LMFDB - Embedded newform 2366.2.a.bg.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.6052921.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 7x^{3} + 33x^{2} - 9x - 27 $ x^6 - x^5 - 11x^4 + 7x^3 + 33x^2 - 9x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.46434$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.46434 q^{3} +1.00000 q^{4} +3.19361 q^{5} -2.46434 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.07299 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.46434 q^{3} +1.00000 q^{4} +3.19361 q^{5} -2.46434 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.07299 q^{9} +3.19361 q^{10} -1.63865 q^{11} -2.46434 q^{12} +1.00000 q^{14} -7.87016 q^{15} +1.00000 q^{16} -3.38651 q^{17} +3.07299 q^{18} +5.90454 q^{19} +3.19361 q^{20} -2.46434 q^{21} -1.63865 q^{22} +6.07281 q^{23} -2.46434 q^{24} +5.19916 q^{25} -0.179860 q^{27} +1.00000 q^{28} -0.769774 q^{29} -7.87016 q^{30} +8.79749 q^{31} +1.00000 q^{32} +4.03821 q^{33} -3.38651 q^{34} +3.19361 q^{35} +3.07299 q^{36} -8.07480 q^{37} +5.90454 q^{38} +3.19361 q^{40} -10.5415 q^{41} -2.46434 q^{42} +10.2648 q^{43} -1.63865 q^{44} +9.81392 q^{45} +6.07281 q^{46} -8.70705 q^{47} -2.46434 q^{48} +1.00000 q^{49} +5.19916 q^{50} +8.34553 q^{51} +3.75334 q^{53} -0.179860 q^{54} -5.23323 q^{55} +1.00000 q^{56} -14.5508 q^{57} -0.769774 q^{58} -8.61816 q^{59} -7.87016 q^{60} +1.62349 q^{61} +8.79749 q^{62} +3.07299 q^{63} +1.00000 q^{64} +4.03821 q^{66} +6.49665 q^{67} -3.38651 q^{68} -14.9655 q^{69} +3.19361 q^{70} +14.7084 q^{71} +3.07299 q^{72} +16.0908 q^{73} -8.07480 q^{74} -12.8125 q^{75} +5.90454 q^{76} -1.63865 q^{77} +4.98223 q^{79} +3.19361 q^{80} -8.77572 q^{81} -10.5415 q^{82} -13.1422 q^{83} -2.46434 q^{84} -10.8152 q^{85} +10.2648 q^{86} +1.89699 q^{87} -1.63865 q^{88} +13.1556 q^{89} +9.81392 q^{90} +6.07281 q^{92} -21.6800 q^{93} -8.70705 q^{94} +18.8568 q^{95} -2.46434 q^{96} -7.70472 q^{97} +1.00000 q^{98} -5.03556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 4 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 4 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 5 * q^9	$ 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 4 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 5 q^{9} + 4 q^{10} + 6 q^{11} + q^{12} + 6 q^{14} - 5 q^{15} + 6 q^{16} - 9 q^{17} + 5 q^{18} + 10 q^{19} + 4 q^{20} + q^{21} + 6 q^{22} + 21 q^{23} + q^{24} + 8 q^{25} + 7 q^{27} + 6 q^{28} - q^{29} - 5 q^{30} + 20 q^{31} + 6 q^{32} + 9 q^{33} - 9 q^{34} + 4 q^{35} + 5 q^{36} + 16 q^{37} + 10 q^{38} + 4 q^{40} + 2 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} + 17 q^{45} + 21 q^{46} - 5 q^{47} + q^{48} + 6 q^{49} + 8 q^{50} - 15 q^{51} + 28 q^{53} + 7 q^{54} - 29 q^{55} + 6 q^{56} + 22 q^{57} - q^{58} - 12 q^{59} - 5 q^{60} - 27 q^{61} + 20 q^{62} + 5 q^{63} + 6 q^{64} + 9 q^{66} + 16 q^{67} - 9 q^{68} - 15 q^{69} + 4 q^{70} + 5 q^{72} + 38 q^{73} + 16 q^{74} - 7 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} + 4 q^{80} - 26 q^{81} + 2 q^{82} - 6 q^{83} + q^{84} + 9 q^{85} + 2 q^{86} - 39 q^{87} + 6 q^{88} - q^{89} + 17 q^{90} + 21 q^{92} - 7 q^{93} - 5 q^{94} + 3 q^{95} + q^{96} + 16 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 4 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 5 * q^9 + 4 * q^10 + 6 * q^11 + q^12 + 6 * q^14 - 5 * q^15 + 6 * q^16 - 9 * q^17 + 5 * q^18 + 10 * q^19 + 4 * q^20 + q^21 + 6 * q^22 + 21 * q^23 + q^24 + 8 * q^25 + 7 * q^27 + 6 * q^28 - q^29 - 5 * q^30 + 20 * q^31 + 6 * q^32 + 9 * q^33 - 9 * q^34 + 4 * q^35 + 5 * q^36 + 16 * q^37 + 10 * q^38 + 4 * q^40 + 2 * q^41 + q^42 + 2 * q^43 + 6 * q^44 + 17 * q^45 + 21 * q^46 - 5 * q^47 + q^48 + 6 * q^49 + 8 * q^50 - 15 * q^51 + 28 * q^53 + 7 * q^54 - 29 * q^55 + 6 * q^56 + 22 * q^57 - q^58 - 12 * q^59 - 5 * q^60 - 27 * q^61 + 20 * q^62 + 5 * q^63 + 6 * q^64 + 9 * q^66 + 16 * q^67 - 9 * q^68 - 15 * q^69 + 4 * q^70 + 5 * q^72 + 38 * q^73 + 16 * q^74 - 7 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 + 4 * q^80 - 26 * q^81 + 2 * q^82 - 6 * q^83 + q^84 + 9 * q^85 + 2 * q^86 - 39 * q^87 + 6 * q^88 - q^89 + 17 * q^90 + 21 * q^92 - 7 * q^93 - 5 * q^94 + 3 * q^95 + q^96 + 16 * q^97 + 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.46434	−1.42279	−0.711394	−	0.702793i	$-0.751936\pi$
$3$	−2.46434	−1.42279	−0.711394	+	0.702793i	$0.751936\pi$
$4$	1.00000	0.500000
$5$	3.19361	1.42823	0.714113	−	0.700030i	$-0.246830\pi$
$5$	3.19361	1.42823	0.714113	+	0.700030i	$0.246830\pi$
$6$	−2.46434	−1.00606
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	3.07299	1.02433
$10$	3.19361	1.00991
$11$	−1.63865	−0.494073	−0.247036	−	0.969006i	$-0.579457\pi$
$11$	−1.63865	−0.494073	−0.247036	+	0.969006i	$0.579457\pi$
$12$	−2.46434	−0.711394
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−7.87016	−2.03207
$16$	1.00000	0.250000
$17$	−3.38651	−0.821350	−0.410675	−	0.911782i	$-0.634707\pi$
$17$	−3.38651	−0.821350	−0.410675	+	0.911782i	$0.634707\pi$
$18$	3.07299	0.724310
$19$	5.90454	1.35459	0.677297	−	0.735710i	$-0.263151\pi$
$19$	5.90454	1.35459	0.677297	+	0.735710i	$0.263151\pi$
$20$	3.19361	0.714113
$21$	−2.46434	−0.537764
$22$	−1.63865	−0.349362
$23$	6.07281	1.26627	0.633134	−	0.774042i	$-0.281768\pi$
$23$	6.07281	1.26627	0.633134	+	0.774042i	$0.281768\pi$
$24$	−2.46434	−0.503032
$25$	5.19916	1.03983
$26$	0	0
$27$	−0.179860	−0.0346141
$28$	1.00000	0.188982
$29$	−0.769774	−0.142943	−0.0714717	−	0.997443i	$-0.522770\pi$
$29$	−0.769774	−0.142943	−0.0714717	+	0.997443i	$0.522770\pi$
$30$	−7.87016	−1.43689
$31$	8.79749	1.58008	0.790038	−	0.613058i	$-0.210061\pi$
$31$	8.79749	1.58008	0.790038	+	0.613058i	$0.210061\pi$
$32$	1.00000	0.176777
$33$	4.03821	0.702961
$34$	−3.38651	−0.580782
$35$	3.19361	0.539819
$36$	3.07299	0.512164
$37$	−8.07480	−1.32749	−0.663744	−	0.747960i	$-0.731034\pi$
$37$	−8.07480	−1.32749	−0.663744	+	0.747960i	$0.731034\pi$
$38$	5.90454	0.957843
$39$	0	0
$40$	3.19361	0.504954
