LMFDB - Embedded newform 9.68.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,68,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, 68, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 68);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 68 $
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:	$255.861316737$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 80\!\cdots\!00 $ x^6 - 3x^5 - 18265801580559590892x^4 - 7523970115455178716247853536x^3 + 78501261395396048023472482629898922880x^2 + 29605717530431234535889524616359650095893868800*x - 80637078962263575025979556823830075867035962985404800000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{46}\cdot 3^{29}\cdot 5^{6}\cdot 7^{2}\cdot 11^{2}\cdot 13\cdot 17 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$9.72648e8$ 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)

$f(q)$	$=$	$q+3.54666e9 q^{2} -1.34995e20 q^{4} -1.66367e23 q^{5} -1.26991e28 q^{7} -1.00218e30 q^{8} +O(q^{10})$	\(q+3.54666e9 q^{2} -1.34995e20 q^{4} -1.66367e23 q^{5} -1.26991e28 q^{7} -1.00218e30 q^{8} -5.90048e32 q^{10} -3.05496e34 q^{11} -2.14767e37 q^{13} -4.50395e37 q^{14} +1.63674e40 q^{16} -1.02290e41 q^{17} +2.26035e42 q^{19} +2.24588e43 q^{20} -1.08349e44 q^{22} +7.58105e45 q^{23} -4.00846e46 q^{25} -7.61705e46 q^{26} +1.71432e48 q^{28} +4.33411e48 q^{29} -3.83579e49 q^{31} +2.05945e50 q^{32} -3.62787e50 q^{34} +2.11272e51 q^{35} +3.81245e52 q^{37} +8.01669e51 q^{38} +1.66729e53 q^{40} +6.60130e53 q^{41} -5.55298e54 q^{43} +4.12405e54 q^{44} +2.68874e55 q^{46} +2.64005e55 q^{47} -2.57110e56 q^{49} -1.42167e56 q^{50} +2.89925e57 q^{52} +1.96065e57 q^{53} +5.08245e57 q^{55} +1.27268e58 q^{56} +1.53716e58 q^{58} +1.16514e59 q^{59} +1.04181e60 q^{61} -1.36043e59 q^{62} -1.68498e60 q^{64} +3.57302e60 q^{65} -5.71388e60 q^{67} +1.38086e61 q^{68} +7.49308e60 q^{70} +3.93949e61 q^{71} +2.89309e62 q^{73} +1.35215e62 q^{74} -3.05136e62 q^{76} +3.87953e62 q^{77} +3.53480e63 q^{79} -2.72299e63 q^{80} +2.34126e63 q^{82} -1.40445e64 q^{83} +1.70176e64 q^{85} -1.96945e64 q^{86} +3.06161e64 q^{88} -3.15803e65 q^{89} +2.72735e65 q^{91} -1.02341e66 q^{92} +9.36338e64 q^{94} -3.76047e65 q^{95} +7.03827e66 q^{97} -9.11883e65 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 13735355166 q^{2} + 46\!\cdots\!52 q^{4}+ \cdots - 17\!\cdots\!92 q^{8}+O(q^{10}) $ 6 * q - 13735355166 * q^2 + 461137328518259214852 * q^4 + 180289059197853505182300 * q^5 - 28067678610591277820235434208 * q^7 - 174428717775449559766832729592 * q^8	$ 6 q - 13735355166 q^{2} + 46\!\cdots\!52 q^{4}+ \cdots - 26\!\cdots\!74 q^{98}+O(q^{100}) $ 6 * q - 13735355166 * q^2 + 461137328518259214852 * q^4 + 180289059197853505182300 * q^5 - 28067678610591277820235434208 * q^7 - 174428717775449559766832729592 * q^8 + 7304190735814693245550459325330100 * q^10 - 1253554983811830341203783945028424 * q^11 - 1032427018834954393824819765456935964 * q^13 + 447380929503565966859381489320173353952 * q^14 - 10777060270558286469269005744606427140080 * q^16 + 22303705201707705421583405421371675716596 * q^17 - 6709513794502265961382038704145157001302152 * q^19 - 46181758835098395119891481090112367056690200 * q^20 + 1406045276258114363650986812146594678084267368 * q^22 - 12239031860950699209155226229708548540686529264 * q^23 + 124984998689116279435075553443500491502742646250 * q^25 - 147728325197899719596176944836466085493373208692 * q^26 - 14712260029031223829746951621139067346976206433344 * q^28 + 18873418589468921842047146695821329699174822684364 * q^29 - 224044794880051525600176726995317503621741761218704 * q^31 + 647694914760137169573449462765066287313897316284448 * q^32 + 693429763914603914127075176718731888866377974041404 * q^34 + 6444089679967517736201498858201618112886103095496000 * q^35 + 27414420131407696449125644786001907623181109991614452 * q^37 - 12552113658955455007053647987482106208988678055446104 * q^38 + 1194094866560066539991934179669093556164670510853198800 * q^40 - 2660548042321177320771169314506367536908331651920652796 * q^41 - 1105961611152903745004520895209354208863582663043308600 * q^43 + 34817398461777279630054811602795668745922518275227441104 * q^44 - 45061363378216725453974438646463842380148485881039366224 * q^46 - 58003762634770246900699775563009450632230835045286599360 * q^47 + 985569916983315185097203394977137449656339808292459655670 * q^49 - 4791887184864825461869475209769884139573386495444648751250 * q^50 - 772447381048143948901083488309399868612217101599766652776 * q^52 + 13674721974185597882029982508413224730588130474226494780636 * q^53 - 51238754618576674303553172437218137404754442562163094366800 * q^55 + 53382539406310631647595973723370754348378361469563798407040 * q^56 - 27334542479326918025552783071893481077859694969007500722812 * q^58 - 432173245375539353201786532564121354794334705181731449983112 * q^59 - 301681480554705175984062079070767927549030780778630557968540 * q^61 - 1319649268553974306953641963470020465251839304368009232497584 * q^62 - 3306273837825060723687391413275118884560206796975317864472512 * q^64 - 9144509139500418095807614952796559412618850636965585264371800 * q^65 - 3659535002024051270225014883853538282826668950514180780948296 * q^67 - 62841982068874697565842994801948402899655187355391437927918088 * q^68 - 17848574477080955030302460292958517135297977483696841850120000 * q^70 - 252155511033891103624460277167902994429076906738358010146768272 * q^71 + 166779610709719144717689715238124518472612391435088881765181724 * q^73 - 1006325717889854285502211107525082701977251477599580185617852868 * q^74 - 517707814526076465205777997582680722788148819042185613752993712 * q^76 - 352534620603367398775736559627568751080150267776772663929922944 * q^77 - 4778664108337215079572742262604077882794836667809906425462078640 * q^79 - 22035563788144287210408960904426824039627000323030751017638600800 * q^80 + 64371214133499796977109337023506169313379178165909274002938946284 * q^82 - 36651193288697208236374412380857358965233031511415957283935392632 * q^83 + 251284152586026236911243321213724923566970783996009477585132585800 * q^85 - 109459654412686722699057856511584566836933916033705406023221718504 * q^86 + 294858564158317243888419031127963434466163056120837408554388440992 * q^88 + 24716082341461782003245292062820103472910477446347105193539129092 * q^89 + 1637449943486433383394466120659741425501433624430401587862051946176 * q^91 - 4192506910423434290693315227336082767370233979633693670230439475872 * q^92 + 10776123537142027626725320636495971787147507990566237758042792171712 * q^94 - 8892438758299572900094061329818154779583617585762349202154337045200 * q^95 + 3864203546244162410999773872217768224094576263762936458169046609164 * q^97 - 26255683859954817683324025976879398726779583524717348419525625709774 * 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 $

