LMFDB - Embedded newform 117.4.q.e.10.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(10,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("117.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, degree $2$, 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:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.5
Root			$-5.36472i$ of defining polynomial
Character	$\chi$	$=$	117.10
Dual form			117.4.q.e.82.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.64599 - 2.68236i) q^{2} +(10.3901 - 17.9962i) q^{4} -2.69631i q^{5} +(13.1657 + 7.60123i) q^{7} -68.5626i q^{8} +O(q^{10})$	\(q+(4.64599 - 2.68236i) q^{2} +(10.3901 - 17.9962i) q^{4} -2.69631i q^{5} +(13.1657 + 7.60123i) q^{7} -68.5626i q^{8} +(-7.23249 - 12.5270i) q^{10} +(-57.9240 + 33.4424i) q^{11} +(46.8650 + 0.818689i) q^{13} +81.5570 q^{14} +(-100.789 - 174.571i) q^{16} +(-2.08177 + 3.60573i) q^{17} +(-22.5903 - 13.0425i) q^{19} +(-48.5235 - 28.0150i) q^{20} +(-179.409 + 310.746i) q^{22} +(-23.6621 - 40.9839i) q^{23} +117.730 q^{25} +(219.930 - 121.905i) q^{26} +(273.587 - 157.956i) q^{28} +(128.503 + 222.575i) q^{29} +206.242i q^{31} +(-461.511 - 266.453i) q^{32} +22.3362i q^{34} +(20.4953 - 35.4989i) q^{35} +(-152.149 + 87.8430i) q^{37} -139.939 q^{38} -184.866 q^{40} +(-135.501 + 78.2313i) q^{41} +(25.9922 - 45.0199i) q^{43} +1389.88i q^{44} +(-219.868 - 126.941i) q^{46} -354.222i q^{47} +(-55.9425 - 96.8953i) q^{49} +(546.972 - 315.794i) q^{50} +(501.667 - 834.888i) q^{52} +10.4723 q^{53} +(90.1712 + 156.181i) q^{55} +(521.160 - 902.676i) q^{56} +(1194.05 + 689.386i) q^{58} +(-385.480 - 222.557i) q^{59} +(-59.8481 + 103.660i) q^{61} +(553.216 + 958.199i) q^{62} -1246.28 q^{64} +(2.20744 - 126.363i) q^{65} +(-19.4057 + 11.2039i) q^{67} +(43.2597 + 74.9281i) q^{68} -219.903i q^{70} +(246.997 + 142.604i) q^{71} -740.989i q^{73} +(-471.253 + 816.235i) q^{74} +(-469.432 + 271.027i) q^{76} -1016.81 q^{77} -547.679 q^{79} +(-470.698 + 271.758i) q^{80} +(-419.689 + 726.923i) q^{82} -603.056i q^{83} +(9.72218 + 5.61310i) q^{85} -278.882i q^{86} +(2292.90 + 3971.42i) q^{88} +(186.774 - 107.834i) q^{89} +(610.789 + 367.011i) q^{91} -983.409 q^{92} +(-950.153 - 1645.71i) q^{94} +(-35.1666 + 60.9104i) q^{95} +(-1253.58 - 723.752i) q^{97} +(-519.817 - 300.116i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) $ 10 * q + 30 * q^4 + 30 * q^7	$ 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29} - 1440 q^{32} - 60 q^{35} - 405 q^{37} + 1380 q^{38} + 2000 q^{40} - 1065 q^{41} - 370 q^{43} - 390 q^{46} + 775 q^{49} + 4320 q^{50} + 2940 q^{52} - 330 q^{53} - 260 q^{55} + 2670 q^{56} + 2040 q^{58} - 780 q^{59} - 1375 q^{61} + 780 q^{62} - 3140 q^{64} - 1605 q^{65} + 1590 q^{67} + 600 q^{68} - 1620 q^{71} - 2190 q^{74} - 5190 q^{76} + 4320 q^{77} + 1100 q^{79} - 8430 q^{80} - 2390 q^{82} + 525 q^{85} + 3170 q^{88} - 2040 q^{89} + 4770 q^{91} + 1740 q^{92} - 3230 q^{94} + 1380 q^{95} - 3750 q^{97} - 180 q^{98}+O(q^{100}) $ 10 * q + 30 * q^4 + 30 * q^7 + 40 * q^10 - 60 * q^11 + 25 * q^13 + 60 * q^14 - 250 * q^16 - 105 * q^17 + 180 * q^19 - 510 * q^20 - 290 * q^22 + 60 * q^23 - 960 * q^25 + 30 * q^26 + 150 * q^28 + 495 * q^29 - 1440 * q^32 - 60 * q^35 - 405 * q^37 + 1380 * q^38 + 2000 * q^40 - 1065 * q^41 - 370 * q^43 - 390 * q^46 + 775 * q^49 + 4320 * q^50 + 2940 * q^52 - 330 * q^53 - 260 * q^55 + 2670 * q^56 + 2040 * q^58 - 780 * q^59 - 1375 * q^61 + 780 * q^62 - 3140 * q^64 - 1605 * q^65 + 1590 * q^67 + 600 * q^68 - 1620 * q^71 - 2190 * q^74 - 5190 * q^76 + 4320 * q^77 + 1100 * q^79 - 8430 * q^80 - 2390 * q^82 + 525 * q^85 + 3170 * q^88 - 2040 * q^89 + 4770 * q^91 + 1740 * q^92 - 3230 * q^94 + 1380 * q^95 - 3750 * q^97 - 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	4.64599	−	2.68236i	1.64260	−	0.948358i	0.662702	−	0.748883i	$-0.269410\pi$
$2$	4.64599	−	2.68236i	1.64260	−	0.948358i	0.979903	−	0.199475i	$-0.0639236\pi$
$3$		0			0
$3$		0			0
$4$	10.3901	−	17.9962i	1.29877	−	2.24953i
$5$		−	2.69631i		−	0.241165i	−0.992703	−	0.120583i	$-0.961524\pi$
$5$		−	2.69631i		−	0.241165i	0.992703	−	0.120583i	$-0.0384763\pi$
$6$		0			0
$7$	13.1657	+	7.60123i	0.710882	+	0.410428i	0.811388	−	0.584509i	$-0.198713\pi$
$7$	13.1657	+	7.60123i	0.710882	+	0.410428i	−0.100505	+	0.994937i	$0.532046\pi$
$8$		−	68.5626i		−	3.03007i
$9$		0			0
$10$	−7.23249	−	12.5270i	−0.228711	−	0.396140i
$11$	−57.9240	+	33.4424i	−1.58770	+	0.916661i	−0.594018	+	0.804451i	$0.702459\pi$
$11$	−57.9240	+	33.4424i	−1.58770	+	0.916661i	−0.993685	+	0.112209i	$0.964207\pi$
$12$		0			0
$13$	46.8650	+	0.818689i	0.999847	+	0.0174664i
$13$	46.8650	+	0.818689i	0.999847	+	0.0174664i
$14$	81.5570			1.55693
$15$		0			0
$16$	−100.789	−	174.571i	−1.57482	−	2.72767i
$17$	−2.08177	+	3.60573i	−0.0297002	+	0.0514422i	−0.880493	−	0.474058i	$-0.842789\pi$
$17$	−2.08177	+	3.60573i	−0.0297002	+	0.0514422i	0.850793	+	0.525501i	$0.176122\pi$
$18$		0			0
$19$	−22.5903	−	13.0425i	−0.272766	−	0.157482i	0.357378	−	0.933960i	$-0.383671\pi$
$19$	−22.5903	−	13.0425i	−0.272766	−	0.157482i	−0.630144	+	0.776478i	$0.717004\pi$
$20$	−48.5235	−	28.0150i	−0.542509	−	0.313218i
$21$		0			0
$22$	−179.409	+	310.746i	−1.73865	+	3.01142i
$23$	−23.6621	−	40.9839i	−0.214517	−	0.371554i	0.738606	−	0.674137i	$-0.235484\pi$
$23$	−23.6621	−	40.9839i	−0.214517	−	0.371554i	−0.953123	+	0.302583i	$0.902151\pi$
$24$		0			0
$25$	117.730			0.941839
$26$	219.930	−	121.905i	1.65892	−	0.919523i
$27$		0			0
$28$	273.587	−	157.956i	1.84654	−	1.06610i
$29$	128.503	+	222.575i	0.822845	+	1.42521i	0.903555	+	0.428471i	$0.140948\pi$
$29$	128.503	+	222.575i	0.822845	+	1.42521i	−0.0807106	+	0.996738i	$0.525719\pi$
$30$		0			0
$31$			206.242i			1.19491i	0.801903	+	0.597455i	$0.203821\pi$
$31$			206.242i			1.19491i	−0.801903	+	0.597455i	$0.796179\pi$
$32$	−461.511	−	266.453i	−2.54951	−	1.47196i
$33$		0			0
$34$			22.3362i			0.112666i
$35$	20.4953	−	35.4989i	0.0989811	−	0.171440i
$36$		0			0
