LMFDB - Embedded newform 6069.2.a.be.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6069,2,Mod(1,6069)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6069, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6069.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 6069 = 3 \cdot 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6069.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,4,10,12,-6,4,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$48.4612089867$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 8x^{8} + 44x^{7} + 5x^{6} - 144x^{5} + 48x^{4} + 160x^{3} - 44x^{2} - 64x - 2 $ x^10 - 4x^9 - 8x^8 + 44x^7 + 5x^6 - 144x^5 + 48x^4 + 160x^3 - 44x^2 - 64*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 357)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.0320370$ of defining polynomial
Character	$\chi$	$=$	6069.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.0320370 q^{2} +1.00000 q^{3} -1.99897 q^{4} -2.49420 q^{5} -0.0320370 q^{6} -1.00000 q^{7} +0.128115 q^{8} +1.00000 q^{9} +0.0799067 q^{10} +1.19691 q^{11} -1.99897 q^{12} +6.07047 q^{13} +0.0320370 q^{14} -2.49420 q^{15} +3.99384 q^{16} -0.0320370 q^{18} +8.11633 q^{19} +4.98584 q^{20} -1.00000 q^{21} -0.0383453 q^{22} -7.69432 q^{23} +0.128115 q^{24} +1.22105 q^{25} -0.194479 q^{26} +1.00000 q^{27} +1.99897 q^{28} -5.27739 q^{29} +0.0799067 q^{30} -0.675631 q^{31} -0.384181 q^{32} +1.19691 q^{33} +2.49420 q^{35} -1.99897 q^{36} +1.44837 q^{37} -0.260023 q^{38} +6.07047 q^{39} -0.319545 q^{40} -7.34574 q^{41} +0.0320370 q^{42} -1.76514 q^{43} -2.39259 q^{44} -2.49420 q^{45} +0.246503 q^{46} -5.15344 q^{47} +3.99384 q^{48} +1.00000 q^{49} -0.0391186 q^{50} -12.1347 q^{52} -4.55283 q^{53} -0.0320370 q^{54} -2.98533 q^{55} -0.128115 q^{56} +8.11633 q^{57} +0.169072 q^{58} +6.26447 q^{59} +4.98584 q^{60} +7.26118 q^{61} +0.0216452 q^{62} -1.00000 q^{63} -7.97538 q^{64} -15.1410 q^{65} -0.0383453 q^{66} +3.54409 q^{67} -7.69432 q^{69} -0.0799067 q^{70} -3.75607 q^{71} +0.128115 q^{72} +15.9665 q^{73} -0.0464015 q^{74} +1.22105 q^{75} -16.2243 q^{76} -1.19691 q^{77} -0.194479 q^{78} +0.616782 q^{79} -9.96145 q^{80} +1.00000 q^{81} +0.235335 q^{82} -0.959545 q^{83} +1.99897 q^{84} +0.0565497 q^{86} -5.27739 q^{87} +0.153342 q^{88} +17.8863 q^{89} +0.0799067 q^{90} -6.07047 q^{91} +15.3807 q^{92} -0.675631 q^{93} +0.165101 q^{94} -20.2438 q^{95} -0.384181 q^{96} -7.68879 q^{97} -0.0320370 q^{98} +1.19691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 10 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} + 12 q^{12} + 6 q^{13} - 4 q^{14} - 6 q^{15} + 20 q^{16} + 4 q^{18} + 6 q^{19} - 16 q^{20} - 10 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 10 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 + 12 * q^12 + 6 * q^13 - 4 * q^14 - 6 * q^15 + 20 * q^16 + 4 * q^18 + 6 * q^19 - 16 * q^20 - 10 * q^21 + 24 * q^22 + 18 * q^23 + 12 * q^24 + 4 * q^25 + 12 * q^26 + 10 * q^27 - 12 * q^28 - 12 * q^29 - 8 * q^31 + 28 * q^32 - 2 * q^33 + 6 * q^35 + 12 * q^36 + 24 * q^37 + 32 * q^38 + 6 * q^39 - 36 * q^40 - 2 * q^41 - 4 * q^42 + 6 * q^43 + 28 * q^44 - 6 * q^45 - 28 * q^46 + 16 * q^47 + 20 * q^48 + 10 * q^49 + 52 * q^50 + 24 * q^52 - 12 * q^53 + 4 * q^54 + 18 * q^55 - 12 * q^56 + 6 * q^57 + 20 * q^58 + 20 * q^59 - 16 * q^60 - 4 * q^61 - 24 * q^62 - 10 * q^63 + 56 * q^64 - 38 * q^65 + 24 * q^66 + 20 * q^67 + 18 * q^69 - 20 * q^71 + 12 * q^72 + 20 * q^73 + 36 * q^74 + 4 * q^75 - 8 * q^76 + 2 * q^77 + 12 * q^78 + 20 * q^79 - 92 * q^80 + 10 * q^81 + 8 * q^82 + 36 * q^83 - 12 * q^84 - 12 * q^87 + 92 * q^88 + 32 * q^89 - 6 * q^91 + 40 * q^92 - 8 * q^93 + 60 * q^94 - 14 * q^95 + 28 * q^96 + 36 * q^97 + 4 * q^98 - 2 * 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 $

$2$	−0.0320370	−0.0226536	−0.0113268	−	0.999936i	$-0.503606\pi$
$2$	−0.0320370	−0.0226536	−0.0113268	+	0.999936i	$0.503606\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.99897	−0.999487
$5$	−2.49420	−1.11544	−0.557721	−	0.830029i	$-0.688324\pi$
$5$	−2.49420	−1.11544	−0.557721	+	0.830029i	$0.688324\pi$
$6$	−0.0320370	−0.0130790
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.128115	0.0452955
$9$	1.00000	0.333333
$10$	0.0799067	0.0252687
$11$	1.19691	0.360881	0.180441	−	0.983586i	$-0.442248\pi$
$11$	1.19691	0.360881	0.180441	+	0.983586i	$0.442248\pi$
$12$	−1.99897	−0.577054
$13$	6.07047	1.68364	0.841822	−	0.539754i	$-0.181483\pi$
$13$	6.07047	1.68364	0.841822	+	0.539754i	$0.181483\pi$
$14$	0.0320370	0.00856224
$15$	−2.49420	−0.644000
$16$	3.99384	0.998461
$17$	0	0
$17$	0	0
$18$	−0.0320370	−0.00755119
$19$	8.11633	1.86201	0.931007	−	0.365001i	$-0.118931\pi$
$19$	8.11633	1.86201	0.931007	+	0.365001i	$0.118931\pi$
$20$	4.98584	1.11487
$21$	−1.00000	−0.218218
$22$	−0.0383453	−0.00817525
$23$	−7.69432	−1.60438	−0.802189	−	0.597071i	$-0.796331\pi$
$23$	−7.69432	−1.60438	−0.802189	+	0.597071i	$0.796331\pi$
$24$	0.128115	0.0261514
$25$	1.22105	0.244209
$26$	−0.194479	−0.0381405
$27$	1.00000	0.192450
$28$	1.99897	0.377771
$29$	−5.27739	−0.979988	−0.489994	−	0.871726i	$-0.663001\pi$
$29$	−5.27739	−0.979988	−0.489994	+	0.871726i	$0.663001\pi$
$30$	0.0799067	0.0145889
$31$	−0.675631	−0.121347	−0.0606734	−	0.998158i	$-0.519325\pi$
$31$	−0.675631	−0.121347	−0.0606734	+	0.998158i	$0.519325\pi$
$32$	−0.384181	−0.0679142
$33$	1.19691	0.208355
$34$	0	0
$35$	2.49420	0.421597
$36$	−1.99897	−0.333162
$37$	1.44837	0.238111	0.119055	−	0.992888i	$-0.462013\pi$
$37$	1.44837	0.238111	0.119055	+	0.992888i	$0.462013\pi$
$38$	−0.260023	−0.0421812
$39$	6.07047	0.972053
$40$	−0.319545	−0.0505245
$41$	−7.34574	−1.14721	−0.573606	−	0.819131i	$-0.694456\pi$
$41$	−7.34574	−1.14721	−0.573606	+	0.819131i	$0.694456\pi$
$42$	0.0320370	0.00494341
$43$	−1.76514	−0.269181	−0.134591	−	0.990901i	$-0.542972\pi$
$43$	−1.76514	−0.269181	−0.134591	+	0.990901i	$0.542972\pi$
$44$	−2.39259	−0.360696
$45$	−2.49420	−0.371814
