LMFDB - Embedded newform 153.10.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,10,Mod(1,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("153.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	153.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:	$78.8004829331$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 $ x^5 - 2x^4 - 1596x^3 + 5754x^2 + 488987x - 2711704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$5.77274$ of defining polynomial
Character	$\chi$	$=$	153.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.22726 q^{2} -510.494 q^{4} +1620.18 q^{5} -1834.42 q^{7} -1254.87 q^{8} +O(q^{10})$	\(q+1.22726 q^{2} -510.494 q^{4} +1620.18 q^{5} -1834.42 q^{7} -1254.87 q^{8} +1988.39 q^{10} +31779.3 q^{11} -132363. q^{13} -2251.32 q^{14} +259833. q^{16} +83521.0 q^{17} -1603.79 q^{19} -827094. q^{20} +39001.6 q^{22} -23254.0 q^{23} +671873. q^{25} -162444. q^{26} +936463. q^{28} -3.73267e6 q^{29} +8.91479e6 q^{31} +961376. q^{32} +102502. q^{34} -2.97211e6 q^{35} -1.20475e7 q^{37} -1968.28 q^{38} -2.03312e6 q^{40} +1.26779e7 q^{41} +2.86352e7 q^{43} -1.62231e7 q^{44} -28538.8 q^{46} +7.17761e6 q^{47} -3.69885e7 q^{49} +824565. q^{50} +6.75705e7 q^{52} +5.96065e7 q^{53} +5.14884e7 q^{55} +2.30196e6 q^{56} -4.58096e6 q^{58} -1.85990e8 q^{59} -2.00037e8 q^{61} +1.09408e7 q^{62} -1.31855e8 q^{64} -2.14453e8 q^{65} -1.27030e8 q^{67} -4.26370e7 q^{68} -3.64756e6 q^{70} +3.27860e8 q^{71} -1.48678e8 q^{73} -1.47854e7 q^{74} +818726. q^{76} -5.82968e7 q^{77} -2.58778e8 q^{79} +4.20977e8 q^{80} +1.55591e7 q^{82} -3.45060e8 q^{83} +1.35319e8 q^{85} +3.51430e7 q^{86} -3.98789e7 q^{88} -4.03936e8 q^{89} +2.42810e8 q^{91} +1.18710e7 q^{92} +8.80881e6 q^{94} -2.59844e6 q^{95} -9.89973e8 q^{97} -4.53946e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 33 q^{2} + 853 q^{4} - 1480 q^{5} - 13202 q^{7} + 42423 q^{8}+O(q^{10}) $ 5 * q + 33 * q^2 + 853 * q^4 - 1480 * q^5 - 13202 * q^7 + 42423 * q^8	\( 5 q + 33 q^{2} + 853 q^{4} - 1480 q^{5} - 13202 q^{7} + 42423 q^{8} - 89328 q^{10} + 68036 q^{11} - 158862 q^{13} + 84700 q^{14} + 350225 q^{16} + 417605 q^{17} - 370992 q^{19} - 1632640 q^{20} + 122290 q^{22} - 1645870 q^{23} + 3270239 q^{25} - 734846 q^{26} + 183372 q^{28} - 3668616 q^{29} - 7262362 q^{31} + 5605919 q^{32} + 2756193 q^{34} + 26503988 q^{35} - 31420708 q^{37} - 18513700 q^{38} - 53930464 q^{40} + 7996938 q^{41} - 56908268 q^{43} - 43323054 q^{44} - 32063472 q^{46} + 16903336 q^{47} - 11784059 q^{49} - 85921093 q^{50} + 173619082 q^{52} + 83362982 q^{53} + 6363364 q^{55} - 317409372 q^{56} + 64577488 q^{58} + 37946604 q^{59} - 77685452 q^{61} - 324855300 q^{62} + 131623105 q^{64} + 40321288 q^{65} - 304503600 q^{67} + 71243413 q^{68} - 122787392 q^{70} + 476602922 q^{71} - 289980486 q^{73} - 262289012 q^{74} - 1031276084 q^{76} + 143385648 q^{77} - 828240610 q^{79} - 912750944 q^{80} - 1109615654 q^{82} - 194681148 q^{83} - 123611080 q^{85} - 1164707144 q^{86} - 1017979978 q^{88} - 376848106 q^{89} + 194543664 q^{91} - 2506713088 q^{92} - 2244811104 q^{94} - 1498679864 q^{95} + 692035246 q^{97} - 871744055 q^{98}+O(q^{100}) \) 5 * q + 33 * q^2 + 853 * q^4 - 1480 * q^5 - 13202 * q^7 + 42423 * q^8 - 89328 * q^10 + 68036 * q^11 - 158862 * q^13 + 84700 * q^14 + 350225 * q^16 + 417605 * q^17 - 370992 * q^19 - 1632640 * q^20 + 122290 * q^22 - 1645870 * q^23 + 3270239 * q^25 - 734846 * q^26 + 183372 * q^28 - 3668616 * q^29 - 7262362 * q^31 + 5605919 * q^32 + 2756193 * q^34 + 26503988 * q^35 - 31420708 * q^37 - 18513700 * q^38 - 53930464 * q^40 + 7996938 * q^41 - 56908268 * q^43 - 43323054 * q^44 - 32063472 * q^46 + 16903336 * q^47 - 11784059 * q^49 - 85921093 * q^50 + 173619082 * q^52 + 83362982 * q^53 + 6363364 * q^55 - 317409372 * q^56 + 64577488 * q^58 + 37946604 * q^59 - 77685452 * q^61 - 324855300 * q^62 + 131623105 * q^64 + 40321288 * q^65 - 304503600 * q^67 + 71243413 * q^68 - 122787392 * q^70 + 476602922 * q^71 - 289980486 * q^73 - 262289012 * q^74 - 1031276084 * q^76 + 143385648 * q^77 - 828240610 * q^79 - 912750944 * q^80 - 1109615654 * q^82 - 194681148 * q^83 - 123611080 * q^85 - 1164707144 * q^86 - 1017979978 * q^88 - 376848106 * q^89 + 194543664 * q^91 - 2506713088 * q^92 - 2244811104 * q^94 - 1498679864 * q^95 + 692035246 * q^97 - 871744055 * 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 $

$2$	1.22726	0.0542379	0.0271189	−	0.999632i	$-0.491367\pi$
$2$	1.22726	0.0542379	0.0271189	+	0.999632i	$0.491367\pi$
$3$	0	0
$3$	0	0
$4$	−510.494	−0.997058
$5$	1620.18	1.15931	0.579655	−	0.814862i	$-0.303187\pi$
$5$	1620.18	1.15931	0.579655	+	0.814862i	$0.303187\pi$
$6$	0	0
$7$	−1834.42	−0.288774	−0.144387	−	0.989521i	$-0.546121\pi$
$7$	−1834.42	−0.288774	−0.144387	+	0.989521i	$0.546121\pi$
$8$	−1254.87	−0.108316
$9$	0	0
$10$	1988.39	0.0628785
$11$	31779.3	0.654452	0.327226	−	0.944946i	$-0.393886\pi$
$11$	31779.3	0.654452	0.327226	+	0.944946i	$0.393886\pi$
$12$	0	0
$13$	−132363.	−1.28535	−0.642675	−	0.766139i	$-0.722176\pi$
$13$	−132363.	−1.28535	−0.642675	+	0.766139i	$0.722176\pi$
$14$	−2251.32	−0.0156625
$15$	0	0
$16$	259833.	0.991183
$17$	83521.0	0.242536
$17$	83521.0	0.242536
$18$	0	0
$19$	−1603.79	−0.00282330	−0.00141165	−	0.999999i	$-0.500449\pi$
$19$	−1603.79	−0.00282330	−0.00141165	+	0.999999i	$0.500449\pi$
$20$	−827094.	−1.15590
$21$	0	0
$22$	39001.6	0.0354961
$23$	−23254.0	−0.0173270	−0.00866348	−	0.999962i	$-0.502758\pi$
$23$	−23254.0	−0.0173270	−0.00866348	+	0.999962i	$0.502758\pi$
$24$	0	0
$25$	671873.	0.343999
$26$	−162444.	−0.0697147
$27$	0	0
$28$	936463.	0.287925
$29$	−3.73267e6	−0.980005	−0.490002	−	0.871721i	$-0.663004\pi$
$29$	−3.73267e6	−0.980005	−0.490002	+	0.871721i	$0.663004\pi$
$30$	0	0
$31$	8.91479e6	1.73374	0.866869	−	0.498536i	$-0.166129\pi$
$31$	8.91479e6	1.73374	0.866869	+	0.498536i	$0.166129\pi$
