LMFDB - Embedded newform 4805.2.a.y.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4805,2,Mod(1,4805)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4805.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4805, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 4805 = 5 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4805.a (trivial)

Newform invariants

comment:select newform

sage:traces = [20,-1,4,15,-20,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$38.3681181712$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 27 x^{18} + 29 x^{17} + 298 x^{16} - 343 x^{15} - 1729 x^{14} + 2127 x^{13} + 5634 x^{12} + \cdots + 1 $ x^20 - x^19 - 27x^18 + 29x^17 + 298x^16 - 343x^15 - 1729x^14 + 2127x^13 + 5634x^12 - 7404x^11 - 10174x^10 + 14381x^9 + 9333x^8 - 14641x^7 - 3440x^6 + 6885x^5 - 5x^4 - 1073x^3 + 89x^2 + 30x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.47391$ of defining polynomial
Character	$\chi$	$=$	4805.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.47391 q^{2} +2.90581 q^{3} +0.172406 q^{4} -1.00000 q^{5} -4.28290 q^{6} +3.45832 q^{7} +2.69371 q^{8} +5.44372 q^{9} +1.47391 q^{10} -2.66743 q^{11} +0.500978 q^{12} +1.40942 q^{13} -5.09725 q^{14} -2.90581 q^{15} -4.31509 q^{16} -2.66581 q^{17} -8.02355 q^{18} +4.61973 q^{19} -0.172406 q^{20} +10.0492 q^{21} +3.93154 q^{22} -7.95912 q^{23} +7.82740 q^{24} +1.00000 q^{25} -2.07735 q^{26} +7.10100 q^{27} +0.596234 q^{28} +9.41305 q^{29} +4.28290 q^{30} +0.972630 q^{32} -7.75103 q^{33} +3.92916 q^{34} -3.45832 q^{35} +0.938529 q^{36} +9.54129 q^{37} -6.80906 q^{38} +4.09550 q^{39} -2.69371 q^{40} -0.204208 q^{41} -14.8116 q^{42} +3.22072 q^{43} -0.459879 q^{44} -5.44372 q^{45} +11.7310 q^{46} -5.59812 q^{47} -12.5388 q^{48} +4.95998 q^{49} -1.47391 q^{50} -7.74633 q^{51} +0.242991 q^{52} +3.88528 q^{53} -10.4662 q^{54} +2.66743 q^{55} +9.31570 q^{56} +13.4240 q^{57} -13.8740 q^{58} -10.5015 q^{59} -0.500978 q^{60} +1.40790 q^{61} +18.8261 q^{63} +7.19661 q^{64} -1.40942 q^{65} +11.4243 q^{66} +4.69098 q^{67} -0.459600 q^{68} -23.1277 q^{69} +5.09725 q^{70} +9.52831 q^{71} +14.6638 q^{72} +1.53135 q^{73} -14.0630 q^{74} +2.90581 q^{75} +0.796467 q^{76} -9.22481 q^{77} -6.03639 q^{78} +9.89107 q^{79} +4.31509 q^{80} +4.30296 q^{81} +0.300984 q^{82} +6.98802 q^{83} +1.73254 q^{84} +2.66581 q^{85} -4.74704 q^{86} +27.3525 q^{87} -7.18526 q^{88} +13.1073 q^{89} +8.02355 q^{90} +4.87421 q^{91} -1.37220 q^{92} +8.25112 q^{94} -4.61973 q^{95} +2.82628 q^{96} +14.8804 q^{97} -7.31056 q^{98} -14.5207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + 4 q^{3} + 15 q^{4} - 20 q^{5} + 4 q^{6} + q^{7} + 9 q^{8} + 8 q^{9} + q^{10} + 17 q^{11} - 13 q^{12} + 9 q^{13} + 6 q^{14} - 4 q^{15} + 9 q^{16} - 20 q^{17} - 28 q^{18} - 7 q^{19} - 15 q^{20}+ \cdots + 53 q^{99}+O(q^{100}) $ 20 * q - q^2 + 4 * q^3 + 15 * q^4 - 20 * q^5 + 4 * q^6 + q^7 + 9 * q^8 + 8 * q^9 + q^10 + 17 * q^11 - 13 * q^12 + 9 * q^13 + 6 * q^14 - 4 * q^15 + 9 * q^16 - 20 * q^17 - 28 * q^18 - 7 * q^19 - 15 * q^20 + 22 * q^21 + 22 * q^22 - 9 * q^23 + 28 * q^24 + 20 * q^25 + 32 * q^26 + 13 * q^27 + 8 * q^28 + 4 * q^29 - 4 * q^30 + 2 * q^32 - 26 * q^33 + 27 * q^34 - q^35 + 13 * q^36 + 12 * q^37 + 15 * q^38 + 11 * q^39 - 9 * q^40 + 9 * q^41 - 14 * q^42 + 42 * q^43 + 49 * q^44 - 8 * q^45 - 24 * q^46 - 32 * q^47 - 31 * q^48 + q^49 - q^50 + 2 * q^51 + 29 * q^52 + 9 * q^53 + 44 * q^54 - 17 * q^55 - 9 * q^56 + 38 * q^57 + 47 * q^58 + 6 * q^59 + 13 * q^60 + 50 * q^61 + 55 * q^63 - 19 * q^64 - 9 * q^65 + 15 * q^66 - 30 * q^67 - 34 * q^68 + 2 * q^69 - 6 * q^70 + 7 * q^71 - 16 * q^72 + 32 * q^73 - 22 * q^74 + 4 * q^75 + 23 * q^76 - 8 * q^77 + 29 * q^78 + 63 * q^79 - 9 * q^80 + 8 * q^81 - 12 * q^82 - 35 * q^83 + 71 * q^84 + 20 * q^85 + 65 * q^86 + 46 * q^87 + 70 * q^88 + 40 * q^89 + 28 * q^90 + 28 * q^91 + 5 * q^92 + 65 * q^94 + 7 * q^95 + 46 * q^96 + 41 * q^97 + 65 * q^98 + 53 * q^99

Coefficient data

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

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

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

$2$	−1.47391	−1.04221	−0.521105	−	0.853492i	$-0.674480\pi$
$2$	−1.47391	−1.04221	−0.521105	+	0.853492i	$0.674480\pi$
$3$	2.90581	1.67767	0.838835	−	0.544386i	$-0.183237\pi$
$3$	2.90581	1.67767	0.838835	+	0.544386i	$0.183237\pi$
$4$	0.172406	0.0862028
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.28290	−1.74848
$7$	3.45832	1.30712	0.653561	−	0.756874i	$-0.273274\pi$
$7$	3.45832	1.30712	0.653561	+	0.756874i	$0.273274\pi$
$8$	2.69371	0.952369
$9$	5.44372	1.81457
$10$	1.47391	0.466091
$11$	−2.66743	−0.804259	−0.402130	−	0.915583i	$-0.631730\pi$
$11$	−2.66743	−0.804259	−0.402130	+	0.915583i	$0.631730\pi$
$12$	0.500978	0.144620
$13$	1.40942	0.390902	0.195451	−	0.980713i	$-0.437383\pi$
$13$	1.40942	0.390902	0.195451	+	0.980713i	$0.437383\pi$
$14$	−5.09725	−1.36230
$15$	−2.90581	−0.750277
$16$	−4.31509	−1.07877
$17$	−2.66581	−0.646553	−0.323277	−	0.946305i	$-0.604784\pi$
$17$	−2.66581	−0.646553	−0.323277	+	0.946305i	$0.604784\pi$
$18$	−8.02355	−1.89117
$19$	4.61973	1.05984	0.529919	−	0.848048i	$-0.322222\pi$
$19$	4.61973	1.05984	0.529919	+	0.848048i	$0.322222\pi$
$20$	−0.172406	−0.0385511
$21$	10.0492	2.19292
$22$	3.93154	0.838207
$23$	−7.95912	−1.65959	−0.829795	−	0.558068i	$-0.811543\pi$
$23$	−7.95912	−1.65959	−0.829795	+	0.558068i	$0.811543\pi$
$24$	7.82740	1.59776
$25$	1.00000	0.200000
$26$	−2.07735	−0.407402
$27$	7.10100	1.36659
$28$	0.596234	0.112678
$29$	9.41305	1.74796	0.873979	−	0.485963i	$-0.161531\pi$
$29$	9.41305	1.74796	0.873979	+	0.485963i	$0.161531\pi$
$30$	4.28290	0.781946
$31$	0	0
$31$	0	0
$32$	0.972630	0.171938
$33$	−7.75103	−1.34928
$34$	3.92916	0.673845
$35$	−3.45832	−0.584563
$36$	0.938529	0.156421
$37$	9.54129	1.56858	0.784290	−	0.620395i	$-0.213028\pi$
$37$	9.54129	1.56858	0.784290	+	0.620395i	$0.213028\pi$
$38$	−6.80906	−1.10457
$39$	4.09550	0.655804
$40$	−2.69371	−0.425912
