LMFDB - Embedded newform 3900.2.bm.b.2293.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3900,2,Mod(2257,3900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3900, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3900.2257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3900.bm (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$31.1416567883$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 780)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2293.8
Character	$\chi$	$=$	3900.2293
Dual form			3900.2.bm.b.2257.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} -4.69969 q^{7} +1.00000i q^{9} +O(q^{10})$	$q+(0.707107 + 0.707107i) q^{3} -4.69969 q^{7} +1.00000i q^{9} +(0.315352 + 0.315352i) q^{11} +(2.17205 - 2.87788i) q^{13} +(1.07992 + 1.07992i) q^{17} +(3.49017 + 3.49017i) q^{19} +(-3.32318 - 3.32318i) q^{21} +(-3.48094 + 3.48094i) q^{23} +(-0.707107 + 0.707107i) q^{27} -2.87828i q^{29} +(-1.13365 + 1.13365i) q^{31} +0.445975i q^{33} -8.92799 q^{37} +(3.57084 - 0.499101i) q^{39} +(6.10267 - 6.10267i) q^{41} +(-0.557675 + 0.557675i) q^{43} -6.16002 q^{47} +15.0871 q^{49} +1.52723i q^{51} +(-8.42127 - 8.42127i) q^{53} +4.93584i q^{57} +(1.44238 - 1.44238i) q^{59} -5.80499 q^{61} -4.69969i q^{63} +4.05741i q^{67} -4.92280 q^{69} +(-6.68803 + 6.68803i) q^{71} -0.734212i q^{73} +(-1.48205 - 1.48205i) q^{77} -12.9137i q^{79} -1.00000 q^{81} +1.05600 q^{83} +(2.03525 - 2.03525i) q^{87} +(-5.36534 + 5.36534i) q^{89} +(-10.2079 + 13.5251i) q^{91} -1.60322 q^{93} -4.56277i q^{97} +(-0.315352 + 0.315352i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q + 8 q^{11} - 4 q^{17} + 16 q^{19} + 8 q^{21} - 8 q^{23} - 24 q^{37} - 8 q^{39} + 12 q^{41} + 16 q^{43} + 24 q^{47} + 36 q^{49} - 36 q^{53} - 16 q^{59} + 8 q^{61} + 8 q^{69} + 8 q^{71} - 48 q^{77} - 28 q^{81} + 24 q^{83} + 24 q^{87} + 36 q^{89} - 24 q^{91} - 8 q^{99}+O(q^{100}) $ 28 * q + 8 * q^11 - 4 * q^17 + 16 * q^19 + 8 * q^21 - 8 * q^23 - 24 * q^37 - 8 * q^39 + 12 * q^41 + 16 * q^43 + 24 * q^47 + 36 * q^49 - 36 * q^53 - 16 * q^59 + 8 * q^61 + 8 * q^69 + 8 * q^71 - 48 * q^77 - 28 * q^81 + 24 * q^83 + 24 * q^87 + 36 * q^89 - 24 * q^91 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1951$	$3277$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.69969			−1.77631			−0.888157	−	0.459539i	$-0.848014\pi$
$7$	−4.69969			−1.77631			−0.888157	+	0.459539i	$0.848014\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	0.315352	+	0.315352i	0.0950822	+	0.0950822i	0.753048	−	0.657966i	$-0.228583\pi$
$11$	0.315352	+	0.315352i	0.0950822	+	0.0950822i	−0.657966	+	0.753048i	$0.728583\pi$
$12$		0			0
$13$	2.17205	−	2.87788i	0.602418	−	0.798181i
$13$	2.17205	−	2.87788i	0.602418	−	0.798181i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.07992	+	1.07992i	0.261918	+	0.261918i	0.825833	−	0.563915i	$-0.190705\pi$
$17$	1.07992	+	1.07992i	0.261918	+	0.261918i	−0.563915	+	0.825833i	$0.690705\pi$
$18$		0			0
$19$	3.49017	+	3.49017i	0.800700	+	0.800700i	0.983205	−	0.182505i	$-0.0584206\pi$
$19$	3.49017	+	3.49017i	0.800700	+	0.800700i	−0.182505	+	0.983205i	$0.558421\pi$
$20$		0			0
$21$	−3.32318	−	3.32318i	−0.725177	−	0.725177i
$22$		0			0
$23$	−3.48094	+	3.48094i	−0.725827	+	0.725827i	−0.969786	−	0.243959i	$-0.921554\pi$
$23$	−3.48094	+	3.48094i	−0.725827	+	0.725827i	0.243959	+	0.969786i	$0.421554\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	2.87828i		−	0.534483i	−0.963630	−	0.267241i	$-0.913888\pi$
$29$		−	2.87828i		−	0.534483i	0.963630	−	0.267241i	$-0.0861121\pi$
$30$		0			0
$31$	−1.13365	+	1.13365i	−0.203610	+	0.203610i	−0.801545	−	0.597935i	$-0.795988\pi$
$31$	−1.13365	+	1.13365i	−0.203610	+	0.203610i	0.597935	+	0.801545i	$0.295988\pi$
$32$		0			0
$33$			0.445975i			0.0776343i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−8.92799			−1.46775			−0.733876	−	0.679283i	$-0.762291\pi$
$37$	−8.92799			−1.46775			−0.733876	+	0.679283i	$0.762291\pi$
$38$		0			0
$39$	3.57084	−	0.499101i	0.571792	−	0.0799202i
$40$		0			0
$41$	6.10267	−	6.10267i	0.953078	−	0.953078i	−0.0458697	−	0.998947i	$-0.514606\pi$
$41$	6.10267	−	6.10267i	0.953078	−	0.953078i	0.998947	+	0.0458697i	$0.0146059\pi$
$42$		0			0
$43$	−0.557675	+	0.557675i	−0.0850447	+	0.0850447i	−0.748349	−	0.663305i	$-0.769153\pi$
$43$	−0.557675	+	0.557675i	−0.0850447	+	0.0850447i	0.663305	+	0.748349i	$0.269153\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.16002			−0.898531			−0.449265	−	0.893398i	$-0.648314\pi$
$47$	−6.16002			−0.898531			−0.449265	+	0.893398i	$0.648314\pi$
$48$		0			0
$49$	15.0871			2.15529
$50$		0			0
$51$			1.52723i			0.213855i
$52$		0			0
$53$	−8.42127	−	8.42127i	−1.15675	−	1.15675i	−0.985170	−	0.171581i	$-0.945113\pi$
$53$	−8.42127	−	8.42127i	−1.15675	−	1.15675i	−0.171581	−	0.985170i	$-0.554887\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			4.93584i			0.653769i
$58$		0			0
$59$	1.44238	−	1.44238i	0.187782	−	0.187782i	−0.606955	−	0.794736i	$-0.707609\pi$
$59$	1.44238	−	1.44238i	0.187782	−	0.187782i	0.794736	+	0.606955i	$0.207609\pi$
$60$		0			0
$61$	−5.80499			−0.743253			−0.371626	−	0.928382i	$-0.621200\pi$
$61$	−5.80499			−0.743253			−0.371626	+	0.928382i	$0.621200\pi$
$62$		0			0
$63$		−	4.69969i		−	0.592105i
$64$		0			0
$65$		0			0
$66$		0			0
$67$			4.05741i			0.495691i	0.968800	+	0.247846i	$0.0797226\pi$
$67$			4.05741i			0.495691i	−0.968800	+	0.247846i	$0.920277\pi$
$68$		0			0
$69$	−4.92280			−0.592635
$70$		0			0
$71$	−6.68803	+	6.68803i	−0.793723	+	0.793723i	−0.982097	−	0.188374i	$-0.939678\pi$
$71$	−6.68803	+	6.68803i	−0.793723	+	0.793723i	0.188374	+	0.982097i	$0.439678\pi$
$72$		0			0
$73$		−	0.734212i		−	0.0859330i	−0.999077	−	0.0429665i	$-0.986319\pi$
$73$		−	0.734212i		−	0.0859330i	0.999077	−	0.0429665i	$-0.0136809\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.48205	−	1.48205i	−0.168896	−	0.168896i
