LMFDB - Embedded newform 625.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(1,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("625.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.6152203125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 26x^{4} - 35x^{3} - 27x^{2} + 16x + 1 $ x^8 - 3x^7 - 8x^6 + 20x^5 + 26x^4 - 35x^3 - 27x^2 + 16*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.0573749$ of defining polynomial
Character	$\chi$	$=$	625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.05737 q^{2} -0.687404 q^{3} -0.881958 q^{4} -0.726843 q^{6} +1.01199 q^{7} -3.04731 q^{8} -2.52748 q^{9} +O(q^{10})$	\(q+1.05737 q^{2} -0.687404 q^{3} -0.881958 q^{4} -0.726843 q^{6} +1.01199 q^{7} -3.04731 q^{8} -2.52748 q^{9} +5.12074 q^{11} +0.606261 q^{12} +6.08528 q^{13} +1.07006 q^{14} -1.45823 q^{16} +3.19320 q^{17} -2.67249 q^{18} +3.42871 q^{19} -0.695649 q^{21} +5.41454 q^{22} +2.91916 q^{23} +2.09473 q^{24} +6.43442 q^{26} +3.79961 q^{27} -0.892537 q^{28} -1.55246 q^{29} -7.99699 q^{31} +4.55272 q^{32} -3.52001 q^{33} +3.37640 q^{34} +2.22913 q^{36} +8.40726 q^{37} +3.62544 q^{38} -4.18304 q^{39} -1.86355 q^{41} -0.735561 q^{42} -5.22402 q^{43} -4.51628 q^{44} +3.08665 q^{46} -4.80081 q^{47} +1.00239 q^{48} -5.97587 q^{49} -2.19501 q^{51} -5.36696 q^{52} +10.0499 q^{53} +4.01761 q^{54} -3.08386 q^{56} -2.35691 q^{57} -1.64153 q^{58} +2.89450 q^{59} -2.30966 q^{61} -8.45582 q^{62} -2.55779 q^{63} +7.73040 q^{64} -3.72197 q^{66} +4.64895 q^{67} -2.81626 q^{68} -2.00664 q^{69} -7.73711 q^{71} +7.70201 q^{72} -0.595540 q^{73} +8.88962 q^{74} -3.02398 q^{76} +5.18216 q^{77} -4.42304 q^{78} +11.0593 q^{79} +4.97057 q^{81} -1.97047 q^{82} +14.2973 q^{83} +0.613533 q^{84} -5.52374 q^{86} +1.06717 q^{87} -15.6045 q^{88} -6.39323 q^{89} +6.15827 q^{91} -2.57458 q^{92} +5.49716 q^{93} -5.07625 q^{94} -3.12956 q^{96} -14.0833 q^{97} -6.31873 q^{98} -12.9425 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} + 5 q^{3} + 11 q^{4} - 4 q^{6} + 10 q^{7} + 15 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q + 5 * q^2 + 5 * q^3 + 11 * q^4 - 4 * q^6 + 10 * q^7 + 15 * q^8 + 9 * q^9	$ 8 q + 5 q^{2} + 5 q^{3} + 11 q^{4} - 4 q^{6} + 10 q^{7} + 15 q^{8} + 9 q^{9} + q^{11} + 10 q^{12} + 10 q^{13} - 8 q^{14} + 13 q^{16} + 15 q^{17} - 5 q^{18} - 10 q^{19} - 14 q^{21} - 5 q^{22} + 30 q^{23} + 5 q^{24} + 11 q^{26} + 20 q^{27} - 5 q^{28} + 10 q^{29} - 9 q^{31} + 30 q^{32} + 5 q^{33} + 7 q^{34} + 3 q^{36} - 10 q^{37} + 20 q^{38} + 8 q^{39} - 4 q^{41} - 35 q^{42} - 18 q^{44} - 9 q^{46} + 30 q^{47} + 5 q^{48} - 4 q^{49} - 14 q^{51} + 5 q^{52} + 10 q^{53} - 20 q^{54} - 10 q^{57} - 30 q^{58} - 5 q^{59} + 6 q^{61} + 10 q^{62} - 9 q^{64} - 18 q^{66} + 10 q^{67} + 40 q^{68} + 3 q^{69} - 9 q^{71} - 15 q^{72} - 18 q^{74} - 10 q^{76} + 5 q^{77} - 30 q^{78} - 20 q^{79} + 8 q^{81} - 45 q^{82} + 40 q^{83} - 28 q^{84} - 24 q^{86} + 40 q^{87} - 40 q^{88} - 5 q^{89} + 6 q^{91} + 15 q^{92} - 40 q^{93} + 47 q^{94} + 71 q^{96} - 30 q^{98} - 22 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 + 5 * q^3 + 11 * q^4 - 4 * q^6 + 10 * q^7 + 15 * q^8 + 9 * q^9 + q^11 + 10 * q^12 + 10 * q^13 - 8 * q^14 + 13 * q^16 + 15 * q^17 - 5 * q^18 - 10 * q^19 - 14 * q^21 - 5 * q^22 + 30 * q^23 + 5 * q^24 + 11 * q^26 + 20 * q^27 - 5 * q^28 + 10 * q^29 - 9 * q^31 + 30 * q^32 + 5 * q^33 + 7 * q^34 + 3 * q^36 - 10 * q^37 + 20 * q^38 + 8 * q^39 - 4 * q^41 - 35 * q^42 - 18 * q^44 - 9 * q^46 + 30 * q^47 + 5 * q^48 - 4 * q^49 - 14 * q^51 + 5 * q^52 + 10 * q^53 - 20 * q^54 - 10 * q^57 - 30 * q^58 - 5 * q^59 + 6 * q^61 + 10 * q^62 - 9 * q^64 - 18 * q^66 + 10 * q^67 + 40 * q^68 + 3 * q^69 - 9 * q^71 - 15 * q^72 - 18 * q^74 - 10 * q^76 + 5 * q^77 - 30 * q^78 - 20 * q^79 + 8 * q^81 - 45 * q^82 + 40 * q^83 - 28 * q^84 - 24 * q^86 + 40 * q^87 - 40 * q^88 - 5 * q^89 + 6 * q^91 + 15 * q^92 - 40 * q^93 + 47 * q^94 + 71 * q^96 - 30 * q^98 - 22 * 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 $

$2$	1.05737	0.747677	0.373838	−	0.927494i	$-0.378041\pi$
$2$	1.05737	0.747677	0.373838	+	0.927494i	$0.378041\pi$
$3$	−0.687404	−0.396873	−0.198436	−	0.980114i	$-0.563586\pi$
$3$	−0.687404	−0.396873	−0.198436	+	0.980114i	$0.563586\pi$
$4$	−0.881958	−0.440979
$5$	0	0
$5$	0	0
$6$	−0.726843	−0.296733
$7$	1.01199	0.382498	0.191249	−	0.981542i	$-0.438746\pi$
$7$	1.01199	0.382498	0.191249	+	0.981542i	$0.438746\pi$
$8$	−3.04731	−1.07739
$9$	−2.52748	−0.842492
$10$	0	0
$11$	5.12074	1.54396	0.771980	−	0.635647i	$-0.219266\pi$
$11$	5.12074	1.54396	0.771980	+	0.635647i	$0.219266\pi$
$12$	0.606261	0.175013
$13$	6.08528	1.68775	0.843876	−	0.536538i	$-0.180268\pi$
$13$	6.08528	1.68775	0.843876	+	0.536538i	$0.180268\pi$
$14$	1.07006	0.285985
$15$	0	0
$16$	−1.45823	−0.364558
$17$	3.19320	0.774464	0.387232	−	0.921982i	$-0.373431\pi$
$17$	3.19320	0.774464	0.387232	+	0.921982i	$0.373431\pi$
$18$	−2.67249	−0.629912
$19$	3.42871	0.786601	0.393300	−	0.919410i	$-0.371333\pi$
$19$	3.42871	0.786601	0.393300	+	0.919410i	$0.371333\pi$
$20$	0	0
$21$	−0.695649	−0.151803
$22$	5.41454	1.15438
$23$	2.91916	0.608687	0.304343	−	0.952562i	$-0.401563\pi$
$23$	2.91916	0.608687	0.304343	+	0.952562i	$0.401563\pi$
$24$	2.09473	0.427585
$25$	0	0
$26$	6.43442	1.26189
$27$	3.79961	0.731235
$28$	−0.892537	−0.168674
$29$	−1.55246	−0.288285	−0.144142	−	0.989557i	$-0.546042\pi$
$29$	−1.55246	−0.288285	−0.144142	+	0.989557i	$0.546042\pi$
$30$	0	0
$31$	−7.99699	−1.43630	−0.718151	−	0.695887i	$-0.755011\pi$
$31$	−7.99699	−1.43630	−0.718151	+	0.695887i	$0.755011\pi$
$32$	4.55272	0.804815
$33$	−3.52001	−0.612756
$34$	3.37640	0.579049
$35$	0	0
$36$	2.22913	0.371521
$37$	8.40726	1.38214	0.691072	−	0.722786i	$-0.257139\pi$
$37$	8.40726	1.38214	0.691072	+	0.722786i	$0.257139\pi$
$38$	3.62544	0.588123
$39$	−4.18304	−0.669823
$40$	0	0
$41$	−1.86355	−0.291037	−0.145519	−	0.989356i	$-0.546485\pi$
