LMFDB - Embedded newform 1300.2.m.c.593.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(57,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("1300.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.m (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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.31678304256.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 8x^{5} + 32x^{4} - 20x^{3} + 8x^{2} + 8x + 4 $ x^8 - 2x^7 + 2x^6 + 8x^5 + 32x^4 - 20x^3 + 8x^2 + 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.2
Root			$0.575868 - 0.575868i$ of defining polynomial
Character	$\chi$	$=$	1300.593
Dual form			1300.2.m.c.57.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.575868 - 0.575868i) q^{3} +2.48849i q^{7} -2.33675i q^{9} +O(q^{10})$	$q+(-0.575868 - 0.575868i) q^{3} +2.48849i q^{7} -2.33675i q^{9} +(-0.160643 + 0.160643i) q^{11} +(-1.42413 - 3.31238i) q^{13} +(-1.58477 - 1.58477i) q^{17} +(-2.91262 + 2.91262i) q^{19} +(1.43304 - 1.43304i) q^{21} +(0.839357 - 0.839357i) q^{23} +(-3.07326 + 3.07326i) q^{27} +2.80977i q^{29} +(-3.31238 - 3.31238i) q^{31} +0.185018 q^{33} -5.33675i q^{37} +(-1.08738 + 2.72760i) q^{39} +(-6.07326 - 6.07326i) q^{41} +(7.48193 - 7.48193i) q^{43} -3.99244i q^{47} +0.807426 q^{49} +1.82524i q^{51} +(0.0154678 + 0.0154678i) q^{53} +3.35457 q^{57} +(-2.91262 - 2.91262i) q^{59} -7.60929 q^{61} +5.81498 q^{63} +1.64022 q^{67} -0.966717 q^{69} +(-11.3702 - 11.3702i) q^{71} -15.2598 q^{73} +(-0.399757 - 0.399757i) q^{77} +15.6017i q^{79} -3.47067 q^{81} +0.681062i q^{83} +(1.61806 - 1.61806i) q^{87} +(-8.11324 - 8.11324i) q^{89} +(8.24281 - 3.54394i) q^{91} +3.81498i q^{93} -10.4322 q^{97} +(0.375382 + 0.375382i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3}+O(q^{10}) $ 8 * q - 2 * q^3	$ 8 q - 2 q^{3} + 14 q^{11} - 14 q^{13} + 2 q^{19} + 4 q^{21} + 22 q^{23} + 16 q^{27} - 6 q^{31} - 16 q^{33} - 34 q^{39} - 8 q^{41} + 14 q^{43} - 24 q^{49} + 8 q^{53} - 16 q^{57} + 2 q^{59} - 12 q^{61} + 64 q^{63} - 20 q^{67} - 20 q^{69} - 22 q^{71} + 28 q^{73} - 8 q^{77} - 20 q^{81} - 12 q^{87} + 4 q^{89} - 12 q^{97} + 10 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 14 * q^11 - 14 * q^13 + 2 * q^19 + 4 * q^21 + 22 * q^23 + 16 * q^27 - 6 * q^31 - 16 * q^33 - 34 * q^39 - 8 * q^41 + 14 * q^43 - 24 * q^49 + 8 * q^53 - 16 * q^57 + 2 * q^59 - 12 * q^61 + 64 * q^63 - 20 * q^67 - 20 * q^69 - 22 * q^71 + 28 * q^73 - 8 * q^77 - 20 * q^81 - 12 * q^87 + 4 * q^89 - 12 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.575868	−	0.575868i	−0.332477	−	0.332477i	0.521049	−	0.853527i	$-0.325541\pi$
$3$	−0.575868	−	0.575868i	−0.332477	−	0.332477i	−0.853527	+	0.521049i	$0.825541\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			2.48849i			0.940560i	0.882517	+	0.470280i	$0.155847\pi$
$7$			2.48849i			0.940560i	−0.882517	+	0.470280i	$0.844153\pi$
$8$		0			0
$9$		−	2.33675i		−	0.778918i
$10$		0			0
$11$	−0.160643	+	0.160643i	−0.0484356	+	0.0484356i	−0.730910	−	0.682474i	$-0.760904\pi$
$11$	−0.160643	+	0.160643i	−0.0484356	+	0.0484356i	0.682474	+	0.730910i	$0.260904\pi$
$12$		0			0
$13$	−1.42413	−	3.31238i	−0.394983	−	0.918688i
$13$	−1.42413	−	3.31238i	−0.394983	−	0.918688i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.58477	−	1.58477i	−0.384364	−	0.384364i	0.488307	−	0.872672i	$-0.337615\pi$
$17$	−1.58477	−	1.58477i	−0.384364	−	0.384364i	−0.872672	+	0.488307i	$0.837615\pi$
$18$		0			0
$19$	−2.91262	+	2.91262i	−0.668201	+	0.668201i	−0.957299	−	0.289098i	$-0.906645\pi$
$19$	−2.91262	+	2.91262i	−0.668201	+	0.668201i	0.289098	+	0.957299i	$0.406645\pi$
$20$		0			0
$21$	1.43304	−	1.43304i	0.312715	−	0.312715i
$22$		0			0
$23$	0.839357	−	0.839357i	0.175018	−	0.175018i	−0.614162	−	0.789180i	$-0.710506\pi$
$23$	0.839357	−	0.839357i	0.175018	−	0.175018i	0.789180	+	0.614162i	$0.210506\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.07326	+	3.07326i	−0.591450	+	0.591450i
$28$		0			0
$29$			2.80977i			0.521762i	0.965371	+	0.260881i	$0.0840130\pi$
$29$			2.80977i			0.521762i	−0.965371	+	0.260881i	$0.915987\pi$
$30$		0			0
$31$	−3.31238	−	3.31238i	−0.594921	−	0.594921i	0.344036	−	0.938957i	$-0.388206\pi$
$31$	−3.31238	−	3.31238i	−0.594921	−	0.594921i	−0.938957	+	0.344036i	$0.888206\pi$
$32$		0			0
$33$	0.185018			0.0322075
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	5.33675i		−	0.877357i	−0.898644	−	0.438678i	$-0.855447\pi$
$37$		−	5.33675i		−	0.877357i	0.898644	−	0.438678i	$-0.144553\pi$
$38$		0			0
$39$	−1.08738	+	2.72760i	−0.174120	+	0.436766i
$40$		0			0
$41$	−6.07326	−	6.07326i	−0.948484	−	0.948484i	0.0502522	−	0.998737i	$-0.483997\pi$
$41$	−6.07326	−	6.07326i	−0.948484	−	0.948484i	−0.998737	+	0.0502522i	$0.983997\pi$
$42$		0			0
$43$	7.48193	−	7.48193i	1.14098	−	1.14098i	0.152713	−	0.988271i	$-0.451199\pi$
$43$	7.48193	−	7.48193i	1.14098	−	1.14098i	0.988271	−	0.152713i	$-0.0488009\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	3.99244i		−	0.582358i	−0.956669	−	0.291179i	$-0.905953\pi$
$47$		−	3.99244i		−	0.582358i	0.956669	−	0.291179i	$-0.0940475\pi$
$48$		0			0
$49$	0.807426			0.115347
$50$		0			0
$51$			1.82524i			0.255585i
$52$		0			0
$53$	0.0154678	+	0.0154678i	0.00212466	+	0.00212466i	0.708168	−	0.706044i	$-0.249522\pi$
$53$	0.0154678	+	0.0154678i	0.00212466	+	0.00212466i	−0.706044	+	0.708168i	$0.749522\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.35457			0.444323
$58$		0			0
$59$	−2.91262	−	2.91262i	−0.379191	−	0.379191i	0.491619	−	0.870810i	$-0.336405\pi$
$59$	−2.91262	−	2.91262i	−0.379191	−	0.379191i	−0.870810	+	0.491619i	$0.836405\pi$
$60$		0			0
$61$	−7.60929			−0.974269			−0.487135	−	0.873327i	$-0.661958\pi$
$61$	−7.60929			−0.974269			−0.487135	+	0.873327i	$0.661958\pi$
$62$		0			0
$63$	5.81498			0.732619
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.64022			0.200385			0.100193	−	0.994968i	$-0.468054\pi$
$67$	1.64022			0.200385			0.100193	+	0.994968i	$0.468054\pi$
$68$		0			0
$69$	−0.966717			−0.116379
$70$		0			0
$71$	−11.3702	−	11.3702i	−1.34939	−	1.34939i	−0.886322	−	0.463069i	$-0.846748\pi$
