LMFDB - Embedded newform 45.10.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,10,Mod(1,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, 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("45.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	45.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:	$23.1766126274$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{241}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 60 $ x^2 - x - 60
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-7.26209$ of defining polynomial
Character	$\chi$	$=$	45.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.78626 q^{2} -451.374 q^{4} -625.000 q^{5} +1839.88 q^{7} -7501.08 q^{8} +O(q^{10})$	\(q+7.78626 q^{2} -451.374 q^{4} -625.000 q^{5} +1839.88 q^{7} -7501.08 q^{8} -4866.41 q^{10} -44385.9 q^{11} +136584. q^{13} +14325.8 q^{14} +172698. q^{16} +253591. q^{17} +85435.7 q^{19} +282109. q^{20} -345600. q^{22} +979409. q^{23} +390625. q^{25} +1.06348e6 q^{26} -830473. q^{28} -2.58640e6 q^{29} +8.94787e6 q^{31} +5.18523e6 q^{32} +1.97452e6 q^{34} -1.14992e6 q^{35} +1.56064e7 q^{37} +665225. q^{38} +4.68818e6 q^{40} -2.44893e7 q^{41} +1.27592e7 q^{43} +2.00346e7 q^{44} +7.62593e6 q^{46} +6.16764e7 q^{47} -3.69685e7 q^{49} +3.04151e6 q^{50} -6.16504e7 q^{52} -5.70418e6 q^{53} +2.77412e7 q^{55} -1.38011e7 q^{56} -2.01384e7 q^{58} -8.35095e7 q^{59} +1.48622e8 q^{61} +6.96704e7 q^{62} -4.80479e7 q^{64} -8.53649e7 q^{65} -1.68003e8 q^{67} -1.14464e8 q^{68} -8.95360e6 q^{70} -2.10986e8 q^{71} -1.43534e8 q^{73} +1.21515e8 q^{74} -3.85635e7 q^{76} -8.16646e7 q^{77} -4.55960e8 q^{79} -1.07936e8 q^{80} -1.90680e8 q^{82} +3.55106e8 q^{83} -1.58494e8 q^{85} +9.93465e7 q^{86} +3.32942e8 q^{88} +4.24540e8 q^{89} +2.51297e8 q^{91} -4.42080e8 q^{92} +4.80228e8 q^{94} -5.33973e7 q^{95} +1.19905e9 q^{97} -2.87846e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 31 q^{2} + 541 q^{4} - 1250 q^{5} + 14112 q^{7} - 26133 q^{8}+O(q^{10}) $ 2 * q - 31 * q^2 + 541 * q^4 - 1250 * q^5 + 14112 * q^7 - 26133 * q^8	\( 2 q - 31 q^{2} + 541 q^{4} - 1250 q^{5} + 14112 q^{7} - 26133 q^{8} + 19375 q^{10} + 21512 q^{11} + 24284 q^{13} - 461664 q^{14} + 387265 q^{16} + 156956 q^{17} - 95896 q^{19} - 338125 q^{20} - 2901532 q^{22} + 735264 q^{23} + 781250 q^{25} + 5419166 q^{26} + 11348064 q^{28} + 2678212 q^{29} + 10782432 q^{31} + 6402523 q^{32} + 5722622 q^{34} - 8820000 q^{35} + 21968332 q^{37} + 7698404 q^{38} + 16333125 q^{40} - 26060372 q^{41} - 7191160 q^{43} + 85429972 q^{44} + 17095392 q^{46} + 31580240 q^{47} + 73282930 q^{49} - 12109375 q^{50} - 173093786 q^{52} - 3131116 q^{53} - 13445000 q^{55} - 242454240 q^{56} - 224332958 q^{58} + 35494664 q^{59} + 341497340 q^{61} - 1485504 q^{62} - 205120471 q^{64} - 15177500 q^{65} - 288195816 q^{67} - 210362042 q^{68} + 288540000 q^{70} - 210286064 q^{71} - 232663084 q^{73} - 125240234 q^{74} - 218512364 q^{76} + 727042176 q^{77} - 24755040 q^{79} - 242040625 q^{80} - 129742346 q^{82} + 372082152 q^{83} - 98097500 q^{85} + 873146372 q^{86} - 894861492 q^{88} + 427639116 q^{89} - 1126859328 q^{91} - 684362592 q^{92} + 1647543896 q^{94} + 59935000 q^{95} + 1771658884 q^{97} - 4564085351 q^{98}+O(q^{100}) \) 2 * q - 31 * q^2 + 541 * q^4 - 1250 * q^5 + 14112 * q^7 - 26133 * q^8 + 19375 * q^10 + 21512 * q^11 + 24284 * q^13 - 461664 * q^14 + 387265 * q^16 + 156956 * q^17 - 95896 * q^19 - 338125 * q^20 - 2901532 * q^22 + 735264 * q^23 + 781250 * q^25 + 5419166 * q^26 + 11348064 * q^28 + 2678212 * q^29 + 10782432 * q^31 + 6402523 * q^32 + 5722622 * q^34 - 8820000 * q^35 + 21968332 * q^37 + 7698404 * q^38 + 16333125 * q^40 - 26060372 * q^41 - 7191160 * q^43 + 85429972 * q^44 + 17095392 * q^46 + 31580240 * q^47 + 73282930 * q^49 - 12109375 * q^50 - 173093786 * q^52 - 3131116 * q^53 - 13445000 * q^55 - 242454240 * q^56 - 224332958 * q^58 + 35494664 * q^59 + 341497340 * q^61 - 1485504 * q^62 - 205120471 * q^64 - 15177500 * q^65 - 288195816 * q^67 - 210362042 * q^68 + 288540000 * q^70 - 210286064 * q^71 - 232663084 * q^73 - 125240234 * q^74 - 218512364 * q^76 + 727042176 * q^77 - 24755040 * q^79 - 242040625 * q^80 - 129742346 * q^82 + 372082152 * q^83 - 98097500 * q^85 + 873146372 * q^86 - 894861492 * q^88 + 427639116 * q^89 - 1126859328 * q^91 - 684362592 * q^92 + 1647543896 * q^94 + 59935000 * q^95 + 1771658884 * q^97 - 4564085351 * 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 $

$2$	7.78626	0.344107	0.172054	−	0.985088i	$-0.444960\pi$
$2$	7.78626	0.344107	0.172054	+	0.985088i	$0.444960\pi$
$3$	0	0
$3$	0	0
$4$	−451.374	−0.881590
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	0	0
$7$	1839.88	0.289633	0.144816	−	0.989459i	$-0.453741\pi$
$7$	1839.88	0.289633	0.144816	+	0.989459i	$0.453741\pi$
$8$	−7501.08	−0.647469
$9$	0	0
$10$	−4866.41	−0.153890
$11$	−44385.9	−0.914066	−0.457033	−	0.889450i	$-0.651088\pi$
$11$	−44385.9	−0.914066	−0.457033	+	0.889450i	$0.651088\pi$
$12$	0	0
$13$	136584.	1.32634	0.663169	−	0.748470i	$-0.269211\pi$
$13$	136584.	1.32634	0.663169	+	0.748470i	$0.269211\pi$
$14$	14325.8	0.0996648
$15$	0	0
$16$	172698.	0.658791
$17$	253591.	0.736399	0.368199	−	0.929747i	$-0.379974\pi$
$17$	253591.	0.736399	0.368199	+	0.929747i	$0.379974\pi$
$18$	0	0
$19$	85435.7	0.150400	0.0752001	−	0.997168i	$-0.476040\pi$
$19$	85435.7	0.150400	0.0752001	+	0.997168i	$0.476040\pi$
$20$	282109.	0.394259
$21$	0	0
$22$	−345600.	−0.314537
$23$	979409.	0.729775	0.364887	−	0.931052i	$-0.381108\pi$
$23$	979409.	0.729775	0.364887	+	0.931052i	$0.381108\pi$
$24$	0	0
$25$	390625.	0.200000
$26$	1.06348e6	0.456403
$27$	0	0
$28$	−830473.	−0.255337
$29$	−2.58640e6	−0.679054	−0.339527	−	0.940596i	$-0.610267\pi$
$29$	−2.58640e6	−0.679054	−0.339527	+	0.940596i	$0.610267\pi$
$30$	0	0
$31$	8.94787e6	1.74017	0.870085	−	0.492901i	$-0.164064\pi$
