LMFDB - Embedded newform 3750.2.a.u.1.3

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			1.3
Root			$-0.0444111$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.70913 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.70913 q^{7} -1.00000 q^{8} +1.00000 q^{9} +5.62045 q^{11} -1.00000 q^{12} +4.84082 q^{13} +2.70913 q^{14} +1.00000 q^{16} -1.04568 q^{17} -1.00000 q^{18} +8.38494 q^{19} +2.70913 q^{21} -5.62045 q^{22} +5.29478 q^{23} +1.00000 q^{24} -4.84082 q^{26} -1.00000 q^{27} -2.70913 q^{28} +4.19039 q^{29} -5.58042 q^{31} -1.00000 q^{32} -5.62045 q^{33} +1.04568 q^{34} +1.00000 q^{36} +2.99179 q^{37} -8.38494 q^{38} -4.84082 q^{39} -1.57743 q^{41} -2.70913 q^{42} -3.29669 q^{43} +5.62045 q^{44} -5.29478 q^{46} +3.07374 q^{47} -1.00000 q^{48} +0.339383 q^{49} +1.04568 q^{51} +4.84082 q^{52} -6.17710 q^{53} +1.00000 q^{54} +2.70913 q^{56} -8.38494 q^{57} -4.19039 q^{58} -14.1876 q^{59} +0.270588 q^{61} +5.58042 q^{62} -2.70913 q^{63} +1.00000 q^{64} +5.62045 q^{66} -6.30981 q^{67} -1.04568 q^{68} -5.29478 q^{69} -4.53276 q^{71} -1.00000 q^{72} +8.16098 q^{73} -2.99179 q^{74} +8.38494 q^{76} -15.2265 q^{77} +4.84082 q^{78} +12.4814 q^{79} +1.00000 q^{81} +1.57743 q^{82} +0.134522 q^{83} +2.70913 q^{84} +3.29669 q^{86} -4.19039 q^{87} -5.62045 q^{88} +11.7902 q^{89} -13.1144 q^{91} +5.29478 q^{92} +5.58042 q^{93} -3.07374 q^{94} +1.00000 q^{96} +2.64031 q^{97} -0.339383 q^{98} +5.62045 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−2.70913	−1.02395	−0.511977	−	0.858999i	$-0.671087\pi$
$7$	−2.70913	−1.02395	−0.511977	+	0.858999i	$0.671087\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	5.62045	1.69463	0.847314	−	0.531092i	$-0.178218\pi$
$11$	5.62045	1.69463	0.847314	+	0.531092i	$0.178218\pi$
$12$	−1.00000	−0.288675
$13$	4.84082	1.34260	0.671301	−	0.741185i	$-0.265736\pi$
$13$	4.84082	1.34260	0.671301	+	0.741185i	$0.265736\pi$
$14$	2.70913	0.724045
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.04568	−0.253614	−0.126807	−	0.991927i	$-0.540473\pi$
$17$	−1.04568	−0.253614	−0.126807	+	0.991927i	$0.540473\pi$
$18$	−1.00000	−0.235702
$19$	8.38494	1.92364	0.961819	−	0.273687i	$-0.0882433\pi$
$19$	8.38494	1.92364	0.961819	+	0.273687i	$0.0882433\pi$
$20$	0	0
$21$	2.70913	0.591181
$22$	−5.62045	−1.19828
$23$	5.29478	1.10404	0.552019	−	0.833832i	$-0.313858\pi$
$23$	5.29478	1.10404	0.552019	+	0.833832i	$0.313858\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−4.84082	−0.949362
$27$	−1.00000	−0.192450
$28$	−2.70913	−0.511977
$29$	4.19039	0.778136	0.389068	−	0.921209i	$-0.372797\pi$
$29$	4.19039	0.778136	0.389068	+	0.921209i	$0.372797\pi$
$30$	0	0
$31$	−5.58042	−1.00227	−0.501136	−	0.865368i	$-0.667084\pi$
$31$	−5.58042	−1.00227	−0.501136	+	0.865368i	$0.667084\pi$
$32$	−1.00000	−0.176777
$33$	−5.62045	−0.978394
$34$	1.04568	0.179332
$35$	0	0
$36$	1.00000	0.166667
$37$	2.99179	0.491847	0.245924	−	0.969289i	$-0.420909\pi$
$37$	2.99179	0.491847	0.245924	+	0.969289i	$0.420909\pi$
$38$	−8.38494	−1.36022
$39$	−4.84082	−0.775151
$40$	0	0
$41$	−1.57743	−0.246353	−0.123177	−	0.992385i	$-0.539308\pi$
$41$	−1.57743	−0.246353	−0.123177	+	0.992385i	$0.539308\pi$
$42$	−2.70913	−0.418028
$43$	−3.29669	−0.502741	−0.251370	−	0.967891i	$-0.580881\pi$
$43$	−3.29669	−0.502741	−0.251370	+	0.967891i	$0.580881\pi$
$44$	5.62045	0.847314
$45$	0	0
$46$	−5.29478	−0.780673
$47$	3.07374	0.448351	0.224176	−	0.974549i	$-0.428031\pi$
$47$	3.07374	0.448351	0.224176	+	0.974549i	$0.428031\pi$
$48$	−1.00000	−0.144338
$49$	0.339383	0.0484833
$50$	0	0
$51$	1.04568	0.146424
$52$	4.84082	0.671301
$53$	−6.17710	−0.848491	−0.424245	−	0.905547i	$-0.639461\pi$
$53$	−6.17710	−0.848491	−0.424245	+	0.905547i	$0.639461\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	2.70913	0.362023
$57$	−8.38494	−1.11061
$58$	−4.19039	−0.550225
$59$	−14.1876	−1.84707	−0.923533	−	0.383520i	$-0.874712\pi$
$59$	−14.1876	−1.84707	−0.923533	+	0.383520i	$0.874712\pi$
$60$	0	0
$61$	0.270588	0.0346453	0.0173226	−	0.999850i	$-0.494486\pi$
$61$	0.270588	0.0346453	0.0173226	+	0.999850i	$0.494486\pi$
$62$	5.58042	0.708714
$63$	−2.70913	−0.341318
$64$	1.00000	0.125000
$65$	0	0
$66$	5.62045	0.691829
$67$	−6.30981	−0.770866	−0.385433	−	0.922736i	$-0.625948\pi$
$67$	−6.30981	−0.770866	−0.385433	+	0.922736i	$0.625948\pi$
$68$	−1.04568	−0.126807
$69$	−5.29478	−0.637417
$70$	0	0
$71$	−4.53276	−0.537940	−0.268970	−	0.963149i	$-0.586683\pi$
$71$	−4.53276	−0.537940	−0.268970	+	0.963149i	$0.586683\pi$
$72$	−1.00000	−0.117851
$73$	8.16098	0.955171	0.477585	−	0.878585i	$-0.341512\pi$
$73$	8.16098	0.955171	0.477585	+	0.878585i	$0.341512\pi$
$74$	−2.99179	−0.347788
$75$	0	0
$76$	8.38494	0.961819
$77$	−15.2265	−1.73522
$78$	4.84082	0.548115
$79$	12.4814	1.40427	0.702135	−	0.712044i	$-0.252230\pi$
$79$	12.4814	1.40427	0.702135	+	0.712044i	$0.252230\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.57743	0.174198
$83$	0.134522	0.0147657	0.00738284	−	0.999973i	$-0.497650\pi$
$83$	0.134522	0.0147657	0.00738284	+	0.999973i	$0.497650\pi$
$84$	2.70913	0.295590
$85$	0	0
$86$	3.29669	0.355492
$87$	−4.19039	−0.449257
$88$	−5.62045	−0.599141
$89$	11.7902	1.24975	0.624877	−	0.780723i	$-0.285149\pi$