$41$	−10.5415	−1.64630	−0.823150	−	0.567823i	$-0.807786\pi$
$41$	−10.5415	−1.64630	−0.823150	+	0.567823i	$0.807786\pi$
$42$	−2.46434	−0.380256
$43$	10.2648	1.56536	0.782681	−	0.622423i	$-0.213851\pi$
$43$	10.2648	1.56536	0.782681	+	0.622423i	$0.213851\pi$
$44$	−1.63865	−0.247036
$45$	9.81392	1.46297
$46$	6.07281	0.895387
$47$	−8.70705	−1.27005	−0.635027	−	0.772490i	$-0.719011\pi$
$47$	−8.70705	−1.27005	−0.635027	+	0.772490i	$0.719011\pi$
$48$	−2.46434	−0.355697
$49$	1.00000	0.142857
$50$	5.19916	0.735272
$51$	8.34553	1.16861
$52$	0	0
$53$	3.75334	0.515561	0.257780	−	0.966204i	$-0.417009\pi$
$53$	3.75334	0.515561	0.257780	+	0.966204i	$0.417009\pi$
$54$	−0.179860	−0.0244759
$55$	−5.23323	−0.705648
$56$	1.00000	0.133631
$57$	−14.5508	−1.92730
$58$	−0.769774	−0.101076
$59$	−8.61816	−1.12199	−0.560994	−	0.827820i	$-0.689581\pi$
$59$	−8.61816	−1.12199	−0.560994	+	0.827820i	$0.689581\pi$
$60$	−7.87016	−1.01603
$61$	1.62349	0.207867	0.103934	−	0.994584i	$-0.466857\pi$
$61$	1.62349	0.207867	0.103934	+	0.994584i	$0.466857\pi$
$62$	8.79749	1.11728
$63$	3.07299	0.387160
$64$	1.00000	0.125000
$65$	0	0
$66$	4.03821	0.497069
$67$	6.49665	0.793692	0.396846	−	0.917885i	$-0.370105\pi$
$67$	6.49665	0.793692	0.396846	+	0.917885i	$0.370105\pi$
$68$	−3.38651	−0.410675
$69$	−14.9655	−1.80163
$70$	3.19361	0.381710
$71$	14.7084	1.74557	0.872783	−	0.488108i	$-0.162313\pi$
$71$	14.7084	1.74557	0.872783	+	0.488108i	$0.162313\pi$
$72$	3.07299	0.362155
$73$	16.0908	1.88329	0.941645	−	0.336608i	$-0.109280\pi$
$73$	16.0908	1.88329	0.941645	+	0.336608i	$0.109280\pi$
$74$	−8.07480	−0.938676
$75$	−12.8125	−1.47946
$76$	5.90454	0.677297
$77$	−1.63865	−0.186742
$78$	0	0
$79$	4.98223	0.560545	0.280272	−	0.959921i	$-0.409575\pi$
$79$	4.98223	0.560545	0.280272	+	0.959921i	$0.409575\pi$
$80$	3.19361	0.357057
$81$	−8.77572	−0.975080
$82$	−10.5415	−1.16411
$83$	−13.1422	−1.44254	−0.721270	−	0.692654i	$-0.756441\pi$
$83$	−13.1422	−1.44254	−0.721270	+	0.692654i	$0.756441\pi$
$84$	−2.46434	−0.268882
$85$	−10.8152	−1.17307
$86$	10.2648	1.10688
$87$	1.89699	0.203378
$88$	−1.63865	−0.174681
$89$	13.1556	1.39449	0.697244	−	0.716834i	$-0.254410\pi$
$89$	13.1556	1.39449	0.697244	+	0.716834i	$0.254410\pi$
$90$	9.81392	1.03448
$91$	0	0
$92$	6.07281	0.633134
$93$	−21.6800	−2.24811
$94$	−8.70705	−0.898064
$95$	18.8568	1.93467
$96$	−2.46434	−0.251516
$97$	−7.70472	−0.782296	−0.391148	−	0.920328i	$-0.627922\pi$
$97$	−7.70472	−0.782296	−0.391148	+	0.920328i	$0.627922\pi$
$98$	1.00000	0.101015
$99$	−5.03556	−0.506093
$100$	5.19916	0.519916
$101$	10.0482	0.999829	0.499914	−	0.866075i	$-0.333365\pi$
$101$	10.0482	0.999829	0.499914	+	0.866075i	$0.333365\pi$
$102$	8.34553	0.826330
$103$	−8.89776	−0.876722	−0.438361	−	0.898799i	$-0.644441\pi$
$103$	−8.89776	−0.876722	−0.438361	+	0.898799i	$0.644441\pi$
$104$	0	0
$105$	−7.87016	−0.768049
$106$	3.75334	0.364556
$107$	6.28307	0.607408	0.303704	−	0.952766i	$-0.401777\pi$
$107$	6.28307	0.607408	0.303704	+	0.952766i	$0.401777\pi$
$108$	−0.179860	−0.0173071
$109$	4.30268	0.412122	0.206061	−	0.978539i	$-0.433935\pi$
$109$	4.30268	0.412122	0.206061	+	0.978539i	$0.433935\pi$
$110$	−5.23323	−0.498969
$111$	19.8991	1.88874
$112$	1.00000	0.0944911
$113$	−10.9027	−1.02564	−0.512820	−	0.858496i	$-0.671399\pi$
$113$	−10.9027	−1.02564	−0.512820	+	0.858496i	$0.671399\pi$
$114$	−14.5508	−1.36281
$115$	19.3942	1.80852
$116$	−0.769774	−0.0714717
$117$	0	0
$118$	−8.61816	−0.793366
$119$	−3.38651	−0.310441
$120$	−7.87016	−0.718444
$121$	−8.31481	−0.755892
$122$	1.62349	0.146984
$123$	25.9778	2.34234
$124$	8.79749	0.790038
$125$	0.636044	0.0568895
$126$	3.07299	0.273763
$127$	7.34110	0.651418	0.325709	−	0.945470i	$-0.394397\pi$
$127$	7.34110	0.651418	0.325709	+	0.945470i	$0.394397\pi$
$128$	1.00000	0.0883883
$129$	−25.2959	−2.22718
$130$	0	0
$131$	−0.984843	−0.0860462	−0.0430231	−	0.999074i	$-0.513699\pi$
$131$	−0.984843	−0.0860462	−0.0430231	+	0.999074i	$0.513699\pi$
$132$	4.03821	0.351481
$133$	5.90454	0.511988
$134$	6.49665	0.561225
$135$	−0.574404	−0.0494369
$136$	−3.38651	−0.290391
$137$	9.24829	0.790135	0.395068	−	0.918652i	$-0.370721\pi$
$137$	9.24829	0.790135	0.395068	+	0.918652i	$0.370721\pi$
$138$	−14.9655	−1.27395
$139$	−1.45279	−0.123224	−0.0616119	−	0.998100i	$-0.519624\pi$
$139$	−1.45279	−0.123224	−0.0616119	+	0.998100i	$0.519624\pi$
$140$	3.19361	0.269910
$141$	21.4572	1.80702
$142$	14.7084	1.23430
$143$	0	0
$144$	3.07299	0.256082
$145$	−2.45836	−0.204156
$146$	16.0908	1.33169
$147$	−2.46434	−0.203256
$148$	−8.07480	−0.663744
$149$	6.23309	0.510634	0.255317	−	0.966857i	$-0.417820\pi$
$149$	6.23309	0.510634	0.255317	+	0.966857i	$0.417820\pi$
$150$	−12.8125	−1.04614
$151$	19.6726	1.60094	0.800468	−	0.599376i	$-0.204584\pi$
$151$	19.6726	1.60094	0.800468	+	0.599376i	$0.204584\pi$
$152$	5.90454	0.478921
$153$	−10.4067	−0.841332
$154$	−1.63865	−0.132047
$155$	28.0958	2.25671
$156$	0	0
$157$	5.01323	0.400099	0.200050	−	0.979786i	$-0.435890\pi$
$157$	5.01323	0.400099	0.200050	+	0.979786i	$0.435890\pi$
$158$	4.98223	0.396365
$159$	−9.24951	−0.733534
$160$	3.19361	0.252477
$161$	6.07281	0.478604
$162$	−8.77572	−0.689486
$163$	19.6322	1.53771	0.768857	−	0.639421i	$-0.220826\pi$
$163$	19.6322	1.53771	0.768857	+	0.639421i	$0.220826\pi$
$164$	−10.5415	−0.823150
$165$	12.8965	1.00399
$166$	−13.1422	−1.02003
$167$	1.34364	0.103974	0.0519869	−	0.998648i	$-0.483445\pi$
$167$	1.34364	0.103974	0.0519869	+	0.998648i	$0.483445\pi$
$168$	−2.46434	−0.190128
$169$	0	0
$170$	−10.8152	−0.829489
$171$	18.1446	1.38755
$172$	10.2648	0.782681
$173$	12.9105	0.981571	0.490785	−	0.871281i	$-0.336710\pi$
$173$	12.9105	0.981571	0.490785	+	0.871281i	$0.336710\pi$
$174$	1.89699	0.143810
$175$	5.19916	0.393020
$176$	−1.63865	−0.123518
$177$	21.2381	1.59635
$178$	13.1556	0.986051
$179$	18.8288	1.40733	0.703664	−	0.710533i	$-0.251546\pi$
$179$	18.8288	1.40733	0.703664	+	0.710533i	$0.251546\pi$
$180$	9.81392	0.731487
