LMFDB - Embedded newform 1617.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.3676752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 8x^{3} + 14x^{2} + 11x - 10 $ x^5 - 2x^4 - 8x^3 + 14x^2 + 11x - 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.49291$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49291 q^{2} +1.00000 q^{3} +4.21460 q^{4} +0.880926 q^{5} -2.49291 q^{6} -5.52081 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.49291 q^{2} +1.00000 q^{3} +4.21460 q^{4} +0.880926 q^{5} -2.49291 q^{6} -5.52081 q^{8} +1.00000 q^{9} -2.19607 q^{10} +1.00000 q^{11} +4.21460 q^{12} -7.12343 q^{13} +0.880926 q^{15} +5.33368 q^{16} +2.49291 q^{17} -2.49291 q^{18} -2.63052 q^{19} +3.71275 q^{20} -2.49291 q^{22} +5.33368 q^{23} -5.52081 q^{24} -4.22397 q^{25} +17.7581 q^{26} +1.00000 q^{27} +0.773136 q^{29} -2.19607 q^{30} +1.21460 q^{31} -2.25476 q^{32} +1.00000 q^{33} -6.21460 q^{34} +4.21460 q^{36} +8.86675 q^{37} +6.55765 q^{38} -7.12343 q^{39} -4.86343 q^{40} +6.19607 q^{41} +3.22921 q^{43} +4.21460 q^{44} +0.880926 q^{45} -13.2964 q^{46} +9.75704 q^{47} +5.33368 q^{48} +10.5300 q^{50} +2.49291 q^{51} -30.0224 q^{52} +8.93672 q^{53} -2.49291 q^{54} +0.880926 q^{55} -2.63052 q^{57} -1.92736 q^{58} -5.33368 q^{59} +3.71275 q^{60} +9.08370 q^{61} -3.02790 q^{62} -5.04643 q^{64} -6.27521 q^{65} -2.49291 q^{66} +11.2704 q^{67} +10.5066 q^{68} +5.33368 q^{69} -7.62963 q^{71} -5.52081 q^{72} +12.7766 q^{73} -22.1040 q^{74} -4.22397 q^{75} -11.0866 q^{76} +17.7581 q^{78} -6.95896 q^{79} +4.69858 q^{80} +1.00000 q^{81} -15.4462 q^{82} +1.20524 q^{83} +2.19607 q^{85} -8.05013 q^{86} +0.773136 q^{87} -5.52081 q^{88} -6.29395 q^{89} -2.19607 q^{90} +22.4793 q^{92} +1.21460 q^{93} -24.3234 q^{94} -2.31729 q^{95} -2.25476 q^{96} -1.29862 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} + 5 q^{3} + 10 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 + 5 * q^3 + 10 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^8 + 5 * q^9	$ 5 q + 2 q^{2} + 5 q^{3} + 10 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{8} + 5 q^{9} - 2 q^{10} + 5 q^{11} + 10 q^{12} - 5 q^{13} + 4 q^{15} + 16 q^{16} - 2 q^{17} + 2 q^{18} + 3 q^{19} + 8 q^{20} + 2 q^{22} + 16 q^{23} + 6 q^{24} + 7 q^{25} + 10 q^{26} + 5 q^{27} - 2 q^{30} - 5 q^{31} + 4 q^{32} + 5 q^{33} - 20 q^{34} + 10 q^{36} + 15 q^{37} - 6 q^{38} - 5 q^{39} + 6 q^{40} + 22 q^{41} + 3 q^{43} + 10 q^{44} + 4 q^{45} + 16 q^{46} + 2 q^{47} + 16 q^{48} + 34 q^{50} - 2 q^{51} - 40 q^{52} + 6 q^{53} + 2 q^{54} + 4 q^{55} + 3 q^{57} + 12 q^{58} - 16 q^{59} + 8 q^{60} - 12 q^{61} + 4 q^{62} - 4 q^{64} - 28 q^{65} + 2 q^{66} + 7 q^{67} - 10 q^{68} + 16 q^{69} + 24 q^{71} + 6 q^{72} - 17 q^{73} - 36 q^{74} + 7 q^{75} - 30 q^{76} + 10 q^{78} + 7 q^{79} - 16 q^{80} + 5 q^{81} - 8 q^{82} + 12 q^{83} + 2 q^{85} - 18 q^{86} + 6 q^{88} + 6 q^{89} - 2 q^{90} + 68 q^{92} - 5 q^{93} - 82 q^{94} - 18 q^{95} + 4 q^{96} + 14 q^{97} + 5 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 + 5 * q^3 + 10 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^8 + 5 * q^9 - 2 * q^10 + 5 * q^11 + 10 * q^12 - 5 * q^13 + 4 * q^15 + 16 * q^16 - 2 * q^17 + 2 * q^18 + 3 * q^19 + 8 * q^20 + 2 * q^22 + 16 * q^23 + 6 * q^24 + 7 * q^25 + 10 * q^26 + 5 * q^27 - 2 * q^30 - 5 * q^31 + 4 * q^32 + 5 * q^33 - 20 * q^34 + 10 * q^36 + 15 * q^37 - 6 * q^38 - 5 * q^39 + 6 * q^40 + 22 * q^41 + 3 * q^43 + 10 * q^44 + 4 * q^45 + 16 * q^46 + 2 * q^47 + 16 * q^48 + 34 * q^50 - 2 * q^51 - 40 * q^52 + 6 * q^53 + 2 * q^54 + 4 * q^55 + 3 * q^57 + 12 * q^58 - 16 * q^59 + 8 * q^60 - 12 * q^61 + 4 * q^62 - 4 * q^64 - 28 * q^65 + 2 * q^66 + 7 * q^67 - 10 * q^68 + 16 * q^69 + 24 * q^71 + 6 * q^72 - 17 * q^73 - 36 * q^74 + 7 * q^75 - 30 * q^76 + 10 * q^78 + 7 * q^79 - 16 * q^80 + 5 * q^81 - 8 * q^82 + 12 * q^83 + 2 * q^85 - 18 * q^86 + 6 * q^88 + 6 * q^89 - 2 * q^90 + 68 * q^92 - 5 * q^93 - 82 * q^94 - 18 * q^95 + 4 * q^96 + 14 * q^97 + 5 * q^99

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 $

$2$	−2.49291	−1.76275	−0.881377	−	0.472414i	$-0.843383\pi$
$2$	−2.49291	−1.76275	−0.881377	+	0.472414i	$0.843383\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.21460	2.10730
$5$	0.880926	0.393962	0.196981	−	0.980407i	$-0.436886\pi$
$5$	0.880926	0.393962	0.196981	+	0.980407i	$0.436886\pi$
$6$	−2.49291	−1.01773
$7$	0	0
$7$	0	0
$8$	−5.52081	−1.95190
$9$	1.00000	0.333333
$10$	−2.19607	−0.694458
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.21460	1.21665
$13$	−7.12343	−1.97568	−0.987842	−	0.155462i	$-0.950313\pi$
$13$	−7.12343	−1.97568	−0.987842	+	0.155462i	$0.950313\pi$
$14$	0	0
$15$	0.880926	0.227454
$16$	5.33368	1.33342
$17$	2.49291	0.604620	0.302310	−	0.953210i	$-0.402242\pi$
$17$	2.49291	0.604620	0.302310	+	0.953210i	$0.402242\pi$
$18$	−2.49291	−0.587585
$19$	−2.63052	−0.603482	−0.301741	−	0.953390i	$-0.597568\pi$
$19$	−2.63052	−0.603482	−0.301741	+	0.953390i	$0.597568\pi$
$20$	3.71275	0.830197
$21$	0	0
$22$	−2.49291	−0.531490
$23$	5.33368	1.11215	0.556074	−	0.831133i	$-0.312307\pi$
$23$	5.33368	1.11215	0.556074	+	0.831133i	$0.312307\pi$
$24$	−5.52081	−1.12693
$25$	−4.22397	−0.844794
$26$	17.7581	3.48264
$27$	1.00000	0.192450
$28$	0	0
$29$	0.773136	0.143568	0.0717839	−	0.997420i	$-0.477131\pi$
$29$	0.773136	0.143568	0.0717839	+	0.997420i	$0.477131\pi$
$30$	−2.19607	−0.400946
$31$	1.21460	0.218149	0.109075	−	0.994034i	$-0.465211\pi$
$31$	1.21460	0.218149	0.109075	+	0.994034i	$0.465211\pi$
$32$	−2.25476	−0.398590
$33$	1.00000	0.174078
$34$	−6.21460	−1.06580
$35$	0	0
$36$	4.21460	0.702434
$37$	8.86675	1.45768	0.728842	−	0.684682i	$-0.240059\pi$
$37$	8.86675	1.45768	0.728842	+	0.684682i	$0.240059\pi$
$38$	6.55765	1.06379
$39$	−7.12343	−1.14066
$40$	−4.86343	−0.768975
$41$	6.19607	0.967664	0.483832	−	0.875161i	$-0.339245\pi$
