LMFDB - Embedded newform 3900.2.r.b.1357.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3900,2,Mod(1357,3900)]

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, 3]))

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

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

chi := DirichletCharacter("3900.1357");

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.r (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			1357.14
Character	$\chi$	$=$	3900.1357
Dual form			3900.2.r.b.3193.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +4.16665i q^{7} -1.00000i q^{9} +O(q^{10})$	$q+(0.707107 - 0.707107i) q^{3} +4.16665i q^{7} -1.00000i q^{9} +(-3.15147 - 3.15147i) q^{11} +(-1.82867 + 3.10741i) q^{13} +(4.18610 - 4.18610i) q^{17} +(-4.37727 - 4.37727i) q^{19} +(2.94627 + 2.94627i) q^{21} +(1.31199 + 1.31199i) q^{23} +(-0.707107 - 0.707107i) q^{27} -3.93181i q^{29} +(3.84918 - 3.84918i) q^{31} -4.45686 q^{33} +8.44004i q^{37} +(0.904203 + 3.49033i) q^{39} +(1.55464 - 1.55464i) q^{41} +(-8.11673 - 8.11673i) q^{43} +1.02013i q^{47} -10.3610 q^{49} -5.92004i q^{51} +(1.36494 - 1.36494i) q^{53} -6.19040 q^{57} +(-1.43740 + 1.43740i) q^{59} +0.293533 q^{61} +4.16665 q^{63} +11.8746 q^{67} +1.85543 q^{69} +(11.3963 - 11.3963i) q^{71} -6.46158 q^{73} +(13.1311 - 13.1311i) q^{77} -8.32607i q^{79} -1.00000 q^{81} -15.1492i q^{83} +(-2.78021 - 2.78021i) q^{87} +(6.44206 - 6.44206i) q^{89} +(-12.9475 - 7.61943i) q^{91} -5.44357i q^{93} +10.9521 q^{97} +(-3.15147 + 3.15147i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q + 8 q^{11} + 4 q^{13} + 4 q^{17} - 16 q^{19} + 8 q^{21} + 8 q^{23} + 8 q^{33} + 8 q^{39} + 12 q^{41} - 16 q^{43} - 36 q^{49} - 36 q^{53} + 16 q^{59} + 8 q^{61} - 48 q^{67} - 8 q^{69} + 8 q^{71} - 48 q^{73} + 48 q^{77} - 28 q^{81} + 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{97} + 8 q^{99}+O(q^{100}) $ 28 * q + 8 * q^11 + 4 * q^13 + 4 * q^17 - 16 * q^19 + 8 * q^21 + 8 * q^23 + 8 * q^33 + 8 * q^39 + 12 * q^41 - 16 * q^43 - 36 * q^49 - 36 * q^53 + 16 * q^59 + 8 * q^61 - 48 * q^67 - 8 * q^69 + 8 * q^71 - 48 * q^73 + 48 * q^77 - 28 * q^81 + 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$			4.16665i			1.57485i	0.616413	+	0.787423i	$0.288585\pi$
$7$			4.16665i			1.57485i	−0.616413	+	0.787423i	$0.711415\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−3.15147	−	3.15147i	−0.950205	−	0.950205i	0.0486129	−	0.998818i	$-0.484520\pi$
$11$	−3.15147	−	3.15147i	−0.950205	−	0.950205i	−0.998818	+	0.0486129i	$0.984520\pi$
$12$		0			0
$13$	−1.82867	+	3.10741i	−0.507182	+	0.861839i
$13$	−1.82867	+	3.10741i	−0.507182	+	0.861839i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.18610	−	4.18610i	1.01528	−	1.01528i	0.0153976	−	0.999881i	$-0.495099\pi$
$17$	4.18610	−	4.18610i	1.01528	−	1.01528i	0.999881	−	0.0153976i	$-0.00490140\pi$
$18$		0			0
$19$	−4.37727	−	4.37727i	−1.00422	−	1.00422i	−0.999991	−	0.00422428i	$-0.998655\pi$
$19$	−4.37727	−	4.37727i	−1.00422	−	1.00422i	−0.00422428	−	0.999991i	$-0.501345\pi$
$20$		0			0
$21$	2.94627	+	2.94627i	0.642928	+	0.642928i
$22$		0			0
$23$	1.31199	+	1.31199i	0.273569	+	0.273569i	0.830535	−	0.556966i	$-0.188035\pi$
$23$	1.31199	+	1.31199i	0.273569	+	0.273569i	−0.556966	+	0.830535i	$0.688035\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	3.93181i		−	0.730119i	−0.930984	−	0.365060i	$-0.881049\pi$
$29$		−	3.93181i		−	0.730119i	0.930984	−	0.365060i	$-0.118951\pi$
$30$		0			0
$31$	3.84918	−	3.84918i	0.691334	−	0.691334i	−0.271192	−	0.962525i	$-0.587418\pi$
$31$	3.84918	−	3.84918i	0.691334	−	0.691334i	0.962525	+	0.271192i	$0.0874177\pi$
$32$		0			0
$33$	−4.45686			−0.775839
$34$		0			0
$35$		0			0
$36$		0			0
$37$			8.44004i			1.38753i	0.720200	+	0.693767i	$0.244050\pi$
$37$			8.44004i			1.38753i	−0.720200	+	0.693767i	$0.755950\pi$
$38$		0			0
$39$	0.904203	+	3.49033i	0.144788	+	0.558900i
$40$		0			0
$41$	1.55464	−	1.55464i	0.242794	−	0.242794i	−0.575211	−	0.818005i	$-0.695080\pi$
$41$	1.55464	−	1.55464i	0.242794	−	0.242794i	0.818005	+	0.575211i	$0.195080\pi$
$42$		0			0
$43$	−8.11673	−	8.11673i	−1.23779	−	1.23779i	−0.960903	−	0.276887i	$-0.910697\pi$
$43$	−8.11673	−	8.11673i	−1.23779	−	1.23779i	−0.276887	−	0.960903i	$-0.589303\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			1.02013i			0.148801i	0.997228	+	0.0744003i	$0.0237043\pi$
$47$			1.02013i			0.148801i	−0.997228	+	0.0744003i	$0.976296\pi$
$48$		0			0
$49$	−10.3610			−1.48014
$50$		0			0
$51$		−	5.92004i		−	0.828972i
$52$		0			0
$53$	1.36494	−	1.36494i	0.187489	−	0.187489i	−0.607121	−	0.794610i	$-0.707676\pi$
$53$	1.36494	−	1.36494i	0.187489	−	0.187489i	0.794610	+	0.607121i	$0.207676\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.19040			−0.819938
$58$		0			0
$59$	−1.43740	+	1.43740i	−0.187134	+	0.187134i	−0.794456	−	0.607322i	$-0.792244\pi$
$59$	−1.43740	+	1.43740i	−0.187134	+	0.187134i	0.607322	+	0.794456i	$0.292244\pi$
$60$		0			0
$61$	0.293533			0.0375831			0.0187915	−	0.999823i	$-0.494018\pi$
$61$	0.293533			0.0375831			0.0187915	+	0.999823i	$0.494018\pi$
$62$		0			0
$63$	4.16665			0.524949
$64$		0			0
$65$		0			0
$66$		0			0
$67$	11.8746			1.45071			0.725357	−	0.688373i	$-0.241675\pi$
$67$	11.8746			1.45071			0.725357	+	0.688373i	$0.241675\pi$
$68$		0			0
$69$	1.85543			0.223368
$70$		0			0
$71$	11.3963	−	11.3963i	1.35249	−	1.35249i	0.469625	−	0.882866i	$-0.344389\pi$
$71$	11.3963	−	11.3963i	1.35249	−	1.35249i	0.882866	−	0.469625i	$-0.155611\pi$
$72$		0			0
$73$	−6.46158			−0.756271			−0.378135	−	0.925750i	$-0.623435\pi$
$73$	−6.46158			−0.756271			−0.378135	+	0.925750i	$0.623435\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	13.1311	−	13.1311i	1.49643	−	1.49643i
$78$		0			0
$79$		−	8.32607i		−	0.936756i	−0.883528	−	0.468378i	$-0.844838\pi$
