LMFDB - Embedded newform 525.2.d.d.274.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 9 $ x^4 + 7*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.1
Root			$-2.30278i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.2.d.d.274.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30278i q^{2} +1.00000i q^{3} -3.30278 q^{4} +2.30278 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.30278i q^{2} +1.00000i q^{3} -3.30278 q^{4} +2.30278 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} -3.00000 q^{11} -3.30278i q^{12} -2.60555i q^{13} -2.30278 q^{14} +0.302776 q^{16} -4.60555i q^{17} +2.30278i q^{18} -6.60555 q^{19} +1.00000 q^{21} +6.90833i q^{22} -6.21110i q^{23} -3.00000 q^{24} -6.00000 q^{26} -1.00000i q^{27} +3.30278i q^{28} +7.60555 q^{29} -7.21110 q^{31} +5.30278i q^{32} -3.00000i q^{33} -10.6056 q^{34} +3.30278 q^{36} +4.21110i q^{37} +15.2111i q^{38} +2.60555 q^{39} -2.30278i q^{42} +9.60555i q^{43} +9.90833 q^{44} -14.3028 q^{46} -10.6056i q^{47} +0.302776i q^{48} -1.00000 q^{49} +4.60555 q^{51} +8.60555i q^{52} +3.21110i q^{53} -2.30278 q^{54} +3.00000 q^{56} -6.60555i q^{57} -17.5139i q^{58} +10.6056 q^{59} -1.21110 q^{61} +16.6056i q^{62} +1.00000i q^{63} +12.8167 q^{64} -6.90833 q^{66} -15.6056i q^{67} +15.2111i q^{68} +6.21110 q^{69} -3.00000 q^{71} -3.00000i q^{72} +0.605551i q^{73} +9.69722 q^{74} +21.8167 q^{76} +3.00000i q^{77} -6.00000i q^{78} +14.8167 q^{79} +1.00000 q^{81} -3.21110i q^{83} -3.30278 q^{84} +22.1194 q^{86} +7.60555i q^{87} -9.00000i q^{88} -7.81665 q^{89} -2.60555 q^{91} +20.5139i q^{92} -7.21110i q^{93} -24.4222 q^{94} -5.30278 q^{96} +0.788897i q^{97} +2.30278i q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 6 * q^4 + 2 * q^6 - 4 * q^9	$ 4 q - 6 q^{4} + 2 q^{6} - 4 q^{9} - 12 q^{11} - 2 q^{14} - 6 q^{16} - 12 q^{19} + 4 q^{21} - 12 q^{24} - 24 q^{26} + 16 q^{29} - 28 q^{34} + 6 q^{36} - 4 q^{39} + 18 q^{44} - 50 q^{46} - 4 q^{49} + 4 q^{51} - 2 q^{54} + 12 q^{56} + 28 q^{59} + 24 q^{61} + 8 q^{64} - 6 q^{66} - 4 q^{69} - 12 q^{71} + 46 q^{74} + 44 q^{76} + 16 q^{79} + 4 q^{81} - 6 q^{84} + 38 q^{86} + 12 q^{89} + 4 q^{91} - 40 q^{94} - 14 q^{96} + 12 q^{99}+O(q^{100}) $ 4 * q - 6 * q^4 + 2 * q^6 - 4 * q^9 - 12 * q^11 - 2 * q^14 - 6 * q^16 - 12 * q^19 + 4 * q^21 - 12 * q^24 - 24 * q^26 + 16 * q^29 - 28 * q^34 + 6 * q^36 - 4 * q^39 + 18 * q^44 - 50 * q^46 - 4 * q^49 + 4 * q^51 - 2 * q^54 + 12 * q^56 + 28 * q^59 + 24 * q^61 + 8 * q^64 - 6 * q^66 - 4 * q^69 - 12 * q^71 + 46 * q^74 + 44 * q^76 + 16 * q^79 + 4 * q^81 - 6 * q^84 + 38 * q^86 + 12 * q^89 + 4 * q^91 - 40 * q^94 - 14 * q^96 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	− 2.30278i	− 1.62831i	−0.580649	−	0.814154i	$-0.697201\pi$
$2$	− 2.30278i	− 1.62831i	0.580649	−	0.814154i	$-0.302799\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−3.30278	−1.65139
$5$	0	0
$5$	0	0
$6$	2.30278	0.940104
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	3.00000i	1.06066i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	− 3.30278i	− 0.953429i
$13$	− 2.60555i	− 0.722650i	−0.932440	−	0.361325i	$-0.882325\pi$
$13$	− 2.60555i	− 0.722650i	0.932440	−	0.361325i	$-0.117675\pi$
$14$	−2.30278	−0.615443
$15$	0	0
$16$	0.302776	0.0756939
$17$	− 4.60555i	− 1.11701i	−0.829501	−	0.558505i	$-0.811375\pi$
$17$	− 4.60555i	− 1.11701i	0.829501	−	0.558505i	$-0.188625\pi$
$18$	2.30278i	0.542769i
$19$	−6.60555	−1.51542	−0.757709	−	0.652593i	$-0.773681\pi$
$19$	−6.60555	−1.51542	−0.757709	+	0.652593i	$0.773681\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	6.90833i	1.47286i
$23$	− 6.21110i	− 1.29510i	−0.762021	−	0.647552i	$-0.775793\pi$
$23$	− 6.21110i	− 1.29510i	0.762021	−	0.647552i	$-0.224207\pi$
$24$	−3.00000	−0.612372
$25$	0	0
$26$	−6.00000	−1.17670
$27$	− 1.00000i	− 0.192450i
$28$	3.30278i	0.624166i
$29$	7.60555	1.41232	0.706158	−	0.708055i	$-0.250427\pi$
$29$	7.60555	1.41232	0.706158	+	0.708055i	$0.250427\pi$
$30$	0	0
$31$	−7.21110	−1.29515	−0.647576	−	0.762001i	$-0.724217\pi$
$31$	−7.21110	−1.29515	−0.647576	+	0.762001i	$0.724217\pi$
$32$	5.30278i	0.937407i
$33$	− 3.00000i	− 0.522233i
$34$	−10.6056	−1.81884
$35$	0	0
$36$	3.30278	0.550463
$37$	4.21110i	0.692301i	0.938179	+	0.346150i	$0.112511\pi$
$37$	4.21110i	0.692301i	−0.938179	+	0.346150i	$0.887489\pi$
$38$	15.2111i	2.46757i
$39$	2.60555	0.417222
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	− 2.30278i	− 0.355326i
$43$	9.60555i	1.46483i	0.680857	+	0.732416i	$0.261608\pi$
$43$	9.60555i	1.46483i	−0.680857	+	0.732416i	$0.738392\pi$
$44$	9.90833	1.49374
$45$	0	0
$46$	−14.3028	−2.10883
$47$	− 10.6056i	− 1.54698i	−0.633809	−	0.773489i	$-0.718510\pi$
$47$	− 10.6056i	− 1.54698i	0.633809	−	0.773489i	$-0.281490\pi$
$48$	0.302776i	0.0437019i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	4.60555	0.644906
$52$	8.60555i	1.19338i
$53$	3.21110i	0.441079i	0.975378	+	0.220539i	$0.0707818\pi$
$53$	3.21110i	0.441079i	−0.975378	+	0.220539i	$0.929218\pi$
$54$	−2.30278	−0.313368
$55$	0	0
$56$	3.00000	0.400892
$57$	− 6.60555i	− 0.874927i
$58$	− 17.5139i	− 2.29968i
$59$	10.6056	1.38073	0.690363	−	0.723464i	$-0.257451\pi$
$59$	10.6056	1.38073	0.690363	+	0.723464i	$0.257451\pi$
$60$	0	0
$61$	−1.21110	−0.155066	−0.0775329	−	0.996990i	$-0.524704\pi$
$61$	−1.21110	−0.155066	−0.0775329	+	0.996990i	$0.524704\pi$
$62$	16.6056i	2.10891i
$63$	1.00000i	0.125988i
$64$	12.8167	1.60208
$65$	0	0
$66$	−6.90833	−0.850356