$41$	6.19607	0.967664	0.483832	+	0.875161i	$0.339245\pi$
$42$	0	0
$43$	3.22921	0.492450	0.246225	−	0.969213i	$-0.420810\pi$
$43$	3.22921	0.492450	0.246225	+	0.969213i	$0.420810\pi$
$44$	4.21460	0.635375
$45$	0.880926	0.131321
$46$	−13.2964	−1.96044
$47$	9.75704	1.42321	0.711605	−	0.702580i	$-0.247969\pi$
$47$	9.75704	1.42321	0.711605	+	0.702580i	$0.247969\pi$
$48$	5.33368	0.769850
$49$	0	0
$50$	10.5300	1.48916
$51$	2.49291	0.349077
$52$	−30.0224	−4.16336
$53$	8.93672	1.22755	0.613777	−	0.789480i	$-0.289650\pi$
$53$	8.93672	1.22755	0.613777	+	0.789480i	$0.289650\pi$
$54$	−2.49291	−0.339242
$55$	0.880926	0.118784
$56$	0	0
$57$	−2.63052	−0.348421
$58$	−1.92736	−0.253075
$59$	−5.33368	−0.694386	−0.347193	−	0.937794i	$-0.612865\pi$
$59$	−5.33368	−0.694386	−0.347193	+	0.937794i	$0.612865\pi$
$60$	3.71275	0.479315
$61$	9.08370	1.16305	0.581524	−	0.813529i	$-0.302457\pi$
$61$	9.08370	1.16305	0.581524	+	0.813529i	$0.302457\pi$
$62$	−3.02790	−0.384544
$63$	0	0
$64$	−5.04643	−0.630804
$65$	−6.27521	−0.778345
$66$	−2.49291	−0.306856
$67$	11.2704	1.37690	0.688449	−	0.725284i	$-0.258292\pi$
$67$	11.2704	1.37690	0.688449	+	0.725284i	$0.258292\pi$
$68$	10.5066	1.27412
$69$	5.33368	0.642099
$70$	0	0
$71$	−7.62963	−0.905471	−0.452735	−	0.891645i	$-0.649552\pi$
$71$	−7.62963	−0.905471	−0.452735	+	0.891645i	$0.649552\pi$
$72$	−5.52081	−0.650634
$73$	12.7766	1.49539	0.747694	−	0.664043i	$-0.231161\pi$
$73$	12.7766	1.49539	0.747694	+	0.664043i	$0.231161\pi$
$74$	−22.1040	−2.56954
$75$	−4.22397	−0.487742
$76$	−11.0866	−1.27172
$77$	0	0
$78$	17.7581	2.01071
$79$	−6.95896	−0.782944	−0.391472	−	0.920190i	$-0.628034\pi$
$79$	−6.95896	−0.782944	−0.391472	+	0.920190i	$0.628034\pi$
$80$	4.69858	0.525317
$81$	1.00000	0.111111
$82$	−15.4462	−1.70575
$83$	1.20524	0.132292	0.0661461	−	0.997810i	$-0.478930\pi$
$83$	1.20524	0.132292	0.0661461	+	0.997810i	$0.478930\pi$
$84$	0	0
$85$	2.19607	0.238197
$86$	−8.05013	−0.868068
$87$	0.773136	0.0828889
$88$	−5.52081	−0.588520
$89$	−6.29395	−0.667157	−0.333578	−	0.942722i	$-0.608256\pi$
$89$	−6.29395	−0.667157	−0.333578	+	0.942722i	$0.608256\pi$
$90$	−2.19607	−0.231486
$91$	0	0
$92$	22.4793	2.34363
$93$	1.21460	0.125949
$94$	−24.3234	−2.50877
$95$	−2.31729	−0.237749
$96$	−2.25476	−0.230126
$97$	−1.29862	−0.131855	−0.0659275	−	0.997824i	$-0.521001\pi$
$97$	−1.29862	−0.131855	−0.0659275	+	0.997824i	$0.521001\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−17.8024	−1.78024
$101$	9.89422	0.984512	0.492256	−	0.870451i	$-0.336172\pi$
$101$	9.89422	0.984512	0.492256	+	0.870451i	$0.336172\pi$
$102$	−6.21460	−0.615337
$103$	−11.1842	−1.10202	−0.551008	−	0.834500i	$-0.685757\pi$
$103$	−11.1842	−1.10202	−0.551008	+	0.834500i	$0.685757\pi$
$104$	39.3271	3.85634
$105$	0	0
$106$	−22.2785	−2.16387
$107$	7.26605	0.702435	0.351218	−	0.936294i	$-0.385768\pi$
$107$	7.26605	0.702435	0.351218	+	0.936294i	$0.385768\pi$
$108$	4.21460	0.405550
$109$	0.456074	0.0436839	0.0218420	−	0.999761i	$-0.493047\pi$
$109$	0.456074	0.0436839	0.0218420	+	0.999761i	$0.493047\pi$
$110$	−2.19607	−0.209387
$111$	8.86675	0.841594
$112$	0	0
$113$	−14.3518	−1.35010	−0.675050	−	0.737772i	$-0.735878\pi$
$113$	−14.3518	−1.35010	−0.675050	+	0.737772i	$0.735878\pi$
$114$	6.55765	0.614180
$115$	4.69858	0.438144
$116$	3.25846	0.302541
$117$	−7.12343	−0.658561
$118$	13.2964	1.22403
$119$	0	0
$120$	−4.86343	−0.443968
$121$	1.00000	0.0909091
$122$	−22.6448	−2.05017
$123$	6.19607	0.558681
$124$	5.11907	0.459706
$125$	−8.12564	−0.726779
$126$	0	0
$127$	8.91977	0.791502	0.395751	−	0.918358i	$-0.370484\pi$
$127$	8.91977	0.791502	0.395751	+	0.918358i	$0.370484\pi$
$128$	17.0898	1.51054
$129$	3.22921	0.284316
$130$	15.6436	1.37203
$131$	−12.3871	−1.08227	−0.541134	−	0.840936i	$-0.682005\pi$
$131$	−12.3871	−1.08227	−0.541134	+	0.840936i	$0.682005\pi$
$132$	4.21460	0.366834
$133$	0	0
$134$	−28.0961	−2.42713
$135$	0.880926	0.0758181
$136$	−13.7629	−1.18016
$137$	22.1256	1.89032	0.945160	−	0.326607i	$-0.105905\pi$
$137$	22.1256	1.89032	0.945160	+	0.326607i	$0.105905\pi$
$138$	−13.2964	−1.13186
$139$	−2.63553	−0.223543	−0.111771	−	0.993734i	$-0.535652\pi$
$139$	−2.63553	−0.223543	−0.111771	+	0.993734i	$0.535652\pi$
$140$	0	0
$141$	9.75704	0.821691
$142$	19.0200	1.59612
$143$	−7.12343	−0.595691
$144$	5.33368	0.444473
$145$	0.681076	0.0565602
$146$	−31.8509	−2.63600
$147$	0	0
$148$	37.3698	3.07178
$149$	0.768125	0.0629273	0.0314636	−	0.999505i	$-0.489983\pi$
$149$	0.768125	0.0629273	0.0314636	+	0.999505i	$0.489983\pi$
$150$	10.5300	0.859769
$151$	−14.0353	−1.14218	−0.571090	−	0.820887i	$-0.693479\pi$
$151$	−14.0353	−1.14218	−0.571090	+	0.820887i	$0.693479\pi$
$152$	14.5226	1.17794
$153$	2.49291	0.201540
$154$	0	0
$155$	1.06998	0.0859426
$156$	−30.0224	−2.40372
$157$	−5.63810	−0.449970	−0.224985	−	0.974362i	$-0.572233\pi$
$157$	−5.63810	−0.449970	−0.224985	+	0.974362i	$0.572233\pi$
$158$	17.3481	1.38014
$159$	8.93672	0.708728
$160$	−1.98628	−0.157029
$161$	0	0
$162$	−2.49291	−0.195862
$163$	10.8997	0.853727	0.426864	−	0.904316i	$-0.359618\pi$
$163$	10.8997	0.853727	0.426864	+	0.904316i	$0.359618\pi$
$164$	26.1140	2.03916
$165$	0.880926	0.0685800
$166$	−3.00455	−0.233198
$167$	−9.17688	−0.710128	−0.355064	−	0.934842i	$-0.615541\pi$
$167$	−9.17688	−0.710128	−0.355064	+	0.934842i	$0.615541\pi$
$168$	0	0
$169$	37.7432	2.90333
$170$	−5.47461	−0.419883
$171$	−2.63052	−0.201161
$172$	13.6098	1.03774
$173$	2.51837	0.191468	0.0957342	−	0.995407i	$-0.469480\pi$
$173$	2.51837	0.191468	0.0957342	+	0.995407i	$0.469480\pi$
$174$	−1.92736	−0.146113
$175$	0	0
$176$	5.33368	0.402041
$177$	−5.33368	−0.400904
$178$	15.6902	1.17603
$179$	24.5313	1.83356	0.916778	−	0.399398i	$-0.130781\pi$
$179$	24.5313	1.83356	0.916778	+	0.399398i	$0.130781\pi$
$180$	3.71275	0.276732