$2$	3.54666e9	0.291954	0.145977	−	0.989288i	$-0.453367\pi$
$2$	3.54666e9	0.291954	0.145977	+	0.989288i	$0.453367\pi$
$3$	0	0
$3$	0	0
$4$	−1.34995e20	−0.914763
$5$	−1.66367e23	−0.639105	−0.319553	−	0.947569i	$-0.603533\pi$
$5$	−1.66367e23	−0.639105	−0.319553	+	0.947569i	$0.603533\pi$
$6$	0	0
$7$	−1.26991e28	−0.620854	−0.310427	−	0.950597i	$-0.600472\pi$
$7$	−1.26991e28	−0.620854	−0.310427	+	0.950597i	$0.600472\pi$
$8$	−1.00218e30	−0.559023
$9$	0	0
$10$	−5.90048e32	−0.186589
$11$	−3.05496e34	−0.396598	−0.198299	−	0.980142i	$-0.563542\pi$
$11$	−3.05496e34	−0.396598	−0.198299	+	0.980142i	$0.563542\pi$
$12$	0	0
$13$	−2.14767e37	−1.03482	−0.517410	−	0.855737i	$-0.673104\pi$
$13$	−2.14767e37	−1.03482	−0.517410	+	0.855737i	$0.673104\pi$
$14$	−4.50395e37	−0.181261
$15$	0	0
$16$	1.63674e40	0.751554
$17$	−1.02290e41	−0.616301	−0.308151	−	0.951338i	$-0.599710\pi$
$17$	−1.02290e41	−0.616301	−0.308151	+	0.951338i	$0.599710\pi$
$18$	0	0
$19$	2.26035e42	0.328042	0.164021	−	0.986457i	$-0.447553\pi$
$19$	2.26035e42	0.328042	0.164021	+	0.986457i	$0.447553\pi$
$20$	2.24588e43	0.584630
$21$	0	0
$22$	−1.08349e44	−0.115789
$23$	7.58105e45	1.82746	0.913728	−	0.406327i	$-0.133190\pi$
$23$	7.58105e45	1.82746	0.913728	+	0.406327i	$0.133190\pi$
$24$	0	0
$25$	−4.00846e46	−0.591545
$26$	−7.61705e46	−0.302120
$27$	0	0
$28$	1.71432e48	0.567934
$29$	4.33411e48	0.443166	0.221583	−	0.975141i	$-0.428878\pi$
$29$	4.33411e48	0.443166	0.221583	+	0.975141i	$0.428878\pi$
$30$	0	0
$31$	−3.83579e49	−0.419989	−0.209995	−	0.977703i	$-0.567345\pi$
$31$	−3.83579e49	−0.419989	−0.209995	+	0.977703i	$0.567345\pi$
$32$	2.05945e50	0.778442
$33$	0	0
$34$	−3.62787e50	−0.179932
$35$	2.11272e51	0.396791
$36$	0	0
$37$	3.81245e52	1.11288	0.556438	−	0.830889i	$-0.312168\pi$
$37$	3.81245e52	1.11288	0.556438	+	0.830889i	$0.312168\pi$
$38$	8.01669e51	0.0957733
$39$	0	0
$40$	1.66729e53	0.357274
$41$	6.60130e53	0.618544	0.309272	−	0.950974i	$-0.399915\pi$
$41$	6.60130e53	0.618544	0.309272	+	0.950974i	$0.399915\pi$
$42$	0	0
$43$	−5.55298e54	−1.05520	−0.527598	−	0.849494i	$-0.676907\pi$
$43$	−5.55298e54	−1.05520	−0.527598	+	0.849494i	$0.676907\pi$
$44$	4.12405e54	0.362793
$45$	0	0
$46$	2.68874e55	0.533533
$47$	2.64005e55	0.254879	0.127440	−	0.991846i	$-0.459324\pi$
$47$	2.64005e55	0.254879	0.127440	+	0.991846i	$0.459324\pi$
$48$	0	0
$49$	−2.57110e56	−0.614541
$50$	−1.42167e56	−0.172704
$51$	0	0
$52$	2.89925e57	0.946616
$53$	1.96065e57	0.338188	0.169094	−	0.985600i	$-0.445916\pi$
$53$	1.96065e57	0.338188	0.169094	+	0.985600i	$0.445916\pi$
$54$	0	0
$55$	5.08245e57	0.253468
$56$	1.27268e58	0.347071
$57$	0	0
$58$	1.53716e58	0.129384
$59$	1.16514e59	0.553139	0.276570	−	0.960994i	$-0.410802\pi$
$59$	1.16514e59	0.553139	0.276570	+	0.960994i	$0.410802\pi$
$60$	0	0
$61$	1.04181e60	1.61898	0.809488	−	0.587137i	$-0.199745\pi$
$61$	1.04181e60	1.61898	0.809488	+	0.587137i	$0.199745\pi$
$62$	−1.36043e59	−0.122618
$63$	0	0
$64$	−1.68498e60	−0.524284
$65$	3.57302e60	0.661359
$66$	0	0
$67$	−5.71388e60	−0.383200	−0.191600	−	0.981473i	$-0.561368\pi$
$67$	−5.71388e60	−0.383200	−0.191600	+	0.981473i	$0.561368\pi$
$68$	1.38086e61	0.563769
$69$	0	0
$70$	7.49308e60	0.115845
$71$	3.93949e61	0.378691	0.189345	−	0.981911i	$-0.439363\pi$
$71$	3.93949e61	0.378691	0.189345	+	0.981911i	$0.439363\pi$
$72$	0	0
$73$	2.89309e62	1.09660	0.548298	−	0.836283i	$-0.315276\pi$
$73$	2.89309e62	1.09660	0.548298	+	0.836283i	$0.315276\pi$
$74$	1.35215e62	0.324909
$75$	0	0
$76$	−3.05136e62	−0.300081
$77$	3.87953e62	0.246230
$78$	0	0
$79$	3.53480e63	0.950292	0.475146	−	0.879907i	$-0.342395\pi$
$79$	3.53480e63	0.950292	0.475146	+	0.879907i	$0.342395\pi$
$80$	−2.72299e63	−0.480322
$81$	0	0
$82$	2.34126e63	0.180587
$83$	−1.40445e64	−0.721754	−0.360877	−	0.932613i	$-0.617523\pi$
$83$	−1.40445e64	−0.721754	−0.360877	+	0.932613i	$0.617523\pi$
$84$	0	0
$85$	1.70176e64	0.393881
$86$	−1.96945e64	−0.308069
$87$	0	0
$88$	3.06161e64	0.221708
$89$	−3.15803e65	−1.56622	−0.783108	−	0.621886i	$-0.786367\pi$
$89$	−3.15803e65	−1.56622	−0.783108	+	0.621886i	$0.786367\pi$
$90$	0	0
$91$	2.72735e65	0.642472
$92$	−1.02341e66	−1.67169
$93$	0	0
$94$	9.36338e64	0.0744131
$95$	−3.76047e65	−0.209653
$96$	0	0
$97$	7.03827e66	1.95260	0.976298	−	0.216429i	$-0.0694410\pi$
$97$	7.03827e66	1.95260	0.976298	+	0.216429i	$0.0694410\pi$
$98$	−9.11883e65	−0.179418
$99$	0	0
$100$	5.41123e66	0.541123
$101$	2.82872e66	0.202686	0.101343	−	0.994852i	$-0.467686\pi$
$101$	2.82872e66	0.202686	0.101343	+	0.994852i	$0.467686\pi$
$102$	0	0
$103$	1.44038e67	0.535095	0.267547	−	0.963545i	$-0.413787\pi$
$103$	1.44038e67	0.535095	0.267547	+	0.963545i	$0.413787\pi$
$104$	2.15234e67	0.578489
$105$	0	0
$106$	6.95376e66	0.0987355
$107$	−1.65663e68	−1.71739	−0.858694	−	0.512488i	$-0.828724\pi$
$107$	−1.65663e68	−1.71739	−0.858694	+	0.512488i	$0.828724\pi$
$108$	0	0
$109$	−1.71048e68	−0.953523	−0.476761	−	0.879033i	$-0.658189\pi$
$109$	−1.71048e68	−0.953523	−0.476761	+	0.879033i	$0.658189\pi$
$110$	1.80257e67	0.0740011
$111$	0	0
$112$	−2.07851e68	−0.466605
$113$	9.98863e68	1.66486	0.832431	−	0.554129i	$-0.186948\pi$
$113$	9.98863e68	1.66486	0.832431	+	0.554129i	$0.186948\pi$
$114$	0	0
$115$	−1.26124e69	−1.16794
$116$	−5.85083e68	−0.405392
$117$	0	0
$118$	4.13234e68	0.161491
$119$	1.29899e69	0.382633
$120$	0	0
$121$	−5.00021e69	−0.842710
$122$	3.69496e69	0.472667
$123$	0	0
$124$	5.17813e69	0.384191
$125$	1.79422e70	1.01716
$126$	0	0
$127$	6.32448e69	0.210669	0.105334	−	0.994437i	$-0.466409\pi$
$127$	6.32448e69	0.210669	0.105334	+	0.994437i	$0.466409\pi$
$128$	−3.63681e70	−0.931509
$129$	0	0
$130$	1.26723e70	0.193087
$131$	−7.81112e70	−0.920714	−0.460357	−	0.887734i	$-0.652279\pi$
$131$	−7.81112e70	−0.920714	−0.460357	+	0.887734i	$0.652279\pi$
$132$	0	0
$133$	−2.87044e70	−0.203666
$134$	−2.02652e70	−0.111877
$135$	0	0
$136$	1.02512e71	0.344527
$137$	−5.13243e71	−1.34954	−0.674768	−	0.738030i	$-0.735756\pi$
