LMFDB - Embedded newform 975.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(1,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("975.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 3 $ x^3 - x^2 - 5*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.51414$ of defining polynomial
Character	$\chi$	$=$	975.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.51414 q^{2} +1.00000 q^{3} +4.32088 q^{4} +2.51414 q^{6} -0.514137 q^{7} +5.83502 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.51414 q^{2} +1.00000 q^{3} +4.32088 q^{4} +2.51414 q^{6} -0.514137 q^{7} +5.83502 q^{8} +1.00000 q^{9} -0.806748 q^{11} +4.32088 q^{12} +1.00000 q^{13} -1.29261 q^{14} +6.02827 q^{16} -2.02827 q^{17} +2.51414 q^{18} +0.292611 q^{19} -0.514137 q^{21} -2.02827 q^{22} +8.34916 q^{23} +5.83502 q^{24} +2.51414 q^{26} +1.00000 q^{27} -2.22153 q^{28} -9.64177 q^{29} +6.22153 q^{31} +3.48586 q^{32} -0.806748 q^{33} -5.09936 q^{34} +4.32088 q^{36} -6.34916 q^{37} +0.735663 q^{38} +1.00000 q^{39} -1.70739 q^{41} -1.29261 q^{42} -7.96265 q^{43} -3.48586 q^{44} +20.9909 q^{46} -10.7694 q^{47} +6.02827 q^{48} -6.73566 q^{49} -2.02827 q^{51} +4.32088 q^{52} +4.70739 q^{53} +2.51414 q^{54} -3.00000 q^{56} +0.292611 q^{57} -24.2407 q^{58} +4.12763 q^{59} -2.61350 q^{61} +15.6418 q^{62} -0.514137 q^{63} -3.29261 q^{64} -2.02827 q^{66} +13.5051 q^{67} -8.76394 q^{68} +8.34916 q^{69} -7.70739 q^{71} +5.83502 q^{72} +11.3209 q^{73} -15.9627 q^{74} +1.26434 q^{76} +0.414779 q^{77} +2.51414 q^{78} -4.73566 q^{79} +1.00000 q^{81} -4.29261 q^{82} -6.57068 q^{83} -2.22153 q^{84} -20.0192 q^{86} -9.64177 q^{87} -4.70739 q^{88} -0.971726 q^{89} -0.514137 q^{91} +36.0757 q^{92} +6.22153 q^{93} -27.0757 q^{94} +3.48586 q^{96} +9.61350 q^{97} -16.9344 q^{98} -0.806748 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 5 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 5 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 5 q^{7} + 3 q^{8} + 3 q^{9} - q^{11} + 5 q^{12} + 3 q^{13} - 9 q^{14} + 5 q^{16} + 7 q^{17} + q^{18} + 6 q^{19} + 5 q^{21} + 7 q^{22} + 4 q^{23} + 3 q^{24} + q^{26} + 3 q^{27} + 5 q^{28} - 13 q^{29} + 7 q^{31} + 17 q^{32} - q^{33} - 19 q^{34} + 5 q^{36} + 2 q^{37} - 16 q^{38} + 3 q^{39} - 9 q^{42} - 17 q^{44} + 26 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} + 7 q^{51} + 5 q^{52} + 9 q^{53} + q^{54} - 9 q^{56} + 6 q^{57} - 11 q^{58} + 3 q^{59} - 5 q^{61} + 31 q^{62} + 5 q^{63} - 15 q^{64} + 7 q^{66} - 3 q^{67} + 5 q^{68} + 4 q^{69} - 18 q^{71} + 3 q^{72} + 26 q^{73} - 24 q^{74} + 22 q^{76} - 9 q^{77} + q^{78} + 4 q^{79} + 3 q^{81} - 18 q^{82} + 13 q^{83} + 5 q^{84} - 10 q^{86} - 13 q^{87} - 9 q^{88} - 16 q^{89} + 5 q^{91} + 32 q^{92} + 7 q^{93} - 5 q^{94} + 17 q^{96} + 26 q^{97} - 40 q^{98} - q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 5 * q^7 + 3 * q^8 + 3 * q^9 - q^11 + 5 * q^12 + 3 * q^13 - 9 * q^14 + 5 * q^16 + 7 * q^17 + q^18 + 6 * q^19 + 5 * q^21 + 7 * q^22 + 4 * q^23 + 3 * q^24 + q^26 + 3 * q^27 + 5 * q^28 - 13 * q^29 + 7 * q^31 + 17 * q^32 - q^33 - 19 * q^34 + 5 * q^36 + 2 * q^37 - 16 * q^38 + 3 * q^39 - 9 * q^42 - 17 * q^44 + 26 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 + 7 * q^51 + 5 * q^52 + 9 * q^53 + q^54 - 9 * q^56 + 6 * q^57 - 11 * q^58 + 3 * q^59 - 5 * q^61 + 31 * q^62 + 5 * q^63 - 15 * q^64 + 7 * q^66 - 3 * q^67 + 5 * q^68 + 4 * q^69 - 18 * q^71 + 3 * q^72 + 26 * q^73 - 24 * q^74 + 22 * q^76 - 9 * q^77 + q^78 + 4 * q^79 + 3 * q^81 - 18 * q^82 + 13 * q^83 + 5 * q^84 - 10 * q^86 - 13 * q^87 - 9 * q^88 - 16 * q^89 + 5 * q^91 + 32 * q^92 + 7 * q^93 - 5 * q^94 + 17 * q^96 + 26 * q^97 - 40 * q^98 - 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 $

$2$	2.51414	1.77776	0.888882	−	0.458137i	$-0.151483\pi$
$2$	2.51414	1.77776	0.888882	+	0.458137i	$0.151483\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.32088	2.16044
$5$	0	0
$5$	0	0
$6$	2.51414	1.02639
$7$	−0.514137	−0.194325	−0.0971627	−	0.995269i	$-0.530977\pi$
$7$	−0.514137	−0.194325	−0.0971627	+	0.995269i	$0.530977\pi$
$8$	5.83502	2.06299
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.806748	−0.243244	−0.121622	−	0.992577i	$-0.538809\pi$
$11$	−0.806748	−0.243244	−0.121622	+	0.992577i	$0.538809\pi$
$12$	4.32088	1.24733
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.29261	−0.345465
$15$	0	0
$16$	6.02827	1.50707
$17$	−2.02827	−0.491929	−0.245964	−	0.969279i	$-0.579105\pi$
$17$	−2.02827	−0.491929	−0.245964	+	0.969279i	$0.579105\pi$
$18$	2.51414	0.592588
$19$	0.292611	0.0671295	0.0335647	−	0.999437i	$-0.489314\pi$
$19$	0.292611	0.0671295	0.0335647	+	0.999437i	$0.489314\pi$
$20$	0	0
$21$	−0.514137	−0.112194
$22$	−2.02827	−0.432429
$23$	8.34916	1.74092	0.870460	−	0.492239i	$-0.163821\pi$
$23$	8.34916	1.74092	0.870460	+	0.492239i	$0.163821\pi$
$24$	5.83502	1.19107
$25$	0	0
$26$	2.51414	0.493063
$27$	1.00000	0.192450
$28$	−2.22153	−0.419829
$29$	−9.64177	−1.79043	−0.895216	−	0.445633i	$-0.852979\pi$
$29$	−9.64177	−1.79043	−0.895216	+	0.445633i	$0.852979\pi$
$30$	0	0
$31$	6.22153	1.11742	0.558710	−	0.829363i	$-0.311297\pi$
$31$	6.22153	1.11742	0.558710	+	0.829363i	$0.311297\pi$
$32$	3.48586	0.616219
$33$	−0.806748	−0.140437
$34$	−5.09936	−0.874533
$35$	0	0
$36$	4.32088	0.720147
$37$	−6.34916	−1.04380	−0.521898	−	0.853008i	$-0.674776\pi$
$37$	−6.34916	−1.04380	−0.521898	+	0.853008i	$0.674776\pi$
$38$	0.735663	0.119340
$39$	1.00000	0.160128
$40$	0	0
$41$	−1.70739	−0.266649	−0.133325	−	0.991072i	$-0.542565\pi$
$41$	−1.70739	−0.266649	−0.133325	+	0.991072i	$0.542565\pi$
$42$	−1.29261	−0.199454
$43$	−7.96265	−1.21429	−0.607147	−	0.794590i	$-0.707686\pi$
