LMFDB - Embedded newform 2523.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2523,2,Mod(1,2523)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2523, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2523.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2523 = 3 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2523.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$20.1462564300$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.8902000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 9x^{4} + 10x^{3} + 13x^{2} - 9x - 1 $ x^6 - x^5 - 9x^4 + 10x^3 + 13x^2 - 9x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.26098$ of defining polynomial
Character	$\chi$	$=$	2523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.26098 q^{2} -1.00000 q^{3} +3.11205 q^{4} +0.694681 q^{5} +2.26098 q^{6} -1.74736 q^{7} -2.51433 q^{8} +1.00000 q^{9} -1.57066 q^{10} -4.36539 q^{11} -3.11205 q^{12} -3.28875 q^{13} +3.95075 q^{14} -0.694681 q^{15} -0.539244 q^{16} -5.78276 q^{17} -2.26098 q^{18} -7.37607 q^{19} +2.16188 q^{20} +1.74736 q^{21} +9.87009 q^{22} +1.73466 q^{23} +2.51433 q^{24} -4.51742 q^{25} +7.43580 q^{26} -1.00000 q^{27} -5.43787 q^{28} +1.57066 q^{30} -5.92335 q^{31} +6.24788 q^{32} +4.36539 q^{33} +13.0747 q^{34} -1.21386 q^{35} +3.11205 q^{36} -2.89863 q^{37} +16.6772 q^{38} +3.28875 q^{39} -1.74666 q^{40} +7.12933 q^{41} -3.95075 q^{42} +10.5602 q^{43} -13.5853 q^{44} +0.694681 q^{45} -3.92203 q^{46} -9.52021 q^{47} +0.539244 q^{48} -3.94673 q^{49} +10.2138 q^{50} +5.78276 q^{51} -10.2347 q^{52} +12.3047 q^{53} +2.26098 q^{54} -3.03256 q^{55} +4.39344 q^{56} +7.37607 q^{57} -6.64954 q^{59} -2.16188 q^{60} +1.89863 q^{61} +13.3926 q^{62} -1.74736 q^{63} -13.0479 q^{64} -2.28463 q^{65} -9.87009 q^{66} -4.62828 q^{67} -17.9962 q^{68} -1.73466 q^{69} +2.74451 q^{70} +4.65874 q^{71} -2.51433 q^{72} +0.735359 q^{73} +6.55375 q^{74} +4.51742 q^{75} -22.9547 q^{76} +7.62791 q^{77} -7.43580 q^{78} +6.69339 q^{79} -0.374603 q^{80} +1.00000 q^{81} -16.1193 q^{82} +14.6306 q^{83} +5.43787 q^{84} -4.01718 q^{85} -23.8764 q^{86} +10.9760 q^{88} +1.66540 q^{89} -1.57066 q^{90} +5.74662 q^{91} +5.39833 q^{92} +5.92335 q^{93} +21.5250 q^{94} -5.12402 q^{95} -6.24788 q^{96} +5.67811 q^{97} +8.92350 q^{98} -4.36539 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 6 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} + 6 q^{8} + 6 q^{9} - 12 q^{10} - 6 q^{11} - 7 q^{12} + 8 q^{13} + 10 q^{14} - 5 q^{15} + 17 q^{16} - 2 q^{17} - q^{18} + q^{19} + 3 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 6 * q - q^2 - 6 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 3 * q^7 + 6 * q^8 + 6 * q^9 - 12 * q^10 - 6 * q^11 - 7 * q^12 + 8 * q^13 + 10 * q^14 - 5 * q^15 + 17 * q^16 - 2 * q^17 - q^18 + q^19 + 3 * q^20 - 3 * q^21 + 9 * q^22 + 7 * q^23 - 6 * q^24 + 9 * q^25 - 7 * q^26 - 6 * q^27 + q^28 + 12 * q^30 - 28 * q^31 + 41 * q^32 + 6 * q^33 - 8 * q^34 - 5 * q^35 + 7 * q^36 - 4 * q^37 + 30 * q^38 - 8 * q^39 - 19 * q^40 + 36 * q^41 - 10 * q^42 - 3 * q^43 - 17 * q^44 + 5 * q^45 + 21 * q^46 + q^47 - 17 * q^48 + 19 * q^49 - 32 * q^50 + 2 * q^51 - 11 * q^52 + 16 * q^53 + q^54 - 15 * q^55 + 63 * q^56 - q^57 + 25 * q^59 - 3 * q^60 - 2 * q^61 - 9 * q^62 + 3 * q^63 + 20 * q^64 + 29 * q^65 - 9 * q^66 - 62 * q^68 - 7 * q^69 + 19 * q^70 - 3 * q^71 + 6 * q^72 - 21 * q^73 + 28 * q^74 - 9 * q^75 - 11 * q^76 + 49 * q^77 + 7 * q^78 + 6 * q^79 - 16 * q^80 + 6 * q^81 - 19 * q^82 + 14 * q^83 - q^84 + 26 * q^85 - 49 * q^86 + 44 * q^88 - 6 * q^89 - 12 * q^90 + 41 * q^91 - 18 * q^92 + 28 * q^93 - 29 * q^95 - 41 * q^96 + 8 * q^97 + 38 * q^98 - 6 * 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 $

$2$	−2.26098	−1.59876	−0.799379	−	0.600828i	$-0.794838\pi$
$2$	−2.26098	−1.59876	−0.799379	+	0.600828i	$0.794838\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.11205	1.55603
$5$	0.694681	0.310671	0.155335	−	0.987862i	$-0.450354\pi$
$5$	0.694681	0.310671	0.155335	+	0.987862i	$0.450354\pi$
$6$	2.26098	0.923043
$7$	−1.74736	−0.660440	−0.330220	−	0.943904i	$-0.607123\pi$
$7$	−1.74736	−0.660440	−0.330220	+	0.943904i	$0.607123\pi$
$8$	−2.51433	−0.888949
$9$	1.00000	0.333333
$10$	−1.57066	−0.496687
$11$	−4.36539	−1.31622	−0.658108	−	0.752924i	$-0.728643\pi$
$11$	−4.36539	−1.31622	−0.658108	+	0.752924i	$0.728643\pi$
$12$	−3.11205	−0.898371
$13$	−3.28875	−0.912134	−0.456067	−	0.889945i	$-0.650742\pi$
$13$	−3.28875	−0.912134	−0.456067	+	0.889945i	$0.650742\pi$
$14$	3.95075	1.05588
$15$	−0.694681	−0.179366
$16$	−0.539244	−0.134811
$17$	−5.78276	−1.40253	−0.701263	−	0.712903i	$-0.747380\pi$
$17$	−5.78276	−1.40253	−0.701263	+	0.712903i	$0.747380\pi$
$18$	−2.26098	−0.532919
$19$	−7.37607	−1.69219	−0.846093	−	0.533035i	$-0.821051\pi$
$19$	−7.37607	−1.69219	−0.846093	+	0.533035i	$0.821051\pi$
$20$	2.16188	0.483412
$21$	1.74736	0.381305
$22$	9.87009	2.10431
$23$	1.73466	0.361701	0.180850	−	0.983511i	$-0.442115\pi$
$23$	1.73466	0.361701	0.180850	+	0.983511i	$0.442115\pi$
$24$	2.51433	0.513235
$25$	−4.51742	−0.903484
$26$	7.43580	1.45828
$27$	−1.00000	−0.192450
$28$	−5.43787	−1.02766
$29$	0	0
$29$	0	0
$30$	1.57066	0.286763
$31$	−5.92335	−1.06387	−0.531933	−	0.846787i	$-0.678534\pi$
$31$	−5.92335	−1.06387	−0.531933	+	0.846787i	$0.678534\pi$
$32$	6.24788	1.10448
$33$	4.36539	0.759918
$34$	13.0747	2.24230
$35$	−1.21386	−0.205179
$36$	3.11205	0.518675
$37$	−2.89863	−0.476531	−0.238266	−	0.971200i	$-0.576579\pi$
$37$	−2.89863	−0.476531	−0.238266	+	0.971200i	$0.576579\pi$
$38$	16.6772	2.70540
$39$	3.28875	0.526621
$40$	−1.74666	−0.276171
$41$	7.12933	1.11341	0.556707	−	0.830709i	$-0.312065\pi$
$41$	7.12933	1.11341	0.556707	+	0.830709i	$0.312065\pi$
$42$	−3.95075	−0.609614
$43$	10.5602	1.61041	0.805205	−	0.592997i	$-0.202055\pi$
$43$	10.5602	1.61041	0.805205	+	0.592997i	$0.202055\pi$