$37$	−152.149	+	87.8430i	−0.676029	+	0.390305i	−0.798357	−	0.602184i	$-0.794297\pi$
$37$	−152.149	+	87.8430i	−0.676029	+	0.390305i	0.122328	+	0.992490i	$0.460964\pi$
$38$	−139.939			−0.597396
$39$		0			0
$40$	−184.866			−0.730748
$41$	−135.501	+	78.2313i	−0.516137	+	0.297992i	−0.735353	−	0.677684i	$-0.762984\pi$
$41$	−135.501	+	78.2313i	−0.516137	+	0.297992i	0.219216	+	0.975676i	$0.429650\pi$
$42$		0			0
$43$	25.9922	−	45.0199i	0.0921809	−	0.159662i	−0.816248	−	0.577702i	$-0.803950\pi$
$43$	25.9922	−	45.0199i	0.0921809	−	0.159662i	0.908429	+	0.418040i	$0.137283\pi$
$44$			1389.88i			4.76211i
$45$		0			0
$46$	−219.868	−	126.941i	−0.704733	−	0.406878i
$47$		−	354.222i		−	1.09933i	−0.835384	−	0.549666i	$-0.814755\pi$
$47$		−	354.222i		−	1.09933i	0.835384	−	0.549666i	$-0.185245\pi$
$48$		0			0
$49$	−55.9425	−	96.8953i	−0.163098	−	0.282494i
$50$	546.972	−	315.794i	1.54707	−	0.893201i
$51$		0			0
$52$	501.667	−	834.888i	1.33786	−	2.22650i
$53$	10.4723			0.0271412			0.0135706	−	0.999908i	$-0.495680\pi$
$53$	10.4723			0.0271412			0.0135706	+	0.999908i	$0.495680\pi$
$54$		0			0
$55$	90.1712	+	156.181i	0.221067	+	0.382899i
$56$	521.160	−	902.676i	1.24362	−	2.15402i
$57$		0			0
$58$	1194.05	+	689.386i	2.70322	+	1.56070i
$59$	−385.480	−	222.557i	−0.850597	−	0.491092i	0.0102552	−	0.999947i	$-0.496736\pi$
$59$	−385.480	−	222.557i	−0.850597	−	0.491092i	−0.860852	+	0.508855i	$0.830069\pi$
$60$		0			0
$61$	−59.8481	+	103.660i	−0.125619	+	0.217579i	−0.921975	−	0.387250i	$-0.873425\pi$
$61$	−59.8481	+	103.660i	−0.125619	+	0.217579i	0.796356	+	0.604829i	$0.206758\pi$
$62$	553.216	+	958.199i	1.13320	+	1.96276i
$63$		0			0
$64$	−1246.28			−2.43413
$65$	2.20744	−	126.363i	0.00421230	−	0.241129i
$66$		0			0
$67$	−19.4057	+	11.2039i	−0.0353848	+	0.0204294i	−0.517588	−	0.855630i	$-0.673170\pi$
$67$	−19.4057	+	11.2039i	−0.0353848	+	0.0204294i	0.482203	+	0.876059i	$0.339837\pi$
$68$	43.2597	+	74.9281i	0.0771473	+	0.133623i
$69$		0			0
$70$		−	219.903i		−	0.375478i
$71$	246.997	+	142.604i	0.412861	+	0.238365i	0.692018	−	0.721880i	$-0.256722\pi$
$71$	246.997	+	142.604i	0.412861	+	0.238365i	−0.279157	+	0.960245i	$0.590055\pi$
$72$		0			0
$73$		−	740.989i		−	1.18803i	−0.804454	−	0.594015i	$-0.797542\pi$
$73$		−	740.989i		−	1.18803i	0.804454	−	0.594015i	$-0.202458\pi$
$74$	−471.253	+	816.235i	−0.740299	+	1.28223i
$75$		0			0
$76$	−469.432	+	271.027i	−0.708520	+	0.409064i
$77$	−1016.81			−1.50489
$78$		0			0
$79$	−547.679			−0.779983			−0.389992	−	0.920818i	$-0.627522\pi$
$79$	−547.679			−0.779983			−0.389992	+	0.920818i	$0.627522\pi$
$80$	−470.698	+	271.758i	−0.657821	+	0.379793i
$81$		0			0
$82$	−419.689	+	726.923i	−0.565206	+	0.978966i
$83$		−	603.056i		−	0.797518i	−0.917056	−	0.398759i	$-0.869441\pi$
$83$		−	603.056i		−	0.797518i	0.917056	−	0.398759i	$-0.130559\pi$
$84$		0			0
$85$	9.72218	+	5.61310i	0.0124061	+	0.00716266i
$86$		−	278.882i		−	0.349682i
$87$		0			0
$88$	2292.90	+	3971.42i	2.77754	+	4.81085i
$89$	186.774	−	107.834i	0.222450	−	0.128431i	−0.384634	−	0.923069i	$-0.625672\pi$
$89$	186.774	−	107.834i	0.222450	−	0.128431i	0.607084	+	0.794638i	$0.292339\pi$
$90$		0			0
$91$	610.789	+	367.011i	0.703605	+	0.422782i
$92$	−983.409			−1.11443
$93$		0			0
$94$	−950.153	−	1645.71i	−1.04256	−	1.80577i
$95$	−35.1666	+	60.9104i	−0.0379792	+	0.0657818i
$96$		0			0
$97$	−1253.58	−	723.752i	−1.31218	−	0.757586i	−0.329722	−	0.944078i	$-0.606955\pi$
$97$	−1253.58	−	723.752i	−1.31218	−	0.757586i	−0.982457	+	0.186492i	$0.940288\pi$
$98$	−519.817	−	300.116i	−0.535810	−	0.309350i
$99$		0			0
$100$	1223.23	−	2118.70i	1.22323	−	2.11870i
$101$	441.725	+	765.090i	0.435181	+	0.753756i	0.997310	−	0.0732935i	$-0.0233510\pi$
$101$	441.725	+	765.090i	0.435181	+	0.753756i	−0.562129	+	0.827049i	$0.690018\pi$
$102$		0			0
$103$	−1251.74			−1.19745			−0.598726	−	0.800954i	$-0.704326\pi$
$103$	−1251.74			−1.19745			−0.598726	+	0.800954i	$0.704326\pi$
$104$	56.1315	−	3213.19i	0.0529244	−	3.02961i
$105$		0			0
$106$	48.6543	−	28.0906i	0.0445823	−	0.0257396i
$107$	−170.807	−	295.846i	−0.154323	−	0.267294i	0.778490	−	0.627658i	$-0.215986\pi$
$107$	−170.807	−	295.846i	−0.154323	−	0.267294i	−0.932812	+	0.360363i	$0.882653\pi$
$108$		0			0
$109$			775.177i			0.681179i	0.940212	+	0.340589i	$0.110627\pi$
$109$			775.177i			0.681179i	−0.940212	+	0.340589i	$0.889373\pi$
$110$	837.869	+	483.744i	0.726251	+	0.419301i
$111$		0			0
$112$		−	3064.47i		−	2.58541i
$113$	639.524	−	1107.69i	0.532402	−	0.922147i	−0.466883	−	0.884319i	$-0.654623\pi$
$113$	639.524	−	1107.69i	0.532402	−	0.922147i	0.999284	−	0.0378273i	$-0.0120437\pi$
$114$		0			0
$115$	−110.505	+	63.8004i	−0.0896060	+	0.0517340i
$116$	5340.67			4.27473
$117$		0			0
$118$	−2387.91			−1.86293
$119$	−54.8160	+	31.6480i	−0.0422267	+	0.0243796i
$120$		0			0
$121$	1571.29	−	2721.55i	1.18053	−	2.04474i
$122$			642.137i			0.476528i
$123$		0			0
$124$	3711.58	+	2142.88i	2.68798	+	1.55191i
$125$		−	654.476i		−	0.468305i
$126$		0			0
$127$	−556.910	−	964.597i	−0.389117	−	0.673970i	0.603214	−	0.797579i	$-0.293886\pi$
$127$	−556.910	−	964.597i	−0.389117	−	0.673970i	−0.992331	+	0.123609i	$0.960553\pi$
$128$	−2098.10	+	1211.34i	−1.44881	+	0.836472i
$129$		0			0
$130$	−328.695	−	593.001i	−0.221757	−	0.400074i
$131$	−2100.12			−1.40068			−0.700339	−	0.713811i	$-0.746968\pi$
$131$	−2100.12			−1.40068			−0.700339	+	0.713811i	$0.746968\pi$
$132$		0			0
$133$	−198.278	−	343.428i	−0.129270	−	0.223902i
$134$	−60.1057	+	104.106i	−0.0387488	+	0.0671150i
$135$		0			0
$136$	247.218	+	142.732i	0.155874	+	0.0899936i
$137$	1043.58	+	602.509i	0.650793	+	0.375736i	0.788760	−	0.614701i	$-0.210723\pi$
$137$	1043.58	+	602.509i	0.650793	+	0.375736i	−0.137967	+	0.990437i	$0.544057\pi$
$138$		0			0
$139$	−161.445	+	279.631i	−0.0985149	+	0.170633i	−0.911070	−	0.412251i	$-0.864743\pi$
$139$	−161.445	+	279.631i	−0.0985149	+	0.170633i	0.812555	+	0.582884i	$0.198076\pi$
$140$	−425.898	−	737.677i	−0.257107	−	0.445322i
