LMFDB - Embedded newform 1617.2.a.bb.1.5

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			1.5
Root			$2.59450$ 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)

$f(q)$	$=$	$q+2.59450 q^{2} +1.00000 q^{3} +4.73141 q^{4} -2.19202 q^{5} +2.59450 q^{6} +7.08664 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.59450 q^{2} +1.00000 q^{3} +4.73141 q^{4} -2.19202 q^{5} +2.59450 q^{6} +7.08664 q^{8} +1.00000 q^{9} -5.68719 q^{10} +1.00000 q^{11} +4.73141 q^{12} +2.95275 q^{13} -2.19202 q^{15} +8.92343 q^{16} -2.59450 q^{17} +2.59450 q^{18} +2.35825 q^{19} -10.3713 q^{20} +2.59450 q^{22} +8.92343 q^{23} +7.08664 q^{24} -0.195048 q^{25} +7.66090 q^{26} +1.00000 q^{27} +4.48640 q^{29} -5.68719 q^{30} +1.73141 q^{31} +8.97854 q^{32} +1.00000 q^{33} -6.73141 q^{34} +4.73141 q^{36} -4.38101 q^{37} +6.11848 q^{38} +2.95275 q^{39} -15.5341 q^{40} +9.68719 q^{41} -10.3132 q^{43} +4.73141 q^{44} -2.19202 q^{45} +23.1518 q^{46} -11.1094 q^{47} +8.92343 q^{48} -0.506050 q^{50} -2.59450 q^{51} +13.9707 q^{52} -9.17630 q^{53} +2.59450 q^{54} -2.19202 q^{55} +2.35825 q^{57} +11.6399 q^{58} -8.92343 q^{59} -10.3713 q^{60} -13.4764 q^{61} +4.49214 q^{62} +5.44792 q^{64} -6.47249 q^{65} +2.59450 q^{66} -3.25287 q^{67} -12.2756 q^{68} +8.92343 q^{69} +0.994758 q^{71} +7.08664 q^{72} -0.294879 q^{73} -11.3665 q^{74} -0.195048 q^{75} +11.1579 q^{76} +7.66090 q^{78} -15.0734 q^{79} -19.5603 q^{80} +1.00000 q^{81} +25.1334 q^{82} +6.26778 q^{83} +5.68719 q^{85} -26.7576 q^{86} +4.48640 q^{87} +7.08664 q^{88} +2.60024 q^{89} -5.68719 q^{90} +42.2204 q^{92} +1.73141 q^{93} -28.8233 q^{94} -5.16934 q^{95} +8.97854 q^{96} -7.51704 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.59450	1.83459	0.917293	−	0.398213i	$-0.130369\pi$
$2$	2.59450	1.83459	0.917293	+	0.398213i	$0.130369\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.73141	2.36571
$5$	−2.19202	−0.980301	−0.490151	−	0.871638i	$-0.663058\pi$
$5$	−2.19202	−0.980301	−0.490151	+	0.871638i	$0.663058\pi$
$6$	2.59450	1.05920
$7$	0	0
$7$	0	0
$8$	7.08664	2.50550
$9$	1.00000	0.333333
$10$	−5.68719	−1.79845
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.73141	1.36584
$13$	2.95275	0.818945	0.409473	−	0.912322i	$-0.365713\pi$
$13$	2.95275	0.818945	0.409473	+	0.912322i	$0.365713\pi$
$14$	0	0
$15$	−2.19202	−0.565977
$16$	8.92343	2.23086
$17$	−2.59450	−0.629258	−0.314629	−	0.949215i	$-0.601880\pi$
$17$	−2.59450	−0.629258	−0.314629	+	0.949215i	$0.601880\pi$
$18$	2.59450	0.611529
$19$	2.35825	0.541020	0.270510	−	0.962717i	$-0.412808\pi$
$19$	2.35825	0.541020	0.270510	+	0.962717i	$0.412808\pi$
$20$	−10.3713	−2.31910
$21$	0	0
$22$	2.59450	0.553148
$23$	8.92343	1.86066	0.930332	−	0.366718i	$-0.119519\pi$
$23$	8.92343	1.86066	0.930332	+	0.366718i	$0.119519\pi$
$24$	7.08664	1.44655
$25$	−0.195048	−0.0390095
$26$	7.66090	1.50243
$27$	1.00000	0.192450
$28$	0	0
$29$	4.48640	0.833103	0.416551	−	0.909112i	$-0.363239\pi$
$29$	4.48640	0.833103	0.416551	+	0.909112i	$0.363239\pi$
$30$	−5.68719	−1.03833
$31$	1.73141	0.310971	0.155485	−	0.987838i	$-0.450306\pi$
$31$	1.73141	0.310971	0.155485	+	0.987838i	$0.450306\pi$
$32$	8.97854	1.58720
$33$	1.00000	0.174078
$34$	−6.73141	−1.15443
$35$	0	0
$36$	4.73141	0.788569
$37$	−4.38101	−0.720234	−0.360117	−	0.932907i	$-0.617263\pi$
$37$	−4.38101	−0.720234	−0.360117	+	0.932907i	$0.617263\pi$
$38$	6.11848	0.992548
$39$	2.95275	0.472818
$40$	−15.5341	−2.45615
$41$	9.68719	1.51288	0.756442	−	0.654060i	$-0.226936\pi$
$41$	9.68719	1.51288	0.756442	+	0.654060i	$0.226936\pi$
$42$	0	0
$43$	−10.3132	−1.57275	−0.786375	−	0.617749i	$-0.788045\pi$
$43$	−10.3132	−1.57275	−0.786375	+	0.617749i	$0.788045\pi$
$44$	4.73141	0.713287
$45$	−2.19202	−0.326767
$46$	23.1518	3.41355
$47$	−11.1094	−1.62047	−0.810236	−	0.586104i	$-0.800661\pi$
$47$	−11.1094	−1.62047	−0.810236	+	0.586104i	$0.800661\pi$
$48$	8.92343	1.28799
$49$	0	0
$50$	−0.506050	−0.0715663
$51$	−2.59450	−0.363302
$52$	13.9707	1.93738
$53$	−9.17630	−1.26046	−0.630231	−	0.776408i	$-0.717040\pi$
$53$	−9.17630	−1.26046	−0.630231	+	0.776408i	$0.717040\pi$
$54$	2.59450	0.353066
$55$	−2.19202	−0.295572
$56$	0	0
$57$	2.35825	0.312358
$58$	11.6399	1.52840
$59$	−8.92343	−1.16173	−0.580866	−	0.813999i	$-0.697286\pi$
$59$	−8.92343	−1.16173	−0.580866	+	0.813999i	$0.697286\pi$
$60$	−10.3713	−1.33894
$61$	−13.4764	−1.72548	−0.862740	−	0.505649i	$-0.831253\pi$
$61$	−13.4764	−1.72548	−0.862740	+	0.505649i	$0.831253\pi$
$62$	4.49214	0.570502
$63$	0	0
$64$	5.44792	0.680990
$65$	−6.47249	−0.802813
$66$	2.59450	0.319360
$67$	−3.25287	−0.397401	−0.198701	−	0.980060i	$-0.563672\pi$
$67$	−3.25287	−0.397401	−0.198701	+	0.980060i	$0.563672\pi$
$68$	−12.2756	−1.48864
$69$	8.92343	1.07425
$70$	0	0
$71$	0.994758	0.118056	0.0590280	−	0.998256i	$-0.481200\pi$
$71$	0.994758	0.118056	0.0590280	+	0.998256i	$0.481200\pi$
$72$	7.08664	0.835168
$73$	−0.294879	−0.0345130	−0.0172565	−	0.999851i	$-0.505493\pi$
$73$	−0.294879	−0.0345130	−0.0172565	+	0.999851i	$0.505493\pi$
$74$	−11.3665	−1.32133
$75$	−0.195048	−0.0225222
$76$	11.1579	1.27990
$77$	0	0
$78$	7.66090	0.867426
$79$	−15.0734	−1.69589	−0.847947	−	0.530080i	$-0.822162\pi$
$79$	−15.0734	−1.69589	−0.847947	+	0.530080i	$0.822162\pi$
$80$	−19.5603	−2.18691
$81$	1.00000	0.111111
