LMFDB - Embedded newform 9295.2.a.bn.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9295,2,Mod(1,9295)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9295, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9295.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9295 = 5 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9295.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:	$74.2209486788$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	9295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.676070 q^{2} +1.15350 q^{3} -1.54293 q^{4} +1.00000 q^{5} +0.779848 q^{6} -4.22950 q^{7} -2.39527 q^{8} -1.66943 q^{9} +O(q^{10})$	\(q+0.676070 q^{2} +1.15350 q^{3} -1.54293 q^{4} +1.00000 q^{5} +0.779848 q^{6} -4.22950 q^{7} -2.39527 q^{8} -1.66943 q^{9} +0.676070 q^{10} +1.00000 q^{11} -1.77977 q^{12} -2.85944 q^{14} +1.15350 q^{15} +1.46649 q^{16} -5.49282 q^{17} -1.12865 q^{18} -3.78464 q^{19} -1.54293 q^{20} -4.87874 q^{21} +0.676070 q^{22} +0.422998 q^{23} -2.76295 q^{24} +1.00000 q^{25} -5.38620 q^{27} +6.52582 q^{28} -5.97550 q^{29} +0.779848 q^{30} +0.372253 q^{31} +5.78199 q^{32} +1.15350 q^{33} -3.71353 q^{34} -4.22950 q^{35} +2.57582 q^{36} -4.70199 q^{37} -2.55868 q^{38} -2.39527 q^{40} +5.96197 q^{41} -3.29837 q^{42} +9.82750 q^{43} -1.54293 q^{44} -1.66943 q^{45} +0.285977 q^{46} -10.8258 q^{47} +1.69160 q^{48} +10.8887 q^{49} +0.676070 q^{50} -6.33598 q^{51} +2.31536 q^{53} -3.64145 q^{54} +1.00000 q^{55} +10.1308 q^{56} -4.36559 q^{57} -4.03985 q^{58} +4.65716 q^{59} -1.77977 q^{60} -3.08942 q^{61} +0.251669 q^{62} +7.06086 q^{63} +0.976047 q^{64} +0.779848 q^{66} +0.431119 q^{67} +8.47504 q^{68} +0.487930 q^{69} -2.85944 q^{70} -3.70524 q^{71} +3.99874 q^{72} +1.36092 q^{73} -3.17888 q^{74} +1.15350 q^{75} +5.83944 q^{76} -4.22950 q^{77} -10.9737 q^{79} +1.46649 q^{80} -1.20470 q^{81} +4.03071 q^{82} +15.4549 q^{83} +7.52755 q^{84} -5.49282 q^{85} +6.64408 q^{86} -6.89275 q^{87} -2.39527 q^{88} +16.1874 q^{89} -1.12865 q^{90} -0.652657 q^{92} +0.429394 q^{93} -7.31901 q^{94} -3.78464 q^{95} +6.66953 q^{96} +17.5648 q^{97} +7.36150 q^{98} -1.66943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9}+O(q^{10}) $ 33 * q + 8 * q^2 + 12 * q^3 + 38 * q^4 + 33 * q^5 + 18 * q^6 + 4 * q^7 + 21 * q^8 + 35 * q^9	\( 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9} + 8 q^{10} + 33 q^{11} + 24 q^{12} - 5 q^{14} + 12 q^{15} + 44 q^{16} + 9 q^{17} + 18 q^{18} + 8 q^{19} + 38 q^{20} + 9 q^{21} + 8 q^{22} + 7 q^{23} + 54 q^{24} + 33 q^{25} + 42 q^{27} + 15 q^{28} - 11 q^{29} + 18 q^{30} + 13 q^{31} + 85 q^{32} + 12 q^{33} + 31 q^{34} + 4 q^{35} + 26 q^{36} + 22 q^{37} - 2 q^{38} + 21 q^{40} + 36 q^{41} + 11 q^{42} + 26 q^{43} + 38 q^{44} + 35 q^{45} - q^{46} + 46 q^{47} + 36 q^{48} + 29 q^{49} + 8 q^{50} - 41 q^{51} + 9 q^{53} + 70 q^{54} + 33 q^{55} - 10 q^{56} + 70 q^{57} - 23 q^{58} + 18 q^{59} + 24 q^{60} - 42 q^{61} - 24 q^{62} + 68 q^{63} + 39 q^{64} + 18 q^{66} + 26 q^{67} + 8 q^{68} + 12 q^{69} - 5 q^{70} + 43 q^{71} + 46 q^{72} + 21 q^{73} - 22 q^{74} + 12 q^{75} + 2 q^{76} + 4 q^{77} - 22 q^{79} + 44 q^{80} + 41 q^{81} + 156 q^{82} + 26 q^{83} + 11 q^{84} + 9 q^{85} + 17 q^{86} - 30 q^{87} + 21 q^{88} + 95 q^{89} + 18 q^{90} + 37 q^{92} + 62 q^{93} - 14 q^{94} + 8 q^{95} + 53 q^{96} + 40 q^{97} + 132 q^{98} + 35 q^{99}+O(q^{100}) \) 33 * q + 8 * q^2 + 12 * q^3 + 38 * q^4 + 33 * q^5 + 18 * q^6 + 4 * q^7 + 21 * q^8 + 35 * q^9 + 8 * q^10 + 33 * q^11 + 24 * q^12 - 5 * q^14 + 12 * q^15 + 44 * q^16 + 9 * q^17 + 18 * q^18 + 8 * q^19 + 38 * q^20 + 9 * q^21 + 8 * q^22 + 7 * q^23 + 54 * q^24 + 33 * q^25 + 42 * q^27 + 15 * q^28 - 11 * q^29 + 18 * q^30 + 13 * q^31 + 85 * q^32 + 12 * q^33 + 31 * q^34 + 4 * q^35 + 26 * q^36 + 22 * q^37 - 2 * q^38 + 21 * q^40 + 36 * q^41 + 11 * q^42 + 26 * q^43 + 38 * q^44 + 35 * q^45 - q^46 + 46 * q^47 + 36 * q^48 + 29 * q^49 + 8 * q^50 - 41 * q^51 + 9 * q^53 + 70 * q^54 + 33 * q^55 - 10 * q^56 + 70 * q^57 - 23 * q^58 + 18 * q^59 + 24 * q^60 - 42 * q^61 - 24 * q^62 + 68 * q^63 + 39 * q^64 + 18 * q^66 + 26 * q^67 + 8 * q^68 + 12 * q^69 - 5 * q^70 + 43 * q^71 + 46 * q^72 + 21 * q^73 - 22 * q^74 + 12 * q^75 + 2 * q^76 + 4 * q^77 - 22 * q^79 + 44 * q^80 + 41 * q^81 + 156 * q^82 + 26 * q^83 + 11 * q^84 + 9 * q^85 + 17 * q^86 - 30 * q^87 + 21 * q^88 + 95 * q^89 + 18 * q^90 + 37 * q^92 + 62 * q^93 - 14 * q^94 + 8 * q^95 + 53 * q^96 + 40 * q^97 + 132 * q^98 + 35 * 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 $

$2$	0.676070	0.478054	0.239027	−	0.971013i	$-0.423172\pi$
$2$	0.676070	0.478054	0.239027	+	0.971013i	$0.423172\pi$
$3$	1.15350	0.665975	0.332987	−	0.942931i	$-0.391943\pi$
$3$	1.15350	0.665975	0.332987	+	0.942931i	$0.391943\pi$
$4$	−1.54293	−0.771465
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.779848	0.318372
$7$	−4.22950	−1.59860	−0.799300	−	0.600932i	$-0.794796\pi$
$7$	−4.22950	−1.59860	−0.799300	+	0.600932i	$0.794796\pi$
$8$	−2.39527	−0.846855
$9$	−1.66943	−0.556478
$10$	0.676070	0.213792
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.77977	−0.513776
$13$	0	0
$13$	0	0
$14$	−2.85944	−0.764217
$15$	1.15350	0.297833
$16$	1.46649	0.366623
$17$	−5.49282	−1.33220	−0.666102	−	0.745860i	$-0.732039\pi$
$17$	−5.49282	−1.33220	−0.666102	+	0.745860i	$0.732039\pi$
$18$	−1.12865	−0.266026
$19$	−3.78464	−0.868257	−0.434128	−	0.900851i	$-0.642944\pi$
$19$	−3.78464	−0.868257	−0.434128	+	0.900851i	$0.642944\pi$
$20$	−1.54293	−0.345010
$21$	−4.87874	−1.06463
$22$	0.676070	0.144139
$23$	0.422998	0.0882013	0.0441006	−	0.999027i	$-0.485958\pi$
$23$	0.422998	0.0882013	0.0441006	+	0.999027i	$0.485958\pi$
$24$	−2.76295	−0.563984
$25$	1.00000	0.200000
$26$	0	0
$27$	−5.38620	−1.03657
$28$	6.52582	1.23326
$29$	−5.97550	−1.10962	−0.554811	−	0.831977i	$-0.687209\pi$
$29$	−5.97550	−1.10962	−0.554811	+	0.831977i	$0.687209\pi$
$30$	0.779848	0.142380
$31$	0.372253	0.0668585	0.0334293	−	0.999441i	$-0.489357\pi$
$31$	0.372253	0.0668585	0.0334293	+	0.999441i	$0.489357\pi$
$32$	5.78199	1.02212
