346	−	0.329729i
$721$		−	26340.3i		−	1.36056i
$722$	5469.91	+	18532.4i	0.281951	+	0.955267i
$723$	−4401.18			−0.226392
$724$	7078.76	+	10947.0i	0.363370	+	0.561934i
$725$		−	1986.99i		−	0.101786i
$726$	8746.77	−	2581.65i	0.447139	−	0.131975i
$727$	7899.54			0.402996			0.201498	−	0.979489i	$-0.435419\pi$
$727$	7899.54			0.402996			0.201498	+	0.979489i	$0.435419\pi$
$728$	−22016.4	+	4305.95i	−1.12086	+	0.219216i
$729$	−729.000			−0.0370370
$730$	−24923.4	+	7356.26i	−1.26364	+	0.372969i
$731$			10733.8i			0.543095i
$732$	−6733.57	+	4354.20i	−0.340000	+	0.219858i
$733$	−18.8350			−0.000949093			−0.000474547	−	1.00000i	$-0.500151\pi$
$733$	−18.8350			−0.000949093			−0.000474547		1.00000i	$0.500151\pi$
$734$	−454.726	−	1540.64i	−0.0228668	−	0.0774741i
$735$			3798.26i			0.190614i
$736$	−17468.5	−	2386.37i	−0.874862	−	0.119515i
$737$	−5046.29			−0.252215
$738$	−2740.53	+	808.879i	−0.136694	+	0.0403459i
$739$	−13711.5			−0.682525			−0.341262	−	0.939968i	$-0.610854\pi$
$739$	−13711.5			−0.682525			−0.341262	+	0.939968i	$0.610854\pi$
$740$	5404.47	−	3494.76i	0.268476	−	0.173608i
$741$	−10189.7	+	12918.0i	−0.505167	+	0.640423i
$742$	−4083.08	−	13833.7i	−0.202014	−	0.684436i
$743$		−	11169.5i		−	0.551506i	−0.961229	−	0.275753i	$-0.911073\pi$
$743$		−	11169.5i		−	0.551506i	0.961229	−	0.275753i	$-0.0889271\pi$
$744$	−7792.86	−	6695.21i	−0.384005	−	0.329917i
$745$	36272.4			1.78378
$746$	−12567.4	+	3709.32i	−0.616789	+	0.182048i
$747$	−7404.16			−0.362656
$748$	4925.44	−	3184.99i	0.240764	−	0.155688i
$749$	−10333.5			−0.504111
$750$	−10158.7	+	2998.37i	−0.494589	+	0.145980i
$751$	−31229.1			−1.51740			−0.758698	−	0.651443i	$-0.774164\pi$
$751$	−31229.1			−1.51740			−0.758698	+	0.651443i	$0.774164\pi$
$752$	−33877.0	−	15241.4i	−1.64278	−	0.739093i
$753$	−14646.4			−0.708822
$754$	11081.3	+	4437.20i	0.535223	+	0.214315i
$755$			27987.0i			1.34907i
$756$	3836.56	−	2480.88i	0.184569	−	0.119350i
$757$			29792.5i			1.43042i	0.698911	+	0.715209i	$0.253668\pi$
$757$			29792.5i			1.43042i	−0.698911	+	0.715209i	$0.746332\pi$
$758$	6409.42	+	21715.5i	0.307125	+	1.04056i
$759$			4677.08i			0.223672i
$760$	24353.7	+	20923.4i	1.16237	+	0.998646i
$761$			3531.27i			0.168211i	0.996457	+	0.0841054i	$0.0268033\pi$
$761$			3531.27i			0.168211i	−0.996457	+	0.0841054i	$0.973197\pi$
$762$	12530.9	−	3698.56i	0.595733	−	0.175833i
$763$			14889.9i			0.706488i
$764$	−31734.3	+	20520.7i	−1.50276	+	0.971746i
$765$	4999.32			0.236275
$766$	−24740.4	+	7302.25i	−1.16698	+	0.344440i
$767$	−11519.0	−	9086.21i	−0.542278	−	0.427750i
$768$	9195.55	−	8150.88i	0.432052	−	0.382968i
$769$			10014.1i			0.469596i	0.972044	+	0.234798i	$0.0754428\pi$
$769$			10014.1i			0.469596i	−0.972044	+	0.234798i	$0.924557\pi$