$137$	−5.13243e71	−1.34954	−0.674768	+	0.738030i	$0.735756\pi$
$138$	0	0
$139$	1.33977e70	0.0216787	0.0108394	−	0.999941i	$-0.496550\pi$
$139$	1.33977e70	0.0216787	0.0108394	+	0.999941i	$0.496550\pi$
$140$	−2.85206e71	−0.362969
$141$	0	0
$142$	1.39720e71	0.110560
$143$	6.56105e71	0.410408
$144$	0	0
$145$	−7.21053e71	−0.283230
$146$	1.02608e72	0.320156
$147$	0	0
$148$	−5.14663e72	−1.01802
$149$	7.90185e72	1.24735	0.623676	−	0.781683i	$-0.285638\pi$
$149$	7.90185e72	1.24735	0.623676	+	0.781683i	$0.285638\pi$
$150$	0	0
$151$	−1.21590e73	−1.22792	−0.613959	−	0.789338i	$-0.710424\pi$
$151$	−1.21590e73	−1.22792	−0.613959	+	0.789338i	$0.710424\pi$
$152$	−2.26527e72	−0.183383
$153$	0	0
$154$	1.37594e72	0.0718878
$155$	6.38150e72	0.268417
$156$	0	0
$157$	2.23950e73	0.613074	0.306537	−	0.951859i	$-0.400830\pi$
$157$	2.23950e73	0.613074	0.306537	+	0.951859i	$0.400830\pi$
$158$	1.25367e73	0.277442
$159$	0	0
$160$	−3.42624e73	−0.497506
$161$	−9.62727e73	−1.13458
$162$	0	0
$163$	1.46906e74	1.14487	0.572434	−	0.819951i	$-0.305999\pi$
$163$	1.46906e74	1.14487	0.572434	+	0.819951i	$0.305999\pi$
$164$	−8.91144e73	−0.565821
$165$	0	0
$166$	−4.98110e73	−0.210719
$167$	−6.76089e73	−0.233885	−0.116943	−	0.993139i	$-0.537309\pi$
$167$	−6.76089e73	−0.233885	−0.116943	+	0.993139i	$0.537309\pi$
$168$	0	0
$169$	3.05190e73	0.0708542
$170$	6.03558e73	0.114995
$171$	0	0
$172$	7.49626e74	0.965254
$173$	1.95747e74	0.207563	0.103782	−	0.994600i	$-0.466906\pi$
$173$	1.95747e74	0.207563	0.103782	+	0.994600i	$0.466906\pi$
$174$	0	0
$175$	5.09039e74	0.367263
$176$	−5.00018e74	−0.298065
$177$	0	0
$178$	−1.12005e75	−0.457263
$179$	5.44647e75	1.84306	0.921528	−	0.388311i	$-0.126941\pi$
$179$	5.44647e75	1.84306	0.921528	+	0.388311i	$0.126941\pi$
$180$	0	0
$181$	−1.80801e74	−0.0421666	−0.0210833	−	0.999778i	$-0.506712\pi$
$181$	−1.80801e74	−0.0421666	−0.0210833	+	0.999778i	$0.506712\pi$
$182$	9.67299e74	0.187572
$183$	0	0
$184$	−7.59755e75	−1.02159
$185$	−6.34267e75	−0.711245
$186$	0	0
$187$	3.12491e75	0.244424
$188$	−3.56395e75	−0.233154
$189$	0	0
$190$	−1.33371e75	−0.0612092
$191$	1.51865e75	0.0584575	0.0292287	−	0.999573i	$-0.490695\pi$
$191$	1.51865e75	0.0584575	0.0292287	+	0.999573i	$0.490695\pi$
$192$	0	0
$193$	−3.48124e76	−0.945288	−0.472644	−	0.881253i	$-0.656700\pi$
$193$	−3.48124e76	−0.945288	−0.472644	+	0.881253i	$0.656700\pi$
$194$	2.49623e76	0.570069
$195$	0	0
$196$	3.47086e76	0.562159
$197$	−1.09636e77	−1.49738	−0.748691	−	0.662919i	$-0.769318\pi$
$197$	−1.09636e77	−1.49738	−0.748691	+	0.662919i	$0.769318\pi$
$198$	0	0
$199$	1.76321e77	1.71683	0.858413	−	0.512959i	$-0.171451\pi$
$199$	1.76321e77	1.71683	0.858413	+	0.512959i	$0.171451\pi$
$200$	4.01719e76	0.330687
$201$	0	0
$202$	1.00325e76	0.0591751
$203$	−5.50393e76	−0.275141
$204$	0	0
$205$	−1.09824e77	−0.395315
$206$	5.10855e76	0.156223
$207$	0	0
$208$	−3.51517e77	−0.777723
$209$	−6.90528e76	−0.130101
$210$	0	0
$211$	−4.62226e77	−0.632983	−0.316491	−	0.948595i	$-0.602505\pi$
$211$	−4.62226e77	−0.632983	−0.316491	+	0.948595i	$0.602505\pi$
$212$	−2.64678e77	−0.309362
$213$	0	0
$214$	−5.87550e77	−0.501399
$215$	9.23833e77	0.674381
$216$	0	0
$217$	4.87112e77	0.260752
$218$	−6.06650e77	−0.278385
$219$	0	0
$220$	−6.86107e77	−0.231863
$221$	2.19684e78	0.637761
$222$	0	0
$223$	4.30563e77	0.0924324	0.0462162	−	0.998931i	$-0.485284\pi$
$223$	4.30563e77	0.0924324	0.0462162	+	0.998931i	$0.485284\pi$
$224$	−2.61532e78	−0.483299
$225$	0	0
$226$	3.54263e78	0.486063
$227$	5.95123e78	0.704272	0.352136	−	0.935949i	$-0.385455\pi$
$227$	5.95123e78	0.704272	0.352136	+	0.935949i	$0.385455\pi$
$228$	0	0
$229$	1.26941e79	1.11973	0.559863	−	0.828585i	$-0.310854\pi$
$229$	1.26941e79	1.11973	0.559863	+	0.828585i	$0.310854\pi$
$230$	−4.47318e78	−0.340984
$231$	0	0
$232$	−4.34354e78	−0.247740
$233$	−2.79863e79	−1.38204	−0.691022	−	0.722834i	$-0.742839\pi$
$233$	−2.79863e79	−1.38204	−0.691022	+	0.722834i	$0.742839\pi$
$234$	0	0
$235$	−4.39218e78	−0.162895
$236$	−1.57288e79	−0.505991
$237$	0	0
$238$	4.60707e78	0.111711
$239$	−3.49525e79	−0.736458	−0.368229	−	0.929735i	$-0.620036\pi$
$239$	−3.49525e79	−0.736458	−0.368229	+	0.929735i	$0.620036\pi$
$240$	0	0
$241$	−1.86931e79	−0.297928	−0.148964	−	0.988843i	$-0.547594\pi$
$241$	−1.86931e79	−0.297928	−0.148964	+	0.988843i	$0.547594\pi$
$242$	−1.77340e79	−0.246033
$243$	0	0
$244$	−1.40640e80	−1.48098
$245$	4.27747e79	0.392756
$246$	0	0
$247$	−4.85448e79	−0.339465
$248$	3.84414e79	0.234784
$249$	0	0
$250$	6.36350e79	0.296965
$251$	7.13517e79	0.291296	0.145648	−	0.989336i	$-0.453473\pi$
$251$	7.13517e79	0.291296	0.145648	+	0.989336i	$0.453473\pi$
$252$	0	0
$253$	−2.31598e80	−0.724766
$254$	2.24308e79	0.0615056
$255$	0	0
$256$	1.19674e80	0.252326
$257$	−7.32793e80	−1.35588	−0.677940	−	0.735117i	$-0.737127\pi$
$257$	−7.32793e80	−1.35588	−0.677940	+	0.735117i	$0.737127\pi$
$258$	0	0
$259$	−4.84148e80	−0.690933
$260$	−4.82340e80	−0.604987
$261$	0	0
$262$	−2.77034e80	−0.268806
$263$	−2.32553e81	−1.98612	−0.993058	−	0.117629i	$-0.962471\pi$
$263$	−2.32553e81	−1.98612	−0.993058	+	0.117629i	$0.962471\pi$
$264$	0	0
$265$	−3.26188e80	−0.216138
$266$	−1.01805e80	−0.0594612
$267$	0	0
$268$	7.71346e80	0.350537
$269$	−3.59341e81	−1.44147	−0.720734	−	0.693211i	$-0.756195\pi$
$269$	−3.59341e81	−1.44147	−0.720734	+	0.693211i	$0.756195\pi$
$270$	0	0
$271$	2.85431e81	0.893367	0.446684	−	0.894692i	$-0.352605\pi$
$271$	2.85431e81	0.893367	0.446684	+	0.894692i	$0.352605\pi$
$272$	−1.67421e81	−0.463183
$273$	0	0
$274$	−1.82030e81	−0.394003
$275$	1.22457e81	0.234606
$276$	0	0
$277$	−1.00709e82	−1.51354	−0.756771	−	0.653680i	$-0.773224\pi$
$277$	−1.00709e82	−1.51354	−0.756771	+	0.653680i	$0.773224\pi$
$278$	4.75170e79	0.00632919
$279$	0	0
$280$	−2.11731e81	−0.221815
$281$	−1.13532e82	−1.05549	−0.527746	−	0.849402i	$-0.676963\pi$
$281$	−1.13532e82	−1.05549	−0.527746	+	0.849402i	$0.676963\pi$
$282$	0	0
$283$	−1.14040e82	−0.836013	−0.418006	−	0.908444i	$-0.637271\pi$
$283$	−1.14040e82	−0.836013	−0.418006	+	0.908444i	$0.637271\pi$
$284$	−5.31811e81	−0.346412
$285$	0	0
$286$	2.32698e81	0.119820
$287$	−8.38307e81	−0.384025
$288$	0	0
$289$	−1.70840e82	−0.620173
$290$	−2.55733e81	−0.0826901
$291$	0	0
$292$	−3.90554e82	−1.00313
$293$	−6.70401e82	−1.53557	−0.767785	−	0.640708i	$-0.778641\pi$
$293$	−6.70401e82	−1.53557	−0.767785	+	0.640708i	$0.778641\pi$
$294$	0	0
$295$	−1.93840e82	−0.353514
$296$	−3.82075e82	−0.622124
$297$	0	0
