LMFDB - Embedded newform 1519.2.a.j.1.10

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			1.10
Root			$1.84239$ 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)

$f(q)$	$=$	$q+1.84239 q^{2} +2.73867 q^{3} +1.39439 q^{4} +3.57831 q^{5} +5.04568 q^{6} -1.11576 q^{8} +4.50029 q^{9} +O(q^{10})$	\(q+1.84239 q^{2} +2.73867 q^{3} +1.39439 q^{4} +3.57831 q^{5} +5.04568 q^{6} -1.11576 q^{8} +4.50029 q^{9} +6.59263 q^{10} -3.61166 q^{11} +3.81878 q^{12} +2.94816 q^{13} +9.79979 q^{15} -4.84445 q^{16} -5.97271 q^{17} +8.29128 q^{18} -0.224697 q^{19} +4.98957 q^{20} -6.65407 q^{22} -4.23895 q^{23} -3.05569 q^{24} +7.80428 q^{25} +5.43166 q^{26} +4.10879 q^{27} +7.95965 q^{29} +18.0550 q^{30} -1.00000 q^{31} -6.69384 q^{32} -9.89112 q^{33} -11.0041 q^{34} +6.27518 q^{36} +2.44243 q^{37} -0.413979 q^{38} +8.07403 q^{39} -3.99253 q^{40} -2.80348 q^{41} -7.15676 q^{43} -5.03607 q^{44} +16.1034 q^{45} -7.80980 q^{46} -0.205954 q^{47} -13.2673 q^{48} +14.3785 q^{50} -16.3573 q^{51} +4.11090 q^{52} +3.45534 q^{53} +7.56998 q^{54} -12.9236 q^{55} -0.615370 q^{57} +14.6648 q^{58} -9.51858 q^{59} +13.6648 q^{60} +4.77442 q^{61} -1.84239 q^{62} -2.64375 q^{64} +10.5494 q^{65} -18.2233 q^{66} -10.0640 q^{67} -8.32832 q^{68} -11.6091 q^{69} +12.0008 q^{71} -5.02124 q^{72} -4.06214 q^{73} +4.49991 q^{74} +21.3733 q^{75} -0.313316 q^{76} +14.8755 q^{78} +12.2894 q^{79} -17.3349 q^{80} -2.24827 q^{81} -5.16510 q^{82} +6.95648 q^{83} -21.3722 q^{85} -13.1855 q^{86} +21.7988 q^{87} +4.02974 q^{88} +16.1716 q^{89} +29.6687 q^{90} -5.91077 q^{92} -2.73867 q^{93} -0.379446 q^{94} -0.804035 q^{95} -18.3322 q^{96} -14.4852 q^{97} -16.2535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.84239	1.30277	0.651383	−	0.758749i	$-0.274189\pi$
$2$	1.84239	1.30277	0.651383	+	0.758749i	$0.274189\pi$
$3$	2.73867	1.58117	0.790585	−	0.612353i	$-0.209777\pi$
$3$	2.73867	1.58117	0.790585	+	0.612353i	$0.209777\pi$
$4$	1.39439	0.697197
$5$	3.57831	1.60027	0.800134	−	0.599821i	$-0.204762\pi$
$5$	3.57831	1.60027	0.800134	+	0.599821i	$0.204762\pi$
$6$	5.04568	2.05989
$7$	0	0
$7$	0	0
$8$	−1.11576	−0.394481
$9$	4.50029	1.50010
$10$	6.59263	2.08477
$11$	−3.61166	−1.08896	−0.544478	−	0.838775i	$-0.683272\pi$
$11$	−3.61166	−1.08896	−0.544478	+	0.838775i	$0.683272\pi$
$12$	3.81878	1.10239
$13$	2.94816	0.817673	0.408837	−	0.912608i	$-0.365935\pi$
$13$	2.94816	0.817673	0.408837	+	0.912608i	$0.365935\pi$
$14$	0	0
$15$	9.79979	2.53029
$16$	−4.84445	−1.21111
$17$	−5.97271	−1.44860	−0.724298	−	0.689487i	$-0.757836\pi$
$17$	−5.97271	−1.44860	−0.724298	+	0.689487i	$0.757836\pi$
$18$	8.29128	1.95427
$19$	−0.224697	−0.0515490	−0.0257745	−	0.999668i	$-0.508205\pi$
$19$	−0.224697	−0.0515490	−0.0257745	+	0.999668i	$0.508205\pi$
$20$	4.98957	1.11570
$21$	0	0
$22$	−6.65407	−1.41865
$23$	−4.23895	−0.883883	−0.441941	−	0.897044i	$-0.645710\pi$
$23$	−4.23895	−0.883883	−0.441941	+	0.897044i	$0.645710\pi$
$24$	−3.05569	−0.623741
$25$	7.80428	1.56086
$26$	5.43166	1.06524
$27$	4.10879	0.790736
$28$	0	0
$29$	7.95965	1.47807	0.739035	−	0.673667i	$-0.235282\pi$
$29$	7.95965	1.47807	0.739035	+	0.673667i	$0.235282\pi$
$30$	18.0550	3.29638
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−6.69384	−1.18332
$33$	−9.89112	−1.72182
$34$	−11.0041	−1.88718
$35$	0	0
$36$	6.27518	1.04586
$37$	2.44243	0.401533	0.200767	−	0.979639i	$-0.435657\pi$
$37$	2.44243	0.401533	0.200767	+	0.979639i	$0.435657\pi$
$38$	−0.413979	−0.0671563
$39$	8.07403	1.29288
$40$	−3.99253	−0.631275
$41$	−2.80348	−0.437830	−0.218915	−	0.975744i	$-0.570252\pi$
$41$	−2.80348	−0.437830	−0.218915	+	0.975744i	$0.570252\pi$
$42$	0	0
$43$	−7.15676	−1.09140	−0.545698	−	0.837982i	$-0.683735\pi$
$43$	−7.15676	−1.09140	−0.545698	+	0.837982i	$0.683735\pi$
$44$	−5.03607	−0.759217
$45$	16.1034	2.40056
$46$	−7.80980	−1.15149
$47$	−0.205954	−0.0300414	−0.0150207	−	0.999887i	$-0.504781\pi$
$47$	−0.205954	−0.0300414	−0.0150207	+	0.999887i	$0.504781\pi$
$48$	−13.2673	−1.91497
$49$	0	0
$50$	14.3785	2.03343
$51$	−16.3573	−2.29048
$52$	4.11090	0.570080
$53$	3.45534	0.474628	0.237314	−	0.971433i	$-0.423733\pi$
$53$	3.45534	0.474628	0.237314	+	0.971433i	$0.423733\pi$
$54$	7.56998	1.03014
$55$	−12.9236	−1.74262
$56$	0	0
$57$	−0.615370	−0.0815077
$58$	14.6648	1.92558
$59$	−9.51858	−1.23921	−0.619607	−	0.784912i	$-0.712708\pi$
$59$	−9.51858	−1.23921	−0.619607	+	0.784912i	$0.712708\pi$
$60$	13.6648	1.76411
$61$	4.77442	0.611302	0.305651	−	0.952144i	$-0.401126\pi$
$61$	4.77442	0.611302	0.305651	+	0.952144i	$0.401126\pi$
$62$	−1.84239	−0.233984
$63$	0	0
$64$	−2.64375	−0.330469
$65$	10.5494	1.30850
$66$	−18.2233	−2.24313
$67$	−10.0640	−1.22952	−0.614758	−	0.788716i	$-0.710746\pi$
$67$	−10.0640	−1.22952	−0.614758	+	0.788716i	$0.710746\pi$
$68$	−8.32832	−1.00996
$69$	−11.6091	−1.39757
$70$	0	0
$71$	12.0008	1.42423	0.712114	−	0.702064i	$-0.247738\pi$
$71$	12.0008	1.42423	0.712114	+	0.702064i	$0.247738\pi$
$72$	−5.02124	−0.591759
$73$	−4.06214	−0.475437	−0.237718	−	0.971334i	$-0.576400\pi$
$73$	−4.06214	−0.475437	−0.237718	+	0.971334i	$0.576400\pi$
$74$	4.49991	0.523104
$75$	21.3733	2.46798
$76$	−0.313316	−0.0359398
$77$	0	0
$78$	14.8755	1.68432
$79$	12.2894	1.38267	0.691334	−	0.722535i	$-0.257023\pi$