$181$	−14.6189	−1.08662	−0.543309	−	0.839533i	$-0.682829\pi$
$181$	−14.6189	−1.08662	−0.543309	+	0.839533i	$0.682829\pi$
$182$	0	0
$183$	−4.00084	−0.295751
$184$	6.07281	0.447693
$185$	−25.7878	−1.89595
$186$	−21.6800	−1.58966
$187$	5.54932	0.405807
$188$	−8.70705	−0.635027
$189$	−0.179860	−0.0130829
$190$	18.8568	1.36802
$191$	−13.8232	−1.00021	−0.500105	−	0.865965i	$-0.666705\pi$
$191$	−13.8232	−1.00021	−0.500105	+	0.865965i	$0.666705\pi$
$192$	−2.46434	−0.177849
$193$	−4.53033	−0.326100	−0.163050	−	0.986618i	$-0.552133\pi$
$193$	−4.53033	−0.326100	−0.163050	+	0.986618i	$0.552133\pi$
$194$	−7.70472	−0.553167
$195$	0	0
$196$	1.00000	0.0714286
$197$	−1.46310	−0.104242	−0.0521209	−	0.998641i	$-0.516598\pi$
$197$	−1.46310	−0.104242	−0.0521209	+	0.998641i	$0.516598\pi$
$198$	−5.03556	−0.357862
$199$	8.08413	0.573069	0.286534	−	0.958070i	$-0.407497\pi$
$199$	8.08413	0.573069	0.286534	+	0.958070i	$0.407497\pi$
$200$	5.19916	0.367636
$201$	−16.0100	−1.12926
$202$	10.0482	0.706986
$203$	−0.769774	−0.0540275
$204$	8.34553	0.584304
$205$	−33.6654	−2.35129
$206$	−8.89776	−0.619936
$207$	18.6617	1.29707
$208$	0	0
$209$	−9.67550	−0.669268
$210$	−7.87016	−0.543092
$211$	6.08392	0.418834	0.209417	−	0.977826i	$-0.432843\pi$
$211$	6.08392	0.418834	0.209417	+	0.977826i	$0.432843\pi$
$212$	3.75334	0.257780
$213$	−36.2465	−2.48357
$214$	6.28307	0.429502
$215$	32.7817	2.23569
$216$	−0.179860	−0.0122379
$217$	8.79749	0.597212
$218$	4.30268	0.291415
$219$	−39.6533	−2.67952
$220$	−5.23323	−0.352824
$221$	0	0
$222$	19.8991	1.33554
$223$	−8.41009	−0.563182	−0.281591	−	0.959535i	$-0.590862\pi$
$223$	−8.41009	−0.563182	−0.281591	+	0.959535i	$0.590862\pi$
$224$	1.00000	0.0668153
$225$	15.9769	1.06513
$226$	−10.9027	−0.725237
$227$	−24.1450	−1.60256	−0.801281	−	0.598288i	$-0.795848\pi$
$227$	−24.1450	−1.60256	−0.801281	+	0.598288i	$0.795848\pi$
$228$	−14.5508	−0.963651
$229$	19.9987	1.32155	0.660774	−	0.750585i	$-0.270228\pi$
$229$	19.9987	1.32155	0.660774	+	0.750585i	$0.270228\pi$
$230$	19.3942	1.27882
$231$	4.03821	0.265694
$232$	−0.769774	−0.0505381
$233$	−8.98014	−0.588309	−0.294154	−	0.955758i	$-0.595038\pi$
$233$	−8.98014	−0.588309	−0.294154	+	0.955758i	$0.595038\pi$
$234$	0	0
$235$	−27.8069	−1.81392
$236$	−8.61816	−0.560994
$237$	−12.2779	−0.797537
$238$	−3.38651	−0.219515
$239$	0.171956	0.0111229	0.00556144	−	0.999985i	$-0.498230\pi$
$239$	0.171956	0.0111229	0.00556144	+	0.999985i	$0.498230\pi$
$240$	−7.87016	−0.508016
$241$	−2.07610	−0.133733	−0.0668667	−	0.997762i	$-0.521300\pi$
$241$	−2.07610	−0.133733	−0.0668667	+	0.997762i	$0.521300\pi$
$242$	−8.31481	−0.534496
$243$	22.1660	1.42195
$244$	1.62349	0.103934
$245$	3.19361	0.204032
$246$	25.9778	1.65628
$247$	0	0
$248$	8.79749	0.558641
$249$	32.3868	2.05243
$250$	0.636044	0.0402269
$251$	−14.8796	−0.939192	−0.469596	−	0.882881i	$-0.655600\pi$
$251$	−14.8796	−0.939192	−0.469596	+	0.882881i	$0.655600\pi$
$252$	3.07299	0.193580
$253$	−9.95124	−0.625629
$254$	7.34110	0.460622
$255$	26.6524	1.66904
$256$	1.00000	0.0625000
$257$	4.08661	0.254916	0.127458	−	0.991844i	$-0.459318\pi$
$257$	4.08661	0.254916	0.127458	+	0.991844i	$0.459318\pi$
$258$	−25.2959	−1.57485
$259$	−8.07480	−0.501743
$260$	0	0
$261$	−2.36550	−0.146421
$262$	−0.984843	−0.0608438
$263$	−8.24162	−0.508200	−0.254100	−	0.967178i	$-0.581779\pi$
$263$	−8.24162	−0.508200	−0.254100	+	0.967178i	$0.581779\pi$
$264$	4.03821	0.248534
$265$	11.9867	0.736338
$266$	5.90454	0.362031
$267$	−32.4198	−1.98406
$268$	6.49665	0.396846
$269$	−21.2899	−1.29807	−0.649034	−	0.760760i	$-0.724827\pi$
$269$	−21.2899	−1.29807	−0.649034	+	0.760760i	$0.724827\pi$
$270$	−0.574404	−0.0349571
$271$	−22.4902	−1.36618	−0.683091	−	0.730333i	$-0.739365\pi$
$271$	−22.4902	−1.36618	−0.683091	+	0.730333i	$0.739365\pi$
$272$	−3.38651	−0.205337
$273$	0	0
$274$	9.24829	0.558710
$275$	−8.51963	−0.513753
$276$	−14.9655	−0.900816
$277$	−16.3535	−0.982589	−0.491294	−	0.870994i	$-0.663476\pi$
$277$	−16.3535	−0.982589	−0.491294	+	0.870994i	$0.663476\pi$
$278$	−1.45279	−0.0871324
$279$	27.0345	1.61852
$280$	3.19361	0.190855
$281$	−0.751897	−0.0448544	−0.0224272	−	0.999748i	$-0.507139\pi$
$281$	−0.751897	−0.0448544	−0.0224272	+	0.999748i	$0.507139\pi$
$282$	21.4572	1.27775
$283$	−20.2736	−1.20514	−0.602570	−	0.798066i	$-0.705857\pi$
$283$	−20.2736	−1.20514	−0.602570	+	0.798066i	$0.705857\pi$
$284$	14.7084	0.872783
$285$	−46.4696	−2.75262
$286$	0	0
$287$	−10.5415	−0.622243
$288$	3.07299	0.181077
$289$	−5.53153	−0.325384
$290$	−2.45836	−0.144360
$291$	18.9871	1.11304
$292$	16.0908	0.941645
$293$	−14.1068	−0.824127	−0.412064	−	0.911155i	$-0.635192\pi$
$293$	−14.1068	−0.824127	−0.412064	+	0.911155i	$0.635192\pi$
$294$	−2.46434	−0.143723
$295$	−27.5231	−1.60245
$296$	−8.07480	−0.469338
$297$	0.294729	0.0171019
$298$	6.23309	0.361073
$299$	0	0
$300$	−12.8125	−0.739731
$301$	10.2648	0.591651
$302$	19.6726	1.13203
$303$	−24.7621	−1.42255
$304$	5.90454	0.338649
$305$	5.18481	0.296881
$306$	−10.4067	−0.594912
$307$	−27.2943	−1.55777	−0.778884	−	0.627168i	$-0.784214\pi$
$307$	−27.2943	−1.55777	−0.778884	+	0.627168i	$0.784214\pi$
$308$	−1.63865	−0.0933710
$309$	21.9271	1.24739
$310$	28.0958	1.59573
$311$	8.30553	0.470964	0.235482	−	0.971879i	$-0.424333\pi$
$311$	8.30553	0.470964	0.235482	+	0.971879i	$0.424333\pi$
$312$	0	0
$313$	−26.3624	−1.49009	−0.745047	−	0.667013i	$-0.767573\pi$
$313$	−26.3624	−1.49009	−0.745047	+	0.667013i	$0.767573\pi$
$314$	5.01323	0.282913
$315$	9.81392	0.552952
$316$	4.98223	0.280272
$317$	22.7491	1.27772	0.638859	−	0.769324i	$-0.279407\pi$
$317$	22.7491	1.27772	0.638859	+	0.769324i	$0.279407\pi$
$318$	−9.24951	−0.518687
$319$	1.26139	0.0706244
$320$	3.19361	0.178528
$321$	−15.4836	−0.864213
$322$	6.07281	0.338424
$323$	−19.9958	−1.11260
$324$	−8.77572	−0.487540
$325$	0	0
$326$	19.6322	1.08733
$327$	−10.6033	−0.586363
$328$	−10.5415	−0.582055
$329$	−8.70705	−0.480035
$330$	12.8965	0.709927
$331$	−17.4096	−0.956919	−0.478460	−	0.878110i	$-0.658805\pi$