$770$	11138.4	−	3287.54i	0.521298	−	0.153863i
$771$		−	5709.68i		−	0.266705i
$772$	−46.4138	−	71.7767i	−0.00216382	−	0.00334624i
$773$	18303.4			0.851652			0.425826	−	0.904805i	$-0.359984\pi$
$773$	18303.4			0.851652			0.425826	+	0.904805i	$0.359984\pi$
$774$	5721.28	−	1688.66i	0.265694	−	0.0784208<

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.800675 + 2.71273i) q^{2} +3.00000i q^{3} +(-6.71784 + 4.34403i) q^{4} -12.1272 q^{5} +(-8.13820 + 2.40203i) q^{6} -21.1519i q^{7} +(-17.1630 - 14.7455i) q^{8} -9.00000 q^{9} +(-9.70993 - 32.8978i) q^{10} -16.0069 q^{11} +(-13.0321 - 20.1535i) q^{12} +(36.8012 + 29.0288i) q^{13} +(57.3793 - 16.9358i) q^{14} -36.3815i q^{15} +(26.2587 - 58.3651i) q^{16} +45.8045 q^{17} +(-7.20608 - 24.4146i) q^{18} +117.007 q^{19} +(81.4684 - 52.6809i) q^{20} +63.4556 q^{21} +(-12.8163 - 43.4224i) q^{22} -97.3972 q^{23} +(44.2366 - 51.4890i) q^{24} +22.0685 q^{25} +(-49.2817 + 123.074i) q^{26} -27.0000i q^{27} +(91.8844 + 142.095i) q^{28} -90.0375i q^{29} +(98.6934 - 29.1298i) q^{30} -151.350i q^{31} +(179.354 + 24.5015i) q^{32} -48.0206i q^{33} +(36.6745 + 124.255i) q^{34} +256.512i q^{35} +(60.4606 - 39.0963i) q^{36} +66.3382 q^{37} +(93.6845 + 317.409i) q^{38} +(-87.0865 + 110.404i) q^{39} +(208.139 + 178.822i) q^{40} -112.250i q^{41} +(50.8073 + 172.138i) q^{42} +234.339i q^{43} +(107.532 - 69.5345i) q^{44} +109.145 q^{45} +(-77.9835 - 264.213i) q^{46} -580.433i q^{47} +(175.095 + 78.7762i) q^{48} -104.401 q^{49} +(17.6697 + 59.8660i) q^{50} +137.414i q^{51} +(-373.327 - 35.1454i) q^{52} -241.092i q^{53} +(73.2438 - 21.6182i) q^{54} +194.118 q^{55} +(-311.896 + 363.029i) q^{56} +351.021i q^{57} +(244.248 - 72.0908i) q^{58} -313.006 q^{59} +(158.043 + 244.405i) q^{60} -334.114i q^{61} +(410.572 - 121.182i) q^{62} +190.367i q^{63} +(77.1380 + 506.156i) q^{64} +(-446.295 - 352.038i) q^{65} +(130.267 - 38.4489i) q^{66} +315.258 q^{67} +(-307.707 + 198.976i) q^{68} -292.192i q^{69} +(-695.849 + 205.383i) q^{70} -503.306i q^{71} +(154.467 + 132.710i) q^{72} -757.602i q^{73} +(53.1154 + 179.958i) q^{74} +66.2055i q^{75} +(-786.034 + 508.282i) q^{76} +338.575i q^{77} +(-369.223 - 147.845i) q^{78} +1134.30 q^{79} +(-318.444 + 707.804i) q^{80} +81.0000 q^{81} +(304.503 - 89.8754i) q^{82} +822.684 q^{83} +(-426.284 + 275.653i) q^{84} -555.480 q^{85} +(-635.698 + 187.629i) q^{86} +270.113 q^{87} +(274.726 + 236.030i) q^{88} +803.525i q^{89} +(87.3894 + 296.080i) q^{90} +(614.014 - 778.413i) q^{91} +(654.299 - 423.097i) q^{92} +454.049 q^{93} +(1574.56 - 464.738i) q^{94} -1418.96 q^{95} +(-73.5044 + 538.061i) q^{96} -750.474i q^{97} +(-83.5911 - 283.211i) q^{98} +144.062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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