$79$	12.2894	1.38267	0.691334	+	0.722535i	$0.257023\pi$
$80$	−17.3349	−1.93811
$81$	−2.24827	−0.249808
$82$	−5.16510	−0.570389
$83$	6.95648	0.763573	0.381787	−	0.924250i	$-0.375309\pi$
$83$	6.95648	0.763573	0.381787	+	0.924250i	$0.375309\pi$
$84$	0	0
$85$	−21.3722	−2.31814
$86$	−13.1855	−1.42183
$87$	21.7988	2.33708
$88$	4.02974	0.429572
$89$	16.1716	1.71419	0.857094	−	0.515160i	$-0.172267\pi$
$89$	16.1716	1.71419	0.857094	+	0.515160i	$0.172267\pi$
$90$	29.6687	3.12736
$91$	0	0
$92$	−5.91077	−0.616241
$93$	−2.73867	−0.283986
$94$	−0.379446	−0.0391369
$95$	−0.804035	−0.0824923
$96$	−18.3322	−1.87102
$97$	−14.4852	−1.47075	−0.735373	−	0.677662i	$-0.762993\pi$
$97$	−14.4852	−1.47075	−0.735373	+	0.677662i	$0.762993\pi$
$98$	0	0
$99$	−16.2535	−1.63354
$100$	10.8823	1.08823
$101$	6.98203	0.694738	0.347369	−	0.937729i	$-0.387075\pi$
$101$	6.98203	0.694738	0.347369	+	0.937729i	$0.387075\pi$
$102$	−30.1364	−2.98395
$103$	−7.61580	−0.750407	−0.375204	−	0.926942i	$-0.622427\pi$
$103$	−7.61580	−0.750407	−0.375204	+	0.926942i	$0.622427\pi$
$104$	−3.28944	−0.322557
$105$	0	0
$106$	6.36608	0.618329
$107$	6.14305	0.593871	0.296935	−	0.954898i	$-0.404035\pi$
$107$	6.14305	0.593871	0.296935	+	0.954898i	$0.404035\pi$
$108$	5.72927	0.551299
$109$	11.3778	1.08980	0.544898	−	0.838503i	$-0.316568\pi$
$109$	11.3778	1.08980	0.544898	+	0.838503i	$0.316568\pi$
$110$	−23.8103	−2.27022
$111$	6.68900	0.634892
$112$	0	0
$113$	−17.3339	−1.63063	−0.815317	−	0.579014i	$-0.803437\pi$
$113$	−17.3339	−1.63063	−0.815317	+	0.579014i	$0.803437\pi$
$114$	−1.13375	−0.106185
$115$	−15.1683	−1.41445
$116$	11.0989	1.03051
$117$	13.2676	1.22659
$118$	−17.5369	−1.61440
$119$	0	0
$120$	−10.9342	−0.998153
$121$	2.04406	0.185823
$122$	8.79634	0.796383
$123$	−7.67779	−0.692283
$124$	−1.39439	−0.125220
$125$	10.0346	0.897521
$126$	0	0
$127$	−5.21651	−0.462890	−0.231445	−	0.972848i	$-0.574345\pi$
$127$	−5.21651	−0.462890	−0.231445	+	0.972848i	$0.574345\pi$
$128$	8.51687	0.752792
$129$	−19.6000	−1.72568
$130$	19.4362	1.70466
$131$	−3.14197	−0.274515	−0.137258	−	0.990535i	$-0.543829\pi$
$131$	−3.14197	−0.274515	−0.137258	+	0.990535i	$0.543829\pi$
$132$	−13.7921	−1.20045
$133$	0	0
$134$	−18.5418	−1.60177
$135$	14.7025	1.26539
$136$	6.66412	0.571443
$137$	17.8081	1.52145	0.760724	−	0.649075i	$-0.224844\pi$
$137$	17.8081	1.52145	0.760724	+	0.649075i	$0.224844\pi$
$138$	−21.3884	−1.82070
$139$	11.4668	0.972599	0.486299	−	0.873792i	$-0.338346\pi$
$139$	11.4668	0.972599	0.486299	+	0.873792i	$0.338346\pi$
$140$	0	0
$141$	−0.564038	−0.0475006
$142$	22.1100	1.85543
$143$	−10.6478	−0.890410
$144$	−21.8014	−1.81679
$145$	28.4821	2.36531
$146$	−7.48403	−0.619383
$147$	0	0
$148$	3.40571	0.279948
$149$	18.9272	1.55058	0.775288	−	0.631608i	$-0.217605\pi$
$149$	18.9272	1.55058	0.775288	+	0.631608i	$0.217605\pi$
$150$	39.3780	3.21520
$151$	−10.1135	−0.823025	−0.411513	−	0.911404i	$-0.634999\pi$
$151$	−10.1135	−0.823025	−0.411513	+	0.911404i	$0.634999\pi$
$152$	0.250708	0.0203351
$153$	−26.8789	−2.17303
$154$	0	0
$155$	−3.57831	−0.287417
$156$	11.2584	0.901392
$157$	7.85833	0.627163	0.313582	−	0.949561i	$-0.398471\pi$
$157$	7.85833	0.627163	0.313582	+	0.949561i	$0.398471\pi$
$158$	22.6419	1.80129
$159$	9.46303	0.750467
$160$	−23.9526	−1.89362
$161$	0	0
$162$	−4.14219	−0.325441
$163$	−16.2569	−1.27334	−0.636671	−	0.771136i	$-0.719689\pi$
$163$	−16.2569	−1.27334	−0.636671	+	0.771136i	$0.719689\pi$
$164$	−3.90916	−0.305254
$165$	−35.3935	−2.75538
$166$	12.8165	0.994757
$167$	−2.87768	−0.222681	−0.111341	−	0.993782i	$-0.535514\pi$
$167$	−2.87768	−0.222681	−0.111341	+	0.993782i	$0.535514\pi$
$168$	0	0
$169$	−4.30833	−0.331410
$170$	−39.3759	−3.01999
$171$	−1.01120	−0.0773285
$172$	−9.97934	−0.760918
$173$	2.08329	0.158390	0.0791949	−	0.996859i	$-0.474765\pi$
$173$	2.08329	0.158390	0.0791949	+	0.996859i	$0.474765\pi$
$174$	40.1619	3.04467
$175$	0	0
$176$	17.4965	1.31885
$177$	−26.0682	−1.95941
$178$	29.7944	2.23318
$179$	13.8738	1.03697	0.518487	−	0.855085i	$-0.326495\pi$
$179$	13.8738	1.03697	0.518487	+	0.855085i	$0.326495\pi$
$180$	22.4545	1.67366
$181$	−0.280540	−0.0208524	−0.0104262	−	0.999946i	$-0.503319\pi$
$181$	−0.280540	−0.0208524	−0.0104262	+	0.999946i	$0.503319\pi$
$182$	0	0
$183$	13.0755	0.966572
$184$	4.72966	0.348675
$185$	8.73977	0.642561
$186$	−5.04568	−0.369968
$187$	21.5714	1.57746
$188$	−0.287181	−0.0209448
$189$	0	0
$190$	−1.48134	−0.107468
$191$	8.96904	0.648977	0.324488	−	0.945890i	$-0.394808\pi$
$191$	8.96904	0.648977	0.324488	+	0.945890i	$0.394808\pi$
$192$	−7.24035	−0.522527
$193$	6.35169	0.457205	0.228602	−	0.973520i	$-0.426584\pi$
$193$	6.35169	0.457205	0.228602	+	0.973520i	$0.426584\pi$
$194$	−26.6873	−1.91604
$195$	28.8914	2.06895
$196$	0	0
$197$	−1.11684	−0.0795717	−0.0397858	−	0.999208i	$-0.512668\pi$
$197$	−1.11684	−0.0795717	−0.0397858	+	0.999208i	$0.512668\pi$
$198$	−29.9452	−2.12812
$199$	−1.83979	−0.130419	−0.0652095	−	0.997872i	$-0.520772\pi$
$199$	−1.83979	−0.130419	−0.0652095	+	0.997872i	$0.520772\pi$
$200$	−8.70771	−0.615728
$201$	−27.5620	−1.94407
$202$	12.8636	0.905081
$203$	0	0
$204$	−22.8085	−1.59691
$205$	−10.0317	−0.700645
$206$	−14.0313	−0.977604
$207$	−19.0765	−1.32591
$208$	−14.2822	−0.990295
$209$	0.811528	0.0561346