$46$	0.246503	0.0363448
$47$	−5.15344	−0.751707	−0.375853	−	0.926679i	$-0.622650\pi$
$47$	−5.15344	−0.751707	−0.375853	+	0.926679i	$0.622650\pi$
$48$	3.99384	0.576462
$49$	1.00000	0.142857
$50$	−0.0391186	−0.00553220
$51$	0	0
$52$	−12.1347	−1.68278
$53$	−4.55283	−0.625380	−0.312690	−	0.949855i	$-0.601230\pi$
$53$	−4.55283	−0.625380	−0.312690	+	0.949855i	$0.601230\pi$
$54$	−0.0320370	−0.00435968
$55$	−2.98533	−0.402542
$56$	−0.128115	−0.0171201
$57$	8.11633	1.07503
$58$	0.169072	0.0222002
$59$	6.26447	0.815564	0.407782	−	0.913079i	$-0.366302\pi$
$59$	6.26447	0.815564	0.407782	+	0.913079i	$0.366302\pi$
$60$	4.98584	0.643670
$61$	7.26118	0.929699	0.464850	−	0.885390i	$-0.346108\pi$
$61$	7.26118	0.929699	0.464850	+	0.885390i	$0.346108\pi$
$62$	0.0216452	0.00274894
$63$	−1.00000	−0.125988
$64$	−7.97538	−0.996922
$65$	−15.1410	−1.87801
$66$	−0.0383453	−0.00471998
$67$	3.54409	0.432980	0.216490	−	0.976285i	$-0.430539\pi$
$67$	3.54409	0.432980	0.216490	+	0.976285i	$0.430539\pi$
$68$	0	0
$69$	−7.69432	−0.926287
$70$	−0.0799067	−0.00955067
$71$	−3.75607	−0.445764	−0.222882	−	0.974845i	$-0.571546\pi$
$71$	−3.75607	−0.445764	−0.222882	+	0.974845i	$0.571546\pi$
$72$	0.128115	0.0150985
$73$	15.9665	1.86874	0.934371	−	0.356302i	$-0.115963\pi$
$73$	15.9665	1.86874	0.934371	+	0.356302i	$0.115963\pi$
$74$	−0.0464015	−0.00539406
$75$	1.22105	0.140994
$76$	−16.2243	−1.86106
$77$	−1.19691	−0.136400
$78$	−0.194479	−0.0220205
$79$	0.616782	0.0693934	0.0346967	−	0.999398i	$-0.488953\pi$
$79$	0.616782	0.0693934	0.0346967	+	0.999398i	$0.488953\pi$
$80$	−9.96145	−1.11372
$81$	1.00000	0.111111
$82$	0.235335	0.0259884
$83$	−0.959545	−0.105324	−0.0526619	−	0.998612i	$-0.516771\pi$
$83$	−0.959545	−0.105324	−0.0526619	+	0.998612i	$0.516771\pi$
$84$	1.99897	0.218106
$85$	0	0
$86$	0.0565497	0.00609791
$87$	−5.27739	−0.565796
$88$	0.153342	0.0163463
$89$	17.8863	1.89594	0.947970	−	0.318359i	$-0.103132\pi$
$89$	17.8863	1.89594	0.947970	+	0.318359i	$0.103132\pi$
$90$	0.0799067	0.00842290
$91$	−6.07047	−0.636358
$92$	15.3807	1.60355
$93$	−0.675631	−0.0700596
$94$	0.165101	0.0170288
$95$	−20.2438	−2.07697
$96$	−0.384181	−0.0392103
$97$	−7.68879	−0.780678	−0.390339	−	0.920671i	$-0.627642\pi$
$97$	−7.68879	−0.780678	−0.390339	+	0.920671i	$0.627642\pi$
$98$	−0.0320370	−0.00323622
$99$	1.19691	0.120294
$100$	−2.44084	−0.244084
$101$	−12.9635	−1.28992	−0.644959	−	0.764217i	$-0.723126\pi$
$101$	−12.9635	−1.28992	−0.644959	+	0.764217i	$0.723126\pi$
$102$	0	0
$103$	7.23801	0.713182	0.356591	−	0.934261i	$-0.383939\pi$
$103$	7.23801	0.713182	0.356591	+	0.934261i	$0.383939\pi$
$104$	0.777718	0.0762615
$105$	2.49420	0.243409
$106$	0.145859	0.0141671
$107$	−0.656429	−0.0634594	−0.0317297	−	0.999496i	$-0.510102\pi$
$107$	−0.656429	−0.0634594	−0.0317297	+	0.999496i	$0.510102\pi$
$108$	−1.99897	−0.192351
$109$	−12.5896	−1.20586	−0.602930	−	0.797794i	$-0.706000\pi$
$109$	−12.5896	−1.20586	−0.602930	+	0.797794i	$0.706000\pi$
$110$	0.0956410	0.00911901
$111$	1.44837	0.137473
$112$	−3.99384	−0.377383
$113$	20.0088	1.88227	0.941137	−	0.338025i	$-0.109759\pi$
$113$	20.0088	1.88227	0.941137	+	0.338025i	$0.109759\pi$
$114$	−0.260023	−0.0243534
$115$	19.1912	1.78959
$116$	10.5494	0.979485
$117$	6.07047	0.561215
$118$	−0.200694	−0.0184754
$119$	0	0
$120$	−0.319545	−0.0291703
$121$	−9.56741	−0.869765
$122$	−0.232626	−0.0210610
$123$	−7.34574	−0.662343
$124$	1.35057	0.121285
$125$	9.42548	0.843040
$126$	0.0320370	0.00285408
$127$	8.82854	0.783406	0.391703	−	0.920092i	$-0.371886\pi$
$127$	8.82854	0.783406	0.391703	+	0.920092i	$0.371886\pi$
$128$	1.02387	0.0904980
$129$	−1.76514	−0.155412
$130$	0.485071	0.0425435
$131$	−4.16622	−0.364004	−0.182002	−	0.983298i	$-0.558258\pi$
$131$	−4.16622	−0.364004	−0.182002	+	0.983298i	$0.558258\pi$
$132$	−2.39259	−0.208248
$133$	−8.11633	−0.703775
$134$	−0.113542	−0.00980853
$135$	−2.49420	−0.214667
$136$	0	0
$137$	−13.0894	−1.11830	−0.559151	−	0.829066i	$-0.688873\pi$
$137$	−13.0894	−1.11830	−0.559151	+	0.829066i	$0.688873\pi$
$138$	0.246503	0.0209837
$139$	19.5822	1.66094	0.830471	−	0.557062i	$-0.188071\pi$
$139$	19.5822	1.66094	0.830471	+	0.557062i	$0.188071\pi$
$140$	−4.98584	−0.421381
$141$	−5.15344	−0.433998
$142$	0.120333	0.0100981
$143$	7.26579	0.607596
$144$	3.99384	0.332820
$145$	13.1629	1.09312
$146$	−0.511519	−0.0423336
$147$	1.00000	0.0824786
$148$	−2.89526	−0.237989
$149$	10.9894	0.900284	0.450142	−	0.892957i	$-0.351373\pi$
$149$	10.9894	0.900284	0.450142	+	0.892957i	$0.351373\pi$
$150$	−0.0391186	−0.00319402
$151$	−4.73844	−0.385609	−0.192804	−	0.981237i	$-0.561758\pi$
$151$	−4.73844	−0.385609	−0.192804	+	0.981237i	$0.561758\pi$
$152$	1.03982	0.0843408
$153$	0	0
$154$	0.0383453	0.00308995
$155$	1.68516	0.135355
$156$	−12.1347	−0.971554
$157$	4.27662	0.341311	0.170656	−	0.985331i	$-0.445411\pi$
$157$	4.27662	0.341311	0.170656	+	0.985331i	$0.445411\pi$
$158$	−0.0197598	−0.00157201
$159$	−4.55283	−0.361063
$160$	0.958224	0.0757543
$161$	7.69432	0.606398
$162$	−0.0320370	−0.00251706
$163$	−3.48148	−0.272691	−0.136345	−	0.990661i	$-0.543536\pi$
$163$	−3.48148	−0.272691	−0.136345	+	0.990661i	$0.543536\pi$
$164$	14.6839	1.14662
$165$	−2.98533	−0.232408
$166$	0.0307409	0.00238596
$167$	17.7583	1.37418	0.687089	−	0.726573i	$-0.258888\pi$
$167$	17.7583	1.37418	0.687089	+	0.726573i	$0.258888\pi$
$168$	−0.128115	−0.00988429
$169$	23.8506	1.83466
$170$	0	0
$171$	8.11633	0.620671
$172$	3.52847	0.269043
$173$	12.1573	0.924303	0.462151	−	0.886801i	$-0.347078\pi$
$173$	12.1573	0.924303	0.462151	+	0.886801i	$0.347078\pi$
$174$	0.169072	0.0128173
$175$	−1.22105	−0.0923023
$176$	4.78026	0.360326
$177$	6.26447	0.470866
$178$	−0.573022	−0.0429498
$179$	−2.15314	−0.160933	−0.0804665	−	0.996757i	$-0.525641\pi$
$179$	−2.15314	−0.160933	−0.0804665	+	0.996757i	$0.525641\pi$
$180$	4.98584	0.371623
$181$	13.1695	0.978884	0.489442	−	0.872036i	$-0.337200\pi$
$181$	13.1695	0.978884	0.489442	+	0.872036i	$0.337200\pi$
