LMFDB - Embedded newform 3887.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3887,2,Mod(1,3887)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3887, 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("3887.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3887 = 13^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3887.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:	$31.0378512657$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 19x^{8} + 18x^{7} + 127x^{6} - 109x^{5} - 357x^{4} + 252x^{3} + 400x^{2} - 192x - 128 $ x^10 - x^9 - 19x^8 + 18x^7 + 127x^6 - 109x^5 - 357x^4 + 252x^3 + 400x^2 - 192x - 128
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 299)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.20349$ of defining polynomial
Character	$\chi$	$=$	3887.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20349 q^{2} -3.23947 q^{3} +2.85538 q^{4} -3.16617 q^{5} +7.13815 q^{6} +0.235798 q^{7} -1.88483 q^{8} +7.49418 q^{9} +O(q^{10})$	\(q-2.20349 q^{2} -3.23947 q^{3} +2.85538 q^{4} -3.16617 q^{5} +7.13815 q^{6} +0.235798 q^{7} -1.88483 q^{8} +7.49418 q^{9} +6.97663 q^{10} -3.79013 q^{11} -9.24994 q^{12} -0.519580 q^{14} +10.2567 q^{15} -1.55755 q^{16} +4.32013 q^{17} -16.5134 q^{18} +1.70609 q^{19} -9.04063 q^{20} -0.763862 q^{21} +8.35152 q^{22} +1.00000 q^{23} +6.10586 q^{24} +5.02462 q^{25} -14.5588 q^{27} +0.673295 q^{28} +1.21141 q^{29} -22.6006 q^{30} +9.90915 q^{31} +7.20172 q^{32} +12.2780 q^{33} -9.51938 q^{34} -0.746578 q^{35} +21.3988 q^{36} +7.10275 q^{37} -3.75935 q^{38} +5.96770 q^{40} +5.91110 q^{41} +1.68317 q^{42} +5.55930 q^{43} -10.8223 q^{44} -23.7278 q^{45} -2.20349 q^{46} +8.57175 q^{47} +5.04564 q^{48} -6.94440 q^{49} -11.0717 q^{50} -13.9949 q^{51} +5.25815 q^{53} +32.0801 q^{54} +12.0002 q^{55} -0.444441 q^{56} -5.52682 q^{57} -2.66932 q^{58} -10.1287 q^{59} +29.2869 q^{60} +3.92523 q^{61} -21.8347 q^{62} +1.76712 q^{63} -12.7538 q^{64} -27.0545 q^{66} +9.95783 q^{67} +12.3356 q^{68} -3.23947 q^{69} +1.64508 q^{70} -15.1592 q^{71} -14.1253 q^{72} +6.96714 q^{73} -15.6509 q^{74} -16.2771 q^{75} +4.87153 q^{76} -0.893706 q^{77} +14.4351 q^{79} +4.93147 q^{80} +24.6801 q^{81} -13.0251 q^{82} -0.579878 q^{83} -2.18112 q^{84} -13.6783 q^{85} -12.2499 q^{86} -3.92431 q^{87} +7.14375 q^{88} -2.75331 q^{89} +52.2841 q^{90} +2.85538 q^{92} -32.1004 q^{93} -18.8878 q^{94} -5.40176 q^{95} -23.3298 q^{96} +7.51768 q^{97} +15.3019 q^{98} -28.4039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9}+O(q^{10}) $ 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9	\( 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9} + 6 q^{10} - 3 q^{11} + 10 q^{12} - 15 q^{14} - 2 q^{15} + 25 q^{16} - 3 q^{17} - q^{18} - 2 q^{19} + 19 q^{20} - 21 q^{21} + 13 q^{22} + 10 q^{23} + 35 q^{24} + 33 q^{25} + 6 q^{27} + 19 q^{28} + 17 q^{29} - 47 q^{30} - 5 q^{31} + 9 q^{32} + 23 q^{33} - 23 q^{34} + 3 q^{35} + 48 q^{36} - 16 q^{37} + 5 q^{38} + 13 q^{40} + 16 q^{41} - 65 q^{42} - 9 q^{43} - 18 q^{44} - 32 q^{45} - q^{46} + 11 q^{47} + 37 q^{48} + 40 q^{49} + 30 q^{50} - 31 q^{51} + 8 q^{53} + 73 q^{54} - 14 q^{55} - 54 q^{56} + 35 q^{57} - 17 q^{58} - 2 q^{59} + 37 q^{60} + 48 q^{61} - 19 q^{62} + 15 q^{63} + 64 q^{64} - 84 q^{66} + 6 q^{67} - 62 q^{68} + 3 q^{69} + 44 q^{70} - 24 q^{71} + 89 q^{72} + 33 q^{73} - 28 q^{74} - 22 q^{75} + 53 q^{76} + 15 q^{77} + 17 q^{79} + 94 q^{80} + 30 q^{81} + 35 q^{82} + 21 q^{83} - 92 q^{84} - 58 q^{85} + 7 q^{86} + 23 q^{87} + 9 q^{88} + 16 q^{89} + 67 q^{90} + 19 q^{92} - 15 q^{93} + 12 q^{94} - 27 q^{95} + 22 q^{96} + 40 q^{97} + 34 q^{98} + 17 q^{99}+O(q^{100}) \) 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9 + 6 * q^10 - 3 * q^11 + 10 * q^12 - 15 * q^14 - 2 * q^15 + 25 * q^16 - 3 * q^17 - q^18 - 2 * q^19 + 19 * q^20 - 21 * q^21 + 13 * q^22 + 10 * q^23 + 35 * q^24 + 33 * q^25 + 6 * q^27 + 19 * q^28 + 17 * q^29 - 47 * q^30 - 5 * q^31 + 9 * q^32 + 23 * q^33 - 23 * q^34 + 3 * q^35 + 48 * q^36 - 16 * q^37 + 5 * q^38 + 13 * q^40 + 16 * q^41 - 65 * q^42 - 9 * q^43 - 18 * q^44 - 32 * q^45 - q^46 + 11 * q^47 + 37 * q^48 + 40 * q^49 + 30 * q^50 - 31 * q^51 + 8 * q^53 + 73 * q^54 - 14 * q^55 - 54 * q^56 + 35 * q^57 - 17 * q^58 - 2 * q^59 + 37 * q^60 + 48 * q^61 - 19 * q^62 + 15 * q^63 + 64 * q^64 - 84 * q^66 + 6 * q^67 - 62 * q^68 + 3 * q^69 + 44 * q^70 - 24 * q^71 + 89 * q^72 + 33 * q^73 - 28 * q^74 - 22 * q^75 + 53 * q^76 + 15 * q^77 + 17 * q^79 + 94 * q^80 + 30 * q^81 + 35 * q^82 + 21 * q^83 - 92 * q^84 - 58 * q^85 + 7 * q^86 + 23 * q^87 + 9 * q^88 + 16 * q^89 + 67 * q^90 + 19 * q^92 - 15 * q^93 + 12 * q^94 - 27 * q^95 + 22 * q^96 + 40 * q^97 + 34 * q^98 + 17 * 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 $

$2$	−2.20349	−1.55811	−0.779053	−	0.626959i	$-0.784300\pi$
$2$	−2.20349	−1.55811	−0.779053	+	0.626959i	$0.784300\pi$
$3$	−3.23947	−1.87031	−0.935155	−	0.354239i	$-0.884740\pi$
$3$	−3.23947	−1.87031	−0.935155	+	0.354239i	$0.884740\pi$
$4$	2.85538	1.42769
$5$	−3.16617	−1.41595	−0.707977	−	0.706236i	$-0.750392\pi$
$5$	−3.16617	−1.41595	−0.707977	+	0.706236i	$0.750392\pi$
$6$	7.13815	2.91414
$7$	0.235798	0.0891234	0.0445617	−	0.999007i	$-0.485811\pi$
$7$	0.235798	0.0891234	0.0445617	+	0.999007i	$0.485811\pi$
$8$	−1.88483	−0.666389
$9$	7.49418	2.49806
$10$	6.97663	2.20620
$11$	−3.79013	−1.14277	−0.571383	−	0.820684i	$-0.693593\pi$
$11$	−3.79013	−1.14277	−0.571383	+	0.820684i	$0.693593\pi$
$12$	−9.24994	−2.67023
$13$	0	0
$13$	0	0
$14$	−0.519580	−0.138864
$15$	10.2567	2.64827
$16$	−1.55755	−0.389388
$17$	4.32013	1.04779	0.523893	−	0.851784i	$-0.324479\pi$
$17$	4.32013	1.04779	0.523893	+	0.851784i	$0.324479\pi$
$18$	−16.5134	−3.89224
$19$	1.70609	0.391403	0.195702	−	0.980663i	$-0.437302\pi$
$19$	1.70609	0.391403	0.195702	+	0.980663i	$0.437302\pi$
$20$	−9.04063	−2.02155
$21$	−0.763862	−0.166688
$22$	8.35152	1.78055
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	6.10586	1.24635
$25$	5.02462	1.00492
$26$	0	0
$27$	−14.5588	−2.80183
$28$	0.673295	0.127241
