LMFDB - Embedded newform 117.5.bd.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,5,Mod(19,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("117.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	117.bd (of order $12$, degree $4$, 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:	$12.0942856808$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + \cdots + 3779136 $ x^16 + 152x^14 + 9190x^12 + 285720x^10 + 4862025x^8 + 43573680x^6 + 169417008x^4 + 100636992*x^2 + 3779136
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 13^{2} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Root			$-0.200628i$ of defining polynomial
Character	$\chi$	$=$	117.37
Dual form			117.5.bd.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59772 + 5.96275i) q^{2} +(-19.1453 - 11.0536i) q^{4} +(5.37551 + 5.37551i) q^{5} +(23.3974 + 87.3205i) q^{7} +(26.6579 - 26.6579i) q^{8} +O(q^{10})$	\(q+(-1.59772 + 5.96275i) q^{2} +(-19.1453 - 11.0536i) q^{4} +(5.37551 + 5.37551i) q^{5} +(23.3974 + 87.3205i) q^{7} +(26.6579 - 26.6579i) q^{8} +(-40.6414 + 23.4643i) q^{10} +(131.169 + 35.1465i) q^{11} +(-164.495 + 38.7617i) q^{13} -558.053 q^{14} +(-60.4944 - 104.779i) q^{16} +(-97.4284 - 56.2503i) q^{17} +(-27.6068 + 7.39723i) q^{19} +(-43.4974 - 162.335i) q^{20} +(-419.140 + 725.972i) q^{22} +(-382.304 + 220.723i) q^{23} -567.208i q^{25} +(31.6895 - 1042.77i) q^{26} +(517.250 - 1930.41i) q^{28} +(-141.434 - 244.970i) q^{29} +(596.807 + 596.807i) q^{31} +(1304.07 - 349.425i) q^{32} +(491.070 - 491.070i) q^{34} +(-343.619 + 595.166i) q^{35} +(-358.208 - 95.9816i) q^{37} -176.431i q^{38} +286.599 q^{40} +(339.191 - 1265.88i) q^{41} +(-37.5303 - 21.6682i) q^{43} +(-2122.77 - 2122.77i) q^{44} +(-705.305 - 2632.24i) q^{46} +(-2361.67 + 2361.67i) q^{47} +(-4998.10 + 2885.65i) q^{49} +(3382.12 + 906.236i) q^{50} +(3577.76 + 1076.15i) q^{52} +150.315 q^{53} +(516.168 + 894.029i) q^{55} +(2951.50 + 1704.05i) q^{56} +(1686.67 - 451.941i) q^{58} +(447.938 + 1671.73i) q^{59} +(1068.49 - 1850.67i) q^{61} +(-4512.14 + 2605.09i) q^{62} +6398.32i q^{64} +(-1092.61 - 675.880i) q^{65} +(-1444.15 + 5389.66i) q^{67} +(1243.53 + 2153.86i) q^{68} +(-2999.82 - 2999.82i) q^{70} +(6954.13 - 1863.35i) q^{71} +(-3856.78 + 3856.78i) q^{73} +(1144.63 - 1982.56i) q^{74} +(610.308 + 163.531i) q^{76} +12276.0i q^{77} +9010.15 q^{79} +(238.055 - 888.432i) q^{80} +(7006.20 + 4045.03i) q^{82} +(2184.19 + 2184.19i) q^{83} +(-221.353 - 826.102i) q^{85} +(189.165 - 189.165i) q^{86} +(4433.61 - 2559.74i) q^{88} +(-1348.94 - 361.446i) q^{89} +(-7233.45 - 13456.8i) q^{91} +9759.11 q^{92} +(-10308.8 - 17855.4i) q^{94} +(-188.165 - 108.637i) q^{95} +(6839.94 - 1832.76i) q^{97} +(-9220.90 - 34412.9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 6 q^{4} - 8 q^{5} + 56 q^{7} - 90 q^{8}+O(q^{10}) $ 16 * q + 4 * q^2 - 6 * q^4 - 8 * q^5 + 56 * q^7 - 90 * q^8	$ 16 q + 4 q^{2} - 6 q^{4} - 8 q^{5} + 56 q^{7} - 90 q^{8} - 486 q^{10} + 100 q^{11} + 294 q^{13} - 808 q^{14} + 230 q^{16} - 984 q^{17} - 1498 q^{19} + 3962 q^{20} - 1524 q^{22} + 1014 q^{23} - 614 q^{26} + 5764 q^{28} - 814 q^{29} + 4060 q^{31} + 4996 q^{32} - 2502 q^{34} + 4892 q^{35} - 1790 q^{37} + 18816 q^{40} - 4280 q^{41} - 1368 q^{43} - 10736 q^{44} - 15246 q^{46} - 1484 q^{47} - 11820 q^{49} + 13574 q^{50} + 1432 q^{52} - 7204 q^{53} + 6936 q^{55} - 8124 q^{56} + 3030 q^{58} + 2380 q^{59} - 162 q^{61} - 19614 q^{62} + 5248 q^{65} - 14854 q^{67} + 6444 q^{68} - 34524 q^{70} + 8050 q^{71} - 15448 q^{73} + 2882 q^{74} + 10622 q^{76} - 17064 q^{79} - 2564 q^{80} - 5346 q^{82} - 12788 q^{83} + 35382 q^{85} - 67260 q^{86} + 40836 q^{88} - 20492 q^{89} + 8996 q^{91} + 49884 q^{92} - 30606 q^{94} + 98574 q^{95} + 50944 q^{97} - 61484 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 6 * q^4 - 8 * q^5 + 56 * q^7 - 90 * q^8 - 486 * q^10 + 100 * q^11 + 294 * q^13 - 808 * q^14 + 230 * q^16 - 984 * q^17 - 1498 * q^19 + 3962 * q^20 - 1524 * q^22 + 1014 * q^23 - 614 * q^26 + 5764 * q^28 - 814 * q^29 + 4060 * q^31 + 4996 * q^32 - 2502 * q^34 + 4892 * q^35 - 1790 * q^37 + 18816 * q^40 - 4280 * q^41 - 1368 * q^43 - 10736 * q^44 - 15246 * q^46 - 1484 * q^47 - 11820 * q^49 + 13574 * q^50 + 1432 * q^52 - 7204 * q^53 + 6936 * q^55 - 8124 * q^56 + 3030 * q^58 + 2380 * q^59 - 162 * q^61 - 19614 * q^62 + 5248 * q^65 - 14854 * q^67 + 6444 * q^68 - 34524 * q^70 + 8050 * q^71 - 15448 * q^73 + 2882 * q^74 + 10622 * q^76 - 17064 * q^79 - 2564 * q^80 - 5346 * q^82 - 12788 * q^83 + 35382 * q^85 - 67260 * q^86 + 40836 * q^88 - 20492 * q^89 + 8996 * q^91 + 49884 * q^92 - 30606 * q^94 + 98574 * q^95 + 50944 * q^97 - 61484 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−1.59772	+	5.96275i	−0.399429	+	1.49069i	0.414675	+	0.909969i	$0.363895\pi$
$2$	−1.59772	+	5.96275i	−0.399429	+	1.49069i	−0.814104	+	0.580719i	$0.802771\pi$
$3$		0			0
$3$		0			0
$4$	−19.1453	−	11.0536i	−1.19658	−	0.690848i
$5$	5.37551	+	5.37551i	0.215021	+	0.215021i	0.806396	−	0.591376i	$-0.201415\pi$
$5$	5.37551	+	5.37551i	0.215021	+	0.215021i	−0.591376	+	0.806396i	$0.701415\pi$
$6$		0			0
$7$	23.3974	+	87.3205i	0.477499	+	1.78205i	0.611693	+	0.791095i	$0.290489\pi$
$7$	23.3974	+	87.3205i	0.477499	+	1.78205i	−0.134194	+	0.990955i	$0.542845\pi$
$8$	26.6579	−	26.6579i	0.416529	−	0.416529i
$9$		0			0
$10$	−40.6414	+	23.4643i	−0.406414	+	0.234643i
$11$	131.169	+	35.1465i	1.08404	+	0.290467i	0.756249	−	0.654284i	$-0.227030\pi$
$11$	131.169	+	35.1465i	1.08404	+	0.290467i	0.327789	+	0.944751i	$0.393696\pi$
$12$		0			0
$13$	−164.495	+	38.7617i	−0.973342	+	0.229359i
$13$	−164.495	+	38.7617i	−0.973342	+	0.229359i
$14$	−558.053			−2.84721
$15$		0			0
$16$	−60.4944	−	104.779i	−0.236306	−	0.409295i
$17$	−97.4284	−	56.2503i	−0.337122	−	0.194638i	0.321876	−	0.946782i	$-0.395686\pi$
$17$	−97.4284	−	56.2503i	−0.337122	−	0.194638i	−0.658999	+	0.752144i	$0.729020\pi$
$18$		0			0
$19$	−27.6068	+	7.39723i	−0.0764732	+	0.0204909i	−0.296853	−	0.954923i	$-0.595937\pi$
$19$	−27.6068	+	7.39723i	−0.0764732	+	0.0204909i	0.220380	+	0.975414i	$0.429270\pi$
$20$	−43.4974	−	162.335i	−0.108744	−	0.405837i
$21$		0			0
$22$	−419.140	+	725.972i	−0.865992	+	1.49994i
$23$	−382.304	+	220.723i	−0.722691	+	0.417246i	−0.815742	−	0.578415i	$-0.803671\pi$
$23$	−382.304	+	220.723i	−0.722691	+	0.417246i	0.0930512	+	0.995661i	$0.470338\pi$
$24$		0			0
$25$		−	567.208i		−	0.907532i
$26$	31.6895	−	1042.77i	0.0468779	−	1.54256i
$27$		0			0
$28$	517.250	−	1930.41i	0.659758	−	2.46225i
$29$	−141.434	−	244.970i	−0.168173	−	0.291284i	0.769604	−	0.638521i	$-0.220453\pi$
$29$	−141.434	−	244.970i	−0.168173	−	0.291284i	−0.937778	+	0.347237i	$0.887120\pi$
$30$		0			0
$31$	596.807	+	596.807i	0.621027	+	0.621027i	0.945794	−	0.324767i	$-0.105286\pi$
$31$	596.807	+	596.807i	0.621027	+	0.621027i	−0.324767	+	0.945794i	$0.605286\pi$
$32$	1304.07	−	349.425i	1.27351	−	0.341235i
$33$		0			0
$34$	491.070	−	491.070i	0.424801	−	0.424801i
$35$	−343.619	+	595.166i	−0.280505	+	0.485850i
$36$		0			0
$37$	−358.208	−	95.9816i	−0.261657	−	0.0701107i	0.125606	−	0.992080i	$-0.459913\pi$
$37$	−358.208	−	95.9816i	−0.261657	−	0.0701107i	−0.387262	+	0.921970i	$0.626579\pi$
$38$		−	176.431i		−	0.122182i
$39$		0			0
$40$	286.599			0.179125
$41$	339.191	−	1265.88i	0.201780	−	0.753051i	−0.788628	−	0.614871i	$-0.789208\pi$
$41$	339.191	−	1265.88i	0.201780	−	0.753051i	0.990407	−	0.138180i	$-0.0441253\pi$
$42$		0			0
$43$	−37.5303	−	21.6682i	−0.0202976	−	0.0117189i	0.489817	−	0.871825i	$-0.337064\pi$
$43$	−37.5303	−	21.6682i	−0.0202976	−	0.0117189i	−0.510114	+	0.860107i	$0.670397\pi$
$44$	−2122.77	−	2122.77i	−1.09647	−	1.09647i
$45$		0			0
$46$	−705.305	−	2632.24i	−0.333320	−	1.24397i
$47$	−2361.67	+	2361.67i	−1.06911	+	1.06911i	−0.0716878	+	0.997427i	$0.522839\pi$
$47$	−2361.67	+	2361.67i	−1.06911	+	1.06911i	−0.997427	+	0.0716878i	$0.977161\pi$
$48$		0			0