$78$		0			0
$79$		−	12.9137i		−	1.45290i	−0.687218	−	0.726451i	$-0.741168\pi$
$79$		−	12.9137i		−	1.45290i	0.687218	−	0.726451i	$-0.258832\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	1.05600			0.115911			0.0579553	−	0.998319i	$-0.481542\pi$
$83$	1.05600			0.115911			0.0579553	+	0.998319i	$0.481542\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.03525	−	2.03525i	0.218202	−	0.218202i
$88$		0			0
$89$	−5.36534	+	5.36534i	−0.568725	+	0.568725i	−0.931771	−	0.363046i	$-0.881737\pi$
$89$	−5.36534	+	5.36534i	−0.568725	+	0.568725i	0.363046	+	0.931771i	$0.381737\pi$
$90$		0			0
$91$	−10.2079	+	13.5251i	−1.07008	+	1.41782i
$92$		0			0
$93$	−1.60322			−0.166246
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	4.56277i		−	0.463279i	−0.972802	−	0.231640i	$-0.925591\pi$
$97$		−	4.56277i		−	0.463279i	0.972802	−	0.231640i	$-0.0744090\pi$
$98$		0			0
$99$	−0.315352	+	0.315352i	−0.0316941	+	0.0316941i
$100$		0			0
$101$		−	8.68921i		−	0.864609i	−0.901728	−	0.432304i	$-0.857701\pi$
$101$		−	8.68921i		−	0.864609i	0.901728	−	0.432304i	$-0.142299\pi$
$102$		0			0
$103$	3.72580	−	3.72580i	0.367114	−	0.367114i	−0.499310	−	0.866424i	$-0.666413\pi$
$103$	3.72580	−	3.72580i	0.367114	−	0.367114i	0.866424	+	0.499310i	$0.166413\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.4478	−	12.4478i	1.20337	−	1.20337i	0.230240	−	0.973134i	$-0.426049\pi$
$107$	12.4478	−	12.4478i	1.20337	−	1.20337i	0.973134	−	0.230240i	$-0.0739512\pi$
$108$		0			0
$109$	−12.0020	−	12.0020i	−1.14958	−	1.14958i	−0.986635	−	0.162949i	$-0.947899\pi$
$109$	−12.0020	−	12.0020i	−1.14958	−	1.14958i	−0.162949	−	0.986635i	$-0.552101\pi$
$110$		0			0
$111$	−6.31304	−	6.31304i	−0.599207	−	0.599207i
$112$		0			0
$113$	−11.3426	−	11.3426i	−1.06702	−	1.06702i	−0.997586	−	0.0694367i	$-0.977880\pi$
$113$	−11.3426	−	11.3426i	−1.06702	−	1.06702i	−0.0694367	−	0.997586i	$-0.522120\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.87788	+	2.17205i	0.266060	+	0.200806i
$118$		0			0
$119$	−5.07526	−	5.07526i	−0.465249	−	0.465249i
$120$		0			0
$121$		−	10.8011i		−	0.981919i
$122$		0			0
$123$	8.63049			0.778185
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.73937	−	6.73937i	−0.598022	−	0.598022i	0.341764	−	0.939786i	$-0.388976\pi$
$127$	−6.73937	−	6.73937i	−0.598022	−	0.598022i	−0.939786	+	0.341764i	$0.888976\pi$
$128$		0			0
$129$	−0.788672			−0.0694387
$130$		0			0
$131$	−5.18022			−0.452598			−0.226299	−	0.974058i	$-0.572663\pi$
$131$	−5.18022			−0.452598			−0.226299	+	0.974058i	$0.572663\pi$
$132$		0			0
$133$	−16.4027	−	16.4027i	−1.42229	−	1.42229i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.8964			−1.44356			−0.721778	−	0.692124i	$-0.756675\pi$
$137$	−16.8964			−1.44356			−0.721778	+	0.692124i	$0.756675\pi$
$138$		0			0
$139$			3.05422i			0.259056i	0.991576	+	0.129528i	$0.0413462\pi$
$139$			3.05422i			0.259056i	−0.991576	+	0.129528i	$0.958654\pi$
$140$		0			0
$141$	−4.35579	−	4.35579i	−0.366824	−	0.366824i
$142$		0			0
$143$	1.59250	−	0.222587i	0.133172	−	0.0186136i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	10.6682	+	10.6682i	0.879895	+	0.879895i
$148$		0			0
$149$	0.623594	+	0.623594i	0.0510868	+	0.0510868i	0.732189	−	0.681102i	$-0.238499\pi$
$149$	0.623594	+	0.623594i	0.0510868	+	0.0510868i	−0.681102	+	0.732189i	$0.738499\pi$
$150$		0			0
$151$	5.84579	+	5.84579i	0.475724	+	0.475724i	0.903761	−	0.428037i	$-0.140795\pi$
$151$	5.84579	+	5.84579i	0.475724	+	0.475724i	−0.428037	+	0.903761i	$0.640795\pi$
$152$		0			0
$153$	−1.07992	+	1.07992i	−0.0873060	+	0.0873060i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−10.2125	+	10.2125i	−0.815046	+	0.815046i	−0.985385	−	0.170339i	$-0.945514\pi$
$157$	−10.2125	+	10.2125i	−0.815046	+	0.815046i	0.170339	+	0.985385i	$0.445514\pi$
$158$		0			0
$159$		−	11.9095i		−	0.944483i
$160$		0			0
$161$	16.3593	−	16.3593i	1.28930	−	1.28930i
$162$		0			0
$163$		−	23.2373i		−	1.82009i	−0.414511	−	0.910044i	$-0.636047\pi$
$163$		−	23.2373i		−	1.82009i	0.414511	−	0.910044i	$-0.363953\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.5054			0.967697			0.483848	−	0.875152i	$-0.339239\pi$
$167$	12.5054			0.967697			0.483848	+	0.875152i	$0.339239\pi$
$168$		0			0
$169$	−3.56442	−	12.5018i	−0.274186	−	0.961677i
$170$		0			0
$171$	−3.49017	+	3.49017i	−0.266900	+	0.266900i
$172$		0			0
$173$	18.3381	−	18.3381i	1.39422	−	1.39422i	0.578618	−	0.815599i	$-0.303592\pi$
$173$	18.3381	−	18.3381i	1.39422	−	1.39422i	0.815599	−	0.578618i	$-0.196408\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.03983			0.153323
$178$		0			0
$179$	−13.9880			−1.04552			−0.522758	−	0.852481i	$-0.675097\pi$
$179$	−13.9880			−1.04552			−0.522758	+	0.852481i	$0.675097\pi$
$180$		0			0
$181$			14.6342i			1.08775i	0.839165	+	0.543877i	$0.183044\pi$
$181$			14.6342i			1.08775i	−0.839165	+	0.543877i	$0.816956\pi$
$182$		0			0
$183$	−4.10475	−	4.10475i	−0.303432	−	0.303432i
$184$		0			0
$185$		0			0
$186$		0			0
$187$			0.681107i			0.0498074i
$188$		0			0
$189$	3.32318	−	3.32318i	0.241726	−	0.241726i
$190$		0			0
$191$	−13.6896			−0.990548			−0.495274	−	0.868737i	$-0.664932\pi$
$191$	−13.6896			−0.990548			−0.495274	+	0.868737i	$0.664932\pi$
$192$		0			0
$193$			11.3452i			0.816647i	0.912837	+	0.408323i	$0.133886\pi$
$193$			11.3452i			0.816647i	−0.912837	+	0.408323i	$0.866114\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			12.7625i			0.909294i	0.890672	+	0.454647i	$0.150234\pi$
$197$			12.7625i			0.909294i	−0.890672	+	0.454647i	$0.849766\pi$
$198$		0			0
$199$	2.52762			0.179178			0.0895892	−	0.995979i	$-0.471445\pi$
$199$	2.52762			0.179178			0.0895892	+	0.995979i	$0.471445\pi$
$200$		0			0
$201$	−2.86902	+	2.86902i	−0.202365	+	0.202365i
$202$		0			0
$203$			13.5270i			0.949409i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.48094	−	3.48094i	−0.241942	−	0.241942i
$208$		0			0