$43$	−7.96265	−1.21429	−0.607147	+	0.794590i	$0.707686\pi$
$44$	−3.48586	−0.525514
$45$	0	0
$46$	20.9909	3.09494
$47$	−10.7694	−1.57088	−0.785439	−	0.618939i	$-0.787563\pi$
$47$	−10.7694	−1.57088	−0.785439	+	0.618939i	$0.787563\pi$
$48$	6.02827	0.870106
$49$	−6.73566	−0.962238
$50$	0	0
$51$	−2.02827	−0.284015
$52$	4.32088	0.599199
$53$	4.70739	0.646610	0.323305	−	0.946295i	$-0.395206\pi$
$53$	4.70739	0.646610	0.323305	+	0.946295i	$0.395206\pi$
$54$	2.51414	0.342131
$55$	0	0
$56$	−3.00000	−0.400892
$57$	0.292611	0.0387572
$58$	−24.2407	−3.18296
$59$	4.12763	0.537372	0.268686	−	0.963228i	$-0.413411\pi$
$59$	4.12763	0.537372	0.268686	+	0.963228i	$0.413411\pi$
$60$	0	0
$61$	−2.61350	−0.334624	−0.167312	−	0.985904i	$-0.553509\pi$
$61$	−2.61350	−0.334624	−0.167312	+	0.985904i	$0.553509\pi$
$62$	15.6418	1.98651
$63$	−0.514137	−0.0647752
$64$	−3.29261	−0.411576
$65$	0	0
$66$	−2.02827	−0.249663
$67$	13.5051	1.64991	0.824953	−	0.565201i	$-0.191201\pi$
$67$	13.5051	1.64991	0.824953	+	0.565201i	$0.191201\pi$
$68$	−8.76394	−1.06278
$69$	8.34916	1.00512
$70$	0	0
$71$	−7.70739	−0.914699	−0.457349	−	0.889287i	$-0.651201\pi$
$71$	−7.70739	−0.914699	−0.457349	+	0.889287i	$0.651201\pi$
$72$	5.83502	0.687664
$73$	11.3209	1.32501	0.662505	−	0.749058i	$-0.269493\pi$
$73$	11.3209	1.32501	0.662505	+	0.749058i	$0.269493\pi$
$74$	−15.9627	−1.85562
$75$	0	0
$76$	1.26434	0.145029
$77$	0.414779	0.0472684
$78$	2.51414	0.284670
$79$	−4.73566	−0.532804	−0.266402	−	0.963862i	$-0.585835\pi$
$79$	−4.73566	−0.532804	−0.266402	+	0.963862i	$0.585835\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−4.29261	−0.474040
$83$	−6.57068	−0.721226	−0.360613	−	0.932715i	$-0.617433\pi$
$83$	−6.57068	−0.721226	−0.360613	+	0.932715i	$0.617433\pi$
$84$	−2.22153	−0.242388
$85$	0	0
$86$	−20.0192	−2.15873
$87$	−9.64177	−1.03371
$88$	−4.70739	−0.501809
$89$	−0.971726	−0.103003	−0.0515014	−	0.998673i	$-0.516401\pi$
$89$	−0.971726	−0.103003	−0.0515014	+	0.998673i	$0.516401\pi$
$90$	0	0
$91$	−0.514137	−0.0538962
$92$	36.0757	3.76116
$93$	6.22153	0.645142
$94$	−27.0757	−2.79265
$95$	0	0
$96$	3.48586	0.355774
$97$	9.61350	0.976103	0.488051	−	0.872815i	$-0.337708\pi$
$97$	9.61350	0.976103	0.488051	+	0.872815i	$0.337708\pi$
$98$	−16.9344	−1.71063
$99$	−0.806748	−0.0810812
$100$	0	0
$101$	0.962653	0.0957876	0.0478938	−	0.998852i	$-0.484749\pi$
$101$	0.962653	0.0957876	0.0478938	+	0.998852i	$0.484749\pi$
$102$	−5.09936	−0.504912
$103$	16.0192	1.57842	0.789209	−	0.614124i	$-0.210491\pi$
$103$	16.0192	1.57842	0.789209	+	0.614124i	$0.210491\pi$
$104$	5.83502	0.572171
$105$	0	0
$106$	11.8350	1.14952
$107$	−15.0848	−1.45830	−0.729152	−	0.684351i	$-0.760085\pi$
$107$	−15.0848	−1.45830	−0.729152	+	0.684351i	$0.760085\pi$
$108$	4.32088	0.415777
$109$	−4.73566	−0.453594	−0.226797	−	0.973942i	$-0.572825\pi$
$109$	−4.73566	−0.453594	−0.226797	+	0.973942i	$0.572825\pi$
$110$	0	0
$111$	−6.34916	−0.602635
$112$	−3.09936	−0.292862
$113$	18.3118	1.72263	0.861315	−	0.508071i	$-0.169641\pi$
$113$	18.3118	1.72263	0.861315	+	0.508071i	$0.169641\pi$
$114$	0.735663	0.0689012
$115$	0	0
$116$	−41.6610	−3.86812
$117$	1.00000	0.0924500
$118$	10.3774	0.955320
$119$	1.04281	0.0955943
$120$	0	0
$121$	−10.3492	−0.940833
$122$	−6.57068	−0.594882
$123$	−1.70739	−0.153950
$124$	26.8825	2.41412
$125$	0	0
$126$	−1.29261	−0.115155
$127$	−2.29261	−0.203436	−0.101718	−	0.994813i	$-0.532434\pi$
$127$	−2.29261	−0.203436	−0.101718	+	0.994813i	$0.532434\pi$
$128$	−15.2498	−1.34790
$129$	−7.96265	−0.701073
$130$	0	0
$131$	−11.1222	−0.971748	−0.485874	−	0.874029i	$-0.661499\pi$
$131$	−11.1222	−0.971748	−0.485874	+	0.874029i	$0.661499\pi$
$132$	−3.48586	−0.303405
$133$	−0.150442	−0.0130450
$134$	33.9536	2.93314
$135$	0	0
$136$	−11.8350	−1.01484
$137$	17.6700	1.50965	0.754827	−	0.655924i	$-0.227721\pi$
$137$	17.6700	1.50965	0.754827	+	0.655924i	$0.227721\pi$
$138$	20.9909	1.78687
$139$	−7.86876	−0.667419	−0.333710	−	0.942676i	$-0.608301\pi$
$139$	−7.86876	−0.667419	−0.333710	+	0.942676i	$0.608301\pi$
$140$	0	0
$141$	−10.7694	−0.906947
$142$	−19.3774	−1.62612
$143$	−0.806748	−0.0674636
$144$	6.02827	0.502356
$145$	0	0
$146$	28.4623	2.35555
$147$	−6.73566	−0.555548
$148$	−27.4340	−2.25506
$149$	14.8970	1.22041	0.610206	−	0.792243i	$-0.291087\pi$
$149$	14.8970	1.22041	0.610206	+	0.792243i	$0.291087\pi$
$150$	0	0
$151$	−9.59896	−0.781152	−0.390576	−	0.920571i	$-0.627724\pi$
$151$	−9.59896	−0.781152	−0.390576	+	0.920571i	$0.627724\pi$
$152$	1.70739	0.138488
$153$	−2.02827	−0.163976
$154$	1.04281	0.0840321
$155$	0	0
$156$	4.32088	0.345948
$157$	1.67912	0.134008	0.0670040	−	0.997753i	$-0.478656\pi$
$157$	1.67912	0.134008	0.0670040	+	0.997753i	$0.478656\pi$
$158$	−11.9061	−0.947199
$159$	4.70739	0.373320
$160$	0	0
$161$	−4.29261	−0.338305
$162$	2.51414	0.197529
$163$	10.3492	0.810609	0.405304	−	0.914182i	$-0.367166\pi$
$163$	10.3492	0.810609	0.405304	+	0.914182i	$0.367166\pi$
$164$	−7.37743	−0.576081
$165$	0	0
$166$	−16.5196	−1.28217
$167$	23.2462	1.79884	0.899422	−	0.437081i	$-0.143988\pi$
$167$	23.2462	1.79884	0.899422	+	0.437081i	$0.143988\pi$
$168$	−3.00000	−0.231455
$169$	1.00000	0.0769231
$170$	0	0
$171$	0.292611	0.0223765
$172$	−34.4057	−2.62341
$173$	9.73566	0.740189	0.370094	−	0.928994i	$-0.379325\pi$
$173$	9.73566	0.740189	0.370094	+	0.928994i	$0.379325\pi$
$174$	−24.2407	−1.83768
$175$	0	0
$176$	−4.86330	−0.366585
$177$	4.12763	0.310252
$178$	−2.44305	−0.183115
$179$	−6.54787	−0.489411	−0.244706	−	0.969597i	$-0.578691\pi$
$179$	−6.54787	−0.489411	−0.244706	+	0.969597i	$0.578691\pi$
$180$	0	0
$181$	21.2745	1.58132	0.790659	−	0.612256i	$-0.209738\pi$
