LMFDB - Embedded newform 4375.2.a.o.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4375,2,Mod(1,4375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4375, 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("4375.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4375 = 5^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4375.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:	$34.9345508843$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 175)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4375.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13370 q^{2} -1.69500 q^{3} +2.55269 q^{4} +3.61663 q^{6} +1.00000 q^{7} -1.17927 q^{8} -0.126975 q^{9} +O(q^{10})$	\(q-2.13370 q^{2} -1.69500 q^{3} +2.55269 q^{4} +3.61663 q^{6} +1.00000 q^{7} -1.17927 q^{8} -0.126975 q^{9} +2.06809 q^{11} -4.32681 q^{12} -1.88008 q^{13} -2.13370 q^{14} -2.58916 q^{16} -2.50557 q^{17} +0.270928 q^{18} +6.09181 q^{19} -1.69500 q^{21} -4.41269 q^{22} -5.67861 q^{23} +1.99887 q^{24} +4.01152 q^{26} +5.30022 q^{27} +2.55269 q^{28} +5.64023 q^{29} +2.89738 q^{31} +7.88304 q^{32} -3.50541 q^{33} +5.34614 q^{34} -0.324129 q^{36} +0.481898 q^{37} -12.9981 q^{38} +3.18673 q^{39} -6.56763 q^{41} +3.61663 q^{42} -10.9911 q^{43} +5.27919 q^{44} +12.1165 q^{46} -5.45312 q^{47} +4.38862 q^{48} +1.00000 q^{49} +4.24694 q^{51} -4.79925 q^{52} +10.5221 q^{53} -11.3091 q^{54} -1.17927 q^{56} -10.3256 q^{57} -12.0346 q^{58} -1.46745 q^{59} -7.25908 q^{61} -6.18216 q^{62} -0.126975 q^{63} -11.6418 q^{64} +7.47951 q^{66} -12.0384 q^{67} -6.39594 q^{68} +9.62524 q^{69} -0.303557 q^{71} +0.149739 q^{72} +13.2568 q^{73} -1.02823 q^{74} +15.5505 q^{76} +2.06809 q^{77} -6.79953 q^{78} +1.92630 q^{79} -8.60295 q^{81} +14.0134 q^{82} -17.9309 q^{83} -4.32681 q^{84} +23.4517 q^{86} -9.56018 q^{87} -2.43884 q^{88} +5.17421 q^{89} -1.88008 q^{91} -14.4957 q^{92} -4.91107 q^{93} +11.6353 q^{94} -13.3618 q^{96} +8.87197 q^{97} -2.13370 q^{98} -0.262596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9}+O(q^{10}) $ 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9	$ 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9} - 16 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{14} + 24 q^{16} - 40 q^{17} - 24 q^{18} + 4 q^{19} - 8 q^{21} - 16 q^{22} - 32 q^{23} + 14 q^{24} + 6 q^{26} - 32 q^{27} + 24 q^{28} - 24 q^{29} + 6 q^{31} - 56 q^{32} - 28 q^{33} + 18 q^{36} - 32 q^{37} - 40 q^{38} - 28 q^{39} + 2 q^{41} - 16 q^{43} - 26 q^{44} - 12 q^{46} - 26 q^{47} - 46 q^{48} + 28 q^{49} - 22 q^{51} - 28 q^{52} - 60 q^{53} + 38 q^{54} - 24 q^{56} - 76 q^{57} - 16 q^{58} + 8 q^{59} + 18 q^{61} - 34 q^{62} + 22 q^{63} + 28 q^{64} + 38 q^{66} - 24 q^{67} - 62 q^{68} + 14 q^{69} - 54 q^{71} - 40 q^{72} - 46 q^{73} - 30 q^{74} + 26 q^{76} - 16 q^{77} - 32 q^{78} - 30 q^{79} + 4 q^{81} - 22 q^{82} - 60 q^{83} - 24 q^{84} - 10 q^{86} - 18 q^{87} - 16 q^{88} + 6 q^{89} - 16 q^{91} - 72 q^{92} - 48 q^{93} + 86 q^{94} + 106 q^{96} - 70 q^{97} - 8 q^{98} - 30 q^{99}+O(q^{100}) $ 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9 - 16 * q^11 - 24 * q^12 - 16 * q^13 - 8 * q^14 + 24 * q^16 - 40 * q^17 - 24 * q^18 + 4 * q^19 - 8 * q^21 - 16 * q^22 - 32 * q^23 + 14 * q^24 + 6 * q^26 - 32 * q^27 + 24 * q^28 - 24 * q^29 + 6 * q^31 - 56 * q^32 - 28 * q^33 + 18 * q^36 - 32 * q^37 - 40 * q^38 - 28 * q^39 + 2 * q^41 - 16 * q^43 - 26 * q^44 - 12 * q^46 - 26 * q^47 - 46 * q^48 + 28 * q^49 - 22 * q^51 - 28 * q^52 - 60 * q^53 + 38 * q^54 - 24 * q^56 - 76 * q^57 - 16 * q^58 + 8 * q^59 + 18 * q^61 - 34 * q^62 + 22 * q^63 + 28 * q^64 + 38 * q^66 - 24 * q^67 - 62 * q^68 + 14 * q^69 - 54 * q^71 - 40 * q^72 - 46 * q^73 - 30 * q^74 + 26 * q^76 - 16 * q^77 - 32 * q^78 - 30 * q^79 + 4 * q^81 - 22 * q^82 - 60 * q^83 - 24 * q^84 - 10 * q^86 - 18 * q^87 - 16 * q^88 + 6 * q^89 - 16 * q^91 - 72 * q^92 - 48 * q^93 + 86 * q^94 + 106 * q^96 - 70 * q^97 - 8 * q^98 - 30 * 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 $

$2$	−2.13370	−1.50876	−0.754378	−	0.656440i	$-0.772061\pi$
$2$	−2.13370	−1.50876	−0.754378	+	0.656440i	$0.772061\pi$
$3$	−1.69500	−0.978609	−0.489304	−	0.872113i	$-0.662749\pi$
$3$	−1.69500	−0.978609	−0.489304	+	0.872113i	$0.662749\pi$
$4$	2.55269	1.27634
$5$	0	0
$5$	0	0
$6$	3.61663	1.47648
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.17927	−0.416936
$9$	−0.126975	−0.0423251
$10$	0	0
$11$	2.06809	0.623553	0.311776	−	0.950156i	$-0.399076\pi$
$11$	2.06809	0.623553	0.311776	+	0.950156i	$0.399076\pi$
$12$	−4.32681	−1.24904
$13$	−1.88008	−0.521439	−0.260720	−	0.965415i	$-0.583960\pi$
$13$	−1.88008	−0.521439	−0.260720	+	0.965415i	$0.583960\pi$
$14$	−2.13370	−0.570256
$15$	0	0
$16$	−2.58916	−0.647290
$17$	−2.50557	−0.607690	−0.303845	−	0.952721i	$-0.598271\pi$
$17$	−2.50557	−0.607690	−0.303845	+	0.952721i	$0.598271\pi$
$18$	0.270928	0.0638583
$19$	6.09181	1.39756	0.698779	−	0.715338i	$-0.253727\pi$
$19$	6.09181	1.39756	0.698779	+	0.715338i	$0.253727\pi$
$20$	0	0
$21$	−1.69500	−0.369879
$22$	−4.41269	−0.940789
$23$	−5.67861	−1.18407	−0.592036	−	0.805911i	$-0.701676\pi$
$23$	−5.67861	−1.18407	−0.592036	+	0.805911i	$0.701676\pi$
$24$	1.99887	0.408017
$25$	0	0
$26$	4.01152	0.786725
$27$	5.30022	1.02003
$28$	2.55269	0.482413
$29$	5.64023	1.04736	0.523682	−	0.851914i	$-0.324558\pi$
$29$	5.64023	1.04736	0.523682	+	0.851914i	$0.324558\pi$
$30$	0	0
$31$	2.89738	0.520386	0.260193	−	0.965557i	$-0.416214\pi$
$31$	2.89738	0.520386	0.260193	+	0.965557i	$0.416214\pi$
$32$	7.88304	1.39354
$33$	−3.50541	−0.610214
$34$	5.34614	0.916856
$35$	0	0
$36$	−0.324129	−0.0540214
$37$	0.481898	0.0792236	0.0396118	−	0.999215i	$-0.487388\pi$
$37$	0.481898	0.0792236	0.0396118	+	0.999215i	$0.487388\pi$