$32$	961376.	0.162076
$33$	0	0
$34$	102502.	0.0131546
$35$	−2.97211e6	−0.334779
$36$	0	0
$37$	−1.20475e7	−1.05679	−0.528395	−	0.848999i	$-0.677206\pi$
$37$	−1.20475e7	−1.05679	−0.528395	+	0.848999i	$0.677206\pi$
$38$	−1968.28	−0.000153130 0
$39$	0	0
$40$	−2.03312e6	−0.125572
$41$	1.26779e7	0.700680	0.350340	−	0.936623i	$-0.386066\pi$
$41$	1.26779e7	0.700680	0.350340	+	0.936623i	$0.386066\pi$
$42$	0	0
$43$	2.86352e7	1.27730	0.638650	−	0.769498i	$-0.279493\pi$
$43$	2.86352e7	1.27730	0.638650	+	0.769498i	$0.279493\pi$
$44$	−1.62231e7	−0.652526
$45$	0	0
$46$	−28538.8	−0.000939777 0
$47$	7.17761e6	0.214555	0.107278	−	0.994229i	$-0.465787\pi$
$47$	7.17761e6	0.214555	0.107278	+	0.994229i	$0.465787\pi$
$48$	0	0
$49$	−3.69885e7	−0.916609
$50$	824565.	0.0186578
$51$	0	0
$52$	6.75705e7	1.28157
$53$	5.96065e7	1.03765	0.518826	−	0.854880i	$-0.326369\pi$
$53$	5.96065e7	1.03765	0.518826	+	0.854880i	$0.326369\pi$
$54$	0	0
$55$	5.14884e7	0.758712
$56$	2.30196e6	0.0312790
$57$	0	0
$58$	−4.58096e6	−0.0531534
$59$	−1.85990e8	−1.99828	−0.999139	−	0.0414925i	$-0.986789\pi$
$59$	−1.85990e8	−1.99828	−0.999139	+	0.0414925i	$0.986789\pi$
$60$	0	0
$61$	−2.00037e8	−1.84981	−0.924905	−	0.380198i	$-0.875856\pi$
$61$	−2.00037e8	−1.84981	−0.924905	+	0.380198i	$0.875856\pi$
$62$	1.09408e7	0.0940343
$63$	0	0
$64$	−1.31855e8	−0.982393
$65$	−2.14453e8	−1.49012
$66$	0	0
$67$	−1.27030e8	−0.770137	−0.385069	−	0.922888i	$-0.625822\pi$
$67$	−1.27030e8	−0.770137	−0.385069	+	0.922888i	$0.625822\pi$
$68$	−4.26370e7	−0.241822
$69$	0	0
$70$	−3.64756e6	−0.0181577
$71$	3.27860e8	1.53118	0.765590	−	0.643329i	$-0.222447\pi$
$71$	3.27860e8	1.53118	0.765590	+	0.643329i	$0.222447\pi$
$72$	0	0
$73$	−1.48678e8	−0.612766	−0.306383	−	0.951908i	$-0.599119\pi$
$73$	−1.48678e8	−0.612766	−0.306383	+	0.951908i	$0.599119\pi$
$74$	−1.47854e7	−0.0573181
$75$	0	0
$76$	818726.	0.00281500
$77$	−5.82968e7	−0.188989
$78$	0	0
$79$	−2.58778e8	−0.747491	−0.373746	−	0.927531i	$-0.621927\pi$
$79$	−2.58778e8	−0.747491	−0.373746	+	0.927531i	$0.621927\pi$
$80$	4.20977e8	1.14909
$81$	0	0
$82$	1.55591e7	0.0380034
$83$	−3.45060e8	−0.798073	−0.399037	−	0.916935i	$-0.630655\pi$
$83$	−3.45060e8	−0.798073	−0.399037	+	0.916935i	$0.630655\pi$
$84$	0	0
$85$	1.35319e8	0.281174
$86$	3.51430e7	0.0692780
$87$	0	0
$88$	−3.98789e7	−0.0708877
$89$	−4.03936e8	−0.682428	−0.341214	−	0.939986i	$-0.610838\pi$
$89$	−4.03936e8	−0.682428	−0.341214	+	0.939986i	$0.610838\pi$
$90$	0	0
$91$	2.42810e8	0.371176
$92$	1.18710e7	0.0172760
$93$	0	0
$94$	8.80881e6	0.0116370
$95$	−2.59844e6	−0.00327308
$96$	0	0
$97$	−9.89973e8	−1.13540	−0.567702	−	0.823234i	$-0.692167\pi$
$97$	−9.89973e8	−1.13540	−0.567702	+	0.823234i	$0.692167\pi$
$98$	−4.53946e7	−0.0497149
$99$	0	0
$100$	−3.42987e8	−0.342987
$101$	1.11917e9	1.07017	0.535084	−	0.844799i	$-0.320280\pi$
$101$	1.11917e9	1.07017	0.535084	+	0.844799i	$0.320280\pi$
$102$	0	0
$103$	6.58796e6	0.00576744	0.00288372	−	0.999996i	$-0.499082\pi$
$103$	6.58796e6	0.00576744	0.00288372	+	0.999996i	$0.499082\pi$
$104$	1.66098e8	0.139224
$105$	0	0
$106$	7.31528e7	0.0562801
$107$	−1.55590e9	−1.14751	−0.573754	−	0.819028i	$-0.694513\pi$
$107$	−1.55590e9	−1.14751	−0.573754	+	0.819028i	$0.694513\pi$
$108$	0	0
$109$	6.94766e8	0.471432	0.235716	−	0.971822i	$-0.424256\pi$
$109$	6.94766e8	0.471432	0.235716	+	0.971822i	$0.424256\pi$
$110$	6.31898e7	0.0411509
$111$	0	0
$112$	−4.76644e8	−0.286228
$113$	−2.09735e9	−1.21009	−0.605047	−	0.796190i	$-0.706846\pi$
$113$	−2.09735e9	−1.21009	−0.605047	+	0.796190i	$0.706846\pi$
$114$	0	0
$115$	−3.76758e7	−0.0200873
$116$	1.90550e9	0.977122
$117$	0	0
$118$	−2.28259e8	−0.108382
$119$	−1.53213e8	−0.0700381
$120$	0	0
$121$	−1.34802e9	−0.571693
$122$	−2.45499e8	−0.100330
$123$	0	0
$124$	−4.55095e9	−1.72864
$125$	−2.07586e9	−0.760508
$126$	0	0
$127$	−4.92229e9	−1.67900	−0.839499	−	0.543361i	$-0.817151\pi$
$127$	−4.92229e9	−1.67900	−0.839499	+	0.543361i	$0.817151\pi$
$128$	−6.54045e8	−0.215359
$129$	0	0
$130$	−2.63190e8	−0.0808209
$131$	−4.54604e9	−1.34869	−0.674345	−	0.738416i	$-0.735574\pi$
$131$	−4.54604e9	−1.34869	−0.674345	+	0.738416i	$0.735574\pi$
$132$	0	0
$133$	2.94204e6	0.000815297 0
$134$	−1.55899e8	−0.0417706
$135$	0	0
$136$	−1.04808e8	−0.0262705
$137$	−5.25313e9	−1.27402	−0.637010	−	0.770856i	$-0.719829\pi$
$137$	−5.25313e9	−1.27402	−0.637010	+	0.770856i	$0.719829\pi$
$138$	0	0
$139$	1.55602e9	0.353549	0.176774	−	0.984251i	$-0.443434\pi$
$139$	1.55602e9	0.353549	0.176774	+	0.984251i	$0.443434\pi$
$140$	1.51724e9	0.333794
$141$	0	0
$142$	4.02371e8	0.0830479
$143$	−4.20641e9	−0.841200
$144$	0	0
$145$	−6.04761e9	−1.13613
$146$	−1.82467e8	−0.0332351
$147$	0	0
$148$	6.15017e9	1.05368
$149$	−2.13936e9	−0.355587	−0.177794	−	0.984068i	$-0.556896\pi$
$149$	−2.13936e9	−0.355587	−0.177794	+	0.984068i	$0.556896\pi$
$150$	0	0
$151$	−1.65162e9	−0.258531	−0.129266	−	0.991610i	$-0.541262\pi$
$151$	−1.65162e9	−0.258531	−0.129266	+	0.991610i	$0.541262\pi$
$152$	2.01255e6	0.000305809 0
$153$	0	0
$154$	−7.15455e7	−0.0102504
$155$	1.44436e10	2.00994
$156$	0	0
$157$	−4.44203e9	−0.583490	−0.291745	−	0.956496i	$-0.594236\pi$
$157$	−4.44203e9	−0.583490	−0.291745	+	0.956496i	$0.594236\pi$
$158$	−3.17589e8	−0.0405423
$159$	0	0
$160$	1.55761e9	0.187896
$161$	4.26577e7	0.00500358
$162$	0	0
$163$	2.66196e9	0.295363	0.147682	−	0.989035i	$-0.452819\pi$
$163$	2.66196e9	0.295363	0.147682	+	0.989035i	$0.452819\pi$
$164$	−6.47198e9	−0.698618
$165$	0	0
$166$	−4.23479e8	−0.0432858
$167$	1.58326e10	1.57518	0.787588	−	0.616203i	$-0.211330\pi$
$167$	1.58326e10	1.57518	0.787588	+	0.616203i	$0.211330\pi$
$168$	0	0
$169$	6.91547e9	0.652126
$170$	1.66073e8	0.0152503
$171$	0	0
$172$	−1.46181e10	−1.27354
$173$	1.27988e10	1.08633	0.543165	−	0.839626i	$-0.317226\pi$
$173$	1.27988e10	1.08633	0.543165	+	0.839626i	$0.317226\pi$
$174$	0	0