$181$	21.2745	1.58132	0.790659	+	0.612256i	$0.209738\pi$
$182$	−1.29261	−0.0958147
$183$	−2.61350	−0.193195
$184$	48.7175	3.59150
$185$	0	0
$186$	15.6418	1.14691
$187$	1.63631	0.119658
$188$	−46.5333	−3.39379
$189$	−0.514137	−0.0373980
$190$	0	0
$191$	−1.30168	−0.0941865	−0.0470932	−	0.998890i	$-0.514996\pi$
$191$	−1.30168	−0.0941865	−0.0470932	+	0.998890i	$0.514996\pi$
$192$	−3.29261	−0.237624
$193$	5.50867	0.396523	0.198261	−	0.980149i	$-0.436470\pi$
$193$	5.50867	0.396523	0.198261	+	0.980149i	$0.436470\pi$
$194$	24.1696	1.73528
$195$	0	0
$196$	−29.1040	−2.07886
$197$	−17.1222	−1.21990	−0.609952	−	0.792438i	$-0.708811\pi$
$197$	−17.1222	−1.21990	−0.609952	+	0.792438i	$0.708811\pi$
$198$	−2.02827	−0.144143
$199$	24.0565	1.70532	0.852662	−	0.522463i	$-0.174987\pi$
$199$	24.0565	1.70532	0.852662	+	0.522463i	$0.174987\pi$
$200$	0	0
$201$	13.5051	0.952574
$202$	2.42024	0.170288
$203$	4.95719	0.347926
$204$	−8.76394	−0.613598
$205$	0	0
$206$	40.2745	2.80605
$207$	8.34916	0.580307
$208$	6.02827	0.417986
$209$	−0.236063	−0.0163288
$210$	0	0
$211$	−10.2179	−0.703430	−0.351715	−	0.936107i	$-0.614401\pi$
$211$	−10.2179	−0.703430	−0.351715	+	0.936107i	$0.614401\pi$
$212$	20.3401	1.39696
$213$	−7.70739	−0.528102
$214$	−37.9253	−2.59252
$215$	0	0
$216$	5.83502	0.397023
$217$	−3.19872	−0.217143
$218$	−11.9061	−0.806383
$219$	11.3209	0.764994
$220$	0	0
$221$	−2.02827	−0.136436
$222$	−15.9627	−1.07134
$223$	−2.93438	−0.196501	−0.0982503	−	0.995162i	$-0.531325\pi$
$223$	−2.93438	−0.196501	−0.0982503	+	0.995162i	$0.531325\pi$
$224$	−1.79221	−0.119747
$225$	0	0
$226$	46.0384	3.06243
$227$	−20.0903	−1.33344	−0.666720	−	0.745309i	$-0.732302\pi$
$227$	−20.0903	−1.33344	−0.666720	+	0.745309i	$0.732302\pi$
$228$	1.26434	0.0837327
$229$	−4.45398	−0.294327	−0.147164	−	0.989112i	$-0.547014\pi$
$229$	−4.45398	−0.294327	−0.147164	+	0.989112i	$0.547014\pi$
$230$	0	0
$231$	0.414779	0.0272904
$232$	−56.2599	−3.69365
$233$	−5.02827	−0.329413	−0.164707	−	0.986343i	$-0.552668\pi$
$233$	−5.02827	−0.329413	−0.164707	+	0.986343i	$0.552668\pi$
$234$	2.51414	0.164354
$235$	0	0
$236$	17.8350	1.16096
$237$	−4.73566	−0.307614
$238$	2.62177	0.169944
$239$	−4.95719	−0.320654	−0.160327	−	0.987064i	$-0.551255\pi$
$239$	−4.95719	−0.320654	−0.160327	+	0.987064i	$0.551255\pi$
$240$	0	0
$241$	13.4340	0.865359	0.432679	−	0.901548i	$-0.357568\pi$
$241$	13.4340	0.865359	0.432679	+	0.901548i	$0.357568\pi$
$242$	−26.0192	−1.67258
$243$	1.00000	0.0641500
$244$	−11.2926	−0.722935
$245$	0	0
$246$	−4.29261	−0.273687
$247$	0.292611	0.0186184
$248$	36.3027	2.30523
$249$	−6.57068	−0.416400
$250$	0	0
$251$	4.60442	0.290629	0.145314	−	0.989386i	$-0.453581\pi$
$251$	4.60442	0.290629	0.145314	+	0.989386i	$0.453581\pi$
$252$	−2.22153	−0.139943
$253$	−6.73566	−0.423468
$254$	−5.76394	−0.361662
$255$	0	0
$256$	−31.7549	−1.98468
$257$	−10.0475	−0.626744	−0.313372	−	0.949630i	$-0.601459\pi$
$257$	−10.0475	−0.626744	−0.313372	+	0.949630i	$0.601459\pi$
$258$	−20.0192	−1.24634
$259$	3.26434	0.202836
$260$	0	0
$261$	−9.64177	−0.596811
$262$	−27.9627	−1.72754
$263$	−16.7922	−1.03545	−0.517726	−	0.855546i	$-0.673221\pi$
$263$	−16.7922	−1.03545	−0.517726	+	0.855546i	$0.673221\pi$
$264$	−4.70739	−0.289720
$265$	0	0
$266$	−0.378232	−0.0231909
$267$	−0.971726	−0.0594687
$268$	58.3538	3.56453
$269$	−22.6135	−1.37877	−0.689385	−	0.724396i	$-0.742119\pi$
$269$	−22.6135	−1.37877	−0.689385	+	0.724396i	$0.742119\pi$
$270$	0	0
$271$	25.2690	1.53498	0.767491	−	0.641059i	$-0.221505\pi$
$271$	25.2690	1.53498	0.767491	+	0.641059i	$0.221505\pi$
$272$	−12.2270	−0.741370
$273$	−0.514137	−0.0311170
$274$	44.4249	2.68381
$275$	0	0
$276$	36.0757	2.17150
$277$	31.0101	1.86322	0.931609	−	0.363462i	$-0.118405\pi$
$277$	31.0101	1.86322	0.931609	+	0.363462i	$0.118405\pi$
$278$	−19.7831	−1.18651
$279$	6.22153	0.372473
$280$	0	0
$281$	−3.86876	−0.230791	−0.115395	−	0.993320i	$-0.536814\pi$
$281$	−3.86876	−0.230791	−0.115395	+	0.993320i	$0.536814\pi$
$282$	−27.0757	−1.61234
$283$	0.0565477	0.00336141	0.00168071	−	0.999999i	$-0.499465\pi$
$283$	0.0565477	0.00336141	0.00168071	+	0.999999i	$0.499465\pi$
$284$	−33.3027	−1.97615
$285$	0	0
$286$	−2.02827	−0.119934
$287$	0.877832	0.0518168
$288$	3.48586	0.205406
$289$	−12.8861	−0.758006
$290$	0	0
$291$	9.61350	0.563553
$292$	48.9162	2.86261
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−16.9344	−0.987633
$295$	0	0
$296$	−37.0475	−2.15334
$297$	−0.806748	−0.0468122
$298$	37.4532	2.16960
$299$	8.34916	0.482844
$300$	0	0
$301$	4.09389	0.235968
$302$	−24.1331	−1.38870
$303$	0.962653	0.0553030
$304$	1.76394	0.101169
$305$	0	0
$306$	−5.09936	−0.291511
$307$	32.7175	1.86729	0.933644	−	0.358203i	$-0.116610\pi$
$307$	32.7175	1.86729	0.933644	+	0.358203i	$0.116610\pi$
$308$	1.79221	0.102121
$309$	16.0192	0.911301
$310$	0	0
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	5.83502	0.330343
$313$	19.2070	1.08564	0.542822	−	0.839848i	$-0.317356\pi$
$313$	19.2070	1.08564	0.542822	+	0.839848i	$0.317356\pi$
$314$	4.22153	0.238235
$315$	0	0
$316$	−20.4623	−1.15109
$317$	−9.96265	−0.559558	−0.279779	−	0.960064i	$-0.590261\pi$
$317$	−9.96265	−0.559558	−0.279779	+	0.960064i	$0.590261\pi$
$318$	11.8350	0.663675
$319$	7.77847	0.435511
$320$	0	0
$321$	−15.0848	−0.841953
$322$	−10.7922	−0.601426
$323$	−0.593495	−0.0330229
$324$	4.32088	0.240049
$325$	0	0
$326$	26.0192	1.44107
$327$	−4.73566	−0.261883
$328$	−9.96265	−0.550096
$329$	5.53695	0.305262
$330$	0	0
$331$	−0.367304	−0.0201888	−0.0100944	−	0.999949i	$-0.503213\pi$
$331$	−0.367304	−0.0201888	−0.0100944	+	0.999949i	$0.503213\pi$
$332$	−28.3912	−1.55817
$333$	−6.34916	−0.347932