$38$	−12.9981	−2.10857
$39$	3.18673	0.510285
$40$	0	0
$41$	−6.56763	−1.02569	−0.512846	−	0.858481i	$-0.671409\pi$
$41$	−6.56763	−1.02569	−0.512846	+	0.858481i	$0.671409\pi$
$42$	3.61663	0.558058
$43$	−10.9911	−1.67612	−0.838060	−	0.545578i	$-0.816310\pi$
$43$	−10.9911	−1.67612	−0.838060	+	0.545578i	$0.816310\pi$
$44$	5.27919	0.795868
$45$	0	0
$46$	12.1165	1.78648
$47$	−5.45312	−0.795419	−0.397709	−	0.917511i	$-0.630195\pi$
$47$	−5.45312	−0.795419	−0.397709	+	0.917511i	$0.630195\pi$
$48$	4.38862	0.633443
$49$	1.00000	0.142857
$50$	0	0
$51$	4.24694	0.594691
$52$	−4.79925	−0.665536
$53$	10.5221	1.44532	0.722659	−	0.691205i	$-0.242920\pi$
$53$	10.5221	1.44532	0.722659	+	0.691205i	$0.242920\pi$
$54$	−11.3091	−1.53897
$55$	0	0
$56$	−1.17927	−0.157587
$57$	−10.3256	−1.36766
$58$	−12.0346	−1.58022
$59$	−1.46745	−0.191046	−0.0955229	−	0.995427i	$-0.530452\pi$
$59$	−1.46745	−0.191046	−0.0955229	+	0.995427i	$0.530452\pi$
$60$	0	0
$61$	−7.25908	−0.929430	−0.464715	−	0.885460i	$-0.653843\pi$
$61$	−7.25908	−0.929430	−0.464715	+	0.885460i	$0.653843\pi$
$62$	−6.18216	−0.785135
$63$	−0.126975	−0.0159974
$64$	−11.6418	−1.45522
$65$	0	0
$66$	7.47951	0.920664
$67$	−12.0384	−1.47072	−0.735360	−	0.677677i	$-0.762987\pi$
$67$	−12.0384	−1.47072	−0.735360	+	0.677677i	$0.762987\pi$
$68$	−6.39594	−0.775622
$69$	9.62524	1.15874
$70$	0	0
$71$	−0.303557	−0.0360256	−0.0180128	−	0.999838i	$-0.505734\pi$
$71$	−0.303557	−0.0360256	−0.0180128	+	0.999838i	$0.505734\pi$
$72$	0.149739	0.0176469
$73$	13.2568	1.55159	0.775797	−	0.630982i	$-0.217348\pi$
$73$	13.2568	1.55159	0.775797	+	0.630982i	$0.217348\pi$
$74$	−1.02823	−0.119529
$75$	0	0
$76$	15.5505	1.78376
$77$	2.06809	0.235681
$78$	−6.79953	−0.769895
$79$	1.92630	0.216725	0.108363	−	0.994111i	$-0.465439\pi$
$79$	1.92630	0.216725	0.108363	+	0.994111i	$0.465439\pi$
$80$	0	0
$81$	−8.60295	−0.955883
$82$	14.0134	1.54752
$83$	−17.9309	−1.96817	−0.984085	−	0.177699i	$-0.943135\pi$
$83$	−17.9309	−1.96817	−0.984085	+	0.177699i	$0.943135\pi$
$84$	−4.32681	−0.472093
$85$	0	0
$86$	23.4517	2.52886
$87$	−9.56018	−1.02496
$88$	−2.43884	−0.259982
$89$	5.17421	0.548465	0.274233	−	0.961663i	$-0.411576\pi$
$89$	5.17421	0.548465	0.274233	+	0.961663i	$0.411576\pi$
$90$	0	0
$91$	−1.88008	−0.197086
$92$	−14.4957	−1.51128
$93$	−4.91107	−0.509254
$94$	11.6353	1.20009
$95$	0	0
$96$	−13.3618	−1.36373
$97$	8.87197	0.900812	0.450406	−	0.892824i	$-0.351279\pi$
$97$	8.87197	0.900812	0.450406	+	0.892824i	$0.351279\pi$
$98$	−2.13370	−0.215537
$99$	−0.262596	−0.0263919
$100$	0	0
$101$	−8.59159	−0.854895	−0.427447	−	0.904040i	$-0.640587\pi$
$101$	−8.59159	−0.854895	−0.427447	+	0.904040i	$0.640587\pi$
$102$	−9.06171	−0.897243
$103$	12.6727	1.24868	0.624339	−	0.781154i	$-0.285369\pi$
$103$	12.6727	1.24868	0.624339	+	0.781154i	$0.285369\pi$
$104$	2.21712	0.217407
$105$	0	0
$106$	−22.4510	−2.18063
$107$	1.20139	0.116143	0.0580714	−	0.998312i	$-0.481505\pi$
$107$	1.20139	0.116143	0.0580714	+	0.998312i	$0.481505\pi$
$108$	13.5298	1.30191
$109$	6.36232	0.609399	0.304700	−	0.952448i	$-0.401444\pi$
$109$	6.36232	0.609399	0.304700	+	0.952448i	$0.401444\pi$
$110$	0	0
$111$	−0.816818	−0.0775289
$112$	−2.58916	−0.244652
$113$	−10.4738	−0.985296	−0.492648	−	0.870229i	$-0.663971\pi$
$113$	−10.4738	−0.985296	−0.492648	+	0.870229i	$0.663971\pi$
$114$	22.0318	2.06347
$115$	0	0
$116$	14.3977	1.33680
$117$	0.238723	0.0220700
$118$	3.13110	0.288242
$119$	−2.50557	−0.229685
$120$	0	0
$121$	−6.72300	−0.611182
$122$	15.4887	1.40228
$123$	11.1321	1.00375
$124$	7.39612	0.664191
$125$	0	0
$126$	0.270928	0.0241362
$127$	16.9336	1.50261	0.751307	−	0.659953i	$-0.229424\pi$
$127$	16.9336	1.50261	0.751307	+	0.659953i	$0.229424\pi$
$128$	9.07396	0.802032
$129$	18.6298	1.64027
$130$	0	0
$131$	6.00146	0.524350	0.262175	−	0.965020i	$-0.415560\pi$
$131$	6.00146	0.524350	0.262175	+	0.965020i	$0.415560\pi$
$132$	−8.94823	−0.778843
$133$	6.09181	0.528227
$134$	25.6863	2.21896
$135$	0	0
$136$	2.95475	0.253368
$137$	14.9956	1.28116	0.640582	−	0.767890i	$-0.278693\pi$
$137$	14.9956	1.28116	0.640582	+	0.767890i	$0.278693\pi$
$138$	−20.5374	−1.74826
$139$	20.1744	1.71117	0.855584	−	0.517664i	$-0.173198\pi$
$139$	20.1744	1.71117	0.855584	+	0.517664i	$0.173198\pi$
$140$	0	0
$141$	9.24303	0.778404
$142$	0.647701	0.0543538
$143$	−3.88817	−0.325145
$144$	0.328759	0.0273966
$145$	0	0
$146$	−28.2861	−2.34098
$147$	−1.69500	−0.139801
$148$	1.23014	0.101117
$149$	−10.3764	−0.850071	−0.425035	−	0.905177i	$-0.639738\pi$
$149$	−10.3764	−0.850071	−0.425035	+	0.905177i	$0.639738\pi$
$150$	0	0
$151$	17.3336	1.41059	0.705294	−	0.708915i	$-0.250815\pi$
$151$	17.3336	1.41059	0.705294	+	0.708915i	$0.250815\pi$
$152$	−7.18391	−0.582692
$153$	0.318146	0.0257206
$154$	−4.41269	−0.355585
$155$	0	0
$156$	8.13473	0.651299
$157$	−12.3970	−0.989385	−0.494692	−	0.869068i	$-0.664719\pi$
$157$	−12.3970	−0.989385	−0.494692	+	0.869068i	$0.664719\pi$
$158$	−4.11015	−0.326986
$159$	−17.8349	−1.41440
$160$	0	0
$161$	−5.67861	−0.447537
$162$	18.3561	1.44219
$163$	9.32260	0.730203	0.365101	−	0.930968i	$-0.381034\pi$
$163$	9.32260	0.730203	0.365101	+	0.930968i	$0.381034\pi$
$164$	−16.7651	−1.30914
$165$	0	0
$166$	38.2592	2.96949
$167$	8.46949	0.655389	0.327695	−	0.944784i	$-0.393728\pi$
$167$	8.46949	0.655389	0.327695	+	0.944784i	$0.393728\pi$
$168$	1.99887	0.154216
$169$	−9.46531	−0.728101
$170$	0	0
$171$	−0.773510	−0.0591518
$172$	−28.0567	−2.13931
$173$	−20.0552	−1.52477	−0.762385	−	0.647124i	$-0.775972\pi$
$173$	−20.0552	−1.52477	−0.762385	+	0.647124i	$0.775972\pi$
$174$	20.3986	1.54641
$175$	0	0
$176$	−5.35461	−0.403619
$177$	2.48733	0.186959
$178$	−11.0402	−0.827500
$179$	9.47680	0.708329	0.354165	−	0.935183i	$-0.384765\pi$