$182$	0.194479	0.0144158
$183$	7.26118	0.536762
$184$	−0.985758	−0.0726710
$185$	−3.61253	−0.265599
$186$	0.0216452	0.00158710
$187$	0	0
$188$	10.3016	0.751321
$189$	−1.00000	−0.0727393
$190$	0.648549	0.0470507
$191$	8.39465	0.607416	0.303708	−	0.952765i	$-0.401775\pi$
$191$	8.39465	0.607416	0.303708	+	0.952765i	$0.401775\pi$
$192$	−7.97538	−0.575573
$193$	−17.7755	−1.27951	−0.639754	−	0.768580i	$-0.720964\pi$
$193$	−17.7755	−1.27951	−0.639754	+	0.768580i	$0.720964\pi$
$194$	0.246325	0.0176851
$195$	−15.1410	−1.08427
$196$	−1.99897	−0.142784
$197$	−8.50221	−0.605757	−0.302879	−	0.953029i	$-0.597948\pi$
$197$	−8.50221	−0.605757	−0.302879	+	0.953029i	$0.597948\pi$
$198$	−0.0383453	−0.00272508
$199$	4.88644	0.346391	0.173195	−	0.984888i	$-0.444591\pi$
$199$	4.88644	0.346391	0.173195	+	0.984888i	$0.444591\pi$
$200$	0.156434	0.0110616
$201$	3.54409	0.249981
$202$	0.415312	0.0292212
$203$	5.27739	0.370400
$204$	0	0
$205$	18.3218	1.27965
$206$	−0.231884	−0.0161561
$207$	−7.69432	−0.534792
$208$	24.2445	1.68105
$209$	9.71451	0.671966
$210$	−0.0799067	−0.00551408
$211$	−2.47918	−0.170674	−0.0853370	−	0.996352i	$-0.527197\pi$
$211$	−2.47918	−0.170674	−0.0853370	+	0.996352i	$0.527197\pi$
$212$	9.10099	0.625059
$213$	−3.75607	−0.257362
$214$	0.0210300	0.00143758
$215$	4.40261	0.300256
$216$	0.128115	0.00871712
$217$	0.675631	0.0458648
$218$	0.403331	0.0273170
$219$	15.9665	1.07892
$220$	5.96760	0.402335
$221$	0	0
$222$	−0.0464015	−0.00311426
$223$	−28.3519	−1.89858	−0.949290	−	0.314401i	$-0.898196\pi$
$223$	−28.3519	−1.89858	−0.949290	+	0.314401i	$0.898196\pi$
$224$	0.384181	0.0256691
$225$	1.22105	0.0814030
$226$	−0.641023	−0.0426402
$227$	0.431744	0.0286559	0.0143279	−	0.999897i	$-0.495439\pi$
$227$	0.431744	0.0286559	0.0143279	+	0.999897i	$0.495439\pi$
$228$	−16.2243	−1.07448
$229$	−18.2795	−1.20795	−0.603973	−	0.797005i	$-0.706417\pi$
$229$	−18.2795	−1.20795	−0.603973	+	0.797005i	$0.706417\pi$
$230$	−0.614828	−0.0405405
$231$	−1.19691	−0.0787508
$232$	−0.676113	−0.0443890
$233$	17.3095	1.13398	0.566990	−	0.823725i	$-0.308108\pi$
$233$	17.3095	1.13398	0.566990	+	0.823725i	$0.308108\pi$
$234$	−0.194479	−0.0127135
$235$	12.8537	0.838484
$236$	−12.5225	−0.815145
$237$	0.616782	0.0400643
$238$	0	0
$239$	22.9147	1.48223	0.741116	−	0.671377i	$-0.234297\pi$
$239$	22.9147	1.48223	0.741116	+	0.671377i	$0.234297\pi$
$240$	−9.96145	−0.643009
$241$	25.8879	1.66758	0.833792	−	0.552079i	$-0.186165\pi$
$241$	25.8879	1.66758	0.833792	+	0.552079i	$0.186165\pi$
$242$	0.306511	0.0197033
$243$	1.00000	0.0641500
$244$	−14.5149	−0.929222
$245$	−2.49420	−0.159349
$246$	0.235335	0.0150044
$247$	49.2699	3.13497
$248$	−0.0865584	−0.00549647
$249$	−0.959545	−0.0608087
$250$	−0.301964	−0.0190979
$251$	29.8362	1.88324	0.941622	−	0.336673i	$-0.109302\pi$
$251$	29.8362	1.88324	0.941622	+	0.336673i	$0.109302\pi$
$252$	1.99897	0.125924
$253$	−9.20940	−0.578990
$254$	−0.282839	−0.0177469
$255$	0	0
$256$	15.9180	0.994872
$257$	8.29710	0.517559	0.258780	−	0.965936i	$-0.416680\pi$
$257$	8.29710	0.517559	0.258780	+	0.965936i	$0.416680\pi$
$258$	0.0565497	0.00352063
$259$	−1.44837	−0.0899975
$260$	30.2664	1.87704
$261$	−5.27739	−0.326663
$262$	0.133473	0.00824599
$263$	−12.3822	−0.763522	−0.381761	−	0.924261i	$-0.624682\pi$
$263$	−12.3822	−0.763522	−0.381761	+	0.924261i	$0.624682\pi$
$264$	0.153342	0.00943754
$265$	11.3557	0.697574
$266$	0.260023	0.0159430
$267$	17.8863	1.09462
$268$	−7.08455	−0.432758
$269$	−14.7850	−0.901459	−0.450729	−	0.892661i	$-0.648836\pi$
$269$	−14.7850	−0.901459	−0.450729	+	0.892661i	$0.648836\pi$
$270$	0.0799067	0.00486297
$271$	7.94792	0.482802	0.241401	−	0.970425i	$-0.422393\pi$
$271$	7.94792	0.482802	0.241401	+	0.970425i	$0.422393\pi$
$272$	0	0
$273$	−6.07047	−0.367401
$274$	0.419345	0.0253335
$275$	1.46148	0.0881305
$276$	15.3807	0.925812
$277$	23.4684	1.41008	0.705041	−	0.709166i	$-0.250928\pi$
$277$	23.4684	1.41008	0.705041	+	0.709166i	$0.250928\pi$
$278$	−0.627355	−0.0376262
$279$	−0.675631	−0.0404490
$280$	0.319545	0.0190964
$281$	20.5627	1.22667	0.613335	−	0.789823i	$-0.289828\pi$
$281$	20.5627	1.22667	0.613335	+	0.789823i	$0.289828\pi$
$282$	0.165101	0.00983160
$283$	−23.6702	−1.40705	−0.703523	−	0.710672i	$-0.748391\pi$
$283$	−23.6702	−1.40705	−0.703523	+	0.710672i	$0.748391\pi$
$284$	7.50829	0.445535
$285$	−20.2438	−1.19914
$286$	−0.232774	−0.0137642
$287$	7.34574	0.433605
$288$	−0.384181	−0.0226381
$289$	0	0
$290$	−0.421699	−0.0247630
$291$	−7.68879	−0.450725
$292$	−31.9167	−1.86778
$293$	17.2639	1.00857	0.504285	−	0.863537i	$-0.331756\pi$
$293$	17.2639	1.00857	0.504285	+	0.863537i	$0.331756\pi$
$294$	−0.0320370	−0.00186843
$295$	−15.6248	−0.909714
$296$	0.185558	0.0107854
$297$	1.19691	0.0694517
$298$	−0.352066	−0.0203946
$299$	−46.7081	−2.70120
$300$	−2.44084	−0.140922
$301$	1.76514	0.101741
$302$	0.151805	0.00873541
$303$	−12.9635	−0.744735
$304$	32.4154	1.85915
$305$	−18.1109	−1.03703
$306$	0	0
$307$	15.4910	0.884117	0.442059	−	0.896986i	$-0.354248\pi$
$307$	15.4910	0.884117	0.442059	+	0.896986i	$0.354248\pi$
$308$	2.39259	0.136330
$309$	7.23801	0.411756
$310$	−0.0539874	−0.00306628
$311$	9.83560	0.557726	0.278863	−	0.960331i	$-0.410043\pi$
$311$	9.83560	0.557726	0.278863	+	0.960331i	$0.410043\pi$
$312$	0.777718	0.0440296
$313$	6.14928	0.347578	0.173789	−	0.984783i	$-0.444399\pi$
$313$	6.14928	0.347578	0.173789	+	0.984783i	$0.444399\pi$
$314$	−0.137010	−0.00773191
$315$	2.49420	0.140532
$316$	−1.23293	−0.0693578
$317$	11.3092	0.635189	0.317595	−	0.948227i	$-0.397125\pi$
$317$	11.3092	0.635189	0.317595	+	0.948227i	$0.397125\pi$
$318$	0.145859	0.00817936
$319$	−6.31656	−0.353659
$320$	19.8922	1.11201
$321$	−0.656429	−0.0366383
$322$	−0.246503	−0.0137371
$323$	0	0
$324$	−1.99897	−0.111054
$325$	7.41232	0.411161
$326$	0.111536	0.00617741
$327$	−12.5896	−0.696204
$328$	−0.941099	−0.0519635
$329$	5.15344	0.284118
$330$	0.0956410	0.00526486
