LMFDB - Embedded newform 9.48.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,48,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 48, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 48);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 48 $
Character orbit:	$[\chi]$	$=$	9.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:	$125.916896390$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 832803191366x^{2} + 3710135215485780x + 13175318942671469337000 $ x^4 - x^3 - 832803191366x^2 + 3710135215485780x + 13175318942671469337000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{11}\cdot 5^{3}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-124721.$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.54692e6 q^{2} -1.38345e14 q^{4} -4.23962e16 q^{5} -3.90714e19 q^{7} -4.31719e20 q^{8} +O(q^{10})$	\(q+1.54692e6 q^{2} -1.38345e14 q^{4} -4.23962e16 q^{5} -3.90714e19 q^{7} -4.31719e20 q^{8} -6.55837e22 q^{10} -2.66558e24 q^{11} +2.26259e26 q^{13} -6.04405e25 q^{14} +1.88024e28 q^{16} -8.41583e28 q^{17} +3.16735e29 q^{19} +5.86528e30 q^{20} -4.12345e30 q^{22} -2.26985e31 q^{23} +1.08689e33 q^{25} +3.50006e32 q^{26} +5.40532e33 q^{28} +3.39685e34 q^{29} +1.81646e35 q^{31} +8.98449e34 q^{32} -1.30186e35 q^{34} +1.65648e36 q^{35} -7.13789e36 q^{37} +4.89965e35 q^{38} +1.83032e37 q^{40} +2.78383e37 q^{41} -4.92777e37 q^{43} +3.68769e38 q^{44} -3.51128e37 q^{46} -1.86825e39 q^{47} -3.71676e39 q^{49} +1.68134e39 q^{50} -3.13017e40 q^{52} +2.48904e40 q^{53} +1.13011e41 q^{55} +1.68679e40 q^{56} +5.25467e40 q^{58} -3.69239e40 q^{59} +3.52589e41 q^{61} +2.80993e41 q^{62} -2.50722e42 q^{64} -9.59253e42 q^{65} -1.26183e42 q^{67} +1.16428e43 q^{68} +2.56245e42 q^{70} +3.26023e43 q^{71} +3.59179e43 q^{73} -1.10418e43 q^{74} -4.38186e43 q^{76} +1.04148e44 q^{77} -5.82596e44 q^{79} -7.97151e44 q^{80} +4.30637e43 q^{82} +3.51619e44 q^{83} +3.56799e45 q^{85} -7.62288e43 q^{86} +1.15078e45 q^{88} +2.92401e45 q^{89} -8.84027e45 q^{91} +3.14021e45 q^{92} -2.89005e45 q^{94} -1.34284e46 q^{95} +2.17182e46 q^{97} -5.74955e45 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5785560 q^{2} + 404807499161152 q^{4} + 31\!\cdots\!00 q^{5}+ \cdots - 23\!\cdots\!20 q^{8}+O(q^{10}) $ 4 * q - 5785560 * q^2 + 404807499161152 * q^4 + 31114680242272200 * q^5 - 39169218725888423200 * q^7 - 2392716988073784337920 * q^8	$ 4 q - 5785560 q^{2} + 404807499161152 q^{4} + 31\!\cdots\!00 q^{5}+ \cdots + 29\!\cdots\!20 q^{98}+O(q^{100}) $ 4 * q - 5785560 * q^2 + 404807499161152 * q^4 + 31114680242272200 * q^5 - 39169218725888423200 * q^7 - 2392716988073784337920 * q^8 + 161126302562215963534800 * q^10 + 1902165515717740404742512 * q^11 + 126959149195199610466858520 * q^13 - 3491363489769461659480835904 * q^14 + 124527684040554167211817897984 * q^16 - 210426285758836687099688769480 * q^17 - 1059119811802437301721159140240 * q^19 + 15129514318106701401937782249600 * q^20 - 79668451994083088127806382590880 * q^22 - 137531418344493639994288859179680 * q^23 + 1009909900344396506188154274977500 * q^25 - 2282338781897562472343866220387088 * q^26 - 36222097928665071743339635065479680 * q^28 + 22743132490172744184500850941726760 * q^29 + 75786540814706434901630981303934848 * q^31 - 1184674767018086471839527432906178560 * q^32 - 1261659118578465318749852382715620816 * q^34 + 1313148822925052387484546800067979200 * q^35 - 11291457045120157869429951769632191560 * q^37 - 29667542464851305273548614410680536480 * q^38 + 70753686685508718175919216681780352000 * q^40 - 130658126291089294119301677048020391528 * q^41 - 445357287738427943170332944488133090800 * q^43 + 1525898906718917337200010663037616115456 * q^44 + 1226146172325422687186041586267533291968 * q^46 - 2031912465958423919194866366997063590720 * q^47 + 9153745744156628626499502447643951451172 * q^49 + 19226200465513908889722489088356697935000 * q^50 - 55272350705889116147839999778699925596800 * q^52 - 29171719896619533806321793123448457437560 * q^53 + 192172580604633896452606078657416872901600 * q^55 - 276101696826518177934513744689489393111040 * q^56 - 732323136683092912071778597620095648941680 * q^58 - 478242858216320686410790860443879577596880 * q^59 + 626683213833907852009669690320782900857688 * q^61 + 6870459615610782098804391369236375065946880 * q^62 + 5525430481808418303700543890989262651523072 * q^64 - 12996735432890074297558542478104126872331600 * q^65 + 18701411419127220668869505853739529194216880 * q^67 + 27469024204738931095482995064729717598496640 * q^68 - 97207317904230285933067401805385458355395200 * q^70 - 22196594617762006008028198712153461686540768 * q^71 + 104911201720506650033573412943840886878191080 * q^73 - 187734656069700274526204928907842421165646544 * q^74 + 351694386032713991264839561028061045130100480 * q^76 + 263490744376507692433815778071300370399209600 * q^77 - 1327995310109394234162785254414226288730352960 * q^79 + 948349663264469859337474495994045561022259200 * q^80 + 3821513842864797430908620724480935919685390320 * q^82 + 1439130627532364606968733068855111784504073360 * q^83 - 1001895286410663502447652611446390227458237200 * q^85 - 9578145533777866709022895861637903827077656928 * q^86 - 15478856320702836436797993507832298416714229760 * q^88 + 7960590522674945421108320896849737731421281880 * q^89 + 5325194479227227497182497798631911205603381568 * q^91 - 13058297350229360275908546071900174502239009280 * q^92 + 3475860200879106349192555645858186353201354624 * q^94 - 75421152415106939771624998522249518123547668000 * q^95 + 95066248961258904822565865801364599382905757320 * q^97 + 296344663186266398350742083591017164797938217320 * q^98

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 $

$2$	1.54692e6	0.130396	0.0651980	−	0.997872i	$-0.479232\pi$
$2$	1.54692e6	0.130396	0.0651980	+	0.997872i	$0.479232\pi$
$3$	0	0
$3$	0	0
$4$	−1.38345e14	−0.982997
$5$	−4.23962e16	−1.59049	−0.795246	−	0.606286i	$-0.792659\pi$
$5$	−4.23962e16	−1.59049	−0.795246	+	0.606286i	$0.792659\pi$
$6$	0	0
$7$	−3.90714e19	−0.539579	−0.269790	−	0.962919i	$-0.586954\pi$
$7$	−3.90714e19	−0.539579	−0.269790	+	0.962919i	$0.586954\pi$
