LMFDB - Embedded newform 4114.2.a.bk.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4114,2,Mod(1,4114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4114, 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("4114.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4114 = 2 \cdot 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4114.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:	$32.8504553916$
Analytic rank:	$1$
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} - 2x^{9} - 19x^{8} + 33x^{7} + 114x^{6} - 152x^{5} - 294x^{4} + 248x^{3} + 346x^{2} - 125x - 145 $ x^10 - 2x^9 - 19x^8 + 33x^7 + 114x^6 - 152x^5 - 294x^4 + 248x^3 + 346x^2 - 125*x - 145
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 374)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.77980$ of defining polynomial
Character	$\chi$	$=$	4114.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.77980 q^{3} +1.00000 q^{4} +2.34877 q^{5} -1.77980 q^{6} -4.53996 q^{7} -1.00000 q^{8} +0.167681 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.77980 q^{3} +1.00000 q^{4} +2.34877 q^{5} -1.77980 q^{6} -4.53996 q^{7} -1.00000 q^{8} +0.167681 q^{9} -2.34877 q^{10} +1.77980 q^{12} +0.401232 q^{13} +4.53996 q^{14} +4.18034 q^{15} +1.00000 q^{16} -1.00000 q^{17} -0.167681 q^{18} +6.80587 q^{19} +2.34877 q^{20} -8.08022 q^{21} -3.73562 q^{23} -1.77980 q^{24} +0.516742 q^{25} -0.401232 q^{26} -5.04096 q^{27} -4.53996 q^{28} -4.60581 q^{29} -4.18034 q^{30} -3.30937 q^{31} -1.00000 q^{32} +1.00000 q^{34} -10.6633 q^{35} +0.167681 q^{36} +6.50680 q^{37} -6.80587 q^{38} +0.714112 q^{39} -2.34877 q^{40} -11.4191 q^{41} +8.08022 q^{42} -6.24378 q^{43} +0.393845 q^{45} +3.73562 q^{46} -3.12096 q^{47} +1.77980 q^{48} +13.6113 q^{49} -0.516742 q^{50} -1.77980 q^{51} +0.401232 q^{52} +12.9032 q^{53} +5.04096 q^{54} +4.53996 q^{56} +12.1131 q^{57} +4.60581 q^{58} -10.5133 q^{59} +4.18034 q^{60} -2.72719 q^{61} +3.30937 q^{62} -0.761265 q^{63} +1.00000 q^{64} +0.942403 q^{65} -4.45469 q^{67} -1.00000 q^{68} -6.64866 q^{69} +10.6633 q^{70} +3.14997 q^{71} -0.167681 q^{72} -1.39211 q^{73} -6.50680 q^{74} +0.919696 q^{75} +6.80587 q^{76} -0.714112 q^{78} -3.51026 q^{79} +2.34877 q^{80} -9.47493 q^{81} +11.4191 q^{82} +9.92155 q^{83} -8.08022 q^{84} -2.34877 q^{85} +6.24378 q^{86} -8.19741 q^{87} -9.88841 q^{89} -0.393845 q^{90} -1.82158 q^{91} -3.73562 q^{92} -5.89000 q^{93} +3.12096 q^{94} +15.9854 q^{95} -1.77980 q^{96} -5.36499 q^{97} -13.6113 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{6} - 2 q^{7} - 10 q^{8} + 12 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^6 - 2 * q^7 - 10 * q^8 + 12 * q^9	$ 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{6} - 2 q^{7} - 10 q^{8} + 12 q^{9} + 2 q^{12} + 2 q^{14} - 5 q^{15} + 10 q^{16} - 10 q^{17} - 12 q^{18} - 9 q^{19} - 19 q^{21} - 6 q^{23} - 2 q^{24} + 4 q^{25} + 11 q^{27} - 2 q^{28} - 20 q^{29} + 5 q^{30} - q^{31} - 10 q^{32} + 10 q^{34} - 13 q^{35} + 12 q^{36} + 17 q^{37} + 9 q^{38} - 11 q^{39} - 39 q^{41} + 19 q^{42} - 16 q^{43} - 26 q^{45} + 6 q^{46} - 14 q^{47} + 2 q^{48} + 18 q^{49} - 4 q^{50} - 2 q^{51} + 8 q^{53} - 11 q^{54} + 2 q^{56} - 24 q^{57} + 20 q^{58} - 4 q^{59} - 5 q^{60} - 22 q^{61} + q^{62} - 29 q^{63} + 10 q^{64} - 52 q^{65} - 13 q^{67} - 10 q^{68} - 30 q^{69} + 13 q^{70} - 7 q^{71} - 12 q^{72} + 6 q^{73} - 17 q^{74} + 45 q^{75} - 9 q^{76} + 11 q^{78} - 19 q^{79} + 34 q^{81} + 39 q^{82} - 19 q^{83} - 19 q^{84} + 16 q^{86} - 29 q^{87} - 8 q^{89} + 26 q^{90} + 9 q^{91} - 6 q^{92} + 3 q^{93} + 14 q^{94} + 27 q^{95} - 2 q^{96} + 39 q^{97} - 18 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^6 - 2 * q^7 - 10 * q^8 + 12 * q^9 + 2 * q^12 + 2 * q^14 - 5 * q^15 + 10 * q^16 - 10 * q^17 - 12 * q^18 - 9 * q^19 - 19 * q^21 - 6 * q^23 - 2 * q^24 + 4 * q^25 + 11 * q^27 - 2 * q^28 - 20 * q^29 + 5 * q^30 - q^31 - 10 * q^32 + 10 * q^34 - 13 * q^35 + 12 * q^36 + 17 * q^37 + 9 * q^38 - 11 * q^39 - 39 * q^41 + 19 * q^42 - 16 * q^43 - 26 * q^45 + 6 * q^46 - 14 * q^47 + 2 * q^48 + 18 * q^49 - 4 * q^50 - 2 * q^51 + 8 * q^53 - 11 * q^54 + 2 * q^56 - 24 * q^57 + 20 * q^58 - 4 * q^59 - 5 * q^60 - 22 * q^61 + q^62 - 29 * q^63 + 10 * q^64 - 52 * q^65 - 13 * q^67 - 10 * q^68 - 30 * q^69 + 13 * q^70 - 7 * q^71 - 12 * q^72 + 6 * q^73 - 17 * q^74 + 45 * q^75 - 9 * q^76 + 11 * q^78 - 19 * q^79 + 34 * q^81 + 39 * q^82 - 19 * q^83 - 19 * q^84 + 16 * q^86 - 29 * q^87 - 8 * q^89 + 26 * q^90 + 9 * q^91 - 6 * q^92 + 3 * q^93 + 14 * q^94 + 27 * q^95 - 2 * q^96 + 39 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.77980	1.02757	0.513783	−	0.857920i	$-0.328243\pi$
$3$	1.77980	1.02757	0.513783	+	0.857920i	$0.328243\pi$
$4$	1.00000	0.500000
$5$	2.34877	1.05040	0.525202	−	0.850978i	$-0.323990\pi$
$5$	2.34877	1.05040	0.525202	+	0.850978i	$0.323990\pi$
$6$	−1.77980	−0.726599
$7$	−4.53996	−1.71594	−0.857972	−	0.513696i	$-0.828276\pi$
$7$	−4.53996	−1.71594	−0.857972	+	0.513696i	$0.828276\pi$
$8$	−1.00000	−0.353553
$9$	0.167681	0.0558936
$10$	−2.34877	−0.742748
$11$	0	0
$11$	0	0
$12$	1.77980	0.513783
$13$	0.401232	0.111282	0.0556408	−	0.998451i	$-0.482280\pi$
$13$	0.401232	0.111282	0.0556408	+	0.998451i	$0.482280\pi$
$14$	4.53996	1.21336
$15$	4.18034	1.07936
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.167681	−0.0395228
$19$	6.80587	1.56137	0.780686	−	0.624923i	$-0.214870\pi$
$19$	6.80587	1.56137	0.780686	+	0.624923i	$0.214870\pi$
$20$	2.34877	0.525202
$21$	−8.08022	−1.76325
$22$	0	0
$23$	−3.73562	−0.778932	−0.389466	−	0.921041i	$-0.627340\pi$
$23$	−3.73562	−0.778932	−0.389466	+	0.921041i	$0.627340\pi$
$24$	−1.77980	−0.363300
$25$	0.516742	0.103348
$26$	−0.401232	−0.0786880
$27$	−5.04096	−0.970132
$28$	−4.53996	−0.857972
$29$	−4.60581	−0.855278	−0.427639	−	0.903950i	$-0.640654\pi$
$29$	−4.60581	−0.855278	−0.427639	+	0.903950i	$0.640654\pi$
$30$	−4.18034	−0.763223
$31$	−3.30937	−0.594380	−0.297190	−	0.954818i	$-0.596049\pi$
