LMFDB - Embedded newform 1519.2.a.k.1.13

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			1.13
Root			$2.64321$ 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)

$f(q)$	$=$	$q+2.64321 q^{2} +2.32634 q^{3} +4.98654 q^{4} +0.354419 q^{5} +6.14899 q^{6} +7.89404 q^{8} +2.41186 q^{9} +O(q^{10})$	\(q+2.64321 q^{2} +2.32634 q^{3} +4.98654 q^{4} +0.354419 q^{5} +6.14899 q^{6} +7.89404 q^{8} +2.41186 q^{9} +0.936803 q^{10} -2.17674 q^{11} +11.6004 q^{12} -4.99524 q^{13} +0.824500 q^{15} +10.8925 q^{16} -6.28607 q^{17} +6.37503 q^{18} +2.83131 q^{19} +1.76733 q^{20} -5.75357 q^{22} +2.91448 q^{23} +18.3642 q^{24} -4.87439 q^{25} -13.2035 q^{26} -1.36822 q^{27} +9.51280 q^{29} +2.17932 q^{30} +1.00000 q^{31} +13.0030 q^{32} -5.06383 q^{33} -16.6154 q^{34} +12.0268 q^{36} +4.77815 q^{37} +7.48374 q^{38} -11.6206 q^{39} +2.79780 q^{40} -2.71610 q^{41} -0.143225 q^{43} -10.8544 q^{44} +0.854808 q^{45} +7.70358 q^{46} -3.53184 q^{47} +25.3396 q^{48} -12.8840 q^{50} -14.6235 q^{51} -24.9090 q^{52} -9.99332 q^{53} -3.61650 q^{54} -0.771478 q^{55} +6.58659 q^{57} +25.1443 q^{58} +9.02557 q^{59} +4.11140 q^{60} -4.62165 q^{61} +2.64321 q^{62} +12.5847 q^{64} -1.77041 q^{65} -13.3848 q^{66} +14.0369 q^{67} -31.3457 q^{68} +6.78008 q^{69} -8.11202 q^{71} +19.0393 q^{72} -7.54534 q^{73} +12.6296 q^{74} -11.3395 q^{75} +14.1185 q^{76} -30.7157 q^{78} -5.31173 q^{79} +3.86051 q^{80} -10.4185 q^{81} -7.17921 q^{82} +8.37314 q^{83} -2.22790 q^{85} -0.378572 q^{86} +22.1300 q^{87} -17.1833 q^{88} +3.38479 q^{89} +2.25943 q^{90} +14.5332 q^{92} +2.32634 q^{93} -9.33537 q^{94} +1.00347 q^{95} +30.2495 q^{96} -2.32530 q^{97} -5.24998 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.64321	1.86903	0.934514	−	0.355925i	$-0.115834\pi$
$2$	2.64321	1.86903	0.934514	+	0.355925i	$0.115834\pi$
$3$	2.32634	1.34311	0.671556	−	0.740953i	$-0.265626\pi$
$3$	2.32634	1.34311	0.671556	+	0.740953i	$0.265626\pi$
$4$	4.98654	2.49327
$5$	0.354419	0.158501	0.0792506	−	0.996855i	$-0.474747\pi$
$5$	0.354419	0.158501	0.0792506	+	0.996855i	$0.474747\pi$
$6$	6.14899	2.51032
$7$	0	0
$7$	0	0
$8$	7.89404	2.79096
$9$	2.41186	0.803952
$10$	0.936803	0.296243
$11$	−2.17674	−0.656311	−0.328156	−	0.944624i	$-0.606427\pi$
$11$	−2.17674	−0.656311	−0.328156	+	0.944624i	$0.606427\pi$
$12$	11.6004	3.34874
$13$	−4.99524	−1.38543	−0.692715	−	0.721211i	$-0.743586\pi$
$13$	−4.99524	−1.38543	−0.692715	+	0.721211i	$0.743586\pi$
$14$	0	0
$15$	0.824500	0.212885
$16$	10.8925	2.72312
$17$	−6.28607	−1.52460	−0.762298	−	0.647226i	$-0.775929\pi$
$17$	−6.28607	−1.52460	−0.762298	+	0.647226i	$0.775929\pi$
$18$	6.37503	1.50261
$19$	2.83131	0.649548	0.324774	−	0.945792i	$-0.394712\pi$
$19$	2.83131	0.649548	0.324774	+	0.945792i	$0.394712\pi$
$20$	1.76733	0.395186
$21$	0	0
$22$	−5.75357	−1.22666
$23$	2.91448	0.607712	0.303856	−	0.952718i	$-0.401726\pi$
$23$	2.91448	0.607712	0.303856	+	0.952718i	$0.401726\pi$
$24$	18.3642	3.74858
$25$	−4.87439	−0.974877
$26$	−13.2035	−2.58941
$27$	−1.36822	−0.263315
$28$	0	0
$29$	9.51280	1.76648	0.883241	−	0.468919i	$-0.155356\pi$
$29$	9.51280	1.76648	0.883241	+	0.468919i	$0.155356\pi$
$30$	2.17932	0.397888
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	13.0030	2.29863
$33$	−5.06383	−0.881500
$34$	−16.6154	−2.84951
$35$	0	0
$36$	12.0268	2.00447
$37$	4.77815	0.785523	0.392761	−	0.919640i	$-0.371520\pi$
$37$	4.77815	0.785523	0.392761	+	0.919640i	$0.371520\pi$
$38$	7.48374	1.21402
$39$	−11.6206	−1.86079
$40$	2.79780	0.442371
$41$	−2.71610	−0.424183	−0.212092	−	0.977250i	$-0.568028\pi$
$41$	−2.71610	−0.424183	−0.212092	+	0.977250i	$0.568028\pi$
$42$	0	0
$43$	−0.143225	−0.0218415	−0.0109208	−	0.999940i	$-0.503476\pi$
$43$	−0.143225	−0.0218415	−0.0109208	+	0.999940i	$0.503476\pi$
$44$	−10.8544	−1.63636
$45$	0.854808	0.127427
$46$	7.70358	1.13583
$47$	−3.53184	−0.515171	−0.257586	−	0.966255i	$-0.582927\pi$
$47$	−3.53184	−0.515171	−0.257586	+	0.966255i	$0.582927\pi$
$48$	25.3396	3.65746
$49$	0	0
$50$	−12.8840	−1.82207
$51$	−14.6235	−2.04770
$52$	−24.9090	−3.45425
$53$	−9.99332	−1.37269	−0.686344	−	0.727277i	$-0.740786\pi$
$53$	−9.99332	−1.37269	−0.686344	+	0.727277i	$0.740786\pi$
$54$	−3.61650	−0.492143
$55$	−0.771478	−0.104026
$56$	0	0
$57$	6.58659	0.872416
$58$	25.1443	3.30161
$59$	9.02557	1.17503	0.587514	−	0.809214i	$-0.300107\pi$
$59$	9.02557	1.17503	0.587514	+	0.809214i	$0.300107\pi$
$60$	4.11140	0.530779
$61$	−4.62165	−0.591742	−0.295871	−	0.955228i	$-0.595610\pi$
$61$	−4.62165	−0.591742	−0.295871	+	0.955228i	$0.595610\pi$
$62$	2.64321	0.335688
$63$	0	0
$64$	12.5847	1.57309
$65$	−1.77041	−0.219592
$66$	−13.3848	−1.64755
$67$	14.0369	1.71488	0.857441	−	0.514582i	$-0.172053\pi$
$67$	14.0369	1.71488	0.857441	+	0.514582i	$0.172053\pi$
$68$	−31.3457	−3.80123
$69$	6.78008	0.816226
$70$	0	0
$71$	−8.11202	−0.962719	−0.481360	−	0.876523i	$-0.659857\pi$
$71$	−8.11202	−0.962719	−0.481360	+	0.876523i	$0.659857\pi$
$72$	19.0393	2.24380
$73$	−7.54534	−0.883116	−0.441558	−	0.897233i	$-0.645574\pi$
$73$	−7.54534	−0.883116	−0.441558	+	0.897233i	$0.645574\pi$
$74$	12.6296	1.46816
$75$	−11.3395	−1.30937
$76$	14.1185	1.61950
$77$	0	0
$78$	−30.7157	−3.47787
$79$	−5.31173	−0.597616	−0.298808	−	0.954313i	$-0.596589\pi$
