LMFDB - Embedded newform 1519.2.a.k.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1519,2,Mod(1,1519)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1519, 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("1519.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1519 = 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1519.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$12.1292760670$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 5 x^{12} - 9 x^{11} + 76 x^{10} - 17 x^{9} - 387 x^{8} + 332 x^{7} + 758 x^{6} - 875 x^{5} + \cdots + 21 $ x^13 - 5x^12 - 9x^11 + 76x^10 - 17x^9 - 387x^8 + 332x^7 + 758x^6 - 875x^5 - 475x^4 + 705x^3 - 48x^2 - 108x + 21
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 217)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.57456$ of defining polynomial
Character	$\chi$	$=$	1519.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.57456 q^{2} -0.536269 q^{3} +4.62836 q^{4} -2.52145 q^{5} -1.38066 q^{6} +6.76686 q^{8} -2.71242 q^{9} +O(q^{10})$	\(q+2.57456 q^{2} -0.536269 q^{3} +4.62836 q^{4} -2.52145 q^{5} -1.38066 q^{6} +6.76686 q^{8} -2.71242 q^{9} -6.49162 q^{10} +5.05724 q^{11} -2.48204 q^{12} +2.83835 q^{13} +1.35218 q^{15} +8.16497 q^{16} +3.86148 q^{17} -6.98328 q^{18} +5.06267 q^{19} -11.6702 q^{20} +13.0202 q^{22} +5.17615 q^{23} -3.62886 q^{24} +1.35771 q^{25} +7.30751 q^{26} +3.06339 q^{27} -2.48767 q^{29} +3.48126 q^{30} +1.00000 q^{31} +7.48748 q^{32} -2.71204 q^{33} +9.94161 q^{34} -12.5540 q^{36} -6.27040 q^{37} +13.0342 q^{38} -1.52212 q^{39} -17.0623 q^{40} +2.36222 q^{41} +9.59880 q^{43} +23.4067 q^{44} +6.83922 q^{45} +13.3263 q^{46} -9.98935 q^{47} -4.37862 q^{48} +3.49550 q^{50} -2.07079 q^{51} +13.1369 q^{52} -8.60842 q^{53} +7.88688 q^{54} -12.7516 q^{55} -2.71495 q^{57} -6.40466 q^{58} +13.3105 q^{59} +6.25835 q^{60} -3.44336 q^{61} +2.57456 q^{62} +2.94702 q^{64} -7.15677 q^{65} -6.98231 q^{66} -8.35132 q^{67} +17.8723 q^{68} -2.77581 q^{69} +0.885293 q^{71} -18.3545 q^{72} -12.1707 q^{73} -16.1435 q^{74} -0.728097 q^{75} +23.4319 q^{76} -3.91879 q^{78} +7.15906 q^{79} -20.5876 q^{80} +6.49445 q^{81} +6.08167 q^{82} -2.67930 q^{83} -9.73653 q^{85} +24.7127 q^{86} +1.33406 q^{87} +34.2216 q^{88} -7.07116 q^{89} +17.6080 q^{90} +23.9571 q^{92} -0.536269 q^{93} -25.7182 q^{94} -12.7653 q^{95} -4.01530 q^{96} -3.20114 q^{97} -13.7173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 5 q^{2} + 17 q^{4} + q^{5} - 2 q^{6} + 12 q^{8} + 25 q^{9}+O(q^{10}) $ 13 * q + 5 * q^2 + 17 * q^4 + q^5 - 2 * q^6 + 12 * q^8 + 25 * q^9	$ 13 q + 5 q^{2} + 17 q^{4} + q^{5} - 2 q^{6} + 12 q^{8} + 25 q^{9} - 7 q^{10} + 15 q^{11} - 5 q^{12} + 4 q^{13} + 4 q^{15} + 29 q^{16} - 4 q^{17} + 16 q^{18} + 2 q^{19} + 26 q^{20} - 10 q^{22} + 14 q^{23} - 28 q^{24} + 24 q^{25} - 7 q^{26} + 12 q^{27} + 22 q^{29} + 6 q^{30} + 13 q^{31} + 19 q^{32} - 5 q^{33} + 20 q^{34} + 11 q^{36} + 12 q^{37} - 11 q^{38} + 11 q^{39} - 6 q^{40} + 4 q^{41} - 3 q^{43} + 52 q^{44} - 12 q^{45} - 3 q^{46} - 14 q^{47} + 48 q^{48} + 15 q^{50} + 16 q^{51} + 4 q^{52} + 19 q^{53} - 25 q^{54} + 18 q^{55} + 13 q^{57} + 24 q^{58} + 19 q^{59} + 6 q^{60} - 11 q^{61} + 5 q^{62} + 10 q^{64} + 68 q^{65} - 52 q^{66} - 25 q^{67} - 26 q^{68} + 52 q^{69} + 28 q^{71} + 52 q^{72} - 29 q^{73} + 54 q^{74} - 71 q^{75} + 37 q^{76} - 71 q^{78} + 30 q^{79} + 3 q^{80} + 25 q^{81} + 5 q^{82} - 10 q^{83} - q^{85} + 10 q^{86} + 50 q^{87} + 18 q^{88} - 11 q^{89} + 81 q^{90} + 35 q^{92} - 36 q^{94} - 20 q^{95} - 12 q^{96} - 3 q^{97} + 42 q^{99}+O(q^{100}) $ 13 * q + 5 * q^2 + 17 * q^4 + q^5 - 2 * q^6 + 12 * q^8 + 25 * q^9 - 7 * q^10 + 15 * q^11 - 5 * q^12 + 4 * q^13 + 4 * q^15 + 29 * q^16 - 4 * q^17 + 16 * q^18 + 2 * q^19 + 26 * q^20 - 10 * q^22 + 14 * q^23 - 28 * q^24 + 24 * q^25 - 7 * q^26 + 12 * q^27 + 22 * q^29 + 6 * q^30 + 13 * q^31 + 19 * q^32 - 5 * q^33 + 20 * q^34 + 11 * q^36 + 12 * q^37 - 11 * q^38 + 11 * q^39 - 6 * q^40 + 4 * q^41 - 3 * q^43 + 52 * q^44 - 12 * q^45 - 3 * q^46 - 14 * q^47 + 48 * q^48 + 15 * q^50 + 16 * q^51 + 4 * q^52 + 19 * q^53 - 25 * q^54 + 18 * q^55 + 13 * q^57 + 24 * q^58 + 19 * q^59 + 6 * q^60 - 11 * q^61 + 5 * q^62 + 10 * q^64 + 68 * q^65 - 52 * q^66 - 25 * q^67 - 26 * q^68 + 52 * q^69 + 28 * q^71 + 52 * q^72 - 29 * q^73 + 54 * q^74 - 71 * q^75 + 37 * q^76 - 71 * q^78 + 30 * q^79 + 3 * q^80 + 25 * q^81 + 5 * q^82 - 10 * q^83 - q^85 + 10 * q^86 + 50 * q^87 + 18 * q^88 - 11 * q^89 + 81 * q^90 + 35 * q^92 - 36 * q^94 - 20 * q^95 - 12 * q^96 - 3 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.57456	1.82049	0.910244	−	0.414072i	$-0.135894\pi$
$2$	2.57456	1.82049	0.910244	+	0.414072i	$0.135894\pi$
$3$	−0.536269	−0.309615	−0.154808	−	0.987945i	$-0.549476\pi$
$3$	−0.536269	−0.309615	−0.154808	+	0.987945i	$0.549476\pi$
$4$	4.62836	2.31418
$5$	−2.52145	−1.12763	−0.563813	−	0.825902i	$-0.690666\pi$
$5$	−2.52145	−1.12763	−0.563813	+	0.825902i	$0.690666\pi$
$6$	−1.38066	−0.563651
$7$	0	0
$7$	0	0
$8$	6.76686	2.39245
$9$	−2.71242	−0.904139
$10$	−6.49162	−2.05283
$11$	5.05724	1.52481	0.762407	−	0.647097i	$-0.224017\pi$
$11$	5.05724	1.52481	0.762407	+	0.647097i	$0.224017\pi$
$12$	−2.48204	−0.716504
$13$	2.83835	0.787218	0.393609	−	0.919278i	$-0.371226\pi$
$13$	2.83835	0.787218	0.393609	+	0.919278i	$0.371226\pi$
$14$	0	0
$15$	1.35218	0.349130
$16$	8.16497	2.04124
$17$	3.86148	0.936547	0.468273	−	0.883584i	$-0.344876\pi$
$17$	3.86148	0.936547	0.468273	+	0.883584i	$0.344876\pi$
$18$	−6.98328	−1.64597
$19$	5.06267	1.16146	0.580728	−	0.814097i	$-0.302768\pi$
$19$	5.06267	1.16146	0.580728	+	0.814097i	$0.302768\pi$
$20$	−11.6702	−2.60953
$21$	0	0
$22$	13.0202	2.77591
$23$	5.17615	1.07930	0.539651	−	0.841889i	$-0.318556\pi$
$23$	5.17615	1.07930	0.539651	+	0.841889i	$0.318556\pi$
$24$	−3.62886	−0.740737
$25$	1.35771	0.271542
$26$	7.30751	1.43312