$49$	−4998.10	+	2885.65i	−2.08167	+	1.20185i
$50$	3382.12	+	906.236i	1.35285	+	0.362495i
$51$		0			0
$52$	3577.76	+	1076.15i	1.32314	+	0.397984i
$53$	150.315			0.0535120			0.0267560	−	0.999642i	$-0.491482\pi$
$53$	150.315			0.0535120			0.0267560	+	0.999642i	$0.491482\pi$
$54$		0			0
$55$	516.168	+	894.029i	0.170634	+	0.295547i
$56$	2951.50	+	1704.05i	0.941168	+	0.543384i
$57$		0			0
$58$	1686.67	−	451.941i	0.501387	−	0.134346i
$59$	447.938	+	1671.73i	0.128681	+	0.480244i	0.999944	−	0.0105725i	$-0.00336538\pi$
$59$	447.938	+	1671.73i	0.128681	+	0.480244i	−0.871263	+	0.490816i	$0.836699\pi$
$60$		0			0
$61$	1068.49	−	1850.67i	0.287150	−	0.497358i	−0.685978	−	0.727622i	$-0.740626\pi$
$61$	1068.49	−	1850.67i	0.287150	−	0.497358i	0.973128	+	0.230264i	$0.0739588\pi$
$62$	−4512.14	+	2605.09i	−1.17381	+	0.677702i
$63$		0			0
$64$			6398.32i			1.56209i
$65$	−1092.61	−	675.880i	−0.258605	−	0.159972i
$66$		0			0
$67$	−1444.15	+	5389.66i	−0.321710	+	1.20064i	0.595869	+	0.803082i	$0.296808\pi$
$67$	−1444.15	+	5389.66i	−0.321710	+	1.20064i	−0.917578	+	0.397555i	$0.869859\pi$
$68$	1243.53	+	2153.86i	0.268930	+	0.465801i
$69$		0			0
$70$	−2999.82	−	2999.82i	−0.612208	−	0.612208i
$71$	6954.13	−	1863.35i	1.37951	−	0.369640i	0.508570	−	0.861021i	$-0.330174\pi$
$71$	6954.13	−	1863.35i	1.37951	−	0.369640i	0.870945	+	0.491381i	$0.163508\pi$
$72$		0			0
$73$	−3856.78	+	3856.78i	−0.723734	+	0.723734i	−0.969364	−	0.245630i	$-0.921005\pi$
$73$	−3856.78	+	3856.78i	−0.723734	+	0.723734i	0.245630	+	0.969364i	$0.421005\pi$
$74$	1144.63	−	1982.56i	0.209026	−	0.362045i
$75$		0			0
$76$	610.308	+	163.531i	0.105663	+	0.0283122i
$77$			12276.0i			2.07051i
$78$		0			0
$79$	9010.15			1.44370			0.721851	−	0.692048i	$-0.243291\pi$
$79$	9010.15			1.44370			0.721851	+	0.692048i	$0.243291\pi$
$80$	238.055	−	888.432i	0.0371960	−	0.138817i
$81$		0			0
$82$	7006.20	+	4045.03i	1.04197	+	0.601581i
$83$	2184.19	+	2184.19i	0.317055	+	0.317055i	0.847635	−	0.530580i	$-0.178026\pi$
$83$	2184.19	+	2184.19i	0.317055	+	0.317055i	−0.530580	+	0.847635i	$0.678026\pi$
$84$		0			0
$85$	−221.353	−	826.102i	−0.0306371	−	0.114339i
$86$	189.165	−	189.165i	0.0255766	−	0.0255766i
$87$		0			0
$88$	4433.61	−	2559.74i	0.572522	−	0.330545i
$89$	−1348.94	−	361.446i	−0.170299	−	0.0456314i	0.172662	−	0.984981i	$-0.444763\pi$
$89$	−1348.94	−	361.446i	−0.170299	−	0.0456314i	−0.342961	+	0.939350i	$0.611430\pi$
$90$		0			0
$91$	−7233.45	−	13456.8i	−0.873499	−	1.62503i
$92$	9759.11			1.15301
$93$		0			0
$94$	−10308.8	−	17855.4i	−1.16668	−	2.02075i
$95$	−188.165	−	108.637i	−0.0208493	−	0.0120373i
$96$		0			0
$97$	6839.94	−	1832.76i	0.726957	−	0.194788i	0.123683	−	0.992322i	$-0.460529\pi$
$97$	6839.94	−	1832.76i	0.726957	−	0.194788i	0.603274	+	0.797534i	$0.293863\pi$
$98$	−9220.90	−	34412.9i	−0.960110	−	3.58318i
$99$		0			0
$100$	−6269.67	+	10859.4i	−0.626967	+	1.08594i
$101$	−3354.45	+	1936.69i	−0.328835	+	0.189853i	−0.655324	−	0.755348i	$-0.727468\pi$
$101$	−3354.45	+	1936.69i	−0.328835	+	0.189853i	0.326489	+	0.945201i	$0.394135\pi$
$102$		0			0
$103$			3372.99i			0.317937i	0.987284	+	0.158968i	$0.0508168\pi$
$103$			3372.99i			0.317937i	−0.987284	+	0.158968i	$0.949183\pi$
$104$	−3351.78	+	5418.38i	−0.309891	+	0.500960i
$105$		0			0
$106$	−240.161	+	896.292i	−0.0213742	+	0.0797697i
$107$	−1930.57	−	3343.84i	−0.168623	−	0.292064i	0.769313	−	0.638872i	$-0.220599\pi$
$107$	−1930.57	−	3343.84i	−0.168623	−	0.292064i	−0.937936	+	0.346808i	$0.887265\pi$
$108$		0			0
$109$	8275.58	+	8275.58i	0.696539	+	0.696539i	0.963662	−	0.267123i	$-0.0860731\pi$
$109$	8275.58	+	8275.58i	0.696539	+	0.696539i	−0.267123	+	0.963662i	$0.586073\pi$
$110$	−6155.57	+	1649.38i	−0.508724	+	0.136312i
$111$		0			0
$112$	7733.97	−	7733.97i	0.616548	−	0.616548i
$113$	−4225.16	+	7318.19i	−0.330892	+	0.573121i	−0.982687	−	0.185274i	$-0.940683\pi$
$113$	−4225.16	+	7318.19i	−0.330892	+	0.573121i	0.651795	+	0.758395i	$0.274016\pi$
$114$		0			0
$115$	−3241.58	−	868.578i	−0.245110	−	0.0656770i
$116$			6253.38i			0.464728i
$117$		0			0
$118$	−10683.8			−0.767292
$119$	2632.23	−	9823.60i	0.185879	−	0.693708i
$120$		0			0
$121$	3290.45	+	1899.74i	0.224742	+	0.129755i
$122$	9327.96	+	9327.96i	0.626711	+	0.626711i
$123$		0			0
$124$	−4829.23	−	18022.9i	−0.314076	−	1.17215i
$125$	6408.73	−	6408.73i	0.410159	−	0.410159i
$126$		0			0
$127$	3336.63	−	1926.41i	0.206872	−	0.119437i	−0.392985	−	0.919545i	$-0.628558\pi$
$127$	3336.63	−	1926.41i	0.206872	−	0.119437i	0.599857	+	0.800107i	$0.295224\pi$
$128$	−17286.5	−	4631.89i	−1.05508	−	0.282708i
$129$		0			0
$130$	5775.78	−	5435.09i	0.341762	−	0.321603i
$131$	18579.1			1.08264			0.541318	−	0.840818i	$-0.317926\pi$
$131$	18579.1			1.08264			0.541318	+	0.840818i	$0.317926\pi$
$132$		0			0
$133$	−1291.86	−	2237.56i	−0.0730318	−	0.126495i
$134$	−29829.9	−	17222.3i	−1.66128	−	0.959138i
$135$		0			0
$136$	−4096.75	+	1097.72i	−0.221494	+	0.0593490i
$137$	7754.09	+	28938.6i	0.413133	+	1.54183i	0.788547	+	0.614975i	$0.210834\pi$
$137$	7754.09	+	28938.6i	0.413133	+	1.54183i	−0.375414	+	0.926857i	$0.622500\pi$
$138$		0			0
$139$	−7596.66	+	13157.8i	−0.393182	+	0.681011i	−0.992867	−	0.119225i	$-0.961959\pi$
$139$	−7596.66	+	13157.8i	−0.393182	+	0.681011i	0.599686	+	0.800236i	$0.295292\pi$
$140$	13157.4	−	7596.43i	0.671296	−	0.387573i
$141$		0			0
$142$			44442.9i			2.20407i
$143$	−22938.9	−	697.105i	−1.12176	−	0.0340899i
$144$		0			0
$145$	556.562	−	2077.12i	0.0264714	−	0.0987928i
$146$	−16835.0	−	29159.1i	−0.789782	−	1.36794i
$147$		0			0
$148$	5797.08	+	5797.08i	0.264658	+	0.264658i
$149$	21511.3	−	5763.93i	0.968933	−	0.259625i	0.260555	−	0.965459i	$-0.416094\pi$
$149$	21511.3	−	5763.93i	0.968933	−	0.259625i	0.708377	+	0.705834i	$0.249428\pi$
$150$		0			0
$151$	−10348.1	+	10348.1i	−0.453845	+	0.453845i	−0.896629	−	0.442783i	$-0.853991\pi$
$151$	−10348.1	+	10348.1i	−0.453845	+	0.453845i	0.442783	+	0.896629i	$0.353991\pi$
$152$	−538.745	+	933.133i	−0.0233182	+	0.0403884i
$153$		0			0
$154$	−73199.0	−	19613.6i	−3.08648	−	0.827021i
$155$			6416.29i			0.267067i
$156$		0			0
$157$	22244.0			0.902431			0.451215	−	0.892415i	$-0.350991\pi$
$157$	22244.0			0.902431			0.451215	+	0.892415i	$0.350991\pi$
$158$	−14395.6	+	53725.3i	−0.576656	+	2.15211i
$159$		0			0
$160$	8888.40	+	5131.72i	0.347203	+	0.200458i
$161$	−28218.6	−	28218.6i	−1.08864	−	1.08864i
$162$		0			0
$163$	−1844.86	−	6885.11i	−0.0694365	−	0.259141i	0.922478	−	0.386050i	$-0.126161\pi$
$163$	−1844.86	−	6885.11i	−0.0694365	−	0.259141i	−0.991914	+	0.126910i	$0.959494\pi$
$164$	−20486.4	+	20486.4i	−0.761690	+	0.761690i
$165$		0			0
$166$	−16513.5	+	9534.08i	−0.599271	+	0.345989i
$167$	−29795.5	−	7983.69i	−1.06836	−	0.286267i	−0.318542	−	0.947909i	$-0.603193\pi$
$167$	−29795.5	−	7983.69i	−1.06836	−	0.286267i	−0.749820	+	0.661642i	$0.769860\pi$
$168$		0			0
$169$	25556.1	−	12752.2i	0.894789	−	0.446489i
$170$	5279.50			0.182682
$171$		0			0
$172$	479.021	+	829.688i	0.0161919	+	0.0280452i
$173$	47178.7	+	27238.7i	1.57636	+	0.910109i	0.995362	+	0.0962012i	$0.0306692\pi$
$173$	47178.7	+	27238.7i	1.57636	+	0.910109i	0.580994	+	0.813908i	$0.302664\pi$
$174$		0			0
$175$	49528.8	−	13271.2i	1.61727	−	0.433346i
$176$	−4252.34	−	15869.9i	−0.137278	−	0.512330i
$177$		0			0
$178$	4310.43	−	7465.88i	0.136044	−	0.235636i
$179$	12658.7	−	7308.50i	0.395078	−	0.228099i	−0.289280	−	0.957245i	$-0.593416\pi$
$179$	12658.7	−	7308.50i	0.395078	−	0.228099i	0.684358	+	0.729146i	$0.260083\pi$
$180$		0			0
$181$		−	15636.6i		−	0.477292i	−0.971107	−	0.238646i	$-0.923296\pi$
$181$		−	15636.6i		−	0.477292i	0.971107	−	0.238646i	$-0.0767036\pi$
$182$	91796.8	−	21631.1i	2.77131	−	0.653033i
$183$		0			0
$184$	−4307.39	+	16075.4i	−0.127227	+	0.474817i
$185$	−1409.60	−	2441.50i	−0.0411863	−	0.0713368i
$186$		0			0
$187$	−10802.5	−	10802.5i	−0.308918	−	0.308918i
$188$	71320.0	−	19110.1i	2.01788	−	0.540690i
$189$		0			0