$331$	−0.0226644	−0.00124575	−0.000622874	−	1.00000i	$-0.500198\pi$
$331$	−0.0226644	−0.00124575	−0.000622874		1.00000i	$0.500198\pi$
$332$	1.91811	0.105270
$333$	1.44837	0.0793703
$334$	−0.568922	−0.0311300
$335$	−8.83969	−0.482964
$336$	−3.99384	−0.217882
$337$	−8.73908	−0.476048	−0.238024	−	0.971259i	$-0.576500\pi$
$337$	−8.73908	−0.476048	−0.238024	+	0.971259i	$0.576500\pi$
$338$	−0.764100	−0.0415616
$339$	20.0088	1.08673
$340$	0	0
$341$	−0.808668	−0.0437918
$342$	−0.260023	−0.0140604
$343$	−1.00000	−0.0539949
$344$	−0.226141	−0.0121927
$345$	19.1912	1.03322
$346$	−0.389483	−0.0209387
$347$	−0.672393	−0.0360959	−0.0180480	−	0.999837i	$-0.505745\pi$
$347$	−0.672393	−0.0360959	−0.0180480	+	0.999837i	$0.505745\pi$
$348$	10.5494	0.565506
$349$	−18.8163	−1.00721	−0.503606	−	0.863934i	$-0.667994\pi$
$349$	−18.8163	−1.00721	−0.503606	+	0.863934i	$0.667994\pi$
$350$	0.0391186	0.00209098
$351$	6.07047	0.324018
$352$	−0.459829	−0.0245090
$353$	−10.7979	−0.574715	−0.287358	−	0.957823i	$-0.592777\pi$
$353$	−10.7979	−0.574715	−0.287358	+	0.957823i	$0.592777\pi$
$354$	−0.200694	−0.0106668
$355$	9.36840	0.497223
$356$	−35.7542	−1.89497
$357$	0	0
$358$	0.0689800	0.00364571
$359$	7.87458	0.415604	0.207802	−	0.978171i	$-0.433369\pi$
$359$	7.87458	0.415604	0.207802	+	0.978171i	$0.433369\pi$
$360$	−0.319545	−0.0168415
$361$	46.8748	2.46710
$362$	−0.421912	−0.0221752
$363$	−9.56741	−0.502159
$364$	12.1347	0.636031
$365$	−39.8238	−2.08447
$366$	−0.232626	−0.0121596
$367$	−12.0687	−0.629979	−0.314990	−	0.949095i	$-0.602001\pi$
$367$	−12.0687	−0.629979	−0.314990	+	0.949095i	$0.602001\pi$
$368$	−30.7299	−1.60191
$369$	−7.34574	−0.382404
$370$	0.115735	0.00601676
$371$	4.55283	0.236371
$372$	1.35057	0.0700237
$373$	4.21469	0.218228	0.109114	−	0.994029i	$-0.465199\pi$
$373$	4.21469	0.218228	0.109114	+	0.994029i	$0.465199\pi$
$374$	0	0
$375$	9.42548	0.486730
$376$	−0.660233	−0.0340489
$377$	−32.0363	−1.64995
$378$	0.0320370	0.00164780
$379$	−12.1018	−0.621628	−0.310814	−	0.950471i	$-0.600602\pi$
$379$	−12.1018	−0.621628	−0.310814	+	0.950471i	$0.600602\pi$
$380$	40.4668	2.07590
$381$	8.82854	0.452300
$382$	−0.268939	−0.0137601
$383$	18.3983	0.940108	0.470054	−	0.882638i	$-0.344234\pi$
$383$	18.3983	0.940108	0.470054	+	0.882638i	$0.344234\pi$
$384$	1.02387	0.0522490
$385$	2.98533	0.152147
$386$	0.569473	0.0289854
$387$	−1.76514	−0.0897270
$388$	15.3697	0.780277
$389$	−27.1775	−1.37795	−0.688976	−	0.724784i	$-0.741939\pi$
$389$	−27.1775	−1.37795	−0.688976	+	0.724784i	$0.741939\pi$
$390$	0.485071	0.0245625
$391$	0	0
$392$	0.128115	0.00647078
$393$	−4.16622	−0.210158
$394$	0.272385	0.0137226
$395$	−1.53838	−0.0774042
$396$	−2.39259	−0.120232
$397$	6.37566	0.319985	0.159993	−	0.987118i	$-0.448853\pi$
$397$	6.37566	0.319985	0.159993	+	0.987118i	$0.448853\pi$
$398$	−0.156547	−0.00784698
$399$	−8.11633	−0.406325
$400$	4.87666	0.243833
$401$	−7.01469	−0.350297	−0.175148	−	0.984542i	$-0.556041\pi$
$401$	−7.01469	−0.350297	−0.175148	+	0.984542i	$0.556041\pi$
$402$	−0.113542	−0.00566296
$403$	−4.10140	−0.204305
$404$	25.9137	1.28926
$405$	−2.49420	−0.123938
$406$	−0.169072	−0.00839089
$407$	1.73357	0.0859298
$408$	0	0
$409$	−2.17117	−0.107358	−0.0536788	−	0.998558i	$-0.517095\pi$
$409$	−2.17117	−0.107358	−0.0536788	+	0.998558i	$0.517095\pi$
$410$	−0.586974	−0.0289886
$411$	−13.0894	−0.645652
$412$	−14.4686	−0.712816
$413$	−6.26447	−0.308254
$414$	0.246503	0.0121149
$415$	2.39330	0.117483
$416$	−2.33216	−0.114343
$417$	19.5822	0.958945
$418$	−0.311223	−0.0152224
$419$	20.9432	1.02314	0.511570	−	0.859242i	$-0.329064\pi$
$419$	20.9432	1.02314	0.511570	+	0.859242i	$0.329064\pi$
$420$	−4.98584	−0.243284
$421$	24.1096	1.17503	0.587514	−	0.809214i	$-0.300107\pi$
$421$	24.1096	1.17503	0.587514	+	0.809214i	$0.300107\pi$
$422$	0.0794255	0.00386637
$423$	−5.15344	−0.250569
$424$	−0.583286	−0.0283269
$425$	0	0
$426$	0.120333	0.00583016
$427$	−7.26118	−0.351393
$428$	1.31218	0.0634268
$429$	7.26579	0.350796
$430$	−0.141046	−0.00680186
$431$	−30.2463	−1.45691	−0.728456	−	0.685092i	$-0.759762\pi$
$431$	−30.2463	−1.45691	−0.728456	+	0.685092i	$0.759762\pi$
$432$	3.99384	0.192154
$433$	16.9171	0.812984	0.406492	−	0.913654i	$-0.366752\pi$
$433$	16.9171	0.812984	0.406492	+	0.913654i	$0.366752\pi$
$434$	−0.0216452	−0.00103900
$435$	13.1629	0.631112
$436$	25.1662	1.20524
$437$	−62.4497	−2.98737
$438$	−0.511519	−0.0244413
$439$	3.35952	0.160341	0.0801706	−	0.996781i	$-0.474453\pi$
$439$	3.35952	0.160341	0.0801706	+	0.996781i	$0.474453\pi$
$440$	−0.382466	−0.0182333
$441$	1.00000	0.0476190
$442$	0	0
$443$	10.0201	0.476067	0.238033	−	0.971257i	$-0.423497\pi$
$443$	10.0201	0.476067	0.238033	+	0.971257i	$0.423497\pi$
$444$	−2.89526	−0.137403
$445$	−44.6120	−2.11481
$446$	0.908307	0.0430096
$447$	10.9894	0.519779
$448$	7.97538	0.376801
$449$	18.0226	0.850541	0.425271	−	0.905066i	$-0.360179\pi$
$449$	18.0226	0.850541	0.425271	+	0.905066i	$0.360179\pi$
$450$	−0.0391186	−0.00184407
$451$	−8.79218	−0.414007
$452$	−39.9972	−1.88131
$453$	−4.73844	−0.222631
$454$	−0.0138318	−0.000649157 0
$455$	15.1410	0.709820
$456$	1.03982	0.0486942
$457$	17.5069	0.818939	0.409470	−	0.912324i	$-0.365714\pi$
$457$	17.5069	0.818939	0.409470	+	0.912324i	$0.365714\pi$
$458$	0.585621	0.0273643
$459$	0	0
$460$	−38.3627	−1.78867
$461$	−35.8718	−1.67071	−0.835357	−	0.549708i	$-0.814739\pi$
$461$	−35.8718	−1.67071	−0.835357	+	0.549708i	$0.814739\pi$
$462$	0.0383453	0.00178399
$463$	−11.1535	−0.518345	−0.259172	−	0.965831i	$-0.583450\pi$
$463$	−11.1535	−0.518345	−0.259172	+	0.965831i	$0.583450\pi$
$464$	−21.0771	−0.978479
$465$	1.68516	0.0781474
$466$	−0.554542	−0.0256887
$467$	31.0692	1.43771	0.718855	−	0.695160i	$-0.244667\pi$
$467$	31.0692	1.43771	0.718855	+	0.695160i	$0.244667\pi$
$468$	−12.1347	−0.560927
$469$	−3.54409	−0.163651
$470$	−0.411794	−0.0189947
$471$	4.27662	0.197056
$472$	0.802572	0.0369414
$473$	−2.11271	−0.0971425