$27$	3.06339	0.589550
$28$	0	0
$29$	−2.48767	−0.461949	−0.230975	−	0.972960i	$-0.574191\pi$
$29$	−2.48767	−0.461949	−0.230975	+	0.972960i	$0.574191\pi$
$30$	3.48126	0.635587
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	7.48748	1.32361
$33$	−2.71204	−0.472106
$34$	9.94161	1.70497
$35$	0	0
$36$	−12.5540	−2.09234
$37$	−6.27040	−1.03085	−0.515423	−	0.856936i	$-0.672365\pi$
$37$	−6.27040	−1.03085	−0.515423	+	0.856936i	$0.672365\pi$
$38$	13.0342	2.11442
$39$	−1.52212	−0.243734
$40$	−17.0623	−2.69779
$41$	2.36222	0.368916	0.184458	−	0.982840i	$-0.440947\pi$
$41$	2.36222	0.368916	0.184458	+	0.982840i	$0.440947\pi$
$42$	0	0
$43$	9.59880	1.46380	0.731901	−	0.681411i	$-0.238633\pi$
$43$	9.59880	1.46380	0.731901	+	0.681411i	$0.238633\pi$
$44$	23.4067	3.52869
$45$	6.83922	1.01953
$46$	13.3263	1.96486
$47$	−9.98935	−1.45710	−0.728549	−	0.684994i	$-0.759805\pi$
$47$	−9.98935	−1.45710	−0.728549	+	0.684994i	$0.759805\pi$
$48$	−4.37862	−0.631999
$49$	0	0
$50$	3.49550	0.494338
$51$	−2.07079	−0.289969
$52$	13.1369	1.82176
$53$	−8.60842	−1.18246	−0.591229	−	0.806504i	$-0.701357\pi$
$53$	−8.60842	−1.18246	−0.591229	+	0.806504i	$0.701357\pi$
$54$	7.88688	1.07327
$55$	−12.7516	−1.71942
$56$	0	0
$57$	−2.71495	−0.359604
$58$	−6.40466	−0.840974
$59$	13.3105	1.73288	0.866438	−	0.499285i	$-0.166404\pi$
$59$	13.3105	1.73288	0.866438	+	0.499285i	$0.166404\pi$
$60$	6.25835	0.807949
$61$	−3.44336	−0.440877	−0.220438	−	0.975401i	$-0.570749\pi$
$61$	−3.44336	−0.440877	−0.220438	+	0.975401i	$0.570749\pi$
$62$	2.57456	0.326969
$63$	0	0
$64$	2.94702	0.368378
$65$	−7.15677	−0.887688
$66$	−6.98231	−0.859463
$67$	−8.35132	−1.02028	−0.510138	−	0.860093i	$-0.670406\pi$
$67$	−8.35132	−1.02028	−0.510138	+	0.860093i	$0.670406\pi$
$68$	17.8723	2.16734
$69$	−2.77581	−0.334168
$70$	0	0
$71$	0.885293	0.105065	0.0525325	−	0.998619i	$-0.483271\pi$
$71$	0.885293	0.105065	0.0525325	+	0.998619i	$0.483271\pi$
$72$	−18.3545	−2.16310
$73$	−12.1707	−1.42447	−0.712233	−	0.701943i	$-0.752316\pi$
$73$	−12.1707	−1.42447	−0.712233	+	0.701943i	$0.752316\pi$
$74$	−16.1435	−1.87664
$75$	−0.728097	−0.0840733
$76$	23.4319	2.68782
$77$	0	0
$78$	−3.91879	−0.443716
$79$	7.15906	0.805457	0.402728	−	0.915320i	$-0.368062\pi$
$79$	7.15906	0.805457	0.402728	+	0.915320i	$0.368062\pi$
$80$	−20.5876	−2.30176
$81$	6.49445	0.721605
$82$	6.08167	0.671608
$83$	−2.67930	−0.294091	−0.147046	−	0.989130i	$-0.546976\pi$
$83$	−2.67930	−0.294091	−0.147046	+	0.989130i	$0.546976\pi$
$84$	0	0
$85$	−9.73653	−1.05607
$86$	24.7127	2.66484
$87$	1.33406	0.143026
$88$	34.2216	3.64804
$89$	−7.07116	−0.749541	−0.374771	−	0.927118i	$-0.622279\pi$
$89$	−7.07116	−0.749541	−0.374771	+	0.927118i	$0.622279\pi$
$90$	17.6080	1.85604
$91$	0	0
$92$	23.9571	2.49770
$93$	−0.536269	−0.0556085
$94$	−25.7182	−2.65263
$95$	−12.7653	−1.30969
$96$	−4.01530	−0.409810
$97$	−3.20114	−0.325026	−0.162513	−	0.986706i	$-0.551960\pi$
$97$	−3.20114	−0.325026	−0.162513	+	0.986706i	$0.551960\pi$
$98$	0	0
$99$	−13.7173	−1.37864
$100$	6.28396	0.628396
$101$	−6.16138	−0.613080	−0.306540	−	0.951858i	$-0.599171\pi$
$101$	−6.16138	−0.613080	−0.306540	+	0.951858i	$0.599171\pi$
$102$	−5.33138	−0.527885
$103$	−13.1908	−1.29973	−0.649864	−	0.760050i	$-0.725174\pi$
$103$	−13.1908	−1.29973	−0.649864	+	0.760050i	$0.725174\pi$
$104$	19.2067	1.88338
$105$	0	0
$106$	−22.1629	−2.15265
$107$	1.38929	0.134308	0.0671539	−	0.997743i	$-0.478608\pi$
$107$	1.38929	0.134308	0.0671539	+	0.997743i	$0.478608\pi$
$108$	14.1785	1.36432
$109$	−2.20055	−0.210774	−0.105387	−	0.994431i	$-0.533608\pi$
$109$	−2.20055	−0.210774	−0.105387	+	0.994431i	$0.533608\pi$
$110$	−32.8297	−3.13019
$111$	3.36262	0.319166
$112$	0	0
$113$	−11.0376	−1.03833	−0.519165	−	0.854674i	$-0.673757\pi$
$113$	−11.0376	−1.03833	−0.519165	+	0.854674i	$0.673757\pi$
$114$	−6.98981	−0.654656
$115$	−13.0514	−1.21705
$116$	−11.5138	−1.06903
$117$	−7.69879	−0.711754
$118$	34.2686	3.15468
$119$	0	0
$120$	9.14998	0.835275
$121$	14.5757	1.32506
$122$	−8.86513	−0.802611
$123$	−1.26678	−0.114222
$124$	4.62836	0.415639
$125$	9.18386	0.821429
$126$	0	0
$127$	9.97576	0.885205	0.442603	−	0.896718i	$-0.354055\pi$
$127$	9.97576	0.885205	0.442603	+	0.896718i	$0.354055\pi$
$128$	−7.38767	−0.652984
$129$	−5.14754	−0.453215
$130$	−18.4255	−1.61602
$131$	11.2507	0.982975	0.491487	−	0.870885i	$-0.336453\pi$
$131$	11.2507	0.982975	0.491487	+	0.870885i	$0.336453\pi$
$132$	−12.5523	−1.09254
$133$	0	0
$134$	−21.5010	−1.85740
$135$	−7.72419	−0.664792
$136$	26.1301	2.24064
$137$	6.21571	0.531044	0.265522	−	0.964105i	$-0.414456\pi$
$137$	6.21571	0.531044	0.265522	+	0.964105i	$0.414456\pi$
$138$	−7.14648	−0.608349
$139$	12.5607	1.06538	0.532691	−	0.846310i	$-0.321181\pi$
$139$	12.5607	1.06538	0.532691	+	0.846310i	$0.321181\pi$
$140$	0	0
$141$	5.35698	0.451139
$142$	2.27924	0.191270
$143$	14.3542	1.20036
$144$	−22.1468	−1.84557
$145$	6.27254	0.520906
$146$	−31.3341	−2.59323
$147$	0	0
$148$	−29.0216	−2.38556
$149$	−7.95149	−0.651412	−0.325706	−	0.945471i	$-0.605602\pi$
$149$	−7.95149	−0.651412	−0.325706	+	0.945471i	$0.605602\pi$
$150$	−1.87453	−0.153055
$151$	−6.75250	−0.549510	−0.274755	−	0.961514i	$-0.588597\pi$
$151$	−6.75250	−0.549510	−0.274755	+	0.961514i	$0.588597\pi$
$152$	34.2584	2.77872
$153$	−10.4739	−0.846768
$154$	0	0
$155$	−2.52145	−0.202528
$156$	−7.04492	−0.564045
$157$	8.95883	0.714992	0.357496	−	0.933915i	$-0.383631\pi$
$157$	8.95883	0.714992	0.357496	+	0.933915i	$0.383631\pi$
$158$	18.4314	1.46632
$159$	4.61643	0.366107
$160$	−18.8793	−1.49254
$161$	0	0
$162$	16.7203	1.31367
$163$	20.8129	1.63019	0.815095	−	0.579327i	$-0.196685\pi$
$163$	20.8129	1.63019	0.815095	+	0.579327i	$0.196685\pi$
$164$	10.9332	0.853738
$165$	6.83827	0.532359
$166$	−6.89802	−0.535390
$167$	−10.0243	−0.775703	−0.387851	−	0.921722i	$-0.626783\pi$