$8$	−4.31719e20	−0.258575
$9$	0	0
$10$	−6.55837e22	−0.207394
$11$	−2.66558e24	−0.897561	−0.448781	−	0.893642i	$-0.648142\pi$
$11$	−2.66558e24	−0.897561	−0.448781	+	0.893642i	$0.648142\pi$
$12$	0	0
$13$	2.26259e26	1.50293	0.751463	−	0.659776i	$-0.229349\pi$
$13$	2.26259e26	1.50293	0.751463	+	0.659776i	$0.229349\pi$
$14$	−6.04405e25	−0.0703589
$15$	0	0
$16$	1.88024e28	0.949280
$17$	−8.41583e28	−1.02223	−0.511114	−	0.859513i	$-0.670767\pi$
$17$	−8.41583e28	−1.02223	−0.511114	+	0.859513i	$0.670767\pi$
$18$	0	0
$19$	3.16735e29	0.281830	0.140915	−	0.990022i	$-0.454996\pi$
$19$	3.16735e29	0.281830	0.140915	+	0.990022i	$0.454996\pi$
$20$	5.86528e30	1.56345
$21$	0	0
$22$	−4.12345e30	−0.117038
$23$	−2.26985e31	−0.226669	−0.113335	−	0.993557i	$-0.536153\pi$
$23$	−2.26985e31	−0.226669	−0.113335	+	0.993557i	$0.536153\pi$
$24$	0	0
$25$	1.08689e33	1.52967
$26$	3.50006e32	0.195975
$27$	0	0
$28$	5.40532e33	0.530405
$29$	3.39685e34	1.46125	0.730624	−	0.682780i	$-0.239229\pi$
$29$	3.39685e34	1.46125	0.730624	+	0.682780i	$0.239229\pi$
$30$	0	0
$31$	1.81646e35	1.63015	0.815074	−	0.579357i	$-0.196696\pi$
$31$	1.81646e35	1.63015	0.815074	+	0.579357i	$0.196696\pi$
$32$	8.98449e34	0.382357
$33$	0	0
$34$	−1.30186e35	−0.133294
$35$	1.65648e36	0.858197
$36$	0	0
$37$	−7.13789e36	−1.00191	−0.500956	−	0.865473i	$-0.667018\pi$
$37$	−7.13789e36	−1.00191	−0.500956	+	0.865473i	$0.667018\pi$
$38$	4.89965e35	0.0367494
$39$	0	0
$40$	1.83032e37	0.411261
$41$	2.78383e37	0.350124	0.175062	−	0.984557i	$-0.443987\pi$
$41$	2.78383e37	0.350124	0.175062	+	0.984557i	$0.443987\pi$
$42$	0	0
$43$	−4.92777e37	−0.202368	−0.101184	−	0.994868i	$-0.532263\pi$
$43$	−4.92777e37	−0.202368	−0.101184	+	0.994868i	$0.532263\pi$
$44$	3.68769e38	0.882300
$45$	0	0
$46$	−3.51128e37	−0.0295567
$47$	−1.86825e39	−0.948716	−0.474358	−	0.880332i	$-0.657320\pi$
$47$	−1.86825e39	−0.948716	−0.474358	+	0.880332i	$0.657320\pi$
$48$	0	0
$49$	−3.71676e39	−0.708854
$50$	1.68134e39	0.199462
$51$	0	0
$52$	−3.13017e40	−1.47737
$53$	2.48904e40	0.750843	0.375421	−	0.926854i	$-0.377498\pi$
$53$	2.48904e40	0.750843	0.375421	+	0.926854i	$0.377498\pi$
$54$	0	0
$55$	1.13011e41	1.42756
$56$	1.68679e40	0.139522
$57$	0	0
$58$	5.25467e40	0.190541
$59$	−3.69239e40	−0.0895953	−0.0447976	−	0.998996i	$-0.514264\pi$
$59$	−3.69239e40	−0.0895953	−0.0447976	+	0.998996i	$0.514264\pi$
$60$	0	0
$61$	3.52589e41	0.390857	0.195429	−	0.980718i	$-0.437390\pi$
$61$	3.52589e41	0.390857	0.195429	+	0.980718i	$0.437390\pi$
$62$	2.80993e41	0.212565
$63$	0	0
$64$	−2.50722e42	−0.899422
$65$	−9.59253e42	−2.39039
$66$	0	0
$67$	−1.26183e42	−0.154257	−0.0771283	−	0.997021i	$-0.524575\pi$
$67$	−1.26183e42	−0.154257	−0.0771283	+	0.997021i	$0.524575\pi$
$68$	1.16428e43	1.00485
$69$	0	0
$70$	2.56245e42	0.111905
$71$	3.26023e43	1.02018	0.510090	−	0.860121i	$-0.329612\pi$
$71$	3.26023e43	1.02018	0.510090	+	0.860121i	$0.329612\pi$
$72$	0	0
$73$	3.59179e43	0.585092	0.292546	−	0.956251i	$-0.405498\pi$
$73$	3.59179e43	0.585092	0.292546	+	0.956251i	$0.405498\pi$
$74$	−1.10418e43	−0.130645
$75$	0	0
$76$	−4.38186e43	−0.277038
$77$	1.04148e44	0.484305
$78$	0	0
$79$	−5.82596e44	−1.48297	−0.741483	−	0.670972i	$-0.765877\pi$
$79$	−5.82596e44	−1.48297	−0.741483	+	0.670972i	$0.765877\pi$
$80$	−7.97151e44	−1.50982
$81$	0	0
$82$	4.30637e43	0.0456547
$83$	3.51619e44	0.280373	0.140187	−	0.990125i	$-0.455230\pi$
$83$	3.51619e44	0.280373	0.140187	+	0.990125i	$0.455230\pi$
$84$	0	0
$85$	3.56799e45	1.62584
$86$	−7.62288e43	−0.0263879
$87$	0	0
$88$	1.15078e45	0.232087
$89$	2.92401e45	0.452182	0.226091	−	0.974106i	$-0.427405\pi$
$89$	2.92401e45	0.452182	0.226091	+	0.974106i	$0.427405\pi$
$90$	0	0
$91$	−8.84027e45	−0.810947
$92$	3.14021e45	0.222815
$93$	0	0
$94$	−2.89005e45	−0.123709
$95$	−1.34284e46	−0.448248
$96$	0	0
$97$	2.17182e46	0.444311	0.222156	−	0.975011i	$-0.428691\pi$
$97$	2.17182e46	0.444311	0.222156	+	0.975011i	$0.428691\pi$
$98$	−5.74955e45	−0.0924317
$99$	0	0
$100$	−1.50366e47	−1.50366
$101$	5.11557e46	0.404894	0.202447	−	0.979293i	$-0.435111\pi$
$101$	5.11557e46	0.404894	0.202447	+	0.979293i	$0.435111\pi$
$102$	0	0
$103$	3.19569e47	1.59547	0.797736	−	0.603006i	$-0.206031\pi$
$103$	3.19569e47	1.59547	0.797736	+	0.603006i	$0.206031\pi$
$104$	−9.76803e46	−0.388618
$105$	0	0
$106$	3.85036e46	0.0979068
$107$	−2.00584e47	−0.409051	−0.204526	−	0.978861i	$-0.565565\pi$
$107$	−2.00584e47	−0.409051	−0.204526	+	0.978861i	$0.565565\pi$
$108$	0	0
$109$	−5.86410e47	−0.773888	−0.386944	−	0.922103i	$-0.626469\pi$
$109$	−5.86410e47	−0.773888	−0.386944	+	0.922103i	$0.626469\pi$
$110$	1.74819e47	0.186149
$111$	0	0
$112$	−7.34637e47	−0.512212
$113$	−3.11593e47	−0.176297	−0.0881484	−	0.996107i	$-0.528095\pi$
$113$	−3.11593e47	−0.176297	−0.0881484	+	0.996107i	$0.528095\pi$
$114$	0	0
$115$	9.62329e47	0.360516
$116$	−4.69936e48	−1.43640
$117$	0	0
$118$	−5.71184e46	−0.0116829
$119$	3.28818e48	0.551572
$120$	0	0
$121$	−1.71442e48	−0.194384
$122$	5.45429e47	0.0509662
$123$	0	0
$124$	−2.51298e49	−1.60243
$125$	−1.59559e49	−0.842432
$126$	0	0
$127$	2.66165e49	0.967749	0.483875	−	0.875137i	$-0.339229\pi$
$127$	2.66165e49	0.967749	0.483875	+	0.875137i	$0.339229\pi$
$128$	−1.65230e49	−0.499638
$129$	0	0
$130$	−1.48389e49	−0.311697
$131$	−6.34924e49	−1.11390	−0.556950	−	0.830546i	$-0.688028\pi$
$131$	−6.34924e49	−1.11390	−0.556950	+	0.830546i	$0.688028\pi$
$132$	0	0
$133$	−1.23753e49	−0.152069
$134$	−1.95196e48	−0.0201144
$135$	0	0
$136$	3.63327e49	0.264322
$137$	−1.99734e50	−1.22326	−0.611631	−	0.791143i	$-0.709486\pi$
$137$	−1.99734e50	−1.22326	−0.611631	+	0.791143i	$0.709486\pi$
$138$	0	0
$139$	−3.16608e50	−1.37935	−0.689674	−	0.724120i	$-0.742246\pi$
$139$	−3.16608e50	−1.37935	−0.689674	+	0.724120i	$0.742246\pi$
$140$	−2.29165e50	−0.843605
$141$	0	0
$142$	5.04332e49	0.133027
$143$	−6.03113e50	−1.34897
$144$	0	0
$145$	−1.44014e51	−2.32410
$146$	5.55623e49	0.0762936
$147$	0	0
$148$	9.87488e50	0.984876
$149$	−1.00267e50	−0.0853651	−0.0426826	−	0.999089i	$-0.513590\pi$
$149$	−1.00267e50	−0.0853651	−0.0426826	+	0.999089i	$0.513590\pi$
$150$	0	0
$151$	−2.40479e49	−0.0149664	−0.00748321	−	0.999972i	$-0.502382\pi$
$151$	−2.40479e49	−0.0149664	−0.00748321	+	0.999972i	$0.502382\pi$