$179$	9.47680	0.708329	0.354165	+	0.935183i	$0.384765\pi$
$180$	0	0
$181$	−16.1951	−1.20377	−0.601886	−	0.798582i	$-0.705584\pi$
$181$	−16.1951	−1.20377	−0.601886	+	0.798582i	$0.705584\pi$
$182$	4.01152	0.297354
$183$	12.3041	0.909548
$184$	6.69663	0.493682
$185$	0	0
$186$	10.4788	0.768340
$187$	−5.18174	−0.378927
$188$	−13.9201	−1.01523
$189$	5.30022	0.385534
$190$	0	0
$191$	−26.9304	−1.94861	−0.974306	−	0.225227i	$-0.927687\pi$
$191$	−26.9304	−1.94861	−0.974306	+	0.225227i	$0.927687\pi$
$192$	19.7328	1.42409
$193$	8.82966	0.635573	0.317786	−	0.948162i	$-0.397061\pi$
$193$	8.82966	0.635573	0.317786	+	0.948162i	$0.397061\pi$
$194$	−18.9301	−1.35910
$195$	0	0
$196$	2.55269	0.182335
$197$	12.8985	0.918981	0.459490	−	0.888183i	$-0.348032\pi$
$197$	12.8985	0.918981	0.459490	+	0.888183i	$0.348032\pi$
$198$	0.560303	0.0398190
$199$	−2.72762	−0.193356	−0.0966778	−	0.995316i	$-0.530822\pi$
$199$	−2.72762	−0.193356	−0.0966778	+	0.995316i	$0.530822\pi$
$200$	0	0
$201$	20.4050	1.43926
$202$	18.3319	1.28983
$203$	5.64023	0.395866
$204$	10.8411	0.759030
$205$	0	0
$206$	−27.0398	−1.88395
$207$	0.721044	0.0501160
$208$	4.86781	0.337522
$209$	12.5984	0.871451
$210$	0	0
$211$	−15.6902	−1.08015	−0.540077	−	0.841615i	$-0.681605\pi$
$211$	−15.6902	−1.08015	−0.540077	+	0.841615i	$0.681605\pi$
$212$	26.8596	1.84472
$213$	0.514529	0.0352550
$214$	−2.56341	−0.175231
$215$	0	0
$216$	−6.25041	−0.425287
$217$	2.89738	0.196687
$218$	−13.5753	−0.919435
$219$	−22.4703	−1.51840
$220$	0	0
$221$	4.71066	0.316873
$222$	1.74285	0.116972
$223$	−5.87222	−0.393233	−0.196616	−	0.980480i	$-0.562995\pi$
$223$	−5.87222	−0.393233	−0.196616	+	0.980480i	$0.562995\pi$
$224$	7.88304	0.526708
$225$	0	0
$226$	22.3481	1.48657
$227$	1.52052	0.100920	0.0504601	−	0.998726i	$-0.483931\pi$
$227$	1.52052	0.100920	0.0504601	+	0.998726i	$0.483931\pi$
$228$	−26.3581	−1.74561
$229$	21.4398	1.41678	0.708391	−	0.705820i	$-0.249421\pi$
$229$	21.4398	1.41678	0.708391	+	0.705820i	$0.249421\pi$
$230$	0	0
$231$	−3.50541	−0.230639
$232$	−6.65137	−0.436684
$233$	20.7338	1.35832	0.679159	−	0.733991i	$-0.262345\pi$
$233$	20.7338	1.35832	0.679159	+	0.733991i	$0.262345\pi$
$234$	−0.509365	−0.0332982
$235$	0	0
$236$	−3.74595	−0.243840
$237$	−3.26507	−0.212089
$238$	5.34614	0.346539
$239$	−17.0369	−1.10203	−0.551013	−	0.834497i	$-0.685758\pi$
$239$	−17.0369	−1.10203	−0.551013	+	0.834497i	$0.685758\pi$
$240$	0	0
$241$	6.08298	0.391839	0.195920	−	0.980620i	$-0.437231\pi$
$241$	6.08298	0.391839	0.195920	+	0.980620i	$0.437231\pi$
$242$	14.3449	0.922125
$243$	−1.31867	−0.0845926
$244$	−18.5302	−1.18627
$245$	0	0
$246$	−23.7527	−1.51441
$247$	−11.4531	−0.728742
$248$	−3.41681	−0.216968
$249$	30.3928	1.92607
$250$	0	0
$251$	−19.1633	−1.20958	−0.604788	−	0.796387i	$-0.706742\pi$
$251$	−19.1633	−1.20958	−0.604788	+	0.796387i	$0.706742\pi$
$252$	−0.324129	−0.0204182
$253$	−11.7439	−0.738331
$254$	−36.1313	−2.26708
$255$	0	0
$256$	3.92237	0.245148
$257$	15.6052	0.973424	0.486712	−	0.873563i	$-0.338196\pi$
$257$	15.6052	0.973424	0.486712	+	0.873563i	$0.338196\pi$
$258$	−39.7505	−2.47476
$259$	0.481898	0.0299437
$260$	0	0
$261$	−0.716170	−0.0443298
$262$	−12.8053	−0.791117
$263$	−22.3707	−1.37944	−0.689719	−	0.724077i	$-0.742266\pi$
$263$	−22.3707	−1.37944	−0.689719	+	0.724077i	$0.742266\pi$
$264$	4.13384	0.254420
$265$	0	0
$266$	−12.9981	−0.796966
$267$	−8.77028	−0.536733
$268$	−30.7302	−1.87714
$269$	1.03680	0.0632148	0.0316074	−	0.999500i	$-0.489937\pi$
$269$	1.03680	0.0632148	0.0316074	+	0.999500i	$0.489937\pi$
$270$	0	0
$271$	−17.4481	−1.05990	−0.529949	−	0.848030i	$-0.677789\pi$
$271$	−17.4481	−1.05990	−0.529949	+	0.848030i	$0.677789\pi$
$272$	6.48732	0.393351
$273$	3.18673	0.192870
$274$	−31.9963	−1.93296
$275$	0	0
$276$	24.5703	1.47896
$277$	22.4984	1.35180	0.675898	−	0.736995i	$-0.263756\pi$
$277$	22.4984	1.35180	0.675898	+	0.736995i	$0.263756\pi$
$278$	−43.0461	−2.58174
$279$	−0.367896	−0.0220254
$280$	0	0
$281$	1.22624	0.0731514	0.0365757	−	0.999331i	$-0.488355\pi$
$281$	1.22624	0.0731514	0.0365757	+	0.999331i	$0.488355\pi$
$282$	−19.7219	−1.17442
$283$	5.71846	0.339927	0.169964	−	0.985450i	$-0.445635\pi$
$283$	5.71846	0.339927	0.169964	+	0.985450i	$0.445635\pi$
$284$	−0.774887	−0.0459811
$285$	0	0
$286$	8.29619	0.490564
$287$	−6.56763	−0.387675
$288$	−1.00095	−0.0589817
$289$	−10.7221	−0.630713
$290$	0	0
$291$	−15.0380	−0.881542
$292$	33.8406	1.98037
$293$	3.57430	0.208813	0.104406	−	0.994535i	$-0.466706\pi$
$293$	3.57430	0.208813	0.104406	+	0.994535i	$0.466706\pi$
$294$	3.61663	0.210926
$295$	0	0
$296$	−0.568290	−0.0330312
$297$	10.9613	0.636041
$298$	22.1402	1.28255
$299$	10.6762	0.617422
$300$	0	0
$301$	−10.9911	−0.633514
$302$	−36.9847	−2.12823
$303$	14.5627	0.836607
$304$	−15.7727	−0.904625
$305$	0	0
$306$	−0.678828	−0.0388060
$307$	19.9639	1.13940	0.569700	−	0.821853i	$-0.307059\pi$
$307$	19.9639	1.13940	0.569700	+	0.821853i	$0.307059\pi$
$308$	5.27919	0.300810
$309$	−21.4802	−1.22197
$310$	0	0
$311$	12.6475	0.717176	0.358588	−	0.933496i	$-0.383258\pi$
$311$	12.6475	0.717176	0.358588	+	0.933496i	$0.383258\pi$
$312$	−3.75802	−0.212756
$313$	−11.8571	−0.670204	−0.335102	−	0.942182i	$-0.608771\pi$
$313$	−11.8571	−0.670204	−0.335102	+	0.942182i	$0.608771\pi$
$314$	26.4514	1.49274
$315$	0	0
$316$	4.91724	0.276616
$317$	−9.33346	−0.524219	−0.262110	−	0.965038i	$-0.584418\pi$
$317$	−9.33346	−0.524219	−0.262110	+	0.965038i	$0.584418\pi$
$318$	38.0544	2.13398
$319$	11.6645	0.653086
$320$	0	0
$321$	−2.03636	−0.113658
$322$	12.1165	0.675224
$323$	−15.2635	−0.849282
$324$	−21.9607	−1.22004
$325$	0	0
$326$	−19.8917	−1.10170
$327$	−10.7841	−0.596363
$328$	7.74503	0.427648
$329$	−5.45312	−0.300640
$330$	0	0