$41$	−1.86355	−0.291037	−0.145519	+	0.989356i	$0.546485\pi$
$42$	−0.735561	−0.113500
$43$	−5.22402	−0.796655	−0.398328	−	0.917243i	$-0.630409\pi$
$43$	−5.22402	−0.796655	−0.398328	+	0.917243i	$0.630409\pi$
$44$	−4.51628	−0.680854
$45$	0	0
$46$	3.08665	0.455101
$47$	−4.80081	−0.700269	−0.350135	−	0.936699i	$-0.613864\pi$
$47$	−4.80081	−0.700269	−0.350135	+	0.936699i	$0.613864\pi$
$48$	1.00239	0.144683
$49$	−5.97587	−0.853695
$50$	0	0
$51$	−2.19501	−0.307363
$52$	−5.36696	−0.744264
$53$	10.0499	1.38046	0.690232	−	0.723588i	$-0.257508\pi$
$53$	10.0499	1.38046	0.690232	+	0.723588i	$0.257508\pi$
$54$	4.01761	0.546727
$55$	0	0
$56$	−3.08386	−0.412098
$57$	−2.35691	−0.312180
$58$	−1.64153	−0.215544
$59$	2.89450	0.376832	0.188416	−	0.982089i	$-0.439665\pi$
$59$	2.89450	0.376832	0.188416	+	0.982089i	$0.439665\pi$
$60$	0	0
$61$	−2.30966	−0.295722	−0.147861	−	0.989008i	$-0.547239\pi$
$61$	−2.30966	−0.295722	−0.147861	+	0.989008i	$0.547239\pi$
$62$	−8.45582	−1.07389
$63$	−2.55779	−0.322252
$64$	7.73040	0.966300
$65$	0	0
$66$	−3.72197	−0.458143
$67$	4.64895	0.567960	0.283980	−	0.958830i	$-0.408345\pi$
$67$	4.64895	0.567960	0.283980	+	0.958830i	$0.408345\pi$
$68$	−2.81626	−0.341522
$69$	−2.00664	−0.241571
$70$	0	0
$71$	−7.73711	−0.918226	−0.459113	−	0.888378i	$-0.651833\pi$
$71$	−7.73711	−0.918226	−0.459113	+	0.888378i	$0.651833\pi$
$72$	7.70201	0.907690
$73$	−0.595540	−0.0697027	−0.0348513	−	0.999393i	$-0.511096\pi$
$73$	−0.595540	−0.0697027	−0.0348513	+	0.999393i	$0.511096\pi$
$74$	8.88962	1.03340
$75$	0	0
$76$	−3.02398	−0.346875
$77$	5.18216	0.590562
$78$	−4.42304	−0.500811
$79$	11.0593	1.24427	0.622134	−	0.782910i	$-0.286266\pi$
$79$	11.0593	1.24427	0.622134	+	0.782910i	$0.286266\pi$
$80$	0	0
$81$	4.97057	0.552285
$82$	−1.97047	−0.217602
$83$	14.2973	1.56933	0.784665	−	0.619920i	$-0.212835\pi$
$83$	14.2973	1.56933	0.784665	+	0.619920i	$0.212835\pi$
$84$	0.613533	0.0669420
$85$	0	0
$86$	−5.52374	−0.595641
$87$	1.06717	0.114412
$88$	−15.6045	−1.66344
$89$	−6.39323	−0.677681	−0.338841	−	0.940844i	$-0.610035\pi$
$89$	−6.39323	−0.677681	−0.338841	+	0.940844i	$0.610035\pi$
$90$	0	0
$91$	6.15827	0.645562
$92$	−2.57458	−0.268418
$93$	5.49716	0.570029
$94$	−5.07625	−0.523575
$95$	0	0
$96$	−3.12956	−0.319409
$97$	−14.0833	−1.42994	−0.714970	−	0.699155i	$-0.753560\pi$
$97$	−14.0833	−1.42994	−0.714970	+	0.699155i	$0.753560\pi$
$98$	−6.31873	−0.638288
$99$	−12.9425	−1.30077
$100$	0	0
$101$	−10.5130	−1.04608	−0.523040	−	0.852308i	$-0.675202\pi$
$101$	−10.5130	−1.04608	−0.523040	+	0.852308i	$0.675202\pi$
$102$	−2.32095	−0.229809
$103$	−3.07770	−0.303254	−0.151627	−	0.988438i	$-0.548451\pi$
$103$	−3.07770	−0.303254	−0.151627	+	0.988438i	$0.548451\pi$
$104$	−18.5437	−1.81836
$105$	0	0
$106$	10.6265	1.03214
$107$	−5.24731	−0.507277	−0.253638	−	0.967299i	$-0.581627\pi$
$107$	−5.24731	−0.507277	−0.253638	+	0.967299i	$0.581627\pi$
$108$	−3.35109	−0.322459
$109$	−6.51906	−0.624413	−0.312206	−	0.950014i	$-0.601068\pi$
$109$	−6.51906	−0.624413	−0.312206	+	0.950014i	$0.601068\pi$
$110$	0	0
$111$	−5.77918	−0.548535
$112$	−1.47572	−0.139443
$113$	0.385555	0.0362699	0.0181350	−	0.999836i	$-0.494227\pi$
$113$	0.385555	0.0362699	0.0181350	+	0.999836i	$0.494227\pi$
$114$	−2.49214	−0.233410
$115$	0	0
$116$	1.36921	0.127128
$117$	−15.3804	−1.42192
$118$	3.06058	0.281749
$119$	3.23150	0.296231
$120$	0	0
$121$	15.2220	1.38381
$122$	−2.44218	−0.221104
$123$	1.28101	0.115505
$124$	7.05301	0.633379
$125$	0	0
$126$	−2.70455	−0.240940
$127$	−4.64324	−0.412021	−0.206010	−	0.978550i	$-0.566048\pi$
$127$	−4.64324	−0.412021	−0.206010	+	0.978550i	$0.566048\pi$
$128$	−0.931513	−0.0823349
$129$	3.59101	0.316171
$130$	0	0
$131$	16.2213	1.41726	0.708630	−	0.705581i	$-0.249314\pi$
$131$	16.2213	1.41726	0.708630	+	0.705581i	$0.249314\pi$
$132$	3.10450	0.270212
$133$	3.46984	0.300873
$134$	4.91568	0.424650
$135$	0	0
$136$	−9.73066	−0.834397
$137$	−19.1801	−1.63867	−0.819335	−	0.573315i	$-0.805657\pi$
$137$	−19.1801	−1.63867	−0.819335	+	0.573315i	$0.805657\pi$
$138$	−2.12177	−0.180617
$139$	3.58765	0.304300	0.152150	−	0.988357i	$-0.451380\pi$
$139$	3.58765	0.304300	0.152150	+	0.988357i	$0.451380\pi$
$140$	0	0
$141$	3.30009	0.277918
$142$	−8.18102	−0.686536
$143$	31.1611	2.60582
$144$	3.68565	0.307137
$145$	0	0
$146$	−0.629709	−0.0521151
$147$	4.10783	0.338808
$148$	−7.41485	−0.609497
$149$	1.60192	0.131234	0.0656170	−	0.997845i	$-0.479098\pi$
$149$	1.60192	0.131234	0.0656170	+	0.997845i	$0.479098\pi$
$150$	0	0
$151$	6.74218	0.548671	0.274336	−	0.961634i	$-0.411542\pi$
$151$	6.74218	0.548671	0.274336	+	0.961634i	$0.411542\pi$
$152$	−10.4484	−0.847474
$153$	−8.07073	−0.652479
$154$	5.47948	0.441549
$155$	0	0
$156$	3.68927	0.295378
$157$	−14.2612	−1.13817	−0.569083	−	0.822280i	$-0.692702\pi$
$157$	−14.2612	−1.13817	−0.569083	+	0.822280i	$0.692702\pi$
$158$	11.6938	0.930311
$159$	−6.90836	−0.547869
$160$	0	0
$161$	2.95417	0.232822
$162$	5.25575	0.412931
$163$	−10.1141	−0.792194	−0.396097	−	0.918209i	$-0.629636\pi$
$163$	−10.1141	−0.792194	−0.396097	+	0.918209i	$0.629636\pi$
$164$	1.64357	0.128341
$165$	0	0
$166$	15.1176	1.17335
$167$	16.7161	1.29353	0.646765	−	0.762689i	$-0.276121\pi$
$167$	16.7161	1.29353	0.646765	+	0.762689i	$0.276121\pi$
$168$	2.11986	0.163551
$169$	24.0306	1.84851
$170$	0	0
$171$	−8.66599	−0.662705
$172$	4.60736	0.351308
$173$	6.44267	0.489827	0.244914	−	0.969545i	$-0.421240\pi$
$173$	6.44267	0.489827	0.244914	+	0.969545i	$0.421240\pi$
$174$	1.12840	0.0855435
$175$	0	0
$176$	−7.46723	−0.562864
$177$	−1.98969	−0.149554
$178$	−6.76004	−0.506687
$179$	−15.4342	−1.15361	−0.576804	−	0.816882i	$-0.695700\pi$
$179$	−15.4342	−1.15361	−0.576804	+	0.816882i	$0.695700\pi$
$180$	0	0
$181$	1.27794	0.0949885	0.0474943	−	0.998872i	$-0.484876\pi$
$181$	1.27794	0.0949885	0.0474943	+	0.998872i	$0.484876\pi$