$79$	−5.31173	−0.597616	−0.298808	+	0.954313i	$0.596589\pi$
$80$	3.86051	0.431618
$81$	−10.4185	−1.15761
$82$	−7.17921	−0.792811
$83$	8.37314	0.919071	0.459536	−	0.888159i	$-0.348016\pi$
$83$	8.37314	0.919071	0.459536	+	0.888159i	$0.348016\pi$
$84$	0	0
$85$	−2.22790	−0.241650
$86$	−0.378572	−0.0408225
$87$	22.1300	2.37259
$88$	−17.1833	−1.83174
$89$	3.38479	0.358787	0.179394	−	0.983777i	$-0.442586\pi$
$89$	3.38479	0.358787	0.179394	+	0.983777i	$0.442586\pi$
$90$	2.25943	0.238165
$91$	0	0
$92$	14.5332	1.51519
$93$	2.32634	0.241230
$94$	−9.33537	−0.962870
$95$	1.00347	0.102954
$96$	30.2495	3.08732
$97$	−2.32530	−0.236098	−0.118049	−	0.993008i	$-0.537664\pi$
$97$	−2.32530	−0.236098	−0.118049	+	0.993008i	$0.537664\pi$
$98$	0	0
$99$	−5.24998	−0.527643
$100$	−24.3063	−2.43063
$101$	8.90630	0.886210	0.443105	−	0.896470i	$-0.353877\pi$
$101$	8.90630	0.886210	0.443105	+	0.896470i	$0.353877\pi$
$102$	−38.6530	−3.82722
$103$	9.65162	0.951003	0.475501	−	0.879715i	$-0.342267\pi$
$103$	9.65162	0.951003	0.475501	+	0.879715i	$0.342267\pi$
$104$	−39.4326	−3.86669
$105$	0	0
$106$	−26.4144	−2.56559
$107$	15.1675	1.46630	0.733149	−	0.680068i	$-0.238050\pi$
$107$	15.1675	1.46630	0.733149	+	0.680068i	$0.238050\pi$
$108$	−6.82270	−0.656515
$109$	8.56409	0.820291	0.410146	−	0.912020i	$-0.365478\pi$
$109$	8.56409	0.820291	0.410146	+	0.912020i	$0.365478\pi$
$110$	−2.03918	−0.194428
$111$	11.1156	1.05505
$112$	0	0
$113$	10.6566	1.00249	0.501243	−	0.865306i	$-0.332876\pi$
$113$	10.6566	1.00249	0.501243	+	0.865306i	$0.332876\pi$
$114$	17.4097	1.63057
$115$	1.03295	0.0963230
$116$	47.4359	4.40432
$117$	−12.0478	−1.11382
$118$	23.8564	2.19616
$119$	0	0
$120$	6.50863	0.594154
$121$	−6.26181	−0.569255
$122$	−12.2160	−1.10598
$123$	−6.31857	−0.569726
$124$	4.98654	0.447804
$125$	−3.49967	−0.313020
$126$	0	0
$127$	1.25322	0.111205	0.0556025	−	0.998453i	$-0.482292\pi$
$127$	1.25322	0.111205	0.0556025	+	0.998453i	$0.482292\pi$
$128$	7.25789	0.641513
$129$	−0.333189	−0.0293356
$130$	−4.67956	−0.410424
$131$	10.9897	0.960179	0.480089	−	0.877220i	$-0.340604\pi$
$131$	10.9897	0.960179	0.480089	+	0.877220i	$0.340604\pi$
$132$	−25.2510	−2.19782
$133$	0	0
$134$	37.1025	3.20517
$135$	−0.484925	−0.0417357
$136$	−49.6225	−4.25509
$137$	−22.0369	−1.88274	−0.941370	−	0.337376i	$-0.890461\pi$
$137$	−22.0369	−1.88274	−0.941370	+	0.337376i	$0.890461\pi$
$138$	17.9211	1.52555
$139$	15.0380	1.27551	0.637754	−	0.770240i	$-0.279864\pi$
$139$	15.0380	1.27551	0.637754	+	0.770240i	$0.279864\pi$
$140$	0	0
$141$	−8.21625	−0.691933
$142$	−21.4417	−1.79935
$143$	10.8733	0.909274
$144$	26.2711	2.18926
$145$	3.37152	0.279989
$146$	−19.9439	−1.65057
$147$	0	0
$148$	23.8264	1.95852
$149$	1.69025	0.138471	0.0692354	−	0.997600i	$-0.477944\pi$
$149$	1.69025	0.138471	0.0692354	+	0.997600i	$0.477944\pi$
$150$	−29.9726	−2.44725
$151$	9.58645	0.780134	0.390067	−	0.920787i	$-0.372452\pi$
$151$	9.58645	0.780134	0.390067	+	0.920787i	$0.372452\pi$
$152$	22.3505	1.81286
$153$	−15.1611	−1.22570
$154$	0	0
$155$	0.354419	0.0284676
$156$	−57.9467	−4.63945
$157$	16.2134	1.29397	0.646987	−	0.762501i	$-0.276029\pi$
$157$	16.2134	1.29397	0.646987	+	0.762501i	$0.276029\pi$
$158$	−14.0400	−1.11696
$159$	−23.2479	−1.84367
$160$	4.60852	0.364336
$161$	0	0
$162$	−27.5383	−2.16361
$163$	−13.0689	−1.02364	−0.511819	−	0.859093i	$-0.671028\pi$
$163$	−13.0689	−1.02364	−0.511819	+	0.859093i	$0.671028\pi$
$164$	−13.5439	−1.05760
$165$	−1.79472	−0.139719
$166$	22.1319	1.71777
$167$	−8.26882	−0.639860	−0.319930	−	0.947441i	$-0.603659\pi$
$167$	−8.26882	−0.639860	−0.319930	+	0.947441i	$0.603659\pi$
$168$	0	0
$169$	11.9524	0.919419
$170$	−5.88881	−0.451651
$171$	6.82872	0.522205
$172$	−0.714195	−0.0544568
$173$	−2.35772	−0.179254	−0.0896272	−	0.995975i	$-0.528568\pi$
$173$	−2.35772	−0.179254	−0.0896272	+	0.995975i	$0.528568\pi$
$174$	58.4942	4.43443
$175$	0	0
$176$	−23.7101	−1.78722
$177$	20.9965	1.57820
$178$	8.94670	0.670584
$179$	−6.84472	−0.511599	−0.255799	−	0.966730i	$-0.582339\pi$
$179$	−6.84472	−0.511599	−0.255799	+	0.966730i	$0.582339\pi$
$180$	4.26253	0.317710
$181$	16.4144	1.22007	0.610035	−	0.792375i	$-0.291156\pi$
$181$	16.4144	1.22007	0.610035	+	0.792375i	$0.291156\pi$
$182$	0	0
$183$	−10.7515	−0.794776
$184$	23.0070	1.69610
$185$	1.69347	0.124506
$186$	6.14899	0.450866
$187$	13.6831	1.00061
$188$	−17.6116	−1.28446
$189$	0	0
$190$	2.65238	0.192424
$191$	−1.87210	−0.135461	−0.0677303	−	0.997704i	$-0.521576\pi$
$191$	−1.87210	−0.135461	−0.0677303	+	0.997704i	$0.521576\pi$
$192$	29.2763	2.11283
$193$	−14.2628	−1.02666	−0.513329	−	0.858192i	$-0.671588\pi$
$193$	−14.2628	−1.02666	−0.513329	+	0.858192i	$0.671588\pi$
$194$	−6.14624	−0.441274
$195$	−4.11858	−0.294937
$196$	0	0
$197$	−13.9854	−0.996419	−0.498209	−	0.867057i	$-0.666009\pi$
$197$	−13.9854	−0.996419	−0.498209	+	0.867057i	$0.666009\pi$
$198$	−13.8768	−0.986179
$199$	−13.6559	−0.968040	−0.484020	−	0.875057i	$-0.660824\pi$
$199$	−13.6559	−0.968040	−0.484020	+	0.875057i	$0.660824\pi$
$200$	−38.4786	−2.72085
$201$	32.6546	2.30328
$202$	23.5412	1.65635
$203$	0	0
$204$	−72.9208	−5.10548
$205$	−0.962638	−0.0672335
$206$	25.5112	1.77745
$207$	7.02931	0.488571
$208$	−54.4106	−3.77270
$209$	−6.16303	−0.426306
$210$	0	0
