LMFDB - Embedded newform 7007.2.a.w.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7007,2,Mod(1,7007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7007 = 7^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7007.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:	$55.9511766963$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 18x^{9} + 15x^{8} + 117x^{7} - 78x^{6} - 326x^{5} + 167x^{4} + 348x^{3} - 143x^{2} - 74x + 24 $ x^11 - x^10 - 18x^9 + 15x^8 + 117x^7 - 78x^6 - 326x^5 + 167x^4 + 348x^3 - 143x^2 - 74*x + 24
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 1001)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.72345$ of defining polynomial
Character	$\chi$	$=$	7007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.72345 q^{2} -1.94436 q^{3} +0.970287 q^{4} -2.87921 q^{5} -3.35102 q^{6} -1.77466 q^{8} +0.780553 q^{9} +O(q^{10})$	\(q+1.72345 q^{2} -1.94436 q^{3} +0.970287 q^{4} -2.87921 q^{5} -3.35102 q^{6} -1.77466 q^{8} +0.780553 q^{9} -4.96218 q^{10} +1.00000 q^{11} -1.88659 q^{12} -1.00000 q^{13} +5.59824 q^{15} -4.99912 q^{16} +1.03513 q^{17} +1.34525 q^{18} +3.77967 q^{19} -2.79366 q^{20} +1.72345 q^{22} +4.81227 q^{23} +3.45059 q^{24} +3.28986 q^{25} -1.72345 q^{26} +4.31541 q^{27} -2.49935 q^{29} +9.64829 q^{30} +3.70030 q^{31} -5.06642 q^{32} -1.94436 q^{33} +1.78400 q^{34} +0.757361 q^{36} +3.10095 q^{37} +6.51408 q^{38} +1.94436 q^{39} +5.10962 q^{40} +3.08866 q^{41} +2.77031 q^{43} +0.970287 q^{44} -2.24738 q^{45} +8.29371 q^{46} +1.01541 q^{47} +9.72011 q^{48} +5.66991 q^{50} -2.01267 q^{51} -0.970287 q^{52} +1.70518 q^{53} +7.43741 q^{54} -2.87921 q^{55} -7.34906 q^{57} -4.30751 q^{58} -12.6864 q^{59} +5.43190 q^{60} +11.8456 q^{61} +6.37729 q^{62} +1.26650 q^{64} +2.87921 q^{65} -3.35102 q^{66} -2.26886 q^{67} +1.00437 q^{68} -9.35680 q^{69} -11.5460 q^{71} -1.38522 q^{72} -3.92496 q^{73} +5.34435 q^{74} -6.39668 q^{75} +3.66737 q^{76} +3.35102 q^{78} -7.80949 q^{79} +14.3935 q^{80} -10.7324 q^{81} +5.32317 q^{82} -1.39326 q^{83} -2.98036 q^{85} +4.77450 q^{86} +4.85965 q^{87} -1.77466 q^{88} +6.58651 q^{89} -3.87325 q^{90} +4.66928 q^{92} -7.19474 q^{93} +1.75000 q^{94} -10.8825 q^{95} +9.85096 q^{96} -15.1174 q^{97} +0.780553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - q^{2} - 2 q^{3} + 15 q^{4} - 7 q^{5} - 3 q^{6} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 11 * q - q^2 - 2 * q^3 + 15 * q^4 - 7 * q^5 - 3 * q^6 - 6 * q^8 + 15 * q^9	$ 11 q - q^{2} - 2 q^{3} + 15 q^{4} - 7 q^{5} - 3 q^{6} - 6 q^{8} + 15 q^{9} - q^{10} + 11 q^{11} + 5 q^{12} - 11 q^{13} + 4 q^{15} + 15 q^{16} - 7 q^{17} - 17 q^{18} - 22 q^{19} - 6 q^{20} - q^{22} + 3 q^{23} - 17 q^{24} + 10 q^{25} + q^{26} - 2 q^{27} - 6 q^{29} - 40 q^{30} - 28 q^{31} - 23 q^{32} - 2 q^{33} - 19 q^{34} + 48 q^{36} + q^{37} + 20 q^{38} + 2 q^{39} - 16 q^{40} + 4 q^{41} - 8 q^{43} + 15 q^{44} - 12 q^{45} + 2 q^{46} - 22 q^{47} + 30 q^{48} - 24 q^{50} - 27 q^{51} - 15 q^{52} + 9 q^{53} - 36 q^{54} - 7 q^{55} - 34 q^{57} - 8 q^{58} + 2 q^{59} + 25 q^{60} - 8 q^{62} - 10 q^{64} + 7 q^{65} - 3 q^{66} + 23 q^{67} - 24 q^{68} - 7 q^{69} + 3 q^{71} - 76 q^{72} - 29 q^{73} + 15 q^{74} - 36 q^{75} - 62 q^{76} + 3 q^{78} + 26 q^{79} + 16 q^{80} + 7 q^{81} + 16 q^{82} - 9 q^{83} - 31 q^{85} + 28 q^{86} - 13 q^{87} - 6 q^{88} - 9 q^{89} + 26 q^{90} - 58 q^{92} - 24 q^{93} + 34 q^{94} - 14 q^{95} - 56 q^{96} - 40 q^{97} + 15 q^{99}+O(q^{100}) $ 11 * q - q^2 - 2 * q^3 + 15 * q^4 - 7 * q^5 - 3 * q^6 - 6 * q^8 + 15 * q^9 - q^10 + 11 * q^11 + 5 * q^12 - 11 * q^13 + 4 * q^15 + 15 * q^16 - 7 * q^17 - 17 * q^18 - 22 * q^19 - 6 * q^20 - q^22 + 3 * q^23 - 17 * q^24 + 10 * q^25 + q^26 - 2 * q^27 - 6 * q^29 - 40 * q^30 - 28 * q^31 - 23 * q^32 - 2 * q^33 - 19 * q^34 + 48 * q^36 + q^37 + 20 * q^38 + 2 * q^39 - 16 * q^40 + 4 * q^41 - 8 * q^43 + 15 * q^44 - 12 * q^45 + 2 * q^46 - 22 * q^47 + 30 * q^48 - 24 * q^50 - 27 * q^51 - 15 * q^52 + 9 * q^53 - 36 * q^54 - 7 * q^55 - 34 * q^57 - 8 * q^58 + 2 * q^59 + 25 * q^60 - 8 * q^62 - 10 * q^64 + 7 * q^65 - 3 * q^66 + 23 * q^67 - 24 * q^68 - 7 * q^69 + 3 * q^71 - 76 * q^72 - 29 * q^73 + 15 * q^74 - 36 * q^75 - 62 * q^76 + 3 * q^78 + 26 * q^79 + 16 * q^80 + 7 * q^81 + 16 * q^82 - 9 * q^83 - 31 * q^85 + 28 * q^86 - 13 * q^87 - 6 * q^88 - 9 * q^89 + 26 * q^90 - 58 * q^92 - 24 * q^93 + 34 * q^94 - 14 * q^95 - 56 * q^96 - 40 * q^97 + 15 * 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 $

$2$	1.72345	1.21866	0.609332	−	0.792915i	$-0.291438\pi$
$2$	1.72345	1.21866	0.609332	+	0.792915i	$0.291438\pi$
$3$	−1.94436	−1.12258	−0.561290	−	0.827619i	$-0.689695\pi$
$3$	−1.94436	−1.12258	−0.561290	+	0.827619i	$0.689695\pi$
$4$	0.970287	0.485144
$5$	−2.87921	−1.28762	−0.643811	−	0.765184i	$-0.722648\pi$
$5$	−2.87921	−1.28762	−0.643811	+	0.765184i	$0.722648\pi$
$6$	−3.35102	−1.36805
$7$	0	0
$7$	0	0
$8$	−1.77466	−0.627437
$9$	0.780553	0.260184
$10$	−4.96218	−1.56918
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.88659	−0.544612
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	5.59824	1.44546
$16$	−4.99912	−1.24978
$17$	1.03513	0.251056	0.125528	−	0.992090i	$-0.459938\pi$
$17$	1.03513	0.251056	0.125528	+	0.992090i	$0.459938\pi$
$18$	1.34525	0.317077
$19$	3.77967	0.867116	0.433558	−	0.901126i	$-0.357258\pi$
$19$	3.77967	0.867116	0.433558	+	0.901126i	$0.357258\pi$
$20$	−2.79366	−0.624682
$21$	0	0
$22$	1.72345	0.367441
$23$	4.81227	1.00343	0.501713	−	0.865034i	$-0.332703\pi$
$23$	4.81227	1.00343	0.501713	+	0.865034i	$0.332703\pi$
$24$	3.45059	0.704348
$25$	3.28986	0.657972
$26$	−1.72345	−0.337997
$27$	4.31541	0.830502
$28$	0	0
$29$	−2.49935	−0.464118	−0.232059	−	0.972702i	$-0.574546\pi$
$29$	−2.49935	−0.464118	−0.232059	+	0.972702i	$0.574546\pi$
$30$	9.64829	1.76153
$31$	3.70030	0.664594	0.332297	−	0.943175i	$-0.392176\pi$