$190$	948.409	−	948.409i	0.0262717	−	0.0262717i
$191$	10415.6	−	18040.4i	0.285508	−	0.494514i	−0.687224	−	0.726445i	$-0.741171\pi$
$191$	10415.6	−	18040.4i	0.285508	−	0.494514i	0.972732	+	0.231931i	$0.0745044\pi$
$192$		0			0
$193$	−47365.6	−	12691.6i	−1.27159	−	0.340722i	−0.440952	−	0.897530i	$-0.645359\pi$
$193$	−47365.6	−	12691.6i	−1.27159	−	0.340722i	−0.830641	+	0.556808i	$0.812026\pi$
$194$			43713.1i			1.16147i
$195$		0			0
$196$	127587.			3.32119
$197$	−16495.3	+	61561.3i	−0.425038	+	1.58626i	0.338803	+	0.940857i	$0.389978\pi$
$197$	−16495.3	+	61561.3i	−0.425038	+	1.58626i	−0.763841	+	0.645405i	$0.776689\pi$
$198$		0			0
$199$	21392.2	+	12350.8i	0.540193	+	0.311881i	0.745157	−	0.666889i	$-0.232374\pi$
$199$	21392.2	+	12350.8i	0.540193	+	0.311881i	−0.204964	+	0.978770i	$0.565708\pi$
$200$	−15120.5	−	15120.5i	−0.378014	−	0.378014i
$201$		0			0
$202$	−6188.56	−	23096.0i	−0.151666	−	0.566024i
$203$	18081.7	−	18081.7i	0.438781	−	0.438781i
$204$		0			0
$205$	8628.08	−	4981.42i	0.205308	−	0.118535i
$206$	−20112.3	−	5389.08i	−0.473945	−	0.126993i
$207$		0			0
$208$	14012.4	+	14890.8i	0.323882	+	0.344185i
$209$	−3881.14			−0.0888518
$210$		0			0
$211$	−7684.22	−	13309.5i	−0.172598	−	0.298948i	0.766730	−	0.641970i	$-0.221883\pi$
$211$	−7684.22	−	13309.5i	−0.172598	−	0.298948i	−0.939327	+	0.343022i	$0.888549\pi$
$212$	−2877.83	−	1661.52i	−0.0640315	−	0.0369686i
$213$		0			0
$214$	23023.0	−	6168.99i	0.502729	−	0.134706i
$215$	−85.2674	−	318.222i	−0.00184462	−	0.00688420i
$216$		0			0
$217$	−38149.7	+	66077.3i	−0.810162	+	1.40324i
$218$	−62567.3	+	36123.2i	−1.31654	+	0.760105i
$219$		0			0
$220$		−	22822.0i		−	0.471529i
$221$	18206.8	+	5476.39i	0.372777	+	0.112127i
$222$		0			0
$223$	−360.162	+	1344.14i	−0.00724250	+	0.0270294i	−0.969453	−	0.245279i	$-0.921120\pi$
$223$	−360.162	+	1344.14i	−0.00724250	+	0.0270294i	0.962210	+	0.272308i	$0.0877871\pi$
$224$	61023.9	+	105697.i	1.21620	+	2.10652i
$225$		0			0
$226$	−36886.0	−	36886.0i	−0.722178	−	0.722178i
$227$	−76619.8	+	20530.2i	−1.48693	+	0.398420i	−0.908698	−	0.417455i	$-0.862922\pi$
$227$	−76619.8	+	20530.2i	−1.48693	+	0.398420i	−0.578228	+	0.815876i	$0.696255\pi$
$228$		0			0
$229$	−49114.8	+	49114.8i	−0.936573	+	0.936573i	−0.998105	−	0.0615317i	$-0.980401\pi$
$229$	−49114.8	+	49114.8i	−0.936573	+	0.936573i	0.0615317	+	0.998105i	$0.480401\pi$
$230$	10358.2	−	17941.0i	0.195808	−	0.339149i
$231$		0			0
$232$	−10300.7	−	2760.06i	−0.191377	−	0.0512794i
$233$		−	90643.7i		−	1.66965i	−0.550515	−	0.834826i	$-0.685568\pi$
$233$		−	90643.7i		−	1.66965i	0.550515	−	0.834826i	$-0.314432\pi$
$234$		0			0
$235$	−25390.4			−0.459763
$236$	9902.63	−	36957.1i	0.177798	−	0.663551i
$237$		0			0
$238$	54370.2	+	31390.6i	0.959858	+	0.554174i
$239$	−53610.9	−	53610.9i	−0.938549	−	0.938549i	0.0596691	−	0.998218i	$-0.480995\pi$
$239$	−53610.9	−	53610.9i	−0.938549	−	0.938549i	−0.998218	+	0.0596691i	$0.980995\pi$
$240$		0			0
$241$	−6713.31	−	25054.4i	−0.115585	−	0.431370i	0.883745	−	0.467969i	$-0.155014\pi$
$241$	−6713.31	−	25054.4i	−0.115585	−	0.431370i	−0.999330	+	0.0365992i	$0.988348\pi$
$242$	−16584.9	+	16584.9i	−0.283193	+	0.283193i
$243$		0			0
$244$	−40913.0	+	23621.1i	−0.687198	+	0.396754i
$245$	−42379.2	−	11355.5i	−0.706026	−	0.189179i
$246$		0			0
$247$	4254.45	−	2286.89i	0.0697348	−	0.0374845i
$248$	31819.2			0.517352
$249$		0			0
$250$	27974.4	+	48453.0i	0.447590	+	0.775248i
$251$	57981.5	+	33475.7i	0.920327	+	0.531351i	0.883739	−	0.467979i	$-0.155018\pi$
$251$	57981.5	+	33475.7i	0.920327	+	0.531351i	0.0365878	+	0.999330i	$0.488351\pi$
$252$		0			0
$253$	−57903.9	+	15515.3i	−0.904621	+	0.242392i
$254$	6155.70	+	22973.4i	0.0954135	+	0.356088i
$255$		0			0
$256$	4051.12	−	7016.75i	0.0618152	−	0.107067i
$257$	32203.7	−	18592.8i	0.487573	−	0.281500i	−0.235994	−	0.971754i	$-0.575835\pi$
$257$	32203.7	−	18592.8i	0.487573	−	0.281500i	0.723567	+	0.690254i	$0.242501\pi$
$258$		0			0
$259$		−	33524.6i		−	0.499763i
$260$	13447.5	+	25017.2i	0.198927	+	0.370076i
$261$		0			0
$262$	−29684.1	+	110783.i	−0.432436	+	1.61387i
$263$	−10900.9	−	18881.0i	−0.157598	−	0.272969i	0.776404	−	0.630236i	$-0.217042\pi$
$263$	−10900.9	−	18881.0i	−0.157598	−	0.272969i	−0.934002	+	0.357267i	$0.883709\pi$
$264$		0			0
$265$	808.021	+	808.021i	0.0115062	+	0.0115062i
$266$	15406.1	−	4128.04i	0.217735	−	0.0583420i
$267$		0			0
$268$	87223.8	−	87223.8i	1.21441	−	1.21441i
$269$	−53948.9	+	93442.2i	−0.745552	+	1.29133i	0.204384	+	0.978891i	$0.434481\pi$
$269$	−53948.9	+	93442.2i	−0.745552	+	1.29133i	−0.949936	+	0.312444i	$0.898852\pi$
$270$		0			0
$271$	42444.4	+	11372.9i	0.577939	+	0.154858i	0.535935	−	0.844259i	$-0.319959\pi$
$271$	42444.4	+	11372.9i	0.577939	+	0.154858i	0.0420036	+	0.999117i	$0.486626\pi$
$272$			13611.3i			0.183976i
$273$		0			0
$274$	−184943.			−2.46341
$275$	19935.4	−	74399.8i	0.263608	−	0.983800i
$276$		0			0
$277$	−1084.76	−	626.285i	−0.0141375	−	0.00816230i	0.492915	−	0.870078i	$-0.335932\pi$
$277$	−1084.76	−	626.285i	−0.0141375	−	0.00816230i	−0.507052	+	0.861915i	$0.669265\pi$
$278$	−66319.5	−	66319.5i	−0.858127	−	0.858127i
$279$		0			0
$280$	6705.70	+	25026.0i	0.0855318	+	0.319209i
$281$	−74905.1	+	74905.1i	−0.948634	+	0.948634i	−0.998744	−	0.0501093i	$-0.984043\pi$
$281$	−74905.1	+	74905.1i	−0.948634	+	0.948634i	0.0501093	+	0.998744i	$0.484043\pi$
$282$		0			0
$283$	−37049.3	+	21390.4i	−0.462601	+	0.267083i	−0.713137	−	0.701024i	$-0.752726\pi$
$283$	−37049.3	+	21390.4i	−0.462601	+	0.267083i	0.250536	+	0.968107i	$0.419393\pi$
$284$	−153736.	−	41193.4i	−1.90607	−	0.510730i
$285$		0			0
$286$	40806.5	−	135665.i	0.498881	−	1.65858i
$287$	118473.			1.43833
$288$		0			0
$289$	−35432.3	−	61370.6i	−0.424232	−	0.734792i
$290$	11496.1	+	6637.29i	0.136696	+	0.0789213i
$291$		0			0
$292$	116471.	−	31208.2i	1.36600	−	0.366018i
$293$	−8238.85	−	30747.8i	−0.0959691	−	0.358162i	0.901195	−	0.433413i	$-0.142691\pi$
$293$	−8238.85	−	30747.8i	−0.0959691	−	0.358162i	−0.997165	+	0.0752512i	$0.976024\pi$
$294$		0			0
$295$	−6578.50	+	11394.3i	−0.0755932	+	0.130931i
$296$	−12107.7	+	6990.40i	−0.138191	+	0.0797845i
$297$		0			0
$298$			137476.i			1.54808i
$299$	54331.4	−	51126.5i	0.607727	−	0.571879i
$300$		0			0
$301$	1013.96	−	3784.15i	0.0111915	−	0.0417672i
$302$	−45170.0	−	78236.7i	−0.495263	−	0.857821i
$303$		0			0
$304$	2445.14	+	2445.14i	0.0264579	+	0.0264579i
$305$	15692.0	−	4204.65i	0.168685	−	0.0451991i
$306$		0			0
$307$	84129.7	−	84129.7i	0.892632	−	0.892632i	−0.102138	−	0.994770i	$-0.532568\pi$
$307$	84129.7	−	84129.7i	0.892632	−	0.892632i	0.994770	+	0.102138i	$0.0325683\pi$
$308$	135694.	−	235029.i	1.43041	−	2.47754i
$309$		0			0
$310$	−38258.8	−	10251.4i	−0.398114	−	0.106674i
$311$		−	13886.4i		−	0.143572i	−0.997420	−	0.0717860i	$-0.977130\pi$
$311$		−	13886.4i		−	0.143572i	0.997420	−	0.0717860i	$-0.0228699\pi$
$312$		0			0
$313$	63260.4			0.645718			0.322859	−	0.946447i	$-0.395356\pi$
$313$	63260.4			0.645718			0.322859	+	0.946447i	$0.395356\pi$
$314$	−35539.6	+	132636.i	−0.360457	+	1.34524i
$315$		0			0
$316$	−172502.	−	99594.3i	−1.72751	−	0.997379i
$317$	10553.4	+	10553.4i	0.105020	+	0.105020i	0.757664	−	0.652644i	$-0.226340\pi$
$317$	10553.4	+	10553.4i	0.105020	+	0.105020i	−0.652644	+	0.757664i	$0.726340\pi$
$318$		0			0
$319$	−9941.79	−	37103.3i	−0.0976975	−	0.364612i
$320$	−34394.3	+	34394.3i	−0.335881	+	0.335881i
$321$		0			0
$322$	213346.	−	123175.i	2.05765	−	1.18799i
$323$	3105.78	+	832.192i	0.0297691	+	0.00797662i
$324$		0			0
$325$	21985.9	+	93302.7i	0.208151	+	0.883339i
$326$	44001.8			0.414033
$327$		0			0
$328$	−24703.5	−	42787.8i	−0.229621	−	0.397715i
$329$	−261480.	−	150965.i	−2.41572	−	1.39472i
$330$		0			0
$331$	−45405.1	+	12166.3i	−0.414428	+	0.111046i	−0.460007	−	0.887915i	$-0.652153\pi$
$331$	−45405.1	+	12166.3i	−0.414428	+	0.111046i	0.0455795	+	0.998961i	$0.485487\pi$
$332$	−17674.0	−	65960.2i	−0.160346	−	0.598419i