$334$	58.4441	3.19792
$335$	0	0
$336$	−3.09936	−0.169084
$337$	31.3492	1.70770	0.853849	−	0.520521i	$-0.174262\pi$
$337$	31.3492	1.70770	0.853849	+	0.520521i	$0.174262\pi$
$338$	2.51414	0.136751
$339$	18.3118	0.994561
$340$	0	0
$341$	−5.01920	−0.271805
$342$	0.735663	0.0397801
$343$	7.06201	0.381313
$344$	−46.4623	−2.50508
$345$	0	0
$346$	24.4768	1.31588
$347$	−6.18779	−0.332178	−0.166089	−	0.986111i	$-0.553114\pi$
$347$	−6.18779	−0.332178	−0.166089	+	0.986111i	$0.553114\pi$
$348$	−41.6610	−2.23326
$349$	−11.7074	−0.626682	−0.313341	−	0.949641i	$-0.601448\pi$
$349$	−11.7074	−0.626682	−0.313341	+	0.949641i	$0.601448\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−2.81221	−0.149891
$353$	15.6508	0.833010	0.416505	−	0.909133i	$-0.363255\pi$
$353$	15.6508	0.833010	0.416505	+	0.909133i	$0.363255\pi$
$354$	10.3774	0.551554
$355$	0	0
$356$	−4.19872	−0.222532
$357$	1.04281	0.0551914
$358$	−16.4623	−0.870057
$359$	30.2407	1.59604	0.798022	−	0.602628i	$-0.205880\pi$
$359$	30.2407	1.59604	0.798022	+	0.602628i	$0.205880\pi$
$360$	0	0
$361$	−18.9144	−0.995494
$362$	53.4869	2.81121
$363$	−10.3492	−0.543190
$364$	−2.22153	−0.116440
$365$	0	0
$366$	−6.57068	−0.343455
$367$	−10.8296	−0.565298	−0.282649	−	0.959223i	$-0.591213\pi$
$367$	−10.8296	−0.565298	−0.282649	+	0.959223i	$0.591213\pi$
$368$	50.3310	2.62369
$369$	−1.70739	−0.0888831
$370$	0	0
$371$	−2.42024	−0.125653
$372$	26.8825	1.39379
$373$	−27.9909	−1.44932	−0.724658	−	0.689109i	$-0.758002\pi$
$373$	−27.9909	−1.44932	−0.724658	+	0.689109i	$0.758002\pi$
$374$	4.11389	0.212724
$375$	0	0
$376$	−62.8397	−3.24071
$377$	−9.64177	−0.496576
$378$	−1.29261	−0.0664847
$379$	25.6929	1.31975	0.659877	−	0.751374i	$-0.270609\pi$
$379$	25.6929	1.31975	0.659877	+	0.751374i	$0.270609\pi$
$380$	0	0
$381$	−2.29261	−0.117454
$382$	−3.27261	−0.167441
$383$	−26.5369	−1.35597	−0.677987	−	0.735074i	$-0.737148\pi$
$383$	−26.5369	−1.35597	−0.677987	+	0.735074i	$0.737148\pi$
$384$	−15.2498	−0.778213
$385$	0	0
$386$	13.8496	0.704924
$387$	−7.96265	−0.404764
$388$	41.5388	2.10881
$389$	−3.74474	−0.189866	−0.0949328	−	0.995484i	$-0.530264\pi$
$389$	−3.74474	−0.189866	−0.0949328	+	0.995484i	$0.530264\pi$
$390$	0	0
$391$	−16.9344	−0.856408
$392$	−39.3027	−1.98509
$393$	−11.1222	−0.561039
$394$	−43.0475	−2.16870
$395$	0	0
$396$	−3.48586	−0.175171
$397$	29.9144	1.50136	0.750680	−	0.660666i	$-0.229726\pi$
$397$	29.9144	1.50136	0.750680	+	0.660666i	$0.229726\pi$
$398$	60.4815	3.03166
$399$	−0.150442	−0.00753152
$400$	0	0
$401$	19.7074	0.984140	0.492070	−	0.870556i	$-0.336240\pi$
$401$	19.7074	0.984140	0.492070	+	0.870556i	$0.336240\pi$
$402$	33.9536	1.69345
$403$	6.22153	0.309916
$404$	4.15951	0.206944
$405$	0	0
$406$	12.4631	0.618531
$407$	5.12217	0.253896
$408$	−11.8350	−0.585921
$409$	12.9344	0.639564	0.319782	−	0.947491i	$-0.396390\pi$
$409$	12.9344	0.639564	0.319782	+	0.947491i	$0.396390\pi$
$410$	0	0
$411$	17.6700	0.871599
$412$	69.2171	3.41008
$413$	−2.12217	−0.104425
$414$	20.9909	1.03165
$415$	0	0
$416$	3.48586	0.170908
$417$	−7.86876	−0.385335
$418$	−0.593495	−0.0290288
$419$	14.8488	0.725409	0.362705	−	0.931904i	$-0.381853\pi$
$419$	14.8488	0.725409	0.362705	+	0.931904i	$0.381853\pi$
$420$	0	0
$421$	23.4148	1.14117	0.570583	−	0.821240i	$-0.306717\pi$
$421$	23.4148	1.14117	0.570583	+	0.821240i	$0.306717\pi$
$422$	−25.6892	−1.25053
$423$	−10.7694	−0.523626
$424$	27.4677	1.33395
$425$	0	0
$426$	−19.3774	−0.938840
$427$	1.34369	0.0650259
$428$	−65.1798	−3.15058
$429$	−0.806748	−0.0389501
$430$	0	0
$431$	−28.9162	−1.39285	−0.696423	−	0.717632i	$-0.745226\pi$
$431$	−28.9162	−1.39285	−0.696423	+	0.717632i	$0.745226\pi$
$432$	6.02827	0.290035
$433$	2.78394	0.133788	0.0668938	−	0.997760i	$-0.478691\pi$
$433$	2.78394	0.133788	0.0668938	+	0.997760i	$0.478691\pi$
$434$	−8.04201	−0.386029
$435$	0	0
$436$	−20.4623	−0.979964
$437$	2.44305	0.116867
$438$	28.4623	1.35998
$439$	−4.42385	−0.211139	−0.105569	−	0.994412i	$-0.533667\pi$
$439$	−4.42385	−0.211139	−0.105569	+	0.994412i	$0.533667\pi$
$440$	0	0
$441$	−6.73566	−0.320746
$442$	−5.09936	−0.242552
$443$	18.0939	0.859667	0.429833	−	0.902908i	$-0.358572\pi$
$443$	18.0939	0.859667	0.429833	+	0.902908i	$0.358572\pi$
$444$	−27.4340	−1.30196
$445$	0	0
$446$	−7.37743	−0.349332
$447$	14.8970	0.704605
$448$	1.69285	0.0799798
$449$	−26.7549	−1.26264	−0.631320	−	0.775522i	$-0.717487\pi$
$449$	−26.7549	−1.26264	−0.631320	+	0.775522i	$0.717487\pi$
$450$	0	0
$451$	1.37743	0.0648607
$452$	79.1232	3.72164
$453$	−9.59896	−0.450998
$454$	−50.5097	−2.37054
$455$	0	0
$456$	1.70739	0.0799558
$457$	4.53695	0.212229	0.106115	−	0.994354i	$-0.466159\pi$
$457$	4.53695	0.212229	0.106115	+	0.994354i	$0.466159\pi$
$458$	−11.1979	−0.523244
$459$	−2.02827	−0.0946717
$460$	0	0
$461$	14.5852	0.679301	0.339651	−	0.940552i	$-0.389691\pi$
$461$	14.5852	0.679301	0.339651	+	0.940552i	$0.389691\pi$
$462$	1.04281	0.0485159
$463$	−36.0903	−1.67726	−0.838629	−	0.544703i	$-0.816642\pi$
$463$	−36.0903	−1.67726	−0.838629	+	0.544703i	$0.816642\pi$
$464$	−58.1232	−2.69830
$465$	0	0
$466$	−12.6418	−0.585619
$467$	−5.48225	−0.253688	−0.126844	−	0.991923i	$-0.540485\pi$
$467$	−5.48225	−0.253688	−0.126844	+	0.991923i	$0.540485\pi$
$468$	4.32088	0.199733
$469$	−6.94345	−0.320619
$470$	0	0
$471$	1.67912	0.0773696
$472$	24.0848	1.10859
$473$	6.42385	0.295369
$474$	−11.9061	−0.546866
$475$	0	0
$476$	4.50586	0.206526
$477$	4.70739	0.215537
$478$	−12.4631	−0.570047
$479$	−36.7886	−1.68091	−0.840457	−	0.541878i	$-0.817713\pi$
$479$	−36.7886	−1.68091	−0.840457	+	0.541878i	$0.817713\pi$
$480$	0	0
$481$	−6.34916	−0.289497
$482$	33.7749	1.53840
