LMFDB - Embedded newform 4334.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 6 x^{14} - 8 x^{13} + 94 x^{12} - 13 x^{11} - 582 x^{10} + 295 x^{9} + 1814 x^{8} - 1056 x^{7} + \cdots - 45 $ x^15 - 6x^14 - 8x^13 + 94x^12 - 13x^11 - 582x^10 + 295x^9 + 1814x^8 - 1056x^7 - 2966x^6 + 1621x^5 + 2328x^4 - 1160x^3 - 589x^2 + 364x - 45
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			1.3
Root			$-1.55193$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -2.55193 q^{3} +1.00000 q^{4} -3.59659 q^{5} -2.55193 q^{6} -3.65108 q^{7} +1.00000 q^{8} +3.51234 q^{9} -3.59659 q^{10} +1.00000 q^{11} -2.55193 q^{12} -1.76088 q^{13} -3.65108 q^{14} +9.17824 q^{15} +1.00000 q^{16} +5.45317 q^{17} +3.51234 q^{18} -3.47915 q^{19} -3.59659 q^{20} +9.31729 q^{21} +1.00000 q^{22} +1.38562 q^{23} -2.55193 q^{24} +7.93544 q^{25} -1.76088 q^{26} -1.30746 q^{27} -3.65108 q^{28} +4.84019 q^{29} +9.17824 q^{30} +5.30041 q^{31} +1.00000 q^{32} -2.55193 q^{33} +5.45317 q^{34} +13.1314 q^{35} +3.51234 q^{36} +7.29674 q^{37} -3.47915 q^{38} +4.49363 q^{39} -3.59659 q^{40} -7.03552 q^{41} +9.31729 q^{42} +5.65561 q^{43} +1.00000 q^{44} -12.6325 q^{45} +1.38562 q^{46} +3.27067 q^{47} -2.55193 q^{48} +6.33036 q^{49} +7.93544 q^{50} -13.9161 q^{51} -1.76088 q^{52} -12.1640 q^{53} -1.30746 q^{54} -3.59659 q^{55} -3.65108 q^{56} +8.87855 q^{57} +4.84019 q^{58} -12.4566 q^{59} +9.17824 q^{60} -1.47899 q^{61} +5.30041 q^{62} -12.8238 q^{63} +1.00000 q^{64} +6.33315 q^{65} -2.55193 q^{66} +1.97721 q^{67} +5.45317 q^{68} -3.53602 q^{69} +13.1314 q^{70} +0.420050 q^{71} +3.51234 q^{72} -4.86379 q^{73} +7.29674 q^{74} -20.2507 q^{75} -3.47915 q^{76} -3.65108 q^{77} +4.49363 q^{78} -11.4819 q^{79} -3.59659 q^{80} -7.20047 q^{81} -7.03552 q^{82} -12.7764 q^{83} +9.31729 q^{84} -19.6128 q^{85} +5.65561 q^{86} -12.3518 q^{87} +1.00000 q^{88} +14.3851 q^{89} -12.6325 q^{90} +6.42909 q^{91} +1.38562 q^{92} -13.5263 q^{93} +3.27067 q^{94} +12.5131 q^{95} -2.55193 q^{96} +8.57250 q^{97} +6.33036 q^{98} +3.51234 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19}+ \cdots + 10 q^{99}+O(q^{100}) $ 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * q^99

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.55193	−1.47336	−0.736679	−	0.676243i	$-0.763607\pi$
$3$	−2.55193	−1.47336	−0.736679	+	0.676243i	$0.763607\pi$
$4$	1.00000	0.500000
$5$	−3.59659	−1.60844	−0.804221	−	0.594330i	$-0.797417\pi$
$5$	−3.59659	−1.60844	−0.804221	+	0.594330i	$0.797417\pi$
$6$	−2.55193	−1.04182
$7$	−3.65108	−1.37998	−0.689989	−	0.723820i	$-0.742384\pi$
$7$	−3.65108	−1.37998	−0.689989	+	0.723820i	$0.742384\pi$
$8$	1.00000	0.353553
$9$	3.51234	1.17078
$10$	−3.59659	−1.13734
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.55193	−0.736679
$13$	−1.76088	−0.488379	−0.244190	−	0.969728i	$-0.578522\pi$
$13$	−1.76088	−0.488379	−0.244190	+	0.969728i	$0.578522\pi$
$14$	−3.65108	−0.975791
$15$	9.17824	2.36981
$16$	1.00000	0.250000
$17$	5.45317	1.32259	0.661294	−	0.750127i	$-0.270008\pi$
$17$	5.45317	1.32259	0.661294	+	0.750127i	$0.270008\pi$
$18$	3.51234	0.827867
$19$	−3.47915	−0.798172	−0.399086	−	0.916913i	$-0.630673\pi$
$19$	−3.47915	−0.798172	−0.399086	+	0.916913i	$0.630673\pi$
$20$	−3.59659	−0.804221
$21$	9.31729	2.03320
$22$	1.00000	0.213201
$23$	1.38562	0.288923	0.144461	−	0.989510i	$-0.453855\pi$
$23$	1.38562	0.288923	0.144461	+	0.989510i	$0.453855\pi$
$24$	−2.55193	−0.520910
$25$	7.93544	1.58709
$26$	−1.76088	−0.345336
$27$	−1.30746	−0.251621
$28$	−3.65108	−0.689989
$29$	4.84019	0.898801	0.449400	−	0.893330i	$-0.351638\pi$
$29$	4.84019	0.898801	0.449400	+	0.893330i	$0.351638\pi$
$30$	9.17824	1.67571
$31$	5.30041	0.951982	0.475991	−	0.879450i	$-0.342089\pi$
$31$	5.30041	0.951982	0.475991	+	0.879450i	$0.342089\pi$
$32$	1.00000	0.176777
$33$	−2.55193	−0.444234
$34$	5.45317	0.935210
$35$	13.1314	2.21961
$36$	3.51234	0.585391
$37$	7.29674	1.19958	0.599788	−	0.800159i	$-0.295252\pi$
$37$	7.29674	1.19958	0.599788	+	0.800159i	$0.295252\pi$
$38$	−3.47915	−0.564393
$39$	4.49363	0.719557
$40$	−3.59659	−0.568670
$41$	−7.03552	−1.09876	−0.549382	−	0.835571i	$-0.685137\pi$
$41$	−7.03552	−1.09876	−0.549382	+	0.835571i	$0.685137\pi$
$42$	9.31729	1.43769
$43$	5.65561	0.862472	0.431236	−	0.902239i	$-0.358078\pi$
$43$	5.65561	0.862472	0.431236	+	0.902239i	$0.358078\pi$
$44$	1.00000	0.150756
$45$	−12.6325	−1.88313
$46$	1.38562	0.204299
$47$	3.27067	0.477076	0.238538	−	0.971133i	$-0.423332\pi$
$47$	3.27067	0.477076	0.238538	+	0.971133i	$0.423332\pi$
$48$	−2.55193	−0.368339
$49$	6.33036	0.904337
$50$	7.93544	1.12224
$51$	−13.9161	−1.94864
$52$	−1.76088	−0.244190
$53$	−12.1640	−1.67086	−0.835429	−	0.549599i	$-0.814781\pi$
$53$	−12.1640	−1.67086	−0.835429	+	0.549599i	$0.814781\pi$
$54$	−1.30746	−0.177923
$55$	−3.59659	−0.484964
$56$	−3.65108	−0.487896
$57$	8.87855	1.17599
$58$	4.84019	0.635548
$59$	−12.4566	−1.62171	−0.810855	−	0.585247i	$-0.800998\pi$
$59$	−12.4566	−1.62171	−0.810855	+	0.585247i	$0.800998\pi$
$60$	9.17824	1.18491
$61$	−1.47899	−0.189365	−0.0946826	−	0.995508i	$-0.530184\pi$
$61$	−1.47899	−0.189365	−0.0946826	+	0.995508i	$0.530184\pi$
$62$	5.30041	0.673153
$63$	−12.8238	−1.61565
$64$	1.00000	0.125000
$65$	6.33315	0.785530
$66$	−2.55193	−0.314121
$67$	1.97721	0.241555	0.120778	−	0.992680i	$-0.461461\pi$
$67$	1.97721	0.241555	0.120778	+	0.992680i	$0.461461\pi$
$68$	5.45317	0.661294
$69$	−3.53602	−0.425686
$70$	13.1314	1.56950
$71$	0.420050	0.0498507	0.0249254	−	0.999689i	$-0.492065\pi$
$71$	0.420050	0.0498507	0.0249254	+	0.999689i	$0.492065\pi$