$31$	3.70030	0.664594	0.332297	+	0.943175i	$0.392176\pi$
$32$	−5.06642	−0.895625
$33$	−1.94436	−0.338470
$34$	1.78400	0.305953
$35$	0	0
$36$	0.757361	0.126227
$37$	3.10095	0.509794	0.254897	−	0.966968i	$-0.417958\pi$
$37$	3.10095	0.509794	0.254897	+	0.966968i	$0.417958\pi$
$38$	6.51408	1.05672
$39$	1.94436	0.311347
$40$	5.10962	0.807902
$41$	3.08866	0.482368	0.241184	−	0.970479i	$-0.422464\pi$
$41$	3.08866	0.482368	0.241184	+	0.970479i	$0.422464\pi$
$42$	0	0
$43$	2.77031	0.422469	0.211234	−	0.977435i	$-0.432252\pi$
$43$	2.77031	0.422469	0.211234	+	0.977435i	$0.432252\pi$
$44$	0.970287	0.146276
$45$	−2.24738	−0.335019
$46$	8.29371	1.22284
$47$	1.01541	0.148112	0.0740561	−	0.997254i	$-0.476406\pi$
$47$	1.01541	0.148112	0.0740561	+	0.997254i	$0.476406\pi$
$48$	9.72011	1.40298
$49$	0	0
$50$	5.66991	0.801847
$51$	−2.01267	−0.281830
$52$	−0.970287	−0.134555
$53$	1.70518	0.234224	0.117112	−	0.993119i	$-0.462636\pi$
$53$	1.70518	0.234224	0.117112	+	0.993119i	$0.462636\pi$
$54$	7.43741	1.01210
$55$	−2.87921	−0.388233
$56$	0	0
$57$	−7.34906	−0.973406
$58$	−4.30751	−0.565604
$59$	−12.6864	−1.65163	−0.825816	−	0.563940i	$-0.809285\pi$
$59$	−12.6864	−1.65163	−0.825816	+	0.563940i	$0.809285\pi$
$60$	5.43190	0.701255
$61$	11.8456	1.51668	0.758338	−	0.651862i	$-0.226012\pi$
$61$	11.8456	1.51668	0.758338	+	0.651862i	$0.226012\pi$
$62$	6.37729	0.809917
$63$	0	0
$64$	1.26650	0.158313
$65$	2.87921	0.357122
$66$	−3.35102	−0.412482
$67$	−2.26886	−0.277185	−0.138593	−	0.990349i	$-0.544258\pi$
$67$	−2.26886	−0.277185	−0.138593	+	0.990349i	$0.544258\pi$
$68$	1.00437	0.121798
$69$	−9.35680	−1.12643
$70$	0	0
$71$	−11.5460	−1.37026	−0.685128	−	0.728423i	$-0.740254\pi$
$71$	−11.5460	−1.37026	−0.685128	+	0.728423i	$0.740254\pi$
$72$	−1.38522	−0.163249
$73$	−3.92496	−0.459382	−0.229691	−	0.973264i	$-0.573772\pi$
$73$	−3.92496	−0.459382	−0.229691	+	0.973264i	$0.573772\pi$
$74$	5.34435	0.621268
$75$	−6.39668	−0.738625
$76$	3.66737	0.420676
$77$	0	0
$78$	3.35102	0.379428
$79$	−7.80949	−0.878636	−0.439318	−	0.898332i	$-0.644780\pi$
$79$	−7.80949	−0.878636	−0.439318	+	0.898332i	$0.644780\pi$
$80$	14.3935	1.60924
$81$	−10.7324	−1.19249
$82$	5.32317	0.587845
$83$	−1.39326	−0.152930	−0.0764650	−	0.997072i	$-0.524363\pi$
$83$	−1.39326	−0.152930	−0.0764650	+	0.997072i	$0.524363\pi$
$84$	0	0
$85$	−2.98036	−0.323265
$86$	4.77450	0.514848
$87$	4.85965	0.521009
$88$	−1.77466	−0.189179
$89$	6.58651	0.698168	0.349084	−	0.937091i	$-0.386493\pi$
$89$	6.58651	0.698168	0.349084	+	0.937091i	$0.386493\pi$
$90$	−3.87325	−0.408276
$91$	0	0
$92$	4.66928	0.486806
$93$	−7.19474	−0.746059
$94$	1.75000	0.180499
$95$	−10.8825	−1.11652
$96$	9.85096	1.00541
$97$	−15.1174	−1.53494	−0.767472	−	0.641082i	$-0.778486\pi$
$97$	−15.1174	−1.53494	−0.767472	+	0.641082i	$0.778486\pi$
$98$	0	0
$99$	0.780553	0.0784485
$100$	3.19211	0.319211
$101$	−10.4474	−1.03955	−0.519775	−	0.854303i	$-0.673984\pi$
$101$	−10.4474	−1.03955	−0.519775	+	0.854303i	$0.673984\pi$
$102$	−3.46874	−0.343457
$103$	−9.02391	−0.889152	−0.444576	−	0.895741i	$-0.646646\pi$
$103$	−9.02391	−0.889152	−0.444576	+	0.895741i	$0.646646\pi$
$104$	1.77466	0.174020
$105$	0	0
$106$	2.93879	0.285441
$107$	2.89837	0.280196	0.140098	−	0.990138i	$-0.455258\pi$
$107$	2.89837	0.280196	0.140098	+	0.990138i	$0.455258\pi$
$108$	4.18719	0.402913
$109$	−15.6973	−1.50353	−0.751764	−	0.659432i	$-0.770797\pi$
$109$	−15.6973	−1.50353	−0.751764	+	0.659432i	$0.770797\pi$
$110$	−4.96218	−0.473126
$111$	−6.02939	−0.572284
$112$	0	0
$113$	15.2593	1.43547	0.717737	−	0.696314i	$-0.245178\pi$
$113$	15.2593	1.43547	0.717737	+	0.696314i	$0.245178\pi$
$114$	−12.6657	−1.18626
$115$	−13.8555	−1.29203
$116$	−2.42509	−0.225164
$117$	−0.780553	−0.0721621
$118$	−21.8644	−2.01279
$119$	0	0
$120$	−9.93497	−0.906934
$121$	1.00000	0.0909091
$122$	20.4153	1.84832
$123$	−6.00549	−0.541497
$124$	3.59036	0.322424
$125$	4.92386	0.440403
$126$	0	0
$127$	16.2764	1.44430	0.722148	−	0.691739i	$-0.243155\pi$
$127$	16.2764	1.44430	0.722148	+	0.691739i	$0.243155\pi$
$128$	12.3156	1.08856
$129$	−5.38650	−0.474255
$130$	4.96218	0.435212
$131$	11.9570	1.04469	0.522345	−	0.852734i	$-0.325057\pi$
$131$	11.9570	1.04469	0.522345	+	0.852734i	$0.325057\pi$
$132$	−1.88659	−0.164207
$133$	0	0
$134$	−3.91027	−0.337796
$135$	−12.4250	−1.06937
$136$	−1.83700	−0.157522
$137$	−8.62065	−0.736512	−0.368256	−	0.929725i	$-0.620045\pi$
$137$	−8.62065	−0.736512	−0.368256	+	0.929725i	$0.620045\pi$
$138$	−16.1260	−1.37274
$139$	−8.50892	−0.721717	−0.360859	−	0.932621i	$-0.617516\pi$
$139$	−8.50892	−0.721717	−0.360859	+	0.932621i	$0.617516\pi$
$140$	0	0
$141$	−1.97432	−0.166268
$142$	−19.8990	−1.66988
$143$	−1.00000	−0.0836242
$144$	−3.90208	−0.325173
$145$	7.19616	0.597609
$146$	−6.76448	−0.559833
$147$	0	0
$148$	3.00882	0.247323
$149$	18.5684	1.52118	0.760591	−	0.649231i	$-0.224909\pi$
$149$	18.5684	1.52118	0.760591	+	0.649231i	$0.224909\pi$
$150$	−11.0244	−0.900137
$151$	−12.2923	−1.00033	−0.500167	−	0.865929i	$-0.666728\pi$
$151$	−12.2923	−1.00033	−0.500167	+	0.865929i	$0.666728\pi$
$152$	−6.70763	−0.544061
$153$	0.807974	0.0653208
$154$	0	0
$155$	−10.6540	−0.855746
$156$	1.88659	0.151048
$157$	3.69196	0.294650	0.147325	−	0.989088i	$-0.452934\pi$
$157$	3.69196	0.294650	0.147325	+	0.989088i	$0.452934\pi$
$158$	−13.4593	−1.07076
$159$	−3.31549	−0.262935
$160$	14.5873	1.15323
$161$	0	0
$162$	−18.4968	−1.45324
$163$	−12.1805	−0.954049	−0.477025	−	0.878890i	$-0.658285\pi$
$163$	−12.1805	−0.954049	−0.477025	+	0.878890i	$0.658285\pi$
$164$	2.99689	0.234018
$165$	5.59824	0.435822
$166$	−2.40122	−0.186371
$167$	−10.6257	−0.822242	−0.411121	−	0.911581i	$-0.634863\pi$
$167$	−10.6257	−0.822242	−0.411121	+	0.911581i	$0.634863\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−5.13651	−0.393952
$171$	2.95023	0.225610
$172$	2.68800	0.204958