$31$	8.94787e6	1.74017	0.870085	+	0.492901i	$0.164064\pi$
$32$	5.18523e6	0.874164
$33$	0	0
$34$	1.97452e6	0.253400
$35$	−1.14992e6	−0.129528
$36$	0	0
$37$	1.56064e7	1.36897	0.684486	−	0.729026i	$-0.260026\pi$
$37$	1.56064e7	1.36897	0.684486	+	0.729026i	$0.260026\pi$
$38$	665225.	0.0517538
$39$	0	0
$40$	4.68818e6	0.289557
$41$	−2.44893e7	−1.35347	−0.676735	−	0.736227i	$-0.736606\pi$
$41$	−2.44893e7	−1.35347	−0.676735	+	0.736227i	$0.736606\pi$
$42$	0	0
$43$	1.27592e7	0.569135	0.284568	−	0.958656i	$-0.408150\pi$
$43$	1.27592e7	0.569135	0.284568	+	0.958656i	$0.408150\pi$
$44$	2.00346e7	0.805832
$45$	0	0
$46$	7.62593e6	0.251121
$47$	6.16764e7	1.84365	0.921825	−	0.387607i	$-0.126698\pi$
$47$	6.16764e7	1.84365	0.921825	+	0.387607i	$0.126698\pi$
$48$	0	0
$49$	−3.69685e7	−0.916113
$50$	3.04151e6	0.0688215
$51$	0	0
$52$	−6.16504e7	−1.16929
$53$	−5.70418e6	−0.0993006	−0.0496503	−	0.998767i	$-0.515811\pi$
$53$	−5.70418e6	−0.0993006	−0.0496503	+	0.998767i	$0.515811\pi$
$54$	0	0
$55$	2.77412e7	0.408783
$56$	−1.38011e7	−0.187528
$57$	0	0
$58$	−2.01384e7	−0.233668
$59$	−8.35095e7	−0.897226	−0.448613	−	0.893726i	$-0.648082\pi$
$59$	−8.35095e7	−0.897226	−0.448613	+	0.893726i	$0.648082\pi$
$60$	0	0
$61$	1.48622e8	1.37435	0.687177	−	0.726490i	$-0.258850\pi$
$61$	1.48622e8	1.37435	0.687177	+	0.726490i	$0.258850\pi$
$62$	6.96704e7	0.598806
$63$	0	0
$64$	−4.80479e7	−0.357985
$65$	−8.53649e7	−0.593156
$66$	0	0
$67$	−1.68003e8	−1.01854	−0.509272	−	0.860606i	$-0.670085\pi$
$67$	−1.68003e8	−1.01854	−0.509272	+	0.860606i	$0.670085\pi$
$68$	−1.14464e8	−0.649202
$69$	0	0
$70$	−8.95360e6	−0.0445714
$71$	−2.10986e8	−0.985349	−0.492675	−	0.870214i	$-0.663981\pi$
$71$	−2.10986e8	−0.985349	−0.492675	+	0.870214i	$0.663981\pi$
$72$	0	0
$73$	−1.43534e8	−0.591566	−0.295783	−	0.955255i	$-0.595580\pi$
$73$	−1.43534e8	−0.591566	−0.295783	+	0.955255i	$0.595580\pi$
$74$	1.21515e8	0.471074
$75$	0	0
$76$	−3.85635e7	−0.132591
$77$	−8.16646e7	−0.264744
$78$	0	0
$79$	−4.55960e8	−1.31706	−0.658529	−	0.752555i	$-0.728821\pi$
$79$	−4.55960e8	−1.31706	−0.658529	+	0.752555i	$0.728821\pi$
$80$	−1.07936e8	−0.294620
$81$	0	0
$82$	−1.90680e8	−0.465739
$83$	3.55106e8	0.821309	0.410655	−	0.911791i	$-0.365300\pi$
$83$	3.55106e8	0.821309	0.410655	+	0.911791i	$0.365300\pi$
$84$	0	0
$85$	−1.58494e8	−0.329328
$86$	9.93465e7	0.195844
$87$	0	0
$88$	3.32942e8	0.591830
$89$	4.24540e8	0.717239	0.358620	−	0.933484i	$-0.383248\pi$
$89$	4.24540e8	0.717239	0.358620	+	0.933484i	$0.383248\pi$
$90$	0	0
$91$	2.51297e8	0.384151
$92$	−4.42080e8	−0.643362
$93$	0	0
$94$	4.80228e8	0.634413
$95$	−5.33973e7	−0.0672610
$96$	0	0
$97$	1.19905e9	1.37520	0.687598	−	0.726092i	$-0.258665\pi$
$97$	1.19905e9	1.37520	0.687598	+	0.726092i	$0.258665\pi$
$98$	−2.87846e8	−0.315241
$99$	0	0
$100$	−1.76318e8	−0.176318
$101$	1.77085e9	1.69331	0.846654	−	0.532144i	$-0.178613\pi$
$101$	1.77085e9	1.69331	0.846654	+	0.532144i	$0.178613\pi$
$102$	0	0
$103$	3.03322e8	0.265544	0.132772	−	0.991147i	$-0.457612\pi$
$103$	3.03322e8	0.265544	0.132772	+	0.991147i	$0.457612\pi$
$104$	−1.02453e9	−0.858763
$105$	0	0
$106$	−4.44142e7	−0.0341701
$107$	1.95414e8	0.144121	0.0720607	−	0.997400i	$-0.477042\pi$
$107$	1.95414e8	0.144121	0.0720607	+	0.997400i	$0.477042\pi$
$108$	0	0
$109$	2.31494e9	1.57080	0.785401	−	0.618988i	$-0.212457\pi$
$109$	2.31494e9	1.57080	0.785401	+	0.618988i	$0.212457\pi$
$110$	2.16000e8	0.140665
$111$	0	0
$112$	3.17743e8	0.190808
$113$	−1.31945e9	−0.761270	−0.380635	−	0.924725i	$-0.624294\pi$
$113$	−1.31945e9	−0.761270	−0.380635	+	0.924725i	$0.624294\pi$
$114$	0	0
$115$	−6.12130e8	−0.326365
$116$	1.16743e9	0.598648
$117$	0	0
$118$	−6.50227e8	−0.308742
$119$	4.66576e8	0.213285
$120$	0	0
$121$	−3.87842e8	−0.164483
$122$	1.15721e9	0.472925
$123$	0	0
$124$	−4.03884e9	−1.53412
$125$	−2.44141e8	−0.0894427
$126$	0	0
$127$	3.18960e9	1.08798	0.543988	−	0.839093i	$-0.316914\pi$
$127$	3.18960e9	1.08798	0.543988	+	0.839093i	$0.316914\pi$
$128$	−3.02895e9	−0.997349
$129$	0	0
$130$	−6.64673e8	−0.204109
$131$	5.40115e9	1.60238	0.801190	−	0.598410i	$-0.204201\pi$
$131$	5.40115e9	1.60238	0.801190	+	0.598410i	$0.204201\pi$
$132$	0	0
$133$	1.57191e8	0.0435608
$134$	−1.30811e9	−0.350488
$135$	0	0
$136$	−1.90220e9	−0.476796
$137$	−1.19903e7	−0.00290795	−0.00145398	−	0.999999i	$-0.500463\pi$
$137$	−1.19903e7	−0.00290795	−0.00145398	+	0.999999i	$0.500463\pi$
$138$	0	0
$139$	9.15482e8	0.208010	0.104005	−	0.994577i	$-0.466834\pi$
$139$	9.15482e8	0.208010	0.104005	+	0.994577i	$0.466834\pi$
$140$	5.19046e8	0.114190
$141$	0	0
$142$	−1.64279e9	−0.339066
$143$	−6.06239e9	−1.21236
$144$	0	0
$145$	1.61650e9	0.303682
$146$	−1.11760e9	−0.203562
$147$	0	0
$148$	−7.04432e9	−1.20687
$149$	−5.00462e9	−0.831827	−0.415913	−	0.909404i	$-0.636538\pi$
$149$	−5.00462e9	−0.831827	−0.415913	+	0.909404i	$0.636538\pi$
$150$	0	0
$151$	3.20554e9	0.501770	0.250885	−	0.968017i	$-0.419278\pi$
$151$	3.20554e9	0.501770	0.250885	+	0.968017i	$0.419278\pi$
$152$	−6.40860e8	−0.0973794
$153$	0	0
$154$	−6.35862e8	−0.0911002
$155$	−5.59242e9	−0.778228
$156$	0	0
$157$	−4.63430e8	−0.0608745	−0.0304373	−	0.999537i	$-0.509690\pi$
$157$	−4.63430e8	−0.0608745	−0.0304373	+	0.999537i	$0.509690\pi$
$158$	−3.55023e9	−0.453210
$159$	0	0
$160$	−3.24077e9	−0.390938
$161$	1.80199e9	0.211367
$162$	0	0
$163$	−1.27948e10	−1.41968	−0.709840	−	0.704363i	$-0.751233\pi$
$163$	−1.27948e10	−1.41968	−0.709840	+	0.704363i	$0.751233\pi$
$164$	1.10538e10	1.19320
$165$	0	0
$166$	2.76495e9	0.282619
$167$	1.85699e10	1.84750	0.923752	−	0.382992i	$-0.125106\pi$
$167$	1.85699e10	1.84750	0.923752	+	0.382992i	$0.125106\pi$
$168$	0	0
$169$	8.05063e9	0.759171
$170$	−1.23408e9	−0.113324
$171$	0	0
$172$	−5.75917e9	−0.501744
$173$	−4.90746e9	−0.416533	−0.208266	−	0.978072i	$-0.566782\pi$
$173$	−4.90746e9	−0.416533	−0.208266	+	0.978072i	$0.566782\pi$
$174$	0	0
$175$	7.18702e8	0.0579266
