LMFDB - Embedded newform 3750.2.a.v.1.6

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			1.6
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	$-0.328913\pi$
$7$	2.70913	1.02395	0.511977	+	0.858999i	$0.328913\pi$
$8$	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	$-0.734264\pi$
$13$	−4.84082	−1.34260	−0.671301	+	0.741185i	$0.734264\pi$
$14$	2.70913	0.724045
$15$	0	0
$16$	1.00000	0.250000
$17$	1.04568	0.253614	0.126807	−	0.991927i	$-0.459527\pi$
$17$	1.04568	0.253614	0.126807	+	0.991927i	$0.459527\pi$
$18$	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	$-0.686142\pi$
$23$	−5.29478	−1.10404	−0.552019	+	0.833832i	$0.686142\pi$
$24$	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	$-0.579091\pi$
$37$	−2.99179	−0.491847	−0.245924	+	0.969289i	$0.579091\pi$
$38$	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	$-0.419119\pi$
$43$	3.29669	0.502741	0.251370	+	0.967891i	$0.419119\pi$
$44$	5.62045	0.847314
$45$	0	0
$46$	−5.29478	−0.780673
$47$	−3.07374	−0.448351	−0.224176	−	0.974549i	$-0.571969\pi$
$47$	−3.07374	−0.448351	−0.224176	+	0.974549i	$0.571969\pi$
$48$	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	$-0.360539\pi$
$53$	6.17710	0.848491	0.424245	+	0.905547i	$0.360539\pi$
$54$	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	$-0.374052\pi$
$67$	6.30981	0.770866	0.385433	+	0.922736i	$0.374052\pi$
$68$	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	$-0.658488\pi$
$73$	−8.16098	−0.955171	−0.477585	+	0.878585i	$0.658488\pi$
$74$	−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	$-0.502350\pi$
$83$	−0.134522	−0.0147657	−0.00738284	+	0.999973i	$0.502350\pi$
$84$	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	$-0.542795\pi$
$97$	−2.64031	−0.268083	−0.134041	+	0.990976i	$0.542795\pi$
$98$	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	$-0.593768\pi$
$103$	−5.89322	−0.580676	−0.290338	+	0.956924i	$0.593768\pi$
$104$	−4.84082	−0.474681
$105$	0	0
$106$	6.17710	0.599973
$107$	−5.90758	−0.571108	−0.285554	−	0.958363i	$-0.592178\pi$
$107$	−5.90758	−0.571108	−0.285554	+	0.958363i	$0.592178\pi$
$108$	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	$-0.423401\pi$
$113$	5.06692	0.476656	0.238328	+	0.971185i	$0.423401\pi$
$114$	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	$-0.638947\pi$
$127$	−9.52909	−0.845570	−0.422785	+	0.906230i	$0.638947\pi$
$128$	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	$-0.374031\pi$
$137$	9.02419	0.770989	0.385494	+	0.922710i	$0.374031\pi$
$138$	−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	$-0.714125\pi$
$157$	−15.6147	−1.24619	−0.623095	+	0.782146i	$0.714125\pi$
$158$	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	$-0.454251\pi$
$163$	3.65730	0.286461	0.143231	+	0.989689i	$0.454251\pi$
$164$	−1.57743	−0.123177
$165$	0	0
$166$	−0.134522	−0.0104409
$167$	6.30307	0.487746	0.243873	−	0.969807i	$-0.421582\pi$
$167$	6.30307	0.487746	0.243873	+	0.969807i	$0.421582\pi$
$168$	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	$-0.632617\pi$
$173$	−10.6455	−0.809360	−0.404680	+	0.914458i	$0.632617\pi$
$174$	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	$-0.773108\pi$
$193$	−21.0202	−1.51307	−0.756533	+	0.653956i	$0.773108\pi$
$194$	−2.64031	−0.189563
$195$	0	0
$196$	0.339383	0.0242417
$197$	24.1574	1.72114	0.860572	−	0.509328i	$-0.170106\pi$
$197$	24.1574	1.72114	0.860572	+	0.509328i	$0.170106\pi$