$298$	2.80252e82	0.364170
$299$	−1.62816e83	−1.89109
$300$	0	0
$301$	7.05180e82	0.655122
$302$	−4.31237e82	−0.358496
$303$	0	0
$304$	3.69960e82	0.246541
$305$	−1.73323e83	−1.03470
$306$	0	0
$307$	−3.19616e83	−1.53283	−0.766414	−	0.642347i	$-0.777961\pi$
$307$	−3.19616e83	−1.53283	−0.766414	+	0.642347i	$0.777961\pi$
$308$	−5.23718e82	−0.225242
$309$	0	0
$310$	2.26330e82	0.0783656
$311$	5.23816e83	1.62819	0.814097	−	0.580730i	$-0.197233\pi$
$311$	5.23816e83	1.62819	0.814097	+	0.580730i	$0.197233\pi$
$312$	0	0
$313$	2.07664e83	0.520745	0.260372	−	0.965508i	$-0.416155\pi$
$313$	2.07664e83	0.520745	0.260372	+	0.965508i	$0.416155\pi$
$314$	7.94275e82	0.178989
$315$	0	0
$316$	−4.77180e83	−0.869291
$317$	−3.07775e83	−0.504369	−0.252185	−	0.967679i	$-0.581149\pi$
$317$	−3.07775e83	−0.504369	−0.252185	+	0.967679i	$0.581149\pi$
$318$	0	0
$319$	−1.32405e83	−0.175759
$320$	2.80326e83	0.335073
$321$	0	0
$322$	−3.41446e83	−0.331246
$323$	−2.31210e83	−0.202173
$324$	0	0
$325$	8.60885e83	0.612143
$326$	5.21027e83	0.334249
$327$	0	0
$328$	−6.61567e83	−0.345780
$329$	−3.35264e83	−0.158243
$330$	0	0
$331$	4.04685e84	1.55912	0.779559	−	0.626328i	$-0.215443\pi$
$331$	4.04685e84	1.55912	0.779559	+	0.626328i	$0.215443\pi$
$332$	1.89594e84	0.660234
$333$	0	0
$334$	−2.39786e83	−0.0682837
$335$	9.50602e83	0.244905
$336$	0	0
$337$	2.49688e84	0.526983	0.263491	−	0.964662i	$-0.415126\pi$
$337$	2.49688e84	0.526983	0.263491	+	0.964662i	$0.415126\pi$
$338$	1.08241e83	0.0206862
$339$	0	0
$340$	−2.29730e84	−0.360308
$341$	1.17182e84	0.166567
$342$	0	0
$343$	8.57810e84	1.00239
$344$	5.56507e84	0.589879
$345$	0	0
$346$	6.94247e83	0.0605989
$347$	1.62541e85	1.28803	0.644013	−	0.765015i	$-0.277268\pi$
$347$	1.62541e85	1.28803	0.644013	+	0.765015i	$0.277268\pi$
$348$	0	0
$349$	2.30166e84	0.150449	0.0752244	−	0.997167i	$-0.476033\pi$
$349$	2.30166e84	0.150449	0.0752244	+	0.997167i	$0.476033\pi$
$350$	1.80539e84	0.107224
$351$	0	0
$352$	−6.29154e84	−0.308729
$353$	9.24470e84	0.412515	0.206258	−	0.978498i	$-0.433871\pi$
$353$	9.24470e84	0.412515	0.206258	+	0.978498i	$0.433871\pi$
$354$	0	0
$355$	−6.55401e84	−0.242023
$356$	4.26319e85	1.43272
$357$	0	0
$358$	1.93168e85	0.538088
$359$	1.12490e85	0.285397	0.142699	−	0.989766i	$-0.454422\pi$
$359$	1.12490e85	0.285397	0.142699	+	0.989766i	$0.454422\pi$
$360$	0	0
$361$	−4.23687e85	−0.892388
$362$	−6.41240e83	−0.0123107
$363$	0	0
$364$	−3.68179e85	−0.587710
$365$	−4.81316e85	−0.700840
$366$	0	0
$367$	1.48969e86	1.80627	0.903134	−	0.429358i	$-0.141260\pi$
$367$	1.48969e86	1.80627	0.903134	+	0.429358i	$0.141260\pi$
$368$	1.24082e86	1.37343
$369$	0	0
$370$	−2.24953e85	−0.207651
$371$	−2.48985e85	−0.209965
$372$	0	0
$373$	2.32298e86	1.63606	0.818031	−	0.575175i	$-0.195066\pi$
$373$	2.32298e86	1.63606	0.818031	+	0.575175i	$0.195066\pi$
$374$	1.10830e85	0.0713606
$375$	0	0
$376$	−2.64580e85	−0.142483
$377$	−9.30823e85	−0.458598
$378$	0	0
$379$	6.80738e85	0.280909	0.140455	−	0.990087i	$-0.455144\pi$
$379$	6.80738e85	0.280909	0.140455	+	0.990087i	$0.455144\pi$
$380$	5.07646e85	0.191783
$381$	0	0
$382$	5.38614e84	0.0170669
$383$	−4.50234e86	−1.30701	−0.653505	−	0.756922i	$-0.726702\pi$
$383$	−4.50234e86	−1.30701	−0.653505	+	0.756922i	$0.726702\pi$
$384$	0	0
$385$	−6.45427e85	−0.157367
$386$	−1.23468e86	−0.275981
$387$	0	0
$388$	−9.50132e86	−1.78616
$389$	−1.57388e86	−0.271431	−0.135715	−	0.990748i	$-0.543333\pi$
$389$	−1.57388e86	−0.271431	−0.135715	+	0.990748i	$0.543333\pi$
$390$	0	0
$391$	−7.75463e86	−1.12626
$392$	2.57670e86	0.343542
$393$	0	0
$394$	−3.88840e86	−0.437167
$395$	−5.88074e86	−0.607336
$396$	0	0
$397$	4.05321e86	0.353441	0.176721	−	0.984261i	$-0.443451\pi$
$397$	4.05321e86	0.353441	0.176721	+	0.984261i	$0.443451\pi$
$398$	6.25351e86	0.501235
$399$	0	0
$400$	−6.56081e86	−0.444578
$401$	−2.28951e87	−1.42694	−0.713470	−	0.700686i	$-0.752878\pi$
$401$	−2.28951e87	−1.42694	−0.713470	+	0.700686i	$0.752878\pi$
$402$	0	0
$403$	8.23801e86	0.434614
$404$	−3.81864e86	−0.185410
$405$	0	0
$406$	−1.95206e86	−0.0803287
$407$	−1.16469e87	−0.441365
$408$	0	0
$409$	2.15532e86	0.0693075	0.0346537	−	0.999399i	$-0.488967\pi$
$409$	2.15532e86	0.0693075	0.0346537	+	0.999399i	$0.488967\pi$
$410$	−3.89508e86	−0.115414
$411$	0	0
$412$	−1.94445e87	−0.489485
$413$	−1.47962e87	−0.343418
$414$	0	0
$415$	2.33654e87	0.461277
$416$	−4.42301e87	−0.805548
$417$	0	0
$418$	−2.44907e86	−0.0379835
$419$	−1.08084e88	−1.54736	−0.773681	−	0.633575i	$-0.781587\pi$
$419$	−1.08084e88	−1.54736	−0.773681	+	0.633575i	$0.781587\pi$
$420$	0	0
$421$	2.71807e87	0.331750	0.165875	−	0.986147i	$-0.446955\pi$
$421$	2.71807e87	0.331750	0.165875	+	0.986147i	$0.446955\pi$
$422$	−1.63936e87	−0.184802
$423$	0	0
$424$	−1.96492e87	−0.189055
$425$	4.10024e87	0.364570
$426$	0	0
$427$	−1.32301e88	−1.00515
$428$	2.23637e88	1.57100
$429$	0	0
$430$	3.27652e87	0.196888
$431$	1.82590e88	1.01505	0.507527	−	0.861636i	$-0.330560\pi$
$431$	1.82590e88	1.01505	0.507527	+	0.861636i	$0.330560\pi$
$432$	0	0
$433$	9.88211e87	0.470441	0.235220	−	0.971942i	$-0.424419\pi$
$433$	9.88211e87	0.470441	0.235220	+	0.971942i	$0.424419\pi$
$434$	1.72762e87	0.0761276
$435$	0	0
$436$	2.30907e88	0.872247
$437$	1.71358e88	0.599482
$438$	0	0
$439$	−3.91460e88	−1.17524	−0.587619	−	0.809138i	$-0.699934\pi$
$439$	−3.91460e88	−1.17524	−0.587619	+	0.809138i	$0.699934\pi$
$440$	−5.09352e87	−0.141694
$441$	0	0
$442$	7.79146e87	0.186197
$443$	5.04930e88	1.11868	0.559341	−	0.828938i	$-0.311054\pi$
$443$	5.04930e88	1.11868	0.559341	+	0.828938i	$0.311054\pi$
$444$	0	0
$445$	5.25393e88	1.00098
$446$	1.52706e87	0.0269860
$447$	0	0
$448$	2.13978e88	0.325504
$449$	6.56038e88	0.926139	0.463070	−	0.886322i	$-0.346748\pi$
$449$	6.56038e88	0.926139	0.463070	+	0.886322i	$0.346748\pi$
$450$	0	0
$451$	−2.01667e88	−0.245314
$452$	−1.34842e89	−1.52295
$453$	0	0
$454$	2.11070e88	0.205615
$455$	−4.53741e88	−0.410607
$456$	0	0
$457$	−1.05473e88	−0.0824039	−0.0412020	−	0.999151i	$-0.513119\pi$
$457$	−1.05473e88	−0.0824039	−0.0412020	+	0.999151i	$0.513119\pi$
$458$	4.50215e88	0.326909
$459$	0	0
$460$	1.70261e89	1.06838
$461$	7.33038e88	0.427706	0.213853	−	0.976866i	$-0.431399\pi$
$461$	7.33038e88	0.427706	0.213853	+	0.976866i	$0.431399\pi$
$462$	0	0
$463$	6.14153e88	0.309966	0.154983	−	0.987917i	$-0.450468\pi$
$463$	6.14153e88	0.309966	0.154983	+	0.987917i	$0.450468\pi$
$464$	7.09380e88	0.333063
$465$	0	0
$466$	−9.92578e88	−0.403493