$44$	−13.5853	−2.04806
$45$	0.694681	0.103557
$46$	−3.92203	−0.578272
$47$	−9.52021	−1.38867	−0.694333	−	0.719654i	$-0.744300\pi$
$47$	−9.52021	−1.38867	−0.694333	+	0.719654i	$0.744300\pi$
$48$	0.539244	0.0778332
$49$	−3.94673	−0.563819
$50$	10.2138	1.44445
$51$	5.78276	0.809749
$52$	−10.2347	−1.41930
$53$	12.3047	1.69018	0.845092	−	0.534620i	$-0.179545\pi$
$53$	12.3047	1.69018	0.845092	+	0.534620i	$0.179545\pi$
$54$	2.26098	0.307681
$55$	−3.03256	−0.408910
$56$	4.39344	0.587097
$57$	7.37607	0.976984
$58$	0	0
$59$	−6.64954	−0.865696	−0.432848	−	0.901467i	$-0.642491\pi$
$59$	−6.64954	−0.865696	−0.432848	+	0.901467i	$0.642491\pi$
$60$	−2.16188	−0.279098
$61$	1.89863	0.243094	0.121547	−	0.992586i	$-0.461214\pi$
$61$	1.89863	0.243094	0.121547	+	0.992586i	$0.461214\pi$
$62$	13.3926	1.70086
$63$	−1.74736	−0.220147
$64$	−13.0479	−1.63098
$65$	−2.28463	−0.283374
$66$	−9.87009	−1.21492
$67$	−4.62828	−0.565434	−0.282717	−	0.959203i	$-0.591236\pi$
$67$	−4.62828	−0.565434	−0.282717	+	0.959203i	$0.591236\pi$
$68$	−17.9962	−2.18237
$69$	−1.73466	−0.208828
$70$	2.74451	0.328032
$71$	4.65874	0.552891	0.276446	−	0.961030i	$-0.410843\pi$
$71$	4.65874	0.552891	0.276446	+	0.961030i	$0.410843\pi$
$72$	−2.51433	−0.296316
$73$	0.735359	0.0860672	0.0430336	−	0.999074i	$-0.486298\pi$
$73$	0.735359	0.0860672	0.0430336	+	0.999074i	$0.486298\pi$
$74$	6.55375	0.761858
$75$	4.51742	0.521626
$76$	−22.9547	−2.63308
$77$	7.62791	0.869281
$78$	−7.43580	−0.841939
$79$	6.69339	0.753065	0.376533	−	0.926403i	$-0.377116\pi$
$79$	6.69339	0.753065	0.376533	+	0.926403i	$0.377116\pi$
$80$	−0.374603	−0.0418819
$81$	1.00000	0.111111
$82$	−16.1193	−1.78008
$83$	14.6306	1.60592	0.802959	−	0.596035i	$-0.203258\pi$
$83$	14.6306	1.60592	0.802959	+	0.596035i	$0.203258\pi$
$84$	5.43787	0.593320
$85$	−4.01718	−0.435724
$86$	−23.8764	−2.57465
$87$	0	0
$88$	10.9760	1.17005
$89$	1.66540	0.176533	0.0882663	−	0.996097i	$-0.471867\pi$
$89$	1.66540	0.176533	0.0882663	+	0.996097i	$0.471867\pi$
$90$	−1.57066	−0.165562
$91$	5.74662	0.602410
$92$	5.39833	0.562815
$93$	5.92335	0.614223
$94$	21.5250	2.22014
$95$	−5.12402	−0.525713
$96$	−6.24788	−0.637671
$97$	5.67811	0.576525	0.288262	−	0.957551i	$-0.406922\pi$
$97$	5.67811	0.576525	0.288262	+	0.957551i	$0.406922\pi$
$98$	8.92350	0.901410
$99$	−4.36539	−0.438739
$100$	−14.0584	−1.40584
$101$	−2.01614	−0.200613	−0.100307	−	0.994957i	$-0.531982\pi$
$101$	−2.01614	−0.200613	−0.100307	+	0.994957i	$0.531982\pi$
$102$	−13.0747	−1.29459
$103$	−14.1152	−1.39081	−0.695405	−	0.718618i	$-0.744775\pi$
$103$	−14.1152	−1.39081	−0.695405	+	0.718618i	$0.744775\pi$
$104$	8.26899	0.810841
$105$	1.21386	0.118460
$106$	−27.8208	−2.70220
$107$	−4.67185	−0.451645	−0.225822	−	0.974168i	$-0.572507\pi$
$107$	−4.67185	−0.451645	−0.225822	+	0.974168i	$0.572507\pi$
$108$	−3.11205	−0.299457
$109$	−13.4642	−1.28963	−0.644816	−	0.764338i	$-0.723066\pi$
$109$	−13.4642	−1.28963	−0.644816	+	0.764338i	$0.723066\pi$
$110$	6.85656	0.653748
$111$	2.89863	0.275125
$112$	0.942254	0.0890346
$113$	3.04283	0.286246	0.143123	−	0.989705i	$-0.454286\pi$
$113$	3.04283	0.286246	0.143123	+	0.989705i	$0.454286\pi$
$114$	−16.6772	−1.56196
$115$	1.20503	0.112370
$116$	0	0
$117$	−3.28875	−0.304045
$118$	15.0345	1.38404
$119$	10.1046	0.926284
$120$	1.74666	0.159447
$121$	8.05666	0.732424
$122$	−4.29277	−0.388649
$123$	−7.12933	−0.642830
$124$	−18.4338	−1.65540
$125$	−6.61157	−0.591357
$126$	3.95075	0.351961
$127$	−5.57137	−0.494379	−0.247189	−	0.968967i	$-0.579507\pi$
$127$	−5.57137	−0.494379	−0.247189	+	0.968967i	$0.579507\pi$
$128$	17.0053	1.50307
$129$	−10.5602	−0.929771
$130$	5.16551	0.453046
$131$	−8.35339	−0.729839	−0.364920	−	0.931039i	$-0.618904\pi$
$131$	−8.35339	−0.729839	−0.364920	+	0.931039i	$0.618904\pi$
$132$	13.5853	1.18245
$133$	12.8886	1.11759
$134$	10.4645	0.903992
$135$	−0.694681	−0.0597886
$136$	14.5398	1.24677
$137$	18.1690	1.55228	0.776142	−	0.630558i	$-0.217174\pi$
$137$	18.1690	1.55228	0.776142	+	0.630558i	$0.217174\pi$
$138$	3.92203	0.333865
$139$	−20.4275	−1.73263	−0.866317	−	0.499494i	$-0.833519\pi$
$139$	−20.4275	−1.73263	−0.866317	+	0.499494i	$0.833519\pi$
$140$	−3.77759	−0.319264
$141$	9.52021	0.801746
$142$	−10.5333	−0.883939
$143$	14.3567	1.20057
$144$	−0.539244	−0.0449370
$145$	0	0
$146$	−1.66263	−0.137601
$147$	3.94673	0.325521
$148$	−9.02067	−0.741495
$149$	−17.4954	−1.43328	−0.716640	−	0.697443i	$-0.754321\pi$
$149$	−17.4954	−1.43328	−0.716640	+	0.697443i	$0.754321\pi$
$150$	−10.2138	−0.833954
$151$	19.7133	1.60425	0.802124	−	0.597158i	$-0.203703\pi$
$151$	19.7133	1.60425	0.802124	+	0.597158i	$0.203703\pi$
$152$	18.5459	1.50427
$153$	−5.78276	−0.467509
$154$	−17.2466	−1.38977
$155$	−4.11484	−0.330512
$156$	10.2347	0.819435
$157$	20.1702	1.60976	0.804878	−	0.593441i	$-0.202231\pi$
$157$	20.1702	1.60976	0.804878	+	0.593441i	$0.202231\pi$
$158$	−15.1337	−1.20397
$159$	−12.3047	−0.975829
$160$	4.34028	0.343130
$161$	−3.03107	−0.238882
$162$	−2.26098	−0.177640
$163$	−8.65350	−0.677794	−0.338897	−	0.940823i	$-0.610054\pi$
$163$	−8.65350	−0.677794	−0.338897	+	0.940823i	$0.610054\pi$
$164$	22.1868	1.73250
$165$	3.03256	0.236084
$166$	−33.0796	−2.56747
$167$	−2.57560	−0.199306	−0.0996529	−	0.995022i	$-0.531773\pi$
$167$	−2.57560	−0.199306	−0.0996529	+	0.995022i	$0.531773\pi$
$168$	−4.39344	−0.338961
$169$	−2.18415	−0.168011
$170$	9.08277	0.696617
$171$	−7.37607	−0.564062
$172$	32.8638	2.50584
$173$	13.0654	0.993343	0.496671	−	0.867939i	$-0.334555\pi$
$173$	13.0654	0.993343	0.496671	+	0.867939i	$0.334555\pi$
$174$	0	0
$175$	7.89355	0.596697
$176$	2.35401	0.177440
$177$	6.64954	0.499810
$178$	−3.76545	−0.282233
$179$	0.551360	0.0412106	0.0206053	−	0.999788i	$-0.493441\pi$
$179$	0.551360	0.0412106	0.0206053	+	0.999788i	$0.493441\pi$
$180$	2.16188	0.161137
$181$	0.881620	0.0655303	0.0327651	−	0.999463i	$-0.489569\pi$
