LMFDB - Embedded newform 1805.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.7537.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 4x + 3 $ x^4 - x^3 - 5x^2 + 4x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.37933$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.09744 q^{2} +0.379334 q^{3} -0.795629 q^{4} +1.00000 q^{5} -0.416295 q^{6} +1.89307 q^{7} +3.06803 q^{8} -2.85611 q^{9} -1.09744 q^{10} +0.134400 q^{11} -0.301809 q^{12} -3.51373 q^{13} -2.07752 q^{14} +0.379334 q^{15} -1.77572 q^{16} -1.66123 q^{17} +3.13440 q^{18} -0.795629 q^{20} +0.718104 q^{21} -0.147496 q^{22} +5.36984 q^{23} +1.16381 q^{24} +1.00000 q^{25} +3.85611 q^{26} -2.22142 q^{27} -1.50618 q^{28} -4.97059 q^{29} -0.416295 q^{30} -6.56472 q^{31} -4.18732 q^{32} +0.0509824 q^{33} +1.82310 q^{34} +1.89307 q^{35} +2.27240 q^{36} +1.69819 q^{37} -1.33288 q^{39} +3.06803 q^{40} -10.6327 q^{41} -0.788075 q^{42} +8.50784 q^{43} -0.106932 q^{44} -2.85611 q^{45} -5.89307 q^{46} -11.1154 q^{47} -0.673589 q^{48} -3.41630 q^{49} -1.09744 q^{50} -0.630160 q^{51} +2.79563 q^{52} +0.264847 q^{53} +2.43787 q^{54} +0.134400 q^{55} +5.80799 q^{56} +5.45492 q^{58} +6.89667 q^{59} -0.301809 q^{60} +9.17589 q^{61} +7.20437 q^{62} -5.40680 q^{63} +8.14676 q^{64} -3.51373 q^{65} -0.0559501 q^{66} +2.95354 q^{67} +1.32172 q^{68} +2.03696 q^{69} -2.07752 q^{70} -1.32835 q^{71} -8.76262 q^{72} -6.34237 q^{73} -1.86366 q^{74} +0.379334 q^{75} +0.254428 q^{77} +1.46275 q^{78} +1.46728 q^{79} -1.77572 q^{80} +7.72566 q^{81} +11.6688 q^{82} +7.44736 q^{83} -0.571345 q^{84} -1.66123 q^{85} -9.33683 q^{86} -1.88551 q^{87} +0.412343 q^{88} -9.73608 q^{89} +3.13440 q^{90} -6.65174 q^{91} -4.27240 q^{92} -2.49022 q^{93} +12.1985 q^{94} -1.58839 q^{96} -17.4689 q^{97} +3.74917 q^{98} -0.383860 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} - 12 q^{8} + q^{9} - q^{10} - 2 q^{11} - 6 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} + 7 q^{16} - q^{17} + 10 q^{18} + 5 q^{20} + 4 q^{21}+ \cdots + 38 q^{99}+O(q^{100}) $ 4 * q - q^2 - 3 * q^3 + 5 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^7 - 12 * q^8 + q^9 - q^10 - 2 * q^11 - 6 * q^12 - 7 * q^13 + q^14 - 3 * q^15 + 7 * q^16 - q^17 + 10 * q^18 + 5 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 23 * q^24 + 4 * q^25 + 3 * q^26 - 12 * q^27 - 19 * q^28 + q^29 + 2 * q^30 - 30 * q^32 - 19 * q^33 - 15 * q^34 - 4 * q^35 - 7 * q^36 + 2 * q^37 + 15 * q^39 - 12 * q^40 + 8 * q^41 - 15 * q^42 + q^43 - 12 * q^44 + q^45 - 12 * q^46 - 12 * q^47 - 23 * q^48 - 10 * q^49 - q^50 - 22 * q^51 + 3 * q^52 + 5 * q^53 - 34 * q^54 - 2 * q^55 + 41 * q^56 - 27 * q^58 + 5 * q^59 - 6 * q^60 + 37 * q^62 - 3 * q^63 + 56 * q^64 - 7 * q^65 - 31 * q^66 - 4 * q^67 + 16 * q^68 + 9 * q^69 + q^70 - 20 * q^71 - 17 * q^72 - 20 * q^73 + 25 * q^74 - 3 * q^75 + 14 * q^77 + 18 * q^78 - 17 * q^79 + 7 * q^80 + 12 * q^81 + 21 * q^82 + q^83 + 20 * q^84 - q^85 - 8 * q^86 - 16 * q^87 + 7 * q^88 - 11 * q^89 + 10 * q^90 - 6 * q^91 - q^92 - 8 * q^93 + 31 * q^94 + 21 * q^96 - q^97 - 9 * q^98 + 38 * q^99

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 $

$2$	−1.09744	−0.776006	−0.388003	−	0.921658i	$-0.626835\pi$
$2$	−1.09744	−0.776006	−0.388003	+	0.921658i	$0.626835\pi$
$3$	0.379334	0.219008	0.109504	−	0.993986i	$-0.465074\pi$
$3$	0.379334	0.219008	0.109504	+	0.993986i	$0.465074\pi$
$4$	−0.795629	−0.397815
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.416295	−0.169952
$7$	1.89307	0.715512	0.357756	−	0.933815i	$-0.383542\pi$
$7$	1.89307	0.715512	0.357756	+	0.933815i	$0.383542\pi$
$8$	3.06803	1.08471
$9$	−2.85611	−0.952035
$10$	−1.09744	−0.347040
$11$	0.134400	0.0405231	0.0202615	−	0.999795i	$-0.493550\pi$
$11$	0.134400	0.0405231	0.0202615	+	0.999795i	$0.493550\pi$
$12$	−0.301809	−0.0871248
$13$	−3.51373	−0.974534	−0.487267	−	0.873253i	$-0.662006\pi$
$13$	−3.51373	−0.974534	−0.487267	+	0.873253i	$0.662006\pi$
$14$	−2.07752	−0.555242
$15$	0.379334	0.0979436
$16$	−1.77572	−0.443929
$17$	−1.66123	−0.402907	−0.201454	−	0.979498i	$-0.564567\pi$
$17$	−1.66123	−0.402907	−0.201454	+	0.979498i	$0.564567\pi$
$18$	3.13440	0.738785
$19$	0	0
$19$	0	0
$20$	−0.795629	−0.177908
$21$	0.718104	0.156703
$22$	−0.147496	−0.0314462
$23$	5.36984	1.11969	0.559844	−	0.828598i	$-0.310861\pi$
$23$	5.36984	1.11969	0.559844	+	0.828598i	$0.310861\pi$
$24$	1.16381	0.237561
$25$	1.00000	0.200000
$26$	3.85611	0.756245
$27$	−2.22142	−0.427512
$28$	−1.50618	−0.284641
$29$	−4.97059	−0.923016	−0.461508	−	0.887136i	$-0.652691\pi$
$29$	−4.97059	−0.923016	−0.461508	+	0.887136i	$0.652691\pi$
$30$	−0.416295	−0.0760048
$31$	−6.56472	−1.17906	−0.589529	−	0.807747i	$-0.700687\pi$
$31$	−6.56472	−1.17906	−0.589529	+	0.807747i	$0.700687\pi$
$32$	−4.18732	−0.740221
$33$	0.0509824	0.00887490
$34$	1.82310	0.312658
$35$	1.89307	0.319987
$36$	2.27240	0.378734
$37$	1.69819	0.279181	0.139590	−	0.990209i	$-0.455421\pi$
$37$	1.69819	0.279181	0.139590	+	0.990209i	$0.455421\pi$
$38$	0	0
$39$	−1.33288	−0.213431
$40$	3.06803	0.485098
$41$	−10.6327	−1.66056	−0.830278	−	0.557349i	$-0.811818\pi$
$41$	−10.6327	−1.66056	−0.830278	+	0.557349i	$0.811818\pi$
$42$	−0.788075	−0.121603
$43$	8.50784	1.29743	0.648717	−	0.761030i	$-0.275306\pi$
$43$	8.50784	1.29743	0.648717	+	0.761030i	$0.275306\pi$
$44$	−0.106932	−0.0161207
$45$	−2.85611	−0.425763
$46$	−5.89307	−0.868885
$47$	−11.1154	−1.62135	−0.810675	−	0.585497i	$-0.800899\pi$
$47$	−11.1154	−1.62135	−0.810675	+	0.585497i	$0.800899\pi$
$48$	−0.673589	−0.0972242
$49$	−3.41630	−0.488042
$50$	−1.09744	−0.155201
$51$	−0.630160	−0.0882401
$52$	2.79563	0.387684
$53$	0.264847	0.0363796	0.0181898	−	0.999835i	$-0.494210\pi$
$53$	0.264847	0.0363796	0.0181898	+	0.999835i	$0.494210\pi$
$54$	2.43787	0.331752
$55$	0.134400	0.0181225
$56$	5.80799	0.776125
$57$	0	0
$58$	5.45492	0.716266
$59$	6.89667	0.897870	0.448935	−	0.893564i	$-0.351804\pi$