$79$		−	8.32607i		−	0.936756i	0.883528	−	0.468378i	$-0.155162\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$		−	15.1492i		−	1.66285i	−0.555640	−	0.831423i	$-0.687527\pi$
$83$		−	15.1492i		−	1.66285i	0.555640	−	0.831423i	$-0.312473\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.78021	−	2.78021i	−0.298070	−	0.298070i
$88$		0			0
$89$	6.44206	−	6.44206i	0.682857	−	0.682857i	−0.277786	−	0.960643i	$-0.589601\pi$
$89$	6.44206	−	6.44206i	0.682857	−	0.682857i	0.960643	+	0.277786i	$0.0896005\pi$
$90$		0			0
$91$	−12.9475	−	7.61943i	−1.35726	−	0.798733i
$92$		0			0
$93$		−	5.44357i		−	0.564472i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	10.9521			1.11201			0.556007	−	0.831178i	$-0.312333\pi$
$97$	10.9521			1.11201			0.556007	+	0.831178i	$0.312333\pi$
$98$		0			0
$99$	−3.15147	+	3.15147i	−0.316735	+	0.316735i
$100$		0			0
$101$			8.05908i			0.801908i	0.916098	+	0.400954i	$0.131321\pi$
$101$			8.05908i			0.801908i	−0.916098	+	0.400954i	$0.868679\pi$
$102$		0			0
$103$	−4.15942	−	4.15942i	−0.409840	−	0.409840i	0.471843	−	0.881683i	$-0.343589\pi$
$103$	−4.15942	−	4.15942i	−0.409840	−	0.409840i	−0.881683	+	0.471843i	$0.843589\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.88527	−	1.88527i	−0.182256	−	0.182256i	0.610082	−	0.792338i	$-0.291137\pi$
$107$	−1.88527	−	1.88527i	−0.182256	−	0.182256i	−0.792338	+	0.610082i	$0.791137\pi$
$108$		0			0
$109$	−3.25319	−	3.25319i	−0.311599	−	0.311599i	0.533930	−	0.845529i	$-0.320715\pi$
$109$	−3.25319	−	3.25319i	−0.311599	−	0.311599i	−0.845529	+	0.533930i	$0.820715\pi$
$110$		0			0
$111$	5.96801	+	5.96801i	0.566458	+	0.566458i
$112$		0			0
$113$	−7.79437	+	7.79437i	−0.733233	+	0.733233i	−0.971259	−	0.238026i	$-0.923500\pi$
$113$	−7.79437	+	7.79437i	−0.733233	+	0.733233i	0.238026	+	0.971259i	$0.423500\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.10741	+	1.82867i	0.287280	+	0.169061i
$118$		0			0
$119$	17.4420	+	17.4420i	1.59891	+	1.59891i
$120$		0			0
$121$			8.86356i			0.805778i
$122$		0			0
$123$		−	2.19859i		−	0.198240i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	4.51457	−	4.51457i	0.400604	−	0.400604i	−0.477842	−	0.878446i	$-0.658581\pi$
$127$	4.51457	−	4.51457i	0.400604	−	0.400604i	0.878446	+	0.477842i	$0.158581\pi$
$128$		0			0
$129$	−11.4788			−1.01065
$130$		0			0
$131$	6.47998			0.566158			0.283079	−	0.959097i	$-0.408644\pi$
$131$	6.47998			0.566158			0.283079	+	0.959097i	$0.408644\pi$
$132$		0			0
$133$	18.2386	−	18.2386i	1.58148	−	1.58148i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	14.7302i		−	1.25848i	−0.777209	−	0.629242i	$-0.783365\pi$
$137$		−	14.7302i		−	1.25848i	0.777209	−	0.629242i	$-0.216635\pi$
$138$		0			0
$139$		−	7.19379i		−	0.610169i	−0.952325	−	0.305085i	$-0.901315\pi$
$139$		−	7.19379i		−	0.610169i	0.952325	−	0.305085i	$-0.0986848\pi$
$140$		0			0
$141$	0.721338	+	0.721338i	0.0607476	+	0.0607476i
$142$		0			0
$143$	15.5559	−	4.02990i	1.30085	−	0.336997i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.32632	+	7.32632i	−0.604265	+	0.604265i
$148$		0			0
$149$	7.19801	+	7.19801i	0.589684	+	0.589684i	0.937546	−	0.347862i	$-0.113092\pi$
$149$	7.19801	+	7.19801i	0.589684	+	0.589684i	−0.347862	+	0.937546i	$0.613092\pi$
$150$		0			0
$151$	6.77767	+	6.77767i	0.551559	+	0.551559i	0.926891	−	0.375332i	$-0.122471\pi$
$151$	6.77767	+	6.77767i	0.551559	+	0.551559i	−0.375332	+	0.926891i	$0.622471\pi$
$152$		0			0
$153$	−4.18610	−	4.18610i	−0.338426	−	0.338426i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−11.4226	−	11.4226i	−0.911626	−	0.911626i	0.0847741	−	0.996400i	$-0.472983\pi$
$157$	−11.4226	−	11.4226i	−0.911626	−	0.911626i	−0.996400	+	0.0847741i	$0.972983\pi$
$158$		0			0
$159$		−	1.93032i		−	0.153084i
$160$		0			0
$161$	−5.46661	+	5.46661i	−0.430829	+	0.430829i
$162$		0			0
$163$	15.5052			1.21446			0.607230	−	0.794526i	$-0.292281\pi$
$163$	15.5052			1.21446			0.607230	+	0.794526i	$0.292281\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			10.8047i			0.836092i	0.908426	+	0.418046i	$0.137285\pi$
$167$			10.8047i			0.836092i	−0.908426	+	0.418046i	$0.862715\pi$
$168$		0			0
$169$	−6.31194	−	11.3648i	−0.485534	−	0.874218i
$170$		0			0
$171$	−4.37727	+	4.37727i	−0.334738	+	0.334738i
$172$		0			0
$173$	−7.61397	−	7.61397i	−0.578879	−	0.578879i	0.355715	−	0.934594i	$-0.384237\pi$
$173$	−7.61397	−	7.61397i	−0.578879	−	0.578879i	−0.934594	+	0.355715i	$0.884237\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			2.03280i			0.152794i
$178$		0			0
$179$	−13.2476			−0.990175			−0.495087	−	0.868843i	$-0.664864\pi$
$179$	−13.2476			−0.990175			−0.495087	+	0.868843i	$0.664864\pi$
$180$		0			0
$181$		−	13.5363i		−	1.00614i	−0.864245	−	0.503072i	$-0.832203\pi$
$181$		−	13.5363i		−	1.00614i	0.864245	−	0.503072i	$-0.167797\pi$
$182$		0			0
$183$	0.207559	−	0.207559i	0.0153432	−	0.0153432i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−26.3848			−1.92945
$188$		0			0
$189$	2.94627	−	2.94627i	0.214309	−	0.214309i
$190$		0			0
$191$	−23.5256			−1.70226			−0.851128	−	0.524959i	$-0.824081\pi$
$191$	−23.5256			−1.70226			−0.851128	+	0.524959i	$0.824081\pi$
$192$		0			0
$193$	−12.6069			−0.907466			−0.453733	−	0.891138i	$-0.649908\pi$
$193$	−12.6069			−0.907466			−0.453733	+	0.891138i	$0.649908\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.4136			0.955681			0.477841	−	0.878447i	$-0.341420\pi$
$197$	13.4136			0.955681			0.477841	+	0.878447i	$0.341420\pi$
$198$		0			0
$199$	22.5835			1.60091			0.800453	−	0.599396i	$-0.204592\pi$
$199$	22.5835			1.60091			0.800453	+	0.599396i	$0.204592\pi$
$200$		0			0
$201$	8.39661	−	8.39661i	0.592251	−	0.592251i
$202$		0			0
$203$	16.3825			1.14983
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.31199	−	1.31199i	0.0911896	−	0.0911896i
$208$		0			0
$209$			27.5897i			1.90842i
$210$		0			0
$211$	−12.0590			−0.830175			−0.415088	−	0.909781i	$-0.636249\pi$
$211$	−12.0590			−0.830175			−0.415088	+	0.909781i	$0.636249\pi$