$181$	−12.8187	−0.952805	−0.476403	−	0.879227i	$-0.658060\pi$
$181$	−12.8187	−0.952805	−0.476403	+	0.879227i	$0.658060\pi$
$182$	0	0
$183$	9.08370	0.671486
$184$	−29.4462	−2.17080
$185$	7.81095	0.574272
$186$	−3.02790	−0.222016
$187$	2.49291	0.182300
$188$	41.1221	2.99913
$189$	0	0
$190$	5.77680	0.419093
$191$	22.0785	1.59755	0.798774	−	0.601631i	$-0.205482\pi$
$191$	22.0785	1.59755	0.798774	+	0.601631i	$0.205482\pi$
$192$	−5.04643	−0.364195
$193$	18.4453	1.32772	0.663860	−	0.747857i	$-0.268917\pi$
$193$	18.4453	1.32772	0.663860	+	0.747857i	$0.268917\pi$
$194$	3.23734	0.232428
$195$	−6.27521	−0.449377
$196$	0	0
$197$	−4.57707	−0.326102	−0.163051	−	0.986618i	$-0.552134\pi$
$197$	−4.57707	−0.326102	−0.163051	+	0.986618i	$0.552134\pi$
$198$	−2.49291	−0.177163
$199$	2.19106	0.155320	0.0776601	−	0.996980i	$-0.475255\pi$
$199$	2.19106	0.155320	0.0776601	+	0.996980i	$0.475255\pi$
$200$	23.3197	1.64895
$201$	11.2704	0.794953
$202$	−24.6654	−1.73545
$203$	0	0
$204$	10.5066	0.735611
$205$	5.45828	0.381223
$206$	27.8813	1.94258
$207$	5.33368	0.370716
$208$	−37.9941	−2.63441
$209$	−2.63052	−0.181957
$210$	0	0
$211$	−9.97047	−0.686395	−0.343198	−	0.939263i	$-0.611510\pi$
$211$	−9.97047	−0.686395	−0.343198	+	0.939263i	$0.611510\pi$
$212$	37.6648	2.58683
$213$	−7.62963	−0.522774
$214$	−18.1136	−1.23822
$215$	2.84469	0.194007
$216$	−5.52081	−0.375644
$217$	0	0
$218$	−1.13695	−0.0770040
$219$	12.7766	0.863363
$220$	3.71275	0.250314
$221$	−17.7581	−1.19454
$222$	−22.1040	−1.48352
$223$	15.2015	1.01796	0.508982	−	0.860777i	$-0.330022\pi$
$223$	15.2015	1.01796	0.508982	+	0.860777i	$0.330022\pi$
$224$	0	0
$225$	−4.22397	−0.281598
$226$	35.7776	2.37989
$227$	11.0661	0.734485	0.367243	−	0.930125i	$-0.380302\pi$
$227$	11.0661	0.734485	0.367243	+	0.930125i	$0.380302\pi$
$228$	−11.0866	−0.734227
$229$	2.86577	0.189375	0.0946877	−	0.995507i	$-0.469815\pi$
$229$	2.86577	0.189375	0.0946877	+	0.995507i	$0.469815\pi$
$230$	−11.7131	−0.772341
$231$	0	0
$232$	−4.26834	−0.280230
$233$	−14.6048	−0.956794	−0.478397	−	0.878144i	$-0.658782\pi$
$233$	−14.6048	−0.956794	−0.478397	+	0.878144i	$0.658782\pi$
$234$	17.7581	1.16088
$235$	8.59523	0.560691
$236$	−22.4793	−1.46328
$237$	−6.95896	−0.452033
$238$	0	0
$239$	18.4800	1.19537	0.597686	−	0.801730i	$-0.296087\pi$
$239$	18.4800	1.19537	0.597686	+	0.801730i	$0.296087\pi$
$240$	4.69858	0.303292
$241$	−25.9433	−1.67115	−0.835577	−	0.549373i	$-0.814866\pi$
$241$	−25.9433	−1.67115	−0.835577	+	0.549373i	$0.814866\pi$
$242$	−2.49291	−0.160250
$243$	1.00000	0.0641500
$244$	38.2842	2.45089
$245$	0	0
$246$	−15.4462	−0.984817
$247$	18.7383	1.19229
$248$	−6.70560	−0.425806
$249$	1.20524	0.0763789
$250$	20.2565	1.28113
$251$	−26.4331	−1.66844	−0.834221	−	0.551430i	$-0.814082\pi$
$251$	−26.4331	−1.66844	−0.834221	+	0.551430i	$0.814082\pi$
$252$	0	0
$253$	5.33368	0.335325
$254$	−22.2362	−1.39522
$255$	2.19607	0.137523
$256$	−32.5106	−2.03191
$257$	4.63900	0.289373	0.144686	−	0.989478i	$-0.453783\pi$
$257$	4.63900	0.289373	0.144686	+	0.989478i	$0.453783\pi$
$258$	−8.05013	−0.501179
$259$	0	0
$260$	−26.4475	−1.64021
$261$	0.773136	0.0478559
$262$	30.8800	1.90777
$263$	19.6266	1.21023	0.605114	−	0.796139i	$-0.293128\pi$
$263$	19.6266	1.21023	0.605114	+	0.796139i	$0.293128\pi$
$264$	−5.52081	−0.339782
$265$	7.87259	0.483610
$266$	0	0
$267$	−6.29395	−0.385183
$268$	47.5003	2.90154
$269$	22.5633	1.37571	0.687855	−	0.725848i	$-0.258553\pi$
$269$	22.5633	1.37571	0.687855	+	0.725848i	$0.258553\pi$
$270$	−2.19607	−0.133649
$271$	17.1535	1.04200	0.521002	−	0.853556i	$-0.325559\pi$
$271$	17.1535	1.04200	0.521002	+	0.853556i	$0.325559\pi$
$272$	13.2964	0.806212
$273$	0	0
$274$	−55.1572	−3.33217
$275$	−4.22397	−0.254715
$276$	22.4793	1.35310
$277$	−26.1496	−1.57117	−0.785587	−	0.618751i	$-0.787639\pi$
$277$	−26.1496	−1.57117	−0.785587	+	0.618751i	$0.787639\pi$
$278$	6.57014	0.394051
$279$	1.21460	0.0727164
$280$	0	0
$281$	8.79972	0.524947	0.262474	−	0.964939i	$-0.415462\pi$
$281$	8.79972	0.524947	0.262474	+	0.964939i	$0.415462\pi$
$282$	−24.3234	−1.44844
$283$	−13.7499	−0.817346	−0.408673	−	0.912681i	$-0.634008\pi$
$283$	−13.7499	−0.817346	−0.408673	+	0.912681i	$0.634008\pi$
$284$	−32.1559	−1.90810
$285$	−2.31729	−0.137265
$286$	17.7581	1.05006
$287$	0	0
$288$	−2.25476	−0.132863
$289$	−10.7854	−0.634435
$290$	−1.69786	−0.0997018
$291$	−1.29862	−0.0761265
$292$	53.8483	3.15124
$293$	−17.4266	−1.01807	−0.509037	−	0.860744i	$-0.669999\pi$
$293$	−17.4266	−1.01807	−0.509037	+	0.860744i	$0.669999\pi$
$294$	0	0
$295$	−4.69858	−0.273562
$296$	−48.9516	−2.84526
$297$	1.00000	0.0580259
$298$	−1.91487	−0.110925
$299$	−37.9941	−2.19725
$300$	−17.8024	−1.02782
$301$	0	0
$302$	34.9889	2.01338
$303$	9.89422	0.568408
$304$	−14.0303	−0.804695
$305$	8.00207	0.458197
$306$	−6.21460	−0.355265
$307$	0.804963	0.0459416	0.0229708	−	0.999736i	$-0.492688\pi$
$307$	0.804963	0.0459416	0.0229708	+	0.999736i	$0.492688\pi$
$308$	0	0
$309$	−11.1842	−0.636249
$310$	−2.66736	−0.151496
$311$	10.8250	0.613830	0.306915	−	0.951737i	$-0.400703\pi$
$311$	10.8250	0.613830	0.306915	+	0.951737i	$0.400703\pi$
$312$	39.3271	2.22646
$313$	−24.7315	−1.39791	−0.698953	−	0.715168i	$-0.746350\pi$
$313$	−24.7315	−1.39791	−0.698953	+	0.715168i	$0.746350\pi$
$314$	14.0553	0.793186
$315$	0	0
$316$	−29.3292	−1.64990
$317$	−12.2819	−0.689821	−0.344911	−	0.938636i	$-0.612091\pi$
$317$	−12.2819	−0.689821	−0.344911	+	0.938636i	$0.612091\pi$
$318$	−22.2785	−1.24931
$319$	0.773136	0.0432873
$320$	−4.44553	−0.248513
$321$	7.26605	0.405551
$322$	0	0
$323$	−6.55765	−0.364877
$324$	4.21460	0.234145
$325$	30.0891	1.66905
$326$	−27.1719	−1.50491
$327$	0.456074	0.0252209
$328$	−34.2073	−1.88878
$329$	0	0
$330$	−2.19607	−0.120890
$331$	−13.1987	−0.725468	−0.362734	−	0.931893i	$-0.618157\pi$
$331$	−13.1987	−0.725468	−0.362734	+	0.931893i	$0.618157\pi$