$33$	1.15350	0.200799
$34$	−3.71353	−0.636865
$35$	−4.22950	−0.714916
$36$	2.57582	0.429303
$37$	−4.70199	−0.773003	−0.386501	−	0.922289i	$-0.626317\pi$
$37$	−4.70199	−0.773003	−0.386501	+	0.922289i	$0.626317\pi$
$38$	−2.55868	−0.415073
$39$	0	0
$40$	−2.39527	−0.378725
$41$	5.96197	0.931104	0.465552	−	0.885021i	$-0.345856\pi$
$41$	5.96197	0.931104	0.465552	+	0.885021i	$0.345856\pi$
$42$	−3.29837	−0.508949
$43$	9.82750	1.49868	0.749340	−	0.662185i	$-0.230371\pi$
$43$	9.82750	1.49868	0.749340	+	0.662185i	$0.230371\pi$
$44$	−1.54293	−0.232605
$45$	−1.66943	−0.248864
$46$	0.285977	0.0421649
$47$	−10.8258	−1.57911	−0.789554	−	0.613681i	$-0.789688\pi$
$47$	−10.8258	−1.57911	−0.789554	+	0.613681i	$0.789688\pi$
$48$	1.69160	0.244161
$49$	10.8887	1.55552
$50$	0.676070	0.0956107
$51$	−6.33598	−0.887215
$52$	0	0
$53$	2.31536	0.318039	0.159020	−	0.987275i	$-0.449167\pi$
$53$	2.31536	0.318039	0.159020	+	0.987275i	$0.449167\pi$
$54$	−3.64145	−0.495538
$55$	1.00000	0.134840
$56$	10.1308	1.35378
$57$	−4.36559	−0.578237
$58$	−4.03985	−0.530459
$59$	4.65716	0.606311	0.303156	−	0.952941i	$-0.401960\pi$
$59$	4.65716	0.606311	0.303156	+	0.952941i	$0.401960\pi$
$60$	−1.77977	−0.229768
$61$	−3.08942	−0.395560	−0.197780	−	0.980246i	$-0.563373\pi$
$61$	−3.08942	−0.395560	−0.197780	+	0.980246i	$0.563373\pi$
$62$	0.251669	0.0319620
$63$	7.06086	0.889585
$64$	0.976047	0.122006
$65$	0	0
$66$	0.779848	0.0959927
$67$	0.431119	0.0526696	0.0263348	−	0.999653i	$-0.491616\pi$
$67$	0.431119	0.0526696	0.0263348	+	0.999653i	$0.491616\pi$
$68$	8.47504	1.02775
$69$	0.487930	0.0587398
$70$	−2.85944	−0.341768
$71$	−3.70524	−0.439731	−0.219865	−	0.975530i	$-0.570562\pi$
$71$	−3.70524	−0.439731	−0.219865	+	0.975530i	$0.570562\pi$
$72$	3.99874	0.471256
$73$	1.36092	0.159283	0.0796415	−	0.996824i	$-0.474622\pi$
$73$	1.36092	0.159283	0.0796415	+	0.996824i	$0.474622\pi$
$74$	−3.17888	−0.369537
$75$	1.15350	0.133195
$76$	5.83944	0.669829
$77$	−4.22950	−0.481996
$78$	0	0
$79$	−10.9737	−1.23463	−0.617316	−	0.786715i	$-0.711780\pi$
$79$	−10.9737	−1.23463	−0.617316	+	0.786715i	$0.711780\pi$
$80$	1.46649	0.163959
$81$	−1.20470	−0.133855
$82$	4.03071	0.445118
$83$	15.4549	1.69639	0.848197	−	0.529680i	$-0.177688\pi$
$83$	15.4549	1.69639	0.848197	+	0.529680i	$0.177688\pi$
$84$	7.52755	0.821323
$85$	−5.49282	−0.595780
$86$	6.64408	0.716450
$87$	−6.89275	−0.738980
$88$	−2.39527	−0.255336
$89$	16.1874	1.71586	0.857932	−	0.513764i	$-0.171749\pi$
$89$	16.1874	1.71586	0.857932	+	0.513764i	$0.171749\pi$
$90$	−1.12865	−0.118970
$91$	0	0
$92$	−0.652657	−0.0680442
$93$	0.429394	0.0445261
$94$	−7.31901	−0.754898
$95$	−3.78464	−0.388296
$96$	6.66953	0.680706
$97$	17.5648	1.78343	0.891717	−	0.452594i	$-0.149501\pi$
$97$	17.5648	1.78343	0.891717	+	0.452594i	$0.149501\pi$
$98$	7.36150	0.743624
$99$	−1.66943	−0.167784
$100$	−1.54293	−0.154293
$101$	−4.50936	−0.448698	−0.224349	−	0.974509i	$-0.572026\pi$
$101$	−4.50936	−0.448698	−0.224349	+	0.974509i	$0.572026\pi$
$102$	−4.28357	−0.424136
$103$	7.08453	0.698060	0.349030	−	0.937112i	$-0.386511\pi$
$103$	7.08453	0.698060	0.349030	+	0.937112i	$0.386511\pi$
$104$	0	0
$105$	−4.87874	−0.476116
$106$	1.56535	0.152040
$107$	2.41678	0.233639	0.116819	−	0.993153i	$-0.462730\pi$
$107$	2.41678	0.233639	0.116819	+	0.993153i	$0.462730\pi$
$108$	8.31053	0.799681
$109$	−1.86522	−0.178656	−0.0893280	−	0.996002i	$-0.528472\pi$
$109$	−1.86522	−0.178656	−0.0893280	+	0.996002i	$0.528472\pi$
$110$	0.676070	0.0644607
$111$	−5.42376	−0.514800
$112$	−6.20252	−0.586083
$113$	−12.3760	−1.16424	−0.582119	−	0.813104i	$-0.697776\pi$
$113$	−12.3760	−1.16424	−0.582119	+	0.813104i	$0.697776\pi$
$114$	−2.95145	−0.276428
$115$	0.422998	0.0394448
$116$	9.21977	0.856034
$117$	0	0
$118$	3.14857	0.289849
$119$	23.2319	2.12966
$120$	−2.76295	−0.252221
$121$	1.00000	0.0909091
$122$	−2.08866	−0.189099
$123$	6.87715	0.620092
$124$	−0.574360	−0.0515790
$125$	1.00000	0.0894427
$126$	4.77364	0.425269
$127$	−19.3958	−1.72110	−0.860549	−	0.509367i	$-0.829880\pi$
$127$	−19.3958	−1.72110	−0.860549	+	0.509367i	$0.829880\pi$
$128$	−10.9041	−0.963795
$129$	11.3360	0.998083
$130$	0	0
$131$	12.6067	1.10145	0.550725	−	0.834687i	$-0.314351\pi$
$131$	12.6067	1.10145	0.550725	+	0.834687i	$0.314351\pi$
$132$	−1.77977	−0.154909
$133$	16.0071	1.38800
$134$	0.291467	0.0251789
$135$	−5.38620	−0.463570
$136$	13.1568	1.12818
$137$	−1.29691	−0.110802	−0.0554011	−	0.998464i	$-0.517644\pi$
$137$	−1.29691	−0.110802	−0.0554011	+	0.998464i	$0.517644\pi$
$138$	0.329875	0.0280808
$139$	18.0165	1.52814	0.764068	−	0.645136i	$-0.223199\pi$
$139$	18.0165	1.52814	0.764068	+	0.645136i	$0.223199\pi$
$140$	6.52582	0.551532
$141$	−12.4876	−1.05165
$142$	−2.50500	−0.210215
$143$	0	0
$144$	−2.44821	−0.204017
$145$	−5.97550	−0.496238
$146$	0.920074	0.0761459
$147$	12.5601	1.03594
$148$	7.25484	0.596344
$149$	−6.12183	−0.501520	−0.250760	−	0.968049i	$-0.580680\pi$
$149$	−6.12183	−0.501520	−0.250760	+	0.968049i	$0.580680\pi$
$150$	0.779848	0.0636743
$151$	−12.4541	−1.01350	−0.506750	−	0.862093i	$-0.669153\pi$
$151$	−12.4541	−1.01350	−0.506750	+	0.862093i	$0.669153\pi$
$152$	9.06523	0.735288
$153$	9.16989	0.741342
$154$	−2.85944	−0.230420
$155$	0.372253	0.0299001
$156$	0	0
$157$	5.63111	0.449412	0.224706	−	0.974427i	$-0.427858\pi$
$157$	5.63111	0.449412	0.224706	+	0.974427i	$0.427858\pi$
$158$	−7.41896	−0.590221
$159$	2.67077	0.211806
$160$	5.78199	0.457106
$161$	−1.78907	−0.140999
$162$	−0.814460	−0.0639900
$163$	−6.70122	−0.524880	−0.262440	−	0.964948i	$-0.584527\pi$
$163$	−6.70122	−0.524880	−0.262440	+	0.964948i	$0.584527\pi$
$164$	−9.19891	−0.718314
$165$	1.15350	0.0898000
$166$	10.4486	0.810968
$167$	16.6890	1.29144	0.645718	−	0.763576i	$-0.276558\pi$
$167$	16.6890	1.29144	0.645718	+	0.763576i	$0.276558\pi$
$168$	11.6859	0.901586
$169$	0	0
$170$	−3.71353	−0.284815
$171$	6.31821	0.483165
$172$	−15.1631	−1.15618
$173$	−1.81151	−0.137727	−0.0688633	−	0.997626i	$-0.521937\pi$
$173$	−1.81151	−0.137727	−0.0688633	+	0.997626i	$0.521937\pi$