$59$	6.89667	0.897870	0.448935	+	0.893564i	$0.351804\pi$
$60$	−0.301809	−0.0389634
$61$	9.17589	1.17485	0.587426	−	0.809278i	$-0.300141\pi$
$61$	9.17589	1.17485	0.587426	+	0.809278i	$0.300141\pi$
$62$	7.20437	0.914956
$63$	−5.40680	−0.681193
$64$	8.14676	1.01834
$65$	−3.51373	−0.435825
$66$	−0.0559501	−0.00688698
$67$	2.95354	0.360833	0.180416	−	0.983590i	$-0.442255\pi$
$67$	2.95354	0.360833	0.180416	+	0.983590i	$0.442255\pi$
$68$	1.32172	0.160282
$69$	2.03696	0.245221
$70$	−2.07752	−0.248312
$71$	−1.32835	−0.157646	−0.0788232	−	0.996889i	$-0.525116\pi$
$71$	−1.32835	−0.157646	−0.0788232	+	0.996889i	$0.525116\pi$
$72$	−8.76262	−1.03268
$73$	−6.34237	−0.742319	−0.371159	−	0.928569i	$-0.621040\pi$
$73$	−6.34237	−0.742319	−0.371159	+	0.928569i	$0.621040\pi$
$74$	−1.86366	−0.216646
$75$	0.379334	0.0438017
$76$	0	0
$77$	0.254428	0.0289948
$78$	1.46275	0.165624
$79$	1.46728	0.165082	0.0825408	−	0.996588i	$-0.473697\pi$
$79$	1.46728	0.165082	0.0825408	+	0.996588i	$0.473697\pi$
$80$	−1.77572	−0.198531
$81$	7.72566	0.858406
$82$	11.6688	1.28860
$83$	7.44736	0.817454	0.408727	−	0.912657i	$-0.365973\pi$
$83$	7.44736	0.817454	0.408727	+	0.912657i	$0.365973\pi$
$84$	−0.571345	−0.0623388
$85$	−1.66123	−0.180186
$86$	−9.33683	−1.00682
$87$	−1.88551	−0.202148
$88$	0.412343	0.0439559
$89$	−9.73608	−1.03202	−0.516011	−	0.856582i	$-0.672584\pi$
$89$	−9.73608	−1.03202	−0.516011	+	0.856582i	$0.672584\pi$
$90$	3.13440	0.330395
$91$	−6.65174	−0.697291
$92$	−4.27240	−0.445429
$93$	−2.49022	−0.258224
$94$	12.1985	1.25818
$95$	0	0
$96$	−1.58839	−0.162115
$97$	−17.4689	−1.77370	−0.886851	−	0.462055i	$-0.847112\pi$
$97$	−17.4689	−1.77370	−0.886851	+	0.462055i	$0.847112\pi$
$98$	3.74917	0.378724
$99$	−0.383860	−0.0385794
$100$	−0.795629	−0.0795629
$101$	5.39731	0.537052	0.268526	−	0.963272i	$-0.413463\pi$
$101$	5.39731	0.537052	0.268526	+	0.963272i	$0.413463\pi$
$102$	0.691562	0.0684749
$103$	−2.14750	−0.211599	−0.105800	−	0.994387i	$-0.533740\pi$
$103$	−2.14750	−0.211599	−0.105800	+	0.994387i	$0.533740\pi$
$104$	−10.7802	−1.05709
$105$	0.718104	0.0700798
$106$	−0.290654	−0.0282308
$107$	1.00093	0.0967631	0.0483815	−	0.998829i	$-0.484594\pi$
$107$	1.00093	0.0967631	0.0483815	+	0.998829i	$0.484594\pi$
$108$	1.76743	0.170071
$109$	−16.2629	−1.55770	−0.778852	−	0.627208i	$-0.784198\pi$
$109$	−16.2629	−1.55770	−0.778852	+	0.627208i	$0.784198\pi$
$110$	−0.147496	−0.0140632
$111$	0.644181	0.0611430
$112$	−3.36155	−0.317637
$113$	−0.843010	−0.0793037	−0.0396519	−	0.999214i	$-0.512625\pi$
$113$	−0.843010	−0.0793037	−0.0396519	+	0.999214i	$0.512625\pi$
$114$	0	0
$115$	5.36984	0.500740
$116$	3.95475	0.367189
$117$	10.0356	0.927791
$118$	−7.56867	−0.696752
$119$	−3.14482	−0.288285
$120$	1.16381	0.106241
$121$	−10.9819	−0.998358
$122$	−10.0700	−0.911692
$123$	−4.03336	−0.363676
$124$	5.22308	0.469046
$125$	1.00000	0.0894427
$126$	5.93363	0.528610
$127$	−18.7397	−1.66288	−0.831439	−	0.555616i	$-0.812482\pi$
$127$	−18.7397	−1.66288	−0.831439	+	0.555616i	$0.812482\pi$
$128$	−0.565920	−0.0500208
$129$	3.22731	0.284149
$130$	3.85611	0.338203
$131$	2.88644	0.252189	0.126095	−	0.992018i	$-0.459756\pi$
$131$	2.88644	0.252189	0.126095	+	0.992018i	$0.459756\pi$
$132$	−0.0405631	−0.00353057
$133$	0	0
$134$	−3.24133	−0.280008
$135$	−2.22142	−0.191189
$136$	−5.09670	−0.437039
$137$	−18.8316	−1.60889	−0.804445	−	0.594027i	$-0.797537\pi$
$137$	−18.8316	−1.60889	−0.804445	+	0.594027i	$0.797537\pi$
$138$	−2.23544	−0.190293
$139$	−18.1795	−1.54196	−0.770982	−	0.636857i	$-0.780234\pi$
$139$	−18.1795	−1.54196	−0.770982	+	0.636857i	$0.780234\pi$
$140$	−1.50618	−0.127295
$141$	−4.21645	−0.355089
$142$	1.45778	0.122334
$143$	−0.472245	−0.0394912
$144$	5.07163	0.422636
$145$	−4.97059	−0.412785
$146$	6.96036	0.576044
$147$	−1.29592	−0.106885
$148$	−1.35113	−0.111062
$149$	−22.2543	−1.82315	−0.911573	−	0.411138i	$-0.865131\pi$
$149$	−22.2543	−1.82315	−0.911573	+	0.411138i	$0.865131\pi$
$150$	−0.416295	−0.0339904
$151$	−3.33482	−0.271384	−0.135692	−	0.990751i	$-0.543326\pi$
$151$	−3.33482	−0.271384	−0.135692	+	0.990751i	$0.543326\pi$
$152$	0	0
$153$	4.74465	0.383582
$154$	−0.279219	−0.0225001
$155$	−6.56472	−0.527291
$156$	1.06048	0.0849061
$157$	7.26291	0.579643	0.289822	−	0.957081i	$-0.406404\pi$
$157$	7.26291	0.579643	0.289822	+	0.957081i	$0.406404\pi$
$158$	−1.61025	−0.128104
$159$	0.100466	0.00796744
$160$	−4.18732	−0.331037
$161$	10.1655	0.801151
$162$	−8.47843	−0.666129
$163$	−19.7783	−1.54916	−0.774578	−	0.632478i	$-0.782038\pi$
$163$	−19.7783	−1.54916	−0.774578	+	0.632478i	$0.782038\pi$
$164$	8.45972	0.660593
$165$	0.0509824	0.00396898
$166$	−8.17302	−0.634350
$167$	3.40320	0.263348	0.131674	−	0.991293i	$-0.457965\pi$
$167$	3.40320	0.263348	0.131674	+	0.991293i	$0.457965\pi$
$168$	2.20317	0.169978
$169$	−0.653675	−0.0502827
$170$	1.82310	0.139825
$171$	0	0
$172$	−6.76909	−0.516138
$173$	10.5857	0.804817	0.402409	−	0.915460i	$-0.368173\pi$
$173$	10.5857	0.804817	0.402409	+	0.915460i	$0.368173\pi$
$174$	2.06923	0.156868
$175$	1.89307	0.143102
$176$	−0.238656	−0.0179894
$177$	2.61614	0.196641
$178$	10.6847	0.800855
$179$	14.6024	1.09144	0.545718	−	0.837969i	$-0.316257\pi$
$179$	14.6024	1.09144	0.545718	+	0.837969i	$0.316257\pi$
$180$	2.27240	0.169375
$181$	5.43261	0.403803	0.201901	−	0.979406i	$-0.435288\pi$
$181$	5.43261	0.403803	0.201901	+	0.979406i	$0.435288\pi$
$182$	7.29987	0.541102
$183$	3.48072	0.257303
$184$	16.4748	1.21454
$185$	1.69819	0.124853
$186$	2.73286	0.200383
$187$	−0.223269	−0.0163271
$188$	8.84375	0.644996
$189$	−4.20530	−0.305890
$190$	0	0
$191$	20.4758	1.48157	0.740787	−	0.671740i	$-0.234453\pi$
$191$	20.4758	1.48157	0.740787	+	0.671740i	$0.234453\pi$
$192$	3.09034	0.223026
$193$	−11.0235	−0.793490	−0.396745	−	0.917929i	$-0.629860\pi$
$193$	−11.0235	−0.793490	−0.396745	+	0.917929i	$0.629860\pi$
$194$	19.1711	1.37640
$195$	−1.33288	−0.0954494