$474$	−0.0197598	−0.000907599 0
$475$	9.91041	0.454721
$476$	0	0
$477$	−4.55283	−0.208460
$478$	−0.734119	−0.0335778
$479$	19.8485	0.906901	0.453451	−	0.891281i	$-0.350193\pi$
$479$	19.8485	0.906901	0.453451	+	0.891281i	$0.350193\pi$
$480$	0.958224	0.0437367
$481$	8.79230	0.400894
$482$	−0.829369	−0.0377767
$483$	7.69432	0.350104
$484$	19.1250	0.869318
$485$	19.1774	0.870800
$486$	−0.0320370	−0.00145323
$487$	3.92615	0.177911	0.0889553	−	0.996036i	$-0.471647\pi$
$487$	3.92615	0.177911	0.0889553	+	0.996036i	$0.471647\pi$
$488$	0.930267	0.0421112
$489$	−3.48148	−0.157438
$490$	0.0799067	0.00360982
$491$	22.0363	0.994486	0.497243	−	0.867611i	$-0.334346\pi$
$491$	22.0363	0.994486	0.497243	+	0.867611i	$0.334346\pi$
$492$	14.6839	0.662003
$493$	0	0
$494$	−1.57846	−0.0710182
$495$	−2.98533	−0.134181
$496$	−2.69836	−0.121160
$497$	3.75607	0.168483
$498$	0.0307409	0.00137753
$499$	29.2650	1.31008	0.655041	−	0.755593i	$-0.272651\pi$
$499$	29.2650	1.31008	0.655041	+	0.755593i	$0.272651\pi$
$500$	−18.8413	−0.842608
$501$	17.7583	0.793382
$502$	−0.955861	−0.0426622
$503$	−2.16558	−0.0965584	−0.0482792	−	0.998834i	$-0.515374\pi$
$503$	−2.16558	−0.0965584	−0.0482792	+	0.998834i	$0.515374\pi$
$504$	−0.128115	−0.00570669
$505$	32.3336	1.43883
$506$	0.295041	0.0131162
$507$	23.8506	1.05924
$508$	−17.6480	−0.783004
$509$	31.4557	1.39425	0.697125	−	0.716950i	$-0.254462\pi$
$509$	31.4557	1.39425	0.697125	+	0.716950i	$0.254462\pi$
$510$	0	0
$511$	−15.9665	−0.706318
$512$	−2.55770	−0.113035
$513$	8.11633	0.358345
$514$	−0.265814	−0.0117246
$515$	−18.0531	−0.795513
$516$	3.52847	0.155332
$517$	−6.16820	−0.271277
$518$	0.0464015	0.00203876
$519$	12.1573	0.533646
$520$	−1.93979	−0.0850652
$521$	−7.19537	−0.315235	−0.157617	−	0.987500i	$-0.550381\pi$
$521$	−7.19537	−0.315235	−0.157617	+	0.987500i	$0.550381\pi$
$522$	0.169072	0.00740007
$523$	−31.6415	−1.38359	−0.691793	−	0.722096i	$-0.743179\pi$
$523$	−31.6415	−1.38359	−0.691793	+	0.722096i	$0.743179\pi$
$524$	8.32816	0.363817
$525$	−1.22105	−0.0532908
$526$	0.396690	0.0172965
$527$	0	0
$528$	4.78026	0.208034
$529$	36.2026	1.57403
$530$	−0.363802	−0.0158025
$531$	6.26447	0.271855
$532$	16.2243	0.703414
$533$	−44.5921	−1.93150
$534$	−0.573022	−0.0247971
$535$	1.63727	0.0707852
$536$	0.454051	0.0196120
$537$	−2.15314	−0.0929147
$538$	0.473667	0.0204213
$539$	1.19691	0.0515545
$540$	4.98584	0.214557
$541$	29.5299	1.26959	0.634794	−	0.772681i	$-0.281085\pi$
$541$	29.5299	1.26959	0.634794	+	0.772681i	$0.281085\pi$
$542$	−0.254627	−0.0109372
$543$	13.1695	0.565159
$544$	0	0
$545$	31.4009	1.34507
$546$	0.194479	0.00832295
$547$	12.8253	0.548370	0.274185	−	0.961677i	$-0.411592\pi$
$547$	12.8253	0.548370	0.274185	+	0.961677i	$0.411592\pi$
$548$	26.1654	1.11773
$549$	7.26118	0.309900
$550$	−0.0468214	−0.00199647
$551$	−42.8331	−1.82475
$552$	−0.985758	−0.0419566
$553$	−0.616782	−0.0262282
$554$	−0.751858	−0.0319434
$555$	−3.61253	−0.153344
$556$	−39.1443	−1.66009
$557$	−8.21543	−0.348099	−0.174050	−	0.984737i	$-0.555685\pi$
$557$	−8.21543	−0.348099	−0.174050	+	0.984737i	$0.555685\pi$
$558$	0.0216452	0.000916313 0
$559$	−10.7152	−0.453205
$560$	9.96145	0.420948
$561$	0	0
$562$	−0.658767	−0.0277884
$563$	40.9986	1.72789	0.863943	−	0.503589i	$-0.167987\pi$
$563$	40.9986	1.72789	0.863943	+	0.503589i	$0.167987\pi$
$564$	10.3016	0.433775
$565$	−49.9061	−2.09957
$566$	0.758321	0.0318746
$567$	−1.00000	−0.0419961
$568$	−0.481209	−0.0201911
$569$	−24.3430	−1.02051	−0.510256	−	0.860022i	$-0.670449\pi$
$569$	−24.3430	−1.02051	−0.510256	+	0.860022i	$0.670449\pi$
$570$	0.648549	0.0271647
$571$	29.6719	1.24173	0.620866	−	0.783917i	$-0.286781\pi$
$571$	29.6719	1.24173	0.620866	+	0.783917i	$0.286781\pi$
$572$	−14.5241	−0.607284
$573$	8.39465	0.350692
$574$	−0.235335	−0.00982270
$575$	−9.39512	−0.391803
$576$	−7.97538	−0.332307
$577$	3.22696	0.134340	0.0671700	−	0.997742i	$-0.478603\pi$
$577$	3.22696	0.134340	0.0671700	+	0.997742i	$0.478603\pi$
$578$	0	0
$579$	−17.7755	−0.738724
$580$	−26.3123	−1.09256
$581$	0.959545	0.0398087
$582$	0.246325	0.0102105
$583$	−5.44932	−0.225688
$584$	2.04555	0.0846455
$585$	−15.1410	−0.626002
$586$	−0.553084	−0.0228477
$587$	−40.0268	−1.65208	−0.826042	−	0.563608i	$-0.809413\pi$
$587$	−40.0268	−1.65208	−0.826042	+	0.563608i	$0.809413\pi$
$588$	−1.99897	−0.0824363
$589$	−5.48364	−0.225950
$590$	0.500573	0.0206082
$591$	−8.50221	−0.349734
$592$	5.78457	0.237744
$593$	−23.2555	−0.954987	−0.477494	−	0.878635i	$-0.658455\pi$
$593$	−23.2555	−0.954987	−0.477494	+	0.878635i	$0.658455\pi$
$594$	−0.0383453	−0.00157333
$595$	0	0
$596$	−21.9675	−0.899822
$597$	4.88644	0.199989
$598$	1.49639	0.0611918
$599$	−1.27348	−0.0520331	−0.0260165	−	0.999662i	$-0.508282\pi$
$599$	−1.27348	−0.0520331	−0.0260165	+	0.999662i	$0.508282\pi$
$600$	0.156434	0.00638640
$601$	−12.6277	−0.515094	−0.257547	−	0.966266i	$-0.582914\pi$
$601$	−12.6277	−0.515094	−0.257547	+	0.966266i	$0.582914\pi$
$602$	−0.0565497	−0.00230479
$603$	3.54409	0.144327
$604$	9.47202	0.385411
$605$	23.8631	0.970171
$606$	0.415312	0.0168709
$607$	22.0549	0.895182	0.447591	−	0.894239i	$-0.352282\pi$
$607$	22.0549	0.895182	0.447591	+	0.894239i	$0.352282\pi$
$608$	−3.11814	−0.126457
$609$	5.27739	0.213851
$610$	0.580217	0.0234923
$611$	−31.2838	−1.26561
$612$	0	0
$613$	−27.7612	−1.12126	−0.560631	−	0.828066i	$-0.689441\pi$
$613$	−27.7612	−1.12126	−0.560631	+	0.828066i	$0.689441\pi$
$614$	−0.496284	−0.0200284
$615$	18.3218	0.738805
$616$	−0.153342	−0.00617832
$617$	−17.9459	−0.722473	−0.361237	−	0.932474i	$-0.617645\pi$
$617$	−17.9459	−0.722473	−0.361237	+	0.932474i	$0.617645\pi$
$618$	−0.231884	−0.00932773
$619$	−31.2149	−1.25463	−0.627317	−	0.778764i	$-0.715847\pi$
$619$	−31.2149	−1.25463	−0.627317	+	0.778764i	$0.715847\pi$
$620$	−3.36859	−0.135286
$621$	−7.69432	−0.308762
$622$	−0.315103	−0.0126345
$623$	−17.8863	−0.716598
$624$	24.2445	0.970557
$625$	−29.6143	−1.18457
