LMFDB - Embedded newform 4598.2.a.bo.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.621.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 3 $ x^3 - 6*x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.14510$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.14510 q^{3} +1.00000 q^{4} -1.60147 q^{5} -2.14510 q^{6} -2.89167 q^{7} +1.00000 q^{8} +1.60147 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.14510 q^{3} +1.00000 q^{4} -1.60147 q^{5} -2.14510 q^{6} -2.89167 q^{7} +1.00000 q^{8} +1.60147 q^{9} -1.60147 q^{10} -2.14510 q^{12} -4.89167 q^{13} -2.89167 q^{14} +3.43531 q^{15} +1.00000 q^{16} +5.74657 q^{17} +1.60147 q^{18} +1.00000 q^{19} -1.60147 q^{20} +6.20293 q^{21} -7.74657 q^{23} -2.14510 q^{24} -2.43531 q^{25} -4.89167 q^{26} +3.00000 q^{27} -2.89167 q^{28} -5.34803 q^{29} +3.43531 q^{30} -7.43531 q^{31} +1.00000 q^{32} +5.74657 q^{34} +4.63091 q^{35} +1.60147 q^{36} -7.49314 q^{37} +1.00000 q^{38} +10.4931 q^{39} -1.60147 q^{40} +2.05783 q^{41} +6.20293 q^{42} +10.6887 q^{43} -2.56469 q^{45} -7.74657 q^{46} -7.08727 q^{47} -2.14510 q^{48} +1.36176 q^{49} -2.43531 q^{50} -12.3270 q^{51} -4.89167 q^{52} +8.32698 q^{53} +3.00000 q^{54} -2.89167 q^{56} -2.14510 q^{57} -5.34803 q^{58} -2.54364 q^{59} +3.43531 q^{60} -13.4931 q^{61} -7.43531 q^{62} -4.63091 q^{63} +1.00000 q^{64} +7.83384 q^{65} -10.3848 q^{67} +5.74657 q^{68} +16.6172 q^{69} +4.63091 q^{70} +14.9789 q^{71} +1.60147 q^{72} +3.74657 q^{73} -7.49314 q^{74} +5.22399 q^{75} +1.00000 q^{76} +10.4931 q^{78} +8.69607 q^{79} -1.60147 q^{80} -11.2397 q^{81} +2.05783 q^{82} +6.10833 q^{83} +6.20293 q^{84} -9.20293 q^{85} +10.6887 q^{86} +11.4721 q^{87} +3.20293 q^{89} -2.56469 q^{90} +14.1451 q^{91} -7.74657 q^{92} +15.9495 q^{93} -7.08727 q^{94} -1.60147 q^{95} -2.14510 q^{96} -6.98627 q^{97} +1.36176 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 6 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 6 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + 6 q^{14} - 9 q^{15} + 3 q^{16} + 9 q^{17} + 3 q^{18} + 3 q^{19} - 3 q^{20} + 15 q^{21} - 15 q^{23} + 12 q^{25} + 9 q^{27} + 6 q^{28} - 6 q^{29} - 9 q^{30} - 3 q^{31} + 3 q^{32} + 9 q^{34} + 3 q^{36} - 6 q^{37} + 3 q^{38} + 15 q^{39} - 3 q^{40} + 9 q^{41} + 15 q^{42} + 21 q^{43} - 27 q^{45} - 15 q^{46} - 12 q^{47} + 27 q^{49} + 12 q^{50} - 3 q^{51} - 9 q^{53} + 9 q^{54} + 6 q^{56} - 6 q^{58} - 3 q^{59} - 9 q^{60} - 24 q^{61} - 3 q^{62} + 3 q^{64} + 6 q^{65} + 9 q^{68} + 3 q^{69} + 21 q^{71} + 3 q^{72} + 3 q^{73} - 6 q^{74} + 36 q^{75} + 3 q^{76} + 15 q^{78} + 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 33 q^{83} + 15 q^{84} - 24 q^{85} + 21 q^{86} - 6 q^{87} + 6 q^{89} - 27 q^{90} + 36 q^{91} - 15 q^{92} + 36 q^{93} - 12 q^{94} - 3 q^{95} + 12 q^{97} + 27 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 6 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + 6 * q^14 - 9 * q^15 + 3 * q^16 + 9 * q^17 + 3 * q^18 + 3 * q^19 - 3 * q^20 + 15 * q^21 - 15 * q^23 + 12 * q^25 + 9 * q^27 + 6 * q^28 - 6 * q^29 - 9 * q^30 - 3 * q^31 + 3 * q^32 + 9 * q^34 + 3 * q^36 - 6 * q^37 + 3 * q^38 + 15 * q^39 - 3 * q^40 + 9 * q^41 + 15 * q^42 + 21 * q^43 - 27 * q^45 - 15 * q^46 - 12 * q^47 + 27 * q^49 + 12 * q^50 - 3 * q^51 - 9 * q^53 + 9 * q^54 + 6 * q^56 - 6 * q^58 - 3 * q^59 - 9 * q^60 - 24 * q^61 - 3 * q^62 + 3 * q^64 + 6 * q^65 + 9 * q^68 + 3 * q^69 + 21 * q^71 + 3 * q^72 + 3 * q^73 - 6 * q^74 + 36 * q^75 + 3 * q^76 + 15 * q^78 + 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 33 * q^83 + 15 * q^84 - 24 * q^85 + 21 * q^86 - 6 * q^87 + 6 * q^89 - 27 * q^90 + 36 * q^91 - 15 * q^92 + 36 * q^93 - 12 * q^94 - 3 * q^95 + 12 * q^97 + 27 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.14510	−1.23848	−0.619238	−	0.785204i	$-0.712558\pi$
$3$	−2.14510	−1.23848	−0.619238	+	0.785204i	$0.712558\pi$
$4$	1.00000	0.500000
$5$	−1.60147	−0.716197	−0.358099	−	0.933684i	$-0.616575\pi$
$5$	−1.60147	−0.716197	−0.358099	+	0.933684i	$0.616575\pi$
$6$	−2.14510	−0.875735
$7$	−2.89167	−1.09295	−0.546474	−	0.837476i	$-0.684030\pi$
$7$	−2.89167	−1.09295	−0.546474	+	0.837476i	$0.684030\pi$
$8$	1.00000	0.353553
$9$	1.60147	0.533822
$10$	−1.60147	−0.506428
$11$	0	0
$11$	0	0
$12$	−2.14510	−0.619238
$13$	−4.89167	−1.35671	−0.678353	−	0.734736i	$-0.737306\pi$
$13$	−4.89167	−1.35671	−0.678353	+	0.734736i	$0.737306\pi$
$14$	−2.89167	−0.772832
$15$	3.43531	0.886993
$16$	1.00000	0.250000
$17$	5.74657	1.39375	0.696874	−	0.717194i	$-0.254574\pi$
$17$	5.74657	1.39375	0.696874	+	0.717194i	$0.254574\pi$
$18$	1.60147	0.377469
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.60147	−0.358099
$21$	6.20293	1.35359
$22$	0	0
$23$	−7.74657	−1.61527	−0.807636	−	0.589682i	$-0.799253\pi$
$23$	−7.74657	−1.61527	−0.807636	+	0.589682i	$0.799253\pi$
$24$	−2.14510	−0.437867
$25$	−2.43531	−0.487062
$26$	−4.89167	−0.959336
$27$	3.00000	0.577350
$28$	−2.89167	−0.546474
$29$	−5.34803	−0.993105	−0.496552	−	0.868007i	$-0.665401\pi$
$29$	−5.34803	−0.993105	−0.496552	+	0.868007i	$0.665401\pi$
$30$	3.43531	0.627199
$31$	−7.43531	−1.33542	−0.667710	−	0.744421i	$-0.732726\pi$
$31$	−7.43531	−1.33542	−0.667710	+	0.744421i	$0.732726\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	5.74657	0.985528
$35$	4.63091	0.782767
$36$	1.60147	0.266911
$37$	−7.49314	−1.23186	−0.615932	−	0.787799i	$-0.711220\pi$
$37$	−7.49314	−1.23186	−0.615932	+	0.787799i	$0.711220\pi$
$38$	1.00000	0.162221
$39$	10.4931	1.68025
$40$	−1.60147	−0.253214
$41$	2.05783	0.321379	0.160689	−	0.987005i	$-0.448628\pi$
$41$	2.05783	0.321379	0.160689	+	0.987005i	$0.448628\pi$
$42$	6.20293	0.957133
$43$	10.6887	1.63002	0.815009	−	0.579449i	$-0.196732\pi$
$43$	10.6887	1.63002	0.815009	+	0.579449i	$0.196732\pi$
$44$	0	0
$45$	−2.56469	−0.382322
$46$	−7.74657	−1.14217