$41$	−0.204208	−0.0318920	−0.0159460	−	0.999873i	$-0.505076\pi$
$41$	−0.204208	−0.0318920	−0.0159460	+	0.999873i	$0.505076\pi$
$42$	−14.8116	−2.28548
$43$	3.22072	0.491155	0.245578	−	0.969377i	$-0.421022\pi$
$43$	3.22072	0.491155	0.245578	+	0.969377i	$0.421022\pi$
$44$	−0.459879	−0.0693294
$45$	−5.44372	−0.811503
$46$	11.7310	1.72964
$47$	−5.59812	−0.816570	−0.408285	−	0.912855i	$-0.633873\pi$
$47$	−5.59812	−0.816570	−0.408285	+	0.912855i	$0.633873\pi$
$48$	−12.5388	−1.80982
$49$	4.95998	0.708569
$50$	−1.47391	−0.208442
$51$	−7.74633	−1.08470
$52$	0.242991	0.0336968
$53$	3.88528	0.533684	0.266842	−	0.963740i	$-0.414020\pi$
$53$	3.88528	0.533684	0.266842	+	0.963740i	$0.414020\pi$
$54$	−10.4662	−1.42427
$55$	2.66743	0.359676
$56$	9.31570	1.24486
$57$	13.4240	1.77806
$58$	−13.8740	−1.82174
$59$	−10.5015	−1.36718	−0.683590	−	0.729866i	$-0.739583\pi$
$59$	−10.5015	−1.36718	−0.683590	+	0.729866i	$0.739583\pi$
$60$	−0.500978	−0.0646760
$61$	1.40790	0.180264	0.0901318	−	0.995930i	$-0.471271\pi$
$61$	1.40790	0.180264	0.0901318	+	0.995930i	$0.471271\pi$
$62$	0	0
$63$	18.8261	2.37187
$64$	7.19661	0.899576
$65$	−1.40942	−0.174817
$66$	11.4243	1.40623
$67$	4.69098	0.573094	0.286547	−	0.958066i	$-0.407493\pi$
$67$	4.69098	0.573094	0.286547	+	0.958066i	$0.407493\pi$
$68$	−0.459600	−0.0557347
$69$	−23.1277	−2.78424
$70$	5.09725	0.609238
$71$	9.52831	1.13080	0.565401	−	0.824816i	$-0.308721\pi$
$71$	9.52831	1.13080	0.565401	+	0.824816i	$0.308721\pi$
$72$	14.6638	1.72814
$73$	1.53135	0.179231	0.0896156	−	0.995976i	$-0.471436\pi$
$73$	1.53135	0.179231	0.0896156	+	0.995976i	$0.471436\pi$
$74$	−14.0630	−1.63479
$75$	2.90581	0.335534
$76$	0.796467	0.0913611
$77$	−9.22481	−1.05126
$78$	−6.03639	−0.683486
$79$	9.89107	1.11283	0.556416	−	0.830904i	$-0.312176\pi$
$79$	9.89107	1.11283	0.556416	+	0.830904i	$0.312176\pi$
$80$	4.31509	0.482441
$81$	4.30296	0.478107
$82$	0.300984	0.0332381
$83$	6.98802	0.767035	0.383518	−	0.923534i	$-0.374713\pi$
$83$	6.98802	0.767035	0.383518	+	0.923534i	$0.374713\pi$
$84$	1.73254	0.189036
$85$	2.66581	0.289147
$86$	−4.74704	−0.511887
$87$	27.3525	2.93250
$88$	−7.18526	−0.765951
$89$	13.1073	1.38937	0.694686	−	0.719313i	$-0.255543\pi$
$89$	13.1073	1.38937	0.694686	+	0.719313i	$0.255543\pi$
$90$	8.02355	0.845757
$91$	4.87421	0.510957
$92$	−1.37220	−0.143061
$93$	0	0
$94$	8.25112	0.851038
$95$	−4.61973	−0.473974
$96$	2.82628	0.288456
$97$	14.8804	1.51087	0.755436	−	0.655223i	$-0.227425\pi$
$97$	14.8804	1.51087	0.755436	+	0.655223i	$0.227425\pi$
$98$	−7.31056	−0.738478
$99$	−14.5207	−1.45939
$100$	0.172406	0.0172406
$101$	−9.00152	−0.895685	−0.447842	−	0.894113i	$-0.647807\pi$
$101$	−9.00152	−0.895685	−0.447842	+	0.894113i	$0.647807\pi$
$102$	11.4174	1.13049
$103$	2.14246	0.211103	0.105551	−	0.994414i	$-0.466339\pi$
$103$	2.14246	0.211103	0.105551	+	0.994414i	$0.466339\pi$
$104$	3.79656	0.372283
$105$	−10.0492	−0.980703
$106$	−5.72654	−0.556211
$107$	6.22162	0.601466	0.300733	−	0.953708i	$-0.402769\pi$
$107$	6.22162	0.601466	0.300733	+	0.953708i	$0.402769\pi$
$108$	1.22425	0.117804
$109$	−14.5905	−1.39751	−0.698756	−	0.715360i	$-0.746263\pi$
$109$	−14.5905	−1.39751	−0.698756	+	0.715360i	$0.746263\pi$
$110$	−3.93154	−0.374858
$111$	27.7252	2.63156
$112$	−14.9230	−1.41009
$113$	11.3201	1.06491	0.532455	−	0.846458i	$-0.321270\pi$
$113$	11.3201	1.06491	0.532455	+	0.846458i	$0.321270\pi$
$114$	−19.7858	−1.85311
$115$	7.95912	0.742191
$116$	1.62286	0.150679
$117$	7.67248	0.709321
$118$	15.4783	1.42489
$119$	−9.21922	−0.845124
$120$	−7.82740	−0.714540
$121$	−3.88484	−0.353167
$122$	−2.07512	−0.187873
$123$	−0.593390	−0.0535042
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	−27.7480	−2.47199
$127$	6.54904	0.581134	0.290567	−	0.956855i	$-0.406156\pi$
$127$	6.54904	0.581134	0.290567	+	0.956855i	$0.406156\pi$
$128$	−12.5524	−1.10949
$129$	9.35879	0.823996
$130$	2.07735	0.182196
$131$	−1.29615	−0.113245	−0.0566226	−	0.998396i	$-0.518033\pi$
$131$	−1.29615	−0.113245	−0.0566226	+	0.998396i	$0.518033\pi$
$132$	−1.33632	−0.116312
$133$	15.9765	1.38534
$134$	−6.91407	−0.597285
$135$	−7.10100	−0.611156
$136$	−7.18090	−0.615757
$137$	−1.02259	−0.0873661	−0.0436830	−	0.999045i	$-0.513909\pi$
$137$	−1.02259	−0.0873661	−0.0436830	+	0.999045i	$0.513909\pi$
$138$	34.0881	2.90177
$139$	−6.96021	−0.590358	−0.295179	−	0.955442i	$-0.595379\pi$
$139$	−6.96021	−0.590358	−0.295179	+	0.955442i	$0.595379\pi$
$140$	−0.596234	−0.0503910
$141$	−16.2671	−1.36993
$142$	−14.0439	−1.17853
$143$	−3.75951	−0.314386
$144$	−23.4901	−1.95751
$145$	−9.41305	−0.781711
$146$	−2.25707	−0.186797
$147$	14.4128	1.18874
$148$	1.64497	0.135216
$149$	−20.7884	−1.70305	−0.851527	−	0.524310i	$-0.824323\pi$
$149$	−20.7884	−1.70305	−0.851527	+	0.524310i	$0.824323\pi$
$150$	−4.28290	−0.349697
$151$	−0.146321	−0.0119074	−0.00595372	−	0.999982i	$-0.501895\pi$
$151$	−0.146321	−0.0119074	−0.00595372	+	0.999982i	$0.501895\pi$
$152$	12.4442	1.00936
$153$	−14.5119	−1.17322
$154$	13.5965	1.09564
$155$	0	0
$156$	0.706087	0.0565322
$157$	0.415184	0.0331353	0.0165676	−	0.999863i	$-0.494726\pi$
$157$	0.415184	0.0331353	0.0165676	+	0.999863i	$0.494726\pi$
$158$	−14.5785	−1.15981
$159$	11.2899	0.895345
$160$	−0.972630	−0.0768932
$161$	−27.5252	−2.16929
$162$	−6.34218	−0.498288
$163$	−10.5405	−0.825598	−0.412799	−	0.910822i	$-0.635449\pi$
$163$	−10.5405	−0.825598	−0.412799	+	0.910822i	$0.635449\pi$
$164$	−0.0352067	−0.00274918
$165$	7.75103	0.603417
$166$	−10.2997	−0.799412
$167$	−14.6974	−1.13732	−0.568660	−	0.822573i	$-0.692538\pi$
$167$	−14.6974	−1.13732	−0.568660	+	0.822573i	$0.692538\pi$
$168$	27.0696	2.08847
$169$	−11.0135	−0.847196
$170$	−3.92916	−0.301352
$171$	25.1485	1.92316
$172$	0.555270	0.0423390
$173$	17.5003	1.33052	0.665262	−	0.746610i	$-0.268320\pi$
$173$	17.5003	1.33052	0.665262	+	0.746610i	$0.268320\pi$
$174$	−40.3151	−3.05628
$175$	3.45832	0.261424
$176$	11.5102	0.867612
$177$	−30.5154	−2.29368
$178$	−19.3190	−1.44802