$173$	23.6962	1.80159	0.900796	−	0.434242i	$-0.142984\pi$
$173$	23.6962	1.80159	0.900796	+	0.434242i	$0.142984\pi$
$174$	8.37537	0.634936
$175$	0	0
$176$	−4.99912	−0.376823
$177$	24.6670	1.85409
$178$	11.3515	0.850833
$179$	11.3529	0.848557	0.424279	−	0.905532i	$-0.360528\pi$
$179$	11.3529	0.848557	0.424279	+	0.905532i	$0.360528\pi$
$180$	−2.18060	−0.162532
$181$	17.5961	1.30791	0.653953	−	0.756535i	$-0.273109\pi$
$181$	17.5961	1.30791	0.653953	+	0.756535i	$0.273109\pi$
$182$	0	0
$183$	−23.0322	−1.70259
$184$	−8.54014	−0.629587
$185$	−8.92830	−0.656422
$186$	−12.3998	−0.909196
$187$	1.03513	0.0756962
$188$	0.985236	0.0718557
$189$	0	0
$190$	−18.7554	−1.36066
$191$	0.551266	0.0398882	0.0199441	−	0.999801i	$-0.493651\pi$
$191$	0.551266	0.0398882	0.0199441	+	0.999801i	$0.493651\pi$
$192$	−2.46254	−0.177719
$193$	−3.94413	−0.283905	−0.141952	−	0.989874i	$-0.545338\pi$
$193$	−3.94413	−0.283905	−0.141952	+	0.989874i	$0.545338\pi$
$194$	−26.0542	−1.87058
$195$	−5.59824	−0.400898
$196$	0	0
$197$	−13.0818	−0.932041	−0.466021	−	0.884774i	$-0.654313\pi$
$197$	−13.0818	−0.932041	−0.466021	+	0.884774i	$0.654313\pi$
$198$	1.34525	0.0956024
$199$	−12.7655	−0.904923	−0.452462	−	0.891784i	$-0.649454\pi$
$199$	−12.7655	−0.904923	−0.452462	+	0.891784i	$0.649454\pi$
$200$	−5.83838	−0.412836
$201$	4.41149	0.311162
$202$	−18.0055	−1.26686
$203$	0	0
$204$	−1.95287	−0.136728
$205$	−8.89292	−0.621108
$206$	−15.5523	−1.08358
$207$	3.75623	0.261076
$208$	4.99912	0.346626
$209$	3.77967	0.261445
$210$	0	0
$211$	−20.0586	−1.38089	−0.690444	−	0.723385i	$-0.742585\pi$
$211$	−20.0586	−1.38089	−0.690444	+	0.723385i	$0.742585\pi$
$212$	1.65451	0.113632
$213$	22.4496	1.53822
$214$	4.99520	0.341465
$215$	−7.97631	−0.543980
$216$	−7.65839	−0.521088
$217$	0	0
$218$	−27.0535	−1.83230
$219$	7.63156	0.515693
$220$	−2.79366	−0.188349
$221$	−1.03513	−0.0696304
$222$	−10.3914	−0.697422
$223$	−10.7719	−0.721338	−0.360669	−	0.932694i	$-0.617452\pi$
$223$	−10.7719	−0.721338	−0.360669	+	0.932694i	$0.617452\pi$
$224$	0	0
$225$	2.56791	0.171194
$226$	26.2987	1.74936
$227$	1.46581	0.0972891	0.0486445	−	0.998816i	$-0.484510\pi$
$227$	1.46581	0.0972891	0.0486445	+	0.998816i	$0.484510\pi$
$228$	−7.13070	−0.472242
$229$	−22.7162	−1.50113	−0.750563	−	0.660799i	$-0.770218\pi$
$229$	−22.7162	−1.50113	−0.750563	+	0.660799i	$0.770218\pi$
$230$	−23.8793	−1.57456
$231$	0	0
$232$	4.43550	0.291205
$233$	13.9802	0.915872	0.457936	−	0.888985i	$-0.348589\pi$
$233$	13.9802	0.915872	0.457936	+	0.888985i	$0.348589\pi$
$234$	−1.34525	−0.0879414
$235$	−2.92357	−0.190713
$236$	−12.3095	−0.801279
$237$	15.1845	0.986339
$238$	0	0
$239$	−3.50685	−0.226839	−0.113420	−	0.993547i	$-0.536180\pi$
$239$	−3.50685	−0.226839	−0.113420	+	0.993547i	$0.536180\pi$
$240$	−27.9862	−1.80650
$241$	9.78814	0.630510	0.315255	−	0.949007i	$-0.397910\pi$
$241$	9.78814	0.630510	0.315255	+	0.949007i	$0.397910\pi$
$242$	1.72345	0.110788
$243$	7.92145	0.508161
$244$	11.4937	0.735806
$245$	0	0
$246$	−10.3502	−0.659903
$247$	−3.77967	−0.240495
$248$	−6.56678	−0.416991
$249$	2.70900	0.171676
$250$	8.48604	0.536704
$251$	−14.0207	−0.884977	−0.442489	−	0.896774i	$-0.645904\pi$
$251$	−14.0207	−0.884977	−0.442489	+	0.896774i	$0.645904\pi$
$252$	0	0
$253$	4.81227	0.302545
$254$	28.0516	1.76011
$255$	5.79490	0.362891
$256$	18.6923	1.16827
$257$	−24.6752	−1.53919	−0.769597	−	0.638530i	$-0.779543\pi$
$257$	−24.6752	−1.53919	−0.769597	+	0.638530i	$0.779543\pi$
$258$	−9.28337	−0.577957
$259$	0	0
$260$	2.79366	0.173256
$261$	−1.95088	−0.120756
$262$	20.6073	1.27313
$263$	7.25020	0.447067	0.223533	−	0.974696i	$-0.428241\pi$
$263$	7.25020	0.447067	0.223533	+	0.974696i	$0.428241\pi$
$264$	3.45059	0.212369
$265$	−4.90957	−0.301592
$266$	0	0
$267$	−12.8066	−0.783749
$268$	−2.20145	−0.134475
$269$	−14.6971	−0.896097	−0.448048	−	0.894009i	$-0.647881\pi$
$269$	−14.6971	−0.896097	−0.448048	+	0.894009i	$0.647881\pi$
$270$	−21.4139	−1.30321
$271$	−4.61422	−0.280294	−0.140147	−	0.990131i	$-0.544758\pi$
$271$	−4.61422	−0.280294	−0.140147	+	0.990131i	$0.544758\pi$
$272$	−5.17474	−0.313765
$273$	0	0
$274$	−14.8573	−0.897561
$275$	3.28986	0.198386
$276$	−9.07878	−0.546479
$277$	−25.0313	−1.50399	−0.751993	−	0.659171i	$-0.770907\pi$
$277$	−25.0313	−1.50399	−0.751993	+	0.659171i	$0.770907\pi$
$278$	−14.6647	−0.879531
$279$	2.88828	0.172917
$280$	0	0
$281$	−13.0057	−0.775855	−0.387927	−	0.921690i	$-0.626809\pi$
$281$	−13.0057	−0.775855	−0.387927	+	0.921690i	$0.626809\pi$
$282$	−3.40264	−0.202625
$283$	−2.68107	−0.159373	−0.0796864	−	0.996820i	$-0.525392\pi$
$283$	−2.68107	−0.159373	−0.0796864	+	0.996820i	$0.525392\pi$
$284$	−11.2029	−0.664771
$285$	21.1595	1.25338
$286$	−1.72345	−0.101910
$287$	0	0
$288$	−3.95461	−0.233027
$289$	−15.9285	−0.936971
$290$	12.4022	0.728285
$291$	29.3938	1.72310
$292$	−3.80834	−0.222866
$293$	−15.9085	−0.929385	−0.464693	−	0.885472i	$-0.653835\pi$
$293$	−15.9085	−0.929385	−0.464693	+	0.885472i	$0.653835\pi$
$294$	0	0
$295$	36.5269	2.12668
$296$	−5.50314	−0.319864
$297$	4.31541	0.250406
$298$	32.0017	1.85381
$299$	−4.81227	−0.278301
$300$	−6.20662	−0.358339
$301$	0	0
$302$	−21.1852	−1.21907
$303$	20.3135	1.16698
$304$	−18.8950	−1.08370
$305$	−34.1060	−1.95291
$306$	1.39250	0.0796042
$307$	−27.0504	−1.54385	−0.771925	−	0.635714i	$-0.780706\pi$
$307$	−27.0504	−1.54385	−0.771925	+	0.635714i	$0.780706\pi$
$308$	0	0
$309$	17.5458	0.998144
$310$	−18.3616	−1.04287
$311$	17.7956	1.00910	0.504548	−	0.863384i	$-0.331659\pi$
$311$	17.7956	1.00910	0.504548	+	0.863384i	$0.331659\pi$
$312$	−3.45059	−0.195351
$313$	22.8496	1.29153	0.645767	−	0.763534i	$-0.276538\pi$
$313$	22.8496	1.29153	0.645767	+	0.763534i	$0.276538\pi$
$314$	6.36291	0.359080
$315$	0	0
$316$	−7.57745	−0.426265
$317$	21.4245	1.20332	0.601660	−	0.798752i	$-0.294506\pi$