$212$		0			0
$213$		−	16.1168i		−	1.10430i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	16.0382	+	16.0382i	1.08874	+	1.08874i
$218$		0			0
$219$	−4.56903	+	4.56903i	−0.308746	+	0.308746i
$220$		0			0
$221$	5.35292	+	20.6629i	0.360076	+	1.38994i
$222$		0			0
$223$			9.25360i			0.619667i	0.950791	+	0.309834i	$0.100273\pi$
$223$			9.25360i			0.619667i	−0.950791	+	0.309834i	$0.899727\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	16.0754			1.06696			0.533481	−	0.845812i	$-0.320884\pi$
$227$	16.0754			1.06696			0.533481	+	0.845812i	$0.320884\pi$
$228$		0			0
$229$	−5.43244	+	5.43244i	−0.358986	+	0.358986i	−0.863439	−	0.504453i	$-0.831694\pi$
$229$	−5.43244	+	5.43244i	−0.358986	+	0.358986i	0.504453	+	0.863439i	$0.331694\pi$
$230$		0			0
$231$		−	18.5702i		−	1.22183i
$232$		0			0
$233$	1.12524	+	1.12524i	0.0737170	+	0.0737170i	0.743004	−	0.669287i	$-0.233400\pi$
$233$	1.12524	+	1.12524i	0.0737170	+	0.0737170i	−0.669287	+	0.743004i	$0.733400\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−5.88742	−	5.88742i	−0.382429	−	0.382429i
$238$		0			0
$239$	−12.4781	−	12.4781i	−0.807144	−	0.807144i	0.177057	−	0.984201i	$-0.443342\pi$
$239$	−12.4781	−	12.4781i	−0.807144	−	0.807144i	−0.984201	+	0.177057i	$0.943342\pi$
$240$		0			0
$241$	1.27702	+	1.27702i	0.0822603	+	0.0822603i	0.747040	−	0.664779i	$-0.231474\pi$
$241$	1.27702	+	1.27702i	0.0822603	+	0.0822603i	−0.664779	+	0.747040i	$0.731474\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	21.6065	−	5.59738i	1.37479	−	0.356153i
$248$		0			0
$249$	−10.7121	−	10.7121i	−0.678854	−	0.678854i
$250$		0			0
$251$		−	19.6566i		−	1.24072i	−0.784319	−	0.620358i	$-0.786987\pi$
$251$		−	19.6566i		−	1.24072i	0.784319	−	0.620358i	$-0.213013\pi$
$252$		0			0
$253$		−	8.26940i		−	0.519893i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−20.8698	+	20.8698i	−1.30182	+	1.30182i	−0.374662	+	0.927162i	$0.622241\pi$
$257$	−20.8698	+	20.8698i	−1.30182	+	1.30182i	−0.927162	+	0.374662i	$0.877759\pi$
$258$		0			0
$259$	−35.1667			−2.18515
$260$		0			0
$261$	−3.93181			−0.243373
$262$		0			0
$263$	−3.80349	+	3.80349i	−0.234533	+	0.234533i	−0.814582	−	0.580049i	$-0.803034\pi$
$263$	−3.80349	+	3.80349i	−0.234533	+	0.234533i	0.580049	+	0.814582i	$0.303034\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	9.11045i		−	0.557551i
$268$		0			0
$269$			3.31848i			0.202332i	0.994870	+	0.101166i	$0.0322572\pi$
$269$			3.31848i			0.202332i	−0.994870	+	0.101166i	$0.967743\pi$
$270$		0			0
$271$	5.56659	+	5.56659i	0.338146	+	0.338146i	0.855669	−	0.517523i	$-0.173146\pi$
$271$	5.56659	+	5.56659i	0.338146	+	0.338146i	−0.517523	+	0.855669i	$0.673146\pi$
$272$		0			0
$273$	−14.5430	+	3.76750i	−0.880182	+	0.228019i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.00278	−	3.00278i	0.180419	−	0.180419i	−0.611119	−	0.791539i	$-0.709280\pi$
$277$	3.00278	−	3.00278i	0.180419	−	0.180419i	0.791539	+	0.611119i	$0.209280\pi$
$278$		0			0
$279$	−3.84918	−	3.84918i	−0.230445	−	0.230445i
$280$		0			0
$281$	2.34615	+	2.34615i	0.139960	+	0.139960i	0.773615	−	0.633656i	$-0.218446\pi$
$281$	2.34615	+	2.34615i	0.139960	+	0.139960i	−0.633656	+	0.773615i	$0.718446\pi$
$282$		0			0
$283$	−16.7918	−	16.7918i	−0.998167	−	0.998167i	0.00183106	−	0.999998i	$-0.499417\pi$
$283$	−16.7918	−	16.7918i	−0.998167	−	0.998167i	−0.999998	+	0.00183106i	$0.999417\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.47764	+	6.47764i	0.382363	+	0.382363i
$288$		0			0
$289$		−	18.0469i		−	1.06158i
$290$		0			0
$291$	7.74428	−	7.74428i	0.453978	−	0.453978i
$292$		0			0
$293$	−10.6729			−0.623516			−0.311758	−	0.950162i	$-0.600918\pi$
$293$	−10.6729			−0.623516			−0.311758	+	0.950162i	$0.600918\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			4.45686i			0.258613i
$298$		0			0
$299$	−6.47608	+	1.67769i	−0.374522	+	0.0970233i
$300$		0			0
$301$	33.8196	−	33.8196i	1.94933	−	1.94933i
$302$		0			0
$303$	5.69863	+	5.69863i	0.327378	+	0.327378i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	9.95047i		−	0.567903i	−0.958839	−	0.283952i	$-0.908355\pi$
$307$		−	9.95047i		−	0.567903i	0.958839	−	0.283952i	$-0.0916455\pi$
$308$		0			0
$309$	−5.88231			−0.334633
$310$		0			0
$311$			5.16651i			0.292966i	0.989213	+	0.146483i	$0.0467954\pi$
$311$			5.16651i			0.292966i	−0.989213	+	0.146483i	$0.953205\pi$
$312$		0			0
$313$	−2.76718	+	2.76718i	−0.156410	+	0.156410i	−0.780974	−	0.624564i	$-0.785277\pi$
$313$	−2.76718	+	2.76718i	−0.156410	+	0.156410i	0.624564	+	0.780974i	$0.285277\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−29.1994			−1.64000			−0.820000	−	0.572363i	$-0.806027\pi$
$317$	−29.1994			−1.64000			−0.820000	+	0.572363i	$0.806027\pi$
$318$		0			0
$319$	−12.3910	+	12.3910i	−0.693763	+	0.693763i
$320$		0			0
$321$	−2.66618			−0.148812
$322$		0			0
$323$	−36.6474			−2.03912
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−4.60071			−0.254420
$328$		0			0
$329$	−4.25051			−0.234338
$330$		0			0
$331$	−8.69091	+	8.69091i	−0.477696	+	0.477696i	−0.904394	−	0.426698i	$-0.859677\pi$
$331$	−8.69091	+	8.69091i	−0.477696	+	0.477696i	0.426698	+	0.904394i	$0.359677\pi$
$332$		0			0
$333$	8.44004			0.462511
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.49283	−	7.49283i	0.408161	−	0.408161i	−0.472936	−	0.881097i	$-0.656806\pi$
$337$	7.49283	−	7.49283i	0.408161	−	0.408161i	0.881097	+	0.472936i	$0.156806\pi$
$338$		0			0
$339$			11.0229i			0.598682i
$340$		0			0
$341$	−24.2612			−1.31382
$342$		0			0
$343$		−	14.0040i		−	0.756147i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.92612	+	9.92612i	0.532862	+	0.532862i	0.921423	−	0.388561i	$-0.127028\pi$
$347$	9.92612	+	9.92612i	0.532862	+	0.532862i	−0.388561	+	0.921423i	$0.627028\pi$
$348$		0			0
$349$	7.52765	−	7.52765i	0.402946	−	0.402946i	−0.476324	−	0.879270i	$-0.658031\pi$
