LMFDB - Embedded newform 3750.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.a (trivial)

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:	yes
Analytic conductor:	$29.9439007580$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.71684000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 18x^{6} + 10x^{5} + 101x^{4} + 40x^{3} - 132x^{2} - 96x - 4 $ x^8 - 2x^7 - 18x^6 + 10x^5 + 101x^4 + 40x^3 - 132x^2 - 96*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 150)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.65651$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -3.23143 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -3.23143 q^{7} -1.00000 q^{8} +1.00000 q^{9} +5.30029 q^{11} -1.00000 q^{12} -5.90441 q^{13} +3.23143 q^{14} +1.00000 q^{16} -1.02469 q^{17} -1.00000 q^{18} -4.50718 q^{19} +3.23143 q^{21} -5.30029 q^{22} -1.92827 q^{23} +1.00000 q^{24} +5.90441 q^{26} -1.00000 q^{27} -3.23143 q^{28} -0.260762 q^{29} -2.24205 q^{31} -1.00000 q^{32} -5.30029 q^{33} +1.02469 q^{34} +1.00000 q^{36} +9.55354 q^{37} +4.50718 q^{38} +5.90441 q^{39} -9.96112 q^{41} -3.23143 q^{42} +5.30164 q^{43} +5.30029 q^{44} +1.92827 q^{46} +10.5282 q^{47} -1.00000 q^{48} +3.44213 q^{49} +1.02469 q^{51} -5.90441 q^{52} +2.31107 q^{53} +1.00000 q^{54} +3.23143 q^{56} +4.50718 q^{57} +0.260762 q^{58} -6.49202 q^{59} -3.94494 q^{61} +2.24205 q^{62} -3.23143 q^{63} +1.00000 q^{64} +5.30029 q^{66} -9.29210 q^{67} -1.02469 q^{68} +1.92827 q^{69} +8.53771 q^{71} -1.00000 q^{72} -3.95422 q^{73} -9.55354 q^{74} -4.50718 q^{76} -17.1275 q^{77} -5.90441 q^{78} -13.3714 q^{79} +1.00000 q^{81} +9.96112 q^{82} -7.48698 q^{83} +3.23143 q^{84} -5.30164 q^{86} +0.260762 q^{87} -5.30029 q^{88} -0.733574 q^{89} +19.0797 q^{91} -1.92827 q^{92} +2.24205 q^{93} -10.5282 q^{94} +1.00000 q^{96} +17.2567 q^{97} -3.44213 q^{98} +5.30029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{11} - 8 q^{12} - 2 q^{13} + 4 q^{14} + 8 q^{16} - 14 q^{17} - 8 q^{18} + 10 q^{19} + 4 q^{21} - 6 q^{22} - 12 q^{23} + 8 q^{24} + 2 q^{26} - 8 q^{27} - 4 q^{28} + 10 q^{29} + 16 q^{31} - 8 q^{32} - 6 q^{33} + 14 q^{34} + 8 q^{36} + 6 q^{37} - 10 q^{38} + 2 q^{39} + 6 q^{41} - 4 q^{42} - 2 q^{43} + 6 q^{44} + 12 q^{46} - 14 q^{47} - 8 q^{48} + 26 q^{49} + 14 q^{51} - 2 q^{52} - 12 q^{53} + 8 q^{54} + 4 q^{56} - 10 q^{57} - 10 q^{58} + 16 q^{61} - 16 q^{62} - 4 q^{63} + 8 q^{64} + 6 q^{66} + 6 q^{67} - 14 q^{68} + 12 q^{69} + 6 q^{71} - 8 q^{72} + 8 q^{73} - 6 q^{74} + 10 q^{76} - 8 q^{77} - 2 q^{78} + 10 q^{79} + 8 q^{81} - 6 q^{82} - 22 q^{83} + 4 q^{84} + 2 q^{86} - 10 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{91} - 12 q^{92} - 16 q^{93} + 14 q^{94} + 8 q^{96} + 16 q^{97} - 26 q^{98} + 6 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^11 - 8 * q^12 - 2 * q^13 + 4 * q^14 + 8 * q^16 - 14 * q^17 - 8 * q^18 + 10 * q^19 + 4 * q^21 - 6 * q^22 - 12 * q^23 + 8 * q^24 + 2 * q^26 - 8 * q^27 - 4 * q^28 + 10 * q^29 + 16 * q^31 - 8 * q^32 - 6 * q^33 + 14 * q^34 + 8 * q^36 + 6 * q^37 - 10 * q^38 + 2 * q^39 + 6 * q^41 - 4 * q^42 - 2 * q^43 + 6 * q^44 + 12 * q^46 - 14 * q^47 - 8 * q^48 + 26 * q^49 + 14 * q^51 - 2 * q^52 - 12 * q^53 + 8 * q^54 + 4 * q^56 - 10 * q^57 - 10 * q^58 + 16 * q^61 - 16 * q^62 - 4 * q^63 + 8 * q^64 + 6 * q^66 + 6 * q^67 - 14 * q^68 + 12 * q^69 + 6 * q^71 - 8 * q^72 + 8 * q^73 - 6 * q^74 + 10 * q^76 - 8 * q^77 - 2 * q^78 + 10 * q^79 + 8 * q^81 - 6 * q^82 - 22 * q^83 + 4 * q^84 + 2 * q^86 - 10 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^91 - 12 * q^92 - 16 * q^93 + 14 * q^94 + 8 * q^96 + 16 * q^97 - 26 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−3.23143	−1.22136	−0.610682	−	0.791876i	$-0.709105\pi$
$7$	−3.23143	−1.22136	−0.610682	+	0.791876i	$0.709105\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	5.30029	1.59810	0.799048	−	0.601267i	$-0.205337\pi$
$11$	5.30029	1.59810	0.799048	+	0.601267i	$0.205337\pi$
$12$	−1.00000	−0.288675
$13$	−5.90441	−1.63759	−0.818795	−	0.574087i	$-0.805357\pi$
$13$	−5.90441	−1.63759	−0.818795	+	0.574087i	$0.805357\pi$
$14$	3.23143	0.863635
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.02469	−0.248525	−0.124262	−	0.992249i	$-0.539656\pi$
$17$	−1.02469	−0.248525	−0.124262	+	0.992249i	$0.539656\pi$
$18$	−1.00000	−0.235702
$19$	−4.50718	−1.03402	−0.517010	−	0.855980i	$-0.672955\pi$
$19$	−4.50718	−1.03402	−0.517010	+	0.855980i	$0.672955\pi$
$20$	0	0
$21$	3.23143	0.705155
$22$	−5.30029	−1.13002
$23$	−1.92827	−0.402073	−0.201037	−	0.979584i	$-0.564431\pi$
$23$	−1.92827	−0.402073	−0.201037	+	0.979584i	$0.564431\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	5.90441	1.15795
$27$	−1.00000	−0.192450
$28$	−3.23143	−0.610682
$29$	−0.260762	−0.0484222	−0.0242111	−	0.999707i	$-0.507707\pi$
$29$	−0.260762	−0.0484222	−0.0242111	+	0.999707i	$0.507707\pi$
$30$	0	0
$31$	−2.24205	−0.402684	−0.201342	−	0.979521i	$-0.564530\pi$
$31$	−2.24205	−0.402684	−0.201342	+	0.979521i	$0.564530\pi$
$32$	−1.00000	−0.176777
$33$	−5.30029	−0.922661
$34$	1.02469	0.175734
$35$	0	0
$36$	1.00000	0.166667
$37$	9.55354	1.57059	0.785296	−	0.619120i	$-0.212511\pi$
$37$	9.55354	1.57059	0.785296	+	0.619120i	$0.212511\pi$
$38$	4.50718	0.731162
$39$	5.90441	0.945463
$40$	0	0
$41$	−9.96112	−1.55567	−0.777833	−	0.628471i	$-0.783681\pi$
$41$	−9.96112	−1.55567	−0.777833	+	0.628471i	$0.783681\pi$
$42$	−3.23143	−0.498620
$43$	5.30164	0.808492	0.404246	−	0.914650i	$-0.367534\pi$
$43$	5.30164	0.808492	0.404246	+	0.914650i	$0.367534\pi$
$44$	5.30029	0.799048
$45$	0	0
$46$	1.92827	0.284309
$47$	10.5282	1.53569	0.767846	−	0.640635i	$-0.221329\pi$
$47$	10.5282	1.53569	0.767846	+	0.640635i	$0.221329\pi$