$317$	21.4245	1.20332	0.601660	+	0.798752i	$0.294506\pi$
$318$	−5.71408	−0.320430
$319$	−2.49935	−0.139937
$320$	−3.64653	−0.203847
$321$	−5.63548	−0.314542
$322$	0	0
$323$	3.91245	0.217695
$324$	−10.4135	−0.578528
$325$	−3.28986	−0.182489
$326$	−20.9925	−1.16267
$327$	30.5213	1.68783
$328$	−5.48133	−0.302656
$329$	0	0
$330$	9.64829	0.531121
$331$	27.9542	1.53650	0.768250	−	0.640150i	$-0.221128\pi$
$331$	27.9542	1.53650	0.768250	+	0.640150i	$0.221128\pi$
$332$	−1.35186	−0.0741931
$333$	2.42046	0.132640
$334$	−18.3129	−1.00204
$335$	6.53253	0.356910
$336$	0	0
$337$	−18.4576	−1.00545	−0.502725	−	0.864446i	$-0.667669\pi$
$337$	−18.4576	−1.00545	−0.502725	+	0.864446i	$0.667669\pi$
$338$	1.72345	0.0937434
$339$	−29.6696	−1.61143
$340$	−2.89180	−0.156830
$341$	3.70030	0.200383
$342$	5.08458	0.274943
$343$	0	0
$344$	−4.91636	−0.265073
$345$	26.9402	1.45041
$346$	40.8394	2.19554
$347$	−2.70175	−0.145037	−0.0725187	−	0.997367i	$-0.523104\pi$
$347$	−2.70175	−0.145037	−0.0725187	+	0.997367i	$0.523104\pi$
$348$	4.71526	0.252764
$349$	19.0171	1.01796	0.508980	−	0.860778i	$-0.330023\pi$
$349$	19.0171	1.01796	0.508980	+	0.860778i	$0.330023\pi$
$350$	0	0
$351$	−4.31541	−0.230340
$352$	−5.06642	−0.270041
$353$	1.19490	0.0635980	0.0317990	−	0.999494i	$-0.489876\pi$
$353$	1.19490	0.0635980	0.0317990	+	0.999494i	$0.489876\pi$
$354$	42.5124	2.25951
$355$	33.2433	1.76437
$356$	6.39081	0.338712
$357$	0	0
$358$	19.5662	1.03411
$359$	−2.19748	−0.115979	−0.0579893	−	0.998317i	$-0.518469\pi$
$359$	−2.19748	−0.115979	−0.0579893	+	0.998317i	$0.518469\pi$
$360$	3.98833	0.210203
$361$	−4.71409	−0.248110
$362$	30.3260	1.59390
$363$	−1.94436	−0.102053
$364$	0	0
$365$	11.3008	0.591511
$366$	−39.6949	−2.07488
$367$	−16.6210	−0.867611	−0.433805	−	0.901007i	$-0.642829\pi$
$367$	−16.6210	−0.867611	−0.433805	+	0.901007i	$0.642829\pi$
$368$	−24.0571	−1.25406
$369$	2.41087	0.125505
$370$	−15.3875	−0.799958
$371$	0	0
$372$	−6.98096	−0.361946
$373$	25.9831	1.34536	0.672678	−	0.739935i	$-0.265144\pi$
$373$	25.9831	1.34536	0.672678	+	0.739935i	$0.265144\pi$
$374$	1.78400	0.0922483
$375$	−9.57378	−0.494388
$376$	−1.80200	−0.0929311
$377$	2.49935	0.128723
$378$	0	0
$379$	−7.62905	−0.391878	−0.195939	−	0.980616i	$-0.562775\pi$
$379$	−7.62905	−0.391878	−0.195939	+	0.980616i	$0.562775\pi$
$380$	−10.5591	−0.541672
$381$	−31.6472	−1.62134
$382$	0.950081	0.0486104
$383$	3.76269	0.192265	0.0961323	−	0.995369i	$-0.469353\pi$
$383$	3.76269	0.192265	0.0961323	+	0.995369i	$0.469353\pi$
$384$	−23.9460	−1.22199
$385$	0	0
$386$	−6.79752	−0.345984
$387$	2.16238	0.109920
$388$	−14.6683	−0.744669
$389$	−25.0146	−1.26829	−0.634145	−	0.773214i	$-0.718648\pi$
$389$	−25.0146	−1.26829	−0.634145	+	0.773214i	$0.718648\pi$
$390$	−9.64829	−0.488560
$391$	4.98132	0.251916
$392$	0	0
$393$	−23.2488	−1.17275
$394$	−22.5459	−1.13585
$395$	22.4852	1.13135
$396$	0.757361	0.0380588
$397$	−32.6317	−1.63774	−0.818869	−	0.573981i	$-0.805399\pi$
$397$	−32.6317	−1.63774	−0.818869	+	0.573981i	$0.805399\pi$
$398$	−22.0008	−1.10280
$399$	0	0
$400$	−16.4464	−0.822319
$401$	7.33420	0.366253	0.183126	−	0.983089i	$-0.441378\pi$
$401$	7.33420	0.366253	0.183126	+	0.983089i	$0.441378\pi$
$402$	7.60299	0.379203
$403$	−3.70030	−0.184325
$404$	−10.1369	−0.504331
$405$	30.9008	1.53547
$406$	0	0
$407$	3.10095	0.153709
$408$	3.57181	0.176831
$409$	3.76552	0.186193	0.0930966	−	0.995657i	$-0.470323\pi$
$409$	3.76552	0.186193	0.0930966	+	0.995657i	$0.470323\pi$
$410$	−15.3265	−0.756923
$411$	16.7617	0.826793
$412$	−8.75579	−0.431367
$413$	0	0
$414$	6.47368	0.318164
$415$	4.01149	0.196916
$416$	5.06642	0.248402
$417$	16.5444	0.810185
$418$	6.51408	0.318614
$419$	10.3298	0.504644	0.252322	−	0.967643i	$-0.418806\pi$
$419$	10.3298	0.504644	0.252322	+	0.967643i	$0.418806\pi$
$420$	0	0
$421$	16.9650	0.826825	0.413413	−	0.910544i	$-0.364337\pi$
$421$	16.9650	0.826825	0.413413	+	0.910544i	$0.364337\pi$
$422$	−34.5700	−1.68284
$423$	0.792578	0.0385365
$424$	−3.02611	−0.146961
$425$	3.40543	0.165188
$426$	38.6908	1.87458
$427$	0	0
$428$	2.81225	0.135935
$429$	1.94436	0.0938748
$430$	−13.7468	−0.662929
$431$	−24.1799	−1.16471	−0.582353	−	0.812936i	$-0.697868\pi$
$431$	−24.1799	−1.16471	−0.582353	+	0.812936i	$0.697868\pi$
$432$	−21.5733	−1.03794
$433$	−19.1566	−0.920608	−0.460304	−	0.887761i	$-0.652260\pi$
$433$	−19.1566	−0.920608	−0.460304	+	0.887761i	$0.652260\pi$
$434$	0	0
$435$	−13.9920	−0.670863
$436$	−15.2309	−0.729427
$437$	18.1888	0.870087
$438$	13.1526	0.628457
$439$	−40.0714	−1.91250	−0.956252	−	0.292545i	$-0.905498\pi$
$439$	−40.0714	−1.91250	−0.956252	+	0.292545i	$0.905498\pi$
$440$	5.10962	0.243592
$441$	0	0
$442$	−1.78400	−0.0848561
$443$	−15.2894	−0.726420	−0.363210	−	0.931707i	$-0.618319\pi$
$443$	−15.2894	−0.726420	−0.363210	+	0.931707i	$0.618319\pi$
$444$	−5.85024	−0.277640
$445$	−18.9639	−0.898977
$446$	−18.5648	−0.879069
$447$	−36.1037	−1.70765
$448$	0	0
$449$	6.65972	0.314292	0.157146	−	0.987575i	$-0.449771\pi$
$449$	6.65972	0.314292	0.157146	+	0.987575i	$0.449771\pi$
$450$	4.42567	0.208628
$451$	3.08866	0.145440
$452$	14.8059	0.696411
$453$	23.9007	1.12295
$454$	2.52625	0.118563
$455$	0	0
$456$	13.0421	0.610751
$457$	2.84735	0.133193	0.0665967	−	0.997780i	$-0.478786\pi$
$457$	2.84735	0.133193	0.0665967	+	0.997780i	$0.478786\pi$
$458$	−39.1502	−1.82937
$459$	4.46702	0.208502
$460$	−13.4438	−0.626823
$461$	−26.4112	−1.23009	−0.615045	−	0.788492i	$-0.710862\pi$
$461$	−26.4112	−1.23009	−0.615045	+	0.788492i	$0.710862\pi$
$462$	0	0
$463$	18.2720	0.849172	0.424586	−	0.905388i	$-0.360420\pi$
$463$	18.2720	0.849172	0.424586	+	0.905388i	$0.360420\pi$
$464$	12.4946	0.580045
$465$	20.7152	0.960643
$466$	24.0942	1.11614
$467$	−4.52674	−0.209472	−0.104736	−	0.994500i	$-0.533400\pi$
$467$	−4.52674	−0.209472	−0.104736	+	0.994500i	$0.533400\pi$
$468$	−0.757361	−0.0350090
$469$	0	0