$211$	−22.2135	−1.52924	−0.764619	−	0.644483i	$-0.777073\pi$
$211$	−22.2135	−1.52924	−0.764619	+	0.644483i	$0.777073\pi$
$212$	−49.8321	−3.42248
$213$	−18.8713	−1.29304
$214$	40.0908	2.74055
$215$	−0.0507615	−0.00346191
$216$	−10.8008	−0.734902
$217$	0	0
$218$	22.6367	1.53315
$219$	−17.5530	−1.18612
$220$	−3.84701	−0.259365
$221$	31.4004	2.11222
$222$	29.3808	1.97191
$223$	−21.7578	−1.45701	−0.728505	−	0.685040i	$-0.759785\pi$
$223$	−21.7578	−1.45701	−0.728505	+	0.685040i	$0.759785\pi$
$224$	0	0
$225$	−11.7563	−0.783754
$226$	28.1675	1.87368
$227$	−1.54952	−0.102845	−0.0514226	−	0.998677i	$-0.516376\pi$
$227$	−1.54952	−0.102845	−0.0514226	+	0.998677i	$0.516376\pi$
$228$	32.8443	2.17517
$229$	1.69033	0.111700	0.0558502	−	0.998439i	$-0.482213\pi$
$229$	1.69033	0.111700	0.0558502	+	0.998439i	$0.482213\pi$
$230$	2.73030	0.180031
$231$	0	0
$232$	75.0944	4.93019
$233$	−5.77383	−0.378256	−0.189128	−	0.981952i	$-0.560566\pi$
$233$	−5.77383	−0.378256	−0.189128	+	0.981952i	$0.560566\pi$
$234$	−31.8448	−2.08176
$235$	−1.25175	−0.0816552
$236$	45.0063	2.92966
$237$	−12.3569	−0.802666
$238$	0	0
$239$	24.6926	1.59723	0.798615	−	0.601842i	$-0.205566\pi$
$239$	24.6926	1.59723	0.798615	+	0.601842i	$0.205566\pi$
$240$	8.98085	0.579712
$241$	−2.24466	−0.144591	−0.0722957	−	0.997383i	$-0.523033\pi$
$241$	−2.24466	−0.144591	−0.0722957	+	0.997383i	$0.523033\pi$
$242$	−16.5513	−1.06395
$243$	−20.1323	−1.29149
$244$	−23.0460	−1.47537
$245$	0	0
$246$	−16.7013	−1.06483
$247$	−14.1431	−0.899903
$248$	7.89404	0.501272
$249$	19.4788	1.23442
$250$	−9.25036	−0.585044
$251$	28.5981	1.80510	0.902549	−	0.430588i	$-0.141694\pi$
$251$	28.5981	1.80510	0.902549	+	0.430588i	$0.141694\pi$
$252$	0	0
$253$	−6.34407	−0.398848
$254$	3.31251	0.207845
$255$	−5.18286	−0.324563
$256$	−5.98529	−0.374081
$257$	−19.2512	−1.20086	−0.600429	−	0.799678i	$-0.705004\pi$
$257$	−19.2512	−1.20086	−0.600429	+	0.799678i	$0.705004\pi$
$258$	−0.880687	−0.0548292
$259$	0	0
$260$	−8.82822	−0.547503
$261$	22.9435	1.42017
$262$	29.0482	1.79460
$263$	11.7553	0.724865	0.362433	−	0.932010i	$-0.381946\pi$
$263$	11.7553	0.724865	0.362433	+	0.932010i	$0.381946\pi$
$264$	−39.9741	−2.46023
$265$	−3.54183	−0.217573
$266$	0	0
$267$	7.87418	0.481892
$268$	69.9956	4.27566
$269$	−10.4927	−0.639753	−0.319876	−	0.947459i	$-0.603641\pi$
$269$	−10.4927	−0.639753	−0.319876	+	0.947459i	$0.603641\pi$
$270$	−1.28176	−0.0780052
$271$	−8.69159	−0.527976	−0.263988	−	0.964526i	$-0.585038\pi$
$271$	−8.69159	−0.527976	−0.263988	+	0.964526i	$0.585038\pi$
$272$	−68.4709	−4.15166
$273$	0	0
$274$	−58.2481	−3.51890
$275$	10.6103	0.639823
$276$	33.8091	2.03507
$277$	−5.99620	−0.360277	−0.180139	−	0.983641i	$-0.557655\pi$
$277$	−5.99620	−0.360277	−0.180139	+	0.983641i	$0.557655\pi$
$278$	39.7486	2.38396
$279$	2.41186	0.144394
$280$	0	0
$281$	25.3627	1.51301	0.756506	−	0.653986i	$-0.226905\pi$
$281$	25.3627	1.51301	0.756506	+	0.653986i	$0.226905\pi$
$282$	−21.7172	−1.29324
$283$	6.67371	0.396711	0.198356	−	0.980130i	$-0.436440\pi$
$283$	6.67371	0.396711	0.198356	+	0.980130i	$0.436440\pi$
$284$	−40.4509	−2.40032
$285$	2.33442	0.138279
$286$	28.7405	1.69946
$287$	0	0
$288$	31.3614	1.84799
$289$	22.5147	1.32439
$290$	8.91162	0.523308
$291$	−5.40943	−0.317106
$292$	−37.6251	−2.20185
$293$	4.55839	0.266304	0.133152	−	0.991096i	$-0.457490\pi$
$293$	4.55839	0.266304	0.133152	+	0.991096i	$0.457490\pi$
$294$	0	0
$295$	3.19883	0.186243
$296$	37.7189	2.19237
$297$	2.97827	0.172817
$298$	4.46768	0.258806
$299$	−14.5586	−0.841943
$300$	−56.5448	−3.26461
$301$	0	0
$302$	25.3390	1.45809
$303$	20.7191	1.19028
$304$	30.8401	1.76880
$305$	−1.63800	−0.0937918
$306$	−40.0739	−2.29087
$307$	30.0271	1.71374	0.856869	−	0.515534i	$-0.172407\pi$
$307$	30.0271	1.71374	0.856869	+	0.515534i	$0.172407\pi$
$308$	0	0
$309$	22.4529	1.27730
$310$	0.936803	0.0532068
$311$	−18.9801	−1.07626	−0.538131	−	0.842861i	$-0.680870\pi$
$311$	−18.9801	−1.07626	−0.538131	+	0.842861i	$0.680870\pi$
$312$	−91.7337	−5.19340
$313$	−10.8415	−0.612799	−0.306399	−	0.951903i	$-0.599124\pi$
$313$	−10.8415	−0.612799	−0.306399	+	0.951903i	$0.599124\pi$
$314$	42.8555	2.41847
$315$	0	0
$316$	−26.4871	−1.49002
$317$	−2.74924	−0.154413	−0.0772063	−	0.997015i	$-0.524600\pi$
$317$	−2.74924	−0.154413	−0.0772063	+	0.997015i	$0.524600\pi$
$318$	−61.4489	−3.44588
$319$	−20.7069	−1.15936
$320$	4.46026	0.249336
$321$	35.2848	1.96940
$322$	0	0
$323$	−17.7978	−0.990298
$324$	−51.9524	−2.88624
$325$	24.3487	1.35063
$326$	−34.5439	−1.91321
$327$	19.9230	1.10174
$328$	−21.4410	−1.18388
$329$	0	0
$330$	−4.74381	−0.261138
$331$	−24.0874	−1.32396	−0.661981	−	0.749521i	$-0.730284\pi$
$331$	−24.0874	−1.32396	−0.661981	+	0.749521i	$0.730284\pi$
$332$	41.7530	2.29149
$333$	11.5242	0.631522
$334$	−21.8562	−1.19592
$335$	4.97496	0.271811
$336$	0	0
$337$	4.50464	0.245383	0.122692	−	0.992445i	$-0.460847\pi$
$337$	4.50464	0.245383	0.122692	+	0.992445i	$0.460847\pi$
$338$	31.5928	1.71842
$339$	24.7908	1.34645
$340$	−11.1095	−0.602499
$341$	−2.17674	−0.117877
$342$	18.0497	0.976016
$343$	0	0
$344$	−1.13062	−0.0609589
$345$	2.40299	0.129373
$346$	−6.23195	−0.335032
$347$	−0.446505	−0.0239697	−0.0119848	−	0.999928i	$-0.503815\pi$
$347$	−0.446505	−0.0239697	−0.0119848	+	0.999928i	$0.503815\pi$