$29$	1.21141	0.224952	0.112476	−	0.993654i	$-0.464122\pi$
$29$	1.21141	0.224952	0.112476	+	0.993654i	$0.464122\pi$
$30$	−22.6006	−4.12629
$31$	9.90915	1.77974	0.889868	−	0.456219i	$-0.150797\pi$
$31$	9.90915	1.77974	0.889868	+	0.456219i	$0.150797\pi$
$32$	7.20172	1.27310
$33$	12.2780	2.13733
$34$	−9.51938	−1.63256
$35$	−0.746578	−0.126195
$36$	21.3988	3.56646
$37$	7.10275	1.16769	0.583843	−	0.811867i	$-0.301549\pi$
$37$	7.10275	1.16769	0.583843	+	0.811867i	$0.301549\pi$
$38$	−3.75935	−0.609847
$39$	0	0
$40$	5.96770	0.943576
$41$	5.91110	0.923159	0.461580	−	0.887099i	$-0.347283\pi$
$41$	5.91110	0.923159	0.461580	+	0.887099i	$0.347283\pi$
$42$	1.68317	0.259718
$43$	5.55930	0.847786	0.423893	−	0.905712i	$-0.360663\pi$
$43$	5.55930	0.847786	0.423893	+	0.905712i	$0.360663\pi$
$44$	−10.8223	−1.63152
$45$	−23.7278	−3.53714
$46$	−2.20349	−0.324887
$47$	8.57175	1.25032	0.625159	−	0.780498i	$-0.285034\pi$
$47$	8.57175	1.25032	0.625159	+	0.780498i	$0.285034\pi$
$48$	5.04564	0.728275
$49$	−6.94440	−0.992057
$50$	−11.0717	−1.56578
$51$	−13.9949	−1.95968
$52$	0	0
$53$	5.25815	0.722262	0.361131	−	0.932515i	$-0.382391\pi$
$53$	5.25815	0.722262	0.361131	+	0.932515i	$0.382391\pi$
$54$	32.0801	4.36555
$55$	12.0002	1.61810
$56$	−0.444441	−0.0593909
$57$	−5.52682	−0.732045
$58$	−2.66932	−0.350499
$59$	−10.1287	−1.31865	−0.659325	−	0.751858i	$-0.729158\pi$
$59$	−10.1287	−1.31865	−0.659325	+	0.751858i	$0.729158\pi$
$60$	29.2869	3.78092
$61$	3.92523	0.502574	0.251287	−	0.967913i	$-0.419146\pi$
$61$	3.92523	0.502574	0.251287	+	0.967913i	$0.419146\pi$
$62$	−21.8347	−2.77302
$63$	1.76712	0.222636
$64$	−12.7538	−1.59423
$65$	0	0
$66$	−27.0545	−3.33018
$67$	9.95783	1.21654	0.608271	−	0.793729i	$-0.291863\pi$
$67$	9.95783	1.21654	0.608271	+	0.793729i	$0.291863\pi$
$68$	12.3356	1.49592
$69$	−3.23947	−0.389987
$70$	1.64508	0.196625
$71$	−15.1592	−1.79907	−0.899536	−	0.436847i	$-0.856095\pi$
$71$	−15.1592	−1.79907	−0.899536	+	0.436847i	$0.856095\pi$
$72$	−14.1253	−1.66468
$73$	6.96714	0.815442	0.407721	−	0.913107i	$-0.366324\pi$
$73$	6.96714	0.815442	0.407721	+	0.913107i	$0.366324\pi$
$74$	−15.6509	−1.81938
$75$	−16.2771	−1.87952
$76$	4.87153	0.558803
$77$	−0.893706	−0.101847
$78$	0	0
$79$	14.4351	1.62407	0.812036	−	0.583607i	$-0.198359\pi$
$79$	14.4351	1.62407	0.812036	+	0.583607i	$0.198359\pi$
$80$	4.93147	0.551355
$81$	24.6801	2.74224
$82$	−13.0251	−1.43838
$83$	−0.579878	−0.0636499	−0.0318250	−	0.999493i	$-0.510132\pi$
$83$	−0.579878	−0.0636499	−0.0318250	+	0.999493i	$0.510132\pi$
$84$	−2.18112	−0.237980
$85$	−13.6783	−1.48362
$86$	−12.2499	−1.32094
$87$	−3.92431	−0.420731
$88$	7.14375	0.761527
$89$	−2.75331	−0.291851	−0.145925	−	0.989296i	$-0.546616\pi$
$89$	−2.75331	−0.291851	−0.145925	+	0.989296i	$0.546616\pi$
$90$	52.2841	5.51123
$91$	0	0
$92$	2.85538	0.297694
$93$	−32.1004	−3.32866
$94$	−18.8878	−1.94813
$95$	−5.40176	−0.554209
$96$	−23.3298	−2.38108
$97$	7.51768	0.763305	0.381653	−	0.924306i	$-0.375355\pi$
$97$	7.51768	0.763305	0.381653	+	0.924306i	$0.375355\pi$
$98$	15.3019	1.54573
$99$	−28.4039	−2.85470
$100$	14.3472	1.43472
$101$	−0.909694	−0.0905180	−0.0452590	−	0.998975i	$-0.514411\pi$
$101$	−0.909694	−0.0905180	−0.0452590	+	0.998975i	$0.514411\pi$
$102$	30.8378	3.05339
$103$	−12.5697	−1.23853	−0.619265	−	0.785182i	$-0.712569\pi$
$103$	−12.5697	−1.23853	−0.619265	+	0.785182i	$0.712569\pi$
$104$	0	0
$105$	2.41852	0.236023
$106$	−11.5863	−1.12536
$107$	−15.7354	−1.52120	−0.760598	−	0.649224i	$-0.775094\pi$
$107$	−15.7354	−1.52120	−0.760598	+	0.649224i	$0.775094\pi$
$108$	−41.5708	−4.00016
$109$	−16.2006	−1.55174	−0.775868	−	0.630896i	$-0.782688\pi$
$109$	−16.2006	−1.55174	−0.775868	+	0.630896i	$0.782688\pi$
$110$	−26.4423	−2.52118
$111$	−23.0092	−2.18393
$112$	−0.367268	−0.0347036
$113$	4.04330	0.380362	0.190181	−	0.981749i	$-0.439093\pi$
$113$	4.04330	0.380362	0.190181	+	0.981749i	$0.439093\pi$
$114$	12.1783	1.14060
$115$	−3.16617	−0.295247
$116$	3.45903	0.321163
$117$	0	0
$118$	22.3186	2.05460
$119$	1.01868	0.0933823
$120$	−19.3322	−1.76478
$121$	3.36505	0.305914
$122$	−8.64921	−0.783063
$123$	−19.1488	−1.72659
$124$	28.2944	2.54091
$125$	−0.0779656	−0.00697345
$126$	−3.89383	−0.346890
$127$	−7.84438	−0.696077	−0.348038	−	0.937480i	$-0.613152\pi$
$127$	−7.84438	−0.696077	−0.348038	+	0.937480i	$0.613152\pi$
$128$	13.6996	1.21088
$129$	−18.0092	−1.58562
$130$	0	0
$131$	1.14696	0.100210	0.0501051	−	0.998744i	$-0.484044\pi$
$131$	1.14696	0.100210	0.0501051	+	0.998744i	$0.484044\pi$
$132$	35.0584	3.05144
$133$	0.402293	0.0348832
$134$	−21.9420	−1.89550
$135$	46.0955	3.96727
$136$	−8.14273	−0.698233
$137$	6.83485	0.583941	0.291970	−	0.956427i	$-0.405689\pi$
$137$	6.83485	0.583941	0.291970	+	0.956427i	$0.405689\pi$
$138$	7.13815	0.607640
$139$	5.71966	0.485136	0.242568	−	0.970134i	$-0.422010\pi$
$139$	5.71966	0.485136	0.242568	+	0.970134i	$0.422010\pi$
$140$	−2.13177	−0.180167
$141$	−27.7679	−2.33848
$142$	33.4033	2.80314
$143$	0	0
$144$	−11.6726	−0.972713
$145$	−3.83551	−0.318522
$146$	−15.3520	−1.27054
$147$	22.4962	1.85545
$148$	20.2811	1.66709
$149$	10.8560	0.889362	0.444681	−	0.895689i	$-0.353317\pi$
$149$	10.8560	0.889362	0.444681	+	0.895689i	$0.353317\pi$
$150$	35.8665	2.92849
$151$	0.713918	0.0580978	0.0290489	−	0.999578i	$-0.490752\pi$
$151$	0.713918	0.0580978	0.0290489	+	0.999578i	$0.490752\pi$
$152$	−3.21569	−0.260827
$153$	32.3758	2.61743
$154$	1.96927	0.158689
$155$	−31.3740	−2.52002
$156$	0	0
$157$	2.92054	0.233085	0.116542	−	0.993186i	$-0.462819\pi$
$157$	2.92054	0.233085	0.116542	+	0.993186i	$0.462819\pi$
$158$	−31.8076	−2.53048
$159$	−17.0336	−1.35085
$160$	−22.8019	−1.80264
$161$	0.235798	0.0185835
$162$	−54.3825	−4.27270
$163$	5.44671	0.426619	0.213310	−	0.976985i	$-0.431576\pi$
$163$	5.44671	0.426619	0.213310	+	0.976985i	$0.431576\pi$
$164$	16.8785	1.31799
$165$	−38.8742	−3.02635
$166$	1.27776	0.0991733
$167$	−19.9006	−1.53995	−0.769976	−	0.638073i	$-0.779732\pi$
$167$	−19.9006	−1.53995	−0.769976	+	0.638073i	$0.779732\pi$
$168$	1.43975	0.111079
$169$	0	0