$333$		0			0
$334$	95209.6	−	164908.i	0.853469	−	1.47825i
$335$	−36735.3	+	21209.1i	−0.327336	+	0.188987i
$336$		0			0
$337$		−	8592.02i		−	0.0756546i	−0.999284	−	0.0378273i	$-0.987956\pi$
$337$		−	8592.02i		−	0.0756546i	0.999284	−	0.0378273i	$-0.0120437\pi$
$338$	35206.8	+	172759.i	0.308172	+	1.51219i
$339$		0			0
$340$	−4893.49	+	18262.7i	−0.0423312	+	0.157982i
$341$	57306.7	+	99258.1i	0.492829	+	0.853605i
$342$		0			0
$343$	−215440.	−	215440.i	−1.83121	−	1.83121i
$344$	−1578.11	+	422.852i	−0.0133358	+	0.00357332i
$345$		0			0
$346$	−237796.	+	237796.i	−1.98633	+	1.98633i
$347$	86232.5	−	149359.i	0.716163	−	1.24043i	−0.246346	−	0.969182i	$-0.579230\pi$
$347$	86232.5	−	149359.i	0.716163	−	1.24043i	0.962509	−	0.271249i	$-0.0874366\pi$
$348$		0			0
$349$	126776.	+	33969.6i	1.04085	+	0.278894i	0.738465	−	0.674292i	$-0.235551\pi$
$349$	126776.	+	33969.6i	1.04085	+	0.278894i	0.302383	+	0.953186i	$0.402218\pi$
$350$			316532.i			2.58393i
$351$		0			0
$352$	183334.			1.47965
$353$	11384.2	−	42486.4i	0.0913593	−	0.340958i	−0.905083	−	0.425235i	$-0.860191\pi$
$353$	11384.2	−	42486.4i	0.0913593	−	0.340958i	0.996442	+	0.0842773i	$0.0268582\pi$
$354$		0			0
$355$	47398.5	+	27365.6i	0.376104	+	0.217144i
$356$	21830.6	+	21830.6i	0.172252	+	0.172252i
$357$		0			0
$358$	23353.8	+	87157.6i	0.182218	+	0.680048i
$359$	15691.6	−	15691.6i	0.121753	−	0.121753i	−0.643605	−	0.765358i	$-0.722562\pi$
$359$	15691.6	−	15691.6i	0.121753	−	0.121753i	0.765358	+	0.643605i	$0.222562\pi$
$360$		0			0
$361$	−112154.	+	64752.1i	−0.860597	+	0.496866i
$362$	93237.1	+	24982.8i	0.711494	+	0.190644i
$363$		0			0
$364$	−10259.3	+	337591.i	−0.0774308	+	2.54793i
$365$	−41464.3			−0.311235
$366$		0			0
$367$	100985.	+	174910.i	0.749761	+	1.29862i	0.947937	+	0.318458i	$0.103165\pi$
$367$	100985.	+	174910.i	0.749761	+	1.29862i	−0.198175	+	0.980167i	$0.563502\pi$
$368$	46254.5	+	26705.0i	0.341553	+	0.197196i
$369$		0			0
$370$	16810.2	−	4504.29i	0.122792	−	0.0329020i
$371$	3516.99	+	13125.6i	0.0255519	+	0.0953610i
$372$		0			0
$373$	124830.	−	216212.i	0.897226	−	1.55404i	0.0662014	−	0.997806i	$-0.478912\pi$
$373$	124830.	−	216212.i	0.897226	−	1.55404i	0.831025	−	0.556235i	$-0.187755\pi$
$374$	81672.3	−	47153.5i	0.583891	−	0.337109i
$375$		0			0
$376$			125914.i			0.890635i
$377$	32760.5	+	34814.1i	0.230499	+	0.244947i
$378$		0			0
$379$	19032.3	−	71029.7i	0.132499	−	0.494494i	−0.867496	−	0.497444i	$-0.834272\pi$
$379$	19032.3	−	71029.7i	0.132499	−	0.494494i	0.999996	+	0.00294932i	$0.000938800\pi$
$380$	2401.65	+	4159.78i	0.0166319	+	0.0288074i
$381$		0			0
$382$	90929.1	+	90929.1i	0.623127	+	0.623127i
$383$	97227.9	−	26052.1i	0.662817	−	0.177601i	0.0882998	−	0.996094i	$-0.471857\pi$
$383$	97227.9	−	26052.1i	0.662817	−	0.177601i	0.574517	+	0.818493i	$0.305190\pi$
$384$		0			0
$385$	−65990.0	+	65990.0i	−0.445202	+	0.445202i
$386$	151353.	−	262152.i	1.01582	−	1.75946i
$387$		0			0
$388$	−151211.	−	40517.0i	−1.00443	−	0.269137i
$389$			214008.i			1.41426i	0.707082	+	0.707131i	$0.250011\pi$
$389$			214008.i			1.41426i	−0.707082	+	0.707131i	$0.749989\pi$
$390$		0			0
$391$	49663.0			0.324847
$392$	−56313.3	+	210164.i	−0.366470	+	1.36768i
$393$		0			0
$394$	−340720.	−	196715.i	−2.19485	−	1.26720i
$395$	48434.2	+	48434.2i	0.310426	+	0.310426i
$396$		0			0
$397$	35355.3	+	131948.i	0.224323	+	0.837184i	0.982675	+	0.185339i	$0.0593382\pi$
$397$	35355.3	+	131948.i	0.224323	+	0.837184i	−0.758352	+	0.651845i	$0.773995\pi$
$398$	−107823.	+	107823.i	−0.680686	+	0.680686i
$399$		0			0
$400$	−59431.7	+	34312.9i	−0.371448	+	0.214456i
$401$	197833.	+	53009.2i	1.23030	+	0.329657i	0.814695	−	0.579890i	$-0.196904\pi$
$401$	197833.	+	53009.2i	1.23030	+	0.329657i	0.415602	+	0.909547i	$0.363571\pi$
$402$		0			0
$403$	−121305.	−	75038.4i	−0.746910	−	0.462034i
$404$	85629.4			0.524638
$405$		0			0
$406$	78927.4	+	136706.i	0.478824	+	0.829347i
$407$	−43612.2	−	25179.5i	−0.263281	−	0.152005i
$408$		0			0
$409$	152546.	−	40874.6i	0.911916	−	0.244347i	0.227789	−	0.973710i	$-0.426850\pi$
$409$	152546.	−	40874.6i	0.911916	−	0.244347i	0.684126	+	0.729363i	$0.260184\pi$
$410$	15917.8	+	59406.0i	0.0946924	+	0.353397i
$411$		0			0
$412$	37283.6	−	64577.0i	0.219646	−	0.380438i
$413$	−135495.	+	78228.3i	−0.794373	+	0.458632i
$414$		0			0
$415$			23482.3i			0.136347i
$416$	−200969.	+	108027.i	−1.16129	+	0.624229i
$417$		0			0
$418$	6200.95	−	23142.3i	0.0354900	−	0.132450i
$419$	−98539.2	−	170675.i	−0.561282	−	0.972168i	−0.997385	−	0.0722718i	$-0.976975\pi$
$419$	−98539.2	−	170675.i	−0.561282	−	0.972168i	0.436103	−	0.899897i	$-0.356358\pi$
$420$		0			0
$421$	107929.	+	107929.i	0.608939	+	0.608939i	0.942669	−	0.333729i	$-0.108307\pi$
$421$	107929.	+	107929.i	0.608939	+	0.608939i	−0.333729	+	0.942669i	$0.608307\pi$
$422$	91638.2	−	24554.4i	0.514579	−	0.137881i
$423$		0			0
$424$	4007.08	−	4007.08i	0.0222893	−	0.0222893i
$425$	−31905.6	+	55262.1i	−0.176640	+	0.305949i
$426$		0			0
$427$	186601.	+	49999.7i	1.02343	+	0.274228i
$428$			85358.6i			0.465972i
$429$		0			0
$430$	2033.71			0.0109990
$431$	−32479.2	+	121214.i	−0.174844	+	0.652528i	0.821734	+	0.569871i	$0.193007\pi$
$431$	−32479.2	+	121214.i	−0.174844	+	0.652528i	−0.996578	+	0.0826563i	$0.973660\pi$
$432$		0			0
$433$	228921.	+	132167.i	1.22098	+	0.704934i	0.965127	−	0.261781i	$-0.0843097\pi$
$433$	228921.	+	132167.i	1.22098	+	0.704934i	0.255855	+	0.966715i	$0.417643\pi$
$434$	−333050.	−	333050.i	−1.76819	−	1.76819i
$435$		0			0
$436$	−66964.1	−	249913.i	−0.352265	−	1.31467i
$437$	8921.45	−	8921.45i	0.0467168	−	0.0467168i
$438$		0			0
$439$	−207852.	+	120004.i	−1.07851	+	0.622680i	−0.930495	−	0.366304i	$-0.880623\pi$
$439$	−207852.	+	120004.i	−1.07851	+	0.622680i	−0.148019	+	0.988985i	$0.547290\pi$
$440$	37592.9	+	10073.0i	0.194178	+	0.0520298i
$441$		0			0
$442$	−61743.7	+	99813.0i	−0.316044	+	0.510908i
$443$	−56485.3			−0.287825			−0.143912	−	0.989590i	$-0.545968\pi$
$443$	−56485.3			−0.287825			−0.143912	+	0.989590i	$0.545968\pi$
$444$		0			0
$445$	−5308.26	−	9194.18i	−0.0268060	−	0.0464294i
$446$	−7439.36	−	4295.12i	−0.0373995	−	0.0215926i
$447$		0			0
$448$	−558704.	+	149704.i	−2.78372	+	0.745896i
$449$	34627.1	+	129230.i	0.171761	+	0.641020i	0.997081	+	0.0763545i	$0.0243281\pi$
$449$	34627.1	+	129230.i	0.171761	+	0.641020i	−0.825320	+	0.564665i	$0.809005\pi$
$450$		0			0
$451$	88982.5	−	154122.i	0.437473	−	0.757726i
$452$	161784.	−	93406.1i	0.791879	−	0.457192i
$453$		0			0
$454$		−	489666.i		−	2.37568i
$455$	33453.9	−	111221.i	0.161594	−	0.537234i
$456$		0			0
$457$	46049.5	−	171859.i	0.220492	−	0.822886i	−0.763669	−	0.645608i	$-0.776604\pi$
$457$	46049.5	−	171859.i	0.220492	−	0.822886i	0.984161	−	0.177278i	$-0.0567293\pi$
$458$	−214388.	−	371331.i	−1.02204	−	1.77023i
$459$		0			0
$460$	52460.2	+	52460.2i	0.247922	+	0.247922i
$461$	303818.	−	81407.7i	1.42959	−	0.383057i	0.540714	−	0.841207i	$-0.318154\pi$
$461$	303818.	−	81407.7i	1.42959	−	0.383057i	0.888875	+	0.458149i	$0.151488\pi$
$462$		0			0
$463$	238507.	−	238507.i	1.11260	−	1.11260i	0.119805	−	0.992797i	$-0.461773\pi$
$463$	238507.	−	238507.i	1.11260	−	1.11260i	0.992797	−	0.119805i	$-0.0382269\pi$
$464$	−17111.9	+	29638.6i	−0.0794807	+	0.137665i
$465$		0			0
$466$	540486.	+	144823.i	2.48893	+	0.666907i
$467$		−	300948.i		−	1.37993i	−0.723842	−	0.689965i	$-0.757626\pi$
$467$		−	300948.i		−	1.37993i	0.723842	−	0.689965i	$-0.242374\pi$
$468$		0			0
$469$	−504417.			−2.29321
$470$	40566.7	−	151397.i	0.183643	−	0.685364i
$471$		0			0
$472$	56505.8	+	32623.6i	0.253635	+	0.146436i
$473$	−4161.24	−	4161.24i	−0.0185995	−	0.0185995i
$474$		0			0
$475$	4195.76	+	15658.8i	0.0185962	+	0.0694019i
$476$	−158981.	+	158981.i	−0.701666	+	0.701666i
$477$		0			0
$478$	405323.	−	234014.i	1.77397	−	1.02420i
$479$	206969.	+	55457.3i	0.902059	+	0.241706i	0.679900	−	0.733304i	$-0.262023\pi$
$479$	206969.	+	55457.3i	0.902059	+	0.241706i	0.222159	+	0.975010i	$0.428690\pi$