$210$	0	0
$211$	−0.185059	−0.0127400	−0.00637001	−	0.999980i	$-0.502028\pi$
$211$	−0.185059	−0.0127400	−0.00637001	+	0.999980i	$0.502028\pi$
$212$	4.81811	0.330909
$213$	32.8660	2.25194
$214$	11.3179	0.773674
$215$	−25.6091	−1.74652
$216$	−4.58442	−0.311930
$217$	0	0
$218$	20.9623	1.41975
$219$	−11.1248	−0.751746
$220$	−18.0206	−1.21495
$221$	−17.6085	−1.18448
$222$	12.3237	0.827115
$223$	15.9748	1.06975	0.534877	−	0.844930i	$-0.320358\pi$
$223$	15.9748	1.06975	0.534877	+	0.844930i	$0.320358\pi$
$224$	0	0
$225$	35.1215	2.34144
$226$	−31.9357	−2.12433
$227$	−19.4658	−1.29199	−0.645997	−	0.763340i	$-0.723558\pi$
$227$	−19.4658	−1.29199	−0.645997	+	0.763340i	$0.723558\pi$
$228$	−0.858069	−0.0568270
$229$	4.37277	0.288961	0.144480	−	0.989508i	$-0.453849\pi$
$229$	4.37277	0.288961	0.144480	+	0.989508i	$0.453849\pi$
$230$	−27.9459	−1.84270
$231$	0	0
$232$	−8.88107	−0.583070
$233$	11.4872	0.752548	0.376274	−	0.926508i	$-0.377205\pi$
$233$	11.4872	0.752548	0.376274	+	0.926508i	$0.377205\pi$
$234$	24.4440	1.59796
$235$	−0.736965	−0.0480743
$236$	−13.2727	−0.863976
$237$	33.6566	2.18623
$238$	0	0
$239$	−13.8908	−0.898522	−0.449261	−	0.893400i	$-0.648313\pi$
$239$	−13.8908	−0.898522	−0.449261	+	0.893400i	$0.648313\pi$
$240$	−47.4746	−3.06447
$241$	8.39619	0.540846	0.270423	−	0.962742i	$-0.412836\pi$
$241$	8.39619	0.540846	0.270423	+	0.962742i	$0.412836\pi$
$242$	3.76595	0.242084
$243$	−18.4836	−1.18573
$244$	6.65743	0.426198
$245$	0	0
$246$	−14.1455	−0.901882
$247$	−0.662444	−0.0421503
$248$	1.11576	0.0708509
$249$	19.0515	1.20734
$250$	18.4876	1.16926
$251$	9.97443	0.629581	0.314790	−	0.949161i	$-0.398066\pi$
$251$	9.97443	0.629581	0.314790	+	0.949161i	$0.398066\pi$
$252$	0	0
$253$	15.3096	0.962509
$254$	−9.61083	−0.603037
$255$	−58.5313	−3.66537
$256$	20.9789	1.31118
$257$	−20.2360	−1.26229	−0.631144	−	0.775666i	$-0.717414\pi$
$257$	−20.2360	−1.26229	−0.631144	+	0.775666i	$0.717414\pi$
$258$	−36.1107	−2.24816
$259$	0	0
$260$	14.7101	0.912280
$261$	35.8207	2.21725
$262$	−5.78873	−0.357629
$263$	−1.79007	−0.110380	−0.0551901	−	0.998476i	$-0.517577\pi$
$263$	−1.79007	−0.110380	−0.0551901	+	0.998476i	$0.517577\pi$
$264$	11.0361	0.679226
$265$	12.3643	0.759532
$266$	0	0
$267$	44.2887	2.71042
$268$	−14.0332	−0.857216
$269$	−5.17191	−0.315337	−0.157668	−	0.987492i	$-0.550398\pi$
$269$	−5.17191	−0.315337	−0.157668	+	0.987492i	$0.550398\pi$
$270$	27.0877	1.64851
$271$	0.918727	0.0558087	0.0279044	−	0.999611i	$-0.491117\pi$
$271$	0.918727	0.0558087	0.0279044	+	0.999611i	$0.491117\pi$
$272$	28.9345	1.75441
$273$	0	0
$274$	32.8094	1.98209
$275$	−28.1864	−1.69970
$276$	−16.1876	−0.974381
$277$	4.21904	0.253497	0.126749	−	0.991935i	$-0.459546\pi$
$277$	4.21904	0.253497	0.126749	+	0.991935i	$0.459546\pi$
$278$	21.1262	1.26707
$279$	−4.50029	−0.269425
$280$	0	0
$281$	15.0257	0.896358	0.448179	−	0.893944i	$-0.352073\pi$
$281$	15.0257	0.896358	0.448179	+	0.893944i	$0.352073\pi$
$282$	−1.03918	−0.0618821
$283$	8.80087	0.523157	0.261579	−	0.965182i	$-0.415757\pi$
$283$	8.80087	0.523157	0.261579	+	0.965182i	$0.415757\pi$
$284$	16.7338	0.992967
$285$	−2.20198	−0.130434
$286$	−19.6173	−1.15999
$287$	0	0
$288$	−30.1242	−1.77509
$289$	18.6733	1.09843
$290$	52.4751	3.08144
$291$	−39.6700	−2.32550
$292$	−5.66422	−0.331473
$293$	−20.9214	−1.22224	−0.611120	−	0.791538i	$-0.709281\pi$
$293$	−20.9214	−1.22224	−0.611120	+	0.791538i	$0.709281\pi$
$294$	0	0
$295$	−34.0604	−1.98307
$296$	−2.72517	−0.158397
$297$	−14.8395	−0.861077
$298$	34.8712	2.02004
$299$	−12.4971	−0.722728
$300$	29.8028	1.72067
$301$	0	0
$302$	−18.6330	−1.07221
$303$	19.1214	1.09850
$304$	1.08853	0.0624317
$305$	17.0844	0.978247
$306$	−49.5214	−2.83095
$307$	−32.4527	−1.85217	−0.926086	−	0.377312i	$-0.876849\pi$
$307$	−32.4527	−1.85217	−0.926086	+	0.377312i	$0.876849\pi$
$308$	0	0
$309$	−20.8571	−1.18652
$310$	−6.59263	−0.374436
$311$	−18.8966	−1.07153	−0.535764	−	0.844367i	$-0.679977\pi$
$311$	−18.8966	−1.07153	−0.535764	+	0.844367i	$0.679977\pi$
$312$	−9.00869	−0.510016
$313$	−26.2855	−1.48575	−0.742873	−	0.669432i	$-0.766538\pi$
$313$	−26.2855	−1.48575	−0.742873	+	0.669432i	$0.766538\pi$
$314$	14.4781	0.817047
$315$	0	0
$316$	17.1363	0.963992
$317$	6.45657	0.362637	0.181319	−	0.983424i	$-0.441963\pi$
$317$	6.45657	0.362637	0.181319	+	0.983424i	$0.441963\pi$
$318$	17.4346	0.977682
$319$	−28.7475	−1.60955
$320$	−9.46015	−0.528839
$321$	16.8238	0.939010
$322$	0	0
$323$	1.34205	0.0746737
$324$	−3.13498	−0.174165
$325$	23.0083	1.27627
$326$	−29.9516	−1.65887
$327$	31.1600	1.72315
$328$	3.12801	0.172715
$329$	0	0
$330$	−65.2085	−3.58961
$331$	17.8615	0.981759	0.490880	−	0.871227i	$-0.336675\pi$
$331$	17.8615	0.981759	0.490880	+	0.871227i	$0.336675\pi$
$332$	9.70008	0.532361
$333$	10.9916	0.602338
$334$	−5.30180	−0.290102
$335$	−36.0122	−1.96756
$336$	0	0
$337$	0.491481	0.0267727	0.0133863	−	0.999910i	$-0.495739\pi$
$337$	0.491481	0.0267727	0.0133863	+	0.999910i	$0.495739\pi$
$338$	−7.93762	−0.431750
$339$	−47.4717	−2.57831
$340$	−29.8013	−1.61620
$341$	3.61166	0.195582
$342$	−1.86303	−0.100741
$343$	0	0
$344$	7.98523	0.430535
$345$	−41.5408	−2.23648
$346$	3.83823	0.206345
$347$	−5.81870	−0.312364	−0.156182	−	0.987728i	$-0.549919\pi$