$331$	2.03647	0.111934	0.0559671	−	0.998433i	$-0.482176\pi$
$331$	2.03647	0.111934	0.0559671	+	0.998433i	$0.482176\pi$
$332$	−45.7720	−2.51206
$333$	−0.0611892	−0.00335315
$334$	−18.0714	−0.988822
$335$	0	0
$336$	4.38862	0.239419
$337$	−19.4939	−1.06190	−0.530951	−	0.847403i	$-0.678165\pi$
$337$	−19.4939	−1.06190	−0.530951	+	0.847403i	$0.678165\pi$
$338$	20.1962	1.09853
$339$	17.7532	0.964219
$340$	0	0
$341$	5.99205	0.324488
$342$	1.65044	0.0892456
$343$	1.00000	0.0539949
$344$	12.9615	0.698835
$345$	0	0
$346$	42.7919	2.30051
$347$	−19.4512	−1.04419	−0.522097	−	0.852886i	$-0.674850\pi$
$347$	−19.4512	−1.04419	−0.522097	+	0.852886i	$0.674850\pi$
$348$	−24.4042	−1.30820
$349$	−10.4238	−0.557973	−0.278987	−	0.960295i	$-0.589999\pi$
$349$	−10.4238	−0.557973	−0.278987	+	0.960295i	$0.589999\pi$
$350$	0	0
$351$	−9.96482	−0.531883
$352$	16.3028	0.868944
$353$	6.40301	0.340798	0.170399	−	0.985375i	$-0.445494\pi$
$353$	6.40301	0.340798	0.170399	+	0.985375i	$0.445494\pi$
$354$	−5.30722	−0.282076
$355$	0	0
$356$	13.2081	0.700030
$357$	4.24694	0.224772
$358$	−20.2207	−1.06870
$359$	−15.0803	−0.795907	−0.397953	−	0.917406i	$-0.630279\pi$
$359$	−15.0803	−0.795907	−0.397953	+	0.917406i	$0.630279\pi$
$360$	0	0
$361$	18.1102	0.953168
$362$	34.5555	1.81620
$363$	11.3955	0.598108
$364$	−4.79925	−0.251549
$365$	0	0
$366$	−26.2534	−1.37229
$367$	−0.784895	−0.0409712	−0.0204856	−	0.999790i	$-0.506521\pi$
$367$	−0.784895	−0.0409712	−0.0204856	+	0.999790i	$0.506521\pi$
$368$	14.7028	0.766437
$369$	0.833927	0.0434125
$370$	0	0
$371$	10.5221	0.546279
$372$	−12.5364	−0.649983
$373$	−25.6527	−1.32824	−0.664122	−	0.747624i	$-0.731195\pi$
$373$	−25.6527	−1.32824	−0.664122	+	0.747624i	$0.731195\pi$
$374$	11.0563	0.571708
$375$	0	0
$376$	6.43072	0.331639
$377$	−10.6041	−0.546136
$378$	−11.3091	−0.581677
$379$	−21.5207	−1.10544	−0.552722	−	0.833366i	$-0.686411\pi$
$379$	−21.5207	−1.10544	−0.552722	+	0.833366i	$0.686411\pi$
$380$	0	0
$381$	−28.7024	−1.47047
$382$	57.4614	2.93998
$383$	−13.0606	−0.667366	−0.333683	−	0.942685i	$-0.608292\pi$
$383$	−13.0606	−0.667366	−0.333683	+	0.942685i	$0.608292\pi$
$384$	−15.3804	−0.784876
$385$	0	0
$386$	−18.8399	−0.958924
$387$	1.39559	0.0709420
$388$	22.6474	1.14975
$389$	−30.1491	−1.52862	−0.764309	−	0.644850i	$-0.776920\pi$
$389$	−30.1491	−1.52862	−0.764309	+	0.644850i	$0.776920\pi$
$390$	0	0
$391$	14.2282	0.719549
$392$	−1.17927	−0.0595623
$393$	−10.1725	−0.513134
$394$	−27.5216	−1.38652
$395$	0	0
$396$	−0.670327	−0.0336852
$397$	13.4298	0.674023	0.337011	−	0.941501i	$-0.390584\pi$
$397$	13.4298	0.674023	0.337011	+	0.941501i	$0.390584\pi$
$398$	5.81993	0.291727
$399$	−10.3256	−0.516928
$400$	0	0
$401$	−21.3013	−1.06373	−0.531867	−	0.846828i	$-0.678510\pi$
$401$	−21.3013	−1.06373	−0.531867	+	0.846828i	$0.678510\pi$
$402$	−43.5382	−2.17149
$403$	−5.44730	−0.271350
$404$	−21.9316	−1.09114
$405$	0	0
$406$	−12.0346	−0.597265
$407$	0.996609	0.0494001
$408$	−5.00830	−0.247948
$409$	4.81575	0.238124	0.119062	−	0.992887i	$-0.462011\pi$
$409$	4.81575	0.238124	0.119062	+	0.992887i	$0.462011\pi$
$410$	0	0
$411$	−25.4176	−1.25376
$412$	32.3494	1.59374
$413$	−1.46745	−0.0722085
$414$	−1.53849	−0.0756128
$415$	0	0
$416$	−14.8207	−0.726645
$417$	−34.1956	−1.67456
$418$	−26.8813	−1.31481
$419$	22.0999	1.07965	0.539826	−	0.841777i	$-0.318490\pi$
$419$	22.0999	1.07965	0.539826	+	0.841777i	$0.318490\pi$
$420$	0	0
$421$	−31.1151	−1.51646	−0.758229	−	0.651988i	$-0.773935\pi$
$421$	−31.1151	−1.51646	−0.758229	+	0.651988i	$0.773935\pi$
$422$	33.4781	1.62969
$423$	0.692412	0.0336662
$424$	−12.4084	−0.602605
$425$	0	0
$426$	−1.09785	−0.0531911
$427$	−7.25908	−0.351291
$428$	3.06677	0.148238
$429$	6.59044	0.318189
$430$	0	0
$431$	−4.23318	−0.203905	−0.101953	−	0.994789i	$-0.532509\pi$
$431$	−4.23318	−0.203905	−0.101953	+	0.994789i	$0.532509\pi$
$432$	−13.7231	−0.660254
$433$	−21.7576	−1.04560	−0.522801	−	0.852455i	$-0.675113\pi$
$433$	−21.7576	−1.04560	−0.522801	+	0.852455i	$0.675113\pi$
$434$	−6.18216	−0.296753
$435$	0	0
$436$	16.2410	0.777803
$437$	−34.5930	−1.65481
$438$	47.9450	2.29090
$439$	−6.07203	−0.289802	−0.144901	−	0.989446i	$-0.546286\pi$
$439$	−6.07203	−0.289802	−0.144901	+	0.989446i	$0.546286\pi$
$440$	0	0
$441$	−0.126975	−0.00604645
$442$	−10.0512	−0.478085
$443$	6.79775	0.322971	0.161485	−	0.986875i	$-0.448372\pi$
$443$	6.79775	0.322971	0.161485	+	0.986875i	$0.448372\pi$
$444$	−2.08508	−0.0989536
$445$	0	0
$446$	12.5296	0.593292
$447$	17.5881	0.831887
$448$	−11.6418	−0.550021
$449$	−25.9097	−1.22275	−0.611376	−	0.791340i	$-0.709384\pi$
$449$	−25.9097	−1.22275	−0.611376	+	0.791340i	$0.709384\pi$
$450$	0	0
$451$	−13.5824	−0.639573
$452$	−26.7365	−1.25758
$453$	−29.3804	−1.38041
$454$	−3.24433	−0.152264
$455$	0	0
$456$	12.1767	0.570228
$457$	−24.0284	−1.12400	−0.562000	−	0.827137i	$-0.689968\pi$
$457$	−24.0284	−1.12400	−0.562000	+	0.827137i	$0.689968\pi$
$458$	−45.7462	−2.13758
$459$	−13.2801	−0.619861
$460$	0	0
$461$	−39.4658	−1.83811	−0.919053	−	0.394134i	$-0.871045\pi$
$461$	−39.4658	−1.83811	−0.919053	+	0.394134i	$0.871045\pi$
$462$	7.47951	0.347978
$463$	29.9086	1.38997	0.694986	−	0.719023i	$-0.255411\pi$
$463$	29.9086	1.38997	0.694986	+	0.719023i	$0.255411\pi$
$464$	−14.6034	−0.677947
$465$	0	0
$466$	−44.2398	−2.04937
$467$	1.29413	0.0598850	0.0299425	−	0.999552i	$-0.490468\pi$
$467$	1.29413	0.0598850	0.0299425	+	0.999552i	$0.490468\pi$
$468$	0.609386	0.0281689
$469$	−12.0384	−0.555880
$470$	0	0
$471$	21.0128	0.968221
$472$	1.73053	0.0796539
$473$	−22.7305	−1.04515
$474$	6.96670	0.319991
$475$	0	0
$476$	−6.39594	−0.293157
$477$	−1.33604	−0.0611732
$478$	36.3517	1.66269
$479$	16.0326	0.732549	0.366274	−	0.930507i	$-0.380633\pi$
$479$	16.0326	0.732549	0.366274	+	0.930507i	$0.380633\pi$