$141$		0			0
$142$	1530.06			0.904223
$143$	−2741.99	+	1519.86i	−1.60347	+	0.888789i
$144$		0			0
$145$	600.131	−	346.486i	0.343711	−	0.198442i
$146$	−1987.60	−	3442.63i	−1.12668	−	1.95146i
$147$		0			0
$148$			3650.80i			2.02766i
$149$	977.620	+	564.429i	0.537515	+	0.310335i	0.744071	−	0.668100i	$-0.232892\pi$
$149$	977.620	+	564.429i	0.537515	+	0.310335i	−0.206556	+	0.978435i	$0.566226\pi$
$150$		0			0
$151$			2940.44i			1.58470i	0.610066	+	0.792350i	$0.291143\pi$
$151$			2940.44i			1.58470i	−0.610066	+	0.792350i	$0.708857\pi$
$152$	−894.228	+	1548.85i	−0.477181	+	0.826501i
$153$		0			0
$154$	−4724.11	+	2727.46i	−2.47194	+	1.42718i
$155$	556.093			0.288171
$156$		0			0
$157$	629.388			0.319940			0.159970	−	0.987122i	$-0.448860\pi$
$157$	629.388			0.319940			0.159970	+	0.987122i	$0.448860\pi$
$158$	−2544.51	+	1469.07i	−1.28120	+	0.739703i
$159$		0			0
$160$	−718.441	+	1244.38i	−0.354986	+	0.614854i
$161$		−	719.444i		−	0.352175i
$162$		0			0
$163$	−342.004	−	197.456i	−0.164343	−	0.0948832i	0.415573	−	0.909560i	$-0.363581\pi$
$163$	−342.004	−	197.456i	−0.164343	−	0.0948832i	−0.579915	+	0.814677i	$0.696914\pi$
$164$			3251.33i			1.54809i
$165$		0			0
$166$	−1617.61	−	2801.79i	−0.756333	−	1.31001i
$167$	−131.515	+	75.9299i	−0.0609395	+	0.0351834i	−0.530160	−	0.847898i	$-0.677868\pi$
$167$	−131.515	+	75.9299i	−0.0609395	+	0.0351834i	0.469221	+	0.883081i	$0.344535\pi$
$168$		0			0
$169$	2195.66	+	76.7357i	0.999390	+	0.0349275i
$170$	60.2255			0.0271711
$171$		0			0
$172$	−540.126	−	935.525i	−0.239443	−	0.414728i
$173$	−269.407	+	466.626i	−0.118397	+	0.205069i	−0.919132	−	0.393949i	$-0.871109\pi$
$173$	−269.407	+	466.626i	−0.118397	+	0.205069i	0.800736	+	0.599018i	$0.204442\pi$
$174$		0			0
$175$	1550.00	+	894.892i	0.669537	+	0.386557i
$176$	11676.2	+	6741.24i	5.00070	+	2.88716i
$177$		0			0
$178$	578.500	−	1001.99i	0.243598	−	0.421924i
$179$	1110.40	+	1923.27i	0.463659	+	0.803081i	0.999140	−	0.0414660i	$-0.0132028\pi$
$179$	1110.40	+	1923.27i	0.463659	+	0.803081i	−0.535481	+	0.844548i	$0.679870\pi$
$180$		0			0
$181$	3822.78			1.56986			0.784932	−	0.619582i	$-0.212698\pi$
$181$	3822.78			1.56986			0.784932	+	0.619582i	$0.212698\pi$
$182$	3822.17	+	66.7698i	1.55669	+	0.0271940i
$183$		0			0
$184$	−2809.97	+	1622.33i	−1.12583	+	0.650001i
$185$	236.852	+	410.240i	0.0941282	+	0.163035i
$186$		0			0
$187$		−	278.478i		−	0.108900i
$188$	−6374.67	−	3680.42i	−2.47298	−	1.42778i
$189$		0			0
$190$			377.319i			0.144071i
$191$	1732.09	−	3000.08i	0.656178	−	1.13653i	−0.325419	−	0.945570i	$-0.605505\pi$
$191$	1732.09	−	3000.08i	0.656178	−	1.13653i	0.981597	−	0.190964i	$-0.0611612\pi$
$192$		0			0
$193$	−4068.07	+	2348.70i	−1.51723	+	0.875975i	−0.517438	+	0.855721i	$0.673114\pi$
$193$	−4068.07	+	2348.70i	−1.51723	+	0.875975i	−0.999795	+	0.0202541i	$0.993552\pi$
$194$	−7765.46			−2.87385
$195$		0			0
$196$	−2325.00			−0.847304
$197$	2500.98	−	1443.94i	0.904506	−	0.522217i	0.0258469	−	0.999666i	$-0.491772\pi$
$197$	2500.98	−	1443.94i	0.904506	−	0.522217i	0.878660	+	0.477449i	$0.158438\pi$
$198$		0			0
$199$	31.5046	−	54.5676i	0.0112226	−	0.0194382i	−0.860360	−	0.509688i	$-0.829761\pi$
$199$	31.5046	−	54.5676i	0.0112226	−	0.0194382i	0.871582	+	0.490249i	$0.163094\pi$
$200$		−	8071.87i		−	2.85384i
$201$		0			0
$202$	4104.50	+	2369.73i	1.42966	+	0.825415i
$203$			3907.14i			1.35087i
$204$		0			0
$205$	210.936	+	365.352i	0.0718654	+	0.124474i
$206$	−5815.57	+	3357.62i	−1.96694	+	1.13561i
$207$		0			0
$208$	−4580.55	−	8263.80i	−1.52694	−	2.75477i
$209$	1744.69			0.577429
$210$		0			0
$211$	524.848	+	909.064i	0.171242	+	0.296600i	0.938854	−	0.344315i	$-0.111889\pi$
$211$	524.848	+	909.064i	0.171242	+	0.296600i	−0.767612	+	0.640914i	$0.778555\pi$
$212$	108.809	−	188.463i	0.0352501	−	0.0610550i
$213$		0			0
$214$	−1587.13	−	916.331i	−0.506982	−	0.292706i
$215$	−121.388	−	70.0832i	−0.0385050	−	0.0222309i
$216$		0			0
$217$	−1567.69	+	2715.33i	−0.490424	+	0.849440i
$218$	2079.30	+	3601.46i	0.646001	+	1.11891i
$219$		0			0
$220$	3747.56			1.14846
$221$	−100.514	+	167.278i	−0.0305942	+	0.0509156i
$222$		0			0
$223$	2003.54	−	1156.75i	0.601647	−	0.347361i	−0.168042	−	0.985780i	$-0.553745\pi$
$223$	2003.54	−	1156.75i	0.601647	−	0.347361i	0.769689	+	0.638419i	$0.220411\pi$
$224$	−4050.75	−	7016.10i	−1.20827	−	2.09278i
$225$		0			0
$226$		−	6861.74i		−	2.01963i
$227$	3290.43	+	1899.73i	0.962085	+	0.555460i	0.896814	−	0.442407i	$-0.145875\pi$
$227$	3290.43	+	1899.73i	0.962085	+	0.555460i	0.0652711	+	0.997868i	$0.479209\pi$
$228$		0			0
$229$			4321.07i			1.24692i	0.781856	+	0.623459i	$0.214273\pi$
$229$			4321.07i			1.24692i	−0.781856	+	0.623459i	$0.785727\pi$
$230$	−342.271	+	592.832i	−0.0981248	+	0.169957i
$231$		0			0
$232$	15260.3	−	8810.54i	4.31848	−	2.49328i
$233$	5279.77			1.48450			0.742251	−	0.670122i	$-0.233758\pi$
$233$	5279.77			1.48450			0.742251	+	0.670122i	$0.233758\pi$
$234$		0			0
$235$	−955.094			−0.265121
$236$	−8010.38	+	4624.79i	−2.20945	+	1.27563i
$237$		0			0
$238$	−169.783	+	294.073i	−0.0462412	+	0.0800920i
$239$		−	1547.92i		−	0.418939i	−0.977815	−	0.209469i	$-0.932826\pi$
$239$		−	1547.92i		−	0.418939i	0.977815	−	0.209469i	$-0.0671737\pi$
$240$		0			0
$241$	−4259.12	−	2459.00i	−1.13840	−	0.657255i	−0.192365	−	0.981323i	$-0.561616\pi$
$241$	−4259.12	−	2459.00i	−1.13840	−	0.657255i	−0.946033	+	0.324069i	$0.894949\pi$
$242$		−	16859.1i		−	4.47828i
$243$		0			0
$244$	1243.66	+	2154.08i	0.326300	+	0.565168i
$245$	−261.260	+	150.839i	−0.0681277	+	0.0393336i
$246$		0			0
$247$	−1048.02	−	629.731i	−0.269974	−	0.162222i
$248$	14140.5			3.62066
$249$		0			0
$250$	−1755.54	−	3040.69i	−0.444121	−	0.769239i
$251$	−577.890	+	1000.94i	−0.145323	+	0.251707i	−0.929493	−	0.368839i	$-0.879756\pi$
$251$	−577.890	+	1000.94i	−0.145323	+	0.251707i	0.784170	+	0.620546i	$0.213089\pi$
$252$		0			0
$253$	2741.20	+	1582.63i	0.681178	+	0.393278i
$254$	−5174.80	−	2987.67i	−1.27833	−	0.738044i