$152$	−1.36740e50	−0.0728740
$153$	0	0
$154$	1.61109e50	0.0631514
$155$	−7.70111e51	−2.59274
$156$	0	0
$157$	−1.42274e51	−0.354391	−0.177196	−	0.984176i	$-0.556702\pi$
$157$	−1.42274e51	−0.354391	−0.177196	+	0.984176i	$0.556702\pi$
$158$	−9.01232e50	−0.193373
$159$	0	0
$160$	−3.80908e51	−0.608136
$161$	8.86862e50	0.122306
$162$	0	0
$163$	−4.79256e51	−0.494492	−0.247246	−	0.968953i	$-0.579525\pi$
$163$	−4.79256e51	−0.494492	−0.247246	+	0.968953i	$0.579525\pi$
$164$	−3.85127e51	−0.344170
$165$	0	0
$166$	5.43927e50	0.0365596
$167$	9.89736e51	0.577673	0.288837	−	0.957378i	$-0.406732\pi$
$167$	9.89736e51	0.577673	0.288837	+	0.957378i	$0.406732\pi$
$168$	0	0
$169$	2.85292e52	1.25878
$170$	5.51941e51	0.212004
$171$	0	0
$172$	6.81729e51	0.198927
$173$	7.43991e52	1.89446	0.947228	−	0.320562i	$-0.103872\pi$
$173$	7.43991e52	1.89446	0.947228	+	0.320562i	$0.103872\pi$
$174$	0	0
$175$	−4.24665e52	−0.825377
$176$	−5.01194e52	−0.852037
$177$	0	0
$178$	4.52321e51	0.0589627
$179$	−3.60632e52	−0.412115	−0.206057	−	0.978540i	$-0.566063\pi$
$179$	−3.60632e52	−0.412115	−0.206057	+	0.978540i	$0.566063\pi$
$180$	0	0
$181$	6.19557e52	0.545299	0.272650	−	0.962113i	$-0.412100\pi$
$181$	6.19557e52	0.545299	0.272650	+	0.962113i	$0.412100\pi$
$182$	−1.36752e52	−0.105744
$183$	0	0
$184$	9.79935e51	0.0586109
$185$	3.02619e53	1.59353
$186$	0	0
$187$	2.24331e53	0.917511
$188$	2.58463e53	0.932585
$189$	0	0
$190$	−2.07727e52	−0.0584497
$191$	3.09862e53	0.770699	0.385349	−	0.922771i	$-0.374081\pi$
$191$	3.09862e53	0.770699	0.385349	+	0.922771i	$0.374081\pi$
$192$	0	0
$193$	4.75475e53	0.925829	0.462914	−	0.886403i	$-0.346804\pi$
$193$	4.75475e53	0.925829	0.462914	+	0.886403i	$0.346804\pi$
$194$	3.35963e52	0.0579364
$195$	0	0
$196$	5.14194e53	0.696802
$197$	7.61644e53	0.915790	0.457895	−	0.889006i	$-0.348604\pi$
$197$	7.61644e53	0.915790	0.457895	+	0.889006i	$0.348604\pi$
$198$	0	0
$199$	−1.90631e54	−1.80778	−0.903890	−	0.427765i	$-0.859301\pi$
$199$	−1.90631e54	−1.80778	−0.903890	+	0.427765i	$0.859301\pi$
$200$	−4.69232e53	−0.395533
$201$	0	0
$202$	7.91339e52	0.0527965
$203$	−1.32720e54	−0.788459
$204$	0	0
$205$	−1.18024e54	−0.556869
$206$	4.94348e53	0.208043
$207$	0	0
$208$	4.25422e54	1.42670
$209$	−8.44284e53	−0.252959
$210$	0	0
$211$	1.25520e54	0.300660	0.150330	−	0.988636i	$-0.451966\pi$
$211$	1.25520e54	0.300660	0.150330	+	0.988636i	$0.451966\pi$
$212$	−3.44345e54	−0.738076
$213$	0	0
$214$	−3.10288e53	−0.0533386
$215$	2.08918e54	0.321864
$216$	0	0
$217$	−7.09718e54	−0.879594
$218$	−9.07131e53	−0.100912
$219$	0	0
$220$	−1.56344e55	−1.40329
$221$	−1.90416e55	−1.53633
$222$	0	0
$223$	−1.43141e54	−0.0934545	−0.0467272	−	0.998908i	$-0.514879\pi$
$223$	−1.43141e54	−0.0934545	−0.0467272	+	0.998908i	$0.514879\pi$
$224$	−3.51037e54	−0.206312
$225$	0	0
$226$	−4.82011e53	−0.0229884
$227$	−3.38487e55	−1.45524	−0.727619	−	0.685982i	$-0.759373\pi$
$227$	−3.38487e55	−1.45524	−0.727619	+	0.685982i	$0.759373\pi$
$228$	0	0
$229$	−4.65218e54	−0.162750	−0.0813752	−	0.996684i	$-0.525931\pi$
$229$	−4.65218e54	−0.162750	−0.0813752	+	0.996684i	$0.525931\pi$
$230$	1.48865e54	0.0470098
$231$	0	0
$232$	−1.46649e55	−0.377842
$233$	6.87236e55	1.60045	0.800225	−	0.599700i	$-0.204713\pi$
$233$	6.87236e55	1.60045	0.800225	+	0.599700i	$0.204713\pi$
$234$	0	0
$235$	7.92068e55	1.50893
$236$	5.10822e54	0.0880719
$237$	0	0
$238$	5.08657e54	0.0719228
$239$	−1.09219e56	−1.39942	−0.699710	−	0.714427i	$-0.746687\pi$
$239$	−1.09219e56	−1.39942	−0.699710	+	0.714427i	$0.746687\pi$
$240$	0	0
$241$	−4.82622e55	−0.508401	−0.254201	−	0.967152i	$-0.581812\pi$
$241$	−4.82622e55	−0.508401	−0.254201	+	0.967152i	$0.581812\pi$
$242$	−2.65207e54	−0.0253468
$243$	0	0
$244$	−4.87788e55	−0.384211
$245$	1.57577e56	1.12743
$246$	0	0
$247$	7.16642e55	0.423569
$248$	−7.84201e55	−0.421515
$249$	0	0
$250$	−2.46825e55	−0.109850
$251$	4.06217e56	1.64599	0.822993	−	0.568052i	$-0.192303\pi$
$251$	4.06217e56	1.64599	0.822993	+	0.568052i	$0.192303\pi$
$252$	0	0
$253$	6.05047e55	0.203450
$254$	4.11736e55	0.126191
$255$	0	0
$256$	3.27300e56	0.834271
$257$	−1.93698e56	−0.450501	−0.225251	−	0.974301i	$-0.572320\pi$
$257$	−1.93698e56	−0.450501	−0.225251	+	0.974301i	$0.572320\pi$
$258$	0	0
$259$	2.78887e56	0.540611
$260$	1.32707e57	2.34975
$261$	0	0
$262$	−9.82178e55	−0.145248
$263$	−8.33659e56	−1.12727	−0.563636	−	0.826023i	$-0.690598\pi$
$263$	−8.33659e56	−1.12727	−0.563636	+	0.826023i	$0.690598\pi$
$264$	0	0
$265$	−1.05526e57	−1.19421
$266$	−1.91436e55	−0.0198292
$267$	0	0
$268$	1.74568e56	0.151634
$269$	1.88490e57	1.50006	0.750032	−	0.661402i	$-0.230038\pi$
$269$	1.88490e57	1.50006	0.750032	+	0.661402i	$0.230038\pi$
$270$	0	0
$271$	2.56612e57	1.71593	0.857963	−	0.513712i	$-0.171730\pi$
$271$	2.56612e57	1.71593	0.857963	+	0.513712i	$0.171730\pi$
$272$	−1.58238e57	−0.970380
$273$	0	0
$274$	−3.08974e56	−0.159508
$275$	−2.89721e57	−1.37297
$276$	0	0
$277$	−8.36679e56	−0.334414	−0.167207	−	0.985922i	$-0.553475\pi$
$277$	−8.36679e56	−0.334414	−0.167207	+	0.985922i	$0.553475\pi$
$278$	−4.89768e56	−0.179861
$279$	0	0
$280$	−7.15133e56	−0.221908
$281$	3.96974e57	1.13283	0.566414	−	0.824121i	$-0.308330\pi$
$281$	3.96974e57	1.13283	0.566414	+	0.824121i	$0.308330\pi$
$282$	0	0
$283$	−4.45361e57	−1.07580	−0.537900	−	0.843009i	$-0.680782\pi$
$283$	−4.45361e57	−1.07580	−0.537900	+	0.843009i	$0.680782\pi$
$284$	−4.51034e57	−1.00283
$285$	0	0
$286$	−9.32969e56	−0.175900
$287$	−1.08768e57	−0.188919
$288$	0	0
$289$	3.04657e56	0.0449481
$290$	−2.22778e57	−0.303054
$291$	0	0
$292$	−4.96905e57	−0.575144
$293$	−1.05167e58	−1.12328	−0.561641	−	0.827381i	$-0.689830\pi$
$293$	−1.05167e58	−1.12328	−0.561641	+	0.827381i	$0.689830\pi$
$294$	0	0
$295$	1.56543e57	0.142501
$296$	3.08156e57	0.259069
$297$	0	0
$298$	−1.55105e56	−0.0111313
$299$	−5.13574e57	−0.340667
$300$	0	0
$301$	1.92535e57	0.109193
$302$	−3.72002e55	−0.00195156
$303$	0	0
$304$	5.95539e57	0.267535
$305$	−1.49484e58	−0.621656
$306$	0	0
$307$	5.43218e57	0.193741	0.0968707	−	0.995297i	$-0.469117\pi$
$307$	5.43218e57	0.193741	0.0968707	+	0.995297i	$0.469117\pi$
$308$	−1.44083e58	−0.476071
$309$	0	0