$89$	11.7902	1.24975	0.624877	+	0.780723i	$0.285149\pi$
$90$	0	0
$91$	−13.1144	−1.37476
$92$	5.29478	0.552019
$93$	5.58042	0.578662
$94$	−3.07374	−0.317032
$95$	0	0
$96$	1.00000	0.102062
$97$	2.64031	0.268083	0.134041	−	0.990976i	$-0.457205\pi$
$97$	2.64031	0.268083	0.134041	+	0.990976i	$0.457205\pi$
$98$	−0.339383	−0.0342829
$99$	5.62045	0.564876
$100$	0	0
$101$	−3.82844	−0.380944	−0.190472	−	0.981693i	$-0.561002\pi$
$101$	−3.82844	−0.380944	−0.190472	+	0.981693i	$0.561002\pi$
$102$	−1.04568	−0.103538
$103$	5.89322	0.580676	0.290338	−	0.956924i	$-0.406232\pi$
$103$	5.89322	0.580676	0.290338	+	0.956924i	$0.406232\pi$
$104$	−4.84082	−0.474681
$105$	0	0
$106$	6.17710	0.599973
$107$	5.90758	0.571108	0.285554	−	0.958363i	$-0.407822\pi$
$107$	5.90758	0.571108	0.285554	+	0.958363i	$0.407822\pi$
$108$	−1.00000	−0.0962250
$109$	5.63805	0.540028	0.270014	−	0.962856i	$-0.412972\pi$
$109$	5.63805	0.540028	0.270014	+	0.962856i	$0.412972\pi$
$110$	0	0
$111$	−2.99179	−0.283968
$112$	−2.70913	−0.255989
$113$	−5.06692	−0.476656	−0.238328	−	0.971185i	$-0.576599\pi$
$113$	−5.06692	−0.476656	−0.238328	+	0.971185i	$0.576599\pi$
$114$	8.38494	0.785322
$115$	0	0
$116$	4.19039	0.389068
$117$	4.84082	0.447534
$118$	14.1876	1.30607
$119$	2.83288	0.259690
$120$	0	0
$121$	20.5894	1.87176
$122$	−0.270588	−0.0244979
$123$	1.57743	0.142232
$124$	−5.58042	−0.501136
$125$	0	0
$126$	2.70913	0.241348
$127$	9.52909	0.845570	0.422785	−	0.906230i	$-0.361053\pi$
$127$	9.52909	0.845570	0.422785	+	0.906230i	$0.361053\pi$
$128$	−1.00000	−0.0883883
$129$	3.29669	0.290258
$130$	0	0
$131$	0.148886	0.0130082	0.00650411	−	0.999979i	$-0.497930\pi$
$131$	0.148886	0.0130082	0.00650411	+	0.999979i	$0.497930\pi$
$132$	−5.62045	−0.489197
$133$	−22.7159	−1.96972
$134$	6.30981	0.545084
$135$	0	0
$136$	1.04568	0.0896662
$137$	−9.02419	−0.770989	−0.385494	−	0.922710i	$-0.625969\pi$
$137$	−9.02419	−0.770989	−0.385494	+	0.922710i	$0.625969\pi$
$138$	5.29478	0.450722
$139$	7.11259	0.603282	0.301641	−	0.953422i	$-0.402466\pi$
$139$	7.11259	0.603282	0.301641	+	0.953422i	$0.402466\pi$
$140$	0	0
$141$	−3.07374	−0.258856
$142$	4.53276	0.380381
$143$	27.2075	2.27521
$144$	1.00000	0.0833333
$145$	0	0
$146$	−8.16098	−0.675408
$147$	−0.339383	−0.0279919
$148$	2.99179	0.245924
$149$	15.4351	1.26449	0.632246	−	0.774768i	$-0.282133\pi$
$149$	15.4351	1.26449	0.632246	+	0.774768i	$0.282133\pi$
$150$	0	0
$151$	−7.99801	−0.650868	−0.325434	−	0.945565i	$-0.605510\pi$
$151$	−7.99801	−0.650868	−0.325434	+	0.945565i	$0.605510\pi$
$152$	−8.38494	−0.680109
$153$	−1.04568	−0.0845381
$154$	15.2265	1.22699
$155$	0	0
$156$	−4.84082	−0.387576
$157$	15.6147	1.24619	0.623095	−	0.782146i	$-0.285875\pi$
$157$	15.6147	1.24619	0.623095	+	0.782146i	$0.285875\pi$
$158$	−12.4814	−0.992969
$159$	6.17710	0.489876
$160$	0	0
$161$	−14.3442	−1.13048
$162$	−1.00000	−0.0785674
$163$	−3.65730	−0.286461	−0.143231	−	0.989689i	$-0.545749\pi$
$163$	−3.65730	−0.286461	−0.143231	+	0.989689i	$0.545749\pi$
$164$	−1.57743	−0.123177
$165$	0	0
$166$	−0.134522	−0.0104409
$167$	−6.30307	−0.487746	−0.243873	−	0.969807i	$-0.578418\pi$
$167$	−6.30307	−0.487746	−0.243873	+	0.969807i	$0.578418\pi$
$168$	−2.70913	−0.209014
$169$	10.4335	0.802578
$170$	0	0
$171$	8.38494	0.641213
$172$	−3.29669	−0.251370
$173$	10.6455	0.809360	0.404680	−	0.914458i	$-0.367383\pi$
$173$	10.6455	0.809360	0.404680	+	0.914458i	$0.367383\pi$
$174$	4.19039	0.317673
$175$	0	0
$176$	5.62045	0.423657
$177$	14.1876	1.06640
$178$	−11.7902	−0.883710
$179$	−0.799304	−0.0597428	−0.0298714	−	0.999554i	$-0.509510\pi$
$179$	−0.799304	−0.0597428	−0.0298714	+	0.999554i	$0.509510\pi$
$180$	0	0
$181$	−16.3240	−1.21335	−0.606676	−	0.794949i	$-0.707497\pi$
$181$	−16.3240	−1.21335	−0.606676	+	0.794949i	$0.707497\pi$
$182$	13.1144	0.972104
$183$	−0.270588	−0.0200025
$184$	−5.29478	−0.390336
$185$	0	0
$186$	−5.58042	−0.409176
$187$	−5.87718	−0.429782
$188$	3.07374	0.224176
$189$	2.70913	0.197060
$190$	0	0
$191$	−15.5301	−1.12372	−0.561858	−	0.827233i	$-0.689913\pi$
$191$	−15.5301	−1.12372	−0.561858	+	0.827233i	$0.689913\pi$
$192$	−1.00000	−0.0721688
$193$	21.0202	1.51307	0.756533	−	0.653956i	$-0.226892\pi$
$193$	21.0202	1.51307	0.756533	+	0.653956i	$0.226892\pi$
$194$	−2.64031	−0.189563
$195$	0	0
$196$	0.339383	0.0242417
$197$	−24.1574	−1.72114	−0.860572	−	0.509328i	$-0.829894\pi$
$197$	−24.1574	−1.72114	−0.860572	+	0.509328i	$0.829894\pi$
$198$	−5.62045	−0.399428
$199$	−25.4930	−1.80715	−0.903574	−	0.428432i	$-0.859066\pi$
$199$	−25.4930	−1.80715	−0.903574	+	0.428432i	$0.859066\pi$
$200$	0	0
$201$	6.30981	0.445060
$202$	3.82844	0.269368
$203$	−11.3523	−0.796776
$204$	1.04568	0.0732121
$205$	0	0
$206$	−5.89322	−0.410600
$207$	5.29478	0.368013
$208$	4.84082	0.335650
$209$	47.1271	3.25985
$210$	0	0
$211$	5.24920	0.361370	0.180685	−	0.983541i	$-0.442169\pi$
$211$	5.24920	0.361370	0.180685	+	0.983541i	$0.442169\pi$
$212$	−6.17710	−0.424245
$213$	4.53276	0.310580
$214$	−5.90758	−0.403834
$215$	0	0
$216$	1.00000	0.0680414
$217$	15.1181	1.02628
$218$	−5.63805	−0.381857
$219$	−8.16098	−0.551468
$220$	0	0
$221$	−5.06194	−0.340503
$222$	2.99179	0.200796