$196$	2.71810	0.194150
$197$	−19.8532	−1.41448	−0.707242	−	0.706971i	$-0.750061\pi$
$197$	−19.8532	−1.41448	−0.707242	+	0.706971i	$0.750061\pi$
$198$	0.421263	0.0299379
$199$	21.0026	1.48883	0.744417	−	0.667715i	$-0.232728\pi$
$199$	21.0026	1.48883	0.744417	+	0.667715i	$0.232728\pi$
$200$	3.06803	0.216943
$201$	1.12038	0.0790254
$202$	−5.92321	−0.416756
$203$	−9.40967	−0.660429
$204$	0.501374	0.0351032
$205$	−10.6327	−0.742623
$206$	2.35674	0.164202
$207$	−15.3368	−1.06598
$208$	6.23939	0.432624
$209$	0	0
$210$	−0.788075	−0.0543824
$211$	12.8257	0.882956	0.441478	−	0.897272i	$-0.354454\pi$
$211$	12.8257	0.882956	0.441478	+	0.897272i	$0.354454\pi$
$212$	−0.210720	−0.0144723
$213$	−0.503889	−0.0345259
$214$	−1.09845	−0.0750887
$215$	8.50784	0.580230
$216$	−6.81538	−0.463728
$217$	−12.4275	−0.843630
$218$	17.8475	1.20879
$219$	−2.40588	−0.162574
$220$	−0.106932	−0.00720939
$221$	5.83712	0.392647
$222$	−0.706949	−0.0474473
$223$	−20.3944	−1.36571	−0.682856	−	0.730553i	$-0.739263\pi$
$223$	−20.3944	−1.36571	−0.682856	+	0.730553i	$0.739263\pi$
$224$	−7.92688	−0.529637
$225$	−2.85611	−0.190407
$226$	0.925152	0.0615402
$227$	−25.4172	−1.68700	−0.843500	−	0.537129i	$-0.819509\pi$
$227$	−25.4172	−1.68700	−0.843500	+	0.537129i	$0.819509\pi$
$228$	0	0
$229$	2.21553	0.146406	0.0732030	−	0.997317i	$-0.476678\pi$
$229$	2.21553	0.146406	0.0732030	+	0.997317i	$0.476678\pi$
$230$	−5.89307	−0.388577
$231$	0.0965132	0.00635010
$232$	−15.2499	−1.00121
$233$	−14.1576	−0.927498	−0.463749	−	0.885967i	$-0.653496\pi$
$233$	−14.1576	−0.927498	−0.463749	+	0.885967i	$0.653496\pi$
$234$	−11.0134	−0.719972
$235$	−11.1154	−0.725089
$236$	−5.48719	−0.357186
$237$	0.556588	0.0361543
$238$	3.45125	0.223711
$239$	3.01476	0.195008	0.0975042	−	0.995235i	$-0.468914\pi$
$239$	3.01476	0.195008	0.0975042	+	0.995235i	$0.468914\pi$
$240$	−0.673589	−0.0434800
$241$	23.7792	1.53175	0.765877	−	0.642987i	$-0.222305\pi$
$241$	23.7792	1.53175	0.765877	+	0.642987i	$0.222305\pi$
$242$	12.0520	0.774732
$243$	9.59486	0.615511
$244$	−7.30060	−0.467373
$245$	−3.41630	−0.218259
$246$	4.42636	0.282215
$247$	0	0
$248$	−20.1407	−1.27894
$249$	2.82504	0.179029
$250$	−1.09744	−0.0694081
$251$	17.1899	1.08502	0.542509	−	0.840050i	$-0.317475\pi$
$251$	17.1899	1.08502	0.542509	+	0.840050i	$0.317475\pi$
$252$	4.30181	0.270988
$253$	0.721706	0.0453733
$254$	20.5656	1.29040
$255$	−0.630160	−0.0394622
$256$	−15.6725	−0.979529
$257$	19.5429	1.21905	0.609525	−	0.792767i	$-0.291360\pi$
$257$	19.5429	1.21905	0.609525	+	0.792767i	$0.291360\pi$
$258$	−3.54178	−0.220501
$259$	3.21479	0.199757
$260$	2.79563	0.173378
$261$	14.1965	0.878744
$262$	−3.16769	−0.195700
$263$	8.81360	0.543470	0.271735	−	0.962372i	$-0.412403\pi$
$263$	8.81360	0.543470	0.271735	+	0.962372i	$0.412403\pi$
$264$	0.156416	0.00962672
$265$	0.264847	0.0162694
$266$	0	0
$267$	−3.69322	−0.226022
$268$	−2.34993	−0.143545
$269$	−0.288362	−0.0175818	−0.00879088	−	0.999961i	$-0.502798\pi$
$269$	−0.288362	−0.0175818	−0.00879088	+	0.999961i	$0.502798\pi$
$270$	2.43787	0.148364
$271$	−24.8712	−1.51082	−0.755409	−	0.655253i	$-0.772562\pi$
$271$	−24.8712	−1.51082	−0.755409	+	0.655253i	$0.772562\pi$
$272$	2.94987	0.178862
$273$	−2.52323	−0.152713
$274$	20.6665	1.24851
$275$	0.134400	0.00810462
$276$	−1.62067	−0.0975526
$277$	−4.40486	−0.264662	−0.132331	−	0.991206i	$-0.542246\pi$
$277$	−4.40486	−0.264662	−0.132331	+	0.991206i	$0.542246\pi$
$278$	19.9509	1.19657
$279$	18.7495	1.12250
$280$	5.80799	0.347094
$281$	32.7214	1.95200	0.975998	−	0.217778i	$-0.0698809\pi$
$281$	32.7214	1.95200	0.975998	+	0.217778i	$0.0698809\pi$
$282$	4.62729	0.275551
$283$	−1.32893	−0.0789964	−0.0394982	−	0.999220i	$-0.512576\pi$
$283$	−1.32893	−0.0789964	−0.0394982	+	0.999220i	$0.512576\pi$
$284$	1.05688	0.0627140
$285$	0	0
$286$	0.518260	0.0306454
$287$	−20.1285	−1.18815
$288$	11.9594	0.704717
$289$	−14.2403	−0.837666
$290$	5.45492	0.320324
$291$	−6.62656	−0.388456
$292$	5.04618	0.295305
$293$	7.72365	0.451220	0.225610	−	0.974218i	$-0.427562\pi$
$293$	7.72365	0.451220	0.225610	+	0.974218i	$0.427562\pi$
$294$	1.42219	0.0829437
$295$	6.89667	0.401540
$296$	5.21010	0.302831
$297$	−0.298558	−0.0173241
$298$	24.4228	1.41477
$299$	−18.8682	−1.09118
$300$	−0.301809	−0.0174250
$301$	16.1059	0.928330
$302$	3.65976	0.210595
$303$	2.04738	0.117619
$304$	0	0
$305$	9.17589	0.525410
$306$	−5.20696	−0.297662
$307$	9.10002	0.519366	0.259683	−	0.965694i	$-0.416382\pi$
$307$	9.10002	0.519366	0.259683	+	0.965694i	$0.416382\pi$
$308$	−0.202430	−0.0115345
$309$	−0.814618	−0.0463420
$310$	7.20437	0.409181
$311$	−12.4569	−0.706364	−0.353182	−	0.935555i	$-0.614900\pi$
$311$	−12.4569	−0.706364	−0.353182	+	0.935555i	$0.614900\pi$
$312$	−4.08931	−0.231512
$313$	2.04553	0.115620	0.0578101	−	0.998328i	$-0.481588\pi$
$313$	2.04553	0.115620	0.0578101	+	0.998328i	$0.481588\pi$
$314$	−7.97059	−0.449807
$315$	−5.40680	−0.304639
$316$	−1.16741	−0.0656719
$317$	−23.5713	−1.32389	−0.661947	−	0.749551i	$-0.730270\pi$
$317$	−23.5713	−1.32389	−0.661947	+	0.749551i	$0.730270\pi$
$318$	−0.110255	−0.00618278
$319$	−0.668047	−0.0374035
$320$	8.14676	0.455418
$321$	0.379685	0.0211919
$322$	−11.1560	−0.621698
$323$	0	0
$324$	−6.14676	−0.341487
$325$	−3.51373	−0.194907
$326$	21.7055	1.20215
$327$	−6.16907	−0.341150
$328$	−32.6216	−1.80123
$329$	−21.0422	−1.16010
$330$	−0.0559501	−0.00307995
$331$	18.7175	1.02881	0.514403	−	0.857549i	$-0.328014\pi$
$331$	18.7175	1.02881	0.514403	+	0.857549i	$0.328014\pi$
$332$	−5.92534	−0.325195
$333$	−4.85021	−0.265790
$334$	−3.73480	−0.204359
$335$	2.95354	0.161369
$336$	−1.27515	−0.0695651
$337$	32.6881	1.78063	0.890316	−	0.455343i	$-0.150483\pi$
$337$	32.6881	1.78063	0.890316	+	0.455343i	$0.150483\pi$
$338$	0.717368	0.0390197
$339$	−0.319782	−0.0173682
$340$	1.32172	0.0716805
$341$	−0.882297	−0.0477791
$342$	0	0
$343$	−19.7188	−1.06471
$344$	26.1023	1.40734