$47$	−7.08727	−1.03379	−0.516893	−	0.856050i	$-0.672911\pi$
$47$	−7.08727	−1.03379	−0.516893	+	0.856050i	$0.672911\pi$
$48$	−2.14510	−0.309619
$49$	1.36176	0.194537
$50$	−2.43531	−0.344405
$51$	−12.3270	−1.72612
$52$	−4.89167	−0.678353
$53$	8.32698	1.14380	0.571899	−	0.820324i	$-0.306207\pi$
$53$	8.32698	1.14380	0.571899	+	0.820324i	$0.306207\pi$
$54$	3.00000	0.408248
$55$	0	0
$56$	−2.89167	−0.386416
$57$	−2.14510	−0.284126
$58$	−5.34803	−0.702231
$59$	−2.54364	−0.331153	−0.165577	−	0.986197i	$-0.552949\pi$
$59$	−2.54364	−0.331153	−0.165577	+	0.986197i	$0.552949\pi$
$60$	3.43531	0.443496
$61$	−13.4931	−1.72762	−0.863810	−	0.503818i	$-0.831928\pi$
$61$	−13.4931	−1.72762	−0.863810	+	0.503818i	$0.831928\pi$
$62$	−7.43531	−0.944285
$63$	−4.63091	−0.583440
$64$	1.00000	0.125000
$65$	7.83384	0.971669
$66$	0	0
$67$	−10.3848	−1.26871	−0.634353	−	0.773043i	$-0.718733\pi$
$67$	−10.3848	−1.26871	−0.634353	+	0.773043i	$0.718733\pi$
$68$	5.74657	0.696874
$69$	16.6172	2.00047
$70$	4.63091	0.553500
$71$	14.9789	1.77767	0.888837	−	0.458224i	$-0.151514\pi$
$71$	14.9789	1.77767	0.888837	+	0.458224i	$0.151514\pi$
$72$	1.60147	0.188735
$73$	3.74657	0.438503	0.219251	−	0.975668i	$-0.429639\pi$
$73$	3.74657	0.438503	0.219251	+	0.975668i	$0.429639\pi$
$74$	−7.49314	−0.871059
$75$	5.22399	0.603214
$76$	1.00000	0.114708
$77$	0	0
$78$	10.4931	1.18811
$79$	8.69607	0.978384	0.489192	−	0.872176i	$-0.337292\pi$
$79$	8.69607	0.978384	0.489192	+	0.872176i	$0.337292\pi$
$80$	−1.60147	−0.179049
$81$	−11.2397	−1.24886
$82$	2.05783	0.227249
$83$	6.10833	0.670476	0.335238	−	0.942133i	$-0.391183\pi$
$83$	6.10833	0.670476	0.335238	+	0.942133i	$0.391183\pi$
$84$	6.20293	0.676795
$85$	−9.20293	−0.998198
$86$	10.6887	1.15260
$87$	11.4721	1.22994
$88$	0	0
$89$	3.20293	0.339510	0.169755	−	0.985486i	$-0.445702\pi$
$89$	3.20293	0.339510	0.169755	+	0.985486i	$0.445702\pi$
$90$	−2.56469	−0.270342
$91$	14.1451	1.48281
$92$	−7.74657	−0.807636
$93$	15.9495	1.65389
$94$	−7.08727	−0.730997
$95$	−1.60147	−0.164307
$96$	−2.14510	−0.218934
$97$	−6.98627	−0.709349	−0.354674	−	0.934990i	$-0.615408\pi$
$97$	−6.98627	−0.709349	−0.354674	+	0.934990i	$0.615408\pi$
$98$	1.36176	0.137559
$99$	0	0
$100$	−2.43531	−0.243531
$101$	1.20293	0.119696	0.0598481	−	0.998207i	$-0.480938\pi$
$101$	1.20293	0.119696	0.0598481	+	0.998207i	$0.480938\pi$
$102$	−12.3270	−1.22055
$103$	16.8779	1.66303	0.831517	−	0.555500i	$-0.187473\pi$
$103$	16.8779	1.66303	0.831517	+	0.555500i	$0.187473\pi$
$104$	−4.89167	−0.479668
$105$	−9.93378	−0.969438
$106$	8.32698	0.808788
$107$	8.03677	0.776944	0.388472	−	0.921460i	$-0.373003\pi$
$107$	8.03677	0.776944	0.388472	+	0.921460i	$0.373003\pi$
$108$	3.00000	0.288675
$109$	−11.5299	−1.10437	−0.552183	−	0.833723i	$-0.686205\pi$
$109$	−11.5299	−1.10437	−0.552183	+	0.833723i	$0.686205\pi$
$110$	0	0
$111$	16.0735	1.52563
$112$	−2.89167	−0.273237
$113$	−8.00000	−0.752577	−0.376288	−	0.926503i	$-0.622800\pi$
$113$	−8.00000	−0.752577	−0.376288	+	0.926503i	$0.622800\pi$
$114$	−2.14510	−0.200907
$115$	12.4059	1.15685
$116$	−5.34803	−0.496552
$117$	−7.83384	−0.724239
$118$	−2.54364	−0.234161
$119$	−16.6172	−1.52329
$120$	3.43531	0.313599
$121$	0	0
$122$	−13.4931	−1.22161
$123$	−4.41425	−0.398020
$124$	−7.43531	−0.667710
$125$	11.9074	1.06503
$126$	−4.63091	−0.412554
$127$	21.2765	1.88798	0.943991	−	0.329971i	$-0.107039\pi$
$127$	21.2765	1.88798	0.943991	+	0.329971i	$0.107039\pi$
$128$	1.00000	0.0883883
$129$	−22.9284	−2.01874
$130$	7.83384	0.687073
$131$	3.43531	0.300144	0.150072	−	0.988675i	$-0.452049\pi$
$131$	3.43531	0.300144	0.150072	+	0.988675i	$0.452049\pi$
$132$	0	0
$133$	−2.89167	−0.250740
$134$	−10.3848	−0.897111
$135$	−4.80440	−0.413497
$136$	5.74657	0.492764
$137$	13.5877	1.16088	0.580439	−	0.814303i	$-0.302881\pi$
$137$	13.5877	1.16088	0.580439	+	0.814303i	$0.302881\pi$
$138$	16.6172	1.41455
$139$	−3.19560	−0.271048	−0.135524	−	0.990774i	$-0.543272\pi$
$139$	−3.19560	−0.271048	−0.135524	+	0.990774i	$0.543272\pi$
$140$	4.63091	0.391383
$141$	15.2029	1.28032
$142$	14.9789	1.25701
$143$	0	0
$144$	1.60147	0.133455
$145$	8.56469	0.711259
$146$	3.74657	0.310068
$147$	−2.92112	−0.240930
$148$	−7.49314	−0.615932
$149$	12.0735	0.989104	0.494552	−	0.869148i	$-0.335332\pi$
$149$	12.0735	0.989104	0.494552	+	0.869148i	$0.335332\pi$
$150$	5.22399	0.426537
$151$	4.91273	0.399792	0.199896	−	0.979817i	$-0.435940\pi$
$151$	4.91273	0.399792	0.199896	+	0.979817i	$0.435940\pi$
$152$	1.00000	0.0811107
$153$	9.20293	0.744013
$154$	0	0
$155$	11.9074	0.956425
$156$	10.4931	0.840123
$157$	8.00733	0.639054	0.319527	−	0.947577i	$-0.396476\pi$
$157$	8.00733	0.639054	0.319527	+	0.947577i	$0.396476\pi$
$158$	8.69607	0.691822
$159$	−17.8622	−1.41657
$160$	−1.60147	−0.126607
$161$	22.4005	1.76541
$162$	−11.2397	−0.883075
$163$	1.88434	0.147593	0.0737966	−	0.997273i	$-0.476488\pi$
$163$	1.88434	0.147593	0.0737966	+	0.997273i	$0.476488\pi$
$164$	2.05783	0.160689
$165$	0	0
$166$	6.10833	0.474098
$167$	4.98627	0.385849	0.192925	−	0.981214i	$-0.438203\pi$
$167$	4.98627	0.385849	0.192925	+	0.981214i	$0.438203\pi$
$168$	6.20293	0.478567
$169$	10.9284	0.840650
$170$	−9.20293	−0.705833
$171$	1.60147	0.122467
$172$	10.6887	0.815009
$173$	−6.51419	−0.495265	−0.247632	−	0.968854i	$-0.579653\pi$
$173$	−6.51419	−0.495265	−0.247632	+	0.968854i	$0.579653\pi$
$174$	11.4721	0.869696
$175$	7.04211	0.532333
$176$	0	0
$177$	5.45636	0.410125
$178$	3.20293	0.240070
$179$	−5.55096	−0.414899	−0.207449	−	0.978246i	$-0.566516\pi$
$179$	−5.55096	−0.414899	−0.207449	+	0.978246i	$0.566516\pi$
$180$	−2.56469	−0.191161
$181$	1.88434	0.140062	0.0700311	−	0.997545i	$-0.477690\pi$
$181$	1.88434	0.140062	0.0700311	+	0.997545i	$0.477690\pi$
$182$	14.1451	1.04850
$183$	28.9442	2.13961
$184$	−7.74657	−0.571085