$223$	14.7970	0.990877	0.495439	−	0.868643i	$-0.335007\pi$
$223$	14.7970	0.990877	0.495439	+	0.868643i	$0.335007\pi$
$224$	2.70913	0.181011
$225$	0	0
$226$	5.06692	0.337047
$227$	−11.8784	−0.788400	−0.394200	−	0.919025i	$-0.628978\pi$
$227$	−11.8784	−0.788400	−0.394200	+	0.919025i	$0.628978\pi$
$228$	−8.38494	−0.555306
$229$	18.2572	1.20647	0.603234	−	0.797565i	$-0.293879\pi$
$229$	18.2572	1.20647	0.603234	+	0.797565i	$0.293879\pi$
$230$	0	0
$231$	15.2265	1.00183
$232$	−4.19039	−0.275113
$233$	2.85842	0.187261	0.0936307	−	0.995607i	$-0.470153\pi$
$233$	2.85842	0.187261	0.0936307	+	0.995607i	$0.470153\pi$
$234$	−4.84082	−0.316454
$235$	0	0
$236$	−14.1876	−0.923533
$237$	−12.4814	−0.810755
$238$	−2.83288	−0.183628
$239$	16.3838	1.05978	0.529889	−	0.848067i	$-0.322234\pi$
$239$	16.3838	1.05978	0.529889	+	0.848067i	$0.322234\pi$
$240$	0	0
$241$	26.3276	1.69591	0.847955	−	0.530069i	$-0.177834\pi$
$241$	26.3276	1.69591	0.847955	+	0.530069i	$0.177834\pi$
$242$	−20.5894	−1.32354
$243$	−1.00000	−0.0641500
$244$	0.270588	0.0173226
$245$	0	0
$246$	−1.57743	−0.100573
$247$	40.5900	2.58268
$248$	5.58042	0.354357
$249$	−0.134522	−0.00852497
$250$	0	0
$251$	−13.8356	−0.873295	−0.436647	−	0.899633i	$-0.643834\pi$
$251$	−13.8356	−0.873295	−0.436647	+	0.899633i	$0.643834\pi$
$252$	−2.70913	−0.170659
$253$	29.7590	1.87093
$254$	−9.52909	−0.597908
$255$	0	0
$256$	1.00000	0.0625000
$257$	−28.6204	−1.78529	−0.892647	−	0.450756i	$-0.851154\pi$
$257$	−28.6204	−1.78529	−0.892647	+	0.450756i	$0.851154\pi$
$258$	−3.29669	−0.205243
$259$	−8.10515	−0.503629
$260$	0	0
$261$	4.19039	0.259379
$262$	−0.148886	−0.00919821
$263$	−3.12306	−0.192576	−0.0962882	−	0.995353i	$-0.530697\pi$
$263$	−3.12306	−0.192576	−0.0962882	+	0.995353i	$0.530697\pi$
$264$	5.62045	0.345914
$265$	0	0
$266$	22.7159	1.39280
$267$	−11.7902	−0.721546
$268$	−6.30981	−0.385433
$269$	9.23200	0.562885	0.281442	−	0.959578i	$-0.409187\pi$
$269$	9.23200	0.562885	0.281442	+	0.959578i	$0.409187\pi$
$270$	0	0
$271$	−21.6845	−1.31724	−0.658620	−	0.752475i	$-0.728860\pi$
$271$	−21.6845	−1.31724	−0.658620	+	0.752475i	$0.728860\pi$
$272$	−1.04568	−0.0634036
$273$	13.1144	0.793720
$274$	9.02419	0.545171
$275$	0	0
$276$	−5.29478	−0.318708
$277$	10.2951	0.618571	0.309285	−	0.950969i	$-0.399910\pi$
$277$	10.2951	0.618571	0.309285	+	0.950969i	$0.399910\pi$
$278$	−7.11259	−0.426585
$279$	−5.58042	−0.334091
$280$	0	0
$281$	−0.798542	−0.0476370	−0.0238185	−	0.999716i	$-0.507582\pi$
$281$	−0.798542	−0.0476370	−0.0238185	+	0.999716i	$0.507582\pi$
$282$	3.07374	0.183039
$283$	−0.730642	−0.0434322	−0.0217161	−	0.999764i	$-0.506913\pi$
$283$	−0.730642	−0.0434322	−0.0217161	+	0.999764i	$0.506913\pi$
$284$	−4.53276	−0.268970
$285$	0	0
$286$	−27.2075	−1.60882
$287$	4.27346	0.252254
$288$	−1.00000	−0.0589256
$289$	−15.9066	−0.935680
$290$	0	0
$291$	−2.64031	−0.154778
$292$	8.16098	0.477585
$293$	−18.4842	−1.07986	−0.539929	−	0.841711i	$-0.681549\pi$
$293$	−18.4842	−1.07986	−0.539929	+	0.841711i	$0.681549\pi$
$294$	0.339383	0.0197932
$295$	0	0
$296$	−2.99179	−0.173894
$297$	−5.62045	−0.326131
$298$	−15.4351	−0.894130
$299$	25.6311	1.48228
$300$	0	0
$301$	8.93117	0.514784
$302$	7.99801	0.460233
$303$	3.82844	0.219938
$304$	8.38494	0.480909
$305$	0	0
$306$	1.04568	0.0597775
$307$	−14.1923	−0.809998	−0.404999	−	0.914317i	$-0.632728\pi$
$307$	−14.1923	−0.809998	−0.404999	+	0.914317i	$0.632728\pi$
$308$	−15.2265	−0.867611
$309$	−5.89322	−0.335254
$310$	0	0
$311$	10.1142	0.573522	0.286761	−	0.958002i	$-0.407421\pi$
$311$	10.1142	0.573522	0.286761	+	0.958002i	$0.407421\pi$
$312$	4.84082	0.274057
$313$	−7.00045	−0.395689	−0.197844	−	0.980233i	$-0.563394\pi$
$313$	−7.00045	−0.395689	−0.197844	+	0.980233i	$0.563394\pi$
$314$	−15.6147	−0.881190
$315$	0	0
$316$	12.4814	0.702135
$317$	15.3385	0.861498	0.430749	−	0.902472i	$-0.358249\pi$
$317$	15.3385	0.861498	0.430749	+	0.902472i	$0.358249\pi$
$318$	−6.17710	−0.346395
$319$	23.5519	1.31865
$320$	0	0
$321$	−5.90758	−0.329729
$322$	14.3442	0.799373
$323$	−8.76795	−0.487862
$324$	1.00000	0.0555556
$325$	0	0
$326$	3.65730	0.202559
$327$	−5.63805	−0.311785
$328$	1.57743	0.0870990
$329$	−8.32716	−0.459091
$330$	0	0
$331$	23.6472	1.29977	0.649883	−	0.760034i	$-0.274818\pi$
$331$	23.6472	1.29977	0.649883	+	0.760034i	$0.274818\pi$
$332$	0.134522	0.00738284
$333$	2.99179	0.163949
$334$	6.30307	0.344889
$335$	0	0
$336$	2.70913	0.147795
$337$	27.7121	1.50957	0.754787	−	0.655969i	$-0.227740\pi$
$337$	27.7121	1.50957	0.754787	+	0.655969i	$0.227740\pi$
$338$	−10.4335	−0.567508
$339$	5.06692	0.275197
$340$	0	0
$341$	−31.3644	−1.69848
$342$	−8.38494	−0.453406
$343$	18.0445	0.974310
$344$	3.29669	0.177746
$345$	0	0
$346$	−10.6455	−0.572304
$347$	−26.6860	−1.43258	−0.716290	−	0.697803i	$-0.754161\pi$
$347$	−26.6860	−1.43258	−0.716290	+	0.697803i	$0.754161\pi$
$348$	−4.19039	−0.224628
$349$	−5.73576	−0.307028	−0.153514	−	0.988146i	$-0.549059\pi$
$349$	−5.73576	−0.307028	−0.153514	+	0.988146i	$0.549059\pi$
$350$	0	0
$351$	−4.84082	−0.258384
$352$	−5.62045	−0.299571
$353$	29.1028	1.54899	0.774494	−	0.632581i	$-0.218004\pi$
$353$	29.1028	1.54899	0.774494	+	0.632581i	$0.218004\pi$
$354$	−14.1876	−0.754061