$67$	− 15.6056i	− 1.90652i	−0.302149	−	0.953261i	$-0.597704\pi$
$67$	− 15.6056i	− 1.90652i	0.302149	−	0.953261i	$-0.402296\pi$
$68$	15.2111i	1.84462i
$69$	6.21110	0.747729
$70$	0	0
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	− 3.00000i	− 0.353553i
$73$	0.605551i	0.0708744i	0.999372	+	0.0354372i	$0.0112824\pi$
$73$	0.605551i	0.0708744i	−0.999372	+	0.0354372i	$0.988718\pi$
$74$	9.69722	1.12728
$75$	0	0
$76$	21.8167	2.50254
$77$	3.00000i	0.341882i
$78$	− 6.00000i	− 0.679366i
$79$	14.8167	1.66700	0.833502	−	0.552517i	$-0.186332\pi$
$79$	14.8167	1.66700	0.833502	+	0.552517i	$0.186332\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	− 3.21110i	− 0.352464i	−0.984349	−	0.176232i	$-0.943609\pi$
$83$	− 3.21110i	− 0.352464i	0.984349	−	0.176232i	$-0.0563909\pi$
$84$	−3.30278	−0.360362
$85$	0	0
$86$	22.1194	2.38520
$87$	7.60555i	0.815401i
$88$	− 9.00000i	− 0.959403i
$89$	−7.81665	−0.828564	−0.414282	−	0.910149i	$-0.635967\pi$
$89$	−7.81665	−0.828564	−0.414282	+	0.910149i	$0.635967\pi$
$90$	0	0
$91$	−2.60555	−0.273136
$92$	20.5139i	2.13872i
$93$	− 7.21110i	− 0.747757i
$94$	−24.4222	−2.51896
$95$	0	0
$96$	−5.30278	−0.541212
$97$	0.788897i	0.0801004i	0.999198	+	0.0400502i	$0.0127518\pi$
$97$	0.788897i	0.0801004i	−0.999198	+	0.0400502i	$0.987248\pi$
$98$	2.30278i	0.232615i
$99$	3.00000	0.301511
$100$	0	0
$101$	16.6056	1.65231	0.826157	−	0.563440i	$-0.190522\pi$
$101$	16.6056	1.65231	0.826157	+	0.563440i	$0.190522\pi$
$102$	− 10.6056i	− 1.05011i
$103$	3.81665i	0.376066i	0.982163	+	0.188033i	$0.0602112\pi$
$103$	3.81665i	0.376066i	−0.982163	+	0.188033i	$0.939789\pi$
$104$	7.81665	0.766486
$105$	0	0
$106$	7.39445	0.718212
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	3.30278i	0.317810i
$109$	−2.21110	−0.211785	−0.105893	−	0.994378i	$-0.533770\pi$
$109$	−2.21110	−0.211785	−0.105893	+	0.994378i	$0.533770\pi$
$110$	0	0
$111$	−4.21110	−0.399700
$112$	− 0.302776i	− 0.0286096i
$113$	− 10.8167i	− 1.01755i	−0.860901	−	0.508773i	$-0.830099\pi$
$113$	− 10.8167i	− 1.01755i	0.860901	−	0.508773i	$-0.169901\pi$
$114$	−15.2111	−1.42465
$115$	0	0
$116$	−25.1194	−2.33228
$117$	2.60555i	0.240883i
$118$	− 24.4222i	− 2.24825i
$119$	−4.60555	−0.422190
$120$	0	0
$121$	−2.00000	−0.181818
$122$	2.78890i	0.252495i
$123$	0	0
$124$	23.8167	2.13880
$125$	0	0
$126$	2.30278	0.205148
$127$	− 12.8167i	− 1.13729i	−0.822582	−	0.568647i	$-0.807467\pi$
$127$	− 12.8167i	− 1.13729i	0.822582	−	0.568647i	$-0.192533\pi$
$128$	− 18.9083i	− 1.67128i
$129$	−9.60555	−0.845722
$130$	0	0
$131$	−7.39445	−0.646056	−0.323028	−	0.946389i	$-0.604701\pi$
$131$	−7.39445	−0.646056	−0.323028	+	0.946389i	$0.604701\pi$
$132$	9.90833i	0.862409i
$133$	6.60555i	0.572774i
$134$	−35.9361	−3.10440
$135$	0	0
$136$	13.8167	1.18477
$137$	3.21110i	0.274343i	0.990547	+	0.137172i	$0.0438011\pi$
$137$	3.21110i	0.274343i	−0.990547	+	0.137172i	$0.956199\pi$
$138$	− 14.3028i	− 1.21753i
$139$	−19.0278	−1.61391	−0.806957	−	0.590611i	$-0.798887\pi$
$139$	−19.0278	−1.61391	−0.806957	+	0.590611i	$0.798887\pi$
$140$	0	0
$141$	10.6056	0.893149
$142$	6.90833i	0.579734i
$143$	7.81665i	0.653661i
$144$	−0.302776	−0.0252313
$145$	0	0
$146$	1.39445	0.115405
$147$	− 1.00000i	− 0.0824786i
$148$	− 13.9083i	− 1.14326i
$149$	16.3944	1.34309	0.671543	−	0.740966i	$-0.265632\pi$
$149$	16.3944	1.34309	0.671543	+	0.740966i	$0.265632\pi$
$150$	0	0
$151$	6.81665	0.554731	0.277366	−	0.960764i	$-0.410539\pi$
$151$	6.81665	0.554731	0.277366	+	0.960764i	$0.410539\pi$
$152$	− 19.8167i	− 1.60734i
$153$	4.60555i	0.372337i
$154$	6.90833	0.556689
$155$	0	0
$156$	−8.60555	−0.688996
$157$	− 14.4222i	− 1.15102i	−0.817796	−	0.575509i	$-0.804804\pi$
$157$	− 14.4222i	− 1.15102i	0.817796	−	0.575509i	$-0.195196\pi$
$158$	− 34.1194i	− 2.71440i
$159$	−3.21110	−0.254657
$160$	0	0
$161$	−6.21110	−0.489503
$162$	− 2.30278i	− 0.180923i
$163$	17.2111i	1.34808i	0.738696	+	0.674039i	$0.235442\pi$
$163$	17.2111i	1.34808i	−0.738696	+	0.674039i	$0.764558\pi$
$164$	0	0
$165$	0	0
$166$	−7.39445	−0.573921
$167$	17.0278i	1.31765i	0.752297	+	0.658824i	$0.228946\pi$
$167$	17.0278i	1.31765i	−0.752297	+	0.658824i	$0.771054\pi$
$168$	3.00000i	0.231455i
$169$	6.21110	0.477777
$170$	0	0
$171$	6.60555	0.505139
$172$	− 31.7250i	− 2.41901i
$173$	− 7.81665i	− 0.594289i	−0.954832	−	0.297145i	$-0.903966\pi$
$173$	− 7.81665i	− 0.594289i	0.954832	−	0.297145i	$-0.0960343\pi$
$174$	17.5139	1.32772
$175$	0	0
$176$	−0.908327	−0.0684677
$177$	10.6056i	0.797162i
$178$	18.0000i	1.34916i
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	12.6056	0.936963	0.468482	−	0.883473i	$-0.344801\pi$
$181$	12.6056	0.936963	0.468482	+	0.883473i	$0.344801\pi$
$182$	6.00000i	0.444750i
$183$	− 1.21110i	− 0.0895273i
$184$	18.6333	1.37367
$185$	0	0
$186$	−16.6056	−1.21758
$187$	13.8167i	1.01037i
$188$	35.0278i	2.55466i
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−2.78890	−0.201798	−0.100899	−	0.994897i	$-0.532172\pi$
$191$	−2.78890	−0.201798	−0.100899	+	0.994897i	$0.532172\pi$
$192$	12.8167i	0.924962i
$193$	8.21110i	0.591048i	0.955335	+	0.295524i	$0.0954942\pi$
$193$	8.21110i	0.591048i	−0.955335	+	0.295524i	$0.904506\pi$
$194$	1.81665	0.130428
$195$	0	0
$196$	3.30278	0.235913
$197$	− 16.8167i	− 1.19814i	−0.800698	−	0.599068i	$-0.795538\pi$
$197$	− 16.8167i	− 1.19814i	0.800698	−	0.599068i	$-0.204462\pi$
$198$	− 6.90833i	− 0.490953i
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	0	0
$201$	15.6056	1.10073
$202$	− 38.2389i	− 2.69048i
$203$	− 7.60555i	− 0.533805i