$48$	−1.00000	−0.144338
$49$	3.44213	0.491732
$50$	0	0
$51$	1.02469	0.143486
$52$	−5.90441	−0.818795
$53$	2.31107	0.317450	0.158725	−	0.987323i	$-0.449262\pi$
$53$	2.31107	0.317450	0.158725	+	0.987323i	$0.449262\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	3.23143	0.431818
$57$	4.50718	0.596991
$58$	0.260762	0.0342397
$59$	−6.49202	−0.845190	−0.422595	−	0.906319i	$-0.638881\pi$
$59$	−6.49202	−0.845190	−0.422595	+	0.906319i	$0.638881\pi$
$60$	0	0
$61$	−3.94494	−0.505098	−0.252549	−	0.967584i	$-0.581269\pi$
$61$	−3.94494	−0.505098	−0.252549	+	0.967584i	$0.581269\pi$
$62$	2.24205	0.284741
$63$	−3.23143	−0.407122
$64$	1.00000	0.125000
$65$	0	0
$66$	5.30029	0.652420
$67$	−9.29210	−1.13521	−0.567605	−	0.823301i	$-0.692130\pi$
$67$	−9.29210	−1.13521	−0.567605	+	0.823301i	$0.692130\pi$
$68$	−1.02469	−0.124262
$69$	1.92827	0.232137
$70$	0	0
$71$	8.53771	1.01324	0.506620	−	0.862170i	$-0.330895\pi$
$71$	8.53771	1.01324	0.506620	+	0.862170i	$0.330895\pi$
$72$	−1.00000	−0.117851
$73$	−3.95422	−0.462806	−0.231403	−	0.972858i	$-0.574332\pi$
$73$	−3.95422	−0.462806	−0.231403	+	0.972858i	$0.574332\pi$
$74$	−9.55354	−1.11058
$75$	0	0
$76$	−4.50718	−0.517010
$77$	−17.1275	−1.95186
$78$	−5.90441	−0.668543
$79$	−13.3714	−1.50440	−0.752199	−	0.658936i	$-0.771007\pi$
$79$	−13.3714	−1.50440	−0.752199	+	0.658936i	$0.771007\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	9.96112	1.10002
$83$	−7.48698	−0.821803	−0.410901	−	0.911680i	$-0.634786\pi$
$83$	−7.48698	−0.821803	−0.410901	+	0.911680i	$0.634786\pi$
$84$	3.23143	0.352578
$85$	0	0
$86$	−5.30164	−0.571691
$87$	0.260762	0.0279566
$88$	−5.30029	−0.565012
$89$	−0.733574	−0.0777587	−0.0388794	−	0.999244i	$-0.512379\pi$
$89$	−0.733574	−0.0777587	−0.0388794	+	0.999244i	$0.512379\pi$
$90$	0	0
$91$	19.0797	2.00009
$92$	−1.92827	−0.201037
$93$	2.24205	0.232490
$94$	−10.5282	−1.08590
$95$	0	0
$96$	1.00000	0.102062
$97$	17.2567	1.75215	0.876075	−	0.482174i	$-0.160153\pi$
$97$	17.2567	1.75215	0.876075	+	0.482174i	$0.160153\pi$
$98$	−3.44213	−0.347707
$99$	5.30029	0.532699
$100$	0	0
$101$	11.8454	1.17866	0.589331	−	0.807892i	$-0.299391\pi$
$101$	11.8454	1.17866	0.589331	+	0.807892i	$0.299391\pi$
$102$	−1.02469	−0.101460
$103$	7.15084	0.704593	0.352297	−	0.935888i	$-0.385401\pi$
$103$	7.15084	0.704593	0.352297	+	0.935888i	$0.385401\pi$
$104$	5.90441	0.578975
$105$	0	0
$106$	−2.31107	−0.224471
$107$	−3.20058	−0.309412	−0.154706	−	0.987961i	$-0.549443\pi$
$107$	−3.20058	−0.309412	−0.154706	+	0.987961i	$0.549443\pi$
$108$	−1.00000	−0.0962250
$109$	9.89555	0.947822	0.473911	−	0.880573i	$-0.342842\pi$
$109$	9.89555	0.947822	0.473911	+	0.880573i	$0.342842\pi$
$110$	0	0
$111$	−9.55354	−0.906782
$112$	−3.23143	−0.305341
$113$	4.24575	0.399406	0.199703	−	0.979856i	$-0.436002\pi$
$113$	4.24575	0.399406	0.199703	+	0.979856i	$0.436002\pi$
$114$	−4.50718	−0.422137
$115$	0	0
$116$	−0.260762	−0.0242111
$117$	−5.90441	−0.545863
$118$	6.49202	0.597639
$119$	3.31122	0.303539
$120$	0	0
$121$	17.0930	1.55391
$122$	3.94494	0.357158
$123$	9.96112	0.898164
$124$	−2.24205	−0.201342
$125$	0	0
$126$	3.23143	0.287878
$127$	9.25090	0.820884	0.410442	−	0.911887i	$-0.365374\pi$
$127$	9.25090	0.820884	0.410442	+	0.911887i	$0.365374\pi$
$128$	−1.00000	−0.0883883
$129$	−5.30164	−0.466783
$130$	0	0
$131$	−4.86497	−0.425054	−0.212527	−	0.977155i	$-0.568169\pi$
$131$	−4.86497	−0.425054	−0.212527	+	0.977155i	$0.568169\pi$
$132$	−5.30029	−0.461331
$133$	14.5646	1.26291
$134$	9.29210	0.802715
$135$	0	0
$136$	1.02469	0.0878668
$137$	−6.01666	−0.514038	−0.257019	−	0.966406i	$-0.582740\pi$
$137$	−6.01666	−0.514038	−0.257019	+	0.966406i	$0.582740\pi$
$138$	−1.92827	−0.164146
$139$	−5.62720	−0.477293	−0.238646	−	0.971107i	$-0.576704\pi$
$139$	−5.62720	−0.477293	−0.238646	+	0.971107i	$0.576704\pi$
$140$	0	0
$141$	−10.5282	−0.886632
$142$	−8.53771	−0.716469
$143$	−31.2951	−2.61703
$144$	1.00000	0.0833333
$145$	0	0
$146$	3.95422	0.327253
$147$	−3.44213	−0.283902
$148$	9.55354	0.785296
$149$	−11.6556	−0.954863	−0.477432	−	0.878669i	$-0.658432\pi$
$149$	−11.6556	−0.954863	−0.477432	+	0.878669i	$0.658432\pi$
$150$	0	0
$151$	5.52354	0.449499	0.224750	−	0.974417i	$-0.427844\pi$
$151$	5.52354	0.449499	0.224750	+	0.974417i	$0.427844\pi$
$152$	4.50718	0.365581
$153$	−1.02469	−0.0828416
$154$	17.1275	1.38017
$155$	0	0
$156$	5.90441	0.472731
$157$	6.84307	0.546136	0.273068	−	0.961995i	$-0.411962\pi$
$157$	6.84307	0.546136	0.273068	+	0.961995i	$0.411962\pi$
$158$	13.3714	1.06377
$159$	−2.31107	−0.183280
$160$	0	0
$161$	6.23108	0.491078
$162$	−1.00000	−0.0785674
$163$	9.38717	0.735260	0.367630	−	0.929972i	$-0.380169\pi$
$163$	9.38717	0.735260	0.367630	+	0.929972i	$0.380169\pi$
$164$	−9.96112	−0.777833
$165$	0	0
$166$	7.48698	0.581102
$167$	−6.82883	−0.528431	−0.264215	−	0.964464i	$-0.585113\pi$
$167$	−6.82883	−0.528431	−0.264215	+	0.964464i	$0.585113\pi$
$168$	−3.23143	−0.249310
$169$	21.8621	1.68170
$170$	0	0
$171$	−4.50718	−0.344673
$172$	5.30164	0.404246
$173$	−18.8604	−1.43393	−0.716966	−	0.697108i	$-0.754470\pi$
$173$	−18.8604	−1.43393	−0.716966	+	0.697108i	$0.754470\pi$
$174$	−0.260762	−0.0197683
$175$	0	0
$176$	5.30029	0.399524
$177$	6.49202	0.487970
$178$	0.733574	0.0549837
$179$	0.941336	0.0703588	0.0351794	−	0.999381i	$-0.488800\pi$
$179$	0.941336	0.0703588	0.0351794	+	0.999381i	$0.488800\pi$
$180$	0	0
$181$	14.1057	1.04847	0.524235	−	0.851573i	$-0.324351\pi$
$181$	14.1057	1.04847	0.524235	+	0.851573i	$0.324351\pi$
$182$	−19.0797	−1.41428
$183$	3.94494	0.291618
$184$	1.92827	0.142154
$185$	0	0
$186$	−2.24205	−0.164395
$187$	−5.43117	−0.397166
$188$	10.5282	0.767846