$185$	12.0000	0.882258
$186$	15.9495	1.16947
$187$	0	0
$188$	−7.08727	−0.516893
$189$	−8.67501	−0.631014
$190$	−1.60147	−0.116183
$191$	2.44264	0.176743	0.0883715	−	0.996088i	$-0.471834\pi$
$191$	2.44264	0.176743	0.0883715	+	0.996088i	$0.471834\pi$
$192$	−2.14510	−0.154809
$193$	9.67501	0.696423	0.348211	−	0.937416i	$-0.386789\pi$
$193$	9.67501	0.696423	0.348211	+	0.937416i	$0.386789\pi$
$194$	−6.98627	−0.501585
$195$	−16.8044	−1.20339
$196$	1.36176	0.0972686
$197$	17.4931	1.24633	0.623167	−	0.782089i	$-0.285846\pi$
$197$	17.4931	1.24633	0.623167	+	0.782089i	$0.285846\pi$
$198$	0	0
$199$	−25.2397	−1.78920	−0.894598	−	0.446873i	$-0.852538\pi$
$199$	−25.2397	−1.78920	−0.894598	+	0.446873i	$0.852538\pi$
$200$	−2.43531	−0.172202
$201$	22.2765	1.57126
$202$	1.20293	0.0846379
$203$	15.4648	1.08541
$204$	−12.3270	−0.863061
$205$	−3.29554	−0.230171
$206$	16.8779	1.17594
$207$	−12.4059	−0.862267
$208$	−4.89167	−0.339176
$209$	0	0
$210$	−9.93378	−0.685496
$211$	14.8338	1.02120	0.510602	−	0.859817i	$-0.329423\pi$
$211$	14.8338	1.02120	0.510602	+	0.859817i	$0.329423\pi$
$212$	8.32698	0.571899
$213$	−32.1314	−2.20161
$214$	8.03677	0.549383
$215$	−17.1176	−1.16741
$216$	3.00000	0.204124
$217$	21.5005	1.45955
$218$	−11.5299	−0.780904
$219$	−8.03677	−0.543075
$220$	0	0
$221$	−28.1103	−1.89090
$222$	16.0735	1.07879
$223$	11.4931	0.769637	0.384819	−	0.922992i	$-0.374264\pi$
$223$	11.4931	0.769637	0.384819	+	0.922992i	$0.374264\pi$
$224$	−2.89167	−0.193208
$225$	−3.90006	−0.260004
$226$	−8.00000	−0.532152
$227$	−8.73284	−0.579619	−0.289810	−	0.957084i	$-0.593592\pi$
$227$	−8.73284	−0.579619	−0.289810	+	0.957084i	$0.593592\pi$
$228$	−2.14510	−0.142063
$229$	7.84117	0.518159	0.259080	−	0.965856i	$-0.416581\pi$
$229$	7.84117	0.518159	0.259080	+	0.965856i	$0.416581\pi$
$230$	12.4059	0.818018
$231$	0	0
$232$	−5.34803	−0.351116
$233$	12.5069	0.819352	0.409676	−	0.912231i	$-0.365642\pi$
$233$	12.5069	0.819352	0.409676	+	0.912231i	$0.365642\pi$
$234$	−7.83384	−0.512114
$235$	11.3500	0.740394
$236$	−2.54364	−0.165577
$237$	−18.6540	−1.21170
$238$	−16.6172	−1.07713
$239$	−24.6245	−1.59283	−0.796414	−	0.604752i	$-0.793272\pi$
$239$	−24.6245	−1.59283	−0.796414	+	0.604752i	$0.793272\pi$
$240$	3.43531	0.221748
$241$	−16.0809	−1.03586	−0.517930	−	0.855423i	$-0.673297\pi$
$241$	−16.0809	−1.03586	−0.517930	+	0.855423i	$0.673297\pi$
$242$	0	0
$243$	15.1103	0.969328
$244$	−13.4931	−0.863810
$245$	−2.18081	−0.139327
$246$	−4.41425	−0.281443
$247$	−4.89167	−0.311250
$248$	−7.43531	−0.472143
$249$	−13.1030	−0.830368
$250$	11.9074	0.753089
$251$	13.0873	0.826061	0.413031	−	0.910717i	$-0.364470\pi$
$251$	13.0873	0.826061	0.413031	+	0.910717i	$0.364470\pi$
$252$	−4.63091	−0.291720
$253$	0	0
$254$	21.2765	1.33500
$255$	19.7412	1.23624
$256$	1.00000	0.0625000
$257$	0.723522	0.0451320	0.0225660	−	0.999745i	$-0.492816\pi$
$257$	0.723522	0.0451320	0.0225660	+	0.999745i	$0.492816\pi$
$258$	−22.9284	−1.42746
$259$	21.6677	1.34636
$260$	7.83384	0.485834
$261$	−8.56469	−0.530141
$262$	3.43531	0.212234
$263$	−13.7760	−0.849465	−0.424733	−	0.905319i	$-0.639632\pi$
$263$	−13.7760	−0.849465	−0.424733	+	0.905319i	$0.639632\pi$
$264$	0	0
$265$	−13.3354	−0.819185
$266$	−2.89167	−0.177300
$267$	−6.87062	−0.420475
$268$	−10.3848	−0.634353
$269$	−19.9579	−1.21685	−0.608427	−	0.793610i	$-0.708199\pi$
$269$	−19.9579	−1.21685	−0.608427	+	0.793610i	$0.708199\pi$
$270$	−4.80440	−0.292386
$271$	−28.7486	−1.74635	−0.873175	−	0.487406i	$-0.837943\pi$
$271$	−28.7486	−1.74635	−0.873175	+	0.487406i	$0.837943\pi$
$272$	5.74657	0.348437
$273$	−30.3427	−1.83642
$274$	13.5877	0.820865
$275$	0	0
$276$	16.6172	1.00024
$277$	−3.08727	−0.185496	−0.0927482	−	0.995690i	$-0.529565\pi$
$277$	−3.08727	−0.185496	−0.0927482	+	0.995690i	$0.529565\pi$
$278$	−3.19560	−0.191660
$279$	−11.9074	−0.712877
$280$	4.63091	0.276750
$281$	−9.09460	−0.542538	−0.271269	−	0.962504i	$-0.587443\pi$
$281$	−9.09460	−0.542538	−0.271269	+	0.962504i	$0.587443\pi$
$282$	15.2029	0.905321
$283$	−13.1451	−0.781395	−0.390698	−	0.920519i	$-0.627766\pi$
$283$	−13.1451	−0.781395	−0.390698	+	0.920519i	$0.627766\pi$
$284$	14.9789	0.888837
$285$	3.43531	0.203490
$286$	0	0
$287$	−5.95056	−0.351251
$288$	1.60147	0.0943673
$289$	16.0230	0.942532
$290$	8.56469	0.502936
$291$	14.9863	0.878511
$292$	3.74657	0.219251
$293$	−3.10833	−0.181591	−0.0907953	−	0.995870i	$-0.528941\pi$
$293$	−3.10833	−0.181591	−0.0907953	+	0.995870i	$0.528941\pi$
$294$	−2.92112	−0.170363
$295$	4.07355	0.237171
$296$	−7.49314	−0.435530
$297$	0	0
$298$	12.0735	0.699402
$299$	37.8937	2.19145
$300$	5.22399	0.301607
$301$	−30.9083	−1.78153
$302$	4.91273	0.282696
$303$	−2.58041	−0.148241
$304$	1.00000	0.0573539
$305$	21.6088	1.23732
$306$	9.20293	0.526097
$307$	−2.18920	−0.124944	−0.0624722	−	0.998047i	$-0.519898\pi$
$307$	−2.18920	−0.124944	−0.0624722	+	0.998047i	$0.519898\pi$
$308$	0	0
$309$	−36.2049	−2.05963
$310$	11.9074	0.676294
$311$	3.92112	0.222346	0.111173	−	0.993801i	$-0.464539\pi$
$311$	3.92112	0.222346	0.111173	+	0.993801i	$0.464539\pi$
$312$	10.4931	0.594057
$313$	−21.7118	−1.22722	−0.613611	−	0.789608i	$-0.710284\pi$
$313$	−21.7118	−1.22722	−0.613611	+	0.789608i	$0.710284\pi$
$314$	8.00733	0.451880
$315$	7.41625	0.417858
$316$	8.69607	0.489192
$317$	6.90739	0.387958	0.193979	−	0.981006i	$-0.437861\pi$
$317$	6.90739	0.387958	0.193979	+	0.981006i	$0.437861\pi$
$318$	−17.8622	−1.00166
$319$	0	0
$320$	−1.60147	−0.0895246
$321$	−17.2397	−0.962226
$322$	22.4005	1.24833
$323$	5.74657	0.319748
$324$	−11.2397	−0.624428
$325$	11.9127	0.660799
$326$	1.88434	0.104364
$327$	24.7328	1.36773
$328$	2.05783	0.113625
$329$	20.4941	1.12987
$330$	0	0
$331$	32.1030	1.76454	0.882270	−	0.470744i	$-0.156014\pi$
$331$	32.1030	1.76454	0.882270	+	0.470744i	$0.156014\pi$