$182$	6.51160	0.482672
$183$	1.58767	0.117364
$184$	−8.89559	−0.655791
$185$	0	0
$186$	5.81256	0.426197
$187$	16.3515	1.19574
$188$	4.23411	0.308804
$189$	3.84518	0.279696
$190$	0	0
$191$	5.83613	0.422287	0.211144	−	0.977455i	$-0.432281\pi$
$191$	5.83613	0.422287	0.211144	+	0.977455i	$0.432281\pi$
$192$	−5.31390	−0.383498
$193$	−4.17773	−0.300719	−0.150360	−	0.988631i	$-0.548043\pi$
$193$	−4.17773	−0.300719	−0.150360	+	0.988631i	$0.548043\pi$
$194$	−14.8913	−1.06913
$195$	0	0
$196$	5.27047	0.376462
$197$	−17.4854	−1.24579	−0.622893	−	0.782307i	$-0.714043\pi$
$197$	−17.4854	−1.24579	−0.622893	+	0.782307i	$0.714043\pi$
$198$	−13.6851	−0.972559
$199$	5.89046	0.417564	0.208782	−	0.977962i	$-0.433050\pi$
$199$	5.89046	0.417564	0.208782	+	0.977962i	$0.433050\pi$
$200$	0	0
$201$	−3.19571	−0.225408
$202$	−11.1162	−0.782130
$203$	−1.57108	−0.110268
$204$	1.93591	0.135541
$205$	0	0
$206$	−3.25428	−0.226736
$207$	−7.37811	−0.512814
$208$	−8.87375	−0.615284
$209$	17.5575	1.21448
$210$	0	0
$211$	−11.9773	−0.824549	−0.412275	−	0.911060i	$-0.635266\pi$
$211$	−11.9773	−0.824549	−0.412275	+	0.911060i	$0.635266\pi$
$212$	−8.86362	−0.608756
$213$	5.31852	0.364419
$214$	−5.54838	−0.379279
$215$	0	0
$216$	−11.5786	−0.787823
$217$	−8.09291	−0.549383
$218$	−6.89309	−0.466859
$219$	0.409376	0.0276631
$220$	0	0
$221$	19.4315	1.30710
$222$	−6.11076	−0.410127
$223$	−1.27716	−0.0855248	−0.0427624	−	0.999085i	$-0.513616\pi$
$223$	−1.27716	−0.0855248	−0.0427624	+	0.999085i	$0.513616\pi$
$224$	4.60733	0.307840
$225$	0	0
$226$	0.407676	0.0271182
$227$	28.1382	1.86760	0.933798	−	0.357802i	$-0.116474\pi$
$227$	28.1382	1.86760	0.933798	+	0.357802i	$0.116474\pi$
$228$	2.07870	0.137665
$229$	11.2821	0.745544	0.372772	−	0.927923i	$-0.378407\pi$
$229$	11.2821	0.745544	0.372772	+	0.927923i	$0.378407\pi$
$230$	0	0
$231$	−3.56223	−0.234378
$232$	4.73083	0.310594
$233$	−13.4719	−0.882576	−0.441288	−	0.897365i	$-0.645478\pi$
$233$	−13.4719	−0.882576	−0.441288	+	0.897365i	$0.645478\pi$
$234$	−16.2628	−1.06314
$235$	0	0
$236$	−2.55283	−0.166175
$237$	−7.60220	−0.493816
$238$	3.41690	0.221485
$239$	1.90251	0.123063	0.0615315	−	0.998105i	$-0.480402\pi$
$239$	1.90251	0.123063	0.0615315	+	0.998105i	$0.480402\pi$
$240$	0	0
$241$	−19.5685	−1.26052	−0.630258	−	0.776386i	$-0.717051\pi$
$241$	−19.5685	−1.26052	−0.630258	+	0.776386i	$0.717051\pi$
$242$	16.0953	1.03465
$243$	−14.8156	−0.950422
$244$	2.03702	0.130407
$245$	0	0
$246$	1.35451	0.0863602
$247$	20.8647	1.32759
$248$	24.3693	1.54745
$249$	−9.82800	−0.622824
$250$	0	0
$251$	20.7096	1.30718	0.653590	−	0.756849i	$-0.273262\pi$
$251$	20.7096	1.30718	0.653590	+	0.756849i	$0.273262\pi$
$252$	2.25587	0.142106
$253$	14.9483	0.939789
$254$	−4.90964	−0.308058
$255$	0	0
$256$	−16.4458	−1.02786
$257$	15.0730	0.940225	0.470113	−	0.882606i	$-0.344213\pi$
$257$	15.0730	0.940225	0.470113	+	0.882606i	$0.344213\pi$
$258$	3.79704	0.236393
$259$	8.50810	0.528667
$260$	0	0
$261$	3.92381	0.242878
$262$	17.1520	1.05965
$263$	5.00327	0.308515	0.154257	−	0.988031i	$-0.450702\pi$
$263$	5.00327	0.308515	0.154257	+	0.988031i	$0.450702\pi$
$264$	10.7266	0.660175
$265$	0	0
$266$	3.66892	0.224956
$267$	4.39473	0.268953
$268$	−4.10018	−0.250458
$269$	−27.6804	−1.68770	−0.843852	−	0.536576i	$-0.819717\pi$
$269$	−27.6804	−1.68770	−0.843852	+	0.536576i	$0.819717\pi$
$270$	0	0
$271$	−26.3928	−1.60325	−0.801624	−	0.597829i	$-0.796030\pi$
$271$	−26.3928	−1.60325	−0.801624	+	0.597829i	$0.796030\pi$
$272$	−4.65642	−0.282337
$273$	−4.23322	−0.256206
$274$	−20.2806	−1.22520
$275$	0	0
$276$	1.76977	0.106528
$277$	−7.12277	−0.427966	−0.213983	−	0.976837i	$-0.568644\pi$
$277$	−7.12277	−0.427966	−0.213983	+	0.976837i	$0.568644\pi$
$278$	3.79349	0.227518
$279$	20.2122	1.21007
$280$	0	0
$281$	−10.3267	−0.616037	−0.308019	−	0.951380i	$-0.599666\pi$
$281$	−10.3267	−0.616037	−0.308019	+	0.951380i	$0.599666\pi$
$282$	3.48943	0.207793
$283$	4.55987	0.271056	0.135528	−	0.990773i	$-0.456727\pi$
$283$	4.55987	0.271056	0.135528	+	0.990773i	$0.456727\pi$
$284$	6.82381	0.404918
$285$	0	0
$286$	32.9490	1.94831
$287$	−1.88590	−0.111321
$288$	−11.5069	−0.678050
$289$	−6.80350	−0.400206
$290$	0	0
$291$	9.68090	0.567504
$292$	0.525241	0.0307374
$293$	−20.8237	−1.21653	−0.608267	−	0.793733i	$-0.708135\pi$
$293$	−20.8237	−1.21653	−0.608267	+	0.793733i	$0.708135\pi$
$294$	4.34352	0.253319
$295$	0	0
$296$	−25.6195	−1.48910
$297$	19.4568	1.12900
$298$	1.69383	0.0981207
$299$	17.7639	1.02731
$300$	0	0
$301$	−5.28668	−0.304719
$302$	7.12902	0.410229
$303$	7.22666	0.415161
$304$	−4.99986	−0.286762
$305$	0	0
$306$	−8.53378	−0.487844
$307$	9.44200	0.538884	0.269442	−	0.963017i	$-0.413161\pi$
$307$	9.44200	0.538884	0.269442	+	0.963017i	$0.413161\pi$
$308$	−4.57045	−0.260425
$309$	2.11562	0.120353
$310$	0	0
$311$	13.3804	0.758732	0.379366	−	0.925247i	$-0.376142\pi$
$311$	13.3804	0.758732	0.379366	+	0.925247i	$0.376142\pi$
$312$	12.7470	0.721658
$313$	23.9947	1.35626	0.678131	−	0.734941i	$-0.262790\pi$
$313$	23.9947	1.35626	0.678131	+	0.734941i	$0.262790\pi$
$314$	−15.0794	−0.850980
$315$	0	0
$316$	−9.75384	−0.548697
$317$	14.5616	0.817862	0.408931	−	0.912565i	$-0.365902\pi$
$317$	14.5616	0.817862	0.408931	+	0.912565i	$0.365902\pi$
$318$	−7.30473	−0.409629
$319$	−7.94975	−0.445100
$320$	0	0
$321$	3.60702	0.201324
$322$	3.12367	0.174075
$323$	10.9486	0.609194
$324$	−4.38383	−0.243546
$325$	0	0
$326$	−10.6944	−0.592305
$327$	4.48122	0.247812
$328$	5.67880	0.313560
$329$	−4.85839	−0.267852
$330$	0	0
$331$	−24.4248	−1.34251	−0.671255	−	0.741226i	$-0.734245\pi$
$331$	−24.4248	−1.34251	−0.671255	+	0.741226i	$0.734245\pi$
$332$	−12.6096	−0.692042
$333$	−21.2491	−1.16445
$334$	17.6752	0.967143
$335$	0	0
$336$	1.01442	0.0553410
$337$	−8.57221	−0.466958	−0.233479	−	0.972362i	$-0.575011\pi$
$337$	−8.57221	−0.466958	−0.233479	+	0.972362i	$0.575011\pi$