$332$	5.07960	0.278779
$333$	8.86675	0.485895
$334$	22.8771	1.25178
$335$	9.92839	0.542446
$336$	0	0
$337$	0.468940	0.0255448	0.0127724	−	0.999918i	$-0.495934\pi$
$337$	0.468940	0.0255448	0.0127724	+	0.999918i	$0.495934\pi$
$338$	−94.0905	−5.11785
$339$	−14.3518	−0.779480
$340$	9.25557	0.501954
$341$	1.21460	0.0657745
$342$	6.55765	0.354597
$343$	0	0
$344$	−17.8278	−0.961213
$345$	4.69858	0.252963
$346$	−6.27808	−0.337512
$347$	3.49417	0.187577	0.0937885	−	0.995592i	$-0.470102\pi$
$347$	3.49417	0.187577	0.0937885	+	0.995592i	$0.470102\pi$
$348$	3.25846	0.174672
$349$	15.7180	0.841365	0.420683	−	0.907208i	$-0.361791\pi$
$349$	15.7180	0.841365	0.420683	+	0.907208i	$0.361791\pi$
$350$	0	0
$351$	−7.12343	−0.380221
$352$	−2.25476	−0.120179
$353$	−35.2242	−1.87480	−0.937398	−	0.348261i	$-0.886772\pi$
$353$	−35.2242	−1.87480	−0.937398	+	0.348261i	$0.886772\pi$
$354$	13.2964	0.706695
$355$	−6.72114	−0.356721
$356$	−26.5265	−1.40590
$357$	0	0
$358$	−61.1543	−3.23211
$359$	23.2190	1.22545	0.612725	−	0.790296i	$-0.290073\pi$
$359$	23.2190	1.22545	0.612725	+	0.790296i	$0.290073\pi$
$360$	−4.86343	−0.256325
$361$	−12.0804	−0.635809
$362$	31.9558	1.67956
$363$	1.00000	0.0524864
$364$	0	0
$365$	11.2552	0.589127
$366$	−22.6448	−1.18366
$367$	−19.7507	−1.03098	−0.515490	−	0.856896i	$-0.672390\pi$
$367$	−19.7507	−1.03098	−0.515490	+	0.856896i	$0.672390\pi$
$368$	28.4481	1.48296
$369$	6.19607	0.322555
$370$	−19.4720	−1.01230
$371$	0	0
$372$	5.11907	0.265412
$373$	−24.9656	−1.29267	−0.646335	−	0.763054i	$-0.723699\pi$
$373$	−24.9656	−1.29267	−0.646335	+	0.763054i	$0.723699\pi$
$374$	−6.21460	−0.321350
$375$	−8.12564	−0.419606
$376$	−53.8668	−2.77797
$377$	−5.50738	−0.283644
$378$	0	0
$379$	−16.3261	−0.838613	−0.419307	−	0.907845i	$-0.637727\pi$
$379$	−16.3261	−0.838613	−0.419307	+	0.907845i	$0.637727\pi$
$380$	−9.76647	−0.501009
$381$	8.91977	0.456974
$382$	−55.0398	−2.81608
$383$	−12.1079	−0.618687	−0.309343	−	0.950950i	$-0.600109\pi$
$383$	−12.1079	−0.618687	−0.309343	+	0.950950i	$0.600109\pi$
$384$	17.0898	0.872112
$385$	0	0
$386$	−45.9824	−2.34044
$387$	3.22921	0.164150
$388$	−5.47317	−0.277858
$389$	−18.1998	−0.922765	−0.461382	−	0.887201i	$-0.652646\pi$
$389$	−18.1998	−0.922765	−0.461382	+	0.887201i	$0.652646\pi$
$390$	15.6436	0.792142
$391$	13.2964	0.672427
$392$	0	0
$393$	−12.3871	−0.624848
$394$	11.4102	0.574838
$395$	−6.13033	−0.308450
$396$	4.21460	0.211792
$397$	0.0579458	0.00290822	0.00145411	−	0.999999i	$-0.499537\pi$
$397$	0.0579458	0.00290822	0.00145411	+	0.999999i	$0.499537\pi$
$398$	−5.46212	−0.273791
$399$	0	0
$400$	−22.5293	−1.12646
$401$	−16.8849	−0.843194	−0.421597	−	0.906783i	$-0.638530\pi$
$401$	−16.8849	−0.843194	−0.421597	+	0.906783i	$0.638530\pi$
$402$	−28.0961	−1.40131
$403$	−8.65214	−0.430994
$404$	41.7002	2.07466
$405$	0.880926	0.0437736
$406$	0	0
$407$	8.86675	0.439508
$408$	−13.7629	−0.681364
$409$	1.08636	0.0537171	0.0268586	−	0.999639i	$-0.491450\pi$
$409$	1.08636	0.0537171	0.0268586	+	0.999639i	$0.491450\pi$
$410$	−13.6070	−0.672002
$411$	22.1256	1.09138
$412$	−47.1371	−2.32228
$413$	0	0
$414$	−13.2964	−0.653482
$415$	1.06173	0.0521181
$416$	16.0616	0.787487
$417$	−2.63553	−0.129062
$418$	6.55765	0.320745
$419$	−18.7222	−0.914638	−0.457319	−	0.889303i	$-0.651190\pi$
$419$	−18.7222	−0.914638	−0.457319	+	0.889303i	$0.651190\pi$
$420$	0	0
$421$	10.6579	0.519433	0.259716	−	0.965685i	$-0.416371\pi$
$421$	10.6579	0.519433	0.259716	+	0.965685i	$0.416371\pi$
$422$	24.8555	1.20995
$423$	9.75704	0.474403
$424$	−49.3380	−2.39606
$425$	−10.5300	−0.510779
$426$	19.0200	0.921522
$427$	0	0
$428$	30.6235	1.48024
$429$	−7.12343	−0.343922
$430$	−7.09157	−0.341986
$431$	19.7490	0.951275	0.475638	−	0.879641i	$-0.342217\pi$
$431$	19.7490	0.951275	0.475638	+	0.879641i	$0.342217\pi$
$432$	5.33368	0.256617
$433$	34.6826	1.66674	0.833370	−	0.552715i	$-0.186408\pi$
$433$	34.6826	1.66674	0.833370	+	0.552715i	$0.186408\pi$
$434$	0	0
$435$	0.681076	0.0326551
$436$	1.92217	0.0920552
$437$	−14.0303	−0.671162
$438$	−31.8509	−1.52190
$439$	5.59033	0.266812	0.133406	−	0.991061i	$-0.457409\pi$
$439$	5.59033	0.266812	0.133406	+	0.991061i	$0.457409\pi$
$440$	−4.86343	−0.231855
$441$	0	0
$442$	44.2693	2.10568
$443$	10.9065	0.518185	0.259093	−	0.965852i	$-0.416577\pi$
$443$	10.9065	0.518185	0.259093	+	0.965852i	$0.416577\pi$
$444$	37.3698	1.77349
$445$	−5.54450	−0.262835
$446$	−37.8959	−1.79442
$447$	0.768125	0.0363311
$448$	0	0
$449$	9.97164	0.470591	0.235295	−	0.971924i	$-0.424394\pi$
$449$	9.97164	0.470591	0.235295	+	0.971924i	$0.424394\pi$
$450$	10.5300	0.496388
$451$	6.19607	0.291762
$452$	−60.4870	−2.84507
$453$	−14.0353	−0.659438
$454$	−27.5869	−1.29472
$455$	0	0
$456$	14.5226	0.680083
$457$	−5.76803	−0.269817	−0.134909	−	0.990858i	$-0.543074\pi$
$457$	−5.76803	−0.269817	−0.134909	+	0.990858i	$0.543074\pi$
$458$	−7.14411	−0.333822
$459$	2.49291	0.116359
$460$	19.8026	0.923303
$461$	25.9921	1.21057	0.605286	−	0.796008i	$-0.293059\pi$
$461$	25.9921	1.21057	0.605286	+	0.796008i	$0.293059\pi$
$462$	0	0
$463$	6.09937	0.283462	0.141731	−	0.989905i	$-0.454733\pi$
$463$	6.09937	0.283462	0.141731	+	0.989905i	$0.454733\pi$
$464$	4.12366	0.191436
$465$	1.06998	0.0496190
$466$	36.4085	1.68659
$467$	23.8540	1.10383	0.551915	−	0.833900i	$-0.313897\pi$
$467$	23.8540	1.10383	0.551915	+	0.833900i	$0.313897\pi$
$468$	−30.0224	−1.38779
$469$	0	0
$470$	−21.4271	−0.988360
$471$	−5.63810	−0.259790
$472$	29.4462	1.35537
$473$	3.22921	0.148479
$474$	17.3481	0.796823
$475$	11.1112	0.509818
$476$	0	0
$477$	8.93672	0.409184
$478$	−46.0690	−2.10715
$479$	9.26889	0.423506	0.211753	−	0.977323i	$-0.432083\pi$
$479$	9.26889	0.423506	0.211753	+	0.977323i	$0.432083\pi$
$480$	−1.98628	−0.0906609
$481$	−63.1616	−2.87992
$482$	64.6743	2.94583
$483$	0	0
$484$	4.21460	0.191573