$480$		0			0
$481$	62643.8	+	1903.72i	0.270762	+	0.00822836i
$482$	160119.			0.689206
$483$		0			0
$484$	−41997.8	−	72742.4i	−0.179282	−	0.310525i
$485$	46620.2	+	26916.2i	0.198194	+	0.114427i
$486$		0			0
$487$	55699.6	−	14924.7i	0.234852	−	0.0629283i	−0.139474	−	0.990226i	$-0.544541\pi$
$487$	55699.6	−	14924.7i	0.234852	−	0.0629283i	0.374325	+	0.927297i	$0.377874\pi$
$488$	−20851.4	−	77818.5i	−0.0875579	−	0.326771i
$489$		0			0
$490$	135420.	−	234554.i	0.564014	−	0.976901i
$491$	−339332.	+	195914.i	−1.40754	+	0.812646i	−0.995151	−	0.0983596i	$-0.968640\pi$
$491$	−339332.	+	195914.i	−1.40754	+	0.812646i	−0.412394	+	0.911006i	$0.635307\pi$
$492$		0			0
$493$			31822.7i			0.130931i
$494$	6838.78	+	29022.0i	0.0280236	+	0.118925i
$495$		0			0
$496$	26429.6	−	98636.6i	0.107430	−	0.400936i
$497$	325418.	+	563640.i	1.31743	+	2.28186i
$498$		0			0
$499$	−49256.6	−	49256.6i	−0.197817	−	0.197817i	0.601247	−	0.799063i	$-0.294671\pi$
$499$	−49256.6	−	49256.6i	−0.197817	−	0.197817i	−0.799063	+	0.601247i	$0.794671\pi$
$500$	−193537.	+	51858.0i	−0.774146	+	0.207432i
$501$		0			0
$502$	−292245.	+	292245.i	−1.15968	+	1.15968i
$503$	207038.	−	358600.i	0.818302	−	1.41734i	−0.0886300	−	0.996065i	$-0.528249\pi$
$503$	207038.	−	358600.i	0.818302	−	1.41734i	0.906932	−	0.421276i	$-0.138418\pi$
$504$		0			0
$505$	−28442.6	−	7621.17i	−0.111529	−	0.0298840i
$506$		−	370056.i		−	1.44533i
$507$		0			0
$508$	−85174.6			−0.330052
$509$	32960.3	−	123010.i	0.127220	−	0.474792i	−0.872689	−	0.488277i	$-0.837626\pi$
$509$	32960.3	−	123010.i	0.127220	−	0.474792i	0.999909	+	0.0134846i	$0.00429240\pi$
$510$		0			0
$511$	−427015.	−	246537.i	−1.63531	−	0.944149i
$512$	−167106.	−	167106.i	−0.637461	−	0.637461i
$513$		0			0
$514$	59412.0	+	221729.i	0.224879	+	0.839258i
$515$	−18131.6	+	18131.6i	−0.0683629	+	0.0683629i
$516$		0			0
$517$	−392782.	+	226773.i	−1.46950	+	0.848419i
$518$	199899.	+	53562.8i	0.744991	+	0.199620i
$519$		0			0
$520$	−47144.1	+	11109.1i	−0.174350	+	0.0410839i
$521$	−288110.			−1.06141			−0.530705	−	0.847557i	$-0.678073\pi$
$521$	−288110.			−1.06141			−0.530705	+	0.847557i	$0.678073\pi$
$522$		0			0
$523$	170871.	+	295958.i	0.624692	+	1.08200i	0.988600	+	0.150563i	$0.0481087\pi$
$523$	170871.	+	295958.i	0.624692	+	1.08200i	−0.363909	+	0.931435i	$0.618558\pi$
$524$	−355703.	−	205365.i	−1.29546	−	0.747937i
$525$		0			0
$526$	129999.	−	34833.2i	0.469861	−	0.125899i
$527$	−24575.4	−	91716.6i	−0.0884869	−	0.330238i
$528$		0			0
$529$	−42483.1	+	73582.9i	−0.151812	+	0.262945i
$530$	−6109.02	+	3527.04i	−0.0217480	+	0.0125562i
$531$		0			0
$532$			57118.6i			0.201815i
$533$	−6727.60	+	221378.i	−0.0236813	+	0.779256i
$534$		0			0
$535$	7597.07	−	28352.7i	0.0265423	−	0.0990572i
$536$	105179.	+	182175.i	0.366099	+	0.634102i
$537$		0			0
$538$	−470978.	−	470978.i	−1.62718	−	1.62718i
$539$	−757014.	+	202841.i	−2.60571	+	0.698198i
$540$		0			0
$541$	−195832.	+	195832.i	−0.669096	+	0.669096i	−0.957507	−	0.288411i	$-0.906873\pi$
$541$	−195832.	+	195832.i	−0.669096	+	0.669096i	0.288411	+	0.957507i	$0.406873\pi$
$542$	−135628.	+	234915.i	−0.461691	+	0.799672i
$543$		0			0
$544$	−146709.	−	39310.5i	−0.495745	−	0.132835i
$545$			88971.0i			0.299540i
$546$		0			0
$547$	232302.			0.776387			0.388194	−	0.921578i	$-0.373099\pi$
$547$	232302.			0.776387			0.388194	+	0.921578i	$0.373099\pi$
$548$	171421.	−	639750.i	0.570824	−	2.13034i
$549$		0			0
$550$	411777.	+	237740.i	1.36125	+	0.785916i
$551$	5716.63	+	5716.63i	0.0188294	+	0.0188294i
$552$		0			0
$553$	210814.	+	786770.i	0.689366	+	2.57275i
$554$	5467.52	−	5467.52i	0.0178144	−	0.0178144i
$555$		0			0
$556$	290881.	−	167940.i	0.940950	−	0.543258i
$557$	−379764.	−	101757.i	−1.22406	−	0.327986i	−0.411797	−	0.911276i	$-0.635099\pi$
$557$	−379764.	−	101757.i	−1.22406	−	0.327986i	−0.812264	+	0.583290i	$0.801765\pi$
$558$		0			0
$559$	7013.44	+	2109.56i	0.0224444	+	0.00675100i
$560$	83148.1			0.265141
$561$		0			0
$562$	−326964.	−	566318.i	−1.03521	−	1.79303i
$563$	270897.	+	156402.i	0.854648	+	0.493431i	0.862216	−	0.506540i	$-0.169076\pi$
$563$	270897.	+	156402.i	0.854648	+	0.493431i	−0.00756835	+	0.999971i	$0.502409\pi$
$564$		0			0
$565$	−62051.4	+	16626.6i	−0.194381	+	0.0520843i
$566$	−68351.5	−	255091.i	−0.213361	−	0.796275i
$567$		0			0
$568$	135709.	−	235055.i	0.420642	−	0.728574i
$569$	−121130.	+	69934.3i	−0.374133	+	0.216006i	−0.675263	−	0.737577i	$-0.735970\pi$
$569$	−121130.	+	69934.3i	−0.374133	+	0.216006i	0.301129	+	0.953583i	$0.402636\pi$
$570$		0			0
$571$		−	53058.0i		−	0.162734i	−0.996684	−	0.0813671i	$-0.974071\pi$
$571$		−	53058.0i		−	0.162734i	0.996684	−	0.0813671i	$-0.0259286\pi$
$572$	431467.	+	266903.i	1.31873	+	0.815758i
$573$		0			0
$574$	−189287.	+	706428.i	−0.574508	+	2.14409i
$575$	125196.	+	216846.i	0.378664	+	0.655866i
$576$		0			0
$577$	−321525.	−	321525.i	−0.965748	−	0.965748i	0.0336847	−	0.999433i	$-0.489276\pi$
$577$	−321525.	−	321525.i	−0.965748	−	0.965748i	−0.999433	+	0.0336847i	$0.989276\pi$
$578$	422548.	−	113221.i	1.26480	−	0.338901i
$579$		0			0
$580$	−33615.1	+	33615.1i	−0.0999261	+	0.0999261i
$581$	−139620.	+	241829.i	−0.413614	+	0.716401i
$582$		0			0
$583$	19716.6	+	5283.05i	0.0580090	+	0.0155435i
$584$			205627.i			0.602913i
$585$		0			0
$586$	196505.			0.572240
$587$	−105377.	+	393271.i	−0.305822	+	1.14134i	0.626414	+	0.779491i	$0.284522\pi$
$587$	−105377.	+	393271.i	−0.305822	+	1.14134i	−0.932236	+	0.361852i	$0.882145\pi$
$588$		0			0
$589$	−20890.7	−	12061.2i	−0.0602174	−	0.0347665i
$590$	−57430.8	−	57430.8i	−0.164984	−	0.164984i
$591$		0			0
$592$	11612.7	+	43339.2i	0.0331352	+	0.123662i
$593$	65134.9	−	65134.9i	0.185227	−	0.185227i	−0.608402	−	0.793629i	$-0.708189\pi$
$593$	65134.9	−	65134.9i	0.185227	−	0.185227i	0.793629	+	0.608402i	$0.208189\pi$
$594$		0			0
$595$	66956.5	−	38657.3i	0.189129	−	0.109194i
$596$	−475552.	−	127424.i	−1.33877	−	0.358722i
$597$		0			0
$598$	218049.	+	405650.i	0.609750	+	1.13436i
$599$	267881.			0.746600			0.373300	−	0.927711i	$-0.378226\pi$
$599$	267881.			0.746600			0.373300	+	0.927711i	$0.378226\pi$
$600$		0			0
$601$	92557.9	+	160315.i	0.256250	+	0.443839i	0.965234	−	0.261386i	$-0.0841795\pi$
$601$	92557.9	+	160315.i	0.256250	+	0.443839i	−0.708984	+	0.705225i	$0.750846\pi$
$602$	20943.9	+	12092.0i	0.0577916	+	0.0333660i
$603$		0			0
$604$	312502.	−	83734.7i	0.856602	−	0.229526i
$605$	7475.76	+	27899.9i	0.0204242	+	0.0762241i
$606$		0			0
$607$	−159586.	+	276411.i	−0.433129	+	0.750201i	−0.997141	−	0.0755656i	$-0.975924\pi$
$607$	−159586.	+	276411.i	−0.433129	+	0.750201i	0.564012	+	0.825766i	$0.309257\pi$
$608$	−33416.5	+	19293.0i	−0.0903970	+	0.0521907i
$609$		0			0
$610$			100285.i			0.269511i
$611$	296941.	−	480026.i	0.795403	−	1.28583i
$612$		0			0
$613$	152708.	−	569912.i	0.406387	−	1.51666i	−0.395097	−	0.918640i	$-0.629289\pi$
$613$	152708.	−	569912.i	0.406387	−	1.51666i	0.801484	−	0.598017i	$-0.204044\pi$
$614$	367229.	+	636060.i	0.974094	+	1.68718i
$615$		0			0
$616$	327253.	+	327253.i	0.862427	+	0.862427i
$617$	473767.	−	126946.i	1.24450	−	0.333463i	0.424290	−	0.905526i	$-0.360524\pi$
$617$	473767.	−	126946.i	1.24450	−	0.333463i	0.820209	+	0.572063i	$0.193857\pi$
$618$		0			0
$619$	−241958.	+	241958.i	−0.631478	+	0.631478i	−0.948439	−	0.316961i	$-0.897338\pi$
$619$	−241958.	+	241958.i	−0.631478	+	0.631478i	0.316961	+	0.948439i	$0.397338\pi$
$620$	70922.9	−	122842.i	0.184503	−	0.319568i
$621$		0			0
$622$	82801.4	+	22186.6i	0.214021	+	0.0573468i
$623$		−	126247.i		−	0.325270i
$624$		0			0
$625$	−285604.			−0.731147
$626$	−101072.	+	377206.i	−0.257918	+	0.962565i
$627$		0			0
$628$	−425869.	−	245876.i	−1.07983	−	0.623442i
$629$	29500.6	+	29500.6i	0.0745642	+	0.0745642i
$630$		0			0
$631$	−79353.2	−	296150.i	−0.199299	−	0.743795i	−0.991112	−	0.133031i	$-0.957529\pi$
$631$	−79353.2	−	296150.i	−0.199299	−	0.743795i	0.791813	−	0.610764i	$-0.209138\pi$