$71$	−11.3702	−	11.3702i	−1.34939	−	1.34939i	−0.463069	−	0.886322i	$-0.653252\pi$
$72$		0			0
$73$	−15.2598			−1.78602			−0.893011	−	0.450036i	$-0.851411\pi$
$73$	−15.2598			−1.78602			−0.893011	+	0.450036i	$0.851411\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.399757	−	0.399757i	−0.0455566	−	0.0455566i
$78$		0			0
$79$			15.6017i			1.75533i	0.479273	+	0.877666i	$0.340900\pi$
$79$			15.6017i			1.75533i	−0.479273	+	0.877666i	$0.659100\pi$
$80$		0			0
$81$	−3.47067			−0.385630
$82$		0			0
$83$			0.681062i			0.0747562i	0.999301	+	0.0373781i	$0.0119006\pi$
$83$			0.681062i			0.0747562i	−0.999301	+	0.0373781i	$0.988099\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.61806	−	1.61806i	0.173474	−	0.173474i
$88$		0			0
$89$	−8.11324	−	8.11324i	−0.860002	−	0.860002i	0.131336	−	0.991338i	$-0.458073\pi$
$89$	−8.11324	−	8.11324i	−0.860002	−	0.860002i	−0.991338	+	0.131336i	$0.958073\pi$
$90$		0			0
$91$	8.24281	−	3.54394i	0.864082	−	0.371506i
$92$		0			0
$93$			3.81498i			0.395595i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.4322			−1.05923			−0.529614	−	0.848239i	$-0.677663\pi$
$97$	−10.4322			−1.05923			−0.529614	+	0.848239i	$0.677663\pi$
$98$		0			0
$99$	0.375382	+	0.375382i	0.0377273	+	0.0377273i
$100$		0			0
$101$		−	4.86608i		−	0.484193i	−0.970252	−	0.242097i	$-0.922165\pi$
$101$		−	4.86608i		−	0.484193i	0.970252	−	0.242097i	$-0.0778351\pi$
$102$		0			0
$103$	7.08217	−	7.08217i	0.697827	−	0.697827i	−0.266114	−	0.963941i	$-0.585740\pi$
$103$	7.08217	−	7.08217i	0.697827	−	0.697827i	0.963941	+	0.266114i	$0.0857399\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.34566	+	9.34566i	−0.903479	+	0.903479i	−0.995735	−	0.0922562i	$-0.970592\pi$
$107$	−9.34566	+	9.34566i	−0.903479	+	0.903479i	0.0922562	+	0.995735i	$0.470592\pi$
$108$		0			0
$109$	−3.88825	+	3.88825i	−0.372426	+	0.372426i	−0.868360	−	0.495934i	$-0.834826\pi$
$109$	−3.88825	+	3.88825i	−0.372426	+	0.372426i	0.495934	+	0.868360i	$0.334826\pi$
$110$		0			0
$111$	−3.07326	+	3.07326i	−0.291701	+	0.291701i
$112$		0			0
$113$	0.265837	+	0.265837i	0.0250078	+	0.0250078i	0.719500	−	0.694492i	$-0.244371\pi$
$113$	0.265837	+	0.265837i	0.0250078	+	0.0250078i	−0.694492	+	0.719500i	$0.744371\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−7.74021	+	3.32785i	−0.715583	+	0.307659i
$118$		0			0
$119$	3.94369	−	3.94369i	0.361518	−	0.361518i
$120$		0			0
$121$			10.9484i			0.995308i
$122$		0			0
$123$			6.99479i			0.630699i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	2.23391	+	2.23391i	0.198227	+	0.198227i	0.799240	−	0.601013i	$-0.205236\pi$
$127$	2.23391	+	2.23391i	0.198227	+	0.198227i	−0.601013	+	0.799240i	$0.705236\pi$
$128$		0			0
$129$	−8.61720			−0.758702
$130$		0			0
$131$	22.5965			1.97427			0.987134	−	0.159897i	$-0.0511162\pi$
$131$	22.5965			1.97427			0.987134	+	0.159897i	$0.0511162\pi$
$132$		0			0
$133$	−7.24802	−	7.24802i	−0.628483	−	0.628483i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	0.128712i		−	0.0109966i	−0.999985	−	0.00549829i	$-0.998250\pi$
$137$		−	0.128712i		−	0.0109966i	0.999985	−	0.00549829i	$-0.00175017\pi$
$138$		0			0
$139$			0.848265i			0.0719489i	0.999353	+	0.0359744i	$0.0114535\pi$
$139$			0.848265i			0.0719489i	−0.999353	+	0.0359744i	$0.988547\pi$
$140$		0			0
$141$	−2.29912	+	2.29912i	−0.193621	+	0.193621i
$142$		0			0
$143$	0.760885	+	0.303333i	0.0636284	+	0.0253660i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.464971	−	0.464971i	−0.0383501	−	0.0383501i
$148$		0			0
$149$	14.3945	−	14.3945i	1.17925	−	1.17925i	0.199311	−	0.979936i	$-0.436130\pi$
$149$	14.3945	−	14.3945i	1.17925	−	1.17925i	0.979936	−	0.199311i	$-0.0638704\pi$
$150$		0			0
$151$	9.06670	−	9.06670i	0.737838	−	0.737838i	−0.234321	−	0.972159i	$-0.575287\pi$
$151$	9.06670	−	9.06670i	0.737838	−	0.737838i	0.972159	+	0.234321i	$0.0752868\pi$
$152$		0			0
$153$	−3.70323	+	3.70323i	−0.299388	+	0.299388i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.56696	−	3.56696i	0.284674	−	0.284674i	−0.550296	−	0.834970i	$-0.685485\pi$
$157$	3.56696	−	3.56696i	0.284674	−	0.284674i	0.834970	+	0.550296i	$0.185485\pi$
$158$		0			0
$159$		−	0.0178148i		−	0.00141280i
$160$		0			0
$161$	2.08873	+	2.08873i	0.164615	+	0.164615i
$162$		0			0
$163$	−18.8763			−1.47851			−0.739254	−	0.673426i	$-0.764822\pi$
$163$	−18.8763			−1.47851			−0.739254	+	0.673426i	$0.764822\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	2.45755i		−	0.190171i	−0.995469	−	0.0950856i	$-0.969688\pi$
$167$		−	2.45755i		−	0.190171i	0.995469	−	0.0950856i	$-0.0303125\pi$
$168$		0			0
$169$	−8.94369	+	9.43453i	−0.687976	+	0.725733i
$170$		0			0
$171$	6.80607	+	6.80607i	0.520474	+	0.520474i
$172$		0			0
$173$	17.4500	−	17.4500i	1.32670	−	1.32670i	0.418466	−	0.908232i	$-0.362568\pi$
$173$	17.4500	−	17.4500i	1.32670	−	1.32670i	0.908232	−	0.418466i	$-0.137432\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			3.35457i			0.252145i
$178$		0			0
$179$	24.4191			1.82517			0.912583	−	0.408891i	$-0.134084\pi$
$179$	24.4191			1.82517			0.912583	+	0.408891i	$0.134084\pi$
$180$		0			0
$181$			6.96672i			0.517832i	0.965900	+	0.258916i	$0.0833653\pi$
$181$			6.96672i			0.517832i	−0.965900	+	0.258916i	$0.916635\pi$
$182$		0			0
$183$	4.38194	+	4.38194i	0.323923	+	0.323923i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.509165			0.0372338
$188$		0			0
$189$	−7.64778	−	7.64778i	−0.556294	−	0.556294i
$190$		0			0
$191$	−19.7304			−1.42764			−0.713822	−	0.700327i	$-0.753038\pi$
$191$	−19.7304			−1.42764			−0.713822	+	0.700327i	$0.753038\pi$
$192$		0			0
$193$	20.5478			1.47906			0.739531	−	0.673123i	$-0.235048\pi$
$193$	20.5478			1.47906			0.739531	+	0.673123i	$0.235048\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.3213			1.02035			0.510175	−	0.860071i	$-0.329581\pi$
$197$	14.3213			1.02035			0.510175	+	0.860071i	$0.329581\pi$
$198$		0			0
$199$	4.63788			0.328770			0.164385	−	0.986396i	$-0.447436\pi$
$199$	4.63788			0.328770			0.164385	+	0.986396i	$0.447436\pi$
$200$		0			0