$170$	30.1400	2.31163
$171$	12.7857	0.977748
$172$	15.8739	1.21038
$173$	6.99238	0.531621	0.265811	−	0.964025i	$-0.414360\pi$
$173$	6.99238	0.531621	0.265811	+	0.964025i	$0.414360\pi$
$174$	8.64720	0.655542
$175$	1.18480	0.0895624
$176$	5.90331	0.444979
$177$	32.8118	2.46628
$178$	6.06691	0.454734
$179$	8.75931	0.654701	0.327351	−	0.944903i	$-0.393844\pi$
$179$	8.75931	0.654701	0.327351	+	0.944903i	$0.393844\pi$
$180$	−67.7521	−5.04994
$181$	−4.76957	−0.354520	−0.177260	−	0.984164i	$-0.556723\pi$
$181$	−4.76957	−0.354520	−0.177260	+	0.984164i	$0.556723\pi$
$182$	0	0
$183$	−12.7157	−0.939969
$184$	−1.88483	−0.138952
$185$	−22.4885	−1.65339
$186$	70.7330	5.18640
$187$	−16.3738	−1.19737
$188$	24.4756	1.78507
$189$	−3.43293	−0.249709
$190$	11.9027	0.863516
$191$	−22.7443	−1.64572	−0.822861	−	0.568243i	$-0.807623\pi$
$191$	−22.7443	−1.64572	−0.822861	+	0.568243i	$0.807623\pi$
$192$	41.3157	2.98170
$193$	8.47048	0.609719	0.304859	−	0.952397i	$-0.401391\pi$
$193$	8.47048	0.609719	0.304859	+	0.952397i	$0.401391\pi$
$194$	−16.5652	−1.18931
$195$	0	0
$196$	−19.8289	−1.41635
$197$	−6.11920	−0.435975	−0.217988	−	0.975952i	$-0.569949\pi$
$197$	−6.11920	−0.435975	−0.217988	+	0.975952i	$0.569949\pi$
$198$	62.5877	4.44792
$199$	17.7018	1.25485	0.627425	−	0.778677i	$-0.284109\pi$
$199$	17.7018	1.25485	0.627425	+	0.778677i	$0.284109\pi$
$200$	−9.47058	−0.669671
$201$	−32.2581	−2.27531
$202$	2.00451	0.141037
$203$	0.285647	0.0200485
$204$	−39.9609	−2.79783
$205$	−18.7155	−1.30715
$206$	27.6973	1.92976
$207$	7.49418	0.520881
$208$	0	0
$209$	−6.46629	−0.447282
$210$	−5.32919	−0.367749
$211$	21.8534	1.50445	0.752226	−	0.658906i	$-0.228980\pi$
$211$	21.8534	1.50445	0.752226	+	0.658906i	$0.228980\pi$
$212$	15.0140	1.03117
$213$	49.1079	3.36482
$214$	34.6728	2.37018
$215$	−17.6017	−1.20043
$216$	27.4408	1.86711
$217$	2.33656	0.158616
$218$	35.6979	2.41777
$219$	−22.5698	−1.52513
$220$	34.2651	2.31015
$221$	0	0
$222$	50.7005	3.40280
$223$	17.7866	1.19108	0.595540	−	0.803325i	$-0.296938\pi$
$223$	17.7866	1.19108	0.595540	+	0.803325i	$0.296938\pi$
$224$	1.69815	0.113463
$225$	37.6554	2.51036
$226$	−8.90939	−0.592644
$227$	−7.90472	−0.524655	−0.262327	−	0.964979i	$-0.584490\pi$
$227$	−7.90472	−0.524655	−0.262327	+	0.964979i	$0.584490\pi$
$228$	−15.7812	−1.04514
$229$	−21.3088	−1.40812	−0.704062	−	0.710139i	$-0.748632\pi$
$229$	−21.3088	−1.40812	−0.704062	+	0.710139i	$0.748632\pi$
$230$	6.97663	0.460026
$231$	2.89513	0.190486
$232$	−2.28330	−0.149906
$233$	−6.36295	−0.416851	−0.208425	−	0.978038i	$-0.566834\pi$
$233$	−6.36295	−0.416851	−0.208425	+	0.978038i	$0.566834\pi$
$234$	0	0
$235$	−27.1396	−1.77039
$236$	−28.9215	−1.88263
$237$	−46.7620	−3.03752
$238$	−2.24466	−0.145499
$239$	−10.1265	−0.655026	−0.327513	−	0.944847i	$-0.606211\pi$
$239$	−10.1265	−0.655026	−0.327513	+	0.944847i	$0.606211\pi$
$240$	−15.9753	−1.03120
$241$	7.66833	0.493961	0.246980	−	0.969021i	$-0.420562\pi$
$241$	7.66833	0.493961	0.246980	+	0.969021i	$0.420562\pi$
$242$	−7.41487	−0.476646
$243$	−36.2744	−2.32700
$244$	11.2080	0.717521
$245$	21.9871	1.40471
$246$	42.1944	2.69021
$247$	0	0
$248$	−18.6771	−1.18600
$249$	1.87850	0.119045
$250$	0.171797	0.0108654
$251$	−25.2235	−1.59209	−0.796047	−	0.605235i	$-0.793079\pi$
$251$	−25.2235	−1.59209	−0.796047	+	0.605235i	$0.793079\pi$
$252$	5.04579	0.317855
$253$	−3.79013	−0.238283
$254$	17.2850	1.08456
$255$	44.3104	2.77482
$256$	−4.67923	−0.292452
$257$	12.1672	0.758969	0.379484	−	0.925198i	$-0.376101\pi$
$257$	12.1672	0.758969	0.379484	+	0.925198i	$0.376101\pi$
$258$	39.6832	2.47057
$259$	1.67482	0.104068
$260$	0	0
$261$	9.07848	0.561944
$262$	−2.52732	−0.156138
$263$	6.82097	0.420599	0.210299	−	0.977637i	$-0.432556\pi$
$263$	6.82097	0.420599	0.210299	+	0.977637i	$0.432556\pi$
$264$	−23.1420	−1.42429
$265$	−16.6482	−1.02269
$266$	−0.886449	−0.0543517
$267$	8.91928	0.545851
$268$	28.4334	1.73685
$269$	0.678927	0.0413949	0.0206975	−	0.999786i	$-0.493411\pi$
$269$	0.678927	0.0413949	0.0206975	+	0.999786i	$0.493411\pi$
$270$	−101.571	−6.18142
$271$	−1.53300	−0.0931231	−0.0465616	−	0.998915i	$-0.514826\pi$
$271$	−1.53300	−0.0931231	−0.0465616	+	0.998915i	$0.514826\pi$
$272$	−6.72882	−0.407995
$273$	0	0
$274$	−15.0606	−0.909841
$275$	−19.0440	−1.14839
$276$	−9.24994	−0.556781
$277$	19.3966	1.16543	0.582716	−	0.812676i	$-0.301990\pi$
$277$	19.3966	1.16543	0.582716	+	0.812676i	$0.301990\pi$
$278$	−12.6032	−0.755892
$279$	74.2609	4.44588
$280$	1.40717	0.0840948
$281$	10.9696	0.654393	0.327196	−	0.944956i	$-0.393896\pi$
$281$	10.9696	0.654393	0.327196	+	0.944956i	$0.393896\pi$
$282$	61.1864	3.64360
$283$	19.2341	1.14335	0.571674	−	0.820481i	$-0.306294\pi$
$283$	19.2341	1.14335	0.571674	+	0.820481i	$0.306294\pi$
$284$	−43.2855	−2.56852
$285$	17.4988	1.03654
$286$	0	0
$287$	1.39383	0.0822751
$288$	53.9709	3.18027
$289$	1.66354	0.0978552
$290$	8.45153	0.496291
$291$	−24.3533	−1.42762
$292$	19.8939	1.16420
$293$	15.6597	0.914851	0.457426	−	0.889248i	$-0.348772\pi$
$293$	15.6597	0.914851	0.457426	+	0.889248i	$0.348772\pi$
$294$	−49.5702	−2.89099
$295$	32.0693	1.86715
$296$	−13.3875	−0.778133
$297$	55.1795	3.20184
$298$	−23.9212	−1.38572
$299$	0	0
$300$	−46.4775	−2.68338
$301$	1.31087	0.0755576
$302$	−1.57311	−0.0905225
$303$	2.94693	0.169297
$304$	−2.65732	−0.152408
$305$	−12.4279	−0.711621
$306$	−71.3399	−4.07823
$307$	−28.2538	−1.61253	−0.806266	−	0.591553i	$-0.798515\pi$
$307$	−28.2538	−1.61253	−0.806266	+	0.591553i	$0.798515\pi$
$308$	−2.55187	−0.145406
$309$	40.7192	2.31643
$310$	69.1325	3.92646
$311$	−2.27688	−0.129110	−0.0645549	−	0.997914i	$-0.520563\pi$
$311$	−2.27688	−0.129110	−0.0645549	+	0.997914i	$0.520563\pi$
$312$	0	0
$313$	23.7113	1.34024	0.670120	−	0.742252i	$-0.266242\pi$
$313$	23.7113	1.34024	0.670120	+	0.742252i	$0.266242\pi$
$314$	−6.43540	−0.363171
$315$	−5.59498	−0.315242
$316$	41.2177	2.31867
$317$	20.4521	1.14870	0.574352	−	0.818609i	$-0.305254\pi$
$317$	20.4521	1.14870	0.574352	+	0.818609i	$0.305254\pi$
$318$	37.5335	2.10477
$319$	−4.59138	−0.257068
