LMFDB - Embedded newform 153.10.a.f.1.1

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:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-43.1213$ 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)

$f(q)$	$=$	$q-43.1213 q^{2} +1347.45 q^{4} -1536.21 q^{5} +3027.69 q^{7} -36025.5 q^{8} +O(q^{10})$	\(q-43.1213 q^{2} +1347.45 q^{4} -1536.21 q^{5} +3027.69 q^{7} -36025.5 q^{8} +66243.5 q^{10} -51964.2 q^{11} -166337. q^{13} -130558. q^{14} +863574. q^{16} -83521.0 q^{17} -1.03482e6 q^{19} -2.06997e6 q^{20} +2.24076e6 q^{22} +647595. q^{23} +406829. q^{25} +7.17269e6 q^{26} +4.07964e6 q^{28} -101038. q^{29} +1.03448e6 q^{31} -1.87934e7 q^{32} +3.60153e6 q^{34} -4.65118e6 q^{35} -5.58601e6 q^{37} +4.46226e7 q^{38} +5.53429e7 q^{40} +4.18736e6 q^{41} -9.60190e6 q^{43} -7.00190e7 q^{44} -2.79251e7 q^{46} -3.98318e7 q^{47} -3.11867e7 q^{49} -1.75430e7 q^{50} -2.24131e8 q^{52} -6.22183e7 q^{53} +7.98282e7 q^{55} -1.09074e8 q^{56} +4.35690e6 q^{58} -9.60858e7 q^{59} -1.86877e8 q^{61} -4.46079e7 q^{62} +3.68245e8 q^{64} +2.55530e8 q^{65} +3.73689e7 q^{67} -1.12540e8 q^{68} +2.00565e8 q^{70} -2.04593e8 q^{71} -1.95705e8 q^{73} +2.40876e8 q^{74} -1.39436e9 q^{76} -1.57331e8 q^{77} +2.72638e8 q^{79} -1.32663e9 q^{80} -1.80564e8 q^{82} +1.96272e8 q^{83} +1.28306e8 q^{85} +4.14046e8 q^{86} +1.87204e9 q^{88} +3.93217e8 q^{89} -5.03618e8 q^{91} +8.72600e8 q^{92} +1.71760e9 q^{94} +1.58970e9 q^{95} +8.75485e8 q^{97} +1.34481e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8}+O(q^{10}) $ 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8} + 154226 q^{10} - 135536 q^{11} + 166122 q^{13} - 447252 q^{14} + 1463585 q^{16} - 584647 q^{17} + 777172 q^{19} + 917162 q^{20} - 1222520 q^{22} - 1357764 q^{23} + 1065785 q^{25} + 14379966 q^{26} - 3328892 q^{28} - 967002 q^{29} + 3546740 q^{31} - 4825461 q^{32} - 83521 q^{34} + 530736 q^{35} + 18296498 q^{37} + 49363020 q^{38} + 127155062 q^{40} - 10285686 q^{41} + 21913204 q^{43} - 96696624 q^{44} - 151509484 q^{46} - 56639800 q^{47} + 27010351 q^{49} + 261150303 q^{50} - 156226378 q^{52} - 121813562 q^{53} + 40793128 q^{55} + 196175436 q^{56} - 236833910 q^{58} - 29222388 q^{59} - 49915846 q^{61} + 73506556 q^{62} + 317922057 q^{64} + 122633668 q^{65} + 301863420 q^{67} - 199531669 q^{68} + 966315960 q^{70} - 652473940 q^{71} + 306656342 q^{73} - 249173874 q^{74} + 128694700 q^{76} + 102442536 q^{77} + 959147884 q^{79} + 692173602 q^{80} + 1046441254 q^{82} + 1512945268 q^{83} + 113755602 q^{85} + 164953236 q^{86} + 1132038848 q^{88} + 1971327114 q^{89} - 1061062864 q^{91} - 901186756 q^{92} + 2534831232 q^{94} + 3249631512 q^{95} + 2006526254 q^{97} + 2170640009 q^{98}+O(q^{100}) \) 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8 + 154226 * q^10 - 135536 * q^11 + 166122 * q^13 - 447252 * q^14 + 1463585 * q^16 - 584647 * q^17 + 777172 * q^19 + 917162 * q^20 - 1222520 * q^22 - 1357764 * q^23 + 1065785 * q^25 + 14379966 * q^26 - 3328892 * q^28 - 967002 * q^29 + 3546740 * q^31 - 4825461 * q^32 - 83521 * q^34 + 530736 * q^35 + 18296498 * q^37 + 49363020 * q^38 + 127155062 * q^40 - 10285686 * q^41 + 21913204 * q^43 - 96696624 * q^44 - 151509484 * q^46 - 56639800 * q^47 + 27010351 * q^49 + 261150303 * q^50 - 156226378 * q^52 - 121813562 * q^53 + 40793128 * q^55 + 196175436 * q^56 - 236833910 * q^58 - 29222388 * q^59 - 49915846 * q^61 + 73506556 * q^62 + 317922057 * q^64 + 122633668 * q^65 + 301863420 * q^67 - 199531669 * q^68 + 966315960 * q^70 - 652473940 * q^71 + 306656342 * q^73 - 249173874 * q^74 + 128694700 * q^76 + 102442536 * q^77 + 959147884 * q^79 + 692173602 * q^80 + 1046441254 * q^82 + 1512945268 * q^83 + 113755602 * q^85 + 164953236 * q^86 + 1132038848 * q^88 + 1971327114 * q^89 - 1061062864 * q^91 - 901186756 * q^92 + 2534831232 * q^94 + 3249631512 * q^95 + 2006526254 * q^97 + 2170640009 * 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 $

$2$	−43.1213	−1.90571	−0.952855	−	0.303426i	$-0.901869\pi$
$2$	−43.1213	−1.90571	−0.952855	+	0.303426i	$0.901869\pi$
$3$	0	0
$3$	0	0
$4$	1347.45	2.63173
$5$	−1536.21	−1.09923	−0.549613	−	0.835420i	$-0.685225\pi$
$5$	−1536.21	−1.09923	−0.549613	+	0.835420i	$0.685225\pi$
$6$	0	0
$7$	3027.69	0.476617	0.238309	−	0.971189i	$-0.423407\pi$
$7$	3027.69	0.476617	0.238309	+	0.971189i	$0.423407\pi$
$8$	−36025.5	−3.10960
$9$	0	0
$10$	66243.5	2.09480
$11$	−51964.2	−1.07013	−0.535066	−	0.844810i	$-0.679713\pi$
$11$	−51964.2	−1.07013	−0.535066	+	0.844810i	$0.679713\pi$
$12$	0	0
$13$	−166337.	−1.61527	−0.807635	−	0.589683i	$-0.799253\pi$
$13$	−166337.	−1.61527	−0.807635	+	0.589683i	$0.799253\pi$
$14$	−130558.	−0.908294
$15$	0	0
$16$	863574.	3.29427
$17$	−83521.0	−0.242536
$17$	−83521.0	−0.242536
$18$	0	0
$19$	−1.03482e6	−1.82168	−0.910840	−	0.412759i	$-0.864565\pi$
$19$	−1.03482e6	−1.82168	−0.910840	+	0.412759i	$0.864565\pi$
$20$	−2.06997e6	−2.89286
$21$	0	0
$22$	2.24076e6	2.03936
$23$	647595.	0.482535	0.241267	−	0.970459i	$-0.422437\pi$
$23$	647595.	0.482535	0.241267	+	0.970459i	$0.422437\pi$
$24$	0	0
$25$	406829.	0.208297
$26$	7.17269e6	3.07824
$27$	0	0
$28$	4.07964e6	1.25433
$29$	−101038.	−0.0265274	−0.0132637	−	0.999912i	$-0.504222\pi$
$29$	−101038.	−0.0265274	−0.0132637	+	0.999912i	$0.504222\pi$
$30$	0	0
$31$	1.03448e6	0.201184	0.100592	−	0.994928i	$-0.467926\pi$
$31$	1.03448e6	0.201184	0.100592	+	0.994928i	$0.467926\pi$
$32$	−1.87934e7	−3.16833
$33$	0	0
$34$	3.60153e6	0.462203
$35$	−4.65118e6	−0.523910
$36$	0	0
$37$	−5.58601e6	−0.489998	−0.244999	−	0.969523i	$-0.578788\pi$
$37$	−5.58601e6	−0.489998	−0.244999	+	0.969523i	$0.578788\pi$
$38$	4.46226e7	3.47159
$39$	0	0
$40$	5.53429e7	3.41816
$41$	4.18736e6	0.231426	0.115713	−	0.993283i	$-0.463085\pi$