$467$	4.75062e89	1.79736	0.898679	−	0.438607i	$-0.144528\pi$
$467$	4.75062e89	1.79736	0.898679	+	0.438607i	$0.144528\pi$
$468$	0	0
$469$	7.25613e88	0.237911
$470$	−1.55776e88	−0.0475578
$471$	0	0
$472$	−1.16767e89	−0.309218
$473$	1.69642e89	0.418489
$474$	0	0
$475$	−9.06052e88	−0.194052
$476$	−1.75357e89	−0.350018
$477$	0	0
$478$	−1.23965e89	−0.215012
$479$	4.59749e89	0.743501	0.371750	−	0.928333i	$-0.378758\pi$
$479$	4.59749e89	0.743501	0.371750	+	0.928333i	$0.378758\pi$
$480$	0	0
$481$	−8.18789e89	−1.15163
$482$	−6.62981e88	−0.0869812
$483$	0	0
$484$	6.75004e89	0.770879
$485$	−1.17094e90	−1.24791
$486$	0	0
$487$	2.89512e89	0.268810	0.134405	−	0.990926i	$-0.457088\pi$
$487$	2.89512e89	0.268810	0.134405	+	0.990926i	$0.457088\pi$
$488$	−1.04408e90	−0.905045
$489$	0	0
$490$	1.51707e89	0.114667
$491$	−2.28241e90	−1.61126	−0.805628	−	0.592422i	$-0.798172\pi$
$491$	−2.28241e90	−1.61126	−0.805628	+	0.592422i	$0.798172\pi$
$492$	0	0
$493$	−4.43334e89	−0.273124
$494$	−1.72172e89	−0.0991082
$495$	0	0
$496$	−6.27819e89	−0.315645
$497$	−5.00280e89	−0.235112
$498$	0	0
$499$	−7.84213e88	−0.0322156	−0.0161078	−	0.999870i	$-0.505127\pi$
$499$	−7.84213e88	−0.0322156	−0.0161078	+	0.999870i	$0.505127\pi$
$500$	−2.42211e90	−0.930464
$501$	0	0
$502$	2.53060e89	0.0850452
$503$	3.29209e90	1.03501	0.517505	−	0.855680i	$-0.326861\pi$
$503$	3.29209e90	1.03501	0.517505	+	0.855680i	$0.326861\pi$
$504$	0	0
$505$	−4.70607e89	−0.129538
$506$	−8.21400e89	−0.211599
$507$	0	0
$508$	−8.53774e89	−0.192712
$509$	−6.95196e90	−1.46914	−0.734568	−	0.678536i	$-0.762615\pi$
$509$	−6.95196e90	−1.46914	−0.734568	+	0.678536i	$0.762615\pi$
$510$	0	0
$511$	−3.67397e90	−0.680826
$512$	5.79144e90	1.00518
$513$	0	0
$514$	−2.59897e90	−0.395855
$515$	−2.39632e90	−0.341982
$516$	0	0
$517$	−8.06527e89	−0.101085
$518$	−1.71711e90	−0.201721
$519$	0	0
$520$	−3.58079e90	−0.369715
$521$	9.53203e89	0.0922830	0.0461415	−	0.998935i	$-0.485307\pi$
$521$	9.53203e89	0.0922830	0.0461415	+	0.998935i	$0.485307\pi$
$522$	0	0
$523$	−9.89851e90	−0.842875	−0.421438	−	0.906857i	$-0.638474\pi$
$523$	−9.89851e90	−0.842875	−0.421438	+	0.906857i	$0.638474\pi$
$524$	1.05446e91	0.842235
$525$	0	0
$526$	−8.24787e90	−0.579855
$527$	3.92362e90	0.258840
$528$	0	0
$529$	4.02630e91	2.33959
$530$	−1.15688e90	−0.0631024
$531$	0	0
$532$	3.87496e90	0.186306
$533$	−1.41774e91	−0.640082
$534$	0	0
$535$	2.75608e91	1.09759
$536$	5.72632e90	0.214218
$537$	0	0
$538$	−1.27446e91	−0.420843
$539$	7.85462e90	0.243726
$540$	0	0
$541$	5.31156e91	1.45584	0.727921	−	0.685661i	$-0.240487\pi$
$541$	5.31156e91	1.45584	0.727921	+	0.685661i	$0.240487\pi$
$542$	1.01233e91	0.260822
$543$	0	0
$544$	−2.10660e91	−0.479755
$545$	2.84568e91	0.609401
$546$	0	0
$547$	−9.06405e90	−0.171691	−0.0858454	−	0.996308i	$-0.527359\pi$
$547$	−9.06405e90	−0.171691	−0.0858454	+	0.996308i	$0.527359\pi$
$548$	6.92854e91	1.23450
$549$	0	0
$550$	4.34314e90	0.0684941
$551$	9.79659e90	0.145377
$552$	0	0
$553$	−4.48888e91	−0.589992
$554$	−3.57179e91	−0.441885
$555$	0	0
$556$	−1.80862e90	−0.0198309
$557$	1.15401e92	1.19141	0.595706	−	0.803203i	$-0.296872\pi$
$557$	1.15401e92	1.19141	0.595706	+	0.803203i	$0.296872\pi$
$558$	0	0
$559$	1.19260e92	1.09194
$560$	3.45796e91	0.298209
$561$	0	0
$562$	−4.02658e91	−0.308155
$563$	6.53348e91	0.471100	0.235550	−	0.971862i	$-0.424311\pi$
$563$	6.53348e91	0.471100	0.235550	+	0.971862i	$0.424311\pi$
$564$	0	0
$565$	−1.66178e92	−1.06402
$566$	−4.04462e91	−0.244077
$567$	0	0
$568$	−3.94806e91	−0.211697
$569$	−6.96531e90	−0.0352111	−0.0176055	−	0.999845i	$-0.505604\pi$
$569$	−6.96531e90	−0.0352111	−0.0176055	+	0.999845i	$0.505604\pi$
$570$	0	0
$571$	−9.46031e91	−0.425202	−0.212601	−	0.977139i	$-0.568193\pi$
$571$	−9.46031e91	−0.425202	−0.212601	+	0.977139i	$0.568193\pi$
$572$	−8.85710e91	−0.375426
$573$	0	0
$574$	−2.97319e91	−0.112118
$575$	−3.03884e92	−1.08102
$576$	0	0
$577$	5.08231e92	1.60943	0.804714	−	0.593663i	$-0.202319\pi$
$577$	5.08231e92	1.60943	0.804714	+	0.593663i	$0.202319\pi$
$578$	−6.05913e91	−0.181062
$579$	0	0
$580$	9.73386e91	0.259088
$581$	1.78352e92	0.448104
$582$	0	0
$583$	−5.98972e91	−0.134125
$584$	−2.89939e92	−0.613022
$585$	0	0
$586$	−2.37769e92	−0.448316
$587$	−4.46800e91	−0.0795678	−0.0397839	−	0.999208i	$-0.512667\pi$
$587$	−4.46800e91	−0.0795678	−0.0397839	+	0.999208i	$0.512667\pi$
$588$	0	0
$589$	−8.67022e91	−0.137774
$590$	−6.87486e91	−0.103210
$591$	0	0
$592$	6.23999e92	0.836386
$593$	−2.14083e92	−0.271175	−0.135588	−	0.990765i	$-0.543292\pi$
$593$	−2.14083e92	−0.271175	−0.135588	+	0.990765i	$0.543292\pi$
$594$	0	0
$595$	−2.16109e92	−0.244543
$596$	−1.06671e93	−1.14103
$597$	0	0
$598$	−5.77453e92	−0.552112
$599$	−1.12807e93	−1.01985	−0.509926	−	0.860219i	$-0.670327\pi$
$599$	−1.12807e93	−1.01985	−0.509926	+	0.860219i	$0.670327\pi$
$600$	0	0
$601$	−1.96269e93	−1.58693	−0.793464	−	0.608617i	$-0.791725\pi$
$601$	−1.96269e93	−1.58693	−0.793464	+	0.608617i	$0.791725\pi$
$602$	2.50103e92	0.191266
$603$	0	0
$604$	1.64140e93	1.12325
$605$	8.31870e92	0.538580
$606$	0	0
$607$	−2.93504e93	−1.70135	−0.850673	−	0.525695i	$-0.823805\pi$
$607$	−2.93504e93	−1.70135	−0.850673	+	0.525695i	$0.823805\pi$
$608$	4.65507e92	0.255362
$609$	0	0
$610$	−6.14719e92	−0.302084
$611$	−5.66997e92	−0.263755
$612$	0	0
$613$	3.78455e92	0.157793	0.0788966	−	0.996883i	$-0.474860\pi$
$613$	3.78455e92	0.157793	0.0788966	+	0.996883i	$0.474860\pi$
$614$	−1.13357e93	−0.447516
$615$	0	0
$616$	−3.88798e92	−0.137648
$617$	8.57063e92	0.287382	0.143691	−	0.989623i	$-0.454103\pi$
$617$	8.57063e92	0.287382	0.143691	+	0.989623i	$0.454103\pi$
$618$	0	0
$619$	2.20381e93	0.663038	0.331519	−	0.943449i	$-0.392439\pi$
$619$	2.20381e93	0.663038	0.331519	+	0.943449i	$0.392439\pi$
$620$	−8.61471e92	−0.245538
$621$	0	0
$622$	1.85780e93	0.475358
$623$	4.01042e93	0.972390
$624$	0	0
$625$	−2.68757e92	−0.0585302
$626$	7.36512e92	0.152034
$627$	0	0
$628$	−3.02322e93	−0.560817
$629$	−3.89975e93	−0.685867
$630$	0	0
$631$	1.10304e94	1.74425	0.872123	−	0.489286i	$-0.162743\pi$
$631$	1.10304e94	1.74425	0.872123	+	0.489286i	$0.162743\pi$
$632$	−3.54249e93	−0.531235
$633$	0	0
$634$	−1.09157e93	−0.147253
$635$	−1.05219e93	−0.134639
$636$	0	0
$637$	5.52188e93	0.635940
$638$	−4.69597e92	−0.0513136
$639$	0	0
$640$	6.05046e93	0.595332
$641$	1.71036e94	1.59714	0.798569	−	0.601903i	$-0.205591\pi$
$641$	1.71036e94	1.59714	0.798569	+	0.601903i	$0.205591\pi$
$642$	0	0