$332$	6.10833	0.335238
$333$	−12.0000	−0.657596
$334$	4.98627	0.272837
$335$	16.6309	0.908644
$336$	6.20293	0.338398
$337$	1.55096	0.0844864	0.0422432	−	0.999107i	$-0.486550\pi$
$337$	1.55096	0.0844864	0.0422432	+	0.999107i	$0.486550\pi$
$338$	10.9284	0.594429
$339$	17.1608	0.932048
$340$	−9.20293	−0.499099
$341$	0	0
$342$	1.60147	0.0865973
$343$	16.3039	0.880330
$344$	10.6887	0.576298
$345$	−26.6118	−1.43273
$346$	−6.51419	−0.350205
$347$	0.506864	0.0272099	0.0136049	−	0.999907i	$-0.495669\pi$
$347$	0.506864	0.0272099	0.0136049	+	0.999907i	$0.495669\pi$
$348$	11.4721	0.614968
$349$	−10.8117	−0.578738	−0.289369	−	0.957218i	$-0.593446\pi$
$349$	−10.8117	−0.578738	−0.289369	+	0.957218i	$0.593446\pi$
$350$	7.04211	0.376417
$351$	−14.6750	−0.783294
$352$	0	0
$353$	27.0966	1.44221	0.721103	−	0.692828i	$-0.243635\pi$
$353$	27.0966	1.44221	0.721103	+	0.692828i	$0.243635\pi$
$354$	5.45636	0.290002
$355$	−23.9883	−1.27316
$356$	3.20293	0.169755
$357$	35.6456	1.88656
$358$	−5.55096	−0.293378
$359$	20.7486	1.09507	0.547534	−	0.836784i	$-0.315567\pi$
$359$	20.7486	1.09507	0.547534	+	0.836784i	$0.315567\pi$
$360$	−2.56469	−0.135171
$361$	1.00000	0.0526316
$362$	1.88434	0.0990389
$363$	0	0
$364$	14.1451	0.741405
$365$	−6.00000	−0.314054
$366$	28.9442	1.51294
$367$	25.6402	1.33841	0.669205	−	0.743078i	$-0.266635\pi$
$367$	25.6402	1.33841	0.669205	+	0.743078i	$0.266635\pi$
$368$	−7.74657	−0.403818
$369$	3.29554	0.171559
$370$	12.0000	0.623850
$371$	−24.0789	−1.25011
$372$	15.9495	0.826943
$373$	−25.2049	−1.30506	−0.652531	−	0.757762i	$-0.726293\pi$
$373$	−25.2049	−1.30506	−0.652531	+	0.757762i	$0.726293\pi$
$374$	0	0
$375$	−25.5426	−1.31901
$376$	−7.08727	−0.365498
$377$	26.1608	1.34735
$378$	−8.67501	−0.446195
$379$	3.47208	0.178349	0.0891744	−	0.996016i	$-0.471577\pi$
$379$	3.47208	0.178349	0.0891744	+	0.996016i	$0.471577\pi$
$380$	−1.60147	−0.0821534
$381$	−45.6402	−2.33822
$382$	2.44264	0.124976
$383$	23.1176	1.18126	0.590628	−	0.806944i	$-0.298880\pi$
$383$	23.1176	1.18126	0.590628	+	0.806944i	$0.298880\pi$
$384$	−2.14510	−0.109467
$385$	0	0
$386$	9.67501	0.492445
$387$	17.1176	0.870139
$388$	−6.98627	−0.354674
$389$	−26.7623	−1.35690	−0.678451	−	0.734646i	$-0.737348\pi$
$389$	−26.7623	−1.35690	−0.678451	+	0.734646i	$0.737348\pi$
$390$	−16.8044	−0.850924
$391$	−44.5162	−2.25128
$392$	1.36176	0.0687793
$393$	−7.36909	−0.371721
$394$	17.4931	0.881291
$395$	−13.9265	−0.700716
$396$	0	0
$397$	−31.1030	−1.56101	−0.780507	−	0.625147i	$-0.785039\pi$
$397$	−31.1030	−1.56101	−0.780507	+	0.625147i	$0.785039\pi$
$398$	−25.2397	−1.26515
$399$	6.20293	0.310535
$400$	−2.43531	−0.121765
$401$	29.3500	1.46567	0.732835	−	0.680406i	$-0.238197\pi$
$401$	29.3500	1.46567	0.732835	+	0.680406i	$0.238197\pi$
$402$	22.2765	1.11105
$403$	36.3711	1.81177
$404$	1.20293	0.0598481
$405$	18.0000	0.894427
$406$	15.4648	0.767503
$407$	0	0
$408$	−12.3270	−0.610276
$409$	−8.58774	−0.424636	−0.212318	−	0.977201i	$-0.568101\pi$
$409$	−8.58774	−0.424636	−0.212318	+	0.977201i	$0.568101\pi$
$410$	−3.29554	−0.162755
$411$	−29.1471	−1.43772
$412$	16.8779	0.831517
$413$	7.35536	0.361934
$414$	−12.4059	−0.609715
$415$	−9.78228	−0.480193
$416$	−4.89167	−0.239834
$417$	6.85490	0.335686
$418$	0	0
$419$	7.59414	0.370998	0.185499	−	0.982644i	$-0.440610\pi$
$419$	7.59414	0.370998	0.185499	+	0.982644i	$0.440610\pi$
$420$	−9.93378	−0.484719
$421$	8.76030	0.426951	0.213475	−	0.976948i	$-0.431522\pi$
$421$	8.76030	0.426951	0.213475	+	0.976948i	$0.431522\pi$
$422$	14.8338	0.722100
$423$	−11.3500	−0.551857
$424$	8.32698	0.404394
$425$	−13.9947	−0.678841
$426$	−32.1314	−1.55677
$427$	39.0177	1.88820
$428$	8.03677	0.388472
$429$	0	0
$430$	−17.1176	−0.825486
$431$	33.6677	1.62172	0.810858	−	0.585243i	$-0.199001\pi$
$431$	33.6677	1.62172	0.810858	+	0.585243i	$0.199001\pi$
$432$	3.00000	0.144338
$433$	30.5383	1.46758	0.733789	−	0.679378i	$-0.237750\pi$
$433$	30.5383	1.46758	0.733789	+	0.679378i	$0.237750\pi$
$434$	21.5005	1.03206
$435$	−18.3721	−0.880877
$436$	−11.5299	−0.552183
$437$	−7.74657	−0.370569
$438$	−8.03677	−0.384012
$439$	12.5069	0.596920	0.298460	−	0.954422i	$-0.403527\pi$
$439$	12.5069	0.596920	0.298460	+	0.954422i	$0.403527\pi$
$440$	0	0
$441$	2.18081	0.103848
$442$	−28.1103	−1.33707
$443$	−17.6677	−0.839417	−0.419709	−	0.907659i	$-0.637868\pi$
$443$	−17.6677	−0.839417	−0.419709	+	0.907659i	$0.637868\pi$
$444$	16.0735	0.762817
$445$	−5.12938	−0.243156
$446$	11.4931	0.544216
$447$	−25.8990	−1.22498
$448$	−2.89167	−0.136619
$449$	−17.7098	−0.835777	−0.417888	−	0.908498i	$-0.637230\pi$
$449$	−17.7098	−0.835777	−0.417888	+	0.908498i	$0.637230\pi$
$450$	−3.90006	−0.183851
$451$	0	0
$452$	−8.00000	−0.376288
$453$	−10.5383	−0.495133
$454$	−8.73284	−0.409853
$455$	−22.6529	−1.06198
$456$	−2.14510	−0.100454
$457$	24.8064	1.16039	0.580197	−	0.814476i	$-0.302976\pi$
$457$	24.8064	1.16039	0.580197	+	0.814476i	$0.302976\pi$
$458$	7.84117	0.366394
$459$	17.2397	0.804681
$460$	12.4059	0.578426
$461$	2.98627	0.139085	0.0695423	−	0.997579i	$-0.477846\pi$
$461$	2.98627	0.139085	0.0695423	+	0.997579i	$0.477846\pi$
$462$	0	0
$463$	−39.5667	−1.83882	−0.919410	−	0.393301i	$-0.871333\pi$
$463$	−39.5667	−1.83882	−0.919410	+	0.393301i	$0.871333\pi$
$464$	−5.34803	−0.248276
$465$	−25.5426	−1.18451
$466$	12.5069	0.579369
$467$	4.46475	0.206604	0.103302	−	0.994650i	$-0.467059\pi$
$467$	4.46475	0.206604	0.103302	+	0.994650i	$0.467059\pi$
$468$	−7.83384	−0.362119
$469$	30.0294	1.38663
$470$	11.3500	0.523538
$471$	−17.1765	−0.791453
$472$	−2.54364	−0.117080
$473$	0	0
$474$	−18.6540	−0.856805
$475$	−2.43531	−0.111740
$476$	−16.6172	−0.761647
$477$	13.3354	0.610585
$478$	−24.6245	−1.12630
$479$	20.8863	0.954321	0.477161	−	0.878816i	$-0.341666\pi$
$479$	20.8863	0.954321	0.477161	+	0.878816i	$0.341666\pi$