$41$	4.18736e6	0.231426	0.115713	+	0.993283i	$0.463085\pi$
$42$	0	0
$43$	−9.60190e6	−0.428301	−0.214151	−	0.976801i	$-0.568698\pi$
$43$	−9.60190e6	−0.428301	−0.214151	+	0.976801i	$0.568698\pi$
$44$	−7.00190e7	−2.81630
$45$	0	0
$46$	−2.79251e7	−0.919571
$47$	−3.98318e7	−1.19067	−0.595333	−	0.803479i	$-0.702980\pi$
$47$	−3.98318e7	−1.19067	−0.595333	+	0.803479i	$0.702980\pi$
$48$	0	0
$49$	−3.11867e7	−0.772836
$50$	−1.75430e7	−0.396953
$51$	0	0
$52$	−2.24131e8	−4.25095
$53$	−6.22183e7	−1.08312	−0.541560	−	0.840662i	$-0.682166\pi$
$53$	−6.22183e7	−1.08312	−0.541560	+	0.840662i	$0.682166\pi$
$54$	0	0
$55$	7.98282e7	1.17632
$56$	−1.09074e8	−1.48209
$57$	0	0
$58$	4.35690e6	0.0505536
$59$	−9.60858e7	−1.03235	−0.516173	−	0.856484i	$-0.672644\pi$
$59$	−9.60858e7	−1.03235	−0.516173	+	0.856484i	$0.672644\pi$
$60$	0	0
$61$	−1.86877e8	−1.72811	−0.864055	−	0.503398i	$-0.832083\pi$
$61$	−1.86877e8	−1.72811	−0.864055	+	0.503398i	$0.832083\pi$
$62$	−4.46079e7	−0.383398
$63$	0	0
$64$	3.68245e8	2.74364
$65$	2.55530e8	1.77555
$66$	0	0
$67$	3.73689e7	0.226555	0.113278	−	0.993563i	$-0.463865\pi$
$67$	3.73689e7	0.226555	0.113278	+	0.993563i	$0.463865\pi$
$68$	−1.12540e8	−0.638288
$69$	0	0
$70$	2.00565e8	0.998420
$71$	−2.04593e8	−0.955495	−0.477748	−	0.878497i	$-0.658547\pi$
$71$	−2.04593e8	−0.955495	−0.477748	+	0.878497i	$0.658547\pi$
$72$	0	0
$73$	−1.95705e8	−0.806581	−0.403291	−	0.915072i	$-0.632134\pi$
$73$	−1.95705e8	−0.806581	−0.403291	+	0.915072i	$0.632134\pi$
$74$	2.40876e8	0.933793
$75$	0	0
$76$	−1.39436e9	−4.79417
$77$	−1.57331e8	−0.510043
$78$	0	0
$79$	2.72638e8	0.787524	0.393762	−	0.919212i	$-0.371173\pi$
$79$	2.72638e8	0.787524	0.393762	+	0.919212i	$0.371173\pi$
$80$	−1.32663e9	−3.62115
$81$	0	0
$82$	−1.80564e8	−0.441032
$83$	1.96272e8	0.453950	0.226975	−	0.973901i	$-0.427116\pi$
$83$	1.96272e8	0.453950	0.226975	+	0.973901i	$0.427116\pi$
$84$	0	0
$85$	1.28306e8	0.266601
$86$	4.14046e8	0.816218
$87$	0	0
$88$	1.87204e9	3.32769
$89$	3.93217e8	0.664319	0.332160	−	0.943223i	$-0.392223\pi$
$89$	3.93217e8	0.664319	0.332160	+	0.943223i	$0.392223\pi$
$90$	0	0
$91$	−5.03618e8	−0.769865
$92$	8.72600e8	1.26990
$93$	0	0
$94$	1.71760e9	2.26906
$95$	1.58970e9	2.00244
$96$	0	0
$97$	8.75485e8	1.00410	0.502049	−	0.864839i	$-0.332580\pi$
$97$	8.75485e8	1.00410	0.502049	+	0.864839i	$0.332580\pi$
$98$	1.34481e9	1.47280
$99$	0	0
$100$	5.48180e8	0.548180
$101$	−2.76987e8	−0.264858	−0.132429	−	0.991192i	$-0.542278\pi$
$101$	−2.76987e8	−0.264858	−0.132429	+	0.991192i	$0.542278\pi$
$102$	0	0
$103$	−5.47928e7	−0.0479685	−0.0239842	−	0.999712i	$-0.507635\pi$
$103$	−5.47928e7	−0.0479685	−0.0239842	+	0.999712i	$0.507635\pi$
$104$	5.99239e9	5.02285
$105$	0	0
$106$	2.68293e9	2.06411
$107$	−1.33346e9	−0.983449	−0.491724	−	0.870751i	$-0.663633\pi$
$107$	−1.33346e9	−0.983449	−0.491724	+	0.870751i	$0.663633\pi$
$108$	0	0
$109$	−7.04251e8	−0.477868	−0.238934	−	0.971036i	$-0.576798\pi$
$109$	−7.04251e8	−0.477868	−0.238934	+	0.971036i	$0.576798\pi$
$110$	−3.44229e9	−2.24172
$111$	0	0
$112$	2.61463e9	1.57011
$113$	−1.40406e9	−0.810091	−0.405045	−	0.914297i	$-0.632744\pi$
$113$	−1.40406e9	−0.810091	−0.405045	+	0.914297i	$0.632744\pi$
$114$	0	0
$115$	−9.94845e8	−0.530414
$116$	−1.36144e8	−0.0698130
$117$	0	0
$118$	4.14335e9	1.96735
$119$	−2.52875e8	−0.115597
$120$	0	0
$121$	3.42331e8	0.145182
$122$	8.05837e9	3.29328
$123$	0	0
$124$	1.39390e9	0.529461
$125$	2.37544e9	0.870261
$126$	0	0
$127$	4.64719e8	0.158516	0.0792581	−	0.996854i	$-0.474745\pi$
$127$	4.64719e8	0.158516	0.0792581	+	0.996854i	$0.474745\pi$
$128$	−6.25697e9	−2.06025
$129$	0	0
$130$	−1.10188e10	−3.38367
$131$	−4.70705e9	−1.39646	−0.698229	−	0.715874i	$-0.746028\pi$
$131$	−4.70705e9	−1.39646	−0.698229	+	0.715874i	$0.746028\pi$
$132$	0	0
$133$	−3.13310e9	−0.868244
$134$	−1.61140e9	−0.431748
$135$	0	0
$136$	3.00889e9	0.754190
$137$	−4.09197e9	−0.992407	−0.496203	−	0.868206i	$-0.665273\pi$
$137$	−4.09197e9	−0.992407	−0.496203	+	0.868206i	$0.665273\pi$
$138$	0	0
$139$	−4.61710e8	−0.104907	−0.0524533	−	0.998623i	$-0.516704\pi$
$139$	−4.61710e8	−0.104907	−0.0524533	+	0.998623i	$0.516704\pi$
$140$	−6.26721e9	−1.37879
$141$	0	0
$142$	8.82232e9	1.82090
$143$	8.64359e9	1.72855
$144$	0	0
$145$	1.55216e8	0.0291596
$146$	8.43904e9	1.53711
$147$	0	0
$148$	−7.52685e9	−1.28954
$149$	−1.87018e9	−0.310847	−0.155423	−	0.987848i	$-0.549674\pi$
$149$	−1.87018e9	−0.310847	−0.155423	+	0.987848i	$0.549674\pi$
$150$	0	0
$151$	−6.04895e9	−0.946856	−0.473428	−	0.880833i	$-0.656984\pi$
$151$	−6.04895e9	−0.946856	−0.473428	+	0.880833i	$0.656984\pi$
$152$	3.72798e10	5.66470
$153$	0	0
$154$	6.78433e9	0.971994
$155$	−1.58918e9	−0.221146
$156$	0	0
$157$	5.87552e9	0.771788	0.385894	−	0.922543i	$-0.373893\pi$
$157$	5.87552e9	0.771788	0.385894	+	0.922543i	$0.373893\pi$
$158$	−1.17565e10	−1.50079
$159$	0	0
$160$	2.88706e10	3.48270
$161$	1.96072e9	0.229984
$162$	0	0
$163$	1.19332e10	1.32408	0.662039	−	0.749470i	$-0.269691\pi$
$163$	1.19332e10	1.32408	0.662039	+	0.749470i	$0.269691\pi$
$164$	5.64224e9	0.609052
$165$	0	0
$166$	−8.46352e9	−0.865096
$167$	−2.11741e9	−0.210659	−0.105330	−	0.994437i	$-0.533590\pi$
$167$	−2.11741e9	−0.210659	−0.105330	+	0.994437i	$0.533590\pi$
$168$	0	0
$169$	1.70637e10	1.60910
$170$	−5.53273e9	−0.508065
$171$	0	0
$172$	−1.29380e10	−1.12717
$173$	−4.37524e9	−0.371359	−0.185680	−	0.982610i	$-0.559449\pi$
$173$	−4.37524e9	−0.371359	−0.185680	+	0.982610i	$0.559449\pi$
$174$	0	0
$175$	1.23175e9	0.0992777
$176$	−4.48749e10	−3.52531
$177$	0	0
$178$	−1.69560e10	−1.26600
$179$	−2.12791e9	−0.154922	−0.0774612	−	0.996995i	$-0.524681\pi$
$179$	−2.12791e9	−0.154922	−0.0774612	+	0.996995i	$0.524681\pi$
$180$	0	0