$209$			2.20126i			0.152265i
$210$		0			0
$211$	10.4839			0.721738			0.360869	−	0.932616i	$-0.382480\pi$
$211$	10.4839			0.721738			0.360869	+	0.932616i	$0.382480\pi$
$212$		0			0
$213$	−9.45830			−0.648072
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.32780	−	5.32780i	0.361675	−	0.361675i
$218$		0			0
$219$	0.519166	−	0.519166i	0.0350820	−	0.0350820i
$220$		0			0
$221$	5.45350	−	0.762243i	0.366842	−	0.0512740i
$222$		0			0
$223$	−1.90938			−0.127861			−0.0639306	−	0.997954i	$-0.520364\pi$
$223$	−1.90938			−0.127861			−0.0639306	+	0.997954i	$0.520364\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			28.0353i			1.86077i	0.366584	+	0.930385i	$0.380527\pi$
$227$			28.0353i			1.86077i	−0.366584	+	0.930385i	$0.619473\pi$
$228$		0			0
$229$	−5.80903	+	5.80903i	−0.383871	+	0.383871i	−0.872495	−	0.488623i	$-0.837499\pi$
$229$	−5.80903	+	5.80903i	−0.383871	+	0.383871i	0.488623	+	0.872495i	$0.337499\pi$
$230$		0			0
$231$		−	2.09594i		−	0.137903i
$232$		0			0
$233$	10.4654	−	10.4654i	0.685613	−	0.685613i	−0.275646	−	0.961259i	$-0.588892\pi$
$233$	10.4654	−	10.4654i	0.685613	−	0.685613i	0.961259	+	0.275646i	$0.0888919\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	9.13135	−	9.13135i	0.593145	−	0.593145i
$238$		0			0
$239$	−0.358095	−	0.358095i	−0.0231633	−	0.0231633i	0.695430	−	0.718594i	$-0.255214\pi$
$239$	−0.358095	−	0.358095i	−0.0231633	−	0.0231633i	−0.718594	+	0.695430i	$0.755214\pi$
$240$		0			0
$241$	−8.96339	−	8.96339i	−0.577383	−	0.577383i	0.356799	−	0.934181i	$-0.383868\pi$
$241$	−8.96339	−	8.96339i	−0.577383	−	0.577383i	−0.934181	+	0.356799i	$0.883868\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	17.6251	−	2.46349i	1.12146	−	0.156748i
$248$		0			0
$249$	0.746702	+	0.746702i	0.0473203	+	0.0473203i
$250$		0			0
$251$			10.3022i			0.650272i	0.945667	+	0.325136i	$0.105410\pi$
$251$			10.3022i			0.650272i	−0.945667	+	0.325136i	$0.894590\pi$
$252$		0			0
$253$	−2.19544			−0.138026
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−20.2281	−	20.2281i	−1.26179	−	1.26179i	−0.950222	−	0.311572i	$-0.899144\pi$
$257$	−20.2281	−	20.2281i	−1.26179	−	1.26179i	−0.311572	−	0.950222i	$-0.600856\pi$
$258$		0			0
$259$	41.9587			2.60719
$260$		0			0
$261$	2.87828			0.178161
$262$		0			0
$263$	5.83060	+	5.83060i	0.359530	+	0.359530i	0.863640	−	0.504110i	$-0.168179\pi$
$263$	5.83060	+	5.83060i	0.359530	+	0.359530i	−0.504110	+	0.863640i	$0.668179\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−7.58774			−0.464362
$268$		0			0
$269$			26.2933i			1.60313i	0.597906	+	0.801566i	$0.295999\pi$
$269$			26.2933i			1.60313i	−0.597906	+	0.801566i	$0.704001\pi$
$270$		0			0
$271$	−21.5497	−	21.5497i	−1.30905	−	1.30905i	−0.922100	−	0.386953i	$-0.873528\pi$
$271$	−21.5497	−	21.5497i	−1.30905	−	1.30905i	−0.386953	−	0.922100i	$-0.626472\pi$
$272$		0			0
$273$	−16.7818	+	2.34562i	−1.01568	+	0.141963i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	11.0701	+	11.0701i	0.665137	+	0.665137i	0.956586	−	0.291449i	$-0.0941375\pi$
$277$	11.0701	+	11.0701i	0.665137	+	0.665137i	−0.291449	+	0.956586i	$0.594137\pi$
$278$		0			0
$279$	−1.13365	−	1.13365i	−0.0678698	−	0.0678698i
$280$		0			0
$281$	13.6165	+	13.6165i	0.812291	+	0.812291i	0.984977	−	0.172686i	$-0.0552446\pi$
$281$	13.6165	+	13.6165i	0.812291	+	0.812291i	−0.172686	+	0.984977i	$0.555245\pi$
$282$		0			0
$283$	12.6708	−	12.6708i	0.753204	−	0.753204i	−0.221872	−	0.975076i	$-0.571217\pi$
$283$	12.6708	−	12.6708i	0.753204	−	0.753204i	0.975076	+	0.221872i	$0.0712168\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−28.6807	+	28.6807i	−1.69297	+	1.69297i
$288$		0			0
$289$		−	14.6676i		−	0.862798i
$290$		0			0
$291$	3.22637	−	3.22637i	0.189133	−	0.189133i
$292$		0			0
$293$			31.1560i			1.82015i	0.414439	+	0.910077i	$0.363978\pi$
$293$			31.1560i			1.82015i	−0.414439	+	0.910077i	$0.636022\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.445975			−0.0258781
$298$		0			0
$299$	2.45697	+	17.5785i	0.142090	+	1.01659i
$300$		0			0
$301$	2.62090	−	2.62090i	0.151066	−	0.151066i
$302$		0			0
$303$	6.14420	−	6.14420i	0.352975	−	0.352975i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−28.0732			−1.60222			−0.801110	−	0.598517i	$-0.795757\pi$
$307$	−28.0732			−1.60222			−0.801110	+	0.598517i	$0.795757\pi$
$308$		0			0
$309$	5.26907			0.299747
$310$		0			0
$311$			12.7252i			0.721579i	0.932647	+	0.360789i	$0.117493\pi$
$311$			12.7252i			0.721579i	−0.932647	+	0.360789i	$0.882507\pi$
$312$		0			0
$313$	14.1806	+	14.1806i	0.801534	+	0.801534i	0.983335	−	0.181801i	$-0.0581928\pi$
$313$	14.1806	+	14.1806i	0.801534	+	0.801534i	−0.181801	+	0.983335i	$0.558193\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			7.64077i			0.429148i	0.976708	+	0.214574i	$0.0688363\pi$
$317$			7.64077i			0.429148i	−0.976708	+	0.214574i	$0.931164\pi$
$318$		0			0
$319$	0.907670	−	0.907670i	0.0508198	−	0.0508198i
$320$		0			0
$321$	17.6038			0.982551
$322$		0			0
$323$			7.53817i			0.419435i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	16.9734i		−	0.938631i
$328$		0			0
$329$	28.9502			1.59607
$330$		0			0
$331$	15.0162	−	15.0162i	0.825365	−	0.825365i	−0.161507	−	0.986872i	$-0.551635\pi$
$331$	15.0162	−	15.0162i	0.825365	−	0.825365i	0.986872	+	0.161507i	$0.0516354\pi$
$332$		0			0
$333$		−	8.92799i		−	0.489251i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−9.44617	−	9.44617i	−0.514566	−	0.514566i	0.401356	−	0.915922i	$-0.368539\pi$
$337$	−9.44617	−	9.44617i	−0.514566	−	0.514566i	−0.915922	+	0.401356i	$0.868539\pi$
$338$		0			0
$339$		−	16.0409i		−	0.871221i
$340$		0			0
$341$	−0.714997			−0.0387193
$342$		0			0
$343$	−38.0066			−2.05217
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.5249	+	20.5249i	−1.10183	+	1.10183i	−0.107642	+	0.994190i	$0.534330\pi$
$347$	−20.5249	+	20.5249i	−1.10183	+	1.10183i	−0.994190	+	0.107642i	$0.965670\pi$
