LMFDB - Embedded newform 5070.2.a.bw.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5070,2,Mod(1,5070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5070, 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("5070.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5070.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:	$40.4841538248$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	5070.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.69202 q^{11} +1.00000 q^{12} +3.35690 q^{14} -1.00000 q^{15} +1.00000 q^{16} +0.939001 q^{17} +1.00000 q^{18} -4.85086 q^{19} -1.00000 q^{20} +3.35690 q^{21} +1.69202 q^{22} +4.04892 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +3.35690 q^{28} -8.12498 q^{29} -1.00000 q^{30} +4.08815 q^{31} +1.00000 q^{32} +1.69202 q^{33} +0.939001 q^{34} -3.35690 q^{35} +1.00000 q^{36} +11.6310 q^{37} -4.85086 q^{38} -1.00000 q^{40} +3.86294 q^{41} +3.35690 q^{42} +4.02177 q^{43} +1.69202 q^{44} -1.00000 q^{45} +4.04892 q^{46} -1.27413 q^{47} +1.00000 q^{48} +4.26875 q^{49} +1.00000 q^{50} +0.939001 q^{51} +5.74094 q^{53} +1.00000 q^{54} -1.69202 q^{55} +3.35690 q^{56} -4.85086 q^{57} -8.12498 q^{58} +0.417895 q^{59} -1.00000 q^{60} +0.198062 q^{61} +4.08815 q^{62} +3.35690 q^{63} +1.00000 q^{64} +1.69202 q^{66} +8.93900 q^{67} +0.939001 q^{68} +4.04892 q^{69} -3.35690 q^{70} -5.15883 q^{71} +1.00000 q^{72} -11.5308 q^{73} +11.6310 q^{74} +1.00000 q^{75} -4.85086 q^{76} +5.67994 q^{77} -4.94869 q^{79} -1.00000 q^{80} +1.00000 q^{81} +3.86294 q^{82} +13.1739 q^{83} +3.35690 q^{84} -0.939001 q^{85} +4.02177 q^{86} -8.12498 q^{87} +1.69202 q^{88} -9.47650 q^{89} -1.00000 q^{90} +4.04892 q^{92} +4.08815 q^{93} -1.27413 q^{94} +4.85086 q^{95} +1.00000 q^{96} +15.4547 q^{97} +4.26875 q^{98} +1.69202 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{12} + 6 q^{14} - 3 q^{15} + 3 q^{16} - 7 q^{17} + 3 q^{18} - q^{19} - 3 q^{20} + 6 q^{21} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{27} + 6 q^{28} - 3 q^{30} + 16 q^{31} + 3 q^{32} - 7 q^{34} - 6 q^{35} + 3 q^{36} + 20 q^{37} - q^{38} - 3 q^{40} + 17 q^{41} + 6 q^{42} + 9 q^{43} - 3 q^{45} + 3 q^{46} + 7 q^{47} + 3 q^{48} + 5 q^{49} + 3 q^{50} - 7 q^{51} + 3 q^{53} + 3 q^{54} + 6 q^{56} - q^{57} + 7 q^{59} - 3 q^{60} + 5 q^{61} + 16 q^{62} + 6 q^{63} + 3 q^{64} + 17 q^{67} - 7 q^{68} + 3 q^{69} - 6 q^{70} - 7 q^{71} + 3 q^{72} + 3 q^{73} + 20 q^{74} + 3 q^{75} - q^{76} - 7 q^{77} + 17 q^{79} - 3 q^{80} + 3 q^{81} + 17 q^{82} + 6 q^{83} + 6 q^{84} + 7 q^{85} + 9 q^{86} - 3 q^{89} - 3 q^{90} + 3 q^{92} + 16 q^{93} + 7 q^{94} + q^{95} + 3 q^{96} + 24 q^{97} + 5 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^12 + 6 * q^14 - 3 * q^15 + 3 * q^16 - 7 * q^17 + 3 * q^18 - q^19 - 3 * q^20 + 6 * q^21 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 + 6 * q^28 - 3 * q^30 + 16 * q^31 + 3 * q^32 - 7 * q^34 - 6 * q^35 + 3 * q^36 + 20 * q^37 - q^38 - 3 * q^40 + 17 * q^41 + 6 * q^42 + 9 * q^43 - 3 * q^45 + 3 * q^46 + 7 * q^47 + 3 * q^48 + 5 * q^49 + 3 * q^50 - 7 * q^51 + 3 * q^53 + 3 * q^54 + 6 * q^56 - q^57 + 7 * q^59 - 3 * q^60 + 5 * q^61 + 16 * q^62 + 6 * q^63 + 3 * q^64 + 17 * q^67 - 7 * q^68 + 3 * q^69 - 6 * q^70 - 7 * q^71 + 3 * q^72 + 3 * q^73 + 20 * q^74 + 3 * q^75 - q^76 - 7 * q^77 + 17 * q^79 - 3 * q^80 + 3 * q^81 + 17 * q^82 + 6 * q^83 + 6 * q^84 + 7 * q^85 + 9 * q^86 - 3 * q^89 - 3 * q^90 + 3 * q^92 + 16 * q^93 + 7 * q^94 + q^95 + 3 * q^96 + 24 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	3.35690	1.26879	0.634394	−	0.773010i	$-0.281250\pi$
$7$	3.35690	1.26879	0.634394	+	0.773010i	$0.281250\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	1.69202	0.510164	0.255082	−	0.966919i	$-0.417898\pi$
$11$	1.69202	0.510164	0.255082	+	0.966919i	$0.417898\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	3.35690	0.897168
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	0.939001	0.227741	0.113871	−	0.993496i	$-0.463675\pi$
$17$	0.939001	0.227741	0.113871	+	0.993496i	$0.463675\pi$
$18$	1.00000	0.235702
$19$	−4.85086	−1.11286	−0.556431	−	0.830894i	$-0.687830\pi$
$19$	−4.85086	−1.11286	−0.556431	+	0.830894i	$0.687830\pi$
$20$	−1.00000	−0.223607
$21$	3.35690	0.732535
$22$	1.69202	0.360740
$23$	4.04892	0.844258	0.422129	−	0.906536i	$-0.361283\pi$
$23$	4.04892	0.844258	0.422129	+	0.906536i	$0.361283\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	3.35690	0.634394
$29$	−8.12498	−1.50877	−0.754386	−	0.656432i	$-0.772065\pi$
$29$	−8.12498	−1.50877	−0.754386	+	0.656432i	$0.772065\pi$
$30$	−1.00000	−0.182574
$31$	4.08815	0.734253	0.367126	−	0.930171i	$-0.380342\pi$
$31$	4.08815	0.734253	0.367126	+	0.930171i	$0.380342\pi$
$32$	1.00000	0.176777
$33$	1.69202	0.294543
$34$	0.939001	0.161037
$35$	−3.35690	−0.567419
$36$	1.00000	0.166667
$37$	11.6310	1.91213	0.956064	−	0.293157i	$-0.0947060\pi$
$37$	11.6310	1.91213	0.956064	+	0.293157i	$0.0947060\pi$
$38$	−4.85086	−0.786913
$39$	0	0
$40$	−1.00000	−0.158114
$41$	3.86294	0.603289	0.301645	−	0.953420i	$-0.402464\pi$
$41$	3.86294	0.603289	0.301645	+	0.953420i	$0.402464\pi$
$42$	3.35690	0.517980
$43$	4.02177	0.613314	0.306657	−	0.951820i	$-0.400790\pi$
$43$	4.02177	0.613314	0.306657	+	0.951820i	$0.400790\pi$
$44$	1.69202	0.255082
$45$	−1.00000	−0.149071
$46$	4.04892	0.596980
$47$	−1.27413	−0.185850	−0.0929252	−	0.995673i	$-0.529622\pi$
$47$	−1.27413	−0.185850	−0.0929252	+	0.995673i	$0.529622\pi$
$48$	1.00000	0.144338
$49$	4.26875	0.609821
$50$	1.00000	0.141421
$51$	0.939001	0.131486
$52$	0	0
$53$	5.74094	0.788579	0.394289	−	0.918986i	$-0.370991\pi$
$53$	5.74094	0.788579	0.394289	+	0.918986i	$0.370991\pi$
$54$	1.00000	0.136083
$55$	−1.69202	−0.228152
$56$	3.35690	0.448584
$57$	−4.85086	−0.642511
$58$	−8.12498	−1.06686