$485$	−1.14399	−0.0519458
$486$	−2.49291	−0.113081
$487$	38.4123	1.74063	0.870313	−	0.492498i	$-0.163916\pi$
$487$	38.4123	1.74063	0.870313	+	0.492498i	$0.163916\pi$
$488$	−50.1494	−2.27015
$489$	10.8997	0.492900
$490$	0	0
$491$	−12.1820	−0.549767	−0.274884	−	0.961477i	$-0.588639\pi$
$491$	−12.1820	−0.549767	−0.274884	+	0.961477i	$0.588639\pi$
$492$	26.1140	1.17731
$493$	1.92736	0.0868039
$494$	−46.7129	−2.10171
$495$	0.880926	0.0395947
$496$	6.47831	0.290884
$497$	0	0
$498$	−3.00455	−0.134637
$499$	7.21460	0.322970	0.161485	−	0.986875i	$-0.448372\pi$
$499$	7.21460	0.322970	0.161485	+	0.986875i	$0.448372\pi$
$500$	−34.2463	−1.53154
$501$	−9.17688	−0.409993
$502$	65.8954	2.94105
$503$	−3.49548	−0.155856	−0.0779280	−	0.996959i	$-0.524830\pi$
$503$	−3.49548	−0.155856	−0.0779280	+	0.996959i	$0.524830\pi$
$504$	0	0
$505$	8.71608	0.387860
$506$	−13.2964	−0.591096
$507$	37.7432	1.67624
$508$	37.5933	1.66793
$509$	−34.2725	−1.51910	−0.759552	−	0.650447i	$-0.774582\pi$
$509$	−34.2725	−1.51910	−0.759552	+	0.650447i	$0.774582\pi$
$510$	−5.47461	−0.242420
$511$	0	0
$512$	46.8663	2.07122
$513$	−2.63052	−0.116140
$514$	−11.5646	−0.510093
$515$	−9.85249	−0.434152
$516$	13.6098	0.599140
$517$	9.75704	0.429114
$518$	0	0
$519$	2.51837	0.110544
$520$	34.6443	1.51925
$521$	6.00786	0.263209	0.131604	−	0.991302i	$-0.457987\pi$
$521$	6.00786	0.263209	0.131604	+	0.991302i	$0.457987\pi$
$522$	−1.92736	−0.0843582
$523$	−2.98731	−0.130626	−0.0653130	−	0.997865i	$-0.520805\pi$
$523$	−2.98731	−0.130626	−0.0653130	+	0.997865i	$0.520805\pi$
$524$	−52.2068	−2.28067
$525$	0	0
$526$	−48.9273	−2.13333
$527$	3.02790	0.131897
$528$	5.33368	0.232119
$529$	5.44812	0.236875
$530$	−19.6257	−0.852485
$531$	−5.33368	−0.231462
$532$	0	0
$533$	−44.1373	−1.91180
$534$	15.6902	0.678983
$535$	6.40085	0.276733
$536$	−62.2217	−2.68757
$537$	24.5313	1.05860
$538$	−56.2483	−2.42504
$539$	0	0
$540$	3.71275	0.159772
$541$	−0.0373463	−0.00160564	−0.000802822	−	1.00000i	$-0.500256\pi$
$541$	−0.0373463	−0.00160564	−0.000802822		1.00000i	$0.500256\pi$
$542$	−42.7622	−1.83680
$543$	−12.8187	−0.550102
$544$	−5.62092	−0.240995
$545$	0.401767	0.0172098
$546$	0	0
$547$	−16.1882	−0.692156	−0.346078	−	0.938206i	$-0.612487\pi$
$547$	−16.1882	−0.692156	−0.346078	+	0.938206i	$0.612487\pi$
$548$	93.2508	3.98348
$549$	9.08370	0.387683
$550$	10.5300	0.449000
$551$	−2.03375	−0.0866406
$552$	−29.4462	−1.25331
$553$	0	0
$554$	65.1885	2.76959
$555$	7.81095	0.331556
$556$	−11.1077	−0.471072
$557$	33.4158	1.41587	0.707937	−	0.706275i	$-0.249626\pi$
$557$	33.4158	1.41587	0.707937	+	0.706275i	$0.249626\pi$
$558$	−3.02790	−0.128181
$559$	−23.0030	−0.972925
$560$	0	0
$561$	2.49291	0.105251
$562$	−21.9369	−0.925353
$563$	−0.284245	−0.0119795	−0.00598974	−	0.999982i	$-0.501907\pi$
$563$	−0.284245	−0.0119795	−0.00598974	+	0.999982i	$0.501907\pi$
$564$	41.1221	1.73155
$565$	−12.6428	−0.531888
$566$	34.2772	1.44078
$567$	0	0
$568$	42.1217	1.76739
$569$	−15.4749	−0.648741	−0.324371	−	0.945930i	$-0.605153\pi$
$569$	−15.4749	−0.648741	−0.324371	+	0.945930i	$0.605153\pi$
$570$	5.77680	0.241964
$571$	−10.7334	−0.449179	−0.224589	−	0.974453i	$-0.572104\pi$
$571$	−10.7334	−0.449179	−0.224589	+	0.974453i	$0.572104\pi$
$572$	−30.0224	−1.25530
$573$	22.0785	0.922345
$574$	0	0
$575$	−22.5293	−0.939536
$576$	−5.04643	−0.210268
$577$	−11.9907	−0.499179	−0.249589	−	0.968352i	$-0.580296\pi$
$577$	−11.9907	−0.499179	−0.249589	+	0.968352i	$0.580296\pi$
$578$	26.8870	1.11835
$579$	18.4453	0.766559
$580$	2.87046	0.119190
$581$	0	0
$582$	3.23734	0.134192
$583$	8.93672	0.370121
$584$	−70.5372	−2.91885
$585$	−6.27521	−0.259448
$586$	43.4430	1.79462
$587$	−34.2223	−1.41251	−0.706254	−	0.707959i	$-0.749616\pi$
$587$	−34.2223	−1.41251	−0.706254	+	0.707959i	$0.749616\pi$
$588$	0	0
$589$	−3.19504	−0.131649
$590$	11.7131	0.482222
$591$	−4.57707	−0.188275
$592$	47.2924	1.94370
$593$	29.5003	1.21143	0.605716	−	0.795681i	$-0.292887\pi$
$593$	29.5003	1.21143	0.605716	+	0.795681i	$0.292887\pi$
$594$	−2.49291	−0.102285
$595$	0	0
$596$	3.23734	0.132607
$597$	2.19106	0.0896741
$598$	94.7158	3.87322
$599$	−21.1061	−0.862373	−0.431186	−	0.902263i	$-0.641905\pi$
$599$	−21.1061	−0.862373	−0.431186	+	0.902263i	$0.641905\pi$
$600$	23.3197	0.952024
$601$	−20.4406	−0.833789	−0.416894	−	0.908955i	$-0.636882\pi$
$601$	−20.4406	−0.833789	−0.416894	+	0.908955i	$0.636882\pi$
$602$	0	0
$603$	11.2704	0.458966
$604$	−59.1534	−2.40692
$605$	0.880926	0.0358147
$606$	−24.6654	−1.00196
$607$	42.5633	1.72759	0.863795	−	0.503843i	$-0.168081\pi$
$607$	42.5633	1.72759	0.863795	+	0.503843i	$0.168081\pi$
$608$	5.93119	0.240542
$609$	0	0
$610$	−19.9484	−0.807689
$611$	−69.5036	−2.81181
$612$	10.5066	0.424705
$613$	−0.696566	−0.0281340	−0.0140670	−	0.999901i	$-0.504478\pi$
$613$	−0.696566	−0.0281340	−0.0140670	+	0.999901i	$0.504478\pi$
$614$	−2.00670	−0.0809838
$615$	5.45828	0.220099
$616$	0	0
$617$	−13.6494	−0.549504	−0.274752	−	0.961515i	$-0.588596\pi$
$617$	−13.6494	−0.549504	−0.274752	+	0.961515i	$0.588596\pi$
$618$	27.8813	1.12155
$619$	35.2791	1.41799	0.708994	−	0.705215i	$-0.249149\pi$
$619$	35.2791	1.41799	0.708994	+	0.705215i	$0.249149\pi$
$620$	4.50953	0.181107
$621$	5.33368	0.214033
$622$	−26.9858	−1.08203
$623$	0	0
$624$	−37.9941	−1.52098
$625$	13.9618	0.558470
$626$	61.6534	2.46416
$627$	−2.63052	−0.105053
$628$	−23.7624	−0.948222
$629$	22.1040	0.881345
$630$	0	0
$631$	16.4853	0.656271	0.328136	−	0.944631i	$-0.393580\pi$
$631$	16.4853	0.656271	0.328136	+	0.944631i	$0.393580\pi$
$632$	38.4191	1.52823
$633$	−9.97047	−0.396291
$634$	30.6177	1.21598
$635$	7.85766	0.311822
$636$	37.6648	1.49350
$637$	0	0
$638$	−1.92736	−0.0763049
$639$	−7.62963	−0.301824
$640$	15.0549	0.595096
$641$	6.46868	0.255497	0.127749	−	0.991807i	$-0.459225\pi$