$175$	−1.23250e9	−0.0993382
$176$	8.25731e9	0.648681
$177$	0	0
$178$	−4.95735e8	−0.0370135
$179$	8.33273e9	0.606665	0.303332	−	0.952885i	$-0.401901\pi$
$179$	8.33273e9	0.606665	0.303332	+	0.952885i	$0.401901\pi$
$180$	0	0
$181$	−8.70236e9	−0.602676	−0.301338	−	0.953517i	$-0.597433\pi$
$181$	−8.70236e9	−0.602676	−0.301338	+	0.953517i	$0.597433\pi$
$182$	2.97992e8	0.0201318
$183$	0	0
$184$	2.91807e7	0.00187679
$185$	−1.95192e10	−1.22515
$186$	0	0
$187$	2.65424e9	0.158728
$188$	−3.66413e9	−0.213924
$189$	0	0
$190$	−3.18897e6	−0.000177525 0
$191$	−2.29558e10	−1.24808	−0.624040	−	0.781392i	$-0.714510\pi$
$191$	−2.29558e10	−1.24808	−0.624040	+	0.781392i	$0.714510\pi$
$192$	0	0
$193$	2.04685e10	1.06189	0.530943	−	0.847407i	$-0.321838\pi$
$193$	2.04685e10	1.06189	0.530943	+	0.847407i	$0.321838\pi$
$194$	−1.21496e9	−0.0615819
$195$	0	0
$196$	1.88824e10	0.913913
$197$	−5.81009e9	−0.274843	−0.137422	−	0.990513i	$-0.543882\pi$
$197$	−5.81009e9	−0.274843	−0.137422	+	0.990513i	$0.543882\pi$
$198$	0	0
$199$	4.49526e9	0.203196	0.101598	−	0.994826i	$-0.467604\pi$
$199$	4.49526e9	0.203196	0.101598	+	0.994826i	$0.467604\pi$
$200$	−8.43113e8	−0.0372607
$201$	0	0
$202$	1.37352e9	0.0580436
$203$	6.84730e9	0.283000
$204$	0	0
$205$	2.05405e10	0.812305
$206$	8.08516e6	0.000312814 0
$207$	0	0
$208$	−3.43922e10	−1.27402
$209$	−5.09674e7	−0.00184771
$210$	0	0
$211$	3.47865e10	1.20820	0.604101	−	0.796908i	$-0.293533\pi$
$211$	3.47865e10	1.20820	0.604101	+	0.796908i	$0.293533\pi$
$212$	−3.04287e10	−1.03460
$213$	0	0
$214$	−1.90950e9	−0.0622384
$215$	4.63944e10	1.48079
$216$	0	0
$217$	−1.63535e10	−0.500659
$218$	8.52661e8	0.0255695
$219$	0	0
$220$	−2.62845e10	−0.756480
$221$	−1.10551e10	−0.311743
$222$	0	0
$223$	−2.46348e10	−0.667078	−0.333539	−	0.942736i	$-0.608243\pi$
$223$	−2.46348e10	−0.667078	−0.333539	+	0.942736i	$0.608243\pi$
$224$	−1.76357e9	−0.0468034
$225$	0	0
$226$	−2.57401e9	−0.0656329
$227$	−4.45657e10	−1.11400	−0.556999	−	0.830513i	$-0.688047\pi$
$227$	−4.45657e10	−1.11400	−0.556999	+	0.830513i	$0.688047\pi$
$228$	0	0
$229$	6.61817e10	1.59030	0.795148	−	0.606415i	$-0.207393\pi$
$229$	6.61817e10	1.59030	0.795148	+	0.606415i	$0.207393\pi$
$230$	−4.62381e7	−0.00108949
$231$	0	0
$232$	4.68401e9	0.106150
$233$	4.35721e10	0.968516	0.484258	−	0.874925i	$-0.339090\pi$
$233$	4.35721e10	0.968516	0.484258	+	0.874925i	$0.339090\pi$
$234$	0	0
$235$	1.16291e10	0.248736
$236$	9.49468e10	1.99240
$237$	0	0
$238$	−1.88033e8	−0.00379872
$239$	−3.67128e10	−0.727825	−0.363912	−	0.931433i	$-0.618559\pi$
$239$	−3.67128e10	−0.727825	−0.363912	+	0.931433i	$0.618559\pi$
$240$	0	0
$241$	3.62693e10	0.692568	0.346284	−	0.938130i	$-0.387443\pi$
$241$	3.62693e10	0.692568	0.346284	+	0.938130i	$0.387443\pi$
$242$	−1.65438e9	−0.0310074
$243$	0	0
$244$	1.02118e11	1.84437
$245$	−5.99282e10	−1.06263
$246$	0	0
$247$	2.12283e8	0.00362893
$248$	−1.11869e10	−0.187792
$249$	0	0
$250$	−2.54763e9	−0.0412484
$251$	9.34890e10	1.48672	0.743359	−	0.668892i	$-0.233231\pi$
$251$	9.34890e10	1.48672	0.743359	+	0.668892i	$0.233231\pi$
$252$	0	0
$253$	−7.38996e8	−0.0113397
$254$	−6.04094e9	−0.0910653
$255$	0	0
$256$	6.67068e10	0.970712
$257$	−1.91619e10	−0.273993	−0.136996	−	0.990572i	$-0.543745\pi$
$257$	−1.91619e10	−0.273993	−0.136996	+	0.990572i	$0.543745\pi$
$258$	0	0
$259$	2.21002e10	0.305174
$260$	1.09477e11	1.48574
$261$	0	0
$262$	−5.57918e9	−0.0731501
$263$	−3.75028e10	−0.483352	−0.241676	−	0.970357i	$-0.577697\pi$
$263$	−3.75028e10	−0.483352	−0.241676	+	0.970357i	$0.577697\pi$
$264$	0	0
$265$	9.65735e10	1.20296
$266$	3.61065e6	4.42200e−5 0
$267$	0	0
$268$	6.48478e10	0.767872
$269$	9.36804e10	1.09085	0.545423	−	0.838161i	$-0.316369\pi$
$269$	9.36804e10	1.09085	0.545423	+	0.838161i	$0.316369\pi$
$270$	0	0
$271$	−9.81985e10	−1.10597	−0.552985	−	0.833191i	$-0.686511\pi$
$271$	−9.81985e10	−1.10597	−0.552985	+	0.833191i	$0.686511\pi$
$272$	2.17015e10	0.240397
$273$	0	0
$274$	−6.44698e9	−0.0691001
$275$	2.13517e10	0.225131
$276$	0	0
$277$	9.27606e9	0.0946683	0.0473341	−	0.998879i	$-0.484927\pi$
$277$	9.27606e9	0.0946683	0.0473341	+	0.998879i	$0.484927\pi$
$278$	1.90965e9	0.0191757
$279$	0	0
$280$	3.72960e9	0.0362620
$281$	1.04165e11	0.996649	0.498325	−	0.866991i	$-0.333949\pi$
$281$	1.04165e11	0.996649	0.498325	+	0.866991i	$0.333949\pi$
$282$	0	0
$283$	−9.57066e10	−0.886958	−0.443479	−	0.896285i	$-0.646256\pi$
$283$	−9.57066e10	−0.886958	−0.443479	+	0.896285i	$0.646256\pi$
$284$	−1.67371e11	−1.52668
$285$	0	0
$286$	−5.16237e9	−0.0456249
$287$	−2.32566e10	−0.202338
$288$	0	0
$289$	6.97576e9	0.0588235
$290$	−7.42201e9	−0.0616212
$291$	0	0
$292$	7.58993e10	0.610963
$293$	1.62664e11	1.28940	0.644698	−	0.764437i	$-0.276983\pi$
$293$	1.62664e11	1.28940	0.644698	+	0.764437i	$0.276983\pi$
$294$	0	0
$295$	−3.01338e11	−2.31662
$296$	1.51180e10	0.114468
$297$	0	0
$298$	−2.62556e9	−0.0192863
$299$	3.07797e9	0.0222712
$300$	0	0
$301$	−5.25292e10	−0.368851
$302$	−2.02697e9	−0.0140222
$303$	0	0
$304$	−4.16718e8	−0.00279841
$305$	−3.24098e11	−2.14450
$306$	0	0
$307$	−2.26286e11	−1.45390	−0.726952	−	0.686688i	$-0.759064\pi$
$307$	−2.26286e11	−1.45390	−0.726952	+	0.686688i	$0.759064\pi$
$308$	2.97601e10	0.188433
$309$	0	0
$310$	1.77261e10	0.109015
$311$	−1.17225e11	−0.710556	−0.355278	−	0.934761i	$-0.615614\pi$
$311$	−1.17225e11	−0.710556	−0.355278	+	0.934761i	$0.615614\pi$
$312$	0	0
$313$	2.85060e11	1.67876	0.839378	−	0.543549i	$-0.182920\pi$
$313$	2.85060e11	1.67876	0.839378	+	0.543549i	$0.182920\pi$
$314$	−5.45154e9	−0.0316472
$315$	0	0
$316$	1.32105e11	0.745292
$317$	9.98016e9	0.0555099	0.0277550	−	0.999615i	$-0.491164\pi$
$317$	9.98016e9	0.0555099	0.0277550	+	0.999615i	$0.491164\pi$
$318$	0	0
$319$	−1.18622e11	−0.641365
$320$	−2.13629e11	−1.13890
$321$	0	0
$322$	5.23522e7	0.000271384 0
$323$	−1.33950e8	−0.000684751 0
$324$	0	0