$201$	−0.944552	−	0.944552i	−0.0666235	−	0.0666235i
$202$		0			0
$203$	−6.99209			−0.490748
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.96137	−	1.96137i	−0.136325	−	0.136325i
$208$		0			0
$209$		−	0.935782i		−	0.0647294i
$210$		0			0
$211$	11.8565			0.816232			0.408116	−	0.912930i	$-0.366186\pi$
$211$	11.8565			0.816232			0.408116	+	0.912930i	$0.366186\pi$
$212$		0			0
$213$			13.0954i			0.897284i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	8.24281	−	8.24281i	0.559559	−	0.559559i
$218$		0			0
$219$	8.78761	+	8.78761i	0.593811	+	0.593811i
$220$		0			0
$221$	−2.99244	+	7.50630i	−0.201294	+	0.504929i
$222$		0			0
$223$			15.1311i			1.01325i	0.862166	+	0.506625i	$0.169107\pi$
$223$			15.1311i			1.01325i	−0.862166	+	0.506625i	$0.830893\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.64492			0.507411			0.253705	−	0.967282i	$-0.418351\pi$
$227$	7.64492			0.507411			0.253705	+	0.967282i	$0.418351\pi$
$228$		0			0
$229$	−5.82759	−	5.82759i	−0.385098	−	0.385098i	0.487837	−	0.872935i	$-0.337786\pi$
$229$	−5.82759	−	5.82759i	−0.385098	−	0.385098i	−0.872935	+	0.487837i	$0.837786\pi$
$230$		0			0
$231$			0.460414i			0.0302931i
$232$		0			0
$233$	−10.1235	+	10.1235i	−0.663213	+	0.663213i	−0.956136	−	0.292923i	$-0.905372\pi$
$233$	−10.1235	+	10.1235i	−0.663213	+	0.663213i	0.292923	+	0.956136i	$0.405372\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	8.98453	−	8.98453i	0.583608	−	0.583608i
$238$		0			0
$239$	6.42562	−	6.42562i	0.415639	−	0.415639i	−0.468059	−	0.883697i	$-0.655046\pi$
$239$	6.42562	−	6.42562i	0.415639	−	0.415639i	0.883697	+	0.468059i	$0.155046\pi$
$240$		0			0
$241$	−6.77500	+	6.77500i	−0.436416	+	0.436416i	−0.890804	−	0.454388i	$-0.849858\pi$
$241$	−6.77500	+	6.77500i	−0.436416	+	0.436416i	0.454388	+	0.890804i	$0.349858\pi$
$242$		0			0
$243$	11.2184	+	11.2184i	0.719663	+	0.719663i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.7957	+	5.49974i	0.877797	+	0.349940i
$248$		0			0
$249$	0.392201	−	0.392201i	0.0248548	−	0.0248548i
$250$		0			0
$251$			10.1643i			0.641568i	0.947152	+	0.320784i	$0.103946\pi$
$251$			10.1643i			0.641568i	−0.947152	+	0.320784i	$0.896054\pi$
$252$		0			0
$253$			0.269673i			0.0169542i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.9437	+	10.9437i	0.682649	+	0.682649i	0.960596	−	0.277947i	$-0.0896541\pi$
$257$	10.9437	+	10.9437i	0.682649	+	0.682649i	−0.277947	+	0.960596i	$0.589654\pi$
$258$		0			0
$259$	13.2804			0.825207
$260$		0			0
$261$	6.56575			0.406410
$262$		0			0
$263$	−6.89715	−	6.89715i	−0.425297	−	0.425297i	0.461726	−	0.887023i	$-0.347230\pi$
$263$	−6.89715	−	6.89715i	−0.425297	−	0.425297i	−0.887023	+	0.461726i	$0.847230\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			9.34431i			0.571862i
$268$		0			0
$269$		−	10.2725i		−	0.626328i	−0.949699	−	0.313164i	$-0.898611\pi$
$269$		−	10.2725i		−	0.626328i	0.949699	−	0.313164i	$-0.101389\pi$
$270$		0			0
$271$	−1.62462	+	1.62462i	−0.0986885	+	0.0986885i	−0.754727	−	0.656039i	$-0.772231\pi$
$271$	−1.62462	+	1.62462i	−0.0986885	+	0.0986885i	0.656039	+	0.754727i	$0.272231\pi$
$272$		0			0
$273$	−6.78761	−	2.70593i	−0.410805	−	0.163770i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−12.2983	−	12.2983i	−0.738931	−	0.738931i	0.233440	−	0.972371i	$-0.425002\pi$
$277$	−12.2983	−	12.2983i	−0.738931	−	0.738931i	−0.972371	+	0.233440i	$0.925002\pi$
$278$		0			0
$279$	−7.74021	+	7.74021i	−0.463394	+	0.463394i
$280$		0			0
$281$	−8.05545	+	8.05545i	−0.480548	+	0.480548i	−0.905307	−	0.424759i	$-0.860359\pi$
$281$	−8.05545	+	8.05545i	−0.480548	+	0.480548i	0.424759	+	0.905307i	$0.360359\pi$
$282$		0			0
$283$	−8.29456	+	8.29456i	−0.493061	+	0.493061i	−0.909269	−	0.416209i	$-0.863359\pi$
$283$	−8.29456	+	8.29456i	−0.493061	+	0.493061i	0.416209	+	0.909269i	$0.363359\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	15.1132	−	15.1132i	0.892107	−	0.892107i
$288$		0			0
$289$		−	11.9770i		−	0.704528i
$290$		0			0
$291$	6.00756	+	6.00756i	0.352169	+	0.352169i
$292$		0			0
$293$	−4.02068			−0.234890			−0.117445	−	0.993079i	$-0.537470\pi$
$293$	−4.02068			−0.234890			−0.117445	+	0.993079i	$0.537470\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	0.987394i		−	0.0572944i
$298$		0			0
$299$	−3.97562	−	1.58491i	−0.229916	−	0.0916579i
$300$		0			0
$301$	18.6187	+	18.6187i	1.07316	+	1.07316i
$302$		0			0
$303$	−2.80222	+	2.80222i	−0.160983	+	0.160983i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			17.4655i			0.996807i	0.866945	+	0.498403i	$0.166080\pi$
$307$			17.4655i			0.996807i	−0.866945	+	0.498403i	$0.833920\pi$
$308$		0			0
$309$	−8.15679			−0.464023
$310$		0			0
$311$		−	3.18267i		−	0.180473i	−0.995920	−	0.0902364i	$-0.971238\pi$
$311$		−	3.18267i		−	0.180473i	0.995920	−	0.0902364i	$-0.0287622\pi$
$312$		0			0
$313$	11.8882	+	11.8882i	0.671963	+	0.671963i	0.958168	−	0.286205i	$-0.0923938\pi$
$313$	11.8882	+	11.8882i	0.671963	+	0.671963i	−0.286205	+	0.958168i	$0.592394\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.7788			0.942393			0.471197	−	0.882028i	$-0.343822\pi$
$317$	16.7788			0.942393			0.471197	+	0.882028i	$0.343822\pi$
$318$		0			0
$319$	−0.451369	−	0.451369i	−0.0252718	−	0.0252718i
$320$		0			0
$321$	10.7637			0.600773
$322$		0			0
$323$	9.23170			0.513665
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4.47823			0.247647
$328$		0			0
$329$	9.93515			0.547743
$330$		0			0
$331$	3.02672	+	3.02672i	0.166364	+	0.166364i	0.785379	−	0.619015i	$-0.212468\pi$
$331$	3.02672	+	3.02672i	0.166364	+	0.166364i	−0.619015	+	0.785379i	$0.712468\pi$
$332$		0			0
$333$	−12.4707			−0.683389
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−17.0193	−	17.0193i	−0.927101	−	0.927101i	0.0704171	−	0.997518i	$-0.477567\pi$
$337$	−17.0193	−	17.0193i	−0.927101	−	0.927101i	−0.997518	+	0.0704171i	$0.977567\pi$
$338$		0			0
$339$		−	0.306174i		−	0.0166291i
$340$		0			0
$341$	1.06422			0.0576306
$342$		0			0
$343$			19.4287i			1.04905i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.9229	+	17.9229i	−0.962151	+	0.962151i	−0.999309	−	0.0371588i	$-0.988169\pi$