$355$	0	0
$356$	11.7902	0.624877
$357$	−2.83288	−0.149932
$358$	0.799304	0.0422445
$359$	−12.9895	−0.685562	−0.342781	−	0.939415i	$-0.611369\pi$
$359$	−12.9895	−0.685562	−0.342781	+	0.939415i	$0.611369\pi$
$360$	0	0
$361$	51.3072	2.70038
$362$	16.3240	0.857970
$363$	−20.5894	−1.08066
$364$	−13.1144	−0.687381
$365$	0	0
$366$	0.270588	0.0141439
$367$	3.68807	0.192516	0.0962578	−	0.995356i	$-0.469313\pi$
$367$	3.68807	0.192516	0.0962578	+	0.995356i	$0.469313\pi$
$368$	5.29478	0.276009
$369$	−1.57743	−0.0821177
$370$	0	0
$371$	16.7346	0.868816
$372$	5.58042	0.289331
$373$	26.0048	1.34648	0.673239	−	0.739425i	$-0.264902\pi$
$373$	26.0048	1.34648	0.673239	+	0.739425i	$0.264902\pi$
$374$	5.87718	0.303902
$375$	0	0
$376$	−3.07374	−0.158516
$377$	20.2849	1.04473
$378$	−2.70913	−0.139343
$379$	−30.1651	−1.54948	−0.774738	−	0.632282i	$-0.782118\pi$
$379$	−30.1651	−1.54948	−0.774738	+	0.632282i	$0.782118\pi$
$380$	0	0
$381$	−9.52909	−0.488190
$382$	15.5301	0.794588
$383$	13.3650	0.682919	0.341460	−	0.939896i	$-0.389079\pi$
$383$	13.3650	0.682919	0.341460	+	0.939896i	$0.389079\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−21.0202	−1.06990
$387$	−3.29669	−0.167580
$388$	2.64031	0.134041
$389$	−9.70031	−0.491825	−0.245913	−	0.969292i	$-0.579088\pi$
$389$	−9.70031	−0.491825	−0.245913	+	0.969292i	$0.579088\pi$
$390$	0	0
$391$	−5.53664	−0.280000
$392$	−0.339383	−0.0171414
$393$	−0.148886	−0.00751030
$394$	24.1574	1.21703
$395$	0	0
$396$	5.62045	0.282438
$397$	7.91246	0.397115	0.198557	−	0.980089i	$-0.436374\pi$
$397$	7.91246	0.397115	0.198557	+	0.980089i	$0.436374\pi$
$398$	25.4930	1.27785
$399$	22.7159	1.13722
$400$	0	0
$401$	−20.1362	−1.00555	−0.502777	−	0.864416i	$-0.667688\pi$
$401$	−20.1362	−1.00555	−0.502777	+	0.864416i	$0.667688\pi$
$402$	−6.30981	−0.314705
$403$	−27.0138	−1.34565
$404$	−3.82844	−0.190472
$405$	0	0
$406$	11.3523	0.563406
$407$	16.8152	0.833498
$408$	−1.04568	−0.0517688
$409$	−2.80742	−0.138818	−0.0694089	−	0.997588i	$-0.522111\pi$
$409$	−2.80742	−0.138818	−0.0694089	+	0.997588i	$0.522111\pi$
$410$	0	0
$411$	9.02419	0.445131
$412$	5.89322	0.290338
$413$	38.4360	1.89131
$414$	−5.29478	−0.260224
$415$	0	0
$416$	−4.84082	−0.237341
$417$	−7.11259	−0.348305
$418$	−47.1271	−2.30506
$419$	−33.1961	−1.62174	−0.810869	−	0.585228i	$-0.801005\pi$
$419$	−33.1961	−1.62174	−0.810869	+	0.585228i	$0.801005\pi$
$420$	0	0
$421$	19.1376	0.932709	0.466355	−	0.884598i	$-0.345567\pi$
$421$	19.1376	0.932709	0.466355	+	0.884598i	$0.345567\pi$
$422$	−5.24920	−0.255527
$423$	3.07374	0.149450
$424$	6.17710	0.299987
$425$	0	0
$426$	−4.53276	−0.219613
$427$	−0.733059	−0.0354752
$428$	5.90758	0.285554
$429$	−27.2075	−1.31359
$430$	0	0
$431$	−20.0314	−0.964877	−0.482438	−	0.875930i	$-0.660249\pi$
$431$	−20.0314	−0.964877	−0.482438	+	0.875930i	$0.660249\pi$
$432$	−1.00000	−0.0481125
$433$	32.3617	1.55520	0.777602	−	0.628757i	$-0.216436\pi$
$433$	32.3617	1.55520	0.777602	+	0.628757i	$0.216436\pi$
$434$	−15.1181	−0.725691
$435$	0	0
$436$	5.63805	0.270014
$437$	44.3964	2.12377
$438$	8.16098	0.389947
$439$	17.3270	0.826973	0.413487	−	0.910510i	$-0.364311\pi$
$439$	17.3270	0.826973	0.413487	+	0.910510i	$0.364311\pi$
$440$	0	0
$441$	0.339383	0.0161611
$442$	5.06194	0.240772
$443$	16.5326	0.785489	0.392745	−	0.919648i	$-0.371526\pi$
$443$	16.5326	0.785489	0.392745	+	0.919648i	$0.371526\pi$
$444$	−2.99179	−0.141984
$445$	0	0
$446$	−14.7970	−0.700656
$447$	−15.4351	−0.730054
$448$	−2.70913	−0.127994
$449$	2.51289	0.118591	0.0592954	−	0.998240i	$-0.481115\pi$
$449$	2.51289	0.118591	0.0592954	+	0.998240i	$0.481115\pi$
$450$	0	0
$451$	−8.86586	−0.417477
$452$	−5.06692	−0.238328
$453$	7.99801	0.375779
$454$	11.8784	0.557483
$455$	0	0
$456$	8.38494	0.392661
$457$	36.7686	1.71996	0.859982	−	0.510324i	$-0.170475\pi$
$457$	36.7686	1.71996	0.859982	+	0.510324i	$0.170475\pi$
$458$	−18.2572	−0.853101
$459$	1.04568	0.0488081
$460$	0	0
$461$	6.07068	0.282740	0.141370	−	0.989957i	$-0.454849\pi$
$461$	6.07068	0.282740	0.141370	+	0.989957i	$0.454849\pi$
$462$	−15.2265	−0.708402
$463$	33.3123	1.54815	0.774077	−	0.633091i	$-0.218214\pi$
$463$	33.3123	1.54815	0.774077	+	0.633091i	$0.218214\pi$
$464$	4.19039	0.194534
$465$	0	0
$466$	−2.85842	−0.132414
$467$	−9.13651	−0.422787	−0.211394	−	0.977401i	$-0.567800\pi$
$467$	−9.13651	−0.422787	−0.211394	+	0.977401i	$0.567800\pi$
$468$	4.84082	0.223767
$469$	17.0941	0.789332
$470$	0	0
$471$	−15.6147	−0.719489
$472$	14.1876	0.653036
$473$	−18.5289	−0.851959
$474$	12.4814	0.573291
$475$	0	0
$476$	2.83288	0.129845
$477$	−6.17710	−0.282830
$478$	−16.3838	−0.749376
$479$	20.8609	0.953158	0.476579	−	0.879132i	$-0.341877\pi$
$479$	20.8609	0.953158	0.476579	+	0.879132i	$0.341877\pi$
$480$	0	0
$481$	14.4827	0.660355
$482$	−26.3276	−1.19919
$483$	14.3442	0.652686
$484$	20.5894	0.935882
$485$	0	0
$486$	1.00000	0.0453609
$487$	−1.27292	−0.0576814	−0.0288407	−	0.999584i	$-0.509182\pi$
$487$	−1.27292	−0.0576814	−0.0288407	+	0.999584i	$0.509182\pi$
$488$	−0.270588	−0.0122490
$489$	3.65730	0.165389
$490$	0	0
$491$	10.6983	0.482805	0.241403	−	0.970425i	$-0.422393\pi$
$491$	10.6983	0.482805	0.241403	+	0.970425i	$0.422393\pi$