$325$	−8.89312e10	−0.442159
$326$	3.26692e9	0.0160199
$327$	0	0
$328$	−1.59091e10	−0.0758949
$329$	−1.31668e10	−0.0619581
$330$	0	0
$331$	−2.14841e11	−0.983766	−0.491883	−	0.870661i	$-0.663691\pi$
$331$	−2.14841e11	−0.983766	−0.491883	+	0.870661i	$0.663691\pi$
$332$	1.76151e11	0.795725
$333$	0	0
$334$	1.94308e10	0.0854342
$335$	−2.05811e11	−0.892828
$336$	0	0
$337$	−3.33228e11	−1.40737	−0.703683	−	0.710514i	$-0.748463\pi$
$337$	−3.33228e11	−1.40737	−0.703683	+	0.710514i	$0.748463\pi$
$338$	8.48710e9	0.0353699
$339$	0	0
$340$	−6.90797e10	−0.280347
$341$	2.83306e11	1.13465
$342$	0	0
$343$	1.41878e11	0.553468
$344$	−3.59335e10	−0.138352
$345$	0	0
$346$	1.57075e10	0.0589203
$347$	1.63241e10	0.0604432	0.0302216	−	0.999543i	$-0.490379\pi$
$347$	1.63241e10	0.0604432	0.0302216	+	0.999543i	$0.490379\pi$
$348$	0	0
$349$	1.61528e11	0.582819	0.291410	−	0.956598i	$-0.405876\pi$
$349$	1.61528e11	0.582819	0.291410	+	0.956598i	$0.405876\pi$
$350$	−1.51260e9	−0.00538789
$351$	0	0
$352$	3.05519e10	0.106071
$353$	−2.89170e11	−0.991212	−0.495606	−	0.868547i	$-0.665054\pi$
$353$	−2.89170e11	−0.991212	−0.495606	+	0.868547i	$0.665054\pi$
$354$	0	0
$355$	5.31194e11	1.77511
$356$	2.06207e11	0.680421
$357$	0	0
$358$	1.02265e10	0.0329042
$359$	−2.34120e11	−0.743898	−0.371949	−	0.928253i	$-0.621310\pi$
$359$	−2.34120e11	−0.743898	−0.371949	+	0.928253i	$0.621310\pi$
$360$	0	0
$361$	−3.22685e11	−0.999992
$362$	−1.06801e10	−0.0326878
$363$	0	0
$364$	−1.23953e11	−0.370084
$365$	−2.40886e11	−0.710385
$366$	0	0
$367$	−1.08932e11	−0.313442	−0.156721	−	0.987643i	$-0.550092\pi$
$367$	−1.08932e11	−0.313442	−0.156721	+	0.987643i	$0.550092\pi$
$368$	−6.04215e9	−0.0171742
$369$	0	0
$370$	−2.39551e10	−0.0664494
$371$	−1.09344e11	−0.299648
$372$	0	0
$373$	−6.82746e11	−1.82629	−0.913145	−	0.407635i	$-0.866353\pi$
$373$	−6.82746e11	−1.82629	−0.913145	+	0.407635i	$0.866353\pi$
$374$	3.25745e9	0.00860906
$375$	0	0
$376$	−9.00696e9	−0.0232398
$377$	4.94067e11	1.25965
$378$	0	0
$379$	1.87645e11	0.467156	0.233578	−	0.972338i	$-0.424957\pi$
$379$	1.87645e11	0.467156	0.233578	+	0.972338i	$0.424957\pi$
$380$	1.32649e9	0.00326345
$381$	0	0
$382$	−2.81728e10	−0.0676932
$383$	−1.01456e11	−0.240925	−0.120462	−	0.992718i	$-0.538438\pi$
$383$	−1.01456e11	−0.240925	−0.120462	+	0.992718i	$0.538438\pi$
$384$	0	0
$385$	−9.44515e10	−0.219097
$386$	2.51202e10	0.0575945
$387$	0	0
$388$	5.05375e11	1.13206
$389$	4.62050e11	1.02310	0.511548	−	0.859255i	$-0.329072\pi$
$389$	4.62050e11	1.02310	0.511548	+	0.859255i	$0.329072\pi$
$390$	0	0
$391$	−1.94220e9	−0.00420240
$392$	4.64157e10	0.0992836
$393$	0	0
$394$	−7.13051e9	−0.0149069
$395$	−4.19269e11	−0.866574
$396$	0	0
$397$	8.72806e11	1.76344	0.881720	−	0.471774i	$-0.156386\pi$
$397$	8.72806e11	1.76344	0.881720	+	0.471774i	$0.156386\pi$
$398$	5.51687e9	0.0110209
$399$	0	0
$400$	1.74575e11	0.340966
$401$	1.68101e11	0.324654	0.162327	−	0.986737i	$-0.448100\pi$
$401$	1.68101e11	0.324654	0.162327	+	0.986737i	$0.448100\pi$
$402$	0	0
$403$	−1.17999e12	−2.22846
$404$	−5.71332e11	−1.06702
$405$	0	0
$406$	8.40343e9	0.0153493
$407$	−3.82861e11	−0.691618
$408$	0	0
$409$	−6.99127e11	−1.23538	−0.617691	−	0.786421i	$-0.711932\pi$
$409$	−6.99127e11	−1.23538	−0.617691	+	0.786421i	$0.711932\pi$
$410$	2.52086e10	0.0440577
$411$	0	0
$412$	−3.36311e9	−0.00575047
$413$	3.41185e11	0.577052
$414$	0	0
$415$	−5.59060e11	−0.925214
$416$	−1.27251e11	−0.208324
$417$	0	0
$418$	−6.25505e7	−0.000100216 0
$419$	−9.68451e11	−1.53502	−0.767511	−	0.641036i	$-0.778505\pi$
$419$	−9.68451e11	−1.53502	−0.767511	+	0.641036i	$0.778505\pi$
$420$	0	0
$421$	−5.47606e11	−0.849569	−0.424784	−	0.905295i	$-0.639650\pi$
$421$	−5.47606e11	−0.849569	−0.424784	+	0.905295i	$0.639650\pi$
$422$	4.26921e10	0.0655303
$423$	0	0
$424$	−7.47983e10	−0.112395
$425$	5.61155e10	0.0834320
$426$	0	0
$427$	3.66954e11	0.534178
$428$	7.94279e11	1.14413
$429$	0	0
$430$	5.69381e10	0.0803147
$431$	−4.80670e11	−0.670964	−0.335482	−	0.942047i	$-0.608899\pi$
$431$	−4.80670e11	−0.670964	−0.335482	+	0.942047i	$0.608899\pi$
$432$	0	0
$433$	−7.09547e11	−0.970031	−0.485016	−	0.874506i	$-0.661186\pi$
$433$	−7.09547e11	−0.970031	−0.485016	+	0.874506i	$0.661186\pi$
$434$	−2.00701e10	−0.0271547
$435$	0	0
$436$	−3.54674e11	−0.470045
$437$	3.72946e7	4.89192e−5 0
$438$	0	0
$439$	1.17101e12	1.50477	0.752387	−	0.658721i	$-0.228902\pi$
$439$	1.17101e12	1.50477	0.752387	+	0.658721i	$0.228902\pi$
$440$	−6.46111e10	−0.0821808
$441$	0	0
$442$	−1.35675e10	−0.0169083
$443$	4.75055e11	0.586040	0.293020	−	0.956106i	$-0.405340\pi$
$443$	4.75055e11	0.586040	0.293020	+	0.956106i	$0.405340\pi$
$444$	0	0
$445$	−6.54450e11	−0.791146
$446$	−3.02333e10	−0.0361809
$447$	0	0
$448$	2.41877e11	0.283690
$449$	9.33820e11	1.08431	0.542156	−	0.840278i	$-0.317608\pi$
$449$	9.33820e11	1.08431	0.542156	+	0.840278i	$0.317608\pi$
$450$	0	0
$451$	4.02895e11	0.458561
$452$	1.07069e12	1.20653
$453$	0	0
$454$	−5.46938e10	−0.0604209
$455$	3.93397e11	0.430308
$456$	0	0
$457$	1.28584e12	1.37900	0.689498	−	0.724288i	$-0.257831\pi$
$457$	1.28584e12	1.37900	0.689498	+	0.724288i	$0.257831\pi$
$458$	8.12223e10	0.0862543
$459$	0	0
$460$	1.92332e10	0.0200282
$461$	−5.18444e11	−0.534623	−0.267311	−	0.963610i	$-0.586135\pi$
$461$	−5.18444e11	−0.534623	−0.267311	+	0.963610i	$0.586135\pi$
$462$	0	0
$463$	−7.76808e11	−0.785596	−0.392798	−	0.919625i	$-0.628493\pi$
$463$	−7.76808e11	−0.785596	−0.392798	+	0.919625i	$0.628493\pi$
$464$	−9.69869e11	−0.971364
$465$	0	0
$466$	5.34744e10	0.0525302
$467$	−8.28768e10	−0.0806319	−0.0403159	−	0.999187i	$-0.512836\pi$
$467$	−8.28768e10	−0.0806319	−0.0403159	+	0.999187i	$0.512836\pi$
$468$	0	0
$469$	2.33026e11	0.222396
$470$	1.42719e10	0.0134909
$471$	0	0
$472$	2.33393e11	0.216446
$473$	9.10008e11	0.835930
$474$	0	0
$475$	−1.07755e9	−0.000971213 0
$476$	7.82143e10	0.0698321
$477$	0	0