$345$	2.03696	0.109666
$346$	−11.6172	−0.624543
$347$	−2.56666	−0.137785	−0.0688927	−	0.997624i	$-0.521947\pi$
$347$	−2.56666	−0.137785	−0.0688927	+	0.997624i	$0.521947\pi$
$348$	1.50017	0.0804175
$349$	16.6195	0.889619	0.444810	−	0.895625i	$-0.353271\pi$
$349$	16.6195	0.889619	0.444810	+	0.895625i	$0.353271\pi$
$350$	−2.07752	−0.111048
$351$	7.80547	0.416625
$352$	−0.562776	−0.0299961
$353$	28.3629	1.50961	0.754803	−	0.655951i	$-0.227732\pi$
$353$	28.3629	1.50961	0.754803	+	0.655951i	$0.227732\pi$
$354$	−2.87105	−0.152595
$355$	−1.32835	−0.0705016
$356$	7.74631	0.410553
$357$	−1.19294	−0.0631369
$358$	−16.0252	−0.846961
$359$	17.3885	0.917733	0.458866	−	0.888505i	$-0.348256\pi$
$359$	17.3885	0.917733	0.458866	+	0.888505i	$0.348256\pi$
$360$	−8.76262	−0.461831
$361$	0	0
$362$	−5.96195	−0.313353
$363$	−4.16582	−0.218649
$364$	5.29231	0.277393
$365$	−6.34237	−0.331975
$366$	−3.81988	−0.199668
$367$	25.8048	1.34700	0.673501	−	0.739186i	$-0.264790\pi$
$367$	25.8048	1.34700	0.673501	+	0.739186i	$0.264790\pi$
$368$	−9.53531	−0.497062
$369$	30.3683	1.58091
$370$	−1.86366	−0.0968871
$371$	0.501374	0.0260300
$372$	1.98129	0.102725
$373$	−27.0663	−1.40144	−0.700719	−	0.713437i	$-0.747138\pi$
$373$	−27.0663	−1.40144	−0.700719	+	0.713437i	$0.747138\pi$
$374$	0.245024	0.0126699
$375$	0.379334	0.0195887
$376$	−34.1024	−1.75870
$377$	17.4653	0.899511
$378$	4.61505	0.237373
$379$	−12.4028	−0.637092	−0.318546	−	0.947907i	$-0.603194\pi$
$379$	−12.4028	−0.637092	−0.318546	+	0.947907i	$0.603194\pi$
$380$	0	0
$381$	−7.10859	−0.364184
$382$	−22.4709	−1.14971
$383$	5.35942	0.273854	0.136927	−	0.990581i	$-0.456277\pi$
$383$	5.35942	0.273854	0.136927	+	0.990581i	$0.456277\pi$
$384$	−0.214673	−0.0109550
$385$	0.254428	0.0129669
$386$	12.0976	0.615753
$387$	−24.2993	−1.23520
$388$	13.8988	0.705605
$389$	8.56933	0.434482	0.217241	−	0.976118i	$-0.430294\pi$
$389$	8.56933	0.434482	0.217241	+	0.976118i	$0.430294\pi$
$390$	1.46275	0.0740693
$391$	−8.92053	−0.451131
$392$	−10.4813	−0.529386
$393$	1.09492	0.0552316
$394$	21.7877	1.09765
$395$	1.46728	0.0738268
$396$	0.305411	0.0153475
$397$	−10.6445	−0.534234	−0.267117	−	0.963664i	$-0.586071\pi$
$397$	−10.6445	−0.534234	−0.267117	+	0.963664i	$0.586071\pi$
$398$	−23.0490	−1.15534
$399$	0	0
$400$	−1.77572	−0.0887858
$401$	−7.65209	−0.382127	−0.191063	−	0.981578i	$-0.561194\pi$
$401$	−7.65209	−0.382127	−0.191063	+	0.981578i	$0.561194\pi$
$402$	−1.22955	−0.0613242
$403$	23.0667	1.14903
$404$	−4.29426	−0.213647
$405$	7.72566	0.383891
$406$	10.3265	0.512497
$407$	0.228237	0.0113133
$408$	−1.93335	−0.0957152
$409$	17.6887	0.874650	0.437325	−	0.899304i	$-0.355926\pi$
$409$	17.6887	0.874650	0.437325	+	0.899304i	$0.355926\pi$
$410$	11.6688	0.576280
$411$	−7.14345	−0.352361
$412$	1.70861	0.0841772
$413$	13.0559	0.642437
$414$	16.8312	0.827210
$415$	7.44736	0.365577
$416$	14.7131	0.721371
$417$	−6.89609	−0.337703
$418$	0	0
$419$	1.18732	0.0580045	0.0290023	−	0.999579i	$-0.490767\pi$
$419$	1.18732	0.0580045	0.0290023	+	0.999579i	$0.490767\pi$
$420$	−0.571345	−0.0278788
$421$	−33.3673	−1.62622	−0.813111	−	0.582109i	$-0.802228\pi$
$421$	−33.3673	−1.62622	−0.813111	+	0.582109i	$0.802228\pi$
$422$	−14.0754	−0.685180
$423$	31.7468	1.54358
$424$	0.812560	0.0394614
$425$	−1.66123	−0.0805815
$426$	0.552987	0.0267923
$427$	17.3706	0.840621
$428$	−0.796365	−0.0384938
$429$	−0.179139	−0.00864890
$430$	−9.33683	−0.450262
$431$	6.17598	0.297486	0.148743	−	0.988876i	$-0.452477\pi$
$431$	6.17598	0.297486	0.148743	+	0.988876i	$0.452477\pi$
$432$	3.94461	0.189785
$433$	18.5552	0.891707	0.445854	−	0.895106i	$-0.352900\pi$
$433$	18.5552	0.891707	0.445854	+	0.895106i	$0.352900\pi$
$434$	13.6384	0.654662
$435$	−1.88551	−0.0904035
$436$	12.9392	0.619677
$437$	0	0
$438$	2.64030	0.126158
$439$	0.227312	0.0108490	0.00542450	−	0.999985i	$-0.498273\pi$
$439$	0.227312	0.0108490	0.00542450	+	0.999985i	$0.498273\pi$
$440$	0.412343	0.0196577
$441$	9.75730	0.464633
$442$	−6.40588	−0.304696
$443$	−34.9827	−1.66208	−0.831038	−	0.556215i	$-0.812253\pi$
$443$	−34.9827	−1.66208	−0.831038	+	0.556215i	$0.812253\pi$
$444$	−0.512529	−0.0243236
$445$	−9.73608	−0.461534
$446$	22.3816	1.05980
$447$	−8.44182	−0.399285
$448$	15.4224	0.728638
$449$	16.9509	0.799961	0.399980	−	0.916524i	$-0.369017\pi$
$449$	16.9509	0.799961	0.399980	+	0.916524i	$0.369017\pi$
$450$	3.13440	0.147757
$451$	−1.42904	−0.0672909
$452$	0.670724	0.0315482
$453$	−1.26501	−0.0594353
$454$	27.8938	1.30912
$455$	−6.65174	−0.311838
$456$	0	0
$457$	1.60241	0.0749578	0.0374789	−	0.999297i	$-0.488067\pi$
$457$	1.60241	0.0749578	0.0374789	+	0.999297i	$0.488067\pi$
$458$	−2.43140	−0.113612
$459$	3.69029	0.172248
$460$	−4.27240	−0.199202
$461$	−8.74162	−0.407138	−0.203569	−	0.979061i	$-0.565254\pi$
$461$	−8.74162	−0.407138	−0.203569	+	0.979061i	$0.565254\pi$
$462$	−0.105917	−0.00492772
$463$	21.1886	0.984718	0.492359	−	0.870392i	$-0.336135\pi$
$463$	21.1886	0.984718	0.492359	+	0.870392i	$0.336135\pi$
$464$	8.82636	0.409753
$465$	−2.49022	−0.115481
$466$	15.5371	0.719744
$467$	20.4516	0.946388	0.473194	−	0.880958i	$-0.343101\pi$
$467$	20.4516	0.946388	0.473194	+	0.880958i	$0.343101\pi$
$468$	−7.98461	−0.369089
$469$	5.59126	0.258180
$470$	12.1985	0.562674
$471$	2.75507	0.126947
$472$	21.1592	0.973931
$473$	1.14345	0.0525760
$474$	−0.610821	−0.0280559
$475$	0	0
$476$	2.50211	0.114684
$477$	−0.756432	−0.0346347
$478$	−3.30851	−0.151328
$479$	23.5491	1.07599	0.537994	−	0.842949i	$-0.319182\pi$
$479$	23.5491	1.07599	0.537994	+	0.842949i	$0.319182\pi$
$480$	−1.58839	−0.0724999
$481$	−5.96699	−0.272071
$482$	−26.0962	−1.18865
$483$	3.85611	0.175459
$484$	8.73755	0.397161
$485$	−17.4689	−0.793224
$486$	−10.5298	−0.477640
$487$	−36.0392	−1.63309	−0.816546	−	0.577280i	$-0.804114\pi$
$487$	−36.0392	−1.63309	−0.816546	+	0.577280i	$0.804114\pi$
$488$	28.1519	1.27438
$489$	−7.50258	−0.339278