$349$	7.52765	−	7.52765i	0.402946	−	0.402946i	0.879270	+	0.476324i	$0.158031\pi$
$350$		0			0
$351$	3.49033	−	0.904203i	0.186300	−	0.0482628i
$352$		0			0
$353$		−	7.33990i		−	0.390664i	−0.980737	−	0.195332i	$-0.937422\pi$
$353$		−	7.33990i		−	0.390664i	0.980737	−	0.195332i	$-0.0625784\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	24.6668			1.30550
$358$		0			0
$359$	24.1816	−	24.1816i	1.27626	−	1.27626i	0.333509	−	0.942747i	$-0.391767\pi$
$359$	24.1816	−	24.1816i	1.27626	−	1.27626i	0.942747	−	0.333509i	$-0.108233\pi$
$360$		0			0
$361$			19.3210i			1.01690i
$362$		0			0
$363$	6.26749	+	6.26749i	0.328958	+	0.328958i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−17.7690	−	17.7690i	−0.927537	−	0.927537i	0.0700097	−	0.997546i	$-0.477697\pi$
$367$	−17.7690	−	17.7690i	−0.927537	−	0.927537i	−0.997546	+	0.0700097i	$0.977697\pi$
$368$		0			0
$369$	−1.55464	−	1.55464i	−0.0809313	−	0.0809313i
$370$		0			0
$371$	5.68722	+	5.68722i	0.295266	+	0.295266i
$372$		0			0
$373$	3.42778	−	3.42778i	0.177484	−	0.177484i	−0.612774	−	0.790258i	$-0.709946\pi$
$373$	3.42778	−	3.42778i	0.177484	−	0.177484i	0.790258	+	0.612774i	$0.209946\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.2177	+	7.18999i	0.629245	+	0.370303i
$378$		0			0
$379$	6.32325	+	6.32325i	0.324804	+	0.324804i	0.850606	−	0.525803i	$-0.176235\pi$
$379$	6.32325	+	6.32325i	0.324804	+	0.324804i	−0.525803	+	0.850606i	$0.676235\pi$
$380$		0			0
$381$		−	6.38457i		−	0.327092i
$382$		0			0
$383$			24.6950i			1.26186i	0.775841	+	0.630928i	$0.217326\pi$
$383$			24.6950i			1.26186i	−0.775841	+	0.630928i	$0.782674\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.11673	+	8.11673i	−0.412596	+	0.412596i
$388$		0			0
$389$	−27.4062			−1.38955			−0.694775	−	0.719228i	$-0.744496\pi$
$389$	−27.4062			−1.38955			−0.694775	+	0.719228i	$0.744496\pi$
$390$		0			0
$391$	10.9843			0.555498
$392$		0			0
$393$	4.58204	−	4.58204i	0.231133	−	0.231133i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			39.1875i			1.96676i	0.181554	+	0.983381i	$0.441887\pi$
$397$			39.1875i			1.96676i	−0.181554	+	0.983381i	$0.558113\pi$
$398$		0			0
$399$		−	25.7932i		−	1.29128i
$400$		0			0
$401$	21.9890	+	21.9890i	1.09808	+	1.09808i	0.994636	+	0.103441i	$0.0329854\pi$
$401$	21.9890	+	21.9890i	1.09808	+	1.09808i	0.103441	+	0.994636i	$0.467015\pi$
$402$		0			0
$403$	4.92209	+	18.9999i	0.245187	+	0.946450i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	26.5985	−	26.5985i	1.31844	−	1.31844i
$408$		0			0
$409$	−2.71373	−	2.71373i	−0.134185	−	0.134185i	0.636824	−	0.771009i	$-0.280248\pi$
$409$	−2.71373	−	2.71373i	−0.134185	−	0.134185i	−0.771009	+	0.636824i	$0.780248\pi$
$410$		0			0
$411$	−10.4158	−	10.4158i	−0.513774	−	0.513774i
$412$		0			0
$413$	−5.98916	−	5.98916i	−0.294707	−	0.294707i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.08678	−	5.08678i	−0.249101	−	0.249101i
$418$		0			0
$419$		−	34.1751i		−	1.66956i	−0.550583	−	0.834780i	$-0.685595\pi$
$419$		−	34.1751i		−	1.66956i	0.550583	−	0.834780i	$-0.314405\pi$
$420$		0			0
$421$	15.5333	−	15.5333i	0.757049	−	0.757049i	−0.218736	−	0.975784i	$-0.570193\pi$
$421$	15.5333	−	15.5333i	0.757049	−	0.757049i	0.975784	+	0.218736i	$0.0701932\pi$
$422$		0			0
$423$	1.02013			0.0496002
$424$		0			0
$425$		0			0
$426$		0			0
$427$			1.22305i			0.0591875i
$428$		0			0
$429$	8.15012	−	13.8493i	0.393491	−	0.668648i
$430$		0			0
$431$	−26.4717	+	26.4717i	−1.27510	+	1.27510i	−0.331722	+	0.943377i	$0.607629\pi$
$431$	−26.4717	+	26.4717i	−1.27510	+	1.27510i	−0.943377	+	0.331722i	$0.892371\pi$
$432$		0			0
$433$	26.0961	+	26.0961i	1.25410	+	1.25410i	0.953866	+	0.300232i	$0.0970641\pi$
$433$	26.0961	+	26.0961i	1.25410	+	1.25410i	0.300232	+	0.953866i	$0.402936\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	11.4859i		−	0.549444i
$438$		0			0
$439$	−12.5133			−0.597226			−0.298613	−	0.954374i	$-0.596524\pi$
$439$	−12.5133			−0.597226			−0.298613	+	0.954374i	$0.596524\pi$
$440$		0			0
$441$			10.3610i			0.493380i
$442$		0			0
$443$	1.48719	−	1.48719i	0.0706585	−	0.0706585i	−0.670894	−	0.741553i	$-0.734090\pi$
$443$	1.48719	−	1.48719i	0.0706585	−	0.0706585i	0.741553	+	0.670894i	$0.234090\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	10.1795			0.481475
$448$		0			0
$449$	11.5904	−	11.5904i	0.546986	−	0.546986i	−0.378582	−	0.925568i	$-0.623588\pi$
$449$	11.5904	−	11.5904i	0.546986	−	0.546986i	0.925568	+	0.378582i	$0.123588\pi$
$450$		0			0
$451$	−9.79880			−0.461408
$452$		0			0
$453$	9.58507			0.450346
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−34.6269			−1.61978			−0.809888	−	0.586584i	$-0.800472\pi$
$457$	−34.6269			−1.61978			−0.809888	+	0.586584i	$0.800472\pi$
$458$		0			0
$459$	−5.92004			−0.276324
$460$		0			0
$461$	−18.8332	+	18.8332i	−0.877149	+	0.877149i	−0.993239	−	0.116090i	$-0.962964\pi$
$461$	−18.8332	+	18.8332i	−0.877149	+	0.877149i	0.116090	+	0.993239i	$0.462964\pi$
$462$		0			0
$463$	−13.5047			−0.627615			−0.313808	−	0.949487i	$-0.601605\pi$
$463$	−13.5047			−0.627615			−0.313808	+	0.949487i	$0.601605\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.20739	−	7.20739i	0.333518	−	0.333518i	−0.520403	−	0.853921i	$-0.674218\pi$
$467$	7.20739	−	7.20739i	0.333518	−	0.333518i	0.853921	+	0.520403i	$0.174218\pi$
$468$		0			0
$469$			49.4773i			2.28465i
$470$		0			0
$471$	−16.1541			−0.744340
$472$		0			0
$473$			51.1593i			2.35231i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.36494	−	1.36494i	−0.0624963	−	0.0624963i
$478$		0			0
$479$	12.3993	−	12.3993i	0.566537	−	0.566537i	−0.364620	−	0.931157i	$-0.618801\pi$
$479$	12.3993	−	12.3993i	0.566537	−	0.566537i	0.931157	+	0.364620i	$0.118801\pi$
$480$		0			0
$481$	−26.2266	−	15.4340i	−1.19583	−	0.703731i
$482$		0			0
$483$			7.73095i			0.351770i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−32.1455			−1.45665			−0.728326	−	0.685230i	$-0.759702\pi$