$198$	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	$-0.664993\pi$
$223$	−14.7970	−0.990877	−0.495439	+	0.868643i	$0.664993\pi$
$224$	2.70913	0.181011
$225$	0	0
$226$	5.06692	0.337047
$227$	11.8784	0.788400	0.394200	−	0.919025i	$-0.371022\pi$
$227$	11.8784	0.788400	0.394200	+	0.919025i	$0.371022\pi$
$228$	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	$-0.529847\pi$
$233$	−2.85842	−0.187261	−0.0936307	+	0.995607i	$0.529847\pi$
$234$	−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	$-0.148846\pi$
$257$	28.6204	1.78529	0.892647	+	0.450756i	$0.148846\pi$
$258$	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	$-0.469303\pi$
$263$	3.12306	0.192576	0.0962882	+	0.995353i	$0.469303\pi$
$264$	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	$-0.600090\pi$
$277$	−10.2951	−0.618571	−0.309285	+	0.950969i	$0.600090\pi$
$278$	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	$-0.493087\pi$
$283$	0.730642	0.0434322	0.0217161	+	0.999764i	$0.493087\pi$
$284$	−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	$-0.318451\pi$
$293$	18.4842	1.07986	0.539929	+	0.841711i	$0.318451\pi$
$294$	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	$-0.367272\pi$
$307$	14.1923	0.809998	0.404999	+	0.914317i	$0.367272\pi$
$308$	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	$-0.436606\pi$
$313$	7.00045	0.395689	0.197844	+	0.980233i	$0.436606\pi$
$314$	−15.6147	−0.881190
$315$	0	0
$316$	12.4814	0.702135
$317$	−15.3385	−0.861498	−0.430749	−	0.902472i	$-0.641751\pi$
$317$	−15.3385	−0.861498	−0.430749	+	0.902472i	$0.641751\pi$
$318$	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	$-0.772260\pi$
$337$	−27.7121	−1.50957	−0.754787	+	0.655969i	$0.772260\pi$
$338$	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	$-0.245839\pi$
$347$	26.6860	1.43258	0.716290	+	0.697803i	$0.245839\pi$
$348$	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	$-0.781996\pi$
$353$	−29.1028	−1.54899	−0.774494	+	0.632581i	$0.781996\pi$
$354$	−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	$-0.530687\pi$
$367$	−3.68807	−0.192516	−0.0962578	+	0.995356i	$0.530687\pi$
$368$	−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	$-0.735098\pi$
$373$	−26.0048	−1.34648	−0.673239	+	0.739425i	$0.735098\pi$
$374$	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	$-0.610921\pi$
$383$	−13.3650	−0.682919	−0.341460	+	0.939896i	$0.610921\pi$
$384$	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	$-0.563626\pi$
$397$	−7.91246	−0.397115	−0.198557	+	0.980089i	$0.563626\pi$
$398$	−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	$-0.783564\pi$
$433$	−32.3617	−1.55520	−0.777602	+	0.628757i	$0.783564\pi$
$434$	−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	$-0.628474\pi$
$443$	−16.5326	−0.785489	−0.392745	+	0.919648i	$0.628474\pi$
$444$	−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	$-0.829525\pi$
$457$	−36.7686	−1.71996	−0.859982	+	0.510324i	$0.829525\pi$
$458$	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	$-0.781786\pi$
$463$	−33.3123	−1.54815	−0.774077	+	0.633091i	$0.781786\pi$
$464$	4.19039	0.194534
$465$	0	0
$466$	−2.85842	−0.132414
$467$	9.13651	0.422787	0.211394	−	0.977401i	$-0.432200\pi$
$467$	9.13651	0.422787	0.211394	+	0.977401i	$0.432200\pi$
$468$	−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	$-0.490818\pi$
$487$	1.27292	0.0576814	0.0288407	+	0.999584i	$0.490818\pi$