$348$		0			0
$349$	1.54929	−	1.54929i	0.0829316	−	0.0829316i	−0.664424	−	0.747356i	$-0.731323\pi$
$349$	1.54929	−	1.54929i	0.0829316	−	0.0829316i	0.747356	+	0.664424i	$0.231323\pi$
$350$		0			0
$351$	0.499101	+	3.57084i	0.0266401	+	0.190597i
$352$		0			0
$353$	−9.75270			−0.519084			−0.259542	−	0.965732i	$-0.583572\pi$
$353$	−9.75270			−0.519084			−0.259542	+	0.965732i	$0.583572\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	7.17751i		−	0.379874i
$358$		0			0
$359$	−2.81152	+	2.81152i	−0.148387	+	0.148387i	−0.777397	−	0.629010i	$-0.783460\pi$
$359$	−2.81152	+	2.81152i	−0.148387	+	0.148387i	0.629010	+	0.777397i	$0.283460\pi$
$360$		0			0
$361$			5.36257i			0.282240i
$362$		0			0
$363$	7.63754	−	7.63754i	0.400867	−	0.400867i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	23.2265	−	23.2265i	1.21241	−	1.21241i	0.242184	−	0.970230i	$-0.422136\pi$
$367$	23.2265	−	23.2265i	1.21241	−	1.21241i	0.970230	−	0.242184i	$-0.0778636\pi$
$368$		0			0
$369$	6.10267	+	6.10267i	0.317693	+	0.317693i
$370$		0			0
$371$	39.5773	+	39.5773i	2.05475	+	2.05475i
$372$		0			0
$373$	3.06758	+	3.06758i	0.158833	+	0.158833i	0.782050	−	0.623216i	$-0.214174\pi$
$373$	3.06758	+	3.06758i	0.158833	+	0.158833i	−0.623216	+	0.782050i	$0.714174\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.28334	−	6.25175i	−0.426614	−	0.321982i
$378$		0			0
$379$	−16.7416	−	16.7416i	−0.859959	−	0.859959i	0.131374	−	0.991333i	$-0.458061\pi$
$379$	−16.7416	−	16.7416i	−0.859959	−	0.859959i	−0.991333	+	0.131374i	$0.958061\pi$
$380$		0			0
$381$		−	9.53091i		−	0.488283i
$382$		0			0
$383$	5.16648			0.263995			0.131997	−	0.991250i	$-0.457861\pi$
$383$	5.16648			0.263995			0.131997	+	0.991250i	$0.457861\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.557675	−	0.557675i	−0.0283482	−	0.0283482i
$388$		0			0
$389$	4.92391			0.249652			0.124826	−	0.992179i	$-0.460163\pi$
$389$	4.92391			0.249652			0.124826	+	0.992179i	$0.460163\pi$
$390$		0			0
$391$	−7.51825			−0.380214
$392$		0			0
$393$	−3.66297	−	3.66297i	−0.184772	−	0.184772i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	26.9445			1.35231			0.676154	−	0.736760i	$-0.263645\pi$
$397$	26.9445			1.35231			0.676154	+	0.736760i	$0.263645\pi$
$398$		0			0
$399$		−	23.1969i		−	1.16130i
$400$		0			0
$401$	−25.1188	−	25.1188i	−1.25437	−	1.25437i	−0.953739	−	0.300635i	$-0.902801\pi$
$401$	−25.1188	−	25.1188i	−1.25437	−	1.25437i	−0.300635	−	0.953739i	$-0.597199\pi$
$402$		0			0
$403$	0.800171	+	5.72485i	0.0398593	+	0.285175i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.81546	−	2.81546i	−0.139557	−	0.139557i
$408$		0			0
$409$	−0.765296	−	0.765296i	−0.0378414	−	0.0378414i	0.687933	−	0.725774i	$-0.258518\pi$
$409$	−0.765296	−	0.765296i	−0.0378414	−	0.0378414i	−0.725774	+	0.687933i	$0.758518\pi$
$410$		0			0
$411$	−11.9476	−	11.9476i	−0.589330	−	0.589330i
$412$		0			0
$413$	−6.77873	+	6.77873i	−0.333559	+	0.333559i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.15966	+	2.15966i	−0.105759	+	0.105759i
$418$		0			0
$419$			6.89257i			0.336724i	0.985725	+	0.168362i	$0.0538477\pi$
$419$			6.89257i			0.336724i	−0.985725	+	0.168362i	$0.946152\pi$
$420$		0			0
$421$	19.8483	−	19.8483i	0.967349	−	0.967349i	−0.0321346	−	0.999484i	$-0.510231\pi$
$421$	19.8483	−	19.8483i	0.967349	−	0.967349i	0.999484	+	0.0321346i	$0.0102305\pi$
$422$		0			0
$423$		−	6.16002i		−	0.299510i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	27.2816			1.32025
$428$		0			0
$429$	1.28346	+	0.968678i	0.0619662	+	0.0467682i
$430$		0			0
$431$	−18.3880	+	18.3880i	−0.885718	+	0.885718i	−0.994108	−	0.108391i	$-0.965430\pi$
$431$	−18.3880	+	18.3880i	−0.885718	+	0.885718i	0.108391	+	0.994108i	$0.465430\pi$
$432$		0			0
$433$	6.17848	−	6.17848i	0.296919	−	0.296919i	−0.542887	−	0.839806i	$-0.682669\pi$
$433$	6.17848	−	6.17848i	0.296919	−	0.296919i	0.839806	+	0.542887i	$0.182669\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−24.2982			−1.16234
$438$		0			0
$439$	−15.7983			−0.754013			−0.377006	−	0.926211i	$-0.623046\pi$
$439$	−15.7983			−0.754013			−0.377006	+	0.926211i	$0.623046\pi$
$440$		0			0
$441$			15.0871i			0.718431i
$442$		0			0
$443$	7.28734	+	7.28734i	0.346232	+	0.346232i	0.858704	−	0.512472i	$-0.171270\pi$
$443$	7.28734	+	7.28734i	0.346232	+	0.346232i	−0.512472	+	0.858704i	$0.671270\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			0.881895i			0.0417122i
$448$		0			0
$449$	11.9047	−	11.9047i	0.561819	−	0.561819i	−0.368005	−	0.929824i	$-0.619959\pi$
$449$	11.9047	−	11.9047i	0.561819	−	0.561819i	0.929824	+	0.368005i	$0.119959\pi$
$450$		0			0
$451$	3.84898			0.181241
$452$		0			0
$453$			8.26719i			0.388427i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	10.4884i		−	0.490628i	−0.969444	−	0.245314i	$-0.921109\pi$
$457$		−	10.4884i		−	0.490628i	0.969444	−	0.245314i	$-0.0788911\pi$
$458$		0			0
$459$	−1.52723			−0.0712850
$460$		0			0
$461$	−17.4899	+	17.4899i	−0.814587	+	0.814587i	−0.985318	−	0.170731i	$-0.945387\pi$
$461$	−17.4899	+	17.4899i	−0.814587	+	0.814587i	0.170731	+	0.985318i	$0.445387\pi$
$462$		0			0
$463$		−	16.3159i		−	0.758266i	−0.925342	−	0.379133i	$-0.876222\pi$
$463$		−	16.3159i		−	0.758266i	0.925342	−	0.379133i	$-0.123778\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.5684	−	13.5684i	−0.627870	−	0.627870i	0.319662	−	0.947532i	$-0.396431\pi$
$467$	−13.5684	−	13.5684i	−0.627870	−	0.627870i	−0.947532	+	0.319662i	$0.896431\pi$
$468$		0			0
$469$		−	19.0686i		−	0.880504i
$470$		0			0
$471$	−14.4427			−0.665482
$472$		0			0
$473$	−0.351728			−0.0161725
$474$		0			0
$475$		0			0
$476$		0			0
$477$	8.42127	−	8.42127i	0.385584	−	0.385584i
$478$		0			0
$479$	−17.7533	+	17.7533i	−0.811171	+	0.811171i	−0.984809	−	0.173639i	$-0.944448\pi$
$479$	−17.7533	+	17.7533i	−0.811171	+	0.811171i	0.173639	+	0.984809i	$0.444448\pi$
$480$		0			0
$481$	−19.3920	+	25.6937i	−0.884200	+	1.17153i