$487$	−32.1455			−1.45665			−0.728326	+	0.685230i	$0.759702\pi$
$488$		0			0
$489$	10.9638	−	10.9638i	0.495801	−	0.495801i
$490$		0			0
$491$		−	3.73137i		−	0.168395i	−0.996449	−	0.0841973i	$-0.973167\pi$
$491$		−	3.73137i		−	0.168395i	0.996449	−	0.0841973i	$-0.0268326\pi$
$492$		0			0
$493$	−16.4590	−	16.4590i	−0.741275	−	0.741275i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	47.4844	+	47.4844i	2.12997	+	2.12997i
$498$		0			0
$499$	5.85645	+	5.85645i	0.262171	+	0.262171i	0.825936	−	0.563765i	$-0.190647\pi$
$499$	5.85645	+	5.85645i	0.262171	+	0.262171i	−0.563765	+	0.825936i	$0.690647\pi$
$500$		0			0
$501$	7.64007	+	7.64007i	0.341333	+	0.341333i
$502$		0			0
$503$	21.0951	−	21.0951i	0.940586	−	0.940586i	−0.0577458	−	0.998331i	$-0.518391\pi$
$503$	21.0951	−	21.0951i	0.940586	−	0.940586i	0.998331	+	0.0577458i	$0.0183913\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−12.4994	−	3.57294i	−0.555116	−	0.158680i
$508$		0			0
$509$	23.2392	+	23.2392i	1.03006	+	1.03006i	0.999534	+	0.0305246i	$0.00971780\pi$
$509$	23.2392	+	23.2392i	1.03006	+	1.03006i	0.0305246	+	0.999534i	$0.490282\pi$
$510$		0			0
$511$		−	26.9231i		−	1.19101i
$512$		0			0
$513$			6.19040i			0.273313i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	3.21490	−	3.21490i	0.141391	−	0.141391i
$518$		0			0
$519$	−10.7678			−0.472653
$520$		0			0
$521$	21.5024			0.942038			0.471019	−	0.882123i	$-0.343886\pi$
$521$	21.5024			0.942038			0.471019	+	0.882123i	$0.343886\pi$
$522$		0			0
$523$	−14.0736	+	14.0736i	−0.615395	+	0.615395i	−0.944347	−	0.328952i	$-0.893305\pi$
$523$	−14.0736	+	14.0736i	−0.615395	+	0.615395i	0.328952	+	0.944347i	$0.393305\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	32.2262i		−	1.40379i
$528$		0			0
$529$		−	19.5574i		−	0.850320i
$530$		0			0
$531$	1.43740	+	1.43740i	0.0623780	+	0.0623780i
$532$		0			0
$533$	1.98797	+	7.67381i	0.0861087	+	0.332390i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−9.36749	+	9.36749i	−0.404237	+	0.404237i
$538$		0			0
$539$	32.6523	+	32.6523i	1.40644	+	1.40644i
$540$		0			0
$541$	11.4516	+	11.4516i	0.492344	+	0.492344i	0.909044	−	0.416700i	$-0.136813\pi$
$541$	11.4516	+	11.4516i	0.492344	+	0.492344i	−0.416700	+	0.909044i	$0.636813\pi$
$542$		0			0
$543$	−9.57160	−	9.57160i	−0.410756	−	0.410756i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−16.7429	−	16.7429i	−0.715874	−	0.715874i	0.251884	−	0.967757i	$-0.418950\pi$
$547$	−16.7429	−	16.7429i	−0.715874	−	0.715874i	−0.967757	+	0.251884i	$0.918950\pi$
$548$		0			0
$549$		−	0.293533i		−	0.0125277i
$550$		0			0
$551$	−17.2106	+	17.2106i	−0.733197	+	0.733197i
$552$		0			0
$553$	34.6918			1.47525
$554$		0			0
$555$		0			0
$556$		0			0
$557$			38.6119i			1.63604i	0.575189	+	0.818020i	$0.304928\pi$
$557$			38.6119i			1.63604i	−0.575189	+	0.818020i	$0.695072\pi$
$558$		0			0
$559$	40.0648	−	10.3792i	1.69456	−	0.438991i
$560$		0			0
$561$	−18.6569	+	18.6569i	−0.787693	+	0.787693i
$562$		0			0
$563$	−9.62289	−	9.62289i	−0.405556	−	0.405556i	0.474629	−	0.880186i	$-0.342582\pi$
$563$	−9.62289	−	9.62289i	−0.405556	−	0.405556i	−0.880186	+	0.474629i	$0.842582\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	4.16665i		−	0.174983i
$568$		0			0
$569$	23.7899			0.997326			0.498663	−	0.866796i	$-0.333825\pi$
$569$	23.7899			0.997326			0.498663	+	0.866796i	$0.333825\pi$
$570$		0			0
$571$		−	11.2205i		−	0.469562i	−0.972048	−	0.234781i	$-0.924563\pi$
$571$		−	11.2205i		−	0.469562i	0.972048	−	0.234781i	$-0.0754373\pi$
$572$		0			0
$573$	−16.6351	+	16.6351i	−0.694943	+	0.694943i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−40.0865			−1.66882			−0.834411	−	0.551143i	$-0.814192\pi$
$577$	−40.0865			−1.66882			−0.834411	+	0.551143i	$0.814192\pi$
$578$		0			0
$579$	−8.91444	+	8.91444i	−0.370471	+	0.370471i
$580$		0			0
$581$	63.1216			2.61873
$582$		0			0
$583$	−8.60314			−0.356305
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.7208			−0.483770			−0.241885	−	0.970305i	$-0.577766\pi$
$587$	−11.7208			−0.483770			−0.241885	+	0.970305i	$0.577766\pi$
$588$		0			0
$589$	−33.6979			−1.38850
$590$		0			0
$591$	9.48487	−	9.48487i	0.390155	−	0.390155i
$592$		0			0
$593$	15.4834			0.635826			0.317913	−	0.948120i	$-0.397018\pi$
$593$	15.4834			0.635826			0.317913	+	0.948120i	$0.397018\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	15.9690	−	15.9690i	0.653567	−	0.653567i
$598$		0			0
$599$			13.5127i			0.552115i	0.961141	+	0.276058i	$0.0890280\pi$
$599$			13.5127i			0.552115i	−0.961141	+	0.276058i	$0.910972\pi$
$600$		0			0
$601$	27.4625			1.12022			0.560108	−	0.828419i	$-0.310759\pi$
$601$	27.4625			1.12022			0.560108	+	0.828419i	$0.310759\pi$
$602$		0			0
$603$		−	11.8746i		−	0.483571i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−9.34983	−	9.34983i	−0.379498	−	0.379498i	0.491423	−	0.870921i	$-0.336477\pi$
$607$	−9.34983	−	9.34983i	−0.379498	−	0.379498i	−0.870921	+	0.491423i	$0.836477\pi$
$608$		0			0
$609$	11.5842	−	11.5842i	0.469414	−	0.469414i
$610$		0			0
$611$	−3.16994	−	1.86547i	−0.128242	−	0.0754689i
$612$		0			0
$613$			16.7293i			0.675690i	0.941202	+	0.337845i	$0.109698\pi$
$613$			16.7293i			0.675690i	−0.941202	+	0.337845i	$0.890302\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	33.3846			1.34401			0.672007	−	0.740544i	$-0.265432\pi$
$617$	33.3846			1.34401			0.672007	+	0.740544i	$0.265432\pi$
$618$		0			0
$619$	12.9465	−	12.9465i	0.520365	−	0.520365i	−0.397316	−	0.917682i	$-0.630058\pi$
$619$	12.9465	−	12.9465i	0.520365	−	0.520365i	0.917682	+	0.397316i	$0.130058\pi$
$620$		0			0
$621$		−	1.85543i		−	0.0744560i
$622$		0			0
$623$	26.8418	+	26.8418i	1.07540	+	1.07540i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	19.5089	+	19.5089i	0.779109	+	0.779109i
$628$		0			0
$629$	35.3309	+	35.3309i	1.40873	+	1.40873i
$630$		0			0
