LMFDB - Embedded newform 315.5.h.a.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,5,Mod(181,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("315.181");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	315.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.5615383714$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 109 x^{10} + 570 x^{9} + 5814 x^{8} - 22512 x^{7} - 151120 x^{6} + 300288 x^{5} + \cdots + 205833600 $ x^12 - 6x^11 - 109x^10 + 570x^9 + 5814x^8 - 22512x^7 - 151120x^6 + 300288x^5 + 2661184x^4 - 1881600x^3 - 12922560x^2 + 25948800*x + 205833600
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3}\cdot 5^{5} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.2
Root			$7.50299 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	315.181
Dual form			315.5.h.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.50299 q^{2} +26.2889 q^{4} +11.1803i q^{5} +(-19.9894 + 44.7373i) q^{7} -66.9085 q^{8} +O(q^{10})$	\(q-6.50299 q^{2} +26.2889 q^{4} +11.1803i q^{5} +(-19.9894 + 44.7373i) q^{7} -66.9085 q^{8} -72.7056i q^{10} +105.424 q^{11} +234.089i q^{13} +(129.991 - 290.926i) q^{14} +14.4831 q^{16} +375.251i q^{17} +45.1673i q^{19} +293.919i q^{20} -685.571 q^{22} -46.3674 q^{23} -125.000 q^{25} -1522.28i q^{26} +(-525.500 + 1176.09i) q^{28} +257.421 q^{29} -194.899i q^{31} +976.352 q^{32} -2440.26i q^{34} +(-500.178 - 223.489i) q^{35} +2523.02 q^{37} -293.723i q^{38} -748.060i q^{40} +2504.06i q^{41} +2288.24 q^{43} +2771.48 q^{44} +301.527 q^{46} -2624.74i q^{47} +(-1601.84 - 1788.55i) q^{49} +812.874 q^{50} +6153.94i q^{52} +358.663 q^{53} +1178.68i q^{55} +(1337.46 - 2993.30i) q^{56} -1674.01 q^{58} -854.723i q^{59} -2085.25i q^{61} +1267.43i q^{62} -6580.94 q^{64} -2617.20 q^{65} -7558.23 q^{67} +9864.94i q^{68} +(3252.65 + 1453.34i) q^{70} +282.660 q^{71} +9190.85i q^{73} -16407.2 q^{74} +1187.40i q^{76} +(-2107.37 + 4716.38i) q^{77} -7184.60 q^{79} +161.926i q^{80} -16283.9i q^{82} +5064.74i q^{83} -4195.44 q^{85} -14880.4 q^{86} -7053.76 q^{88} -10243.7i q^{89} +(-10472.5 - 4679.31i) q^{91} -1218.95 q^{92} +17068.6i q^{94} -504.986 q^{95} -608.860i q^{97} +(10416.8 + 11630.9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 122 q^{4} - 50 q^{7} + 186 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 122 * q^4 - 50 * q^7 + 186 * q^8	$ 12 q + 6 q^{2} + 122 q^{4} - 50 q^{7} + 186 q^{8} - 126 q^{11} - 78 q^{14} + 578 q^{16} + 2264 q^{22} + 756 q^{23} - 1500 q^{25} + 1414 q^{28} + 2190 q^{29} + 8682 q^{32} + 150 q^{35} + 5564 q^{37} + 3944 q^{43} + 11196 q^{44} + 7844 q^{46} - 8796 q^{49} - 750 q^{50} - 11760 q^{53} + 6606 q^{56} - 18496 q^{58} + 20146 q^{64} + 750 q^{65} - 24096 q^{67} + 14400 q^{70} + 5664 q^{71} - 17604 q^{74} - 26904 q^{77} - 1590 q^{79} + 1050 q^{85} - 17604 q^{86} - 7268 q^{88} - 7182 q^{91} + 60252 q^{92} + 3000 q^{95} - 57714 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 122 * q^4 - 50 * q^7 + 186 * q^8 - 126 * q^11 - 78 * q^14 + 578 * q^16 + 2264 * q^22 + 756 * q^23 - 1500 * q^25 + 1414 * q^28 + 2190 * q^29 + 8682 * q^32 + 150 * q^35 + 5564 * q^37 + 3944 * q^43 + 11196 * q^44 + 7844 * q^46 - 8796 * q^49 - 750 * q^50 - 11760 * q^53 + 6606 * q^56 - 18496 * q^58 + 20146 * q^64 + 750 * q^65 - 24096 * q^67 + 14400 * q^70 + 5664 * q^71 - 17604 * q^74 - 26904 * q^77 - 1590 * q^79 + 1050 * q^85 - 17604 * q^86 - 7268 * q^88 - 7182 * q^91 + 60252 * q^92 + 3000 * q^95 - 57714 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−6.50299			−1.62575			−0.812874	−	0.582440i	$-0.802098\pi$
$2$	−6.50299			−1.62575			−0.812874	+	0.582440i	$0.802098\pi$
$3$		0			0
$3$		0			0
$4$	26.2889			1.64305
$5$			11.1803i			0.447214i
$5$			11.1803i			0.447214i
$6$		0			0
$7$	−19.9894	+	44.7373i	−0.407948	+	0.913005i
$7$	−19.9894	+	44.7373i	−0.407948	+	0.913005i
$8$	−66.9085			−1.04545
$9$		0			0
$10$		−	72.7056i		−	0.727056i
$11$	105.424			0.871273			0.435636	−	0.900123i	$-0.356523\pi$
$11$	105.424			0.871273			0.435636	+	0.900123i	$0.356523\pi$
$12$		0			0
$13$			234.089i			1.38514i	0.721349	+	0.692571i	$0.243522\pi$
$13$			234.089i			1.38514i	−0.721349	+	0.692571i	$0.756478\pi$
$14$	129.991	−	290.926i	0.663220	−	1.48432i
$15$		0			0
$16$	14.4831			0.0565747
$17$			375.251i			1.29845i	0.760597	+	0.649224i	$0.224906\pi$
$17$			375.251i			1.29845i	−0.760597	+	0.649224i	$0.775094\pi$
$18$		0			0
$19$			45.1673i			0.125117i	0.998041	+	0.0625586i	$0.0199260\pi$
$19$			45.1673i			0.125117i	−0.998041	+	0.0625586i	$0.980074\pi$
$20$			293.919i			0.734797i
$21$		0			0
$22$	−685.571			−1.41647
$23$	−46.3674			−0.0876510			−0.0438255	−	0.999039i	$-0.513955\pi$
$23$	−46.3674			−0.0876510			−0.0438255	+	0.999039i	$0.513955\pi$
$24$		0			0
$25$	−125.000			−0.200000
$26$		−	1522.28i		−	2.25189i
$27$		0			0
$28$	−525.500	+	1176.09i	−0.670280	+	1.50012i
$29$	257.421			0.306089			0.153045	−	0.988219i	$-0.451092\pi$
$29$	257.421			0.306089			0.153045	+	0.988219i	$0.451092\pi$
$30$		0			0
$31$		−	194.899i		−	0.202809i	−0.994845	−	0.101404i	$-0.967666\pi$
$31$		−	194.899i		−	0.202809i	0.994845	−	0.101404i	$-0.0323336\pi$
$32$	976.352			0.953469
$33$		0			0
$34$		−	2440.26i		−	2.11095i
$35$	−500.178	−	223.489i	−0.408308	−	0.182440i
$36$		0			0
$37$	2523.02			1.84296			0.921482	−	0.388421i	$-0.126979\pi$
$37$	2523.02			1.84296			0.921482	+	0.388421i	$0.126979\pi$
$38$		−	293.723i		−	0.203409i
$39$		0			0
$40$		−	748.060i		−	0.467537i
$41$			2504.06i			1.48963i	0.667274	+	0.744813i	$0.267461\pi$
$41$			2504.06i			1.48963i	−0.667274	+	0.744813i	$0.732539\pi$
$42$		0			0
$43$	2288.24			1.23756			0.618779	−	0.785565i	$-0.287628\pi$
$43$	2288.24			1.23756			0.618779	+	0.785565i	$0.287628\pi$
$44$	2771.48			1.43155
$45$		0			0
$46$	301.527			0.142498
$47$		−	2624.74i		−	1.18820i	−0.804391	−	0.594101i	$-0.797508\pi$
$47$		−	2624.74i		−	1.18820i	0.804391	−	0.594101i	$-0.202492\pi$
$48$		0			0
$49$	−1601.84	−	1788.55i	−0.667157	−	0.744917i
$50$	812.874			0.325150
$51$		0			0
$52$			6153.94i			2.27587i
$53$	358.663			0.127683			0.0638417	−	0.997960i	$-0.479665\pi$
$53$	358.663			0.127683			0.0638417	+	0.997960i	$0.479665\pi$
$54$		0			0
