LMFDB - Embedded newform 1512.2.r.e.505.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(505,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("1512.505");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.2091141441.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 $ x^8 - x^7 + x^6 + 3x^5 - 15x^4 + 9x^3 + 9x^2 - 27*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.3
Root			$0.199732 - 1.72050i$ of defining polynomial
Character	$\chi$	$=$	1512.505
Dual form			1512.2.r.e.1009.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.300268 + 0.520080i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(0.300268 + 0.520080i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.800268 + 1.38611i) q^{11} +(-0.165178 - 0.286096i) q^{13} +1.44990 q^{17} +2.57918 q^{19} +(0.924682 + 1.60160i) q^{23} +(2.31968 - 4.01780i) q^{25} +(1.75950 - 3.04755i) q^{29} +(4.81034 + 8.33176i) q^{31} +0.600537 q^{35} +0.600537 q^{37} +(3.31034 + 5.73368i) q^{41} +(-1.81481 + 3.14334i) q^{43} +(1.95477 - 3.38576i) q^{47} +(-0.500000 - 0.866025i) q^{49} +9.27166 q^{53} -0.961181 q^{55} +(-6.93476 - 12.0113i) q^{59} +(2.59433 - 4.49351i) q^{61} +(0.0991952 - 0.171811i) q^{65} +(5.90467 + 10.2272i) q^{67} +4.17972 q^{71} +4.13969 q^{73} +(0.800268 + 1.38611i) q^{77} +(-4.06538 + 7.04144i) q^{79} +(-2.78959 + 4.83171i) q^{83} +(0.435359 + 0.754064i) q^{85} +3.83069 q^{89} -0.330355 q^{91} +(0.774447 + 1.34138i) q^{95} +(0.974782 - 1.68837i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q + 3 * q^5 + 4 * q^7	$ 8 q + 3 q^{5} + 4 q^{7} - 7 q^{11} + 3 q^{13} - 6 q^{17} - 8 q^{19} - 2 q^{23} - 5 q^{25} + 9 q^{29} + 3 q^{31} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 8 q^{43} - 3 q^{47} - 4 q^{49} - 12 q^{53} - 56 q^{55} - 10 q^{59} + 20 q^{61} - q^{65} + 11 q^{67} + 6 q^{71} - 48 q^{73} + 7 q^{77} + 21 q^{79} - 8 q^{83} + 9 q^{85} - 12 q^{89} + 6 q^{91} - 36 q^{95} + 16 q^{97}+O(q^{100}) $ 8 * q + 3 * q^5 + 4 * q^7 - 7 * q^11 + 3 * q^13 - 6 * q^17 - 8 * q^19 - 2 * q^23 - 5 * q^25 + 9 * q^29 + 3 * q^31 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 8 * q^43 - 3 * q^47 - 4 * q^49 - 12 * q^53 - 56 * q^55 - 10 * q^59 + 20 * q^61 - q^65 + 11 * q^67 + 6 * q^71 - 48 * q^73 + 7 * q^77 + 21 * q^79 - 8 * q^83 + 9 * q^85 - 12 * q^89 + 6 * q^91 - 36 * q^95 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.300268	+	0.520080i	0.134284	+	0.232587i	0.925324	−	0.379178i	$-0.123793\pi$
$5$	0.300268	+	0.520080i	0.134284	+	0.232587i	−0.791040	+	0.611765i	$0.790460\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.800268	+	1.38611i	−0.241290	+	0.417926i	−0.961082	−	0.276263i	$-0.910904\pi$
$11$	−0.800268	+	1.38611i	−0.241290	+	0.417926i	0.719792	+	0.694190i	$0.244237\pi$
$12$		0			0
$13$	−0.165178	−	0.286096i	−0.0458120	−	0.0793487i	0.842210	−	0.539149i	$-0.181254\pi$
$13$	−0.165178	−	0.286096i	−0.0458120	−	0.0793487i	−0.888022	+	0.459801i	$0.847921\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.44990			0.351652			0.175826	−	0.984421i	$-0.443740\pi$
$17$	1.44990			0.351652			0.175826	+	0.984421i	$0.443740\pi$
$18$		0			0
$19$	2.57918			0.591705			0.295852	−	0.955234i	$-0.404396\pi$
$19$	2.57918			0.591705			0.295852	+	0.955234i	$0.404396\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.924682	+	1.60160i	0.192809	+	0.333956i	0.946180	−	0.323640i	$-0.104907\pi$
$23$	0.924682	+	1.60160i	0.192809	+	0.333956i	−0.753371	+	0.657596i	$0.771573\pi$
$24$		0			0
$25$	2.31968	−	4.01780i	0.463936	−	0.803560i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.75950	−	3.04755i	0.326732	−	0.565916i	−0.655130	−	0.755517i	$-0.727386\pi$
$29$	1.75950	−	3.04755i	0.326732	−	0.565916i	0.981861	+	0.189601i	$0.0607193\pi$
$30$		0			0
$31$	4.81034	+	8.33176i	0.863963	+	1.49643i	0.868073	+	0.496436i	$0.165358\pi$
$31$	4.81034	+	8.33176i	0.863963	+	1.49643i	−0.00411031	+	0.999992i	$0.501308\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.600537			0.101509
$36$		0			0
$37$	0.600537			0.0987276			0.0493638	−	0.998781i	$-0.484281\pi$
$37$	0.600537			0.0987276			0.0493638	+	0.998781i	$0.484281\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.31034	+	5.73368i	0.516989	+	0.895450i	0.999805	+	0.0197291i	$0.00628037\pi$
$41$	3.31034	+	5.73368i	0.516989	+	0.895450i	−0.482817	+	0.875721i	$0.660386\pi$
$42$		0			0
$43$	−1.81481	+	3.14334i	−0.276756	+	0.479355i	−0.970577	−	0.240793i	$-0.922593\pi$
$43$	−1.81481	+	3.14334i	−0.276756	+	0.479355i	0.693821	+	0.720148i	$0.255926\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.95477	−	3.38576i	0.285132	−	0.493864i	−0.687509	−	0.726176i	$-0.741296\pi$
$47$	1.95477	−	3.38576i	0.285132	−	0.493864i	0.972641	+	0.232312i	$0.0746291\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.27166			1.27356			0.636780	−	0.771046i	$-0.280266\pi$
$53$	9.27166			1.27356			0.636780	+	0.771046i	$0.280266\pi$
$54$		0			0
$55$	−0.961181			−0.129606
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.93476	−	12.0113i	−0.902828	−	1.56374i	−0.823806	−	0.566872i	$-0.808154\pi$
$59$	−6.93476	−	12.0113i	−0.902828	−	1.56374i	−0.0790221	−	0.996873i	$-0.525180\pi$
$60$		0			0
$61$	2.59433	−	4.49351i	0.332169	−	0.575334i	−0.650768	−	0.759277i	$-0.725553\pi$
$61$	2.59433	−	4.49351i	0.332169	−	0.575334i	0.982937	+	0.183943i	$0.0588861\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.0991952	−	0.171811i	0.0123036	−	0.0213105i
$66$		0			0
$67$	5.90467	+	10.2272i	0.721370	+	1.24945i	0.960451	+	0.278450i	$0.0898206\pi$
$67$	5.90467	+	10.2272i	0.721370	+	1.24945i	−0.239081	+	0.971000i	$0.576846\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.17972			0.496041			0.248021	−	0.968755i	$-0.420220\pi$
$71$	4.17972			0.496041			0.248021	+	0.968755i	$0.420220\pi$
$72$		0			0
$73$	4.13969			0.484514			0.242257	−	0.970212i	$-0.422112\pi$