$176$	−7.66536e9	−0.602179
$177$	0	0
$178$	3.30558e9	0.246807
$179$	1.28930e10	0.938678	0.469339	−	0.883018i	$-0.344492\pi$
$179$	1.28930e10	0.938678	0.469339	+	0.883018i	$0.344492\pi$
$180$	0	0
$181$	2.66233e10	1.84378	0.921889	−	0.387453i	$-0.126645\pi$
$181$	2.66233e10	1.84378	0.921889	+	0.387453i	$0.126645\pi$
$182$	1.95667e9	0.132189
$183$	0	0
$184$	−7.34663e9	−0.472506
$185$	−9.75400e9	−0.612223
$186$	0	0
$187$	−1.12558e10	−0.673117
$188$	−2.78391e10	−1.62534
$189$	0	0
$190$	−4.15766e8	−0.0231450
$191$	2.72802e10	1.48319	0.741595	−	0.670848i	$-0.234070\pi$
$191$	2.72802e10	1.48319	0.741595	+	0.670848i	$0.234070\pi$
$192$	0	0
$193$	−9.65442e9	−0.500862	−0.250431	−	0.968134i	$-0.580572\pi$
$193$	−9.65442e9	−0.500862	−0.250431	+	0.968134i	$0.580572\pi$
$194$	9.33612e9	0.473215
$195$	0	0
$196$	1.66866e10	0.807636
$197$	−1.21091e10	−0.572812	−0.286406	−	0.958108i	$-0.592461\pi$
$197$	−1.21091e10	−0.572812	−0.286406	+	0.958108i	$0.592461\pi$
$198$	0	0
$199$	1.89741e10	0.857673	0.428837	−	0.903382i	$-0.358924\pi$
$199$	1.89741e10	0.857673	0.428837	+	0.903382i	$0.358924\pi$
$200$	−2.93011e9	−0.129494
$201$	0	0
$202$	1.37883e10	0.582680
$203$	−4.75866e9	−0.196676
$204$	0	0
$205$	1.53058e10	0.605290
$206$	2.36174e9	0.0913757
$207$	0	0
$208$	2.35878e10	0.873779
$209$	−3.79214e9	−0.137476
$210$	0	0
$211$	−8.91928e9	−0.309784	−0.154892	−	0.987931i	$-0.549503\pi$
$211$	−8.91928e9	−0.309784	−0.154892	+	0.987931i	$0.549503\pi$
$212$	2.57472e9	0.0875424
$213$	0	0
$214$	1.52154e9	0.0495933
$215$	−7.97450e9	−0.254525
$216$	0	0
$217$	1.64630e10	0.504010
$218$	1.80248e10	0.540524
$219$	0	0
$220$	−1.25216e10	−0.360379
$221$	3.46364e10	0.976714
$222$	0	0
$223$	−4.42755e10	−1.19892	−0.599462	−	0.800403i	$-0.704619\pi$
$223$	−4.42755e10	−1.19892	−0.599462	+	0.800403i	$0.704619\pi$
$224$	9.54018e9	0.253187
$225$	0	0
$226$	−1.02735e10	−0.261959
$227$	5.40045e10	1.34994	0.674968	−	0.737847i	$-0.264157\pi$
$227$	5.40045e10	1.34994	0.674968	+	0.737847i	$0.264157\pi$
$228$	0	0
$229$	5.80250e9	0.139430	0.0697149	−	0.997567i	$-0.477791\pi$
$229$	5.80250e9	0.139430	0.0697149	+	0.997567i	$0.477791\pi$
$230$	−4.76621e9	−0.112305
$231$	0	0
$232$	1.94008e10	0.439667
$233$	−5.41865e10	−1.20445	−0.602226	−	0.798326i	$-0.705719\pi$
$233$	−5.41865e10	−1.20445	−0.602226	+	0.798326i	$0.705719\pi$
$234$	0	0
$235$	−3.85477e10	−0.824505
$236$	3.76940e10	0.790986
$237$	0	0
$238$	3.63288e9	0.0733930
$239$	−7.91761e10	−1.56965	−0.784826	−	0.619716i	$-0.787248\pi$
$239$	−7.91761e10	−1.56965	−0.784826	+	0.619716i	$0.787248\pi$
$240$	0	0
$241$	−6.14920e10	−1.17420	−0.587100	−	0.809514i	$-0.699730\pi$
$241$	−6.14920e10	−1.17420	−0.587100	+	0.809514i	$0.699730\pi$
$242$	−3.01984e9	−0.0565998
$243$	0	0
$244$	−6.70841e10	−1.21162
$245$	2.31053e10	0.409698
$246$	0	0
$247$	1.16691e10	0.199481
$248$	−6.71187e10	−1.12671
$249$	0	0
$250$	−1.90094e9	−0.0307779
$251$	−2.89319e10	−0.460093	−0.230046	−	0.973180i	$-0.573888\pi$
$251$	−2.89319e10	−0.460093	−0.230046	+	0.973180i	$0.573888\pi$
$252$	0	0
$253$	−4.34719e10	−0.667062
$254$	2.48350e10	0.374381
$255$	0	0
$256$	1.01633e9	0.0147896
$257$	−1.22388e11	−1.75001	−0.875005	−	0.484114i	$-0.839142\pi$
$257$	−1.22388e11	−1.75001	−0.875005	+	0.484114i	$0.839142\pi$
$258$	0	0
$259$	2.87139e10	0.396499
$260$	3.85315e10	0.522921
$261$	0	0
$262$	4.20548e10	0.551391
$263$	6.24892e10	0.805386	0.402693	−	0.915335i	$-0.368074\pi$
$263$	6.24892e10	0.805386	0.402693	+	0.915335i	$0.368074\pi$
$264$	0	0
$265$	3.56511e9	0.0444086
$266$	1.22393e9	0.0149896
$267$	0	0
$268$	7.58321e10	0.897938
$269$	−1.27214e11	−1.48132	−0.740659	−	0.671881i	$-0.765487\pi$
$269$	−1.27214e11	−1.48132	−0.740659	+	0.671881i	$0.765487\pi$
$270$	0	0
$271$	1.54116e10	0.173574	0.0867871	−	0.996227i	$-0.472340\pi$
$271$	1.54116e10	0.173574	0.0867871	+	0.996227i	$0.472340\pi$
$272$	4.37946e10	0.485133
$273$	0	0
$274$	−9.33596e7	−0.00100065
$275$	−1.73382e10	−0.182813
$276$	0	0
$277$	−9.20867e10	−0.939806	−0.469903	−	0.882718i	$-0.655711\pi$
$277$	−9.20867e10	−0.939806	−0.469903	+	0.882718i	$0.655711\pi$
$278$	7.12818e9	0.0715776
$279$	0	0
$280$	8.62567e9	0.0838652
$281$	7.78782e10	0.745139	0.372570	−	0.928004i	$-0.378477\pi$
$281$	7.78782e10	0.745139	0.372570	+	0.928004i	$0.378477\pi$
$282$	0	0
$283$	2.92463e10	0.271039	0.135520	−	0.990775i	$-0.456730\pi$
$283$	2.92463e10	0.271039	0.135520	+	0.990775i	$0.456730\pi$
$284$	9.52334e10	0.868674
$285$	0	0
$286$	−4.72034e10	−0.417182
$287$	−4.50572e10	−0.392009
$288$	0	0
$289$	−5.42796e10	−0.457717
$290$	1.25865e10	0.104499
$291$	0	0
$292$	6.47877e10	0.521519
$293$	2.27403e11	1.80257	0.901285	−	0.433227i	$-0.142625\pi$
$293$	2.27403e11	1.80257	0.901285	+	0.433227i	$0.142625\pi$
$294$	0	0
$295$	5.21935e10	0.401252
$296$	−1.17065e11	−0.886368
$297$	0	0
$298$	−3.89673e10	−0.286238
$299$	1.33771e11	0.967927
$300$	0	0
$301$	2.34754e10	0.164840
$302$	2.49592e10	0.172663
$303$	0	0
$304$	1.47546e10	0.0990823
$305$	−9.28887e10	−0.614630
$306$	0	0
$307$	−6.02579e10	−0.387160	−0.193580	−	0.981084i	$-0.562010\pi$
$307$	−6.02579e10	−0.387160	−0.193580	+	0.981084i	$0.562010\pi$
$308$	3.68613e10	0.233395
$309$	0	0
$310$	−4.35440e10	−0.267794
$311$	−1.36816e11	−0.829308	−0.414654	−	0.909979i	$-0.636097\pi$
$311$	−1.36816e11	−0.829308	−0.414654	+	0.909979i	$0.636097\pi$
$312$	0	0
$313$	2.25535e11	1.32820	0.664101	−	0.747643i	$-0.268815\pi$
$313$	2.25535e11	1.32820	0.664101	+	0.747643i	$0.268815\pi$
$314$	−3.60839e9	−0.0209474
$315$	0	0
$316$	2.05809e11	1.16111
$317$	1.28386e11	0.714089	0.357045	−	0.934087i	$-0.383784\pi$
$317$	1.28386e11	0.714089	0.357045	+	0.934087i	$0.383784\pi$
$318$	0	0
$319$	1.14800e11	0.620701
$320$	3.00299e10	0.160096
$321$	0	0
$322$	1.40308e10	0.0727328
$323$	2.16657e10	0.110755
$324$	0	0
$325$	5.33530e10	0.265268
$326$	−9.96239e10	−0.488522
$327$	0	0
$328$	1.83696e11	0.876329