$167$	−10.0243	−0.775703	−0.387851	+	0.921722i	$0.626783\pi$
$168$	0	0
$169$	−4.94375	−0.380288
$170$	−25.0673	−1.92257
$171$	−13.7321	−1.05012
$172$	44.4266	3.38750
$173$	−1.25485	−0.0954042	−0.0477021	−	0.998862i	$-0.515190\pi$
$173$	−1.25485	−0.0954042	−0.0477021	+	0.998862i	$0.515190\pi$
$174$	3.43462	0.260378
$175$	0	0
$176$	41.2922	3.11252
$177$	−7.13799	−0.536524
$178$	−18.2051	−1.36453
$179$	−11.7036	−0.874771	−0.437386	−	0.899274i	$-0.644096\pi$
$179$	−11.7036	−0.874771	−0.437386	+	0.899274i	$0.644096\pi$
$180$	31.6543	2.35938
$181$	−15.9491	−1.18549	−0.592743	−	0.805392i	$-0.701955\pi$
$181$	−15.9491	−1.18549	−0.592743	+	0.805392i	$0.701955\pi$
$182$	0	0
$183$	1.84657	0.136502
$184$	35.0263	2.58217
$185$	15.8105	1.16241
$186$	−1.38066	−0.101235
$187$	19.5284	1.42806
$188$	−46.2343	−3.37198
$189$	0	0
$190$	−32.8650	−2.38427
$191$	−11.3810	−0.823497	−0.411749	−	0.911298i	$-0.635082\pi$
$191$	−11.3810	−0.823497	−0.411749	+	0.911298i	$0.635082\pi$
$192$	−1.58040	−0.114055
$193$	−7.17233	−0.516276	−0.258138	−	0.966108i	$-0.583109\pi$
$193$	−7.17233	−0.516276	−0.258138	+	0.966108i	$0.583109\pi$
$194$	−8.24152	−0.591706
$195$	3.83795	0.274841
$196$	0	0
$197$	7.12810	0.507856	0.253928	−	0.967223i	$-0.418277\pi$
$197$	7.12810	0.507856	0.253928	+	0.967223i	$0.418277\pi$
$198$	−35.3161	−2.50980
$199$	−9.14704	−0.648416	−0.324208	−	0.945986i	$-0.605098\pi$
$199$	−9.14704	−0.648416	−0.324208	+	0.945986i	$0.605098\pi$
$200$	9.18742	0.649649
$201$	4.47855	0.315893
$202$	−15.8628	−1.11611
$203$	0	0
$204$	−9.58436	−0.671040
$205$	−5.95621	−0.416000
$206$	−33.9605	−2.36614
$207$	−14.0399	−0.975838
$208$	23.1751	1.60690
$209$	25.6031	1.77101
$210$	0	0
$211$	1.40878	0.0969846	0.0484923	−	0.998824i	$-0.484558\pi$
$211$	1.40878	0.0969846	0.0484923	+	0.998824i	$0.484558\pi$
$212$	−39.8429	−2.73642
$213$	−0.474755	−0.0325297
$214$	3.57681	0.244506
$215$	−24.2029	−1.65062
$216$	20.7295	1.41047
$217$	0	0
$218$	−5.66544	−0.383712
$219$	6.52674	0.441036
$220$	−59.0188	−3.97905
$221$	10.9602	0.737266
$222$	8.65726	0.581037
$223$	24.2321	1.62270	0.811350	−	0.584561i	$-0.198733\pi$
$223$	24.2321	1.62270	0.811350	+	0.584561i	$0.198733\pi$
$224$	0	0
$225$	−3.68267	−0.245511
$226$	−28.4170	−1.89027
$227$	22.5006	1.49342	0.746710	−	0.665150i	$-0.231632\pi$
$227$	22.5006	1.49342	0.746710	+	0.665150i	$0.231632\pi$
$228$	−12.5658	−0.832189
$229$	−25.6075	−1.69219	−0.846096	−	0.533030i	$-0.821053\pi$
$229$	−25.6075	−1.69219	−0.846096	+	0.533030i	$0.821053\pi$
$230$	−33.6016	−2.21562
$231$	0	0
$232$	−16.8337	−1.10519
$233$	19.5929	1.28357	0.641786	−	0.766884i	$-0.278194\pi$
$233$	19.5929	1.28357	0.641786	+	0.766884i	$0.278194\pi$
$234$	−19.8210	−1.29574
$235$	25.1877	1.64306
$236$	61.6056	4.01018
$237$	−3.83918	−0.249382
$238$	0	0
$239$	19.9855	1.29276	0.646378	−	0.763018i	$-0.276283\pi$
$239$	19.9855	1.29276	0.646378	+	0.763018i	$0.276283\pi$
$240$	11.0405	0.712659
$241$	3.93552	0.253509	0.126755	−	0.991934i	$-0.459544\pi$
$241$	3.93552	0.253509	0.126755	+	0.991934i	$0.459544\pi$
$242$	37.5259	2.41226
$243$	−12.6729	−0.812970
$244$	−15.9371	−1.02027
$245$	0	0
$246$	−3.26141	−0.207940
$247$	14.3697	0.914319
$248$	6.76686	0.429696
$249$	1.43683	0.0910551
$250$	23.6444	1.49540
$251$	−14.5654	−0.919360	−0.459680	−	0.888085i	$-0.652036\pi$
$251$	−14.5654	−0.919360	−0.459680	+	0.888085i	$0.652036\pi$
$252$	0	0
$253$	26.1770	1.64573
$254$	25.6832	1.61151
$255$	5.22140	0.326977
$256$	−24.9141	−1.55713
$257$	−10.6895	−0.666790	−0.333395	−	0.942787i	$-0.608194\pi$
$257$	−10.6895	−0.666790	−0.333395	+	0.942787i	$0.608194\pi$
$258$	−13.2526	−0.825073
$259$	0	0
$260$	−33.1241	−2.05427
$261$	6.74760	0.417666
$262$	28.9655	1.78949
$263$	−14.1585	−0.873048	−0.436524	−	0.899693i	$-0.643791\pi$
$263$	−14.1585	−0.873048	−0.436524	+	0.899693i	$0.643791\pi$
$264$	−18.3520	−1.12949
$265$	21.7057	1.33337
$266$	0	0
$267$	3.79204	0.232069
$268$	−38.6529	−2.36110
$269$	−2.07431	−0.126473	−0.0632365	−	0.997999i	$-0.520142\pi$
$269$	−2.07431	−0.126473	−0.0632365	+	0.997999i	$0.520142\pi$
$270$	−19.8864	−1.21025
$271$	−9.07981	−0.551559	−0.275780	−	0.961221i	$-0.588936\pi$
$271$	−9.07981	−0.551559	−0.275780	+	0.961221i	$0.588936\pi$
$272$	31.5289	1.91172
$273$	0	0
$274$	16.0027	0.966760
$275$	6.86625	0.414051
$276$	−12.8474	−0.773324
$277$	−19.3294	−1.16139	−0.580697	−	0.814120i	$-0.697220\pi$
$277$	−19.3294	−1.16139	−0.580697	+	0.814120i	$0.697220\pi$
$278$	32.3382	1.93952
$279$	−2.71242	−0.162388
$280$	0	0
$281$	21.2825	1.26960	0.634802	−	0.772675i	$-0.281082\pi$
$281$	21.2825	1.26960	0.634802	+	0.772675i	$0.281082\pi$
$282$	13.7919	0.821294
$283$	3.44385	0.204715	0.102358	−	0.994748i	$-0.467361\pi$
$283$	3.44385	0.204715	0.102358	+	0.994748i	$0.467361\pi$
$284$	4.09745	0.243139
$285$	6.84562	0.405499
$286$	36.9558	2.18524
$287$	0	0
$288$	−20.3092	−1.19673
$289$	−2.08897	−0.122880
$290$	16.1490	0.948304
$291$	1.71667	0.100633
$292$	−56.3301	−3.29647
$293$	19.7785	1.15547	0.577735	−	0.816224i	$-0.303937\pi$
$293$	19.7785	1.15547	0.577735	+	0.816224i	$0.303937\pi$
$294$	0	0
$295$	−33.5617	−1.95404
$296$	−42.4309	−2.46625
$297$	15.4923	0.898954
$298$	−20.4716	−1.18589
$299$	14.6917	0.849645
$300$	−3.36989	−0.194561
$301$	0	0
$302$	−17.3847	−1.00038
$303$	3.30416	0.189819
$304$	41.3366	2.37081
$305$	8.68225	0.497144
$306$	−26.9658	−1.54153
$307$	−27.4654	−1.56753	−0.783766	−	0.621056i	$-0.786704\pi$
$307$	−27.4654	−1.56753	−0.783766	+	0.621056i	$0.786704\pi$
$308$	0	0
$309$	7.07382	0.402415
$310$	−6.49162	−0.368699
$311$	25.7799	1.46184	0.730921	−	0.682462i	$-0.239091\pi$
$311$	25.7799	1.46184	0.730921	+	0.682462i	$0.239091\pi$
$312$	−10.3000	−0.583121
$313$	6.41612	0.362660	0.181330	−	0.983422i	$-0.441960\pi$
$313$	6.41612	0.362660	0.181330	+	0.983422i	$0.441960\pi$
$314$	23.0650	1.30164
$315$	0	0
$316$	33.1347	1.86397