$174$	−4.65998	−0.353272
$175$	−4.22950	−0.319720
$176$	1.46649	0.110541
$177$	5.37205	0.403788
$178$	10.9438	0.820275
$179$	−2.07295	−0.154940	−0.0774699	−	0.996995i	$-0.524684\pi$
$179$	−2.07295	−0.154940	−0.0774699	+	0.996995i	$0.524684\pi$
$180$	2.57582	0.191990
$181$	1.61565	0.120090	0.0600451	−	0.998196i	$-0.480876\pi$
$181$	1.61565	0.120090	0.0600451	+	0.998196i	$0.480876\pi$
$182$	0	0
$183$	−3.56365	−0.263433
$184$	−1.01319	−0.0746937
$185$	−4.70199	−0.345697
$186$	0.290301	0.0212859
$187$	−5.49282	−0.401675
$188$	16.7035	1.21823
$189$	22.7809	1.65707
$190$	−2.55868	−0.185626
$191$	−25.9406	−1.87700	−0.938499	−	0.345281i	$-0.887784\pi$
$191$	−25.9406	−1.87700	−0.938499	+	0.345281i	$0.887784\pi$
$192$	1.12587	0.0812528
$193$	−6.68661	−0.481312	−0.240656	−	0.970610i	$-0.577363\pi$
$193$	−6.68661	−0.481312	−0.240656	+	0.970610i	$0.577363\pi$
$194$	11.8750	0.852577
$195$	0	0
$196$	−16.8004	−1.20003
$197$	23.3899	1.66646	0.833231	−	0.552925i	$-0.186488\pi$
$197$	23.3899	1.66646	0.833231	+	0.552925i	$0.186488\pi$
$198$	−1.12865	−0.0802099
$199$	7.66068	0.543051	0.271526	−	0.962431i	$-0.412472\pi$
$199$	7.66068	0.543051	0.271526	+	0.962431i	$0.412472\pi$
$200$	−2.39527	−0.169371
$201$	0.497297	0.0350766
$202$	−3.04864	−0.214502
$203$	25.2734	1.77384
$204$	9.77597	0.684455
$205$	5.96197	0.416402
$206$	4.78964	0.333710
$207$	−0.706167	−0.0490820
$208$	0	0
$209$	−3.78464	−0.261789
$210$	−3.29837	−0.227609
$211$	7.98160	0.549476	0.274738	−	0.961519i	$-0.411409\pi$
$211$	7.98160	0.549476	0.274738	+	0.961519i	$0.411409\pi$
$212$	−3.57244	−0.245356
$213$	−4.27400	−0.292850
$214$	1.63391	0.111692
$215$	9.82750	0.670230
$216$	12.9014	0.877829
$217$	−1.57444	−0.106880
$218$	−1.26102	−0.0854071
$219$	1.56982	0.106079
$220$	−1.54293	−0.104024
$221$	0	0
$222$	−3.66684	−0.246102
$223$	−12.3306	−0.825719	−0.412859	−	0.910795i	$-0.635470\pi$
$223$	−12.3306	−0.825719	−0.412859	+	0.910795i	$0.635470\pi$
$224$	−24.4549	−1.63396
$225$	−1.66943	−0.111296
$226$	−8.36705	−0.556568
$227$	10.2327	0.679168	0.339584	−	0.940576i	$-0.389714\pi$
$227$	10.2327	0.679168	0.339584	+	0.940576i	$0.389714\pi$
$228$	6.73580	0.446090
$229$	6.33736	0.418784	0.209392	−	0.977832i	$-0.432851\pi$
$229$	6.33736	0.418784	0.209392	+	0.977832i	$0.432851\pi$
$230$	0.285977	0.0188567
$231$	−4.87874	−0.320997
$232$	14.3129	0.939689
$233$	20.2746	1.32823	0.664116	−	0.747630i	$-0.268808\pi$
$233$	20.2746	1.32823	0.664116	+	0.747630i	$0.268808\pi$
$234$	0	0
$235$	−10.8258	−0.706199
$236$	−7.18568	−0.467748
$237$	−12.6581	−0.822234
$238$	15.7064	1.01809
$239$	−29.8160	−1.92864	−0.964319	−	0.264742i	$-0.914713\pi$
$239$	−29.8160	−1.92864	−0.964319	+	0.264742i	$0.914713\pi$
$240$	1.69160	0.109192
$241$	−14.9852	−0.965282	−0.482641	−	0.875818i	$-0.660322\pi$
$241$	−14.9852	−0.965282	−0.482641	+	0.875818i	$0.660322\pi$
$242$	0.676070	0.0434594
$243$	14.7690	0.947431
$244$	4.76676	0.305160
$245$	10.8887	0.695651
$246$	4.64944	0.296437
$247$	0	0
$248$	−0.891645	−0.0566195
$249$	17.8273	1.12976
$250$	0.676070	0.0427584
$251$	−2.98566	−0.188453	−0.0942267	−	0.995551i	$-0.530038\pi$
$251$	−2.98566	−0.188453	−0.0942267	+	0.995551i	$0.530038\pi$
$252$	−10.8944	−0.686284
$253$	0.422998	0.0265937
$254$	−13.1129	−0.822778
$255$	−6.33598	−0.396775
$256$	−9.32402	−0.582752
$257$	14.3635	0.895971	0.447985	−	0.894041i	$-0.352142\pi$
$257$	14.3635	0.895971	0.447985	+	0.894041i	$0.352142\pi$
$258$	7.66396	0.477137
$259$	19.8871	1.23572
$260$	0	0
$261$	9.97569	0.617479
$262$	8.52298	0.526552
$263$	7.23024	0.445836	0.222918	−	0.974837i	$-0.428442\pi$
$263$	7.23024	0.445836	0.222918	+	0.974837i	$0.428442\pi$
$264$	−2.76295	−0.170048
$265$	2.31536	0.142231
$266$	10.8220	0.663536
$267$	18.6722	1.14272
$268$	−0.665187	−0.0406328
$269$	−14.6557	−0.893573	−0.446786	−	0.894641i	$-0.647432\pi$
$269$	−14.6557	−0.893573	−0.446786	+	0.894641i	$0.647432\pi$
$270$	−3.64145	−0.221612
$271$	29.5085	1.79251	0.896257	−	0.443536i	$-0.146276\pi$
$271$	29.5085	1.79251	0.896257	+	0.443536i	$0.146276\pi$
$272$	−8.05517	−0.488416
$273$	0	0
$274$	−0.876799	−0.0529694
$275$	1.00000	0.0603023
$276$	−0.752841	−0.0453157
$277$	−25.1682	−1.51221	−0.756106	−	0.654449i	$-0.772901\pi$
$277$	−25.1682	−1.51221	−0.756106	+	0.654449i	$0.772901\pi$
$278$	12.1804	0.730531
$279$	−0.621451	−0.0372053
$280$	10.1308	0.605430
$281$	−9.39555	−0.560491	−0.280246	−	0.959928i	$-0.590416\pi$
$281$	−9.39555	−0.560491	−0.280246	+	0.959928i	$0.590416\pi$
$282$	−8.44250	−0.502743
$283$	−29.3745	−1.74613	−0.873067	−	0.487600i	$-0.837873\pi$
$283$	−29.3745	−1.74613	−0.873067	+	0.487600i	$0.837873\pi$
$284$	5.71692	0.339237
$285$	−4.36559	−0.258595
$286$	0	0
$287$	−25.2162	−1.48846
$288$	−9.65264	−0.568787
$289$	13.1711	0.774770
$290$	−4.03985	−0.237228
$291$	20.2610	1.18772
$292$	−2.09980	−0.122881
$293$	10.9355	0.638858	0.319429	−	0.947610i	$-0.396509\pi$
$293$	10.9355	0.638858	0.319429	+	0.947610i	$0.396509\pi$
$294$	8.49151	0.495235
$295$	4.65716	0.271151
$296$	11.2625	0.654621
$297$	−5.38620	−0.312539
$298$	−4.13878	−0.239753
$299$	0	0
$300$	−1.77977	−0.102755
$301$	−41.5654	−2.39579
$302$	−8.41984	−0.484507
$303$	−5.20155	−0.298821
$304$	−5.55014	−0.318322
$305$	−3.08942	−0.176900
$306$	6.19949	0.354401
$307$	17.8022	1.01603	0.508013	−	0.861350i	$-0.330380\pi$
$307$	17.8022	1.01603	0.508013	+	0.861350i	$0.330380\pi$
$308$	6.52582	0.371843
$309$	8.17203	0.464890
$310$	0.251669	0.0142938
$311$	21.7080	1.23095	0.615473	−	0.788158i	$-0.288965\pi$
$311$	21.7080	1.23095	0.615473	+	0.788158i	$0.288965\pi$
$312$	0	0
$313$	7.36948	0.416548	0.208274	−	0.978071i	$-0.433215\pi$
$313$	7.36948	0.416548	0.208274	+	0.978071i	$0.433215\pi$
$314$	3.80703	0.214843
$315$	7.06086	0.397835
$316$	16.9316	0.952475
$317$	25.1520	1.41268	0.706339	−	0.707874i	$-0.250346\pi$
$317$	25.1520	1.41268	0.706339	+	0.707874i	$0.250346\pi$
$318$	1.80563	0.101255
$319$	−5.97550	−0.334564
$320$	0.976047	0.0545627
$321$	2.78776	0.155598
$322$	−1.20954	−0.0674049
$323$	20.7884	1.15670