$492$	1.57743	0.0711160
$493$	−4.38180	−0.197346
$494$	−40.5900	−1.82623
$495$	0	0
$496$	−5.58042	−0.250568
$497$	12.2798	0.550826
$498$	0.134522	0.00602807
$499$	−7.08035	−0.316960	−0.158480	−	0.987362i	$-0.550659\pi$
$499$	−7.08035	−0.316960	−0.158480	+	0.987362i	$0.550659\pi$
$500$	0	0
$501$	6.30307	0.281601
$502$	13.8356	0.617513
$503$	−5.53082	−0.246607	−0.123304	−	0.992369i	$-0.539349\pi$
$503$	−5.53082	−0.246607	−0.123304	+	0.992369i	$0.539349\pi$
$504$	2.70913	0.120674
$505$	0	0
$506$	−29.7590	−1.32295
$507$	−10.4335	−0.463368
$508$	9.52909	0.422785
$509$	9.63792	0.427193	0.213597	−	0.976922i	$-0.431482\pi$
$509$	9.63792	0.427193	0.213597	+	0.976922i	$0.431482\pi$
$510$	0	0
$511$	−22.1092	−0.978052
$512$	−1.00000	−0.0441942
$513$	−8.38494	−0.370204
$514$	28.6204	1.26239
$515$	0	0
$516$	3.29669	0.145129
$517$	17.2758	0.759789
$518$	8.10515	0.356120
$519$	−10.6455	−0.467284
$520$	0	0
$521$	20.2613	0.887665	0.443832	−	0.896110i	$-0.353619\pi$
$521$	20.2613	0.887665	0.443832	+	0.896110i	$0.353619\pi$
$522$	−4.19039	−0.183408
$523$	−25.6681	−1.12239	−0.561193	−	0.827685i	$-0.689658\pi$
$523$	−25.6681	−1.12239	−0.561193	+	0.827685i	$0.689658\pi$
$524$	0.148886	0.00650411
$525$	0	0
$526$	3.12306	0.136172
$527$	5.83532	0.254191
$528$	−5.62045	−0.244598
$529$	5.03469	0.218899
$530$	0	0
$531$	−14.1876	−0.615688
$532$	−22.7159	−0.984859
$533$	−7.63605	−0.330754
$534$	11.7902	0.510210
$535$	0	0
$536$	6.30981	0.272542
$537$	0.799304	0.0344925
$538$	−9.23200	−0.398020
$539$	1.90749	0.0821612
$540$	0	0
$541$	−3.96094	−0.170294	−0.0851471	−	0.996368i	$-0.527136\pi$
$541$	−3.96094	−0.170294	−0.0851471	+	0.996368i	$0.527136\pi$
$542$	21.6845	0.931430
$543$	16.3240	0.700529
$544$	1.04568	0.0448331
$545$	0	0
$546$	−13.1144	−0.561245
$547$	−9.95096	−0.425472	−0.212736	−	0.977110i	$-0.568237\pi$
$547$	−9.95096	−0.425472	−0.212736	+	0.977110i	$0.568237\pi$
$548$	−9.02419	−0.385494
$549$	0.270588	0.0115484
$550$	0	0
$551$	35.1362	1.49685
$552$	5.29478	0.225361
$553$	−33.8138	−1.43791
$554$	−10.2951	−0.437396
$555$	0	0
$556$	7.11259	0.301641
$557$	18.7017	0.792415	0.396207	−	0.918161i	$-0.370326\pi$
$557$	18.7017	0.792415	0.396207	+	0.918161i	$0.370326\pi$
$558$	5.58042	0.236238
$559$	−15.9587	−0.674981
$560$	0	0
$561$	5.87718	0.248135
$562$	0.798542	0.0336845
$563$	38.3865	1.61780	0.808898	−	0.587949i	$-0.200064\pi$
$563$	38.3865	1.61780	0.808898	+	0.587949i	$0.200064\pi$
$564$	−3.07374	−0.129428
$565$	0	0
$566$	0.730642	0.0307112
$567$	−2.70913	−0.113773
$568$	4.53276	0.190190
$569$	−15.8679	−0.665216	−0.332608	−	0.943065i	$-0.607929\pi$
$569$	−15.8679	−0.665216	−0.332608	+	0.943065i	$0.607929\pi$
$570$	0	0
$571$	32.2596	1.35002	0.675012	−	0.737807i	$-0.264139\pi$
$571$	32.2596	1.35002	0.675012	+	0.737807i	$0.264139\pi$
$572$	27.2075	1.13760
$573$	15.5301	0.648778
$574$	−4.27346	−0.178371
$575$	0	0
$576$	1.00000	0.0416667
$577$	28.0399	1.16732	0.583659	−	0.811999i	$-0.301621\pi$
$577$	28.0399	1.16732	0.583659	+	0.811999i	$0.301621\pi$
$578$	15.9066	0.661626
$579$	−21.0202	−0.873569
$580$	0	0
$581$	−0.364437	−0.0151194
$582$	2.64031	0.109444
$583$	−34.7181	−1.43788
$584$	−8.16098	−0.337704
$585$	0	0
$586$	18.4842	0.763575
$587$	−11.3870	−0.469992	−0.234996	−	0.971996i	$-0.575508\pi$
$587$	−11.3870	−0.469992	−0.234996	+	0.971996i	$0.575508\pi$
$588$	−0.339383	−0.0139959
$589$	−46.7915	−1.92801
$590$	0	0
$591$	24.1574	0.993703
$592$	2.99179	0.122962
$593$	−34.9063	−1.43343	−0.716715	−	0.697366i	$-0.754355\pi$
$593$	−34.9063	−1.43343	−0.716715	+	0.697366i	$0.754355\pi$
$594$	5.62045	0.230610
$595$	0	0
$596$	15.4351	0.632246
$597$	25.4930	1.04336
$598$	−25.6311	−1.04813
$599$	21.2325	0.867535	0.433768	−	0.901025i	$-0.357184\pi$
$599$	21.2325	0.867535	0.433768	+	0.901025i	$0.357184\pi$
$600$	0	0
$601$	−22.6617	−0.924389	−0.462195	−	0.886779i	$-0.652938\pi$
$601$	−22.6617	−0.924389	−0.462195	+	0.886779i	$0.652938\pi$
$602$	−8.93117	−0.364007
$603$	−6.30981	−0.256955
$604$	−7.99801	−0.325434
$605$	0	0
$606$	−3.82844	−0.155520
$607$	−21.3752	−0.867591	−0.433796	−	0.901011i	$-0.642826\pi$
$607$	−21.3752	−0.867591	−0.433796	+	0.901011i	$0.642826\pi$
$608$	−8.38494	−0.340054
$609$	11.3523	0.460019
$610$	0	0
$611$	14.8794	0.601957
$612$	−1.04568	−0.0422691
$613$	−34.0087	−1.37360	−0.686799	−	0.726848i	$-0.740985\pi$
$613$	−34.0087	−1.37360	−0.686799	+	0.726848i	$0.740985\pi$
$614$	14.1923	0.572755
$615$	0	0
$616$	15.2265	0.613494
$617$	24.3930	0.982027	0.491014	−	0.871152i	$-0.336627\pi$
$617$	24.3930	0.982027	0.491014	+	0.871152i	$0.336627\pi$
$618$	5.89322	0.237060
$619$	−24.2876	−0.976202	−0.488101	−	0.872787i	$-0.662310\pi$
$619$	−24.2876	−0.976202	−0.488101	+	0.872787i	$0.662310\pi$
$620$	0	0
$621$	−5.29478	−0.212472
$622$	−10.1142	−0.405542
$623$	−31.9411	−1.27969
$624$	−4.84082	−0.193788
$625$	0	0
$626$	7.00045	0.279794
$627$	−47.1271	−1.88208
$628$	15.6147	0.623095
$629$	−3.12845	−0.124739
$630$	0	0
$631$	1.03394	0.0411606	0.0205803	−	0.999788i	$-0.493449\pi$
$631$	1.03394	0.0411606	0.0205803	+	0.999788i	$0.493449\pi$
$632$	−12.4814	−0.496484
$633$	−5.24920	−0.208637
$634$	−15.3385	−0.609171
$635$	0	0
$636$	6.17710	0.244938