$483$	−4.29261	−0.195321
$484$	−44.7175	−2.03261
$485$	0	0
$486$	2.51414	0.114044
$487$	−14.2034	−0.643617	−0.321808	−	0.946805i	$-0.604291\pi$
$487$	−14.2034	−0.643617	−0.321808	+	0.946805i	$0.604291\pi$
$488$	−15.2498	−0.690326
$489$	10.3492	0.468005
$490$	0	0
$491$	−1.30168	−0.0587441	−0.0293721	−	0.999569i	$-0.509351\pi$
$491$	−1.30168	−0.0587441	−0.0293721	+	0.999569i	$0.509351\pi$
$492$	−7.37743	−0.332600
$493$	19.5561	0.880765
$494$	0.735663	0.0330991
$495$	0	0
$496$	37.5051	1.68403
$497$	3.96265	0.177749
$498$	−16.5196	−0.740261
$499$	17.3437	0.776410	0.388205	−	0.921573i	$-0.373095\pi$
$499$	17.3437	0.776410	0.388205	+	0.921573i	$0.373095\pi$
$500$	0	0
$501$	23.2462	1.03856
$502$	11.5761	0.516669
$503$	−19.7074	−0.878709	−0.439355	−	0.898314i	$-0.644793\pi$
$503$	−19.7074	−0.878709	−0.439355	+	0.898314i	$0.644793\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	−16.9344	−0.752825
$507$	1.00000	0.0444116
$508$	−9.90611	−0.439512
$509$	−15.9627	−0.707532	−0.353766	−	0.935334i	$-0.615099\pi$
$509$	−15.9627	−0.707532	−0.353766	+	0.935334i	$0.615099\pi$
$510$	0	0
$511$	−5.82048	−0.257483
$512$	−49.3365	−2.18038
$513$	0.292611	0.0129191
$514$	−25.2607	−1.11420
$515$	0	0
$516$	−34.4057	−1.51463
$517$	8.68819	0.382106
$518$	8.20699	0.360594
$519$	9.73566	0.427348
$520$	0	0
$521$	21.2270	0.929971	0.464986	−	0.885318i	$-0.346059\pi$
$521$	21.2270	0.929971	0.464986	+	0.885318i	$0.346059\pi$
$522$	−24.2407	−1.06099
$523$	−25.5388	−1.11673	−0.558367	−	0.829594i	$-0.688572\pi$
$523$	−25.5388	−1.11673	−0.558367	+	0.829594i	$0.688572\pi$
$524$	−48.0576	−2.09941
$525$	0	0
$526$	−42.2179	−1.84079
$527$	−12.6190	−0.549690
$528$	−4.86330	−0.211648
$529$	46.7084	2.03080
$530$	0	0
$531$	4.12763	0.179124
$532$	−0.650042	−0.0281829
$533$	−1.70739	−0.0739552
$534$	−2.44305	−0.105721
$535$	0	0
$536$	78.8023	3.40374
$537$	−6.54787	−0.282562
$538$	−56.8534	−2.45113
$539$	5.43398	0.234058
$540$	0	0
$541$	21.3774	0.919088	0.459544	−	0.888155i	$-0.348013\pi$
$541$	21.3774	0.919088	0.459544	+	0.888155i	$0.348013\pi$
$542$	63.5297	2.72884
$543$	21.2745	0.912975
$544$	−7.07028	−0.303136
$545$	0	0
$546$	−1.29261	−0.0553186
$547$	−39.4340	−1.68608	−0.843038	−	0.537855i	$-0.819235\pi$
$547$	−39.4340	−1.68608	−0.843038	+	0.537855i	$0.819235\pi$
$548$	76.3502	3.26152
$549$	−2.61350	−0.111541
$550$	0	0
$551$	−2.82128	−0.120191
$552$	48.7175	2.07356
$553$	2.43478	0.103537
$554$	77.9637	3.31236
$555$	0	0
$556$	−34.0000	−1.44192
$557$	15.3027	0.648398	0.324199	−	0.945989i	$-0.394905\pi$
$557$	15.3027	0.648398	0.324199	+	0.945989i	$0.394905\pi$
$558$	15.6418	0.662169
$559$	−7.96265	−0.336784
$560$	0	0
$561$	1.63631	0.0690849
$562$	−9.72659	−0.410291
$563$	−4.27447	−0.180147	−0.0900736	−	0.995935i	$-0.528710\pi$
$563$	−4.27447	−0.180147	−0.0900736	+	0.995935i	$0.528710\pi$
$564$	−46.5333	−1.95941
$565$	0	0
$566$	0.142169	0.00597580
$567$	−0.514137	−0.0215917
$568$	−44.9728	−1.88702
$569$	11.6610	0.488853	0.244427	−	0.969668i	$-0.421400\pi$
$569$	11.6610	0.488853	0.244427	+	0.969668i	$0.421400\pi$
$570$	0	0
$571$	33.0475	1.38299	0.691497	−	0.722379i	$-0.256952\pi$
$571$	33.0475	1.38299	0.691497	+	0.722379i	$0.256952\pi$
$572$	−3.48586	−0.145751
$573$	−1.30168	−0.0543786
$574$	2.20699	0.0921180
$575$	0	0
$576$	−3.29261	−0.137192
$577$	44.9536	1.87144	0.935721	−	0.352741i	$-0.114750\pi$
$577$	44.9536	1.87144	0.935721	+	0.352741i	$0.114750\pi$
$578$	−32.3974	−1.34756
$579$	5.50867	0.228933
$580$	0	0
$581$	3.37823	0.140153
$582$	24.1696	1.00186
$583$	−3.79767	−0.157284
$584$	66.0576	2.73348
$585$	0	0
$586$	15.0848	0.623148
$587$	14.5899	0.602189	0.301095	−	0.953594i	$-0.402648\pi$
$587$	14.5899	0.602189	0.301095	+	0.953594i	$0.402648\pi$
$588$	−29.1040	−1.20023
$589$	1.82048	0.0750118
$590$	0	0
$591$	−17.1222	−0.704312
$592$	−38.2745	−1.57307
$593$	−37.2654	−1.53031	−0.765153	−	0.643848i	$-0.777337\pi$
$593$	−37.2654	−1.53031	−0.765153	+	0.643848i	$0.777337\pi$
$594$	−2.02827	−0.0832211
$595$	0	0
$596$	64.3684	2.63663
$597$	24.0565	0.984569
$598$	20.9909	0.858383
$599$	−34.2745	−1.40042	−0.700208	−	0.713939i	$-0.746910\pi$
$599$	−34.2745	−1.40042	−0.700208	+	0.713939i	$0.746910\pi$
$600$	0	0
$601$	7.67912	0.313238	0.156619	−	0.987659i	$-0.449941\pi$
$601$	7.67912	0.313238	0.156619	+	0.987659i	$0.449941\pi$
$602$	10.2926	0.419495
$603$	13.5051	0.549969
$604$	−41.4760	−1.68763
$605$	0	0
$606$	2.42024	0.0983156
$607$	−8.84049	−0.358824	−0.179412	−	0.983774i	$-0.557420\pi$
$607$	−8.84049	−0.358824	−0.179412	+	0.983774i	$0.557420\pi$
$608$	1.02000	0.0413665
$609$	4.95719	0.200875
$610$	0	0
$611$	−10.7694	−0.435683
$612$	−8.76394	−0.354261
$613$	−8.05655	−0.325401	−0.162700	−	0.986676i	$-0.552020\pi$
$613$	−8.05655	−0.325401	−0.162700	+	0.986676i	$0.552020\pi$
$614$	82.2563	3.31959
$615$	0	0
$616$	2.42024	0.0975144
$617$	−13.1414	−0.529052	−0.264526	−	0.964379i	$-0.585215\pi$
$617$	−13.1414	−0.529052	−0.264526	+	0.964379i	$0.585215\pi$
$618$	40.2745	1.62008
$619$	17.7749	0.714432	0.357216	−	0.934022i	$-0.383726\pi$
$619$	17.7749	0.714432	0.357216	+	0.934022i	$0.383726\pi$
$620$	0	0
$621$	8.34916	0.335040
$622$	−45.2545	−1.81454
$623$	0.499600	0.0200161
$624$	6.02827	0.241324
$625$	0	0
$626$	48.2890	1.93002
$627$	−0.236063	−0.00942745
$628$	7.25526	0.289517
$629$	12.8778	0.513473
$630$	0	0
$631$	−9.26434	−0.368807	−0.184404	−	0.982851i	$-0.559035\pi$
$631$	−9.26434	−0.368807	−0.184404	+	0.982851i	$0.559035\pi$
$632$	−27.6327	−1.09917
$633$	−10.2179	−0.406126
$634$	−25.0475	−0.994762
$635$	0	0
$636$	20.3401	0.806537
$637$	−6.73566	−0.266877
$638$	19.5561	0.774235
$639$	−7.70739	−0.304900
$640$	0	0