$181$	1.80496e10	1.25001	0.625007	−	0.780619i	$-0.285096\pi$
$181$	1.80496e10	1.25001	0.625007	+	0.780619i	$0.285096\pi$
$182$	2.17166e10	1.46714
$183$	0	0
$184$	−2.33299e10	−1.50049
$185$	8.58131e9	0.538618
$186$	0	0
$187$	4.34010e9	0.259545
$188$	−5.36713e10	−3.13351
$189$	0	0
$190$	−6.85499e10	−3.81606
$191$	6.31774e8	0.0343488	0.0171744	−	0.999853i	$-0.494533\pi$
$191$	6.31774e8	0.0343488	0.0171744	+	0.999853i	$0.494533\pi$
$192$	0	0
$193$	1.51993e10	0.788524	0.394262	−	0.918998i	$-0.371000\pi$
$193$	1.51993e10	0.788524	0.394262	+	0.918998i	$0.371000\pi$
$194$	−3.77520e10	−1.91352
$195$	0	0
$196$	−4.20224e10	−2.03390
$197$	2.63264e10	1.24535	0.622677	−	0.782479i	$-0.286045\pi$
$197$	2.63264e10	1.24535	0.622677	+	0.782479i	$0.286045\pi$
$198$	0	0
$199$	3.40221e10	1.53788	0.768940	−	0.639321i	$-0.220784\pi$
$199$	3.40221e10	1.53788	0.768940	+	0.639321i	$0.220784\pi$
$200$	−1.46562e10	−0.647720
$201$	0	0
$202$	1.19440e10	0.504743
$203$	−3.05912e8	−0.0126434
$204$	0	0
$205$	−6.43268e9	−0.254390
$206$	2.36273e9	0.0914140
$207$	0	0
$208$	−1.43645e11	−5.32114
$209$	5.37734e10	1.94944
$210$	0	0
$211$	−2.29918e10	−0.798550	−0.399275	−	0.916831i	$-0.630738\pi$
$211$	−2.29918e10	−0.798550	−0.399275	+	0.916831i	$0.630738\pi$
$212$	−8.38358e10	−2.85048
$213$	0	0
$214$	5.75003e10	1.87417
$215$	1.47506e10	0.470800
$216$	0	0
$217$	3.13207e9	0.0958876
$218$	3.03682e10	0.910678
$219$	0	0
$220$	1.07564e11	3.09575
$221$	1.38927e10	0.391760
$222$	0	0
$223$	−5.81614e10	−1.57494	−0.787468	−	0.616355i	$-0.788609\pi$
$223$	−5.81614e10	−1.57494	−0.787468	+	0.616355i	$0.788609\pi$
$224$	−5.69004e10	−1.51008
$225$	0	0
$226$	6.05450e10	1.54380
$227$	6.36497e9	0.159104	0.0795518	−	0.996831i	$-0.474651\pi$
$227$	6.36497e9	0.159104	0.0795518	+	0.996831i	$0.474651\pi$
$228$	0	0
$229$	−7.25334e10	−1.74292	−0.871461	−	0.490464i	$-0.836827\pi$
$229$	−7.25334e10	−1.74292	−0.871461	+	0.490464i	$0.836827\pi$
$230$	4.28990e10	1.01082
$231$	0	0
$232$	3.63996e9	0.0824898
$233$	8.13370e10	1.80795	0.903975	−	0.427585i	$-0.140635\pi$
$233$	8.13370e10	1.80795	0.903975	+	0.427585i	$0.140635\pi$
$234$	0	0
$235$	6.11902e10	1.30881
$236$	−1.29470e11	−2.71686
$237$	0	0
$238$	1.09043e10	0.220294
$239$	−7.48651e10	−1.48419	−0.742094	−	0.670296i	$-0.766167\pi$
$239$	−7.48651e10	−1.48419	−0.742094	+	0.670296i	$0.766167\pi$
$240$	0	0
$241$	−1.06255e10	−0.202896	−0.101448	−	0.994841i	$-0.532348\pi$
$241$	−1.06255e10	−0.202896	−0.101448	+	0.994841i	$0.532348\pi$
$242$	−1.47618e10	−0.276674
$243$	0	0
$244$	−2.51806e11	−4.54792
$245$	4.79095e10	0.849521
$246$	0	0
$247$	1.72129e11	2.94250
$248$	−3.72675e10	−0.625602
$249$	0	0
$250$	−1.02432e11	−1.65846
$251$	9.55285e10	1.51915	0.759576	−	0.650418i	$-0.225406\pi$
$251$	9.55285e10	1.51915	0.759576	+	0.650418i	$0.225406\pi$
$252$	0	0
$253$	−3.36518e10	−0.516376
$254$	−2.00393e10	−0.302086
$255$	0	0
$256$	8.12676e10	1.18260
$257$	−6.50855e10	−0.930647	−0.465324	−	0.885141i	$-0.654062\pi$
$257$	−6.50855e10	−0.930647	−0.465324	+	0.885141i	$0.654062\pi$
$258$	0	0
$259$	−1.69127e10	−0.233541
$260$	3.44313e11	4.67276
$261$	0	0
$262$	2.02974e11	2.66124
$263$	6.33984e10	0.817104	0.408552	−	0.912735i	$-0.366034\pi$
$263$	6.33984e10	0.817104	0.408552	+	0.912735i	$0.366034\pi$
$264$	0	0
$265$	9.55806e10	1.19059
$266$	1.35103e11	1.65462
$267$	0	0
$268$	5.03526e10	0.596232
$269$	7.50317e10	0.873695	0.436847	−	0.899536i	$-0.356095\pi$
$269$	7.50317e10	0.873695	0.436847	+	0.899536i	$0.356095\pi$
$270$	0	0
$271$	−9.55753e10	−1.07643	−0.538213	−	0.842809i	$-0.680900\pi$
$271$	−9.55753e10	−1.07643	−0.538213	+	0.842809i	$0.680900\pi$
$272$	−7.21266e10	−0.798979
$273$	0	0
$274$	1.76451e11	1.89124
$275$	−2.11406e10	−0.222905
$276$	0	0
$277$	−1.40532e10	−0.143422	−0.0717110	−	0.997425i	$-0.522846\pi$
$277$	−1.40532e10	−0.143422	−0.0717110	+	0.997425i	$0.522846\pi$
$278$	1.99095e10	0.199922
$279$	0	0
$280$	1.67561e11	1.62915
$281$	−1.00661e11	−0.963124	−0.481562	−	0.876412i	$-0.659930\pi$
$281$	−1.00661e11	−0.963124	−0.481562	+	0.876412i	$0.659930\pi$
$282$	0	0
$283$	7.78714e10	0.721670	0.360835	−	0.932630i	$-0.382492\pi$
$283$	7.78714e10	0.721670	0.360835	+	0.932630i	$0.382492\pi$
$284$	−2.75678e11	−2.51461
$285$	0	0
$286$	−3.72723e11	−3.29412
$287$	1.26780e10	0.110302
$288$	0	0
$289$	6.97576e9	0.0588235
$290$	−6.69314e9	−0.0555698
$291$	0	0
$292$	−2.63701e11	−2.12270
$293$	8.86150e10	0.702429	0.351215	−	0.936295i	$-0.385769\pi$
$293$	8.86150e10	0.702429	0.351215	+	0.936295i	$0.385769\pi$
$294$	0	0
$295$	1.47608e11	1.13478
$296$	2.01239e11	1.52370
$297$	0	0
$298$	8.06447e10	0.592383
$299$	−1.07719e11	−0.779423
$300$	0	0
$301$	−2.90716e10	−0.204136
$302$	2.60839e11	1.80443
$303$	0	0
$304$	−8.93641e11	−6.00111
$305$	2.87083e11	1.89958
$306$	0	0
$307$	−1.69929e11	−1.09180	−0.545902	−	0.837849i	$-0.683813\pi$
$307$	−1.69929e11	−1.09180	−0.545902	+	0.837849i	$0.683813\pi$
$308$	−2.11995e11	−1.34230
$309$	0	0
$310$	6.85274e10	0.421441
$311$	−1.18662e11	−0.719265	−0.359633	−	0.933094i	$-0.617098\pi$
$311$	−1.18662e11	−0.719265	−0.359633	+	0.933094i	$0.617098\pi$
$312$	0	0
$313$	2.52103e11	1.48467	0.742333	−	0.670032i	$-0.233719\pi$
$313$	2.52103e11	1.48467	0.742333	+	0.670032i	$0.233719\pi$
$314$	−2.53360e11	−1.47080
$315$	0	0
$316$	3.67365e11	2.07255
$317$	−7.54487e10	−0.419648	−0.209824	−	0.977739i	$-0.567289\pi$
$317$	−7.54487e10	−0.419648	−0.209824	+	0.977739i	$0.567289\pi$
$318$	0	0
$319$	5.25038e9	0.0283878
$320$	−5.65702e11	−3.01587
$321$	0	0
$322$	−8.45486e10	−0.438283
$323$	8.64289e10	0.441822
$324$	0	0
$325$	−6.76709e10	−0.336455
$326$	−5.14576e11	−2.52331
$327$	0	0
$328$	−1.50852e11	−0.719645
$329$	−1.20598e11	−0.567492
$330$	0	0
$331$	−2.39508e11	−1.09672	−0.548358	−	0.836244i	$-0.684747\pi$