$181$	0.881620	0.0655303	0.0327651	+	0.999463i	$0.489569\pi$
$182$	−12.9930	−0.963107
$183$	−1.89863	−0.140351
$184$	−4.36149	−0.321533
$185$	−2.01362	−0.148044
$186$	−13.3926	−0.981994
$187$	25.2440	1.84603
$188$	−29.6274	−2.16080
$189$	1.74736	0.127102
$190$	11.5853	0.840488
$191$	−1.63034	−0.117967	−0.0589835	−	0.998259i	$-0.518786\pi$
$191$	−1.63034	−0.117967	−0.0589835	+	0.998259i	$0.518786\pi$
$192$	13.0479	0.941649
$193$	−7.08096	−0.509699	−0.254849	−	0.966981i	$-0.582026\pi$
$193$	−7.08096	−0.509699	−0.254849	+	0.966981i	$0.582026\pi$
$194$	−12.8381	−0.921723
$195$	2.28463	0.163606
$196$	−12.2824	−0.877317
$197$	13.7732	0.981298	0.490649	−	0.871357i	$-0.336760\pi$
$197$	13.7732	0.981298	0.490649	+	0.871357i	$0.336760\pi$
$198$	9.87009	0.701437
$199$	−5.84299	−0.414199	−0.207099	−	0.978320i	$-0.566402\pi$
$199$	−5.84299	−0.414199	−0.207099	+	0.978320i	$0.566402\pi$
$200$	11.3583	0.803151
$201$	4.62828	0.326453
$202$	4.55846	0.320732
$203$	0	0
$204$	17.9962	1.25999
$205$	4.95261	0.345905
$206$	31.9142	2.22357
$207$	1.73466	0.120567
$208$	1.77344	0.122966
$209$	32.1995	2.22728
$210$	−2.74451	−0.189389
$211$	23.4620	1.61519	0.807594	−	0.589738i	$-0.200769\pi$
$211$	23.4620	1.61519	0.807594	+	0.589738i	$0.200769\pi$
$212$	38.2929	2.62997
$213$	−4.65874	−0.319212
$214$	10.5630	0.722070
$215$	7.33595	0.500307
$216$	2.51433	0.171078
$217$	10.3502	0.702619
$218$	30.4422	2.06181
$219$	−0.735359	−0.0496909
$220$	−9.43747	−0.636274
$221$	19.0180	1.27929
$222$	−6.55375	−0.439859
$223$	−3.33324	−0.223210	−0.111605	−	0.993753i	$-0.535599\pi$
$223$	−3.33324	−0.223210	−0.111605	+	0.993753i	$0.535599\pi$
$224$	−10.9173	−0.729442
$225$	−4.51742	−0.301161
$226$	−6.87980	−0.457637
$227$	−8.50125	−0.564248	−0.282124	−	0.959378i	$-0.591039\pi$
$227$	−8.50125	−0.564248	−0.282124	+	0.959378i	$0.591039\pi$
$228$	22.9547	1.52021
$229$	−24.9056	−1.64581	−0.822904	−	0.568180i	$-0.807648\pi$
$229$	−24.9056	−1.64581	−0.822904	+	0.568180i	$0.807648\pi$
$230$	−2.72456	−0.179652
$231$	−7.62791	−0.501880
$232$	0	0
$233$	−6.81039	−0.446164	−0.223082	−	0.974800i	$-0.571612\pi$
$233$	−6.81039	−0.446164	−0.223082	+	0.974800i	$0.571612\pi$
$234$	7.43580	0.486094
$235$	−6.61351	−0.431418
$236$	−20.6937	−1.34704
$237$	−6.69339	−0.434782
$238$	−22.8463	−1.48090
$239$	4.88184	0.315780	0.157890	−	0.987457i	$-0.449531\pi$
$239$	4.88184	0.315780	0.157890	+	0.987457i	$0.449531\pi$
$240$	0.374603	0.0241805
$241$	−3.85069	−0.248045	−0.124022	−	0.992279i	$-0.539579\pi$
$241$	−3.85069	−0.248045	−0.124022	+	0.992279i	$0.539579\pi$
$242$	−18.2160	−1.17097
$243$	−1.00000	−0.0641500
$244$	5.90862	0.378261
$245$	−2.74172	−0.175162
$246$	16.1193	1.02773
$247$	24.2580	1.54350
$248$	14.8933	0.945722
$249$	−14.6306	−0.927177
$250$	14.9487	0.945436
$251$	5.91306	0.373229	0.186614	−	0.982433i	$-0.440248\pi$
$251$	5.91306	0.373229	0.186614	+	0.982433i	$0.440248\pi$
$252$	−5.43787	−0.342554
$253$	−7.57245	−0.476076
$254$	12.5968	0.790392
$255$	4.01718	0.251565
$256$	−12.3529	−0.772057
$257$	−7.92041	−0.494061	−0.247031	−	0.969008i	$-0.579455\pi$
$257$	−7.92041	−0.494061	−0.247031	+	0.969008i	$0.579455\pi$
$258$	23.8764	1.48648
$259$	5.06494	0.314720
$260$	−7.10988	−0.440936
$261$	0	0
$262$	18.8869	1.16684
$263$	4.63022	0.285512	0.142756	−	0.989758i	$-0.454404\pi$
$263$	4.63022	0.285512	0.142756	+	0.989758i	$0.454404\pi$
$264$	−10.9760	−0.675528
$265$	8.54787	0.525091
$266$	−29.1410	−1.78675
$267$	−1.66540	−0.101921
$268$	−14.4034	−0.879829
$269$	27.3742	1.66903	0.834516	−	0.550984i	$-0.185747\pi$
$269$	27.3742	1.66903	0.834516	+	0.550984i	$0.185747\pi$
$270$	1.57066	0.0955875
$271$	−3.93007	−0.238735	−0.119367	−	0.992850i	$-0.538087\pi$
$271$	−3.93007	−0.238735	−0.119367	+	0.992850i	$0.538087\pi$
$272$	3.11832	0.189076
$273$	−5.74662	−0.347801
$274$	−41.0799	−2.48173
$275$	19.7203	1.18918
$276$	−5.39833	−0.324942
$277$	26.6161	1.59921	0.799605	−	0.600527i	$-0.205042\pi$
$277$	26.6161	1.59921	0.799605	+	0.600527i	$0.205042\pi$
$278$	46.1862	2.77006
$279$	−5.92335	−0.354622
$280$	3.05204	0.182394
$281$	12.5229	0.747054	0.373527	−	0.927619i	$-0.378148\pi$
$281$	12.5229	0.747054	0.373527	+	0.927619i	$0.378148\pi$
$282$	−21.5250	−1.28180
$283$	−17.5097	−1.04084	−0.520422	−	0.853909i	$-0.674225\pi$
$283$	−17.5097	−1.04084	−0.520422	+	0.853909i	$0.674225\pi$
$284$	14.4982	0.860313
$285$	5.12402	0.303521
$286$	−32.4602	−1.91941
$287$	−12.4575	−0.735343
$288$	6.24788	0.368160
$289$	16.4403	0.967079
$290$	0	0
$291$	−5.67811	−0.332857
$292$	2.28847	0.133923
$293$	5.94551	0.347341	0.173670	−	0.984804i	$-0.444437\pi$
$293$	5.94551	0.347341	0.173670	+	0.984804i	$0.444437\pi$
$294$	−8.92350	−0.520429
$295$	−4.61931	−0.268946
$296$	7.28810	0.423612
$297$	4.36539	0.253306
$298$	39.5569	2.29147
$299$	−5.70484	−0.329920
$300$	14.0584	0.811664
$301$	−18.4524	−1.06358
$302$	−44.5715	−2.56480
$303$	2.01614	0.115824
$304$	3.97750	0.228125
$305$	1.31894	0.0755223
$306$	13.0747	0.747433
$307$	−12.2335	−0.698203	−0.349102	−	0.937085i	$-0.613513\pi$
$307$	−12.2335	−0.698203	−0.349102	+	0.937085i	$0.613513\pi$
$308$	23.7384	1.35262
$309$	14.1152	0.802984
$310$	9.30359	0.528409
$311$	10.4087	0.590226	0.295113	−	0.955462i	$-0.404643\pi$
$311$	10.4087	0.590226	0.295113	+	0.955462i	$0.404643\pi$
$312$	−8.26899	−0.468139
$313$	7.57216	0.428004	0.214002	−	0.976833i	$-0.431350\pi$
$313$	7.57216	0.428004	0.214002	+	0.976833i	$0.431350\pi$
$314$	−45.6045	−2.57361
$315$	−1.21386	−0.0683932
$316$	20.8302	1.17179
$317$	−7.30476	−0.410276	−0.205138	−	0.978733i	$-0.565764\pi$
$317$	−7.30476	−0.410276	−0.205138	+	0.978733i	$0.565764\pi$
$318$	27.8208	1.56011
$319$	0	0
$320$	−9.06411	−0.506699
$321$	4.67185	0.260757
$322$	6.85319	0.381914
$323$	42.6541	2.37334
$324$	3.11205	0.172892
$325$	14.8566	0.824098
$326$	19.5654	1.08363
$327$	13.4642	0.744569
$328$	−17.9255	−0.989768