$82$	25.1334	2.77552
$83$	6.26778	0.687978	0.343989	−	0.938974i	$-0.388222\pi$
$83$	6.26778	0.687978	0.343989	+	0.938974i	$0.388222\pi$
$84$	0	0
$85$	5.68719	0.616862
$86$	−26.7576	−2.88535
$87$	4.48640	0.480992
$88$	7.08664	0.755438
$89$	2.60024	0.275625	0.137813	−	0.990458i	$-0.455993\pi$
$89$	2.60024	0.275625	0.137813	+	0.990458i	$0.455993\pi$
$90$	−5.68719	−0.599482
$91$	0	0
$92$	42.2204	4.40178
$93$	1.73141	0.179539
$94$	−28.8233	−2.97290
$95$	−5.16934	−0.530363
$96$	8.97854	0.916368
$97$	−7.51704	−0.763239	−0.381620	−	0.924319i	$-0.624634\pi$
$97$	−7.51704	−0.763239	−0.381620	+	0.924319i	$0.624634\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−0.922850	−0.0922850
$101$	13.3605	1.32942	0.664708	−	0.747103i	$-0.268556\pi$
$101$	13.3605	1.32942	0.664708	+	0.747103i	$0.268556\pi$
$102$	−6.73141	−0.666509
$103$	5.32863	0.525045	0.262523	−	0.964926i	$-0.415446\pi$
$103$	5.32863	0.525045	0.262523	+	0.964926i	$0.415446\pi$
$104$	20.9251	2.05187
$105$	0	0
$106$	−23.8079	−2.31243
$107$	5.89190	0.569591	0.284796	−	0.958588i	$-0.408074\pi$
$107$	5.89190	0.569591	0.284796	+	0.958588i	$0.408074\pi$
$108$	4.73141	0.455280
$109$	−16.7996	−1.60911	−0.804556	−	0.593877i	$-0.797596\pi$
$109$	−16.7996	−1.60911	−0.804556	+	0.593877i	$0.797596\pi$
$110$	−5.68719	−0.542252
$111$	−4.38101	−0.415827
$112$	0	0
$113$	12.9025	1.21376	0.606881	−	0.794793i	$-0.292420\pi$
$113$	12.9025	1.21376	0.606881	+	0.794793i	$0.292420\pi$
$114$	6.11848	0.573048
$115$	−19.5603	−1.82401
$116$	21.2270	1.97088
$117$	2.95275	0.272982
$118$	−23.1518	−2.13130
$119$	0	0
$120$	−15.5341	−1.41806
$121$	1.00000	0.0909091
$122$	−34.9645	−3.16554
$123$	9.68719	0.873464
$124$	8.19202	0.735665
$125$	11.3876	1.01854
$126$	0	0
$127$	14.6951	1.30398	0.651992	−	0.758226i	$-0.273934\pi$
$127$	14.6951	1.30398	0.651992	+	0.758226i	$0.273934\pi$
$128$	−3.82247	−0.337862
$129$	−10.3132	−0.908028
$130$	−16.7928	−1.47283
$131$	−10.7660	−0.940627	−0.470314	−	0.882499i	$-0.655859\pi$
$131$	−10.7660	−0.940627	−0.470314	+	0.882499i	$0.655859\pi$
$132$	4.73141	0.411817
$133$	0	0
$134$	−8.43956	−0.729067
$135$	−2.19202	−0.188659
$136$	−18.3863	−1.57661
$137$	2.61235	0.223188	0.111594	−	0.993754i	$-0.464404\pi$
$137$	2.61235	0.223188	0.111594	+	0.993754i	$0.464404\pi$
$138$	23.1518	1.97081
$139$	−6.25015	−0.530131	−0.265066	−	0.964230i	$-0.585394\pi$
$139$	−6.25015	−0.530131	−0.265066	+	0.964230i	$0.585394\pi$
$140$	0	0
$141$	−11.1094	−0.935580
$142$	2.58090	0.216584
$143$	2.95275	0.246921
$144$	8.92343	0.743619
$145$	−9.83427	−0.816692
$146$	−0.765062	−0.0633170
$147$	0	0
$148$	−20.7284	−1.70386
$149$	−4.12201	−0.337688	−0.168844	−	0.985643i	$-0.554003\pi$
$149$	−4.12201	−0.337688	−0.168844	+	0.985643i	$0.554003\pi$
$150$	−0.506050	−0.0413188
$151$	12.4353	1.01197	0.505985	−	0.862542i	$-0.331129\pi$
$151$	12.4353	1.01197	0.505985	+	0.862542i	$0.331129\pi$
$152$	16.7121	1.35553
$153$	−2.59450	−0.209753
$154$	0	0
$155$	−3.79529	−0.304845
$156$	13.9707	1.11855
$157$	18.6933	1.49189	0.745945	−	0.666007i	$-0.231998\pi$
$157$	18.6933	1.49189	0.745945	+	0.666007i	$0.231998\pi$
$158$	−39.1080	−3.11126
$159$	−9.17630	−0.727728
$160$	−19.6811	−1.55593
$161$	0	0
$162$	2.59450	0.203843
$163$	−1.26475	−0.0990627	−0.0495314	−	0.998773i	$-0.515773\pi$
$163$	−1.26475	−0.0990627	−0.0495314	+	0.998773i	$0.515773\pi$
$164$	45.8341	3.57904
$165$	−2.19202	−0.170649
$166$	16.2617	1.26215
$167$	6.11021	0.472822	0.236411	−	0.971653i	$-0.424029\pi$
$167$	6.11021	0.472822	0.236411	+	0.971653i	$0.424029\pi$
$168$	0	0
$169$	−4.28127	−0.329328
$170$	14.7554	1.13169
$171$	2.35825	0.180340
$172$	−48.7961	−3.72067
$173$	17.4649	1.32783	0.663917	−	0.747806i	$-0.268893\pi$
$173$	17.4649	1.32783	0.663917	+	0.747806i	$0.268893\pi$
$174$	11.6399	0.882421
$175$	0	0
$176$	8.92343	0.672629
$177$	−8.92343	−0.670726
$178$	6.74632	0.505658
$179$	0.422545	0.0315825	0.0157912	−	0.999875i	$-0.494973\pi$
$179$	0.422545	0.0315825	0.0157912	+	0.999875i	$0.494973\pi$
$180$	−10.3713	−0.773035
$181$	−2.40197	−0.178537	−0.0892686	−	0.996008i	$-0.528453\pi$
$181$	−2.40197	−0.178537	−0.0892686	+	0.996008i	$0.528453\pi$
$182$	0	0
$183$	−13.4764	−0.996206
$184$	63.2371	4.66190
$185$	9.60327	0.706046
$186$	4.49214	0.329380
$187$	−2.59450	−0.189728
$188$	−52.5631	−3.83356
$189$	0	0
$190$	−13.4118	−0.972996
$191$	−8.69291	−0.628997	−0.314498	−	0.949258i	$-0.601836\pi$
$191$	−8.69291	−0.628997	−0.314498	+	0.949258i	$0.601836\pi$
$192$	5.44792	0.393170
$193$	−8.04513	−0.579101	−0.289551	−	0.957163i	$-0.593506\pi$
$193$	−8.04513	−0.579101	−0.289551	+	0.957163i	$0.593506\pi$
$194$	−19.5029	−1.40023
$195$	−6.47249	−0.463504
$196$	0	0
$197$	−4.79921	−0.341929	−0.170965	−	0.985277i	$-0.554688\pi$
$197$	−4.79921	−0.341929	−0.170965	+	0.985277i	$0.554688\pi$
$198$	2.59450	0.184383
$199$	−2.92122	−0.207080	−0.103540	−	0.994625i	$-0.533017\pi$
$199$	−2.92122	−0.207080	−0.103540	+	0.994625i	$0.533017\pi$
$200$	−1.38223	−0.0977385
$201$	−3.25287	−0.229440
$202$	34.6637	2.43893
$203$	0	0
$204$	−12.2756	−0.859466
$205$	−21.2345	−1.48308
$206$	13.8251	0.963240
$207$	8.92343	0.620221
$208$	26.3487	1.82695
$209$	2.35825	0.163124
$210$	0	0
$211$	−9.82721	−0.676533	−0.338266	−	0.941050i	$-0.609841\pi$
$211$	−9.82721	−0.676533	−0.338266	+	0.941050i	$0.609841\pi$