$482$		0			0
$483$	23.1356			1.05271
$484$		0			0
$485$		0			0
$486$		0			0
$487$			33.7675i			1.53015i	0.643941	+	0.765075i	$0.277298\pi$
$487$			33.7675i			1.53015i	−0.643941	+	0.765075i	$0.722702\pi$
$488$		0			0
$489$	16.4313	−	16.4313i	0.743048	−	0.743048i
$490$		0			0
$491$		−	22.9938i		−	1.03770i	−0.854866	−	0.518849i	$-0.826361\pi$
$491$		−	22.9938i		−	1.03770i	0.854866	−	0.518849i	$-0.173639\pi$
$492$		0			0
$493$	3.10830	−	3.10830i	0.139991	−	0.139991i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	31.4317	−	31.4317i	1.40990	−	1.40990i
$498$		0			0
$499$	6.02065	+	6.02065i	0.269521	+	0.269521i	0.828907	−	0.559386i	$-0.188963\pi$
$499$	6.02065	+	6.02065i	0.269521	+	0.269521i	−0.559386	+	0.828907i	$0.688963\pi$
$500$		0			0
$501$	8.84265	+	8.84265i	0.395060	+	0.395060i
$502$		0			0
$503$	10.3721	+	10.3721i	0.462470	+	0.462470i	0.899464	−	0.436995i	$-0.143957\pi$
$503$	10.3721	+	10.3721i	0.462470	+	0.462470i	−0.436995	+	0.899464i	$0.643957\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.31968	−	11.3605i	0.280667	−	0.504539i
$508$		0			0
$509$	−5.39148	−	5.39148i	−0.238973	−	0.238973i	0.577452	−	0.816425i	$-0.304047\pi$
$509$	−5.39148	−	5.39148i	−0.238973	−	0.238973i	−0.816425	+	0.577452i	$0.804047\pi$
$510$		0			0
$511$			3.45057i			0.152644i
$512$		0			0
$513$	−4.93584			−0.217923
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.94257	−	1.94257i	−0.0854343	−	0.0854343i
$518$		0			0
$519$	25.9339			1.13837
$520$		0			0
$521$	42.1874			1.84826			0.924131	−	0.382076i	$-0.124791\pi$
$521$	42.1874			1.84826			0.924131	+	0.382076i	$0.124791\pi$
$522$		0			0
$523$	−11.3298	−	11.3298i	−0.495417	−	0.495417i	0.414591	−	0.910008i	$-0.363925\pi$
$523$	−11.3298	−	11.3298i	−0.495417	−	0.495417i	−0.910008	+	0.414591i	$0.863925\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.44849			−0.106658
$528$		0			0
$529$		−	1.23393i		−	0.0536492i
$530$		0			0
$531$	1.44238	+	1.44238i	0.0625939	+	0.0625939i
$532$		0			0
$533$	−4.30749	−	30.8181i	−0.186578	−	1.33488i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−9.89104	−	9.89104i	−0.426830	−	0.426830i
$538$		0			0
$539$	4.75773	+	4.75773i	0.204930	+	0.204930i
$540$		0			0
$541$	−11.3903	−	11.3903i	−0.489709	−	0.489709i	0.418506	−	0.908214i	$-0.362554\pi$
$541$	−11.3903	−	11.3903i	−0.489709	−	0.489709i	−0.908214	+	0.418506i	$0.862554\pi$
$542$		0			0
$543$	−10.3480	+	10.3480i	−0.444074	+	0.444074i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−11.3855	+	11.3855i	−0.486809	+	0.486809i	−0.907298	−	0.420489i	$-0.861859\pi$
$547$	−11.3855	+	11.3855i	−0.486809	+	0.486809i	0.420489	+	0.907298i	$0.361859\pi$
$548$		0			0
$549$		−	5.80499i		−	0.247751i
$550$		0			0
$551$	10.0457	−	10.0457i	0.427960	−	0.427960i
$552$		0			0
$553$			60.6902i			2.58081i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−34.1016			−1.44493			−0.722465	−	0.691408i	$-0.756991\pi$
$557$	−34.1016			−1.44493			−0.722465	+	0.691408i	$0.756991\pi$
$558$		0			0
$559$	0.393627	+	2.81622i	0.0166487	+	0.119113i
$560$		0			0
$561$	−0.481615	+	0.481615i	−0.0203338	+	0.0203338i
$562$		0			0
$563$	−25.7769	+	25.7769i	−1.08637	+	1.08637i	−0.0904666	+	0.995899i	$0.528836\pi$
$563$	−25.7769	+	25.7769i	−1.08637	+	1.08637i	−0.995899	+	0.0904666i	$0.971164\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	4.69969			0.197368
$568$		0			0
$569$	−26.2934			−1.10228			−0.551138	−	0.834414i	$-0.685806\pi$
$569$	−26.2934			−1.10228			−0.551138	+	0.834414i	$0.685806\pi$
$570$		0			0
$571$		−	14.6838i		−	0.614496i	−0.951629	−	0.307248i	$-0.900592\pi$
$571$		−	14.6838i		−	0.614496i	0.951629	−	0.307248i	$-0.0994082\pi$
$572$		0			0
$573$	−9.68004	−	9.68004i	−0.404389	−	0.404389i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			23.1978i			0.965735i	0.875693	+	0.482868i	$0.160405\pi$
$577$			23.1978i			0.965735i	−0.875693	+	0.482868i	$0.839595\pi$
$578$		0			0
$579$	−8.02228	+	8.02228i	−0.333395	+	0.333395i
$580$		0			0
$581$	−4.96285			−0.205894
$582$		0			0
$583$		−	5.31133i		−	0.219973i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			7.91675i			0.326759i	0.986563	+	0.163380i	$0.0522395\pi$
$587$			7.91675i			0.326759i	−0.986563	+	0.163380i	$0.947760\pi$
$588$		0			0
$589$	−7.91326			−0.326060
$590$		0			0
$591$	−9.02448	+	9.02448i	−0.371218	+	0.371218i
$592$		0			0
$593$			43.6618i			1.79297i	0.443071	+	0.896487i	$0.353889\pi$
$593$			43.6618i			1.79297i	−0.443071	+	0.896487i	$0.646111\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.78730	+	1.78730i	0.0731492	+	0.0731492i
$598$		0			0
$599$			15.5444i			0.635126i	0.948237	+	0.317563i	$0.102864\pi$
$599$			15.5444i			0.635126i	−0.948237	+	0.317563i	$0.897136\pi$
$600$		0			0
$601$	−7.39443			−0.301625			−0.150813	−	0.988562i	$-0.548189\pi$
$601$	−7.39443			−0.301625			−0.150813	+	0.988562i	$0.548189\pi$
$602$		0			0
$603$	−4.05741			−0.165230
$604$		0			0
$605$		0			0
$606$		0			0
$607$	29.2174	−	29.2174i	1.18590	−	1.18590i	0.207705	−	0.978192i	$-0.433401\pi$
$607$	29.2174	−	29.2174i	1.18590	−	1.18590i	0.978192	−	0.207705i	$-0.0665994\pi$
$608$		0			0
$609$	−9.56503	+	9.56503i	−0.387595	+	0.387595i
$610$		0			0
$611$	−13.3798	+	17.7278i	−0.541291	+	0.717190i
$612$		0			0
$613$	−39.5039			−1.59555			−0.797774	−	0.602957i	$-0.793989\pi$
$613$	−39.5039			−1.59555			−0.797774	+	0.602957i	$0.793989\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			2.88852i			0.116288i	0.998308	+	0.0581438i	$0.0185182\pi$
$617$			2.88852i			0.116288i	−0.998308	+	0.0581438i	$0.981482\pi$
$618$		0			0
$619$	−13.1526	+	13.1526i	−0.528649	+	0.528649i	−0.920169	−	0.391520i	$-0.871949\pi$
$619$	−13.1526	+	13.1526i	−0.528649	+	0.528649i	0.391520	+	0.920169i	$0.371949\pi$
$620$		0			0
$621$		−	4.92280i		−	0.197545i
$622$		0			0
$623$	25.2154	−	25.2154i	1.01023	−	1.01023i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.55653	+	1.55653i	−0.0621617	+	0.0621617i