$310$	−1.19130e58	−0.338082
$311$	4.80030e58	1.26299	0.631493	−	0.775381i	$-0.282442\pi$
$311$	4.80030e58	1.26299	0.631493	+	0.775381i	$0.282442\pi$
$312$	0	0
$313$	−2.50321e58	−0.566507	−0.283253	−	0.959045i	$-0.591414\pi$
$313$	−2.50321e58	−0.566507	−0.283253	+	0.959045i	$0.591414\pi$
$314$	−2.20087e57	−0.0462111
$315$	0	0
$316$	8.05990e58	1.45775
$317$	6.65301e58	1.11719	0.558593	−	0.829442i	$-0.311341\pi$
$317$	6.65301e58	1.11719	0.558593	+	0.829442i	$0.311341\pi$
$318$	0	0
$319$	−9.05460e58	−1.31156
$320$	1.06297e59	1.43052
$321$	0	0
$322$	1.37191e57	0.0159482
$323$	−2.66559e58	−0.288094
$324$	0	0
$325$	2.45920e59	2.29898
$326$	−7.41372e57	−0.0644797
$327$	0	0
$328$	−1.20183e58	−0.0905331
$329$	7.29953e58	0.511907
$330$	0	0
$331$	−1.52984e58	−0.0930438	−0.0465219	−	0.998917i	$-0.514814\pi$
$331$	−1.52984e58	−0.0930438	−0.0465219	+	0.998917i	$0.514814\pi$
$332$	−4.86445e58	−0.275606
$333$	0	0
$334$	1.53105e58	0.0753262
$335$	5.34969e58	0.245344
$336$	0	0
$337$	−1.19696e59	−0.477284	−0.238642	−	0.971108i	$-0.576702\pi$
$337$	−1.19696e59	−0.477284	−0.238642	+	0.971108i	$0.576702\pi$
$338$	4.41324e58	0.164140
$339$	0	0
$340$	−4.93612e59	−1.59820
$341$	−4.84194e59	−1.46316
$342$	0	0
$343$	3.50084e59	0.922062
$344$	2.12741e58	0.0523272
$345$	0	0
$346$	1.15090e59	0.247029
$347$	6.60768e59	1.32528	0.662638	−	0.748940i	$-0.269437\pi$
$347$	6.60768e59	1.32528	0.662638	+	0.748940i	$0.269437\pi$
$348$	0	0
$349$	7.13810e59	1.25079	0.625396	−	0.780308i	$-0.284937\pi$
$349$	7.13810e59	1.25079	0.625396	+	0.780308i	$0.284937\pi$
$350$	−6.56924e58	−0.107626
$351$	0	0
$352$	−2.39489e59	−0.343189
$353$	−4.98386e58	−0.0668129	−0.0334064	−	0.999442i	$-0.510636\pi$
$353$	−4.98386e58	−0.0668129	−0.0334064	+	0.999442i	$0.510636\pi$
$354$	0	0
$355$	−1.38221e60	−1.62259
$356$	−4.04520e59	−0.444493
$357$	0	0
$358$	−5.57870e58	−0.0537381
$359$	−2.08989e60	−1.88540	−0.942700	−	0.333641i	$-0.891723\pi$
$359$	−2.08989e60	−1.88540	−0.942700	+	0.333641i	$0.891723\pi$
$360$	0	0
$361$	−1.16273e60	−0.920572
$362$	9.58408e58	0.0711048
$363$	0	0
$364$	1.22300e60	0.797159
$365$	−1.52278e60	−0.930585
$366$	0	0
$367$	−1.22059e59	−0.0656021	−0.0328011	−	0.999462i	$-0.510443\pi$
$367$	−1.22059e59	−0.0656021	−0.0328011	+	0.999462i	$0.510443\pi$
$368$	−4.26786e59	−0.215173
$369$	0	0
$370$	4.68129e59	0.207790
$371$	−9.72503e59	−0.405139
$372$	0	0
$373$	−2.41910e60	−0.888172	−0.444086	−	0.895984i	$-0.646472\pi$
$373$	−2.41910e60	−0.888172	−0.444086	+	0.895984i	$0.646472\pi$
$374$	3.47023e59	0.119640
$375$	0	0
$376$	8.06560e59	0.245314
$377$	7.68569e60	2.19615
$378$	0	0
$379$	6.29795e60	1.58920	0.794598	−	0.607135i	$-0.207681\pi$
$379$	6.29795e60	1.58920	0.794598	+	0.607135i	$0.207681\pi$
$380$	1.85774e60	0.440626
$381$	0	0
$382$	4.79333e59	0.100496
$383$	−3.88964e60	−0.766898	−0.383449	−	0.923562i	$-0.625264\pi$
$383$	−3.88964e60	−0.766898	−0.383449	+	0.923562i	$0.625264\pi$
$384$	0	0
$385$	−4.41548e60	−0.770284
$386$	7.35523e59	0.120724
$387$	0	0
$388$	−3.00459e60	−0.436757
$389$	−5.15774e60	−0.705739	−0.352869	−	0.935673i	$-0.614794\pi$
$389$	−5.15774e60	−0.705739	−0.352869	+	0.935673i	$0.614794\pi$
$390$	0	0
$391$	1.91027e60	0.231707
$392$	1.60460e60	0.183292
$393$	0	0
$394$	1.17821e60	0.119415
$395$	2.46999e61	2.35865
$396$	0	0
$397$	−1.92619e61	−1.63351	−0.816754	−	0.576986i	$-0.804229\pi$
$397$	−1.92619e61	−1.63351	−0.816754	+	0.576986i	$0.804229\pi$
$398$	−2.94891e60	−0.235727
$399$	0	0
$400$	2.04362e61	1.45208
$401$	−5.06490e58	−0.00339374	−0.00169687	−	0.999999i	$-0.500540\pi$
$401$	−5.06490e58	−0.00339374	−0.00169687	+	0.999999i	$0.500540\pi$
$402$	0	0
$403$	4.10992e61	2.44999
$404$	−7.07710e60	−0.398010
$405$	0	0
$406$	−2.05308e60	−0.102812
$407$	1.90266e61	0.899277
$408$	0	0
$409$	1.50217e61	0.632733	0.316367	−	0.948637i	$-0.397537\pi$
$409$	1.50217e61	0.632733	0.316367	+	0.948637i	$0.397537\pi$
$410$	−1.82574e60	−0.0726135
$411$	0	0
$412$	−4.42106e61	−1.56834
$413$	1.44267e60	0.0483437
$414$	0	0
$415$	−1.49073e61	−0.445932
$416$	2.03282e61	0.574654
$417$	0	0
$418$	−1.30604e60	−0.0329849
$419$	−6.95944e61	−1.66167	−0.830835	−	0.556518i	$-0.812137\pi$
$419$	−6.95944e61	−1.66167	−0.830835	+	0.556518i	$0.812137\pi$
$420$	0	0
$421$	−3.78966e61	−0.809042	−0.404521	−	0.914529i	$-0.632562\pi$
$421$	−3.78966e61	−0.809042	−0.404521	+	0.914529i	$0.632562\pi$
$422$	1.94170e60	0.0392049
$423$	0	0
$424$	−1.07457e61	−0.194149
$425$	−9.14712e61	−1.56367
$426$	0	0
$427$	−1.37762e61	−0.210898
$428$	2.77497e61	0.402096
$429$	0	0
$430$	3.23181e60	0.0419698
$431$	−4.06747e60	−0.0500160	−0.0250080	−	0.999687i	$-0.507961\pi$
$431$	−4.06747e60	−0.0500160	−0.0250080	+	0.999687i	$0.507961\pi$
$432$	0	0
$433$	−2.59125e61	−0.285788	−0.142894	−	0.989738i	$-0.545641\pi$
$433$	−2.59125e61	−0.285788	−0.142894	+	0.989738i	$0.545641\pi$
$434$	−1.09788e61	−0.114695
$435$	0	0
$436$	8.11265e61	0.760730
$437$	−7.18941e60	−0.0638821
$438$	0	0
$439$	3.51058e61	0.280196	0.140098	−	0.990138i	$-0.455258\pi$
$439$	3.51058e61	0.280196	0.140098	+	0.990138i	$0.455258\pi$
$440$	−4.87888e61	−0.369132
$441$	0	0
$442$	−2.94559e61	−0.200331
$443$	4.43894e61	0.286281	0.143140	−	0.989702i	$-0.454280\pi$
$443$	4.43894e61	0.286281	0.143140	+	0.989702i	$0.454280\pi$
$444$	0	0
$445$	−1.23967e62	−0.719192
$446$	−2.21428e60	−0.0121861
$447$	0	0
$448$	9.79607e61	0.485309
$449$	−3.43198e62	−1.61345	−0.806725	−	0.590927i	$-0.798762\pi$
$449$	−3.43198e62	−1.61345	−0.806725	+	0.590927i	$0.798762\pi$
$450$	0	0
$451$	−7.42052e61	−0.314257
$452$	4.31072e61	0.173299
$453$	0	0
$454$	−5.23613e61	−0.189757
$455$	3.74794e62	1.28981
$456$	0	0
$457$	−9.64466e60	−0.0299403	−0.0149701	−	0.999888i	$-0.504765\pi$
$457$	−9.64466e60	−0.0299403	−0.0149701	+	0.999888i	$0.504765\pi$
$458$	−7.19656e60	−0.0212220
$459$	0	0
$460$	−1.33133e62	−0.354386
$461$	6.32143e61	0.159898	0.0799491	−	0.996799i	$-0.474524\pi$
$461$	6.32143e61	0.159898	0.0799491	+	0.996799i	$0.474524\pi$
$462$	0	0
$463$	6.86213e62	1.56785	0.783927	−	0.620853i	$-0.213214\pi$
$463$	6.86213e62	1.56785	0.783927	+	0.620853i	$0.213214\pi$
$464$	6.38691e62	1.38713
$465$	0	0
$466$	1.06310e62	0.208692