$73$	4.13969			0.484514			0.242257	+	0.970212i	$0.422112\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.800268	+	1.38611i	0.0911990	+	0.157961i
$78$		0			0
$79$	−4.06538	+	7.04144i	−0.457391	+	0.792224i	−0.998822	−	0.0485208i	$-0.984549\pi$
$79$	−4.06538	+	7.04144i	−0.457391	+	0.792224i	0.541431	+	0.840745i	$0.317883\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.78959	+	4.83171i	−0.306197	+	0.530349i	−0.977527	−	0.210809i	$-0.932390\pi$
$83$	−2.78959	+	4.83171i	−0.306197	+	0.530349i	0.671330	+	0.741159i	$0.265723\pi$
$84$		0			0
$85$	0.435359	+	0.754064i	0.0472213	+	0.0817897i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.83069			0.406053			0.203026	−	0.979173i	$-0.434922\pi$
$89$	3.83069			0.406053			0.203026	+	0.979173i	$0.434922\pi$
$90$		0			0
$91$	−0.330355			−0.0346306
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.774447	+	1.34138i	0.0794565	+	0.137623i
$96$		0			0
$97$	0.974782	−	1.68837i	0.0989741	−	0.171428i	−0.812286	−	0.583259i	$-0.801777\pi$
$97$	0.974782	−	1.68837i	0.0989741	−	0.171428i	0.911260	+	0.411831i	$0.135111\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.79520	−	15.2337i	0.875155	−	1.51581i	0.0185572	−	0.999828i	$-0.494093\pi$
$101$	8.79520	−	15.2337i	0.875155	−	1.51581i	0.856598	−	0.515985i	$-0.172574\pi$
$102$		0			0
$103$	5.30547	+	9.18935i	0.522764	+	0.905454i	0.999649	+	0.0264880i	$0.00843237\pi$
$103$	5.30547	+	9.18935i	0.522764	+	0.905454i	−0.476885	+	0.878966i	$0.658234\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.43949			0.332508			0.166254	−	0.986083i	$-0.446833\pi$
$107$	3.43949			0.332508			0.166254	+	0.986083i	$0.446833\pi$
$108$		0			0
$109$	−5.55010			−0.531603			−0.265802	−	0.964028i	$-0.585637\pi$
$109$	−5.55010			−0.531603			−0.265802	+	0.964028i	$0.585637\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.38079	+	7.58775i	0.412110	+	0.713796i	0.995120	−	0.0986691i	$-0.0314585\pi$
$113$	4.38079	+	7.58775i	0.412110	+	0.713796i	−0.583010	+	0.812465i	$0.698125\pi$
$114$		0			0
$115$	−0.555305	+	0.961817i	−0.0517825	+	0.0896899i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.724950	−	1.25565i	0.0664561	−	0.115105i
$120$		0			0
$121$	4.21914	+	7.30777i	0.383558	+	0.664342i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.78879			0.517765
$126$		0			0
$127$	−11.1521			−0.989590			−0.494795	−	0.869010i	$-0.664757\pi$
$127$	−11.1521			−0.989590			−0.494795	+	0.869010i	$0.664757\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.59993	−	4.50322i	−0.227157	−	0.393448i	0.729807	−	0.683653i	$-0.239610\pi$
$131$	−2.59993	−	4.50322i	−0.227157	−	0.393448i	−0.956964	+	0.290205i	$0.906276\pi$
$132$		0			0
$133$	1.28959	−	2.23364i	0.111822	−	0.193681i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.39399	−	7.61062i	0.375404	−	0.650219i	−0.614983	−	0.788540i	$-0.710837\pi$
$137$	4.39399	−	7.61062i	0.375404	−	0.650219i	0.990387	+	0.138321i	$0.0441706\pi$
$138$		0			0
$139$	4.50934	+	7.81040i	0.382477	+	0.662469i	0.991416	−	0.130748i	$-0.0417378\pi$
$139$	4.50934	+	7.81040i	0.382477	+	0.662469i	−0.608939	+	0.793217i	$0.708404\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.528746			0.0442159
$144$		0			0
$145$	2.11329			0.175499
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.525620	−	0.910400i	−0.0430604	−	0.0745829i	0.843692	−	0.536828i	$-0.180377\pi$
$149$	−0.525620	−	0.910400i	−0.0430604	−	0.0745829i	−0.886752	+	0.462245i	$0.847044\pi$
$150$		0			0
$151$	6.48932	−	11.2398i	0.528094	−	0.914685i	−0.471370	−	0.881936i	$-0.656240\pi$
$151$	6.48932	−	11.2398i	0.528094	−	0.914685i	0.999464	−	0.0327494i	$-0.0104263\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.88879	+	5.00352i	−0.232033	+	0.401893i
$156$		0			0
$157$	9.86699	+	17.0901i	0.787471	+	1.36394i	0.927511	+	0.373795i	$0.121944\pi$
$157$	9.86699	+	17.0901i	0.787471	+	1.36394i	−0.140040	+	0.990146i	$0.544723\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.84936			0.145750
$162$		0			0
$163$	−22.9214			−1.79534			−0.897672	−	0.440664i	$-0.854743\pi$
$163$	−22.9214			−1.79534			−0.897672	+	0.440664i	$0.854743\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.61508	+	2.79740i	0.124978	+	0.216469i	0.921725	−	0.387845i	$-0.126780\pi$
$167$	1.61508	+	2.79740i	0.124978	+	0.216469i	−0.796746	+	0.604314i	$0.793447\pi$
$168$		0			0
$169$	6.44543	−	11.1638i	0.495803	−	0.858755i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.08052	−	12.2638i	0.538322	−	0.932401i	−0.460672	−	0.887570i	$-0.652392\pi$
$173$	7.08052	−	12.2638i	0.538322	−	0.932401i	0.998995	−	0.0448312i	$-0.0142750\pi$
$174$		0			0
$175$	−2.31968	−	4.01780i	−0.175351	−	0.303717i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−7.06790			−0.528280			−0.264140	−	0.964484i	$-0.585088\pi$
$179$	−7.06790			−0.528280			−0.264140	+	0.964484i	$0.585088\pi$
$180$		0			0
$181$	−19.6207			−1.45839			−0.729197	−	0.684304i	$-0.760106\pi$
$181$	−19.6207			−1.45839			−0.729197	+	0.684304i	$0.760106\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.180322	+	0.312327i	0.0132575	+	0.0229627i
$186$		0			0
$187$	−1.16031	+	2.00971i	−0.0848502	+	0.146965i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.1096	+	17.5104i	−0.731505	+	1.26700i	0.224734	+	0.974420i	$0.427849\pi$
$191$	−10.1096	+	17.5104i	−0.731505	+	1.26700i	−0.956240	+	0.292584i	$0.905485\pi$
$192$		0			0
$193$	−8.89473	−	15.4061i	−0.640257	−	1.10896i	−0.985375	−	0.170398i	$-0.945495\pi$
$193$	−8.89473	−	15.4061i	−0.640257	−	1.10896i	0.345119	−	0.938559i	$-0.387839\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.04150			−0.572933			−0.286467	−	0.958090i	$-0.592481\pi$
$197$	−8.04150			−0.572933			−0.286467	+	0.958090i	$0.592481\pi$
$198$		0			0
$199$	14.0332			0.994790			0.497395	−	0.867524i	$-0.334290\pi$
$199$	14.0332			0.994790			0.497395	+	0.867524i	$0.334290\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.75950	−	3.04755i	−0.123493	−	0.213896i