$331$	−17.4096	−0.956919	−0.478460	+	0.878110i	$0.658805\pi$
$332$	−13.1422	−0.721270
$333$	−24.8137	−1.35978
$334$	1.34364	0.0735205
$335$	20.7478	1.13357
$336$	−2.46434	−0.134441
$337$	13.3497	0.727206	0.363603	−	0.931554i	$-0.381546\pi$
$337$	13.3497	0.727206	0.363603	+	0.931554i	$0.381546\pi$
$338$	0	0
$339$	26.8680	1.45927
$340$	−10.8152	−0.586537
$341$	−14.4160	−0.780672
$342$	18.1446	0.981146
$343$	1.00000	0.0539949
$344$	10.2648	0.553439
$345$	−47.7940	−2.57314
$346$	12.9105	0.694075
$347$	−10.0705	−0.540614	−0.270307	−	0.962774i	$-0.587125\pi$
$347$	−10.0705	−0.540614	−0.270307	+	0.962774i	$0.587125\pi$
$348$	1.89699	0.101689
$349$	8.40589	0.449957	0.224978	−	0.974364i	$-0.427769\pi$
$349$	8.40589	0.449957	0.224978	+	0.974364i	$0.427769\pi$
$350$	5.19916	0.277907
$351$	0	0
$352$	−1.63865	−0.0873406
$353$	26.4575	1.40819	0.704096	−	0.710105i	$-0.251353\pi$
$353$	26.4575	1.40819	0.704096	+	0.710105i	$0.251353\pi$
$354$	21.2381	1.12879
$355$	46.9729	2.49306
$356$	13.1556	0.697244
$357$	8.34553	0.441692
$358$	18.8288	0.995132
$359$	−10.6006	−0.559477	−0.279738	−	0.960076i	$-0.590248\pi$
$359$	−10.6006	−0.559477	−0.279738	+	0.960076i	$0.590248\pi$
$360$	9.81392	0.517239
$361$	15.8636	0.834926
$362$	−14.6189	−0.768355
$363$	20.4905	1.07547
$364$	0	0
$365$	51.3879	2.68977
$366$	−4.00084	−0.209127
$367$	14.0310	0.732413	0.366207	−	0.930534i	$-0.380656\pi$
$367$	14.0310	0.732413	0.366207	+	0.930534i	$0.380656\pi$
$368$	6.07281	0.316567
$369$	−32.3938	−1.68635
$370$	−25.7878	−1.34064
$371$	3.75334	0.194864
$372$	−21.6800	−1.12406
$373$	−29.2117	−1.51253	−0.756263	−	0.654268i	$-0.772977\pi$
$373$	−29.2117	−1.51253	−0.756263	+	0.654268i	$0.772977\pi$
$374$	5.54932	0.286949
$375$	−1.56743	−0.0809417
$376$	−8.70705	−0.449032
$377$	0	0
$378$	−0.179860	−0.00925102
$379$	20.8150	1.06919	0.534597	−	0.845107i	$-0.320464\pi$
$379$	20.8150	1.06919	0.534597	+	0.845107i	$0.320464\pi$
$380$	18.8568	0.967334
$381$	−18.0910	−0.926830
$382$	−13.8232	−0.707255
$383$	−22.1878	−1.13374	−0.566872	−	0.823806i	$-0.691847\pi$
$383$	−22.1878	−1.13374	−0.566872	+	0.823806i	$0.691847\pi$
$384$	−2.46434	−0.125758
$385$	−5.23323	−0.266710
$386$	−4.53033	−0.230588
$387$	31.5435	1.60345
$388$	−7.70472	−0.391148
$389$	1.98048	0.100414	0.0502070	−	0.998739i	$-0.484012\pi$
$389$	1.98048	0.100414	0.0502070	+	0.998739i	$0.484012\pi$
$390$	0	0
$391$	−20.5656	−1.04005
$392$	1.00000	0.0505076
$393$	2.42699	0.122426
$394$	−1.46310	−0.0737100
$395$	15.9113	0.800585
$396$	−5.03556	−0.253046
$397$	−4.03678	−0.202600	−0.101300	−	0.994856i	$-0.532300\pi$
$397$	−4.03678	−0.202600	−0.101300	+	0.994856i	$0.532300\pi$
$398$	8.08413	0.405221
$399$	−14.5508	−0.728452
$400$	5.19916	0.259958
$401$	−10.6442	−0.531544	−0.265772	−	0.964036i	$-0.585627\pi$
$401$	−10.6442	−0.531544	−0.265772	+	0.964036i	$0.585627\pi$
$402$	−16.0100	−0.798505
$403$	0	0
$404$	10.0482	0.499914
$405$	−28.0262	−1.39264
$406$	−0.769774	−0.0382032
$407$	13.2318	0.655876
$408$	8.34553	0.413165
$409$	12.0943	0.598026	0.299013	−	0.954249i	$-0.403343\pi$
$409$	12.0943	0.598026	0.299013	+	0.954249i	$0.403343\pi$
$410$	−33.6654	−1.66261
$411$	−22.7910	−1.12420
$412$	−8.89776	−0.438361
$413$	−8.61816	−0.424072
$414$	18.6617	0.917170
$415$	−41.9710	−2.06027
$416$	0	0
$417$	3.58017	0.175321
$418$	−9.67550	−0.473244
$419$	−3.34008	−0.163173	−0.0815867	−	0.996666i	$-0.525999\pi$
$419$	−3.34008	−0.163173	−0.0815867	+	0.996666i	$0.525999\pi$
$420$	−7.87016	−0.384024
$421$	−10.8214	−0.527403	−0.263701	−	0.964604i	$-0.584943\pi$
$421$	−10.8214	−0.527403	−0.263701	+	0.964604i	$0.584943\pi$
$422$	6.08392	0.296160
$423$	−26.7566	−1.30095
$424$	3.75334	0.182278
$425$	−17.6070	−0.854066
$426$	−36.2465	−1.75615
$427$	1.62349	0.0785664
$428$	6.28307	0.303704
$429$	0	0
$430$	32.7817	1.58087
$431$	−31.5076	−1.51767	−0.758834	−	0.651284i	$-0.774231\pi$
$431$	−31.5076	−1.51767	−0.758834	+	0.651284i	$0.774231\pi$
$432$	−0.179860	−0.00865354
$433$	−16.3267	−0.784612	−0.392306	−	0.919835i	$-0.628323\pi$
$433$	−16.3267	−0.784612	−0.392306	+	0.919835i	$0.628323\pi$
$434$	8.79749	0.422293
$435$	6.05824	0.290470
$436$	4.30268	0.206061
$437$	35.8571	1.71528
$438$	−39.6533	−1.89471
$439$	−22.8205	−1.08916	−0.544582	−	0.838708i	$-0.683312\pi$
$439$	−22.8205	−1.08916	−0.544582	+	0.838708i	$0.683312\pi$
$440$	−5.23323	−0.249484
$441$	3.07299	0.146333
$442$	0	0
$443$	21.7611	1.03390	0.516950	−	0.856015i	$-0.327067\pi$
$443$	21.7611	1.03390	0.516950	+	0.856015i	$0.327067\pi$
$444$	19.8991	0.944368
$445$	42.0138	1.99164
$446$	−8.41009	−0.398230
$447$	−15.3605	−0.726525
$448$	1.00000	0.0472456
$449$	−12.5827	−0.593814	−0.296907	−	0.954906i	$-0.595955\pi$
$449$	−12.5827	−0.593814	−0.296907	+	0.954906i	$0.595955\pi$
$450$	15.9769	0.753160
$451$	17.2738	0.813393
$452$	−10.9027	−0.512820
$453$	−48.4801	−2.27779
$454$	−24.1450	−1.13318
$455$	0	0
$456$	−14.5508	−0.681404
$457$	18.9984	0.888707	0.444354	−	0.895851i	$-0.353433\pi$
$457$	18.9984	0.888707	0.444354	+	0.895851i	$0.353433\pi$
$458$	19.9987	0.934476
$459$	0.609099	0.0284303
$460$	19.3942	0.904259
$461$	28.6344	1.33364	0.666818	−	0.745221i	$-0.267656\pi$
$461$	28.6344	1.33364	0.666818	+	0.745221i	$0.267656\pi$
$462$	4.03821	0.187874
$463$	−30.7909	−1.43097	−0.715487	−	0.698626i	$-0.753795\pi$
$463$	−30.7909	−1.43097	−0.715487	+	0.698626i	$0.753795\pi$
$464$	−0.769774	−0.0357358
$465$	−69.2376	−3.21082
$466$	−8.98014	−0.415997
$467$	3.95166	0.182861	0.0914305	−	0.995811i	$-0.470856\pi$
$467$	3.95166	0.182861	0.0914305	+	0.995811i	$0.470856\pi$
$468$	0	0
$469$	6.49665	0.299988
$470$	−27.8069	−1.28264
$471$	−12.3543	−0.569256
$472$	−8.61816	−0.396683
$473$	−16.8204	−0.773403
$474$	−12.2779	−0.563943
$475$	30.6987	1.40855
$476$	−3.38651	−0.155221
$477$	11.5340	0.528103
$478$	0.171956	0.00786506
$479$	−1.62076	−0.0740546	−0.0370273	−	0.999314i	$-0.511789\pi$
$479$	−1.62076	−0.0740546	−0.0370273	+	0.999314i	$0.511789\pi$