$329$	1.13477e11	0.533981
$330$	0	0
$331$	1.15018e10	0.0526673	0.0263337	−	0.999653i	$-0.491617\pi$
$331$	1.15018e10	0.0526673	0.0263337	+	0.999653i	$0.491617\pi$
$332$	−1.60286e11	−0.724058
$333$	0	0
$334$	1.44590e11	0.635740
$335$	1.05002e11	0.455506
$336$	0	0
$337$	−2.79631e11	−1.18100	−0.590502	−	0.807036i	$-0.701070\pi$
$337$	−2.79631e11	−1.18100	−0.590502	+	0.807036i	$0.701070\pi$
$338$	6.26843e10	0.261236
$339$	0	0
$340$	7.15402e10	0.290332
$341$	−3.97159e11	−1.59063
$342$	0	0
$343$	−1.42263e11	−0.554969
$344$	−9.57078e10	−0.368497
$345$	0	0
$346$	−3.82107e10	−0.143332
$347$	−9.07088e10	−0.335867	−0.167933	−	0.985798i	$-0.553709\pi$
$347$	−9.07088e10	−0.335867	−0.167933	+	0.985798i	$0.553709\pi$
$348$	0	0
$349$	−3.98825e11	−1.43902	−0.719511	−	0.694481i	$-0.755634\pi$
$349$	−3.98825e11	−1.43902	−0.719511	+	0.694481i	$0.755634\pi$
$350$	5.59600e9	0.0199330
$351$	0	0
$352$	−2.30151e11	−0.799044
$353$	4.56192e11	1.56373	0.781865	−	0.623448i	$-0.214269\pi$
$353$	4.56192e11	1.56373	0.781865	+	0.623448i	$0.214269\pi$
$354$	0	0
$355$	1.31866e11	0.440662
$356$	−1.91627e11	−0.632311
$357$	0	0
$358$	1.00389e11	0.323006
$359$	−1.89176e11	−0.601094	−0.300547	−	0.953767i	$-0.597169\pi$
$359$	−1.89176e11	−0.601094	−0.300547	+	0.953767i	$0.597169\pi$
$360$	0	0
$361$	−3.15388e11	−0.977380
$362$	2.07296e11	0.634458
$363$	0	0
$364$	−1.13429e11	−0.338664
$365$	8.97090e10	0.264556
$366$	0	0
$367$	−3.17920e10	−0.0914787	−0.0457394	−	0.998953i	$-0.514564\pi$
$367$	−3.17920e10	−0.0914787	−0.0457394	+	0.998953i	$0.514564\pi$
$368$	1.69142e11	0.480769
$369$	0	0
$370$	−7.59472e10	−0.210671
$371$	−1.04950e10	−0.0287607
$372$	0	0
$373$	−4.46388e11	−1.19405	−0.597025	−	0.802222i	$-0.703651\pi$
$373$	−4.46388e11	−1.19405	−0.597025	+	0.802222i	$0.703651\pi$
$374$	−8.76409e10	−0.231625
$375$	0	0
$376$	−4.62639e11	−1.19371
$377$	−3.53260e11	−0.900655
$378$	0	0
$379$	3.53467e11	0.879978	0.439989	−	0.898003i	$-0.354982\pi$
$379$	3.53467e11	0.879978	0.439989	+	0.898003i	$0.354982\pi$
$380$	2.41022e10	0.0592966
$381$	0	0
$382$	2.12411e11	0.510377
$383$	−3.14974e11	−0.747963	−0.373981	−	0.927436i	$-0.622008\pi$
$383$	−3.14974e11	−0.747963	−0.373981	+	0.927436i	$0.622008\pi$
$384$	0	0
$385$	5.10403e10	0.118397
$386$	−7.51718e10	−0.172350
$387$	0	0
$388$	−5.41220e11	−1.21236
$389$	4.20729e11	0.931600	0.465800	−	0.884890i	$-0.345767\pi$
$389$	4.20729e11	0.931600	0.465800	+	0.884890i	$0.345767\pi$
$390$	0	0
$391$	2.48369e11	0.537405
$392$	2.77303e11	0.593155
$393$	0	0
$394$	−9.42843e10	−0.197109
$395$	2.84975e11	0.589007
$396$	0	0
$397$	5.63093e11	1.13769	0.568844	−	0.822446i	$-0.307391\pi$
$397$	5.63093e11	1.13769	0.568844	+	0.822446i	$0.307391\pi$
$398$	1.47737e11	0.295132
$399$	0	0
$400$	6.74602e10	0.131758
$401$	−2.75897e11	−0.532841	−0.266420	−	0.963857i	$-0.585841\pi$
$401$	−2.75897e11	−0.532841	−0.266420	+	0.963857i	$0.585841\pi$
$402$	0	0
$403$	1.22213e12	2.30805
$404$	−7.99317e11	−1.49280
$405$	0	0
$406$	−3.70521e10	−0.0676778
$407$	−6.92703e11	−1.25133
$408$	0	0
$409$	−6.54552e10	−0.115662	−0.0578308	−	0.998326i	$-0.518418\pi$
$409$	−6.54552e10	−0.115662	−0.0578308	+	0.998326i	$0.518418\pi$
$410$	1.19175e11	0.208285
$411$	0	0
$412$	−1.36912e11	−0.234101
$413$	−1.53647e11	−0.259866
$414$	0	0
$415$	−2.21941e11	−0.367301
$416$	7.08218e11	1.15944
$417$	0	0
$418$	−2.95266e10	−0.0473064
$419$	−2.70250e10	−0.0428354	−0.0214177	−	0.999771i	$-0.506818\pi$
$419$	−2.70250e10	−0.0428354	−0.0214177	+	0.999771i	$0.506818\pi$
$420$	0	0
$421$	−4.29698e11	−0.666644	−0.333322	−	0.942813i	$-0.608170\pi$
$421$	−4.29698e11	−0.666644	−0.333322	+	0.942813i	$0.608170\pi$
$422$	−6.94478e10	−0.106599
$423$	0	0
$424$	4.27875e10	0.0642940
$425$	9.90589e10	0.147280
$426$	0	0
$427$	2.73446e11	0.398058
$428$	−8.82048e10	−0.127056
$429$	0	0
$430$	−6.20915e10	−0.0875839
$431$	9.44700e11	1.31870	0.659350	−	0.751836i	$-0.270831\pi$
$431$	9.44700e11	1.31870	0.659350	+	0.751836i	$0.270831\pi$
$432$	0	0
$433$	2.10762e11	0.288136	0.144068	−	0.989568i	$-0.453982\pi$
$433$	2.10762e11	0.288136	0.144068	+	0.989568i	$0.453982\pi$
$434$	1.28185e11	0.173434
$435$	0	0
$436$	−1.04491e12	−1.38480
$437$	8.36765e10	0.109758
$438$	0	0
$439$	7.69079e11	0.988282	0.494141	−	0.869382i	$-0.335483\pi$
$439$	7.69079e11	0.988282	0.494141	+	0.869382i	$0.335483\pi$
$440$	−2.08089e11	−0.264674
$441$	0	0
$442$	2.69688e11	0.336094
$443$	6.49894e11	0.801726	0.400863	−	0.916138i	$-0.368710\pi$
$443$	6.49894e11	0.801726	0.400863	+	0.916138i	$0.368710\pi$
$444$	0	0
$445$	−2.65338e11	−0.320759
$446$	−3.44741e11	−0.412559
$447$	0	0
$448$	−8.84023e10	−0.103684
$449$	4.51858e11	0.524679	0.262339	−	0.964976i	$-0.415506\pi$
$449$	4.51858e11	0.524679	0.262339	+	0.964976i	$0.415506\pi$
$450$	0	0
$451$	1.08698e12	1.23716
$452$	5.95564e11	0.671128
$453$	0	0
$454$	4.20493e11	0.464523
$455$	−1.57061e11	−0.171797
$456$	0	0
$457$	−6.18434e11	−0.663240	−0.331620	−	0.943413i	$-0.607595\pi$
$457$	−6.18434e11	−0.663240	−0.331620	+	0.943413i	$0.607595\pi$
$458$	4.51798e10	0.0479788
$459$	0	0
$460$	2.76300e11	0.287720
$461$	2.76450e11	0.285078	0.142539	−	0.989789i	$-0.454473\pi$
$461$	2.76450e11	0.285078	0.142539	+	0.989789i	$0.454473\pi$
$462$	0	0
$463$	6.09969e11	0.616870	0.308435	−	0.951245i	$-0.400195\pi$
$463$	6.09969e11	0.616870	0.308435	+	0.951245i	$0.400195\pi$
$464$	−4.46666e11	−0.447355
$465$	0	0
$466$	−4.21910e11	−0.414461
$467$	−2.83260e11	−0.275587	−0.137794	−	0.990461i	$-0.544001\pi$
$467$	−2.83260e11	−0.275587	−0.137794	+	0.990461i	$0.544001\pi$
$468$	0	0
$469$	−3.09104e11	−0.295004
$470$	−3.00143e11	−0.283718
$471$	0	0
$472$	6.26412e11	0.580926
$473$	−5.66328e11	−0.520227
$474$	0	0
$475$	3.33733e10	0.0300800
$476$	−2.10600e11	−0.188030
$477$	0	0
$478$	−6.16485e11	−0.540129
$479$	1.39149e12	1.20773	0.603865	−	0.797087i	$-0.293627\pi$