$55$			1178.68i			0.389645i
$56$	1337.46	−	2993.30i	0.426487	−	0.954497i
$57$		0			0
$58$	−1674.01			−0.497624
$59$		−	854.723i		−	0.245540i	−0.992435	−	0.122770i	$-0.960822\pi$
$59$		−	854.723i		−	0.245540i	0.992435	−	0.122770i	$-0.0391777\pi$
$60$		0			0
$61$		−	2085.25i		−	0.560400i	−0.959942	−	0.280200i	$-0.909599\pi$
$61$		−	2085.25i		−	0.560400i	0.959942	−	0.280200i	$-0.0904007\pi$
$62$			1267.43i			0.329716i
$63$		0			0
$64$	−6580.94			−1.60667
$65$	−2617.20			−0.619455
$66$		0			0
$67$	−7558.23			−1.68372			−0.841862	−	0.539693i	$-0.818540\pi$
$67$	−7558.23			−1.68372			−0.841862	+	0.539693i	$0.818540\pi$
$68$			9864.94i			2.13342i
$69$		0			0
$70$	3252.65	+	1453.34i	0.663806	+	0.296601i
$71$	282.660			0.0560722			0.0280361	−	0.999607i	$-0.491075\pi$
$71$	282.660			0.0560722			0.0280361	+	0.999607i	$0.491075\pi$
$72$		0			0
$73$			9190.85i			1.72469i	0.506325	+	0.862343i	$0.331004\pi$
$73$			9190.85i			1.72469i	−0.506325	+	0.862343i	$0.668996\pi$
$74$	−16407.2			−2.99619
$75$		0			0
$76$			1187.40i			0.205575i
$77$	−2107.37	+	4716.38i	−0.355434	+	0.795477i
$78$		0			0
$79$	−7184.60			−1.15119			−0.575597	−	0.817734i	$-0.695230\pi$
$79$	−7184.60			−1.15119			−0.575597	+	0.817734i	$0.695230\pi$
$80$			161.926i			0.0253010i
$81$		0			0
$82$		−	16283.9i		−	2.42175i
$83$			5064.74i			0.735192i	0.929986	+	0.367596i	$0.119819\pi$
$83$			5064.74i			0.735192i	−0.929986	+	0.367596i	$0.880181\pi$
$84$		0			0
$85$	−4195.44			−0.580683
$86$	−14880.4			−2.01196
$87$		0			0
$88$	−7053.76			−0.910868
$89$		−	10243.7i		−	1.29323i	−0.762817	−	0.646614i	$-0.776184\pi$
$89$		−	10243.7i		−	1.29323i	0.762817	−	0.646614i	$-0.223816\pi$
$90$		0			0
$91$	−10472.5	−	4679.31i	−1.26464	−	0.565066i
$92$	−1218.95			−0.144015
$93$		0			0
$94$			17068.6i			1.93172i
$95$	−504.986			−0.0559541
$96$		0			0
$97$		−	608.860i		−	0.0647104i	−0.999476	−	0.0323552i	$-0.989699\pi$
$97$		−	608.860i		−	0.0647104i	0.999476	−	0.0323552i	$-0.0103008\pi$
$98$	10416.8	+	11630.9i	1.08463	+	1.21105i
$99$		0			0
$100$	−3286.11			−0.328611
$101$			14966.3i			1.46714i	0.679616	+	0.733568i	$0.262146\pi$
$101$			14966.3i			1.46714i	−0.679616	+	0.733568i	$0.737854\pi$
$102$		0			0
$103$			18840.1i			1.77586i	0.459979	+	0.887930i	$0.347857\pi$
$103$			18840.1i			1.77586i	−0.459979	+	0.887930i	$0.652143\pi$
$104$		−	15662.5i		−	1.44809i
$105$		0			0
$106$	−2332.38			−0.207581
$107$	−3903.78			−0.340971			−0.170485	−	0.985360i	$-0.554534\pi$
$107$	−3903.78			−0.340971			−0.170485	+	0.985360i	$0.554534\pi$
$108$		0			0
$109$	16429.7			1.38285			0.691427	−	0.722447i	$-0.256982\pi$
$109$	16429.7			1.38285			0.691427	+	0.722447i	$0.256982\pi$
$110$		−	7664.92i		−	0.633464i
$111$		0			0
$112$	−289.510	+	647.935i	−0.0230795	+	0.0516530i
$113$	−19430.8			−1.52172			−0.760858	−	0.648918i	$-0.775222\pi$
$113$	−19430.8			−1.52172			−0.760858	+	0.648918i	$0.775222\pi$
$114$		0			0
$115$		−	518.403i		−	0.0391987i
$116$	6767.31			0.502922
$117$		0			0
$118$			5558.26i			0.399185i
$119$	−16787.7	−	7501.06i	−1.18549	−	0.529699i
$120$		0			0
$121$	−3526.78			−0.240884
$122$			13560.3i			0.911068i
$123$		0			0
$124$		−	5123.68i		−	0.333226i
$125$		−	1397.54i		−	0.0894427i
$126$		0			0
$127$	−3473.63			−0.215365			−0.107683	−	0.994185i	$-0.534343\pi$
$127$	−3473.63			−0.215365			−0.107683	+	0.994185i	$0.534343\pi$
$128$	27174.1			1.65858
$129$		0			0
$130$	17019.6			1.00708
$131$		−	5214.48i		−	0.303856i	−0.988392	−	0.151928i	$-0.951452\pi$
$131$		−	5214.48i		−	0.303856i	0.988392	−	0.151928i	$-0.0485482\pi$
$132$		0			0
$133$	−2020.66	−	902.870i	−0.114233	−	0.0510413i
$134$	49151.1			2.73731
$135$		0			0
$136$		−	25107.5i		−	1.35746i
$137$	−25017.6			−1.33292			−0.666461	−	0.745540i	$-0.732192\pi$
$137$	−25017.6			−1.33292			−0.666461	+	0.745540i	$0.732192\pi$
$138$		0			0
$139$		−	9723.25i		−	0.503248i	−0.967825	−	0.251624i	$-0.919035\pi$
$139$		−	9723.25i		−	0.503248i	0.967825	−	0.251624i	$-0.0809646\pi$
$140$	−13149.1	−	5875.27i	−0.670873	−	0.299759i
$141$		0			0
$142$	−1838.14			−0.0911593
$143$			24678.6i			1.20684i
$144$		0			0
$145$			2878.06i			0.136887i
$146$		−	59768.0i		−	2.80390i
$147$		0			0
$148$	66327.3			3.02809
$149$	−4969.64			−0.223847			−0.111924	−	0.993717i	$-0.535701\pi$
$149$	−4969.64			−0.223847			−0.111924	+	0.993717i	$0.535701\pi$
$150$		0			0
$151$	−15572.0			−0.682954			−0.341477	−	0.939890i	$-0.610927\pi$
$151$	−15572.0			−0.682954			−0.341477	+	0.939890i	$0.610927\pi$
$152$		−	3022.08i		−	0.130803i
$153$		0			0
$154$	13704.2	−	30670.6i	0.577845	−	1.29324i
$155$	2179.04			0.0906988
$156$		0			0
$157$		−	2245.97i		−	0.0911180i	−0.998962	−	0.0455590i	$-0.985493\pi$
$157$		−	2245.97i		−	0.0911180i	0.998962	−	0.0455590i	$-0.0145069\pi$
$158$	46721.4			1.87155
$159$		0			0
$160$			10915.9i			0.426404i
$161$	926.858	−	2074.35i	0.0357570	−	0.0800259i
$162$		0			0
$163$	27048.4			1.01804			0.509021	−	0.860754i	$-0.330007\pi$
$163$	27048.4			1.01804			0.509021	+	0.860754i	$0.330007\pi$
$164$			65828.9i			2.44754i
$165$		0			0
$166$		−	32936.0i		−	1.19524i
$167$		−	36693.5i		−	1.31570i	−0.753149	−	0.657849i	$-0.771466\pi$
$167$		−	36693.5i		−	1.31570i	0.753149	−	0.657849i	$-0.228534\pi$
$168$		0			0
$169$	−26236.7			−0.918620
$170$	27282.9			0.944045
$171$		0			0
$172$	60155.4			2.03338
$173$		−	3132.59i		−	0.104667i	−0.998630	−	0.0523337i	$-0.983334\pi$
$173$		−	3132.59i		−	0.104667i	0.998630	−	0.0523337i	$-0.0166660\pi$
$174$		0			0
$175$	2498.68	−	5592.16i	0.0815895	−	0.182601i
$176$	1526.87			0.0492920
$177$		0			0
$178$			66614.4i			2.10246i
$179$	25816.5			0.805732			0.402866	−	0.915259i	$-0.368014\pi$
$179$	25816.5			0.805732			0.402866	+	0.915259i	$0.368014\pi$
$180$		0			0
$181$		−	31614.4i		−	0.965002i	−0.875895	−	0.482501i	$-0.839728\pi$
$181$		−	31614.4i		−	0.965002i	0.875895	−	0.482501i	$-0.160272\pi$
$182$	68102.6	+	30429.5i	2.05599	+	0.918654i
$183$		0			0
$184$	3102.37			0.0916343
$185$			28208.2i			0.824199i
$186$		0			0
$187$			39560.5i			1.13130i
$188$		−	69001.4i		−	1.95228i
$189$		0			0
$190$	3283.92			0.0909673
$191$	4727.49			0.129588			0.0647938	−	0.997899i	$-0.479361\pi$