$317$	−6.33133	−0.355603	−0.177801	−	0.984066i	$-0.556898\pi$
$317$	−6.33133	−0.355603	−0.177801	+	0.984066i	$0.556898\pi$
$318$	11.8853	0.666493
$319$	−12.5808	−0.704387
$320$	−7.43077	−0.415393
$321$	−0.745033	−0.0415837
$322$	0	0
$323$	19.5494	1.08776
$324$	30.0586	1.66992
$325$	3.85366	0.213762
$326$	53.5840	2.96774
$327$	1.18008	0.0652588
$328$	15.9848	0.882613
$329$	0	0
$330$	17.6055	0.969153
$331$	−18.7683	−1.03160	−0.515799	−	0.856710i	$-0.672505\pi$
$331$	−18.7683	−1.03160	−0.515799	+	0.856710i	$0.672505\pi$
$332$	−12.4008	−0.680580
$333$	17.0079	0.932028
$334$	−25.8081	−1.41216
$335$	21.0574	1.15049
$336$	0	0
$337$	−30.2984	−1.65046	−0.825230	−	0.564797i	$-0.808955\pi$
$337$	−30.2984	−1.65046	−0.825230	+	0.564797i	$0.808955\pi$
$338$	−12.7280	−0.692311
$339$	5.91912	0.321483
$340$	−45.0641	−2.44395
$341$	5.05724	0.273865
$342$	−35.3540	−1.91173
$343$	0	0
$344$	64.9537	3.50207
$345$	6.99906	0.376817
$346$	−3.23068	−0.173682
$347$	−18.0656	−0.969812	−0.484906	−	0.874566i	$-0.661146\pi$
$347$	−18.0656	−0.969812	−0.484906	+	0.874566i	$0.661146\pi$
$348$	6.17451	0.330989
$349$	−31.5485	−1.68875	−0.844377	−	0.535750i	$-0.820029\pi$
$349$	−31.5485	−1.68875	−0.844377	+	0.535750i	$0.820029\pi$
$350$	0	0
$351$	8.69499	0.464104
$352$	37.8660	2.01826
$353$	−14.3506	−0.763806	−0.381903	−	0.924202i	$-0.624731\pi$
$353$	−14.3506	−0.763806	−0.381903	+	0.924202i	$0.624731\pi$
$354$	−18.3772	−0.976736
$355$	−2.23222	−0.118474
$356$	−32.7278	−1.73457
$357$	0	0
$358$	−30.1317	−1.59251
$359$	17.9840	0.949161	0.474581	−	0.880212i	$-0.342600\pi$
$359$	17.9840	0.949161	0.474581	+	0.880212i	$0.342600\pi$
$360$	46.2800	2.43917
$361$	6.63065	0.348982
$362$	−41.0618	−2.15816
$363$	−7.81647	−0.410258
$364$	0	0
$365$	30.6877	1.60627
$366$	4.75409	0.248500
$367$	−18.1314	−0.946449	−0.473225	−	0.880942i	$-0.656910\pi$
$367$	−18.1314	−0.946449	−0.473225	+	0.880942i	$0.656910\pi$
$368$	42.2631	2.20312
$369$	−6.40732	−0.333552
$370$	40.7050	2.11615
$371$	0	0
$372$	−2.48204	−0.128688
$373$	7.04848	0.364956	0.182478	−	0.983210i	$-0.441588\pi$
$373$	7.04848	0.364956	0.182478	+	0.983210i	$0.441588\pi$
$374$	50.2771	2.59977
$375$	−4.92502	−0.254327
$376$	−67.5966	−3.48603
$377$	−7.06090	−0.363655
$378$	0	0
$379$	−24.1407	−1.24003	−0.620013	−	0.784592i	$-0.712873\pi$
$379$	−24.1407	−1.24003	−0.620013	+	0.784592i	$0.712873\pi$
$380$	−59.0822	−3.03085
$381$	−5.34969	−0.274073
$382$	−29.3009	−1.49917
$383$	4.13656	0.211368	0.105684	−	0.994400i	$-0.466297\pi$
$383$	4.13656	0.211368	0.105684	+	0.994400i	$0.466297\pi$
$384$	3.96178	0.202174
$385$	0	0
$386$	−18.4656	−0.939874
$387$	−26.0359	−1.32348
$388$	−14.8160	−0.752168
$389$	1.51828	0.0769796	0.0384898	−	0.999259i	$-0.487745\pi$
$389$	1.51828	0.0769796	0.0384898	+	0.999259i	$0.487745\pi$
$390$	9.88103	0.500346
$391$	19.9876	1.01082
$392$	0	0
$393$	−6.03338	−0.304344
$394$	18.3517	0.924546
$395$	−18.0512	−0.908254
$396$	−63.4887	−3.19043
$397$	30.3079	1.52111	0.760554	−	0.649275i	$-0.224927\pi$
$397$	30.3079	1.52111	0.760554	+	0.649275i	$0.224927\pi$
$398$	−23.5496	−1.18043
$399$	0	0
$400$	11.0856	0.554282
$401$	13.8858	0.693426	0.346713	−	0.937971i	$-0.387298\pi$
$401$	13.8858	0.693426	0.346713	+	0.937971i	$0.387298\pi$
$402$	11.5303	0.575079
$403$	2.83835	0.141388
$404$	−28.5171	−1.41878
$405$	−16.3754	−0.813701
$406$	0	0
$407$	−31.7109	−1.57185
$408$	−14.0128	−0.693735
$409$	−0.318596	−0.0157535	−0.00787677	−	0.999969i	$-0.502507\pi$
$409$	−0.318596	−0.0157535	−0.00787677	+	0.999969i	$0.502507\pi$
$410$	−15.3346	−0.757323
$411$	−3.33329	−0.164419
$412$	−61.0517	−3.00780
$413$	0	0
$414$	−36.1465	−1.77650
$415$	6.75572	0.331625
$416$	21.2521	1.04197
$417$	−6.73590	−0.329858
$418$	65.9168	3.22410
$419$	−3.06925	−0.149943	−0.0749713	−	0.997186i	$-0.523887\pi$
$419$	−3.06925	−0.149943	−0.0749713	+	0.997186i	$0.523887\pi$
$420$	0	0
$421$	−2.64920	−0.129114	−0.0645571	−	0.997914i	$-0.520563\pi$
$421$	−2.64920	−0.129114	−0.0645571	+	0.997914i	$0.520563\pi$
$422$	3.62700	0.176559
$423$	27.0953	1.31742
$424$	−58.2520	−2.82897
$425$	5.24276	0.254311
$426$	−1.22229	−0.0592199
$427$	0	0
$428$	6.43013	0.310812
$429$	−7.69773	−0.371650
$430$	−62.3118	−3.00494
$431$	−17.8480	−0.859710	−0.429855	−	0.902898i	$-0.641435\pi$
$431$	−17.8480	−0.859710	−0.429855	+	0.902898i	$0.641435\pi$
$432$	25.0125	1.20341
$433$	2.23115	0.107222	0.0536112	−	0.998562i	$-0.482927\pi$
$433$	2.23115	0.107222	0.0536112	+	0.998562i	$0.482927\pi$
$434$	0	0
$435$	−3.36377	−0.161280
$436$	−10.1849	−0.487769
$437$	26.2051	1.25356
$438$	16.8035	0.802902
$439$	−12.2223	−0.583338	−0.291669	−	0.956519i	$-0.594211\pi$
$439$	−12.2223	−0.583338	−0.291669	+	0.956519i	$0.594211\pi$
$440$	−86.2881	−4.11362
$441$	0	0
$442$	28.2178	1.34218
$443$	20.8124	0.988828	0.494414	−	0.869226i	$-0.335383\pi$
$443$	20.8124	0.988828	0.494414	+	0.869226i	$0.335383\pi$
$444$	15.5634	0.738606
$445$	17.8296	0.845203
$446$	62.3869	2.95411
$447$	4.26414	0.201687
$448$	0	0
$449$	27.3096	1.28882	0.644409	−	0.764681i	$-0.277103\pi$
$449$	27.3096	1.28882	0.644409	+	0.764681i	$0.277103\pi$
$450$	−9.48125	−0.446950
$451$	11.9463	0.562529
$452$	−51.0860	−2.40288
$453$	3.62115	0.170137
$454$	57.9292	2.71875
$455$	0	0
$456$	−18.3717	−0.860334
$457$	−19.6882	−0.920975	−0.460487	−	0.887666i	$-0.652325\pi$
$457$	−19.6882	−0.920975	−0.460487	+	0.887666i	$0.652325\pi$
$458$	−65.9281	−3.08062
$459$	11.8292	0.552141
$460$	−60.4065	−2.81647
$461$	−26.0563	−1.21356	−0.606781	−	0.794869i	$-0.707540\pi$
$461$	−26.0563	−1.21356	−0.606781	+	0.794869i	$0.707540\pi$
$462$	0	0
$463$	31.2370	1.45170	0.725852	−	0.687851i	$-0.241446\pi$
$463$	31.2370	1.45170	0.725852	+	0.687851i	$0.241446\pi$
$464$	−20.3118	−0.942951
$465$	1.35218	0.0627056
$466$	50.4430	2.33673
$467$	24.2951	1.12424	0.562122	−	0.827054i	$-0.309985\pi$
$467$	24.2951	1.12424	0.562122	+	0.827054i	$0.309985\pi$