$643$	−9.74742e93	−0.820016	−0.410008	−	0.912082i	$-0.634474\pi$
$643$	−9.74742e93	−0.820016	−0.410008	+	0.912082i	$0.634474\pi$
$644$	1.29963e94	1.03787
$645$	0	0
$646$	−8.20024e92	−0.0590252
$647$	2.06058e93	0.140830	0.0704150	−	0.997518i	$-0.477568\pi$
$647$	2.06058e93	0.140830	0.0704150	+	0.997518i	$0.477568\pi$
$648$	0	0
$649$	−3.55945e93	−0.219374
$650$	3.05327e93	0.178718
$651$	0	0
$652$	−1.98316e94	−1.04728
$653$	2.00922e94	1.00794	0.503970	−	0.863721i	$-0.331872\pi$
$653$	2.00922e94	1.00794	0.503970	+	0.863721i	$0.331872\pi$
$654$	0	0
$655$	1.29951e94	0.588433
$656$	1.08046e94	0.464869
$657$	0	0
$658$	−1.18907e93	−0.0461996
$659$	−8.21097e93	−0.303203	−0.151601	−	0.988442i	$-0.548443\pi$
$659$	−8.21097e93	−0.303203	−0.151601	+	0.988442i	$0.548443\pi$
$660$	0	0
$661$	2.48802e94	0.830052	0.415026	−	0.909810i	$-0.363772\pi$
$661$	2.48802e94	0.830052	0.415026	+	0.909810i	$0.363772\pi$
$662$	1.43528e94	0.455191
$663$	0	0
$664$	1.40750e94	0.403477
$665$	4.77547e93	0.130164
$666$	0	0
$667$	3.28571e94	0.809867
$668$	9.12688e93	0.213949
$669$	0	0
$670$	3.37146e93	0.0715010
$671$	−3.18270e94	−0.642083
$672$	0	0
$673$	−2.98741e94	−0.545495	−0.272747	−	0.962086i	$-0.587932\pi$
$673$	−2.98741e94	−0.545495	−0.272747	+	0.962086i	$0.587932\pi$
$674$	8.85559e93	0.153855
$675$	0	0
$676$	−4.11992e93	−0.0648148
$677$	−1.11284e95	−1.66615	−0.833073	−	0.553164i	$-0.813420\pi$
$677$	−1.11284e95	−1.66615	−0.833073	+	0.553164i	$0.813420\pi$
$678$	0	0
$679$	−8.93798e94	−1.21228
$680$	−1.70547e94	−0.220189
$681$	0	0
$682$	4.15605e93	0.0486300
$683$	−1.62723e95	−1.81282	−0.906409	−	0.422401i	$-0.861187\pi$
$683$	−1.62723e95	−1.81282	−0.906409	+	0.422401i	$0.861187\pi$
$684$	0	0
$685$	8.53868e94	0.862495
$686$	3.04236e94	0.292653
$687$	0	0
$688$	−9.08878e94	−0.793036
$689$	−4.21083e94	−0.349964
$690$	0	0
$691$	−1.41176e95	−1.06474	−0.532372	−	0.846510i	$-0.678699\pi$
$691$	−1.41176e95	−1.06474	−0.532372	+	0.846510i	$0.678699\pi$
$692$	−2.64249e94	−0.189871
$693$	0	0
$694$	5.76476e94	0.376045
$695$	−2.22893e93	−0.0138550
$696$	0	0
$697$	−6.75245e94	−0.381209
$698$	8.16319e93	0.0439242
$699$	0	0
$700$	−6.87179e94	−0.335958
$701$	2.96929e95	1.38388	0.691941	−	0.721954i	$-0.256756\pi$
$701$	2.96929e95	1.38388	0.691941	+	0.721954i	$0.256756\pi$
$702$	0	0
$703$	8.61747e94	0.365070
$704$	5.14756e94	0.207930
$705$	0	0
$706$	3.27878e94	0.120436
$707$	−3.59223e94	−0.125839
$708$	0	0
$709$	−2.38690e95	−0.760650	−0.380325	−	0.924853i	$-0.624188\pi$
$709$	−2.38690e95	−0.760650	−0.380325	+	0.924853i	$0.624188\pi$
$710$	−2.32448e94	−0.0706597
$711$	0	0
$712$	3.16491e95	0.875550
$713$	−2.90793e95	−0.767512
$714$	0	0
$715$	−1.09154e95	−0.262294
$716$	−7.35247e95	−1.68596
$717$	0	0
$718$	3.98964e94	0.0833229
$719$	4.92960e95	0.982638	0.491319	−	0.870980i	$-0.336515\pi$
$719$	4.92960e95	0.982638	0.491319	+	0.870980i	$0.336515\pi$
$720$	0	0
$721$	−1.82916e95	−0.332215
$722$	−1.50267e95	−0.260537
$723$	0	0
$724$	2.44073e94	0.0385725
$725$	−1.73731e95	−0.262153
$726$	0	0
$727$	2.83726e95	0.390388	0.195194	−	0.980765i	$-0.437466\pi$
$727$	2.83726e95	0.390388	0.195194	+	0.980765i	$0.437466\pi$
$728$	−2.73329e95	−0.359157
$729$	0	0
$730$	−1.70706e95	−0.204613
$731$	5.68013e95	0.650318
$732$	0	0
$733$	1.53710e96	1.60590	0.802950	−	0.596046i	$-0.203262\pi$
$733$	1.53710e96	1.60590	0.802950	+	0.596046i	$0.203262\pi$
$734$	5.28342e95	0.527348
$735$	0	0
$736$	1.56128e96	1.42257
$737$	1.74557e95	0.151976
$738$	0	0
$739$	−1.56801e96	−1.24670	−0.623349	−	0.781944i	$-0.714228\pi$
$739$	−1.56801e96	−1.24670	−0.623349	+	0.781944i	$0.714228\pi$
$740$	8.56230e95	0.650620
$741$	0	0
$742$	−8.83066e94	−0.0613003
$743$	1.24019e96	0.822927	0.411464	−	0.911426i	$-0.365018\pi$
$743$	1.24019e96	0.822927	0.411464	+	0.911426i	$0.365018\pi$
$744$	0	0
$745$	−1.31461e96	−0.797189
$746$	8.23882e95	0.477655
$747$	0	0
$748$	−4.21848e95	−0.223590
$749$	2.10377e96	1.06625
$750$	0	0
$751$	2.53507e95	0.117504	0.0587519	−	0.998273i	$-0.481288\pi$
$751$	2.53507e95	0.117504	0.0587519	+	0.998273i	$0.481288\pi$
$752$	4.32108e95	0.191556
$753$	0	0
$754$	−3.30131e95	−0.133890
$755$	2.02285e96	0.784768
$756$	0	0
$757$	1.18981e94	0.00422440	0.00211220	−	0.999998i	$-0.499328\pi$
$757$	1.18981e94	0.00422440	0.00211220	+	0.999998i	$0.499328\pi$
$758$	2.41435e95	0.0820127
$759$	0	0
$760$	3.76866e95	0.117201
$761$	−3.12153e96	−0.928926	−0.464463	−	0.885593i	$-0.653753\pi$
$761$	−3.12153e96	−0.928926	−0.464463	+	0.885593i	$0.653753\pi$
$762$	0	0
$763$	2.17216e96	0.591998
$764$	−2.05010e95	−0.0534747
$765$	0	0
$766$	−1.59683e96	−0.381587
$767$	−2.50233e96	−0.572400
$768$	0	0
$769$	2.83694e95	0.0594726	0.0297363	−	0.999558i	$-0.490533\pi$
$769$	2.83694e95	0.0594726	0.0297363	+	0.999558i	$0.490533\pi$
$770$	−2.28911e95	−0.0459438
$771$	0	0
$772$	4.69951e96	0.864714
$773$	−4.89330e95	−0.0862162	−0.0431081	−	0.999070i	$-0.513726\pi$
$773$	−4.89330e95	−0.0862162	−0.0431081	+	0.999070i	$0.513726\pi$
$774$	0	0
$775$	1.53756e96	0.248443
$776$	−7.05359e96	−1.09155
$777$	0	0
$778$	−5.58201e95	−0.0792454
$779$	1.49212e96	0.202908
$780$	0	0
$781$	−1.20350e96	−0.150188
$782$	−2.75030e96	−0.328817
$783$	0	0
$784$	−4.20822e96	−0.461860
$785$	−3.72579e96	−0.391819
$786$	0	0
$787$	1.83342e97	1.77055	0.885276	−	0.465065i	$-0.153969\pi$
$787$	1.83342e97	1.77055	0.885276	+	0.465065i	$0.153969\pi$
$788$	1.48003e97	1.36975
$789$	0	0
$790$	−2.08570e96	−0.177314
$791$	−1.26847e97	−1.03364
$792$	0	0
$793$	−2.23747e97	−1.67535
$794$	1.43754e96	0.103189
$795$	0	0
$796$	−2.38025e97	−1.57049
$797$	−6.71228e96	−0.424636	−0.212318	−	0.977201i	$-0.568101\pi$
$797$	−6.71228e96	−0.424636	−0.212318	+	0.977201i	$0.568101\pi$
$798$	0	0
$799$	−2.70050e96	−0.157082
$800$	−8.25522e96	−0.460483
$801$	0	0
$802$	−8.12011e96	−0.416601
$803$	−8.83829e96	−0.434908
$804$	0	0
$805$	1.60166e97	0.725117
$806$	2.92174e96	0.126887
$807$	0	0
$808$	−2.83488e96	−0.113306
$809$	−1.23268e97	−0.472688	−0.236344	−	0.971669i	$-0.575949\pi$
$809$	−1.23268e97	−0.472688	−0.236344	+	0.971669i	$0.575949\pi$
$810$	0	0
$811$	−2.90320e97	−1.02489	−0.512447	−	0.858719i	$-0.671261\pi$
$811$	−2.90320e97	−1.02489	−0.512447	+	0.858719i	$0.671261\pi$
$812$	7.43004e96	0.251689
$813$	0	0
$814$	−4.13076e96	−0.128858
$815$	−2.44404e97	−0.731692
$816$	0	0
$817$	−1.25517e97	−0.346149
$818$	7.64418e95	0.0202346
$819$	0	0
$820$	1.48257e97	0.361619
$821$	1.62725e97	0.381029	0.190515	−	0.981684i	$-0.438984\pi$