$255$		0			0
$256$	−1513.40	+	2621.28i	−0.369482	+	0.639962i
$257$	−1175.98	−	2036.85i	−0.285429	−	0.494378i	0.687284	−	0.726389i	$-0.258803\pi$
$257$	−1175.98	−	2036.85i	−0.285429	−	0.494378i	−0.972713	+	0.232011i	$0.925470\pi$
$258$		0			0
$259$	−2670.86			−0.640769
$260$	−2251.12	−	1352.65i	−0.536956	−	0.322646i
$261$		0			0
$262$	−9757.15	+	5633.29i	−2.30076	+	1.32834i
$263$	2760.94	+	4782.09i	0.647326	+	1.12120i	0.983759	+	0.179494i	$0.0574461\pi$
$263$	2760.94	+	4782.09i	0.647326	+	1.12120i	−0.336433	+	0.941707i	$0.609221\pi$
$264$		0			0
$265$		−	28.2367i		−	0.00654553i
$266$	−1842.39	−	1063.71i	−0.424678	−	0.245188i
$267$		0			0
$268$			465.639i			0.106132i
$269$	1958.48	−	3392.18i	0.443905	−	0.768866i	−0.554070	−	0.832470i	$-0.686926\pi$
$269$	1958.48	−	3392.18i	0.443905	−	0.768866i	0.997975	+	0.0636038i	$0.0202594\pi$
$270$		0			0
$271$	2405.41	−	1388.76i	0.539182	−	0.311297i	−0.205566	−	0.978643i	$-0.565903\pi$
$271$	2405.41	−	1388.76i	0.539182	−	0.311297i	0.744747	+	0.667347i	$0.232570\pi$
$272$	839.276			0.187090
$273$		0			0
$274$	6464.58			1.42533
$275$	−6819.38	+	3937.17i	−1.49536	+	0.863347i
$276$		0			0
$277$	3291.54	−	5701.12i	0.713969	−	1.23663i	−0.249386	−	0.968404i	$-0.580229\pi$
$277$	3291.54	−	5701.12i	0.713969	−	1.23663i	0.963356	−	0.268227i	$-0.0864378\pi$
$278$			1732.21i			0.373710i
$279$		0			0
$280$	−2433.90	−	1405.21i	−0.519476	−	0.299919i
$281$			2871.66i			0.609640i	0.952410	+	0.304820i	$0.0985963\pi$
$281$			2871.66i			0.609640i	−0.952410	+	0.304820i	$0.901404\pi$
$282$		0			0
$283$	3759.02	+	6510.81i	0.789578	+	1.36759i	0.926226	+	0.376969i	$0.123034\pi$
$283$	3759.02	+	6510.81i	0.789578	+	1.36759i	−0.136648	+	0.990620i	$0.543633\pi$
$284$	5132.66	−	2963.34i	1.07242	−	0.619162i
$285$		0			0
$286$	−8662.43	+	14416.2i	−1.79098	+	2.98060i
$287$	−2378.62			−0.489217
$288$		0			0
$289$	2447.83	+	4239.77i	0.498236	+	0.862970i
$290$	1858.80	−	3219.54i	0.376388	−	0.651923i
$291$		0			0
$292$	−13335.0	−	7698.97i	−2.67251	−	1.54297i
$293$	−3902.80	−	2253.28i	−0.778171	−	0.449278i	0.0576104	−	0.998339i	$-0.481652\pi$
$293$	−3902.80	−	2253.28i	−0.778171	−	0.449278i	−0.835782	+	0.549062i	$0.814985\pi$
$294$		0			0
$295$	−600.083	+	1039.37i	−0.118435	+	0.205135i
$296$	6022.75	+	10431.7i	1.18265	+	2.04841i
$297$		0			0
$298$	6056.02			1.17723
$299$	−1075.37	−	1940.08i	−0.207994	−	0.375244i
$300$		0			0
$301$	684.413	−	395.146i	0.131060	−	0.0756673i
$302$	7887.33	+	13661.3i	1.50286	+	2.60304i
$303$		0			0
$304$			5258.15i			0.992024i
$305$	279.500	+	161.369i	0.0524725	+	0.0302950i
$306$		0			0
$307$		−	9538.89i		−	1.77333i	−0.462409	−	0.886667i	$-0.653015\pi$
$307$		−	9538.89i		−	1.77333i	0.462409	−	0.886667i	$-0.346985\pi$
$308$	−10564.8	+	18298.8i	−1.95450	+	3.38530i
$309$		0			0
$310$	2583.60	−	1491.64i	0.473351	−	0.273289i
$311$	−7466.28			−1.36133			−0.680666	−	0.732594i	$-0.738309\pi$
$311$	−7466.28			−1.36133			−0.680666	+	0.732594i	$0.738309\pi$
$312$		0			0
$313$	−1821.65			−0.328964			−0.164482	−	0.986380i	$-0.552595\pi$
$313$	−1821.65			−0.328964			−0.164482	+	0.986380i	$0.552595\pi$
$314$	2924.13	−	1688.25i	0.525536	−	0.303418i
$315$		0			0
$316$	−5690.46	+	9856.16i	−1.01302	+	1.75460i
$317$		−	3125.14i		−	0.553708i	−0.960912	−	0.276854i	$-0.910708\pi$
$317$		−	3125.14i		−	0.553708i	0.960912	−	0.276854i	$-0.0892918\pi$
$318$		0			0
$319$	−14886.9	−	8594.93i	−2.61287	−	1.50854i
$320$			3360.35i			0.587029i
$321$		0			0
$322$	−1929.81	−	3342.53i	−0.333988	−	0.578484i
$323$	94.0554	−	54.3029i	0.0162024	−	0.00935448i
$324$		0			0
$325$	5517.41	+	96.3842i	0.941696	+	0.0164506i
$326$	−2118.60			−0.359933
$327$		0			0
$328$	5363.74	+	9290.27i	0.902936	+	1.56393i
$329$	2692.53	−	4663.59i	0.451197	−	0.781496i
$330$		0			0
$331$	1345.52	+	776.836i	0.223433	+	0.128999i	0.607539	−	0.794290i	$-0.292157\pi$
$331$	1345.52	+	776.836i	0.223433	+	0.128999i	−0.384106	+	0.923289i	$0.625490\pi$
$332$	−10852.7	−	6265.83i	−1.79404	−	1.03579i
$333$		0			0
$334$	−407.343	+	705.539i	−0.0667330	+	0.115585i
$335$	30.2092	+	52.3238i	0.00492688	+	0.00853360i
$336$		0			0
$337$	3190.43			0.515709			0.257855	−	0.966184i	$-0.416984\pi$
$337$	3190.43			0.515709			0.257855	+	0.966184i	$0.416984\pi$
$338$	10406.8	−	5533.04i	1.67473	−	0.890408i
$339$		0			0
$340$	202.029	−	116.642i	0.0322252	−	0.0186053i
$341$	−6897.24	−	11946.4i	−1.09533	−	1.89716i
$342$		0			0
$343$		−	6915.37i		−	1.08862i
$344$	−3086.68	−	1782.10i	−0.483787	−	0.279315i
$345$		0			0
$346$			2890.59i			0.449130i
$347$	−2859.34	+	4952.53i	−0.442356	+	0.766183i	−0.997864	−	0.0653283i	$-0.979191\pi$
$347$	−2859.34	+	4952.53i	−0.442356	+	0.766183i	0.555508	+	0.831511i	$0.312524\pi$
$348$		0			0
$349$	2882.53	−	1664.23i	0.442116	−	0.255256i	−0.262379	−	0.964965i	$-0.584507\pi$
$349$	2882.53	−	1664.23i	0.442116	−	0.255256i	0.704495	+	0.709709i	$0.251174\pi$
$350$	9601.70			1.46638
$351$		0			0
$352$	35643.4			5.39715
$353$	10657.7	−	6153.25i	1.60695	−	0.927774i	0.616905	−	0.787037i	$-0.288386\pi$
$353$	10657.7	−	6153.25i	1.60695	−	0.927774i	0.990047	−	0.140737i	$-0.0449472\pi$
$354$		0			0
$355$	384.504	−	665.981i	0.0574855	−	0.0995679i
$356$		−	4481.64i		−	0.667210i
$357$		0			0
$358$	10317.8	+	5956.98i	1.52322	+	0.879430i
$359$			8539.97i			1.25549i	0.778418	+	0.627747i	$0.216023\pi$
$359$			8539.97i			1.25549i	−0.778418	+	0.627747i	$0.783977\pi$
$360$		0			0
$361$	−3089.29	−	5350.80i	−0.450399	−	0.780114i
$362$	17760.6	−	10254.1i	2.57866	−	1.48879i
$363$		0			0
$364$	12951.0	−	7178.61i	1.86488	−	1.03369i
$365$	−1997.94			−0.286512
$366$		0			0
$367$	−1248.33	−	2162.17i	−0.177553	−	0.307532i	0.763489	−	0.645821i	$-0.223485\pi$
$367$	−1248.33	−	2162.17i	−0.177553	−	0.307532i	−0.941042	+	0.338290i	$0.890152\pi$
$368$	−4769.74	+	8261.44i	−0.675652	+	1.17026i
$369$		0			0
$370$	2200.82	+	1270.65i	0.309231	+	0.178535i
$371$	137.876	+	79.6026i	0.0192942	+	0.0111395i
$372$		0			0