$72$	3.51234	0.413934
$73$	−4.86379	−0.569263	−0.284632	−	0.958637i	$-0.591871\pi$
$73$	−4.86379	−0.569263	−0.284632	+	0.958637i	$0.591871\pi$
$74$	7.29674	0.848228
$75$	−20.2507	−2.33835
$76$	−3.47915	−0.399086
$77$	−3.65108	−0.416079
$78$	4.49363	0.508804
$79$	−11.4819	−1.29181	−0.645907	−	0.763416i	$-0.723521\pi$
$79$	−11.4819	−1.29181	−0.645907	+	0.763416i	$0.723521\pi$
$80$	−3.59659	−0.402111
$81$	−7.20047	−0.800053
$82$	−7.03552	−0.776943
$83$	−12.7764	−1.40239	−0.701197	−	0.712968i	$-0.747350\pi$
$83$	−12.7764	−1.40239	−0.701197	+	0.712968i	$0.747350\pi$
$84$	9.31729	1.01660
$85$	−19.6128	−2.12731
$86$	5.65561	0.609860
$87$	−12.3518	−1.32425
$88$	1.00000	0.106600
$89$	14.3851	1.52482	0.762408	−	0.647096i	$-0.224017\pi$
$89$	14.3851	1.52482	0.762408	+	0.647096i	$0.224017\pi$
$90$	−12.6325	−1.33158
$91$	6.42909	0.673952
$92$	1.38562	0.144461
$93$	−13.5263	−1.40261
$94$	3.27067	0.337343
$95$	12.5131	1.28381
$96$	−2.55193	−0.260455
$97$	8.57250	0.870406	0.435203	−	0.900332i	$-0.356677\pi$
$97$	8.57250	0.870406	0.435203	+	0.900332i	$0.356677\pi$
$98$	6.33036	0.639463
$99$	3.51234	0.353004
$100$	7.93544	0.793544
$101$	20.0227	1.99233	0.996165	−	0.0874995i	$-0.0278876\pi$
$101$	20.0227	1.99233	0.996165	+	0.0874995i	$0.0278876\pi$
$102$	−13.9161	−1.37790
$103$	−4.28639	−0.422351	−0.211175	−	0.977448i	$-0.567729\pi$
$103$	−4.28639	−0.422351	−0.211175	+	0.977448i	$0.567729\pi$
$104$	−1.76088	−0.172668
$105$	−33.5104	−3.27028
$106$	−12.1640	−1.18147
$107$	9.62271	0.930263	0.465131	−	0.885242i	$-0.346007\pi$
$107$	9.62271	0.930263	0.465131	+	0.885242i	$0.346007\pi$
$108$	−1.30746	−0.125811
$109$	4.95125	0.474244	0.237122	−	0.971480i	$-0.423796\pi$
$109$	4.95125	0.474244	0.237122	+	0.971480i	$0.423796\pi$
$110$	−3.59659	−0.342921
$111$	−18.6208	−1.76740
$112$	−3.65108	−0.344994
$113$	3.27079	0.307690	0.153845	−	0.988095i	$-0.450834\pi$
$113$	3.27079	0.307690	0.153845	+	0.988095i	$0.450834\pi$
$114$	8.87855	0.831553
$115$	−4.98352	−0.464716
$116$	4.84019	0.449400
$117$	−6.18480	−0.571785
$118$	−12.4566	−1.14672
$119$	−19.9099	−1.82514
$120$	9.17824	0.837855
$121$	1.00000	0.0909091
$122$	−1.47899	−0.133901
$123$	17.9541	1.61887
$124$	5.30041	0.475991
$125$	−10.5576	−0.944299
$126$	−12.8238	−1.14244
$127$	8.41574	0.746776	0.373388	−	0.927675i	$-0.378196\pi$
$127$	8.41574	0.746776	0.373388	+	0.927675i	$0.378196\pi$
$128$	1.00000	0.0883883
$129$	−14.4327	−1.27073
$130$	6.33315	0.555454
$131$	−12.1450	−1.06112	−0.530558	−	0.847649i	$-0.678017\pi$
$131$	−12.1450	−1.06112	−0.530558	+	0.847649i	$0.678017\pi$
$132$	−2.55193	−0.222117
$133$	12.7027	1.10146
$134$	1.97721	0.170805
$135$	4.70241	0.404719
$136$	5.45317	0.467605
$137$	10.0744	0.860714	0.430357	−	0.902659i	$-0.358388\pi$
$137$	10.0744	0.860714	0.430357	+	0.902659i	$0.358388\pi$
$138$	−3.53602	−0.301006
$139$	5.45014	0.462275	0.231137	−	0.972921i	$-0.425755\pi$
$139$	5.45014	0.462275	0.231137	+	0.972921i	$0.425755\pi$
$140$	13.1314	1.10981
$141$	−8.34651	−0.702903
$142$	0.420050	0.0352498
$143$	−1.76088	−0.147252
$144$	3.51234	0.292695
$145$	−17.4082	−1.44567
$146$	−4.86379	−0.402530
$147$	−16.1546	−1.33241
$148$	7.29674	0.599788
$149$	−3.01150	−0.246712	−0.123356	−	0.992362i	$-0.539366\pi$
$149$	−3.01150	−0.246712	−0.123356	+	0.992362i	$0.539366\pi$
$150$	−20.2507	−1.65346
$151$	−11.5591	−0.940669	−0.470335	−	0.882488i	$-0.655867\pi$
$151$	−11.5591	−0.940669	−0.470335	+	0.882488i	$0.655867\pi$
$152$	−3.47915	−0.282197
$153$	19.1534	1.54846
$154$	−3.65108	−0.294212
$155$	−19.0634	−1.53121
$156$	4.49363	0.359778
$157$	−8.04051	−0.641703	−0.320851	−	0.947130i	$-0.603969\pi$
$157$	−8.04051	−0.641703	−0.320851	+	0.947130i	$0.603969\pi$
$158$	−11.4819	−0.913450
$159$	31.0417	2.46177
$160$	−3.59659	−0.284335
$161$	−5.05902	−0.398707
$162$	−7.20047	−0.565723
$163$	9.62932	0.754227	0.377113	−	0.926167i	$-0.376917\pi$
$163$	9.62932	0.754227	0.377113	+	0.926167i	$0.376917\pi$
$164$	−7.03552	−0.549382
$165$	9.17824	0.714525
$166$	−12.7764	−0.991642
$167$	2.08668	0.161472	0.0807362	−	0.996736i	$-0.474273\pi$
$167$	2.08668	0.161472	0.0807362	+	0.996736i	$0.474273\pi$
$168$	9.31729	0.718844
$169$	−9.89931	−0.761486
$170$	−19.6128	−1.50423
$171$	−12.2200	−0.934485
$172$	5.65561	0.431236
$173$	−19.4859	−1.48148	−0.740742	−	0.671789i	$-0.765526\pi$
$173$	−19.4859	−1.48148	−0.740742	+	0.671789i	$0.765526\pi$
$174$	−12.3518	−0.936389
$175$	−28.9729	−2.19015
$176$	1.00000	0.0753778
$177$	31.7883	2.38936
$178$	14.3851	1.07821
$179$	−15.4103	−1.15182	−0.575909	−	0.817514i	$-0.695352\pi$
$179$	−15.4103	−1.15182	−0.575909	+	0.817514i	$0.695352\pi$
$180$	−12.6325	−0.941567
$181$	−19.2831	−1.43330	−0.716650	−	0.697433i	$-0.754325\pi$
$181$	−19.2831	−1.43330	−0.716650	+	0.697433i	$0.754325\pi$
$182$	6.42909	0.476556
$183$	3.77428	0.279002
$184$	1.38562	0.102150
$185$	−26.2434	−1.92945
$186$	−13.5263	−0.991795
$187$	5.45317	0.398775
$188$	3.27067	0.238538
$189$	4.77365	0.347232
$190$	12.5131	0.907794
$191$	−7.25201	−0.524737	−0.262368	−	0.964968i	$-0.584504\pi$
$191$	−7.25201	−0.524737	−0.262368	+	0.964968i	$0.584504\pi$
$192$	−2.55193	−0.184170
$193$	15.0222	1.08132	0.540660	−	0.841241i	$-0.318175\pi$
$193$	15.0222	1.08132	0.540660	+	0.841241i	$0.318175\pi$
$194$	8.57250	0.615470
$195$	−16.1617	−1.15737
$196$	6.33036	0.452169
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	3.51234	0.249611
$199$	4.24552	0.300957	0.150479	−	0.988613i	$-0.451919\pi$
$199$	4.24552	0.300957	0.150479	+	0.988613i	$0.451919\pi$
$200$	7.93544	0.561121