$338$	25.4094	1.38209
$339$	−0.265032	−0.0143945
$340$	0	0
$341$	−40.9505	−2.21759
$342$	−9.16320	−0.495489
$343$	−13.1315	−0.709035
$344$	15.9192	0.858306
$345$	0	0
$346$	6.81232	0.366233
$347$	10.8076	0.580182	0.290091	−	0.956999i	$-0.406314\pi$
$347$	10.8076	0.580182	0.290091	+	0.956999i	$0.406314\pi$
$348$	−0.941197	−0.0504535
$349$	−8.13956	−0.435701	−0.217850	−	0.975982i	$-0.569904\pi$
$349$	−8.13956	−0.435701	−0.217850	+	0.975982i	$0.569904\pi$
$350$	0	0
$351$	23.1217	1.23414
$352$	23.3133	1.24260
$353$	21.1661	1.12656	0.563279	−	0.826267i	$-0.309540\pi$
$353$	21.1661	1.12656	0.563279	+	0.826267i	$0.309540\pi$
$354$	−2.10385	−0.111818
$355$	0	0
$356$	5.63856	0.298843
$357$	−2.22134	−0.117566
$358$	−16.3198	−0.862527
$359$	−5.32585	−0.281087	−0.140544	−	0.990074i	$-0.544885\pi$
$359$	−5.32585	−0.281087	−0.140544	+	0.990074i	$0.544885\pi$
$360$	0	0
$361$	−7.24392	−0.381259
$362$	1.35126	0.0710207
$363$	−10.4636	−0.549198
$364$	−5.43134	−0.284679
$365$	0	0
$366$	1.67876	0.0877502
$367$	−17.0272	−0.888812	−0.444406	−	0.895826i	$-0.646585\pi$
$367$	−17.0272	−0.888812	−0.444406	+	0.895826i	$0.646585\pi$
$368$	−4.25682	−0.221902
$369$	4.71007	0.245196
$370$	0	0
$371$	10.1705	0.528025
$372$	−4.84826	−0.251371
$373$	−6.85131	−0.354748	−0.177374	−	0.984144i	$-0.556760\pi$
$373$	−6.85131	−0.354748	−0.177374	+	0.984144i	$0.556760\pi$
$374$	17.2897	0.894028
$375$	0	0
$376$	14.6295	0.754461
$377$	−9.44716	−0.486554
$378$	4.06580	0.209122
$379$	−7.38816	−0.379504	−0.189752	−	0.981832i	$-0.560768\pi$
$379$	−7.38816	−0.379504	−0.189752	+	0.981832i	$0.560768\pi$
$380$	0	0
$381$	3.19178	0.163520
$382$	6.17097	0.315734
$383$	20.2032	1.03233	0.516167	−	0.856488i	$-0.327359\pi$
$383$	20.2032	1.03233	0.516167	+	0.856488i	$0.327359\pi$
$384$	0.640325	0.0326764
$385$	0	0
$386$	−4.41742	−0.224841
$387$	13.2036	0.671176
$388$	12.4209	0.630574
$389$	8.80029	0.446192	0.223096	−	0.974796i	$-0.428384\pi$
$389$	8.80029	0.446192	0.223096	+	0.974796i	$0.428384\pi$
$390$	0	0
$391$	9.32145	0.471406
$392$	18.2103	0.919760
$393$	−11.1506	−0.562471
$394$	−18.4887	−0.931446
$395$	0	0
$396$	11.4148	0.573614
$397$	6.09306	0.305802	0.152901	−	0.988242i	$-0.451138\pi$
$397$	6.09306	0.305802	0.152901	+	0.988242i	$0.451138\pi$
$398$	6.22842	0.312203
$399$	−2.38518	−0.119408
$400$	0	0
$401$	−1.71924	−0.0858547	−0.0429274	−	0.999078i	$-0.513668\pi$
$401$	−1.71924	−0.0858547	−0.0429274	+	0.999078i	$0.513668\pi$
$402$	−3.37906	−0.168532
$403$	−48.6639	−2.42412
$404$	9.27201	0.461300
$405$	0	0
$406$	−1.66122	−0.0824451
$407$	43.0514	2.13398
$408$	6.68889	0.331149
$409$	−27.7414	−1.37173	−0.685863	−	0.727731i	$-0.740575\pi$
$409$	−27.7414	−1.37173	−0.685863	+	0.727731i	$0.740575\pi$
$410$	0	0
$411$	13.1845	0.650343
$412$	2.71440	0.133729
$413$	2.92922	0.144138
$414$	−7.80143	−0.383419
$415$	0	0
$416$	27.7046	1.35833
$417$	−2.46616	−0.120768
$418$	18.5649	0.908039
$419$	16.3540	0.798944	0.399472	−	0.916745i	$-0.369193\pi$
$419$	16.3540	0.798944	0.399472	+	0.916745i	$0.369193\pi$
$420$	0	0
$421$	−9.94561	−0.484719	−0.242360	−	0.970186i	$-0.577921\pi$
$421$	−9.94561	−0.484719	−0.242360	+	0.970186i	$0.577921\pi$
$422$	−12.6645	−0.616496
$423$	12.1339	0.589972
$424$	−30.6253	−1.48729
$425$	0	0
$426$	5.62367	0.272467
$427$	−2.33736	−0.113113
$428$	4.62791	0.223699
$429$	−21.4203	−1.03418
$430$	0	0
$431$	−20.5302	−0.988903	−0.494452	−	0.869205i	$-0.664631\pi$
$431$	−20.5302	−0.988903	−0.494452	+	0.869205i	$0.664631\pi$
$432$	−5.54071	−0.266578
$433$	−25.9469	−1.24693	−0.623463	−	0.781853i	$-0.714275\pi$
$433$	−25.9469	−1.24693	−0.623463	+	0.781853i	$0.714275\pi$
$434$	−8.55724	−0.410761
$435$	0	0
$436$	5.74954	0.275353
$437$	10.0090	0.478794
$438$	0.432864	0.0206831
$439$	25.1284	1.19931	0.599656	−	0.800258i	$-0.295304\pi$
$439$	25.1284	1.19931	0.599656	+	0.800258i	$0.295304\pi$
$440$	0	0
$441$	15.1039	0.719232
$442$	20.5464	0.977291
$443$	27.0262	1.28405	0.642027	−	0.766682i	$-0.278094\pi$
$443$	27.0262	1.28405	0.642027	+	0.766682i	$0.278094\pi$
$444$	5.09699	0.241893
$445$	0	0
$446$	−1.35043	−0.0639449
$447$	−1.10116	−0.0520832
$448$	7.82312	0.369608
$449$	37.9871	1.79272	0.896361	−	0.443325i	$-0.146201\pi$
$449$	37.9871	1.79272	0.896361	+	0.443325i	$0.146201\pi$
$450$	0	0
$451$	−9.54273	−0.449350
$452$	−0.340043	−0.0159943
$453$	−4.63460	−0.217753
$454$	29.7526	1.39636
$455$	0	0
$456$	7.18224	0.336339
$457$	−29.9832	−1.40256	−0.701278	−	0.712888i	$-0.747387\pi$
$457$	−29.9832	−1.40256	−0.701278	+	0.712888i	$0.747387\pi$
$458$	11.9294	0.557426
$459$	12.1329	0.566315
$460$	0	0
$461$	−2.13364	−0.0993734	−0.0496867	−	0.998765i	$-0.515822\pi$
$461$	−2.13364	−0.0993734	−0.0496867	+	0.998765i	$0.515822\pi$
$462$	−3.76662	−0.175239
$463$	−21.9804	−1.02151	−0.510757	−	0.859725i	$-0.670635\pi$
$463$	−21.9804	−1.02151	−0.510757	+	0.859725i	$0.670635\pi$
$464$	2.26385	0.105097
$465$	0	0
$466$	−14.2449	−0.659882
$467$	5.31093	0.245761	0.122880	−	0.992421i	$-0.460787\pi$
$467$	5.31093	0.245761	0.122880	+	0.992421i	$0.460787\pi$
$468$	13.5649	0.627036
$469$	4.70471	0.217243
$470$	0	0
$471$	9.80318	0.451707
$472$	−8.82045	−0.405994
$473$	−26.7508	−1.23000
$474$	−8.03838	−0.369215
$475$	0	0
$476$	−2.85005	−0.130632
$477$	−25.4010	−1.16303
$478$	2.01166	0.0920113
$479$	−21.0877	−0.963522	−0.481761	−	0.876303i	$-0.660003\pi$
$479$	−21.0877	−0.963522	−0.481761	+	0.876303i	$0.660003\pi$
$480$	0	0
$481$	51.1605	2.33272
$482$	−20.6912	−0.942459
$483$	−2.03071	−0.0924005
$484$	−13.4251	−0.610233
$485$	0	0
$486$	−15.6656	−0.710608
$487$	−26.6121	−1.20591	−0.602954	−	0.797776i	$-0.706010\pi$
$487$	−26.6121	−1.20591	−0.602954	+	0.797776i	$0.706010\pi$
$488$	7.03825	0.318607
$489$	6.95244	0.314400
$490$	0	0
$491$	1.80069	0.0812638	0.0406319	−	0.999174i	$-0.487063\pi$
$491$	1.80069	0.0812638	0.0406319	+	0.999174i	$0.487063\pi$