$331$	−2.39508e11	−1.09672	−0.548358	+	0.836244i	$0.684747\pi$
$332$	2.64466e11	1.19467
$333$	0	0
$334$	9.13054e10	0.401455
$335$	−5.74067e10	−0.249035
$336$	0	0
$337$	8.05715e10	0.340288	0.170144	−	0.985419i	$-0.445577\pi$
$337$	8.05715e10	0.340288	0.170144	+	0.985419i	$0.445577\pi$
$338$	−7.35807e11	−3.06647
$339$	0	0
$340$	1.72886e11	0.701623
$341$	−5.37557e10	−0.215293
$342$	0	0
$343$	−2.16602e11	−0.844964
$344$	3.45913e11	1.33185
$345$	0	0
$346$	1.88666e11	0.707703
$347$	3.81897e11	1.41405	0.707024	−	0.707190i	$-0.250037\pi$
$347$	3.81897e11	1.41405	0.707024	+	0.707190i	$0.250037\pi$
$348$	0	0
$349$	−2.86306e11	−1.03304	−0.516518	−	0.856276i	$-0.672772\pi$
$349$	−2.86306e11	−1.03304	−0.516518	+	0.856276i	$0.672772\pi$
$350$	−5.31147e10	−0.189195
$351$	0	0
$352$	9.76583e11	3.39053
$353$	−3.83234e10	−0.131364	−0.0656822	−	0.997841i	$-0.520922\pi$
$353$	−3.83234e10	−0.131364	−0.0656822	+	0.997841i	$0.520922\pi$
$354$	0	0
$355$	3.14299e11	1.05030
$356$	5.29838e11	1.74831
$357$	0	0
$358$	9.17581e10	0.295237
$359$	8.46163e10	0.268862	0.134431	−	0.990923i	$-0.457079\pi$
$359$	8.46163e10	0.268862	0.134431	+	0.990923i	$0.457079\pi$
$360$	0	0
$361$	7.48157e11	2.31852
$362$	−7.78323e11	−2.38216
$363$	0	0
$364$	−6.78598e11	−2.02608
$365$	3.00644e11	0.886615
$366$	0	0
$367$	6.52825e11	1.87845	0.939225	−	0.343301i	$-0.111545\pi$
$367$	6.52825e11	1.87845	0.939225	+	0.343301i	$0.111545\pi$
$368$	5.59246e11	1.58960
$369$	0	0
$370$	−3.70037e11	−1.02645
$371$	−1.88377e11	−0.516234
$372$	0	0
$373$	−9.69405e10	−0.259308	−0.129654	−	0.991559i	$-0.541387\pi$
$373$	−9.69405e10	−0.259308	−0.129654	+	0.991559i	$0.541387\pi$
$374$	−1.87151e11	−0.494618
$375$	0	0
$376$	1.43496e12	3.70250
$377$	1.68065e10	0.0428489
$378$	0	0
$379$	−6.80659e11	−1.69454	−0.847272	−	0.531159i	$-0.821757\pi$
$379$	−6.80659e11	−1.69454	−0.847272	+	0.531159i	$0.821757\pi$
$380$	2.14203e12	5.26987
$381$	0	0
$382$	−2.72429e10	−0.0654589
$383$	−1.56533e11	−0.371717	−0.185858	−	0.982577i	$-0.559507\pi$
$383$	−1.56533e11	−0.371717	−0.185858	+	0.982577i	$0.559507\pi$
$384$	0	0
$385$	2.41695e11	0.560652
$386$	−6.55412e11	−1.50270
$387$	0	0
$388$	1.17967e12	2.64251
$389$	5.55777e11	1.23063	0.615315	−	0.788282i	$-0.289029\pi$
$389$	5.55777e11	1.23063	0.615315	+	0.788282i	$0.289029\pi$
$390$	0	0
$391$	−5.40878e10	−0.117032
$392$	1.12352e12	2.40321
$393$	0	0
$394$	−1.13523e12	−2.37328
$395$	−4.18830e11	−0.865667
$396$	0	0
$397$	−2.61410e11	−0.528159	−0.264079	−	0.964501i	$-0.585068\pi$
$397$	−2.61410e11	−0.528159	−0.264079	+	0.964501i	$0.585068\pi$
$398$	−1.46708e12	−2.93075
$399$	0	0
$400$	3.51327e11	0.686186
$401$	−8.04746e10	−0.155421	−0.0777104	−	0.996976i	$-0.524761\pi$
$401$	−8.04746e10	−0.155421	−0.0777104	+	0.996976i	$0.524761\pi$
$402$	0	0
$403$	−1.72072e11	−0.324966
$404$	−3.73225e11	−0.697035
$405$	0	0
$406$	1.31913e10	0.0240947
$407$	2.90273e11	0.524362
$408$	0	0
$409$	4.96676e11	0.877643	0.438822	−	0.898574i	$-0.355396\pi$
$409$	4.96676e11	0.877643	0.438822	+	0.898574i	$0.355396\pi$
$410$	2.77386e11	0.484793
$411$	0	0
$412$	−7.38303e10	−0.126240
$413$	−2.90918e11	−0.492034
$414$	0	0
$415$	−3.01516e11	−0.498993
$416$	3.12604e12	5.11770
$417$	0	0
$418$	−2.31878e12	−3.71506
$419$	−5.00093e11	−0.792661	−0.396331	−	0.918108i	$-0.629717\pi$
$419$	−5.00093e11	−0.792661	−0.396331	+	0.918108i	$0.629717\pi$
$420$	0	0
$421$	9.47398e11	1.46982	0.734908	−	0.678167i	$-0.237225\pi$
$421$	9.47398e11	1.46982	0.734908	+	0.678167i	$0.237225\pi$
$422$	9.91436e11	1.52180
$423$	0	0
$424$	2.24145e12	3.36808
$425$	−3.39788e10	−0.0505193
$426$	0	0
$427$	−5.65805e11	−0.823647
$428$	−1.79676e12	−2.58817
$429$	0	0
$430$	−6.36064e11	−0.897207
$431$	5.09374e11	0.711032	0.355516	−	0.934670i	$-0.384305\pi$
$431$	5.09374e11	0.711032	0.355516	+	0.934670i	$0.384305\pi$
$432$	0	0
$433$	1.25104e12	1.71032	0.855160	−	0.518365i	$-0.173459\pi$
$433$	1.25104e12	1.71032	0.855160	+	0.518365i	$0.173459\pi$
$434$	−1.35059e11	−0.182734
$435$	0	0
$436$	−9.48940e11	−1.25762
$437$	−6.70142e11	−0.879024
$438$	0	0
$439$	−1.15261e12	−1.48112	−0.740561	−	0.671989i	$-0.765440\pi$
$439$	−1.15261e12	−1.48112	−0.740561	+	0.671989i	$0.765440\pi$
$440$	−2.87585e12	−3.65788
$441$	0	0
$442$	−5.99070e11	−0.746582
$443$	−1.57617e12	−1.94440	−0.972199	−	0.234155i	$-0.924768\pi$
$443$	−1.57617e12	−1.94440	−0.972199	+	0.234155i	$0.924768\pi$
$444$	0	0
$445$	−6.04065e11	−0.730237
$446$	2.50800e12	3.00137
$447$	0	0
$448$	1.11493e12	1.30766
$449$	1.39885e12	1.62428	0.812141	−	0.583461i	$-0.198302\pi$
$449$	1.39885e12	1.62428	0.812141	+	0.583461i	$0.198302\pi$
$450$	0	0
$451$	−2.17593e11	−0.247657
$452$	−1.89190e12	−2.13194
$453$	0	0
$454$	−2.74466e11	−0.303205
$455$	7.73665e11	0.846255
$456$	0	0
$457$	3.76472e11	0.403747	0.201874	−	0.979412i	$-0.435297\pi$
$457$	3.76472e11	0.403747	0.201874	+	0.979412i	$0.435297\pi$
$458$	3.12773e12	3.32151
$459$	0	0
$460$	−1.34050e12	−1.39591
$461$	−2.03996e11	−0.210362	−0.105181	−	0.994453i	$-0.533542\pi$
$461$	−2.03996e11	−0.210362	−0.105181	+	0.994453i	$0.533542\pi$
$462$	0	0
$463$	−1.19166e12	−1.20514	−0.602571	−	0.798065i	$-0.705857\pi$
$463$	−1.19166e12	−1.20514	−0.602571	+	0.798065i	$0.705857\pi$
$464$	−8.72541e10	−0.0873886
$465$	0	0
$466$	−3.50736e12	−3.44543
$467$	1.20046e12	1.16795	0.583973	−	0.811773i	$-0.301497\pi$
$467$	1.20046e12	1.16795	0.583973	+	0.811773i	$0.301497\pi$
$468$	0	0
$469$	1.13141e11	0.107980
$470$	−2.63860e12	−2.49421
$471$	0	0
$472$	3.46154e12	3.21019
$473$	4.98955e11	0.458339
$474$	0	0
$475$	−4.20994e11	−0.379450
$476$	−3.40736e11	−0.304219
$477$	0	0
$478$	3.22828e12	2.82843
$479$	3.78765e10	0.0328746	0.0164373	−	0.999865i	$-0.494768\pi$
$479$	3.78765e10	0.0328746	0.0164373	+	0.999865i	$0.494768\pi$