$201$	−5.04571	−0.355897
$202$	20.0227	1.40879
$203$	−17.6719	−1.24032
$204$	−13.9161	−0.974322
$205$	25.3039	1.76730
$206$	−4.28639	−0.298647
$207$	4.86679	0.338265
$208$	−1.76088	−0.122095
$209$	−3.47915	−0.240658
$210$	−33.5104	−2.31244
$211$	−4.87147	−0.335366	−0.167683	−	0.985841i	$-0.553629\pi$
$211$	−4.87147	−0.335366	−0.167683	+	0.985841i	$0.553629\pi$
$212$	−12.1640	−0.835429
$213$	−1.07194	−0.0734479
$214$	9.62271	0.657795
$215$	−20.3409	−1.38724
$216$	−1.30746	−0.0889616
$217$	−19.3522	−1.31371
$218$	4.95125	0.335341
$219$	12.4120	0.838728
$220$	−3.59659	−0.242482
$221$	−9.60235	−0.645924
$222$	−18.6208	−1.24974
$223$	−20.6190	−1.38075	−0.690376	−	0.723451i	$-0.742555\pi$
$223$	−20.6190	−1.38075	−0.690376	+	0.723451i	$0.742555\pi$
$224$	−3.65108	−0.243948
$225$	27.8720	1.85813
$226$	3.27079	0.217570
$227$	−10.9218	−0.724907	−0.362454	−	0.932002i	$-0.618061\pi$
$227$	−10.9218	−0.724907	−0.362454	+	0.932002i	$0.618061\pi$
$228$	8.87855	0.587996
$229$	−24.0175	−1.58712	−0.793560	−	0.608492i	$-0.791775\pi$
$229$	−24.0175	−1.58712	−0.793560	+	0.608492i	$0.791775\pi$
$230$	−4.98352	−0.328604
$231$	9.31729	0.613033
$232$	4.84019	0.317774
$233$	21.1742	1.38717	0.693583	−	0.720377i	$-0.256031\pi$
$233$	21.1742	1.38717	0.693583	+	0.720377i	$0.256031\pi$
$234$	−6.18480	−0.404313
$235$	−11.7632	−0.767349
$236$	−12.4566	−0.810855
$237$	29.3010	1.90330
$238$	−19.9099	−1.29057
$239$	−20.4319	−1.32163	−0.660814	−	0.750549i	$-0.729789\pi$
$239$	−20.4319	−1.32163	−0.660814	+	0.750549i	$0.729789\pi$
$240$	9.17824	0.592453
$241$	13.4047	0.863475	0.431737	−	0.901999i	$-0.357901\pi$
$241$	13.4047	0.863475	0.431737	+	0.901999i	$0.357901\pi$
$242$	1.00000	0.0642824
$243$	22.2975	1.43038
$244$	−1.47899	−0.0946826
$245$	−22.7677	−1.45457
$246$	17.9541	1.14471
$247$	6.12636	0.389811
$248$	5.30041	0.336576
$249$	32.6045	2.06623
$250$	−10.5576	−0.667720
$251$	−6.43782	−0.406352	−0.203176	−	0.979142i	$-0.565126\pi$
$251$	−6.43782	−0.406352	−0.203176	+	0.979142i	$0.565126\pi$
$252$	−12.8238	−0.807826
$253$	1.38562	0.0871135
$254$	8.41574	0.528050
$255$	50.0505	3.13428
$256$	1.00000	0.0625000
$257$	−2.00537	−0.125091	−0.0625457	−	0.998042i	$-0.519922\pi$
$257$	−2.00537	−0.125091	−0.0625457	+	0.998042i	$0.519922\pi$
$258$	−14.4327	−0.898541
$259$	−26.6409	−1.65539
$260$	6.33315	0.392765
$261$	17.0004	1.05230
$262$	−12.1450	−0.750322
$263$	5.24913	0.323675	0.161838	−	0.986817i	$-0.448258\pi$
$263$	5.24913	0.323675	0.161838	+	0.986817i	$0.448258\pi$
$264$	−2.55193	−0.157060
$265$	43.7490	2.68748
$266$	12.7027	0.778850
$267$	−36.7097	−2.24660
$268$	1.97721	0.120778
$269$	13.2839	0.809935	0.404968	−	0.914331i	$-0.367283\pi$
$269$	13.2839	0.809935	0.404968	+	0.914331i	$0.367283\pi$
$270$	4.70241	0.286179
$271$	17.8247	1.08277	0.541386	−	0.840774i	$-0.317900\pi$
$271$	17.8247	1.08277	0.541386	+	0.840774i	$0.317900\pi$
$272$	5.45317	0.330647
$273$	−16.4066	−0.992972
$274$	10.0744	0.608616
$275$	7.93544	0.478525
$276$	−3.53602	−0.212843
$277$	16.1952	0.973075	0.486537	−	0.873660i	$-0.338260\pi$
$277$	16.1952	0.973075	0.486537	+	0.873660i	$0.338260\pi$
$278$	5.45014	0.326878
$279$	18.6169	1.11456
$280$	13.1314	0.784752
$281$	17.2704	1.03027	0.515134	−	0.857109i	$-0.327742\pi$
$281$	17.2704	1.03027	0.515134	+	0.857109i	$0.327742\pi$
$282$	−8.34651	−0.497027
$283$	−3.26640	−0.194168	−0.0970838	−	0.995276i	$-0.530951\pi$
$283$	−3.26640	−0.194168	−0.0970838	+	0.995276i	$0.530951\pi$
$284$	0.420050	0.0249254
$285$	−31.9325	−1.89152
$286$	−1.76088	−0.104123
$287$	25.6872	1.51627
$288$	3.51234	0.206967
$289$	12.7370	0.749237
$290$	−17.4082	−1.02224
$291$	−21.8764	−1.28242
$292$	−4.86379	−0.284632
$293$	23.4211	1.36827	0.684136	−	0.729354i	$-0.260179\pi$
$293$	23.4211	1.36827	0.684136	+	0.729354i	$0.260179\pi$
$294$	−16.1546	−0.942157
$295$	44.8012	2.60843
$296$	7.29674	0.424114
$297$	−1.30746	−0.0758667
$298$	−3.01150	−0.174452
$299$	−2.43991	−0.141104
$300$	−20.2507	−1.16917
$301$	−20.6490	−1.19019
$302$	−11.5591	−0.665154
$303$	−51.0964	−2.93541
$304$	−3.47915	−0.199543
$305$	5.31931	0.304583
$306$	19.1534	1.09493
$307$	−22.8135	−1.30203	−0.651017	−	0.759063i	$-0.725658\pi$
$307$	−22.8135	−1.30203	−0.651017	+	0.759063i	$0.725658\pi$
$308$	−3.65108	−0.208039
$309$	10.9386	0.622273
$310$	−19.0634	−1.08273
$311$	13.0418	0.739535	0.369767	−	0.929124i	$-0.379437\pi$
$311$	13.0418	0.739535	0.369767	+	0.929124i	$0.379437\pi$
$312$	4.49363	0.254402
$313$	−20.9748	−1.18557	−0.592784	−	0.805362i	$-0.701971\pi$
$313$	−20.9748	−1.18557	−0.592784	+	0.805362i	$0.701971\pi$
$314$	−8.04051	−0.453752
$315$	46.1220	2.59868
$316$	−11.4819	−0.645907
$317$	−24.2887	−1.36419	−0.682096	−	0.731263i	$-0.738931\pi$
$317$	−24.2887	−1.36419	−0.682096	+	0.731263i	$0.738931\pi$
$318$	31.0417	1.74073
$319$	4.84019	0.270999
$320$	−3.59659	−0.201055
$321$	−24.5565	−1.37061
$322$	−5.05902	−0.281928
$323$	−18.9724	−1.05565
$324$	−7.20047	−0.400026
$325$	−13.9733	−0.775101
$326$	9.62932	0.533319
$327$	−12.6352	−0.698730
$328$	−7.03552	−0.388472
$329$	−11.9415	−0.658354
$330$	9.17824	0.505245
$331$	−0.628339	−0.0345366	−0.0172683	−	0.999851i	$-0.505497\pi$
$331$	−0.628339	−0.0345366	−0.0172683	+	0.999851i	$0.505497\pi$
$332$	−12.7764	−0.701197
$333$	25.6286	1.40444
$334$	2.08668	0.114178
$335$	−7.11122	−0.388527
$336$	9.31729	0.508300
$337$	−27.4542	−1.49552	−0.747762	−	0.663967i	$-0.768871\pi$
$337$	−27.4542	−1.49552	−0.747762	+	0.663967i	$0.768871\pi$
$338$	−9.89931	−0.538452
$339$	−8.34683	−0.453338
$340$	−19.6128	−1.06365