$31$	−3.30937	−0.594380	−0.297190	+	0.954818i	$0.596049\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.00000	0.171499
$35$	−10.6633	−1.80243
$36$	0.167681	0.0279468
$37$	6.50680	1.06971	0.534856	−	0.844943i	$-0.320366\pi$
$37$	6.50680	1.06971	0.534856	+	0.844943i	$0.320366\pi$
$38$	−6.80587	−1.10406
$39$	0.714112	0.114349
$40$	−2.34877	−0.371374
$41$	−11.4191	−1.78337	−0.891684	−	0.452658i	$-0.850476\pi$
$41$	−11.4191	−1.78337	−0.891684	+	0.452658i	$0.850476\pi$
$42$	8.08022	1.24680
$43$	−6.24378	−0.952168	−0.476084	−	0.879400i	$-0.657944\pi$
$43$	−6.24378	−0.952168	−0.476084	+	0.879400i	$0.657944\pi$
$44$	0	0
$45$	0.393845	0.0587109
$46$	3.73562	0.550788
$47$	−3.12096	−0.455239	−0.227619	−	0.973750i	$-0.573094\pi$
$47$	−3.12096	−0.455239	−0.227619	+	0.973750i	$0.573094\pi$
$48$	1.77980	0.256892
$49$	13.6113	1.94446
$50$	−0.516742	−0.0730783
$51$	−1.77980	−0.249222
$52$	0.401232	0.0556408
$53$	12.9032	1.77239	0.886193	−	0.463316i	$-0.153341\pi$
$53$	12.9032	1.77239	0.886193	+	0.463316i	$0.153341\pi$
$54$	5.04096	0.685987
$55$	0	0
$56$	4.53996	0.606678
$57$	12.1131	1.60441
$58$	4.60581	0.604773
$59$	−10.5133	−1.36871	−0.684355	−	0.729149i	$-0.739916\pi$
$59$	−10.5133	−1.36871	−0.684355	+	0.729149i	$0.739916\pi$
$60$	4.18034	0.539680
$61$	−2.72719	−0.349181	−0.174590	−	0.984641i	$-0.555860\pi$
$61$	−2.72719	−0.349181	−0.174590	+	0.984641i	$0.555860\pi$
$62$	3.30937	0.420290
$63$	−0.761265	−0.0959104
$64$	1.00000	0.125000
$65$	0.942403	0.116891
$66$	0	0
$67$	−4.45469	−0.544227	−0.272114	−	0.962265i	$-0.587723\pi$
$67$	−4.45469	−0.544227	−0.272114	+	0.962265i	$0.587723\pi$
$68$	−1.00000	−0.121268
$69$	−6.64866	−0.800404
$70$	10.6633	1.27451
$71$	3.14997	0.373833	0.186916	−	0.982376i	$-0.440151\pi$
$71$	3.14997	0.373833	0.186916	+	0.982376i	$0.440151\pi$
$72$	−0.167681	−0.0197614
$73$	−1.39211	−0.162934	−0.0814671	−	0.996676i	$-0.525961\pi$
$73$	−1.39211	−0.162934	−0.0814671	+	0.996676i	$0.525961\pi$
$74$	−6.50680	−0.756400
$75$	0.919696	0.106197
$76$	6.80587	0.780686
$77$	0	0
$78$	−0.714112	−0.0808572
$79$	−3.51026	−0.394935	−0.197468	−	0.980309i	$-0.563272\pi$
$79$	−3.51026	−0.394935	−0.197468	+	0.980309i	$0.563272\pi$
$80$	2.34877	0.262601
$81$	−9.47493	−1.05277
$82$	11.4191	1.26103
$83$	9.92155	1.08903	0.544516	−	0.838750i	$-0.316713\pi$
$83$	9.92155	1.08903	0.544516	+	0.838750i	$0.316713\pi$
$84$	−8.08022	−0.881624
$85$	−2.34877	−0.254760
$86$	6.24378	0.673284
$87$	−8.19741	−0.878855
$88$	0	0
$89$	−9.88841	−1.04817	−0.524085	−	0.851666i	$-0.675592\pi$
$89$	−9.88841	−1.04817	−0.524085	+	0.851666i	$0.675592\pi$
$90$	−0.393845	−0.0415149
$91$	−1.82158	−0.190953
$92$	−3.73562	−0.389466
$93$	−5.89000	−0.610765
$94$	3.12096	0.321903
$95$	15.9854	1.64007
$96$	−1.77980	−0.181650
$97$	−5.36499	−0.544732	−0.272366	−	0.962194i	$-0.587806\pi$
$97$	−5.36499	−0.544732	−0.272366	+	0.962194i	$0.587806\pi$
$98$	−13.6113	−1.37494
$99$	0	0
$100$	0.516742	0.0516742
$101$	11.0205	1.09658	0.548291	−	0.836288i	$-0.315279\pi$
$101$	11.0205	1.09658	0.548291	+	0.836288i	$0.315279\pi$
$102$	1.77980	0.176226
$103$	−18.9448	−1.86669	−0.933345	−	0.358980i	$-0.883125\pi$
$103$	−18.9448	−1.86669	−0.933345	+	0.358980i	$0.883125\pi$
$104$	−0.401232	−0.0393440
$105$	−18.9786	−1.85212
$106$	−12.9032	−1.25327
$107$	12.1554	1.17511	0.587555	−	0.809184i	$-0.300090\pi$
$107$	12.1554	1.17511	0.587555	+	0.809184i	$0.300090\pi$
$108$	−5.04096	−0.485066
$109$	−0.568643	−0.0544661	−0.0272330	−	0.999629i	$-0.508670\pi$
$109$	−0.568643	−0.0544661	−0.0272330	+	0.999629i	$0.508670\pi$
$110$	0	0
$111$	11.5808	1.09920
$112$	−4.53996	−0.428986
$113$	−18.3328	−1.72460	−0.862301	−	0.506397i	$-0.830977\pi$
$113$	−18.3328	−1.72460	−0.862301	+	0.506397i	$0.830977\pi$
$114$	−12.1131	−1.13449
$115$	−8.77414	−0.818193
$116$	−4.60581	−0.427639
$117$	0.0672789	0.00621994
$118$	10.5133	0.967823
$119$	4.53996	0.416178
$120$	−4.18034	−0.381611
$121$	0	0
$122$	2.72719	0.246908
$123$	−20.3237	−1.83253
$124$	−3.30937	−0.297190
$125$	−10.5302	−0.941846
$126$	0.761265	0.0678189
$127$	−17.3031	−1.53540	−0.767701	−	0.640808i	$-0.778599\pi$
$127$	−17.3031	−1.53540	−0.767701	+	0.640808i	$0.778599\pi$
$128$	−1.00000	−0.0883883
$129$	−11.1127	−0.978416
$130$	−0.942403	−0.0826542
$131$	−6.34476	−0.554344	−0.277172	−	0.960820i	$-0.589397\pi$
$131$	−6.34476	−0.554344	−0.277172	+	0.960820i	$0.589397\pi$
$132$	0	0
$133$	−30.8984	−2.67923
$134$	4.45469	0.384827
$135$	−11.8401	−1.01903
$136$	1.00000	0.0857493
$137$	15.9646	1.36395	0.681974	−	0.731377i	$-0.261122\pi$
$137$	15.9646	1.36395	0.681974	+	0.731377i	$0.261122\pi$
$138$	6.64866	0.565971
$139$	2.29985	0.195071	0.0975354	−	0.995232i	$-0.468904\pi$
$139$	2.29985	0.195071	0.0975354	+	0.995232i	$0.468904\pi$
$140$	−10.6633	−0.901217
$141$	−5.55468	−0.467788
$142$	−3.14997	−0.264339
$143$	0	0
$144$	0.167681	0.0139734
$145$	−10.8180	−0.898387
$146$	1.39211	0.115212
$147$	24.2253	1.99807
$148$	6.50680	0.534856
$149$	−11.8231	−0.968588	−0.484294	−	0.874905i	$-0.660923\pi$
$149$	−11.8231	−0.968588	−0.484294	+	0.874905i	$0.660923\pi$
$150$	−0.919696	−0.0750928
$151$	−8.30105	−0.675530	−0.337765	−	0.941231i	$-0.609671\pi$
$151$	−8.30105	−0.675530	−0.337765	+	0.941231i	$0.609671\pi$
$152$	−6.80587	−0.552029
$153$	−0.167681	−0.0135562
$154$	0	0
$155$	−7.77295	−0.624339
$156$	0.714112	0.0571747
$157$	8.35107	0.666488	0.333244	−	0.942841i	$-0.391857\pi$
$157$	8.35107	0.666488	0.333244	+	0.942841i	$0.391857\pi$
$158$	3.51026	0.279261
$159$	22.9650	1.82125
$160$	−2.34877	−0.185687
$161$	16.9596	1.33660
$162$	9.47493	0.744420
$163$	7.05459	0.552558	0.276279	−	0.961077i	$-0.410899\pi$
$163$	7.05459	0.552558	0.276279	+	0.961077i	$0.410899\pi$
$164$	−11.4191	−0.891684
$165$	0	0
$166$	−9.92155	−0.770062
$167$	12.2506	0.947979	0.473990	−	0.880530i	$-0.342813\pi$
$167$	12.2506	0.947979	0.473990	+	0.880530i	$0.342813\pi$
$168$	8.08022	0.623402
$169$	−12.8390	−0.987616
$170$	2.34877	0.180143
$171$	1.14121	0.0872708
$172$	−6.24378	−0.476084