$490$	3.74917	0.169370
$491$	20.0595	0.905271	0.452635	−	0.891696i	$-0.350484\pi$
$491$	20.0595	0.905271	0.452635	+	0.891696i	$0.350484\pi$
$492$	3.20906	0.144676
$493$	8.25729	0.371890
$494$	0	0
$495$	−0.383860	−0.0172532
$496$	11.6571	0.523418
$497$	−2.51466	−0.112798
$498$	−3.10030	−0.138928
$499$	−36.8729	−1.65066	−0.825328	−	0.564653i	$-0.809010\pi$
$499$	−36.8729	−1.65066	−0.825328	+	0.564653i	$0.809010\pi$
$500$	−0.795629	−0.0355816
$501$	1.29095	0.0576753
$502$	−18.8649	−0.841980
$503$	−21.6487	−0.965268	−0.482634	−	0.875822i	$-0.660320\pi$
$503$	−21.6487	−0.965268	−0.482634	+	0.875822i	$0.660320\pi$
$504$	−16.5882	−0.738899
$505$	5.39731	0.240177
$506$	−0.792028	−0.0352099
$507$	−0.247961	−0.0110123
$508$	14.9098	0.661517
$509$	36.4558	1.61588	0.807938	−	0.589267i	$-0.200583\pi$
$509$	36.4558	1.61588	0.807938	+	0.589267i	$0.200583\pi$
$510$	0.691562	0.0306229
$511$	−12.0065	−0.531138
$512$	18.3314	0.810141
$513$	0	0
$514$	−21.4471	−0.945990
$515$	−2.14750	−0.0946300
$516$	−2.56774	−0.113039
$517$	−1.49391	−0.0657021
$518$	−3.52803	−0.155013
$519$	4.01552	0.176262
$520$	−10.7802	−0.472745
$521$	22.6092	0.990528	0.495264	−	0.868742i	$-0.335071\pi$
$521$	22.6092	0.990528	0.495264	+	0.868742i	$0.335071\pi$
$522$	−15.5798	−0.681910
$523$	−0.532911	−0.0233026	−0.0116513	−	0.999932i	$-0.503709\pi$
$523$	−0.532911	−0.0233026	−0.0116513	+	0.999932i	$0.503709\pi$
$524$	−2.29654	−0.100325
$525$	0.718104	0.0313406
$526$	−9.67238	−0.421736
$527$	10.9055	0.475051
$528$	−0.0905303	−0.00393983
$529$	5.83518	0.253703
$530$	−0.290654	−0.0126252
$531$	−19.6976	−0.854804
$532$	0	0
$533$	37.3606	1.61827
$534$	4.05308	0.175394
$535$	1.00093	0.0432738
$536$	9.06156	0.391400
$537$	5.53919	0.239034
$538$	0.316460	0.0136436
$539$	−0.459150	−0.0197770
$540$	1.76743	0.0760579
$541$	5.01640	0.215672	0.107836	−	0.994169i	$-0.465608\pi$
$541$	5.01640	0.215672	0.107836	+	0.994169i	$0.465608\pi$
$542$	27.2946	1.17240
$543$	2.06077	0.0884362
$544$	6.95610	0.298240
$545$	−16.2629	−0.696626
$546$	2.76909	0.118506
$547$	−22.6299	−0.967584	−0.483792	−	0.875183i	$-0.660741\pi$
$547$	−22.6299	−0.967584	−0.483792	+	0.875183i	$0.660741\pi$
$548$	14.9830	0.640040
$549$	−26.2073	−1.11850
$550$	−0.147496	−0.00628923
$551$	0	0
$552$	6.24946	0.265995
$553$	2.77766	0.118118
$554$	4.83406	0.205380
$555$	0.644181	0.0273440
$556$	14.4641	0.613416
$557$	35.2554	1.49382	0.746910	−	0.664925i	$-0.231537\pi$
$557$	35.2554	1.49382	0.746910	+	0.664925i	$0.231537\pi$
$558$	−20.5764	−0.871070
$559$	−29.8943	−1.26439
$560$	−3.36155	−0.142051
$561$	−0.0846935	−0.00357576
$562$	−35.9097	−1.51476
$563$	24.6295	1.03801	0.519005	−	0.854771i	$-0.326302\pi$
$563$	24.6295	1.03801	0.519005	+	0.854771i	$0.326302\pi$
$564$	3.35473	0.141260
$565$	−0.843010	−0.0354657
$566$	1.45841	0.0613017
$567$	14.6252	0.614200
$568$	−4.07542	−0.171001
$569$	20.0193	0.839252	0.419626	−	0.907697i	$-0.362161\pi$
$569$	20.0193	0.839252	0.419626	+	0.907697i	$0.362161\pi$
$570$	0	0
$571$	−16.6121	−0.695195	−0.347597	−	0.937644i	$-0.613002\pi$
$571$	−16.6121	−0.695195	−0.347597	+	0.937644i	$0.613002\pi$
$572$	0.375732	0.0157102
$573$	7.76715	0.324477
$574$	22.0898	0.922010
$575$	5.36984	0.223938
$576$	−23.2680	−0.969500
$577$	12.4486	0.518244	0.259122	−	0.965845i	$-0.416567\pi$
$577$	12.4486	0.518244	0.259122	+	0.965845i	$0.416567\pi$
$578$	15.6279	0.650034
$579$	−4.18159	−0.173781
$580$	3.95475	0.164212
$581$	14.0984	0.584899
$582$	7.27224	0.301444
$583$	0.0355955	0.00147421
$584$	−19.4586	−0.805202
$585$	10.0356	0.414921
$586$	−8.47623	−0.350150
$587$	4.51144	0.186207	0.0931036	−	0.995656i	$-0.470321\pi$
$587$	4.51144	0.186207	0.0931036	+	0.995656i	$0.470321\pi$
$588$	1.03107	0.0425206
$589$	0	0
$590$	−7.56867	−0.311597
$591$	−7.53101	−0.309784
$592$	−3.01550	−0.123936
$593$	19.6082	0.805213	0.402606	−	0.915373i	$-0.368104\pi$
$593$	19.6082	0.805213	0.402606	+	0.915373i	$0.368104\pi$
$594$	0.327650	0.0134436
$595$	−3.14482	−0.128925
$596$	17.7062	0.725274
$597$	7.96699	0.326067
$598$	20.7067	0.846759
$599$	−10.7759	−0.440292	−0.220146	−	0.975467i	$-0.570653\pi$
$599$	−10.7759	−0.440292	−0.220146	+	0.975467i	$0.570653\pi$
$600$	1.16381	0.0475122
$601$	−15.0244	−0.612860	−0.306430	−	0.951893i	$-0.599134\pi$
$601$	−15.0244	−0.612860	−0.306430	+	0.951893i	$0.599134\pi$
$602$	−17.6753	−0.720389
$603$	−8.43563	−0.343526
$604$	2.65328	0.107960
$605$	−10.9819	−0.446479
$606$	−2.24687	−0.0912730
$607$	−25.1901	−1.02243	−0.511217	−	0.859452i	$-0.670805\pi$
$607$	−25.1901	−1.02243	−0.511217	+	0.859452i	$0.670805\pi$
$608$	0	0
$609$	−3.56940	−0.144640
$610$	−10.0700	−0.407721
$611$	39.0566	1.58006
$612$	−3.77498	−0.152595
$613$	16.2351	0.655728	0.327864	−	0.944725i	$-0.393671\pi$
$613$	16.2351	0.655728	0.327864	+	0.944725i	$0.393671\pi$
$614$	−9.98672	−0.403031
$615$	−4.03336	−0.162641
$616$	0.780593	0.0314510
$617$	6.51826	0.262415	0.131208	−	0.991355i	$-0.458115\pi$
$617$	6.51826	0.262415	0.131208	+	0.991355i	$0.458115\pi$
$618$	0.893993	0.0359617
$619$	−4.39112	−0.176494	−0.0882470	−	0.996099i	$-0.528126\pi$
$619$	−4.39112	−0.176494	−0.0882470	+	0.996099i	$0.528126\pi$
$620$	5.22308	0.209764
$621$	−11.9287	−0.478681
$622$	13.6706	0.548142
$623$	−18.4311	−0.738425
$624$	2.36681	0.0947483
$625$	1.00000	0.0400000
$626$	−2.24484	−0.0897220
$627$	0	0
$628$	−5.77858	−0.230590
$629$	−2.82108	−0.112484
$630$	5.93363	0.236402
$631$	−34.6209	−1.37824	−0.689118	−	0.724650i	$-0.742002\pi$
$631$	−34.6209	−1.37824	−0.689118	+	0.724650i	$0.742002\pi$
$632$	4.50165	0.179066
$633$	4.86521	0.193375
$634$	25.8680	1.02735
$635$	−18.7397	−0.743661
$636$	−0.0799333	−0.00316956
$637$	12.0040	0.475614
$638$	0.733141	0.0290253
$639$	3.79391	0.150085
$640$	−0.565920	−0.0223700
$641$	−7.41241	−0.292773	−0.146386	−	0.989227i	$-0.546764\pi$
$641$	−7.41241	−0.292773	−0.146386	+	0.989227i	$0.546764\pi$