$59$	0.417895	0.0544053	0.0272026	−	0.999630i	$-0.491340\pi$
$59$	0.417895	0.0544053	0.0272026	+	0.999630i	$0.491340\pi$
$60$	−1.00000	−0.129099
$61$	0.198062	0.0253593	0.0126796	−	0.999920i	$-0.495964\pi$
$61$	0.198062	0.0253593	0.0126796	+	0.999920i	$0.495964\pi$
$62$	4.08815	0.519195
$63$	3.35690	0.422929
$64$	1.00000	0.125000
$65$	0	0
$66$	1.69202	0.208273
$67$	8.93900	1.09207	0.546036	−	0.837761i	$-0.316136\pi$
$67$	8.93900	1.09207	0.546036	+	0.837761i	$0.316136\pi$
$68$	0.939001	0.113871
$69$	4.04892	0.487432
$70$	−3.35690	−0.401226
$71$	−5.15883	−0.612241	−0.306120	−	0.951993i	$-0.599031\pi$
$71$	−5.15883	−0.612241	−0.306120	+	0.951993i	$0.599031\pi$
$72$	1.00000	0.117851
$73$	−11.5308	−1.34958	−0.674789	−	0.738011i	$-0.735765\pi$
$73$	−11.5308	−1.34958	−0.674789	+	0.738011i	$0.735765\pi$
$74$	11.6310	1.35208
$75$	1.00000	0.115470
$76$	−4.85086	−0.556431
$77$	5.67994	0.647289
$78$	0	0
$79$	−4.94869	−0.556771	−0.278386	−	0.960469i	$-0.589799\pi$
$79$	−4.94869	−0.556771	−0.278386	+	0.960469i	$0.589799\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	3.86294	0.426590
$83$	13.1739	1.44602	0.723012	−	0.690836i	$-0.242757\pi$
$83$	13.1739	1.44602	0.723012	+	0.690836i	$0.242757\pi$
$84$	3.35690	0.366267
$85$	−0.939001	−0.101849
$86$	4.02177	0.433679
$87$	−8.12498	−0.871089
$88$	1.69202	0.180370
$89$	−9.47650	−1.00451	−0.502254	−	0.864720i	$-0.667496\pi$
$89$	−9.47650	−1.00451	−0.502254	+	0.864720i	$0.667496\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	4.04892	0.422129
$93$	4.08815	0.423921
$94$	−1.27413	−0.131416
$95$	4.85086	0.497687
$96$	1.00000	0.102062
$97$	15.4547	1.56919	0.784595	−	0.620009i	$-0.212871\pi$
$97$	15.4547	1.56919	0.784595	+	0.620009i	$0.212871\pi$
$98$	4.26875	0.431209
$99$	1.69202	0.170055
$100$	1.00000	0.100000
$101$	5.38404	0.535732	0.267866	−	0.963456i	$-0.413682\pi$
$101$	5.38404	0.535732	0.267866	+	0.963456i	$0.413682\pi$
$102$	0.939001	0.0929750
$103$	4.08575	0.402581	0.201291	−	0.979532i	$-0.435486\pi$
$103$	4.08575	0.402581	0.201291	+	0.979532i	$0.435486\pi$
$104$	0	0
$105$	−3.35690	−0.327599
$106$	5.74094	0.557609
$107$	−16.1196	−1.55834	−0.779171	−	0.626812i	$-0.784359\pi$
$107$	−16.1196	−1.55834	−0.779171	+	0.626812i	$0.784359\pi$
$108$	1.00000	0.0962250
$109$	−14.2325	−1.36323	−0.681613	−	0.731713i	$-0.738721\pi$
$109$	−14.2325	−1.36323	−0.681613	+	0.731713i	$0.738721\pi$
$110$	−1.69202	−0.161328
$111$	11.6310	1.10397
$112$	3.35690	0.317197
$113$	−13.3274	−1.25373	−0.626866	−	0.779127i	$-0.715663\pi$
$113$	−13.3274	−1.25373	−0.626866	+	0.779127i	$0.715663\pi$
$114$	−4.85086	−0.454324
$115$	−4.04892	−0.377563
$116$	−8.12498	−0.754386
$117$	0	0
$118$	0.417895	0.0384703
$119$	3.15213	0.288955
$120$	−1.00000	−0.0912871
$121$	−8.13706	−0.739733
$122$	0.198062	0.0179317
$123$	3.86294	0.348309
$124$	4.08815	0.367126
$125$	−1.00000	−0.0894427
$126$	3.35690	0.299056
$127$	−12.8509	−1.14033	−0.570164	−	0.821531i	$-0.693121\pi$
$127$	−12.8509	−1.14033	−0.570164	+	0.821531i	$0.693121\pi$
$128$	1.00000	0.0883883
$129$	4.02177	0.354097
$130$	0	0
$131$	−0.570024	−0.0498032	−0.0249016	−	0.999690i	$-0.507927\pi$
$131$	−0.570024	−0.0498032	−0.0249016	+	0.999690i	$0.507927\pi$
$132$	1.69202	0.147272
$133$	−16.2838	−1.41199
$134$	8.93900	0.772212
$135$	−1.00000	−0.0860663
$136$	0.939001	0.0805187
$137$	21.5405	1.84033	0.920164	−	0.391533i	$-0.128055\pi$
$137$	21.5405	1.84033	0.920164	+	0.391533i	$0.128055\pi$
$138$	4.04892	0.344667
$139$	7.09783	0.602030	0.301015	−	0.953619i	$-0.402674\pi$
$139$	7.09783	0.602030	0.301015	+	0.953619i	$0.402674\pi$
$140$	−3.35690	−0.283709
$141$	−1.27413	−0.107301
$142$	−5.15883	−0.432920
$143$	0	0
$144$	1.00000	0.0833333
$145$	8.12498	0.674743
$146$	−11.5308	−0.954295
$147$	4.26875	0.352081
$148$	11.6310	0.956064
$149$	−1.14914	−0.0941416	−0.0470708	−	0.998892i	$-0.514989\pi$
$149$	−1.14914	−0.0941416	−0.0470708	+	0.998892i	$0.514989\pi$
$150$	1.00000	0.0816497
$151$	0.0217703	0.00177164	0.000885819	−	1.00000i	$-0.499718\pi$
$151$	0.0217703	0.00177164	0.000885819		1.00000i	$0.499718\pi$
$152$	−4.85086	−0.393456
$153$	0.939001	0.0759137
$154$	5.67994	0.457703
$155$	−4.08815	−0.328368
$156$	0	0
$157$	−10.1588	−0.810763	−0.405382	−	0.914148i	$-0.632861\pi$
$157$	−10.1588	−0.810763	−0.405382	+	0.914148i	$0.632861\pi$
$158$	−4.94869	−0.393697
$159$	5.74094	0.455286
$160$	−1.00000	−0.0790569
$161$	13.5918	1.07118
$162$	1.00000	0.0785674
$163$	19.1511	1.50003	0.750014	−	0.661422i	$-0.230047\pi$
$163$	19.1511	1.50003	0.750014	+	0.661422i	$0.230047\pi$
$164$	3.86294	0.301645
$165$	−1.69202	−0.131724
$166$	13.1739	1.02249
$167$	−15.2174	−1.17756	−0.588780	−	0.808293i	$-0.700392\pi$
$167$	−15.2174	−1.17756	−0.588780	+	0.808293i	$0.700392\pi$
$168$	3.35690	0.258990
$169$	0	0
$170$	−0.939001	−0.0720181
$171$	−4.85086	−0.370954
$172$	4.02177	0.306657
$173$	21.8213	1.65904	0.829522	−	0.558474i	$-0.188613\pi$
$173$	21.8213	1.65904	0.829522	+	0.558474i	$0.188613\pi$
$174$	−8.12498	−0.615953
$175$	3.35690	0.253757
$176$	1.69202	0.127541
$177$	0.417895	0.0314109
$178$	−9.47650	−0.710294
$179$	−20.2513	−1.51365	−0.756826	−	0.653616i	$-0.773251\pi$
$179$	−20.2513	−1.51365	−0.756826	+	0.653616i	$0.773251\pi$
$180$	−1.00000	−0.0745356
$181$	14.4969	1.07755	0.538775	−	0.842450i	$-0.318887\pi$
$181$	14.4969	1.07755	0.538775	+	0.842450i	$0.318887\pi$
$182$	0	0
$183$	0.198062	0.0146412
$184$	4.04892	0.298490
$185$	−11.6310	−0.855130
$186$	4.08815	0.299757
$187$	1.58881	0.116185
$188$	−1.27413	−0.0929252
$189$	3.35690	0.244178
$190$	4.85086	0.351918
$191$	−10.1806	−0.736643	−0.368321	−	0.929699i	$-0.620067\pi$
$191$	−10.1806	−0.736643	−0.368321	+	0.929699i	$0.620067\pi$
$192$	1.00000	0.0721688
$193$	27.6407	1.98962	0.994811	−	0.101741i	$-0.0324412\pi$
$193$	27.6407	1.98962	0.994811	+	0.101741i	$0.0324412\pi$