$480$	−7.87016	−0.359222
$481$	0	0
$482$	−2.07610	−0.0945638
$483$	−14.9655	−0.680953
$484$	−8.31481	−0.377946
$485$	−24.6059	−1.11730
$486$	22.1660	1.00547
$487$	−22.6802	−1.02774	−0.513868	−	0.857869i	$-0.671788\pi$
$487$	−22.6802	−1.02774	−0.513868	+	0.857869i	$0.671788\pi$
$488$	1.62349	0.0734921
$489$	−48.3805	−2.18784
$490$	3.19361	0.144273
$491$	12.8913	0.581775	0.290887	−	0.956757i	$-0.406050\pi$
$491$	12.8913	0.581775	0.290887	+	0.956757i	$0.406050\pi$
$492$	25.9778	1.17117
$493$	2.60685	0.117407
$494$	0	0
$495$	−16.0816	−0.722816
$496$	8.79749	0.395019
$497$	14.7084	0.659762
$498$	32.3868	1.45129
$499$	9.71178	0.434759	0.217379	−	0.976087i	$-0.430249\pi$
$499$	9.71178	0.434759	0.217379	+	0.976087i	$0.430249\pi$
$500$	0.636044	0.0284447
$501$	−3.31118	−0.147933
$502$	−14.8796	−0.664109
$503$	−12.3313	−0.549824	−0.274912	−	0.961469i	$-0.588649\pi$
$503$	−12.3313	−0.549824	−0.274912	+	0.961469i	$0.588649\pi$
$504$	3.07299	0.136882
$505$	32.0899	1.42798
$506$	−9.95124	−0.442386
$507$	0	0
$508$	7.34110	0.325709
$509$	21.9985	0.975065	0.487532	−	0.873105i	$-0.337897\pi$
$509$	21.9985	0.975065	0.487532	+	0.873105i	$0.337897\pi$
$510$	26.6524	1.18019
$511$	16.0908	0.711817
$512$	1.00000	0.0441942
$513$	−1.06199	−0.0468881
$514$	4.08661	0.180253
$515$	−28.4160	−1.25216
$516$	−25.2959	−1.11359
$517$	14.2678	0.627499
$518$	−8.07480	−0.354786
$519$	−31.8160	−1.39657
$520$	0	0
$521$	−20.9806	−0.919175	−0.459588	−	0.888132i	$-0.652003\pi$
$521$	−20.9806	−0.919175	−0.459588	+	0.888132i	$0.652003\pi$
$522$	−2.36550	−0.103535
$523$	−3.58213	−0.156636	−0.0783178	−	0.996928i	$-0.524955\pi$
$523$	−3.58213	−0.156636	−0.0783178	+	0.996928i	$0.524955\pi$
$524$	−0.984843	−0.0430231
$525$	−12.8125	−0.559184
$526$	−8.24162	−0.359352
$527$	−29.7928	−1.29779
$528$	4.03821	0.175740
$529$	13.8790	0.603435
$530$	11.9867	0.520669
$531$	−26.4835	−1.14928
$532$	5.90454	0.255994
$533$	0	0
$534$	−32.4198	−1.40294
$535$	20.0657	0.867516
$536$	6.49665	0.280613
$537$	−46.4006	−2.00233
$538$	−21.2899	−0.917872
$539$	−1.63865	−0.0705818
$540$	−0.574404	−0.0247184
$541$	−2.63882	−0.113452	−0.0567259	−	0.998390i	$-0.518066\pi$
$541$	−2.63882	−0.113452	−0.0567259	+	0.998390i	$0.518066\pi$
$542$	−22.4902	−0.966037
$543$	36.0261	1.54603
$544$	−3.38651	−0.145196
$545$	13.7411	0.588604
$546$	0	0
$547$	−22.3465	−0.955466	−0.477733	−	0.878505i	$-0.658541\pi$
$547$	−22.3465	−0.955466	−0.477733	+	0.878505i	$0.658541\pi$
$548$	9.24829	0.395068
$549$	4.98897	0.212924
$550$	−8.51963	−0.363278
$551$	−4.54516	−0.193630
$552$	−14.9655	−0.636973
$553$	4.98223	0.211866
$554$	−16.3535	−0.694795
$555$	63.5499	2.69754
$556$	−1.45279	−0.0616119
$557$	14.5821	0.617862	0.308931	−	0.951084i	$-0.400029\pi$
$557$	14.5821	0.617862	0.308931	+	0.951084i	$0.400029\pi$
$558$	27.0345	1.14446
$559$	0	0
$560$	3.19361	0.134955
$561$	−13.6754	−0.577377
$562$	−0.751897	−0.0317169
$563$	−36.7959	−1.55076	−0.775382	−	0.631492i	$-0.782443\pi$
$563$	−36.7959	−1.55076	−0.775382	+	0.631492i	$0.782443\pi$
$564$	21.4572	0.903509
$565$	−34.8190	−1.46485
$566$	−20.2736	−0.852163
$567$	−8.77572	−0.368546
$568$	14.7084	0.617151
$569$	−10.5094	−0.440576	−0.220288	−	0.975435i	$-0.570700\pi$
$569$	−10.5094	−0.440576	−0.220288	+	0.975435i	$0.570700\pi$
$570$	−46.4696	−1.94640
$571$	24.1650	1.01128	0.505638	−	0.862746i	$-0.331257\pi$
$571$	24.1650	1.01128	0.505638	+	0.862746i	$0.331257\pi$
$572$	0	0
$573$	34.0650	1.42309
$574$	−10.5415	−0.439992
$575$	31.5735	1.31671
$576$	3.07299	0.128041
$577$	−31.4403	−1.30888	−0.654439	−	0.756115i	$-0.727095\pi$
$577$	−31.4403	−1.30888	−0.654439	+	0.756115i	$0.727095\pi$
$578$	−5.53153	−0.230081
$579$	11.1643	0.463972
$580$	−2.45836	−0.102078
$581$	−13.1422	−0.545229
$582$	18.9871	0.787039
$583$	−6.15042	−0.254725
$584$	16.0908	0.665844
$585$	0	0
$586$	−14.1068	−0.582746
$587$	−2.09548	−0.0864898	−0.0432449	−	0.999065i	$-0.513770\pi$
$587$	−2.09548	−0.0864898	−0.0432449	+	0.999065i	$0.513770\pi$
$588$	−2.46434	−0.101628
$589$	51.9451	2.14036
$590$	−27.5231	−1.13311
$591$	3.60559	0.148314
$592$	−8.07480	−0.331872
$593$	7.57495	0.311066	0.155533	−	0.987831i	$-0.450291\pi$
$593$	7.57495	0.311066	0.155533	+	0.987831i	$0.450291\pi$
$594$	0.294729	0.0120929
$595$	−10.8152	−0.443380
$596$	6.23309	0.255317
$597$	−19.9221	−0.815356
$598$	0	0
$599$	−38.0720	−1.55558	−0.777791	−	0.628524i	$-0.783660\pi$
$599$	−38.0720	−1.55558	−0.777791	+	0.628524i	$0.783660\pi$
$600$	−12.8125	−0.523069
$601$	27.6065	1.12609	0.563047	−	0.826425i	$-0.309629\pi$
$601$	27.6065	1.12609	0.563047	+	0.826425i	$0.309629\pi$
$602$	10.2648	0.418361
$603$	19.9641	0.813002
$604$	19.6726	0.800468
$605$	−26.5543	−1.07959
$606$	−24.7621	−1.00589
$607$	6.37552	0.258774	0.129387	−	0.991594i	$-0.458699\pi$
$607$	6.37552	0.258774	0.129387	+	0.991594i	$0.458699\pi$
$608$	5.90454	0.239461
$609$	1.89699	0.0768697
$610$	5.18481	0.209927
$611$	0	0
$612$	−10.4067	−0.420666
$613$	−39.6315	−1.60070	−0.800350	−	0.599533i	$-0.795353\pi$
$613$	−39.6315	−1.60070	−0.800350	+	0.599533i	$0.795353\pi$
$614$	−27.2943	−1.10151
$615$	82.9630	3.34539
$616$	−1.63865	−0.0660233
$617$	−26.5931	−1.07060	−0.535299	−	0.844662i	$-0.679801\pi$
$617$	−26.5931	−1.07060	−0.535299	+	0.844662i	$0.679801\pi$
$618$	21.9271	0.882039
$619$	26.9329	1.08253	0.541263	−	0.840854i	$-0.317946\pi$
$619$	26.9329	1.08253	0.541263	+	0.840854i	$0.317946\pi$
$620$	28.0958	1.12835
$621$	−1.09226	−0.0438308
$622$	8.30553	0.333022
$623$	13.1556	0.527067
$624$	0	0
$625$	−23.9645	−0.958581
$626$	−26.3624	−1.05365
$627$	23.8437	0.952228
$628$	5.01323	0.200050
$629$	27.3454	1.09033
$630$	9.81392	0.390996
$631$	26.6357	1.06035	0.530175	−	0.847888i	$-0.322126\pi$
$631$	26.6357	1.06035	0.530175	+	0.847888i	$0.322126\pi$
$632$	4.98223	0.198182
$633$	−14.9929	−0.595912
$634$	22.7491	0.903483
$635$	23.4446	0.930372
$636$	−9.24951	−0.366767
$637$	0	0
$638$	1.26139	0.0499390
$639$	45.1987	1.78803
$640$	3.19361	0.126239