$480$	0	0
$481$	9.29163e11	0.791478
$482$	4.58187e11	0.386662
$483$	0	0
$484$	4.61273e11	0.382079
$485$	−1.34493e12	−1.10373
$486$	0	0
$487$	1.88071e12	1.51510	0.757550	−	0.652778i	$-0.226396\pi$
$487$	1.88071e12	1.51510	0.757550	+	0.652778i	$0.226396\pi$
$488$	6.73233e12	5.37374
$489$	0	0
$490$	−2.06592e12	−1.61894
$491$	2.42874e11	0.188588	0.0942942	−	0.995544i	$-0.469941\pi$
$491$	2.42874e11	0.188588	0.0942942	+	0.995544i	$0.469941\pi$
$492$	0	0
$493$	8.43882e9	0.00643384
$494$	−7.42241e12	−5.60756
$495$	0	0
$496$	8.93347e11	0.662754
$497$	−6.19444e11	−0.455405
$498$	0	0
$499$	7.88648e11	0.569417	0.284709	−	0.958614i	$-0.408103\pi$
$499$	7.88648e11	0.569417	0.284709	+	0.958614i	$0.408103\pi$
$500$	3.20078e12	2.29029
$501$	0	0
$502$	−4.11931e12	−2.89506
$503$	−1.92372e12	−1.33994	−0.669972	−	0.742386i	$-0.733694\pi$
$503$	−1.92372e12	−1.33994	−0.669972	+	0.742386i	$0.733694\pi$
$504$	0	0
$505$	4.25512e11	0.291139
$506$	1.45111e12	0.984062
$507$	0	0
$508$	6.26184e11	0.417172
$509$	−2.87805e12	−1.90050	−0.950250	−	0.311487i	$-0.899173\pi$
$509$	−2.87805e12	−1.90050	−0.950250	+	0.311487i	$0.899173\pi$
$510$	0	0
$511$	−5.92532e11	−0.384431
$512$	−3.00794e11	−0.193443
$513$	0	0
$514$	2.80657e12	1.77354
$515$	8.41734e10	0.0527281
$516$	0	0
$517$	2.06983e12	1.27417
$518$	7.29297e11	0.445062
$519$	0	0
$520$	−9.20560e12	−5.52124
$521$	−2.41942e12	−1.43861	−0.719303	−	0.694697i	$-0.755539\pi$
$521$	−2.41942e12	−1.43861	−0.719303	+	0.694697i	$0.755539\pi$
$522$	0	0
$523$	2.25636e12	1.31872	0.659358	−	0.751829i	$-0.270828\pi$
$523$	2.25636e12	1.31872	0.659358	+	0.751829i	$0.270828\pi$
$524$	−6.34249e12	−3.67510
$525$	0	0
$526$	−2.73382e12	−1.55716
$527$	−8.64005e10	−0.0487942
$528$	0	0
$529$	−1.38177e12	−0.767160
$530$	−4.12156e12	−2.26893
$531$	0	0
$532$	−4.22168e12	−2.28498
$533$	−6.96515e11	−0.373816
$534$	0	0
$535$	2.04847e12	1.08103
$536$	−1.34623e12	−0.704497
$537$	0	0
$538$	−3.23547e12	−1.66501
$539$	1.62059e12	0.827036
$540$	0	0
$541$	−2.18649e12	−1.09739	−0.548694	−	0.836023i	$-0.684875\pi$
$541$	−2.18649e12	−1.09739	−0.548694	+	0.836023i	$0.684875\pi$
$542$	4.12133e12	2.05135
$543$	0	0
$544$	1.56964e12	0.768432
$545$	1.08188e12	0.525285
$546$	0	0
$547$	−7.53862e11	−0.360039	−0.180019	−	0.983663i	$-0.557616\pi$
$547$	−7.53862e11	−0.360039	−0.180019	+	0.983663i	$0.557616\pi$
$548$	−5.51371e12	−2.61175
$549$	0	0
$550$	9.11608e11	0.424792
$551$	1.04556e11	0.0483245
$552$	0	0
$553$	8.25462e11	0.375348
$554$	6.05991e11	0.273321
$555$	0	0
$556$	−6.22130e11	−0.276086
$557$	2.08949e12	0.919797	0.459898	−	0.887972i	$-0.347886\pi$
$557$	2.08949e12	0.919797	0.459898	+	0.887972i	$0.347886\pi$
$558$	0	0
$559$	1.59716e12	0.691822
$560$	−4.01663e12	−1.72590
$561$	0	0
$562$	4.34063e12	1.83544
$563$	6.61278e11	0.277393	0.138697	−	0.990335i	$-0.455709\pi$
$563$	6.61278e11	0.277393	0.138697	+	0.990335i	$0.455709\pi$
$564$	0	0
$565$	2.15694e12	0.890472
$566$	−3.35791e12	−1.37529
$567$	0	0
$568$	7.37057e12	2.97121
$569$	1.47797e12	0.591100	0.295550	−	0.955327i	$-0.404497\pi$
$569$	1.47797e12	0.591100	0.295550	+	0.955327i	$0.404497\pi$
$570$	0	0
$571$	−2.27003e12	−0.893652	−0.446826	−	0.894621i	$-0.647446\pi$
$571$	−2.27003e12	−0.893652	−0.446826	+	0.894621i	$0.647446\pi$
$572$	1.16468e13	4.54908
$573$	0	0
$574$	−5.46692e11	−0.210203
$575$	2.63461e11	0.100510
$576$	0	0
$577$	−1.93038e12	−0.725021	−0.362511	−	0.931980i	$-0.618080\pi$
$577$	−1.93038e12	−0.725021	−0.362511	+	0.931980i	$0.618080\pi$
$578$	−3.00804e11	−0.112101
$579$	0	0
$580$	2.09146e11	0.0767402
$581$	5.94251e11	0.216360
$582$	0	0
$583$	3.23312e12	1.15908
$584$	7.05036e12	2.50815
$585$	0	0
$586$	−3.82119e12	−1.33863
$587$	−2.62778e12	−0.913518	−0.456759	−	0.889590i	$-0.650990\pi$
$587$	−2.62778e12	−0.913518	−0.456759	+	0.889590i	$0.650990\pi$
$588$	0	0
$589$	−1.07049e12	−0.366492
$590$	−6.36507e12	−2.16256
$591$	0	0
$592$	−4.82393e12	−1.61419
$593$	−5.85157e12	−1.94324	−0.971620	−	0.236548i	$-0.923984\pi$
$593$	−5.85157e12	−1.94324	−0.971620	+	0.236548i	$0.923984\pi$
$594$	0	0
$595$	3.88471e11	0.127067
$596$	−2.51997e12	−0.818064
$597$	0	0
$598$	4.64500e12	1.48535
$599$	−4.56968e11	−0.145033	−0.0725163	−	0.997367i	$-0.523103\pi$
$599$	−4.56968e11	−0.145033	−0.0725163	+	0.997367i	$0.523103\pi$
$600$	0	0
$601$	−4.72333e12	−1.47677	−0.738385	−	0.674379i	$-0.764411\pi$
$601$	−4.72333e12	−1.47677	−0.738385	+	0.674379i	$0.764411\pi$
$602$	1.25360e12	0.389023
$603$	0	0
$604$	−8.15063e12	−2.49187
$605$	−5.25894e11	−0.159588
$606$	0	0
$607$	1.89920e12	0.567836	0.283918	−	0.958849i	$-0.408366\pi$
$607$	1.89920e12	0.567836	0.283918	+	0.958849i	$0.408366\pi$
$608$	1.94477e13	5.77168
$609$	0	0
$610$	−1.23794e13	−3.62005
$611$	6.62553e12	1.92325
$612$	0	0
$613$	−5.38704e12	−1.54091	−0.770456	−	0.637493i	$-0.779971\pi$
$613$	−5.38704e12	−1.54091	−0.770456	+	0.637493i	$0.779971\pi$
$614$	7.32756e12	2.08066
$615$	0	0
$616$	5.66794e12	1.58603
$617$	5.80011e11	0.161121	0.0805607	−	0.996750i	$-0.474329\pi$
$617$	5.80011e11	0.161121	0.0805607	+	0.996750i	$0.474329\pi$
$618$	0	0
$619$	−1.58371e12	−0.433579	−0.216790	−	0.976218i	$-0.569559\pi$
$619$	−1.58371e12	−0.433579	−0.216790	+	0.976218i	$0.569559\pi$
$620$	−2.14133e12	−0.581997
$621$	0	0
$622$	5.11685e12	1.37071
$623$	1.19054e12	0.316626
$624$	0	0
$625$	−4.44378e12	−1.16491
$626$	−1.08710e13	−2.82934
$627$	0	0
$628$	7.91695e12	2.03114
$629$	4.66549e11	0.118842
$630$	0	0
$631$	3.36740e12	0.845595	0.422797	−	0.906224i	$-0.361048\pi$
$631$	3.36740e12	0.845595	0.422797	+	0.906224i	$0.361048\pi$
$632$	−9.82191e12	−2.44889
$633$	0	0
$634$	3.25344e12	0.799727
$635$	−7.13908e11	−0.174245
$636$	0	0
$637$	5.18752e12	1.24834
$638$	−2.26403e11	−0.0540990