$480$	3.43531	0.156800
$481$	36.6540	1.67128
$482$	−16.0809	−0.732464
$483$	−48.0514	−2.18642
$484$	0	0
$485$	11.1883	0.508033
$486$	15.1103	0.685418
$487$	15.2838	0.692575	0.346288	−	0.938128i	$-0.387442\pi$
$487$	15.2838	0.692575	0.346288	+	0.938128i	$0.387442\pi$
$488$	−13.4931	−0.610806
$489$	−4.04211	−0.182791
$490$	−2.18081	−0.0985191
$491$	−3.31965	−0.149814	−0.0749069	−	0.997191i	$-0.523866\pi$
$491$	−3.31965	−0.149814	−0.0749069	+	0.997191i	$0.523866\pi$
$492$	−4.41425	−0.199010
$493$	−30.7328	−1.38414
$494$	−4.89167	−0.220087
$495$	0	0
$496$	−7.43531	−0.333855
$497$	−43.3142	−1.94291
$498$	−13.1030	−0.587159
$499$	−2.07355	−0.0928247	−0.0464124	−	0.998922i	$-0.514779\pi$
$499$	−2.07355	−0.0928247	−0.0464124	+	0.998922i	$0.514779\pi$
$500$	11.9074	0.532515
$501$	−10.6961	−0.477865
$502$	13.0873	0.584114
$503$	1.11672	0.0497921	0.0248960	−	0.999690i	$-0.492075\pi$
$503$	1.11672	0.0497921	0.0248960	+	0.999690i	$0.492075\pi$
$504$	−4.63091	−0.206277
$505$	−1.92645	−0.0857260
$506$	0	0
$507$	−23.4426	−1.04112
$508$	21.2765	0.943991
$509$	−38.2481	−1.69532	−0.847659	−	0.530542i	$-0.821988\pi$
$509$	−38.2481	−1.69532	−0.847659	+	0.530542i	$0.821988\pi$
$510$	19.7412	0.874156
$511$	−10.8338	−0.479261
$512$	1.00000	0.0441942
$513$	3.00000	0.132453
$514$	0.723522	0.0319132
$515$	−27.0294	−1.19106
$516$	−22.9284	−1.00937
$517$	0	0
$518$	21.6677	0.952023
$519$	13.9736	0.613373
$520$	7.83384	0.343537
$521$	10.8853	0.476892	0.238446	−	0.971156i	$-0.423362\pi$
$521$	10.8853	0.476892	0.238446	+	0.971156i	$0.423362\pi$
$522$	−8.56469	−0.374866
$523$	15.7191	0.687349	0.343674	−	0.939089i	$-0.388328\pi$
$523$	15.7191	0.687349	0.343674	+	0.939089i	$0.388328\pi$
$524$	3.43531	0.150072
$525$	−15.1060	−0.659282
$526$	−13.7760	−0.600663
$527$	−42.7275	−1.86124
$528$	0	0
$529$	37.0093	1.60910
$530$	−13.3354	−0.579251
$531$	−4.07355	−0.176777
$532$	−2.89167	−0.125370
$533$	−10.0662	−0.436016
$534$	−6.87062	−0.297321
$535$	−12.8706	−0.556445
$536$	−10.3848	−0.448555
$537$	11.9074	0.513842
$538$	−19.9579	−0.860446
$539$	0	0
$540$	−4.80440	−0.206748
$541$	26.4373	1.13663	0.568314	−	0.822812i	$-0.307596\pi$
$541$	26.4373	1.13663	0.568314	+	0.822812i	$0.307596\pi$
$542$	−28.7486	−1.23486
$543$	−4.04211	−0.173464
$544$	5.74657	0.246382
$545$	18.4648	0.790943
$546$	−30.3427	−1.29855
$547$	24.9588	1.06716	0.533581	−	0.845749i	$-0.320846\pi$
$547$	24.9588	1.06716	0.533581	+	0.845749i	$0.320846\pi$
$548$	13.5877	0.580439
$549$	−21.6088	−0.922241
$550$	0	0
$551$	−5.34803	−0.227834
$552$	16.6172	0.707274
$553$	−25.1462	−1.06932
$554$	−3.08727	−0.131166
$555$	−25.7412	−1.09265
$556$	−3.19560	−0.135524
$557$	−8.30486	−0.351888	−0.175944	−	0.984400i	$-0.556298\pi$
$557$	−8.30486	−0.351888	−0.175944	+	0.984400i	$0.556298\pi$
$558$	−11.9074	−0.504080
$559$	−52.2858	−2.21145
$560$	4.63091	0.195692
$561$	0	0
$562$	−9.09460	−0.383633
$563$	−41.6402	−1.75493	−0.877463	−	0.479644i	$-0.840766\pi$
$563$	−41.6402	−1.75493	−0.877463	+	0.479644i	$0.840766\pi$
$564$	15.2029	0.640159
$565$	12.8117	0.538993
$566$	−13.1451	−0.552530
$567$	32.5015	1.36494
$568$	14.9789	0.628503
$569$	14.9138	0.625219	0.312609	−	0.949882i	$-0.398797\pi$
$569$	14.9138	0.625219	0.312609	+	0.949882i	$0.398797\pi$
$570$	3.43531	0.143889
$571$	23.0020	0.962603	0.481302	−	0.876555i	$-0.340164\pi$
$571$	23.0020	0.962603	0.481302	+	0.876555i	$0.340164\pi$
$572$	0	0
$573$	−5.23970	−0.218892
$574$	−5.95056	−0.248372
$575$	18.8653	0.786737
$576$	1.60147	0.0667277
$577$	−33.6613	−1.40134	−0.700669	−	0.713487i	$-0.747115\pi$
$577$	−33.6613	−1.40134	−0.700669	+	0.713487i	$0.747115\pi$
$578$	16.0230	0.666471
$579$	−20.7539	−0.862502
$580$	8.56469	0.355629
$581$	−17.6633	−0.732796
$582$	14.9863	0.621201
$583$	0	0
$584$	3.74657	0.155034
$585$	12.5456	0.518698
$586$	−3.10833	−0.128404
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	−2.92112	−0.120465
$589$	−7.43531	−0.306367
$590$	4.07355	0.167705
$591$	−37.5246	−1.54355
$592$	−7.49314	−0.307966
$593$	30.9588	1.27133	0.635663	−	0.771967i	$-0.280727\pi$
$593$	30.9588	1.27133	0.635663	+	0.771967i	$0.280727\pi$
$594$	0	0
$595$	26.6118	1.09098
$596$	12.0735	0.494552
$597$	54.1418	2.21587
$598$	37.8937	1.54959
$599$	3.93378	0.160730	0.0803650	−	0.996766i	$-0.474391\pi$
$599$	3.93378	0.160730	0.0803650	+	0.996766i	$0.474391\pi$
$600$	5.22399	0.213268
$601$	−23.1451	−0.944108	−0.472054	−	0.881570i	$-0.656487\pi$
$601$	−23.1451	−0.944108	−0.472054	+	0.881570i	$0.656487\pi$
$602$	−30.9083	−1.25973
$603$	−16.6309	−0.677263
$604$	4.91273	0.199896
$605$	0	0
$606$	−2.58041	−0.104822
$607$	1.78334	0.0723836	0.0361918	−	0.999345i	$-0.488477\pi$
$607$	1.78334	0.0723836	0.0361918	+	0.999345i	$0.488477\pi$
$608$	1.00000	0.0405554
$609$	−33.1735	−1.34426
$610$	21.6088	0.874914
$611$	34.6686	1.40254
$612$	9.20293	0.372006
$613$	33.0598	1.33527	0.667637	−	0.744487i	$-0.267306\pi$
$613$	33.0598	1.33527	0.667637	+	0.744487i	$0.267306\pi$
$614$	−2.18920	−0.0883491
$615$	7.06927	0.285061
$616$	0	0
$617$	−21.8412	−0.879292	−0.439646	−	0.898171i	$-0.644896\pi$
$617$	−21.8412	−0.879292	−0.439646	+	0.898171i	$0.644896\pi$
$618$	−36.2049	−1.45638
$619$	−46.2206	−1.85776	−0.928882	−	0.370375i	$-0.879229\pi$
$619$	−46.2206	−1.85776	−0.928882	+	0.370375i	$0.879229\pi$
$620$	11.9074	0.478212
$621$	−23.2397	−0.932577
$622$	3.92112	0.157222
$623$	−9.26182	−0.371067
$624$	10.4931	0.420062
$625$	−6.89273	−0.275709
$626$	−21.7118	−0.867778
$627$	0	0
$628$	8.00733	0.319527
$629$	−43.0598	−1.71691
$630$	7.41625	0.295470
$631$	0.317659	0.0126458	0.00632291	−	0.999980i	$-0.497987\pi$
$631$	0.317659	0.0126458	0.00632291	+	0.999980i	$0.497987\pi$
$632$	8.69607	0.345911
$633$	−31.8201	−1.26474
$634$	6.90739	0.274327
$635$	−34.0735	−1.35217
$636$	−17.8622	−0.708283