$492$	−1.12980	−0.0509351
$493$	−4.95731	−0.223266
$494$	22.0618	0.992607
$495$	0	0
$496$	11.6615	0.523616
$497$	−7.82991	−0.351220
$498$	−10.3919	−0.465671
$499$	28.6962	1.28462	0.642309	−	0.766446i	$-0.277977\pi$
$499$	28.6962	1.28462	0.642309	+	0.766446i	$0.277977\pi$
$500$	0	0
$501$	−11.4907	−0.513367
$502$	21.8978	0.977349
$503$	−23.6827	−1.05596	−0.527980	−	0.849257i	$-0.677051\pi$
$503$	−23.6827	−1.05596	−0.527980	+	0.849257i	$0.677051\pi$
$504$	7.79439	0.347190
$505$	0	0
$506$	15.8059	0.702658
$507$	−16.5187	−0.733622
$508$	4.09514	0.181693
$509$	17.6957	0.784346	0.392173	−	0.919891i	$-0.371723\pi$
$509$	17.6957	0.784346	0.392173	+	0.919891i	$0.371723\pi$
$510$	0	0
$511$	−0.602683	−0.0266611
$512$	−15.5263	−0.686172
$513$	13.0278	0.575190
$514$	15.9378	0.702985
$515$	0	0
$516$	−3.16712	−0.139425
$517$	−24.5837	−1.08119
$518$	8.99625	0.395273
$519$	−4.42872	−0.194399
$520$	0	0
$521$	22.9756	1.00658	0.503289	−	0.864118i	$-0.332123\pi$
$521$	22.9756	1.00658	0.503289	+	0.864118i	$0.332123\pi$
$522$	4.14894	0.181594
$523$	−28.9773	−1.26709	−0.633544	−	0.773707i	$-0.718400\pi$
$523$	−28.9773	−1.26709	−0.633544	+	0.773707i	$0.718400\pi$
$524$	−14.3065	−0.624982
$525$	0	0
$526$	5.29033	0.230669
$527$	−25.5359	−1.11236
$528$	5.13300	0.223385
$529$	−14.4785	−0.629500
$530$	0	0
$531$	−7.31579	−0.317478
$532$	−3.06025	−0.132679
$533$	−11.3402	−0.491199
$534$	4.64688	0.201090
$535$	0	0
$536$	−14.1668	−0.611912
$537$	10.6095	0.457836
$538$	−29.2686	−1.26186
$539$	−30.6008	−1.31807
$540$	0	0
$541$	24.4505	1.05121	0.525605	−	0.850729i	$-0.323839\pi$
$541$	24.4505	1.05121	0.525605	+	0.850729i	$0.323839\pi$
$542$	−27.9071	−1.19871
$543$	−0.878460	−0.0376983
$544$	14.5377	0.623300
$545$	0	0
$546$	−4.47610	−0.191559
$547$	−6.50334	−0.278063	−0.139031	−	0.990288i	$-0.544399\pi$
$547$	−6.50334	−0.278063	−0.139031	+	0.990288i	$0.544399\pi$
$548$	16.9161	0.722619
$549$	5.83761	0.249143
$550$	0	0
$551$	−5.32295	−0.226765
$552$	6.11486	0.260266
$553$	11.1920	0.475930
$554$	−7.53144	−0.319980
$555$	0	0
$556$	−3.16416	−0.134190
$557$	3.12305	0.132328	0.0661640	−	0.997809i	$-0.478924\pi$
$557$	3.12305	0.132328	0.0661640	+	0.997809i	$0.478924\pi$
$558$	21.3719	0.904744
$559$	−31.7896	−1.34456
$560$	0	0
$561$	−11.2401	−0.474557
$562$	−10.9192	−0.460597
$563$	−36.5252	−1.53935	−0.769677	−	0.638433i	$-0.779583\pi$
$563$	−36.5252	−1.53935	−0.769677	+	0.638433i	$0.779583\pi$
$564$	−2.91054	−0.122556
$565$	0	0
$566$	4.82149	0.202663
$567$	5.03019	0.211248
$568$	23.5774	0.989285
$569$	−37.7676	−1.58330	−0.791650	−	0.610975i	$-0.790778\pi$
$569$	−37.7676	−1.58330	−0.791650	+	0.610975i	$0.790778\pi$
$570$	0	0
$571$	−41.2370	−1.72571	−0.862857	−	0.505448i	$-0.831327\pi$
$571$	−41.2370	−1.72571	−0.862857	+	0.505448i	$0.831327\pi$
$572$	−27.4828	−1.14911
$573$	−4.01177	−0.167594
$574$	−1.99410	−0.0832322
$575$	0	0
$576$	−19.5384	−0.814100
$577$	−4.26929	−0.177733	−0.0888663	−	0.996044i	$-0.528324\pi$
$577$	−4.26929	−0.177733	−0.0888663	+	0.996044i	$0.528324\pi$
$578$	−7.19385	−0.299225
$579$	2.87178	0.119347
$580$	0	0
$581$	14.4688	0.600266
$582$	10.2363	0.424310
$583$	51.4631	2.13138
$584$	1.81480	0.0750968
$585$	0	0
$586$	−22.0185	−0.909574
$587$	11.4331	0.471893	0.235947	−	0.971766i	$-0.424181\pi$
$587$	11.4331	0.471893	0.235947	+	0.971766i	$0.424181\pi$
$588$	−3.62294	−0.149407
$589$	−27.4194	−1.12980
$590$	0	0
$591$	12.0196	0.494418
$592$	−12.2597	−0.503872
$593$	30.9375	1.27045	0.635225	−	0.772327i	$-0.280908\pi$
$593$	30.9375	1.27045	0.635225	+	0.772327i	$0.280908\pi$
$594$	20.5731	0.844125
$595$	0	0
$596$	−1.41282	−0.0578715
$597$	−4.04912	−0.165720
$598$	18.7831	0.768098
$599$	−46.1912	−1.88732	−0.943660	−	0.330916i	$-0.892642\pi$
$599$	−46.1912	−1.88732	−0.943660	+	0.330916i	$0.892642\pi$
$600$	0	0
$601$	−38.0963	−1.55398	−0.776990	−	0.629513i	$-0.783254\pi$
$601$	−38.0963	−1.55398	−0.776990	+	0.629513i	$0.783254\pi$
$602$	−5.59000	−0.227831
$603$	−11.7501	−0.478502
$604$	−5.94632	−0.241953
$605$	0	0
$606$	7.64129	0.310406
$607$	38.6361	1.56819	0.784095	−	0.620641i	$-0.213127\pi$
$607$	38.6361	1.56819	0.784095	+	0.620641i	$0.213127\pi$
$608$	15.6100	0.633068
$609$	1.07997	0.0437625
$610$	0	0
$611$	−29.2142	−1.18188
$612$	7.11804	0.287730
$613$	−10.7561	−0.434434	−0.217217	−	0.976123i	$-0.569698\pi$
$613$	−10.7561	−0.434434	−0.217217	+	0.976123i	$0.569698\pi$
$614$	9.98374	0.402911
$615$	0	0
$616$	−15.7916	−0.636264
$617$	−10.8072	−0.435082	−0.217541	−	0.976051i	$-0.569804\pi$
$617$	−10.8072	−0.435082	−0.217541	+	0.976051i	$0.569804\pi$
$618$	2.23700	0.0899855
$619$	−36.8938	−1.48289	−0.741443	−	0.671016i	$-0.765858\pi$
$619$	−36.8938	−1.48289	−0.741443	+	0.671016i	$0.765858\pi$
$620$	0	0
$621$	11.0917	0.445093
$622$	14.1481	0.567286
$623$	−6.46992	−0.259212
$624$	6.09985	0.244189
$625$	0	0
$626$	25.3714	1.01405
$627$	−12.0691	−0.481994
$628$	12.5778	0.501907
$629$	26.8460	1.07042
$630$	0	0
$631$	39.2593	1.56289	0.781445	−	0.623974i	$-0.214483\pi$
$631$	39.2593	1.56289	0.781445	+	0.623974i	$0.214483\pi$
$632$	−33.7011	−1.34056
$633$	8.23322	0.327241
$634$	15.3971	0.611497
$635$	0	0
$636$	6.09289	0.241599
$637$	−36.3648	−1.44083
$638$	−8.40586	−0.332791
$639$	19.5554	0.773598
$640$	0	0
$641$	8.34833	0.329739	0.164870	−	0.986315i	$-0.447280\pi$
$641$	8.34833	0.329739	0.164870	+	0.986315i	$0.447280\pi$
$642$	3.81397	0.150526
$643$	−13.1408	−0.518223	−0.259112	−	0.965847i	$-0.583430\pi$
$643$	−13.1408	−0.518223	−0.259112	+	0.965847i	$0.583430\pi$
$644$	−2.60546	−0.102669
$645$	0	0
$646$	11.5767	0.455480
$647$	26.0801	1.02531	0.512656	−	0.858594i	$-0.328661\pi$
$647$	26.0801	1.02531	0.512656	+	0.858594i	$0.328661\pi$
$648$	−15.1469	−0.595025
$649$	14.8220	0.581814
$650$	0	0
$651$	5.56310	0.218035
$652$	8.92018	0.349341
$653$	23.0295	0.901213	0.450606	−	0.892723i	$-0.351208\pi$