$480$	0	0
$481$	−0.906006	−0.0413103
$482$	−12.9793	−0.591190
$483$	9.62524	0.437964
$484$	−17.1617	−0.780079
$485$	0	0
$486$	2.81364	0.127630
$487$	−5.64007	−0.255576	−0.127788	−	0.991802i	$-0.540788\pi$
$487$	−5.64007	−0.255576	−0.127788	+	0.991802i	$0.540788\pi$
$488$	8.56044	0.387513
$489$	−15.8018	−0.714583
$490$	0	0
$491$	−3.61351	−0.163075	−0.0815377	−	0.996670i	$-0.525983\pi$
$491$	−3.61351	−0.163075	−0.0815377	+	0.996670i	$0.525983\pi$
$492$	28.4169	1.28113
$493$	−14.1320	−0.636472
$494$	24.4375	1.09949
$495$	0	0
$496$	−7.50179	−0.336840
$497$	−0.303557	−0.0136164
$498$	−64.8493	−2.90597
$499$	−14.4978	−0.649010	−0.324505	−	0.945884i	$-0.605198\pi$
$499$	−14.4978	−0.649010	−0.324505	+	0.945884i	$0.605198\pi$
$500$	0	0
$501$	−14.3558	−0.641369
$502$	40.8887	1.82495
$503$	−29.2466	−1.30404	−0.652021	−	0.758201i	$-0.726078\pi$
$503$	−29.2466	−1.30404	−0.652021	+	0.758201i	$0.726078\pi$
$504$	0.149739	0.00666989
$505$	0	0
$506$	25.0579	1.11396
$507$	16.0437	0.712526
$508$	43.2262	1.91785
$509$	20.3314	0.901173	0.450586	−	0.892733i	$-0.351215\pi$
$509$	20.3314	0.901173	0.450586	+	0.892733i	$0.351215\pi$
$510$	0	0
$511$	13.2568	0.586448
$512$	−26.5171	−1.17190
$513$	32.2880	1.42555
$514$	−33.2968	−1.46866
$515$	0	0
$516$	47.5562	2.09354
$517$	−11.2775	−0.495986
$518$	−1.02823	−0.0451778
$519$	33.9936	1.49215
$520$	0	0
$521$	9.68703	0.424396	0.212198	−	0.977227i	$-0.431938\pi$
$521$	9.68703	0.424396	0.212198	+	0.977227i	$0.431938\pi$
$522$	1.52809	0.0668828
$523$	−27.0805	−1.18415	−0.592074	−	0.805884i	$-0.701691\pi$
$523$	−27.0805	−1.18415	−0.592074	+	0.805884i	$0.701691\pi$
$524$	15.3199	0.669252
$525$	0	0
$526$	47.7325	2.08124
$527$	−7.25960	−0.316233
$528$	9.07607	0.394985
$529$	9.24662	0.402027
$530$	0	0
$531$	0.186330	0.00808604
$532$	15.5505	0.674200
$533$	12.3476	0.534836
$534$	18.7132	0.809799
$535$	0	0
$536$	14.1965	0.613196
$537$	−16.0632	−0.693177
$538$	−2.21222	−0.0953757
$539$	2.06809	0.0890789
$540$	0	0
$541$	36.2949	1.56044	0.780220	−	0.625506i	$-0.215107\pi$
$541$	36.2949	1.56044	0.780220	+	0.625506i	$0.215107\pi$
$542$	37.2291	1.59913
$543$	27.4507	1.17802
$544$	−19.7515	−0.846839
$545$	0	0
$546$	−6.79953	−0.290993
$547$	−42.7082	−1.82607	−0.913035	−	0.407882i	$-0.866267\pi$
$547$	−42.7082	−1.82607	−0.913035	+	0.407882i	$0.866267\pi$
$548$	38.2792	1.63521
$549$	0.921724	0.0393382
$550$	0	0
$551$	34.3592	1.46375
$552$	−11.3508	−0.483122
$553$	1.92630	0.0819145
$554$	−48.0048	−2.03953
$555$	0	0
$556$	51.4989	2.18404
$557$	−29.3580	−1.24394	−0.621969	−	0.783042i	$-0.713667\pi$
$557$	−29.3580	−1.24394	−0.621969	+	0.783042i	$0.713667\pi$
$558$	0.784982	0.0332309
$559$	20.6640	0.873995
$560$	0	0
$561$	8.78306	0.370821
$562$	−2.61643	−0.110368
$563$	6.63864	0.279785	0.139893	−	0.990167i	$-0.455324\pi$
$563$	6.63864	0.279785	0.139893	+	0.990167i	$0.455324\pi$
$564$	23.5946	0.993511
$565$	0	0
$566$	−12.2015	−0.512867
$567$	−8.60295	−0.361290
$568$	0.357977	0.0150204
$569$	−2.90189	−0.121654	−0.0608269	−	0.998148i	$-0.519374\pi$
$569$	−2.90189	−0.121654	−0.0608269	+	0.998148i	$0.519374\pi$
$570$	0	0
$571$	9.03302	0.378020	0.189010	−	0.981975i	$-0.439472\pi$
$571$	9.03302	0.378020	0.189010	+	0.981975i	$0.439472\pi$
$572$	−9.92528	−0.414997
$573$	45.6470	1.90693
$574$	14.0134	0.584907
$575$	0	0
$576$	1.47822	0.0615923
$577$	14.7692	0.614851	0.307426	−	0.951572i	$-0.400532\pi$
$577$	14.7692	0.614851	0.307426	+	0.951572i	$0.400532\pi$
$578$	22.8778	0.951592
$579$	−14.9663	−0.621977
$580$	0	0
$581$	−17.9309	−0.743898
$582$	32.0866	1.33003
$583$	21.7606	0.901231
$584$	−15.6334	−0.646916
$585$	0	0
$586$	−7.62649	−0.315047
$587$	−14.9838	−0.618449	−0.309224	−	0.950989i	$-0.600069\pi$
$587$	−14.9838	−0.618449	−0.309224	+	0.950989i	$0.600069\pi$
$588$	−4.32681	−0.178435
$589$	17.6503	0.727269
$590$	0	0
$591$	−21.8630	−0.899322
$592$	−1.24771	−0.0512806
$593$	−38.4718	−1.57985	−0.789924	−	0.613205i	$-0.789880\pi$
$593$	−38.4718	−1.57985	−0.789924	+	0.613205i	$0.789880\pi$
$594$	−23.3882	−0.959631
$595$	0	0
$596$	−26.4878	−1.08498
$597$	4.62331	0.189220
$598$	−22.7799	−0.931539
$599$	−26.7785	−1.09414	−0.547070	−	0.837087i	$-0.684257\pi$
$599$	−26.7785	−1.09414	−0.547070	+	0.837087i	$0.684257\pi$
$600$	0	0
$601$	−6.15561	−0.251093	−0.125546	−	0.992088i	$-0.540068\pi$
$601$	−6.15561	−0.251093	−0.125546	+	0.992088i	$0.540068\pi$
$602$	23.4517	0.955818
$603$	1.52857	0.0622484
$604$	44.2473	1.80040
$605$	0	0
$606$	−31.0726	−1.26224
$607$	−5.96735	−0.242207	−0.121104	−	0.992640i	$-0.538643\pi$
$607$	−5.96735	−0.242207	−0.121104	+	0.992640i	$0.538643\pi$
$608$	48.0220	1.94755
$609$	−9.56018	−0.387398
$610$	0	0
$611$	10.2523	0.414763
$612$	0.812127	0.0328283
$613$	−14.9168	−0.602483	−0.301241	−	0.953548i	$-0.597401\pi$
$613$	−14.9168	−0.602483	−0.301241	+	0.953548i	$0.597401\pi$
$614$	−42.5970	−1.71908
$615$	0	0
$616$	−2.43884	−0.0982638
$617$	−15.2139	−0.612487	−0.306243	−	0.951953i	$-0.599072\pi$
$617$	−15.2139	−0.612487	−0.306243	+	0.951953i	$0.599072\pi$
$618$	45.8324	1.84365
$619$	35.7713	1.43777	0.718884	−	0.695130i	$-0.244653\pi$
$619$	35.7713	1.43777	0.718884	+	0.695130i	$0.244653\pi$
$620$	0	0
$621$	−30.0979	−1.20779
$622$	−26.9861	−1.08204
$623$	5.17421	0.207300
$624$	−8.25094	−0.330302
$625$	0	0
$626$	25.2996	1.01117
$627$	−21.3543	−0.852809
$628$	−31.6456	−1.26280
$629$	−1.20743	−0.0481434
$630$	0	0
$631$	39.0342	1.55393	0.776963	−	0.629546i	$-0.216759\pi$
$631$	39.0342	1.55393	0.776963	+	0.629546i	$0.216759\pi$
$632$	−2.27163	−0.0903606
$633$	26.5948	1.05705
$634$	19.9148	0.790919
$635$	0	0
$636$	−45.5270	−1.80526
$637$	−1.88008	−0.0744913
$638$	−24.8886	−0.985348
$639$	0.0385443	0.00152479
$640$	0	0