$324$	1.85876	0.103265
$325$	0	0
$326$	−4.53049	−0.250921
$327$	−2.15154	−0.118980
$328$	−14.2805	−0.788510
$329$	45.7878	2.52436
$330$	0.779848	0.0429292
$331$	5.71137	0.313926	0.156963	−	0.987605i	$-0.449830\pi$
$331$	5.71137	0.313926	0.156963	+	0.987605i	$0.449830\pi$
$332$	−23.8458	−1.30871
$333$	7.84966	0.430159
$334$	11.2829	0.617375
$335$	0.431119	0.0235546
$336$	−7.15462	−0.390317
$337$	15.4336	0.840723	0.420361	−	0.907357i	$-0.361903\pi$
$337$	15.4336	0.840723	0.420361	+	0.907357i	$0.361903\pi$
$338$	0	0
$339$	−14.2758	−0.775353
$340$	8.47504	0.459623
$341$	0.372253	0.0201586
$342$	4.27155	0.230979
$343$	−16.4471	−0.888061
$344$	−23.5395	−1.26917
$345$	0.487930	0.0262693
$346$	−1.22471	−0.0658407
$347$	−4.22394	−0.226753	−0.113377	−	0.993552i	$-0.536167\pi$
$347$	−4.22394	−0.226753	−0.113377	+	0.993552i	$0.536167\pi$
$348$	10.6350	0.570097
$349$	−1.87909	−0.100585	−0.0502926	−	0.998735i	$-0.516015\pi$
$349$	−1.87909	−0.100585	−0.0502926	+	0.998735i	$0.516015\pi$
$350$	−2.85944	−0.152843
$351$	0	0
$352$	5.78199	0.308181
$353$	11.8816	0.632394	0.316197	−	0.948694i	$-0.397594\pi$
$353$	11.8816	0.632394	0.316197	+	0.948694i	$0.397594\pi$
$354$	3.63188	0.193032
$355$	−3.70524	−0.196654
$356$	−24.9760	−1.32373
$357$	26.7980	1.41830
$358$	−1.40146	−0.0740695
$359$	0.455705	0.0240512	0.0120256	−	0.999928i	$-0.496172\pi$
$359$	0.455705	0.0240512	0.0120256	+	0.999928i	$0.496172\pi$
$360$	3.99874	0.210752
$361$	−4.67648	−0.246130
$362$	1.09229	0.0574095
$363$	1.15350	0.0605432
$364$	0	0
$365$	1.36092	0.0712336
$366$	−2.40928	−0.125935
$367$	29.3482	1.53196	0.765981	−	0.642863i	$-0.222253\pi$
$367$	29.3482	1.53196	0.765981	+	0.642863i	$0.222253\pi$
$368$	0.620323	0.0323366
$369$	−9.95311	−0.518138
$370$	−3.17888	−0.165262
$371$	−9.79282	−0.508418
$372$	−0.662525	−0.0343503
$373$	−25.3186	−1.31095	−0.655474	−	0.755218i	$-0.727531\pi$
$373$	−25.3186	−1.31095	−0.655474	+	0.755218i	$0.727531\pi$
$374$	−3.71353	−0.192022
$375$	1.15350	0.0595666
$376$	25.9307	1.33728
$377$	0	0
$378$	15.4015	0.792168
$379$	28.9019	1.48459	0.742296	−	0.670072i	$-0.233737\pi$
$379$	28.9019	1.48459	0.742296	+	0.670072i	$0.233737\pi$
$380$	5.83944	0.299557
$381$	−22.3731	−1.14621
$382$	−17.5377	−0.897306
$383$	21.9756	1.12290	0.561449	−	0.827511i	$-0.310244\pi$
$383$	21.9756	1.12290	0.561449	+	0.827511i	$0.310244\pi$
$384$	−12.5779	−0.641863
$385$	−4.22950	−0.215555
$386$	−4.52061	−0.230093
$387$	−16.4064	−0.833982
$388$	−27.1012	−1.37586
$389$	−4.61448	−0.233964	−0.116982	−	0.993134i	$-0.537322\pi$
$389$	−4.61448	−0.233964	−0.116982	+	0.993134i	$0.537322\pi$
$390$	0	0
$391$	−2.32345	−0.117502
$392$	−26.0813	−1.31730
$393$	14.5418	0.733537
$394$	15.8132	0.796658
$395$	−10.9737	−0.552144
$396$	2.57582	0.129440
$397$	33.3689	1.67474	0.837369	−	0.546638i	$-0.184093\pi$
$397$	33.3689	1.67474	0.837369	+	0.546638i	$0.184093\pi$
$398$	5.17916	0.259608
$399$	18.4643	0.924370
$400$	1.46649	0.0733245
$401$	37.5230	1.87381	0.936904	−	0.349587i	$-0.113678\pi$
$401$	37.5230	1.87381	0.936904	+	0.349587i	$0.113678\pi$
$402$	0.336208	0.0167685
$403$	0	0
$404$	6.95762	0.346154
$405$	−1.20470	−0.0598619
$406$	17.0866	0.847992
$407$	−4.70199	−0.233069
$408$	15.1764	0.751342
$409$	3.59487	0.177755	0.0888774	−	0.996043i	$-0.471672\pi$
$409$	3.59487	0.177755	0.0888774	+	0.996043i	$0.471672\pi$
$410$	4.03071	0.199063
$411$	−1.49598	−0.0737914
$412$	−10.9309	−0.538529
$413$	−19.6975	−0.969249
$414$	−0.477419	−0.0234638
$415$	15.4549	0.758651
$416$	0	0
$417$	20.7820	1.01770
$418$	−2.55868	−0.125149
$419$	−28.4516	−1.38995	−0.694976	−	0.719033i	$-0.744585\pi$
$419$	−28.4516	−1.38995	−0.694976	+	0.719033i	$0.744585\pi$
$420$	7.52755	0.367307
$421$	8.69745	0.423888	0.211944	−	0.977282i	$-0.432021\pi$
$421$	8.69745	0.423888	0.211944	+	0.977282i	$0.432021\pi$
$422$	5.39612	0.262679
$423$	18.0730	0.878738
$424$	−5.54591	−0.269333
$425$	−5.49282	−0.266441
$426$	−2.88952	−0.139998
$427$	13.0667	0.632342
$428$	−3.72892	−0.180244
$429$	0	0
$430$	6.64408	0.320406
$431$	−23.4080	−1.12752	−0.563762	−	0.825937i	$-0.690647\pi$
$431$	−23.4080	−1.12752	−0.563762	+	0.825937i	$0.690647\pi$
$432$	−7.89881	−0.380032
$433$	−2.21727	−0.106555	−0.0532776	−	0.998580i	$-0.516967\pi$
$433$	−2.21727	−0.106555	−0.0532776	+	0.998580i	$0.516967\pi$
$434$	−1.06443	−0.0510944
$435$	−6.89275	−0.330482
$436$	2.87791	0.137827
$437$	−1.60090	−0.0765813
$438$	1.06131	0.0507112
$439$	−36.4253	−1.73848	−0.869242	−	0.494387i	$-0.835392\pi$
$439$	−36.4253	−1.73848	−0.869242	+	0.494387i	$0.835392\pi$
$440$	−2.39527	−0.114190
$441$	−18.1779	−0.865614
$442$	0	0
$443$	−8.63539	−0.410280	−0.205140	−	0.978733i	$-0.565765\pi$
$443$	−8.63539	−0.410280	−0.205140	+	0.978733i	$0.565765\pi$
$444$	8.36848	0.397150
$445$	16.1874	0.767357
$446$	−8.33636	−0.394738
$447$	−7.06154	−0.333999
$448$	−4.12819	−0.195039
$449$	−31.1669	−1.47086	−0.735428	−	0.677603i	$-0.763019\pi$
$449$	−31.1669	−1.47086	−0.735428	+	0.677603i	$0.763019\pi$
$450$	−1.12865	−0.0532052
$451$	5.96197	0.280738
$452$	19.0953	0.898168
$453$	−14.3658	−0.674965
$454$	6.91802	0.324679
$455$	0	0
$456$	10.4568	0.489683
$457$	−3.76445	−0.176094	−0.0880468	−	0.996116i	$-0.528063\pi$
$457$	−3.76445	−0.176094	−0.0880468	+	0.996116i	$0.528063\pi$
$458$	4.28450	0.200201
$459$	29.5854	1.38093
$460$	−0.652657	−0.0304303
$461$	−9.31078	−0.433646	−0.216823	−	0.976211i	$-0.569570\pi$
$461$	−9.31078	−0.433646	−0.216823	+	0.976211i	$0.569570\pi$
$462$	−3.29837	−0.153454
$463$	34.3864	1.59807	0.799035	−	0.601284i	$-0.205344\pi$
$463$	34.3864	1.59807	0.799035	+	0.601284i	$0.205344\pi$
$464$	−8.76300	−0.406812
$465$	0.429394	0.0199127
$466$	13.7070	0.634966
$467$	3.77792	0.174821	0.0874106	−	0.996172i	$-0.472141\pi$
$467$	3.77792	0.174821	0.0874106	+	0.996172i	$0.472141\pi$
$468$	0	0
$469$	−1.82342	−0.0841977
$470$	−7.31901	−0.337601
$471$	6.49550	0.299297
$472$	−11.1552	−0.513458
$473$	9.82750	0.451869
$474$	−8.55778	−0.393072
$475$	−3.78464	−0.173651
$476$	−35.8452	−1.64296
$477$	−3.86534	−0.176982