$653$	23.0295	0.901213	0.450606	+	0.892723i	$0.351208\pi$
$654$	4.73833	0.185284
$655$	0	0
$656$	2.71749	0.106100
$657$	1.50521	0.0587240
$658$	−5.13714	−0.200267
$659$	34.7580	1.35398	0.676990	−	0.735992i	$-0.263284\pi$
$659$	34.7580	1.35398	0.676990	+	0.735992i	$0.263284\pi$
$660$	0	0
$661$	18.0033	0.700249	0.350124	−	0.936703i	$-0.386139\pi$
$661$	18.0033	0.700249	0.350124	+	0.936703i	$0.386139\pi$
$662$	−25.8262	−1.00376
$663$	−13.3573	−0.518753
$664$	−43.5682	−1.69078
$665$	0	0
$666$	−22.4683	−0.870629
$667$	−4.53188	−0.175475
$668$	−14.7429	−0.570420
$669$	0.877923	0.0339425
$670$	0	0
$671$	−11.8272	−0.456583
$672$	−3.16709	−0.122173
$673$	14.8622	0.572896	0.286448	−	0.958096i	$-0.407526\pi$
$673$	14.8622	0.572896	0.286448	+	0.958096i	$0.407526\pi$
$674$	−9.06404	−0.349134
$675$	0	0
$676$	−21.1940	−0.815153
$677$	−23.1238	−0.888720	−0.444360	−	0.895848i	$-0.646569\pi$
$677$	−23.1238	−0.888720	−0.444360	+	0.895848i	$0.646569\pi$
$678$	−0.280238	−0.0107625
$679$	−14.2522	−0.546949
$680$	0	0
$681$	−19.3423	−0.741197
$682$	−43.3000	−1.65804
$683$	−19.6347	−0.751302	−0.375651	−	0.926761i	$-0.622581\pi$
$683$	−19.6347	−0.751302	−0.375651	+	0.926761i	$0.622581\pi$
$684$	7.64304	0.292239
$685$	0	0
$686$	−13.8849	−0.530129
$687$	−7.75538	−0.295886
$688$	7.61783	0.290427
$689$	61.1566	2.32988
$690$	0	0
$691$	−5.87782	−0.223603	−0.111801	−	0.993731i	$-0.535662\pi$
$691$	−5.87782	−0.223603	−0.111801	+	0.993731i	$0.535662\pi$
$692$	−5.68217	−0.216004
$693$	−13.0978	−0.497544
$694$	11.4277	0.433788
$695$	0	0
$696$	−3.25199	−0.123266
$697$	−5.95067	−0.225398
$698$	−8.60657	−0.325763
$699$	9.26066	0.350270
$700$	0	0
$701$	−50.0581	−1.89067	−0.945334	−	0.326103i	$-0.894264\pi$
$701$	−50.0581	−1.89067	−0.945334	+	0.326103i	$0.894264\pi$
$702$	24.4483	0.922740
$703$	28.8261	1.08720
$704$	39.5853	1.49193
$705$	0	0
$706$	22.3805	0.842301
$707$	−10.6391	−0.400124
$708$	1.75483	0.0659504
$709$	13.7506	0.516414	0.258207	−	0.966090i	$-0.416868\pi$
$709$	13.7506	0.516414	0.258207	+	0.966090i	$0.416868\pi$
$710$	0	0
$711$	−27.9521	−1.04829
$712$	19.4822	0.730125
$713$	−23.3445	−0.874258
$714$	−2.34879	−0.0879013
$715$	0	0
$716$	13.6123	0.508717
$717$	−1.30779	−0.0488403
$718$	−5.63142	−0.210163
$719$	−10.5000	−0.391582	−0.195791	−	0.980646i	$-0.562727\pi$
$719$	−10.5000	−0.391582	−0.195791	+	0.980646i	$0.562727\pi$
$720$	0	0
$721$	−3.11461	−0.115994
$722$	−7.65954	−0.285059
$723$	13.4514	0.500264
$724$	−1.12709	−0.0418880
$725$	0	0
$726$	−11.0640	−0.410623
$727$	−6.06366	−0.224889	−0.112444	−	0.993658i	$-0.535868\pi$
$727$	−6.06366	−0.224889	−0.112444	+	0.993658i	$0.535868\pi$
$728$	−18.7662	−0.695520
$729$	−4.72740	−0.175089
$730$	0	0
$731$	−16.6813	−0.616980
$732$	−1.40026	−0.0517550
$733$	2.34070	0.0864558	0.0432279	−	0.999065i	$-0.486236\pi$
$733$	2.34070	0.0864558	0.0432279	+	0.999065i	$0.486236\pi$
$734$	−18.0041	−0.664544
$735$	0	0
$736$	13.2901	0.489880
$737$	23.8061	0.876907
$738$	4.98031	0.183328
$739$	−41.5352	−1.52790	−0.763949	−	0.645276i	$-0.776742\pi$
$739$	−41.5352	−1.52790	−0.763949	+	0.645276i	$0.776742\pi$
$740$	0	0
$741$	−14.3425	−0.526883
$742$	10.7540	0.394792
$743$	−0.813821	−0.0298562	−0.0149281	−	0.999889i	$-0.504752\pi$
$743$	−0.813821	−0.0298562	−0.0149281	+	0.999889i	$0.504752\pi$
$744$	−16.7515	−0.614142
$745$	0	0
$746$	−7.24441	−0.265237
$747$	−36.1360	−1.32215
$748$	−14.4214	−0.527297
$749$	−5.31025	−0.194032
$750$	0	0
$751$	31.8919	1.16375	0.581877	−	0.813277i	$-0.302319\pi$
$751$	31.8919	1.16375	0.581877	+	0.813277i	$0.302319\pi$
$752$	7.00069	0.255289
$753$	−14.2359	−0.518784
$754$	−9.98919	−0.363785
$755$	0	0
$756$	−3.39129	−0.123340
$757$	26.7040	0.970572	0.485286	−	0.874355i	$-0.338715\pi$
$757$	26.7040	0.970572	0.485286	+	0.874355i	$0.338715\pi$
$758$	−7.81205	−0.283746
$759$	−10.2755	−0.372976
$760$	0	0
$761$	43.0644	1.56108	0.780542	−	0.625103i	$-0.214943\pi$
$761$	43.0644	1.56108	0.780542	+	0.625103i	$0.214943\pi$
$762$	3.37491	0.122260
$763$	−6.59725	−0.238837
$764$	−5.14722	−0.186220
$765$	0	0
$766$	21.3623	0.771852
$767$	17.6139	0.636000
$768$	11.3049	0.407929
$769$	−1.05358	−0.0379930	−0.0189965	−	0.999820i	$-0.506047\pi$
$769$	−1.05358	−0.0379930	−0.0189965	+	0.999820i	$0.506047\pi$
$770$	0	0
$771$	−10.3612	−0.373150
$772$	3.68458	0.132611
$773$	−13.2299	−0.475845	−0.237923	−	0.971284i	$-0.576466\pi$
$773$	−13.2299	−0.475845	−0.237923	+	0.971284i	$0.576466\pi$
$774$	13.9611	0.501823
$775$	0	0
$776$	42.9161	1.54060
$777$	−5.84850	−0.209814
$778$	9.30521	0.333608
$779$	−6.38957	−0.228930
$780$	0	0
$781$	−39.6197	−1.41770
$782$	9.85627	0.352459
$783$	−5.89874	−0.210804
$784$	8.71421	0.311222
$785$	0	0
$786$	−11.7903	−0.420547
$787$	33.6378	1.19906	0.599528	−	0.800354i	$-0.295355\pi$
$787$	33.6378	1.19906	0.599528	+	0.800354i	$0.295355\pi$
$788$	15.4214	0.549366
$789$	−3.43926	−0.122441
$790$	0	0
$791$	0.390179	0.0138732
$792$	39.4399	1.40144
$793$	−14.0549	−0.499105
$794$	6.44264	0.228641
$795$	0	0
$796$	−5.19514	−0.184137
$797$	6.89741	0.244319	0.122159	−	0.992511i	$-0.461018\pi$
$797$	6.89741	0.244319	0.122159	+	0.992511i	$0.461018\pi$
$798$	−2.52203	−0.0892789
$799$	−15.3299	−0.542333
$800$	0	0
$801$	16.1587	0.570941
$802$	−1.81788	−0.0641916
$803$	−3.04960	−0.107618
$804$	2.81848	0.0994001
$805$	0	0
$806$	−51.4560	−1.81246
$807$	19.0276	0.669803
$808$	32.0363	1.12703
$809$	−35.3330	−1.24224	−0.621121	−	0.783715i	$-0.713322\pi$
$809$	−35.3330	−1.24224	−0.621121	+	0.783715i	$0.713322\pi$
$810$	0	0
$811$	−3.97201	−0.139476	−0.0697380	−	0.997565i	$-0.522216\pi$
$811$	−3.97201	−0.139476	−0.0697380	+	0.997565i	$0.522216\pi$
$812$	1.38563	0.0486261
$813$	18.1425	0.636285
$814$	45.5214	1.59552
$815$	0	0
$816$	3.20084	0.112052
$817$	−17.9117	−0.626650
$818$	−29.3331	−1.02561
$819$	−15.5649	−0.543881
$820$	0	0