$341$	5.30041	0.287033
$342$	−12.2200	−0.660781
$343$	2.44491	0.132013
$344$	5.65561	0.304930
$345$	12.7176	0.684692
$346$	−19.4859	−1.04757
$347$	4.94438	0.265428	0.132714	−	0.991154i	$-0.457631\pi$
$347$	4.94438	0.265428	0.132714	+	0.991154i	$0.457631\pi$
$348$	−12.3518	−0.662127
$349$	−11.6426	−0.623213	−0.311606	−	0.950211i	$-0.600867\pi$
$349$	−11.6426	−0.623213	−0.311606	+	0.950211i	$0.600867\pi$
$350$	−28.9729	−1.54867
$351$	2.30228	0.122887
$352$	1.00000	0.0533002
$353$	6.70944	0.357108	0.178554	−	0.983930i	$-0.442858\pi$
$353$	6.70944	0.357108	0.178554	+	0.983930i	$0.442858\pi$
$354$	31.7883	1.68953
$355$	−1.51075	−0.0801820
$356$	14.3851	0.762408
$357$	50.8087	2.68908
$358$	−15.4103	−0.814458
$359$	−26.6711	−1.40764	−0.703822	−	0.710376i	$-0.748525\pi$
$359$	−26.6711	−1.40764	−0.703822	+	0.710376i	$0.748525\pi$
$360$	−12.6325	−0.665789
$361$	−6.89550	−0.362921
$362$	−19.2831	−1.01350
$363$	−2.55193	−0.133942
$364$	6.42909	0.336976
$365$	17.4930	0.915628
$366$	3.77428	0.197285
$367$	35.0539	1.82980	0.914899	−	0.403683i	$-0.132270\pi$
$367$	35.0539	1.82980	0.914899	+	0.403683i	$0.132270\pi$
$368$	1.38562	0.0722307
$369$	−24.7112	−1.28641
$370$	−26.2434	−1.36433
$371$	44.4118	2.30575
$372$	−13.5263	−0.701305
$373$	−8.43979	−0.436996	−0.218498	−	0.975837i	$-0.570116\pi$
$373$	−8.43979	−0.436996	−0.218498	+	0.975837i	$0.570116\pi$
$374$	5.45317	0.281977
$375$	26.9422	1.39129
$376$	3.27067	0.168672
$377$	−8.52298	−0.438956
$378$	4.77365	0.245530
$379$	−0.378997	−0.0194678	−0.00973389	−	0.999953i	$-0.503098\pi$
$379$	−0.378997	−0.0194678	−0.00973389	+	0.999953i	$0.503098\pi$
$380$	12.5131	0.641907
$381$	−21.4764	−1.10027
$382$	−7.25201	−0.371045
$383$	−25.5842	−1.30729	−0.653645	−	0.756802i	$-0.726761\pi$
$383$	−25.5842	−1.30729	−0.653645	+	0.756802i	$0.726761\pi$
$384$	−2.55193	−0.130228
$385$	13.1314	0.669239
$386$	15.0222	0.764608
$387$	19.8644	1.00977
$388$	8.57250	0.435203
$389$	−12.7199	−0.644923	−0.322461	−	0.946583i	$-0.604510\pi$
$389$	−12.7199	−0.644923	−0.322461	+	0.946583i	$0.604510\pi$
$390$	−16.1617	−0.818382
$391$	7.55604	0.382125
$392$	6.33036	0.319731
$393$	30.9932	1.56340
$394$	−1.00000	−0.0503793
$395$	41.2956	2.07781
$396$	3.51234	0.176502
$397$	−30.2380	−1.51760	−0.758801	−	0.651323i	$-0.774215\pi$
$397$	−30.2380	−1.51760	−0.758801	+	0.651323i	$0.774215\pi$
$398$	4.24552	0.212809
$399$	−32.4163	−1.62284
$400$	7.93544	0.396772
$401$	−7.27342	−0.363217	−0.181609	−	0.983371i	$-0.558130\pi$
$401$	−7.27342	−0.363217	−0.181609	+	0.983371i	$0.558130\pi$
$402$	−5.04571	−0.251657
$403$	−9.33337	−0.464928
$404$	20.0227	0.996165
$405$	25.8971	1.28684
$406$	−17.6719	−0.877042
$407$	7.29674	0.361686
$408$	−13.9161	−0.688949
$409$	23.0892	1.14169	0.570843	−	0.821059i	$-0.306616\pi$
$409$	23.0892	1.14169	0.570843	+	0.821059i	$0.306616\pi$
$410$	25.3039	1.24967
$411$	−25.7091	−1.26814
$412$	−4.28639	−0.211175
$413$	45.4800	2.23792
$414$	4.86679	0.239190
$415$	45.9515	2.25567
$416$	−1.76088	−0.0863341
$417$	−13.9084	−0.681096
$418$	−3.47915	−0.170171
$419$	−8.60996	−0.420624	−0.210312	−	0.977634i	$-0.567448\pi$
$419$	−8.60996	−0.420624	−0.210312	+	0.977634i	$0.567448\pi$
$420$	−33.5104	−1.63514
$421$	6.58646	0.321004	0.160502	−	0.987035i	$-0.448689\pi$
$421$	6.58646	0.321004	0.160502	+	0.987035i	$0.448689\pi$
$422$	−4.87147	−0.237140
$423$	11.4877	0.558551
$424$	−12.1640	−0.590737
$425$	43.2733	2.09906
$426$	−1.07194	−0.0519355
$427$	5.39990	0.261320
$428$	9.62271	0.465131
$429$	4.49363	0.216955
$430$	−20.3409	−0.980924
$431$	17.5106	0.843454	0.421727	−	0.906723i	$-0.361424\pi$
$431$	17.5106	0.843454	0.421727	+	0.906723i	$0.361424\pi$
$432$	−1.30746	−0.0629054
$433$	12.7712	0.613745	0.306872	−	0.951751i	$-0.400718\pi$
$433$	12.7712	0.613745	0.306872	+	0.951751i	$0.400718\pi$
$434$	−19.3522	−0.928936
$435$	44.4244	2.12999
$436$	4.95125	0.237122
$437$	−4.82080	−0.230610
$438$	12.4120	0.593070
$439$	−8.23514	−0.393042	−0.196521	−	0.980500i	$-0.562964\pi$
$439$	−8.23514	−0.393042	−0.196521	+	0.980500i	$0.562964\pi$
$440$	−3.59659	−0.171461
$441$	22.2344	1.05878
$442$	−9.60235	−0.456737
$443$	−4.73625	−0.225026	−0.112513	−	0.993650i	$-0.535890\pi$
$443$	−4.73625	−0.225026	−0.112513	+	0.993650i	$0.535890\pi$
$444$	−18.6208	−0.883702
$445$	−51.7372	−2.45258
$446$	−20.6190	−0.976339
$447$	7.68514	0.363495
$448$	−3.65108	−0.172497
$449$	13.2461	0.625122	0.312561	−	0.949898i	$-0.398813\pi$
$449$	13.2461	0.625122	0.312561	+	0.949898i	$0.398813\pi$
$450$	27.8720	1.31390
$451$	−7.03552	−0.331290
$452$	3.27079	0.153845
$453$	29.4981	1.38594
$454$	−10.9218	−0.512587
$455$	−23.1228	−1.08401
$456$	8.87855	0.415776
$457$	22.0381	1.03090	0.515448	−	0.856921i	$-0.327625\pi$
$457$	22.0381	1.03090	0.515448	+	0.856921i	$0.327625\pi$
$458$	−24.0175	−1.12226
$459$	−7.12982	−0.332791
$460$	−4.98352	−0.232358
$461$	−34.8532	−1.62328	−0.811638	−	0.584161i	$-0.801424\pi$
$461$	−34.8532	−1.62328	−0.811638	+	0.584161i	$0.801424\pi$
$462$	9.31729	0.433480
$463$	0.838941	0.0389889	0.0194945	−	0.999810i	$-0.493794\pi$
$463$	0.838941	0.0389889	0.0194945	+	0.999810i	$0.493794\pi$
$464$	4.84019	0.224700
$465$	48.6484	2.25602
$466$	21.1742	0.980875
$467$	10.1902	0.471548	0.235774	−	0.971808i	$-0.424238\pi$
$467$	10.1902	0.471548	0.235774	+	0.971808i	$0.424238\pi$
$468$	−6.18480	−0.285893
$469$	−7.21896	−0.333340
$470$	−11.7632	−0.542598
$471$	20.5188	0.945457
$472$	−12.4566	−0.573361
$473$	5.65561	0.260045
$474$	29.3010	1.34584
$475$	−27.6086	−1.26677
$476$	−19.9099	−0.912570