$329$	16.6352	0.917130
$330$	−6.85656	−0.377441
$331$	20.2190	1.11134	0.555669	−	0.831404i	$-0.312462\pi$
$331$	20.2190	1.11134	0.555669	+	0.831404i	$0.312462\pi$
$332$	45.5312	2.49885
$333$	−2.89863	−0.158844
$334$	5.82339	0.318642
$335$	−3.21518	−0.175664
$336$	−0.942254	−0.0514042
$337$	22.5657	1.22923	0.614617	−	0.788826i	$-0.289311\pi$
$337$	22.5657	1.22923	0.614617	+	0.788826i	$0.289311\pi$
$338$	4.93832	0.268609
$339$	−3.04283	−0.165264
$340$	−12.5017	−0.677997
$341$	25.8578	1.40028
$342$	16.6772	0.901799
$343$	19.1279	1.03281
$344$	−26.5517	−1.43157
$345$	−1.20503	−0.0648768
$346$	−29.5406	−1.58811
$347$	25.0587	1.34522	0.672611	−	0.739996i	$-0.265173\pi$
$347$	25.0587	1.34522	0.672611	+	0.739996i	$0.265173\pi$
$348$	0	0
$349$	13.7348	0.735209	0.367605	−	0.929982i	$-0.380178\pi$
$349$	13.7348	0.735209	0.367605	+	0.929982i	$0.380178\pi$
$350$	−17.8472	−0.953973
$351$	3.28875	0.175540
$352$	−27.2745	−1.45373
$353$	−20.0703	−1.06824	−0.534118	−	0.845410i	$-0.679356\pi$
$353$	−20.0703	−1.06824	−0.534118	+	0.845410i	$0.679356\pi$
$354$	−15.0345	−0.799074
$355$	3.23634	0.171767
$356$	5.18282	0.274689
$357$	−10.1046	−0.534790
$358$	−1.24662	−0.0658858
$359$	−33.7750	−1.78258	−0.891289	−	0.453436i	$-0.850198\pi$
$359$	−33.7750	−1.78258	−0.891289	+	0.453436i	$0.850198\pi$
$360$	−1.74666	−0.0920569
$361$	35.4064	1.86350
$362$	−1.99333	−0.104767
$363$	−8.05666	−0.422865
$364$	17.8838	0.937365
$365$	0.510840	0.0267386
$366$	4.29277	0.224386
$367$	−30.8220	−1.60889	−0.804447	−	0.594025i	$-0.797538\pi$
$367$	−30.8220	−1.60889	−0.804447	+	0.594025i	$0.797538\pi$
$368$	−0.935403	−0.0487612
$369$	7.12933	0.371138
$370$	4.55277	0.236687
$371$	−21.5008	−1.11627
$372$	18.4338	0.955746
$373$	27.7259	1.43559	0.717797	−	0.696253i	$-0.245151\pi$
$373$	27.7259	1.43559	0.717797	+	0.696253i	$0.245151\pi$
$374$	−57.0764	−2.95135
$375$	6.61157	0.341420
$376$	23.9369	1.23445
$377$	0	0
$378$	−3.95075	−0.203205
$379$	−10.4155	−0.535010	−0.267505	−	0.963557i	$-0.586199\pi$
$379$	−10.4155	−0.535010	−0.267505	+	0.963557i	$0.586199\pi$
$380$	−15.9462	−0.818023
$381$	5.57137	0.285430
$382$	3.68617	0.188601
$383$	3.73020	0.190604	0.0953022	−	0.995448i	$-0.469618\pi$
$383$	3.73020	0.190604	0.0953022	+	0.995448i	$0.469618\pi$
$384$	−17.0053	−0.867796
$385$	5.29897	0.270060
$386$	16.0099	0.814885
$387$	10.5602	0.536803
$388$	17.6706	0.897087
$389$	−25.4297	−1.28934	−0.644668	−	0.764463i	$-0.723004\pi$
$389$	−25.4297	−1.28934	−0.644668	+	0.764463i	$0.723004\pi$
$390$	−5.16551	−0.261566
$391$	−10.0311	−0.507295
$392$	9.92338	0.501207
$393$	8.35339	0.421373
$394$	−31.1409	−1.56886
$395$	4.64977	0.233955
$396$	−13.5853	−0.682688
$397$	−30.9208	−1.55187	−0.775935	−	0.630813i	$-0.782722\pi$
$397$	−30.9208	−1.55187	−0.775935	+	0.630813i	$0.782722\pi$
$398$	13.2109	0.662203
$399$	−12.8886	−0.645239
$400$	2.43599	0.121800
$401$	2.48245	0.123968	0.0619838	−	0.998077i	$-0.480257\pi$
$401$	2.48245	0.123968	0.0619838	+	0.998077i	$0.480257\pi$
$402$	−10.4645	−0.521920
$403$	19.4804	0.970388
$404$	−6.27432	−0.312159
$405$	0.694681	0.0345190
$406$	0	0
$407$	12.6536	0.627218
$408$	−14.5398	−0.719825
$409$	−0.575334	−0.0284484	−0.0142242	−	0.999899i	$-0.504528\pi$
$409$	−0.575334	−0.0284484	−0.0142242	+	0.999899i	$0.504528\pi$
$410$	−11.1978	−0.553018
$411$	−18.1690	−0.896212
$412$	−43.9271	−2.16413
$413$	11.6191	0.571740
$414$	−3.92203	−0.192757
$415$	10.1636	0.498912
$416$	−20.5477	−1.00743
$417$	20.4275	1.00034
$418$	−72.8025	−3.56088
$419$	−30.7334	−1.50142	−0.750712	−	0.660630i	$-0.770289\pi$
$419$	−30.7334	−1.50142	−0.750712	+	0.660630i	$0.770289\pi$
$420$	3.77759	0.184327
$421$	−23.1624	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$421$	−23.1624	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$422$	−53.0472	−2.58229
$423$	−9.52021	−0.462888
$424$	−30.9381	−1.50249
$425$	26.1232	1.26716
$426$	10.5333	0.510342
$427$	−3.31758	−0.160549
$428$	−14.5390	−0.702771
$429$	−14.3567	−0.693147
$430$	−16.5865	−0.799870
$431$	−34.4994	−1.66178	−0.830889	−	0.556438i	$-0.812168\pi$
$431$	−34.4994	−1.66178	−0.830889	+	0.556438i	$0.812168\pi$
$432$	0.539244	0.0259444
$433$	16.5174	0.793776	0.396888	−	0.917867i	$-0.370090\pi$
$433$	16.5174	0.793776	0.396888	+	0.917867i	$0.370090\pi$
$434$	−23.4017	−1.12332
$435$	0	0
$436$	−41.9011	−2.00670
$437$	−12.7949	−0.612065
$438$	1.66263	0.0794437
$439$	−25.3234	−1.20862	−0.604309	−	0.796750i	$-0.706551\pi$
$439$	−25.3234	−1.20862	−0.604309	+	0.796750i	$0.706551\pi$
$440$	7.62484	0.363500
$441$	−3.94673	−0.187940
$442$	−42.9995	−2.04528
$443$	8.31671	0.395139	0.197569	−	0.980289i	$-0.436695\pi$
$443$	8.31671	0.395139	0.197569	+	0.980289i	$0.436695\pi$
$444$	9.02067	0.428102
$445$	1.15693	0.0548435
$446$	7.53640	0.356859
$447$	17.4954	0.827505
$448$	22.7993	1.07717
$449$	−21.5337	−1.01624	−0.508118	−	0.861287i	$-0.669659\pi$
$449$	−21.5337	−1.01624	−0.508118	+	0.861287i	$0.669659\pi$
$450$	10.2138	0.481484
$451$	−31.1223	−1.46549
$452$	9.46945	0.445405
$453$	−19.7133	−0.926213
$454$	19.2212	0.902095
$455$	3.99207	0.187151
$456$	−18.5459	−0.868489
$457$	31.1654	1.45785	0.728927	−	0.684591i	$-0.240019\pi$
$457$	31.1654	1.45785	0.728927	+	0.684591i	$0.240019\pi$
$458$	56.3112	2.63125
$459$	5.78276	0.269916
$460$	3.75012	0.174850
$461$	3.11409	0.145038	0.0725188	−	0.997367i	$-0.476896\pi$
$461$	3.11409	0.145038	0.0725188	+	0.997367i	$0.476896\pi$
$462$	17.2466	0.802384
$463$	−18.1671	−0.844296	−0.422148	−	0.906527i	$-0.638724\pi$
$463$	−18.1671	−0.844296	−0.422148	+	0.906527i	$0.638724\pi$
$464$	0	0
$465$	4.11484	0.190821
$466$	15.3982	0.713307
$467$	−10.9579	−0.507073	−0.253536	−	0.967326i	$-0.581594\pi$
$467$	−10.9579	−0.507073	−0.253536	+	0.967326i	$0.581594\pi$
$468$	−10.2347	−0.473101
$469$	8.08726	0.373435
$470$	14.9530	0.689733
$471$	−20.1702	−0.929393