$179$	14.2118	1.06224	0.531121	−	0.847296i	$-0.321771\pi$
$179$	14.2118	1.06224	0.531121	+	0.847296i	$0.321771\pi$
$180$	−0.938529	−0.0699538
$181$	21.2848	1.58209	0.791044	−	0.611759i	$-0.209538\pi$
$181$	21.2848	1.58209	0.791044	+	0.611759i	$0.209538\pi$
$182$	−7.18415	−0.532524
$183$	4.09110	0.302423
$184$	−21.4395	−1.58054
$185$	−9.54129	−0.701490
$186$	0	0
$187$	7.11084	0.519996
$188$	−0.965148	−0.0703906
$189$	24.5575	1.78630
$190$	6.80906	0.493981
$191$	13.7537	0.995180	0.497590	−	0.867412i	$-0.334218\pi$
$191$	13.7537	0.995180	0.497590	+	0.867412i	$0.334218\pi$
$192$	20.9120	1.50919
$193$	−20.4043	−1.46873	−0.734366	−	0.678754i	$-0.762520\pi$
$193$	−20.4043	−1.46873	−0.734366	+	0.678754i	$0.762520\pi$
$194$	−21.9323	−1.57465
$195$	−4.09550	−0.293285
$196$	0.855129	0.0610806
$197$	−15.3471	−1.09344	−0.546719	−	0.837316i	$-0.684123\pi$
$197$	−15.3471	−1.09344	−0.546719	+	0.837316i	$0.684123\pi$
$198$	21.4022	1.52099
$199$	−14.8692	−1.05405	−0.527024	−	0.849850i	$-0.676692\pi$
$199$	−14.8692	−1.05405	−0.527024	+	0.849850i	$0.676692\pi$
$200$	2.69371	0.190474
$201$	13.6311	0.961462
$202$	13.2674	0.933492
$203$	32.5533	2.28480
$204$	−1.33551	−0.0935044
$205$	0.204208	0.0142625
$206$	−3.15779	−0.220014
$207$	−43.3272	−3.01145
$208$	−6.08176	−0.421694
$209$	−12.3228	−0.852385
$210$	14.8116	1.02210
$211$	8.86815	0.610509	0.305254	−	0.952271i	$-0.401259\pi$
$211$	8.86815	0.610509	0.305254	+	0.952271i	$0.401259\pi$
$212$	0.669844	0.0460051
$213$	27.6875	1.89711
$214$	−9.17009	−0.626855
$215$	−3.22072	−0.219651
$216$	19.1280	1.30150
$217$	0	0
$218$	21.5050	1.45650
$219$	4.44982	0.300691
$220$	0.459879	0.0310051
$221$	−3.75723	−0.252739
$222$	−40.8644	−2.74264
$223$	21.6759	1.45152	0.725762	−	0.687946i	$-0.241487\pi$
$223$	21.6759	1.45152	0.725762	+	0.687946i	$0.241487\pi$
$224$	3.36367	0.224744
$225$	5.44372	0.362915
$226$	−16.6849	−1.10986
$227$	−3.19371	−0.211974	−0.105987	−	0.994368i	$-0.533800\pi$
$227$	−3.19371	−0.211974	−0.105987	+	0.994368i	$0.533800\pi$
$228$	2.31438	0.153274
$229$	8.63771	0.570796	0.285398	−	0.958409i	$-0.407874\pi$
$229$	8.63771	0.570796	0.285398	+	0.958409i	$0.407874\pi$
$230$	−11.7310	−0.773520
$231$	−26.8055	−1.76368
$232$	25.3560	1.66470
$233$	7.43891	0.487339	0.243669	−	0.969858i	$-0.421649\pi$
$233$	7.43891	0.487339	0.243669	+	0.969858i	$0.421649\pi$
$234$	−11.3085	−0.739262
$235$	5.59812	0.365181
$236$	−1.81052	−0.117855
$237$	28.7416	1.86697
$238$	13.5883	0.880797
$239$	24.5101	1.58543	0.792713	−	0.609595i	$-0.208668\pi$
$239$	24.5101	1.58543	0.792713	+	0.609595i	$0.208668\pi$
$240$	12.5388	0.809377
$241$	7.53725	0.485517	0.242759	−	0.970087i	$-0.421948\pi$
$241$	7.53725	0.485517	0.242759	+	0.970087i	$0.421948\pi$
$242$	5.72590	0.368075
$243$	−8.79940	−0.564482
$244$	0.242731	0.0155392
$245$	−4.95998	−0.316882
$246$	0.874603	0.0557626
$247$	6.51112	0.414293
$248$	0	0
$249$	20.3059	1.28683
$250$	1.47391	0.0932181
$251$	−9.72288	−0.613703	−0.306851	−	0.951757i	$-0.599275\pi$
$251$	−9.72288	−0.613703	−0.306851	+	0.951757i	$0.599275\pi$
$252$	3.24573	0.204462
$253$	21.2303	1.33474
$254$	−9.65269	−0.605664
$255$	7.74633	0.485094
$256$	4.10787	0.256742
$257$	−2.58779	−0.161422	−0.0807110	−	0.996738i	$-0.525719\pi$
$257$	−2.58779	−0.161422	−0.0807110	+	0.996738i	$0.525719\pi$
$258$	−13.7940	−0.858777
$259$	32.9969	2.05032
$260$	−0.242991	−0.0150697
$261$	51.2420	3.17180
$262$	1.91041	0.118025
$263$	13.7013	0.844860	0.422430	−	0.906395i	$-0.361177\pi$
$263$	13.7013	0.844860	0.422430	+	0.906395i	$0.361177\pi$
$264$	−20.8790	−1.28501
$265$	−3.88528	−0.238671
$266$	−23.5479	−1.44381
$267$	38.0873	2.33091
$268$	0.808751	0.0494023
$269$	−20.3407	−1.24019	−0.620097	−	0.784525i	$-0.712907\pi$
$269$	−20.3407	−1.24019	−0.620097	+	0.784525i	$0.712907\pi$
$270$	10.4662	0.636954
$271$	27.7920	1.68824	0.844121	−	0.536152i	$-0.180123\pi$
$271$	27.7920	1.68824	0.844121	+	0.536152i	$0.180123\pi$
$272$	11.5032	0.697483
$273$	14.1635	0.857216
$274$	1.50721	0.0910538
$275$	−2.66743	−0.160852
$276$	−3.98734	−0.240010
$277$	−5.10182	−0.306539	−0.153269	−	0.988184i	$-0.548980\pi$
$277$	−5.10182	−0.306539	−0.153269	+	0.988184i	$0.548980\pi$
$278$	10.2587	0.615277
$279$	0	0
$280$	−9.31570	−0.556720
$281$	−4.90667	−0.292708	−0.146354	−	0.989232i	$-0.546754\pi$
$281$	−4.90667	−0.292708	−0.146354	+	0.989232i	$0.546754\pi$
$282$	23.9762	1.42776
$283$	−15.4008	−0.915482	−0.457741	−	0.889086i	$-0.651341\pi$
$283$	−15.4008	−0.915482	−0.457741	+	0.889086i	$0.651341\pi$
$284$	1.64273	0.0974784
$285$	−13.4240	−0.795172
$286$	5.54118	0.327657
$287$	−0.706217	−0.0416867
$288$	5.29473	0.311995
$289$	−9.89347	−0.581969
$290$	13.8740	0.814707
$291$	43.2395	2.53474
$292$	0.264014	0.0154502
$293$	−14.8543	−0.867799	−0.433899	−	0.900961i	$-0.642863\pi$
$293$	−14.8543	−0.867799	−0.433899	+	0.900961i	$0.642863\pi$
$294$	−21.2431	−1.23892
$295$	10.5015	0.611422
$296$	25.7014	1.49387
$297$	−18.9414	−1.09909
$298$	30.6402	1.77494
$299$	−11.2177	−0.648737
$300$	0.500978	0.0289240
$301$	11.1383	0.642000
$302$	0.215664	0.0124101
$303$	−26.1567	−1.50266
$304$	−19.9345	−1.14332
$305$	−1.40790	−0.0806163
$306$	21.3892	1.22274
$307$	−22.5176	−1.28515	−0.642573	−	0.766224i	$-0.722133\pi$
$307$	−22.5176	−1.28515	−0.642573	+	0.766224i	$0.722133\pi$
$308$	−1.59041	−0.0906220
$309$	6.22558	0.354161
$310$	0	0
$311$	9.55538	0.541836	0.270918	−	0.962602i	$-0.412673\pi$
$311$	9.55538	0.541836	0.270918	+	0.962602i	$0.412673\pi$
$312$	11.0321	0.624568
$313$	−13.7285	−0.775979	−0.387989	−	0.921664i	$-0.626830\pi$
$313$	−13.7285	−0.775979	−0.387989	+	0.921664i	$0.626830\pi$
$314$	−0.611943	−0.0345339
$315$	−18.8261	−1.06073
$316$	1.70528	0.0959293
$317$	29.8871	1.67863	0.839314	−	0.543647i	$-0.182957\pi$
$317$	29.8871	1.67863	0.839314	+	0.543647i	$0.182957\pi$
$318$	−16.6402	−0.933138
$319$	−25.1086	−1.40581
$320$	−7.19661	−0.402303
$321$	18.0788	1.00906
$322$	40.5696	2.26085
$323$	−12.3153	−0.685242
$324$	0.741855	0.0412142