$204$		0			0
$205$	−1.98798	+	3.44328i	−0.138847	+	0.240489i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.06404	+	3.57502i	−0.142772	+	0.247289i
$210$		0			0
$211$	−7.32622	−	12.6894i	−0.504358	−	0.873574i	−0.999987	−	0.00503962i	$-0.998396\pi$
$211$	−7.32622	−	12.6894i	−0.504358	−	0.873574i	0.495629	−	0.868534i	$-0.334938\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.17972			−0.148656
$216$		0			0
$217$	9.62068			0.653095
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.239491	−	0.414811i	−0.0161099	−	0.0279032i
$222$		0			0
$223$	7.02696	−	12.1711i	0.470560	−	0.815034i	−0.528873	−	0.848701i	$-0.677385\pi$
$223$	7.02696	−	12.1711i	0.470560	−	0.815034i	0.999433	+	0.0336670i	$0.0107185\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.40601	−	4.16733i	0.159692	−	0.276596i	−0.775065	−	0.631881i	$-0.782283\pi$
$227$	2.40601	−	4.16733i	0.159692	−	0.276596i	0.934758	+	0.355286i	$0.115616\pi$
$228$		0			0
$229$	−1.68419	−	2.91710i	−0.111294	−	0.192767i	0.804998	−	0.593277i	$-0.202166\pi$
$229$	−1.68419	−	2.91710i	−0.111294	−	0.192767i	−0.916292	+	0.400510i	$0.868833\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−20.9137			−1.37010			−0.685051	−	0.728495i	$-0.740220\pi$
$233$	−20.9137			−1.37010			−0.685051	+	0.728495i	$0.740220\pi$
$234$		0			0
$235$	2.34782			0.153155
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.60614	+	16.6383i	0.621370	+	1.07624i	0.989231	+	0.146363i	$0.0467568\pi$
$239$	9.60614	+	16.6383i	0.621370	+	1.07624i	−0.367861	+	0.929881i	$0.619910\pi$
$240$		0			0
$241$	8.88912	−	15.3964i	0.572599	−	0.991770i	−0.423699	−	0.905803i	$-0.639269\pi$
$241$	8.88912	−	15.3964i	0.572599	−	0.991770i	0.996298	−	0.0859672i	$-0.0273980\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.300268	−	0.520080i	0.0191834	−	0.0332267i
$246$		0			0
$247$	−0.426023	−	0.737894i	−0.0271072	−	0.0469510i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−20.5531			−1.29730			−0.648649	−	0.761088i	$-0.724665\pi$
$251$	−20.5531			−1.29730			−0.648649	+	0.761088i	$0.724665\pi$
$252$		0			0
$253$	−2.95997			−0.186092
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.6943	−	21.9871i	−0.791846	−	1.37152i	−0.924823	−	0.380399i	$-0.875787\pi$
$257$	−12.6943	−	21.9871i	−0.791846	−	1.37152i	0.132976	−	0.991119i	$-0.457547\pi$
$258$		0			0
$259$	0.300268	−	0.520080i	0.0186578	−	0.0323162i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.3557	+	26.5969i	−0.946874	+	1.64003i	−0.194918	+	0.980820i	$0.562444\pi$
$263$	−15.3557	+	26.5969i	−0.946874	+	1.64003i	−0.751956	+	0.659213i	$0.770889\pi$
$264$		0			0
$265$	2.78398	+	4.82200i	0.171019	+	0.296213i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−13.7402			−0.837757			−0.418878	−	0.908042i	$-0.637577\pi$
$269$	−13.7402			−0.837757			−0.418878	+	0.908042i	$0.637577\pi$
$270$		0			0
$271$	7.64977			0.464690			0.232345	−	0.972633i	$-0.425360\pi$
$271$	7.64977			0.464690			0.232345	+	0.972633i	$0.425360\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.71273	+	6.43064i	0.223886	+	0.387782i
$276$		0			0
$277$	4.19174	−	7.26030i	0.251857	−	0.436229i	−0.712180	−	0.701997i	$-0.752292\pi$
$277$	4.19174	−	7.26030i	0.251857	−	0.436229i	0.964037	+	0.265768i	$0.0856254\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.7786	+	22.1333i	−0.762310	+	1.32036i	0.179347	+	0.983786i	$0.442602\pi$
$281$	−12.7786	+	22.1333i	−0.762310	+	1.32036i	−0.941657	+	0.336574i	$0.890732\pi$
$282$		0			0
$283$	−5.46132	−	9.45928i	−0.324641	−	0.562296i	0.656798	−	0.754066i	$-0.271910\pi$
$283$	−5.46132	−	9.45928i	−0.324641	−	0.562296i	−0.981440	+	0.191771i	$0.938577\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.62068			0.390807
$288$		0			0
$289$	−14.8978			−0.876341
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.9994	+	24.2477i	0.817853	+	1.41656i	0.907261	+	0.420569i	$0.138169\pi$
$293$	13.9994	+	24.2477i	0.817853	+	1.41656i	−0.0894073	+	0.995995i	$0.528497\pi$
$294$		0			0
$295$	4.16457	−	7.21325i	0.242471	−	0.419972i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.305473	−	0.529095i	0.0176660	−	0.0305984i
$300$		0			0
$301$	1.81481	+	3.14334i	0.104604	+	0.181179i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.11598			0.178420
$306$		0			0
$307$	−33.0259			−1.88489			−0.942443	−	0.334367i	$-0.891477\pi$
$307$	−33.0259			−1.88489			−0.942443	+	0.334367i	$0.891477\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−13.0143	−	22.5415i	−0.737975	−	1.27821i	−0.953406	−	0.301692i	$-0.902449\pi$
$311$	−13.0143	−	22.5415i	−0.737975	−	1.27821i	0.215430	−	0.976519i	$-0.430885\pi$
$312$		0			0
$313$	5.46618	−	9.46771i	0.308967	−	0.535146i	−0.669170	−	0.743110i	$-0.733350\pi$
$313$	5.46618	−	9.46771i	0.308967	−	0.535146i	0.978137	+	0.207963i	$0.0666834\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.98593	+	10.3679i	−0.336203	+	0.582321i	−0.983715	−	0.179734i	$-0.942476\pi$
$317$	−5.98593	+	10.3679i	−0.336203	+	0.582321i	0.647512	+	0.762055i	$0.275810\pi$
$318$		0			0
$319$	2.81615	+	4.87772i	0.157674	+	0.273100i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.73956			0.208074
$324$		0			0
$325$	−1.53264			−0.0850153
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.95477	−	3.38576i	−0.107770	−	0.186663i
$330$		0			0
$331$	−11.6176	+	20.1223i	−0.638561	+	1.10602i	0.347188	+	0.937796i	$0.387137\pi$
$331$	−11.6176	+	20.1223i	−0.638561	+	1.10602i	−0.985749	+	0.168224i	$0.946197\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.54597	+	6.14180i	−0.193737	+	0.335562i
$336$		0			0
$337$	−3.89594	−	6.74796i	−0.212225	−	0.367585i	0.740185	−	0.672403i	$-0.234738\pi$
$337$	−3.89594	−	6.74796i	−0.212225	−	0.367585i	−0.952411	+	0.304818i	$0.901404\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.3983			−0.833862
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.26198	−	16.0422i	−0.497209	−	0.861192i	0.502785	−	0.864411i	$-0.332309\pi$