$478$	−4.50562e10	−0.0394757
$479$	2.08230e12	1.80731	0.903657	−	0.428257i	$-0.140872\pi$
$479$	2.08230e12	1.80731	0.903657	+	0.428257i	$0.140872\pi$
$480$	0	0
$481$	1.59464e12	1.35835
$482$	4.45120e10	0.0375634
$483$	0	0
$484$	6.88157e11	0.570011
$485$	−1.60394e12	−1.31629
$486$	0	0
$487$	−2.69427e11	−0.217051	−0.108525	−	0.994094i	$-0.534613\pi$
$487$	−2.69427e11	−0.217051	−0.108525	+	0.994094i	$0.534613\pi$
$488$	2.51021e11	0.200364
$489$	0	0
$490$	−7.35477e10	−0.0576350
$491$	5.87772e10	0.0456396	0.0228198	−	0.999740i	$-0.492736\pi$
$491$	5.87772e10	0.0456396	0.0228198	+	0.999740i	$0.492736\pi$
$492$	0	0
$493$	−3.11756e11	−0.237686
$494$	2.60527e8	0.000196826 0
$495$	0	0
$496$	2.31635e12	1.71845
$497$	−6.01435e11	−0.442166
$498$	0	0
$499$	−3.13142e11	−0.226094	−0.113047	−	0.993590i	$-0.536061\pi$
$499$	−3.13142e11	−0.226094	−0.113047	+	0.993590i	$0.536061\pi$
$500$	1.05972e12	0.758271
$501$	0	0
$502$	1.14736e11	0.0806365
$503$	−7.31761e11	−0.509699	−0.254849	−	0.966981i	$-0.582026\pi$
$503$	−7.31761e11	−0.509699	−0.254849	+	0.966981i	$0.582026\pi$
$504$	0	0
$505$	1.81327e12	1.24066
$506$	−9.06943e8	−0.000615039 0
$507$	0	0
$508$	2.51280e12	1.67406
$509$	−2.84601e12	−1.87935	−0.939673	−	0.342073i	$-0.888871\pi$
$509$	−2.84601e12	−1.87935	−0.939673	+	0.342073i	$0.888871\pi$
$510$	0	0
$511$	2.72739e11	0.176951
$512$	4.16738e11	0.268008
$513$	0	0
$514$	−2.35167e10	−0.0148608
$515$	1.06737e10	0.00668625
$516$	0	0
$517$	2.28100e11	0.140416
$518$	2.71228e10	0.0165520
$519$	0	0
$520$	2.69110e11	0.161404
$521$	1.42270e10	0.00845949	0.00422974	−	0.999991i	$-0.498654\pi$
$521$	1.42270e10	0.00845949	0.00422974	+	0.999991i	$0.498654\pi$
$522$	0	0
$523$	1.20853e12	0.706316	0.353158	−	0.935564i	$-0.385108\pi$
$523$	1.20853e12	0.706316	0.353158	+	0.935564i	$0.385108\pi$
$524$	2.32072e12	1.34472
$525$	0	0
$526$	−4.60259e10	−0.0262160
$527$	7.44572e11	0.420493
$528$	0	0
$529$	−1.80061e12	−0.999700
$530$	1.18521e11	0.0652460
$531$	0	0
$532$	−1.50189e9	−0.000812899 0
$533$	−1.67808e12	−0.900619
$534$	0	0
$535$	−2.52085e12	−1.33032
$536$	1.59405e11	0.0834184
$537$	0	0
$538$	1.14971e11	0.0591652
$539$	−1.17547e12	−0.599876
$540$	0	0
$541$	2.35337e12	1.18115	0.590573	−	0.806985i	$-0.298902\pi$
$541$	2.35337e12	1.18115	0.590573	+	0.806985i	$0.298902\pi$
$542$	−1.20515e11	−0.0599854
$543$	0	0
$544$	8.02951e10	0.0393092
$545$	1.12565e12	0.546536
$546$	0	0
$547$	1.30236e12	0.621996	0.310998	−	0.950411i	$-0.399337\pi$
$547$	1.30236e12	0.621996	0.310998	+	0.950411i	$0.399337\pi$
$548$	2.68169e12	1.27027
$549$	0	0
$550$	2.62041e10	0.0122106
$551$	5.98642e9	0.00276685
$552$	0	0
$553$	4.74710e11	0.215856
$554$	1.13842e10	0.00513461
$555$	0	0
$556$	−7.94340e11	−0.352509
$557$	−3.33519e12	−1.46816	−0.734078	−	0.679065i	$-0.762385\pi$
$557$	−3.33519e12	−1.46816	−0.734078	+	0.679065i	$0.762385\pi$
$558$	0	0
$559$	−3.79025e12	−1.64178
$560$	−7.72251e11	−0.331827
$561$	0	0
$562$	1.27838e11	0.0540561
$563$	9.51343e11	0.399070	0.199535	−	0.979891i	$-0.436057\pi$
$563$	9.51343e11	0.399070	0.199535	+	0.979891i	$0.436057\pi$
$564$	0	0
$565$	−3.39810e12	−1.40287
$566$	−1.17457e11	−0.0481067
$567$	0	0
$568$	−4.11422e11	−0.165852
$569$	8.14899e10	0.0325911	0.0162955	−	0.999867i	$-0.494813\pi$
$569$	8.14899e10	0.0325911	0.0162955	+	0.999867i	$0.494813\pi$
$570$	0	0
$571$	1.06368e12	0.418744	0.209372	−	0.977836i	$-0.432858\pi$
$571$	1.06368e12	0.418744	0.209372	+	0.977836i	$0.432858\pi$
$572$	2.14734e12	0.838725
$573$	0	0
$574$	−2.85420e10	−0.0109744
$575$	−1.56237e10	−0.00596046
$576$	0	0
$577$	−3.44925e12	−1.29549	−0.647743	−	0.761859i	$-0.724287\pi$
$577$	−3.44925e12	−1.29549	−0.647743	+	0.761859i	$0.724287\pi$
$578$	8.56109e9	0.00319046
$579$	0	0
$580$	3.08727e12	1.13279
$581$	6.32986e11	0.230463
$582$	0	0
$583$	1.89425e12	0.679093
$584$	1.86572e11	0.0663725
$585$	0	0
$586$	1.99631e11	0.0699341
$587$	3.31180e12	1.15131	0.575655	−	0.817693i	$-0.304747\pi$
$587$	3.31180e12	1.15131	0.575655	+	0.817693i	$0.304747\pi$
$588$	0	0
$589$	−1.42975e10	−0.00489486
$590$	−3.69821e11	−0.125649
$591$	0	0
$592$	−3.13033e12	−1.04747
$593$	−9.22763e10	−0.0306439	−0.0153219	−	0.999883i	$-0.504877\pi$
$593$	−9.22763e10	−0.0306439	−0.0153219	+	0.999883i	$0.504877\pi$
$594$	0	0
$595$	−2.48233e11	−0.0811958
$596$	1.09213e12	0.354541
$597$	0	0
$598$	3.77748e9	0.00120794
$599$	4.28034e11	0.135849	0.0679246	−	0.997690i	$-0.478362\pi$
$599$	4.28034e11	0.135849	0.0679246	+	0.997690i	$0.478362\pi$
$600$	0	0
$601$	2.92420e12	0.914266	0.457133	−	0.889398i	$-0.348876\pi$
$601$	2.92420e12	0.914266	0.457133	+	0.889398i	$0.348876\pi$
$602$	−6.44671e10	−0.0200057
$603$	0	0
$604$	8.43140e11	0.257771
$605$	−2.18405e12	−0.662770
$606$	0	0
$607$	−1.45237e12	−0.434237	−0.217118	−	0.976145i	$-0.569666\pi$
$607$	−1.45237e12	−0.434237	−0.217118	+	0.976145i	$0.569666\pi$
$608$	−1.54185e9	−0.000457589 0
$609$	0	0
$610$	−3.97753e11	−0.116313
$611$	−9.50050e11	−0.275779
$612$	0	0
$613$	5.13743e12	1.46951	0.734757	−	0.678331i	$-0.237296\pi$
$613$	5.13743e12	1.46951	0.734757	+	0.678331i	$0.237296\pi$
$614$	−2.77713e11	−0.0788567
$615$	0	0
$616$	7.31548e10	0.0204706
$617$	5.31905e12	1.47758	0.738790	−	0.673936i	$-0.235397\pi$
$617$	5.31905e12	1.47758	0.738790	+	0.673936i	$0.235397\pi$
$618$	0	0
$619$	−3.23470e12	−0.885577	−0.442789	−	0.896626i	$-0.646011\pi$
$619$	−3.23470e12	−0.885577	−0.442789	+	0.896626i	$0.646011\pi$
$620$	−7.37337e12	−2.00403
$621$	0	0
$622$	−1.43866e11	−0.0385391
$623$	7.40989e11	0.197068
$624$	0	0
$625$	−4.67554e12	−1.22566
$626$	3.49844e11	0.0910521
$627$	0	0
$628$	2.26763e12	0.581773
$629$	−1.00622e12	−0.256309
$630$	0	0
$631$	−7.91021e12	−1.98635	−0.993175	−	0.116630i	$-0.962791\pi$
$631$	−7.91021e12	−1.98635	−0.993175	+	0.116630i	$0.962791\pi$
$632$	3.24733e11	0.0809654
$633$	0	0
$634$	1.22483e10	0.00301074