$637$	−6.66129	−0.263930
$638$	0	0
$639$	23.9883	0.948961
$640$	−1.60147	−0.0633035
$641$	−41.5246	−1.64012	−0.820061	−	0.572276i	$-0.806061\pi$
$641$	−41.5246	−1.64012	−0.820061	+	0.572276i	$0.806061\pi$
$642$	−17.2397	−0.680397
$643$	7.26182	0.286378	0.143189	−	0.989695i	$-0.454264\pi$
$643$	7.26182	0.286378	0.143189	+	0.989695i	$0.454264\pi$
$644$	22.4005	0.882704
$645$	36.7191	1.44581
$646$	5.74657	0.226096
$647$	29.0819	1.14333	0.571664	−	0.820487i	$-0.306298\pi$
$647$	29.0819	1.14333	0.571664	+	0.820487i	$0.306298\pi$
$648$	−11.2397	−0.441537
$649$	0	0
$650$	11.9127	0.467256
$651$	−46.1207	−1.80761
$652$	1.88434	0.0737966
$653$	12.6529	0.495146	0.247573	−	0.968869i	$-0.420367\pi$
$653$	12.6529	0.495146	0.247573	+	0.968869i	$0.420367\pi$
$654$	24.7328	0.967131
$655$	−5.50153	−0.214962
$656$	2.05783	0.0803447
$657$	6.00000	0.234082
$658$	20.4941	0.798942
$659$	−49.4878	−1.92777	−0.963886	−	0.266317i	$-0.914193\pi$
$659$	−49.4878	−1.92777	−0.963886	+	0.266317i	$0.914193\pi$
$660$	0	0
$661$	4.94950	0.192513	0.0962566	−	0.995357i	$-0.469313\pi$
$661$	4.94950	0.192513	0.0962566	+	0.995357i	$0.469313\pi$
$662$	32.1030	1.24772
$663$	60.2995	2.34184
$664$	6.10833	0.237049
$665$	4.63091	0.179579
$666$	−12.0000	−0.464991
$667$	41.4289	1.60413
$668$	4.98627	0.192925
$669$	−24.6540	−0.953177
$670$	16.6309	0.642508
$671$	0	0
$672$	6.20293	0.239283
$673$	−21.9001	−0.844185	−0.422093	−	0.906553i	$-0.638704\pi$
$673$	−21.9001	−0.844185	−0.422093	+	0.906553i	$0.638704\pi$
$674$	1.55096	0.0597409
$675$	−7.30592	−0.281205
$676$	10.9284	0.420325
$677$	−26.4353	−1.01599	−0.507996	−	0.861360i	$-0.669613\pi$
$677$	−26.4353	−1.01599	−0.507996	+	0.861360i	$0.669613\pi$
$678$	17.1608	0.659057
$679$	20.2020	0.775282
$680$	−9.20293	−0.352916
$681$	18.7328	0.717844
$682$	0	0
$683$	9.82545	0.375960	0.187980	−	0.982173i	$-0.439806\pi$
$683$	9.82545	0.375960	0.187980	+	0.982173i	$0.439806\pi$
$684$	1.60147	0.0612336
$685$	−21.7603	−0.831418
$686$	16.3039	0.622487
$687$	−16.8201	−0.641727
$688$	10.6887	0.407504
$689$	−40.7328	−1.55180
$690$	−26.6118	−1.01310
$691$	−19.8255	−0.754196	−0.377098	−	0.926173i	$-0.623078\pi$
$691$	−19.8255	−0.754196	−0.377098	+	0.926173i	$0.623078\pi$
$692$	−6.51419	−0.247632
$693$	0	0
$694$	0.506864	0.0192403
$695$	5.11765	0.194123
$696$	11.4721	0.434848
$697$	11.8255	0.447921
$698$	−10.8117	−0.409230
$699$	−26.8285	−1.01475
$700$	7.04211	0.266167
$701$	10.7550	0.406209	0.203105	−	0.979157i	$-0.434897\pi$
$701$	10.7550	0.406209	0.203105	+	0.979157i	$0.434897\pi$
$702$	−14.6750	−0.553873
$703$	−7.49314	−0.282609
$704$	0	0
$705$	−24.3470	−0.916960
$706$	27.0966	1.01979
$707$	−3.47848	−0.130822
$708$	5.45636	0.205063
$709$	−1.82651	−0.0685962	−0.0342981	−	0.999412i	$-0.510920\pi$
$709$	−1.82651	−0.0685962	−0.0342981	+	0.999412i	$0.510920\pi$
$710$	−23.9883	−0.900264
$711$	13.9265	0.522283
$712$	3.20293	0.120035
$713$	57.5981	2.15707
$714$	35.6456	1.33400
$715$	0	0
$716$	−5.55096	−0.207449
$717$	52.8221	1.97268
$718$	20.7486	0.774329
$719$	−4.65929	−0.173762	−0.0868812	−	0.996219i	$-0.527690\pi$
$719$	−4.65929	−0.173762	−0.0868812	+	0.996219i	$0.527690\pi$
$720$	−2.56469	−0.0955804
$721$	−48.8055	−1.81761
$722$	1.00000	0.0372161
$723$	34.4951	1.28289
$724$	1.88434	0.0700311
$725$	13.0241	0.483703
$726$	0	0
$727$	19.9358	0.739377	0.369688	−	0.929156i	$-0.379464\pi$
$727$	19.9358	0.739377	0.369688	+	0.929156i	$0.379464\pi$
$728$	14.1451	0.524252
$729$	1.30592	0.0483676
$730$	−6.00000	−0.222070
$731$	61.4236	2.27183
$732$	28.9442	1.06981
$733$	−13.7687	−0.508558	−0.254279	−	0.967131i	$-0.581838\pi$
$733$	−13.7687	−0.508558	−0.254279	+	0.967131i	$0.581838\pi$
$734$	25.6402	0.946398
$735$	4.67807	0.172553
$736$	−7.74657	−0.285542
$737$	0	0
$738$	3.29554	0.121311
$739$	−22.4867	−0.827188	−0.413594	−	0.910461i	$-0.635727\pi$
$739$	−22.4867	−0.827188	−0.413594	+	0.910461i	$0.635727\pi$
$740$	12.0000	0.441129
$741$	10.4931	0.385475
$742$	−24.0789	−0.883964
$743$	50.6540	1.85831	0.929157	−	0.369686i	$-0.120535\pi$
$743$	50.6540	1.85831	0.929157	+	0.369686i	$0.120535\pi$
$744$	15.9495	0.584737
$745$	−19.3354	−0.708393
$746$	−25.2049	−0.922818
$747$	9.78228	0.357915
$748$	0	0
$749$	−23.2397	−0.849160
$750$	−25.5426	−0.932683
$751$	−38.9127	−1.41995	−0.709973	−	0.704229i	$-0.751293\pi$
$751$	−38.9127	−1.41995	−0.709973	+	0.704229i	$0.751293\pi$
$752$	−7.08727	−0.258446
$753$	−28.0735	−1.02306
$754$	26.1608	0.952721
$755$	−7.86756	−0.286330
$756$	−8.67501	−0.315507
$757$	−20.5877	−0.748274	−0.374137	−	0.927373i	$-0.622061\pi$
$757$	−20.5877	−0.748274	−0.374137	+	0.927373i	$0.622061\pi$
$758$	3.47208	0.126112
$759$	0	0
$760$	−1.60147	−0.0580913
$761$	−10.6025	−0.384341	−0.192171	−	0.981362i	$-0.561553\pi$
$761$	−10.6025	−0.384341	−0.192171	+	0.981362i	$0.561553\pi$
$762$	−45.6402	−1.65337
$763$	33.3407	1.20701
$764$	2.44264	0.0883715
$765$	−14.7382	−0.532860
$766$	23.1176	0.835275
$767$	12.4426	0.449278
$768$	−2.14510	−0.0774047
$769$	8.77495	0.316433	0.158216	−	0.987404i	$-0.449426\pi$
$769$	8.77495	0.316433	0.158216	+	0.987404i	$0.449426\pi$
$770$	0	0
$771$	−1.55203	−0.0558949
$772$	9.67501	0.348211
$773$	−46.8653	−1.68563	−0.842813	−	0.538206i	$-0.819102\pi$
$773$	−46.8653	−1.68563	−0.842813	+	0.538206i	$0.819102\pi$
$774$	17.1176	0.615281
$775$	18.1073	0.650432
$776$	−6.98627	−0.250793
$777$	−46.4794	−1.66744
$778$	−26.7623	−0.959474
$779$	2.05783	0.0737294
$780$	−16.8044	−0.601694
$781$	0	0
$782$	−44.5162	−1.59190
$783$	−16.0441	−0.573369
$784$	1.36176	0.0486343
$785$	−12.8235	−0.457689
$786$	−7.36909	−0.262847
$787$	27.4143	0.977213	0.488606	−	0.872504i	$-0.337505\pi$
$787$	27.4143	0.977213	0.488606	+	0.872504i	$0.337505\pi$
$788$	17.4931	0.623167
$789$	29.5510	1.05204
$790$	−13.9265	−0.495481
$791$	23.1334	0.822528