$467$	2.91371e62	0.543876	0.271938	−	0.962315i	$-0.412335\pi$
$467$	2.91371e62	0.543876	0.271938	+	0.962315i	$0.412335\pi$
$468$	0	0
$469$	4.93016e61	0.0832337
$470$	1.22527e62	0.196758
$471$	0	0
$472$	1.59407e61	0.0231671
$473$	1.31354e62	0.181637
$474$	0	0
$475$	3.44258e62	0.431106
$476$	−4.54902e62	−0.542194
$477$	0	0
$478$	−1.68954e62	−0.182479
$479$	9.39830e62	0.966417	0.483209	−	0.875505i	$-0.339471\pi$
$479$	9.39830e62	0.966417	0.483209	+	0.875505i	$0.339471\pi$
$480$	0	0
$481$	−1.61501e63	−1.50580
$482$	−7.46579e61	−0.0662934
$483$	0	0
$484$	2.37180e62	0.191079
$485$	−9.20767e62	−0.706674
$486$	0	0
$487$	2.39350e63	1.66764	0.833820	−	0.552037i	$-0.186149\pi$
$487$	2.39350e63	1.66764	0.833820	+	0.552037i	$0.186149\pi$
$488$	−1.52219e62	−0.101066
$489$	0	0
$490$	2.43759e62	0.147012
$491$	−1.23586e63	−0.710481	−0.355241	−	0.934775i	$-0.615601\pi$
$491$	−1.23586e63	−0.710481	−0.355241	+	0.934775i	$0.615601\pi$
$492$	0	0
$493$	−2.85874e63	−1.49373
$494$	1.10859e62	0.0552317
$495$	0	0
$496$	3.41539e63	1.54747
$497$	−1.27382e63	−0.550468
$498$	0	0
$499$	−2.94657e63	−1.15865	−0.579327	−	0.815095i	$-0.696684\pi$
$499$	−2.94657e63	−1.15865	−0.579327	+	0.815095i	$0.696684\pi$
$500$	2.20741e63	0.828108
$501$	0	0
$502$	6.28387e62	0.214630
$503$	1.27808e63	0.416591	0.208296	−	0.978066i	$-0.433208\pi$
$503$	1.27808e63	0.416591	0.208296	+	0.978066i	$0.433208\pi$
$504$	0	0
$505$	−2.16880e63	−0.643981
$506$	9.35961e61	0.0265290
$507$	0	0
$508$	−3.68224e63	−0.951294
$509$	−7.25177e63	−1.78886	−0.894429	−	0.447209i	$-0.852418\pi$
$509$	−7.25177e63	−1.78886	−0.894429	+	0.447209i	$0.852418\pi$
$510$	0	0
$511$	−1.40336e63	−0.315704
$512$	2.83172e63	0.608423
$513$	0	0
$514$	−2.99635e62	−0.0587435
$515$	−1.35485e64	−2.53759
$516$	0	0
$517$	4.97998e63	0.851531
$518$	4.31418e62	0.0704934
$519$	0	0
$520$	4.14127e63	0.618095
$521$	9.84138e63	1.40401	0.702004	−	0.712173i	$-0.252289\pi$
$521$	9.84138e63	1.40401	0.702004	+	0.712173i	$0.252289\pi$
$522$	0	0
$523$	4.91409e62	0.0640698	0.0320349	−	0.999487i	$-0.489801\pi$
$523$	4.91409e62	0.0640698	0.0320349	+	0.999487i	$0.489801\pi$
$524$	8.78382e63	1.09496
$525$	0	0
$526$	−1.28961e63	−0.146992
$527$	−1.52871e64	−1.66638
$528$	0	0
$529$	−9.51264e63	−0.948621
$530$	−1.63240e63	−0.155720
$531$	0	0
$532$	1.71205e63	0.149484
$533$	6.29866e63	0.526210
$534$	0	0
$535$	8.50400e63	0.650593
$536$	5.44756e62	0.0398869
$537$	0	0
$538$	2.91580e63	0.195602
$539$	9.90734e63	0.636240
$540$	0	0
$541$	6.71742e61	0.00395428	0.00197714	−	0.999998i	$-0.499371\pi$
$541$	6.71742e61	0.00395428	0.00197714	+	0.999998i	$0.499371\pi$
$542$	3.96959e63	0.223750
$543$	0	0
$544$	−7.56119e63	−0.390856
$545$	2.48615e64	1.23086
$546$	0	0
$547$	4.01645e62	0.0182449	0.00912243	−	0.999958i	$-0.497096\pi$
$547$	4.01645e62	0.0182449	0.00912243	+	0.999958i	$0.497096\pi$
$548$	2.76322e64	1.20246
$549$	0	0
$550$	−4.48176e63	−0.179030
$551$	1.07590e64	0.411823
$552$	0	0
$553$	2.27629e64	0.800177
$554$	−1.29428e63	−0.0436062
$555$	0	0
$556$	4.38010e64	1.35589
$557$	−6.03614e64	−1.79127	−0.895637	−	0.444785i	$-0.853280\pi$
$557$	−6.03614e64	−1.79127	−0.895637	+	0.444785i	$0.853280\pi$
$558$	0	0
$559$	−1.11495e64	−0.304144
$560$	3.11458e64	0.814669
$561$	0	0
$562$	6.14089e63	0.147716
$563$	3.47404e63	0.0801470	0.0400735	−	0.999197i	$-0.487241\pi$
$563$	3.47404e63	0.0801470	0.0400735	+	0.999197i	$0.487241\pi$
$564$	0	0
$565$	1.32104e64	0.280399
$566$	−6.88940e63	−0.140280
$567$	0	0
$568$	−1.40750e64	−0.263793
$569$	−9.25178e64	−1.66375	−0.831873	−	0.554966i	$-0.812731\pi$
$569$	−9.25178e64	−1.66375	−0.831873	+	0.554966i	$0.812731\pi$
$570$	0	0
$571$	−1.04188e65	−1.72532	−0.862658	−	0.505787i	$-0.831202\pi$
$571$	−1.04188e65	−1.72532	−0.862658	+	0.505787i	$0.831202\pi$
$572$	8.34373e64	1.32603
$573$	0	0
$574$	−1.68256e63	−0.0246343
$575$	−2.46708e64	−0.346728
$576$	0	0
$577$	−8.68105e64	−1.12445	−0.562225	−	0.826984i	$-0.690055\pi$
$577$	−8.68105e64	−1.12445	−0.562225	+	0.826984i	$0.690055\pi$
$578$	4.71281e62	0.00586105
$579$	0	0
$580$	1.99235e65	2.28459
$581$	−1.37382e64	−0.151284
$582$	0	0
$583$	−6.63474e64	−0.673928
$584$	−1.55064e64	−0.151290
$585$	0	0
$586$	−1.62685e64	−0.146471
$587$	−5.04453e64	−0.436340	−0.218170	−	0.975911i	$-0.570009\pi$
$587$	−5.04453e64	−0.436340	−0.218170	+	0.975911i	$0.570009\pi$
$588$	0	0
$589$	5.75338e64	0.459424
$590$	2.42160e63	0.0185815
$591$	0	0
$592$	−1.34210e65	−0.951094
$593$	−1.82757e65	−1.24477	−0.622385	−	0.782712i	$-0.713836\pi$
$593$	−1.82757e65	−1.24477	−0.622385	+	0.782712i	$0.713836\pi$
$594$	0	0
$595$	−1.39406e65	−0.877272
$596$	1.38714e64	0.0839137
$597$	0	0
$598$	−7.94459e63	−0.0444216
$599$	−6.30818e64	−0.339136	−0.169568	−	0.985519i	$-0.554237\pi$
$599$	−6.30818e64	−0.339136	−0.169568	+	0.985519i	$0.554237\pi$
$600$	0	0
$601$	1.16613e65	0.579693	0.289847	−	0.957073i	$-0.406396\pi$
$601$	1.16613e65	0.579693	0.289847	+	0.957073i	$0.406396\pi$
$602$	2.97837e63	0.0142384
$603$	0	0
$604$	3.32689e63	0.0147119
$605$	7.26847e64	0.309166
$606$	0	0
$607$	−8.69736e64	−0.342337	−0.171168	−	0.985242i	$-0.554754\pi$
$607$	−8.69736e64	−0.342337	−0.171168	+	0.985242i	$0.554754\pi$
$608$	2.84570e64	0.107760
$609$	0	0
$610$	−2.31241e64	−0.0810614
$611$	−4.22709e65	−1.42585
$612$	0	0
$613$	3.95467e65	1.23535	0.617674	−	0.786435i	$-0.288075\pi$
$613$	3.95467e65	1.23535	0.617674	+	0.786435i	$0.288075\pi$
$614$	8.40317e63	0.0252631
$615$	0	0
$616$	−4.49627e64	−0.125229
$617$	4.10300e65	1.10002	0.550009	−	0.835159i	$-0.314624\pi$
$617$	4.10300e65	1.10002	0.550009	+	0.835159i	$0.314624\pi$
$618$	0	0
$619$	1.39273e65	0.346047	0.173024	−	0.984918i	$-0.444646\pi$
$619$	1.39273e65	0.346047	0.173024	+	0.984918i	$0.444646\pi$
$620$	1.06541e66	2.54865
$621$	0	0
$622$	7.42569e64	0.164688
$623$	−1.14245e65	−0.243988
$624$	0	0
$625$	−9.58171e64	−0.189785
$626$	−3.87227e64	−0.0738702
$627$	0	0
$628$	1.96828e65	0.348365
$629$	6.00713e65	1.02418
$630$	0	0
$631$	1.54026e65	0.243728	0.121864	−	0.992547i	$-0.461113\pi$
$631$	1.54026e65	0.243728	0.121864	+	0.992547i	$0.461113\pi$
$632$	2.51518e65	0.383457
$633$	0	0
$634$	1.02917e65	0.145677
$635$	−1.12844e66	−1.53920
$636$	0	0
$637$	−8.40952e65	−1.06536