$347$	−17.9229	+	17.9229i	−0.962151	+	0.962151i	0.0371588	+	0.999309i	$0.488169\pi$
$348$		0			0
$349$	−8.47302	−	8.47302i	−0.453550	−	0.453550i	0.442981	−	0.896531i	$-0.353921\pi$
$349$	−8.47302	−	8.47302i	−0.453550	−	0.453550i	−0.896531	+	0.442981i	$0.853921\pi$
$350$		0			0
$351$	14.5565	+	5.80308i	0.776971	+	0.309745i
$352$		0			0
$353$			12.2472i			0.651851i	0.945395	+	0.325925i	$0.105676\pi$
$353$			12.2472i			0.651851i	−0.945395	+	0.325925i	$0.894324\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.54209			−0.240393
$358$		0			0
$359$	17.0770	+	17.0770i	0.901288	+	0.901288i	0.995548	−	0.0942600i	$-0.0300485\pi$
$359$	17.0770	+	17.0770i	0.901288	+	0.901288i	−0.0942600	+	0.995548i	$0.530049\pi$
$360$		0			0
$361$			2.03328i			0.107015i
$362$		0			0
$363$	6.30482	−	6.30482i	0.330917	−	0.330917i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−23.4910	+	23.4910i	−1.22622	+	1.22622i	−0.260836	+	0.965383i	$0.583998\pi$
$367$	−23.4910	+	23.4910i	−1.22622	+	1.22622i	−0.965383	+	0.260836i	$0.916002\pi$
$368$		0			0
$369$	−14.1917	+	14.1917i	−0.738791	+	0.738791i
$370$		0			0
$371$	−0.0384913	+	0.0384913i	−0.00199837	+	0.00199837i
$372$		0			0
$373$	2.57487	+	2.57487i	0.133322	+	0.133322i	0.770619	−	0.637297i	$-0.219947\pi$
$373$	2.57487	+	2.57487i	0.133322	+	0.133322i	−0.637297	+	0.770619i	$0.719947\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.30703	−	4.00149i	0.479336	−	0.206087i
$378$		0			0
$379$	3.16299	−	3.16299i	0.162472	−	0.162472i	−0.621189	−	0.783661i	$-0.713350\pi$
$379$	3.16299	−	3.16299i	0.162472	−	0.162472i	0.783661	+	0.621189i	$0.213350\pi$
$380$		0			0
$381$		−	2.57287i		−	0.131812i
$382$		0			0
$383$		−	38.4781i		−	1.96614i	−0.183237	−	0.983069i	$-0.558658\pi$
$383$		−	38.4781i		−	1.96614i	0.183237	−	0.983069i	$-0.441342\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−17.4834	−	17.4834i	−0.888732	−	0.888732i
$388$		0			0
$389$	26.2574			1.33130			0.665652	−	0.746262i	$-0.268153\pi$
$389$	26.2574			1.33130			0.665652	+	0.746262i	$0.268153\pi$
$390$		0			0
$391$	−2.66039			−0.134541
$392$		0			0
$393$	−13.0126	−	13.0126i	−0.656399	−	0.656399i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			14.8051i			0.743046i	0.928424	+	0.371523i	$0.121164\pi$
$397$			14.8051i			0.743046i	−0.928424	+	0.371523i	$0.878836\pi$
$398$		0			0
$399$			8.34780i			0.417913i
$400$		0			0
$401$	23.9207	−	23.9207i	1.19454	−	1.19454i	0.218763	−	0.975778i	$-0.429798\pi$
$401$	23.9207	−	23.9207i	1.19454	−	1.19454i	0.975778	−	0.218763i	$-0.0702023\pi$
$402$		0			0
$403$	−6.25458	+	15.6891i	−0.311563	+	0.781530i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.857310	+	0.857310i	0.0424953	+	0.0424953i
$408$		0			0
$409$	20.7646	−	20.7646i	1.02674	−	1.02674i	0.0271101	−	0.999632i	$-0.491370\pi$
$409$	20.7646	−	20.7646i	1.02674	−	1.02674i	0.999632	−	0.0271101i	$-0.00863048\pi$
$410$		0			0
$411$	−0.0741209	+	0.0741209i	−0.00365611	+	0.00365611i
$412$		0			0
$413$	7.24802	−	7.24802i	0.356652	−	0.356652i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.488488	−	0.488488i	0.0239214	−	0.0239214i
$418$		0			0
$419$		−	28.3908i		−	1.38698i	−0.720465	−	0.693491i	$-0.756072\pi$
$419$		−	28.3908i		−	1.38698i	0.720465	−	0.693491i	$-0.243928\pi$
$420$		0			0
$421$	0.0630043	+	0.0630043i	0.00307064	+	0.00307064i	0.708640	−	0.705570i	$-0.249309\pi$
$421$	0.0630043	+	0.0630043i	0.00307064	+	0.00307064i	−0.705570	+	0.708640i	$0.749309\pi$
$422$		0			0
$423$	−9.32936			−0.453609
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	18.9356i		−	0.916359i
$428$		0			0
$429$	−0.263490	−	0.612849i	−0.0127214	−	0.0295886i
$430$		0			0
$431$	−4.28935	−	4.28935i	−0.206611	−	0.206611i	0.596214	−	0.802825i	$-0.296671\pi$
$431$	−4.28935	−	4.28935i	−0.206611	−	0.206611i	−0.802825	+	0.596214i	$0.796671\pi$
$432$		0			0
$433$	3.57573	−	3.57573i	0.171839	−	0.171839i	−0.615948	−	0.787787i	$-0.711227\pi$
$433$	3.57573	−	3.57573i	0.171839	−	0.171839i	0.787787	+	0.615948i	$0.211227\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			4.88946i			0.233895i
$438$		0			0
$439$	−25.6505			−1.22423			−0.612115	−	0.790768i	$-0.709681\pi$
$439$	−25.6505			−1.22423			−0.612115	+	0.790768i	$0.709681\pi$
$440$		0			0
$441$		−	1.88676i		−	0.0898455i
$442$		0			0
$443$	17.7454	+	17.7454i	0.843110	+	0.843110i	0.989262	−	0.146152i	$-0.0466888\pi$
$443$	17.7454	+	17.7454i	0.843110	+	0.843110i	−0.146152	+	0.989262i	$0.546689\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−16.5787			−0.784146
$448$		0			0
$449$	−19.5256	−	19.5256i	−0.921470	−	0.921470i	0.0756631	−	0.997133i	$-0.475893\pi$
$449$	−19.5256	−	19.5256i	−0.921470	−	0.921470i	−0.997133	+	0.0756631i	$0.975893\pi$
$450$		0			0
$451$	1.95125			0.0918808
$452$		0			0
$453$	−10.4424			−0.490629
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−22.6248			−1.05834			−0.529171	−	0.848515i	$-0.677497\pi$
$457$	−22.6248			−1.05834			−0.529171	+	0.848515i	$0.677497\pi$
$458$		0			0
$459$	9.74086			0.454664
$460$		0			0
$461$	−11.6379	−	11.6379i	−0.542030	−	0.542030i	0.382094	−	0.924124i	$-0.375203\pi$
$461$	−11.6379	−	11.6379i	−0.542030	−	0.542030i	−0.924124	+	0.382094i	$0.875203\pi$
$462$		0			0
$463$	24.1258			1.12122			0.560612	−	0.828079i	$-0.310566\pi$
$463$	24.1258			1.12122			0.560612	+	0.828079i	$0.310566\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.6478	+	25.6478i	1.18684	+	1.18684i	0.977937	+	0.208900i	$0.0669882\pi$
$467$	25.6478	+	25.6478i	1.18684	+	1.18684i	0.208900	+	0.977937i	$0.433012\pi$
$468$		0			0
$469$			4.08168i			0.188474i
$470$		0			0
$471$	−4.10819			−0.189296
$472$		0			0
$473$			2.40383i			0.110528i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.0361443	−	0.0361443i	0.00165494	−	0.00165494i
$478$		0			0
$479$	14.4035	+	14.4035i	0.658111	+	0.658111i	0.954933	−	0.296822i	$-0.0959268\pi$
$479$	14.4035	+	14.4035i	0.658111	+	0.658111i	−0.296822	+	0.954933i	$0.595927\pi$
$480$		0			0
$481$	−17.6773	+	7.60024i	−0.806017	+	0.346541i