$320$	40.3808	2.25736
$321$	50.9743	2.84511
$322$	−0.519580	−0.0289551
$323$	7.37052	0.410107
$324$	70.4713	3.91507
$325$	0	0
$326$	−12.0018	−0.664718
$327$	52.4814	2.90223
$328$	−11.1414	−0.615183
$329$	2.02120	0.111433
$330$	85.6591	4.71538
$331$	−16.5340	−0.908788	−0.454394	−	0.890801i	$-0.650144\pi$
$331$	−16.5340	−0.908788	−0.454394	+	0.890801i	$0.650144\pi$
$332$	−1.65578	−0.0908725
$333$	53.2293	2.91695
$334$	43.8507	2.39941
$335$	−31.5282	−1.72257
$336$	1.18975	0.0649064
$337$	−3.64158	−0.198370	−0.0991848	−	0.995069i	$-0.531623\pi$
$337$	−3.64158	−0.198370	−0.0991848	+	0.995069i	$0.531623\pi$
$338$	0	0
$339$	−13.0982	−0.711395
$340$	−39.0567	−2.11815
$341$	−37.5569	−2.03382
$342$	−28.1732	−1.52343
$343$	−3.28807	−0.177539
$344$	−10.4784	−0.564955
$345$	10.2567	0.552203
$346$	−15.4077	−0.828322
$347$	−5.03984	−0.270553	−0.135276	−	0.990808i	$-0.543192\pi$
$347$	−5.03984	−0.270553	−0.135276	+	0.990808i	$0.543192\pi$
$348$	−11.2054	−0.600674
$349$	−9.06627	−0.485306	−0.242653	−	0.970113i	$-0.578018\pi$
$349$	−9.06627	−0.485306	−0.242653	+	0.970113i	$0.578018\pi$
$350$	−2.61070	−0.139548
$351$	0	0
$352$	−27.2954	−1.45485
$353$	−16.0812	−0.855916	−0.427958	−	0.903799i	$-0.640767\pi$
$353$	−16.0812	−0.855916	−0.427958	+	0.903799i	$0.640767\pi$
$354$	−72.3006	−3.84273
$355$	47.9967	2.54740
$356$	−7.86177	−0.416673
$357$	−3.29999	−0.174654
$358$	−19.3011	−1.02009
$359$	9.49369	0.501058	0.250529	−	0.968109i	$-0.419395\pi$
$359$	9.49369	0.501058	0.250529	+	0.968109i	$0.419395\pi$
$360$	44.7230	2.35711
$361$	−16.0893	−0.846803
$362$	10.5097	0.552379
$363$	−10.9010	−0.572154
$364$	0	0
$365$	−22.0591	−1.15463
$366$	28.0189	1.46457
$367$	24.7931	1.29419	0.647094	−	0.762410i	$-0.275984\pi$
$367$	24.7931	1.29419	0.647094	+	0.762410i	$0.275984\pi$
$368$	−1.55755	−0.0811929
$369$	44.2988	2.30611
$370$	49.5533	2.57615
$371$	1.23986	0.0643705
$372$	−91.6590	−4.75230
$373$	−0.0784580	−0.00406240	−0.00203120	−	0.999998i	$-0.500647\pi$
$373$	−0.0784580	−0.00406240	−0.00203120	+	0.999998i	$0.500647\pi$
$374$	36.0797	1.86563
$375$	0.252567	0.0130425
$376$	−16.1563	−0.833198
$377$	0	0
$378$	7.56444	0.389073
$379$	−32.3741	−1.66294	−0.831472	−	0.555567i	$-0.812501\pi$
$379$	−32.3741	−1.66294	−0.831472	+	0.555567i	$0.812501\pi$
$380$	−15.4241	−0.791240
$381$	25.4117	1.30188
$382$	50.1170	2.56421
$383$	9.92132	0.506956	0.253478	−	0.967341i	$-0.418425\pi$
$383$	9.92132	0.506956	0.253478	+	0.967341i	$0.418425\pi$
$384$	−44.3794	−2.26472
$385$	2.82962	0.144211
$386$	−18.6647	−0.950006
$387$	41.6624	2.11782
$388$	21.4659	1.08976
$389$	32.1131	1.62820	0.814099	−	0.580726i	$-0.197231\pi$
$389$	32.1131	1.62820	0.814099	+	0.580726i	$0.197231\pi$
$390$	0	0
$391$	4.32013	0.218478
$392$	13.0890	0.661096
$393$	−3.71554	−0.187424
$394$	13.4836	0.679295
$395$	−45.7039	−2.29961
$396$	−81.1040	−4.07563
$397$	−25.2034	−1.26492	−0.632460	−	0.774593i	$-0.717955\pi$
$397$	−25.2034	−1.26492	−0.632460	+	0.774593i	$0.717955\pi$
$398$	−39.0059	−1.95519
$399$	−1.30322	−0.0652424
$400$	−7.82610	−0.391305
$401$	7.35628	0.367355	0.183678	−	0.982987i	$-0.441200\pi$
$401$	7.35628	0.367355	0.183678	+	0.982987i	$0.441200\pi$
$402$	71.0805	3.54517
$403$	0	0
$404$	−2.59753	−0.129232
$405$	−78.1415	−3.88288
$406$	−0.629422	−0.0312377
$407$	−26.9203	−1.33439
$408$	26.3781	1.30591
$409$	34.8746	1.72444	0.862218	−	0.506537i	$-0.169075\pi$
$409$	34.8746	1.72444	0.862218	+	0.506537i	$0.169075\pi$
$410$	41.2396	2.03668
$411$	−22.1413	−1.09215
$412$	−35.8913	−1.76824
$413$	−2.38834	−0.117523
$414$	−16.5134	−0.811588
$415$	1.83599	0.0901254
$416$	0	0
$417$	−18.5287	−0.907354
$418$	14.2484	0.696913
$419$	20.9702	1.02446	0.512231	−	0.858848i	$-0.328819\pi$
$419$	20.9702	1.02446	0.512231	+	0.858848i	$0.328819\pi$
$420$	6.90580	0.336968
$421$	−1.80263	−0.0878549	−0.0439275	−	0.999035i	$-0.513987\pi$
$421$	−1.80263	−0.0878549	−0.0439275	+	0.999035i	$0.513987\pi$
$422$	−48.1539	−2.34409
$423$	64.2382	3.12337
$424$	−9.91073	−0.481308
$425$	21.7070	1.05295
$426$	−108.209	−5.24275
$427$	0.925562	0.0447911
$428$	−44.9305	−2.17180
$429$	0	0
$430$	38.7852	1.87039
$431$	−11.7955	−0.568169	−0.284084	−	0.958799i	$-0.591690\pi$
$431$	−11.7955	−0.568169	−0.284084	+	0.958799i	$0.591690\pi$
$432$	22.6760	1.09100
$433$	−10.3628	−0.498002	−0.249001	−	0.968503i	$-0.580102\pi$
$433$	−10.3628	−0.498002	−0.249001	+	0.968503i	$0.580102\pi$
$434$	−5.14860	−0.247141
$435$	12.4250	0.595735
$436$	−46.2589	−2.21540
$437$	1.70609	0.0816132
$438$	49.7325	2.37631
$439$	−27.0965	−1.29324	−0.646622	−	0.762811i	$-0.723819\pi$
$439$	−27.0965	−1.29324	−0.646622	+	0.762811i	$0.723819\pi$
$440$	−22.6183	−1.07829
$441$	−52.0425	−2.47822
$442$	0	0
$443$	31.9676	1.51883	0.759413	−	0.650609i	$-0.225486\pi$
$443$	31.9676	1.51883	0.759413	+	0.650609i	$0.225486\pi$
$444$	−65.7000	−3.11798
$445$	8.71746	0.413247
$446$	−39.1927	−1.85583
$447$	−35.1679	−1.66338
$448$	−3.00734	−0.142083
$449$	12.2815	0.579599	0.289800	−	0.957087i	$-0.406411\pi$
$449$	12.2815	0.579599	0.289800	+	0.957087i	$0.406411\pi$
$450$	−82.9735	−3.91141
$451$	−22.4038	−1.05495
$452$	11.5452	0.543040
$453$	−2.31272	−0.108661
$454$	17.4180	0.817467
$455$	0	0
$456$	10.4171	0.487827
$457$	16.6559	0.779132	0.389566	−	0.920999i	$-0.372625\pi$
$457$	16.6559	0.779132	0.389566	+	0.920999i	$0.372625\pi$
$458$	46.9538	2.19400
$459$	−62.8957	−2.93572
$460$	−9.04063	−0.421521
$461$	3.40671	0.158666	0.0793332	−	0.996848i	$-0.474721\pi$
$461$	3.40671	0.158666	0.0793332	+	0.996848i	$0.474721\pi$
$462$	−6.37941	−0.296797
$463$	4.05946	0.188659	0.0943296	−	0.995541i	$-0.469929\pi$
$463$	4.05946	0.188659	0.0943296	+	0.995541i	$0.469929\pi$
$464$	−1.88682	−0.0875936
$465$	101.635	4.71322
$466$	14.0207	0.649497
$467$	−9.94601	−0.460246	−0.230123	−	0.973162i	$-0.573913\pi$
$467$	−9.94601	−0.460246	−0.230123	+	0.973162i	$0.573913\pi$
$468$	0	0
$469$	2.34804	0.108422
$470$	59.8019	2.75846
$471$	−9.46102	−0.435941
$472$	19.0910	0.878734
$473$	−21.0705	−0.968821
$474$	103.040	4.73277
$475$	8.57245	0.393331
$476$	2.90872	0.133321