$477$	−42.7242	−1.95621
$478$	−20.4319	−0.934533
$479$	−29.3423	−1.34068	−0.670342	−	0.742052i	$-0.733853\pi$
$479$	−29.3423	−1.34068	−0.670342	+	0.742052i	$0.733853\pi$
$480$	9.17824	0.418927
$481$	−12.8486	−0.585848
$482$	13.4047	0.610569
$483$	12.9103	0.587437
$484$	1.00000	0.0454545
$485$	−30.8318	−1.40000
$486$	22.2975	1.01143
$487$	36.3905	1.64901	0.824506	−	0.565854i	$-0.191453\pi$
$487$	36.3905	1.64901	0.824506	+	0.565854i	$0.191453\pi$
$488$	−1.47899	−0.0669507
$489$	−24.5734	−1.11125
$490$	−22.7677	−1.02854
$491$	25.4213	1.14725	0.573623	−	0.819119i	$-0.305537\pi$
$491$	25.4213	1.14725	0.573623	+	0.819119i	$0.305537\pi$
$492$	17.9541	0.809436
$493$	26.3944	1.18874
$494$	6.12636	0.275638
$495$	−12.6325	−0.567786
$496$	5.30041	0.237995
$497$	−1.53363	−0.0687929
$498$	32.6045	1.46104
$499$	−6.10391	−0.273248	−0.136624	−	0.990623i	$-0.543625\pi$
$499$	−6.10391	−0.273248	−0.136624	+	0.990623i	$0.543625\pi$
$500$	−10.5576	−0.472149
$501$	−5.32507	−0.237907
$502$	−6.43782	−0.287334
$503$	−9.59903	−0.428000	−0.214000	−	0.976834i	$-0.568649\pi$
$503$	−9.59903	−0.428000	−0.214000	+	0.976834i	$0.568649\pi$
$504$	−12.8238	−0.571219
$505$	−72.0133	−3.20455
$506$	1.38562	0.0615985
$507$	25.2624	1.12194
$508$	8.41574	0.373388
$509$	−9.37518	−0.415547	−0.207774	−	0.978177i	$-0.566622\pi$
$509$	−9.37518	−0.415547	−0.207774	+	0.978177i	$0.566622\pi$
$510$	50.0505	2.21627
$511$	17.7581	0.785571
$512$	1.00000	0.0441942
$513$	4.54887	0.200837
$514$	−2.00537	−0.0884529
$515$	15.4164	0.679327
$516$	−14.4327	−0.635364
$517$	3.27067	0.143844
$518$	−26.6409	−1.17054
$519$	49.7266	2.18276
$520$	6.33315	0.277727
$521$	18.5900	0.814443	0.407222	−	0.913329i	$-0.366498\pi$
$521$	18.5900	0.814443	0.407222	+	0.913329i	$0.366498\pi$
$522$	17.0004	0.744088
$523$	17.1864	0.751507	0.375753	−	0.926720i	$-0.377384\pi$
$523$	17.1864	0.751507	0.375753	+	0.926720i	$0.377384\pi$
$524$	−12.1450	−0.530558
$525$	73.9368	3.22687
$526$	5.24913	0.228873
$527$	28.9040	1.25908
$528$	−2.55193	−0.111058
$529$	−21.0800	−0.916524
$530$	43.7490	1.90033
$531$	−43.7518	−1.89867
$532$	12.7027	0.550730
$533$	12.3887	0.536613
$534$	−36.7097	−1.58859
$535$	−34.6089	−1.49627
$536$	1.97721	0.0854026
$537$	39.3259	1.69704
$538$	13.2839	0.572711
$539$	6.33036	0.272668
$540$	4.70241	0.202359
$541$	5.78441	0.248691	0.124346	−	0.992239i	$-0.460317\pi$
$541$	5.78441	0.248691	0.124346	+	0.992239i	$0.460317\pi$
$542$	17.8247	0.765636
$543$	49.2090	2.11176
$544$	5.45317	0.233803
$545$	−17.8076	−0.762794
$546$	−16.4066	−0.702137
$547$	−10.3837	−0.443974	−0.221987	−	0.975050i	$-0.571254\pi$
$547$	−10.3837	−0.443974	−0.221987	+	0.975050i	$0.571254\pi$
$548$	10.0744	0.430357
$549$	−5.19472	−0.221705
$550$	7.93544	0.338368
$551$	−16.8398	−0.717398
$552$	−3.53602	−0.150503
$553$	41.9213	1.78267
$554$	16.1952	0.688068
$555$	66.9712	2.84277
$556$	5.45014	0.231137
$557$	18.0343	0.764139	0.382069	−	0.924134i	$-0.375212\pi$
$557$	18.0343	0.764139	0.382069	+	0.924134i	$0.375212\pi$
$558$	18.6169	0.788115
$559$	−9.95882	−0.421213
$560$	13.1314	0.554904
$561$	−13.9161	−0.587538
$562$	17.2704	0.728510
$563$	8.79775	0.370781	0.185390	−	0.982665i	$-0.440645\pi$
$563$	8.79775	0.370781	0.185390	+	0.982665i	$0.440645\pi$
$564$	−8.34651	−0.351451
$565$	−11.7637	−0.494902
$566$	−3.26640	−0.137297
$567$	26.2895	1.10405
$568$	0.420050	0.0176249
$569$	−12.5906	−0.527825	−0.263913	−	0.964547i	$-0.585013\pi$
$569$	−12.5906	−0.527825	−0.263913	+	0.964547i	$0.585013\pi$
$570$	−31.9325	−1.33750
$571$	−28.9127	−1.20996	−0.604979	−	0.796242i	$-0.706818\pi$
$571$	−28.9127	−1.20996	−0.604979	+	0.796242i	$0.706818\pi$
$572$	−1.76088	−0.0736259
$573$	18.5066	0.773125
$574$	25.6872	1.07216
$575$	10.9955	0.458546
$576$	3.51234	0.146348
$577$	−37.2934	−1.55255	−0.776273	−	0.630397i	$-0.782892\pi$
$577$	−37.2934	−1.55255	−0.776273	+	0.630397i	$0.782892\pi$
$578$	12.7370	0.529790
$579$	−38.3355	−1.59317
$580$	−17.4082	−0.722835
$581$	46.6476	1.93527
$582$	−21.8764	−0.906807
$583$	−12.1640	−0.503782
$584$	−4.86379	−0.201265
$585$	22.2442	0.919684
$586$	23.4211	0.967515
$587$	−38.9179	−1.60631	−0.803157	−	0.595767i	$-0.796848\pi$
$587$	−38.9179	−1.60631	−0.803157	+	0.595767i	$0.796848\pi$
$588$	−16.1546	−0.666206
$589$	−18.4409	−0.759846
$590$	44.8012	1.84444
$591$	2.55193	0.104972
$592$	7.29674	0.299894
$593$	15.0548	0.618225	0.309112	−	0.951025i	$-0.399968\pi$
$593$	15.0548	0.618225	0.309112	+	0.951025i	$0.399968\pi$
$594$	−1.30746	−0.0536459
$595$	71.6078	2.93563
$596$	−3.01150	−0.123356
$597$	−10.8343	−0.443417
$598$	−2.43991	−0.0997755
$599$	−41.6441	−1.70153	−0.850766	−	0.525544i	$-0.823862\pi$
$599$	−41.6441	−1.70153	−0.850766	+	0.525544i	$0.823862\pi$
$600$	−20.2507	−0.826731
$601$	−5.80113	−0.236633	−0.118317	−	0.992976i	$-0.537750\pi$
$601$	−5.80113	−0.236633	−0.118317	+	0.992976i	$0.537750\pi$
$602$	−20.6490	−0.841592
$603$	6.94465	0.282808
$604$	−11.5591	−0.470335
$605$	−3.59659	−0.146222
$606$	−51.0964	−2.07565
$607$	−31.5860	−1.28204	−0.641018	−	0.767526i	$-0.721488\pi$
$607$	−31.5860	−1.28204	−0.641018	+	0.767526i	$0.721488\pi$
$608$	−3.47915	−0.141098
$609$	45.0974	1.82744
$610$	5.31931	0.215373
$611$	−5.75924	−0.232994
$612$	19.1534	0.774230
$613$	−26.8984	−1.08642	−0.543209	−	0.839598i	$-0.682791\pi$
$613$	−26.8984	−1.08642	−0.543209	+	0.839598i	$0.682791\pi$
$614$	−22.8135	−0.920678
$615$	−64.5737	−2.60386
$616$	−3.65108	−0.147106
$617$	24.8821	1.00172	0.500858	−	0.865530i	$-0.333018\pi$
$617$	24.8821	1.00172	0.500858	+	0.865530i	$0.333018\pi$