$325$	1.40942	0.0781804
$326$	15.5358	0.860447
$327$	−42.3971	−2.34456
$328$	−0.550077	−0.0303729
$329$	−19.3601	−1.06736
$330$	−11.4243	−0.628887
$331$	13.6978	0.752898	0.376449	−	0.926437i	$-0.377145\pi$
$331$	13.6978	0.752898	0.376449	+	0.926437i	$0.377145\pi$
$332$	1.20477	0.0661206
$333$	51.9402	2.84630
$334$	21.6626	1.18533
$335$	−4.69098	−0.256295
$336$	−43.3633	−2.36566
$337$	9.90110	0.539347	0.269674	−	0.962952i	$-0.413084\pi$
$337$	9.90110	0.539347	0.269674	+	0.962952i	$0.413084\pi$
$338$	16.2330	0.882956
$339$	32.8942	1.78657
$340$	0.459600	0.0249253
$341$	0	0
$342$	−37.0666	−2.00433
$343$	−7.05504	−0.380936
$344$	8.67567	0.467761
$345$	23.1277	1.24515
$346$	−25.7938	−1.38669
$347$	22.0447	1.18342	0.591711	−	0.806150i	$-0.298453\pi$
$347$	22.0447	1.18342	0.591711	+	0.806150i	$0.298453\pi$
$348$	4.71573	0.252790
$349$	−16.6541	−0.891473	−0.445737	−	0.895164i	$-0.647058\pi$
$349$	−16.6541	−0.891473	−0.445737	+	0.895164i	$0.647058\pi$
$350$	−5.09725	−0.272459
$351$	10.0083	0.534202
$352$	−2.59442	−0.138283
$353$	8.70819	0.463490	0.231745	−	0.972777i	$-0.425556\pi$
$353$	8.70819	0.463490	0.231745	+	0.972777i	$0.425556\pi$
$354$	44.9769	2.39050
$355$	−9.52831	−0.505710
$356$	2.25977	0.119768
$357$	−26.7893	−1.41784
$358$	−20.9469	−1.10708
$359$	−14.5051	−0.765550	−0.382775	−	0.923842i	$-0.625032\pi$
$359$	−14.5051	−0.765550	−0.382775	+	0.923842i	$0.625032\pi$
$360$	−14.6638	−0.772850
$361$	2.34190	0.123258
$362$	−31.3719	−1.64887
$363$	−11.2886	−0.592498
$364$	0.840342	0.0440459
$365$	−1.53135	−0.0801547
$366$	−6.02991	−0.315188
$367$	−14.3868	−0.750985	−0.375493	−	0.926825i	$-0.622526\pi$
$367$	−14.3868	−0.750985	−0.375493	+	0.926825i	$0.622526\pi$
$368$	34.3443	1.79032
$369$	−1.11165	−0.0578704
$370$	14.0630	0.731100
$371$	13.4365	0.697590
$372$	0	0
$373$	−18.6605	−0.966203	−0.483102	−	0.875564i	$-0.660490\pi$
$373$	−18.6605	−0.966203	−0.483102	+	0.875564i	$0.660490\pi$
$374$	−10.4807	−0.541946
$375$	−2.90581	−0.150055
$376$	−15.0797	−0.777676
$377$	13.2669	0.683280
$378$	−36.1955	−1.86170
$379$	12.8204	0.658541	0.329270	−	0.944236i	$-0.393197\pi$
$379$	12.8204	0.658541	0.329270	+	0.944236i	$0.393197\pi$
$380$	−0.796467	−0.0408579
$381$	19.0303	0.974950
$382$	−20.2716	−1.03719
$383$	−27.9245	−1.42688	−0.713438	−	0.700718i	$-0.752863\pi$
$383$	−27.9245	−1.42688	−0.713438	+	0.700718i	$0.752863\pi$
$384$	−36.4749	−1.86135
$385$	9.22481	0.470140
$386$	30.0740	1.53073
$387$	17.5327	0.891238
$388$	2.56546	0.130241
$389$	−3.87595	−0.196518	−0.0982592	−	0.995161i	$-0.531327\pi$
$389$	−3.87595	−0.196518	−0.0982592	+	0.995161i	$0.531327\pi$
$390$	6.03639	0.305664
$391$	21.2175	1.07301
$392$	13.3607	0.674819
$393$	−3.76637	−0.189988
$394$	22.6203	1.13959
$395$	−9.89107	−0.497674
$396$	−2.50346	−0.125803
$397$	27.5481	1.38260	0.691300	−	0.722568i	$-0.257038\pi$
$397$	27.5481	1.38260	0.691300	+	0.722568i	$0.257038\pi$
$398$	21.9158	1.09854
$399$	46.4247	2.32414
$400$	−4.31509	−0.215754
$401$	11.1280	0.555704	0.277852	−	0.960624i	$-0.410378\pi$
$401$	11.1280	0.555704	0.277852	+	0.960624i	$0.410378\pi$
$402$	−20.0910	−1.00205
$403$	0	0
$404$	−1.55191	−0.0772105
$405$	−4.30296	−0.213816
$406$	−47.9806	−2.38124
$407$	−25.4507	−1.26154
$408$	−20.8663	−1.03304
$409$	2.53795	0.125494	0.0627468	−	0.998029i	$-0.480014\pi$
$409$	2.53795	0.125494	0.0627468	+	0.998029i	$0.480014\pi$
$410$	−0.300984	−0.0148645
$411$	−2.97146	−0.146571
$412$	0.369372	0.0181977
$413$	−36.3176	−1.78707
$414$	63.8604	3.13857
$415$	−6.98802	−0.343028
$416$	1.37084	0.0672110
$417$	−20.2251	−0.990425
$418$	18.1627	0.888364
$419$	18.0607	0.882321	0.441160	−	0.897428i	$-0.354567\pi$
$419$	18.0607	0.882321	0.441160	+	0.897428i	$0.354567\pi$
$420$	−1.73254	−0.0845394
$421$	−1.76859	−0.0861958	−0.0430979	−	0.999071i	$-0.513723\pi$
$421$	−1.76859	−0.0861958	−0.0430979	+	0.999071i	$0.513723\pi$
$422$	−13.0708	−0.636279
$423$	−30.4746	−1.48173
$424$	10.4658	0.508264
$425$	−2.66581	−0.129311
$426$	−40.8088	−1.97719
$427$	4.86898	0.235627
$428$	1.07264	0.0518481
$429$	−10.9244	−0.527436
$430$	4.74704	0.228923
$431$	0.292706	0.0140991	0.00704957	−	0.999975i	$-0.497756\pi$
$431$	0.292706	0.0140991	0.00704957	+	0.999975i	$0.497756\pi$
$432$	−30.6414	−1.47424
$433$	−4.00282	−0.192363	−0.0961816	−	0.995364i	$-0.530663\pi$
$433$	−4.00282	−0.192363	−0.0961816	+	0.995364i	$0.530663\pi$
$434$	0	0
$435$	−27.3525	−1.31145
$436$	−2.51548	−0.120470
$437$	−36.7690	−1.75890
$438$	−6.55862	−0.313383
$439$	−4.06612	−0.194065	−0.0970325	−	0.995281i	$-0.530935\pi$
$439$	−4.06612	−0.194065	−0.0970325	+	0.995281i	$0.530935\pi$
$440$	7.18526	0.342544
$441$	27.0008	1.28575
$442$	5.53782	0.263407
$443$	9.09675	0.432200	0.216100	−	0.976371i	$-0.430666\pi$
$443$	9.09675	0.432200	0.216100	+	0.976371i	$0.430666\pi$
$444$	4.77998	0.226848
$445$	−13.1073	−0.621346
$446$	−31.9483	−1.51279
$447$	−60.4072	−2.85716
$448$	24.8882	1.17586
$449$	5.31542	0.250850	0.125425	−	0.992103i	$-0.459971\pi$
$449$	5.31542	0.250850	0.125425	+	0.992103i	$0.459971\pi$
$450$	−8.02355	−0.378234
$451$	0.544710	0.0256494
$452$	1.95166	0.0917982
$453$	−0.425181	−0.0199767
$454$	4.70724	0.220922
$455$	−4.87421	−0.228507
$456$	36.1604	1.69337
$457$	6.23934	0.291864	0.145932	−	0.989295i	$-0.453382\pi$
$457$	6.23934	0.291864	0.145932	+	0.989295i	$0.453382\pi$
$458$	−12.7312	−0.594890
$459$	−18.9299	−0.883572
$460$	1.37220	0.0639790
$461$	−26.9998	−1.25750	−0.628752	−	0.777606i	$-0.716434\pi$
$461$	−26.9998	−1.25750	−0.628752	+	0.777606i	$0.716434\pi$
$462$	39.5089	1.83812
$463$	14.7117	0.683710	0.341855	−	0.939753i	$-0.388945\pi$
$463$	14.7117	0.683710	0.341855	+	0.939753i	$0.388945\pi$
$464$	−40.6181	−1.88565
$465$	0	0
$466$	−10.9643	−0.507910
$467$	28.3349	1.31118	0.655591	−	0.755116i	$-0.272419\pi$
$467$	28.3349	1.31118	0.655591	+	0.755116i	$0.272419\pi$
$468$	1.32278	0.0611455
$469$	16.2229	0.749104
$470$	−8.25112	−0.380596
$471$	1.20644	0.0555900
$472$	−28.2880	−1.30206
$473$	−8.59103	−0.395016