$626$	−0.197004	−0.00787387
$627$	9.71451	0.387960
$628$	−8.54884	−0.341136
$629$	0	0
$630$	−0.0799067	−0.00318356
$631$	−3.93329	−0.156582	−0.0782908	−	0.996931i	$-0.524946\pi$
$631$	−3.93329	−0.156582	−0.0782908	+	0.996931i	$0.524946\pi$
$632$	0.0790190	0.00314321
$633$	−2.47918	−0.0985387
$634$	−0.362313	−0.0143893
$635$	−22.0202	−0.873843
$636$	9.10099	0.360878
$637$	6.07047	0.240521
$638$	0.202363	0.00801164
$639$	−3.75607	−0.148588
$640$	−2.55373	−0.100945
$641$	−24.7916	−0.979210	−0.489605	−	0.871944i	$-0.662859\pi$
$641$	−24.7916	−0.979210	−0.489605	+	0.871944i	$0.662859\pi$
$642$	0.0210300	0.000829988 0
$643$	−14.7505	−0.581702	−0.290851	−	0.956768i	$-0.593938\pi$
$643$	−14.7505	−0.581702	−0.290851	+	0.956768i	$0.593938\pi$
$644$	−15.3807	−0.606086
$645$	4.40261	0.173353
$646$	0	0
$647$	25.0562	0.985060	0.492530	−	0.870295i	$-0.336072\pi$
$647$	25.0562	0.985060	0.492530	+	0.870295i	$0.336072\pi$
$648$	0.128115	0.00503283
$649$	7.49799	0.294322
$650$	−0.237468	−0.00931427
$651$	0.675631	0.0264801
$652$	6.95939	0.272551
$653$	7.35352	0.287765	0.143883	−	0.989595i	$-0.454041\pi$
$653$	7.35352	0.287765	0.143883	+	0.989595i	$0.454041\pi$
$654$	0.403331	0.0157715
$655$	10.3914	0.406025
$656$	−29.3377	−1.14545
$657$	15.9665	0.622914
$658$	−0.165101	−0.00643629
$659$	21.9466	0.854917	0.427458	−	0.904035i	$-0.359409\pi$
$659$	21.9466	0.854917	0.427458	+	0.904035i	$0.359409\pi$
$660$	5.96760	0.232288
$661$	10.2441	0.398451	0.199225	−	0.979954i	$-0.436157\pi$
$661$	10.2441	0.398451	0.199225	+	0.979954i	$0.436157\pi$
$662$	0.000726098 0	2.82206e−5 0
$663$	0	0
$664$	−0.122932	−0.00477069
$665$	20.2438	0.785020
$666$	−0.0464015	−0.00179802
$667$	40.6060	1.57227
$668$	−35.4984	−1.37347
$669$	−28.3519	−1.09615
$670$	0.283197	0.0109408
$671$	8.69097	0.335511
$672$	0.384181	0.0148201
$673$	−30.7568	−1.18559	−0.592794	−	0.805354i	$-0.701975\pi$
$673$	−30.7568	−1.18559	−0.592794	+	0.805354i	$0.701975\pi$
$674$	0.279974	0.0107842
$675$	1.22105	0.0469981
$676$	−47.6767	−1.83372
$677$	−50.0728	−1.92445	−0.962227	−	0.272250i	$-0.912232\pi$
$677$	−50.0728	−1.92445	−0.962227	+	0.272250i	$0.912232\pi$
$678$	−0.641023	−0.0246183
$679$	7.68879	0.295069
$680$	0	0
$681$	0.431744	0.0165445
$682$	0.0259073	0.000992041 0
$683$	−28.2130	−1.07954	−0.539771	−	0.841812i	$-0.681489\pi$
$683$	−28.2130	−1.07954	−0.539771	+	0.841812i	$0.681489\pi$
$684$	−16.2243	−0.620353
$685$	32.6476	1.24740
$686$	0.0320370	0.00122318
$687$	−18.2795	−0.697408
$688$	−7.04969	−0.268767
$689$	−27.6378	−1.05292
$690$	−0.614828	−0.0234061
$691$	−32.2264	−1.22595	−0.612975	−	0.790102i	$-0.710028\pi$
$691$	−32.2264	−1.22595	−0.612975	+	0.790102i	$0.710028\pi$
$692$	−24.3021	−0.923828
$693$	−1.19691	−0.0454668
$694$	0.0215414	0.000817701 0
$695$	−48.8420	−1.85268
$696$	−0.676113	−0.0256280
$697$	0	0
$698$	0.602816	0.0228169
$699$	17.3095	0.654704
$700$	2.44084	0.0922550
$701$	−1.84962	−0.0698592	−0.0349296	−	0.999390i	$-0.511121\pi$
$701$	−1.84962	−0.0698592	−0.0349296	+	0.999390i	$0.511121\pi$
$702$	−0.194479	−0.00734015
$703$	11.7555	0.443366
$704$	−9.54580	−0.359771
$705$	12.8537	0.484099
$706$	0.345933	0.0130193
$707$	12.9635	0.487543
$708$	−12.5225	−0.470624
$709$	37.0619	1.39189	0.695944	−	0.718096i	$-0.254986\pi$
$709$	37.0619	1.39189	0.695944	+	0.718096i	$0.254986\pi$
$710$	−0.300135	−0.0112639
$711$	0.616782	0.0231311
$712$	2.29150	0.0858775
$713$	5.19852	0.194686
$714$	0	0
$715$	−18.1224	−0.677738
$716$	4.30406	0.160850
$717$	22.9147	0.855767
$718$	−0.252278	−0.00941492
$719$	22.1881	0.827476	0.413738	−	0.910396i	$-0.364223\pi$
$719$	22.1881	0.827476	0.413738	+	0.910396i	$0.364223\pi$
$720$	−9.96145	−0.371241
$721$	−7.23801	−0.269557
$722$	−1.50173	−0.0558885
$723$	25.8879	0.962780
$724$	−26.3256	−0.978382
$725$	−6.44394	−0.239322
$726$	0.306511	0.0113757
$727$	24.5756	0.911459	0.455730	−	0.890118i	$-0.349378\pi$
$727$	24.5756	0.911459	0.455730	+	0.890118i	$0.349378\pi$
$728$	−0.777718	−0.0288241
$729$	1.00000	0.0370370
$730$	1.27583	0.0472207
$731$	0	0
$732$	−14.5149	−0.536487
$733$	16.3286	0.603112	0.301556	−	0.953448i	$-0.402494\pi$
$733$	16.3286	0.603112	0.301556	+	0.953448i	$0.402494\pi$
$734$	0.386643	0.0142713
$735$	−2.49420	−0.0920000
$736$	2.95601	0.108960
$737$	4.24196	0.156254
$738$	0.235335	0.00866281
$739$	−35.6148	−1.31011	−0.655055	−	0.755581i	$-0.727355\pi$
$739$	−35.6148	−1.31011	−0.655055	+	0.755581i	$0.727355\pi$
$740$	7.22136	0.265462
$741$	49.2699	1.80998
$742$	−0.145859	−0.00535465
$743$	−23.8891	−0.876406	−0.438203	−	0.898876i	$-0.644385\pi$
$743$	−23.8891	−0.876406	−0.438203	+	0.898876i	$0.644385\pi$
$744$	−0.0865584	−0.00317339
$745$	−27.4097	−1.00421
$746$	−0.135026	−0.00494365
$747$	−0.959545	−0.0351079
$748$	0	0
$749$	0.656429	0.0239854
$750$	−0.301964	−0.0110262
$751$	34.8469	1.27158	0.635791	−	0.771861i	$-0.280674\pi$
$751$	34.8469	1.27158	0.635791	+	0.771861i	$0.280674\pi$
$752$	−20.5820	−0.750549
$753$	29.8362	1.08729
$754$	1.02634	0.0373773
$755$	11.8186	0.430124
$756$	1.99897	0.0727020
$757$	−11.9402	−0.433973	−0.216986	−	0.976175i	$-0.569623\pi$
$757$	−11.9402	−0.433973	−0.216986	+	0.976175i	$0.569623\pi$
$758$	0.387705	0.0140821
$759$	−9.20940	−0.334280
$760$	−2.59353	−0.0940773
$761$	31.8811	1.15569	0.577845	−	0.816146i	$-0.303894\pi$
$761$	31.8811	1.15569	0.577845	+	0.816146i	$0.303894\pi$
$762$	−0.282839	−0.0102462
$763$	12.5896	0.455772
$764$	−16.7807	−0.607104
$765$	0	0
$766$	−0.589425	−0.0212968
$767$	38.0282	1.37312
$768$	15.9180	0.574390
$769$	−14.6114	−0.526901	−0.263451	−	0.964673i	$-0.584861\pi$
$769$	−14.6114	−0.526901	−0.263451	+	0.964673i	$0.584861\pi$
$770$	−0.0956410	−0.00344666
$771$	8.29710	0.298813
$772$	35.5327	1.27885
$773$	−29.0677	−1.04549	−0.522746	−	0.852489i	$-0.675092\pi$
$773$	−29.0677	−1.04549	−0.522746	+	0.852489i	$0.675092\pi$
$774$	0.0565497	0.00203264
$775$	−0.824976	−0.0296340
$776$	−0.985049	−0.0353612
$777$	−1.44837	−0.0519601