$641$	−35.4249	−1.39920	−0.699600	−	0.714535i	$-0.746638\pi$
$641$	−35.4249	−1.39920	−0.699600	+	0.714535i	$0.746638\pi$
$642$	−37.9253	−1.49679
$643$	6.27447	0.247441	0.123720	−	0.992317i	$-0.460517\pi$
$643$	6.27447	0.247441	0.123720	+	0.992317i	$0.460517\pi$
$644$	−18.5479	−0.730889
$645$	0	0
$646$	−1.49213	−0.0587069
$647$	−27.9144	−1.09743	−0.548714	−	0.836010i	$-0.684882\pi$
$647$	−27.9144	−1.09743	−0.548714	+	0.836010i	$0.684882\pi$
$648$	5.83502	0.229221
$649$	−3.32996	−0.130712
$650$	0	0
$651$	−3.19872	−0.125368
$652$	44.7175	1.75127
$653$	4.98907	0.195237	0.0976187	−	0.995224i	$-0.468877\pi$
$653$	4.98907	0.195237	0.0976187	+	0.995224i	$0.468877\pi$
$654$	−11.9061	−0.465566
$655$	0	0
$656$	−10.2926	−0.401859
$657$	11.3209	0.441670
$658$	13.9206	0.542683
$659$	8.47318	0.330068	0.165034	−	0.986288i	$-0.447227\pi$
$659$	8.47318	0.330068	0.165034	+	0.986288i	$0.447227\pi$
$660$	0	0
$661$	−24.9728	−0.971329	−0.485664	−	0.874145i	$-0.661422\pi$
$661$	−24.9728	−0.971329	−0.485664	+	0.874145i	$0.661422\pi$
$662$	−0.923452	−0.0358910
$663$	−2.02827	−0.0787716
$664$	−38.3401	−1.48788
$665$	0	0
$666$	−15.9627	−0.618540
$667$	−80.5007	−3.11700
$668$	100.444	3.88630
$669$	−2.93438	−0.113450
$670$	0	0
$671$	2.10843	0.0813951
$672$	−1.79221	−0.0691360
$673$	0.519601	0.0200291	0.0100146	−	0.999950i	$-0.496812\pi$
$673$	0.519601	0.0200291	0.0100146	+	0.999950i	$0.496812\pi$
$674$	78.8161	3.03588
$675$	0	0
$676$	4.32088	0.166188
$677$	42.1515	1.62001	0.810007	−	0.586420i	$-0.199463\pi$
$677$	42.1515	1.62001	0.810007	+	0.586420i	$0.199463\pi$
$678$	46.0384	1.76809
$679$	−4.94265	−0.189682
$680$	0	0
$681$	−20.0903	−0.769861
$682$	−12.6190	−0.483205
$683$	16.2034	0.620005	0.310003	−	0.950736i	$-0.399670\pi$
$683$	16.2034	0.620005	0.310003	+	0.950736i	$0.399670\pi$
$684$	1.26434	0.0483431
$685$	0	0
$686$	17.7549	0.677884
$687$	−4.45398	−0.169930
$688$	−48.0011	−1.83002
$689$	4.70739	0.179337
$690$	0	0
$691$	41.6555	1.58465	0.792325	−	0.610099i	$-0.208870\pi$
$691$	41.6555	1.58465	0.792325	+	0.610099i	$0.208870\pi$
$692$	42.0667	1.59914
$693$	0.414779	0.0157561
$694$	−15.5569	−0.590534
$695$	0	0
$696$	−56.2599	−2.13253
$697$	3.46305	0.131172
$698$	−29.4340	−1.11409
$699$	−5.02827	−0.190187
$700$	0	0
$701$	35.3009	1.33330	0.666648	−	0.745373i	$-0.267728\pi$
$701$	35.3009	1.33330	0.666648	+	0.745373i	$0.267728\pi$
$702$	2.51414	0.0948900
$703$	−1.85783	−0.0700694
$704$	2.65631	0.100113
$705$	0	0
$706$	39.3484	1.48090
$707$	−0.494936	−0.0186140
$708$	17.8350	0.670281
$709$	−40.3876	−1.51679	−0.758393	−	0.651797i	$-0.774015\pi$
$709$	−40.3876	−1.51679	−0.758393	+	0.651797i	$0.774015\pi$
$710$	0	0
$711$	−4.73566	−0.177601
$712$	−5.67004	−0.212494
$713$	51.9445	1.94534
$714$	2.62177	0.0981172
$715$	0	0
$716$	−28.2926	−1.05734
$717$	−4.95719	−0.185130
$718$	76.0293	2.83739
$719$	43.5471	1.62403	0.812016	−	0.583635i	$-0.198370\pi$
$719$	43.5471	1.62403	0.812016	+	0.583635i	$0.198370\pi$
$720$	0	0
$721$	−8.23606	−0.306727
$722$	−47.5533	−1.76975
$723$	13.4340	0.499615
$724$	91.9245	3.41635
$725$	0	0
$726$	−26.0192	−0.965663
$727$	19.2462	0.713802	0.356901	−	0.934142i	$-0.383833\pi$
$727$	19.2462	0.713802	0.356901	+	0.934142i	$0.383833\pi$
$728$	−3.00000	−0.111187
$729$	1.00000	0.0370370
$730$	0	0
$731$	16.1504	0.597346
$732$	−11.2926	−0.417387
$733$	−23.3017	−0.860667	−0.430334	−	0.902670i	$-0.641604\pi$
$733$	−23.3017	−0.860667	−0.430334	+	0.902670i	$0.641604\pi$
$734$	−27.2270	−1.00497
$735$	0	0
$736$	29.1040	1.07279
$737$	−10.8952	−0.401329
$738$	−4.29261	−0.158013
$739$	−29.4941	−1.08496	−0.542480	−	0.840069i	$-0.682514\pi$
$739$	−29.4941	−1.08496	−0.542480	+	0.840069i	$0.682514\pi$
$740$	0	0
$741$	0.292611	0.0107493
$742$	−6.08482	−0.223381
$743$	25.1642	0.923184	0.461592	−	0.887092i	$-0.347278\pi$
$743$	25.1642	0.923184	0.461592	+	0.887092i	$0.347278\pi$
$744$	36.3027	1.33092
$745$	0	0
$746$	−70.3730	−2.57654
$747$	−6.57068	−0.240409
$748$	7.07028	0.258515
$749$	7.75566	0.283386
$750$	0	0
$751$	−22.5935	−0.824448	−0.412224	−	0.911082i	$-0.635248\pi$
$751$	−22.5935	−0.824448	−0.412224	+	0.911082i	$0.635248\pi$
$752$	−64.9209	−2.36742
$753$	4.60442	0.167794
$754$	−24.2407	−0.882795
$755$	0	0
$756$	−2.22153	−0.0807961
$757$	−27.3009	−0.992268	−0.496134	−	0.868246i	$-0.665247\pi$
$757$	−27.3009	−0.992268	−0.496134	+	0.868246i	$0.665247\pi$
$758$	64.5953	2.34621
$759$	−6.73566	−0.244489
$760$	0	0
$761$	25.5652	0.926739	0.463369	−	0.886165i	$-0.346640\pi$
$761$	25.5652	0.926739	0.463369	+	0.886165i	$0.346640\pi$
$762$	−5.76394	−0.208805
$763$	2.43478	0.0881449
$764$	−5.62442	−0.203484
$765$	0	0
$766$	−66.7175	−2.41060
$767$	4.12763	0.149040
$768$	−31.7549	−1.14585
$769$	−24.2371	−0.874013	−0.437006	−	0.899458i	$-0.643961\pi$
$769$	−24.2371	−0.874013	−0.437006	+	0.899458i	$0.643961\pi$
$770$	0	0
$771$	−10.0475	−0.361851
$772$	23.8023	0.856665
$773$	4.84049	0.174100	0.0870501	−	0.996204i	$-0.472256\pi$
$773$	4.84049	0.174100	0.0870501	+	0.996204i	$0.472256\pi$
$774$	−20.0192	−0.719575
$775$	0	0
$776$	56.0950	2.01369
$777$	3.26434	0.117107
$778$	−9.41478	−0.337536
$779$	−0.499600	−0.0179000
$780$	0	0
$781$	6.21792	0.222495
$782$	−42.5753	−1.52249
$783$	−9.64177	−0.344569
$784$	−40.6044	−1.45016
$785$	0	0
$786$	−27.9627	−0.997395
$787$	34.2599	1.22123	0.610617	−	0.791926i	$-0.290921\pi$
$787$	34.2599	1.22123	0.610617	+	0.791926i	$0.290921\pi$
$788$	−73.9829	−2.63553
$789$	−16.7922	−0.597819
$790$	0	0
$791$	−9.41478	−0.334751
$792$	−4.70739	−0.167270
$793$	−2.61350	−0.0928079
$794$	75.2088	2.66906
$795$	0	0
$796$	103.946	3.68425
$797$	−53.7367	−1.90345	−0.951726	−	0.306949i	$-0.900692\pi$