$189$	3.23143	0.235052
$190$	0	0
$191$	25.4719	1.84308	0.921541	−	0.388280i	$-0.126931\pi$
$191$	25.4719	1.84308	0.921541	+	0.388280i	$0.126931\pi$
$192$	−1.00000	−0.0721688
$193$	6.63439	0.477554	0.238777	−	0.971074i	$-0.423254\pi$
$193$	6.63439	0.477554	0.238777	+	0.971074i	$0.423254\pi$
$194$	−17.2567	−1.23896
$195$	0	0
$196$	3.44213	0.245866
$197$	10.1777	0.725133	0.362567	−	0.931958i	$-0.381900\pi$
$197$	10.1777	0.725133	0.362567	+	0.931958i	$0.381900\pi$
$198$	−5.30029	−0.376675
$199$	−2.52238	−0.178807	−0.0894035	−	0.995995i	$-0.528496\pi$
$199$	−2.52238	−0.178807	−0.0894035	+	0.995995i	$0.528496\pi$
$200$	0	0
$201$	9.29210	0.655414
$202$	−11.8454	−0.833440
$203$	0.842633	0.0591412
$204$	1.02469	0.0717429
$205$	0	0
$206$	−7.15084	−0.498223
$207$	−1.92827	−0.134024
$208$	−5.90441	−0.409397
$209$	−23.8894	−1.65246
$210$	0	0
$211$	15.7638	1.08523	0.542613	−	0.839983i	$-0.317435\pi$
$211$	15.7638	1.08523	0.542613	+	0.839983i	$0.317435\pi$
$212$	2.31107	0.158725
$213$	−8.53771	−0.584994
$214$	3.20058	0.218787
$215$	0	0
$216$	1.00000	0.0680414
$217$	7.24502	0.491824
$218$	−9.89555	−0.670211
$219$	3.95422	0.267201
$220$	0	0
$221$	6.05021	0.406981
$222$	9.55354	0.641192
$223$	9.29534	0.622462	0.311231	−	0.950334i	$-0.399259\pi$
$223$	9.29534	0.622462	0.311231	+	0.950334i	$0.399259\pi$
$224$	3.23143	0.215909
$225$	0	0
$226$	−4.24575	−0.282423
$227$	3.63809	0.241468	0.120734	−	0.992685i	$-0.461475\pi$
$227$	3.63809	0.241468	0.120734	+	0.992685i	$0.461475\pi$
$228$	4.50718	0.298496
$229$	9.93181	0.656312	0.328156	−	0.944623i	$-0.393573\pi$
$229$	9.93181	0.656312	0.328156	+	0.944623i	$0.393573\pi$
$230$	0	0
$231$	17.1275	1.12691
$232$	0.260762	0.0171198
$233$	−18.7893	−1.23093	−0.615465	−	0.788164i	$-0.711032\pi$
$233$	−18.7893	−1.23093	−0.615465	+	0.788164i	$0.711032\pi$
$234$	5.90441	0.385984
$235$	0	0
$236$	−6.49202	−0.422595
$237$	13.3714	0.868565
$238$	−3.31122	−0.214635
$239$	−9.75186	−0.630795	−0.315398	−	0.948960i	$-0.602138\pi$
$239$	−9.75186	−0.630795	−0.315398	+	0.948960i	$0.602138\pi$
$240$	0	0
$241$	18.9211	1.21881	0.609407	−	0.792858i	$-0.291408\pi$
$241$	18.9211	1.21881	0.609407	+	0.792858i	$0.291408\pi$
$242$	−17.0930	−1.09878
$243$	−1.00000	−0.0641500
$244$	−3.94494	−0.252549
$245$	0	0
$246$	−9.96112	−0.635098
$247$	26.6123	1.69330
$248$	2.24205	0.142370
$249$	7.48698	0.474468
$250$	0	0
$251$	−1.98608	−0.125360	−0.0626801	−	0.998034i	$-0.519965\pi$
$251$	−1.98608	−0.125360	−0.0626801	+	0.998034i	$0.519965\pi$
$252$	−3.23143	−0.203561
$253$	−10.2204	−0.642551
$254$	−9.25090	−0.580453
$255$	0	0
$256$	1.00000	0.0625000
$257$	19.2797	1.20263	0.601317	−	0.799010i	$-0.294643\pi$
$257$	19.2797	1.20263	0.601317	+	0.799010i	$0.294643\pi$
$258$	5.30164	0.330066
$259$	−30.8716	−1.91827
$260$	0	0
$261$	−0.260762	−0.0161407
$262$	4.86497	0.300559
$263$	−12.5297	−0.772613	−0.386307	−	0.922370i	$-0.626249\pi$
$263$	−12.5297	−0.772613	−0.386307	+	0.922370i	$0.626249\pi$
$264$	5.30029	0.326210
$265$	0	0
$266$	−14.5646	−0.893016
$267$	0.733574	0.0448940
$268$	−9.29210	−0.567605
$269$	13.4929	0.822680	0.411340	−	0.911482i	$-0.365061\pi$
$269$	13.4929	0.822680	0.411340	+	0.911482i	$0.365061\pi$
$270$	0	0
$271$	−26.8135	−1.62880	−0.814402	−	0.580301i	$-0.802935\pi$
$271$	−26.8135	−1.62880	−0.814402	+	0.580301i	$0.802935\pi$
$272$	−1.02469	−0.0621312
$273$	−19.0797	−1.15475
$274$	6.01666	0.363480
$275$	0	0
$276$	1.92827	0.116068
$277$	−8.16724	−0.490722	−0.245361	−	0.969432i	$-0.578906\pi$
$277$	−8.16724	−0.490722	−0.245361	+	0.969432i	$0.578906\pi$
$278$	5.62720	0.337497
$279$	−2.24205	−0.134228
$280$	0	0
$281$	31.3418	1.86970	0.934848	−	0.355049i	$-0.115536\pi$
$281$	31.3418	1.86970	0.934848	+	0.355049i	$0.115536\pi$
$282$	10.5282	0.626943
$283$	16.3503	0.971927	0.485964	−	0.873979i	$-0.338469\pi$
$283$	16.3503	0.971927	0.485964	+	0.873979i	$0.338469\pi$
$284$	8.53771	0.506620
$285$	0	0
$286$	31.2951	1.85052
$287$	32.1886	1.90004
$288$	−1.00000	−0.0589256
$289$	−15.9500	−0.938235
$290$	0	0
$291$	−17.2567	−1.01160
$292$	−3.95422	−0.231403
$293$	28.1867	1.64669	0.823343	−	0.567545i	$-0.192107\pi$
$293$	28.1867	1.64669	0.823343	+	0.567545i	$0.192107\pi$
$294$	3.44213	0.200749
$295$	0	0
$296$	−9.55354	−0.555288
$297$	−5.30029	−0.307554
$298$	11.6556	0.675190
$299$	11.3853	0.658431
$300$	0	0
$301$	−17.1319	−0.987464
$302$	−5.52354	−0.317844
$303$	−11.8454	−0.680501
$304$	−4.50718	−0.258505
$305$	0	0
$306$	1.02469	0.0585778
$307$	14.5372	0.829680	0.414840	−	0.909894i	$-0.363837\pi$
$307$	14.5372	0.829680	0.414840	+	0.909894i	$0.363837\pi$
$308$	−17.1275	−0.975929
$309$	−7.15084	−0.406797
$310$	0	0
$311$	14.4924	0.821791	0.410896	−	0.911682i	$-0.365216\pi$
$311$	14.4924	0.821791	0.410896	+	0.911682i	$0.365216\pi$
$312$	−5.90441	−0.334272
$313$	31.5288	1.78211	0.891057	−	0.453892i	$-0.149965\pi$
$313$	31.5288	1.78211	0.891057	+	0.453892i	$0.149965\pi$
$314$	−6.84307	−0.386177
$315$	0	0
$316$	−13.3714	−0.752199
$317$	14.9810	0.841419	0.420710	−	0.907195i	$-0.361781\pi$
$317$	14.9810	0.841419	0.420710	+	0.907195i	$0.361781\pi$
$318$	2.31107	0.129598
$319$	−1.38211	−0.0773834
$320$	0	0
$321$	3.20058	0.178639
$322$	−6.23108	−0.347245
$323$	4.61848	0.256979
$324$	1.00000	0.0555556
$325$	0	0
$326$	−9.38717	−0.519907
$327$	−9.89555	−0.547225
$328$	9.96112	0.550011
$329$	−34.0210	−1.87564
$330$	0	0
$331$	−21.6174	−1.18820	−0.594100	−	0.804391i	$-0.702492\pi$
$331$	−21.6174	−1.18820	−0.594100	+	0.804391i	$0.702492\pi$
$332$	−7.48698	−0.410901
$333$	9.55354	0.523531
$334$	6.82883	0.373657
$335$	0	0
$336$	3.23143	0.176289
$337$	7.59495	0.413723	0.206862	−	0.978370i	$-0.433675\pi$
$337$	7.59495	0.413723	0.206862	+	0.978370i	$0.433675\pi$