$778$	0.870683	0.0312155
$779$	−59.6205	−2.13612
$780$	30.2664	1.08371
$781$	−4.49567	−0.160868
$782$	0	0
$783$	−5.27739	−0.188599
$784$	3.99384	0.142637
$785$	−10.6667	−0.380713
$786$	0.133473	0.00476082
$787$	7.95596	0.283599	0.141800	−	0.989895i	$-0.454711\pi$
$787$	7.95596	0.283599	0.141800	+	0.989895i	$0.454711\pi$
$788$	16.9957	0.605446
$789$	−12.3822	−0.440820
$790$	0.0492850	0.00175348
$791$	−20.0088	−0.711433
$792$	0.153342	0.00544877
$793$	44.0788	1.56528
$794$	−0.204257	−0.00724880
$795$	11.3557	0.402745
$796$	−9.76786	−0.346213
$797$	−30.5849	−1.08337	−0.541686	−	0.840581i	$-0.682214\pi$
$797$	−30.5849	−1.08337	−0.541686	+	0.840581i	$0.682214\pi$
$798$	0.260023	0.00920470
$799$	0	0
$800$	−0.469102	−0.0165853
$801$	17.8863	0.631980
$802$	0.224729	0.00793547
$803$	19.1105	0.674394
$804$	−7.08455	−0.249853
$805$	−19.1912	−0.676401
$806$	0.131396	0.00462824
$807$	−14.7850	−0.520458
$808$	−1.66082	−0.0584275
$809$	47.1770	1.65866	0.829328	−	0.558762i	$-0.188724\pi$
$809$	47.1770	1.65866	0.829328	+	0.558762i	$0.188724\pi$
$810$	0.0799067	0.00280763
$811$	16.3345	0.573581	0.286791	−	0.957993i	$-0.407412\pi$
$811$	16.3345	0.573581	0.286791	+	0.957993i	$0.407412\pi$
$812$	−10.5494	−0.370210
$813$	7.94792	0.278746
$814$	−0.0555383	−0.00194662
$815$	8.68351	0.304170
$816$	0	0
$817$	−14.3265	−0.501219
$818$	0.0695578	0.00243203
$819$	−6.07047	−0.212119
$820$	−36.6247	−1.27899
$821$	−21.7554	−0.759269	−0.379635	−	0.925136i	$-0.623950\pi$
$821$	−21.7554	−0.759269	−0.379635	+	0.925136i	$0.623950\pi$
$822$	0.419345	0.0146263
$823$	−24.4219	−0.851296	−0.425648	−	0.904889i	$-0.639954\pi$
$823$	−24.4219	−0.851296	−0.425648	+	0.904889i	$0.639954\pi$
$824$	0.927297	0.0323039
$825$	1.46148	0.0508822
$826$	0.200694	0.00698305
$827$	28.8981	1.00489	0.502443	−	0.864610i	$-0.332435\pi$
$827$	28.8981	1.00489	0.502443	+	0.864610i	$0.332435\pi$
$828$	15.3807	0.534518
$829$	−14.9474	−0.519146	−0.259573	−	0.965723i	$-0.583582\pi$
$829$	−14.9474	−0.519146	−0.259573	+	0.965723i	$0.583582\pi$
$830$	−0.0766741	−0.00266140
$831$	23.4684	0.814111
$832$	−48.4143	−1.67846
$833$	0	0
$834$	−0.627355	−0.0217235
$835$	−44.2928	−1.53281
$836$	−19.4190	−0.671622
$837$	−0.675631	−0.0233532
$838$	−0.670955	−0.0231778
$839$	23.8981	0.825055	0.412528	−	0.910945i	$-0.364646\pi$
$839$	23.8981	0.825055	0.412528	+	0.910945i	$0.364646\pi$
$840$	0.319545	0.0110253
$841$	−1.14911	−0.0396244
$842$	−0.772397	−0.0266186
$843$	20.5627	0.708218
$844$	4.95582	0.170586
$845$	−59.4882	−2.04646
$846$	0.165101	0.00567628
$847$	9.56741	0.328740
$848$	−18.1833	−0.624417
$849$	−23.6702	−0.812358
$850$	0	0
$851$	−11.1442	−0.382020
$852$	7.50829	0.257230
$853$	12.6177	0.432021	0.216011	−	0.976391i	$-0.430695\pi$
$853$	12.6177	0.432021	0.216011	+	0.976391i	$0.430695\pi$
$854$	0.232626	0.00796031
$855$	−20.2438	−0.692322
$856$	−0.0840984	−0.00287442
$857$	53.2353	1.81848	0.909241	−	0.416271i	$-0.136663\pi$
$857$	53.2353	1.81848	0.909241	+	0.416271i	$0.136663\pi$
$858$	−0.232774	−0.00794677
$859$	−13.7646	−0.469642	−0.234821	−	0.972039i	$-0.575450\pi$
$859$	−13.7646	−0.469642	−0.234821	+	0.972039i	$0.575450\pi$
$860$	−8.80071	−0.300102
$861$	7.34574	0.250342
$862$	0.968999	0.0330043
$863$	17.1090	0.582399	0.291199	−	0.956662i	$-0.405946\pi$
$863$	17.1090	0.582399	0.291199	+	0.956662i	$0.405946\pi$
$864$	−0.384181	−0.0130701
$865$	−30.3228	−1.03101
$866$	−0.541972	−0.0184170
$867$	0	0
$868$	−1.35057	−0.0458413
$869$	0.738231	0.0250428
$870$	−0.421699	−0.0142969
$871$	21.5143	0.728984
$872$	−1.61291	−0.0546200
$873$	−7.68879	−0.260226
$874$	2.00070	0.0676746
$875$	−9.42548	−0.318639
$876$	−31.9167	−1.07836
$877$	45.3777	1.53230	0.766148	−	0.642664i	$-0.222171\pi$
$877$	45.3777	1.53230	0.766148	+	0.642664i	$0.222171\pi$
$878$	−0.107629	−0.00363230
$879$	17.2639	0.582298
$880$	−11.9229	−0.401922
$881$	−10.0513	−0.338638	−0.169319	−	0.985561i	$-0.554157\pi$
$881$	−10.0513	−0.338638	−0.169319	+	0.985561i	$0.554157\pi$
$882$	−0.0320370	−0.00107874
$883$	−45.8540	−1.54311	−0.771554	−	0.636163i	$-0.780520\pi$
$883$	−45.8540	−1.54311	−0.771554	+	0.636163i	$0.780520\pi$
$884$	0	0
$885$	−15.6248	−0.525223
$886$	−0.321012	−0.0107846
$887$	24.4053	0.819451	0.409726	−	0.912209i	$-0.365624\pi$
$887$	24.4053	0.819451	0.409726	+	0.912209i	$0.365624\pi$
$888$	0.185558	0.00622693
$889$	−8.82854	−0.296100
$890$	1.42923	0.0479080
$891$	1.19691	0.0400979
$892$	56.6746	1.89761
$893$	−41.8270	−1.39969
$894$	−0.352066	−0.0117748
$895$	5.37036	0.179511
$896$	−1.02387	−0.0342050
$897$	−46.7081	−1.55954
$898$	−0.577391	−0.0192678
$899$	3.56557	0.118918
$900$	−2.44084	−0.0813612
$901$	0	0
$902$	0.281675	0.00937874
$903$	1.76514	0.0587401
$904$	2.56343	0.0852585
$905$	−32.8475	−1.09189
$906$	0.151805	0.00504339
$907$	9.77194	0.324472	0.162236	−	0.986752i	$-0.448129\pi$
$907$	9.77194	0.324472	0.162236	+	0.986752i	$0.448129\pi$
$908$	−0.863045	−0.0286412
$909$	−12.9635	−0.429973
$910$	−0.485071	−0.0160799
$911$	−11.1010	−0.367792	−0.183896	−	0.982946i	$-0.558871\pi$
$911$	−11.1010	−0.367792	−0.183896	+	0.982946i	$0.558871\pi$
$912$	32.4154	1.07338
$913$	−1.14849	−0.0380094
$914$	−0.560869	−0.0185519
$915$	−18.1109	−0.598727
$916$	36.5403	1.20733
$917$	4.16622	0.137581
$918$	0	0
$919$	18.9671	0.625668	0.312834	−	0.949808i	$-0.398722\pi$
$919$	18.9671	0.625668	0.312834	+	0.949808i	$0.398722\pi$
$920$	2.45868	0.0810603
$921$	15.4910	0.510445
$922$	1.14922	0.0378476
$923$	−22.8011	−0.750508
$924$	2.39259	0.0787104
$925$	1.76853	0.0581489
$926$	0.357323	0.0117424
$927$	7.23801	0.237727
$928$	2.02747	0.0665550
$929$	−5.60311	−0.183832	−0.0919160	−	0.995767i	$-0.529299\pi$
$929$	−5.60311	−0.183832	−0.0919160	+	0.995767i	$0.529299\pi$
$930$	−0.0539874	−0.00177032
$931$	8.11633	0.266002
$932$	−34.6011	−1.13340
$933$	9.83560	0.322003
$934$	−0.995362	−0.0325692
$935$	0	0
$936$	0.777718	0.0254205
$937$	20.5013	0.669749	0.334875	−	0.942263i	$-0.391306\pi$