$482$		0			0
$483$		−	2.40567i		−	0.109462i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−4.63231			−0.209910			−0.104955	−	0.994477i	$-0.533470\pi$
$487$	−4.63231			−0.209910			−0.104955	+	0.994477i	$0.533470\pi$
$488$		0			0
$489$	10.8703	+	10.8703i	0.491571	+	0.491571i
$490$		0			0
$491$			21.9852i			0.992177i	0.868272	+	0.496088i	$0.165231\pi$
$491$			21.9852i			0.992177i	−0.868272	+	0.496088i	$0.834769\pi$
$492$		0			0
$493$	4.45286	−	4.45286i	0.200547	−	0.200547i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	28.2945	−	28.2945i	1.26918	−	1.26918i
$498$		0			0
$499$	−11.0901	+	11.0901i	−0.496460	+	0.496460i	−0.910334	−	0.413874i	$-0.864175\pi$
$499$	−11.0901	+	11.0901i	−0.496460	+	0.496460i	0.413874	+	0.910334i	$0.364175\pi$
$500$		0			0
$501$	−1.41523	+	1.41523i	−0.0632276	+	0.0632276i
$502$		0			0
$503$	−28.8526	−	28.8526i	−1.28647	−	1.28647i	−0.936914	−	0.349559i	$-0.886331\pi$
$503$	−28.8526	−	28.8526i	−1.28647	−	1.28647i	−0.349559	−	0.936914i	$-0.613669\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	10.5834	−	0.282656i	0.470026	−	0.0125532i
$508$		0			0
$509$	−18.7792	+	18.7792i	−0.832373	+	0.832373i	−0.987841	−	0.155468i	$-0.950312\pi$
$509$	−18.7792	+	18.7792i	−0.832373	+	0.832373i	0.155468	+	0.987841i	$0.450312\pi$
$510$		0			0
$511$		−	37.9738i		−	1.67986i
$512$		0			0
$513$		−	17.9025i		−	0.790415i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.641357	+	0.641357i	0.0282068	+	0.0282068i
$518$		0			0
$519$	−20.0978			−0.882194
$520$		0			0
$521$	−4.85411			−0.212662			−0.106331	−	0.994331i	$-0.533910\pi$
$521$	−4.85411			−0.212662			−0.106331	+	0.994331i	$0.533910\pi$
$522$		0			0
$523$	13.2053	+	13.2053i	0.577428	+	0.577428i	0.934194	−	0.356766i	$-0.116121\pi$
$523$	13.2053	+	13.2053i	0.577428	+	0.577428i	−0.356766	+	0.934194i	$0.616121\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			10.4987i			0.457333i
$528$		0			0
$529$			21.5910i			0.938737i
$530$		0			0
$531$	−6.80607	+	6.80607i	−0.295358	+	0.295358i
$532$		0			0
$533$	−11.4678	+	28.7661i	−0.496726	+	1.24600i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−14.0621	−	14.0621i	−0.606826	−	0.606826i
$538$		0			0
$539$	−0.129707	+	0.129707i	−0.00558688	+	0.00558688i
$540$		0			0
$541$	−15.6350	+	15.6350i	−0.672202	+	0.672202i	−0.958223	−	0.286021i	$-0.907667\pi$
$541$	−15.6350	+	15.6350i	−0.672202	+	0.672202i	0.286021	+	0.958223i	$0.407667\pi$
$542$		0			0
$543$	4.01191	−	4.01191i	0.172167	−	0.172167i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.0244	−	13.0244i	0.556882	−	0.556882i	−0.371536	−	0.928418i	$-0.621169\pi$
$547$	13.0244	−	13.0244i	0.556882	−	0.556882i	0.928418	+	0.371536i	$0.121169\pi$
$548$		0			0
$549$			17.7810i			0.758876i
$550$		0			0
$551$	−8.18380	−	8.18380i	−0.348642	−	0.348642i
$552$		0			0
$553$	−38.8247			−1.65100
$554$		0			0
$555$		0			0
$556$		0			0
$557$			3.94839i			0.167299i	0.996495	+	0.0836493i	$0.0266575\pi$
$557$			3.94839i			0.167299i	−0.996495	+	0.0836493i	$0.973342\pi$
$558$		0			0
$559$	−35.4382	−	14.1277i	−1.49888	−	0.597539i
$560$		0			0
$561$	−0.293212	−	0.293212i	−0.0123794	−	0.0123794i
$562$		0			0
$563$	3.06287	−	3.06287i	0.129084	−	0.129084i	−0.639613	−	0.768697i	$-0.720905\pi$
$563$	3.06287	−	3.06287i	0.129084	−	0.129084i	0.768697	+	0.639613i	$0.220905\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	8.63673i		−	0.362709i
$568$		0			0
$569$	23.1291			0.969621			0.484810	−	0.874619i	$-0.338889\pi$
$569$	23.1291			0.969621			0.484810	+	0.874619i	$0.338889\pi$
$570$		0			0
$571$		−	28.5374i		−	1.19425i	−0.802148	−	0.597126i	$-0.796309\pi$
$571$		−	28.5374i		−	1.19425i	0.802148	−	0.597126i	$-0.203691\pi$
$572$		0			0
$573$	11.3621	+	11.3621i	0.474660	+	0.474660i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.740230			0.0308162			0.0154081	−	0.999881i	$-0.495095\pi$
$577$	0.740230			0.0308162			0.0154081	+	0.999881i	$0.495095\pi$
$578$		0			0
$579$	−11.8328	−	11.8328i	−0.491754	−	0.491754i
$580$		0			0
$581$	−1.69481			−0.0703127
$582$		0			0
$583$	−0.00496956			−0.000205818
$584$		0			0
$585$		0			0
$586$		0			0
$587$	37.3368			1.54105			0.770526	−	0.637408i	$-0.219993\pi$
$587$	37.3368			1.54105			0.770526	+	0.637408i	$0.219993\pi$
$588$		0			0
$589$	19.2954			0.795053
$590$		0			0
$591$	−8.24716	−	8.24716i	−0.339243	−	0.339243i
$592$		0			0
$593$	42.5834			1.74869			0.874345	−	0.485304i	$-0.161291\pi$
$593$	42.5834			1.74869			0.874345	+	0.485304i	$0.161291\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.67080	−	2.67080i	−0.109309	−	0.109309i
$598$		0			0
$599$			10.3983i			0.424862i	0.977176	+	0.212431i	$0.0681380\pi$
$599$			10.3983i			0.424862i	−0.977176	+	0.212431i	$0.931862\pi$
$600$		0			0
$601$	−36.8896			−1.50476			−0.752379	−	0.658731i	$-0.771094\pi$
$601$	−36.8896			−1.50476			−0.752379	+	0.658731i	$0.771094\pi$
$602$		0			0
$603$		−	3.83280i		−	0.156084i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−7.66695	+	7.66695i	−0.311192	+	0.311192i	−0.845371	−	0.534179i	$-0.820621\pi$
$607$	−7.66695	+	7.66695i	−0.311192	+	0.311192i	0.534179	+	0.845371i	$0.320621\pi$
$608$		0			0
$609$	4.02652	+	4.02652i	0.163163	+	0.163163i
$610$		0			0
$611$	−13.2245	+	5.68577i	−0.535005	+	0.230022i
$612$		0			0
$613$			20.2723i			0.818789i	0.912357	+	0.409394i	$0.134260\pi$
$613$			20.2723i			0.818789i	−0.912357	+	0.409394i	$0.865740\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−36.3465			−1.46325			−0.731627	−	0.681705i	$-0.761239\pi$
$617$	−36.3465			−1.46325			−0.731627	+	0.681705i	$0.761239\pi$
$618$		0			0
$619$	−21.2208	−	21.2208i	−0.852935	−	0.852935i	0.137558	−	0.990494i	$-0.456075\pi$
$619$	−21.2208	−	21.2208i	−0.852935	−	0.852935i	−0.990494	+	0.137558i	$0.956075\pi$
$620$		0			0
$621$			5.15913i			0.207029i
$622$		0			0
$623$	20.1897	−	20.1897i	0.808884	−	0.808884i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.538887	+	0.538887i	−0.0215211	+	0.0215211i
$628$		0			0
$629$	−8.45755	+	8.45755i	−0.337225	+	0.337225i
$630$		0			0