$472$	16.7191	0.769560
$473$	−46.0993	−2.11965
$474$	15.1337	0.695112
$475$	33.3208	1.52886
$476$	31.4459	1.44132
$477$	12.3047	0.563395
$478$	−11.0378	−0.504856
$479$	−15.7087	−0.717748	−0.358874	−	0.933386i	$-0.616839\pi$
$479$	−15.7087	−0.717748	−0.358874	+	0.933386i	$0.616839\pi$
$480$	−4.34028	−0.198106
$481$	9.53285	0.434660
$482$	8.70635	0.396563
$483$	3.03107	0.137918
$484$	25.0727	1.13967
$485$	3.94448	0.179109
$486$	2.26098	0.102560
$487$	−0.758980	−0.0343927	−0.0171963	−	0.999852i	$-0.505474\pi$
$487$	−0.758980	−0.0343927	−0.0171963	+	0.999852i	$0.505474\pi$
$488$	−4.77377	−0.216098
$489$	8.65350	0.391325
$490$	6.19899	0.280042
$491$	−20.3493	−0.918349	−0.459175	−	0.888346i	$-0.651855\pi$
$491$	−20.3493	−0.918349	−0.459175	+	0.888346i	$0.651855\pi$
$492$	−22.1868	−1.00026
$493$	0	0
$494$	−54.8470	−2.46768
$495$	−3.03256	−0.136303
$496$	3.19413	0.143421
$497$	−8.14050	−0.365151
$498$	33.0796	1.48233
$499$	17.5627	0.786213	0.393106	−	0.919493i	$-0.371400\pi$
$499$	17.5627	0.786213	0.393106	+	0.919493i	$0.371400\pi$
$500$	−20.5755	−0.920166
$501$	2.57560	0.115069
$502$	−13.3693	−0.596702
$503$	7.62305	0.339895	0.169948	−	0.985453i	$-0.445640\pi$
$503$	7.62305	0.339895	0.169948	+	0.985453i	$0.445640\pi$
$504$	4.39344	0.195699
$505$	−1.40057	−0.0623247
$506$	17.1212	0.761130
$507$	2.18415	0.0970014
$508$	−17.3384	−0.769266
$509$	17.2662	0.765310	0.382655	−	0.923891i	$-0.375010\pi$
$509$	17.2662	0.765310	0.382655	+	0.923891i	$0.375010\pi$
$510$	−9.08277	−0.402192
$511$	−1.28494	−0.0568422
$512$	−6.08081	−0.268736
$513$	7.37607	0.325661
$514$	17.9079	0.789884
$515$	−9.80555	−0.432084
$516$	−32.8638	−1.44675
$517$	41.5595	1.82778
$518$	−11.4518	−0.503161
$519$	−13.0654	−0.573507
$520$	5.74431	0.251905
$521$	13.2985	0.582616	0.291308	−	0.956629i	$-0.405910\pi$
$521$	13.2985	0.582616	0.291308	+	0.956629i	$0.405910\pi$
$522$	0	0
$523$	−1.96887	−0.0860928	−0.0430464	−	0.999073i	$-0.513706\pi$
$523$	−1.96887	−0.0860928	−0.0430464	+	0.999073i	$0.513706\pi$
$524$	−25.9962	−1.13565
$525$	−7.89355	−0.344503
$526$	−10.4689	−0.456464
$527$	34.2533	1.49210
$528$	−2.35401	−0.102445
$529$	−19.9910	−0.869173
$530$	−19.3266	−0.839493
$531$	−6.64954	−0.288565
$532$	40.1101	1.73899
$533$	−23.4465	−1.01558
$534$	3.76545	0.162947
$535$	−3.24545	−0.140313
$536$	11.6370	0.502642
$537$	−0.551360	−0.0237930
$538$	−61.8925	−2.66838
$539$	17.2290	0.742108
$540$	−2.16188	−0.0930326
$541$	23.1317	0.994510	0.497255	−	0.867604i	$-0.334341\pi$
$541$	23.1317	0.994510	0.497255	+	0.867604i	$0.334341\pi$
$542$	8.88582	0.381679
$543$	−0.881620	−0.0378339
$544$	−36.1300	−1.54906
$545$	−9.35329	−0.400651
$546$	12.9930	0.556050
$547$	3.78367	0.161778	0.0808890	−	0.996723i	$-0.474224\pi$
$547$	3.78367	0.161778	0.0808890	+	0.996723i	$0.474224\pi$
$548$	56.5429	2.41539
$549$	1.89863	0.0810314
$550$	−44.5873	−1.90121
$551$	0	0
$552$	4.36149	0.185637
$553$	−11.6958	−0.497354
$554$	−60.1787	−2.55675
$555$	2.01362	0.0854735
$556$	−63.5713	−2.69602
$557$	−18.1703	−0.769899	−0.384950	−	0.922938i	$-0.625781\pi$
$557$	−18.1703	−0.769899	−0.384950	+	0.922938i	$0.625781\pi$
$558$	13.3926	0.566954
$559$	−34.7297	−1.46891
$560$	0.654566	0.0276605
$561$	−25.2440	−1.06580
$562$	−28.3141	−1.19436
$563$	42.0074	1.77040	0.885201	−	0.465208i	$-0.154021\pi$
$563$	42.0074	1.77040	0.885201	+	0.465208i	$0.154021\pi$
$564$	29.6274	1.24754
$565$	2.11380	0.0889282
$566$	39.5892	1.66406
$567$	−1.74736	−0.0733822
$568$	−11.7136	−0.491492
$569$	−29.0279	−1.21691	−0.608457	−	0.793587i	$-0.708211\pi$
$569$	−29.0279	−1.21691	−0.608457	+	0.793587i	$0.708211\pi$
$570$	−11.5853	−0.485256
$571$	11.0087	0.460700	0.230350	−	0.973108i	$-0.426013\pi$
$571$	11.0087	0.460700	0.230350	+	0.973108i	$0.426013\pi$
$572$	44.6787	1.86811
$573$	1.63034	0.0681083
$574$	28.1662	1.17563
$575$	−7.83616	−0.326791
$576$	−13.0479	−0.543661
$577$	17.3892	0.723921	0.361960	−	0.932194i	$-0.382108\pi$
$577$	17.3892	0.723921	0.361960	+	0.932194i	$0.382108\pi$
$578$	−37.1714	−1.54612
$579$	7.08096	0.294275
$580$	0	0
$581$	−25.5649	−1.06061
$582$	12.8381	0.532157
$583$	−53.7150	−2.22465
$584$	−1.84893	−0.0765094
$585$	−2.28463	−0.0944578
$586$	−13.4427	−0.555313
$587$	5.00210	0.206459	0.103229	−	0.994658i	$-0.467082\pi$
$587$	5.00210	0.206459	0.103229	+	0.994658i	$0.467082\pi$
$588$	12.2824	0.506519
$589$	43.6911	1.80026
$590$	10.4442	0.429980
$591$	−13.7732	−0.566552
$592$	1.56307	0.0642417
$593$	11.4607	0.470634	0.235317	−	0.971919i	$-0.424387\pi$
$593$	11.4607	0.470634	0.235317	+	0.971919i	$0.424387\pi$
$594$	−9.87009	−0.404975
$595$	7.01945	0.287770
$596$	−54.4466	−2.23022
$597$	5.84299	0.239138
$598$	12.8986	0.527461
$599$	26.7654	1.09361	0.546803	−	0.837262i	$-0.315845\pi$
$599$	26.7654	1.09361	0.546803	+	0.837262i	$0.315845\pi$
$600$	−11.3583	−0.463699
$601$	−9.36535	−0.382021	−0.191010	−	0.981588i	$-0.561176\pi$
$601$	−9.36535	−0.382021	−0.191010	+	0.981588i	$0.561176\pi$
$602$	41.7206	1.70040
$603$	−4.62828	−0.188478
$604$	61.3489	2.49625
$605$	5.59681	0.227543
$606$	−4.55846	−0.185175
$607$	−38.6946	−1.57057	−0.785283	−	0.619137i	$-0.787483\pi$
$607$	−38.6946	−1.57057	−0.785283	+	0.619137i	$0.787483\pi$
$608$	−46.0848	−1.86899
$609$	0	0
$610$	−2.98210	−0.120742
$611$	31.3096	1.26665
$612$	−17.9962	−0.727455
$613$	30.0381	1.21323	0.606613	−	0.794997i	$-0.292528\pi$
$613$	30.0381	1.21323	0.606613	+	0.794997i	$0.292528\pi$
$614$	27.6598	1.11626
$615$	−4.95261	−0.199708
$616$	−19.1791	−0.772747
$617$	−44.5841	−1.79489	−0.897444	−	0.441128i	$-0.854579\pi$
$617$	−44.5841	−1.79489	−0.897444	+	0.441128i	$0.854579\pi$
$618$	−31.9142	−1.28378
$619$	15.9491	0.641049	0.320524	−	0.947240i	$-0.396141\pi$
$619$	15.9491	0.641049	0.320524	+	0.947240i	$0.396141\pi$
$620$	−12.8056	−0.514285
$621$	−1.73466	−0.0696093
$622$	−23.5340	−0.943628
$623$	−2.91006	−0.116589
$624$	−1.77344	−0.0709943