$347$	−9.26198	−	16.0422i	−0.497209	−	0.861192i	−0.999995	+	0.00321932i	$0.998975\pi$
$348$		0			0
$349$	0.958498	−	1.66017i	0.0513072	−	0.0888667i	−0.839231	−	0.543775i	$-0.816995\pi$
$349$	0.958498	−	1.66017i	0.0513072	−	0.0888667i	0.890538	+	0.454908i	$0.150328\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.869778	+	1.50650i	−0.0462936	+	0.0801829i	−0.888244	−	0.459372i	$-0.848074\pi$
$353$	−0.869778	+	1.50650i	−0.0462936	+	0.0801829i	0.841950	+	0.539555i	$0.181408\pi$
$354$		0			0
$355$	1.25504	+	2.17379i	0.0666104	+	0.115373i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.07616			0.162354			0.0811768	−	0.996700i	$-0.474132\pi$
$359$	3.07616			0.162354			0.0811768	+	0.996700i	$0.474132\pi$
$360$		0			0
$361$	−12.3478			−0.649885
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.24302	+	2.15297i	0.0650625	+	0.112692i
$366$		0			0
$367$	6.17871	−	10.7018i	0.322526	−	0.558632i	−0.658482	−	0.752596i	$-0.728801\pi$
$367$	6.17871	−	10.7018i	0.322526	−	0.558632i	0.981009	+	0.193964i	$0.0621346\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.63583	−	8.02949i	0.240680	−	0.416870i
$372$		0			0
$373$	−12.3999	−	21.4773i	−0.642044	−	1.11205i	−0.984976	−	0.172693i	$-0.944753\pi$
$373$	−12.3999	−	21.4773i	−0.642044	−	1.11205i	0.342931	−	0.939360i	$-0.388580\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.16252			−0.0598730
$378$		0			0
$379$	−11.9650			−0.614602			−0.307301	−	0.951612i	$-0.599426\pi$
$379$	−11.9650			−0.614602			−0.307301	+	0.951612i	$0.599426\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.85810	+	10.1465i	0.299335	+	0.518463i	0.975984	−	0.217843i	$-0.0699020\pi$
$383$	5.85810	+	10.1465i	0.299335	+	0.518463i	−0.676649	+	0.736306i	$0.736569\pi$
$384$		0			0
$385$	−0.480590	+	0.832407i	−0.0244932	+	0.0424234i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	19.1360	−	33.1445i	0.970232	−	1.68049i	0.275384	−	0.961334i	$-0.411195\pi$
$389$	19.1360	−	33.1445i	0.970232	−	1.68049i	0.694848	−	0.719156i	$-0.255472\pi$
$390$		0			0
$391$	1.34070	+	2.32215i	0.0678019	+	0.117436i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.88282			−0.245681
$396$		0			0
$397$	12.8396			0.644402			0.322201	−	0.946671i	$-0.395577\pi$
$397$	12.8396			0.644402			0.322201	+	0.946671i	$0.395577\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.1570	+	19.3245i	0.557155	+	0.965021i	0.997732	+	0.0673063i	$0.0214405\pi$
$401$	11.1570	+	19.3245i	0.557155	+	0.965021i	−0.440577	+	0.897715i	$0.645226\pi$
$402$		0			0
$403$	1.58912	−	2.75244i	0.0791598	−	0.137109i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.480590	+	0.832407i	−0.0238220	+	0.0412609i
$408$		0			0
$409$	3.76605	+	6.52299i	0.186219	+	0.322541i	0.943987	−	0.329984i	$-0.107043\pi$
$409$	3.76605	+	6.52299i	0.186219	+	0.322541i	−0.757767	+	0.652525i	$0.773710\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.8695			−0.682474
$414$		0			0
$415$	−3.35050			−0.164470
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.1245	−	24.4644i	−0.690029	−	1.19517i	−0.971828	−	0.235692i	$-0.924264\pi$
$419$	−14.1245	−	24.4644i	−0.690029	−	1.19517i	0.281798	−	0.959474i	$-0.409069\pi$
$420$		0			0
$421$	−9.53395	+	16.5133i	−0.464656	+	0.804808i	−0.999186	−	0.0403414i	$-0.987155\pi$
$421$	−9.53395	+	16.5133i	−0.464656	+	0.804808i	0.534530	+	0.845150i	$0.320489\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.36330	−	5.82541i	0.163144	−	0.282574i
$426$		0			0
$427$	−2.59433	−	4.49351i	−0.125548	−	0.217456i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	22.9786			1.10684			0.553421	−	0.832902i	$-0.313322\pi$
$431$	22.9786			1.10684			0.553421	+	0.832902i	$0.313322\pi$
$432$		0			0
$433$	−29.0806			−1.39752			−0.698762	−	0.715354i	$-0.746265\pi$
$433$	−29.0806			−1.39752			−0.698762	+	0.715354i	$0.746265\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.38492	+	4.13081i	0.114086	+	0.197603i
$438$		0			0
$439$	7.36777	−	12.7613i	0.351644	−	0.609066i	−0.634893	−	0.772600i	$-0.718956\pi$
$439$	7.36777	−	12.7613i	0.351644	−	0.609066i	0.986538	+	0.163534i	$0.0522893\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−17.2548	+	29.8861i	−0.819799	+	1.41993i	0.0860314	+	0.996292i	$0.472581\pi$
$443$	−17.2548	+	29.8861i	−0.819799	+	1.41993i	−0.905830	+	0.423641i	$0.860752\pi$
$444$		0			0
$445$	1.15024	+	1.99227i	0.0545264	+	0.0944425i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11.5508			−0.545115			−0.272557	−	0.962140i	$-0.587869\pi$
$449$	−11.5508			−0.545115			−0.272557	+	0.962140i	$0.587869\pi$
$450$		0			0
$451$	−10.5966			−0.498977
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0991952	−	0.171811i	−0.00465034	−	0.00805463i
$456$		0			0
$457$	−18.6995	+	32.3884i	−0.874724	+	1.51507i	−0.0176677	+	0.999844i	$0.505624\pi$
$457$	−18.6995	+	32.3884i	−0.874724	+	1.51507i	−0.857056	+	0.515223i	$0.827709\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.13929	+	15.8297i	−0.425659	+	0.737263i	−0.996482	−	0.0838101i	$-0.973291\pi$
$461$	−9.13929	+	15.8297i	−0.425659	+	0.737263i	0.570823	+	0.821073i	$0.306624\pi$
$462$		0			0
$463$	−4.24610	−	7.35447i	−0.197333	−	0.341791i	0.750330	−	0.661064i	$-0.229895\pi$
$463$	−4.24610	−	7.35447i	−0.197333	−	0.341791i	−0.947663	+	0.319273i	$0.896561\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.6746			0.679060			0.339530	−	0.940595i	$-0.389732\pi$
$467$	14.6746			0.679060			0.339530	+	0.940595i	$0.389732\pi$
$468$		0			0
$469$	11.8093			0.545305
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.90467	−	5.03103i	−0.133557	−	0.231327i
$474$		0			0
$475$	5.98287	−	10.3626i	0.274513	−	0.475470i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	18.7151	−	32.4156i	0.855117	−	1.48111i	−0.0214198	−	0.999771i	$-0.506819\pi$
$479$	18.7151	−	32.4156i	0.855117	−	1.48111i	0.876537	−	0.481335i	$-0.159848\pi$