$488$	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	$-0.460651\pi$
$503$	5.53082	0.246607	0.123304	+	0.992369i	$0.460651\pi$
$504$	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	$-0.310342\pi$
$523$	25.6681	1.12239	0.561193	+	0.827685i	$0.310342\pi$
$524$	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	$-0.431763\pi$
$547$	9.95096	0.425472	0.212736	+	0.977110i	$0.431763\pi$
$548$	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	$-0.629674\pi$
$557$	−18.7017	−0.792415	−0.396207	+	0.918161i	$0.629674\pi$
$558$	−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	$-0.799936\pi$
$563$	−38.3865	−1.61780	−0.808898	+	0.587949i	$0.799936\pi$
$564$	−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	$-0.698379\pi$
$577$	−28.0399	−1.16732	−0.583659	+	0.811999i	$0.698379\pi$
$578$	−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	$-0.424492\pi$
$587$	11.3870	0.469992	0.234996	+	0.971996i	$0.424492\pi$
$588$	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	$-0.245645\pi$
$593$	34.9063	1.43343	0.716715	+	0.697366i	$0.245645\pi$
$594$	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	$-0.357174\pi$
$607$	21.3752	0.867591	0.433796	+	0.901011i	$0.357174\pi$
$608$	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	$-0.259015\pi$
$613$	34.0087	1.37360	0.686799	+	0.726848i	$0.259015\pi$
$614$	14.1923	0.572755
$615$	0	0
$616$	15.2265	0.613494
$617$	−24.3930	−0.982027	−0.491014	−	0.871152i	$-0.663373\pi$
$617$	−24.3930	−0.982027	−0.491014	+	0.871152i	$0.663373\pi$
$618$	−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	$-0.245880\pi$
$643$	36.3220	1.43240	0.716199	+	0.697896i	$0.245880\pi$
$644$	−14.3442	−0.565242
$645$	0	0
$646$	8.76795	0.344971
$647$	14.2736	0.561151	0.280576	−	0.959832i	$-0.409475\pi$
$647$	14.2736	0.561151	0.280576	+	0.959832i	$0.409475\pi$
$648$	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	$-0.464008\pi$
$653$	5.76651	0.225661	0.112830	+	0.993614i	$0.464008\pi$
$654$	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	$-0.325545\pi$
$673$	27.0338	1.04208	0.521039	+	0.853533i	$0.325545\pi$
$674$	−27.7121	−1.06743
$675$	0	0
$676$	10.4335	0.401289
$677$	−8.65077	−0.332476	−0.166238	−	0.986086i	$-0.553162\pi$
$677$	−8.65077	−0.332476	−0.166238	+	0.986086i	$0.553162\pi$
$678$	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	$-0.848664\pi$
$683$	−46.4716	−1.77819	−0.889093	+	0.457727i	$0.848664\pi$
$684$	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	$-0.370533\pi$
$727$	21.3336	0.791221	0.395610	+	0.918418i	$0.370533\pi$
$728$	−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	$-0.625953\pi$
$733$	−20.8712	−0.770895	−0.385448	+	0.922730i	$0.625953\pi$
$734$	−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	$-0.279803\pi$
$743$	34.7758	1.27580	0.637900	+	0.770120i	$0.279803\pi$
$744$	−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	$-0.937096\pi$
$757$	−53.9563	−1.96107	−0.980537	+	0.196335i	$0.937096\pi$
$758$	−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	$-0.284395\pi$
$773$	34.8495	1.25345	0.626724	+	0.779241i	$0.284395\pi$
$774$	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	$-0.592304\pi$
$787$	−16.0429	−0.571869	−0.285935	+	0.958249i	$0.592304\pi$
$788$	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	$-0.729290\pi$
$797$	−37.2447	−1.31928	−0.659638	+	0.751584i	$0.729290\pi$