$373$	571.454	−	989.787i	0.0793264	−	0.137397i	−0.823633	−	0.567123i	$-0.808056\pi$
$373$	571.454	−	989.787i	0.0793264	−	0.137397i	0.902960	+	0.429726i	$0.141390\pi$
$374$	−746.978	−	1293.80i	−0.103276	−	0.178880i
$375$		0			0
$376$	−24286.4			−3.33105
$377$	5840.10	+	10536.2i	0.797826	+	1.43936i
$378$		0			0
$379$	−10549.8	+	6090.91i	−1.42983	+	0.825512i	−0.997107	−	0.0760146i	$-0.975780\pi$
$379$	−10549.8	+	6090.91i	−1.42983	+	0.825512i	−0.432723	+	0.901527i	$0.642447\pi$
$380$	730.772	+	1265.73i	0.0986522	+	0.170871i
$381$		0			0
$382$		−	18584.4i		−	2.48917i
$383$	−8816.66	−	5090.30i	−1.17627	−	0.679118i	−0.221119	−	0.975247i	$-0.570971\pi$
$383$	−8816.66	−	5090.30i	−1.17627	−	0.679118i	−0.955148	+	0.296129i	$0.904304\pi$
$384$		0			0
$385$			2741.65i			0.362928i
$386$	−12600.1	+	21824.1i	−1.66148	+	2.87776i
$387$		0			0
$388$	−26049.6	+	15039.8i	−3.40843	+	1.96786i
$389$	5845.83			0.761941			0.380971	−	0.924587i	$-0.375590\pi$
$389$	5845.83			0.761941			0.380971	+	0.924587i	$0.375590\pi$
$390$		0			0
$391$	197.036			0.0254848
$392$	−6643.40	+	3835.57i	−0.855975	+	0.494197i
$393$		0			0
$394$	7746.36	−	13417.1i	0.990498	−	1.71559i
$395$			1476.71i			0.188105i
$396$		0			0
$397$	−2165.86	−	1250.46i	−0.273807	−	0.158083i	0.356809	−	0.934177i	$-0.383865\pi$
$397$	−2165.86	−	1250.46i	−0.273807	−	0.158083i	−0.630617	+	0.776094i	$0.717198\pi$
$398$		−	338.027i		−	0.0425723i
$399$		0			0
$400$	−11865.8	−	20552.2i	−1.48323	−	2.56903i
$401$	−7958.12	+	4594.62i	−0.991046	+	0.572181i	−0.905587	−	0.424161i	$-0.860569\pi$
$401$	−7958.12	+	4594.62i	−0.991046	+	0.572181i	−0.0854594	+	0.996342i	$0.527236\pi$
$402$		0			0
$403$	−168.848	+	9665.54i	−0.0208708	+	1.19473i
$404$	18358.3			2.26080
$405$		0			0
$406$	10480.4	+	18152.5i	1.28111	+	2.21895i
$407$	5875.36	−	10176.4i	0.715555	−	1.23938i
$408$		0			0
$409$	−7979.89	−	4607.19i	−0.964744	−	0.556995i	−0.0671140	−	0.997745i	$-0.521379\pi$
$409$	−7979.89	−	4607.19i	−0.964744	−	0.556995i	−0.897630	+	0.440750i	$0.854712\pi$
$410$	1960.01	+	1131.61i	0.236093	+	0.136308i
$411$		0			0
$412$	−13005.8	+	22526.6i	−1.55521	+	2.69371i
$413$	−3383.42	−	5860.25i	−0.403116	−	0.698218i
$414$		0			0
$415$	−1626.03			−0.192334
$416$	−21410.6	−	12865.2i	−2.52341	−	1.51627i
$417$		0			0
$418$	8105.81	−	4679.89i	0.948488	−	0.547610i
$419$	−3247.20	−	5624.32i	−0.378607	−	0.655767i	0.612253	−	0.790662i	$-0.290263\pi$
$419$	−3247.20	−	5624.32i	−0.378607	−	0.655767i	−0.990860	+	0.134895i	$0.956930\pi$
$420$		0			0
$421$			3059.56i			0.354190i	0.984194	+	0.177095i	$0.0566699\pi$
$421$			3059.56i			0.354190i	−0.984194	+	0.177095i	$0.943330\pi$
$422$	4876.88	+	2815.67i	0.562566	+	0.324797i
$423$		0			0
$424$		−	718.010i		−	0.0822398i
$425$	−245.087	+	424.502i	−0.0279728	+	0.0484503i
$426$		0			0
$427$	−1575.89	+	909.839i	−0.178601	+	0.103115i
$428$	−7098.82			−0.801716
$429$		0			0
$430$	−751.954			−0.0843313
$431$	−6873.69	+	3968.53i	−0.768199	+	0.443520i	−0.832232	−	0.554428i	$-0.812937\pi$
$431$	−6873.69	+	3968.53i	−0.768199	+	0.443520i	0.0640325	+	0.997948i	$0.479604\pi$
$432$		0			0
$433$	3647.19	−	6317.11i	0.404786	−	0.701111i	−0.589510	−	0.807761i	$-0.700679\pi$
$433$	3647.19	−	6317.11i	0.404786	−	0.701111i	0.994297	+	0.106650i	$0.0340125\pi$
$434$			16820.5i			1.86039i
$435$		0			0
$436$	13950.3	+	8054.19i	1.53233	+	0.884692i
$437$			1234.45i			0.135130i
$438$		0			0
$439$	7607.35	+	13176.3i	0.827059	+	1.43251i	0.900335	+	0.435197i	$0.143321\pi$
$439$	7607.35	+	13176.3i	0.827059	+	1.43251i	−0.0732765	+	0.997312i	$0.523346\pi$
$440$	10708.2	−	6182.37i	1.16021	−	0.669848i
$441$		0			0
$442$	−18.2864	+	1046.79i	−0.00196787	+	0.112649i
$443$	−1517.05			−0.162703			−0.0813515	−	0.996685i	$-0.525924\pi$
$443$	−1517.05			−0.162703			−0.0813515	+	0.996685i	$0.525924\pi$
$444$		0			0
$445$	−290.754	−	503.601i	−0.0309732	−	0.0536472i
$446$	6205.63	−	10748.5i	0.658845	−	1.14115i
$447$		0			0
$448$	−16408.1	−	9473.24i	−1.73038	−	0.999037i
$449$	610.761	+	352.623i	0.0641951	+	0.0370631i	0.531754	−	0.846899i	$-0.321533\pi$
$449$	610.761	+	352.623i	0.0641951	+	0.0370631i	−0.467559	+	0.883962i	$0.654866\pi$
$450$		0			0
$451$	5232.48	−	9062.93i	0.546315	−	0.946245i
$452$	−13289.5	−	23018.1i	−1.38293	−	2.39531i
$453$		0			0
$454$	20383.1			2.10710
$455$	989.575	−	1646.88i	0.101960	−	0.169685i
$456$		0			0
$457$	−6302.69	+	3638.86i	−0.645137	+	0.372470i	−0.786591	−	0.617475i	$-0.788156\pi$
$457$	−6302.69	+	3638.86i	−0.645137	+	0.372470i	0.141454	+	0.989945i	$0.454822\pi$
$458$	11590.7	+	20075.6i	1.18253	+	2.04820i
$459$		0			0
$460$			2651.58i			0.268762i
$461$	1699.04	+	980.941i	0.171653	+	0.0991041i	0.583365	−	0.812210i	$-0.301736\pi$
$461$	1699.04	+	980.941i	0.171653	+	0.0991041i	−0.411712	+	0.911314i	$0.635069\pi$
$462$		0			0
$463$			10374.1i			1.04131i	0.853768	+	0.520653i	$0.174311\pi$
$463$			10374.1i			1.04131i	−0.853768	+	0.520653i	$0.825689\pi$
$464$	25903.4	−	44866.0i	2.59167	−	4.48891i
$465$		0			0
$466$	24529.7	−	14162.2i	2.43845	−	1.40784i
$467$	8788.92			0.870883			0.435442	−	0.900217i	$-0.356592\pi$
$467$	8788.92			0.870883			0.435442	+	0.900217i	$0.356592\pi$
$468$		0			0
$469$	−340.653			−0.0335392
$470$	−4437.36	+	2561.91i	−0.435489	+	0.251430i
$471$		0			0
$472$	−15259.1	+	26429.5i	−1.48804	+	2.57737i
$473$			3476.97i			0.337995i
$474$		0			0
$475$	−2659.55	−	1535.49i	−0.256902	−	0.148322i
$476$			1315.31i			0.126654i
$477$		0			0
$478$	−4152.07	−	7191.60i	−0.397304	−	0.688151i
$479$	−9648.96	+	5570.83i	−0.920401	+	0.531394i	−0.883763	−	0.467935i	$-0.844998\pi$
$479$	−9648.96	+	5570.83i	−0.920401	+	0.531394i	−0.0366382	+	0.999329i	$0.511665\pi$
$480$		0			0
$481$	−7202.36	+	3992.20i	−0.682743	+	0.378438i
$482$	−26383.8			−2.49325
$483$		0			0
$484$	−32651.8	−	56554.6i	−3.06648	−	5.31129i
$485$	−1951.46	+	3380.03i	−0.182704	+	0.316452i
$486$		0			0
$487$	17009.1	+	9820.23i	1.58266	+	0.913752i	0.994469	+	0.105033i	$0.0334948\pi$
$487$	17009.1	+	9820.23i	1.58266	+	0.913752i	0.588195	+	0.808719i	$0.299839\pi$