$348$	110.352	5.91549
$349$	−11.7175	−0.627221	−0.313611	−	0.949552i	$-0.601539\pi$
$349$	−11.7175	−0.627221	−0.313611	+	0.949552i	$0.601539\pi$
$350$	0	0
$351$	6.83461	0.364805
$352$	−28.3042	−1.50862
$353$	16.3366	0.869510	0.434755	−	0.900549i	$-0.356835\pi$
$353$	16.3366	0.869510	0.434755	+	0.900549i	$0.356835\pi$
$354$	55.4982	2.94969
$355$	−2.87505	−0.152592
$356$	16.8784	0.894553
$357$	0	0
$358$	−18.0920	−0.956193
$359$	−3.86854	−0.204174	−0.102087	−	0.994775i	$-0.532552\pi$
$359$	−3.86854	−0.204174	−0.102087	+	0.994775i	$0.532552\pi$
$360$	6.74789	0.355645
$361$	−10.9837	−0.578088
$362$	43.3865	2.28034
$363$	−14.5671	−0.764574
$364$	0	0
$365$	−2.67422	−0.139975
$366$	−28.4185	−1.48546
$367$	−1.67607	−0.0874901	−0.0437451	−	0.999043i	$-0.513929\pi$
$367$	−1.67607	−0.0874901	−0.0437451	+	0.999043i	$0.513929\pi$
$368$	31.7460	1.65487
$369$	−6.55084	−0.341023
$370$	4.47618	0.232706
$371$	0	0
$372$	11.6004	0.601452
$373$	−10.0023	−0.517898	−0.258949	−	0.965891i	$-0.583376\pi$
$373$	−10.0023	−0.517898	−0.258949	+	0.965891i	$0.583376\pi$
$374$	36.1673	1.87017
$375$	−8.14143	−0.420422
$376$	−27.8804	−1.43782
$377$	−47.5187	−2.44734
$378$	0	0
$379$	4.64969	0.238839	0.119419	−	0.992844i	$-0.461897\pi$
$379$	4.64969	0.238839	0.119419	+	0.992844i	$0.461897\pi$
$380$	5.00385	0.256692
$381$	2.91541	0.149361
$382$	−4.94836	−0.253180
$383$	−9.65621	−0.493409	−0.246705	−	0.969091i	$-0.579348\pi$
$383$	−9.65621	−0.493409	−0.246705	+	0.969091i	$0.579348\pi$
$384$	16.8843	0.861624
$385$	0	0
$386$	−37.6995	−1.91885
$387$	−0.345437	−0.0175595
$388$	−11.5952	−0.588656
$389$	8.28222	0.419925	0.209963	−	0.977709i	$-0.432666\pi$
$389$	8.28222	0.419925	0.209963	+	0.977709i	$0.432666\pi$
$390$	−10.8862	−0.551246
$391$	−18.3206	−0.926515
$392$	0	0
$393$	25.5659	1.28963
$394$	−36.9663	−1.86234
$395$	−1.88258	−0.0947228
$396$	−26.1792	−1.31556
$397$	−7.08145	−0.355408	−0.177704	−	0.984084i	$-0.556867\pi$
$397$	−7.08145	−0.355408	−0.177704	+	0.984084i	$0.556867\pi$
$398$	−36.0953	−1.80929
$399$	0	0
$400$	−53.0942	−2.65471
$401$	5.70335	0.284812	0.142406	−	0.989808i	$-0.454516\pi$
$401$	5.70335	0.284812	0.142406	+	0.989808i	$0.454516\pi$
$402$	86.3129	4.30490
$403$	−4.99524	−0.248831
$404$	44.4116	2.20956
$405$	−3.69252	−0.183483
$406$	0	0
$407$	−10.4008	−0.515547
$408$	−115.439	−5.71507
$409$	6.64606	0.328626	0.164313	−	0.986408i	$-0.447459\pi$
$409$	6.64606	0.328626	0.164313	+	0.986408i	$0.447459\pi$
$410$	−2.54445	−0.125661
$411$	−51.2653	−2.52873
$412$	48.1282	2.37111
$413$	0	0
$414$	18.5799	0.913154
$415$	2.96760	0.145674
$416$	−64.9533	−3.18460
$417$	34.9835	1.71315
$418$	−16.2902	−0.796777
$419$	9.06221	0.442718	0.221359	−	0.975192i	$-0.428951\pi$
$419$	9.06221	0.442718	0.221359	+	0.975192i	$0.428951\pi$
$420$	0	0
$421$	−4.93098	−0.240321	−0.120161	−	0.992754i	$-0.538341\pi$
$421$	−4.93098	−0.240321	−0.120161	+	0.992754i	$0.538341\pi$
$422$	−58.7147	−2.85819
$423$	−8.51828	−0.414173
$424$	−78.8877	−3.83112
$425$	30.6407	1.48629
$426$	−49.8807	−2.41673
$427$	0	0
$428$	75.6333	3.65588
$429$	25.2951	1.22126
$430$	−0.134173	−0.00647041
$431$	25.4703	1.22686	0.613430	−	0.789749i	$-0.289789\pi$
$431$	25.4703	1.22686	0.613430	+	0.789749i	$0.289789\pi$
$432$	−14.9034	−0.717039
$433$	9.39902	0.451688	0.225844	−	0.974163i	$-0.427486\pi$
$433$	9.39902	0.451688	0.225844	+	0.974163i	$0.427486\pi$
$434$	0	0
$435$	7.84330	0.376057
$436$	42.7052	2.04521
$437$	8.25182	0.394738
$438$	−46.3963	−2.21690
$439$	39.9665	1.90749	0.953747	−	0.300609i	$-0.0971900\pi$
$439$	39.9665	1.90749	0.953747	+	0.300609i	$0.0971900\pi$
$440$	−6.09008	−0.290333
$441$	0	0
$442$	82.9978	3.94780
$443$	14.2263	0.675911	0.337955	−	0.941162i	$-0.390265\pi$
$443$	14.2263	0.675911	0.337955	+	0.941162i	$0.390265\pi$
$444$	55.4283	2.63051
$445$	1.19964	0.0568682
$446$	−57.5104	−2.72320
$447$	3.93210	0.185982
$448$	0	0
$449$	−1.38464	−0.0653451	−0.0326726	−	0.999466i	$-0.510402\pi$
$449$	−1.38464	−0.0653451	−0.0326726	+	0.999466i	$0.510402\pi$
$450$	−31.0744	−1.46486
$451$	5.91224	0.278396
$452$	53.1395	2.49947
$453$	22.3013	1.04781
$454$	−4.09570	−0.192221
$455$	0	0
$456$	51.9948	2.43488
$457$	−17.5760	−0.822168	−0.411084	−	0.911597i	$-0.634850\pi$
$457$	−17.5760	−0.822168	−0.411084	+	0.911597i	$0.634850\pi$
$458$	4.46790	0.208771
$459$	8.60075	0.401449
$460$	5.15084	0.240159
$461$	−27.1063	−1.26247	−0.631234	−	0.775593i	$-0.717451\pi$
$461$	−27.1063	−1.26247	−0.631234	+	0.775593i	$0.717451\pi$
$462$	0	0
$463$	−18.7308	−0.870494	−0.435247	−	0.900311i	$-0.643339\pi$
$463$	−18.7308	−0.870494	−0.435247	+	0.900311i	$0.643339\pi$
$464$	103.618	4.81035
$465$	0.824500	0.0382353
$466$	−15.2614	−0.706972
$467$	−10.2196	−0.472904	−0.236452	−	0.971643i	$-0.575985\pi$
$467$	−10.2196	−0.472904	−0.236452	+	0.971643i	$0.575985\pi$
$468$	−60.0768	−2.77705
$469$	0	0
$470$	−3.30863	−0.152616
$471$	37.7180	1.73795
$472$	71.2482	3.27946
$473$	0.311762	0.0143348
$474$	−32.6618	−1.50021
$475$	−13.8009	−0.633229
$476$	0	0
$477$	−24.1024	−1.10358
$478$	65.2676	2.98527
$479$	−24.4638	−1.11778	−0.558889	−	0.829242i	$-0.688772\pi$
$479$	−24.4638	−1.11778	−0.558889	+	0.829242i	$0.688772\pi$
$480$	10.7210	0.489344
$481$	−23.8680	−1.08829