$631$	29.0903	+	29.0903i	1.15807	+	1.15807i	0.984891	+	0.173174i	$0.0554024\pi$
$631$	29.0903	+	29.0903i	1.15807	+	1.15807i	0.173174	+	0.984891i	$0.444598\pi$
$632$		0			0
$633$	−8.52700	+	8.52700i	−0.338918	+	0.338918i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	18.9468	−	32.1958i	0.750700	−	1.27564i
$638$		0			0
$639$	−11.3963	−	11.3963i	−0.450830	−	0.450830i
$640$		0			0
$641$		−	27.5037i		−	1.08633i	−0.839626	−	0.543165i	$-0.817226\pi$
$641$		−	27.5037i		−	1.08633i	0.839626	−	0.543165i	$-0.182774\pi$
$642$		0			0
$643$			3.97198i			0.156640i	0.996928	+	0.0783198i	$0.0249555\pi$
$643$			3.97198i			0.156640i	−0.996928	+	0.0783198i	$0.975044\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.2989	−	24.2989i	0.955290	−	0.955290i	−0.0437527	−	0.999042i	$-0.513931\pi$
$647$	24.2989	−	24.2989i	0.955290	−	0.955290i	0.999042	+	0.0437527i	$0.0139314\pi$
$648$		0			0
$649$	9.05987			0.355631
$650$		0			0
$651$	22.6814			0.888956
$652$		0			0
$653$	6.39282	−	6.39282i	0.250170	−	0.250170i	−0.570870	−	0.821040i	$-0.693394\pi$
$653$	6.39282	−	6.39282i	0.250170	−	0.250170i	0.821040	+	0.570870i	$0.193394\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			6.46158i			0.252090i
$658$		0			0
$659$			11.4763i			0.447052i	0.974698	+	0.223526i	$0.0717567\pi$
$659$			11.4763i			0.447052i	−0.974698	+	0.223526i	$0.928243\pi$
$660$		0			0
$661$	−19.3374	−	19.3374i	−0.752139	−	0.752139i	0.222739	−	0.974878i	$-0.428500\pi$
$661$	−19.3374	−	19.3374i	−0.752139	−	0.752139i	−0.974878	+	0.222739i	$0.928500\pi$
$662$		0			0
$663$	18.3960	+	10.8258i	0.714440	+	0.420439i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5.15850	−	5.15850i	0.199738	−	0.199738i
$668$		0			0
$669$	6.54329	+	6.54329i	0.252978	+	0.252978i
$670$		0			0
$671$	−0.925062	−	0.925062i	−0.0357116	−	0.0357116i
$672$		0			0
$673$	−6.06351	−	6.06351i	−0.233731	−	0.233731i	0.580517	−	0.814248i	$-0.302850\pi$
$673$	−6.06351	−	6.06351i	−0.233731	−	0.233731i	−0.814248	+	0.580517i	$0.802850\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.6902	+	10.6902i	0.410859	+	0.410859i	0.882038	−	0.471179i	$-0.156171\pi$
$677$	10.6902	+	10.6902i	0.410859	+	0.410859i	−0.471179	+	0.882038i	$0.656171\pi$
$678$		0			0
$679$			45.6334i			1.75125i
$680$		0			0
$681$	11.3670	−	11.3670i	0.435585	−	0.435585i
$682$		0			0
$683$	1.96421			0.0751586			0.0375793	−	0.999294i	$-0.488035\pi$
$683$	1.96421			0.0751586			0.0375793	+	0.999294i	$0.488035\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			7.68263i			0.293111i
$688$		0			0
$689$	1.74540	+	6.73744i	0.0664943	+	0.256676i
$690$		0			0
$691$	−29.0749	+	29.0749i	−1.10606	+	1.10606i	−0.112400	+	0.993663i	$0.535854\pi$
$691$	−29.0749	+	29.0749i	−1.10606	+	1.10606i	−0.993663	+	0.112400i	$0.964146\pi$
$692$		0			0
$693$	−13.1311	−	13.1311i	−0.498809	−	0.498809i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	13.0158i		−	0.493007i
$698$		0			0
$699$	1.59133			0.0601897
$700$		0			0
$701$			31.8458i			1.20280i	0.798949	+	0.601399i	$0.205390\pi$
$701$			31.8458i			1.20280i	−0.798949	+	0.601399i	$0.794610\pi$
$702$		0			0
$703$	36.9443	−	36.9443i	1.39338	−	1.39338i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−33.5794			−1.26288
$708$		0			0
$709$	−20.4104	+	20.4104i	−0.766528	+	0.766528i	−0.977493	−	0.210966i	$-0.932339\pi$
$709$	−20.4104	+	20.4104i	−0.766528	+	0.766528i	0.210966	+	0.977493i	$0.432339\pi$
$710$		0			0
$711$	−8.32607			−0.312252
$712$		0			0
$713$	10.1002			0.378255
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−17.6468			−0.659030
$718$		0			0
$719$	31.3675			1.16981			0.584905	−	0.811102i	$-0.301132\pi$
$719$	31.3675			1.16981			0.584905	+	0.811102i	$0.301132\pi$
$720$		0			0
$721$	17.3309	−	17.3309i	0.645435	−	0.645435i
$722$		0			0
$723$	1.80598			0.0671652
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−13.3838	+	13.3838i	−0.496379	+	0.496379i	−0.910309	−	0.413930i	$-0.864156\pi$
$727$	−13.3838	+	13.3838i	−0.496379	+	0.496379i	0.413930	+	0.910309i	$0.364156\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−67.9549			−2.51340
$732$		0			0
$733$		−	23.1954i		−	0.856740i	−0.903603	−	0.428370i	$-0.859088\pi$
$733$		−	23.1954i		−	0.856740i	0.903603	−	0.428370i	$-0.140912\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−37.4225	−	37.4225i	−1.37847	−	1.37847i
$738$		0			0
$739$	−3.46527	+	3.46527i	−0.127472	+	0.127472i	−0.767965	−	0.640492i	$-0.778730\pi$
$739$	−3.46527	+	3.46527i	−0.127472	+	0.127472i	0.640492	+	0.767965i	$0.278730\pi$
$740$		0			0
$741$	11.3202	−	19.2361i	0.415858	−	0.706655i
$742$		0			0
$743$		−	1.29558i		−	0.0475301i	−0.999718	−	0.0237650i	$-0.992435\pi$
$743$		−	1.29558i		−	0.0475301i	0.999718	−	0.0237650i	$-0.00756536\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−15.1492			−0.554282
$748$		0			0
$749$	7.85528	−	7.85528i	0.287026	−	0.287026i
$750$		0			0
$751$		−	1.38749i		−	0.0506301i	−0.999680	−	0.0253150i	$-0.991941\pi$
$751$		−	1.38749i		−	0.0506301i	0.999680	−	0.0253150i	$-0.00805889\pi$
$752$		0			0
$753$	−13.8993	−	13.8993i	−0.506520	−	0.506520i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	9.11127	+	9.11127i	0.331155	+	0.331155i	0.853025	−	0.521870i	$-0.174765\pi$
$757$	9.11127	+	9.11127i	0.331155	+	0.331155i	−0.521870	+	0.853025i	$0.674765\pi$
$758$		0			0
$759$	−5.84735	−	5.84735i	−0.212245	−	0.212245i
$760$		0			0
$761$	−19.8539	−	19.8539i	−0.719703	−	0.719703i	0.248841	−	0.968544i	$-0.419950\pi$
$761$	−19.8539	−	19.8539i	−0.719703	−	0.719703i	−0.968544	+	0.248841i	$0.919950\pi$
$762$		0			0
$763$	13.5549	−	13.5549i	0.490721	−	0.490721i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.83806	−	7.09513i	−0.0663685	−	0.256190i
$768$		0			0
$769$	22.6182	+	22.6182i	0.815634	+	0.815634i	0.985472	−	0.169838i	$-0.0543243\pi$
$769$	22.6182	+	22.6182i	0.815634	+	0.815634i	−0.169838	+	0.985472i	$0.554324\pi$
$770$		0			0