$635$	−7.97501e12	−1.94648
$636$	0	0
$637$	4.89591e12	1.17816
$638$	−1.45580e11	−0.0347863
$639$	0	0
$640$	−1.05967e12	−0.249668
$641$	2.28438e12	0.534451	0.267225	−	0.963634i	$-0.413893\pi$
$641$	2.28438e12	0.534451	0.267225	+	0.963634i	$0.413893\pi$
$642$	0	0
$643$	7.52203e11	0.173534	0.0867672	−	0.996229i	$-0.472346\pi$
$643$	7.52203e11	0.173534	0.0867672	+	0.996229i	$0.472346\pi$
$644$	−2.17765e10	−0.00498886
$645$	0	0
$646$	−1.64392e8	−3.71394e−5 0
$647$	4.59159e12	1.03013	0.515067	−	0.857150i	$-0.327767\pi$
$647$	4.59159e12	1.03013	0.515067	+	0.857150i	$0.327767\pi$
$648$	0	0
$649$	−5.91064e12	−1.30778
$650$	−1.09142e11	−0.0239818
$651$	0	0
$652$	−1.35891e12	−0.294495
$653$	−4.27664e12	−0.920436	−0.460218	−	0.887806i	$-0.652229\pi$
$653$	−4.27664e12	−0.920436	−0.460218	+	0.887806i	$0.652229\pi$
$654$	0	0
$655$	−7.36542e12	−1.56355
$656$	3.29413e12	0.694502
$657$	0	0
$658$	−1.61591e10	−0.00336048
$659$	8.26860e12	1.70784	0.853920	−	0.520404i	$-0.174218\pi$
$659$	8.26860e12	1.70784	0.853920	+	0.520404i	$0.174218\pi$
$660$	0	0
$661$	4.45784e12	0.908276	0.454138	−	0.890931i	$-0.349947\pi$
$661$	4.45784e12	0.908276	0.454138	+	0.890931i	$0.349947\pi$
$662$	−2.63667e11	−0.0533574
$663$	0	0
$664$	4.33005e11	0.0864442
$665$	4.76664e9	0.000945182 0
$666$	0	0
$667$	8.67994e10	0.0169805
$668$	−8.08246e12	−1.57054
$669$	0	0
$670$	−2.52585e11	−0.0484251
$671$	−6.35705e12	−1.21061
$672$	0	0
$673$	3.90397e12	0.733566	0.366783	−	0.930307i	$-0.380459\pi$
$673$	3.90397e12	0.733566	0.366783	+	0.930307i	$0.380459\pi$
$674$	−4.08959e11	−0.0763326
$675$	0	0
$676$	−3.53030e12	−0.650207
$677$	−4.84414e12	−0.886273	−0.443137	−	0.896454i	$-0.646134\pi$
$677$	−4.84414e12	−0.886273	−0.443137	+	0.896454i	$0.646134\pi$
$678$	0	0
$679$	1.81603e12	0.327876
$680$	−1.69808e11	−0.0304557
$681$	0	0
$682$	3.47691e11	0.0615409
$683$	3.67160e12	0.645598	0.322799	−	0.946468i	$-0.395376\pi$
$683$	3.67160e12	0.645598	0.322799	+	0.946468i	$0.395376\pi$
$684$	0	0
$685$	−8.51105e12	−1.47698
$686$	1.74122e11	0.0300189
$687$	0	0
$688$	7.44037e12	1.26604
$689$	−7.88969e12	−1.33375
$690$	0	0
$691$	3.94359e12	0.658023	0.329011	−	0.944326i	$-0.393285\pi$
$691$	3.94359e12	0.658023	0.329011	+	0.944326i	$0.393285\pi$
$692$	−6.53371e12	−1.08314
$693$	0	0
$694$	2.00340e10	0.00327831
$695$	2.52104e12	0.409873
$696$	0	0
$697$	1.05887e12	0.169940
$698$	1.98238e11	0.0316109
$699$	0	0
$700$	6.29184e11	0.0990459
$701$	9.80834e12	1.53414	0.767069	−	0.641564i	$-0.221714\pi$
$701$	9.80834e12	1.53414	0.767069	+	0.641564i	$0.221714\pi$
$702$	0	0
$703$	1.93217e10	0.00298364
$704$	−4.19025e12	−0.642928
$705$	0	0
$706$	−3.54887e11	−0.0537613
$707$	−2.05304e12	−0.309037
$708$	0	0
$709$	4.04313e12	0.600910	0.300455	−	0.953796i	$-0.402861\pi$
$709$	4.04313e12	0.600910	0.300455	+	0.953796i	$0.402861\pi$
$710$	6.51915e11	0.0962783
$711$	0	0
$712$	5.06886e11	0.0739180
$713$	−2.07305e11	−0.0300404
$714$	0	0
$715$	−6.81515e12	−0.975211
$716$	−4.25381e12	−0.604880
$717$	0	0
$718$	−2.87327e11	−0.0403475
$719$	4.48823e12	0.626319	0.313159	−	0.949701i	$-0.398613\pi$
$719$	4.48823e12	0.626319	0.313159	+	0.949701i	$0.398613\pi$
$720$	0	0
$721$	−1.20851e10	−0.00166549
$722$	−3.96020e11	−0.0542374
$723$	0	0
$724$	4.44250e12	0.600903
$725$	−2.50788e12	−0.337121
$726$	0	0
$727$	−1.02503e13	−1.36092	−0.680459	−	0.732786i	$-0.738220\pi$
$727$	−1.02503e13	−1.36092	−0.680459	+	0.732786i	$0.738220\pi$
$728$	−3.04695e11	−0.0402044
$729$	0	0
$730$	−2.95631e11	−0.0385298
$731$	2.39164e12	0.309791
$732$	0	0
$733$	−1.77332e12	−0.226892	−0.113446	−	0.993544i	$-0.536189\pi$
$733$	−1.77332e12	−0.226892	−0.113446	+	0.993544i	$0.536189\pi$
$734$	−1.33688e11	−0.0170004
$735$	0	0
$736$	−2.23558e10	−0.00280828
$737$	−4.03691e12	−0.504018
$738$	0	0
$739$	2.07204e12	0.255563	0.127781	−	0.991802i	$-0.459214\pi$
$739$	2.07204e12	0.255563	0.127781	+	0.991802i	$0.459214\pi$
$740$	9.96441e12	1.22154
$741$	0	0
$742$	−1.34193e11	−0.0162523
$743$	−7.60966e12	−0.916042	−0.458021	−	0.888941i	$-0.651442\pi$
$743$	−7.60966e12	−0.916042	−0.458021	+	0.888941i	$0.651442\pi$
$744$	0	0
$745$	−3.46616e12	−0.412236
$746$	−8.37909e11	−0.0990541
$747$	0	0
$748$	−1.35497e12	−0.158261
$749$	2.85419e12	0.331371
$750$	0	0
$751$	−7.56877e12	−0.868252	−0.434126	−	0.900852i	$-0.642943\pi$
$751$	−7.56877e12	−0.868252	−0.434126	+	0.900852i	$0.642943\pi$
$752$	1.86498e12	0.212664
$753$	0	0
$754$	6.06350e11	0.0683207
$755$	−2.67592e12	−0.299718
$756$	0	0
$757$	−6.86633e12	−0.759965	−0.379982	−	0.924994i	$-0.624070\pi$
$757$	−6.86633e12	−0.759965	−0.379982	+	0.924994i	$0.624070\pi$
$758$	2.30290e11	0.0253375
$759$	0	0
$760$	3.26070e9	0.000354528 0
$761$	−9.51816e12	−1.02878	−0.514389	−	0.857557i	$-0.671981\pi$
$761$	−9.51816e12	−1.02878	−0.514389	+	0.857557i	$0.671981\pi$
$762$	0	0
$763$	−1.27450e12	−0.136138
$764$	1.17188e13	1.24441
$765$	0	0
$766$	−1.24513e11	−0.0130672
$767$	2.46182e13	2.56849
$768$	0	0
$769$	−6.30061e12	−0.649702	−0.324851	−	0.945765i	$-0.605314\pi$
$769$	−6.30061e12	−0.649702	−0.324851	+	0.945765i	$0.605314\pi$
$770$	−1.15917e11	−0.0118833
$771$	0	0
$772$	−1.04490e13	−1.05876
$773$	1.40318e13	1.41354	0.706768	−	0.707446i	$-0.250153\pi$
$773$	1.40318e13	1.41354	0.706768	+	0.707446i	$0.250153\pi$
$774$	0	0
$775$	5.98961e12	0.596404
$776$	1.24229e12	0.122983
$777$	0	0
$778$	5.67057e11	0.0554905
$779$	−2.03327e10	−0.00197823
$780$	0	0
$781$	1.04192e13	1.00208
$782$	−2.38359e9	−0.000227930 0
$783$	0	0
$784$	−9.61082e12	−0.908528
$785$	−7.19691e12	−0.676445
$786$	0	0
$787$	1.03038e13	0.957440	0.478720	−	0.877968i	$-0.341101\pi$
$787$	1.03038e13	0.957440	0.478720	+	0.877968i	$0.341101\pi$
$788$	2.96602e12	0.274035
$789$	0	0
$790$	−5.14553e11	−0.0470011
$791$	3.84744e12	0.349444
$792$	0	0
$793$	2.64776e13	2.37765
$794$	1.07116e12	0.0956452
$795$	0	0
$796$	−2.29480e12	−0.202599