$631$	−18.7084	+	18.7084i	−0.744770	+	0.744770i	−0.973492	−	0.228722i	$-0.926545\pi$
$631$	−18.7084	+	18.7084i	−0.744770	+	0.744770i	0.228722	+	0.973492i	$0.426545\pi$
$632$		0			0
$633$	−6.82775	−	6.82775i	−0.271379	−	0.271379i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.14988	−	2.67450i	−0.0455600	−	0.105968i
$638$		0			0
$639$	−26.5693	+	26.5693i	−1.05106	+	1.05106i
$640$		0			0
$641$		−	42.7477i		−	1.68843i	−0.536001	−	0.844217i	$-0.680066\pi$
$641$		−	42.7477i		−	1.68843i	0.536001	−	0.844217i	$-0.319934\pi$
$642$		0			0
$643$		−	33.0231i		−	1.30231i	−0.758947	−	0.651153i	$-0.774286\pi$
$643$		−	33.0231i		−	1.30231i	0.758947	−	0.651153i	$-0.225714\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−25.6478	−	25.6478i	−1.00832	−	1.00832i	−0.999965	−	0.00835231i	$-0.997341\pi$
$647$	−25.6478	−	25.6478i	−1.00832	−	1.00832i	−0.00835231	−	0.999965i	$-0.502659\pi$
$648$		0			0
$649$	0.935782			0.0367327
$650$		0			0
$651$	−9.49354			−0.372081
$652$		0			0
$653$	−22.0733	−	22.0733i	−0.863794	−	0.863794i	0.127983	−	0.991776i	$-0.459150\pi$
$653$	−22.0733	−	22.0733i	−0.863794	−	0.863794i	−0.991776	+	0.127983i	$0.959150\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			35.6583i			1.39116i
$658$		0			0
$659$			8.15965i			0.317855i	0.987290	+	0.158927i	$0.0508036\pi$
$659$			8.15965i			0.317855i	−0.987290	+	0.158927i	$0.949196\pi$
$660$		0			0
$661$	19.3969	−	19.3969i	0.754452	−	0.754452i	−0.220855	−	0.975307i	$-0.570885\pi$
$661$	19.3969	−	19.3969i	0.754452	−	0.754452i	0.975307	+	0.220855i	$0.0708847\pi$
$662$		0			0
$663$	6.04589	−	2.59939i	0.234803	−	0.100952i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.35840	+	2.35840i	0.0913178	+	0.0913178i
$668$		0			0
$669$	8.71349	−	8.71349i	0.336883	−	0.336883i
$670$		0			0
$671$	1.22238	−	1.22238i	0.0471893	−	0.0471893i
$672$		0			0
$673$	27.7182	−	27.7182i	1.06846	−	1.06846i	0.0709796	−	0.997478i	$-0.477387\pi$
$673$	27.7182	−	27.7182i	1.06846	−	1.06846i	0.997478	−	0.0709796i	$-0.0226125\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.8328	−	16.8328i	0.646937	−	0.646937i	−0.305315	−	0.952252i	$-0.598762\pi$
$677$	16.8328	−	16.8328i	0.646937	−	0.646937i	0.952252	+	0.305315i	$0.0987616\pi$
$678$		0			0
$679$		−	25.9604i		−	0.996267i
$680$		0			0
$681$	−4.40246	−	4.40246i	−0.168703	−	0.168703i
$682$		0			0
$683$	−41.7558			−1.59774			−0.798871	−	0.601503i	$-0.794569\pi$
$683$	−41.7558			−1.59774			−0.798871	+	0.601503i	$0.794569\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			6.71184i			0.256073i
$688$		0			0
$689$	0.0292069	−	0.0732632i	0.00111270	−	0.00279111i
$690$		0			0
$691$	15.4589	+	15.4589i	0.588084	+	0.588084i	0.937112	−	0.349028i	$-0.113488\pi$
$691$	15.4589	+	15.4589i	0.588084	+	0.588084i	−0.349028	+	0.937112i	$0.613488\pi$
$692$		0			0
$693$	−0.934134	+	0.934134i	−0.0354848	+	0.0354848i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			19.2495i			0.729127i
$698$		0			0
$699$	11.6596			0.441006
$700$		0			0
$701$		−	23.2495i		−	0.878122i	−0.898457	−	0.439061i	$-0.855311\pi$
$701$		−	23.2495i		−	0.878122i	0.898457	−	0.439061i	$-0.144689\pi$
$702$		0			0
$703$	15.5439	+	15.5439i	0.586251	+	0.586251i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	12.1092			0.455413
$708$		0			0
$709$	12.1623	+	12.1623i	0.456764	+	0.456764i	0.897592	−	0.440828i	$-0.145315\pi$
$709$	12.1623	+	12.1623i	0.456764	+	0.456764i	−0.440828	+	0.897592i	$0.645315\pi$
$710$		0			0
$711$	36.4574			1.36726
$712$		0			0
$713$	−5.56054			−0.208244
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−7.40061			−0.276381
$718$		0			0
$719$	17.8565			0.665933			0.332967	−	0.942939i	$-0.391950\pi$
$719$	17.8565			0.665933			0.332967	+	0.942939i	$0.391950\pi$
$720$		0			0
$721$	17.6239	+	17.6239i	0.656348	+	0.656348i
$722$		0			0
$723$	7.80301			0.290197
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−13.4866	−	13.4866i	−0.500191	−	0.500191i	0.411306	−	0.911497i	$-0.365073\pi$
$727$	−13.4866	−	13.4866i	−0.500191	−	0.500191i	−0.911497	+	0.411306i	$0.865073\pi$
$728$		0			0
$729$		−	2.50865i		−	0.0929130i
$730$		0			0
$731$	−23.7143			−0.877107
$732$		0			0
$733$		−	13.3958i		−	0.494784i	−0.968916	−	0.247392i	$-0.920426\pi$
$733$		−	13.3958i		−	0.494784i	0.968916	−	0.247392i	$-0.0795735\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.263490	+	0.263490i	−0.00970577	+	0.00970577i
$738$		0			0
$739$	16.6491	+	16.6491i	0.612448	+	0.612448i	0.943583	−	0.331135i	$-0.107432\pi$
$739$	16.6491	+	16.6491i	0.612448	+	0.612448i	−0.331135	+	0.943583i	$0.607432\pi$
$740$		0			0
$741$	−4.77735	−	11.1116i	−0.175500	−	0.408195i
$742$		0			0
$743$		−	37.0984i		−	1.36101i	−0.732744	−	0.680504i	$-0.761761\pi$
$743$		−	37.0984i		−	1.36101i	0.732744	−	0.680504i	$-0.238239\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.59147			0.0582290
$748$		0			0
$749$	−23.2566	−	23.2566i	−0.849776	−	0.849776i
$750$		0			0
$751$		−	29.9361i		−	1.09239i	−0.837660	−	0.546193i	$-0.816077\pi$
$751$		−	29.9361i		−	1.09239i	0.837660	−	0.546193i	$-0.183923\pi$
$752$		0			0
$753$	5.85331	−	5.85331i	0.213307	−	0.213307i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−24.7792	+	24.7792i	−0.900615	+	0.900615i	−0.995489	−	0.0948741i	$-0.969755\pi$
$757$	−24.7792	+	24.7792i	−0.900615	+	0.900615i	0.0948741	+	0.995489i	$0.469755\pi$
$758$		0			0
$759$	0.155296	−	0.155296i	0.00563689	−	0.00563689i
$760$		0			0
$761$	15.2396	−	15.2396i	0.552435	−	0.552435i	−0.374708	−	0.927143i	$-0.622257\pi$
$761$	15.2396	−	15.2396i	0.552435	−	0.552435i	0.927143	+	0.374708i	$0.122257\pi$
$762$		0			0
$763$	−9.67585	−	9.67585i	−0.350289	−	0.350289i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.49974	+	13.7957i	−0.198584	+	0.498132i
$768$		0			0
$769$	−12.9644	+	12.9644i	−0.467507	+	0.467507i	−0.901106	−	0.433599i	$-0.857243\pi$
$769$	−12.9644	+	12.9644i	−0.467507	+	0.467507i	0.433599	+	0.901106i	$0.357243\pi$
$770$		0			0
$771$		−	12.6042i		−	0.453931i
$772$		0			0
$773$		−	38.9949i		−	1.40255i	−0.712891	−	0.701275i	$-0.752615\pi$