$338$	−21.8621	−1.18914
$339$	−4.24575	−0.230597
$340$	0	0
$341$	−11.8835	−0.643528
$342$	4.50718	0.243721
$343$	11.4970	0.620780
$344$	−5.30164	−0.285845
$345$	0	0
$346$	18.8604	1.01394
$347$	7.53304	0.404395	0.202197	−	0.979345i	$-0.435192\pi$
$347$	7.53304	0.404395	0.202197	+	0.979345i	$0.435192\pi$
$348$	0.260762	0.0139783
$349$	18.7527	1.00381	0.501904	−	0.864923i	$-0.332633\pi$
$349$	18.7527	1.00381	0.501904	+	0.864923i	$0.332633\pi$
$350$	0	0
$351$	5.90441	0.315154
$352$	−5.30029	−0.282506
$353$	−4.36607	−0.232383	−0.116191	−	0.993227i	$-0.537069\pi$
$353$	−4.36607	−0.232383	−0.116191	+	0.993227i	$0.537069\pi$
$354$	−6.49202	−0.345047
$355$	0	0
$356$	−0.733574	−0.0388794
$357$	−3.31122	−0.175249
$358$	−0.941336	−0.0497512
$359$	0.737212	0.0389086	0.0194543	−	0.999811i	$-0.493807\pi$
$359$	0.737212	0.0389086	0.0194543	+	0.999811i	$0.493807\pi$
$360$	0	0
$361$	1.31471	0.0691954
$362$	−14.1057	−0.741381
$363$	−17.0930	−0.897151
$364$	19.0797	1.00005
$365$	0	0
$366$	−3.94494	−0.206205
$367$	−18.8600	−0.984486	−0.492243	−	0.870458i	$-0.663823\pi$
$367$	−18.8600	−0.984486	−0.492243	+	0.870458i	$0.663823\pi$
$368$	−1.92827	−0.100518
$369$	−9.96112	−0.518555
$370$	0	0
$371$	−7.46806	−0.387722
$372$	2.24205	0.116245
$373$	29.8366	1.54488	0.772441	−	0.635086i	$-0.219035\pi$
$373$	29.8366	1.54488	0.772441	+	0.635086i	$0.219035\pi$
$374$	5.43117	0.280839
$375$	0	0
$376$	−10.5282	−0.542949
$377$	1.53964	0.0792958
$378$	−3.23143	−0.166207
$379$	25.4826	1.30895	0.654477	−	0.756082i	$-0.272889\pi$
$379$	25.4826	1.30895	0.654477	+	0.756082i	$0.272889\pi$
$380$	0	0
$381$	−9.25090	−0.473938
$382$	−25.4719	−1.30326
$383$	−31.6433	−1.61690	−0.808449	−	0.588566i	$-0.799693\pi$
$383$	−31.6433	−1.61690	−0.808449	+	0.588566i	$0.799693\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−6.63439	−0.337682
$387$	5.30164	0.269497
$388$	17.2567	0.876075
$389$	12.0480	0.610858	0.305429	−	0.952215i	$-0.401200\pi$
$389$	12.0480	0.610858	0.305429	+	0.952215i	$0.401200\pi$
$390$	0	0
$391$	1.97589	0.0999251
$392$	−3.44213	−0.173854
$393$	4.86497	0.245405
$394$	−10.1777	−0.512747
$395$	0	0
$396$	5.30029	0.266349
$397$	−25.7565	−1.29268	−0.646341	−	0.763049i	$-0.723702\pi$
$397$	−25.7565	−1.29268	−0.646341	+	0.763049i	$0.723702\pi$
$398$	2.52238	0.126436
$399$	−14.5646	−0.729144
$400$	0	0
$401$	26.3196	1.31434	0.657169	−	0.753743i	$-0.271754\pi$
$401$	26.3196	1.31434	0.657169	+	0.753743i	$0.271754\pi$
$402$	−9.29210	−0.463448
$403$	13.2380	0.659431
$404$	11.8454	0.589331
$405$	0	0
$406$	−0.842633	−0.0418192
$407$	50.6365	2.50996
$408$	−1.02469	−0.0507299
$409$	36.7714	1.81823	0.909113	−	0.416549i	$-0.136761\pi$
$409$	36.7714	1.81823	0.909113	+	0.416549i	$0.136761\pi$
$410$	0	0
$411$	6.01666	0.296780
$412$	7.15084	0.352297
$413$	20.9785	1.03229
$414$	1.92827	0.0947695
$415$	0	0
$416$	5.90441	0.289488
$417$	5.62720	0.275565
$418$	23.8894	1.16847
$419$	−31.7245	−1.54984	−0.774922	−	0.632057i	$-0.782211\pi$
$419$	−31.7245	−1.54984	−0.774922	+	0.632057i	$0.782211\pi$
$420$	0	0
$421$	8.81726	0.429727	0.214864	−	0.976644i	$-0.431069\pi$
$421$	8.81726	0.429727	0.214864	+	0.976644i	$0.431069\pi$
$422$	−15.7638	−0.767371
$423$	10.5282	0.511897
$424$	−2.31107	−0.112236
$425$	0	0
$426$	8.53771	0.413653
$427$	12.7478	0.616908
$428$	−3.20058	−0.154706
$429$	31.2951	1.51094
$430$	0	0
$431$	23.5065	1.13227	0.566135	−	0.824313i	$-0.308438\pi$
$431$	23.5065	1.13227	0.566135	+	0.824313i	$0.308438\pi$
$432$	−1.00000	−0.0481125
$433$	8.40312	0.403828	0.201914	−	0.979403i	$-0.435284\pi$
$433$	8.40312	0.403828	0.201914	+	0.979403i	$0.435284\pi$
$434$	−7.24502	−0.347772
$435$	0	0
$436$	9.89555	0.473911
$437$	8.69109	0.415751
$438$	−3.95422	−0.188940
$439$	35.6325	1.70065	0.850324	−	0.526260i	$-0.176406\pi$
$439$	35.6325	1.70065	0.850324	+	0.526260i	$0.176406\pi$
$440$	0	0
$441$	3.44213	0.163911
$442$	−6.05021	−0.287779
$443$	6.79550	0.322864	0.161432	−	0.986884i	$-0.448389\pi$
$443$	6.79550	0.322864	0.161432	+	0.986884i	$0.448389\pi$
$444$	−9.55354	−0.453391
$445$	0	0
$446$	−9.29534	−0.440147
$447$	11.6556	0.551291
$448$	−3.23143	−0.152671
$449$	8.75011	0.412943	0.206472	−	0.978453i	$-0.433802\pi$
$449$	8.75011	0.412943	0.206472	+	0.978453i	$0.433802\pi$
$450$	0	0
$451$	−52.7968	−2.48610
$452$	4.24575	0.199703
$453$	−5.52354	−0.259519
$454$	−3.63809	−0.170744
$455$	0	0
$456$	−4.50718	−0.211068
$457$	−38.1474	−1.78446	−0.892230	−	0.451581i	$-0.850860\pi$
$457$	−38.1474	−1.78446	−0.892230	+	0.451581i	$0.850860\pi$
$458$	−9.93181	−0.464083
$459$	1.02469	0.0478286
$460$	0	0
$461$	−1.27077	−0.0591856	−0.0295928	−	0.999562i	$-0.509421\pi$
$461$	−1.27077	−0.0591856	−0.0295928	+	0.999562i	$0.509421\pi$
$462$	−17.1275	−0.796843
$463$	8.93349	0.415175	0.207587	−	0.978216i	$-0.433439\pi$
$463$	8.93349	0.415175	0.207587	+	0.978216i	$0.433439\pi$
$464$	−0.260762	−0.0121056
$465$	0	0
$466$	18.7893	0.870399
$467$	−5.75682	−0.266394	−0.133197	−	0.991090i	$-0.542524\pi$
$467$	−5.75682	−0.266394	−0.133197	+	0.991090i	$0.542524\pi$
$468$	−5.90441	−0.272932
$469$	30.0268	1.38651
$470$	0	0
$471$	−6.84307	−0.315312
$472$	6.49202	0.298820
$473$	28.1002	1.29205
$474$	−13.3714	−0.614168
$475$	0	0
$476$	3.31122	0.151770
$477$	2.31107	0.105817
$478$	9.75186	0.446040
$479$	−4.63051	−0.211573	−0.105787	−	0.994389i	$-0.533736\pi$
$479$	−4.63051	−0.211573	−0.105787	+	0.994389i	$0.533736\pi$
$480$	0	0
$481$	−56.4080	−2.57199
$482$	−18.9211	−0.861832
$483$	−6.23108	−0.283524
$484$	17.0930	0.776956
$485$	0	0
$486$	1.00000	0.0453609
$487$	15.9235	0.721564	0.360782	−	0.932650i	$-0.382510\pi$
$487$	15.9235	0.721564	0.360782	+	0.932650i	$0.382510\pi$