$821$	24.3758	0.850720	0.425360	−	0.905024i	$-0.360147\pi$
$821$	24.3758	0.850720	0.425360	+	0.905024i	$0.360147\pi$
$822$	13.9410	0.486247
$823$	22.2604	0.775947	0.387974	−	0.921670i	$-0.373175\pi$
$823$	22.2604	0.775947	0.387974	+	0.921670i	$0.373175\pi$
$824$	9.37870	0.326722
$825$	0	0
$826$	3.09729	0.107768
$827$	26.6196	0.925656	0.462828	−	0.886448i	$-0.346835\pi$
$827$	26.6196	0.925656	0.462828	+	0.886448i	$0.346835\pi$
$828$	6.50718	0.226140
$829$	−7.83334	−0.272063	−0.136032	−	0.990704i	$-0.543435\pi$
$829$	−7.83334	−0.272063	−0.136032	+	0.990704i	$0.543435\pi$
$830$	0	0
$831$	4.89622	0.169848
$832$	47.0416	1.63088
$833$	−19.0821	−0.661156
$834$	−2.60766	−0.0902958
$835$	0	0
$836$	−15.4850	−0.535561
$837$	−30.3854	−1.05027
$838$	17.2923	0.597352
$839$	5.87401	0.202793	0.101397	−	0.994846i	$-0.467669\pi$
$839$	5.87401	0.202793	0.101397	+	0.994846i	$0.467669\pi$
$840$	0	0
$841$	−26.5899	−0.916892
$842$	−10.5162	−0.362413
$843$	7.09859	0.244488
$844$	10.5635	0.363609
$845$	0	0
$846$	12.8301	0.441108
$847$	15.4045	0.529306
$848$	−14.6551	−0.503260
$849$	−3.13447	−0.107575
$850$	0	0
$851$	24.5421	0.841293
$852$	−4.69071	−0.160701
$853$	−28.1446	−0.963654	−0.481827	−	0.876266i	$-0.660027\pi$
$853$	−28.1446	−0.963654	−0.481827	+	0.876266i	$0.660027\pi$
$854$	−2.47147	−0.0845719
$855$	0	0
$856$	15.9902	0.546534
$857$	−36.2976	−1.23990	−0.619951	−	0.784640i	$-0.712848\pi$
$857$	−36.2976	−1.23990	−0.619951	+	0.784640i	$0.712848\pi$
$858$	−22.6492	−0.773232
$859$	3.82400	0.130473	0.0652366	−	0.997870i	$-0.479220\pi$
$859$	3.82400	0.130473	0.0652366	+	0.997870i	$0.479220\pi$
$860$	0	0
$861$	1.29637	0.0441803
$862$	−21.7081	−0.739380
$863$	25.5955	0.871280	0.435640	−	0.900121i	$-0.356522\pi$
$863$	25.5955	0.871280	0.435640	+	0.900121i	$0.356522\pi$
$864$	17.2986	0.588509
$865$	0	0
$866$	−27.4356	−0.932298
$867$	4.67675	0.158831
$868$	7.13761	0.242266
$869$	56.6318	1.92110
$870$	0	0
$871$	28.2902	0.958575
$872$	19.8656	0.672734
$873$	35.5952	1.20471
$874$	10.5832	0.357983
$875$	0	0
$876$	−0.361053	−0.0121988
$877$	14.8579	0.501715	0.250857	−	0.968024i	$-0.419287\pi$
$877$	14.8579	0.501715	0.250857	+	0.968024i	$0.419287\pi$
$878$	26.5701	0.896697
$879$	14.3143	0.482809
$880$	0	0
$881$	2.11362	0.0712096	0.0356048	−	0.999366i	$-0.488664\pi$
$881$	2.11362	0.0712096	0.0356048	+	0.999366i	$0.488664\pi$
$882$	15.9704	0.537753
$883$	−51.0828	−1.71907	−0.859537	−	0.511074i	$-0.829248\pi$
$883$	−51.0828	−1.71907	−0.859537	+	0.511074i	$0.829248\pi$
$884$	−17.1378	−0.576405
$885$	0	0
$886$	28.5768	0.960058
$887$	45.5799	1.53042	0.765212	−	0.643779i	$-0.222634\pi$
$887$	45.5799	1.53042	0.765212	+	0.643779i	$0.222634\pi$
$888$	17.6109	0.590985
$889$	−4.69893	−0.157597
$890$	0	0
$891$	25.4530	0.852706
$892$	1.12640	0.0377147
$893$	−16.4606	−0.550833
$894$	−1.16434	−0.0389414
$895$	0	0
$896$	−0.942686	−0.0314929
$897$	−12.2110	−0.407712
$898$	40.1666	1.34038
$899$	12.4150	0.414064
$900$	0	0
$901$	32.0914	1.06912
$902$	−10.0902	−0.335968
$903$	3.63408	0.120935
$904$	−1.17490	−0.0390767
$905$	0	0
$906$	−4.90051	−0.162809
$907$	−27.5215	−0.913837	−0.456919	−	0.889508i	$-0.651047\pi$
$907$	−27.5215	−0.913837	−0.456919	+	0.889508i	$0.651047\pi$
$908$	−24.8167	−0.823570
$909$	26.5713	0.881315
$910$	0	0
$911$	50.4110	1.67019	0.835096	−	0.550104i	$-0.185412\pi$
$911$	50.4110	1.67019	0.835096	+	0.550104i	$0.185412\pi$
$912$	3.43692	0.113808
$913$	73.2126	2.42298
$914$	−31.7035	−1.04866
$915$	0	0
$916$	−9.95037	−0.328770
$917$	16.4158	0.542099
$918$	12.8290	0.423420
$919$	12.6543	0.417427	0.208714	−	0.977977i	$-0.433072\pi$
$919$	12.6543	0.417427	0.208714	+	0.977977i	$0.433072\pi$
$920$	0	0
$921$	−6.49047	−0.213868
$922$	−2.25606	−0.0742992
$923$	−47.0825	−1.54974
$924$	3.14174	0.103356
$925$	0	0
$926$	−23.2415	−0.763763
$927$	7.77881	0.255489
$928$	−7.06793	−0.232016
$929$	−3.03961	−0.0997265	−0.0498633	−	0.998756i	$-0.515879\pi$
$929$	−3.03961	−0.0997265	−0.0498633	+	0.998756i	$0.515879\pi$
$930$	0	0
$931$	−20.4895	−0.671517
$932$	11.8817	0.389198
$933$	−9.19772	−0.301120
$934$	5.61565	0.183750
$935$	0	0
$936$	46.8688	1.53196
$937$	0.0480749	0.00157054	0.000785268	−	1.00000i	$-0.499750\pi$
$937$	0.0480749	0.00157054	0.000785268		1.00000i	$0.499750\pi$
$938$	4.97465	0.162428
$939$	−16.4941	−0.538263
$940$	0	0
$941$	−1.25393	−0.0408769	−0.0204384	−	0.999791i	$-0.506506\pi$
$941$	−1.25393	−0.0408769	−0.0204384	+	0.999791i	$0.506506\pi$
$942$	10.3656	0.337731
$943$	−5.43999	−0.177150
$944$	−4.22086	−0.137377
$945$	0	0
$946$	−28.2856	−0.919646
$947$	44.5985	1.44926	0.724628	−	0.689140i	$-0.242011\pi$
$947$	44.5985	1.44926	0.724628	+	0.689140i	$0.242011\pi$
$948$	6.70483	0.217763
$949$	−3.62403	−0.117641
$950$	0	0
$951$	−10.0097	−0.324587
$952$	−9.84737	−0.319155
$953$	−41.8227	−1.35477	−0.677385	−	0.735629i	$-0.736887\pi$
$953$	−41.8227	−1.35477	−0.677385	+	0.735629i	$0.736887\pi$
$954$	−26.8584	−0.869571
$955$	0	0
$956$	−1.67793	−0.0542682
$957$	5.46469	0.176648
$958$	−22.2976	−0.720404
$959$	−19.4102	−0.626788
$960$	0	0
$961$	32.9518	1.06296
$962$	54.0958	1.74412
$963$	13.2625	0.427377
$964$	17.2586	0.555861
$965$	0	0
$966$	−2.14722	−0.0690857
$967$	44.4986	1.43098	0.715490	−	0.698623i	$-0.246204\pi$
$967$	44.4986	1.43098	0.715490	+	0.698623i	$0.246204\pi$
$968$	−46.3860	−1.49090
$969$	−7.52607	−0.241772
$970$	0	0
$971$	3.66499	0.117615	0.0588076	−	0.998269i	$-0.481270\pi$
$971$	3.66499	0.117615	0.0588076	+	0.998269i	$0.481270\pi$
$972$	13.0667	0.419116
$973$	3.63068	0.116394
$974$	−28.1389	−0.901629
$975$	0	0
$976$	3.36802	0.107808
$977$	15.7554	0.504060	0.252030	−	0.967719i	$-0.418902\pi$
$977$	15.7554	0.504060	0.252030	+	0.967719i	$0.418902\pi$
$978$	7.35133	0.235070
$979$	−32.7381	−1.04631
$980$	0	0
$981$	16.4768	0.526063
$982$	1.90400	0.0607591
$983$	26.9019	0.858036	0.429018	−	0.903296i	$-0.358860\pi$