$212$	−43.4169	−2.98188
$213$	0.994758	0.0681597
$214$	15.2865	1.04496
$215$	22.6068	1.54177
$216$	7.08664	0.482185
$217$	0	0
$218$	−43.5865	−2.95205
$219$	−0.294879	−0.0199261
$220$	−10.3713	−0.699236
$221$	−7.66090	−0.515328
$222$	−11.3665	−0.762871
$223$	16.3127	1.09238	0.546190	−	0.837661i	$-0.316078\pi$
$223$	16.3127	1.09238	0.546190	+	0.837661i	$0.316078\pi$
$224$	0	0
$225$	−0.195048	−0.0130032
$226$	33.4754	2.22675
$227$	−22.6089	−1.50060	−0.750302	−	0.661095i	$-0.770092\pi$
$227$	−22.6089	−1.50060	−0.750302	+	0.661095i	$0.770092\pi$
$228$	11.1579	0.738948
$229$	3.70723	0.244981	0.122490	−	0.992470i	$-0.460912\pi$
$229$	3.70723	0.244981	0.122490	+	0.992470i	$0.460912\pi$
$230$	−50.7492	−3.34631
$231$	0	0
$232$	31.7935	2.08734
$233$	−7.69899	−0.504377	−0.252189	−	0.967678i	$-0.581150\pi$
$233$	−7.69899	−0.504377	−0.252189	+	0.967678i	$0.581150\pi$
$234$	7.66090	0.500809
$235$	24.3520	1.58855
$236$	−42.2204	−2.74832
$237$	−15.0734	−0.979125
$238$	0	0
$239$	−4.12986	−0.267139	−0.133569	−	0.991039i	$-0.542644\pi$
$239$	−4.12986	−0.267139	−0.133569	+	0.991039i	$0.542644\pi$
$240$	−19.5603	−1.26261
$241$	14.7560	0.950516	0.475258	−	0.879847i	$-0.342355\pi$
$241$	14.7560	0.950516	0.475258	+	0.879847i	$0.342355\pi$
$242$	2.59450	0.166781
$243$	1.00000	0.0641500
$244$	−63.7625	−4.08198
$245$	0	0
$246$	25.1334	1.60245
$247$	6.96333	0.443066
$248$	12.2699	0.779138
$249$	6.26778	0.397204
$250$	29.5452	1.86860
$251$	13.5521	0.855399	0.427700	−	0.903921i	$-0.359324\pi$
$251$	13.5521	0.855399	0.427700	+	0.903921i	$0.359324\pi$
$252$	0	0
$253$	8.92343	0.561011
$254$	38.1265	2.39227
$255$	5.68719	0.356146
$256$	−20.8132	−1.30083
$257$	−8.53112	−0.532157	−0.266078	−	0.963951i	$-0.585728\pi$
$257$	−8.53112	−0.532157	−0.266078	+	0.963951i	$0.585728\pi$
$258$	−26.7576	−1.66586
$259$	0	0
$260$	−30.6240	−1.89922
$261$	4.48640	0.277701
$262$	−27.9323	−1.72566
$263$	3.55290	0.219081	0.109540	−	0.993982i	$-0.465062\pi$
$263$	3.55290	0.219081	0.109540	+	0.993982i	$0.465062\pi$
$264$	7.08664	0.436152
$265$	20.1146	1.23563
$266$	0	0
$267$	2.60024	0.159132
$268$	−15.3907	−0.940135
$269$	−11.6234	−0.708692	−0.354346	−	0.935114i	$-0.615296\pi$
$269$	−11.6234	−0.708692	−0.354346	+	0.935114i	$0.615296\pi$
$270$	−5.68719	−0.346111
$271$	−9.87979	−0.600154	−0.300077	−	0.953915i	$-0.597012\pi$
$271$	−9.87979	−0.600154	−0.300077	+	0.953915i	$0.597012\pi$
$272$	−23.1518	−1.40378
$273$	0	0
$274$	6.77774	0.409458
$275$	−0.195048	−0.0117618
$276$	42.2204	2.54137
$277$	−1.28210	−0.0770339	−0.0385169	−	0.999258i	$-0.512263\pi$
$277$	−1.28210	−0.0770339	−0.0385169	+	0.999258i	$0.512263\pi$
$278$	−16.2160	−0.972571
$279$	1.73141	0.103657
$280$	0	0
$281$	25.5914	1.52665	0.763327	−	0.646013i	$-0.223565\pi$
$281$	25.5914	1.52665	0.763327	+	0.646013i	$0.223565\pi$
$282$	−28.8233	−1.71640
$283$	12.0079	0.713798	0.356899	−	0.934143i	$-0.383834\pi$
$283$	12.0079	0.713798	0.356899	+	0.934143i	$0.383834\pi$
$284$	4.70661	0.279286
$285$	−5.16934	−0.306205
$286$	7.66090	0.452998
$287$	0	0
$288$	8.97854	0.529065
$289$	−10.2686	−0.604035
$290$	−25.5150	−1.49829
$291$	−7.51704	−0.440657
$292$	−1.39519	−0.0816475
$293$	17.6972	1.03388	0.516939	−	0.856022i	$-0.327071\pi$
$293$	17.6972	1.03388	0.516939	+	0.856022i	$0.327071\pi$
$294$	0	0
$295$	19.5603	1.13885
$296$	−31.0466	−1.80455
$297$	1.00000	0.0580259
$298$	−10.6945	−0.619518
$299$	26.3487	1.52378
$300$	−0.922850	−0.0532808
$301$	0	0
$302$	32.2634	1.85655
$303$	13.3605	0.767539
$304$	21.0437	1.20694
$305$	29.5406	1.69149
$306$	−6.73141	−0.384809
$307$	8.08311	0.461327	0.230664	−	0.973034i	$-0.425910\pi$
$307$	8.08311	0.461327	0.230664	+	0.973034i	$0.425910\pi$
$308$	0	0
$309$	5.32863	0.303135
$310$	−9.84686	−0.559264
$311$	−11.5867	−0.657024	−0.328512	−	0.944500i	$-0.606547\pi$
$311$	−11.5867	−0.657024	−0.328512	+	0.944500i	$0.606547\pi$
$312$	20.9251	1.18465
$313$	−1.55592	−0.0879460	−0.0439730	−	0.999033i	$-0.514002\pi$
$313$	−1.55592	−0.0879460	−0.0439730	+	0.999033i	$0.514002\pi$
$314$	48.4998	2.73700
$315$	0	0
$316$	−71.3187	−4.01199
$317$	10.4991	0.589688	0.294844	−	0.955545i	$-0.404732\pi$
$317$	10.4991	0.589688	0.294844	+	0.955545i	$0.404732\pi$
$318$	−23.8079	−1.33508
$319$	4.48640	0.251190
$320$	−11.9419	−0.667575
$321$	5.89190	0.328854
$322$	0	0
$323$	−6.11848	−0.340441
$324$	4.73141	0.262856
$325$	−0.575927	−0.0319467
$326$	−3.28138	−0.181739
$327$	−16.7996	−0.929021
$328$	68.6496	3.79054
$329$	0	0
$330$	−5.68719	−0.313069
$331$	28.9811	1.59294	0.796471	−	0.604676i	$-0.206698\pi$
$331$	28.9811	1.59294	0.796471	+	0.604676i	$0.206698\pi$
$332$	29.6554	1.62755
$333$	−4.38101	−0.240078
$334$	15.8529	0.867433
$335$	7.13036	0.389573
$336$	0	0
$337$	13.9865	0.761893	0.380946	−	0.924597i	$-0.375598\pi$
$337$	13.9865	0.761893	0.380946	+	0.924597i	$0.375598\pi$
$338$	−11.1077	−0.604181
$339$	12.9025	0.700766
$340$	26.9084	1.45931
$341$	1.73141	0.0937612
$342$	6.11848	0.330849
$343$	0	0
$344$	−73.0860	−3.94053
$345$	−19.5603	−1.05309
$346$	45.3127	2.43603
$347$	−8.94087	−0.479971	−0.239986	−	0.970776i	$-0.577143\pi$
$347$	−8.94087	−0.479971	−0.239986	+	0.970776i	$0.577143\pi$
$348$	21.2270	1.13789
$349$	−0.353903	−0.0189440	−0.00947199	−	0.999955i	$-0.503015\pi$