$173$	−1.43585	−0.109165	−0.0545827	−	0.998509i	$-0.517383\pi$
$173$	−1.43585	−0.109165	−0.0545827	+	0.998509i	$0.517383\pi$
$174$	8.19741	0.621444
$175$	−2.34599	−0.177340
$176$	0	0
$177$	−18.7115	−1.40644
$178$	9.88841	0.741167
$179$	−14.4379	−1.07914	−0.539569	−	0.841941i	$-0.681413\pi$
$179$	−14.4379	−1.07914	−0.539569	+	0.841941i	$0.681413\pi$
$180$	0.393845	0.0293555
$181$	9.77109	0.726280	0.363140	−	0.931735i	$-0.381705\pi$
$181$	9.77109	0.726280	0.363140	+	0.931735i	$0.381705\pi$
$182$	1.82158	0.135024
$183$	−4.85385	−0.358807
$184$	3.73562	0.275394
$185$	15.2830	1.12363
$186$	5.89000	0.431876
$187$	0	0
$188$	−3.12096	−0.227619
$189$	22.8857	1.66469
$190$	−15.9854	−1.15971
$191$	1.55160	0.112270	0.0561350	−	0.998423i	$-0.482122\pi$
$191$	1.55160	0.112270	0.0561350	+	0.998423i	$0.482122\pi$
$192$	1.77980	0.128446
$193$	5.97039	0.429758	0.214879	−	0.976641i	$-0.431064\pi$
$193$	5.97039	0.429758	0.214879	+	0.976641i	$0.431064\pi$
$194$	5.36499	0.385184
$195$	1.67729	0.120113
$196$	13.6113	0.972232
$197$	−4.12660	−0.294008	−0.147004	−	0.989136i	$-0.546963\pi$
$197$	−4.12660	−0.294008	−0.147004	+	0.989136i	$0.546963\pi$
$198$	0	0
$199$	−2.45497	−0.174028	−0.0870142	−	0.996207i	$-0.527733\pi$
$199$	−2.45497	−0.174028	−0.0870142	+	0.996207i	$0.527733\pi$
$200$	−0.516742	−0.0365392
$201$	−7.92846	−0.559230
$202$	−11.0205	−0.775401
$203$	20.9102	1.46761
$204$	−1.77980	−0.124611
$205$	−26.8210	−1.87326
$206$	18.9448	1.31995
$207$	−0.626393	−0.0435373
$208$	0.401232	0.0278204
$209$	0	0
$210$	18.9786	1.30965
$211$	−5.38046	−0.370406	−0.185203	−	0.982700i	$-0.559294\pi$
$211$	−5.38046	−0.370406	−0.185203	+	0.982700i	$0.559294\pi$
$212$	12.9032	0.886193
$213$	5.60631	0.384138
$214$	−12.1554	−0.830929
$215$	−14.6652	−1.00016
$216$	5.04096	0.342994
$217$	15.0244	1.01992
$218$	0.568643	0.0385133
$219$	−2.47767	−0.167426
$220$	0	0
$221$	−0.401232	−0.0269898
$222$	−11.5808	−0.777252
$223$	−8.67385	−0.580844	−0.290422	−	0.956899i	$-0.593796\pi$
$223$	−8.67385	−0.580844	−0.290422	+	0.956899i	$0.593796\pi$
$224$	4.53996	0.303339
$225$	0.0866477	0.00577652
$226$	18.3328	1.21948
$227$	27.9473	1.85493	0.927463	−	0.373915i	$-0.121985\pi$
$227$	27.9473	1.85493	0.927463	+	0.373915i	$0.121985\pi$
$228$	12.1131	0.802207
$229$	−21.8451	−1.44356	−0.721782	−	0.692120i	$-0.756677\pi$
$229$	−21.8451	−1.44356	−0.721782	+	0.692120i	$0.756677\pi$
$230$	8.77414	0.578550
$231$	0	0
$232$	4.60581	0.302386
$233$	−0.0684939	−0.00448719	−0.00224359	−	0.999997i	$-0.500714\pi$
$233$	−0.0684939	−0.00448719	−0.00224359	+	0.999997i	$0.500714\pi$
$234$	−0.0672789	−0.00439816
$235$	−7.33043	−0.478185
$236$	−10.5133	−0.684355
$237$	−6.24756	−0.405822
$238$	−4.53996	−0.294282
$239$	−7.36507	−0.476407	−0.238203	−	0.971215i	$-0.576559\pi$
$239$	−7.36507	−0.476407	−0.238203	+	0.971215i	$0.576559\pi$
$240$	4.18034	0.269840
$241$	23.8852	1.53858	0.769291	−	0.638899i	$-0.220610\pi$
$241$	23.8852	1.53858	0.769291	+	0.638899i	$0.220610\pi$
$242$	0	0
$243$	−1.74059	−0.111659
$244$	−2.72719	−0.174590
$245$	31.9698	2.04247
$246$	20.3237	1.29579
$247$	2.73073	0.173752
$248$	3.30937	0.210145
$249$	17.6584	1.11905
$250$	10.5302	0.665986
$251$	−13.2111	−0.833879	−0.416939	−	0.908934i	$-0.636897\pi$
$251$	−13.2111	−0.833879	−0.416939	+	0.908934i	$0.636897\pi$
$252$	−0.761265	−0.0479552
$253$	0	0
$254$	17.3031	1.08569
$255$	−4.18034	−0.261783
$256$	1.00000	0.0625000
$257$	−15.7297	−0.981191	−0.490595	−	0.871387i	$-0.663221\pi$
$257$	−15.7297	−0.981191	−0.490595	+	0.871387i	$0.663221\pi$
$258$	11.1127	0.691845
$259$	−29.5406	−1.83556
$260$	0.942403	0.0584454
$261$	−0.772307	−0.0478046
$262$	6.34476	0.391980
$263$	−29.4792	−1.81777	−0.908883	−	0.417051i	$-0.863064\pi$
$263$	−29.4792	−1.81777	−0.908883	+	0.417051i	$0.863064\pi$
$264$	0	0
$265$	30.3066	1.86172
$266$	30.8984	1.89450
$267$	−17.5994	−1.07706
$268$	−4.45469	−0.272114
$269$	−1.96163	−0.119603	−0.0598013	−	0.998210i	$-0.519047\pi$
$269$	−1.96163	−0.119603	−0.0598013	+	0.998210i	$0.519047\pi$
$270$	11.8401	0.720564
$271$	−20.3344	−1.23523	−0.617615	−	0.786481i	$-0.711901\pi$
$271$	−20.3344	−1.23523	−0.617615	+	0.786481i	$0.711901\pi$
$272$	−1.00000	−0.0606339
$273$	−3.24204	−0.196217
$274$	−15.9646	−0.964456
$275$	0	0
$276$	−6.64866	−0.400202
$277$	14.2083	0.853692	0.426846	−	0.904324i	$-0.359625\pi$
$277$	14.2083	0.853692	0.426846	+	0.904324i	$0.359625\pi$
$278$	−2.29985	−0.137936
$279$	−0.554917	−0.0332220
$280$	10.6633	0.637257
$281$	−8.61758	−0.514081	−0.257041	−	0.966401i	$-0.582747\pi$
$281$	−8.61758	−0.514081	−0.257041	+	0.966401i	$0.582747\pi$
$282$	5.55468	0.330776
$283$	18.9842	1.12849	0.564247	−	0.825606i	$-0.309166\pi$
$283$	18.9842	1.12849	0.564247	+	0.825606i	$0.309166\pi$
$284$	3.14997	0.186916
$285$	28.4509	1.68528
$286$	0	0
$287$	51.8424	3.06016
$288$	−0.167681	−0.00988069
$289$	1.00000	0.0588235
$290$	10.8180	0.635255
$291$	−9.54860	−0.559749
$292$	−1.39211	−0.0814671
$293$	0.972761	0.0568293	0.0284146	−	0.999596i	$-0.490954\pi$
$293$	0.972761	0.0568293	0.0284146	+	0.999596i	$0.490954\pi$
$294$	−24.2253	−1.41285
$295$	−24.6933	−1.43770
$296$	−6.50680	−0.378200
$297$	0	0
$298$	11.8231	0.684895
$299$	−1.49885	−0.0866808
$300$	0.919696	0.0530987
$301$	28.3465	1.63387
$302$	8.30105	0.477672
$303$	19.6143	1.12681
$304$	6.80587	0.390343
$305$	−6.40555	−0.366781
$306$	0.167681	0.00958568
$307$	28.8312	1.64548	0.822741	−	0.568416i	$-0.192444\pi$
$307$	28.8312	1.64548	0.822741	+	0.568416i	$0.192444\pi$
$308$	0	0
$309$	−33.7180	−1.91815
$310$	7.77295	0.441474
$311$	−8.48624	−0.481211	−0.240605	−	0.970623i	$-0.577346\pi$
$311$	−8.48624	−0.481211	−0.240605	+	0.970623i	$0.577346\pi$
$312$	−0.714112	−0.0404286
$313$	−2.97111	−0.167937	−0.0839686	−	0.996468i	$-0.526760\pi$
$313$	−2.97111	−0.167937	−0.0839686	+	0.996468i	$0.526760\pi$
$314$	−8.35107	−0.471278
$315$	−1.78804	−0.100745
$316$	−3.51026	−0.197468
$317$	14.2834	0.802238	0.401119	−	0.916026i	$-0.368621\pi$
$317$	14.2834	0.802238	0.401119	+	0.916026i	$0.368621\pi$