$191$	4727.49			0.129588			0.0647938	+	0.997899i	$0.479361\pi$
$192$		0			0
$193$	−36953.1			−0.992057			−0.496028	−	0.868306i	$-0.665209\pi$
$193$	−36953.1			−0.992057			−0.496028	+	0.868306i	$0.665209\pi$
$194$			3959.41i			0.105203i
$195$		0			0
$196$	−42110.7	−	47018.8i	−1.09618	−	1.22394i
$197$	3222.40			0.0830322			0.0415161	−	0.999138i	$-0.486781\pi$
$197$	3222.40			0.0830322			0.0415161	+	0.999138i	$0.486781\pi$
$198$		0			0
$199$			51984.5i			1.31271i	0.754453	+	0.656354i	$0.227902\pi$
$199$			51984.5i			1.31271i	−0.754453	+	0.656354i	$0.772098\pi$
$200$	8363.56			0.209089
$201$		0			0
$202$		−	97325.4i		−	2.38519i
$203$	−5145.70	+	11516.3i	−0.124868	+	0.279461i
$204$		0			0
$205$	−27996.2			−0.666181
$206$		−	122517.i		−	2.88710i
$207$		0			0
$208$			3390.34i			0.0783641i
$209$			4761.72i			0.109011i
$210$		0			0
$211$	−15750.2			−0.353770			−0.176885	−	0.984232i	$-0.556602\pi$
$211$	−15750.2			−0.353770			−0.176885	+	0.984232i	$0.556602\pi$
$212$	9428.84			0.209791
$213$		0			0
$214$	25386.2			0.554333
$215$			25583.3i			0.553453i
$216$		0			0
$217$	8719.26	+	3895.93i	0.185165	+	0.0827354i
$218$	−106842.			−2.24817
$219$		0			0
$220$			30986.1i			0.640208i
$221$	−87842.3			−1.79854
$222$		0			0
$223$			11942.3i			0.240148i	0.992765	+	0.120074i	$0.0383133\pi$
$223$			11942.3i			0.240148i	−0.992765	+	0.120074i	$0.961687\pi$
$224$	−19516.7	+	43679.3i	−0.388965	+	0.870522i
$225$		0			0
$226$	126358.			2.47393
$227$			79946.4i			1.55148i	0.631051	+	0.775742i	$0.282624\pi$
$227$			79946.4i			1.55148i	−0.631051	+	0.775742i	$0.717376\pi$
$228$		0			0
$229$		−	40487.1i		−	0.772050i	−0.922488	−	0.386025i	$-0.873848\pi$
$229$		−	40487.1i		−	0.772050i	0.922488	−	0.386025i	$-0.126152\pi$
$230$			3371.17i			0.0637272i
$231$		0			0
$232$	−17223.7			−0.320000
$233$	40236.2			0.741148			0.370574	−	0.928803i	$-0.379161\pi$
$233$	40236.2			0.741148			0.370574	+	0.928803i	$0.379161\pi$
$234$		0			0
$235$	29345.5			0.531380
$236$		−	22469.7i		−	0.403435i
$237$		0			0
$238$	109170.	+	48779.3i	1.92731	+	0.861156i
$239$	12346.0			0.216137			0.108069	−	0.994143i	$-0.465533\pi$
$239$	12346.0			0.216137			0.108069	+	0.994143i	$0.465533\pi$
$240$		0			0
$241$		−	20969.2i		−	0.361034i	−0.983572	−	0.180517i	$-0.942223\pi$
$241$		−	20969.2i		−	0.361034i	0.983572	−	0.180517i	$-0.0577771\pi$
$242$	22934.6			0.391616
$243$		0			0
$244$		−	54818.8i		−	0.920767i
$245$	19996.5	−	17909.2i	0.333137	−	0.298362i
$246$		0			0
$247$	−10573.2			−0.173305
$248$			13040.4i			0.212025i
$249$		0			0
$250$			9088.20i			0.145411i
$251$		−	82331.2i		−	1.30682i	−0.757003	−	0.653411i	$-0.773337\pi$
$251$		−	82331.2i		−	1.30682i	0.757003	−	0.653411i	$-0.226663\pi$
$252$		0			0
$253$	−4888.24			−0.0763680
$254$	22589.0			0.350130
$255$		0			0
$256$	−71418.2			−1.08975
$257$		−	6751.23i		−	0.102216i	−0.998693	−	0.0511078i	$-0.983725\pi$
$257$		−	6751.23i		−	0.102216i	0.998693	−	0.0511078i	$-0.0162752\pi$
$258$		0			0
$259$	−50433.7	+	112873.i	−0.751833	+	1.68264i
$260$	−68803.2			−1.01780
$261$		0			0
$262$			33909.7i			0.493994i
$263$	−23786.1			−0.343884			−0.171942	−	0.985107i	$-0.555004\pi$
$263$	−23786.1			−0.343884			−0.171942	+	0.985107i	$0.555004\pi$
$264$		0			0
$265$			4009.97i			0.0571018i
$266$	13140.4	+	5871.35i	0.185714	+	0.0829803i
$267$		0			0
$268$	−198697.			−2.76645
$269$			74052.1i			1.02337i	0.859173	+	0.511685i	$0.170979\pi$
$269$			74052.1i			1.02337i	−0.859173	+	0.511685i	$0.829021\pi$
$270$		0			0
$271$		−	61472.9i		−	0.837037i	−0.908208	−	0.418519i	$-0.862549\pi$
$271$		−	61472.9i		−	0.837037i	0.908208	−	0.418519i	$-0.137451\pi$
$272$			5434.81i			0.0734593i
$273$		0			0
$274$	162689.			2.16699
$275$	−13178.0			−0.174255
$276$		0			0
$277$	−73318.6			−0.955552			−0.477776	−	0.878482i	$-0.658557\pi$
$277$	−73318.6			−0.955552			−0.477776	+	0.878482i	$0.658557\pi$
$278$			63230.2i			0.818154i
$279$		0			0
$280$	33466.1	+	14953.3i	0.426864	+	0.190731i
$281$	63569.9			0.805080			0.402540	−	0.915403i	$-0.368128\pi$
$281$	63569.9			0.805080			0.402540	+	0.915403i	$0.368128\pi$
$282$		0			0
$283$		−	99674.3i		−	1.24454i	−0.782801	−	0.622272i	$-0.786210\pi$
$283$		−	99674.3i		−	1.24454i	0.782801	−	0.622272i	$-0.213790\pi$
$284$	7430.82			0.0921298
$285$		0			0
$286$		−	160485.i		−	1.96201i
$287$	−112025.	−	50054.7i	−1.36004	−	0.607689i
$288$		0			0
$289$	−57292.6			−0.685967
$290$		−	18716.0i		−	0.222544i
$291$		0			0
$292$			241617.i			2.83375i
$293$			33390.9i			0.388949i	0.980908	+	0.194475i	$0.0623002\pi$
$293$			33390.9i			0.388949i	−0.980908	+	0.194475i	$0.937700\pi$
$294$		0			0
$295$	9556.10			0.109809
$296$	−168811.			−1.92672
$297$		0			0
$298$	32317.5			0.363919
$299$		−	10854.1i		−	0.121409i
$300$		0			0
$301$	−45740.7	+	102370.i	−0.504859	+	1.12990i
$302$	101265.			1.11031
$303$		0			0
$304$			654.164i			0.00707847i
$305$	23313.8			0.250618
$306$		0			0
$307$		−	81081.7i		−	0.860292i	−0.902759	−	0.430146i	$-0.858462\pi$
$307$		−	81081.7i		−	0.860292i	0.902759	−	0.430146i	$-0.141538\pi$
$308$	−55400.3	+	123988.i	−0.583997	+	1.30701i
$309$		0			0
$310$	−14170.3			−0.147453
$311$			58811.2i			0.608050i	0.952664	+	0.304025i	$0.0983306\pi$
$311$			58811.2i			0.608050i	−0.952664	+	0.304025i	$0.901669\pi$
$312$		0			0
$313$			146677.i			1.49718i	0.663033	+	0.748590i	$0.269269\pi$
$313$			146677.i			1.49718i	−0.663033	+	0.748590i	$0.730731\pi$
$314$			14605.5i			0.148135i
$315$		0			0
$316$	−188875.			−1.89147
$317$	−106159.			−1.05642			−0.528210	−	0.849114i	$-0.677137\pi$
$317$	−106159.			−1.05642			−0.528210	+	0.849114i	$0.677137\pi$
$318$		0			0
$319$	27138.4			0.266687
$320$		−	73577.1i		−	0.718527i
$321$		0			0
$322$	−6027.35	+	13489.5i	−0.0581319	+	0.130102i
$323$	−16949.1			−0.162458
$324$		0			0
$325$		−	29261.1i		−	0.277029i
$326$	−175895.			−1.65508
$327$		0			0
$328$		−	167543.i		−	1.55732i
$329$	117424.	+	52467.0i	1.08483	+	0.484724i
$330$		0			0
$331$	−24297.3			−0.221769			−0.110885	−	0.993833i	$-0.535368\pi$
$331$	−24297.3			−0.221769			−0.110885	+	0.993833i	$0.535368\pi$
$332$			133146.i			1.20796i
$333$		0			0
$334$			238618.i			2.13899i
$335$		−	84503.6i		−	0.752984i
$336$		0			0