$632$	240191.	−	240191.i	0.601344	−	0.601344i
$633$		0			0
$634$	−79788.5	+	46065.9i	−0.198501	+	0.114604i
$635$	28291.5	+	7580.70i	0.0701632	+	0.0188002i
$636$		0			0
$637$	710308.	−	668409.i	1.75052	−	1.64727i
$638$	237122.			0.582546
$639$		0			0
$640$	−68024.8	−	117822.i	−0.166076	−	0.287652i
$641$	−98429.5	−	56828.3i	−0.239557	−	0.138308i	0.375416	−	0.926856i	$-0.377500\pi$
$641$	−98429.5	−	56828.3i	−0.239557	−	0.138308i	−0.614973	+	0.788548i	$0.710833\pi$
$642$		0			0
$643$	−14225.1	+	3811.61i	−0.0344060	+	0.00921906i	−0.275981	−	0.961163i	$-0.589003\pi$
$643$	−14225.1	+	3811.61i	−0.0344060	+	0.00921906i	0.241575	+	0.970382i	$0.422336\pi$
$644$	228338.	+	852170.i	0.550563	+	2.05473i
$645$		0			0
$646$	−9924.32	+	17189.4i	−0.0237813	+	0.0411904i
$647$	213468.	−	123246.i	0.509946	−	0.294417i	−0.222866	−	0.974849i	$-0.571541\pi$
$647$	213468.	−	123246.i	0.509946	−	0.294417i	0.732811	+	0.680432i	$0.238208\pi$
$648$		0			0
$649$			235022.i			0.557980i
$650$	−591468.	−	17974.5i	−1.39993	−	0.0425432i
$651$		0			0
$652$	−40784.5	+	152210.i	−0.0959401	+	0.358053i
$653$	−114446.	−	198226.i	−0.268394	−	0.464872i	0.700053	−	0.714091i	$-0.253160\pi$
$653$	−114446.	−	198226.i	−0.268394	−	0.464872i	−0.968447	+	0.249219i	$0.919826\pi$
$654$		0			0
$655$	99872.3	+	99872.3i	0.232789	+	0.232789i
$656$	−153157.	+	41038.4i	−0.355902	+	0.0953636i
$657$		0			0
$658$	1.31794e6	−	1.31794e6i	3.04399	−	3.04399i
$659$	139582.	−	241763.i	0.321409	−	0.556697i	−0.659370	−	0.751819i	$-0.729177\pi$
$659$	139582.	−	241763.i	0.321409	−	0.556697i	0.980779	+	0.195122i	$0.0625103\pi$
$660$		0			0
$661$	85509.9	+	22912.3i	0.195710	+	0.0524404i	0.355343	−	0.934736i	$-0.384364\pi$
$661$	85509.9	+	22912.3i	0.195710	+	0.0524404i	−0.159632	+	0.987177i	$0.551031\pi$
$662$		−	290178.i		−	0.662138i
$663$		0			0
$664$	116452.			0.264125
$665$	5083.66	−	18972.5i	0.0114956	−	0.0429023i
$666$		0			0
$667$	108141.	+	62435.3i	0.243074	+	0.140339i
$668$	482197.	+	482197.i	1.08062	+	1.08062i
$669$		0			0
$670$	−67772.2	−	252929.i	−0.150974	−	0.563443i
$671$	205196.	−	205196.i	0.455748	−	0.455748i
$672$		0			0
$673$	130883.	−	75565.6i	0.288971	−	0.166838i	−0.348507	−	0.937306i	$-0.613311\pi$
$673$	130883.	−	75565.6i	0.288971	−	0.166838i	0.637478	+	0.770469i	$0.279978\pi$
$674$	51232.1	+	13727.6i	0.112777	+	0.0302186i
$675$		0			0
$676$	−630237.	−	38340.7i	−1.37915	−	0.0839010i
$677$	−752917.			−1.64274			−0.821372	−	0.570393i	$-0.806791\pi$
$677$	−752917.			−1.64274			−0.821372	+	0.570393i	$0.806791\pi$
$678$		0			0
$679$	320074.	+	554385.i	0.694243	+	1.20246i
$680$	−27922.9	−	16121.3i	−0.0603869	−	0.0348644i
$681$		0			0
$682$	−683411.	+	183120.i	−1.46931	+	0.393700i
$683$	145592.	+	543357.i	0.312102	+	1.16478i	0.926657	+	0.375907i	$0.122669\pi$
$683$	145592.	+	543357.i	0.312102	+	1.16478i	−0.614555	+	0.788874i	$0.710665\pi$
$684$		0			0
$685$	−113878.	+	197242.i	−0.242694	+	0.420358i
$686$	1.62883e6	−	940404.i	3.46120	−	1.99833i
$687$		0			0
$688$			5243.21i			0.0110770i
$689$	−24726.1	+	5826.47i	−0.0520854	+	0.0122735i
$690$		0			0
$691$	−103894.	+	387737.i	−0.217588	+	0.812048i	0.767652	+	0.640867i	$0.221425\pi$
$691$	−103894.	+	387737.i	−0.217588	+	0.812048i	−0.985240	+	0.171181i	$0.945242\pi$
$692$	−602169.	−	1.04299e6i	−1.25749	−	2.17804i
$693$		0			0
$694$	752816.	+	752816.i	1.56304	+	1.56304i
$695$	−111566.	+	29894.0i	−0.230973	+	0.0618892i
$696$		0			0
$697$	−104253.	+	104253.i	−0.214597	+	0.214597i
$698$	−405105.	+	701662.i	−0.831489	+	1.44018i
$699$		0			0
$700$	−1.09494e6	−	293388.i	−2.23457	−	0.598752i
$701$		−	465668.i		−	0.947634i	−0.880623	−	0.473817i	$-0.842876\pi$
$701$		−	465668.i		−	0.947634i	0.880623	−	0.473817i	$-0.157124\pi$
$702$		0			0
$703$	10599.0			0.0214464
$704$	−224879.	+	839259.i	−0.453736	+	1.69336i
$705$		0			0
$706$	235147.	+	135762.i	0.471770	+	0.272377i
$707$	−247598.	−	247598.i	−0.495346	−	0.495346i
$708$		0			0
$709$	−198348.	−	740245.i	−0.394581	−	1.47259i	−0.822493	−	0.568775i	$-0.807418\pi$
$709$	−198348.	−	740245.i	−0.394581	−	1.47259i	0.427913	−	0.903820i	$-0.359249\pi$
$710$	−238903.	+	238903.i	−0.473921	+	0.473921i
$711$		0			0
$712$	−45595.1	+	26324.4i	−0.0899412	+	0.0519276i
$713$	−359891.	−	96432.5i	−0.707932	−	0.189690i
$714$		0			0
$715$	−119561.	−	127056.i	−0.233872	−	0.248532i
$716$	−323140.			−0.630326
$717$		0			0
$718$	68494.5	+	118636.i	0.132864	+	0.230127i
$719$	579881.	+	334794.i	1.12171	+	0.647620i	0.941837	−	0.336070i	$-0.109098\pi$
$719$	579881.	+	334794.i	1.12171	+	0.647620i	0.179874	+	0.983690i	$0.442431\pi$
$720$		0			0
$721$	−294531.	+	78919.4i	−0.566579	+	0.151814i
$722$	−206911.	−	772201.i	−0.396925	−	1.48134i
$723$		0			0
$724$	−172840.	+	299368.i	−0.329736	+	0.571120i
$725$	−138949.	+	80222.2i	−0.264350	+	0.152622i
$726$		0			0
$727$		−	852719.i		−	1.61338i	−0.590974	−	0.806690i	$-0.701257\pi$
$727$		−	852719.i		−	1.61338i	0.590974	−	0.806690i	$-0.298743\pi$
$728$	−551559.	−	165902.i	−1.04071	−	0.313033i
$729$		0			0
$730$	66248.2	−	247242.i	0.124316	−	0.463955i
$731$	2437.68	+	4222.19i	0.00456186	+	0.00790137i
$732$		0			0
$733$	195353.	+	195353.i	0.363590	+	0.363590i	0.865133	−	0.501543i	$-0.167234\pi$
$733$	195353.	+	195353.i	0.363590	+	0.363590i	−0.501543	+	0.865133i	$0.667234\pi$
$734$	−1.20429e6	+	322689.i	−2.23532	+	0.598953i
$735$		0			0
$736$	−421425.	+	421425.i	−0.777974	+	0.777974i
$737$	−378855.	+	656197.i	−0.697491	+	1.20809i
$738$		0			0
$739$	341809.	+	91587.4i	0.625885	+	0.167705i	0.557802	−	0.829974i	$-0.311645\pi$
$739$	341809.	+	91587.4i	0.625885	+	0.167705i	0.0680832	+	0.997680i	$0.478312\pi$
$740$			62324.5i			0.113814i
$741$		0			0
$742$	−83883.8			−0.152360
$743$	107468.	−	401075.i	0.194671	−	0.726520i	−0.797681	−	0.603079i	$-0.793940\pi$
$743$	107468.	−	401075.i	0.194671	−	0.726520i	0.992352	−	0.123441i	$-0.0393930\pi$
$744$		0			0
$745$	146618.	+	84650.1i	0.264165	+	0.152516i
$746$	1.08978e6	+	1.08978e6i	1.95821	+	1.95821i
$747$		0			0
$748$	87411.7	+	326225.i	0.156231	+	0.583061i
$749$	246815.	−	246815.i	0.439955	−	0.439955i
$750$		0			0
$751$	163029.	−	94124.8i	0.289058	−	0.166888i	−0.348459	−	0.937324i	$-0.613295\pi$
$751$	163029.	−	94124.8i	0.289058	−	0.166888i	0.637517	+	0.770436i	$0.279962\pi$
$752$	390323.	+	104587.i	0.690222	+	0.184944i
$753$		0			0
$754$	−259930.	+	139720.i	−0.457208	+	0.245763i
$755$	−111253.			−0.195172
$756$		0			0
$757$	−399242.	−	691507.i	−0.696698	−	1.20672i	−0.969605	−	0.244675i	$-0.921319\pi$
$757$	−399242.	−	691507.i	−0.696698	−	1.20672i	0.272908	−	0.962040i	$-0.412015\pi$
$758$	393124.	+	226970.i	0.684213	+	0.395031i
$759$		0			0
$760$	−7912.10	+	2120.04i	−0.0136982	+	0.00367043i
$761$	−24628.2	−	91913.9i	−0.0425269	−	0.158713i	0.941397	−	0.337300i	$-0.109514\pi$
$761$	−24628.2	−	91913.9i	−0.0425269	−	0.158713i	−0.983924	+	0.178588i	$0.942847\pi$
$762$		0			0
$763$	−529000.	+	916255.i	−0.908671	+	1.57386i
$764$	−398821.	+	230259.i	−0.683268	+	0.394485i
$765$		0			0
$766$			621370.i			1.05899i
$767$	−138482.	−	257628.i	−0.235399	−	0.437927i
$768$		0			0
$769$	110548.	−	412572.i	0.186939	−	0.697666i	−0.807268	−	0.590185i	$-0.799055\pi$
$769$	110548.	−	412572.i	0.186939	−	0.697666i	0.994207	−	0.107481i	$-0.0342784\pi$
$770$	−288049.	−	498916.i	−0.485831	−	0.841484i
$771$		0			0
$772$	766543.	+	766543.i	1.28618	+	1.28618i
$773$	931158.	−	249503.i	1.55835	−	0.417558i	0.626208	−	0.779656i	$-0.284606\pi$
$773$	931158.	−	249503.i	1.55835	−	0.417558i	0.932140	+	0.362097i	$0.117939\pi$
$774$		0			0
$775$	338514.	−	338514.i	0.563602	−	0.563602i
$776$	133481.	−	231196.i	0.221664	−	0.383934i
$777$		0			0
$778$	−1.27607e6	−	341923.i	−2.10822	−	0.564897i
$779$			37456.0i			0.0617229i
$780$		0			0
$781$	977654.			1.60281
$782$	−79347.3	+	296128.i	−0.129753	+	0.484246i
$783$		0			0
$784$	604714.	+	349132.i	0.983825	+	0.568012i