$637$	1.64289	0.0650938
$638$	−23.5519	−0.932427
$639$	−4.53276	−0.179313
$640$	0	0
$641$	4.93979	0.195110	0.0975550	−	0.995230i	$-0.468898\pi$
$641$	4.93979	0.195110	0.0975550	+	0.995230i	$0.468898\pi$
$642$	5.90758	0.233154
$643$	−36.3220	−1.43240	−0.716199	−	0.697896i	$-0.754120\pi$
$643$	−36.3220	−1.43240	−0.716199	+	0.697896i	$0.754120\pi$
$644$	−14.3442	−0.565242
$645$	0	0
$646$	8.76795	0.344971
$647$	−14.2736	−0.561151	−0.280576	−	0.959832i	$-0.590525\pi$
$647$	−14.2736	−0.561151	−0.280576	+	0.959832i	$0.590525\pi$
$648$	−1.00000	−0.0392837
$649$	−79.7405	−3.13009
$650$	0	0
$651$	−15.1181	−0.592524
$652$	−3.65730	−0.143231
$653$	−5.76651	−0.225661	−0.112830	−	0.993614i	$-0.535992\pi$
$653$	−5.76651	−0.225661	−0.112830	+	0.993614i	$0.535992\pi$
$654$	5.63805	0.220465
$655$	0	0
$656$	−1.57743	−0.0615883
$657$	8.16098	0.318390
$658$	8.32716	0.324627
$659$	10.0701	0.392275	0.196138	−	0.980576i	$-0.437160\pi$
$659$	10.0701	0.392275	0.196138	+	0.980576i	$0.437160\pi$
$660$	0	0
$661$	−36.9291	−1.43637	−0.718187	−	0.695850i	$-0.755028\pi$
$661$	−36.9291	−1.43637	−0.718187	+	0.695850i	$0.755028\pi$
$662$	−23.6472	−0.919073
$663$	5.06194	0.196589
$664$	−0.134522	−0.00522046
$665$	0	0
$666$	−2.99179	−0.115929
$667$	22.1872	0.859091
$668$	−6.30307	−0.243873
$669$	−14.7970	−0.572083
$670$	0	0
$671$	1.52083	0.0587109
$672$	−2.70913	−0.104507
$673$	−27.0338	−1.04208	−0.521039	−	0.853533i	$-0.674455\pi$
$673$	−27.0338	−1.04208	−0.521039	+	0.853533i	$0.674455\pi$
$674$	−27.7121	−1.06743
$675$	0	0
$676$	10.4335	0.401289
$677$	8.65077	0.332476	0.166238	−	0.986086i	$-0.446838\pi$
$677$	8.65077	0.332476	0.166238	+	0.986086i	$0.446838\pi$
$678$	−5.06692	−0.194594
$679$	−7.15293	−0.274504
$680$	0	0
$681$	11.8784	0.455183
$682$	31.3644	1.20101
$683$	46.4716	1.77819	0.889093	−	0.457727i	$-0.151336\pi$
$683$	46.4716	1.77819	0.889093	+	0.457727i	$0.151336\pi$
$684$	8.38494	0.320606
$685$	0	0
$686$	−18.0445	−0.688941
$687$	−18.2572	−0.696554
$688$	−3.29669	−0.125685
$689$	−29.9022	−1.13918
$690$	0	0
$691$	−47.2883	−1.79893	−0.899466	−	0.436991i	$-0.856044\pi$
$691$	−47.2883	−1.79893	−0.899466	+	0.436991i	$0.856044\pi$
$692$	10.6455	0.404680
$693$	−15.2265	−0.578407
$694$	26.6860	1.01299
$695$	0	0
$696$	4.19039	0.158836
$697$	1.64948	0.0624787
$698$	5.73576	0.217102
$699$	−2.85842	−0.108115
$700$	0	0
$701$	30.1858	1.14010	0.570052	−	0.821609i	$-0.306923\pi$
$701$	30.1858	1.14010	0.570052	+	0.821609i	$0.306923\pi$
$702$	4.84082	0.182705
$703$	25.0860	0.946136
$704$	5.62045	0.211828
$705$	0	0
$706$	−29.1028	−1.09530
$707$	10.3717	0.390069
$708$	14.1876	0.533202
$709$	−17.3299	−0.650837	−0.325419	−	0.945570i	$-0.605505\pi$
$709$	−17.3299	−0.650837	−0.325419	+	0.945570i	$0.605505\pi$
$710$	0	0
$711$	12.4814	0.468090
$712$	−11.7902	−0.441855
$713$	−29.5471	−1.10655
$714$	2.83288	0.106018
$715$	0	0
$716$	−0.799304	−0.0298714
$717$	−16.3838	−0.611863
$718$	12.9895	0.484765
$719$	−18.8364	−0.702479	−0.351240	−	0.936286i	$-0.614240\pi$
$719$	−18.8364	−0.702479	−0.351240	+	0.936286i	$0.614240\pi$
$720$	0	0
$721$	−15.9655	−0.594586
$722$	−51.3072	−1.90946
$723$	−26.3276	−0.979134
$724$	−16.3240	−0.606676
$725$	0	0
$726$	20.5894	0.764144
$727$	−21.3336	−0.791221	−0.395610	−	0.918418i	$-0.629467\pi$
$727$	−21.3336	−0.791221	−0.395610	+	0.918418i	$0.629467\pi$
$728$	13.1144	0.486052
$729$	1.00000	0.0370370
$730$	0	0
$731$	3.44728	0.127502
$732$	−0.270588	−0.0100012
$733$	20.8712	0.770895	0.385448	−	0.922730i	$-0.374047\pi$
$733$	20.8712	0.770895	0.385448	+	0.922730i	$0.374047\pi$
$734$	−3.68807	−0.136129
$735$	0	0
$736$	−5.29478	−0.195168
$737$	−35.4639	−1.30633
$738$	1.57743	0.0580660
$739$	−16.2084	−0.596236	−0.298118	−	0.954529i	$-0.596359\pi$
$739$	−16.2084	−0.596236	−0.298118	+	0.954529i	$0.596359\pi$
$740$	0	0
$741$	−40.5900	−1.49111
$742$	−16.7346	−0.614346
$743$	−34.7758	−1.27580	−0.637900	−	0.770120i	$-0.720197\pi$
$743$	−34.7758	−1.27580	−0.637900	+	0.770120i	$0.720197\pi$
$744$	−5.58042	−0.204588
$745$	0	0
$746$	−26.0048	−0.952104
$747$	0.134522	0.00492190
$748$	−5.87718	−0.214891
$749$	−16.0044	−0.584788
$750$	0	0
$751$	21.2393	0.775034	0.387517	−	0.921863i	$-0.373333\pi$
$751$	21.2393	0.775034	0.387517	+	0.921863i	$0.373333\pi$
$752$	3.07374	0.112088
$753$	13.8356	0.504197
$754$	−20.2849	−0.738733
$755$	0	0
$756$	2.70913	0.0985301
$757$	53.9563	1.96107	0.980537	−	0.196335i	$-0.0629040\pi$
$757$	53.9563	1.96107	0.980537	+	0.196335i	$0.0629040\pi$
$758$	30.1651	1.09565
$759$	−29.7590	−1.08018
$760$	0	0
$761$	−42.3959	−1.53685	−0.768426	−	0.639939i	$-0.778960\pi$
$761$	−42.3959	−1.53685	−0.768426	+	0.639939i	$0.778960\pi$
$762$	9.52909	0.345202
$763$	−15.2742	−0.552964
$764$	−15.5301	−0.561858
$765$	0	0
$766$	−13.3650	−0.482897
$767$	−68.6795	−2.47987
$768$	−1.00000	−0.0360844
$769$	5.04642	0.181979	0.0909893	−	0.995852i	$-0.470997\pi$
$769$	5.04642	0.181979	0.0909893	+	0.995852i	$0.470997\pi$
$770$	0	0
$771$	28.6204	1.03074
$772$	21.0202	0.756533
$773$	−34.8495	−1.25345	−0.626724	−	0.779241i	$-0.715605\pi$
$773$	−34.8495	−1.25345	−0.626724	+	0.779241i	$0.715605\pi$
$774$	3.29669	0.118497
$775$	0	0
$776$	−2.64031	−0.0947815
$777$	8.10515	0.290770