$194$	15.4547	1.10958
$195$	0	0
$196$	4.26875	0.304911
$197$	−13.0261	−0.928070	−0.464035	−	0.885817i	$-0.653599\pi$
$197$	−13.0261	−0.928070	−0.464035	+	0.885817i	$0.653599\pi$
$198$	1.69202	0.120247
$199$	6.67563	0.473223	0.236611	−	0.971604i	$-0.423963\pi$
$199$	6.67563	0.473223	0.236611	+	0.971604i	$0.423963\pi$
$200$	1.00000	0.0707107
$201$	8.93900	0.630509
$202$	5.38404	0.378820
$203$	−27.2747	−1.91431
$204$	0.939001	0.0657432
$205$	−3.86294	−0.269799
$206$	4.08575	0.284668
$207$	4.04892	0.281419
$208$	0	0
$209$	−8.20775	−0.567742
$210$	−3.35690	−0.231648
$211$	−11.3056	−0.778309	−0.389154	−	0.921173i	$-0.627233\pi$
$211$	−11.3056	−0.778309	−0.389154	+	0.921173i	$0.627233\pi$
$212$	5.74094	0.394289
$213$	−5.15883	−0.353477
$214$	−16.1196	−1.10191
$215$	−4.02177	−0.274282
$216$	1.00000	0.0680414
$217$	13.7235	0.931611
$218$	−14.2325	−0.963947
$219$	−11.5308	−0.779179
$220$	−1.69202	−0.114076
$221$	0	0
$222$	11.6310	0.780623
$223$	18.0911	1.21147	0.605736	−	0.795666i	$-0.292879\pi$
$223$	18.0911	1.21147	0.605736	+	0.795666i	$0.292879\pi$
$224$	3.35690	0.224292
$225$	1.00000	0.0666667
$226$	−13.3274	−0.886523
$227$	−9.37196	−0.622039	−0.311019	−	0.950404i	$-0.600670\pi$
$227$	−9.37196	−0.622039	−0.311019	+	0.950404i	$0.600670\pi$
$228$	−4.85086	−0.321256
$229$	21.2664	1.40532	0.702660	−	0.711526i	$-0.251995\pi$
$229$	21.2664	1.40532	0.702660	+	0.711526i	$0.251995\pi$
$230$	−4.04892	−0.266978
$231$	5.67994	0.373713
$232$	−8.12498	−0.533431
$233$	2.03146	0.133085	0.0665427	−	0.997784i	$-0.478803\pi$
$233$	2.03146	0.133085	0.0665427	+	0.997784i	$0.478803\pi$
$234$	0	0
$235$	1.27413	0.0831149
$236$	0.417895	0.0272026
$237$	−4.94869	−0.321452
$238$	3.15213	0.204322
$239$	−11.9903	−0.775589	−0.387794	−	0.921746i	$-0.626763\pi$
$239$	−11.9903	−0.775589	−0.387794	+	0.921746i	$0.626763\pi$
$240$	−1.00000	−0.0645497
$241$	21.7627	1.40186	0.700930	−	0.713230i	$-0.252769\pi$
$241$	21.7627	1.40186	0.700930	+	0.713230i	$0.252769\pi$
$242$	−8.13706	−0.523070
$243$	1.00000	0.0641500
$244$	0.198062	0.0126796
$245$	−4.26875	−0.272720
$246$	3.86294	0.246292
$247$	0	0
$248$	4.08815	0.259598
$249$	13.1739	0.834862
$250$	−1.00000	−0.0632456
$251$	13.7506	0.867932	0.433966	−	0.900929i	$-0.357114\pi$
$251$	13.7506	0.867932	0.433966	+	0.900929i	$0.357114\pi$
$252$	3.35690	0.211465
$253$	6.85086	0.430710
$254$	−12.8509	−0.806334
$255$	−0.939001	−0.0588025
$256$	1.00000	0.0625000
$257$	−24.1782	−1.50820	−0.754098	−	0.656762i	$-0.771925\pi$
$257$	−24.1782	−1.50820	−0.754098	+	0.656762i	$0.771925\pi$
$258$	4.02177	0.250384
$259$	39.0441	2.42608
$260$	0	0
$261$	−8.12498	−0.502924
$262$	−0.570024	−0.0352162
$263$	0.960771	0.0592437	0.0296218	−	0.999561i	$-0.490570\pi$
$263$	0.960771	0.0592437	0.0296218	+	0.999561i	$0.490570\pi$
$264$	1.69202	0.104137
$265$	−5.74094	−0.352663
$266$	−16.2838	−0.998425
$267$	−9.47650	−0.579952
$268$	8.93900	0.546036
$269$	10.0761	0.614348	0.307174	−	0.951653i	$-0.400617\pi$
$269$	10.0761	0.614348	0.307174	+	0.951653i	$0.400617\pi$
$270$	−1.00000	−0.0608581
$271$	−14.9584	−0.908657	−0.454328	−	0.890834i	$-0.650121\pi$
$271$	−14.9584	−0.908657	−0.454328	+	0.890834i	$0.650121\pi$
$272$	0.939001	0.0569353
$273$	0	0
$274$	21.5405	1.30131
$275$	1.69202	0.102033
$276$	4.04892	0.243716
$277$	−13.0465	−0.783890	−0.391945	−	0.919989i	$-0.628198\pi$
$277$	−13.0465	−0.783890	−0.391945	+	0.919989i	$0.628198\pi$
$278$	7.09783	0.425700
$279$	4.08815	0.244751
$280$	−3.35690	−0.200613
$281$	16.2881	0.971668	0.485834	−	0.874051i	$-0.338516\pi$
$281$	16.2881	0.971668	0.485834	+	0.874051i	$0.338516\pi$
$282$	−1.27413	−0.0758731
$283$	−12.3773	−0.735756	−0.367878	−	0.929874i	$-0.619916\pi$
$283$	−12.3773	−0.735756	−0.367878	+	0.929874i	$0.619916\pi$
$284$	−5.15883	−0.306120
$285$	4.85086	0.287340
$286$	0	0
$287$	12.9675	0.765446
$288$	1.00000	0.0589256
$289$	−16.1183	−0.948134
$290$	8.12498	0.477115
$291$	15.4547	0.905972
$292$	−11.5308	−0.674789
$293$	−1.73663	−0.101455	−0.0507274	−	0.998713i	$-0.516154\pi$
$293$	−1.73663	−0.101455	−0.0507274	+	0.998713i	$0.516154\pi$
$294$	4.26875	0.248959
$295$	−0.417895	−0.0243308
$296$	11.6310	0.676039
$297$	1.69202	0.0981810
$298$	−1.14914	−0.0665682
$299$	0	0
$300$	1.00000	0.0577350
$301$	13.5007	0.778165
$302$	0.0217703	0.00125274
$303$	5.38404	0.309305
$304$	−4.85086	−0.278216
$305$	−0.198062	−0.0113410
$306$	0.939001	0.0536791
$307$	25.4403	1.45195	0.725976	−	0.687720i	$-0.241388\pi$
$307$	25.4403	1.45195	0.725976	+	0.687720i	$0.241388\pi$
$308$	5.67994	0.323645
$309$	4.08575	0.232430
$310$	−4.08815	−0.232191
$311$	−10.0325	−0.568892	−0.284446	−	0.958692i	$-0.591810\pi$
$311$	−10.0325	−0.568892	−0.284446	+	0.958692i	$0.591810\pi$
$312$	0	0
$313$	−22.3274	−1.26202	−0.631008	−	0.775776i	$-0.717359\pi$
$313$	−22.3274	−1.26202	−0.631008	+	0.775776i	$0.717359\pi$
$314$	−10.1588	−0.573296
$315$	−3.35690	−0.189140
$316$	−4.94869	−0.278386
$317$	−5.33811	−0.299818	−0.149909	−	0.988700i	$-0.547898\pi$
$317$	−5.33811	−0.299818	−0.149909	+	0.988700i	$0.547898\pi$
$318$	5.74094	0.321936
$319$	−13.7476	−0.769720
$320$	−1.00000	−0.0559017
$321$	−16.1196	−0.899709
$322$	13.5918	0.757441
$323$	−4.55496	−0.253445
$324$	1.00000	0.0555556
$325$	0	0
$326$	19.1511	1.06068
$327$	−14.2325	−0.787059
$328$	3.86294	0.213295
$329$	−4.27711	−0.235805
$330$	−1.69202	−0.0931427
$331$	−4.49827	−0.247247	−0.123624	−	0.992329i	$-0.539452\pi$
$331$	−4.49827	−0.247247	−0.123624	+	0.992329i	$0.539452\pi$
$332$	13.1739	0.723012
$333$	11.6310	0.637376
$334$	−15.2174	−0.832661
$335$	−8.93900	−0.488390
$336$	3.35690	0.183134
$337$	−11.5676	−0.630129	−0.315064	−	0.949070i	$-0.602026\pi$
$337$	−11.5676	−0.630129	−0.315064	+	0.949070i	$0.602026\pi$
$338$	0	0
$339$	−13.3274	−0.723843