$639$	0	0
$640$	9.61205e12	2.26468
$641$	7.80868e12	1.82691	0.913454	−	0.406943i	$-0.133405\pi$
$641$	7.80868e12	1.82691	0.913454	+	0.406943i	$0.133405\pi$
$642$	0	0
$643$	−2.11639e12	−0.488255	−0.244128	−	0.969743i	$-0.578502\pi$
$643$	−2.11639e12	−0.488255	−0.244128	+	0.969743i	$0.578502\pi$
$644$	2.64196e12	0.605257
$645$	0	0
$646$	−3.72693e12	−0.841985
$647$	−3.18454e12	−0.714460	−0.357230	−	0.934016i	$-0.616279\pi$
$647$	−3.18454e12	−0.714460	−0.357230	+	0.934016i	$0.616279\pi$
$648$	0	0
$649$	4.99302e12	1.10475
$650$	2.91806e12	0.641186
$651$	0	0
$652$	1.60794e13	3.48462
$653$	−1.82854e12	−0.393545	−0.196772	−	0.980449i	$-0.563046\pi$
$653$	−1.82854e12	−0.393545	−0.196772	+	0.980449i	$0.563046\pi$
$654$	0	0
$655$	7.23104e12	1.53502
$656$	3.61609e12	0.762382
$657$	0	0
$658$	5.20036e12	1.08148
$659$	−7.92252e11	−0.163636	−0.0818181	−	0.996647i	$-0.526073\pi$
$659$	−7.92252e11	−0.163636	−0.0818181	+	0.996647i	$0.526073\pi$
$660$	0	0
$661$	−7.49133e11	−0.152634	−0.0763172	−	0.997084i	$-0.524316\pi$
$661$	−7.49133e11	−0.152634	−0.0763172	+	0.997084i	$0.524316\pi$
$662$	1.03279e13	2.09002
$663$	0	0
$664$	−7.07081e12	−1.41160
$665$	4.81311e12	0.954396
$666$	0	0
$667$	−6.54319e10	−0.0128004
$668$	−2.85309e12	−0.554398
$669$	0	0
$670$	2.47545e12	0.474589
$671$	9.71091e12	1.84931
$672$	0	0
$673$	7.01486e12	1.31811	0.659055	−	0.752095i	$-0.270957\pi$
$673$	7.01486e12	1.31811	0.659055	+	0.752095i	$0.270957\pi$
$674$	−3.47435e12	−0.648490
$675$	0	0
$676$	2.29923e13	4.23471
$677$	−7.71992e12	−1.41242	−0.706210	−	0.708002i	$-0.749597\pi$
$677$	−7.71992e12	−1.41242	−0.706210	+	0.708002i	$0.749597\pi$
$678$	0	0
$679$	2.65069e12	0.478570
$680$	−4.62229e12	−0.829025
$681$	0	0
$682$	2.31802e12	0.410286
$683$	4.25216e12	0.747680	0.373840	−	0.927493i	$-0.378041\pi$
$683$	4.25216e12	0.747680	0.373840	+	0.927493i	$0.378041\pi$
$684$	0	0
$685$	6.28614e12	1.09088
$686$	9.34014e12	1.61026
$687$	0	0
$688$	−8.29195e12	−1.41094
$689$	1.03492e13	1.74953
$690$	0	0
$691$	−2.49111e12	−0.415664	−0.207832	−	0.978165i	$-0.566641\pi$
$691$	−2.49111e12	−0.415664	−0.207832	+	0.978165i	$0.566641\pi$
$692$	−5.89539e12	−0.977317
$693$	0	0
$694$	−1.64679e13	−2.69476
$695$	7.09286e11	0.115316
$696$	0	0
$697$	−3.49732e11	−0.0561291
$698$	1.23459e13	1.96867
$699$	0	0
$700$	1.65972e12	0.261272
$701$	3.08136e11	0.0481961	0.0240980	−	0.999710i	$-0.492329\pi$
$701$	3.08136e11	0.0481961	0.0240980	+	0.999710i	$0.492329\pi$
$702$	0	0
$703$	5.78049e12	0.892619
$704$	−1.91355e13	−2.93605
$705$	0	0
$706$	1.65255e12	0.250342
$707$	−8.38630e11	−0.126236
$708$	0	0
$709$	−6.98388e12	−1.03798	−0.518990	−	0.854780i	$-0.673692\pi$
$709$	−6.98388e12	−1.03798	−0.518990	+	0.854780i	$0.673692\pi$
$710$	−1.35530e13	−2.00158
$711$	0	0
$712$	−1.41658e13	−2.06577
$713$	6.69922e11	0.0970781
$714$	0	0
$715$	−1.32784e13	−1.90007
$716$	−2.86724e12	−0.407714
$717$	0	0
$718$	−3.64876e12	−0.512373
$719$	1.30686e13	1.82368	0.911842	−	0.410540i	$-0.134660\pi$
$719$	1.30686e13	1.82368	0.911842	+	0.410540i	$0.134660\pi$
$720$	0	0
$721$	−1.65895e11	−0.0228626
$722$	−3.22615e13	−4.41842
$723$	0	0
$724$	2.43209e13	3.28970
$725$	−4.11053e10	−0.00552557
$726$	0	0
$727$	−1.13650e12	−0.150891	−0.0754456	−	0.997150i	$-0.524038\pi$
$727$	−1.13650e12	−0.150891	−0.0754456	+	0.997150i	$0.524038\pi$
$728$	1.81431e13	2.39398
$729$	0	0
$730$	−1.29642e13	−1.68963
$731$	8.01960e11	0.103878
$732$	0	0
$733$	5.78287e12	0.739904	0.369952	−	0.929051i	$-0.379374\pi$
$733$	5.78287e12	0.739904	0.369952	+	0.929051i	$0.379374\pi$
$734$	−2.81507e13	−3.57978
$735$	0	0
$736$	−1.21705e13	−1.52883
$737$	−1.94185e12	−0.242444
$738$	0	0
$739$	−1.05562e13	−1.30199	−0.650996	−	0.759081i	$-0.725649\pi$
$739$	−1.05562e13	−1.30199	−0.650996	+	0.759081i	$0.725649\pi$
$740$	1.15628e13	1.41750
$741$	0	0
$742$	8.12308e12	0.983792
$743$	−1.33049e13	−1.60163	−0.800815	−	0.598912i	$-0.795600\pi$
$743$	−1.33049e13	−1.60163	−0.800815	+	0.598912i	$0.795600\pi$
$744$	0	0
$745$	2.87300e12	0.341690
$746$	4.18020e12	0.494165
$747$	0	0
$748$	5.84805e12	0.683053
$749$	−4.03729e12	−0.468729
$750$	0	0
$751$	−2.33606e12	−0.267982	−0.133991	−	0.990983i	$-0.542779\pi$
$751$	−2.33606e12	−0.267982	−0.133991	+	0.990983i	$0.542779\pi$
$752$	−3.43977e13	−3.92238
$753$	0	0
$754$	−7.24716e11	−0.0816576
$755$	9.29248e12	1.04081
$756$	0	0
$757$	−1.17644e13	−1.30208	−0.651039	−	0.759045i	$-0.725666\pi$
$757$	−1.17644e13	−1.30208	−0.651039	+	0.759045i	$0.725666\pi$
$758$	2.93509e13	3.22931
$759$	0	0
$760$	−5.72697e13	−6.22679
$761$	−3.21795e12	−0.347815	−0.173907	−	0.984762i	$-0.555639\pi$
$761$	−3.21795e12	−0.347815	−0.173907	+	0.984762i	$0.555639\pi$
$762$	0	0
$763$	−2.13225e12	−0.227760
$764$	8.51281e11	0.0903968
$765$	0	0
$766$	6.74991e12	0.708384
$767$	1.59827e13	1.66752
$768$	0	0
$769$	−9.65995e12	−0.996108	−0.498054	−	0.867146i	$-0.665952\pi$
$769$	−9.65995e12	−0.996108	−0.498054	+	0.867146i	$0.665952\pi$
$770$	−1.04222e13	−1.06844
$771$	0	0
$772$	2.04802e13	2.07518
$773$	3.02219e12	0.304449	0.152224	−	0.988346i	$-0.451356\pi$
$773$	3.02219e12	0.304449	0.152224	+	0.988346i	$0.451356\pi$
$774$	0	0
$775$	4.20855e11	0.0419059
$776$	−3.15398e13	−3.12235
$777$	0	0
$778$	−2.39658e13	−2.34522
$779$	−4.33315e12	−0.421585
$780$	0	0
$781$	1.06315e13	1.02251
$782$	2.33234e12	0.223029
$783$	0	0
$784$	−2.69320e13	−2.54593
$785$	−9.02606e12	−0.848369
$786$	0	0
$787$	−1.47037e13	−1.36628	−0.683141	−	0.730286i	$-0.739387\pi$
$787$	−1.47037e13	−1.36628	−0.683141	+	0.730286i	$0.739387\pi$
$788$	3.54734e13	3.27744
$789$	0	0
$790$	1.80605e13	1.64971
$791$	−4.25106e12	−0.386103
$792$	0	0
$793$	3.10846e13	2.79136
$794$	1.12723e13	1.00652
$795$	0	0
$796$	4.58430e13	4.04729