$642$	−0.416681	−0.0164451
$643$	−16.5459	−0.652506	−0.326253	−	0.945282i	$-0.605786\pi$
$643$	−16.5459	−0.652506	−0.326253	+	0.945282i	$0.605786\pi$
$644$	−8.08794	−0.318710
$645$	3.22731	0.127075
$646$	0	0
$647$	29.4822	1.15907	0.579533	−	0.814949i	$-0.303235\pi$
$647$	29.4822	1.15907	0.579533	+	0.814949i	$0.303235\pi$
$648$	23.7026	0.931124
$649$	0.926912	0.0363845
$650$	3.85611	0.151249
$651$	−4.71415	−0.184762
$652$	15.7362	0.616277
$653$	6.57421	0.257269	0.128634	−	0.991692i	$-0.458941\pi$
$653$	6.57421	0.257269	0.128634	+	0.991692i	$0.458941\pi$
$654$	6.77017	0.264735
$655$	2.88644	0.112782
$656$	18.8807	0.737169
$657$	18.1145	0.706713
$658$	23.0925	0.900241
$659$	26.3370	1.02594	0.512972	−	0.858405i	$-0.328544\pi$
$659$	26.3370	1.02594	0.512972	+	0.858405i	$0.328544\pi$
$660$	−0.0405631	−0.00157892
$661$	−3.78419	−0.147188	−0.0735941	−	0.997288i	$-0.523447\pi$
$661$	−3.78419	−0.147188	−0.0735941	+	0.997288i	$0.523447\pi$
$662$	−20.5413	−0.798359
$663$	2.21422	0.0859930
$664$	22.8487	0.886703
$665$	0	0
$666$	5.32281	0.206255
$667$	−26.6913	−1.03349
$668$	−2.70769	−0.104763
$669$	−7.73630	−0.299103
$670$	−3.24133	−0.125224
$671$	1.23324	0.0476086
$672$	−3.00694	−0.115995
$673$	21.0431	0.811150	0.405575	−	0.914062i	$-0.367071\pi$
$673$	21.0431	0.811150	0.405575	+	0.914062i	$0.367071\pi$
$674$	−35.8731	−1.38178
$675$	−2.22142	−0.0855025
$676$	0.520083	0.0200032
$677$	15.2744	0.587043	0.293522	−	0.955952i	$-0.405173\pi$
$677$	15.2744	0.587043	0.293522	+	0.955952i	$0.405173\pi$
$678$	0.350941	0.0134778
$679$	−33.0699	−1.26911
$680$	−5.09670	−0.195450
$681$	−9.64161	−0.369467
$682$	0.968267	0.0370769
$683$	8.60225	0.329156	0.164578	−	0.986364i	$-0.447374\pi$
$683$	8.60225	0.329156	0.164578	+	0.986364i	$0.447374\pi$
$684$	0	0
$685$	−18.8316	−0.719518
$686$	21.6401	0.826223
$687$	0.840424	0.0320642
$688$	−15.1075	−0.575968
$689$	−0.930603	−0.0354532
$690$	−2.23544	−0.0851017
$691$	34.1079	1.29753	0.648763	−	0.760990i	$-0.275286\pi$
$691$	34.1079	1.29753	0.648763	+	0.760990i	$0.275286\pi$
$692$	−8.42231	−0.320168
$693$	−0.726674	−0.0276040
$694$	2.81675	0.106922
$695$	−18.1795	−0.689587
$696$	−5.78481	−0.219273
$697$	17.6634	0.669050
$698$	−18.2388	−0.690350
$699$	−5.37047	−0.203130
$700$	−1.50618	−0.0569282
$701$	10.7293	0.405239	0.202619	−	0.979258i	$-0.435055\pi$
$701$	10.7293	0.405239	0.202619	+	0.979258i	$0.435055\pi$
$702$	−8.56603	−0.323304
$703$	0	0
$704$	1.09492	0.0412665
$705$	−4.21645	−0.158801
$706$	−31.1266	−1.17146
$707$	10.2175	0.384267
$708$	−2.08148	−0.0782267
$709$	−28.8476	−1.08339	−0.541697	−	0.840574i	$-0.682218\pi$
$709$	−28.8476	−1.08339	−0.541697	+	0.840574i	$0.682218\pi$
$710$	1.45778	0.0547096
$711$	−4.19070	−0.157164
$712$	−29.8706	−1.11945
$713$	−35.2515	−1.32018
$714$	1.30917	0.0489946
$715$	−0.472245	−0.0176610
$716$	−11.6181	−0.434189
$717$	1.14360	0.0427085
$718$	−19.0829	−0.712166
$719$	−20.0555	−0.747944	−0.373972	−	0.927440i	$-0.622004\pi$
$719$	−20.0555	−0.747944	−0.373972	+	0.927440i	$0.622004\pi$
$720$	5.07163	0.189009
$721$	−4.06535	−0.151402
$722$	0	0
$723$	9.02026	0.335467
$724$	−4.32234	−0.160639
$725$	−4.97059	−0.184603
$726$	4.57173	0.169673
$727$	−0.780521	−0.0289479	−0.0144740	−	0.999895i	$-0.504607\pi$
$727$	−0.780521	−0.0289479	−0.0144740	+	0.999895i	$0.504607\pi$
$728$	−20.4077	−0.756361
$729$	−19.5373	−0.723604
$730$	6.96036	0.257615
$731$	−14.1335	−0.522745
$732$	−2.76937	−0.102359
$733$	−26.8391	−0.991326	−0.495663	−	0.868515i	$-0.665075\pi$
$733$	−26.8391	−0.991326	−0.495663	+	0.868515i	$0.665075\pi$
$734$	−28.3192	−1.04528
$735$	−1.29592	−0.0478006
$736$	−22.4853	−0.828817
$737$	0.396956	0.0146221
$738$	−33.3273	−1.22679
$739$	20.6530	0.759735	0.379867	−	0.925041i	$-0.375970\pi$
$739$	20.6530	0.759735	0.379867	+	0.925041i	$0.375970\pi$
$740$	−1.35113	−0.0496685
$741$	0	0
$742$	−0.550227	−0.0201995
$743$	−1.47317	−0.0540454	−0.0270227	−	0.999635i	$-0.508603\pi$
$743$	−1.47317	−0.0540454	−0.0270227	+	0.999635i	$0.508603\pi$
$744$	−7.64007	−0.280098
$745$	−22.2543	−0.815336
$746$	29.7036	1.08752
$747$	−21.2705	−0.778245
$748$	0.177639	0.00649514
$749$	1.89482	0.0692352
$750$	−0.416295	−0.0152010
$751$	−15.5624	−0.567881	−0.283940	−	0.958842i	$-0.591642\pi$
$751$	−15.5624	−0.567881	−0.283940	+	0.958842i	$0.591642\pi$
$752$	19.7378	0.719764
$753$	6.52071	0.237628
$754$	−19.1671	−0.698026
$755$	−3.33482	−0.121366
$756$	3.34586	0.121688
$757$	20.1756	0.733295	0.366647	−	0.930360i	$-0.380506\pi$
$757$	20.1756	0.733295	0.366647	+	0.930360i	$0.380506\pi$
$758$	13.6114	0.494387
$759$	0.273767	0.00993713
$760$	0	0
$761$	−15.1076	−0.547649	−0.273825	−	0.961780i	$-0.588289\pi$
$761$	−15.1076	−0.547649	−0.273825	+	0.961780i	$0.588289\pi$
$762$	7.80124	0.282609
$763$	−30.7868	−1.11456
$764$	−16.2911	−0.589392
$765$	4.74465	0.171543
$766$	−5.88163	−0.212512
$767$	−24.2331	−0.875005
$768$	−5.94509	−0.214525
$769$	51.6580	1.86284	0.931418	−	0.363951i	$-0.118573\pi$
$769$	51.6580	1.86284	0.931418	+	0.363951i	$0.118573\pi$
$770$	−0.279219	−0.0100624
$771$	7.41327	0.266982
$772$	8.77063	0.315662
$773$	−30.1558	−1.08463	−0.542314	−	0.840176i	$-0.682452\pi$
$773$	−30.1558	−1.08463	−0.542314	+	0.840176i	$0.682452\pi$
$774$	26.6670	0.958525
$775$	−6.56472	−0.235812
$776$	−53.5952	−1.92396
$777$	1.21948	0.0437485
$778$	−9.40431	−0.337161
$779$	0	0
$780$	1.06048	0.0379712
$781$	−0.178530	−0.00638832
$782$	9.78974	0.350080
$783$	11.0418	0.394601
$784$	6.06637	0.216656
$785$	7.26291	0.259224
$786$	−1.20161	−0.0428601
$787$	−43.0969	−1.53624	−0.768119	−	0.640307i	$-0.778807\pi$
$787$	−43.0969	−1.53624	−0.768119	+	0.640307i	$0.778807\pi$
$788$	15.7958	0.562703
$789$	3.34330	0.119025
$790$	−1.61025	−0.0572900
$791$	−1.59588	−0.0567428
$792$	−1.17770	−0.0418476
$793$	−32.2416	−1.14493
$794$	11.6817	0.414569
$795$	0.100466	0.00356315
$796$	−16.7103	−0.592280
$797$	50.5062	1.78902	0.894510	−	0.447048i	$-0.147525\pi$