$937$	20.5013	0.669749	0.334875	+	0.942263i	$0.391306\pi$
$938$	0.113542	0.00370728
$939$	6.14928	0.200674
$940$	−25.6943	−0.838054
$941$	49.7248	1.62098	0.810490	−	0.585752i	$-0.199201\pi$
$941$	49.7248	1.62098	0.810490	+	0.585752i	$0.199201\pi$
$942$	−0.137010	−0.00446402
$943$	56.5205	1.84056
$944$	25.0193	0.814309
$945$	2.49420	0.0811364
$946$	0.0676848	0.00220062
$947$	56.7708	1.84480	0.922401	−	0.386233i	$-0.126224\pi$
$947$	56.7708	1.84480	0.922401	+	0.386233i	$0.126224\pi$
$948$	−1.23293	−0.0400437
$949$	96.9243	3.14630
$950$	−0.317499	−0.0103010
$951$	11.3092	0.366727
$952$	0	0
$953$	32.2040	1.04319	0.521594	−	0.853194i	$-0.325338\pi$
$953$	32.2040	1.04319	0.521594	+	0.853194i	$0.325338\pi$
$954$	0.145859	0.00472236
$955$	−20.9380	−0.677536
$956$	−45.8060	−1.48147
$957$	−6.31656	−0.204185
$958$	−0.635886	−0.0205445
$959$	13.0894	0.422679
$960$	19.8922	0.642018
$961$	−30.5435	−0.985275
$962$	−0.281679	−0.00908168
$963$	−0.656429	−0.0211531
$964$	−51.7492	−1.66673
$965$	44.3357	1.42722
$966$	−0.246503	−0.00793110
$967$	39.1577	1.25923	0.629613	−	0.776909i	$-0.283213\pi$
$967$	39.1577	1.25923	0.629613	+	0.776909i	$0.283213\pi$
$968$	−1.22573	−0.0393964
$969$	0	0
$970$	−0.614385	−0.0197267
$971$	39.1476	1.25631	0.628153	−	0.778090i	$-0.283811\pi$
$971$	39.1476	1.25631	0.628153	+	0.778090i	$0.283811\pi$
$972$	−1.99897	−0.0641171
$973$	−19.5822	−0.627777
$974$	−0.125782	−0.00403031
$975$	7.41232	0.237384
$976$	29.0000	0.928268
$977$	42.4663	1.35862	0.679308	−	0.733853i	$-0.262280\pi$
$977$	42.4663	1.35862	0.679308	+	0.733853i	$0.262280\pi$
$978$	0.111536	0.00356653
$979$	21.4082	0.684210
$980$	4.98584	0.159267
$981$	−12.5896	−0.401953
$982$	−0.705978	−0.0225286
$983$	26.0435	0.830659	0.415329	−	0.909671i	$-0.363666\pi$
$983$	26.0435	0.830659	0.415329	+	0.909671i	$0.363666\pi$
$984$	−0.941099	−0.0300012
$985$	21.2062	0.675686
$986$	0	0
$987$	5.15344	0.164036
$988$	−98.4893	−3.13336
$989$	13.5815	0.431868
$990$	0.0956410	0.00303967
$991$	−47.1316	−1.49718	−0.748592	−	0.663031i	$-0.769270\pi$
$991$	−47.1316	−1.49718	−0.748592	+	0.663031i	$0.769270\pi$
$992$	0.259564	0.00824117
$993$	−0.0226644	−0.000719233 0
$994$	−0.120333	−0.00381673
$995$	−12.1878	−0.386378
$996$	1.91811	0.0607775
$997$	−2.41793	−0.0765767	−0.0382883	−	0.999267i	$-0.512191\pi$
$997$	−2.41793	−0.0765767	−0.0382883	+	0.999267i	$0.512191\pi$
$998$	−0.937563	−0.0296780
$999$	1.44837	0.0458245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6069.2.a.be.1.5		10
17.2	even	8		357.2.k.b.106.5	yes	20
17.9	even	8		357.2.k.b.64.6	✓	20
17.16	even	2		6069.2.a.bd.1.5		10
51.2	odd	8		1071.2.n.b.820.6		20
51.26	odd	8		1071.2.n.b.64.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.b.64.6	✓	20	17.9	even	8
357.2.k.b.106.5	yes	20	17.2	even	8
1071.2.n.b.64.5		20	51.26	odd	8
1071.2.n.b.820.6		20	51.2	odd	8
6069.2.a.bd.1.5		10	17.16	even	2
6069.2.a.be.1.5		10	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:	\( N \)	\(=\)	\( 6069 = 3 \cdot 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6069.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0320370 q^{2} +1.00000 q^{3} -1.99897 q^{4} -2.49420 q^{5} -0.0320370 q^{6} -1.00000 q^{7} +0.128115 q^{8} +1.00000 q^{9} +0.0799067 q^{10} +1.19691 q^{11} -1.99897 q^{12} +6.07047 q^{13} +0.0320370 q^{14} -2.49420 q^{15} +3.99384 q^{16} -0.0320370 q^{18} +8.11633 q^{19} +4.98584 q^{20} -1.00000 q^{21} -0.0383453 q^{22} -7.69432 q^{23} +0.128115 q^{24} +1.22105 q^{25} -0.194479 q^{26} +1.00000 q^{27} +1.99897 q^{28} -5.27739 q^{29} +0.0799067 q^{30} -0.675631 q^{31} -0.384181 q^{32} +1.19691 q^{33} +2.49420 q^{35} -1.99897 q^{36} +1.44837 q^{37} -0.260023 q^{38} +6.07047 q^{39} -0.319545 q^{40} -7.34574 q^{41} +0.0320370 q^{42} -1.76514 q^{43} -2.39259 q^{44} -2.49420 q^{45} +0.246503 q^{46} -5.15344 q^{47} +3.99384 q^{48} +1.00000 q^{49} -0.0391186 q^{50} -12.1347 q^{52} -4.55283 q^{53} -0.0320370 q^{54} -2.98533 q^{55} -0.128115 q^{56} +8.11633 q^{57} +0.169072 q^{58} +6.26447 q^{59} +4.98584 q^{60} +7.26118 q^{61} +0.0216452 q^{62} -1.00000 q^{63} -7.97538 q^{64} -15.1410 q^{65} -0.0383453 q^{66} +3.54409 q^{67} -7.69432 q^{69} -0.0799067 q^{70} -3.75607 q^{71} +0.128115 q^{72} +15.9665 q^{73} -0.0464015 q^{74} +1.22105 q^{75} -16.2243 q^{76} -1.19691 q^{77} -0.194479 q^{78} +0.616782 q^{79} -9.96145 q^{80} +1.00000 q^{81} +0.235335 q^{82} -0.959545 q^{83} +1.99897 q^{84} +0.0565497 q^{86} -5.27739 q^{87} +0.153342 q^{88} +17.8863 q^{89} +0.0799067 q^{90} -6.07047 q^{91} +15.3807 q^{92} -0.675631 q^{93} +0.165101 q^{94} -20.2438 q^{95} -0.384181 q^{96} -7.68879 q^{97} -0.0320370 q^{98} +1.19691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} + 12 q^{12} + 6 q^{13} - 4 q^{14} - 6 q^{15} + 20 q^{16} + 4 q^{18} + 6 q^{19} - 16 q^{20} - 10 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 10 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 + 12 * q^12 + 6 * q^13 - 4 * q^14 - 6 * q^15 + 20 * q^16 + 4 * q^18 + 6 * q^19 - 16 * q^20 - 10 * q^21 + 24 * q^22 + 18 * q^23 + 12 * q^24 + 4 * q^25 + 12 * q^26 + 10 * q^27 - 12 * q^28 - 12 * q^29 - 8 * q^31 + 28 * q^32 - 2 * q^33 + 6 * q^35 + 12 * q^36 + 24 * q^37 + 32 * q^38 + 6 * q^39 - 36 * q^40 - 2 * q^41 - 4 * q^42 + 6 * q^43 + 28 * q^44 - 6 * q^45 - 28 * q^46 + 16 * q^47 + 20 * q^48 + 10 * q^49 + 52 * q^50 + 24 * q^52 - 12 * q^53 + 4 * q^54 + 18 * q^55 - 12 * q^56 + 6 * q^57 + 20 * q^58 + 20 * q^59 - 16 * q^60 - 4 * q^61 - 24 * q^62 - 10 * q^63 + 56 * q^64 - 38 * q^65 + 24 * q^66 + 20 * q^67 + 18 * q^69 - 20 * q^71 + 12 * q^72 + 20 * q^73 + 36 * q^74 + 4 * q^75 - 8 * q^76 + 2 * q^77 + 12 * q^78 + 20 * q^79 - 92 * q^80 + 10 * q^81 + 8 * q^82 + 36 * q^83 - 12 * q^84 - 12 * q^87 + 92 * q^88 + 32 * q^89 - 6 * q^91 + 40 * q^92 - 8 * q^93 + 60 * q^94 - 14 * q^95 + 28 * q^96 + 36 * q^97 + 4 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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