$771$			29.5144i			1.06293i
$772$		0			0
$773$		−	20.5557i		−	0.739336i	−0.929164	−	0.369668i	$-0.879471\pi$
$773$		−	20.5557i		−	0.739336i	0.929164	−	0.369668i	$-0.120529\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−24.8666	+	24.8666i	−0.892084	+	0.892084i
$778$		0			0
$779$	−13.6102			−0.487634
$780$		0			0
$781$	−71.8302			−2.57029
$782$		0			0
$783$	−2.78021	+	2.78021i	−0.0993567	+	0.0993567i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			13.3191i			0.474774i	0.971415	+	0.237387i	$0.0762909\pi$
$787$			13.3191i			0.474774i	−0.971415	+	0.237387i	$0.923709\pi$
$788$		0			0
$789$			5.37895i			0.191496i
$790$		0			0
$791$	−32.4764	−	32.4764i	−1.15473	−	1.15473i
$792$		0			0
$793$	−0.536775	+	0.912126i	−0.0190614	+	0.0323906i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−20.3474	+	20.3474i	−0.720743	+	0.720743i	−0.968757	−	0.248014i	$-0.920222\pi$
$797$	−20.3474	+	20.3474i	−0.720743	+	0.720743i	0.248014	+	0.968757i	$0.420222\pi$
$798$		0			0
$799$	4.27035	+	4.27035i	0.151074	+	0.151074i
$800$		0			0
$801$	−6.44206	−	6.44206i	−0.227619	−	0.227619i
$802$		0			0
$803$	20.3635	+	20.3635i	0.718612	+	0.718612i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.34652	+	2.34652i	0.0826015	+	0.0826015i
$808$		0			0
$809$			42.5767i			1.49692i	0.663182	+	0.748458i	$0.269205\pi$
$809$			42.5767i			1.49692i	−0.663182	+	0.748458i	$0.730795\pi$
$810$		0			0
$811$	22.7142	−	22.7142i	0.797603	−	0.797603i	−0.185114	−	0.982717i	$-0.559265\pi$
$811$	22.7142	−	22.7142i	0.797603	−	0.797603i	0.982717	+	0.185114i	$0.0592655\pi$
$812$		0			0
$813$	7.87235			0.276095
$814$		0			0
$815$		0			0
$816$		0			0
$817$			71.0583i			2.48601i
$818$		0			0
$819$	−7.61943	+	12.9475i	−0.266244	+	0.452421i
$820$		0			0
$821$	7.60013	−	7.60013i	0.265246	−	0.265246i	−0.561935	−	0.827181i	$-0.689943\pi$
$821$	7.60013	−	7.60013i	0.265246	−	0.265246i	0.827181	+	0.561935i	$0.189943\pi$
$822$		0			0
$823$	−25.4074	−	25.4074i	−0.885648	−	0.885648i	0.108454	−	0.994101i	$-0.465410\pi$
$823$	−25.4074	−	25.4074i	−0.885648	−	0.885648i	−0.994101	+	0.108454i	$0.965410\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	37.7770i		−	1.31363i	−0.754050	−	0.656817i	$-0.771902\pi$
$827$		−	37.7770i		−	1.31363i	0.754050	−	0.656817i	$-0.228098\pi$
$828$		0			0
$829$	−32.0493			−1.11312			−0.556559	−	0.830808i	$-0.687878\pi$
$829$	−32.0493			−1.11312			−0.556559	+	0.830808i	$0.687878\pi$
$830$		0			0
$831$		−	4.24657i		−	0.147312i
$832$		0			0
$833$	−43.3721	+	43.3721i	−1.50276	+	1.50276i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−5.44357			−0.188157
$838$		0			0
$839$	−9.17521	+	9.17521i	−0.316763	+	0.316763i	−0.847523	−	0.530759i	$-0.821907\pi$
$839$	−9.17521	+	9.17521i	−0.316763	+	0.316763i	0.530759	+	0.847523i	$0.321907\pi$
$840$		0			0
$841$	13.5408			0.466926
$842$		0			0
$843$	3.31796			0.114277
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−36.9314			−1.26898
$848$		0			0
$849$	−23.7472			−0.815000
$850$		0			0
$851$	−11.0732	+	11.0732i	−0.379586	+	0.379586i
$852$		0			0
$853$	−25.1821			−0.862220			−0.431110	−	0.902299i	$-0.641878\pi$
$853$	−25.1821			−0.862220			−0.431110	+	0.902299i	$0.641878\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.17990	−	7.17990i	0.245261	−	0.245261i	−0.573762	−	0.819022i	$-0.694516\pi$
$857$	7.17990	−	7.17990i	0.245261	−	0.245261i	0.819022	+	0.573762i	$0.194516\pi$
$858$		0			0
$859$		−	44.4341i		−	1.51607i	−0.652213	−	0.758036i	$-0.726159\pi$
$859$		−	44.4341i		−	1.51607i	0.652213	−	0.758036i	$-0.273841\pi$
$860$		0			0
$861$	9.16076			0.312198
$862$		0			0
$863$			21.1546i			0.720111i	0.932931	+	0.360055i	$0.117242\pi$
$863$			21.1546i			0.720111i	−0.932931	+	0.360055i	$0.882758\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−12.7611	−	12.7611i	−0.433389	−	0.433389i
$868$		0			0
$869$	−26.2394	+	26.2394i	−0.890111	+	0.890111i
$870$		0			0
$871$	−21.7147	+	36.8992i	−0.735775	+	1.25028i
$872$		0			0
$873$		−	10.9521i		−	0.370671i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−38.6352			−1.30462			−0.652309	−	0.757953i	$-0.726200\pi$
$877$	−38.6352			−1.30462			−0.652309	+	0.757953i	$0.726200\pi$
$878$		0			0
$879$	−7.54686	+	7.54686i	−0.254549	+	0.254549i
$880$		0			0
$881$		−	17.4550i		−	0.588072i	−0.955794	−	0.294036i	$-0.905001\pi$
$881$		−	17.4550i		−	0.588072i	0.955794	−	0.294036i	$-0.0949986\pi$
$882$		0			0
$883$	22.8569	+	22.8569i	0.769196	+	0.769196i	0.977965	−	0.208769i	$-0.0669457\pi$
$883$	22.8569	+	22.8569i	0.769196	+	0.769196i	−0.208769	+	0.977965i	$0.566946\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.6394	−	12.6394i	−0.424390	−	0.424390i	0.462322	−	0.886712i	$-0.347016\pi$
$887$	−12.6394	−	12.6394i	−0.424390	−	0.424390i	−0.886712	+	0.462322i	$0.847016\pi$
$888$		0			0
$889$	18.8107	+	18.8107i	0.630889	+	0.630889i
$890$		0			0
$891$	3.15147	+	3.15147i	0.105578	+	0.105578i
$892$		0			0
$893$	4.46537	−	4.46537i	0.149428	−	0.149428i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−3.39298	+	5.76559i	−0.113288	+	0.192507i
$898$		0			0
$899$	−15.1343	−	15.1343i	−0.504756	−	0.504756i
$900$		0			0
$901$		−	11.4275i		−	0.380707i
$902$		0			0
$903$		−	47.8281i		−	1.59162i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.4274	−	16.4274i	0.545462	−	0.545462i	−0.379663	−	0.925125i	$-0.623960\pi$
$907$	16.4274	−	16.4274i	0.545462	−	0.545462i	0.925125	+	0.379663i	$0.123960\pi$
$908$		0			0
$909$	8.05908			0.267303
$910$		0			0
$911$	−2.40393			−0.0796456			−0.0398228	−	0.999207i	$-0.512679\pi$
$911$	−2.40393			−0.0796456			−0.0398228	+	0.999207i	$0.512679\pi$
$912$		0			0
$913$	−47.7424	+	47.7424i	−1.58004	+	1.58004i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			26.9998i			0.891612i
$918$		0			0
$919$			7.76783i			0.256237i	0.991759	+	0.128118i	$0.0408938\pi$
$919$			7.76783i			0.256237i	−0.991759	+	0.128118i	$0.959106\pi$