$488$	3.94494	0.178579
$489$	−9.38717	−0.424503
$490$	0	0
$491$	−6.38076	−0.287959	−0.143980	−	0.989581i	$-0.545990\pi$
$491$	−6.38076	−0.287959	−0.143980	+	0.989581i	$0.545990\pi$
$492$	9.96112	0.449082
$493$	0.267201	0.0120341
$494$	−26.6123	−1.19734
$495$	0	0
$496$	−2.24205	−0.100671
$497$	−27.5890	−1.23754
$498$	−7.48698	−0.335500
$499$	12.9135	0.578087	0.289044	−	0.957316i	$-0.406663\pi$
$499$	12.9135	0.578087	0.289044	+	0.957316i	$0.406663\pi$
$500$	0	0
$501$	6.82883	0.305090
$502$	1.98608	0.0886431
$503$	−1.45203	−0.0647429	−0.0323714	−	0.999476i	$-0.510306\pi$
$503$	−1.45203	−0.0647429	−0.0323714	+	0.999476i	$0.510306\pi$
$504$	3.23143	0.143939
$505$	0	0
$506$	10.2204	0.454352
$507$	−21.8621	−0.970929
$508$	9.25090	0.410442
$509$	−12.4097	−0.550051	−0.275026	−	0.961437i	$-0.588686\pi$
$509$	−12.4097	−0.550051	−0.275026	+	0.961437i	$0.588686\pi$
$510$	0	0
$511$	12.7778	0.565255
$512$	−1.00000	−0.0441942
$513$	4.50718	0.198997
$514$	−19.2797	−0.850391
$515$	0	0
$516$	−5.30164	−0.233392
$517$	55.8023	2.45418
$518$	30.8716	1.35642
$519$	18.8604	0.827881
$520$	0	0
$521$	7.94615	0.348127	0.174064	−	0.984734i	$-0.444310\pi$
$521$	7.94615	0.348127	0.174064	+	0.984734i	$0.444310\pi$
$522$	0.260762	0.0114132
$523$	−34.8305	−1.52303	−0.761517	−	0.648145i	$-0.775545\pi$
$523$	−34.8305	−1.52303	−0.761517	+	0.648145i	$0.775545\pi$
$524$	−4.86497	−0.212527
$525$	0	0
$526$	12.5297	0.546320
$527$	2.29741	0.100077
$528$	−5.30029	−0.230665
$529$	−19.2818	−0.838337
$530$	0	0
$531$	−6.49202	−0.281730
$532$	14.5646	0.631457
$533$	58.8146	2.54754
$534$	−0.733574	−0.0317449
$535$	0	0
$536$	9.29210	0.401358
$537$	−0.941336	−0.0406216
$538$	−13.4929	−0.581722
$539$	18.2443	0.785836
$540$	0	0
$541$	28.1723	1.21122	0.605610	−	0.795762i	$-0.292929\pi$
$541$	28.1723	1.21122	0.605610	+	0.795762i	$0.292929\pi$
$542$	26.8135	1.15174
$543$	−14.1057	−0.605335
$544$	1.02469	0.0439334
$545$	0	0
$546$	19.0797	0.816535
$547$	−27.1778	−1.16204	−0.581019	−	0.813890i	$-0.697346\pi$
$547$	−27.1778	−1.16204	−0.581019	+	0.813890i	$0.697346\pi$
$548$	−6.01666	−0.257019
$549$	−3.94494	−0.168366
$550$	0	0
$551$	1.17530	0.0500695
$552$	−1.92827	−0.0820728
$553$	43.2087	1.83742
$554$	8.16724	0.346993
$555$	0	0
$556$	−5.62720	−0.238646
$557$	6.74857	0.285946	0.142973	−	0.989727i	$-0.454334\pi$
$557$	6.74857	0.285946	0.142973	+	0.989727i	$0.454334\pi$
$558$	2.24205	0.0949135
$559$	−31.3031	−1.32398
$560$	0	0
$561$	5.43117	0.229304
$562$	−31.3418	−1.32207
$563$	−11.3076	−0.476561	−0.238280	−	0.971196i	$-0.576584\pi$
$563$	−11.3076	−0.476561	−0.238280	+	0.971196i	$0.576584\pi$
$564$	−10.5282	−0.443316
$565$	0	0
$566$	−16.3503	−0.687256
$567$	−3.23143	−0.135707
$568$	−8.53771	−0.358234
$569$	25.2185	1.05721	0.528607	−	0.848867i	$-0.322714\pi$
$569$	25.2185	1.05721	0.528607	+	0.848867i	$0.322714\pi$
$570$	0	0
$571$	−27.8001	−1.16340	−0.581699	−	0.813404i	$-0.697612\pi$
$571$	−27.8001	−1.16340	−0.581699	+	0.813404i	$0.697612\pi$
$572$	−31.2951	−1.30851
$573$	−25.4719	−1.06410
$574$	−32.1886	−1.34353
$575$	0	0
$576$	1.00000	0.0416667
$577$	11.4935	0.478479	0.239240	−	0.970961i	$-0.423102\pi$
$577$	11.4935	0.478479	0.239240	+	0.970961i	$0.423102\pi$
$578$	15.9500	0.663433
$579$	−6.63439	−0.275716
$580$	0	0
$581$	24.1936	1.00372
$582$	17.2567	0.715313
$583$	12.2493	0.507316
$584$	3.95422	0.163627
$585$	0	0
$586$	−28.1867	−1.16438
$587$	−42.2281	−1.74294	−0.871469	−	0.490450i	$-0.836832\pi$
$587$	−42.2281	−1.74294	−0.871469	+	0.490450i	$0.836832\pi$
$588$	−3.44213	−0.141951
$589$	10.1053	0.416383
$590$	0	0
$591$	−10.1777	−0.418656
$592$	9.55354	0.392648
$593$	0.0131121	0.000538451 0	0.000269225	−	1.00000i	$-0.499914\pi$
$593$	0.0131121	0.000538451 0	0.000269225		1.00000i	$0.499914\pi$
$594$	5.30029	0.217473
$595$	0	0
$596$	−11.6556	−0.477432
$597$	2.52238	0.103234
$598$	−11.3853	−0.465581
$599$	2.38072	0.0972738	0.0486369	−	0.998817i	$-0.484512\pi$
$599$	2.38072	0.0972738	0.0486369	+	0.998817i	$0.484512\pi$
$600$	0	0
$601$	−19.6020	−0.799581	−0.399790	−	0.916607i	$-0.630917\pi$
$601$	−19.6020	−0.799581	−0.399790	+	0.916607i	$0.630917\pi$
$602$	17.1319	0.698243
$603$	−9.29210	−0.378404
$604$	5.52354	0.224750
$605$	0	0
$606$	11.8454	0.481187
$607$	−10.7155	−0.434930	−0.217465	−	0.976068i	$-0.569779\pi$
$607$	−10.7155	−0.434930	−0.217465	+	0.976068i	$0.569779\pi$
$608$	4.50718	0.182790
$609$	−0.842633	−0.0341452
$610$	0	0
$611$	−62.1627	−2.51483
$612$	−1.02469	−0.0414208
$613$	−1.16434	−0.0470273	−0.0235137	−	0.999724i	$-0.507485\pi$
$613$	−1.16434	−0.0470273	−0.0235137	+	0.999724i	$0.507485\pi$
$614$	−14.5372	−0.586673
$615$	0	0
$616$	17.1275	0.690086
$617$	−22.6435	−0.911594	−0.455797	−	0.890084i	$-0.650646\pi$
$617$	−22.6435	−0.911594	−0.455797	+	0.890084i	$0.650646\pi$
$618$	7.15084	0.287649
$619$	24.7725	0.995689	0.497844	−	0.867266i	$-0.334125\pi$
$619$	24.7725	0.995689	0.497844	+	0.867266i	$0.334125\pi$
$620$	0	0
$621$	1.92827	0.0773790
$622$	−14.4924	−0.581094
$623$	2.37049	0.0949718
$624$	5.90441	0.236366
$625$	0	0
$626$	−31.5288	−1.26014
$627$	23.8894	0.954049
$628$	6.84307	0.273068
$629$	−9.78945	−0.390331
$630$	0	0
$631$	−32.6515	−1.29983	−0.649917	−	0.760005i	$-0.725196\pi$
$631$	−32.6515	−1.29983	−0.649917	+	0.760005i	$0.725196\pi$
$632$	13.3714	0.531885
$633$	−15.7638	−0.626556
$634$	−14.9810	−0.594973
$635$	0	0
$636$	−2.31107	−0.0916400
$637$	−20.3237	−0.805256
$638$	1.38211	0.0547183
$639$	8.53771	0.337747
$640$	0	0
$641$	−26.8543	−1.06068	−0.530340	−	0.847785i	$-0.677936\pi$
$641$	−26.8543	−1.06068	−0.530340	+	0.847785i	$0.677936\pi$
$642$	−3.20058	−0.126317
$643$	−17.1051	−0.674559	−0.337279	−	0.941405i	$-0.609507\pi$