$778$	9.70031	0.347773
$779$	−13.2267	−0.473894
$780$	0	0
$781$	−25.4761	−0.911608
$782$	5.53664	0.197990
$783$	−4.19039	−0.149752
$784$	0.339383	0.0121208
$785$	0	0
$786$	0.148886	0.00531059
$787$	16.0429	0.571869	0.285935	−	0.958249i	$-0.407696\pi$
$787$	16.0429	0.571869	0.285935	+	0.958249i	$0.407696\pi$
$788$	−24.1574	−0.860572
$789$	3.12306	0.111184
$790$	0	0
$791$	13.7269	0.488074
$792$	−5.62045	−0.199714
$793$	1.30987	0.0465148
$794$	−7.91246	−0.280803
$795$	0	0
$796$	−25.4930	−0.903574
$797$	37.2447	1.31928	0.659638	−	0.751584i	$-0.270710\pi$
$797$	37.2447	1.31928	0.659638	+	0.751584i	$0.270710\pi$
$798$	−22.7159	−0.804134
$799$	−3.21415	−0.113708
$800$	0	0
$801$	11.7902	0.416585
$802$	20.1362	0.711034
$803$	45.8684	1.61866
$804$	6.30981	0.222530
$805$	0	0
$806$	27.0138	0.951520
$807$	−9.23200	−0.324982
$808$	3.82844	0.134684
$809$	−8.62369	−0.303193	−0.151596	−	0.988442i	$-0.548441\pi$
$809$	−8.62369	−0.303193	−0.151596	+	0.988442i	$0.548441\pi$
$810$	0	0
$811$	0.183808	0.00645438	0.00322719	−	0.999995i	$-0.498973\pi$
$811$	0.183808	0.00645438	0.00322719	+	0.999995i	$0.498973\pi$
$812$	−11.3523	−0.398388
$813$	21.6845	0.760509
$814$	−16.8152	−0.589372
$815$	0	0
$816$	1.04568	0.0366061
$817$	−27.6426	−0.967091
$818$	2.80742	0.0981591
$819$	−13.1144	−0.458254
$820$	0	0
$821$	27.4060	0.956476	0.478238	−	0.878230i	$-0.341276\pi$
$821$	27.4060	0.956476	0.478238	+	0.878230i	$0.341276\pi$
$822$	−9.02419	−0.314755
$823$	32.5985	1.13631	0.568156	−	0.822921i	$-0.307657\pi$
$823$	32.5985	1.13631	0.568156	+	0.822921i	$0.307657\pi$
$824$	−5.89322	−0.205300
$825$	0	0
$826$	−38.4360	−1.33736
$827$	−38.6082	−1.34254	−0.671270	−	0.741213i	$-0.734251\pi$
$827$	−38.6082	−1.34254	−0.671270	+	0.741213i	$0.734251\pi$
$828$	5.29478	0.184006
$829$	36.1007	1.25383	0.626915	−	0.779088i	$-0.284317\pi$
$829$	36.1007	1.25383	0.626915	+	0.779088i	$0.284317\pi$
$830$	0	0
$831$	−10.2951	−0.357132
$832$	4.84082	0.167825
$833$	−0.354886	−0.0122961
$834$	7.11259	0.246289
$835$	0	0
$836$	47.1271	1.62992
$837$	5.58042	0.192887
$838$	33.1961	1.14674
$839$	33.0852	1.14223	0.571113	−	0.820871i	$-0.306512\pi$
$839$	33.0852	1.14223	0.571113	+	0.820871i	$0.306512\pi$
$840$	0	0
$841$	−11.4406	−0.394505
$842$	−19.1376	−0.659525
$843$	0.798542	0.0275033
$844$	5.24920	0.180685
$845$	0	0
$846$	−3.07374	−0.105677
$847$	−55.7794	−1.91660
$848$	−6.17710	−0.212123
$849$	0.730642	0.0250756
$850$	0	0
$851$	15.8409	0.543018
$852$	4.53276	0.155290
$853$	20.1475	0.689836	0.344918	−	0.938633i	$-0.387907\pi$
$853$	20.1475	0.689836	0.344918	+	0.938633i	$0.387907\pi$
$854$	0.733059	0.0250848
$855$	0	0
$856$	−5.90758	−0.201917
$857$	−55.8400	−1.90746	−0.953729	−	0.300668i	$-0.902790\pi$
$857$	−55.8400	−1.90746	−0.953729	+	0.300668i	$0.902790\pi$
$858$	27.2075	0.928850
$859$	−50.9315	−1.73776	−0.868880	−	0.495023i	$-0.835159\pi$
$859$	−50.9315	−1.73776	−0.868880	+	0.495023i	$0.835159\pi$
$860$	0	0
$861$	−4.27346	−0.145639
$862$	20.0314	0.682271
$863$	27.6734	0.942012	0.471006	−	0.882130i	$-0.343891\pi$
$863$	27.6734	0.942012	0.471006	+	0.882130i	$0.343891\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−32.3617	−1.09970
$867$	15.9066	0.540215
$868$	15.1181	0.513141
$869$	70.1511	2.37971
$870$	0	0
$871$	−30.5446	−1.03497
$872$	−5.63805	−0.190929
$873$	2.64031	0.0893608
$874$	−44.3964	−1.50173
$875$	0	0
$876$	−8.16098	−0.275734
$877$	−33.6019	−1.13466	−0.567328	−	0.823492i	$-0.692023\pi$
$877$	−33.6019	−1.13466	−0.567328	+	0.823492i	$0.692023\pi$
$878$	−17.3270	−0.584758
$879$	18.4842	0.623456
$880$	0	0
$881$	2.59498	0.0874272	0.0437136	−	0.999044i	$-0.486081\pi$
$881$	2.59498	0.0874272	0.0437136	+	0.999044i	$0.486081\pi$
$882$	−0.339383	−0.0114276
$883$	39.9789	1.34540	0.672698	−	0.739917i	$-0.265135\pi$
$883$	39.9789	1.34540	0.672698	+	0.739917i	$0.265135\pi$
$884$	−5.06194	−0.170251
$885$	0	0
$886$	−16.5326	−0.555425
$887$	−21.8845	−0.734811	−0.367405	−	0.930061i	$-0.619754\pi$
$887$	−21.8845	−0.734811	−0.367405	+	0.930061i	$0.619754\pi$
$888$	2.99179	0.100398
$889$	−25.8155	−0.865825
$890$	0	0
$891$	5.62045	0.188292
$892$	14.7970	0.495439
$893$	25.7731	0.862465
$894$	15.4351	0.516226
$895$	0	0
$896$	2.70913	0.0905057
$897$	−25.6311	−0.855796
$898$	−2.51289	−0.0838563
$899$	−23.3841	−0.779904
$900$	0	0
$901$	6.45927	0.215189
$902$	8.86586	0.295201
$903$	−8.93117	−0.297211
$904$	5.06692	0.168523
$905$	0	0
$906$	−7.99801	−0.265716
$907$	−22.6784	−0.753025	−0.376512	−	0.926412i	$-0.622877\pi$
$907$	−22.6784	−0.753025	−0.376512	+	0.926412i	$0.622877\pi$
$908$	−11.8784	−0.394200
$909$	−3.82844	−0.126981
$910$	0	0
$911$	48.3310	1.60128	0.800638	−	0.599148i	$-0.204494\pi$
$911$	48.3310	1.60128	0.800638	+	0.599148i	$0.204494\pi$
$912$	−8.38494	−0.277653
$913$	0.756073	0.0250223
$914$	−36.7686	−1.21620
$915$	0	0
$916$	18.2572	0.603234
$917$	−0.403351	−0.0133198
$918$	−1.04568	−0.0345125
$919$	−43.0761	−1.42095	−0.710474	−	0.703723i	$-0.751519\pi$
$919$	−43.0761	−1.42095	−0.710474	+	0.703723i	$0.751519\pi$
$920$	0	0
$921$	14.1923	0.467652
$922$	−6.07068	−0.199927
$923$	−21.9423	−0.722238
$924$	15.2265	0.500916
$925$	0	0
$926$	−33.3123	−1.09471
$927$	5.89322	0.193559