$468$	−35.6328	−1.64713
$469$	0	0
$470$	64.8471	2.99117
$471$	−4.80434	−0.221372
$472$	90.0701	4.14581
$473$	48.5434	2.23203
$474$	−9.88420	−0.453996
$475$	6.87363	0.315384
$476$	0	0
$477$	23.3496	1.06911
$478$	51.4539	2.35345
$479$	18.1957	0.831383	0.415691	−	0.909506i	$-0.363540\pi$
$479$	18.1957	0.831383	0.415691	+	0.909506i	$0.363540\pi$
$480$	10.1244	0.462113
$481$	−17.7976	−0.811501
$482$	10.1322	0.461511
$483$	0	0
$484$	67.4613	3.06642
$485$	8.07150	0.366508
$486$	−32.6272	−1.48000
$487$	−9.90826	−0.448986	−0.224493	−	0.974476i	$-0.572073\pi$
$487$	−9.90826	−0.448986	−0.224493	+	0.974476i	$0.572073\pi$
$488$	−23.3007	−1.05477
$489$	−11.1613	−0.504731
$490$	0	0
$491$	−28.9101	−1.30469	−0.652347	−	0.757920i	$-0.726216\pi$
$491$	−28.9101	−1.30469	−0.652347	+	0.757920i	$0.726216\pi$
$492$	−5.86313	−0.264330
$493$	−9.60610	−0.432637
$494$	36.9955	1.66451
$495$	34.5876	1.55460
$496$	8.16497	0.366618
$497$	0	0
$498$	3.69919	0.165765
$499$	−10.7721	−0.482227	−0.241113	−	0.970497i	$-0.577513\pi$
$499$	−10.7721	−0.482227	−0.241113	+	0.970497i	$0.577513\pi$
$500$	42.5062	1.90093
$501$	5.37572	0.240169
$502$	−37.4995	−1.67368
$503$	31.4852	1.40385	0.701927	−	0.712249i	$-0.252323\pi$
$503$	31.4852	1.40385	0.701927	+	0.712249i	$0.252323\pi$
$504$	0	0
$505$	15.5356	0.691326
$506$	67.3943	2.99604
$507$	2.65118	0.117743
$508$	46.1714	2.04852
$509$	−36.8745	−1.63443	−0.817216	−	0.576331i	$-0.804484\pi$
$509$	−36.8745	−1.63443	−0.817216	+	0.576331i	$0.804484\pi$
$510$	13.4428	0.595257
$511$	0	0
$512$	−49.3674	−2.18175
$513$	15.5089	0.684737
$514$	−27.5206	−1.21388
$515$	33.2599	1.46561
$516$	−23.8246	−1.04882
$517$	−50.5185	−2.22180
$518$	0	0
$519$	0.672935	0.0295386
$520$	−48.4288	−2.12374
$521$	−37.1360	−1.62696	−0.813480	−	0.581593i	$-0.802430\pi$
$521$	−37.1360	−1.62696	−0.813480	+	0.581593i	$0.802430\pi$
$522$	17.3721	0.760357
$523$	−18.9069	−0.826740	−0.413370	−	0.910563i	$-0.635648\pi$
$523$	−18.9069	−0.826740	−0.413370	+	0.910563i	$0.635648\pi$
$524$	52.0721	2.27478
$525$	0	0
$526$	−36.4518	−1.58937
$527$	3.86148	0.168209
$528$	−22.1437	−0.963682
$529$	3.79249	0.164891
$530$	55.8826	2.42739
$531$	−36.1035	−1.56676
$532$	0	0
$533$	6.70481	0.290418
$534$	9.76284	0.422479
$535$	−3.50302	−0.151449
$536$	−56.5122	−2.44096
$537$	6.27630	0.270842
$538$	−5.34043	−0.230242
$539$	0	0
$540$	−35.7503	−1.53845
$541$	31.8502	1.36935	0.684674	−	0.728849i	$-0.259945\pi$
$541$	31.8502	1.36935	0.684674	+	0.728849i	$0.259945\pi$
$542$	−23.3765	−1.00411
$543$	8.55299	0.367044
$544$	28.9128	1.23962
$545$	5.54857	0.237674
$546$	0	0
$547$	−3.92580	−0.167855	−0.0839276	−	0.996472i	$-0.526746\pi$
$547$	−3.92580	−0.167855	−0.0839276	+	0.996472i	$0.526746\pi$
$548$	28.7685	1.22893
$549$	9.33982	0.398614
$550$	17.6776	0.753774
$551$	−12.5943	−0.536534
$552$	−18.7835	−0.799479
$553$	0	0
$554$	−49.7648	−2.11430
$555$	−8.47868	−0.359900
$556$	58.1353	2.46548
$557$	−21.4484	−0.908797	−0.454399	−	0.890798i	$-0.650146\pi$
$557$	−21.4484	−0.908797	−0.454399	+	0.890798i	$0.650146\pi$
$558$	−6.98328	−0.295626
$559$	27.2448	1.15233
$560$	0	0
$561$	−10.4725	−0.442149
$562$	54.7929	2.31130
$563$	−4.60636	−0.194135	−0.0970674	−	0.995278i	$-0.530946\pi$
$563$	−4.60636	−0.194135	−0.0970674	+	0.995278i	$0.530946\pi$
$564$	24.7940	1.04402
$565$	27.8308	1.17085
$566$	8.86639	0.372682
$567$	0	0
$568$	5.99066	0.251362
$569$	35.9352	1.50648	0.753240	−	0.657745i	$-0.228490\pi$
$569$	35.9352	1.50648	0.753240	+	0.657745i	$0.228490\pi$
$570$	17.6245	0.738207
$571$	22.2670	0.931846	0.465923	−	0.884825i	$-0.345722\pi$
$571$	22.2670	0.931846	0.465923	+	0.884825i	$0.345722\pi$
$572$	66.4365	2.77785
$573$	6.10325	0.254967
$574$	0	0
$575$	7.02769	0.293075
$576$	−7.99355	−0.333065
$577$	−12.3015	−0.512117	−0.256058	−	0.966661i	$-0.582424\pi$
$577$	−12.3015	−0.512117	−0.256058	+	0.966661i	$0.582424\pi$
$578$	−5.37817	−0.223702
$579$	3.84630	0.159847
$580$	29.0316	1.20547
$581$	0	0
$582$	4.41967	0.183201
$583$	−43.5349	−1.80303
$584$	−82.3571	−3.40796
$585$	19.4121	0.802593
$586$	50.9208	2.10352
$587$	−2.49334	−0.102911	−0.0514555	−	0.998675i	$-0.516386\pi$
$587$	−2.49334	−0.102911	−0.0514555	+	0.998675i	$0.516386\pi$
$588$	0	0
$589$	5.06267	0.208604
$590$	−86.4065	−3.55730
$591$	−3.82258	−0.157240
$592$	−51.1976	−2.10421
$593$	7.81289	0.320837	0.160418	−	0.987049i	$-0.448716\pi$
$593$	7.81289	0.320837	0.160418	+	0.987049i	$0.448716\pi$
$594$	39.8858	1.63654
$595$	0	0
$596$	−36.8023	−1.50748
$597$	4.90527	0.200759
$598$	37.8247	1.54677
$599$	11.4676	0.468554	0.234277	−	0.972170i	$-0.424728\pi$
$599$	11.4676	0.468554	0.234277	+	0.972170i	$0.424728\pi$
$600$	−4.92693	−0.201141
$601$	29.1335	1.18838	0.594190	−	0.804325i	$-0.297473\pi$
$601$	29.1335	1.18838	0.594190	+	0.804325i	$0.297473\pi$
$602$	0	0
$603$	22.6522	0.922471
$604$	−31.2530	−1.27166
$605$	−36.7518	−1.49417
$606$	8.50675	0.345563
$607$	−30.0629	−1.22022	−0.610108	−	0.792318i	$-0.708874\pi$
$607$	−30.0629	−1.22022	−0.610108	+	0.792318i	$0.708874\pi$
$608$	37.9067	1.53732
$609$	0	0
$610$	22.3530	0.905046
$611$	−28.3533	−1.14705
$612$	−48.4771	−1.95957
$613$	40.4373	1.63325	0.816624	−	0.577170i	$-0.195843\pi$
$613$	40.4373	1.63325	0.816624	+	0.577170i	$0.195843\pi$
$614$	−70.7112	−2.85367
$615$	3.19413	0.128800
$616$	0	0
$617$	−5.87760	−0.236623	−0.118312	−	0.992977i	$-0.537748\pi$
$617$	−5.87760	−0.236623	−0.118312	+	0.992977i	$0.537748\pi$
$618$	18.2120	0.732593
$619$	22.7024	0.912487	0.456244	−	0.889855i	$-0.349195\pi$
$619$	22.7024	0.912487	0.456244	+	0.889855i	$0.349195\pi$
$620$	−11.6702	−0.468685
$621$	15.8566	0.636302
$622$	66.3718	2.66127
$623$	0	0
$624$	−12.4281	−0.497521
$625$	−29.9452	−1.19781
$626$	16.5187	0.660219
$627$	−13.7302	−0.548330
$628$	41.4647	1.65462
$629$	−24.2130	−0.965436
$630$	0	0
$631$	30.3599	1.20861	0.604305	−	0.796753i	$-0.293451\pi$