$478$	−20.1577	−0.921993
$479$	14.7358	0.673297	0.336649	−	0.941630i	$-0.390707\pi$
$479$	14.7358	0.673297	0.336649	+	0.941630i	$0.390707\pi$
$480$	6.66953	0.304421
$481$	0	0
$482$	−10.1310	−0.461457
$483$	−2.06370	−0.0939015
$484$	−1.54293	−0.0701332
$485$	17.5648	0.797576
$486$	9.98486	0.452923
$487$	42.8837	1.94325	0.971624	−	0.236532i	$-0.0760108\pi$
$487$	42.8837	1.94325	0.971624	+	0.236532i	$0.0760108\pi$
$488$	7.39999	0.334982
$489$	−7.72987	−0.349557
$490$	7.36150	0.332559
$491$	−7.34766	−0.331595	−0.165798	−	0.986160i	$-0.553020\pi$
$491$	−7.34766	−0.331595	−0.165798	+	0.986160i	$0.553020\pi$
$492$	−10.6110	−0.478379
$493$	32.8223	1.47824
$494$	0	0
$495$	−1.66943	−0.0750354
$496$	0.545905	0.0245119
$497$	15.6713	0.702954
$498$	12.0525	0.540084
$499$	36.7452	1.64494	0.822470	−	0.568809i	$-0.192596\pi$
$499$	36.7452	1.64494	0.822470	+	0.568809i	$0.192596\pi$
$500$	−1.54293	−0.0690019
$501$	19.2508	0.860063
$502$	−2.01852	−0.0900908
$503$	−3.38063	−0.150735	−0.0753675	−	0.997156i	$-0.524013\pi$
$503$	−3.38063	−0.150735	−0.0753675	+	0.997156i	$0.524013\pi$
$504$	−16.9127	−0.753350
$505$	−4.50936	−0.200664
$506$	0.285977	0.0127132
$507$	0	0
$508$	29.9263	1.32777
$509$	−14.0285	−0.621801	−0.310901	−	0.950442i	$-0.600631\pi$
$509$	−14.0285	−0.621801	−0.310901	+	0.950442i	$0.600631\pi$
$510$	−4.28357	−0.189680
$511$	−5.75599	−0.254630
$512$	15.5045	0.685209
$513$	20.3848	0.900013
$514$	9.71073	0.428322
$515$	7.08453	0.312182
$516$	−17.4907	−0.769986
$517$	−10.8258	−0.476119
$518$	13.4451	0.590742
$519$	−2.08958	−0.0917225
$520$	0	0
$521$	38.1528	1.67151	0.835753	−	0.549106i	$-0.185032\pi$
$521$	38.1528	1.67151	0.835753	+	0.549106i	$0.185032\pi$
$522$	6.74426	0.295188
$523$	23.2722	1.01762	0.508812	−	0.860878i	$-0.330085\pi$
$523$	23.2722	1.01762	0.508812	+	0.860878i	$0.330085\pi$
$524$	−19.4512	−0.849729
$525$	−4.87874	−0.212926
$526$	4.88815	0.213133
$527$	−2.04472	−0.0890693
$528$	1.69160	0.0736174
$529$	−22.8211	−0.992221
$530$	1.56535	0.0679943
$531$	−7.77482	−0.337399
$532$	−24.6979	−1.07079
$533$	0	0
$534$	12.6237	0.546282
$535$	2.41678	0.104486
$536$	−1.03265	−0.0446035
$537$	−2.39115	−0.103186
$538$	−9.90827	−0.427176
$539$	10.8887	0.469008
$540$	8.31053	0.357628
$541$	−32.2447	−1.38631	−0.693154	−	0.720790i	$-0.743779\pi$
$541$	−32.2447	−1.38631	−0.693154	+	0.720790i	$0.743779\pi$
$542$	19.9498	0.856917
$543$	1.86365	0.0799770
$544$	−31.7594	−1.36167
$545$	−1.86522	−0.0798974
$546$	0	0
$547$	−43.5448	−1.86184	−0.930921	−	0.365222i	$-0.880993\pi$
$547$	−43.5448	−1.86184	−0.930921	+	0.365222i	$0.880993\pi$
$548$	2.00103	0.0854799
$549$	5.15758	0.220120
$550$	0.676070	0.0288277
$551$	22.6151	0.963436
$552$	−1.16872	−0.0497441
$553$	46.4131	1.97368
$554$	−17.0155	−0.722919
$555$	−5.42376	−0.230226
$556$	−27.7981	−1.17890
$557$	10.0780	0.427019	0.213509	−	0.976941i	$-0.431511\pi$
$557$	10.0780	0.427019	0.213509	+	0.976941i	$0.431511\pi$
$558$	−0.420144	−0.0177861
$559$	0	0
$560$	−6.20252	−0.262104
$561$	−6.33598	−0.267505
$562$	−6.35205	−0.267945
$563$	−18.5259	−0.780775	−0.390388	−	0.920651i	$-0.627659\pi$
$563$	−18.5259	−0.780775	−0.390388	+	0.920651i	$0.627659\pi$
$564$	19.2675	0.811308
$565$	−12.3760	−0.520663
$566$	−19.8592	−0.834746
$567$	5.09527	0.213981
$568$	8.87503	0.372388
$569$	−18.1241	−0.759802	−0.379901	−	0.925027i	$-0.624042\pi$
$569$	−18.1241	−0.759802	−0.379901	+	0.925027i	$0.624042\pi$
$570$	−2.95145	−0.123623
$571$	−2.61277	−0.109341	−0.0546704	−	0.998504i	$-0.517411\pi$
$571$	−2.61277	−0.109341	−0.0546704	+	0.998504i	$0.517411\pi$
$572$	0	0
$573$	−29.9226	−1.25003
$574$	−17.0479	−0.711565
$575$	0.422998	0.0176403
$576$	−1.62944	−0.0678935
$577$	−21.2343	−0.883995	−0.441998	−	0.897016i	$-0.645730\pi$
$577$	−21.2343	−0.883995	−0.441998	+	0.897016i	$0.645730\pi$
$578$	8.90457	0.370381
$579$	−7.71301	−0.320542
$580$	9.21977	0.382830
$581$	−65.3665	−2.71186
$582$	13.6979	0.567795
$583$	2.31536	0.0958924
$584$	−3.25976	−0.134890
$585$	0	0
$586$	7.39316	0.305408
$587$	−19.9086	−0.821715	−0.410857	−	0.911700i	$-0.634771\pi$
$587$	−19.9086	−0.821715	−0.410857	+	0.911700i	$0.634771\pi$
$588$	−19.3794	−0.799191
$589$	−1.40884	−0.0580504
$590$	3.14857	0.129625
$591$	26.9803	1.10982
$592$	−6.89543	−0.283400
$593$	−38.6914	−1.58887	−0.794433	−	0.607352i	$-0.792232\pi$
$593$	−38.6914	−1.58887	−0.794433	+	0.607352i	$0.792232\pi$
$594$	−3.64145	−0.149410
$595$	23.2319	0.952414
$596$	9.44555	0.386905
$597$	8.83661	0.361659
$598$	0	0
$599$	20.4687	0.836330	0.418165	−	0.908371i	$-0.362673\pi$
$599$	20.4687	0.836330	0.418165	+	0.908371i	$0.362673\pi$
$600$	−2.76295	−0.112797
$601$	26.6153	1.08566	0.542831	−	0.839842i	$-0.317352\pi$
$601$	26.6153	1.08566	0.542831	+	0.839842i	$0.317352\pi$
$602$	−28.1011	−1.14532
$603$	−0.719725	−0.0293095
$604$	19.2158	0.781879
$605$	1.00000	0.0406558
$606$	−3.51661	−0.142853
$607$	6.60457	0.268071	0.134036	−	0.990977i	$-0.457206\pi$
$607$	6.60457	0.268071	0.134036	+	0.990977i	$0.457206\pi$
$608$	−21.8828	−0.887463
$609$	29.1529	1.18133
$610$	−2.08866	−0.0845675
$611$	0	0
$612$	−14.1485	−0.571919
$613$	10.6223	0.429029	0.214515	−	0.976721i	$-0.431183\pi$
$613$	10.6223	0.429029	0.214515	+	0.976721i	$0.431183\pi$
$614$	12.0355	0.485714
$615$	6.87715	0.277313
$616$	10.1308	0.408181
$617$	19.9578	0.803472	0.401736	−	0.915756i	$-0.368407\pi$
$617$	19.9578	0.803472	0.401736	+	0.915756i	$0.368407\pi$
$618$	5.52486	0.222242
$619$	−40.4667	−1.62650	−0.813248	−	0.581918i	$-0.802303\pi$
$619$	−40.4667	−1.62650	−0.813248	+	0.581918i	$0.802303\pi$
$620$	−0.574360	−0.0230668
$621$	−2.27835	−0.0914272
$622$	14.6761	0.588459
$623$	−68.4647	−2.74298
$624$	0	0
$625$	1.00000	0.0400000
$626$	4.98228	0.199132
$627$	−4.36559	−0.174345
$628$	−8.68841	−0.346705
$629$	25.8272	1.02980
$630$	4.77364	0.190186
$631$	1.04621	0.0416490	0.0208245	−	0.999783i	$-0.493371\pi$
$631$	1.04621	0.0416490	0.0208245	+	0.999783i	$0.493371\pi$
$632$	26.2848	1.04555
$633$	9.20679	0.365937
$634$	17.0045	0.675336
$635$	−19.3958	−0.769699