$618$	10.9386	0.440014
$619$	18.6551	0.749811	0.374905	−	0.927063i	$-0.377675\pi$
$619$	18.6551	0.749811	0.374905	+	0.927063i	$0.377675\pi$
$620$	−19.0634	−0.765604
$621$	−1.81165	−0.0726992
$622$	13.0418	0.522930
$623$	−52.5211	−2.10421
$624$	4.49363	0.179889
$625$	−1.70595	−0.0682382
$626$	−20.9748	−0.838323
$627$	8.87855	0.354575
$628$	−8.04051	−0.320851
$629$	39.7903	1.58654
$630$	46.1220	1.83755
$631$	−17.2461	−0.686558	−0.343279	−	0.939233i	$-0.611538\pi$
$631$	−17.2461	−0.686558	−0.343279	+	0.939233i	$0.611538\pi$
$632$	−11.4819	−0.456725
$633$	12.4317	0.494114
$634$	−24.2887	−0.964629
$635$	−30.2679	−1.20115
$636$	31.0417	1.23088
$637$	−11.1470	−0.441659
$638$	4.84019	0.191625
$639$	1.47536	0.0583643
$640$	−3.59659	−0.142168
$641$	−21.2999	−0.841294	−0.420647	−	0.907224i	$-0.638197\pi$
$641$	−21.2999	−0.841294	−0.420647	+	0.907224i	$0.638197\pi$
$642$	−24.5565	−0.969167
$643$	−23.9968	−0.946342	−0.473171	−	0.880971i	$-0.656891\pi$
$643$	−23.9968	−0.946342	−0.473171	+	0.880971i	$0.656891\pi$
$644$	−5.05902	−0.199353
$645$	51.9085	2.04389
$646$	−18.9724	−0.746459
$647$	−13.8514	−0.544554	−0.272277	−	0.962219i	$-0.587777\pi$
$647$	−13.8514	−0.544554	−0.272277	+	0.962219i	$0.587777\pi$
$648$	−7.20047	−0.282861
$649$	−12.4566	−0.488964
$650$	−13.9733	−0.548079
$651$	49.3855	1.93557
$652$	9.62932	0.377113
$653$	47.7504	1.86862	0.934309	−	0.356465i	$-0.116018\pi$
$653$	47.7504	1.86862	0.934309	+	0.356465i	$0.116018\pi$
$654$	−12.6352	−0.494077
$655$	43.6806	1.70674
$656$	−7.03552	−0.274691
$657$	−17.0833	−0.666483
$658$	−11.9415	−0.465526
$659$	28.6664	1.11668	0.558342	−	0.829611i	$-0.311438\pi$
$659$	28.6664	1.11668	0.558342	+	0.829611i	$0.311438\pi$
$660$	9.17824	0.357262
$661$	−32.3845	−1.25961	−0.629806	−	0.776753i	$-0.716865\pi$
$661$	−32.3845	−1.25961	−0.629806	+	0.776753i	$0.716865\pi$
$662$	−0.628339	−0.0244211
$663$	24.5045	0.951677
$664$	−12.7764	−0.495821
$665$	−45.6862	−1.77164
$666$	25.6286	0.993090
$667$	6.70669	0.259684
$668$	2.08668	0.0807362
$669$	52.6183	2.03434
$670$	−7.11122	−0.274730
$671$	−1.47899	−0.0570957
$672$	9.31729	0.359422
$673$	24.0242	0.926065	0.463032	−	0.886341i	$-0.346761\pi$
$673$	24.0242	0.926065	0.463032	+	0.886341i	$0.346761\pi$
$674$	−27.4542	−1.05749
$675$	−10.3753	−0.399346
$676$	−9.89931	−0.380743
$677$	15.8925	0.610799	0.305400	−	0.952224i	$-0.401210\pi$
$677$	15.8925	0.610799	0.305400	+	0.952224i	$0.401210\pi$
$678$	−8.34683	−0.320558
$679$	−31.2989	−1.20114
$680$	−19.6128	−0.752116
$681$	27.8717	1.06805
$682$	5.30041	0.202963
$683$	24.7925	0.948659	0.474330	−	0.880347i	$-0.342690\pi$
$683$	24.7925	0.948659	0.474330	+	0.880347i	$0.342690\pi$
$684$	−12.2200	−0.467243
$685$	−36.2334	−1.38441
$686$	2.44491	0.0933471
$687$	61.2909	2.33840
$688$	5.65561	0.215618
$689$	21.4193	0.816012
$690$	12.7176	0.484150
$691$	−5.74345	−0.218491	−0.109246	−	0.994015i	$-0.534844\pi$
$691$	−5.74345	−0.218491	−0.109246	+	0.994015i	$0.534844\pi$
$692$	−19.4859	−0.740742
$693$	−12.8238	−0.487137
$694$	4.94438	0.187686
$695$	−19.6019	−0.743543
$696$	−12.3518	−0.468195
$697$	−38.3659	−1.45321
$698$	−11.6426	−0.440678
$699$	−54.0350	−2.04379
$700$	−28.9729	−1.09507
$701$	−38.8853	−1.46868	−0.734338	−	0.678784i	$-0.762507\pi$
$701$	−38.8853	−1.46868	−0.734338	+	0.678784i	$0.762507\pi$
$702$	2.30228	0.0868940
$703$	−25.3865	−0.957469
$704$	1.00000	0.0376889
$705$	30.0190	1.13058
$706$	6.70944	0.252513
$707$	−73.1043	−2.74937
$708$	31.7883	1.19468
$709$	10.1995	0.383049	0.191525	−	0.981488i	$-0.438657\pi$
$709$	10.1995	0.383049	0.191525	+	0.981488i	$0.438657\pi$
$710$	−1.51075	−0.0566973
$711$	−40.3283	−1.51243
$712$	14.3851	0.539104
$713$	7.34438	0.275049
$714$	50.8087	1.90147
$715$	6.33315	0.236846
$716$	−15.4103	−0.575909
$717$	52.1407	1.94723
$718$	−26.6711	−0.995355
$719$	10.6469	0.397061	0.198531	−	0.980095i	$-0.436383\pi$
$719$	10.6469	0.397061	0.198531	+	0.980095i	$0.436383\pi$
$720$	−12.6325	−0.470784
$721$	15.6499	0.582834
$722$	−6.89550	−0.256624
$723$	−34.2079	−1.27221
$724$	−19.2831	−0.716650
$725$	38.4091	1.42648
$726$	−2.55193	−0.0947110
$727$	7.01470	0.260161	0.130080	−	0.991503i	$-0.458476\pi$
$727$	7.01470	0.260161	0.130080	+	0.991503i	$0.458476\pi$
$728$	6.42909	0.238278
$729$	−35.3002	−1.30741
$730$	17.4930	0.647447
$731$	30.8410	1.14069
$732$	3.77428	0.139501
$733$	40.1943	1.48461	0.742305	−	0.670062i	$-0.233733\pi$
$733$	40.1943	1.48461	0.742305	+	0.670062i	$0.233733\pi$
$734$	35.0539	1.29386
$735$	58.1015	2.14311
$736$	1.38562	0.0510748
$737$	1.97721	0.0728316
$738$	−24.7112	−0.909630
$739$	−4.92852	−0.181299	−0.0906493	−	0.995883i	$-0.528894\pi$
$739$	−4.92852	−0.181299	−0.0906493	+	0.995883i	$0.528894\pi$
$740$	−26.2434	−0.964725
$741$	−15.6340	−0.574330
$742$	44.4118	1.63041
$743$	−47.6088	−1.74660	−0.873298	−	0.487186i	$-0.838023\pi$
$743$	−47.6088	−1.74660	−0.873298	+	0.487186i	$0.838023\pi$
$744$	−13.5263	−0.495897
$745$	10.8311	0.396822
$746$	−8.43979	−0.309003
$747$	−44.8751	−1.64190
$748$	5.45317	0.199388
$749$	−35.1333	−1.28374
$750$	26.9422	0.983790
$751$	−44.1684	−1.61173	−0.805865	−	0.592100i	$-0.798299\pi$
$751$	−44.1684	−1.61173	−0.805865	+	0.592100i	$0.798299\pi$
$752$	3.27067	0.119269
$753$	16.4289	0.598701
$754$	−8.52298	−0.310388
$755$	41.5734	1.51301
$756$	4.77365	0.173616
$757$	34.2984	1.24660	0.623298	−	0.781984i	$-0.285792\pi$
$757$	34.2984	1.24660	0.623298	+	0.781984i	$0.285792\pi$
$758$	−0.378997	−0.0137658
$759$	−3.53602	−0.128349
$760$	12.5131	0.453897
$761$	7.90680	0.286621	0.143311	−	0.989678i	$-0.454225\pi$