$641$	−39.1633	−1.54686	−0.773429	−	0.633883i	$-0.781460\pi$
$641$	−39.1633	−1.54686	−0.773429	+	0.633883i	$0.781460\pi$
$642$	4.34498	0.171483
$643$	26.9293	1.06199	0.530994	−	0.847376i	$-0.321819\pi$
$643$	26.9293	1.06199	0.530994	+	0.847376i	$0.321819\pi$
$644$	−14.4957	−0.571212
$645$	0	0
$646$	32.5677	1.28136
$647$	−14.0917	−0.554002	−0.277001	−	0.960870i	$-0.589341\pi$
$647$	−14.0917	−0.554002	−0.277001	+	0.960870i	$0.589341\pi$
$648$	10.1452	0.398542
$649$	−3.03482	−0.119127
$650$	0	0
$651$	−4.91107	−0.192480
$652$	23.7977	0.931990
$653$	−29.0854	−1.13820	−0.569101	−	0.822268i	$-0.692709\pi$
$653$	−29.0854	−1.13820	−0.569101	+	0.822268i	$0.692709\pi$
$654$	23.0101	0.899767
$655$	0	0
$656$	17.0046	0.663919
$657$	−1.68329	−0.0656714
$658$	11.6353	0.453593
$659$	−20.6865	−0.805831	−0.402915	−	0.915237i	$-0.632003\pi$
$659$	−20.6865	−0.805831	−0.402915	+	0.915237i	$0.632003\pi$
$660$	0	0
$661$	28.6284	1.11352	0.556759	−	0.830674i	$-0.312045\pi$
$661$	28.6284	1.11352	0.556759	+	0.830674i	$0.312045\pi$
$662$	−4.34521	−0.168881
$663$	−7.98457	−0.310095
$664$	21.1454	0.820601
$665$	0	0
$666$	0.130560	0.00505908
$667$	−32.0286	−1.24015
$668$	21.6200	0.836502
$669$	9.95341	0.384821
$670$	0	0
$671$	−15.0124	−0.579548
$672$	−13.3618	−0.515441
$673$	37.3147	1.43837	0.719187	−	0.694816i	$-0.244514\pi$
$673$	37.3147	1.43837	0.719187	+	0.694816i	$0.244514\pi$
$674$	41.5942	1.60215
$675$	0	0
$676$	−24.1620	−0.929308
$677$	−16.7901	−0.645298	−0.322649	−	0.946519i	$-0.604573\pi$
$677$	−16.7901	−0.645298	−0.322649	+	0.946519i	$0.604573\pi$
$678$	−37.8800	−1.45477
$679$	8.87197	0.340475
$680$	0	0
$681$	−2.57728	−0.0987614
$682$	−12.7853	−0.489573
$683$	−16.6137	−0.635707	−0.317853	−	0.948140i	$-0.602962\pi$
$683$	−16.6137	−0.635707	−0.317853	+	0.948140i	$0.602962\pi$
$684$	−1.97453	−0.0754981
$685$	0	0
$686$	−2.13370	−0.0814652
$687$	−36.3405	−1.38648
$688$	28.4576	1.08494
$689$	−19.7823	−0.753645
$690$	0	0
$691$	32.4497	1.23445	0.617223	−	0.786789i	$-0.288258\pi$
$691$	32.4497	1.23445	0.617223	+	0.786789i	$0.288258\pi$
$692$	−51.1947	−1.94613
$693$	−0.262596	−0.00997521
$694$	41.5030	1.57543
$695$	0	0
$696$	11.2741	0.427342
$697$	16.4557	0.623303
$698$	22.2413	0.841845
$699$	−35.1438	−1.32926
$700$	0	0
$701$	−0.758935	−0.0286646	−0.0143323	−	0.999897i	$-0.504562\pi$
$701$	−0.758935	−0.0286646	−0.0143323	+	0.999897i	$0.504562\pi$
$702$	21.2620	0.802481
$703$	2.93564	0.110720
$704$	−24.0762	−0.907406
$705$	0	0
$706$	−13.6621	−0.514181
$707$	−8.59159	−0.323120
$708$	6.34938	0.238624
$709$	−22.5988	−0.848715	−0.424358	−	0.905495i	$-0.639500\pi$
$709$	−22.5988	−0.848715	−0.424358	+	0.905495i	$0.639500\pi$
$710$	0	0
$711$	−0.244592	−0.00917293
$712$	−6.10181	−0.228675
$713$	−16.4531	−0.616174
$714$	−9.06171	−0.339126
$715$	0	0
$716$	24.1913	0.904072
$717$	28.8776	1.07845
$718$	32.1768	1.20083
$719$	−10.8929	−0.406237	−0.203118	−	0.979154i	$-0.565108\pi$
$719$	−10.8929	−0.406237	−0.203118	+	0.979154i	$0.565108\pi$
$720$	0	0
$721$	12.6727	0.471956
$722$	−38.6418	−1.43810
$723$	−10.3106	−0.383457
$724$	−41.3410	−1.53643
$725$	0	0
$726$	−24.3146	−0.902399
$727$	11.4704	0.425412	0.212706	−	0.977116i	$-0.431772\pi$
$727$	11.4704	0.425412	0.212706	+	0.977116i	$0.431772\pi$
$728$	2.21712	0.0821721
$729$	28.0440	1.03867
$730$	0	0
$731$	27.5389	1.01856
$732$	31.4086	1.16090
$733$	−17.4399	−0.644158	−0.322079	−	0.946713i	$-0.604382\pi$
$733$	−17.4399	−0.644158	−0.322079	+	0.946713i	$0.604382\pi$
$734$	1.67473	0.0618155
$735$	0	0
$736$	−44.7647	−1.65005
$737$	−24.8964	−0.917071
$738$	−1.77935	−0.0654989
$739$	−14.0250	−0.515920	−0.257960	−	0.966156i	$-0.583050\pi$
$739$	−14.0250	−0.515920	−0.257960	+	0.966156i	$0.583050\pi$
$740$	0	0
$741$	19.4130	0.713153
$742$	−22.4510	−0.824201
$743$	−0.956607	−0.0350945	−0.0175473	−	0.999846i	$-0.505586\pi$
$743$	−0.956607	−0.0350945	−0.0175473	+	0.999846i	$0.505586\pi$
$744$	5.79149	0.212326
$745$	0	0
$746$	54.7352	2.00400
$747$	2.27678	0.0833030
$748$	−13.2274	−0.483641
$749$	1.20139	0.0438978
$750$	0	0
$751$	1.86740	0.0681425	0.0340713	−	0.999419i	$-0.489153\pi$
$751$	1.86740	0.0681425	0.0340713	+	0.999419i	$0.489153\pi$
$752$	14.1190	0.514866
$753$	32.4818	1.18370
$754$	22.6259	0.823987
$755$	0	0
$756$	13.5298	0.492075
$757$	13.4048	0.487207	0.243604	−	0.969875i	$-0.421670\pi$
$757$	13.4048	0.487207	0.243604	+	0.969875i	$0.421670\pi$
$758$	45.9188	1.66785
$759$	19.9059	0.722537
$760$	0	0
$761$	−37.4322	−1.35691	−0.678457	−	0.734640i	$-0.737351\pi$
$761$	−37.4322	−1.35691	−0.678457	+	0.734640i	$0.737351\pi$
$762$	61.2425	2.21858
$763$	6.36232	0.230331
$764$	−68.7448	−2.48710
$765$	0	0
$766$	27.8675	1.00689
$767$	2.75892	0.0996188
$768$	−6.64841	−0.239904
$769$	−44.5195	−1.60542	−0.802708	−	0.596373i	$-0.796608\pi$
$769$	−44.5195	−1.60542	−0.802708	+	0.596373i	$0.796608\pi$
$770$	0	0
$771$	−26.4508	−0.952601
$772$	22.5394	0.811210
$773$	31.4534	1.13130	0.565651	−	0.824645i	$-0.308625\pi$
$773$	31.4534	1.13130	0.565651	+	0.824645i	$0.308625\pi$
$774$	−2.97778	−0.107034
$775$	0	0
$776$	−10.4625	−0.375581
$777$	−0.816818	−0.0293032
$778$	64.3292	2.30631
$779$	−40.0088	−1.43346
$780$	0	0
$781$	−0.627783	−0.0224639
$782$	−30.3587	−1.08562
$783$	29.8945	1.06834
$784$	−2.58916	−0.0924699
$785$	0	0
$786$	21.7051	0.774194
$787$	21.7804	0.776387	0.388193	−	0.921578i	$-0.373099\pi$
$787$	21.7804	0.776387	0.388193	+	0.921578i	$0.373099\pi$
$788$	32.9259	1.17294
$789$	37.9184	1.34993
$790$	0	0
$791$	−10.4738	−0.372407
$792$	0.309673	0.0110038
$793$	13.6476	0.484641
$794$	−28.6552	−1.01694
$795$	0	0
$796$	−6.96276	−0.246788
$797$	−46.9836	−1.66425	−0.832123	−	0.554591i	$-0.812875\pi$
$797$	−46.9836	−1.66425	−0.832123	+	0.554591i	$0.812875\pi$
$798$	22.0318	0.779918