$340$	−0.939001	−0.0509245
$341$	6.91723	0.374589
$342$	−4.85086	−0.262304
$343$	−9.16852	−0.495054
$344$	4.02177	0.216839
$345$	−4.04892	−0.217986
$346$	21.8213	1.17312
$347$	27.1226	1.45602	0.728008	−	0.685568i	$-0.240446\pi$
$347$	27.1226	1.45602	0.728008	+	0.685568i	$0.240446\pi$
$348$	−8.12498	−0.435545
$349$	12.8562	0.688178	0.344089	−	0.938937i	$-0.388188\pi$
$349$	12.8562	0.688178	0.344089	+	0.938937i	$0.388188\pi$
$350$	3.35690	0.179434
$351$	0	0
$352$	1.69202	0.0901850
$353$	24.6262	1.31072	0.655361	−	0.755316i	$-0.272516\pi$
$353$	24.6262	1.31072	0.655361	+	0.755316i	$0.272516\pi$
$354$	0.417895	0.0222109
$355$	5.15883	0.273802
$356$	−9.47650	−0.502254
$357$	3.15213	0.166828
$358$	−20.2513	−1.07031
$359$	−23.8629	−1.25944	−0.629719	−	0.776823i	$-0.716830\pi$
$359$	−23.8629	−1.25944	−0.629719	+	0.776823i	$0.716830\pi$
$360$	−1.00000	−0.0527046
$361$	4.53079	0.238463
$362$	14.4969	0.761942
$363$	−8.13706	−0.427085
$364$	0	0
$365$	11.5308	0.603549
$366$	0.198062	0.0103529
$367$	33.1933	1.73267	0.866337	−	0.499459i	$-0.166468\pi$
$367$	33.1933	1.73267	0.866337	+	0.499459i	$0.166468\pi$
$368$	4.04892	0.211064
$369$	3.86294	0.201096
$370$	−11.6310	−0.604668
$371$	19.2717	1.00054
$372$	4.08815	0.211960
$373$	−10.8465	−0.561613	−0.280806	−	0.959764i	$-0.590602\pi$
$373$	−10.8465	−0.561613	−0.280806	+	0.959764i	$0.590602\pi$
$374$	1.58881	0.0821554
$375$	−1.00000	−0.0516398
$376$	−1.27413	−0.0657081
$377$	0	0
$378$	3.35690	0.172660
$379$	−6.09485	−0.313071	−0.156536	−	0.987672i	$-0.550033\pi$
$379$	−6.09485	−0.313071	−0.156536	+	0.987672i	$0.550033\pi$
$380$	4.85086	0.248844
$381$	−12.8509	−0.658369
$382$	−10.1806	−0.520885
$383$	−7.95407	−0.406434	−0.203217	−	0.979134i	$-0.565140\pi$
$383$	−7.95407	−0.406434	−0.203217	+	0.979134i	$0.565140\pi$
$384$	1.00000	0.0510310
$385$	−5.67994	−0.289477
$386$	27.6407	1.40688
$387$	4.02177	0.204438
$388$	15.4547	0.784595
$389$	1.50365	0.0762380	0.0381190	−	0.999273i	$-0.487863\pi$
$389$	1.50365	0.0762380	0.0381190	+	0.999273i	$0.487863\pi$
$390$	0	0
$391$	3.80194	0.192272
$392$	4.26875	0.215604
$393$	−0.570024	−0.0287539
$394$	−13.0261	−0.656245
$395$	4.94869	0.248996
$396$	1.69202	0.0850273
$397$	34.9627	1.75473	0.877364	−	0.479826i	$-0.159300\pi$
$397$	34.9627	1.75473	0.877364	+	0.479826i	$0.159300\pi$
$398$	6.67563	0.334619
$399$	−16.2838	−0.815210
$400$	1.00000	0.0500000
$401$	−31.1148	−1.55380	−0.776900	−	0.629624i	$-0.783209\pi$
$401$	−31.1148	−1.55380	−0.776900	+	0.629624i	$0.783209\pi$
$402$	8.93900	0.445837
$403$	0	0
$404$	5.38404	0.267866
$405$	−1.00000	−0.0496904
$406$	−27.2747	−1.35362
$407$	19.6799	0.975498
$408$	0.939001	0.0464875
$409$	−32.7318	−1.61849	−0.809243	−	0.587474i	$-0.800122\pi$
$409$	−32.7318	−1.61849	−0.809243	+	0.587474i	$0.800122\pi$
$410$	−3.86294	−0.190777
$411$	21.5405	1.06251
$412$	4.08575	0.201291
$413$	1.40283	0.0690287
$414$	4.04892	0.198993
$415$	−13.1739	−0.646681
$416$	0	0
$417$	7.09783	0.347582
$418$	−8.20775	−0.401454
$419$	13.0694	0.638480	0.319240	−	0.947674i	$-0.396572\pi$
$419$	13.0694	0.638480	0.319240	+	0.947674i	$0.396572\pi$
$420$	−3.35690	−0.163800
$421$	16.4789	0.803132	0.401566	−	0.915830i	$-0.368466\pi$
$421$	16.4789	0.803132	0.401566	+	0.915830i	$0.368466\pi$
$422$	−11.3056	−0.550347
$423$	−1.27413	−0.0619502
$424$	5.74094	0.278805
$425$	0.939001	0.0455482
$426$	−5.15883	−0.249946
$427$	0.664874	0.0321755
$428$	−16.1196	−0.779171
$429$	0	0
$430$	−4.02177	−0.193947
$431$	−41.0640	−1.97798	−0.988991	−	0.147974i	$-0.952725\pi$
$431$	−41.0640	−1.97798	−0.988991	+	0.147974i	$0.952725\pi$
$432$	1.00000	0.0481125
$433$	−6.04593	−0.290549	−0.145275	−	0.989391i	$-0.546407\pi$
$433$	−6.04593	−0.290549	−0.145275	+	0.989391i	$0.546407\pi$
$434$	13.7235	0.658748
$435$	8.12498	0.389563
$436$	−14.2325	−0.681613
$437$	−19.6407	−0.939543
$438$	−11.5308	−0.550963
$439$	−26.2543	−1.25305	−0.626524	−	0.779402i	$-0.715523\pi$
$439$	−26.2543	−1.25305	−0.626524	+	0.779402i	$0.715523\pi$
$440$	−1.69202	−0.0806640
$441$	4.26875	0.203274
$442$	0	0
$443$	−39.3846	−1.87122	−0.935610	−	0.353035i	$-0.885150\pi$
$443$	−39.3846	−1.87122	−0.935610	+	0.353035i	$0.885150\pi$
$444$	11.6310	0.551984
$445$	9.47650	0.449229
$446$	18.0911	0.856640
$447$	−1.14914	−0.0543527
$448$	3.35690	0.158598
$449$	−9.39075	−0.443177	−0.221588	−	0.975140i	$-0.571124\pi$
$449$	−9.39075	−0.443177	−0.221588	+	0.975140i	$0.571124\pi$
$450$	1.00000	0.0471405
$451$	6.53617	0.307776
$452$	−13.3274	−0.626866
$453$	0.0217703	0.00102286
$454$	−9.37196	−0.439848
$455$	0	0
$456$	−4.85086	−0.227162
$457$	−2.66487	−0.124658	−0.0623288	−	0.998056i	$-0.519853\pi$
$457$	−2.66487	−0.124658	−0.0623288	+	0.998056i	$0.519853\pi$
$458$	21.2664	0.993712
$459$	0.939001	0.0438288
$460$	−4.04892	−0.188782
$461$	−24.5284	−1.14240	−0.571201	−	0.820810i	$-0.693522\pi$
$461$	−24.5284	−1.14240	−0.571201	+	0.820810i	$0.693522\pi$
$462$	5.67994	0.264255
$463$	−4.50498	−0.209364	−0.104682	−	0.994506i	$-0.533382\pi$
$463$	−4.50498	−0.209364	−0.104682	+	0.994506i	$0.533382\pi$
$464$	−8.12498	−0.377193
$465$	−4.08815	−0.189583
$466$	2.03146	0.0941055
$467$	21.3317	0.987112	0.493556	−	0.869714i	$-0.335697\pi$
$467$	21.3317	0.987112	0.493556	+	0.869714i	$0.335697\pi$
$468$	0	0
$469$	30.0073	1.38561
$470$	1.27413	0.0587711
$471$	−10.1588	−0.468094
$472$	0.417895	0.0192352
$473$	6.80492	0.312891
$474$	−4.94869	−0.227301
$475$	−4.85086	−0.222572
$476$	3.15213	0.144478
$477$	5.74094	0.262860
$478$	−11.9903	−0.548424
$479$	−32.9517	−1.50560	−0.752800	−	0.658249i	$-0.771297\pi$
$479$	−32.9517	−1.50560	−0.752800	+	0.658249i	$0.771297\pi$
$480$	−1.00000	−0.0456435
$481$	0	0
$482$	21.7627	0.991264
$483$	13.5918	0.618448
$484$	−8.13706	−0.369867
$485$	−15.4547	−0.701763
$486$	1.00000	0.0453609