$204$	−15.2111	−1.06499
$205$	0	0
$206$	8.78890	0.612352
$207$	6.21110i	0.431701i
$208$	− 0.788897i	− 0.0547002i
$209$	19.8167	1.37075
$210$	0	0
$211$	26.4222	1.81898	0.909490	−	0.415726i	$-0.136473\pi$
$211$	26.4222	1.81898	0.909490	+	0.415726i	$0.136473\pi$
$212$	− 10.6056i	− 0.728392i
$213$	− 3.00000i	− 0.205557i
$214$	0	0
$215$	0	0
$216$	3.00000	0.204124
$217$	7.21110i	0.489522i
$218$	5.09167i	0.344852i
$219$	−0.605551	−0.0409194
$220$	0	0
$221$	−12.0000	−0.807207
$222$	9.69722i	0.650835i
$223$	15.3944i	1.03089i	0.856923	+	0.515444i	$0.172373\pi$
$223$	15.3944i	1.03089i	−0.856923	+	0.515444i	$0.827627\pi$
$224$	5.30278	0.354307
$225$	0	0
$226$	−24.9083	−1.65688
$227$	− 22.6056i	− 1.50038i	−0.661221	−	0.750192i	$-0.729961\pi$
$227$	− 22.6056i	− 1.50038i	0.661221	−	0.750192i	$-0.270039\pi$
$228$	21.8167i	1.44484i
$229$	7.21110	0.476523	0.238262	−	0.971201i	$-0.423422\pi$
$229$	7.21110	0.476523	0.238262	+	0.971201i	$0.423422\pi$
$230$	0	0
$231$	−3.00000	−0.197386
$232$	22.8167i	1.49799i
$233$	− 1.18335i	− 0.0775236i	−0.999248	−	0.0387618i	$-0.987659\pi$
$233$	− 1.18335i	− 0.0775236i	0.999248	−	0.0387618i	$-0.0123414\pi$
$234$	6.00000	0.392232
$235$	0	0
$236$	−35.0278	−2.28011
$237$	14.8167i	0.962445i
$238$	10.6056i	0.687456i
$239$	−14.7889	−0.956614	−0.478307	−	0.878193i	$-0.658749\pi$
$239$	−14.7889	−0.956614	−0.478307	+	0.878193i	$0.658749\pi$
$240$	0	0
$241$	9.39445	0.605150	0.302575	−	0.953126i	$-0.402154\pi$
$241$	9.39445	0.605150	0.302575	+	0.953126i	$0.402154\pi$
$242$	4.60555i	0.296056i
$243$	1.00000i	0.0641500i
$244$	4.00000	0.256074
$245$	0	0
$246$	0	0
$247$	17.2111i	1.09512i
$248$	− 21.6333i	− 1.37372i
$249$	3.21110	0.203495
$250$	0	0
$251$	−13.8167	−0.872099	−0.436050	−	0.899923i	$-0.643623\pi$
$251$	−13.8167	−0.872099	−0.436050	+	0.899923i	$0.643623\pi$
$252$	− 3.30278i	− 0.208055i
$253$	18.6333i	1.17147i
$254$	−29.5139	−1.85187
$255$	0	0
$256$	−17.9083	−1.11927
$257$	21.6333i	1.34945i	0.738070	+	0.674724i	$0.235737\pi$
$257$	21.6333i	1.34945i	−0.738070	+	0.674724i	$0.764263\pi$
$258$	22.1194i	1.37710i
$259$	4.21110	0.261665
$260$	0	0
$261$	−7.60555	−0.470772
$262$	17.0278i	1.05198i
$263$	− 5.78890i	− 0.356959i	−0.983944	−	0.178479i	$-0.942882\pi$
$263$	− 5.78890i	− 0.356959i	0.983944	−	0.178479i	$-0.0571178\pi$
$264$	9.00000	0.553912
$265$	0	0
$266$	15.2111	0.932653
$267$	− 7.81665i	− 0.478371i
$268$	51.5416i	3.14841i
$269$	3.21110	0.195784	0.0978922	−	0.995197i	$-0.468790\pi$
$269$	3.21110	0.195784	0.0978922	+	0.995197i	$0.468790\pi$
$270$	0	0
$271$	−26.6056	−1.61617	−0.808086	−	0.589064i	$-0.799496\pi$
$271$	−26.6056	−1.61617	−0.808086	+	0.589064i	$0.799496\pi$
$272$	− 1.39445i	− 0.0845509i
$273$	− 2.60555i	− 0.157695i
$274$	7.39445	0.446715
$275$	0	0
$276$	−20.5139	−1.23479
$277$	10.0000i	0.600842i	0.953807	+	0.300421i	$0.0971271\pi$
$277$	10.0000i	0.600842i	−0.953807	+	0.300421i	$0.902873\pi$
$278$	43.8167i	2.62795i
$279$	7.21110	0.431717
$280$	0	0
$281$	−1.18335	−0.0705925	−0.0352963	−	0.999377i	$-0.511237\pi$
$281$	−1.18335	−0.0705925	−0.0352963	+	0.999377i	$0.511237\pi$
$282$	− 24.4222i	− 1.45432i
$283$	− 13.6333i	− 0.810416i	−0.914225	−	0.405208i	$-0.867199\pi$
$283$	− 13.6333i	− 0.810416i	0.914225	−	0.405208i	$-0.132801\pi$
$284$	9.90833	0.587951
$285$	0	0
$286$	18.0000	1.06436
$287$	0	0
$288$	− 5.30278i	− 0.312469i
$289$	−4.21110	−0.247712
$290$	0	0
$291$	−0.788897	−0.0462460
$292$	− 2.00000i	− 0.117041i
$293$	10.6056i	0.619583i	0.950805	+	0.309791i	$0.100259\pi$
$293$	10.6056i	0.619583i	−0.950805	+	0.309791i	$0.899741\pi$
$294$	−2.30278	−0.134301
$295$	0	0
$296$	−12.6333	−0.734296
$297$	3.00000i	0.174078i
$298$	− 37.7527i	− 2.18696i
$299$	−16.1833	−0.935907
$300$	0	0
$301$	9.60555	0.553655
$302$	− 15.6972i	− 0.903274i
$303$	16.6056i	0.953964i
$304$	−2.00000	−0.114708
$305$	0	0
$306$	10.6056	0.606279
$307$	8.60555i	0.491145i	0.969378	+	0.245572i	$0.0789759\pi$
$307$	8.60555i	0.491145i	−0.969378	+	0.245572i	$0.921024\pi$
$308$	− 9.90833i	− 0.564579i
$309$	−3.81665	−0.217122
$310$	0	0
$311$	13.8167	0.783471	0.391735	−	0.920078i	$-0.371875\pi$
$311$	13.8167	0.783471	0.391735	+	0.920078i	$0.371875\pi$
$312$	7.81665i	0.442531i
$313$	− 23.8167i	− 1.34620i	−0.739553	−	0.673098i	$-0.764963\pi$
$313$	− 23.8167i	− 1.34620i	0.739553	−	0.673098i	$-0.235037\pi$
$314$	−33.2111	−1.87421
$315$	0	0
$316$	−48.9361	−2.75287
$317$	16.3944i	0.920804i	0.887711	+	0.460402i	$0.152295\pi$
$317$	16.3944i	0.920804i	−0.887711	+	0.460402i	$0.847705\pi$
$318$	7.39445i	0.414660i
$319$	−22.8167	−1.27749
$320$	0	0
$321$	0	0
$322$	14.3028i	0.797063i
$323$	30.4222i	1.69274i
$324$	−3.30278	−0.183488
$325$	0	0
$326$	39.6333	2.19509
$327$	− 2.21110i	− 0.122274i
$328$	0	0
$329$	−10.6056	−0.584703
$330$	0	0
$331$	−21.2389	−1.16739	−0.583697	−	0.811972i	$-0.698394\pi$
$331$	−21.2389	−1.16739	−0.583697	+	0.811972i	$0.698394\pi$
$332$	10.6056i	0.582055i
$333$	− 4.21110i	− 0.230767i
$334$	39.2111	2.14554
$335$	0	0
$336$	0.302776	0.0165178
$337$	7.21110i	0.392814i	0.980522	+	0.196407i	$0.0629273\pi$
$337$	7.21110i	0.392814i	−0.980522	+	0.196407i	$0.937073\pi$
$338$	− 14.3028i	− 0.777968i
$339$	10.8167	0.587480
$340$	0	0
$341$	21.6333	1.17151
$342$	− 15.2111i	− 0.822522i
$343$	1.00000i	0.0539949i
$344$	−28.8167	−1.55369
$345$	0	0
$346$	−18.0000	−0.967686
$347$	− 30.2111i	− 1.62182i	−0.585173	−	0.810908i	$-0.698973\pi$
$347$	− 30.2111i	− 1.62182i	0.585173	−	0.810908i	$-0.301027\pi$