$482$	−5.93310	−0.270245
$483$	0	0
$484$	−31.2248	−1.41931
$485$	−0.824130	−0.0374218
$486$	−53.2139	−2.41383
$487$	4.39995	0.199381	0.0996905	−	0.995018i	$-0.468215\pi$
$487$	4.39995	0.199381	0.0996905	+	0.995018i	$0.468215\pi$
$488$	−36.4835	−1.65153
$489$	−30.4028	−1.37486
$490$	0	0
$491$	26.9170	1.21475	0.607374	−	0.794416i	$-0.292223\pi$
$491$	26.9170	1.21475	0.607374	+	0.794416i	$0.292223\pi$
$492$	−31.5078	−1.42048
$493$	−59.7981	−2.69317
$494$	−37.3831	−1.68195
$495$	−1.86069	−0.0836320
$496$	10.8925	0.489087
$497$	0	0
$498$	51.4864	2.30716
$499$	0.0837718	0.00375014	0.00187507	−	0.999998i	$-0.499403\pi$
$499$	0.0837718	0.00375014	0.00187507	+	0.999998i	$0.499403\pi$
$500$	−17.4513	−0.780444
$501$	−19.2361	−0.859404
$502$	75.5907	3.37378
$503$	−3.94084	−0.175713	−0.0878566	−	0.996133i	$-0.528002\pi$
$503$	−3.94084	−0.175713	−0.0878566	+	0.996133i	$0.528002\pi$
$504$	0	0
$505$	3.15657	0.140465
$506$	−16.7687	−0.745459
$507$	27.8054	1.23488
$508$	6.24921	0.277264
$509$	−8.81784	−0.390844	−0.195422	−	0.980719i	$-0.562608\pi$
$509$	−8.81784	−0.390844	−0.195422	+	0.980719i	$0.562608\pi$
$510$	−13.6994	−0.606618
$511$	0	0
$512$	−30.3361	−1.34068
$513$	−3.87387	−0.171036
$514$	−50.8850	−2.24444
$515$	3.42072	0.150735
$516$	−1.66146	−0.0731417
$517$	7.68788	0.338113
$518$	0	0
$519$	−5.48486	−0.240759
$520$	−13.9757	−0.612874
$521$	−13.4148	−0.587712	−0.293856	−	0.955850i	$-0.594939\pi$
$521$	−13.4148	−0.587712	−0.293856	+	0.955850i	$0.594939\pi$
$522$	60.6444	2.65433
$523$	−17.7610	−0.776635	−0.388318	−	0.921526i	$-0.626944\pi$
$523$	−17.7610	−0.776635	−0.388318	+	0.921526i	$0.626944\pi$
$524$	54.8008	2.39398
$525$	0	0
$526$	31.0718	1.35479
$527$	−6.28607	−0.273825
$528$	−55.1578	−2.40043
$529$	−14.5058	−0.630686
$530$	−9.36178	−0.406650
$531$	21.7684	0.944666
$532$	0	0
$533$	13.5676	0.587677
$534$	20.8131	0.900670
$535$	5.37566	0.232410
$536$	110.808	4.78618
$537$	−15.9231	−0.687135
$538$	−27.7344	−1.19572
$539$	0	0
$540$	−2.41810	−0.104058
$541$	−10.5221	−0.452378	−0.226189	−	0.974083i	$-0.572627\pi$
$541$	−10.5221	−0.452378	−0.226189	+	0.974083i	$0.572627\pi$
$542$	−22.9737	−0.986803
$543$	38.1854	1.63869
$544$	−81.7379	−3.50448
$545$	3.03528	0.130017
$546$	0	0
$547$	24.2290	1.03596	0.517978	−	0.855394i	$-0.326685\pi$
$547$	24.2290	1.03596	0.517978	+	0.855394i	$0.326685\pi$
$548$	−109.888	−4.69418
$549$	−11.1468	−0.475732
$550$	28.0451	1.19585
$551$	26.9337	1.14741
$552$	53.5222	2.27806
$553$	0	0
$554$	−15.8492	−0.673368
$555$	3.93958	0.167226
$556$	74.9877	3.18019
$557$	−22.7619	−0.964453	−0.482227	−	0.876047i	$-0.660172\pi$
$557$	−22.7619	−0.964453	−0.482227	+	0.876047i	$0.660172\pi$
$558$	6.37503	0.269877
$559$	0.715441	0.0302599
$560$	0	0
$561$	31.8316	1.34393
$562$	67.0389	2.82786
$563$	−18.6412	−0.785633	−0.392816	−	0.919617i	$-0.628499\pi$
$563$	−18.6412	−0.785633	−0.392816	+	0.919617i	$0.628499\pi$
$564$	−40.9706	−1.72518
$565$	3.77690	0.158895
$566$	17.6400	0.741465
$567$	0	0
$568$	−64.0366	−2.68691
$569$	19.7690	0.828760	0.414380	−	0.910104i	$-0.363999\pi$
$569$	19.7690	0.828760	0.414380	+	0.910104i	$0.363999\pi$
$570$	6.17034	0.258447
$571$	−19.6037	−0.820391	−0.410196	−	0.911998i	$-0.634540\pi$
$571$	−19.6037	−0.820391	−0.410196	+	0.911998i	$0.634540\pi$
$572$	54.2203	2.26707
$573$	−4.35515	−0.181939
$574$	0	0
$575$	−14.2063	−0.592445
$576$	30.3525	1.26469
$577$	2.06307	0.0858865	0.0429433	−	0.999078i	$-0.486327\pi$
$577$	2.06307	0.0858865	0.0429433	+	0.999078i	$0.486327\pi$
$578$	59.5109	2.47533
$579$	−33.1801	−1.37892
$580$	16.8122	0.698089
$581$	0	0
$582$	−14.2982	−0.592681
$583$	21.7528	0.900911
$584$	−59.5632	−2.46474
$585$	−4.26997	−0.176542
$586$	12.0488	0.497729
$587$	9.20613	0.379978	0.189989	−	0.981786i	$-0.439155\pi$
$587$	9.20613	0.379978	0.189989	+	0.981786i	$0.439155\pi$
$588$	0	0
$589$	2.83131	0.116662
$590$	8.45518	0.348094
$591$	−32.5348	−1.33830
$592$	52.0459	2.13907
$593$	42.7927	1.75729	0.878643	−	0.477479i	$-0.158449\pi$
$593$	42.7927	1.75729	0.878643	+	0.477479i	$0.158449\pi$
$594$	7.87217	0.322999
$595$	0	0
$596$	8.42850	0.345245
$597$	−31.7682	−1.30019
$598$	−38.4813	−1.57362
$599$	14.9797	0.612052	0.306026	−	0.952023i	$-0.401000\pi$
$599$	14.9797	0.612052	0.306026	+	0.952023i	$0.401000\pi$
$600$	−89.5143	−3.65440
$601$	35.5248	1.44909	0.724544	−	0.689228i	$-0.242050\pi$
$601$	35.5248	1.44909	0.724544	+	0.689228i	$0.242050\pi$
$602$	0	0
$603$	33.8550	1.37868
$604$	47.8032	1.94508
$605$	−2.21931	−0.0902276
$606$	54.7648	2.22467
$607$	−33.2770	−1.35067	−0.675336	−	0.737510i	$-0.736001\pi$
$607$	−33.2770	−1.35067	−0.675336	+	0.737510i	$0.736001\pi$
$608$	36.8156	1.49307
$609$	0	0
$610$	−4.32958	−0.175300
$611$	17.6424	0.713734
$612$	−75.6014	−3.05600
$613$	40.1397	1.62123	0.810614	−	0.585581i	$-0.199134\pi$
$613$	40.1397	1.62123	0.810614	+	0.585581i	$0.199134\pi$
$614$	79.3679	3.20303
$615$	−2.23942	−0.0903022
$616$	0	0
$617$	−19.7106	−0.793518	−0.396759	−	0.917923i	$-0.629865\pi$
$617$	−19.7106	−0.793518	−0.396759	+	0.917923i	$0.629865\pi$
$618$	59.3478	2.38732
$619$	19.5282	0.784906	0.392453	−	0.919772i	$-0.371627\pi$
$619$	19.5282	0.784906	0.392453	+	0.919772i	$0.371627\pi$
$620$	1.76733	0.0709775
$621$	−3.98767	−0.160020
$622$	−50.1683	−2.01157