$792$	0	0
$793$	66.0040	2.34387
$794$	−31.1030	−1.10380
$795$	28.6057	1.01454
$796$	−25.2397	−0.894598
$797$	−9.16616	−0.324682	−0.162341	−	0.986735i	$-0.551904\pi$
$797$	−9.16616	−0.324682	−0.162341	+	0.986735i	$0.551904\pi$
$798$	6.20293	0.219581
$799$	−40.7275	−1.44084
$800$	−2.43531	−0.0861011
$801$	5.12938	0.181238
$802$	29.3500	1.03639
$803$	0	0
$804$	22.2765	0.785631
$805$	−35.8737	−1.26438
$806$	36.3711	1.28112
$807$	42.8117	1.50704
$808$	1.20293	0.0423190
$809$	−48.0829	−1.69050	−0.845252	−	0.534368i	$-0.820550\pi$
$809$	−48.0829	−1.69050	−0.845252	+	0.534368i	$0.820550\pi$
$810$	18.0000	0.632456
$811$	2.67395	0.0938951	0.0469475	−	0.998897i	$-0.485051\pi$
$811$	2.67395	0.0938951	0.0469475	+	0.998897i	$0.485051\pi$
$812$	15.4648	0.542706
$813$	61.6686	2.16281
$814$	0	0
$815$	−3.01771	−0.105706
$816$	−12.3270	−0.431531
$817$	10.6887	0.373952
$818$	−8.58774	−0.300263
$819$	22.6529	0.791556
$820$	−3.29554	−0.115085
$821$	−29.5078	−1.02983	−0.514915	−	0.857242i	$-0.672176\pi$
$821$	−29.5078	−1.02983	−0.514915	+	0.857242i	$0.672176\pi$
$822$	−29.1471	−1.01662
$823$	−2.39654	−0.0835382	−0.0417691	−	0.999127i	$-0.513299\pi$
$823$	−2.39654	−0.0835382	−0.0417691	+	0.999127i	$0.513299\pi$
$824$	16.8779	0.587971
$825$	0	0
$826$	7.35536	0.255926
$827$	−7.78868	−0.270839	−0.135419	−	0.990788i	$-0.543238\pi$
$827$	−7.78868	−0.270839	−0.135419	+	0.990788i	$0.543238\pi$
$828$	−12.4059	−0.431134
$829$	13.2818	0.461296	0.230648	−	0.973037i	$-0.425915\pi$
$829$	13.2818	0.461296	0.230648	+	0.973037i	$0.425915\pi$
$830$	−9.78228	−0.339548
$831$	6.62252	0.229733
$832$	−4.89167	−0.169588
$833$	7.82545	0.271136
$834$	6.85490	0.237366
$835$	−7.98534	−0.276344
$836$	0	0
$837$	−22.3059	−0.771006
$838$	7.59414	0.262335
$839$	−33.9063	−1.17058	−0.585288	−	0.810825i	$-0.699019\pi$
$839$	−33.9063	−1.17058	−0.585288	+	0.810825i	$0.699019\pi$
$840$	−9.93378	−0.342748
$841$	−0.398534	−0.0137426
$842$	8.76030	0.301900
$843$	19.5089	0.671921
$844$	14.8338	0.510602
$845$	−17.5015	−0.602071
$846$	−11.3500	−0.390222
$847$	0	0
$848$	8.32698	0.285950
$849$	28.1976	0.967739
$850$	−13.9947	−0.480013
$851$	58.0461	1.98979
$852$	−32.1314	−1.10080
$853$	−40.0735	−1.37209	−0.686046	−	0.727558i	$-0.740655\pi$
$853$	−40.0735	−1.37209	−0.686046	+	0.727558i	$0.740655\pi$
$854$	39.0177	1.33516
$855$	−2.56469	−0.0877106
$856$	8.03677	0.274691
$857$	−0.665693	−0.0227396	−0.0113698	−	0.999935i	$-0.503619\pi$
$857$	−0.665693	−0.0227396	−0.0113698	+	0.999935i	$0.503619\pi$
$858$	0	0
$859$	13.8990	0.474228	0.237114	−	0.971482i	$-0.423799\pi$
$859$	13.8990	0.474228	0.237114	+	0.971482i	$0.423799\pi$
$860$	−17.1176	−0.583707
$861$	12.7646	0.435015
$862$	33.6677	1.14673
$863$	−40.3941	−1.37503	−0.687516	−	0.726169i	$-0.741299\pi$
$863$	−40.3941	−1.37503	−0.687516	+	0.726169i	$0.741299\pi$
$864$	3.00000	0.102062
$865$	10.4323	0.354707
$866$	30.5383	1.03773
$867$	−34.3711	−1.16730
$868$	21.5005	0.729773
$869$	0	0
$870$	−18.3721	−0.622874
$871$	50.7991	1.72126
$872$	−11.5299	−0.390452
$873$	−11.1883	−0.378666
$874$	−7.74657	−0.262032
$875$	−34.4323	−1.16402
$876$	−8.03677	−0.271537
$877$	−15.6108	−0.527139	−0.263569	−	0.964640i	$-0.584900\pi$
$877$	−15.6108	−0.527139	−0.263569	+	0.964640i	$0.584900\pi$
$878$	12.5069	0.422086
$879$	6.66769	0.224895
$880$	0	0
$881$	19.9843	0.673288	0.336644	−	0.941632i	$-0.390708\pi$
$881$	19.9843	0.673288	0.336644	+	0.941632i	$0.390708\pi$
$882$	2.18081	0.0734318
$883$	20.2167	0.680345	0.340172	−	0.940363i	$-0.389515\pi$
$883$	20.2167	0.680345	0.340172	+	0.940363i	$0.389515\pi$
$884$	−28.1103	−0.945452
$885$	−8.73818	−0.293731
$886$	−17.6677	−0.593557
$887$	−20.1471	−0.676473	−0.338237	−	0.941061i	$-0.609830\pi$
$887$	−20.1471	−0.676473	−0.338237	+	0.941061i	$0.609830\pi$
$888$	16.0735	0.539393
$889$	−61.5246	−2.06347
$890$	−5.12938	−0.171937
$891$	0	0
$892$	11.4931	0.384819
$893$	−7.08727	−0.237167
$894$	−25.8990	−0.866192
$895$	8.88968	0.297149
$896$	−2.89167	−0.0966039
$897$	−81.2858	−2.71405
$898$	−17.7098	−0.590984
$899$	39.7643	1.32621
$900$	−3.90006	−0.130002
$901$	47.8516	1.59417
$902$	0	0
$903$	66.3015	2.20638
$904$	−8.00000	−0.266076
$905$	−3.01771	−0.100312
$906$	−10.5383	−0.350112
$907$	4.57109	0.151781	0.0758903	−	0.997116i	$-0.475820\pi$
$907$	4.57109	0.151781	0.0758903	+	0.997116i	$0.475820\pi$
$908$	−8.73284	−0.289810
$909$	1.92645	0.0638964
$910$	−22.6529	−0.750936
$911$	51.6402	1.71092	0.855459	−	0.517871i	$-0.173275\pi$
$911$	51.6402	1.71092	0.855459	+	0.517871i	$0.173275\pi$
$912$	−2.14510	−0.0710314
$913$	0	0
$914$	24.8064	0.820522
$915$	−46.3531	−1.53239
$916$	7.84117	0.259080
$917$	−9.93378	−0.328042
$918$	17.2397	0.568995
$919$	48.8412	1.61112	0.805561	−	0.592513i	$-0.201864\pi$
$919$	48.8412	1.61112	0.805561	+	0.592513i	$0.201864\pi$
$920$	12.4059	0.409009
$921$	4.69607	0.154741
$922$	2.98627	0.0983477
$923$	−73.2721	−2.41178
$924$	0	0
$925$	18.2481	0.599994
$926$	−39.5667	−1.30024
$927$	27.0294	0.887763
$928$	−5.34803	−0.175558
$929$	−57.8819	−1.89904	−0.949522	−	0.313700i	$-0.898431\pi$
$929$	−57.8819	−1.89904	−0.949522	+	0.313700i	$0.898431\pi$
$930$	−25.5426	−0.837574
$931$	1.36176	0.0446299
$932$	12.5069	0.409676
$933$	−8.41120	−0.275370
$934$	4.46475	0.146091
$935$	0	0
$936$	−7.83384	−0.256057
$937$	57.6496	1.88333	0.941664	−	0.336553i	$-0.109261\pi$
$937$	57.6496	1.88333	0.941664	+	0.336553i	$0.109261\pi$
$938$	30.0294	0.980496
$939$	46.5740	1.51989
$940$	11.3500	0.370197
$941$	15.0966	0.492135	0.246067	−	0.969253i	$-0.420862\pi$
$941$	15.0966	0.492135	0.246067	+	0.969253i	$0.420862\pi$
$942$	−17.1765	−0.559642
$943$	−15.9411	−0.519114
$944$	−2.54364	−0.0827883
$945$	13.8927	0.451931
$946$	0	0
$947$	33.3775	1.08462	0.542311	−	0.840178i	$-0.317549\pi$
$947$	33.3775	1.08462	0.542311	+	0.840178i	$0.317549\pi$