$773$		−	38.9949i		−	1.40255i	0.712891	−	0.701275i	$-0.247385\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−7.64778	−	7.64778i	−0.274363	−	0.274363i
$778$		0			0
$779$	35.3782			1.26756
$780$		0			0
$781$	3.65307			0.130717
$782$		0			0
$783$	−8.63517	−	8.63517i	−0.308596	−	0.308596i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	39.0675i		−	1.39260i	−0.717748	−	0.696302i	$-0.754827\pi$
$787$		−	39.0675i		−	1.39260i	0.717748	−	0.696302i	$-0.245173\pi$
$788$		0			0
$789$			7.94369i			0.282803i
$790$		0			0
$791$	−0.661532	+	0.661532i	−0.0235214	+	0.0235214i
$792$		0			0
$793$	10.8366	+	25.2048i	0.384820	+	0.895050i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.79345	−	3.79345i	−0.134371	−	0.134371i	0.636722	−	0.771093i	$-0.280290\pi$
$797$	−3.79345	−	3.79345i	−0.134371	−	0.134371i	−0.771093	+	0.636722i	$0.780290\pi$
$798$		0			0
$799$	−6.32713	+	6.32713i	−0.223838	+	0.223838i
$800$		0			0
$801$	−18.9586	+	18.9586i	−0.669871	+	0.669871i
$802$		0			0
$803$	2.45137	−	2.45137i	0.0865069	−	0.0865069i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.91562	+	5.91562i	−0.208240	+	0.208240i
$808$		0			0
$809$			5.90406i			0.207576i	0.994599	+	0.103788i	$0.0330963\pi$
$809$			5.90406i			0.207576i	−0.994599	+	0.103788i	$0.966904\pi$
$810$		0			0
$811$	26.4406	+	26.4406i	0.928454	+	0.928454i	0.997606	−	0.0691520i	$-0.0220293\pi$
$811$	26.4406	+	26.4406i	0.928454	+	0.928454i	−0.0691520	+	0.997606i	$0.522029\pi$
$812$		0			0
$813$	1.87113			0.0656234
$814$		0			0
$815$		0			0
$816$		0			0
$817$			43.5840i			1.52481i
$818$		0			0
$819$	−8.28130	−	19.2614i	−0.289372	−	0.673048i
$820$		0			0
$821$	−13.7728	−	13.7728i	−0.480673	−	0.480673i	0.424674	−	0.905347i	$-0.360389\pi$
$821$	−13.7728	−	13.7728i	−0.480673	−	0.480673i	−0.905347	+	0.424674i	$0.860389\pi$
$822$		0			0
$823$	−1.57821	+	1.57821i	−0.0550131	+	0.0550131i	−0.734078	−	0.679065i	$-0.762385\pi$
$823$	−1.57821	+	1.57821i	−0.0550131	+	0.0550131i	0.679065	+	0.734078i	$0.262385\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	34.0311i		−	1.18338i	−0.806167	−	0.591688i	$-0.798462\pi$
$827$		−	34.0311i		−	1.18338i	0.806167	−	0.591688i	$-0.201538\pi$
$828$		0			0
$829$	−42.7271			−1.48397			−0.741986	−	0.670415i	$-0.766116\pi$
$829$	−42.7271			−1.48397			−0.741986	+	0.670415i	$0.766116\pi$
$830$		0			0
$831$			14.1643i			0.491356i
$832$		0			0
$833$	−1.27959	−	1.27959i	−0.0443351	−	0.0443351i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	20.3596			0.703731
$838$		0			0
$839$	−30.7469	−	30.7469i	−1.06150	−	1.06150i	−0.997981	−	0.0635206i	$-0.979767\pi$
$839$	−30.7469	−	30.7469i	−1.06150	−	1.06150i	−0.0635206	−	0.997981i	$-0.520233\pi$
$840$		0			0
$841$	21.1052			0.727765
$842$		0			0
$843$	9.27774			0.319542
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−27.2449			−0.936147
$848$		0			0
$849$	9.55314			0.327863
$850$		0			0
$851$	−4.47944	−	4.47944i	−0.153553	−	0.153553i
$852$		0			0
$853$	−11.1085			−0.380350			−0.190175	−	0.981750i	$-0.560905\pi$
$853$	−11.1085			−0.380350			−0.190175	+	0.981750i	$0.560905\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.36248	−	9.36248i	−0.319816	−	0.319816i	0.528880	−	0.848696i	$-0.322612\pi$
$857$	−9.36248	−	9.36248i	−0.319816	−	0.319816i	−0.848696	+	0.528880i	$0.822612\pi$
$858$		0			0
$859$			31.9099i			1.08875i	0.838841	+	0.544376i	$0.183233\pi$
$859$			31.9099i			1.08875i	−0.838841	+	0.544376i	$0.816767\pi$
$860$		0			0
$861$	−17.4065			−0.593210
$862$		0			0
$863$			23.4655i			0.798774i	0.916782	+	0.399387i	$0.130777\pi$
$863$			23.4655i			0.798774i	−0.916782	+	0.399387i	$0.869223\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.89715	+	6.89715i	−0.234240	+	0.234240i
$868$		0			0
$869$	−2.50630	−	2.50630i	−0.0850205	−	0.0850205i
$870$		0			0
$871$	−2.33590	−	5.43304i	−0.0791488	−	0.184092i
$872$		0			0
$873$			24.3774i			0.825051i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.9685			−0.640522			−0.320261	−	0.947329i	$-0.603771\pi$
$877$	−18.9685			−0.640522			−0.320261	+	0.947329i	$0.603771\pi$
$878$		0			0
$879$	2.31538	+	2.31538i	0.0780957	+	0.0780957i
$880$		0			0
$881$		−	6.29619i		−	0.212124i	−0.994360	−	0.106062i	$-0.966176\pi$
$881$		−	6.29619i		−	0.212124i	0.994360	−	0.106062i	$-0.0338242\pi$
$882$		0			0
$883$	−24.5284	+	24.5284i	−0.825448	+	0.825448i	−0.986883	−	0.161435i	$-0.948388\pi$
$883$	−24.5284	+	24.5284i	−0.825448	+	0.825448i	0.161435	+	0.986883i	$0.448388\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.8820	+	24.8820i	−0.835457	+	0.835457i	−0.988257	−	0.152800i	$-0.951171\pi$
$887$	−24.8820	+	24.8820i	−0.835457	+	0.835457i	0.152800	+	0.988257i	$0.451171\pi$
$888$		0			0
$889$	−5.55905	+	5.55905i	−0.186444	+	0.186444i
$890$		0			0
$891$	0.557538	−	0.557538i	0.0186782	−	0.0186782i
$892$		0			0
$893$	11.6285	+	11.6285i	0.389132	+	0.389132i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.37673	+	3.20213i	0.0459678	+	0.106916i
$898$		0			0
$899$	9.30703	−	9.30703i	0.310407	−	0.310407i
$900$		0			0
$901$		−	0.0490258i		−	0.00163329i
$902$		0			0
$903$		−	21.4438i		−	0.713605i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	24.3213	+	24.3213i	0.807574	+	0.807574i	0.984266	−	0.176692i	$-0.0565396\pi$
$907$	24.3213	+	24.3213i	0.807574	+	0.807574i	−0.176692	+	0.984266i	$0.556540\pi$
$908$		0			0
$909$	−11.3708			−0.377146
$910$		0			0
$911$	−41.3903			−1.37132			−0.685661	−	0.727921i	$-0.740487\pi$
$911$	−41.3903			−1.37132			−0.685661	+	0.727921i	$0.740487\pi$
$912$		0			0
$913$	−0.109408	−	0.109408i	−0.00362086	−	0.00362086i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			56.2312i			1.85692i
$918$		0			0
$919$			0.148517i			0.00489913i	0.999997	+	0.00244957i	$0.000779722\pi$
$919$			0.148517i			0.00489913i	−0.999997	+	0.00244957i	$0.999220\pi$
$920$		0			0
$921$	10.0578	−	10.0578i	0.331416	−	0.331416i
$922$		0			0
$923$	−21.4697	+	53.8549i	−0.706683	+	1.77266i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−16.5493	−	16.5493i	−0.543550	−	0.543550i
$928$		0			0