$623$	0	0
$624$	−126.578	−5.06716
$625$	23.1316	0.925263
$626$	−28.6564	−1.14534
$627$	−14.3373	−0.572576
$628$	80.8489	3.22622
$629$	−30.0358	−1.19760
$630$	0	0
$631$	−12.8837	−0.512891	−0.256446	−	0.966559i	$-0.582551\pi$
$631$	−12.8837	−0.512891	−0.256446	+	0.966559i	$0.582551\pi$
$632$	−41.9310	−1.66793
$633$	−51.6760	−2.05394
$634$	−7.26680	−0.288601
$635$	0.444164	0.0176261
$636$	−115.926	−4.59678
$637$	0	0
$638$	−54.7325	−2.16688
$639$	−19.5650	−0.773980
$640$	2.57234	0.101680
$641$	40.3069	1.59203	0.796013	−	0.605280i	$-0.206939\pi$
$641$	40.3069	1.59203	0.796013	+	0.605280i	$0.206939\pi$
$642$	93.2649	3.68087
$643$	−4.71734	−0.186034	−0.0930169	−	0.995665i	$-0.529651\pi$
$643$	−4.71734	−0.186034	−0.0930169	+	0.995665i	$0.529651\pi$
$644$	0	0
$645$	−0.118089	−0.00464973
$646$	−47.0433	−1.85089
$647$	12.1692	0.478420	0.239210	−	0.970968i	$-0.423112\pi$
$647$	12.1692	0.478420	0.239210	+	0.970968i	$0.423112\pi$
$648$	−82.2442	−3.23086
$649$	−19.6463	−0.771185
$650$	64.3588	2.52436
$651$	0	0
$652$	−65.1687	−2.55220
$653$	5.64254	0.220810	0.110405	−	0.993887i	$-0.464785\pi$
$653$	5.64254	0.220810	0.110405	+	0.993887i	$0.464785\pi$
$654$	52.6605	2.05919
$655$	3.89498	0.152189
$656$	−29.5851	−1.15510
$657$	−18.1983	−0.709982
$658$	0	0
$659$	−18.3995	−0.716742	−0.358371	−	0.933579i	$-0.616668\pi$
$659$	−18.3995	−0.716742	−0.358371	+	0.933579i	$0.616668\pi$
$660$	−8.94944	−0.348357
$661$	−29.4676	−1.14616	−0.573079	−	0.819500i	$-0.694251\pi$
$661$	−29.4676	−1.14616	−0.573079	+	0.819500i	$0.694251\pi$
$662$	−63.6679	−2.47452
$663$	73.0481	2.83695
$664$	66.0979	2.56510
$665$	0	0
$666$	30.4608	1.18033
$667$	27.7249	1.07351
$668$	−41.2328	−1.59534
$669$	−50.6160	−1.95693
$670$	13.1498	0.508022
$671$	10.0601	0.388367
$672$	0	0
$673$	23.7875	0.916940	0.458470	−	0.888710i	$-0.348398\pi$
$673$	23.7875	0.916940	0.458470	+	0.888710i	$0.348398\pi$
$674$	11.9067	0.458628
$675$	6.66925	0.256700
$676$	59.6013	2.29236
$677$	−17.6902	−0.679891	−0.339945	−	0.940445i	$-0.610409\pi$
$677$	−17.6902	−0.679891	−0.339945	+	0.940445i	$0.610409\pi$
$678$	65.5273	2.51656
$679$	0	0
$680$	−17.5872	−0.674437
$681$	−3.60471	−0.138133
$682$	−5.75357	−0.220316
$683$	−15.6996	−0.600728	−0.300364	−	0.953825i	$-0.597108\pi$
$683$	−15.6996	−0.600728	−0.300364	+	0.953825i	$0.597108\pi$
$684$	34.0517	1.30200
$685$	−7.81031	−0.298416
$686$	0	0
$687$	3.93229	0.150026
$688$	−1.56007	−0.0594772
$689$	49.9191	1.90176
$690$	6.35160	0.241801
$691$	45.6324	1.73594	0.867969	−	0.496618i	$-0.165425\pi$
$691$	45.6324	1.73594	0.867969	+	0.496618i	$0.165425\pi$
$692$	−11.7569	−0.446929
$693$	0	0
$694$	−1.18021	−0.0448000
$695$	5.32976	0.202169
$696$	174.695	6.62180
$697$	17.0736	0.646708
$698$	−30.9717	−1.17230
$699$	−13.4319	−0.508041
$700$	0	0
$701$	42.6332	1.61023	0.805116	−	0.593117i	$-0.202103\pi$
$701$	42.6332	1.61023	0.805116	+	0.593117i	$0.202103\pi$
$702$	18.0653	0.681830
$703$	13.5284	0.510234
$704$	−27.3936	−1.03243
$705$	−2.91200	−0.109672
$706$	43.1810	1.62514
$707$	0	0
$708$	104.700	3.93487
$709$	−11.5388	−0.433351	−0.216675	−	0.976244i	$-0.569521\pi$
$709$	−11.5388	−0.433351	−0.216675	+	0.976244i	$0.569521\pi$
$710$	−7.59936	−0.285199
$711$	−12.8111	−0.480455
$712$	26.7197	1.00136
$713$	2.91448	0.109148
$714$	0	0
$715$	3.85372	0.144121
$716$	−34.1315	−1.27555
$717$	57.4433	2.14526
$718$	−10.2254	−0.381607
$719$	−9.19248	−0.342822	−0.171411	−	0.985200i	$-0.554833\pi$
$719$	−9.19248	−0.342822	−0.171411	+	0.985200i	$0.554833\pi$
$720$	9.31099	0.347000
$721$	0	0
$722$	−29.0321	−1.08046
$723$	−5.22185	−0.194203
$724$	81.8508	3.04196
$725$	−46.3691	−1.72210
$726$	−38.5038	−1.42901
$727$	−31.3235	−1.16172	−0.580862	−	0.814002i	$-0.697284\pi$
$727$	−31.3235	−1.16172	−0.580862	+	0.814002i	$0.697284\pi$
$728$	0	0
$729$	−15.5791	−0.577004
$730$	−7.06850	−0.261617
$731$	0.900319	0.0332995
$732$	−53.6129	−1.98159
$733$	39.9736	1.47646	0.738229	−	0.674550i	$-0.235662\pi$
$733$	39.9736	1.47646	0.738229	+	0.674550i	$0.235662\pi$
$734$	−4.43020	−0.163522
$735$	0	0
$736$	37.8971	1.39691
$737$	−30.5547	−1.12550
$738$	−17.3152	−0.637382
$739$	−6.97061	−0.256418	−0.128209	−	0.991747i	$-0.540923\pi$
$739$	−6.97061	−0.256418	−0.128209	+	0.991747i	$0.540923\pi$
$740$	8.44454	0.310428
$741$	−32.9016	−1.20867
$742$	0	0
$743$	−12.0493	−0.442046	−0.221023	−	0.975269i	$-0.570940\pi$
$743$	−12.0493	−0.442046	−0.221023	+	0.975269i	$0.570940\pi$
$744$	18.3642	0.673265
$745$	0.599058	0.0219478
$746$	−26.4381	−0.967967
$747$	20.1948	0.738889
$748$	68.2314	2.49479
$749$	0	0
$750$	−21.5195	−0.785780
$751$	−9.96963	−0.363797	−0.181898	−	0.983317i	$-0.558224\pi$
$751$	−9.96963	−0.363797	−0.181898	+	0.983317i	$0.558224\pi$
$752$	−38.4705	−1.40287
$753$	66.5289	2.42445
$754$	−125.602	−4.57415
$755$	3.39762	0.123652
$756$	0	0
$757$	−51.7659	−1.88146	−0.940732	−	0.339151i	$-0.889860\pi$
$757$	−51.7659	−1.88146	−0.940732	+	0.339151i	$0.889860\pi$
$758$	12.2901	0.446396
$759$	−14.7585	−0.535698
$760$	7.92144	0.287341
$761$	−21.8136	−0.790741	−0.395371	−	0.918522i	$-0.629384\pi$
$761$	−21.8136	−0.790741	−0.395371	+	0.918522i	$0.629384\pi$
$762$	7.70602	0.279160
$763$	0	0
$764$	−9.33532	−0.337740
$765$	−5.37338	−0.194275
$766$	−25.5233	−0.922196
$767$	−45.0849	−1.62792