$479$	1.39149e12	1.20773	0.603865	+	0.797087i	$0.293627\pi$
$480$	0	0
$481$	2.13158e12	1.81572
$482$	−4.78793e11	−0.404051
$483$	0	0
$484$	1.75062e11	0.145007
$485$	−7.49406e11	−0.615006
$486$	0	0
$487$	−1.41532e11	−0.114018	−0.0570092	−	0.998374i	$-0.518156\pi$
$487$	−1.41532e11	−0.114018	−0.0570092	+	0.998374i	$0.518156\pi$
$488$	−1.11483e12	−0.889851
$489$	0	0
$490$	1.79904e11	0.140980
$491$	4.66246e11	0.362034	0.181017	−	0.983480i	$-0.442061\pi$
$491$	4.66246e11	0.362034	0.181017	+	0.983480i	$0.442061\pi$
$492$	0	0
$493$	−6.55887e11	−0.500055
$494$	9.08589e10	0.0686430
$495$	0	0
$496$	1.54528e12	1.14641
$497$	−3.88188e11	−0.285389
$498$	0	0
$499$	−2.21254e12	−1.59749	−0.798746	−	0.601668i	$-0.794503\pi$
$499$	−2.21254e12	−1.59749	−0.798746	+	0.601668i	$0.794503\pi$
$500$	1.10199e11	0.0788518
$501$	0	0
$502$	−2.25271e11	−0.158321
$503$	−3.39574e11	−0.236526	−0.118263	−	0.992982i	$-0.537733\pi$
$503$	−3.39574e11	−0.236526	−0.118263	+	0.992982i	$0.537733\pi$
$504$	0	0
$505$	−1.10678e12	−0.757270
$506$	−3.38484e11	−0.229541
$507$	0	0
$508$	−1.43970e12	−0.959149
$509$	5.66691e11	0.374211	0.187106	−	0.982340i	$-0.440089\pi$
$509$	5.66691e11	0.374211	0.187106	+	0.982340i	$0.440089\pi$
$510$	0	0
$511$	−2.64086e11	−0.171337
$512$	1.55874e12	1.00244
$513$	0	0
$514$	−9.52947e11	−0.602191
$515$	−1.89576e11	−0.118755
$516$	0	0
$517$	−2.73756e12	−1.68522
$518$	2.23574e11	0.136438
$519$	0	0
$520$	6.40329e11	0.384050
$521$	−4.42970e11	−0.263393	−0.131697	−	0.991290i	$-0.542042\pi$
$521$	−4.42970e11	−0.263393	−0.131697	+	0.991290i	$0.542042\pi$
$522$	0	0
$523$	−1.44683e11	−0.0845591	−0.0422796	−	0.999106i	$-0.513462\pi$
$523$	−1.44683e11	−0.0845591	−0.0422796	+	0.999106i	$0.513462\pi$
$524$	−2.43794e12	−1.41264
$525$	0	0
$526$	4.86557e11	0.277139
$527$	2.26910e12	1.28146
$528$	0	0
$529$	−8.41911e11	−0.467429
$530$	2.77589e10	0.0152813
$531$	0	0
$532$	−7.09520e10	−0.0384028
$533$	−3.34484e12	−1.79516
$534$	0	0
$535$	−1.22134e11	−0.0644531
$536$	1.26020e12	0.659475
$537$	0	0
$538$	−9.90519e11	−0.509733
$539$	1.64088e12	0.837388
$540$	0	0
$541$	−3.10308e11	−0.155742	−0.0778710	−	0.996963i	$-0.524812\pi$
$541$	−3.10308e11	−0.155742	−0.0778710	+	0.996963i	$0.524812\pi$
$542$	1.19999e11	0.0597281
$543$	0	0
$544$	1.31493e12	0.643733
$545$	−1.44684e12	−0.702484
$546$	0	0
$547$	1.68502e12	0.804750	0.402375	−	0.915475i	$-0.368185\pi$
$547$	1.68502e12	0.804750	0.402375	+	0.915475i	$0.368185\pi$
$548$	5.41211e9	0.00256362
$549$	0	0
$550$	−1.35000e11	−0.0629074
$551$	−2.20971e11	−0.102130
$552$	0	0
$553$	−8.38911e11	−0.381463
$554$	−7.17011e11	−0.323394
$555$	0	0
$556$	−4.13225e11	−0.183379
$557$	2.31328e12	1.01831	0.509156	−	0.860674i	$-0.329958\pi$
$557$	2.31328e12	1.01831	0.509156	+	0.860674i	$0.329958\pi$
$558$	0	0
$559$	1.74270e12	0.754865
$560$	−1.98590e11	−0.0853317
$561$	0	0
$562$	6.06380e11	0.256408
$563$	−7.03648e11	−0.295167	−0.147583	−	0.989050i	$-0.547150\pi$
$563$	−7.03648e11	−0.295167	−0.147583	+	0.989050i	$0.547150\pi$
$564$	0	0
$565$	8.24653e11	0.340450
$566$	2.27720e11	0.0932666
$567$	0	0
$568$	1.58262e12	0.637983
$569$	−3.21997e12	−1.28779	−0.643896	−	0.765113i	$-0.722683\pi$
$569$	−3.21997e12	−1.28779	−0.643896	+	0.765113i	$0.722683\pi$
$570$	0	0
$571$	−1.21116e12	−0.476801	−0.238401	−	0.971167i	$-0.576623\pi$
$571$	−1.21116e12	−0.476801	−0.238401	+	0.971167i	$0.576623\pi$
$572$	2.73641e12	1.06880
$573$	0	0
$574$	−3.50827e11	−0.134893
$575$	3.82582e11	0.145955
$576$	0	0
$577$	7.30673e11	0.274430	0.137215	−	0.990541i	$-0.456185\pi$
$577$	7.30673e11	0.274430	0.137215	+	0.990541i	$0.456185\pi$
$578$	−4.22635e11	−0.157504
$579$	0	0
$580$	−7.29646e11	−0.267723
$581$	6.53352e11	0.237878
$582$	0	0
$583$	2.53185e11	0.0907673
$584$	1.07666e12	0.383021
$585$	0	0
$586$	1.77062e12	0.620278
$587$	−4.55331e12	−1.58291	−0.791453	−	0.611230i	$-0.790675\pi$
$587$	−4.55331e12	−1.58291	−0.791453	+	0.611230i	$0.790675\pi$
$588$	0	0
$589$	7.64467e11	0.261722
$590$	4.06392e11	0.138074
$591$	0	0
$592$	2.69520e12	0.901867
$593$	−3.00074e12	−0.996510	−0.498255	−	0.867030i	$-0.666026\pi$
$593$	−3.00074e12	−0.996510	−0.498255	+	0.867030i	$0.666026\pi$
$594$	0	0
$595$	−2.91610e11	−0.0953841
$596$	2.25896e12	0.733330
$597$	0	0
$598$	1.04158e12	0.333071
$599$	4.03514e12	1.28067	0.640336	−	0.768095i	$-0.278795\pi$
$599$	4.03514e12	1.28067	0.640336	+	0.768095i	$0.278795\pi$
$600$	0	0
$601$	2.04760e12	0.640192	0.320096	−	0.947385i	$-0.396285\pi$
$601$	2.04760e12	0.640192	0.320096	+	0.947385i	$0.396285\pi$
$602$	1.82785e11	0.0567227
$603$	0	0
$604$	−1.44690e12	−0.442355
$605$	2.42401e11	0.0735590
$606$	0	0
$607$	3.15792e12	0.944175	0.472088	−	0.881552i	$-0.343501\pi$
$607$	3.15792e12	0.944175	0.472088	+	0.881552i	$0.343501\pi$
$608$	4.43004e11	0.131474
$609$	0	0
$610$	−7.23256e11	−0.211499
$611$	8.42399e12	2.44530
$612$	0	0
$613$	−2.89302e12	−0.827520	−0.413760	−	0.910386i	$-0.635785\pi$
$613$	−2.89302e12	−0.827520	−0.413760	+	0.910386i	$0.635785\pi$
$614$	−4.69183e11	−0.133225
$615$	0	0
$616$	6.12573e11	0.171413
$617$	−6.03603e12	−1.67675	−0.838375	−	0.545094i	$-0.816494\pi$
$617$	−6.03603e12	−1.67675	−0.838375	+	0.545094i	$0.816494\pi$
$618$	0	0
$619$	4.05606e12	1.11044	0.555222	−	0.831702i	$-0.312633\pi$
$619$	4.05606e12	1.11044	0.555222	+	0.831702i	$0.312633\pi$
$620$	2.52427e12	0.686078
$621$	0	0
$622$	−1.06529e12	−0.285371
$623$	7.81102e11	0.207736
$624$	0	0
$625$	1.52588e11	0.0400000
$626$	1.75607e12	0.457044
$627$	0	0
$628$	2.09180e11	0.0536664
$629$	3.95764e12	1.00811
$630$	0	0
$631$	−5.34498e12	−1.34219	−0.671095	−	0.741372i	$-0.734176\pi$
$631$	−5.34498e12	−1.34219	−0.671095	+	0.741372i	$0.734176\pi$
$632$	3.42020e12	0.852755
$633$	0	0
$634$	9.99651e11	0.245723
$635$	−1.99350e12	−0.486558
$636$	0	0
$637$	−5.04929e12	−1.21507
$638$	8.93859e11	0.213588
$639$	0	0
$640$	1.89309e12	0.446028
$641$	−4.81739e12	−1.12707	−0.563534	−	0.826093i	$-0.690559\pi$