$470$	−5.03863	−0.232415
$471$	−7.17851	−0.330768
$472$	22.5141	1.03630
$473$	2.77031	0.127379
$474$	26.1698	1.20202
$475$	12.4346	0.570538
$476$	0	0
$477$	1.33098	0.0609415
$478$	−6.04389	−0.276441
$479$	8.24909	0.376911	0.188455	−	0.982082i	$-0.439652\pi$
$479$	8.24909	0.376911	0.188455	+	0.982082i	$0.439652\pi$
$480$	−28.3630	−1.29459
$481$	−3.10095	−0.141391
$482$	16.8694	0.768380
$483$	0	0
$484$	0.970287	0.0441040
$485$	43.5263	1.97643
$486$	13.6522	0.619278
$487$	20.4246	0.925527	0.462763	−	0.886482i	$-0.346858\pi$
$487$	20.4246	0.925527	0.462763	+	0.886482i	$0.346858\pi$
$488$	−21.0219	−0.951619
$489$	23.6833	1.07100
$490$	0	0
$491$	37.6909	1.70097	0.850483	−	0.526003i	$-0.176310\pi$
$491$	37.6909	1.70097	0.850483	+	0.526003i	$0.176310\pi$
$492$	−5.82705	−0.262704
$493$	−2.58715	−0.116520
$494$	−6.51408	−0.293082
$495$	−2.24738	−0.101012
$496$	−18.4982	−0.830596
$497$	0	0
$498$	4.66884	0.209216
$499$	35.5360	1.59081	0.795404	−	0.606080i	$-0.207259\pi$
$499$	35.5360	1.59081	0.795404	+	0.606080i	$0.207259\pi$
$500$	4.77756	0.213659
$501$	20.6602	0.923032
$502$	−24.1640	−1.07849
$503$	4.37096	0.194892	0.0974458	−	0.995241i	$-0.468933\pi$
$503$	4.37096	0.194892	0.0974458	+	0.995241i	$0.468933\pi$
$504$	0	0
$505$	30.0801	1.33855
$506$	8.29371	0.368700
$507$	−1.94436	−0.0863523
$508$	15.7928	0.700691
$509$	−4.03288	−0.178754	−0.0893772	−	0.995998i	$-0.528488\pi$
$509$	−4.03288	−0.178754	−0.0893772	+	0.995998i	$0.528488\pi$
$510$	9.98724	0.442242
$511$	0	0
$512$	7.58415	0.335175
$513$	16.3108	0.720141
$514$	−42.5265	−1.87576
$515$	25.9817	1.14489
$516$	−5.22645	−0.230082
$517$	1.01541	0.0446575
$518$	0	0
$519$	−46.0741	−2.02243
$520$	−5.10962	−0.224072
$521$	10.7797	0.472267	0.236134	−	0.971721i	$-0.424120\pi$
$521$	10.7797	0.472267	0.236134	+	0.971721i	$0.424120\pi$
$522$	−3.36224	−0.147161
$523$	−23.9060	−1.04533	−0.522667	−	0.852537i	$-0.675063\pi$
$523$	−23.9060	−1.04533	−0.522667	+	0.852537i	$0.675063\pi$
$524$	11.6017	0.506825
$525$	0	0
$526$	12.4954	0.544824
$527$	3.83029	0.166850
$528$	9.72011	0.423013
$529$	0.157900	0.00686521
$530$	−8.46141	−0.367540
$531$	−9.90242	−0.429729
$532$	0	0
$533$	−3.08866	−0.133785
$534$	−22.0715	−0.955128
$535$	−8.34501	−0.360786
$536$	4.02645	0.173916
$537$	−22.0742	−0.952573
$538$	−25.3297	−1.09204
$539$	0	0
$540$	−12.0558	−0.518800
$541$	40.2380	1.72996	0.864982	−	0.501802i	$-0.167330\pi$
$541$	40.2380	1.72996	0.864982	+	0.501802i	$0.167330\pi$
$542$	−7.95239	−0.341585
$543$	−34.2132	−1.46823
$544$	−5.24440	−0.224852
$545$	45.1958	1.93598
$546$	0	0
$547$	−4.01979	−0.171874	−0.0859369	−	0.996301i	$-0.527388\pi$
$547$	−4.01979	−0.171874	−0.0859369	+	0.996301i	$0.527388\pi$
$548$	−8.36451	−0.357314
$549$	9.24613	0.394615
$550$	5.66991	0.241766
$551$	−9.44672	−0.402444
$552$	16.6051	0.706762
$553$	0	0
$554$	−43.1403	−1.83285
$555$	17.3599	0.736886
$556$	−8.25610	−0.350137
$557$	−12.8281	−0.543545	−0.271773	−	0.962362i	$-0.587610\pi$
$557$	−12.8281	−0.543545	−0.271773	+	0.962362i	$0.587610\pi$
$558$	4.97781	0.210728
$559$	−2.77031	−0.117172
$560$	0	0
$561$	−2.01267	−0.0849750
$562$	−22.4147	−0.945507
$563$	6.18807	0.260796	0.130398	−	0.991462i	$-0.458374\pi$
$563$	6.18807	0.260796	0.130398	+	0.991462i	$0.458374\pi$
$564$	−1.91566	−0.0806637
$565$	−43.9347	−1.84835
$566$	−4.62069	−0.194222
$567$	0	0
$568$	20.4902	0.859750
$569$	−37.7901	−1.58424	−0.792121	−	0.610364i	$-0.791023\pi$
$569$	−37.7901	−1.58424	−0.792121	+	0.610364i	$0.791023\pi$
$570$	36.4674	1.52745
$571$	−22.2849	−0.932592	−0.466296	−	0.884629i	$-0.654412\pi$
$571$	−22.2849	−0.932592	−0.466296	+	0.884629i	$0.654412\pi$
$572$	−0.970287	−0.0405698
$573$	−1.07186	−0.0447777
$574$	0	0
$575$	15.8317	0.660226
$576$	0.988573	0.0411905
$577$	−31.8317	−1.32517	−0.662585	−	0.748987i	$-0.730541\pi$
$577$	−31.8317	−1.32517	−0.662585	+	0.748987i	$0.730541\pi$
$578$	−27.4520	−1.14185
$579$	7.66882	0.318705
$580$	6.98235	0.289926
$581$	0	0
$582$	50.6589	2.09988
$583$	1.70518	0.0706213
$584$	6.96547	0.288233
$585$	2.24738	0.0929176
$586$	−27.4176	−1.13261
$587$	5.99885	0.247599	0.123800	−	0.992307i	$-0.460492\pi$
$587$	5.99885	0.247599	0.123800	+	0.992307i	$0.460492\pi$
$588$	0	0
$589$	13.9859	0.576280
$590$	62.9524	2.59171
$591$	25.4358	1.04629
$592$	−15.5020	−0.637130
$593$	−3.90931	−0.160536	−0.0802681	−	0.996773i	$-0.525578\pi$
$593$	−3.90931	−0.160536	−0.0802681	+	0.996773i	$0.525578\pi$
$594$	7.43741	0.305161
$595$	0	0
$596$	18.0167	0.737992
$597$	24.8208	1.01585
$598$	−8.29371	−0.339155
$599$	−4.07150	−0.166357	−0.0831786	−	0.996535i	$-0.526507\pi$
$599$	−4.07150	−0.166357	−0.0831786	+	0.996535i	$0.526507\pi$
$600$	11.3519	0.463441
$601$	42.7755	1.74485	0.872425	−	0.488747i	$-0.162546\pi$
$601$	42.7755	1.74485	0.872425	+	0.488747i	$0.162546\pi$
$602$	0	0
$603$	−1.77096	−0.0721193
$604$	−11.9271	−0.485306
$605$	−2.87921	−0.117057
$606$	35.0093	1.42215
$607$	−7.75409	−0.314729	−0.157364	−	0.987541i	$-0.550300\pi$
$607$	−7.75409	−0.314729	−0.157364	+	0.987541i	$0.550300\pi$
$608$	−19.1494	−0.776610
$609$	0	0
$610$	−58.7801	−2.37994
$611$	−1.01541	−0.0410789
$612$	0.783967	0.0316900
$613$	28.4076	1.14737	0.573686	−	0.819075i	$-0.305513\pi$
$613$	28.4076	1.14737	0.573686	+	0.819075i	$0.305513\pi$
$614$	−46.6201	−1.88143
$615$	17.2911	0.697243
$616$	0	0
$617$	−18.3782	−0.739880	−0.369940	−	0.929056i	$-0.620622\pi$
$617$	−18.3782	−0.739880	−0.369940	+	0.929056i	$0.620622\pi$
$618$	30.2393	1.21640
$619$	24.0955	0.968482	0.484241	−	0.874935i	$-0.339096\pi$
$619$	24.0955	0.968482	0.484241	+	0.874935i	$0.339096\pi$
$620$	−10.3374	−0.415160
$621$	20.7669	0.833348
$622$	30.6698	1.22975
$623$	0	0
$624$	−9.72011	−0.389116
$625$	−30.6261	−1.22504
$626$	39.3801	1.57395
$627$	−7.34906	−0.293493
$628$	3.58226	0.142948
$629$	3.20989	0.127987
$630$	0	0