$643$	−17.1051	−0.674559	−0.337279	+	0.941405i	$0.609507\pi$
$644$	6.23108	0.245539
$645$	0	0
$646$	−4.61848	−0.181712
$647$	45.8135	1.80112	0.900558	−	0.434736i	$-0.143158\pi$
$647$	45.8135	1.80112	0.900558	+	0.434736i	$0.143158\pi$
$648$	−1.00000	−0.0392837
$649$	−34.4096	−1.35069
$650$	0	0
$651$	−7.24502	−0.283955
$652$	9.38717	0.367630
$653$	11.4555	0.448288	0.224144	−	0.974556i	$-0.428041\pi$
$653$	11.4555	0.448288	0.224144	+	0.974556i	$0.428041\pi$
$654$	9.89555	0.386947
$655$	0	0
$656$	−9.96112	−0.388916
$657$	−3.95422	−0.154269
$658$	34.0210	1.32628
$659$	39.9982	1.55811	0.779054	−	0.626957i	$-0.215700\pi$
$659$	39.9982	1.55811	0.779054	+	0.626957i	$0.215700\pi$
$660$	0	0
$661$	−5.69132	−0.221367	−0.110683	−	0.993856i	$-0.535304\pi$
$661$	−5.69132	−0.221367	−0.110683	+	0.993856i	$0.535304\pi$
$662$	21.6174	0.840184
$663$	−6.05021	−0.234971
$664$	7.48698	0.290551
$665$	0	0
$666$	−9.55354	−0.370192
$667$	0.502820	0.0194693
$668$	−6.82883	−0.264215
$669$	−9.29534	−0.359379
$670$	0	0
$671$	−20.9093	−0.807194
$672$	−3.23143	−0.124655
$673$	48.4527	1.86772	0.933858	−	0.357645i	$-0.116420\pi$
$673$	48.4527	1.86772	0.933858	+	0.357645i	$0.116420\pi$
$674$	−7.59495	−0.292547
$675$	0	0
$676$	21.8621	0.840849
$677$	18.5092	0.711367	0.355683	−	0.934607i	$-0.384248\pi$
$677$	18.5092	0.711367	0.355683	+	0.934607i	$0.384248\pi$
$678$	4.24575	0.163057
$679$	−55.7637	−2.14002
$680$	0	0
$681$	−3.63809	−0.139412
$682$	11.8835	0.455043
$683$	−36.0242	−1.37843	−0.689214	−	0.724558i	$-0.742044\pi$
$683$	−36.0242	−1.37843	−0.689214	+	0.724558i	$0.742044\pi$
$684$	−4.50718	−0.172337
$685$	0	0
$686$	−11.4970	−0.438958
$687$	−9.93181	−0.378922
$688$	5.30164	0.202123
$689$	−13.6455	−0.519853
$690$	0	0
$691$	−14.4695	−0.550446	−0.275223	−	0.961380i	$-0.588752\pi$
$691$	−14.4695	−0.550446	−0.275223	+	0.961380i	$0.588752\pi$
$692$	−18.8604	−0.716966
$693$	−17.1275	−0.650620
$694$	−7.53304	−0.285950
$695$	0	0
$696$	−0.260762	−0.00988415
$697$	10.2071	0.386621
$698$	−18.7527	−0.709799
$699$	18.7893	0.710678
$700$	0	0
$701$	8.31284	0.313972	0.156986	−	0.987601i	$-0.449822\pi$
$701$	8.31284	0.313972	0.156986	+	0.987601i	$0.449822\pi$
$702$	−5.90441	−0.222848
$703$	−43.0596	−1.62402
$704$	5.30029	0.199762
$705$	0	0
$706$	4.36607	0.164319
$707$	−38.2776	−1.43958
$708$	6.49202	0.243985
$709$	−8.97215	−0.336956	−0.168478	−	0.985705i	$-0.553885\pi$
$709$	−8.97215	−0.336956	−0.168478	+	0.985705i	$0.553885\pi$
$710$	0	0
$711$	−13.3714	−0.501466
$712$	0.733574	0.0274919
$713$	4.32329	0.161908
$714$	3.31122	0.123919
$715$	0	0
$716$	0.941336	0.0351794
$717$	9.75186	0.364190
$718$	−0.737212	−0.0275125
$719$	28.1138	1.04847	0.524234	−	0.851574i	$-0.324352\pi$
$719$	28.1138	1.04847	0.524234	+	0.851574i	$0.324352\pi$
$720$	0	0
$721$	−23.1074	−0.860566
$722$	−1.31471	−0.0489286
$723$	−18.9211	−0.703683
$724$	14.1057	0.524235
$725$	0	0
$726$	17.0930	0.634382
$727$	−24.8767	−0.922627	−0.461314	−	0.887237i	$-0.652622\pi$
$727$	−24.8767	−0.922627	−0.461314	+	0.887237i	$0.652622\pi$
$728$	−19.0797	−0.707140
$729$	1.00000	0.0370370
$730$	0	0
$731$	−5.43256	−0.200930
$732$	3.94494	0.145809
$733$	6.75601	0.249539	0.124769	−	0.992186i	$-0.460181\pi$
$733$	6.75601	0.249539	0.124769	+	0.992186i	$0.460181\pi$
$734$	18.8600	0.696136
$735$	0	0
$736$	1.92827	0.0710771
$737$	−49.2508	−1.81418
$738$	9.96112	0.366674
$739$	−5.09161	−0.187298	−0.0936490	−	0.995605i	$-0.529853\pi$
$739$	−5.09161	−0.187298	−0.0936490	+	0.995605i	$0.529853\pi$
$740$	0	0
$741$	−26.6123	−0.977626
$742$	7.46806	0.274161
$743$	−16.0999	−0.590647	−0.295324	−	0.955397i	$-0.595427\pi$
$743$	−16.0999	−0.590647	−0.295324	+	0.955397i	$0.595427\pi$
$744$	−2.24205	−0.0821975
$745$	0	0
$746$	−29.8366	−1.09240
$747$	−7.48698	−0.273934
$748$	−5.43117	−0.198583
$749$	10.3424	0.377905
$750$	0	0
$751$	−25.4366	−0.928196	−0.464098	−	0.885784i	$-0.653622\pi$
$751$	−25.4366	−0.928196	−0.464098	+	0.885784i	$0.653622\pi$
$752$	10.5282	0.383923
$753$	1.98608	0.0723768
$754$	−1.53964	−0.0560706
$755$	0	0
$756$	3.23143	0.117526
$757$	12.4947	0.454129	0.227064	−	0.973880i	$-0.427087\pi$
$757$	12.4947	0.454129	0.227064	+	0.973880i	$0.427087\pi$
$758$	−25.4826	−0.925570
$759$	10.2204	0.370977
$760$	0	0
$761$	−11.5890	−0.420101	−0.210051	−	0.977691i	$-0.567363\pi$
$761$	−11.5890	−0.420101	−0.210051	+	0.977691i	$0.567363\pi$
$762$	9.25090	0.335125
$763$	−31.9768	−1.15764
$764$	25.4719	0.921541
$765$	0	0
$766$	31.6433	1.14332
$767$	38.3316	1.38407
$768$	−1.00000	−0.0360844
$769$	−23.7516	−0.856505	−0.428253	−	0.903659i	$-0.640871\pi$
$769$	−23.7516	−0.856505	−0.428253	+	0.903659i	$0.640871\pi$
$770$	0	0
$771$	−19.2797	−0.694341
$772$	6.63439	0.238777
$773$	12.0949	0.435024	0.217512	−	0.976058i	$-0.430206\pi$
$773$	12.0949	0.435024	0.217512	+	0.976058i	$0.430206\pi$
$774$	−5.30164	−0.190564
$775$	0	0
$776$	−17.2567	−0.619479
$777$	30.8716	1.10751
$778$	−12.0480	−0.431942
$779$	44.8966	1.60859
$780$	0	0
$781$	45.2523	1.61925
$782$	−1.97589	−0.0706577
$783$	0.260762	0.00931887
$784$	3.44213	0.122933
$785$	0	0
$786$	−4.86497	−0.173528
$787$	−20.3022	−0.723694	−0.361847	−	0.932237i	$-0.617854\pi$
$787$	−20.3022	−0.723694	−0.361847	+	0.932237i	$0.617854\pi$
$788$	10.1777	0.362567
$789$	12.5297	0.446068
$790$	0	0
$791$	−13.7198	−0.487821
$792$	−5.30029	−0.188337
$793$	23.2925	0.827142
$794$	25.7565	0.914064
$795$	0	0
$796$	−2.52238	−0.0894035
$797$	−31.7025	−1.12296	−0.561480	−	0.827490i	$-0.689768\pi$
$797$	−31.7025	−1.12296	−0.561480	+	0.827490i	$0.689768\pi$
$798$	14.5646	0.515583
$799$	−10.7881	−0.381657
$800$	0	0
$801$	−0.733574	−0.0259196
$802$	−26.3196	−0.929378