$318$	−22.9650	−1.28781
$319$	0	0
$320$	2.34877	0.131300
$321$	21.6342	1.20750
$322$	−16.9596	−0.945121
$323$	−6.80587	−0.378688
$324$	−9.47493	−0.526385
$325$	0.207333	0.0115008
$326$	−7.05459	−0.390718
$327$	−1.01207	−0.0559675
$328$	11.4191	0.630516
$329$	14.1690	0.781165
$330$	0	0
$331$	28.2359	1.55199	0.775993	−	0.630742i	$-0.217249\pi$
$331$	28.2359	1.55199	0.775993	+	0.630742i	$0.217249\pi$
$332$	9.92155	0.544516
$333$	1.09107	0.0597901
$334$	−12.2506	−0.670322
$335$	−10.4631	−0.571659
$336$	−8.08022	−0.440812
$337$	28.8607	1.57214	0.786070	−	0.618137i	$-0.212112\pi$
$337$	28.8607	1.57214	0.786070	+	0.618137i	$0.212112\pi$
$338$	12.8390	0.698350
$339$	−32.6286	−1.77214
$340$	−2.34877	−0.127380
$341$	0	0
$342$	−1.14121	−0.0617098
$343$	−30.0148	−1.62065
$344$	6.24378	0.336642
$345$	−15.6162	−0.840748
$346$	1.43585	0.0771916
$347$	−11.9221	−0.640011	−0.320006	−	0.947416i	$-0.603685\pi$
$347$	−11.9221	−0.640011	−0.320006	+	0.947416i	$0.603685\pi$
$348$	−8.19741	−0.439427
$349$	12.8069	0.685540	0.342770	−	0.939419i	$-0.388635\pi$
$349$	12.8069	0.685540	0.342770	+	0.939419i	$0.388635\pi$
$350$	2.34599	0.125398
$351$	−2.02259	−0.107958
$352$	0	0
$353$	27.6343	1.47082	0.735412	−	0.677620i	$-0.236989\pi$
$353$	27.6343	1.47082	0.735412	+	0.677620i	$0.236989\pi$
$354$	18.7115	0.994503
$355$	7.39857	0.392675
$356$	−9.88841	−0.524085
$357$	8.08022	0.427650
$358$	14.4379	0.763066
$359$	−35.0559	−1.85018	−0.925090	−	0.379749i	$-0.876010\pi$
$359$	−35.0559	−1.85018	−0.925090	+	0.379749i	$0.876010\pi$
$360$	−0.393845	−0.0207574
$361$	27.3198	1.43788
$362$	−9.77109	−0.513557
$363$	0	0
$364$	−1.82158	−0.0954766
$365$	−3.26975	−0.171147
$366$	4.85385	0.253715
$367$	17.4556	0.911175	0.455587	−	0.890191i	$-0.349429\pi$
$367$	17.4556	0.911175	0.455587	+	0.890191i	$0.349429\pi$
$368$	−3.73562	−0.194733
$369$	−1.91477	−0.0996790
$370$	−15.2830	−0.794526
$371$	−58.5799	−3.04132
$372$	−5.89000	−0.305382
$373$	−31.0299	−1.60667	−0.803333	−	0.595530i	$-0.796942\pi$
$373$	−31.0299	−1.60667	−0.803333	+	0.595530i	$0.796942\pi$
$374$	0	0
$375$	−18.7416	−0.967810
$376$	3.12096	0.160951
$377$	−1.84800	−0.0951767
$378$	−22.8857	−1.17712
$379$	−29.0940	−1.49446	−0.747229	−	0.664567i	$-0.768616\pi$
$379$	−29.0940	−1.49446	−0.747229	+	0.664567i	$0.768616\pi$
$380$	15.9854	0.820036
$381$	−30.7960	−1.57773
$382$	−1.55160	−0.0793869
$383$	−9.30679	−0.475555	−0.237777	−	0.971320i	$-0.576419\pi$
$383$	−9.30679	−0.475555	−0.237777	+	0.971320i	$0.576419\pi$
$384$	−1.77980	−0.0908249
$385$	0	0
$386$	−5.97039	−0.303885
$387$	−1.04696	−0.0532201
$388$	−5.36499	−0.272366
$389$	−0.724310	−0.0367240	−0.0183620	−	0.999831i	$-0.505845\pi$
$389$	−0.724310	−0.0367240	−0.0183620	+	0.999831i	$0.505845\pi$
$390$	−1.67729	−0.0849327
$391$	3.73562	0.188919
$392$	−13.6113	−0.687472
$393$	−11.2924	−0.569625
$394$	4.12660	0.207895
$395$	−8.24481	−0.414842
$396$	0	0
$397$	12.4930	0.627005	0.313503	−	0.949587i	$-0.398498\pi$
$397$	12.4930	0.627005	0.313503	+	0.949587i	$0.398498\pi$
$398$	2.45497	0.123057
$399$	−54.9929	−2.75309
$400$	0.516742	0.0258371
$401$	−10.6942	−0.534044	−0.267022	−	0.963690i	$-0.586040\pi$
$401$	−10.6942	−0.534044	−0.267022	+	0.963690i	$0.586040\pi$
$402$	7.92846	0.395435
$403$	−1.32782	−0.0661436
$404$	11.0205	0.548291
$405$	−22.2545	−1.10583
$406$	−20.9102	−1.03776
$407$	0	0
$408$	1.77980	0.0881131
$409$	15.4640	0.764647	0.382324	−	0.924028i	$-0.375124\pi$
$409$	15.4640	0.764647	0.382324	+	0.924028i	$0.375124\pi$
$410$	26.8210	1.32459
$411$	28.4137	1.40155
$412$	−18.9448	−0.933345
$413$	47.7298	2.34863
$414$	0.626393	0.0307855
$415$	23.3035	1.14392
$416$	−0.401232	−0.0196720
$417$	4.09327	0.200448
$418$	0	0
$419$	−3.05415	−0.149205	−0.0746026	−	0.997213i	$-0.523769\pi$
$419$	−3.05415	−0.149205	−0.0746026	+	0.997213i	$0.523769\pi$
$420$	−18.9786	−0.926061
$421$	11.7076	0.570592	0.285296	−	0.958439i	$-0.407908\pi$
$421$	11.7076	0.570592	0.285296	+	0.958439i	$0.407908\pi$
$422$	5.38046	0.261917
$423$	−0.523326	−0.0254450
$424$	−12.9032	−0.626633
$425$	−0.516742	−0.0250657
$426$	−5.60631	−0.271627
$427$	12.3813	0.599175
$428$	12.1554	0.587555
$429$	0	0
$430$	14.6652	0.707221
$431$	−24.3493	−1.17286	−0.586432	−	0.809999i	$-0.699468\pi$
$431$	−24.3493	−1.17286	−0.586432	+	0.809999i	$0.699468\pi$
$432$	−5.04096	−0.242533
$433$	28.4107	1.36533	0.682666	−	0.730730i	$-0.260820\pi$
$433$	28.4107	1.36533	0.682666	+	0.730730i	$0.260820\pi$
$434$	−15.0244	−0.721194
$435$	−19.2539	−0.923153
$436$	−0.568643	−0.0272330
$437$	−25.4242	−1.21620
$438$	2.47767	0.118388
$439$	7.35267	0.350924	0.175462	−	0.984486i	$-0.443858\pi$
$439$	7.35267	0.350924	0.175462	+	0.984486i	$0.443858\pi$
$440$	0	0
$441$	2.28235	0.108683
$442$	0.401232	0.0190847
$443$	−7.79033	−0.370130	−0.185065	−	0.982726i	$-0.559250\pi$
$443$	−7.79033	−0.370130	−0.185065	+	0.982726i	$0.559250\pi$
$444$	11.5808	0.549600
$445$	−23.2256	−1.10100
$446$	8.67385	0.410719
$447$	−21.0428	−0.995289
$448$	−4.53996	−0.214493
$449$	32.9849	1.55666	0.778328	−	0.627858i	$-0.216068\pi$
$449$	32.9849	1.55666	0.778328	+	0.627858i	$0.216068\pi$
$450$	−0.0866477	−0.00408461
$451$	0	0
$452$	−18.3328	−0.862301
$453$	−14.7742	−0.694152
$454$	−27.9473	−1.31163
$455$	−4.27847	−0.200578
$456$	−12.1131	−0.567246
$457$	5.13787	0.240339	0.120170	−	0.992753i	$-0.461656\pi$
$457$	5.13787	0.240339	0.120170	+	0.992753i	$0.461656\pi$
$458$	21.8451	1.02075
$459$	5.04096	0.235292
$460$	−8.77414	−0.409096
$461$	−38.2472	−1.78135	−0.890676	−	0.454639i	$-0.849768\pi$
$461$	−38.2472	−1.78135	−0.890676	+	0.454639i	$0.849768\pi$
$462$	0	0
$463$	−37.0096	−1.71998	−0.859992	−	0.510308i	$-0.829531\pi$
$463$	−37.0096	−1.71998	−0.859992	+	0.510308i	$0.829531\pi$
$464$	−4.60581	−0.213819
$465$	−13.8343	−0.641550
$466$	0.0684939	0.00317292
$467$	12.5766	0.581973	0.290987	−	0.956727i	$-0.406016\pi$
$467$	12.5766	0.581973	0.290987	+	0.956727i	$0.406016\pi$
$468$	0.0672789	0.00310997
$469$	20.2241	0.933864
$470$	7.33043	0.338128