$347$	−5.81870	−0.312364	−0.156182	+	0.987728i	$0.549919\pi$
$348$	30.3962	1.62941
$349$	5.16754	0.276612	0.138306	−	0.990390i	$-0.455834\pi$
$349$	5.16754	0.276612	0.138306	+	0.990390i	$0.455834\pi$
$350$	0	0
$351$	12.1134	0.646564
$352$	24.1759	1.28858
$353$	−32.1373	−1.71049	−0.855247	−	0.518220i	$-0.826595\pi$
$353$	−32.1373	−1.71049	−0.855247	+	0.518220i	$0.826595\pi$
$354$	−48.0277	−2.55265
$355$	42.9424	2.27914
$356$	22.5496	1.19513
$357$	0	0
$358$	25.5609	1.35093
$359$	−1.98881	−0.104965	−0.0524826	−	0.998622i	$-0.516713\pi$
$359$	−1.98881	−0.104965	−0.0524826	+	0.998622i	$0.516713\pi$
$360$	−17.9676	−0.946973
$361$	−18.9495	−0.997343
$362$	−0.516864	−0.0271658
$363$	5.59799	0.293818
$364$	0	0
$365$	−14.5356	−0.760826
$366$	24.0902	1.25922
$367$	23.8282	1.24382	0.621911	−	0.783088i	$-0.286357\pi$
$367$	23.8282	1.24382	0.621911	+	0.783088i	$0.286357\pi$
$368$	20.5354	1.07048
$369$	−12.6165	−0.656787
$370$	16.1021	0.837106
$371$	0	0
$372$	−3.81878	−0.197995
$373$	−0.639709	−0.0331229	−0.0165614	−	0.999863i	$-0.505272\pi$
$373$	−0.639709	−0.0331229	−0.0165614	+	0.999863i	$0.505272\pi$
$374$	39.7429	2.05506
$375$	27.4814	1.41913
$376$	0.229795	0.0118508
$377$	23.4664	1.20858
$378$	0	0
$379$	16.6485	0.855178	0.427589	−	0.903973i	$-0.359363\pi$
$379$	16.6485	0.855178	0.427589	+	0.903973i	$0.359363\pi$
$380$	−1.12114	−0.0575134
$381$	−14.2863	−0.731908
$382$	16.5245	0.845464
$383$	26.7009	1.36435	0.682177	−	0.731187i	$-0.261034\pi$
$383$	26.7009	1.36435	0.682177	+	0.731187i	$0.261034\pi$
$384$	23.3249	1.19029
$385$	0	0
$386$	11.7023	0.595631
$387$	−32.2075	−1.63720
$388$	−20.1980	−1.02540
$389$	−12.1364	−0.615341	−0.307671	−	0.951493i	$-0.599549\pi$
$389$	−12.1364	−0.615341	−0.307671	+	0.951493i	$0.599549\pi$
$390$	53.2291	2.69536
$391$	25.3181	1.28039
$392$	0	0
$393$	−8.60481	−0.434055
$394$	−2.05766	−0.103663
$395$	43.9753	2.21264
$396$	−22.6638	−1.13890
$397$	−14.9019	−0.747903	−0.373952	−	0.927448i	$-0.621997\pi$
$397$	−14.9019	−0.747903	−0.373952	+	0.927448i	$0.621997\pi$
$398$	−3.38960	−0.169905
$399$	0	0
$400$	−37.8075	−1.89037
$401$	35.9073	1.79313	0.896564	−	0.442915i	$-0.146056\pi$
$401$	35.9073	1.79313	0.896564	+	0.442915i	$0.146056\pi$
$402$	−50.7799	−2.53267
$403$	−2.94816	−0.146858
$404$	9.73571	0.484369
$405$	−8.04501	−0.399760
$406$	0	0
$407$	−8.82122	−0.437252
$408$	18.2508	0.903549
$409$	−4.59478	−0.227197	−0.113599	−	0.993527i	$-0.536238\pi$
$409$	−4.59478	−0.227197	−0.113599	+	0.993527i	$0.536238\pi$
$410$	−18.4823	−0.912776
$411$	48.7704	2.40567
$412$	−10.6194	−0.523182
$413$	0	0
$414$	−35.1463	−1.72735
$415$	24.8924	1.22192
$416$	−19.7345	−0.967566
$417$	31.4037	1.53784
$418$	1.49515	0.0731302
$419$	−21.6844	−1.05935	−0.529676	−	0.848200i	$-0.677687\pi$
$419$	−21.6844	−1.05935	−0.529676	+	0.848200i	$0.677687\pi$
$420$	0	0
$421$	38.1573	1.85967	0.929837	−	0.367973i	$-0.119948\pi$
$421$	38.1573	1.85967	0.929837	+	0.367973i	$0.119948\pi$
$422$	−0.340951	−0.0165973
$423$	−0.926850	−0.0450650
$424$	−3.85534	−0.187232
$425$	−46.6128	−2.26105
$426$	60.5520	2.93375
$427$	0	0
$428$	8.56583	0.414045
$429$	−29.1606	−1.40789
$430$	−47.1819	−2.27531
$431$	30.9184	1.48929	0.744644	−	0.667462i	$-0.232619\pi$
$431$	30.9184	1.48929	0.744644	+	0.667462i	$0.232619\pi$
$432$	−19.9048	−0.957671
$433$	−35.5499	−1.70842	−0.854209	−	0.519930i	$-0.825958\pi$
$433$	−35.5499	−1.70842	−0.854209	+	0.519930i	$0.825958\pi$
$434$	0	0
$435$	78.0029	3.73995
$436$	15.8651	0.759802
$437$	0.952480	0.0455633
$438$	−20.4963	−0.979349
$439$	7.36099	0.351321	0.175660	−	0.984451i	$-0.443794\pi$
$439$	7.36099	0.351321	0.175660	+	0.984451i	$0.443794\pi$
$440$	14.4197	0.687430
$441$	0	0
$442$	−32.4418	−1.54310
$443$	−15.0571	−0.715385	−0.357693	−	0.933839i	$-0.616436\pi$
$443$	−15.0571	−0.715385	−0.357693	+	0.933839i	$0.616436\pi$
$444$	9.32711	0.442645
$445$	57.8670	2.74316
$446$	29.4319	1.39364
$447$	51.8352	2.45172
$448$	0	0
$449$	−5.54732	−0.261794	−0.130897	−	0.991396i	$-0.541786\pi$
$449$	−5.54732	−0.261794	−0.130897	+	0.991396i	$0.541786\pi$
$450$	64.7075	3.05034
$451$	10.1252	0.476777
$452$	−24.1703	−1.13687
$453$	−27.6975	−1.30134
$454$	−35.8636	−1.68316
$455$	0	0
$456$	0.686606	0.0321532
$457$	−10.2476	−0.479363	−0.239681	−	0.970852i	$-0.577043\pi$
$457$	−10.2476	−0.479363	−0.239681	+	0.970852i	$0.577043\pi$
$458$	8.05635	0.376448
$459$	−24.5406	−1.14546
$460$	−21.1506	−0.986150
$461$	−9.55351	−0.444952	−0.222476	−	0.974938i	$-0.571414\pi$
$461$	−9.55351	−0.444952	−0.222476	+	0.974938i	$0.571414\pi$
$462$	0	0
$463$	−16.6305	−0.772886	−0.386443	−	0.922313i	$-0.626296\pi$
$463$	−16.6305	−0.772886	−0.386443	+	0.922313i	$0.626296\pi$
$464$	−38.5602	−1.79011
$465$	−9.79979	−0.454454
$466$	21.1638	0.980394
$467$	−14.5713	−0.674281	−0.337140	−	0.941454i	$-0.609460\pi$
$467$	−14.5713	−0.674281	−0.337140	+	0.941454i	$0.609460\pi$
$468$	18.5002	0.855174
$469$	0	0
$470$	−1.35778	−0.0626295
$471$	21.5213	0.991651
$472$	10.6205	0.488846
$473$	25.8477	1.18848
$474$	62.0085	2.84815
$475$	−1.75360	−0.0804607
$476$	0	0
$477$	15.5500	0.711987
$478$	−25.5923	−1.17056
$479$	−6.37438	−0.291253	−0.145626	−	0.989340i	$-0.546520\pi$
$479$	−6.37438	−0.291253	−0.145626	+	0.989340i	$0.546520\pi$
$480$	−65.5982	−2.99414
$481$	7.20069	0.328323