$768$	−13.9238	−0.502433
$769$	−33.2768	−1.19999	−0.599995	−	0.800003i	$-0.704831\pi$
$769$	−33.2768	−1.19999	−0.599995	+	0.800003i	$0.704831\pi$
$770$	0	0
$771$	−44.7849	−1.61289
$772$	−71.1219	−2.55973
$773$	−12.6696	−0.455694	−0.227847	−	0.973697i	$-0.573169\pi$
$773$	−12.6696	−0.455694	−0.227847	+	0.973697i	$0.573169\pi$
$774$	−0.913061	−0.0328193
$775$	−4.87439	−0.175093
$776$	−18.3560	−0.658941
$777$	0	0
$778$	21.8916	0.784852
$779$	−7.69012	−0.275527
$780$	−20.5374	−0.735358
$781$	17.6577	0.631844
$782$	−48.4252	−1.73168
$783$	−13.0156	−0.465141
$784$	0	0
$785$	5.74635	0.205096
$786$	67.5759	2.41035
$787$	−33.0489	−1.17807	−0.589033	−	0.808109i	$-0.700491\pi$
$787$	−33.0489	−1.17807	−0.589033	+	0.808109i	$0.700491\pi$
$788$	−69.7387	−2.48434
$789$	27.3469	0.973576
$790$	−4.97605	−0.177040
$791$	0	0
$792$	−41.4435	−1.47263
$793$	23.0863	0.819818
$794$	−18.7177	−0.664267
$795$	−8.23949	−0.292225
$796$	−68.0956	−2.41358
$797$	−31.1760	−1.10431	−0.552156	−	0.833741i	$-0.686195\pi$
$797$	−31.1760	−1.10431	−0.552156	+	0.833741i	$0.686195\pi$
$798$	0	0
$799$	22.2014	0.785428
$800$	−63.3818	−2.24088
$801$	8.16363	0.288448
$802$	15.0751	0.532321
$803$	16.4242	0.579599
$804$	162.834	5.74270
$805$	0	0
$806$	−13.2035	−0.465072
$807$	−24.4096	−0.859260
$808$	70.3067	2.47338
$809$	−0.770850	−0.0271016	−0.0135508	−	0.999908i	$-0.504313\pi$
$809$	−0.770850	−0.0271016	−0.0135508	+	0.999908i	$0.504313\pi$
$810$	−9.76010	−0.342935
$811$	41.1256	1.44412	0.722058	−	0.691832i	$-0.243196\pi$
$811$	41.1256	1.44412	0.722058	+	0.691832i	$0.243196\pi$
$812$	0	0
$813$	−20.2196	−0.709132
$814$	−27.4914	−0.963573
$815$	−4.63188	−0.162248
$816$	−159.287	−5.57615
$817$	−0.405513	−0.0141871
$818$	17.5669	0.614212
$819$	0	0
$820$	−4.80023	−0.167631
$821$	−3.56797	−0.124523	−0.0622615	−	0.998060i	$-0.519831\pi$
$821$	−3.56797	−0.124523	−0.0622615	+	0.998060i	$0.519831\pi$
$822$	−135.505	−4.72627
$823$	18.2856	0.637396	0.318698	−	0.947856i	$-0.396754\pi$
$823$	18.2856	0.637396	0.318698	+	0.947856i	$0.396754\pi$
$824$	76.1903	2.65421
$825$	24.6831	0.859355
$826$	0	0
$827$	−5.17728	−0.180032	−0.0900159	−	0.995940i	$-0.528692\pi$
$827$	−5.17728	−0.180032	−0.0900159	+	0.995940i	$0.528692\pi$
$828$	35.0519	1.21814
$829$	−35.6623	−1.23860	−0.619302	−	0.785153i	$-0.712584\pi$
$829$	−35.6623	−1.23860	−0.619302	+	0.785153i	$0.712584\pi$
$830$	7.84398	0.272269
$831$	−13.9492	−0.483893
$832$	−62.8636	−2.17940
$833$	0	0
$834$	92.4687	3.20193
$835$	−2.93063	−0.101419
$836$	−30.7322	−1.06289
$837$	−1.36822	−0.0472927
$838$	23.9533	0.827452
$839$	33.2844	1.14910	0.574552	−	0.818468i	$-0.305176\pi$
$839$	33.2844	1.14910	0.574552	+	0.818468i	$0.305176\pi$
$840$	0	0
$841$	61.4934	2.12046
$842$	−13.0336	−0.449167
$843$	59.0023	2.03215
$844$	−110.768	−3.81280
$845$	4.23618	0.145729
$846$	−22.5156	−0.774101
$847$	0	0
$848$	−108.852	−3.73800
$849$	15.5253	0.532828
$850$	80.9898	2.77793
$851$	13.9258	0.477371
$852$	−94.1025	−3.22390
$853$	−19.9660	−0.683623	−0.341811	−	0.939769i	$-0.611040\pi$
$853$	−19.9660	−0.683623	−0.341811	+	0.939769i	$0.611040\pi$
$854$	0	0
$855$	2.42023	0.0827701
$856$	119.733	4.09238
$857$	38.0655	1.30029	0.650146	−	0.759809i	$-0.274708\pi$
$857$	38.0655	1.30029	0.650146	+	0.759809i	$0.274708\pi$
$858$	66.8601	2.28257
$859$	34.3211	1.17102	0.585511	−	0.810664i	$-0.300894\pi$
$859$	34.3211	1.17102	0.585511	+	0.810664i	$0.300894\pi$
$860$	−0.253124	−0.00863147
$861$	0	0
$862$	67.3232	2.29304
$863$	−31.7584	−1.08107	−0.540534	−	0.841322i	$-0.681778\pi$
$863$	−31.7584	−1.08107	−0.540534	+	0.841322i	$0.681778\pi$
$864$	−17.7911	−0.605264
$865$	−0.835623	−0.0284120
$866$	24.8436	0.844218
$867$	52.3767	1.77881
$868$	0	0
$869$	11.5622	0.392222
$870$	20.7315	0.702862
$871$	−70.1178	−2.37585
$872$	67.6053	2.28940
$873$	−5.60828	−0.189812
$874$	21.8113	0.737777
$875$	0	0
$876$	−87.5289	−2.95733
$877$	−50.6498	−1.71032	−0.855161	−	0.518363i	$-0.826542\pi$
$877$	−50.6498	−1.71032	−0.855161	+	0.518363i	$0.826542\pi$
$878$	105.640	3.56516
$879$	10.6044	0.357676
$880$	−8.40332	−0.283276
$881$	−8.31830	−0.280251	−0.140125	−	0.990134i	$-0.544751\pi$
$881$	−8.31830	−0.280251	−0.140125	+	0.990134i	$0.544751\pi$
$882$	0	0
$883$	−54.6299	−1.83844	−0.919221	−	0.393743i	$-0.871180\pi$
$883$	−54.6299	−1.83844	−0.919221	+	0.393743i	$0.871180\pi$
$884$	156.579	5.26634
$885$	7.44158	0.250146
$886$	37.6030	1.26330
$887$	10.7364	0.360493	0.180246	−	0.983622i	$-0.442311\pi$
$887$	10.7364	0.360493	0.180246	+	0.983622i	$0.442311\pi$
$888$	87.7469	2.94459
$889$	0	0
$890$	3.17088	0.106288
$891$	22.6784	0.759755
$892$	−108.496	−3.63272
$893$	−9.99973	−0.334628
$894$	10.3933	0.347605
$895$	−2.42590	−0.0810890
$896$	0	0
$897$	−33.8681	−1.13082
$898$	−3.65989	−0.122132
$899$	9.51280	0.317270
$900$	−58.6233	−1.95411
$901$	62.8187	2.09279
$902$	15.6273	0.520331
$903$	0	0
$904$	84.1235	2.79790
$905$	5.81756	0.193382
$906$	58.9470	1.95838
$907$	20.0274	0.664999	0.332500	−	0.943103i	$-0.392108\pi$
$907$	20.0274	0.664999	0.332500	+	0.943103i	$0.392108\pi$
$908$	−7.72674	−0.256421
$909$	21.4807	0.712470
$910$	0	0
$911$	19.7955	0.655854	0.327927	−	0.944703i	$-0.393650\pi$
$911$	19.7955	0.655854	0.327927	+	0.944703i	$0.393650\pi$