$631$	30.3599	1.20861	0.604305	+	0.796753i	$0.293451\pi$
$632$	48.4443	1.92701
$633$	−0.755487	−0.0300279
$634$	−16.3004	−0.647371
$635$	−25.1534	−0.998181
$636$	21.3665	0.847236
$637$	0	0
$638$	−32.3899	−1.28233
$639$	−2.40128	−0.0949933
$640$	18.6276	0.736322
$641$	37.8917	1.49663	0.748316	−	0.663342i	$-0.230863\pi$
$641$	37.8917	1.49663	0.748316	+	0.663342i	$0.230863\pi$
$642$	−1.91813	−0.0757026
$643$	−28.8236	−1.13669	−0.568346	−	0.822790i	$-0.692416\pi$
$643$	−28.8236	−1.13669	−0.568346	+	0.822790i	$0.692416\pi$
$644$	0	0
$645$	12.9793	0.511058
$646$	50.3311	1.98025
$647$	−34.8092	−1.36849	−0.684246	−	0.729252i	$-0.739868\pi$
$647$	−34.8092	−1.36849	−0.684246	+	0.729252i	$0.739868\pi$
$648$	43.9470	1.72640
$649$	67.3142	2.64231
$650$	9.92146	0.389152
$651$	0	0
$652$	96.3294	3.77255
$653$	30.5743	1.19646	0.598232	−	0.801323i	$-0.295870\pi$
$653$	30.5743	1.19646	0.598232	+	0.801323i	$0.295870\pi$
$654$	3.03820	0.118803
$655$	−28.3680	−1.10843
$656$	19.2874	0.753048
$657$	33.0119	1.28792
$658$	0	0
$659$	9.88136	0.384923	0.192462	−	0.981305i	$-0.438353\pi$
$659$	9.88136	0.384923	0.192462	+	0.981305i	$0.438353\pi$
$660$	31.6500	1.23197
$661$	15.7835	0.613905	0.306953	−	0.951725i	$-0.400691\pi$
$661$	15.7835	0.613905	0.306953	+	0.951725i	$0.400691\pi$
$662$	−48.3200	−1.87801
$663$	−5.87764	−0.228269
$664$	−18.1305	−0.703598
$665$	0	0
$666$	43.7879	1.69675
$667$	−12.8766	−0.498583
$668$	−46.3960	−1.79511
$669$	−12.9949	−0.502412
$670$	54.2136	2.09445
$671$	−17.4139	−0.672256
$672$	0	0
$673$	20.7326	0.799185	0.399592	−	0.916693i	$-0.369152\pi$
$673$	20.7326	0.799185	0.399592	+	0.916693i	$0.369152\pi$
$674$	−78.0051	−3.00464
$675$	4.15919	0.160087
$676$	−22.8814	−0.880055
$677$	33.8383	1.30051	0.650255	−	0.759716i	$-0.274662\pi$
$677$	33.8383	1.30051	0.650255	+	0.759716i	$0.274662\pi$
$678$	15.2391	0.585255
$679$	0	0
$680$	−65.8857	−2.52660
$681$	−12.0664	−0.462385
$682$	13.0202	0.498568
$683$	−2.76332	−0.105735	−0.0528677	−	0.998602i	$-0.516836\pi$
$683$	−2.76332	−0.105735	−0.0528677	+	0.998602i	$0.516836\pi$
$684$	−63.5569	−2.43016
$685$	−15.6726	−0.598819
$686$	0	0
$687$	13.7325	0.523928
$688$	78.3739	2.98798
$689$	−24.4338	−0.930852
$690$	18.0195	0.685990
$691$	3.37019	0.128208	0.0641040	−	0.997943i	$-0.479581\pi$
$691$	3.37019	0.128208	0.0641040	+	0.997943i	$0.479581\pi$
$692$	−5.80787	−0.220782
$693$	0	0
$694$	−46.5109	−1.76553
$695$	−31.6711	−1.20135
$696$	9.02741	0.342183
$697$	9.12166	0.345507
$698$	−81.2235	−3.07436
$699$	−10.5071	−0.397413
$700$	0	0
$701$	2.80980	0.106125	0.0530623	−	0.998591i	$-0.483102\pi$
$701$	2.80980	0.106125	0.0530623	+	0.998591i	$0.483102\pi$
$702$	22.3858	0.844896
$703$	−31.7450	−1.19728
$704$	14.9038	0.561708
$705$	−13.5074	−0.508717
$706$	−36.9465	−1.39050
$707$	0	0
$708$	−33.0372	−1.24161
$709$	−24.6810	−0.926916	−0.463458	−	0.886119i	$-0.653391\pi$
$709$	−24.6810	−0.926916	−0.463458	+	0.886119i	$0.653391\pi$
$710$	−5.74699	−0.215681
$711$	−19.4183	−0.728244
$712$	−47.8495	−1.79324
$713$	5.17615	0.193848
$714$	0	0
$715$	−36.1935	−1.35356
$716$	−54.1686	−2.02438
$717$	−10.7176	−0.400256
$718$	46.3010	1.72794
$719$	−8.48290	−0.316359	−0.158179	−	0.987410i	$-0.550562\pi$
$719$	−8.48290	−0.316359	−0.158179	+	0.987410i	$0.550562\pi$
$720$	55.8420	2.08111
$721$	0	0
$722$	17.0710	0.635317
$723$	−2.11050	−0.0784903
$724$	−73.8180	−2.74342
$725$	−3.37753	−0.125438
$726$	−20.1240	−0.746871
$727$	−10.6348	−0.394424	−0.197212	−	0.980361i	$-0.563189\pi$
$727$	−10.6348	−0.394424	−0.197212	+	0.980361i	$0.563189\pi$
$728$	0	0
$729$	−12.6872	−0.469897
$730$	79.0073	2.92419
$731$	37.0656	1.37092
$732$	8.54657	0.315890
$733$	5.15685	0.190473	0.0952363	−	0.995455i	$-0.469639\pi$
$733$	5.15685	0.190473	0.0952363	+	0.995455i	$0.469639\pi$
$734$	−46.6803	−1.72300
$735$	0	0
$736$	38.7563	1.42858
$737$	−42.2346	−1.55573
$738$	−16.4960	−0.607227
$739$	24.0431	0.884441	0.442220	−	0.896906i	$-0.354191\pi$
$739$	24.0431	0.884441	0.442220	+	0.896906i	$0.354191\pi$
$740$	73.1766	2.69002
$741$	−7.70600	−0.283087
$742$	0	0
$743$	7.39593	0.271330	0.135665	−	0.990755i	$-0.456683\pi$
$743$	7.39593	0.271330	0.135665	+	0.990755i	$0.456683\pi$
$744$	−3.62886	−0.133040
$745$	20.0493	0.734549
$746$	18.1467	0.664399
$747$	7.26738	0.265899
$748$	90.3845	3.30479
$749$	0	0
$750$	−12.6797	−0.462999
$751$	7.63920	0.278758	0.139379	−	0.990239i	$-0.455489\pi$
$751$	7.63920	0.278758	0.139379	+	0.990239i	$0.455489\pi$
$752$	−81.5628	−2.97429
$753$	7.81097	0.284648
$754$	−18.1787	−0.662029
$755$	17.0261	0.619642
$756$	0	0
$757$	−21.1310	−0.768018	−0.384009	−	0.923329i	$-0.625457\pi$
$757$	−21.1310	−0.768018	−0.384009	+	0.923329i	$0.625457\pi$
$758$	−62.1517	−2.25745
$759$	−14.0379	−0.509544
$760$	−86.3808	−3.13336
$761$	10.1785	0.368971	0.184485	−	0.982835i	$-0.440938\pi$
$761$	10.1785	0.368971	0.184485	+	0.982835i	$0.440938\pi$
$762$	−13.7731	−0.498946
$763$	0	0
$764$	−52.6751	−1.90572
$765$	26.4095	0.954838
$766$	10.6498	0.384793
$767$	37.7798	1.36415
$768$	13.3606	0.482110
$769$	−16.5066	−0.595244	−0.297622	−	0.954684i	$-0.596193\pi$
$769$	−16.5066	−0.595244	−0.297622	+	0.954684i	$0.596193\pi$
$770$	0	0
$771$	5.73242	0.206448
$772$	−33.1961	−1.19475
$773$	12.7067	0.457027	0.228513	−	0.973541i	$-0.426614\pi$
$773$	12.7067	0.457027	0.228513	+	0.973541i	$0.426614\pi$
$774$	−67.0310	−2.40938
$775$	1.35771	0.0487703
$776$	−21.6616	−0.777608
$777$	0	0
$778$	3.90889	0.140141
$779$	11.9591	0.428480
$780$	17.7634	0.636032
$781$	4.47714	0.160205
$782$	51.4592	1.84018
$783$	−7.62072	−0.272342
$784$	0	0
$785$	−22.5892	−0.806244
$786$	−15.5333	−0.554054
$787$	−27.8919	−0.994239	−0.497120	−	0.867682i	$-0.665609\pi$
$787$	−27.8919	−0.994239	−0.497120	+	0.867682i	$0.665609\pi$
$788$	32.9914	1.17527
$789$	7.59274	0.270309
$790$	−46.4739	−1.65347
$791$	0	0