$474$	−42.3624	−1.94577
$475$	4.61973	0.211968
$476$	−1.58944	−0.0728521
$477$	21.1504	0.968409
$478$	−36.1256	−1.65235
$479$	−6.09919	−0.278679	−0.139340	−	0.990245i	$-0.544498\pi$
$479$	−6.09919	−0.278679	−0.139340	+	0.990245i	$0.544498\pi$
$480$	−2.82628	−0.129001
$481$	13.4477	0.613161
$482$	−11.1092	−0.506011
$483$	−79.9829	−3.63935
$484$	−0.669769	−0.0304440
$485$	−14.8804	−0.675682
$486$	12.9695	0.588309
$487$	21.6339	0.980326	0.490163	−	0.871631i	$-0.336937\pi$
$487$	21.6339	0.980326	0.490163	+	0.871631i	$0.336937\pi$
$488$	3.79248	0.171678
$489$	−30.6288	−1.38508
$490$	7.31056	0.330257
$491$	0.677158	0.0305597	0.0152798	−	0.999883i	$-0.495136\pi$
$491$	0.677158	0.0305597	0.0152798	+	0.999883i	$0.495136\pi$
$492$	−0.102304	−0.00461221
$493$	−25.0934	−1.13015
$494$	−9.59680	−0.431780
$495$	14.5207	0.652658
$496$	0	0
$497$	32.9520	1.47810
$498$	−29.9290	−1.34115
$499$	−30.7228	−1.37534	−0.687671	−	0.726022i	$-0.741367\pi$
$499$	−30.7228	−1.37534	−0.687671	+	0.726022i	$0.741367\pi$
$500$	−0.172406	−0.00771021
$501$	−42.7079	−1.90805
$502$	14.3306	0.639607
$503$	14.7318	0.656858	0.328429	−	0.944529i	$-0.393481\pi$
$503$	14.7318	0.656858	0.328429	+	0.944529i	$0.393481\pi$
$504$	50.7121	2.25890
$505$	9.00152	0.400562
$506$	−31.2916	−1.39108
$507$	−32.0033	−1.42131
$508$	1.12909	0.0500954
$509$	−28.0832	−1.24477	−0.622383	−	0.782713i	$-0.713835\pi$
$509$	−28.0832	−1.24477	−0.622383	+	0.782713i	$0.713835\pi$
$510$	−11.4174	−0.505570
$511$	5.29591	0.234277
$512$	19.0502	0.841907
$513$	32.8047	1.44836
$514$	3.81417	0.168236
$515$	−2.14246	−0.0944081
$516$	1.61351	0.0710308
$517$	14.9326	0.656734
$518$	−48.6343	−2.13687
$519$	50.8525	2.23218
$520$	−3.79656	−0.166490
$521$	1.31642	0.0576733	0.0288366	−	0.999584i	$-0.490820\pi$
$521$	1.31642	0.0576733	0.0288366	+	0.999584i	$0.490820\pi$
$522$	−75.5261	−3.30569
$523$	20.6601	0.903402	0.451701	−	0.892169i	$-0.350817\pi$
$523$	20.6601	0.903402	0.451701	+	0.892169i	$0.350817\pi$
$524$	−0.223464	−0.00976206
$525$	10.0492	0.438584
$526$	−20.1945	−0.880522
$527$	0	0
$528$	33.4464	1.45557
$529$	40.3475	1.75424
$530$	5.72654	0.248745
$531$	−57.1674	−2.48085
$532$	2.75444	0.119420
$533$	−0.287815	−0.0124666
$534$	−56.1372	−2.42929
$535$	−6.22162	−0.268984
$536$	12.6361	0.545797
$537$	41.2968	1.78209
$538$	29.9803	1.29254
$539$	−13.2304	−0.569873
$540$	−1.22425	−0.0526834
$541$	45.1612	1.94163	0.970815	−	0.239829i	$-0.0770914\pi$
$541$	45.1612	1.94163	0.970815	+	0.239829i	$0.0770914\pi$
$542$	−40.9628	−1.75950
$543$	61.8496	2.65422
$544$	−2.59285	−0.111167
$545$	14.5905	0.624987
$546$	−20.8758	−0.893400
$547$	−39.8573	−1.70418	−0.852088	−	0.523399i	$-0.824664\pi$
$547$	−39.8573	−1.70418	−0.852088	+	0.523399i	$0.824664\pi$
$548$	−0.176301	−0.00753120
$549$	7.66424	0.327102
$550$	3.93154	0.167641
$551$	43.4857	1.85255
$552$	−62.2992	−2.65163
$553$	34.2065	1.45461
$554$	7.51962	0.319478
$555$	−27.7252	−1.17687
$556$	−1.19998	−0.0508905
$557$	19.9182	0.843963	0.421982	−	0.906604i	$-0.361335\pi$
$557$	19.9182	0.843963	0.421982	+	0.906604i	$0.361335\pi$
$558$	0	0
$559$	4.53934	0.191993
$560$	14.9230	0.630610
$561$	20.6627	0.872382
$562$	7.23199	0.305063
$563$	32.5583	1.37217	0.686085	−	0.727521i	$-0.259328\pi$
$563$	32.5583	1.37217	0.686085	+	0.727521i	$0.259328\pi$
$564$	−2.80453	−0.118092
$565$	−11.3201	−0.476242
$566$	22.6994	0.954125
$567$	14.8810	0.624945
$568$	25.6665	1.07694
$569$	−3.25103	−0.136290	−0.0681452	−	0.997675i	$-0.521708\pi$
$569$	−3.25103	−0.136290	−0.0681452	+	0.997675i	$0.521708\pi$
$570$	19.7858	0.828737
$571$	−8.04060	−0.336488	−0.168244	−	0.985745i	$-0.553810\pi$
$571$	−8.04060	−0.336488	−0.168244	+	0.985745i	$0.553810\pi$
$572$	−0.648161	−0.0271010
$573$	39.9655	1.66958
$574$	1.04090	0.0434463
$575$	−7.95912	−0.331918
$576$	39.1763	1.63235
$577$	−25.7938	−1.07381	−0.536904	−	0.843643i	$-0.680406\pi$
$577$	−25.7938	−1.07381	−0.536904	+	0.843643i	$0.680406\pi$
$578$	14.5821	0.606534
$579$	−59.2909	−2.46405
$580$	−1.62286	−0.0673857
$581$	24.1668	1.00261
$582$	−63.7310	−2.64174
$583$	−10.3637	−0.429220
$584$	4.12501	0.170694
$585$	−7.67248	−0.317218
$586$	21.8939	0.904429
$587$	−1.91959	−0.0792299	−0.0396149	−	0.999215i	$-0.512613\pi$
$587$	−1.91959	−0.0792299	−0.0396149	+	0.999215i	$0.512613\pi$
$588$	2.48484	0.102473
$589$	0	0
$590$	−15.4783	−0.637230
$591$	−44.5958	−1.83443
$592$	−41.1715	−1.69214
$593$	−12.2707	−0.503898	−0.251949	−	0.967741i	$-0.581071\pi$
$593$	−12.2707	−0.503898	−0.251949	+	0.967741i	$0.581071\pi$
$594$	27.9179	1.14548
$595$	9.21922	0.377951
$596$	−3.58404	−0.146808
$597$	−43.2070	−1.76835
$598$	16.5339	0.676121
$599$	−1.76287	−0.0720288	−0.0360144	−	0.999351i	$-0.511466\pi$
$599$	−1.76287	−0.0720288	−0.0360144	+	0.999351i	$0.511466\pi$
$600$	7.82740	0.319552
$601$	7.78880	0.317712	0.158856	−	0.987302i	$-0.449219\pi$
$601$	7.78880	0.317712	0.158856	+	0.987302i	$0.449219\pi$
$602$	−16.4168	−0.669099
$603$	25.5364	1.03992
$604$	−0.0252266	−0.00102645
$605$	3.88484	0.157941
$606$	38.5526	1.56609
$607$	1.71885	0.0697659	0.0348829	−	0.999391i	$-0.488894\pi$
$607$	1.71885	0.0697659	0.0348829	+	0.999391i	$0.488894\pi$
$608$	4.49329	0.182227
$609$	94.5937	3.83313
$610$	2.07512	0.0840192
$611$	−7.89008	−0.319199
$612$	−2.50194	−0.101135
$613$	−21.3044	−0.860477	−0.430239	−	0.902715i	$-0.641571\pi$
$613$	−21.3044	−0.860477	−0.430239	+	0.902715i	$0.641571\pi$
$614$	33.1888	1.33939
$615$	0.593390	0.0239278
$616$	−24.8489	−1.00119
$617$	14.3276	0.576808	0.288404	−	0.957509i	$-0.406875\pi$
$617$	14.3276	0.576808	0.288404	+	0.957509i	$0.406875\pi$
$618$	−9.17594	−0.369110
$619$	9.19099	0.369417	0.184709	−	0.982793i	$-0.440866\pi$
$619$	9.19099	0.369417	0.184709	+	0.982793i	$0.440866\pi$
$620$	0	0
$621$	−56.5177	−2.26798
$622$	−14.0837	−0.564707
$623$	45.3293	1.81608
$624$	−17.6724	−0.707463
$625$	1.00000	0.0400000
$626$	20.2345	0.808733
$627$	−35.8077	−1.43002
$628$	0.0715800	0.00285635
$629$	−25.4353	−1.01417