$761$	7.90680	0.286621	0.143311	+	0.989678i	$0.454225\pi$
$762$	−21.4764	−0.778006
$763$	−18.0774	−0.654445
$764$	−7.25201	−0.262368
$765$	−68.8869	−2.49061
$766$	−25.5842	−0.924393
$767$	21.9345	0.792009
$768$	−2.55193	−0.0920848
$769$	14.9981	0.540844	0.270422	−	0.962742i	$-0.412837\pi$
$769$	14.9981	0.540844	0.270422	+	0.962742i	$0.412837\pi$
$770$	13.1314	0.473223
$771$	5.11755	0.184304
$772$	15.0222	0.540660
$773$	−4.35181	−0.156524	−0.0782619	−	0.996933i	$-0.524937\pi$
$773$	−4.35181	−0.156524	−0.0782619	+	0.996933i	$0.524937\pi$
$774$	19.8644	0.714012
$775$	42.0611	1.51088
$776$	8.57250	0.307735
$777$	67.9858	2.43898
$778$	−12.7199	−0.456029
$779$	24.4776	0.877003
$780$	−16.1617	−0.578683
$781$	0.420050	0.0150306
$782$	7.55604	0.270203
$783$	−6.32837	−0.226158
$784$	6.33036	0.226084
$785$	28.9184	1.03214
$786$	30.9932	1.10549
$787$	−7.96580	−0.283950	−0.141975	−	0.989870i	$-0.545345\pi$
$787$	−7.96580	−0.283950	−0.141975	+	0.989870i	$0.545345\pi$
$788$	−1.00000	−0.0356235
$789$	−13.3954	−0.476889
$790$	41.2956	1.46923
$791$	−11.9419	−0.424606
$792$	3.51234	0.124806
$793$	2.60432	0.0924820
$794$	−30.2380	−1.07311
$795$	−111.644	−3.95962
$796$	4.24552	0.150479
$797$	26.8845	0.952297	0.476149	−	0.879365i	$-0.342032\pi$
$797$	26.8845	0.952297	0.476149	+	0.879365i	$0.342032\pi$
$798$	−32.4163	−1.14752
$799$	17.8355	0.630974
$800$	7.93544	0.280560
$801$	50.5254	1.78523
$802$	−7.27342	−0.256833
$803$	−4.86379	−0.171639
$804$	−5.04571	−0.177948
$805$	18.1952	0.641297
$806$	−9.33337	−0.328754
$807$	−33.8996	−1.19332
$808$	20.0227	0.704395
$809$	54.4202	1.91331	0.956656	−	0.291222i	$-0.0940618\pi$
$809$	54.4202	1.91331	0.956656	+	0.291222i	$0.0940618\pi$
$810$	25.8971	0.909933
$811$	−49.1449	−1.72571	−0.862856	−	0.505451i	$-0.831326\pi$
$811$	−49.1449	−1.72571	−0.862856	+	0.505451i	$0.831326\pi$
$812$	−17.6719	−0.620162
$813$	−45.4873	−1.59531
$814$	7.29674	0.255750
$815$	−34.6327	−1.21313
$816$	−13.9161	−0.487161
$817$	−19.6767	−0.688401
$818$	23.0892	0.807294
$819$	22.5812	0.789050
$820$	25.3039	0.883649
$821$	5.05250	0.176333	0.0881667	−	0.996106i	$-0.471899\pi$
$821$	5.05250	0.176333	0.0881667	+	0.996106i	$0.471899\pi$
$822$	−25.7091	−0.896709
$823$	−25.3831	−0.884799	−0.442400	−	0.896818i	$-0.645873\pi$
$823$	−25.3831	−0.884799	−0.442400	+	0.896818i	$0.645873\pi$
$824$	−4.28639	−0.149323
$825$	−20.2507	−0.705039
$826$	45.4800	1.58245
$827$	−20.2794	−0.705184	−0.352592	−	0.935777i	$-0.614700\pi$
$827$	−20.2794	−0.705184	−0.352592	+	0.935777i	$0.614700\pi$
$828$	4.86679	0.169133
$829$	−54.1938	−1.88223	−0.941114	−	0.338088i	$-0.890220\pi$
$829$	−54.1938	−1.88223	−0.941114	+	0.338088i	$0.890220\pi$
$830$	45.9515	1.59500
$831$	−41.3290	−1.43369
$832$	−1.76088	−0.0610474
$833$	34.5205	1.19606
$834$	−13.9084	−0.481607
$835$	−7.50494	−0.259719
$836$	−3.47915	−0.120329
$837$	−6.93009	−0.239539
$838$	−8.60996	−0.297426
$839$	1.16416	0.0401911	0.0200956	−	0.999798i	$-0.493603\pi$
$839$	1.16416	0.0401911	0.0200956	+	0.999798i	$0.493603\pi$
$840$	−33.5104	−1.15622
$841$	−5.57256	−0.192157
$842$	6.58646	0.226984
$843$	−44.0730	−1.51795
$844$	−4.87147	−0.167683
$845$	35.6038	1.22481
$846$	11.4877	0.394955
$847$	−3.65108	−0.125452
$848$	−12.1640	−0.417714
$849$	8.33563	0.286078
$850$	43.2733	1.48426
$851$	10.1105	0.346585
$852$	−1.07194	−0.0367240
$853$	−55.3325	−1.89455	−0.947274	−	0.320424i	$-0.896175\pi$
$853$	−55.3325	−1.89455	−0.947274	+	0.320424i	$0.896175\pi$
$854$	5.39990	0.184781
$855$	43.9502	1.50307
$856$	9.62271	0.328898
$857$	51.8766	1.77207	0.886035	−	0.463618i	$-0.153449\pi$
$857$	51.8766	1.77207	0.886035	+	0.463618i	$0.153449\pi$
$858$	4.49363	0.153410
$859$	−6.47642	−0.220973	−0.110486	−	0.993878i	$-0.535241\pi$
$859$	−6.47642	−0.220973	−0.110486	+	0.993878i	$0.535241\pi$
$860$	−20.3409	−0.693618
$861$	−65.5520	−2.23401
$862$	17.5106	0.596412
$863$	39.6907	1.35109	0.675544	−	0.737320i	$-0.263909\pi$
$863$	39.6907	1.35109	0.675544	+	0.737320i	$0.263909\pi$
$864$	−1.30746	−0.0444808
$865$	70.0827	2.38288
$866$	12.7712	0.433983
$867$	−32.5040	−1.10389
$868$	−19.3522	−0.656857
$869$	−11.4819	−0.389496
$870$	44.4244	1.50613
$871$	−3.48163	−0.117970
$872$	4.95125	0.167670
$873$	30.1096	1.01905
$874$	−4.82080	−0.163066
$875$	38.5465	1.30311
$876$	12.4120	0.419364
$877$	16.8049	0.567461	0.283731	−	0.958904i	$-0.408428\pi$
$877$	16.8049	0.567461	0.283731	+	0.958904i	$0.408428\pi$
$878$	−8.23514	−0.277923
$879$	−59.7689	−2.01595
$880$	−3.59659	−0.121241
$881$	30.3341	1.02198	0.510991	−	0.859586i	$-0.329279\pi$
$881$	30.3341	1.02198	0.510991	+	0.859586i	$0.329279\pi$
$882$	22.2344	0.748671
$883$	−51.5177	−1.73371	−0.866854	−	0.498561i	$-0.833862\pi$
$883$	−51.5177	−1.73371	−0.866854	+	0.498561i	$0.833862\pi$
$884$	−9.60235	−0.322962
$885$	−114.330	−3.84315
$886$	−4.73625	−0.159117
$887$	−38.8548	−1.30462	−0.652309	−	0.757953i	$-0.726200\pi$
$887$	−38.8548	−1.30462	−0.652309	+	0.757953i	$0.726200\pi$
$888$	−18.6208	−0.624872
$889$	−30.7265	−1.03053
$890$	−51.7372	−1.73424
$891$	−7.20047	−0.241225
$892$	−20.6190	−0.690376
$893$	−11.3791	−0.380789
$894$	7.68514	0.257030
$895$	55.4244	1.85263
$896$	−3.65108	−0.121974
$897$	6.22649	0.207896
$898$	13.2461	0.442028
$899$	25.6550	0.855642
$900$	27.8720	0.929067
$901$	−66.3325	−2.20985
$902$	−7.03552	−0.234257
$903$	52.6949	1.75358
$904$	3.27079	0.108785
$905$	69.3533	2.30538
$906$	29.4981	0.980009
$907$	−15.0676	−0.500311	−0.250156	−	0.968206i	$-0.580482\pi$
$907$	−15.0676	−0.500311	−0.250156	+	0.968206i	$0.580482\pi$