$797$	50.5062	1.78902	0.894510	+	0.447048i	$0.147525\pi$
$798$	0	0
$799$	18.4652	0.653253
$800$	−4.18732	−0.148044
$801$	27.8073	0.982522
$802$	8.39769	0.296533
$803$	−0.852414	−0.0300810
$804$	−0.891406	−0.0314375
$805$	10.1655	0.358286
$806$	−25.3142	−0.891656
$807$	−0.109386	−0.00385056
$808$	16.5591	0.582547
$809$	−30.0872	−1.05781	−0.528905	−	0.848681i	$-0.677397\pi$
$809$	−30.0872	−1.05781	−0.528905	+	0.848681i	$0.677397\pi$
$810$	−8.47843	−0.297902
$811$	−22.9509	−0.805916	−0.402958	−	0.915218i	$-0.632018\pi$
$811$	−22.9509	−0.805916	−0.402958	+	0.915218i	$0.632018\pi$
$812$	7.48661	0.262728
$813$	−9.43449	−0.330882
$814$	−0.250476	−0.00877917
$815$	−19.7783	−0.692804
$816$	1.11899	0.0391723
$817$	0	0
$818$	−19.4123	−0.678734
$819$	18.9981	0.663846
$820$	8.45972	0.295426
$821$	−38.0807	−1.32903	−0.664513	−	0.747277i	$-0.731361\pi$
$821$	−38.0807	−1.32903	−0.664513	+	0.747277i	$0.731361\pi$
$822$	7.83950	0.273434
$823$	53.7932	1.87511	0.937556	−	0.347835i	$-0.113083\pi$
$823$	53.7932	1.87511	0.937556	+	0.347835i	$0.113083\pi$
$824$	−6.58858	−0.229524
$825$	0.0509824	0.00177498
$826$	−14.3280	−0.498535
$827$	−32.4092	−1.12698	−0.563490	−	0.826123i	$-0.690542\pi$
$827$	−32.4092	−1.12698	−0.563490	+	0.826123i	$0.690542\pi$
$828$	12.2024	0.424064
$829$	18.5305	0.643592	0.321796	−	0.946809i	$-0.395713\pi$
$829$	18.5305	0.643592	0.321796	+	0.946809i	$0.395713\pi$
$830$	−8.17302	−0.283690
$831$	−1.67091	−0.0579633
$832$	−28.6255	−0.992412
$833$	5.67525	0.196636
$834$	7.56804	0.262060
$835$	3.40320	0.117773
$836$	0	0
$837$	14.5830	0.504062
$838$	−1.30301	−0.0450118
$839$	−0.826608	−0.0285377	−0.0142688	−	0.999898i	$-0.504542\pi$
$839$	−0.826608	−0.0285377	−0.0142688	+	0.999898i	$0.504542\pi$
$840$	2.20317	0.0760165
$841$	−4.29321	−0.148042
$842$	36.6185	1.26196
$843$	12.4123	0.427504
$844$	−10.2045	−0.351253
$845$	−0.653675	−0.0224871
$846$	−34.8401	−1.19783
$847$	−20.7895	−0.714337
$848$	−0.470294	−0.0161500
$849$	−0.504106	−0.0173009
$850$	1.82310	0.0625317
$851$	9.11901	0.312596
$852$	0.400908	0.0137349
$853$	−7.34938	−0.251638	−0.125819	−	0.992053i	$-0.540156\pi$
$853$	−7.34938	−0.251638	−0.125819	+	0.992053i	$0.540156\pi$
$854$	−19.0631	−0.652327
$855$	0	0
$856$	3.07087	0.104960
$857$	45.3496	1.54911	0.774556	−	0.632506i	$-0.217974\pi$
$857$	45.3496	1.54911	0.774556	+	0.632506i	$0.217974\pi$
$858$	0.196594	0.00671160
$859$	29.6285	1.01091	0.505456	−	0.862852i	$-0.331324\pi$
$859$	29.6285	1.01091	0.505456	+	0.862852i	$0.331324\pi$
$860$	−6.76909	−0.230824
$861$	−7.63542	−0.260215
$862$	−6.77775	−0.230851
$863$	−41.0807	−1.39840	−0.699201	−	0.714925i	$-0.746461\pi$
$863$	−41.0807	−1.39840	−0.699201	+	0.714925i	$0.746461\pi$
$864$	9.30180	0.316454
$865$	10.5857	0.359925
$866$	−20.3632	−0.691970
$867$	−5.40183	−0.183456
$868$	9.88764	0.335608
$869$	0.197202	0.00668962
$870$	2.06923	0.0701536
$871$	−10.3780	−0.351644
$872$	−49.8951	−1.68966
$873$	49.8931	1.68863
$874$	0	0
$875$	1.89307	0.0639974
$876$	1.91419	0.0646743
$877$	−54.6307	−1.84475	−0.922374	−	0.386298i	$-0.873754\pi$
$877$	−54.6307	−1.84475	−0.922374	+	0.386298i	$0.873754\pi$
$878$	−0.249460	−0.00841888
$879$	2.92984	0.0988211
$880$	−0.238656	−0.00804509
$881$	−15.4805	−0.521552	−0.260776	−	0.965399i	$-0.583978\pi$
$881$	−15.4805	−0.521552	−0.260776	+	0.965399i	$0.583978\pi$
$882$	−10.7080	−0.360558
$883$	−45.3495	−1.52613	−0.763066	−	0.646321i	$-0.776307\pi$
$883$	−45.3495	−1.52613	−0.763066	+	0.646321i	$0.776307\pi$
$884$	−4.64418	−0.156201
$885$	2.61614	0.0879406
$886$	38.3913	1.28978
$887$	31.1399	1.04558	0.522788	−	0.852463i	$-0.324892\pi$
$887$	31.1399	1.04558	0.522788	+	0.852463i	$0.324892\pi$
$888$	1.97637	0.0663226
$889$	−35.4755	−1.18981
$890$	10.6847	0.358153
$891$	1.03833	0.0347853
$892$	16.2264	0.543301
$893$	0	0
$894$	9.26438	0.309847
$895$	14.6024	0.488105
$896$	−1.07133	−0.0357905
$897$	−7.15734	−0.238977
$898$	−18.6025	−0.620775
$899$	32.6305	1.08829
$900$	2.27240	0.0757467
$901$	−0.439972	−0.0146576
$902$	1.56828	0.0522181
$903$	6.10952	0.203312
$904$	−2.58638	−0.0860218
$905$	5.43261	0.180586
$906$	1.38827	0.0461222
$907$	−43.5415	−1.44577	−0.722886	−	0.690967i	$-0.757185\pi$
$907$	−43.5415	−1.44577	−0.722886	+	0.690967i	$0.757185\pi$
$908$	20.2227	0.671113
$909$	−15.4153	−0.511293
$910$	7.29987	0.241988
$911$	−5.72789	−0.189774	−0.0948868	−	0.995488i	$-0.530249\pi$
$911$	−5.72789	−0.189774	−0.0948868	+	0.995488i	$0.530249\pi$
$912$	0	0
$913$	1.00093	0.0331258
$914$	−1.75855	−0.0581677
$915$	3.48072	0.115069
$916$	−1.76274	−0.0582425
$917$	5.46422	0.180445
$918$	−4.04986	−0.133665
$919$	7.93860	0.261870	0.130935	−	0.991391i	$-0.458202\pi$
$919$	7.93860	0.261870	0.130935	+	0.991391i	$0.458202\pi$
$920$	16.4748	0.543159
$921$	3.45195	0.113746
$922$	9.59339	0.315941
$923$	4.66747	0.153632
$924$	−0.0767887	−0.00252616
$925$	1.69819	0.0558362
$926$	−23.2532	−0.764147
$927$	6.13347	0.201450
$928$	20.8135	0.683236
$929$	−28.9567	−0.950039	−0.475019	−	0.879975i	$-0.657559\pi$
$929$	−28.9567	−0.950039	−0.475019	+	0.879975i	$0.657559\pi$
$930$	2.73286	0.0896141
$931$	0	0
$932$	11.2642	0.368972
$933$	−4.72531	−0.154700
$934$	−22.4444	−0.734403
$935$	−0.223269	−0.00730168
$936$	30.7895	1.00639
$937$	−14.6816	−0.479627	−0.239813	−	0.970819i	$-0.577086\pi$
$937$	−14.6816	−0.479627	−0.239813	+	0.970819i	$0.577086\pi$
$938$	−6.13606	−0.200349
$939$	0.775939	0.0253218
$940$	8.84375	0.288451
$941$	0.154755	0.00504485	0.00252243	−	0.999997i	$-0.499197\pi$
$941$	0.154755	0.00504485	0.00252243	+	0.999997i	$0.499197\pi$
$942$	−3.02352	−0.0985114
$943$	−57.0961	−1.85931
$944$	−12.2465	−0.398590
$945$	−4.20530	−0.136798
$946$	−1.25487	−0.0407993
$947$	−7.51807	−0.244304	−0.122152	−	0.992511i	$-0.538980\pi$
$947$	−7.51807	−0.244304	−0.122152	+	0.992511i	$0.538980\pi$
$948$	−0.442838	−0.0143827
$949$	22.2854	0.723415
$950$	0	0