$480$		0			0
$481$	−0.0991952	−	0.171811i	−0.00452291	−	0.00783391i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.17078			0.0531626
$486$		0			0
$487$	33.3216			1.50994			0.754972	−	0.655757i	$-0.227650\pi$
$487$	33.3216			1.50994			0.754972	+	0.655757i	$0.227650\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−19.9456	−	34.5467i	−0.900131	−	1.55907i	−0.827323	−	0.561726i	$-0.810137\pi$
$491$	−19.9456	−	34.5467i	−0.900131	−	1.55907i	−0.0728078	−	0.997346i	$-0.523196\pi$
$492$		0			0
$493$	2.55110	−	4.41864i	0.114896	−	0.199006i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.08986	−	3.61974i	0.0937430	−	0.162368i
$498$		0			0
$499$	−11.0370	−	19.1167i	−0.494086	−	0.855781i	0.505891	−	0.862597i	$-0.331164\pi$
$499$	−11.0370	−	19.1167i	−0.494086	−	0.855781i	−0.999977	+	0.00681602i	$0.997830\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.30820			0.415032			0.207516	−	0.978232i	$-0.433462\pi$
$503$	9.30820			0.415032			0.207516	+	0.978232i	$0.433462\pi$
$504$		0			0
$505$	10.5637			0.470077
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.88466	−	4.99637i	−0.127860	−	0.221460i	0.794987	−	0.606626i	$-0.207478\pi$
$509$	−2.88466	−	4.99637i	−0.127860	−	0.221460i	−0.922847	+	0.385166i	$0.874144\pi$
$510$		0			0
$511$	2.06985	−	3.58508i	0.0915646	−	0.158595i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.18613	+	5.51854i	−0.140398	+	0.243176i
$516$		0			0
$517$	3.12868	+	5.41903i	0.137599	+	0.238329i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.2989			0.582634			0.291317	−	0.956627i	$-0.405907\pi$
$521$	13.2989			0.582634			0.291317	+	0.956627i	$0.405907\pi$
$522$		0			0
$523$	4.27523			0.186943			0.0934713	−	0.995622i	$-0.470204\pi$
$523$	4.27523			0.186943			0.0934713	+	0.995622i	$0.470204\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.97451	+	12.0802i	0.303815	+	0.526222i
$528$		0			0
$529$	9.78993	−	16.9567i	0.425649	−	0.737246i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.09359	−	1.89415i	0.0473686	−	0.0820448i
$534$		0			0
$535$	1.03277	+	1.78881i	0.0446505	+	0.0773370i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.60054			0.0689400
$540$		0			0
$541$	−12.2130			−0.525076			−0.262538	−	0.964922i	$-0.584560\pi$
$541$	−12.2130			−0.525076			−0.262538	+	0.964922i	$0.584560\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.66652	−	2.88650i	−0.0713858	−	0.123644i
$546$		0			0
$547$	−19.0910	+	33.0666i	−0.816272	+	1.41382i	0.0921387	+	0.995746i	$0.470630\pi$
$547$	−19.0910	+	33.0666i	−0.816272	+	1.41382i	−0.908411	+	0.418079i	$0.862704\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.53808	−	7.86019i	0.193329	−	0.334855i
$552$		0			0
$553$	4.06538	+	7.04144i	0.172877	+	0.299433i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−36.8404			−1.56098			−0.780490	−	0.625169i	$-0.785030\pi$
$557$	−36.8404			−1.56098			−0.780490	+	0.625169i	$0.785030\pi$
$558$		0			0
$559$	1.19906			0.0507150
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.56265	+	16.5630i	0.403018	+	0.698047i	0.994089	−	0.108572i	$-0.0346279\pi$
$563$	9.56265	+	16.5630i	0.403018	+	0.698047i	−0.591071	+	0.806620i	$0.701295\pi$
$564$		0			0
$565$	−2.63083	+	4.55672i	−0.110680	+	0.191703i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.9576	+	22.4433i	−0.543212	+	0.940871i	0.455505	+	0.890233i	$0.349459\pi$
$569$	−12.9576	+	22.4433i	−0.543212	+	0.940871i	−0.998717	+	0.0506376i	$0.983875\pi$
$570$		0			0
$571$	19.5679	+	33.8925i	0.818889	+	1.41836i	0.906501	+	0.422203i	$0.138743\pi$
$571$	19.5679	+	33.8925i	0.818889	+	1.41836i	−0.0876117	+	0.996155i	$0.527923\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.57985			0.357805
$576$		0			0
$577$	9.72008			0.404652			0.202326	−	0.979318i	$-0.435150\pi$
$577$	9.72008			0.404652			0.202326	+	0.979318i	$0.435150\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.78959	+	4.83171i	0.115732	+	0.200453i
$582$		0			0
$583$	−7.41981	+	12.8515i	−0.307297	+	0.532254i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.91088	−	11.9700i	0.285242	−	0.494054i	−0.687425	−	0.726255i	$-0.741259\pi$
$587$	6.91088	−	11.9700i	0.285242	−	0.494054i	0.972668	+	0.232200i	$0.0745925\pi$
$588$		0			0
$589$	12.4067	+	21.4891i	0.511211	+	0.885444i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	22.1361			0.909022			0.454511	−	0.890741i	$-0.349814\pi$
$593$	22.1361			0.909022			0.454511	+	0.890741i	$0.349814\pi$
$594$		0			0
$595$	0.870718			0.0356960
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.28059	+	3.95010i	0.0931824	+	0.161397i	0.908849	−	0.417126i	$-0.136963\pi$
$599$	2.28059	+	3.95010i	0.0931824	+	0.161397i	−0.815666	+	0.578523i	$0.803629\pi$
$600$		0			0
$601$	−10.2116	+	17.6870i	−0.416541	+	0.721469i	−0.995589	−	0.0938238i	$-0.970091\pi$
$601$	−10.2116	+	17.6870i	−0.416541	+	0.721469i	0.579048	+	0.815293i	$0.303424\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.53375	+	4.38858i	−0.103012	+	0.178421i
$606$		0			0
$607$	−7.11206	−	12.3184i	−0.288670	−	0.499990i	0.684823	−	0.728710i	$-0.259880\pi$
$607$	−7.11206	−	12.3184i	−0.288670	−	0.499990i	−0.973492	+	0.228719i	$0.926546\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.29154			−0.0522499
$612$		0			0
$613$	−31.3892			−1.26780			−0.633899	−	0.773416i	$-0.718546\pi$
$613$	−31.3892			−1.26780			−0.633899	+	0.773416i	$0.718546\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.51767	+	4.36073i	0.101357	+	0.175556i	0.912244	−	0.409647i	$-0.134348\pi$
$617$	2.51767	+	4.36073i	0.101357	+	0.175556i	−0.810887	+	0.585203i	$0.801015\pi$
$618$		0			0
$619$	19.1803	−	33.2212i	0.770920	−	1.33527i	−0.166140	−	0.986102i	$-0.553130\pi$
$619$	19.1803	−	33.2212i	0.770920	−	1.33527i	0.937060	−	0.349170i	$-0.113536\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.91535	−	3.31748i	0.0767367	−	0.132912i
$624$		0			0