$928$	−4.19039	−0.137556
$929$	−37.9242	−1.24425	−0.622126	−	0.782917i	$-0.713731\pi$
$929$	−37.9242	−1.24425	−0.622126	+	0.782917i	$0.713731\pi$
$930$	0	0
$931$	2.84571	0.0932644
$932$	2.85842	0.0936307
$933$	−10.1142	−0.331123
$934$	9.13651	0.298956
$935$	0	0
$936$	−4.84082	−0.158227
$937$	−16.5775	−0.541563	−0.270782	−	0.962641i	$-0.587282\pi$
$937$	−16.5775	−0.541563	−0.270782	+	0.962641i	$0.587282\pi$
$938$	−17.0941	−0.558142
$939$	7.00045	0.228451
$940$	0	0
$941$	25.6063	0.834743	0.417371	−	0.908736i	$-0.362951\pi$
$941$	25.6063	0.834743	0.417371	+	0.908736i	$0.362951\pi$
$942$	15.6147	0.508755
$943$	−8.35214	−0.271983
$944$	−14.1876	−0.461766
$945$	0	0
$946$	18.5289	0.602426
$947$	19.9638	0.648735	0.324368	−	0.945931i	$-0.394849\pi$
$947$	19.9638	0.648735	0.324368	+	0.945931i	$0.394849\pi$
$948$	−12.4814	−0.405378
$949$	39.5058	1.28241
$950$	0	0
$951$	−15.3385	−0.497386
$952$	−2.83288	−0.0918141
$953$	−45.1335	−1.46202	−0.731010	−	0.682367i	$-0.760951\pi$
$953$	−45.1335	−1.46202	−0.731010	+	0.682367i	$0.760951\pi$
$954$	6.17710	0.199991
$955$	0	0
$956$	16.3838	0.529889
$957$	−23.5519	−0.761323
$958$	−20.8609	−0.673984
$959$	24.4477	0.789458
$960$	0	0
$961$	0.141061	0.00455036
$962$	−14.4827	−0.466941
$963$	5.90758	0.190369
$964$	26.3276	0.847955
$965$	0	0
$966$	−14.3442	−0.461518
$967$	−7.84915	−0.252412	−0.126206	−	0.992004i	$-0.540280\pi$
$967$	−7.84915	−0.252412	−0.126206	+	0.992004i	$0.540280\pi$
$968$	−20.5894	−0.661768
$969$	8.76795	0.281667
$970$	0	0
$971$	4.30228	0.138067	0.0690333	−	0.997614i	$-0.478009\pi$
$971$	4.30228	0.138067	0.0690333	+	0.997614i	$0.478009\pi$
$972$	−1.00000	−0.0320750
$973$	−19.2689	−0.617733
$974$	1.27292	0.0407869
$975$	0	0
$976$	0.270588	0.00866132
$977$	−0.426335	−0.0136397	−0.00681983	−	0.999977i	$-0.502171\pi$
$977$	−0.426335	−0.0136397	−0.00681983	+	0.999977i	$0.502171\pi$
$978$	−3.65730	−0.116947
$979$	66.2659	2.11787
$980$	0	0
$981$	5.63805	0.180009
$982$	−10.6983	−0.341395
$983$	59.5909	1.90066	0.950328	−	0.311251i	$-0.100748\pi$
$983$	59.5909	1.90066	0.950328	+	0.311251i	$0.100748\pi$
$984$	−1.57743	−0.0502866
$985$	0	0
$986$	4.38180	0.139545
$987$	8.32716	0.265057
$988$	40.5900	1.29134
$989$	−17.4553	−0.555045
$990$	0	0
$991$	21.9785	0.698169	0.349084	−	0.937091i	$-0.386493\pi$
$991$	21.9785	0.698169	0.349084	+	0.937091i	$0.386493\pi$
$992$	5.58042	0.177178
$993$	−23.6472	−0.750420
$994$	−12.2798	−0.389493
$995$	0	0
$996$	−0.134522	−0.00426249
$997$	44.8454	1.42027	0.710135	−	0.704066i	$-0.248634\pi$
$997$	44.8454	1.42027	0.710135	+	0.704066i	$0.248634\pi$
$998$	7.08035	0.224124
$999$	−2.99179	−0.0946560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.u.1.3		8
5.2	odd	4		3750.2.c.k.1249.3		16
5.3	odd	4		3750.2.c.k.1249.14		16
5.4	even	2		3750.2.a.v.1.6		8
25.3	odd	20		150.2.h.b.109.4	✓	16
25.4	even	10		750.2.g.f.451.3		16
25.6	even	5		750.2.g.g.301.2		16
25.8	odd	20		750.2.h.d.199.2		16
25.17	odd	20		150.2.h.b.139.4	yes	16
25.19	even	10		750.2.g.f.301.3		16
25.21	even	5		750.2.g.g.451.2		16
25.22	odd	20		750.2.h.d.49.1		16
75.17	even	20		450.2.l.c.289.1		16
75.53	even	20		450.2.l.c.109.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.4	✓	16	25.3	odd	20
150.2.h.b.139.4	yes	16	25.17	odd	20
450.2.l.c.109.1		16	75.53	even	20
450.2.l.c.289.1		16	75.17	even	20
750.2.g.f.301.3		16	25.19	even	10
750.2.g.f.451.3		16	25.4	even	10
750.2.g.g.301.2		16	25.6	even	5
750.2.g.g.451.2		16	25.21	even	5
750.2.h.d.49.1		16	25.22	odd	20
750.2.h.d.199.2		16	25.8	odd	20
3750.2.a.u.1.3		8	1.1	even	1	trivial
3750.2.a.v.1.6		8	5.4	even	2
3750.2.c.k.1249.3		16	5.2	odd	4
3750.2.c.k.1249.14		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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.70913 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.70913 q^{7} -1.00000 q^{8} +1.00000 q^{9} +5.62045 q^{11} -1.00000 q^{12} +4.84082 q^{13} +2.70913 q^{14} +1.00000 q^{16} -1.04568 q^{17} -1.00000 q^{18} +8.38494 q^{19} +2.70913 q^{21} -5.62045 q^{22} +5.29478 q^{23} +1.00000 q^{24} -4.84082 q^{26} -1.00000 q^{27} -2.70913 q^{28} +4.19039 q^{29} -5.58042 q^{31} -1.00000 q^{32} -5.62045 q^{33} +1.04568 q^{34} +1.00000 q^{36} +2.99179 q^{37} -8.38494 q^{38} -4.84082 q^{39} -1.57743 q^{41} -2.70913 q^{42} -3.29669 q^{43} +5.62045 q^{44} -5.29478 q^{46} +3.07374 q^{47} -1.00000 q^{48} +0.339383 q^{49} +1.04568 q^{51} +4.84082 q^{52} -6.17710 q^{53} +1.00000 q^{54} +2.70913 q^{56} -8.38494 q^{57} -4.19039 q^{58} -14.1876 q^{59} +0.270588 q^{61} +5.58042 q^{62} -2.70913 q^{63} +1.00000 q^{64} +5.62045 q^{66} -6.30981 q^{67} -1.04568 q^{68} -5.29478 q^{69} -4.53276 q^{71} -1.00000 q^{72} +8.16098 q^{73} -2.99179 q^{74} +8.38494 q^{76} -15.2265 q^{77} +4.84082 q^{78} +12.4814 q^{79} +1.00000 q^{81} +1.57743 q^{82} +0.134522 q^{83} +2.70913 q^{84} +3.29669 q^{86} -4.19039 q^{87} -5.62045 q^{88} +11.7902 q^{89} -13.1144 q^{91} +5.29478 q^{92} +5.58042 q^{93} -3.07374 q^{94} +1.00000 q^{96} +2.64031 q^{97} -0.339383 q^{98} +5.62045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 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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