$951$	−8.94137	−0.289944
$952$	−9.64840	−0.312706
$953$	−22.6743	−0.734493	−0.367247	−	0.930124i	$-0.619700\pi$
$953$	−22.6743	−0.734493	−0.367247	+	0.930124i	$0.619700\pi$
$954$	0.830138	0.0268767
$955$	20.4758	0.662580
$956$	−2.39863	−0.0775772
$957$	−0.253413	−0.00819167
$958$	−25.8437	−0.834973
$959$	−35.6494	−1.15118
$960$	3.09034	0.0997403
$961$	12.0955	0.390177
$962$	6.54840	0.211129
$963$	−2.85875	−0.0921219
$964$	−18.9194	−0.609354
$965$	−11.0235	−0.354860
$966$	−4.23184	−0.136157
$967$	28.8344	0.927253	0.463627	−	0.886031i	$-0.346548\pi$
$967$	28.8344	0.927253	0.463627	+	0.886031i	$0.346548\pi$
$968$	−33.6929	−1.08293
$969$	0	0
$970$	19.1711	0.615546
$971$	−26.3661	−0.846130	−0.423065	−	0.906099i	$-0.639046\pi$
$971$	−26.3661	−0.846130	−0.423065	+	0.906099i	$0.639046\pi$
$972$	−7.63395	−0.244859
$973$	−34.4150	−1.10329
$974$	39.5508	1.26729
$975$	−1.33288	−0.0426863
$976$	−16.2938	−0.521551
$977$	−4.59218	−0.146917	−0.0734585	−	0.997298i	$-0.523404\pi$
$977$	−4.59218	−0.146917	−0.0734585	+	0.997298i	$0.523404\pi$
$978$	8.23362	0.263282
$979$	−1.30853	−0.0418207
$980$	2.71810	0.0868267
$981$	46.4486	1.48299
$982$	−22.0140	−0.702496
$983$	−6.91473	−0.220546	−0.110273	−	0.993901i	$-0.535172\pi$
$983$	−6.91473	−0.220546	−0.110273	+	0.993901i	$0.535172\pi$
$984$	−12.3745	−0.394484
$985$	−19.8532	−0.632577
$986$	−9.06187	−0.288589
$987$	−7.98203	−0.254071
$988$	0	0
$989$	45.6857	1.45272
$990$	0.421263	0.0133886
$991$	38.0070	1.20733	0.603666	−	0.797237i	$-0.293706\pi$
$991$	38.0070	1.20733	0.603666	+	0.797237i	$0.293706\pi$
$992$	27.4886	0.872763
$993$	7.10017	0.225317
$994$	2.75968	0.0875318
$995$	21.0026	0.665827
$996$	−2.24768	−0.0712205
$997$	16.2265	0.513899	0.256950	−	0.966425i	$-0.417283\pi$
$997$	16.2265	0.513899	0.256950	+	0.966425i	$0.417283\pi$
$998$	40.4657	1.28092
$999$	−3.77239	−0.119353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.i.1.2		4
5.4	even	2		9025.2.a.bp.1.3		4
19.8	odd	6		95.2.e.c.26.2	yes	8
19.12	odd	6		95.2.e.c.11.2	✓	8
19.18	odd	2		1805.2.a.o.1.3		4
57.8	even	6		855.2.k.h.406.3		8
57.50	even	6		855.2.k.h.676.3		8
76.27	even	6		1520.2.q.o.881.2		8
76.31	even	6		1520.2.q.o.961.2		8
95.8	even	12		475.2.j.c.349.4		16
95.12	even	12		475.2.j.c.49.4		16
95.27	even	12		475.2.j.c.349.5		16
95.69	odd	6		475.2.e.e.201.3		8
95.84	odd	6		475.2.e.e.26.3		8
95.88	even	12		475.2.j.c.49.5		16
95.94	odd	2		9025.2.a.bg.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.2	✓	8	19.12	odd	6
95.2.e.c.26.2	yes	8	19.8	odd	6
475.2.e.e.26.3		8	95.84	odd	6
475.2.e.e.201.3		8	95.69	odd	6
475.2.j.c.49.4		16	95.12	even	12
475.2.j.c.49.5		16	95.88	even	12
475.2.j.c.349.4		16	95.8	even	12
475.2.j.c.349.5		16	95.27	even	12
855.2.k.h.406.3		8	57.8	even	6
855.2.k.h.676.3		8	57.50	even	6
1520.2.q.o.881.2		8	76.27	even	6
1520.2.q.o.961.2		8	76.31	even	6
1805.2.a.i.1.2		4	1.1	even	1	trivial
1805.2.a.o.1.3		4	19.18	odd	2
9025.2.a.bg.1.2		4	95.94	odd	2
9025.2.a.bp.1.3		4	5.4	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-1.09744 q^{2} +0.379334 q^{3} -0.795629 q^{4} +1.00000 q^{5} -0.416295 q^{6} +1.89307 q^{7} +3.06803 q^{8} -2.85611 q^{9} -1.09744 q^{10} +0.134400 q^{11} -0.301809 q^{12} -3.51373 q^{13} -2.07752 q^{14} +0.379334 q^{15} -1.77572 q^{16} -1.66123 q^{17} +3.13440 q^{18} -0.795629 q^{20} +0.718104 q^{21} -0.147496 q^{22} +5.36984 q^{23} +1.16381 q^{24} +1.00000 q^{25} +3.85611 q^{26} -2.22142 q^{27} -1.50618 q^{28} -4.97059 q^{29} -0.416295 q^{30} -6.56472 q^{31} -4.18732 q^{32} +0.0509824 q^{33} +1.82310 q^{34} +1.89307 q^{35} +2.27240 q^{36} +1.69819 q^{37} -1.33288 q^{39} +3.06803 q^{40} -10.6327 q^{41} -0.788075 q^{42} +8.50784 q^{43} -0.106932 q^{44} -2.85611 q^{45} -5.89307 q^{46} -11.1154 q^{47} -0.673589 q^{48} -3.41630 q^{49} -1.09744 q^{50} -0.630160 q^{51} +2.79563 q^{52} +0.264847 q^{53} +2.43787 q^{54} +0.134400 q^{55} +5.80799 q^{56} +5.45492 q^{58} +6.89667 q^{59} -0.301809 q^{60} +9.17589 q^{61} +7.20437 q^{62} -5.40680 q^{63} +8.14676 q^{64} -3.51373 q^{65} -0.0559501 q^{66} +2.95354 q^{67} +1.32172 q^{68} +2.03696 q^{69} -2.07752 q^{70} -1.32835 q^{71} -8.76262 q^{72} -6.34237 q^{73} -1.86366 q^{74} +0.379334 q^{75} +0.254428 q^{77} +1.46275 q^{78} +1.46728 q^{79} -1.77572 q^{80} +7.72566 q^{81} +11.6688 q^{82} +7.44736 q^{83} -0.571345 q^{84} -1.66123 q^{85} -9.33683 q^{86} -1.88551 q^{87} +0.412343 q^{88} -9.73608 q^{89} +3.13440 q^{90} -6.65174 q^{91} -4.27240 q^{92} -2.49022 q^{93} +12.1985 q^{94} -1.58839 q^{96} -17.4689 q^{97} +3.74917 q^{98} -0.383860 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} - 12 q^{8} + q^{9} - q^{10} - 2 q^{11} - 6 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} + 7 q^{16} - q^{17} + 10 q^{18} + 5 q^{20} + 4 q^{21}+ \cdots + 38 q^{99}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 + 5 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^7 - 12 * q^8 + q^9 - q^10 - 2 * q^11 - 6 * q^12 - 7 * q^13 + q^14 - 3 * q^15 + 7 * q^16 - q^17 + 10 * q^18 + 5 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 23 * q^24 + 4 * q^25 + 3 * q^26 - 12 * q^27 - 19 * q^28 + q^29 + 2 * q^30 - 30 * q^32 - 19 * q^33 - 15 * q^34 - 4 * q^35 - 7 * q^36 + 2 * q^37 + 15 * q^39 - 12 * q^40 + 8 * q^41 - 15 * q^42 + q^43 - 12 * q^44 + q^45 - 12 * q^46 - 12 * q^47 - 23 * q^48 - 10 * q^49 - q^50 - 22 * q^51 + 3 * q^52 + 5 * q^53 - 34 * q^54 - 2 * q^55 + 41 * q^56 - 27 * q^58 + 5 * q^59 - 6 * q^60 + 37 * q^62 - 3 * q^63 + 56 * q^64 - 7 * q^65 - 31 * q^66 - 4 * q^67 + 16 * q^68 + 9 * q^69 + q^70 - 20 * q^71 - 17 * q^72 - 20 * q^73 + 25 * q^74 - 3 * q^75 + 14 * q^77 + 18 * q^78 - 17 * q^79 + 7 * q^80 + 12 * q^81 + 21 * q^82 + q^83 + 20 * q^84 - q^85 - 8 * q^86 - 16 * q^87 + 7 * q^88 - 11 * q^89 + 10 * q^90 - 6 * q^91 - q^92 - 8 * q^93 + 31 * q^94 + 21 * q^96 - q^97 - 9 * q^98 + 38 * q^99

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