$625$	−9.86020	−	17.0784i	−0.394408	−	0.683135i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.870718			0.0347178
$630$		0			0
$631$	24.0768			0.958480			0.479240	−	0.877684i	$-0.340912\pi$
$631$	24.0768			0.958480			0.479240	+	0.877684i	$0.340912\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.34863	−	5.79999i	−0.132886	−	0.230166i
$636$		0			0
$637$	−0.165178	+	0.286096i	−0.00654457	+	0.0113355i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.7800	−	35.9920i	0.820760	−	1.42160i	−0.0843567	−	0.996436i	$-0.526884\pi$
$641$	20.7800	−	35.9920i	0.820760	−	1.42160i	0.905117	−	0.425163i	$-0.139783\pi$
$642$		0			0
$643$	0.924345	+	1.60101i	0.0364526	+	0.0631378i	0.883676	−	0.468099i	$-0.155061\pi$
$643$	0.924345	+	1.60101i	0.0364526	+	0.0631378i	−0.847224	+	0.531237i	$0.821728\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	38.8480			1.52727			0.763637	−	0.645646i	$-0.223412\pi$
$647$	38.8480			1.52727			0.763637	+	0.645646i	$0.223412\pi$
$648$		0			0
$649$	22.1987			0.871374
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.3225	+	35.1996i	0.795281	+	1.37747i	0.922661	+	0.385613i	$0.126010\pi$
$653$	20.3225	+	35.1996i	0.795281	+	1.37747i	−0.127380	+	0.991854i	$0.540657\pi$
$654$		0			0
$655$	1.56135	−	2.70435i	0.0610072	−	0.105668i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.2140	−	33.2796i	0.748471	−	1.29639i	−0.200084	−	0.979779i	$-0.564121\pi$
$659$	19.2140	−	33.2796i	0.748471	−	1.29639i	0.948555	−	0.316612i	$-0.102545\pi$
$660$		0			0
$661$	5.72841	+	9.92190i	0.222809	+	0.385917i	0.955660	−	0.294472i	$-0.0951439\pi$
$661$	5.72841	+	9.92190i	0.222809	+	0.385917i	−0.732851	+	0.680390i	$0.761811\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.54889			0.0600635
$666$		0			0
$667$	6.50793			0.251988
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.15231	+	7.19202i	0.160298	+	0.277645i
$672$		0			0
$673$	−23.4933	+	40.6916i	−0.905601	+	1.56855i	−0.0854925	+	0.996339i	$0.527246\pi$
$673$	−23.4933	+	40.6916i	−0.905601	+	1.56855i	−0.820108	+	0.572208i	$0.806087\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.03942	+	13.9247i	−0.308980	+	0.535169i	−0.978140	−	0.207950i	$-0.933321\pi$
$677$	−8.03942	+	13.9247i	−0.308980	+	0.535169i	0.669159	+	0.743119i	$0.266654\pi$
$678$		0			0
$679$	−0.974782	−	1.68837i	−0.0374087	−	0.0647938i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	5.20464			0.199150			0.0995750	−	0.995030i	$-0.468252\pi$
$683$	5.20464			0.199150			0.0995750	+	0.995030i	$0.468252\pi$
$684$		0			0
$685$	5.27750			0.201643
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.53147	−	2.65258i	−0.0583444	−	0.101055i
$690$		0			0
$691$	−0.783381	+	1.35686i	−0.0298012	+	0.0516172i	−0.880541	−	0.473969i	$-0.842821\pi$
$691$	−0.783381	+	1.35686i	−0.0298012	+	0.0516172i	0.850740	+	0.525587i	$0.176154\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.70802	+	4.69043i	−0.102721	+	0.177918i
$696$		0			0
$697$	4.79966	+	8.31326i	0.181800	+	0.314887i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−5.94479			−0.224532			−0.112266	−	0.993678i	$-0.535811\pi$
$701$	−5.94479			−0.224532			−0.112266	+	0.993678i	$0.535811\pi$
$702$		0			0
$703$	1.54889			0.0584176
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.79520	−	15.2337i	−0.330777	−	0.572923i
$708$		0			0
$709$	6.53916	−	11.3262i	0.245583	−	0.425362i	−0.716712	−	0.697369i	$-0.754354\pi$
$709$	6.53916	−	11.3262i	0.245583	−	0.425362i	0.962295	+	0.272007i	$0.0876872\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−8.89607	+	15.4084i	−0.333160	+	0.577051i
$714$		0			0
$715$	0.158766	+	0.274990i	0.00593749	+	0.0102840i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.5600			0.393821			0.196910	−	0.980422i	$-0.436909\pi$
$719$	10.5600			0.393821			0.196910	+	0.980422i	$0.436909\pi$
$720$		0			0
$721$	10.6109			0.395172
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−8.16297	−	14.1387i	−0.303165	−	0.525097i
$726$		0			0
$727$	5.08052	−	8.79972i	0.188426	−	0.326364i	−0.756300	−	0.654226i	$-0.772995\pi$
$727$	5.08052	−	8.79972i	0.188426	−	0.326364i	0.944726	+	0.327862i	$0.106328\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.63129	+	4.55753i	−0.0973218	+	0.168566i
$732$		0			0
$733$	−13.2280	−	22.9116i	−0.488589	−	0.846260i	0.511325	−	0.859387i	$-0.329155\pi$
$733$	−13.2280	−	22.9116i	−0.488589	−	0.846260i	−0.999914	+	0.0131270i	$0.995821\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.9013			−0.696237
$738$		0			0
$739$	24.3880			0.897127			0.448563	−	0.893751i	$-0.351936\pi$
$739$	24.3880			0.897127			0.448563	+	0.893751i	$0.351936\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	8.21961	+	14.2368i	0.301548	+	0.522297i	0.976487	−	0.215577i	$-0.0691632\pi$
$743$	8.21961	+	14.2368i	0.301548	+	0.522297i	−0.674939	+	0.737874i	$0.735830\pi$
$744$		0			0
$745$	0.315654	−	0.546728i	0.0115647	−	0.0200306i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.71974	−	2.97869i	0.0628381	−	0.108839i
$750$		0			0
$751$	0.0653789	+	0.113240i	0.00238571	+	0.00413217i	0.867216	−	0.497932i	$-0.165907\pi$
$751$	0.0653789	+	0.113240i	0.00238571	+	0.00413217i	−0.864830	+	0.502065i	$0.832574\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.79415			0.283658
$756$		0			0
$757$	36.1017			1.31214			0.656069	−	0.754701i	$-0.272218\pi$
$757$	36.1017			1.31214			0.656069	+	0.754701i	$0.272218\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.61027	−	7.98523i	−0.167122	−	0.289464i	0.770285	−	0.637700i	$-0.220114\pi$
$761$	−4.61027	−	7.98523i	−0.167122	−	0.289464i	−0.937407	+	0.348236i	$0.886781\pi$
$762$		0			0
$763$	−2.77505	+	4.80653i	−0.100464	+	0.174008i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.29093	+	3.96801i	−0.0827208	+	0.143277i
$768$		0			0
$769$	22.8660	+	39.6050i	0.824568	+	1.42819i	0.902249	+	0.431216i	$0.141915\pi$