$641$	42.1351	1.66424	0.832118	−	0.554599i	$-0.187128\pi$
$641$	42.1351	1.66424	0.832118	+	0.554599i	$0.187128\pi$
$642$	−15.4836	−0.611091
$643$	−4.22815	−0.166742	−0.0833710	−	0.996519i	$-0.526569\pi$
$643$	−4.22815	−0.166742	−0.0833710	+	0.996519i	$0.526569\pi$
$644$	6.07281	0.239302
$645$	−80.7853	−3.18092
$646$	−19.9958	−0.786724
$647$	7.10186	0.279203	0.139602	−	0.990208i	$-0.455418\pi$
$647$	7.10186	0.279203	0.139602	+	0.990208i	$0.455418\pi$
$648$	−8.77572	−0.344743
$649$	14.1222	0.554344
$650$	0	0
$651$	−21.6800	−0.849707
$652$	19.6322	0.768857
$653$	−1.69816	−0.0664543	−0.0332271	−	0.999448i	$-0.510578\pi$
$653$	−1.69816	−0.0664543	−0.0332271	+	0.999448i	$0.510578\pi$
$654$	−10.6033	−0.414621
$655$	−3.14521	−0.122893
$656$	−10.5415	−0.411575
$657$	49.4469	1.92911
$658$	−8.70705	−0.339436
$659$	−14.7170	−0.573294	−0.286647	−	0.958036i	$-0.592541\pi$
$659$	−14.7170	−0.573294	−0.286647	+	0.958036i	$0.592541\pi$
$660$	12.8965	0.501994
$661$	−23.9005	−0.929622	−0.464811	−	0.885410i	$-0.653878\pi$
$661$	−23.9005	−0.929622	−0.464811	+	0.885410i	$0.653878\pi$
$662$	−17.4096	−0.676644
$663$	0	0
$664$	−13.1422	−0.510015
$665$	18.8568	0.731236
$666$	−24.8137	−0.961513
$667$	−4.67469	−0.181005
$668$	1.34364	0.0519869
$669$	20.7254	0.801289
$670$	20.7478	0.801557
$671$	−2.66034	−0.102701
$672$	−2.46434	−0.0950641
$673$	−44.0942	−1.69971	−0.849853	−	0.527020i	$-0.823309\pi$
$673$	−44.0942	−1.69971	−0.849853	+	0.527020i	$0.823309\pi$
$674$	13.3497	0.514212
$675$	−0.935123	−0.0359929
$676$	0	0
$677$	12.7037	0.488243	0.244122	−	0.969745i	$-0.421500\pi$
$677$	12.7037	0.488243	0.244122	+	0.969745i	$0.421500\pi$
$678$	26.8680	1.03186
$679$	−7.70472	−0.295680
$680$	−10.8152	−0.414744
$681$	59.5016	2.28011
$682$	−14.4160	−0.552019
$683$	0.300984	0.0115168	0.00575841	−	0.999983i	$-0.498167\pi$
$683$	0.300984	0.0115168	0.00575841	+	0.999983i	$0.498167\pi$
$684$	18.1446	0.693775
$685$	29.5355	1.12849
$686$	1.00000	0.0381802
$687$	−49.2835	−1.88028
$688$	10.2648	0.391341
$689$	0	0
$690$	−47.7940	−1.81948
$691$	14.7054	0.559420	0.279710	−	0.960084i	$-0.409762\pi$
$691$	14.7054	0.559420	0.279710	+	0.960084i	$0.409762\pi$
$692$	12.9105	0.490785
$693$	−5.03556	−0.191285
$694$	−10.0705	−0.382271
$695$	−4.63964	−0.175992
$696$	1.89699	0.0719051
$697$	35.6988	1.35219
$698$	8.40589	0.318167
$699$	22.1302	0.837039
$700$	5.19916	0.196510
$701$	7.80661	0.294852	0.147426	−	0.989073i	$-0.452901\pi$
$701$	7.80661	0.294852	0.147426	+	0.989073i	$0.452901\pi$
$702$	0	0
$703$	−47.6780	−1.79821
$704$	−1.63865	−0.0617591
$705$	68.5258	2.58083
$706$	26.4575	0.995741
$707$	10.0482	0.377900
$708$	21.2381	0.798177
$709$	−41.5600	−1.56082	−0.780410	−	0.625268i	$-0.784990\pi$
$709$	−41.5600	−1.56082	−0.780410	+	0.625268i	$0.784990\pi$
$710$	46.9729	1.76286
$711$	15.3103	0.574182
$712$	13.1556	0.493026
$713$	53.4255	2.00080
$714$	8.34553	0.312324
$715$	0	0
$716$	18.8288	0.703664
$717$	−0.423757	−0.0158255
$718$	−10.6006	−0.395610
$719$	41.8350	1.56018	0.780091	−	0.625666i	$-0.215173\pi$
$719$	41.8350	1.56018	0.780091	+	0.625666i	$0.215173\pi$
$720$	9.81392	0.365743
$721$	−8.89776	−0.331370
$722$	15.8636	0.590381
$723$	5.11622	0.190274
$724$	−14.6189	−0.543309
$725$	−4.00218	−0.148637
$726$	20.4905	0.760475
$727$	−20.1568	−0.747576	−0.373788	−	0.927514i	$-0.621941\pi$
$727$	−20.1568	−0.747576	−0.373788	+	0.927514i	$0.621941\pi$
$728$	0	0
$729$	−28.2974	−1.04805
$730$	51.3879	1.90195
$731$	−34.7618	−1.28571
$732$	−4.00084	−0.147875
$733$	−15.8117	−0.584017	−0.292009	−	0.956416i	$-0.594324\pi$
$733$	−15.8117	−0.584017	−0.292009	+	0.956416i	$0.594324\pi$
$734$	14.0310	0.517894
$735$	−7.87016	−0.290295
$736$	6.07281	0.223847
$737$	−10.6458	−0.392142
$738$	−32.3938	−1.19243
$739$	25.4638	0.936700	0.468350	−	0.883543i	$-0.344849\pi$
$739$	25.4638	0.936700	0.468350	+	0.883543i	$0.344849\pi$
$740$	−25.7878	−0.947977
$741$	0	0
$742$	3.75334	0.137789
$743$	7.30218	0.267891	0.133946	−	0.990989i	$-0.457235\pi$
$743$	7.30218	0.267891	0.133946	+	0.990989i	$0.457235\pi$
$744$	−21.6800	−0.794828
$745$	19.9061	0.729302
$746$	−29.2117	−1.06952
$747$	−40.3857	−1.47763
$748$	5.54932	0.202903
$749$	6.28307	0.229579
$750$	−1.56743	−0.0572345
$751$	24.5893	0.897276	0.448638	−	0.893714i	$-0.351909\pi$
$751$	24.5893	0.897276	0.448638	+	0.893714i	$0.351909\pi$
$752$	−8.70705	−0.317513
$753$	36.6684	1.33627
$754$	0	0
$755$	62.8268	2.28650
$756$	−0.179860	−0.00654146
$757$	22.6861	0.824542	0.412271	−	0.911061i	$-0.364736\pi$
$757$	22.6861	0.824542	0.412271	+	0.911061i	$0.364736\pi$
$758$	20.8150	0.756034
$759$	24.5233	0.890138
$760$	18.8568	0.684008
$761$	−38.1199	−1.38185	−0.690923	−	0.722928i	$-0.742796\pi$
$761$	−38.1199	−1.38185	−0.690923	+	0.722928i	$0.742796\pi$
$762$	−18.0910	−0.655368
$763$	4.30268	0.155768
$764$	−13.8232	−0.500105
$765$	−33.2350	−1.20161
$766$	−22.1878	−0.801679
$767$	0	0
$768$	−2.46434	−0.0889243
$769$	24.2249	0.873572	0.436786	−	0.899565i	$-0.356117\pi$
$769$	24.2249	0.873572	0.436786	+	0.899565i	$0.356117\pi$
$770$	−5.23323	−0.188592
$771$	−10.0708	−0.362691
$772$	−4.53033	−0.163050
$773$	−19.5080	−0.701653	−0.350827	−	0.936440i	$-0.614099\pi$
$773$	−19.5080	−0.701653	−0.350827	+	0.936440i	$0.614099\pi$
$774$	31.5435	1.13381
$775$	45.7396	1.64301
$776$	−7.70472	−0.276583
$777$	19.8991	0.713875
$778$	1.98048	0.0710035
$779$	−62.2425	−2.23007
$780$	0	0
$781$	−24.1020	−0.862437
$782$	−20.5656	−0.735426
$783$	0.138452	0.00494786
$784$	1.00000	0.0357143
$785$	16.0103	0.571432
$786$	2.42699	0.0865679
$787$	16.8232	0.599683	0.299842	−	0.953989i	$-0.403066\pi$
$787$	16.8232	0.599683	0.299842	+	0.953989i	$0.403066\pi$
$788$	−1.46310	−0.0521209
$789$	20.3102	0.723062
$790$	15.9113	0.566099
$791$	−10.9027	−0.387656
$792$	−5.03556	−0.178931
$793$	0	0
$794$	−4.03678	−0.143260
$795$	−29.5394	−1.04765
$796$	8.08413	0.286534
$797$	−23.3039	−0.825467	−0.412733	−	0.910852i	$-0.635426\pi$
$797$	−23.3039	−0.825467	−0.412733	+	0.910852i	$0.635426\pi$