$792$	−92.8233	−3.29833
$793$	−9.77347	−0.347066
$794$	78.0294	2.76916
$795$	−11.6401	−0.412832
$796$	−42.3357	−1.50055
$797$	44.5837	1.57924	0.789618	−	0.613599i	$-0.210279\pi$
$797$	44.5837	1.57924	0.789618	+	0.613599i	$0.210279\pi$
$798$	0	0
$799$	−38.5737	−1.36464
$800$	10.1658	0.359416
$801$	19.1799	0.677689
$802$	35.7499	1.26237
$803$	−61.5499	−2.17205
$804$	20.7283	0.731032
$805$	0	0
$806$	7.30751	0.257396
$807$	1.11239	0.0391579
$808$	−41.6932	−1.46676
$809$	10.0819	0.354460	0.177230	−	0.984170i	$-0.443286\pi$
$809$	10.0819	0.354460	0.177230	+	0.984170i	$0.443286\pi$
$810$	−42.1595	−1.48133
$811$	−11.6028	−0.407428	−0.203714	−	0.979030i	$-0.565301\pi$
$811$	−11.6028	−0.407428	−0.203714	+	0.979030i	$0.565301\pi$
$812$	0	0
$813$	4.86922	0.170771
$814$	−81.6416	−2.86154
$815$	−52.4786	−1.83825
$816$	−16.9080	−0.591897
$817$	48.5956	1.70014
$818$	−0.820243	−0.0286791
$819$	0	0
$820$	−27.5675	−0.962698
$821$	39.0212	1.36185	0.680924	−	0.732354i	$-0.261578\pi$
$821$	39.0212	1.36185	0.680924	+	0.732354i	$0.261578\pi$
$822$	−8.58176	−0.299323
$823$	−25.8282	−0.900314	−0.450157	−	0.892949i	$-0.648632\pi$
$823$	−25.8282	−0.900314	−0.450157	+	0.892949i	$0.648632\pi$
$824$	−89.2603	−3.10953
$825$	−3.68216	−0.128196
$826$	0	0
$827$	−48.7414	−1.69491	−0.847453	−	0.530871i	$-0.821865\pi$
$827$	−48.7414	−1.69491	−0.847453	+	0.530871i	$0.821865\pi$
$828$	−64.9815	−2.25826
$829$	−47.3229	−1.64359	−0.821796	−	0.569781i	$-0.807028\pi$
$829$	−47.3229	−1.64359	−0.821796	+	0.569781i	$0.807028\pi$
$830$	17.3930	0.603720
$831$	10.3658	0.359585
$832$	8.36469	0.289994
$833$	0	0
$834$	−17.3420	−0.600503
$835$	25.2757	0.874703
$836$	118.500	4.09842
$837$	3.06339	0.105886
$838$	−7.90197	−0.272969
$839$	19.4483	0.671432	0.335716	−	0.941963i	$-0.391022\pi$
$839$	19.4483	0.671432	0.335716	+	0.941963i	$0.391022\pi$
$840$	0	0
$841$	−22.8115	−0.786603
$842$	−6.82053	−0.235051
$843$	−11.4131	−0.393089
$844$	6.52035	0.224440
$845$	12.4654	0.428823
$846$	69.7584	2.39834
$847$	0	0
$848$	−70.2875	−2.41368
$849$	−1.84683	−0.0633830
$850$	13.4978	0.462971
$851$	−32.4565	−1.11259
$852$	−2.19734	−0.0752795
$853$	−23.2042	−0.794498	−0.397249	−	0.917711i	$-0.630035\pi$
$853$	−23.2042	−0.794498	−0.397249	+	0.917711i	$0.630035\pi$
$854$	0	0
$855$	34.6247	1.18414
$856$	9.40113	0.321324
$857$	−36.7971	−1.25696	−0.628482	−	0.777824i	$-0.716323\pi$
$857$	−36.7971	−1.25696	−0.628482	+	0.777824i	$0.716323\pi$
$858$	−19.8183	−0.676584
$859$	8.16720	0.278661	0.139331	−	0.990246i	$-0.455505\pi$
$859$	8.16720	0.278661	0.139331	+	0.990246i	$0.455505\pi$
$860$	−112.020	−3.81983
$861$	0	0
$862$	−45.9508	−1.56509
$863$	−47.8219	−1.62788	−0.813938	−	0.580952i	$-0.802681\pi$
$863$	−47.8219	−1.62788	−0.813938	+	0.580952i	$0.802681\pi$
$864$	22.9371	0.780335
$865$	3.16403	0.107580
$866$	5.74424	0.195197
$867$	1.12025	0.0380456
$868$	0	0
$869$	36.2051	1.22817
$870$	−8.66023	−0.293609
$871$	−23.7040	−0.803179
$872$	−14.8908	−0.504266
$873$	8.68281	0.293869
$874$	67.4667	2.28209
$875$	0	0
$876$	30.2081	1.02064
$877$	−8.45874	−0.285631	−0.142816	−	0.989749i	$-0.545616\pi$
$877$	−8.45874	−0.285631	−0.142816	+	0.989749i	$0.545616\pi$
$878$	−31.4670	−1.06196
$879$	−10.6066	−0.357751
$880$	−104.116	−3.50976
$881$	28.1301	0.947728	0.473864	−	0.880598i	$-0.342859\pi$
$881$	28.1301	0.947728	0.473864	+	0.880598i	$0.342859\pi$
$882$	0	0
$883$	29.8400	1.00419	0.502097	−	0.864811i	$-0.332562\pi$
$883$	29.8400	1.00419	0.502097	+	0.864811i	$0.332562\pi$
$884$	50.7279	1.70617
$885$	17.9981	0.604999
$886$	53.5828	1.80015
$887$	−11.9128	−0.399994	−0.199997	−	0.979797i	$-0.564093\pi$
$887$	−11.9128	−0.399994	−0.199997	+	0.979797i	$0.564093\pi$
$888$	22.7544	0.763587
$889$	0	0
$890$	45.9033	1.53868
$891$	32.8440	1.10031
$892$	112.155	3.75522
$893$	−50.5728	−1.69236
$894$	10.9783	0.367169
$895$	29.5101	0.986415
$896$	0	0
$897$	−7.87872	−0.263063
$898$	70.3101	2.34628
$899$	−2.48767	−0.0829686
$900$	−17.0447	−0.568157
$901$	−33.2413	−1.10743
$902$	30.7565	1.02408
$903$	0	0
$904$	−74.6899	−2.48415
$905$	40.2148	1.33678
$906$	9.32288	0.309732
$907$	−30.4238	−1.01021	−0.505103	−	0.863059i	$-0.668545\pi$
$907$	−30.4238	−1.01021	−0.505103	+	0.863059i	$0.668545\pi$
$908$	104.141	3.45604
$909$	16.7122	0.554310
$910$	0	0
$911$	−1.48333	−0.0491451	−0.0245725	−	0.999698i	$-0.507822\pi$
$911$	−1.48333	−0.0491451	−0.0245725	+	0.999698i	$0.507822\pi$
$912$	−22.1675	−0.734040
$913$	−13.5499	−0.448435
$914$	−50.6884	−1.67662
$915$	−4.65602	−0.153923
$916$	−118.521	−3.91603
$917$	0	0
$918$	30.4550	1.00517
$919$	3.86079	0.127356	0.0636778	−	0.997971i	$-0.479717\pi$
$919$	3.86079	0.127356	0.0636778	+	0.997971i	$0.479717\pi$
$920$	−88.3169	−2.91172
$921$	14.7288	0.485331
$922$	−67.0835	−2.20928
$923$	2.51278	0.0827090
$924$	0	0
$925$	−8.51337	−0.279918
$926$	80.4214	2.64281
$927$	35.7789	1.17513
$928$	−18.6264	−0.611442
$929$	53.8315	1.76615	0.883077	−	0.469227i	$-0.155468\pi$
$929$	53.8315	1.76615	0.883077	+	0.469227i	$0.155468\pi$
$930$	3.48126	0.114155
$931$	0	0
$932$	90.6828	2.97041
$933$	−13.8249	−0.452608
$934$	62.5493	2.04667
$935$	−49.2399	−1.61032
$936$	−52.0967	−1.70283
$937$	−1.26675	−0.0413829	−0.0206914	−	0.999786i	$-0.506587\pi$
$937$	−1.26675	−0.0413829	−0.0206914	+	0.999786i	$0.506587\pi$
$938$	0	0
$939$	−3.44077	−0.112285
$940$	116.577	3.80234
$941$	47.8797	1.56083	0.780417	−	0.625260i	$-0.215007\pi$
$941$	47.8797	1.56083	0.780417	+	0.625260i	$0.215007\pi$
$942$	−12.3691	−0.403006
$943$	12.2272	0.398172
$944$	108.680	3.53722
$945$	0	0
$946$	124.978	4.06338
$947$	−5.85485	−0.190257	−0.0951285	−	0.995465i	$-0.530326\pi$
$947$	−5.85485	−0.190257	−0.0951285	+	0.995465i	$0.530326\pi$
$948$	−17.7691	−0.577113
$949$	−34.5446	−1.12137
$950$	17.6966	0.574152
$951$	3.39529	0.110100
$952$	0	0
$953$	−7.36461	−0.238563	−0.119282	−	0.992860i	$-0.538059\pi$