$799$	13.6632	0.483368
$800$	0	0
$801$	−0.656997	−0.0232138
$802$	45.4506	1.60492
$803$	27.4163	0.967501
$804$	52.0877	1.83699
$805$	0	0
$806$	11.6229	0.409400
$807$	−1.75738	−0.0618625
$808$	10.1318	0.356436
$809$	4.65140	0.163534	0.0817672	−	0.996651i	$-0.473944\pi$
$809$	4.65140	0.163534	0.0817672	+	0.996651i	$0.473944\pi$
$810$	0	0
$811$	43.5223	1.52828	0.764138	−	0.645053i	$-0.223165\pi$
$811$	43.5223	1.52828	0.764138	+	0.645053i	$0.223165\pi$
$812$	14.3977	0.505262
$813$	29.5746	1.03723
$814$	−2.12647	−0.0745327
$815$	0	0
$816$	−10.9960	−0.384937
$817$	−66.9555	−2.34248
$818$	−10.2754	−0.359270
$819$	0.238723	0.00834167
$820$	0	0
$821$	18.0139	0.628688	0.314344	−	0.949309i	$-0.398215\pi$
$821$	18.0139	0.628688	0.314344	+	0.949309i	$0.398215\pi$
$822$	54.2336	1.89162
$823$	33.7176	1.17532	0.587660	−	0.809108i	$-0.300049\pi$
$823$	33.7176	1.17532	0.587660	+	0.809108i	$0.300049\pi$
$824$	−14.9446	−0.520619
$825$	0	0
$826$	3.13110	0.108945
$827$	−19.6192	−0.682227	−0.341114	−	0.940022i	$-0.610804\pi$
$827$	−19.6192	−0.682227	−0.341114	+	0.940022i	$0.610804\pi$
$828$	1.84060	0.0639653
$829$	−49.9467	−1.73472	−0.867360	−	0.497681i	$-0.834185\pi$
$829$	−49.9467	−1.73472	−0.867360	+	0.497681i	$0.834185\pi$
$830$	0	0
$831$	−38.1347	−1.32288
$832$	21.8874	0.758808
$833$	−2.50557	−0.0868129
$834$	72.9632	2.52651
$835$	0	0
$836$	32.1598	1.11227
$837$	15.3568	0.530808
$838$	−47.1546	−1.62893
$839$	0.459449	0.0158619	0.00793097	−	0.999969i	$-0.497475\pi$
$839$	0.459449	0.0158619	0.00793097	+	0.999969i	$0.497475\pi$
$840$	0	0
$841$	2.81214	0.0969704
$842$	66.3905	2.28797
$843$	−2.07848	−0.0715866
$844$	−40.0521	−1.37865
$845$	0	0
$846$	−1.47740	−0.0507941
$847$	−6.72300	−0.231005
$848$	−27.2433	−0.935539
$849$	−9.69279	−0.332656
$850$	0	0
$851$	−2.73651	−0.0938065
$852$	1.31343	0.0449975
$853$	−9.15890	−0.313595	−0.156797	−	0.987631i	$-0.550117\pi$
$853$	−9.15890	−0.313595	−0.156797	+	0.987631i	$0.550117\pi$
$854$	15.4887	0.530013
$855$	0	0
$856$	−1.41677	−0.0484241
$857$	−37.3998	−1.27755	−0.638777	−	0.769392i	$-0.720559\pi$
$857$	−37.3998	−1.27755	−0.638777	+	0.769392i	$0.720559\pi$
$858$	−14.0620	−0.480070
$859$	0.371396	0.0126719	0.00633594	−	0.999980i	$-0.497983\pi$
$859$	0.371396	0.0126719	0.00633594	+	0.999980i	$0.497983\pi$
$860$	0	0
$861$	11.1321	0.379382
$862$	9.03235	0.307643
$863$	2.58450	0.0879773	0.0439886	−	0.999032i	$-0.485993\pi$
$863$	2.58450	0.0879773	0.0439886	+	0.999032i	$0.485993\pi$
$864$	41.7819	1.42145
$865$	0	0
$866$	46.4242	1.57756
$867$	18.1740	0.617221
$868$	7.39612	0.251041
$869$	3.98376	0.135140
$870$	0	0
$871$	22.6330	0.766891
$872$	−7.50291	−0.254081
$873$	−1.12652	−0.0381270
$874$	73.8113	2.49670
$875$	0	0
$876$	−57.3597	−1.93801
$877$	−4.50486	−0.152118	−0.0760591	−	0.997103i	$-0.524234\pi$
$877$	−4.50486	−0.152118	−0.0760591	+	0.997103i	$0.524234\pi$
$878$	12.9559	0.437241
$879$	−6.05843	−0.204346
$880$	0	0
$881$	21.2183	0.714864	0.357432	−	0.933939i	$-0.383652\pi$
$881$	21.2183	0.714864	0.357432	+	0.933939i	$0.383652\pi$
$882$	0.270928	0.00912261
$883$	−43.4584	−1.46249	−0.731245	−	0.682115i	$-0.761060\pi$
$883$	−43.4584	−1.46249	−0.731245	+	0.682115i	$0.761060\pi$
$884$	12.0249	0.404440
$885$	0	0
$886$	−14.5044	−0.487284
$887$	14.2921	0.479883	0.239941	−	0.970787i	$-0.422872\pi$
$887$	14.2921	0.479883	0.239941	+	0.970787i	$0.422872\pi$
$888$	0.963252	0.0323246
$889$	16.9336	0.567935
$890$	0	0
$891$	−17.7917	−0.596044
$892$	−14.9899	−0.501900
$893$	−33.2194	−1.11164
$894$	−37.5277	−1.25511
$895$	0	0
$896$	9.07396	0.303140
$897$	−18.0962	−0.604214
$898$	55.2835	1.84483
$899$	16.3419	0.545033
$900$	0	0
$901$	−26.3638	−0.878305
$902$	28.9809	0.964959
$903$	18.6298	0.619962
$904$	12.3515	0.410806
$905$	0	0
$906$	62.6891	2.08271
$907$	17.3448	0.575926	0.287963	−	0.957641i	$-0.407022\pi$
$907$	17.3448	0.575926	0.287963	+	0.957641i	$0.407022\pi$
$908$	3.88141	0.128809
$909$	1.09092	0.0361835
$910$	0	0
$911$	27.8590	0.923011	0.461506	−	0.887137i	$-0.347309\pi$
$911$	27.8590	0.923011	0.461506	+	0.887137i	$0.347309\pi$
$912$	26.7347	0.885273
$913$	−37.0827	−1.22726
$914$	51.2694	1.69584
$915$	0	0
$916$	54.7291	1.80830
$917$	6.00146	0.198186
$918$	28.3357	0.935219
$919$	−25.5765	−0.843690	−0.421845	−	0.906668i	$-0.638617\pi$
$919$	−25.5765	−0.843690	−0.421845	+	0.906668i	$0.638617\pi$
$920$	0	0
$921$	−33.8388	−1.11503
$922$	84.2083	2.77325
$923$	0.570710	0.0187852
$924$	−8.94823	−0.294375
$925$	0	0
$926$	−63.8161	−2.09713
$927$	−1.60912	−0.0528504
$928$	44.4621	1.45954
$929$	12.1852	0.399784	0.199892	−	0.979818i	$-0.435941\pi$
$929$	12.1852	0.399784	0.199892	+	0.979818i	$0.435941\pi$
$930$	0	0
$931$	6.09181	0.199651
$932$	52.9270	1.73368
$933$	−21.4376	−0.701834
$934$	−2.76128	−0.0903519
$935$	0	0
$936$	−0.281520	−0.00920177
$937$	−0.868400	−0.0283694	−0.0141847	−	0.999899i	$-0.504515\pi$
$937$	−0.868400	−0.0283694	−0.0141847	+	0.999899i	$0.504515\pi$
$938$	25.6863	0.838687
$939$	20.0978	0.655867
$940$	0	0
$941$	−20.9589	−0.683240	−0.341620	−	0.939838i	$-0.610976\pi$
$941$	−20.9589	−0.683240	−0.341620	+	0.939838i	$0.610976\pi$
$942$	−44.8352	−1.46081
$943$	37.2950	1.21449
$944$	3.79946	0.123662
$945$	0	0
$946$	48.5001	1.57688
$947$	34.8640	1.13293	0.566463	−	0.824087i	$-0.308311\pi$
$947$	34.8640	1.13293	0.566463	+	0.824087i	$0.308311\pi$
$948$	−8.33472	−0.270699
$949$	−24.9238	−0.809062
$950$	0	0
$951$	15.8202	0.513006
$952$	2.95475	0.0957641
$953$	−55.0246	−1.78242	−0.891211	−	0.453589i	$-0.850143\pi$
$953$	−55.0246	−1.78242	−0.891211	+	0.453589i	$0.850143\pi$
$954$	2.85072	0.0922955
$955$	0	0
$956$	−43.4899	−1.40656
$957$	−19.7713	−0.639116
$958$	−34.2088	−1.10524
$959$	14.9956	0.484235
$960$	0	0
$961$	−22.6052	−0.729199