$641$	−4.81739e12	−1.12707	−0.563534	+	0.826093i	$0.690559\pi$
$642$	0	0
$643$	−5.85505e11	−0.135077	−0.0675385	−	0.997717i	$-0.521515\pi$
$643$	−5.85505e11	−0.135077	−0.0675385	+	0.997717i	$0.521515\pi$
$644$	−8.13372e11	−0.186339
$645$	0	0
$646$	1.68695e11	0.0381114
$647$	−4.54903e12	−1.02059	−0.510293	−	0.860001i	$-0.670463\pi$
$647$	−4.54903e12	−1.02059	−0.510293	+	0.860001i	$0.670463\pi$
$648$	0	0
$649$	3.70664e12	0.820124
$650$	4.15421e11	0.0912805
$651$	0	0
$652$	5.77526e12	1.25158
$653$	7.04350e12	1.51593	0.757965	−	0.652295i	$-0.226194\pi$
$653$	7.04350e12	1.51593	0.757965	+	0.652295i	$0.226194\pi$
$654$	0	0
$655$	−3.37572e12	−0.716606
$656$	−4.22925e12	−0.891653
$657$	0	0
$658$	8.83561e11	0.183747
$659$	−5.23559e12	−1.08139	−0.540694	−	0.841219i	$-0.681838\pi$
$659$	−5.23559e12	−1.08139	−0.540694	+	0.841219i	$0.681838\pi$
$660$	0	0
$661$	−5.79017e12	−1.17974	−0.589868	−	0.807500i	$-0.700820\pi$
$661$	−5.79017e12	−1.17974	−0.589868	+	0.807500i	$0.700820\pi$
$662$	8.95563e10	0.0181232
$663$	0	0
$664$	−2.66368e12	−0.531772
$665$	−9.82445e10	−0.0194810
$666$	0	0
$667$	−2.53314e12	−0.495557
$668$	−8.38197e12	−1.62874
$669$	0	0
$670$	8.17570e11	0.156743
$671$	−6.59671e12	−1.25625
$672$	0	0
$673$	−5.92328e10	−0.0111300	−0.00556499	−	0.999985i	$-0.501771\pi$
$673$	−5.92328e10	−0.0111300	−0.00556499	+	0.999985i	$0.501771\pi$
$674$	−2.17728e12	−0.406392
$675$	0	0
$676$	−3.63385e12	−0.669278
$677$	−4.57177e12	−0.836440	−0.418220	−	0.908346i	$-0.637346\pi$
$677$	−4.57177e12	−0.836440	−0.418220	+	0.908346i	$0.637346\pi$
$678$	0	0
$679$	2.20611e12	0.398302
$680$	1.18888e12	0.213229
$681$	0	0
$682$	−3.09238e12	−0.547348
$683$	9.71286e12	1.70787	0.853934	−	0.520382i	$-0.174210\pi$
$683$	9.71286e12	1.70787	0.853934	+	0.520382i	$0.174210\pi$
$684$	0	0
$685$	7.49393e9	0.00130048
$686$	−1.10770e12	−0.190969
$687$	0	0
$688$	2.20349e12	0.374941
$689$	−7.79098e11	−0.131706
$690$	0	0
$691$	2.23726e12	0.373306	0.186653	−	0.982426i	$-0.440236\pi$
$691$	2.23726e12	0.373306	0.186653	+	0.982426i	$0.440236\pi$
$692$	2.21510e12	0.367211
$693$	0	0
$694$	−7.06282e11	−0.115574
$695$	−5.72176e11	−0.0930247
$696$	0	0
$697$	−6.21025e12	−0.996693
$698$	−3.10535e12	−0.495178
$699$	0	0
$700$	−3.24404e11	−0.0510675
$701$	2.29477e10	0.00358929	0.00179464	−	0.999998i	$-0.499429\pi$
$701$	2.29477e10	0.00358929	0.00179464	+	0.999998i	$0.499429\pi$
$702$	0	0
$703$	1.33334e12	0.205894
$704$	2.13265e12	0.327222
$705$	0	0
$706$	3.55203e12	0.538091
$707$	3.25815e12	0.490438
$708$	0	0
$709$	−9.57637e12	−1.42329	−0.711644	−	0.702540i	$-0.752049\pi$
$709$	−9.57637e12	−1.42329	−0.711644	+	0.702540i	$0.752049\pi$
$710$	1.02674e12	0.151635
$711$	0	0
$712$	−3.18451e12	−0.464390
$713$	8.76362e12	1.26993
$714$	0	0
$715$	3.78899e12	0.542184
$716$	−5.81959e12	−0.827529
$717$	0	0
$718$	−1.47298e12	−0.206841
$719$	5.46390e12	0.762469	0.381235	−	0.924478i	$-0.375499\pi$
$719$	5.46390e12	0.762469	0.381235	+	0.924478i	$0.375499\pi$
$720$	0	0
$721$	5.58075e11	0.0769102
$722$	−2.45570e12	−0.336324
$723$	0	0
$724$	−1.20171e13	−1.62546
$725$	−1.01031e12	−0.135811
$726$	0	0
$727$	6.59842e12	0.876062	0.438031	−	0.898960i	$-0.355676\pi$
$727$	6.59842e12	0.876062	0.438031	+	0.898960i	$0.355676\pi$
$728$	−1.88500e12	−0.248726
$729$	0	0
$730$	6.98498e11	0.0910358
$731$	3.23561e12	0.419111
$732$	0	0
$733$	6.91041e11	0.0884170	0.0442085	−	0.999022i	$-0.485923\pi$
$733$	6.91041e11	0.0884170	0.0442085	+	0.999022i	$0.485923\pi$
$734$	−2.47541e11	−0.0314785
$735$	0	0
$736$	5.07846e12	0.637943
$737$	7.45694e12	0.931016
$738$	0	0
$739$	7.60189e12	0.937608	0.468804	−	0.883302i	$-0.344685\pi$
$739$	7.60189e12	0.937608	0.468804	+	0.883302i	$0.344685\pi$
$740$	4.40270e12	0.539730
$741$	0	0
$742$	−8.17167e10	−0.00989677
$743$	2.23002e12	0.268448	0.134224	−	0.990951i	$-0.457146\pi$
$743$	2.23002e12	0.268448	0.134224	+	0.990951i	$0.457146\pi$
$744$	0	0
$745$	3.12789e12	0.372004
$746$	−3.47569e12	−0.410882
$747$	0	0
$748$	5.08060e12	0.593414
$749$	3.59538e11	0.0417423
$750$	0	0
$751$	1.65708e12	0.190092	0.0950459	−	0.995473i	$-0.469700\pi$
$751$	1.65708e12	0.190092	0.0950459	+	0.995473i	$0.469700\pi$
$752$	1.06514e13	1.21458
$753$	0	0
$754$	−2.75058e12	−0.309922
$755$	−2.00346e12	−0.224398
$756$	0	0
$757$	−1.28420e13	−1.42135	−0.710675	−	0.703521i	$-0.751610\pi$
$757$	−1.28420e13	−1.42135	−0.710675	+	0.703521i	$0.751610\pi$
$758$	2.75218e12	0.302807
$759$	0	0
$760$	4.00538e11	0.0435494
$761$	−1.61852e13	−1.74939	−0.874694	−	0.484676i	$-0.838937\pi$
$761$	−1.61852e13	−1.74939	−0.874694	+	0.484676i	$0.838937\pi$
$762$	0	0
$763$	4.25921e12	0.454955
$764$	−1.23136e13	−1.30757
$765$	0	0
$766$	−2.45247e12	−0.257380
$767$	−1.14060e13	−1.19002
$768$	0	0
$769$	5.30462e12	0.546998	0.273499	−	0.961872i	$-0.411819\pi$
$769$	5.30462e12	0.546998	0.273499	+	0.961872i	$0.411819\pi$
$770$	3.97414e11	0.0407413
$771$	0	0
$772$	4.35775e12	0.441555
$773$	1.26188e13	1.27119	0.635596	−	0.772022i	$-0.280755\pi$
$773$	1.26188e13	1.27119	0.635596	+	0.772022i	$0.280755\pi$
$774$	0	0
$775$	3.49526e12	0.348034
$776$	−8.99418e12	−0.890397
$777$	0	0
$778$	3.27591e12	0.320571
$779$	−2.09226e12	−0.203562
$780$	0	0
$781$	9.36478e12	0.900675
$782$	1.93387e12	0.184925
$783$	0	0
$784$	−6.38438e12	−0.603527
$785$	2.89644e11	0.0272239
$786$	0	0
$787$	1.22887e13	1.14188	0.570941	−	0.820991i	$-0.306579\pi$
$787$	1.22887e13	1.14188	0.570941	+	0.820991i	$0.306579\pi$
$788$	5.46571e12	0.504985
$789$	0	0
$790$	2.21889e12	0.202682
$791$	−2.42762e12	−0.220489
$792$	0	0
$793$	2.02993e13	1.82286
$794$	4.38439e12	0.391487
$795$	0	0
$796$	−8.56441e12	−0.756116
$797$	3.56495e12	0.312962	0.156481	−	0.987681i	$-0.449985\pi$
$797$	3.56495e12	0.312962	0.156481	+	0.987681i	$0.449985\pi$
$798$	0	0
$799$	1.56405e13	1.35766
$800$	2.02548e12	0.174833
$801$	0	0
$802$	−2.14821e12	−0.183354