$488$	7107.20	+	4103.34i	0.659278	+	0.380634i
$489$		0			0
$490$	−809.207	+	1401.59i	−0.0746046	+	0.129219i
$491$	1705.16	+	2953.42i	0.156726	+	0.271458i	0.933686	−	0.358092i	$-0.116573\pi$
$491$	1705.16	+	2953.42i	0.156726	+	0.271458i	−0.776960	+	0.629550i	$0.783239\pi$
$492$		0			0
$493$	−1070.06			−0.0977546
$494$	−6558.23	−	114.566i	−0.597305	−	0.0104344i
$495$		0			0
$496$	36003.9	−	20786.9i	3.25932	−	1.88177i
$497$	2167.93	+	3754.96i	0.195664	+	0.338899i
$498$		0			0
$499$		−	5032.44i		−	0.451469i	−0.974189	−	0.225735i	$-0.927522\pi$
$499$		−	5032.44i		−	0.451469i	0.974189	−	0.225735i	$-0.0724782\pi$
$500$	−11778.1	−	6800.09i	−1.05347	−	0.608219i
$501$		0			0
$502$			6200.44i			0.551274i
$503$	8594.69	−	14886.4i	0.761866	−	1.31959i	−0.180022	−	0.983663i	$-0.557617\pi$
$503$	8594.69	−	14886.4i	0.761866	−	1.31959i	0.941888	−	0.335927i	$-0.109050\pi$
$504$		0			0
$505$	2062.92	−	1191.03i	0.181780	−	0.104951i
$506$	16980.8			1.49187
$507$		0			0
$508$	−23145.5			−2.02149
$509$	805.889	−	465.280i	0.0701776	−	0.0405170i	−0.464501	−	0.885573i	$-0.653766\pi$
$509$	805.889	−	465.280i	0.0701776	−	0.0405170i	0.534678	+	0.845056i	$0.320433\pi$
$510$		0			0
$511$	5632.43	−	9755.65i	0.487601	−	0.844549i
$512$		−	3143.50i		−	0.271337i
$513$		0			0
$514$	−10927.1	−	6308.79i	−0.937695	−	0.541379i
$515$			3375.08i			0.288784i
$516$		0			0
$517$	11846.1	+	20518.0i	1.00772	+	1.74541i
$518$	−12408.8	+	7164.21i	−1.05253	+	0.607679i
$519$		0			0
$520$	−8663.76	−	151.348i	−0.730637	−	0.0127636i
$521$	9869.60			0.829933			0.414966	−	0.909837i	$-0.363793\pi$
$521$	9869.60			0.829933			0.414966	+	0.909837i	$0.363793\pi$
$522$		0			0
$523$	10710.3	+	18550.8i	0.895466	+	1.55099i	0.833226	+	0.552932i	$0.186491\pi$
$523$	10710.3	+	18550.8i	0.895466	+	1.55099i	0.0622398	+	0.998061i	$0.480176\pi$
$524$	−21820.6	+	37794.3i	−1.81915	+	3.15087i
$525$		0			0
$526$	25654.6	+	14811.7i	2.12660	+	1.22779i
$527$	−743.654	−	429.349i	−0.0614688	−	0.0354890i
$528$		0			0
$529$	4963.71	−	8597.40i	0.407965	−	0.706616i
$530$	−75.7410	−	131.187i	−0.00620750	−	0.0107517i
$531$		0			0
$532$	−8240.54			−0.671565
$533$	−6414.28	+	3555.38i	−0.521263	+	0.288931i
$534$		0			0
$535$	−797.693	+	460.548i	−0.0644622	+	0.0372173i
$536$	768.168	+	1330.51i	0.0619026	+	0.107218i
$537$		0			0
$538$		−	21013.4i		−	1.68392i
$539$	6480.83	+	3741.71i	0.517902	+	0.299011i
$540$		0			0
$541$		−	7771.50i		−	0.617602i	−0.951127	−	0.308801i	$-0.900072\pi$
$541$		−	7771.50i		−	0.617602i	0.951127	−	0.308801i	$-0.0999277\pi$
$542$	7450.34	−	12904.4i	0.590442	−	1.02267i
$543$		0			0
$544$	1921.52	−	1109.39i	0.151442	−	0.0874350i
$545$	2090.12			0.164277
$546$		0			0
$547$	−15577.5			−1.21763			−0.608817	−	0.793310i	$-0.708356\pi$
$547$	−15577.5			−1.21763			−0.608817	+	0.793310i	$0.708356\pi$
$548$	21685.8	−	12520.3i	1.69046	−	0.975986i
$549$		0			0
$550$	−21121.8	+	36584.1i	−1.63752	+	2.83628i
$551$		−	6704.02i		−	0.518332i
$552$		0			0
$553$	−7210.58	−	4163.03i	−0.554476	−	0.320127i
$554$		−	35316.4i		−	2.70840i
$555$		0			0
$556$	3354.87	+	5810.80i	0.255896	+	0.443225i
$557$	−19749.3	+	11402.3i	−1.50234	+	0.867377i	−0.502345	+	0.864667i	$0.667529\pi$
$557$	−19749.3	+	11402.3i	−1.50234	+	0.867377i	−0.999996	+	0.00270962i	$0.999138\pi$
$558$		0			0
$559$	1254.98	−	2088.58i	0.0949556	−	0.158028i
$560$	−8262.78			−0.623511
$561$		0			0
$562$	7702.83	+	13341.7i	0.578157	+	1.00140i
$563$	1758.71	−	3046.17i	0.131653	−	0.228030i	−0.792661	−	0.609663i	$-0.791305\pi$
$563$	1758.71	−	3046.17i	0.131653	−	0.228030i	0.924314	+	0.381633i	$0.124638\pi$
$564$		0			0
$565$	−2986.67	−	1724.36i	−0.222390	−	0.128397i
$566$	34928.7	+	20166.1i	2.59393	+	1.49761i
$567$		0			0
$568$	9777.29	−	16934.8i	0.722264	−	1.25100i
$569$	3046.72	+	5277.08i	0.224473	+	0.388799i	0.956161	−	0.292841i	$-0.0946006\pi$
$569$	3046.72	+	5277.08i	0.224473	+	0.388799i	−0.731688	+	0.681640i	$0.761267\pi$
$570$		0			0
$571$	−10460.2			−0.766630			−0.383315	−	0.923618i	$-0.625218\pi$
$571$	−10460.2			−0.766630			−0.383315	+	0.923618i	$0.625218\pi$
$572$	−1137.88	+	65137.0i	−0.0831771	+	4.76139i
$573$		0			0
$574$	−11051.0	+	6380.31i	−0.803590	+	0.463953i
$575$	−2785.74	−	4825.03i	−0.202040	−	0.349944i
$576$		0			0
$577$		−	9648.19i		−	0.696117i	−0.937473	−	0.348058i	$-0.886841\pi$
$577$		−	9648.19i		−	0.696117i	0.937473	−	0.348058i	$-0.113159\pi$
$578$	22745.2	+	13131.9i	1.63681	+	0.945012i
$579$		0			0
$580$		−	14400.1i		−	1.03092i
$581$	4583.97	−	7939.66i	0.327324	−	0.566941i
$582$		0			0
$583$	−606.599	+	350.220i	−0.0430922	+	0.0248793i
$584$	−50804.1			−3.59981
$585$		0			0
$586$	−24176.5			−1.70430
$587$	−1879.91	+	1085.37i	−0.132184	+	0.0763166i	−0.564634	−	0.825341i	$-0.690983\pi$
$587$	−1879.91	+	1085.37i	−0.132184	+	0.0763166i	0.432450	+	0.901658i	$0.357649\pi$
$588$		0			0
$589$	2689.91	−	4659.06i	0.188176	−	0.325931i
$590$			6438.56i			0.449274i
$591$		0			0
$592$	30669.7	+	17707.2i	2.12925	+	1.22932i
$593$			22885.9i			1.58484i	0.609975	+	0.792421i	$0.291180\pi$
$593$			22885.9i			1.58484i	−0.609975	+	0.792421i	$0.708820\pi$
$594$		0			0
$595$	85.3330	+	147.801i	0.00587951	+	0.0101836i
$596$	20315.2	−	11729.0i	1.39621	−	0.806105i
$597$		0			0
$598$	−10200.2	−	6129.08i	−0.697518	−	0.419125i
$599$	23978.7			1.63563			0.817815	−	0.575482i	$-0.195185\pi$
$599$	23978.7			1.63563			0.817815	+	0.575482i	$0.195185\pi$
$600$		0			0
$601$	−6436.62	−	11148.6i	−0.436864	−	0.756671i	0.560582	−	0.828099i	$-0.310578\pi$
$601$	−6436.62	−	11148.6i	−0.436864	−	0.756671i	−0.997446	+	0.0714284i	$0.977244\pi$
$602$	2119.85	−	3671.69i	0.143519	−	0.248583i
$603$		0			0
$604$	52916.9	+	30551.6i	3.56483	+	2.05816i
$605$	−7338.16	−	4236.69i	−0.493122	−	0.284704i
$606$		0			0
$607$	3558.57	−	6163.63i	0.237954	−	0.412148i	−0.722173	−	0.691712i	$-0.756857\pi$
$607$	3558.57	−	6163.63i	0.237954	−	0.412148i	0.960127	+	0.279564i	$0.0901899\pi$