$798$	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	$-0.692343\pi$
$823$	−32.5985	−1.13631	−0.568156	+	0.822921i	$0.692343\pi$
$824$	−5.89322	−0.205300
$825$	0	0
$826$	−38.4360	−1.33736
$827$	38.6082	1.34254	0.671270	−	0.741213i	$-0.265749\pi$
$827$	38.6082	1.34254	0.671270	+	0.741213i	$0.265749\pi$
$828$	−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	$-0.612093\pi$
$853$	−20.1475	−0.689836	−0.344918	+	0.938633i	$0.612093\pi$
$854$	0.733059	0.0250848
$855$	0	0
$856$	−5.90758	−0.201917
$857$	55.8400	1.90746	0.953729	−	0.300668i	$-0.0972098\pi$
$857$	55.8400	1.90746	0.953729	+	0.300668i	$0.0972098\pi$
$858$	−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	$-0.656109\pi$
$863$	−27.6734	−0.942012	−0.471006	+	0.882130i	$0.656109\pi$
$864$	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	$-0.307977\pi$
$877$	33.6019	1.13466	0.567328	+	0.823492i	$0.307977\pi$
$878$	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	$-0.734865\pi$
$883$	−39.9789	−1.34540	−0.672698	+	0.739917i	$0.734865\pi$
$884$	−5.06194	−0.170251
$885$	0	0
$886$	−16.5326	−0.555425
$887$	21.8845	0.734811	0.367405	−	0.930061i	$-0.380246\pi$
$887$	21.8845	0.734811	0.367405	+	0.930061i	$0.380246\pi$
$888$	−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	$-0.377123\pi$
$907$	22.6784	0.753025	0.376512	+	0.926412i	$0.377123\pi$
$908$	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	$-0.412718\pi$
$937$	16.5775	0.541563	0.270782	+	0.962641i	$0.412718\pi$
$938$	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	$-0.605151\pi$
$947$	−19.9638	−0.648735	−0.324368	+	0.945931i	$0.605151\pi$
$948$	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	$-0.239049\pi$
$953$	45.1335	1.46202	0.731010	+	0.682367i	$0.239049\pi$
$954$	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	$-0.459720\pi$
$967$	7.84915	0.252412	0.126206	+	0.992004i	$0.459720\pi$
$968$	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	$-0.497829\pi$
$977$	0.426335	0.0136397	0.00681983	+	0.999977i	$0.497829\pi$
$978$	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	$-0.899252\pi$
$983$	−59.5909	−1.90066	−0.950328	+	0.311251i	$0.899252\pi$
$984$	−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	$-0.751366\pi$
$997$	−44.8454	−1.42027	−0.710135	+	0.704066i	$0.751366\pi$
$998$	−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.v.1.6		8
5.2	odd	4		3750.2.c.k.1249.14		16
5.3	odd	4		3750.2.c.k.1249.3		16
5.4	even	2		3750.2.a.u.1.3		8
25.3	odd	20		750.2.h.d.49.1		16
25.4	even	10		750.2.g.g.451.2		16
25.6	even	5		750.2.g.f.301.3		16
25.8	odd	20		150.2.h.b.139.4	yes	16
25.17	odd	20		750.2.h.d.199.2		16
25.19	even	10		750.2.g.g.301.2		16
25.21	even	5		750.2.g.f.451.3		16
25.22	odd	20		150.2.h.b.109.4	✓	16
75.8	even	20		450.2.l.c.289.1		16
75.47	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	25.22	odd	20
150.2.h.b.139.4	yes	16	25.8	odd	20
450.2.l.c.109.1		16	75.47	even	20
450.2.l.c.289.1		16	75.8	even	20
750.2.g.f.301.3		16	25.6	even	5
750.2.g.f.451.3		16	25.21	even	5
750.2.g.g.301.2		16	25.19	even	10
750.2.g.g.451.2		16	25.4	even	10
750.2.h.d.49.1		16	25.3	odd	20
750.2.h.d.199.2		16	25.17	odd	20
3750.2.a.u.1.3		8	5.4	even	2
3750.2.a.v.1.6		8	1.1	even	1	trivial
3750.2.c.k.1249.3		16	5.3	odd	4
3750.2.c.k.1249.14		16	5.2	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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