$631$	23.1221	0.920477	0.460239	−	0.887795i	$-0.347764\pi$
$631$	23.1221	0.920477	0.460239	+	0.887795i	$0.347764\pi$
$632$	13.8592	0.551289
$633$	39.0012	1.55016
$634$	36.9241	1.46644
$635$	−46.8632	−1.85971
$636$	−3.21698	−0.127561
$637$	0	0
$638$	−4.30751	−0.170536
$639$	−9.01225	−0.356519
$640$	−35.4592	−1.40165
$641$	−38.2805	−1.51199	−0.755994	−	0.654578i	$-0.772846\pi$
$641$	−38.2805	−1.51199	−0.755994	+	0.654578i	$0.772846\pi$
$642$	−9.71249	−0.383321
$643$	−46.6257	−1.83874	−0.919369	−	0.393397i	$-0.871300\pi$
$643$	−46.6257	−1.83874	−0.919369	+	0.393397i	$0.871300\pi$
$644$	0	0
$645$	15.5089	0.610661
$646$	6.74292	0.265297
$647$	44.7530	1.75942	0.879711	−	0.475509i	$-0.157736\pi$
$647$	44.7530	1.75942	0.879711	+	0.475509i	$0.157736\pi$
$648$	19.0464	0.748212
$649$	−12.6864	−0.497986
$650$	−5.66991	−0.222392
$651$	0	0
$652$	−11.8186	−0.462851
$653$	0.202996	0.00794384	0.00397192	−	0.999992i	$-0.498736\pi$
$653$	0.202996	0.00794384	0.00397192	+	0.999992i	$0.498736\pi$
$654$	52.6019	2.05690
$655$	−34.4268	−1.34517
$656$	−15.4406	−0.602854
$657$	−3.06364	−0.119524
$658$	0	0
$659$	−19.7867	−0.770779	−0.385389	−	0.922754i	$-0.625933\pi$
$659$	−19.7867	−0.770779	−0.385389	+	0.922754i	$0.625933\pi$
$660$	5.43190	0.211436
$661$	31.3250	1.21840	0.609201	−	0.793016i	$-0.291490\pi$
$661$	31.3250	1.21840	0.609201	+	0.793016i	$0.291490\pi$
$662$	48.1777	1.87248
$663$	2.01267	0.0781656
$664$	2.47256	0.0959540
$665$	0	0
$666$	4.17155	0.161644
$667$	−12.0275	−0.465708
$668$	−10.3100	−0.398905
$669$	20.9444	0.809759
$670$	11.2585	0.434954
$671$	11.8456	0.457295
$672$	0	0
$673$	21.2057	0.817419	0.408710	−	0.912665i	$-0.365979\pi$
$673$	21.2057	0.817419	0.408710	+	0.912665i	$0.365979\pi$
$674$	−31.8108	−1.22531
$675$	14.1971	0.546447
$676$	0.970287	0.0373187
$677$	11.8192	0.454249	0.227124	−	0.973866i	$-0.427068\pi$
$677$	11.8192	0.454249	0.227124	+	0.973866i	$0.427068\pi$
$678$	−51.1342	−1.96380
$679$	0	0
$680$	5.28912	0.202829
$681$	−2.85006	−0.109215
$682$	6.37729	0.244199
$683$	5.78690	0.221430	0.110715	−	0.993852i	$-0.464686\pi$
$683$	5.78690	0.221430	0.110715	+	0.993852i	$0.464686\pi$
$684$	2.86257	0.109453
$685$	24.8207	0.948349
$686$	0	0
$687$	44.1685	1.68513
$688$	−13.8491	−0.527993
$689$	−1.70518	−0.0649621
$690$	46.4301	1.76757
$691$	16.2134	0.616787	0.308393	−	0.951259i	$-0.400209\pi$
$691$	16.2134	0.616787	0.308393	+	0.951259i	$0.400209\pi$
$692$	22.9922	0.874031
$693$	0	0
$694$	−4.65633	−0.176752
$695$	24.4990	0.929299
$696$	−8.62423	−0.326901
$697$	3.19717	0.121101
$698$	32.7750	1.24055
$699$	−27.1826	−1.02814
$700$	0	0
$701$	−27.6708	−1.04511	−0.522555	−	0.852606i	$-0.675021\pi$
$701$	−27.6708	−1.04511	−0.522555	+	0.852606i	$0.675021\pi$
$702$	−7.43741	−0.280707
$703$	11.7206	0.442050
$704$	1.26650	0.0477331
$705$	5.68448	0.214090
$706$	2.05935	0.0775046
$707$	0	0
$708$	23.9341	0.899499
$709$	−9.31849	−0.349963	−0.174982	−	0.984572i	$-0.555987\pi$
$709$	−9.31849	−0.349963	−0.174982	+	0.984572i	$0.555987\pi$
$710$	57.2933	2.15018
$711$	−6.09572	−0.228607
$712$	−11.6888	−0.438057
$713$	17.8068	0.666871
$714$	0	0
$715$	2.87921	0.107676
$716$	11.0156	0.411672
$717$	6.81860	0.254645
$718$	−3.78725	−0.141339
$719$	−42.3895	−1.58086	−0.790430	−	0.612552i	$-0.790143\pi$
$719$	−42.3895	−1.58086	−0.790430	+	0.612552i	$0.790143\pi$
$720$	11.2349	0.418700
$721$	0	0
$722$	−8.12452	−0.302363
$723$	−19.0317	−0.707797
$724$	17.0732	0.634522
$725$	−8.22251	−0.305376
$726$	−3.35102	−0.124368
$727$	−17.6216	−0.653549	−0.326775	−	0.945102i	$-0.605962\pi$
$727$	−17.6216	−0.653549	−0.326775	+	0.945102i	$0.605962\pi$
$728$	0	0
$729$	16.7950	0.622037
$730$	19.4764	0.720853
$731$	2.86763	0.106063
$732$	−22.3478	−0.826000
$733$	−42.1457	−1.55669	−0.778343	−	0.627839i	$-0.783940\pi$
$733$	−42.1457	−1.55669	−0.778343	+	0.627839i	$0.783940\pi$
$734$	−28.6455	−1.05733
$735$	0	0
$736$	−24.3810	−0.898694
$737$	−2.26886	−0.0835745
$738$	4.15501	0.152948
$739$	18.6080	0.684506	0.342253	−	0.939608i	$-0.388810\pi$
$739$	18.6080	0.684506	0.342253	+	0.939608i	$0.388810\pi$
$740$	−8.66302	−0.318459
$741$	7.34906	0.269974
$742$	0	0
$743$	6.81625	0.250064	0.125032	−	0.992153i	$-0.460097\pi$
$743$	6.81625	0.250064	0.125032	+	0.992153i	$0.460097\pi$
$744$	12.7682	0.468105
$745$	−53.4623	−1.95871
$746$	44.7807	1.63954
$747$	−1.08751	−0.0397900
$748$	1.00437	0.0367235
$749$	0	0
$750$	−16.4999	−0.602493
$751$	−40.2134	−1.46741	−0.733704	−	0.679469i	$-0.762210\pi$
$751$	−40.2134	−1.46741	−0.733704	+	0.679469i	$0.762210\pi$
$752$	−5.07613	−0.185108
$753$	27.2613	0.993457
$754$	4.30751	0.156870
$755$	35.3921	1.28805
$756$	0	0
$757$	−19.9894	−0.726526	−0.363263	−	0.931687i	$-0.618337\pi$
$757$	−19.9894	−0.726526	−0.363263	+	0.931687i	$0.618337\pi$
$758$	−13.1483	−0.477568
$759$	−9.35680	−0.339630
$760$	19.3127	0.700545
$761$	−24.0360	−0.871304	−0.435652	−	0.900115i	$-0.643482\pi$
$761$	−24.0360	−0.871304	−0.435652	+	0.900115i	$0.643482\pi$
$762$	−54.5425	−1.97587
$763$	0	0
$764$	0.534887	0.0193515
$765$	−2.32633	−0.0841085
$766$	6.48482	0.234306
$767$	12.6864	0.458080
$768$	−36.3447	−1.31148
$769$	−13.0814	−0.471729	−0.235864	−	0.971786i	$-0.575792\pi$
$769$	−13.0814	−0.471729	−0.235864	+	0.971786i	$0.575792\pi$
$770$	0	0
$771$	47.9775	1.72787
$772$	−3.82694	−0.137735
$773$	−5.98717	−0.215343	−0.107672	−	0.994187i	$-0.534340\pi$
$773$	−5.98717	−0.215343	−0.107672	+	0.994187i	$0.534340\pi$
$774$	3.72675	0.133955
$775$	12.1735	0.437284
$776$	26.8283	0.963081
$777$	0	0
$778$	−43.1115	−1.54562
$779$	11.6741	0.418269
$780$	−5.43190	−0.194493
$781$	−11.5460	−0.413148
$782$	8.58507	0.307001
$783$	−10.7857	−0.385451
$784$	0	0
$785$	−10.6299	−0.379398
$786$	−40.0682	−1.42919
$787$	14.3995	0.513287	0.256644	−	0.966506i	$-0.417383\pi$
$787$	14.3995	0.513287	0.256644	+	0.966506i	$0.417383\pi$
$788$	−12.6931	−0.452174