$349$	−0.353903	−0.0189440	−0.00947199	+	0.999955i	$0.503015\pi$
$350$	0	0
$351$	2.95275	0.157606
$352$	8.97854	0.478558
$353$	−20.6041	−1.09664	−0.548322	−	0.836267i	$-0.684733\pi$
$353$	−20.6041	−1.09664	−0.548322	+	0.836267i	$0.684733\pi$
$354$	−23.1518	−1.23050
$355$	−2.18053	−0.115731
$356$	12.3028	0.652048
$357$	0	0
$358$	1.09629	0.0579408
$359$	10.5866	0.558742	0.279371	−	0.960183i	$-0.409874\pi$
$359$	10.5866	0.558742	0.279371	+	0.960183i	$0.409874\pi$
$360$	−15.5341	−0.818716
$361$	−13.4386	−0.707297
$362$	−6.23191	−0.327542
$363$	1.00000	0.0524864
$364$	0	0
$365$	0.646381	0.0338331
$366$	−34.9645	−1.82763
$367$	−10.8793	−0.567896	−0.283948	−	0.958840i	$-0.591644\pi$
$367$	−10.8793	−0.567896	−0.283948	+	0.958840i	$0.591644\pi$
$368$	79.6276	4.15088
$369$	9.68719	0.504295
$370$	24.9156	1.29530
$371$	0	0
$372$	8.19202	0.424736
$373$	14.7567	0.764072	0.382036	−	0.924147i	$-0.375223\pi$
$373$	14.7567	0.764072	0.382036	+	0.924147i	$0.375223\pi$
$374$	−6.73141	−0.348073
$375$	11.3876	0.588056
$376$	−78.7283	−4.06010
$377$	13.2472	0.682266
$378$	0	0
$379$	12.8452	0.659815	0.329908	−	0.944013i	$-0.392982\pi$
$379$	12.8452	0.659815	0.329908	+	0.944013i	$0.392982\pi$
$380$	−24.4583	−1.25468
$381$	14.6951	0.752855
$382$	−22.5537	−1.15395
$383$	−12.4554	−0.636440	−0.318220	−	0.948017i	$-0.603085\pi$
$383$	−12.4554	−0.636440	−0.318220	+	0.948017i	$0.603085\pi$
$384$	−3.82247	−0.195065
$385$	0	0
$386$	−20.8731	−1.06241
$387$	−10.3132	−0.524250
$388$	−35.5662	−1.80560
$389$	13.2108	0.669812	0.334906	−	0.942252i	$-0.391295\pi$
$389$	13.2108	0.669812	0.334906	+	0.942252i	$0.391295\pi$
$390$	−16.7928	−0.850339
$391$	−23.1518	−1.17084
$392$	0	0
$393$	−10.7660	−0.543071
$394$	−12.4515	−0.627299
$395$	33.0413	1.66249
$396$	4.73141	0.237762
$397$	−18.6942	−0.938233	−0.469116	−	0.883136i	$-0.655427\pi$
$397$	−18.6942	−0.938233	−0.469116	+	0.883136i	$0.655427\pi$
$398$	−7.57909	−0.379905
$399$	0	0
$400$	−1.74049	−0.0870247
$401$	−7.17208	−0.358157	−0.179078	−	0.983835i	$-0.557312\pi$
$401$	−7.17208	−0.358157	−0.179078	+	0.983835i	$0.557312\pi$
$402$	−8.43956	−0.420927
$403$	5.11242	0.254668
$404$	63.2139	3.14501
$405$	−2.19202	−0.108922
$406$	0	0
$407$	−4.38101	−0.217159
$408$	−18.3863	−0.910255
$409$	−3.04120	−0.150377	−0.0751887	−	0.997169i	$-0.523956\pi$
$409$	−3.04120	−0.150377	−0.0751887	+	0.997169i	$0.523956\pi$
$410$	−55.0929	−2.72084
$411$	2.61235	0.128858
$412$	25.2119	1.24210
$413$	0	0
$414$	23.1518	1.13785
$415$	−13.7391	−0.674425
$416$	26.5114	1.29983
$417$	−6.25015	−0.306071
$418$	6.11848	0.299265
$419$	−24.9508	−1.21893	−0.609464	−	0.792814i	$-0.708615\pi$
$419$	−24.9508	−1.21893	−0.609464	+	0.792814i	$0.708615\pi$
$420$	0	0
$421$	−11.9958	−0.584638	−0.292319	−	0.956321i	$-0.594427\pi$
$421$	−11.9958	−0.584638	−0.292319	+	0.956321i	$0.594427\pi$
$422$	−25.4967	−1.24116
$423$	−11.1094	−0.540157
$424$	−65.0291	−3.15809
$425$	0.506050	0.0245470
$426$	2.58090	0.125045
$427$	0	0
$428$	27.8770	1.34749
$429$	2.95275	0.142560
$430$	58.6532	2.82851
$431$	−17.1701	−0.827057	−0.413528	−	0.910491i	$-0.635704\pi$
$431$	−17.1701	−0.827057	−0.413528	+	0.910491i	$0.635704\pi$
$432$	8.92343	0.429329
$433$	−7.02235	−0.337472	−0.168736	−	0.985661i	$-0.553969\pi$
$433$	−7.02235	−0.337472	−0.168736	+	0.985661i	$0.553969\pi$
$434$	0	0
$435$	−9.83427	−0.471517
$436$	−79.4859	−3.80668
$437$	21.0437	1.00666
$438$	−0.765062	−0.0365561
$439$	−39.7521	−1.89726	−0.948631	−	0.316385i	$-0.897531\pi$
$439$	−39.7521	−1.89726	−0.948631	+	0.316385i	$0.897531\pi$
$440$	−15.5341	−0.740557
$441$	0	0
$442$	−19.8762	−0.945413
$443$	35.0012	1.66296	0.831479	−	0.555557i	$-0.187495\pi$
$443$	35.0012	1.66296	0.831479	+	0.555557i	$0.187495\pi$
$444$	−20.7284	−0.983725
$445$	−5.69978	−0.270196
$446$	42.3233	2.00407
$447$	−4.12201	−0.194964
$448$	0	0
$449$	−10.3780	−0.489767	−0.244884	−	0.969552i	$-0.578750\pi$
$449$	−10.3780	−0.489767	−0.244884	+	0.969552i	$0.578750\pi$
$450$	−0.506050	−0.0238554
$451$	9.68719	0.456152
$452$	61.0469	2.87140
$453$	12.4353	0.584262
$454$	−58.6587	−2.75299
$455$	0	0
$456$	16.7121	0.782615
$457$	−18.6027	−0.870199	−0.435100	−	0.900382i	$-0.643287\pi$
$457$	−18.6027	−0.870199	−0.435100	+	0.900382i	$0.643287\pi$
$458$	9.61840	0.449438
$459$	−2.59450	−0.121101
$460$	−92.5480	−4.31507
$461$	17.0730	0.795171	0.397585	−	0.917565i	$-0.369848\pi$
$461$	17.0730	0.795171	0.397585	+	0.917565i	$0.369848\pi$
$462$	0	0
$463$	32.3530	1.50357	0.751786	−	0.659408i	$-0.229193\pi$
$463$	32.3530	1.50357	0.751786	+	0.659408i	$0.229193\pi$
$464$	40.0340	1.85853
$465$	−3.79529	−0.176002
$466$	−19.9750	−0.925324
$467$	0.217409	0.0100605	0.00503024	−	0.999987i	$-0.498399\pi$
$467$	0.217409	0.0100605	0.00503024	+	0.999987i	$0.498399\pi$
$468$	13.9707	0.645795
$469$	0	0
$470$	63.1812	2.91433
$471$	18.6933	0.861344
$472$	−63.2371	−2.91072
$473$	−10.3132	−0.474202
$474$	−39.1080	−1.79629
$475$	−0.459972	−0.0211049
$476$	0	0
$477$	−9.17630	−0.420154
$478$	−10.7149	−0.490089
$479$	21.4612	0.980587	0.490294	−	0.871557i	$-0.336890\pi$
$479$	21.4612	0.980587	0.490294	+	0.871557i	$0.336890\pi$
$480$	−19.6811	−0.898317
$481$	−12.9360	−0.589832
$482$	38.2843	1.74380
$483$	0	0
$484$	4.73141	0.215064
$485$	16.4775	0.748205
$486$	2.59450	0.117689