$625$	17.9942	0.719766
$626$	−17.1205	−0.684274
$627$	−32.1995	−1.28592
$628$	62.7706	2.50482
$629$	16.7621	0.668348
$630$	2.74451	0.109344
$631$	−8.28342	−0.329758	−0.164879	−	0.986314i	$-0.552723\pi$
$631$	−8.28342	−0.329758	−0.164879	+	0.986314i	$0.552723\pi$
$632$	−16.8294	−0.669437
$633$	−23.4620	−0.932530
$634$	16.5160	0.655932
$635$	−3.87032	−0.153589
$636$	−38.2929	−1.51841
$637$	12.9798	0.514279
$638$	0	0
$639$	4.65874	0.184297
$640$	11.8132	0.466959
$641$	−1.48489	−0.0586497	−0.0293248	−	0.999570i	$-0.509336\pi$
$641$	−1.48489	−0.0586497	−0.0293248	+	0.999570i	$0.509336\pi$
$642$	−10.5630	−0.416888
$643$	47.4253	1.87027	0.935136	−	0.354289i	$-0.115277\pi$
$643$	47.4253	1.87027	0.935136	+	0.354289i	$0.115277\pi$
$644$	−9.43283	−0.371706
$645$	−7.33595	−0.288853
$646$	−96.4402	−3.79439
$647$	−15.0276	−0.590796	−0.295398	−	0.955374i	$-0.595452\pi$
$647$	−15.0276	−0.590796	−0.295398	+	0.955374i	$0.595452\pi$
$648$	−2.51433	−0.0987721
$649$	29.0278	1.13944
$650$	−33.5906	−1.31753
$651$	−10.3502	−0.405657
$652$	−26.9301	−1.05466
$653$	19.3474	0.757121	0.378560	−	0.925577i	$-0.376419\pi$
$653$	19.3474	0.757121	0.378560	+	0.925577i	$0.376419\pi$
$654$	−30.4422	−1.19039
$655$	−5.80295	−0.226740
$656$	−3.84445	−0.150100
$657$	0.735359	0.0286891
$658$	−37.6120	−1.46627
$659$	29.7738	1.15982	0.579912	−	0.814679i	$-0.303087\pi$
$659$	29.7738	1.15982	0.579912	+	0.814679i	$0.303087\pi$
$660$	9.43747	0.367353
$661$	−34.7735	−1.35253	−0.676266	−	0.736657i	$-0.736403\pi$
$661$	−34.7735	−1.35253	−0.676266	+	0.736657i	$0.736403\pi$
$662$	−45.7149	−1.77676
$663$	−19.0180	−0.738599
$664$	−36.7861	−1.42758
$665$	8.95350	0.347202
$666$	6.55375	0.253953
$667$	0	0
$668$	−8.01539	−0.310125
$669$	3.33324	0.128870
$670$	7.26946	0.280844
$671$	−8.28825	−0.319964
$672$	10.9173	0.421144
$673$	15.4494	0.595532	0.297766	−	0.954639i	$-0.403759\pi$
$673$	15.4494	0.595532	0.297766	+	0.954639i	$0.403759\pi$
$674$	−51.0208	−1.96525
$675$	4.51742	0.173875
$676$	−6.79717	−0.261430
$677$	13.4157	0.515608	0.257804	−	0.966197i	$-0.417001\pi$
$677$	13.4157	0.515608	0.257804	+	0.966197i	$0.417001\pi$
$678$	6.87980	0.264217
$679$	−9.92170	−0.380760
$680$	10.1005	0.387336
$681$	8.50125	0.325768
$682$	−58.4640	−2.23870
$683$	−33.1479	−1.26837	−0.634185	−	0.773181i	$-0.718664\pi$
$683$	−33.1479	−1.26837	−0.634185	+	0.773181i	$0.718664\pi$
$684$	−22.9547	−0.877695
$685$	12.6217	0.482250
$686$	−43.2478	−1.65121
$687$	24.9056	0.950208
$688$	−5.69451	−0.217101
$689$	−40.4671	−1.54168
$690$	2.72456	0.103722
$691$	−13.0512	−0.496490	−0.248245	−	0.968697i	$-0.579854\pi$
$691$	−13.0512	−0.496490	−0.248245	+	0.968697i	$0.579854\pi$
$692$	40.6601	1.54567
$693$	7.62791	0.289760
$694$	−56.6573	−2.15068
$695$	−14.1906	−0.538279
$696$	0	0
$697$	−41.2272	−1.56159
$698$	−31.0543	−1.17542
$699$	6.81039	0.257593
$700$	24.5651	0.928475
$701$	−16.0420	−0.605898	−0.302949	−	0.953007i	$-0.597971\pi$
$701$	−16.0420	−0.605898	−0.302949	+	0.953007i	$0.597971\pi$
$702$	−7.43580	−0.280646
$703$	21.3805	0.806380
$704$	56.9591	2.14673
$705$	6.61351	0.249079
$706$	45.3787	1.70785
$707$	3.52292	0.132493
$708$	20.6937	0.777716
$709$	23.4747	0.881610	0.440805	−	0.897603i	$-0.354693\pi$
$709$	23.4747	0.881610	0.440805	+	0.897603i	$0.354693\pi$
$710$	−7.31732	−0.274614
$711$	6.69339	0.251022
$712$	−4.18737	−0.156928
$713$	−10.2750	−0.384801
$714$	22.8463	0.855000
$715$	9.97331	0.372981
$716$	1.71586	0.0641247
$717$	−4.88184	−0.182316
$718$	76.3648	2.84991
$719$	−24.3340	−0.907507	−0.453753	−	0.891127i	$-0.649915\pi$
$719$	−24.3340	−0.907507	−0.453753	+	0.891127i	$0.649915\pi$
$720$	−0.374603	−0.0139606
$721$	24.6643	0.918546
$722$	−80.0534	−2.97928
$723$	3.85069	0.143209
$724$	2.74365	0.101967
$725$	0	0
$726$	18.2160	0.676059
$727$	−16.1534	−0.599096	−0.299548	−	0.954081i	$-0.596836\pi$
$727$	−16.1534	−0.599096	−0.299548	+	0.954081i	$0.596836\pi$
$728$	−14.4489	−0.535512
$729$	1.00000	0.0370370
$730$	−1.15500	−0.0427485
$731$	−61.0669	−2.25864
$732$	−5.90862	−0.218389
$733$	11.6756	0.431247	0.215623	−	0.976477i	$-0.430822\pi$
$733$	11.6756	0.431247	0.215623	+	0.976477i	$0.430822\pi$
$734$	69.6880	2.57223
$735$	2.74172	0.101130
$736$	10.8379	0.399491
$737$	20.2042	0.744233
$738$	−16.1193	−0.593359
$739$	23.4275	0.861796	0.430898	−	0.902401i	$-0.358197\pi$
$739$	23.4275	0.861796	0.430898	+	0.902401i	$0.358197\pi$
$740$	−6.26649	−0.230361
$741$	−24.2580	−0.891141
$742$	48.6130	1.78464
$743$	−18.7709	−0.688637	−0.344318	−	0.938853i	$-0.611890\pi$
$743$	−18.7709	−0.688637	−0.344318	+	0.938853i	$0.611890\pi$
$744$	−14.8933	−0.546013
$745$	−12.1537	−0.445279
$746$	−62.6879	−2.29517
$747$	14.6306	0.535306
$748$	78.5607	2.87246
$749$	8.16340	0.298284
$750$	−14.9487	−0.545848
$751$	15.7969	0.576438	0.288219	−	0.957564i	$-0.406937\pi$
$751$	15.7969	0.576438	0.288219	+	0.957564i	$0.406937\pi$
$752$	5.13372	0.187207
$753$	−5.91306	−0.215484
$754$	0	0
$755$	13.6945	0.498393
$756$	5.43787	0.197773
$757$	−37.1786	−1.35128	−0.675639	−	0.737232i	$-0.736132\pi$
$757$	−37.1786	−1.35128	−0.675639	+	0.737232i	$0.736132\pi$
$758$	23.5493	0.855351
$759$	7.57245	0.274863
$760$	12.8835	0.467332
$761$	4.88513	0.177086	0.0885429	−	0.996072i	$-0.471779\pi$
$761$	4.88513	0.177086	0.0885429	+	0.996072i	$0.471779\pi$
$762$	−12.5968	−0.456333
$763$	23.5267	0.851724
$764$	−5.07369	−0.183560
$765$	−4.01718	−0.145241
$766$	−8.43392	−0.304730
$767$	21.8686	0.789631
$768$	12.3529	0.445747
$769$	7.88824	0.284457	0.142229	−	0.989834i	$-0.454573\pi$
$769$	7.88824	0.284457	0.142229	+	0.989834i	$0.454573\pi$
$770$	−11.9809	−0.431761
$771$	7.92041	0.285247
$772$	−22.0363	−0.793104
$773$	−38.0905	−1.37002	−0.685009	−	0.728534i	$-0.740202\pi$
$773$	−38.0905	−1.37002	−0.685009	+	0.728534i	$0.740202\pi$
$774$	−23.8764	−0.858218
$775$	26.7583	0.961185
$776$	−14.2766	−0.512501