$477$	39.4055	1.80425
$478$	22.3136	1.02060
$479$	27.6591	1.26378	0.631888	−	0.775059i	$-0.282280\pi$
$479$	27.6591	1.26378	0.631888	+	0.775059i	$0.282280\pi$
$480$	73.8660	3.37150
$481$	0	0
$482$	−16.8971	−0.769642
$483$	−0.763862	−0.0347569
$484$	9.60852	0.436751
$485$	−23.8023	−1.08080
$486$	79.9303	3.62571
$487$	7.20231	0.326368	0.163184	−	0.986596i	$-0.447824\pi$
$487$	7.20231	0.326368	0.163184	+	0.986596i	$0.447824\pi$
$488$	−7.39840	−0.334910
$489$	−17.6445	−0.797911
$490$	−48.4485	−2.18868
$491$	−9.65647	−0.435790	−0.217895	−	0.975972i	$-0.569919\pi$
$491$	−9.65647	−0.435790	−0.217895	+	0.975972i	$0.569919\pi$
$492$	−54.6773	−2.46504
$493$	5.23343	0.235702
$494$	0	0
$495$	89.9314	4.04212
$496$	−15.4340	−0.693007
$497$	−3.57453	−0.160339
$498$	−4.13926	−0.185485
$499$	14.5438	0.651069	0.325534	−	0.945530i	$-0.394456\pi$
$499$	14.5438	0.651069	0.325534	+	0.945530i	$0.394456\pi$
$500$	−0.222622	−0.00995594
$501$	64.4673	2.88019
$502$	55.5799	2.48065
$503$	27.0631	1.20668	0.603342	−	0.797483i	$-0.293836\pi$
$503$	27.0631	1.20668	0.603342	+	0.797483i	$0.293836\pi$
$504$	−3.33072	−0.148362
$505$	2.88025	0.128169
$506$	8.35152	0.371270
$507$	0	0
$508$	−22.3987	−0.993783
$509$	2.63712	0.116888	0.0584440	−	0.998291i	$-0.481386\pi$
$509$	2.63712	0.116888	0.0584440	+	0.998291i	$0.481386\pi$
$510$	−97.6376	−4.32346
$511$	1.64284	0.0726750
$512$	−17.0885	−0.755211
$513$	−24.8385	−1.09665
$514$	−26.8103	−1.18255
$515$	39.7978	1.75370
$516$	−51.4232	−2.26378
$517$	−32.4880	−1.42882
$518$	−3.69045	−0.162149
$519$	−22.6516	−0.994296
$520$	0	0
$521$	19.3631	0.848314	0.424157	−	0.905589i	$-0.360570\pi$
$521$	19.3631	0.848314	0.424157	+	0.905589i	$0.360570\pi$
$522$	−20.0044	−0.875568
$523$	−26.8206	−1.17278	−0.586392	−	0.810028i	$-0.699452\pi$
$523$	−26.8206	−1.17278	−0.586392	+	0.810028i	$0.699452\pi$
$524$	3.27501	0.143069
$525$	−3.83812	−0.167509
$526$	−15.0300	−0.655337
$527$	42.8088	1.86478
$528$	−19.1236	−0.832248
$529$	1.00000	0.0434783
$530$	36.6842	1.59346
$531$	−75.9066	−3.29407
$532$	1.14870	0.0498025
$533$	0	0
$534$	−19.6536	−0.850494
$535$	49.8208	2.15394
$536$	−18.7688	−0.810690
$537$	−28.3755	−1.22449
$538$	−1.49601	−0.0644977
$539$	26.3201	1.13369
$540$	131.620	5.66404
$541$	−4.98239	−0.214210	−0.107105	−	0.994248i	$-0.534158\pi$
$541$	−4.98239	−0.214210	−0.107105	+	0.994248i	$0.534158\pi$
$542$	3.37796	0.145096
$543$	15.4509	0.663062
$544$	31.1124	1.33393
$545$	51.2938	2.19719
$546$	0	0
$547$	−13.4452	−0.574874	−0.287437	−	0.957800i	$-0.592803\pi$
$547$	−13.4452	−0.574874	−0.287437	+	0.957800i	$0.592803\pi$
$548$	19.5161	0.833688
$549$	29.4163	1.25546
$550$	41.9632	1.78932
$551$	2.06676	0.0880471
$552$	6.10586	0.259883
$553$	3.40377	0.144743
$554$	−42.7404	−1.81587
$555$	72.8509	3.09235
$556$	16.3318	0.692624
$557$	−15.8357	−0.670982	−0.335491	−	0.942043i	$-0.608902\pi$
$557$	−15.8357	−0.670982	−0.335491	+	0.942043i	$0.608902\pi$
$558$	−163.633	−6.92715
$559$	0	0
$560$	1.16283	0.0491386
$561$	53.0426	2.23946
$562$	−24.1715	−1.01961
$563$	19.4488	0.819671	0.409835	−	0.912160i	$-0.365586\pi$
$563$	19.4488	0.819671	0.409835	+	0.912160i	$0.365586\pi$
$564$	−79.2881	−3.33863
$565$	−12.8018	−0.538575
$566$	−42.3822	−1.78146
$567$	5.81954	0.244398
$568$	28.5727	1.19888
$569$	−36.5966	−1.53421	−0.767105	−	0.641521i	$-0.778304\pi$
$569$	−36.5966	−1.53421	−0.767105	+	0.641521i	$0.778304\pi$
$570$	−38.5586	−1.61504
$571$	−29.3054	−1.22639	−0.613197	−	0.789930i	$-0.710117\pi$
$571$	−29.3054	−1.22639	−0.613197	+	0.789930i	$0.710117\pi$
$572$	0	0
$573$	73.6796	3.07801
$574$	−3.07129	−0.128193
$575$	5.02462	0.209541
$576$	−95.5795	−3.98248
$577$	8.62392	0.359018	0.179509	−	0.983756i	$-0.442549\pi$
$577$	8.62392	0.359018	0.179509	+	0.983756i	$0.442549\pi$
$578$	−3.66559	−0.152469
$579$	−27.4399	−1.14036
$580$	−10.9519	−0.454751
$581$	−0.136734	−0.00567270
$582$	53.6624	2.22438
$583$	−19.9290	−0.825377
$584$	−13.1319	−0.543402
$585$	0	0
$586$	−34.5061	−1.42543
$587$	−24.2951	−1.00276	−0.501382	−	0.865226i	$-0.667175\pi$
$587$	−24.2951	−1.00276	−0.501382	+	0.865226i	$0.667175\pi$
$588$	64.2352	2.64902
$589$	16.9059	0.696594
$590$	−70.6645	−2.90921
$591$	19.8230	0.815408
$592$	−11.0629	−0.454682
$593$	−31.7110	−1.30221	−0.651107	−	0.758986i	$-0.725695\pi$
$593$	−31.7110	−1.30221	−0.651107	+	0.758986i	$0.725695\pi$
$594$	−121.588	−4.98880
$595$	−3.22531	−0.132225
$596$	30.9982	1.26973
$597$	−57.3446	−2.34696
$598$	0	0
$599$	23.4202	0.956922	0.478461	−	0.878109i	$-0.341195\pi$
$599$	23.4202	0.956922	0.478461	+	0.878109i	$0.341195\pi$
$600$	30.6797	1.25249
$601$	7.03284	0.286876	0.143438	−	0.989659i	$-0.454184\pi$
$601$	7.03284	0.286876	0.143438	+	0.989659i	$0.454184\pi$
$602$	−2.88850	−0.117727
$603$	74.6257	3.03899
$604$	2.03851	0.0829458
$605$	−10.6543	−0.433160
$606$	−6.49354	−0.263782
$607$	27.8193	1.12915	0.564575	−	0.825381i	$-0.309040\pi$
$607$	27.8193	1.12915	0.564575	+	0.825381i	$0.309040\pi$
$608$	12.2868	0.498294
$609$	−0.925347	−0.0374969
$610$	27.3849	1.10878
$611$	0	0
$612$	92.4454	3.73688
$613$	3.52670	0.142442	0.0712210	−	0.997461i	$-0.477310\pi$
$613$	3.52670	0.142442	0.0712210	+	0.997461i	$0.477310\pi$
$614$	62.2572	2.51249
$615$	60.6285	2.44478
$616$	1.68449	0.0678699
$617$	−22.4828	−0.905122	−0.452561	−	0.891733i	$-0.649490\pi$
$617$	−22.4828	−0.905122	−0.452561	+	0.891733i	$0.649490\pi$
$618$	−89.7245	−3.60925
$619$	−14.3338	−0.576126	−0.288063	−	0.957612i	$-0.593011\pi$
$619$	−14.3338	−0.576126	−0.288063	+	0.957612i	$0.593011\pi$
$620$	−89.5849	−3.59782
$621$	−14.5588	−0.584223
$622$	5.01708	0.201167
$623$	−0.649227	−0.0260107
$624$	0	0
$625$	−24.8763	−0.995051
$626$	−52.2477	−2.08824
$627$	20.9473	0.836556
$628$	8.33927	0.332773
$629$	30.6848	1.22348
$630$	12.3285	0.491180
$631$	−26.3765	−1.05003	−0.525016	−	0.851092i	$-0.675941\pi$
$631$	−26.3765	−1.05003	−0.525016	+	0.851092i	$0.675941\pi$
$632$	−27.2077	−1.08226
$633$	−70.7935	−2.81379
$634$	−45.0660	−1.78980
$635$	24.8366	0.985612
$636$	−48.6375	−1.92860
$637$	0	0