$348$	− 25.1194i	− 1.34654i
$349$	−31.4500	−1.68348	−0.841739	−	0.539885i	$-0.818468\pi$
$349$	−31.4500	−1.68348	−0.841739	+	0.539885i	$0.818468\pi$
$350$	0	0
$351$	−2.60555	−0.139074
$352$	− 15.9083i	− 0.847917i
$353$	− 30.0000i	− 1.59674i	−0.602168	−	0.798369i	$-0.705696\pi$
$353$	− 30.0000i	− 1.59674i	0.602168	−	0.798369i	$-0.294304\pi$
$354$	24.4222	1.29803
$355$	0	0
$356$	25.8167	1.36828
$357$	− 4.60555i	− 0.243752i
$358$	0	0
$359$	−24.6333	−1.30010	−0.650048	−	0.759893i	$-0.725251\pi$
$359$	−24.6333	−1.30010	−0.650048	+	0.759893i	$0.725251\pi$
$360$	0	0
$361$	24.6333	1.29649
$362$	− 29.0278i	− 1.52567i
$363$	− 2.00000i	− 0.104973i
$364$	8.60555	0.451053
$365$	0	0
$366$	−2.78890	−0.145778
$367$	− 14.4222i	− 0.752833i	−0.926451	−	0.376416i	$-0.877156\pi$
$367$	− 14.4222i	− 0.752833i	0.926451	−	0.376416i	$-0.122844\pi$
$368$	− 1.88057i	− 0.0980315i
$369$	0	0
$370$	0	0
$371$	3.21110	0.166712
$372$	23.8167i	1.23484i
$373$	− 1.00000i	− 0.0517780i	−0.999665	−	0.0258890i	$-0.991758\pi$
$373$	− 1.00000i	− 0.0517780i	0.999665	−	0.0258890i	$-0.00824165\pi$
$374$	31.8167	1.64520
$375$	0	0
$376$	31.8167	1.64082
$377$	− 19.8167i	− 1.02061i
$378$	2.30278i	0.118442i
$379$	14.8167	0.761080	0.380540	−	0.924764i	$-0.375738\pi$
$379$	14.8167	0.761080	0.380540	+	0.924764i	$0.375738\pi$
$380$	0	0
$381$	12.8167	0.656617
$382$	6.42221i	0.328589i
$383$	− 26.2389i	− 1.34074i	−0.742026	−	0.670372i	$-0.766135\pi$
$383$	− 26.2389i	− 1.34074i	0.742026	−	0.670372i	$-0.233865\pi$
$384$	18.9083	0.964912
$385$	0	0
$386$	18.9083	0.962408
$387$	− 9.60555i	− 0.488278i
$388$	− 2.60555i	− 0.132277i
$389$	28.8167	1.46106	0.730531	−	0.682879i	$-0.239273\pi$
$389$	28.8167	1.46106	0.730531	+	0.682879i	$0.239273\pi$
$390$	0	0
$391$	−28.6056	−1.44664
$392$	− 3.00000i	− 0.151523i
$393$	− 7.39445i	− 0.373001i
$394$	−38.7250	−1.95094
$395$	0	0
$396$	−9.90833	−0.497912
$397$	− 2.00000i	− 0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$	− 2.00000i	− 0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$	18.4222i	0.923422i
$399$	−6.60555	−0.330691
$400$	0	0
$401$	−16.8167	−0.839784	−0.419892	−	0.907574i	$-0.637932\pi$
$401$	−16.8167	−0.839784	−0.419892	+	0.907574i	$0.637932\pi$
$402$	− 35.9361i	− 1.79233i
$403$	18.7889i	0.935942i
$404$	−54.8444	−2.72861
$405$	0	0
$406$	−17.5139	−0.869199
$407$	− 12.6333i	− 0.626210i
$408$	13.8167i	0.684026i
$409$	11.8167	0.584296	0.292148	−	0.956373i	$-0.405630\pi$
$409$	11.8167	0.584296	0.292148	+	0.956373i	$0.405630\pi$
$410$	0	0
$411$	−3.21110	−0.158392
$412$	− 12.6056i	− 0.621031i
$413$	− 10.6056i	− 0.521865i
$414$	14.3028	0.702943
$415$	0	0
$416$	13.8167	0.677417
$417$	− 19.0278i	− 0.931793i
$418$	− 45.6333i	− 2.23200i
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	0	0
$421$	−10.2111	−0.497659	−0.248829	−	0.968547i	$-0.580046\pi$
$421$	−10.2111	−0.497659	−0.248829	+	0.968547i	$0.580046\pi$
$422$	− 60.8444i	− 2.96186i
$423$	10.6056i	0.515660i
$424$	−9.63331	−0.467835
$425$	0	0
$426$	−6.90833	−0.334710
$427$	1.21110i	0.0586094i
$428$	0	0
$429$	−7.81665	−0.377392
$430$	0	0
$431$	5.57779	0.268673	0.134336	−	0.990936i	$-0.457110\pi$
$431$	5.57779	0.268673	0.134336	+	0.990936i	$0.457110\pi$
$432$	− 0.302776i	− 0.0145673i
$433$	− 37.2111i	− 1.78825i	−0.447816	−	0.894126i	$-0.647798\pi$
$433$	− 37.2111i	− 1.78825i	0.447816	−	0.894126i	$-0.352202\pi$
$434$	16.6056	0.797092
$435$	0	0
$436$	7.30278	0.349740
$437$	41.0278i	1.96262i
$438$	1.39445i	0.0666293i
$439$	−6.60555	−0.315266	−0.157633	−	0.987498i	$-0.550386\pi$
$439$	−6.60555	−0.315266	−0.157633	+	0.987498i	$0.550386\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	27.6333i	1.31438i
$443$	15.6333i	0.742761i	0.928481	+	0.371380i	$0.121115\pi$
$443$	15.6333i	0.742761i	−0.928481	+	0.371380i	$0.878885\pi$
$444$	13.9083	0.660060
$445$	0	0
$446$	35.4500	1.67860
$447$	16.3944i	0.775431i
$448$	− 12.8167i	− 0.605530i
$449$	34.8167	1.64310	0.821550	−	0.570137i	$-0.193110\pi$
$449$	34.8167	1.64310	0.821550	+	0.570137i	$0.193110\pi$
$450$	0	0
$451$	0	0
$452$	35.7250i	1.68036i
$453$	6.81665i	0.320274i
$454$	−52.0555	−2.44309
$455$	0	0
$456$	19.8167	0.928000
$457$	3.78890i	0.177237i	0.996066	+	0.0886186i	$0.0282452\pi$
$457$	3.78890i	0.177237i	−0.996066	+	0.0886186i	$0.971755\pi$
$458$	− 16.6056i	− 0.775926i
$459$	−4.60555	−0.214969
$460$	0	0
$461$	−26.2389	−1.22207	−0.611033	−	0.791605i	$-0.709246\pi$
$461$	−26.2389	−1.22207	−0.611033	+	0.791605i	$0.709246\pi$
$462$	6.90833i	0.321404i
$463$	17.2111i	0.799868i	0.916544	+	0.399934i	$0.130967\pi$
$463$	17.2111i	0.799868i	−0.916544	+	0.399934i	$0.869033\pi$
$464$	2.30278	0.106904
$465$	0	0
$466$	−2.72498	−0.126232
$467$	0.422205i	0.0195373i	0.999952	+	0.00976866i	$0.00310951\pi$
$467$	0.422205i	0.0195373i	−0.999952	+	0.00976866i	$0.996890\pi$
$468$	− 8.60555i	− 0.397792i
$469$	−15.6056	−0.720597
$470$	0	0
$471$	14.4222	0.664540
$472$	31.8167i	1.46448i
$473$	− 28.8167i	− 1.32499i
$474$	34.1194	1.56716
$475$	0	0
$476$	15.2111	0.697200
$477$	− 3.21110i	− 0.147026i
$478$	34.0555i	1.55766i
$479$	−34.6056	−1.58117	−0.790584	−	0.612354i	$-0.790223\pi$
$479$	−34.6056	−1.58117	−0.790584	+	0.612354i	$0.790223\pi$
$480$	0	0
$481$	10.9722	0.500291
$482$	− 21.6333i	− 0.985370i
$483$	− 6.21110i	− 0.282615i
$484$	6.60555	0.300252
$485$	0	0
$486$	2.30278	0.104456
$487$	20.8167i	0.943293i	0.881788	+	0.471646i	$0.156340\pi$
$487$	20.8167i	0.943293i	−0.881788	+	0.471646i	$0.843660\pi$
$488$	− 3.63331i	− 0.164472i