$821$	1.62725e97	0.381029	0.190515	+	0.981684i	$0.438984\pi$
$822$	0	0
$823$	7.54690e97	1.62882	0.814412	−	0.580287i	$-0.197059\pi$
$823$	7.54690e97	1.62882	0.814412	+	0.580287i	$0.197059\pi$
$824$	−1.44352e97	−0.299130
$825$	0	0
$826$	−5.24771e96	−0.100262
$827$	4.70909e96	0.0863977	0.0431988	−	0.999066i	$-0.486245\pi$
$827$	4.70909e96	0.0863977	0.0431988	+	0.999066i	$0.486245\pi$
$828$	0	0
$829$	5.63395e97	0.953315	0.476657	−	0.879089i	$-0.341848\pi$
$829$	5.63395e97	0.953315	0.476657	+	0.879089i	$0.341848\pi$
$830$	8.28690e96	0.134672
$831$	0	0
$832$	3.61879e97	0.542540
$833$	2.62997e97	0.378742
$834$	0	0
$835$	1.12479e97	0.149477
$836$	9.32179e96	0.119012
$837$	0	0
$838$	−3.83338e97	−0.451759
$839$	9.35016e97	1.05875	0.529375	−	0.848388i	$-0.322427\pi$
$839$	9.35016e97	1.05875	0.529375	+	0.848388i	$0.322427\pi$
$840$	0	0
$841$	−7.68613e97	−0.803604
$842$	9.64007e96	0.0968557
$843$	0	0
$844$	6.23982e97	0.579029
$845$	−5.07736e96	−0.0452833
$846$	0	0
$847$	6.34982e97	0.523199
$848$	3.20907e97	0.254167
$849$	0	0
$850$	1.45422e97	0.106438
$851$	2.89024e98	2.03373
$852$	0	0
$853$	−1.53678e98	−0.999586	−0.499793	−	0.866145i	$-0.666591\pi$
$853$	−1.53678e98	−0.999586	−0.499793	+	0.866145i	$0.666591\pi$
$854$	−4.69227e97	−0.293457
$855$	0	0
$856$	1.66023e98	0.960060
$857$	−3.74053e97	−0.208006	−0.104003	−	0.994577i	$-0.533165\pi$
$857$	−3.74053e97	−0.208006	−0.104003	+	0.994577i	$0.533165\pi$
$858$	0	0
$859$	−1.70881e98	−0.878865	−0.439433	−	0.898276i	$-0.644820\pi$
$859$	−1.70881e98	−0.878865	−0.439433	+	0.898276i	$0.644820\pi$
$860$	−1.24713e98	−0.616898
$861$	0	0
$862$	6.47586e97	0.296349
$863$	2.97133e98	1.30794	0.653972	−	0.756519i	$-0.273102\pi$
$863$	2.97133e98	1.30794	0.653972	+	0.756519i	$0.273102\pi$
$864$	0	0
$865$	−3.25658e97	−0.132655
$866$	3.50485e97	0.137347
$867$	0	0
$868$	−6.57577e97	−0.238526
$869$	−1.07987e98	−0.376884
$870$	0	0
$871$	1.22715e98	0.396543
$872$	1.71421e98	0.533041
$873$	0	0
$874$	6.07749e97	0.175021
$875$	−2.27851e98	−0.631510
$876$	0	0
$877$	4.18737e97	0.107512	0.0537558	−	0.998554i	$-0.482881\pi$
$877$	4.18737e97	0.107512	0.0537558	+	0.998554i	$0.482881\pi$
$878$	−1.38837e98	−0.343115
$879$	0	0
$880$	8.31865e97	0.190495
$881$	−3.25627e98	−0.717839	−0.358919	−	0.933369i	$-0.616855\pi$
$881$	−3.25627e98	−0.717839	−0.358919	+	0.933369i	$0.616855\pi$
$882$	0	0
$883$	1.02307e97	0.0209037	0.0104518	−	0.999945i	$-0.496673\pi$
$883$	1.02307e97	0.0209037	0.0104518	+	0.999945i	$0.496673\pi$
$884$	−2.96563e98	−0.583400
$885$	0	0
$886$	1.79082e98	0.326604
$887$	−8.62313e98	−1.51434	−0.757171	−	0.653217i	$-0.773419\pi$
$887$	−8.62313e98	−1.51434	−0.757171	+	0.653217i	$0.773419\pi$
$888$	0	0
$889$	−8.03153e97	−0.130794
$890$	1.86339e98	0.292239
$891$	0	0
$892$	−5.81240e97	−0.0845537
$893$	5.96744e97	0.0836112
$894$	0	0
$895$	−9.06114e98	−1.17791
$896$	4.61843e98	0.578331
$897$	0	0
$898$	2.32674e98	0.270390
$899$	−1.66247e98	−0.186125
$900$	0	0
$901$	−2.00554e98	−0.208426
$902$	−7.15246e97	−0.0716203
$903$	0	0
$904$	−1.00104e99	−0.930696
$905$	3.00794e97	0.0269489
$906$	0	0
$907$	4.77849e97	0.0397601	0.0198800	−	0.999802i	$-0.493672\pi$
$907$	4.77849e97	0.0397601	0.0198800	+	0.999802i	$0.493672\pi$
$908$	−8.03387e98	−0.644242
$909$	0	0
$910$	−1.60927e98	−0.119879
$911$	−1.36204e99	−0.977964	−0.488982	−	0.872294i	$-0.662632\pi$
$911$	−1.36204e99	−0.977964	−0.488982	+	0.872294i	$0.662632\pi$
$912$	0	0
$913$	4.29053e98	0.286247
$914$	−3.74076e97	−0.0240582
$915$	0	0
$916$	−1.71364e99	−1.02428
$917$	9.91943e98	0.571629
$918$	0	0
$919$	1.87215e99	1.00293	0.501466	−	0.865177i	$-0.332794\pi$
$919$	1.87215e99	1.00293	0.501466	+	0.865177i	$0.332794\pi$
$920$	1.26398e99	0.652903
$921$	0	0
$922$	2.59984e98	0.124871
$923$	−8.46071e98	−0.391877
$924$	0	0
$925$	−1.52821e99	−0.658316
$926$	2.17819e98	0.0904958
$927$	0	0
$928$	8.92587e98	0.344979
$929$	−1.09697e99	−0.408947	−0.204474	−	0.978872i	$-0.565548\pi$
$929$	−1.09697e99	−0.408947	−0.204474	+	0.978872i	$0.565548\pi$
$930$	0	0
$931$	−5.81159e98	−0.201595
$932$	3.77801e99	1.26424
$933$	0	0
$934$	1.68488e99	0.524746
$935$	−5.19882e98	−0.156213
$936$	0	0
$937$	3.10631e99	0.868898	0.434449	−	0.900696i	$-0.356943\pi$
$937$	3.10631e99	0.868898	0.434449	+	0.900696i	$0.356943\pi$
$938$	2.57350e98	0.0694591
$939$	0	0
$940$	5.92923e98	0.149010
$941$	−7.31696e99	−1.77451	−0.887255	−	0.461280i	$-0.847390\pi$
$941$	−7.31696e99	−1.77451	−0.887255	+	0.461280i	$0.847390\pi$
$942$	0	0
$943$	5.00448e99	1.13036
$944$	1.90702e99	0.415714
$945$	0	0
$946$	6.01661e98	0.122180
$947$	3.58770e99	0.703221	0.351610	−	0.936146i	$-0.385634\pi$
$947$	3.58770e99	0.703221	0.351610	+	0.936146i	$0.385634\pi$
$948$	0	0
$949$	−6.21341e99	−1.13478
$950$	−3.21346e98	−0.0566542
$951$	0	0
$952$	−1.30182e99	−0.213901
$953$	3.77034e99	0.598093	0.299047	−	0.954239i	$-0.403331\pi$
$953$	3.77034e99	0.598093	0.299047	+	0.954239i	$0.403331\pi$
$954$	0	0
$955$	−2.52653e98	−0.0373605
$956$	4.71841e99	0.673685
$957$	0	0
$958$	1.63058e99	0.217068
$959$	6.51774e99	0.837864
$960$	0	0
$961$	−6.86996e99	−0.823609
$962$	−2.90397e99	−0.336223
$963$	0	0
$964$	2.52348e99	0.272533
$965$	5.79164e99	0.604138
$966$	0	0
$967$	−3.34294e98	−0.0325344	−0.0162672	−	0.999868i	$-0.505178\pi$
$967$	−3.34294e98	−0.0325344	−0.0162672	+	0.999868i	$0.505178\pi$
$968$	5.01109e99	0.471094
$969$	0	0
$970$	−4.15291e99	−0.364334
$971$	1.09912e100	0.931541	0.465771	−	0.884905i	$-0.345777\pi$
$971$	1.09912e100	0.931541	0.465771	+	0.884905i	$0.345777\pi$
$972$	0	0
$973$	−1.70139e98	−0.0134593
$974$	1.02680e99	0.0784803
$975$	0	0
$976$	1.70518e100	1.21675
$977$	1.76276e100	1.21542	0.607710	−	0.794159i	$-0.292088\pi$
$977$	1.76276e100	1.21542	0.607710	+	0.794159i	$0.292088\pi$
$978$	0	0
$979$	9.64767e99	0.621158
$980$	−5.77438e99	−0.359279
$981$	0	0
$982$	−8.09495e99	−0.470413
$983$	−1.83321e100	−1.02960	−0.514801	−	0.857310i	$-0.672134\pi$
$983$	−1.83321e100	−1.02960	−0.514801	+	0.857310i	$0.672134\pi$
$984$	0	0
$985$	1.82397e100	0.956985
$986$	−1.57236e99	−0.0797397
$987$	0	0
$988$	6.55331e99	0.310530
$989$	−4.20974e100	−1.92832
$990$	0	0
$991$	−9.79963e99	−0.419510	−0.209755	−	0.977754i	$-0.567267\pi$
$991$	−9.79963e99	−0.419510	−0.209755	+	0.977754i	$0.567267\pi$
$992$	−7.89961e99	−0.326938
$993$	0	0
$994$	−1.77432e99	−0.0686418
$995$	−2.93340e100	−1.09723
$996$	0	0
$997$	−2.14429e100	−0.749888	−0.374944	−	0.927047i	$-0.622338\pi$