$641$	6.46868	0.255497	0.127749	+	0.991807i	$0.459225\pi$
$642$	−18.1136	−0.714887
$643$	18.2913	0.721338	0.360669	−	0.932694i	$-0.382548\pi$
$643$	18.2913	0.721338	0.360669	+	0.932694i	$0.382548\pi$
$644$	0	0
$645$	2.84469	0.112010
$646$	16.3476	0.643189
$647$	18.0021	0.707734	0.353867	−	0.935296i	$-0.384867\pi$
$647$	18.0021	0.707734	0.353867	+	0.935296i	$0.384867\pi$
$648$	−5.52081	−0.216878
$649$	−5.33368	−0.209365
$650$	−75.0095	−2.94212
$651$	0	0
$652$	45.9377	1.79906
$653$	−5.00885	−0.196011	−0.0980057	−	0.995186i	$-0.531246\pi$
$653$	−5.00885	−0.196011	−0.0980057	+	0.995186i	$0.531246\pi$
$654$	−1.13695	−0.0444583
$655$	−10.9121	−0.426373
$656$	33.0478	1.29030
$657$	12.7766	0.498463
$658$	0	0
$659$	43.2762	1.68580	0.842901	−	0.538068i	$-0.180846\pi$
$659$	43.2762	1.68580	0.842901	+	0.538068i	$0.180846\pi$
$660$	3.71275	0.144519
$661$	−19.0415	−0.740628	−0.370314	−	0.928907i	$-0.620750\pi$
$661$	−19.0415	−0.740628	−0.370314	+	0.928907i	$0.620750\pi$
$662$	32.9033	1.27882
$663$	−17.7581	−0.689666
$664$	−6.65389	−0.258221
$665$	0	0
$666$	−22.1040	−0.856513
$667$	4.12366	0.159669
$668$	−38.6769	−1.49645
$669$	15.2015	0.587722
$670$	−24.7506	−0.956199
$671$	9.08370	0.350672
$672$	0	0
$673$	9.68181	0.373206	0.186603	−	0.982435i	$-0.440252\pi$
$673$	9.68181	0.373206	0.186603	+	0.982435i	$0.440252\pi$
$674$	−1.16903	−0.0450292
$675$	−4.22397	−0.162581
$676$	159.073	6.11818
$677$	−23.4995	−0.903160	−0.451580	−	0.892231i	$-0.649139\pi$
$677$	−23.4995	−0.903160	−0.451580	+	0.892231i	$0.649139\pi$
$678$	35.7776	1.37403
$679$	0	0
$680$	−12.1241	−0.464937
$681$	11.0661	0.424055
$682$	−3.02790	−0.115944
$683$	−26.4226	−1.01103	−0.505517	−	0.862817i	$-0.668698\pi$
$683$	−26.4226	−1.01103	−0.505517	+	0.862817i	$0.668698\pi$
$684$	−11.0866	−0.423906
$685$	19.4911	0.744715
$686$	0	0
$687$	2.86577	0.109336
$688$	17.2236	0.656642
$689$	−63.6601	−2.42526
$690$	−11.7131	−0.445911
$691$	−29.0351	−1.10455	−0.552274	−	0.833663i	$-0.686240\pi$
$691$	−29.0351	−1.10455	−0.552274	+	0.833663i	$0.686240\pi$
$692$	10.6139	0.403482
$693$	0	0
$694$	−8.71066	−0.330652
$695$	−2.32171	−0.0880673
$696$	−4.26834	−0.161791
$697$	15.4462	0.585068
$698$	−39.1836	−1.48312
$699$	−14.6048	−0.552405
$700$	0	0
$701$	14.9866	0.566037	0.283019	−	0.959114i	$-0.408664\pi$
$701$	14.9866	0.566037	0.283019	+	0.959114i	$0.408664\pi$
$702$	17.7581	0.670235
$703$	−23.3241	−0.879687
$704$	−5.04643	−0.190195
$705$	8.59523	0.323715
$706$	87.8108	3.30480
$707$	0	0
$708$	−22.4793	−0.844825
$709$	−4.29492	−0.161299	−0.0806496	−	0.996743i	$-0.525699\pi$
$709$	−4.29492	−0.161299	−0.0806496	+	0.996743i	$0.525699\pi$
$710$	16.7552	0.628812
$711$	−6.95896	−0.260981
$712$	34.7477	1.30222
$713$	6.47831	0.242614
$714$	0	0
$715$	−6.27521	−0.234680
$716$	103.390	3.86385
$717$	18.4800	0.690148
$718$	−57.8828	−2.16017
$719$	−26.0471	−0.971395	−0.485697	−	0.874127i	$-0.661434\pi$
$719$	−26.0471	−0.971395	−0.485697	+	0.874127i	$0.661434\pi$
$720$	4.69858	0.175106
$721$	0	0
$722$	30.1153	1.12078
$723$	−25.9433	−0.964841
$724$	−54.0257	−2.00785
$725$	−3.26570	−0.121285
$726$	−2.49291	−0.0925206
$727$	−39.2855	−1.45702	−0.728510	−	0.685035i	$-0.759787\pi$
$727$	−39.2855	−1.45702	−0.728510	+	0.685035i	$0.759787\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−28.0583	−1.03849
$731$	8.05013	0.297745
$732$	38.2842	1.41502
$733$	−8.55811	−0.316101	−0.158050	−	0.987431i	$-0.550521\pi$
$733$	−8.55811	−0.316101	−0.158050	+	0.987431i	$0.550521\pi$
$734$	49.2368	1.81736
$735$	0	0
$736$	−12.0262	−0.443291
$737$	11.2704	0.415151
$738$	−15.4462	−0.568584
$739$	−12.2262	−0.449747	−0.224874	−	0.974388i	$-0.572197\pi$
$739$	−12.2262	−0.449747	−0.224874	+	0.974388i	$0.572197\pi$
$740$	32.9201	1.21017
$741$	18.7383	0.688369
$742$	0	0
$743$	−24.0257	−0.881416	−0.440708	−	0.897650i	$-0.645273\pi$
$743$	−24.0257	−0.881416	−0.440708	+	0.897650i	$0.645273\pi$
$744$	−6.70560	−0.245839
$745$	0.676662	0.0247910
$746$	62.2370	2.27866
$747$	1.20524	0.0440974
$748$	10.5066	0.384160
$749$	0	0
$750$	20.2565	0.739662
$751$	7.51318	0.274160	0.137080	−	0.990560i	$-0.456228\pi$
$751$	7.51318	0.274160	0.137080	+	0.990560i	$0.456228\pi$
$752$	52.0409	1.89774
$753$	−26.4331	−0.963276
$754$	13.7294	0.499995
$755$	−12.3641	−0.449976
$756$	0	0
$757$	8.97814	0.326316	0.163158	−	0.986600i	$-0.447832\pi$
$757$	8.97814	0.326316	0.163158	+	0.986600i	$0.447832\pi$
$758$	40.6994	1.47827
$759$	5.33368	0.193600
$760$	12.7933	0.464063
$761$	−2.79331	−0.101257	−0.0506287	−	0.998718i	$-0.516123\pi$
$761$	−2.79331	−0.101257	−0.0506287	+	0.998718i	$0.516123\pi$
$762$	−22.2362	−0.805532
$763$	0	0
$764$	93.0523	3.36652
$765$	2.19607	0.0793991
$766$	30.1840	1.09059
$767$	37.9941	1.37189
$768$	−32.5106	−1.17312
$769$	5.83905	0.210561	0.105281	−	0.994443i	$-0.466426\pi$
$769$	5.83905	0.210561	0.105281	+	0.994443i	$0.466426\pi$
$770$	0	0
$771$	4.63900	0.167069
$772$	77.7395	2.79791
$773$	−5.13156	−0.184570	−0.0922848	−	0.995733i	$-0.529417\pi$
$773$	−5.13156	−0.184570	−0.0922848	+	0.995733i	$0.529417\pi$
$774$	−8.05013	−0.289356
$775$	−5.13045	−0.184291
$776$	7.16944	0.257368
$777$	0	0
$778$	45.3704	1.62661
$779$	−16.2989	−0.583968
$780$	−26.4475	−0.946974
$781$	−7.62963	−0.273010
$782$	−33.1467	−1.18532
$783$	0.773136	0.0276296
$784$	0	0
$785$	−4.96675	−0.177271
$786$	30.8800	1.10145
$787$	−10.8644	−0.387273	−0.193636	−	0.981073i	$-0.562028\pi$
$787$	−10.8644	−0.387273	−0.193636	+	0.981073i	$0.562028\pi$
$788$	−19.2905	−0.687196
$789$	19.6266	0.698725
$790$	15.2824	0.543722
$791$	0	0
$792$	−5.52081	−0.196173
$793$	−64.7071	−2.29782
$794$	−0.144454	−0.00512647
$795$	7.87259	0.279212
$796$	9.23445	0.327306
$797$	−15.9000	−0.563208	−0.281604	−	0.959531i	$-0.590866\pi$
$797$	−15.9000	−0.563208	−0.281604	+	0.959531i	$0.590866\pi$
$798$	0	0
$799$	24.3234	0.860501
$800$	9.52405	0.336726