$487$	36.0891	1.63535	0.817676	−	0.575679i	$-0.195262\pi$
$487$	36.0891	1.63535	0.817676	+	0.575679i	$0.195262\pi$
$488$	−95.5025	−4.32320
$489$	−1.26475	−0.0571939
$490$	0	0
$491$	−5.10627	−0.230443	−0.115221	−	0.993340i	$-0.536758\pi$
$491$	−5.10627	−0.230443	−0.115221	+	0.993340i	$0.536758\pi$
$492$	45.8341	2.06636
$493$	−11.6399	−0.524236
$494$	18.0663	0.812843
$495$	−2.19202	−0.0985240
$496$	15.4501	0.693731
$497$	0	0
$498$	16.2617	0.728705
$499$	7.73141	0.346106	0.173053	−	0.984913i	$-0.444637\pi$
$499$	7.73141	0.346106	0.173053	+	0.984913i	$0.444637\pi$
$500$	53.8797	2.40957
$501$	6.11021	0.272984
$502$	35.1608	1.56930
$503$	−34.5655	−1.54120	−0.770599	−	0.637320i	$-0.780043\pi$
$503$	−34.5655	−1.54120	−0.770599	+	0.637320i	$0.780043\pi$
$504$	0	0
$505$	−29.2864	−1.30323
$506$	23.1518	1.02922
$507$	−4.28127	−0.190138
$508$	69.5288	3.08484
$509$	28.5408	1.26505	0.632524	−	0.774541i	$-0.282019\pi$
$509$	28.5408	1.26505	0.632524	+	0.774541i	$0.282019\pi$
$510$	14.7554	0.653380
$511$	0	0
$512$	−46.3549	−2.04862
$513$	2.35825	0.104119
$514$	−22.1340	−0.976287
$515$	−11.6805	−0.514702
$516$	−48.7961	−2.14813
$517$	−11.1094	−0.488591
$518$	0	0
$519$	17.4649	0.766625
$520$	−45.8682	−2.01145
$521$	28.1777	1.23449	0.617244	−	0.786772i	$-0.288249\pi$
$521$	28.1777	1.23449	0.617244	+	0.786772i	$0.288249\pi$
$522$	11.6399	0.509466
$523$	−31.4514	−1.37527	−0.687637	−	0.726054i	$-0.741352\pi$
$523$	−31.4514	−1.37527	−0.687637	+	0.726054i	$0.741352\pi$
$524$	−50.9382	−2.22525
$525$	0	0
$526$	9.21797	0.401923
$527$	−4.49214	−0.195681
$528$	8.92343	0.388343
$529$	56.6276	2.46207
$530$	52.1874	2.26687
$531$	−8.92343	−0.387244
$532$	0	0
$533$	28.6038	1.23897
$534$	6.74632	0.291942
$535$	−12.9152	−0.558371
$536$	−23.0519	−0.995691
$537$	0.422545	0.0182342
$538$	−30.1569	−1.30016
$539$	0	0
$540$	−10.3713	−0.446312
$541$	37.2790	1.60275	0.801374	−	0.598164i	$-0.204103\pi$
$541$	37.2790	1.60275	0.801374	+	0.598164i	$0.204103\pi$
$542$	−25.6331	−1.10104
$543$	−2.40197	−0.103079
$544$	−23.2948	−0.998755
$545$	36.8251	1.57741
$546$	0	0
$547$	−10.7602	−0.460074	−0.230037	−	0.973182i	$-0.573885\pi$
$547$	−10.7602	−0.460074	−0.230037	+	0.973182i	$0.573885\pi$
$548$	12.3601	0.527998
$549$	−13.4764	−0.575160
$550$	−0.506050	−0.0215781
$551$	10.5801	0.450726
$552$	63.2371	2.69155
$553$	0	0
$554$	−3.32640	−0.141325
$555$	9.60327	0.407636
$556$	−29.5720	−1.25413
$557$	−10.9427	−0.463656	−0.231828	−	0.972757i	$-0.574471\pi$
$557$	−10.9427	−0.463656	−0.231828	+	0.972757i	$0.574471\pi$
$558$	4.49214	0.190167
$559$	−30.4523	−1.28800
$560$	0	0
$561$	−2.59450	−0.109540
$562$	66.3967	2.80078
$563$	−2.44499	−0.103044	−0.0515221	−	0.998672i	$-0.516407\pi$
$563$	−2.44499	−0.103044	−0.0515221	+	0.998672i	$0.516407\pi$
$564$	−52.5631	−2.21331
$565$	−28.2825	−1.18985
$566$	31.1545	1.30952
$567$	0	0
$568$	7.04949	0.295790
$569$	28.5971	1.19885	0.599426	−	0.800430i	$-0.295395\pi$
$569$	28.5971	1.19885	0.599426	+	0.800430i	$0.295395\pi$
$570$	−13.4118	−0.561760
$571$	−1.96272	−0.0821374	−0.0410687	−	0.999156i	$-0.513076\pi$
$571$	−1.96272	−0.0821374	−0.0410687	+	0.999156i	$0.513076\pi$
$572$	13.9707	0.584143
$573$	−8.69291	−0.363151
$574$	0	0
$575$	−1.74049	−0.0725836
$576$	5.44792	0.226997
$577$	−41.3949	−1.72329	−0.861646	−	0.507509i	$-0.830566\pi$
$577$	−41.3949	−1.72329	−0.861646	+	0.507509i	$0.830566\pi$
$578$	−26.6418	−1.10815
$579$	−8.04513	−0.334344
$580$	−46.5300	−1.93205
$581$	0	0
$582$	−19.5029	−0.808422
$583$	−9.17630	−0.380044
$584$	−2.08970	−0.0864724
$585$	−6.47249	−0.267604
$586$	45.9152	1.89674
$587$	−22.5301	−0.929917	−0.464959	−	0.885332i	$-0.653931\pi$
$587$	−22.5301	−0.929917	−0.464959	+	0.885332i	$0.653931\pi$
$588$	0	0
$589$	4.08311	0.168241
$590$	50.7492	2.08931
$591$	−4.79921	−0.197413
$592$	−39.0937	−1.60674
$593$	18.7131	0.768454	0.384227	−	0.923239i	$-0.374468\pi$
$593$	18.7131	0.768454	0.384227	+	0.923239i	$0.374468\pi$
$594$	2.59450	0.106453
$595$	0	0
$596$	−19.5029	−0.798871
$597$	−2.92122	−0.119557
$598$	68.3615	2.79551
$599$	45.4471	1.85692	0.928459	−	0.371435i	$-0.121134\pi$
$599$	45.4471	1.85692	0.928459	+	0.371435i	$0.121134\pi$
$600$	−1.38223	−0.0564294
$601$	−13.6085	−0.555103	−0.277551	−	0.960711i	$-0.589523\pi$
$601$	−13.6085	−0.555103	−0.277551	+	0.960711i	$0.589523\pi$
$602$	0	0
$603$	−3.25287	−0.132467
$604$	58.8365	2.39403
$605$	−2.19202	−0.0891183
$606$	34.6637	1.40812
$607$	29.1530	1.18329	0.591643	−	0.806200i	$-0.298480\pi$
$607$	29.1530	1.18329	0.591643	+	0.806200i	$0.298480\pi$
$608$	21.1737	0.858705
$609$	0	0
$610$	76.6430	3.10318
$611$	−32.8033	−1.32708
$612$	−12.2756	−0.496213
$613$	20.2424	0.817583	0.408791	−	0.912628i	$-0.365950\pi$
$613$	20.2424	0.817583	0.408791	+	0.912628i	$0.365950\pi$
$614$	20.9716	0.846345
$615$	−21.2345	−0.856258
$616$	0	0
$617$	−6.70281	−0.269845	−0.134922	−	0.990856i	$-0.543079\pi$
$617$	−6.70281	−0.269845	−0.134922	+	0.990856i	$0.543079\pi$
$618$	13.8251	0.556127
$619$	−5.54241	−0.222768	−0.111384	−	0.993777i	$-0.535528\pi$
$619$	−5.54241	−0.222768	−0.111384	+	0.993777i	$0.535528\pi$
$620$	−17.9571	−0.721173
$621$	8.92343	0.358085
$622$	−30.0617	−1.20537
$623$	0	0
$624$	26.3487	1.05479
$625$	−23.9867	−0.959469
$626$	−4.03684	−0.161344
$627$	2.35825	0.0941796
$628$	88.4459	3.52937