$789$	−14.0970	−0.501868
$790$	38.7521	1.37874
$791$	0	0
$792$	−1.38522	−0.0492215
$793$	−11.8456	−0.420650
$794$	−56.2392	−1.99585
$795$	9.54599	0.338561
$796$	−12.3862	−0.439018
$797$	−14.6705	−0.519656	−0.259828	−	0.965655i	$-0.583666\pi$
$797$	−14.6705	−0.519656	−0.259828	+	0.965655i	$0.583666\pi$
$798$	0	0
$799$	1.05108	0.0371844
$800$	−16.6678	−0.589296
$801$	5.14112	0.181652
$802$	12.6401	0.446339
$803$	−3.92496	−0.138509
$804$	4.28041	0.150959
$805$	0	0
$806$	−6.37729	−0.224631
$807$	28.5765	1.00594
$808$	18.5405	0.652252
$809$	−16.1263	−0.566969	−0.283485	−	0.958977i	$-0.591491\pi$
$809$	−16.1263	−0.566969	−0.283485	+	0.958977i	$0.591491\pi$
$810$	53.2561	1.87123
$811$	22.8313	0.801715	0.400857	−	0.916140i	$-0.368712\pi$
$811$	22.8313	0.801715	0.400857	+	0.916140i	$0.368712\pi$
$812$	0	0
$813$	8.97173	0.314652
$814$	5.34435	0.187319
$815$	35.0702	1.22846
$816$	10.0616	0.352226
$817$	10.4709	0.366329
$818$	6.48970	0.226907
$819$	0	0
$820$	−8.62869	−0.301327
$821$	−27.6232	−0.964057	−0.482029	−	0.876155i	$-0.660100\pi$
$821$	−27.6232	−0.964057	−0.482029	+	0.876155i	$0.660100\pi$
$822$	28.8880	1.00758
$823$	9.96213	0.347258	0.173629	−	0.984811i	$-0.444451\pi$
$823$	9.96213	0.347258	0.173629	+	0.984811i	$0.444451\pi$
$824$	16.0144	0.557887
$825$	−6.39668	−0.222704
$826$	0	0
$827$	33.3161	1.15851	0.579257	−	0.815145i	$-0.303343\pi$
$827$	33.3161	1.15851	0.579257	+	0.815145i	$0.303343\pi$
$828$	3.64462	0.126659
$829$	15.3982	0.534803	0.267401	−	0.963585i	$-0.413835\pi$
$829$	15.3982	0.534803	0.267401	+	0.963585i	$0.413835\pi$
$830$	6.91361	0.239975
$831$	48.6700	1.68834
$832$	−1.26650	−0.0439081
$833$	0	0
$834$	28.5135	0.987343
$835$	30.5937	1.05874
$836$	3.66737	0.126839
$837$	15.9683	0.551946
$838$	17.8029	0.614992
$839$	−23.6333	−0.815914	−0.407957	−	0.913001i	$-0.633759\pi$
$839$	−23.6333	−0.815914	−0.407957	+	0.913001i	$0.633759\pi$
$840$	0	0
$841$	−22.7532	−0.784595
$842$	29.2384	1.00762
$843$	25.2878	0.870958
$844$	−19.4626	−0.669930
$845$	−2.87921	−0.0990479
$846$	1.36597	0.0469630
$847$	0	0
$848$	−8.52438	−0.292729
$849$	5.21297	0.178909
$850$	5.86910	0.201308
$851$	14.9226	0.511541
$852$	21.7826	0.746258
$853$	−8.42663	−0.288522	−0.144261	−	0.989540i	$-0.546081\pi$
$853$	−8.42663	−0.288522	−0.144261	+	0.989540i	$0.546081\pi$
$854$	0	0
$855$	−8.49434	−0.290500
$856$	−5.14362	−0.175805
$857$	40.1845	1.37268	0.686338	−	0.727283i	$-0.259217\pi$
$857$	40.1845	1.37268	0.686338	+	0.727283i	$0.259217\pi$
$858$	3.35102	0.114402
$859$	29.9007	1.02020	0.510099	−	0.860116i	$-0.329609\pi$
$859$	29.9007	1.02020	0.510099	+	0.860116i	$0.329609\pi$
$860$	−7.73932	−0.263909
$861$	0	0
$862$	−41.6729	−1.41939
$863$	−31.5382	−1.07357	−0.536786	−	0.843718i	$-0.680362\pi$
$863$	−31.5382	−1.07357	−0.536786	+	0.843718i	$0.680362\pi$
$864$	−21.8637	−0.743818
$865$	−68.2265	−2.31977
$866$	−33.0155	−1.12191
$867$	30.9708	1.05182
$868$	0	0
$869$	−7.80949	−0.264919
$870$	−24.1145	−0.817557
$871$	2.26886	0.0768774
$872$	27.8574	0.943369
$873$	−11.8000	−0.399368
$874$	31.3475	1.06034
$875$	0	0
$876$	7.40480	0.250185
$877$	−27.2502	−0.920174	−0.460087	−	0.887874i	$-0.652182\pi$
$877$	−27.2502	−0.920174	−0.460087	+	0.887874i	$0.652182\pi$
$878$	−69.0611	−2.33070
$879$	30.9320	1.04331
$880$	14.3935	0.485205
$881$	13.0723	0.440415	0.220208	−	0.975453i	$-0.429326\pi$
$881$	13.0723	0.440415	0.220208	+	0.975453i	$0.429326\pi$
$882$	0	0
$883$	25.2435	0.849512	0.424756	−	0.905308i	$-0.360360\pi$
$883$	25.2435	0.849512	0.424756	+	0.905308i	$0.360360\pi$
$884$	−1.00437	−0.0337807
$885$	−71.0216	−2.38736
$886$	−26.3505	−0.885262
$887$	−46.8983	−1.57469	−0.787345	−	0.616512i	$-0.788545\pi$
$887$	−46.8983	−1.57469	−0.787345	+	0.616512i	$0.788545\pi$
$888$	10.7001	0.359072
$889$	0	0
$890$	−32.6835	−1.09555
$891$	−10.7324	−0.359549
$892$	−10.4518	−0.349953
$893$	3.83790	0.128430
$894$	−62.2231	−2.08105
$895$	−32.6875	−1.09262
$896$	0	0
$897$	9.35680	0.312414
$898$	11.4777	0.383016
$899$	−9.24836	−0.308450
$900$	2.49161	0.0830536
$901$	1.76508	0.0588034
$902$	5.32317	0.177242
$903$	0	0
$904$	−27.0801	−0.900670
$905$	−50.6628	−1.68409
$906$	41.1917	1.36850
$907$	32.5039	1.07928	0.539638	−	0.841897i	$-0.318561\pi$
$907$	32.5039	1.07928	0.539638	+	0.841897i	$0.318561\pi$
$908$	1.42225	0.0471992
$909$	−8.15471	−0.270475
$910$	0	0
$911$	15.8733	0.525905	0.262952	−	0.964809i	$-0.415304\pi$
$911$	15.8733	0.525905	0.262952	+	0.964809i	$0.415304\pi$
$912$	36.7388	1.21654
$913$	−1.39326	−0.0461102
$914$	4.90727	0.162318
$915$	66.3145	2.19229
$916$	−22.0412	−0.728262
$917$	0	0
$918$	7.69869	0.254095
$919$	9.14281	0.301593	0.150797	−	0.988565i	$-0.451816\pi$
$919$	9.14281	0.301593	0.150797	+	0.988565i	$0.451816\pi$
$920$	24.5889	0.810671
$921$	52.5959	1.73309
$922$	−45.5184	−1.49907
$923$	11.5460	0.380041
$924$	0	0
$925$	10.2017	0.335430
$926$	31.4909	1.03486
$927$	−7.04364	−0.231343
$928$	12.6628	0.415676
$929$	32.5858	1.06911	0.534553	−	0.845135i	$-0.320480\pi$
$929$	32.5858	1.06911	0.534553	+	0.845135i	$0.320480\pi$
$930$	35.7016	1.17070
$931$	0	0
$932$	13.5648	0.444329
$933$	−34.6011	−1.13279
$934$	−7.80162	−0.255277
$935$	−2.98036	−0.0974681
$936$	1.38522	0.0452772
$937$	19.3244	0.631302	0.315651	−	0.948875i	$-0.397777\pi$
$937$	19.3244	0.631302	0.315651	+	0.948875i	$0.397777\pi$
$938$	0	0
$939$	−44.4279	−1.44985
$940$	−2.83670	−0.0925230
$941$	39.2795	1.28047	0.640237	−	0.768177i	$-0.278836\pi$
$941$	39.2795	1.28047	0.640237	+	0.768177i	$0.278836\pi$
$942$	−12.3718	−0.403096
$943$	14.8635	0.484021
$944$	63.4209	2.06417
$945$	0	0
$946$	4.77450	0.155232
$947$	−46.0788	−1.49736	−0.748679	−	0.662932i	$-0.769312\pi$
$947$	−46.0788	−1.49736	−0.748679	+	0.662932i	$0.769312\pi$
$948$	14.7333	0.478516
$949$	3.92496	0.127410
$950$	21.4304	0.695294
$951$	−41.6570	−1.35082
$952$	0	0