$628$		0			0
$629$	−9.64147	−	9.64147i	−0.384431	−	0.384431i
$630$		0			0
$631$	−26.9044	−	26.9044i	−1.07105	−	1.07105i	−0.997275	−	0.0737713i	$-0.976497\pi$
$631$	−26.9044	−	26.9044i	−1.07105	−	1.07105i	−0.0737713	−	0.997275i	$-0.523503\pi$
$632$		0			0
$633$	7.41320	+	7.41320i	0.294648	+	0.294648i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	32.7698	−	43.4188i	1.29839	−	1.72032i
$638$		0			0
$639$	−6.68803	−	6.68803i	−0.264574	−	0.264574i
$640$		0			0
$641$			7.72592i			0.305156i	0.988291	+	0.152578i	$0.0487575\pi$
$641$			7.72592i			0.305156i	−0.988291	+	0.152578i	$0.951243\pi$
$642$		0			0
$643$	17.3325			0.683528			0.341764	−	0.939786i	$-0.388976\pi$
$643$	17.3325			0.683528			0.341764	+	0.939786i	$0.388976\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.2911	+	11.2911i	0.443898	+	0.443898i	0.893320	−	0.449421i	$-0.148370\pi$
$647$	11.2911	+	11.2911i	0.443898	+	0.443898i	−0.449421	+	0.893320i	$0.648370\pi$
$648$		0			0
$649$	0.909714			0.0357094
$650$		0			0
$651$	7.53465			0.295306
$652$		0			0
$653$	19.3452	+	19.3452i	0.757037	+	0.757037i	0.975782	−	0.218745i	$-0.0701963\pi$
$653$	19.3452	+	19.3452i	0.757037	+	0.757037i	−0.218745	+	0.975782i	$0.570196\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.734212			0.0286443
$658$		0			0
$659$			41.8280i			1.62939i	0.579890	+	0.814695i	$0.303095\pi$
$659$			41.8280i			1.62939i	−0.579890	+	0.814695i	$0.696905\pi$
$660$		0			0
$661$	−14.9894	−	14.9894i	−0.583022	−	0.583022i	0.352711	−	0.935732i	$-0.385260\pi$
$661$	−14.9894	−	14.9894i	−0.583022	−	0.583022i	−0.935732	+	0.352711i	$0.885260\pi$
$662$		0			0
$663$	4.39519	+	3.31722i	0.170695	+	0.128830i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	10.0191	+	10.0191i	0.387942	+	0.387942i
$668$		0			0
$669$	−1.35013	−	1.35013i	−0.0521991	−	0.0521991i
$670$		0			0
$671$	−1.83061	−	1.83061i	−0.0706701	−	0.0706701i
$672$		0			0
$673$	11.3096	−	11.3096i	0.435952	−	0.435952i	−0.454695	−	0.890647i	$-0.650252\pi$
$673$	11.3096	−	11.3096i	0.435952	−	0.435952i	0.890647	+	0.454695i	$0.150252\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.2625	−	14.2625i	0.548153	−	0.548153i	−0.377753	−	0.925906i	$-0.623303\pi$
$677$	14.2625	−	14.2625i	0.548153	−	0.548153i	0.925906	+	0.377753i	$0.123303\pi$
$678$		0			0
$679$			21.4436i			0.822930i
$680$		0			0
$681$	−19.8240	+	19.8240i	−0.759656	+	0.759656i
$682$		0			0
$683$		−	24.2502i		−	0.927910i	−0.885859	−	0.463955i	$-0.846430\pi$
$683$		−	24.2502i		−	0.927910i	0.885859	−	0.463955i	$-0.153570\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.21520			−0.313430
$688$		0			0
$689$	−42.5268	+	5.94404i	−1.62014	+	0.226450i
$690$		0			0
$691$	18.8507	−	18.8507i	0.717116	−	0.717116i	−0.250898	−	0.968014i	$-0.580726\pi$
$691$	18.8507	−	18.8507i	0.717116	−	0.717116i	0.968014	+	0.250898i	$0.0807257\pi$
$692$		0			0
$693$	1.48205	−	1.48205i	0.0562986	−	0.0562986i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	13.1807			0.499256
$698$		0			0
$699$	14.8003			0.559800
$700$		0			0
$701$		−	23.7436i		−	0.896783i	−0.893837	−	0.448392i	$-0.851997\pi$
$701$		−	23.7436i		−	0.896783i	0.893837	−	0.448392i	$-0.148003\pi$
$702$		0			0
$703$	−31.1602	−	31.1602i	−1.17523	−	1.17523i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			40.8366i			1.53582i
$708$		0			0
$709$	−6.02523	+	6.02523i	−0.226282	+	0.226282i	−0.811138	−	0.584855i	$-0.801151\pi$
$709$	−6.02523	+	6.02523i	−0.226282	+	0.226282i	0.584855	+	0.811138i	$0.301151\pi$
$710$		0			0
$711$	12.9137			0.484301
$712$		0			0
$713$		−	7.89234i		−	0.295571i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	0.506423i		−	0.0189127i
$718$		0			0
$719$	−5.39301			−0.201125			−0.100563	−	0.994931i	$-0.532064\pi$
$719$	−5.39301			−0.201125			−0.100563	+	0.994931i	$0.532064\pi$
$720$		0			0
$721$	−17.5101	+	17.5101i	−0.652109	+	0.652109i
$722$		0			0
$723$		−	12.6761i		−	0.471431i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	27.4677	+	27.4677i	1.01872	+	1.01872i	0.999821	+	0.0188979i	$0.00601576\pi$
$727$	27.4677	+	27.4677i	1.01872	+	1.01872i	0.0188979	+	0.999821i	$0.493984\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−1.20448			−0.0445495
$732$		0			0
$733$	40.5951			1.49941			0.749707	−	0.661770i	$-0.230194\pi$
$733$	40.5951			1.49941			0.749707	+	0.661770i	$0.230194\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.27951	+	1.27951i	−0.0471314	+	0.0471314i
$738$		0			0
$739$	−19.5815	+	19.5815i	−0.720315	+	0.720315i	−0.968669	−	0.248354i	$-0.920110\pi$
$739$	−19.5815	+	19.5815i	−0.720315	+	0.720315i	0.248354	+	0.968669i	$0.420110\pi$
$740$		0			0
$741$	14.2048	+	10.7209i	0.521826	+	0.393842i
$742$		0			0
$743$	−33.1542			−1.21631			−0.608155	−	0.793818i	$-0.708090\pi$
$743$	−33.1542			−1.21631			−0.608155	+	0.793818i	$0.708090\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			1.05600i			0.0386369i
$748$		0			0
$749$	−58.5008	+	58.5008i	−2.13757	+	2.13757i
$750$		0			0
$751$			9.49285i			0.346399i	0.984887	+	0.173200i	$0.0554105\pi$
$751$			9.49285i			0.346399i	−0.984887	+	0.173200i	$0.944589\pi$
$752$		0			0
$753$	−7.28479	+	7.28479i	−0.265472	+	0.265472i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−2.84463	+	2.84463i	−0.103390	+	0.103390i	−0.756909	−	0.653520i	$-0.773292\pi$
$757$	−2.84463	+	2.84463i	−0.103390	+	0.103390i	0.653520	+	0.756909i	$0.273292\pi$
$758$		0			0
$759$	−1.55241	−	1.55241i	−0.0563490	−	0.0563490i
$760$		0			0
$761$	33.6477	+	33.6477i	1.21973	+	1.21973i	0.967727	+	0.252002i	$0.0810888\pi$
$761$	33.6477	+	33.6477i	1.21973	+	1.21973i	0.252002	+	0.967727i	$0.418911\pi$
$762$		0			0
$763$	56.4057	+	56.4057i	2.04202	+	2.04202i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.01808	−	7.28391i	−0.0367608	−	0.263007i
$768$		0			0