$629$	11.3665	0.453213
$630$	0	0
$631$	−34.6139	−1.37796	−0.688979	−	0.724782i	$-0.741941\pi$
$631$	−34.6139	−1.37796	−0.688979	+	0.724782i	$0.741941\pi$
$632$	−106.820	−4.24907
$633$	−9.82721	−0.390596
$634$	27.2399	1.08183
$635$	−32.2121	−1.27830
$636$	−43.4169	−1.72159
$637$	0	0
$638$	11.6399	0.460830
$639$	0.994758	0.0393520
$640$	8.37893	0.331206
$641$	−14.0006	−0.552990	−0.276495	−	0.961015i	$-0.589173\pi$
$641$	−14.0006	−0.552990	−0.276495	+	0.961015i	$0.589173\pi$
$642$	15.2865	0.603311
$643$	−9.03547	−0.356324	−0.178162	−	0.984001i	$-0.557015\pi$
$643$	−9.03547	−0.356324	−0.178162	+	0.984001i	$0.557015\pi$
$644$	0	0
$645$	22.6068	0.890141
$646$	−15.8744	−0.624569
$647$	39.5406	1.55450	0.777250	−	0.629191i	$-0.216614\pi$
$647$	39.5406	1.55450	0.777250	+	0.629191i	$0.216614\pi$
$648$	7.08664	0.278389
$649$	−8.92343	−0.350275
$650$	−1.49424	−0.0586089
$651$	0	0
$652$	−5.98404	−0.234353
$653$	21.6815	0.848461	0.424231	−	0.905554i	$-0.360545\pi$
$653$	21.6815	0.848461	0.424231	+	0.905554i	$0.360545\pi$
$654$	−43.5865	−1.70437
$655$	23.5992	0.922098
$656$	86.4430	3.37503
$657$	−0.294879	−0.0115043
$658$	0	0
$659$	9.66475	0.376485	0.188243	−	0.982123i	$-0.439721\pi$
$659$	9.66475	0.376485	0.188243	+	0.982123i	$0.439721\pi$
$660$	−10.3713	−0.403704
$661$	5.78135	0.224869	0.112434	−	0.993659i	$-0.464135\pi$
$661$	5.78135	0.224869	0.112434	+	0.993659i	$0.464135\pi$
$662$	75.1912	2.92239
$663$	−7.66090	−0.297525
$664$	44.4175	1.72373
$665$	0	0
$666$	−11.3665	−0.440444
$667$	40.0340	1.55012
$668$	28.9099	1.11856
$669$	16.3127	0.630686
$670$	18.4997	0.714705
$671$	−13.4764	−0.520252
$672$	0	0
$673$	−4.33155	−0.166969	−0.0834846	−	0.996509i	$-0.526605\pi$
$673$	−4.33155	−0.166969	−0.0834846	+	0.996509i	$0.526605\pi$
$674$	36.2879	1.39776
$675$	−0.195048	−0.00750738
$676$	−20.2565	−0.779094
$677$	−20.6844	−0.794965	−0.397483	−	0.917610i	$-0.630116\pi$
$677$	−20.6844	−0.794965	−0.397483	+	0.917610i	$0.630116\pi$
$678$	33.4754	1.28562
$679$	0	0
$680$	40.3030	1.54555
$681$	−22.6089	−0.866375
$682$	4.49214	0.172013
$683$	−5.46446	−0.209092	−0.104546	−	0.994520i	$-0.533339\pi$
$683$	−5.46446	−0.209092	−0.104546	+	0.994520i	$0.533339\pi$
$684$	11.1579	0.426632
$685$	−5.72633	−0.218792
$686$	0	0
$687$	3.70723	0.141440
$688$	−92.0293	−3.50858
$689$	−27.0953	−1.03225
$690$	−50.7492	−1.93199
$691$	43.4221	1.65185	0.825927	−	0.563777i	$-0.190652\pi$
$691$	43.4221	1.65185	0.825927	+	0.563777i	$0.190652\pi$
$692$	82.6338	3.14127
$693$	0	0
$694$	−23.1971	−0.880548
$695$	13.7005	0.519688
$696$	31.7935	1.20513
$697$	−25.1334	−0.951994
$698$	−0.918199	−0.0347543
$699$	−7.69899	−0.291202
$700$	0	0
$701$	−30.4055	−1.14840	−0.574200	−	0.818715i	$-0.694687\pi$
$701$	−30.4055	−1.14840	−0.574200	+	0.818715i	$0.694687\pi$
$702$	7.66090	0.289142
$703$	−10.3315	−0.389661
$704$	5.44792	0.205326
$705$	24.3520	0.917150
$706$	−53.4572	−2.01189
$707$	0	0
$708$	−42.2204	−1.58674
$709$	18.6885	0.701861	0.350930	−	0.936402i	$-0.385865\pi$
$709$	18.6885	0.701861	0.350930	+	0.936402i	$0.385865\pi$
$710$	−5.65738	−0.212318
$711$	−15.0734	−0.565298
$712$	18.4270	0.690580
$713$	15.4501	0.578612
$714$	0	0
$715$	−6.47249	−0.242057
$716$	1.99923	0.0747149
$717$	−4.12986	−0.154233
$718$	27.4670	1.02506
$719$	32.5232	1.21291	0.606456	−	0.795117i	$-0.292591\pi$
$719$	32.5232	1.21291	0.606456	+	0.795117i	$0.292591\pi$
$720$	−19.5603	−0.728971
$721$	0	0
$722$	−34.8665	−1.29760
$723$	14.7560	0.548780
$724$	−11.3647	−0.422367
$725$	−0.875061	−0.0324989
$726$	2.59450	0.0962908
$727$	23.7302	0.880103	0.440051	−	0.897973i	$-0.354960\pi$
$727$	23.7302	0.880103	0.440051	+	0.897973i	$0.354960\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.67703	0.0620698
$731$	26.7576	0.989666
$732$	−63.7625	−2.35673
$733$	−35.9886	−1.32927	−0.664635	−	0.747168i	$-0.731413\pi$
$733$	−35.9886	−1.32927	−0.664635	+	0.747168i	$0.731413\pi$
$734$	−28.2263	−1.04185
$735$	0	0
$736$	80.1194	2.95324
$737$	−3.25287	−0.119821
$738$	25.1334	0.925172
$739$	1.23985	0.0456087	0.0228043	−	0.999740i	$-0.492741\pi$
$739$	1.23985	0.0456087	0.0228043	+	0.999740i	$0.492741\pi$
$740$	45.4370	1.67030
$741$	6.96333	0.255804
$742$	0	0
$743$	18.6353	0.683662	0.341831	−	0.939761i	$-0.388953\pi$
$743$	18.6353	0.683662	0.341831	+	0.939761i	$0.388953\pi$
$744$	12.2699	0.449836
$745$	9.03553	0.331036
$746$	38.2862	1.40176
$747$	6.26778	0.229326
$748$	−12.2756	−0.448841
$749$	0	0
$750$	29.5452	1.07884
$751$	−45.3810	−1.65598	−0.827988	−	0.560745i	$-0.810515\pi$
$751$	−45.3810	−1.65598	−0.827988	+	0.560745i	$0.810515\pi$
$752$	−99.1339	−3.61504
$753$	13.5521	0.493865
$754$	34.3698	1.25168
$755$	−27.2584	−0.992036
$756$	0	0
$757$	35.8708	1.30375	0.651874	−	0.758327i	$-0.273983\pi$
$757$	35.8708	1.30375	0.651874	+	0.758327i	$0.273983\pi$
$758$	33.3269	1.21049
$759$	8.92343	0.323900
$760$	−36.6332	−1.32883
$761$	−18.7213	−0.678645	−0.339323	−	0.940670i	$-0.610198\pi$
$761$	−18.7213	−0.678645	−0.339323	+	0.940670i	$0.610198\pi$
$762$	38.1265	1.38118
$763$	0	0
$764$	−41.1297	−1.48802
$765$	5.68719	0.205621
$766$	−32.3154	−1.16760
$767$	−26.3487	−0.951395
$768$	−20.8132	−0.751032
$769$	−6.00582	−0.216576	−0.108288	−	0.994120i	$-0.534537\pi$
$769$	−6.00582	−0.216576	−0.108288	+	0.994120i	$0.534537\pi$