$489$	−17.2111	−0.778313
$490$	0	0
$491$	−3.00000	−0.135388	−0.0676941	−	0.997706i	$-0.521564\pi$
$491$	−3.00000	−0.135388	−0.0676941	+	0.997706i	$0.521564\pi$
$492$	0	0
$493$	− 35.0278i	− 1.57757i
$494$	39.6333	1.78319
$495$	0	0
$496$	−2.18335	−0.0980351
$497$	3.00000i	0.134568i
$498$	− 7.39445i	− 0.331353i
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	0	0
$501$	−17.0278	−0.760744
$502$	31.8167i	1.42005i
$503$	− 8.78890i	− 0.391878i	−0.980616	−	0.195939i	$-0.937225\pi$
$503$	− 8.78890i	− 0.391878i	0.980616	−	0.195939i	$-0.0627754\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	42.9083	1.90751
$507$	6.21110i	0.275845i
$508$	42.3305i	1.87811i
$509$	−1.39445	−0.0618079	−0.0309039	−	0.999522i	$-0.509839\pi$
$509$	−1.39445	−0.0618079	−0.0309039	+	0.999522i	$0.509839\pi$
$510$	0	0
$511$	0.605551	0.0267880
$512$	3.42221i	0.151242i
$513$	6.60555i	0.291642i
$514$	49.8167	2.19732
$515$	0	0
$516$	31.7250	1.39661
$517$	31.8167i	1.39929i
$518$	− 9.69722i	− 0.426072i
$519$	7.81665	0.343113
$520$	0	0
$521$	−36.4222	−1.59569	−0.797843	−	0.602865i	$-0.794026\pi$
$521$	−36.4222	−1.59569	−0.797843	+	0.602865i	$0.794026\pi$
$522$	17.5139i	0.766562i
$523$	− 16.0000i	− 0.699631i	−0.936819	−	0.349816i	$-0.886244\pi$
$523$	− 16.0000i	− 0.699631i	0.936819	−	0.349816i	$-0.113756\pi$
$524$	24.4222	1.06689
$525$	0	0
$526$	−13.3305	−0.581239
$527$	33.2111i	1.44670i
$528$	− 0.908327i	− 0.0395299i
$529$	−15.5778	−0.677295
$530$	0	0
$531$	−10.6056	−0.460242
$532$	− 21.8167i	− 0.945872i
$533$	0	0
$534$	−18.0000	−0.778936
$535$	0	0
$536$	46.8167	2.02217
$537$	0	0
$538$	− 7.39445i	− 0.318797i
$539$	3.00000	0.129219
$540$	0	0
$541$	−31.4222	−1.35095	−0.675473	−	0.737385i	$-0.736061\pi$
$541$	−31.4222	−1.35095	−0.675473	+	0.737385i	$0.736061\pi$
$542$	61.2666i	2.63163i
$543$	12.6056i	0.540956i
$544$	24.4222	1.04709
$545$	0	0
$546$	−6.00000	−0.256776
$547$	29.6056i	1.26584i	0.774216	+	0.632921i	$0.218144\pi$
$547$	29.6056i	1.26584i	−0.774216	+	0.632921i	$0.781856\pi$
$548$	− 10.6056i	− 0.453047i
$549$	1.21110	0.0516886
$550$	0	0
$551$	−50.2389	−2.14025
$552$	18.6333i	0.793086i
$553$	− 14.8167i	− 0.630068i
$554$	23.0278	0.978356
$555$	0	0
$556$	62.8444	2.66520
$557$	− 11.2389i	− 0.476206i	−0.971240	−	0.238103i	$-0.923474\pi$
$557$	− 11.2389i	− 0.476206i	0.971240	−	0.238103i	$-0.0765255\pi$
$558$	− 16.6056i	− 0.702969i
$559$	25.0278	1.05856
$560$	0	0
$561$	−13.8167	−0.583340
$562$	2.72498i	0.114946i
$563$	15.2111i	0.641072i	0.947236	+	0.320536i	$0.103863\pi$
$563$	15.2111i	0.641072i	−0.947236	+	0.320536i	$0.896137\pi$
$564$	−35.0278	−1.47493
$565$	0	0
$566$	−31.3944	−1.31961
$567$	− 1.00000i	− 0.0419961i
$568$	− 9.00000i	− 0.377632i
$569$	1.18335	0.0496085	0.0248042	−	0.999692i	$-0.492104\pi$
$569$	1.18335	0.0496085	0.0248042	+	0.999692i	$0.492104\pi$
$570$	0	0
$571$	−5.60555	−0.234585	−0.117293	−	0.993097i	$-0.537422\pi$
$571$	−5.60555	−0.234585	−0.117293	+	0.993097i	$0.537422\pi$
$572$	− 25.8167i	− 1.07945i
$573$	− 2.78890i	− 0.116508i
$574$	0	0
$575$	0	0
$576$	−12.8167	−0.534027
$577$	− 30.6056i	− 1.27413i	−0.770812	−	0.637063i	$-0.780149\pi$
$577$	− 30.6056i	− 1.27413i	0.770812	−	0.637063i	$-0.219851\pi$
$578$	9.69722i	0.403351i
$579$	−8.21110	−0.341242
$580$	0	0
$581$	−3.21110	−0.133219
$582$	1.81665i	0.0753027i
$583$	− 9.63331i	− 0.398971i
$584$	−1.81665	−0.0751737
$585$	0	0
$586$	24.4222	1.00887
$587$	− 37.8167i	− 1.56086i	−0.625243	−	0.780430i	$-0.715000\pi$
$587$	− 37.8167i	− 1.56086i	0.625243	−	0.780430i	$-0.285000\pi$
$588$	3.30278i	0.136204i
$589$	47.6333	1.96270
$590$	0	0
$591$	16.8167	0.691745
$592$	1.27502i	0.0524030i
$593$	27.6333i	1.13476i	0.823455	+	0.567382i	$0.192044\pi$
$593$	27.6333i	1.13476i	−0.823455	+	0.567382i	$0.807956\pi$
$594$	6.90833	0.283452
$595$	0	0
$596$	−54.1472	−2.21796
$597$	− 8.00000i	− 0.327418i
$598$	37.2666i	1.52395i
$599$	−5.78890	−0.236528	−0.118264	−	0.992982i	$-0.537733\pi$
$599$	−5.78890	−0.236528	−0.118264	+	0.992982i	$0.537733\pi$
$600$	0	0
$601$	17.2111	0.702056	0.351028	−	0.936365i	$-0.385832\pi$
$601$	17.2111	0.702056	0.351028	+	0.936365i	$0.385832\pi$
$602$	− 22.1194i	− 0.901521i
$603$	15.6056i	0.635507i
$604$	−22.5139	−0.916077
$605$	0	0
$606$	38.2389	1.55335
$607$	23.8167i	0.966688i	0.875430	+	0.483344i	$0.160578\pi$
$607$	23.8167i	0.966688i	−0.875430	+	0.483344i	$0.839422\pi$
$608$	− 35.0278i	− 1.42056i
$609$	7.60555	0.308192
$610$	0	0
$611$	−27.6333	−1.11792
$612$	− 15.2111i	− 0.614872i
$613$	− 49.4222i	− 1.99614i	−0.0620663	−	0.998072i	$-0.519769\pi$
$613$	− 49.4222i	− 1.99614i	0.0620663	−	0.998072i	$-0.480231\pi$
$614$	19.8167	0.799735
$615$	0	0
$616$	−9.00000	−0.362620
$617$	− 22.8167i	− 0.918564i	−0.888291	−	0.459282i	$-0.848107\pi$
$617$	− 22.8167i	− 0.918564i	0.888291	−	0.459282i	$-0.151893\pi$
$618$	8.78890i	0.353541i
$619$	2.60555	0.104726	0.0523630	−	0.998628i	$-0.483325\pi$
$619$	2.60555	0.104726	0.0523630	+	0.998628i	$0.483325\pi$
$620$	0	0
$621$	−6.21110	−0.249243
$622$	− 31.8167i	− 1.27573i
$623$	7.81665i	0.313168i
$624$	0.788897	0.0315812
$625$	0	0
$626$	−54.8444	−2.19202
$627$	19.8167i	0.791401i
$628$	47.6333i	1.90078i
$629$	19.3944	0.773307
$630$	0	0
$631$	22.0278	0.876911	0.438456	−	0.898753i	$-0.355526\pi$
$631$	22.0278	0.876911	0.438456	+	0.898753i	$0.355526\pi$
$632$	44.4500i	1.76812i
$633$	26.4222i	1.05019i
$634$	37.7527	1.49935
$635$	0	0
$636$	10.6056	0.420537
$637$	2.60555i	0.103236i
$638$	52.5416i	2.08014i
$639$	3.00000	0.118678