$769$	22.8660	+	39.6050i	0.824568	+	1.42819i	−0.0776802	+	0.996978i	$0.524751\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−25.9709			−0.934109			−0.467054	−	0.884229i	$-0.654685\pi$
$773$	−25.9709			−0.934109			−0.467054	+	0.884229i	$0.654685\pi$
$774$		0			0
$775$	44.6338			1.60329
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.53797	+	14.7882i	0.305905	+	0.529842i
$780$		0			0
$781$	−3.34490	+	5.79353i	−0.119690	+	0.207309i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.92549	+	10.2632i	−0.211490	+	0.366311i
$786$		0			0
$787$	−25.3821	−	43.9630i	−0.904773	−	1.56711i	−0.821222	−	0.570609i	$-0.806707\pi$
$787$	−25.3821	−	43.9630i	−0.904773	−	1.56711i	−0.0835512	−	0.996503i	$-0.526626\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	8.76158			0.311526
$792$		0			0
$793$	−1.71410			−0.0608694
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.2977	+	23.0322i	0.471027	+	0.815843i	0.999451	−	0.0331379i	$-0.0105501\pi$
$797$	13.2977	+	23.0322i	0.471027	+	0.815843i	−0.528424	+	0.848981i	$0.677217\pi$
$798$		0			0
$799$	2.83422	−	4.90901i	0.100267	−	0.173668i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.31286	+	5.73805i	−0.116908	+	0.202491i
$804$		0			0
$805$	0.555305	+	0.961817i	0.0195719	+	0.0338996i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	21.1540			0.743735			0.371867	−	0.928286i	$-0.378718\pi$
$809$	21.1540			0.743735			0.371867	+	0.928286i	$0.378718\pi$
$810$		0			0
$811$	−15.4615			−0.542927			−0.271464	−	0.962449i	$-0.587508\pi$
$811$	−15.4615			−0.542927			−0.271464	+	0.962449i	$0.587508\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.88258	−	11.9210i	−0.241086	−	0.417573i
$816$		0			0
$817$	−4.68072	+	8.10725i	−0.163758	+	0.283637i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	13.2843	−	23.0091i	0.463626	−	0.803024i	−0.535512	−	0.844527i	$-0.679881\pi$
$821$	13.2843	−	23.0091i	0.463626	−	0.803024i	0.999138	+	0.0415036i	$0.0132148\pi$
$822$		0			0
$823$	12.5469	+	21.7318i	0.437357	+	0.757524i	0.997485	−	0.0708819i	$-0.0225813\pi$
$823$	12.5469	+	21.7318i	0.437357	+	0.757524i	−0.560128	+	0.828406i	$0.689248\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.8156			−0.445642			−0.222821	−	0.974859i	$-0.571526\pi$
$827$	−12.8156			−0.445642			−0.222821	+	0.974859i	$0.571526\pi$
$828$		0			0
$829$	37.9832			1.31921			0.659605	−	0.751613i	$-0.270724\pi$
$829$	37.9832			1.31921			0.659605	+	0.751613i	$0.270724\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.724950	−	1.25565i	−0.0251180	−	0.0435057i
$834$		0			0
$835$	−0.969913	+	1.67994i	−0.0335652	+	0.0581367i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2.95638	+	5.12060i	−0.102065	+	0.176783i	−0.912535	−	0.408998i	$-0.865878\pi$
$839$	−2.95638	+	5.12060i	−0.102065	+	0.176783i	0.810470	+	0.585780i	$0.199212\pi$
$840$		0			0
$841$	8.30829	+	14.3904i	0.286493	+	0.496220i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	7.74144			0.266313
$846$		0			0
$847$	8.43828			0.289943
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.555305	+	0.961817i	0.0190356	+	0.0329707i
$852$		0			0
$853$	9.72609	−	16.8461i	0.333015	−	0.576799i	−0.650087	−	0.759860i	$-0.725267\pi$
$853$	9.72609	−	16.8461i	0.333015	−	0.576799i	0.983101	+	0.183061i	$0.0586007\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.42502	+	5.93231i	−0.116996	+	0.202644i	−0.918576	−	0.395244i	$-0.870660\pi$
$857$	−3.42502	+	5.93231i	−0.116996	+	0.202644i	0.801580	+	0.597888i	$0.203993\pi$
$858$		0			0
$859$	−3.04742	−	5.27828i	−0.103977	−	0.180093i	0.809343	−	0.587336i	$-0.199823\pi$
$859$	−3.04742	−	5.27828i	−0.103977	−	0.180093i	−0.913320	+	0.407244i	$0.866490\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	33.6568			1.14569			0.572846	−	0.819663i	$-0.305839\pi$
$863$	33.6568			1.14569			0.572846	+	0.819663i	$0.305839\pi$
$864$		0			0
$865$	8.50423			0.289152
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.50679	−	11.2701i	−0.220728	−	0.382312i
$870$		0			0
$871$	1.95064	−	3.37860i	0.0660948	−	0.114480i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.89439	−	5.01324i	0.0978483	−	0.169478i
$876$		0			0
$877$	−8.18905	−	14.1839i	−0.276525	−	0.478955i	0.693994	−	0.719981i	$-0.255849\pi$
$877$	−8.18905	−	14.1839i	−0.276525	−	0.478955i	−0.970519	+	0.241026i	$0.922516\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−22.0864			−0.744108			−0.372054	−	0.928211i	$-0.621346\pi$
$881$	−22.0864			−0.744108			−0.372054	+	0.928211i	$0.621346\pi$
$882$		0			0
$883$	13.1872			0.443784			0.221892	−	0.975071i	$-0.428777\pi$
$883$	13.1872			0.443784			0.221892	+	0.975071i	$0.428777\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.7174	+	25.4912i	0.494160	+	0.855911i	0.999977	−	0.00672982i	$-0.00214218\pi$
$887$	14.7174	+	25.4912i	0.494160	+	0.855911i	−0.505817	+	0.862641i	$0.668809\pi$
$888$		0			0
$889$	−5.57606	+	9.65801i	−0.187015	+	0.323919i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.04170	−	8.73249i	0.168714	−	0.292222i
$894$		0			0
$895$	−2.12227	−	3.67587i	−0.0709395	−	0.122871i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	33.8553			1.12914
$900$		0			0
$901$	13.4430			0.447850
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.89147	−	10.2043i	−0.195839	−	0.339203i
$906$		0			0
$907$	−9.03916	+	15.6563i	−0.300140	+	0.519858i	−0.976167	−	0.217018i	$-0.930367\pi$
$907$	−9.03916	+	15.6563i	−0.300140	+	0.519858i	0.676027	+	0.736877i	$0.263700\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.24050	−	7.34475i	0.140494	−	0.243343i	−0.787189	−	0.616712i	$-0.788464\pi$
$911$	4.24050	−	7.34475i	0.140494	−	0.243343i	0.927683	+	0.373369i	$0.121798\pi$
$912$		0			0
$913$	−4.46484	−	7.73333i	−0.147765	−	0.255936i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.19987			−0.171715
$918$		0			0
$919$	22.0092			0.726017			0.363008	−	0.931786i	$-0.381750\pi$