$471$	14.8632	0.684861
$472$	10.5133	0.483912
$473$	0	0
$474$	6.24756	0.286960
$475$	3.51687	0.161365
$476$	4.53996	0.208089
$477$	2.16361	0.0990651
$478$	7.36507	0.336871
$479$	−2.63284	−0.120298	−0.0601488	−	0.998189i	$-0.519158\pi$
$479$	−2.63284	−0.120298	−0.0601488	+	0.998189i	$0.519158\pi$
$480$	−4.18034	−0.190806
$481$	2.61073	0.119039
$482$	−23.8852	−1.08794
$483$	30.1847	1.37345
$484$	0	0
$485$	−12.6011	−0.572189
$486$	1.74059	0.0789546
$487$	17.3982	0.788386	0.394193	−	0.919028i	$-0.371024\pi$
$487$	17.3982	0.788386	0.394193	+	0.919028i	$0.371024\pi$
$488$	2.72719	0.123454
$489$	12.5558	0.567791
$490$	−31.9698	−1.44425
$491$	18.1235	0.817904	0.408952	−	0.912556i	$-0.365894\pi$
$491$	18.1235	0.817904	0.408952	+	0.912556i	$0.365894\pi$
$492$	−20.3237	−0.916265
$493$	4.60581	0.207435
$494$	−2.73073	−0.122861
$495$	0	0
$496$	−3.30937	−0.148595
$497$	−14.3007	−0.641476
$498$	−17.6584	−0.791290
$499$	1.78545	0.0799275	0.0399638	−	0.999201i	$-0.487276\pi$
$499$	1.78545	0.0799275	0.0399638	+	0.999201i	$0.487276\pi$
$500$	−10.5302	−0.470923
$501$	21.8036	0.974112
$502$	13.2111	0.589641
$503$	30.9099	1.37821	0.689103	−	0.724664i	$-0.258005\pi$
$503$	30.9099	1.37821	0.689103	+	0.724664i	$0.258005\pi$
$504$	0.761265	0.0339094
$505$	25.8847	1.15185
$506$	0	0
$507$	−22.8508	−1.01484
$508$	−17.3031	−0.767701
$509$	10.5546	0.467823	0.233912	−	0.972258i	$-0.424847\pi$
$509$	10.5546	0.467823	0.233912	+	0.972258i	$0.424847\pi$
$510$	4.18034	0.185109
$511$	6.32013	0.279586
$512$	−1.00000	−0.0441942
$513$	−34.3081	−1.51474
$514$	15.7297	0.693807
$515$	−44.4972	−1.96078
$516$	−11.1127	−0.489208
$517$	0	0
$518$	29.5406	1.29794
$519$	−2.55552	−0.112175
$520$	−0.942403	−0.0413271
$521$	−12.3274	−0.540074	−0.270037	−	0.962850i	$-0.587036\pi$
$521$	−12.3274	−0.540074	−0.270037	+	0.962850i	$0.587036\pi$
$522$	0.772307	0.0338029
$523$	−35.9922	−1.57383	−0.786914	−	0.617063i	$-0.788322\pi$
$523$	−35.9922	−1.57383	−0.786914	+	0.617063i	$0.788322\pi$
$524$	−6.34476	−0.277172
$525$	−4.17538	−0.182229
$526$	29.4792	1.28535
$527$	3.30937	0.144158
$528$	0	0
$529$	−9.04511	−0.393265
$530$	−30.3066	−1.31644
$531$	−1.76287	−0.0765021
$532$	−30.8984	−1.33961
$533$	−4.58172	−0.198456
$534$	17.5994	0.761599
$535$	28.5504	1.23434
$536$	4.45469	0.192413
$537$	−25.6965	−1.10889
$538$	1.96163	0.0845718
$539$	0	0
$540$	−11.8401	−0.509515
$541$	−11.2526	−0.483787	−0.241893	−	0.970303i	$-0.577768\pi$
$541$	−11.2526	−0.483787	−0.241893	+	0.970303i	$0.577768\pi$
$542$	20.3344	0.873439
$543$	17.3906	0.746301
$544$	1.00000	0.0428746
$545$	−1.33561	−0.0572114
$546$	3.24204	0.138746
$547$	34.8504	1.49010	0.745049	−	0.667010i	$-0.232426\pi$
$547$	34.8504	1.49010	0.745049	+	0.667010i	$0.232426\pi$
$548$	15.9646	0.681974
$549$	−0.457298	−0.0195170
$550$	0	0
$551$	−31.3465	−1.33541
$552$	6.64866	0.282986
$553$	15.9365	0.677687
$554$	−14.2083	−0.603651
$555$	27.2007	1.15460
$556$	2.29985	0.0975354
$557$	−26.2898	−1.11394	−0.556968	−	0.830534i	$-0.688035\pi$
$557$	−26.2898	−1.11394	−0.556968	+	0.830534i	$0.688035\pi$
$558$	0.554917	0.0234915
$559$	−2.50520	−0.105959
$560$	−10.6633	−0.450609
$561$	0	0
$562$	8.61758	0.363510
$563$	−31.6877	−1.33548	−0.667740	−	0.744395i	$-0.732738\pi$
$563$	−31.6877	−1.33548	−0.667740	+	0.744395i	$0.732738\pi$
$564$	−5.55468	−0.233894
$565$	−43.0595	−1.81153
$566$	−18.9842	−0.797966
$567$	43.0158	1.80649
$568$	−3.14997	−0.132170
$569$	17.4674	0.732271	0.366135	−	0.930562i	$-0.380681\pi$
$569$	17.4674	0.732271	0.366135	+	0.930562i	$0.380681\pi$
$570$	−28.4509	−1.19168
$571$	11.0988	0.464469	0.232235	−	0.972660i	$-0.425396\pi$
$571$	11.0988	0.464469	0.232235	+	0.972660i	$0.425396\pi$
$572$	0	0
$573$	2.76154	0.115365
$574$	−51.8424	−2.16386
$575$	−1.93035	−0.0805013
$576$	0.167681	0.00698671
$577$	2.00126	0.0833136	0.0416568	−	0.999132i	$-0.486736\pi$
$577$	2.00126	0.0833136	0.0416568	+	0.999132i	$0.486736\pi$
$578$	−1.00000	−0.0415945
$579$	10.6261	0.441605
$580$	−10.8180	−0.449193
$581$	−45.0435	−1.86872
$582$	9.54860	0.395802
$583$	0	0
$584$	1.39211	0.0576059
$585$	0.158023	0.00653345
$586$	−0.972761	−0.0401844
$587$	−4.90422	−0.202419	−0.101209	−	0.994865i	$-0.532271\pi$
$587$	−4.90422	−0.202419	−0.101209	+	0.994865i	$0.532271\pi$
$588$	24.2253	0.999034
$589$	−22.5231	−0.928048
$590$	24.6933	1.01661
$591$	−7.34452	−0.302113
$592$	6.50680	0.267428
$593$	5.84556	0.240048	0.120024	−	0.992771i	$-0.461703\pi$
$593$	5.84556	0.240048	0.120024	+	0.992771i	$0.461703\pi$
$594$	0	0
$595$	10.6633	0.437155
$596$	−11.8231	−0.484294
$597$	−4.36935	−0.178826
$598$	1.49885	0.0612926
$599$	−11.8661	−0.484836	−0.242418	−	0.970172i	$-0.577941\pi$
$599$	−11.8661	−0.484836	−0.242418	+	0.970172i	$0.577941\pi$
$600$	−0.919696	−0.0375464
$601$	26.4312	1.07815	0.539076	−	0.842257i	$-0.318773\pi$
$601$	26.4312	1.07815	0.539076	+	0.842257i	$0.318773\pi$
$602$	−28.3465	−1.15532
$603$	−0.746967	−0.0304189
$604$	−8.30105	−0.337765
$605$	0	0
$606$	−19.6143	−0.796776
$607$	37.1179	1.50657	0.753284	−	0.657695i	$-0.228468\pi$
$607$	37.1179	1.50657	0.753284	+	0.657695i	$0.228468\pi$
$608$	−6.80587	−0.276014
$609$	37.2159	1.50807
$610$	6.40555	0.259353
$611$	−1.25223	−0.0506598
$612$	−0.167681	−0.00677810
$613$	20.2181	0.816601	0.408300	−	0.912848i	$-0.366122\pi$
$613$	20.2181	0.816601	0.408300	+	0.912848i	$0.366122\pi$
$614$	−28.8312	−1.16353
$615$	−47.7359	−1.92490
$616$	0	0
$617$	1.81082	0.0729007	0.0364503	−	0.999335i	$-0.488395\pi$
$617$	1.81082	0.0729007	0.0364503	+	0.999335i	$0.488395\pi$
$618$	33.7180	1.35634
$619$	−24.4225	−0.981625	−0.490812	−	0.871265i	$-0.663300\pi$
$619$	−24.4225	−0.981625	−0.490812	+	0.871265i	$0.663300\pi$
$620$	−7.77295	−0.312169
$621$	18.8311	0.755667
$622$	8.48624	0.340267
$623$	44.8930	1.79860
$624$	0.714112	0.0285873
$625$	−27.3167	−1.09267
$626$	2.97111	0.118749
$627$	0	0
$628$	8.35107	0.333244
$629$	−6.50680	−0.259443
$630$	1.78804	0.0712372
$631$	−12.1565	−0.483943	−0.241972	−	0.970283i	$-0.577794\pi$