$636$	−4.12082	−0.163401
$637$	0	0
$638$	−4.03985	−0.159939
$639$	6.18564	0.244700
$640$	−10.9041	−0.431022
$641$	−29.1017	−1.14945	−0.574724	−	0.818347i	$-0.694891\pi$
$641$	−29.1017	−1.14945	−0.574724	+	0.818347i	$0.694891\pi$
$642$	1.88472	0.0743840
$643$	27.8017	1.09639	0.548196	−	0.836350i	$-0.315315\pi$
$643$	27.8017	1.09639	0.548196	+	0.836350i	$0.315315\pi$
$644$	2.76041	0.108775
$645$	11.3360	0.446356
$646$	14.0544	0.552963
$647$	−38.4851	−1.51301	−0.756503	−	0.653990i	$-0.773094\pi$
$647$	−38.4851	−1.51301	−0.756503	+	0.653990i	$0.773094\pi$
$648$	2.88557	0.113356
$649$	4.65716	0.182810
$650$	0	0
$651$	−1.81612	−0.0711795
$652$	10.3395	0.404926
$653$	13.0070	0.509002	0.254501	−	0.967072i	$-0.418089\pi$
$653$	13.0070	0.509002	0.254501	+	0.967072i	$0.418089\pi$
$654$	−1.45459	−0.0568790
$655$	12.6067	0.492583
$656$	8.74318	0.341364
$657$	−2.27196	−0.0886375
$658$	30.9558	1.20678
$659$	−41.7397	−1.62595	−0.812974	−	0.582300i	$-0.802153\pi$
$659$	−41.7397	−1.62595	−0.812974	+	0.582300i	$0.802153\pi$
$660$	−1.77977	−0.0692776
$661$	−12.7520	−0.495997	−0.247998	−	0.968760i	$-0.579773\pi$
$661$	−12.7520	−0.495997	−0.247998	+	0.968760i	$0.579773\pi$
$662$	3.86129	0.150073
$663$	0	0
$664$	−37.0186	−1.43660
$665$	16.0071	0.620731
$666$	5.30692	0.205639
$667$	−2.52763	−0.0978700
$668$	−25.7500	−0.996297
$669$	−14.2234	−0.549908
$670$	0.291467	0.0112603
$671$	−3.08942	−0.119266
$672$	−28.2088	−1.08818
$673$	−20.2732	−0.781475	−0.390737	−	0.920502i	$-0.627780\pi$
$673$	−20.2732	−0.781475	−0.390737	+	0.920502i	$0.627780\pi$
$674$	10.4342	0.401911
$675$	−5.38620	−0.207315
$676$	0	0
$677$	−25.4567	−0.978380	−0.489190	−	0.872177i	$-0.662708\pi$
$677$	−25.4567	−0.978380	−0.489190	+	0.872177i	$0.662708\pi$
$678$	−9.65141	−0.370660
$679$	−74.2902	−2.85100
$680$	13.1568	0.504539
$681$	11.8034	0.452309
$682$	0.251669	0.00963690
$683$	−11.6295	−0.444989	−0.222495	−	0.974934i	$-0.571420\pi$
$683$	−11.6295	−0.444989	−0.222495	+	0.974934i	$0.571420\pi$
$684$	−9.74855	−0.372745
$685$	−1.29691	−0.0495522
$686$	−11.1194	−0.424541
$687$	7.31016	0.278900
$688$	14.4119	0.549450
$689$	0	0
$690$	0.329875	0.0125581
$691$	37.6651	1.43285	0.716424	−	0.697665i	$-0.245778\pi$
$691$	37.6651	1.43285	0.716424	+	0.697665i	$0.245778\pi$
$692$	2.79503	0.106251
$693$	7.06086	0.268220
$694$	−2.85568	−0.108400
$695$	18.0165	0.683403
$696$	16.5100	0.625809
$697$	−32.7481	−1.24042
$698$	−1.27039	−0.0480851
$699$	23.3868	0.884568
$700$	6.52582	0.246653
$701$	−18.7118	−0.706737	−0.353368	−	0.935484i	$-0.614964\pi$
$701$	−18.7118	−0.706737	−0.353368	+	0.935484i	$0.614964\pi$
$702$	0	0
$703$	17.7954	0.671165
$704$	0.976047	0.0367861
$705$	−12.4876	−0.470311
$706$	8.03280	0.302318
$707$	19.0723	0.717288
$708$	−8.28869	−0.311508
$709$	34.8970	1.31058	0.655292	−	0.755375i	$-0.272545\pi$
$709$	34.8970	1.31058	0.655292	+	0.755375i	$0.272545\pi$
$710$	−2.50500	−0.0940109
$711$	18.3198	0.687045
$712$	−38.7732	−1.45309
$713$	0.157462	0.00589701
$714$	18.1173	0.678025
$715$	0	0
$716$	3.19842	0.119531
$717$	−34.3929	−1.28442
$718$	0.308089	0.0114978
$719$	23.4439	0.874311	0.437155	−	0.899386i	$-0.355986\pi$
$719$	23.4439	0.874311	0.437155	+	0.899386i	$0.355986\pi$
$720$	−2.44821	−0.0912393
$721$	−29.9640	−1.11592
$722$	−3.16163	−0.117664
$723$	−17.2855	−0.642854
$724$	−2.49283	−0.0926453
$725$	−5.97550	−0.221924
$726$	0.779848	0.0289429
$727$	0.492442	0.0182637	0.00913183	−	0.999958i	$-0.497093\pi$
$727$	0.492442	0.0182637	0.00913183	+	0.999958i	$0.497093\pi$
$728$	0	0
$729$	20.6501	0.764820
$730$	0.920074	0.0340535
$731$	−53.9807	−1.99655
$732$	5.49847	0.203229
$733$	−36.6922	−1.35526	−0.677628	−	0.735405i	$-0.736992\pi$
$733$	−36.6922	−1.35526	−0.677628	+	0.735405i	$0.736992\pi$
$734$	19.8414	0.732360
$735$	12.5601	0.463286
$736$	2.44577	0.0901523
$737$	0.431119	0.0158805
$738$	−6.72900	−0.247698
$739$	−36.5957	−1.34620	−0.673098	−	0.739553i	$-0.735037\pi$
$739$	−36.5957	−1.34620	−0.673098	+	0.739553i	$0.735037\pi$
$740$	7.25484	0.266693
$741$	0	0
$742$	−6.62063	−0.243051
$743$	−33.5036	−1.22913	−0.614564	−	0.788867i	$-0.710668\pi$
$743$	−33.5036	−1.22913	−0.614564	+	0.788867i	$0.710668\pi$
$744$	−1.02851	−0.0377072
$745$	−6.12183	−0.224286
$746$	−17.1171	−0.626703
$747$	−25.8009	−0.944006
$748$	8.47504	0.309878
$749$	−10.2218	−0.373495
$750$	0.779848	0.0284760
$751$	1.42960	0.0521669	0.0260835	−	0.999660i	$-0.491696\pi$
$751$	1.42960	0.0521669	0.0260835	+	0.999660i	$0.491696\pi$
$752$	−15.8760	−0.578937
$753$	−3.44397	−0.125505
$754$	0	0
$755$	−12.4541	−0.453251
$756$	−35.1494	−1.27837
$757$	−3.32507	−0.120852	−0.0604258	−	0.998173i	$-0.519246\pi$
$757$	−3.32507	−0.120852	−0.0604258	+	0.998173i	$0.519246\pi$
$758$	19.5397	0.709714
$759$	0.487930	0.0177107
$760$	9.06523	0.328831
$761$	18.1121	0.656565	0.328282	−	0.944580i	$-0.393530\pi$
$761$	18.1121	0.656565	0.328282	+	0.944580i	$0.393530\pi$
$762$	−15.1258	−0.547949
$763$	7.88896	0.285599
$764$	40.0246	1.44804
$765$	9.16989	0.331538
$766$	14.8570	0.536806
$767$	0	0
$768$	−10.7553	−0.388098
$769$	50.8749	1.83460	0.917298	−	0.398201i	$-0.130365\pi$
$769$	50.8749	1.83460	0.917298	+	0.398201i	$0.130365\pi$
$770$	−2.85944	−0.103047
$771$	16.5683	0.596694
$772$	10.3170	0.371316
$773$	−4.09629	−0.147333	−0.0736666	−	0.997283i	$-0.523470\pi$
$773$	−4.09629	−0.147333	−0.0736666	+	0.997283i	$0.523470\pi$
$774$	−11.0918	−0.398688
$775$	0.372253	0.0133717
$776$	−42.0724	−1.51031
$777$	22.9398	0.822960
$778$	−3.11971	−0.111847
$779$	−22.5639	−0.808437
$780$	0	0
$781$	−3.70524	−0.132584
$782$	−1.57082	−0.0561723
$783$	32.1852	1.15021
$784$	15.9681	0.570290
$785$	5.63111	0.200983
$786$	9.83128	0.350670
$787$	19.4736	0.694158	0.347079	−	0.937836i	$-0.387173\pi$
$787$	19.4736	0.694158	0.347079	+	0.937836i	$0.387173\pi$
$788$	−36.0890	−1.28562
$789$	8.34010	0.296915
$790$	−7.41896	−0.263955
$791$	52.3443	1.86115
$792$	3.99874	0.142089
$793$	0	0
$794$	22.5597	0.800614
$795$	2.67077	0.0947226
$796$	−11.8199	−0.418945