$770$	0	0
$771$	−8.53112	−0.307241
$772$	−38.0648	−1.36998
$773$	14.1425	0.508669	0.254334	−	0.967116i	$-0.418144\pi$
$773$	14.1425	0.508669	0.254334	+	0.967116i	$0.418144\pi$
$774$	−26.7576	−0.961782
$775$	−0.337708	−0.0121308
$776$	−53.2705	−1.91230
$777$	0	0
$778$	34.2753	1.22883
$779$	22.8448	0.818501
$780$	−30.6240	−1.09651
$781$	0.994758	0.0355953
$782$	−60.0673	−2.14800
$783$	4.48640	0.160331
$784$	0	0
$785$	−40.9762	−1.46250
$786$	−27.9323	−0.996311
$787$	−50.0291	−1.78334	−0.891672	−	0.452681i	$-0.850467\pi$
$787$	−50.0291	−1.78334	−0.891672	+	0.452681i	$0.850467\pi$
$788$	−22.7070	−0.808904
$789$	3.55290	0.126486
$790$	85.7255	3.04998
$791$	0	0
$792$	7.08664	0.251813
$793$	−39.7925	−1.41307
$794$	−48.5019	−1.72127
$795$	20.1146	0.713393
$796$	−13.8215	−0.489889
$797$	7.24763	0.256724	0.128362	−	0.991727i	$-0.459028\pi$
$797$	7.24763	0.256724	0.128362	+	0.991727i	$0.459028\pi$
$798$	0	0
$799$	28.8233	1.01969
$800$	−1.75124	−0.0619157
$801$	2.60024	0.0918750
$802$	−18.6079	−0.657069
$803$	−0.294879	−0.0104061
$804$	−15.3907	−0.542787
$805$	0	0
$806$	13.2642	0.467210
$807$	−11.6234	−0.409163
$808$	94.6808	3.33086
$809$	0.512279	0.0180108	0.00900538	−	0.999959i	$-0.497133\pi$
$809$	0.512279	0.0180108	0.00900538	+	0.999959i	$0.497133\pi$
$810$	−5.68719	−0.199827
$811$	−40.5892	−1.42528	−0.712640	−	0.701530i	$-0.752501\pi$
$811$	−40.5892	−1.42528	−0.712640	+	0.701530i	$0.752501\pi$
$812$	0	0
$813$	−9.87979	−0.346499
$814$	−11.3665	−0.398396
$815$	2.77235	0.0971113
$816$	−23.1518	−0.810476
$817$	−24.3212	−0.850890
$818$	−7.89037	−0.275880
$819$	0	0
$820$	−100.469	−3.50854
$821$	−22.6189	−0.789405	−0.394702	−	0.918809i	$-0.629152\pi$
$821$	−22.6189	−0.789405	−0.394702	+	0.918809i	$0.629152\pi$
$822$	6.77774	0.236401
$823$	6.03629	0.210412	0.105206	−	0.994450i	$-0.466450\pi$
$823$	6.03629	0.210412	0.105206	+	0.994450i	$0.466450\pi$
$824$	37.7620	1.31550
$825$	−0.195048	−0.00679068
$826$	0	0
$827$	4.54161	0.157927	0.0789636	−	0.996878i	$-0.474839\pi$
$827$	4.54161	0.157927	0.0789636	+	0.996878i	$0.474839\pi$
$828$	42.2204	1.46726
$829$	−25.8717	−0.898560	−0.449280	−	0.893391i	$-0.648319\pi$
$829$	−25.8717	−0.898560	−0.449280	+	0.893391i	$0.648319\pi$
$830$	−35.6460	−1.23729
$831$	−1.28210	−0.0444755
$832$	16.0863	0.557693
$833$	0	0
$834$	−16.2160	−0.561514
$835$	−13.3937	−0.463508
$836$	11.1579	0.385903
$837$	1.73141	0.0598463
$838$	−64.7348	−2.23623
$839$	28.9458	0.999319	0.499660	−	0.866222i	$-0.333458\pi$
$839$	28.9458	0.999319	0.499660	+	0.866222i	$0.333458\pi$
$840$	0	0
$841$	−8.87225	−0.305940
$842$	−31.1230	−1.07257
$843$	25.5914	0.881414
$844$	−46.4966	−1.60048
$845$	9.38463	0.322841
$846$	−28.8233	−0.990965
$847$	0	0
$848$	−81.8841	−2.81191
$849$	12.0079	0.412111
$850$	1.31295	0.0450337
$851$	−39.0937	−1.34011
$852$	4.70661	0.161246
$853$	4.72334	0.161724	0.0808620	−	0.996725i	$-0.474233\pi$
$853$	4.72334	0.161724	0.0808620	+	0.996725i	$0.474233\pi$
$854$	0	0
$855$	−5.16934	−0.176788
$856$	41.7538	1.42711
$857$	−28.2092	−0.963606	−0.481803	−	0.876279i	$-0.660018\pi$
$857$	−28.2092	−0.963606	−0.481803	+	0.876279i	$0.660018\pi$
$858$	7.66090	0.261539
$859$	7.43580	0.253706	0.126853	−	0.991922i	$-0.459512\pi$
$859$	7.43580	0.253706	0.126853	+	0.991922i	$0.459512\pi$
$860$	106.962	3.64737
$861$	0	0
$862$	−44.5479	−1.51731
$863$	45.6002	1.55225	0.776125	−	0.630579i	$-0.217183\pi$
$863$	45.6002	1.55225	0.776125	+	0.630579i	$0.217183\pi$
$864$	8.97854	0.305456
$865$	−38.2835	−1.30168
$866$	−18.2194	−0.619122
$867$	−10.2686	−0.348740
$868$	0	0
$869$	−15.0734	−0.511332
$870$	−25.5150	−0.865039
$871$	−9.60491	−0.325450
$872$	−119.053	−4.03164
$873$	−7.51704	−0.254413
$874$	54.5978	1.84680
$875$	0	0
$876$	−1.39519	−0.0471392
$877$	−39.7363	−1.34180	−0.670900	−	0.741548i	$-0.734092\pi$
$877$	−39.7363	−1.34180	−0.670900	+	0.741548i	$0.734092\pi$
$878$	−103.137	−3.48069
$879$	17.6972	0.596910
$880$	−19.5603	−0.659379
$881$	−28.1813	−0.949452	−0.474726	−	0.880134i	$-0.657453\pi$
$881$	−28.1813	−0.949452	−0.474726	+	0.880134i	$0.657453\pi$
$882$	0	0
$883$	40.6909	1.36936	0.684679	−	0.728845i	$-0.259942\pi$
$883$	40.6909	1.36936	0.684679	+	0.728845i	$0.259942\pi$
$884$	−36.2469	−1.21911
$885$	19.5603	0.657514
$886$	90.8105	3.05084
$887$	18.4938	0.620960	0.310480	−	0.950580i	$-0.399510\pi$
$887$	18.4938	0.620960	0.310480	+	0.950580i	$0.399510\pi$
$888$	−31.0466	−1.04186
$889$	0	0
$890$	−14.7881	−0.495697
$891$	1.00000	0.0335013
$892$	77.1822	2.58425
$893$	−26.1988	−0.876708
$894$	−10.6945	−0.357679
$895$	−0.926227	−0.0309604
$896$	0	0
$897$	26.3487	0.879756
$898$	−26.9256	−0.898520
$899$	7.76780	0.259071
$900$	−0.922850	−0.0307617
$901$	23.8079	0.793156
$902$	25.1334	0.836850
$903$	0	0
$904$	91.4351	3.04109
$905$	5.26517	0.175020
$906$	32.2634	1.07188
$907$	−47.9651	−1.59266	−0.796328	−	0.604865i	$-0.793227\pi$
$907$	−47.9651	−1.59266	−0.796328	+	0.604865i	$0.793227\pi$
$908$	−106.972	−3.54999
$909$	13.3605	0.443139
$910$	0	0
$911$	11.9369	0.395489	0.197744	−	0.980254i	$-0.436638\pi$
$911$	11.9369	0.395489	0.197744	+	0.980254i	$0.436638\pi$
$912$	21.0437	0.696827
$913$	6.26778	0.207433
$914$	−48.2647	−1.59646
$915$	29.5406	0.976582
$916$	17.5404	0.579552
$917$	0	0
$918$	−6.73141	−0.222170