$803$	6.37090e12	0.540730
$804$	0	0
$805$	−1.12624e12	−0.0945260
$806$	9.51585e12	0.794218
$807$	0	0
$808$	−1.32833e13	−1.09636
$809$	3.11624e12	0.255778	0.127889	−	0.991789i	$-0.459180\pi$
$809$	3.11624e12	0.255778	0.127889	+	0.991789i	$0.459180\pi$
$810$	0	0
$811$	−2.30256e12	−0.186904	−0.0934518	−	0.995624i	$-0.529790\pi$
$811$	−2.30256e12	−0.186904	−0.0934518	+	0.995624i	$0.529790\pi$
$812$	2.14793e12	0.173388
$813$	0	0
$814$	−5.39357e12	−0.430593
$815$	7.99677e12	0.634900
$816$	0	0
$817$	1.09009e12	0.0855980
$818$	−5.09651e11	−0.0398000
$819$	0	0
$820$	−6.90864e12	−0.533617
$821$	6.28720e12	0.482962	0.241481	−	0.970406i	$-0.422367\pi$
$821$	6.28720e12	0.482962	0.241481	+	0.970406i	$0.422367\pi$
$822$	0	0
$823$	3.76056e12	0.285728	0.142864	−	0.989742i	$-0.454369\pi$
$823$	3.76056e12	0.285728	0.142864	+	0.989742i	$0.454369\pi$
$824$	−2.27524e12	−0.171932
$825$	0	0
$826$	−1.19634e12	−0.0894219
$827$	−1.75054e13	−1.30136	−0.650679	−	0.759353i	$-0.725516\pi$
$827$	−1.75054e13	−1.30136	−0.650679	+	0.759353i	$0.725516\pi$
$828$	0	0
$829$	−2.42570e12	−0.178378	−0.0891891	−	0.996015i	$-0.528428\pi$
$829$	−2.42570e12	−0.178378	−0.0891891	+	0.996015i	$0.528428\pi$
$830$	−1.72809e12	−0.126391
$831$	0	0
$832$	−6.56257e12	−0.474809
$833$	−9.37486e12	−0.674625
$834$	0	0
$835$	−1.16062e13	−0.826229
$836$	1.71167e12	0.121197
$837$	0	0
$838$	−2.10424e11	−0.0147400
$839$	−9.69596e11	−0.0675557	−0.0337778	−	0.999429i	$-0.510754\pi$
$839$	−9.69596e11	−0.0675557	−0.0337778	+	0.999429i	$0.510754\pi$
$840$	0	0
$841$	−7.81769e12	−0.538885
$842$	−3.34574e12	−0.229397
$843$	0	0
$844$	4.02593e12	0.273102
$845$	−5.03164e12	−0.339512
$846$	0	0
$847$	−7.13582e11	−0.0476397
$848$	−9.85101e11	−0.0654183
$849$	0	0
$850$	7.71298e11	0.0506801
$851$	1.52850e13	0.999042
$852$	0	0
$853$	−2.11898e13	−1.37043	−0.685215	−	0.728340i	$-0.740292\pi$
$853$	−2.11898e13	−1.37043	−0.685215	+	0.728340i	$0.740292\pi$
$854$	2.12912e12	0.136975
$855$	0	0
$856$	−1.46582e12	−0.0933142
$857$	−8.34904e12	−0.528717	−0.264358	−	0.964425i	$-0.585160\pi$
$857$	−8.34904e12	−0.528717	−0.264358	+	0.964425i	$0.585160\pi$
$858$	0	0
$859$	−8.24621e12	−0.516755	−0.258378	−	0.966044i	$-0.583188\pi$
$859$	−8.24621e12	−0.516755	−0.258378	+	0.966044i	$0.583188\pi$
$860$	3.59948e12	0.224387
$861$	0	0
$862$	7.35568e12	0.453775
$863$	−4.35663e12	−0.267364	−0.133682	−	0.991024i	$-0.542680\pi$
$863$	−4.35663e12	−0.267364	−0.133682	+	0.991024i	$0.542680\pi$
$864$	0	0
$865$	3.06716e12	0.186279
$866$	1.64105e12	0.0991497
$867$	0	0
$868$	−7.43096e12	−0.444331
$869$	2.02382e13	1.20388
$870$	0	0
$871$	−2.29464e13	−1.35093
$872$	−1.73646e13	−1.01705
$873$	0	0
$874$	6.51527e11	0.0377686
$875$	−4.49189e11	−0.0259055
$876$	0	0
$877$	−1.21873e12	−0.0695680	−0.0347840	−	0.999395i	$-0.511074\pi$
$877$	−1.21873e12	−0.0695680	−0.0347840	+	0.999395i	$0.511074\pi$
$878$	5.98825e12	0.340075
$879$	0	0
$880$	4.79085e12	0.269303
$881$	−3.98577e12	−0.222905	−0.111453	−	0.993770i	$-0.535550\pi$
$881$	−3.98577e12	−0.222905	−0.111453	+	0.993770i	$0.535550\pi$
$882$	0	0
$883$	2.19963e13	1.21766	0.608831	−	0.793300i	$-0.291639\pi$
$883$	2.19963e13	1.21766	0.608831	+	0.793300i	$0.291639\pi$
$884$	−1.56340e13	−0.861061
$885$	0	0
$886$	5.06025e12	0.275880
$887$	−1.39860e13	−0.758640	−0.379320	−	0.925266i	$-0.623842\pi$
$887$	−1.39860e13	−0.758640	−0.379320	+	0.925266i	$0.623842\pi$
$888$	0	0
$889$	5.86847e12	0.315113
$890$	−2.06599e12	−0.110376
$891$	0	0
$892$	1.99848e13	1.05696
$893$	5.26936e12	0.277285
$894$	0	0
$895$	−8.05815e12	−0.419790
$896$	−5.57290e12	−0.288865
$897$	0	0
$898$	3.51829e12	0.180546
$899$	−2.31428e13	−1.18167
$900$	0	0
$901$	−1.44653e12	−0.0731248
$902$	8.46349e12	0.425716
$903$	0	0
$904$	9.89727e12	0.492899
$905$	−1.66396e13	−0.824563
$906$	0	0
$907$	−8.00749e12	−0.392884	−0.196442	−	0.980515i	$-0.562939\pi$
$907$	−8.00749e12	−0.392884	−0.196442	+	0.980515i	$0.562939\pi$
$908$	−2.43762e13	−1.19009
$909$	0	0
$910$	−1.22292e12	−0.0591168
$911$	4.09248e13	1.96858	0.984291	−	0.176555i	$-0.0564953\pi$
$911$	4.09248e13	1.96858	0.984291	+	0.176555i	$0.0564953\pi$
$912$	0	0
$913$	−1.57617e13	−0.750731
$914$	−4.81529e12	−0.228226
$915$	0	0
$916$	−2.61910e12	−0.122920
$917$	9.93745e12	0.464102
$918$	0	0
$919$	8.12730e12	0.375860	0.187930	−	0.982182i	$-0.439822\pi$
$919$	8.12730e12	0.375860	0.187930	+	0.982182i	$0.439822\pi$
$920$	4.59164e12	0.211311
$921$	0	0
$922$	2.15252e12	0.0980973
$923$	−2.88172e13	−1.30691
$924$	0	0
$925$	6.09625e12	0.273795
$926$	4.74938e12	0.212269
$927$	0	0
$928$	−1.34111e13	−0.593605
$929$	4.43436e13	1.95326	0.976631	−	0.214923i	$-0.0689500\pi$
$929$	4.43436e13	1.95326	0.976631	+	0.214923i	$0.0689500\pi$
$930$	0	0
$931$	−3.15843e12	−0.137783
$932$	2.44584e13	1.06183
$933$	0	0
$934$	−2.20554e12	−0.0948317
$935$	7.03490e12	0.301027
$936$	0	0
$937$	−3.56882e13	−1.51250	−0.756251	−	0.654281i	$-0.772971\pi$
$937$	−3.56882e13	−1.51250	−0.756251	+	0.654281i	$0.772971\pi$
$938$	−2.40677e12	−0.101513
$939$	0	0
$940$	1.73994e13	0.726875
$941$	−3.76351e13	−1.56473	−0.782366	−	0.622818i	$-0.785988\pi$
$941$	−3.76351e13	−1.56473	−0.782366	+	0.622818i	$0.785988\pi$
$942$	0	0
$943$	−2.39850e13	−0.987727
$944$	−1.44219e13	−0.591085
$945$	0	0
$946$	−4.40958e12	−0.179014
$947$	1.01014e13	0.408139	0.204070	−	0.978956i	$-0.434583\pi$
$947$	1.01014e13	0.408139	0.204070	+	0.978956i	$0.434583\pi$
$948$	0	0
$949$	−1.96045e13	−0.784616
$950$	2.59853e11	0.0103508
$951$	0	0
$952$	−3.49982e12	−0.138096
$953$	−1.49469e13	−0.586993	−0.293497	−	0.955960i	$-0.594819\pi$
$953$	−1.49469e13	−0.586993	−0.293497	+	0.955960i	$0.594819\pi$
$954$	0	0
$955$	−1.70501e13	−0.663303
$956$	3.57380e13	1.38379
$957$	0	0
$958$	1.08345e13	0.415589
$959$	−2.20607e10	−0.000842238 0
$960$	0	0
$961$	5.36247e13	2.02819
$962$	1.65970e13	0.624803
$963$	0	0
$964$	2.77559e13	1.03516