$638$	10.1171	0.400539
$639$	−113.606	−4.49419
$640$	−43.3751	−1.71455
$641$	−12.9715	−0.512342	−0.256171	−	0.966632i	$-0.582461\pi$
$641$	−12.9715	−0.512342	−0.256171	+	0.966632i	$0.582461\pi$
$642$	−112.321	−4.43297
$643$	−4.79214	−0.188984	−0.0944919	−	0.995526i	$-0.530123\pi$
$643$	−4.79214	−0.188984	−0.0944919	+	0.995526i	$0.530123\pi$
$644$	0.673295	0.0265315
$645$	57.0202	2.24517
$646$	−16.2409	−0.638990
$647$	−13.2742	−0.521863	−0.260932	−	0.965357i	$-0.584030\pi$
$647$	−13.2742	−0.521863	−0.260932	+	0.965357i	$0.584030\pi$
$648$	−46.5180	−1.82740
$649$	38.3892	1.50691
$650$	0	0
$651$	−7.56922	−0.296661
$652$	15.5525	0.609081
$653$	9.74330	0.381285	0.190642	−	0.981660i	$-0.438943\pi$
$653$	9.74330	0.381285	0.190642	+	0.981660i	$0.438943\pi$
$654$	−115.642	−4.52197
$655$	−3.63147	−0.141893
$656$	−9.20684	−0.359467
$657$	52.2130	2.03702
$658$	−4.45371	−0.173624
$659$	−10.0441	−0.391263	−0.195631	−	0.980677i	$-0.562676\pi$
$659$	−10.0441	−0.391263	−0.195631	+	0.980677i	$0.562676\pi$
$660$	−111.001	−4.32070
$661$	39.3115	1.52904	0.764521	−	0.644599i	$-0.222976\pi$
$661$	39.3115	1.52904	0.764521	+	0.644599i	$0.222976\pi$
$662$	36.4325	1.41599
$663$	0	0
$664$	1.09297	0.0424156
$665$	−1.27373	−0.0493930
$666$	−117.290	−4.54491
$667$	1.21141	0.0469058
$668$	−56.8237	−2.19858
$669$	−57.6193	−2.22769
$670$	69.4721	2.68394
$671$	−14.8771	−0.574324
$672$	−5.50112	−0.212210
$673$	−3.74979	−0.144544	−0.0722720	−	0.997385i	$-0.523025\pi$
$673$	−3.74979	−0.144544	−0.0722720	+	0.997385i	$0.523025\pi$
$674$	8.02420	0.309081
$675$	−73.1523	−2.81563
$676$	0	0
$677$	44.8654	1.72432	0.862160	−	0.506637i	$-0.169112\pi$
$677$	44.8654	1.72432	0.862160	+	0.506637i	$0.169112\pi$
$678$	28.8617	1.10843
$679$	1.77266	0.0680284
$680$	25.7812	0.988666
$681$	25.6071	0.981267
$682$	82.7564	3.16891
$683$	4.48406	0.171578	0.0857889	−	0.996313i	$-0.472659\pi$
$683$	4.48406	0.171578	0.0857889	+	0.996313i	$0.472659\pi$
$684$	36.5081	1.39592
$685$	−21.6403	−0.826833
$686$	7.24524	0.276624
$687$	69.0292	2.63363
$688$	−8.65889	−0.330117
$689$	0	0
$690$	−22.6006	−0.860390
$691$	0.957020	0.0364068	0.0182034	−	0.999834i	$-0.494205\pi$
$691$	0.957020	0.0364068	0.0182034	+	0.999834i	$0.494205\pi$
$692$	19.9659	0.758991
$693$	−6.69759	−0.254420
$694$	11.1053	0.421550
$695$	−18.1094	−0.686930
$696$	7.39668	0.280370
$697$	25.5367	0.967273
$698$	19.9775	0.756158
$699$	20.6126	0.779640
$700$	3.38306	0.127867
$701$	−4.50088	−0.169996	−0.0849980	−	0.996381i	$-0.527088\pi$
$701$	−4.50088	−0.169996	−0.0849980	+	0.996381i	$0.527088\pi$
$702$	0	0
$703$	12.1179	0.457036
$704$	48.3387	1.82183
$705$	87.9179	3.31118
$706$	35.4348	1.33361
$707$	−0.214504	−0.00806727
$708$	93.6902	3.52110
$709$	−42.0648	−1.57978	−0.789888	−	0.613252i	$-0.789861\pi$
$709$	−42.0648	−1.57978	−0.789888	+	0.613252i	$0.789861\pi$
$710$	−105.760	−3.96912
$711$	108.179	4.05703
$712$	5.18954	0.194486
$713$	9.90915	0.371100
$714$	7.27150	0.272129
$715$	0	0
$716$	25.0112	0.934712
$717$	32.8044	1.22510
$718$	−20.9193	−0.780701
$719$	16.4724	0.614317	0.307159	−	0.951658i	$-0.400622\pi$
$719$	16.4724	0.614317	0.307159	+	0.951658i	$0.400622\pi$
$720$	36.9573	1.37732
$721$	−2.96392	−0.110382
$722$	35.4526	1.31941
$723$	−24.8413	−0.923859
$724$	−13.6190	−0.506145
$725$	6.08686	0.226060
$726$	24.0203	0.891476
$727$	14.9530	0.554576	0.277288	−	0.960787i	$-0.410564\pi$
$727$	14.9530	0.554576	0.277288	+	0.960787i	$0.410564\pi$
$728$	0	0
$729$	43.4693	1.60998
$730$	48.6072	1.79903
$731$	24.0169	0.888298
$732$	−36.3081	−1.34199
$733$	1.61289	0.0595736	0.0297868	−	0.999556i	$-0.490517\pi$
$733$	1.61289	0.0595736	0.0297868	+	0.999556i	$0.490517\pi$
$734$	−54.6314	−2.01648
$735$	−71.2267	−2.62724
$736$	7.20172	0.265459
$737$	−37.7414	−1.39022
$738$	−97.6122	−3.59316
$739$	52.4404	1.92905	0.964526	−	0.263987i	$-0.0850376\pi$
$739$	52.4404	1.92905	0.964526	+	0.263987i	$0.0850376\pi$
$740$	−64.2133	−2.36053
$741$	0	0
$742$	−2.73203	−0.100296
$743$	25.7314	0.943994	0.471997	−	0.881600i	$-0.343533\pi$
$743$	25.7314	0.943994	0.471997	+	0.881600i	$0.343533\pi$
$744$	60.5039	2.21818
$745$	−34.3721	−1.25930
$746$	0.172882	0.00632965
$747$	−4.34571	−0.159001
$748$	−46.7536	−1.70948
$749$	−3.71037	−0.135574
$750$	−0.556530	−0.0203216
$751$	−20.7203	−0.756094	−0.378047	−	0.925786i	$-0.623404\pi$
$751$	−20.7203	−0.756094	−0.378047	+	0.925786i	$0.623404\pi$
$752$	−13.3509	−0.486858
$753$	81.7109	2.97771
$754$	0	0
$755$	−2.26038	−0.0822638
$756$	−9.80234	−0.356508
$757$	−6.21515	−0.225893	−0.112947	−	0.993601i	$-0.536029\pi$
$757$	−6.21515	−0.225893	−0.112947	+	0.993601i	$0.536029\pi$
$758$	71.3360	2.59104
$759$	12.2780	0.445663
$760$	10.1814	0.369319
$761$	50.5107	1.83101	0.915506	−	0.402303i	$-0.131790\pi$
$761$	50.5107	1.83101	0.915506	+	0.402303i	$0.131790\pi$
$762$	−55.9944	−2.02846
$763$	−3.82007	−0.138296
$764$	−64.9438	−2.34958
$765$	−102.507	−3.70616
$766$	−21.8616	−0.789891
$767$	0	0
$768$	15.1582	0.546976
$769$	−41.3515	−1.49117	−0.745586	−	0.666409i	$-0.767830\pi$
$769$	−41.3515	−1.49117	−0.745586	+	0.666409i	$0.767830\pi$
$770$	−6.23506	−0.224696
$771$	−39.4153	−1.41951
$772$	24.1865	0.870491
$773$	−12.6236	−0.454040	−0.227020	−	0.973890i	$-0.572898\pi$
$773$	−12.6236	−0.454040	−0.227020	+	0.973890i	$0.572898\pi$
$774$	−91.8028	−3.29978
$775$	49.7897	1.78850
$776$	−14.1696	−0.508658
$777$	−5.42552	−0.194640
$778$	−70.7610	−2.53690
$779$	10.0849	0.361327
$780$	0	0
$781$	57.4554	2.05592
$782$	−9.51938	−0.340412
$783$	−17.6366	−0.630279
$784$	10.8162	0.386295
$785$	−9.24693	−0.330037
$786$	8.18717	0.292027
$787$	31.0508	1.10684	0.553421	−	0.832902i	$-0.313322\pi$
$787$	31.0508	1.10684	0.553421	+	0.832902i	$0.313322\pi$
$788$	−17.4727	−0.622438
$789$	−22.0963	−0.786650
$790$	100.708	3.58304
$791$	0.953404	0.0338992
$792$	53.5366	1.90234
$793$	0	0
$794$	55.5354	1.97088
$795$	53.9313	1.91275
$796$	50.5456	1.79154
$797$	19.6770	0.696996	0.348498	−	0.937310i	$-0.386692\pi$
$797$	19.6770	0.696996	0.348498	+	0.937310i	$0.386692\pi$
$798$	2.87163	0.101655
$799$	37.0311	1.31007