$769$	2.09238	+	2.09238i	0.0754532	+	0.0754532i	0.743826	−	0.668373i	$-0.233009\pi$
$769$	2.09238	+	2.09238i	0.0754532	+	0.0754532i	−0.668373	+	0.743826i	$0.733009\pi$
$770$		0			0
$771$		−	28.6069i		−	1.03025i
$772$		0			0
$773$	33.8949			1.21911			0.609557	−	0.792742i	$-0.291347\pi$
$773$	33.8949			1.21911			0.609557	+	0.792742i	$0.291347\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	29.6693	+	29.6693i	1.06438	+	1.06438i
$778$		0			0
$779$	42.5987			1.52626
$780$		0			0
$781$	−4.21817			−0.150938
$782$		0			0
$783$	2.03525	+	2.03525i	0.0727339	+	0.0727339i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−13.3356			−0.475363			−0.237682	−	0.971343i	$-0.576388\pi$
$787$	−13.3356			−0.475363			−0.237682	+	0.971343i	$0.576388\pi$
$788$		0			0
$789$			8.24571i			0.293555i
$790$		0			0
$791$	53.3067	+	53.3067i	1.89537	+	1.89537i
$792$		0			0
$793$	−12.6087	+	16.7061i	−0.447748	+	0.593250i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.21618	−	2.21618i	−0.0785012	−	0.0785012i	0.666766	−	0.745267i	$-0.267678\pi$
$797$	−2.21618	−	2.21618i	−0.0785012	−	0.0785012i	−0.745267	+	0.666766i	$0.767678\pi$
$798$		0			0
$799$	−6.65230	−	6.65230i	−0.235341	−	0.235341i
$800$		0			0
$801$	−5.36534	−	5.36534i	−0.189575	−	0.189575i
$802$		0			0
$803$	0.231535	−	0.231535i	0.00817069	−	0.00817069i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−18.5922	+	18.5922i	−0.654476	+	0.654476i
$808$		0			0
$809$			10.3854i			0.365131i	0.983194	+	0.182565i	$0.0584401\pi$
$809$			10.3854i			0.365131i	−0.983194	+	0.182565i	$0.941560\pi$
$810$		0			0
$811$	−2.72201	+	2.72201i	−0.0955825	+	0.0955825i	−0.753281	−	0.657699i	$-0.771530\pi$
$811$	−2.72201	+	2.72201i	−0.0955825	+	0.0955825i	0.657699	+	0.753281i	$0.271530\pi$
$812$		0			0
$813$		−	30.4759i		−	1.06884i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.89276			−0.136191
$818$		0			0
$819$	−13.5251	−	10.2079i	−0.472607	−	0.356694i
$820$		0			0
$821$	3.79821	−	3.79821i	0.132558	−	0.132558i	−0.637714	−	0.770273i	$-0.720120\pi$
$821$	3.79821	−	3.79821i	0.132558	−	0.132558i	0.770273	+	0.637714i	$0.220120\pi$
$822$		0			0
$823$	36.2441	−	36.2441i	1.26339	−	1.26339i	0.313951	−	0.949439i	$-0.398347\pi$
$823$	36.2441	−	36.2441i	1.26339	−	1.26339i	0.949439	−	0.313951i	$-0.101653\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.2770			1.26147			0.630737	−	0.775996i	$-0.282753\pi$
$827$	36.2770			1.26147			0.630737	+	0.775996i	$0.282753\pi$
$828$		0			0
$829$	−11.4935			−0.399185			−0.199592	−	0.979879i	$-0.563962\pi$
$829$	−11.4935			−0.399185			−0.199592	+	0.979879i	$0.563962\pi$
$830$		0			0
$831$			15.6555i			0.543082i
$832$		0			0
$833$	16.2927	+	16.2927i	0.564510	+	0.564510i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	1.60322i		−	0.0554155i
$838$		0			0
$839$	−20.5056	+	20.5056i	−0.707931	+	0.707931i	−0.966100	−	0.258169i	$-0.916881\pi$
$839$	−20.5056	+	20.5056i	−0.707931	+	0.707931i	0.258169	+	0.966100i	$0.416881\pi$
$840$		0			0
$841$	20.7155			0.714328
$842$		0			0
$843$			19.2566i			0.663233i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			50.7618i			1.74420i
$848$		0			0
$849$	17.9193			0.614988
$850$		0			0
$851$	31.0778	−	31.0778i	1.06533	−	1.06533i
$852$		0			0
$853$			10.6968i			0.366253i	0.983089	+	0.183126i	$0.0586217\pi$
$853$			10.6968i			0.366253i	−0.983089	+	0.183126i	$0.941378\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−20.4311	−	20.4311i	−0.697912	−	0.697912i	0.266048	−	0.963960i	$-0.414282\pi$
$857$	−20.4311	−	20.4311i	−0.697912	−	0.697912i	−0.963960	+	0.266048i	$0.914282\pi$
$858$		0			0
$859$			31.0854i			1.06062i	0.847803	+	0.530311i	$0.177925\pi$
$859$			31.0854i			1.06062i	−0.847803	+	0.530311i	$0.822075\pi$
$860$		0			0
$861$	−40.5606			−1.38230
$862$		0			0
$863$	32.6466			1.11130			0.555651	−	0.831415i	$-0.312469\pi$
$863$	32.6466			1.11130			0.555651	+	0.831415i	$0.312469\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	10.3715	−	10.3715i	0.352236	−	0.352236i
$868$		0			0
$869$	4.07235	−	4.07235i	0.138145	−	0.138145i
$870$		0			0
$871$	11.6768	+	8.81289i	0.395652	+	0.298613i
$872$		0			0
$873$	4.56277			0.154426
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	24.8946i		−	0.840629i	−0.907378	−	0.420315i	$-0.861920\pi$
$877$		−	24.8946i		−	0.840629i	0.907378	−	0.420315i	$-0.138080\pi$
$878$		0			0
$879$	−22.0306	+	22.0306i	−0.743075	+	0.743075i
$880$		0			0
$881$		−	57.1910i		−	1.92681i	−0.268046	−	0.963406i	$-0.586378\pi$
$881$		−	57.1910i		−	1.92681i	0.268046	−	0.963406i	$-0.413622\pi$
$882$		0			0
$883$	−18.8928	+	18.8928i	−0.635793	+	0.635793i	−0.949515	−	0.313722i	$-0.898424\pi$
$883$	−18.8928	+	18.8928i	−0.635793	+	0.635793i	0.313722	+	0.949515i	$0.398424\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.5287	−	14.5287i	0.487826	−	0.487826i	−0.419794	−	0.907620i	$-0.637898\pi$
$887$	14.5287	−	14.5287i	0.487826	−	0.487826i	0.907620	+	0.419794i	$0.137898\pi$
$888$		0			0
$889$	31.6729	+	31.6729i	1.06228	+	1.06228i
$890$		0			0
$891$	−0.315352	−	0.315352i	−0.0105647	−	0.0105647i
$892$		0			0
$893$	−21.4995	−	21.4995i	−0.719454	−	0.719454i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−10.6925	+	14.1672i	−0.357014	+	0.473030i
$898$		0			0
$899$	3.26296	+	3.26296i	0.108826	+	0.108826i
$900$		0			0
$901$		−	18.1885i		−	0.605948i
$902$		0			0
$903$	3.70651			0.123345
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−14.2325	−	14.2325i	−0.472583	−	0.472583i	0.430166	−	0.902750i	$-0.358455\pi$
$907$	−14.2325	−	14.2325i	−0.472583	−	0.472583i	−0.902750	+	0.430166i	$0.858455\pi$
$908$		0			0
$909$	8.68921			0.288203
$910$		0			0
$911$	32.2436			1.06828			0.534139	−	0.845397i	$-0.320636\pi$
$911$	32.2436			1.06828			0.534139	+	0.845397i	$0.320636\pi$
$912$		0			0
$913$	0.333010	+	0.333010i	0.0110210	+	0.0110210i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.3454			0.803956
$918$		0			0