$487$	−9.33034	−0.422798	−0.211399	−	0.977400i	$-0.567802\pi$
$487$	−9.33034	−0.422798	−0.211399	+	0.977400i	$0.567802\pi$
$488$	0.198062	0.00896586
$489$	19.1511	0.866041
$490$	−4.26875	−0.192842
$491$	−20.4349	−0.922213	−0.461107	−	0.887345i	$-0.652547\pi$
$491$	−20.4349	−0.922213	−0.461107	+	0.887345i	$0.652547\pi$
$492$	3.86294	0.174155
$493$	−7.62937	−0.343609
$494$	0	0
$495$	−1.69202	−0.0760507
$496$	4.08815	0.183563
$497$	−17.3177	−0.776804
$498$	13.1739	0.590337
$499$	3.54958	0.158901	0.0794505	−	0.996839i	$-0.474683\pi$
$499$	3.54958	0.158901	0.0794505	+	0.996839i	$0.474683\pi$
$500$	−1.00000	−0.0447214
$501$	−15.2174	−0.679865
$502$	13.7506	0.613721
$503$	−19.8146	−0.883490	−0.441745	−	0.897141i	$-0.645640\pi$
$503$	−19.8146	−0.883490	−0.441745	+	0.897141i	$0.645640\pi$
$504$	3.35690	0.149528
$505$	−5.38404	−0.239587
$506$	6.85086	0.304558
$507$	0	0
$508$	−12.8509	−0.570164
$509$	32.4325	1.43754	0.718772	−	0.695246i	$-0.244704\pi$
$509$	32.4325	1.43754	0.718772	+	0.695246i	$0.244704\pi$
$510$	−0.939001	−0.0415797
$511$	−38.7077	−1.71233
$512$	1.00000	0.0441942
$513$	−4.85086	−0.214170
$514$	−24.1782	−1.06646
$515$	−4.08575	−0.180040
$516$	4.02177	0.177049
$517$	−2.15585	−0.0948142
$518$	39.0441	1.71550
$519$	21.8213	0.957849
$520$	0	0
$521$	7.87694	0.345095	0.172547	−	0.985001i	$-0.444800\pi$
$521$	7.87694	0.345095	0.172547	+	0.985001i	$0.444800\pi$
$522$	−8.12498	−0.355621
$523$	−23.4276	−1.02442	−0.512208	−	0.858861i	$-0.671172\pi$
$523$	−23.4276	−1.02442	−0.512208	+	0.858861i	$0.671172\pi$
$524$	−0.570024	−0.0249016
$525$	3.35690	0.146507
$526$	0.960771	0.0418916
$527$	3.83877	0.167220
$528$	1.69202	0.0736358
$529$	−6.60627	−0.287229
$530$	−5.74094	−0.249370
$531$	0.417895	0.0181351
$532$	−16.2838	−0.705993
$533$	0	0
$534$	−9.47650	−0.410088
$535$	16.1196	0.696911
$536$	8.93900	0.386106
$537$	−20.2513	−0.873908
$538$	10.0761	0.434410
$539$	7.22282	0.311109
$540$	−1.00000	−0.0430331
$541$	−1.21552	−0.0522593	−0.0261297	−	0.999659i	$-0.508318\pi$
$541$	−1.21552	−0.0522593	−0.0261297	+	0.999659i	$0.508318\pi$
$542$	−14.9584	−0.642517
$543$	14.4969	0.622123
$544$	0.939001	0.0402593
$545$	14.2325	0.609654
$546$	0	0
$547$	−15.1371	−0.647214	−0.323607	−	0.946192i	$-0.604896\pi$
$547$	−15.1371	−0.647214	−0.323607	+	0.946192i	$0.604896\pi$
$548$	21.5405	0.920164
$549$	0.198062	0.00845309
$550$	1.69202	0.0721480
$551$	39.4131	1.67905
$552$	4.04892	0.172333
$553$	−16.6122	−0.706424
$554$	−13.0465	−0.554294
$555$	−11.6310	−0.493709
$556$	7.09783	0.301015
$557$	0.147817	0.00626321	0.00313160	−	0.999995i	$-0.499003\pi$
$557$	0.147817	0.00626321	0.00313160	+	0.999995i	$0.499003\pi$
$558$	4.08815	0.173065
$559$	0	0
$560$	−3.35690	−0.141855
$561$	1.58881	0.0670796
$562$	16.2881	0.687073
$563$	40.6945	1.71507	0.857535	−	0.514426i	$-0.171995\pi$
$563$	40.6945	1.71507	0.857535	+	0.514426i	$0.171995\pi$
$564$	−1.27413	−0.0536504
$565$	13.3274	0.560686
$566$	−12.3773	−0.520258
$567$	3.35690	0.140976
$568$	−5.15883	−0.216460
$569$	−26.2433	−1.10017	−0.550087	−	0.835107i	$-0.685406\pi$
$569$	−26.2433	−1.10017	−0.550087	+	0.835107i	$0.685406\pi$
$570$	4.85086	0.203180
$571$	2.31575	0.0969110	0.0484555	−	0.998825i	$-0.484570\pi$
$571$	2.31575	0.0969110	0.0484555	+	0.998825i	$0.484570\pi$
$572$	0	0
$573$	−10.1806	−0.425301
$574$	12.9675	0.541252
$575$	4.04892	0.168852
$576$	1.00000	0.0416667
$577$	−14.5241	−0.604646	−0.302323	−	0.953206i	$-0.597762\pi$
$577$	−14.5241	−0.604646	−0.302323	+	0.953206i	$0.597762\pi$
$578$	−16.1183	−0.670432
$579$	27.6407	1.14871
$580$	8.12498	0.337372
$581$	44.2234	1.83470
$582$	15.4547	0.640619
$583$	9.71379	0.402304
$584$	−11.5308	−0.477148
$585$	0	0
$586$	−1.73663	−0.0717394
$587$	−32.9028	−1.35804	−0.679021	−	0.734119i	$-0.737596\pi$
$587$	−32.9028	−1.35804	−0.679021	+	0.734119i	$0.737596\pi$
$588$	4.26875	0.176040
$589$	−19.8310	−0.817122
$590$	−0.417895	−0.0172045
$591$	−13.0261	−0.535821
$592$	11.6310	0.478032
$593$	−36.0146	−1.47894	−0.739471	−	0.673188i	$-0.764924\pi$
$593$	−36.0146	−1.47894	−0.739471	+	0.673188i	$0.764924\pi$
$594$	1.69202	0.0694245
$595$	−3.15213	−0.129225
$596$	−1.14914	−0.0470708
$597$	6.67563	0.273215
$598$	0	0
$599$	−29.4644	−1.20388	−0.601942	−	0.798540i	$-0.705606\pi$
$599$	−29.4644	−1.20388	−0.601942	+	0.798540i	$0.705606\pi$
$600$	1.00000	0.0408248
$601$	−28.4004	−1.15848	−0.579239	−	0.815158i	$-0.696650\pi$
$601$	−28.4004	−1.15848	−0.579239	+	0.815158i	$0.696650\pi$
$602$	13.5007	0.550246
$603$	8.93900	0.364024
$604$	0.0217703	0.000885819 0
$605$	8.13706	0.330819
$606$	5.38404	0.218712
$607$	15.6450	0.635012	0.317506	−	0.948256i	$-0.397155\pi$
$607$	15.6450	0.635012	0.317506	+	0.948256i	$0.397155\pi$
$608$	−4.85086	−0.196728
$609$	−27.2747	−1.10523
$610$	−0.198062	−0.00801931
$611$	0	0
$612$	0.939001	0.0379569
$613$	−17.6329	−0.712188	−0.356094	−	0.934450i	$-0.615892\pi$
$613$	−17.6329	−0.712188	−0.356094	+	0.934450i	$0.615892\pi$
$614$	25.4403	1.02669
$615$	−3.86294	−0.155769
$616$	5.67994	0.228851
$617$	10.8582	0.437133	0.218566	−	0.975822i	$-0.429862\pi$
$617$	10.8582	0.437133	0.218566	+	0.975822i	$0.429862\pi$
$618$	4.08575	0.164353
$619$	−34.2083	−1.37495	−0.687475	−	0.726208i	$-0.741281\pi$
$619$	−34.2083	−1.37495	−0.687475	+	0.726208i	$0.741281\pi$
$620$	−4.08815	−0.164184
$621$	4.04892	0.162477
$622$	−10.0325	−0.402268
$623$	−31.8116	−1.27451
$624$	0	0
$625$	1.00000	0.0400000
$626$	−22.3274	−0.892381
$627$	−8.20775	−0.327786
$628$	−10.1588	−0.405382
$629$	10.9215	0.435470
$630$	−3.35690	−0.133742
$631$	31.9571	1.27219	0.636095	−	0.771611i	$-0.280549\pi$
$631$	31.9571	1.27219	0.636095	+	0.771611i	$0.280549\pi$
$632$	−4.94869	−0.196848
$633$	−11.3056	−0.449357
$634$	−5.33811	−0.212003
$635$	12.8509	0.509971
$636$	5.74094	0.227643
$637$	0	0