$797$	−1.57641e13	−1.38390	−0.691952	−	0.721944i	$-0.743249\pi$
$797$	−1.57641e13	−1.38390	−0.691952	+	0.721944i	$0.743249\pi$
$798$	0	0
$799$	5.99481e11	0.0520373
$800$	6.45923e11	0.0557540
$801$	0	0
$802$	2.06304e11	0.0176086
$803$	−4.72489e12	−0.401026
$804$	0	0
$805$	6.91134e10	0.00580070
$806$	−1.44816e12	−0.120867
$807$	0	0
$808$	−1.40442e12	−0.115916
$809$	−1.37214e13	−1.12623	−0.563117	−	0.826377i	$-0.690398\pi$
$809$	−1.37214e13	−1.12623	−0.563117	+	0.826377i	$0.690398\pi$
$810$	0	0
$811$	1.55198e13	1.25977	0.629887	−	0.776687i	$-0.283101\pi$
$811$	1.55198e13	1.25977	0.629887	+	0.776687i	$0.283101\pi$
$812$	−3.49550e12	−0.282168
$813$	0	0
$814$	−4.69871e11	−0.0375119
$815$	4.31286e12	0.342418
$816$	0	0
$817$	−4.59250e10	−0.00360620
$818$	−8.58013e11	−0.0670045
$819$	0	0
$820$	−1.04858e13	−0.809915
$821$	−3.40134e12	−0.261280	−0.130640	−	0.991430i	$-0.541703\pi$
$821$	−3.40134e12	−0.261280	−0.130640	+	0.991430i	$0.541703\pi$
$822$	0	0
$823$	4.01848e12	0.305325	0.152663	−	0.988278i	$-0.451215\pi$
$823$	4.01848e12	0.305325	0.152663	+	0.988278i	$0.451215\pi$
$824$	−8.26702e9	−0.000624707 0
$825$	0	0
$826$	4.18724e11	0.0312981
$827$	4.31147e12	0.320517	0.160258	−	0.987075i	$-0.448767\pi$
$827$	4.31147e12	0.320517	0.160258	+	0.987075i	$0.448767\pi$
$828$	0	0
$829$	4.42248e12	0.325215	0.162608	−	0.986691i	$-0.448010\pi$
$829$	4.42248e12	0.325215	0.162608	+	0.986691i	$0.448010\pi$
$830$	−6.86114e11	−0.0501816
$831$	0	0
$832$	1.74527e13	1.26272
$833$	−3.08932e12	−0.222310
$834$	0	0
$835$	2.56518e13	1.82612
$836$	2.60186e10	0.00184228
$837$	0	0
$838$	−1.18854e12	−0.0832563
$839$	−1.12787e13	−0.785835	−0.392917	−	0.919574i	$-0.628534\pi$
$839$	−1.12787e13	−0.785835	−0.392917	+	0.919574i	$0.628534\pi$
$840$	0	0
$841$	−5.74353e11	−0.0395910
$842$	−6.72056e11	−0.0460788
$843$	0	0
$844$	−1.77583e13	−1.20465
$845$	1.12043e13	0.756016
$846$	0	0
$847$	2.47285e12	0.165090
$848$	1.54877e13	1.02850
$849$	0	0
$850$	6.88685e10	0.00452518
$851$	2.80152e11	0.0183110
$852$	0	0
$853$	−3.07683e12	−0.198991	−0.0994954	−	0.995038i	$-0.531723\pi$
$853$	−3.07683e12	−0.198991	−0.0994954	+	0.995038i	$0.531723\pi$
$854$	4.50349e11	0.0289727
$855$	0	0
$856$	1.95246e12	0.124294
$857$	3.10840e13	1.96845	0.984223	−	0.176930i	$-0.0566166\pi$
$857$	3.10840e13	1.96845	0.984223	+	0.176930i	$0.0566166\pi$
$858$	0	0
$859$	−7.61893e12	−0.477446	−0.238723	−	0.971088i	$-0.576729\pi$
$859$	−7.61893e12	−0.477446	−0.238723	+	0.971088i	$0.576729\pi$
$860$	−2.36840e13	−1.47643
$861$	0	0
$862$	−5.89908e11	−0.0363917
$863$	2.61427e13	1.60436	0.802179	−	0.597083i	$-0.203674\pi$
$863$	2.61427e13	1.60436	0.802179	+	0.597083i	$0.203674\pi$
$864$	0	0
$865$	2.07364e13	1.25939
$866$	−8.70801e11	−0.0526124
$867$	0	0
$868$	8.34837e12	0.499186
$869$	−8.22380e12	−0.489197
$870$	0	0
$871$	1.68140e13	0.989896
$872$	−8.71840e11	−0.0510638
$873$	0	0
$874$	4.57703e7	2.65327e−6 0
$875$	3.80802e12	0.219615
$876$	0	0
$877$	−3.00641e13	−1.71613	−0.858065	−	0.513541i	$-0.828333\pi$
$877$	−3.00641e13	−1.71613	−0.858065	+	0.513541i	$0.828333\pi$
$878$	1.43714e12	0.0816158
$879$	0	0
$880$	1.33784e13	0.752023
$881$	2.06409e13	1.15435	0.577175	−	0.816620i	$-0.304155\pi$
$881$	2.06409e13	1.15435	0.577175	+	0.816620i	$0.304155\pi$
$882$	0	0
$883$	1.85711e13	1.02805	0.514026	−	0.857774i	$-0.328153\pi$
$883$	1.85711e13	1.02805	0.514026	+	0.857774i	$0.328153\pi$
$884$	5.64356e12	0.310826
$885$	0	0
$886$	5.83017e11	0.0317855
$887$	−1.35590e11	−0.00735482	−0.00367741	−	0.999993i	$-0.501171\pi$
$887$	−1.35590e11	−0.00735482	−0.00367741	+	0.999993i	$0.501171\pi$
$888$	0	0
$889$	9.02957e12	0.484852
$890$	−8.03182e11	−0.0429101
$891$	0	0
$892$	1.25759e13	0.665115
$893$	−1.15114e10	−0.000605754 0
$894$	0	0
$895$	1.35006e13	0.703313
$896$	1.19980e12	0.0621901
$897$	0	0
$898$	1.14604e12	0.0588108
$899$	−3.32759e13	−1.69907
$900$	0	0
$901$	4.97839e12	0.251668
$902$	4.94458e11	0.0248714
$903$	0	0
$904$	2.63190e12	0.131073
$905$	−1.40994e13	−0.698688
$906$	0	0
$907$	−1.36972e13	−0.672045	−0.336022	−	0.941854i	$-0.609082\pi$
$907$	−1.36972e13	−0.672045	−0.336022	+	0.941854i	$0.609082\pi$
$908$	2.27505e13	1.11072
$909$	0	0
$910$	4.82802e11	0.0233390
$911$	2.24844e13	1.08156	0.540778	−	0.841165i	$-0.318130\pi$
$911$	2.24844e13	1.08156	0.540778	+	0.841165i	$0.318130\pi$
$912$	0	0
$913$	−1.09658e13	−0.522300
$914$	1.57806e12	0.0747938
$915$	0	0
$916$	−3.37853e13	−1.58562
$917$	8.33936e12	0.389467
$918$	0	0
$919$	9.66637e12	0.447037	0.223519	−	0.974700i	$-0.428246\pi$
$919$	9.66637e12	0.447037	0.223519	+	0.974700i	$0.428246\pi$
$920$	4.72781e10	0.00217578
$921$	0	0
$922$	−6.36267e11	−0.0289968
$923$	−4.33966e13	−1.96810
$924$	0	0
$925$	−8.09439e12	−0.363535
$926$	−9.53348e11	−0.0426091
$927$	0	0
$928$	−3.58850e12	−0.158835
$929$	−8.19216e12	−0.360851	−0.180425	−	0.983589i	$-0.557747\pi$
$929$	−8.19216e12	−0.360851	−0.180425	+	0.983589i	$0.557747\pi$
$930$	0	0
$931$	5.93219e10	0.00258786
$932$	−2.22433e13	−0.965667
$933$	0	0
$934$	−1.01712e11	−0.00437330
$935$	4.30036e12	0.184015
$936$	0	0
$937$	3.49872e12	0.148279	0.0741396	−	0.997248i	$-0.476379\pi$
$937$	3.49872e12	0.148279	0.0741396	+	0.997248i	$0.476379\pi$
$938$	2.85984e11	0.0120623
$939$	0	0
$940$	−5.93656e12	−0.248004
$941$	1.51926e12	0.0631655	0.0315827	−	0.999501i	$-0.489945\pi$
$941$	1.51926e12	0.0631655	0.0315827	+	0.999501i	$0.489945\pi$
$942$	0	0
$943$	−2.94811e11	−0.0121406
$944$	−4.83263e13	−1.98066
$945$	0	0
$946$	1.11682e12	0.0453391
$947$	2.12785e13	0.859738	0.429869	−	0.902891i	$-0.358560\pi$
$947$	2.12785e13	0.859738	0.429869	+	0.902891i	$0.358560\pi$
$948$	0	0
$949$	1.96795e13	0.787619
$950$	−1.32243e9	−5.26765e−5 0
$951$	0	0
$952$	1.92262e11	0.00758626
$953$	−9.61359e12	−0.377544	−0.188772	−	0.982021i	$-0.560451\pi$
$953$	−9.61359e12	−0.377544	−0.188772	+	0.982021i	$0.560451\pi$