$919$	59.0449	1.94771	0.973856	−	0.227167i	$-0.0729462\pi$
$919$	59.0449	1.94771	0.973856	+	0.227167i	$0.0729462\pi$
$920$	−138.617	−4.57007
$921$	8.08311	0.266347
$922$	44.2959	1.45881
$923$	2.93727	0.0966815
$924$	0	0
$925$	0.854506	0.0280960
$926$	83.9397	2.75843
$927$	5.32863	0.175015
$928$	40.2813	1.32230
$929$	38.0748	1.24919	0.624597	−	0.780948i	$-0.285263\pi$
$929$	38.0748	1.24919	0.624597	+	0.780948i	$0.285263\pi$
$930$	−9.84686	−0.322891
$931$	0	0
$932$	−36.4271	−1.19321
$933$	−11.5867	−0.379333
$934$	0.564066	0.0184568
$935$	5.68719	0.185991
$936$	20.9251	0.683957
$937$	19.4407	0.635099	0.317550	−	0.948242i	$-0.397140\pi$
$937$	19.4407	0.635099	0.317550	+	0.948242i	$0.397140\pi$
$938$	0	0
$939$	−1.55592	−0.0507756
$940$	115.219	3.75804
$941$	39.7534	1.29592	0.647961	−	0.761673i	$-0.275622\pi$
$941$	39.7534	1.29592	0.647961	+	0.761673i	$0.275622\pi$
$942$	48.4998	1.58021
$943$	86.4430	2.81497
$944$	−79.6276	−2.59166
$945$	0	0
$946$	−26.7576	−0.869965
$947$	32.3542	1.05137	0.525686	−	0.850679i	$-0.323809\pi$
$947$	32.3542	1.05137	0.525686	+	0.850679i	$0.323809\pi$
$948$	−71.3187	−2.31632
$949$	−0.870704	−0.0282642
$950$	−1.19339	−0.0387188
$951$	10.4991	0.340457
$952$	0	0
$953$	8.56486	0.277443	0.138722	−	0.990331i	$-0.455701\pi$
$953$	8.56486	0.277443	0.138722	+	0.990331i	$0.455701\pi$
$954$	−23.8079	−0.770809
$955$	19.0550	0.616606
$956$	−19.5401	−0.631972
$957$	4.48640	0.145025
$958$	55.6810	1.79897
$959$	0	0
$960$	−11.9419	−0.385425
$961$	−28.0022	−0.903297
$962$	−33.5625	−1.08210
$963$	5.89190	0.189864
$964$	69.8166	2.24864
$965$	17.6351	0.567694
$966$	0	0
$967$	11.2215	0.360858	0.180429	−	0.983588i	$-0.442251\pi$
$967$	11.2215	0.360858	0.180429	+	0.983588i	$0.442251\pi$
$968$	7.08664	0.227773
$969$	−6.11848	−0.196554
$970$	42.7508	1.37265
$971$	42.7645	1.37238	0.686188	−	0.727424i	$-0.259283\pi$
$971$	42.7645	1.37238	0.686188	+	0.727424i	$0.259283\pi$
$972$	4.73141	0.151760
$973$	0	0
$974$	93.6329	3.00019
$975$	−0.575927	−0.0184444
$976$	−120.256	−3.84930
$977$	24.7195	0.790848	0.395424	−	0.918499i	$-0.370598\pi$
$977$	24.7195	0.790848	0.395424	+	0.918499i	$0.370598\pi$
$978$	−3.28138	−0.104927
$979$	2.60024	0.0831041
$980$	0	0
$981$	−16.7996	−0.536370
$982$	−13.2482	−0.422767
$983$	40.7257	1.29895	0.649475	−	0.760383i	$-0.274989\pi$
$983$	40.7257	1.29895	0.649475	+	0.760383i	$0.274989\pi$
$984$	68.6496	2.18847
$985$	10.5200	0.335194
$986$	−30.1998	−0.961757
$987$	0	0
$988$	32.9464	1.04816
$989$	−92.0293	−2.92636
$990$	−5.68719	−0.180751
$991$	−57.5124	−1.82694	−0.913471	−	0.406905i	$-0.866608\pi$
$991$	−57.5124	−1.82694	−0.913471	+	0.406905i	$0.866608\pi$
$992$	15.5455	0.493571
$993$	28.9811	0.919686
$994$	0	0
$995$	6.40337	0.203000
$996$	29.6554	0.939668
$997$	37.8183	1.19772	0.598858	−	0.800855i	$-0.295621\pi$
$997$	37.8183	1.19772	0.598858	+	0.800855i	$0.295621\pi$
$998$	20.0591	0.634960
$999$	−4.38101	−0.138609

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.bb.1.5		5
3.2	odd	2		4851.2.a.bz.1.1		5
7.3	odd	6		231.2.i.f.100.1	yes	10
7.5	odd	6		231.2.i.f.67.1	✓	10
7.6	odd	2		1617.2.a.ba.1.5		5
21.5	even	6		693.2.i.j.298.5		10
21.17	even	6		693.2.i.j.100.5		10
21.20	even	2		4851.2.a.ca.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.1	✓	10	7.5	odd	6
231.2.i.f.100.1	yes	10	7.3	odd	6
693.2.i.j.100.5		10	21.17	even	6
693.2.i.j.298.5		10	21.5	even	6
1617.2.a.ba.1.5		5	7.6	odd	2
1617.2.a.bb.1.5		5	1.1	even	1	trivial
4851.2.a.bz.1.1		5	3.2	odd	2
4851.2.a.ca.1.1		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)

\(f(q)\)	\(=\)	\(q+2.59450 q^{2} +1.00000 q^{3} +4.73141 q^{4} -2.19202 q^{5} +2.59450 q^{6} +7.08664 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.59450 q^{2} +1.00000 q^{3} +4.73141 q^{4} -2.19202 q^{5} +2.59450 q^{6} +7.08664 q^{8} +1.00000 q^{9} -5.68719 q^{10} +1.00000 q^{11} +4.73141 q^{12} +2.95275 q^{13} -2.19202 q^{15} +8.92343 q^{16} -2.59450 q^{17} +2.59450 q^{18} +2.35825 q^{19} -10.3713 q^{20} +2.59450 q^{22} +8.92343 q^{23} +7.08664 q^{24} -0.195048 q^{25} +7.66090 q^{26} +1.00000 q^{27} +4.48640 q^{29} -5.68719 q^{30} +1.73141 q^{31} +8.97854 q^{32} +1.00000 q^{33} -6.73141 q^{34} +4.73141 q^{36} -4.38101 q^{37} +6.11848 q^{38} +2.95275 q^{39} -15.5341 q^{40} +9.68719 q^{41} -10.3132 q^{43} +4.73141 q^{44} -2.19202 q^{45} +23.1518 q^{46} -11.1094 q^{47} +8.92343 q^{48} -0.506050 q^{50} -2.59450 q^{51} +13.9707 q^{52} -9.17630 q^{53} +2.59450 q^{54} -2.19202 q^{55} +2.35825 q^{57} +11.6399 q^{58} -8.92343 q^{59} -10.3713 q^{60} -13.4764 q^{61} +4.49214 q^{62} +5.44792 q^{64} -6.47249 q^{65} +2.59450 q^{66} -3.25287 q^{67} -12.2756 q^{68} +8.92343 q^{69} +0.994758 q^{71} +7.08664 q^{72} -0.294879 q^{73} -11.3665 q^{74} -0.195048 q^{75} +11.1579 q^{76} +7.66090 q^{78} -15.0734 q^{79} -19.5603 q^{80} +1.00000 q^{81} +25.1334 q^{82} +6.26778 q^{83} +5.68719 q^{85} -26.7576 q^{86} +4.48640 q^{87} +7.08664 q^{88} +2.60024 q^{89} -5.68719 q^{90} +42.2204 q^{92} +1.73141 q^{93} -28.8233 q^{94} -5.16934 q^{95} +8.97854 q^{96} -7.51704 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + 5 q^{3} + 10 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 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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