$638$	−13.7476	−0.544274
$639$	−5.15883	−0.204080
$640$	−1.00000	−0.0395285
$641$	−45.8297	−1.81016	−0.905082	−	0.425238i	$-0.860190\pi$
$641$	−45.8297	−1.81016	−0.905082	+	0.425238i	$0.860190\pi$
$642$	−16.1196	−0.636190
$643$	20.6418	0.814032	0.407016	−	0.913421i	$-0.366569\pi$
$643$	20.6418	0.814032	0.407016	+	0.913421i	$0.366569\pi$
$644$	13.5918	0.535592
$645$	−4.02177	−0.158357
$646$	−4.55496	−0.179212
$647$	1.40389	0.0551928	0.0275964	−	0.999619i	$-0.491215\pi$
$647$	1.40389	0.0551928	0.0275964	+	0.999619i	$0.491215\pi$
$648$	1.00000	0.0392837
$649$	0.707087	0.0277556
$650$	0	0
$651$	13.7235	0.537866
$652$	19.1511	0.750014
$653$	−4.54229	−0.177753	−0.0888767	−	0.996043i	$-0.528328\pi$
$653$	−4.54229	−0.177753	−0.0888767	+	0.996043i	$0.528328\pi$
$654$	−14.2325	−0.556535
$655$	0.570024	0.0222727
$656$	3.86294	0.150822
$657$	−11.5308	−0.449859
$658$	−4.27711	−0.166739
$659$	17.4161	0.678435	0.339217	−	0.940708i	$-0.389838\pi$
$659$	17.4161	0.678435	0.339217	+	0.940708i	$0.389838\pi$
$660$	−1.69202	−0.0658618
$661$	43.3682	1.68683	0.843415	−	0.537263i	$-0.180542\pi$
$661$	43.3682	1.68683	0.843415	+	0.537263i	$0.180542\pi$
$662$	−4.49827	−0.174830
$663$	0	0
$664$	13.1739	0.511246
$665$	16.2838	0.631459
$666$	11.6310	0.450693
$667$	−32.8974	−1.27379
$668$	−15.2174	−0.588780
$669$	18.0911	0.699443
$670$	−8.93900	−0.345344
$671$	0.335126	0.0129374
$672$	3.35690	0.129495
$673$	−3.49875	−0.134867	−0.0674334	−	0.997724i	$-0.521481\pi$
$673$	−3.49875	−0.134867	−0.0674334	+	0.997724i	$0.521481\pi$
$674$	−11.5676	−0.445568
$675$	1.00000	0.0384900
$676$	0	0
$677$	−13.3284	−0.512253	−0.256126	−	0.966643i	$-0.582446\pi$
$677$	−13.3284	−0.512253	−0.256126	+	0.966643i	$0.582446\pi$
$678$	−13.3274	−0.511834
$679$	51.8799	1.99097
$680$	−0.939001	−0.0360090
$681$	−9.37196	−0.359134
$682$	6.91723	0.264874
$683$	−24.1739	−0.924989	−0.462494	−	0.886622i	$-0.653045\pi$
$683$	−24.1739	−0.924989	−0.462494	+	0.886622i	$0.653045\pi$
$684$	−4.85086	−0.185477
$685$	−21.5405	−0.823020
$686$	−9.16852	−0.350056
$687$	21.2664	0.811362
$688$	4.02177	0.153329
$689$	0	0
$690$	−4.04892	−0.154140
$691$	−37.8810	−1.44106	−0.720530	−	0.693423i	$-0.756102\pi$
$691$	−37.8810	−1.44106	−0.720530	+	0.693423i	$0.756102\pi$
$692$	21.8213	0.829522
$693$	5.67994	0.215763
$694$	27.1226	1.02956
$695$	−7.09783	−0.269236
$696$	−8.12498	−0.307977
$697$	3.62730	0.137394
$698$	12.8562	0.486616
$699$	2.03146	0.0768368
$700$	3.35690	0.126879
$701$	−21.5967	−0.815696	−0.407848	−	0.913050i	$-0.633721\pi$
$701$	−21.5967	−0.815696	−0.407848	+	0.913050i	$0.633721\pi$
$702$	0	0
$703$	−56.4204	−2.12794
$704$	1.69202	0.0637705
$705$	1.27413	0.0479864
$706$	24.6262	0.926821
$707$	18.0737	0.679730
$708$	0.417895	0.0157054
$709$	41.3062	1.55129	0.775643	−	0.631172i	$-0.217426\pi$
$709$	41.3062	1.55129	0.775643	+	0.631172i	$0.217426\pi$
$710$	5.15883	0.193608
$711$	−4.94869	−0.185590
$712$	−9.47650	−0.355147
$713$	16.5526	0.619898
$714$	3.15213	0.117965
$715$	0	0
$716$	−20.2513	−0.756826
$717$	−11.9903	−0.447786
$718$	−23.8629	−0.890557
$719$	−35.5338	−1.32519	−0.662593	−	0.748980i	$-0.730544\pi$
$719$	−35.5338	−1.32519	−0.662593	+	0.748980i	$0.730544\pi$
$720$	−1.00000	−0.0372678
$721$	13.7154	0.510790
$722$	4.53079	0.168619
$723$	21.7627	0.809364
$724$	14.4969	0.538775
$725$	−8.12498	−0.301754
$726$	−8.13706	−0.301995
$727$	19.6635	0.729281	0.364640	−	0.931148i	$-0.381192\pi$
$727$	19.6635	0.729281	0.364640	+	0.931148i	$0.381192\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	11.5308	0.426774
$731$	3.77645	0.139677
$732$	0.198062	0.00732059
$733$	−46.8702	−1.73119	−0.865596	−	0.500743i	$-0.833060\pi$
$733$	−46.8702	−1.73119	−0.865596	+	0.500743i	$0.833060\pi$
$734$	33.1933	1.22519
$735$	−4.26875	−0.157455
$736$	4.04892	0.149245
$737$	15.1250	0.557136
$738$	3.86294	0.142197
$739$	−8.57779	−0.315539	−0.157770	−	0.987476i	$-0.550430\pi$
$739$	−8.57779	−0.315539	−0.157770	+	0.987476i	$0.550430\pi$
$740$	−11.6310	−0.427565
$741$	0	0
$742$	19.2717	0.707488
$743$	−44.9506	−1.64908	−0.824539	−	0.565805i	$-0.808565\pi$
$743$	−44.9506	−1.64908	−0.824539	+	0.565805i	$0.808565\pi$
$744$	4.08815	0.149879
$745$	1.14914	0.0421014
$746$	−10.8465	−0.397120
$747$	13.1739	0.482008
$748$	1.58881	0.0580926
$749$	−54.1118	−1.97720
$750$	−1.00000	−0.0365148
$751$	44.0374	1.60695	0.803474	−	0.595339i	$-0.202982\pi$
$751$	44.0374	1.60695	0.803474	+	0.595339i	$0.202982\pi$
$752$	−1.27413	−0.0464626
$753$	13.7506	0.501101
$754$	0	0
$755$	−0.0217703	−0.000792301 0
$756$	3.35690	0.122089
$757$	−13.2798	−0.482661	−0.241331	−	0.970443i	$-0.577584\pi$
$757$	−13.2798	−0.482661	−0.241331	+	0.970443i	$0.577584\pi$
$758$	−6.09485	−0.221375
$759$	6.85086	0.248670
$760$	4.85086	0.175959
$761$	9.11231	0.330321	0.165160	−	0.986267i	$-0.447186\pi$
$761$	9.11231	0.330321	0.165160	+	0.986267i	$0.447186\pi$
$762$	−12.8509	−0.465537
$763$	−47.7770	−1.72964
$764$	−10.1806	−0.368321
$765$	−0.939001	−0.0339497
$766$	−7.95407	−0.287392
$767$	0	0
$768$	1.00000	0.0360844
$769$	−31.7784	−1.14596	−0.572979	−	0.819570i	$-0.694212\pi$
$769$	−31.7784	−1.14596	−0.572979	+	0.819570i	$0.694212\pi$
$770$	−5.67994	−0.204691
$771$	−24.1782	−0.870757
$772$	27.6407	0.994811
$773$	7.11960	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$773$	7.11960	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$774$	4.02177	0.144560
$775$	4.08815	0.146851
$776$	15.4547	0.554792
$777$	39.0441	1.40070
$778$	1.50365	0.0539084
$779$	−18.7385	−0.671378
$780$	0	0
$781$	−8.72886	−0.312343
$782$	3.80194	0.135957
$783$	−8.12498	−0.290363
$784$	4.26875	0.152455
$785$	10.1588	0.362584
$786$	−0.570024	−0.0203321
$787$	−44.2121	−1.57599	−0.787995	−	0.615682i	$-0.788881\pi$
$787$	−44.2121	−1.57599	−0.787995	+	0.615682i	$0.788881\pi$