$997$	−2.14429e100	−0.749888	−0.374944	+	0.927047i	$0.622338\pi$
$998$	−2.78134e98	−0.00940547
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.68.a.c.1.4		6
3.2	odd	2		3.68.a.b.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.68.a.b.1.3	✓	6	3.2	odd	2
9.68.a.c.1.4		6	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 68 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+3.54666e9 q^{2} -1.34995e20 q^{4} -1.66367e23 q^{5} -1.26991e28 q^{7} -1.00218e30 q^{8} +O(q^{10})\)	\(q+3.54666e9 q^{2} -1.34995e20 q^{4} -1.66367e23 q^{5} -1.26991e28 q^{7} -1.00218e30 q^{8} -5.90048e32 q^{10} -3.05496e34 q^{11} -2.14767e37 q^{13} -4.50395e37 q^{14} +1.63674e40 q^{16} -1.02290e41 q^{17} +2.26035e42 q^{19} +2.24588e43 q^{20} -1.08349e44 q^{22} +7.58105e45 q^{23} -4.00846e46 q^{25} -7.61705e46 q^{26} +1.71432e48 q^{28} +4.33411e48 q^{29} -3.83579e49 q^{31} +2.05945e50 q^{32} -3.62787e50 q^{34} +2.11272e51 q^{35} +3.81245e52 q^{37} +8.01669e51 q^{38} +1.66729e53 q^{40} +6.60130e53 q^{41} -5.55298e54 q^{43} +4.12405e54 q^{44} +2.68874e55 q^{46} +2.64005e55 q^{47} -2.57110e56 q^{49} -1.42167e56 q^{50} +2.89925e57 q^{52} +1.96065e57 q^{53} +5.08245e57 q^{55} +1.27268e58 q^{56} +1.53716e58 q^{58} +1.16514e59 q^{59} +1.04181e60 q^{61} -1.36043e59 q^{62} -1.68498e60 q^{64} +3.57302e60 q^{65} -5.71388e60 q^{67} +1.38086e61 q^{68} +7.49308e60 q^{70} +3.93949e61 q^{71} +2.89309e62 q^{73} +1.35215e62 q^{74} -3.05136e62 q^{76} +3.87953e62 q^{77} +3.53480e63 q^{79} -2.72299e63 q^{80} +2.34126e63 q^{82} -1.40445e64 q^{83} +1.70176e64 q^{85} -1.96945e64 q^{86} +3.06161e64 q^{88} -3.15803e65 q^{89} +2.72735e65 q^{91} -1.02341e66 q^{92} +9.36338e64 q^{94} -3.76047e65 q^{95} +7.03827e66 q^{97} -9.11883e65 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 13735355166 q^{2} + 46\!\cdots\!52 q^{4}+ \cdots - 17\!\cdots\!92 q^{8}+O(q^{10}) \) 6 * q - 13735355166 * q^2 + 461137328518259214852 * q^4 + 180289059197853505182300 * q^5 - 28067678610591277820235434208 * q^7 - 174428717775449559766832729592 * q^8	\( 6 q - 13735355166 q^{2} + 46\!\cdots\!52 q^{4}+ \cdots - 26\!\cdots\!74 q^{98}+O(q^{100}) \) 6 * q - 13735355166 * q^2 + 461137328518259214852 * q^4 + 180289059197853505182300 * q^5 - 28067678610591277820235434208 * q^7 - 174428717775449559766832729592 * q^8 + 7304190735814693245550459325330100 * q^10 - 1253554983811830341203783945028424 * q^11 - 1032427018834954393824819765456935964 * q^13 + 447380929503565966859381489320173353952 * q^14 - 10777060270558286469269005744606427140080 * q^16 + 22303705201707705421583405421371675716596 * q^17 - 6709513794502265961382038704145157001302152 * q^19 - 46181758835098395119891481090112367056690200 * q^20 + 1406045276258114363650986812146594678084267368 * q^22 - 12239031860950699209155226229708548540686529264 * q^23 + 124984998689116279435075553443500491502742646250 * q^25 - 147728325197899719596176944836466085493373208692 * q^26 - 14712260029031223829746951621139067346976206433344 * q^28 + 18873418589468921842047146695821329699174822684364 * q^29 - 224044794880051525600176726995317503621741761218704 * q^31 + 647694914760137169573449462765066287313897316284448 * q^32 + 693429763914603914127075176718731888866377974041404 * q^34 + 6444089679967517736201498858201618112886103095496000 * q^35 + 27414420131407696449125644786001907623181109991614452 * q^37 - 12552113658955455007053647987482106208988678055446104 * q^38 + 1194094866560066539991934179669093556164670510853198800 * q^40 - 2660548042321177320771169314506367536908331651920652796 * q^41 - 1105961611152903745004520895209354208863582663043308600 * q^43 + 34817398461777279630054811602795668745922518275227441104 * q^44 - 45061363378216725453974438646463842380148485881039366224 * q^46 - 58003762634770246900699775563009450632230835045286599360 * q^47 + 985569916983315185097203394977137449656339808292459655670 * q^49 - 4791887184864825461869475209769884139573386495444648751250 * q^50 - 772447381048143948901083488309399868612217101599766652776 * q^52 + 13674721974185597882029982508413224730588130474226494780636 * q^53 - 51238754618576674303553172437218137404754442562163094366800 * q^55 + 53382539406310631647595973723370754348378361469563798407040 * q^56 - 27334542479326918025552783071893481077859694969007500722812 * q^58 - 432173245375539353201786532564121354794334705181731449983112 * q^59 - 301681480554705175984062079070767927549030780778630557968540 * q^61 - 1319649268553974306953641963470020465251839304368009232497584 * q^62 - 3306273837825060723687391413275118884560206796975317864472512 * q^64 - 9144509139500418095807614952796559412618850636965585264371800 * q^65 - 3659535002024051270225014883853538282826668950514180780948296 * q^67 - 62841982068874697565842994801948402899655187355391437927918088 * q^68 - 17848574477080955030302460292958517135297977483696841850120000 * q^70 - 252155511033891103624460277167902994429076906738358010146768272 * q^71 + 166779610709719144717689715238124518472612391435088881765181724 * q^73 - 1006325717889854285502211107525082701977251477599580185617852868 * q^74 - 517707814526076465205777997582680722788148819042185613752993712 * q^76 - 352534620603367398775736559627568751080150267776772663929922944 * q^77 - 4778664108337215079572742262604077882794836667809906425462078640 * q^79 - 22035563788144287210408960904426824039627000323030751017638600800 * q^80 + 64371214133499796977109337023506169313379178165909274002938946284 * q^82 - 36651193288697208236374412380857358965233031511415957283935392632 * q^83 + 251284152586026236911243321213724923566970783996009477585132585800 * q^85 - 109459654412686722699057856511584566836933916033705406023221718504 * q^86 + 294858564158317243888419031127963434466163056120837408554388440992 * q^88 + 24716082341461782003245292062820103472910477446347105193539129092 * q^89 + 1637449943486433383394466120659741425501433624430401587862051946176 * q^91 - 4192506910423434290693315227336082767370233979633693670230439475872 * q^92 + 10776123537142027626725320636495971787147507990566237758042792171712 * q^94 - 8892438758299572900094061329818154779583617585762349202154337045200 * q^95 + 3864203546244162410999773872217768224094576263762936458169046609164 * q^97 - 26255683859954817683324025976879398726779583524717348419525625709774 * q^98

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