$953$	−7.36461	−0.238563	−0.119282	+	0.992860i	$0.538059\pi$
$954$	60.1150	1.94629
$955$	28.6965	0.928597
$956$	92.5001	2.99167
$957$	6.74667	0.218089
$958$	46.8459	1.51352
$959$	0	0
$960$	3.98489	0.128612
$961$	1.00000	0.0322581
$962$	−45.8210	−1.47733
$963$	−3.76833	−0.121433
$964$	18.2150	0.586666
$965$	18.0847	0.582166
$966$	0	0
$967$	−34.2691	−1.10202	−0.551010	−	0.834498i	$-0.685758\pi$
$967$	−34.2691	−1.10202	−0.551010	+	0.834498i	$0.685758\pi$
$968$	98.6314	3.17013
$969$	−10.4837	−0.336786
$970$	20.7806	0.667224
$971$	9.53577	0.306017	0.153009	−	0.988225i	$-0.451104\pi$
$971$	9.53577	0.306017	0.153009	+	0.988225i	$0.451104\pi$
$972$	−58.6549	−1.88136
$973$	0	0
$974$	−25.5094	−0.817374
$975$	−2.06660	−0.0661840
$976$	−28.1149	−0.899936
$977$	−19.5002	−0.623865	−0.311933	−	0.950104i	$-0.600976\pi$
$977$	−19.5002	−0.623865	−0.311933	+	0.950104i	$0.600976\pi$
$978$	−28.7354	−0.918857
$979$	−35.7605	−1.14291
$980$	0	0
$981$	5.96880	0.190569
$982$	−74.4308	−2.37518
$983$	−6.81115	−0.217242	−0.108621	−	0.994083i	$-0.534644\pi$
$983$	−6.81115	−0.217242	−0.108621	+	0.994083i	$0.534644\pi$
$984$	−8.57215	−0.273270
$985$	−17.9731	−0.572672
$986$	−24.7315	−0.787611
$987$	0	0
$988$	66.5079	2.11590
$989$	49.6848	1.57988
$990$	89.0477	2.83012
$991$	38.4656	1.22190	0.610951	−	0.791669i	$-0.290787\pi$
$991$	38.4656	1.22190	0.610951	+	0.791669i	$0.290787\pi$
$992$	7.48748	0.237728
$993$	10.0648	0.319398
$994$	0	0
$995$	23.0638	0.731171
$996$	6.65014	0.210718
$997$	18.5301	0.586853	0.293426	−	0.955982i	$-0.405204\pi$
$997$	18.5301	0.586853	0.293426	+	0.955982i	$0.405204\pi$
$998$	−27.7335	−0.877888
$999$	−19.2087	−0.607736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1519.2.a.k.1.12		13
7.2	even	3		217.2.f.b.32.2	✓	26
7.4	even	3		217.2.f.b.156.2	yes	26
7.6	odd	2		1519.2.a.j.1.12		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
217.2.f.b.32.2	✓	26	7.2	even	3
217.2.f.b.156.2	yes	26	7.4	even	3
1519.2.a.j.1.12		13	7.6	odd	2
1519.2.a.k.1.12		13	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1519 = 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1519.a (trivial)

\(f(q)\)	\(=\)	\(q+2.57456 q^{2} -0.536269 q^{3} +4.62836 q^{4} -2.52145 q^{5} -1.38066 q^{6} +6.76686 q^{8} -2.71242 q^{9} +O(q^{10})\)	\(q+2.57456 q^{2} -0.536269 q^{3} +4.62836 q^{4} -2.52145 q^{5} -1.38066 q^{6} +6.76686 q^{8} -2.71242 q^{9} -6.49162 q^{10} +5.05724 q^{11} -2.48204 q^{12} +2.83835 q^{13} +1.35218 q^{15} +8.16497 q^{16} +3.86148 q^{17} -6.98328 q^{18} +5.06267 q^{19} -11.6702 q^{20} +13.0202 q^{22} +5.17615 q^{23} -3.62886 q^{24} +1.35771 q^{25} +7.30751 q^{26} +3.06339 q^{27} -2.48767 q^{29} +3.48126 q^{30} +1.00000 q^{31} +7.48748 q^{32} -2.71204 q^{33} +9.94161 q^{34} -12.5540 q^{36} -6.27040 q^{37} +13.0342 q^{38} -1.52212 q^{39} -17.0623 q^{40} +2.36222 q^{41} +9.59880 q^{43} +23.4067 q^{44} +6.83922 q^{45} +13.3263 q^{46} -9.98935 q^{47} -4.37862 q^{48} +3.49550 q^{50} -2.07079 q^{51} +13.1369 q^{52} -8.60842 q^{53} +7.88688 q^{54} -12.7516 q^{55} -2.71495 q^{57} -6.40466 q^{58} +13.3105 q^{59} +6.25835 q^{60} -3.44336 q^{61} +2.57456 q^{62} +2.94702 q^{64} -7.15677 q^{65} -6.98231 q^{66} -8.35132 q^{67} +17.8723 q^{68} -2.77581 q^{69} +0.885293 q^{71} -18.3545 q^{72} -12.1707 q^{73} -16.1435 q^{74} -0.728097 q^{75} +23.4319 q^{76} -3.91879 q^{78} +7.15906 q^{79} -20.5876 q^{80} +6.49445 q^{81} +6.08167 q^{82} -2.67930 q^{83} -9.73653 q^{85} +24.7127 q^{86} +1.33406 q^{87} +34.2216 q^{88} -7.07116 q^{89} +17.6080 q^{90} +23.9571 q^{92} -0.536269 q^{93} -25.7182 q^{94} -12.7653 q^{95} -4.01530 q^{96} -3.20114 q^{97} -13.7173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 5 q^{2} + 17 q^{4} + q^{5} - 2 q^{6} + 12 q^{8} + 25 q^{9}+O(q^{10}) \) 13 * q + 5 * q^2 + 17 * q^4 + q^5 - 2 * q^6 + 12 * q^8 + 25 * q^9	\( 13 q + 5 q^{2} + 17 q^{4} + q^{5} - 2 q^{6} + 12 q^{8} + 25 q^{9} - 7 q^{10} + 15 q^{11} - 5 q^{12} + 4 q^{13} + 4 q^{15} + 29 q^{16} - 4 q^{17} + 16 q^{18} + 2 q^{19} + 26 q^{20} - 10 q^{22} + 14 q^{23} - 28 q^{24} + 24 q^{25} - 7 q^{26} + 12 q^{27} + 22 q^{29} + 6 q^{30} + 13 q^{31} + 19 q^{32} - 5 q^{33} + 20 q^{34} + 11 q^{36} + 12 q^{37} - 11 q^{38} + 11 q^{39} - 6 q^{40} + 4 q^{41} - 3 q^{43} + 52 q^{44} - 12 q^{45} - 3 q^{46} - 14 q^{47} + 48 q^{48} + 15 q^{50} + 16 q^{51} + 4 q^{52} + 19 q^{53} - 25 q^{54} + 18 q^{55} + 13 q^{57} + 24 q^{58} + 19 q^{59} + 6 q^{60} - 11 q^{61} + 5 q^{62} + 10 q^{64} + 68 q^{65} - 52 q^{66} - 25 q^{67} - 26 q^{68} + 52 q^{69} + 28 q^{71} + 52 q^{72} - 29 q^{73} + 54 q^{74} - 71 q^{75} + 37 q^{76} - 71 q^{78} + 30 q^{79} + 3 q^{80} + 25 q^{81} + 5 q^{82} - 10 q^{83} - q^{85} + 10 q^{86} + 50 q^{87} + 18 q^{88} - 11 q^{89} + 81 q^{90} + 35 q^{92} - 36 q^{94} - 20 q^{95} - 12 q^{96} - 3 q^{97} + 42 q^{99}+O(q^{100}) \) 13 * q + 5 * q^2 + 17 * q^4 + q^5 - 2 * q^6 + 12 * q^8 + 25 * q^9 - 7 * q^10 + 15 * q^11 - 5 * q^12 + 4 * q^13 + 4 * q^15 + 29 * q^16 - 4 * q^17 + 16 * q^18 + 2 * q^19 + 26 * q^20 - 10 * q^22 + 14 * q^23 - 28 * q^24 + 24 * q^25 - 7 * q^26 + 12 * q^27 + 22 * q^29 + 6 * q^30 + 13 * q^31 + 19 * q^32 - 5 * q^33 + 20 * q^34 + 11 * q^36 + 12 * q^37 - 11 * q^38 + 11 * q^39 - 6 * q^40 + 4 * q^41 - 3 * q^43 + 52 * q^44 - 12 * q^45 - 3 * q^46 - 14 * q^47 + 48 * q^48 + 15 * q^50 + 16 * q^51 + 4 * q^52 + 19 * q^53 - 25 * q^54 + 18 * q^55 + 13 * q^57 + 24 * q^58 + 19 * q^59 + 6 * q^60 - 11 * q^61 + 5 * q^62 + 10 * q^64 + 68 * q^65 - 52 * q^66 - 25 * q^67 - 26 * q^68 + 52 * q^69 + 28 * q^71 + 52 * q^72 - 29 * q^73 + 54 * q^74 - 71 * q^75 + 37 * q^76 - 71 * q^78 + 30 * q^79 + 3 * q^80 + 25 * q^81 + 5 * q^82 - 10 * q^83 - q^85 + 10 * q^86 + 50 * q^87 + 18 * q^88 - 11 * q^89 + 81 * q^90 + 35 * q^92 - 36 * q^94 - 20 * q^95 - 12 * q^96 - 3 * q^97 + 42 * q^99

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