$920$		0			0
$921$	−7.03604	−	7.03604i	−0.231845	−	0.231845i
$922$		0			0
$923$	14.5729	+	56.2530i	0.479671	+	1.85159i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.15942	+	4.15942i	−0.136613	+	0.136613i
$928$		0			0
$929$	17.0133	+	17.0133i	0.558189	+	0.558189i	0.928792	−	0.370602i	$-0.120849\pi$
$929$	17.0133	+	17.0133i	0.558189	+	0.558189i	−0.370602	+	0.928792i	$0.620849\pi$
$930$		0			0
$931$	45.3528	+	45.3528i	1.48638	+	1.48638i
$932$		0			0
$933$	3.65328	+	3.65328i	0.119603	+	0.119603i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−6.62978	−	6.62978i	−0.216586	−	0.216586i	0.590472	−	0.807058i	$-0.298941\pi$
$937$	−6.62978	−	6.62978i	−0.216586	−	0.216586i	−0.807058	+	0.590472i	$0.798941\pi$
$938$		0			0
$939$			3.91338i			0.127708i
$940$		0			0
$941$	−23.5888	+	23.5888i	−0.768973	+	0.768973i	−0.977926	−	0.208953i	$-0.932994\pi$
$941$	−23.5888	+	23.5888i	−0.768973	+	0.768973i	0.208953	+	0.977926i	$0.432994\pi$
$942$		0			0
$943$	4.07934			0.132842
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	6.31026i		−	0.205056i	−0.994730	−	0.102528i	$-0.967307\pi$
$947$		−	6.31026i		−	0.205056i	0.994730	−	0.102528i	$-0.0326931\pi$
$948$		0			0
$949$	11.8161	−	20.0787i	0.383567	−	0.651784i
$950$		0			0
$951$	−20.6471	+	20.6471i	−0.669527	+	0.669527i
$952$		0			0
$953$	4.37109	+	4.37109i	0.141594	+	0.141594i	0.774350	−	0.632757i	$-0.218077\pi$
$953$	4.37109	+	4.37109i	0.141594	+	0.141594i	−0.632757	+	0.774350i	$0.718077\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			17.5235i			0.566455i
$958$		0			0
$959$	61.3755			1.98192
$960$		0			0
$961$			1.36757i			0.0441152i
$962$		0			0
$963$	−1.88527	+	1.88527i	−0.0607521	+	0.0607521i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	39.7361			1.27783			0.638914	−	0.769278i	$-0.279384\pi$
$967$	39.7361			1.27783			0.638914	+	0.769278i	$0.279384\pi$
$968$		0			0
$969$	−25.9136	+	25.9136i	−0.832466	+	0.832466i
$970$		0			0
$971$	31.5420			1.01223			0.506115	−	0.862466i	$-0.331081\pi$
$971$	31.5420			1.01223			0.506115	+	0.862466i	$0.331081\pi$
$972$		0			0
$973$	29.9740			0.960923
$974$		0			0
$975$		0			0
$976$		0			0
$977$	39.9665			1.27864			0.639322	−	0.768940i	$-0.279215\pi$
$977$	39.9665			1.27864			0.639322	+	0.768940i	$0.279215\pi$
$978$		0			0
$979$	−40.6040			−1.29771
$980$		0			0
$981$	−3.25319	+	3.25319i	−0.103866	+	0.103866i
$982$		0			0
$983$	23.4700			0.748577			0.374289	−	0.927312i	$-0.377887\pi$
$983$	23.4700			0.748577			0.374289	+	0.927312i	$0.377887\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−3.00556	+	3.00556i	−0.0956681	+	0.0956681i
$988$		0			0
$989$		−	21.2981i		−	0.677241i
$990$		0			0
$991$	33.6588			1.06921			0.534604	−	0.845103i	$-0.320461\pi$
$991$	33.6588			1.06921			0.534604	+	0.845103i	$0.320461\pi$
$992$		0			0
$993$			12.2908i			0.390037i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	16.7331	+	16.7331i	0.529943	+	0.529943i	0.920555	−	0.390613i	$-0.127737\pi$
$997$	16.7331	+	16.7331i	0.529943	+	0.529943i	−0.390613	+	0.920555i	$0.627737\pi$
$998$		0			0
$999$	5.96801	−	5.96801i	0.188819	−	0.188819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3900.2.r.b.1357.14		28
5.2	odd	4		780.2.bm.a.733.2	yes	28
5.3	odd	4		3900.2.bm.b.2293.14		28
5.4	even	2		780.2.r.a.577.5	yes	28
13.8	odd	4		3900.2.bm.b.2257.14		28
15.2	even	4		2340.2.bp.i.1513.13		28
15.14	odd	2		2340.2.u.i.577.6		28
65.8	even	4	inner	3900.2.r.b.3193.14		28
65.34	odd	4		780.2.bm.a.697.2	yes	28
65.47	even	4		780.2.r.a.73.5	✓	28
195.47	odd	4		2340.2.u.i.73.6		28
195.164	even	4		2340.2.bp.i.1477.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.5	✓	28	65.47	even	4
780.2.r.a.577.5	yes	28	5.4	even	2
780.2.bm.a.697.2	yes	28	65.34	odd	4
780.2.bm.a.733.2	yes	28	5.2	odd	4
2340.2.u.i.73.6		28	195.47	odd	4
2340.2.u.i.577.6		28	15.14	odd	2
2340.2.bp.i.1477.13		28	195.164	even	4
2340.2.bp.i.1513.13		28	15.2	even	4
3900.2.r.b.1357.14		28	1.1	even	1	trivial
3900.2.r.b.3193.14		28	65.8	even	4	inner
3900.2.bm.b.2257.14		28	13.8	odd	4
3900.2.bm.b.2293.14		28	5.3	odd	4

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.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +4.16665i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +4.16665i q^{7} -1.00000i q^{9} +(-3.15147 - 3.15147i) q^{11} +(-1.82867 + 3.10741i) q^{13} +(4.18610 - 4.18610i) q^{17} +(-4.37727 - 4.37727i) q^{19} +(2.94627 + 2.94627i) q^{21} +(1.31199 + 1.31199i) q^{23} +(-0.707107 - 0.707107i) q^{27} -3.93181i q^{29} +(3.84918 - 3.84918i) q^{31} -4.45686 q^{33} +8.44004i q^{37} +(0.904203 + 3.49033i) q^{39} +(1.55464 - 1.55464i) q^{41} +(-8.11673 - 8.11673i) q^{43} +1.02013i q^{47} -10.3610 q^{49} -5.92004i q^{51} +(1.36494 - 1.36494i) q^{53} -6.19040 q^{57} +(-1.43740 + 1.43740i) q^{59} +0.293533 q^{61} +4.16665 q^{63} +11.8746 q^{67} +1.85543 q^{69} +(11.3963 - 11.3963i) q^{71} -6.46158 q^{73} +(13.1311 - 13.1311i) q^{77} -8.32607i q^{79} -1.00000 q^{81} -15.1492i q^{83} +(-2.78021 - 2.78021i) q^{87} +(6.44206 - 6.44206i) q^{89} +(-12.9475 - 7.61943i) q^{91} -5.44357i q^{93} +10.9521 q^{97} +(-3.15147 + 3.15147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q + 8 q^{11} + 4 q^{13} + 4 q^{17} - 16 q^{19} + 8 q^{21} + 8 q^{23} + 8 q^{33} + 8 q^{39} + 12 q^{41} - 16 q^{43} - 36 q^{49} - 36 q^{53} + 16 q^{59} + 8 q^{61} - 48 q^{67} - 8 q^{69} + 8 q^{71} - 48 q^{73} + 48 q^{77} - 28 q^{81} + 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{97} + 8 q^{99}+O(q^{100}) \) 28 * q + 8 * q^11 + 4 * q^13 + 4 * q^17 - 16 * q^19 + 8 * q^21 + 8 * q^23 + 8 * q^33 + 8 * q^39 + 12 * q^41 - 16 * q^43 - 36 * q^49 - 36 * q^53 + 16 * q^59 + 8 * q^61 - 48 * q^67 - 8 * q^69 + 8 * q^71 - 48 * q^73 + 48 * q^77 - 28 * q^81 + 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^97 + 8 * q^99

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