$631$	−12.1565	−0.483943	−0.241972	+	0.970283i	$0.577794\pi$
$632$	3.51026	0.139631
$633$	−9.57613	−0.380617
$634$	−14.2834	−0.567268
$635$	−40.6411	−1.61279
$636$	22.9650	0.910623
$637$	5.46127	0.216383
$638$	0	0
$639$	0.528190	0.0208949
$640$	−2.34877	−0.0928435
$641$	15.9542	0.630152	0.315076	−	0.949066i	$-0.397970\pi$
$641$	15.9542	0.630152	0.315076	+	0.949066i	$0.397970\pi$
$642$	−21.6342	−0.853835
$643$	7.18743	0.283445	0.141722	−	0.989906i	$-0.454736\pi$
$643$	7.18743	0.283445	0.141722	+	0.989906i	$0.454736\pi$
$644$	16.9596	0.668302
$645$	−26.1012	−1.02773
$646$	6.80587	0.267773
$647$	35.0476	1.37786	0.688931	−	0.724827i	$-0.258080\pi$
$647$	35.0476	1.37786	0.688931	+	0.724827i	$0.258080\pi$
$648$	9.47493	0.372210
$649$	0	0
$650$	−0.207333	−0.00813228
$651$	26.7404	1.04804
$652$	7.05459	0.276279
$653$	47.6735	1.86561	0.932804	−	0.360384i	$-0.117354\pi$
$653$	47.6735	1.86561	0.932804	+	0.360384i	$0.117354\pi$
$654$	1.01207	0.0395750
$655$	−14.9024	−0.582285
$656$	−11.4191	−0.445842
$657$	−0.233430	−0.00910698
$658$	−14.1690	−0.552367
$659$	21.6584	0.843693	0.421846	−	0.906667i	$-0.361382\pi$
$659$	21.6584	0.843693	0.421846	+	0.906667i	$0.361382\pi$
$660$	0	0
$661$	5.96122	0.231865	0.115932	−	0.993257i	$-0.463014\pi$
$661$	5.96122	0.231865	0.115932	+	0.993257i	$0.463014\pi$
$662$	−28.2359	−1.09742
$663$	−0.714112	−0.0277338
$664$	−9.92155	−0.385031
$665$	−72.5733	−2.81427
$666$	−1.09107	−0.0422780
$667$	17.2056	0.666203
$668$	12.2506	0.473990
$669$	−15.4377	−0.596856
$670$	10.4631	0.404224
$671$	0	0
$672$	8.08022	0.311701
$673$	37.4745	1.44453	0.722267	−	0.691614i	$-0.243100\pi$
$673$	37.4745	1.44453	0.722267	+	0.691614i	$0.243100\pi$
$674$	−28.8607	−1.11167
$675$	−2.60487	−0.100262
$676$	−12.8390	−0.493808
$677$	−41.7591	−1.60493	−0.802467	−	0.596697i	$-0.796480\pi$
$677$	−41.7591	−1.60493	−0.802467	+	0.596697i	$0.796480\pi$
$678$	32.6286	1.25309
$679$	24.3568	0.934730
$680$	2.34877	0.0900714
$681$	49.7405	1.90606
$682$	0	0
$683$	43.1623	1.65156	0.825779	−	0.563993i	$-0.190736\pi$
$683$	43.1623	1.65156	0.825779	+	0.563993i	$0.190736\pi$
$684$	1.14121	0.0436354
$685$	37.4972	1.43270
$686$	30.0148	1.14597
$687$	−38.8799	−1.48336
$688$	−6.24378	−0.238042
$689$	5.17716	0.197234
$690$	15.6162	0.594498
$691$	20.4847	0.779276	0.389638	−	0.920968i	$-0.372600\pi$
$691$	20.4847	0.779276	0.389638	+	0.920968i	$0.372600\pi$
$692$	−1.43585	−0.0545827
$693$	0	0
$694$	11.9221	0.452556
$695$	5.40183	0.204903
$696$	8.19741	0.310722
$697$	11.4191	0.432530
$698$	−12.8069	−0.484750
$699$	−0.121905	−0.00461088
$700$	−2.34599	−0.0886700
$701$	5.17910	0.195612	0.0978060	−	0.995205i	$-0.468818\pi$
$701$	5.17910	0.195612	0.0978060	+	0.995205i	$0.468818\pi$
$702$	2.02259	0.0763378
$703$	44.2844	1.67022
$704$	0	0
$705$	−13.0467	−0.491367
$706$	−27.6343	−1.04003
$707$	−50.0327	−1.88167
$708$	−18.7115	−0.703220
$709$	−5.06579	−0.190250	−0.0951248	−	0.995465i	$-0.530325\pi$
$709$	−5.06579	−0.190250	−0.0951248	+	0.995465i	$0.530325\pi$
$710$	−7.39857	−0.277663
$711$	−0.588604	−0.0220744
$712$	9.88841	0.370584
$713$	12.3625	0.462981
$714$	−8.08022	−0.302394
$715$	0	0
$716$	−14.4379	−0.539569
$717$	−13.1083	−0.489540
$718$	35.0559	1.30827
$719$	−10.0443	−0.374591	−0.187295	−	0.982304i	$-0.559972\pi$
$719$	−10.0443	−0.374591	−0.187295	+	0.982304i	$0.559972\pi$
$720$	0.393845	0.0146777
$721$	86.0089	3.20314
$722$	−27.3198	−1.01674
$723$	42.5109	1.58100
$724$	9.77109	0.363140
$725$	−2.38001	−0.0883915
$726$	0	0
$727$	−43.5582	−1.61549	−0.807743	−	0.589535i	$-0.799311\pi$
$727$	−43.5582	−1.61549	−0.807743	+	0.589535i	$0.799311\pi$
$728$	1.82158	0.0675121
$729$	25.3269	0.938033
$730$	3.26975	0.121019
$731$	6.24378	0.230935
$732$	−4.85385	−0.179403
$733$	−49.2175	−1.81789	−0.908945	−	0.416915i	$-0.863111\pi$
$733$	−49.2175	−1.81789	−0.908945	+	0.416915i	$0.863111\pi$
$734$	−17.4556	−0.644298
$735$	56.8997	2.09878
$736$	3.73562	0.137697
$737$	0	0
$738$	1.91477	0.0704837
$739$	−11.3312	−0.416825	−0.208412	−	0.978041i	$-0.566830\pi$
$739$	−11.3312	−0.416825	−0.208412	+	0.978041i	$0.566830\pi$
$740$	15.2830	0.561814
$741$	4.86015	0.178542
$742$	58.5799	2.15053
$743$	−30.5555	−1.12097	−0.560486	−	0.828164i	$-0.689386\pi$
$743$	−30.5555	−1.12097	−0.560486	+	0.828164i	$0.689386\pi$
$744$	5.89000	0.215938
$745$	−27.7698	−1.01741
$746$	31.0299	1.13608
$747$	1.66366	0.0608700
$748$	0	0
$749$	−55.1852	−2.01642
$750$	18.7416	0.684345
$751$	29.3586	1.07131	0.535655	−	0.844437i	$-0.320065\pi$
$751$	29.3586	1.07131	0.535655	+	0.844437i	$0.320065\pi$
$752$	−3.12096	−0.113810
$753$	−23.5131	−0.856866
$754$	1.84800	0.0673001
$755$	−19.4973	−0.709579
$756$	22.8857	0.832347
$757$	−13.5778	−0.493495	−0.246748	−	0.969080i	$-0.579362\pi$
$757$	−13.5778	−0.493495	−0.246748	+	0.969080i	$0.579362\pi$
$758$	29.0940	1.05674
$759$	0	0
$760$	−15.9854	−0.579853
$761$	−8.64428	−0.313355	−0.156677	−	0.987650i	$-0.550078\pi$
$761$	−8.64428	−0.313355	−0.156677	+	0.987650i	$0.550078\pi$
$762$	30.7960	1.11562
$763$	2.58162	0.0934608
$764$	1.55160	0.0561350
$765$	−0.393845	−0.0142395
$766$	9.30679	0.336268
$767$	−4.21825	−0.152312
$768$	1.77980	0.0642229
$769$	4.03103	0.145363	0.0726813	−	0.997355i	$-0.476844\pi$
$769$	4.03103	0.145363	0.0726813	+	0.997355i	$0.476844\pi$
$770$	0	0
$771$	−27.9957	−1.00824
$772$	5.97039	0.214879
$773$	3.91904	0.140958	0.0704790	−	0.997513i	$-0.477547\pi$
$773$	3.91904	0.140958	0.0704790	+	0.997513i	$0.477547\pi$
$774$	1.04696	0.0376323
$775$	−1.71009	−0.0614281
$776$	5.36499	0.192592
$777$	−52.5763	−1.88617
$778$	0.724310	0.0259678
$779$	−77.7171	−2.78450
$780$	1.67729	0.0600565
$781$	0	0
$782$	−3.73562	−0.133586
$783$	23.2177	0.829732
$784$	13.6113	0.486116
$785$	19.6148	0.700081
$786$	11.2924	0.402786
$787$	−14.7558	−0.525987	−0.262994	−	0.964798i	$-0.584710\pi$
$787$	−14.7558	−0.525987	−0.262994	+	0.964798i	$0.584710\pi$
$788$	−4.12660	−0.147004
$789$	−52.4670	−1.86788
$790$	8.24481	0.293337
$791$	83.2301	2.95932
$792$	0	0