$798$	−14.5508	−0.515093
$799$	29.4865	1.04316
$800$	5.19916	0.183818
$801$	40.4269	1.42841
$802$	−10.6442	−0.375858
$803$	−26.3673	−0.930483
$804$	−16.0100	−0.564628
$805$	19.3942	0.683556
$806$	0	0
$807$	52.4656	1.84688
$808$	10.0482	0.353493
$809$	−36.2228	−1.27353	−0.636763	−	0.771060i	$-0.719727\pi$
$809$	−36.2228	−1.27353	−0.636763	+	0.771060i	$0.719727\pi$
$810$	−28.0262	−0.984742
$811$	20.9842	0.736855	0.368427	−	0.929657i	$-0.379896\pi$
$811$	20.9842	0.736855	0.368427	+	0.929657i	$0.379896\pi$
$812$	−0.769774	−0.0270138
$813$	55.4236	1.94379
$814$	13.2318	0.463774
$815$	62.6977	2.19620
$816$	8.34553	0.292152
$817$	60.6087	2.12043
$818$	12.0943	0.422869
$819$	0	0
$820$	−33.6654	−1.17565
$821$	26.1491	0.912610	0.456305	−	0.889824i	$-0.349173\pi$
$821$	26.1491	0.912610	0.456305	+	0.889824i	$0.349173\pi$
$822$	−22.7910	−0.794926
$823$	−9.09620	−0.317074	−0.158537	−	0.987353i	$-0.550678\pi$
$823$	−9.09620	−0.317074	−0.158537	+	0.987353i	$0.550678\pi$
$824$	−8.89776	−0.309968
$825$	20.9953	0.730962
$826$	−8.61816	−0.299864
$827$	44.6342	1.55208	0.776042	−	0.630681i	$-0.217224\pi$
$827$	44.6342	1.55208	0.776042	+	0.630681i	$0.217224\pi$
$828$	18.6617	0.648537
$829$	−49.6565	−1.72464	−0.862320	−	0.506363i	$-0.830989\pi$
$829$	−49.6565	−1.72464	−0.862320	+	0.506363i	$0.830989\pi$
$830$	−41.9710	−1.45683
$831$	40.3007	1.39802
$832$	0	0
$833$	−3.38651	−0.117336
$834$	3.58017	0.123971
$835$	4.29106	0.148498
$836$	−9.67550	−0.334634
$837$	−1.58232	−0.0546930
$838$	−3.34008	−0.115381
$839$	−28.5826	−0.986781	−0.493391	−	0.869808i	$-0.664243\pi$
$839$	−28.5826	−0.986781	−0.493391	+	0.869808i	$0.664243\pi$
$840$	−7.87016	−0.271546
$841$	−28.4074	−0.979567
$842$	−10.8214	−0.372930
$843$	1.85293	0.0638184
$844$	6.08392	0.209417
$845$	0	0
$846$	−26.7566	−0.919912
$847$	−8.31481	−0.285700
$848$	3.75334	0.128890
$849$	49.9611	1.71466
$850$	−17.6070	−0.603916
$851$	−49.0367	−1.68096
$852$	−36.2465	−1.24179
$853$	24.4117	0.835840	0.417920	−	0.908484i	$-0.362759\pi$
$853$	24.4117	0.835840	0.417920	+	0.908484i	$0.362759\pi$
$854$	1.62349	0.0555548
$855$	57.9467	1.98174
$856$	6.28307	0.214751
$857$	−19.4606	−0.664762	−0.332381	−	0.943145i	$-0.607852\pi$
$857$	−19.4606	−0.664762	−0.332381	+	0.943145i	$0.607852\pi$
$858$	0	0
$859$	31.4100	1.07169	0.535847	−	0.844315i	$-0.319992\pi$
$859$	31.4100	1.07169	0.535847	+	0.844315i	$0.319992\pi$
$860$	32.7817	1.11785
$861$	25.9778	0.885321
$862$	−31.5076	−1.07315
$863$	−30.9732	−1.05434	−0.527169	−	0.849760i	$-0.676747\pi$
$863$	−30.9732	−1.05434	−0.527169	+	0.849760i	$0.676747\pi$
$864$	−0.179860	−0.00611897
$865$	41.2313	1.40191
$866$	−16.3267	−0.554805
$867$	13.6316	0.462953
$868$	8.79749	0.298606
$869$	−8.16415	−0.276950
$870$	6.05824	0.205393
$871$	0	0
$872$	4.30268	0.145707
$873$	−23.6765	−0.801328
$874$	35.8571	1.21289
$875$	0.636044	0.0215022
$876$	−39.6533	−1.33976
$877$	24.8370	0.838687	0.419344	−	0.907828i	$-0.362260\pi$
$877$	24.8370	0.838687	0.419344	+	0.907828i	$0.362260\pi$
$878$	−22.8205	−0.770155
$879$	34.7640	1.17256
$880$	−5.23323	−0.176412
$881$	−30.1352	−1.01528	−0.507640	−	0.861569i	$-0.669482\pi$
$881$	−30.1352	−1.01528	−0.507640	+	0.861569i	$0.669482\pi$
$882$	3.07299	0.103473
$883$	41.6442	1.40144	0.700719	−	0.713437i	$-0.252863\pi$
$883$	41.6442	1.40144	0.700719	+	0.713437i	$0.252863\pi$
$884$	0	0
$885$	67.8263	2.27995
$886$	21.7611	0.731078
$887$	−32.7821	−1.10071	−0.550357	−	0.834929i	$-0.685508\pi$
$887$	−32.7821	−1.10071	−0.550357	+	0.834929i	$0.685508\pi$
$888$	19.8991	0.667769
$889$	7.34110	0.246213
$890$	42.0138	1.40831
$891$	14.3804	0.481760
$892$	−8.41009	−0.281591
$893$	−51.4111	−1.72041
$894$	−15.3605	−0.513731
$895$	60.1318	2.00998
$896$	1.00000	0.0334077
$897$	0	0
$898$	−12.5827	−0.419890
$899$	−6.77207	−0.225861
$900$	15.9769	0.532565
$901$	−12.7107	−0.423456
$902$	17.2738	0.575155
$903$	−25.2959	−0.841795
$904$	−10.9027	−0.362619
$905$	−46.6873	−1.55194
$906$	−48.4801	−1.61064
$907$	39.5137	1.31203	0.656016	−	0.754747i	$-0.272240\pi$
$907$	39.5137	1.31203	0.656016	+	0.754747i	$0.272240\pi$
$908$	−24.1450	−0.801281
$909$	30.8778	1.02415
$910$	0	0
$911$	−53.8969	−1.78568	−0.892842	−	0.450369i	$-0.851292\pi$
$911$	−53.8969	−1.78568	−0.892842	+	0.450369i	$0.851292\pi$
$912$	−14.5508	−0.481825
$913$	21.5355	0.712720
$914$	18.9984	0.628411
$915$	−12.7771	−0.422399
$916$	19.9987	0.660774
$917$	−0.984843	−0.0325224
$918$	0.609099	0.0201033
$919$	7.57856	0.249994	0.124997	−	0.992157i	$-0.460108\pi$
$919$	7.57856	0.249994	0.124997	+	0.992157i	$0.460108\pi$
$920$	19.3942	0.639408
$921$	67.2625	2.21638
$922$	28.6344	0.943023
$923$	0	0
$924$	4.03821	0.132847
$925$	−41.9822	−1.38037
$926$	−30.7909	−1.01185
$927$	−27.3427	−0.898052
$928$	−0.769774	−0.0252691
$929$	48.4711	1.59029	0.795143	−	0.606422i	$-0.207396\pi$
$929$	48.4711	1.59029	0.795143	+	0.606422i	$0.207396\pi$
$930$	−69.2376	−2.27039
$931$	5.90454	0.193513
$932$	−8.98014	−0.294154
$933$	−20.4677	−0.670082
$934$	3.95166	0.129302
$935$	17.7224	0.579584
$936$	0	0
$937$	−16.6631	−0.544361	−0.272181	−	0.962246i	$-0.587745\pi$
$937$	−16.6631	−0.544361	−0.272181	+	0.962246i	$0.587745\pi$
$938$	6.49665	0.212123
$939$	64.9661	2.12009
$940$	−27.8069	−0.906962
$941$	−30.8001	−1.00406	−0.502028	−	0.864851i	$-0.667413\pi$
$941$	−30.8001	−1.00406	−0.502028	+	0.864851i	$0.667413\pi$
$942$	−12.3543	−0.402525
$943$	−64.0163	−2.08466
$944$	−8.61816	−0.280497
$945$	−0.574404	−0.0186854
$946$	−16.8204	−0.546879
$947$	36.2300	1.17732	0.588659	−	0.808381i	$-0.299656\pi$
$947$	36.2300	1.17732	0.588659	+	0.808381i	$0.299656\pi$
$948$	−12.2779	−0.398768
$949$	0	0
$950$	30.6987	0.995996
$951$	−56.0616	−1.81792
$952$	−3.38651	−0.109757
$953$	−57.8916	−1.87529	−0.937646	−	0.347592i	$-0.887000\pi$
$953$	−57.8916	−1.87529	−0.937646	+	0.347592i	$0.887000\pi$
$954$	11.5340	0.373425
$955$	−44.1458	−1.42853
$956$	0.171956	0.00556144
$957$	−3.10850	−0.100484