$482$	15.4690	0.704595
$483$	0	0
$484$	2.85022	0.129556
$485$	−51.8324	−2.35359
$486$	−34.0540	−1.54472
$487$	−28.5269	−1.29268	−0.646339	−	0.763051i	$-0.723701\pi$
$487$	−28.5269	−1.29268	−0.646339	+	0.763051i	$0.723701\pi$
$488$	−5.32711	−0.241147
$489$	−44.5223	−2.01337
$490$	0	0
$491$	11.2486	0.507641	0.253820	−	0.967251i	$-0.418313\pi$
$491$	11.2486	0.507641	0.253820	+	0.967251i	$0.418313\pi$
$492$	−10.7059	−0.482658
$493$	−47.5407	−2.14113
$494$	−1.22048	−0.0549119
$495$	−58.1600	−2.61410
$496$	4.84445	0.217522
$497$	0	0
$498$	35.1002	1.57288
$499$	−7.78381	−0.348451	−0.174226	−	0.984706i	$-0.555742\pi$
$499$	−7.78381	−0.348451	−0.174226	+	0.984706i	$0.555742\pi$
$500$	13.9922	0.625749
$501$	−7.88100	−0.352097
$502$	18.3768	0.820196
$503$	4.31584	0.192434	0.0962168	−	0.995360i	$-0.469326\pi$
$503$	4.31584	0.192434	0.0962168	+	0.995360i	$0.469326\pi$
$504$	0	0
$505$	24.9839	1.11177
$506$	28.2063	1.25392
$507$	−11.7991	−0.524015
$508$	−7.27387	−0.322726
$509$	−14.3440	−0.635786	−0.317893	−	0.948127i	$-0.602975\pi$
$509$	−14.3440	−0.635786	−0.317893	+	0.948127i	$0.602975\pi$
$510$	−107.837	−4.77512
$511$	0	0
$512$	21.6175	0.955368
$513$	−0.923232	−0.0407617
$514$	−37.2826	−1.64446
$515$	−27.2517	−1.20085
$516$	−27.3301	−1.20314
$517$	0.743833	0.0327138
$518$	0	0
$519$	5.70544	0.250441
$520$	−11.7706	−0.516177
$521$	−13.3904	−0.586642	−0.293321	−	0.956014i	$-0.594760\pi$
$521$	−13.3904	−0.586642	−0.293321	+	0.956014i	$0.594760\pi$
$522$	65.9957	2.88855
$523$	−14.6230	−0.639420	−0.319710	−	0.947515i	$-0.603585\pi$
$523$	−14.6230	−0.639420	−0.319710	+	0.947515i	$0.603585\pi$
$524$	−4.38115	−0.191391
$525$	0	0
$526$	−3.29800	−0.143800
$527$	5.97271	0.260176
$528$	47.9171	2.08532
$529$	−5.03127	−0.218751
$530$	22.7798	0.989492
$531$	−42.8363	−1.85894
$532$	0	0
$533$	−8.26511	−0.358002
$534$	81.5969	3.53104
$535$	21.9817	0.950352
$536$	11.2290	0.485021
$537$	37.9956	1.63963
$538$	−9.52866	−0.410810
$539$	0	0
$540$	20.5011	0.882226
$541$	9.30525	0.400064	0.200032	−	0.979789i	$-0.435895\pi$
$541$	9.30525	0.400064	0.200032	+	0.979789i	$0.435895\pi$
$542$	1.69265	0.0727057
$543$	−0.768306	−0.0329712
$544$	39.9804	1.71415
$545$	40.7133	1.74396
$546$	0	0
$547$	13.3520	0.570890	0.285445	−	0.958395i	$-0.407859\pi$
$547$	13.3520	0.570890	0.285445	+	0.958395i	$0.407859\pi$
$548$	24.8315	1.06075
$549$	21.4863	0.917012
$550$	−51.9303	−2.21431
$551$	−1.78851	−0.0761931
$552$	12.9529	0.551314
$553$	0	0
$554$	7.77310	0.330247
$555$	23.9353	1.01600
$556$	15.9892	0.678093
$557$	−9.19697	−0.389688	−0.194844	−	0.980834i	$-0.562420\pi$
$557$	−9.19697	−0.389688	−0.194844	+	0.980834i	$0.562420\pi$
$558$	−8.29128	−0.350998
$559$	−21.0993	−0.892405
$560$	0	0
$561$	59.0768	2.49423
$562$	27.6832	1.16774
$563$	36.3207	1.53073	0.765367	−	0.643594i	$-0.222558\pi$
$563$	36.3207	1.53073	0.765367	+	0.643594i	$0.222558\pi$
$564$	−0.786491	−0.0331173
$565$	−62.0260	−2.60945
$566$	16.2146	0.681551
$567$	0	0
$568$	−13.3900	−0.561830
$569$	34.7599	1.45721	0.728606	−	0.684933i	$-0.240169\pi$
$569$	34.7599	1.45721	0.728606	+	0.684933i	$0.240169\pi$
$570$	−4.05691	−0.169925
$571$	20.0804	0.840339	0.420170	−	0.907446i	$-0.361971\pi$
$571$	20.0804	0.840339	0.420170	+	0.907446i	$0.361971\pi$
$572$	−14.8472	−0.620791
$573$	24.5632	1.02614
$574$	0	0
$575$	−33.0820	−1.37961
$576$	−11.8976	−0.495735
$577$	−26.5913	−1.10701	−0.553504	−	0.832846i	$-0.686710\pi$
$577$	−26.5913	−1.10701	−0.553504	+	0.832846i	$0.686710\pi$
$578$	34.4035	1.43100
$579$	17.3952	0.722918
$580$	39.7153	1.64909
$581$	0	0
$582$	−73.0876	−3.02958
$583$	−12.4795	−0.516849
$584$	4.53237	0.187551
$585$	47.4755	1.96287
$586$	−38.5453	−1.59229
$587$	47.4629	1.95900	0.979501	−	0.201437i	$-0.0645612\pi$
$587$	47.4629	1.95900	0.979501	+	0.201437i	$0.0645612\pi$
$588$	0	0
$589$	0.224697	0.00925848
$590$	−62.7525	−2.58348
$591$	−3.05865	−0.125816
$592$	−11.8322	−0.486302
$593$	−1.71227	−0.0703145	−0.0351572	−	0.999382i	$-0.511193\pi$
$593$	−1.71227	−0.0703145	−0.0351572	+	0.999382i	$0.511193\pi$
$594$	−27.3402	−1.12178
$595$	0	0
$596$	26.3920	1.08106
$597$	−5.03856	−0.206214
$598$	−23.0246	−0.941544
$599$	−20.6087	−0.842048	−0.421024	−	0.907050i	$-0.638329\pi$
$599$	−20.6087	−0.842048	−0.421024	+	0.907050i	$0.638329\pi$
$600$	−23.8475	−0.973570
$601$	−15.5198	−0.633065	−0.316533	−	0.948582i	$-0.602519\pi$
$601$	−15.5198	−0.633065	−0.316533	+	0.948582i	$0.602519\pi$
$602$	0	0
$603$	−45.2910	−1.84439
$604$	−14.1022	−0.573811
$605$	7.31427	0.297367
$606$	35.2291	1.43109
$607$	5.50905	0.223605	0.111803	−	0.993730i	$-0.464338\pi$
$607$	5.50905	0.223605	0.111803	+	0.993730i	$0.464338\pi$
$608$	1.50409	0.0609988
$609$	0	0
$610$	31.4760	1.27443
$611$	−0.607185	−0.0245641
$612$	−37.4798	−1.51503
$613$	−35.3914	−1.42945	−0.714723	−	0.699407i	$-0.753447\pi$
$613$	−35.3914	−1.42945	−0.714723	+	0.699407i	$0.753447\pi$
$614$	−59.7905	−2.41295
$615$	−27.4735	−1.10784
$616$	0	0
$617$	5.49216	0.221106	0.110553	−	0.993870i	$-0.464738\pi$
$617$	5.49216	0.221106	0.110553	+	0.993870i	$0.464738\pi$
$618$	−38.4269	−1.54576
$619$	−26.9204	−1.08202	−0.541012	−	0.841015i	$-0.681959\pi$
$619$	−26.9204	−1.08202	−0.541012	+	0.841015i	$0.681959\pi$
$620$	−4.98957	−0.200386