$777$	−5.06494	−0.181704
$778$	57.4961	2.06134
$779$	−52.5864	−1.88410
$780$	7.10988	0.254575
$781$	−20.3373	−0.727724
$782$	22.6802	0.811041
$783$	0	0
$784$	2.12825	0.0760091
$785$	14.0118	0.500104
$786$	−18.8869	−0.673673
$787$	7.47041	0.266291	0.133146	−	0.991096i	$-0.457492\pi$
$787$	7.47041	0.266291	0.133146	+	0.991096i	$0.457492\pi$
$788$	42.8628	1.52692
$789$	−4.63022	−0.164840
$790$	−10.5131	−0.374038
$791$	−5.31692	−0.189048
$792$	10.9760	0.390016
$793$	−6.24410	−0.221735
$794$	69.9114	2.48106
$795$	−8.54787	−0.303162
$796$	−18.1837	−0.644503
$797$	−25.2857	−0.895667	−0.447833	−	0.894117i	$-0.647804\pi$
$797$	−25.2857	−0.895667	−0.447833	+	0.894117i	$0.647804\pi$
$798$	29.1410	1.03158
$799$	55.0531	1.94764
$800$	−28.2243	−0.997879
$801$	1.66540	0.0588442
$802$	−5.61278	−0.198194
$803$	−3.21013	−0.113283
$804$	14.4034	0.507970
$805$	−2.10563	−0.0742135
$806$	−44.0449	−1.55142
$807$	−27.3742	−0.963616
$808$	5.06923	0.178335
$809$	49.3907	1.73648	0.868242	−	0.496142i	$-0.165250\pi$
$809$	49.3907	1.73648	0.868242	+	0.496142i	$0.165250\pi$
$810$	−1.57066	−0.0551875
$811$	14.0420	0.493080	0.246540	−	0.969133i	$-0.420706\pi$
$811$	14.0420	0.493080	0.246540	+	0.969133i	$0.420706\pi$
$812$	0	0
$813$	3.93007	0.137833
$814$	−28.6097	−1.00277
$815$	−6.01142	−0.210571
$816$	−3.11832	−0.109163
$817$	−77.8925	−2.72511
$818$	1.30082	0.0454821
$819$	5.74662	0.200803
$820$	15.4128	0.538237
$821$	37.3810	1.30461	0.652303	−	0.757959i	$-0.273803\pi$
$821$	37.3810	1.30461	0.652303	+	0.757959i	$0.273803\pi$
$822$	41.0799	1.43283
$823$	−45.9010	−1.60001	−0.800005	−	0.599994i	$-0.795170\pi$
$823$	−45.9010	−1.60001	−0.800005	+	0.599994i	$0.795170\pi$
$824$	35.4902	1.23636
$825$	−19.7203	−0.686573
$826$	−26.2707	−0.914074
$827$	6.14281	0.213606	0.106803	−	0.994280i	$-0.465939\pi$
$827$	6.14281	0.213606	0.106803	+	0.994280i	$0.465939\pi$
$828$	5.39833	0.187605
$829$	28.4301	0.987417	0.493709	−	0.869627i	$-0.335641\pi$
$829$	28.4301	0.987417	0.493709	+	0.869627i	$0.335641\pi$
$830$	−22.9798	−0.797639
$831$	−26.6161	−0.923304
$832$	42.9111	1.48768
$833$	22.8230	0.790771
$834$	−46.1862	−1.59930
$835$	−1.78922	−0.0619185
$836$	100.206	3.46571
$837$	5.92335	0.204741
$838$	69.4877	2.40041
$839$	18.0221	0.622194	0.311097	−	0.950378i	$-0.399304\pi$
$839$	18.0221	0.622194	0.311097	+	0.950378i	$0.399304\pi$
$840$	−3.05204	−0.105305
$841$	0	0
$842$	52.3698	1.80478
$843$	−12.5229	−0.431312
$844$	73.0148	2.51327
$845$	−1.51729	−0.0521962
$846$	21.5250	0.740046
$847$	−14.0779	−0.483722
$848$	−6.63526	−0.227856
$849$	17.5097	0.600932
$850$	−59.0640	−2.02588
$851$	−5.02812	−0.172362
$852$	−14.4982	−0.496702
$853$	−21.4123	−0.733144	−0.366572	−	0.930390i	$-0.619469\pi$
$853$	−21.4123	−0.733144	−0.366572	+	0.930390i	$0.619469\pi$
$854$	7.50101	0.256679
$855$	−5.12402	−0.175238
$856$	11.7466	0.401489
$857$	20.2783	0.692693	0.346346	−	0.938107i	$-0.387422\pi$
$857$	20.2783	0.692693	0.346346	+	0.938107i	$0.387422\pi$
$858$	32.4602	1.10817
$859$	−12.5045	−0.426650	−0.213325	−	0.976981i	$-0.568429\pi$
$859$	−12.5045	−0.426650	−0.213325	+	0.976981i	$0.568429\pi$
$860$	22.8298	0.778491
$861$	12.4575	0.424550
$862$	78.0026	2.65678
$863$	36.3437	1.23716	0.618578	−	0.785724i	$-0.287709\pi$
$863$	36.3437	1.23716	0.618578	+	0.785724i	$0.287709\pi$
$864$	−6.24788	−0.212557
$865$	9.07628	0.308603
$866$	−37.3456	−1.26906
$867$	−16.4403	−0.558343
$868$	32.2104	1.09329
$869$	−29.2193	−0.991196
$870$	0	0
$871$	15.2212	0.515752
$872$	33.8533	1.14642
$873$	5.67811	0.192175
$874$	28.9292	0.978543
$875$	11.5528	0.390556
$876$	−2.28847	−0.0773203
$877$	8.06605	0.272371	0.136186	−	0.990683i	$-0.456516\pi$
$877$	8.06605	0.272371	0.136186	+	0.990683i	$0.456516\pi$
$878$	57.2558	1.93229
$879$	−5.94551	−0.200537
$880$	1.63529	0.0551256
$881$	−15.6384	−0.526870	−0.263435	−	0.964677i	$-0.584855\pi$
$881$	−15.6384	−0.526870	−0.263435	+	0.964677i	$0.584855\pi$
$882$	8.92350	0.300470
$883$	7.14821	0.240556	0.120278	−	0.992740i	$-0.461621\pi$
$883$	7.14821	0.240556	0.120278	+	0.992740i	$0.461621\pi$
$884$	59.1851	1.99061
$885$	4.61931	0.155276
$886$	−18.8039	−0.631731
$887$	−42.9360	−1.44165	−0.720825	−	0.693117i	$-0.756237\pi$
$887$	−42.9360	−1.44165	−0.720825	+	0.693117i	$0.756237\pi$
$888$	−7.28810	−0.244573
$889$	9.73518	0.326508
$890$	−2.61579	−0.0876815
$891$	−4.36539	−0.146246
$892$	−10.3732	−0.347321
$893$	70.2217	2.34988
$894$	−39.5569	−1.32298
$895$	0.383020	0.0128029
$896$	−29.7143	−0.992686
$897$	5.70484	0.190479
$898$	48.6873	1.62472
$899$	0	0
$900$	−14.0584	−0.468614
$901$	−71.1553	−2.37053
$902$	70.3671	2.34297
$903$	18.4524	0.614058
$904$	−7.65068	−0.254458
$905$	0.612445	0.0203584
$906$	44.5715	1.48079
$907$	4.67367	0.155187	0.0775934	−	0.996985i	$-0.475276\pi$
$907$	4.67367	0.155187	0.0775934	+	0.996985i	$0.475276\pi$
$908$	−26.4563	−0.877983
$909$	−2.01614	−0.0668711
$910$	−9.02601	−0.299209
$911$	30.7046	1.01729	0.508645	−	0.860977i	$-0.330147\pi$
$911$	30.7046	1.01729	0.508645	+	0.860977i	$0.330147\pi$
$912$	−3.97750	−0.131708
$913$	−63.8684	−2.11373
$914$	−70.4644	−2.33075
$915$	−1.31894	−0.0436028
$916$	−77.5075	−2.56092
$917$	14.5964	0.482015
$918$	−13.0747	−0.431531
$919$	−5.90273	−0.194713	−0.0973565	−	0.995250i	$-0.531039\pi$
$919$	−5.90273	−0.194713	−0.0973565	+	0.995250i	$0.531039\pi$
$920$	−3.02985	−0.0998911
$921$	12.2335	0.403108
$922$	−7.04090	−0.231880
$923$	−15.3214	−0.504311
$924$	−23.7384	−0.780938
$925$	13.0943	0.430538
$926$	41.0755	1.34982
$927$	−14.1152	−0.463603
$928$	0	0
$929$	20.7621	0.681183	0.340592	−	0.940211i	$-0.389373\pi$
$929$	20.7621	0.681183	0.340592	+	0.940211i	$0.389373\pi$
$930$	−9.30359	−0.305077
$931$	29.1114	0.954087
$932$	−21.1943	−0.694242
$933$	−10.4087	−0.340767
$934$	24.7757	0.810686
$935$	17.5366	0.573507
$936$	8.26899	0.270280
$937$	45.1087	1.47364	0.736819	−	0.676090i	$-0.236327\pi$