$958$	−1.62076	−0.0523645
$959$	9.24829	0.298643
$960$	−7.87016	−0.254008
$961$	46.3958	1.49664
$962$	0	0
$963$	19.3078	0.622185
$964$	−2.07610	−0.0668667
$965$	−14.4681	−0.465745
$966$	−14.9655	−0.481507
$967$	1.99785	0.0642464	0.0321232	−	0.999484i	$-0.489773\pi$
$967$	1.99785	0.0642464	0.0321232	+	0.999484i	$0.489773\pi$
$968$	−8.31481	−0.267248
$969$	49.2765	1.58299
$970$	−24.6059	−0.790048
$971$	−30.4186	−0.976179	−0.488089	−	0.872794i	$-0.662306\pi$
$971$	−30.4186	−0.976179	−0.488089	+	0.872794i	$0.662306\pi$
$972$	22.1660	0.710973
$973$	−1.45279	−0.0465742
$974$	−22.6802	−0.726719
$975$	0	0
$976$	1.62349	0.0519668
$977$	4.37381	0.139930	0.0699652	−	0.997549i	$-0.477711\pi$
$977$	4.37381	0.139930	0.0699652	+	0.997549i	$0.477711\pi$
$978$	−48.3805	−1.54704
$979$	−21.5574	−0.688978
$980$	3.19361	0.102016
$981$	13.2221	0.422149
$982$	12.8913	0.411377
$983$	26.3471	0.840341	0.420171	−	0.907445i	$-0.361970\pi$
$983$	26.3471	0.840341	0.420171	+	0.907445i	$0.361970\pi$
$984$	25.9778	0.828142
$985$	−4.67258	−0.148881
$986$	2.60685	0.0830189
$987$	21.4572	0.682989
$988$	0	0
$989$	62.3360	1.98217
$990$	−16.0816	−0.511108
$991$	13.4926	0.428606	0.214303	−	0.976767i	$-0.431252\pi$
$991$	13.4926	0.428606	0.214303	+	0.976767i	$0.431252\pi$
$992$	8.79749	0.279321
$993$	42.9033	1.36149
$994$	14.7084	0.466522
$995$	25.8176	0.818472
$996$	32.3868	1.02621
$997$	31.2272	0.988976	0.494488	−	0.869185i	$-0.335356\pi$
$997$	31.2272	0.988976	0.494488	+	0.869185i	$0.335356\pi$
$998$	9.71178	0.307421
$999$	1.45234	0.0459499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.bg.1.1	yes	6
13.5	odd	4		2366.2.d.q.337.1		12
13.8	odd	4		2366.2.d.q.337.7		12
13.12	even	2		2366.2.a.be.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.be.1.1	✓	6	13.12	even	2
2366.2.a.bg.1.1	yes	6	1.1	even	1	trivial
2366.2.d.q.337.1		12	13.5	odd	4
2366.2.d.q.337.7		12	13.8	odd	4

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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.46434 q^{3} +1.00000 q^{4} +3.19361 q^{5} -2.46434 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.07299 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.46434 q^{3} +1.00000 q^{4} +3.19361 q^{5} -2.46434 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.07299 q^{9} +3.19361 q^{10} -1.63865 q^{11} -2.46434 q^{12} +1.00000 q^{14} -7.87016 q^{15} +1.00000 q^{16} -3.38651 q^{17} +3.07299 q^{18} +5.90454 q^{19} +3.19361 q^{20} -2.46434 q^{21} -1.63865 q^{22} +6.07281 q^{23} -2.46434 q^{24} +5.19916 q^{25} -0.179860 q^{27} +1.00000 q^{28} -0.769774 q^{29} -7.87016 q^{30} +8.79749 q^{31} +1.00000 q^{32} +4.03821 q^{33} -3.38651 q^{34} +3.19361 q^{35} +3.07299 q^{36} -8.07480 q^{37} +5.90454 q^{38} +3.19361 q^{40} -10.5415 q^{41} -2.46434 q^{42} +10.2648 q^{43} -1.63865 q^{44} +9.81392 q^{45} +6.07281 q^{46} -8.70705 q^{47} -2.46434 q^{48} +1.00000 q^{49} +5.19916 q^{50} +8.34553 q^{51} +3.75334 q^{53} -0.179860 q^{54} -5.23323 q^{55} +1.00000 q^{56} -14.5508 q^{57} -0.769774 q^{58} -8.61816 q^{59} -7.87016 q^{60} +1.62349 q^{61} +8.79749 q^{62} +3.07299 q^{63} +1.00000 q^{64} +4.03821 q^{66} +6.49665 q^{67} -3.38651 q^{68} -14.9655 q^{69} +3.19361 q^{70} +14.7084 q^{71} +3.07299 q^{72} +16.0908 q^{73} -8.07480 q^{74} -12.8125 q^{75} +5.90454 q^{76} -1.63865 q^{77} +4.98223 q^{79} +3.19361 q^{80} -8.77572 q^{81} -10.5415 q^{82} -13.1422 q^{83} -2.46434 q^{84} -10.8152 q^{85} +10.2648 q^{86} +1.89699 q^{87} -1.63865 q^{88} +13.1556 q^{89} +9.81392 q^{90} +6.07281 q^{92} -21.6800 q^{93} -8.70705 q^{94} +18.8568 q^{95} -2.46434 q^{96} -7.70472 q^{97} +1.00000 q^{98} -5.03556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 4 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 4 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 5 * q^9	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 4 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 5 q^{9} + 4 q^{10} + 6 q^{11} + q^{12} + 6 q^{14} - 5 q^{15} + 6 q^{16} - 9 q^{17} + 5 q^{18} + 10 q^{19} + 4 q^{20} + q^{21} + 6 q^{22} + 21 q^{23} + q^{24} + 8 q^{25} + 7 q^{27} + 6 q^{28} - q^{29} - 5 q^{30} + 20 q^{31} + 6 q^{32} + 9 q^{33} - 9 q^{34} + 4 q^{35} + 5 q^{36} + 16 q^{37} + 10 q^{38} + 4 q^{40} + 2 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} + 17 q^{45} + 21 q^{46} - 5 q^{47} + q^{48} + 6 q^{49} + 8 q^{50} - 15 q^{51} + 28 q^{53} + 7 q^{54} - 29 q^{55} + 6 q^{56} + 22 q^{57} - q^{58} - 12 q^{59} - 5 q^{60} - 27 q^{61} + 20 q^{62} + 5 q^{63} + 6 q^{64} + 9 q^{66} + 16 q^{67} - 9 q^{68} - 15 q^{69} + 4 q^{70} + 5 q^{72} + 38 q^{73} + 16 q^{74} - 7 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} + 4 q^{80} - 26 q^{81} + 2 q^{82} - 6 q^{83} + q^{84} + 9 q^{85} + 2 q^{86} - 39 q^{87} + 6 q^{88} - q^{89} + 17 q^{90} + 21 q^{92} - 7 q^{93} - 5 q^{94} + 3 q^{95} + q^{96} + 16 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 4 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 5 * q^9 + 4 * q^10 + 6 * q^11 + q^12 + 6 * q^14 - 5 * q^15 + 6 * q^16 - 9 * q^17 + 5 * q^18 + 10 * q^19 + 4 * q^20 + q^21 + 6 * q^22 + 21 * q^23 + q^24 + 8 * q^25 + 7 * q^27 + 6 * q^28 - q^29 - 5 * q^30 + 20 * q^31 + 6 * q^32 + 9 * q^33 - 9 * q^34 + 4 * q^35 + 5 * q^36 + 16 * q^37 + 10 * q^38 + 4 * q^40 + 2 * q^41 + q^42 + 2 * q^43 + 6 * q^44 + 17 * q^45 + 21 * q^46 - 5 * q^47 + q^48 + 6 * q^49 + 8 * q^50 - 15 * q^51 + 28 * q^53 + 7 * q^54 - 29 * q^55 + 6 * q^56 + 22 * q^57 - q^58 - 12 * q^59 - 5 * q^60 - 27 * q^61 + 20 * q^62 + 5 * q^63 + 6 * q^64 + 9 * q^66 + 16 * q^67 - 9 * q^68 - 15 * q^69 + 4 * q^70 + 5 * q^72 + 38 * q^73 + 16 * q^74 - 7 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 + 4 * q^80 - 26 * q^81 + 2 * q^82 - 6 * q^83 + q^84 + 9 * q^85 + 2 * q^86 - 39 * q^87 + 6 * q^88 - q^89 + 17 * q^90 + 21 * q^92 - 7 * q^93 - 5 * q^94 + 3 * q^95 + q^96 + 16 * q^97 + 6 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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