$337$	−170981.			−1.50553			−0.752763	−	0.658292i	$-0.771279\pi$
$337$	−170981.			−1.50553			−0.752763	+	0.658292i	$0.771279\pi$
$338$	170617.			1.49344
$339$		0			0
$340$	−110293.			−0.954095
$341$		−	20547.1i		−	0.176702i
$342$		0			0
$343$	112035.	−	35910.1i	0.952278	−	0.305231i
$344$	−153103.			−1.29380
$345$		0			0
$346$			20371.2i			0.170163i
$347$	202470.			1.68152			0.840761	−	0.541406i	$-0.182108\pi$
$347$	202470.			1.68152			0.840761	+	0.541406i	$0.182108\pi$
$348$		0			0
$349$			90133.9i			0.740009i	0.929030	+	0.370005i	$0.120644\pi$
$349$			90133.9i			0.740009i	−0.929030	+	0.370005i	$0.879356\pi$
$350$	−16248.9	+	36365.7i	−0.132644	+	0.296863i
$351$		0			0
$352$	102931.			0.830732
$353$		−	118178.i		−	0.948388i	−0.880420	−	0.474194i	$-0.842739\pi$
$353$		−	118178.i		−	0.948388i	0.880420	−	0.474194i	$-0.157261\pi$
$354$		0			0
$355$			3160.24i			0.0250763i
$356$		−	269294.i		−	2.12485i
$357$		0			0
$358$	−167884.			−1.30992
$359$	−194552.			−1.50955			−0.754774	−	0.655985i	$-0.772253\pi$
$359$	−194552.			−1.50955			−0.754774	+	0.655985i	$0.772253\pi$
$360$		0			0
$361$	128281.			0.984346
$362$			205588.i			1.56885i
$363$		0			0
$364$	−275310.	−	123014.i	−2.07788	−	0.928434i
$365$	−102757.			−0.771303
$366$		0			0
$367$		−	105692.i		−	0.784710i	−0.919814	−	0.392355i	$-0.871661\pi$
$367$		−	105692.i		−	0.784710i	0.919814	−	0.392355i	$-0.128339\pi$
$368$	−671.545			−0.00495883
$369$		0			0
$370$		−	183438.i		−	1.33994i
$371$	−7169.46	+	16045.6i	−0.0520881	+	0.116576i
$372$		0			0
$373$	66392.5			0.477201			0.238600	−	0.971118i	$-0.423311\pi$
$373$	66392.5			0.477201			0.238600	+	0.971118i	$0.423311\pi$
$374$		−	257262.i		−	1.83921i
$375$		0			0
$376$			175617.i			1.24220i
$377$			60259.5i			0.423978i
$378$		0			0
$379$	175353.			1.22077			0.610387	−	0.792103i	$-0.291014\pi$
$379$	175353.			1.22077			0.610387	+	0.792103i	$0.291014\pi$
$380$	−13275.5			−0.0919357
$381$		0			0
$382$	−30742.8			−0.210677
$383$		−	4098.21i		−	0.0279381i	−0.999902	−	0.0139690i	$-0.995553\pi$
$383$		−	4098.21i		−	0.0279381i	0.999902	−	0.0139690i	$-0.00444662\pi$
$384$		0			0
$385$	−52730.7	−	23561.1i	−0.355748	−	0.158955i
$386$	240306.			1.61283
$387$		0			0
$388$		−	16006.2i		−	0.106323i
$389$	207427.			1.37077			0.685387	−	0.728179i	$-0.259633\pi$
$389$	207427.			1.37077			0.685387	+	0.728179i	$0.259633\pi$
$390$		0			0
$391$		−	17399.4i		−	0.113810i
$392$	107177.	+	119669.i	0.697476	+	0.778770i
$393$		0			0
$394$	−20955.2			−0.134989
$395$		−	80326.3i		−	0.514829i
$396$		0			0
$397$		−	115680.i		−	0.733968i	−0.930227	−	0.366984i	$-0.880390\pi$
$397$		−	115680.i		−	0.733968i	0.930227	−	0.366984i	$-0.119610\pi$
$398$		−	338055.i		−	2.13413i
$399$		0			0
$400$	−1810.39			−0.0113149
$401$	198641.			1.23532			0.617661	−	0.786444i	$-0.288080\pi$
$401$	198641.			1.23532			0.617661	+	0.786444i	$0.288080\pi$
$402$		0			0
$403$	45623.8			0.280919
$404$			393446.i			2.41059i
$405$		0			0
$406$	33462.5	−	74890.5i	0.203005	−	0.454333i
$407$	265987.			1.60572
$408$		0			0
$409$			39642.8i			0.236983i	0.992955	+	0.118492i	$0.0378059\pi$
$409$			39642.8i			0.236983i	−0.992955	+	0.118492i	$0.962194\pi$
$410$	182059.			1.08304
$411$		0			0
$412$			495285.i			2.91783i
$413$	38238.0	+	17085.4i	0.224179	+	0.100167i
$414$		0			0
$415$	−56625.5			−0.328788
$416$			228553.i			1.32069i
$417$		0			0
$418$		−	30965.4i		−	0.177225i
$419$		−	157716.i		−	0.898354i	−0.893443	−	0.449177i	$-0.851717\pi$
$419$		−	157716.i		−	0.898354i	0.893443	−	0.449177i	$-0.148283\pi$
$420$		0			0
$421$	9811.94			0.0553593			0.0276797	−	0.999617i	$-0.491188\pi$
$421$	9811.94			0.0553593			0.0276797	+	0.999617i	$0.491188\pi$
$422$	102423.			0.575141
$423$		0			0
$424$	−23997.6			−0.133486
$425$		−	46906.4i		−	0.259690i
$426$		0			0
$427$	93288.2	+	41682.9i	0.511648	+	0.228614i
$428$	−102626.			−0.560234
$429$		0			0
$430$		−	166368.i		−	0.899774i
$431$	−223189.			−1.20149			−0.600743	−	0.799442i	$-0.705128\pi$
$431$	−223189.			−1.20149			−0.600743	+	0.799442i	$0.705128\pi$
$432$		0			0
$433$			112634.i			0.600748i	0.953821	+	0.300374i	$0.0971115\pi$
$433$			112634.i			0.600748i	−0.953821	+	0.300374i	$0.902888\pi$
$434$	−56701.2	−	25335.2i	−0.301032	−	0.134507i
$435$		0			0
$436$	431918.			2.27210
$437$		−	2094.29i		−	0.0109667i
$438$		0			0
$439$		−	73105.8i		−	0.379335i	−0.981848	−	0.189667i	$-0.939259\pi$
$439$		−	73105.8i		−	0.379335i	0.981848	−	0.189667i	$-0.0607410\pi$
$440$		−	78863.4i		−	0.407353i
$441$		0			0
$442$	571237.			2.92396
$443$	−50089.8			−0.255236			−0.127618	−	0.991823i	$-0.540733\pi$
$443$	−50089.8			−0.255236			−0.127618	+	0.991823i	$0.540733\pi$
$444$		0			0
$445$	114528.			0.578349
$446$		−	77660.9i		−	0.390421i
$447$		0			0
$448$	131549.	−	294413.i	0.655439	−	1.46690i
$449$	5042.02			0.0250099			0.0125049	−	0.999922i	$-0.496019\pi$
$449$	5042.02			0.0250099			0.0125049	+	0.999922i	$0.496019\pi$
$450$		0			0
$451$			263988.i			1.29787i
$452$	−510814.			−2.50026
$453$		0			0
$454$		−	519891.i		−	2.52232i
$455$	52316.3	−	117086.i	0.252705	−	0.565565i
$456$		0			0
$457$	−38281.4			−0.183297			−0.0916486	−	0.995791i	$-0.529214\pi$
$457$	−38281.4			−0.183297			−0.0916486	+	0.995791i	$0.529214\pi$
$458$			263287.i			1.25516i
$459$		0			0
$460$		−	13628.2i		−	0.0644057i
$461$			37749.3i			0.177626i	0.996048	+	0.0888132i	$0.0283074\pi$
$461$			37749.3i			0.177626i	−0.996048	+	0.0888132i	$0.971693\pi$
$462$		0			0
$463$	−343927.			−1.60437			−0.802185	−	0.597075i	$-0.796329\pi$
$463$	−343927.			−1.60437			−0.802185	+	0.597075i	$0.796329\pi$
$464$	3728.26			0.0173169
$465$		0			0
$466$	−261656.			−1.20492
$467$		−	96841.6i		−	0.444046i	−0.975041	−	0.222023i	$-0.928734\pi$
$467$		−	96841.6i		−	0.444046i	0.975041	−	0.222023i	$-0.0712661\pi$
$468$		0			0
$469$	151085.	−	338135.i	0.686871	−	1.53725i
$470$	−190833.			−0.863890
$471$		0			0
$472$			57188.2i			0.256698i
$473$	241236.			1.07825
$474$		0			0
$475$		−	5645.92i		−	0.0250235i
$476$	−441330.	−	197195.i	−1.94782	−	0.870324i
$477$		0			0
$478$	−80285.7			−0.351384
$479$			41421.1i			0.180530i	0.995918	+	0.0902652i	$0.0287715\pi$