$797$	13.3398	0.472519	0.236259	−	0.971690i	$-0.424079\pi$
$797$	13.3398	0.472519	0.236259	+	0.971690i	$0.424079\pi$
$798$	12.4831	0.441899
$799$	59.4643	2.10370
$800$	5.78199	0.204424
$801$	−27.0238	−0.954839
$802$	25.3682	0.895781
$803$	1.36092	0.0480257
$804$	−0.767295	−0.0270604
$805$	−1.78907	−0.0630565
$806$	0	0
$807$	−16.9054	−0.595097
$808$	10.8011	0.379982
$809$	35.0573	1.23255	0.616274	−	0.787532i	$-0.288642\pi$
$809$	35.0573	1.23255	0.616274	+	0.787532i	$0.288642\pi$
$810$	−0.814460	−0.0286172
$811$	0.339698	0.0119284	0.00596421	−	0.999982i	$-0.498102\pi$
$811$	0.339698	0.0119284	0.00596421	+	0.999982i	$0.498102\pi$
$812$	−38.9950	−1.36846
$813$	34.0381	1.19377
$814$	−3.17888	−0.111420
$815$	−6.70122	−0.234733
$816$	−9.29165	−0.325273
$817$	−37.1936	−1.30124
$818$	2.43038	0.0849764
$819$	0	0
$820$	−9.19891	−0.321240
$821$	4.23372	0.147758	0.0738790	−	0.997267i	$-0.476462\pi$
$821$	4.23372	0.147758	0.0738790	+	0.997267i	$0.476462\pi$
$822$	−1.01139	−0.0352763
$823$	27.4813	0.957937	0.478969	−	0.877832i	$-0.341011\pi$
$823$	27.4813	0.957937	0.478969	+	0.877832i	$0.341011\pi$
$824$	−16.9694	−0.591156
$825$	1.15350	0.0401598
$826$	−13.3169	−0.463353
$827$	−10.4452	−0.363215	−0.181608	−	0.983371i	$-0.558130\pi$
$827$	−10.4452	−0.363215	−0.181608	+	0.983371i	$0.558130\pi$
$828$	1.08957	0.0378651
$829$	−48.5054	−1.68466	−0.842330	−	0.538961i	$-0.818817\pi$
$829$	−48.5054	−1.68466	−0.842330	+	0.538961i	$0.818817\pi$
$830$	10.4486	0.362676
$831$	−29.0316	−1.00710
$832$	0	0
$833$	−59.8095	−2.07228
$834$	14.0501	0.486515
$835$	16.6890	0.577547
$836$	5.83944	0.201961
$837$	−2.00503	−0.0693039
$838$	−19.2353	−0.664472
$839$	−34.8814	−1.20424	−0.602120	−	0.798406i	$-0.705677\pi$
$839$	−34.8814	−1.20424	−0.602120	+	0.798406i	$0.705677\pi$
$840$	11.6859	0.403201
$841$	6.70654	0.231260
$842$	5.88009	0.202641
$843$	−10.8378	−0.373273
$844$	−12.3150	−0.423901
$845$	0	0
$846$	12.2186	0.420084
$847$	−4.22950	−0.145327
$848$	3.39545	0.116600
$849$	−33.8836	−1.16288
$850$	−3.71353	−0.127373
$851$	−1.98894	−0.0681798
$852$	6.59448	0.225923
$853$	−3.13108	−0.107206	−0.0536030	−	0.998562i	$-0.517071\pi$
$853$	−3.13108	−0.107206	−0.0536030	+	0.998562i	$0.517071\pi$
$854$	8.83400	0.302293
$855$	6.31821	0.216078
$856$	−5.78883	−0.197858
$857$	−17.0323	−0.581812	−0.290906	−	0.956752i	$-0.593957\pi$
$857$	−17.0323	−0.581812	−0.290906	+	0.956752i	$0.593957\pi$
$858$	0	0
$859$	43.0926	1.47030	0.735150	−	0.677904i	$-0.237112\pi$
$859$	43.0926	1.47030	0.735150	+	0.677904i	$0.237112\pi$
$860$	−15.1631	−0.517059
$861$	−29.0869	−0.991279
$862$	−15.8255	−0.539017
$863$	2.29209	0.0780235	0.0390118	−	0.999239i	$-0.487579\pi$
$863$	2.29209	0.0780235	0.0390118	+	0.999239i	$0.487579\pi$
$864$	−31.1429	−1.05950
$865$	−1.81151	−0.0615932
$866$	−1.49903	−0.0509391
$867$	15.1929	0.515977
$868$	2.42925	0.0824542
$869$	−10.9737	−0.372256
$870$	−4.65998	−0.157988
$871$	0	0
$872$	4.46771	0.151296
$873$	−29.3232	−0.992441
$874$	−1.08232	−0.0366100
$875$	−4.22950	−0.142983
$876$	−2.42212	−0.0818358
$877$	−1.73862	−0.0587090	−0.0293545	−	0.999569i	$-0.509345\pi$
$877$	−1.73862	−0.0587090	−0.0293545	+	0.999569i	$0.509345\pi$
$878$	−24.6260	−0.831088
$879$	12.6141	0.425463
$880$	1.46649	0.0494354
$881$	53.5576	1.80440	0.902201	−	0.431315i	$-0.141950\pi$
$881$	53.5576	1.80440	0.902201	+	0.431315i	$0.141950\pi$
$882$	−12.2895	−0.413810
$883$	5.95369	0.200358	0.100179	−	0.994969i	$-0.468059\pi$
$883$	5.95369	0.200358	0.100179	+	0.994969i	$0.468059\pi$
$884$	0	0
$885$	5.37205	0.180579
$886$	−5.83813	−0.196136
$887$	−33.9268	−1.13915	−0.569575	−	0.821939i	$-0.692892\pi$
$887$	−33.9268	−1.13915	−0.569575	+	0.821939i	$0.692892\pi$
$888$	12.9914	0.435961
$889$	82.0345	2.75135
$890$	10.9438	0.366838
$891$	−1.20470	−0.0403589
$892$	19.0253	0.637013
$893$	40.9719	1.37107
$894$	−4.77409	−0.159670
$895$	−2.07295	−0.0692911
$896$	46.1189	1.54072
$897$	0	0
$898$	−21.0710	−0.703148
$899$	−2.22439	−0.0741877
$900$	2.57582	0.0858606
$901$	−12.7179	−0.423693
$902$	4.03071	0.134208
$903$	−47.9458	−1.59554
$904$	29.6439	0.985941
$905$	1.61565	0.0537060
$906$	−9.71230	−0.322670
$907$	−42.3042	−1.40469	−0.702344	−	0.711838i	$-0.747863\pi$
$907$	−42.3042	−1.40469	−0.702344	+	0.711838i	$0.747863\pi$
$908$	−15.7883	−0.523954
$909$	7.52807	0.249690
$910$	0	0
$911$	1.83800	0.0608956	0.0304478	−	0.999536i	$-0.490307\pi$
$911$	1.83800	0.0608956	0.0304478	+	0.999536i	$0.490307\pi$
$912$	−6.40210	−0.211995
$913$	15.4549	0.511482
$914$	−2.54503	−0.0841822
$915$	−3.56365	−0.117811
$916$	−9.77810	−0.323077
$917$	−53.3199	−1.76078
$918$	20.0018	0.660159
$919$	5.01610	0.165466	0.0827330	−	0.996572i	$-0.473635\pi$
$919$	5.01610	0.165466	0.0827330	+	0.996572i	$0.473635\pi$
$920$	−1.01319	−0.0334040
$921$	20.5349	0.676647
$922$	−6.29474	−0.207306
$923$	0	0
$924$	7.52755	0.247638
$925$	−4.70199	−0.154601
$926$	23.2476	0.763963
$927$	−11.8272	−0.388455
$928$	−34.5502	−1.13417
$929$	−25.9211	−0.850443	−0.425222	−	0.905089i	$-0.639804\pi$
$929$	−25.9211	−0.850443	−0.425222	+	0.905089i	$0.639804\pi$
$930$	0.290301	0.00951933
$931$	−41.2097	−1.35059
$932$	−31.2822	−1.02468
$933$	25.0402	0.819780
$934$	2.55414	0.0835739
$935$	−5.49282	−0.179634
$936$	0	0
$937$	−8.81499	−0.287973	−0.143987	−	0.989580i	$-0.545992\pi$
$937$	−8.81499	−0.287973	−0.143987	+	0.989580i	$0.545992\pi$
$938$	−1.23276	−0.0402510
$939$	8.50071	0.277410
$940$	16.7035	0.544807
$941$	6.90735	0.225173	0.112587	−	0.993642i	$-0.464086\pi$
$941$	6.90735	0.225173	0.112587	+	0.993642i	$0.464086\pi$
$942$	4.39141	0.143080
$943$	2.52191	0.0821246
$944$	6.82969	0.222287
$945$	22.7809	0.741064
$946$	6.64408	0.216018
$947$	−4.78221	−0.155401	−0.0777005	−	0.996977i	$-0.524758\pi$
$947$	−4.78221	−0.155401	−0.0777005	+	0.996977i	$0.524758\pi$
$948$	19.5306	0.634325
$949$	0	0
$950$	−2.55868	−0.0830146
$951$	29.0129	0.940808
$952$	−55.6466	−1.80352
$953$	35.1931	1.14002	0.570009	−	0.821639i	$-0.306940\pi$
$953$	35.1931	1.14002	0.570009	+	0.821639i	$0.306940\pi$
$954$	−2.61324	−0.0846067