$954$	0	0
$955$	−3.71927e13	−1.44691
$956$	1.87417e13	0.725684
$957$	0	0
$958$	2.55553e12	0.0980249
$959$	9.63648e12	0.367904
$960$	0	0
$961$	5.30339e13	2.00585
$962$	1.95705e12	0.0736738
$963$	0	0
$964$	−1.85153e13	−0.690531
$965$	3.31627e13	1.23106
$966$	0	0
$967$	−1.08700e13	−0.399772	−0.199886	−	0.979819i	$-0.564057\pi$
$967$	−1.08700e13	−0.399772	−0.199886	+	0.979819i	$0.564057\pi$
$968$	1.69159e12	0.0619236
$969$	0	0
$970$	−1.96846e12	−0.0713925
$971$	−2.79438e13	−1.00879	−0.504393	−	0.863474i	$-0.668284\pi$
$971$	−2.79438e13	−1.00879	−0.504393	+	0.863474i	$0.668284\pi$
$972$	0	0
$973$	−2.85441e12	−0.102096
$974$	−3.30658e11	−0.0117724
$975$	0	0
$976$	−5.19763e13	−1.83350
$977$	1.49620e13	0.525369	0.262685	−	0.964882i	$-0.415392\pi$
$977$	1.49620e13	0.525369	0.262685	+	0.964882i	$0.415392\pi$
$978$	0	0
$979$	−1.28368e13	−0.446616
$980$	3.05930e13	1.05951
$981$	0	0
$982$	7.21350e10	0.00247540
$983$	−2.54966e13	−0.870946	−0.435473	−	0.900202i	$-0.643419\pi$
$983$	−2.54966e13	−0.870946	−0.435473	+	0.900202i	$0.643419\pi$
$984$	0	0
$985$	−9.41343e12	−0.318629
$986$	−3.82607e11	−0.0128916
$987$	0	0
$988$	−1.08369e11	−0.00361826
$989$	−6.65884e11	−0.0221317
$990$	0	0
$991$	−9.59893e12	−0.316149	−0.158074	−	0.987427i	$-0.550529\pi$
$991$	−9.59893e12	−0.316149	−0.158074	+	0.987427i	$0.550529\pi$
$992$	8.57047e12	0.280997
$993$	0	0
$994$	−7.38119e11	−0.0239821
$995$	7.28315e12	0.235568
$996$	0	0
$997$	−3.17533e13	−1.01780	−0.508898	−	0.860827i	$-0.669947\pi$
$997$	−3.17533e13	−1.01780	−0.508898	+	0.860827i	$0.669947\pi$
$998$	−3.84308e11	−0.0122629
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.10.a.c.1.3		5
3.2	odd	2		17.10.a.a.1.3	✓	5
12.11	even	2		272.10.a.f.1.1		5
51.50	odd	2		289.10.a.a.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.a.1.3	✓	5	3.2	odd	2
153.10.a.c.1.3		5	1.1	even	1	trivial
272.10.a.f.1.1		5	12.11	even	2
289.10.a.a.1.3		5	51.50	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	153.a (trivial)

\(f(q)\)	\(=\)	\(q+1.22726 q^{2} -510.494 q^{4} +1620.18 q^{5} -1834.42 q^{7} -1254.87 q^{8} +O(q^{10})\)	\(q+1.22726 q^{2} -510.494 q^{4} +1620.18 q^{5} -1834.42 q^{7} -1254.87 q^{8} +1988.39 q^{10} +31779.3 q^{11} -132363. q^{13} -2251.32 q^{14} +259833. q^{16} +83521.0 q^{17} -1603.79 q^{19} -827094. q^{20} +39001.6 q^{22} -23254.0 q^{23} +671873. q^{25} -162444. q^{26} +936463. q^{28} -3.73267e6 q^{29} +8.91479e6 q^{31} +961376. q^{32} +102502. q^{34} -2.97211e6 q^{35} -1.20475e7 q^{37} -1968.28 q^{38} -2.03312e6 q^{40} +1.26779e7 q^{41} +2.86352e7 q^{43} -1.62231e7 q^{44} -28538.8 q^{46} +7.17761e6 q^{47} -3.69885e7 q^{49} +824565. q^{50} +6.75705e7 q^{52} +5.96065e7 q^{53} +5.14884e7 q^{55} +2.30196e6 q^{56} -4.58096e6 q^{58} -1.85990e8 q^{59} -2.00037e8 q^{61} +1.09408e7 q^{62} -1.31855e8 q^{64} -2.14453e8 q^{65} -1.27030e8 q^{67} -4.26370e7 q^{68} -3.64756e6 q^{70} +3.27860e8 q^{71} -1.48678e8 q^{73} -1.47854e7 q^{74} +818726. q^{76} -5.82968e7 q^{77} -2.58778e8 q^{79} +4.20977e8 q^{80} +1.55591e7 q^{82} -3.45060e8 q^{83} +1.35319e8 q^{85} +3.51430e7 q^{86} -3.98789e7 q^{88} -4.03936e8 q^{89} +2.42810e8 q^{91} +1.18710e7 q^{92} +8.80881e6 q^{94} -2.59844e6 q^{95} -9.89973e8 q^{97} -4.53946e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 33 q^{2} + 853 q^{4} - 1480 q^{5} - 13202 q^{7} + 42423 q^{8}+O(q^{10}) \) 5 * q + 33 * q^2 + 853 * q^4 - 1480 * q^5 - 13202 * q^7 + 42423 * q^8	\( 5 q + 33 q^{2} + 853 q^{4} - 1480 q^{5} - 13202 q^{7} + 42423 q^{8} - 89328 q^{10} + 68036 q^{11} - 158862 q^{13} + 84700 q^{14} + 350225 q^{16} + 417605 q^{17} - 370992 q^{19} - 1632640 q^{20} + 122290 q^{22} - 1645870 q^{23} + 3270239 q^{25} - 734846 q^{26} + 183372 q^{28} - 3668616 q^{29} - 7262362 q^{31} + 5605919 q^{32} + 2756193 q^{34} + 26503988 q^{35} - 31420708 q^{37} - 18513700 q^{38} - 53930464 q^{40} + 7996938 q^{41} - 56908268 q^{43} - 43323054 q^{44} - 32063472 q^{46} + 16903336 q^{47} - 11784059 q^{49} - 85921093 q^{50} + 173619082 q^{52} + 83362982 q^{53} + 6363364 q^{55} - 317409372 q^{56} + 64577488 q^{58} + 37946604 q^{59} - 77685452 q^{61} - 324855300 q^{62} + 131623105 q^{64} + 40321288 q^{65} - 304503600 q^{67} + 71243413 q^{68} - 122787392 q^{70} + 476602922 q^{71} - 289980486 q^{73} - 262289012 q^{74} - 1031276084 q^{76} + 143385648 q^{77} - 828240610 q^{79} - 912750944 q^{80} - 1109615654 q^{82} - 194681148 q^{83} - 123611080 q^{85} - 1164707144 q^{86} - 1017979978 q^{88} - 376848106 q^{89} + 194543664 q^{91} - 2506713088 q^{92} - 2244811104 q^{94} - 1498679864 q^{95} + 692035246 q^{97} - 871744055 q^{98}+O(q^{100}) \) 5 * q + 33 * q^2 + 853 * q^4 - 1480 * q^5 - 13202 * q^7 + 42423 * q^8 - 89328 * q^10 + 68036 * q^11 - 158862 * q^13 + 84700 * q^14 + 350225 * q^16 + 417605 * q^17 - 370992 * q^19 - 1632640 * q^20 + 122290 * q^22 - 1645870 * q^23 + 3270239 * q^25 - 734846 * q^26 + 183372 * q^28 - 3668616 * q^29 - 7262362 * q^31 + 5605919 * q^32 + 2756193 * q^34 + 26503988 * q^35 - 31420708 * q^37 - 18513700 * q^38 - 53930464 * q^40 + 7996938 * q^41 - 56908268 * q^43 - 43323054 * q^44 - 32063472 * q^46 + 16903336 * q^47 - 11784059 * q^49 - 85921093 * q^50 + 173619082 * q^52 + 83362982 * q^53 + 6363364 * q^55 - 317409372 * q^56 + 64577488 * q^58 + 37946604 * q^59 - 77685452 * q^61 - 324855300 * q^62 + 131623105 * q^64 + 40321288 * q^65 - 304503600 * q^67 + 71243413 * q^68 - 122787392 * q^70 + 476602922 * q^71 - 289980486 * q^73 - 262289012 * q^74 - 1031276084 * q^76 + 143385648 * q^77 - 828240610 * q^79 - 912750944 * q^80 - 1109615654 * q^82 - 194681148 * q^83 - 123611080 * q^85 - 1164707144 * q^86 - 1017979978 * q^88 - 376848106 * q^89 + 194543664 * q^91 - 2506713088 * q^92 - 2244811104 * q^94 - 1498679864 * q^95 + 692035246 * q^97 - 871744055 * q^98

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