$983$	26.9019	0.858036	0.429018	+	0.903296i	$0.358860\pi$
$984$	−3.90363	−0.124443
$985$	0	0
$986$	−5.24174	−0.166931
$987$	3.33967	0.106303
$988$	−18.4018	−0.585438
$989$	−15.2497	−0.484914
$990$	0	0
$991$	14.0680	0.446885	0.223442	−	0.974717i	$-0.428271\pi$
$991$	14.0680	0.446885	0.223442	+	0.974717i	$0.428271\pi$
$992$	−36.4081	−1.15596
$993$	16.7897	0.532806
$994$	−8.27915	−0.262599
$995$	0	0
$996$	8.66788	0.274652
$997$	0.618644	0.0195926	0.00979632	−	0.999952i	$-0.496882\pi$
$997$	0.618644	0.0195926	0.00979632	+	0.999952i	$0.496882\pi$
$998$	30.3426	0.960479
$999$	31.9443	1.01067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.a.g.1.5	yes	8
3.2	odd	2		5625.2.a.s.1.4		8
4.3	odd	2		10000.2.a.be.1.6		8
5.2	odd	4		625.2.b.d.624.11		16
5.3	odd	4		625.2.b.d.624.6		16
5.4	even	2		625.2.a.e.1.4	✓	8
15.14	odd	2		5625.2.a.be.1.5		8
20.19	odd	2		10000.2.a.bn.1.3		8
25.2	odd	20		625.2.e.j.124.6		32
25.3	odd	20		625.2.e.k.249.3		32
25.4	even	10		625.2.d.p.376.3		16
25.6	even	5		625.2.d.n.251.2		16
25.8	odd	20		625.2.e.k.374.6		32
25.9	even	10		625.2.d.q.126.2		16
25.11	even	5		625.2.d.m.501.3		16
25.12	odd	20		625.2.e.j.499.3		32
25.13	odd	20		625.2.e.j.499.6		32
25.14	even	10		625.2.d.q.501.2		16
25.16	even	5		625.2.d.m.126.3		16
25.17	odd	20		625.2.e.k.374.3		32
25.19	even	10		625.2.d.p.251.3		16
25.21	even	5		625.2.d.n.376.2		16
25.22	odd	20		625.2.e.k.249.6		32
25.23	odd	20		625.2.e.j.124.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.4	✓	8	5.4	even	2
625.2.a.g.1.5	yes	8	1.1	even	1	trivial
625.2.b.d.624.6		16	5.3	odd	4
625.2.b.d.624.11		16	5.2	odd	4
625.2.d.m.126.3		16	25.16	even	5
625.2.d.m.501.3		16	25.11	even	5
625.2.d.n.251.2		16	25.6	even	5
625.2.d.n.376.2		16	25.21	even	5
625.2.d.p.251.3		16	25.19	even	10
625.2.d.p.376.3		16	25.4	even	10
625.2.d.q.126.2		16	25.9	even	10
625.2.d.q.501.2		16	25.14	even	10
625.2.e.j.124.3		32	25.23	odd	20
625.2.e.j.124.6		32	25.2	odd	20
625.2.e.j.499.3		32	25.12	odd	20
625.2.e.j.499.6		32	25.13	odd	20
625.2.e.k.249.3		32	25.3	odd	20
625.2.e.k.249.6		32	25.22	odd	20
625.2.e.k.374.3		32	25.17	odd	20
625.2.e.k.374.6		32	25.8	odd	20
5625.2.a.s.1.4		8	3.2	odd	2
5625.2.a.be.1.5		8	15.14	odd	2
10000.2.a.be.1.6		8	4.3	odd	2
10000.2.a.bn.1.3		8	20.19	odd	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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.a (trivial)

\(f(q)\)	\(=\)	\(q+1.05737 q^{2} -0.687404 q^{3} -0.881958 q^{4} -0.726843 q^{6} +1.01199 q^{7} -3.04731 q^{8} -2.52748 q^{9} +O(q^{10})\)	\(q+1.05737 q^{2} -0.687404 q^{3} -0.881958 q^{4} -0.726843 q^{6} +1.01199 q^{7} -3.04731 q^{8} -2.52748 q^{9} +5.12074 q^{11} +0.606261 q^{12} +6.08528 q^{13} +1.07006 q^{14} -1.45823 q^{16} +3.19320 q^{17} -2.67249 q^{18} +3.42871 q^{19} -0.695649 q^{21} +5.41454 q^{22} +2.91916 q^{23} +2.09473 q^{24} +6.43442 q^{26} +3.79961 q^{27} -0.892537 q^{28} -1.55246 q^{29} -7.99699 q^{31} +4.55272 q^{32} -3.52001 q^{33} +3.37640 q^{34} +2.22913 q^{36} +8.40726 q^{37} +3.62544 q^{38} -4.18304 q^{39} -1.86355 q^{41} -0.735561 q^{42} -5.22402 q^{43} -4.51628 q^{44} +3.08665 q^{46} -4.80081 q^{47} +1.00239 q^{48} -5.97587 q^{49} -2.19501 q^{51} -5.36696 q^{52} +10.0499 q^{53} +4.01761 q^{54} -3.08386 q^{56} -2.35691 q^{57} -1.64153 q^{58} +2.89450 q^{59} -2.30966 q^{61} -8.45582 q^{62} -2.55779 q^{63} +7.73040 q^{64} -3.72197 q^{66} +4.64895 q^{67} -2.81626 q^{68} -2.00664 q^{69} -7.73711 q^{71} +7.70201 q^{72} -0.595540 q^{73} +8.88962 q^{74} -3.02398 q^{76} +5.18216 q^{77} -4.42304 q^{78} +11.0593 q^{79} +4.97057 q^{81} -1.97047 q^{82} +14.2973 q^{83} +0.613533 q^{84} -5.52374 q^{86} +1.06717 q^{87} -15.6045 q^{88} -6.39323 q^{89} +6.15827 q^{91} -2.57458 q^{92} +5.49716 q^{93} -5.07625 q^{94} -3.12956 q^{96} -14.0833 q^{97} -6.31873 q^{98} -12.9425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} + 5 q^{3} + 11 q^{4} - 4 q^{6} + 10 q^{7} + 15 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q + 5 * q^2 + 5 * q^3 + 11 * q^4 - 4 * q^6 + 10 * q^7 + 15 * q^8 + 9 * q^9	\( 8 q + 5 q^{2} + 5 q^{3} + 11 q^{4} - 4 q^{6} + 10 q^{7} + 15 q^{8} + 9 q^{9} + q^{11} + 10 q^{12} + 10 q^{13} - 8 q^{14} + 13 q^{16} + 15 q^{17} - 5 q^{18} - 10 q^{19} - 14 q^{21} - 5 q^{22} + 30 q^{23} + 5 q^{24} + 11 q^{26} + 20 q^{27} - 5 q^{28} + 10 q^{29} - 9 q^{31} + 30 q^{32} + 5 q^{33} + 7 q^{34} + 3 q^{36} - 10 q^{37} + 20 q^{38} + 8 q^{39} - 4 q^{41} - 35 q^{42} - 18 q^{44} - 9 q^{46} + 30 q^{47} + 5 q^{48} - 4 q^{49} - 14 q^{51} + 5 q^{52} + 10 q^{53} - 20 q^{54} - 10 q^{57} - 30 q^{58} - 5 q^{59} + 6 q^{61} + 10 q^{62} - 9 q^{64} - 18 q^{66} + 10 q^{67} + 40 q^{68} + 3 q^{69} - 9 q^{71} - 15 q^{72} - 18 q^{74} - 10 q^{76} + 5 q^{77} - 30 q^{78} - 20 q^{79} + 8 q^{81} - 45 q^{82} + 40 q^{83} - 28 q^{84} - 24 q^{86} + 40 q^{87} - 40 q^{88} - 5 q^{89} + 6 q^{91} + 15 q^{92} - 40 q^{93} + 47 q^{94} + 71 q^{96} - 30 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 + 5 * q^3 + 11 * q^4 - 4 * q^6 + 10 * q^7 + 15 * q^8 + 9 * q^9 + q^11 + 10 * q^12 + 10 * q^13 - 8 * q^14 + 13 * q^16 + 15 * q^17 - 5 * q^18 - 10 * q^19 - 14 * q^21 - 5 * q^22 + 30 * q^23 + 5 * q^24 + 11 * q^26 + 20 * q^27 - 5 * q^28 + 10 * q^29 - 9 * q^31 + 30 * q^32 + 5 * q^33 + 7 * q^34 + 3 * q^36 - 10 * q^37 + 20 * q^38 + 8 * q^39 - 4 * q^41 - 35 * q^42 - 18 * q^44 - 9 * q^46 + 30 * q^47 + 5 * q^48 - 4 * q^49 - 14 * q^51 + 5 * q^52 + 10 * q^53 - 20 * q^54 - 10 * q^57 - 30 * q^58 - 5 * q^59 + 6 * q^61 + 10 * q^62 - 9 * q^64 - 18 * q^66 + 10 * q^67 + 40 * q^68 + 3 * q^69 - 9 * q^71 - 15 * q^72 - 18 * q^74 - 10 * q^76 + 5 * q^77 - 30 * q^78 - 20 * q^79 + 8 * q^81 - 45 * q^82 + 40 * q^83 - 28 * q^84 - 24 * q^86 + 40 * q^87 - 40 * q^88 - 5 * q^89 + 6 * q^91 + 15 * q^92 - 40 * q^93 + 47 * q^94 + 71 * q^96 - 30 * q^98 - 22 * q^99

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