$785$	119573.	+	119573.i	0.194041	+	0.194041i
$786$		0			0
$787$	−179306.	−	669180.i	−0.289498	−	1.08042i	−0.945489	−	0.325653i	$-0.894416\pi$
$787$	−179306.	−	669180.i	−0.289498	−	1.08042i	0.655991	−	0.754769i	$-0.272251\pi$
$788$	996279.	−	996279.i	1.60446	−	1.60446i
$789$		0			0
$790$	−366185.	+	211417.i	−0.586741	+	0.338755i
$791$	−737885.	−	197716.i	−1.17933	−	0.316001i
$792$		0			0
$793$	−104025.	+	345842.i	−0.165422	+	0.549960i
$794$	−843260.			−1.33758
$795$		0			0
$796$	−273041.	−	472920.i	−0.430924	−	0.746383i
$797$	−806320.	−	465529.i	−1.26938	−	0.732875i	−0.294507	−	0.955649i	$-0.595155\pi$
$797$	−806320.	−	465529.i	−1.26938	−	0.732875i	−0.974870	+	0.222774i	$0.928489\pi$
$798$		0			0
$799$	362939.	−	97249.2i	0.568513	−	0.152333i
$800$	−198197.	−	739680.i	−0.309682	−	1.15575i
$801$		0			0
$802$	−632161.	+	1.09494e6i	−0.982832	+	1.70231i
$803$	−641441.	+	370336.i	−0.994777	+	0.574334i
$804$		0			0
$805$		−	303379.i		−	0.468159i
$806$	641247.	−	603422.i	0.987086	−	0.928861i
$807$		0			0
$808$	−37794.4	+	141051.i	−0.0578901	+	0.216049i
$809$	−26946.9	−	46673.5i	−0.0411730	−	0.0713137i	0.844705	−	0.535233i	$-0.179776\pi$
$809$	−26946.9	−	46673.5i	−0.0411730	−	0.0713137i	−0.885878	+	0.463919i	$0.846443\pi$
$810$		0			0
$811$	−867670.	−	867670.i	−1.31921	−	1.31921i	−0.914404	−	0.404803i	$-0.867340\pi$
$811$	−867670.	−	867670.i	−1.31921	−	1.31921i	−0.404803	−	0.914404i	$-0.632660\pi$
$812$	−546048.	+	146313.i	−0.828169	+	0.221907i
$813$		0			0
$814$	219819.	−	219819.i	0.331755	−	0.331755i
$815$	27093.9	−	46928.0i	0.0407903	−	0.0706508i
$816$		0			0
$817$	1196.38	+	320.569i	0.00179236	+	0.000480260i
$818$			974901.i			1.45698i
$819$		0			0
$820$	−220250.			−0.327558
$821$	277240.	−	1.03468e6i	0.411311	−	1.53503i	−0.380801	−	0.924657i	$-0.624352\pi$
$821$	277240.	−	1.03468e6i	0.411311	−	1.53503i	0.792112	−	0.610376i	$-0.208982\pi$
$822$		0			0
$823$	948821.	+	547802.i	1.40083	+	0.808768i	0.994478	−	0.104950i	$-0.0334682\pi$
$823$	948821.	+	547802.i	1.40083	+	0.808768i	0.406350	+	0.913718i	$0.366801\pi$
$824$	89916.7	+	89916.7i	0.132430	+	0.132430i
$825$		0			0
$826$	−249973.	−	932913.i	−0.366381	−	1.36735i
$827$	118484.	−	118484.i	0.173240	−	0.173240i	−0.615161	−	0.788401i	$-0.710909\pi$
$827$	118484.	−	118484.i	0.173240	−	0.173240i	0.788401	+	0.615161i	$0.210909\pi$
$828$		0			0
$829$	−598258.	+	345405.i	−0.870522	+	0.502596i	−0.867522	−	0.497399i	$-0.834288\pi$
$829$	−598258.	+	345405.i	−0.870522	+	0.502596i	−0.00300029	+	0.999995i	$0.500955\pi$
$830$	−140019.	−	37518.0i	−0.203250	−	0.0544608i
$831$		0			0
$832$	−248010.	−	1.05249e6i	−0.358279	−	1.52045i
$833$	649275.			0.935705
$834$		0			0
$835$	−117250.	−	203083.i	−0.168166	−	0.291273i
$836$	74305.7	+	42900.4i	0.106319	+	0.0613831i
$837$		0			0
$838$	1.17513e6	−	314875.i	1.67339	−	0.448384i
$839$	−43984.2	−	164151.i	−0.0624845	−	0.233195i	0.927620	−	0.373524i	$-0.121851\pi$
$839$	−43984.2	−	164151.i	−0.0624845	−	0.233195i	−0.990105	+	0.140329i	$0.955184\pi$
$840$		0			0
$841$	313634.	−	543229.i	0.443436	−	0.768053i
$842$	−815994.	+	471114.i	−1.15097	+	0.664511i
$843$		0			0
$844$			339752.i			0.476955i
$845$	205927.	+	68827.4i	0.288402	+	0.0963936i
$846$		0			0
$847$	−88898.2	+	331773.i	−0.123916	+	0.462459i
$848$	−9093.23	−	15749.9i	−0.0126452	−	0.0219022i
$849$		0			0
$850$	−278538.	−	278538.i	−0.385520	−	0.385520i
$851$	158130.	−	42370.7i	0.218350	−	0.0585068i
$852$		0			0
$853$	−621614.	+	621614.i	−0.854324	+	0.854324i	−0.990662	−	0.136338i	$-0.956467\pi$
$853$	−621614.	+	621614.i	−0.854324	+	0.854324i	0.136338	+	0.990662i	$0.456467\pi$
$854$	−596271.	+	1.03277e6i	−0.817576	+	1.41608i
$855$		0			0
$856$	−140604.	−	37674.9i	−0.191890	−	0.0514167i
$857$			433050.i			0.589626i	0.955555	+	0.294813i	$0.0952574\pi$
$857$			433050.i			0.589626i	−0.955555	+	0.294813i	$0.904743\pi$
$858$		0			0
$859$	264929.			0.359040			0.179520	−	0.983754i	$-0.442546\pi$
$859$	264929.			0.359040			0.179520	+	0.983754i	$0.442546\pi$
$860$	−1885.02	+	7034.98i	−0.00254870	+	0.00951188i
$861$		0			0
$862$	−670878.	−	387332.i	−0.902878	−	0.521277i
$863$	−344574.	−	344574.i	−0.462659	−	0.462659i	0.436867	−	0.899526i	$-0.356088\pi$
$863$	−344574.	−	344574.i	−0.462659	−	0.462659i	−0.899526	+	0.436867i	$0.856088\pi$
$864$		0			0
$865$	107188.	+	400032.i	0.143257	+	0.534641i
$866$	−1.15383e6	+	1.15383e6i	−1.53853	+	1.53853i
$867$		0			0
$868$	1.46078e6	−	843381.i	1.93885	−	1.11940i
$869$	1.18185e6	+	316675.i	1.56503	+	0.419348i
$870$		0			0
$871$	28643.7	−	942548.i	0.0377566	−	1.24242i
$872$	441219.			0.580258
$873$		0			0
$874$	38942.5	+	67450.4i	0.0509801	+	0.0883002i
$875$	709561.	+	409665.i	0.926774	+	0.535073i
$876$		0			0
$877$	910707.	−	244023.i	1.18408	−	0.317272i	0.387534	−	0.921855i	$-0.373327\pi$
$877$	910707.	−	244023.i	1.18408	−	0.317272i	0.796542	+	0.604583i	$0.206660\pi$
$878$	−383463.	−	1.43110e6i	−0.497433	−	1.85644i
$879$		0			0
$880$	62450.6	−	108168.i	0.0806438	−	0.139679i
$881$	896268.	−	517461.i	1.15475	−	0.666692i	0.204706	−	0.978823i	$-0.434376\pi$
$881$	896268.	−	517461.i	1.15475	−	0.666692i	0.950039	+	0.312131i	$0.101043\pi$
$882$		0			0
$883$			200330.i			0.256936i	0.991714	+	0.128468i	$0.0410059\pi$
$883$			200330.i			0.256936i	−0.991714	+	0.128468i	$0.958994\pi$
$884$	−288042.	−	306098.i	−0.368596	−	0.391702i
$885$		0			0
$886$	90247.5	−	336808.i	0.114966	−	0.429057i
$887$	−661285.	−	1.14538e6i	−0.840507	−	1.45580i	−0.889466	−	0.457001i	$-0.848924\pi$
$887$	−661285.	−	1.14538e6i	−0.840507	−	1.45580i	0.0489590	−	0.998801i	$-0.484410\pi$
$888$		0			0
$889$	246283.	+	246283.i	0.311625	+	0.311625i
$890$	63303.7	−	16962.2i	0.0799189	−	0.0214142i
$891$		0			0
$892$	21753.0	−	21753.0i	0.0273394	−	0.0273394i
$893$	47728.5	−	82668.2i	0.0598515	−	0.103666i
$894$		0			0
$895$	107334.	+	28760.1i	0.133996	+	0.0359041i
$896$		−	1.61784e6i		−	2.01520i
$897$		0			0
$898$	−825892.			−1.02417
$899$	61791.4	−	230609.i	0.0764554	−	0.285336i
$900$		0			0
$901$	−14645.0	−	8455.27i	−0.0180401	−	0.0104154i
$902$	776824.	+	776824.i	0.954794	+	0.954794i
$903$		0			0
$904$	82453.6	+	307721.i	0.100896	+	0.376548i
$905$	84054.6	−	84054.6i	0.102628	−	0.102628i
$906$		0			0
$907$	−1.13720e6	+	656563.i	−1.38236	+	0.798108i	−0.992439	−	0.122738i	$-0.960832\pi$
$907$	−1.13720e6	+	656563.i	−1.38236	+	0.798108i	−0.389925	+	0.920847i	$0.627499\pi$
$908$	1.69384e6	+	453864.i	2.05448	+	0.550496i
$909$		0			0
$910$	609733.	+	377177.i	0.736304	+	0.455473i
$911$	773793.			0.932370			0.466185	−	0.884687i	$-0.345628\pi$
$911$	773793.			0.932370			0.466185	+	0.884687i	$0.345628\pi$
$912$		0			0
$913$	209731.	+	363264.i	0.251605	+	0.435793i
$914$	951179.	+	549164.i	1.13860	+	0.657369i
$915$		0			0
$916$	1.48321e6	−	397426.i	1.76772	−	0.473659i
$917$	434704.	+	1.62234e6i	0.516957	+	1.92931i
$918$		0			0
$919$	6404.07	−	11092.2i	0.00758272	−	0.0131337i	−0.862209	−	0.506552i	$-0.830920\pi$
$919$	6404.07	−	11092.2i	0.00758272	−	0.0131337i	0.869792	+	0.493419i	$0.164253\pi$
$920$	−109568.	+	63259.1i	−0.129452	+	0.0747390i
$921$		0			0
$922$			1.94166e6i			2.28408i
$923$	−1.07169e6	+	576066.i	−1.25796	+	0.676190i
$924$		0			0
$925$	−54441.5	+	203178.i	−0.0636277	+	0.237462i
$926$	1.04109e6	+	1.80323e6i	1.21414	+	2.10295i
$927$		0			0
$928$	−270038.	−	270038.i	−0.313566	−	0.313566i
$929$	552161.	−	147951.i	0.639786	−	0.171430i	0.0756793	−	0.997132i	$-0.475887\pi$
$929$	552161.	−	147951.i	0.639786	−	0.171430i	0.564106	+	0.825702i	$0.309221\pi$
$930$		0			0
$931$	116636.	−	116636.i	0.134565	−	0.134565i
$932$	−1.00194e6	+	1.73540e6i	−1.15347	+	1.99788i
$933$		0			0
$934$	1.79448e6	+	480829.i	2.05705	+	0.551184i
$935$		−	116138.i		−	0.132847i
$936$		0			0
$937$	−763773.			−0.869931			−0.434966	−	0.900447i	$-0.643239\pi$
$937$	−763773.			−0.869931			−0.434966	+	0.900447i	$0.643239\pi$
$938$	805915.	−	3.00771e6i	0.915975	−	3.41846i
$939$		0			0