$908$	−10.9218	−0.362454
$909$	70.3265	2.33258
$910$	−23.1228	−0.766513
$911$	26.5121	0.878386	0.439193	−	0.898393i	$-0.355264\pi$
$911$	26.5121	0.878386	0.439193	+	0.898393i	$0.355264\pi$
$912$	8.87855	0.293998
$913$	−12.7764	−0.422837
$914$	22.0381	0.728954
$915$	−13.5745	−0.448760
$916$	−24.0175	−0.793560
$917$	44.3424	1.46431
$918$	−7.12982	−0.235319
$919$	−7.35644	−0.242667	−0.121333	−	0.992612i	$-0.538717\pi$
$919$	−7.35644	−0.242667	−0.121333	+	0.992612i	$0.538717\pi$
$920$	−4.98352	−0.164302
$921$	58.2184	1.91836
$922$	−34.8532	−1.14783
$923$	−0.739656	−0.0243461
$924$	9.31729	0.306516
$925$	57.9028	1.90383
$926$	0.838941	0.0275693
$927$	−15.0553	−0.494480
$928$	4.84019	0.158887
$929$	−10.5762	−0.346994	−0.173497	−	0.984834i	$-0.555507\pi$
$929$	−10.5762	−0.346994	−0.173497	+	0.984834i	$0.555507\pi$
$930$	48.6484	1.59524
$931$	−22.0243	−0.721817
$932$	21.1742	0.693583
$933$	−33.2819	−1.08960
$934$	10.1902	0.333435
$935$	−19.6128	−0.641407
$936$	−6.18480	−0.202157
$937$	34.9545	1.14191	0.570956	−	0.820980i	$-0.306573\pi$
$937$	34.9545	1.14191	0.570956	+	0.820980i	$0.306573\pi$
$938$	−7.21896	−0.235707
$939$	53.5263	1.74676
$940$	−11.7632	−0.383675
$941$	39.7026	1.29427	0.647135	−	0.762376i	$-0.275967\pi$
$941$	39.7026	1.29427	0.647135	+	0.762376i	$0.275967\pi$
$942$	20.5188	0.668539
$943$	−9.74859	−0.317458
$944$	−12.4566	−0.405428
$945$	−17.1688	−0.558503
$946$	5.65561	0.183880
$947$	13.2878	0.431796	0.215898	−	0.976416i	$-0.430732\pi$
$947$	13.2878	0.431796	0.215898	+	0.976416i	$0.430732\pi$
$948$	29.3010	0.951651
$949$	8.56453	0.278016
$950$	−27.6086	−0.895742
$951$	61.9831	2.00994
$952$	−19.9099	−0.645284
$953$	11.7639	0.381071	0.190536	−	0.981680i	$-0.438978\pi$
$953$	11.7639	0.381071	0.190536	+	0.981680i	$0.438978\pi$
$954$	−42.7242	−1.38325
$955$	26.0825	0.844010
$956$	−20.4319	−0.660814
$957$	−12.3518	−0.399278
$958$	−29.3423	−0.948007
$959$	−36.7824	−1.18777
$960$	9.17824	0.296226
$961$	−2.90564	−0.0937304
$962$	−12.8486	−0.414257
$963$	33.7983	1.08913
$964$	13.4047	0.431737
$965$	−54.0285	−1.73924
$966$	12.9103	0.415381
$967$	−50.2178	−1.61490	−0.807448	−	0.589939i	$-0.799152\pi$
$967$	−50.2178	−1.61490	−0.807448	+	0.589939i	$0.799152\pi$
$968$	1.00000	0.0321412
$969$	48.4162	1.55535
$970$	−30.8318	−0.989948
$971$	32.0552	1.02870	0.514351	−	0.857580i	$-0.328033\pi$
$971$	32.0552	1.02870	0.514351	+	0.857580i	$0.328033\pi$
$972$	22.2975	0.715192
$973$	−19.8989	−0.637929
$974$	36.3905	1.16603
$975$	35.6590	1.14200
$976$	−1.47899	−0.0473413
$977$	5.16212	0.165151	0.0825754	−	0.996585i	$-0.473685\pi$
$977$	5.16212	0.165151	0.0825754	+	0.996585i	$0.473685\pi$
$978$	−24.5734	−0.785769
$979$	14.3851	0.459750
$980$	−22.7677	−0.727287
$981$	17.3905	0.555235
$982$	25.4213	0.811226
$983$	25.4454	0.811583	0.405791	−	0.913966i	$-0.366996\pi$
$983$	25.4454	0.811583	0.405791	+	0.913966i	$0.366996\pi$
$984$	17.9541	0.572357
$985$	3.59659	0.114597
$986$	26.3944	0.840568
$987$	30.4737	0.969990
$988$	6.12636	0.194905
$989$	7.83655	0.249188
$990$	−12.6325	−0.401486
$991$	−47.1774	−1.49864	−0.749320	−	0.662208i	$-0.769620\pi$
$991$	−47.1774	−1.49864	−0.749320	+	0.662208i	$0.769620\pi$
$992$	5.30041	0.168288
$993$	1.60348	0.0508848
$994$	−1.53363	−0.0486439
$995$	−15.2694	−0.484072
$996$	32.6045	1.03311
$997$	32.9634	1.04396	0.521980	−	0.852958i	$-0.325194\pi$
$997$	32.9634	1.04396	0.521980	+	0.852958i	$0.325194\pi$
$998$	−6.10391	−0.193216
$999$	−9.54022	−0.301839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.b.1.3	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.b.1.3	✓	15	1.1	even	1	trivial

Overview	Random
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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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.55193 q^{3} +1.00000 q^{4} -3.59659 q^{5} -2.55193 q^{6} -3.65108 q^{7} +1.00000 q^{8} +3.51234 q^{9} -3.59659 q^{10} +1.00000 q^{11} -2.55193 q^{12} -1.76088 q^{13} -3.65108 q^{14} +9.17824 q^{15} +1.00000 q^{16} +5.45317 q^{17} +3.51234 q^{18} -3.47915 q^{19} -3.59659 q^{20} +9.31729 q^{21} +1.00000 q^{22} +1.38562 q^{23} -2.55193 q^{24} +7.93544 q^{25} -1.76088 q^{26} -1.30746 q^{27} -3.65108 q^{28} +4.84019 q^{29} +9.17824 q^{30} +5.30041 q^{31} +1.00000 q^{32} -2.55193 q^{33} +5.45317 q^{34} +13.1314 q^{35} +3.51234 q^{36} +7.29674 q^{37} -3.47915 q^{38} +4.49363 q^{39} -3.59659 q^{40} -7.03552 q^{41} +9.31729 q^{42} +5.65561 q^{43} +1.00000 q^{44} -12.6325 q^{45} +1.38562 q^{46} +3.27067 q^{47} -2.55193 q^{48} +6.33036 q^{49} +7.93544 q^{50} -13.9161 q^{51} -1.76088 q^{52} -12.1640 q^{53} -1.30746 q^{54} -3.59659 q^{55} -3.65108 q^{56} +8.87855 q^{57} +4.84019 q^{58} -12.4566 q^{59} +9.17824 q^{60} -1.47899 q^{61} +5.30041 q^{62} -12.8238 q^{63} +1.00000 q^{64} +6.33315 q^{65} -2.55193 q^{66} +1.97721 q^{67} +5.45317 q^{68} -3.53602 q^{69} +13.1314 q^{70} +0.420050 q^{71} +3.51234 q^{72} -4.86379 q^{73} +7.29674 q^{74} -20.2507 q^{75} -3.47915 q^{76} -3.65108 q^{77} +4.49363 q^{78} -11.4819 q^{79} -3.59659 q^{80} -7.20047 q^{81} -7.03552 q^{82} -12.7764 q^{83} +9.31729 q^{84} -19.6128 q^{85} +5.65561 q^{86} -12.3518 q^{87} +1.00000 q^{88} +14.3851 q^{89} -12.6325 q^{90} +6.42909 q^{91} +1.38562 q^{92} -13.5263 q^{93} +3.27067 q^{94} +12.5131 q^{95} -2.55193 q^{96} +8.57250 q^{97} +6.33036 q^{98} +3.51234 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19}+ \cdots + 10 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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