$621$	−17.4170	−0.698918
$622$	−34.8149	−1.39595
$623$	0	0
$624$	−39.1143	−1.56582
$625$	−3.11457	−0.124583
$626$	−48.4282	−1.93558
$627$	2.22250	0.0887583
$628$	10.9576	0.437257
$629$	−14.5879	−0.581659
$630$	0	0
$631$	−3.35946	−0.133738	−0.0668690	−	0.997762i	$-0.521301\pi$
$631$	−3.35946	−0.133738	−0.0668690	+	0.997762i	$0.521301\pi$
$632$	−13.7121	−0.545436
$633$	−0.506816	−0.0201441
$634$	11.8955	0.472431
$635$	−18.6663	−0.740748
$636$	13.1952	0.523224
$637$	0	0
$638$	−52.9641	−2.09687
$639$	54.0068	2.13648
$640$	30.4760	1.20467
$641$	34.0492	1.34486	0.672432	−	0.740159i	$-0.265250\pi$
$641$	34.0492	1.34486	0.672432	+	0.740159i	$0.265250\pi$
$642$	30.9959	1.22331
$643$	13.0746	0.515613	0.257806	−	0.966197i	$-0.417000\pi$
$643$	13.0746	0.515613	0.257806	+	0.966197i	$0.417000\pi$
$644$	0	0
$645$	−70.1347	−2.76155
$646$	2.47258	0.0972823
$647$	42.0859	1.65457	0.827284	−	0.561784i	$-0.189885\pi$
$647$	42.0859	1.65457	0.827284	+	0.561784i	$0.189885\pi$
$648$	2.50853	0.0985445
$649$	34.3778	1.34945
$650$	42.3902	1.66268
$651$	0	0
$652$	−22.6686	−0.887770
$653$	3.77401	0.147688	0.0738442	−	0.997270i	$-0.476473\pi$
$653$	3.77401	0.147688	0.0738442	+	0.997270i	$0.476473\pi$
$654$	57.4088	2.24486
$655$	−11.2429	−0.439298
$656$	13.5813	0.530261
$657$	−18.2808	−0.713201
$658$	0	0
$659$	32.1270	1.25149	0.625744	−	0.780028i	$-0.284795\pi$
$659$	32.1270	1.25149	0.625744	+	0.780028i	$0.284795\pi$
$660$	−49.3524	−1.92104
$661$	34.4529	1.34006	0.670032	−	0.742332i	$-0.266280\pi$
$661$	34.4529	1.34006	0.670032	+	0.742332i	$0.266280\pi$
$662$	32.9079	1.27900
$663$	−48.2239	−1.87286
$664$	−7.76177	−0.301215
$665$	0	0
$666$	20.2509	0.784706
$667$	−33.7406	−1.30644
$668$	−4.01262	−0.155253
$669$	43.7498	1.69146
$670$	−66.3484	−2.56326
$671$	−17.2436	−0.665681
$672$	0	0
$673$	−40.3629	−1.55588	−0.777938	−	0.628341i	$-0.783734\pi$
$673$	−40.3629	−1.55588	−0.777938	+	0.628341i	$0.783734\pi$
$674$	0.905499	0.0348785
$675$	32.0661	1.23423
$676$	−6.00751	−0.231058
$677$	30.0626	1.15540	0.577699	−	0.816250i	$-0.303951\pi$
$677$	30.0626	1.15540	0.577699	+	0.816250i	$0.303951\pi$
$678$	−87.4613	−3.35893
$679$	0	0
$680$	23.8463	0.914462
$681$	−53.3104	−2.04286
$682$	6.65407	0.254798
$683$	−42.7137	−1.63439	−0.817197	−	0.576358i	$-0.804473\pi$
$683$	−42.7137	−1.63439	−0.817197	+	0.576358i	$0.804473\pi$
$684$	−1.41001	−0.0539132
$685$	63.7229	2.43473
$686$	0	0
$687$	11.9756	0.456896
$688$	34.6706	1.32180
$689$	10.1869	0.388091
$690$	−76.5344	−2.91361
$691$	0.906495	0.0344847	0.0172423	−	0.999851i	$-0.494511\pi$
$691$	0.906495	0.0344847	0.0172423	+	0.999851i	$0.494511\pi$
$692$	2.90493	0.110429
$693$	0	0
$694$	−10.7203	−0.406937
$695$	41.0316	1.55642
$696$	−24.3223	−0.921933
$697$	16.7444	0.634238
$698$	9.52062	0.360361
$699$	31.4595	1.18991
$700$	0	0
$701$	7.99378	0.301921	0.150960	−	0.988540i	$-0.451763\pi$
$701$	7.99378	0.301921	0.150960	+	0.988540i	$0.451763\pi$
$702$	22.3175	0.842321
$703$	−0.548807	−0.0206987
$704$	9.54832	0.359866
$705$	−2.01830	−0.0760136
$706$	−59.2093	−2.22837
$707$	0	0
$708$	−36.3494	−1.36609
$709$	−16.6589	−0.625640	−0.312820	−	0.949812i	$-0.601274\pi$
$709$	−16.6589	−0.625640	−0.312820	+	0.949812i	$0.601274\pi$
$710$	79.1165	2.96919
$711$	55.3059	2.07413
$712$	−18.0437	−0.676214
$713$	4.23895	0.158750
$714$	0	0
$715$	−38.1009	−1.42489
$716$	19.3455	0.722975
$717$	−38.0423	−1.42072
$718$	−3.66415	−0.136745
$719$	−3.76552	−0.140430	−0.0702152	−	0.997532i	$-0.522369\pi$
$719$	−3.76552	−0.140430	−0.0702152	+	0.997532i	$0.522369\pi$
$720$	−78.0122	−2.90734
$721$	0	0
$722$	−34.9124	−1.29930
$723$	22.9943	0.855169
$724$	−0.391184	−0.0145382
$725$	62.1194	2.30706
$726$	10.3137	0.382776
$727$	−21.4256	−0.794631	−0.397316	−	0.917682i	$-0.630058\pi$
$727$	−21.4256	−0.794631	−0.397316	+	0.917682i	$0.630058\pi$
$728$	0	0
$729$	−43.8756	−1.62502
$730$	−26.7802	−0.991178
$731$	42.7453	1.58099
$732$	18.2325	0.673891
$733$	36.6833	1.35493	0.677464	−	0.735556i	$-0.263079\pi$
$733$	36.6833	1.35493	0.677464	+	0.735556i	$0.263079\pi$
$734$	43.9008	1.62041
$735$	0	0
$736$	28.3749	1.04591
$737$	36.3478	1.33889
$738$	−23.2444	−0.855639
$739$	−2.60081	−0.0956724	−0.0478362	−	0.998855i	$-0.515233\pi$
$739$	−2.60081	−0.0956724	−0.0478362	+	0.998855i	$0.515233\pi$
$740$	12.1867	0.447992
$741$	−1.81421	−0.0666467
$742$	0	0
$743$	28.9539	1.06221	0.531107	−	0.847305i	$-0.321776\pi$
$743$	28.9539	1.06221	0.531107	+	0.847305i	$0.321776\pi$
$744$	3.05569	0.112027
$745$	67.7273	2.48134
$746$	−1.17859	−0.0431513
$747$	31.3062	1.14543
$748$	30.0790	1.09980
$749$	0	0
$750$	50.6314	1.84880
$751$	0.895914	0.0326924	0.0163462	−	0.999866i	$-0.494797\pi$
$751$	0.895914	0.0326924	0.0163462	+	0.999866i	$0.494797\pi$
$752$	0.997732	0.0363836
$753$	27.3166	0.995474
$754$	43.2341	1.57449
$755$	−36.1892	−1.31706
$756$	0	0
$757$	9.43200	0.342812	0.171406	−	0.985200i	$-0.445169\pi$
$757$	9.43200	0.342812	0.171406	+	0.985200i	$0.445169\pi$
$758$	30.6731	1.11410
$759$	41.9280	1.52189
$760$	0.897111	0.0325416
$761$	41.0241	1.48712	0.743561	−	0.668668i	$-0.233135\pi$
$761$	41.0241	1.48712	0.743561	+	0.668668i	$0.233135\pi$
$762$	−26.3209	−0.953504
$763$	0	0
$764$	12.5064	0.452465
$765$	−96.1811	−3.47743
$766$	49.1935	1.77743
$767$	−28.0623	−1.01327