$640$	0	0
$641$	22.8167	0.901204	0.450602	−	0.892725i	$-0.351209\pi$
$641$	22.8167	0.901204	0.450602	+	0.892725i	$0.351209\pi$
$642$	0	0
$643$	38.4222i	1.51522i	0.652705	+	0.757612i	$0.273634\pi$
$643$	38.4222i	1.51522i	−0.652705	+	0.757612i	$0.726366\pi$
$644$	20.5139	0.808360
$645$	0	0
$646$	70.0555	2.75630
$647$	− 6.00000i	− 0.235884i	−0.993020	−	0.117942i	$-0.962370\pi$
$647$	− 6.00000i	− 0.235884i	0.993020	−	0.117942i	$-0.0376297\pi$
$648$	3.00000i	0.117851i
$649$	−31.8167	−1.24891
$650$	0	0
$651$	−7.21110	−0.282625
$652$	− 56.8444i	− 2.22620i
$653$	− 3.21110i	− 0.125660i	−0.998024	−	0.0628301i	$-0.979987\pi$
$653$	− 3.21110i	− 0.125660i	0.998024	−	0.0628301i	$-0.0200126\pi$
$654$	−5.09167	−0.199100
$655$	0	0
$656$	0	0
$657$	− 0.605551i	− 0.0236248i
$658$	24.4222i	0.952077i
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	−20.1833	−0.785041	−0.392521	−	0.919743i	$-0.628397\pi$
$661$	−20.1833	−0.785041	−0.392521	+	0.919743i	$0.628397\pi$
$662$	48.9083i	1.90088i
$663$	− 12.0000i	− 0.466041i
$664$	9.63331	0.373845
$665$	0	0
$666$	−9.69722	−0.375760
$667$	− 47.2389i	− 1.82910i
$668$	− 56.2389i	− 2.17595i
$669$	−15.3944	−0.595184
$670$	0	0
$671$	3.63331	0.140262
$672$	5.30278i	0.204559i
$673$	− 10.0000i	− 0.385472i	−0.981251	−	0.192736i	$-0.938264\pi$
$673$	− 10.0000i	− 0.385472i	0.981251	−	0.192736i	$-0.0617360\pi$
$674$	16.6056	0.639622
$675$	0	0
$676$	−20.5139	−0.788995
$677$	8.78890i	0.337785i	0.985634	+	0.168892i	$0.0540190\pi$
$677$	8.78890i	0.337785i	−0.985634	+	0.168892i	$0.945981\pi$
$678$	− 24.9083i	− 0.956599i
$679$	0.788897	0.0302751
$680$	0	0
$681$	22.6056	0.866247
$682$	− 49.8167i	− 1.90758i
$683$	− 18.6333i	− 0.712984i	−0.934298	−	0.356492i	$-0.883973\pi$
$683$	− 18.6333i	− 0.712984i	0.934298	−	0.356492i	$-0.116027\pi$
$684$	−21.8167	−0.834181
$685$	0	0
$686$	2.30278	0.0879204
$687$	7.21110i	0.275121i
$688$	2.90833i	0.110879i
$689$	8.36669	0.318746
$690$	0	0
$691$	41.2111	1.56774	0.783872	−	0.620922i	$-0.213242\pi$
$691$	41.2111	1.56774	0.783872	+	0.620922i	$0.213242\pi$
$692$	25.8167i	0.981402i
$693$	− 3.00000i	− 0.113961i
$694$	−69.5694	−2.64082
$695$	0	0
$696$	−22.8167	−0.864863
$697$	0	0
$698$	72.4222i	2.74122i
$699$	1.18335	0.0447583
$700$	0	0
$701$	−20.7889	−0.785186	−0.392593	−	0.919712i	$-0.628422\pi$
$701$	−20.7889	−0.785186	−0.392593	+	0.919712i	$0.628422\pi$
$702$	6.00000i	0.226455i
$703$	− 27.8167i	− 1.04912i
$704$	−38.4500	−1.44914
$705$	0	0
$706$	−69.0833	−2.59998
$707$	− 16.6056i	− 0.624516i
$708$	− 35.0278i	− 1.31642i
$709$	34.8444	1.30861	0.654305	−	0.756231i	$-0.272961\pi$
$709$	34.8444	1.30861	0.654305	+	0.756231i	$0.272961\pi$
$710$	0	0
$711$	−14.8167	−0.555668
$712$	− 23.4500i	− 0.878824i
$713$	44.7889i	1.67736i
$714$	−10.6056	−0.396903
$715$	0	0
$716$	0	0
$717$	− 14.7889i	− 0.552301i
$718$	56.7250i	2.11696i
$719$	−26.7889	−0.999057	−0.499529	−	0.866297i	$-0.666493\pi$
$719$	−26.7889	−0.999057	−0.499529	+	0.866297i	$0.666493\pi$
$720$	0	0
$721$	3.81665	0.142140
$722$	− 56.7250i	− 2.11109i
$723$	9.39445i	0.349383i
$724$	−41.6333	−1.54729
$725$	0	0
$726$	−4.60555	−0.170928
$727$	23.3944i	0.867652i	0.900997	+	0.433826i	$0.142837\pi$
$727$	23.3944i	0.867652i	−0.900997	+	0.433826i	$0.857163\pi$
$728$	− 7.81665i	− 0.289704i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	44.2389	1.63623
$732$	4.00000i	0.147844i
$733$	20.0000i	0.738717i	0.929287	+	0.369358i	$0.120423\pi$
$733$	20.0000i	0.738717i	−0.929287	+	0.369358i	$0.879577\pi$
$734$	−33.2111	−1.22584
$735$	0	0
$736$	32.9361	1.21404
$737$	46.8167i	1.72451i
$738$	0	0
$739$	−3.18335	−0.117101	−0.0585506	−	0.998284i	$-0.518648\pi$
$739$	−3.18335	−0.117101	−0.0585506	+	0.998284i	$0.518648\pi$
$740$	0	0
$741$	−17.2111	−0.632266
$742$	− 7.39445i	− 0.271459i
$743$	− 27.6333i	− 1.01377i	−0.862014	−	0.506884i	$-0.830797\pi$
$743$	− 27.6333i	− 1.01377i	0.862014	−	0.506884i	$-0.169203\pi$
$744$	21.6333	0.793116
$745$	0	0
$746$	−2.30278	−0.0843106
$747$	3.21110i	0.117488i
$748$	− 45.6333i	− 1.66852i
$749$	0	0
$750$	0	0
$751$	−0.366692	−0.0133808	−0.00669040	−	0.999978i	$-0.502130\pi$
$751$	−0.366692	−0.0133808	−0.00669040	+	0.999978i	$0.502130\pi$
$752$	− 3.21110i	− 0.117097i
$753$	− 13.8167i	− 0.503507i
$754$	−45.6333	−1.66187
$755$	0	0
$756$	3.30278	0.120121
$757$	− 41.0000i	− 1.49017i	−0.666969	−	0.745085i	$-0.732409\pi$
$757$	− 41.0000i	− 1.49017i	0.666969	−	0.745085i	$-0.267591\pi$
$758$	− 34.1194i	− 1.23927i
$759$	−18.6333	−0.676346
$760$	0	0
$761$	−27.6333	−1.00171	−0.500853	−	0.865532i	$-0.666980\pi$
$761$	−27.6333	−1.00171	−0.500853	+	0.865532i	$0.666980\pi$
$762$	− 29.5139i	− 1.06917i
$763$	2.21110i	0.0800473i
$764$	9.21110	0.333246
$765$	0	0
$766$	−60.4222	−2.18314
$767$	− 27.6333i	− 0.997781i
$768$	− 17.9083i	− 0.646211i
$769$	31.6333	1.14073	0.570363	−	0.821393i	$-0.306802\pi$
$769$	31.6333	1.14073	0.570363	+	0.821393i	$0.306802\pi$
$770$	0	0
$771$	−21.6333	−0.779105
$772$	− 27.1194i	− 0.976050i
$773$	6.00000i	0.215805i	0.994161	+	0.107903i	$0.0344134\pi$
$773$	6.00000i	0.215805i	−0.994161	+	0.107903i	$0.965587\pi$
$774$	−22.1194	−0.795066
$775$	0	0
$776$	−2.36669	−0.0849593
$777$	4.21110i	0.151072i
$778$	− 66.3583i	− 2.37906i
$779$	0	0
$780$	0	0
$781$	9.00000	0.322045
$782$	65.8722i	2.35558i
$783$	− 7.60555i	− 0.271800i
$784$	−0.302776	−0.0108134
$785$	0	0
$786$	−17.0278	−0.607360
$787$	− 28.2389i	− 1.00661i	−0.864110	−	0.503303i	$-0.832118\pi$
$787$	− 28.2389i	− 1.00661i	0.864110	−	0.503303i	$-0.167882\pi$