$630$	27.7480	1.10551
$631$	17.0178	0.677469	0.338734	−	0.940882i	$-0.390001\pi$
$631$	17.0178	0.677469	0.338734	+	0.940882i	$0.390001\pi$
$632$	26.6437	1.05983
$633$	25.7691	1.02423
$634$	−44.0509	−1.74948
$635$	−6.54904	−0.259891
$636$	1.94644	0.0771813
$637$	6.99068	0.276981
$638$	37.0078	1.46515
$639$	51.8695	2.05193
$640$	12.5524	0.496177
$641$	−3.87955	−0.153233	−0.0766164	−	0.997061i	$-0.524412\pi$
$641$	−3.87955	−0.153233	−0.0766164	+	0.997061i	$0.524412\pi$
$642$	−26.6465	−1.05165
$643$	−22.1064	−0.871791	−0.435896	−	0.899997i	$-0.643568\pi$
$643$	−22.1064	−0.871791	−0.435896	+	0.899997i	$0.643568\pi$
$644$	−4.74550	−0.186999
$645$	−9.35879	−0.368502
$646$	18.1516	0.714167
$647$	−37.9030	−1.49012	−0.745059	−	0.666998i	$-0.767579\pi$
$647$	−37.9030	−1.49012	−0.745059	+	0.666998i	$0.767579\pi$
$648$	11.5909	0.455334
$649$	28.0120	1.09957
$650$	−2.07735	−0.0814804
$651$	0	0
$652$	−1.81725	−0.0711689
$653$	6.41241	0.250937	0.125469	−	0.992098i	$-0.459957\pi$
$653$	6.41241	0.250937	0.125469	+	0.992098i	$0.459957\pi$
$654$	62.4894	2.44353
$655$	1.29615	0.0506448
$656$	0.881176	0.0344042
$657$	8.33626	0.325229
$658$	28.5350	1.11241
$659$	11.9679	0.466205	0.233103	−	0.972452i	$-0.425112\pi$
$659$	11.9679	0.466205	0.233103	+	0.972452i	$0.425112\pi$
$660$	1.33632	0.0520162
$661$	9.87244	0.383994	0.191997	−	0.981396i	$-0.438504\pi$
$661$	9.87244	0.383994	0.191997	+	0.981396i	$0.438504\pi$
$662$	−20.1893	−0.784679
$663$	−10.9178	−0.424012
$664$	18.8237	0.730500
$665$	−15.9765	−0.619542
$666$	−76.5551	−2.96645
$667$	−74.9195	−2.90090
$668$	−2.53392	−0.0980402
$669$	62.9860	2.43518
$670$	6.91407	0.267114
$671$	−3.75548	−0.144979
$672$	9.77417	0.377047
$673$	10.1976	0.393090	0.196545	−	0.980495i	$-0.437028\pi$
$673$	10.1976	0.393090	0.196545	+	0.980495i	$0.437028\pi$
$674$	−14.5933	−0.562113
$675$	7.10100	0.273317
$676$	−1.89880	−0.0730307
$677$	−24.8036	−0.953281	−0.476641	−	0.879098i	$-0.658146\pi$
$677$	−24.8036	−0.953281	−0.476641	+	0.879098i	$0.658146\pi$
$678$	−48.4830	−1.86198
$679$	51.4610	1.97489
$680$	7.18090	0.275375
$681$	−9.28031	−0.355622
$682$	0	0
$683$	−27.4082	−1.04875	−0.524373	−	0.851489i	$-0.675700\pi$
$683$	−27.4082	−1.04875	−0.524373	+	0.851489i	$0.675700\pi$
$684$	4.33575	0.165782
$685$	1.02259	0.0390713
$686$	10.3985	0.397016
$687$	25.0995	0.957607
$688$	−13.8977	−0.529844
$689$	5.47597	0.208618
$690$	−34.0881	−1.29771
$691$	14.9810	0.569902	0.284951	−	0.958542i	$-0.408023\pi$
$691$	14.9810	0.569902	0.284951	+	0.958542i	$0.408023\pi$
$692$	3.01715	0.114695
$693$	−50.2173	−1.90760
$694$	−32.4919	−1.23338
$695$	6.96021	0.264016
$696$	73.6796	2.79282
$697$	0.544380	0.0206199
$698$	24.5466	0.929103
$699$	21.6160	0.817594
$700$	0.596234	0.0225355
$701$	−40.5555	−1.53176	−0.765880	−	0.642984i	$-0.777696\pi$
$701$	−40.5555	−1.53176	−0.765880	+	0.642984i	$0.777696\pi$
$702$	−14.7513	−0.556751
$703$	44.0782	1.66244
$704$	−19.1964	−0.723492
$705$	16.2671	0.612653
$706$	−12.8351	−0.483054
$707$	−31.1301	−1.17077
$708$	−5.26103	−0.197721
$709$	−40.8323	−1.53349	−0.766745	−	0.641952i	$-0.778125\pi$
$709$	−40.8323	−1.53349	−0.766745	+	0.641952i	$0.778125\pi$
$710$	14.0439	0.527057
$711$	53.8443	2.01932
$712$	35.3072	1.32319
$713$	0	0
$714$	39.4849	1.47769
$715$	3.75951	0.140598
$716$	2.45020	0.0915682
$717$	71.2217	2.65982
$718$	21.3792	0.797865
$719$	−6.30206	−0.235027	−0.117514	−	0.993071i	$-0.537492\pi$
$719$	−6.30206	−0.235027	−0.117514	+	0.993071i	$0.537492\pi$
$720$	23.4901	0.875426
$721$	7.40932	0.275937
$722$	−3.45174	−0.128461
$723$	21.9018	0.814537
$724$	3.66962	0.136380
$725$	9.41305	0.349592
$726$	16.6384	0.617508
$727$	−32.3549	−1.19998	−0.599988	−	0.800009i	$-0.704828\pi$
$727$	−32.3549	−1.19998	−0.599988	+	0.800009i	$0.704828\pi$
$728$	13.1297	0.486619
$729$	−38.4783	−1.42512
$730$	2.25707	0.0835380
$731$	−8.58582	−0.317558
$732$	0.705329	0.0260697
$733$	20.5902	0.760516	0.380258	−	0.924881i	$-0.375835\pi$
$733$	20.5902	0.760516	0.380258	+	0.924881i	$0.375835\pi$
$734$	21.2048	0.782685
$735$	−14.4128	−0.531622
$736$	−7.74128	−0.285347
$737$	−12.5128	−0.460916
$738$	1.63848	0.0603131
$739$	37.3538	1.37408	0.687041	−	0.726618i	$-0.258909\pi$
$739$	37.3538	1.37408	0.687041	+	0.726618i	$0.258909\pi$
$740$	−1.64497	−0.0604704
$741$	18.9201	0.695047
$742$	−19.8042	−0.727036
$743$	−6.28553	−0.230594	−0.115297	−	0.993331i	$-0.536782\pi$
$743$	−6.28553	−0.230594	−0.115297	+	0.993331i	$0.536782\pi$
$744$	0	0
$745$	20.7884	0.761629
$746$	27.5038	1.00699
$747$	38.0409	1.39184
$748$	1.22595	0.0448251
$749$	21.5163	0.786190
$750$	4.28290	0.156389
$751$	4.39903	0.160523	0.0802614	−	0.996774i	$-0.474424\pi$
$751$	4.39903	0.160523	0.0802614	+	0.996774i	$0.474424\pi$
$752$	24.1564	0.880892
$753$	−28.2528	−1.02959
$754$	−19.5542	−0.712122
$755$	0.146321	0.00532517
$756$	4.23386	0.153984
$757$	1.82986	0.0665075	0.0332537	−	0.999447i	$-0.489413\pi$
$757$	1.82986	0.0665075	0.0332537	+	0.999447i	$0.489413\pi$
$758$	−18.8961	−0.686338
$759$	61.6913	2.23925
$760$	−12.4442	−0.451398
$761$	17.9862	0.651998	0.325999	−	0.945370i	$-0.394299\pi$
$761$	17.9862	0.651998	0.325999	+	0.945370i	$0.394299\pi$
$762$	−28.0489	−1.01610
$763$	−50.4585	−1.82672
$764$	2.37121	0.0857873
$765$	14.5119	0.524680
$766$	41.1582	1.48710
$767$	−14.8010	−0.534434
$768$	11.9367	0.430728
$769$	−18.9297	−0.682623	−0.341311	−	0.939950i	$-0.610871\pi$
$769$	−18.9297	−0.682623	−0.341311	+	0.939950i	$0.610871\pi$
$770$	−13.5965	−0.489985
$771$	−7.51963	−0.270813
$772$	−3.51781	−0.126609
$773$	21.0091	0.755643	0.377822	−	0.925878i	$-0.376673\pi$
$773$	21.0091	0.755643	0.377822	+	0.925878i	$0.376673\pi$
$774$	−25.8416	−0.928857
$775$	0	0
$776$	40.0833	1.43891
$777$	95.8825	3.43977
$778$	5.71279	0.204813
$779$	−0.943387	−0.0338003
$780$	−0.706087	−0.0252820
$781$	−25.4161	−0.909458
$782$	−31.2726	−1.11831
$783$	66.8420	2.38874
$784$	−21.4027	−0.764384
$785$	−0.415184	−0.0148185
$786$	5.55128	0.198008
$787$	23.5993	0.841223	0.420612	−	0.907241i	$-0.361816\pi$