$793$	−1.09423	−0.0388574
$794$	−12.4930	−0.443360
$795$	53.9397	1.91304
$796$	−2.45497	−0.0870142
$797$	20.0704	0.710930	0.355465	−	0.934690i	$-0.384322\pi$
$797$	20.0704	0.710930	0.355465	+	0.934690i	$0.384322\pi$
$798$	54.9929	1.94673
$799$	3.12096	0.110412
$800$	−0.516742	−0.0182696
$801$	−1.65810	−0.0585860
$802$	10.6942	0.377626
$803$	0	0
$804$	−7.92846	−0.279615
$805$	39.8343	1.40397
$806$	1.32782	0.0467706
$807$	−3.49130	−0.122900
$808$	−11.0205	−0.387700
$809$	5.94181	0.208903	0.104451	−	0.994530i	$-0.466691\pi$
$809$	5.94181	0.208903	0.104451	+	0.994530i	$0.466691\pi$
$810$	22.2545	0.781942
$811$	−45.7596	−1.60684	−0.803418	−	0.595415i	$-0.796988\pi$
$811$	−45.7596	−1.60684	−0.803418	+	0.595415i	$0.796988\pi$
$812$	20.9102	0.733804
$813$	−36.1912	−1.26928
$814$	0	0
$815$	16.5696	0.580409
$816$	−1.77980	−0.0623054
$817$	−42.4943	−1.48669
$818$	−15.4640	−0.540687
$819$	−0.305444	−0.0106731
$820$	−26.8210	−0.936629
$821$	34.5342	1.20525	0.602626	−	0.798023i	$-0.294121\pi$
$821$	34.5342	1.20525	0.602626	+	0.798023i	$0.294121\pi$
$822$	−28.4137	−0.991043
$823$	44.4609	1.54981	0.774904	−	0.632079i	$-0.217798\pi$
$823$	44.4609	1.54981	0.774904	+	0.632079i	$0.217798\pi$
$824$	18.9448	0.659975
$825$	0	0
$826$	−47.7298	−1.66073
$827$	21.5308	0.748701	0.374350	−	0.927287i	$-0.377866\pi$
$827$	21.5308	0.748701	0.374350	+	0.927287i	$0.377866\pi$
$828$	−0.626393	−0.0217687
$829$	44.6660	1.55131	0.775657	−	0.631155i	$-0.217419\pi$
$829$	44.6660	1.55131	0.775657	+	0.631155i	$0.217419\pi$
$830$	−23.3035	−0.808876
$831$	25.2878	0.877225
$832$	0.401232	0.0139102
$833$	−13.6113	−0.471602
$834$	−4.09327	−0.141738
$835$	28.7739	0.995761
$836$	0	0
$837$	16.6824	0.576627
$838$	3.05415	0.105504
$839$	−3.94504	−0.136198	−0.0680990	−	0.997679i	$-0.521693\pi$
$839$	−3.94504	−0.136198	−0.0680990	+	0.997679i	$0.521693\pi$
$840$	18.9786	0.654824
$841$	−7.78651	−0.268500
$842$	−11.7076	−0.403470
$843$	−15.3375	−0.528253
$844$	−5.38046	−0.185203
$845$	−30.1559	−1.03740
$846$	0.523326	0.0179923
$847$	0	0
$848$	12.9032	0.443097
$849$	33.7881	1.15960
$850$	0.516742	0.0177241
$851$	−24.3070	−0.833232
$852$	5.60631	0.192069
$853$	−13.9167	−0.476498	−0.238249	−	0.971204i	$-0.576573\pi$
$853$	−13.9167	−0.476498	−0.238249	+	0.971204i	$0.576573\pi$
$854$	−12.3813	−0.423681
$855$	2.68045	0.0916696
$856$	−12.1554	−0.415464
$857$	−29.0885	−0.993645	−0.496822	−	0.867852i	$-0.665500\pi$
$857$	−29.0885	−0.993645	−0.496822	+	0.867852i	$0.665500\pi$
$858$	0	0
$859$	1.76082	0.0600785	0.0300392	−	0.999549i	$-0.490437\pi$
$859$	1.76082	0.0600785	0.0300392	+	0.999549i	$0.490437\pi$
$860$	−14.6652	−0.500080
$861$	92.2690	3.14452
$862$	24.3493	0.829340
$863$	−30.6933	−1.04481	−0.522406	−	0.852697i	$-0.674965\pi$
$863$	−30.6933	−1.04481	−0.522406	+	0.852697i	$0.674965\pi$
$864$	5.04096	0.171497
$865$	−3.37248	−0.114668
$866$	−28.4107	−0.965436
$867$	1.77980	0.0604451
$868$	15.0244	0.509961
$869$	0	0
$870$	19.2539	0.652767
$871$	−1.78736	−0.0605625
$872$	0.568643	0.0192567
$873$	−0.899606	−0.0304471
$874$	25.4242	0.859985
$875$	47.8065	1.61616
$876$	−2.47767	−0.0837129
$877$	−28.0813	−0.948237	−0.474118	−	0.880461i	$-0.657233\pi$
$877$	−28.0813	−0.948237	−0.474118	+	0.880461i	$0.657233\pi$
$878$	−7.35267	−0.248141
$879$	1.73132	0.0583959
$880$	0	0
$881$	29.0569	0.978951	0.489476	−	0.872017i	$-0.337188\pi$
$881$	29.0569	0.978951	0.489476	+	0.872017i	$0.337188\pi$
$882$	−2.28235	−0.0768506
$883$	18.5528	0.624351	0.312175	−	0.950025i	$-0.398942\pi$
$883$	18.5528	0.624351	0.312175	+	0.950025i	$0.398942\pi$
$884$	−0.401232	−0.0134949
$885$	−43.9490	−1.47733
$886$	7.79033	0.261721
$887$	−20.3470	−0.683187	−0.341593	−	0.939848i	$-0.610967\pi$
$887$	−20.3470	−0.683187	−0.341593	+	0.939848i	$0.610967\pi$
$888$	−11.5808	−0.388626
$889$	78.5554	2.63466
$890$	23.2256	0.778525
$891$	0	0
$892$	−8.67385	−0.290422
$893$	−21.2408	−0.710798
$894$	21.0428	0.703776
$895$	−33.9113	−1.13353
$896$	4.53996	0.151669
$897$	−2.66765	−0.0890703
$898$	−32.9849	−1.10072
$899$	15.2423	0.508359
$900$	0.0866477	0.00288826
$901$	−12.9032	−0.429867
$902$	0	0
$903$	50.4511	1.67891
$904$	18.3328	0.609739
$905$	22.9501	0.762887
$906$	14.7742	0.490840
$907$	9.46247	0.314196	0.157098	−	0.987583i	$-0.449786\pi$
$907$	9.46247	0.314196	0.157098	+	0.987583i	$0.449786\pi$
$908$	27.9473	0.927463
$909$	1.84793	0.0612920
$910$	4.27847	0.141830
$911$	3.79584	0.125762	0.0628808	−	0.998021i	$-0.479971\pi$
$911$	3.79584	0.125762	0.0628808	+	0.998021i	$0.479971\pi$
$912$	12.1131	0.401104
$913$	0	0
$914$	−5.13787	−0.169946
$915$	−11.4006	−0.376892
$916$	−21.8451	−0.721782
$917$	28.8050	0.951223
$918$	−5.04096	−0.166376
$919$	−31.9088	−1.05258	−0.526288	−	0.850307i	$-0.676417\pi$
$919$	−31.9088	−1.05258	−0.526288	+	0.850307i	$0.676417\pi$
$920$	8.77414	0.289275
$921$	51.3137	1.69084
$922$	38.2472	1.25961
$923$	1.26387	0.0416007
$924$	0	0
$925$	3.36233	0.110553
$926$	37.0096	1.21621
$927$	−3.17669	−0.104336
$928$	4.60581	0.151193
$929$	20.6108	0.676217	0.338109	−	0.941107i	$-0.390213\pi$
$929$	20.6108	0.676217	0.338109	+	0.941107i	$0.390213\pi$
$930$	13.8343	0.453644
$931$	92.6364	3.03603
$932$	−0.0684939	−0.00224359
$933$	−15.1038	−0.494476
$934$	−12.5766	−0.411517
$935$	0	0
$936$	−0.0672789	−0.00219908
$937$	−31.5345	−1.03019	−0.515094	−	0.857134i	$-0.672243\pi$
$937$	−31.5345	−1.03019	−0.515094	+	0.857134i	$0.672243\pi$
$938$	−20.2241	−0.660342
$939$	−5.28798	−0.172567
$940$	−7.33043	−0.239092
$941$	−22.1543	−0.722211	−0.361105	−	0.932525i	$-0.617601\pi$
$941$	−22.1543	−0.722211	−0.361105	+	0.932525i	$0.617601\pi$
$942$	−14.8632	−0.484270
$943$	42.6576	1.38912
$944$	−10.5133	−0.342177
$945$	53.7535	1.74860
$946$	0	0
$947$	−24.1814	−0.785789	−0.392894	−	0.919584i	$-0.628526\pi$
$947$	−24.1814	−0.785789	−0.392894	+	0.919584i	$0.628526\pi$
$948$	−6.24756	−0.202911
$949$	−0.558559	−0.0181316
$950$	−3.51687	−0.114102
$951$	25.4216	0.824353
$952$	−4.53996	−0.147141