$608$	6950.43	+	12038.5i	0.463614	+	0.803002i
$609$		0			0
$610$	1731.40			0.114922
$611$	289.998	−	16600.6i	0.0192014	−	1.09917i
$612$		0			0
$613$	150.079	−	86.6484i	0.00988850	−	0.00570913i	−0.495048	−	0.868866i	$-0.664849\pi$
$613$	150.079	−	86.6484i	0.00988850	−	0.00570913i	0.504936	+	0.863157i	$0.331516\pi$
$614$	−25586.8	−	44317.6i	−1.68176	−	2.91289i
$615$		0			0
$616$			69715.5i			4.55993i
$617$	−5285.14	−	3051.38i	−0.344849	−	0.199099i	0.317565	−	0.948236i	$-0.397135\pi$
$617$	−5285.14	−	3051.38i	−0.344849	−	0.199099i	−0.662414	+	0.749138i	$0.730468\pi$
$618$		0			0
$619$			14867.8i			0.965409i	0.875783	+	0.482705i	$0.160346\pi$
$619$			14867.8i			0.965409i	−0.875783	+	0.482705i	$0.839654\pi$
$620$	5777.88	−	10007.6i	0.374267	−	0.648249i
$621$		0			0
$622$	−34688.3	+	20027.3i	−2.23613	+	1.29103i
$623$	3278.69			0.210847
$624$		0			0
$625$	12951.6			0.828900
$626$	−8463.35	+	4886.32i	−0.540357	+	0.311975i
$627$		0			0
$628$	6539.43	−	11326.6i	0.415528	−	0.719716i
$629$		−	731.475i		−	0.0463686i
$630$		0			0
$631$	−14904.8	−	8605.29i	−0.940334	−	0.542902i	−0.0502690	−	0.998736i	$-0.516008\pi$
$631$	−14904.8	−	8605.29i	−0.940334	−	0.542902i	−0.890065	+	0.455834i	$0.849341\pi$
$632$			37550.3i			2.36340i
$633$		0			0
$634$	−8382.76	−	14519.4i	−0.525113	−	0.909523i
$635$	−2600.86	+	1501.60i	−0.162538	+	0.0938415i
$636$		0			0
$637$	−2542.42	−	4586.80i	−0.158139	−	0.285299i
$638$	−92218.9			−5.72254
$639$		0			0
$640$	3266.15	+	5657.14i	0.201728	+	0.349403i
$641$	6318.01	−	10943.1i	0.389308	−	0.674301i	−0.603049	−	0.797704i	$-0.706047\pi$
$641$	6318.01	−	10943.1i	0.389308	−	0.674301i	0.992357	+	0.123403i	$0.0393808\pi$
$642$		0			0
$643$	8302.04	+	4793.19i	0.509177	+	0.293973i	0.732495	−	0.680772i	$-0.238356\pi$
$643$	8302.04	+	4793.19i	0.509177	+	0.293973i	−0.223318	+	0.974746i	$0.571689\pi$
$644$	−12947.3	−	7475.12i	−0.792228	−	0.457393i
$645$		0			0
$646$	291.320	−	504.581i	0.0177428	−	0.0307314i
$647$	−2622.16	−	4541.72i	−0.159332	−	0.275971i	0.775296	−	0.631598i	$-0.217601\pi$
$647$	−2622.16	−	4541.72i	−0.159332	−	0.275971i	−0.934628	+	0.355627i	$0.884267\pi$
$648$		0			0
$649$	29771.4			1.80066
$650$	25892.4	−	14351.9i	1.56243	−	0.866043i
$651$		0			0
$652$	−7106.94	+	4103.19i	−0.426885	+	0.246462i
$653$	9434.51	+	16341.1i	0.565392	+	0.979288i	0.997013	+	0.0772326i	$0.0246084\pi$
$653$	9434.51	+	16341.1i	0.565392	+	0.979288i	−0.431621	+	0.902055i	$0.642058\pi$
$654$		0			0
$655$			5662.59i			0.337795i
$656$	27313.8	+	15769.7i	1.62565	+	0.938570i
$657$		0			0
$658$		−	28889.3i		−	1.71159i
$659$	−12149.9	+	21044.2i	−0.718197	+	1.24395i	0.243516	+	0.969897i	$0.421699\pi$
$659$	−12149.9	+	21044.2i	−0.718197	+	1.24395i	−0.961713	+	0.274057i	$0.911634\pi$
$660$		0			0
$661$	−25907.2	+	14957.5i	−1.52447	+	0.880151i	−0.524886	+	0.851173i	$0.675892\pi$
$661$	−25907.2	+	14957.5i	−1.52447	+	0.880151i	−0.999580	+	0.0289779i	$0.990775\pi$
$662$	8335.03			0.489350
$663$		0			0
$664$	−41347.1			−2.41653
$665$	−925.988	+	534.620i	−0.0539974	+	0.0311754i
$666$		0			0
$667$	6081.32	−	10533.2i	0.353028	−	0.611462i
$668$			3155.69i			0.182780i
$669$		0			0
$670$	280.703	+	162.064i	0.0161858	+	0.00934489i
$671$		−	8005.86i		−	0.460600i
$672$		0			0
$673$	7746.84	+	13417.9i	0.443713	+	0.768533i	0.997962	−	0.0638177i	$-0.0203276\pi$
$673$	7746.84	+	13417.9i	0.443713	+	0.768533i	−0.554249	+	0.832351i	$0.686994\pi$
$674$	14822.7	−	8557.90i	0.847106	−	0.489077i
$675$		0			0
$676$	24194.2	−	38716.3i	1.37654	−	2.20279i
$677$	−11729.7			−0.665891			−0.332945	−	0.942946i	$-0.608042\pi$
$677$	−11729.7			−0.665891			−0.332945	+	0.942946i	$0.608042\pi$
$678$		0			0
$679$	−11002.8	−	19057.4i	−0.621869	−	1.07711i
$680$	384.849	−	666.578i	0.0217034	−	0.0375913i
$681$		0			0
$682$	−64088.9	−	37001.8i	−3.59838	−	2.07752i
$683$	1011.88	+	584.210i	0.0566889	+	0.0327294i	0.528077	−	0.849197i	$-0.322913\pi$
$683$	1011.88	+	584.210i	0.0566889	+	0.0327294i	−0.471388	+	0.881926i	$0.656247\pi$
$684$		0			0
$685$	1624.55	−	2813.81i	0.0906145	−	0.156949i
$686$	−18549.5	−	32128.7i	−1.03240	−	1.78816i
$687$		0			0
$688$	−10478.9			−0.580675
$689$	490.786	+	8.57358i	0.0271371	+	0.000474060i
$690$		0			0
$691$	28572.7	−	16496.4i	1.57302	−	0.908183i	0.577222	−	0.816587i	$-0.304137\pi$
$691$	28572.7	−	16496.4i	1.57302	−	0.908183i	0.995796	−	0.0915952i	$-0.0291966\pi$
$692$	5598.34	+	9696.62i	0.307539	+	0.532673i
$693$		0			0
$694$			30679.2i			1.67805i
$695$	753.972	+	435.306i	0.0411508	+	0.0237584i
$696$		0			0
$697$		−	651.438i		−	0.0354017i
$698$	8928.14	−	15464.0i	0.484147	−	0.838568i
$699$		0			0
$700$	32209.4	−	18596.1i	1.73914	−	1.00410i
$701$	−14785.8			−0.796651			−0.398326	−	0.917244i	$-0.630409\pi$
$701$	−14785.8			−0.796651			−0.398326	+	0.917244i	$0.630409\pi$
$702$		0			0
$703$	4582.77			0.245864
$704$	72189.3	−	41678.5i	3.86468	−	2.23128i
$705$		0			0
$706$	33010.5	−	57175.8i	1.75973	−	3.04793i
$707$			13430.6i			0.714442i
$708$		0			0
$709$	10941.4	+	6317.00i	0.579565	+	0.334612i	0.760961	−	0.648798i	$-0.224728\pi$
$709$	10941.4	+	6317.00i	0.579565	+	0.334612i	−0.181395	+	0.983410i	$0.558061\pi$
$710$		−	4125.52i		−	0.218067i
$711$		0			0
$712$	−7393.39	−	12805.7i	−0.389156	−	0.674038i
$713$	8452.62	−	4880.12i	0.443973	−	0.256328i
$714$		0			0
$715$	4098.01	+	7393.25i	0.214345	+	0.386702i
$716$	46148.7			2.40874
$717$		0			0
$718$	22907.3	+	39676.6i	1.19066	+	2.06228i
$719$	13648.3	−	23639.5i	0.707920	−	1.22615i	−0.257707	−	0.966223i	$-0.582967\pi$
$719$	13648.3	−	23639.5i	0.707920	−	1.22615i	0.965627	−	0.259931i	$-0.0836998\pi$
$720$		0			0
$721$	−16480.1	−	9514.77i	−0.851248	−	0.491468i
$722$	−28705.6	−	16573.2i	−1.47966	−	0.854279i
$723$		0			0
$724$	39719.2	−	68795.7i	2.03889	−	3.53145i
$725$	15128.7	+	26203.7i	0.774987	+	1.34232i
$726$		0			0
$727$	−4658.21			−0.237639			−0.118819	−	0.992916i	$-0.537911\pi$
$727$	−4658.21			−0.237639			−0.118819	+	0.992916i	$0.537911\pi$