$801$	−6.29395	−0.222386
$802$	42.0927	1.48634
$803$	12.7766	0.450877
$804$	47.5003	1.67521
$805$	0	0
$806$	21.5690	0.759736
$807$	22.5633	0.794266
$808$	−54.6241	−1.92167
$809$	−39.4022	−1.38531	−0.692653	−	0.721271i	$-0.743558\pi$
$809$	−39.4022	−1.38531	−0.692653	+	0.721271i	$0.743558\pi$
$810$	−2.19607	−0.0771620
$811$	−14.2370	−0.499928	−0.249964	−	0.968255i	$-0.580419\pi$
$811$	−14.2370	−0.499928	−0.249964	+	0.968255i	$0.580419\pi$
$812$	0	0
$813$	17.1535	0.601601
$814$	−22.1040	−0.774745
$815$	9.60179	0.336336
$816$	13.2964	0.465466
$817$	−8.49449	−0.297185
$818$	−2.70820	−0.0946901
$819$	0	0
$820$	23.0045	0.803352
$821$	−31.2643	−1.09113	−0.545565	−	0.838068i	$-0.683685\pi$
$821$	−31.2643	−1.09113	−0.545565	+	0.838068i	$0.683685\pi$
$822$	−55.1572	−1.92383
$823$	34.7684	1.21195	0.605975	−	0.795483i	$-0.292783\pi$
$823$	34.7684	1.21195	0.605975	+	0.795483i	$0.292783\pi$
$824$	61.7460	2.15103
$825$	−4.22397	−0.147060
$826$	0	0
$827$	8.62027	0.299756	0.149878	−	0.988704i	$-0.452112\pi$
$827$	8.62027	0.299756	0.149878	+	0.988704i	$0.452112\pi$
$828$	22.4793	0.781211
$829$	−4.55830	−0.158316	−0.0791582	−	0.996862i	$-0.525223\pi$
$829$	−4.55830	−0.158316	−0.0791582	+	0.996862i	$0.525223\pi$
$830$	−2.64679	−0.0918714
$831$	−26.1496	−0.907118
$832$	35.9479	1.24627
$833$	0	0
$834$	6.57014	0.227505
$835$	−8.08415	−0.279764
$836$	−11.0866	−0.383438
$837$	1.21460	0.0419828
$838$	46.6727	1.61228
$839$	−5.51585	−0.190428	−0.0952141	−	0.995457i	$-0.530354\pi$
$839$	−5.51585	−0.190428	−0.0952141	+	0.995457i	$0.530354\pi$
$840$	0	0
$841$	−28.4023	−0.979388
$842$	−26.5691	−0.915632
$843$	8.79972	0.303079
$844$	−42.0216	−1.44644
$845$	33.2490	1.14380
$846$	−24.3234	−0.836257
$847$	0	0
$848$	47.6656	1.63684
$849$	−13.7499	−0.471895
$850$	26.2503	0.900378
$851$	47.2924	1.62116
$852$	−32.1559	−1.10164
$853$	−41.9614	−1.43673	−0.718366	−	0.695666i	$-0.755110\pi$
$853$	−41.9614	−1.43673	−0.718366	+	0.695666i	$0.755110\pi$
$854$	0	0
$855$	−2.31729	−0.0792497
$856$	−40.1145	−1.37108
$857$	−9.11350	−0.311311	−0.155656	−	0.987811i	$-0.549749\pi$
$857$	−9.11350	−0.311311	−0.155656	+	0.987811i	$0.549749\pi$
$858$	17.7581	0.606251
$859$	−42.2991	−1.44323	−0.721614	−	0.692296i	$-0.756599\pi$
$859$	−42.2991	−1.44323	−0.721614	+	0.692296i	$0.756599\pi$
$860$	11.9893	0.408830
$861$	0	0
$862$	−49.2325	−1.67686
$863$	−13.7735	−0.468855	−0.234427	−	0.972134i	$-0.575322\pi$
$863$	−13.7735	−0.468855	−0.234427	+	0.972134i	$0.575322\pi$
$864$	−2.25476	−0.0767086
$865$	2.21850	0.0754313
$866$	−86.4607	−2.93805
$867$	−10.7854	−0.366291
$868$	0	0
$869$	−6.95896	−0.236066
$870$	−1.69786	−0.0575629
$871$	−80.2839	−2.72032
$872$	−2.51790	−0.0852667
$873$	−1.29862	−0.0439516
$874$	34.9764	1.18309
$875$	0	0
$876$	53.8483	1.81937
$877$	44.1197	1.48982	0.744908	−	0.667167i	$-0.232493\pi$
$877$	44.1197	1.48982	0.744908	+	0.667167i	$0.232493\pi$
$878$	−13.9362	−0.470324
$879$	−17.4266	−0.587786
$880$	4.69858	0.158389
$881$	57.8355	1.94853	0.974263	−	0.225414i	$-0.0723734\pi$
$881$	57.8355	1.94853	0.974263	+	0.225414i	$0.0723734\pi$
$882$	0	0
$883$	−11.2117	−0.377303	−0.188651	−	0.982044i	$-0.560412\pi$
$883$	−11.2117	−0.377303	−0.188651	+	0.982044i	$0.560412\pi$
$884$	−74.8432	−2.51725
$885$	−4.69858	−0.157941
$886$	−27.1890	−0.913433
$887$	22.1324	0.743134	0.371567	−	0.928406i	$-0.378821\pi$
$887$	22.1324	0.743134	0.371567	+	0.928406i	$0.378821\pi$
$888$	−48.9516	−1.64271
$889$	0	0
$890$	13.8219	0.463313
$891$	1.00000	0.0335013
$892$	64.0681	2.14516
$893$	−25.6661	−0.858882
$894$	−1.91487	−0.0640428
$895$	21.6103	0.722351
$896$	0	0
$897$	−37.9941	−1.26859
$898$	−24.8584	−0.829536
$899$	0.939054	0.0313192
$900$	−17.8024	−0.593412
$901$	22.2785	0.742203
$902$	−15.4462	−0.514304
$903$	0	0
$904$	79.2333	2.63526
$905$	−11.2923	−0.375369
$906$	34.9889	1.16243
$907$	−26.0093	−0.863624	−0.431812	−	0.901964i	$-0.642126\pi$
$907$	−26.0093	−0.863624	−0.431812	+	0.901964i	$0.642126\pi$
$908$	46.6394	1.54778
$909$	9.89422	0.328171
$910$	0	0
$911$	32.6978	1.08333	0.541664	−	0.840595i	$-0.317795\pi$
$911$	32.6978	1.08333	0.541664	+	0.840595i	$0.317795\pi$
$912$	−14.0303	−0.464591
$913$	1.20524	0.0398876
$914$	14.3792	0.475621
$915$	8.00207	0.264540
$916$	12.0781	0.399071
$917$	0	0
$918$	−6.21460	−0.205112
$919$	−0.123800	−0.00408377	−0.00204189	−	0.999998i	$-0.500650\pi$
$919$	−0.123800	−0.00408377	−0.00204189	+	0.999998i	$0.500650\pi$
$920$	−25.9399	−0.855215
$921$	0.804963	0.0265244
$922$	−64.7960	−2.13394
$923$	54.3491	1.78892
$924$	0	0
$925$	−37.4529	−1.23144
$926$	−15.2052	−0.499673
$927$	−11.1842	−0.367339
$928$	−1.74324	−0.0572246
$929$	6.93559	0.227549	0.113775	−	0.993507i	$-0.463706\pi$
$929$	6.93559	0.227549	0.113775	+	0.993507i	$0.463706\pi$
$930$	−2.66736	−0.0874660
$931$	0	0
$932$	−61.5536	−2.01625
$933$	10.8250	0.354395
$934$	−59.4658	−1.94578
$935$	2.19607	0.0718192
$936$	39.3271	1.28545
$937$	29.6703	0.969288	0.484644	−	0.874712i	$-0.338949\pi$
$937$	29.6703	0.969288	0.484644	+	0.874712i	$0.338949\pi$
$938$	0	0
$939$	−24.7315	−0.807082
$940$	36.2255	1.18155
$941$	36.2313	1.18111	0.590554	−	0.806998i	$-0.298909\pi$
$941$	36.2313	1.18111	0.590554	+	0.806998i	$0.298909\pi$
$942$	14.0553	0.457946
$943$	33.0478	1.07619
$944$	−28.4481	−0.925907
$945$	0	0
$946$	−8.05013	−0.261732
$947$	18.1200	0.588820	0.294410	−	0.955679i	$-0.404877\pi$
$947$	18.1200	0.588820	0.294410	+	0.955679i	$0.404877\pi$
$948$	−29.3292	−0.952569
$949$	−91.0132	−2.95441
$950$	−27.6993	−0.898684
$951$	−12.2819	−0.398268
$952$	0	0
$953$	−58.5262	−1.89585	−0.947924	−	0.318496i	$-0.896822\pi$
$953$	−58.5262	−1.89585	−0.947924	+	0.318496i	$0.896822\pi$
$954$	−22.2785	−0.721292
$955$	19.4496	0.629373
$956$	77.8859	2.51901
$957$	0.773136	0.0249919
$958$	−23.1065	−0.746538
$959$	0	0
$960$	−4.44553	−0.143479