$940$	486108.	+	280655.i	0.550145	+	0.317627i
$941$	−408742.	−	408742.i	−0.461604	−	0.461604i	0.437577	−	0.899181i	$-0.355837\pi$
$941$	−408742.	−	408742.i	−0.461604	−	0.461604i	−0.899181	+	0.437577i	$0.855837\pi$
$942$		0			0
$943$	149735.	+	558818.i	0.168383	+	0.628415i
$944$	148065.	−	148065.i	0.166153	−	0.166153i
$945$		0			0
$946$	31460.9	−	18164.0i	0.0351552	−	0.0202969i
$947$	−70724.2	−	18950.5i	−0.0788620	−	0.0211310i	0.219172	−	0.975686i	$-0.429664\pi$
$947$	−70724.2	−	18950.5i	−0.0788620	−	0.0211310i	−0.298034	+	0.954555i	$0.596331\pi$
$948$		0			0
$949$	484925.	−	783915.i	0.538446	−	0.870436i
$950$	−100073.			−0.110884
$951$		0			0
$952$	−191707.	−	332046.i	−0.211526	−	0.366374i
$953$	−896707.	−	517714.i	−0.987335	−	0.570038i	−0.0828585	−	0.996561i	$-0.526405\pi$
$953$	−896707.	−	517714.i	−0.987335	−	0.570038i	−0.904477	+	0.426523i	$0.859738\pi$
$954$		0			0
$955$	152966.	−	40987.0i	0.167721	−	0.0449406i
$956$	433807.	+	1.61899e6i	0.474658	+	1.77145i
$957$		0			0
$958$	−661356.	+	1.14550e6i	−0.720617	+	1.24815i
$959$	−2.34551e6	+	1.35418e6i	−2.55035	+	1.47245i
$960$		0			0
$961$		−	211163.i		−	0.228650i
$962$	−111438.	+	370488.i	−0.120416	+	0.400335i
$963$		0			0
$964$	−148412.	+	553881.i	−0.159704	+	0.596022i
$965$	−186391.	−	322838.i	−0.200156	−	0.346681i
$966$		0			0
$967$	−191562.	−	191562.i	−0.204860	−	0.204860i	0.597219	−	0.802078i	$-0.296272\pi$
$967$	−191562.	−	191562.i	−0.204860	−	0.204860i	−0.802078	+	0.597219i	$0.796272\pi$
$968$	138359.	−	37073.3i	0.147658	−	0.0395649i
$969$		0			0
$970$	−234980.	+	234980.i	−0.249740	+	0.249740i
$971$	−544139.	+	942477.i	−0.577127	+	0.999614i	0.418680	+	0.908134i	$0.362493\pi$
$971$	−544139.	+	942477.i	−0.577127	+	0.999614i	−0.995807	+	0.0914796i	$0.970840\pi$
$972$		0			0
$973$	−1.32669e6	−	355485.i	−1.40134	−	0.375488i
$974$			355968.i			0.375226i
$975$		0			0
$976$	−258550.			−0.271421
$977$	1357.53	−	5066.37i	0.00142220	−	0.00530771i	−0.965211	−	0.261472i	$-0.915792\pi$
$977$	1357.53	−	5066.37i	0.00142220	−	0.00530771i	0.966633	+	0.256164i	$0.0824588\pi$
$978$		0			0
$979$	−164234.	−	94820.8i	−0.171356	−	0.0989323i
$980$	685846.	+	685846.i	0.714125	+	0.714125i
$981$		0			0
$982$	−626028.	−	2.33637e6i	−0.649189	−	2.42280i
$983$	−779317.	+	779317.i	−0.806505	+	0.806505i	−0.984103	−	0.177598i	$-0.943167\pi$
$983$	−779317.	+	779317.i	−0.806505	+	0.806505i	0.177598	+	0.984103i	$0.443167\pi$
$984$		0			0
$985$	−419594.	+	242253.i	−0.432471	+	0.249687i
$986$	−189751.	−	50843.6i	−0.195178	−	0.0522977i
$987$		0			0
$988$	−106731.	−	3243.52i	−0.109340	−	0.00332279i
$989$	19130.7			0.0195586
$990$		0			0
$991$	−67246.2	−	116474.i	−0.0684732	−	0.118599i	0.829756	−	0.558126i	$-0.188479\pi$
$991$	−67246.2	−	116474.i	−0.0684732	−	0.118599i	−0.898229	+	0.439527i	$0.855146\pi$
$992$	986819.	+	569740.i	1.00280	+	0.578967i
$993$		0			0
$994$	−3.88077e6	+	1.03985e6i	−3.92777	+	1.05244i
$995$	48602.2	+	181386.i	0.0490919	+	0.183213i
$996$		0			0
$997$	−949605.	+	1.64476e6i	−0.955329	+	1.65468i	−0.221715	+	0.975112i	$0.571165\pi$
$997$	−949605.	+	1.64476e6i	−0.955329	+	1.65468i	−0.733614	+	0.679567i	$0.762168\pi$
$998$	372403.	−	215007.i	0.373897	−	0.215870i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.5.bd.c.37.1		16
3.2	odd	2		13.5.f.a.11.4	yes	16
13.6	odd	12	inner	117.5.bd.c.19.1		16
39.2	even	12		169.5.d.d.70.7		16
39.11	even	12		169.5.d.c.70.2		16
39.23	odd	6		169.5.d.c.99.2		16
39.29	odd	6		169.5.d.d.99.7		16
39.32	even	12		13.5.f.a.6.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.6.4	✓	16	39.32	even	12
13.5.f.a.11.4	yes	16	3.2	odd	2
117.5.bd.c.19.1		16	13.6	odd	12	inner
117.5.bd.c.37.1		16	1.1	even	1	trivial
169.5.d.c.70.2		16	39.11	even	12
169.5.d.c.99.2		16	39.23	odd	6
169.5.d.d.70.7		16	39.2	even	12
169.5.d.d.99.7		16	39.29	odd	6

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	117.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59772 + 5.96275i) q^{2} +(-19.1453 - 11.0536i) q^{4} +(5.37551 + 5.37551i) q^{5} +(23.3974 + 87.3205i) q^{7} +(26.6579 - 26.6579i) q^{8} +O(q^{10})\)	\(q+(-1.59772 + 5.96275i) q^{2} +(-19.1453 - 11.0536i) q^{4} +(5.37551 + 5.37551i) q^{5} +(23.3974 + 87.3205i) q^{7} +(26.6579 - 26.6579i) q^{8} +(-40.6414 + 23.4643i) q^{10} +(131.169 + 35.1465i) q^{11} +(-164.495 + 38.7617i) q^{13} -558.053 q^{14} +(-60.4944 - 104.779i) q^{16} +(-97.4284 - 56.2503i) q^{17} +(-27.6068 + 7.39723i) q^{19} +(-43.4974 - 162.335i) q^{20} +(-419.140 + 725.972i) q^{22} +(-382.304 + 220.723i) q^{23} -567.208i q^{25} +(31.6895 - 1042.77i) q^{26} +(517.250 - 1930.41i) q^{28} +(-141.434 - 244.970i) q^{29} +(596.807 + 596.807i) q^{31} +(1304.07 - 349.425i) q^{32} +(491.070 - 491.070i) q^{34} +(-343.619 + 595.166i) q^{35} +(-358.208 - 95.9816i) q^{37} -176.431i q^{38} +286.599 q^{40} +(339.191 - 1265.88i) q^{41} +(-37.5303 - 21.6682i) q^{43} +(-2122.77 - 2122.77i) q^{44} +(-705.305 - 2632.24i) q^{46} +(-2361.67 + 2361.67i) q^{47} +(-4998.10 + 2885.65i) q^{49} +(3382.12 + 906.236i) q^{50} +(3577.76 + 1076.15i) q^{52} +150.315 q^{53} +(516.168 + 894.029i) q^{55} +(2951.50 + 1704.05i) q^{56} +(1686.67 - 451.941i) q^{58} +(447.938 + 1671.73i) q^{59} +(1068.49 - 1850.67i) q^{61} +(-4512.14 + 2605.09i) q^{62} +6398.32i q^{64} +(-1092.61 - 675.880i) q^{65} +(-1444.15 + 5389.66i) q^{67} +(1243.53 + 2153.86i) q^{68} +(-2999.82 - 2999.82i) q^{70} +(6954.13 - 1863.35i) q^{71} +(-3856.78 + 3856.78i) q^{73} +(1144.63 - 1982.56i) q^{74} +(610.308 + 163.531i) q^{76} +12276.0i q^{77} +9010.15 q^{79} +(238.055 - 888.432i) q^{80} +(7006.20 + 4045.03i) q^{82} +(2184.19 + 2184.19i) q^{83} +(-221.353 - 826.102i) q^{85} +(189.165 - 189.165i) q^{86} +(4433.61 - 2559.74i) q^{88} +(-1348.94 - 361.446i) q^{89} +(-7233.45 - 13456.8i) q^{91} +9759.11 q^{92} +(-10308.8 - 17855.4i) q^{94} +(-188.165 - 108.637i) q^{95} +(6839.94 - 1832.76i) q^{97} +(-9220.90 - 34412.9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 6 q^{4} - 8 q^{5} + 56 q^{7} - 90 q^{8}+O(q^{10}) \) 16 * q + 4 * q^2 - 6 * q^4 - 8 * q^5 + 56 * q^7 - 90 * q^8	\( 16 q + 4 q^{2} - 6 q^{4} - 8 q^{5} + 56 q^{7} - 90 q^{8} - 486 q^{10} + 100 q^{11} + 294 q^{13} - 808 q^{14} + 230 q^{16} - 984 q^{17} - 1498 q^{19} + 3962 q^{20} - 1524 q^{22} + 1014 q^{23} - 614 q^{26} + 5764 q^{28} - 814 q^{29} + 4060 q^{31} + 4996 q^{32} - 2502 q^{34} + 4892 q^{35} - 1790 q^{37} + 18816 q^{40} - 4280 q^{41} - 1368 q^{43} - 10736 q^{44} - 15246 q^{46} - 1484 q^{47} - 11820 q^{49} + 13574 q^{50} + 1432 q^{52} - 7204 q^{53} + 6936 q^{55} - 8124 q^{56} + 3030 q^{58} + 2380 q^{59} - 162 q^{61} - 19614 q^{62} + 5248 q^{65} - 14854 q^{67} + 6444 q^{68} - 34524 q^{70} + 8050 q^{71} - 15448 q^{73} + 2882 q^{74} + 10622 q^{76} - 17064 q^{79} - 2564 q^{80} - 5346 q^{82} - 12788 q^{83} + 35382 q^{85} - 67260 q^{86} + 40836 q^{88} - 20492 q^{89} + 8996 q^{91} + 49884 q^{92} - 30606 q^{94} + 98574 q^{95} + 50944 q^{97} - 61484 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 6 * q^4 - 8 * q^5 + 56 * q^7 - 90 * q^8 - 486 * q^10 + 100 * q^11 + 294 * q^13 - 808 * q^14 + 230 * q^16 - 984 * q^17 - 1498 * q^19 + 3962 * q^20 - 1524 * q^22 + 1014 * q^23 - 614 * q^26 + 5764 * q^28 - 814 * q^29 + 4060 * q^31 + 4996 * q^32 - 2502 * q^34 + 4892 * q^35 - 1790 * q^37 + 18816 * q^40 - 4280 * q^41 - 1368 * q^43 - 10736 * q^44 - 15246 * q^46 - 1484 * q^47 - 11820 * q^49 + 13574 * q^50 + 1432 * q^52 - 7204 * q^53 + 6936 * q^55 - 8124 * q^56 + 3030 * q^58 + 2380 * q^59 - 162 * q^61 - 19614 * q^62 + 5248 * q^65 - 14854 * q^67 + 6444 * q^68 - 34524 * q^70 + 8050 * q^71 - 15448 * q^73 + 2882 * q^74 + 10622 * q^76 - 17064 * q^79 - 2564 * q^80 - 5346 * q^82 - 12788 * q^83 + 35382 * q^85 - 67260 * q^86 + 40836 * q^88 - 20492 * q^89 + 8996 * q^91 + 49884 * q^92 - 30606 * q^94 + 98574 * q^95 + 50944 * q^97 - 61484 * q^98

Introduction

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