$728$	25163.2	−	41877.3i	1.28106	−	2.13197i
$729$		0			0
$730$	−9282.39	+	5359.19i	−0.470626	+	0.271716i
$731$	108.220	+	187.442i	0.00547558	+	0.00948399i
$732$		0			0
$733$		−	166.474i		−	0.00838864i	−0.999991	−	0.00419432i	$-0.998665\pi$
$733$		−	166.474i		−	0.00838864i	0.999991	−	0.00419432i	$-0.00133510\pi$
$734$	−11599.4	−	6696.93i	−0.583300	−	0.336769i
$735$		0			0
$736$			25219.4i			1.26304i
$737$	749.370	−	1297.95i	0.0374537	−	0.0648718i
$738$		0			0
$739$	−11031.5	+	6369.03i	−0.549120	+	0.317035i	−0.748767	−	0.662833i	$-0.769354\pi$
$739$	−11031.5	+	6369.03i	−0.549120	+	0.317035i	0.199647	+	0.979868i	$0.436020\pi$
$740$	9843.70			0.489002
$741$		0			0
$742$	854.092			0.0422570
$743$	26608.2	−	15362.2i	1.31381	−	0.758527i	0.331083	−	0.943602i	$-0.392586\pi$
$743$	26608.2	−	15362.2i	1.31381	−	0.758527i	0.982725	+	0.185074i	$0.0592526\pi$
$744$		0			0
$745$	1521.88	−	2635.97i	0.0748420	−	0.129630i
$746$		−	6131.38i		−	0.300919i
$747$		0			0
$748$	−5011.55	−	2893.42i	−0.244974	−	0.141436i
$749$		−	5193.37i		−	0.253353i
$750$		0			0
$751$	−19769.3	−	34241.4i	−0.960575	−	1.66376i	−0.721061	−	0.692872i	$-0.756345\pi$
$751$	−19769.3	−	34241.4i	−0.960575	−	1.66376i	−0.239514	−	0.970893i	$-0.576988\pi$
$752$	−61837.0	+	35701.6i	−2.99862	+	1.73126i
$753$		0			0
$754$	55394.8	+	33285.6i	2.67555	+	1.60768i
$755$	7928.35			0.382175
$756$		0			0
$757$	−11517.6	−	19949.0i	−0.552990	−	0.957807i	−0.998057	−	0.0623093i	$-0.980153\pi$
$757$	−11517.6	−	19949.0i	−0.552990	−	0.957807i	0.445067	−	0.895497i	$-0.353180\pi$
$758$	−32676.1	+	56596.6i	−1.56576	+	2.71198i
$759$		0			0
$760$	4176.18	+	2411.12i	0.199323	+	0.115079i
$761$	−28106.0	−	16227.0i	−1.33882	−	0.772968i	−0.352187	−	0.935930i	$-0.614562\pi$
$761$	−28106.0	−	16227.0i	−1.33882	−	0.772968i	−0.986632	+	0.162962i	$0.947895\pi$
$762$		0			0
$763$	−5892.30	+	10205.8i	−0.279575	+	0.484238i
$764$	−35993.4	−	62342.4i	−1.70444	−	2.95218i
$765$		0			0
$766$	−54616.1			−2.57619
$767$	−17883.3	−	10745.7i	−0.841890	−	0.505874i
$768$		0			0
$769$	−27900.1	+	16108.1i	−1.30833	+	0.755362i	−0.981817	−	0.189831i	$-0.939206\pi$
$769$	−27900.1	+	16108.1i	−1.30833	+	0.755362i	−0.326509	+	0.945194i	$0.605873\pi$
$770$	7354.10	+	12737.7i	0.344186	+	0.596148i
$771$		0			0
$772$			97613.2i			4.55075i
$773$	2532.78	+	1462.30i	0.117849	+	0.0680404i	0.557766	−	0.829998i	$-0.311659\pi$
$773$	2532.78	+	1462.30i	0.117849	+	0.0680404i	−0.439917	+	0.898039i	$0.644992\pi$
$774$		0			0
$775$			24280.9i			1.12541i
$776$	−49622.3	+	85948.4i	−2.29554	+	3.97599i
$777$		0			0
$778$	27159.6	−	15680.6i	1.25157	−	0.722593i
$779$	4081.32

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.64599 - 2.68236i) q^{2} +(10.3901 - 17.9962i) q^{4} -2.69631i q^{5} +(13.1657 + 7.60123i) q^{7} -68.5626i q^{8} +O(q^{10})\)	\(q+(4.64599 - 2.68236i) q^{2} +(10.3901 - 17.9962i) q^{4} -2.69631i q^{5} +(13.1657 + 7.60123i) q^{7} -68.5626i q^{8} +(-7.23249 - 12.5270i) q^{10} +(-57.9240 + 33.4424i) q^{11} +(46.8650 + 0.818689i) q^{13} +81.5570 q^{14} +(-100.789 - 174.571i) q^{16} +(-2.08177 + 3.60573i) q^{17} +(-22.5903 - 13.0425i) q^{19} +(-48.5235 - 28.0150i) q^{20} +(-179.409 + 310.746i) q^{22} +(-23.6621 - 40.9839i) q^{23} +117.730 q^{25} +(219.930 - 121.905i) q^{26} +(273.587 - 157.956i) q^{28} +(128.503 + 222.575i) q^{29} +206.242i q^{31} +(-461.511 - 266.453i) q^{32} +22.3362i q^{34} +(20.4953 - 35.4989i) q^{35} +(-152.149 + 87.8430i) q^{37} -139.939 q^{38} -184.866 q^{40} +(-135.501 + 78.2313i) q^{41} +(25.9922 - 45.0199i) q^{43} +1389.88i q^{44} +(-219.868 - 126.941i) q^{46} -354.222i q^{47} +(-55.9425 - 96.8953i) q^{49} +(546.972 - 315.794i) q^{50} +(501.667 - 834.888i) q^{52} +10.4723 q^{53} +(90.1712 + 156.181i) q^{55} +(521.160 - 902.676i) q^{56} +(1194.05 + 689.386i) q^{58} +(-385.480 - 222.557i) q^{59} +(-59.8481 + 103.660i) q^{61} +(553.216 + 958.199i) q^{62} -1246.28 q^{64} +(2.20744 - 126.363i) q^{65} +(-19.4057 + 11.2039i) q^{67} +(43.2597 + 74.9281i) q^{68} -219.903i q^{70} +(246.997 + 142.604i) q^{71} -740.989i q^{73} +(-471.253 + 816.235i) q^{74} +(-469.432 + 271.027i) q^{76} -1016.81 q^{77} -547.679 q^{79} +(-470.698 + 271.758i) q^{80} +(-419.689 + 726.923i) q^{82} -603.056i q^{83} +(9.72218 + 5.61310i) q^{85} -278.882i q^{86} +(2292.90 + 3971.42i) q^{88} +(186.774 - 107.834i) q^{89} +(610.789 + 367.011i) q^{91} -983.409 q^{92} +(-950.153 - 1645.71i) q^{94} +(-35.1666 + 60.9104i) q^{95} +(-1253.58 - 723.752i) q^{97} +(-519.817 - 300.116i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) \) 10 * q + 30 * q^4 + 30 * q^7	\( 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29} - 1440 q^{32} - 60 q^{35} - 405 q^{37} + 1380 q^{38} + 2000 q^{40} - 1065 q^{41} - 370 q^{43} - 390 q^{46} + 775 q^{49} + 4320 q^{50} + 2940 q^{52} - 330 q^{53} - 260 q^{55} + 2670 q^{56} + 2040 q^{58} - 780 q^{59} - 1375 q^{61} + 780 q^{62} - 3140 q^{64} - 1605 q^{65} + 1590 q^{67} + 600 q^{68} - 1620 q^{71} - 2190 q^{74} - 5190 q^{76} + 4320 q^{77} + 1100 q^{79} - 8430 q^{80} - 2390 q^{82} + 525 q^{85} + 3170 q^{88} - 2040 q^{89} + 4770 q^{91} + 1740 q^{92} - 3230 q^{94} + 1380 q^{95} - 3750 q^{97} - 180 q^{98}+O(q^{100}) \) 10 * q + 30 * q^4 + 30 * q^7 + 40 * q^10 - 60 * q^11 + 25 * q^13 + 60 * q^14 - 250 * q^16 - 105 * q^17 + 180 * q^19 - 510 * q^20 - 290 * q^22 + 60 * q^23 - 960 * q^25 + 30 * q^26 + 150 * q^28 + 495 * q^29 - 1440 * q^32 - 60 * q^35 - 405 * q^37 + 1380 * q^38 + 2000 * q^40 - 1065 * q^41 - 370 * q^43 - 390 * q^46 + 775 * q^49 + 4320 * q^50 + 2940 * q^52 - 330 * q^53 - 260 * q^55 + 2670 * q^56 + 2040 * q^58 - 780 * q^59 - 1375 * q^61 + 780 * q^62 - 3140 * q^64 - 1605 * q^65 + 1590 * q^67 + 600 * q^68 - 1620 * q^71 - 2190 * q^74 - 5190 * q^76 + 4320 * q^77 + 1100 * q^79 - 8430 * q^80 - 2390 * q^82 + 525 * q^85 + 3170 * q^88 - 2040 * q^89 + 4770 * q^91 + 1740 * q^92 - 3230 * q^94 + 1380 * q^95 - 3750 * q^97 - 180 * q^98

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