$965$	6.03401e12	0.223992
$966$	0	0
$967$	2.42942e13	0.893475	0.446738	−	0.894665i	$-0.352586\pi$
$967$	2.42942e13	0.893475	0.446738	+	0.894665i	$0.352586\pi$
$968$	2.90924e12	0.106498
$969$	0	0
$970$	−5.83507e12	−0.211628
$971$	1.07032e13	0.386392	0.193196	−	0.981160i	$-0.438115\pi$
$971$	1.07032e13	0.386392	0.193196	+	0.981160i	$0.438115\pi$
$972$	0	0
$973$	1.68437e12	0.0602464
$974$	−1.10201e12	−0.0392346
$975$	0	0
$976$	2.56667e13	0.905412
$977$	1.53038e13	0.537372	0.268686	−	0.963228i	$-0.413411\pi$
$977$	1.53038e13	0.537372	0.268686	+	0.963228i	$0.413411\pi$
$978$	0	0
$979$	−1.88436e13	−0.655604
$980$	−1.04291e13	−0.361186
$981$	0	0
$982$	3.63032e12	0.124578
$983$	−3.27251e13	−1.11787	−0.558934	−	0.829212i	$-0.688790\pi$
$983$	−3.27251e13	−1.11787	−0.558934	+	0.829212i	$0.688790\pi$
$984$	0	0
$985$	7.56816e12	0.256169
$986$	−5.10691e12	−0.172073
$987$	0	0
$988$	−5.26714e12	−0.175861
$989$	1.24965e13	0.415340
$990$	0	0
$991$	3.05488e13	1.00615	0.503075	−	0.864243i	$-0.332202\pi$
$991$	3.05488e13	1.00615	0.503075	+	0.864243i	$0.332202\pi$
$992$	4.63967e13	1.52119
$993$	0	0
$994$	−3.02253e12	−0.0982046
$995$	−1.18588e13	−0.383563
$996$	0	0
$997$	4.87857e13	1.56374	0.781870	−	0.623441i	$-0.214266\pi$
$997$	4.87857e13	1.56374	0.781870	+	0.623441i	$0.214266\pi$
$998$	−1.72274e13	−0.549709
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.10.a.d.1.2		2
3.2	odd	2		15.10.a.d.1.1	✓	2
5.2	odd	4		225.10.b.i.199.3		4
5.3	odd	4		225.10.b.i.199.2		4
5.4	even	2		225.10.a.k.1.1		2
12.11	even	2		240.10.a.r.1.2		2
15.2	even	4		75.10.b.f.49.2		4
15.8	even	4		75.10.b.f.49.3		4
15.14	odd	2		75.10.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.a.d.1.1	✓	2	3.2	odd	2
45.10.a.d.1.2		2	1.1	even	1	trivial
75.10.a.f.1.2		2	15.14	odd	2
75.10.b.f.49.2		4	15.2	even	4
75.10.b.f.49.3		4	15.8	even	4
225.10.a.k.1.1		2	5.4	even	2
225.10.b.i.199.2		4	5.3	odd	4
225.10.b.i.199.3		4	5.2	odd	4
240.10.a.r.1.2		2	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	45.a (trivial)

\(f(q)\)	\(=\)	\(q+7.78626 q^{2} -451.374 q^{4} -625.000 q^{5} +1839.88 q^{7} -7501.08 q^{8} +O(q^{10})\)	\(q+7.78626 q^{2} -451.374 q^{4} -625.000 q^{5} +1839.88 q^{7} -7501.08 q^{8} -4866.41 q^{10} -44385.9 q^{11} +136584. q^{13} +14325.8 q^{14} +172698. q^{16} +253591. q^{17} +85435.7 q^{19} +282109. q^{20} -345600. q^{22} +979409. q^{23} +390625. q^{25} +1.06348e6 q^{26} -830473. q^{28} -2.58640e6 q^{29} +8.94787e6 q^{31} +5.18523e6 q^{32} +1.97452e6 q^{34} -1.14992e6 q^{35} +1.56064e7 q^{37} +665225. q^{38} +4.68818e6 q^{40} -2.44893e7 q^{41} +1.27592e7 q^{43} +2.00346e7 q^{44} +7.62593e6 q^{46} +6.16764e7 q^{47} -3.69685e7 q^{49} +3.04151e6 q^{50} -6.16504e7 q^{52} -5.70418e6 q^{53} +2.77412e7 q^{55} -1.38011e7 q^{56} -2.01384e7 q^{58} -8.35095e7 q^{59} +1.48622e8 q^{61} +6.96704e7 q^{62} -4.80479e7 q^{64} -8.53649e7 q^{65} -1.68003e8 q^{67} -1.14464e8 q^{68} -8.95360e6 q^{70} -2.10986e8 q^{71} -1.43534e8 q^{73} +1.21515e8 q^{74} -3.85635e7 q^{76} -8.16646e7 q^{77} -4.55960e8 q^{79} -1.07936e8 q^{80} -1.90680e8 q^{82} +3.55106e8 q^{83} -1.58494e8 q^{85} +9.93465e7 q^{86} +3.32942e8 q^{88} +4.24540e8 q^{89} +2.51297e8 q^{91} -4.42080e8 q^{92} +4.80228e8 q^{94} -5.33973e7 q^{95} +1.19905e9 q^{97} -2.87846e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 31 q^{2} + 541 q^{4} - 1250 q^{5} + 14112 q^{7} - 26133 q^{8}+O(q^{10}) \) 2 * q - 31 * q^2 + 541 * q^4 - 1250 * q^5 + 14112 * q^7 - 26133 * q^8	\( 2 q - 31 q^{2} + 541 q^{4} - 1250 q^{5} + 14112 q^{7} - 26133 q^{8} + 19375 q^{10} + 21512 q^{11} + 24284 q^{13} - 461664 q^{14} + 387265 q^{16} + 156956 q^{17} - 95896 q^{19} - 338125 q^{20} - 2901532 q^{22} + 735264 q^{23} + 781250 q^{25} + 5419166 q^{26} + 11348064 q^{28} + 2678212 q^{29} + 10782432 q^{31} + 6402523 q^{32} + 5722622 q^{34} - 8820000 q^{35} + 21968332 q^{37} + 7698404 q^{38} + 16333125 q^{40} - 26060372 q^{41} - 7191160 q^{43} + 85429972 q^{44} + 17095392 q^{46} + 31580240 q^{47} + 73282930 q^{49} - 12109375 q^{50} - 173093786 q^{52} - 3131116 q^{53} - 13445000 q^{55} - 242454240 q^{56} - 224332958 q^{58} + 35494664 q^{59} + 341497340 q^{61} - 1485504 q^{62} - 205120471 q^{64} - 15177500 q^{65} - 288195816 q^{67} - 210362042 q^{68} + 288540000 q^{70} - 210286064 q^{71} - 232663084 q^{73} - 125240234 q^{74} - 218512364 q^{76} + 727042176 q^{77} - 24755040 q^{79} - 242040625 q^{80} - 129742346 q^{82} + 372082152 q^{83} - 98097500 q^{85} + 873146372 q^{86} - 894861492 q^{88} + 427639116 q^{89} - 1126859328 q^{91} - 684362592 q^{92} + 1647543896 q^{94} + 59935000 q^{95} + 1771658884 q^{97} - 4564085351 q^{98}+O(q^{100}) \) 2 * q - 31 * q^2 + 541 * q^4 - 1250 * q^5 + 14112 * q^7 - 26133 * q^8 + 19375 * q^10 + 21512 * q^11 + 24284 * q^13 - 461664 * q^14 + 387265 * q^16 + 156956 * q^17 - 95896 * q^19 - 338125 * q^20 - 2901532 * q^22 + 735264 * q^23 + 781250 * q^25 + 5419166 * q^26 + 11348064 * q^28 + 2678212 * q^29 + 10782432 * q^31 + 6402523 * q^32 + 5722622 * q^34 - 8820000 * q^35 + 21968332 * q^37 + 7698404 * q^38 + 16333125 * q^40 - 26060372 * q^41 - 7191160 * q^43 + 85429972 * q^44 + 17095392 * q^46 + 31580240 * q^47 + 73282930 * q^49 - 12109375 * q^50 - 173093786 * q^52 - 3131116 * q^53 - 13445000 * q^55 - 242454240 * q^56 - 224332958 * q^58 + 35494664 * q^59 + 341497340 * q^61 - 1485504 * q^62 - 205120471 * q^64 - 15177500 * q^65 - 288195816 * q^67 - 210362042 * q^68 + 288540000 * q^70 - 210286064 * q^71 - 232663084 * q^73 - 125240234 * q^74 - 218512364 * q^76 + 727042176 * q^77 - 24755040 * q^79 - 242040625 * q^80 - 129742346 * q^82 + 372082152 * q^83 - 98097500 * q^85 + 873146372 * q^86 - 894861492 * q^88 + 427639116 * q^89 - 1126859328 * q^91 - 684362592 * q^92 + 1647543896 * q^94 + 59935000 * q^95 + 1771658884 * q^97 - 4564085351 * q^98

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