$948$	−18.6540	−0.605852
$949$	−18.3270	−0.594919
$950$	−2.43531	−0.0790118
$951$	−14.8171	−0.480476
$952$	−16.6172	−0.538566
$953$	12.4794	0.404248	0.202124	−	0.979360i	$-0.435216\pi$
$953$	12.4794	0.404248	0.202124	+	0.979360i	$0.435216\pi$
$954$	13.3354	0.431749
$955$	−3.91180	−0.126583
$956$	−24.6245	−0.796414
$957$	0	0
$958$	20.8863	0.674807
$959$	−39.2913	−1.26878
$960$	3.43531	0.110874
$961$	24.2838	0.783349
$962$	36.6540	1.18177
$963$	12.8706	0.414750
$964$	−16.0809	−0.517930
$965$	−15.4942	−0.498776
$966$	−48.0514	−1.54603
$967$	12.5804	0.404559	0.202279	−	0.979328i	$-0.435165\pi$
$967$	12.5804	0.404559	0.202279	+	0.979328i	$0.435165\pi$
$968$	0	0
$969$	−12.3270	−0.396000
$970$	11.1883	0.359234
$971$	−1.79067	−0.0574653	−0.0287327	−	0.999587i	$-0.509147\pi$
$971$	−1.79067	−0.0574653	−0.0287327	+	0.999587i	$0.509147\pi$
$972$	15.1103	0.484664
$973$	9.24063	0.296241
$974$	15.2838	0.489725
$975$	−25.5540	−0.818384
$976$	−13.4931	−0.431905
$977$	6.40586	0.204942	0.102471	−	0.994736i	$-0.467325\pi$
$977$	6.40586	0.204942	0.102471	+	0.994736i	$0.467325\pi$
$978$	−4.04211	−0.129252
$979$	0	0
$980$	−2.18081	−0.0696635
$981$	−18.4648	−0.589534
$982$	−3.31965	−0.105934
$983$	−20.5647	−0.655912	−0.327956	−	0.944693i	$-0.606360\pi$
$983$	−20.5647	−0.655912	−0.327956	+	0.944693i	$0.606360\pi$
$984$	−4.41425	−0.140721
$985$	−28.0147	−0.892621
$986$	−30.7328	−0.978733
$987$	−43.9619	−1.39932
$988$	−4.89167	−0.155625
$989$	−82.8011	−2.63292
$990$	0	0
$991$	−29.0166	−0.921744	−0.460872	−	0.887467i	$-0.652463\pi$
$991$	−29.0166	−0.921744	−0.460872	+	0.887467i	$0.652463\pi$
$992$	−7.43531	−0.236071
$993$	−68.8642	−2.18534
$994$	−43.3142	−1.37384
$995$	40.4205	1.28142
$996$	−13.1030	−0.415184
$997$	−42.3638	−1.34167	−0.670837	−	0.741605i	$-0.734065\pi$
$997$	−42.3638	−1.34167	−0.670837	+	0.741605i	$0.734065\pi$
$998$	−2.07355	−0.0656370
$999$	−22.4794	−0.711217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bo.1.1		3
11.10	odd	2		418.2.a.g.1.1	✓	3
33.32	even	2		3762.2.a.bg.1.2		3
44.43	even	2		3344.2.a.q.1.3		3
209.208	even	2		7942.2.a.bi.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.g.1.1	✓	3	11.10	odd	2
3344.2.a.q.1.3		3	44.43	even	2
3762.2.a.bg.1.2		3	33.32	even	2
4598.2.a.bo.1.1		3	1.1	even	1	trivial
7942.2.a.bi.1.3		3	209.208	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.14510 q^{3} +1.00000 q^{4} -1.60147 q^{5} -2.14510 q^{6} -2.89167 q^{7} +1.00000 q^{8} +1.60147 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.14510 q^{3} +1.00000 q^{4} -1.60147 q^{5} -2.14510 q^{6} -2.89167 q^{7} +1.00000 q^{8} +1.60147 q^{9} -1.60147 q^{10} -2.14510 q^{12} -4.89167 q^{13} -2.89167 q^{14} +3.43531 q^{15} +1.00000 q^{16} +5.74657 q^{17} +1.60147 q^{18} +1.00000 q^{19} -1.60147 q^{20} +6.20293 q^{21} -7.74657 q^{23} -2.14510 q^{24} -2.43531 q^{25} -4.89167 q^{26} +3.00000 q^{27} -2.89167 q^{28} -5.34803 q^{29} +3.43531 q^{30} -7.43531 q^{31} +1.00000 q^{32} +5.74657 q^{34} +4.63091 q^{35} +1.60147 q^{36} -7.49314 q^{37} +1.00000 q^{38} +10.4931 q^{39} -1.60147 q^{40} +2.05783 q^{41} +6.20293 q^{42} +10.6887 q^{43} -2.56469 q^{45} -7.74657 q^{46} -7.08727 q^{47} -2.14510 q^{48} +1.36176 q^{49} -2.43531 q^{50} -12.3270 q^{51} -4.89167 q^{52} +8.32698 q^{53} +3.00000 q^{54} -2.89167 q^{56} -2.14510 q^{57} -5.34803 q^{58} -2.54364 q^{59} +3.43531 q^{60} -13.4931 q^{61} -7.43531 q^{62} -4.63091 q^{63} +1.00000 q^{64} +7.83384 q^{65} -10.3848 q^{67} +5.74657 q^{68} +16.6172 q^{69} +4.63091 q^{70} +14.9789 q^{71} +1.60147 q^{72} +3.74657 q^{73} -7.49314 q^{74} +5.22399 q^{75} +1.00000 q^{76} +10.4931 q^{78} +8.69607 q^{79} -1.60147 q^{80} -11.2397 q^{81} +2.05783 q^{82} +6.10833 q^{83} +6.20293 q^{84} -9.20293 q^{85} +10.6887 q^{86} +11.4721 q^{87} +3.20293 q^{89} -2.56469 q^{90} +14.1451 q^{91} -7.74657 q^{92} +15.9495 q^{93} -7.08727 q^{94} -1.60147 q^{95} -2.14510 q^{96} -6.98627 q^{97} +1.36176 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 6 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + 6 q^{14} - 9 q^{15} + 3 q^{16} + 9 q^{17} + 3 q^{18} + 3 q^{19} - 3 q^{20} + 15 q^{21} - 15 q^{23} + 12 q^{25} + 9 q^{27} + 6 q^{28} - 6 q^{29} - 9 q^{30} - 3 q^{31} + 3 q^{32} + 9 q^{34} + 3 q^{36} - 6 q^{37} + 3 q^{38} + 15 q^{39} - 3 q^{40} + 9 q^{41} + 15 q^{42} + 21 q^{43} - 27 q^{45} - 15 q^{46} - 12 q^{47} + 27 q^{49} + 12 q^{50} - 3 q^{51} - 9 q^{53} + 9 q^{54} + 6 q^{56} - 6 q^{58} - 3 q^{59} - 9 q^{60} - 24 q^{61} - 3 q^{62} + 3 q^{64} + 6 q^{65} + 9 q^{68} + 3 q^{69} + 21 q^{71} + 3 q^{72} + 3 q^{73} - 6 q^{74} + 36 q^{75} + 3 q^{76} + 15 q^{78} + 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 33 q^{83} + 15 q^{84} - 24 q^{85} + 21 q^{86} - 6 q^{87} + 6 q^{89} - 27 q^{90} + 36 q^{91} - 15 q^{92} + 36 q^{93} - 12 q^{94} - 3 q^{95} + 12 q^{97} + 27 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 6 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + 6 * q^14 - 9 * q^15 + 3 * q^16 + 9 * q^17 + 3 * q^18 + 3 * q^19 - 3 * q^20 + 15 * q^21 - 15 * q^23 + 12 * q^25 + 9 * q^27 + 6 * q^28 - 6 * q^29 - 9 * q^30 - 3 * q^31 + 3 * q^32 + 9 * q^34 + 3 * q^36 - 6 * q^37 + 3 * q^38 + 15 * q^39 - 3 * q^40 + 9 * q^41 + 15 * q^42 + 21 * q^43 - 27 * q^45 - 15 * q^46 - 12 * q^47 + 27 * q^49 + 12 * q^50 - 3 * q^51 - 9 * q^53 + 9 * q^54 + 6 * q^56 - 6 * q^58 - 3 * q^59 - 9 * q^60 - 24 * q^61 - 3 * q^62 + 3 * q^64 + 6 * q^65 + 9 * q^68 + 3 * q^69 + 21 * q^71 + 3 * q^72 + 3 * q^73 - 6 * q^74 + 36 * q^75 + 3 * q^76 + 15 * q^78 + 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 33 * q^83 + 15 * q^84 - 24 * q^85 + 21 * q^86 - 6 * q^87 + 6 * q^89 - 27 * q^90 + 36 * q^91 - 15 * q^92 + 36 * q^93 - 12 * q^94 - 3 * q^95 + 12 * q^97 + 27 * q^98

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