$800$	36.1859	1.27937
$801$	−20.6338	−0.729060
$802$	−16.2095	−0.572378
$803$	−26.4063	−0.931859
$804$	−92.1092	−3.24844
$805$	−0.746578	−0.0263134
$806$	0	0
$807$	−2.19937	−0.0774213
$808$	1.71462	0.0603202
$809$	−16.1703	−0.568518	−0.284259	−	0.958747i	$-0.591748\pi$
$809$	−16.1703	−0.568518	−0.284259	+	0.958747i	$0.591748\pi$
$810$	172.184	6.04994
$811$	46.4655	1.63162	0.815811	−	0.578318i	$-0.196291\pi$
$811$	46.4655	1.63162	0.815811	+	0.578318i	$0.196291\pi$
$812$	0.815633	0.0286231
$813$	4.96611	0.174169
$814$	59.3187	2.07912
$815$	−17.2452	−0.604073
$816$	21.7978	0.763077
$817$	9.48466	0.331826
$818$	−76.8459	−2.68685
$819$	0	0
$820$	−53.4401	−1.86621
$821$	23.3058	0.813378	0.406689	−	0.913567i	$-0.366683\pi$
$821$	23.3058	0.813378	0.406689	+	0.913567i	$0.366683\pi$
$822$	48.7882	1.70169
$823$	−38.7054	−1.34918	−0.674592	−	0.738191i	$-0.735680\pi$
$823$	−38.7054	−1.34918	−0.674592	+	0.738191i	$0.735680\pi$
$824$	23.6918	0.825343
$825$	61.6924	2.14785
$826$	5.26270	0.183113
$827$	−10.1889	−0.354302	−0.177151	−	0.984184i	$-0.556688\pi$
$827$	−10.1889	−0.354302	−0.177151	+	0.984184i	$0.556688\pi$
$828$	21.3988	0.743658
$829$	40.4574	1.40514	0.702571	−	0.711613i	$-0.252035\pi$
$829$	40.4574	1.40514	0.702571	+	0.711613i	$0.252035\pi$
$830$	−4.04560	−0.140425
$831$	−62.8349	−2.17972
$832$	0	0
$833$	−30.0007	−1.03946
$834$	40.8278	1.41375
$835$	63.0085	2.18050
$836$	−18.4637	−0.638581
$837$	−144.265	−4.98652
$838$	−46.2078	−1.59622
$839$	−48.3656	−1.66977	−0.834883	−	0.550428i	$-0.814465\pi$
$839$	−48.3656	−1.66977	−0.834883	+	0.550428i	$0.814465\pi$
$840$	−4.55850	−0.157283
$841$	−27.5325	−0.949396
$842$	3.97209	0.136887
$843$	−35.5358	−1.22392
$844$	62.3999	2.14789
$845$	0	0
$846$	−141.548	−4.86653
$847$	0.793474	0.0272641
$848$	−8.18983	−0.281240
$849$	−62.3083	−2.13842
$850$	−47.8313	−1.64060
$851$	7.10275	0.243479
$852$	140.222	4.80393
$853$	14.6921	0.503048	0.251524	−	0.967851i	$-0.419068\pi$
$853$	14.6921	0.503048	0.251524	+	0.967851i	$0.419068\pi$
$854$	−2.03947	−0.0697893
$855$	−40.4817	−1.38445
$856$	29.6585	1.01371
$857$	28.5527	0.975343	0.487671	−	0.873027i	$-0.337846\pi$
$857$	28.5527	0.975343	0.487671	+	0.873027i	$0.337846\pi$
$858$	0	0
$859$	−33.8909	−1.15634	−0.578172	−	0.815915i	$-0.696234\pi$
$859$	−33.8909	−1.15634	−0.578172	+	0.815915i	$0.696234\pi$
$860$	−50.2596	−1.71384
$861$	−4.51527	−0.153880
$862$	25.9913	0.885267
$863$	2.41592	0.0822389	0.0411194	−	0.999154i	$-0.486908\pi$
$863$	2.41592	0.0822389	0.0411194	+	0.999154i	$0.486908\pi$
$864$	−104.848	−3.56700
$865$	−22.1391	−0.752751
$866$	22.8343	0.775940
$867$	−5.38898	−0.183019
$868$	6.67178	0.226455
$869$	−54.7107	−1.85593
$870$	−27.3785	−0.928218
$871$	0	0
$872$	30.5354	1.03406
$873$	56.3388	1.90678
$874$	−3.75935	−0.127162
$875$	−0.0183842	−0.000621498 0
$876$	−64.4456	−2.17741
$877$	−33.2177	−1.12168	−0.560841	−	0.827924i	$-0.689522\pi$
$877$	−33.2177	−1.12168	−0.560841	+	0.827924i	$0.689522\pi$
$878$	59.7069	2.01501
$879$	−50.7292	−1.71105
$880$	−18.6909	−0.630069
$881$	4.80819	0.161992	0.0809961	−	0.996714i	$-0.474190\pi$
$881$	4.80819	0.161992	0.0809961	+	0.996714i	$0.474190\pi$
$882$	114.675	3.86132
$883$	22.8140	0.767753	0.383877	−	0.923384i	$-0.374589\pi$
$883$	22.8140	0.767753	0.383877	+	0.923384i	$0.374589\pi$
$884$	0	0
$885$	−103.888	−3.49215
$886$	−70.4404	−2.36649
$887$	−19.4532	−0.653174	−0.326587	−	0.945167i	$-0.605899\pi$
$887$	−19.4532	−0.653174	−0.326587	+	0.945167i	$0.605899\pi$
$888$	43.3684	1.45535
$889$	−1.84969	−0.0620367
$890$	−19.2089	−0.643882
$891$	−93.5409	−3.13374
$892$	50.7877	1.70050
$893$	14.6241	0.489378
$894$	77.4921	2.59172
$895$	−27.7335	−0.927027
$896$	3.23034	0.107918
$897$	0	0
$898$	−27.0622	−0.903076
$899$	12.0040	0.400356
$900$	107.521	3.58402
$901$	22.7159	0.756776
$902$	49.3667	1.64373
$903$	−4.24654	−0.141316
$904$	−7.62095	−0.253469
$905$	15.1013	0.501983
$906$	5.09606	0.169305
$907$	−33.4148	−1.10952	−0.554760	−	0.832011i	$-0.687190\pi$
$907$	−33.4148	−1.10952	−0.554760	+	0.832011i	$0.687190\pi$
$908$	−22.5710	−0.749046
$909$	−6.81741	−0.226119
$910$	0	0
$911$	−6.42423	−0.212844	−0.106422	−	0.994321i	$-0.533939\pi$
$911$	−6.42423	−0.212844	−0.106422	+	0.994321i	$0.533939\pi$
$912$	8.60830	0.285049
$913$	2.19781	0.0727370
$914$	−36.7012	−1.21397
$915$	40.2599	1.33095
$916$	−60.8447	−2.01037
$917$	0.270451	0.00893108
$918$	138.590	4.57416
$919$	−56.4522	−1.86219	−0.931093	−	0.364782i	$-0.881144\pi$
$919$	−56.4522	−1.86219	−0.931093	+	0.364782i	$0.881144\pi$
$920$	5.96770	0.196749
$921$	91.5275	3.01593
$922$	−7.50667	−0.247219
$923$	0	0
$924$	8.26672	0.271955
$925$	35.6887	1.17344
$926$	−8.94500	−0.293951
$927$	−94.1996	−3.09392
$928$	8.72420	0.286386
$929$	33.3641	1.09464	0.547320	−	0.836924i	$-0.315648\pi$
$929$	33.3641	1.09464	0.547320	+	0.836924i	$0.315648\pi$
$930$	−223.953	−7.34370
$931$	−11.8478	−0.388294
$932$	−18.1687	−0.595134
$933$	7.37588	0.241475
$934$	21.9160	0.717112
$935$	51.8423	1.69543
$936$	0	0
$937$	−16.8979	−0.552030	−0.276015	−	0.961153i	$-0.589014\pi$
$937$	−16.8979	−0.552030	−0.276015	+	0.961153i	$0.589014\pi$
$938$	−5.17389	−0.168934
$939$	−76.8120	−2.50667
$940$	−77.4940	−2.52757
$941$	17.2529	0.562430	0.281215	−	0.959645i	$-0.409263\pi$
$941$	17.2529	0.562430	0.281215	+	0.959645i	$0.409263\pi$
$942$	20.8473	0.679241
$943$	5.91110	0.192492
$944$	15.7760	0.513466
$945$	10.8692	0.353576
$946$	46.4286	1.50952
$947$	−12.8930	−0.418967	−0.209483	−	0.977812i	$-0.567178\pi$
$947$	−12.8930	−0.418967	−0.209483	+	0.977812i	$0.567178\pi$
$948$	−133.523	−4.33664
$949$	0	0
$950$	−18.8893	−0.612851
$951$	−66.2539	−2.14843
$952$	−1.92004	−0.0622289
$953$	−53.1278	−1.72098	−0.860489	−	0.509470i	$-0.829842\pi$
$953$	−53.1278	−1.72098	−0.860489	+	0.509470i	$0.829842\pi$
$954$	−86.8298	−2.81122
$955$	72.0124	2.33027
$956$	−28.9149	−0.935176
$957$	14.8736	0.480796
$958$	−60.9467	−1.96910
$959$	1.61165	0.0520428
$960$	−130.812	−4.22195
$961$	67.1912	2.16746
$962$	0	0
$963$	−117.924	−3.80003
$964$	21.8960	0.705224