$788$	55.5416i	1.97859i
$789$	5.78890	0.206090
$790$	0	0
$791$	−10.8167	−0.384596
$792$	9.00000i	0.319801i
$793$	3.15559i	0.112058i
$794$	−4.60555	−0.163445
$795$	0	0
$796$	26.4222	0.936510
$797$	29.4500i	1.04317i	0.853199	+	0.521586i	$0.174659\pi$
$797$	29.4500i	1.04317i	−0.853199	+	0.521586i	$0.825341\pi$
$798$	15.2111i	0.538467i
$799$	−48.8444	−1.72799
$800$	0	0
$801$	7.81665	0.276188
$802$	38.7250i	1.36743i
$803$	− 1.81665i	− 0.0641083i
$804$	−51.5416	−1.81773
$805$	0	0
$806$	43.2666	1.52400
$807$	3.21110i	0.113036i
$808$	49.8167i	1.75254i
$809$	−32.4500	−1.14088	−0.570440	−	0.821339i	$-0.693227\pi$
$809$	−32.4500	−1.14088	−0.570440	+	0.821339i	$0.693227\pi$
$810$	0	0
$811$	14.8444	0.521258	0.260629	−	0.965439i	$-0.416070\pi$
$811$	14.8444	0.521258	0.260629	+	0.965439i	$0.416070\pi$
$812$	25.1194i	0.881519i
$813$	− 26.6056i	− 0.933097i
$814$	−29.0917	−1.01966
$815$	0	0
$816$	1.39445	0.0488155
$817$	− 63.4500i	− 2.21983i
$818$	− 27.2111i	− 0.951414i
$819$	2.60555	0.0910453
$820$	0	0
$821$	49.2666	1.71942	0.859708	−	0.510785i	$-0.170645\pi$
$821$	49.2666	1.71942	0.859708	+	0.510785i	$0.170645\pi$
$822$	7.39445i	0.257911i
$823$	24.8167i	0.865054i	0.901621	+	0.432527i	$0.142378\pi$
$823$	24.8167i	0.865054i	−0.901621	+	0.432527i	$0.857622\pi$
$824$	−11.4500	−0.398878
$825$	0	0
$826$	−24.4222	−0.849757
$827$	30.6333i	1.06522i	0.846359	+	0.532612i	$0.178790\pi$
$827$	30.6333i	1.06522i	−0.846359	+	0.532612i	$0.821210\pi$
$828$	− 20.5139i	− 0.712907i
$829$	0.238859	0.00829591	0.00414796	−	0.999991i	$-0.498680\pi$
$829$	0.238859	0.00829591	0.00414796	+	0.999991i	$0.498680\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	− 33.3944i	− 1.15774i
$833$	4.60555i	0.159573i
$834$	−43.8167	−1.51725
$835$	0	0
$836$	−65.4500	−2.26363
$837$	7.21110i	0.249252i
$838$	13.8167i	0.477288i
$839$	22.1833	0.765854	0.382927	−	0.923779i	$-0.374916\pi$
$839$	22.1833	0.765854	0.382927	+	0.923779i	$0.374916\pi$
$840$	0	0
$841$	28.8444	0.994635
$842$	23.5139i	0.810342i
$843$	− 1.18335i	− 0.0407566i
$844$	−87.2666	−3.00384
$845$	0	0
$846$	24.4222	0.839653
$847$	2.00000i	0.0687208i
$848$	0.972244i	0.0333870i
$849$	13.6333	0.467894
$850$	0	0
$851$	26.1556	0.896602
$852$	9.90833i	0.339454i
$853$	− 6.78890i	− 0.232447i	−0.993223	−	0.116224i	$-0.962921\pi$
$853$	− 6.78890i	− 0.232447i	0.993223	−	0.116224i	$-0.0370790\pi$
$854$	2.78890	0.0954341
$855$	0	0
$856$	0	0
$857$	− 27.6333i	− 0.943936i	−0.881616	−	0.471968i	$-0.843544\pi$
$857$	− 27.6333i	− 0.943936i	0.881616	−	0.471968i	$-0.156456\pi$
$858$	18.0000i	0.614510i
$859$	49.6333	1.69347	0.846733	−	0.532018i	$-0.178566\pi$
$859$	49.6333	1.69347	0.846733	+	0.532018i	$0.178566\pi$
$860$	0	0
$861$	0	0
$862$	− 12.8444i	− 0.437482i
$863$	5.36669i	0.182684i	0.995820	+	0.0913422i	$0.0291157\pi$
$863$	5.36669i	0.182684i	−0.995820	+	0.0913422i	$0.970884\pi$
$864$	5.30278	0.180404
$865$	0	0
$866$	−85.6888	−2.91182
$867$	− 4.21110i	− 0.143017i
$868$	− 23.8167i	− 0.808390i
$869$	−44.4500	−1.50786
$870$	0	0
$871$	−40.6611	−1.37775
$872$	− 6.63331i	− 0.224632i
$873$	− 0.788897i	− 0.0267001i
$874$	94.4777	3.19576
$875$	0	0
$876$	2.00000	0.0675737
$877$	22.0000i	0.742887i	0.928456	+	0.371444i	$0.121137\pi$
$877$	22.0000i	0.742887i	−0.928456	+	0.371444i	$0.878863\pi$
$878$	15.2111i	0.513350i
$879$	−10.6056	−0.357716
$880$	0	0
$881$	33.6333	1.13313	0.566567	−	0.824015i	$-0.308271\pi$
$881$	33.6333	1.13313	0.566567	+	0.824015i	$0.308271\pi$
$882$	− 2.30278i	− 0.0775385i
$883$	15.6056i	0.525169i	0.964909	+	0.262584i	$0.0845748\pi$
$883$	15.6056i	0.525169i	−0.964909	+	0.262584i	$0.915425\pi$
$884$	39.6333	1.33301
$885$	0	0
$886$	36.0000	1.20944
$887$	14.7889i	0.496563i	0.968688	+	0.248281i	$0.0798657\pi$
$887$	14.7889i	0.496563i	−0.968688	+	0.248281i	$0.920134\pi$
$888$	− 12.6333i	− 0.423946i
$889$	−12.8167	−0.429857
$890$	0	0
$891$	−3.00000	−0.100504
$892$	− 50.8444i	− 1.70240i
$893$	70.0555i	2.34432i
$894$	37.7527	1.26264
$895$	0	0
$896$	−18.9083	−0.631683
$897$	− 16.1833i	− 0.540346i
$898$	− 80.1749i	− 2.67547i
$899$	−54.8444	−1.82916
$900$	0	0
$901$	14.7889	0.492690
$902$	0	0
$903$	9.60555i	0.319653i
$904$	32.4500	1.07927
$905$	0	0
$906$	15.6972	0.521505
$907$	13.2111i	0.438667i	0.975650	+	0.219334i	$0.0703883\pi$
$907$	13.2111i	0.438667i	−0.975650	+	0.219334i	$0.929612\pi$
$908$	74.6611i	2.47771i
$909$	−16.6056	−0.550771
$910$	0	0
$911$	15.0000	0.496972	0.248486	−	0.968635i	$-0.420067\pi$
$911$	15.0000	0.496972	0.248486	+	0.968635i	$0.420067\pi$
$912$	− 2.00000i	− 0.0662266i
$913$	9.63331i	0.318816i
$914$	8.72498	0.288597
$915$	0	0
$916$	−23.8167	−0.786924
$917$	7.39445i	0.244186i
$918$	10.6056i	0.350035i
$919$	17.6056	0.580754	0.290377	−	0.956912i	$-0.406219\pi$
$919$	17.6056	0.580754	0.290377	+	0.956912i	$0.406219\pi$
$920$	0	0
$921$	−8.60555	−0.283563
$922$	60.4222i	1.98990i
$923$	7.81665i	0.257288i
$924$	9.90833	0.325960
$925$	0	0
$926$	39.6333	1.30243
$927$	− 3.81665i	− 0.125355i
$928$	40.3305i	1.32391i
$929$	20.2389	0.664015	0.332008	−	0.943277i	$-0.392274\pi$
$929$	20.2389	0.664015	0.332008	+	0.943277i	$0.392274\pi$
$930$	0	0
$931$	6.60555	0.216488
$932$	3.90833i	0.128022i
$933$	13.8167i	0.452337i
$934$	0.972244	0.0318128
$935$	0	0
$936$	−7.81665	−0.255495
$937$	56.4777i	1.84505i	0.385941	+	0.922523i	$0.373877\pi$
$937$	56.4777i	1.84505i	−0.385941	+	0.922523i	$0.626123\pi$
$938$	35.9361i	1.17335i
$939$	23.8167	0.777227
$940$	0	0