$768$	57.4541	2.07320
$769$	0.137102	0.00494403	0.00247201	−	0.999997i	$-0.499213\pi$
$769$	0.137102	0.00494403	0.00247201	+	0.999997i	$0.499213\pi$
$770$	0	0
$771$	−55.4196	−1.99589
$772$	8.85677	0.318762
$773$	44.7967	1.61123	0.805614	−	0.592441i	$-0.201836\pi$
$773$	44.7967	1.61123	0.805614	+	0.592441i	$0.201836\pi$
$774$	−59.3387	−2.13288
$775$	−7.80428	−0.280338
$776$	16.1620	0.580181
$777$	0	0
$778$	−22.3600	−0.801645
$779$	0.629933	0.0225697
$780$	40.2860	1.44247
$781$	−43.3426	−1.55092
$782$	46.6457	1.66805
$783$	32.7045	1.16876
$784$	0	0
$785$	28.1195	1.00363
$786$	−15.8534	−0.565472
$787$	21.0386	0.749945	0.374973	−	0.927036i	$-0.377652\pi$
$787$	21.0386	0.749945	0.374973	+	0.927036i	$0.377652\pi$
$788$	−1.55732	−0.0554771
$789$	−4.90240	−0.174530
$790$	81.0196	2.88255
$791$	0	0
$792$	18.1350	0.644399
$793$	14.0758	0.499846
$794$	−27.4550	−0.974343
$795$	33.8616	1.20095
$796$	−2.56539	−0.0909278
$797$	0.771492	0.0273276	0.0136638	−	0.999907i	$-0.495651\pi$
$797$	0.771492	0.0273276	0.0136638	+	0.999907i	$0.495651\pi$
$798$	0	0
$799$	1.23010	0.0435179
$800$	−52.2406	−1.84699
$801$	72.7769	2.57145
$802$	66.1553	2.33602
$803$	14.6710	0.517730
$804$	−38.4323	−1.35540
$805$	0	0
$806$	−5.43166	−0.191322
$807$	−14.1641	−0.498601
$808$	−7.79027	−0.274061
$809$	−12.1082	−0.425702	−0.212851	−	0.977085i	$-0.568275\pi$
$809$	−12.1082	−0.425702	−0.212851	+	0.977085i	$0.568275\pi$
$810$	−14.8220	−0.520793
$811$	−16.5626	−0.581593	−0.290796	−	0.956785i	$-0.593920\pi$
$811$	−16.5626	−0.581593	−0.290796	+	0.956785i	$0.593920\pi$
$812$	0	0
$813$	2.51609	0.0882430
$814$	−16.2521	−0.569636
$815$	−58.1723	−2.03769
$816$	79.2420	2.77403
$817$	1.60810	0.0562604
$818$	−8.46536	−0.295984
$819$	0	0
$820$	−13.9882	−0.488488
$821$	−7.13045	−0.248854	−0.124427	−	0.992229i	$-0.539709\pi$
$821$	−7.13045	−0.248854	−0.124427	+	0.992229i	$0.539709\pi$
$822$	89.8541	3.13402
$823$	8.55974	0.298374	0.149187	−	0.988809i	$-0.452334\pi$
$823$	8.55974	0.298374	0.149187	+	0.988809i	$0.452334\pi$
$824$	8.49741	0.296021
$825$	−77.1931	−2.68752
$826$	0	0
$827$	46.0574	1.60157	0.800786	−	0.598951i	$-0.204416\pi$
$827$	46.0574	1.60157	0.800786	+	0.598951i	$0.204416\pi$
$828$	−26.6002	−0.924420
$829$	−10.3843	−0.360661	−0.180331	−	0.983606i	$-0.557717\pi$
$829$	−10.3843	−0.360661	−0.180331	+	0.983606i	$0.557717\pi$
$830$	45.8615	1.59188
$831$	11.5545	0.400822
$832$	−7.79421	−0.270216
$833$	0	0
$834$	57.8577	2.00345
$835$	−10.2972	−0.356350
$836$	1.13159	0.0391369
$837$	−4.10879	−0.142020
$838$	−39.9511	−1.38009
$839$	−31.6615	−1.09308	−0.546538	−	0.837435i	$-0.684054\pi$
$839$	−31.6615	−1.09308	−0.546538	+	0.837435i	$0.684054\pi$
$840$	0	0
$841$	34.3561	1.18469
$842$	70.3006	2.42272
$843$	41.1504	1.41729
$844$	−0.258046	−0.00888231
$845$	−15.4165	−0.530345
$846$	−1.70762	−0.0587091
$847$	0	0
$848$	−16.7392	−0.574828
$849$	24.1026	0.827200
$850$	−85.8788	−2.94562
$851$	−10.3534	−0.354908
$852$	45.8282	1.57005
$853$	31.0507	1.06316	0.531578	−	0.847010i	$-0.321599\pi$
$853$	31.0507	1.06316	0.531578	+	0.847010i	$0.321599\pi$
$854$	0	0
$855$	−3.61839	−0.123746
$856$	−6.85417	−0.234271
$857$	−28.6448	−0.978486	−0.489243	−	0.872147i	$-0.662727\pi$
$857$	−28.6448	−0.978486	−0.489243	+	0.872147i	$0.662727\pi$
$858$	−53.7252	−1.83415
$859$	0.0818649	0.00279319	0.00139660	−	0.999999i	$-0.499555\pi$
$859$	0.0818649	0.00279319	0.00139660	+	0.999999i	$0.499555\pi$
$860$	−35.7092	−1.21767
$861$	0	0
$862$	56.9637	1.94019
$863$	15.1237	0.514815	0.257408	−	0.966303i	$-0.417132\pi$
$863$	15.1237	0.514815	0.257408	+	0.966303i	$0.417132\pi$
$864$	−27.5036	−0.935691
$865$	7.45466	0.253466
$866$	−65.4966	−2.22567
$867$	51.1400	1.73680
$868$	0	0
$869$	−44.3852	−1.50566
$870$	143.712	4.87228
$871$	−29.6704	−1.00534
$872$	−12.6949	−0.429903
$873$	−65.1874	−2.20626
$874$	1.75484	0.0593583
$875$	0	0
$876$	−15.5124	−0.524115
$877$	8.37346	0.282752	0.141376	−	0.989956i	$-0.454847\pi$
$877$	8.37346	0.282752	0.141376	+	0.989956i	$0.454847\pi$
$878$	13.5618	0.457689
$879$	−57.2967	−1.93257
$880$	62.6078	2.11051
$881$	21.6067	0.727947	0.363974	−	0.931409i	$-0.381420\pi$
$881$	21.6067	0.727947	0.363974	+	0.931409i	$0.381420\pi$
$882$	0	0
$883$	48.7046	1.63904	0.819520	−	0.573050i	$-0.194240\pi$
$883$	48.7046	1.63904	0.819520	+	0.573050i	$0.194240\pi$
$884$	−24.5532	−0.825815
$885$	−93.2800	−3.13557
$886$	−27.7411	−0.931979
$887$	49.3711	1.65772	0.828860	−	0.559457i	$-0.188990\pi$
$887$	49.3711	1.65772	0.828860	+	0.559457i	$0.188990\pi$
$888$	−7.46332	−0.250453
$889$	0	0
$890$	106.614	3.57369
$891$	8.11998	0.272030
$892$	22.2752	0.745830
$893$	0.0462772	0.00154861
$894$	95.5006	3.19402
$895$	49.6446	1.65944
$896$	0	0
$897$	−34.2255	−1.14275
$898$	−10.2203	−0.341056
$899$	−7.95965	−0.265469
$900$	48.9733	1.63244
$901$	−20.6378	−0.687544
$902$	18.6545	0.621129
$903$	0	0
$904$	19.3405	0.643254
$905$	−1.00386	−0.0333694
$906$	−51.0295	−1.69534
$907$	20.7996	0.690639	0.345319	−	0.938485i	$-0.387771\pi$
$907$	20.7996	0.690639	0.345319	+	0.938485i	$0.387771\pi$
$908$	−27.1431	−0.900774
$909$	31.4212	1.04217
$910$	0	0
$911$	−8.39246	−0.278054	−0.139027	−	0.990289i	$-0.544398\pi$
$911$	−8.39246	−0.278054	−0.139027	+	0.990289i	$0.544398\pi$