$937$	45.1087	1.47364	0.736819	+	0.676090i	$0.236327\pi$
$938$	−18.2852	−0.597032
$939$	−7.57216	−0.247108
$940$	−20.5816	−0.671297
$941$	−22.6049	−0.736900	−0.368450	−	0.929648i	$-0.620111\pi$
$941$	−22.6049	−0.736900	−0.368450	+	0.929648i	$0.620111\pi$
$942$	45.6045	1.48587
$943$	12.3669	0.402722
$944$	3.58572	0.116705
$945$	1.21386	0.0394868
$946$	104.230	3.38880
$947$	28.8923	0.938874	0.469437	−	0.882966i	$-0.344457\pi$
$947$	28.8923	0.938874	0.469437	+	0.882966i	$0.344457\pi$
$948$	−20.8302	−0.676532
$949$	−2.41841	−0.0785049
$950$	−75.3378	−2.44428
$951$	7.30476	0.236873
$952$	−25.4062	−0.823419
$953$	11.4122	0.369678	0.184839	−	0.982769i	$-0.440824\pi$
$953$	11.4122	0.369678	0.184839	+	0.982769i	$0.440824\pi$
$954$	−27.8208	−0.900732
$955$	−1.13256	−0.0366489
$956$	15.1925	0.491362
$957$	0	0
$958$	35.5171	1.14751
$959$	−31.7478	−1.02519
$960$	9.06411	0.292543
$961$	4.08611	0.131810
$962$	−21.5536	−0.694917
$963$	−4.67185	−0.150548
$964$	−11.9835	−0.385964
$965$	−4.91901	−0.158349
$966$	−6.85319	−0.220498
$967$	−29.5811	−0.951265	−0.475632	−	0.879644i	$-0.657781\pi$
$967$	−29.5811	−0.951265	−0.475632	+	0.879644i	$0.657781\pi$
$968$	−20.2571	−0.651088
$969$	−42.6541	−1.37025
$970$	−8.91840	−0.286352
$971$	20.4243	0.655447	0.327723	−	0.944774i	$-0.393719\pi$
$971$	20.4243	0.655447	0.327723	+	0.944774i	$0.393719\pi$
$972$	−3.11205	−0.0998191
$973$	35.6941	1.14430
$974$	1.71604	0.0549855
$975$	−14.8566	−0.475793
$976$	−1.02382	−0.0327718
$977$	14.4236	0.461453	0.230727	−	0.973019i	$-0.425890\pi$
$977$	14.4236	0.461453	0.230727	+	0.973019i	$0.425890\pi$
$978$	−19.5654	−0.625633
$979$	−7.27015	−0.232355
$980$	−8.53238	−0.272557
$981$	−13.4642	−0.429877
$982$	46.0093	1.46822
$983$	48.2410	1.53865	0.769325	−	0.638858i	$-0.220593\pi$
$983$	48.2410	1.53865	0.769325	+	0.638858i	$0.220593\pi$
$984$	17.9255	0.571443
$985$	9.56796	0.304861
$986$	0	0
$987$	−16.6352	−0.529505
$988$	75.4922	2.40173
$989$	18.3182	0.582486
$990$	6.85656	0.217916
$991$	−9.81769	−0.311869	−0.155935	−	0.987767i	$-0.549839\pi$
$991$	−9.81769	−0.311869	−0.155935	+	0.987767i	$0.549839\pi$
$992$	−37.0084	−1.17502
$993$	−20.2190	−0.641631
$994$	18.4055	0.583789
$995$	−4.05902	−0.128679
$996$	−45.5312	−1.44271
$997$	26.8908	0.851641	0.425820	−	0.904808i	$-0.359986\pi$
$997$	26.8908	0.851641	0.425820	+	0.904808i	$0.359986\pi$
$998$	−39.7089	−1.25696
$999$	2.89863	0.0917085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2523.2.a.k.1.1	✓	6
3.2	odd	2		7569.2.a.bb.1.6		6
29.28	even	2		2523.2.a.l.1.6	yes	6
87.86	odd	2		7569.2.a.z.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2523.2.a.k.1.1	✓	6	1.1	even	1	trivial
2523.2.a.l.1.6	yes	6	29.28	even	2
7569.2.a.z.1.1		6	87.86	odd	2
7569.2.a.bb.1.6		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2523.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26098 q^{2} -1.00000 q^{3} +3.11205 q^{4} +0.694681 q^{5} +2.26098 q^{6} -1.74736 q^{7} -2.51433 q^{8} +1.00000 q^{9} -1.57066 q^{10} -4.36539 q^{11} -3.11205 q^{12} -3.28875 q^{13} +3.95075 q^{14} -0.694681 q^{15} -0.539244 q^{16} -5.78276 q^{17} -2.26098 q^{18} -7.37607 q^{19} +2.16188 q^{20} +1.74736 q^{21} +9.87009 q^{22} +1.73466 q^{23} +2.51433 q^{24} -4.51742 q^{25} +7.43580 q^{26} -1.00000 q^{27} -5.43787 q^{28} +1.57066 q^{30} -5.92335 q^{31} +6.24788 q^{32} +4.36539 q^{33} +13.0747 q^{34} -1.21386 q^{35} +3.11205 q^{36} -2.89863 q^{37} +16.6772 q^{38} +3.28875 q^{39} -1.74666 q^{40} +7.12933 q^{41} -3.95075 q^{42} +10.5602 q^{43} -13.5853 q^{44} +0.694681 q^{45} -3.92203 q^{46} -9.52021 q^{47} +0.539244 q^{48} -3.94673 q^{49} +10.2138 q^{50} +5.78276 q^{51} -10.2347 q^{52} +12.3047 q^{53} +2.26098 q^{54} -3.03256 q^{55} +4.39344 q^{56} +7.37607 q^{57} -6.64954 q^{59} -2.16188 q^{60} +1.89863 q^{61} +13.3926 q^{62} -1.74736 q^{63} -13.0479 q^{64} -2.28463 q^{65} -9.87009 q^{66} -4.62828 q^{67} -17.9962 q^{68} -1.73466 q^{69} +2.74451 q^{70} +4.65874 q^{71} -2.51433 q^{72} +0.735359 q^{73} +6.55375 q^{74} +4.51742 q^{75} -22.9547 q^{76} +7.62791 q^{77} -7.43580 q^{78} +6.69339 q^{79} -0.374603 q^{80} +1.00000 q^{81} -16.1193 q^{82} +14.6306 q^{83} +5.43787 q^{84} -4.01718 q^{85} -23.8764 q^{86} +10.9760 q^{88} +1.66540 q^{89} -1.57066 q^{90} +5.74662 q^{91} +5.39833 q^{92} +5.92335 q^{93} +21.5250 q^{94} -5.12402 q^{95} -6.24788 q^{96} +5.67811 q^{97} +8.92350 q^{98} -4.36539 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 6 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} + 6 q^{8} + 6 q^{9} - 12 q^{10} - 6 q^{11} - 7 q^{12} + 8 q^{13} + 10 q^{14} - 5 q^{15} + 17 q^{16} - 2 q^{17} - q^{18} + q^{19} + 3 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 6 * q - q^2 - 6 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 3 * q^7 + 6 * q^8 + 6 * q^9 - 12 * q^10 - 6 * q^11 - 7 * q^12 + 8 * q^13 + 10 * q^14 - 5 * q^15 + 17 * q^16 - 2 * q^17 - q^18 + q^19 + 3 * q^20 - 3 * q^21 + 9 * q^22 + 7 * q^23 - 6 * q^24 + 9 * q^25 - 7 * q^26 - 6 * q^27 + q^28 + 12 * q^30 - 28 * q^31 + 41 * q^32 + 6 * q^33 - 8 * q^34 - 5 * q^35 + 7 * q^36 - 4 * q^37 + 30 * q^38 - 8 * q^39 - 19 * q^40 + 36 * q^41 - 10 * q^42 - 3 * q^43 - 17 * q^44 + 5 * q^45 + 21 * q^46 + q^47 - 17 * q^48 + 19 * q^49 - 32 * q^50 + 2 * q^51 - 11 * q^52 + 16 * q^53 + q^54 - 15 * q^55 + 63 * q^56 - q^57 + 25 * q^59 - 3 * q^60 - 2 * q^61 - 9 * q^62 + 3 * q^63 + 20 * q^64 + 29 * q^65 - 9 * q^66 - 62 * q^68 - 7 * q^69 + 19 * q^70 - 3 * q^71 + 6 * q^72 - 21 * q^73 + 28 * q^74 - 9 * q^75 - 11 * q^76 + 49 * q^77 + 7 * q^78 + 6 * q^79 - 16 * q^80 + 6 * q^81 - 19 * q^82 + 14 * q^83 - q^84 + 26 * q^85 - 49 * q^86 + 44 * q^88 - 6 * q^89 - 12 * q^90 + 41 * q^91 - 18 * q^92 + 28 * q^93 - 29 * q^95 - 41 * q^96 + 8 * q^97 + 38 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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