$962$	1.93315	0.0623272
$963$	−0.152547	−0.00491576
$964$	15.5280	0.500122
$965$	0	0
$966$	−20.5374	−0.660780
$967$	−23.0541	−0.741370	−0.370685	−	0.928759i	$-0.620877\pi$
$967$	−23.0541	−0.741370	−0.370685	+	0.928759i	$0.620877\pi$
$968$	7.92826	0.254824
$969$	25.8716	0.831115
$970$	0	0
$971$	14.1902	0.455387	0.227693	−	0.973733i	$-0.426882\pi$
$971$	14.1902	0.455387	0.227693	+	0.973733i	$0.426882\pi$
$972$	−3.36615	−0.107969
$973$	20.1744	0.646761
$974$	12.0342	0.385601
$975$	0	0
$976$	18.7949	0.601610
$977$	19.4215	0.621348	0.310674	−	0.950517i	$-0.399445\pi$
$977$	19.4215	0.621348	0.310674	+	0.950517i	$0.399445\pi$
$978$	33.7164	1.07813
$979$	10.7007	0.341997
$980$	0	0
$981$	−0.807857	−0.0257929
$982$	7.71015	0.246041
$983$	26.8758	0.857204	0.428602	−	0.903494i	$-0.359006\pi$
$983$	26.8758	0.857204	0.428602	+	0.903494i	$0.359006\pi$
$984$	−13.1278	−0.418500
$985$	0	0
$986$	30.1535	0.960281
$987$	9.24303	0.294209
$988$	−29.2361	−0.930125
$989$	62.4139	1.98465
$990$	0	0
$991$	−28.1354	−0.893749	−0.446875	−	0.894597i	$-0.647463\pi$
$991$	−28.1354	−0.893749	−0.446875	+	0.894597i	$0.647463\pi$
$992$	22.8402	0.725177
$993$	−3.45181	−0.109540
$994$	0.647701	0.0205438
$995$	0	0
$996$	77.5835	2.45833
$997$	−11.7856	−0.373254	−0.186627	−	0.982431i	$-0.559756\pi$
$997$	−11.7856	−0.373254	−0.186627	+	0.982431i	$0.559756\pi$
$998$	30.9340	0.979198
$999$	2.55417	0.0808103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4375.2.a.o.1.5		28
5.4	even	2		4375.2.a.p.1.24		28
25.3	odd	20		175.2.n.a.134.12	yes	56
25.4	even	10		875.2.h.d.701.3		56
25.6	even	5		875.2.h.e.176.12		56
25.8	odd	20		875.2.n.c.449.3		56
25.17	odd	20		175.2.n.a.64.12	✓	56
25.19	even	10		875.2.h.d.176.3		56
25.21	even	5		875.2.h.e.701.12		56
25.22	odd	20		875.2.n.c.799.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.64.12	✓	56	25.17	odd	20
175.2.n.a.134.12	yes	56	25.3	odd	20
875.2.h.d.176.3		56	25.19	even	10
875.2.h.d.701.3		56	25.4	even	10
875.2.h.e.176.12		56	25.6	even	5
875.2.h.e.701.12		56	25.21	even	5
875.2.n.c.449.3		56	25.8	odd	20
875.2.n.c.799.3		56	25.22	odd	20
4375.2.a.o.1.5		28	1.1	even	1	trivial
4375.2.a.p.1.24		28	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4375 = 5^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4375.a (trivial)

\(f(q)\)	\(=\)	\(q-2.13370 q^{2} -1.69500 q^{3} +2.55269 q^{4} +3.61663 q^{6} +1.00000 q^{7} -1.17927 q^{8} -0.126975 q^{9} +O(q^{10})\)	\(q-2.13370 q^{2} -1.69500 q^{3} +2.55269 q^{4} +3.61663 q^{6} +1.00000 q^{7} -1.17927 q^{8} -0.126975 q^{9} +2.06809 q^{11} -4.32681 q^{12} -1.88008 q^{13} -2.13370 q^{14} -2.58916 q^{16} -2.50557 q^{17} +0.270928 q^{18} +6.09181 q^{19} -1.69500 q^{21} -4.41269 q^{22} -5.67861 q^{23} +1.99887 q^{24} +4.01152 q^{26} +5.30022 q^{27} +2.55269 q^{28} +5.64023 q^{29} +2.89738 q^{31} +7.88304 q^{32} -3.50541 q^{33} +5.34614 q^{34} -0.324129 q^{36} +0.481898 q^{37} -12.9981 q^{38} +3.18673 q^{39} -6.56763 q^{41} +3.61663 q^{42} -10.9911 q^{43} +5.27919 q^{44} +12.1165 q^{46} -5.45312 q^{47} +4.38862 q^{48} +1.00000 q^{49} +4.24694 q^{51} -4.79925 q^{52} +10.5221 q^{53} -11.3091 q^{54} -1.17927 q^{56} -10.3256 q^{57} -12.0346 q^{58} -1.46745 q^{59} -7.25908 q^{61} -6.18216 q^{62} -0.126975 q^{63} -11.6418 q^{64} +7.47951 q^{66} -12.0384 q^{67} -6.39594 q^{68} +9.62524 q^{69} -0.303557 q^{71} +0.149739 q^{72} +13.2568 q^{73} -1.02823 q^{74} +15.5505 q^{76} +2.06809 q^{77} -6.79953 q^{78} +1.92630 q^{79} -8.60295 q^{81} +14.0134 q^{82} -17.9309 q^{83} -4.32681 q^{84} +23.4517 q^{86} -9.56018 q^{87} -2.43884 q^{88} +5.17421 q^{89} -1.88008 q^{91} -14.4957 q^{92} -4.91107 q^{93} +11.6353 q^{94} -13.3618 q^{96} +8.87197 q^{97} -2.13370 q^{98} -0.262596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9}+O(q^{10}) \) 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9	\( 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9} - 16 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{14} + 24 q^{16} - 40 q^{17} - 24 q^{18} + 4 q^{19} - 8 q^{21} - 16 q^{22} - 32 q^{23} + 14 q^{24} + 6 q^{26} - 32 q^{27} + 24 q^{28} - 24 q^{29} + 6 q^{31} - 56 q^{32} - 28 q^{33} + 18 q^{36} - 32 q^{37} - 40 q^{38} - 28 q^{39} + 2 q^{41} - 16 q^{43} - 26 q^{44} - 12 q^{46} - 26 q^{47} - 46 q^{48} + 28 q^{49} - 22 q^{51} - 28 q^{52} - 60 q^{53} + 38 q^{54} - 24 q^{56} - 76 q^{57} - 16 q^{58} + 8 q^{59} + 18 q^{61} - 34 q^{62} + 22 q^{63} + 28 q^{64} + 38 q^{66} - 24 q^{67} - 62 q^{68} + 14 q^{69} - 54 q^{71} - 40 q^{72} - 46 q^{73} - 30 q^{74} + 26 q^{76} - 16 q^{77} - 32 q^{78} - 30 q^{79} + 4 q^{81} - 22 q^{82} - 60 q^{83} - 24 q^{84} - 10 q^{86} - 18 q^{87} - 16 q^{88} + 6 q^{89} - 16 q^{91} - 72 q^{92} - 48 q^{93} + 86 q^{94} + 106 q^{96} - 70 q^{97} - 8 q^{98} - 30 q^{99}+O(q^{100}) \) 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9 - 16 * q^11 - 24 * q^12 - 16 * q^13 - 8 * q^14 + 24 * q^16 - 40 * q^17 - 24 * q^18 + 4 * q^19 - 8 * q^21 - 16 * q^22 - 32 * q^23 + 14 * q^24 + 6 * q^26 - 32 * q^27 + 24 * q^28 - 24 * q^29 + 6 * q^31 - 56 * q^32 - 28 * q^33 + 18 * q^36 - 32 * q^37 - 40 * q^38 - 28 * q^39 + 2 * q^41 - 16 * q^43 - 26 * q^44 - 12 * q^46 - 26 * q^47 - 46 * q^48 + 28 * q^49 - 22 * q^51 - 28 * q^52 - 60 * q^53 + 38 * q^54 - 24 * q^56 - 76 * q^57 - 16 * q^58 + 8 * q^59 + 18 * q^61 - 34 * q^62 + 22 * q^63 + 28 * q^64 + 38 * q^66 - 24 * q^67 - 62 * q^68 + 14 * q^69 - 54 * q^71 - 40 * q^72 - 46 * q^73 - 30 * q^74 + 26 * q^76 - 16 * q^77 - 32 * q^78 - 30 * q^79 + 4 * q^81 - 22 * q^82 - 60 * q^83 - 24 * q^84 - 10 * q^86 - 18 * q^87 - 16 * q^88 + 6 * q^89 - 16 * q^91 - 72 * q^92 - 48 * q^93 + 86 * q^94 + 106 * q^96 - 70 * q^97 - 8 * q^98 - 30 * q^99

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