$919$	22.0092			0.726017			0.363008	+	0.931786i	$0.381750\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.690396	−	1.19580i	−0.0227247	−	0.0393603i
$924$		0			0
$925$	1.39305	−	2.41284i	0.0458032	−	0.0793336i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	21.4107	−	37.0845i	0.702464	−	1.21670i	−0.265135	−	0.964211i	$-0.585417\pi$
$929$	21.4107	−	37.0845i	0.702464	−	1.21670i	0.967599	−	0.252492i	$-0.0812501\pi$
$930$		0			0
$931$	−1.28959	−	2.23364i	−0.0422646	−	0.0732045i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.39362			−0.0455761
$936$		0			0
$937$	8.65749			0.282828			0.141414	−	0.989951i	$-0.454835\pi$
$937$	8.65749			0.282828			0.141414	+	0.989951i	$0.454835\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	25.9474	+	44.9421i	0.845859	+	1.46507i	0.884873	+	0.465833i	$0.154245\pi$
$941$	25.9474	+	44.9421i	0.845859	+	1.46507i	−0.0390132	+	0.999239i	$0.512421\pi$
$942$		0			0
$943$	−6.12203	+	10.6037i	−0.199361	+	0.345303i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.5394	+	19.9869i	−0.374981	+	0.649486i	−0.990324	−	0.138773i	$-0.955684\pi$
$947$	−11.5394	+	19.9869i	−0.374981	+	0.649486i	0.615343	+	0.788259i	$0.289017\pi$
$948$		0			0
$949$	−0.683784	−	1.18435i	−0.0221966	−	0.0384456i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	22.9656			0.743927			0.371964	−	0.928247i	$-0.378685\pi$
$953$	22.9656			0.743927			0.371964	+	0.928247i	$0.378685\pi$
$954$		0			0
$955$	−12.1424			−0.392918
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.39399	−	7.61062i	−0.141889	−	0.245760i
$960$		0			0
$961$	−30.7788	+	53.3104i	−0.992864	+	1.71969i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	5.34161	−	9.25194i	0.171953	−	0.297830i
$966$		0			0
$967$	−29.4696	−	51.0429i	−0.947680	−	1.64143i	−0.750294	−	0.661104i	$-0.770088\pi$
$967$	−29.4696	−	51.0429i	−0.947680	−	1.64143i	−0.197386	−	0.980326i	$-0.563245\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−25.8074			−0.828198			−0.414099	−	0.910232i	$-0.635903\pi$
$971$	−25.8074			−0.828198			−0.414099	+	0.910232i	$0.635903\pi$
$972$		0			0
$973$	9.01867			0.289125
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22.4774	−	38.9321i	−0.719117	−	1.24555i	−0.961350	−	0.275329i	$-0.911213\pi$
$977$	−22.4774	−	38.9321i	−0.719117	−	1.24555i	0.242233	−	0.970218i	$-0.422120\pi$
$978$		0			0
$979$	−3.06558	+	5.30974i	−0.0979764	+	0.169700i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.33576	+	7.50976i	−0.138289	+	0.239524i	−0.926849	−	0.375434i	$-0.877494\pi$
$983$	−4.33576	+	7.50976i	−0.138289	+	0.239524i	0.788560	+	0.614958i	$0.210827\pi$
$984$		0			0
$985$	−2.41461	−	4.18222i	−0.0769358	−	0.133257i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.71248			−0.213445
$990$		0			0
$991$	−3.39241			−0.107763			−0.0538817	−	0.998547i	$-0.517159\pi$
$991$	−3.39241			−0.107763			−0.0538817	+	0.998547i	$0.517159\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.21374	+	7.29841i	0.133584	+	0.231375i
$996$		0			0
$997$	−14.0201	+	24.2836i	−0.444023	+	0.769070i	−0.997984	−	0.0634730i	$-0.979782\pi$
$997$	−14.0201	+	24.2836i	−0.444023	+	0.769070i	0.553961	+	0.832543i	$0.313116\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.r.e.505.3		8
3.2	odd	2		504.2.r.e.169.4	✓	8
4.3	odd	2		3024.2.r.m.2017.3		8
9.2	odd	6		4536.2.a.z.1.3		4
9.4	even	3	inner	1512.2.r.e.1009.3		8
9.5	odd	6		504.2.r.e.337.4	yes	8
9.7	even	3		4536.2.a.y.1.2		4
12.11	even	2		1008.2.r.l.673.1		8
36.7	odd	6		9072.2.a.cg.1.2		4
36.11	even	6		9072.2.a.cj.1.3		4
36.23	even	6		1008.2.r.l.337.1		8
36.31	odd	6		3024.2.r.m.1009.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.e.169.4	✓	8	3.2	odd	2
504.2.r.e.337.4	yes	8	9.5	odd	6
1008.2.r.l.337.1		8	36.23	even	6
1008.2.r.l.673.1		8	12.11	even	2
1512.2.r.e.505.3		8	1.1	even	1	trivial
1512.2.r.e.1009.3		8	9.4	even	3	inner
3024.2.r.m.1009.3		8	36.31	odd	6
3024.2.r.m.2017.3		8	4.3	odd	2
4536.2.a.y.1.2		4	9.7	even	3
4536.2.a.z.1.3		4	9.2	odd	6
9072.2.a.cg.1.2		4	36.7	odd	6
9072.2.a.cj.1.3		4	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.300268 + 0.520080i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(0.300268 + 0.520080i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.800268 + 1.38611i) q^{11} +(-0.165178 - 0.286096i) q^{13} +1.44990 q^{17} +2.57918 q^{19} +(0.924682 + 1.60160i) q^{23} +(2.31968 - 4.01780i) q^{25} +(1.75950 - 3.04755i) q^{29} +(4.81034 + 8.33176i) q^{31} +0.600537 q^{35} +0.600537 q^{37} +(3.31034 + 5.73368i) q^{41} +(-1.81481 + 3.14334i) q^{43} +(1.95477 - 3.38576i) q^{47} +(-0.500000 - 0.866025i) q^{49} +9.27166 q^{53} -0.961181 q^{55} +(-6.93476 - 12.0113i) q^{59} +(2.59433 - 4.49351i) q^{61} +(0.0991952 - 0.171811i) q^{65} +(5.90467 + 10.2272i) q^{67} +4.17972 q^{71} +4.13969 q^{73} +(0.800268 + 1.38611i) q^{77} +(-4.06538 + 7.04144i) q^{79} +(-2.78959 + 4.83171i) q^{83} +(0.435359 + 0.754064i) q^{85} +3.83069 q^{89} -0.330355 q^{91} +(0.774447 + 1.34138i) q^{95} +(0.974782 - 1.68837i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q + 3 * q^5 + 4 * q^7	\( 8 q + 3 q^{5} + 4 q^{7} - 7 q^{11} + 3 q^{13} - 6 q^{17} - 8 q^{19} - 2 q^{23} - 5 q^{25} + 9 q^{29} + 3 q^{31} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 8 q^{43} - 3 q^{47} - 4 q^{49} - 12 q^{53} - 56 q^{55} - 10 q^{59} + 20 q^{61} - q^{65} + 11 q^{67} + 6 q^{71} - 48 q^{73} + 7 q^{77} + 21 q^{79} - 8 q^{83} + 9 q^{85} - 12 q^{89} + 6 q^{91} - 36 q^{95} + 16 q^{97}+O(q^{100}) \) 8 * q + 3 * q^5 + 4 * q^7 - 7 * q^11 + 3 * q^13 - 6 * q^17 - 8 * q^19 - 2 * q^23 - 5 * q^25 + 9 * q^29 + 3 * q^31 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 8 * q^43 - 3 * q^47 - 4 * q^49 - 12 * q^53 - 56 * q^55 - 10 * q^59 + 20 * q^61 - q^65 + 11 * q^67 + 6 * q^71 - 48 * q^73 + 7 * q^77 + 21 * q^79 - 8 * q^83 + 9 * q^85 - 12 * q^89 + 6 * q^91 - 36 * q^95 + 16 * q^97

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