$797$	1.44405e13	1.26771	0.633856	−	0.773451i	$-0.281471\pi$
$797$	1.44405e13	1.26771	0.633856	+	0.773451i	$0.281471\pi$
$798$	0	0
$799$	3.32680e12	0.288779
$800$	−7.64569e12	−0.659951
$801$	0	0
$802$	3.47017e12	0.296187
$803$	1.01696e13	0.863148
$804$	0	0
$805$	−3.01208e12	−0.252805
$806$	7.41997e12	0.619291
$807$	0	0
$808$	9.97860e12	0.823604
$809$	−1.10265e13	−0.905041	−0.452521	−	0.891754i	$-0.649475\pi$
$809$	−1.10265e13	−0.905041	−0.452521	+	0.891754i	$0.649475\pi$
$810$	0	0
$811$	1.97221e12	0.160088	0.0800440	−	0.996791i	$-0.474494\pi$
$811$	1.97221e12	0.160088	0.0800440	+	0.996791i	$0.474494\pi$
$812$	−4.12200e11	−0.0332741
$813$	0	0
$814$	−1.25169e13	−0.999282
$815$	−1.83320e13	−1.45546
$816$	0	0
$817$	9.93621e12	0.780228
$818$	−2.14173e13	−1.67253
$819$	0	0
$820$	−8.66769e12	−0.669485
$821$	1.24725e13	0.958093	0.479047	−	0.877789i	$-0.340982\pi$
$821$	1.24725e13	0.958093	0.479047	+	0.877789i	$0.340982\pi$
$822$	0	0
$823$	5.63904e12	0.428455	0.214228	−	0.976784i	$-0.431277\pi$
$823$	5.63904e12	0.428455	0.214228	+	0.976784i	$0.431277\pi$
$824$	1.97394e12	0.149163
$825$	0	0
$826$	1.25448e13	0.937674
$827$	6.43118e12	0.478097	0.239048	−	0.971008i	$-0.423165\pi$
$827$	6.43118e12	0.478097	0.239048	+	0.971008i	$0.423165\pi$
$828$	0	0
$829$	−4.51844e12	−0.332272	−0.166136	−	0.986103i	$-0.553129\pi$
$829$	−4.51844e12	−0.332272	−0.166136	+	0.986103i	$0.553129\pi$
$830$	1.30018e13	0.950936
$831$	0	0
$832$	−6.12529e13	−4.43171
$833$	2.60475e12	0.187440
$834$	0	0
$835$	3.25279e12	0.231562
$836$	7.24568e13	5.13039
$837$	0	0
$838$	2.15647e13	1.51058
$839$	−1.73764e13	−1.21068	−0.605342	−	0.795965i	$-0.706964\pi$
$839$	−1.73764e13	−1.21068	−0.605342	+	0.795965i	$0.706964\pi$
$840$	0	0
$841$	−1.44969e13	−0.999296
$842$	−4.08530e13	−2.80104
$843$	0	0
$844$	−3.09802e13	−2.10157
$845$	−2.62134e13	−1.76876
$846$	0	0
$847$	1.03647e12	0.0691962
$848$	−5.37301e13	−3.56809
$849$	0	0
$850$	1.46521e12	0.0962752
$851$	−3.61747e12	−0.236441
$852$	0	0
$853$	−3.23489e12	−0.209213	−0.104607	−	0.994514i	$-0.533358\pi$
$853$	−3.23489e12	−0.209213	−0.104607	+	0.994514i	$0.533358\pi$
$854$	2.43982e13	1.56963
$855$	0	0
$856$	4.80384e13	3.05814
$857$	−6.56773e12	−0.415912	−0.207956	−	0.978138i	$-0.566681\pi$
$857$	−6.56773e12	−0.415912	−0.207956	+	0.978138i	$0.566681\pi$
$858$	0	0
$859$	−1.06597e13	−0.668001	−0.334000	−	0.942573i	$-0.608399\pi$
$859$	−1.06597e13	−0.668001	−0.334000	+	0.942573i	$0.608399\pi$
$860$	1.98756e13	1.23902
$861$	0	0
$862$	−2.19649e13	−1.35502
$863$	2.96333e12	0.181857	0.0909287	−	0.995857i	$-0.471016\pi$
$863$	2.96333e12	0.181857	0.0909287	+	0.995857i	$0.471016\pi$
$864$	0	0
$865$	6.72130e12	0.408207
$866$	−5.39466e13	−3.25937
$867$	0	0
$868$	4.22029e12	0.252350
$869$	−1.41674e13	−0.842755
$870$	0	0
$871$	−6.21585e12	−0.365948
$872$	2.53710e13	1.48598
$873$	0	0
$874$	2.88974e13	1.67516
$875$	7.19209e12	0.414781
$876$	0	0
$877$	−1.22652e13	−0.700128	−0.350064	−	0.936726i	$-0.613840\pi$
$877$	−1.22652e13	−0.700128	−0.350064	+	0.936726i	$0.613840\pi$
$878$	4.97019e13	2.82259
$879$	0	0
$880$	6.89375e13	3.87511
$881$	−2.36185e13	−1.32087	−0.660435	−	0.750883i	$-0.729628\pi$
$881$	−2.36185e13	−1.32087	−0.660435	+	0.750883i	$0.729628\pi$
$882$	0	0
$883$	2.46792e13	1.36618	0.683089	−	0.730335i	$-0.260636\pi$
$883$	2.46792e13	1.36618	0.683089	+	0.730335i	$0.260636\pi$
$884$	1.87196e13	1.03101
$885$	0	0
$886$	6.79663e13	3.70546
$887$	8.49974e12	0.461051	0.230526	−	0.973066i	$-0.425955\pi$
$887$	8.49974e12	0.461051	0.230526	+	0.973066i	$0.425955\pi$
$888$	0	0
$889$	1.40702e12	0.0755516
$890$	2.60481e13	1.39162
$891$	0	0
$892$	−7.83694e13	−4.14481
$893$	4.12186e13	2.16901
$894$	0	0
$895$	3.26892e12	0.170295
$896$	−1.89442e13	−0.981950
$897$	0	0
$898$	−6.03201e13	−3.09541
$899$	−1.04522e11	−0.00533689
$900$	0	0
$901$	5.19653e12	0.262695
$902$	9.38288e12	0.471962
$903$	0	0
$904$	5.05821e13	2.51906
$905$	−2.77281e13	−1.37405
$906$	0	0
$907$	−1.51717e13	−0.744390	−0.372195	−	0.928155i	$-0.621395\pi$
$907$	−1.51717e13	−0.744390	−0.372195	+	0.928155i	$0.621395\pi$
$908$	8.57645e12	0.418718
$909$	0	0
$910$	−3.33614e13	−1.61272
$911$	2.65044e12	0.127493	0.0637464	−	0.997966i	$-0.479695\pi$
$911$	2.65044e12	0.127493	0.0637464	+	0.997966i	$0.479695\pi$
$912$	0	0
$913$	−1.01991e13	−0.485786
$914$	−1.62340e13	−0.769425
$915$	0	0
$916$	−9.77348e13	−4.58690
$917$	−1.42515e13	−0.665576
$918$	0	0
$919$	−1.10783e13	−0.512336	−0.256168	−	0.966632i	$-0.582460\pi$
$919$	−1.10783e13	−0.512336	−0.256168	+	0.966632i	$0.582460\pi$
$920$	3.58398e13	1.64938
$921$	0	0
$922$	8.79656e12	0.400889
$923$	3.40315e13	1.54338
$924$	0	0
$925$	−2.27255e12	−0.102065
$926$	5.13860e13	2.29665
$927$	0	0
$928$	1.89885e12	0.0840475
$929$	1.10570e13	0.487044	0.243522	−	0.969895i	$-0.421697\pi$
$929$	1.10570e13	0.487044	0.243522	+	0.969895i	$0.421697\pi$
$930$	0	0
$931$	3.22725e13	1.40786
$932$	1.09597e14	4.75804
$933$	0	0
$934$	−5.17655e13	−2.22577
$935$	−6.66733e12	−0.285299
$936$	0	0
$937$	−3.12152e13	−1.32293	−0.661466	−	0.749975i	$-0.730065\pi$
$937$	−3.12152e13	−1.32293	−0.661466	+	0.749975i	$0.730065\pi$
$938$	−4.87880e12	−0.205779
$939$	0	0
$940$	8.24505e13	3.44444
$941$	−3.48495e13	−1.44891	−0.724457	−	0.689320i	$-0.757910\pi$
$941$	−3.48495e13	−1.44891	−0.724457	+	0.689320i	$0.757910\pi$
$942$	0	0
$943$	2.71171e12	0.111671
$944$	−8.29772e13	−3.40083
$945$	0	0
$946$	−2.15156e13	−0.873460
$947$	−2.89060e13	−1.16792	−0.583960	−	0.811783i	$-0.698497\pi$
$947$	−2.89060e13	−1.16792	−0.583960	+	0.811783i	$0.698497\pi$
$948$	0	0
$949$	3.25530e13	1.30285
$950$	1.81538e13	0.723121
$951$	0	0
$952$	9.10996e12	0.359460
$953$	−1.17377e13	−0.460963	−0.230482	−	0.973077i	$-0.574030\pi$