$955$	−25.9406	−0.839419
$956$	46.0040	1.48788
$957$	−6.89275	−0.222811
$958$	9.96245	0.321872
$959$	5.48526	0.177128
$960$	1.12587	0.0363374
$961$	−30.8614	−0.995530
$962$	0	0
$963$	−4.03465	−0.130015
$964$	23.1211	0.744681
$965$	−6.68661	−0.215249
$966$	−1.39520	−0.0448900
$967$	17.1642	0.551965	0.275982	−	0.961163i	$-0.410997\pi$
$967$	17.1642	0.551965	0.275982	+	0.961163i	$0.410997\pi$
$968$	−2.39527	−0.0769868
$969$	23.9794	0.770330
$970$	11.8750	0.381284
$971$	47.1989	1.51468	0.757342	−	0.653018i	$-0.226497\pi$
$971$	47.1989	1.51468	0.757342	+	0.653018i	$0.226497\pi$
$972$	−22.7875	−0.730909
$973$	−76.2006	−2.44288
$974$	28.9924	0.928976
$975$	0	0
$976$	−4.53060	−0.145021
$977$	−14.8802	−0.476060	−0.238030	−	0.971258i	$-0.576502\pi$
$977$	−14.8802	−0.476060	−0.238030	+	0.971258i	$0.576502\pi$
$978$	−5.22593	−0.167107
$979$	16.1874	0.517352
$980$	−16.8004	−0.536671
$981$	3.11386	0.0994180
$982$	−4.96753	−0.158520
$983$	43.8833	1.39966	0.699830	−	0.714310i	$-0.253259\pi$
$983$	43.8833	1.39966	0.699830	+	0.714310i	$0.253259\pi$
$984$	−16.4726	−0.525128
$985$	23.3899	0.745265
$986$	22.1902	0.706680
$987$	52.8163	1.68116
$988$	0	0
$989$	4.15702	0.132186
$990$	−1.12865	−0.0358710
$991$	−9.09001	−0.288754	−0.144377	−	0.989523i	$-0.546118\pi$
$991$	−9.09001	−0.288754	−0.144377	+	0.989523i	$0.546118\pi$
$992$	2.15236	0.0683375
$993$	6.58808	0.209066
$994$	10.5949	0.336050
$995$	7.66068	0.242860
$996$	−27.5062	−0.871567
$997$	45.1648	1.43038	0.715192	−	0.698928i	$-0.246339\pi$
$997$	45.1648	1.43038	0.715192	+	0.698928i	$0.246339\pi$
$998$	24.8423	0.786369
$999$	25.3259	0.801275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9295.2.a.bn.1.17	yes	33
13.12	even	2		9295.2.a.bm.1.17	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9295.2.a.bm.1.17	✓	33	13.12	even	2
9295.2.a.bn.1.17	yes	33	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9295 = 5 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9295.a (trivial)

\(f(q)\)	\(=\)	\(q+0.676070 q^{2} +1.15350 q^{3} -1.54293 q^{4} +1.00000 q^{5} +0.779848 q^{6} -4.22950 q^{7} -2.39527 q^{8} -1.66943 q^{9} +O(q^{10})\)	\(q+0.676070 q^{2} +1.15350 q^{3} -1.54293 q^{4} +1.00000 q^{5} +0.779848 q^{6} -4.22950 q^{7} -2.39527 q^{8} -1.66943 q^{9} +0.676070 q^{10} +1.00000 q^{11} -1.77977 q^{12} -2.85944 q^{14} +1.15350 q^{15} +1.46649 q^{16} -5.49282 q^{17} -1.12865 q^{18} -3.78464 q^{19} -1.54293 q^{20} -4.87874 q^{21} +0.676070 q^{22} +0.422998 q^{23} -2.76295 q^{24} +1.00000 q^{25} -5.38620 q^{27} +6.52582 q^{28} -5.97550 q^{29} +0.779848 q^{30} +0.372253 q^{31} +5.78199 q^{32} +1.15350 q^{33} -3.71353 q^{34} -4.22950 q^{35} +2.57582 q^{36} -4.70199 q^{37} -2.55868 q^{38} -2.39527 q^{40} +5.96197 q^{41} -3.29837 q^{42} +9.82750 q^{43} -1.54293 q^{44} -1.66943 q^{45} +0.285977 q^{46} -10.8258 q^{47} +1.69160 q^{48} +10.8887 q^{49} +0.676070 q^{50} -6.33598 q^{51} +2.31536 q^{53} -3.64145 q^{54} +1.00000 q^{55} +10.1308 q^{56} -4.36559 q^{57} -4.03985 q^{58} +4.65716 q^{59} -1.77977 q^{60} -3.08942 q^{61} +0.251669 q^{62} +7.06086 q^{63} +0.976047 q^{64} +0.779848 q^{66} +0.431119 q^{67} +8.47504 q^{68} +0.487930 q^{69} -2.85944 q^{70} -3.70524 q^{71} +3.99874 q^{72} +1.36092 q^{73} -3.17888 q^{74} +1.15350 q^{75} +5.83944 q^{76} -4.22950 q^{77} -10.9737 q^{79} +1.46649 q^{80} -1.20470 q^{81} +4.03071 q^{82} +15.4549 q^{83} +7.52755 q^{84} -5.49282 q^{85} +6.64408 q^{86} -6.89275 q^{87} -2.39527 q^{88} +16.1874 q^{89} -1.12865 q^{90} -0.652657 q^{92} +0.429394 q^{93} -7.31901 q^{94} -3.78464 q^{95} +6.66953 q^{96} +17.5648 q^{97} +7.36150 q^{98} -1.66943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9}+O(q^{10}) \) 33 * q + 8 * q^2 + 12 * q^3 + 38 * q^4 + 33 * q^5 + 18 * q^6 + 4 * q^7 + 21 * q^8 + 35 * q^9	\( 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9} + 8 q^{10} + 33 q^{11} + 24 q^{12} - 5 q^{14} + 12 q^{15} + 44 q^{16} + 9 q^{17} + 18 q^{18} + 8 q^{19} + 38 q^{20} + 9 q^{21} + 8 q^{22} + 7 q^{23} + 54 q^{24} + 33 q^{25} + 42 q^{27} + 15 q^{28} - 11 q^{29} + 18 q^{30} + 13 q^{31} + 85 q^{32} + 12 q^{33} + 31 q^{34} + 4 q^{35} + 26 q^{36} + 22 q^{37} - 2 q^{38} + 21 q^{40} + 36 q^{41} + 11 q^{42} + 26 q^{43} + 38 q^{44} + 35 q^{45} - q^{46} + 46 q^{47} + 36 q^{48} + 29 q^{49} + 8 q^{50} - 41 q^{51} + 9 q^{53} + 70 q^{54} + 33 q^{55} - 10 q^{56} + 70 q^{57} - 23 q^{58} + 18 q^{59} + 24 q^{60} - 42 q^{61} - 24 q^{62} + 68 q^{63} + 39 q^{64} + 18 q^{66} + 26 q^{67} + 8 q^{68} + 12 q^{69} - 5 q^{70} + 43 q^{71} + 46 q^{72} + 21 q^{73} - 22 q^{74} + 12 q^{75} + 2 q^{76} + 4 q^{77} - 22 q^{79} + 44 q^{80} + 41 q^{81} + 156 q^{82} + 26 q^{83} + 11 q^{84} + 9 q^{85} + 17 q^{86} - 30 q^{87} + 21 q^{88} + 95 q^{89} + 18 q^{90} + 37 q^{92} + 62 q^{93} - 14 q^{94} + 8 q^{95} + 53 q^{96} + 40 q^{97} + 132 q^{98} + 35 q^{99}+O(q^{100}) \) 33 * q + 8 * q^2 + 12 * q^3 + 38 * q^4 + 33 * q^5 + 18 * q^6 + 4 * q^7 + 21 * q^8 + 35 * q^9 + 8 * q^10 + 33 * q^11 + 24 * q^12 - 5 * q^14 + 12 * q^15 + 44 * q^16 + 9 * q^17 + 18 * q^18 + 8 * q^19 + 38 * q^20 + 9 * q^21 + 8 * q^22 + 7 * q^23 + 54 * q^24 + 33 * q^25 + 42 * q^27 + 15 * q^28 - 11 * q^29 + 18 * q^30 + 13 * q^31 + 85 * q^32 + 12 * q^33 + 31 * q^34 + 4 * q^35 + 26 * q^36 + 22 * q^37 - 2 * q^38 + 21 * q^40 + 36 * q^41 + 11 * q^42 + 26 * q^43 + 38 * q^44 + 35 * q^45 - q^46 + 46 * q^47 + 36 * q^48 + 29 * q^49 + 8 * q^50 - 41 * q^51 + 9 * q^53 + 70 * q^54 + 33 * q^55 - 10 * q^56 + 70 * q^57 - 23 * q^58 + 18 * q^59 + 24 * q^60 - 42 * q^61 - 24 * q^62 + 68 * q^63 + 39 * q^64 + 18 * q^66 + 26 * q^67 + 8 * q^68 + 12 * q^69 - 5 * q^70 + 43 * q^71 + 46 * q^72 + 21 * q^73 - 22 * q^74 + 12 * q^75 + 2 * q^76 + 4 * q^77 - 22 * q^79 + 44 * q^80 + 41 * q^81 + 156 * q^82 + 26 * q^83 + 11 * q^84 + 9 * q^85 + 17 * q^86 - 30 * q^87 + 21 * q^88 + 95 * q^89 + 18 * q^90 + 37 * q^92 + 62 * q^93 - 14 * q^94 + 8 * q^95 + 53 * q^96 + 40 * q^97 + 132 * q^98 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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