$638$	−1.40068e65	−0.171022
$639$	0	0
$640$	7.00513e65	0.794670
$641$	1.65837e65	0.181350	0.0906752	−	0.995881i	$-0.471097\pi$
$641$	1.65837e65	0.181350	0.0906752	+	0.995881i	$0.471097\pi$
$642$	0	0
$643$	−1.22213e66	−1.24211	−0.621053	−	0.783768i	$-0.713295\pi$
$643$	−1.22213e66	−1.24211	−0.621053	+	0.783768i	$0.713295\pi$
$644$	−1.22692e65	−0.120226
$645$	0	0
$646$	−4.12346e64	−0.0375663
$647$	9.62351e65	0.845440	0.422720	−	0.906260i	$-0.361075\pi$
$647$	9.62351e65	0.845440	0.422720	+	0.906260i	$0.361075\pi$
$648$	0	0
$649$	9.84237e64	0.0804173
$650$	3.80419e65	0.299777
$651$	0	0
$652$	6.63024e65	0.486084
$653$	−3.91841e65	−0.277109	−0.138554	−	0.990355i	$-0.544246\pi$
$653$	−3.91841e65	−0.277109	−0.138554	+	0.990355i	$0.544246\pi$
$654$	0	0
$655$	2.69183e66	1.77165
$656$	5.23427e65	0.332365
$657$	0	0
$658$	1.12918e65	0.0667506
$659$	−2.16961e66	−1.23758	−0.618792	−	0.785555i	$-0.712378\pi$
$659$	−2.16961e66	−1.23758	−0.618792	+	0.785555i	$0.712378\pi$
$660$	0	0
$661$	−9.87453e65	−0.524544	−0.262272	−	0.964994i	$-0.584472\pi$
$661$	−9.87453e65	−0.524544	−0.262272	+	0.964994i	$0.584472\pi$
$662$	−2.36654e64	−0.0121325
$663$	0	0
$664$	−1.51800e65	−0.0724975
$665$	5.24665e65	0.241865
$666$	0	0
$667$	−7.71034e65	−0.331220
$668$	−1.36925e66	−0.567851
$669$	0	0
$670$	8.27556e64	0.0319919
$671$	−9.39857e65	−0.350818
$672$	0	0
$673$	−5.18176e66	−1.80353	−0.901765	−	0.432227i	$-0.857728\pi$
$673$	−5.18176e66	−1.80353	−0.901765	+	0.432227i	$0.857728\pi$
$674$	−1.85161e65	−0.0622359
$675$	0	0
$676$	−3.94685e66	−1.23738
$677$	−5.62905e66	−1.70452	−0.852259	−	0.523120i	$-0.824768\pi$
$677$	−5.62905e66	−1.70452	−0.852259	+	0.523120i	$0.824768\pi$
$678$	0	0
$679$	−8.48559e65	−0.239741
$680$	−1.54037e66	−0.420402
$681$	0	0
$682$	−7.49010e65	−0.190790
$683$	2.17309e66	0.534800	0.267400	−	0.963586i	$-0.413835\pi$
$683$	2.17309e66	0.534800	0.267400	+	0.963586i	$0.413835\pi$
$684$	0	0
$685$	8.46798e66	1.94559
$686$	5.41553e65	0.120233
$687$	0	0
$688$	−9.26539e65	−0.192104
$689$	5.63168e66	1.12846
$690$	0	0
$691$	3.80507e66	0.712244	0.356122	−	0.934439i	$-0.384099\pi$
$691$	3.80507e66	0.712244	0.356122	+	0.934439i	$0.384099\pi$
$692$	−1.02927e67	−1.86224
$693$	0	0
$694$	1.02216e66	0.172811
$695$	1.34230e67	2.19384
$696$	0	0
$697$	−2.34282e66	−0.357906
$698$	1.10421e66	0.163098
$699$	0	0
$700$	5.87500e66	0.811343
$701$	−4.48575e66	−0.599048	−0.299524	−	0.954089i	$-0.596828\pi$
$701$	−4.48575e66	−0.599048	−0.299524	+	0.954089i	$0.596828\pi$
$702$	0	0
$703$	−2.26082e66	−0.282368
$704$	6.68321e66	0.807286
$705$	0	0
$706$	−7.70965e64	−0.00871212
$707$	−1.99872e66	−0.218472
$708$	0	0
$709$	−1.23589e67	−1.26414	−0.632068	−	0.774913i	$-0.717794\pi$
$709$	−1.23589e67	−1.26414	−0.632068	+	0.774913i	$0.717794\pi$
$710$	−2.13818e66	−0.211579
$711$	0	0
$712$	−1.26235e66	−0.116923
$713$	−4.12310e66	−0.369504
$714$	0	0
$715$	2.55697e67	2.14552
$716$	4.98915e66	0.405108
$717$	0	0
$718$	−3.23290e66	−0.245848
$719$	5.05205e66	0.371825	0.185913	−	0.982566i	$-0.440476\pi$
$719$	5.05205e66	0.371825	0.185913	+	0.982566i	$0.440476\pi$
$720$	0	0
$721$	−1.24860e67	−0.860884
$722$	−1.79865e66	−0.120039
$723$	0	0
$724$	−8.57124e66	−0.536028
$725$	3.69202e67	2.23522
$726$	0	0
$727$	2.10795e67	1.19619	0.598097	−	0.801424i	$-0.295924\pi$
$727$	2.10795e67	1.19619	0.598097	+	0.801424i	$0.295924\pi$
$728$	3.81651e66	0.209690
$729$	0	0
$730$	−2.35563e66	−0.121344
$731$	4.14712e66	0.206866
$732$	0	0
$733$	2.34941e67	1.09905	0.549523	−	0.835478i	$-0.314809\pi$
$733$	2.34941e67	1.09905	0.549523	+	0.835478i	$0.314809\pi$
$734$	−1.88816e65	−0.00855425
$735$	0	0
$736$	−2.03934e66	−0.0866685
$737$	3.36352e66	0.138455
$738$	0	0
$739$	−8.69448e66	−0.335814	−0.167907	−	0.985803i	$-0.553701\pi$
$739$	−8.69448e66	−0.335814	−0.167907	+	0.985803i	$0.553701\pi$
$740$	−4.18657e67	−1.56644
$741$	0	0
$742$	−1.50439e66	−0.0528285
$743$	−1.83903e67	−0.625679	−0.312840	−	0.949806i	$-0.601280\pi$
$743$	−1.83903e67	−0.625679	−0.312840	+	0.949806i	$0.601280\pi$
$744$	0	0
$745$	4.25094e66	0.135773
$746$	−3.74217e66	−0.115814
$747$	0	0
$748$	−3.10350e67	−0.901911
$749$	7.83710e66	0.220715
$750$	0	0
$751$	−2.92872e67	−0.774709	−0.387355	−	0.921931i	$-0.626611\pi$
$751$	−2.92872e67	−0.774709	−0.387355	+	0.921931i	$0.626611\pi$
$752$	−3.51277e67	−0.900597
$753$	0	0
$754$	1.18892e67	0.286369
$755$	1.01954e66	0.0238040
$756$	0	0
$757$	−3.60671e67	−0.791330	−0.395665	−	0.918395i	$-0.629486\pi$
$757$	−3.60671e67	−0.791330	−0.395665	+	0.918395i	$0.629486\pi$
$758$	9.74245e66	0.207225
$759$	0	0
$760$	5.79727e66	0.115906
$761$	−6.36047e67	−1.23296	−0.616481	−	0.787370i	$-0.711442\pi$
$761$	−6.36047e67	−1.23296	−0.616481	+	0.787370i	$0.711442\pi$
$762$	0	0
$763$	2.29118e67	0.417574
$764$	−4.28678e67	−0.757595
$765$	0	0
$766$	−6.01697e66	−0.100000
$767$	−8.35437e66	−0.134655
$768$	0	0
$769$	−1.58030e67	−0.239591	−0.119795	−	0.992799i	$-0.538224\pi$
$769$	−1.58030e67	−0.239591	−0.119795	+	0.992799i	$0.538224\pi$
$770$	−6.83041e66	−0.100442
$771$	0	0
$772$	−6.57793e67	−0.910087
$773$	1.20430e68	1.61628	0.808142	−	0.588988i	$-0.200474\pi$
$773$	1.20430e68	1.61628	0.808142	+	0.588988i	$0.200474\pi$
$774$	0	0
$775$	1.97430e68	2.49358
$776$	−9.37613e66	−0.114888
$777$	0	0
$778$	−7.97864e66	−0.0920255
$779$	8.81736e66	0.0986752
$780$	0	0
$781$	−8.69040e67	−0.915674
$782$	2.95503e66	0.0302137
$783$	0	0
$784$	−6.98842e67	−0.672901
$785$	6.03186e67	0.563656
$786$	0	0
$787$	−1.72836e68	−1.52134	−0.760671	−	0.649137i	$-0.775130\pi$
$787$	−1.72836e68	−1.52134	−0.760671	+	0.649137i	$0.775130\pi$
$788$	−1.05369e68	−0.900219
$789$	0	0
$790$	3.82088e67	0.307558
$791$	1.21744e67	0.0951261
$792$	0	0
$793$	7.97766e67	0.587429
$794$	−2.97966e67	−0.213003
$795$	0	0
$796$	2.63727e68	1.77704
$797$	5.17743e67	0.338722	0.169361	−	0.985554i	$-0.445830\pi$
$797$	5.17743e67	0.338722	0.169361	+	0.985554i	$0.445830\pi$
$798$	0	0
$799$	1.57229e68	0.969803
$800$	9.76519e67	0.584879
$801$	0	0
$802$	−7.83502e64	−0.000442530 0
$803$	−9.57423e67	−0.525156
$804$	0	0
$805$	−3.75995e67	−0.194527
$806$	6.35773e67	0.319469
$807$	0	0
$808$	−2.20848e67	−0.104695
$809$	1.34819e68	0.620812	0.310406	−	0.950604i	$-0.399535\pi$