$961$	−29.5247	−0.952411
$962$	157.456	5.07660
$963$	7.26605	0.234145
$964$	−109.341	−3.52163
$965$	16.2489	0.523071
$966$	0	0
$967$	50.1143	1.61157	0.805783	−	0.592210i	$-0.201745\pi$
$967$	50.1143	1.61157	0.805783	+	0.592210i	$0.201745\pi$
$968$	−5.52081	−0.177446
$969$	−6.55765	−0.210662
$970$	2.85186	0.0915678
$971$	−6.63946	−0.213070	−0.106535	−	0.994309i	$-0.533976\pi$
$971$	−6.63946	−0.213070	−0.106535	+	0.994309i	$0.533976\pi$
$972$	4.21460	0.135183
$973$	0	0
$974$	−95.7584	−3.06830
$975$	30.0891	0.963624
$976$	48.4495	1.55083
$977$	−28.6357	−0.916136	−0.458068	−	0.888917i	$-0.651458\pi$
$977$	−28.6357	−0.916136	−0.458068	+	0.888917i	$0.651458\pi$
$978$	−27.1719	−0.868861
$979$	−6.29395	−0.201155
$980$	0	0
$981$	0.456074	0.0145613
$982$	30.3687	0.969105
$983$	−3.66881	−0.117017	−0.0585084	−	0.998287i	$-0.518634\pi$
$983$	−3.66881	−0.117017	−0.0585084	+	0.998287i	$0.518634\pi$
$984$	−34.2073	−1.09049
$985$	−4.03206	−0.128472
$986$	−4.80473	−0.153014
$987$	0	0
$988$	78.9745	2.51252
$989$	17.2236	0.547677
$990$	−2.19607	−0.0697957
$991$	−33.0334	−1.04934	−0.524670	−	0.851305i	$-0.675811\pi$
$991$	−33.0334	−1.04934	−0.524670	+	0.851305i	$0.675811\pi$
$992$	−2.73864	−0.0869520
$993$	−13.1987	−0.418849
$994$	0	0
$995$	1.93016	0.0611902
$996$	5.07960	0.160953
$997$	−12.3774	−0.391996	−0.195998	−	0.980604i	$-0.562795\pi$
$997$	−12.3774	−0.391996	−0.195998	+	0.980604i	$0.562795\pi$
$998$	−17.9854	−0.569317
$999$	8.86675	0.280531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.bb.1.1		5
3.2	odd	2		4851.2.a.bz.1.5		5
7.3	odd	6		231.2.i.f.100.5	yes	10
7.5	odd	6		231.2.i.f.67.5	✓	10
7.6	odd	2		1617.2.a.ba.1.1		5
21.5	even	6		693.2.i.j.298.1		10
21.17	even	6		693.2.i.j.100.1		10
21.20	even	2		4851.2.a.ca.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.5	✓	10	7.5	odd	6
231.2.i.f.100.5	yes	10	7.3	odd	6
693.2.i.j.100.1		10	21.17	even	6
693.2.i.j.298.1		10	21.5	even	6
1617.2.a.ba.1.1		5	7.6	odd	2
1617.2.a.bb.1.1		5	1.1	even	1	trivial
4851.2.a.bz.1.5		5	3.2	odd	2
4851.2.a.ca.1.5		5	21.20	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49291 q^{2} +1.00000 q^{3} +4.21460 q^{4} +0.880926 q^{5} -2.49291 q^{6} -5.52081 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.49291 q^{2} +1.00000 q^{3} +4.21460 q^{4} +0.880926 q^{5} -2.49291 q^{6} -5.52081 q^{8} +1.00000 q^{9} -2.19607 q^{10} +1.00000 q^{11} +4.21460 q^{12} -7.12343 q^{13} +0.880926 q^{15} +5.33368 q^{16} +2.49291 q^{17} -2.49291 q^{18} -2.63052 q^{19} +3.71275 q^{20} -2.49291 q^{22} +5.33368 q^{23} -5.52081 q^{24} -4.22397 q^{25} +17.7581 q^{26} +1.00000 q^{27} +0.773136 q^{29} -2.19607 q^{30} +1.21460 q^{31} -2.25476 q^{32} +1.00000 q^{33} -6.21460 q^{34} +4.21460 q^{36} +8.86675 q^{37} +6.55765 q^{38} -7.12343 q^{39} -4.86343 q^{40} +6.19607 q^{41} +3.22921 q^{43} +4.21460 q^{44} +0.880926 q^{45} -13.2964 q^{46} +9.75704 q^{47} +5.33368 q^{48} +10.5300 q^{50} +2.49291 q^{51} -30.0224 q^{52} +8.93672 q^{53} -2.49291 q^{54} +0.880926 q^{55} -2.63052 q^{57} -1.92736 q^{58} -5.33368 q^{59} +3.71275 q^{60} +9.08370 q^{61} -3.02790 q^{62} -5.04643 q^{64} -6.27521 q^{65} -2.49291 q^{66} +11.2704 q^{67} +10.5066 q^{68} +5.33368 q^{69} -7.62963 q^{71} -5.52081 q^{72} +12.7766 q^{73} -22.1040 q^{74} -4.22397 q^{75} -11.0866 q^{76} +17.7581 q^{78} -6.95896 q^{79} +4.69858 q^{80} +1.00000 q^{81} -15.4462 q^{82} +1.20524 q^{83} +2.19607 q^{85} -8.05013 q^{86} +0.773136 q^{87} -5.52081 q^{88} -6.29395 q^{89} -2.19607 q^{90} +22.4793 q^{92} +1.21460 q^{93} -24.3234 q^{94} -2.31729 q^{95} -2.25476 q^{96} -1.29862 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + 5 q^{3} + 10 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 + 5 * q^3 + 10 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^8 + 5 * q^9	\( 5 q + 2 q^{2} + 5 q^{3} + 10 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{8} + 5 q^{9} - 2 q^{10} + 5 q^{11} + 10 q^{12} - 5 q^{13} + 4 q^{15} + 16 q^{16} - 2 q^{17} + 2 q^{18} + 3 q^{19} + 8 q^{20} + 2 q^{22} + 16 q^{23} + 6 q^{24} + 7 q^{25} + 10 q^{26} + 5 q^{27} - 2 q^{30} - 5 q^{31} + 4 q^{32} + 5 q^{33} - 20 q^{34} + 10 q^{36} + 15 q^{37} - 6 q^{38} - 5 q^{39} + 6 q^{40} + 22 q^{41} + 3 q^{43} + 10 q^{44} + 4 q^{45} + 16 q^{46} + 2 q^{47} + 16 q^{48} + 34 q^{50} - 2 q^{51} - 40 q^{52} + 6 q^{53} + 2 q^{54} + 4 q^{55} + 3 q^{57} + 12 q^{58} - 16 q^{59} + 8 q^{60} - 12 q^{61} + 4 q^{62} - 4 q^{64} - 28 q^{65} + 2 q^{66} + 7 q^{67} - 10 q^{68} + 16 q^{69} + 24 q^{71} + 6 q^{72} - 17 q^{73} - 36 q^{74} + 7 q^{75} - 30 q^{76} + 10 q^{78} + 7 q^{79} - 16 q^{80} + 5 q^{81} - 8 q^{82} + 12 q^{83} + 2 q^{85} - 18 q^{86} + 6 q^{88} + 6 q^{89} - 2 q^{90} + 68 q^{92} - 5 q^{93} - 82 q^{94} - 18 q^{95} + 4 q^{96} + 14 q^{97} + 5 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 5 * q^3 + 10 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^8 + 5 * q^9 - 2 * q^10 + 5 * q^11 + 10 * q^12 - 5 * q^13 + 4 * q^15 + 16 * q^16 - 2 * q^17 + 2 * q^18 + 3 * q^19 + 8 * q^20 + 2 * q^22 + 16 * q^23 + 6 * q^24 + 7 * q^25 + 10 * q^26 + 5 * q^27 - 2 * q^30 - 5 * q^31 + 4 * q^32 + 5 * q^33 - 20 * q^34 + 10 * q^36 + 15 * q^37 - 6 * q^38 - 5 * q^39 + 6 * q^40 + 22 * q^41 + 3 * q^43 + 10 * q^44 + 4 * q^45 + 16 * q^46 + 2 * q^47 + 16 * q^48 + 34 * q^50 - 2 * q^51 - 40 * q^52 + 6 * q^53 + 2 * q^54 + 4 * q^55 + 3 * q^57 + 12 * q^58 - 16 * q^59 + 8 * q^60 - 12 * q^61 + 4 * q^62 - 4 * q^64 - 28 * q^65 + 2 * q^66 + 7 * q^67 - 10 * q^68 + 16 * q^69 + 24 * q^71 + 6 * q^72 - 17 * q^73 - 36 * q^74 + 7 * q^75 - 30 * q^76 + 10 * q^78 + 7 * q^79 - 16 * q^80 + 5 * q^81 - 8 * q^82 + 12 * q^83 + 2 * q^85 - 18 * q^86 + 6 * q^88 + 6 * q^89 - 2 * q^90 + 68 * q^92 - 5 * q^93 - 82 * q^94 - 18 * q^95 + 4 * q^96 + 14 * q^97 + 5 * q^99

Introduction

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