$953$	6.09708	0.197504	0.0987518	−	0.995112i	$-0.468515\pi$
$953$	6.09708	0.197504	0.0987518	+	0.995112i	$0.468515\pi$
$954$	−2.16361	−0.0700496
$955$	3.64437	0.117929
$956$	−7.36507	−0.238203
$957$	0	0
$958$	2.63284	0.0850632
$959$	−72.4786	−2.34046
$960$	4.18034	0.134920
$961$	−20.0481	−0.646713
$962$	−2.61073	−0.0841735
$963$	2.03824	0.0656812
$964$	23.8852	0.769291
$965$	14.0231	0.451419
$966$	−30.1847	−0.971175
$967$	−42.8736	−1.37872	−0.689361	−	0.724418i	$-0.742108\pi$
$967$	−42.8736	−1.37872	−0.689361	+	0.724418i	$0.742108\pi$
$968$	0	0
$969$	−12.1131	−0.389128
$970$	12.6011	0.404599
$971$	−43.6916	−1.40213	−0.701064	−	0.713098i	$-0.747291\pi$
$971$	−43.6916	−1.40213	−0.701064	+	0.713098i	$0.747291\pi$
$972$	−1.74059	−0.0558293
$973$	−10.4412	−0.334731
$974$	−17.3982	−0.557473
$975$	0.369011	0.0118178
$976$	−2.72719	−0.0872952
$977$	38.2194	1.22275	0.611373	−	0.791342i	$-0.290617\pi$
$977$	38.2194	1.22275	0.611373	+	0.791342i	$0.290617\pi$
$978$	−12.5558	−0.401489
$979$	0	0
$980$	31.9698	1.02124
$981$	−0.0953505	−0.00304431
$982$	−18.1235	−0.578346
$983$	−48.0310	−1.53195	−0.765975	−	0.642870i	$-0.777744\pi$
$983$	−48.0310	−1.53195	−0.765975	+	0.642870i	$0.777744\pi$
$984$	20.3237	0.647897
$985$	−9.69246	−0.308827
$986$	−4.60581	−0.146679
$987$	25.2180	0.802699
$988$	2.73073	0.0868761
$989$	23.3244	0.741674
$990$	0	0
$991$	33.9815	1.07946	0.539729	−	0.841839i	$-0.318527\pi$
$991$	33.9815	1.07946	0.539729	+	0.841839i	$0.318527\pi$
$992$	3.30937	0.105072
$993$	50.2542	1.59477
$994$	14.3007	0.453592
$995$	−5.76618	−0.182800
$996$	17.6584	0.559527
$997$	−15.5000	−0.490891	−0.245446	−	0.969410i	$-0.578934\pi$
$997$	−15.5000	−0.490891	−0.245446	+	0.969410i	$0.578934\pi$
$998$	−1.78545	−0.0565173
$999$	−32.8005	−1.03776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4114.2.a.bk.1.8		10
11.3	even	5		374.2.g.g.273.2	yes	20
11.4	even	5		374.2.g.g.137.2	✓	20
11.10	odd	2		4114.2.a.bl.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.g.137.2	✓	20	11.4	even	5
374.2.g.g.273.2	yes	20	11.3	even	5
4114.2.a.bk.1.8		10	1.1	even	1	trivial
4114.2.a.bl.1.8		10	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4114 = 2 \cdot 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4114.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.77980 q^{3} +1.00000 q^{4} +2.34877 q^{5} -1.77980 q^{6} -4.53996 q^{7} -1.00000 q^{8} +0.167681 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.77980 q^{3} +1.00000 q^{4} +2.34877 q^{5} -1.77980 q^{6} -4.53996 q^{7} -1.00000 q^{8} +0.167681 q^{9} -2.34877 q^{10} +1.77980 q^{12} +0.401232 q^{13} +4.53996 q^{14} +4.18034 q^{15} +1.00000 q^{16} -1.00000 q^{17} -0.167681 q^{18} +6.80587 q^{19} +2.34877 q^{20} -8.08022 q^{21} -3.73562 q^{23} -1.77980 q^{24} +0.516742 q^{25} -0.401232 q^{26} -5.04096 q^{27} -4.53996 q^{28} -4.60581 q^{29} -4.18034 q^{30} -3.30937 q^{31} -1.00000 q^{32} +1.00000 q^{34} -10.6633 q^{35} +0.167681 q^{36} +6.50680 q^{37} -6.80587 q^{38} +0.714112 q^{39} -2.34877 q^{40} -11.4191 q^{41} +8.08022 q^{42} -6.24378 q^{43} +0.393845 q^{45} +3.73562 q^{46} -3.12096 q^{47} +1.77980 q^{48} +13.6113 q^{49} -0.516742 q^{50} -1.77980 q^{51} +0.401232 q^{52} +12.9032 q^{53} +5.04096 q^{54} +4.53996 q^{56} +12.1131 q^{57} +4.60581 q^{58} -10.5133 q^{59} +4.18034 q^{60} -2.72719 q^{61} +3.30937 q^{62} -0.761265 q^{63} +1.00000 q^{64} +0.942403 q^{65} -4.45469 q^{67} -1.00000 q^{68} -6.64866 q^{69} +10.6633 q^{70} +3.14997 q^{71} -0.167681 q^{72} -1.39211 q^{73} -6.50680 q^{74} +0.919696 q^{75} +6.80587 q^{76} -0.714112 q^{78} -3.51026 q^{79} +2.34877 q^{80} -9.47493 q^{81} +11.4191 q^{82} +9.92155 q^{83} -8.08022 q^{84} -2.34877 q^{85} +6.24378 q^{86} -8.19741 q^{87} -9.88841 q^{89} -0.393845 q^{90} -1.82158 q^{91} -3.73562 q^{92} -5.89000 q^{93} +3.12096 q^{94} +15.9854 q^{95} -1.77980 q^{96} -5.36499 q^{97} -13.6113 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{6} - 2 q^{7} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^6 - 2 * q^7 - 10 * q^8 + 12 * q^9	\( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{6} - 2 q^{7} - 10 q^{8} + 12 q^{9} + 2 q^{12} + 2 q^{14} - 5 q^{15} + 10 q^{16} - 10 q^{17} - 12 q^{18} - 9 q^{19} - 19 q^{21} - 6 q^{23} - 2 q^{24} + 4 q^{25} + 11 q^{27} - 2 q^{28} - 20 q^{29} + 5 q^{30} - q^{31} - 10 q^{32} + 10 q^{34} - 13 q^{35} + 12 q^{36} + 17 q^{37} + 9 q^{38} - 11 q^{39} - 39 q^{41} + 19 q^{42} - 16 q^{43} - 26 q^{45} + 6 q^{46} - 14 q^{47} + 2 q^{48} + 18 q^{49} - 4 q^{50} - 2 q^{51} + 8 q^{53} - 11 q^{54} + 2 q^{56} - 24 q^{57} + 20 q^{58} - 4 q^{59} - 5 q^{60} - 22 q^{61} + q^{62} - 29 q^{63} + 10 q^{64} - 52 q^{65} - 13 q^{67} - 10 q^{68} - 30 q^{69} + 13 q^{70} - 7 q^{71} - 12 q^{72} + 6 q^{73} - 17 q^{74} + 45 q^{75} - 9 q^{76} + 11 q^{78} - 19 q^{79} + 34 q^{81} + 39 q^{82} - 19 q^{83} - 19 q^{84} + 16 q^{86} - 29 q^{87} - 8 q^{89} + 26 q^{90} + 9 q^{91} - 6 q^{92} + 3 q^{93} + 14 q^{94} + 27 q^{95} - 2 q^{96} + 39 q^{97} - 18 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^6 - 2 * q^7 - 10 * q^8 + 12 * q^9 + 2 * q^12 + 2 * q^14 - 5 * q^15 + 10 * q^16 - 10 * q^17 - 12 * q^18 - 9 * q^19 - 19 * q^21 - 6 * q^23 - 2 * q^24 + 4 * q^25 + 11 * q^27 - 2 * q^28 - 20 * q^29 + 5 * q^30 - q^31 - 10 * q^32 + 10 * q^34 - 13 * q^35 + 12 * q^36 + 17 * q^37 + 9 * q^38 - 11 * q^39 - 39 * q^41 + 19 * q^42 - 16 * q^43 - 26 * q^45 + 6 * q^46 - 14 * q^47 + 2 * q^48 + 18 * q^49 - 4 * q^50 - 2 * q^51 + 8 * q^53 - 11 * q^54 + 2 * q^56 - 24 * q^57 + 20 * q^58 - 4 * q^59 - 5 * q^60 - 22 * q^61 + q^62 - 29 * q^63 + 10 * q^64 - 52 * q^65 - 13 * q^67 - 10 * q^68 - 30 * q^69 + 13 * q^70 - 7 * q^71 - 12 * q^72 + 6 * q^73 - 17 * q^74 + 45 * q^75 - 9 * q^76 + 11 * q^78 - 19 * q^79 + 34 * q^81 + 39 * q^82 - 19 * q^83 - 19 * q^84 + 16 * q^86 - 29 * q^87 - 8 * q^89 + 26 * q^90 + 9 * q^91 - 6 * q^92 + 3 * q^93 + 14 * q^94 + 27 * q^95 - 2 * q^96 + 39 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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