$809$	1.34819e68	0.620812	0.310406	+	0.950604i	$0.399535\pi$
$810$	0	0
$811$	−1.29768e68	−0.563869	−0.281934	−	0.959434i	$-0.590976\pi$
$811$	−1.29768e68	−0.563869	−0.281934	+	0.959434i	$0.590976\pi$
$812$	1.83611e68	0.775053
$813$	0	0
$814$	2.94328e67	0.117262
$815$	2.03186e68	0.786485
$816$	0	0
$817$	−1.56080e67	−0.0570332
$818$	2.32374e67	0.0825059
$819$	0	0
$820$	1.63279e68	0.547401
$821$	3.05518e68	0.995342	0.497671	−	0.867366i	$-0.334189\pi$
$821$	3.05518e68	0.995342	0.497671	+	0.867366i	$0.334189\pi$
$822$	0	0
$823$	−3.54128e68	−1.08959	−0.544796	−	0.838568i	$-0.683393\pi$
$823$	−3.54128e68	−1.08959	−0.544796	+	0.838568i	$0.683393\pi$
$824$	−1.37964e68	−0.412549
$825$	0	0
$826$	2.23170e66	0.00630383
$827$	−5.88899e68	−1.61682	−0.808410	−	0.588620i	$-0.799672\pi$
$827$	−5.88899e68	−1.61682	−0.808410	+	0.588620i	$0.799672\pi$
$828$	0	0
$829$	7.14204e68	1.85264	0.926319	−	0.376740i	$-0.122955\pi$
$829$	7.14204e68	1.85264	0.926319	+	0.376740i	$0.122955\pi$
$830$	−2.30604e67	−0.0581477
$831$	0	0
$832$	−5.67282e68	−1.35176
$833$	3.12797e68	0.724610
$834$	0	0
$835$	−4.19610e68	−0.918785
$836$	1.16802e68	0.248658
$837$	0	0
$838$	−1.07657e68	−0.216675
$839$	−4.08251e68	−0.798953	−0.399477	−	0.916743i	$-0.630808\pi$
$839$	−4.08251e68	−0.798953	−0.399477	+	0.916743i	$0.630808\pi$
$840$	0	0
$841$	6.13474e68	1.13525
$842$	−5.86231e67	−0.105496
$843$	0	0
$844$	−1.73650e68	−0.295548
$845$	−1.20953e69	−2.00209
$846$	0	0
$847$	6.69846e67	0.104885
$848$	4.68000e68	0.712760
$849$	0	0
$850$	−1.41499e68	−0.203896
$851$	1.62019e68	0.227102
$852$	0	0
$853$	6.69695e68	0.888331	0.444166	−	0.895945i	$-0.353500\pi$
$853$	6.69695e68	0.888331	0.444166	+	0.895945i	$0.353500\pi$
$854$	−2.13107e67	−0.0275003
$855$	0	0
$856$	8.65958e67	0.105770
$857$	−1.01115e69	−1.20162	−0.600809	−	0.799393i	$-0.705155\pi$
$857$	−1.01115e69	−1.20162	−0.600809	+	0.799393i	$0.705155\pi$
$858$	0	0
$859$	−4.13647e68	−0.465361	−0.232681	−	0.972553i	$-0.574750\pi$
$859$	−4.13647e68	−0.465361	−0.232681	+	0.972553i	$0.574750\pi$
$860$	−2.89027e68	−0.316392
$861$	0	0
$862$	−6.29207e66	−0.00652188
$863$	−6.85332e68	−0.691270	−0.345635	−	0.938369i	$-0.612336\pi$
$863$	−6.85332e68	−0.691270	−0.345635	+	0.938369i	$0.612336\pi$
$864$	0	0
$865$	−3.15424e69	−3.01312
$866$	−4.00847e67	−0.0372656
$867$	0	0
$868$	9.81856e68	0.864638
$869$	1.55296e69	1.33105
$870$	0	0
$871$	−2.85501e68	−0.231836
$872$	2.53164e68	0.200108
$873$	0	0
$874$	−1.11215e67	−0.00832997
$875$	6.23418e68	0.454559
$876$	0	0
$877$	6.43840e68	0.444925	0.222463	−	0.974941i	$-0.428590\pi$
$877$	6.43840e68	0.444925	0.222463	+	0.974941i	$0.428590\pi$
$878$	5.43059e67	0.0365364
$879$	0	0
$880$	2.12487e69	1.35516
$881$	−8.86127e68	−0.550253	−0.275126	−	0.961408i	$-0.588720\pi$
$881$	−8.86127e68	−0.550253	−0.275126	+	0.961408i	$0.588720\pi$
$882$	0	0
$883$	4.16643e68	0.245294	0.122647	−	0.992450i	$-0.460862\pi$
$883$	4.16643e68	0.245294	0.122647	+	0.992450i	$0.460862\pi$
$884$	2.63430e69	1.51021
$885$	0	0
$886$	6.86670e67	0.0373298
$887$	−2.94393e69	−1.55856	−0.779278	−	0.626679i	$-0.784414\pi$
$887$	−2.94393e69	−1.55856	−0.779278	+	0.626679i	$0.784414\pi$
$888$	0	0
$889$	−1.03994e69	−0.522177
$890$	−1.91767e68	−0.0937797
$891$	0	0
$892$	1.98028e68	0.0918654
$893$	−5.91742e68	−0.267376
$894$	0	0
$895$	1.52894e69	0.655466
$896$	6.45578e68	0.269594
$897$	0	0
$898$	−5.30901e68	−0.210387
$899$	6.17026e69	2.38205
$900$	0	0
$901$	−2.09473e69	−0.767532
$902$	−1.14790e68	−0.0409779
$903$	0	0
$904$	1.34521e68	0.0455859
$905$	−2.62669e69	−0.867295
$906$	0	0
$907$	3.36233e69	1.05407	0.527034	−	0.849844i	$-0.323304\pi$
$907$	3.36233e69	1.05407	0.527034	+	0.849844i	$0.323304\pi$
$908$	4.68278e69	1.43049
$909$	0	0
$910$	5.79777e68	0.168185
$911$	−4.29823e69	−1.21509	−0.607544	−	0.794286i	$-0.707845\pi$
$911$	−4.29823e69	−1.21509	−0.607544	+	0.794286i	$0.707845\pi$
$912$	0	0
$913$	−9.37269e68	−0.251652
$914$	−1.49195e67	−0.00390409
$915$	0	0
$916$	6.43603e68	0.159983
$917$	2.48074e69	0.601037
$918$	0	0
$919$	5.89124e69	1.35610	0.678050	−	0.735015i	$-0.262825\pi$
$919$	5.89124e69	1.35610	0.678050	+	0.735015i	$0.262825\pi$
$920$	−4.15455e68	−0.0932202
$921$	0	0
$922$	9.77877e67	0.0208501
$923$	7.37656e69	1.53325
$924$	0	0
$925$	−7.75813e69	−1.53259
$926$	1.06152e69	0.204442
$927$	0	0
$928$	3.05190e69	0.558718
$929$	3.81127e69	0.680301	0.340150	−	0.940371i	$-0.389522\pi$
$929$	3.81127e69	0.680301	0.340150	+	0.940371i	$0.389522\pi$
$930$	0	0
$931$	−1.17723e69	−0.199776
$932$	−9.50754e69	−1.57324
$933$	0	0
$934$	4.50729e68	0.0709192
$935$	−9.51078e69	−1.45930
$936$	0	0
$937$	−3.18868e69	−0.465298	−0.232649	−	0.972561i	$-0.574739\pi$
$937$	−3.18868e69	−0.465298	−0.232649	+	0.972561i	$0.574739\pi$
$938$	7.62658e67	0.0108533
$939$	0	0
$940$	−1.09578e70	−1.48327
$941$	−7.20176e69	−0.950785	−0.475393	−	0.879774i	$-0.657694\pi$
$941$	−7.20176e69	−0.950785	−0.475393	+	0.879774i	$0.657694\pi$
$942$	0	0
$943$	−6.31886e68	−0.0793623
$944$	−6.94259e68	−0.0850510
$945$	0	0
$946$	2.03194e68	0.0236848
$947$	−7.19607e69	−0.818222	−0.409111	−	0.912485i	$-0.634161\pi$
$947$	−7.19607e69	−0.818222	−0.409111	+	0.912485i	$0.634161\pi$
$948$	0	0
$949$	8.12676e69	0.879350
$950$	5.32540e68	0.0562144
$951$	0	0
$952$	−1.41957e69	−0.142623
$953$	−1.03533e70	−1.01483	−0.507417	−	0.861700i	$-0.669400\pi$
$953$	−1.03533e70	−1.01483	−0.507417	+	0.861700i	$0.669400\pi$
$954$	0	0
$955$	−1.31370e70	−1.22579
$956$	1.51099e70	1.37563
$957$	0	0
$958$	1.45384e69	0.126017
$959$	7.80391e69	0.660047
$960$	0	0
$961$	2.05789e70	1.65738
$962$	−2.49830e69	−0.196350
$963$	0	0
$964$	6.67681e69	0.499757
$965$	−2.01583e70	−1.47252
$966$	0	0
$967$	−1.88655e70	−1.31264	−0.656321	−	0.754482i	$-0.727888\pi$
$967$	−1.88655e70	−1.31264	−0.656321	+	0.754482i	$0.727888\pi$
$968$	7.40145e68	0.0502627
$969$	0	0
$970$	−1.42436e69	−0.0921474
$971$	1.54065e70	0.972862	0.486431	−	0.873719i	$-0.338299\pi$
$971$	1.54065e70	0.972862	0.486431	+	0.873719i	$0.338299\pi$
$972$	0	0
$973$	1.23703e70	0.744268
$974$	3.70256e69	0.217453
$975$	0	0
$976$	6.62954e69	0.371033
$977$	1.28077e70	0.699760	0.349880	−	0.936795i	$-0.386222\pi$