$797$	−53.7367	−1.90345	−0.951726	+	0.306949i	$0.900692\pi$
$798$	−0.378232	−0.0133893
$799$	21.8433	0.772760
$800$	0	0
$801$	−0.971726	−0.0343343
$802$	49.5471	1.74957
$803$	−9.13310	−0.322300
$804$	58.3538	2.05798
$805$	0	0
$806$	15.6418	0.550958
$807$	−22.6135	−0.796033
$808$	5.61710	0.197609
$809$	0.329957	0.0116007	0.00580034	−	0.999983i	$-0.498154\pi$
$809$	0.329957	0.0116007	0.00580034	+	0.999983i	$0.498154\pi$
$810$	0	0
$811$	7.28715	0.255886	0.127943	−	0.991782i	$-0.459162\pi$
$811$	7.28715	0.255886	0.127943	+	0.991782i	$0.459162\pi$
$812$	21.4194	0.751675
$813$	25.2690	0.886223
$814$	12.8778	0.451368
$815$	0	0
$816$	−12.2270	−0.428030
$817$	−2.32996	−0.0815149
$818$	32.5188	1.13699
$819$	−0.514137	−0.0179654
$820$	0	0
$821$	21.6508	0.755620	0.377810	−	0.925883i	$-0.376677\pi$
$821$	21.6508	0.755620	0.377810	+	0.925883i	$0.376677\pi$
$822$	44.4249	1.54950
$823$	28.0493	0.977738	0.488869	−	0.872357i	$-0.337410\pi$
$823$	28.0493	0.977738	0.488869	+	0.872357i	$0.337410\pi$
$824$	93.4724	3.25626
$825$	0	0
$826$	−5.33542	−0.185643
$827$	−19.3245	−0.671978	−0.335989	−	0.941866i	$-0.609071\pi$
$827$	−19.3245	−0.671978	−0.335989	+	0.941866i	$0.609071\pi$
$828$	36.0757	1.25372
$829$	−57.4249	−1.99445	−0.997225	−	0.0744502i	$-0.976280\pi$
$829$	−57.4249	−1.99445	−0.997225	+	0.0744502i	$0.976280\pi$
$830$	0	0
$831$	31.0101	1.07573
$832$	−3.29261	−0.114151
$833$	13.6618	0.473352
$834$	−19.7831	−0.685034
$835$	0	0
$836$	−1.02000	−0.0352775
$837$	6.22153	0.215047
$838$	37.3318	1.28961
$839$	−38.3492	−1.32396	−0.661980	−	0.749522i	$-0.730284\pi$
$839$	−38.3492	−1.32396	−0.661980	+	0.749522i	$0.730284\pi$
$840$	0	0
$841$	63.9637	2.20565
$842$	58.8680	2.02872
$843$	−3.86876	−0.133247
$844$	−44.1504	−1.51972
$845$	0	0
$846$	−27.0757	−0.930883
$847$	5.32088	0.182828
$848$	28.3774	0.974485
$849$	0.0565477	0.00194071
$850$	0	0
$851$	−53.0101	−1.81716
$852$	−33.3027	−1.14093
$853$	−32.8861	−1.12600	−0.562999	−	0.826457i	$-0.690353\pi$
$853$	−32.8861	−1.12600	−0.562999	+	0.826457i	$0.690353\pi$
$854$	3.37823	0.115601
$855$	0	0
$856$	−88.0203	−3.00847
$857$	44.9427	1.53521	0.767606	−	0.640922i	$-0.221448\pi$
$857$	44.9427	1.53521	0.767606	+	0.640922i	$0.221448\pi$
$858$	−2.02827	−0.0692441
$859$	0.622568	0.0212417	0.0106209	−	0.999944i	$-0.496619\pi$
$859$	0.622568	0.0212417	0.0106209	+	0.999944i	$0.496619\pi$
$860$	0	0
$861$	0.877832	0.0299164
$862$	−72.6994	−2.47615
$863$	−23.9590	−0.815575	−0.407788	−	0.913077i	$-0.633700\pi$
$863$	−23.9590	−0.815575	−0.407788	+	0.913077i	$0.633700\pi$
$864$	3.48586	0.118591
$865$	0	0
$866$	6.99920	0.237843
$867$	−12.8861	−0.437635
$868$	−13.8213	−0.469125
$869$	3.82048	0.129601
$870$	0	0
$871$	13.5051	0.457602
$872$	−27.6327	−0.935761
$873$	9.61350	0.325368
$874$	6.14217	0.207762
$875$	0	0
$876$	48.9162	1.65273
$877$	−45.6338	−1.54094	−0.770471	−	0.637475i	$-0.779979\pi$
$877$	−45.6338	−1.54094	−0.770471	+	0.637475i	$0.779979\pi$
$878$	−11.1222	−0.375355
$879$	6.00000	0.202375
$880$	0	0
$881$	28.6711	0.965954	0.482977	−	0.875633i	$-0.339555\pi$
$881$	28.6711	0.965954	0.482977	+	0.875633i	$0.339555\pi$
$882$	−16.9344	−0.570210
$883$	−43.7266	−1.47152	−0.735758	−	0.677244i	$-0.763174\pi$
$883$	−43.7266	−1.47152	−0.735758	+	0.677244i	$0.763174\pi$
$884$	−8.76394	−0.294763
$885$	0	0
$886$	45.4905	1.52828
$887$	9.13310	0.306659	0.153330	−	0.988175i	$-0.451000\pi$
$887$	9.13310	0.306659	0.153330	+	0.988175i	$0.451000\pi$
$888$	−37.0475	−1.24323
$889$	1.17872	0.0395329
$890$	0	0
$891$	−0.806748	−0.0270271
$892$	−12.6791	−0.424528
$893$	−3.15124	−0.105452
$894$	37.4532	1.25262
$895$	0	0
$896$	7.84049	0.261932
$897$	8.34916	0.278770
$898$	−67.2654	−2.24468
$899$	−59.9865	−2.00066
$900$	0	0
$901$	−9.54787	−0.318086
$902$	3.46305	0.115307
$903$	4.09389	0.136236
$904$	106.850	3.55377
$905$	0	0
$906$	−24.1331	−0.801768
$907$	−16.6599	−0.553183	−0.276592	−	0.960988i	$-0.589205\pi$
$907$	−16.6599	−0.553183	−0.276592	+	0.960988i	$0.589205\pi$
$908$	−86.8078	−2.88082
$909$	0.962653	0.0319292
$910$	0	0
$911$	4.93438	0.163483	0.0817416	−	0.996654i	$-0.473952\pi$
$911$	4.93438	0.163483	0.0817416	+	0.996654i	$0.473952\pi$
$912$	1.76394	0.0584098
$913$	5.30088	0.175434
$914$	11.4065	0.377294
$915$	0	0
$916$	−19.2451	−0.635877
$917$	5.71832	0.188835
$918$	−5.09936	−0.168304
$919$	14.4996	0.478298	0.239149	−	0.970983i	$-0.423132\pi$
$919$	14.4996	0.478298	0.239149	+	0.970983i	$0.423132\pi$
$920$	0	0
$921$	32.7175	1.07808
$922$	36.6692	1.20764
$923$	−7.70739	−0.253692
$924$	1.79221	0.0589594
$925$	0	0
$926$	−90.7359	−2.98177
$927$	16.0192	0.526140
$928$	−33.6099	−1.10330
$929$	−7.09575	−0.232804	−0.116402	−	0.993202i	$-0.537136\pi$
$929$	−7.09575	−0.232804	−0.116402	+	0.993202i	$0.537136\pi$
$930$	0	0
$931$	−1.97093	−0.0645945
$932$	−21.7266	−0.711678
$933$	−18.0000	−0.589294
$934$	−13.7831	−0.450998
$935$	0	0
$936$	5.83502	0.190724
$937$	1.25526	0.0410077	0.0205038	−	0.999790i	$-0.493473\pi$
$937$	1.25526	0.0410077	0.0205038	+	0.999790i	$0.493473\pi$
$938$	−17.4568	−0.569984
$939$	19.2070	0.626796
$940$	0	0
$941$	1.00186	0.0326596	0.0163298	−	0.999867i	$-0.494802\pi$
$941$	1.00186	0.0326596	0.0163298	+	0.999867i	$0.494802\pi$
$942$	4.22153	0.137545
$943$	−14.2553	−0.464215
$944$	24.8825	0.809856
$945$	0	0
$946$	16.1504	0.525096
$947$	−29.0055	−0.942551	−0.471275	−	0.881986i	$-0.656206\pi$
$947$	−29.0055	−0.942551	−0.471275	+	0.881986i	$0.656206\pi$
$948$	−20.4623	−0.664583
$949$	11.3209	0.367491
$950$	0	0
$951$	−9.96265	−0.323061
$952$	6.08482	0.197210
$953$	−38.8698	−1.25912	−0.629558	−	0.776953i	$-0.716764\pi$