$479$			41421.1i			0.180530i	−0.995918	+	0.0902652i	$0.971229\pi$
$480$		0			0
$481$			590611.i			2.55277i
$482$			136363.i			0.586951i
$483$		0			0
$484$	−92715.0			−0.395785
$485$	6807.26			0.0289394
$486$		0			0
$487$	−29470.2			−0.124258			−0.0621290	−	0.998068i	$-0.519789\pi$
$487$	−29470.2			−0.124258			−0.0621290	+	0.998068i	$0.519789\pi$
$488$			139521.i			0.585867i
$489$		0			0
$490$	−130037.	+	116463.i	−0.541596	+	0.485061i
$491$	198756.			0.824437			0.412218	−	0.911085i	$-0.364754\pi$
$491$	198756.			0.824437			0.412218	+	0.911085i	$0.364754\pi$
$492$		0			0
$493$			96597.7i			0.397441i
$494$	68757.3			0.281751
$495$		0			0
$496$		−	2822.75i		−	0.0114738i
$497$	−5650.22	+	12645.4i	−0.0228745	+	0.0511942i
$498$		0			0
$499$	62009.6			0.249034			0.124517	−	0.992218i	$-0.460262\pi$
$499$	62009.6			0.249034			0.124517	+	0.992218i	$0.460262\pi$
$500$		−	36739.8i		−	0.146959i
$501$		0			0
$502$			535399.i			2.12456i
$503$			335191.i			1.32482i	0.749143	+	0.662409i	$0.230466\pi$
$503$			335191.i			1.32482i	−0.749143	+	0.662409i	$0.769534\pi$
$504$		0			0
$505$	−167328.			−0.656123
$506$	31788.2			0.124155
$507$		0			0
$508$	−91317.8			−0.353857
$509$		−	27607.7i		−	0.106560i	−0.998580	−	0.0532800i	$-0.983032\pi$
$509$		−	27607.7i		−	0.106560i	0.998580	−	0.0532800i	$-0.0169676\pi$
$510$		0			0
$511$	−411173.	−	183720.i	−1.57465	−	0.703581i
$512$	29645.3			0.113088
$513$		0			0
$514$			43903.2i			0.166177i
$515$	−210639.			−0.794188
$516$		0			0
$517$		−	276710.i		−	1.03525i
$518$	327970.	−	734011.i	1.22229	−	2.73554i
$519$		0			0
$520$	175113.			0.647606
$521$		−	73225.7i		−	0.269767i	−0.990861	−	0.134883i	$-0.956934\pi$
$521$		−	73225.7i		−	0.269767i	0.990861	−	0.134883i	$-0.0430660\pi$
$522$		0			0
$523$		−	208338.i		−	0.761668i	−0.924643	−	0.380834i	$-0.875637\pi$
$523$		−	208338.i		−	0.761668i	0.924643	−	0.380834i	$-0.124363\pi$
$524$		−	137083.i		−	0.499253i
$525$		0			0
$526$	154681.			0.559069
$527$	73136.2			0.263337
$528$		0			0
$529$	−277691.			−0.992317
$530$		−	26076.8i		−	0.0928330i
$531$		0			0
$532$	−53121.0	−	23735.4i	−0.187691	−	0.0838637i
$533$	−586173.			−2.06334
$534$		0			0
$535$		−	43645.5i		−	0.152487i
$536$	505710.			1.76024
$537$		0			0
$538$		−	481560.i		−	1.66374i
$539$	−168873.	−	188556.i	−0.581276	−	0.649026i
$540$		0			0
$541$	71741.5			0.245118			0.122559	−	0.992461i	$-0.460890\pi$
$541$	71741.5			0.245118			0.122559	+	0.992461i	$0.460890\pi$
$542$			399757.i			1.36081i
$543$		0			0
$544$			366377.i			1.23803i
$545$			183689.i			0.618431i
$546$		0			0
$547$	184265.			0.615839			0.307919	−	0.951412i	$-0.400367\pi$
$547$	184265.			0.615839			0.307919	+	0.951412i	$0.400367\pi$
$548$	−657685.			−2.19006
$549$		0			0
$550$	85696.4			0.283294
$551$			11627.0i			0.0382971i
$552$		0			0
$553$	143616.	−	321419.i	0.469627	−	1.05105i
$554$	476790.			1.55349
$555$		0			0
$556$		−	255613.i		−	0.826864i
$557$	−386198.			−1.24480			−0.622399	−	0.782700i	$-0.713842\pi$
$557$	−386198.			−1.24480			−0.622399	+	0.782700i	$0.713842\pi$
$558$		0			0
$559$			535653.i			1.71419i
$560$	−7244.14	−	3236.82i	−0.0230999	−	0.0103215i
$561$		0			0
$562$	−413394.			−1.30886
$563$			352409.i			1.11181i	0.831246	+	0.555904i	$0.187628\pi$
$563$			352409.i			1.11181i	−0.831246	+	0.555904i	$0.812372\pi$
$564$		0			0
$565$		−	217243.i		−	0.680532i
$566$			648181.i			2.02332i
$567$		0			0
$568$	−18912.4			−0.0586204
$569$	−265786.			−0.820932			−0.410466	−	0.911876i	$-0.634634\pi$
$569$	−265786.			−0.820932			−0.410466	+	0.911876i	$0.634634\pi$
$570$		0			0
$571$	455939.			1.39841			0.699205	−	0.714921i	$-0.253537\pi$
$571$	455939.			1.39841			0.699205	+	0.714921i	$0.253537\pi$
$572$			648773.i			1.98290i
$573$		0			0
$574$	728496.	+	325505.i	2.21107	+	0.987949i
$575$	5795.92			0.0175302
$576$		0			0
$577$			211395.i			0.634956i	0.948266	+	0.317478i	$0.102836\pi$
$577$			211395.i			0.634956i	−0.948266	+	0.317478i	$0.897164\pi$
$578$	372573.			1.11521
$579$		0			0
$580$			75660.9i			0.224913i
$581$	−226583.	−	101241.i	−0.671234	−	0.299920i
$582$		0			0
$583$	37811.7			0.111247
$584$		−	614946.i		−	1.80306i
$585$		0			0
$586$		−	217141.i		−	0.632333i
$587$			158002.i			0.458550i	0.973362	+	0.229275i	$0.0736355\pi$
$587$			158002.i			0.458550i	−0.973362	+	0.229275i	$0.926365\pi$
$588$		0			0
$589$	8803.08			0.0253749
$590$	−62143.2			−0.178521
$591$		0			0
$592$	36541.2			0.104265
$593$		−	239670.i		−	0.681561i	−0.940143	−	0.340780i	$-0.889309\pi$
$593$		−	239670.i		−	0.681561i	0.940143	−	0.340780i	$-0.110691\pi$
$594$		0			0
$595$	83864.4	−	187692.i	0.236888	−	0.530167i
$596$	−130646.			−0.367794
$597$		0			0
$598$			70584.1i			0.197381i
$599$	−183572.			−0.511626			−0.255813	−	0.966726i	$-0.582343\pi$
$599$	−183572.			−0.511626			−0.255813	+	0.966726i	$0.582343\pi$
$600$		0			0
$601$		−	14783.5i		−	0.0409287i	−0.999791	−	0.0204643i	$-0.993486\pi$
$601$		−	14783.5i		−	0.0409287i	0.999791	−	0.0204643i	$-0.00651446\pi$
$602$	297451.	−	665710.i	0.820773	−	1.83693i
$603$		0			0
$604$	−409371.			−1.12213
$605$		−	39430.6i		−	0.107726i
$606$		0			0
$607$		−	591265.i		−	1.60474i	−0.596827	−	0.802370i	$-0.703572\pi$
$607$		−	591265.i		−	1.60474i	0.596827	−	0.802370i	$-0.296428\pi$
$608$			44099.2i			0.119295i
$609$		0			0
$610$	−151609.			−0.407442
$611$	614422.			1.64583
$612$		0			0
$613$	−90639.8			−0.241212			−0.120606	−	0.992700i	$-0.538484\pi$
$613$	−90639.8			−0.241212			−0.120606	+	0.992700i	$0.538484\pi$
$614$			527273.i			1.39862i
$615$		0			0
$616$	141001.	−	315566.i	0.371586	−	0.831627i
$617$	504471.			1.32515			0.662576	−	0.748995i	$-0.269463\pi$
$617$	504471.			1.32515			0.662576	+	0.748995i	$0.269463\pi$
$618$		0			0
$619$			732305.i			1.91122i	0.294634	+	0.955610i	$0.404802\pi$
$619$			732305.i			1.91122i	−0.294634	+	0.955610i	$0.595198\pi$
$620$	57284.5			0.149023
$621$		0			0
$622$		−	382448.i		−	0.988535i
$623$	458273.	+	204765.i	1.18072	+	0.527569i
$624$		0			0
$625$	15625.0			0.0400000
$626$		−	953841.i		−	2.43404i
$627$		0			0
$628$		−	59044.0i		−	0.149712i
$629$			946766.i			2.39299i
$630$		0			0
$631$	537983.			1.35117			0.675585	−	0.737282i	$-0.263891\pi$