$912$	2.98113	0.0987151
$913$	−25.1244	−0.831497
$914$	−18.8801	−0.624497
$915$	46.7883	1.54677
$916$	6.09737	0.201463
$917$	0	0
$918$	−45.2133	−1.49226
$919$	0.0284221	0.000937558 0	0.000468779	−	1.00000i	$-0.499851\pi$
$919$	0.0284221	0.000937558 0	0.000468779		1.00000i	$0.499851\pi$
$920$	16.9242	0.557973
$921$	−88.8771	−2.92860
$922$	−17.6013	−0.579667
$923$	35.3802	1.16455
$924$	0	0
$925$	19.0614	0.626736
$926$	−30.6399	−1.00689
$927$	−34.2733	−1.12568
$928$	−53.2807	−1.74902
$929$	−11.7031	−0.383965	−0.191982	−	0.981398i	$-0.561492\pi$
$929$	−11.7031	−0.383965	−0.191982	+	0.981398i	$0.561492\pi$
$930$	−18.0550	−0.592047
$931$	0	0
$932$	16.0176	0.524675
$933$	−51.7515	−1.69427
$934$	−26.8460	−0.878429
$935$	77.1891	2.52435
$936$	−14.8034	−0.483866
$937$	−21.4568	−0.700964	−0.350482	−	0.936570i	$-0.613982\pi$
$937$	−21.4568	−0.700964	−0.350482	+	0.936570i	$0.613982\pi$
$938$	0	0
$939$	−71.9873	−2.34922
$940$	−1.02762	−0.0335173
$941$	−45.9270	−1.49718	−0.748588	−	0.663036i	$-0.769268\pi$
$941$	−45.9270	−1.49718	−0.748588	+	0.663036i	$0.769268\pi$
$942$	39.6507	1.29189
$943$	11.8838	0.386990
$944$	46.1123	1.50083
$945$	0	0
$946$	47.6216	1.54831
$947$	−46.2336	−1.50239	−0.751195	−	0.660080i	$-0.770522\pi$
$947$	−46.2336	−1.50239	−0.751195	+	0.660080i	$0.770522\pi$
$948$	46.9306	1.52423
$949$	−11.9758	−0.388752
$950$	−3.23081	−0.104821
$951$	17.6824	0.573391
$952$	0	0
$953$	−51.7628	−1.67676	−0.838381	−	0.545084i	$-0.816498\pi$
$953$	−51.7628	−1.67676	−0.838381	+	0.545084i	$0.816498\pi$
$954$	28.6492	0.927553
$955$	32.0940	1.03854
$956$	−19.3693	−0.626447
$957$	−78.7298	−2.54497
$958$	−11.7441	−0.379434
$959$	0	0
$960$	−25.9082	−0.836183
$961$	1.00000	0.0322581
$962$	13.2665	0.427728
$963$	27.6455	0.890863
$964$	11.7076	0.377076
$965$	22.7283	0.731650
$966$	0	0
$967$	−31.8519	−1.02429	−0.512144	−	0.858899i	$-0.671149\pi$
$967$	−31.8519	−1.02429	−0.512144	+	0.858899i	$0.671149\pi$
$968$	−2.28068	−0.0733038
$969$	3.67543	0.118072
$970$	−95.4954	−3.06617
$971$	−11.1667	−0.358358	−0.179179	−	0.983816i	$-0.557344\pi$
$971$	−11.1667	−0.358358	−0.179179	+	0.983816i	$0.557344\pi$
$972$	−25.7735	−0.826684
$973$	0	0
$974$	−52.5576	−1.68405
$975$	63.0121	2.01800
$976$	−23.1295	−0.740356
$977$	16.1348	0.516199	0.258099	−	0.966118i	$-0.416904\pi$
$977$	16.1348	0.516199	0.258099	+	0.966118i	$0.416904\pi$
$978$	−82.0274	−2.62295
$979$	−58.4063	−1.86667
$980$	0	0
$981$	51.2034	1.63480
$982$	20.7242	0.661337
$983$	2.37682	0.0758088	0.0379044	−	0.999281i	$-0.487932\pi$
$983$	2.37682	0.0758088	0.0379044	+	0.999281i	$0.487932\pi$
$984$	8.56657	0.273092
$985$	−3.99640	−0.127336
$986$	−87.5885	−2.78939
$987$	0	0
$988$	−0.923708	−0.0293871
$989$	30.3372	0.964666
$990$	−107.153	−3.40555
$991$	−28.6376	−0.909703	−0.454852	−	0.890567i	$-0.650308\pi$
$991$	−28.6376	−0.909703	−0.454852	+	0.890567i	$0.650308\pi$
$992$	6.69384	0.212530
$993$	48.9168	1.55233
$994$	0	0
$995$	−6.58332	−0.208705
$996$	26.5653	0.841753
$997$	34.9729	1.10760	0.553802	−	0.832648i	$-0.313176\pi$
$997$	34.9729	1.10760	0.553802	+	0.832648i	$0.313176\pi$
$998$	−14.3408	−0.453950
$999$	10.0354	0.317507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1519.2.a.j.1.10		13
7.3	odd	6		217.2.f.b.156.4	yes	26
7.5	odd	6		217.2.f.b.32.4	✓	26
7.6	odd	2		1519.2.a.k.1.10		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
217.2.f.b.32.4	✓	26	7.5	odd	6
217.2.f.b.156.4	yes	26	7.3	odd	6
1519.2.a.j.1.10		13	1.1	even	1	trivial
1519.2.a.k.1.10		13	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.84239 q^{2} +2.73867 q^{3} +1.39439 q^{4} +3.57831 q^{5} +5.04568 q^{6} -1.11576 q^{8} +4.50029 q^{9} +O(q^{10})\)	\(q+1.84239 q^{2} +2.73867 q^{3} +1.39439 q^{4} +3.57831 q^{5} +5.04568 q^{6} -1.11576 q^{8} +4.50029 q^{9} +6.59263 q^{10} -3.61166 q^{11} +3.81878 q^{12} +2.94816 q^{13} +9.79979 q^{15} -4.84445 q^{16} -5.97271 q^{17} +8.29128 q^{18} -0.224697 q^{19} +4.98957 q^{20} -6.65407 q^{22} -4.23895 q^{23} -3.05569 q^{24} +7.80428 q^{25} +5.43166 q^{26} +4.10879 q^{27} +7.95965 q^{29} +18.0550 q^{30} -1.00000 q^{31} -6.69384 q^{32} -9.89112 q^{33} -11.0041 q^{34} +6.27518 q^{36} +2.44243 q^{37} -0.413979 q^{38} +8.07403 q^{39} -3.99253 q^{40} -2.80348 q^{41} -7.15676 q^{43} -5.03607 q^{44} +16.1034 q^{45} -7.80980 q^{46} -0.205954 q^{47} -13.2673 q^{48} +14.3785 q^{50} -16.3573 q^{51} +4.11090 q^{52} +3.45534 q^{53} +7.56998 q^{54} -12.9236 q^{55} -0.615370 q^{57} +14.6648 q^{58} -9.51858 q^{59} +13.6648 q^{60} +4.77442 q^{61} -1.84239 q^{62} -2.64375 q^{64} +10.5494 q^{65} -18.2233 q^{66} -10.0640 q^{67} -8.32832 q^{68} -11.6091 q^{69} +12.0008 q^{71} -5.02124 q^{72} -4.06214 q^{73} +4.49991 q^{74} +21.3733 q^{75} -0.313316 q^{76} +14.8755 q^{78} +12.2894 q^{79} -17.3349 q^{80} -2.24827 q^{81} -5.16510 q^{82} +6.95648 q^{83} -21.3722 q^{85} -13.1855 q^{86} +21.7988 q^{87} +4.02974 q^{88} +16.1716 q^{89} +29.6687 q^{90} -5.91077 q^{92} -2.73867 q^{93} -0.379446 q^{94} -0.804035 q^{95} -18.3322 q^{96} -14.4852 q^{97} -16.2535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 5 q^{2} + 17 q^{4} - q^{5} + 2 q^{6} + 12 q^{8} + 25 q^{9}+O(q^{10}) \) 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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