$912$	71.7444	2.37570
$913$	−18.2261	−0.603197
$914$	−46.4569	−1.53666
$915$	−3.81055	−0.125973
$916$	8.42891	0.278499
$917$	0	0
$918$	22.7336	0.750319
$919$	−40.3280	−1.33030	−0.665150	−	0.746710i	$-0.731632\pi$
$919$	−40.3280	−1.33030	−0.665150	+	0.746710i	$0.731632\pi$
$920$	8.15414	0.268834
$921$	69.8533	2.30174
$922$	−71.6476	−2.35959
$923$	40.5215	1.33378
$924$	0	0
$925$	−23.2905	−0.765788
$926$	−49.5094	−1.62698
$927$	23.2783	0.764560
$928$	123.695	4.06049
$929$	5.36391	0.175984	0.0879921	−	0.996121i	$-0.471955\pi$
$929$	5.36391	0.175984	0.0879921	+	0.996121i	$0.471955\pi$
$930$	2.17932	0.0714628
$931$	0	0
$932$	−28.7914	−0.943095
$933$	−44.1542	−1.44554
$934$	−27.0124	−0.883872
$935$	4.84956	0.158598
$936$	−95.1058	−3.10863
$937$	48.2187	1.57524	0.787619	−	0.616163i	$-0.211314\pi$
$937$	48.2187	1.57524	0.787619	+	0.616163i	$0.211314\pi$
$938$	0	0
$939$	−25.2211	−0.823058
$940$	−6.24190	−0.203588
$941$	24.9474	0.813264	0.406632	−	0.913592i	$-0.366703\pi$
$941$	24.9474	0.813264	0.406632	+	0.913592i	$0.366703\pi$
$942$	99.6963	3.24828
$943$	−7.91603	−0.257781
$944$	98.3109	3.19975
$945$	0	0
$946$	0.824052	0.0267922
$947$	2.03448	0.0661117	0.0330558	−	0.999454i	$-0.489476\pi$
$947$	2.03448	0.0661117	0.0330558	+	0.999454i	$0.489476\pi$
$948$	−61.6181	−2.00126
$949$	37.6908	1.22350
$950$	−36.4787	−1.18352
$951$	−6.39566	−0.207393
$952$	0	0
$953$	−5.39082	−0.174626	−0.0873130	−	0.996181i	$-0.527828\pi$
$953$	−5.39082	−0.174626	−0.0873130	+	0.996181i	$0.527828\pi$
$954$	−63.7077	−2.06261
$955$	−0.663510	−0.0214707
$956$	123.130	3.98232
$957$	−48.1712	−1.55715
$958$	−64.6628	−2.08916
$959$	0	0
$960$	10.3761	0.334886
$961$	1.00000	0.0322581
$962$	−63.0881	−2.03404
$963$	36.5818	1.17883
$964$	−11.1931	−0.360505
$965$	−5.05501	−0.162726
$966$	0	0
$967$	10.4887	0.337295	0.168647	−	0.985676i	$-0.446060\pi$
$967$	10.4887	0.337295	0.168647	+	0.985676i	$0.446060\pi$
$968$	−49.4310	−1.58877
$969$	−41.4038	−1.33008
$970$	−2.17835	−0.0699425
$971$	53.3663	1.71260	0.856302	−	0.516475i	$-0.172756\pi$
$971$	53.3663	1.71260	0.856302	+	0.516475i	$0.172756\pi$
$972$	−100.391	−3.22003
$973$	0	0
$974$	11.6300	0.372649
$975$	56.6434	1.81404
$976$	−50.3413	−1.61139
$977$	58.2089	1.86227	0.931134	−	0.364677i	$-0.118821\pi$
$977$	58.2089	1.86227	0.931134	+	0.364677i	$0.118821\pi$
$978$	−80.3608	−2.56966
$979$	−7.36781	−0.235476
$980$	0	0
$981$	20.6553	0.659474
$982$	71.1472	2.27040
$983$	26.8145	0.855251	0.427626	−	0.903956i	$-0.359350\pi$
$983$	26.8145	0.855251	0.427626	+	0.903956i	$0.359350\pi$
$984$	−49.8790	−1.59008
$985$	−4.95670	−0.157933
$986$	−158.059	−5.03362
$987$	0	0
$988$	−70.5251	−2.24370
$989$	−0.417426	−0.0132734
$990$	−4.91820	−0.156311
$991$	−51.2497	−1.62800	−0.814000	−	0.580864i	$-0.802715\pi$
$991$	−51.2497	−1.62800	−0.814000	+	0.580864i	$0.802715\pi$
$992$	13.0030	0.412846
$993$	−56.0354	−1.77823
$994$	0	0
$995$	−4.83991	−0.153435
$996$	97.1316	3.07773
$997$	29.8303	0.944735	0.472367	−	0.881402i	$-0.343400\pi$
$997$	29.8303	0.944735	0.472367	+	0.881402i	$0.343400\pi$
$998$	0.221426	0.00700912
$999$	−6.53758	−0.206840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1519.2.a.k.1.13		13
7.2	even	3		217.2.f.b.32.1	✓	26
7.4	even	3		217.2.f.b.156.1	yes	26
7.6	odd	2		1519.2.a.j.1.13		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
217.2.f.b.32.1	✓	26	7.2	even	3
217.2.f.b.156.1	yes	26	7.4	even	3
1519.2.a.j.1.13		13	7.6	odd	2
1519.2.a.k.1.13		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)

\(f(q)\)	\(=\)	\(q+2.64321 q^{2} +2.32634 q^{3} +4.98654 q^{4} +0.354419 q^{5} +6.14899 q^{6} +7.89404 q^{8} +2.41186 q^{9} +O(q^{10})\)	\(q+2.64321 q^{2} +2.32634 q^{3} +4.98654 q^{4} +0.354419 q^{5} +6.14899 q^{6} +7.89404 q^{8} +2.41186 q^{9} +0.936803 q^{10} -2.17674 q^{11} +11.6004 q^{12} -4.99524 q^{13} +0.824500 q^{15} +10.8925 q^{16} -6.28607 q^{17} +6.37503 q^{18} +2.83131 q^{19} +1.76733 q^{20} -5.75357 q^{22} +2.91448 q^{23} +18.3642 q^{24} -4.87439 q^{25} -13.2035 q^{26} -1.36822 q^{27} +9.51280 q^{29} +2.17932 q^{30} +1.00000 q^{31} +13.0030 q^{32} -5.06383 q^{33} -16.6154 q^{34} +12.0268 q^{36} +4.77815 q^{37} +7.48374 q^{38} -11.6206 q^{39} +2.79780 q^{40} -2.71610 q^{41} -0.143225 q^{43} -10.8544 q^{44} +0.854808 q^{45} +7.70358 q^{46} -3.53184 q^{47} +25.3396 q^{48} -12.8840 q^{50} -14.6235 q^{51} -24.9090 q^{52} -9.99332 q^{53} -3.61650 q^{54} -0.771478 q^{55} +6.58659 q^{57} +25.1443 q^{58} +9.02557 q^{59} +4.11140 q^{60} -4.62165 q^{61} +2.64321 q^{62} +12.5847 q^{64} -1.77041 q^{65} -13.3848 q^{66} +14.0369 q^{67} -31.3457 q^{68} +6.78008 q^{69} -8.11202 q^{71} +19.0393 q^{72} -7.54534 q^{73} +12.6296 q^{74} -11.3395 q^{75} +14.1185 q^{76} -30.7157 q^{78} -5.31173 q^{79} +3.86051 q^{80} -10.4185 q^{81} -7.17921 q^{82} +8.37314 q^{83} -2.22790 q^{85} -0.378572 q^{86} +22.1300 q^{87} -17.1833 q^{88} +3.38479 q^{89} +2.25943 q^{90} +14.5332 q^{92} +2.32634 q^{93} -9.33537 q^{94} +1.00347 q^{95} +30.2495 q^{96} -2.32530 q^{97} -5.24998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 5 q^{2} + 17 q^{4} + q^{5} - 2 q^{6} + 12 q^{8} + 25 q^{9}+O(q^{10}) \) 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

Introduction

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