$631$	537983.			1.35117			0.675585	+	0.737282i	$0.263891\pi$
$632$	480711.			1.20351
$633$		0			0
$634$	690348.			1.71747
$635$		−	38836.4i		−	0.0963144i
$636$		0			0
$637$	418679.	−	374974.i	1.03182	−	0.924108i
$638$	−176481.			−0.433566
$639$		0			0
$640$			303816.i			0.741739i
$641$	−226234.			−0.550608			−0.275304	−	0.961357i	$-0.588779\pi$
$641$	−226234.			−0.550608			−0.275304	+	0.961357i	$0.588779\pi$
$642$		0			0
$643$			186548.i			0.451199i	0.974220	+	0.225599i	$0.0724340\pi$
$643$			186548.i			0.451199i	−0.974220	+	0.225599i	$0.927566\pi$
$644$	24366.1	−	54532.3i	0.0587508	−	0.131487i
$645$		0			0
$646$	110220.			0.264116
$647$		−	580904.i		−	1.38770i	−0.720120	−	0.693850i	$-0.755913\pi$
$647$		−	580904.i		−	1.38770i	0.720120	−	0.693850i	$-0.244087\pi$
$648$		0			0
$649$		−	90108.4i		−	0.213932i
$650$			190285.i			0.450378i
$651$		0			0
$652$	711072.			1.67270
$653$	−242502.			−0.568707			−0.284354	−	0.958720i	$-0.591779\pi$
$653$	−242502.			−0.568707			−0.284354	+	0.958720i	$0.591779\pi$
$654$		0			0
$655$	58299.6			0.135889
$656$			36266.6i			0.0842751i
$657$		0			0
$658$	−763604.	−	341192.i	−1.76367	−	0.788039i
$659$	377939.			0.870265			0.435132	−	0.900367i	$-0.356702\pi$
$659$	377939.			0.870265			0.435132	+	0.900367i	$0.356702\pi$
$660$		0			0
$661$			377336.i			0.863625i	0.901963	+	0.431812i	$0.142126\pi$
$661$			377336.i			0.863625i	−0.901963	+	0.431812i	$0.857874\pi$
$662$	158005.			0.360541
$663$		0			0
$664$		−	338874.i		−	0.768603i
$665$	10094.4	−	22591.7i	0.0228264	−	0.0510864i
$666$		0			0
$667$	−11936.0			−0.0268291
$668$		−	964632.i		−	2.16177i
$669$		0			0
$670$			549526.i			1.22416i
$671$		−	219835.i		−	0.488261i
$672$		0			0
$673$	334342.			0.738177			0.369088	−	0.929394i	$-0.379670\pi$
$673$	334342.			0.738177			0.369088	+	0.929394i	$0.379670\pi$
$674$	1.11189e6			2.44760
$675$		0			0
$676$	−689734.			−1.50934
$677$		−	823510.i		−	1.79677i	−0.439212	−	0.898383i	$-0.644742\pi$
$677$		−	823510.i		−	1.79677i	0.439212	−	0.898383i	$-0.355258\pi$
$678$		0			0
$679$	27238.7	+	12170.8i	0.0590809	+	0.0263984i
$680$	280710.			0.607073
$681$		0			0
$682$			133617.i			0.287272i
$683$	821787.			1.76164			0.880822	−	0.473448i	$-0.156991\pi$
$683$	821787.			1.76164			0.880822	+	0.473448i	$0.156991\pi$
$684$		0			0
$685$		−	279705.i		−	0.596101i
$686$	−728560.	+	233523.i	−1.54816	+	0.496229i
$687$		0			0
$688$	33140.9			0.0700145
$689$			83959.0i			0.176860i
$690$		0			0
$691$		−	744548.i		−	1.55933i	−0.626200	−	0.779663i	$-0.715391\pi$
$691$		−	744548.i		−	1.55933i	0.626200	−	0.779663i	$-0.284609\pi$
$692$		−	82352.3i		−	0.171974i
$693$		0			0
$694$	−1.31666e6			−2.73373
$695$	108709.			0.225059
$696$		0			0
$697$	−939652.			−1.93420
$698$		−	586140.i		−	1.20307i
$699$		0			0
$700$	65687.5	−	147012.i	0.134056	−	0.300024i
$701$	−318730.			−0.648616			−0.324308	−	0.945952i	$-0.605131\pi$
$701$	−318730.			−0.648616			−0.324308	+	0.945952i	$0.605131\pi$
$702$		0			0
$703$			113958.i			0.230587i
$704$	−693789.			−1.39985
$705$		0			0
$706$			768509.i			1.54184i
$707$	−669549.	−	299167.i	−1.33950	−	0.598515i
$708$		0			0
$709$	150036.			0.298471			0.149235	−	0.988802i	$-0.452319\pi$
$709$	150036.			0.298471			0.149235	+	0.988802i	$0.452319\pi$
$710$		−	20551.0i		−	0.0407677i
$711$		0			0
$712$			685388.i			1.35200i
$713$			9036.97i			0.0177764i
$714$		0			0
$715$	−275915.			−0.539714
$716$	678686.			1.32386
$717$		0			0
$718$	1.26517e6			2.45414
$719$			124427.i			0.240690i	0.992732	+	0.120345i	$0.0384001\pi$
$719$			124427.i			0.240690i	−0.992732	+	0.120345i	$0.961600\pi$
$720$		0			0
$721$	−842854.	−	376603.i	−1.62137	−	0.724458i
$722$	−834209.			−1.60030
$723$		0			0
$724$		−	831108.i		−	1.58555i
$725$	−32177.6			−0.0612179
$726$		0			0
$727$			534357.i			1.01103i	0.862819	+	0.505513i	$0.168697\pi$
$727$			534357.i			1.01103i	−0.862819	+	0.505513i	$0.831303\pi$
$728$	700700.	+	313085.i	1.32211	+	0.590745i
$729$		0			0
$730$	668227.			1.25394
$731$			858667.i			1.60690i
$732$		0			0
$733$			638734.i			1.18881i	0.804166	+	0.594404i	$0.202612\pi$
$733$			638734.i			1.18881i	−0.804166	+	0.594404i	$0.797388\pi$
$734$			687312.i			1.27574i
$735$		0			0
$736$	−45270.9			−0.0835725
$737$	−796819.			−1.46698
$738$		0			0
$739$	198812.			0.364044			0.182022	−	0.983295i	$-0.441736\pi$
$739$	198812.			0.364044			0.182022	+	0.983295i	$0.441736\pi$
$740$			741562.i			1.35420i
$741$		0			0
$742$	46623.0	−	104344.i	0.0846822	−	0.189523i
$743$	−865398.			−1.56761			−0.783806	−	0.621006i	$-0.786724\pi$
$743$	−865398.			−1.56761			−0.783806	+	0.621006i	$0.786724\pi$
$744$		0			0
$745$		−	55562.2i		−	0.100108i
$746$	−431750.			−0.775808
$747$		0			0
$748$			1.04000e6i			1.85879i
$749$	78034.3	−	174644.i	0.139098	−	0.311308i
$750$		0			0
$751$	−18813.0			−0.0333564			−0.0166782	−	0.999861i	$-0.505309\pi$
$751$	−18813.0			−0.0333564			−0.0166782	+	0.999861i	$0.505309\pi$
$752$		−	38014.4i		−	0.0672222i
$753$		0			0
$754$		−	391867.i		−	0.689280i
$755$		−	174101.i		−	0.305426i
$756$		0			0
$757$	−247909.			−0.432614			−0.216307	−	0.976325i	$-0.569401\pi$
$757$	−247909.			−0.432614			−0.216307	+	0.976325i	$0.569401\pi$
$758$	−1.14032e6			−1.98467
$759$		0			0
$760$	33787.9			0.0584970
$761$			882187.i			1.52332i	0.647976	+	0.761661i	$0.275616\pi$
$761$			882187.i			1.52332i	−0.647976	+	0.761661i	$0.724384\pi$
$762$		0			0
$763$	−328420.	+	735019.i	−0.564132	+	1.26255i
$764$	124280.			0.212920
$765$		0			0
$766$			26650.6i			0.0454202i
$767$	200081.			0.340107
$768$		0			0
$769$		−	10006.5i		−	0.0169212i	−0.999964	−	0.00846060i	$-0.997307\pi$
$769$		−	10006.5i		−	0.0169212i	0.999964	−	0.00846060i	$-0.00269312\pi$
$770$	342908.	+	153217.i	0.578356	+	0.258420i
$771$		0			0
$772$	−971456.			−1.63000
$773$		−	148529.i		−	0.248573i	−0.992246	−	0.124286i	$-0.960336\pi$
$773$		−	148529.i		−	0.248573i	0.992246	−	0.124286i	$-0.0396641\pi$
$774$		0			0
$775$			24362.4i			0.0405618i
$776$			40737.9i			0.0676511i
$777$		0			0
$778$	−1.34889e6			−2.22853
$779$	−113102.			−0.186378
$780$		0			0
$781$	29799.2			0.0488542
$782$			113148.i			0.185027i
$783$		0			0
$784$	−23199.7	−	25903.7i	−0.0377442	−	0.0421435i