$803$	−20.9585	−0.739609
$804$	9.29210	0.327707
$805$	0	0
$806$	−13.2380	−0.466288
$807$	−13.4929	−0.474974
$808$	−11.8454	−0.416720
$809$	8.72562	0.306777	0.153388	−	0.988166i	$-0.450981\pi$
$809$	8.72562	0.306777	0.153388	+	0.988166i	$0.450981\pi$
$810$	0	0
$811$	15.2022	0.533821	0.266911	−	0.963721i	$-0.413997\pi$
$811$	15.2022	0.533821	0.266911	+	0.963721i	$0.413997\pi$
$812$	0.842633	0.0295706
$813$	26.8135	0.940391
$814$	−50.6365	−1.77481
$815$	0	0
$816$	1.02469	0.0358715
$817$	−23.8955	−0.835997
$818$	−36.7714	−1.28568
$819$	19.0797	0.666698
$820$	0	0
$821$	16.4595	0.574441	0.287220	−	0.957865i	$-0.407269\pi$
$821$	16.4595	0.574441	0.287220	+	0.957865i	$0.407269\pi$
$822$	−6.01666	−0.209855
$823$	−22.9985	−0.801676	−0.400838	−	0.916149i	$-0.631281\pi$
$823$	−22.9985	−0.801676	−0.400838	+	0.916149i	$0.631281\pi$
$824$	−7.15084	−0.249111
$825$	0	0
$826$	−20.9785	−0.729936
$827$	−24.7319	−0.860011	−0.430006	−	0.902826i	$-0.641488\pi$
$827$	−24.7319	−0.860011	−0.430006	+	0.902826i	$0.641488\pi$
$828$	−1.92827	−0.0670122
$829$	20.8634	0.724617	0.362308	−	0.932058i	$-0.381989\pi$
$829$	20.8634	0.724617	0.362308	+	0.932058i	$0.381989\pi$
$830$	0	0
$831$	8.16724	0.283318
$832$	−5.90441	−0.204699
$833$	−3.52713	−0.122208
$834$	−5.62720	−0.194854
$835$	0	0
$836$	−23.8894	−0.826231
$837$	2.24205	0.0774966
$838$	31.7245	1.09591
$839$	−23.5963	−0.814635	−0.407317	−	0.913287i	$-0.633536\pi$
$839$	−23.5963	−0.814635	−0.407317	+	0.913287i	$0.633536\pi$
$840$	0	0
$841$	−28.9320	−0.997655
$842$	−8.81726	−0.303863
$843$	−31.3418	−1.07947
$844$	15.7638	0.542613
$845$	0	0
$846$	−10.5282	−0.361966
$847$	−55.2349	−1.89789
$848$	2.31107	0.0793625
$849$	−16.3503	−0.561142
$850$	0	0
$851$	−18.4218	−0.631493
$852$	−8.53771	−0.292497
$853$	26.3629	0.902647	0.451324	−	0.892360i	$-0.350952\pi$
$853$	26.3629	0.902647	0.451324	+	0.892360i	$0.350952\pi$
$854$	−12.7478	−0.436220
$855$	0	0
$856$	3.20058	0.109394
$857$	16.0891	0.549593	0.274797	−	0.961502i	$-0.411389\pi$
$857$	16.0891	0.549593	0.274797	+	0.961502i	$0.411389\pi$
$858$	−31.2951	−1.06840
$859$	10.5770	0.360882	0.180441	−	0.983586i	$-0.442248\pi$
$859$	10.5770	0.360882	0.180441	+	0.983586i	$0.442248\pi$
$860$	0	0
$861$	−32.1886	−1.09699
$862$	−23.5065	−0.800636
$863$	−41.7617	−1.42158	−0.710792	−	0.703403i	$-0.751663\pi$
$863$	−41.7617	−1.42158	−0.710792	+	0.703403i	$0.751663\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−8.40312	−0.285550
$867$	15.9500	0.541690
$868$	7.24502	0.245912
$869$	−70.8721	−2.40417
$870$	0	0
$871$	54.8644	1.85901
$872$	−9.89555	−0.335106
$873$	17.2567	0.584050
$874$	−8.69109	−0.293980
$875$	0	0
$876$	3.95422	0.133601
$877$	31.8267	1.07471	0.537355	−	0.843356i	$-0.319423\pi$
$877$	31.8267	1.07471	0.537355	+	0.843356i	$0.319423\pi$
$878$	−35.6325	−1.20254
$879$	−28.1867	−0.950714
$880$	0	0
$881$	−49.6324	−1.67216	−0.836079	−	0.548609i	$-0.815158\pi$
$881$	−49.6324	−1.67216	−0.836079	+	0.548609i	$0.815158\pi$
$882$	−3.44213	−0.115902
$883$	5.06098	0.170316	0.0851578	−	0.996367i	$-0.472861\pi$
$883$	5.06098	0.170316	0.0851578	+	0.996367i	$0.472861\pi$
$884$	6.05021	0.203491
$885$	0	0
$886$	−6.79550	−0.228299
$887$	−11.0542	−0.371164	−0.185582	−	0.982629i	$-0.559417\pi$
$887$	−11.0542	−0.371164	−0.185582	+	0.982629i	$0.559417\pi$
$888$	9.55354	0.320596
$889$	−29.8936	−1.00260
$890$	0	0
$891$	5.30029	0.177566
$892$	9.29534	0.311231
$893$	−47.4524	−1.58793
$894$	−11.6556	−0.389821
$895$	0	0
$896$	3.23143	0.107954
$897$	−11.3853	−0.380145
$898$	−8.75011	−0.291995
$899$	0.584641	0.0194989
$900$	0	0
$901$	−2.36814	−0.0788942
$902$	52.7968	1.75794
$903$	17.1319	0.570113
$904$	−4.24575	−0.141211
$905$	0	0
$906$	5.52354	0.183507
$907$	7.57086	0.251386	0.125693	−	0.992069i	$-0.459885\pi$
$907$	7.57086	0.251386	0.125693	+	0.992069i	$0.459885\pi$
$908$	3.63809	0.120734
$909$	11.8454	0.392887
$910$	0	0
$911$	35.7684	1.18506	0.592529	−	0.805549i	$-0.298129\pi$
$911$	35.7684	1.18506	0.592529	+	0.805549i	$0.298129\pi$
$912$	4.50718	0.149248
$913$	−39.6831	−1.31332
$914$	38.1474	1.26180
$915$	0	0
$916$	9.93181	0.328156
$917$	15.7208	0.519147
$918$	−1.02469	−0.0338199
$919$	−49.6236	−1.63693	−0.818466	−	0.574555i	$-0.805175\pi$
$919$	−49.6236	−1.63693	−0.818466	+	0.574555i	$0.805175\pi$
$920$	0	0
$921$	−14.5372	−0.479016
$922$	1.27077	0.0418505
$923$	−50.4101	−1.65927
$924$	17.1275	0.563453
$925$	0	0
$926$	−8.93349	−0.293573
$927$	7.15084	0.234864
$928$	0.260762	0.00855992
$929$	−16.2616	−0.533527	−0.266764	−	0.963762i	$-0.585954\pi$
$929$	−16.2616	−0.533527	−0.266764	+	0.963762i	$0.585954\pi$
$930$	0	0
$931$	−15.5143	−0.508461
$932$	−18.7893	−0.615465
$933$	−14.4924	−0.474461
$934$	5.75682	0.188369
$935$	0	0
$936$	5.90441	0.192992
$937$	−0.569874	−0.0186170	−0.00930849	−	0.999957i	$-0.502963\pi$
$937$	−0.569874	−0.0186170	−0.00930849	+	0.999957i	$0.502963\pi$
$938$	−30.0268	−0.980408
$939$	−31.5288	−1.02890
$940$	0	0
$941$	6.99538	0.228043	0.114021	−	0.993478i	$-0.463627\pi$
$941$	6.99538	0.228043	0.114021	+	0.993478i	$0.463627\pi$
$942$	6.84307	0.222959
$943$	19.2078	0.625491
$944$	−6.49202	−0.211297
$945$	0	0
$946$	−28.1002	−0.913616
$947$	−34.4620	−1.11987	−0.559933	−	0.828538i	$-0.689173\pi$
$947$	−34.4620	−1.11987	−0.559933	+	0.828538i	$0.689173\pi$
$948$	13.3714	0.434282
$949$	23.3473	0.757886
$950$	0	0
$951$	−14.9810	−0.485794
$952$	−3.31122	−0.107317
$953$	−42.0363	−1.36169	−0.680845	−	0.732427i	$-0.738387\pi$
$953$	−42.0363	−1.36169	−0.680845	+	0.732427i	$0.738387\pi$
$954$	−2.31107	−0.0748237
$955$	0	0
$956$	−9.75186	−0.315398
$957$	1.38211	0.0446773
$958$	4.63051	0.149605
$959$	19.4424	0.627828
$960$	0	0
$961$	−25.9732	−0.837846