$788$	−13.0261	−0.464035
$789$	0.960771	0.0342044
$790$	4.94869	0.176066
$791$	−44.7385	−1.59072
$792$	1.69202	0.0601234
$793$	0	0
$794$	34.9627	1.24078
$795$	−5.74094	−0.203610
$796$	6.67563	0.236611
$797$	19.2241	0.680954	0.340477	−	0.940253i	$-0.389411\pi$
$797$	19.2241	0.680954	0.340477	+	0.940253i	$0.389411\pi$
$798$	−16.2838	−0.576441
$799$	−1.19641	−0.0423258
$800$	1.00000	0.0353553
$801$	−9.47650	−0.334836
$802$	−31.1148	−1.09870
$803$	−19.5104	−0.688505
$804$	8.93900	0.315254
$805$	−13.5918	−0.479048
$806$	0	0
$807$	10.0761	0.354694
$808$	5.38404	0.189410
$809$	0.0988996	0.00347713	0.00173856	−	0.999998i	$-0.499447\pi$
$809$	0.0988996	0.00347713	0.00173856	+	0.999998i	$0.499447\pi$
$810$	−1.00000	−0.0351364
$811$	6.70304	0.235376	0.117688	−	0.993051i	$-0.462452\pi$
$811$	6.70304	0.235376	0.117688	+	0.993051i	$0.462452\pi$
$812$	−27.2747	−0.957155
$813$	−14.9584	−0.524613
$814$	19.6799	0.689782
$815$	−19.1511	−0.670833
$816$	0.939001	0.0328716
$817$	−19.5090	−0.682534
$818$	−32.7318	−1.14444
$819$	0	0
$820$	−3.86294	−0.134900
$821$	−23.7450	−0.828706	−0.414353	−	0.910116i	$-0.635992\pi$
$821$	−23.7450	−0.828706	−0.414353	+	0.910116i	$0.635992\pi$
$822$	21.5405	0.751311
$823$	18.0049	0.627611	0.313806	−	0.949487i	$-0.398396\pi$
$823$	18.0049	0.627611	0.313806	+	0.949487i	$0.398396\pi$
$824$	4.08575	0.142334
$825$	1.69202	0.0589086
$826$	1.40283	0.0488107
$827$	40.4566	1.40682	0.703408	−	0.710787i	$-0.251661\pi$
$827$	40.4566	1.40682	0.703408	+	0.710787i	$0.251661\pi$
$828$	4.04892	0.140710
$829$	8.56704	0.297546	0.148773	−	0.988871i	$-0.452468\pi$
$829$	8.56704	0.297546	0.148773	+	0.988871i	$0.452468\pi$
$830$	−13.1739	−0.457273
$831$	−13.0465	−0.452579
$832$	0	0
$833$	4.00836	0.138881
$834$	7.09783	0.245778
$835$	15.2174	0.526621
$836$	−8.20775	−0.283871
$837$	4.08815	0.141307
$838$	13.0694	0.451474
$839$	−6.75600	−0.233243	−0.116622	−	0.993176i	$-0.537206\pi$
$839$	−6.75600	−0.233243	−0.116622	+	0.993176i	$0.537206\pi$
$840$	−3.35690	−0.115824
$841$	37.0153	1.27639
$842$	16.4789	0.567900
$843$	16.2881	0.560993
$844$	−11.3056	−0.389154
$845$	0	0
$846$	−1.27413	−0.0438054
$847$	−27.3153	−0.938564
$848$	5.74094	0.197145
$849$	−12.3773	−0.424789
$850$	0.939001	0.0322075
$851$	47.0930	1.61433
$852$	−5.15883	−0.176739
$853$	−37.1269	−1.27120	−0.635600	−	0.772018i	$-0.719247\pi$
$853$	−37.1269	−1.27120	−0.635600	+	0.772018i	$0.719247\pi$
$854$	0.664874	0.0227515
$855$	4.85086	0.165896
$856$	−16.1196	−0.550957
$857$	−24.3937	−0.833274	−0.416637	−	0.909073i	$-0.636791\pi$
$857$	−24.3937	−0.833274	−0.416637	+	0.909073i	$0.636791\pi$
$858$	0	0
$859$	43.9366	1.49910	0.749549	−	0.661949i	$-0.230270\pi$
$859$	43.9366	1.49910	0.749549	+	0.661949i	$0.230270\pi$
$860$	−4.02177	−0.137141
$861$	12.9675	0.441930
$862$	−41.0640	−1.39864
$863$	16.3846	0.557739	0.278870	−	0.960329i	$-0.410040\pi$
$863$	16.3846	0.557739	0.278870	+	0.960329i	$0.410040\pi$
$864$	1.00000	0.0340207
$865$	−21.8213	−0.741947
$866$	−6.04593	−0.205449
$867$	−16.1183	−0.547405
$868$	13.7235	0.465805
$869$	−8.37329	−0.284044
$870$	8.12498	0.275463
$871$	0	0
$872$	−14.2325	−0.481973
$873$	15.4547	0.523063
$874$	−19.6407	−0.664357
$875$	−3.35690	−0.113484
$876$	−11.5308	−0.389589
$877$	28.1347	0.950040	0.475020	−	0.879975i	$-0.342441\pi$
$877$	28.1347	0.950040	0.475020	+	0.879975i	$0.342441\pi$
$878$	−26.2543	−0.886039
$879$	−1.73663	−0.0585750
$880$	−1.69202	−0.0570380
$881$	39.1454	1.31884	0.659421	−	0.751773i	$-0.270801\pi$
$881$	39.1454	1.31884	0.659421	+	0.751773i	$0.270801\pi$
$882$	4.26875	0.143736
$883$	46.2833	1.55756	0.778779	−	0.627298i	$-0.215839\pi$
$883$	46.2833	1.55756	0.778779	+	0.627298i	$0.215839\pi$
$884$	0	0
$885$	−0.417895	−0.0140474
$886$	−39.3846	−1.32315
$887$	−3.08097	−0.103449	−0.0517244	−	0.998661i	$-0.516472\pi$
$887$	−3.08097	−0.103449	−0.0517244	+	0.998661i	$0.516472\pi$
$888$	11.6310	0.390312
$889$	−43.1390	−1.44684
$890$	9.47650	0.317653
$891$	1.69202	0.0566849
$892$	18.0911	0.605736
$893$	6.18060	0.206826
$894$	−1.14914	−0.0384332
$895$	20.2513	0.676926
$896$	3.35690	0.112146
$897$	0	0
$898$	−9.39075	−0.313373
$899$	−33.2161	−1.10782
$900$	1.00000	0.0333333
$901$	5.39075	0.179592
$902$	6.53617	0.217631
$903$	13.5007	0.449274
$904$	−13.3274	−0.443261
$905$	−14.4969	−0.481895
$906$	0.0217703	0.000723269 0
$907$	−2.61224	−0.0867379	−0.0433689	−	0.999059i	$-0.513809\pi$
$907$	−2.61224	−0.0867379	−0.0433689	+	0.999059i	$0.513809\pi$
$908$	−9.37196	−0.311019
$909$	5.38404	0.178577
$910$	0	0
$911$	24.9302	0.825973	0.412987	−	0.910737i	$-0.364486\pi$
$911$	24.9302	0.825973	0.412987	+	0.910737i	$0.364486\pi$
$912$	−4.85086	−0.160628
$913$	22.2905	0.737709
$914$	−2.66487	−0.0881462
$915$	−0.198062	−0.00654774
$916$	21.2664	0.702660
$917$	−1.91351	−0.0631897
$918$	0.939001	0.0309917
$919$	−54.4462	−1.79602	−0.898008	−	0.439980i	$-0.854986\pi$
$919$	−54.4462	−1.79602	−0.898008	+	0.439980i	$0.854986\pi$
$920$	−4.04892	−0.133489
$921$	25.4403	0.838285
$922$	−24.5284	−0.807800
$923$	0	0
$924$	5.67994	0.186856
$925$	11.6310	0.382426
$926$	−4.50498	−0.148043
$927$	4.08575	0.134194
$928$	−8.12498	−0.266716
$929$	−40.8267	−1.33948	−0.669740	−	0.742596i	$-0.733595\pi$
$929$	−40.8267	−1.33948	−0.669740	+	0.742596i	$0.733595\pi$
$930$	−4.08815	−0.134056
$931$	−20.7071	−0.678647
$932$	2.03146	0.0665427
$933$	−10.0325	−0.328450
$934$	21.3317	0.697993
$935$	−1.58881	−0.0519596
$936$	0	0
$937$	−46.9571	−1.53402	−0.767010	−	0.641635i	$-0.778256\pi$
$937$	−46.9571	−1.53402	−0.767010	+	0.641635i	$0.778256\pi$
$938$	30.0073	0.979773
$939$	−22.3274	−0.728626
$940$	1.27413	0.0415574
$941$	35.8525	1.16876	0.584379	−	0.811481i	$-0.301338\pi$
$941$	35.8525	1.16876	0.584379	+	0.811481i	$0.301338\pi$
$942$	−10.1588	−0.330993