$785$	25110.7			0.0407492
$786$		0			0
$787$		−	954103.i		−	1.54044i	−0.637776	−	0.770222i	$-0.720145\pi$
$787$		−	954103.i		−	1.54044i	0.637776	−	0.770222i	$-0.279855\pi$
$788$	84713.2			0.136426
$789$		0			0
$790$			522361.i			0.836983i
$791$	388411.	−	869281.i	0.620781	−	1.38934i
$792$		0			0
$793$	488134.			0.776233
$794$			752266.i			1.19325i
$795$		0			0
$796$			1.36662e6i			2.15685i
$797$			105180.i			0.165583i	0.996567	+	0.0827914i	$0.0263835\pi$
$797$			105180.i			0.165583i	−0.996567	+	0.0827914i	$0.973616\pi$
$798$		0			0
$799$	984936.			1.54282
$800$	−122044.			−0.190694
$801$		0			0
$802$	−1.29176e6			−2.00832
$803$			968936.i			1.50267i
$804$		0			0
$805$	23191.9	+	10362.6i	0.0357887	+	0.0159910i
$806$	−296691.			−0.456704
$807$		0			0
$808$		−	1.00137e6i		−	1.53381i
$809$	−13264.8			−0.0202677			−0.0101338	−	0.999949i	$-0.503226\pi$
$809$	−13264.8			−0.0202677			−0.0101338	+	0.999949i	$0.503226\pi$
$810$		0			0
$811$			68424.4i			0.104033i	0.998646	+	0.0520163i	$0.0165648\pi$
$811$			68424.4i			0.104033i	−0.998646	+	0.0520163i	$0.983435\pi$
$812$	−135275.	+	302751.i	−0.205166	+	0.459170i
$813$		0			0
$814$	−1.72971e6			−2.61050
$815$			302410.i			0.455283i
$816$		0			0
$817$			103354.i			0.154840i
$818$		−	257797.i		−	0.385275i
$819$		0			0
$820$	−735990.			−1.09457
$821$	−23666.0			−0.0351107			−0.0175553	−	0.999846i	$-0.505588\pi$
$821$	−23666.0			−0.0351107			−0.0175553	+	0.999846i	$0.505588\pi$
$822$		0			0
$823$	541429.			0.799358			0.399679	−	0.916655i	$-0.369122\pi$
$823$	541429.			0.799358			0.399679	+	0.916655i	$0.369122\pi$
$824$		−	1.26056e6i		−	1.85656i
$825$		0			0
$826$	−248661.	−	111106.i	−0.364458	−	0.162847i
$827$	486140.			0.710805			0.355402	−	0.934713i	$-0.384344\pi$
$827$	486140.			0.710805			0.355402	+	0.934713i	$0.384344\pi$
$828$		0			0
$829$		−	199179.i		−	0.289824i	−0.989445	−	0.144912i	$-0.953710\pi$
$829$		−	199179.i		−	0.289824i	0.989445	−	0.144912i	$-0.0462900\pi$
$830$	368235.			0.534526
$831$		0			0
$832$		−	1.54053e6i		−	2.22547i
$833$	671154.	−	601095.i	0.967236	−	0.866269i
$834$		0			0
$835$	410246.			0.588398
$836$			125180.i			0.179112i
$837$		0			0
$838$			1.02562e6i			1.46050i
$839$		−	1.05803e6i		−	1.50306i	−0.659701	−	0.751528i	$-0.729317\pi$
$839$		−	1.05803e6i		−	1.50306i	0.659701	−	0.751528i	$-0.270683\pi$
$840$		0			0
$841$	−641015.			−0.906309
$842$	−63806.9			−0.0900003
$843$		0			0
$844$	−414055.			−0.581263
$845$		−	293335.i		−	0.410820i
$846$		0			0
$847$	70498.3	−	157778.i	0.0982679	−	0.219928i
$848$	5194.56			0.00722365
$849$		0			0
$850$			305032.i			0.422190i
$851$	−116986.			−0.161538
$852$		0			0
$853$			659921.i			0.906972i	0.891263	+	0.453486i	$0.149820\pi$
$853$			659921.i			0.906972i	−0.891263	+	0.453486i	$0.850180\pi$
$854$	−606652.	−	271064.i	−0.831810	−	0.371668i
$855$		0			0
$856$	261196.			0.356466
$857$			776880.i			1.05777i	0.848693	+	0.528886i	$0.177390\pi$
$857$			776880.i			1.05777i	−0.848693	+	0.528886i	$0.822610\pi$
$858$		0			0
$859$			31227.0i			0.0423198i	0.999776	+	0.0211599i	$0.00673591\pi$
$859$			31227.0i			0.0423198i	−0.999776	+	0.0211599i	$0.993264\pi$
$860$			672557.i			0.909353i
$861$		0			0
$862$	1.45140e6			1.95331
$863$	−197197.			−0.264776			−0.132388	−	0.991198i	$-0.542264\pi$
$863$	−197197.			−0.264776			−0.132388	+	0.991198i	$0.542264\pi$
$864$		0			0
$865$	35023.4			0.0468087
$866$		−	732456.i		−	0.976665i
$867$		0			0
$868$	229220.	+	102420.i	0.304237	+	0.135939i
$869$	−757429.			−1.00300
$870$		0			0
$871$		−	1.76930e6i		−	2.33220i
$872$	−1.09929e6			−1.44570
$873$		0			0
$874$			13619.2i			0.0178290i
$875$	62522.2	+	27936.1i	0.0816617	+	0.0364879i
$876$		0			0
$877$	−1.22846e6			−1.59720			−0.798602	−	0.601860i	$-0.794427\pi$
$877$	−1.22846e6			−1.59720			−0.798602	+	0.601860i	$0.794427\pi$
$878$			475406.i			0.616703i
$879$		0			0
$880$			17070.9i			0.0220441i
$881$			1.23726e6i			1.59408i	0.603927	+	0.797040i	$0.293602\pi$
$881$			1.23726e6i			1.59408i	−0.603927	+	0.797040i	$0.706398\pi$
$882$		0			0
$883$	708608.			0.908835			0.454417	−	0.890789i	$-0.349848\pi$
$883$	708608.			0.908835			0.454417	+	0.890789i	$0.349848\pi$
$884$	−2.30927e6			−2.95509
$885$		0			0
$886$	325733.			0.414949
$887$			48621.1i			0.0617984i	0.999523	+	0.0308992i	$0.00983709\pi$
$887$			48621.1i			0.0617984i	−0.999523	+	0.0308992i	$0.990163\pi$
$888$		0			0
$889$	69435.9	−	155401.i	0.0878578	−	0.196630i
$890$	−744772.			−0.940250
$891$		0			0
$892$			313951.i			0.394577i
$893$	118552.			0.148665
$894$		0			0
$895$			288637.i			0.360334i
$896$	−543196.	+	1.21570e6i	−0.676613	+	1.51429i
$897$		0			0
$898$	−32788.2			−0.0406597
$899$		−	50171.2i		−	0.0620776i
$900$		0			0
$901$			134589.i			0.165790i
$902$		−	1.71671e6i		−	2.11001i
$903$		0			0
$904$	1.30009e6			1.59087
$905$	353460.			0.431562
$906$		0			0
$907$	1.42767e6			1.73546			0.867730	−	0.497036i	$-0.165578\pi$
$907$	1.42767e6			1.73546			0.867730	+	0.497036i	$0.165578\pi$
$908$			2.10170e6i			2.54917i
$909$		0			0
$910$	−340212.	+	761410.i	−0.410835	+	0.919467i
$911$	583391.			0.702947			0.351474	−	0.936198i	$-0.385681\pi$
$911$	583391.			0.702947			0.351474	+	0.936198i	$0.385681\pi$
$912$		0			0
$913$			533945.i			0.640553i
$914$	248944.			0.297995
$915$		0			0
$916$		−	1.06436e6i		−	1.26852i
$917$	233281.	+	104234.i	0.277422	+	0.123957i
$918$		0			0
$919$	911636.			1.07942			0.539710	−	0.841851i	$-0.318534\pi$
$919$	911636.			1.07942			0.539710	+	0.841851i	$0.318534\pi$
$920$			34685.6i			0.0409801i
$921$		0			0
$922$		−	245484.i		−	0.288776i
$923$			66167.7i			0.0776681i
$924$		0			0
$925$	−315377.			−0.368593
$926$	2.23656e6			2.60830
$927$		0			0
$928$	251334.			0.291847
$929$		−	1.18209e6i		−	1.36968i	−0.728696	−	0.684838i	$-0.759873\pi$
$929$		−	1.18209e6i		−	1.36968i	0.728696	−	0.684838i	$-0.240127\pi$
$930$		0			0
$931$	80783.8	−	72351.1i	0.0932020	−	0.0834729i
$932$	1.05776e6			1.21775
$933$		0			0
$934$			629760.i			0.721907i
$935$	−442300.			−0.505934
$936$		0			0
$937$			648753.i			0.738925i	0.929246	+	0.369463i	$0.120458\pi$
$937$			648753.i			0.738925i	−0.929246	+	0.369463i	$0.879542\pi$