$787$	23.5993	0.841223	0.420612	+	0.907241i	$0.361816\pi$
$788$	−2.64593	−0.0942574
$789$	39.8135	1.41740
$790$	14.5785	0.518681
$791$	39.1487	1.39197
$792$	−39.1146	−1.38988
$793$	1.98432	0.0704654
$794$	−40.6034	−1.44096
$795$	−11.2899	−0.400410
$796$	−2.56353	−0.0908620
$797$	−24.6740	−0.873996	−0.436998	−	0.899462i	$-0.643958\pi$
$797$	−24.6740	−0.873996	−0.436998	+	0.899462i	$0.643958\pi$
$798$	−68.4257	−2.42224
$799$	14.9235	0.527956
$800$	0.972630	0.0343877
$801$	71.3526	2.52112
$802$	−16.4016	−0.579160
$803$	−4.08477	−0.144148
$804$	2.35008	0.0828808
$805$	27.5252	0.970135
$806$	0	0
$807$	−59.1061	−2.08063
$808$	−24.2474	−0.853022
$809$	12.3918	0.435671	0.217835	−	0.975986i	$-0.430100\pi$
$809$	12.3918	0.435671	0.217835	+	0.975986i	$0.430100\pi$
$810$	6.34218	0.222841
$811$	−54.3793	−1.90952	−0.954758	−	0.297384i	$-0.903886\pi$
$811$	−54.3793	−1.90952	−0.954758	+	0.297384i	$0.903886\pi$
$812$	5.61238	0.196956
$813$	80.7582	2.83231
$814$	37.5120	1.31479
$815$	10.5405	0.369219
$816$	33.4261	1.17015
$817$	14.8789	0.520545
$818$	−3.74070	−0.130791
$819$	26.5339	0.927169
$820$	0.0352067	0.00122947
$821$	−24.6258	−0.859446	−0.429723	−	0.902961i	$-0.641389\pi$
$821$	−24.6258	−0.859446	−0.429723	+	0.902961i	$0.641389\pi$
$822$	4.37966	0.152758
$823$	−9.56851	−0.333537	−0.166769	−	0.985996i	$-0.553333\pi$
$823$	−9.56851	−0.333537	−0.166769	+	0.985996i	$0.553333\pi$
$824$	5.77116	0.201048
$825$	−7.75103	−0.269856
$826$	53.5288	1.86251
$827$	39.7057	1.38070	0.690352	−	0.723474i	$-0.257456\pi$
$827$	39.7057	1.38070	0.690352	+	0.723474i	$0.257456\pi$
$828$	−7.46986	−0.259596
$829$	−44.3247	−1.53946	−0.769730	−	0.638369i	$-0.779609\pi$
$829$	−44.3247	−1.53946	−0.769730	+	0.638369i	$0.779609\pi$
$830$	10.2997	0.357508
$831$	−14.8249	−0.514271
$832$	10.1430	0.351646
$833$	−13.2224	−0.458127
$834$	29.8099	1.03223
$835$	14.6974	0.508625
$836$	−2.12452	−0.0734780
$837$	0	0
$838$	−26.6197	−0.919564
$839$	−49.7663	−1.71812	−0.859061	−	0.511873i	$-0.828952\pi$
$839$	−49.7663	−1.71812	−0.859061	+	0.511873i	$0.828952\pi$
$840$	−27.0696	−0.933991
$841$	59.6054	2.05536
$842$	2.60674	0.0898341
$843$	−14.2579	−0.491067
$844$	1.52892	0.0526276
$845$	11.0135	0.378877
$846$	44.9168	1.54427
$847$	−13.4350	−0.461633
$848$	−16.7653	−0.575723
$849$	−44.7517	−1.53588
$850$	3.92916	0.134769
$851$	−75.9403	−2.60320
$852$	4.77347	0.163537
$853$	−23.4872	−0.804188	−0.402094	−	0.915598i	$-0.631718\pi$
$853$	−23.4872	−0.804188	−0.402094	+	0.915598i	$0.631718\pi$
$854$	−7.17643	−0.245573
$855$	−25.1485	−0.860062
$856$	16.7592	0.572818
$857$	−25.9974	−0.888055	−0.444028	−	0.896013i	$-0.646451\pi$
$857$	−25.9974	−0.888055	−0.444028	+	0.896013i	$0.646451\pi$
$858$	16.1016	0.549700
$859$	−14.2764	−0.487105	−0.243553	−	0.969888i	$-0.578313\pi$
$859$	−14.2764	−0.487105	−0.243553	+	0.969888i	$0.578313\pi$
$860$	−0.555270	−0.0189346
$861$	−2.05213	−0.0699365
$862$	−0.431421	−0.0146943
$863$	−39.8738	−1.35732	−0.678659	−	0.734453i	$-0.737439\pi$
$863$	−39.8738	−1.35732	−0.678659	+	0.734453i	$0.737439\pi$
$864$	6.90665	0.234969
$865$	−17.5003	−0.595028
$866$	5.89979	0.200483
$867$	−28.7485	−0.976351
$868$	0	0
$869$	−26.3837	−0.895006
$870$	40.3151	1.36681
$871$	6.61154	0.224024
$872$	−39.3024	−1.33095
$873$	81.0046	2.74159
$874$	54.1941	1.83314
$875$	−3.45832	−0.116913
$876$	0.767174	0.0259204
$877$	14.0150	0.473252	0.236626	−	0.971601i	$-0.423958\pi$
$877$	14.0150	0.473252	0.236626	+	0.971601i	$0.423958\pi$
$878$	5.99308	0.202257
$879$	−43.1638	−1.45588
$880$	−11.5102	−0.388008
$881$	−50.4724	−1.70046	−0.850229	−	0.526413i	$-0.823537\pi$
$881$	−50.4724	−1.70046	−0.850229	+	0.526413i	$0.823537\pi$
$882$	−39.7967	−1.34002
$883$	−16.1577	−0.543750	−0.271875	−	0.962333i	$-0.587644\pi$
$883$	−16.1577	−0.543750	−0.271875	+	0.962333i	$0.587644\pi$
$884$	−0.647768	−0.0217868
$885$	30.5154	1.02576
$886$	−13.4078	−0.450443
$887$	3.19982	0.107439	0.0537197	−	0.998556i	$-0.482892\pi$
$887$	3.19982	0.107439	0.0537197	+	0.998556i	$0.482892\pi$
$888$	74.6835	2.50621
$889$	22.6487	0.759613
$890$	19.3190	0.647573
$891$	−11.4778	−0.384522
$892$	3.73704	0.125126
$893$	−25.8618	−0.865432
$894$	89.0347	2.97776
$895$	−14.2118	−0.475049
$896$	−43.4102	−1.45023
$897$	−32.5965	−1.08837
$898$	−7.83444	−0.261439
$899$	0	0
$900$	0.938529	0.0312843
$901$	−10.3574	−0.345055
$902$	−0.802853	−0.0267321
$903$	32.3657	1.07706
$904$	30.4931	1.01419
$905$	−21.2848	−0.707531
$906$	0.626678	0.0208200
$907$	−33.9047	−1.12579	−0.562894	−	0.826529i	$-0.690312\pi$
$907$	−33.9047	−1.12579	−0.562894	+	0.826529i	$0.690312\pi$
$908$	−0.550614	−0.0182728
$909$	−49.0018	−1.62529
$910$	7.18415	0.238152
$911$	−13.9927	−0.463598	−0.231799	−	0.972764i	$-0.574461\pi$
$911$	−13.9927	−0.463598	−0.231799	+	0.972764i	$0.574461\pi$
$912$	−57.9259	−1.91812
$913$	−18.6400	−0.616895
$914$	−9.19621	−0.304184
$915$	−4.09110	−0.135248
$916$	1.48919	0.0492042
$917$	−4.48251	−0.148025
$918$	27.9009	0.920868
$919$	39.4083	1.29996	0.649980	−	0.759951i	$-0.274777\pi$
$919$	39.4083	1.29996	0.649980	+	0.759951i	$0.274777\pi$
$920$	21.4395	0.706840
$921$	−65.4318	−2.15605
$922$	39.7952	1.31058
$923$	13.4294	0.442033
$924$	−4.62143	−0.152034
$925$	9.54129	0.313716
$926$	−21.6837	−0.712570
$927$	11.6630	0.383062
$928$	9.15541	0.300541
$929$	12.8728	0.422342	0.211171	−	0.977449i	$-0.432272\pi$
$929$	12.8728	0.422342	0.211171	+	0.977449i	$0.432272\pi$
$930$	0	0
$931$	22.9138	0.750968
$932$	1.28251	0.0420100
$933$	27.7661	0.909021
$934$	−41.7630	−1.36653
$935$	−7.11084	−0.232549
$936$	20.6674	0.675535
$937$	−28.6284	−0.935250	−0.467625	−	0.883927i	$-0.654890\pi$
$937$	−28.6284	−0.935250	−0.467625	+	0.883927i	$0.654890\pi$
$938$	−23.9111	−0.780724
$939$	−39.8923	−1.30184
$940$	0.965148	0.0314796
$941$	20.3133	0.662196	0.331098	−	0.943596i	$-0.392581\pi$
$941$	20.3133	0.662196	0.331098	+	0.943596i	$0.392581\pi$
$942$	−1.77819	−0.0579365
$943$	1.62532	0.0529276
$944$	45.3150	1.47488