$953$	−36.2870	−1.17545	−0.587725	−	0.809061i	$-0.699976\pi$
$953$	−36.2870	−1.17545	−0.587725	+	0.809061i	$0.699976\pi$
$954$	2.29388	0.0742672
$955$	−1.58721	−0.0513610
$956$	−3.40265	−0.110050
$957$	4.85965	0.157090
$958$	14.2169	0.459328
$959$	0	0
$960$	7.09019	0.228835
$961$	−17.3078	−0.558315
$962$	−5.34435	−0.172309
$963$	2.26233	0.0729025
$964$	9.49731	0.305888
$965$	11.3560	0.365562
$966$	0	0
$967$	5.48989	0.176543	0.0882715	−	0.996096i	$-0.471866\pi$
$967$	5.48989	0.176543	0.0882715	+	0.996096i	$0.471866\pi$
$968$	−1.77466	−0.0570397
$969$	−7.60723	−0.244379
$970$	75.0156	2.40860
$971$	54.5126	1.74939	0.874696	−	0.484672i	$-0.161061\pi$
$971$	54.5126	1.74939	0.874696	+	0.484672i	$0.161061\pi$
$972$	7.68608	0.246531
$973$	0	0
$974$	35.2008	1.12791
$975$	6.39668	0.204858
$976$	−59.2176	−1.89551
$977$	−53.4887	−1.71126	−0.855628	−	0.517592i	$-0.826829\pi$
$977$	−53.4887	−1.71126	−0.855628	+	0.517592i	$0.826829\pi$
$978$	40.8170	1.30518
$979$	6.58651	0.210506
$980$	0	0
$981$	−12.2526	−0.391194
$982$	64.9584	2.07291
$983$	21.0796	0.672336	0.336168	−	0.941802i	$-0.390869\pi$
$983$	21.0796	0.672336	0.336168	+	0.941802i	$0.390869\pi$
$984$	10.6577	0.339755
$985$	37.6653	1.20012
$986$	−4.45884	−0.141998
$987$	0	0
$988$	−3.66737	−0.116674
$989$	13.3315	0.423916
$990$	−3.87325	−0.123100
$991$	−35.9904	−1.14327	−0.571636	−	0.820507i	$-0.693691\pi$
$991$	−35.9904	−1.14327	−0.571636	+	0.820507i	$0.693691\pi$
$992$	−18.7473	−0.595227
$993$	−54.3531	−1.72484
$994$	0	0
$995$	36.7546	1.16520
$996$	2.62851	0.0832876
$997$	−16.6810	−0.528291	−0.264146	−	0.964483i	$-0.585090\pi$
$997$	−16.6810	−0.528291	−0.264146	+	0.964483i	$0.585090\pi$
$998$	61.2445	1.93866
$999$	13.3819	0.423385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7007.2.a.w.1.9		11
7.6	odd	2		1001.2.a.n.1.9	✓	11
21.20	even	2		9009.2.a.bs.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.a.n.1.9	✓	11	7.6	odd	2
7007.2.a.w.1.9		11	1.1	even	1	trivial
9009.2.a.bs.1.3		11	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7007 = 7^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7007.a (trivial)

\(f(q)\)	\(=\)	\(q+1.72345 q^{2} -1.94436 q^{3} +0.970287 q^{4} -2.87921 q^{5} -3.35102 q^{6} -1.77466 q^{8} +0.780553 q^{9} +O(q^{10})\)	\(q+1.72345 q^{2} -1.94436 q^{3} +0.970287 q^{4} -2.87921 q^{5} -3.35102 q^{6} -1.77466 q^{8} +0.780553 q^{9} -4.96218 q^{10} +1.00000 q^{11} -1.88659 q^{12} -1.00000 q^{13} +5.59824 q^{15} -4.99912 q^{16} +1.03513 q^{17} +1.34525 q^{18} +3.77967 q^{19} -2.79366 q^{20} +1.72345 q^{22} +4.81227 q^{23} +3.45059 q^{24} +3.28986 q^{25} -1.72345 q^{26} +4.31541 q^{27} -2.49935 q^{29} +9.64829 q^{30} +3.70030 q^{31} -5.06642 q^{32} -1.94436 q^{33} +1.78400 q^{34} +0.757361 q^{36} +3.10095 q^{37} +6.51408 q^{38} +1.94436 q^{39} +5.10962 q^{40} +3.08866 q^{41} +2.77031 q^{43} +0.970287 q^{44} -2.24738 q^{45} +8.29371 q^{46} +1.01541 q^{47} +9.72011 q^{48} +5.66991 q^{50} -2.01267 q^{51} -0.970287 q^{52} +1.70518 q^{53} +7.43741 q^{54} -2.87921 q^{55} -7.34906 q^{57} -4.30751 q^{58} -12.6864 q^{59} +5.43190 q^{60} +11.8456 q^{61} +6.37729 q^{62} +1.26650 q^{64} +2.87921 q^{65} -3.35102 q^{66} -2.26886 q^{67} +1.00437 q^{68} -9.35680 q^{69} -11.5460 q^{71} -1.38522 q^{72} -3.92496 q^{73} +5.34435 q^{74} -6.39668 q^{75} +3.66737 q^{76} +3.35102 q^{78} -7.80949 q^{79} +14.3935 q^{80} -10.7324 q^{81} +5.32317 q^{82} -1.39326 q^{83} -2.98036 q^{85} +4.77450 q^{86} +4.85965 q^{87} -1.77466 q^{88} +6.58651 q^{89} -3.87325 q^{90} +4.66928 q^{92} -7.19474 q^{93} +1.75000 q^{94} -10.8825 q^{95} +9.85096 q^{96} -15.1174 q^{97} +0.780553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - q^{2} - 2 q^{3} + 15 q^{4} - 7 q^{5} - 3 q^{6} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 11 * q - q^2 - 2 * q^3 + 15 * q^4 - 7 * q^5 - 3 * q^6 - 6 * q^8 + 15 * q^9	\( 11 q - q^{2} - 2 q^{3} + 15 q^{4} - 7 q^{5} - 3 q^{6} - 6 q^{8} + 15 q^{9} - q^{10} + 11 q^{11} + 5 q^{12} - 11 q^{13} + 4 q^{15} + 15 q^{16} - 7 q^{17} - 17 q^{18} - 22 q^{19} - 6 q^{20} - q^{22} + 3 q^{23} - 17 q^{24} + 10 q^{25} + q^{26} - 2 q^{27} - 6 q^{29} - 40 q^{30} - 28 q^{31} - 23 q^{32} - 2 q^{33} - 19 q^{34} + 48 q^{36} + q^{37} + 20 q^{38} + 2 q^{39} - 16 q^{40} + 4 q^{41} - 8 q^{43} + 15 q^{44} - 12 q^{45} + 2 q^{46} - 22 q^{47} + 30 q^{48} - 24 q^{50} - 27 q^{51} - 15 q^{52} + 9 q^{53} - 36 q^{54} - 7 q^{55} - 34 q^{57} - 8 q^{58} + 2 q^{59} + 25 q^{60} - 8 q^{62} - 10 q^{64} + 7 q^{65} - 3 q^{66} + 23 q^{67} - 24 q^{68} - 7 q^{69} + 3 q^{71} - 76 q^{72} - 29 q^{73} + 15 q^{74} - 36 q^{75} - 62 q^{76} + 3 q^{78} + 26 q^{79} + 16 q^{80} + 7 q^{81} + 16 q^{82} - 9 q^{83} - 31 q^{85} + 28 q^{86} - 13 q^{87} - 6 q^{88} - 9 q^{89} + 26 q^{90} - 58 q^{92} - 24 q^{93} + 34 q^{94} - 14 q^{95} - 56 q^{96} - 40 q^{97} + 15 q^{99}+O(q^{100}) \) 11 * q - q^2 - 2 * q^3 + 15 * q^4 - 7 * q^5 - 3 * q^6 - 6 * q^8 + 15 * q^9 - q^10 + 11 * q^11 + 5 * q^12 - 11 * q^13 + 4 * q^15 + 15 * q^16 - 7 * q^17 - 17 * q^18 - 22 * q^19 - 6 * q^20 - q^22 + 3 * q^23 - 17 * q^24 + 10 * q^25 + q^26 - 2 * q^27 - 6 * q^29 - 40 * q^30 - 28 * q^31 - 23 * q^32 - 2 * q^33 - 19 * q^34 + 48 * q^36 + q^37 + 20 * q^38 + 2 * q^39 - 16 * q^40 + 4 * q^41 - 8 * q^43 + 15 * q^44 - 12 * q^45 + 2 * q^46 - 22 * q^47 + 30 * q^48 - 24 * q^50 - 27 * q^51 - 15 * q^52 + 9 * q^53 - 36 * q^54 - 7 * q^55 - 34 * q^57 - 8 * q^58 + 2 * q^59 + 25 * q^60 - 8 * q^62 - 10 * q^64 + 7 * q^65 - 3 * q^66 + 23 * q^67 - 24 * q^68 - 7 * q^69 + 3 * q^71 - 76 * q^72 - 29 * q^73 + 15 * q^74 - 36 * q^75 - 62 * q^76 + 3 * q^78 + 26 * q^79 + 16 * q^80 + 7 * q^81 + 16 * q^82 - 9 * q^83 - 31 * q^85 + 28 * q^86 - 13 * q^87 - 6 * q^88 - 9 * q^89 + 26 * q^90 - 58 * q^92 - 24 * q^93 + 34 * q^94 - 14 * q^95 - 56 * q^96 - 40 * q^97 + 15 * q^99

Introduction

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