$938$	−982503.	+	2.19889e6i	−1.11668	+	2.49918i
$939$		0			0
$940$	771459.			0.873086
$941$		−	539679.i		−	0.609475i	−0.952436	−	0.304738i	$-0.901431\pi$
$941$		−	539679.i		−	0.609475i	0.952436	−	0.304738i	$-0.0985688\pi$
$942$		0			0
$943$		−	116107.i		−	0.130567i
$944$		−	12379.1i		−	0.0138913i
$945$		0			0
$946$	−1.56875e6			−1.75296
$947$	−380310.			−0.424071			−0.212035	−	0.977262i	$-0.568009\pi$
$947$	−380310.			−0.424071			−0.212035	+	0.977262i	$0.568009\pi$
$948$		0			0
$949$	−2.15148e6			−2.38894
$950$			36715.3i			0.0406818i
$951$		0			0
$952$	1.12324e6	+	501885.i	1.23936	+	0.553771i
$953$	1.51323e6			1.66617			0.833084	−	0.553147i	$-0.186573\pi$
$953$	1.51323e6			1.66617			0.833084	+	0.553147i	$0.186573\pi$
$954$		0			0
$955$			52854.9i			0.0579534i
$956$	324562.			0.355125
$957$		0			0
$958$		−	269361.i		−	0.293497i
$959$	500088.	−	1.11922e6i	0.543762	−	1.21696i
$960$		0			0
$961$	885535.			0.958869
$962$		−	3.84074e6i		−	4.15016i
$963$		0			0
$964$		−	551258.i		−	0.593199i
$965$		−	413148.i		−	0.443661i
$966$		0			0
$967$	−393218.			−0.420514			−0.210257	−	0.977646i	$-0.567430\pi$
$967$	−393218.			−0.420514			−0.210257	+	0.977646i	$0.567430\pi$
$968$	235971.			0.251831
$969$		0			0
$970$	−44267.6			−0.0470481
$971$			957332.i			1.01537i	0.861543	+	0.507685i	$0.169498\pi$
$971$			957332.i			1.01537i	−0.861543	+	0.507685i	$0.830502\pi$
$972$		0			0
$973$	434992.	+	194362.i	0.459468	+	0.205299i
$974$	191644.			0.202012
$975$		0			0
$976$		−	30200.9i		−	0.0317044i
$977$	−1.33928e6			−1.40308			−0.701539	−	0.712631i	$-0.747503\pi$
$977$	−1.33928e6			−1.40308			−0.701539	+	0.712631i	$0.747503\pi$
$978$		0			0
$979$		−	1.07993e6i		−	1.12675i
$980$	525687.	−	470812.i	0.547362	−	0.490225i
$981$		0			0
$982$	−1.29251e6			−1.34033
$983$			1.72782e6i			1.78810i	0.447968	+	0.894050i	$0.352148\pi$
$983$			1.72782e6i			1.78810i	−0.447968	+	0.894050i	$0.647852\pi$
$984$		0			0
$985$			36027.5i			0.0371331i
$986$		−	628174.i		−	0.646139i
$987$		0			0
$988$	−277957.			−0.284750
$989$	−106100.			−0.108473
$990$		0			0
$991$	946703.			0.963977			0.481988	−	0.876178i	$-0.339915\pi$
$991$	946703.			0.963977			0.481988	+	0.876178i	$0.339915\pi$
$992$		−	190290.i		−	0.193372i
$993$		0			0
$994$	36743.3	−	82233.2i	0.0371882	−	0.0832289i
$995$	−581205.			−0.587061
$996$		0			0
$997$		−	552328.i		−	0.555657i	−0.960631	−	0.277829i	$-0.910385\pi$
$997$		−	552328.i		−	0.555657i	0.960631	−	0.277829i	$-0.0896148\pi$
$998$	−403248.			−0.404866
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.5.h.a.181.2		12
3.2	odd	2		35.5.d.a.6.11	✓	12
7.6	odd	2	inner	315.5.h.a.181.1		12
12.11	even	2		560.5.f.b.321.8		12
15.2	even	4		175.5.c.d.174.18		24
15.8	even	4		175.5.c.d.174.7		24
15.14	odd	2		175.5.d.i.76.2		12
21.20	even	2		35.5.d.a.6.12	yes	12
84.83	odd	2		560.5.f.b.321.5		12
105.62	odd	4		175.5.c.d.174.8		24
105.83	odd	4		175.5.c.d.174.17		24
105.104	even	2		175.5.d.i.76.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.d.a.6.11	✓	12	3.2	odd	2
35.5.d.a.6.12	yes	12	21.20	even	2
175.5.c.d.174.7		24	15.8	even	4
175.5.c.d.174.8		24	105.62	odd	4
175.5.c.d.174.17		24	105.83	odd	4
175.5.c.d.174.18		24	15.2	even	4
175.5.d.i.76.1		12	105.104	even	2
175.5.d.i.76.2		12	15.14	odd	2
315.5.h.a.181.1		12	7.6	odd	2	inner
315.5.h.a.181.2		12	1.1	even	1	trivial
560.5.f.b.321.5		12	84.83	odd	2
560.5.f.b.321.8		12	12.11	even	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	315.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.50299 q^{2} +26.2889 q^{4} +11.1803i q^{5} +(-19.9894 + 44.7373i) q^{7} -66.9085 q^{8} +O(q^{10})\)	\(q-6.50299 q^{2} +26.2889 q^{4} +11.1803i q^{5} +(-19.9894 + 44.7373i) q^{7} -66.9085 q^{8} -72.7056i q^{10} +105.424 q^{11} +234.089i q^{13} +(129.991 - 290.926i) q^{14} +14.4831 q^{16} +375.251i q^{17} +45.1673i q^{19} +293.919i q^{20} -685.571 q^{22} -46.3674 q^{23} -125.000 q^{25} -1522.28i q^{26} +(-525.500 + 1176.09i) q^{28} +257.421 q^{29} -194.899i q^{31} +976.352 q^{32} -2440.26i q^{34} +(-500.178 - 223.489i) q^{35} +2523.02 q^{37} -293.723i q^{38} -748.060i q^{40} +2504.06i q^{41} +2288.24 q^{43} +2771.48 q^{44} +301.527 q^{46} -2624.74i q^{47} +(-1601.84 - 1788.55i) q^{49} +812.874 q^{50} +6153.94i q^{52} +358.663 q^{53} +1178.68i q^{55} +(1337.46 - 2993.30i) q^{56} -1674.01 q^{58} -854.723i q^{59} -2085.25i q^{61} +1267.43i q^{62} -6580.94 q^{64} -2617.20 q^{65} -7558.23 q^{67} +9864.94i q^{68} +(3252.65 + 1453.34i) q^{70} +282.660 q^{71} +9190.85i q^{73} -16407.2 q^{74} +1187.40i q^{76} +(-2107.37 + 4716.38i) q^{77} -7184.60 q^{79} +161.926i q^{80} -16283.9i q^{82} +5064.74i q^{83} -4195.44 q^{85} -14880.4 q^{86} -7053.76 q^{88} -10243.7i q^{89} +(-10472.5 - 4679.31i) q^{91} -1218.95 q^{92} +17068.6i q^{94} -504.986 q^{95} -608.860i q^{97} +(10416.8 + 11630.9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 122 q^{4} - 50 q^{7} + 186 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 122 * q^4 - 50 * q^7 + 186 * q^8	\( 12 q + 6 q^{2} + 122 q^{4} - 50 q^{7} + 186 q^{8} - 126 q^{11} - 78 q^{14} + 578 q^{16} + 2264 q^{22} + 756 q^{23} - 1500 q^{25} + 1414 q^{28} + 2190 q^{29} + 8682 q^{32} + 150 q^{35} + 5564 q^{37} + 3944 q^{43} + 11196 q^{44} + 7844 q^{46} - 8796 q^{49} - 750 q^{50} - 11760 q^{53} + 6606 q^{56} - 18496 q^{58} + 20146 q^{64} + 750 q^{65} - 24096 q^{67} + 14400 q^{70} + 5664 q^{71} - 17604 q^{74} - 26904 q^{77} - 1590 q^{79} + 1050 q^{85} - 17604 q^{86} - 7268 q^{88} - 7182 q^{91} + 60252 q^{92} + 3000 q^{95} - 57714 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 122 * q^4 - 50 * q^7 + 186 * q^8 - 126 * q^11 - 78 * q^14 + 578 * q^16 + 2264 * q^22 + 756 * q^23 - 1500 * q^25 + 1414 * q^28 + 2190 * q^29 + 8682 * q^32 + 150 * q^35 + 5564 * q^37 + 3944 * q^43 + 11196 * q^44 + 7844 * q^46 - 8796 * q^49 - 750 * q^50 - 11760 * q^53 + 6606 * q^56 - 18496 * q^58 + 20146 * q^64 + 750 * q^65 - 24096 * q^67 + 14400 * q^70 + 5664 * q^71 - 17604 * q^74 - 26904 * q^77 - 1590 * q^79 + 1050 * q^85 - 17604 * q^86 - 7268 * q^88 - 7182 * q^91 + 60252 * q^92 + 3000 * q^95 - 57714 * q^98

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