$977$	1.28077e70	0.699760	0.349880	+	0.936795i	$0.386222\pi$
$978$	0	0
$979$	−7.79418e69	−0.405861
$980$	−2.17999e70	−1.10826
$981$	0	0
$982$	−1.91177e69	−0.0926438
$983$	−1.22658e70	−0.580349	−0.290174	−	0.956974i	$-0.593713\pi$
$983$	−1.22658e70	−0.580349	−0.290174	+	0.956974i	$0.593713\pi$
$984$	0	0
$985$	−3.22908e70	−1.45656
$986$	−4.42225e69	−0.194776
$987$	0	0
$988$	−9.91435e69	−0.416367
$989$	1.11853e69	0.0458705
$990$	0	0
$991$	2.78865e70	1.09059	0.545296	−	0.838244i	$-0.316417\pi$
$991$	2.78865e70	1.09059	0.545296	+	0.838244i	$0.316417\pi$
$992$	1.63200e70	0.623298
$993$	0	0
$994$	−1.97050e69	−0.0717787
$995$	8.08202e70	2.87526
$996$	0	0
$997$	2.05189e70	0.696336	0.348168	−	0.937432i	$-0.386804\pi$
$997$	2.05189e70	0.696336	0.348168	+	0.937432i	$0.386804\pi$
$998$	−4.55812e69	−0.151084
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.48.a.c.1.3		4
3.2	odd	2		1.48.a.a.1.2	✓	4
12.11	even	2		16.48.a.d.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.48.a.a.1.2	✓	4	3.2	odd	2
9.48.a.c.1.3		4	1.1	even	1	trivial
16.48.a.d.1.1		4	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 48 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+1.54692e6 q^{2} -1.38345e14 q^{4} -4.23962e16 q^{5} -3.90714e19 q^{7} -4.31719e20 q^{8} +O(q^{10})\)	\(q+1.54692e6 q^{2} -1.38345e14 q^{4} -4.23962e16 q^{5} -3.90714e19 q^{7} -4.31719e20 q^{8} -6.55837e22 q^{10} -2.66558e24 q^{11} +2.26259e26 q^{13} -6.04405e25 q^{14} +1.88024e28 q^{16} -8.41583e28 q^{17} +3.16735e29 q^{19} +5.86528e30 q^{20} -4.12345e30 q^{22} -2.26985e31 q^{23} +1.08689e33 q^{25} +3.50006e32 q^{26} +5.40532e33 q^{28} +3.39685e34 q^{29} +1.81646e35 q^{31} +8.98449e34 q^{32} -1.30186e35 q^{34} +1.65648e36 q^{35} -7.13789e36 q^{37} +4.89965e35 q^{38} +1.83032e37 q^{40} +2.78383e37 q^{41} -4.92777e37 q^{43} +3.68769e38 q^{44} -3.51128e37 q^{46} -1.86825e39 q^{47} -3.71676e39 q^{49} +1.68134e39 q^{50} -3.13017e40 q^{52} +2.48904e40 q^{53} +1.13011e41 q^{55} +1.68679e40 q^{56} +5.25467e40 q^{58} -3.69239e40 q^{59} +3.52589e41 q^{61} +2.80993e41 q^{62} -2.50722e42 q^{64} -9.59253e42 q^{65} -1.26183e42 q^{67} +1.16428e43 q^{68} +2.56245e42 q^{70} +3.26023e43 q^{71} +3.59179e43 q^{73} -1.10418e43 q^{74} -4.38186e43 q^{76} +1.04148e44 q^{77} -5.82596e44 q^{79} -7.97151e44 q^{80} +4.30637e43 q^{82} +3.51619e44 q^{83} +3.56799e45 q^{85} -7.62288e43 q^{86} +1.15078e45 q^{88} +2.92401e45 q^{89} -8.84027e45 q^{91} +3.14021e45 q^{92} -2.89005e45 q^{94} -1.34284e46 q^{95} +2.17182e46 q^{97} -5.74955e45 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5785560 q^{2} + 404807499161152 q^{4} + 31\!\cdots\!00 q^{5}+ \cdots - 23\!\cdots\!20 q^{8}+O(q^{10}) \) 4 * q - 5785560 * q^2 + 404807499161152 * q^4 + 31114680242272200 * q^5 - 39169218725888423200 * q^7 - 2392716988073784337920 * q^8	\( 4 q - 5785560 q^{2} + 404807499161152 q^{4} + 31\!\cdots\!00 q^{5}+ \cdots + 29\!\cdots\!20 q^{98}+O(q^{100}) \) 4 * q - 5785560 * q^2 + 404807499161152 * q^4 + 31114680242272200 * q^5 - 39169218725888423200 * q^7 - 2392716988073784337920 * q^8 + 161126302562215963534800 * q^10 + 1902165515717740404742512 * q^11 + 126959149195199610466858520 * q^13 - 3491363489769461659480835904 * q^14 + 124527684040554167211817897984 * q^16 - 210426285758836687099688769480 * q^17 - 1059119811802437301721159140240 * q^19 + 15129514318106701401937782249600 * q^20 - 79668451994083088127806382590880 * q^22 - 137531418344493639994288859179680 * q^23 + 1009909900344396506188154274977500 * q^25 - 2282338781897562472343866220387088 * q^26 - 36222097928665071743339635065479680 * q^28 + 22743132490172744184500850941726760 * q^29 + 75786540814706434901630981303934848 * q^31 - 1184674767018086471839527432906178560 * q^32 - 1261659118578465318749852382715620816 * q^34 + 1313148822925052387484546800067979200 * q^35 - 11291457045120157869429951769632191560 * q^37 - 29667542464851305273548614410680536480 * q^38 + 70753686685508718175919216681780352000 * q^40 - 130658126291089294119301677048020391528 * q^41 - 445357287738427943170332944488133090800 * q^43 + 1525898906718917337200010663037616115456 * q^44 + 1226146172325422687186041586267533291968 * q^46 - 2031912465958423919194866366997063590720 * q^47 + 9153745744156628626499502447643951451172 * q^49 + 19226200465513908889722489088356697935000 * q^50 - 55272350705889116147839999778699925596800 * q^52 - 29171719896619533806321793123448457437560 * q^53 + 192172580604633896452606078657416872901600 * q^55 - 276101696826518177934513744689489393111040 * q^56 - 732323136683092912071778597620095648941680 * q^58 - 478242858216320686410790860443879577596880 * q^59 + 626683213833907852009669690320782900857688 * q^61 + 6870459615610782098804391369236375065946880 * q^62 + 5525430481808418303700543890989262651523072 * q^64 - 12996735432890074297558542478104126872331600 * q^65 + 18701411419127220668869505853739529194216880 * q^67 + 27469024204738931095482995064729717598496640 * q^68 - 97207317904230285933067401805385458355395200 * q^70 - 22196594617762006008028198712153461686540768 * q^71 + 104911201720506650033573412943840886878191080 * q^73 - 187734656069700274526204928907842421165646544 * q^74 + 351694386032713991264839561028061045130100480 * q^76 + 263490744376507692433815778071300370399209600 * q^77 - 1327995310109394234162785254414226288730352960 * q^79 + 948349663264469859337474495994045561022259200 * q^80 + 3821513842864797430908620724480935919685390320 * q^82 + 1439130627532364606968733068855111784504073360 * q^83 - 1001895286410663502447652611446390227458237200 * q^85 - 9578145533777866709022895861637903827077656928 * q^86 - 15478856320702836436797993507832298416714229760 * q^88 + 7960590522674945421108320896849737731421281880 * q^89 + 5325194479227227497182497798631911205603381568 * q^91 - 13058297350229360275908546071900174502239009280 * q^92 + 3475860200879106349192555645858186353201354624 * q^94 - 75421152415106939771624998522249518123547668000 * q^95 + 95066248961258904822565865801364599382905757320 * q^97 + 296344663186266398350742083591017164797938217320 * q^98

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