$953$	−1.17377e13	−0.460963	−0.230482	+	0.973077i	$0.574030\pi$
$954$	0	0
$955$	−9.70540e11	−0.0377571
$956$	−1.00877e14	−3.90598
$957$	0	0
$958$	−1.63328e12	−0.0626494
$959$	−1.23892e13	−0.472998
$960$	0	0
$961$	−2.53695e13	−0.959525
$962$	−4.00667e13	−1.50833
$963$	0	0
$964$	−1.43173e13	−0.533969
$965$	−2.33493e13	−0.866765
$966$	0	0
$967$	4.64159e13	1.70705	0.853527	−	0.521048i	$-0.174459\pi$
$967$	4.64159e13	1.70705	0.853527	+	0.521048i	$0.174459\pi$
$968$	−1.23327e13	−0.451458
$969$	0	0
$970$	5.79952e13	2.10339
$971$	3.56315e12	0.128632	0.0643158	−	0.997930i	$-0.479514\pi$
$971$	3.56315e12	0.128632	0.0643158	+	0.997930i	$0.479514\pi$
$972$	0	0
$973$	−1.39791e12	−0.0500003
$974$	−8.10986e13	−2.88734
$975$	0	0
$976$	−1.61382e14	−5.69287
$977$	1.39593e13	0.490160	0.245080	−	0.969503i	$-0.421186\pi$
$977$	1.39593e13	0.490160	0.245080	+	0.969503i	$0.421186\pi$
$978$	0	0
$979$	−2.04332e13	−0.710909
$980$	6.45554e13	2.23571
$981$	0	0
$982$	−1.04731e13	−0.359395
$983$	6.28271e12	0.214613	0.107306	−	0.994226i	$-0.465777\pi$
$983$	6.28271e12	0.214613	0.107306	+	0.994226i	$0.465777\pi$
$984$	0	0
$985$	−4.04429e13	−1.36893
$986$	−3.63893e11	−0.0122610
$987$	0	0
$988$	2.31934e14	7.74388
$989$	−6.21815e12	−0.206670
$990$	0	0
$991$	−4.49640e13	−1.48093	−0.740463	−	0.672097i	$-0.765394\pi$
$991$	−4.49640e13	−1.48093	−0.740463	+	0.672097i	$0.765394\pi$
$992$	−1.94413e13	−0.637416
$993$	0	0
$994$	2.67112e13	0.867871
$995$	−5.22653e13	−1.69048
$996$	0	0
$997$	−1.21770e13	−0.390311	−0.195156	−	0.980772i	$-0.562521\pi$
$997$	−1.21770e13	−0.390311	−0.195156	+	0.980772i	$0.562521\pi$
$998$	−3.40075e13	−1.08514
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.10.a.f.1.1		7
3.2	odd	2		17.10.a.b.1.7	✓	7
12.11	even	2		272.10.a.g.1.6		7
51.50	odd	2		289.10.a.b.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.7	✓	7	3.2	odd	2
153.10.a.f.1.1		7	1.1	even	1	trivial
272.10.a.g.1.6		7	12.11	even	2
289.10.a.b.1.7		7	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)

\(f(q)\)	\(=\)	\(q-43.1213 q^{2} +1347.45 q^{4} -1536.21 q^{5} +3027.69 q^{7} -36025.5 q^{8} +O(q^{10})\)	\(q-43.1213 q^{2} +1347.45 q^{4} -1536.21 q^{5} +3027.69 q^{7} -36025.5 q^{8} +66243.5 q^{10} -51964.2 q^{11} -166337. q^{13} -130558. q^{14} +863574. q^{16} -83521.0 q^{17} -1.03482e6 q^{19} -2.06997e6 q^{20} +2.24076e6 q^{22} +647595. q^{23} +406829. q^{25} +7.17269e6 q^{26} +4.07964e6 q^{28} -101038. q^{29} +1.03448e6 q^{31} -1.87934e7 q^{32} +3.60153e6 q^{34} -4.65118e6 q^{35} -5.58601e6 q^{37} +4.46226e7 q^{38} +5.53429e7 q^{40} +4.18736e6 q^{41} -9.60190e6 q^{43} -7.00190e7 q^{44} -2.79251e7 q^{46} -3.98318e7 q^{47} -3.11867e7 q^{49} -1.75430e7 q^{50} -2.24131e8 q^{52} -6.22183e7 q^{53} +7.98282e7 q^{55} -1.09074e8 q^{56} +4.35690e6 q^{58} -9.60858e7 q^{59} -1.86877e8 q^{61} -4.46079e7 q^{62} +3.68245e8 q^{64} +2.55530e8 q^{65} +3.73689e7 q^{67} -1.12540e8 q^{68} +2.00565e8 q^{70} -2.04593e8 q^{71} -1.95705e8 q^{73} +2.40876e8 q^{74} -1.39436e9 q^{76} -1.57331e8 q^{77} +2.72638e8 q^{79} -1.32663e9 q^{80} -1.80564e8 q^{82} +1.96272e8 q^{83} +1.28306e8 q^{85} +4.14046e8 q^{86} +1.87204e9 q^{88} +3.93217e8 q^{89} -5.03618e8 q^{91} +8.72600e8 q^{92} +1.71760e9 q^{94} +1.58970e9 q^{95} +8.75485e8 q^{97} +1.34481e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8}+O(q^{10}) \) 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8} + 154226 q^{10} - 135536 q^{11} + 166122 q^{13} - 447252 q^{14} + 1463585 q^{16} - 584647 q^{17} + 777172 q^{19} + 917162 q^{20} - 1222520 q^{22} - 1357764 q^{23} + 1065785 q^{25} + 14379966 q^{26} - 3328892 q^{28} - 967002 q^{29} + 3546740 q^{31} - 4825461 q^{32} - 83521 q^{34} + 530736 q^{35} + 18296498 q^{37} + 49363020 q^{38} + 127155062 q^{40} - 10285686 q^{41} + 21913204 q^{43} - 96696624 q^{44} - 151509484 q^{46} - 56639800 q^{47} + 27010351 q^{49} + 261150303 q^{50} - 156226378 q^{52} - 121813562 q^{53} + 40793128 q^{55} + 196175436 q^{56} - 236833910 q^{58} - 29222388 q^{59} - 49915846 q^{61} + 73506556 q^{62} + 317922057 q^{64} + 122633668 q^{65} + 301863420 q^{67} - 199531669 q^{68} + 966315960 q^{70} - 652473940 q^{71} + 306656342 q^{73} - 249173874 q^{74} + 128694700 q^{76} + 102442536 q^{77} + 959147884 q^{79} + 692173602 q^{80} + 1046441254 q^{82} + 1512945268 q^{83} + 113755602 q^{85} + 164953236 q^{86} + 1132038848 q^{88} + 1971327114 q^{89} - 1061062864 q^{91} - 901186756 q^{92} + 2534831232 q^{94} + 3249631512 q^{95} + 2006526254 q^{97} + 2170640009 q^{98}+O(q^{100}) \) 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8 + 154226 * q^10 - 135536 * q^11 + 166122 * q^13 - 447252 * q^14 + 1463585 * q^16 - 584647 * q^17 + 777172 * q^19 + 917162 * q^20 - 1222520 * q^22 - 1357764 * q^23 + 1065785 * q^25 + 14379966 * q^26 - 3328892 * q^28 - 967002 * q^29 + 3546740 * q^31 - 4825461 * q^32 - 83521 * q^34 + 530736 * q^35 + 18296498 * q^37 + 49363020 * q^38 + 127155062 * q^40 - 10285686 * q^41 + 21913204 * q^43 - 96696624 * q^44 - 151509484 * q^46 - 56639800 * q^47 + 27010351 * q^49 + 261150303 * q^50 - 156226378 * q^52 - 121813562 * q^53 + 40793128 * q^55 + 196175436 * q^56 - 236833910 * q^58 - 29222388 * q^59 - 49915846 * q^61 + 73506556 * q^62 + 317922057 * q^64 + 122633668 * q^65 + 301863420 * q^67 - 199531669 * q^68 + 966315960 * q^70 - 652473940 * q^71 + 306656342 * q^73 - 249173874 * q^74 + 128694700 * q^76 + 102442536 * q^77 + 959147884 * q^79 + 692173602 * q^80 + 1046441254 * q^82 + 1512945268 * q^83 + 113755602 * q^85 + 164953236 * q^86 + 1132038848 * q^88 + 1971327114 * q^89 - 1061062864 * q^91 - 901186756 * q^92 + 2534831232 * q^94 + 3249631512 * q^95 + 2006526254 * q^97 + 2170640009 * q^98

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