$943$	15.6407	0.509332
$944$	0.417895	0.0136013
$945$	−3.35690	−0.109200
$946$	6.80492	0.221247
$947$	−8.73019	−0.283693	−0.141846	−	0.989889i	$-0.545304\pi$
$947$	−8.73019	−0.283693	−0.141846	+	0.989889i	$0.545304\pi$
$948$	−4.94869	−0.160726
$949$	0	0
$950$	−4.85086	−0.157383
$951$	−5.33811	−0.173100
$952$	3.15213	0.102161
$953$	10.2107	0.330758	0.165379	−	0.986230i	$-0.447115\pi$
$953$	10.2107	0.330758	0.165379	+	0.986230i	$0.447115\pi$
$954$	5.74094	0.185870
$955$	10.1806	0.329437
$956$	−11.9903	−0.387794
$957$	−13.7476	−0.444398
$958$	−32.9517	−1.06462
$959$	72.3092	2.33498
$960$	−1.00000	−0.0322749
$961$	−14.2871	−0.460873
$962$	0	0
$963$	−16.1196	−0.519447
$964$	21.7627	0.700930
$965$	−27.6407	−0.889786
$966$	13.5918	0.437309
$967$	−34.6907	−1.11558	−0.557789	−	0.829983i	$-0.688350\pi$
$967$	−34.6907	−1.11558	−0.557789	+	0.829983i	$0.688350\pi$
$968$	−8.13706	−0.261535
$969$	−4.55496	−0.146326
$970$	−15.4547	−0.496221
$971$	34.8039	1.11691	0.558454	−	0.829535i	$-0.311395\pi$
$971$	34.8039	1.11691	0.558454	+	0.829535i	$0.311395\pi$
$972$	1.00000	0.0320750
$973$	23.8267	0.763849
$974$	−9.33034	−0.298963
$975$	0	0
$976$	0.198062	0.00633982
$977$	23.3086	0.745707	0.372854	−	0.927890i	$-0.378379\pi$
$977$	23.3086	0.745707	0.372854	+	0.927890i	$0.378379\pi$
$978$	19.1511	0.612383
$979$	−16.0344	−0.512463
$980$	−4.26875	−0.136360
$981$	−14.2325	−0.454409
$982$	−20.4349	−0.652103
$983$	41.3639	1.31930	0.659652	−	0.751571i	$-0.270704\pi$
$983$	41.3639	1.31930	0.659652	+	0.751571i	$0.270704\pi$
$984$	3.86294	0.123146
$985$	13.0261	0.415045
$986$	−7.62937	−0.242969
$987$	−4.27711	−0.136142
$988$	0	0
$989$	16.2838	0.517795
$990$	−1.69202	−0.0537760
$991$	49.4209	1.56991	0.784953	−	0.619555i	$-0.212687\pi$
$991$	49.4209	1.56991	0.784953	+	0.619555i	$0.212687\pi$
$992$	4.08815	0.129799
$993$	−4.49827	−0.142748
$994$	−17.3177	−0.549283
$995$	−6.67563	−0.211632
$996$	13.1739	0.417431
$997$	44.1879	1.39944	0.699722	−	0.714415i	$-0.253307\pi$
$997$	44.1879	1.39944	0.699722	+	0.714415i	$0.253307\pi$
$998$	3.54958	0.112360
$999$	11.6310	0.367989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5070.2.a.bw.1.2	yes	3
13.5	odd	4		5070.2.b.z.1351.2		6
13.8	odd	4		5070.2.b.z.1351.5		6
13.12	even	2		5070.2.a.bp.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5070.2.a.bp.1.2	✓	3	13.12	even	2
5070.2.a.bw.1.2	yes	3	1.1	even	1	trivial
5070.2.b.z.1351.2		6	13.5	odd	4
5070.2.b.z.1351.5		6	13.8	odd	4

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:	\( N \)	\(=\)	\( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5070.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.35690 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.69202 q^{11} +1.00000 q^{12} +3.35690 q^{14} -1.00000 q^{15} +1.00000 q^{16} +0.939001 q^{17} +1.00000 q^{18} -4.85086 q^{19} -1.00000 q^{20} +3.35690 q^{21} +1.69202 q^{22} +4.04892 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +3.35690 q^{28} -8.12498 q^{29} -1.00000 q^{30} +4.08815 q^{31} +1.00000 q^{32} +1.69202 q^{33} +0.939001 q^{34} -3.35690 q^{35} +1.00000 q^{36} +11.6310 q^{37} -4.85086 q^{38} -1.00000 q^{40} +3.86294 q^{41} +3.35690 q^{42} +4.02177 q^{43} +1.69202 q^{44} -1.00000 q^{45} +4.04892 q^{46} -1.27413 q^{47} +1.00000 q^{48} +4.26875 q^{49} +1.00000 q^{50} +0.939001 q^{51} +5.74094 q^{53} +1.00000 q^{54} -1.69202 q^{55} +3.35690 q^{56} -4.85086 q^{57} -8.12498 q^{58} +0.417895 q^{59} -1.00000 q^{60} +0.198062 q^{61} +4.08815 q^{62} +3.35690 q^{63} +1.00000 q^{64} +1.69202 q^{66} +8.93900 q^{67} +0.939001 q^{68} +4.04892 q^{69} -3.35690 q^{70} -5.15883 q^{71} +1.00000 q^{72} -11.5308 q^{73} +11.6310 q^{74} +1.00000 q^{75} -4.85086 q^{76} +5.67994 q^{77} -4.94869 q^{79} -1.00000 q^{80} +1.00000 q^{81} +3.86294 q^{82} +13.1739 q^{83} +3.35690 q^{84} -0.939001 q^{85} +4.02177 q^{86} -8.12498 q^{87} +1.69202 q^{88} -9.47650 q^{89} -1.00000 q^{90} +4.04892 q^{92} +4.08815 q^{93} -1.27413 q^{94} +4.85086 q^{95} +1.00000 q^{96} +15.4547 q^{97} +4.26875 q^{98} +1.69202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{12} + 6 q^{14} - 3 q^{15} + 3 q^{16} - 7 q^{17} + 3 q^{18} - q^{19} - 3 q^{20} + 6 q^{21} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{27} + 6 q^{28} - 3 q^{30} + 16 q^{31} + 3 q^{32} - 7 q^{34} - 6 q^{35} + 3 q^{36} + 20 q^{37} - q^{38} - 3 q^{40} + 17 q^{41} + 6 q^{42} + 9 q^{43} - 3 q^{45} + 3 q^{46} + 7 q^{47} + 3 q^{48} + 5 q^{49} + 3 q^{50} - 7 q^{51} + 3 q^{53} + 3 q^{54} + 6 q^{56} - q^{57} + 7 q^{59} - 3 q^{60} + 5 q^{61} + 16 q^{62} + 6 q^{63} + 3 q^{64} + 17 q^{67} - 7 q^{68} + 3 q^{69} - 6 q^{70} - 7 q^{71} + 3 q^{72} + 3 q^{73} + 20 q^{74} + 3 q^{75} - q^{76} - 7 q^{77} + 17 q^{79} - 3 q^{80} + 3 q^{81} + 17 q^{82} + 6 q^{83} + 6 q^{84} + 7 q^{85} + 9 q^{86} - 3 q^{89} - 3 q^{90} + 3 q^{92} + 16 q^{93} + 7 q^{94} + q^{95} + 3 q^{96} + 24 q^{97} + 5 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^12 + 6 * q^14 - 3 * q^15 + 3 * q^16 - 7 * q^17 + 3 * q^18 - q^19 - 3 * q^20 + 6 * q^21 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 + 6 * q^28 - 3 * q^30 + 16 * q^31 + 3 * q^32 - 7 * q^34 - 6 * q^35 + 3 * q^36 + 20 * q^37 - q^38 - 3 * q^40 + 17 * q^41 + 6 * q^42 + 9 * q^43 - 3 * q^45 + 3 * q^46 + 7 * q^47 + 3 * q^48 + 5 * q^49 + 3 * q^50 - 7 * q^51 + 3 * q^53 + 3 * q^54 + 6 * q^56 - q^57 + 7 * q^59 - 3 * q^60 + 5 * q^61 + 16 * q^62 + 6 * q^63 + 3 * q^64 + 17 * q^67 - 7 * q^68 + 3 * q^69 - 6 * q^70 - 7 * q^71 + 3 * q^72 + 3 * q^73 + 20 * q^74 + 3 * q^75 - q^76 - 7 * q^77 + 17 * q^79 - 3 * q^80 + 3 * q^81 + 17 * q^82 + 6 * q^83 + 6 * q^84 + 7 * q^85 + 9 * q^86 - 3 * q^89 - 3 * q^90 + 3 * q^92 + 16 * q^93 + 7 * q^94 + q^95 + 3 * q^96 + 24 * q^97 + 5 * q^98

Introduction

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