$962$	56.4080	1.81867
$963$	−3.20058	−0.103137
$964$	18.9211	0.609407
$965$	0	0
$966$	6.23108	0.200482
$967$	11.9686	0.384885	0.192443	−	0.981308i	$-0.438359\pi$
$967$	11.9686	0.384885	0.192443	+	0.981308i	$0.438359\pi$
$968$	−17.0930	−0.549391
$969$	−4.61848	−0.148367
$970$	0	0
$971$	1.35194	0.0433858	0.0216929	−	0.999765i	$-0.493094\pi$
$971$	1.35194	0.0433858	0.0216929	+	0.999765i	$0.493094\pi$
$972$	−1.00000	−0.0320750
$973$	18.1839	0.582949
$974$	−15.9235	−0.510223
$975$	0	0
$976$	−3.94494	−0.126274
$977$	−18.5448	−0.593300	−0.296650	−	0.954986i	$-0.595869\pi$
$977$	−18.5448	−0.593300	−0.296650	+	0.954986i	$0.595869\pi$
$978$	9.38717	0.300169
$979$	−3.88815	−0.124266
$980$	0	0
$981$	9.89555	0.315941
$982$	6.38076	0.203618
$983$	16.3821	0.522508	0.261254	−	0.965270i	$-0.415864\pi$
$983$	16.3821	0.522508	0.261254	+	0.965270i	$0.415864\pi$
$984$	−9.96112	−0.317549
$985$	0	0
$986$	−0.267201	−0.00850941
$987$	34.0210	1.08290
$988$	26.6123	0.846649
$989$	−10.2230	−0.325073
$990$	0	0
$991$	19.8303	0.629930	0.314965	−	0.949103i	$-0.398007\pi$
$991$	19.8303	0.629930	0.314965	+	0.949103i	$0.398007\pi$
$992$	2.24205	0.0711851
$993$	21.6174	0.686007
$994$	27.5890	0.875070
$995$	0	0
$996$	7.48698	0.237234
$997$	10.4675	0.331508	0.165754	−	0.986167i	$-0.446994\pi$
$997$	10.4675	0.331508	0.165754	+	0.986167i	$0.446994\pi$
$998$	−12.9135	−0.408769
$999$	−9.55354	−0.302261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.u.1.2		8
5.2	odd	4		3750.2.c.k.1249.2		16
5.3	odd	4		3750.2.c.k.1249.15		16
5.4	even	2		3750.2.a.v.1.7		8
25.2	odd	20		750.2.h.d.649.1		16
25.9	even	10		750.2.g.f.151.4		16
25.11	even	5		750.2.g.g.601.1		16
25.12	odd	20		150.2.h.b.19.3	✓	16
25.13	odd	20		750.2.h.d.349.2		16
25.14	even	10		750.2.g.f.601.4		16
25.16	even	5		750.2.g.g.151.1		16
25.23	odd	20		150.2.h.b.79.3	yes	16
75.23	even	20		450.2.l.c.379.2		16
75.62	even	20		450.2.l.c.19.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.3	✓	16	25.12	odd	20
150.2.h.b.79.3	yes	16	25.23	odd	20
450.2.l.c.19.2		16	75.62	even	20
450.2.l.c.379.2		16	75.23	even	20
750.2.g.f.151.4		16	25.9	even	10
750.2.g.f.601.4		16	25.14	even	10
750.2.g.g.151.1		16	25.16	even	5
750.2.g.g.601.1		16	25.11	even	5
750.2.h.d.349.2		16	25.13	odd	20
750.2.h.d.649.1		16	25.2	odd	20
3750.2.a.u.1.2		8	1.1	even	1	trivial
3750.2.a.v.1.7		8	5.4	even	2
3750.2.c.k.1249.2		16	5.2	odd	4
3750.2.c.k.1249.15		16	5.3	odd	4

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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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -3.23143 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -3.23143 q^{7} -1.00000 q^{8} +1.00000 q^{9} +5.30029 q^{11} -1.00000 q^{12} -5.90441 q^{13} +3.23143 q^{14} +1.00000 q^{16} -1.02469 q^{17} -1.00000 q^{18} -4.50718 q^{19} +3.23143 q^{21} -5.30029 q^{22} -1.92827 q^{23} +1.00000 q^{24} +5.90441 q^{26} -1.00000 q^{27} -3.23143 q^{28} -0.260762 q^{29} -2.24205 q^{31} -1.00000 q^{32} -5.30029 q^{33} +1.02469 q^{34} +1.00000 q^{36} +9.55354 q^{37} +4.50718 q^{38} +5.90441 q^{39} -9.96112 q^{41} -3.23143 q^{42} +5.30164 q^{43} +5.30029 q^{44} +1.92827 q^{46} +10.5282 q^{47} -1.00000 q^{48} +3.44213 q^{49} +1.02469 q^{51} -5.90441 q^{52} +2.31107 q^{53} +1.00000 q^{54} +3.23143 q^{56} +4.50718 q^{57} +0.260762 q^{58} -6.49202 q^{59} -3.94494 q^{61} +2.24205 q^{62} -3.23143 q^{63} +1.00000 q^{64} +5.30029 q^{66} -9.29210 q^{67} -1.02469 q^{68} +1.92827 q^{69} +8.53771 q^{71} -1.00000 q^{72} -3.95422 q^{73} -9.55354 q^{74} -4.50718 q^{76} -17.1275 q^{77} -5.90441 q^{78} -13.3714 q^{79} +1.00000 q^{81} +9.96112 q^{82} -7.48698 q^{83} +3.23143 q^{84} -5.30164 q^{86} +0.260762 q^{87} -5.30029 q^{88} -0.733574 q^{89} +19.0797 q^{91} -1.92827 q^{92} +2.24205 q^{93} -10.5282 q^{94} +1.00000 q^{96} +17.2567 q^{97} -3.44213 q^{98} +5.30029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{11} - 8 q^{12} - 2 q^{13} + 4 q^{14} + 8 q^{16} - 14 q^{17} - 8 q^{18} + 10 q^{19} + 4 q^{21} - 6 q^{22} - 12 q^{23} + 8 q^{24} + 2 q^{26} - 8 q^{27} - 4 q^{28} + 10 q^{29} + 16 q^{31} - 8 q^{32} - 6 q^{33} + 14 q^{34} + 8 q^{36} + 6 q^{37} - 10 q^{38} + 2 q^{39} + 6 q^{41} - 4 q^{42} - 2 q^{43} + 6 q^{44} + 12 q^{46} - 14 q^{47} - 8 q^{48} + 26 q^{49} + 14 q^{51} - 2 q^{52} - 12 q^{53} + 8 q^{54} + 4 q^{56} - 10 q^{57} - 10 q^{58} + 16 q^{61} - 16 q^{62} - 4 q^{63} + 8 q^{64} + 6 q^{66} + 6 q^{67} - 14 q^{68} + 12 q^{69} + 6 q^{71} - 8 q^{72} + 8 q^{73} - 6 q^{74} + 10 q^{76} - 8 q^{77} - 2 q^{78} + 10 q^{79} + 8 q^{81} - 6 q^{82} - 22 q^{83} + 4 q^{84} + 2 q^{86} - 10 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{91} - 12 q^{92} - 16 q^{93} + 14 q^{94} + 8 q^{96} + 16 q^{97} - 26 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^11 - 8 * q^12 - 2 * q^13 + 4 * q^14 + 8 * q^16 - 14 * q^17 - 8 * q^18 + 10 * q^19 + 4 * q^21 - 6 * q^22 - 12 * q^23 + 8 * q^24 + 2 * q^26 - 8 * q^27 - 4 * q^28 + 10 * q^29 + 16 * q^31 - 8 * q^32 - 6 * q^33 + 14 * q^34 + 8 * q^36 + 6 * q^37 - 10 * q^38 + 2 * q^39 + 6 * q^41 - 4 * q^42 - 2 * q^43 + 6 * q^44 + 12 * q^46 - 14 * q^47 - 8 * q^48 + 26 * q^49 + 14 * q^51 - 2 * q^52 - 12 * q^53 + 8 * q^54 + 4 * q^56 - 10 * q^57 - 10 * q^58 + 16 * q^61 - 16 * q^62 - 4 * q^63 + 8 * q^64 + 6 * q^66 + 6 * q^67 - 14 * q^68 + 12 * q^69 + 6 * q^71 - 8 * q^72 + 8 * q^73 - 6 * q^74 + 10 * q^76 - 8 * q^77 - 2 * q^78 + 10 * q^79 + 8 * q^81 - 6 * q^82 - 22 * q^83 + 4 * q^84 + 2 * q^86 - 10 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^91 - 12 * q^92 - 16 * q^93 + 14 * q^94 + 8 * q^96 + 16 * q^97 - 26 * q^98 + 6 * q^99

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