$919$		−	9.73620i		−	0.321168i	−0.987022	−	0.160584i	$-0.948662\pi$
$919$		−	9.73620i		−	0.321168i	0.987022	−	0.160584i	$-0.0513377\pi$
$920$		0			0
$921$	−19.8507	−	19.8507i	−0.654103	−	0.654103i
$922$		0			0
$923$	4.72065	+	33.7741i	0.155382	+	1.11169i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.72580	+	3.72580i	0.122371	+	0.122371i
$928$		0			0
$929$	−9.82032	−	9.82032i	−0.322194	−	0.322194i	0.527414	−	0.849608i	$-0.323162\pi$
$929$	−9.82032	−	9.82032i	−0.322194	−	0.322194i	−0.849608	+	0.527414i	$0.823162\pi$
$930$		0			0
$931$	52.6564	+	52.6564i	1.72574	+	1.72574i
$932$		0			0
$933$	−8.99806	+	8.99806i	−0.294583	+	0.294583i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	6.29485	−	6.29485i	0.205644	−	0.205644i	−0.596769	−	0.802413i	$-0.703549\pi$
$937$	6.29485	−	6.29485i	0.205644	−	0.205644i	0.802413	+	0.596769i	$0.203549\pi$
$938$		0			0
$939$			20.0544i			0.654450i
$940$		0			0
$941$	32.4276	−	32.4276i	1.05711	−	1.05711i	0.0588409	−	0.998267i	$-0.481260\pi$
$941$	32.4276	−	32.4276i	1.05711	−	1.05711i	0.998267	−	0.0588409i	$-0.0187405\pi$
$942$		0			0
$943$			42.4861i			1.38354i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	41.1923			1.33857			0.669285	−	0.743006i	$-0.266601\pi$
$947$	41.1923			1.33857			0.669285	+	0.743006i	$0.266601\pi$
$948$		0			0
$949$	−2.11298	−	1.59474i	−0.0685901	−	0.0517675i
$950$		0			0
$951$	−5.40284	+	5.40284i	−0.175199	+	0.175199i
$952$		0			0
$953$	−33.0574	+	33.0574i	−1.07083	+	1.07083i	−0.0735423	+	0.997292i	$0.523430\pi$
$953$	−33.0574	+	33.0574i	−1.07083	+	1.07083i	−0.997292	+	0.0735423i	$0.976570\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.28364			0.0414942
$958$		0			0
$959$	79.4078			2.56421
$960$		0			0
$961$			28.4297i			0.917086i
$962$		0			0
$963$	12.4478	+	12.4478i	0.401125	+	0.401125i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			54.2975i			1.74609i	0.487640	+	0.873045i	$0.337858\pi$
$967$			54.2975i			1.74609i	−0.487640	+	0.873045i	$0.662142\pi$
$968$		0			0
$969$	−5.33029	+	5.33029i	−0.171234	+	0.171234i
$970$		0			0
$971$	−48.8468			−1.56757			−0.783785	−	0.621033i	$-0.786713\pi$
$971$	−48.8468			−1.56757			−0.783785	+	0.621033i	$0.786713\pi$
$972$		0			0
$973$		−	14.3539i		−	0.460165i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	56.8534i		−	1.81890i	−0.415811	−	0.909451i	$-0.636502\pi$
$977$		−	56.8534i		−	1.81890i	0.415811	−	0.909451i	$-0.363498\pi$
$978$		0			0
$979$	−3.38394			−0.108151
$980$		0			0
$981$	12.0020	−	12.0020i	0.383194	−	0.383194i
$982$		0			0
$983$			15.7995i			0.503924i	0.967737	+	0.251962i	$0.0810759\pi$
$983$			15.7995i			0.503924i	−0.967737	+	0.251962i	$0.918924\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	20.4709	+	20.4709i	0.651594	+	0.651594i
$988$		0			0
$989$		−	3.88247i		−	0.123455i
$990$		0			0
$991$	−17.8662			−0.567538			−0.283769	−	0.958893i	$-0.591585\pi$
$991$	−17.8662			−0.567538			−0.283769	+	0.958893i	$0.591585\pi$
$992$		0			0
$993$	21.2361			0.673907
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−5.03661	+	5.03661i	−0.159511	+	0.159511i	−0.782350	−	0.622839i	$-0.785979\pi$
$997$	−5.03661	+	5.03661i	−0.159511	+	0.159511i	0.622839	+	0.782350i	$0.285979\pi$
$998$		0			0
$999$	6.31304	−	6.31304i	0.199736	−	0.199736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3900.2.bm.b.2293.8		28
5.2	odd	4		3900.2.r.b.1357.8		28
5.3	odd	4		780.2.r.a.577.4	yes	28
5.4	even	2		780.2.bm.a.733.1	yes	28
13.8	odd	4		3900.2.r.b.3193.8		28
15.8	even	4		2340.2.u.i.577.7		28
15.14	odd	2		2340.2.bp.i.1513.14		28
65.8	even	4		780.2.bm.a.697.1	yes	28
65.34	odd	4		780.2.r.a.73.4	✓	28
65.47	even	4	inner	3900.2.bm.b.2257.8		28
195.8	odd	4		2340.2.bp.i.1477.14		28
195.164	even	4		2340.2.u.i.73.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.4	✓	28	65.34	odd	4
780.2.r.a.577.4	yes	28	5.3	odd	4
780.2.bm.a.697.1	yes	28	65.8	even	4
780.2.bm.a.733.1	yes	28	5.4	even	2
2340.2.u.i.73.7		28	195.164	even	4
2340.2.u.i.577.7		28	15.8	even	4
2340.2.bp.i.1477.14		28	195.8	odd	4
2340.2.bp.i.1513.14		28	15.14	odd	2
3900.2.r.b.1357.8		28	5.2	odd	4
3900.2.r.b.3193.8		28	13.8	odd	4
3900.2.bm.b.2257.8		28	65.47	even	4	inner
3900.2.bm.b.2293.8		28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} -4.69969 q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} -4.69969 q^{7} +1.00000i q^{9} +(0.315352 + 0.315352i) q^{11} +(2.17205 - 2.87788i) q^{13} +(1.07992 + 1.07992i) q^{17} +(3.49017 + 3.49017i) q^{19} +(-3.32318 - 3.32318i) q^{21} +(-3.48094 + 3.48094i) q^{23} +(-0.707107 + 0.707107i) q^{27} -2.87828i q^{29} +(-1.13365 + 1.13365i) q^{31} +0.445975i q^{33} -8.92799 q^{37} +(3.57084 - 0.499101i) q^{39} +(6.10267 - 6.10267i) q^{41} +(-0.557675 + 0.557675i) q^{43} -6.16002 q^{47} +15.0871 q^{49} +1.52723i q^{51} +(-8.42127 - 8.42127i) q^{53} +4.93584i q^{57} +(1.44238 - 1.44238i) q^{59} -5.80499 q^{61} -4.69969i q^{63} +4.05741i q^{67} -4.92280 q^{69} +(-6.68803 + 6.68803i) q^{71} -0.734212i q^{73} +(-1.48205 - 1.48205i) q^{77} -12.9137i q^{79} -1.00000 q^{81} +1.05600 q^{83} +(2.03525 - 2.03525i) q^{87} +(-5.36534 + 5.36534i) q^{89} +(-10.2079 + 13.5251i) q^{91} -1.60322 q^{93} -4.56277i q^{97} +(-0.315352 + 0.315352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q + 8 q^{11} - 4 q^{17} + 16 q^{19} + 8 q^{21} - 8 q^{23} - 24 q^{37} - 8 q^{39} + 12 q^{41} + 16 q^{43} + 24 q^{47} + 36 q^{49} - 36 q^{53} - 16 q^{59} + 8 q^{61} + 8 q^{69} + 8 q^{71} - 48 q^{77} - 28 q^{81} + 24 q^{83} + 24 q^{87} + 36 q^{89} - 24 q^{91} - 8 q^{99}+O(q^{100}) \) 28 * q + 8 * q^11 - 4 * q^17 + 16 * q^19 + 8 * q^21 - 8 * q^23 - 24 * q^37 - 8 * q^39 + 12 * q^41 + 16 * q^43 + 24 * q^47 + 36 * q^49 - 36 * q^53 - 16 * q^59 + 8 * q^61 + 8 * q^69 + 8 * q^71 - 48 * q^77 - 28 * q^81 + 24 * q^83 + 24 * q^87 + 36 * q^89 - 24 * q^91 - 8 * q^99

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