$941$	6.00000	0.195594	0.0977972	−	0.995206i	$-0.468820\pi$
$941$	6.00000	0.195594	0.0977972	+	0.995206i	$0.468820\pi$
$942$	− 33.2111i	− 1.08208i
$943$	0	0
$944$	3.21110	0.104512
$945$	0	0
$946$	−66.3583	−2.15749
$947$	0.844410i	0.0274396i	0.999906	+	0.0137198i	$0.00436729\pi$
$947$	0.844410i	0.0274396i	−0.999906	+	0.0137198i	$0.995633\pi$
$948$	− 48.9361i	− 1.58937i
$949$	1.57779	0.0512174
$950$	0	0
$951$	−16.3944	−0.531626
$952$	− 13.8167i	− 0.447800i
$953$	− 13.6056i	− 0.440727i	−0.975418	−	0.220364i	$-0.929276\pi$
$953$	− 13.6056i	− 0.440727i	0.975418	−	0.220364i	$-0.0707244\pi$
$954$	−7.39445	−0.239404
$955$	0	0
$956$	48.8444	1.57974
$957$	− 22.8167i	− 0.737558i
$958$	79.6888i	2.57463i
$959$	3.21110	0.103692
$960$	0	0
$961$	21.0000	0.677419
$962$	− 25.2666i	− 0.814628i
$963$	0	0
$964$	−31.0278	−0.999337
$965$	0	0
$966$	−14.3028	−0.460184
$967$	40.8444i	1.31347i	0.754122	+	0.656734i	$0.228063\pi$
$967$	40.8444i	1.31347i	−0.754122	+	0.656734i	$0.771937\pi$
$968$	− 6.00000i	− 0.192847i
$969$	−30.4222	−0.977302
$970$	0	0
$971$	53.8722	1.72884	0.864420	−	0.502770i	$-0.167686\pi$
$971$	53.8722	1.72884	0.864420	+	0.502770i	$0.167686\pi$
$972$	− 3.30278i	− 0.105937i
$973$	19.0278i	0.610002i
$974$	47.9361	1.53597
$975$	0	0
$976$	−0.366692	−0.0117375
$977$	2.02776i	0.0648737i	0.999474	+	0.0324368i	$0.0103268\pi$
$977$	2.02776i	0.0648737i	−0.999474	+	0.0324368i	$0.989673\pi$
$978$	39.6333i	1.26733i
$979$	23.4500	0.749464
$980$	0	0
$981$	2.21110	0.0705951
$982$	6.90833i	0.220454i
$983$	40.0555i	1.27757i	0.769384	+	0.638786i	$0.220563\pi$
$983$	40.0555i	1.27757i	−0.769384	+	0.638786i	$0.779437\pi$
$984$	0	0
$985$	0	0
$986$	−80.6611	−2.56877
$987$	− 10.6056i	− 0.337578i
$988$	− 56.8444i	− 1.80846i
$989$	59.6611	1.89711
$990$	0	0
$991$	46.0278	1.46212	0.731060	−	0.682313i	$-0.239026\pi$
$991$	46.0278	1.46212	0.731060	+	0.682313i	$0.239026\pi$
$992$	− 38.2389i	− 1.21408i
$993$	− 21.2389i	− 0.673995i
$994$	6.90833	0.219119
$995$	0	0
$996$	−10.6056	−0.336050
$997$	15.4500i	0.489305i	0.969611	+	0.244653i	$0.0786739\pi$
$997$	15.4500i	0.489305i	−0.969611	+	0.244653i	$0.921326\pi$
$998$	− 64.4777i	− 2.04101i
$999$	4.21110	0.133233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.d.d.274.1		4
3.2	odd	2		1575.2.d.g.1324.4		4
5.2	odd	4		525.2.a.h.1.2	yes	2
5.3	odd	4		525.2.a.f.1.1	✓	2
5.4	even	2	inner	525.2.d.d.274.4		4
15.2	even	4		1575.2.a.o.1.1		2
15.8	even	4		1575.2.a.t.1.2		2
15.14	odd	2		1575.2.d.g.1324.1		4
20.3	even	4		8400.2.a.df.1.2		2
20.7	even	4		8400.2.a.cw.1.1		2
35.13	even	4		3675.2.a.w.1.1		2
35.27	even	4		3675.2.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.a.f.1.1	✓	2	5.3	odd	4
525.2.a.h.1.2	yes	2	5.2	odd	4
525.2.d.d.274.1		4	1.1	even	1	trivial
525.2.d.d.274.4		4	5.4	even	2	inner
1575.2.a.o.1.1		2	15.2	even	4
1575.2.a.t.1.2		2	15.8	even	4
1575.2.d.g.1324.1		4	15.14	odd	2
1575.2.d.g.1324.4		4	3.2	odd	2
3675.2.a.w.1.1		2	35.13	even	4
3675.2.a.bb.1.2		2	35.27	even	4
8400.2.a.cw.1.1		2	20.7	even	4
8400.2.a.df.1.2		2	20.3	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.30278i q^{2} +1.00000i q^{3} -3.30278 q^{4} +2.30278 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.30278i q^{2} +1.00000i q^{3} -3.30278 q^{4} +2.30278 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} -3.00000 q^{11} -3.30278i q^{12} -2.60555i q^{13} -2.30278 q^{14} +0.302776 q^{16} -4.60555i q^{17} +2.30278i q^{18} -6.60555 q^{19} +1.00000 q^{21} +6.90833i q^{22} -6.21110i q^{23} -3.00000 q^{24} -6.00000 q^{26} -1.00000i q^{27} +3.30278i q^{28} +7.60555 q^{29} -7.21110 q^{31} +5.30278i q^{32} -3.00000i q^{33} -10.6056 q^{34} +3.30278 q^{36} +4.21110i q^{37} +15.2111i q^{38} +2.60555 q^{39} -2.30278i q^{42} +9.60555i q^{43} +9.90833 q^{44} -14.3028 q^{46} -10.6056i q^{47} +0.302776i q^{48} -1.00000 q^{49} +4.60555 q^{51} +8.60555i q^{52} +3.21110i q^{53} -2.30278 q^{54} +3.00000 q^{56} -6.60555i q^{57} -17.5139i q^{58} +10.6056 q^{59} -1.21110 q^{61} +16.6056i q^{62} +1.00000i q^{63} +12.8167 q^{64} -6.90833 q^{66} -15.6056i q^{67} +15.2111i q^{68} +6.21110 q^{69} -3.00000 q^{71} -3.00000i q^{72} +0.605551i q^{73} +9.69722 q^{74} +21.8167 q^{76} +3.00000i q^{77} -6.00000i q^{78} +14.8167 q^{79} +1.00000 q^{81} -3.21110i q^{83} -3.30278 q^{84} +22.1194 q^{86} +7.60555i q^{87} -9.00000i q^{88} -7.81665 q^{89} -2.60555 q^{91} +20.5139i q^{92} -7.21110i q^{93} -24.4222 q^{94} -5.30278 q^{96} +0.788897i q^{97} +2.30278i q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 6 * q^4 + 2 * q^6 - 4 * q^9	\( 4 q - 6 q^{4} + 2 q^{6} - 4 q^{9} - 12 q^{11} - 2 q^{14} - 6 q^{16} - 12 q^{19} + 4 q^{21} - 12 q^{24} - 24 q^{26} + 16 q^{29} - 28 q^{34} + 6 q^{36} - 4 q^{39} + 18 q^{44} - 50 q^{46} - 4 q^{49} + 4 q^{51} - 2 q^{54} + 12 q^{56} + 28 q^{59} + 24 q^{61} + 8 q^{64} - 6 q^{66} - 4 q^{69} - 12 q^{71} + 46 q^{74} + 44 q^{76} + 16 q^{79} + 4 q^{81} - 6 q^{84} + 38 q^{86} + 12 q^{89} + 4 q^{91} - 40 q^{94} - 14 q^{96} + 12 q^{99}+O(q^{100}) \) 4 * q - 6 * q^4 + 2 * q^6 - 4 * q^9 - 12 * q^11 - 2 * q^14 - 6 * q^16 - 12 * q^19 + 4 * q^21 - 12 * q^24 - 24 * q^26 + 16 * q^29 - 28 * q^34 + 6 * q^36 - 4 * q^39 + 18 * q^44 - 50 * q^46 - 4 * q^49 + 4 * q^51 - 2 * q^54 + 12 * q^56 + 28 * q^59 + 24 * q^61 + 8 * q^64 - 6 * q^66 - 4 * q^69 - 12 * q^71 + 46 * q^74 + 44 * q^76 + 16 * q^79 + 4 * q^81 - 6 * q^84 + 38 * q^86 + 12 * q^89 + 4 * q^91 - 40 * q^94 - 14 * q^96 + 12 * q^99

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