$945$	−24.5575	−0.798856
$946$	12.6624	0.411690
$947$	47.7334	1.55113	0.775563	−	0.631270i	$-0.217466\pi$
$947$	47.7334	1.55113	0.775563	+	0.631270i	$0.217466\pi$
$948$	4.95521	0.160938
$949$	2.15831	0.0700618
$950$	−6.80906	−0.220915
$951$	86.8463	2.81618
$952$	−24.8339	−0.804870
$953$	9.76064	0.316178	0.158089	−	0.987425i	$-0.449467\pi$
$953$	9.76064	0.316178	0.158089	+	0.987425i	$0.449467\pi$
$954$	−31.1737	−1.00929
$955$	−13.7537	−0.445058
$956$	4.22568	0.136668
$957$	−72.9608	−2.35849
$958$	8.98965	0.290442
$959$	−3.53646	−0.114198
$960$	−20.9120	−0.674931
$961$	0	0
$962$	−19.8206	−0.639042
$963$	33.8688	1.09141
$964$	1.29946	0.0418529
$965$	20.4043	0.656837
$966$	117.887	3.79297
$967$	−42.9460	−1.38105	−0.690525	−	0.723308i	$-0.742620\pi$
$967$	−42.9460	−1.38105	−0.690525	+	0.723308i	$0.742620\pi$
$968$	−10.4646	−0.336346
$969$	−35.7859	−1.14961
$970$	21.9323	0.704203
$971$	19.5012	0.625822	0.312911	−	0.949782i	$-0.398696\pi$
$971$	19.5012	0.625822	0.312911	+	0.949782i	$0.398696\pi$
$972$	−1.51707	−0.0486599
$973$	−24.0707	−0.771670
$974$	−31.8864	−1.02171
$975$	4.09550	0.131161
$976$	−6.07523	−0.194463
$977$	−11.0256	−0.352739	−0.176370	−	0.984324i	$-0.556435\pi$
$977$	−11.0256	−0.352739	−0.176370	+	0.984324i	$0.556435\pi$
$978$	45.1440	1.44355
$979$	−34.9628	−1.11741
$980$	−0.855129	−0.0273161
$981$	−79.4264	−2.53589
$982$	−0.998068	−0.0318496
$983$	41.3053	1.31743	0.658717	−	0.752391i	$-0.271100\pi$
$983$	41.3053	1.31743	0.658717	+	0.752391i	$0.271100\pi$
$984$	−1.59842	−0.0509557
$985$	15.3471	0.489000
$986$	36.9853	1.17785
$987$	−56.2567	−1.79067
$988$	1.12255	0.0357132
$989$	−25.6341	−0.815116
$990$	−21.4022	−0.680207
$991$	19.5359	0.620579	0.310290	−	0.950642i	$-0.399574\pi$
$991$	19.5359	0.620579	0.310290	+	0.950642i	$0.399574\pi$
$992$	0	0
$993$	39.8031	1.26311
$994$	−48.5682	−1.54049
$995$	14.8692	0.471385
$996$	3.50084	0.110928
$997$	5.26675	0.166800	0.0833998	−	0.996516i	$-0.473422\pi$
$997$	5.26675	0.166800	0.0833998	+	0.996516i	$0.473422\pi$
$998$	45.2826	1.43340
$999$	67.7527	2.14360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4805.2.a.y.1.6		20
31.22	odd	30		155.2.q.a.81.4	✓	40
31.24	odd	30		155.2.q.a.111.4	yes	40
31.30	odd	2		4805.2.a.x.1.6		20
155.22	even	60		775.2.ck.c.174.3		80
155.24	odd	30		775.2.bl.c.576.2		40
155.53	even	60		775.2.ck.c.174.8		80
155.84	odd	30		775.2.bl.c.701.2		40
155.117	even	60		775.2.ck.c.49.8		80
155.148	even	60		775.2.ck.c.49.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.81.4	✓	40	31.22	odd	30
155.2.q.a.111.4	yes	40	31.24	odd	30
775.2.bl.c.576.2		40	155.24	odd	30
775.2.bl.c.701.2		40	155.84	odd	30
775.2.ck.c.49.3		80	155.148	even	60
775.2.ck.c.49.8		80	155.117	even	60
775.2.ck.c.174.3		80	155.22	even	60
775.2.ck.c.174.8		80	155.53	even	60
4805.2.a.x.1.6		20	31.30	odd	2
4805.2.a.y.1.6		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4805 = 5 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4805.a (trivial)

\(f(q)\)	\(=\)	\(q-1.47391 q^{2} +2.90581 q^{3} +0.172406 q^{4} -1.00000 q^{5} -4.28290 q^{6} +3.45832 q^{7} +2.69371 q^{8} +5.44372 q^{9} +1.47391 q^{10} -2.66743 q^{11} +0.500978 q^{12} +1.40942 q^{13} -5.09725 q^{14} -2.90581 q^{15} -4.31509 q^{16} -2.66581 q^{17} -8.02355 q^{18} +4.61973 q^{19} -0.172406 q^{20} +10.0492 q^{21} +3.93154 q^{22} -7.95912 q^{23} +7.82740 q^{24} +1.00000 q^{25} -2.07735 q^{26} +7.10100 q^{27} +0.596234 q^{28} +9.41305 q^{29} +4.28290 q^{30} +0.972630 q^{32} -7.75103 q^{33} +3.92916 q^{34} -3.45832 q^{35} +0.938529 q^{36} +9.54129 q^{37} -6.80906 q^{38} +4.09550 q^{39} -2.69371 q^{40} -0.204208 q^{41} -14.8116 q^{42} +3.22072 q^{43} -0.459879 q^{44} -5.44372 q^{45} +11.7310 q^{46} -5.59812 q^{47} -12.5388 q^{48} +4.95998 q^{49} -1.47391 q^{50} -7.74633 q^{51} +0.242991 q^{52} +3.88528 q^{53} -10.4662 q^{54} +2.66743 q^{55} +9.31570 q^{56} +13.4240 q^{57} -13.8740 q^{58} -10.5015 q^{59} -0.500978 q^{60} +1.40790 q^{61} +18.8261 q^{63} +7.19661 q^{64} -1.40942 q^{65} +11.4243 q^{66} +4.69098 q^{67} -0.459600 q^{68} -23.1277 q^{69} +5.09725 q^{70} +9.52831 q^{71} +14.6638 q^{72} +1.53135 q^{73} -14.0630 q^{74} +2.90581 q^{75} +0.796467 q^{76} -9.22481 q^{77} -6.03639 q^{78} +9.89107 q^{79} +4.31509 q^{80} +4.30296 q^{81} +0.300984 q^{82} +6.98802 q^{83} +1.73254 q^{84} +2.66581 q^{85} -4.74704 q^{86} +27.3525 q^{87} -7.18526 q^{88} +13.1073 q^{89} +8.02355 q^{90} +4.87421 q^{91} -1.37220 q^{92} +8.25112 q^{94} -4.61973 q^{95} +2.82628 q^{96} +14.8804 q^{97} -7.31056 q^{98} -14.5207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + 4 q^{3} + 15 q^{4} - 20 q^{5} + 4 q^{6} + q^{7} + 9 q^{8} + 8 q^{9} + q^{10} + 17 q^{11} - 13 q^{12} + 9 q^{13} + 6 q^{14} - 4 q^{15} + 9 q^{16} - 20 q^{17} - 28 q^{18} - 7 q^{19} - 15 q^{20}+ \cdots + 53 q^{99}+O(q^{100}) \) 20 * q - q^2 + 4 * q^3 + 15 * q^4 - 20 * q^5 + 4 * q^6 + q^7 + 9 * q^8 + 8 * q^9 + q^10 + 17 * q^11 - 13 * q^12 + 9 * q^13 + 6 * q^14 - 4 * q^15 + 9 * q^16 - 20 * q^17 - 28 * q^18 - 7 * q^19 - 15 * q^20 + 22 * q^21 + 22 * q^22 - 9 * q^23 + 28 * q^24 + 20 * q^25 + 32 * q^26 + 13 * q^27 + 8 * q^28 + 4 * q^29 - 4 * q^30 + 2 * q^32 - 26 * q^33 + 27 * q^34 - q^35 + 13 * q^36 + 12 * q^37 + 15 * q^38 + 11 * q^39 - 9 * q^40 + 9 * q^41 - 14 * q^42 + 42 * q^43 + 49 * q^44 - 8 * q^45 - 24 * q^46 - 32 * q^47 - 31 * q^48 + q^49 - q^50 + 2 * q^51 + 29 * q^52 + 9 * q^53 + 44 * q^54 - 17 * q^55 - 9 * q^56 + 38 * q^57 + 47 * q^58 + 6 * q^59 + 13 * q^60 + 50 * q^61 + 55 * q^63 - 19 * q^64 - 9 * q^65 + 15 * q^66 - 30 * q^67 - 34 * q^68 + 2 * q^69 - 6 * q^70 + 7 * q^71 - 16 * q^72 + 32 * q^73 - 22 * q^74 + 4 * q^75 + 23 * q^76 - 8 * q^77 + 29 * q^78 + 63 * q^79 - 9 * q^80 + 8 * q^81 - 12 * q^82 - 35 * q^83 + 71 * q^84 + 20 * q^85 + 65 * q^86 + 46 * q^87 + 70 * q^88 + 40 * q^89 + 28 * q^90 + 28 * q^91 + 5 * q^92 + 65 * q^94 + 7 * q^95 + 46 * q^96 + 41 * q^97 + 65 * q^98 + 53 * q^99

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