$965$	−26.8190	−0.863334
$966$	1.68317	0.0541550
$967$	−30.1482	−0.969501	−0.484751	−	0.874652i	$-0.661090\pi$
$967$	−30.1482	−0.969501	−0.484751	+	0.874652i	$0.661090\pi$
$968$	−6.34256	−0.203858
$969$	−23.8766	−0.767027
$970$	52.4481	1.68401
$971$	−13.1449	−0.421840	−0.210920	−	0.977503i	$-0.567646\pi$
$971$	−13.1449	−0.421840	−0.210920	+	0.977503i	$0.567646\pi$
$972$	−103.577	−3.32224
$973$	1.34869	0.0432369
$974$	−15.8703	−0.508516
$975$	0	0
$976$	−6.11374	−0.195696
$977$	−7.90910	−0.253034	−0.126517	−	0.991964i	$-0.540380\pi$
$977$	−7.90910	−0.253034	−0.126517	+	0.991964i	$0.540380\pi$
$978$	38.8795	1.24323
$979$	10.4354	0.333517
$980$	62.7817	2.00549
$981$	−121.410	−3.87633
$982$	21.2780	0.679007
$983$	4.70807	0.150164	0.0750821	−	0.997177i	$-0.476078\pi$
$983$	4.70807	0.150164	0.0750821	+	0.997177i	$0.476078\pi$
$984$	36.0924	1.15058
$985$	19.3744	0.617321
$986$	−11.5318	−0.367248
$987$	−6.54763	−0.208413
$988$	0	0
$989$	5.55930	0.176776
$990$	−198.163	−6.29804
$991$	13.2635	0.421329	0.210664	−	0.977558i	$-0.432437\pi$
$991$	13.2635	0.421329	0.210664	+	0.977558i	$0.432437\pi$
$992$	71.3629	2.26577
$993$	53.5613	1.69972
$994$	7.87645	0.249826
$995$	−56.0470	−1.77681
$996$	5.36384	0.169960
$997$	6.29796	0.199458	0.0997292	−	0.995015i	$-0.468202\pi$
$997$	6.29796	0.199458	0.0997292	+	0.995015i	$0.468202\pi$
$998$	−32.0471	−1.01443
$999$	−103.407	−3.27166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3887.2.a.p.1.3		10
13.12	even	2		299.2.a.g.1.8	✓	10
39.38	odd	2		2691.2.a.bc.1.3		10
52.51	odd	2		4784.2.a.bh.1.10		10
65.64	even	2		7475.2.a.w.1.3		10
299.298	odd	2		6877.2.a.o.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.a.g.1.8	✓	10	13.12	even	2
2691.2.a.bc.1.3		10	39.38	odd	2
3887.2.a.p.1.3		10	1.1	even	1	trivial
4784.2.a.bh.1.10		10	52.51	odd	2
6877.2.a.o.1.8		10	299.298	odd	2
7475.2.a.w.1.3		10	65.64	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3887 = 13^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3887.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20349 q^{2} -3.23947 q^{3} +2.85538 q^{4} -3.16617 q^{5} +7.13815 q^{6} +0.235798 q^{7} -1.88483 q^{8} +7.49418 q^{9} +O(q^{10})\)	\(q-2.20349 q^{2} -3.23947 q^{3} +2.85538 q^{4} -3.16617 q^{5} +7.13815 q^{6} +0.235798 q^{7} -1.88483 q^{8} +7.49418 q^{9} +6.97663 q^{10} -3.79013 q^{11} -9.24994 q^{12} -0.519580 q^{14} +10.2567 q^{15} -1.55755 q^{16} +4.32013 q^{17} -16.5134 q^{18} +1.70609 q^{19} -9.04063 q^{20} -0.763862 q^{21} +8.35152 q^{22} +1.00000 q^{23} +6.10586 q^{24} +5.02462 q^{25} -14.5588 q^{27} +0.673295 q^{28} +1.21141 q^{29} -22.6006 q^{30} +9.90915 q^{31} +7.20172 q^{32} +12.2780 q^{33} -9.51938 q^{34} -0.746578 q^{35} +21.3988 q^{36} +7.10275 q^{37} -3.75935 q^{38} +5.96770 q^{40} +5.91110 q^{41} +1.68317 q^{42} +5.55930 q^{43} -10.8223 q^{44} -23.7278 q^{45} -2.20349 q^{46} +8.57175 q^{47} +5.04564 q^{48} -6.94440 q^{49} -11.0717 q^{50} -13.9949 q^{51} +5.25815 q^{53} +32.0801 q^{54} +12.0002 q^{55} -0.444441 q^{56} -5.52682 q^{57} -2.66932 q^{58} -10.1287 q^{59} +29.2869 q^{60} +3.92523 q^{61} -21.8347 q^{62} +1.76712 q^{63} -12.7538 q^{64} -27.0545 q^{66} +9.95783 q^{67} +12.3356 q^{68} -3.23947 q^{69} +1.64508 q^{70} -15.1592 q^{71} -14.1253 q^{72} +6.96714 q^{73} -15.6509 q^{74} -16.2771 q^{75} +4.87153 q^{76} -0.893706 q^{77} +14.4351 q^{79} +4.93147 q^{80} +24.6801 q^{81} -13.0251 q^{82} -0.579878 q^{83} -2.18112 q^{84} -13.6783 q^{85} -12.2499 q^{86} -3.92431 q^{87} +7.14375 q^{88} -2.75331 q^{89} +52.2841 q^{90} +2.85538 q^{92} -32.1004 q^{93} -18.8878 q^{94} -5.40176 q^{95} -23.3298 q^{96} +7.51768 q^{97} +15.3019 q^{98} -28.4039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9}+O(q^{10}) \) 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9	\( 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9} + 6 q^{10} - 3 q^{11} + 10 q^{12} - 15 q^{14} - 2 q^{15} + 25 q^{16} - 3 q^{17} - q^{18} - 2 q^{19} + 19 q^{20} - 21 q^{21} + 13 q^{22} + 10 q^{23} + 35 q^{24} + 33 q^{25} + 6 q^{27} + 19 q^{28} + 17 q^{29} - 47 q^{30} - 5 q^{31} + 9 q^{32} + 23 q^{33} - 23 q^{34} + 3 q^{35} + 48 q^{36} - 16 q^{37} + 5 q^{38} + 13 q^{40} + 16 q^{41} - 65 q^{42} - 9 q^{43} - 18 q^{44} - 32 q^{45} - q^{46} + 11 q^{47} + 37 q^{48} + 40 q^{49} + 30 q^{50} - 31 q^{51} + 8 q^{53} + 73 q^{54} - 14 q^{55} - 54 q^{56} + 35 q^{57} - 17 q^{58} - 2 q^{59} + 37 q^{60} + 48 q^{61} - 19 q^{62} + 15 q^{63} + 64 q^{64} - 84 q^{66} + 6 q^{67} - 62 q^{68} + 3 q^{69} + 44 q^{70} - 24 q^{71} + 89 q^{72} + 33 q^{73} - 28 q^{74} - 22 q^{75} + 53 q^{76} + 15 q^{77} + 17 q^{79} + 94 q^{80} + 30 q^{81} + 35 q^{82} + 21 q^{83} - 92 q^{84} - 58 q^{85} + 7 q^{86} + 23 q^{87} + 9 q^{88} + 16 q^{89} + 67 q^{90} + 19 q^{92} - 15 q^{93} + 12 q^{94} - 27 q^{95} + 22 q^{96} + 40 q^{97} + 34 q^{98} + 17 q^{99}+O(q^{100}) \) 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9 + 6 * q^10 - 3 * q^11 + 10 * q^12 - 15 * q^14 - 2 * q^15 + 25 * q^16 - 3 * q^17 - q^18 - 2 * q^19 + 19 * q^20 - 21 * q^21 + 13 * q^22 + 10 * q^23 + 35 * q^24 + 33 * q^25 + 6 * q^27 + 19 * q^28 + 17 * q^29 - 47 * q^30 - 5 * q^31 + 9 * q^32 + 23 * q^33 - 23 * q^34 + 3 * q^35 + 48 * q^36 - 16 * q^37 + 5 * q^38 + 13 * q^40 + 16 * q^41 - 65 * q^42 - 9 * q^43 - 18 * q^44 - 32 * q^45 - q^46 + 11 * q^47 + 37 * q^48 + 40 * q^49 + 30 * q^50 - 31 * q^51 + 8 * q^53 + 73 * q^54 - 14 * q^55 - 54 * q^56 + 35 * q^57 - 17 * q^58 - 2 * q^59 + 37 * q^60 + 48 * q^61 - 19 * q^62 + 15 * q^63 + 64 * q^64 - 84 * q^66 + 6 * q^67 - 62 * q^68 + 3 * q^69 + 44 * q^70 - 24 * q^71 + 89 * q^72 + 33 * q^73 - 28 * q^74 - 22 * q^75 + 53 * q^76 + 15 * q^77 + 17 * q^79 + 94 * q^80 + 30 * q^81 + 35 * q^82 + 21 * q^83 - 92 * q^84 - 58 * q^85 + 7 * q^86 + 23 * q^87 + 9 * q^88 + 16 * q^89 + 67 * q^90 + 19 * q^92 - 15 * q^93 + 12 * q^94 - 27 * q^95 + 22 * q^96 + 40 * q^97 + 34 * q^98 + 17 * q^99

Introduction

L-functions

Modular forms

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Database

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