$929$	−9.98575	+	9.98575i	−0.327622	+	0.327622i	−0.851681	−	0.524060i	$-0.824417\pi$
$929$	−9.98575	+	9.98575i	−0.327622	+	0.327622i	0.524060	+	0.851681i	$0.324417\pi$
$930$		0			0
$931$	−2.35173	+	2.35173i	−0.0770747	+	0.0770747i
$932$		0			0
$933$	−1.83280	+	1.83280i	−0.0600031	+	0.0600031i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	26.5218	−	26.5218i	0.866428	−	0.866428i	−0.125647	−	0.992075i	$-0.540101\pi$
$937$	26.5218	−	26.5218i	0.866428	−	0.866428i	0.992075	+	0.125647i	$0.0401005\pi$
$938$		0			0
$939$		−	13.6921i		−	0.446825i
$940$		0			0
$941$	31.4142	+	31.4142i	1.02407	+	1.02407i	0.999703	+	0.0243710i	$0.00775828\pi$
$941$	31.4142	+	31.4142i	1.02407	+	1.02407i	0.0243710	+	0.999703i	$0.492242\pi$
$942$		0			0
$943$	−10.1953			−0.332004
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	45.5303i		−	1.47954i	−0.672862	−	0.739768i	$-0.734935\pi$
$947$		−	45.5303i		−	1.47954i	0.672862	−	0.739768i	$-0.265065\pi$
$948$		0			0
$949$	21.7319	+	50.5461i	0.705448	+	1.64080i
$950$		0			0
$951$	−9.66239	−	9.66239i	−0.313324	−	0.313324i
$952$		0			0
$953$	8.04640	−	8.04640i	0.260649	−	0.260649i	−0.564669	−	0.825318i	$-0.690996\pi$
$953$	8.04640	−	8.04640i	0.260649	−	0.260649i	0.825318	+	0.564669i	$0.190996\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			0.519858i			0.0168046i
$958$		0			0
$959$	0.320297			0.0103429
$960$		0			0
$961$		−	9.05631i		−	0.292139i
$962$		0			0
$963$	21.8385	+	21.8385i	0.703736	+	0.703736i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	12.6838			0.407882			0.203941	−	0.978983i	$-0.434625\pi$
$967$	12.6838			0.407882			0.203941	+	0.978983i	$0.434625\pi$
$968$		0			0
$969$	−5.31624	−	5.31624i	−0.170782	−	0.170782i
$970$		0			0
$971$	−25.3336			−0.812994			−0.406497	−	0.913652i	$-0.633250\pi$
$971$	−25.3336			−0.812994			−0.406497	+	0.913652i	$0.633250\pi$
$972$		0			0
$973$	−2.11090			−0.0676722
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.07213			−0.0662933			−0.0331467	−	0.999450i	$-0.510553\pi$
$977$	−2.07213			−0.0662933			−0.0331467	+	0.999450i	$0.510553\pi$
$978$		0			0
$979$	2.60667			0.0833094
$980$		0			0
$981$	9.08587	+	9.08587i	0.290089	+	0.290089i
$982$		0			0
$983$	−35.5838			−1.13495			−0.567473	−	0.823392i	$-0.692079\pi$
$983$	−35.5838			−1.13495			−0.567473	+	0.823392i	$0.692079\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.72133	−	5.72133i	−0.182112	−	0.182112i
$988$		0			0
$989$		−	12.5600i		−	0.399385i
$990$		0			0
$991$	5.33989			0.169627			0.0848136	−	0.996397i	$-0.472971\pi$
$991$	5.33989			0.169627			0.0848136	+	0.996397i	$0.472971\pi$
$992$		0			0
$993$		−	3.48598i		−	0.110624i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	31.9902	−	31.9902i	1.01314	−	1.01314i	0.0132277	−	0.999913i	$-0.495789\pi$
$997$	31.9902	−	31.9902i	1.01314	−	1.01314i	0.999913	−	0.0132277i	$-0.00421064\pi$
$998$		0			0
$999$	16.4012	+	16.4012i	0.518912	+	0.518912i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.m.c.593.2		8
5.2	odd	4		1300.2.r.c.957.2		8
5.3	odd	4		260.2.r.c.177.3	yes	8
5.4	even	2		260.2.m.c.73.3	yes	8
13.5	odd	4		1300.2.r.c.993.2		8
15.8	even	4		2340.2.bp.g.1477.3		8
15.14	odd	2		2340.2.u.g.73.1		8
20.3	even	4		1040.2.cd.m.177.2		8
20.19	odd	2		1040.2.bg.m.593.2		8
65.18	even	4		260.2.m.c.57.3	✓	8
65.44	odd	4		260.2.r.c.213.3	yes	8
65.57	even	4	inner	1300.2.m.c.57.2		8
195.44	even	4		2340.2.bp.g.1513.3		8
195.83	odd	4		2340.2.u.g.577.1		8
260.83	odd	4		1040.2.bg.m.577.2		8
260.239	even	4		1040.2.cd.m.993.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.m.c.57.3	✓	8	65.18	even	4
260.2.m.c.73.3	yes	8	5.4	even	2
260.2.r.c.177.3	yes	8	5.3	odd	4
260.2.r.c.213.3	yes	8	65.44	odd	4
1040.2.bg.m.577.2		8	260.83	odd	4
1040.2.bg.m.593.2		8	20.19	odd	2
1040.2.cd.m.177.2		8	20.3	even	4
1040.2.cd.m.993.2		8	260.239	even	4
1300.2.m.c.57.2		8	65.57	even	4	inner
1300.2.m.c.593.2		8	1.1	even	1	trivial
1300.2.r.c.957.2		8	5.2	odd	4
1300.2.r.c.993.2		8	13.5	odd	4
2340.2.u.g.73.1		8	15.14	odd	2
2340.2.u.g.577.1		8	195.83	odd	4
2340.2.bp.g.1477.3		8	15.8	even	4
2340.2.bp.g.1513.3		8	195.44	even	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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.575868 - 0.575868i) q^{3} +2.48849i q^{7} -2.33675i q^{9} +O(q^{10})\)	\(q+(-0.575868 - 0.575868i) q^{3} +2.48849i q^{7} -2.33675i q^{9} +(-0.160643 + 0.160643i) q^{11} +(-1.42413 - 3.31238i) q^{13} +(-1.58477 - 1.58477i) q^{17} +(-2.91262 + 2.91262i) q^{19} +(1.43304 - 1.43304i) q^{21} +(0.839357 - 0.839357i) q^{23} +(-3.07326 + 3.07326i) q^{27} +2.80977i q^{29} +(-3.31238 - 3.31238i) q^{31} +0.185018 q^{33} -5.33675i q^{37} +(-1.08738 + 2.72760i) q^{39} +(-6.07326 - 6.07326i) q^{41} +(7.48193 - 7.48193i) q^{43} -3.99244i q^{47} +0.807426 q^{49} +1.82524i q^{51} +(0.0154678 + 0.0154678i) q^{53} +3.35457 q^{57} +(-2.91262 - 2.91262i) q^{59} -7.60929 q^{61} +5.81498 q^{63} +1.64022 q^{67} -0.966717 q^{69} +(-11.3702 - 11.3702i) q^{71} -15.2598 q^{73} +(-0.399757 - 0.399757i) q^{77} +15.6017i q^{79} -3.47067 q^{81} +0.681062i q^{83} +(1.61806 - 1.61806i) q^{87} +(-8.11324 - 8.11324i) q^{89} +(8.24281 - 3.54394i) q^{91} +3.81498i q^{93} -10.4322 q^{97} +(0.375382 + 0.375382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3}+O(q^{10}) \) 8 * q - 2 * q^3	\( 8 q - 2 q^{3} + 14 q^{11} - 14 q^{13} + 2 q^{19} + 4 q^{21} + 22 q^{23} + 16 q^{27} - 6 q^{31} - 16 q^{33} - 34 q^{39} - 8 q^{41} + 14 q^{43} - 24 q^{49} + 8 q^{53} - 16 q^{57} + 2 q^{59} - 12 q^{61} + 64 q^{63} - 20 q^{67} - 20 q^{69} - 22 q^{71} + 28 q^{73} - 8 q^{77} - 20 q^{81} - 12 q^{87} + 4 q^{89} - 12 q^{97} + 10 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 14 * q^11 - 14 * q^13 + 2 * q^19 + 4 * q^21 + 22 * q^23 + 16 * q^27 - 6 * q^31 - 16 * q^33 - 34 * q^39 - 8 * q^41 + 14 * q^43 - 24 * q^49 + 8 * q^53 - 16 * q^57 + 2 * q^59 - 12 * q^61 + 64 * q^63 - 20 * q^67 - 20 * q^69 - 22 * q^71 + 28 * q^73 - 8 * q^77 - 20 * q^81 - 12 * q^87 + 4 * q^89 - 12 * q^97 + 10 * q^99

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