$953$	−38.8698	−1.25912	−0.629558	+	0.776953i	$0.716764\pi$
$954$	11.8350	0.383173
$955$	0	0
$956$	−21.4194	−0.692754
$957$	7.77847	0.251442
$958$	−92.4916	−2.98827
$959$	−9.08482	−0.293364
$960$	0	0
$961$	7.70739	0.248625
$962$	−15.9627	−0.514657
$963$	−15.0848	−0.486102
$964$	58.0467	1.86956
$965$	0	0
$966$	−10.7922	−0.347234
$967$	−38.6755	−1.24372	−0.621860	−	0.783128i	$-0.713623\pi$
$967$	−38.6755	−1.24372	−0.621860	+	0.783128i	$0.713623\pi$
$968$	−60.3876	−1.94093
$969$	−0.593495	−0.0190658
$970$	0	0
$971$	−47.0101	−1.50863	−0.754313	−	0.656514i	$-0.772030\pi$
$971$	−47.0101	−1.50863	−0.754313	+	0.656514i	$0.772030\pi$
$972$	4.32088	0.138592
$973$	4.04562	0.129697
$974$	−35.7092	−1.14420
$975$	0	0
$976$	−15.7549	−0.504301
$977$	−8.58522	−0.274666	−0.137333	−	0.990525i	$-0.543853\pi$
$977$	−8.58522	−0.274666	−0.137333	+	0.990525i	$0.543853\pi$
$978$	26.0192	0.832002
$979$	0.783938	0.0250548
$980$	0	0
$981$	−4.73566	−0.151198
$982$	−3.27261	−0.104433
$983$	−6.49494	−0.207156	−0.103578	−	0.994621i	$-0.533029\pi$
$983$	−6.49494	−0.207156	−0.103578	+	0.994621i	$0.533029\pi$
$984$	−9.96265	−0.317598
$985$	0	0
$986$	49.1668	1.56579
$987$	5.53695	0.176243
$988$	1.26434	0.0402239
$989$	−66.4815	−2.11399
$990$	0	0
$991$	−33.9336	−1.07794	−0.538968	−	0.842326i	$-0.681186\pi$
$991$	−33.9336	−1.07794	−0.538968	+	0.842326i	$0.681186\pi$
$992$	21.6874	0.688575
$993$	−0.367304	−0.0116560
$994$	9.96265	0.315996
$995$	0	0
$996$	−28.3912	−0.899609
$997$	−46.2545	−1.46489	−0.732447	−	0.680824i	$-0.761622\pi$
$997$	−46.2545	−1.46489	−0.732447	+	0.680824i	$0.761622\pi$
$998$	43.6044	1.38027
$999$	−6.34916	−0.200878

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.a.p.1.3	yes	3
3.2	odd	2		2925.2.a.bg.1.1		3
5.2	odd	4		975.2.c.j.274.6		6
5.3	odd	4		975.2.c.j.274.1		6
5.4	even	2		975.2.a.n.1.1	✓	3
15.2	even	4		2925.2.c.x.2224.1		6
15.8	even	4		2925.2.c.x.2224.6		6
15.14	odd	2		2925.2.a.bi.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.a.n.1.1	✓	3	5.4	even	2
975.2.a.p.1.3	yes	3	1.1	even	1	trivial
975.2.c.j.274.1		6	5.3	odd	4
975.2.c.j.274.6		6	5.2	odd	4
2925.2.a.bg.1.1		3	3.2	odd	2
2925.2.a.bi.1.3		3	15.14	odd	2
2925.2.c.x.2224.1		6	15.2	even	4
2925.2.c.x.2224.6		6	15.8	even	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.a (trivial)

\(f(q)\)	\(=\)	\(q+2.51414 q^{2} +1.00000 q^{3} +4.32088 q^{4} +2.51414 q^{6} -0.514137 q^{7} +5.83502 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.51414 q^{2} +1.00000 q^{3} +4.32088 q^{4} +2.51414 q^{6} -0.514137 q^{7} +5.83502 q^{8} +1.00000 q^{9} -0.806748 q^{11} +4.32088 q^{12} +1.00000 q^{13} -1.29261 q^{14} +6.02827 q^{16} -2.02827 q^{17} +2.51414 q^{18} +0.292611 q^{19} -0.514137 q^{21} -2.02827 q^{22} +8.34916 q^{23} +5.83502 q^{24} +2.51414 q^{26} +1.00000 q^{27} -2.22153 q^{28} -9.64177 q^{29} +6.22153 q^{31} +3.48586 q^{32} -0.806748 q^{33} -5.09936 q^{34} +4.32088 q^{36} -6.34916 q^{37} +0.735663 q^{38} +1.00000 q^{39} -1.70739 q^{41} -1.29261 q^{42} -7.96265 q^{43} -3.48586 q^{44} +20.9909 q^{46} -10.7694 q^{47} +6.02827 q^{48} -6.73566 q^{49} -2.02827 q^{51} +4.32088 q^{52} +4.70739 q^{53} +2.51414 q^{54} -3.00000 q^{56} +0.292611 q^{57} -24.2407 q^{58} +4.12763 q^{59} -2.61350 q^{61} +15.6418 q^{62} -0.514137 q^{63} -3.29261 q^{64} -2.02827 q^{66} +13.5051 q^{67} -8.76394 q^{68} +8.34916 q^{69} -7.70739 q^{71} +5.83502 q^{72} +11.3209 q^{73} -15.9627 q^{74} +1.26434 q^{76} +0.414779 q^{77} +2.51414 q^{78} -4.73566 q^{79} +1.00000 q^{81} -4.29261 q^{82} -6.57068 q^{83} -2.22153 q^{84} -20.0192 q^{86} -9.64177 q^{87} -4.70739 q^{88} -0.971726 q^{89} -0.514137 q^{91} +36.0757 q^{92} +6.22153 q^{93} -27.0757 q^{94} +3.48586 q^{96} +9.61350 q^{97} -16.9344 q^{98} -0.806748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 5 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 5 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 5 q^{7} + 3 q^{8} + 3 q^{9} - q^{11} + 5 q^{12} + 3 q^{13} - 9 q^{14} + 5 q^{16} + 7 q^{17} + q^{18} + 6 q^{19} + 5 q^{21} + 7 q^{22} + 4 q^{23} + 3 q^{24} + q^{26} + 3 q^{27} + 5 q^{28} - 13 q^{29} + 7 q^{31} + 17 q^{32} - q^{33} - 19 q^{34} + 5 q^{36} + 2 q^{37} - 16 q^{38} + 3 q^{39} - 9 q^{42} - 17 q^{44} + 26 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} + 7 q^{51} + 5 q^{52} + 9 q^{53} + q^{54} - 9 q^{56} + 6 q^{57} - 11 q^{58} + 3 q^{59} - 5 q^{61} + 31 q^{62} + 5 q^{63} - 15 q^{64} + 7 q^{66} - 3 q^{67} + 5 q^{68} + 4 q^{69} - 18 q^{71} + 3 q^{72} + 26 q^{73} - 24 q^{74} + 22 q^{76} - 9 q^{77} + q^{78} + 4 q^{79} + 3 q^{81} - 18 q^{82} + 13 q^{83} + 5 q^{84} - 10 q^{86} - 13 q^{87} - 9 q^{88} - 16 q^{89} + 5 q^{91} + 32 q^{92} + 7 q^{93} - 5 q^{94} + 17 q^{96} + 26 q^{97} - 40 q^{98} - q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 5 * q^7 + 3 * q^8 + 3 * q^9 - q^11 + 5 * q^12 + 3 * q^13 - 9 * q^14 + 5 * q^16 + 7 * q^17 + q^18 + 6 * q^19 + 5 * q^21 + 7 * q^22 + 4 * q^23 + 3 * q^24 + q^26 + 3 * q^27 + 5 * q^28 - 13 * q^29 + 7 * q^31 + 17 * q^32 - q^33 - 19 * q^34 + 5 * q^36 + 2 * q^37 - 16 * q^38 + 3 * q^39 - 9 * q^42 - 17 * q^44 + 26 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 + 7 * q^51 + 5 * q^52 + 9 * q^53 + q^54 - 9 * q^56 + 6 * q^57 - 11 * q^58 + 3 * q^59 - 5 * q^61 + 31 * q^62 + 5 * q^63 - 15 * q^64 + 7 * q^66 - 3 * q^67 + 5 * q^68 + 4 * q^69 - 18 * q^71 + 3 * q^72 + 26 * q^73 - 24 * q^74 + 22 * q^76 - 9 * q^77 + q^78 + 4 * q^79 + 3 * q^81 - 18 * q^82 + 13 * q^83 + 5 * q^84 - 10 * q^86 - 13 * q^87 - 9 * q^88 - 16 * q^89 + 5 * q^91 + 32 * q^92 + 7 * q^93 - 5 * q^94 + 17 * q^96 + 26 * q^97 - 40 * q^98 - q^99

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